Finite Group Databasebeta

← #32905752

Subgroups — #32905752

Order 18176.

7190 conjugacy classes of subgroups.

The subgroup lattice has 1350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22602450C212yesmaximal, complemented
2#22602446C216yesmaximal, complemented
3#22602354C213yesmaximal, complemented
4#22602352C211yesmaximal, characteristic, complemented
5#22602347C211yesmaximal, characteristic, complemented
6#22602345C213yesmaximal, complemented
7#22602193C213yesmaximal, complemented
8#22602190C213yesmaximal, complemented
9#22602144C211yesmaximal, characteristic, complemented
10#22602110C211yesmaximal, characteristic, complemented
11#22602058C216yesmaximal, complemented
12#22601997C212yesmaximal, complemented
13#22601966C211yesmaximal, characteristic, complemented
14#22601966C213yesmaximal, complemented
15#22601958C213yesmaximal, complemented
16#22601935C212yesmaximal, complemented
17#22601931C216yesmaximal, complemented
18#22601761C216yesmaximal, complemented
19#22601637C213yesmaximal, complemented
20#22601633C213yesmaximal, complemented
21C4×#14556176C212yesmaximal, complemented
22C4×#41×D71C211yesmaximal, characteristic, complemented
23C71×#3482C211yesmaximal, characteristic, complemented
24C2×#14556176C2212yes—
25C2×#41×D71C2211yescharacteristic
26#17986734C2216yescomplemented
27#17986733C22112yescomplemented
28#17986731C2216yescomplemented
29Q8×Dic142C2211yescharacteristic, complemented
30Q8×Dic142C2213yescomplemented
31#17986728C2212yescomplemented
32#17986726C2216yescomplemented
33#17986724C2213yescomplemented
34#17986723C2213yescomplemented
35#17986722C2216yescomplemented
36#17986720C2216yescomplemented
37#17986720C2216yescomplemented
38#17986716C22112yescomplemented
39#17986714C2216yescomplemented
40#17986714C2213yescomplemented
41#17986714C2213yescomplemented
42#17986712C2216yescomplemented
43#17986712C22112yescomplemented
44#17986712C2216yescomplemented
45#17986702C2216yescomplemented
46#17986700C22112yescomplemented
47#17986697C2216yescomplemented
48#17986697C2216yescomplemented
49#17986696C2216yescomplemented
50#17986694C22112yescomplemented
51#17986683C2216yescomplemented
52#17986681C22112yescomplemented
53#17986671C2212yes—
54#17986671C2211yescharacteristic, complemented
55#17986671C2213yescomplemented
56#17986670C2216yes—
57#17986670C2213yescomplemented
58#17986670C2213yescomplemented
59#17986668C2212yes—
60#17986668C2216yescomplemented
61#17986667C2216yes—
62#17986664C2213yescomplemented
63#17986660C2212yes—
64#17986660C2212yescomplemented
65#17986659C2216yes—
66#17986659C2216yescomplemented
67#17986657C2216yes—
68#17986652C2213yescomplemented
69#17986651C2216yescomplemented
70#17986629C2216yes—
71#17986622C2216yescomplemented
72#17986618C2216yescomplemented
73#17986615C22112yescomplemented
74#17986605C2216yescomplemented
75#17986602C2216yescomplemented
76#17986601C22112yescomplemented
77#17986588C22112yes—
78#17986585C22112yes—
79#17986579C2216yes—
80#17986567C2216yes—
81#17986565C2216yes—
82#17986554C2213yes—
83#17986554C2213yescomplemented
84#17986553C2213yes—
85#17986553C2213yescomplemented
86#17986552C2213yescomplemented
87#17986550C2213yes—
88#17986550C2213yescomplemented
89#17986549C2216yescomplemented
90#17986549C2213yescomplemented
91#17986546C2213yes—
92#17986546C2216yescomplemented
93#17986546C22112yescomplemented
94#17986546C2213yescomplemented
95#17986545C2213yescomplemented
96#17986536C2213yes—
97#17986536C2216yescomplemented
98#17986536C2213yescomplemented
99#17986536C2216yescomplemented
100#17986535C2216yescomplemented
101#17986535C2216yescomplemented
102#17986534C2216yes—
103#17986534C2216yescomplemented
104#17986531C2211yescharacteristic
105#17986531C2213yescomplemented
106#17986529C2216yescomplemented
107#17986529C2216yescomplemented
108#17986527C2216yes—
109#17986527C22112yescomplemented
110#17986527C2216yescomplemented
111#17986512C2216yes—
112#17986512C2216yes—
113#17986511C2216yes—
114#17986511C2213yes—
115#17986508C2216yes—
116#17986508C2216yes—
117#17986506C2213yes—
118#17986481C2216yes—
119#17986481C2212yescomplemented
120#17986480C2216yes—
121#17986480C2216yescomplemented
122#17986477C2212yescomplemented
123#17986475C2212yes—
124#17986475C2216yescomplemented
125#41×Dic71C2211yescharacteristic
126C4×#11765866C2216yes—
127C4×#11765866C2211yescharacteristic
128C4×#11765866C2211yescharacteristic
129C4×#11765866C2212yescomplemented
130C4×#11765866C2216yescomplemented
131C4×#11765865C2216yes—
132C4×#11765865C2213yes—
133C4×#11765865C2216yescomplemented
134C4×#11765865C2216yescomplemented
135C4×#11765865C2213yescomplemented
136#17986467C2213yes—
137#17986467C2216yescomplemented
138C4×#11765864C2213yes—
139C4×#11765864C2213yes—
140C4×Q8×D71C2211yescharacteristic
141C4×Q8×D71C2211yescharacteristic
142C4×Q8×D71C2216yescomplemented
143C4×D4×D71C2213yes—
144C4×D4×D71C2213yes—
145#117×D71C2213yes—
146C2×C42×D71C2213yes—
147#557×C71C2211yescharacteristic, complemented
148#556×C71C2213yescomplemented
149#552×C71C2216yescomplemented
150D4×Q8×C71C2211yescharacteristic, complemented
151#548×C71C2212yes—
152#547×C71C2213yescomplemented
153#533×C71C2213yescomplemented
154#529×C71C2216yescomplemented
155C4×#41×C71C2211yescharacteristic
156C4×#41×C71C2213yescomplemented
157C2×C4×Q8×C71C2212yescomplemented
158#14556176—216no—
159C2×#11765866C2316yes—
160C2×#11765866C2311yescharacteristic
161C2×#11765866C2312yes—
162C2×#11765866C2316yes—
163C2×#11765865C2316yes—
164C2×#11765865C2313yes—
165C2×#11765865C2316yes—
166C2×#11765865C2313yes—
167C2×#11765865C2316yes—
168C2×#11765865C2316yes—
169C2×#11765864C2313yes—
170#41×D71—28no—
171C2×Q8×D71C2316yes—
172C2×Q8×D71C2311yescharacteristic
173C2×D4×D71C2313yes—
174C22×C4×D71C2313yes—
175C22×C4×D71C2313yes—
176C22×C4×D71C2313yes—
177#14556128C2316yes—
178#14556128C2313yes—
179#14556127C23112yes—
180#14556127C2316yes—
181#14556127C2313yes—
182#14556127C2313yes—
183#14556126C2313yes—
184#14556125C2316yes—
185#14556125C2313yes—
186#14556124C23112yes—
187#14556124C2316yes—
188#14556124C2313yes—
189#14556123C23112yes—
190#14556123C23112yes—
191#14556123C23112yes—
192#14556123C2316yes—
193#14556123C2316yes—
194#14556121C23112yes—
195#14556121C2316yes—
196#14556121C2312yes—
197#14556119C2316yes—
198#14556119C2316yes—
199#14556119C2311yescharacteristic
200#14556119C2313yes—
201#14556118C23112yes—
202#14556118C2316yes—
203#14556118C2316yes—
204#14556117C2316yes—
205#14556117C2316yes—
206#14556117C2313yes—
207#14556116C23112yes—
208#14556116C2316yes—
209#14556115C2311yescharacteristic
210#14556114C23112yes—
211#14556114C23112yes—
212#14556114C23112yes—
213#14556114C23112yes—
214#14556114C2316yes—
215#14556114C2316yes—
216#14556113C23112yes—
217#14556113C23112yes—
218#14556113C2316yes—
219#14556113C23112yes—
220#14556113C2316yes—
221#14556112C23112yes—
222#14556112C2316yes—
223#14556110C23112yes—
224#14556110C2316yes—
225#14556110C2312yes—
226#14556109C2316yes—
227#14556108C2316yes—
228#14556108C2316yes—
229#14556108C2313yes—
230#14556108C2311yescharacteristic
231#14556106C23112yes—
232#14556106C2316yes—
233#14556106C2316yes—
234#14556105C2316yes—
235#14556105C2316yes—
236#14556104C2316yes—
237#14556104C2313yes—
238#14556104C2316yes—
239#14556104C2313yes—
240#14556103C2316yes—
241#14556103C2316yes—
242#14556103C2316yes—
243#14556103C23112yes—
244#14556103C2316yes—
245#14556103C2316yes—
246#14556103C2313yes—
247#14556103C2313yes—
248#14556102C2316yes—
249#14556102C2316yes—
250#14556102C23112yes—
251#14556102C2316yes—
252#14556102C2316yes—
253#14556101C23112yes—
254#14556101C23112yes—
255#14556101C2316yes—
256#14556101C23112yes—
257#14556101C23112yes—
258#14556101C2316yes—
259#14556100C2316yes—
260#14556100C2316yes—
261#14556099C2316yes—
262#14556099C23112yes—
263#14556099C2313yes—
264#14556099C2311yescharacteristic
265#14556098C23112yes—
266#14556098C2316yes—
267#14556096C2316yes—
268Q8×Dic71C2316yes—
269Q8×Dic71C2312yes—
270Q8×Dic71C2311yescharacteristic
271Q8×Dic71C2316yes—
272Q8×Dic71C2316yes—
273Q8×Dic71C2311yescharacteristic
274C4×Dic142C2316yes—
275C4×Dic142C2316yes—
276C4×Dic142C2313yes—
277C4×Dic142C2313yes—
278C4×Dic142C2316yes—
279C4×Dic142C2313yes—
280C4×Dic142C2316yes—
281C4×Dic142C2311yescharacteristic
282C4×Dic142C2316yes—
283#14556093C2316yes—
284#14556093C2313yes—
285#14556093C23112yes—
286#14556093C2316yes—
287#14556093C2313yes—
288#14556093C2316yes—
289C4×D284C2316yes—
290C4×D284C2313yes—
291C4×D284C2313yes—
292C4×D284C2316yes—
293C4×D284C2316yes—
294C4×D284C2316yes—
295C4×D284C2313yes—
296C4×D284C2316yes—
297C4×D284C2316yes—
298C4×D284C2313yes—
299C4×D284C23112yes—
300D4×Dic71C2313yes—
301D4×Dic71C2313yes—
302#14556090C23112yes—
303#14556090C2316yes—
304#14556090C2313yes—
305#14556090C2316yes—
306#14556090C23112yes—
307#14556090C2316yes—
308#14556090C2316yes—
309#14556090C2316yes—
310#14556090C2313yes—
311C4×C22⋊D71C2316yes—
312C4×C22⋊D71C2316yes—
313C4×C22⋊D71C2316yes—
314C4×C22⋊D71C2316yes—
315C4×C22⋊D71C2316yes—
316C4×C22⋊D71C2316yes—
317C4×C22⋊D71C23112yes—
318C4×C22⋊D71C2316yes—
319C4×C22⋊D71C2316yes—
320C4×C22⋊D71C2316yes—
321C4×C22⋊D71C2312yes—
322C4×C22⋊D71C2316yes—
323C4×C22⋊D71C2316yes—
324(C22⋊D71)⋊C4C2316yes—
325(C22⋊D71)⋊C4C23112yes—
326(C22⋊D71)⋊C4C23112yes—
327(C22⋊D71)⋊C4C2316yes—
328#14556087C2316yes—
329#14556087C2313yes—
330#14556087C2316yes—
331#14556087C2313yes—
332#14556087C2312yes—
333#14556086C2316yes—
334#14556086C23112yes—
335#14556086C23112yes—
336#14556086C2313yes—
337#14556086C2316yes—
338#14556086C2313yes—
339#14556086C2316yes—
340#14556085C2316yes—
341#14556085C2316yes—
342#14556085C2316yes—
343#14556085C2316yes—
344#14556085C23112yes—
345#14556085C2316yes—
346#14556085C2316yes—
347#14556084C2316yes—
348C4⋊C4×D71C2313yes—
349C4⋊C4×D71C23112yes—
350C4⋊C4×D71C2316yes—
351C4⋊C4×D71C2313yes—
352C22⋊C4×D71C2316yes—
353C2×C4×Dic71C2313yes—
354C2×C4×Dic71C2313yes—
355C2×C4×Dic71C2313yes—
356C42×D71C2311yescharacteristic
357C42×D71C2313yes—
358C42×D71C2313yes—
359C42×D71C2313yes—
360C42×D71C2313yes—
361C42×D71C2313yes—
362C42×D71C2313yes—
363C42×D71C2313yes—
364C42×D71C23112yes—
365C42×D71C2316yes—
366C2×#41×C71C2311yescharacteristic
367C2×#41×C71C2313yes—
368C22×Q8×C71C2312yes—
369C4⋊Q8×C71C2313yes—
370C4⋊Q8×C71C2313yes—
371#126×C71C23112yes—
372#125×C71C2316yes—
373#125×C71C2316yes—
374#124×C71C2316yes—
375#123×C71C23112yes—
376C22⋊Q8×C71C2316yes—
377C22⋊Q8×C71C2316yes—
378C22⋊Q8×C71C2316yes—
379#121×C71C2316yes—
380C4×Q8×C71C2311yescharacteristic
381C4×Q8×C71C2312yes—
382C4×Q8×C71C2316yes—
383C4×Q8×C71C2316yes—
384C4×Q8×C71C2311yescharacteristic
385C4×Q8×C71C2313yes—
386C4×Q8×C71C2313yes—
387C4×D4×C71C2316yes—
388C4×D4×C71C2313yes—
389C4×D4×C71C2313yes—
390C4×D4×C71C2313yes—
391C4×D4×C71C2311yescharacteristic
392C4×D4×C71C2316yes—
393#117×C71C2313yes—
394#117×C71C2316yes—
395#117×C71C2313yes—
396#117×C71C2316yes—
397C2×C4⋊C4×C71C2316yes—
398C2×C42×C71C2316yes—
399C2×C42×C71C2313yes—
400C23×D71C2413yes—
401#11765866—24no—
402#11765866—28no—
403#11765866—224no—
404#11765866—412no—
405#11765865—224no—
406#11765865—212no—
407#11765865—224no—
408#11765865—46no—
409#11765865—412no—
410#11765865—412no—
411#11765864—212no—
412C2×Dic142C2416yes—
413C2×Dic142C2411yescharacteristic
414C2×Dic142C2416yes—
415C2×Dic142C2416yes—
416C2×Dic142C2413yes—
417Q8×D71—224no—
418Q8×D71#4118yescomplemented
419C2×D284C2413yes—
420C2×D284C2416yes—
421C2×D284C2416yes—
422C2×D284C2413yes—
423C2×D284C2416yes—
424C2×D284C2416yes—
425C2×D284C24112yes—
426C2×C22⋊D71C2416yes—
427C2×C22⋊D71C2412yes—
428C2×C22⋊D71C2416yes—
429C2×C22⋊D71C24112yes—
430C2×C22⋊D71C2416yes—
431C2×C22⋊D71C2416yes—
432C2×C22⋊D71C2416yes—
433D4×D71—212no—
434C22×Dic71C2413yes—
435C22×Dic71C2413yes—
436C22×Dic71C2413yes—
437C2×C4×D71—212no—
438C2×C4×D71—46no—
439C2×C4×D71—46no—
440C2×C4×D71C2411yescharacteristic
441C2×C4×D71C2411yescharacteristic
442C2×C4×D71C2411yescharacteristic
443C2×C4×D71C2413yes—
444C2×C4×D71C2413yes—
445C2×C4×D71C2413yes—
446C2×C4×D71C2413yes—
447C2×C4×D71C24112yes—
448C2×C4×D71C2416yes—
449C2×C4×D71C2416yes—
450C2×C4×D71C2413yes—
451C2×C4×D71C2413yes—
452C2×C4×D71C2413yes—
453C2×C4×D71C2413yes—
454C2×C4×D71C2416yes—
455C2×C4×D71C24112yes—
456C2×C4×D71C2413yes—
457C4⋊Dic71C2413yes—
458C4⋊Dic71C2416yes—
459C4⋊Dic71C2413yes—
460C4⋊Dic71C2416yes—
461C4⋊Dic71C2413yes—
462C4⋊Dic71C2416yes—
463C4⋊Dic71C24112yes—
464C4⋊Dic71C2411yescharacteristic
465C4⋊Dic71C2412yes—
466C4⋊Dic71C2412yes—
467Dic71⋊C4C2416yes—
468Dic71⋊C4C2416yes—
469Dic71⋊C4C2416yes—
470Dic71⋊C4C2416yes—
471Dic71⋊C4C2412yes—
472Dic71⋊C4C2416yes—
473Dic71⋊C4C2412yes—
474Dic71⋊C4C2416yes—
475Dic71⋊C4C2416yes—
476Dic71⋊C4C2416yes—
477Dic71⋊C4C2416yes—
478Dic71⋊C4C2416yes—
479C22⋊Dic71C2416yes—
480C22⋊Dic71C2416yes—
481C22⋊Dic71C2412yes—
482C22⋊Dic71C2412yes—
483C22⋊Dic71C2412yes—
484C22⋊Dic71C2416yes—
485(C2×D71)⋊C4C2416yes—
486(C2×D71)⋊C4C2416yes—
487(C2×D71)⋊C4C2412yes—
488(C2×D71)⋊C4C2416yes—
489(C2×D71)⋊C4C2416yes—
490(C2×D71)⋊C4C2416yes—
491(C2×D71)⋊C4C2416yes—
492(C2×D71)⋊C4C24112yes—
493(C2×D71)⋊C4C2416yes—
494(C2×D71)⋊C4C2416yes—
495(C2×D71)⋊C4C2416yes—
496(C2×D71)⋊C4C2416yes—
497(C2×D71)⋊C4C2416yes—
498(C2×D71)⋊C4C24112yes—
499(C2×D71)⋊C4C24112yes—
500C4×Dic71C2413yes—
501C4×Dic71C2411yescharacteristic
502C4×Dic71C2411yescharacteristic
503C4×Dic71C2411yescharacteristic
504C4×Dic71C2412yes—
505C4×Dic71C2413yes—
506C4×Dic71C2413yes—
507C4×Dic71C2413yes—
508C4×Dic71C2413yes—
509C4×Dic71C2413yes—
510C4×Dic71C2413yes—
511C4×Dic71C2413yes—
512C4×Dic71C2413yes—
513C4×Dic71C24112yes—
514C4×Dic71C2416yes—
515C4×Dic71C2416yes—
516C4×Dic71C24112yes—
517#41×C71—24no—
518#41×C71—46no—
519C2×Q8×C71—28no—
520C2×Q8×C71C2416yes—
521C2×Q8×C71C2413yes—
522C2×Q8×C71C2411yescharacteristic
523C2×D4×C71C2413yes—
524C2×D4×C71C2411yescharacteristic
525C2×D4×C71C2416yes—
526C22×C4×C71C2413yes—
527C22×C4×C71C2413yes—
528C22×C4×C71C2413yes—
529C22×C4×C71C2412yes—
530C22×C4×C71C2416yes—
531C22×C4×C71C2416yes—
532C4⋊C4×C71C2413yes—
533C4⋊C4×C71C2416yes—
534C4⋊C4×C71C24112yes—
535C4⋊C4×C71C2411yescharacteristic
536C4⋊C4×C71C2413yes—
537C4⋊C4×C71C2416yes—
538C4⋊C4×C71C2413yes—
539C4⋊C4×C71C2416yes—
540C4⋊C4×C71C2416yes—
541C4⋊C4×C71C2416yes—
542C22⋊C4×C71C2412yes—
543C22⋊C4×C71C2416yes—
544C22⋊C4×C71C2416yes—
545C22⋊C4×C71C2416yes—
546C22⋊C4×C71C24112yes—
547C42×C71C2413yes—
548C42×C71C2411yescharacteristic
549C42×C71C2413yes—
550C42×C71C2416yes—
551C42×C71C2416yes—
552C42×C71C2413yes—
553C42×C71C2416yes—
554C23×C71C2513yes—
555C23×C71C2512yes—
556C22×D71—26no—
557C22×D71—43no—
558C22×D71—43no—
559C22×D71C2513yes—
560C22×D71C2516yes—
561C22×D71C2511yescharacteristic
562Q8×C71—212no—
563Q8×C71—26no—
564Q8×C71C2×#4114yes—
565D4×C71—26no—
566D4×C71—22no—
567D4×C71—46no—
568C2×C4×C71—212no—
569C2×C4×C71—26no—
570C2×C4×C71—26no—
571C2×C4×C71—26no—
572C2×C4×C71—24no—
573C2×C4×C71—46no—
574C2×C4×C71C2512yes—
575C2×C4×C71C2511yescharacteristic
576C2×C4×C71C2513yes—
577C2×C4×C71C2513yes—
578C2×C4×C71C2516yes—
579C2×C4×C71C2516yes—
580C2×C4×C71C2513yes—
581C2×C4×C71C2511yescharacteristic
582C2×C4×C71C2511yescharacteristic
583C22⋊D71—24no—
584C22⋊D71—212no—
585C22⋊D71—212no—
586C22⋊D71—46no—
587C22⋊D71—46no—
588C22⋊D71—412no—
589C22⋊D71—46no—
590C2×Dic71—26no—
591C2×Dic71—43no—
592C2×Dic71—43no—
593C2×Dic71C2511yescharacteristic
594C2×Dic71C2511yescharacteristic
595C2×Dic71C2511yescharacteristic
596C2×Dic71C2513yes—
597C2×Dic71C2516yes—
598C2×Dic71C2512yes—
599C2×Dic71C2513yes—
600C2×Dic71C2512yes—
601C2×Dic71C2513yes—
602D284—212no—
603D284—26no—
604D284—212no—
605D284—26no—
606D284—46no—
607D284—46no—
608D284—412no—
609C4×D71—22no—
610C4×D71—26no—
611C4×D71—212no—
612C4×D71—22no—
613C4×D71—22no—
614C4×D71—26no—
615C4×D71—26no—
616C4×D71—212no—
617C4×D71—26no—
618C4×D71—224no—
619C4×D71—43no—
620C4×D71—43no—
621C4×D71—43no—
622C4×D71—43no—
623C4×D71—46no—
624C4×D71—412no—
625C4×D71C2×#41112yes—
626Dic142—22no—
627Dic142—212no—
628Dic142—46no—
629Dic142—46no—
630Dic142C2×#41112yes—
631C22×C71—23no—
632C22×C71—22no—
633C22×C71—23no—
634C22×C71—23no—
635C22×C71—22no—
636C22×C71—22no—
637C22×C71C2611yescharacteristic
638C2×D71—21no—
639C2×D71—21no—
640C2×D71—26no—
641C2×D71—23no—
642C2×D71—23no—
643C2×D71—23no—
644C2×D71—26no—
645C2×D71—26no—
646C2×D71—412no—
647C2×D71C22×#4112yes—
648C4×C71—26no—
649C4×C71—21no—
650C4×C71—22no—
651C4×C71—23no—
652C4×C71—23no—
653C4×C71—26no—
654C4×C71C22×#4116yes—
655C4×C71#58512yes—
656C4×C71#58512yes—
657Dic71—22no—
658Dic71—21no—
659Dic71—22no—
660Dic71—26no—
661Dic71—23no—
662Dic71—23no—
663Dic71—21no—
664Dic71—21no—
665Dic71C22×#4116yes—
666#62793—711nomaximal, Sylow
667C2×C71—43no—
668C2×C71—42no—
669C2×C71C23×#4111yescharacteristic
670C2×C71C2×#58511yescharacteristic
671C2×C71C2×#58511yescharacteristic
672D71—22no—
673D71—46no—
674D71—43no—
675#3524—716no—
676#3524—712no—
677#3518—713no—
678#3518—711no—
679#3517—711no—
680#3517—713no—
681#3506—713no—
682#3506—713no—
683#3502—711no—
684#3497—711no—
685#3493—716no—
686#3487—712no—
687#3483—711no—
688#3483—713no—
689#3482—713no—
690#3482D7111yescharacteristic, complemented
691#3480—716no—
692#3480—712no—
693#3460—716no—
694#3444—713no—
695#3444—713no—
696C4×2−1+4—712no—
697C2×C4×#41—711no—
698C71#6279311yescharacteristic, complemented, Sylow
699C2×2−1+4—712no—
700C22×#41—711no—
701#559—716no—
702#559—7112no—
703#559—716no—
704Q82—711no—
705Q82—713no—
706#557—713no—
707#557—716no—
708#557—712no—
709#557C2×D7111yescharacteristic, complemented
710#556—713no—
711#556—7112no—
712#556—716no—
713#556—716no—
714#556—716no—
715#556C2×D7113yescomplemented
716#555—716no—
717#555—713no—
718#555—713no—
719#555—716no—
720#555—7112no—
721#555—716no—
722#553—7112no—
723#553—716no—
724#553—7112no—
725#553—716no—
726#553—716no—
727#553—716no—
728#552—7112no—
729#552—716no—
730#552C2×D7116yescomplemented
731#550—712no—
732#550—716no—
733#550—716no—
734#550—712no—
735#550—711no—
736#550—713no—
737#550—716no—
738#550—713no—
739#550—713no—
740D4×Q8—713no—
741D4×Q8C2×D7111yescharacteristic, complemented
742#548—712no—
743#548—712no—
744#548—716no—
745#548—716no—
746#548—716no—
747#548C2×D7112yes—
748#547—713no—
749#547—716no—
750#547C2×D7113yescomplemented
751#544—716no—
752#542—7112no—
753#542—716no—
754#542—716no—
755#540—716no—
756#540—7112no—
757#540—716no—
758#538—7112no—
759#538—7112no—
760#537—716no—
761#535—716no—
762#535—716no—
763#533—713no—
764#533—713no—
765#533—713no—
766#533—713no—
767#533—713no—
768#533C2×D7113yescomplemented
769#532—713no—
770#532—713no—
771#532—713no—
772#532—713no—
773#532—713no—
774#532—7112no—
775#532—716no—
776#532—713no—
777#532—716no—
778#529—716no—
779#529—716no—
780#529—716no—
781#529—716no—
782#529—713no—
783#529—716no—
784#529—713no—
785#529—716no—
786#529—711no—
787#529—716no—
788#529—713no—
789#529—716no—
790#529—716no—
791#529—716no—
792#529—7112no—
793#529C2×D7116yescomplemented
794#525—713no—
795#525—716no—
796#525—716no—
797#525—716no—
798#525—716no—
799#525—716no—
800#525—713no—
801#520—716no—
802#520—712no—
803#520—716no—
804#520—716no—
805#519—712no—
806#519—712no—
807#519—716no—
808C4×#41—711no—
809C4×#41—711no—
810C4×#41—711no—
811C4×#41—716no—
812C4×#41—712no—
813C4×#41—716no—
814C4×#41—713no—
815C4×#41—713no—
816C4×#41—713no—
817C4×#41—716no—
818C4×#41—713no—
819C4×#41—716no—
820C4×#41—716no—
821C4×#41—716no—
822C4×#41—713no—
823C4×#41C2×D7111yescharacteristic
824C4×#41C2×D7113yescomplemented
825C2×C4×Q8—711no—
826C2×C4×Q8—711no—
827C2×C4×Q8—716no—
828C2×C4×Q8C2×D7112yescomplemented
829C2×C4×D4—713no—
830C2×C4×D4—713no—
831C2×#117—713no—
832C22×C42—713no—
8332−1+4—14216no—
834C2×#41—716no—
835C2×#41—711no—
836C2×#41—716no—
837C2×#41—712no—
838C2×#41—713no—
839C2×#41—716no—
840C2×#41—716no—
841C2×#41—713no—
842C2×#41—713no—
843C2×#41—716no—
844C2×#41—716no—
845C2×#41—1428no—
846C2×#41C22×D7111yescharacteristic
847C2×#41C22×D7113yes—
848C22×Q8—711no—
849C22×Q8—716no—
850C22×Q8C22×D7112yes—
851C22×D4—713no—
852C23×C4—713no—
853C23×C4—713no—
854C23×C4—713no—
855C4⋊Q8—713no—
856C4⋊Q8—713no—
857C4⋊Q8—713no—
858C4⋊Q8—7112no—
859C4⋊Q8—716no—
860C4⋊Q8—713no—
861C4⋊Q8—716no—
862C4⋊Q8C22×D7113yes—
863C4⋊Q8C22×D7113yes—
864#127—713no—
865#127—716no—
866#127—7112no—
867#127—713no—
868#127—716no—
869#126—716no—
870#126—716no—
871#126—7112no—
872#126—7112no—
873#126—7112no—
874#126—712no—
875#126—716no—
876#126—7112no—
877#126C22×D71112yes—
878#125—711no—
879#125—713no—
880#125—716no—
881#125—716no—
882#125—716no—
883#125—7112no—
884#125—716no—
885#125C22×D7116yes—
886#125C22×D7116yes—
887#124—713no—
888#124—716no—
889#124—716no—
890#124—711no—
891#124—716no—
892#124—716no—
893#124—7112no—
894#124—7112no—
895#124—7112no—
896#124—7112no—
897#124—716no—
898#124—7112no—
899#124C22×D7116yes—
900#123—716no—
901#123—716no—
902#123—716no—
903#123—7112no—
904#123—7112no—
905#123—7112no—
906#123—712no—
907#123—716no—
908#123—7112no—
909#123—716no—
910#123—7112no—
911#123C22×D71112yes—
912C22⋊Q8—713no—
913C22⋊Q8—713no—
914C22⋊Q8—716no—
915C22⋊Q8—716no—
916C22⋊Q8—711no—
917C22⋊Q8—716no—
918C22⋊Q8—716no—
919C22⋊Q8—716no—
920C22⋊Q8—713no—
921C22⋊Q8—716no—
922C22⋊Q8—7112no—
923C22⋊Q8—716no—
924C22⋊Q8—716no—
925C22⋊Q8C22×D7116yes—
926C22⋊Q8C22×D7116yes—
927C22⋊Q8C22×D7116yes—
928#121—711no—
929#121—716no—
930#121—716no—
931#121—713no—
932#121—716no—
933#121—7112no—
934#121—716no—
935#121—716no—
936#121—716no—
937#121—716no—
938#121—7112no—
939#121—713no—
940#121—716no—
941#121—716no—
942#121—716no—
943#121—713no—
944#121—716no—
945#121—716no—
946#121—7112no—
947#121—716no—
948#121—716no—
949#121—7112no—
950#121—7112no—
951#121—7112no—
952#121—7112no—
953#121C22×D7116yes—
954#120—716no—
955#120—716no—
956#120—7112no—
957C4×Q8—711no—
958C4×Q8—711no—
959C4×Q8—716no—
960C4×Q8—716no—
961C4×Q8—712no—
962C4×Q8—716no—
963C4×Q8—713no—
964C4×Q8—713no—
965C4×Q8—716no—
966C4×Q8—7112no—
967C4×Q8—716no—
968C4×Q8—716no—
969C4×Q8—713no—
970C4×Q8—716no—
971C4×Q8—713no—
972C4×Q8—711no—
973C4×Q8—716no—
974C4×Q8—716no—
975C4×Q8—713no—
976C4×Q8—716no—
977C4×Q8—716no—
978C4×Q8C22×D7111yescharacteristic
979C4×Q8C22×D7116yes—
980C4×Q8C22×D7111yescharacteristic
981C4×Q8C22×D7112yes—
982C4×Q8C22×D7116yes—
983C4×Q8C22×D7113yes—
984C4×Q8C22×D7113yes—
985C4×D4—713no—
986C4×D4—713no—
987C4×D4—716no—
988C4×D4—716no—
989C4×D4—712no—
990C4×D4—716no—
991C4×D4—716no—
992C4×D4—716no—
993C4×D4—7112no—
994C4×D4—716no—
995C4×D4—716no—
996C4×D4—716no—
997C4×D4—716no—
998C4×D4—716no—
999C4×D4—716no—
1000C4×D4—713no—
1001C4×D4—713no—
1002C4×D4—7112no—
1003C4×D4—716no—
1004C4×D4—716no—
1005C4×D4—7112no—
1006C4×D4—716no—
1007C4×D4—716no—
1008C4×D4—716no—
1009C4×D4—716no—
1010C4×D4—716no—
1011C4×D4—7112no—
1012C4×D4—7112no—
1013C4×D4—713no—
1014C4×D4—713no—
1015C4×D4—716no—
1016C4×D4—716no—
1017C4×D4—713no—
1018C4×D4—716no—
1019C4×D4—716no—
1020C4×D4—7112no—
1021C4×D4—716no—
1022C4×D4—716no—
1023C4×D4—713no—
1024C4×D4C22×D7113yes—
1025C4×D4C22×D7113yes—
1026C4×D4C22×D7111yescharacteristic
1027C4×D4C22×D7116yes—
1028C4×D4C22×D7116yes—
1029C4×D4C22×D7113yes—
1030#117—713no—
1031#117—712no—
1032#117—716no—
1033#117—716no—
1034#117—713no—
1035#117—713no—
1036#117—713no—
1037#117—716no—
1038#117—7112no—
1039#117—716no—
1040#117—716no—
1041#117—7112no—
1042#117—716no—
1043#117—716no—
1044#117—716no—
1045#117—716no—
1046#117—716no—
1047#117—7112no—
1048#117—716no—
1049#117—716no—
1050#117C22×D7113yes—
1051#117C22×D7116yes—
1052#117C22×D7113yes—
1053#117C22×D7116yes—
1054C2×C4⋊C4—713no—
1055C2×C4⋊C4—713no—
1056C2×C4⋊C4—7112no—
1057C2×C4⋊C4—716no—
1058C2×C4⋊C4C22×D7116yes—
1059C2×C22⋊C4—716no—
1060C2×C42—713no—
1061C2×C42—713no—
1062C2×C42—713no—
1063C2×C42—713no—
1064C2×C42—713no—
1065C2×C42—713no—
1066C2×C42—7112no—
1067C2×C42—716no—
1068C2×C42—713no—
1069C2×C42—713no—
1070C2×C42—713no—
1071C2×C42—713no—
1072C2×C42—711no—
1073C2×C42C22×D7116yes—
1074C2×C42C22×D7113yes—
1075C24—713no—
1076#41—24no—
1077#41—46no—
1078#41—2846no—
1079#41—28412no—
1080#41—28412no—
1081#41—28412no—
1082#41—14224no—
1083#41—14212no—
1084#41—14224no—
1085#41—14224no—
1086#41—14212no—
1087#41—1424no—
1088#41—1428no—
1089C2×Q8—28no—
1090C2×Q8—718no—
1091C2×Q8—716no—
1092C2×Q8—716no—
1093C2×Q8—713no—
1094C2×Q8—716no—
1095C2×Q8—711no—
1096C2×Q8—14224no—
1097C2×Q8C23×D7116yes—
1098C2×Q8C23×D7113yes—
1099C2×Q8C23×D7111yescharacteristic
1100C2×D4—716no—
1101C2×D4—716no—
1102C2×D4—7112no—
1103C2×D4—716no—
1104C2×D4—712no—
1105C2×D4—716no—
1106C2×D4—716no—
1107C2×D4—7112no—
1108C2×D4—716no—
1109C2×D4—716no—
1110C2×D4—716no—
1111C2×D4—713no—
1112C2×D4—716no—
1113C2×D4—713no—
1114C2×D4—14212no—
1115C2×D4C23×D7113yes—
1116C2×D4C23×D7111yescharacteristic
1117C2×D4C23×D7116yes—
1118C22×C4—2846no—
1119C22×C4—2846no—
1120C22×C4—713no—
1121C22×C4—713no—
1122C22×C4—713no—
1123C22×C4—713no—
1124C22×C4—713no—
1125C22×C4—713no—
1126C22×C4—7112no—
1127C22×C4—716no—
1128C22×C4—713no—
1129C22×C4—713no—
1130C22×C4—711no—
1131C22×C4—711no—
1132C22×C4—713no—
1133C22×C4—713no—
1134C22×C4—713no—
1135C22×C4—7112no—
1136C22×C4—716no—
1137C22×C4—711no—
1138C22×C4—716no—
1139C22×C4—713no—
1140C22×C4—14212no—
1141C22×C4C23×D7113yes—
1142C22×C4C23×D7113yes—
1143C22×C4C23×D7116yes—
1144C22×C4C23×D7113yes—
1145C22×C4C23×D7112yes—
1146C22×C4C23×D7116yes—
1147C4⋊C4—716no—
1148C4⋊C4—716no—
1149C4⋊C4—716no—
1150C4⋊C4—716no—
1151C4⋊C4—712no—
1152C4⋊C4—716no—
1153C4⋊C4—712no—
1154C4⋊C4—716no—
1155C4⋊C4—716no—
1156C4⋊C4—716no—
1157C4⋊C4—716no—
1158C4⋊C4—716no—
1159C4⋊C4—713no—
1160C4⋊C4—716no—
1161C4⋊C4—713no—
1162C4⋊C4—711no—
1163C4⋊C4—716no—
1164C4⋊C4—713no—
1165C4⋊C4—716no—
1166C4⋊C4—712no—
1167C4⋊C4—712no—
1168C4⋊C4—7112no—
1169C4⋊C4C23×D7113yes—
1170C4⋊C4C23×D7116yes—
1171C4⋊C4C23×D71112yes—
1172C4⋊C4C23×D7113yes—
1173C4⋊C4C23×D7113yes—
1174C4⋊C4C23×D7116yes—
1175C4⋊C4C23×D7111yescharacteristic
1176C4⋊C4C23×D7116yes—
1177C4⋊C4C23×D7116yes—
1178C4⋊C4C23×D7116yes—
1179C22⋊C4—716no—
1180C22⋊C4—712no—
1181C22⋊C4—716no—
1182C22⋊C4—712no—
1183C22⋊C4—712no—
1184C22⋊C4—716no—
1185C22⋊C4—716no—
1186C22⋊C4—716no—
1187C22⋊C4—716no—
1188C22⋊C4—712no—
1189C22⋊C4—716no—
1190C22⋊C4—716no—
1191C22⋊C4—7112no—
1192C22⋊C4—716no—
1193C22⋊C4—716no—
1194C22⋊C4—716no—
1195C22⋊C4—716no—
1196C22⋊C4—716no—
1197C22⋊C4—7112no—
1198C22⋊C4—716no—
1199C22⋊C4—7112no—
1200C22⋊C4C23×D7116yes—
1201C22⋊C4C23×D7112yes—
1202C22⋊C4C23×D71112yes—
1203C22⋊C4C23×D7116yes—
1204C22⋊C4C23×D7116yes—
1205C42—711no—
1206C42—711no—
1207C42—713no—
1208C42—713no—
1209C42—713no—
1210C42—713no—
1211C42—713no—
1212C42—713no—
1213C42—713no—
1214C42—713no—
1215C42—7112no—
1216C42—716no—
1217C42—7112no—
1218C42—716no—
1219C42—711no—
1220C42—713no—
1221C42—712no—
1222C42C23×D7113yes—
1223C42C23×D7113yes—
1224C42C23×D7116yes—
1225C42C23×D7116yes—
1226C42C23×D7113yes—
1227C42C23×D7111yescharacteristic
1228C42C23×D7116yes—
1229C23—2843no—
1230C23—2843no—
1231C23—711no—
1232C23—713no—
1233C23—716no—
1234C23—1426no—
1235C23C24×D7112yes—
1236C23C24×D7113yes—
1237Q8—212no—
1238Q8—26no—
1239Q8—2846no—
1240Q8—2846no—
1241Q8—7112no—
1242Q8—14212no—
1243Q8—1422no—
1244Q8#41×D7114yes—
1245D4—26no—
1246D4—22no—
1247D4—46no—
1248D4—28412no—
1249D4—2846no—
1250D4—2846no—
1251D4—2846no—
1252D4—2846no—
1253D4—28412no—
1254D4—2846no—
1255D4—14212no—
1256D4—14212no—
1257D4—14212no—
1258D4—1424no—
1259D4—1426no—
1260D4—14212no—
1261D4—1426no—
1262C2×C4—26no—
1263C2×C4—212no—
1264C2×C4—26no—
1265C2×C4—26no—
1266C2×C4—24no—
1267C2×C4—46no—
1268C2×C4—2843no—
1269C2×C4—2843no—
1270C2×C4—2843no—
1271C2×C4—2843no—
1272C2×C4—2846no—
1273C2×C4—28412no—
1274C2×C4—2843no—
1275C2×C4—2843no—
1276C2×C4—713no—
1277C2×C4—7112no—
1278C2×C4—711no—
1279C2×C4—711no—
1280C2×C4—713no—
1281C2×C4—711no—
1282C2×C4—716no—
1283C2×C4—712no—
1284C2×C4—713no—
1285C2×C4—712no—
1286C2×C4—1426no—
1287C2×C4—14224no—
1288C2×C4—1422no—
1289C2×C4—1426no—
1290C2×C4—1426no—
1291C2×C4—14212no—
1292C2×C4—1422no—
1293C2×C4—1426no—
1294C2×C4—1422no—
1295C2×C4—1426no—
1296C2×C4—14212no—
1297C2×C4C24×D7111yescharacteristic
1298C2×C4C24×D7113yes—
1299C2×C4C24×D7116yes—
1300C2×C4C24×D7113yes—
1301C2×C4C24×D7116yes—
1302C2×C4C24×D7112yes—
1303C2×C4C24×D7113yes—
1304C2×C4C24×D7111yescharacteristic
1305C2×C4C24×D7111yescharacteristic
1306C22—22no—
1307C22—23no—
1308C22—23no—
1309C22—22no—
1310C22—23no—
1311C22—22no—
1312C22—28412no—
1313C22—712no—
1314C22—1426no—
1315C22—1423no—
1316C22—1426no—
1317C22—1423no—
1318C22—1423no—
1319C22—1426no—
1320C22—1421no—
1321C22—1421no—
1322C22C25×D7111yescharacteristic
1323C4—21no—
1324C4—26no—
1325C4—23no—
1326C4—26no—
1327C4—23no—
1328C4—22no—
1329C4—716no—
1330C4—1421no—
1331C4—1422no—
1332C4—1421no—
1333C4—1423no—
1334C4—1422no—
1335C4—1421no—
1336C4—1423no—
1337C4—1426no—
1338C4C2×#41×D7116yes—
1339C4#1798683512yes—
1340C4#1798683612yes—
1341C2—43no—
1342C2—42no—
1343C2—2843no—
1344C2—2846no—
1345C2—1422no—
1346C2C22×#41×D7111yescharacteristic
1347C2C2×#1798683511yescharacteristic
1348C2C2×#1798683611yescharacteristic
subgroupG/H
centerC2×C4C24×D71
commutator, socle, cosocleC22×C71C26
FrattiniC22C25×D71
FittingC71×#3482C2
hypercenter#3482D71
hypocenterC71#62793
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C2×C4 ◁ #3482

Complements

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

NH ≅ G/Ntype
1. #22602450C2semidirect
2. #22602446C2semidirect
3. #22602354C2semidirect
4. #22602352C2semidirect
5. #22602347C2semidirect
6. #22602345C2semidirect
7. #22602193C2semidirect
8. #22602190C2semidirect
9. #22602144C2semidirect
10. #22602110C2semidirect
11. #22602058C2semidirect
12. #22601997C2semidirect
13. #22601966C2semidirect
14. #22601966C2semidirect
15. #22601958C2semidirect
16. #22601935C2semidirect
17. #22601931C2semidirect
18. #22601761C2semidirect
19. #22601637C2semidirect
20. #22601633C2semidirect
21. C4×#14556176C2semidirect
22. C4×#41×D71C2semidirect
23. C71×#3482C2semidirect
26. #17986734C22semidirect
27. #17986733C22semidirect
28. #17986731C22semidirect
29. Q8×Dic142C22semidirect
30. Q8×Dic142C22semidirect
31. #17986728C22semidirect
32. #17986726C22semidirect
33. #17986724C22semidirect
34. #17986723C22semidirect
35. #17986722C22semidirect
36. #17986720C22semidirect
37. #17986720C22semidirect
38. #17986716C22semidirect
39. #17986714C22semidirect
40. #17986714C22semidirect
41. #17986714C22semidirect
42. #17986712C22semidirect
43. #17986712C22semidirect
44. #17986712C22semidirect
45. #17986702C22semidirect
46. #17986700C22semidirect
47. #17986697C22semidirect
48. #17986697C22semidirect
49. #17986696C22semidirect
50. #17986694C22semidirect
51. #17986683C22semidirect
52. #17986681C22semidirect
54. #17986671C22semidirect
55. #17986671C22semidirect
57. #17986670C22semidirect
58. #17986670C22semidirect
60. #17986668C22semidirect
62. #17986664C22semidirect
64. #17986660C22semidirect
66. #17986659C22semidirect
68. #17986652C22semidirect
69. #17986651C22semidirect
71. #17986622C22semidirect
72. #17986618C22semidirect
73. #17986615C22semidirect
74. #17986605C22semidirect
75. #17986602C22semidirect
76. #17986601C22semidirect
83. #17986554C22semidirect
85. #17986553C22semidirect
86. #17986552C22semidirect
88. #17986550C22semidirect
89. #17986549C22semidirect
90. #17986549C22semidirect
92. #17986546C22semidirect
93. #17986546C22semidirect
94. #17986546C22semidirect
95. #17986545C22semidirect
97. #17986536C22semidirect
98. #17986536C22semidirect
99. #17986536C22semidirect
100. #17986535C22semidirect
101. #17986535C22semidirect
103. #17986534C22semidirect
105. #17986531C22semidirect
106. #17986529C22semidirect
107. #17986529C22semidirect
109. #17986527C22semidirect
110. #17986527C22semidirect
119. #17986481C22semidirect
121. #17986480C22semidirect
122. #17986477C22semidirect
124. #17986475C22semidirect
129. C4×#11765866C22semidirect
130. C4×#11765866C22semidirect
133. C4×#11765865C22semidirect
134. C4×#11765865C22semidirect
135. C4×#11765865C22semidirect
137. #17986467C22semidirect
142. C4×Q8×D71C22semidirect
147. #557×C71C22semidirect
148. #556×C71C22semidirect
149. #552×C71C22semidirect
150. D4×Q8×C71C22semidirect
152. #547×C71C22semidirect
153. #533×C71C22semidirect
154. #529×C71C22semidirect
156. C4×#41×C71C22semidirect
157. C2×C4×Q8×C71C22semidirect
418. Q8×D71#41semidirect
690. #3482D71semidirect
698. C71#62793semidirect
709. #557C2×D71semidirect
715. #556C2×D71semidirect
730. #552C2×D71semidirect
741. D4×Q8C2×D71semidirect
750. #547C2×D71semidirect
768. #533C2×D71semidirect
793. #529C2×D71semidirect
824. C4×#41C2×D71semidirect
828. C2×C4×Q8C2×D71semidirect

Maximal subgroups

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

subgroupindex
#226024502
#226024462
#226023542
#226023522
#226023472
#226023452
#226021932
#226021902
#226021442
#226021102
#226020582
#226019972
#226019662
#226019582
#226019352
#226019312
#226017612
#226016372
#226016332
C4×#145561762
C4×#41×D712
C71×#34822
#6279371