Finite Group Databasebeta

← #3388×D67 #31736350

Subgroups — #3388×D67 #31736350

Order 17152.

1822 conjugacy classes of subgroups.

The subgroup lattice has 1612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#557×D67C211yesmaximal, characteristic, complemented
2#554×D67C211yesmaximal, characteristic
3#22573161C211yesmaximal, characteristic, complemented
4#22573160C211yesmaximal, characteristic, complemented
5#22573159C211yesmaximal, characteristic, complemented
6#22573158C211yesmaximal, characteristic, complemented
7#22573157C211yesmaximal, characteristic, complemented
8#22573156C211yesmaximal, characteristic, complemented
9#22573155C211yesmaximal, characteristic, complemented
10#22573154C211yesmaximal, characteristic, complemented
11#22573153C211yesmaximal, characteristic, complemented
12#22573152C211yesmaximal, characteristic, complemented
13#22573151C211yesmaximal, characteristic, complemented
14#22573150C211yesmaximal, characteristic, complemented
15#22573149C211yesmaximal, characteristic, complemented
16#22573148C211yesmaximal, characteristic, complemented
17#22573147C211yesmaximal, characteristic, complemented
18#501×D67C211yesmaximal, characteristic, complemented
19#501×D67C211yesmaximal, characteristic, complemented
20#499×D67C211yesmaximal, characteristic, complemented
21#479×D67C211yesmaximal, characteristic, complemented
22#479×D67C211yesmaximal, characteristic, complemented
23#475×D67C211yesmaximal, characteristic, complemented
24#478×D67C211yesmaximal, characteristic
25#478×D67C211yesmaximal, characteristic
26#476×D67C211yesmaximal, characteristic
27#446×D67C211yesmaximal, characteristic, complemented
28#440×D67C211yesmaximal, characteristic
29#440×D67C211yesmaximal, characteristic
30C4×SD16×D67C211yesmaximal, characteristic
31C67×#3388C211yesmaximal, characteristic, complemented
32C2×SD16×D67C2211yescharacteristic
33#16864125C2211yescharacteristic, complemented
34#16864124—21no—
35#16864124C2211yescharacteristic, complemented
36#16864123—21no—
37#16864123—21no—
38#16864123C2211yescharacteristic, complemented
39#16864123C2211yescharacteristic, complemented
40#16864122C2211yescharacteristic, complemented
41#16864122C2211yescharacteristic, complemented
42#16864121—21no—
43#16864121C2211yescharacteristic, complemented
44#16864107C2211yescharacteristic
45#16864106C2211yescharacteristic
46#16864105C2211yescharacteristic
47#16864105C2211yescharacteristic
48#16864104—21no—
49#16864103C2211yescharacteristic
50#16864102C2211yescharacteristic
51#16864102C2211yescharacteristic
52#16864101—21no—
53#16864100—21no—
54#16864100—21no—
55C4⋊Q8×D67—21no—
56C4⋊Q8×D67C2211yescharacteristic
57C4⋊Q8×D67C2211yescharacteristic
58#125×D67—21no—
59#125×D67—21no—
60#125×D67C2211yescharacteristic
61#125×D67C2211yescharacteristic
62#125×D67C2211yescharacteristic
63#125×D67C2211yescharacteristic
64C22⋊Q8×D67—21no—
65C22⋊Q8×D67—21no—
66C22⋊Q8×D67—21no—
67C4×Q8×D67—21no—
68C4×Q8×D67C2211yescharacteristic
69C4×Q8×D67C2211yescharacteristic
70C4×Q8×D67C2211yescharacteristic
71C4×Q8×D67C2211yescharacteristic
72C4×D4×D67C2211yescharacteristic
73C4×D4×D67C2211yescharacteristic
74C4×D4×D67C2211yescharacteristic
75C2×C4⋊C4×D67—21no—
76#16863806C2211yescharacteristic, complemented
77#16863806C2211yescharacteristic, complemented
78#16863805C2211yescharacteristic, complemented
79#16863805C2211yescharacteristic, complemented
80#16863804C2211yescharacteristic, complemented
81#16863804C2211yescharacteristic, complemented
82#16863804C2211yescharacteristic, complemented
83#16863804C2211yescharacteristic, complemented
84#16863803C2211yescharacteristic, complemented
85#16863803C2211yescharacteristic, complemented
86#16863803C2211yescharacteristic, complemented
87#16863803C2211yescharacteristic, complemented
88#16863802C2211yescharacteristic, complemented
89#16863802C2211yescharacteristic, complemented
90#16863798C2211yescharacteristic, complemented
91#16863797C2211yescharacteristic, complemented
92#16863797C2211yescharacteristic, complemented
93#16863796C2211yescharacteristic, complemented
94#16863796C2211yescharacteristic, complemented
95#16863795C2211yescharacteristic, complemented
96#16863795C2211yescharacteristic, complemented
97#16863706C2211yescharacteristic, complemented
98#16863706C2211yescharacteristic, complemented
99#16863705C2211yescharacteristic, complemented
100#16863705C2211yescharacteristic, complemented
101#16863704C2211yescharacteristic, complemented
102#16863704C2211yescharacteristic, complemented
103#16863703C2211yescharacteristic, complemented
104#16863703C2211yescharacteristic, complemented
105#16863702C2211yescharacteristic, complemented
106#16863702C2211yescharacteristic, complemented
107#16863701C2211yescharacteristic, complemented
108#16863701C2211yescharacteristic, complemented
109#16863700C2211yescharacteristic, complemented
110#16863700C2211yescharacteristic, complemented
111#16863699C2211yescharacteristic
112#16863699C2211yescharacteristic
113#16863698C2211yescharacteristic
114#16863698C2211yescharacteristic
115#16863697C2211yescharacteristic
116#16863697C2211yescharacteristic
117#16863696C2211yescharacteristic
118#16863696C2211yescharacteristic
119#16863695C2211yescharacteristic
120#16863695C2211yescharacteristic
121#16863694C2211yescharacteristic
122#16863694C2211yescharacteristic
123#16863693C2211yescharacteristic
124#16863693C2211yescharacteristic
125#16863687C2211yescharacteristic
126#16863686C2211yescharacteristic
127#16863685C2211yescharacteristic
128#16863685C2211yescharacteristic
129#16863684C2211yescharacteristic
130#16863684C2211yescharacteristic
131#16863683C2211yescharacteristic
132#16863682C2211yescharacteristic, complemented
133#16863681C2211yescharacteristic, complemented
134#16863680C2211yescharacteristic, complemented
135#16863680C2211yescharacteristic, complemented
136#16863679C2211yescharacteristic, complemented
137#16863679C2211yescharacteristic, complemented
138#16863678C2211yescharacteristic, complemented
139#16863527C2211yescharacteristic, complemented
140#16863526C2211yescharacteristic, complemented
141#16863525C2211yescharacteristic, complemented
142#16863525C2211yescharacteristic, complemented
143#16863524C2211yescharacteristic, complemented
144#16863524C2211yescharacteristic, complemented
145#16863523C2211yescharacteristic, complemented
146#16863499C2211yescharacteristic
147#16863499C2211yescharacteristic
148#16863498C2211yescharacteristic
149#16863498C2211yescharacteristic
150#16863497C2211yescharacteristic
151#16863497C2211yescharacteristic
152#16863496C2211yescharacteristic
153#16863496C2211yescharacteristic
154#16863495C2211yescharacteristic
155#16863495C2211yescharacteristic
156#16863494C2211yescharacteristic
157#16863494C2211yescharacteristic
158#16863493C2211yescharacteristic
159#16863493C2211yescharacteristic
160#16863487C2211yescharacteristic
161C4×#11761617C2211yescharacteristic
162SD16×Dic67C2211yescharacteristic
163C4×#11761615C2211yescharacteristic
164#16863483C2211yescharacteristic
165C4×#11761616C2211yescharacteristic
166#16863481C2211yescharacteristic
167#107×D67C2211yescharacteristic
168#107×D67C2211yescharacteristic
169#107×D67C2211yescharacteristic
170#107×D67C2211yescharacteristic
171#106×D67C2211yescharacteristic
172#106×D67C2211yescharacteristic
173#106×D67C2211yescharacteristic
174#106×D67C2211yescharacteristic
175#106×D67C2211yescharacteristic
176C4⋊C8×D67C2211yescharacteristic
177C4⋊C8×D67C2211yescharacteristic
178C4⋊C8×D67C2211yescharacteristic
179#103×D67C2211yescharacteristic
180#103×D67C2211yescharacteristic
181#103×D67C2211yescharacteristic
182#102×D67C2211yescharacteristic
183#102×D67C2211yescharacteristic
184#102×D67C2211yescharacteristic
185#97×D67C2211yescharacteristic
186#97×D67C2211yescharacteristic
187C4×C8×D67C2211yescharacteristic
188#557×C67C2211yescharacteristic, complemented
189#554×C67C2211yescharacteristic
190#501×C67C2211yescharacteristic, complemented
191#501×C67C2211yescharacteristic, complemented
192#499×C67C2211yescharacteristic, complemented
193#479×C67C2211yescharacteristic, complemented
194#479×C67C2211yescharacteristic, complemented
195#478×C67C2211yescharacteristic
196#478×C67C2211yescharacteristic
197#476×C67C2211yescharacteristic
198#475×C67C2211yescharacteristic, complemented
199#446×C67C2211yescharacteristic, complemented
200#440×C67C2211yescharacteristic
201#440×C67C2211yescharacteristic
202C4×SD16×C67C2211yescharacteristic
203C2×Q8×D67—21no—
204C2×Q8×D67—21no—
205C2×Q8×D67D411yescharacteristic
206C2×Q8×D67C2311yescharacteristic
207C2×D4×D67C2311yescharacteristic
208C22×C4×D67—21no—
209C22×C4×D67—21no—
210C22×C4×D67—21no—
211C2×#11761617C2311yescharacteristic
212C2×#11761616C2311yescharacteristic
213C2×#11761615C2311yescharacteristic
214SD16×D67Q818yescomplemented
215C2×C8×D67C2311yescharacteristic
216C2×C8×D67C2311yescharacteristic
217C2×C8×D67C2311yescharacteristic
218C2×C8×D67C2311yescharacteristic
219#14524043—21no—
220#14524043C2311yescharacteristic
221#14524043C2311yescharacteristic
222#14524042—21no—
223#14524042—21no—
224#14524042—21no—
225#14524042—21no—
226#14524042—21no—
227#14524042—21no—
228#14524042C2311yescharacteristic
229#14524042C2311yescharacteristic
230#14524042C2311yescharacteristic
231#14524042C2311yescharacteristic
232#14524041—21no—
233#14524041—21no—
234#14524041—21no—
235#14524041—21no—
236#14524035—21no—
237#14524035—21no—
238#14524035C2311yescharacteristic
239#14524035C2311yescharacteristic
240#14524035C2311yescharacteristic
241#14524035C2311yescharacteristic
242#14524034—21no—
243#14524034—21no—
244#14524034—21no—
245#14524034—21no—
246#14524034C2311yescharacteristic
247#14524034C2311yescharacteristic
248#14524034C2311yescharacteristic
249#14524034C2311yescharacteristic
250#14524034C2311yescharacteristic
251#14524034C2311yescharacteristic
252#14524034C2311yescharacteristic
253#14524034C2311yescharacteristic
254#14524033—21no—
255#14524033—21no—
256#14524033—21no—
257#14524033—21no—
258#14524033—21no—
259#14524033—21no—
260#14524033—21no—
261#14524033—21no—
262#14524033—21no—
263#14524033—21no—
264#14524033—21no—
265#14524033—21no—
266#14524033—21no—
267#14524033—21no—
268#14524033—21no—
269#14524033—21no—
270#14524023—21no—
271#14524023—21no—
272#14524023—21no—
273#14524022—21no—
274#14524022—21no—
275#14524022—21no—
276#14524021—21no—
277#14524021—21no—
278#14524021—21no—
279#14524021—21no—
280#14524021—21no—
281#14524021—21no—
282#14524020—21no—
283#14524020—21no—
284#14524020—21no—
285#14524020—21no—
286#14524020—21no—
287#14524020—21no—
288#14524019—21no—
289#14524019—21no—
290#14524019—21no—
291Q8×Dic67—21no—
292Q8×Dic67D411yescharacteristic
293Q8×Dic67C2311yescharacteristic
294Q8×Dic67C2311yescharacteristic
295Q8×Dic67C2311yescharacteristic
296C4×Dic134—21no—
297C4×Dic134—21no—
298C4×Dic134—21no—
299C4×Dic134—21no—
300C4×Dic134—21no—
301C4×Dic134—21no—
302C4×Dic134C2311yescharacteristic
303C4×Dic134C2311yescharacteristic
304C4×Dic134C2311yescharacteristic
305C4×Dic134C2311yescharacteristic
306C4×Dic134C2311yescharacteristic
307C4×Dic134C2311yescharacteristic
308#14524008—21no—
309#14524008—21no—
310#14524008—21no—
311#14524008—21no—
312#14524008—21no—
313#14524008—21no—
314#14524008D411yescharacteristic
315#14524008D411yescharacteristic
316#14524008D411yescharacteristic
317#14524008C2311yescharacteristic
318#14524008C2311yescharacteristic
319#14524008C2311yescharacteristic
320C4×D268C2311yescharacteristic
321C4×D268C2311yescharacteristic
322C4×D268C2311yescharacteristic
323D4×Dic67C2311yescharacteristic
324D4×Dic67C2311yescharacteristic
325D4×Dic67C2311yescharacteristic
326#14524005C2311yescharacteristic
327#14524005C2311yescharacteristic
328#14524005C2311yescharacteristic
329C4×C22⋊D67—21no—
330C4×C22⋊D67—21no—
331C4×C22⋊D67—21no—
332(C22⋊D67)⋊C4—21no—
333(C22⋊D67)⋊C4—21no—
334(C22⋊D67)⋊C4—21no—
335C2×C4⋊Dic67—21no—
336C2×Dic67⋊C4—21no—
337C2×Dic67⋊C4—21no—
338C4⋊C4×D67—21no—
339C4⋊C4×D67—21no—
340C4⋊C4×D67—21no—
341C4⋊C4×D67—21no—
342C4⋊C4×D67—21no—
343C4⋊C4×D67—21no—
344C4⋊C4×D67—21no—
345C4⋊C4×D67—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×D67D411yescharacteristic
356C4⋊C4×D67D411yescharacteristic
357C4⋊C4×D67D411yescharacteristic
358C4⋊C4×D67C2311yescharacteristic
359C4⋊C4×D67C2311yescharacteristic
360C4⋊C4×D67C2311yescharacteristic
361C4⋊C4×D67C2311yescharacteristic
362C4⋊C4×D67C2311yescharacteristic
363C4⋊C4×D67C2311yescharacteristic
364C22⋊C4×D67—21no—
365C22⋊C4×D67—21no—
366C22⋊C4×D67—21no—
367C42×D67—21no—
368C42×D67—21no—
369C42×D67—21no—
370C42×D67C2311yescharacteristic
371C42×D67C2311yescharacteristic
372C42×D67C2311yescharacteristic
373#14523977C2311yescharacteristic
374#14523977C2311yescharacteristic
375#14523977C2311yescharacteristic
376#14523977C2311yescharacteristic
377#14523976C2311yescharacteristic
378#14523976C2311yescharacteristic
379#14523976C2311yescharacteristic
380#14523976C2311yescharacteristic
381#14523976C2311yescharacteristic
382#14523976C2311yescharacteristic
383#14523976C2311yescharacteristic
384#14523976C2311yescharacteristic
385#14523975C2311yescharacteristic
386#14523975C2311yescharacteristic
387#14523975C2311yescharacteristic
388#14523975C2311yescharacteristic
389#14523975C2311yescharacteristic
390#14523974C2311yescharacteristic
391#14523974C2311yescharacteristic
392#14523974C2311yescharacteristic
393#14523974C2311yescharacteristic
394#14523974C2311yescharacteristic
395#14523974C2311yescharacteristic
396#14523974C2311yescharacteristic
397#14523974C2311yescharacteristic
398#14523974C2311yescharacteristic
399#14523974C2311yescharacteristic
400C4⋊(C67⋊C8)C2311yescharacteristic
401C4⋊(C67⋊C8)C2311yescharacteristic
402C4⋊(C67⋊C8)C2311yescharacteristic
403Dic67⋊C8C2311yescharacteristic
404Dic67⋊C8C2311yescharacteristic
405Dic67⋊C8C2311yescharacteristic
406Dic67⋊C8C2311yescharacteristic
407Dic67⋊C8C2311yescharacteristic
408Dic67⋊C8C2311yescharacteristic
409#14523968C2311yescharacteristic
410#14523968C2311yescharacteristic
411#14523968C2311yescharacteristic
412#14523967C2311yescharacteristic
413#14523967C2311yescharacteristic
414#14523967C2311yescharacteristic
415#14523966C2311yescharacteristic
416#14523966C2311yescharacteristic
417#14523966C2311yescharacteristic
418#14523965C2311yescharacteristic
419#14523965C2311yescharacteristic
420#14523965C2311yescharacteristic
421#14523964C2311yescharacteristic
422#14523964C2311yescharacteristic
423#14523964C2311yescharacteristic
424#14523963C2311yescharacteristic
425#14523963C2311yescharacteristic
426#14523963C2311yescharacteristic
427#14523954C2311yescharacteristic
428#14523954C2311yescharacteristic
429#14523953C2311yescharacteristic
430#14523953C2311yescharacteristic
431#14523953C2311yescharacteristic
432#14523953C2311yescharacteristic
433C4×C67⋊C8C2311yescharacteristic
434C8×Dic67C2311yescharacteristic
435C8×Dic67C2311yescharacteristic
436C2×SD16×C67C2311yescharacteristic
437C4⋊Q8×C67—21no—
438C4⋊Q8×C67C2311yescharacteristic
439C4⋊Q8×C67C2311yescharacteristic
440#125×C67—21no—
441#125×C67—21no—
442#125×C67C2311yescharacteristic
443#125×C67C2311yescharacteristic
444#125×C67C2311yescharacteristic
445#125×C67C2311yescharacteristic
446C22⋊Q8×C67—21no—
447C22⋊Q8×C67—21no—
448C22⋊Q8×C67—21no—
449C4×Q8×C67—21no—
450C4×Q8×C67C2311yescharacteristic
451C4×Q8×C67C2311yescharacteristic
452C4×Q8×C67C2311yescharacteristic
453C4×Q8×C67C2311yescharacteristic
454C4×D4×C67C2311yescharacteristic
455C4×D4×C67C2311yescharacteristic
456C4×D4×C67C2311yescharacteristic
457C2×C4⋊C4×C67—21no—
458#107×C67C2311yescharacteristic
459#107×C67C2311yescharacteristic
460#107×C67C2311yescharacteristic
461#107×C67C2311yescharacteristic
462#106×C67C2311yescharacteristic
463#106×C67C2311yescharacteristic
464#106×C67C2311yescharacteristic
465#106×C67C2311yescharacteristic
466#106×C67C2311yescharacteristic
467C4⋊C8×C67C2311yescharacteristic
468C4⋊C8×C67C2311yescharacteristic
469C4⋊C8×C67C2311yescharacteristic
470#103×C67C2311yescharacteristic
471#103×C67C2311yescharacteristic
472#103×C67C2311yescharacteristic
473#102×C67C2311yescharacteristic
474#102×C67C2311yescharacteristic
475#102×C67C2311yescharacteristic
476#97×C67C2311yescharacteristic
477#97×C67C2311yescharacteristic
478C4×C8×C67C2311yescharacteristic
479C23×D67—21no—
480C2×Dic134—21no—
481C2×Dic134—21no—
482C2×Dic134—21no—
483C2×Dic134—21no—
484C2×Dic134—21no—
485C2×Dic134—21no—
486C2×Dic134—21no—
487C2×Dic134C2×D411yescharacteristic
488C2×Dic134C2×D411yescharacteristic
489C2×Dic134C2×D411yescharacteristic
490C2×Dic134C2411yescharacteristic
491Q8×D67—22no—
492Q8×D67—42no—
493Q8×D67—44no—
494Q8×D67—82no—
495Q8×D67C2×Q814yes—
496C2×D268C2411yescharacteristic
497C2×C22⋊D67—21no—
498D4×D67—22no—
499D4×D67C2×Q814yes—
500C22×Dic67—21no—
501C22×Dic67—21no—
502C22×Dic67—21no—
503C2×C4×D67—21no—
504C2×C4×D67—21no—
505C2×C4×D67—21no—
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×D67—82no—
518C2×C4×D67—82no—
519C2×C4×D67C2×D411yescharacteristic
520C2×C4×D67C2×D411yescharacteristic
521C2×C4×D67C2×D411yescharacteristic
522C2×C4×D67C2×D411yescharacteristic
523C2×C4×D67C2×D411yescharacteristic
524C2×C4×D67C2×D411yescharacteristic
525C2×C4×D67C2411yescharacteristic
526#11761617C2×Q814yescomplemented
527#11761616C2×Q814yescomplemented
528#11761615C2×Q814yescomplemented
529C2×C67⋊C8C2411yescharacteristic
530C2×C67⋊C8C2411yescharacteristic
531C2×C67⋊C8C2411yescharacteristic
532C2×C67⋊C8C2411yescharacteristic
533C8×D67—22no—
534C8×D67—22no—
535C8×D67—22no—
536C8×D67C2×Q814yes—
537C4⋊Dic67—21no—
538C4⋊Dic67—21no—
539C4⋊Dic67—21no—
540C4⋊Dic67—21no—
541C4⋊Dic67—21no—
542C4⋊Dic67—21no—
543C4⋊Dic67—21no—
544C4⋊Dic67—21no—
545C4⋊Dic67—21no—
546C4⋊Dic67—21no—
547C4⋊Dic67—21no—
548C4⋊Dic67—21no—
549C4⋊Dic67—21no—
550C4⋊Dic67C2×D411yescharacteristic
551C4⋊Dic67C2×D411yescharacteristic
552C4⋊Dic67C2×D411yescharacteristic
553C4⋊Dic67C2411yescharacteristic
554C4⋊Dic67C2411yescharacteristic
555C4⋊Dic67C2411yescharacteristic
556C4⋊Dic67C2411yescharacteristic
557C4⋊Dic67C2411yescharacteristic
558C4⋊Dic67C2411yescharacteristic
559Dic67⋊C4—21no—
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⋊C4—21no—
587Dic67⋊C4—21no—
588Dic67⋊C4—21no—
589Dic67⋊C4—21no—
590Dic67⋊C4—21no—
591Dic67⋊C4C2×D411yescharacteristic
592Dic67⋊C4C2×D411yescharacteristic
593Dic67⋊C4C2×D411yescharacteristic
594Dic67⋊C4C2×D411yescharacteristic
595Dic67⋊C4C2×D411yescharacteristic
596Dic67⋊C4C2×D411yescharacteristic
597C22⋊Dic67—21no—
598C22⋊Dic67—21no—
599C22⋊Dic67—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—
606C4×Dic67—21no—
607C4×Dic67—21no—
608C4×Dic67—21no—
609C4×Dic67—21no—
610C4×Dic67—21no—
611C4×Dic67—21no—
612C4×Dic67—21no—
613C4×Dic67—21no—
614C4×Dic67—21no—
615C4×Dic67C2×D411yescharacteristic
616C4×Dic67C2×D411yescharacteristic
617C4×Dic67C2×D411yescharacteristic
618C4×Dic67C2×D411yescharacteristic
619C4×Dic67C2×D411yescharacteristic
620C4×Dic67C2×D411yescharacteristic
621C4×Dic67C2411yescharacteristic
622C4×Dic67C2411yescharacteristic
623C4×Dic67C2411yescharacteristic
624C2×Q8×C67—21no—
625C2×Q8×C67—21no—
626C2×Q8×C67C2×D411yescharacteristic
627C2×Q8×C67C2411yescharacteristic
628C2×D4×C67C2411yescharacteristic
629C22×C4×C67—21no—
630C22×C4×C67—21no—
631C22×C4×C67—21no—
632SD16×C67C2×Q814yescomplemented
633C2×C8×C67C2411yescharacteristic
634C2×C8×C67C2411yescharacteristic
635C2×C8×C67C2411yescharacteristic
636C2×C8×C67C2411yescharacteristic
637C4⋊C4×C67—21no—
638C4⋊C4×C67—21no—
639C4⋊C4×C67—21no—
640C4⋊C4×C67—21no—
641C4⋊C4×C67—21no—
642C4⋊C4×C67—21no—
643C4⋊C4×C67—21no—
644C4⋊C4×C67—21no—
645C4⋊C4×C67—21no—
646C4⋊C4×C67—21no—
647C4⋊C4×C67—21no—
648C4⋊C4×C67—21no—
649C4⋊C4×C67—21no—
650C4⋊C4×C67C2×D411yescharacteristic
651C4⋊C4×C67C2×D411yescharacteristic
652C4⋊C4×C67C2×D411yescharacteristic
653C4⋊C4×C67C2411yescharacteristic
654C4⋊C4×C67C2411yescharacteristic
655C4⋊C4×C67C2411yescharacteristic
656C4⋊C4×C67C2411yescharacteristic
657C4⋊C4×C67C2411yescharacteristic
658C4⋊C4×C67C2411yescharacteristic
659C22⋊C4×C67—21no—
660C22⋊C4×C67—21no—
661C22⋊C4×C67—21no—
662C42×C67—21no—
663C42×C67—21no—
664C42×C67—21no—
665C42×C67C2411yescharacteristic
666C42×C67C2411yescharacteristic
667C42×C67C2411yescharacteristic
668C23×C67—21no—
669C22×D67—21no—
670C22×D67—24no—
671C22×D67—42no—
672C22×D67—42no—
673C22×D67C22×D411yescharacteristic
674Q8×C67—21no—
675Q8×C67—41no—
676Q8×C67—42no—
677Q8×C67—81no—
678Q8×C67C22×Q812yes—
679D4×C67—21no—
680D4×C67C22×Q812yes—
681C2×C4×C67—21no—
682C2×C4×C67—21no—
683C2×C4×C67—21no—
684C2×C4×C67—21no—
685C2×C4×C67—21no—
686C2×C4×C67—21no—
687C2×C4×C67—21no—
688C2×C4×C67—42no—
689C2×C4×C67—81no—
690C2×C4×C67—81no—
691C2×C4×C67C22×D411yescharacteristic
692C2×C4×C67C22×D411yescharacteristic
693C2×C4×C67C22×D411yescharacteristic
694C2×C4×C67C22×D411yescharacteristic
695C2×C4×C67C22×D411yescharacteristic
696C2×C4×C67C22×D411yescharacteristic
697C2×C4×C67C2511yescharacteristic
698C22⋊D67—24no—
699C2×Dic67—21no—
700C2×Dic67—21no—
701C2×Dic67—21no—
702C2×Dic67—21no—
703C2×Dic67—21no—
704C2×Dic67—21no—
705C2×Dic67—21no—
706C2×Dic67—42no—
707C2×Dic67—81no—
708C2×Dic67—81no—
709C2×Dic67C22×D411yescharacteristic
710C2×Dic67C22×D411yescharacteristic
711C2×Dic67C22×D411yescharacteristic
712C2×Dic67C22×D411yescharacteristic
713C2×Dic67C22×D411yescharacteristic
714C2×Dic67C22×D411yescharacteristic
715C2×Dic67C22×D411yescharacteristic
716D268—21no—
717D268C22×Q812yes—
718C4×D67—24no—
719C4×D67—22no—
720C4×D67—22no—
721C4×D67—22no—
722C4×D67—22no—
723C4×D67—22no—
724C4×D67—22no—
725C4×D67—42no—
726C4×D67—42no—
727C4×D67—42no—
728C4×D67—42no—
729C4×D67—42no—
730C4×D67—42no—
731C4×D67—42no—
732C4×D67—42no—
733C4×D67—81no—
734C4×D67—81no—
735C4×D67—81no—
736C4×D67—81no—
737C4×D67C22×Q812yes—
738C4×D672−1+412yes—
739Dic134—21no—
740Dic134—24no—
741Dic134—41no—
742Dic134—41no—
743Dic134—41no—
744Dic134—42no—
745Dic134—42no—
746Dic134—42no—
747Dic134—81no—
748Dic134—81no—
749Dic134—81no—
750Dic134C22×Q812yes—
751C8×C67—21no—
752C8×C67—21no—
753C8×C67—21no—
754C8×C67C22×Q812yes—
755C67⋊C8—21no—
756C67⋊C8—21no—
757C67⋊C8—21no—
758C67⋊C8C22×Q812yes—
759C22×C67—22no—
760C22×C67—41no—
761C22×C67—41no—
762C22×C67C23×D411yescharacteristic
763C2×D67—22no—
764C2×D67—41no—
765C2×D67—41no—
766C2×D67—48no—
767C2×D67D4×Q812yes—
768C2×D67#57512yes—
769C2×D67#57712yes—
770C4×C67—22no—
771C4×C67—21no—
772C4×C67—21no—
773C4×C67—21no—
774C4×C67—21no—
775C4×C67—21no—
776C4×C67—21no—
777C4×C67—41no—
778C4×C67—41no—
779C4×C67—41no—
780C4×C67—41no—
781C4×C67—41no—
782C4×C67—41no—
783C4×C67C23×Q811yescharacteristic
784C4×C67C2×2−1+411yescharacteristic
785Dic67—22no—
786Dic67—21no—
787Dic67—21no—
788Dic67—21no—
789Dic67—21no—
790Dic67—21no—
791Dic67—21no—
792Dic67—41no—
793Dic67—41no—
794Dic67—41no—
795Dic67—41no—
796Dic67—41no—
797Dic67—41no—
798Dic67D4×Q812yes—
799C2×#3388—671nomaximal, Sylow
800C2×C67—42no—
801C2×C67C2×D4×Q811yescharacteristic
802C2×C67C2×#57511yescharacteristic
803C2×C67C2×#57711yescharacteristic
804D67—42no—
805D67#338814yesdirect product factor
806C2×#557—671no—
807C2×#554—671no—
808#3388—671no—
809#3388—671no—
810#3388—671no—
811#3388—671no—
812#3388—671no—
813#3388—671no—
814#3388—671no—
815#3388—671no—
816#3388—671no—
817#3388—671no—
818#3388—671no—
819#3388—671no—
820#3388—671no—
821#3388—671no—
822#3388—671no—
823#3388D6711yescharacteristic, direct product factor
824C2×#501—671no—
825C2×#501—671no—
826C2×#499—671no—
827C2×#479—671no—
828C2×#479—671no—
829C2×#475—671no—
830C2×#478—671no—
831C2×#478—671no—
832C2×#476—671no—
833C2×#446—671no—
834C2×#440—671no—
835C2×#440—671no—
836C2×C4×SD16—671no—
837C67C2×#338811yescharacteristic, complemented, Sylow
838C22×SD16—671no—
839#557—671no—
840#557—671no—
841#557—671no—
842#557—671no—
843#557—671no—
844#557—671no—
845#557—671no—
846#557—1341no—
847#557—1341no—
848#557—1341no—
849#557—1341no—
850#557C2×D6711yescharacteristic, complemented
851#554—671no—
852#554—671no—
853#554—671no—
854#554—671no—
855#554—671no—
856#554—671no—
857#554—671no—
858#554—1341no—
859#554—1341no—
860#554—1341no—
861#554—1341no—
862#554C2×D6711yescharacteristic
863C2×C4⋊Q8—671no—
864C2×C4⋊Q8—671no—
865C2×C4⋊Q8—1341no—
866C2×#125—671no—
867C2×#125—671no—
868C2×#125—671no—
869C2×#125—671no—
870C2×#125—1341no—
871C2×#125—1341no—
872C2×C22⋊Q8—1341no—
873C2×C22⋊Q8—1341no—
874C2×C22⋊Q8—1341no—
875C2×C4×Q8—671no—
876C2×C4×Q8—671no—
877C2×C4×Q8—671no—
878C2×C4×Q8—671no—
879C2×C4×Q8—1341no—
880C2×C4×D4—671no—
881C2×C4×D4—671no—
882C2×C4×D4—671no—
883C22×C4⋊C4—1341no—
884#501—671no—
885#501—671no—
886#501—671no—
887#501—671no—
888#501—671no—
889#501—671no—
890#501—671no—
891#501—671no—
892#501—671no—
893#501—671no—
894#501—671no—
895#501—671no—
896#501—671no—
897#501—671no—
898#501C2×D6711yescharacteristic, complemented
899#501C2×D6711yescharacteristic, complemented
900#499—671no—
901#499—671no—
902#499—671no—
903#499—671no—
904#499—671no—
905#499—671no—
906#499—671no—
907#499C2×D6711yescharacteristic, complemented
908#479—671no—
909#479—671no—
910#479—671no—
911#479—671no—
912#479—671no—
913#479—671no—
914#479—671no—
915#479—671no—
916#479—671no—
917#479—671no—
918#479—671no—
919#479—671no—
920#479—671no—
921#479—671no—
922#479C2×D6711yescharacteristic, complemented
923#479C2×D6711yescharacteristic, complemented
924#478—671no—
925#478—671no—
926#478—671no—
927#478—671no—
928#478—671no—
929#478—671no—
930#478—671no—
931#478—671no—
932#478—671no—
933#478—671no—
934#478—671no—
935#478—671no—
936#478—671no—
937#478—671no—
938#478C2×D6711yescharacteristic
939#478C2×D6711yescharacteristic
940#476—671no—
941#476—671no—
942#476—671no—
943#476—671no—
944#476—671no—
945#476—671no—
946#476—671no—
947#476C2×D6711yescharacteristic
948#475—671no—
949#475—671no—
950#475—671no—
951#475—671no—
952#475—671no—
953#475—671no—
954#475—671no—
955#475C2×D6711yescharacteristic, complemented
956#446—671no—
957#446—671no—
958#446—671no—
959#446—671no—
960#446—671no—
961#446—671no—
962#446—671no—
963#446C2×D6711yescharacteristic, complemented
964#440—671no—
965#440—671no—
966#440—671no—
967#440—671no—
968#440—671no—
969#440—671no—
970#440—671no—
971#440—671no—
972#440—671no—
973#440—671no—
974#440—671no—
975#440—671no—
976#440—671no—
977#440—671no—
978#440C2×D6711yescharacteristic
979#440C2×D6711yescharacteristic
980C4×SD16—671no—
981C4×SD16—671no—
982C4×SD16—671no—
983C4×SD16—671no—
984C4×SD16—671no—
985C4×SD16—671no—
986C4×SD16—671no—
987C4×SD16C2×D6711yescharacteristic
988C2×#107—671no—
989C2×#107—671no—
990C2×#107—671no—
991C2×#107—671no—
992C2×#106—671no—
993C2×#106—671no—
994C2×#106—671no—
995C2×#106—671no—
996C2×#106—671no—
997C2×C4⋊C8—671no—
998C2×C4⋊C8—671no—
999C2×C4⋊C8—671no—
1000C2×#103—671no—
1001C2×#103—671no—
1002C2×#103—671no—
1003C2×#102—671no—
1004C2×#102—671no—
1005C2×#102—671no—
1006C2×#97—671no—
1007C2×#97—671no—
1008C2×C4×C8—671no—
1009C22×Q8—671no—
1010C22×Q8—671no—
1011C22×Q8—1341no—
1012C22×Q8—1341no—
1013C22×D4—671no—
1014C23×C4—1341no—
1015C23×C4—1341no—
1016C23×C4—1341no—
1017C2×SD16—671no—
1018C2×SD16—671no—
1019C2×SD16—678no—
1020C2×SD16—671no—
1021C2×SD16C22×D6711yescharacteristic
1022C22×C8—671no—
1023C22×C8—671no—
1024C22×C8—671no—
1025C22×C8—671no—
1026C4⋊Q8—21no—
1027C4⋊Q8—671no—
1028C4⋊Q8—671no—
1029C4⋊Q8—671no—
1030C4⋊Q8—671no—
1031C4⋊Q8—671no—
1032C4⋊Q8—671no—
1033C4⋊Q8—1341no—
1034C4⋊Q8—1341no—
1035C4⋊Q8—1341no—
1036C4⋊Q8—1341no—
1037C4⋊Q8—1341no—
1038C4⋊Q8—1341no—
1039C4⋊Q8—1341no—
1040C4⋊Q8—1341no—
1041C4⋊Q8—1341no—
1042C4⋊Q8—1341no—
1043C4⋊Q8—1341no—
1044C4⋊Q8C22×D6711yescharacteristic
1045C4⋊Q8C22×D6711yescharacteristic
1046#125—21no—
1047#125—21no—
1048#125—671no—
1049#125—671no—
1050#125—671no—
1051#125—671no—
1052#125—671no—
1053#125—671no—
1054#125—671no—
1055#125—671no—
1056#125—671no—
1057#125—671no—
1058#125—671no—
1059#125—671no—
1060#125—1341no—
1061#125—1341no—
1062#125—1341no—
1063#125—1341no—
1064#125—1341no—
1065#125—1341no—
1066#125—1341no—
1067#125—1341no—
1068#125—1341no—
1069#125—1341no—
1070#125—1341no—
1071#125—1341no—
1072#125—1341no—
1073#125—1341no—
1074#125—1341no—
1075#125—1341no—
1076#125—1341no—
1077#125—1341no—
1078#125—1341no—
1079#125—1341no—
1080#125—1341no—
1081#125—1341no—
1082#125C22×D6711yescharacteristic
1083#125C22×D6711yescharacteristic
1084#125C22×D6711yescharacteristic
1085#125C22×D6711yescharacteristic
1086C22⋊Q8—21no—
1087C22⋊Q8—21no—
1088C22⋊Q8—21no—
1089C22⋊Q8—1341no—
1090C22⋊Q8—1341no—
1091C22⋊Q8—1341no—
1092C22⋊Q8—1341no—
1093C22⋊Q8—1341no—
1094C22⋊Q8—1341no—
1095C22⋊Q8—1341no—
1096C22⋊Q8—1341no—
1097C22⋊Q8—1341no—
1098C22⋊Q8—1341no—
1099C22⋊Q8—1341no—
1100C22⋊Q8—1341no—
1101C22⋊Q8—1341no—
1102C22⋊Q8—1341no—
1103C22⋊Q8—1341no—
1104C22⋊Q8—1341no—
1105C22⋊Q8—1341no—
1106C22⋊Q8—1341no—
1107C22⋊Q8—1341no—
1108C22⋊Q8—1341no—
1109C22⋊Q8—1341no—
1110C4×Q8—21no—
1111C4×Q8—671no—
1112C4×Q8—671no—
1113C4×Q8—671no—
1114C4×Q8—671no—
1115C4×Q8—671no—
1116C4×Q8—671no—
1117C4×Q8—671no—
1118C4×Q8—671no—
1119C4×Q8—671no—
1120C4×Q8—671no—
1121C4×Q8—671no—
1122C4×Q8—671no—
1123C4×Q8—671no—
1124C4×Q8—671no—
1125C4×Q8—671no—
1126C4×Q8—671no—
1127C4×Q8—1341no—
1128C4×Q8—1341no—
1129C4×Q8—1341no—
1130C4×Q8—1341no—
1131C4×Q8—1341no—
1132C4×Q8—1341no—
1133C4×Q8—1341no—
1134C4×Q8—1341no—
1135C4×Q8—1341no—
1136C4×Q8—1341no—
1137C4×Q8—1341no—
1138C4×Q8—1341no—
1139C4×Q8—1341no—
1140C4×Q8C22×D6711yescharacteristic
1141C4×Q8C22×D6711yescharacteristic
1142C4×Q8C22×D6711yescharacteristic
1143C4×Q8C22×D6711yescharacteristic
1144C4×D4—671no—
1145C4×D4—671no—
1146C4×D4—671no—
1147C4×D4—671no—
1148C4×D4—671no—
1149C4×D4—671no—
1150C4×D4—671no—
1151C4×D4—671no—
1152C4×D4—671no—
1153C4×D4—1341no—
1154C4×D4—1341no—
1155C4×D4—1341no—
1156C4×D4—1341no—
1157C4×D4—1341no—
1158C4×D4—1341no—
1159C4×D4C22×D6711yescharacteristic
1160C4×D4C22×D6711yescharacteristic
1161C4×D4C22×D6711yescharacteristic
1162C2×C4⋊C4—21no—
1163C2×C4⋊C4—671no—
1164C2×C4⋊C4—671no—
1165C2×C4⋊C4—671no—
1166C2×C4⋊C4—671no—
1167C2×C4⋊C4—671no—
1168C2×C4⋊C4—671no—
1169C2×C4⋊C4—671no—
1170C2×C4⋊C4—671no—
1171C2×C4⋊C4—671no—
1172C2×C4⋊C4—1341no—
1173C2×C4⋊C4—1341no—
1174C2×C4⋊C4—1341no—
1175C2×C4⋊C4—1341no—
1176C2×C4⋊C4—1341no—
1177C2×C4⋊C4—1341no—
1178C2×C4⋊C4—1341no—
1179C2×C4⋊C4—1341no—
1180C2×C4⋊C4—1341no—
1181C2×C4⋊C4—1341no—
1182C2×C4⋊C4—1341no—
1183C2×C4⋊C4—1341no—
1184C2×C4⋊C4—1341no—
1185C2×C4⋊C4—1341no—
1186C2×C4⋊C4—1341no—
1187C2×C4⋊C4—1341no—
1188C2×C4⋊C4—1341no—
1189C2×C4⋊C4—1341no—
1190C2×C4⋊C4—1341no—
1191C2×C4⋊C4—1341no—
1192C2×C22⋊C4—1341no—
1193C2×C22⋊C4—1341no—
1194C2×C22⋊C4—1341no—
1195C2×C42—671no—
1196C2×C42—671no—
1197C2×C42—671no—
1198C2×C42—1341no—
1199C2×C42—1341no—
1200C2×C42—1341no—
1201#107—671no—
1202#107—671no—
1203#107—671no—
1204#107—671no—
1205#107—671no—
1206#107—671no—
1207#107—671no—
1208#107—671no—
1209#107—671no—
1210#107—671no—
1211#107—671no—
1212#107—671no—
1213#107C22×D6711yescharacteristic
1214#107C22×D6711yescharacteristic
1215#107C22×D6711yescharacteristic
1216#107C22×D6711yescharacteristic
1217#106—671no—
1218#106—671no—
1219#106—671no—
1220#106—671no—
1221#106—671no—
1222#106—671no—
1223#106—671no—
1224#106—671no—
1225#106—671no—
1226#106—671no—
1227#106—671no—
1228#106—671no—
1229#106—671no—
1230#106—671no—
1231#106—671no—
1232#106C22×D6711yescharacteristic
1233#106C22×D6711yescharacteristic
1234#106C22×D6711yescharacteristic
1235#106C22×D6711yescharacteristic
1236#106C22×D6711yescharacteristic
1237C4⋊C8—671no—
1238C4⋊C8—671no—
1239C4⋊C8—671no—
1240C4⋊C8—671no—
1241C4⋊C8—671no—
1242C4⋊C8—671no—
1243C4⋊C8—671no—
1244C4⋊C8—671no—
1245C4⋊C8—671no—
1246C4⋊C8C22×D6711yescharacteristic
1247C4⋊C8C22×D6711yescharacteristic
1248C4⋊C8C22×D6711yescharacteristic
1249#103—671no—
1250#103—671no—
1251#103—671no—
1252#103—671no—
1253#103—671no—
1254#103—671no—
1255#103—671no—
1256#103—671no—
1257#103—671no—
1258#103C22×D6711yescharacteristic
1259#103C22×D6711yescharacteristic
1260#103C22×D6711yescharacteristic
1261#102—671no—
1262#102—671no—
1263#102—671no—
1264#102—671no—
1265#102—671no—
1266#102—671no—
1267#102—671no—
1268#102—671no—
1269#102—671no—
1270#102C22×D6711yescharacteristic
1271#102C22×D6711yescharacteristic
1272#102C22×D6711yescharacteristic
1273#97—671no—
1274#97—671no—
1275#97—671no—
1276#97—671no—
1277#97—671no—
1278#97—671no—
1279#97C22×D6711yescharacteristic
1280#97C22×D6711yescharacteristic
1281C4×C8—671no—
1282C4×C8—671no—
1283C4×C8—671no—
1284C4×C8C22×D6711yescharacteristic
1285C24—1341no—
1286C2×Q8—21no—
1287C2×Q8—21no—
1288C2×Q8—2684no—
1289C2×Q8—2682no—
1290C2×Q8—5362no—
1291C2×Q8—671no—
1292C2×Q8—671no—
1293C2×Q8—671no—
1294C2×Q8—674no—
1295C2×Q8—671no—
1296C2×Q8—1341no—
1297C2×Q8—1341no—
1298C2×Q8—1341no—
1299C2×Q8—1341no—
1300C2×Q8—1341no—
1301C2×Q8—1342no—
1302C2×Q8—1341no—
1303C2×Q8—1341no—
1304C2×Q8D4×D6711yescharacteristic
1305C2×Q8C23×D6711yescharacteristic
1306C2×D4—674no—
1307C2×D4—671no—
1308C2×D4—1342no—
1309C2×D4—1341no—
1310C2×D4C23×D6711yescharacteristic
1311C22×C4—21no—
1312C22×C4—21no—
1313C22×C4—21no—
1314C22×C4—2684no—
1315C22×C4—5362no—
1316C22×C4—5362no—
1317C22×C4—671no—
1318C22×C4—671no—
1319C22×C4—671no—
1320C22×C4—671no—
1321C22×C4—671no—
1322C22×C4—671no—
1323C22×C4—671no—
1324C22×C4—1341no—
1325C22×C4—1341no—
1326C22×C4—1341no—
1327C22×C4—1341no—
1328C22×C4—1341no—
1329C22×C4—1341no—
1330C22×C4—1341no—
1331C22×C4—1341no—
1332C22×C4—1341no—
1333C22×C4—1341no—
1334C22×C4—1341no—
1335C22×C4—1341no—
1336C22×C4—1341no—
1337C22×C4—1341no—
1338C22×C4—1341no—
1339C22×C4—1341no—
1340SD16—674no—
1341SD16—674no—
1342SD16—674no—
1343SD16Q8×D6714yescomplemented
1344C2×C8—671no—
1345C2×C8—674no—
1346C2×C8—671no—
1347C2×C8—671no—
1348C2×C8—671no—
1349C2×C8—1342no—
1350C2×C8—1342no—
1351C2×C8—1342no—
1352C2×C8C23×D6711yescharacteristic
1353C2×C8C23×D6711yescharacteristic
1354C2×C8C23×D6711yescharacteristic
1355C2×C8C23×D6711yescharacteristic
1356C4⋊C4—21no—
1357C4⋊C4—21no—
1358C4⋊C4—21no—
1359C4⋊C4—21no—
1360C4⋊C4—21no—
1361C4⋊C4—21no—
1362C4⋊C4—21no—
1363C4⋊C4—21no—
1364C4⋊C4—21no—
1365C4⋊C4—21no—
1366C4⋊C4—21no—
1367C4⋊C4—21no—
1368C4⋊C4—21no—
1369C4⋊C4—671no—
1370C4⋊C4—671no—
1371C4⋊C4—671no—
1372C4⋊C4—671no—
1373C4⋊C4—671no—
1374C4⋊C4—671no—
1375C4⋊C4—671no—
1376C4⋊C4—671no—
1377C4⋊C4—671no—
1378C4⋊C4—671no—
1379C4⋊C4—671no—
1380C4⋊C4—671no—
1381C4⋊C4—671no—
1382C4⋊C4—671no—
1383C4⋊C4—671no—
1384C4⋊C4—1341no—
1385C4⋊C4—1341no—
1386C4⋊C4—1341no—
1387C4⋊C4—1341no—
1388C4⋊C4—1341no—
1389C4⋊C4—1341no—
1390C4⋊C4—1341no—
1391C4⋊C4—1341no—
1392C4⋊C4—1341no—
1393C4⋊C4—1341no—
1394C4⋊C4—1341no—
1395C4⋊C4—1341no—
1396C4⋊C4—1341no—
1397C4⋊C4—1341no—
1398C4⋊C4—1341no—
1399C4⋊C4—1341no—
1400C4⋊C4—1341no—
1401C4⋊C4—1341no—
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⋊C4D4×D6711yescharacteristic
1430C4⋊C4D4×D6711yescharacteristic
1431C4⋊C4D4×D6711yescharacteristic
1432C4⋊C4C23×D6711yescharacteristic
1433C4⋊C4C23×D6711yescharacteristic
1434C4⋊C4C23×D6711yescharacteristic
1435C4⋊C4C23×D6711yescharacteristic
1436C4⋊C4C23×D6711yescharacteristic
1437C4⋊C4C23×D6711yescharacteristic
1438C22⋊C4—21no—
1439C22⋊C4—21no—
1440C22⋊C4—21no—
1441C22⋊C4—1341no—
1442C22⋊C4—1341no—
1443C22⋊C4—1341no—
1444C22⋊C4—1341no—
1445C22⋊C4—1341no—
1446C22⋊C4—1341no—
1447C22⋊C4—1341no—
1448C22⋊C4—1341no—
1449C22⋊C4—1341no—
1450C42—21no—
1451C42—21no—
1452C42—21no—
1453C42—671no—
1454C42—671no—
1455C42—671no—
1456C42—671no—
1457C42—671no—
1458C42—671no—
1459C42—671no—
1460C42—671no—
1461C42—671no—
1462C42—1341no—
1463C42—1341no—
1464C42—1341no—
1465C42—1341no—
1466C42—1341no—
1467C42—1341no—
1468C42—1341no—
1469C42—1341no—
1470C42—1341no—
1471C42C23×D6711yescharacteristic
1472C42C23×D6711yescharacteristic
1473C42C23×D6711yescharacteristic
1474C23—21no—
1475C23—2682no—
1476C23—2682no—
1477C23—671no—
1478C23—1344no—
1479C23—1341no—
1480Q8—21no—
1481Q8—41no—
1482Q8—42no—
1483Q8—81no—
1484Q8—2682no—
1485Q8—2681no—
1486Q8—2681no—
1487Q8—2681no—
1488Q8—2682no—
1489Q8—2682no—
1490Q8—5361no—
1491Q8—5361no—
1492Q8—5361no—
1493Q8—672no—
1494Q8—1344no—
1495Q8—1341no—
1496Q8C2×Q8×D6712yes—
1497D4—21no—
1498D4—672no—
1499D4—1344no—
1500D4—1341no—
1501D4C2×Q8×D6712yes—
1502C2×C4—21no—
1503C2×C4—21no—
1504C2×C4—21no—
1505C2×C4—21no—
1506C2×C4—21no—
1507C2×C4—21no—
1508C2×C4—21no—
1509C2×C4—42no—
1510C2×C4—81no—
1511C2×C4—81no—
1512C2×C4—2682no—
1513C2×C4—2682no—
1514C2×C4—2682no—
1515C2×C4—2682no—
1516C2×C4—2682no—
1517C2×C4—2682no—
1518C2×C4—2682no—
1519C2×C4—2682no—
1520C2×C4—2682no—
1521C2×C4—5361no—
1522C2×C4—5361no—
1523C2×C4—5361no—
1524C2×C4—5361no—
1525C2×C4—5361no—
1526C2×C4—5361no—
1527C2×C4—671no—
1528C2×C4—672no—
1529C2×C4—672no—
1530C2×C4—671no—
1531C2×C4—671no—
1532C2×C4—671no—
1533C2×C4—671no—
1534C2×C4—671no—
1535C2×C4—671no—
1536C2×C4—1342no—
1537C2×C4—1342no—
1538C2×C4—1342no—
1539C2×C4—1342no—
1540C2×C4—1342no—
1541C2×C4—1342no—
1542C2×C4—1344no—
1543C2×C4—1341no—
1544C2×C4—1341no—
1545C2×C4—1341no—
1546C2×C4—1341no—
1547C2×C4—1341no—
1548C2×C4—1341no—
1549C2×C4—1341no—
1550C2×C4C2×D4×D6711yescharacteristic
1551C2×C4C2×D4×D6711yescharacteristic
1552C2×C4C2×D4×D6711yescharacteristic
1553C2×C4C2×D4×D6711yescharacteristic
1554C2×C4C2×D4×D6711yescharacteristic
1555C2×C4C2×D4×D6711yescharacteristic
1556C2×C4C24×D6711yescharacteristic
1557C8—21no—
1558C8—21no—
1559C8—21no—
1560C8—672no—
1561C8—1341no—
1562C8—1341no—
1563C8—1341no—
1564C8C2×Q8×D6712yes—
1565C22—22no—
1566C22—41no—
1567C22—41no—
1568C22—2688no—
1569C22—2681no—
1570C22—2681no—
1571C22—672no—
1572C22—672no—
1573C22—672no—
1574C22—1342no—
1575C22C22×D4×D6711yescharacteristic
1576C4—21no—
1577C4—21no—
1578C4—21no—
1579C4—22no—
1580C4—21no—
1581C4—21no—
1582C4—21no—
1583C4—41no—
1584C4—41no—
1585C4—41no—
1586C4—41no—
1587C4—41no—
1588C4—41no—
1589C4—2681no—
1590C4—2681no—
1591C4—2681no—
1592C4—2681no—
1593C4—2681no—
1594C4—2681no—
1595C4—672no—
1596C4—1341no—
1597C4—1341no—
1598C4—1341no—
1599C4—1342no—
1600C4—1341no—
1601C4—1341no—
1602C4—1341no—
1603C4C22×Q8×D6711yescharacteristic
1604C42−1+4×D6711yescharacteristic
1605C2—42no—
1606C2—2682no—
1607C2—674no—
1608C2D4×Q8×D6711yescharacteristic
1609C2#575×D6711yescharacteristic
1610C2#577×D6711yescharacteristic
subgroupG/H
centerC22C22×D4×D67
commutator, cosocleC2×C4×C67C25
FrattiniC2×C4C24×D67
FittingC67×#3388C2
socleC22×C67C23×D4
prime radicalC2×D4×D67C23
hypercenter#3388D67
hypocenterC67C2×#3388
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #3388

Complements

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

NH ≅ G/Ntype
1. #557×D67C2semidirect
3. #22573161C2semidirect
4. #22573160C2semidirect
5. #22573159C2semidirect
6. #22573158C2semidirect
7. #22573157C2semidirect
8. #22573156C2semidirect
9. #22573155C2semidirect
10. #22573154C2semidirect
11. #22573153C2semidirect
12. #22573152C2semidirect
13. #22573151C2semidirect
14. #22573150C2semidirect
15. #22573149C2semidirect
16. #22573148C2semidirect
17. #22573147C2semidirect
18. #501×D67C2semidirect
19. #501×D67C2semidirect
20. #499×D67C2semidirect
21. #479×D67C2semidirect
22. #479×D67C2semidirect
23. #475×D67C2semidirect
27. #446×D67C2semidirect
31. C67×#3388C2semidirect
33. #16864125C22semidirect
35. #16864124C22semidirect
38. #16864123C22semidirect
39. #16864123C22semidirect
40. #16864122C22semidirect
41. #16864122C22semidirect
43. #16864121C22semidirect
76. #16863806C22semidirect
77. #16863806C22semidirect
78. #16863805C22semidirect
79. #16863805C22semidirect
80. #16863804C22semidirect
81. #16863804C22semidirect
82. #16863804C22semidirect
83. #16863804C22semidirect
84. #16863803C22semidirect
85. #16863803C22semidirect
86. #16863803C22semidirect
87. #16863803C22semidirect
88. #16863802C22semidirect
89. #16863802C22semidirect
90. #16863798C22semidirect
91. #16863797C22semidirect
92. #16863797C22semidirect
93. #16863796C22semidirect
94. #16863796C22semidirect
95. #16863795C22semidirect
96. #16863795C22semidirect
97. #16863706C22semidirect
98. #16863706C22semidirect
99. #16863705C22semidirect
100. #16863705C22semidirect
101. #16863704C22semidirect
102. #16863704C22semidirect
103. #16863703C22semidirect
104. #16863703C22semidirect
105. #16863702C22semidirect
106. #16863702C22semidirect
107. #16863701C22semidirect
108. #16863701C22semidirect
109. #16863700C22semidirect
110. #16863700C22semidirect
132. #16863682C22semidirect
133. #16863681C22semidirect
134. #16863680C22semidirect
135. #16863680C22semidirect
136. #16863679C22semidirect
137. #16863679C22semidirect
138. #16863678C22semidirect
139. #16863527C22semidirect
140. #16863526C22semidirect
141. #16863525C22semidirect
142. #16863525C22semidirect
143. #16863524C22semidirect
144. #16863524C22semidirect
145. #16863523C22semidirect
188. #557×C67C22semidirect
190. #501×C67C22semidirect
191. #501×C67C22semidirect
192. #499×C67C22semidirect
193. #479×C67C22semidirect
194. #479×C67C22semidirect
198. #475×C67C22semidirect
199. #446×C67C22semidirect
214. SD16×D67Q8semidirect
526. #11761617C2×Q8semidirect
527. #11761616C2×Q8semidirect
528. #11761615C2×Q8semidirect
632. SD16×C67C2×Q8semidirect
805. D67#3388direct (N × H)
823. #3388D67direct (N × H)
837. C67C2×#3388semidirect
850. #557C2×D67semidirect
898. #501C2×D67semidirect
899. #501C2×D67semidirect
907. #499C2×D67semidirect
922. #479C2×D67semidirect
923. #479C2×D67semidirect
955. #475C2×D67semidirect
963. #446C2×D67semidirect
1343. SD16Q8×D67semidirect

Maximal subgroups

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

subgroupindex
#557×D672
#554×D672
#225731612
#225731602
#225731592
#225731582
#225731572
#225731562
#225731552
#225731542
#225731532
#225731522
#225731512
#225731502
#225731492
#225731482
#225731472
#501×D672
#499×D672
#479×D672
#475×D672
#478×D672
#476×D672
#446×D672
#440×D672
C4×SD16×D672
C67×#33882
C2×#338867