Finite Group Databasebeta

← #32905680

Subgroups — #32905680

Order 18176.

7094 conjugacy classes of subgroups.

The subgroup lattice has 1746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22602434C212yesmaximal, complemented
2#22602428C212yesmaximal, complemented
3#22602423C212yesmaximal, complemented
4#22602417C212yesmaximal, complemented
5#22602329C214yesmaximal, complemented
6#22602323C214yesmaximal, complemented
7#22602207C211yesmaximal, characteristic, complemented
8#22602202C211yesmaximal, characteristic, complemented
9#22602196C214yesmaximal, complemented
10#22602145C211yesmaximal, characteristic, complemented
11#22602106C211yesmaximal, characteristic, complemented
12#22602046C212yesmaximal, complemented
13#22602041C214yesmaximal, complemented
14#22601987C212yesmaximal, complemented
15#22601955C214yesmaximal, complemented
16#22601953C214yesmaximal, complemented
17#22601937C212yesmaximal, complemented
18#22601933C212yesmaximal, complemented
19#41×Dic142C212yesmaximal, complemented
20#22601918C212yesmaximal, complemented
21#22601769C214yesmaximal, complemented
22#22601767C212yesmaximal, complemented
23#22601636C211yesmaximal, characteristic, complemented
24#22601632C214yesmaximal, complemented
25C4×#14556175C212yesmaximal, complemented
26C22×C4×Dic142C211yesmaximal, characteristic, complemented
27C71×#3444C211yesmaximal, characteristic, complemented
28C2×#14556175C2212yes—
29C23×Dic142C2211yescharacteristic
30#17986735C2212yescomplemented
31#17986734C2212yescomplemented
32#17986732C2214yescomplemented
33#17986731C2214yescomplemented
34Q8×Dic142C2212yescomplemented
35#17986729C2212yescomplemented
36#17986728C2212yescomplemented
37#17986727C2214yescomplemented
38#17986727C2212yescomplemented
39#17986726C2214yescomplemented
40#17986726C2214yescomplemented
41#17986725C2214yescomplemented
42#17986724C2212yescomplemented
43#17986724C2212yescomplemented
44#17986723C2212yescomplemented
45#17986722C2214yescomplemented
46#17986721C2214yescomplemented
47#17986719C2212yescomplemented
48#17986718C2214yescomplemented
49#17986718C2214yescomplemented
50#17986717C2218yescomplemented
51#17986716C2218yescomplemented
52#17986710C2212yescomplemented
53#17986708C2218yes—
54#17986708C2214yescomplemented
55#17986707C2214yes—
56#17986706C2214yes—
57#17986706C2212yescomplemented
58#17986705C2214yescomplemented
59#17986703C2218yes—
60#17986701C2214yes—
61#17986698C2218yes—
62#17986695C2214yes—
63#17986692C2218yes—
64#17986691C2214yes—
65#17986689C2214yes—
66#17986689C2214yescomplemented
67#17986687C2214yescomplemented
68#17986686C2218yes—
69#17986685C2218yescomplemented
70#17986682C2218yes—
71#17986682C2218yescomplemented
72#17986670C2212yescomplemented
73#17986669C2212yescomplemented
74D4×Dic142C2214yes—
75D4×Dic142C2214yes—
76D4×Dic142C2212yescomplemented
77#17986664C2212yescomplemented
78#17986662C2214yes—
79#17986662C2214yes—
80#17986658C2214yes—
81#17986658C2214yes—
82#17986658C2214yescomplemented
83#17986657C2214yescomplemented
84#17986655C2214yes—
85#17986655C2214yes—
86#17986653C2214yes—
87#17986649C2214yes—
88#17986648C2218yes—
89#17986647C2218yes—
90#17986628C2214yes—
91#17986627C2212yes—
92#17986620C2214yescomplemented
93#17986615C2218yescomplemented
94#17986614C2214yescomplemented
95#17986613C2218yescomplemented
96#17986611C2214yescomplemented
97#17986608C2218yescomplemented
98#17986607C2214yescomplemented
99#17986606C2218yescomplemented
100#17986598C2214yes—
101#17986594C2214yes—
102#17986593C2218yes—
103#17986591C2218yes—
104#17986577C2212yes—
105#17986576C2214yes—
106#17986575C2212yes—
107#17986571C2218yes—
108#17986570C2212yes—
109#17986556C2211yescharacteristic
110#17986556C2211yescharacteristic
111#17986556C2211yescharacteristic
112#17986556C2214yescomplemented
113#17986553C2214yescomplemented
114#17986553C2218yescomplemented
115#17986552C2214yes—
116#17986552C2218yescomplemented
117#17986551C2214yes—
118#17986551C2214yes—
119#17986549C2211yescharacteristic
120#17986549C2211yescharacteristic
121#17986549C2211yescharacteristic
122#17986545C2214yes—
123#17986544C2214yes—
124#17986544C2214yes—
125#17986535C2214yes—
126#17986535C2214yes—
127#17986533C2212yes—
128#17986533C2212yes—
129#17986533C2212yes—
130#17986533C2212yes—
131#17986533C2212yes—
132#17986533C2212yes—
133#17986533C2214yescomplemented
134#17986531C2214yescomplemented
135#17986530C2214yes—
136#17986530C2214yes—
137#17986529C2218yes—
138#17986529C2218yes—
139#17986529C2218yescomplemented
140#17986527C2218yescomplemented
141#17986526C2218yes—
142#17986526C2218yes—
143#17986510C2212yes—
144#17986510C2212yes—
145#17986510C2212yes—
146#17986505C2218yes—
147#17986505C2218yes—
148#17986482C2212yes—
149#17986479C2212yes—
150#17986479C2214yescomplemented
151#17986478C2218yes—
152#17986478C2214yescomplemented
153#17986476C2212yes—
154#17986476C2214yescomplemented
155#17986475C2214yescomplemented
156#41×Dic71C2214yes—
157C4×#11765865C2212yes—
158C4×#11765865C2212yes—
159C4×#11765865C2212yes—
160C4×#11765865C2214yescomplemented
161#17986467C2214yes—
162C4×#11765864C2218yes—
163C4×#11765864C2218yes—
164C4×#11765864C2214yescomplemented
165C2×C4×Dic142C2211yescharacteristic
166C2×C4×Dic142C2212yes—
167C2×C4×Dic142C2211yescharacteristic
168C2×C4×Dic142C2212yes—
169C2×C4×Dic142C2212yes—
170C2×C4×Dic142C2211yescharacteristic
171C2×C4×Dic142C2212yes—
172C2×C4×Dic142C2212yes—
173C2×C4×Dic142C2212yes—
174C2×C4×Dic142C2212yes—
175C2×C4×Dic142C2212yes—
176C2×C4×Dic142C2211yescharacteristic
177C2×C4×Dic142C2212yes—
178C2×C4×Dic142C2212yes—
179C2×C4×Dic142C2214yescomplemented
180C4×Q8×D71C2214yescomplemented
181C22×C4⋊Dic71C2211yescharacteristic
182C22×Dic71⋊C4C2212yes—
183C22×C4×Dic71C2212yes—
184#533×C71C2211yescharacteristic
185#533×C71C2211yescharacteristic
186#533×C71C2211yescharacteristic
187#532×C71C2211yescharacteristic
188#532×C71C2211yescharacteristic
189#532×C71C2211yescharacteristic
190#529×C71C2212yes—
191#529×C71C2212yes—
192#529×C71C2212yes—
193#529×C71C2212yes—
194#529×C71C2212yes—
195#529×C71C2212yes—
196#525×C71C2212yes—
197#525×C71C2212yes—
198#525×C71C2212yes—
199C4×#41×C71C2212yes—
200C4×#41×C71C2212yes—
201C4×#41×C71C2212yes—
202C22×C42×C71C2211yescharacteristic
203#14556175—216no—
204C2×#11765865C2312yes—
205C2×#11765865C2314yes—
206C2×#11765865C2312yes—
207C2×#11765865C2312yes—
208C2×#11765864C2318yes—
209C2×#11765864C2314yes—
210C2×#11765864C2318yes—
211C22×Dic142—28no—
212C22×Dic142C2311yescharacteristic
213C22×Dic142C2312yes—
214C22×Dic142C2312yes—
215C22×Dic142C2312yes—
216C22×Dic142C2312yes—
217C22×Dic142C2312yes—
218C22×Dic142C2314yes—
219C22×Dic142C2311yescharacteristic
220C2×Q8×D71C2314yes—
221C23×Dic71C2312yes—
222C23×Dic71C2312yes—
223#14556128C2314yes—
224#14556128C2314yes—
225#14556128C2311yescharacteristic
226#14556128C2311yescharacteristic
227#14556128C2311yescharacteristic
228#14556127C2318yes—
229#14556127C2318yes—
230#14556127C2314yes—
231#14556127C2318yes—
232#14556127C2314yes—
233#14556127C2314yes—
234#14556126C2314yes—
235#14556126C2318yes—
236#14556126C2314yes—
237#14556125C2311yescharacteristic
238#14556124C2314yes—
239#14556123C2318yes—
240#14556123C2318yes—
241#14556123C2318yes—
242#14556123C2318yes—
243#14556122C2318yes—
244#14556122C2314yes—
245#14556122C2314yes—
246#14556121C2318yes—
247#14556121C2318yes—
248#14556121C2318yes—
249#14556121C2318yes—
250#14556121C2318yes—
251#14556120C2318yes—
252#14556120C2312yes—
253#14556120C2314yes—
254#14556120C2312yes—
255#14556120C2312yes—
256#14556119C2318yes—
257#14556119C2318yes—
258#14556119C2314yes—
259#14556119C2314yes—
260#14556119C2314yes—
261#14556118C2318yes—
262#14556118C2318yes—
263#14556118C2318yes—
264#14556118C2318yes—
265#14556118C2318yes—
266#14556118C2318yes—
267#14556118C2318yes—
268#14556117C2314yes—
269#14556116C2314yes—
270#14556116C2312yes—
271#14556116C2312yes—
272#14556116C2312yes—
273#14556115C2314yes—
274#14556115C2314yes—
275#14556114C2318yes—
276#14556114C2318yes—
277#14556114C2318yes—
278#14556114C2318yes—
279#14556113C2318yes—
280#14556112C2318yes—
281#14556112C2318yes—
282#14556112C2318yes—
283#14556111C2314yes—
284#14556111C2318yes—
285#14556111C2314yes—
286#14556111C2314yes—
287#14556110C2318yes—
288#14556110C2318yes—
289#14556109C2318yes—
290#14556109C2318yes—
291#14556109C2318yes—
292#14556108C2314yes—
293#14556108C2314yes—
294#14556108C2318yes—
295#14556107C2314yes—
296#14556107C2314yes—
297#14556107C2314yes—
298#14556107C2318yes—
299#14556107C2312yes—
300#14556107C2312yes—
301#14556107C2312yes—
302#14556107C2312yes—
303#14556107C2312yes—
304#14556107C2312yes—
305#14556106C2318yes—
306#14556106C2318yes—
307#14556106C2318yes—
308#14556106C2318yes—
309#14556105C2318yes—
310#14556105C2318yes—
311#14556105C2318yes—
312#14556105C2318yes—
313#14556105C2318yes—
314#14556105C2318yes—
315#14556105C2318yes—
316#14556105C2318yes—
317#14556105C2318yes—
318#14556104C2314yes—
319#14556104C2318yes—
320#14556102C2312yes—
321#14556102C2314yes—
322#14556102C2312yes—
323#14556102C2312yes—
324#14556102C2312yes—
325#14556102C2312yes—
326#14556102C2312yes—
327#14556101C2318yes—
328#14556100C2318yes—
329#14556100C2318yes—
330#14556100C2318yes—
331#14556100C2318yes—
332#14556100C2318yes—
333#14556099C2314yes—
334#14556097C2314yes—
335Q8×Dic71C2314yes—
336Q8×Dic71C2314yes—
337Q8×Dic71C2314yes—
338C4×Dic142C2314yes—
339C4×Dic142C2312yes—
340C4×Dic142C2314yes—
341C4×Dic142C2312yes—
342C4×Dic142C2312yes—
343C4×Dic142C2312yes—
344C4×Dic142C2314yes—
345C4×Dic142C2314yes—
346C4×Dic142C2312yes—
347C4×Dic142C2312yes—
348C4×Dic142C2312yes—
349C4×Dic142C2318yes—
350C4×Dic142C2314yes—
351C4×Dic142C2314yes—
352C4×Dic142C2312yes—
353C4×Dic142C2314yes—
354C4×Dic142C2312yes—
355C4×Dic142C2314yes—
356C4×Dic142C2312yes—
357C4×Dic142C2314yes—
358C4×Dic142C2312yes—
359C4×Dic142C2312yes—
360C4×Dic142C2318yes—
361C4×Dic142C2312yes—
362C4×Dic142C2312yes—
363C4×Dic142C2312yes—
364C4×Dic142C2312yes—
365C4×Dic142C2312yes—
366C4×Dic142C2314yes—
367C4×Dic142C2314yes—
368C4×Dic142C2312yes—
369C4×Dic142C2312yes—
370C4×Dic142C2312yes—
371C4×Dic142C2318yes—
372C4×Dic142C2312yes—
373C4×Dic142C2312yes—
374#14556093C2318yes—
375#14556093C2314yes—
376#14556093C2314yes—
377#14556093C2318yes—
378#14556093C2318yes—
379#14556093C2314yes—
380#14556093C2314yes—
381C4×D284C2312yes—
382C4×D284C2314yes—
383C4×D284C2312yes—
384C4×D284C2312yes—
385C4×D284C2312yes—
386C4×D284C2312yes—
387C4×D284C2312yes—
388D4×Dic71C2318yes—
389D4×Dic71C2318yes—
390D4×Dic71C2314yes—
391D4×Dic71C2318yes—
392D4×Dic71C2314yes—
393D4×Dic71C2318yes—
394D4×Dic71C2314yes—
395#14556090C2314yes—
396#14556090C2314yes—
397C4×C22⋊D71C2314yes—
398C4×C22⋊D71C2318yes—
399C4×C22⋊D71C2314yes—
400C4×C22⋊D71C2314yes—
401C4×C22⋊D71C2314yes—
402C4×C22⋊D71C2314yes—
403C4×C22⋊D71C2314yes—
404C4×C22⋊D71C2318yes—
405C4×C22⋊D71C2318yes—
406(C22⋊D71)⋊C4C2318yes—
407(C22⋊D71)⋊C4C2318yes—
408(C22⋊D71)⋊C4C2318yes—
409(C22⋊D71)⋊C4C2318yes—
410(C22⋊D71)⋊C4C2318yes—
411(C22⋊D71)⋊C4C2318yes—
412(C22⋊D71)⋊C4C2318yes—
413#14556087C2312yes—
414#14556087C2312yes—
415#14556087C2314yes—
416#14556087C2312yes—
417#14556087C2318yes—
418#14556086C2318yes—
419#14556086C2318yes—
420#14556086C2314yes—
421#14556085C2314yes—
422#14556085C2318yes—
423#14556085C2314yes—
424#14556085C2318yes—
425#14556085C2314yes—
426#14556084C2318yes—
427#14556084C2318yes—
428#14556084C2318yes—
429#14556084C2318yes—
430#14556084C2318yes—
431C2×C4⋊Dic71C2311yescharacteristic
432C2×C4⋊Dic71C2312yes—
433C2×C4⋊Dic71C2312yes—
434C2×C4⋊Dic71C2312yes—
435C2×C4⋊Dic71C2314yes—
436C2×C4⋊Dic71C2312yes—
437C2×C4⋊Dic71C2312yes—
438C2×C4⋊Dic71C2311yescharacteristic
439C2×Dic71⋊C4C2312yes—
440C2×Dic71⋊C4C2312yes—
441C2×Dic71⋊C4C2312yes—
442C2×Dic71⋊C4C2314yes—
443C2×Dic71⋊C4C2314yes—
444C2×Dic71⋊C4C2318yes—
445C2×Dic71⋊C4C2314yes—
446C2×Dic71⋊C4C2314yes—
447C2×Dic71⋊C4C2312yes—
448C4⋊C4×D71C2318yes—
449C4⋊C4×D71C2314yes—
450C2×C4×Dic71C2312yes—
451C2×C4×Dic71C2314yes—
452C2×C4×Dic71C2314yes—
453C2×C4×Dic71C2314yes—
454C2×C4×Dic71C2312yes—
455C2×C4×Dic71C2312yes—
456C2×C4×Dic71C2314yes—
457C2×C4×Dic71C2312yes—
458C2×C4×Dic71C2318yes—
459C42×D71C2318yes—
460C42×D71C2314yes—
461C2×#41×C71C2312yes—
462C2×#41×C71C2312yes—
463C2×#41×C71C2312yes—
464C23×C4×C71C2311yescharacteristic
465C23×C4×C71C2311yescharacteristic
466C23×C4×C71C2311yescharacteristic
467C4⋊Q8×C71C2311yescharacteristic
468C4⋊Q8×C71C2311yescharacteristic
469C4⋊Q8×C71C2311yescharacteristic
470#127×C71C2311yescharacteristic
471#126×C71C2314yes—
472#126×C71C2314yes—
473#125×C71C2312yes—
474#125×C71C2312yes—
475#125×C71C2312yes—
476#124×C71C2312yes—
477#124×C71C2312yes—
478#124×C71C2312yes—
479#123×C71C2314yes—
480#123×C71C2314yes—
481#123×C71C2314yes—
482C22⋊Q8×C71C2312yes—
483C22⋊Q8×C71C2312yes—
484C22⋊Q8×C71C2312yes—
485C22⋊Q8×C71C2312yes—
486C22⋊Q8×C71C2312yes—
487C22⋊Q8×C71C2312yes—
488#121×C71C2312yes—
489#121×C71C2312yes—
490#121×C71C2312yes—
491#121×C71C2312yes—
492#121×C71C2312yes—
493#121×C71C2312yes—
494#120×C71C2314yes—
495C4×Q8×C71C2312yes—
496C4×Q8×C71C2312yes—
497C4×Q8×C71C2312yes—
498C4×Q8×C71C2312yes—
499C4×Q8×C71C2312yes—
500C4×Q8×C71C2312yes—
501C4×D4×C71C2314yes—
502C4×D4×C71C2312yes—
503C4×D4×C71C2314yes—
504C4×D4×C71C2314yes—
505C4×D4×C71C2312yes—
506C4×D4×C71C2312yes—
507C4×D4×C71C2314yes—
508C4×D4×C71C2314yes—
509C4×D4×C71C2314yes—
510C4×D4×C71C2312yes—
511C4×D4×C71C2312yes—
512C4×D4×C71C2312yes—
513#117×C71C2312yes—
514#117×C71C2314yes—
515#117×C71C2312yes—
516#117×C71C2312yes—
517#117×C71C2314yes—
518#117×C71C2314yes—
519C2×C42×C71C2311yescharacteristic
520C2×C42×C71C2311yescharacteristic
521C2×C42×C71C2311yescharacteristic
522C2×C42×C71C2311yescharacteristic
523C2×C42×C71C2311yescharacteristic
524C2×C42×C71C2311yescharacteristic
525C2×C42×C71C2311yescharacteristic
526C2×C42×C71C2311yescharacteristic
527C2×C42×C71C2311yescharacteristic
528C2×C42×C71C2311yescharacteristic
529C2×C42×C71C2311yescharacteristic
530C2×C42×C71C2311yescharacteristic
531C2×C42×C71C2314yes—
532#11765865—28no—
533#11765865—28no—
534#11765865—216no—
535#11765865—44no—
536#11765864—232no—
537#11765864—216no—
538#11765864—416no—
539C2×Dic142—24no—
540C2×Dic142—28no—
541C2×Dic142—28no—
542C2×Dic142—28no—
543C2×Dic142—28no—
544C2×Dic142—28no—
545C2×Dic142—216no—
546C2×Dic142#4118yescomplemented
547C2×Dic142C2418yes—
548C2×Dic142C2414yes—
549C2×Dic142C2414yes—
550C2×Dic142C2412yes—
551C2×Dic142C2412yes—
552C2×Dic142C2412yes—
553C2×Dic142C2412yes—
554C2×Dic142C2418yes—
555C2×Dic142C2412yes—
556C2×Dic142C2412yes—
557C2×Dic142C2412yes—
558Q8×D71—216no—
559C2×D284C2412yes—
560C2×D284C2412yes—
561C2×D284C2412yes—
562C2×C22⋊D71C2414yes—
563C2×C22⋊D71C2414yes—
564C2×C22⋊D71C2418yes—
565C2×C22⋊D71C2414yes—
566C2×C22⋊D71C2418yes—
567C22×Dic71—28no—
568C22×Dic71—44no—
569C22×Dic71C2414yes—
570C22×Dic71C2414yes—
571C22×Dic71C2412yes—
572C22×Dic71C2414yes—
573C22×Dic71C2418yes—
574C22×Dic71C2412yes—
575C22×Dic71C2414yes—
576C22×Dic71C2412yes—
577C22×Dic71C2418yes—
578C22×Dic71C2412yes—
579C2×C4×D71C2418yes—
580C2×C4×D71C2414yes—
581C2×C4×D71C2414yes—
582C2×C4×D71C2418yes—
583C2×C4×D71C2414yes—
584C4⋊Dic71C2412yes—
585C4⋊Dic71C2418yes—
586C4⋊Dic71C2412yes—
587C4⋊Dic71C2412yes—
588C4⋊Dic71C2412yes—
589C4⋊Dic71C2414yes—
590C4⋊Dic71C2414yes—
591C4⋊Dic71C2412yes—
592C4⋊Dic71C2418yes—
593C4⋊Dic71C2412yes—
594C4⋊Dic71C2412yes—
595C4⋊Dic71C2412yes—
596C4⋊Dic71C2418yes—
597C4⋊Dic71C2418yes—
598C4⋊Dic71C2412yes—
599C4⋊Dic71C2412yes—
600Dic71⋊C4C2414yes—
601Dic71⋊C4C2418yes—
602Dic71⋊C4C2418yes—
603Dic71⋊C4C2414yes—
604Dic71⋊C4C2414yes—
605Dic71⋊C4C2414yes—
606Dic71⋊C4C2414yes—
607Dic71⋊C4C2414yes—
608Dic71⋊C4C2414yes—
609Dic71⋊C4C2414yes—
610Dic71⋊C4C2414yes—
611Dic71⋊C4C2418yes—
612Dic71⋊C4C2414yes—
613Dic71⋊C4C2414yes—
614Dic71⋊C4C2418yes—
615Dic71⋊C4C2418yes—
616Dic71⋊C4C2418yes—
617Dic71⋊C4C2418yes—
618Dic71⋊C4C2418yes—
619Dic71⋊C4C2414yes—
620Dic71⋊C4C2414yes—
621Dic71⋊C4C2414yes—
622C22⋊Dic71C2414yes—
623C22⋊Dic71C2414yes—
624C22⋊Dic71C2418yes—
625C22⋊Dic71C2418yes—
626C22⋊Dic71C2414yes—
627C22⋊Dic71C2418yes—
628C22⋊Dic71C2418yes—
629(C2×D71)⋊C4C2414yes—
630(C2×D71)⋊C4C2418yes—
631(C2×D71)⋊C4C2414yes—
632(C2×D71)⋊C4C2414yes—
633(C2×D71)⋊C4C2418yes—
634(C2×D71)⋊C4C2418yes—
635(C2×D71)⋊C4C2414yes—
636(C2×D71)⋊C4C2414yes—
637(C2×D71)⋊C4C2414yes—
638(C2×D71)⋊C4C2418yes—
639C4×Dic71C2414yes—
640C4×Dic71C2414yes—
641C4×Dic71C2418yes—
642C4×Dic71C2414yes—
643C4×Dic71C2418yes—
644C4×Dic71C2414yes—
645C4×Dic71C2414yes—
646C4×Dic71C2414yes—
647C4×Dic71C2414yes—
648C4×Dic71C2414yes—
649C4×Dic71C2414yes—
650C4×Dic71C2414yes—
651C4×Dic71C2414yes—
652C4×Dic71C2418yes—
653C4×Dic71C2418yes—
654C24×C71C2411yescharacteristic
655#41×C71—28no—
656#41×C71—28no—
657#41×C71—44no—
658C2×Q8×C71C2412yes—
659C2×Q8×C71C2412yes—
660C2×Q8×C71C2412yes—
661C2×D4×C71C2414yes—
662C2×D4×C71C2414yes—
663C2×D4×C71C2412yes—
664C2×D4×C71C2414yes—
665C2×D4×C71C2412yes—
666C2×D4×C71C2412yes—
667C22×C4×C71—24no—
668C22×C4×C71—24no—
669C22×C4×C71—42no—
670C22×C4×C71C2411yescharacteristic
671C22×C4×C71C2411yescharacteristic
672C22×C4×C71C2411yescharacteristic
673C22×C4×C71C2411yescharacteristic
674C22×C4×C71C2411yescharacteristic
675C22×C4×C71C2414yes—
676C22×C4×C71C2411yescharacteristic
677C22×C4×C71C2411yescharacteristic
678C22×C4×C71C2411yescharacteristic
679C22×C4×C71C2411yescharacteristic
680C22×C4×C71C2411yescharacteristic
681C22×C4×C71C2411yescharacteristic
682C22×C4×C71C2411yescharacteristic
683C22×C4×C71C2414yes—
684C22×C4×C71C2411yescharacteristic
685C22×C4×C71C2411yescharacteristic
686C22×C4×C71C2411yescharacteristic
687C22×C4×C71C2411yescharacteristic
688C22×C4×C71C2414yes—
689C22×C4×C71C2411yescharacteristic
690C22×C4×C71C2411yescharacteristic
691C4⋊C4×C71C2412yes—
692C4⋊C4×C71C2412yes—
693C4⋊C4×C71C2412yes—
694C4⋊C4×C71C2412yes—
695C4⋊C4×C71C2412yes—
696C4⋊C4×C71C2412yes—
697C4⋊C4×C71C2414yes—
698C4⋊C4×C71C2414yes—
699C4⋊C4×C71C2414yes—
700C4⋊C4×C71C2414yes—
701C4⋊C4×C71C2414yes—
702C4⋊C4×C71C2414yes—
703C22⋊C4×C71C2414yes—
704C22⋊C4×C71C2414yes—
705C22⋊C4×C71C2414yes—
706C22⋊C4×C71C2414yes—
707C22⋊C4×C71C2414yes—
708C22⋊C4×C71C2414yes—
709C22⋊C4×C71C2414yes—
710C22⋊C4×C71C2414yes—
711C22⋊C4×C71C2414yes—
712C42×C71C2411yescharacteristic
713C42×C71C2411yescharacteristic
714C42×C71C2411yescharacteristic
715C42×C71C2411yescharacteristic
716C42×C71C2411yescharacteristic
717C42×C71C2411yescharacteristic
718C42×C71C2411yescharacteristic
719C42×C71C2411yescharacteristic
720C42×C71C2411yescharacteristic
721C42×C71C2411yescharacteristic
722C42×C71C2411yescharacteristic
723C42×C71C2411yescharacteristic
724C42×C71C2411yescharacteristic
725C42×C71C2411yescharacteristic
726C42×C71C2411yescharacteristic
727C42×C71C2411yescharacteristic
728C42×C71C2414yes—
729C42×C71C2414yes—
730C42×C71C2414yes—
731C23×C71—22no—
732C23×C71—22no—
733C23×C71—22no—
734C23×C71C2514yes—
735C23×C71C2511yescharacteristic
736C23×C71C2511yescharacteristic
737C23×C71C2511yescharacteristic
738C22×D71C2514yes—
739Q8×C71—24no—
740Q8×C71—24no—
741Q8×C71—42no—
742D4×C71—28no—
743D4×C71—28no—
744D4×C71—28no—
745D4×C71—24no—
746D4×C71—24no—
747D4×C71—42no—
748C2×C4×C71—22no—
749C2×C4×C71—22no—
750C2×C4×C71—22no—
751C2×C4×C71—22no—
752C2×C4×C71—22no—
753C2×C4×C71—22no—
754C2×C4×C71—22no—
755C2×C4×C71—22no—
756C2×C4×C71—28no—
757C2×C4×C71—22no—
758C2×C4×C71—22no—
759C2×C4×C71—22no—
760C2×C4×C71—22no—
761C2×C4×C71—28no—
762C2×C4×C71—41no—
763C2×C4×C71—41no—
764C2×C4×C71—41no—
765C2×C4×C71—41no—
766C2×C4×C71—44no—
767C2×C4×C71C2×#4114yes—
768C2×C4×C712−1+414yescomplemented
769C2×C4×C71C2511yescharacteristic
770C2×C4×C71C2511yescharacteristic
771C2×C4×C71C2511yescharacteristic
772C2×C4×C71C2511yescharacteristic
773C2×C4×C71C2511yescharacteristic
774C2×C4×C71C2511yescharacteristic
775C2×C4×C71C2511yescharacteristic
776C2×C4×C71C2511yescharacteristic
777C2×C4×C71C2514yes—
778C2×C4×C71C2514yes—
779C2×C4×C71C2514yes—
780C2×C4×C71C2511yescharacteristic
781C2×C4×C71C2511yescharacteristic
782C2×C4×C71C2511yescharacteristic
783C2×C4×C71C2511yescharacteristic
784C22⋊D71—28no—
785C22⋊D71—28no—
786C22⋊D71—28no—
787C22⋊D71—216no—
788C22⋊D71—48no—
789C2×Dic71—24no—
790C2×Dic71—28no—
791C2×Dic71—28no—
792C2×Dic71—28no—
793C2×Dic71—216no—
794C2×Dic71—42no—
795C2×Dic71—44no—
796C2×Dic71—42no—
797C2×Dic71—48no—
798C2×Dic71C2×#4118yes—
799C2×Dic71C2514yes—
800C2×Dic71C2514yes—
801C2×Dic71C2514yes—
802C2×Dic71C2514yes—
803C2×Dic71C2514yes—
804C2×Dic71C2514yes—
805C2×Dic71C2514yes—
806D284—24no—
807D284—24no—
808D284—42no—
809C4×D71—28no—
810C4×D71—28no—
811C4×D71—216no—
812C4×D71—48no—
813C4×D71—44no—
814Dic142—24no—
815Dic142—24no—
816Dic142—24no—
817Dic142—24no—
818Dic142—216no—
819Dic142—28no—
820Dic142—28no—
821Dic142—48no—
822Dic142—42no—
823Dic142C2×#4118yes—
824Dic142C2×#4118yes—
825C22×C71—28no—
826C22×C71—21no—
827C22×C71—21no—
828C22×C71—21no—
829C22×C71—21no—
830C22×C71—21no—
831C22×C71—21no—
832C22×C71—24no—
833C22×C71—24no—
834C22×C71—24no—
835C22×C71C22×#4112yes—
836C22×C71C2×2−1+412yes—
837C22×C71#58512yes—
838C22×C71C2611yescharacteristic
839C2×D71—24no—
840C2×D71—24no—
841C2×D71—24no—
842C4×C71—21no—
843C4×C71—21no—
844C4×C71—24no—
845C4×C71—21no—
846C4×C71—21no—
847C4×C71—24no—
848C4×C71—24no—
849C4×C71—21no—
850C4×C71—21no—
851C4×C71—21no—
852C4×C71—21no—
853C4×C71C22×#4112yes—
854C4×C71C22×#4112yes—
855C4×C71C2×2−1+412yes—
856C4×C71C2×2−1+412yes—
857Dic71—24no—
858Dic71—24no—
859Dic71—24no—
860Dic71—24no—
861Dic71—24no—
862Dic71—24no—
863Dic71C22×#4118yes—
864#62788—711nomaximal, Sylow
865C2×C71—22no—
866C2×C71—22no—
867C2×C71—22no—
868C2×C71—44no—
869C2×C71C23×#4111yescharacteristic
870C2×C71C22×2−1+411yescharacteristic
871C2×C71C2×#58511yescharacteristic
872D71—44no—
873#3523—712no—
874#3523—712no—
875#3522—712no—
876#3522—712no—
877#3516—714no—
878#3516—714no—
879#3507—711no—
880#3507—711no—
881#3507—714no—
882#3502—711no—
883#3497—711no—
884#3492—714no—
885#3492—712no—
886#3486—712no—
887#3482—714no—
888#3482—714no—
889#3480—712no—
890#3480—712no—
891Q8×#41—712no—
892Q8×#41—712no—
893#3461—714no—
894#3461—712no—
895#3444—711no—
896#3444—714no—
897#3444D7111yescharacteristic, complemented
898C4×2−1+4—712no—
899C22×C4×Q8—711no—
900C71#6278811yescharacteristic, complemented, Sylow
901C2×2−1+4—712no—
902C23×Q8—711no—
903#559—712no—
904#559—714no—
905#559—712no—
906#559—714no—
907Q82—712no—
908Q82—712no—
909#557—712no—
910#557—712no—
911#557—714no—
912#557—714no—
913#557—714no—
914#557—712no—
915#557—712no—
916#557—714no—
917#556—712no—
918#556—718no—
919#556—714no—
920#556—714no—
921#556—714no—
922#556—714no—
923#556—712no—
924#556—718no—
925#554—712no—
926#554—714no—
927#554—718no—
928#554—714no—
929#554—714no—
930#554—712no—
931#554—718no—
932#554—714no—
933#553—718no—
934#553—714no—
935#553—714no—
936#553—718no—
937#552—718no—
938#552—714no—
939#552—718no—
940#552—714no—
941#552—714no—
942#552—714no—
943#552—718no—
944#552—718no—
945#550—712no—
946#550—712no—
947D4×Q8—712no—
948D4×Q8—714no—
949D4×Q8—714no—
950D4×Q8—714no—
951D4×Q8—714no—
952D4×Q8—712no—
953#548—714no—
954#548—714no—
955#548—714no—
956#548—714no—
957#548—714no—
958#548—714no—
959#547—718no—
960#547—718no—
961#547—714no—
962#547—714no—
963#544—714no—
964#544—712no—
965#542—718no—
966#542—718no—
967#542—714no—
968#542—714no—
969#541—718no—
970#541—718no—
971#541—714no—
972#541—714no—
973#539—718no—
974#539—714no—
975#539—714no—
976#539—718no—
977#537—712no—
978#537—714no—
979#536—712no—
980#536—718no—
981#536—712no—
982#533—714no—
983#533—714no—
984#533—718no—
985#533—714no—
986#533—714no—
987#533—718no—
988#533—711no—
989#533—711no—
990#533—711no—
991#533—714no—
992#533C2×D7111yescharacteristic
993#533C2×D7111yescharacteristic
994#533C2×D7111yescharacteristic
995#532—714no—
996#532—714no—
997#532—714no—
998#532—711no—
999#532—711no—
1000#532—711no—
1001#532C2×D7111yescharacteristic
1002#532C2×D7111yescharacteristic
1003#532C2×D7111yescharacteristic
1004#529—718no—
1005#529—718no—
1006#529—714no—
1007#529—714no—
1008#529—714no—
1009#529—714no—
1010#529—718no—
1011#529—718no—
1012#529—718no—
1013#529—714no—
1014#529—718no—
1015#529—712no—
1016#529—712no—
1017#529—712no—
1018#529—712no—
1019#529—712no—
1020#529—712no—
1021#529—714no—
1022#529C2×D7112yes—
1023#529C2×D7112yes—
1024#529C2×D7112yes—
1025#529C2×D7112yes—
1026#529C2×D7112yes—
1027#529C2×D7112yes—
1028#525—712no—
1029#525—712no—
1030#525—712no—
1031#525—718no—
1032#525—718no—
1033#525C2×D7112yes—
1034#525C2×D7112yes—
1035#525C2×D7112yes—
1036#520—712no—
1037#520—718no—
1038#520—714no—
1039#520—712no—
1040#520—714no—
1041#519—714no—
1042#519—712no—
1043#519—714no—
1044C4×#41—714no—
1045C4×#41—718no—
1046C4×#41—714no—
1047C4×#41—718no—
1048C4×#41—714no—
1049C4×#41—712no—
1050C4×#41—714no—
1051C4×#41—712no—
1052C4×#41—712no—
1053C4×#41C2×D7112yes—
1054C4×#41C2×D7112yes—
1055C4×#41C2×D7112yes—
1056C2×C4×Q8—714no—
1057C2×C4×Q8—711no—
1058C2×C4×Q8—712no—
1059C2×C4×Q8—711no—
1060C2×C4×Q8—712no—
1061C2×C4×Q8—712no—
1062C2×C4×Q8—712no—
1063C2×C4×Q8—712no—
1064C2×C4×Q8—711no—
1065C2×C4×Q8—711no—
1066C2×C4×Q8—712no—
1067C2×C4×Q8—712no—
1068C2×C4×Q8—712no—
1069C2×C4×Q8—712no—
1070C2×C4×Q8—712no—
1071C2×C4×Q8—714no—
1072C22×C4⋊C4—712no—
1073C22×C4⋊C4—711no—
1074C22×C42—712no—
1075C22×C42C2×D7111yescharacteristic
10762−1+4—14216no—
1077C2×#41—718no—
1078C2×#41—718no—
1079C2×#41—714no—
1080C2×#41—712no—
1081C2×#41—712no—
1082C2×#41—712no—
1083C2×#41—714no—
1084C2×#41C22×D7112yes—
1085C2×#41C22×D7112yes—
1086C2×#41C22×D7112yes—
1087C22×Q8—714no—
1088C22×Q8—711no—
1089C22×Q8—712no—
1090C22×Q8—711no—
1091C22×Q8—712no—
1092C22×Q8—712no—
1093C22×Q8—712no—
1094C22×Q8—712no—
1095C22×Q8—714no—
1096C22×Q8—1428no—
1097C23×C4—712no—
1098C23×C4—712no—
1099C23×C4C22×D7111yescharacteristic
1100C23×C4C22×D7111yescharacteristic
1101C23×C4C22×D7111yescharacteristic
1102C4⋊Q8—714no—
1103C4⋊Q8—714no—
1104C4⋊Q8—718no—
1105C4⋊Q8—714no—
1106C4⋊Q8—714no—
1107C4⋊Q8—718no—
1108C4⋊Q8—718no—
1109C4⋊Q8—718no—
1110C4⋊Q8—714no—
1111C4⋊Q8—711no—
1112C4⋊Q8—711no—
1113C4⋊Q8—711no—
1114C4⋊Q8—714no—
1115C4⋊Q8—714no—
1116C4⋊Q8C22×D7111yescharacteristic
1117C4⋊Q8C22×D7111yescharacteristic
1118C4⋊Q8C22×D7111yescharacteristic
1119#127—714no—
1120#127—711no—
1121#127C22×D7111yescharacteristic
1122#126—718no—
1123#126—718no—
1124#126—718no—
1125#126—718no—
1126#126—718no—
1127#126—718no—
1128#126—718no—
1129#126—718no—
1130#126—718no—
1131#126—714no—
1132#126—714no—
1133#126—718no—
1134#126C22×D7114yes—
1135#126C22×D7114yes—
1136#125—718no—
1137#125—718no—
1138#125—714no—
1139#125—714no—
1140#125—718no—
1141#125—718no—
1142#125—714no—
1143#125—718no—
1144#125—718no—
1145#125—718no—
1146#125—718no—
1147#125—718no—
1148#125—712no—
1149#125—712no—
1150#125—712no—
1151#125—714no—
1152#125—718no—
1153#125C22×D7112yes—
1154#125C22×D7112yes—
1155#125C22×D7112yes—
1156#124—714no—
1157#124—714no—
1158#124—714no—
1159#124—718no—
1160#124—718no—
1161#124—718no—
1162#124—718no—
1163#124—712no—
1164#124—712no—
1165#124—712no—
1166#124—714no—
1167#124C22×D7112yes—
1168#124C22×D7112yes—
1169#124C22×D7112yes—
1170#123—718no—
1171#123—718no—
1172#123—718no—
1173#123—714no—
1174#123—714no—
1175#123—714no—
1176#123—718no—
1177#123—718no—
1178#123—718no—
1179#123—718no—
1180#123—718no—
1181#123—718no—
1182#123—718no—
1183#123C22×D7114yes—
1184#123C22×D7114yes—
1185#123C22×D7114yes—
1186C22⋊Q8—714no—
1187C22⋊Q8—718no—
1188C22⋊Q8—712no—
1189C22⋊Q8—712no—
1190C22⋊Q8—712no—
1191C22⋊Q8—712no—
1192C22⋊Q8—712no—
1193C22⋊Q8—712no—
1194C22⋊Q8—714no—
1195C22⋊Q8—714no—
1196C22⋊Q8—714no—
1197C22⋊Q8—718no—
1198C22⋊Q8—718no—
1199C22⋊Q8—714no—
1200C22⋊Q8—718no—
1201C22⋊Q8—714no—
1202C22⋊Q8—718no—
1203C22⋊Q8—718no—
1204C22⋊Q8—718no—
1205C22⋊Q8—718no—
1206C22⋊Q8—718no—
1207C22⋊Q8—718no—
1208C22⋊Q8—718no—
1209C22⋊Q8—718no—
1210C22⋊Q8—718no—
1211C22⋊Q8—718no—
1212C22⋊Q8—718no—
1213C22⋊Q8—718no—
1214C22⋊Q8C22×D7112yes—
1215C22⋊Q8C22×D7112yes—
1216C22⋊Q8C22×D7112yes—
1217C22⋊Q8C22×D7112yes—
1218C22⋊Q8C22×D7112yes—
1219C22⋊Q8C22×D7112yes—
1220#121—718no—
1221#121—718no—
1222#121—718no—
1223#121—718no—
1224#121—714no—
1225#121—718no—
1226#121—712no—
1227#121—712no—
1228#121—712no—
1229#121—712no—
1230#121—712no—
1231#121—712no—
1232#121—714no—
1233#121—718no—
1234#121C22×D7112yes—
1235#121C22×D7112yes—
1236#121C22×D7112yes—
1237#121C22×D7112yes—
1238#121C22×D7112yes—
1239#121C22×D7112yes—
1240#120—714no—
1241#120C22×D7114yes—
1242C4×Q8—714no—
1243C4×Q8—714no—
1244C4×Q8—714no—
1245C4×Q8—714no—
1246C4×Q8—718no—
1247C4×Q8—718no—
1248C4×Q8—714no—
1249C4×Q8—714no—
1250C4×Q8—718no—
1251C4×Q8—714no—
1252C4×Q8—712no—
1253C4×Q8—712no—
1254C4×Q8—712no—
1255C4×Q8—712no—
1256C4×Q8—714no—
1257C4×Q8—714no—
1258C4×Q8—712no—
1259C4×Q8—712no—
1260C4×Q8—714no—
1261C4×Q8—714no—
1262C4×Q8—712no—
1263C4×Q8—712no—
1264C4×Q8—712no—
1265C4×Q8—712no—
1266C4×Q8—712no—
1267C4×Q8—712no—
1268C4×Q8—712no—
1269C4×Q8—712no—
1270C4×Q8—714no—
1271C4×Q8—714no—
1272C4×Q8—712no—
1273C4×Q8—712no—
1274C4×Q8—714no—
1275C4×Q8—714no—
1276C4×Q8—718no—
1277C4×Q8—712no—
1278C4×Q8—714no—
1279C4×Q8—714no—
1280C4×Q8—718no—
1281C4×Q8—712no—
1282C4×Q8—714no—
1283C4×Q8—718no—
1284C4×Q8—712no—
1285C4×Q8—712no—
1286C4×Q8—712no—
1287C4×Q8—712no—
1288C4×Q8C22×D7112yes—
1289C4×Q8C22×D7112yes—
1290C4×Q8C22×D7112yes—
1291C4×Q8C22×D7112yes—
1292C4×Q8C22×D7112yes—
1293C4×Q8C22×D7112yes—
1294C4×D4—718no—
1295C4×D4—714no—
1296C4×D4—718no—
1297C4×D4—718no—
1298C4×D4—718no—
1299C4×D4—714no—
1300C4×D4—714no—
1301C4×D4—714no—
1302C4×D4—714no—
1303C4×D4—718no—
1304C4×D4—714no—
1305C4×D4—718no—
1306C4×D4—714no—
1307C4×D4—714no—
1308C4×D4—714no—
1309C4×D4—718no—
1310C4×D4—714no—
1311C4×D4—714no—
1312C4×D4—718no—
1313C4×D4—718no—
1314C4×D4—718no—
1315C4×D4—718no—
1316C4×D4—718no—
1317C4×D4—718no—
1318C4×D4—718no—
1319C4×D4—712no—
1320C4×D4—712no—
1321C4×D4—714no—
1322C4×D4—712no—
1323C4×D4—712no—
1324C4×D4—712no—
1325C4×D4—712no—
1326C4×D4C22×D7114yes—
1327C4×D4C22×D7114yes—
1328C4×D4C22×D7112yes—
1329C4×D4C22×D7114yes—
1330C4×D4C22×D7112yes—
1331C4×D4C22×D7114yes—
1332C4×D4C22×D7114yes—
1333C4×D4C22×D7114yes—
1334C4×D4C22×D7112yes—
1335C4×D4C22×D7112yes—
1336C4×D4C22×D7112yes—
1337C4×D4C22×D7112yes—
1338#117—712no—
1339#117—712no—
1340#117—714no—
1341#117—712no—
1342#117—718no—
1343#117—718no—
1344#117—714no—
1345#117—718no—
1346#117—718no—
1347#117—718no—
1348#117—718no—
1349#117—718no—
1350#117—718no—
1351#117—714no—
1352#117—718no—
1353#117—718no—
1354#117—714no—
1355#117—714no—
1356#117C22×D7112yes—
1357#117C22×D7112yes—
1358#117C22×D7114yes—
1359#117C22×D7112yes—
1360#117C22×D7114yes—
1361#117C22×D7114yes—
1362C2×C4⋊C4—712no—
1363C2×C4⋊C4—711no—
1364C2×C4⋊C4—712no—
1365C2×C4⋊C4—711no—
1366C2×C4⋊C4—712no—
1367C2×C4⋊C4—712no—
1368C2×C4⋊C4—712no—
1369C2×C4⋊C4—714no—
1370C2×C4⋊C4—714no—
1371C2×C4⋊C4—712no—
1372C2×C4⋊C4—712no—
1373C2×C4⋊C4—714no—
1374C2×C4⋊C4—714no—
1375C2×C4⋊C4—712no—
1376C2×C4⋊C4—712no—
1377C2×C4⋊C4—718no—
1378C2×C4⋊C4—714no—
1379C2×C4⋊C4—718no—
1380C2×C4⋊C4—714no—
1381C2×C42—712no—
1382C2×C42—714no—
1383C2×C42—714no—
1384C2×C42—714no—
1385C2×C42—712no—
1386C2×C42—712no—
1387C2×C42—714no—
1388C2×C42—712no—
1389C2×C42—718no—
1390C2×C42—718no—
1391C2×C42—714no—
1392C2×C42C22×D7111yescharacteristic
1393C2×C42C22×D7111yescharacteristic
1394C2×C42C22×D7111yescharacteristic
1395C2×C42C22×D7111yescharacteristic
1396C2×C42C22×D7111yescharacteristic
1397C2×C42C22×D7111yescharacteristic
1398C2×C42C22×D7111yescharacteristic
1399C2×C42C22×D7111yescharacteristic
1400C2×C42C22×D7111yescharacteristic
1401C2×C42C22×D7111yescharacteristic
1402C2×C42C22×D7111yescharacteristic
1403C2×C42C22×D7111yescharacteristic
1404C2×C42C22×D7114yes—
1405C24C23×D7111yescharacteristic
1406#41—28no—
1407#41—28no—
1408#41—44no—
1409#41—2844no—
1410#41—28416no—
1411#41—14216no—
1412#41—14232no—
1413#41—14216no—
1414#41—1428no—
1415#41—1428no—
1416C2×Q8—718no—
1417C2×Q8—712no—
1418C2×Q8—718no—
1419C2×Q8—712no—
1420C2×Q8—712no—
1421C2×Q8—712no—
1422C2×Q8—714no—
1423C2×Q8—714no—
1424C2×Q8—712no—
1425C2×Q8—712no—
1426C2×Q8—718no—
1427C2×Q8—712no—
1428C2×Q8—1428no—
1429C2×Q8—1428no—
1430C2×Q8—1428no—
1431C2×Q8—1428no—
1432C2×Q8—1428no—
1433C2×Q8—14216no—
1434C2×Q8—14216no—
1435C2×Q8—1424no—
1436C2×Q8C23×D7112yes—
1437C2×Q8C23×D7112yes—
1438C2×Q8C23×D7112yes—
1439C2×D4—718no—
1440C2×D4—714no—
1441C2×D4—714no—
1442C2×D4—714no—
1443C2×D4—718no—
1444C2×D4—712no—
1445C2×D4—712no—
1446C2×D4—712no—
1447C2×D4C23×D7114yes—
1448C2×D4C23×D7112yes—
1449C2×D4C23×D7114yes—
1450C2×D4C23×D7114yes—
1451C2×D4C23×D7112yes—
1452C2×D4C23×D7112yes—
1453C22×C4—24no—
1454C22×C4—24no—
1455C22×C4—42no—
1456C22×C4—2844no—
1457C22×C4—712no—
1458C22×C4—714no—
1459C22×C4—712no—
1460C22×C4—718no—
1461C22×C4—718no—
1462C22×C4—714no—
1463C22×C4—712no—
1464C22×C4—714no—
1465C22×C4—714no—
1466C22×C4—714no—
1467C22×C4—712no—
1468C22×C4—718no—
1469C22×C4—718no—
1470C22×C4—714no—
1471C22×C4—714no—
1472C22×C4—1428no—
1473C22×C4C23×D7111yescharacteristic
1474C22×C4C23×D7111yescharacteristic
1475C22×C4C23×D7111yescharacteristic
1476C22×C4C23×D7111yescharacteristic
1477C22×C4C23×D7111yescharacteristic
1478C22×C4C23×D7111yescharacteristic
1479C22×C4C23×D7111yescharacteristic
1480C22×C4C23×D7111yescharacteristic
1481C22×C4C23×D7111yescharacteristic
1482C22×C4C23×D7111yescharacteristic
1483C22×C4C23×D7114yes—
1484C22×C4C23×D7111yescharacteristic
1485C22×C4C23×D7111yescharacteristic
1486C22×C4C23×D7114yes—
1487C22×C4C23×D7111yescharacteristic
1488C22×C4C23×D7111yescharacteristic
1489C22×C4C23×D7111yescharacteristic
1490C22×C4C23×D7111yescharacteristic
1491C22×C4C23×D7114yes—
1492C22×C4C23×D7111yescharacteristic
1493C22×C4C23×D7111yescharacteristic
1494C4⋊C4—714no—
1495C4⋊C4—714no—
1496C4⋊C4—714no—
1497C4⋊C4—714no—
1498C4⋊C4—714no—
1499C4⋊C4—714no—
1500C4⋊C4—714no—
1501C4⋊C4—714no—
1502C4⋊C4—718no—
1503C4⋊C4—718no—
1504C4⋊C4—714no—
1505C4⋊C4—718no—
1506C4⋊C4—714no—
1507C4⋊C4—714no—
1508C4⋊C4—718no—
1509C4⋊C4—718no—
1510C4⋊C4—718no—
1511C4⋊C4—714no—
1512C4⋊C4—718no—
1513C4⋊C4—714no—
1514C4⋊C4—714no—
1515C4⋊C4—718no—
1516C4⋊C4—712no—
1517C4⋊C4—712no—
1518C4⋊C4—712no—
1519C4⋊C4—712no—
1520C4⋊C4—714no—
1521C4⋊C4—714no—
1522C4⋊C4—712no—
1523C4⋊C4—718no—
1524C4⋊C4—712no—
1525C4⋊C4—712no—
1526C4⋊C4—712no—
1527C4⋊C4—712no—
1528C4⋊C4—712no—
1529C4⋊C4—718no—
1530C4⋊C4—718no—
1531C4⋊C4—718no—
1532C4⋊C4C23×D7112yes—
1533C4⋊C4C23×D7114yes—
1534C4⋊C4C23×D7112yes—
1535C4⋊C4C23×D7114yes—
1536C4⋊C4C23×D7114yes—
1537C4⋊C4C23×D7112yes—
1538C4⋊C4C23×D7112yes—
1539C4⋊C4C23×D7112yes—
1540C4⋊C4C23×D7112yes—
1541C4⋊C4C23×D7114yes—
1542C4⋊C4C23×D7114yes—
1543C4⋊C4C23×D7114yes—
1544C22⋊C4—714no—
1545C22⋊C4—714no—
1546C22⋊C4—718no—
1547C22⋊C4—714no—
1548C22⋊C4—718no—
1549C22⋊C4—718no—
1550C22⋊C4—718no—
1551C22⋊C4—718no—
1552C22⋊C4—714no—
1553C22⋊C4—714no—
1554C22⋊C4—714no—
1555C22⋊C4—714no—
1556C22⋊C4—718no—
1557C22⋊C4—718no—
1558C22⋊C4—714no—
1559C22⋊C4—714no—
1560C22⋊C4—718no—
1561C22⋊C4C23×D7114yes—
1562C22⋊C4C23×D7114yes—
1563C22⋊C4C23×D7114yes—
1564C22⋊C4C23×D7114yes—
1565C22⋊C4C23×D7114yes—
1566C22⋊C4C23×D7114yes—
1567C22⋊C4C23×D7114yes—
1568C22⋊C4C23×D7114yes—
1569C22⋊C4C23×D7114yes—
1570C42—714no—
1571C42—714no—
1572C42—714no—
1573C42—714no—
1574C42—714no—
1575C42—714no—
1576C42—718no—
1577C42—718no—
1578C42—714no—
1579C42—718no—
1580C42—718no—
1581C42—714no—
1582C42—714no—
1583C42—714no—
1584C42—714no—
1585C42C23×D7111yescharacteristic
1586C42C23×D7111yescharacteristic
1587C42C23×D7111yescharacteristic
1588C42C23×D7111yescharacteristic
1589C42C23×D7111yescharacteristic
1590C42C23×D7111yescharacteristic
1591C42C23×D7111yescharacteristic
1592C42C23×D7111yescharacteristic
1593C42C23×D7111yescharacteristic
1594C42C23×D7111yescharacteristic
1595C42C23×D7111yescharacteristic
1596C42C23×D7111yescharacteristic
1597C42C23×D7114yes—
1598C42C23×D7114yes—
1599C42C23×D7111yescharacteristic
1600C42C23×D7114yes—
1601C42C23×D7111yescharacteristic
1602C42C23×D7111yescharacteristic
1603C42C23×D7111yescharacteristic
1604C23—22no—
1605C23—22no—
1606C23—22no—
1607C23—714no—
1608C23C24×D7114yes—
1609C23C24×D7111yescharacteristic
1610C23C24×D7111yescharacteristic
1611C23C24×D7111yescharacteristic
1612Q8—24no—
1613Q8—24no—
1614Q8—42no—
1615Q8—2842no—
1616Q8—2848no—
1617Q8—718no—
1618Q8—718no—
1619Q8—1428no—
1620Q8—1428no—
1621Q8—14216no—
1622Q8—1424no—
1623Q8—1424no—
1624Q8—1424no—
1625Q8—1424no—
1626D4—28no—
1627D4—28no—
1628D4—28no—
1629D4—24no—
1630D4—24no—
1631D4—42no—
1632D4—2842no—
1633D4—2848no—
1634D4—14216no—
1635D4—1428no—
1636D4—1428no—
1637D4—1428no—
1638D4—1424no—
1639D4—1424no—
1640C2×C4—22no—
1641C2×C4—22no—
1642C2×C4—22no—
1643C2×C4—22no—
1644C2×C4—22no—
1645C2×C4—22no—
1646C2×C4—22no—
1647C2×C4—22no—
1648C2×C4—28no—
1649C2×C4—22no—
1650C2×C4—22no—
1651C2×C4—22no—
1652C2×C4—22no—
1653C2×C4—28no—
1654C2×C4—41no—
1655C2×C4—41no—
1656C2×C4—41no—
1657C2×C4—41no—
1658C2×C4—44no—
1659C2×C4—2844no—
1660C2×C4—2848no—
1661C2×C4—2842no—
1662C2×C4—2844no—
1663C2×C4—2842no—
1664C2×C4—2848no—
1665C2×C4—718no—
1666C2×C4—714no—
1667C2×C4—714no—
1668C2×C4—714no—
1669C2×C4—714no—
1670C2×C4—714no—
1671C2×C4—714no—
1672C2×C4—714no—
1673C2×C4—14216no—
1674C2×C4—1428no—
1675C2×C4—1428no—
1676C2×C4—14216no—
1677C2×C4—1424no—
1678C2×C4—1428no—
1679C2×C4—1428no—
1680C2×C4—1428no—
1681C2×C4#41×D7114yes—
1682C2×C4#1455617514yescomplemented
1683C2×C4C24×D7111yescharacteristic
1684C2×C4C24×D7111yescharacteristic
1685C2×C4C24×D7111yescharacteristic
1686C2×C4C24×D7114yes—
1687C2×C4C24×D7114yes—
1688C2×C4C24×D7114yes—
1689C2×C4C24×D7111yescharacteristic
1690C2×C4C24×D7111yescharacteristic
1691C2×C4C24×D7111yescharacteristic
1692C2×C4C24×D7111yescharacteristic
1693C2×C4C24×D7111yescharacteristic
1694C2×C4C24×D7111yescharacteristic
1695C2×C4C24×D7111yescharacteristic
1696C2×C4C24×D7111yescharacteristic
1697C2×C4C24×D7111yescharacteristic
1698C22—28no—
1699C22—21no—
1700C22—21no—
1701C22—21no—
1702C22—21no—
1703C22—21no—
1704C22—21no—
1705C22—24no—
1706C22—24no—
1707C22—24no—
1708C22—1424no—
1709C22—1424no—
1710C22—1424no—
1711C22C2×#41×D7112yes—
1712C22C2×#1455617512yes—
1713C22#1798683512yes—
1714C22C25×D7111yescharacteristic
1715C4—21no—
1716C4—21no—
1717C4—24no—
1718C4—21no—
1719C4—21no—
1720C4—24no—
1721C4—21no—
1722C4—21no—
1723C4—21no—
1724C4—21no—
1725C4—24no—
1726C4—718no—
1727C4—1424no—
1728C4—1424no—
1729C4—1424no—
1730C4—1424no—
1731C4—1424no—
1732C4—1424no—
1733C4C2×#41×D7112yes—
1734C4C2×#41×D7112yes—
1735C4C2×#1455617512yes—
1736C4C2×#1455617512yes—
1737C2—22no—
1738C2—22no—
1739C2—22no—
1740C2—44no—
1741C2—2844no—
1742C2C22×#41×D7111yescharacteristic
1743C2C22×#1455617511yescharacteristic
1744C2C2×#1798683511yescharacteristic
subgroupG/H
centerC2×C4C24×D71
commutator, socle, cosocleC22×C71C26
FrattiniC22C25×D71
FittingC71×#3444C2
hypercenter#3444D71
hypocenterC71#62788
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C2×C4 ◁ #3444

Complements

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

NH ≅ G/Ntype
1. #22602434C2semidirect
2. #22602428C2semidirect
3. #22602423C2semidirect
4. #22602417C2semidirect
5. #22602329C2semidirect
6. #22602323C2semidirect
7. #22602207C2semidirect
8. #22602202C2semidirect
9. #22602196C2semidirect
10. #22602145C2semidirect
11. #22602106C2semidirect
12. #22602046C2semidirect
13. #22602041C2semidirect
14. #22601987C2semidirect
15. #22601955C2semidirect
16. #22601953C2semidirect
17. #22601937C2semidirect
18. #22601933C2semidirect
19. #41×Dic142C2semidirect
20. #22601918C2semidirect
21. #22601769C2semidirect
22. #22601767C2semidirect
23. #22601636C2semidirect
24. #22601632C2semidirect
25. C4×#14556175C2semidirect
26. C22×C4×Dic142C2semidirect
27. C71×#3444C2semidirect
30. #17986735C22semidirect
31. #17986734C22semidirect
32. #17986732C22semidirect
33. #17986731C22semidirect
34. Q8×Dic142C22semidirect
35. #17986729C22semidirect
36. #17986728C22semidirect
37. #17986727C22semidirect
38. #17986727C22semidirect
39. #17986726C22semidirect
40. #17986726C22semidirect
41. #17986725C22semidirect
42. #17986724C22semidirect
43. #17986724C22semidirect
44. #17986723C22semidirect
45. #17986722C22semidirect
46. #17986721C22semidirect
47. #17986719C22semidirect
48. #17986718C22semidirect
49. #17986718C22semidirect
50. #17986717C22semidirect
51. #17986716C22semidirect
52. #17986710C22semidirect
54. #17986708C22semidirect
57. #17986706C22semidirect
58. #17986705C22semidirect
66. #17986689C22semidirect
67. #17986687C22semidirect
69. #17986685C22semidirect
71. #17986682C22semidirect
72. #17986670C22semidirect
73. #17986669C22semidirect
76. D4×Dic142C22semidirect
77. #17986664C22semidirect
82. #17986658C22semidirect
83. #17986657C22semidirect
92. #17986620C22semidirect
93. #17986615C22semidirect
94. #17986614C22semidirect
95. #17986613C22semidirect
96. #17986611C22semidirect
97. #17986608C22semidirect
98. #17986607C22semidirect
99. #17986606C22semidirect
112. #17986556C22semidirect
113. #17986553C22semidirect
114. #17986553C22semidirect
116. #17986552C22semidirect
133. #17986533C22semidirect
134. #17986531C22semidirect
139. #17986529C22semidirect
140. #17986527C22semidirect
150. #17986479C22semidirect
152. #17986478C22semidirect
154. #17986476C22semidirect
155. #17986475C22semidirect
160. C4×#11765865C22semidirect
164. C4×#11765864C22semidirect
179. C2×C4×Dic142C22semidirect
180. C4×Q8×D71C22semidirect
546. C2×Dic142#41semidirect
768. C2×C4×C712−1+4semidirect
897. #3444D71semidirect
900. C71#62788semidirect
1682. C2×C4#14556175semidirect

Maximal subgroups

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

subgroupindex
#226024342
#226024282
#226024232
#226024172
#226023292
#226023232
#226022072
#226022022
#226021962
#226021452
#226021062
#226020462
#226020412
#226019872
#226019552
#226019532
#226019372
#226019332
#41×Dic1422
#226019182
#226017692
#226017672
#226016362
#226016322
C4×#145561752
C22×C4×Dic1422
C71×#34442
#6278871