Finite Group Databasebeta

← C2×#22598199 #32865042

Subgroups — C2×#22598199 #32865042

Order 18176.

2094 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986626C211yesmaximal, characteristic, complemented
2C2×#17986481C211yesmaximal, characteristic
3#22598199C2116yesmaximal, direct product factor
4C2×#17986308C211yesmaximal, characteristic, complemented
5C2×#17986306C211yesmaximal, characteristic, complemented
6C2×#17986282C211yesmaximal, characteristic, complemented
7C2×#17986300C211yesmaximal, characteristic, complemented
8C2×#17986298C211yesmaximal, characteristic, complemented
9C2×#17986288C211yesmaximal, characteristic, complemented
10C2×#17986286C211yesmaximal, characteristic, complemented
11C2×#17986038C211yesmaximal, characteristic, complemented
12C2×#106×D71C211yesmaximal, characteristic, complemented
13C2×#17986024C211yesmaximal, characteristic, complemented
14C2×#17985999C211yesmaximal, characteristic
15C2×#17985994C211yesmaximal, characteristic
16C2×#475×C71C211yesmaximal, characteristic, complemented
17C22×#11765866C2211yescharacteristic
18C22×#11765848C2211yescharacteristic
19C22×C8×D71C2211yescharacteristic
20#17986626—24no—
21#17986626C2218yescomplemented
22C2×#14556127C2211yescharacteristic
23C2×#14556126—21no—
24C2×#14556120C2211yescharacteristic
25C2×#14556119C2211yescharacteristic
26C2×#14556118—21no—
27C2×#14556106—21no—
28C2×#14556104—21no—
29#17986481—24no—
30#17986481C2218yes—
31C2×Q8×Dic71C2211yescharacteristic
32C2×C4×D284—21no—
33C2×C4×D284C2211yescharacteristic
34C2×#14556090—21no—
35C2×#14556090C2211yescharacteristic
36C2×#14556086C2211yescharacteristic
37C2×#14556085—21no—
38C2×#14556085C2211yescharacteristic
39C2×C4⋊C4×D71—21no—
40C2×C4⋊C4×D71C2211yescharacteristic
41C2×C4⋊C4×D71C2211yescharacteristic
42#17986308C2218yescomplemented
43#17986306C2218yescomplemented
44#17986300C2218yescomplemented
45#17986298C2218yescomplemented
46#17986288C2218yescomplemented
47#17986286C2218yescomplemented
48#17986282C2218yescomplemented
49#17986038C2218yescomplemented
50C2×#14556062C2211yescharacteristic
51C2×#14556061C2211yescharacteristic
52C2×#14556060C2211yescharacteristic
53C2×#14556059C2211yescharacteristic
54C2×#14556059C2211yescharacteristic
55C2×#14556059C2211yescharacteristic
56#106×D71C2218yescomplemented
57#17986024C2218yescomplemented
58C2×C4⋊(C71⋊C8)C2211yescharacteristic
59C2×Dic71⋊C8C2211yescharacteristic
60C2×Dic71⋊C8C2211yescharacteristic
61#17985999C2218yes—
62#17985994C2218yes—
63C2×#14556052C2211yescharacteristic
64C2×#14556052C2211yescharacteristic
65C2×#14556050C2211yescharacteristic
66C2×#14556050C2211yescharacteristic
67C2×#14556048C2211yescharacteristic
68C2×#14556048C2211yescharacteristic
69C2×C4⋊Q8×C71C2211yescharacteristic
70C2×C4×Q8×C71C2211yescharacteristic
71#475×C71C2218yescomplemented
72C2×#106×C71C2211yescharacteristic
73C2×#106×C71C2211yescharacteristic
74C2×C4⋊C8×C71C2211yescharacteristic
75C2×#103×C71C2211yescharacteristic
76C2×#103×C71C2211yescharacteristic
77C2×#11765866—22no—
78C2×#11765866—24no—
79C2×#11765866Q818yescomplemented
80C2×#11765866C2314yes—
81C22×Dic142—21no—
82C22×D284—21no—
83C22×D284C2311yescharacteristic
84C22×C4×D71—21no—
85C22×C4×D71—21no—
86C22×C4×D71—21no—
87C22×C4×D71—21no—
88C22×C4×D71—21no—
89C22×C4×D71C2311yescharacteristic
90C2×#11765848—24no—
91C2×#11765848C2314yes—
92C22×C71⋊C8C2311yescharacteristic
93C22×C71⋊C8C2311yescharacteristic
94C2×C8×D71—24no—
95C2×C8×D71C2314yes—
96#14556127—22no—
97#14556127C2314yes—
98#14556126—28no—
99#14556120—22no—
100#14556120C2314yes—
101#14556119—22no—
102#14556119C2314yes—
103#14556118—28no—
104#14556106—28no—
105#14556104—28no—
106Q8×Dic71—22no—
107Q8×Dic71C2314yes—
108C4×D284—28no—
109C4×D284—22no—
110C4×D284C2314yes—
111#14556090—28no—
112#14556090—22no—
113#14556090C2314yes—
114#14556086—22no—
115#14556086C2314yes—
116#14556085—28no—
117#14556085D414yes—
118#14556085C2314yes—
119C2×C4⋊Dic71—21no—
120C2×C4⋊Dic71—21no—
121C2×C4⋊Dic71C2311yescharacteristic
122C2×C4⋊Dic71C2311yescharacteristic
123C2×C4⋊Dic71C2311yescharacteristic
124C2×Dic71⋊C4—21no—
125C2×Dic71⋊C4—21no—
126C2×Dic71⋊C4—21no—
127C2×Dic71⋊C4—21no—
128C2×Dic71⋊C4—21no—
129C2×Dic71⋊C4—21no—
130C2×Dic71⋊C4D411yescharacteristic
131C2×Dic71⋊C4D411yescharacteristic
132C4⋊C4×D71—22no—
133C4⋊C4×D71—22no—
134C4⋊C4×D71—28no—
135C4⋊C4×D71C2314yes—
136C4⋊C4×D71C2314yes—
137C2×(C2×D71)⋊C4—21no—
138C2×(C2×D71)⋊C4—21no—
139C2×(C2×D71)⋊C4—21no—
140C2×(C2×D71)⋊C4D411yescharacteristic
141C2×(C2×D71)⋊C4D411yescharacteristic
142C2×C4×Dic71—21no—
143C2×C4×Dic71—21no—
144C2×C4×Dic71C2311yescharacteristic
145#14556062C2314yes—
146#14556061C2314yes—
147#14556060C2314yes—
148#14556059C2314yes—
149#14556059C2314yes—
150#14556059C2314yes—
151C4⋊(C71⋊C8)C2314yes—
152Dic71⋊C8C2314yes—
153Dic71⋊C8C2314yes—
154#14556052C2314yes—
155#14556052C2314yes—
156#14556050C2314yes—
157#14556050C2314yes—
158#14556048C2314yes—
159#14556048C2314yes—
160C22×Q8×C71—21no—
161C22×Q8×C71C2311yescharacteristic
162C22×C8×C71C2311yescharacteristic
163C22×C8×C71C2311yescharacteristic
164C4⋊Q8×C71—22no—
165C4⋊Q8×C71C2314yes—
166C4×Q8×C71—22no—
167C4×Q8×C71C2314yes—
168C2×C4⋊C4×C71—21no—
169C2×C4⋊C4×C71—21no—
170C2×C4⋊C4×C71C2311yescharacteristic
171C2×C4⋊C4×C71C2311yescharacteristic
172C2×C4⋊C4×C71C2311yescharacteristic
173C2×C42×C71—21no—
174C2×C42×C71C2311yescharacteristic
175#106×C71C2314yes—
176#106×C71C2314yes—
177C4⋊C8×C71C2314yes—
178#103×C71C2314yes—
179#103×C71C2314yes—
180C23×D71—21no—
181C23×D71C2×D411yescharacteristic
182#11765866—216no—
183#11765866—28no—
184#11765866C2×Q8116yescomplemented
185C2×Dic142—24no—
186C2×Dic142—82no—
187C2×D284—28no—
188C2×D284—24no—
189C2×D284—21no—
190C2×D284—22no—
191C2×D284C2×Q814yes—
192C2×D284C2412yes—
193C22×Dic71—21no—
194C22×Dic71—21no—
195C22×Dic71—21no—
196C22×Dic71C2×D411yescharacteristic
197C22×Dic71C2×D411yescharacteristic
198C22×Dic71C2×D411yescharacteristic
199C2×C4×D71—28no—
200C2×C4×D71—24no—
201C2×C4×D71—24no—
202C2×C4×D71—24no—
203C2×C4×D71—24no—
204C2×C4×D71—24no—
205C2×C4×D71—82no—
206C2×C4×D71—82no—
207C2×C4×D71—82no—
208C2×C4×D71—82no—
209C2×C4×D71C2×D412yes—
210C2×C4×D71C2×Q814yes—
211C2×C4×D71#4114yes—
212C2×C4×D71C2412yes—
213#11765848—28no—
214C2×C71⋊C8—22no—
215C2×C71⋊C8—22no—
216C2×C71⋊C8C2412yes—
217C2×C71⋊C8C2412yes—
218C8×D71—28no—
219C4⋊Dic71—21no—
220C4⋊Dic71—21no—
221C4⋊Dic71—21no—
222C4⋊Dic71—24no—
223C4⋊Dic71—24no—
224C4⋊Dic71C2412yes—
225C4⋊Dic71C2412yes—
226C4⋊Dic71C2412yes—
227Dic71⋊C4—24no—
228Dic71⋊C4—24no—
229Dic71⋊C4—24no—
230Dic71⋊C4—24no—
231Dic71⋊C4—24no—
232Dic71⋊C4—24no—
233Dic71⋊C4C2×D414yes—
234Dic71⋊C4C2×D414yes—
235(C2×D71)⋊C4—24no—
236(C2×D71)⋊C4—24no—
237(C2×D71)⋊C4—24no—
238(C2×D71)⋊C4C2×D414yes—
239(C2×D71)⋊C4C2×D414yes—
240C4×Dic71—24no—
241C4×Dic71—24no—
242C4×Dic71C2×D412yes—
243C4×Dic71C2412yes—
244C2×Q8×C71—21no—
245C2×Q8×C71—24no—
246C2×Q8×C71—22no—
247C2×Q8×C71—82no—
248C2×Q8×C71C2×Q814yes—
249C2×Q8×C71C2412yes—
250C22×C4×C71—21no—
251C22×C4×C71—21no—
252C22×C4×C71—21no—
253C22×C4×C71—21no—
254C22×C4×C71C2×D411yescharacteristic
255C22×C4×C71C2×D411yescharacteristic
256C22×C4×C71C2411yescharacteristic
257C2×C8×C71—22no—
258C2×C8×C71—22no—
259C2×C8×C71C2412yes—
260C2×C8×C71C2412yes—
261C4⋊C4×C71—24no—
262C4⋊C4×C71—24no—
263C4⋊C4×C71—21no—
264C4⋊C4×C71—21no—
265C4⋊C4×C71—21no—
266C4⋊C4×C71C2412yes—
267C4⋊C4×C71C2412yes—
268C4⋊C4×C71C2412yes—
269C42×C71—24no—
270C42×C71C2×D412yes—
271C42×C71C2412yes—
272C23×C71C22×D411yescharacteristic
273C22×D71—22no—
274C22×D71—22no—
275C22×D71—24no—
276C22×D71—22no—
277C22×D71—42no—
278C22×D71—42no—
279C22×D71C22⋊Q814yes—
280C22×D71C22×D412yes—
281Q8×C71—24no—
282Q8×C71—22no—
283Q8×C71—84no—
284Q8×C71C22×Q814yes—
285C2×C4×C71—24no—
286C2×C4×C71—22no—
287C2×C4×C71—22no—
288C2×C4×C71—22no—
289C2×C4×C71—22no—
290C2×C4×C71—22no—
291C2×C4×C71—22no—
292C2×C4×C71—42no—
293C2×C4×C71—42no—
294C2×C4×C71—42no—
295C2×C4×C71C22×D412yes—
296C2×C4×C71C22×D412yes—
297C2×C4×C71C22×D411yescharacteristic
298C2×C4×C71C22×Q812yes—
299C2×C4×C71C2×#4112yes—
300C2×C4×C71C2511yescharacteristic
301C2×Dic71—22no—
302C2×Dic71—22no—
303C2×Dic71—22no—
304C2×Dic71—22no—
305C2×Dic71—22no—
306C2×Dic71—42no—
307C2×Dic71—42no—
308C2×Dic71—42no—
309C2×Dic71C22⋊Q814yes—
310C2×Dic71C22×D412yes—
311C2×Dic71C22×D412yes—
312C2×Dic71C22×D412yes—
313D284—216no—
314D284—24no—
315D284—22no—
316D284C22×Q814yes—
317C4×D71—216no—
318C4×D71—84no—
319C4×D71—84no—
320C4×D71—84no—
321C4×D71—84no—
322C4×D71C22⋊Q818yes—
323C4×D71C22×Q814yes—
324C4×D71C2×#4114yes—
325Dic142—84no—
326C8×C71—22no—
327C8×C71—22no—
328C71⋊C8—22no—
329C71⋊C8—22no—
330C22×C71C2×C22⋊Q812yes—
331C22×C71#57712yes—
332C22×C71#57712yes—
333C22×C71C23×D411yescharacteristic
334C2×D71—28no—
335C2×D71—22no—
336C2×D71—22no—
337C2×D71—24no—
338C2×D71—48no—
339C2×D71—42no—
340C2×D71—42no—
341C2×D71C2×C22⋊Q814yes—
342C4×C71—24no—
343C4×C71—22no—
344C4×C71—22no—
345C4×C71—42no—
346C4×C71—42no—
347C4×C71—42no—
348C4×C71C2×C22⋊Q812yes—
349C4×C71C23×Q811yescharacteristic
350C4×C71C22×#4111yescharacteristic
351Dic71—22no—
352Dic71—22no—
353Dic71—42no—
354Dic71—42no—
355Dic71—42no—
356Dic71C2×C22⋊Q814yes—
357C2×#3084—711nomaximal, Sylow
358C2×C71#308414yescomplemented
359C2×C71C22×C22⋊Q811yescharacteristic
360C2×C71C2×#57711yescharacteristic
361C2×C71C2×#57711yescharacteristic
362D71—24no—
363D71—44no—
364C2×#544—711no—
365C2×#520—711no—
366#3084—7116no—
367C2×#479—711no—
368C2×#479—711no—
369C2×#475—711no—
370C2×#475D7111yescharacteristic, complemented
371C2×#478—711no—
372C2×#478—711no—
373C2×#476—711no—
374C2×#476—711no—
375C2×#428—711no—
376C22×#106—711no—
377C2×#424—711no—
378C2×#417—711no—
379C2×#416—711no—
380C71C2×#308411yescharacteristic, complemented, Sylow
381C22×#41—711no—
382C22×M16—711no—
383C23×C8—711no—
384#544—718no—
385#544—1424no—
386C2×C4⋊Q8—711no—
387C2×C4⋊Q8—1421no—
388C2×C4⋊Q8C2×D7111yescharacteristic
389C2×#125—711no—
390C2×#125—711no—
391C2×#125—1421no—
392C2×C22⋊Q8—1421no—
393C2×C22⋊Q8—1421no—
394#520—718no—
395#520—1424no—
396C2×C4×Q8—711no—
397C2×C4×Q8C2×D7111yescharacteristic
398C2×C4×D4—711no—
399C2×C4×D4—711no—
400C2×C4×D4—1421no—
401C2×C4×D4—1421no—
402C2×#117—711no—
403C2×#117—711no—
404C2×#117—1421no—
405C22×C4⋊C4—711no—
406C22×C4⋊C4—711no—
407C22×C4⋊C4—1421no—
408#479—718no—
409#479—718no—
410#478—718no—
411#478—718no—
412#476—718no—
413#476—718no—
414#475—718no—
415#475C2×D7118yescomplemented
416#428—718no—
417C2×#107—711no—
418C2×#107—711no—
419C2×#106—711no—
420C2×#106—711no—
421C2×#106—711no—
422C2×#106—711no—
423C2×#106—718no—
424C2×#106C2×D7111yescharacteristic
425C2×#106C2×D7111yescharacteristic
426#424—718no—
427C2×C4⋊C8—711no—
428C2×C4⋊C8—711no—
429C2×C4⋊C8—711no—
430C2×C4⋊C8C2×D7111yescharacteristic
431#417—718no—
432#416—718no—
433C2×#103—711no—
434C2×#103—711no—
435C2×#103C2×D7111yescharacteristic
436C2×#103C2×D7111yescharacteristic
437C2×#102—711no—
438C2×#102—711no—
439C2×#102—711no—
440C2×#102—711no—
441C2×#41—718no—
442C2×#41—714no—
443C2×#41—1422no—
444C2×#41—1424no—
445C22×Q8—21no—
446C22×Q8—1421no—
447C22×Q8C22×D7111yescharacteristic
448C22×D4—711no—
449C22×D4—1421no—
450C23×C4—711no—
451C23×C4—1421no—
452C23×C4—1421no—
453C23×C4—1421no—
454C23×C4—1421no—
455C23×C4—1421no—
456C2×M16—714no—
457C2×M16—1424no—
458C22×C8—711no—
459C22×C8—711no—
460C22×C8—714no—
461C22×C8—1424no—
462C22×C8C22×D7111yescharacteristic
463C22×C8C22×D7111yescharacteristic
464C4⋊Q8—22no—
465C4⋊Q8—714no—
466C4⋊Q8—1422no—
467C4⋊Q8—1428no—
468C4⋊Q8C22×D7114yes—
469#125—714no—
470#125—714no—
471#125—1422no—
472#125—1428no—
473#125—1422no—
474C22⋊Q8—1428no—
475C22⋊Q8—1428no—
476C4×Q8—22no—
477C4×Q8—714no—
478C4×Q8—1422no—
479C4×Q8C22×D7114yes—
480C4×D4—714no—
481C4×D4—714no—
482C4×D4—1428no—
483C4×D4—1422no—
484C4×D4—1428no—
485C4×D4—1422no—
486#117—714no—
487#117—714no—
488#117—714no—
489#117—1428no—
490#117—1422no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—711no—
494C2×C4⋊C4—711no—
495C2×C4⋊C4—711no—
496C2×C4⋊C4—711no—
497C2×C4⋊C4—711no—
498C2×C4⋊C4—714no—
499C2×C4⋊C4—714no—
500C2×C4⋊C4—1428no—
501C2×C4⋊C4—1422no—
502C2×C4⋊C4—1422no—
503C2×C4⋊C4—1421no—
504C2×C4⋊C4—1421no—
505C2×C4⋊C4—1421no—
506C2×C4⋊C4—1421no—
507C2×C4⋊C4—1421no—
508C2×C4⋊C4—1421no—
509C2×C4⋊C4—1421no—
510C2×C4⋊C4—1421no—
511C2×C4⋊C4C22×D7111yescharacteristic
512C2×C4⋊C4C22×D7111yescharacteristic
513C2×C4⋊C4C22×D7111yescharacteristic
514C2×C22⋊C4—711no—
515C2×C22⋊C4—711no—
516C2×C22⋊C4—1421no—
517C2×C22⋊C4—1421no—
518C2×C22⋊C4—1421no—
519C2×C42—21no—
520C2×C42—711no—
521C2×C42—1421no—
522C2×C42—1421no—
523C2×C42C22×D7111yescharacteristic
524#107—714no—
525#107—714no—
526#106—714no—
527#106—714no—
528#106—714no—
529#106—714no—
530#106C22×D7114yes—
531#106C22×D7114yes—
532C4⋊C8—714no—
533C4⋊C8—714no—
534C4⋊C8—714no—
535C4⋊C8C22×D7114yes—
536#103—714no—
537#103—714no—
538#103C22×D7114yes—
539#103C22×D7114yes—
540#102—714no—
541#102—714no—
542#102—714no—
543#102—714no—
544C24—711no—
545C24—1421no—
546#41—7116no—
547#41—1428no—
548#41—14216no—
549C2×Q8—21no—
550C2×Q8—24no—
551C2×Q8—22no—
552C2×Q8—82no—
553C2×Q8—5682no—
554C2×Q8—1424no—
555C2×Q8Q8×D7114yes—
556C2×Q8C23×D7112yes—
557C2×D4—714no—
558C2×D4—712no—
559C2×D4—1424no—
560C2×D4—1428no—
561C2×D4—1421no—
562C2×D4—1422no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—5682no—
568C22×C4—5682no—
569C22×C4—5682no—
570C22×C4—5682no—
571C22×C4—711no—
572C22×C4—712no—
573C22×C4—714no—
574C22×C4—714no—
575C22×C4—712no—
576C22×C4—711no—
577C22×C4—711no—
578C22×C4—1424no—
579C22×C4—1424no—
580C22×C4—1424no—
581C22×C4—1424no—
582C22×C4—1428no—
583C22×C4—1421no—
584C22×C4—1421no—
585C22×C4—1421no—
586C22×C4—1424no—
587C22×C4D4×D7111yescharacteristic
588C22×C4D4×D7111yescharacteristic
589C22×C4C23×D7111yescharacteristic
590M16—1428no—
591C2×C8—22no—
592C2×C8—22no—
593C2×C8—712no—
594C2×C8—712no—
595C2×C8—1428no—
596C2×C8—1422no—
597C2×C8—1422no—
598C2×C8C23×D7112yes—
599C2×C8C23×D7112yes—
600C4⋊C4—24no—
601C4⋊C4—24no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—714no—
606C4⋊C4—714no—
607C4⋊C4—712no—
608C4⋊C4—712no—
609C4⋊C4—712no—
610C4⋊C4—1424no—
611C4⋊C4—1424no—
612C4⋊C4—1424no—
613C4⋊C4—1424no—
614C4⋊C4—1424no—
615C4⋊C4—1424no—
616C4⋊C4—1424no—
617C4⋊C4—1424no—
618C4⋊C4—1421no—
619C4⋊C4—1421no—
620C4⋊C4—1421no—
621C4⋊C4C23×D7112yes—
622C4⋊C4C23×D7112yes—
623C4⋊C4C23×D7112yes—
624C22⋊C4—714no—
625C22⋊C4—714no—
626C22⋊C4—1424no—
627C22⋊C4—1424no—
628C22⋊C4—1424no—
629C42—24no—
630C42—712no—
631C42—712no—
632C42—1424no—
633C42—1424no—
634C42D4×D7112yes—
635C42C23×D7112yes—
636C23—2842no—
637C23—2842no—
638C23—712no—
639C23—714no—
640C23—1422no—
641C23—1424no—
642C23—1422no—
643C23—1422no—
644C23C2×D4×D7111yescharacteristic
645Q8—22no—
646Q8—24no—
647Q8—84no—
648Q8—5684no—
649Q8C2×Q8×D7114yes—
650D4—714no—
651D4—14216no—
652D4—1422no—
653D4—1424no—
654C2×C4—22no—
655C2×C4—24no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—2842no—
665C2×C4—2842no—
666C2×C4—2842no—
667C2×C4—5684no—
668C2×C4—5684no—
669C2×C4—5684no—
670C2×C4—5684no—
671C2×C4—712no—
672C2×C4—714no—
673C2×C4—714no—
674C2×C4—714no—
675C2×C4—718no—
676C2×C4—712no—
677C2×C4—712no—
678C2×C4—14216no—
679C2×C4—1422no—
680C2×C4—1422no—
681C2×C4—1422no—
682C2×C4—1422no—
683C2×C4—1422no—
684C2×C4C2×D4×D7112yes—
685C2×C4C2×D4×D7112yes—
686C2×C4C2×D4×D7111yescharacteristic
687C2×C4C2×Q8×D7112yes—
688C2×C4#41×D7112yes—
689C2×C4C24×D7111yescharacteristic
690C8—22no—
691C8—22no—
692C8—1422no—
693C8—1422no—
694C22—2848no—
695C22—2842no—
696C22—2842no—
697C22—714no—
698C22—1424no—
699C22—1428no—
700C22—1422no—
701C22—1422no—
702C22C22⋊Q8×D7112yes—
703C22#1798680512yes—
704C22#1798680812yes—
705C22C22×D4×D7111yescharacteristic
706C4—22no—
707C4—22no—
708C4—24no—
709C4—42no—
710C4—42no—
711C4—42no—
712C4—2842no—
713C4—2842no—
714C4—2842no—
715C4—714no—
716C4—1422no—
717C4—1422no—
718C4C22⋊Q8×D7112yes—
719C4C22×Q8×D7111yescharacteristic
720C4C2×#41×D7111yescharacteristic
721C2—2844no—
722C2—1424no—
723C2#2259819914yesdirect product factor
724C2C2×C22⋊Q8×D7111yescharacteristic
725C2C2×#1798680511yescharacteristic
726C2C2×#1798680811yescharacteristic
subgroupG/H
centerC23C2×D4×D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#475×C71C2
socleC23×C71C22×D4
prime radicalC22×#11765866C22
hypercenterC2×#475D71
hypocenterC71C2×#3084
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#475

Complements

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

NH ≅ G/Ntype
1. C2×#17986626C2semidirect
3. #22598199C2direct (N × H)
4. C2×#17986308C2semidirect
5. C2×#17986306C2semidirect
6. C2×#17986282C2semidirect
7. C2×#17986300C2semidirect
8. C2×#17986298C2semidirect
9. C2×#17986288C2semidirect
10. C2×#17986286C2semidirect
11. C2×#17986038C2semidirect
12. C2×#106×D71C2semidirect
13. C2×#17986024C2semidirect
16. C2×#475×C71C2semidirect
21. #17986626C22semidirect
42. #17986308C22semidirect
43. #17986306C22semidirect
44. #17986300C22semidirect
45. #17986298C22semidirect
46. #17986288C22semidirect
47. #17986286C22semidirect
48. #17986282C22semidirect
49. #17986038C22semidirect
56. #106×D71C22semidirect
57. #17986024C22semidirect
71. #475×C71C22semidirect
79. C2×#11765866Q8semidirect
184. #11765866C2×Q8semidirect
358. C2×C71#3084semidirect
370. C2×#475D71semidirect
380. C71C2×#3084semidirect
415. #475C2×D71semidirect
723. C2#22598199direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179866262
C2×#179864812
#225981992
C2×#179863082
C2×#179863062
C2×#179862822
C2×#179863002
C2×#179862982
C2×#179862882
C2×#179862862
C2×#179860382
C2×#106×D712
C2×#179860242
C2×#179859992
C2×#179859942
C2×#475×C712
C2×#308471