Finite Group Databasebeta

← #31763568

Subgroups — #31763568

Order 17152.

6528 conjugacy classes of subgroups.

The subgroup lattice has 1602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22574854C214yesmaximal, complemented
2#22574833C214yesmaximal, complemented
3#22574815C212yesmaximal, complemented
4#22574812C212yesmaximal, complemented
5#22574781C212yesmaximal, complemented
6#22574740C212yesmaximal, complemented
7#22574699C212yesmaximal, complemented
8#22574646C212yesmaximal, complemented
9#22574600C212yesmaximal, complemented
10#22574549C212yesmaximal, complemented
11#22574454C212yesmaximal, complemented
12#22574431C212yesmaximal, complemented
13#22574422C214yesmaximal, complemented
14#22574354C214yesmaximal, complemented
15#22573822C214yesmaximal, complemented
16Q8×#11761628C212yesmaximal, complemented
17#22573767C214yesmaximal, complemented
18#22573767C212yesmaximal, complemented
19#22573638C214yesmaximal, complemented
20#22573634C214yesmaximal, complemented
21#22573614C212yesmaximal, complemented
22#22573599C212yesmaximal, complemented
23#22573505C211yesmaximal, characteristic, complemented
24C2×#16863953C211yesmaximal, characteristic, complemented
25C2×#529×C67C211yesmaximal, characteristic, complemented
26C67⋊#564C2214yescomplemented
27#16864150C2214yescomplemented
28#16864149C2218yescomplemented
29#16864148C2218yescomplemented
30#16864148C2218yescomplemented
31#16864147C2218yescomplemented
32#16864146C2214yescomplemented
33#16864143C2218yescomplemented
34#16864141C2218yes—
35#16864140C2214yescomplemented
36Q8×Dic134C2212yescomplemented
37#16864124C2214yescomplemented
38#16864124C2212yescomplemented
39#16864123C2214yescomplemented
40#16864116C2214yescomplemented
41#16864116C2212yescomplemented
42#16864115C2214yescomplemented
43#16864113C2218yescomplemented
44#16864111C2214yescomplemented
45#16864111C2212yescomplemented
46#16864106C2214yescomplemented
47#16864106C2212yescomplemented
48#16864103C2214yescomplemented
49#16864103C2212yescomplemented
50#16864101C2218yes—
51#16864101C2214yes—
52#16864092C2214yescomplemented
53#16864092C2214yescomplemented
54#16864092C2214yescomplemented
55#16864088C2214yescomplemented
56#16864086C2214yescomplemented
57#16864086C2214yescomplemented
58#16864086C2214yescomplemented
59#16864084C2214yescomplemented
60#16864083C2218yescomplemented
61#16864082C2218yescomplemented
62#16864081C2214yes—
63#16864081C2218yes—
64#16864072C2218yes—
65#16864072C2218yes—
66#16864072C2218yes—
67Q8×D268C2212yescomplemented
68Q8×C22⋊D67C2214yes—
69#16864059C2214yescomplemented
70#16864054C2214yescomplemented
71#16864052C2214yes—
72#16864050C2212yescomplemented
73#16864050C2214yescomplemented
74#16864046C2214yes—
75#16864044C2218yescomplemented
76#16864040C2218yes—
77#16864040C2214yes—
78#16864027C2214yes—
79#16864027C2214yes—
80#16864026C2214yescomplemented
81#16864025C2214yescomplemented
82#16864024C2214yescomplemented
83#16864024C2214yescomplemented
84#16864024C2214yescomplemented
85#16864024C2214yescomplemented
86#16864022C2214yes—
87#16864022C2214yes—
88#16864017C2214yescomplemented
89#16864017C2214yescomplemented
90#16864015C2214yescomplemented
91#16864014C2218yescomplemented
92#16864013C2214yes—
93#16864012C2218yescomplemented
94#16864010C2218yescomplemented
95#16864009C2214yescomplemented
96#16864008C2214yescomplemented
97#16864006C2214yescomplemented
98#16864005C2218yescomplemented
99#16864003C2218yescomplemented
100#16864003C2218yescomplemented
101#16864001C2214yescomplemented
102#16863995C2214yescomplemented
103#16863993C2214yes—
104#16863993C2214yes—
105#16863991C2214yes—
106#16863990C2218yescomplemented
107#16863989C2218yescomplemented
108#16863987C2218yescomplemented
109#16863984C2214yes—
110#16863984C2214yes—
111#16863975C2214yes—
112#16863973C2214yes—
113#16863969C2214yescomplemented
114#16863968C2218yescomplemented
115#16863966C2214yescomplemented
116#16863953C2212yes—
117#16863953C2211yescharacteristic
118#16863953C2214yes—
119#16863953C2212yes—
120#16863953C2212yes—
121#16863953C2212yes—
122#16863953C2212yescomplemented
123#16863953C2212yescomplemented
124#16863953C2212yescomplemented
125#16863953C2212yescomplemented
126#16863953C2211yescharacteristic, complemented
127#16863953C2211yescharacteristic, complemented
128#16863950C2218yescomplemented
129#16863950C2214yescomplemented
130#16863949C2218yescomplemented
131#16863949C2218yescomplemented
132#16863946C2211yescharacteristic
133#16863946C2211yescharacteristic, complemented
134#16863946C2211yescharacteristic, complemented
135C2×#14524043C2211yescharacteristic, complemented
136C2×#14524043C2211yescharacteristic, complemented
137#16863930C2212yes—
138#16863930C2212yes—
139#16863930C2212yescomplemented
140#16863930C2212yescomplemented
141#16863930C2212yescomplemented
142#16863930C2212yescomplemented
143#16863928C2218yescomplemented
144#16863928C2214yescomplemented
145#16863926C2218yescomplemented
146#16863926C2218yescomplemented
147#16863926C2218yescomplemented
148#16863924C2218yescomplemented
149#16863924C2218yescomplemented
150C2×#14524035C2212yescomplemented
151#16863907C2214yes—
152#16863907C2212yes—
153#16863907C2212yes—
154#16863907C2212yes—
155C2×#14524022C2212yes—
156C2×#14524022C2212yes—
157C4×#11761628C2214yes—
158C4×#11761628C2212yes—
159C4×#11761628C2212yescomplemented
160C4×#11761628C2212yescomplemented
161C4×#11761627C2214yescomplemented
162C4×#11761627C2218yescomplemented
163C2×C4×Dic134C2212yescomplemented
164C2×C4×Dic134C2212yescomplemented
165C4×Q8×D67C2214yescomplemented
166C2×#14524002C2214yes—
167C2×#14524002C2212yes—
168#529×C67C2212yes—
169#529×C67C2212yes—
170#529×C67C2212yes—
171#529×C67C2212yes—
172#529×C67C2212yes—
173#529×C67C2212yes—
174#529×C67C2212yes—
175#529×C67C2212yes—
176C2×#126×C67C2212yes—
177C2×#125×C67C2211yescharacteristic
178C2×#124×C67C2211yescharacteristic
179C2×#123×C67C2212yes—
180C2×C22⋊Q8×C67C2211yescharacteristic
181C2×#121×C67C2211yescharacteristic
182C2×C4×Q8×C67C2211yescharacteristic
183C2×C4×D4×C67C2211yescharacteristic
184C2×C4×D4×C67C2212yes—
185C2×#117×C67C2212yes—
186C22×C42×C67C2211yescharacteristic
187C2×#11761628C2312yes—
188C2×#11761628C2312yes—
189C2×#11761628C2312yes—
190C2×#11761627C2318yes—
191C2×#11761627C2314yes—
192C22×Dic134C2312yes—
193C22×Dic134C2312yes—
194C2×Q8×D67C2314yes—
195#14524043C2311yescharacteristic
196#14524043C2312yes—
197#14524043C2312yes—
198#14524043C2312yes—
199#14524043C2312yes—
200#14524043C2311yescharacteristic
201#14524043C2311yescharacteristic
202#14524043C2314yes—
203#14524043C2314yes—
204#14524043C2312yes—
205#14524043C2312yes—
206#14524043C2312yes—
207#14524043C2312yes—
208#14524042C2318yes—
209#14524042C2318yes—
210#14524042C2318yes—
211#14524042C2314yes—
212#14524042C2318yes—
213#14524042C2318yes—
214#14524041C2314yes—
215#14524041C2318yes—
216#14524040C2311yescharacteristic
217#14524038C2318yes—
218#14524038C2318yes—
219#14524038C2318yes—
220#14524038C2318yes—
221#14524038C2318yes—
222#14524037C2314yes—
223#14524037C2314yes—
224#14524036C2318yes—
225#14524036C2318yes—
226#14524036C2318yes—
227#14524036C2318yes—
228#14524036C2318yes—
229#14524036C2318yes—
230#14524036C2318yes—
231#14524036C2318yes—
232#14524035C2314yes—
233#14524035C2312yes—
234#14524035C2314yes—
235#14524035C2312yes—
236#14524035C2314yes—
237#14524035C2314yes—
238#14524035C2314yes—
239#14524035C2314yes—
240#14524035C2312yes—
241#14524034C2318yes—
242#14524034C2318yes—
243#14524034C2318yes—
244#14524034C2314yes—
245#14524034C2318yes—
246#14524034C2318yes—
247#14524033C2318yes—
248#14524033C2318yes—
249#14524033C2318yes—
250#14524033C2318yes—
251#14524033C2318yes—
252#14524033C2318yes—
253#14524033C2318yes—
254#14524033C2318yes—
255#14524031C2312yes—
256#14524031C2312yes—
257#14524031C2312yes—
258#14524030C2318yes—
259#14524030C2314yes—
260#14524029C2318yes—
261#14524029C2318yes—
262#14524029C2318yes—
263#14524029C2318yes—
264#14524029C2318yes—
265#14524028C2318yes—
266#14524028C2318yes—
267#14524027C2318yes—
268#14524027C2318yes—
269#14524027C2318yes—
270#14524026C2314yes—
271#14524026C2318yes—
272#14524026C2314yes—
273#14524026C2314yes—
274#14524025C2318yes—
275#14524025C2318yes—
276#14524025C2318yes—
277#14524025C2318yes—
278#14524025C2318yes—
279#14524024C2318yes—
280#14524024C2318yes—
281#14524024C2318yes—
282#14524023C2314yes—
283#14524023C2314yes—
284#14524023C2318yes—
285#14524023C2318yes—
286#14524022C2314yes—
287#14524022C2314yes—
288#14524022C2314yes—
289#14524022C2314yes—
290#14524022C2312yes—
291#14524022C2312yes—
292#14524022C2318yes—
293#14524022C2318yes—
294#14524022C2314yes—
295#14524022C2314yes—
296#14524022C2312yes—
297#14524022C2314yes—
298#14524022C2314yes—
299#14524022C2312yes—
300#14524022C2312yes—
301#14524022C2314yes—
302#14524022C2314yes—
303#14524022C2312yes—
304#14524021C2318yes—
305#14524021C2318yes—
306#14524021C2318yes—
307#14524021C2318yes—
308#14524021C2318yes—
309#14524020C2318yes—
310#14524020C2318yes—
311#14524020C2318yes—
312#14524020C2318yes—
313#14524020C2318yes—
314#14524020C2318yes—
315#14524020C2318yes—
316#14524020C2318yes—
317#14524020C2318yes—
318#14524020C2318yes—
319#14524020C2318yes—
320#14524019C2318yes—
321#14524019C2314yes—
322#14524017C2314yes—
323#14524017C2314yes—
324#14524017C2312yes—
325#14524017C2312yes—
326#14524017C2312yes—
327#14524017C2312yes—
328#14524017C2312yes—
329#14524017C2312yes—
330#14524016C2318yes—
331#14524016C2318yes—
332#14524015C2318yes—
333#14524015C2318yes—
334#14524015C2318yes—
335#14524014C2314yes—
336#14524014C2318yes—
337#14524012C2314yes—
338#14524012C2318yes—
339Q8×Dic67C2314yes—
340C4×Dic134C2312yes—
341C4×Dic134C2314yes—
342C4×Dic134C2314yes—
343C4×Dic134C2314yes—
344C4×Dic134C2314yes—
345C4×Dic134C2314yes—
346C4×Dic134C2314yes—
347C4×Dic134C2312yes—
348C4×Dic134C2312yes—
349C4×Dic134C2314yes—
350C4×Dic134C2318yes—
351C4×Dic134C2312yes—
352C4×Dic134C2314yes—
353C4×Dic134C2314yes—
354C4×Dic134C2314yes—
355C4×Dic134C2318yes—
356C4×Dic134C2312yes—
357C4×Dic134C2312yes—
358#14524008C2318yes—
359#14524008C2318yes—
360#14524008C2314yes—
361#14524008C2314yes—
362C4×D268C2314yes—
363C4×D268C2314yes—
364C4×D268C2312yes—
365C4×D268C2312yes—
366C4×D268C2312yes—
367C4×D268C2312yes—
368C4×D268C2312yes—
369C4×D268C2312yes—
370D4×Dic67C2314yes—
371D4×Dic67C2318yes—
372C4×C22⋊D67C2314yes—
373C4×C22⋊D67C2314yes—
374C4×C22⋊D67C2318yes—
375C4×C22⋊D67C2314yes—
376C4×C22⋊D67C2318yes—
377C4×C22⋊D67C2314yes—
378C4×C22⋊D67C2314yes—
379C4×C22⋊D67C2318yes—
380C4×C22⋊D67C2318yes—
381C4×C22⋊D67C2314yes—
382(C22⋊D67)⋊C4C2318yes—
383(C22⋊D67)⋊C4C2318yes—
384(C22⋊D67)⋊C4C2318yes—
385#14524002C2312yes—
386#14524002C2314yes—
387#14524002C2314yes—
388#14524002C2318yes—
389#14524002C2314yes—
390#14524002C2312yes—
391#14524002C2314yes—
392#14524002C2312yes—
393#14524002C2314yes—
394#14524002C2318yes—
395#14524002C2314yes—
396#14524001C2318yes—
397#14524001C2314yes—
398#14524000C2314yes—
399#14524000C2314yes—
400#14524000C2318yes—
401#14524000C2314yes—
402#14523999C2318yes—
403#14523999C2318yes—
404#14523999C2318yes—
405C2×C4⋊Dic67C2314yes—
406C2×C4⋊Dic67C2314yes—
407C2×C4⋊Dic67C2312yes—
408C2×C4⋊Dic67C2312yes—
409C2×C4⋊Dic67C2312yes—
410C2×C4⋊Dic67C2312yes—
411C2×Dic67⋊C4C2314yes—
412C2×Dic67⋊C4C2314yes—
413C4⋊C4×D67C2314yes—
414C4⋊C4×D67C2318yes—
415C2×C22⋊Dic67C2318yes—
416C2×C22⋊Dic67C2314yes—
417C2×C4×Dic67C2314yes—
418C2×C4×Dic67C2318yes—
419C42×D67C2314yes—
420C42×D67C2318yes—
421C22×Q8×C67C2311yescharacteristic
422C22×D4×C67C2312yes—
423C22×D4×C67C2311yescharacteristic
424C23×C4×C67C2311yescharacteristic
425C23×C4×C67C2312yes—
426C23×C4×C67C2311yescharacteristic
427C23×C4×C67C2311yescharacteristic
428#126×C67C2314yes—
429#126×C67C2314yes—
430#126×C67C2314yes—
431#126×C67C2314yes—
432#125×C67C2312yes—
433#125×C67C2312yes—
434#125×C67C2312yes—
435#125×C67C2312yes—
436#124×C67C2312yes—
437#124×C67C2312yes—
438#124×C67C2312yes—
439#124×C67C2312yes—
440#123×C67C2314yes—
441#123×C67C2314yes—
442#123×C67C2314yes—
443#123×C67C2314yes—
444C22⋊Q8×C67C2312yes—
445C22⋊Q8×C67C2312yes—
446C22⋊Q8×C67C2312yes—
447C22⋊Q8×C67C2312yes—
448#121×C67C2312yes—
449#121×C67C2312yes—
450#121×C67C2312yes—
451#121×C67C2312yes—
452C4×Q8×C67C2312yes—
453C4×Q8×C67C2312yes—
454C4×Q8×C67C2312yes—
455C4×Q8×C67C2312yes—
456C4×D4×C67C2314yes—
457C4×D4×C67C2312yes—
458C4×D4×C67C2312yes—
459C4×D4×C67C2314yes—
460C4×D4×C67C2314yes—
461C4×D4×C67C2312yes—
462C4×D4×C67C2312yes—
463C4×D4×C67C2314yes—
464#117×C67C2314yes—
465#117×C67C2314yes—
466#117×C67C2314yes—
467#117×C67C2314yes—
468C2×C4⋊C4×C67C2312yes—
469C2×C4⋊C4×C67C2312yes—
470C2×C4⋊C4×C67C2311yescharacteristic
471C2×C4⋊C4×C67C2312yes—
472C2×C4⋊C4×C67C2311yescharacteristic
473C2×C4⋊C4×C67C2312yes—
474C2×C22⋊C4×C67C2312yes—
475C2×C22⋊C4×C67C2312yes—
476C2×C22⋊C4×C67C2312yes—
477C2×C22⋊C4×C67C2312yes—
478C2×C22⋊C4×C67C2312yes—
479C2×C42×C67C2311yescharacteristic
480C2×C42×C67C2311yescharacteristic
481C2×C42×C67C2311yescharacteristic
482C2×C42×C67C2311yescharacteristic
483C2×C42×C67C2311yescharacteristic
484C2×C42×C67C2311yescharacteristic
485C2×C42×C67C2311yescharacteristic
486C2×C42×C67C2311yescharacteristic
487C2×C42×C67C2311yescharacteristic
488C2×C42×C67C2311yescharacteristic
489C2×C42×C67C2311yescharacteristic
490C2×C42×C67C2311yescharacteristic
491C2×C42×C67C2312yes—
492#11761628—28no—
493#11761628—44no—
494#11761628—44no—
495#11761627—48no—
496#11761627—416no—
497C2×Dic134—44no—
498C2×Dic134—44no—
499C2×Dic134C2414yes—
500C2×Dic134C2412yes—
501C2×Dic134C2418yes—
502C2×Dic134C2418yes—
503C2×Dic134C2412yes—
504C2×Dic134C2412yes—
505C2×Dic134C2414yes—
506C2×Dic134C2414yes—
507C2×Dic134C2414yes—
508Q8×D67—48no—
509C2×D268C2412yes—
510C2×D268C2412yes—
511C2×D268C2412yes—
512C2×C22⋊D67C2414yes—
513C2×C22⋊D67C2414yes—
514C2×C22⋊D67C2418yes—
515C2×C22⋊D67C2418yes—
516C2×C22⋊D67C2414yes—
517C22×Dic67C2414yes—
518C22×Dic67C2414yes—
519C22×Dic67C2418yes—
520C22×Dic67C2418yes—
521C2×C4×D67C2414yes—
522C2×C4×D67C2414yes—
523C2×C4×D67C2414yes—
524C2×C4×D67C2418yes—
525C2×C4×D67C2418yes—
526C4⋊Dic67C2414yes—
527C4⋊Dic67C2418yes—
528C4⋊Dic67C2412yes—
529C4⋊Dic67C2412yes—
530C4⋊Dic67C2414yes—
531C4⋊Dic67C2414yes—
532C4⋊Dic67C2414yes—
533C4⋊Dic67C2418yes—
534C4⋊Dic67C2418yes—
535C4⋊Dic67C2414yes—
536C4⋊Dic67C2414yes—
537C4⋊Dic67C2414yes—
538C4⋊Dic67C2414yes—
539C4⋊Dic67C2418yes—
540C4⋊Dic67C2412yes—
541C4⋊Dic67C2412yes—
542C4⋊Dic67C2412yes—
543C4⋊Dic67C2412yes—
544Dic67⋊C4C2418yes—
545Dic67⋊C4C2418yes—
546Dic67⋊C4C2418yes—
547Dic67⋊C4C2418yes—
548Dic67⋊C4C2418yes—
549Dic67⋊C4C2418yes—
550Dic67⋊C4C2414yes—
551Dic67⋊C4C2418yes—
552Dic67⋊C4C2418yes—
553Dic67⋊C4C2418yes—
554Dic67⋊C4C2418yes—
555Dic67⋊C4C2414yes—
556Dic67⋊C4C2414yes—
557Dic67⋊C4C2418yes—
558Dic67⋊C4C2414yes—
559Dic67⋊C4C2414yes—
560Dic67⋊C4C2418yes—
561Dic67⋊C4C2414yes—
562C22⋊Dic67C2414yes—
563C22⋊Dic67C2418yes—
564C22⋊Dic67C2418yes—
565C22⋊Dic67C2418yes—
566C22⋊Dic67C2418yes—
567C22⋊Dic67C2414yes—
568C22⋊Dic67C2418yes—
569C22⋊Dic67C2418yes—
570C22⋊Dic67C2414yes—
571(C2×D67)⋊C4C2414yes—
572(C2×D67)⋊C4C2418yes—
573(C2×D67)⋊C4C2414yes—
574(C2×D67)⋊C4C2418yes—
575(C2×D67)⋊C4C2414yes—
576(C2×D67)⋊C4C2414yes—
577(C2×D67)⋊C4C2414yes—
578(C2×D67)⋊C4C2414yes—
579(C2×D67)⋊C4C2418yes—
580(C2×D67)⋊C4C2418yes—
581C4×Dic67C2414yes—
582C4×Dic67C2418yes—
583C4×Dic67C2414yes—
584C4×Dic67C2418yes—
585C4×Dic67C2414yes—
586C4×Dic67C2418yes—
587C4×Dic67C2418yes—
588C4×Dic67C2418yes—
589C4×Dic67C2418yes—
590C24×C67C2411yescharacteristic
591C24×C67C2412yes—
592C2×Q8×C67—42no—
593C2×Q8×C67C2412yes—
594C2×Q8×C67C2412yes—
595C2×D4×C67—42no—
596C2×D4×C67—44no—
597C2×D4×C67C2414yes—
598C2×D4×C67C2412yes—
599C2×D4×C67C2414yes—
600C2×D4×C67C2412yes—
601C22×C4×C67—24no—
602C22×C4×C67—28no—
603C22×C4×C67—42no—
604C22×C4×C67—42no—
605C22×C4×C67C2411yescharacteristic
606C22×C4×C67C2411yescharacteristic
607C22×C4×C67C2411yescharacteristic
608C22×C4×C67C2411yescharacteristic
609C22×C4×C67C2411yescharacteristic
610C22×C4×C67C2411yescharacteristic
611C22×C4×C67C2411yescharacteristic
612C22×C4×C67C2411yescharacteristic
613C22×C4×C67C2411yescharacteristic
614C22×C4×C67C2411yescharacteristic
615C22×C4×C67C2412yes—
616C22×C4×C67C2414yes—
617C22×C4×C67C2414yes—
618C22×C4×C67C2411yescharacteristic
619C22×C4×C67C2411yescharacteristic
620C22×C4×C67C2411yescharacteristic
621C22×C4×C67C2411yescharacteristic
622C22×C4×C67C2411yescharacteristic
623C22×C4×C67C2411yescharacteristic
624C22×C4×C67C2411yescharacteristic
625C22×C4×C67C2412yes—
626C22×C4×C67C2412yes—
627C22×C4×C67C2411yescharacteristic
628C4⋊C4×C67C2414yes—
629C4⋊C4×C67C2414yes—
630C4⋊C4×C67C2414yes—
631C4⋊C4×C67C2414yes—
632C4⋊C4×C67C2412yes—
633C4⋊C4×C67C2412yes—
634C4⋊C4×C67C2414yes—
635C4⋊C4×C67C2414yes—
636C4⋊C4×C67C2412yes—
637C4⋊C4×C67C2412yes—
638C4⋊C4×C67C2414yes—
639C4⋊C4×C67C2414yes—
640C22⋊C4×C67C2414yes—
641C22⋊C4×C67C2414yes—
642C22⋊C4×C67C2414yes—
643C22⋊C4×C67C2414yes—
644C22⋊C4×C67C2414yes—
645C22⋊C4×C67C2414yes—
646C22⋊C4×C67C2414yes—
647C22⋊C4×C67C2414yes—
648C22⋊C4×C67C2414yes—
649C22⋊C4×C67C2414yes—
650C42×C67C2411yescharacteristic
651C42×C67C2411yescharacteristic
652C42×C67C2411yescharacteristic
653C42×C67C2411yescharacteristic
654C42×C67C2411yescharacteristic
655C42×C67C2411yescharacteristic
656C42×C67C2411yescharacteristic
657C42×C67C2411yescharacteristic
658C42×C67C2411yescharacteristic
659C42×C67C2411yescharacteristic
660C42×C67C2411yescharacteristic
661C42×C67C2411yescharacteristic
662C42×C67C2411yescharacteristic
663C42×C67C2411yescharacteristic
664C42×C67C2411yescharacteristic
665C42×C67C2411yescharacteristic
666C42×C67C2414yes—
667C42×C67C2414yes—
668C23×C67—22no—
669C23×C67—22no—
670C23×C67—24no—
671C23×C67—41no—
672C23×C67—42no—
673C23×C67—42no—
674C23×C67C2514yes—
675C23×C67C2511yescharacteristic
676C23×C67C2511yescharacteristic
677C23×C67C2511yescharacteristic
678C22×D67C2514yes—
679Q8×C67—24no—
680Q8×C67—42no—
681D4×C67—28no—
682D4×C67—24no—
683D4×C67—44no—
684D4×C67—42no—
685C2×C4×C67—22no—
686C2×C4×C67—24no—
687C2×C4×C67—22no—
688C2×C4×C67—22no—
689C2×C4×C67—22no—
690C2×C4×C67—22no—
691C2×C4×C67—28no—
692C2×C4×C67—22no—
693C2×C4×C67—22no—
694C2×C4×C67—28no—
695C2×C4×C67—22no—
696C2×C4×C67—22no—
697C2×C4×C67—22no—
698C2×C4×C67—41no—
699C2×C4×C67—41no—
700C2×C4×C67—41no—
701C2×C4×C67—41no—
702C2×C4×C67—41no—
703C2×C4×C67—41no—
704C2×C4×C67—41no—
705C2×C4×C67—42no—
706C2×C4×C67—42no—
707C2×C4×C672−1+414yes—
708C2×C4×C67C2511yescharacteristic
709C2×C4×C67C2511yescharacteristic
710C2×C4×C67C2511yescharacteristic
711C2×C4×C67C2511yescharacteristic
712C2×C4×C67C2511yescharacteristic
713C2×C4×C67C2511yescharacteristic
714C2×C4×C67C2511yescharacteristic
715C2×C4×C67C2511yescharacteristic
716C2×C4×C67C2511yescharacteristic
717C2×C4×C67C2514yes—
718C2×C4×C67C2514yes—
719C2×C4×C67C2514yes—
720C2×C4×C67C2511yescharacteristic
721C2×C4×C67C2511yescharacteristic
722C2×C4×C67C2511yescharacteristic
723C22⋊D67—28no—
724C22⋊D67—28no—
725C22⋊D67—48no—
726C22⋊D67—48no—
727C22⋊D67—44no—
728C2×Dic67—28no—
729C2×Dic67—44no—
730C2×Dic67—48no—
731C2×Dic67—48no—
732C2×Dic67C2514yes—
733C2×Dic67C2518yes—
734C2×Dic67C2514yes—
735C2×Dic67C2518yes—
736C2×Dic67C2514yes—
737D268—24no—
738D268—42no—
739D268—42no—
740C4×D67—28no—
741C4×D67—28no—
742C4×D67—48no—
743C4×D67—48no—
744C4×D67—44no—
745Dic134—24no—
746Dic134—28no—
747Dic134—48no—
748Dic134—44no—
749Dic134—44no—
750Dic134—44no—
751Dic134—48no—
752Dic134—42no—
753Dic134—42no—
754C22×C67—21no—
755C22×C67—21no—
756C22×C67—21no—
757C22×C67—21no—
758C22×C67—21no—
759C22×C67—24no—
760C22×C67—24no—
761C22×C67—24no—
762C22×C67—21no—
763C22×C67—21no—
764C22×C67—44no—
765C22×C67—84no—
766C22×C67C2×2−1+412yes—
767C22×C67#58512yes—
768C22×C67C2611yescharacteristic
769C2×D67—24no—
770C2×D67—24no—
771C2×D67—24no—
772C4×C67—21no—
773C4×C67—21no—
774C4×C67—24no—
775C4×C67—21no—
776C4×C67—21no—
777C4×C67—21no—
778C4×C67—24no—
779C4×C67—24no—
780C4×C67—21no—
781C4×C67—21no—
782C4×C67—21no—
783C4×C67—21no—
784C4×C67C2×2−1+412yes—
785C4×C67C2×2−1+412yes—
786C4×C67#58512yes—
787Dic67—24no—
788Dic67—28no—
789Dic67—24no—
790Dic67—28no—
791Dic67—24no—
792#62752—671nomaximal, Sylow
793C2×C67—22no—
794C2×C67—22no—
795C2×C67—41no—
796C2×C67—44no—
797C2×C67C22×2−1+411yescharacteristic
798C2×C67C2×#58511yescharacteristic
799C2×C67C2×#58511yescharacteristic
800D67—44no—
801#3565—674no—
802#3564—674no—
803#3563—672no—
804#3563—672no—
805#3561—672no—
806#3559—672no—
807#3555—672no—
808#3552—672no—
809#3547—672no—
810#3544—672no—
811#3538—672no—
812#3536—672no—
813#3535—674no—
814#3531—674no—
815#3482—674no—
816Q8×#41—672no—
817#3475—674no—
818#3475—672no—
819#3461—674no—
820#3461—674no—
821#3458—672no—
822#3455—672no—
823#3444—671no—
824C2×#533—671no—
825C2×#529D6711yescharacteristic, complemented
826C67#6275211yescharacteristic, complemented, Sylow
827#564—674no—
828#563—678no—
829#563—678no—
830#563—674no—
831#563—674no—
832#563—678no—
833#563—678no—
834#562—674no—
835#562—678no—
836#562—678no—
837Q82—672no—
838#557—674no—
839#557—672no—
840#557—674no—
841#556—678no—
842#556—674no—
843#556—672no—
844#556—674no—
845#555—672no—
846#555—674no—
847#554—672no—
848#554—674no—
849#554—672no—
850#554—674no—
851#554—678no—
852#554—674no—
853#553—674no—
854#553—674no—
855#553—674no—
856#552—678no—
857#552—674no—
858#552—678no—
859#552—674no—
860#552—674no—
861#552—674no—
862#552—674no—
863#552—674no—
864#552—678no—
865#551—678no—
866#551—678no—
867#551—678no—
868D4×Q8—674no—
869D4×Q8—674no—
870D4×Q8—672no—
871#548—674no—
872#548—674no—
873#547—678no—
874#547—674no—
875#547—674no—
876#547—672no—
877#546—678no—
878#546—674no—
879#544—674no—
880#544—674no—
881#544—674no—
882#544—674no—
883#544—674no—
884#544—674no—
885#544—674no—
886#544—674no—
887#543—674no—
888#543—674no—
889#542—678no—
890#542—678no—
891#542—674no—
892#542—678no—
893#542—674no—
894#542—674no—
895#542—674no—
896#541—678no—
897#541—678no—
898#541—678no—
899#541—674no—
900#541—674no—
901#541—674no—
902#540—674no—
903#539—678no—
904#539—678no—
905#539—678no—
906#539—674no—
907#539—674no—
908#539—674no—
909#539—674no—
910#538—674no—
911#538—674no—
912#537—674no—
913#537—674no—
914#536—674no—
915#536—678no—
916#536—674no—
917#533—674no—
918#533—678no—
919#533—678no—
920#533—678no—
921#533—672no—
922#533—672no—
923#533—672no—
924#533—672no—
925#533—672no—
926#533—672no—
927#533—672no—
928#533—672no—
929#533—671no—
930#533—671no—
931#533—671no—
932#533—674no—
933#532—671no—
934#532—671no—
935#532—671no—
936C2×C4⋊Q8—671no—
937C2×C4⋊Q8—671no—
938#529—678no—
939#529—674no—
940#529—678no—
941#529—678no—
942#529—678no—
943#529—678no—
944#529—678no—
945#529—672no—
946#529—672no—
947#529—672no—
948#529—672no—
949#529—672no—
950#529—672no—
951#529C2×D6712yes—
952#529C2×D6712yes—
953#529C2×D6712yes—
954#529C2×D6712yes—
955#529C2×D6712yes—
956#529C2×D6712yes—
957#529C2×D6712yes—
958#529C2×D6712yes—
959C2×#126C2×D6712yes—
960C2×#125—672no—
961C2×#125C2×D6711yescharacteristic
962C2×#124C2×D6711yescharacteristic
963#525—672no—
964#525—672no—
965#525—672no—
966#525—674no—
967C2×#123C2×D6712yes—
968C2×C22⋊Q8—672no—
969C2×C22⋊Q8—672no—
970C2×C22⋊Q8C2×D6711yescharacteristic
971C2×#121C2×D6711yescharacteristic
972C4×#41—678no—
973C4×#41—674no—
974C4×#41—672no—
975C4×#41—672no—
976C4×#41—672no—
977C4×#41—674no—
978C2×C4×Q8—674no—
979C2×C4×Q8—672no—
980C2×C4×Q8—672no—
981C2×C4×Q8C2×D6711yescharacteristic
982C2×C4×D4C2×D6712yes—
983C2×C4×D4C2×D6711yescharacteristic
984C2×#117—672no—
985C2×#117—674no—
986C2×#117C2×D6712yes—
987C22×C42C2×D6711yescharacteristic
988C2×#41—678no—
989C2×#41—674no—
990C2×#41—672no—
991C2×#41—672no—
992C2×#41—672no—
993C22×Q8—674no—
994C22×Q8—672no—
995C22×Q8—672no—
996C22×Q8C22×D6711yescharacteristic
997C22×D4C22×D6712yes—
998C22×D4C22×D6711yescharacteristic
999C23×C4C22×D6712yes—
1000C23×C4C22×D6711yescharacteristic
1001C23×C4C22×D6711yescharacteristic
1002C23×C4C22×D6711yescharacteristic
1003C4⋊Q8—674no—
1004C4⋊Q8—678no—
1005C4⋊Q8—678no—
1006C4⋊Q8—678no—
1007C4⋊Q8—678no—
1008C4⋊Q8—674no—
1009C4⋊Q8—678no—
1010C4⋊Q8—678no—
1011C4⋊Q8—672no—
1012C4⋊Q8—672no—
1013C4⋊Q8—672no—
1014C4⋊Q8—672no—
1015C4⋊Q8—672no—
1016C4⋊Q8—672no—
1017C4⋊Q8—672no—
1018C4⋊Q8—672no—
1019C4⋊Q8—671no—
1020C4⋊Q8—671no—
1021C4⋊Q8—671no—
1022C4⋊Q8—674no—
1023C4⋊Q8—674no—
1024#127—671no—
1025#126—678no—
1026#126—678no—
1027#126—678no—
1028#126—678no—
1029#126—678no—
1030#126—678no—
1031#126—678no—
1032#126—678no—
1033#126—678no—
1034#126—678no—
1035#126—678no—
1036#126—678no—
1037#126—678no—
1038#126—674no—
1039#126—674no—
1040#126C22×D6714yes—
1041#126C22×D6714yes—
1042#126C22×D6714yes—
1043#126C22×D6714yes—
1044#125—678no—
1045#125—678no—
1046#125—678no—
1047#125—678no—
1048#125—674no—
1049#125—678no—
1050#125—678no—
1051#125—678no—
1052#125—678no—
1053#125—678no—
1054#125—678no—
1055#125—678no—
1056#125—678no—
1057#125—678no—
1058#125—674no—
1059#125—674no—
1060#125—674no—
1061#125—674no—
1062#125—672no—
1063#125—672no—
1064#125—672no—
1065#125—674no—
1066#125—674no—
1067#125C22×D6712yes—
1068#125C22×D6712yes—
1069#125C22×D6712yes—
1070#125C22×D6712yes—
1071#124—674no—
1072#124—678no—
1073#124—678no—
1074#124—678no—
1075#124—678no—
1076#124—678no—
1077#124—678no—
1078#124—672no—
1079#124—672no—
1080#124—672no—
1081#124C22×D6712yes—
1082#124C22×D6712yes—
1083#124C22×D6712yes—
1084#124C22×D6712yes—
1085#123—678no—
1086#123—678no—
1087#123—678no—
1088#123—674no—
1089#123—674no—
1090#123—674no—
1091#123—678no—
1092#123—678no—
1093#123—678no—
1094#123—678no—
1095#123—678no—
1096#123—678no—
1097#123—678no—
1098#123—678no—
1099#123—678no—
1100#123—678no—
1101#123—678no—
1102#123C22×D6714yes—
1103#123C22×D6714yes—
1104#123C22×D6714yes—
1105#123C22×D6714yes—
1106C22⋊Q8—674no—
1107C22⋊Q8—678no—
1108C22⋊Q8—674no—
1109C22⋊Q8—674no—
1110C22⋊Q8—674no—
1111C22⋊Q8—674no—
1112C22⋊Q8—674no—
1113C22⋊Q8—674no—
1114C22⋊Q8—674no—
1115C22⋊Q8—674no—
1116C22⋊Q8—672no—
1117C22⋊Q8—672no—
1118C22⋊Q8—672no—
1119C22⋊Q8—672no—
1120C22⋊Q8—672no—
1121C22⋊Q8—672no—
1122C22⋊Q8—674no—
1123C22⋊Q8—674no—
1124C22⋊Q8—678no—
1125C22⋊Q8—678no—
1126C22⋊Q8—678no—
1127C22⋊Q8—674no—
1128C22⋊Q8—678no—
1129C22⋊Q8—678no—
1130C22⋊Q8—678no—
1131C22⋊Q8—674no—
1132C22⋊Q8—678no—
1133C22⋊Q8—678no—
1134C22⋊Q8—678no—
1135C22⋊Q8—678no—
1136C22⋊Q8—678no—
1137C22⋊Q8—678no—
1138C22⋊Q8—678no—
1139C22⋊Q8—678no—
1140C22⋊Q8—678no—
1141C22⋊Q8—678no—
1142C22⋊Q8—678no—
1143C22⋊Q8—678no—
1144C22⋊Q8—678no—
1145C22⋊Q8—678no—
1146C22⋊Q8C22×D6712yes—
1147C22⋊Q8C22×D6712yes—
1148C22⋊Q8C22×D6712yes—
1149C22⋊Q8C22×D6712yes—
1150#121—678no—
1151#121—678no—
1152#121—674no—
1153#121—678no—
1154#121—678no—
1155#121—672no—
1156#121—672no—
1157#121—672no—
1158#121—672no—
1159#121—672no—
1160#121—672no—
1161#121—674no—
1162#121—674no—
1163#121—678no—
1164#121—678no—
1165#121C22×D6712yes—
1166#121C22×D6712yes—
1167#121C22×D6712yes—
1168#121C22×D6712yes—
1169#120—674no—
1170#120—678no—
1171C4×Q8—674no—
1172C4×Q8—674no—
1173C4×Q8—678no—
1174C4×Q8—674no—
1175C4×Q8—678no—
1176C4×Q8—674no—
1177C4×Q8—678no—
1178C4×Q8—674no—
1179C4×Q8—674no—
1180C4×Q8—674no—
1181C4×Q8—674no—
1182C4×Q8—674no—
1183C4×Q8—674no—
1184C4×Q8—674no—
1185C4×Q8—678no—
1186C4×Q8—672no—
1187C4×Q8—672no—
1188C4×Q8—672no—
1189C4×Q8—672no—
1190C4×Q8—672no—
1191C4×Q8—672no—
1192C4×Q8—674no—
1193C4×Q8—674no—
1194C4×Q8C22×D6712yes—
1195C4×Q8C22×D6712yes—
1196C4×Q8C22×D6712yes—
1197C4×Q8C22×D6712yes—
1198C4×D4—678no—
1199C4×D4—674no—
1200C4×D4—674no—
1201C4×D4—678no—
1202C4×D4—678no—
1203C4×D4—674no—
1204C4×D4—674no—
1205C4×D4—674no—
1206C4×D4—674no—
1207C4×D4—674no—
1208C4×D4—678no—
1209C4×D4—678no—
1210C4×D4—678no—
1211C4×D4—678no—
1212C4×D4—678no—
1213C4×D4—672no—
1214C4×D4—672no—
1215C4×D4—672no—
1216C4×D4—672no—
1217C4×D4—672no—
1218C4×D4—672no—
1219C4×D4—674no—
1220C4×D4—674no—
1221C4×D4C22×D6712yes—
1222C4×D4C22×D6714yes—
1223C4×D4C22×D6714yes—
1224C4×D4C22×D6712yes—
1225C4×D4C22×D6714yes—
1226C4×D4C22×D6712yes—
1227C4×D4C22×D6712yes—
1228C4×D4C22×D6714yes—
1229#117—674no—
1230#117—672no—
1231#117—678no—
1232#117—674no—
1233#117—674no—
1234#117—674no—
1235#117—678no—
1236#117—674no—
1237#117—674no—
1238#117—672no—
1239#117—672no—
1240#117—674no—
1241#117—678no—
1242#117—678no—
1243#117—678no—
1244#117—678no—
1245#117—678no—
1246#117—674no—
1247#117—674no—
1248#117—674no—
1249#117C22×D6714yes—
1250#117C22×D6714yes—
1251#117C22×D6714yes—
1252#117C22×D6714yes—
1253C2×C4⋊C4—672no—
1254C2×C4⋊C4—672no—
1255C2×C4⋊C4—674no—
1256C2×C4⋊C4—674no—
1257C2×C4⋊C4—674no—
1258C2×C4⋊C4—674no—
1259C2×C4⋊C4—672no—
1260C2×C4⋊C4—672no—
1261C2×C4⋊C4—674no—
1262C2×C4⋊C4—678no—
1263C2×C4⋊C4C22×D6712yes—
1264C2×C4⋊C4C22×D6712yes—
1265C2×C4⋊C4C22×D6711yescharacteristic
1266C2×C4⋊C4C22×D6712yes—
1267C2×C4⋊C4C22×D6711yescharacteristic
1268C2×C4⋊C4C22×D6712yes—
1269C2×C22⋊C4—674no—
1270C2×C22⋊C4—678no—
1271C2×C22⋊C4C22×D6712yes—
1272C2×C22⋊C4C22×D6712yes—
1273C2×C22⋊C4C22×D6712yes—
1274C2×C22⋊C4C22×D6712yes—
1275C2×C22⋊C4C22×D6712yes—
1276C2×C42—674no—
1277C2×C42—678no—
1278C2×C42—674no—
1279C2×C42—678no—
1280C2×C42C22×D6711yescharacteristic
1281C2×C42C22×D6712yes—
1282C2×C42C22×D6711yescharacteristic
1283C2×C42C22×D6711yescharacteristic
1284C2×C42C22×D6711yescharacteristic
1285C2×C42C22×D6711yescharacteristic
1286C2×C42C22×D6711yescharacteristic
1287C2×C42C22×D6711yescharacteristic
1288C2×C42C22×D6711yescharacteristic
1289C2×C42C22×D6711yescharacteristic
1290C2×C42C22×D6711yescharacteristic
1291C2×C42C22×D6711yescharacteristic
1292C2×C42C22×D6711yescharacteristic
1293C24C23×D6711yescharacteristic
1294C24C23×D6712yes—
1295#41—2684no—
1296#41—2684no—
1297#41—2688no—
1298#41—26816no—
1299#41—1348no—
1300C2×Q8—42no—
1301C2×Q8—2684no—
1302C2×Q8—2684no—
1303C2×Q8—2688no—
1304C2×Q8—678no—
1305C2×Q8—674no—
1306C2×Q8—674no—
1307C2×Q8—674no—
1308C2×Q8—678no—
1309C2×Q8—672no—
1310C2×Q8—672no—
1311C2×Q8—672no—
1312C2×Q8—674no—
1313C2×Q8C23×D6712yes—
1314C2×Q8C23×D6712yes—
1315C2×D4—42no—
1316C2×D4—44no—
1317C2×D4—674no—
1318C2×D4—678no—
1319C2×D4—678no—
1320C2×D4—674no—
1321C2×D4—674no—
1322C2×D4—672no—
1323C2×D4—672no—
1324C2×D4—672no—
1325C2×D4C23×D6714yes—
1326C2×D4C23×D6712yes—
1327C2×D4C23×D6712yes—
1328C2×D4C23×D6714yes—
1329C22×C4—24no—
1330C22×C4—28no—
1331C22×C4—42no—
1332C22×C4—42no—
1333C22×C4—674no—
1334C22×C4—678no—
1335C22×C4—678no—
1336C22×C4—674no—
1337C22×C4—678no—
1338C22×C4—678no—
1339C22×C4—674no—
1340C22×C4—674no—
1341C22×C4—674no—
1342C22×C4C23×D6711yescharacteristic
1343C22×C4C23×D6711yescharacteristic
1344C22×C4C23×D6711yescharacteristic
1345C22×C4C23×D6711yescharacteristic
1346C22×C4C23×D6711yescharacteristic
1347C22×C4C23×D6711yescharacteristic
1348C22×C4C23×D6711yescharacteristic
1349C22×C4C23×D6711yescharacteristic
1350C22×C4C23×D6712yes—
1351C22×C4C23×D6714yes—
1352C22×C4C23×D6711yescharacteristic
1353C22×C4C23×D6714yes—
1354C22×C4C23×D6711yescharacteristic
1355C22×C4C23×D6711yescharacteristic
1356C22×C4C23×D6711yescharacteristic
1357C22×C4C23×D6711yescharacteristic
1358C22×C4C23×D6711yescharacteristic
1359C22×C4C23×D6711yescharacteristic
1360C22×C4C23×D6711yescharacteristic
1361C22×C4C23×D6711yescharacteristic
1362C22×C4C23×D6712yes—
1363C22×C4C23×D6712yes—
1364C22×C4C23×D6711yescharacteristic
1365C4⋊C4—674no—
1366C4⋊C4—674no—
1367C4⋊C4—672no—
1368C4⋊C4—672no—
1369C4⋊C4—674no—
1370C4⋊C4—678no—
1371C4⋊C4—678no—
1372C4⋊C4—678no—
1373C4⋊C4—674no—
1374C4⋊C4—674no—
1375C4⋊C4—678no—
1376C4⋊C4—678no—
1377C4⋊C4—678no—
1378C4⋊C4—678no—
1379C4⋊C4—678no—
1380C4⋊C4—678no—
1381C4⋊C4—674no—
1382C4⋊C4—674no—
1383C4⋊C4—674no—
1384C4⋊C4—674no—
1385C4⋊C4—678no—
1386C4⋊C4—672no—
1387C4⋊C4—672no—
1388C4⋊C4—672no—
1389C4⋊C4—672no—
1390C4⋊C4—678no—
1391C4⋊C4—678no—
1392C4⋊C4—674no—
1393C4⋊C4—674no—
1394C4⋊C4—678no—
1395C4⋊C4—678no—
1396C4⋊C4—674no—
1397C4⋊C4—678no—
1398C4⋊C4—674no—
1399C4⋊C4—678no—
1400C4⋊C4—674no—
1401C4⋊C4C23×D6712yes—
1402C4⋊C4C23×D6714yes—
1403C4⋊C4C23×D6712yes—
1404C4⋊C4C23×D6714yes—
1405C4⋊C4C23×D6714yes—
1406C4⋊C4C23×D6714yes—
1407C4⋊C4C23×D6714yes—
1408C4⋊C4C23×D6714yes—
1409C4⋊C4C23×D6714yes—
1410C4⋊C4C23×D6712yes—
1411C4⋊C4C23×D6712yes—
1412C4⋊C4C23×D6714yes—
1413C22⋊C4—678no—
1414C22⋊C4—674no—
1415C22⋊C4—678no—
1416C22⋊C4—678no—
1417C22⋊C4—678no—
1418C22⋊C4—674no—
1419C22⋊C4—674no—
1420C22⋊C4—678no—
1421C22⋊C4—678no—
1422C22⋊C4—674no—
1423C22⋊C4—678no—
1424C22⋊C4—674no—
1425C22⋊C4—678no—
1426C22⋊C4—674no—
1427C22⋊C4—678no—
1428C22⋊C4—678no—
1429C22⋊C4—674no—
1430C22⋊C4—674no—
1431C22⋊C4—674no—
1432C22⋊C4C23×D6714yes—
1433C22⋊C4C23×D6714yes—
1434C22⋊C4C23×D6714yes—
1435C22⋊C4C23×D6714yes—
1436C22⋊C4C23×D6714yes—
1437C22⋊C4C23×D6714yes—
1438C22⋊C4C23×D6714yes—
1439C22⋊C4C23×D6714yes—
1440C22⋊C4C23×D6714yes—
1441C22⋊C4C23×D6714yes—
1442C42—678no—
1443C42—674no—
1444C42—678no—
1445C42—674no—
1446C42—678no—
1447C42—678no—
1448C42—678no—
1449C42—678no—
1450C42—674no—
1451C42C23×D6711yescharacteristic
1452C42C23×D6711yescharacteristic
1453C42C23×D6711yescharacteristic
1454C42C23×D6711yescharacteristic
1455C42C23×D6711yescharacteristic
1456C42C23×D6711yescharacteristic
1457C42C23×D6711yescharacteristic
1458C42C23×D6711yescharacteristic
1459C42C23×D6711yescharacteristic
1460C42C23×D6711yescharacteristic
1461C42C23×D6711yescharacteristic
1462C42C23×D6711yescharacteristic
1463C42C23×D6714yes—
1464C42C23×D6711yescharacteristic
1465C42C23×D6714yes—
1466C42C23×D6711yescharacteristic
1467C42C23×D6711yescharacteristic
1468C42C23×D6711yescharacteristic
1469C23—22no—
1470C23—22no—
1471C23—24no—
1472C23—41no—
1473C23—42no—
1474C23—42no—
1475C23—674no—
1476C23C24×D6711yescharacteristic
1477C23C24×D6714yes—
1478C23C24×D6711yescharacteristic
1479C23C24×D6711yescharacteristic
1480Q8—24no—
1481Q8—42no—
1482Q8—2684no—
1483Q8—2684no—
1484Q8—2684no—
1485Q8—2688no—
1486Q8—2682no—
1487Q8—2682no—
1488Q8—2688no—
1489Q8—1344no—
1490Q8—1348no—
1491D4—28no—
1492D4—24no—
1493D4—42no—
1494D4—44no—
1495D4—2682no—
1496D4—2682no—
1497D4—2688no—
1498D4—2684no—
1499D4—2688no—
1500D4—1348no—
1501D4—1348no—
1502D4—1344no—
1503C2×C4—22no—
1504C2×C4—24no—
1505C2×C4—22no—
1506C2×C4—22no—
1507C2×C4—22no—
1508C2×C4—28no—
1509C2×C4—22no—
1510C2×C4—22no—
1511C2×C4—22no—
1512C2×C4—28no—
1513C2×C4—22no—
1514C2×C4—22no—
1515C2×C4—22no—
1516C2×C4—41no—
1517C2×C4—41no—
1518C2×C4—41no—
1519C2×C4—41no—
1520C2×C4—41no—
1521C2×C4—41no—
1522C2×C4—41no—
1523C2×C4—42no—
1524C2×C4—42no—
1525C2×C4—2688no—
1526C2×C4—2684no—
1527C2×C4—2688no—
1528C2×C4—2684no—
1529C2×C4—2688no—
1530C2×C4—2688no—
1531C2×C4—674no—
1532C2×C4—678no—
1533C2×C4—674no—
1534C2×C4—674no—
1535C2×C4—678no—
1536C2×C4—1348no—
1537C2×C4—1348no—
1538C2×C4—1348no—
1539C2×C4#1452409014yes—
1540C2×C4C24×D6711yescharacteristic
1541C2×C4C24×D6711yescharacteristic
1542C2×C4C24×D6714yes—
1543C2×C4C24×D6714yes—
1544C2×C4C24×D6714yes—
1545C2×C4C24×D6711yescharacteristic
1546C2×C4C24×D6711yescharacteristic
1547C2×C4C24×D6711yescharacteristic
1548C2×C4C24×D6711yescharacteristic
1549C2×C4C24×D6711yescharacteristic
1550C2×C4C24×D6711yescharacteristic
1551C2×C4C24×D6711yescharacteristic
1552C2×C4C24×D6711yescharacteristic
1553C2×C4C24×D6711yescharacteristic
1554C2×C4C24×D6711yescharacteristic
1555C22—21no—
1556C22—21no—
1557C22—21no—
1558C22—21no—
1559C22—21no—
1560C22—24no—
1561C22—21no—
1562C22—21no—
1563C22—24no—
1564C22—24no—
1565C22—44no—
1566C22—84no—
1567C22—1344no—
1568C22—1344no—
1569C22—1344no—
1570C22C2×#1452409012yes—
1571C22#1686423212yes—
1572C22C25×D6711yescharacteristic
1573C4—21no—
1574C4—24no—
1575C4—21no—
1576C4—21no—
1577C4—21no—
1578C4—21no—
1579C4—21no—
1580C4—21no—
1581C4—21no—
1582C4—21no—
1583C4—24no—
1584C4—24no—
1585C4—1344no—
1586C4—1348no—
1587C4—1344no—
1588C4—1348no—
1589C4—1344no—
1590C4C2×#1452409012yes—
1591C4C2×#1452409012yes—
1592C4#1686423212yes—
1593C2—22no—
1594C2—22no—
1595C2—41no—
1596C2—44no—
1597C2—2684no—
1598C2C22×#1452409011yescharacteristic
1599C2C2×#1686423211yescharacteristic
1600C2C2×#1686423211yescharacteristic
subgroupG/H
centerC2×C4C24×D67
commutator, socle, cosocleC22×C67C26
FrattiniC22C25×D67
FittingC2×#529×C67C2
hypercenterC2×#529D67
hypocenterC67#62752
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C2×C4 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
1. #22574854C2semidirect
2. #22574833C2semidirect
3. #22574815C2semidirect
4. #22574812C2semidirect
5. #22574781C2semidirect
6. #22574740C2semidirect
7. #22574699C2semidirect
8. #22574646C2semidirect
9. #22574600C2semidirect
10. #22574549C2semidirect
11. #22574454C2semidirect
12. #22574431C2semidirect
13. #22574422C2semidirect
14. #22574354C2semidirect
15. #22573822C2semidirect
16. Q8×#11761628C2semidirect
17. #22573767C2semidirect
18. #22573767C2semidirect
19. #22573638C2semidirect
20. #22573634C2semidirect
21. #22573614C2semidirect
22. #22573599C2semidirect
23. #22573505C2semidirect
24. C2×#16863953C2semidirect
25. C2×#529×C67C2semidirect
26. C67⋊#564C22semidirect
27. #16864150C22semidirect
28. #16864149C22semidirect
29. #16864148C22semidirect
30. #16864148C22semidirect
31. #16864147C22semidirect
32. #16864146C22semidirect
33. #16864143C22semidirect
35. #16864140C22semidirect
36. Q8×Dic134C22semidirect
37. #16864124C22semidirect
38. #16864124C22semidirect
39. #16864123C22semidirect
40. #16864116C22semidirect
41. #16864116C22semidirect
42. #16864115C22semidirect
43. #16864113C22semidirect
44. #16864111C22semidirect
45. #16864111C22semidirect
46. #16864106C22semidirect
47. #16864106C22semidirect
48. #16864103C22semidirect
49. #16864103C22semidirect
52. #16864092C22semidirect
53. #16864092C22semidirect
54. #16864092C22semidirect
55. #16864088C22semidirect
56. #16864086C22semidirect
57. #16864086C22semidirect
58. #16864086C22semidirect
59. #16864084C22semidirect
60. #16864083C22semidirect
61. #16864082C22semidirect
67. Q8×D268C22semidirect
69. #16864059C22semidirect
70. #16864054C22semidirect
72. #16864050C22semidirect
73. #16864050C22semidirect
75. #16864044C22semidirect
80. #16864026C22semidirect
81. #16864025C22semidirect
82. #16864024C22semidirect
83. #16864024C22semidirect
84. #16864024C22semidirect
85. #16864024C22semidirect
88. #16864017C22semidirect
89. #16864017C22semidirect
90. #16864015C22semidirect
91. #16864014C22semidirect
93. #16864012C22semidirect
94. #16864010C22semidirect
95. #16864009C22semidirect
96. #16864008C22semidirect
97. #16864006C22semidirect
98. #16864005C22semidirect
99. #16864003C22semidirect
100. #16864003C22semidirect
101. #16864001C22semidirect
102. #16863995C22semidirect
106. #16863990C22semidirect
107. #16863989C22semidirect
108. #16863987C22semidirect
113. #16863969C22semidirect
114. #16863968C22semidirect
115. #16863966C22semidirect
122. #16863953C22semidirect
123. #16863953C22semidirect
124. #16863953C22semidirect
125. #16863953C22semidirect
126. #16863953C22semidirect
127. #16863953C22semidirect
128. #16863950C22semidirect
129. #16863950C22semidirect
130. #16863949C22semidirect
131. #16863949C22semidirect
133. #16863946C22semidirect
134. #16863946C22semidirect
135. C2×#14524043C22semidirect
136. C2×#14524043C22semidirect
139. #16863930C22semidirect
140. #16863930C22semidirect
141. #16863930C22semidirect
142. #16863930C22semidirect
143. #16863928C22semidirect
144. #16863928C22semidirect
145. #16863926C22semidirect
146. #16863926C22semidirect
147. #16863926C22semidirect
148. #16863924C22semidirect
149. #16863924C22semidirect
150. C2×#14524035C22semidirect
159. C4×#11761628C22semidirect
160. C4×#11761628C22semidirect
161. C4×#11761627C22semidirect
162. C4×#11761627C22semidirect
163. C2×C4×Dic134C22semidirect
164. C2×C4×Dic134C22semidirect
165. C4×Q8×D67C22semidirect
825. C2×#529D67semidirect
826. C67#62752semidirect

Maximal subgroups

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

subgroupindex
#225748542
#225748332
#225748152
#225748122
#225747812
#225747402
#225746992
#225746462
#225746002
#225745492
#225744542
#225744312
#225744222
#225743542
#225738222
Q8×#117616282
#225737672
#225736382
#225736342
#225736142
#225735992
#225735052
C2×#168639532
C2×#529×C672
#6275267