Finite Group Databasebeta

← C2×#20255446 #27092891

Subgroups — C2×#20255446 #27092891

Order 12032.

2094 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689814C211yesmaximal, characteristic
2C2×#15689788C211yesmaximal, characteristic
3#20255446C2116yesmaximal, direct product factor
4C2×#15689491C211yesmaximal, characteristic, complemented
5C2×#15689463C211yesmaximal, characteristic, complemented
6C2×#15689452C211yesmaximal, characteristic, complemented
7C2×#15689431C211yesmaximal, characteristic, complemented
8C2×#15689378C211yesmaximal, characteristic, complemented
9C2×#15689361C211yesmaximal, characteristic, complemented
10C2×#15689277C211yesmaximal, characteristic, complemented
11C2×#15689277C211yesmaximal, characteristic, complemented
12C2×#15689228C211yesmaximal, characteristic, complemented
13C2×#15689193C211yesmaximal, characteristic
14C2×#15689130C211yesmaximal, characteristic, complemented
15C2×#103×D47C211yesmaximal, characteristic, complemented
16C2×C47×#462C211yesmaximal, characteristic, complemented
17C22×Q8×D47C2211yescharacteristic
18C22×Q8×D47C2211yescharacteristic
19C22×#10625337C2211yescharacteristic
20C22×#10625324C2211yescharacteristic
21C22×C8×D47C2211yescharacteristic
22#15689814—24no—
23#15689814C2218yes—
24#15689788—24no—
25#15689788C2218yes—
26C2×#13094023—21no—
27C2×#13094018—21no—
28C2×#13094016C2211yescharacteristic
29C2×#13094014—21no—
30C2×#13094009—21no—
31C2×#13094002—21no—
32C2×#13094002—21no—
33C2×#13094000C2211yescharacteristic
34C2×#13094000C2211yescharacteristic
35C2×#13094000C2211yescharacteristic
36C2×#13094000C2211yescharacteristic
37C2×C4×Dic94C2211yescharacteristic
38C2×C4×D188C2211yescharacteristic
39C2×#13093986—21no—
40C2×#13093982C2211yescharacteristic
41C2×#13093981—21no—
42C2×C4⋊C4×D47C2211yescharacteristic
43#15689491C2218yescomplemented
44#15689463C2218yescomplemented
45#15689452C2218yescomplemented
46#15689431C2218yescomplemented
47#15689378C2218yescomplemented
48#15689361C2218yescomplemented
49#15689277C2218yescomplemented
50#15689277C2218yescomplemented
51#15689228C2218yescomplemented
52#15689193C2218yes—
53C2×#13093958C2211yescharacteristic
54C2×#13093956C2211yescharacteristic
55C2×#13093955C2211yescharacteristic
56#15689130C2218yescomplemented
57C2×#13093949C2211yescharacteristic
58C2×#13093949C2211yescharacteristic
59C2×#13093948C2211yescharacteristic
60C2×#13093948C2211yescharacteristic
61C2×#13093948C2211yescharacteristic
62C2×#13093948C2211yescharacteristic
63C2×#13093948C2211yescharacteristic
64C2×#13093947C2211yescharacteristic
65#103×D47C2218yescomplemented
66C2×(C2×D47)⋊C8C2211yescharacteristic
67C2×(C2×D47)⋊C8C2211yescharacteristic
68C2×#13093935C2211yescharacteristic
69C22×Q16×C47C2211yescharacteristic
70C22×Q16×C47C2211yescharacteristic
71C2×C4⋊Q8×C47C2211yescharacteristic
72C2×C4×Q8×C47C2211yescharacteristic
73C47×#462C2218yescomplemented
74C2×C4⋊C8×C47C2211yescharacteristic
75C2×#103×C47C2211yescharacteristic
76C2×#103×C47C2211yescharacteristic
77C22×Dic94—21no—
78C22×Dic94—21no—
79C22×Dic94C2311yescharacteristic
80C2×Q8×D47—22no—
81C2×Q8×D47—22no—
82C2×Q8×D47—24no—
83C2×Q8×D47—24no—
84C2×Q8×D47—42no—
85C2×Q8×D47—42no—
86C2×Q8×D47C2314yes—
87C2×Q8×D47C2314yes—
88C22×D188D411yescharacteristic
89C22×C4×D47—21no—
90C22×C4×D47—21no—
91C22×C4×D47—21no—
92C22×C4×D47C2311yescharacteristic
93C22×C4×D47C2311yescharacteristic
94C2×#10625337—24no—
95C2×#10625337C2314yes—
96C2×#10625324—42no—
97C2×#10625324C2314yes—
98C22×C47⋊C8C2311yescharacteristic
99C22×C47⋊C8C2311yescharacteristic
100C2×C8×D47—42no—
101C2×C8×D47C2314yes—
102#13094023—28no—
103#13094018—28no—
104#13094016—22no—
105#13094016C2314yes—
106#13094014—28no—
107#13094009—28no—
108#13094002—28no—
109#13094002—28no—
110#13094000—22no—
111#13094000—22no—
112#13094000—22no—
113#13094000—22no—
114#13094000C2314yes—
115#13094000C2314yes—
116#13094000C2314yes—
117#13094000C2314yes—
118C4×Dic94—22no—
119C4×Dic94C2314yes—
120C4×D188D414yes—
121C4×D188C2314yes—
122#13093986—28no—
123#13093982—22no—
124#13093982C2314yes—
125#13093981—28no—
126C2×C4⋊Dic47D411yescharacteristic
127C2×C4⋊Dic47C2311yescharacteristic
128C2×C4⋊Dic47C2311yescharacteristic
129C2×C4⋊Dic47C2311yescharacteristic
130C2×Dic47⋊C4—21no—
131C2×Dic47⋊C4—21no—
132C2×Dic47⋊C4—21no—
133C2×Dic47⋊C4—21no—
134C2×Dic47⋊C4—21no—
135C2×Dic47⋊C4—21no—
136C2×Dic47⋊C4—21no—
137C2×Dic47⋊C4—21no—
138C4⋊C4×D47—22no—
139C4⋊C4×D47C2314yes—
140C2×(C2×D47)⋊C4—21no—
141C2×(C2×D47)⋊C4—21no—
142C2×(C2×D47)⋊C4—21no—
143C2×(C2×D47)⋊C4—21no—
144C2×(C2×D47)⋊C4—21no—
145C2×(C2×D47)⋊C4D411yescharacteristic
146C2×(C2×D47)⋊C4D411yescharacteristic
147C2×C4×Dic47—21no—
148C2×C4×Dic47—21no—
149#13093958C2314yes—
150#13093956C2314yes—
151#13093955C2314yes—
152#13093949C2314yes—
153#13093949C2314yes—
154#13093948C2314yes—
155#13093948C2314yes—
156#13093948C2314yes—
157#13093948C2314yes—
158#13093948C2314yes—
159#13093947C2314yes—
160(C2×D47)⋊C8C2314yes—
161(C2×D47)⋊C8C2314yes—
162#13093935C2314yes—
163C22×Q8×C47C2311yescharacteristic
164C22×Q8×C47C2311yescharacteristic
165C22×Q8×C47C2311yescharacteristic
166C2×Q16×C47—42no—
167C2×Q16×C47—42no—
168C2×Q16×C47C2314yes—
169C2×Q16×C47C2314yes—
170C22×C8×C47C2311yescharacteristic
171C22×C8×C47C2311yescharacteristic
172C4⋊Q8×C47—22no—
173C4⋊Q8×C47C2314yes—
174C4×Q8×C47—22no—
175C4×Q8×C47C2314yes—
176C2×C4⋊C4×C47—21no—
177C2×C4⋊C4×C47—21no—
178C2×C4⋊C4×C47—21no—
179C2×C4⋊C4×C47C2311yescharacteristic
180C2×C42×C47—21no—
181C2×C42×C47C2311yescharacteristic
182C4⋊C8×C47C2314yes—
183#103×C47C2314yes—
184#103×C47C2314yes—
185C23×D47C2×D411yescharacteristic
186C23×D47C2×D411yescharacteristic
187C2×Q8×C47—21no—
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×C47—22no—
195C2×Q8×C47—22no—
196C2×Q8×C47C2412yes—
197C2×Q8×C47C2412yes—
198C2×Q8×C47C2412yes—
199C22×C4×C47—21no—
200C22×C4×C47—21no—
201C22×C4×C47—21no—
202C22×C4×C47—21no—
203C22×C4×C47C2×D411yescharacteristic
204C22×C4×C47C2×D411yescharacteristic
205C22×C4×C47C2411yescharacteristic
206C22×Dic47—21no—
207C22×Dic47—21no—
208C22×Dic47—21no—
209C22×Dic47—21no—
210C22×Dic47C2×D411yescharacteristic
211C22×Dic47C2×D411yescharacteristic
212Q8×D47—28no—
213Q8×D47—28no—
214Q8×D47—44no—
215Q8×D47—44no—
216Q8×D47—48no—
217Q8×D47—48no—
218C2×D188—24no—
219C2×D188C2×D414yes—
220C2×C4×D47—22no—
221C2×C4×D47—22no—
222C2×C4×D47—22no—
223C2×C4×D47—22no—
224C2×C4×D47—24no—
225C2×C4×D47—24no—
226C2×C4×D47—24no—
227C2×C4×D47—44no—
228C2×C4×D47—44no—
229C2×C4×D47—44no—
230C2×C4×D47C2×D412yes—
231C2×C4×D47C2×D412yes—
232C2×C4×D47C2412yes—
233C2×C4×D47C2412yes—
234C2×Dic94—21no—
235C2×Dic94—22no—
236C2×Dic94—24no—
237C2×Dic94—24no—
238C2×Dic94—44no—
239C2×Dic94—44no—
240C2×Dic94#4114yes—
241C2×Dic94C2412yes—
242Q16×C47—44no—
243Q16×C47—44no—
244C2×C8×C47—22no—
245C2×C8×C47—22no—
246C2×C8×C47C2412yes—
247C2×C8×C47C2412yes—
248C4⋊C4×C47—24no—
249C4⋊C4×C47—24no—
250C4⋊C4×C47—24no—
251C4⋊C4×C47—21no—
252C4⋊C4×C47C2412yes—
253C42×C47—24no—
254C42×C47C2×D412yes—
255C42×C47C2412yes—
256#10625337—28no—
257(C2×D47)⋊C4—24no—
258(C2×D47)⋊C4—24no—
259(C2×D47)⋊C4—24no—
260(C2×D47)⋊C4—24no—
261(C2×D47)⋊C4—24no—
262(C2×D47)⋊C4C2×D414yes—
263(C2×D47)⋊C4C2×D414yes—
264C4⋊Dic47—21no—
265C4⋊Dic47—21no—
266C4⋊Dic47—21no—
267C4⋊Dic47C2×D414yes—
268C4⋊Dic47C2412yes—
269C4⋊Dic47C2412yes—
270C4⋊Dic47C2412yes—
271Dic47⋊C4—24no—
272Dic47⋊C4—24no—
273Dic47⋊C4—24no—
274Dic47⋊C4—24no—
275Dic47⋊C4—24no—
276Dic47⋊C4—24no—
277Dic47⋊C4—24no—
278Dic47⋊C4—24no—
279C4×Dic47—24no—
280C4×Dic47—24no—
281C2×C47⋊C8—22no—
282C2×C47⋊C8—22no—
283C2×C47⋊C8C2412yes—
284C2×C47⋊C8C2412yes—
285#10625324—44no—
286C8×D47—44no—
287C23×C47C22×D411yescharacteristic
288C22×D47—22no—
289C22×D47—22no—
290C22×D47—22no—
291C22×D47—22no—
292C22×D47—22no—
293C22×D47#13714yes—
294C22×D47C22×D412yes—
295C22×D47C22×D412yes—
296Q8×C47—22no—
297Q8×C47—22no—
298Q8×C47—22no—
299Q8×C47—22no—
300Q8×C47—22no—
301Q8×C47—22no—
302Q8×C47—42no—
303Q8×C47—42no—
304Q8×C47—42no—
305C2×C4×C47—22no—
306C2×C4×C47—22no—
307C2×C4×C47—22no—
308C2×C4×C47—22no—
309C2×C4×C47—22no—
310C2×C4×C47—22no—
311C2×C4×C47—42no—
312C2×C4×C47—42no—
313C2×C4×C47—42no—
314C2×C4×C47—42no—
315C2×C4×C47C22×D412yes—
316C2×C4×C47C22×D412yes—
317C2×C4×C47C22×D411yescharacteristic
318C2×C4×C47C2×#4112yes—
319C2×C4×C47H(5,𝔽2)12yes—
320C2×C4×C47C2511yescharacteristic
321C2×Dic47—24no—
322C2×Dic47—22no—
323C2×Dic47—22no—
324C2×Dic47—22no—
325C2×Dic47—22no—
326C2×Dic47—22no—
327C2×Dic47—22no—
328C2×Dic47—42no—
329C2×Dic47—42no—
330C2×Dic47—42no—
331C2×Dic47C22×D412yes—
332C2×Dic47C22×D412yes—
333D188—28no—
334C4×D47—24no—
335C4×D47—24no—
336C4×D47—22no—
337C4×D47—22no—
338C4×D47—22no—
339C4×D47—22no—
340C4×D47—48no—
341C4×D47—48no—
342C4×D47—48no—
343Dic94—24no—
344Dic94—22no—
345Dic94—48no—
346Dic94—48no—
347Dic94C2×#4114yes—
348C8×C47—22no—
349C8×C47—22no—
350C47⋊C8—22no—
351C47⋊C8—22no—
352C2×#3312—471nomaximal, Sylow
353C22×C47#54612yes—
354C22×C47C2×#13712yes—
355C22×C47#57812yes—
356C22×C47C23×D411yescharacteristic
357C2×D47—22no—
358C2×D47—28no—
359C2×D47—22no—
360C2×D47—22no—
361C2×D47—22no—
362C2×D47—22no—
363C2×D47—44no—
364C2×D47C2×#13714yes—
365C4×C47—22no—
366C4×C47—22no—
367C4×C47—42no—
368C4×C47—42no—
369C4×C47—42no—
370C4×C47—42no—
371C4×C47#54612yes—
372C4×C47C22×#4111yescharacteristic
373C4×C47C2×H(5,𝔽2)11yescharacteristic
374Dic47—24no—
375Dic47—22no—
376Dic47—22no—
377Dic47—42no—
378Dic47—42no—
379Dic47—42no—
380C2×#552—471no—
381C2×D4×Q8—471no—
382#3312—4716no—
383C2×#491—471no—
384C2×#485—471no—
385C2×#483—471no—
386C2×#479—471no—
387C2×#470—471no—
388C2×#467—471no—
389C2×#462D4711yescharacteristic, complemented
390C2×#451—471no—
391C2×#451—471no—
392C2×#441—471no—
393C2×#435—471no—
394C2×#419—471no—
395C22×#103—471no—
396C2×C47#331214yescomplemented
397C2×C47C2×#54611yescharacteristic
398C2×C47C22×#13711yescharacteristic
399C2×C47C2×#57811yescharacteristic
400D47—24no—
401D47—42no—
402C23×Q8—471no—
403C23×Q8—471no—
404C22×Q16—471no—
405C22×Q16C2×D4711yescharacteristic
406C22×Q16C2×D4711yescharacteristic
407C22×M16—471no—
408C23×C8—471no—
409#552—478no—
410#552—944no—
411D4×Q8—478no—
412D4×Q8—944no—
413C2×C4⋊Q8—941no—
414C2×C4⋊Q8C2×D4711yescharacteristic
415C2×#126—941no—
416C2×#125—471no—
417C2×#125—941no—
418C2×#123—941no—
419C2×C22⋊Q8—471no—
420C2×C22⋊Q8—471no—
421C2×C22⋊Q8—471no—
422C2×C22⋊Q8—471no—
423C2×C22⋊Q8—941no—
424C2×C22⋊Q8—941no—
425C2×C4×Q8—471no—
426C2×C4×Q8C2×D4711yescharacteristic
427C2×C4×D4—471no—
428C2×C4×D4—941no—
429C2×#117—471no—
430C2×#117—941no—
431C22×C4⋊C4—471no—
432#491—478no—
433#485—478no—
434#483—478no—
435#479—478no—
436#470—478no—
437#467—478no—
438#462C2×D4718yescomplemented
439#451—478no—
440#451—478no—
441#441—478no—
442#435—478no—
443C2×#107—471no—
444C2×#106—471no—
445C2×#106—471no—
446C2×C4⋊C8C2×D4711yescharacteristic
447#419—478no—
448C2×#103—471no—
449C2×#103—471no—
450C2×#103—471no—
451C2×#103—471no—
452C2×#103—471no—
453C2×#103—471no—
454C2×#103—471no—
455C2×#103—471no—
456C2×#103—478no—
457C2×#103C2×D4711yescharacteristic
458C2×#103C2×D4711yescharacteristic
459C2×C22⋊C8—471no—
460C2×C22⋊C8—471no—
461C2×#97—471no—
462C47C2×#331211yescharacteristic, complemented, Sylow
463C22×Q8—474no—
464C22×Q8—474no—
465C22×Q8—471no—
466C22×Q8—941no—
467C22×Q8—941no—
468C22×Q8—942no—
469C22×Q8—942no—
470C22×Q8—944no—
471C22×Q8—944no—
472C22×Q8—1882no—
473C22×Q8—1882no—
474C22×Q8C22×D4711yescharacteristic
475C22×Q8C22×D4711yescharacteristic
476C22×Q8C22×D4711yescharacteristic
477C22×D4—471no—
478C23×C4—471no—
479C23×C4—471no—
480C23×C4—941no—
481C23×C4—941no—
482C23×C4—941no—
483C2×Q16—42no—
484C2×Q16—42no—
485C2×Q16—474no—
486C2×Q16—944no—
487C2×Q16C22×D4714yes—
488C2×Q16C22×D4714yes—
489C2×M16—474no—
490C2×M16—1882no—
491C22×C8—471no—
492C22×C8—471no—
493C22×C8—474no—
494C22×C8—1882no—
495C22×C8C22×D4711yescharacteristic
496C22×C8C22×D4711yescharacteristic
497C4⋊Q8—22no—
498C4⋊Q8—948no—
499C4⋊Q8C22×D4714yes—
500#126—948no—
501#125—474no—
502#125—948no—
503#125—942no—
504#123—948no—
505C22⋊Q8—474no—
506C22⋊Q8—474no—
507C22⋊Q8—474no—
508C22⋊Q8—474no—
509C22⋊Q8—948no—
510C22⋊Q8—948no—
511C22⋊Q8—942no—
512C22⋊Q8—942no—
513C22⋊Q8—942no—
514C22⋊Q8—942no—
515C4×Q8—22no—
516C4×Q8—474no—
517C4×Q8—942no—
518C4×Q8C22×D4714yes—
519C4×D4—474no—
520C4×D4—474no—
521C4×D4—948no—
522#117—474no—
523#117—948no—
524#117—942no—
525C2×C4⋊C4—21no—
526C2×C4⋊C4—21no—
527C2×C4⋊C4—21no—
528C2×C4⋊C4—471no—
529C2×C4⋊C4—471no—
530C2×C4⋊C4—471no—
531C2×C4⋊C4—471no—
532C2×C4⋊C4—474no—
533C2×C4⋊C4—942no—
534C2×C4⋊C4—941no—
535C2×C4⋊C4—941no—
536C2×C4⋊C4—941no—
537C2×C4⋊C4—941no—
538C2×C4⋊C4—941no—
539C2×C4⋊C4—941no—
540C2×C4⋊C4—941no—
541C2×C4⋊C4—941no—
542C2×C4⋊C4C22×D4711yescharacteristic
543C2×C22⋊C4—471no—
544C2×C22⋊C4—471no—
545C2×C22⋊C4—941no—
546C2×C22⋊C4—941no—
547C2×C22⋊C4—941no—
548C2×C22⋊C4—941no—
549C2×C22⋊C4—941no—
550C2×C42—21no—
551C2×C42—941no—
552C2×C42—941no—
553C2×C42C22×D4711yescharacteristic
554#107—474no—
555#106—474no—
556#106—474no—
557C4⋊C8C22×D4714yes—
558#103—474no—
559#103—474no—
560#103—474no—
561#103—474no—
562#103—474no—
563#103—474no—
564#103—474no—
565#103—474no—
566#103C22×D4714yes—
567#103C22×D4714yes—
568C22⋊C8—474no—
569C22⋊C8—474no—
570#97—474no—
571C24—471no—
572C24—471no—
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—22no—
577C2×Q8—22no—
578C2×Q8—22no—
579C2×Q8—22no—
580C2×Q8—22no—
581C2×Q8—22no—
582C2×Q8—474no—
583C2×Q8—472no—
584C2×Q8—944no—
585C2×Q8—944no—
586C2×Q8—941no—
587C2×Q8—942no—
588C2×Q8—948no—
589C2×Q8—948no—
590C2×Q8—1884no—
591C2×Q8—1884no—
592C2×Q8—1884no—
593C2×Q8—1884no—
594C2×Q8—1888no—
595C2×Q8—1888no—
596C2×Q8C23×D4712yes—
597C2×Q8C23×D4712yes—
598C2×Q8C23×D4712yes—
599C2×D4—474no—
600C2×D4—944no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—471no—
606C22×C4—471no—
607C22×C4—472no—
608C22×C4—472no—
609C22×C4—472no—
610C22×C4—472no—
611C22×C4—944no—
612C22×C4—944no—
613C22×C4—944no—
614C22×C4—941no—
615C22×C4—942no—
616C22×C4—942no—
617C22×C4—942no—
618C22×C4—942no—
619C22×C4—941no—
620C22×C4—941no—
621C22×C4—941no—
622C22×C4—1884no—
623C22×C4—1884no—
624C22×C4—1884no—
625C22×C4D4×D4711yescharacteristic
626C22×C4D4×D4711yescharacteristic
627C22×C4C23×D4711yescharacteristic
628Q16—44no—
629Q16—44no—
630Q16—948no—
631M16—1884no—
632C2×C8—22no—
633C2×C8—22no—
634C2×C8—472no—
635C2×C8—472no—
636C2×C8—942no—
637C2×C8—942no—
638C2×C8—1884no—
639C2×C8C23×D4712yes—
640C2×C8C23×D4712yes—
641C4⋊C4—24no—
642C4⋊C4—24no—
643C4⋊C4—24no—
644C4⋊C4—21no—
645C4⋊C4—474no—
646C4⋊C4—472no—
647C4⋊C4—472no—
648C4⋊C4—472no—
649C4⋊C4—944no—
650C4⋊C4—944no—
651C4⋊C4—944no—
652C4⋊C4—944no—
653C4⋊C4—944no—
654C4⋊C4—944no—
655C4⋊C4—944no—
656C4⋊C4—944no—
657C4⋊C4—941no—
658C4⋊C4—941no—
659C4⋊C4—941no—
660C4⋊C4C23×D4712yes—
661C22⋊C4—474no—
662C22⋊C4—474no—
663C22⋊C4—944no—
664C22⋊C4—944no—
665C22⋊C4—944no—
666C22⋊C4—944no—
667C22⋊C4—944no—
668C42—24no—
669C42—944no—
670C42—944no—
671C42D4×D4712yes—
672C42C23×D4712yes—
673C23—474no—
674C23—472no—
675C23—472no—
676C23—942no—
677C23—942no—
678C23—942no—
679C23—942no—
680C23—942no—
681C23C2×D4×D4711yescharacteristic
682Q8—22no—
683Q8—22no—
684Q8—22no—
685Q8—22no—
686Q8—22no—
687Q8—22no—
688Q8—42no—
689Q8—42no—
690Q8—42no—
691Q8—474no—
692Q8—944no—
693Q8—942no—
694Q8—1888no—
695Q8—1888no—
696D4—948no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—472no—
708C2×C4—472no—
709C2×C4—942no—
710C2×C4—942no—
711C2×C4—944no—
712C2×C4—942no—
713C2×C4—944no—
714C2×C4—944no—
715C2×C4—942no—
716C2×C4—942no—
717C2×C4—942no—
718C2×C4—942no—
719C2×C4—942no—
720C2×C4—942no—
721C2×C4—942no—
722C2×C4—1888no—
723C2×C4—1888no—
724C2×C4—1888no—
725C2×C4—1882no—
726C2×C4—1882no—
727C2×C4—1882no—
728C2×C4C2×D4×D4712yes—
729C2×C4C2×D4×D4712yes—
730C2×C4C2×D4×D4711yescharacteristic
731C2×C4#41×D4712yes—
732C2×C4#1309406912yes—
733C2×C4C24×D4711yescharacteristic
734C8—22no—
735C8—22no—
736C8—942no—
737C8—942no—
738C22—474no—
739C22—942no—
740C22—942no—
741C22—948no—
742C22—942no—
743C22—942no—
744C22—942no—
745C22—1884no—
746C22#1568977012yes—
747C22#137×D4712yes—
748C22#1568993612yes—
749C22C22×D4×D4711yescharacteristic
750C4—22no—
751C4—22no—
752C4—42no—
753C4—42no—
754C4—42no—
755C4—42no—
756C4—942no—
757C4—942no—
758C4—944no—
759C4—1882no—
760C4—1882no—
761C4—1882no—
762C4#1568977012yes—
763C4C2×#41×D4711yescharacteristic
764C4C2×#1309406911yescharacteristic
765C2—944no—
766C2—1882no—
767C2#2025544614yesdirect product factor
768C2C2×#1568977011yescharacteristic
769C2C2×#137×D4711yescharacteristic
770C2C2×#1568993611yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#462C2
socleC23×C47C22×D4
prime radicalC22×D188D4
hypercenterC2×#462D47
hypocenterC47C2×#3312
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#462

Complements

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

NH ≅ G/Ntype
3. #20255446C2direct (N × H)
4. C2×#15689491C2semidirect
5. C2×#15689463C2semidirect
6. C2×#15689452C2semidirect
7. C2×#15689431C2semidirect
8. C2×#15689378C2semidirect
9. C2×#15689361C2semidirect
10. C2×#15689277C2semidirect
11. C2×#15689277C2semidirect
12. C2×#15689228C2semidirect
14. C2×#15689130C2semidirect
15. C2×#103×D47C2semidirect
16. C2×C47×#462C2semidirect
43. #15689491C22semidirect
44. #15689463C22semidirect
45. #15689452C22semidirect
46. #15689431C22semidirect
47. #15689378C22semidirect
48. #15689361C22semidirect
49. #15689277C22semidirect
50. #15689277C22semidirect
51. #15689228C22semidirect
56. #15689130C22semidirect
65. #103×D47C22semidirect
73. C47×#462C22semidirect
389. C2×#462D47semidirect
396. C2×C47#3312semidirect
438. #462C2×D47semidirect
462. C47C2×#3312semidirect
767. C2#20255446direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156898142
C2×#156897882
#202554462
C2×#156894912
C2×#156894632
C2×#156894522
C2×#156894312
C2×#156893782
C2×#156893612
C2×#156892772
C2×#156892282
C2×#156891932
C2×#156891302
C2×#103×D472
C2×C47×#4622
C2×#331247