Finite Group Databasebeta

← #31736625

Subgroups — #31736625

Order 17152.

1794 conjugacy classes of subgroups.

The subgroup lattice has 1628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22574020C211yesmaximal, characteristic, complemented
2#22574008C211yesmaximal, characteristic, complemented
3#22573156C211yesmaximal, characteristic, complemented
4#22573154C211yesmaximal, characteristic, complemented
5#22573149C211yesmaximal, characteristic, complemented
6#22573147C211yesmaximal, characteristic, complemented
7#22573116C211yesmaximal, characteristic, complemented
8#22573114C211yesmaximal, characteristic, complemented
9#22573111C211yesmaximal, characteristic, complemented
10#22573109C211yesmaximal, characteristic, complemented
11#22573109C211yesmaximal, characteristic, complemented
12#22573104C211yesmaximal, characteristic, complemented
13#22573103C211yesmaximal, characteristic, complemented
14#22573076C211yesmaximal, characteristic, complemented
15#22573071C211yesmaximal, characteristic, complemented
16#22573066C211yesmaximal, characteristic, complemented
17#22573064C211yesmaximal, characteristic, complemented
18#22570754C211yesmaximal, characteristic, complemented
19#22570736C211yesmaximal, characteristic, complemented
20#22570734C211yesmaximal, characteristic, complemented
21#22570072C211yesmaximal, characteristic, complemented
22#22570066C211yesmaximal, characteristic, complemented
23#22570035C211yesmaximal, characteristic, complemented
24#22570033C211yesmaximal, characteristic, complemented
25#22569994C211yesmaximal, characteristic, complemented
26#476×D67C211yesmaximal, characteristic, complemented
27#22569154C211yesmaximal, characteristic, complemented
28#22569038C211yesmaximal, characteristic
29#22569034C211yesmaximal, characteristic
30#22569020C211yesmaximal, characteristic
31C67×#3384C211yesmaximal, characteristic, complemented
32C2×#14524067C2211yescharacteristic
33#16864126C2211yescharacteristic, complemented
34#16864126C2211yescharacteristic, complemented
35#16864124C2211yescharacteristic, complemented
36#16864121C2211yescharacteristic, complemented
37#16864106C2211yescharacteristic
38#16864105C2211yescharacteristic
39#16864105C2211yescharacteristic
40#16864105C2211yescharacteristic, complemented
41#16864105C2211yescharacteristic, complemented
42#16864102C2211yescharacteristic
43#16864102C2211yescharacteristic
44#16864101—21no—
45#16864100—21no—
46#16864100—21no—
47#16864100—21no—
48#16864100—21no—
49D4×Dic134C2211yescharacteristic
50D4×Dic134C2211yescharacteristic, complemented
51#16864061C2211yescharacteristic
52Q8×C22⋊D67—21no—
53#16864059—21no—
54#16864059—21no—
55#16864026C2211yescharacteristic
56#16864025—21no—
57#16864025—21no—
58#16864023C2211yescharacteristic
59#16864023C2211yescharacteristic
60#16864023C2211yescharacteristic
61#16864021—21no—
62#16864021—21no—
63#16863952C2211yescharacteristic
64#16863950C2211yescharacteristic
65#16863948—21no—
66C2×#14524041—21no—
67C4⋊Q8×D67C2211yescharacteristic
68C2×#14524021—21no—
69C22⋊Q8×D67—21no—
70#16863875C2211yescharacteristic
71#16863875C2211yescharacteristic
72#16863868C2211yescharacteristic
73#16863868C2211yescharacteristic
74C4×#11761627C2211yescharacteristic
75C4×D4×D67C2211yescharacteristic
76#16863806C2211yescharacteristic, complemented
77#16863805C2211yescharacteristic, complemented
78#16863805C2211yescharacteristic, complemented
79#16863804C2211yescharacteristic, complemented
80#16863803C2211yescharacteristic, complemented
81#16863803C2211yescharacteristic, complemented
82#16863803C2211yescharacteristic, complemented
83#16863802C2211yescharacteristic, complemented
84#16863802C2211yescharacteristic, complemented
85#16863802C2211yescharacteristic, complemented
86#16863800C2211yescharacteristic, complemented
87#16863800C2211yescharacteristic, complemented
88#16863798C2211yescharacteristic, complemented
89#16863797C2211yescharacteristic, complemented
90#16863796C2211yescharacteristic, complemented
91#16863795C2211yescharacteristic, complemented
92#16863793C2211yescharacteristic, complemented
93#16863793C2211yescharacteristic, complemented
94#16863793C2211yescharacteristic, complemented
95#16863793C2211yescharacteristic, complemented
96#16863792C2211yescharacteristic, complemented
97#16863706C2211yescharacteristic, complemented
98#16863704C2211yescharacteristic, complemented
99#16863704C2211yescharacteristic, complemented
100#16863702C2211yescharacteristic, complemented
101#16863700C2211yescharacteristic, complemented
102#16863700C2211yescharacteristic, complemented
103#16863699C2211yescharacteristic
104#16863698C2211yescharacteristic
105#16863698C2211yescharacteristic, complemented
106#16863697C2211yescharacteristic
107#16863697C2211yescharacteristic
108#16863696C2211yescharacteristic
109#16863696C2211yescharacteristic
110#16863696C2211yescharacteristic, complemented
111#16863696C2211yescharacteristic, complemented
112#16863695C2211yescharacteristic
113#16863694C2211yescharacteristic
114#16863694C2211yescharacteristic, complemented
115#16863690C2211yescharacteristic, complemented
116#16863687C2211yescharacteristic
117#16863686C2211yescharacteristic
118#16863686C2211yescharacteristic, complemented
119#16863685C2211yescharacteristic
120#16863685C2211yescharacteristic
121#16863685C2211yescharacteristic
122#16863684C2211yescharacteristic
123#16863684C2211yescharacteristic
124#16863684C2211yescharacteristic
125#16863684C2211yescharacteristic, complemented
126#16863684C2211yescharacteristic, complemented
127#16863684C2211yescharacteristic, complemented
128#16863683C2211yescharacteristic
129#16863683C2211yescharacteristic
130#16863682C2211yescharacteristic, complemented
131#16863680C2211yescharacteristic, complemented
132#16863680C2211yescharacteristic, complemented
133#16863680C2211yescharacteristic, complemented
134#16863678C2211yescharacteristic, complemented
135#16863675C2211yescharacteristic
136#16863674C2211yescharacteristic
137#16863674C2211yescharacteristic, complemented
138#16863673C2211yescharacteristic
139#16863527C2211yescharacteristic, complemented
140#16863525C2211yescharacteristic, complemented
141#16863525C2211yescharacteristic, complemented
142#16863524C2211yescharacteristic, complemented
143#16863524C2211yescharacteristic, complemented
144C8×Dic134C2211yescharacteristic, complemented
145#16863520C2211yescharacteristic, complemented
146#16863508C2211yescharacteristic
147#16863506C2211yescharacteristic
148#16863506C2211yescharacteristic
149#16863505C2211yescharacteristic
150#16863498C2211yescharacteristic
151#16863498C2211yescharacteristic
152#16863496C2211yescharacteristic
153#16863496C2211yescharacteristic
154#16863495C2211yescharacteristic
155#16863493C2211yescharacteristic
156#16863487C2211yescharacteristic
157#16863487C2211yescharacteristic
158C4×#11761617C2211yescharacteristic
159#16863483C2211yescharacteristic
160#16863483C2211yescharacteristic
161C4×#11761616C2211yescharacteristic
162D8×Dic67C2211yescharacteristic
163D8×Dic67C2211yescharacteristic
164C4×#11761613C2211yescharacteristic
165#16863476C2211yescharacteristic
166#16863476C2211yescharacteristic
167#16863437C2211yescharacteristic
168#16863437C2211yescharacteristic
169#16863435C2211yescharacteristic
170#16863435C2211yescharacteristic
171#16863435C2211yescharacteristic
172#16863433C2211yescharacteristic
173#16863431C2211yescharacteristic
174#106×D67C2211yescharacteristic
175#106×D67C2211yescharacteristic
176#16863421C2211yescharacteristic
177#16863421C2211yescharacteristic
178C4⋊C8×D67C2211yescharacteristic
179#16863399C2211yescharacteristic
180#16863394C2211yescharacteristic
181#16863389C2211yescharacteristic
182#16863389C2211yescharacteristic
183#102×D67C2211yescharacteristic
184#102×D67C2211yescharacteristic
185#16863353C2211yescharacteristic
186#16863350C2211yescharacteristic
187#16863348C2211yescharacteristic
188#554×C67C2211yescharacteristic
189D4×Q8×C67C2211yescharacteristic, complemented
190#501×C67C2211yescharacteristic, complemented
191#501×C67C2211yescharacteristic, complemented
192#498×C67C2211yescharacteristic, complemented
193#478×C67C2211yescharacteristic, complemented
194#478×C67C2211yescharacteristic, complemented
195#476×C67C2211yescharacteristic
196#476×C67C2211yescharacteristic
197#476×C67C2211yescharacteristic, complemented
198#474×C67C2211yescharacteristic
199#446×C67C2211yescharacteristic, complemented
200#442×C67C2211yescharacteristic
201#442×C67C2211yescharacteristic
202C4×D8×C67C2211yescharacteristic
203C2×#11761627C2311yescharacteristic
204C22×Dic134—21no—
205C22×Dic134—21no—
206C2×Q8×D67—21no—
207C2×Q8×D67—21no—
208C2×D4×D67C2311yescharacteristic
209C22×C4×D67—21no—
210#14524067Q818yescomplemented
211C2×#11761617C2311yescharacteristic
212C2×#11761616C2311yescharacteristic
213C2×#11761613C2311yescharacteristic
214C2×#11761611C2311yescharacteristic
215C2×#11761611C2311yescharacteristic
216C2×C8×D67C2311yescharacteristic
217C2×C8×D67C2311yescharacteristic
218#14524043C2311yescharacteristic
219#14524043C2311yescharacteristic
220#14524042—21no—
221#14524042—21no—
222#14524042—21no—
223#14524042—21no—
224#14524042D411yescharacteristic
225#14524042C2311yescharacteristic
226#14524042C2311yescharacteristic
227#14524042C2311yescharacteristic
228#14524042C2311yescharacteristic
229#14524042C2311yescharacteristic
230#14524042C2311yescharacteristic
231#14524042C2311yescharacteristic
232#14524042C2311yescharacteristic
233#14524041—21no—
234#14524041—21no—
235#14524041—21no—
236#14524041—21no—
237#14524041—21no—
238#14524041—21no—
239#14524041—21no—
240#14524041—21no—
241#14524041—21no—
242#14524041—21no—
243#14524041D411yescharacteristic
244#14524035C2311yescharacteristic
245#14524035C2311yescharacteristic
246#14524035C2311yescharacteristic
247#14524035C2311yescharacteristic
248#14524034C2311yescharacteristic
249#14524034C2311yescharacteristic
250#14524034C2311yescharacteristic
251#14524034C2311yescharacteristic
252#14524033—21no—
253#14524033—21no—
254#14524033—21no—
255#14524033—21no—
256#14524033—21no—
257#14524033—21no—
258#14524033—21no—
259#14524033—21no—
260#14524033D411yescharacteristic
261#14524033D411yescharacteristic
262#14524023—21no—
263#14524023—21no—
264#14524023—21no—
265#14524023D411yescharacteristic
266#14524022—21no—
267#14524022—21no—
268#14524022—21no—
269#14524022—21no—
270#14524022—21no—
271#14524022—21no—
272#14524021—21no—
273#14524021—21no—
274#14524021—21no—
275#14524021—21no—
276#14524021—21no—
277#14524021—21no—
278#14524021—21no—
279#14524021—21no—
280#14524021—21no—
281#14524021—21no—
282#14524021—21no—
283#14524021—21no—
284#14524021—21no—
285#14524021—21no—
286#14524021D411yescharacteristic
287#14524021D411yescharacteristic
288#14524020—21no—
289#14524020—21no—
290#14524020—21no—
291#14524020—21no—
292#14524020—21no—
293#14524020—21no—
294#14524020—21no—
295#14524020—21no—
296#14524020—21no—
297#14524020—21no—
298#14524020—21no—
299#14524020—21no—
300#14524019—21no—
301#14524019—21no—
302#14524019—21no—
303#14524019—21no—
304#14524019—21no—
305#14524019D411yescharacteristic
306Q8×Dic67—21no—
307C4×Dic134C2311yescharacteristic
308C4×Dic134C2311yescharacteristic
309C4×Dic134C2311yescharacteristic
310C4×Dic134C2311yescharacteristic
311C4×Dic134C2311yescharacteristic
312C4×Dic134C2311yescharacteristic
313#14524008—21no—
314#14524008—21no—
315#14524008—21no—
316#14524008—21no—
317#14524008—21no—
318#14524008C2311yescharacteristic
319#14524008C2311yescharacteristic
320#14524008C2311yescharacteristic
321C4×D268C2311yescharacteristic
322C4×D268C2311yescharacteristic
323C4×D268C2311yescharacteristic
324D4×Dic67C2311yescharacteristic
325D4×Dic67C2311yescharacteristic
326D4×Dic67C2311yescharacteristic
327D4×Dic67C2311yescharacteristic
328D4×Dic67C2311yescharacteristic
329D4×Dic67C2311yescharacteristic
330#14524005C2311yescharacteristic
331#14524005C2311yescharacteristic
332#14524005C2311yescharacteristic
333C4×C22⋊D67—21no—
334C4×C22⋊D67—21no—
335C4×C22⋊D67—21no—
336C4×C22⋊D67—21no—
337C4×C22⋊D67—21no—
338C4×C22⋊D67—21no—
339(C22⋊D67)⋊C4—21no—
340(C22⋊D67)⋊C4—21no—
341(C22⋊D67)⋊C4—21no—
342(C22⋊D67)⋊C4—21no—
343(C22⋊D67)⋊C4—21no—
344(C22⋊D67)⋊C4—21no—
345#14524001C2311yescharacteristic
346#14524001C2311yescharacteristic
347#14524001C2311yescharacteristic
348#14524000C2311yescharacteristic
349#14524000C2311yescharacteristic
350#14523999—21no—
351#14523999—21no—
352#14523999—21no—
353C2×Dic67⋊C4—21no—
354C2×Dic67⋊C4—21no—
355C2×Dic67⋊C4—21no—
356C2×Dic67⋊C4—21no—
357C2×Dic67⋊C4—21no—
358C2×Dic67⋊C4—21no—
359C4⋊C4×D67—21no—
360C4⋊C4×D67—21no—
361C4⋊C4×D67—21no—
362C4⋊C4×D67—21no—
363C4⋊C4×D67C2311yescharacteristic
364C4⋊C4×D67C2311yescharacteristic
365C4⋊C4×D67C2311yescharacteristic
366C2×(C2×D67)⋊C4—21no—
367C2×(C2×D67)⋊C4—21no—
368C22⋊C4×D67—21no—
369C22⋊C4×D67—21no—
370C22⋊C4×D67—21no—
371C2×C4×Dic67—21no—
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#14523975C2311yescharacteristic
385#14523975C2311yescharacteristic
386#14523975C2311yescharacteristic
387#14523975C2311yescharacteristic
388#14523975C2311yescharacteristic
389#14523974C2311yescharacteristic
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#14523966C2311yescharacteristic
413#14523966C2311yescharacteristic
414#14523966C2311yescharacteristic
415#14523965C2311yescharacteristic
416#14523965C2311yescharacteristic
417#14523965C2311yescharacteristic
418#14523964C2311yescharacteristic
419#14523964C2311yescharacteristic
420#14523964C2311yescharacteristic
421#14523964C2311yescharacteristic
422#14523964C2311yescharacteristic
423#14523964C2311yescharacteristic
424#14523963C2311yescharacteristic
425#14523963C2311yescharacteristic
426#14523963C2311yescharacteristic
427#14523954C2311yescharacteristic
428#14523954C2311yescharacteristic
429#14523953C2311yescharacteristic
430#14523953C2311yescharacteristic
431C4×C67⋊C8C2311yescharacteristic
432C8×Dic67C2311yescharacteristic
433C8×Dic67C2311yescharacteristic
434C8×Dic67C2311yescharacteristic
435C8×Dic67C2311yescharacteristic
436C22×Q8×C67—21no—
437C2×D8×C67C2311yescharacteristic
438C4⋊Q8×C67C2311yescharacteristic
439C4⋊Q8×C67C2311yescharacteristic
440C4⋊Q8×C67C2311yescharacteristic
441C4⋊Q8×C67C2311yescharacteristic
442#125×C67C2311yescharacteristic
443#125×C67C2311yescharacteristic
444C22⋊Q8×C67—21no—
445C22⋊Q8×C67—21no—
446C22⋊Q8×C67—21no—
447C22⋊Q8×C67—21no—
448C22⋊Q8×C67—21no—
449C22⋊Q8×C67—21no—
450C4×Q8×C67C2311yescharacteristic
451C4×D4×C67C2311yescharacteristic
452C4×D4×C67C2311yescharacteristic
453C4×D4×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#106×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#102×C67C2311yescharacteristic
471#102×C67C2311yescharacteristic
472#102×C67C2311yescharacteristic
473#102×C67C2311yescharacteristic
474#102×C67C2311yescharacteristic
475#102×C67C2311yescharacteristic
476#97×C67C2311yescharacteristic
477#97×C67C2311yescharacteristic
478C4×C8×C67C2311yescharacteristic
479C23×D67—21no—
480#11761627—22no—
481#11761627C2×Q814yescomplemented
482C2×Dic134—21no—
483C2×Dic134—21no—
484C2×Dic134—21no—
485C2×Dic134—21no—
486C2×Dic134—21no—
487C2×Dic134—21no—
488C2×Dic134—21no—
489C2×Dic134—21no—
490C2×Dic134—21no—
491C2×Dic134—21no—
492C2×Dic134—82no—
493C2×Dic134—82no—
494C2×Dic134C2×D411yescharacteristic
495C2×Dic134C2×D411yescharacteristic
496C2×Dic134C2×D411yescharacteristic
497C2×Dic134C2411yescharacteristic
498Q8×D67—82no—
499Q8×D67—82no—
500C2×D268C2411yescharacteristic
501C2×C22⋊D67—21no—
502C2×C22⋊D67—21no—
503D4×D67—22no—
504D4×D67C2×Q814yescomplemented
505C22×Dic67—21no—
506C22×Dic67—21no—
507C22×Dic67—21no—
508C22×Dic67—21no—
509C22×Dic67—21no—
510C22×Dic67—21no—
511C22×Dic67—21no—
512C2×C4×D67—21no—
513C2×C4×D67—21no—
514C2×C4×D67—21no—
515C2×C4×D67—21no—
516C2×C4×D67—21no—
517C2×C4×D67—21no—
518C2×C4×D67—21no—
519C2×C4×D67—21no—
520C2×C4×D67—21no—
521C2×C4×D67—82no—
522C2×C4×D67C2×D411yescharacteristic
523C2×C4×D67C2×D411yescharacteristic
524C2×C4×D67C2411yescharacteristic
525#11761617C2×Q814yescomplemented
526#11761616C2×Q814yescomplemented
527#11761613C2×Q814yescomplemented
528#11761611—22no—
529#11761611C2×Q814yescomplemented
530C2×C67⋊C8C2411yescharacteristic
531C2×C67⋊C8C2411yescharacteristic
532C2×C67⋊C8C2411yescharacteristic
533C2×C67⋊C8C2411yescharacteristic
534C8×D67—22no—
535C8×D67—22no—
536C4⋊Dic67—21no—
537C4⋊Dic67—21no—
538C4⋊Dic67—21no—
539C4⋊Dic67—21no—
540C4⋊Dic67—21no—
541C4⋊Dic67—21no—
542C4⋊Dic67C2×D411yescharacteristic
543C4⋊Dic67C2×D411yescharacteristic
544C4⋊Dic67C2×D411yescharacteristic
545C4⋊Dic67C2411yescharacteristic
546C4⋊Dic67C2411yescharacteristic
547C4⋊Dic67C2411yescharacteristic
548C4⋊Dic67C2411yescharacteristic
549C4⋊Dic67C2411yescharacteristic
550C4⋊Dic67C2411yescharacteristic
551Dic67⋊C4—21no—
552Dic67⋊C4—21no—
553Dic67⋊C4—21no—
554Dic67⋊C4—21no—
555Dic67⋊C4—21no—
556Dic67⋊C4—21no—
557Dic67⋊C4—21no—
558Dic67⋊C4—21no—
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⋊C4C2×D411yescharacteristic
581Dic67⋊C4C2×D411yescharacteristic
582Dic67⋊C4C2×D411yescharacteristic
583Dic67⋊C4C2×D411yescharacteristic
584Dic67⋊C4C2×D411yescharacteristic
585Dic67⋊C4C2×D411yescharacteristic
586Dic67⋊C4C2×D411yescharacteristic
587Dic67⋊C4C2×D411yescharacteristic
588Dic67⋊C4C2×D411yescharacteristic
589Dic67⋊C4C2×D411yescharacteristic
590C22⋊Dic67—21no—
591C22⋊Dic67—21no—
592C22⋊Dic67—21no—
593C22⋊Dic67—21no—
594C22⋊Dic67—21no—
595C22⋊Dic67—21no—
596(C2×D67)⋊C4—21no—
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)⋊C4C2×D411yescharacteristic
606(C2×D67)⋊C4C2×D411yescharacteristic
607(C2×D67)⋊C4C2×D411yescharacteristic
608(C2×D67)⋊C4C2×D411yescharacteristic
609C4×Dic67—21no—
610C4×Dic67—21no—
611C4×Dic67—21no—
612C4×Dic67—21no—
613C4×Dic67—21no—
614C4×Dic67—21no—
615C4×Dic67—21no—
616C4×Dic67—21no—
617C4×Dic67—21no—
618C4×Dic67C2×D411yescharacteristic
619C4×Dic67C2×D411yescharacteristic
620C4×Dic67C2411yescharacteristic
621C4×Dic67C2411yescharacteristic
622C4×Dic67C2411yescharacteristic
623C2×Q8×C67—21no—
624C2×Q8×C67—21no—
625C2×Q8×C67—21no—
626C2×Q8×C67—21no—
627C2×Q8×C67—82no—
628C2×Q8×C67C2×D411yescharacteristic
629C2×D4×C67C2411yescharacteristic
630C2×D4×C67C2411yescharacteristic
631C22×C4×C67—21no—
632C22×C4×C67—21no—
633C22×C4×C67—21no—
634C22×C4×C67—21no—
635C22×C4×C67—21no—
636C22×C4×C67—21no—
637D8×C67C2×Q814yescomplemented
638C2×C8×C67C2411yescharacteristic
639C2×C8×C67C2411yescharacteristic
640C2×C8×C67C2411yescharacteristic
641C2×C8×C67C2411yescharacteristic
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—
662C22⋊C4×C67—21no—
663C22⋊C4×C67—21no—
664C22⋊C4×C67—21no—
665C42×C67C2411yescharacteristic
666C42×C67C2411yescharacteristic
667C42×C67C2411yescharacteristic
668C23×C67—21no—
669C23×C67—21no—
670C22×D67—21no—
671C22×D67—24no—
672C22×D67—81no—
673C22×D67—81no—
674C22×D67C22×D411yescharacteristic
675Q8×C67—41no—
676Q8×C67—42no—
677Q8×C67—81no—
678Q8×C67—81no—
679Q8×C67—81no—
680D4×C67—21no—
681D4×C67—21no—
682D4×C67C22×Q812yes—
683D4×C67C22×Q812yes—
684C2×C4×C67—21no—
685C2×C4×C67—21no—
686C2×C4×C67—21no—
687C2×C4×C67—21no—
688C2×C4×C67—21no—
689C2×C4×C67—21no—
690C2×C4×C67—42no—
691C2×C4×C67—81no—
692C2×C4×C67—81no—
693C2×C4×C67—81no—
694C2×C4×C67—81no—
695C2×C4×C67—81no—
696C2×C4×C67C22×D411yescharacteristic
697C2×C4×C67C22×D411yescharacteristic
698C2×C4×C67C22×D411yescharacteristic
699C2×C4×C67C22×D411yescharacteristic
700C2×C4×C67C22×D411yescharacteristic
701C2×C4×C67C22×D411yescharacteristic
702C2×C4×C67C2511yescharacteristic
703C22⋊D67—24no—
704C22⋊D67—24no—
705C2×Dic67—21no—
706C2×Dic67—24no—
707C2×Dic67—21no—
708C2×Dic67—21no—
709C2×Dic67—21no—
710C2×Dic67—21no—
711C2×Dic67—21no—
712C2×Dic67—21no—
713C2×Dic67—42no—
714C2×Dic67—42no—
715C2×Dic67—81no—
716C2×Dic67—81no—
717C2×Dic67—81no—
718C2×Dic67—81no—
719C2×Dic67C22×D411yescharacteristic
720C2×Dic67C22×D411yescharacteristic
721C2×Dic67C22×D411yescharacteristic
722C2×Dic67C22×D411yescharacteristic
723C2×Dic67C22×D411yescharacteristic
724C2×Dic67C22×D411yescharacteristic
725C2×Dic67C22×D411yescharacteristic
726D268—21no—
727D268C22×Q812yes—
728C4×D67—22no—
729C4×D67—41no—
730C4×D67—42no—
731C4×D67—81no—
732C4×D67—81no—
733C4×D67—81no—
734C4×D67—81no—
735C4×D67—81no—
736C4×D67—81no—
737C4×D67—81no—
738C4×D67—81no—
739C4×D67C22×Q812yes—
740C4×D672−1+412yes—
741Dic134—21no—
742Dic134—22no—
743Dic134—22no—
744Dic134—41no—
745Dic134—42no—
746Dic134—42no—
747Dic134—81no—
748Dic134—81no—
749Dic134—81no—
750Dic134—81no—
751Dic134—81no—
752Dic134—81no—
753Dic134—81no—
754Dic134—81no—
755Dic134C22×Q812yes—
756C8×C67—21no—
757C8×C67—21no—
758C8×C67—21no—
759C8×C67C22×Q812yes—
760C67⋊C8—21no—
761C67⋊C8—21no—
762C67⋊C8—21no—
763C67⋊C8C22×Q812yes—
764C22×C67—22no—
765C22×C67—22no—
766C22×C67—41no—
767C22×C67—41no—
768C22×C67—41no—
769C22×C67—41no—
770C22×C67C23×D411yescharacteristic
771C2×D67—21no—
772C2×D67—21no—
773C2×D67—22no—
774C2×D67—41no—
775C2×D67—41no—
776C2×D67—84no—
777C2×D67D4×Q812yes—
778C4×C67—21no—
779C4×C67—21no—
780C4×C67—21no—
781C4×C67—21no—
782C4×C67—21no—
783C4×C67—21no—
784C4×C67—41no—
785C4×C67—41no—
786C4×C67—41no—
787C4×C67—41no—
788C4×C67—41no—
789C4×C67—41no—
790C4×C67C23×Q811yescharacteristic
791C4×C67C2×2−1+411yescharacteristic
792Dic67—21no—
793Dic67—21no—
794Dic67—21no—
795Dic67—22no—
796Dic67—21no—
797Dic67—21no—
798Dic67—41no—
799Dic67—41no—
800Dic67—41no—
801Dic67—41no—
802Dic67—41no—
803Dic67—41no—
804Dic67D4×Q812yes—
805Dic67#57712yes—
806#61382—671nomaximal, Sylow
807C2×C67—42no—
808C2×C67—42no—
809C2×C67C2×D4×Q811yescharacteristic
810C2×C67C2×#57711yescharacteristic
811C2×C67#358511yescharacteristic
812D67—22no—
813D67—42no—
814#3503—671no—
815#3501—671no—
816#3388—671no—
817#3388—671no—
818#3388—671no—
819#3388—671no—
820#3385—671no—
821#3385—671no—
822#3384—671no—
823#3384—671no—
824#3384—671no—
825#3384—671no—
826#3384—671no—
827#3384D6711yescharacteristic, complemented
828#3380—671no—
829#3380—671no—
830Q8×SD16—671no—
831Q8×SD16—671no—
832#3165—671no—
833#3163—671no—
834#3163—671no—
835#3084—671no—
836#3084—671no—
837#3081—671no—
838#3081—671no—
839#3076—671no—
840C2×#476—671no—
841#2962—671no—
842#2946—671no—
843#2946—671no—
844C4×AGL(1,ℤ/8)—671no—
845C67#6138211yescharacteristic, complemented, Sylow
846C2×AGL(1,ℤ/8)—671no—
847Q82—671no—
848Q82—671no—
849#557—671no—
850#557—671no—
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#554—1341no—
863#554C2×D6711yescharacteristic
864D4×Q8—671no—
865D4×Q8—671no—
866D4×Q8—671no—
867D4×Q8—1341no—
868D4×Q8—1341no—
869D4×Q8—1341no—
870D4×Q8C2×D6711yescharacteristic, complemented
871#544—671no—
872#544—671no—
873#544—671no—
874#544—671no—
875#544—1341no—
876#544—1341no—
877#543—1341no—
878#543—1341no—
879#533—671no—
880#533—671no—
881#533—1341no—
882C2×C4⋊Q8—671no—
883C2×C4⋊Q8—1341no—
884C2×C22⋊Q8—1341no—
885C2×C22⋊Q8—1341no—
886#520—671no—
887#520—671no—
888#518—671no—
889#518—671no—
890C4×#41—671no—
891C2×C4×D4—671no—
892#501—671no—
893#501—671no—
894#501—671no—
895#501—671no—
896#501—671no—
897#501—671no—
898#501—671no—
899#501—671no—
900#501—671no—
901#501—671no—
902#501C2×D6711yescharacteristic, complemented
903#501C2×D6711yescharacteristic, complemented
904#500—671no—
905#500—671no—
906#499—671no—
907#499—671no—
908#499—671no—
909#499—671no—
910#498—671no—
911#498—671no—
912#498—671no—
913#498—671no—
914#498—671no—
915#498C2×D6711yescharacteristic, complemented
916#479—671no—
917#479—671no—
918#479—671no—
919#479—671no—
920#479—671no—
921#479—671no—
922#478—671no—
923#478—671no—
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#478C2×D6711yescharacteristic, complemented
935#478C2×D6711yescharacteristic, complemented
936#477—671no—
937#476—671no—
938#476—671no—
939#476—671no—
940#476—671no—
941#476—671no—
942#476—671no—
943#476—671no—
944#476—671no—
945#476—671no—
946#476—671no—
947#476—671no—
948#476—671no—
949#476—671no—
950#476—671no—
951#476C2×D6711yescharacteristic
952#476C2×D6711yescharacteristic
953#476C2×D6711yescharacteristic, complemented
954#475—671no—
955#475—671no—
956#475—671no—
957#475—671no—
958#475—671no—
959#474—671no—
960#474—671no—
961#474—671no—
962#474—671no—
963#474C2×D6711yescharacteristic
964#446—671no—
965#446—671no—
966#446—671no—
967#446—671no—
968#446—671no—
969#446C2×D6711yescharacteristic, complemented
970C8×Q8—671no—
971C8×Q8—671no—
972#442—671no—
973#442—671no—
974#442—671no—
975#442—671no—
976#442C2×D6711yescharacteristic
977#442C2×D6711yescharacteristic
978#440—671no—
979#440—671no—
980#440—671no—
981#440—671no—
982#440—671no—
983#440—671no—
984C4×SD16—671no—
985C4×SD16—671no—
986C4×SD16—671no—
987C4×SD16—671no—
988C4×SD16—671no—
989C4×SD16—671no—
990C4×D8—671no—
991C4×D8—671no—
992C4×D8—671no—
993C4×D8—671no—
994C4×D8—671no—
995C4×D8C2×D6711yescharacteristic
996#428—671no—
997#428—671no—
998#428—671no—
999#428—671no—
1000#428—671no—
1001#427—671no—
1002#427—671no—
1003C2×#106—671no—
1004C2×#106—671no—
1005#424—671no—
1006#424—671no—
1007C2×C4⋊C8—671no—
1008#418—671no—
1009#417—671no—
1010#416—671no—
1011#416—671no—
1012C2×#102—671no—
1013C2×#102—671no—
1014#405—671no—
1015#405—671no—
1016C4×M16—671no—
1017C2×#41—671no—
1018C22×Q8—21no—
1019C22×Q8—1341no—
1020C22×Q8—1341no—
1021C22×Q8—1341no—
1022C22×Q8—1341no—
1023C22×D4—671no—
1024C23×C4—1341no—
1025AGL(1,ℤ/8)—678no—
1026C2×SD16—671no—
1027C2×SD16—671no—
1028C2×D8—671no—
1029C2×D8C22×D6711yescharacteristic
1030C2×M16—671no—
1031C2×M16—671no—
1032C22×C8—671no—
1033C22×C8—671no—
1034C4⋊Q8—671no—
1035C4⋊Q8—671no—
1036C4⋊Q8—671no—
1037C4⋊Q8—671no—
1038C4⋊Q8—671no—
1039C4⋊Q8—671no—
1040C4⋊Q8—671no—
1041C4⋊Q8—671no—
1042C4⋊Q8—671no—
1043C4⋊Q8—671no—
1044C4⋊Q8—671no—
1045C4⋊Q8—671no—
1046C4⋊Q8—1341no—
1047C4⋊Q8—1341no—
1048C4⋊Q8—1341no—
1049C4⋊Q8—1341no—
1050C4⋊Q8—1341no—
1051C4⋊Q8—1341no—
1052C4⋊Q8—1341no—
1053C4⋊Q8—1341no—
1054C4⋊Q8—1341no—
1055C4⋊Q8—1341no—
1056C4⋊Q8—1341no—
1057C4⋊Q8—1341no—
1058C4⋊Q8—1341no—
1059C4⋊Q8—1341no—
1060C4⋊Q8C22×D6711yescharacteristic
1061C4⋊Q8C22×D6711yescharacteristic
1062C4⋊Q8C22×D6711yescharacteristic
1063C4⋊Q8C22×D6711yescharacteristic
1064#125—671no—
1065#125—671no—
1066#125—671no—
1067#125—671no—
1068#125—671no—
1069#125—671no—
1070#125—671no—
1071#125—671no—
1072#125—671no—
1073#125—671no—
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
1084C22⋊Q8—21no—
1085C22⋊Q8—21no—
1086C22⋊Q8—21no—
1087C22⋊Q8—21no—
1088C22⋊Q8—21no—
1089C22⋊Q8—21no—
1090C22⋊Q8—671no—
1091C22⋊Q8—671no—
1092C22⋊Q8—671no—
1093C22⋊Q8—671no—
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—
1110C22⋊Q8—1341no—
1111C22⋊Q8—1341no—
1112C22⋊Q8—1341no—
1113C22⋊Q8—1341no—
1114C22⋊Q8—1341no—
1115C22⋊Q8—1341no—
1116C22⋊Q8—1341no—
1117C22⋊Q8—1341no—
1118C22⋊Q8—1341no—
1119C22⋊Q8—1341no—
1120C22⋊Q8—1341no—
1121C22⋊Q8—1341no—
1122C22⋊Q8—1341no—
1123C22⋊Q8—1341no—
1124C22⋊Q8—1341no—
1125C22⋊Q8—1341no—
1126C22⋊Q8—1341no—
1127C22⋊Q8—1341no—
1128C22⋊Q8—1341no—
1129C22⋊Q8—1341no—
1130C22⋊Q8—1341no—
1131C22⋊Q8—1341no—
1132C22⋊Q8—1341no—
1133C22⋊Q8—1341no—
1134C4×Q8—671no—
1135C4×Q8—671no—
1136C4×Q8—671no—
1137C4×Q8—671no—
1138C4×Q8—671no—
1139C4×Q8—671no—
1140C4×Q8—671no—
1141C4×Q8—671no—
1142C4×Q8—671no—
1143C4×Q8—1341no—
1144C4×Q8—1341no—
1145C4×Q8—1341no—
1146C4×Q8—1341no—
1147C4×Q8—1341no—
1148C4×Q8—1341no—
1149C4×Q8C22×D6711yescharacteristic
1150C4×D4—671no—
1151C4×D4—671no—
1152C4×D4—671no—
1153C4×D4—671no—
1154C4×D4—671no—
1155C4×D4—671no—
1156C4×D4—671no—
1157C4×D4—671no—
1158C4×D4—671no—
1159C4×D4—671no—
1160C4×D4—671no—
1161C4×D4—671no—
1162C4×D4—1341no—
1163C4×D4—1341no—
1164C4×D4—1341no—
1165C4×D4—1341no—
1166C4×D4—1341no—
1167C4×D4—1341no—
1168C4×D4—1341no—
1169C4×D4—1341no—
1170C4×D4—1341no—
1171C4×D4—1341no—
1172C4×D4—1341no—
1173C4×D4—1341no—
1174C4×D4C22×D6711yescharacteristic
1175C4×D4C22×D6711yescharacteristic
1176C4×D4C22×D6711yescharacteristic
1177C4×D4C22×D6711yescharacteristic
1178C4×D4C22×D6711yescharacteristic
1179C4×D4C22×D6711yescharacteristic
1180#117—671no—
1181#117—671no—
1182#117—671no—
1183#117—671no—
1184#117—671no—
1185#117—1341no—
1186#117—1341no—
1187#117—1341no—
1188C2×C4⋊C4—21no—
1189C2×C4⋊C4—671no—
1190C2×C4⋊C4—671no—
1191C2×C4⋊C4—671no—
1192C2×C4⋊C4—1341no—
1193C2×C4⋊C4—1341no—
1194C2×C4⋊C4—1341no—
1195C2×C4⋊C4—1341no—
1196C2×C4⋊C4—1341no—
1197C2×C4⋊C4—1341no—
1198C2×C4⋊C4—1341no—
1199C2×C4⋊C4—1341no—
1200C2×C4⋊C4—1341no—
1201C2×C4⋊C4—1341no—
1202C2×C22⋊C4—1341no—
1203C2×C22⋊C4—1341no—
1204C2×C22⋊C4—1341no—
1205C2×C22⋊C4—1341no—
1206C2×C22⋊C4—1341no—
1207C2×C42—671no—
1208C2×C42—1341no—
1209#107—671no—
1210#107—671no—
1211#107—671no—
1212#107—671no—
1213#107—671no—
1214#107—671no—
1215#107—671no—
1216#107—671no—
1217#107—671no—
1218#107—671no—
1219#107—671no—
1220#107C22×D6711yescharacteristic
1221#107C22×D6711yescharacteristic
1222#107C22×D6711yescharacteristic
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#106—671no—
1233#106—671no—
1234#106—671no—
1235#106—671no—
1236#106—671no—
1237#106—671no—
1238#106—671no—
1239#106C22×D6711yescharacteristic
1240#106C22×D6711yescharacteristic
1241#106C22×D6711yescharacteristic
1242#106C22×D6711yescharacteristic
1243#106C22×D6711yescharacteristic
1244#106C22×D6711yescharacteristic
1245C4⋊C8—671no—
1246C4⋊C8—671no—
1247C4⋊C8—671no—
1248C4⋊C8—671no—
1249C4⋊C8—671no—
1250C4⋊C8—671no—
1251C4⋊C8—671no—
1252C4⋊C8—671no—
1253C4⋊C8—671no—
1254C4⋊C8C22×D6711yescharacteristic
1255C4⋊C8C22×D6711yescharacteristic
1256C4⋊C8C22×D6711yescharacteristic
1257#103—671no—
1258#103—671no—
1259#103—671no—
1260#103—671no—
1261#103—671no—
1262#103—671no—
1263#102—671no—
1264#102—671no—
1265#102—671no—
1266#102—671no—
1267#102—671no—
1268#102—671no—
1269#102—671no—
1270#102—671no—
1271#102—671no—
1272#102—671no—
1273#102—671no—
1274#102—671no—
1275#102C22×D6711yescharacteristic
1276#102C22×D6711yescharacteristic
1277#102C22×D6711yescharacteristic
1278#102C22×D6711yescharacteristic
1279#102C22×D6711yescharacteristic
1280#102C22×D6711yescharacteristic
1281#97—671no—
1282#97—671no—
1283#97—671no—
1284#97—671no—
1285#97C22×D6711yescharacteristic
1286#97C22×D6711yescharacteristic
1287C4×C8—671no—
1288C4×C8—671no—
1289C4×C8—671no—
1290C4×C8—671no—
1291C4×C8—671no—
1292C4×C8C22×D6711yescharacteristic
1293C24—1341no—
1294#41—674no—
1295#41—1342no—
1296C2×Q8—21no—
1297C2×Q8—21no—
1298C2×Q8—21no—
1299C2×Q8—21no—
1300C2×Q8—82no—
1301C2×Q8—5362no—
1302C2×Q8—5362no—
1303C2×Q8—5362no—
1304C2×Q8—5362no—
1305C2×Q8—671no—
1306C2×Q8—671no—
1307C2×Q8—671no—
1308C2×Q8—671no—
1309C2×Q8—1341no—
1310C2×Q8—1341no—
1311C2×Q8—1341no—
1312C2×Q8—1341no—
1313C2×Q8—1341no—
1314C2×Q8—1341no—
1315C2×Q8—1341no—
1316C2×Q8—1341no—
1317C2×Q8—1341no—
1318C2×Q8—1341no—
1319C2×Q8D4×D6711yescharacteristic
1320C2×D4—674no—
1321C2×D4—671no—
1322C2×D4—1342no—
1323C2×D4—1341no—
1324C2×D4—1341no—
1325C2×D4C23×D6711yescharacteristic
1326C2×D4C23×D6711yescharacteristic
1327C22×C4—21no—
1328C22×C4—21no—
1329C22×C4—21no—
1330C22×C4—21no—
1331C22×C4—21no—
1332C22×C4—21no—
1333C22×C4—5362no—
1334C22×C4—671no—
1335C22×C4—671no—
1336C22×C4—671no—
1337C22×C4—1341no—
1338C22×C4—1341no—
1339C22×C4—1341no—
1340C22×C4—1341no—
1341C22×C4—1341no—
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—1341no—
1353SD16—674no—
1354SD16—674no—
1355D8—674no—
1356D8Q8×D6714yescomplemented
1357M16—674no—
1358M16—1342no—
1359C2×C8—671no—
1360C2×C8—671no—
1361C2×C8—671no—
1362C2×C8—671no—
1363C2×C8—1342no—
1364C2×C8—1342no—
1365C2×C8C23×D6711yescharacteristic
1366C2×C8C23×D6711yescharacteristic
1367C2×C8C23×D6711yescharacteristic
1368C2×C8C23×D6711yescharacteristic
1369C4⋊C4—21no—
1370C4⋊C4—21no—
1371C4⋊C4—21no—
1372C4⋊C4—21no—
1373C4⋊C4—21no—
1374C4⋊C4—21no—
1375C4⋊C4—21no—
1376C4⋊C4—21no—
1377C4⋊C4—671no—
1378C4⋊C4—671no—
1379C4⋊C4—671no—
1380C4⋊C4—671no—
1381C4⋊C4—671no—
1382C4⋊C4—671no—
1383C4⋊C4—671no—
1384C4⋊C4—671no—
1385C4⋊C4—671no—
1386C4⋊C4—671no—
1387C4⋊C4—671no—
1388C4⋊C4—671no—
1389C4⋊C4—671no—
1390C4⋊C4—671no—
1391C4⋊C4—671no—
1392C4⋊C4—671no—
1393C4⋊C4—671no—
1394C4⋊C4—671no—
1395C4⋊C4—671no—
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⋊C4—1341no—
1430C4⋊C4—1341no—
1431C4⋊C4D4×D6711yescharacteristic
1432C4⋊C4D4×D6711yescharacteristic
1433C4⋊C4D4×D6711yescharacteristic
1434C4⋊C4C23×D6711yescharacteristic
1435C4⋊C4C23×D6711yescharacteristic
1436C4⋊C4C23×D6711yescharacteristic
1437C4⋊C4C23×D6711yescharacteristic
1438C4⋊C4C23×D6711yescharacteristic
1439C4⋊C4C23×D6711yescharacteristic
1440C22⋊C4—21no—
1441C22⋊C4—21no—
1442C22⋊C4—21no—
1443C22⋊C4—21no—
1444C22⋊C4—21no—
1445C22⋊C4—21no—
1446C22⋊C4—671no—
1447C22⋊C4—671no—
1448C22⋊C4—671no—
1449C22⋊C4—671no—
1450C22⋊C4—1341no—
1451C22⋊C4—1341no—
1452C22⋊C4—1341no—
1453C22⋊C4—1341no—
1454C22⋊C4—1341no—
1455C22⋊C4—1341no—
1456C22⋊C4—1341no—
1457C22⋊C4—1341no—
1458C22⋊C4—1341no—
1459C22⋊C4—1341no—
1460C22⋊C4—1341no—
1461C22⋊C4—1341no—
1462C22⋊C4—1341no—
1463C22⋊C4—1341no—
1464C22⋊C4—1341no—
1465C42—671no—
1466C42—671no—
1467C42—671no—
1468C42—671no—
1469C42—671no—
1470C42—1341no—
1471C42—1341no—
1472C42—1341no—
1473C42—1341no—
1474C42—1341no—
1475C42—1341no—
1476C42—1341no—
1477C42—1341no—
1478C42—1341no—
1479C42C23×D6711yescharacteristic
1480C42C23×D6711yescharacteristic
1481C42C23×D6711yescharacteristic
1482C23—21no—
1483C23—21no—
1484C23—5361no—
1485C23—5361no—
1486C23—671no—
1487C23—1344no—
1488C23—1341no—
1489Q8—41no—
1490Q8—42no—
1491Q8—81no—
1492Q8—81no—
1493Q8—81no—
1494Q8—2682no—
1495Q8—2681no—
1496Q8—2682no—
1497Q8—5361no—
1498Q8—5361no—
1499Q8—5361no—
1500Q8—5361no—
1501Q8—5361no—
1502Q8—5361no—
1503Q8—5361no—
1504Q8—5361no—
1505Q8—672no—
1506Q8—1342no—
1507Q8—1342no—
1508Q8—1341no—
1509D4—21no—
1510D4—21no—
1511D4—672no—
1512D4—1344no—
1513D4—1344no—
1514D4—1341no—
1515D4C2×Q8×D6712yes—
1516D4C2×Q8×D6712yes—
1517C2×C4—21no—
1518C2×C4—21no—
1519C2×C4—21no—
1520C2×C4—21no—
1521C2×C4—21no—
1522C2×C4—21no—
1523C2×C4—42no—
1524C2×C4—81no—
1525C2×C4—81no—
1526C2×C4—81no—
1527C2×C4—81no—
1528C2×C4—81no—
1529C2×C4—2681no—
1530C2×C4—2682no—
1531C2×C4—2682no—
1532C2×C4—2682no—
1533C2×C4—5361no—
1534C2×C4—5361no—
1535C2×C4—5361no—
1536C2×C4—5361no—
1537C2×C4—5361no—
1538C2×C4—5361no—
1539C2×C4—5361no—
1540C2×C4—5361no—
1541C2×C4—5361no—
1542C2×C4—5361no—
1543C2×C4—5361no—
1544C2×C4—5361no—
1545C2×C4—671no—
1546C2×C4—671no—
1547C2×C4—672no—
1548C2×C4—672no—
1549C2×C4—671no—
1550C2×C4—671no—
1551C2×C4—671no—
1552C2×C4—671no—
1553C2×C4—671no—
1554C2×C4—1342no—
1555C2×C4—1341no—
1556C2×C4—1341no—
1557C2×C4—1341no—
1558C2×C4—1341no—
1559C2×C4—1341no—
1560C2×C4—1341no—
1561C2×C4—1344no—
1562C2×C4—1341no—
1563C2×C4C2×D4×D6711yescharacteristic
1564C2×C4C2×D4×D6711yescharacteristic
1565C2×C4C2×D4×D6711yescharacteristic
1566C2×C4C2×D4×D6711yescharacteristic
1567C2×C4C2×D4×D6711yescharacteristic
1568C2×C4C2×D4×D6711yescharacteristic
1569C2×C4C24×D6711yescharacteristic
1570C8—21no—
1571C8—21no—
1572C8—21no—
1573C8—672no—
1574C8—1341no—
1575C8—1341no—
1576C8—1341no—
1577C8C2×Q8×D6712yes—
1578C22—22no—
1579C22—22no—
1580C22—41no—
1581C22—41no—
1582C22—41no—
1583C22—41no—
1584C22—2681no—
1585C22—2681no—
1586C22—5364no—
1587C22—672no—
1588C22—1342no—
1589C22—1341no—
1590C22—1341no—
1591C22C22×D4×D6711yescharacteristic
1592C4—21no—
1593C4—21no—
1594C4—21no—
1595C4—21no—
1596C4—21no—
1597C4—21no—
1598C4—41no—
1599C4—41no—
1600C4—41no—
1601C4—41no—
1602C4—41no—
1603C4—41no—
1604C4—2681no—
1605C4—2681no—
1606C4—2681no—
1607C4—2681no—
1608C4—2681no—
1609C4—2681no—
1610C4—672no—
1611C4—672no—
1612C4—1342no—
1613C4—1341no—
1614C4—1341no—
1615C4—1341no—
1616C4—1341no—
1617C4—1341no—
1618C4C22×Q8×D6711yescharacteristic
1619C42−1+4×D6711yescharacteristic
1620C2—42no—
1621C2—42no—
1622C2—2682no—
1623C2—1342no—
1624C2D4×Q8×D6711yescharacteristic
1625C2#577×D6711yescharacteristic
1626C2#2257498511yescharacteristic
subgroupG/H
centerC22C22×D4×D67
commutator, cosocleC2×C4×C67C25
FrattiniC2×C4C24×D67
FittingC67×#3384C2
socleC22×C67C23×D4
prime radicalC2×#14524067C22
hypercenter#3384D67
hypocenterC67#61382
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #3384

Complements

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

NH ≅ G/Ntype
1. #22574020C2semidirect
2. #22574008C2semidirect
3. #22573156C2semidirect
4. #22573154C2semidirect
5. #22573149C2semidirect
6. #22573147C2semidirect
7. #22573116C2semidirect
8. #22573114C2semidirect
9. #22573111C2semidirect
10. #22573109C2semidirect
11. #22573109C2semidirect
12. #22573104C2semidirect
13. #22573103C2semidirect
14. #22573076C2semidirect
15. #22573071C2semidirect
16. #22573066C2semidirect
17. #22573064C2semidirect
18. #22570754C2semidirect
19. #22570736C2semidirect
20. #22570734C2semidirect
21. #22570072C2semidirect
22. #22570066C2semidirect
23. #22570035C2semidirect
24. #22570033C2semidirect
25. #22569994C2semidirect
26. #476×D67C2semidirect
27. #22569154C2semidirect
31. C67×#3384C2semidirect
33. #16864126C22semidirect
34. #16864126C22semidirect
35. #16864124C22semidirect
36. #16864121C22semidirect
40. #16864105C22semidirect
41. #16864105C22semidirect
50. D4×Dic134C22semidirect
76. #16863806C22semidirect
77. #16863805C22semidirect
78. #16863805C22semidirect
79. #16863804C22semidirect
80. #16863803C22semidirect
81. #16863803C22semidirect
82. #16863803C22semidirect
83. #16863802C22semidirect
84. #16863802C22semidirect
85. #16863802C22semidirect
86. #16863800C22semidirect
87. #16863800C22semidirect
88. #16863798C22semidirect
89. #16863797C22semidirect
90. #16863796C22semidirect
91. #16863795C22semidirect
92. #16863793C22semidirect
93. #16863793C22semidirect
94. #16863793C22semidirect
95. #16863793C22semidirect
96. #16863792C22semidirect
97. #16863706C22semidirect
98. #16863704C22semidirect
99. #16863704C22semidirect
100. #16863702C22semidirect
101. #16863700C22semidirect
102. #16863700C22semidirect
105. #16863698C22semidirect
110. #16863696C22semidirect
111. #16863696C22semidirect
114. #16863694C22semidirect
115. #16863690C22semidirect
118. #16863686C22semidirect
125. #16863684C22semidirect
126. #16863684C22semidirect
127. #16863684C22semidirect
130. #16863682C22semidirect
131. #16863680C22semidirect
132. #16863680C22semidirect
133. #16863680C22semidirect
134. #16863678C22semidirect
137. #16863674C22semidirect
139. #16863527C22semidirect
140. #16863525C22semidirect
141. #16863525C22semidirect
142. #16863524C22semidirect
143. #16863524C22semidirect
144. C8×Dic134C22semidirect
145. #16863520C22semidirect
189. D4×Q8×C67C22semidirect
190. #501×C67C22semidirect
191. #501×C67C22semidirect
192. #498×C67C22semidirect
193. #478×C67C22semidirect
194. #478×C67C22semidirect
197. #476×C67C22semidirect
199. #446×C67C22semidirect
210. #14524067Q8semidirect
481. #11761627C2×Q8semidirect
504. D4×D67C2×Q8semidirect
525. #11761617C2×Q8semidirect
526. #11761616C2×Q8semidirect
527. #11761613C2×Q8semidirect
529. #11761611C2×Q8semidirect
637. D8×C67C2×Q8semidirect
827. #3384D67semidirect
845. C67#61382semidirect
870. D4×Q8C2×D67semidirect
902. #501C2×D67semidirect
903. #501C2×D67semidirect
915. #498C2×D67semidirect
934. #478C2×D67semidirect
935. #478C2×D67semidirect
953. #476C2×D67semidirect
969. #446C2×D67semidirect
1356. D8Q8×D67semidirect

Maximal subgroups

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

subgroupindex
#225740202
#225740082
#225731562
#225731542
#225731492
#225731472
#225731162
#225731142
#225731112
#225731092
#225731042
#225731032
#225730762
#225730712
#225730662
#225730642
#225707542
#225707362
#225707342
#225700722
#225700662
#225700352
#225700332
#225699942
#476×D672
#225691542
#225690382
#225690342
#225690202
C67×#33842
#6138267