Finite Group Databasebeta

← C2×#22598518 #32865677

Subgroups — C2×#22598518 #32865677

Order 18176.

2274 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986473C211yesmaximal, characteristic, complemented
2#22598518C2116yesmaximal, direct product factor
3C2×#17986337C211yesmaximal, characteristic, complemented
4C2×#17986320C211yesmaximal, characteristic, complemented
5C2×#17986286C211yesmaximal, characteristic, complemented
6C2×#17986276C211yesmaximal, characteristic, complemented
7C2×#17986211C211yesmaximal, characteristic, complemented
8C2×#17986211C211yesmaximal, characteristic, complemented
9C2×#17986149C211yesmaximal, characteristic, complemented
10C2×#17986132C211yesmaximal, characteristic
11C2×#17986109C211yesmaximal, characteristic, complemented
12C2×#17986097C211yesmaximal, characteristic, complemented
13C2×C4×#11765852C211yesmaximal, characteristic, complemented
14C2×C4×#11765850C211yesmaximal, characteristic, complemented
15C2×#17986060C211yesmaximal, characteristic, complemented
16C2×#542×C71C211yesmaximal, characteristic, complemented
17C23×D284C2211yescharacteristic
18C22×#11765852C2211yescharacteristic
19C22×#11765852C2211yescharacteristic
20C22×#11765850C2211yescharacteristic
21C22×#11765850C2211yescharacteristic
22#17986473—24no—
23#17986473C2218yescomplemented
24C2×C4×D284C2211yescharacteristic
25C2×C4×D284C2211yescharacteristic
26C2×C4×D284C2211yescharacteristic
27C2×C4×D284C2211yescharacteristic
28C2×#14556090—21no—
29C2×#14556090—21no—
30C2×#14556087C2211yescharacteristic
31C2×C22⋊C4×D71—21no—
32C2×C22⋊C4×D71—21no—
33#17986337C2218yescomplemented
34#17986320C2218yescomplemented
35#17986286C2218yescomplemented
36#17986276C2218yescomplemented
37#17986211C2218yescomplemented
38#17986211C2218yescomplemented
39#17986149C2218yescomplemented
40#17986132C2218yes—
41#17986109C2218yescomplemented
42#17986097C2218yescomplemented
43C4×#11765852C2218yescomplemented
44C4×#11765850C2218yescomplemented
45#17986060C2218yescomplemented
46C2×#14556061C2211yescharacteristic, complemented
47C2×#14556061C2211yescharacteristic, complemented
48C2×#14556059C2211yescharacteristic, complemented
49C2×#14556059C2211yescharacteristic, complemented
50C2×C4⋊(C71⋊C8)C2211yescharacteristic, complemented
51C2×C4⋊(C71⋊C8)C2211yescharacteristic, complemented
52C2×#14556052C2211yescharacteristic, complemented
53C2×#14556052C2211yescharacteristic, complemented
54C2×#14556049C2211yescharacteristic, complemented
55C2×#14556049C2211yescharacteristic, complemented
56C2×#14556048C2211yescharacteristic
57C2×#14556048C2211yescharacteristic
58C2×#14556048C2211yescharacteristic
59C2×#14556048C2211yescharacteristic
60C2×C22⋊(C71⋊C8)C2211yescharacteristic
61C2×C22⋊(C71⋊C8)C2211yescharacteristic
62C2×#14556039C2211yescharacteristic, complemented
63C2×C4×C71⋊C8C2211yescharacteristic, complemented
64#542×C71—24no—
65#542×C71C2218yescomplemented
66C2×C4⋊Q8×C71C2211yescharacteristic, complemented
67C2×#126×C71—21no—
68C2×#124×C71—21no—
69C2×#124×C71C2211yescharacteristic, complemented
70C2×#123×C71—21no—
71C2×C22⋊Q8×C71—21no—
72C2×C22⋊Q8×C71C2211yescharacteristic
73C2×#121×C71C2211yescharacteristic
74C2×C4×Q8×C71C2211yescharacteristic, complemented
75C2×C4×D4×C71C2211yescharacteristic, complemented
76C2×#117×C71C2211yescharacteristic
77C24×D71—21no—
78C22×D284—24no—
79C22×D284—24no—
80C22×D284—21no—
81C22×D284—22no—
82C22×D284C2314yes—
83C22×D284C2311yescharacteristic
84C22×D284C2311yescharacteristic
85C22×C4×D71—21no—
86C22×C4×D71—21no—
87C22×C4×D71—21no—
88C22×C4×D71—21no—
89C2×#11765852—24no—
90C2×#11765852—24no—
91C2×#11765852C2314yes—
92C2×#11765852C2314yes—
93C2×#11765850—24no—
94C2×#11765850—24no—
95C2×#11765850C2314yes—
96C2×#11765850C2314yes—
97C22×C71⋊C8C2311yescharacteristic
98C22×C71⋊C8C2311yescharacteristic
99C22×C71⋊C8C2311yescharacteristic
100C22×C71⋊C8C2311yescharacteristic
101C4×D284—22no—
102C4×D284—22no—
103C4×D284—22no—
104C4×D284—22no—
105C4×D284C2314yes—
106C4×D284C2314yes—
107C4×D284C2314yes—
108C4×D284C2314yes—
109#14556090—28no—
110#14556090—28no—
111#14556087—22no—
112#14556087C2314yes—
113C2×C4⋊Dic71C2311yescharacteristic
114C2×C4⋊Dic71C2311yescharacteristic
115C2×C22⋊Dic71—21no—
116C2×(C2×D71)⋊C4—21no—
117C2×(C2×D71)⋊C4—21no—
118C2×(C2×D71)⋊C4—21no—
119C2×(C2×D71)⋊C4—21no—
120C22⋊C4×D71—28no—
121C22⋊C4×D71—28no—
122C2×C4×Dic71—21no—
123#14556061C2314yescomplemented
124#14556061C2314yescomplemented
125#14556059C2314yescomplemented
126#14556059C2314yescomplemented
127C4⋊(C71⋊C8)C2314yescomplemented
128C4⋊(C71⋊C8)C2314yescomplemented
129#14556052C2314yescomplemented
130#14556052C2314yescomplemented
131#14556049C2314yescomplemented
132#14556049C2314yescomplemented
133#14556048C2314yes—
134#14556048C2314yes—
135#14556048C2314yes—
136#14556048C2314yes—
137C22⋊(C71⋊C8)C2314yes—
138C22⋊(C71⋊C8)C2314yes—
139#14556039C2314yescomplemented
140C4×C71⋊C8C2314yescomplemented
141C22×Q8×C71—21no—
142C22×Q8×C71C2311yescharacteristic
143C22×D4×C71—21no—
144C22×D4×C71C2311yescharacteristic
145C23×C4×C71—21no—
146C23×C4×C71C2311yescharacteristic
147C4⋊Q8×C71—22no—
148C4⋊Q8×C71C2314yescomplemented
149#126×C71—28no—
150#124×C71—28no—
151#124×C71—22no—
152#124×C71C2314yescomplemented
153#123×C71—28no—
154C22⋊Q8×C71—22no—
155C22⋊Q8×C71—28no—
156C22⋊Q8×C71C2314yes—
157#121×C71—22no—
158#121×C71C2314yes—
159C4×Q8×C71—22no—
160C4×Q8×C71C2314yescomplemented
161C4×D4×C71—22no—
162C4×D4×C71C2314yescomplemented
163#117×C71D414yes—
164#117×C71C2314yes—
165C2×C4⋊C4×C71—21no—
166C2×C4⋊C4×C71—21no—
167C2×C4⋊C4×C71—21no—
168C2×C4⋊C4×C71D411yescharacteristic
169C2×C4⋊C4×C71D411yescharacteristic
170C2×C4⋊C4×C71C2311yescharacteristic
171C2×C4⋊C4×C71C2311yescharacteristic
172C2×C22⋊C4×C71—21no—
173C2×C22⋊C4×C71—21no—
174C2×C22⋊C4×C71—21no—
175C2×C22⋊C4×C71—21no—
176C2×C22⋊C4×C71—21no—
177C2×C22⋊C4×C71D411yescharacteristic
178C2×C22⋊C4×C71D411yescharacteristic
179C2×C42×C71—21no—
180C2×C42×C71C2311yescharacteristic
181C2×C42×C71C2311yescharacteristic
182C23×D71—21no—
183C23×D71—21no—
184C23×D71—28no—
185C23×D71—24no—
186C23×D71—82no—
187C23×D71—82no—
188C2×D284—28no—
189C2×D284—216no—
190C2×D284—24no—
191C2×D284—21no—
192C2×D284—21no—
193C2×D284—22no—
194C2×D284—22no—
195C2×D284—28no—
196C2×D284—28no—
197C2×D284#4114yes—
198C2×D284#4114yes—
199C2×D284C2412yes—
200C2×D284C2412yes—
201C22×Dic71—21no—
202C22×Dic71—21no—
203C2×C4×D71—24no—
204C2×C4×D71—24no—
205C2×C4×D71—24no—
206C2×C4×D71—24no—
207C2×C4×D71—82no—
208C2×C4×D71—82no—
209C2×C4×D71—82no—
210C2×C4×D71—82no—
211#11765852—28no—
212#11765852—28no—
213#11765850—28no—
214#11765850—28no—
215C2×C71⋊C8—22no—
216C2×C71⋊C8—22no—
217C2×C71⋊C8—22no—
218C2×C71⋊C8—22no—
219C2×C71⋊C8C2412yes—
220C2×C71⋊C8C2412yes—
221C2×C71⋊C8C2412yes—
222C2×C71⋊C8C2412yes—
223C4⋊Dic71—21no—
224C4⋊Dic71—21no—
225C4⋊Dic71C2412yes—
226C4⋊Dic71C2412yes—
227C22⋊Dic71—24no—
228(C2×D71)⋊C4—24no—
229(C2×D71)⋊C4—24no—
230(C2×D71)⋊C4—24no—
231(C2×D71)⋊C4—24no—
232C4×Dic71—24no—
233C24×C71—21no—
234C24×C71C2×D411yescharacteristic
235C2×Q8×C71—21no—
236C2×Q8×C71—24no—
237C2×Q8×C71—22no—
238C2×Q8×C71—22no—
239C2×Q8×C71—82no—
240C2×Q8×C71C2412yes—
241C2×D4×C71—24no—
242C2×D4×C71—21no—
243C2×D4×C71—22no—
244C2×D4×C71—22no—
245C2×D4×C71—82no—
246C2×D4×C71C2412yes—
247C22×C4×C71—22no—
248C22×C4×C71—22no—
249C22×C4×C71—21no—
250C22×C4×C71—21no—
251C22×C4×C71—21no—
252C22×C4×C71—24no—
253C22×C4×C71—82no—
254C22×C4×C71C2×D411yescharacteristic
255C22×C4×C71C2×D411yescharacteristic
256C22×C4×C71C2×D411yescharacteristic
257C22×C4×C71C2×D411yescharacteristic
258C22×C4×C71C2×D411yescharacteristic
259C22×C4×C71C2×D412yes—
260C22×C4×C71C2412yes—
261C22×C4×C71C2411yescharacteristic
262C4⋊C4×C71—24no—
263C4⋊C4×C71—24no—
264C4⋊C4×C71—24no—
265C4⋊C4×C71—21no—
266C4⋊C4×C71—21no—
267C4⋊C4×C71C2×D414yes—
268C4⋊C4×C71C2×D414yes—
269C4⋊C4×C71C2412yes—
270C4⋊C4×C71C2412yes—
271C22⋊C4×C71—24no—
272C22⋊C4×C71—24no—
273C22⋊C4×C71—24no—
274C22⋊C4×C71—24no—
275C22⋊C4×C71—24no—
276C22⋊C4×C71C2×D414yes—
277C22⋊C4×C71C2×D414yes—
278C42×C71—24no—
279C42×C71C2×D412yes—
280C42×C71C2×D412yes—
281C42×C71C2412yes—
282C42×C71C2412yes—
283C23×C71—22no—
284C23×C71—22no—
285C23×C71—22no—
286C23×C71—22no—
287C23×C71—42no—
288C23×C71—42no—
289C23×C71—42no—
290C23×C71C22×D412yes—
291C23×C71C22×D411yescharacteristic
292C22×D71—24no—
293C22×D71—24no—
294C22×D71—22no—
295C22×D71—22no—
296C22×D71—216no—
297C22×D71—42no—
298C22×D71—42no—
299C22×D71—42no—
300C22×D71—42no—
301C22×D71—84no—
302C22×D71—84no—
303C22×D71—816no—
304Q8×C71—22no—
305Q8×C71—22no—
306Q8×C71—42no—
307Q8×C71—84no—
308D4×C71—22no—
309D4×C71—22no—
310D4×C71—42no—
311D4×C71—84no—
312C2×C4×C71—22no—
313C2×C4×C71—22no—
314C2×C4×C71—22no—
315C2×C4×C71—22no—
316C2×C4×C71—22no—
317C2×C4×C71—24no—
318C2×C4×C71—22no—
319C2×C4×C71—22no—
320C2×C4×C71—22no—
321C2×C4×C71—22no—
322C2×C4×C71—22no—
323C2×C4×C71—42no—
324C2×C4×C71—42no—
325C2×C4×C71—42no—
326C2×C4×C71—84no—
327C2×C4×C71C22×D412yes—
328C2×C4×C71C22×D412yes—
329C2×C4×C71C22×D412yes—
330C2×C4×C71C22×D412yes—
331C2×C4×C71C22×D412yes—
332C2×C4×C71C22×D411yescharacteristic
333C2×C4×C71C2×#4112yes—
334C2×C4×C71C2×#4112yes—
335C2×C4×C71C2511yescharacteristic
336C2×Dic71—22no—
337C2×Dic71—22no—
338C2×Dic71—42no—
339C2×Dic71—42no—
340D284—216no—
341D284—24no—
342D284—24no—
343D284—22no—
344D284—22no—
345D284C2×#4114yes—
346D284C2×#4114yes—
347C4×D71—84no—
348C4×D71—84no—
349C4×D71—84no—
350C4×D71—84no—
351C71⋊C8—22no—
352C71⋊C8—22no—
353C71⋊C8—22no—
354C71⋊C8—22no—
355C22×C71—22no—
356C22×C71—22no—
357C22×C71—22no—
358C22×C71—44no—
359C22×C71—42no—
360C22×C71—42no—
361C22×C71—42no—
362C22×C71—84no—
363C22×C71#52512yes—
364C22×C71#57612yes—
365C22×C71#57712yes—
366C22×C71C23×D411yescharacteristic
367C2×D71—24no—
368C2×D71—24no—
369C2×D71—48no—
370C2×D71—48no—
371C2×D71—42no—
372C2×D71—42no—
373C2×D71—42no—
374C2×D71—42no—
375C2×D71—816no—
376C4×C71—22no—
377C4×C71—22no—
378C4×C71—22no—
379C4×C71—22no—
380C4×C71—22no—
381C4×C71—42no—
382C4×C71—42no—
383C4×C71—42no—
384C4×C71#52512yes—
385C4×C71C22×#4111yescharacteristic
386C4×C71C22×#4111yescharacteristic
387Dic71—42no—
388Dic71—42no—
389C2×#3118—711nomaximal, Sylow
390C2×C71—42no—
391C2×C71—82no—
392C2×C71#311814yescomplemented
393C2×C71C2×#52511yescharacteristic
394C2×C71C2×#57611yescharacteristic
395C2×C71C2×#57711yescharacteristic
396D71—44no—
397D71—44no—
398C2×#542D7111yescharacteristic, complemented
399C2×#518—711no—
400#3118—7116no—
401C2×#485—711no—
402C2×#482—711no—
403C2×#476—711no—
404C2×#474—711no—
405C2×#463—711no—
406C2×#463—711no—
407C2×#450—711no—
408C2×#447—711no—
409C2×#442—711no—
410C2×#440—711no—
411C2×C4×SD16—711no—
412C2×C4×D8—711no—
413C2×#433—711no—
414C71C2×#311811yescharacteristic, complemented, Sylow
415C23×D4—711no—
416C22×SD16—711no—
417C22×SD16—711no—
418C22×D8—711no—
419C22×D8—711no—
420#542—24no—
421#542C2×D7118yescomplemented
422C2×C4⋊Q8C2×D7111yescharacteristic, complemented
423C2×#126—21no—
424C2×#124—21no—
425C2×#124C2×D7111yescharacteristic, complemented
426C2×#123—21no—
427C2×C22⋊Q8—21no—
428C2×C22⋊Q8C2×D7111yescharacteristic
429C2×#121C2×D7111yescharacteristic
430#518—718no—
431#518—1424no—
432C2×C4×Q8C2×D7111yescharacteristic, complemented
433C2×C4×D4—711no—
434C2×C4×D4—711no—
435C2×C4×D4—711no—
436C2×C4×D4—711no—
437C2×C4×D4—1421no—
438C2×C4×D4—1421no—
439C2×C4×D4C2×D7111yescharacteristic, complemented
440C2×#117—711no—
441C2×#117C2×D7111yescharacteristic
442C22×C22⋊C4—1421no—
443C22×C22⋊C4—1421no—
444#485—718no—
445#482—718no—
446#476—718no—
447#474—718no—
448#463—718no—
449#463—718no—
450#450—718no—
451#447—718no—
452#442—718no—
453#440—718no—
454C4×SD16—718no—
455C4×D8—718no—
456#433—718no—
457C2×#107—711no—
458C2×#107—711no—
459C2×#106—711no—
460C2×#106—711no—
461C2×C4⋊C8—711no—
462C2×C4⋊C8—711no—
463C2×#103—711no—
464C2×#103—711no—
465C2×#102—711no—
466C2×#102—711no—
467C2×#102—711no—
468C2×#102—711no—
469C2×#102—711no—
470C2×#102—711no—
471C2×C22⋊C8—711no—
472C2×C22⋊C8—711no—
473C2×#97—711no—
474C2×C4×C8—711no—
475C25—1421no—
476C22×Q8—21no—
477C22×Q8C22×D7111yescharacteristic
478C22×D4—21no—
479C22×D4—711no—
480C22×D4—711no—
481C22×D4—714no—
482C22×D4—1424no—
483C22×D4—1424no—
484C22×D4—1421no—
485C22×D4—1422no—
486C22×D4C22×D7111yescharacteristic
487C23×C4—21no—
488C23×C4—1421no—
489C23×C4—1421no—
490C23×C4—1421no—
491C23×C4—1421no—
492C23×C4C22×D7111yescharacteristic
493C2×SD16—714no—
494C2×SD16—714no—
495C2×SD16—1424no—
496C2×SD16—1424no—
497C2×D8—714no—
498C2×D8—714no—
499C2×D8—1424no—
500C2×D8—1424no—
501C22×C8—711no—
502C22×C8—711no—
503C22×C8—711no—
504C22×C8—711no—
505C4⋊Q8—22no—
506C4⋊Q8C22×D7114yescomplemented
507#126—28no—
508#124—28no—
509#124—22no—
510#124C22×D7114yescomplemented
511#123—28no—
512C22⋊Q8—22no—
513C22⋊Q8—28no—
514C22⋊Q8C22×D7114yes—
515#121—22no—
516#121C22×D7114yes—
517C4×Q8—22no—
518C4×Q8C22×D7114yescomplemented
519C4×D4—22no—
520C4×D4—714no—
521C4×D4—714no—
522C4×D4—714no—
523C4×D4—714no—
524C4×D4—1428no—
525C4×D4—1428no—
526C4×D4—1422no—
527C4×D4—1422no—
528C4×D4—1422no—
529C4×D4—1422no—
530C4×D4C22×D7114yescomplemented
531#117—714no—
532#117—1422no—
533#117C22⋊D7114yes—
534#117C22×D7114yes—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4—711no—
539C2×C4⋊C4—711no—
540C2×C4⋊C4C22⋊D7111yescharacteristic
541C2×C4⋊C4C22⋊D7111yescharacteristic
542C2×C4⋊C4C22×D7111yescharacteristic
543C2×C4⋊C4C22×D7111yescharacteristic
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—1421no—
550C2×C22⋊C4—1421no—
551C2×C22⋊C4—1421no—
552C2×C22⋊C4—1421no—
553C2×C22⋊C4—1421no—
554C2×C22⋊C4—1428no—
555C2×C22⋊C4—1428no—
556C2×C22⋊C4C22⋊D7111yescharacteristic
557C2×C22⋊C4C22⋊D7111yescharacteristic
558C2×C42—21no—
559C2×C42—1421no—
560C2×C42C22×D7111yescharacteristic
561C2×C42C22×D7111yescharacteristic
562#107—714no—
563#107—714no—
564#106—714no—
565#106—714no—
566C4⋊C8—714no—
567C4⋊C8—714no—
568#103—714no—
569#103—714no—
570#102—714no—
571#102—714no—
572#102—714no—
573#102—714no—
574#102—714no—
575#102—714no—
576C22⋊C8—714no—
577C22⋊C8—714no—
578#97—714no—
579C4×C8—714no—
580C24—21no—
581C24—5682no—
582C24—5682no—
583C24—1428no—
584C24—1421no—
585C24—1421no—
586C24—1424no—
587C24C2×C22⋊D7111yescharacteristic
588C2×Q8—21no—
589C2×Q8—24no—
590C2×Q8—22no—
591C2×Q8—22no—
592C2×Q8—82no—
593C2×Q8C23×D7112yes—
594C2×D4—24no—
595C2×D4—21no—
596C2×D4—22no—
597C2×D4—22no—
598C2×D4—82no—
599C2×D4—714no—
600C2×D4—714no—
601C2×D4—712no—
602C2×D4—712no—
603C2×D4—1428no—
604C2×D4—1428no—
605C2×D4—1428no—
606C2×D4—14216no—
607C2×D4—1424no—
608C2×D4—1421no—
609C2×D4—1421no—
610C2×D4—1422no—
611C2×D4—1422no—
612C2×D4C23×D7112yes—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—24no—
619C22×C4—82no—
620C22×C4—5682no—
621C22×C4—5682no—
622C22×C4—5682no—
623C22×C4—5682no—
624C22×C4—1421no—
625C22×C4—1421no—
626C22×C4—1424no—
627C22×C4—1424no—
628C22×C4—1424no—
629C22×C4—1424no—
630C22×C4C2×C22⋊D7112yes—
631C22×C4C2×C22⋊D7111yescharacteristic
632C22×C4C2×C22⋊D7111yescharacteristic
633C22×C4C2×C22⋊D7111yescharacteristic
634C22×C4C2×C22⋊D7111yescharacteristic
635C22×C4C2×C22⋊D7111yescharacteristic
636C22×C4C23×D7112yes—
637C22×C4C23×D7111yescharacteristic
638SD16—1428no—
639SD16—1428no—
640D8—1428no—
641D8—1428no—
642C2×C8—712no—
643C2×C8—712no—
644C2×C8—712no—
645C2×C8—712no—
646C2×C8—1422no—
647C2×C8—1422no—
648C2×C8—1422no—
649C2×C8—1422no—
650C4⋊C4—24no—
651C4⋊C4—24no—
652C4⋊C4—24no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—712no—
656C4⋊C4—712no—
657C4⋊C4—1421no—
658C4⋊C4—1421no—
659C4⋊C4C2×C22⋊D7114yes—
660C4⋊C4C2×C22⋊D7114yes—
661C4⋊C4C23×D7112yes—
662C4⋊C4C23×D7112yes—
663C22⋊C4—24no—
664C22⋊C4—24no—
665C22⋊C4—24no—
666C22⋊C4—24no—
667C22⋊C4—24no—
668C22⋊C4—1424no—
669C22⋊C4—1424no—
670C22⋊C4—1424no—
671C22⋊C4—1424no—
672C22⋊C4—1424no—
673C22⋊C4C2×C22⋊D7114yes—
674C22⋊C4C2×C22⋊D7114yes—
675C42—24no—
676C42—1424no—
677C42C2×C22⋊D7112yes—
678C42C2×C22⋊D7112yes—
679C42C23×D7112yes—
680C42C23×D7112yes—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—2842no—
689C23—2842no—
690C23—2842no—
691C23—2842no—
692C23—5684no—
693C23—5684no—
694C23—56816no—
695C23—14216no—
696C23—1422no—
697C23—1422no—
698C23—1424no—
699C23—1424no—
700C23C22×C22⋊D7112yes—
701C23C22×C22⋊D7111yescharacteristic
702Q8—22no—
703Q8—22no—
704Q8—42no—
705Q8—84no—
706D4—22no—
707D4—22no—
708D4—42no—
709D4—84no—
710D4—714no—
711D4—714no—
712D4—14216no—
713D4—1422no—
714D4—1422no—
715D4—1424no—
716D4—1424no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—24no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—84no—
732C2×C4—2842no—
733C2×C4—2842no—
734C2×C4—5684no—
735C2×C4—5684no—
736C2×C4—5684no—
737C2×C4—5684no—
738C2×C4—1422no—
739C2×C4—1422no—
740C2×C4C22×C22⋊D7112yes—
741C2×C4C22×C22⋊D7112yes—
742C2×C4C22×C22⋊D7112yes—
743C2×C4C22×C22⋊D7112yes—
744C2×C4C22×C22⋊D7112yes—
745C2×C4C22×C22⋊D7111yescharacteristic
746C2×C4#41×D7112yes—
747C2×C4#41×D7112yes—
748C2×C4C24×D7111yescharacteristic
749C8—1422no—
750C8—1422no—
751C8—1422no—
752C8—1422no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—44no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22—84no—
761C22—2842no—
762C22—2842no—
763C22—2842no—
764C22—2842no—
765C22—2848no—
766C22—2848no—
767C22—56816no—
768C22—1424no—
769C22—1424no—
770C22#1798650612yes—
771C22#1798680212yes—
772C22#1798680712yes—
773C22C23×C22⋊D7111yescharacteristic
774C4—22no—
775C4—22no—
776C4—22no—
777C4—22no—
778C4—22no—
779C4—42no—
780C4—42no—
781C4—42no—
782C4—2842no—
783C4—2842no—
784C4#1798650612yes—
785C4C2×#41×D7111yescharacteristic
786C4C2×#41×D7111yescharacteristic
787C2—42no—
788C2—82no—
789C2—2844no—
790C2—2844no—
791C2#2259851814yesdirect product factor
792C2C2×#1798650611yescharacteristic
793C2C2×#1798680211yescharacteristic
794C2C2×#1798680711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#542×C71C2
socleC23×C71C22×D4
prime radicalC2×#17986132C2
hypercenterC2×#542D71
hypocenterC71C2×#3118
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
1. C2×#17986473C2semidirect
2. #22598518C2direct (N × H)
3. C2×#17986337C2semidirect
4. C2×#17986320C2semidirect
5. C2×#17986286C2semidirect
6. C2×#17986276C2semidirect
7. C2×#17986211C2semidirect
8. C2×#17986211C2semidirect
9. C2×#17986149C2semidirect
11. C2×#17986109C2semidirect
12. C2×#17986097C2semidirect
13. C2×C4×#11765852C2semidirect
14. C2×C4×#11765850C2semidirect
15. C2×#17986060C2semidirect
16. C2×#542×C71C2semidirect
23. #17986473C22semidirect
33. #17986337C22semidirect
34. #17986320C22semidirect
35. #17986286C22semidirect
36. #17986276C22semidirect
37. #17986211C22semidirect
38. #17986211C22semidirect
39. #17986149C22semidirect
41. #17986109C22semidirect
42. #17986097C22semidirect
43. C4×#11765852C22semidirect
44. C4×#11765850C22semidirect
45. #17986060C22semidirect
46. C2×#14556061C22semidirect
47. C2×#14556061C22semidirect
48. C2×#14556059C22semidirect
49. C2×#14556059C22semidirect
50. C2×C4⋊(C71⋊C8)C22semidirect
51. C2×C4⋊(C71⋊C8)C22semidirect
52. C2×#14556052C22semidirect
53. C2×#14556052C22semidirect
54. C2×#14556049C22semidirect
55. C2×#14556049C22semidirect
62. C2×#14556039C22semidirect
63. C2×C4×C71⋊C8C22semidirect
65. #542×C71C22semidirect
66. C2×C4⋊Q8×C71C22semidirect
69. C2×#124×C71C22semidirect
74. C2×C4×Q8×C71C22semidirect
75. C2×C4×D4×C71C22semidirect
123. #14556061C23semidirect
124. #14556061C23semidirect
125. #14556059C23semidirect
126. #14556059C23semidirect
127. C4⋊(C71⋊C8)C23semidirect
128. C4⋊(C71⋊C8)C23semidirect
129. #14556052C23semidirect
130. #14556052C23semidirect
131. #14556049C23semidirect
132. #14556049C23semidirect
139. #14556039C23semidirect
140. C4×C71⋊C8C23semidirect
148. C4⋊Q8×C71C23semidirect
152. #124×C71C23semidirect
160. C4×Q8×C71C23semidirect
162. C4×D4×C71C23semidirect
392. C2×C71#3118semidirect
398. C2×#542D71semidirect
414. C71C2×#3118semidirect
421. #542C2×D71semidirect
422. C2×C4⋊Q8C2×D71semidirect
425. C2×#124C2×D71semidirect
432. C2×C4×Q8C2×D71semidirect
439. C2×C4×D4C2×D71semidirect
506. C4⋊Q8C22×D71semidirect
510. #124C22×D71semidirect
518. C4×Q8C22×D71semidirect
530. C4×D4C22×D71semidirect
791. C2#22598518direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179864732
#225985182
C2×#179863372
C2×#179863202
C2×#179862862
C2×#179862762
C2×#179862112
C2×#179861492
C2×#179861322
C2×#179861092
C2×#179860972
C2×C4×#117658522
C2×C4×#117658502
C2×#179860602
C2×#542×C712
C2×#311871