Finite Group Databasebeta

← C2×#22601087 #32877195

Subgroups — C2×#22601087 #32877195

Order 18176.

1950 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986709C211yesmaximal, characteristic, complemented
2#22601087C2116yesmaximal, direct product factor
3C2×#17986363C211yesmaximal, characteristic, complemented
4C2×#17986358C211yesmaximal, characteristic, complemented
5C2×#17986353C211yesmaximal, characteristic, complemented
6C2×#17986306C211yesmaximal, characteristic, complemented
7C2×#17986299C211yesmaximal, characteristic, complemented
8C2×#17986279C211yesmaximal, characteristic, complemented
9C2×#17986211C211yesmaximal, characteristic, complemented
10C2×#17986211C211yesmaximal, characteristic, complemented
11C2×#17986191C211yesmaximal, characteristic
12C2×#17986130C211yesmaximal, characteristic, complemented
13C2×#17986109C211yesmaximal, characteristic, complemented
14C2×#17986097C211yesmaximal, characteristic, complemented
15C2×C4×#11765850C211yesmaximal, characteristic, complemented
16C2×#559×C71C211yesmaximal, characteristic, complemented
17C22×#11765852C2211yescharacteristic
18C22×#11765850C2211yescharacteristic
19C22×#11765850C2211yescharacteristic
20#17986709—24no—
21#17986709C2218yescomplemented
22C2×#14556128C2211yescharacteristic
23C2×#14556120C2211yescharacteristic
24C2×#14556120C2211yescharacteristic
25C2×#14556106—21no—
26C2×#14556106—21no—
27C2×#14556104—21no—
28C2×C4×D284C2211yescharacteristic
29C2×C4×D284C2211yescharacteristic
30C2×C4×D284C2211yescharacteristic
31C2×C4⋊C4×D71—21no—
32#17986363C2218yescomplemented
33#17986358C2218yescomplemented
34#17986353C2218yescomplemented
35#17986306C2218yescomplemented
36#17986299C2218yescomplemented
37#17986279C2218yescomplemented
38#17986211C2218yescomplemented
39#17986211C2218yescomplemented
40#17986191C2218yes—
41#17986130C2218yescomplemented
42#17986109C2218yescomplemented
43#17986097C2218yescomplemented
44C4×#11765850C2218yescomplemented
45C2×#14556061C2211yescharacteristic
46C2×#14556061C2211yescharacteristic
47C2×#14556059C2211yescharacteristic
48C2×C4⋊(C71⋊C8)C2211yescharacteristic
49C2×C4⋊(C71⋊C8)C2211yescharacteristic
50C2×C4⋊(C71⋊C8)C2211yescharacteristic
51C2×#14556052C2211yescharacteristic
52C2×#14556052C2211yescharacteristic
53C2×#14556052C2211yescharacteristic
54C2×#14556049C2211yescharacteristic
55C2×#14556049C2211yescharacteristic
56C2×#14556049C2211yescharacteristic
57C2×#14556049C2211yescharacteristic
58C2×#14556049C2211yescharacteristic
59C2×#14556049C2211yescharacteristic
60C2×#14556048C2211yescharacteristic
61C2×#14556039C2211yescharacteristic
62C2×#14556039C2211yescharacteristic
63C2×C4×C71⋊C8C2211yescharacteristic
64#559×C71—24no—
65#559×C71C2218yescomplemented
66C2×#127×C71C2211yescharacteristic
67C2×#124×C71—21no—
68C2×#124×C71C2211yescharacteristic
69C2×#124×C71C2211yescharacteristic
70C2×#123×C71—21no—
71C2×#123×C71—21no—
72C2×C4×Q8×C71C2211yescharacteristic
73C2×C4×Q8×C71C2211yescharacteristic
74C2×C4×D4×C71—21no—
75C2×C4×D4×C71C2211yescharacteristic
76C2×C4×D4×C71C2211yescharacteristic
77C22×Dic142—21no—
78C22×D284C2311yescharacteristic
79C22×C4×D71—21no—
80C22×C4×D71—21no—
81C22×C4×D71—21no—
82C2×#11765852—24no—
83C2×#11765852C2314yes—
84C2×#11765850—24no—
85C2×#11765850—24no—
86C2×#11765850C2314yes—
87C2×#11765850C2314yes—
88C22×C71⋊C8C2311yescharacteristic
89C22×C71⋊C8C2311yescharacteristic
90C22×C71⋊C8C2311yescharacteristic
91C22×C71⋊C8C2311yescharacteristic
92#14556128—22no—
93#14556128C2314yes—
94#14556120—22no—
95#14556120—22no—
96#14556120C2314yes—
97#14556120C2314yes—
98#14556106—28no—
99#14556106—28no—
100#14556104—28no—
101C4×D284—22no—
102C4×D284—22no—
103C4×D284—22no—
104C4×D284C2314yes—
105C4×D284C2314yes—
106C4×D284C2314yes—
107C2×C4⋊Dic71—21no—
108C2×C4⋊Dic71C2311yescharacteristic
109C2×C4⋊Dic71C2311yescharacteristic
110C2×C4⋊Dic71C2311yescharacteristic
111C2×Dic71⋊C4—21no—
112C2×Dic71⋊C4—21no—
113C2×Dic71⋊C4—21no—
114C2×Dic71⋊C4—21no—
115C4⋊C4×D71—28no—
116C2×(C2×D71)⋊C4—21no—
117C2×(C2×D71)⋊C4—21no—
118C2×(C2×D71)⋊C4—21no—
119#14556061C2314yes—
120#14556061C2314yes—
121#14556059C2314yes—
122C4⋊(C71⋊C8)C2314yes—
123C4⋊(C71⋊C8)C2314yes—
124C4⋊(C71⋊C8)C2314yes—
125#14556052C2314yes—
126#14556052C2314yes—
127#14556052C2314yes—
128#14556049C2314yes—
129#14556049C2314yes—
130#14556049C2314yes—
131#14556049C2314yes—
132#14556049C2314yes—
133#14556049C2314yes—
134#14556048C2314yes—
135#14556039C2314yes—
136#14556039C2314yes—
137C4×C71⋊C8C2314yes—
138C22×Q8×C71D411yescharacteristic
139C22×Q8×C71C2311yescharacteristic
140C22×D4×C71—21no—
141C22×D4×C71—21no—
142C22×D4×C71C2311yescharacteristic
143C22×D4×C71C2311yescharacteristic
144C23×C4×C71—21no—
145C23×C4×C71—21no—
146#127×C71—22no—
147#127×C71C2314yes—
148#124×C71—28no—
149#124×C71—22no—
150#124×C71—22no—
151#124×C71C2314yes—
152#124×C71C2314yes—
153#123×C71—28no—
154#123×C71—28no—
155C4×Q8×C71—22no—
156C4×Q8×C71D414yes—
157C4×Q8×C71C2314yes—
158C4×Q8×C71C2314yes—
159C4×D4×C71—28no—
160C4×D4×C71—22no—
161C4×D4×C71—22no—
162C4×D4×C71C2314yes—
163C4×D4×C71C2314yes—
164C2×C4⋊C4×C71—21no—
165C2×C4⋊C4×C71D411yescharacteristic
166C2×C4⋊C4×C71D411yescharacteristic
167C2×C4⋊C4×C71D411yescharacteristic
168C2×C4⋊C4×C71C2311yescharacteristic
169C2×C22⋊C4×C71—21no—
170C2×C22⋊C4×C71—21no—
171C2×C22⋊C4×C71—21no—
172C2×C22⋊C4×C71—21no—
173C2×C22⋊C4×C71—21no—
174C2×C22⋊C4×C71—21no—
175C2×C42×C71—21no—
176C2×C42×C71C2311yescharacteristic
177C2×C42×C71C2311yescharacteristic
178C2×C42×C71C2311yescharacteristic
179C23×D71—21no—
180C2×Dic142—24no—
181C2×Dic142—82no—
182C2×D284—21no—
183C2×D284—22no—
184C2×D284#4114yes—
185C2×D284C2412yes—
186C22×Dic71—21no—
187C22×Dic71—21no—
188C22×Dic71—21no—
189C2×C4×D71—24no—
190C2×C4×D71—24no—
191C2×C4×D71—24no—
192C2×C4×D71—44no—
193C2×C4×D71—82no—
194C2×C4×D71—82no—
195#11765852—28no—
196#11765850—28no—
197#11765850—28no—
198C2×C71⋊C8—22no—
199C2×C71⋊C8—22no—
200C2×C71⋊C8—22no—
201C2×C71⋊C8—22no—
202C2×C71⋊C8C2412yes—
203C2×C71⋊C8C2412yes—
204C2×C71⋊C8C2412yes—
205C2×C71⋊C8C2412yes—
206C4⋊Dic71—24no—
207C4⋊Dic71—21no—
208C4⋊Dic71—21no—
209C4⋊Dic71—21no—
210C4⋊Dic71C2412yes—
211C4⋊Dic71C2412yes—
212C4⋊Dic71C2412yes—
213Dic71⋊C4—24no—
214Dic71⋊C4—24no—
215Dic71⋊C4—24no—
216Dic71⋊C4—24no—
217(C2×D71)⋊C4—24no—
218(C2×D71)⋊C4—24no—
219(C2×D71)⋊C4—24no—
220C24×C71—21no—
221C24×C71—21no—
222C2×Q8×C71—21no—
223C2×Q8×C71—22no—
224C2×Q8×C71—22no—
225C2×Q8×C71—42no—
226C2×Q8×C71C2×D414yes—
227C2×Q8×C71C2412yes—
228C2×D4×C71—21no—
229C2×D4×C71—21no—
230C2×D4×C71—24no—
231C2×D4×C71—24no—
232C2×D4×C71—22no—
233C2×D4×C71—22no—
234C2×D4×C71—22no—
235C2×D4×C71—22no—
236C2×D4×C71—44no—
237C2×D4×C71—82no—
238C2×D4×C71C2412yes—
239C2×D4×C71C2412yes—
240C22×C4×C71—21no—
241C22×C4×C71—21no—
242C22×C4×C71—24no—
243C22×C4×C71—24no—
244C22×C4×C71—82no—
245C22×C4×C71—82no—
246C22×C4×C71C2×D411yescharacteristic
247C22×C4×C71C2×D411yescharacteristic
248C22×C4×C71C2×D411yescharacteristic
249C22×C4×C71C2×D411yescharacteristic
250C22×C4×C71C2×D411yescharacteristic
251C22×C4×C71C2×D411yescharacteristic
252C22×C4×C71C2411yescharacteristic
253C4⋊C4×C71—24no—
254C4⋊C4×C71—21no—
255C4⋊C4×C71C2×D414yes—
256C4⋊C4×C71C2×D414yes—
257C4⋊C4×C71C2×D414yes—
258C4⋊C4×C71C2412yes—
259C22⋊C4×C71—24no—
260C22⋊C4×C71—24no—
261C22⋊C4×C71—24no—
262C22⋊C4×C71—24no—
263C22⋊C4×C71—24no—
264C22⋊C4×C71—24no—
265C42×C71—24no—
266C42×C71C2×D412yes—
267C42×C71C2×D412yes—
268C42×C71C2×D412yes—
269C42×C71C2412yes—
270C42×C71C2412yes—
271C42×C71C2412yes—
272C23×C71—22no—
273C23×C71—22no—
274C23×C71—42no—
275C23×C71—42no—
276C23×C71—42no—
277C23×C71—42no—
278C23×C71—42no—
279C23×C71—42no—
280C23×C71C22×D411yescharacteristic
281C22×D71—24no—
282C22×D71—22no—
283C22×D71—42no—
284C22×D71—42no—
285Q8×C71—22no—
286Q8×C71—22no—
287Q8×C71—44no—
288Q8×C71—42no—
289D4×C71—22no—
290D4×C71—22no—
291D4×C71—22no—
292D4×C71—22no—
293D4×C71—48no—
294D4×C71—42no—
295D4×C71—42no—
296D4×C71—84no—
297C2×C4×C71—22no—
298C2×C4×C71—22no—
299C2×C4×C71—22no—
300C2×C4×C71—22no—
301C2×C4×C71—22no—
302C2×C4×C71—22no—
303C2×C4×C71—22no—
304C2×C4×C71—22no—
305C2×C4×C71—42no—
306C2×C4×C71—42no—
307C2×C4×C71—84no—
308C2×C4×C71—84no—
309C2×C4×C71C22×D412yes—
310C2×C4×C71C22×D412yes—
311C2×C4×C71C22×D412yes—
312C2×C4×C71C22×D412yes—
313C2×C4×C71C22×D412yes—
314C2×C4×C71C22×D412yes—
315C2×C4×C71C22×D411yescharacteristic
316C2×C4×C71C2×#4112yes—
317C2×C4×C712−1+412yes—
318C2×C4×C71C2511yescharacteristic
319C2×Dic71—22no—
320C2×Dic71—22no—
321C2×Dic71—22no—
322C2×Dic71—42no—
323C2×Dic71—42no—
324C2×Dic71—42no—
325D284—24no—
326D284—22no—
327D284C2×#4114yes—
328C4×D71—48no—
329C4×D71—84no—
330C4×D71—84no—
331Dic142—84no—
332C71⋊C8—22no—
333C71⋊C8—22no—
334C71⋊C8—22no—
335C71⋊C8—22no—
336C22×C71—42no—
337C22×C71—42no—
338C22×C71—42no—
339C22×C71—42no—
340C22×C71—42no—
341C22×C71—42no—
342C22×C71—84no—
343C22×C71—84no—
344C22×C71#54812yes—
345C22×C71#57512yes—
346C22×C71#57612yes—
347C22×C71C23×D411yescharacteristic
348C2×D71—24no—
349C2×D71—48no—
350C2×D71—42no—
351C2×D71—42no—
352C4×C71—22no—
353C4×C71—22no—
354C4×C71—22no—
355C4×C71—22no—
356C4×C71—22no—
357C4×C71—22no—
358C4×C71—42no—
359C4×C71—42no—
360C4×C71#54812yes—
361C4×C71C22×#4111yescharacteristic
362C4×C71C2×2−1+411yescharacteristic
363Dic71—42no—
364Dic71—42no—
365Dic71—42no—
366C2×#3370—711nomaximal, Sylow
367C2×C71—82no—
368C2×C71—82no—
369C2×C71#337014yescomplemented
370C2×C71C2×#54811yescharacteristic
371C2×C71C2×#57511yescharacteristic
372C2×C71C2×#57611yescharacteristic
373D71—44no—
374C2×#559D7111yescharacteristic, complemented
375C2×#554—711no—
376#3370—7116no—
377C2×#490—711no—
378C2×#489—711no—
379C2×#488—711no—
380C2×#479—711no—
381C2×#478—711no—
382C2×#474—711no—
383C2×#463—711no—
384C2×#463—711no—
385C2×#459—711no—
386C2×#446—711no—
387C2×#442—711no—
388C2×#440—711no—
389C2×C4×D8—711no—
390C71C2×#337011yescharacteristic, complemented, Sylow
391C22×SD16—711no—
392C22×D8—711no—
393C22×D8—711no—
394#559—24no—
395#559C2×D7118yescomplemented
396#554—718no—
397#554—1424no—
398C2×C4⋊Q8—711no—
399C2×#127C2×D7111yescharacteristic
400C2×#125—711no—
401C2×#125—711no—
402C2×#124—21no—
403C2×#124C2×D7111yescharacteristic
404C2×#124C2×D7111yescharacteristic
405C2×#123—21no—
406C2×#123—21no—
407C2×C22⋊Q8—1421no—
408C2×C22⋊Q8—1421no—
409C2×C22⋊Q8—1421no—
410C2×C4×Q8C2×D7111yescharacteristic
411C2×C4×Q8C2×D7111yescharacteristic
412C2×C4×D4—21no—
413C2×C4×D4—711no—
414C2×C4×D4—711no—
415C2×C4×D4—711no—
416C2×C4×D4C2×D7111yescharacteristic
417C2×C4×D4C2×D7111yescharacteristic
418C22×C4⋊C4—1421no—
419#490—718no—
420#489—718no—
421#488—718no—
422#479—718no—
423#478—718no—
424#474—718no—
425#463—718no—
426#463—718no—
427#459—718no—
428#446—718no—
429#442—718no—
430#440—718no—
431C4×D8—718no—
432C2×#107—711no—
433C2×#107—711no—
434C2×#106—711no—
435C2×C4⋊C8—711no—
436C2×C4⋊C8—711no—
437C2×C4⋊C8—711no—
438C2×#103—711no—
439C2×#103—711no—
440C2×#103—711no—
441C2×#102—711no—
442C2×#102—711no—
443C2×#102—711no—
444C2×#102—711no—
445C2×#102—711no—
446C2×#102—711no—
447C2×#102—711no—
448C2×#97—711no—
449C2×#97—711no—
450C2×C4×C8—711no—
451C22×Q8—1421no—
452C22×Q8C22⋊D7111yescharacteristic
453C22×Q8C22×D7111yescharacteristic
454C22×D4—21no—
455C22×D4—21no—
456C22×D4—711no—
457C22×D4C22×D7111yescharacteristic
458C22×D4C22×D7111yescharacteristic
459C23×C4—21no—
460C23×C4—21no—
461C23×C4—1421no—
462C23×C4—1421no—
463C23×C4—1421no—
464C2×SD16—714no—
465C2×SD16—1424no—
466C2×D8—714no—
467C2×D8—714no—
468C2×D8—1424no—
469C2×D8—1424no—
470C22×C8—711no—
471C22×C8—711no—
472C22×C8—711no—
473C22×C8—711no—
474C4⋊Q8—714no—
475C4⋊Q8—1422no—
476#127—22no—
477#127C22×D7114yes—
478#125—714no—
479#125—714no—
480#125—1422no—
481#125—1422no—
482#124—28no—
483#124—22no—
484#124—22no—
485#124C22×D7114yes—
486#124C22×D7114yes—
487#123—28no—
488#123—28no—
489C22⋊Q8—1428no—
490C22⋊Q8—1428no—
491C22⋊Q8—1428no—
492C4×Q8—22no—
493C4×Q8C22⋊D7114yes—
494C4×Q8C22×D7114yes—
495C4×Q8C22×D7114yes—
496C4×D4—28no—
497C4×D4—22no—
498C4×D4—22no—
499C4×D4—714no—
500C4×D4—714no—
501C4×D4—714no—
502C4×D4—1422no—
503C4×D4—1422no—
504C4×D4—1422no—
505C4×D4C22×D7114yes—
506C4×D4C22×D7114yes—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—711no—
509C2×C4⋊C4—711no—
510C2×C4⋊C4—711no—
511C2×C4⋊C4—1421no—
512C2×C4⋊C4—1421no—
513C2×C4⋊C4—1421no—
514C2×C4⋊C4—1421no—
515C2×C4⋊C4—1421no—
516C2×C4⋊C4—1428no—
517C2×C4⋊C4C22⋊D7111yescharacteristic
518C2×C4⋊C4C22⋊D7111yescharacteristic
519C2×C4⋊C4C22⋊D7111yescharacteristic
520C2×C4⋊C4C22×D7111yescharacteristic
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—1421no—
528C2×C22⋊C4—1421no—
529C2×C22⋊C4—1421no—
530C2×C42—21no—
531C2×C42C22×D7111yescharacteristic
532C2×C42C22×D7111yescharacteristic
533C2×C42C22×D7111yescharacteristic
534#107—714no—
535#107—714no—
536#106—714no—
537C4⋊C8—714no—
538C4⋊C8—714no—
539C4⋊C8—714no—
540#103—714no—
541#103—714no—
542#103—714no—
543#102—714no—
544#102—714no—
545#102—714no—
546#102—714no—
547#102—714no—
548#102—714no—
549#102—714no—
550#97—714no—
551#97—714no—
552C4×C8—714no—
553C24—21no—
554C24—21no—
555C24—1421no—
556C2×Q8—21no—
557C2×Q8—22no—
558C2×Q8—22no—
559C2×Q8—42no—
560C2×Q8—5682no—
561C2×Q8—1424no—
562C2×Q8C2×C22⋊D7114yes—
563C2×Q8C23×D7112yes—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—24no—
567C2×D4—24no—
568C2×D4—22no—
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—22no—
572C2×D4—44no—
573C2×D4—82no—
574C2×D4—714no—
575C2×D4—712no—
576C2×D4—1421no—
577C2×D4—1422no—
578C2×D4C23×D7112yes—
579C2×D4C23×D7112yes—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—24no—
583C22×C4—24no—
584C22×C4—82no—
585C22×C4—82no—
586C22×C4—2844no—
587C22×C4—5682no—
588C22×C4—5682no—
589C22×C4—1421no—
590C22×C4—1421no—
591C22×C4—1421no—
592C22×C4—1424no—
593C22×C4—1424no—
594C22×C4—1424no—
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×C4C23×D7111yescharacteristic
602SD16—1428no—
603D8—1428no—
604D8—1428no—
605C2×C8—712no—
606C2×C8—712no—
607C2×C8—712no—
608C2×C8—712no—
609C2×C8—1422no—
610C2×C8—1422no—
611C2×C8—1422no—
612C2×C8—1422no—
613C4⋊C4—24no—
614C4⋊C4—21no—
615C4⋊C4—712no—
616C4⋊C4—712no—
617C4⋊C4—712no—
618C4⋊C4—1424no—
619C4⋊C4—1424no—
620C4⋊C4—1424no—
621C4⋊C4—1424no—
622C4⋊C4—1421no—
623C4⋊C4—1421no—
624C4⋊C4—1421no—
625C4⋊C4—1424no—
626C4⋊C4C2×C22⋊D7114yes—
627C4⋊C4C2×C22⋊D7114yes—
628C4⋊C4C2×C22⋊D7114yes—
629C4⋊C4C23×D7112yes—
630C22⋊C4—24no—
631C22⋊C4—24no—
632C22⋊C4—24no—
633C22⋊C4—24no—
634C22⋊C4—24no—
635C22⋊C4—24no—
636C22⋊C4—1424no—
637C22⋊C4—1424no—
638C22⋊C4—1424no—
639C42—24no—
640C42C2×C22⋊D7112yes—
641C42C2×C22⋊D7112yes—
642C42C2×C22⋊D7112yes—
643C42C23×D7112yes—
644C42C23×D7112yes—
645C42C23×D7112yes—
646C23—22no—
647C23—22no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—2842no—
655C23—2842no—
656C23—1422no—
657C23—1424no—
658C23C22×C22⋊D7111yescharacteristic
659Q8—22no—
660Q8—22no—
661Q8—44no—
662Q8—42no—
663Q8—5684no—
664D4—22no—
665D4—22no—
666D4—22no—
667D4—22no—
668D4—48no—
669D4—42no—
670D4—42no—
671D4—84no—
672D4—714no—
673D4—1422no—
674D4—1424no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—84no—
686C2×C4—84no—
687C2×C4—2848no—
688C2×C4—2842no—
689C2×C4—2842no—
690C2×C4—2842no—
691C2×C4—5684no—
692C2×C4—5684no—
693C2×C4—1422no—
694C2×C4—1422no—
695C2×C4—1422no—
696C2×C4C22×C22⋊D7112yes—
697C2×C4C22×C22⋊D7112yes—
698C2×C4C22×C22⋊D7112yes—
699C2×C4C22×C22⋊D7112yes—
700C2×C4C22×C22⋊D7112yes—
701C2×C4C22×C22⋊D7112yes—
702C2×C4C22×C22⋊D7111yescharacteristic
703C2×C4#41×D7112yes—
704C2×C4#1455617512yes—
705C2×C4C24×D7111yescharacteristic
706C8—1422no—
707C8—1422no—
708C8—1422no—
709C8—1422no—
710C22—42no—
711C22—42no—
712C22—42no—
713C22—42no—
714C22—42no—
715C22—42no—
716C22—84no—
717C22—84no—
718C22—2842no—
719C22—2842no—
720C22—2848no—
721C22—1424no—
722C22#1798665612yes—
723C22#1798679712yes—
724C22#1798680212yes—
725C22C23×C22⋊D7111yescharacteristic
726C4—22no—
727C4—22no—
728C4—22no—
729C4—22no—
730C4—22no—
731C4—22no—
732C4—42no—
733C4—42no—
734C4—2842no—
735C4—2842no—
736C4—2842no—
737C4#1798665612yes—
738C4C2×#41×D7111yescharacteristic
739C4C2×#1455617511yescharacteristic
740C2—82no—
741C2—82no—
742C2—2844no—
743C2#2260108714yesdirect product factor
744C2C2×#1798665611yescharacteristic
745C2C2×#1798679711yescharacteristic
746C2C2×#1798680211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#559×C71C2
socleC23×C71C22×D4
prime radicalC2×#17986191C2
hypercenterC2×#559D71
hypocenterC71C2×#3370
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#559

Complements

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

NH ≅ G/Ntype
1. C2×#17986709C2semidirect
2. #22601087C2direct (N × H)
3. C2×#17986363C2semidirect
4. C2×#17986358C2semidirect
5. C2×#17986353C2semidirect
6. C2×#17986306C2semidirect
7. C2×#17986299C2semidirect
8. C2×#17986279C2semidirect
9. C2×#17986211C2semidirect
10. C2×#17986211C2semidirect
12. C2×#17986130C2semidirect
13. C2×#17986109C2semidirect
14. C2×#17986097C2semidirect
15. C2×C4×#11765850C2semidirect
16. C2×#559×C71C2semidirect
21. #17986709C22semidirect
32. #17986363C22semidirect
33. #17986358C22semidirect
34. #17986353C22semidirect
35. #17986306C22semidirect
36. #17986299C22semidirect
37. #17986279C22semidirect
38. #17986211C22semidirect
39. #17986211C22semidirect
41. #17986130C22semidirect
42. #17986109C22semidirect
43. #17986097C22semidirect
44. C4×#11765850C22semidirect
65. #559×C71C22semidirect
369. C2×C71#3370semidirect
374. C2×#559D71semidirect
390. C71C2×#3370semidirect
395. #559C2×D71semidirect
743. C2#22601087direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179867092
#226010872
C2×#179863632
C2×#179863582
C2×#179863532
C2×#179863062
C2×#179862992
C2×#179862792
C2×#179862112
C2×#179861912
C2×#179861302
C2×#179861092
C2×#179860972
C2×C4×#117658502
C2×#559×C712
C2×#337071