Finite Group Databasebeta

← #32869786

Subgroups — #32869786

Order 18176.

1788 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986533C211yesmaximal, characteristic
2#22599580C214yesmaximal, complemented
3#22599570C212yesmaximal, complemented
4#22599561C212yesmaximal, complemented
5#22599519C214yesmaximal, complemented
6#22599508C214yesmaximal, complemented
7#22598893C212yesmaximal, complemented
8#22598729C212yesmaximal, complemented
9#22598288C212yesmaximal, complemented
10#22598280C212yesmaximal
11#22598141C212yesmaximal, complemented
12#22598133C212yesmaximal, complemented
13#22596973C211yesmaximal, characteristic, complemented
14C2×#533×C71C211yesmaximal, characteristic, complemented
15#17986533—21no—
16#17986533—21no—
17#17986533—21no—
18#17986533—21no—
19#17986533C2212yes—
20#17986533C2212yes—
21#17986533C2212yes—
22#17986533C2212yes—
23C2×#14556122—21no—
24C2×#14556120C2211yescharacteristic
25C2×#14556116C2211yescharacteristic
26C2×#14556111—21no—
27C2×#14556107C2211yescharacteristic
28C2×#14556102C2211yescharacteristic
29C2×C4×Dic142C2211yescharacteristic
30C2×C4×D284C2211yescharacteristic
31C2×C4×C22⋊D71—21no—
32C2×#14556085—21no—
33#17986405C2214yescomplemented
34#17986405C2214yescomplemented
35#17986398C2218yescomplemented
36#17986361C2214yescomplemented
37#17986361C2214yescomplemented
38#17986356C2218yescomplemented
39#17986340C2218yescomplemented
40#17986334C2214yescomplemented
41#17986329C2214yescomplemented
42#17986323C2218yes—
43#17986317C2214yes—
44#17986312C2214yes—
45#17986303C2218yescomplemented
46#17986296C2218yescomplemented
47#17986291C2214yescomplemented
48#17986286C2214yescomplemented
49#17986281C2214yescomplemented
50#17986276C2214yescomplemented
51#17986056C2212yescomplemented
52#17986056C2212yescomplemented
53#17986052C2212yescomplemented
54#17986052C2212yescomplemented
55#17986042C2214yes—
56#17986042C2214yes—
57#17986023C2212yes—
58#17986007C2214yes—
59#17986003C2214yes—
60#17985963C2212yes—
61C4×#11765849C2212yes—
62#533×C71—21no—
63#533×C71—21no—
64#533×C71—21no—
65#533×C71—21no—
66#533×C71C2212yes—
67#533×C71C2212yes—
68#533×C71C2212yescomplemented
69#533×C71C2212yescomplemented
70C2×C4⋊Q8×C71C2211yescharacteristic, complemented
71C2×C4⋊Q8×C71C2211yescharacteristic, complemented
72C2×#125×C71C2212yescomplemented
73C2×C22⋊Q8×C71—21no—
74C2×C22⋊Q8×C71—21no—
75C2×C4×Q8×C71—21no—
76C2×C4×Q8×C71—21no—
77C2×#117×C71C2212yes—
78C22×C42×C71C2211yescharacteristic
79C22×Dic142C2311yescharacteristic
80C22×D284C2311yescharacteristic
81C22×C22⋊D71—21no—
82C22×C4×D71—21no—
83C2×#11765849C2314yes—
84#14556122—22no—
85#14556122—22no—
86#14556122—22no—
87#14556122—22no—
88#14556120—21no—
89#14556120—21no—
90#14556120C2312yes—
91#14556120C2312yes—
92#14556116—21no—
93#14556116—21no—
94#14556116C2312yes—
95#14556116C2312yes—
96#14556111—22no—
97#14556111—22no—
98#14556111—22no—
99#14556111—22no—
100#14556107—21no—
101#14556107—21no—
102#14556107C2312yes—
103#14556107C2312yes—
104#14556102—21no—
105#14556102—21no—
106#14556102C2312yes—
107#14556102C2312yes—
108C4×Dic142—21no—
109C4×Dic142—21no—
110C4×Dic142C2312yes—
111C4×Dic142C2312yes—
112C4×D284—21no—
113C4×D284—21no—
114C4×D284C2312yes—
115C4×D284C2312yes—
116C4×C22⋊D71—22no—
117C4×C22⋊D71—22no—
118C4×C22⋊D71—22no—
119C4×C22⋊D71—22no—
120#14556085—22no—
121#14556085—22no—
122#14556085—22no—
123#14556085—22no—
124C2×C4⋊Dic71C2311yescharacteristic
125C2×C4⋊Dic71C2311yescharacteristic
126C2×Dic71⋊C4—21no—
127C2×Dic71⋊C4—21no—
128C2×Dic71⋊C4—21no—
129C2×Dic71⋊C4—21no—
130C2×C22⋊Dic71—21no—
131C2×(C2×D71)⋊C4—21no—
132C2×(C2×D71)⋊C4—21no—
133C2×(C2×D71)⋊C4—21no—
134C2×(C2×D71)⋊C4—21no—
135C2×C4×Dic71—21no—
136#14556061C2318yes—
137#14556061C2318yes—
138#14556059C2318yes—
139#14556059C2318yes—
140C4⋊(C71⋊C8)C2314yes—
141C4⋊(C71⋊C8)C2314yes—
142#14556051C2318yes—
143#14556051C2318yes—
144#14556048C2318yes—
145#14556048C2318yes—
146C22⋊(C71⋊C8)C2314yes—
147C22⋊(C71⋊C8)C2314yes—
148#14556039C2314yes—
149C4×C71⋊C8C2314yes—
150C22×Q8×C71—21no—
151C22×Q8×C71—21no—
152C23×C4×C71D411yescharacteristic
153C23×C4×C71D411yescharacteristic
154C23×C4×C71C2311yescharacteristic
155C4⋊Q8×C71—21no—
156C4⋊Q8×C71—21no—
157C4⋊Q8×C71—21no—
158C4⋊Q8×C71—21no—
159C4⋊Q8×C71C2312yes—
160C4⋊Q8×C71C2312yes—
161C4⋊Q8×C71C2312yes—
162C4⋊Q8×C71C2312yes—
163#125×C71—22no—
164#125×C71—22no—
165#125×C71C2314yes—
166#125×C71C2314yes—
167C22⋊Q8×C71—22no—
168C22⋊Q8×C71—22no—
169C22⋊Q8×C71—22no—
170C22⋊Q8×C71—22no—
171C22⋊Q8×C71—22no—
172C22⋊Q8×C71—22no—
173C22⋊Q8×C71—22no—
174C22⋊Q8×C71—22no—
175C4×Q8×C71—22no—
176C4×Q8×C71—22no—
177C4×Q8×C71—22no—
178C4×Q8×C71—22no—
179C4×Q8×C71—22no—
180C4×Q8×C71—22no—
181C4×Q8×C71—22no—
182C4×Q8×C71—22no—
183#117×C71—22no—
184#117×C71—22no—
185#117×C71C2314yes—
186#117×C71C2314yes—
187C2×C4⋊C4×C71—22no—
188C2×C4⋊C4×C71—22no—
189C2×C4⋊C4×C71—21no—
190C2×C4⋊C4×C71—21no—
191C2×C4⋊C4×C71C2312yes—
192C2×C4⋊C4×C71C2312yes—
193C2×C22⋊C4×C71—22no—
194C2×C42×C71—22no—
195C2×C42×C71D411yescharacteristic
196C2×C42×C71D411yescharacteristic
197C2×C42×C71D411yescharacteristic
198C2×C42×C71D411yescharacteristic
199C2×C42×C71D411yescharacteristic
200C2×C42×C71D411yescharacteristic
201C2×C42×C71C2311yescharacteristic
202C2×C42×C71C2311yescharacteristic
203C2×C42×C71C2311yescharacteristic
204C2×C42×C71C2311yescharacteristic
205C2×C42×C71C2311yescharacteristic
206C2×C42×C71C2311yescharacteristic
207C23×D71—21no—
208C2×Dic142—24no—
209C2×Dic142—21no—
210C2×Dic142C2412yes—
211C2×D284—24no—
212C2×D284—21no—
213C2×D284C2412yes—
214C2×C22⋊D71—22no—
215C2×C22⋊D71—22no—
216C2×C22⋊D71—44no—
217C22×Dic71—21no—
218C22×Dic71—21no—
219C22×Dic71—21no—
220C2×C4×D71—22no—
221C2×C4×D71—22no—
222C2×C4×D71—44no—
223#11765849—28no—
224C2×C71⋊C8C2418yes—
225C4⋊Dic71—21no—
226C4⋊Dic71—21no—
227C4⋊Dic71C2412yes—
228C4⋊Dic71C2412yes—
229Dic71⋊C4—22no—
230Dic71⋊C4—22no—
231Dic71⋊C4—22no—
232Dic71⋊C4—22no—
233Dic71⋊C4—22no—
234Dic71⋊C4—22no—
235Dic71⋊C4—22no—
236Dic71⋊C4—22no—
237C22⋊Dic71—22no—
238C22⋊Dic71—22no—
239(C2×D71)⋊C4—22no—
240(C2×D71)⋊C4—22no—
241(C2×D71)⋊C4—22no—
242(C2×D71)⋊C4—22no—
243(C2×D71)⋊C4—22no—
244(C2×D71)⋊C4—22no—
245(C2×D71)⋊C4—22no—
246(C2×D71)⋊C4—22no—
247C4×Dic71—22no—
248C4×Dic71—22no—
249C24×C71C2×D411yescharacteristic
250C2×Q8×C71—22no—
251C2×Q8×C71—22no—
252C2×Q8×C71—22no—
253C2×Q8×C71—22no—
254C2×Q8×C71—44no—
255C2×Q8×C71—44no—
256C22×C4×C71—24no—
257C22×C4×C71—22no—
258C22×C4×C71—22no—
259C22×C4×C71—42no—
260C22×C4×C71—42no—
261C22×C4×C71C2×D411yescharacteristic
262C22×C4×C71C2×D411yescharacteristic
263C22×C4×C71C2×D411yescharacteristic
264C22×C4×C71C2×D411yescharacteristic
265C22×C4×C71C2×D411yescharacteristic
266C22×C4×C71C2×D411yescharacteristic
267C22×C4×C71C2×D411yescharacteristic
268C22×C4×C71C2×D411yescharacteristic
269C22×C4×C71C2×D411yescharacteristic
270C22×C4×C71C2×D411yescharacteristic
271C22×C4×C71C2×D411yescharacteristic
272C22×C4×C71C2×D411yescharacteristic
273C22×C4×C71C2×D411yescharacteristic
274C22×C4×C71C2×D411yescharacteristic
275C22×C4×C71C2×D411yescharacteristic
276C22×C4×C71C2411yescharacteristic
277C22×C4×C71C2411yescharacteristic
278C22×C4×C71C2411yescharacteristic
279C4⋊C4×C71—24no—
280C4⋊C4×C71—24no—
281C4⋊C4×C71—24no—
282C4⋊C4×C71—24no—
283C4⋊C4×C71—22no—
284C4⋊C4×C71—22no—
285C4⋊C4×C71—22no—
286C4⋊C4×C71—22no—
287C4⋊C4×C71—22no—
288C4⋊C4×C71—22no—
289C4⋊C4×C71C2414yes—
290C4⋊C4×C71C2414yes—
291C22⋊C4×C71—24no—
292C22⋊C4×C71—24no—
293C42×C71—24no—
294C42×C71—24no—
295C42×C71C2×D411yescharacteristic
296C42×C71C2×D411yescharacteristic
297C42×C71C2×D411yescharacteristic
298C42×C71C2×D411yescharacteristic
299C42×C71C2×D411yescharacteristic
300C42×C71C2×D411yescharacteristic
301C42×C71C2×D411yescharacteristic
302C42×C71C2×D411yescharacteristic
303C42×C71C2×D411yescharacteristic
304C42×C71C2×D411yescharacteristic
305C42×C71C2×D411yescharacteristic
306C42×C71C2×D411yescharacteristic
307C42×C71C2411yescharacteristic
308C42×C71C2411yescharacteristic
309C42×C71C2411yescharacteristic
310C42×C71C2411yescharacteristic
311C23×C71—22no—
312C23×C71—22no—
313C23×C71—41no—
314C23×C71C22×D411yescharacteristic
315C23×C71C22×D411yescharacteristic
316C23×C71C22×D411yescharacteristic
317C22×D71—22no—
318C22×D71—42no—
319C22×D71—42no—
320C22×D71—42no—
321Q8×C71—44no—
322Q8×C71—44no—
323Q8×C71—44no—
324Q8×C71—44no—
325C2×C4×C71—22no—
326C2×C4×C71—22no—
327C2×C4×C71—22no—
328C2×C4×C71—22no—
329C2×C4×C71—22no—
330C2×C4×C71—22no—
331C2×C4×C71—22no—
332C2×C4×C71—22no—
333C2×C4×C71—22no—
334C2×C4×C71—22no—
335C2×C4×C71—24no—
336C2×C4×C71—24no—
337C2×C4×C71—41no—
338C2×C4×C71—41no—
339C2×C4×C71—41no—
340C2×C4×C71—41no—
341C2×C4×C71—41no—
342C2×C4×C71—41no—
343C2×C4×C71—41no—
344C2×C4×C71—44no—
345C2×C4×C71—44no—
346C2×C4×C71C22×D411yescharacteristic
347C2×C4×C71C22×D411yescharacteristic
348C2×C4×C71C22×D411yescharacteristic
349C2×C4×C71C22×D411yescharacteristic
350C2×C4×C71C22×D411yescharacteristic
351C2×C4×C71C22×D411yescharacteristic
352C2×C4×C71C22×D411yescharacteristic
353C2×C4×C71C22×D411yescharacteristic
354C2×C4×C71C22×D411yescharacteristic
355C2×C4×C71C22×D411yescharacteristic
356C2×C4×C71C22×D411yescharacteristic
357C2×C4×C712−1+414yes—
358C2×C4×C71C2511yescharacteristic
359C22⋊D71—44no—
360C22⋊D71—44no—
361C2×Dic71—22no—
362C2×Dic71—22no—
363C2×Dic71—22no—
364C2×Dic71—42no—
365C2×Dic71—42no—
366C2×Dic71—42no—
367D284—24no—
368D284—42no—
369C4×D71—44no—
370C4×D71—44no—
371Dic142—24no—
372Dic142—42no—
373C71⋊C8—28no—
374C22×C71—21no—
375C22×C71—21no—
376C22×C71—21no—
377C22×C71—21no—
378C22×C71—21no—
379C22×C71—21no—
380C22×C71—21no—
381C22×C71—44no—
382C22×C71#53612yes—
383C22×C71#57512yes—
384C22×C71C23×D411yescharacteristic
385C2×D71—42no—
386C2×D71—42no—
387C2×D71—42no—
388C2×D71—84no—
389C4×C71—21no—
390C4×C71—21no—
391C4×C71—21no—
392C4×C71—21no—
393C4×C71—21no—
394C4×C71—21no—
395C4×C71—21no—
396C4×C71—21no—
397C4×C71—21no—
398C4×C71—44no—
399C4×C71—44no—
400C4×C71#53612yes—
401C4×C71#57512yes—
402C4×C71C2×2−1+412yes—
403Dic71—42no—
404Dic71—42no—
405Dic71—42no—
406#60866—711nomaximal, Sylow
407C2×C71—22no—
408C2×C71—22no—
409C2×C71—41no—
410C2×C71C2×#53611yescharacteristic
411C2×C71C2×#57511yescharacteristic
412C2×C71C2×#57511yescharacteristic
413D71—82no—
414C2×#533D7111yescharacteristic, complemented
415C2×#529—711no—
416#3240—714no—
417#3239—712no—
418#3238—712no—
419#3233—714no—
420#3232—714no—
421#3166—712no—
422#3140—712no—
423#3095—712no—
424#3094—712no—
425#3078—712no—
426#3077—712no—
427#2920—711no—
428C71#6086611yescharacteristic, complemented, Sylow
429#533—21no—
430#533—21no—
431#533—21no—
432#533—21no—
433#533C2×D7112yes—
434#533C2×D7112yes—
435#533C2×D7112yescomplemented
436#533C2×D7112yescomplemented
437C2×C4⋊Q8C2×D7111yescharacteristic, complemented
438C2×C4⋊Q8C2×D7111yescharacteristic, complemented
439#529—712no—
440#529—712no—
441#529—712no—
442#529—712no—
443#529—1421no—
444#529—1421no—
445#529—1421no—
446#529—1421no—
447C2×#126—1421no—
448C2×#125—711no—
449C2×#125C2×D7112yescomplemented
450C2×#124—711no—
451C2×#123—1421no—
452C2×C22⋊Q8—21no—
453C2×C22⋊Q8—21no—
454C2×C22⋊Q8—711no—
455C2×#121—711no—
456C2×C4×Q8—21no—
457C2×C4×Q8—21no—
458C2×C4×Q8—711no—
459C2×C4×D4—711no—
460C2×C4×D4—1421no—
461C2×#117—1421no—
462C2×#117C2×D7112yes—
463C22×C42C2×D7111yescharacteristic
464#501—714no—
465#501—714no—
466#499—718no—
467#489—714no—
468#489—714no—
469#488—718no—
470#485—718no—
471#484—714no—
472#483—714no—
473#482—718no—
474#481—714no—
475#480—714no—
476#479—718no—
477#478—718no—
478#477—714no—
479#476—714no—
480#475—714no—
481#474—714no—
482#432—712no—
483#432—712no—
484#431—712no—
485#431—712no—
486#428—714no—
487#428—714no—
488#423—712no—
489#419—714no—
490#418—714no—
491#407—712no—
492C4×M16—712no—
493C22×Q8—21no—
494C22×Q8—21no—
495C22×Q8—711no—
496C22×D4—711no—
497C22×D4—1421no—
498C23×C4—1421no—
499C23×C4C22⋊D7111yescharacteristic
500C23×C4C22⋊D7111yescharacteristic
501C23×C4C22×D7111yescharacteristic
502C2×M16—714no—
503C4⋊Q8—21no—
504C4⋊Q8—21no—
505C4⋊Q8—21no—
506C4⋊Q8—21no—
507C4⋊Q8C22×D7112yes—
508C4⋊Q8C22×D7112yes—
509C4⋊Q8C22×D7112yes—
510C4⋊Q8C22×D7112yes—
511#126—1422no—
512#126—1422no—
513#126—1422no—
514#126—1422no—
515#125—22no—
516#125—22no—
517#125—712no—
518#125—712no—
519#125—1421no—
520#125—1421no—
521#125C22×D7114yes—
522#125C22×D7114yes—
523#124—712no—
524#124—712no—
525#124—1421no—
526#124—1421no—
527#123—1422no—
528#123—1422no—
529#123—1422no—
530#123—1422no—
531C22⋊Q8—22no—
532C22⋊Q8—22no—
533C22⋊Q8—22no—
534C22⋊Q8—22no—
535C22⋊Q8—22no—
536C22⋊Q8—22no—
537C22⋊Q8—22no—
538C22⋊Q8—22no—
539C22⋊Q8—712no—
540C22⋊Q8—712no—
541C22⋊Q8—1421no—
542C22⋊Q8—1421no—
543#121—712no—
544#121—712no—
545#121—1421no—
546#121—1421no—
547C4×Q8—22no—
548C4×Q8—22no—
549C4×Q8—22no—
550C4×Q8—22no—
551C4×Q8—22no—
552C4×Q8—22no—
553C4×Q8—22no—
554C4×Q8—22no—
555C4×Q8—712no—
556C4×Q8—712no—
557C4×Q8—1421no—
558C4×Q8—1421no—
559C4×D4—712no—
560C4×D4—712no—
561C4×D4—1422no—
562C4×D4—1422no—
563C4×D4—1422no—
564C4×D4—1422no—
565C4×D4—1421no—
566C4×D4—1421no—
567#117—22no—
568#117—22no—
569#117—1422no—
570#117—1422no—
571#117—1422no—
572#117—1422no—
573#117C22×D7114yes—
574#117C22×D7114yes—
575C2×C4⋊C4—22no—
576C2×C4⋊C4—22no—
577C2×C4⋊C4—21no—
578C2×C4⋊C4—21no—
579C2×C4⋊C4—711no—
580C2×C4⋊C4—711no—
581C2×C4⋊C4—1421no—
582C2×C4⋊C4—1421no—
583C2×C4⋊C4—1421no—
584C2×C4⋊C4—1421no—
585C2×C4⋊C4C22×D7112yes—
586C2×C4⋊C4C22×D7112yes—
587C2×C22⋊C4—22no—
588C2×C22⋊C4—1421no—
589C2×C22⋊C4—1421no—
590C2×C22⋊C4—1421no—
591C2×C22⋊C4—1421no—
592C2×C22⋊C4—1421no—
593C2×C42—22no—
594C2×C42—1421no—
595C2×C42C22⋊D7111yescharacteristic
596C2×C42C22⋊D7111yescharacteristic
597C2×C42C22⋊D7111yescharacteristic
598C2×C42C22⋊D7111yescharacteristic
599C2×C42C22⋊D7111yescharacteristic
600C2×C42C22⋊D7111yescharacteristic
601C2×C42C22×D7111yescharacteristic
602C2×C42C22×D7111yescharacteristic
603C2×C42C22×D7111yescharacteristic
604C2×C42C22×D7111yescharacteristic
605C2×C42C22×D7111yescharacteristic
606C2×C42C22×D7111yescharacteristic
607#107—718no—
608#107—718no—
609#106—718no—
610#106—718no—
611C4⋊C8—714no—
612C4⋊C8—714no—
613#103—718no—
614#103—718no—
615#102—718no—
616#102—718no—
617C22⋊C8—714no—
618C22⋊C8—714no—
619#97—714no—
620C4×C8—714no—
621C24—1421no—
622C24C2×C22⋊D7111yescharacteristic
623C2×Q8—22no—
624C2×Q8—22no—
625C2×Q8—22no—
626C2×Q8—22no—
627C2×Q8—44no—
628C2×Q8—44no—
629C2×Q8—712no—
630C2×Q8—1424no—
631C2×Q8—1421no—
632C2×D4—2844no—
633C2×D4—712no—
634C2×D4—1422no—
635C2×D4—1422no—
636C2×D4—1421no—
637C2×D4—1424no—
638C22×C4—24no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—42no—
642C22×C4—42no—
643C22×C4—2844no—
644C22×C4—1421no—
645C22×C4—1421no—
646C22×C4—1421no—
647C22×C4—1422no—
648C22×C4—1422no—
649C22×C4C2×C22⋊D7111yescharacteristic
650C22×C4C2×C22⋊D7111yescharacteristic
651C22×C4C2×C22⋊D7111yescharacteristic
652C22×C4C2×C22⋊D7111yescharacteristic
653C22×C4C2×C22⋊D7111yescharacteristic
654C22×C4C2×C22⋊D7111yescharacteristic
655C22×C4C2×C22⋊D7111yescharacteristic
656C22×C4C2×C22⋊D7111yescharacteristic
657C22×C4C2×C22⋊D7111yescharacteristic
658C22×C4C2×C22⋊D7111yescharacteristic
659C22×C4C2×C22⋊D7111yescharacteristic
660C22×C4C2×C22⋊D7111yescharacteristic
661C22×C4C2×C22⋊D7111yescharacteristic
662C22×C4C2×C22⋊D7111yescharacteristic
663C22×C4C2×C22⋊D7111yescharacteristic
664C22×C4C23×D7111yescharacteristic
665C22×C4C23×D7111yescharacteristic
666C22×C4C23×D7111yescharacteristic
667M16—1428no—
668C2×C8—718no—
669C4⋊C4—24no—
670C4⋊C4—24no—
671C4⋊C4—24no—
672C4⋊C4—24no—
673C4⋊C4—22no—
674C4⋊C4—22no—
675C4⋊C4—22no—
676C4⋊C4—22no—
677C4⋊C4—22no—
678C4⋊C4—22no—
679C4⋊C4—712no—
680C4⋊C4—712no—
681C4⋊C4—1422no—
682C4⋊C4—1422no—
683C4⋊C4—1422no—
684C4⋊C4—1422no—
685C4⋊C4—1422no—
686C4⋊C4—1422no—
687C4⋊C4—1422no—
688C4⋊C4—1422no—
689C4⋊C4—1421no—
690C4⋊C4—1421no—
691C4⋊C4C23×D7114yes—
692C4⋊C4C23×D7114yes—
693C22⋊C4—24no—
694C22⋊C4—24no—
695C22⋊C4—1422no—
696C22⋊C4—1422no—
697C22⋊C4—1422no—
698C22⋊C4—1422no—
699C22⋊C4—1422no—
700C22⋊C4—1422no—
701C22⋊C4—1422no—
702C22⋊C4—1422no—
703C22⋊C4—1422no—
704C22⋊C4—1422no—
705C42—24no—
706C42—24no—
707C42—1422no—
708C42—1422no—
709C42C2×C22⋊D7111yescharacteristic
710C42C2×C22⋊D7111yescharacteristic
711C42C2×C22⋊D7111yescharacteristic
712C42C2×C22⋊D7111yescharacteristic
713C42C2×C22⋊D7111yescharacteristic
714C42C2×C22⋊D7111yescharacteristic
715C42C2×C22⋊D7111yescharacteristic
716C42C2×C22⋊D7111yescharacteristic
717C42C2×C22⋊D7111yescharacteristic
718C42C2×C22⋊D7111yescharacteristic
719C42C2×C22⋊D7111yescharacteristic
720C42C2×C22⋊D7111yescharacteristic
721C42C23×D7111yescharacteristic
722C42C23×D7111yescharacteristic
723C42C23×D7111yescharacteristic
724C42C23×D7111yescharacteristic
725C23—22no—
726C23—22no—
727C23—41no—
728C23—2842no—
729C23—2842no—
730C23—2842no—
731C23—1422no—
732C23C22×C22⋊D7111yescharacteristic
733C23C22×C22⋊D7111yescharacteristic
734C23C22×C22⋊D7111yescharacteristic
735Q8—44no—
736Q8—44no—
737Q8—44no—
738Q8—44no—
739Q8—2842no—
740Q8—1424no—
741D4—2844no—
742D4—2844no—
743D4—2842no—
744D4—1424no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—24no—
756C2×C4—24no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—44no—
765C2×C4—44no—
766C2×C4—2844no—
767C2×C4—2842no—
768C2×C4—2842no—
769C2×C4—2842no—
770C2×C4—2844no—
771C2×C4—1422no—
772C2×C4—1422no—
773C2×C4—1422no—
774C2×C4C22×C22⋊D7111yescharacteristic
775C2×C4C22×C22⋊D7111yescharacteristic
776C2×C4C22×C22⋊D7111yescharacteristic
777C2×C4C22×C22⋊D7111yescharacteristic
778C2×C4C22×C22⋊D7111yescharacteristic
779C2×C4C22×C22⋊D7111yescharacteristic
780C2×C4C22×C22⋊D7111yescharacteristic
781C2×C4C22×C22⋊D7111yescharacteristic
782C2×C4C22×C22⋊D7111yescharacteristic
783C2×C4C22×C22⋊D7111yescharacteristic
784C2×C4C22×C22⋊D7111yescharacteristic
785C2×C4#1455617614yes—
786C2×C4C24×D7111yescharacteristic
787C8—1428no—
788C22—21no—
789C22—21no—
790C22—21no—
791C22—21no—
792C22—21no—
793C22—21no—
794C22—21no—
795C22—44no—
796C22—2842no—
797C22—2842no—
798C22—2842no—
799C22—5684no—
800C22#1798657312yes—
801C22#1798679712yes—
802C22C23×C22⋊D7111yescharacteristic
803C4—21no—
804C4—21no—
805C4—21no—
806C4—21no—
807C4—21no—
808C4—21no—
809C4—21no—
810C4—21no—
811C4—21no—
812C4—44no—
813C4—44no—
814C4—2842no—
815C4—2842no—
816C4—2842no—
817C4#1798657312yes—
818C4#1798679712yes—
819C4C2×#1455617612yes—
820C2—22no—
821C2—22no—
822C2—41no—
823C2—5682no—
824C2C2×#1798657311yescharacteristic
825C2C2×#1798679711yescharacteristic
826C2C2×#1798679711yescharacteristic
subgroupG/H
centerC22C23×C22⋊D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#533×C71C2
socleC22×C71C23×D4
prime radicalC2×#14556102C22
hypercenterC2×#533D71
hypocenterC71#60866
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C22×C42 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
2. #22599580C2semidirect
3. #22599570C2semidirect
4. #22599561C2semidirect
5. #22599519C2semidirect
6. #22599508C2semidirect
7. #22598893C2semidirect
8. #22598729C2semidirect
9. #22598288C2semidirect
11. #22598141C2semidirect
12. #22598133C2semidirect
13. #22596973C2semidirect
14. C2×#533×C71C2semidirect
33. #17986405C22semidirect
34. #17986405C22semidirect
35. #17986398C22semidirect
36. #17986361C22semidirect
37. #17986361C22semidirect
38. #17986356C22semidirect
39. #17986340C22semidirect
40. #17986334C22semidirect
41. #17986329C22semidirect
45. #17986303C22semidirect
46. #17986296C22semidirect
47. #17986291C22semidirect
48. #17986286C22semidirect
49. #17986281C22semidirect
50. #17986276C22semidirect
51. #17986056C22semidirect
52. #17986056C22semidirect
53. #17986052C22semidirect
54. #17986052C22semidirect
68. #533×C71C22semidirect
69. #533×C71C22semidirect
70. C2×C4⋊Q8×C71C22semidirect
71. C2×C4⋊Q8×C71C22semidirect
72. C2×#125×C71C22semidirect
414. C2×#533D71semidirect
428. C71#60866semidirect
435. #533C2×D71semidirect
436. #533C2×D71semidirect
437. C2×C4⋊Q8C2×D71semidirect
438. C2×C4⋊Q8C2×D71semidirect
449. C2×#125C2×D71semidirect

Maximal subgroups

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

subgroupindex
C2×#179865332
#225995802
#225995702
#225995612
#225995192
#225995082
#225988932
#225987292
#225982882
#225982802
#225981412
#225981332
#225969732
C2×#533×C712
#6086671