Finite Group Databasebeta

← C2×#22600382 #32874128

Subgroups — C2×#22600382 #32874128

Order 18176.

2254 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986720C211yesmaximal, characteristic, complemented
2C2×#17986646C211yesmaximal, characteristic
3#22600382C2116yesmaximal, direct product factor
4C2×#17986357C211yesmaximal, characteristic, complemented
5C2×#17986343C211yesmaximal, characteristic, complemented
6C2×#17986320C211yesmaximal, characteristic, complemented
7C2×#17986288C211yesmaximal, characteristic, complemented
8C2×#17986256C211yesmaximal, characteristic, complemented
9C2×#17986219C211yesmaximal, characteristic, complemented
10C2×#17986159C211yesmaximal, characteristic, complemented
11C2×#17986148C211yesmaximal, characteristic, complemented
12C2×#17986102C211yesmaximal, characteristic, complemented
13C2×#17986070C211yesmaximal, characteristic, complemented
14C2×#17986002C211yesmaximal, characteristic, complemented
15C2×#17985996C211yesmaximal, characteristic, complemented
16C2×#465×C71C211yesmaximal, characteristic, complemented
17C22×#11765865C2211yescharacteristic
18C22×D4×D71C2211yescharacteristic
19C22×#11765855C2211yescharacteristic, complemented
20C22×#11765852C2211yescharacteristic
21C22×#11765848C2211yescharacteristic
22#17986720—24no—
23#17986720C2218yescomplemented
24#17986646—24no—
25#17986646C2218yes—
26C2×#14556127C2211yescharacteristic, complemented
27C2×#14556123—21no—
28C2×#14556121—21no—
29C2×#14556115C2211yescharacteristic
30C2×#14556114—21no—
31C2×#14556110—21no—
32C2×#14556108C2211yescharacteristic
33C2×#14556104C2211yescharacteristic
34C2×#14556099—21no—
35C2×#14556096—21no—
36C2×Q8×Dic71C2211yescharacteristic, complemented
37C2×#14556093—21no—
38C2×#14556090C2211yescharacteristic
39C2×C4×C22⋊D71C2211yescharacteristic
40C2×#14556087C2211yescharacteristic, complemented
41C2×#14556086C2211yescharacteristic
42C2×C22⋊C4×D71—21no—
43#17986357C2218yescomplemented
44#17986343C2218yescomplemented
45#17986320C2218yescomplemented
46#17986288C2218yescomplemented
47#17986256C2218yescomplemented
48#17986219C2218yescomplemented
49#17986159C2218yescomplemented
50#17986148C2218yescomplemented
51#17986102C2218yescomplemented
52#17986070C2218yescomplemented
53C2×#14556061C2211yescharacteristic, complemented
54C2×#14556059C2211yescharacteristic, complemented
55C2×Dic71⋊C8C2211yescharacteristic, complemented
56#17986002C2218yescomplemented
57#17985996C2218yescomplemented
58C2×#14556053C2211yescharacteristic, complemented
59C2×#14556053C2211yescharacteristic, complemented
60C2×#14556051C2211yescharacteristic, complemented
61C2×#14556050C2211yescharacteristic
62C2×#14556050C2211yescharacteristic
63C2×#14556049C2211yescharacteristic
64C2×#14556049C2211yescharacteristic
65C2×#14556048C2211yescharacteristic
66C2×C22⋊(C71⋊C8)C2211yescharacteristic, complemented
67C2×(C2×D71)⋊C8C2211yescharacteristic
68C2×#14556038C2211yescharacteristic, complemented
69C22×SD16×C71C2211yescharacteristic
70C23×C8×C71C2211yescharacteristic, complemented
71C2×C22⋊Q8×C71C2211yescharacteristic, complemented
72C2×#121×C71C2211yescharacteristic
73#465×C71C2218yescomplemented
74C2×#106×C71C2211yescharacteristic, complemented
75C2×#103×C71C2211yescharacteristic, complemented
76C2×#102×C71C2211yescharacteristic
77C24×D71—21no—
78C2×#11765865—24no—
79C2×#11765865—22no—
80C2×#11765865—42no—
81C2×#11765865C2314yes—
82C22×Dic142—21no—
83C22×Dic142C2311yescharacteristic
84C22×D284C2311yescharacteristic
85C22×C22⋊D71—21no—
86C22×C22⋊D71—21no—
87C22×C22⋊D71D411yescharacteristic
88C2×D4×D71—24no—
89C2×D4×D71—22no—
90C2×D4×D71—42no—
91C2×D4×D71C2314yes—
92C22×C4×D71—21no—
93C22×C4×D71—21no—
94C22×C4×D71C2311yescharacteristic
95C2×#11765855—42no—
96C2×#11765855C2314yescomplemented
97C2×#11765852—24no—
98C2×#11765852C2314yes—
99C2×#11765848—42no—
100C2×#11765848C2314yes—
101C22×C71⋊C8C2311yescharacteristic
102C22×C71⋊C8C2311yescharacteristic
103#14556127—22no—
104#14556127C2314yescomplemented
105#14556123—28no—
106#14556121—28no—
107#14556115—22no—
108#14556115C2314yes—
109#14556114—28no—
110#14556110—28no—
111#14556108—22no—
112#14556108C2314yes—
113#14556104—22no—
114#14556104C2314yes—
115#14556099—28no—
116#14556096—28no—
117Q8×Dic71—22no—
118Q8×Dic71C2314yescomplemented
119#14556093—28no—
120#14556090—22no—
121#14556090C2314yes—
122C4×C22⋊D71D414yes—
123C4×C22⋊D71C2314yes—
124#14556087—22no—
125#14556087C2314yescomplemented
126#14556086—22no—
127#14556086C2314yes—
128C2×C4⋊Dic71—21no—
129C2×C4⋊Dic71—21no—
130C2×C4⋊Dic71C2311yescharacteristic
131C2×C4⋊Dic71C2311yescharacteristic
132C2×Dic71⋊C4—21no—
133C2×Dic71⋊C4—21no—
134C2×Dic71⋊C4D411yescharacteristic
135C2×C22⋊Dic71—21no—
136C2×C22⋊Dic71—21no—
137C2×C22⋊Dic71—21no—
138C2×C22⋊Dic71D411yescharacteristic
139C2×(C2×D71)⋊C4—21no—
140C2×(C2×D71)⋊C4—21no—
141C2×(C2×D71)⋊C4—21no—
142C2×(C2×D71)⋊C4—21no—
143C2×(C2×D71)⋊C4D411yescharacteristic
144C22⋊C4×D71—28no—
145C2×C4×Dic71—21no—
146C2×C4×Dic71—21no—
147C2×C4×Dic71—21no—
148C2×C4×Dic71C2311yescharacteristic
149#14556061C2314yescomplemented
150#14556059C2314yescomplemented
151Dic71⋊C8C2314yescomplemented
152#14556053C2314yescomplemented
153#14556053C2314yescomplemented
154#14556051C2314yescomplemented
155#14556050C2314yes—
156#14556050C2314yes—
157#14556049C2314yes—
158#14556049C2314yes—
159#14556048C2314yes—
160C22⋊(C71⋊C8)C2314yescomplemented
161(C2×D71)⋊C8C2314yes—
162#14556038C2314yescomplemented
163C22×Q8×C71C2311yescharacteristic
164C22×D4×C71—21no—
165C22×D4×C71C2311yescharacteristic
166C23×C4×C71C2311yescharacteristic
167C2×SD16×C71—42no—
168C2×SD16×C71C2314yes—
169C22×C8×C71—42no—
170C22×C8×C71C2311yescharacteristic
171C22×C8×C71C2311yescharacteristic
172C22×C8×C71C2314yescomplemented
173C22⋊Q8×C71—22no—
174C22⋊Q8×C71C2314yescomplemented
175#121×C71—22no—
176#121×C71C2314yes—
177C2×C4⋊C4×C71—21no—
178C2×C4⋊C4×C71C2311yescharacteristic
179C2×C4⋊C4×C71C2311yescharacteristic
180C2×C22⋊C4×C71—21no—
181C2×C22⋊C4×C71—21no—
182#106×C71C2314yescomplemented
183#103×C71C2314yescomplemented
184#102×C71C2314yes—
185C23×D71—21no—
186C23×D71—24no—
187C23×D71—44no—
188C23×D71—44no—
189C23×D71—82no—
190C23×D71C2×D411yescharacteristic
191#11765865—28no—
192#11765865—44no—
193#11765865—48no—
194C2×Dic142—22no—
195C2×Dic142—22no—
196C2×Dic142—21no—
197C2×Dic142—24no—
198C2×Dic142—44no—
199C2×Dic142C2412yes—
200C2×D284—21no—
201C2×D284—22no—
202C2×D284#4114yes—
203C2×D284C2412yes—
204C2×C22⋊D71—24no—
205C2×C22⋊D71—24no—
206C2×C22⋊D71—42no—
207C2×C22⋊D71—44no—
208C2×C22⋊D71—44no—
209C2×C22⋊D71C2×D414yes—
210D4×D71—28no—
211D4×D71—44no—
212D4×D71—48no—
213C22×Dic71—21no—
214C22×Dic71—21no—
215C22×Dic71—21no—
216C22×Dic71C2×D411yescharacteristic
217C22×Dic71C2×D411yescharacteristic
218C22×Dic71C2×D411yescharacteristic
219C2×C4×D71—22no—
220C2×C4×D71—22no—
221C2×C4×D71—24no—
222C2×C4×D71—24no—
223C2×C4×D71—44no—
224C2×C4×D71—82no—
225C2×C4×D71C2×D412yes—
226C2×C4×D71C2412yes—
227#11765855—44no—
228#11765852—28no—
229#11765848—44no—
230C2×C71⋊C8—22no—
231C2×C71⋊C8—22no—
232C2×C71⋊C8C2412yes—
233C2×C71⋊C8C2412yes—
234C4⋊Dic71—21no—
235C4⋊Dic71—21no—
236C4⋊Dic71—24no—
237C4⋊Dic71—24no—
238C4⋊Dic71C2412yes—
239C4⋊Dic71C2412yes—
240Dic71⋊C4—24no—
241Dic71⋊C4—24no—
242Dic71⋊C4C2×D414yes—
243C22⋊Dic71—24no—
244C22⋊Dic71—24no—
245C22⋊Dic71—24no—
246C22⋊Dic71C2×D414yes—
247(C2×D71)⋊C4—24no—
248(C2×D71)⋊C4—24no—
249(C2×D71)⋊C4—24no—
250(C2×D71)⋊C4—24no—
251(C2×D71)⋊C4C2×D414yes—
252C4×Dic71—24no—
253C4×Dic71—24no—
254C4×Dic71—24no—
255C4×Dic71C2×D412yes—
256C4×Dic71C2412yes—
257C24×C71—21no—
258C24×C71C2×D411yescharacteristic
259C2×Q8×C71—21no—
260C2×Q8×C71—22no—
261C2×Q8×C71—22no—
262C2×Q8×C71C2412yes—
263C2×D4×C71—24no—
264C2×D4×C71—21no—
265C2×D4×C71—22no—
266C2×D4×C71—22no—
267C2×D4×C71—82no—
268C2×D4×C71C2412yes—
269C22×C4×C71—22no—
270C22×C4×C71—22no—
271C22×C4×C71—21no—
272C22×C4×C71—21no—
273C22×C4×C71—21no—
274C22×C4×C71C2×D411yescharacteristic
275C22×C4×C71C2×D412yes—
276C22×C4×C71C2412yes—
277C22×C4×C71C2411yescharacteristic
278SD16×C71—44no—
279C2×C8×C71—22no—
280C2×C8×C71—22no—
281C2×C8×C71—44no—
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—
290C22⋊C4×C71—24no—
291C23×C71—22no—
292C23×C71—22no—
293C23×C71—22no—
294C23×C71—22no—
295C23×C71—42no—
296C23×C71—42no—
297C23×C71—42no—
298C23×C71C22×D412yes—
299C23×C71C22×D411yescharacteristic
300C22×D71—22no—
301C22×D71—24no—
302C22×D71—22no—
303C22×D71—22no—
304C22×D71—22no—
305C22×D71—48no—
306C22×D71—48no—
307C22×D71—42no—
308C22×D71—42no—
309C22×D71—84no—
310C22×D71—816no—
311C22×D71C22×D412yes—
312Q8×C71—22no—
313Q8×C71—22no—
314Q8×C71—42no—
315D4×C71—22no—
316D4×C71—22no—
317D4×C71—42no—
318D4×C71—84no—
319C2×C4×C71—22no—
320C2×C4×C71—24no—
321C2×C4×C71—22no—
322C2×C4×C71—22no—
323C2×C4×C71—22no—
324C2×C4×C71—22no—
325C2×C4×C71—22no—
326C2×C4×C71—42no—
327C2×C4×C71—42no—
328C2×C4×C71—42no—
329C2×C4×C71C22×D412yes—
330C2×C4×C71C22×D411yescharacteristic
331C2×C4×C71C2×#4112yes—
332C2×C4×C71H(5,𝔽2)12yes—
333C2×C4×C71C2511yescharacteristic
334C22⋊D71—44no—
335C22⋊D71—48no—
336C22⋊D71—48no—
337C2×Dic71—22no—
338C2×Dic71—22no—
339C2×Dic71—22no—
340C2×Dic71—22no—
341C2×Dic71—22no—
342C2×Dic71—22no—
343C2×Dic71—42no—
344C2×Dic71—42no—
345C2×Dic71—42no—
346C2×Dic71C22×D412yes—
347C2×Dic71C22×D412yes—
348C2×Dic71C22×D412yes—
349D284—24no—
350D284—22no—
351D284C2×#4114yes—
352C4×D71—24no—
353C4×D71—22no—
354C4×D71—22no—
355C4×D71—48no—
356C4×D71—84no—
357Dic142—22no—
358Dic142—22no—
359Dic142—48no—
360Dic142—42no—
361C8×C71—22no—
362C8×C71—22no—
363C71⋊C8—22no—
364C71⋊C8—22no—
365C22×C71—22no—
366C22×C71—22no—
367C22×C71—22no—
368C22×C71—44no—
369C22×C71—42no—
370C22×C71—42no—
371C22×C71—42no—
372C22×C71—84no—
373C22×C71#54612yes—
374C22×C71#57512yes—
375C22×C71#57712yes—
376C22×C71C23×D411yescharacteristic
377C2×D71—22no—
378C2×D71—24no—
379C2×D71—22no—
380C2×D71—22no—
381C2×D71—44no—
382C2×D71—48no—
383C2×D71—42no—
384C2×D71—42no—
385C2×D71—816no—
386C4×C71—22no—
387C4×C71—42no—
388C4×C71—42no—
389C4×C71—42no—
390C4×C71#54612yes—
391C4×C71C22×#4111yescharacteristic
392C4×C71C2×H(5,𝔽2)11yescharacteristic
393Dic71—22no—
394Dic71—22no—
395Dic71—22no—
396Dic71—42no—
397Dic71—42no—
398Dic71—42no—
399C2×#3311—711nomaximal, Sylow
400C2×C71—42no—
401C2×C71—82no—
402C2×C71#331114yescomplemented
403C2×C71C2×#54611yescharacteristic
404C2×C71C2×#57511yescharacteristic
405C2×C71C2×#57711yescharacteristic
406D71—42no—
407D71—44no—
408C2×#556—711no—
409C2×#546—711no—
410#3311—7116no—
411C2×#489—711no—
412C2×#485—711no—
413C2×#482—711no—
414C2×#476—711no—
415C2×#470—711no—
416C2×#465D7111yescharacteristic, complemented
417C2×#464—711no—
418C2×#452—711no—
419C2×#450—711no—
420C2×#440—711no—
421C2×#435—711no—
422C2×#418—711no—
423C2×#416—711no—
424C71C2×#331111yescharacteristic, complemented, Sylow
425C22×#41—711no—
426C23×D4—711no—
427C22×Q16—711no—
428C22×SD16—711no—
429C22×SD16C2×D7111yescharacteristic
430C22×M16—711no—
431C23×C8C2×D7111yescharacteristic, complemented
432#556—718no—
433#556—1424no—
434#546—718no—
435#546—1424no—
436C2×C4⋊Q8—711no—
437C2×#126—1421no—
438C2×#126—1421no—
439C2×#124—711no—
440C2×#124—1421no—
441C2×#123—1421no—
442C2×C22⋊Q8—711no—
443C2×C22⋊Q8—711no—
444C2×C22⋊Q8C2×D7111yescharacteristic, complemented
445C2×#121—1421no—
446C2×#121C2×D7111yescharacteristic
447C2×#120—1421no—
448C2×C4×Q8—711no—
449C2×C4×Q8—1421no—
450C2×C4×D4—711no—
451C2×C4×D4—711no—
452C2×#117—711no—
453C2×#117—711no—
454C22×C22⋊C4—1421no—
455#489—718no—
456#485—718no—
457#482—718no—
458#476—718no—
459#470—718no—
460#465C2×D7118yescomplemented
461#464—718no—
462#452—718no—
463#450—718no—
464#440—718no—
465#435—718no—
466C2×#107—711no—
467C2×#106—711no—
468C2×#106C2×D7111yescharacteristic, complemented
469C2×C4⋊C8—711no—
470#418—718no—
471#416—718no—
472C2×#103—711no—
473C2×#103—711no—
474C2×#103—711no—
475C2×#103C2×D7111yescharacteristic, complemented
476C2×#102—711no—
477C2×#102—711no—
478C2×#102—711no—
479C2×#102—711no—
480C2×#102—711no—
481C2×#102C2×D7111yescharacteristic
482C2×C22⋊C8—711no—
483C2×C22⋊C8—711no—
484C2×#97—711no—
485C25—1421no—
486C2×#41—2842no—
487C2×#41—714no—
488C2×#41—1424no—
489C2×#41—1422no—
490C22×Q8—711no—
491C22×Q8—1421no—
492C22×Q8C22×D7111yescharacteristic
493C22×D4—21no—
494C22×D4—2842no—
495C22×D4—711no—
496C22×D4—714no—
497C22×D4—711no—
498C22×D4—1422no—
499C22×D4—1421no—
500C22×D4—1424no—
501C22×D4—1421no—
502C22×D4C22×D7111yescharacteristic
503C23×C4—711no—
504C23×C4—1421no—
505C23×C4—1421no—
506C23×C4C22×D7111yescharacteristic
507C2×Q16—2842no—
508C2×Q16—714no—
509C2×SD16—42no—
510C2×SD16—714no—
511C2×SD16—1424no—
512C2×SD16C22×D7114yes—
513C2×M16—2842no—
514C2×M16—714no—
515C22×C8—42no—
516C22×C8—711no—
517C22×C8—711no—
518C22×C8C22×D7111yescharacteristic
519C22×C8C22×D7111yescharacteristic
520C22×C8C22×D7114yescomplemented
521C4⋊Q8—714no—
522C4⋊Q8—1422no—
523#126—1428no—
524#126—1428no—
525#124—714no—
526#124—1422no—
527#124—1428no—
528#123—1428no—
529C22⋊Q8—22no—
530C22⋊Q8—714no—
531C22⋊Q8—714no—
532C22⋊Q8—1422no—
533C22⋊Q8—1422no—
534C22⋊Q8C22×D7114yescomplemented
535#121—22no—
536#121—1428no—
537#121C22×D7114yes—
538#120—1428no—
539C4×Q8—714no—
540C4×Q8—1422no—
541C4×Q8—1428no—
542C4×D4—714no—
543C4×D4—714no—
544C4×D4—714no—
545C4×D4—1422no—
546#117—714no—
547#117—714no—
548#117—1422no—
549#117—1422no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—711no—
552C2×C4⋊C4—711no—
553C2×C4⋊C4—711no—
554C2×C4⋊C4—1421no—
555C2×C4⋊C4—1421no—
556C2×C4⋊C4—1421no—
557C2×C4⋊C4—1421no—
558C2×C4⋊C4C22×D7111yescharacteristic
559C2×C4⋊C4C22×D7111yescharacteristic
560C2×C22⋊C4—21no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—711no—
563C2×C22⋊C4—711no—
564C2×C22⋊C4—1428no—
565C2×C22⋊C4—1421no—
566C2×C22⋊C4—1421no—
567C2×C22⋊C4—1421no—
568C2×C22⋊C4—1421no—
569C2×C22⋊C4—1421no—
570C2×C22⋊C4—1421no—
571C2×C22⋊C4—1421no—
572C2×C42—711no—
573C2×C42—1421no—
574C2×C42—1421no—
575C2×C42—1421no—
576#107—714no—
577#106—714no—
578#106C22×D7114yescomplemented
579C4⋊C8—714no—
580#103—714no—
581#103—714no—
582#103—714no—
583#103C22×D7114yescomplemented
584#102—714no—
585#102—714no—
586#102—714no—
587#102—714no—
588#102—714no—
589#102C22×D7114yes—
590C22⋊C8—714no—
591C22⋊C8—714no—
592#97—714no—
593C24—21no—
594C24—2844no—
595C24—2844no—
596C24—5682no—
597C24—711no—
598C24—1424no—
599C24—1421no—
600C24D4×D7111yescharacteristic
601#41—2848no—
602#41—2844no—
603#41—1428no—
604C2×Q8—21no—
605C2×Q8—22no—
606C2×Q8—22no—
607C2×Q8—2844no—
608C2×Q8—712no—
609C2×Q8—1424no—
610C2×Q8—1422no—
611C2×Q8—1422no—
612C2×Q8—1421no—
613C2×Q8C23×D7112yes—
614C2×D4—24no—
615C2×D4—21no—
616C2×D4—22no—
617C2×D4—22no—
618C2×D4—82no—
619C2×D4—2844no—
620C2×D4—2844no—
621C2×D4—2848no—
622C2×D4—2842no—
623C2×D4—2844no—
624C2×D4—714no—
625C2×D4—714no—
626C2×D4—712no—
627C2×D4—1424no—
628C2×D4—1428no—
629C2×D4—1424no—
630C2×D4—1421no—
631C2×D4—1422no—
632C2×D4C23×D7112yes—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—2844no—
639C22×C4—5682no—
640C22×C4—711no—
641C22×C4—711no—
642C22×C4—711no—
643C22×C4—712no—
644C22×C4—712no—
645C22×C4—1424no—
646C22×C4—1421no—
647C22×C4—1421no—
648C22×C4—1421no—
649C22×C4—1424no—
650C22×C4—1422no—
651C22×C4—1422no—
652C22×C4D4×D7112yes—
653C22×C4D4×D7111yescharacteristic
654C22×C4C23×D7112yes—
655C22×C4C23×D7111yescharacteristic
656Q16—2844no—
657SD16—44no—
658SD16—1428no—
659M16—2844no—
660C2×C8—22no—
661C2×C8—22no—
662C2×C8—44no—
663C2×C8—712no—
664C2×C8—712no—
665C2×C8—1422no—
666C2×C8—1422no—
667C2×C8C23×D7112yes—
668C2×C8C23×D7112yes—
669C4⋊C4—24no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—714no—
673C4⋊C4—712no—
674C4⋊C4—712no—
675C4⋊C4—1424no—
676C4⋊C4—1424no—
677C4⋊C4—1424no—
678C4⋊C4—1424no—
679C4⋊C4—1421no—
680C4⋊C4—1421no—
681C4⋊C4C23×D7112yes—
682C4⋊C4C23×D7112yes—
683C22⋊C4—24no—
684C22⋊C4—24no—
685C22⋊C4—714no—
686C22⋊C4—714no—
687C22⋊C4—1424no—
688C22⋊C4—1424no—
689C22⋊C4—1424no—
690C22⋊C4—1424no—
691C22⋊C4—1424no—
692C22⋊C4—1424no—
693C22⋊C4—1424no—
694C42—712no—
695C42—712no—
696C42—1424no—
697C42—1424no—
698C42—1424no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—2848no—
707C23—2848no—
708C23—2842no—
709C23—2842no—
710C23—5684no—
711C23—56816no—
712C23—712no—
713C23—1422no—
714C23—1424no—
715C23—1422no—
716C23—1422no—
717C23—1422no—
718C23C2×D4×D7112yes—
719C23C2×D4×D7111yescharacteristic
720Q8—22no—
721Q8—22no—
722Q8—42no—
723Q8—2848no—
724Q8—2842no—
725Q8—1422no—
726Q8—1422no—
727D4—22no—
728D4—22no—
729D4—42no—
730D4—84no—
731D4—2848no—
732D4—2844no—
733D4—2848no—
734D4—714no—
735D4—1422no—
736D4—1424no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—24no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—2848no—
748C2×C4—2842no—
749C2×C4—2842no—
750C2×C4—2842no—
751C2×C4—5684no—
752C2×C4—712no—
753C2×C4—712no—
754C2×C4—712no—
755C2×C4—1422no—
756C2×C4—1422no—
757C2×C4—1422no—
758C2×C4—1422no—
759C2×C4—1422no—
760C2×C4—1422no—
761C2×C4—1422no—
762C2×C4—1422no—
763C2×C4—1424no—
764C2×C4C2×D4×D7112yes—
765C2×C4C2×D4×D7111yescharacteristic
766C2×C4#41×D7112yes—
767C2×C4#1455617312yes—
768C2×C4C24×D7111yescharacteristic
769C8—22no—
770C8—22no—
771C8—1422no—
772C8—1422no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—44no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22—84no—
781C22—2842no—
782C22—2842no—
783C22—2848no—
784C22—2844no—
785C22—56816no—
786C22—1424no—
787C22—1422no—
788C22—1422no—
789C22—1422no—
790C22#1798663812yes—
791C22#1798679612yes—
792C22#1798680512yes—
793C22C22×D4×D7111yescharacteristic
794C4—22no—
795C4—42no—
796C4—42no—
797C4—42no—
798C4—2842no—
799C4—2842no—
800C4—2842no—
801C4—1422no—
802C4—1422no—
803C4—1422no—
804C4#1798663812yes—
805C4C2×#41×D7111yescharacteristic
806C4C2×#1455617311yescharacteristic
807C2—42no—
808C2—82no—
809C2—2844no—
810C2—2842no—
811C2#2260038214yesdirect product factor
812C2C2×#1798663811yescharacteristic
813C2C2×#1798679611yescharacteristic
814C2C2×#1798680511yescharacteristic
subgroupG/H
centerC23C2×D4×D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#465×C71C2
socleC23×C71C22×D4
prime radicalC2×#17986646C2
hypercenterC2×#465D71
hypocenterC71C2×#3311
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#465

Complements

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

NH ≅ G/Ntype
1. C2×#17986720C2semidirect
3. #22600382C2direct (N × H)
4. C2×#17986357C2semidirect
5. C2×#17986343C2semidirect
6. C2×#17986320C2semidirect
7. C2×#17986288C2semidirect
8. C2×#17986256C2semidirect
9. C2×#17986219C2semidirect
10. C2×#17986159C2semidirect
11. C2×#17986148C2semidirect
12. C2×#17986102C2semidirect
13. C2×#17986070C2semidirect
14. C2×#17986002C2semidirect
15. C2×#17985996C2semidirect
16. C2×#465×C71C2semidirect
19. C22×#11765855C22semidirect
23. #17986720C22semidirect
26. C2×#14556127C22semidirect
36. C2×Q8×Dic71C22semidirect
40. C2×#14556087C22semidirect
43. #17986357C22semidirect
44. #17986343C22semidirect
45. #17986320C22semidirect
46. #17986288C22semidirect
47. #17986256C22semidirect
48. #17986219C22semidirect
49. #17986159C22semidirect
50. #17986148C22semidirect
51. #17986102C22semidirect
52. #17986070C22semidirect
53. C2×#14556061C22semidirect
54. C2×#14556059C22semidirect
55. C2×Dic71⋊C8C22semidirect
56. #17986002C22semidirect
57. #17985996C22semidirect
58. C2×#14556053C22semidirect
59. C2×#14556053C22semidirect
60. C2×#14556051C22semidirect
66. C2×C22⋊(C71⋊C8)C22semidirect
68. C2×#14556038C22semidirect
70. C23×C8×C71C22semidirect
71. C2×C22⋊Q8×C71C22semidirect
73. #465×C71C22semidirect
74. C2×#106×C71C22semidirect
75. C2×#103×C71C22semidirect
96. C2×#11765855C23semidirect
104. #14556127C23semidirect
118. Q8×Dic71C23semidirect
125. #14556087C23semidirect
149. #14556061C23semidirect
150. #14556059C23semidirect
151. Dic71⋊C8C23semidirect
152. #14556053C23semidirect
153. #14556053C23semidirect
154. #14556051C23semidirect
160. C22⋊(C71⋊C8)C23semidirect
162. #14556038C23semidirect
172. C22×C8×C71C23semidirect
174. C22⋊Q8×C71C23semidirect
182. #106×C71C23semidirect
183. #103×C71C23semidirect
402. C2×C71#3311semidirect
416. C2×#465D71semidirect
424. C71C2×#3311semidirect
431. C23×C8C2×D71semidirect
444. C2×C22⋊Q8C2×D71semidirect
460. #465C2×D71semidirect
468. C2×#106C2×D71semidirect
475. C2×#103C2×D71semidirect
520. C22×C8C22×D71semidirect
534. C22⋊Q8C22×D71semidirect
578. #106C22×D71semidirect
583. #103C22×D71semidirect
811. C2#22600382direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179867202
C2×#179866462
#226003822
C2×#179863572
C2×#179863432
C2×#179863202
C2×#179862882
C2×#179862562
C2×#179862192
C2×#179861592
C2×#179861482
C2×#179861022
C2×#179860702
C2×#179860022
C2×#179859962
C2×#465×C712
C2×#331171