Finite Group Databasebeta

← C2×#20255651 #27093142

Subgroups — C2×#20255651 #27093142

Order 12032.

2114 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689815C211yesmaximal, characteristic, complemented
2C2×#15689783C211yesmaximal, characteristic
3#20255651C2116yesmaximal, direct product factor
4C2×#15689479C211yesmaximal, characteristic, complemented
5C2×#15689456C211yesmaximal, characteristic, complemented
6C2×#15689449C211yesmaximal, characteristic, complemented
7C2×#15689433C211yesmaximal, characteristic, complemented
8C2×#15689372C211yesmaximal, characteristic, complemented
9C2×#15689347C211yesmaximal, characteristic, complemented
10C2×#15689283C211yesmaximal, characteristic, complemented
11C2×#15689277C211yesmaximal, characteristic, complemented
12C2×#15689215C211yesmaximal, characteristic, complemented
13C2×#15689199C211yesmaximal, characteristic, complemented
14C2×#15689125C211yesmaximal, characteristic, complemented
15C2×#15689130C211yesmaximal, characteristic, complemented
16C2×C47×#470C211yesmaximal, characteristic, complemented
17C22×#10625350C2211yescharacteristic
18C22×Q8×D47C2211yescharacteristic
19C22×#10625337C2211yescharacteristic
20C22×#10625336C2211yescharacteristic
21C22×#10625324C2211yescharacteristic
22#15689815—24no—
23#15689815C2218yescomplemented
24#15689783—24no—
25#15689783C2218yes—
26C2×#13094019—21no—
27C2×#13094015—21no—
28C2×#13094015C2211yescharacteristic
29C2×#13094013C2211yescharacteristic
30C2×#13094010—21no—
31C2×#13094008—21no—
32C2×#13094002—21no—
33C2×#13094000C2211yescharacteristic
34C2×#13093999C2211yescharacteristic
35C2×#13093997—21no—
36C2×Q8×Dic47C2211yescharacteristic
37C2×#13093989C2211yescharacteristic
38C2×#13093986—21no—
39C2×C4×C22⋊D47C2211yescharacteristic
40C2×#13093982C2211yescharacteristic
41C2×#13093980—21no—
42C22×C4⋊Dic47C2211yescharacteristic
43#15689479C2218yescomplemented
44#15689456C2218yescomplemented
45#15689449C2218yescomplemented
46#15689433C2218yescomplemented
47#15689372C2218yescomplemented
48#15689347C2218yescomplemented
49#15689283C2218yescomplemented
50#15689277C2218yescomplemented
51#15689215C2218yescomplemented
52#15689199C2218yescomplemented
53C2×#13093957C2211yescharacteristic
54C2×#13093957C2211yescharacteristic
55C2×Dic47⋊C8C2211yescharacteristic
56#15689130C2218yescomplemented
57#15689125C2218yescomplemented
58C2×#13093949C2211yescharacteristic
59C2×#13093949C2211yescharacteristic
60C2×#13093948C2211yescharacteristic
61C2×#13093948C2211yescharacteristic
62C2×#13093947C2211yescharacteristic
63C2×#13093946C2211yescharacteristic
64C2×#13093946C2211yescharacteristic
65C2×#13093944C2211yescharacteristic
66C2×C22⋊(C47⋊C8)C2211yescharacteristic
67C2×(C2×D47)⋊C8C2211yescharacteristic
68C2×C8×Dic47C2211yescharacteristic
69C22×Q16×C47C2211yescharacteristic
70C22×M16×C47C2211yescharacteristic
71C2×C22⋊Q8×C47C2211yescharacteristic
72C2×C22⋊Q8×C47C2211yescharacteristic
73C47×#470C2218yescomplemented
74C2×#106×C47C2211yescharacteristic
75C2×#103×C47C2211yescharacteristic
76C2×#103×C47C2211yescharacteristic
77C2×#10625350—22no—
78C2×#10625350—24no—
79C2×#10625350—42no—
80C2×#10625350C2314yes—
81C22×Dic94—21no—
82C22×Dic94C2311yescharacteristic
83C2×Q8×D47—22no—
84C2×Q8×D47—24no—
85C2×Q8×D47—42no—
86C2×Q8×D47C2314yes—
87C22×D188—21no—
88C22×D188C2311yescharacteristic
89C22×C22⋊D47—21no—
90C22×C22⋊D47D411yescharacteristic
91C23×Dic47—21no—
92C22×C4×D47—21no—
93C22×C4×D47—21no—
94C22×C4×D47C2311yescharacteristic
95C2×#10625337—24no—
96C2×#10625337C2314yes—
97C2×#10625336—42no—
98C2×#10625336C2314yes—
99C2×#10625324—42no—
100C2×#10625324C2314yes—
101C22×C47⋊C8C2311yescharacteristic
102C22×C47⋊C8C2311yescharacteristic
103#13094019—28no—
104#13094015—28no—
105#13094015—22no—
106#13094015C2314yes—
107#13094013—22no—
108#13094013C2314yes—
109#13094010—28no—
110#13094008—28no—
111#13094002—28no—
112#13094000—22no—
113#13094000C2314yes—
114#13093999—22no—
115#13093999C2314yes—
116#13093997—28no—
117Q8×Dic47—22no—
118Q8×Dic47C2314yes—
119#13093989—22no—
120#13093989C2314yes—
121#13093986—28no—
122C4×C22⋊D47D414yes—
123C4×C22⋊D47C2314yes—
124#13093982—22no—
125#13093982C2314yes—
126#13093980—28no—
127C2×C4⋊Dic47—22no—
128C2×C4⋊Dic47—21no—
129C2×C4⋊Dic47—21no—
130C2×C4⋊Dic47—21no—
131C2×C4⋊Dic47C2314yes—
132C2×C4⋊Dic47C2311yescharacteristic
133C2×C4⋊Dic47C2311yescharacteristic
134C2×Dic47⋊C4—21no—
135C2×Dic47⋊C4—21no—
136C2×Dic47⋊C4—21no—
137C2×Dic47⋊C4D411yescharacteristic
138C2×C22⋊Dic47D411yescharacteristic
139C2×(C2×D47)⋊C4—21no—
140C2×(C2×D47)⋊C4—21no—
141C2×(C2×D47)⋊C4—21no—
142C2×(C2×D47)⋊C4—21no—
143C2×(C2×D47)⋊C4—21no—
144C2×(C2×D47)⋊C4D411yescharacteristic
145C2×C4×Dic47—21no—
146C2×C4×Dic47—21no—
147C2×C4×Dic47—21no—
148C2×C4×Dic47C2311yescharacteristic
149#13093957C2314yes—
150#13093957C2314yes—
151Dic47⋊C8C2314yes—
152#13093949C2314yes—
153#13093949C2314yes—
154#13093948C2314yes—
155#13093948C2314yes—
156#13093947C2314yes—
157#13093946C2314yes—
158#13093946C2314yes—
159#13093944C2314yes—
160C22⋊(C47⋊C8)C2314yes—
161(C2×D47)⋊C8C2314yes—
162C8×Dic47C2314yes—
163C22×Q8×C47C2311yescharacteristic
164C22×Q8×C47C2311yescharacteristic
165C23×C4×C47C2311yescharacteristic
166C2×Q16×C47—42no—
167C2×Q16×C47C2314yes—
168C2×M16×C47—42no—
169C2×M16×C47C2314yes—
170C22×C8×C47C2311yescharacteristic
171C22×C8×C47C2311yescharacteristic
172C22⋊Q8×C47—22no—
173C22⋊Q8×C47—22no—
174C22⋊Q8×C47C2314yes—
175C22⋊Q8×C47C2314yes—
176C2×C4⋊C4×C47—21no—
177C2×C4⋊C4×C47—21no—
178C2×C4⋊C4×C47C2311yescharacteristic
179C2×C4⋊C4×C47C2311yescharacteristic
180C2×C22⋊C4×C47—21no—
181C2×C22⋊C4×C47—21no—
182#106×C47C2314yes—
183#103×C47C2314yes—
184#103×C47C2314yes—
185C24×C47C2×D411yescharacteristic
186C23×D47—21no—
187C23×D47C2×D411yescharacteristic
188C2×Q8×C47—21no—
189C2×Q8×C47—21no—
190C2×Q8×C47—22no—
191C2×Q8×C47—22no—
192C2×Q8×C47—22no—
193C2×Q8×C47—22no—
194C2×Q8×C47C2412yes—
195C2×Q8×C47C2412yes—
196C22×C4×C47—22no—
197C22×C4×C47—22no—
198C22×C4×C47—21no—
199C22×C4×C47—21no—
200C22×C4×C47—21no—
201C22×C4×C47—21no—
202C22×C4×C47C2×D411yescharacteristic
203C22×C4×C47C2×D412yes—
204C22×C4×C47C2412yes—
205C22×C4×C47C2411yescharacteristic
206C2×C22⋊D47—24no—
207C2×C22⋊D47—42no—
208C2×C22⋊D47—44no—
209C2×C22⋊D47C2×D414yes—
210C22×Dic47—21no—
211C22×Dic47—21no—
212C22×Dic47—21no—
213C22×Dic47—24no—
214C22×Dic47—44no—
215C22×Dic47C2×D411yescharacteristic
216C22×Dic47C2×D411yescharacteristic
217C22×Dic47C2×D411yescharacteristic
218Q8×D47—28no—
219Q8×D47—44no—
220Q8×D47—48no—
221#10625350—28no—
222#10625350—44no—
223#10625350—48no—
224C2×D188—22no—
225C2×D188—22no—
226C2×D188—24no—
227C2×D188—21no—
228C2×D188—44no—
229C2×D188C2412yes—
230C2×C4×D47—22no—
231C2×C4×D47—22no—
232C2×C4×D47—24no—
233C2×C4×D47—24no—
234C2×C4×D47—44no—
235C2×C4×D47—44no—
236C2×C4×D47C2×D412yes—
237C2×C4×D47C2412yes—
238C2×Dic94—21no—
239C2×Dic94—22no—
240C2×Dic94—24no—
241C2×Dic94—44no—
242C2×Dic94#4114yes—
243C2×Dic94C2412yes—
244Q16×C47—44no—
245M16×C47—44no—
246C2×C8×C47—22no—
247C2×C8×C47—22no—
248C2×C8×C47C2412yes—
249C2×C8×C47C2412yes—
250C4⋊C4×C47—24no—
251C4⋊C4×C47—24no—
252C4⋊C4×C47—21no—
253C4⋊C4×C47—21no—
254C4⋊C4×C47C2412yes—
255C4⋊C4×C47C2412yes—
256C22⋊C4×C47—24no—
257C22⋊C4×C47—24no—
258C22⋊Dic47C2×D414yes—
259#10625337—28no—
260#10625336—44no—
261(C2×D47)⋊C4—24no—
262(C2×D47)⋊C4—24no—
263(C2×D47)⋊C4—24no—
264(C2×D47)⋊C4—24no—
265(C2×D47)⋊C4—24no—
266(C2×D47)⋊C4C2×D414yes—
267C4⋊Dic47—21no—
268C4⋊Dic47—21no—
269C4⋊Dic47—24no—
270C4⋊Dic47—24no—
271C4⋊Dic47—24no—
272C4⋊Dic47C2412yes—
273C4⋊Dic47C2412yes—
274Dic47⋊C4—24no—
275Dic47⋊C4—24no—
276Dic47⋊C4—24no—
277Dic47⋊C4C2×D414yes—
278C4×Dic47—24no—
279C4×Dic47—24no—
280C4×Dic47—24no—
281C4×Dic47C2×D412yes—
282C4×Dic47C2412yes—
283C2×C47⋊C8—22no—
284C2×C47⋊C8—22no—
285C2×C47⋊C8C2412yes—
286C2×C47⋊C8C2412yes—
287#10625324—44no—
288C23×C47—22no—
289C23×C47—22no—
290C23×C47—22no—
291C23×C47C22×D412yes—
292C23×C47C22×D411yescharacteristic
293C22×D47—22no—
294C22×D47—22no—
295C22×D47—22no—
296C22×D47—22no—
297C22×D47—42no—
298C22×D47—42no—
299C22×D47—42no—
300C22×D47C22×D412yes—
301Q8×C47—22no—
302Q8×C47—22no—
303Q8×C47—22no—
304Q8×C47—22no—
305Q8×C47—42no—
306Q8×C47—42no—
307C2×C4×C47—22no—
308C2×C4×C47—24no—
309C2×C4×C47—22no—
310C2×C4×C47—22no—
311C2×C4×C47—22no—
312C2×C4×C47—22no—
313C2×C4×C47—22no—
314C2×C4×C47—22no—
315C2×C4×C47—42no—
316C2×C4×C47—42no—
317C2×C4×C47—42no—
318C2×C4×C47—42no—
319C2×C4×C47C22×D412yes—
320C2×C4×C47C22×D411yescharacteristic
321C2×C4×C47C2×#4112yes—
322C2×C4×C47H(5,𝔽2)12yes—
323C2×C4×C47C2511yescharacteristic
324C22⋊D47—44no—
325C22⋊D47—48no—
326C2×Dic47—24no—
327C2×Dic47—22no—
328C2×Dic47—22no—
329C2×Dic47—22no—
330C2×Dic47—22no—
331C2×Dic47—22no—
332C2×Dic47—22no—
333C2×Dic47—48no—
334C2×Dic47—42no—
335C2×Dic47—42no—
336C2×Dic47C22×D412yes—
337C2×Dic47C22×D412yes—
338C2×Dic47C22×D412yes—
339D188—22no—
340D188—22no—
341D188—48no—
342D188—42no—
343C4×D47—24no—
344C4×D47—22no—
345C4×D47—22no—
346C4×D47—48no—
347C4×D47—48no—
348Dic94—24no—
349Dic94—22no—
350Dic94—48no—
351Dic94C2×#4114yes—
352C8×C47—22no—
353C8×C47—22no—
354C47⋊C8—22no—
355C47⋊C8—22no—
356C2×#3327—471nomaximal, Sylow
357C22×C47—22no—
358C22×C47—22no—
359C22×C47—22no—
360C22×C47—44no—
361C22×C47#54612yes—
362C22×C47#57512yes—
363C22×C47#57812yes—
364C22×C47C23×D411yescharacteristic
365C2×D47—22no—
366C2×D47—22no—
367C2×D47—22no—
368C2×D47—44no—
369C2×D47—42no—
370C2×D47—42no—
371C2×D47—42no—
372C2×D47—84no—
373C4×C47—22no—
374C4×C47—42no—
375C4×C47—42no—
376C4×C47—42no—
377C4×C47—42no—
378C4×C47#54612yes—
379C4×C47C22×#4111yescharacteristic
380C4×C47C2×H(5,𝔽2)11yescharacteristic
381Dic47—24no—
382Dic47—22no—
383Dic47—22no—
384Dic47—22no—
385Dic47—42no—
386Dic47—42no—
387C2×#552—471no—
388C2×#548—471no—
389#3327—4716no—
390C2×#488—471no—
391C2×#484—471no—
392C2×#482—471no—
393C2×#479—471no—
394C2×#470D4711yescharacteristic, complemented
395C2×#468—471no—
396C2×#464—471no—
397C2×#452—471no—
398C2×#451—471no—
399C2×C4×Q16—471no—
400C2×#436—471no—
401C2×#417—471no—
402C2×#419—471no—
403C2×C47—42no—
404C2×C47#332714yescomplemented
405C2×C47C2×#54611yescharacteristic
406C2×C47C2×#57511yescharacteristic
407C2×C47C2×#57811yescharacteristic
408D47—42no—
409D47—82no—
410C22×#41—471no—
411C23×Q8—471no—
412C22×Q16—471no—
413C22×Q16C2×D4711yescharacteristic
414C22×SD16—471no—
415C22×M16—471no—
416C22×M16C2×D4711yescharacteristic
417#552—478no—
418#552—944no—
419#548—478no—
420#548—944no—
421C2×#126—941no—
422C2×#125—471no—
423C2×#125—941no—
424C2×#124—471no—
425C2×#124—941no—
426C2×#123—941no—
427C2×C22⋊Q8—471no—
428C2×C22⋊Q8—941no—
429C2×C22⋊Q8C2×D4711yescharacteristic
430C2×C22⋊Q8C2×D4711yescharacteristic
431C2×#121—471no—
432C2×#121—941no—
433C2×C4×Q8—471no—
434C2×C4×Q8—471no—
435C2×C4×D4—471no—
436C2×C4×D4—941no—
437C2×#117—471no—
438C2×#117—941no—
439C22×C4⋊C4—471no—
440#488—478no—
441#484—478no—
442#482—478no—
443#479—478no—
444#470C2×D4718yescomplemented
445#468—478no—
446#464—478no—
447#452—478no—
448#451—478no—
449C4×Q16—478no—
450#436—478no—
451C2×#107—471no—
452C2×#107—471no—
453C2×#106C2×D4711yescharacteristic
454C2×C4⋊C8—471no—
455#419—478no—
456#417—478no—
457C2×#103—471no—
458C2×#103—471no—
459C2×#103—471no—
460C2×#103—471no—
461C2×#103—471no—
462C2×#103C2×D4711yescharacteristic
463C2×#103C2×D4711yescharacteristic
464C2×#102—471no—
465C2×#102—471no—
466C2×#102—471no—
467C2×C22⋊C8—471no—
468C2×C22⋊C8—471no—
469C2×C4×C8—471no—
470C47C2×#332711yescharacteristic, complemented, Sylow
471C2×#41—474no—
472C2×#41—944no—
473C2×#41—942no—
474C2×#41—1882no—
475C22×Q8—474no—
476C22×Q8—471no—
477C22×Q8—941no—
478C22×Q8—942no—
479C22×Q8—944no—
480C22×Q8—1882no—
481C22×Q8C22×D4711yescharacteristic
482C22×Q8C22×D4711yescharacteristic
483C22×D4—471no—
484C22×D4—471no—
485C22×D4—941no—
486C22×D4—941no—
487C23×C4—471no—
488C23×C4—941no—
489C23×C4—941no—
490C23×C4—941no—
491C23×C4C22×D4711yescharacteristic
492C2×Q16—42no—
493C2×Q16—474no—
494C2×Q16—944no—
495C2×Q16C22×D4714yes—
496C2×SD16—474no—
497C2×SD16—1882no—
498C2×M16—42no—
499C2×M16—474no—
500C2×M16—1882no—
501C2×M16C22×D4714yes—
502C22×C8—471no—
503C22×C8—471no—
504C22×C8C22×D4711yescharacteristic
505C22×C8C22×D4711yescharacteristic
506#126—948no—
507#125—474no—
508#125—942no—
509#125—948no—
510#124—474no—
511#124—942no—
512#124—948no—
513#123—948no—
514C22⋊Q8—22no—
515C22⋊Q8—22no—
516C22⋊Q8—474no—
517C22⋊Q8—948no—
518C22⋊Q8—942no—
519C22⋊Q8C22×D4714yes—
520C22⋊Q8C22×D4714yes—
521#121—474no—
522#121—948no—
523#121—942no—
524C4×Q8—474no—
525C4×Q8—474no—
526C4×Q8—942no—
527C4×Q8—942no—
528C4×D4—474no—
529C4×D4—474no—
530C4×D4—948no—
531#117—474no—
532#117—948no—
533#117—942no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—471no—
537C2×C4⋊C4—471no—
538C2×C4⋊C4—471no—
539C2×C4⋊C4—474no—
540C2×C4⋊C4—941no—
541C2×C4⋊C4—941no—
542C2×C4⋊C4—941no—
543C2×C4⋊C4—941no—
544C2×C4⋊C4—941no—
545C2×C4⋊C4—941no—
546C2×C4⋊C4—942no—
547C2×C4⋊C4C22×D4711yescharacteristic
548C2×C4⋊C4C22×D4711yescharacteristic
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—471no—
552C2×C22⋊C4—471no—
553C2×C22⋊C4—941no—
554C2×C22⋊C4—941no—
555C2×C22⋊C4—941no—
556C2×C22⋊C4—941no—
557C2×C22⋊C4—941no—
558C2×C42—471no—
559C2×C42—941no—
560C2×C42—941no—
561C2×C42—941no—
562#107—474no—
563#107—474no—
564#106C22×D4714yes—
565C4⋊C8—474no—
566#103—474no—
567#103—474no—
568#103—474no—
569#103—474no—
570#103—474no—
571#103C22×D4714yes—
572#103C22×D4714yes—
573#102—474no—
574#102—474no—
575#102—474no—
576C22⋊C8—474no—
577C22⋊C8—474no—
578C4×C8—474no—
579C24—471no—
580C24—941no—
581C24D4×D4711yescharacteristic
582#41—948no—
583#41—1884no—
584#41—1888no—
585C2×Q8—21no—
586C2×Q8—21no—
587C2×Q8—22no—
588C2×Q8—22no—
589C2×Q8—22no—
590C2×Q8—22no—
591C2×Q8—474no—
592C2×Q8—472no—
593C2×Q8—944no—
594C2×Q8—941no—
595C2×Q8—942no—
596C2×Q8—948no—
597C2×Q8—1884no—
598C2×Q8—1884no—
599C2×Q8—1888no—
600C2×Q8C23×D4712yes—
601C2×Q8C23×D4712yes—
602C2×D4—474no—
603C2×D4—472no—
604C2×D4—944no—
605C2×D4—944no—
606C2×D4—941no—
607C2×D4—942no—
608C2×D4—942no—
609C2×D4—1884no—
610C2×D4—1882no—
611C2×D4—1884no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—471no—
619C22×C4—471no—
620C22×C4—471no—
621C22×C4—472no—
622C22×C4—472no—
623C22×C4—944no—
624C22×C4—941no—
625C22×C4—942no—
626C22×C4—942no—
627C22×C4—944no—
628C22×C4—941no—
629C22×C4—941no—
630C22×C4—944no—
631C22×C4—1884no—
632C22×C4—1884no—
633C22×C4—1884no—
634C22×C4D4×D4712yes—
635C22×C4D4×D4711yescharacteristic
636C22×C4C23×D4712yes—
637C22×C4C23×D4711yescharacteristic
638Q16—44no—
639Q16—948no—
640SD16—1884no—
641M16—44no—
642M16—1884no—
643C2×C8—22no—
644C2×C8—22no—
645C2×C8—472no—
646C2×C8—472no—
647C2×C8—942no—
648C2×C8—942no—
649C2×C8C23×D4712yes—
650C2×C8C23×D4712yes—
651C4⋊C4—24no—
652C4⋊C4—24no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—474no—
656C4⋊C4—472no—
657C4⋊C4—472no—
658C4⋊C4—944no—
659C4⋊C4—944no—
660C4⋊C4—944no—
661C4⋊C4—944no—
662C4⋊C4—944no—
663C4⋊C4—941no—
664C4⋊C4—941no—
665C4⋊C4—944no—
666C4⋊C4C23×D4712yes—
667C4⋊C4C23×D4712yes—
668C22⋊C4—24no—
669C22⋊C4—24no—
670C22⋊C4—474no—
671C22⋊C4—474no—
672C22⋊C4—944no—
673C22⋊C4—944no—
674C22⋊C4—944no—
675C22⋊C4—944no—
676C22⋊C4—944no—
677C42—472no—
678C42—472no—
679C42—944no—
680C42—944no—
681C42—944no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—472no—
686C23—942no—
687C23—942no—
688C23—942no—
689C23—942no—
690C23—1882no—
691C23—1882no—
692C23—1882no—
693C23C2×D4×D4712yes—
694C23C2×D4×D4711yescharacteristic
695Q8—22no—
696Q8—22no—
697Q8—22no—
698Q8—22no—
699Q8—42no—
700Q8—42no—
701Q8—474no—
702Q8—944no—
703Q8—942no—
704Q8—1888no—
705D4—942no—
706D4—942no—
707D4—1888no—
708D4—1884no—
709D4—1888no—
710D4—1882no—
711C2×C4—22no—
712C2×C4—24no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—472no—
724C2×C4—472no—
725C2×C4—472no—
726C2×C4—942no—
727C2×C4—944no—
728C2×C4—942no—
729C2×C4—942no—
730C2×C4—942no—
731C2×C4—944no—
732C2×C4—942no—
733C2×C4—942no—
734C2×C4—942no—
735C2×C4—942no—
736C2×C4—1888no—
737C2×C4—1888no—
738C2×C4—1888no—
739C2×C4—1882no—
740C2×C4—1882no—
741C2×C4C2×D4×D4712yes—
742C2×C4C2×D4×D4711yescharacteristic
743C2×C4#41×D4712yes—
744C2×C4#1309406912yes—
745C2×C4C24×D4711yescharacteristic
746C8—22no—
747C8—22no—
748C8—942no—
749C8—942no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—44no—
754C22—942no—
755C22—942no—
756C22—942no—
757C22—3764no—
758C22—1882no—
759C22—1882no—
760C22—1882no—
761C22—1884no—
762C22#1568976212yes—
763C22#1568992212yes—
764C22#1568993912yes—
765C22C22×D4×D4711yescharacteristic
766C4—22no—
767C4—42no—
768C4—42no—
769C4—42no—
770C4—42no—
771C4—942no—
772C4—944no—
773C4—942no—
774C4—942no—
775C4—1882no—
776C4—1882no—
777C4#1568976212yes—
778C4C2×#41×D4711yescharacteristic
779C4C2×#1309406911yescharacteristic
780C2—42no—
781C2—3762no—
782C2—1882no—
783C2#2025565114yesdirect product factor
784C2C2×#1568976211yescharacteristic
785C2C2×#1568992211yescharacteristic
786C2C2×#1568993911yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#470C2
socleC23×C47C22×D4
prime radicalC2×#15689783C2
hypercenterC2×#470D47
hypocenterC47C2×#3327
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#470

Complements

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

NH ≅ G/Ntype
1. C2×#15689815C2semidirect
3. #20255651C2direct (N × H)
4. C2×#15689479C2semidirect
5. C2×#15689456C2semidirect
6. C2×#15689449C2semidirect
7. C2×#15689433C2semidirect
8. C2×#15689372C2semidirect
9. C2×#15689347C2semidirect
10. C2×#15689283C2semidirect
11. C2×#15689277C2semidirect
12. C2×#15689215C2semidirect
13. C2×#15689199C2semidirect
14. C2×#15689125C2semidirect
15. C2×#15689130C2semidirect
16. C2×C47×#470C2semidirect
23. #15689815C22semidirect
43. #15689479C22semidirect
44. #15689456C22semidirect
45. #15689449C22semidirect
46. #15689433C22semidirect
47. #15689372C22semidirect
48. #15689347C22semidirect
49. #15689283C22semidirect
50. #15689277C22semidirect
51. #15689215C22semidirect
52. #15689199C22semidirect
56. #15689130C22semidirect
57. #15689125C22semidirect
73. C47×#470C22semidirect
394. C2×#470D47semidirect
404. C2×C47#3327semidirect
444. #470C2×D47semidirect
470. C47C2×#3327semidirect
783. C2#20255651direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156898152
C2×#156897832
#202556512
C2×#156894792
C2×#156894562
C2×#156894492
C2×#156894332
C2×#156893722
C2×#156893472
C2×#156892832
C2×#156892772
C2×#156892152
C2×#156891992
C2×#156891252
C2×#156891302
C2×C47×#4702
C2×#332747