Finite Group Databasebeta

← C2×#22600426 #32873983

Subgroups — C2×#22600426 #32873983

Order 18176.

2298 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986709C211yesmaximal, characteristic, complemented
2C2×#17986644C211yesmaximal, characteristic
3#22600426C2116yesmaximal, direct product factor
4C2×#17986359C211yesmaximal, characteristic, complemented
5C2×#17986336C211yesmaximal, characteristic, complemented
6C2×#17986314C211yesmaximal, characteristic, complemented
7C2×#17986279C211yesmaximal, characteristic, complemented
8C2×#17986248C211yesmaximal, characteristic, complemented
9C2×#17986239C211yesmaximal, characteristic, complemented
10C2×#17986221C211yesmaximal, characteristic, complemented
11C2×#17986158C211yesmaximal, characteristic, complemented
12C2×#17986148C211yesmaximal, characteristic, complemented
13C2×#17986072C211yesmaximal, characteristic, complemented
14C2×#17985997C211yesmaximal, characteristic, complemented
15C2×#102×D71C211yesmaximal, characteristic, complemented
16C2×#440×C71C211yesmaximal, characteristic, complemented
17C22×#11765864C2211yescharacteristic
18C22×D4×D71C2211yescharacteristic
19C22×#11765855C2211yescharacteristic, complemented
20C22×#11765852C2211yescharacteristic
21C22×#11765848C2211yescharacteristic, complemented
22C22×C8×D71C2211yescharacteristic
23#17986709—24no—
24#17986709C2218yescomplemented
25#17986644—24no—
26#17986644C2218yes—
27C2×#14556128C2211yescharacteristic, complemented
28C2×#14556120—21no—
29C2×#14556116C2211yescharacteristic
30C2×#14556112—21no—
31C2×#14556108C2211yescharacteristic
32C2×#14556106—21no—
33C2×#14556106—21no—
34C2×#14556104C2211yescharacteristic
35C2×#14556104C2211yescharacteristic, complemented
36C2×#14556103C2211yescharacteristic
37C2×#14556102—21no—
38C2×#14556098—21no—
39C2×C4×D284—21no—
40C2×C4×D284C2211yescharacteristic
41C2×C4⋊C4×D71C2211yescharacteristic
42C2×C4⋊C4×D71C2211yescharacteristic, complemented
43C22×(C2×D71)⋊C4—21no—
44#17986359C2218yescomplemented
45#17986336C2218yescomplemented
46#17986314C2218yescomplemented
47#17986279C2218yescomplemented
48#17986248C2218yescomplemented
49#17986239C2218yescomplemented
50#17986221C2218yescomplemented
51#17986158C2218yescomplemented
52#17986148C2218yescomplemented
53#17986072C2218yescomplemented
54C2×#14556061C2211yescharacteristic, complemented
55C2×#14556061C2211yescharacteristic, complemented
56C2×C4⋊(C71⋊C8)C2211yescharacteristic, complemented
57#17985997C2218yescomplemented
58C2×#14556053C2211yescharacteristic, complemented
59C2×#14556053C2211yescharacteristic, complemented
60C2×#14556051C2211yescharacteristic, complemented
61C2×#14556050C2211yescharacteristic
62C2×#14556050C2211yescharacteristic
63C2×#14556049C2211yescharacteristic
64C2×#14556049C2211yescharacteristic
65C2×#14556048C2211yescharacteristic
66#102×D71C2218yescomplemented
67C2×(C2×D71)⋊C8C2211yescharacteristic
68C2×(C2×D71)⋊C8C2211yescharacteristic, complemented
69C22×SD16×C71C2211yescharacteristic
70C2×C4×Q8×C71C2211yescharacteristic, complemented
71C2×C4×D4×C71C2211yescharacteristic
72#440×C71C2218yescomplemented
73C2×#107×C71C2211yescharacteristic, complemented
74C2×#103×C71C2211yescharacteristic, complemented
75C2×#102×C71C2211yescharacteristic
76C2×#97×C71C2211yescharacteristic, complemented
77C24×D71—21no—
78C2×#11765864—22no—
79C2×#11765864—24no—
80C2×#11765864—42no—
81C2×#11765864C2314yes—
82C22×Dic142—21no—
83C22×Dic142C2311yescharacteristic
84C22×D284—21no—
85C22×D284D411yescharacteristic
86C22×D284C2311yescharacteristic
87C22×C22⋊D71—21no—
88C22×C22⋊D71—21no—
89C2×D4×D71—22no—
90C2×D4×D71—24no—
91C2×D4×D71—42no—
92C2×D4×D71C2314yes—
93C23×Dic71—21no—
94C22×C4×D71—21no—
95C22×C4×D71—21no—
96C22×C4×D71C2311yescharacteristic
97C22×C4×D71C2311yescharacteristic
98C2×#11765855—42no—
99C2×#11765855C2314yescomplemented
100C2×#11765852—42no—
101C2×#11765852C2314yes—
102C2×#11765848—42no—
103C2×#11765848C2314yescomplemented
104C22×C71⋊C8C2311yescharacteristic
105C22×C71⋊C8C2311yescharacteristic
106C2×C8×D71—42no—
107C2×C8×D71C2314yes—
108#14556128—22no—
109#14556128C2314yescomplemented
110#14556120—28no—
111#14556116—22no—
112#14556116C2314yes—
113#14556112—28no—
114#14556108—22no—
115#14556108C2314yes—
116#14556106—28no—
117#14556106—28no—
118#14556104—22no—
119#14556104—22no—
120#14556104C2314yes—
121#14556104C2314yescomplemented
122#14556103—22no—
123#14556103C2314yes—
124#14556102—28no—
125#14556098—28no—
126C4×D284—28no—
127C4×D284D414yes—
128C4×D284C2314yes—
129C2×C4⋊Dic71—21no—
130C2×C4⋊Dic71—21no—
131C2×C4⋊Dic71D411yescharacteristic
132C2×C4⋊Dic71C2311yescharacteristic
133C2×C4⋊Dic71C2311yescharacteristic
134C2×Dic71⋊C4—21no—
135C2×Dic71⋊C4—21no—
136C2×Dic71⋊C4—21no—
137C2×Dic71⋊C4—21no—
138C4⋊C4×D71—22no—
139C4⋊C4×D71—22no—
140C4⋊C4×D71C2314yes—
141C4⋊C4×D71C2314yescomplemented
142C2×(C2×D71)⋊C4—21no—
143C2×(C2×D71)⋊C4—21no—
144C2×(C2×D71)⋊C4—21no—
145C2×(C2×D71)⋊C4—21no—
146C2×(C2×D71)⋊C4—28no—
147C2×(C2×D71)⋊C4—21no—
148C2×(C2×D71)⋊C4—21no—
149C2×(C2×D71)⋊C4D411yescharacteristic
150C2×(C2×D71)⋊C4D411yescharacteristic
151#14556061C2314yescomplemented
152#14556061C2314yescomplemented
153C4⋊(C71⋊C8)C2314yescomplemented
154#14556053C2314yescomplemented
155#14556053C2314yescomplemented
156#14556051C2314yescomplemented
157#14556050C2314yes—
158#14556050C2314yes—
159#14556049C2314yes—
160#14556049C2314yes—
161#14556048C2314yes—
162(C2×D71)⋊C8C2314yes—
163(C2×D71)⋊C8C2314yescomplemented
164C22×Q8×C71C2311yescharacteristic
165C22×D4×C71C2311yescharacteristic
166C23×C4×C71—21no—
167C2×SD16×C71—24no—
168C2×SD16×C71C2314yes—
169C22×C8×C71C2311yescharacteristic
170C22×C8×C71C2311yescharacteristic
171C4×Q8×C71—22no—
172C4×Q8×C71C2314yescomplemented
173C4×D4×C71—22no—
174C4×D4×C71C2314yes—
175C2×C4⋊C4×C71—21no—
176C2×C4⋊C4×C71C2311yescharacteristic
177C2×C4⋊C4×C71C2311yescharacteristic
178C2×C22⋊C4×C71—21no—
179C2×C42×C71—21no—
180C2×C42×C71C2311yescharacteristic
181#107×C71C2314yescomplemented
182#103×C71C2314yescomplemented
183#102×C71C2314yes—
184#97×C71C2314yescomplemented
185C23×D71—21no—
186C23×D71—24no—
187C23×D71—44no—
188C23×D71—44no—
189C23×D71—82no—
190C23×D71C2×D411yescharacteristic
191C23×D71C2×D411yescharacteristic
192#11765864—28no—
193#11765864—44no—
194#11765864—48no—
195C2×Dic142—22no—
196C2×Dic142—22no—
197C2×Dic142—21no—
198C2×Dic142—24no—
199C2×Dic142—82no—
200C2×Dic142C2412yes—
201C2×D284—24no—
202C2×D284—22no—
203C2×D284—22no—
204C2×D284—21no—
205C2×D284—24no—
206C2×D284—82no—
207C2×D284C2×D414yes—
208C2×D284C2412yes—
209C2×C22⋊D71—24no—
210C2×C22⋊D71—24no—
211C2×C22⋊D71—44no—
212C2×C22⋊D71—44no—
213D4×D71—28no—
214D4×D71—44no—
215D4×D71—48no—
216C22×Dic71—21no—
217C22×Dic71—21no—
218C22×Dic71—21no—
219C22×Dic71—24no—
220C22×Dic71—44no—
221C22×Dic71C2×D411yescharacteristic
222C22×Dic71C2×D411yescharacteristic
223C2×C4×D71—22no—
224C2×C4×D71—22no—
225C2×C4×D71—22no—
226C2×C4×D71—22no—
227C2×C4×D71—24no—
228C2×C4×D71—24no—
229C2×C4×D71—82no—
230C2×C4×D71—82no—
231C2×C4×D71C2×D412yes—
232C2×C4×D71C2×D412yes—
233C2×C4×D71C2412yes—
234C2×C4×D71C2412yes—
235#11765855—44no—
236#11765852—44no—
237#11765848—44no—
238C2×C71⋊C8—22no—
239C2×C71⋊C8—22no—
240C2×C71⋊C8C2412yes—
241C2×C71⋊C8C2412yes—
242C8×D71—44no—
243C4⋊Dic71—21no—
244C4⋊Dic71—21no—
245C4⋊Dic71—24no—
246C4⋊Dic71—24no—
247C4⋊Dic71C2×D414yes—
248C4⋊Dic71C2412yes—
249C4⋊Dic71C2412yes—
250Dic71⋊C4—24no—
251Dic71⋊C4—24no—
252Dic71⋊C4—24no—
253Dic71⋊C4—24no—
254(C2×D71)⋊C4—24no—
255(C2×D71)⋊C4—24no—
256(C2×D71)⋊C4—24no—
257(C2×D71)⋊C4—24no—
258(C2×D71)⋊C4—24no—
259(C2×D71)⋊C4—24no—
260(C2×D71)⋊C4C2×D414yes—
261(C2×D71)⋊C4C2×D414yes—
262C24×C71—21no—
263C2×Q8×C71—21no—
264C2×Q8×C71—22no—
265C2×Q8×C71—22no—
266C2×Q8×C71C2412yes—
267C2×D4×C71—21no—
268C2×D4×C71—22no—
269C2×D4×C71#4114yes—
270C2×D4×C71C2412yes—
271C22×C4×C71—21no—
272C22×C4×C71—21no—
273C22×C4×C71—21no—
274C22×C4×C71—24no—
275C22×C4×C71—82no—
276C22×C4×C71C2×D411yescharacteristic
277C22×C4×C71C2×D411yescharacteristic
278C22×C4×C71C2411yescharacteristic
279SD16×C71—28no—
280C2×C8×C71—22no—
281C2×C8×C71—22no—
282C2×C8×C71C2412yes—
283C2×C8×C71C2412yes—
284C4⋊C4×C71—24no—
285C4⋊C4×C71—21no—
286C4⋊C4×C71—21no—
287C4⋊C4×C71C2412yes—
288C4⋊C4×C71C2412yes—
289C22⋊C4×C71—24no—
290C42×C71—24no—
291C42×C71C2×D412yes—
292C42×C71C2412yes—
293C23×C71—24no—
294C23×C71—22no—
295C23×C71—42no—
296C23×C71—42no—
297C23×C71C22×D411yescharacteristic
298C22×D71—22no—
299C22×D71—22no—
300C22×D71—22no—
301C22×D71—22no—
302C22×D71—22no—
303C22×D71—22no—
304C22×D71—48no—
305C22×D71—42no—
306C22×D71—42no—
307C22×D71—42no—
308C22×D71—48no—
309C22×D71—84no—
310C22×D71—816no—
311C22×D71#13714yes—
312C22×D71C22×D412yes—
313C22×D71C22×D412yes—
314Q8×C71—22no—
315Q8×C71—22no—
316Q8×C71—42no—
317D4×C71—24no—
318D4×C71—22no—
319D4×C71C2×#4114yes—
320C2×C4×C71—22no—
321C2×C4×C71—22no—
322C2×C4×C71—22no—
323C2×C4×C71—22no—
324C2×C4×C71—22no—
325C2×C4×C71—42no—
326C2×C4×C71—42no—
327C2×C4×C71—42no—
328C2×C4×C71—84no—
329C2×C4×C71C22×D412yes—
330C2×C4×C71C22×D412yes—
331C2×C4×C71C22×D411yescharacteristic
332C2×C4×C71C2×#4112yes—
333C2×C4×C71H(5,𝔽2)12yes—
334C2×C4×C71C2511yescharacteristic
335C22⋊D71—48no—
336C22⋊D71—48no—
337C2×Dic71—22no—
338C2×Dic71—22no—
339C2×Dic71—22no—
340C2×Dic71—22no—
341C2×Dic71—22no—
342C2×Dic71—48no—
343C2×Dic71—42no—
344C2×Dic71—42no—
345C2×Dic71—42no—
346C2×Dic71C22×D412yes—
347C2×Dic71C22×D412yes—
348D284—28no—
349D284—22no—
350D284—22no—
351D284—42no—
352D284—84no—
353C4×D71—24no—
354C4×D71—24no—
355C4×D71—22no—
356C4×D71—22no—
357C4×D71—22no—
358C4×D71—22no—
359C4×D71—84no—
360C4×D71—84no—
361Dic142—22no—
362Dic142—22no—
363Dic142—42no—
364Dic142—84no—
365C8×C71—22no—
366C8×C71—22no—
367C71⋊C8—22no—
368C71⋊C8—22no—
369C22×C71—24no—
370C22×C71—48no—
371C22×C71—42no—
372C22×C71—42no—
373C22×C71#54612yes—
374C22×C71C2×#13712yes—
375C22×C71#57612yes—
376C22×C71C23×D411yescharacteristic
377C2×D71—22no—
378C2×D71—28no—
379C2×D71—22no—
380C2×D71—22no—
381C2×D71—22no—
382C2×D71—22no—
383C2×D71—44no—
384C2×D71—42no—
385C2×D71—42no—
386C2×D71—42no—
387C2×D71—816no—
388C2×D71—84no—
389C2×D71C2×#13714yes—
390C4×C71—22no—
391C4×C71—22no—
392C4×C71—42no—
393C4×C71—42no—
394C4×C71—42no—
395C4×C71#54612yes—
396C4×C71C22×#4111yescharacteristic
397C4×C71C2×H(5,𝔽2)11yescharacteristic
398Dic71—22no—
399Dic71—22no—
400Dic71—42no—
401Dic71—42no—
402Dic71—42no—
403C2×#3314—711nomaximal, Sylow
404C2×C71—44no—
405C2×C71#331414yescomplemented
406C2×C71C2×#54611yescharacteristic
407C2×C71C22×#13711yescharacteristic
408C2×C71C2×#57611yescharacteristic
409D71—24no—
410D71—42no—
411D71—82no—
412C2×#554—711no—
413C2×#546—711no—
414#3314—7116no—
415C2×#489—711no—
416C2×#484—711no—
417C2×#480—711no—
418C2×#474—711no—
419C2×#468—711no—
420C2×#467—711no—
421C2×#464—711no—
422C2×#452—711no—
423C2×#450—711no—
424C2×#440D7111yescharacteristic, complemented
425C2×#435—711no—
426C2×#417—711no—
427C22×#102—711no—
428C71C2×#331411yescharacteristic, complemented, Sylow
429C22×#41—711no—
430C23×D4—711no—
431C22×Q16—711no—
432C22×SD16—711no—
433C22×SD16C2×D7111yescharacteristic
434C22×M16—711no—
435C23×C8—711no—
436#554—718no—
437#554—1424no—
438#546—718no—
439#546—1424no—
440C2×C4⋊Q8—711no—
441C2×#125—1421no—
442C2×#124—711no—
443C2×#123—1421no—
444C2×C22⋊Q8—711no—
445C2×C22⋊Q8—711no—
446C2×C22⋊Q8—711no—
447C2×C22⋊Q8—1421no—
448C2×C22⋊Q8—1421no—
449C2×#121—711no—
450C2×#121—1421no—
451C2×#120—1421no—
452C2×C4×Q8C2×D7111yescharacteristic, complemented
453C2×C4×D4—711no—
454C2×C4×D4—1421no—
455C2×C4×D4C2×D7111yescharacteristic
456C22×C4⋊C4—711no—
457C22×C4⋊C4—711no—
458C22×C22⋊C4—1421no—
459#489—718no—
460#484—718no—
461#480—718no—
462#474—718no—
463#468—718no—
464#467—718no—
465#464—718no—
466#452—718no—
467#450—718no—
468#440C2×D7118yescomplemented
469#435—718no—
470C2×#107—711no—
471C2×#107—711no—
472C2×#107C2×D7111yescharacteristic, complemented
473C2×C4⋊C8—711no—
474#417—718no—
475C2×#103—711no—
476C2×#103—711no—
477C2×#103—711no—
478C2×#103C2×D7111yescharacteristic, complemented
479C2×#102—711no—
480C2×#102—711no—
481C2×#102—711no—
482C2×#102—711no—
483C2×#102—711no—
484C2×#102—718no—
485C2×#102C2×D7111yescharacteristic
486C2×C22⋊C8—711no—
487C2×C22⋊C8—711no—
488C2×#97C2×D7111yescharacteristic, complemented
489C25—1421no—
490C2×#41—2842no—
491C2×#41—714no—
492C2×#41—1424no—
493C2×#41—1422no—
494C22×Q8—711no—
495C22×Q8—1421no—
496C22×Q8C22×D7111yescharacteristic
497C22×D4—2842no—
498C22×D4—714no—
499C22×D4—711no—
500C22×D4—711no—
501C22×D4—1421no—
502C22×D4—1422no—
503C22×D4—1421no—
504C22×D4—1421no—
505C22×D4—1424no—
506C22×D4C22×D7111yescharacteristic
507C23×C4—21no—
508C23×C4—711no—
509C23×C4—711no—
510C23×C4—1421no—
511C23×C4—1421no—
512C23×C4—1421no—
513C2×Q16—2842no—
514C2×Q16—714no—
515C2×SD16—24no—
516C2×SD16—2842no—
517C2×SD16—714no—
518C2×SD16C22×D7114yes—
519C2×M16—2842no—
520C2×M16—714no—
521C22×C8—2842no—
522C22×C8—714no—
523C22×C8—711no—
524C22×C8—711no—
525C22×C8C22×D7111yescharacteristic
526C22×C8C22×D7111yescharacteristic
527C4⋊Q8—714no—
528C4⋊Q8—1422no—
529#125—1428no—
530#124—714no—
531#124—1422no—
532#123—1428no—
533C22⋊Q8—714no—
534C22⋊Q8—714no—
535C22⋊Q8—714no—
536C22⋊Q8—1428no—
537C22⋊Q8—1428no—
538C22⋊Q8—1422no—
539C22⋊Q8—1422no—
540C22⋊Q8—1422no—
541#121—714no—
542#121—1428no—
543#121—1422no—
544#120—1428no—
545C4×Q8—22no—
546C4×Q8C22×D7114yescomplemented
547C4×D4—22no—
548C4×D4—714no—
549C4×D4—714no—
550C4×D4—1428no—
551C4×D4C22×D7114yes—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—711no—
554C2×C4⋊C4—711no—
555C2×C4⋊C4—711no—
556C2×C4⋊C4—714no—
557C2×C4⋊C4—714no—
558C2×C4⋊C4—1422no—
559C2×C4⋊C4—1422no—
560C2×C4⋊C4—1421no—
561C2×C4⋊C4—1421no—
562C2×C4⋊C4—1421no—
563C2×C4⋊C4—1421no—
564C2×C4⋊C4—1421no—
565C2×C4⋊C4—1421no—
566C2×C4⋊C4C22×D7111yescharacteristic
567C2×C4⋊C4C22×D7111yescharacteristic
568C2×C22⋊C4—21no—
569C2×C22⋊C4—711no—
570C2×C22⋊C4—711no—
571C2×C22⋊C4—1428no—
572C2×C22⋊C4—1421no—
573C2×C22⋊C4—1421no—
574C2×C22⋊C4—1421no—
575C2×C22⋊C4—1421no—
576C2×C22⋊C4—1421no—
577C2×C22⋊C4—1421no—
578C2×C42—21no—
579C2×C42C22×D7111yescharacteristic
580#107—714no—
581#107—714no—
582#107C22×D7114yescomplemented
583C4⋊C8—714no—
584#103—714no—
585#103—714no—
586#103—714no—
587#103C22×D7114yescomplemented
588#102—714no—
589#102—714no—
590#102—714no—
591#102—714no—
592#102—714no—
593#102C22×D7114yes—
594C22⋊C8—714no—
595C22⋊C8—714no—
596#97C22×D7114yescomplemented
597C24—21no—
598C24—2844no—
599C24—2844no—
600C24—5682no—
601C24—711no—
602C24—711no—
603C24—1424no—
604C24—1421no—
605#41—2848no—
606#41—2844no—
607#41—1428no—
608C2×Q8—21no—
609C2×Q8—22no—
610C2×Q8—22no—
611C2×Q8—5682no—
612C2×Q8—712no—
613C2×Q8—1422no—
614C2×Q8—1422no—
615C2×Q8—1421no—
616C2×Q8—1424no—
617C2×Q8C23×D7112yes—
618C2×D4—21no—
619C2×D4—22no—
620C2×D4—2844no—
621C2×D4—2848no—
622C2×D4—2844no—
623C2×D4—2844no—
624C2×D4—5682no—
625C2×D4—714no—
626C2×D4—712no—
627C2×D4—1424no—
628C2×D4—1424no—
629C2×D4—1424no—
630C2×D4—1424no—
631C2×D4—1428no—
632C2×D4—1421no—
633C2×D4—1422no—
634C2×D4—1422no—
635C2×D4#1176586514yes—
636C2×D4C23×D7112yes—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—24no—
641C22×C4—82no—
642C22×C4—2844no—
643C22×C4—5682no—
644C22×C4—5682no—
645C22×C4—711no—
646C22×C4—711no—
647C22×C4—712no—
648C22×C4—712no—
649C22×C4—712no—
650C22×C4—712no—
651C22×C4—1424no—
652C22×C4—1424no—
653C22×C4—1424no—
654C22×C4—1421no—
655C22×C4—1421no—
656C22×C4—1421no—
657C22×C4—1422no—
658C22×C4—1422no—
659C22×C4—1422no—
660C22×C4—1422no—
661C22×C4D4×D7111yescharacteristic
662C22×C4D4×D7111yescharacteristic
663C22×C4C23×D7111yescharacteristic
664Q16—2844no—
665SD16—28no—
666SD16—2844no—
667M16—2844no—
668C2×C8—22no—
669C2×C8—22no—
670C2×C8—2844no—
671C2×C8—712no—
672C2×C8—712no—
673C2×C8—1422no—
674C2×C8—1422no—
675C2×C8C23×D7112yes—
676C2×C8C23×D7112yes—
677C4⋊C4—24no—
678C4⋊C4—21no—
679C4⋊C4—21no—
680C4⋊C4—714no—
681C4⋊C4—712no—
682C4⋊C4—712no—
683C4⋊C4—1424no—
684C4⋊C4—1424no—
685C4⋊C4—1424no—
686C4⋊C4—1424no—
687C4⋊C4—1424no—
688C4⋊C4—1421no—
689C4⋊C4—1421no—
690C4⋊C4—1424no—
691C4⋊C4C23×D7112yes—
692C4⋊C4C23×D7112yes—
693C22⋊C4—24no—
694C22⋊C4—714no—
695C22⋊C4—714no—
696C22⋊C4—1424no—
697C22⋊C4—1424no—
698C22⋊C4—1424no—
699C22⋊C4—1424no—
700C22⋊C4—1424no—
701C22⋊C4—1424no—
702C42—24no—
703C42D4×D7112yes—
704C42C23×D7112yes—
705C23—22no—
706C23—24no—
707C23—42no—
708C23—42no—
709C23—2848no—
710C23—2848no—
711C23—2842no—
712C23—2842no—
713C23—2842no—
714C23—5684no—
715C23—56816no—
716C23—712no—
717C23—714no—
718C23—712no—
719C23—1422no—
720C23—1422no—
721C23—1422no—
722C23—1422no—
723C23—1422no—
724C23—1422no—
725C23C2×D4×D7111yescharacteristic
726Q8—22no—
727Q8—22no—
728Q8—42no—
729Q8—2842no—
730Q8—5684no—
731Q8—1422no—
732Q8—1422no—
733D4—22no—
734D4—24no—
735D4—2848no—
736D4—2848no—
737D4—2842no—
738D4—5684no—
739D4—1428no—
740D4—1422no—
741D4—1422no—
742D4C2×#1176586514yes—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—84no—
752C2×C4—2842no—
753C2×C4—2842no—
754C2×C4—2842no—
755C2×C4—2848no—
756C2×C4—5684no—
757C2×C4—5684no—
758C2×C4—712no—
759C2×C4—712no—
760C2×C4—1422no—
761C2×C4—1422no—
762C2×C4—1422no—
763C2×C4—1422no—
764C2×C4—1422no—
765C2×C4—1422no—
766C2×C4—1422no—
767C2×C4—1422no—
768C2×C4—1422no—
769C2×C4—1424no—
770C2×C4—1424no—
771C2×C4C2×D4×D7112yes—
772C2×C4C2×D4×D7112yes—
773C2×C4C2×D4×D7111yescharacteristic
774C2×C4C2×#1176586512yes—
775C2×C4#1455617412yes—
776C2×C4C24×D7111yescharacteristic
777C8—22no—
778C8—22no—
779C8—1422no—
780C8—1422no—
781C22—24no—
782C22—42no—
783C22—42no—
784C22—48no—
785C22—2844no—
786C22—2842no—
787C22—2842no—
788C22—2842no—
789C22—56816no—
790C22—5684no—
791C22—714no—
792C22—1422no—
793C22—1422no—
794C22—1422no—
795C22—1422no—
796C22—1422no—
797C22—1428no—
798C22#1798664512yes—
799C22#137×D7112yes—
800C22#1798680312yes—
801C22C22×D4×D7111yescharacteristic
802C4—22no—
803C4—22no—
804C4—42no—
805C4—42no—
806C4—42no—
807C4—2842no—
808C4—2842no—
809C4—2842no—
810C4—1422no—
811C4—1422no—
812C4#1798664512yes—
813C4C22×#1176586511yescharacteristic
814C4C2×#1455617411yescharacteristic
815C2—44no—
816C2—2842no—
817C2—5682no—
818C2—1424no—
819C2#2260042614yesdirect product factor
820C2C2×#1798664511yescharacteristic
821C2C2×#137×D7111yescharacteristic
822C2C2×#1798680311yescharacteristic
subgroupG/H
centerC23C2×D4×D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#440×C71C2
socleC23×C71C22×D4
prime radicalC2×#17986644C2
hypercenterC2×#440D71
hypocenterC71C2×#3314
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
1. C2×#17986709C2semidirect
3. #22600426C2direct (N × H)
4. C2×#17986359C2semidirect
5. C2×#17986336C2semidirect
6. C2×#17986314C2semidirect
7. C2×#17986279C2semidirect
8. C2×#17986248C2semidirect
9. C2×#17986239C2semidirect
10. C2×#17986221C2semidirect
11. C2×#17986158C2semidirect
12. C2×#17986148C2semidirect
13. C2×#17986072C2semidirect
14. C2×#17985997C2semidirect
15. C2×#102×D71C2semidirect
16. C2×#440×C71C2semidirect
19. C22×#11765855C22semidirect
21. C22×#11765848C22semidirect
24. #17986709C22semidirect
27. C2×#14556128C22semidirect
35. C2×#14556104C22semidirect
42. C2×C4⋊C4×D71C22semidirect
44. #17986359C22semidirect
45. #17986336C22semidirect
46. #17986314C22semidirect
47. #17986279C22semidirect
48. #17986248C22semidirect
49. #17986239C22semidirect
50. #17986221C22semidirect
51. #17986158C22semidirect
52. #17986148C22semidirect
53. #17986072C22semidirect
54. C2×#14556061C22semidirect
55. C2×#14556061C22semidirect
56. C2×C4⋊(C71⋊C8)C22semidirect
57. #17985997C22semidirect
58. C2×#14556053C22semidirect
59. C2×#14556053C22semidirect
60. C2×#14556051C22semidirect
66. #102×D71C22semidirect
68. C2×(C2×D71)⋊C8C22semidirect
70. C2×C4×Q8×C71C22semidirect
72. #440×C71C22semidirect
73. C2×#107×C71C22semidirect
74. C2×#103×C71C22semidirect
76. C2×#97×C71C22semidirect
99. C2×#11765855C23semidirect
103. C2×#11765848C23semidirect
109. #14556128C23semidirect
121. #14556104C23semidirect
141. C4⋊C4×D71C23semidirect
151. #14556061C23semidirect
152. #14556061C23semidirect
153. C4⋊(C71⋊C8)C23semidirect
154. #14556053C23semidirect
155. #14556053C23semidirect
156. #14556051C23semidirect
163. (C2×D71)⋊C8C23semidirect
172. C4×Q8×C71C23semidirect
181. #107×C71C23semidirect
182. #103×C71C23semidirect
184. #97×C71C23semidirect
405. C2×C71#3314semidirect
424. C2×#440D71semidirect
428. C71C2×#3314semidirect
452. C2×C4×Q8C2×D71semidirect
468. #440C2×D71semidirect
472. C2×#107C2×D71semidirect
478. C2×#103C2×D71semidirect
488. C2×#97C2×D71semidirect
546. C4×Q8C22×D71semidirect
582. #107C22×D71semidirect
587. #103C22×D71semidirect
596. #97C22×D71semidirect
819. C2#22600426direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179867092
C2×#179866442
#226004262
C2×#179863592
C2×#179863362
C2×#179863142
C2×#179862792
C2×#179862482
C2×#179862392
C2×#179862212
C2×#179861582
C2×#179861482
C2×#179860722
C2×#179859972
C2×#102×D712
C2×#440×C712
C2×#331471