Finite Group Databasebeta

← #32870870

Subgroups — #32870870

Order 18176.

2082 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986549C211yesmaximal, characteristic
2#22599652C214yesmaximal, complemented
3#22599481C212yesmaximal, complemented
4#22599468C212yesmaximal, complemented
5#22599278C212yesmaximal, complemented
6#22599265C212yesmaximal, complemented
7#22599093C214yesmaximal, complemented
8#22598900C214yesmaximal, complemented
9#22598371C214yesmaximal, complemented
10#22598344C214yesmaximal, complemented
11C2×#17986052C211yesmaximal, characteristic, complemented
12C2×#533×C71C211yesmaximal, characteristic, complemented
13C22×#11765865—21no—
14#17986549—21no—
15#17986549—21no—
16#17986549—21no—
17#17986549—21no—
18#17986549C2212yes—
19#17986549C2212yes—
20#17986549C2212yes—
21#17986549C2212yes—
22C2×#14556128C2211yescharacteristic
23C2×#14556125C2211yescharacteristic
24C2×#14556116—21no—
25C2×#14556102—21no—
26C2×#14556102C2212yes—
27C2×C4×D284—21no—
28C2×C4×D284C2212yes—
29#17986395C2214yescomplemented
30#17986373C2214yescomplemented
31#17986349C2214yescomplemented
32#17986347C2214yescomplemented
33#17986327C2218yes—
34#17986317C2218yescomplemented
35#17986286C2218yescomplemented
36#17986284C2218yescomplemented
37#17986230C22116yescomplemented
38#17986201C2218yescomplemented
39#17986199C2218yescomplemented
40#17986149C2218yes—
41#17986138C2218yescomplemented
42C4×#11765852C22116yescomplemented
43#17986052C2212yes—
44#17986052C2212yes—
45#17986052C2212yescomplemented
46#17986052C2212yescomplemented
47C2×C4⋊(C71⋊C8)C2212yescomplemented
48C2×C22⋊(C71⋊C8)C2212yes—
49C2×C4×C71⋊C8C2212yescomplemented
50#533×C71—21no—
51#533×C71—21no—
52#533×C71—21no—
53#533×C71—21no—
54#533×C71C2212yes—
55#533×C71C2212yes—
56#533×C71C2212yescomplemented
57#533×C71C2212yescomplemented
58C2×C4⋊Q8×C71C2211yescharacteristic, complemented
59C2×C4⋊Q8×C71C2211yescharacteristic, complemented
60C2×#125×C71—21no—
61C2×C22⋊Q8×C71—21no—
62C2×C22⋊Q8×C71C2212yes—
63C2×C4×Q8×C71—21no—
64C2×C4×Q8×C71C2212yescomplemented
65C2×#117×C71—21no—
66C22×C42×C71C2211yescharacteristic
67C2×#11765865—22no—
68C2×#11765865—22no—
69C2×#11765865—22no—
70C2×#11765865—22no—
71C2×#11765865—48no—
72C22×Dic142—21no—
73C22×D284—21no—
74C22×D284—21no—
75C22×D284C2312yes—
76C22×C22⋊D71—22no—
77C22×C4×D71—22no—
78C2×#11765852C23116yes—
79C22×C71⋊C8C2314yes—
80#14556128—21no—
81#14556128—21no—
82#14556128C2312yes—
83#14556128C2312yes—
84#14556125—21no—
85#14556125—21no—
86#14556125C2312yes—
87#14556125C2312yes—
88#14556116—22no—
89#14556116—22no—
90#14556116—22no—
91#14556116—22no—
92#14556102—22no—
93#14556102—22no—
94#14556102—22no—
95#14556102—22no—
96#14556102—22no—
97#14556102—22no—
98#14556102C2314yes—
99#14556102C2314yes—
100C4×D284—22no—
101C4×D284—22no—
102C4×D284—22no—
103C4×D284—22no—
104C4×D284—22no—
105C4×D284—22no—
106C4×D284C2314yes—
107C4×D284C2314yes—
108C2×C4⋊Dic71—21no—
109C2×C4⋊Dic71C2312yes—
110C2×(C2×D71)⋊C4—22no—
111C2×(C2×D71)⋊C4—22no—
112#14556059C23116yes—
113C4⋊(C71⋊C8)C2314yes—
114C4⋊(C71⋊C8)C2314yes—
115#14556052C23116yes—
116#14556048C23116yes—
117C22⋊(C71⋊C8)C2314yes—
118C22⋊(C71⋊C8)C2314yes—
119C4×C71⋊C8C2314yes—
120C4×C71⋊C8C2314yes—
121C22×Q8×C71—21no—
122C22×Q8×C71C2312yes—
123C23×C4×C71D411yescharacteristic
124C23×C4×C71D411yescharacteristic
125C23×C4×C71C2311yescharacteristic
126C4⋊Q8×C71—21no—
127C4⋊Q8×C71—21no—
128C4⋊Q8×C71—21no—
129C4⋊Q8×C71—21no—
130C4⋊Q8×C71C2312yes—
131C4⋊Q8×C71C2312yes—
132C4⋊Q8×C71C2312yes—
133C4⋊Q8×C71C2312yes—
134#125×C71—22no—
135#125×C71—22no—
136#125×C71—22no—
137#125×C71—22no—
138C22⋊Q8×C71—22no—
139C22⋊Q8×C71—22no—
140C22⋊Q8×C71—22no—
141C22⋊Q8×C71—22no—
142C22⋊Q8×C71—22no—
143C22⋊Q8×C71—22no—
144C22⋊Q8×C71C2314yes—
145C22⋊Q8×C71C2314yes—
146C4×Q8×C71—22no—
147C4×Q8×C71—22no—
148C4×Q8×C71—22no—
149C4×Q8×C71—22no—
150C4×Q8×C71—22no—
151C4×Q8×C71—22no—
152C4×Q8×C71C2314yes—
153C4×Q8×C71C2314yes—
154#117×C71—22no—
155#117×C71—22no—
156#117×C71—22no—
157#117×C71—22no—
158C2×C4⋊C4×C71—21no—
159C2×C4⋊C4×C71—21no—
160C2×C4⋊C4×C71—21no—
161C2×C4⋊C4×C71—22no—
162C2×C4⋊C4×C71—22no—
163C2×C4⋊C4×C71C2312yes—
164C2×C22⋊C4×C71—22no—
165C2×C42×C71—22no—
166C2×C42×C71D411yescharacteristic
167C2×C42×C71D411yescharacteristic
168C2×C42×C71D411yescharacteristic
169C2×C42×C71D411yescharacteristic
170C2×C42×C71D411yescharacteristic
171C2×C42×C71D411yescharacteristic
172C2×C42×C71C2311yescharacteristic
173C2×C42×C71C2311yescharacteristic
174C2×C42×C71C2311yescharacteristic
175C2×C42×C71C2311yescharacteristic
176C2×C42×C71C2311yescharacteristic
177C2×C42×C71C2311yescharacteristic
178C23×D71—22no—
179#11765865—48no—
180#11765865—48no—
181#11765865—48no—
182#11765865—48no—
183C2×Dic142—22no—
184C2×Dic142—22no—
185C2×Dic142—44no—
186C2×D284—22no—
187C2×D284—22no—
188C2×D284—22no—
189C2×D284—22no—
190C2×D284—22no—
191C2×D284—44no—
192C2×D284—44no—
193C2×D284—44no—
194C2×D284C2414yes—
195C2×C22⋊D71—24no—
196C2×C22⋊D71—24no—
197C2×C22⋊D71—48no—
198C22×Dic71—22no—
199C2×C4×D71—24no—
200C2×C4×D71—24no—
201C2×C4×D71—48no—
202#11765852—416no—
203C2×C71⋊C8—44no—
204C2×C71⋊C8C2418yes—
205C4⋊Dic71—22no—
206C4⋊Dic71—22no—
207C4⋊Dic71—22no—
208C4⋊Dic71C2414yes—
209(C2×D71)⋊C4—24no—
210(C2×D71)⋊C4—24no—
211(C2×D71)⋊C4—24no—
212(C2×D71)⋊C4—24no—
213C24×C71C2×D411yescharacteristic
214C2×Q8×C71—22no—
215C2×Q8×C71—22no—
216C2×Q8×C71—22no—
217C2×Q8×C71—44no—
218C2×Q8×C71—44no—
219C2×Q8×C71C2414yes—
220C22×C4×C71—22no—
221C22×C4×C71—22no—
222C22×C4×C71—42no—
223C22×C4×C71—42no—
224C22×C4×C71SD1618yescomplemented
225C22×C4×C71C2×D411yescharacteristic
226C22×C4×C71C2×D411yescharacteristic
227C22×C4×C71C2×D411yescharacteristic
228C22×C4×C71C2×D411yescharacteristic
229C22×C4×C71C2×D411yescharacteristic
230C22×C4×C71C2×D411yescharacteristic
231C22×C4×C71C2×D411yescharacteristic
232C22×C4×C71C2×D411yescharacteristic
233C22×C4×C71C2×D411yescharacteristic
234C22×C4×C71C2×D411yescharacteristic
235C22×C4×C71C2×D411yescharacteristic
236C22×C4×C71C2×D411yescharacteristic
237C22×C4×C71C2×D411yescharacteristic
238C22×C4×C71C2×D411yescharacteristic
239C22×C4×C71C2×D411yescharacteristic
240C22×C4×C71C2411yescharacteristic
241C22×C4×C71C2411yescharacteristic
242C22×C4×C71C2411yescharacteristic
243C4⋊C4×C71—22no—
244C4⋊C4×C71—22no—
245C4⋊C4×C71—22no—
246C4⋊C4×C71—22no—
247C4⋊C4×C71—22no—
248C4⋊C4×C71—22no—
249C4⋊C4×C71—24no—
250C4⋊C4×C71—24no—
251C4⋊C4×C71—24no—
252C4⋊C4×C71—24no—
253C4⋊C4×C71—22no—
254C4⋊C4×C71C2414yes—
255C22⋊C4×C71—24no—
256C22⋊C4×C71—24no—
257C42×C71—24no—
258C42×C71—24no—
259C42×C71C2×D411yescharacteristic
260C42×C71C2×D411yescharacteristic
261C42×C71C2×D411yescharacteristic
262C42×C71C2×D411yescharacteristic
263C42×C71C2×D411yescharacteristic
264C42×C71C2×D411yescharacteristic
265C42×C71C2×D411yescharacteristic
266C42×C71C2×D411yescharacteristic
267C42×C71C2×D411yescharacteristic
268C42×C71C2×D411yescharacteristic
269C42×C71C2×D411yescharacteristic
270C42×C71C2×D411yescharacteristic
271C42×C71C2411yescharacteristic
272C42×C71C2411yescharacteristic
273C42×C71C2411yescharacteristic
274C42×C71C2411yescharacteristic
275C23×C71—41no—
276C23×C71—41no—
277C23×C71C2×SD1614yes—
278C23×C71C22×D411yescharacteristic
279C23×C71C22×D411yescharacteristic
280C23×C71C22×D411yescharacteristic
281C22×D71—24no—
282C22×D71—44no—
283C22×D71—44no—
284C22×D71—44no—
285Q8×C71—28no—
286Q8×C71—44no—
287Q8×C71—44no—
288Q8×C71—44no—
289C2×C4×C71—22no—
290C2×C4×C71—22no—
291C2×C4×C71—22no—
292C2×C4×C71—22no—
293C2×C4×C71—22no—
294C2×C4×C71—22no—
295C2×C4×C71—24no—
296C2×C4×C71—24no—
297C2×C4×C71—41no—
298C2×C4×C71—41no—
299C2×C4×C71—41no—
300C2×C4×C71—41no—
301C2×C4×C71—41no—
302C2×C4×C71—41no—
303C2×C4×C71—44no—
304C2×C4×C71—44no—
305C2×C4×C71C2×SD1614yes—
306C2×C4×C71C2×SD1614yes—
307C2×C4×C71C2×SD1614yes—
308C2×C4×C71C2×SD1614yes—
309C2×C4×C71C2×SD1614yes—
310C2×C4×C71C2×SD1614yes—
311C2×C4×C71C22×D411yescharacteristic
312C2×C4×C71C22×D411yescharacteristic
313C2×C4×C71C22×D411yescharacteristic
314C2×C4×C71C22×D411yescharacteristic
315C2×C4×C71C22×D411yescharacteristic
316C2×C4×C71C22×D411yescharacteristic
317C2×C4×C71C22×D411yescharacteristic
318C2×C4×C71C22×D411yescharacteristic
319C2×C4×C71C22×D411yescharacteristic
320C2×C4×C71C22×D411yescharacteristic
321C2×C4×C71C22×D411yescharacteristic
322C2×C4×C71C2511yescharacteristic
323C22⋊D71—48no—
324C22⋊D71—48no—
325C2×Dic71—24no—
326C2×Dic71—44no—
327D284—28no—
328D284—44no—
329D284—44no—
330D284—44no—
331D284—44no—
332D284—44no—
333C4×D71—48no—
334C4×D71—48no—
335Dic142—44no—
336Dic142—44no—
337C71⋊C8—28no—
338C22×C71—21no—
339C22×C71—21no—
340C22×C71—21no—
341C22×C71—21no—
342C22×C71—21no—
343C22×C71—21no—
344C22×C71—44no—
345C22×C71C22×SD1612yes—
346C22×C71C22×SD1612yes—
347C22×C71C22×SD1612yes—
348C22×C71C23×D411yescharacteristic
349C2×D71—44no—
350C2×D71—44no—
351C2×D71—44no—
352C2×D71—88no—
353C4×C71—21no—
354C4×C71—21no—
355C4×C71—21no—
356C4×C71—21no—
357C4×C71—21no—
358C4×C71—21no—
359C4×C71—44no—
360C4×C71—44no—
361C4×C71C22×SD1612yes—
362C4×C71C22×SD1612yes—
363C4×C71C22×SD1612yes—
364C4×C71C22×SD1612yes—
365C4×C71#57512yes—
366C4×C71#58512yes—
367Dic71—44no—
368#60941—711nomaximal, Sylow
369C2×C71—22no—
370C2×C71—22no—
371C2×C71—22no—
372C2×C71#344911yescharacteristic
373C2×C71C23×SD1611yescharacteristic
374C2×C71C2×#57511yescharacteristic
375D71—84no—
376C2×#533D7111yescharacteristic, complemented
377C2×#532—711no—
378#3246—714no—
379#3229—712no—
380#3227—712no—
381#3208—712no—
382#3206—712no—
383#3187—714no—
384#3167—714no—
385#3103—714no—
386#3101—714no—
387C2×#431—711no—
388C71#6094111yescharacteristic, complemented, Sylow
389C22×#41—1421no—
390#533—21no—
391#533—21no—
392#533—21no—
393#533—21no—
394#533C2×D7112yes—
395#533C2×D7112yes—
396#533C2×D7112yescomplemented
397#533C2×D7112yescomplemented
398#532—712no—
399#532—712no—
400#532—712no—
401#532—712no—
402#532—1421no—
403#532—1421no—
404#532—1421no—
405#532—1421no—
406C2×C4⋊Q8—711no—
407C2×C4⋊Q8C2×D7111yescharacteristic, complemented
408C2×C4⋊Q8C2×D7111yescharacteristic, complemented
409C2×#127—711no—
410C2×#125—21no—
411C2×#124—1421no—
412C2×C22⋊Q8—21no—
413C2×C22⋊Q8C2×D7112yes—
414C2×#121—712no—
415C2×#121—1421no—
416C2×C4×Q8—21no—
417C2×C4×Q8C2×D7112yescomplemented
418C2×C4×D4—712no—
419C2×C4×D4—1421no—
420C2×#117—21no—
421C22×C42C2×D7111yescharacteristic
422#498—714no—
423#492—714no—
424#487—714no—
425#486—714no—
426#483—718no—
427#481—718no—
428#476—718no—
429#475—718no—
430#465—7116no—
431#461—718no—
432#460—718no—
433#450—718no—
434#448—718no—
435C4×SD16—7116no—
436#431—712no—
437#431—712no—
438#431—712no—
439#431—712no—
440C2×C4⋊C8—712no—
441C2×C22⋊C8—712no—
442C2×C4×C8—712no—
443C2×#41—2848no—
444C2×#41—1422no—
445C2×#41—1422no—
446C2×#41—1422no—
447C2×#41—1422no—
448C22×Q8—21no—
449C22×Q8—1421no—
450C22×Q8C22×D7112yes—
451C22×D4—712no—
452C22×D4—1422no—
453C22×D4—1421no—
454C22×D4—1421no—
455C23×C4—1422no—
456C23×C4C22⋊D7111yescharacteristic
457C23×C4C22⋊D7111yescharacteristic
458C23×C4C22×D7111yescharacteristic
459C2×SD16—7116no—
460C22×C8—714no—
461C4⋊Q8—21no—
462C4⋊Q8—21no—
463C4⋊Q8—21no—
464C4⋊Q8—21no—
465C4⋊Q8—712no—
466C4⋊Q8—712no—
467C4⋊Q8—1421no—
468C4⋊Q8—1421no—
469C4⋊Q8C22×D7112yes—
470C4⋊Q8C22×D7112yes—
471C4⋊Q8C22×D7112yes—
472C4⋊Q8C22×D7112yes—
473#127—712no—
474#127—712no—
475#127—1421no—
476#127—1421no—
477#125—22no—
478#125—22no—
479#125—22no—
480#125—22no—
481#124—1422no—
482#124—1422no—
483#124—1422no—
484#124—1422no—
485C22⋊Q8—22no—
486C22⋊Q8—22no—
487C22⋊Q8—22no—
488C22⋊Q8—22no—
489C22⋊Q8—22no—
490C22⋊Q8—22no—
491C22⋊Q8C22×D7114yes—
492C22⋊Q8C22×D7114yes—
493#121—714no—
494#121—714no—
495#121—1422no—
496#121—1422no—
497#121—1422no—
498#121—1422no—
499#121—1422no—
500#121—1422no—
501C4×Q8—22no—
502C4×Q8—22no—
503C4×Q8—22no—
504C4×Q8—22no—
505C4×Q8—22no—
506C4×Q8—22no—
507C4×Q8C22×D7114yes—
508C4×Q8C22×D7114yes—
509C4×D4—714no—
510C4×D4—714no—
511C4×D4—1422no—
512C4×D4—1422no—
513C4×D4—1422no—
514C4×D4—1422no—
515C4×D4—1422no—
516C4×D4—1422no—
517#117—22no—
518#117—22no—
519#117—22no—
520#117—22no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—21no—
523C2×C4⋊C4—21no—
524C2×C4⋊C4—22no—
525C2×C4⋊C4—22no—
526C2×C4⋊C4—712no—
527C2×C4⋊C4—1421no—
528C2×C4⋊C4C22×D7112yes—
529C2×C22⋊C4—22no—
530C2×C22⋊C4—1422no—
531C2×C22⋊C4—1422no—
532C2×C42—22no—
533C2×C42C22⋊D7111yescharacteristic
534C2×C42C22⋊D7111yescharacteristic
535C2×C42C22⋊D7111yescharacteristic
536C2×C42C22⋊D7111yescharacteristic
537C2×C42C22⋊D7111yescharacteristic
538C2×C42C22⋊D7111yescharacteristic
539C2×C42C22×D7111yescharacteristic
540C2×C42C22×D7111yescharacteristic
541C2×C42C22×D7111yescharacteristic
542C2×C42C22×D7111yescharacteristic
543C2×C42C22×D7111yescharacteristic
544C2×C42C22×D7111yescharacteristic
545#106—7116no—
546C4⋊C8—714no—
547C4⋊C8—714no—
548#103—7116no—
549#102—7116no—
550C22⋊C8—714no—
551C22⋊C8—714no—
552C4×C8—714no—
553C4×C8—714no—
554C24—1422no—
555C24C2×C22⋊D7111yescharacteristic
556#41—2848no—
557#41—2848no—
558#41—2848no—
559#41—2848no—
560C2×Q8—22no—
561C2×Q8—22no—
562C2×Q8—22no—
563C2×Q8—44no—
564C2×Q8—44no—
565C2×Q8—2844no—
566C2×Q8—1422no—
567C2×Q8—1422no—
568C2×Q8C23×D7114yes—
569C2×D4—2844no—
570C2×D4—2844no—
571C2×D4—2848no—
572C2×D4—2844no—
573C2×D4—714no—
574C2×D4—1424no—
575C2×D4—1424no—
576C2×D4—1422no—
577C2×D4—1422no—
578C2×D4—1422no—
579C2×D4—1422no—
580C2×D4—1422no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—42no—
584C22×C4—42no—
585C22×C4—2848no—
586C22×C4—1422no—
587C22×C4—1424no—
588C22×C4—1424no—
589C22×C4#1176585218yescomplemented
590C22×C4C2×C22⋊D7111yescharacteristic
591C22×C4C2×C22⋊D7111yescharacteristic
592C22×C4C2×C22⋊D7111yescharacteristic
593C22×C4C2×C22⋊D7111yescharacteristic
594C22×C4C2×C22⋊D7111yescharacteristic
595C22×C4C2×C22⋊D7111yescharacteristic
596C22×C4C2×C22⋊D7111yescharacteristic
597C22×C4C2×C22⋊D7111yescharacteristic
598C22×C4C2×C22⋊D7111yescharacteristic
599C22×C4C2×C22⋊D7111yescharacteristic
600C22×C4C2×C22⋊D7111yescharacteristic
601C22×C4C2×C22⋊D7111yescharacteristic
602C22×C4C2×C22⋊D7111yescharacteristic
603C22×C4C2×C22⋊D7111yescharacteristic
604C22×C4C2×C22⋊D7111yescharacteristic
605C22×C4C23×D7111yescharacteristic
606C22×C4C23×D7111yescharacteristic
607C22×C4C23×D7111yescharacteristic
608SD16—28416no—
609C2×C8—2844no—
610C2×C8—718no—
611C4⋊C4—22no—
612C4⋊C4—22no—
613C4⋊C4—22no—
614C4⋊C4—22no—
615C4⋊C4—22no—
616C4⋊C4—22no—
617C4⋊C4—24no—
618C4⋊C4—24no—
619C4⋊C4—24no—
620C4⋊C4—24no—
621C4⋊C4—22no—
622C4⋊C4—714no—
623C4⋊C4—1422no—
624C4⋊C4—1422no—
625C4⋊C4—1422no—
626C4⋊C4C23×D7114yes—
627C22⋊C4—24no—
628C22⋊C4—24no—
629C22⋊C4—1424no—
630C22⋊C4—1424no—
631C22⋊C4—1424no—
632C22⋊C4—1424no—
633C42—24no—
634C42—24no—
635C42C2×C22⋊D7111yescharacteristic
636C42C2×C22⋊D7111yescharacteristic
637C42C2×C22⋊D7111yescharacteristic
638C42C2×C22⋊D7111yescharacteristic
639C42C2×C22⋊D7111yescharacteristic
640C42C2×C22⋊D7111yescharacteristic
641C42C2×C22⋊D7111yescharacteristic
642C42C2×C22⋊D7111yescharacteristic
643C42C2×C22⋊D7111yescharacteristic
644C42C2×C22⋊D7111yescharacteristic
645C42C2×C22⋊D7111yescharacteristic
646C42C2×C22⋊D7111yescharacteristic
647C42C23×D7111yescharacteristic
648C42C23×D7111yescharacteristic
649C42C23×D7111yescharacteristic
650C42C23×D7111yescharacteristic
651C23—41no—
652C23—41no—
653C23—2844no—
654C23—2844no—
655C23—2844no—
656C23—1424no—
657C23C2×#1176585214yes—
658C23C22×C22⋊D7111yescharacteristic
659C23C22×C22⋊D7111yescharacteristic
660C23C22×C22⋊D7111yescharacteristic
661Q8—28no—
662Q8—44no—
663Q8—44no—
664Q8—44no—
665Q8—2844no—
666Q8—2844no—
667D4—2844no—
668D4—2844no—
669D4—2848no—
670D4—2848no—
671D4—2844no—
672D4—2844no—
673D4—2844no—
674D4—1428no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—24no—
682C2×C4—24no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—44no—
690C2×C4—44no—
691C2×C4—2844no—
692C2×C4—2848no—
693C2×C4—2848no—
694C2×C4—1424no—
695C2×C4C2×#1176585214yes—
696C2×C4C2×#1176585214yes—
697C2×C4C2×#1176585214yes—
698C2×C4C2×#1176585214yes—
699C2×C4C2×#1176585214yes—
700C2×C4C2×#1176585214yes—
701C2×C4C22×C22⋊D7111yescharacteristic
702C2×C4C22×C22⋊D7111yescharacteristic
703C2×C4C22×C22⋊D7111yescharacteristic
704C2×C4C22×C22⋊D7111yescharacteristic
705C2×C4C22×C22⋊D7111yescharacteristic
706C2×C4C22×C22⋊D7111yescharacteristic
707C2×C4C22×C22⋊D7111yescharacteristic
708C2×C4C22×C22⋊D7111yescharacteristic
709C2×C4C22×C22⋊D7111yescharacteristic
710C2×C4C22×C22⋊D7111yescharacteristic
711C2×C4C22×C22⋊D7111yescharacteristic
712C2×C4C24×D7111yescharacteristic
713C8—1428no—
714C22—21no—
715C22—21no—
716C22—21no—
717C22—21no—
718C22—21no—
719C22—21no—
720C22—44no—
721C22—2844no—
722C22—2844no—
723C22—2844no—
724C22—5688no—
725C22C22×#1176585212yes—
726C22C22×#1176585212yes—
727C22C22×#1176585212yes—
728C22C23×C22⋊D7111yescharacteristic
729C4—21no—
730C4—21no—
731C4—21no—
732C4—21no—
733C4—21no—
734C4—21no—
735C4—44no—
736C4—44no—
737C4—2844no—
738C4C22×#1176585212yes—
739C4C22×#1176585212yes—
740C4C22×#1176585212yes—
741C4C22×#1176585212yes—
742C4#1798679712yes—
743C4#1798683512yes—
744C2—22no—
745C2—22no—
746C2—22no—
747C2—5684no—
748C2#2260166911yescharacteristic
749C2C23×#1176585211yescharacteristic
750C2C2×#1798679711yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#533×C71C2
socleC22×C71C23×D4
prime radicalC2×#17986549C2
hypercenterC2×#533D71
hypocenterC71#60941
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C2×C4 ◁ C22×C42 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
2. #22599652C2semidirect
3. #22599481C2semidirect
4. #22599468C2semidirect
5. #22599278C2semidirect
6. #22599265C2semidirect
7. #22599093C2semidirect
8. #22598900C2semidirect
9. #22598371C2semidirect
10. #22598344C2semidirect
11. C2×#17986052C2semidirect
12. C2×#533×C71C2semidirect
29. #17986395C22semidirect
30. #17986373C22semidirect
31. #17986349C22semidirect
32. #17986347C22semidirect
34. #17986317C22semidirect
35. #17986286C22semidirect
36. #17986284C22semidirect
37. #17986230C22semidirect
38. #17986201C22semidirect
39. #17986199C22semidirect
41. #17986138C22semidirect
42. C4×#11765852C22semidirect
45. #17986052C22semidirect
46. #17986052C22semidirect
47. C2×C4⋊(C71⋊C8)C22semidirect
49. C2×C4×C71⋊C8C22semidirect
56. #533×C71C22semidirect
57. #533×C71C22semidirect
58. C2×C4⋊Q8×C71C22semidirect
59. C2×C4⋊Q8×C71C22semidirect
64. C2×C4×Q8×C71C22semidirect
224. C22×C4×C71SD16semidirect
376. C2×#533D71semidirect
388. C71#60941semidirect
396. #533C2×D71semidirect
397. #533C2×D71semidirect
407. C2×C4⋊Q8C2×D71semidirect
408. C2×C4⋊Q8C2×D71semidirect
417. C2×C4×Q8C2×D71semidirect
589. C22×C4#11765852semidirect

Maximal subgroups

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

subgroupindex
C2×#179865492
#225996522
#225994812
#225994682
#225992782
#225992652
#225990932
#225989002
#225983712
#225983442
C2×#179860522
C2×#533×C712
#6094171