Finite Group Databasebeta

← #3349×D67 #31734450

Subgroups — #3349×D67 #31734450

Order 17152.

1834 conjugacy classes of subgroups.

The subgroup lattice has 1652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#556×D67C211yesmaximal, characteristic
2#552×D67C211yesmaximal, characteristic
3#22572746C211yesmaximal, characteristic, complemented
4#22572745C211yesmaximal, characteristic, complemented
5#22572744C211yesmaximal, characteristic, complemented
6#22572743C211yesmaximal, characteristic, complemented
7#22572742C211yesmaximal, characteristic, complemented
8#22572741C211yesmaximal, characteristic, complemented
9#22572740C211yesmaximal, characteristic, complemented
10#22572739C211yesmaximal, characteristic, complemented
11#22572738C211yesmaximal, characteristic, complemented
12#22572737C211yesmaximal, characteristic, complemented
13#22572736C211yesmaximal, characteristic, complemented
14#22572735C211yesmaximal, characteristic, complemented
15#22572734C211yesmaximal, characteristic, complemented
16#22572733C211yesmaximal, characteristic, complemented
17#22572732C211yesmaximal, characteristic, complemented
18#501×D67C211yesmaximal, characteristic, complemented
19#484×D67C211yesmaximal, characteristic, complemented
20#485×D67C211yesmaximal, characteristic, complemented
21#485×D67C211yesmaximal, characteristic, complemented
22#485×D67C211yesmaximal, characteristic, complemented
23#479×D67C211yesmaximal, characteristic, complemented
24#477×D67C211yesmaximal, characteristic, complemented
25#470×D67C211yesmaximal, characteristic, complemented
26#467×D67C211yesmaximal, characteristic, complemented
27#441×D67C211yesmaximal, characteristic, complemented
28#435×D67C211yesmaximal, characteristic
29#428×D67C211yesmaximal, characteristic, complemented
30#427×D67C211yesmaximal, characteristic, complemented
31C67×#3349C211yesmaximal, characteristic, complemented
32C2×Q16×D67C2211yescharacteristic
33C2×M16×D67C2211yescharacteristic
34C22×C8×D67C2211yescharacteristic
35#16864120C2211yescharacteristic
36#16864119C2211yescharacteristic
37#16864118—21no—
38#16864117C2211yescharacteristic
39#16864117C2211yescharacteristic
40#16864116C2211yescharacteristic
41#16864115—21no—
42#16864114C2211yescharacteristic
43#16864114C2211yescharacteristic
44#16864113—21no—
45#16864113—21no—
46#16864088C2211yescharacteristic
47#16864087C2211yescharacteristic
48#16864086C2211yescharacteristic
49#16864085C2211yescharacteristic
50#16864084C2211yescharacteristic
51#16864083—21no—
52#16864082—21no—
53#16864081C2211yescharacteristic
54#16864080C2211yescharacteristic
55#16864079—21no—
56#16864078—21no—
57C4⋊Q8×D67C2211yescharacteristic
58#126×D67—21no—
59#126×D67—21no—
60#126×D67—21no—
61#125×D67—21no—
62#125×D67C2211yescharacteristic
63#124×D67—21no—
64#123×D67—21no—
65C22⋊Q8×D67C2211yescharacteristic
66C22⋊Q8×D67C2211yescharacteristic
67C22⋊Q8×D67C2211yescharacteristic
68C22⋊Q8×D67C2211yescharacteristic
69C4×Q8×D67—21no—
70C4×Q8×D67C2211yescharacteristic
71C4×Q8×D67C2211yescharacteristic
72C4×D4×D67C2211yescharacteristic
73#117×D67—21no—
74#117×D67C2211yescharacteristic
75#117×D67C2211yescharacteristic
76#117×D67C2211yescharacteristic
77C2×C4⋊C4×D67C2211yescharacteristic
78#16863806C2211yescharacteristic, complemented
79#16863805C2211yescharacteristic, complemented
80#16863804C2211yescharacteristic, complemented
81#16863804C2211yescharacteristic, complemented
82#16863803C2211yescharacteristic, complemented
83#16863803C2211yescharacteristic, complemented
84#16863802C2211yescharacteristic, complemented
85#16863740C2211yescharacteristic, complemented
86#16863740C2211yescharacteristic, complemented
87#16863740C2211yescharacteristic, complemented
88#16863739C2211yescharacteristic, complemented
89#16863739C2211yescharacteristic, complemented
90#16863739C2211yescharacteristic, complemented
91#16863738C2211yescharacteristic, complemented
92#16863738C2211yescharacteristic, complemented
93#16863738C2211yescharacteristic, complemented
94#16863737C2211yescharacteristic, complemented
95#16863737C2211yescharacteristic, complemented
96#16863737C2211yescharacteristic, complemented
97#16863736C2211yescharacteristic, complemented
98#16863736C2211yescharacteristic, complemented
99#16863736C2211yescharacteristic, complemented
100#16863735C2211yescharacteristic, complemented
101#16863735C2211yescharacteristic, complemented
102#16863735C2211yescharacteristic, complemented
103#16863734C2211yescharacteristic, complemented
104#16863734C2211yescharacteristic, complemented
105#16863734C2211yescharacteristic, complemented
106#16863733C2211yescharacteristic, complemented
107#16863733C2211yescharacteristic, complemented
108#16863732C2211yescharacteristic, complemented
109#16863731C2211yescharacteristic, complemented
110#16863730C2211yescharacteristic, complemented
111#16863730C2211yescharacteristic, complemented
112#16863729C2211yescharacteristic, complemented
113#16863706C2211yescharacteristic, complemented
114#16863705C2211yescharacteristic, complemented
115#16863704C2211yescharacteristic, complemented
116#16863703C2211yescharacteristic, complemented
117#16863702C2211yescharacteristic, complemented
118#16863701C2211yescharacteristic, complemented
119#16863700C2211yescharacteristic, complemented
120#16863692C2211yescharacteristic, complemented
121#16863691C2211yescharacteristic, complemented
122#16863690C2211yescharacteristic, complemented
123#16863690C2211yescharacteristic, complemented
124#16863689C2211yescharacteristic, complemented
125#16863689C2211yescharacteristic, complemented
126#16863688C2211yescharacteristic, complemented
127#16863655C2211yescharacteristic, complemented
128#16863654C2211yescharacteristic, complemented
129#16863653C2211yescharacteristic, complemented
130#16863653C2211yescharacteristic, complemented
131#16863652C2211yescharacteristic, complemented
132#16863652C2211yescharacteristic, complemented
133#16863651C2211yescharacteristic, complemented
134#16863638C2211yescharacteristic, complemented
135#16863637C2211yescharacteristic, complemented
136#16863636C2211yescharacteristic, complemented
137#16863636C2211yescharacteristic, complemented
138#16863635C2211yescharacteristic, complemented
139#16863635C2211yescharacteristic, complemented
140#16863634C2211yescharacteristic, complemented
141#16863504C2211yescharacteristic, complemented
142#16863503C2211yescharacteristic, complemented
143#16863502C2211yescharacteristic, complemented
144#16863501C2211yescharacteristic, complemented
145#16863501C2211yescharacteristic, complemented
146#16863500C2211yescharacteristic, complemented
147#16863500C2211yescharacteristic, complemented
148#16863470C2211yescharacteristic
149#16863469C2211yescharacteristic
150#16863468C2211yescharacteristic
151#16863467C2211yescharacteristic
152#16863466C2211yescharacteristic
153#16863465C2211yescharacteristic
154#16863464C2211yescharacteristic
155#16863439C2211yescharacteristic, complemented
156#16863438C2211yescharacteristic, complemented
157#16863437C2211yescharacteristic, complemented
158#16863437C2211yescharacteristic, complemented
159#16863436C2211yescharacteristic, complemented
160#16863435C2211yescharacteristic, complemented
161#16863435C2211yescharacteristic, complemented
162#16863434C2211yescharacteristic, complemented
163#16863433C2211yescharacteristic, complemented
164#16863433C2211yescharacteristic, complemented
165#16863432C2211yescharacteristic, complemented
166#16863432C2211yescharacteristic, complemented
167#16863431C2211yescharacteristic, complemented
168#16863431C2211yescharacteristic, complemented
169#107×D67C2211yescharacteristic
170#107×D67C2211yescharacteristic
171#107×D67C2211yescharacteristic
172#107×D67C2211yescharacteristic
173#107×D67C2211yescharacteristic
174#106×D67C2211yescharacteristic
175#106×D67C2211yescharacteristic
176#106×D67C2211yescharacteristic
177#106×D67C2211yescharacteristic
178C4⋊C8×D67C2211yescharacteristic
179#103×D67C2211yescharacteristic
180#103×D67C2211yescharacteristic
181#103×D67C2211yescharacteristic
182#103×D67C2211yescharacteristic
183#103×D67C2211yescharacteristic
184#103×D67C2211yescharacteristic
185C22⋊C8×D67C2211yescharacteristic
186C22⋊C8×D67C2211yescharacteristic
187#97×D67C2211yescharacteristic
188#556×C67C2211yescharacteristic
189#552×C67C2211yescharacteristic
190#501×C67C2211yescharacteristic, complemented
191#485×C67C2211yescharacteristic, complemented
192#485×C67C2211yescharacteristic, complemented
193#485×C67C2211yescharacteristic, complemented
194#484×C67C2211yescharacteristic, complemented
195#479×C67C2211yescharacteristic, complemented
196#477×C67C2211yescharacteristic, complemented
197#470×C67C2211yescharacteristic, complemented
198#467×C67C2211yescharacteristic, complemented
199#441×C67C2211yescharacteristic, complemented
200#435×C67C2211yescharacteristic
201#428×C67C2211yescharacteristic, complemented
202#427×C67C2211yescharacteristic, complemented
203C2×Q8×D67—21no—
204C2×Q8×D67C2311yescharacteristic
205C2×Q8×D67C2311yescharacteristic
206C2×D4×D67D411yescharacteristic
207C22×C4×D67—21no—
208C22×C4×D67C2311yescharacteristic
209C22×C4×D67C2311yescharacteristic
210C2×Dic268C2311yescharacteristic
211C2×#11761618C2311yescharacteristic
212C2×#11761618C2311yescharacteristic
213Q16×D67—24no—
214C2×#11761612C2311yescharacteristic
215C2×#11761611C2311yescharacteristic
216C2×#11761611C2311yescharacteristic
217M16×D67—24no—
218C22×C67⋊C8C2311yescharacteristic
219C2×C8×D67—24no—
220C2×C8×D67C2311yescharacteristic
221C2×C8×D67C2311yescharacteristic
222C2×C8×D67C2311yescharacteristic
223C2×C8×D67C2311yescharacteristic
224C2×C8×D67C2311yescharacteristic
225C2×C8×D67C2311yescharacteristic
226#14524043C2311yescharacteristic
227#14524042—21no—
228#14524042C2311yescharacteristic
229#14524042C2311yescharacteristic
230#14524041—21no—
231#14524038—21no—
232#14524038—21no—
233#14524038—21no—
234#14524038—21no—
235#14524038—21no—
236#14524038—21no—
237#14524038—21no—
238#14524038—21no—
239#14524038—21no—
240#14524037—21no—
241#14524037—21no—
242#14524037—21no—
243#14524036—21no—
244#14524036—21no—
245#14524036—21no—
246#14524036—21no—
247#14524036—21no—
248#14524036—21no—
249#14524036—21no—
250#14524036—21no—
251#14524036—21no—
252#14524035—21no—
253#14524035C2311yescharacteristic
254#14524034—21no—
255#14524034—21no—
256#14524034C2311yescharacteristic
257#14524034C2311yescharacteristic
258#14524033—21no—
259#14524033—21no—
260#14524033—21no—
261#14524033—21no—
262#14524033—21no—
263#14524033—21no—
264#14524032—21no—
265#14524031—21no—
266#14524030—21no—
267#14524029—21no—
268#14524029—21no—
269#14524029—21no—
270#14524029—21no—
271#14524028—21no—
272#14524028—21no—
273#14524027—21no—
274#14524026—21no—
275#14524025—21no—
276#14524025—21no—
277#14524024—21no—
278#14524023C2311yescharacteristic
279#14524023C2311yescharacteristic
280#14524023C2311yescharacteristic
281#14524023C2311yescharacteristic
282#14524022C2311yescharacteristic
283#14524022C2311yescharacteristic
284#14524022C2311yescharacteristic
285#14524022C2311yescharacteristic
286#14524021—21no—
287#14524021—21no—
288#14524021—21no—
289#14524021—21no—
290#14524020—21no—
291#14524020—21no—
292#14524020—21no—
293#14524020—21no—
294#14524019C2311yescharacteristic
295#14524019C2311yescharacteristic
296#14524019C2311yescharacteristic
297#14524019C2311yescharacteristic
298Q8×Dic67—21no—
299Q8×Dic67C2311yescharacteristic
300Q8×Dic67C2311yescharacteristic
301C4×Dic134—21no—
302C4×Dic134—21no—
303C4×Dic134—21no—
304C4×Dic134—21no—
305C4×Dic134—21no—
306C4×Dic134C2311yescharacteristic
307C4×Dic134C2311yescharacteristic
308#14524008—21no—
309#14524008—21no—
310#14524008—21no—
311#14524008—21no—
312#14524008—21no—
313#14524008C2311yescharacteristic
314#14524008C2311yescharacteristic
315C4×D268C2311yescharacteristic
316D4×Dic67D411yescharacteristic
317#14524005D411yescharacteristic
318C4×C22⋊D67C2311yescharacteristic
319C4×C22⋊D67C2311yescharacteristic
320(C22⋊D67)⋊C4D411yescharacteristic
321(C22⋊D67)⋊C4D411yescharacteristic
322#14524002—21no—
323#14524002C2311yescharacteristic
324#14524002C2311yescharacteristic
325#14524002C2311yescharacteristic
326#14524001—21no—
327#14524001—21no—
328#14524001C2311yescharacteristic
329#14524001C2311yescharacteristic
330#14524001C2311yescharacteristic
331#14524001C2311yescharacteristic
332#14524001C2311yescharacteristic
333#14524001C2311yescharacteristic
334#14524000—21no—
335#14524000—21no—
336#14524000—21no—
337#14524000—21no—
338#14524000—21no—
339#14523999—21no—
340#14523999—21no—
341#14523999—21no—
342#14523999—21no—
343#14523999—21no—
344C2×C4⋊Dic67C2311yescharacteristic
345C2×Dic67⋊C4—21no—
346C4⋊C4×D67—21no—
347C4⋊C4×D67—21no—
348C4⋊C4×D67—21no—
349C4⋊C4×D67—21no—
350C4⋊C4×D67—21no—
351C4⋊C4×D67—21no—
352C4⋊C4×D67—21no—
353C4⋊C4×D67—21no—
354C4⋊C4×D67—21no—
355C4⋊C4×D67—21no—
356C4⋊C4×D67—21no—
357C4⋊C4×D67D411yescharacteristic
358C4⋊C4×D67C2311yescharacteristic
359C4⋊C4×D67C2311yescharacteristic
360C4⋊C4×D67C2311yescharacteristic
361C4⋊C4×D67C2311yescharacteristic
362C4⋊C4×D67C2311yescharacteristic
363C4⋊C4×D67C2311yescharacteristic
364C4⋊C4×D67C2311yescharacteristic
365C4⋊C4×D67C2311yescharacteristic
366C22⋊C4×D67—21no—
367C22⋊C4×D67—21no—
368C22⋊C4×D67—21no—
369C22⋊C4×D67—21no—
370C22⋊C4×D67—21no—
371C22⋊C4×D67—21no—
372C22⋊C4×D67—21no—
373C22⋊C4×D67D411yescharacteristic
374C22⋊C4×D67D411yescharacteristic
375C42×D67—21no—
376C42×D67—21no—
377C42×D67—21no—
378C42×D67—21no—
379C42×D67—21no—
380C42×D67C2311yescharacteristic
381#14523977C2311yescharacteristic
382#14523977C2311yescharacteristic
383#14523977C2311yescharacteristic
384#14523977C2311yescharacteristic
385#14523977C2311yescharacteristic
386#14523976C2311yescharacteristic
387#14523976C2311yescharacteristic
388#14523976C2311yescharacteristic
389#14523976C2311yescharacteristic
390#14523976C2311yescharacteristic
391#14523976C2311yescharacteristic
392#14523976C2311yescharacteristic
393#14523976C2311yescharacteristic
394#14523976C2311yescharacteristic
395#14523976C2311yescharacteristic
396#14523975C2311yescharacteristic
397#14523975C2311yescharacteristic
398#14523975C2311yescharacteristic
399#14523975C2311yescharacteristic
400#14523974C2311yescharacteristic
401#14523974C2311yescharacteristic
402#14523974C2311yescharacteristic
403#14523974C2311yescharacteristic
404#14523974C2311yescharacteristic
405#14523974C2311yescharacteristic
406#14523974C2311yescharacteristic
407#14523974C2311yescharacteristic
408C4⋊(C67⋊C8)C2311yescharacteristic
409Dic67⋊C8C2311yescharacteristic
410Dic67⋊C8C2311yescharacteristic
411#14523968C2311yescharacteristic
412#14523968C2311yescharacteristic
413#14523968C2311yescharacteristic
414#14523968C2311yescharacteristic
415#14523968C2311yescharacteristic
416#14523968C2311yescharacteristic
417#14523967C2311yescharacteristic
418#14523967C2311yescharacteristic
419#14523967C2311yescharacteristic
420#14523967C2311yescharacteristic
421#14523967C2311yescharacteristic
422#14523967C2311yescharacteristic
423#14523966C2311yescharacteristic
424#14523966C2311yescharacteristic
425#14523966C2311yescharacteristic
426#14523966C2311yescharacteristic
427#14523966C2311yescharacteristic
428#14523966C2311yescharacteristic
429C22⋊(C67⋊C8)C2311yescharacteristic
430C22⋊(C67⋊C8)C2311yescharacteristic
431(C2×D67)⋊C8C2311yescharacteristic
432(C2×D67)⋊C8C2311yescharacteristic
433(C2×D67)⋊C8C2311yescharacteristic
434(C2×D67)⋊C8C2311yescharacteristic
435#14523954C2311yescharacteristic
436#14523953C2311yescharacteristic
437#14523953C2311yescharacteristic
438C2×Q16×C67C2311yescharacteristic
439C2×M16×C67C2311yescharacteristic
440C22×C8×C67C2311yescharacteristic
441C4⋊Q8×C67C2311yescharacteristic
442#126×C67—21no—
443#126×C67—21no—
444#126×C67—21no—
445#125×C67—21no—
446#125×C67C2311yescharacteristic
447#124×C67—21no—
448#123×C67—21no—
449C22⋊Q8×C67C2311yescharacteristic
450C22⋊Q8×C67C2311yescharacteristic
451C22⋊Q8×C67C2311yescharacteristic
452C22⋊Q8×C67C2311yescharacteristic
453C4×Q8×C67—21no—
454C4×Q8×C67C2311yescharacteristic
455C4×Q8×C67C2311yescharacteristic
456C4×D4×C67C2311yescharacteristic
457#117×C67—21no—
458#117×C67C2311yescharacteristic
459#117×C67C2311yescharacteristic
460#117×C67C2311yescharacteristic
461C2×C4⋊C4×C67C2311yescharacteristic
462#107×C67C2311yescharacteristic
463#107×C67C2311yescharacteristic
464#107×C67C2311yescharacteristic
465#107×C67C2311yescharacteristic
466#107×C67C2311yescharacteristic
467#106×C67C2311yescharacteristic
468#106×C67C2311yescharacteristic
469#106×C67C2311yescharacteristic
470#106×C67C2311yescharacteristic
471C4⋊C8×C67C2311yescharacteristic
472#103×C67C2311yescharacteristic
473#103×C67C2311yescharacteristic
474#103×C67C2311yescharacteristic
475#103×C67C2311yescharacteristic
476#103×C67C2311yescharacteristic
477#103×C67C2311yescharacteristic
478C22⋊C8×C67C2311yescharacteristic
479C22⋊C8×C67C2311yescharacteristic
480#97×C67C2311yescharacteristic
481C23×D67C2×D411yescharacteristic
482C23×D67C2×D411yescharacteristic
483C2×Dic134—21no—
484C2×Dic134—21no—
485C2×Dic134—21no—
486C2×Dic134—21no—
487C2×Dic134—21no—
488C2×Dic134C2411yescharacteristic
489C2×Dic134C2411yescharacteristic
490Q8×D67—22no—
491Q8×D67—22no—
492Q8×D67—22no—
493Q8×D67—22no—
494Q8×D67—44no—
495C2×D268C2×D411yescharacteristic
496C2×C22⋊D67C2×D411yescharacteristic
497C2×C22⋊D67C2×D411yescharacteristic
498D4×D67—42no—
499C22×Dic67—21no—
500C22×Dic67C2×D411yescharacteristic
501C22×Dic67C2×D411yescharacteristic
502C2×C4×D67—22no—
503C2×C4×D67—22no—
504C2×C4×D67—22no—
505C2×C4×D67—22no—
506C2×C4×D67—21no—
507C2×C4×D67—21no—
508C2×C4×D67—21no—
509C2×C4×D67—21no—
510C2×C4×D67—21no—
511C2×C4×D67—21no—
512C2×C4×D67—21no—
513C2×C4×D67—21no—
514C2×C4×D67—21no—
515C2×C4×D67—21no—
516C2×C4×D67—44no—
517C2×C4×D67C2×D411yescharacteristic
518C2×C4×D67C2×D411yescharacteristic
519C2×C4×D67C2×D411yescharacteristic
520C2×C4×D67C2×D411yescharacteristic
521C2×C4×D67C2×D411yescharacteristic
522C2×C4×D67C2×D411yescharacteristic
523C2×C4×D67C2411yescharacteristic
524C2×C4×D67C2411yescharacteristic
525C2×C4×D67C2411yescharacteristic
526Dic268—22no—
527#11761618—22no—
528#11761618—22no—
529#11761612—22no—
530#11761611—22no—
531#11761611—22no—
532C2×C67⋊C8—22no—
533C2×C67⋊C8C2411yescharacteristic
534C2×C67⋊C8C2411yescharacteristic
535C2×C67⋊C8C2411yescharacteristic
536C2×C67⋊C8C2411yescharacteristic
537C8×D67—22no—
538C8×D67—22no—
539C8×D67—22no—
540C8×D67—22no—
541C8×D67—22no—
542C8×D67#4114yes—
543C4⋊Dic67—21no—
544C4⋊Dic67—21no—
545C4⋊Dic67—21no—
546C4⋊Dic67—21no—
547C4⋊Dic67—21no—
548C4⋊Dic67—21no—
549C4⋊Dic67—21no—
550C4⋊Dic67—21no—
551C4⋊Dic67—21no—
552C4⋊Dic67—21no—
553C4⋊Dic67C2×D411yescharacteristic
554C4⋊Dic67C2411yescharacteristic
555C4⋊Dic67C2411yescharacteristic
556C4⋊Dic67C2411yescharacteristic
557C4⋊Dic67C2411yescharacteristic
558C4⋊Dic67C2411yescharacteristic
559C4⋊Dic67C2411yescharacteristic
560Dic67⋊C4—21no—
561Dic67⋊C4—21no—
562Dic67⋊C4—21no—
563Dic67⋊C4—21no—
564Dic67⋊C4—21no—
565Dic67⋊C4—21no—
566Dic67⋊C4—21no—
567Dic67⋊C4—21no—
568Dic67⋊C4—21no—
569Dic67⋊C4—21no—
570Dic67⋊C4—21no—
571Dic67⋊C4—21no—
572Dic67⋊C4—21no—
573Dic67⋊C4—21no—
574Dic67⋊C4—21no—
575Dic67⋊C4—21no—
576Dic67⋊C4—21no—
577Dic67⋊C4—21no—
578Dic67⋊C4—21no—
579Dic67⋊C4—21no—
580Dic67⋊C4—21no—
581Dic67⋊C4—21no—
582Dic67⋊C4—21no—
583Dic67⋊C4—21no—
584Dic67⋊C4—21no—
585Dic67⋊C4—21no—
586Dic67⋊C4C2×D411yescharacteristic
587Dic67⋊C4C2×D411yescharacteristic
588C22⋊Dic67—21no—
589C22⋊Dic67—21no—
590C22⋊Dic67—21no—
591C22⋊Dic67—21no—
592C22⋊Dic67—21no—
593C22⋊Dic67—21no—
594C22⋊Dic67—21no—
595C22⋊Dic67C2×D411yescharacteristic
596C22⋊Dic67C2×D411yescharacteristic
597(C2×D67)⋊C4—21no—
598(C2×D67)⋊C4—21no—
599(C2×D67)⋊C4—21no—
600(C2×D67)⋊C4—21no—
601(C2×D67)⋊C4—21no—
602(C2×D67)⋊C4—21no—
603(C2×D67)⋊C4—21no—
604(C2×D67)⋊C4—21no—
605(C2×D67)⋊C4—21no—
606(C2×D67)⋊C4—21no—
607(C2×D67)⋊C4—21no—
608(C2×D67)⋊C4—21no—
609(C2×D67)⋊C4—21no—
610(C2×D67)⋊C4—21no—
611(C2×D67)⋊C4C2×D411yescharacteristic
612(C2×D67)⋊C4C2×D411yescharacteristic
613(C2×D67)⋊C4C2×D411yescharacteristic
614(C2×D67)⋊C4C2×D411yescharacteristic
615C4×Dic67—21no—
616C4×Dic67—21no—
617C4×Dic67—21no—
618C4×Dic67—21no—
619C4×Dic67—21no—
620C4×Dic67—21no—
621C4×Dic67—21no—
622C4×Dic67—21no—
623C4×Dic67—21no—
624C4×Dic67—21no—
625C4×Dic67—21no—
626C4×Dic67—21no—
627C4×Dic67—21no—
628C4×Dic67—21no—
629C4×Dic67—21no—
630C4×Dic67C2×D411yescharacteristic
631C4×Dic67C2×D411yescharacteristic
632C4×Dic67C2411yescharacteristic
633C2×Q8×C67—21no—
634C2×Q8×C67C2411yescharacteristic
635C2×Q8×C67C2411yescharacteristic
636C2×D4×C67C2×D411yescharacteristic
637C22×C4×C67—21no—
638C22×C4×C67C2411yescharacteristic
639C22×C4×C67C2411yescharacteristic
640Q16×C67—22no—
641M16×C67—22no—
642C2×C8×C67—22no—
643C2×C8×C67C2411yescharacteristic
644C2×C8×C67C2411yescharacteristic
645C2×C8×C67C2411yescharacteristic
646C2×C8×C67C2411yescharacteristic
647C4⋊C4×C67—21no—
648C4⋊C4×C67—21no—
649C4⋊C4×C67—21no—
650C4⋊C4×C67—21no—
651C4⋊C4×C67—21no—
652C4⋊C4×C67—21no—
653C4⋊C4×C67—21no—
654C4⋊C4×C67—21no—
655C4⋊C4×C67—21no—
656C4⋊C4×C67—21no—
657C4⋊C4×C67C2×D411yescharacteristic
658C4⋊C4×C67C2411yescharacteristic
659C4⋊C4×C67C2411yescharacteristic
660C4⋊C4×C67C2411yescharacteristic
661C4⋊C4×C67C2411yescharacteristic
662C4⋊C4×C67C2411yescharacteristic
663C4⋊C4×C67C2411yescharacteristic
664C22⋊C4×C67—21no—
665C22⋊C4×C67—21no—
666C22⋊C4×C67—21no—
667C22⋊C4×C67—21no—
668C22⋊C4×C67—21no—
669C22⋊C4×C67—21no—
670C22⋊C4×C67—21no—
671C22⋊C4×C67C2×D411yescharacteristic
672C22⋊C4×C67C2×D411yescharacteristic
673C42×C67—21no—
674C42×C67—21no—
675C42×C67—21no—
676C42×C67—21no—
677C42×C67—21no—
678C42×C67C2411yescharacteristic
679C23×C67C22×D411yescharacteristic
680C23×C67C22×D411yescharacteristic
681C22×D67—22no—
682C22×D67—22no—
683C22×D67—22no—
684C22×D67—22no—
685C22×D67—22no—
686C22×D67—22no—
687C22×D67C22×D411yescharacteristic
688C22×D67C22×D411yescharacteristic
689C22×D67C22×D411yescharacteristic
690Q8×C67—21no—
691Q8×C67—21no—
692Q8×C67—21no—
693Q8×C67—21no—
694Q8×C67—42no—
695D4×C67—41no—
696C2×C4×C67—21no—
697C2×C4×C67—21no—
698C2×C4×C67—21no—
699C2×C4×C67—21no—
700C2×C4×C67—21no—
701C2×C4×C67—21no—
702C2×C4×C67—21no—
703C2×C4×C67—21no—
704C2×C4×C67—21no—
705C2×C4×C67—21no—
706C2×C4×C67—21no—
707C2×C4×C67—21no—
708C2×C4×C67—42no—
709C2×C4×C67C22×D411yescharacteristic
710C2×C4×C67C22×D411yescharacteristic
711C2×C4×C67C22×D411yescharacteristic
712C2×C4×C67C22×D411yescharacteristic
713C2×C4×C67C2511yescharacteristic
714C22⋊D67—41no—
715C22⋊D67—41no—
716C2×Dic67—22no—
717C2×Dic67—22no—
718C2×Dic67—21no—
719C2×Dic67—21no—
720C2×Dic67—21no—
721C2×Dic67—21no—
722C2×Dic67—21no—
723C2×Dic67—21no—
724C2×Dic67—21no—
725C2×Dic67—21no—
726C2×Dic67—42no—
727C2×Dic67C22×D411yescharacteristic
728C2×Dic67C22×D411yescharacteristic
729C2×Dic67C22×D411yescharacteristic
730C2×Dic67C22×D411yescharacteristic
731C2×Dic67C22×D411yescharacteristic
732D268—41no—
733C4×D67—22no—
734C4×D67—22no—
735C4×D67—22no—
736C4×D67—22no—
737C4×D67—21no—
738C4×D67—21no—
739C4×D67—21no—
740C4×D67—21no—
741C4×D67—22no—
742C4×D67—22no—
743C4×D67—42no—
744C4×D67—42no—
745C4×D67—42no—
746C4×D67—42no—
747C4×D67—42no—
748C4×D67—42no—
749C4×D67—42no—
750C4×D67—42no—
751C4×D67—42no—
752C4×D67—42no—
753C4×D67C2×#4112yes—
754C4×D672−1+412yes—
755Dic134—21no—
756Dic134—21no—
757Dic134—21no—
758Dic134—21no—
759Dic134—42no—
760Dic134—42no—
761Dic134—42no—
762Dic134—42no—
763Dic134—42no—
764C8×C67—21no—
765C8×C67—21no—
766C8×C67—21no—
767C8×C67C2×#4112yes—
768C67⋊C8—21no—
769C67⋊C8—21no—
770C67⋊C8—21no—
771C67⋊C8C2×#4112yes—
772C22×C67—21no—
773C22×C67—21no—
774C22×C67—21no—
775C22×C67—21no—
776C22×C67—21no—
777C22×C67—21no—
778C22×C67C23×D411yescharacteristic
779C2×D67—21no—
780C2×D67—21no—
781C2×D67—21no—
782C2×D67—21no—
783C2×D67—21no—
784C2×D67—21no—
785C2×D67—44no—
786C2×D67—44no—
787C2×D67#54712yes—
788C2×D67#57512yes—
789C2×D67#57812yes—
790C4×C67—21no—
791C4×C67—21no—
792C4×C67—21no—
793C4×C67—21no—
794C4×C67—41no—
795C4×C67—41no—
796C4×C67—41no—
797C4×C67—41no—
798C4×C67—41no—
799C4×C67—41no—
800C4×C67—41no—
801C4×C67—41no—
802C4×C67C22×#4111yescharacteristic
803C4×C67C2×2−1+411yescharacteristic
804Dic67—21no—
805Dic67—21no—
806Dic67—21no—
807Dic67—21no—
808Dic67—41no—
809Dic67—41no—
810Dic67—41no—
811Dic67—41no—
812Dic67—41no—
813Dic67—41no—
814Dic67—41no—
815Dic67—41no—
816Dic67#54712yes—
817C2×#3349—671nomaximal, Sylow
818C2×C67—41no—
819C2×C67—41no—
820C2×C67C2×#54711yescharacteristic
821C2×C67C2×#57511yescharacteristic
822C2×C67C2×#57811yescharacteristic
823D67—41no—
824D67—41no—
825D67#334914yesdirect product factor
826C2×#556—671no—
827C2×#552—671no—
828#3349—671no—
829#3349—671no—
830#3349—671no—
831#3349—671no—
832#3349—671no—
833#3349—671no—
834#3349—671no—
835#3349—671no—
836#3349—671no—
837#3349—671no—
838#3349—671no—
839#3349—671no—
840#3349—671no—
841#3349—671no—
842#3349—671no—
843#3349D6711yescharacteristic, direct product factor
844C2×#501—671no—
845C2×#484—671no—
846C2×#485—671no—
847C2×#485—671no—
848C2×#485—671no—
849C2×#479—671no—
850C2×#477—671no—
851C2×#470—671no—
852C2×#467—671no—
853C2×#441—671no—
854C2×#435—671no—
855C2×#428—671no—
856C2×#427—671no—
857C67C2×#334911yescharacteristic, complemented, Sylow
858C22×Q16—671no—
859C22×M16—671no—
860C23×C8—671no—
861#556—671no—
862#556—671no—
863#556—671no—
864#556—671no—
865#556—671no—
866#556—671no—
867#556—671no—
868#556—1341no—
869#556—1341no—
870#556—1341no—
871#556—1341no—
872#556C2×D6711yescharacteristic
873#552—671no—
874#552—671no—
875#552—671no—
876#552—671no—
877#552—671no—
878#552—671no—
879#552—671no—
880#552—1341no—
881#552—1341no—
882#552—1341no—
883#552—1341no—
884#552C2×D6711yescharacteristic
885C2×C4⋊Q8—671no—
886C2×#126—1341no—
887C2×#126—1341no—
888C2×#126—1341no—
889C2×#125—671no—
890C2×#125—1341no—
891C2×#124—1341no—
892C2×#123—1341no—
893C2×C22⋊Q8—671no—
894C2×C22⋊Q8—671no—
895C2×C22⋊Q8—671no—
896C2×C22⋊Q8—671no—
897C2×C4×Q8—671no—
898C2×C4×Q8—671no—
899C2×C4×Q8—1341no—
900C2×C4×D4—671no—
901C2×#117—671no—
902C2×#117—671no—
903C2×#117—671no—
904C2×#117—1341no—
905C22×C4⋊C4—671no—
906#501—671no—
907#501—671no—
908#501—671no—
909#501—671no—
910#501—671no—
911#501—671no—
912#501—671no—
913#501C2×D6711yescharacteristic, complemented
914#485—671no—
915#485—671no—
916#485—671no—
917#485—671no—
918#485—671no—
919#485—671no—
920#485—671no—
921#485—671no—
922#485—671no—
923#485—671no—
924#485—671no—
925#485—671no—
926#485—671no—
927#485—671no—
928#485—671no—
929#485—671no—
930#485—671no—
931#485—671no—
932#485—671no—
933#485—671no—
934#485—671no—
935#485C2×D6711yescharacteristic, complemented
936#485C2×D6711yescharacteristic, complemented
937#485C2×D6711yescharacteristic, complemented
938#484—671no—
939#484—671no—
940#484—671no—
941#484—671no—
942#484—671no—
943#484—671no—
944#484—671no—
945#484C2×D6711yescharacteristic, complemented
946#479—671no—
947#479—671no—
948#479—671no—
949#479—671no—
950#479—671no—
951#479—671no—
952#479—671no—
953#479C2×D6711yescharacteristic, complemented
954#477—671no—
955#477—671no—
956#477—671no—
957#477—671no—
958#477—671no—
959#477—671no—
960#477—671no—
961#477C2×D6711yescharacteristic, complemented
962#470—671no—
963#470—671no—
964#470—671no—
965#470—671no—
966#470—671no—
967#470—671no—
968#470—671no—
969#470C2×D6711yescharacteristic, complemented
970#467—671no—
971#467—671no—
972#467—671no—
973#467—671no—
974#467—671no—
975#467—671no—
976#467—671no—
977#467C2×D6711yescharacteristic, complemented
978#441—671no—
979#441—671no—
980#441—671no—
981#441—671no—
982#441—671no—
983#441—671no—
984#441—671no—
985#441C2×D6711yescharacteristic, complemented
986#435—671no—
987#435—671no—
988#435—671no—
989#435—671no—
990#435—671no—
991#435—671no—
992#435—671no—
993#435C2×D6711yescharacteristic
994#428—671no—
995#428—671no—
996#428—671no—
997#428—671no—
998#428—671no—
999#428—671no—
1000#428—671no—
1001#428C2×D6711yescharacteristic, complemented
1002#427—671no—
1003#427—671no—
1004#427—671no—
1005#427—671no—
1006#427—671no—
1007#427—671no—
1008#427—671no—
1009#427C2×D6711yescharacteristic, complemented
1010C2×#107—671no—
1011C2×#107—671no—
1012C2×#107—671no—
1013C2×#107—671no—
1014C2×#107—671no—
1015C2×#106—671no—
1016C2×#106—671no—
1017C2×#106—671no—
1018C2×#106—671no—
1019C2×C4⋊C8—671no—
1020C2×#103—671no—
1021C2×#103—671no—
1022C2×#103—671no—
1023C2×#103—671no—
1024C2×#103—671no—
1025C2×#103—671no—
1026C2×C22⋊C8—671no—
1027C2×C22⋊C8—671no—
1028C2×#97—671no—
1029C22×Q8—671no—
1030C22×Q8—671no—
1031C22×Q8—1341no—
1032C22×D4—671no—
1033C23×C4—671no—
1034C23×C4—671no—
1035C23×C4—1341no—
1036C2×Q16—671no—
1037C2×Q16—671no—
1038C2×Q16—671no—
1039C2×Q16—1344no—
1040C2×Q16C22×D6711yescharacteristic
1041C2×M16—671no—
1042C2×M16—671no—
1043C2×M16—671no—
1044C2×M16—1344no—
1045C2×M16C22×D6711yescharacteristic
1046C22×C8—671no—
1047C22×C8—671no—
1048C22×C8—671no—
1049C22×C8—671no—
1050C22×C8—671no—
1051C22×C8—671no—
1052C22×C8—671no—
1053C22×C8—1344no—
1054C22×C8C22×D6711yescharacteristic
1055C4⋊Q8—671no—
1056C4⋊Q8—671no—
1057C4⋊Q8—671no—
1058C4⋊Q8—1341no—
1059C4⋊Q8—1341no—
1060C4⋊Q8C22×D6711yescharacteristic
1061#126—21no—
1062#126—21no—
1063#126—21no—
1064#126—1341no—
1065#126—1341no—
1066#126—1341no—
1067#126—1341no—
1068#126—1341no—
1069#126—1341no—
1070#126—1341no—
1071#126—1341no—
1072#126—1341no—
1073#126—1341no—
1074#126—1341no—
1075#126—1341no—
1076#126—1341no—
1077#126—1341no—
1078#126—1341no—
1079#126—1341no—
1080#126—1341no—
1081#126—1341no—
1082#126—1341no—
1083#126—1341no—
1084#126—1341no—
1085#125—21no—
1086#125—671no—
1087#125—671no—
1088#125—671no—
1089#125—1341no—
1090#125—1341no—
1091#125—1341no—
1092#125—1341no—
1093#125—1341no—
1094#125—1341no—
1095#125—1341no—
1096#125—1341no—
1097#125—1341no—
1098#125C22×D6711yescharacteristic
1099#124—21no—
1100#124—1341no—
1101#124—1341no—
1102#124—1341no—
1103#124—1341no—
1104#124—1341no—
1105#124—1341no—
1106#124—1341no—
1107#123—21no—
1108#123—1341no—
1109#123—1341no—
1110#123—1341no—
1111#123—1341no—
1112#123—1341no—
1113#123—1341no—
1114#123—1341no—
1115C22⋊Q8—671no—
1116C22⋊Q8—671no—
1117C22⋊Q8—671no—
1118C22⋊Q8—671no—
1119C22⋊Q8—671no—
1120C22⋊Q8—671no—
1121C22⋊Q8—671no—
1122C22⋊Q8—671no—
1123C22⋊Q8—671no—
1124C22⋊Q8—671no—
1125C22⋊Q8—671no—
1126C22⋊Q8—671no—
1127C22⋊Q8—1341no—
1128C22⋊Q8—1341no—
1129C22⋊Q8—1341no—
1130C22⋊Q8—1341no—
1131C22⋊Q8—1341no—
1132C22⋊Q8—1341no—
1133C22⋊Q8—1341no—
1134C22⋊Q8—1341no—
1135C22⋊Q8C22×D6711yescharacteristic
1136C22⋊Q8C22×D6711yescharacteristic
1137C22⋊Q8C22×D6711yescharacteristic
1138C22⋊Q8C22×D6711yescharacteristic
1139C4×Q8—21no—
1140C4×Q8—671no—
1141C4×Q8—671no—
1142C4×Q8—671no—
1143C4×Q8—671no—
1144C4×Q8—671no—
1145C4×Q8—671no—
1146C4×Q8—1341no—
1147C4×Q8—1341no—
1148C4×Q8—1341no—
1149C4×Q8—1341no—
1150C4×Q8—1341no—
1151C4×Q8—1341no—
1152C4×Q8—1341no—
1153C4×Q8—1341no—
1154C4×Q8—1341no—
1155C4×Q8—1341no—
1156C4×Q8—1341no—
1157C4×Q8C22×D6711yescharacteristic
1158C4×Q8C22×D6711yescharacteristic
1159C4×D4—671no—
1160C4×D4—671no—
1161C4×D4—671no—
1162C4×D4—671no—
1163C4×D4—671no—
1164C4×D4—671no—
1165C4×D4—671no—
1166C4×D4C22×D6711yescharacteristic
1167#117—21no—
1168#117—671no—
1169#117—671no—
1170#117—671no—
1171#117—671no—
1172#117—671no—
1173#117—671no—
1174#117—671no—
1175#117—671no—
1176#117—671no—
1177#117—1341no—
1178#117—1341no—
1179#117—1341no—
1180#117—1341no—
1181#117—1341no—
1182#117—1341no—
1183#117—1341no—
1184#117—1341no—
1185#117—1341no—
1186#117—1341no—
1187#117—1341no—
1188#117—1341no—
1189#117—1341no—
1190#117C22×D6711yescharacteristic
1191#117C22×D6711yescharacteristic
1192#117C22×D6711yescharacteristic
1193C2×C4⋊C4—671no—
1194C2×C4⋊C4—671no—
1195C2×C4⋊C4—671no—
1196C2×C4⋊C4—671no—
1197C2×C4⋊C4—671no—
1198C2×C4⋊C4—671no—
1199C2×C4⋊C4—671no—
1200C2×C4⋊C4—671no—
1201C2×C4⋊C4—671no—
1202C2×C4⋊C4—671no—
1203C2×C4⋊C4—1341no—
1204C2×C4⋊C4—1341no—
1205C2×C4⋊C4—1341no—
1206C2×C4⋊C4—1341no—
1207C2×C4⋊C4—1341no—
1208C2×C4⋊C4—1341no—
1209C2×C4⋊C4—1341no—
1210C2×C4⋊C4—1341no—
1211C2×C4⋊C4—1341no—
1212C2×C4⋊C4—1341no—
1213C2×C4⋊C4—1341no—
1214C2×C4⋊C4—1341no—
1215C2×C4⋊C4C22×D6711yescharacteristic
1216C2×C22⋊C4—671no—
1217C2×C22⋊C4—671no—
1218C2×C22⋊C4—1341no—
1219C2×C22⋊C4—1341no—
1220C2×C22⋊C4—1341no—
1221C2×C22⋊C4—1341no—
1222C2×C22⋊C4—1341no—
1223C2×C22⋊C4—1341no—
1224C2×C22⋊C4—1341no—
1225C2×C42—671no—
1226C2×C42—1341no—
1227C2×C42—1341no—
1228C2×C42—1341no—
1229C2×C42—1341no—
1230C2×C42—1341no—
1231#107—671no—
1232#107—671no—
1233#107—671no—
1234#107—671no—
1235#107—671no—
1236#107—671no—
1237#107—671no—
1238#107—671no—
1239#107—671no—
1240#107—671no—
1241#107—671no—
1242#107—671no—
1243#107—671no—
1244#107—671no—
1245#107—671no—
1246#107C22×D6711yescharacteristic
1247#107C22×D6711yescharacteristic
1248#107C22×D6711yescharacteristic
1249#107C22×D6711yescharacteristic
1250#107C22×D6711yescharacteristic
1251#106—671no—
1252#106—671no—
1253#106—671no—
1254#106—671no—
1255#106—671no—
1256#106—671no—
1257#106—671no—
1258#106—671no—
1259#106—671no—
1260#106—671no—
1261#106—671no—
1262#106—671no—
1263#106C22×D6711yescharacteristic
1264#106C22×D6711yescharacteristic
1265#106C22×D6711yescharacteristic
1266#106C22×D6711yescharacteristic
1267C4⋊C8—671no—
1268C4⋊C8—671no—
1269C4⋊C8—671no—
1270C4⋊C8C22×D6711yescharacteristic
1271#103—671no—
1272#103—671no—
1273#103—671no—
1274#103—671no—
1275#103—671no—
1276#103—671no—
1277#103—671no—
1278#103—671no—
1279#103—671no—
1280#103—671no—
1281#103—671no—
1282#103—671no—
1283#103—671no—
1284#103—671no—
1285#103—671no—
1286#103—671no—
1287#103—671no—
1288#103—671no—
1289#103C22×D6711yescharacteristic
1290#103C22×D6711yescharacteristic
1291#103C22×D6711yescharacteristic
1292#103C22×D6711yescharacteristic
1293#103C22×D6711yescharacteristic
1294#103C22×D6711yescharacteristic
1295C22⋊C8—671no—
1296C22⋊C8—671no—
1297C22⋊C8—671no—
1298C22⋊C8—671no—
1299C22⋊C8—671no—
1300C22⋊C8—671no—
1301C22⋊C8C22×D6711yescharacteristic
1302C22⋊C8C22×D6711yescharacteristic
1303#97—671no—
1304#97—671no—
1305#97—671no—
1306#97C22×D6711yescharacteristic
1307C24—671no—
1308C24—671no—
1309C2×Q8—21no—
1310C2×Q8—2684no—
1311C2×Q8—671no—
1312C2×Q8—671no—
1313C2×Q8—1341no—
1314C2×Q8—1341no—
1315C2×Q8—1341no—
1316C2×Q8—1341no—
1317C2×Q8—1342no—
1318C2×Q8—1342no—
1319C2×Q8—1342no—
1320C2×Q8—1342no—
1321C2×Q8—1341no—
1322C2×Q8C23×D6711yescharacteristic
1323C2×Q8C23×D6711yescharacteristic
1324C2×D4—2682no—
1325C2×D4—671no—
1326C2×D4—671no—
1327C2×D4—671no—
1328C2×D4D4×D6711yescharacteristic
1329C22×C4—21no—
1330C22×C4—2684no—
1331C22×C4—671no—
1332C22×C4—671no—
1333C22×C4—671no—
1334C22×C4—671no—
1335C22×C4—671no—
1336C22×C4—671no—
1337C22×C4—671no—
1338C22×C4—671no—
1339C22×C4—671no—
1340C22×C4—671no—
1341C22×C4—671no—
1342C22×C4—1341no—
1343C22×C4—1341no—
1344C22×C4—1341no—
1345C22×C4—1341no—
1346C22×C4—1341no—
1347C22×C4—1341no—
1348C22×C4—1341no—
1349C22×C4—1341no—
1350C22×C4—1341no—
1351C22×C4—1341no—
1352C22×C4—1342no—
1353C22×C4—1342no—
1354C22×C4—1342no—
1355C22×C4—1342no—
1356C22×C4—1341no—
1357C22×C4C23×D6711yescharacteristic
1358C22×C4C23×D6711yescharacteristic
1359Q16—22no—
1360Q16—1342no—
1361Q16—1342no—
1362Q16—1342no—
1363M16—22no—
1364M16—1342no—
1365M16—1342no—
1366M16—1342no—
1367C2×C8—22no—
1368C2×C8—671no—
1369C2×C8—674no—
1370C2×C8—671no—
1371C2×C8—671no—
1372C2×C8—671no—
1373C2×C8—1342no—
1374C2×C8—1342no—
1375C2×C8—1342no—
1376C2×C8—1342no—
1377C2×C8—1342no—
1378C2×C8—1342no—
1379C2×C8C23×D6711yescharacteristic
1380C2×C8C23×D6711yescharacteristic
1381C2×C8C23×D6711yescharacteristic
1382C2×C8C23×D6711yescharacteristic
1383C4⋊C4—21no—
1384C4⋊C4—21no—
1385C4⋊C4—21no—
1386C4⋊C4—21no—
1387C4⋊C4—21no—
1388C4⋊C4—21no—
1389C4⋊C4—21no—
1390C4⋊C4—21no—
1391C4⋊C4—21no—
1392C4⋊C4—21no—
1393C4⋊C4—671no—
1394C4⋊C4—671no—
1395C4⋊C4—671no—
1396C4⋊C4—671no—
1397C4⋊C4—671no—
1398C4⋊C4—671no—
1399C4⋊C4—671no—
1400C4⋊C4—671no—
1401C4⋊C4—671no—
1402C4⋊C4—1341no—
1403C4⋊C4—1341no—
1404C4⋊C4—1341no—
1405C4⋊C4—1341no—
1406C4⋊C4—1341no—
1407C4⋊C4—1341no—
1408C4⋊C4—1341no—
1409C4⋊C4—1341no—
1410C4⋊C4—1341no—
1411C4⋊C4—1341no—
1412C4⋊C4—1341no—
1413C4⋊C4—1341no—
1414C4⋊C4—1341no—
1415C4⋊C4—1341no—
1416C4⋊C4—1341no—
1417C4⋊C4—1341no—
1418C4⋊C4—1341no—
1419C4⋊C4—1341no—
1420C4⋊C4—1341no—
1421C4⋊C4—1341no—
1422C4⋊C4—1341no—
1423C4⋊C4—1341no—
1424C4⋊C4—1341no—
1425C4⋊C4—1341no—
1426C4⋊C4—1341no—
1427C4⋊C4—1341no—
1428C4⋊C4—1341no—
1429C4⋊C4—1341no—
1430C4⋊C4—1341no—
1431C4⋊C4—1341no—
1432C4⋊C4—1341no—
1433C4⋊C4—1341no—
1434C4⋊C4—1341no—
1435C4⋊C4—1341no—
1436C4⋊C4—1341no—
1437C4⋊C4—1341no—
1438C4⋊C4D4×D6711yescharacteristic
1439C4⋊C4C23×D6711yescharacteristic
1440C4⋊C4C23×D6711yescharacteristic
1441C4⋊C4C23×D6711yescharacteristic
1442C4⋊C4C23×D6711yescharacteristic
1443C4⋊C4C23×D6711yescharacteristic
1444C4⋊C4C23×D6711yescharacteristic
1445C22⋊C4—21no—
1446C22⋊C4—21no—
1447C22⋊C4—21no—
1448C22⋊C4—21no—
1449C22⋊C4—21no—
1450C22⋊C4—21no—
1451C22⋊C4—21no—
1452C22⋊C4—671no—
1453C22⋊C4—671no—
1454C22⋊C4—671no—
1455C22⋊C4—671no—
1456C22⋊C4—671no—
1457C22⋊C4—671no—
1458C22⋊C4—1341no—
1459C22⋊C4—1341no—
1460C22⋊C4—1341no—
1461C22⋊C4—1341no—
1462C22⋊C4—1341no—
1463C22⋊C4—1341no—
1464C22⋊C4—1341no—
1465C22⋊C4—1341no—
1466C22⋊C4—1341no—
1467C22⋊C4—1341no—
1468C22⋊C4—1341no—
1469C22⋊C4—1341no—
1470C22⋊C4—1341no—
1471C22⋊C4—1341no—
1472C22⋊C4—1341no—
1473C22⋊C4—1341no—
1474C22⋊C4—1341no—
1475C22⋊C4—1341no—
1476C22⋊C4—1341no—
1477C22⋊C4—1341no—
1478C22⋊C4—1341no—
1479C22⋊C4D4×D6711yescharacteristic
1480C22⋊C4D4×D6711yescharacteristic
1481C42—21no—
1482C42—21no—
1483C42—21no—
1484C42—21no—
1485C42—21no—
1486C42—671no—
1487C42—671no—
1488C42—671no—
1489C42—1341no—
1490C42—1341no—
1491C42—1341no—
1492C42—1341no—
1493C42—1341no—
1494C42—1341no—
1495C42—1341no—
1496C42—1341no—
1497C42—1341no—
1498C42—1341no—
1499C42—1341no—
1500C42—1341no—
1501C42—1341no—
1502C42—1341no—
1503C42—1341no—
1504C42C23×D6711yescharacteristic
1505C23—671no—
1506C23—671no—
1507C23—671no—
1508C23—1342no—
1509C23—1342no—
1510C23—1342no—
1511C23—1342no—
1512C23—1342no—
1513C23—1342no—
1514C23C2×D4×D6711yescharacteristic
1515C23C2×D4×D6711yescharacteristic
1516Q8—21no—
1517Q8—21no—
1518Q8—21no—
1519Q8—21no—
1520Q8—42no—
1521Q8—2682no—
1522Q8—2682no—
1523Q8—2682no—
1524Q8—2682no—
1525Q8—2682no—
1526Q8—1341no—
1527Q8—1341no—
1528Q8—1341no—
1529Q8—1341no—
1530D4—41no—
1531D4—2681no—
1532D4—2681no—
1533D4—2681no—
1534C2×C4—21no—
1535C2×C4—21no—
1536C2×C4—21no—
1537C2×C4—21no—
1538C2×C4—21no—
1539C2×C4—21no—
1540C2×C4—21no—
1541C2×C4—21no—
1542C2×C4—21no—
1543C2×C4—21no—
1544C2×C4—21no—
1545C2×C4—21no—
1546C2×C4—42no—
1547C2×C4—2682no—
1548C2×C4—2682no—
1549C2×C4—2682no—
1550C2×C4—2682no—
1551C2×C4—2682no—
1552C2×C4—2682no—
1553C2×C4—2682no—
1554C2×C4—2682no—
1555C2×C4—2682no—
1556C2×C4—2682no—
1557C2×C4—2682no—
1558C2×C4—671no—
1559C2×C4—672no—
1560C2×C4—672no—
1561C2×C4—671no—
1562C2×C4—671no—
1563C2×C4—671no—
1564C2×C4—671no—
1565C2×C4—1342no—
1566C2×C4—1342no—
1567C2×C4—1342no—
1568C2×C4—1342no—
1569C2×C4—1342no—
1570C2×C4—1342no—
1571C2×C4—1341no—
1572C2×C4—1341no—
1573C2×C4—1341no—
1574C2×C4—1341no—
1575C2×C4—1341no—
1576C2×C4—1341no—
1577C2×C4—1341no—
1578C2×C4—1341no—
1579C2×C4—1342no—
1580C2×C4—1342no—
1581C2×C4—1341no—
1582C2×C4—1341no—
1583C2×C4—1341no—
1584C2×C4—1341no—
1585C2×C4C2×D4×D6711yescharacteristic
1586C2×C4C2×D4×D6711yescharacteristic
1587C2×C4C2×D4×D6711yescharacteristic
1588C2×C4C2×D4×D6711yescharacteristic
1589C2×C4C24×D6711yescharacteristic
1590C8—21no—
1591C8—21no—
1592C8—21no—
1593C8—672no—
1594C8—1341no—
1595C8—1341no—
1596C8—1341no—
1597C8#41×D6712yes—
1598C22—21no—
1599C22—21no—
1600C22—21no—
1601C22—21no—
1602C22—21no—
1603C22—21no—
1604C22—2684no—
1605C22—2684no—
1606C22—672no—
1607C22—672no—
1608C22—672no—
1609C22—1341no—
1610C22—1341no—
1611C22—1341no—
1612C22—1341no—
1613C22—1341no—
1614C22—1341no—
1615C22C22×D4×D6711yescharacteristic
1616C4—21no—
1617C4—21no—
1618C4—21no—
1619C4—21no—
1620C4—41no—
1621C4—41no—
1622C4—41no—
1623C4—41no—
1624C4—41no—
1625C4—41no—
1626C4—41no—
1627C4—41no—
1628C4—2681no—
1629C4—2681no—
1630C4—2681no—
1631C4—2681no—
1632C4—2681no—
1633C4—2681no—
1634C4—2681no—
1635C4—2681no—
1636C4—672no—
1637C4—1341no—
1638C4—1341no—
1639C4—1341no—
1640C4—1341no—
1641C4C2×#41×D6711yescharacteristic
1642C42−1+4×D6711yescharacteristic
1643C2—41no—
1644C2—41no—
1645C2—2681no—
1646C2—2681no—
1647C2—674no—
1648C2#547×D6711yescharacteristic
1649C2#575×D6711yescharacteristic
1650C2#578×D6711yescharacteristic
subgroupG/H
centerC22C22×D4×D67
commutator, cosocleC2×C4×C67C25
FrattiniC2×C4C24×D67
FittingC67×#3349C2
socleC22×C67C23×D4
prime radicalC2×D4×D67D4
hypercenter#3349D67
hypocenterC67C2×#3349
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C22 ◁ C4×D4 ◁ #3349

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. #22572746C2semidirect
4. #22572745C2semidirect
5. #22572744C2semidirect
6. #22572743C2semidirect
7. #22572742C2semidirect
8. #22572741C2semidirect
9. #22572740C2semidirect
10. #22572739C2semidirect
11. #22572738C2semidirect
12. #22572737C2semidirect
13. #22572736C2semidirect
14. #22572735C2semidirect
15. #22572734C2semidirect
16. #22572733C2semidirect
17. #22572732C2semidirect
18. #501×D67C2semidirect
19. #484×D67C2semidirect
20. #485×D67C2semidirect
21. #485×D67C2semidirect
22. #485×D67C2semidirect
23. #479×D67C2semidirect
24. #477×D67C2semidirect
25. #470×D67C2semidirect
26. #467×D67C2semidirect
27. #441×D67C2semidirect
29. #428×D67C2semidirect
30. #427×D67C2semidirect
31. C67×#3349C2semidirect
78. #16863806C22semidirect
79. #16863805C22semidirect
80. #16863804C22semidirect
81. #16863804C22semidirect
82. #16863803C22semidirect
83. #16863803C22semidirect
84. #16863802C22semidirect
85. #16863740C22semidirect
86. #16863740C22semidirect
87. #16863740C22semidirect
88. #16863739C22semidirect
89. #16863739C22semidirect
90. #16863739C22semidirect
91. #16863738C22semidirect
92. #16863738C22semidirect
93. #16863738C22semidirect
94. #16863737C22semidirect
95. #16863737C22semidirect
96. #16863737C22semidirect
97. #16863736C22semidirect
98. #16863736C22semidirect
99. #16863736C22semidirect
100. #16863735C22semidirect
101. #16863735C22semidirect
102. #16863735C22semidirect
103. #16863734C22semidirect
104. #16863734C22semidirect
105. #16863734C22semidirect
106. #16863733C22semidirect
107. #16863733C22semidirect
108. #16863732C22semidirect
109. #16863731C22semidirect
110. #16863730C22semidirect
111. #16863730C22semidirect
112. #16863729C22semidirect
113. #16863706C22semidirect
114. #16863705C22semidirect
115. #16863704C22semidirect
116. #16863703C22semidirect
117. #16863702C22semidirect
118. #16863701C22semidirect
119. #16863700C22semidirect
120. #16863692C22semidirect
121. #16863691C22semidirect
122. #16863690C22semidirect
123. #16863690C22semidirect
124. #16863689C22semidirect
125. #16863689C22semidirect
126. #16863688C22semidirect
127. #16863655C22semidirect
128. #16863654C22semidirect
129. #16863653C22semidirect
130. #16863653C22semidirect
131. #16863652C22semidirect
132. #16863652C22semidirect
133. #16863651C22semidirect
134. #16863638C22semidirect
135. #16863637C22semidirect
136. #16863636C22semidirect
137. #16863636C22semidirect
138. #16863635C22semidirect
139. #16863635C22semidirect
140. #16863634C22semidirect
141. #16863504C22semidirect
142. #16863503C22semidirect
143. #16863502C22semidirect
144. #16863501C22semidirect
145. #16863501C22semidirect
146. #16863500C22semidirect
147. #16863500C22semidirect
155. #16863439C22semidirect
156. #16863438C22semidirect
157. #16863437C22semidirect
158. #16863437C22semidirect
159. #16863436C22semidirect
160. #16863435C22semidirect
161. #16863435C22semidirect
162. #16863434C22semidirect
163. #16863433C22semidirect
164. #16863433C22semidirect
165. #16863432C22semidirect
166. #16863432C22semidirect
167. #16863431C22semidirect
168. #16863431C22semidirect
190. #501×C67C22semidirect
191. #485×C67C22semidirect
192. #485×C67C22semidirect
193. #485×C67C22semidirect
194. #484×C67C22semidirect
195. #479×C67C22semidirect
196. #477×C67C22semidirect
197. #470×C67C22semidirect
198. #467×C67C22semidirect
199. #441×C67C22semidirect
201. #428×C67C22semidirect
202. #427×C67C22semidirect
825. D67#3349direct (N × H)
843. #3349D67direct (N × H)
857. C67C2×#3349semidirect
913. #501C2×D67semidirect
935. #485C2×D67semidirect
936. #485C2×D67semidirect
937. #485C2×D67semidirect
945. #484C2×D67semidirect
953. #479C2×D67semidirect
961. #477C2×D67semidirect
969. #470C2×D67semidirect
977. #467C2×D67semidirect
985. #441C2×D67semidirect
1001. #428C2×D67semidirect
1009. #427C2×D67semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#556×D672
#552×D672
#225727462
#225727452
#225727442
#225727432
#225727422
#225727412
#225727402
#225727392
#225727382
#225727372
#225727362
#225727352
#225727342
#225727332
#225727322
#501×D672
#484×D672
#485×D672
#479×D672
#477×D672
#470×D672
#467×D672
#441×D672
#435×D672
#428×D672
#427×D672
C67×#33492
C2×#334967