Finite Group Databasebeta

← #32905678

Subgroups — #32905678

Order 18176.

7094 conjugacy classes of subgroups.

The subgroup lattice has 1344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22602437C211yesmaximal, characteristic, complemented
2#22602435C213yesmaximal, complemented
3#22602422C213yesmaximal, complemented
4#22602420C211yesmaximal, characteristic, complemented
5#22602324C216yesmaximal, complemented
6#22602322C212yesmaximal, complemented
7#22602197C213yesmaximal, complemented
8#22602195C213yesmaximal, complemented
9#22602144C211yesmaximal, characteristic, complemented
10#22602105C211yesmaximal, characteristic, complemented
11#22602044C216yesmaximal, complemented
12#22601986C212yesmaximal, complemented
13#22601962C212yesmaximal, complemented
14#22601953C216yesmaximal, complemented
15#22601937C213yesmaximal, complemented
16Q8×#11765865C211yesmaximal, characteristic, complemented
17#41×Dic142C213yesmaximal, complemented
18#22601765C216yesmaximal, complemented
19#22601635C213yesmaximal, complemented
20#22601633C213yesmaximal, complemented
21C4×#14556175C212yesmaximal, complemented
22C2×C4×Q8×D71C211yesmaximal, characteristic, complemented
23C71×#3480C211yesmaximal, characteristic, complemented
24C2×#14556175C2212yes—
25C22×Q8×D71C2211yescharacteristic
26#17986735C2213yescomplemented
27#17986731C2216yescomplemented
28Q8×Dic142C2211yescharacteristic, complemented
29Q8×Dic142C2213yescomplemented
30#17986728C2212yescomplemented
31#17986728C2213yescomplemented
32#17986727C2213yescomplemented
33#17986726C2216yescomplemented
34#17986725C2216yescomplemented
35#17986724C2213yescomplemented
36#17986723C2213yescomplemented
37#17986719C2216yescomplemented
38#17986718C2216yescomplemented
39#17986718C2216yescomplemented
40#17986716C22112yescomplemented
41#17986709C2213yescomplemented
42#17986708C22112yes—
43#17986708C2216yescomplemented
44#17986706C2216yes—
45#17986706C2213yescomplemented
46#17986704C2216yes—
47#17986701C2216yes—
48#17986692C22112yes—
49#17986691C2216yescomplemented
50#17986688C2216yes—
51#17986688C2216yescomplemented
52#17986687C2216yes—
53#17986686C22112yescomplemented
54#17986685C22112yes—
55#17986669C2213yescomplemented
56Q8×D284C2212yes—
57Q8×D284C2211yescharacteristic, complemented
58D4×Dic142C2216yes—
59D4×Dic142C2213yescomplemented
60Q8×C22⋊D71C2212yes—
61#17986662C2216yes—
62#17986657C2216yes—
63#17986656C2212yes—
64#17986656C2212yescomplemented
65#17986655C2216yes—
66#17986655C2216yescomplemented
67#17986654C2216yes—
68#17986649C2216yes—
69#17986647C22112yes—
70#17986629C2216yes—
71#17986618C2216yescomplemented
72#17986617C22112yescomplemented
73#17986616C2216yescomplemented
74#17986612C2216yescomplemented
75#17986609C2216yescomplemented
76#17986606C22112yescomplemented
77#17986592C22112yes—
78#17986590C22112yes—
79#17986578C2216yes—
80#17986572C2216yes—
81#17986569C2216yes—
82#17986556C2213yes—
83#17986556C2216yescomplemented
84#17986554C2213yes—
85#17986554C2213yes—
86#17986553C2213yes—
87#17986553C2213yes—
88#17986553C2216yescomplemented
89#17986552C2213yes—
90#17986552C22112yescomplemented
91#17986547C2213yes—
92#17986547C2213yes—
93#17986546C2213yes—
94#17986546C2213yes—
95#17986545C2213yes—
96#17986536C2213yes—
97#17986536C2213yes—
98#17986531C2216yes—
99#17986531C2213yes—
100#17986531C2213yes—
101#17986531C2216yes—
102#17986531C2216yescomplemented
103#17986530C2216yes—
104#17986530C2216yes—
105#17986529C2216yes—
106#17986529C2216yes—
107#17986529C22112yescomplemented
108#17986528C2216yes—
109#17986528C2216yes—
110#17986527C2216yes—
111#17986527C2216yes—
112#17986511C2211yescharacteristic
113#17986509C2216yes—
114#17986509C2216yes—
115#17986508C2216yes—
116#17986508C2216yes—
117#17986506C2213yes—
118#17986482C2212yescomplemented
119#17986479C2216yes—
120#17986478C2216yes—
121#17986478C2216yescomplemented
122#17986476C2216yescomplemented
123#17986475C2212yes—
124#17986475C2212yescomplemented
125#41×Dic71C2216yes—
126C4×#11765865C2216yes—
127C4×#11765865C2213yes—
128C4×#11765865C2216yes—
129C4×#11765864C2216yes—
130C4×#11765864C2216yes—
131C4×#11765864C2216yescomplemented
132C2×Q8×Dic71C2211yescharacteristic
133C2×C4×Dic142C2213yes—
134C2×C4×Dic142C2216yescomplemented
135C2×#14556093C2213yes—
136C4×Q8×D71C2213yes—
137C4×Q8×D71C2211yescharacteristic
138C4×Q8×D71C2211yescharacteristic
139C4×Q8×D71C2211yescharacteristic
140C4×Q8×D71C2213yes—
141C4×Q8×D71C2213yes—
142C4×Q8×D71C2213yes—
143C4×Q8×D71C2211yescharacteristic
144C4×Q8×D71C2212yescomplemented
145C2×C4⋊C4×D71C2213yes—
146C2×C42×D71C2213yes—
147#559×C71C2213yescomplemented
148#557×C71C2211yescharacteristic, complemented
149#556×C71C2213yescomplemented
150#553×C71C2216yes—
151#550×C71C2211yescharacteristic, complemented
152#548×C71C2212yes—
153#532×C71C2213yes—
154#529×C71C2216yescomplemented
155C4×#41×C71C2213yes—
156C4×#41×C71C2212yescomplemented
157C2×C4×Q8×C71C2211yescharacteristic
158#14556175—216no—
159C2×#11765865C2316yes—
160C2×#11765865C2311yescharacteristic
161C2×#11765865C2316yes—
162C2×#11765864C2316yes—
163C2×#11765864C2316yes—
164C2×#11765864C2316yes—
165C22×Dic142C2313yes—
166C22×Dic142C2316yes—
167C2×Q8×D71—28no—
168C2×Q8×D71C2313yes—
169C2×Q8×D71C2311yescharacteristic
170C2×Q8×D71C2313yes—
171C2×Q8×D71C2312yes—
172C2×Q8×D71C2311yescharacteristic
173C22×C4×D71C2313yes—
174C22×C4×D71C2311yescharacteristic
175C22×C4×D71C2313yes—
176#14556128C2316yes—
177#14556128C2316yes—
178#14556128C2313yes—
179#14556128C2313yes—
180#14556127C23112yes—
181#14556127C2316yes—
182#14556127C23112yes—
183#14556127C2313yes—
184#14556127C2313yes—
185#14556126C2316yes—
186#14556126C2313yes—
187#14556124C2313yes—
188#14556123C23112yes—
189#14556123C2316yes—
190#14556123C2316yes—
191#14556121C23112yes—
192#14556121C23112yes—
193#14556121C2316yes—
194#14556121C23112yes—
195#14556121C2316yes—
196#14556121C23112yes—
197#14556120C23112yes—
198#14556120C2316yes—
199#14556119C23112yes—
200#14556119C23112yes—
201#14556119C2316yes—
202#14556119C2316yes—
203#14556119C2316yes—
204#14556119C2313yes—
205#14556119C2313yes—
206#14556118C23112yes—
207#14556118C2316yes—
208#14556118C23112yes—
209#14556118C2316yes—
210#14556117C2313yes—
211#14556115C2316yes—
212#14556115C2316yes—
213#14556115C2316yes—
214#14556115C2313yes—
215#14556114C23112yes—
216#14556114C2316yes—
217#14556114C2316yes—
218#14556113C2316yes—
219#14556113C2316yes—
220#14556112C23112yes—
221#14556112C2312yes—
222#14556110C2316yes—
223#14556110C23112yes—
224#14556110C23112yes—
225#14556110C23112yes—
226#14556110C2316yes—
227#14556109C23112yes—
228#14556109C2316yes—
229#14556108C2316yes—
230#14556108C2316yes—
231#14556108C2316yes—
232#14556108C2316yes—
233#14556108C2311yescharacteristic
234#14556108C2311yescharacteristic
235#14556107C2316yes—
236#14556107C2316yes—
237#14556107C23112yes—
238#14556107C2316yes—
239#14556107C2316yes—
240#14556106C23112yes—
241#14556106C2316yes—
242#14556106C2316yes—
243#14556105C23112yes—
244#14556105C23112yes—
245#14556105C23112yes—
246#14556105C23112yes—
247#14556105C23112yes—
248#14556105C2316yes—
249#14556105C2316yes—
250#14556104C2316yes—
251#14556104C2313yes—
252#14556104C2313yes—
253#14556103C2311yescharacteristic
254#14556103C2311yescharacteristic
255#14556101C2316yes—
256#14556101C2316yes—
257#14556100C23112yes—
258#14556100C2316yes—
259#14556100C2316yes—
260#14556099C2316yes—
261#14556099C2316yes—
262#14556099C2316yes—
263#14556099C2313yes—
264#14556099C2313yes—
265#14556098C2312yes—
266#14556096C2316yes—
267Q8×Dic71C2313yes—
268Q8×Dic71C2312yes—
269Q8×Dic71C2311yescharacteristic
270Q8×Dic71C2313yes—
271Q8×Dic71C2311yescharacteristic
272Q8×Dic71C2316yes—
273Q8×Dic71C2316yes—
274C4×Dic142C2316yes—
275C4×Dic142C2316yes—
276C4×Dic142C2313yes—
277C4×Dic142C23112yes—
278C4×Dic142C2316yes—
279C4×Dic142C2313yes—
280C4×Dic142C2316yes—
281C4×Dic142C2313yes—
282C4×Dic142C2316yes—
283C4×Dic142C2313yes—
284C4×Dic142C2316yes—
285C4×Dic142C2313yes—
286C4×Dic142C2316yes—
287C4×Dic142C2316yes—
288C4×Dic142C2316yes—
289C4×Dic142C2313yes—
290C4×Dic142C2316yes—
291#14556093C2316yes—
292#14556093C2316yes—
293#14556093C2313yes—
294#14556093C2316yes—
295#14556093C2313yes—
296#14556093C2316yes—
297#14556093C2316yes—
298#14556093C2313yes—
299#14556093C2316yes—
300#14556093C2313yes—
301C4×D284C2316yes—
302C4×D284C2316yes—
303C4×D284C2313yes—
304C4×D284C2313yes—
305C4×D284C2312yes—
306C4×D284C2312yes—
307D4×Dic71C2316yes—
308D4×Dic71C2316yes—
309D4×Dic71C23112yes—
310D4×Dic71C2316yes—
311D4×Dic71C2316yes—
312D4×Dic71C23112yes—
313D4×Dic71C2316yes—
314C4×C22⋊D71C2316yes—
315C4×C22⋊D71C2316yes—
316C4×C22⋊D71C2316yes—
317C4×C22⋊D71C2316yes—
318C4×C22⋊D71C2316yes—
319C4×C22⋊D71C2316yes—
320C4×C22⋊D71C2316yes—
321C4×C22⋊D71C2316yes—
322C4×C22⋊D71C2316yes—
323C4×C22⋊D71C2316yes—
324(C22⋊D71)⋊C4C23112yes—
325(C22⋊D71)⋊C4C23112yes—
326(C22⋊D71)⋊C4C23112yes—
327#14556087C2316yes—
328#14556087C2316yes—
329#14556087C2313yes—
330#14556087C23112yes—
331#14556086C2316yes—
332#14556086C2316yes—
333#14556086C2316yes—
334#14556085C2316yes—
335#14556085C2316yes—
336#14556085C2316yes—
337#14556085C2316yes—
338#14556085C2316yes—
339#14556084C23112yes—
340#14556084C23112yes—
341#14556084C23112yes—
342C2×C4⋊Dic71C2316yes—
343C2×C4⋊Dic71C2313yes—
344C2×Dic71⋊C4C23112yes—
345C2×Dic71⋊C4C2316yes—
346C4⋊C4×D71C2313yes—
347C4⋊C4×D71C2316yes—
348C4⋊C4×D71C2316yes—
349C4⋊C4×D71C2313yes—
350C4⋊C4×D71C2313yes—
351C4⋊C4×D71C2316yes—
352C4⋊C4×D71C2313yes—
353C2×C4×Dic71C2313yes—
354C2×C4×Dic71C2313yes—
355C2×C4×Dic71C2313yes—
356C2×C4×Dic71C23112yes—
357C42×D71C2313yes—
358C42×D71C2313yes—
359C42×D71C2313yes—
360C42×D71C2313yes—
361C42×D71C2313yes—
362C42×D71C2313yes—
363C42×D71C2313yes—
364C42×D71C2313yes—
365C42×D71C2316yes—
366C2×#41×C71C2312yes—
367C2×#41×C71C2313yes—
368C22×Q8×C71C2311yescharacteristic
369C4⋊Q8×C71C2313yes—
370#127×C71C2313yes—
371#126×C71C23112yes—
372#125×C71C2316yes—
373#124×C71C2316yes—
374#124×C71C2316yes—
375#123×C71C23112yes—
376C22⋊Q8×C71C2316yes—
377#121×C71C2316yes—
378#121×C71C2316yes—
379#121×C71C2316yes—
380C4×Q8×C71C2312yes—
381C4×Q8×C71C2311yescharacteristic
382C4×Q8×C71C2311yescharacteristic
383C4×Q8×C71C2313yes—
384C4×Q8×C71C2313yes—
385C4×Q8×C71C2313yes—
386C4×Q8×C71C2313yes—
387C4×D4×C71C2316yes—
388C4×D4×C71C2316yes—
389C4×D4×C71C2313yes—
390C4×D4×C71C2316yes—
391C4×D4×C71C2313yes—
392C4×D4×C71C2316yes—
393C4×D4×C71C2316yes—
394#117×C71C2311yescharacteristic
395#117×C71C2316yes—
396#117×C71C2316yes—
397C2×C4⋊C4×C71C2313yes—
398C2×C42×C71C2313yes—
399C2×C42×C71C2316yes—
400C23×D71C2411yescharacteristic
401#11765865—24no—
402#11765865—224no—
403#11765865—412no—
404#11765864—224no—
405#11765864—224no—
406#11765864—412no—
407C2×Dic142—212no—
408C2×Dic142—224no—
409C2×Dic142C2416yes—
410C2×Dic142C2413yes—
411C2×Dic142C2416yes—
412C2×Dic142C2416yes—
413C2×Dic142C2411yescharacteristic
414C2×Dic142C2416yes—
415C2×Dic142C2416yes—
416C2×Dic142C2413yes—
417Q8×D71—24no—
418Q8×D71—28no—
419Q8×D71—212no—
420Q8×D71—212no—
421Q8×D71#4118yescomplemented
422C2×D284C2412yes—
423C2×D284C2412yes—
424C2×D284C2411yescharacteristic
425C2×C22⋊D71C2416yes—
426C2×C22⋊D71C2416yes—
427C2×C22⋊D71C2416yes—
428C2×C22⋊D71C2412yes—
429C2×C22⋊D71C2416yes—
430C22×Dic71C2413yes—
431C22×Dic71C2411yescharacteristic
432C22×Dic71C24112yes—
433C22×Dic71C2413yes—
434C22×Dic71C24112yes—
435C2×C4×D71—24no—
436C2×C4×D71—212no—
437C2×C4×D71—46no—
438C2×C4×D71C2413yes—
439C2×C4×D71C2413yes—
440C2×C4×D71C2413yes—
441C2×C4×D71C2413yes—
442C2×C4×D71C2413yes—
443C2×C4×D71C2411yescharacteristic
444C2×C4×D71C2411yescharacteristic
445C2×C4×D71C2411yescharacteristic
446C2×C4×D71C2411yescharacteristic
447C2×C4×D71C2416yes—
448C2×C4×D71C2412yes—
449C2×C4×D71C2413yes—
450C2×C4×D71C2413yes—
451C2×C4×D71C2416yes—
452C2×C4×D71C2413yes—
453C4⋊Dic71C2413yes—
454C4⋊Dic71C2413yes—
455C4⋊Dic71C2416yes—
456C4⋊Dic71C2416yes—
457C4⋊Dic71C2416yes—
458C4⋊Dic71C2416yes—
459C4⋊Dic71C2412yes—
460C4⋊Dic71C2412yes—
461C4⋊Dic71C2413yes—
462C4⋊Dic71C2413yes—
463C4⋊Dic71C24112yes—
464C4⋊Dic71C24112yes—
465C4⋊Dic71C2416yes—
466Dic71⋊C4C2416yes—
467Dic71⋊C4C2416yes—
468Dic71⋊C4C2416yes—
469Dic71⋊C4C2416yes—
470Dic71⋊C4C24112yes—
471Dic71⋊C4C2416yes—
472Dic71⋊C4C2416yes—
473Dic71⋊C4C2416yes—
474Dic71⋊C4C2416yes—
475Dic71⋊C4C2416yes—
476Dic71⋊C4C24112yes—
477Dic71⋊C4C2416yes—
478Dic71⋊C4C2416yes—
479Dic71⋊C4C2416yes—
480Dic71⋊C4C2416yes—
481Dic71⋊C4C2416yes—
482C22⋊Dic71C2416yes—
483C22⋊Dic71C2416yes—
484C22⋊Dic71C2416yes—
485C22⋊Dic71C2416yes—
486C22⋊Dic71C2416yes—
487C22⋊Dic71C24112yes—
488C22⋊Dic71C24112yes—
489(C2×D71)⋊C4C2412yes—
490(C2×D71)⋊C4C2412yes—
491(C2×D71)⋊C4C2412yes—
492(C2×D71)⋊C4C2412yes—
493(C2×D71)⋊C4C2416yes—
494(C2×D71)⋊C4C2416yes—
495(C2×D71)⋊C4C2416yes—
496(C2×D71)⋊C4C2416yes—
497(C2×D71)⋊C4C2416yes—
498(C2×D71)⋊C4C2416yes—
499C4×Dic71C2413yes—
500C4×Dic71C2413yes—
501C4×Dic71C2413yes—
502C4×Dic71C2413yes—
503C4×Dic71C2413yes—
504C4×Dic71C2413yes—
505C4×Dic71C2413yes—
506C4×Dic71C2413yes—
507C4×Dic71C2413yes—
508C4×Dic71C2413yes—
509C4×Dic71C2413yes—
510C4×Dic71C2413yes—
511C4×Dic71C2416yes—
512C4×Dic71C2416yes—
513C4×Dic71C2416yes—
514C4×Dic71C24112yes—
515C4×Dic71C24112yes—
516#41×C71—28no—
517#41×C71—212no—
518C2×Q8×C71—24no—
519C2×Q8×C71C2413yes—
520C2×Q8×C71C2413yes—
521C2×Q8×C71C2411yescharacteristic
522C2×D4×C71C2416yes—
523C2×D4×C71C2416yes—
524C2×D4×C71C2413yes—
525C2×D4×C71C2416yes—
526C22×C4×C71C2413yes—
527C22×C4×C71C2416yes—
528C22×C4×C71C2416yes—
529C22×C4×C71C2413yes—
530C22×C4×C71C2416yes—
531C22×C4×C71C2411yescharacteristic
532C4⋊C4×C71C2413yes—
533C4⋊C4×C71C2413yes—
534C4⋊C4×C71C2416yes—
535C4⋊C4×C71C2411yescharacteristic
536C4⋊C4×C71C2411yescharacteristic
537C4⋊C4×C71C2416yes—
538C4⋊C4×C71C2416yes—
539C4⋊C4×C71C2416yes—
540C4⋊C4×C71C2416yes—
541C22⋊C4×C71C2412yes—
542C22⋊C4×C71C2416yes—
543C22⋊C4×C71C24112yes—
544C22⋊C4×C71C2416yes—
545C22⋊C4×C71C24112yes—
546C42×C71C2412yes—
547C42×C71C2413yes—
548C42×C71C2413yes—
549C42×C71C2416yes—
550C42×C71C2416yes—
551C42×C71C2413yes—
552C42×C71C2413yes—
553C23×C71C2516yes—
554C23×C71C2511yescharacteristic
555C22×D71—22no—
556C22×D71—22no—
557C22×D71—22no—
558C22×D71C2512yes—
559C22×D71C2511yescharacteristic
560C22×D71C2511yescharacteristic
561Q8×C71—26no—
562Q8×C71—26no—
563Q8×C71C2×#4114yes—
564D4×C71—212no—
565D4×C71—212no—
566D4×C71—26no—
567D4×C71—46no—
568C2×C4×C71—26no—
569C2×C4×C71—212no—
570C2×C4×C71—212no—
571C2×C4×C71—43no—
572C2×C4×C71—46no—
573C2×C4×C712−1+414yescomplemented
574C2×C4×C71C2513yes—
575C2×C4×C71C2512yes—
576C2×C4×C71C2512yes—
577C2×C4×C71C2513yes—
578C2×C4×C71C2516yes—
579C2×C4×C71C2513yes—
580C2×C4×C71C2513yes—
581C2×C4×C71C2511yescharacteristic
582C2×C4×C71C2511yescharacteristic
583C22⋊D71—24no—
584C22⋊D71—212no—
585C22⋊D71—212no—
586C22⋊D71—212no—
587C22⋊D71—46no—
588C2×Dic71—22no—
589C2×Dic71—26no—
590C2×Dic71—224no—
591C2×Dic71—43no—
592C2×Dic71—412no—
593C2×Dic71C2511yescharacteristic
594C2×Dic71C2511yescharacteristic
595C2×Dic71C2513yes—
596C2×Dic71C2512yes—
597C2×Dic71C2513yes—
598C2×Dic71C2516yes—
599C2×Dic71C2516yes—
600C2×Dic71C2513yes—
601C2×Dic71C2513yes—
602D284—24no—
603D284—24no—
604D284—22no—
605C4×D71—26no—
606C4×D71—26no—
607C4×D71—26no—
608C4×D71—26no—
609C4×D71—212no—
610C4×D71—22no—
611C4×D71—22no—
612C4×D71—22no—
613C4×D71—22no—
614C4×D71—24no—
615C4×D71—26no—
616C4×D71—43no—
617C4×D71—43no—
618C4×D71—46no—
619C4×D71C2×#41112yes—
620Dic142—26no—
621Dic142—212no—
622Dic142—22no—
623Dic142—212no—
624Dic142—212no—
625Dic142—46no—
626Dic142—46no—
627Dic142C2×#41112yes—
628C22×C71—21no—
629C22×C71—21no—
630C22×C71—26no—
631C22×C71—26no—
632C22×C71—26no—
633C22×C71C2×2−1+412yes—
634C22×C71C2611yescharacteristic
635C2×D71—28no—
636C2×D71—21no—
637C2×D71—21no—
638C2×D71—21no—
639C2×D71—21no—
640C2×D71—22no—
641C2×D71—22no—
642C2×D71—22no—
643C2×D71C22×#4112yes—
644C2×D71#58512yes—
645C4×C71—22no—
646C4×C71—23no—
647C4×C71—26no—
648C4×C71—22no—
649C4×C71—23no—
650C4×C71—23no—
651C4×C71C22×#4116yes—
652C4×C71C2×2−1+412yes—
653C4×C71C2×2−1+412yes—
654Dic71—23no—
655Dic71—26no—
656Dic71—22no—
657Dic71—21no—
658Dic71—21no—
659Dic71—26no—
660Dic71—23no—
661Dic71—23no—
662Dic71C22×#4116yes—
663#62788—711nomaximal, Sylow
664C2×C71—22no—
665C2×C71—46no—
666C2×C71C23×#4111yescharacteristic
667C2×C71C22×2−1+411yescharacteristic
668C2×C71C2×#58511yescharacteristic
669D71—22no—
670D71—22no—
671D71—42no—
672#3523—711no—
673#3523—713no—
674#3522—713no—
675#3522—711no—
676#3516—716no—
677#3516—712no—
678#3507—713no—
679#3507—713no—
680#3502—711no—
681#3497—711no—
682#3492—716no—
683#3486—712no—
684#3482—716no—
685#3482—712no—
686#3480—713no—
687#3480D7111yescharacteristic, complemented
688Q8×#41—713no—
689Q8×#41—711no—
690#3461—716no—
691#3444—713no—
692#3444—713no—
693C4×2−1+4—712no—
694C22×C4×Q8—711no—
695C71#6278811yescharacteristic, complemented, Sylow
696C2×2−1+4—712no—
697C23×Q8—711no—
698#559—713no—
699#559—716no—
700#559C2×D7113yescomplemented
701Q82—711no—
702Q82—713no—
703#557—713no—
704#557—716no—
705#557—716no—
706#557—713no—
707#557—713no—
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#554—713no—
717#554—716no—
718#554—713no—
719#554—7112no—
720#554—716no—
721#554—716no—
722#553—7112no—
723#553—716no—
724#553C2×D7116yes—
725#552—7112no—
726#552—716no—
727#552—7112no—
728#552—716no—
729#552—716no—
730#552—716no—
731#550—713no—
732#550C2×D7111yescharacteristic, complemented
733D4×Q8—712no—
734D4×Q8—716no—
735D4×Q8—712no—
736D4×Q8—711no—
737D4×Q8—716no—
738D4×Q8—713no—
739#548—712no—
740#548—712no—
741#548—716no—
742#548—716no—
743#548—716no—
744#548C2×D7112yes—
745#547—7112no—
746#547—716no—
747#547—716no—
748#544—716no—
749#542—716no—
750#542—7112no—
751#542—716no—
752#541—7112no—
753#541—716no—
754#541—716no—
755#539—7112no—
756#539—7112no—
757#537—716no—
758#536—716no—
759#536—716no—
760#533—713no—
761#533—713no—
762#533—713no—
763#533—713no—
764#533—716no—
765#533—713no—
766#533—7112no—
767#533—713no—
768#533—716no—
769#532—713no—
770#532—713no—
771#532—713no—
772#532—713no—
773#532—713no—
774#532C2×D7113yes—
775#529—716no—
776#529—716no—
777#529—716no—
778#529—716no—
779#529—713no—
780#529—713no—
781#529—716no—
782#529—716no—
783#529—713no—
784#529—716no—
785#529—716no—
786#529—713no—
787#529—7112no—
788#529—716no—
789#529—716no—
790#529—716no—
791#529C2×D7116yescomplemented
792#525—713no—
793#525—716no—
794#525—716no—
795#525—716no—
796#525—716no—
797#525—711no—
798#520—712no—
799#520—716no—
800#520—716no—
801#520—716no—
802#519—712no—
803#519—712no—
804#519—716no—
805C4×#41—716no—
806C4×#41—716no—
807C4×#41—716no—
808C4×#41—716no—
809C4×#41—716no—
810C4×#41—713no—
811C4×#41—716no—
812C4×#41C2×D7113yes—
813C4×#41C2×D7112yescomplemented
814C2×C4×Q8—711no—
815C2×C4×Q8—711no—
816C2×C4×Q8—713no—
817C2×C4×Q8—711no—
818C2×C4×Q8—713no—
819C2×C4×Q8—711no—
820C2×C4×Q8—713no—
821C2×C4×Q8—711no—
822C2×C4×Q8—713no—
823C2×C4×Q8—712no—
824C2×C4×Q8—713no—
825C2×C4×Q8—713no—
826C2×C4×Q8—716no—
827C2×C4×Q8C2×D7111yescharacteristic
828C22×C4⋊C4—713no—
829C22×C42—713no—
8302−1+4—14216no—
831C2×#41—716no—
832C2×#41—716no—
833C2×#41—716no—
834C2×#41—716no—
835C2×#41—711no—
836C2×#41—716no—
837C2×#41C22×D7113yes—
838C2×#41C22×D7112yes—
839C22×Q8—711no—
840C22×Q8—713no—
841C22×Q8—713no—
842C22×Q8—711no—
843C22×Q8—712no—
844C22×Q8—713no—
845C22×Q8—716no—
846C22×Q8—1428no—
847C22×Q8C22×D7111yescharacteristic
848C23×C4—713no—
849C23×C4—713no—
850C23×C4—711no—
851C4⋊Q8—713no—
852C4⋊Q8—716no—
853C4⋊Q8—713no—
854C4⋊Q8—713no—
855C4⋊Q8—7112no—
856C4⋊Q8—7112no—
857C4⋊Q8—716no—
858C4⋊Q8—713no—
859C4⋊Q8—713no—
860C4⋊Q8—716no—
861C4⋊Q8—716no—
862C4⋊Q8C22×D7113yes—
863#127—713no—
864#127C22×D7113yes—
865#126—716no—
866#126—716no—
867#126—7112no—
868#126—7112no—
869#126—716no—
870#126—716no—
871#126—7112no—
872#126—7112no—
873#126—7112no—
874#126C22×D71112yes—
875#125—716no—
876#125—716no—
877#125—716no—
878#125—716no—
879#125—713no—
880#125—713no—
881#125—7112no—
882#125—716no—
883#125—7112no—
884#125—7112no—
885#125—7112no—
886#125—716no—
887#125—7112no—
888#125C22×D7116yes—
889#124—713no—
890#124—716no—
891#124—716no—
892#124—713no—
893#124—716no—
894#124—716no—
895#124—716no—
896#124—7112no—
897#124C22×D7116yes—
898#124C22×D7116yes—
899#123—716no—
900#123—7112no—
901#123—716no—
902#123—716no—
903#123—712no—
904#123—7112no—
905#123—716no—
906#123—716no—
907#123—7112no—
908#123—7112no—
909#123—7112no—
910#123C22×D71112yes—
911C22⋊Q8—713no—
912C22⋊Q8—713no—
913C22⋊Q8—716no—
914C22⋊Q8—716no—
915C22⋊Q8—716no—
916C22⋊Q8—716no—
917C22⋊Q8—716no—
918C22⋊Q8—7112no—
919C22⋊Q8—711no—
920C22⋊Q8—711no—
921C22⋊Q8—716no—
922C22⋊Q8—716no—
923C22⋊Q8—716no—
924C22⋊Q8—716no—
925C22⋊Q8—716no—
926C22⋊Q8—716no—
927C22⋊Q8—7112no—
928C22⋊Q8—716no—
929C22⋊Q8—716no—
930C22⋊Q8—7112no—
931C22⋊Q8—7112no—
932C22⋊Q8—7112no—
933C22⋊Q8—7112no—
934C22⋊Q8—7112no—
935C22⋊Q8C22×D7116yes—
936#121—713no—
937#121—713no—
938#121—716no—
939#121—716no—
940#121—716no—
941#121—716no—
942#121—716no—
943#121—7112no—
944#121—711no—
945#121—711no—
946#121—716no—
947#121—716no—
948#121C22×D7116yes—
949#121C22×D7116yes—
950#121C22×D7116yes—
951#120—716no—
952#120—712no—
953C4×Q8—711no—
954C4×Q8—713no—
955C4×Q8—711no—
956C4×Q8—713no—
957C4×Q8—712no—
958C4×Q8—716no—
959C4×Q8—716no—
960C4×Q8—713no—
961C4×Q8—716no—
962C4×Q8—713no—
963C4×Q8—713no—
964C4×Q8—716no—
965C4×Q8—713no—
966C4×Q8—716no—
967C4×Q8—716no—
968C4×Q8—716no—
969C4×Q8—716no—
970C4×Q8—713no—
971C4×Q8—716no—
972C4×Q8—713no—
973C4×Q8—713no—
974C4×Q8—713no—
975C4×Q8—716no—
976C4×Q8—716no—
977C4×Q8—716no—
978C4×Q8—716no—
979C4×Q8—716no—
980C4×Q8—7112no—
981C4×Q8—716no—
982C4×Q8—716no—
983C4×Q8—716no—
984C4×Q8—716no—
985C4×Q8—713no—
986C4×Q8—713no—
987C4×Q8C22×D7111yescharacteristic
988C4×Q8C22×D7113yes—
989C4×Q8C22×D7111yescharacteristic
990C4×Q8C22×D7113yes—
991C4×Q8C22×D7113yes—
992C4×Q8C22×D7113yes—
993C4×Q8C22×D7112yes—
994C4×D4—716no—
995C4×D4—716no—
996C4×D4—7112no—
997C4×D4—7112no—
998C4×D4—716no—
999C4×D4—716no—
1000C4×D4—716no—
1001C4×D4—716no—
1002C4×D4—716no—
1003C4×D4—716no—
1004C4×D4—716no—
1005C4×D4—716no—
1006C4×D4—716no—
1007C4×D4—716no—
1008C4×D4—716no—
1009C4×D4—716no—
1010C4×D4—716no—
1011C4×D4—7112no—
1012C4×D4—7112no—
1013C4×D4—7112no—
1014C4×D4—712no—
1015C4×D4—712no—
1016C4×D4—716no—
1017C4×D4—716no—
1018C4×D4—713no—
1019C4×D4—713no—
1020C4×D4C22×D7116yes—
1021C4×D4C22×D7116yes—
1022C4×D4C22×D7116yes—
1023C4×D4C22×D7116yes—
1024C4×D4C22×D7113yes—
1025C4×D4C22×D7113yes—
1026C4×D4C22×D7116yes—
1027#117—713no—
1028#117—716no—
1029#117—7112no—
1030#117—716no—
1031#117—716no—
1032#117—716no—
1033#117—716no—
1034#117—7112no—
1035#117—7112no—
1036#117—7112no—
1037#117—716no—
1038#117—716no—
1039#117—716no—
1040#117—716no—
1041#117—716no—
1042#117C22×D7111yescharacteristic
1043#117C22×D7116yes—
1044#117C22×D7116yes—
1045C2×C4⋊C4—716no—
1046C2×C4⋊C4—713no—
1047C2×C4⋊C4—7112no—
1048C2×C4⋊C4—716no—
1049C2×C4⋊C4—713no—
1050C2×C4⋊C4—713no—
1051C2×C4⋊C4—716no—
1052C2×C4⋊C4—716no—
1053C2×C4⋊C4—713no—
1054C2×C4⋊C4—713no—
1055C2×C4⋊C4—716no—
1056C2×C4⋊C4C22×D7113yes—
1057C2×C42—713no—
1058C2×C42—713no—
1059C2×C42—713no—
1060C2×C42—7112no—
1061C2×C42—713no—
1062C2×C42—713no—
1063C2×C42—713no—
1064C2×C42—713no—
1065C2×C42—713no—
1066C2×C42—713no—
1067C2×C42—713no—
1068C2×C42—713no—
1069C2×C42—716no—
1070C2×C42C22×D7113yes—
1071C2×C42C22×D7116yes—
1072C24—711no—
1073#41—28no—
1074#41—212no—
1075#41—28412no—
1076#41—28412no—
1077#41—14224no—
1078#41—14224no—
1079#41—14224no—
1080#41—1424no—
1081C2×Q8—24no—
1082C2×Q8—718no—
1083C2×Q8—716no—
1084C2×Q8—716no—
1085C2×Q8—713no—
1086C2×Q8—711no—
1087C2×Q8—716no—
1088C2×Q8—713no—
1089C2×Q8—716no—
1090C2×Q8—716no—
1091C2×Q8—14212no—
1092C2×Q8—14224no—
1093C2×Q8—14212no—
1094C2×Q8—14212no—
1095C2×Q8—1424no—
1096C2×Q8—1428no—
1097C2×Q8C23×D7113yes—
1098C2×Q8C23×D7113yes—
1099C2×Q8C23×D7111yescharacteristic
1100C2×D4—716no—
1101C2×D4—712no—
1102C2×D4—716no—
1103C2×D4—716no—
1104C2×D4—716no—
1105C2×D4—711no—
1106C2×D4—712no—
1107C2×D4—712no—
1108C2×D4C23×D7116yes—
1109C2×D4C23×D7113yes—
1110C2×D4C23×D7116yes—
1111C2×D4C23×D7116yes—
1112C22×C4—2846no—
1113C22×C4—713no—
1114C22×C4—7112no—
1115C22×C4—713no—
1116C22×C4—713no—
1117C22×C4—716no—
1118C22×C4—713no—
1119C22×C4—711no—
1120C22×C4—713no—
1121C22×C4—7112no—
1122C22×C4—711no—
1123C22×C4—711no—
1124C22×C4—713no—
1125C22×C4—713no—
1126C22×C4—713no—
1127C22×C4—713no—
1128C22×C4—713no—
1129C22×C4—716no—
1130C22×C4—711no—
1131C22×C4—711no—
1132C22×C4—712no—
1133C22×C4—14212no—
1134C22×C4—1424no—
1135C22×C4C23×D7113yes—
1136C22×C4C23×D7116yes—
1137C22×C4C23×D7116yes—
1138C22×C4C23×D7113yes—
1139C22×C4C23×D7116yes—
1140C22×C4C23×D7111yescharacteristic
1141C4⋊C4—716no—
1142C4⋊C4—716no—
1143C4⋊C4—716no—
1144C4⋊C4—716no—
1145C4⋊C4—716no—
1146C4⋊C4—716no—
1147C4⋊C4—7112no—
1148C4⋊C4—716no—
1149C4⋊C4—716no—
1150C4⋊C4—716no—
1151C4⋊C4—716no—
1152C4⋊C4—716no—
1153C4⋊C4—716no—
1154C4⋊C4—7112no—
1155C4⋊C4—716no—
1156C4⋊C4—716no—
1157C4⋊C4—713no—
1158C4⋊C4—713no—
1159C4⋊C4—716no—
1160C4⋊C4—716no—
1161C4⋊C4—716no—
1162C4⋊C4—712no—
1163C4⋊C4—712no—
1164C4⋊C4—713no—
1165C4⋊C4—713no—
1166C4⋊C4—716no—
1167C4⋊C4—716no—
1168C4⋊C4—7112no—
1169C4⋊C4—7112no—
1170C4⋊C4C23×D7113yes—
1171C4⋊C4C23×D7113yes—
1172C4⋊C4C23×D7116yes—
1173C4⋊C4C23×D7116yes—
1174C4⋊C4C23×D7116yes—
1175C4⋊C4C23×D7111yescharacteristic
1176C4⋊C4C23×D7111yescharacteristic
1177C4⋊C4C23×D7116yes—
1178C4⋊C4C23×D7116yes—
1179C22⋊C4—716no—
1180C22⋊C4—716no—
1181C22⋊C4—716no—
1182C22⋊C4—716no—
1183C22⋊C4—7112no—
1184C22⋊C4—7112no—
1185C22⋊C4—716no—
1186C22⋊C4—712no—
1187C22⋊C4—712no—
1188C22⋊C4—716no—
1189C22⋊C4—716no—
1190C22⋊C4—716no—
1191C22⋊C4—712no—
1192C22⋊C4—712no—
1193C22⋊C4—716no—
1194C22⋊C4—716no—
1195C22⋊C4—716no—
1196C22⋊C4C23×D71112yes—
1197C22⋊C4C23×D71112yes—
1198C22⋊C4C23×D7112yes—
1199C22⋊C4C23×D7116yes—
1200C22⋊C4C23×D7116yes—
1201C42—713no—
1202C42—713no—
1203C42—713no—
1204C42—713no—
1205C42—713no—
1206C42—713no—
1207C42—713no—
1208C42—713no—
1209C42—713no—
1210C42—713no—
1211C42—7112no—
1212C42—716no—
1213C42—7112no—
1214C42—716no—
1215C42—713no—
1216C42—713no—
1217C42—716no—
1218C42C23×D7113yes—
1219C42C23×D7113yes—
1220C42C23×D7116yes—
1221C42C23×D7116yes—
1222C42C23×D7113yes—
1223C42C23×D7113yes—
1224C42C23×D7112yes—
1225C23—711no—
1226C23—711no—
1227C23—712no—
1228C23—1422no—
1229C23—1422no—
1230C23—1422no—
1231C23C24×D7116yes—
1232C23C24×D7111yescharacteristic
1233Q8—26no—
1234Q8—26no—
1235Q8—2846no—
1236Q8—2846no—
1237Q8—7112no—
1238Q8—14212no—
1239Q8—14212no—
1240Q8—1426no—
1241Q8—14212no—
1242Q8—1422no—
1243Q8#41×D7114yes—
1244D4—212no—
1245D4—212no—
1246D4—26no—
1247D4—46no—
1248D4—2846no—
1249D4—1424no—
1250D4—1424no—
1251D4—14212no—
1252D4—14212no—
1253D4—14212no—
1254D4—1424no—
1255D4—1422no—
1256C2×C4—26no—
1257C2×C4—212no—
1258C2×C4—212no—
1259C2×C4—43no—
1260C2×C4—46no—
1261C2×C4—2843no—
1262C2×C4—2843no—
1263C2×C4—2846no—
1264C2×C4—2843no—
1265C2×C4—28412no—
1266C2×C4—713no—
1267C2×C4—7112no—
1268C2×C4—711no—
1269C2×C4—711no—
1270C2×C4—713no—
1271C2×C4—712no—
1272C2×C4—713no—
1273C2×C4—716no—
1274C2×C4—716no—
1275C2×C4—713no—
1276C2×C4—1426no—
1277C2×C4—1426no—
1278C2×C4—1426no—
1279C2×C4—1426no—
1280C2×C4—1426no—
1281C2×C4—14224no—
1282C2×C4—1422no—
1283C2×C4—1426no—
1284C2×C4—14212no—
1285C2×C4—1422no—
1286C2×C4—1422no—
1287C2×C4—1422no—
1288C2×C4—1422no—
1289C2×C4—1424no—
1290C2×C4#1455617514yescomplemented
1291C2×C4C24×D7113yes—
1292C2×C4C24×D7116yes—
1293C2×C4C24×D7113yes—
1294C2×C4C24×D7113yes—
1295C2×C4C24×D7112yes—
1296C2×C4C24×D7112yes—
1297C2×C4C24×D7113yes—
1298C2×C4C24×D7111yescharacteristic
1299C2×C4C24×D7111yescharacteristic
1300C22—21no—
1301C22—21no—
1302C22—26no—
1303C22—26no—
1304C22—26no—
1305C22—712no—
1306C22—712no—
1307C22—1428no—
1308C22—1422no—
1309C22—1422no—
1310C22—1422no—
1311C22—1421no—
1312C22—1421no—
1313C22—1421no—
1314C22—1421no—
1315C22C2×#1455617512yes—
1316C22C25×D7111yescharacteristic
1317C4—22no—
1318C4—23no—
1319C4—26no—
1320C4—23no—
1321C4—22no—
1322C4—23no—
1323C4—716no—
1324C4—1426no—
1325C4—1423no—
1326C4—1421no—
1327C4—1421no—
1328C4—1422no—
1329C4—1423no—
1330C4—1426no—
1331C4—1423no—
1332C4C2×#41×D7116yes—
1333C4C2×#1455617512yes—
1334C4C2×#1455617512yes—
1335C2—22no—
1336C2—46no—
1337C2—2842no—
1338C2—1422no—
1339C2—1422no—
1340C2C22×#41×D7111yescharacteristic
1341C2C22×#1455617511yescharacteristic
1342C2#585×D7111yescharacteristic
subgroupG/H
centerC2×C4C24×D71
commutator, socle, cosocleC22×C71C26
FrattiniC22C25×D71
FittingC71×#3480C2
hypercenter#3480D71
hypocenterC71#62788
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C2×C4 ◁ #3480

Complements

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

NH ≅ G/Ntype
1. #22602437C2semidirect
2. #22602435C2semidirect
3. #22602422C2semidirect
4. #22602420C2semidirect
5. #22602324C2semidirect
6. #22602322C2semidirect
7. #22602197C2semidirect
8. #22602195C2semidirect
9. #22602144C2semidirect
10. #22602105C2semidirect
11. #22602044C2semidirect
12. #22601986C2semidirect
13. #22601962C2semidirect
14. #22601953C2semidirect
15. #22601937C2semidirect
16. Q8×#11765865C2semidirect
17. #41×Dic142C2semidirect
18. #22601765C2semidirect
19. #22601635C2semidirect
20. #22601633C2semidirect
21. C4×#14556175C2semidirect
22. C2×C4×Q8×D71C2semidirect
23. C71×#3480C2semidirect
26. #17986735C22semidirect
27. #17986731C22semidirect
28. Q8×Dic142C22semidirect
29. Q8×Dic142C22semidirect
30. #17986728C22semidirect
31. #17986728C22semidirect
32. #17986727C22semidirect
33. #17986726C22semidirect
34. #17986725C22semidirect
35. #17986724C22semidirect
36. #17986723C22semidirect
37. #17986719C22semidirect
38. #17986718C22semidirect
39. #17986718C22semidirect
40. #17986716C22semidirect
41. #17986709C22semidirect
43. #17986708C22semidirect
45. #17986706C22semidirect
49. #17986691C22semidirect
51. #17986688C22semidirect
53. #17986686C22semidirect
55. #17986669C22semidirect
57. Q8×D284C22semidirect
59. D4×Dic142C22semidirect
64. #17986656C22semidirect
66. #17986655C22semidirect
71. #17986618C22semidirect
72. #17986617C22semidirect
73. #17986616C22semidirect
74. #17986612C22semidirect
75. #17986609C22semidirect
76. #17986606C22semidirect
83. #17986556C22semidirect
88. #17986553C22semidirect
90. #17986552C22semidirect
102. #17986531C22semidirect
107. #17986529C22semidirect
118. #17986482C22semidirect
121. #17986478C22semidirect
122. #17986476C22semidirect
124. #17986475C22semidirect
131. C4×#11765864C22semidirect
134. C2×C4×Dic142C22semidirect
144. C4×Q8×D71C22semidirect
147. #559×C71C22semidirect
148. #557×C71C22semidirect
149. #556×C71C22semidirect
151. #550×C71C22semidirect
154. #529×C71C22semidirect
156. C4×#41×C71C22semidirect
421. Q8×D71#41semidirect
573. C2×C4×C712−1+4semidirect
687. #3480D71semidirect
695. C71#62788semidirect
700. #559C2×D71semidirect
709. #557C2×D71semidirect
715. #556C2×D71semidirect
732. #550C2×D71semidirect
791. #529C2×D71semidirect
813. C4×#41C2×D71semidirect
1290. C2×C4#14556175semidirect

Maximal subgroups

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

subgroupindex
#226024372
#226024352
#226024222
#226024202
#226023242
#226023222
#226021972
#226021952
#226021442
#226021052
#226020442
#226019862
#226019622
#226019532
#226019372
Q8×#117658652
#41×Dic1422
#226017652
#226016352
#226016332
C4×#145561752
C2×C4×Q8×D712
C71×#34802
#6278871