Finite Group Databasebeta

← C2×#20255441 #27092886

Subgroups — C2×#20255441 #27092886

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×#15689813C211yesmaximal, characteristic
2C2×D4×Dic94C211yesmaximal, characteristic
3#20255441C2116yesmaximal, direct product factor
4C2×#15689492C211yesmaximal, characteristic, complemented
5C2×#15689465C211yesmaximal, characteristic, complemented
6C2×#15689454C211yesmaximal, characteristic, complemented
7C2×#15689431C211yesmaximal, characteristic, complemented
8C2×#15689381C211yesmaximal, characteristic, complemented
9C2×#15689364C211yesmaximal, characteristic, complemented
10C2×#15689334C211yesmaximal, characteristic, complemented
11C2×#15689281C211yesmaximal, characteristic, complemented
12C2×#15689281C211yesmaximal, characteristic, complemented
13C2×#15689231C211yesmaximal, characteristic, complemented
14C2×#15689133C211yesmaximal, characteristic, complemented
15C22×#13093949C211yesmaximal, characteristic, complemented
16C2×C47×#435C211yesmaximal, characteristic
17C23×Dic94C2211yescharacteristic
18C23×Dic94C2211yescharacteristic
19C22×Dic188C2211yescharacteristic
20C22×Dic188C2211yescharacteristic
21C22×Dic188C2211yescharacteristic
22#15689813—24no—
23#15689813C2218yes—
24D4×Dic94—24no—
25D4×Dic94C2218yes—
26C2×#13094024C2211yescharacteristic
27C2×#13094023—21no—
28C2×#13094017—21no—
29C2×#13094016C2211yescharacteristic
30C2×#13094014—21no—
31C2×#13094005—21no—
32C2×#13094003C2211yescharacteristic
33C2×#13094003C2211yescharacteristic
34C2×#13094003C2211yescharacteristic
35C2×#13094003C2211yescharacteristic
36C2×#13094001—21no—
37C2×#13094001—21no—
38C2×C4×Dic94C2211yescharacteristic
39C2×C4×Dic94C2211yescharacteristic
40C2×D4×Dic47—21no—
41C2×#13093983C2211yescharacteristic
42C2×#13093980—21no—
43C22×C4⋊Dic47C2211yescharacteristic
44#15689492C2218yescomplemented
45#15689465C2218yescomplemented
46#15689454C2218yescomplemented
47#15689431C2218yescomplemented
48#15689381C2218yescomplemented
49#15689364C2218yescomplemented
50#15689334C2218yescomplemented
51#15689281C2218yescomplemented
52#15689281C2218yescomplemented
53#15689231C2218yescomplemented
54C2×#13093958C2211yescharacteristic
55C2×#13093956C2211yescharacteristic
56C2×#13093956C2211yescharacteristic
57#15689133C2218yescomplemented
58C2×#13093949C2211yescharacteristic
59C2×#13093949C2211yescharacteristic
60C2×#13093949C2211yescharacteristic
61C2×#13093949C2211yescharacteristic
62C2×#13093949C2211yescharacteristic
63C2×#13093949C2211yescharacteristic
64C2×#13093949C2211yescharacteristic
65C2×#13093949C2211yescharacteristic
66C2×#13093949C2211yescharacteristic
67C2×#13093949C2211yescharacteristic
68C2×#13093949C2218yescomplemented
69C22×M16×C47C2211yescharacteristic
70C23×C8×C47C2211yescharacteristic
71C2×C4×D4×C47C2211yescharacteristic
72C47×#435C2218yes—
73C2×C4⋊C8×C47C2211yescharacteristic
74C2×C22⋊C8×C47C2211yescharacteristic
75C2×C22⋊C8×C47C2211yescharacteristic
76C2×#97×C47C2211yescharacteristic
77C22×Dic94—24no—
78C22×Dic94—24no—
79C22×Dic94—22no—
80C22×Dic94—22no—
81C22×Dic94—21no—
82C22×Dic94—21no—
83C22×Dic94—42no—
84C22×Dic94—42no—
85C22×Dic94C2311yescharacteristic
86C22×Dic94C2311yescharacteristic
87C22×Dic94C2311yescharacteristic
88C22×Dic94C2314yes—
89C22×Dic94C2314yes—
90C22×Dic94C2311yescharacteristic
91C23×Dic47—21no—
92C23×Dic47—21no—
93C23×Dic47—21no—
94C2×Dic188—24no—
95C2×Dic188—42no—
96C2×Dic188—42no—
97C2×Dic188C2314yes—
98C2×Dic188C2314yes—
99C2×Dic188C2314yes—
100#13094024—22no—
101#13094024C2314yes—
102#13094023—28no—
103#13094017—28no—
104#13094016—22no—
105#13094016C2314yes—
106#13094014—28no—
107#13094005—28no—
108#13094003—22no—
109#13094003—22no—
110#13094003—22no—
111#13094003—22no—
112#13094003C2314yes—
113#13094003C2314yes—
114#13094003C2314yes—
115#13094003C2314yes—
116#13094001—28no—
117#13094001—28no—
118C4×Dic94—22no—
119C4×Dic94—22no—
120C4×Dic94C2314yes—
121C4×Dic94C2314yes—
122D4×Dic47—28no—
123#13093983—22no—
124#13093983C2314yes—
125#13093980—28no—
126C2×C4⋊Dic47—22no—
127C2×C4⋊Dic47—21no—
128C2×C4⋊Dic47—21no—
129C2×C4⋊Dic47—21no—
130C2×C4⋊Dic47C2314yes—
131C2×C4⋊Dic47C2311yescharacteristic
132C2×C4⋊Dic47C2311yescharacteristic
133C2×C4⋊Dic47C2311yescharacteristic
134C2×C4⋊Dic47C2311yescharacteristic
135C2×Dic47⋊C4—21no—
136C2×Dic47⋊C4—21no—
137C2×Dic47⋊C4—21no—
138C2×Dic47⋊C4—21no—
139C2×Dic47⋊C4—21no—
140C2×Dic47⋊C4—21no—
141C2×Dic47⋊C4—21no—
142C2×Dic47⋊C4—21no—
143C2×C22⋊Dic47—21no—
144C2×C22⋊Dic47—21no—
145C2×C22⋊Dic47—21no—
146C2×C22⋊Dic47—21no—
147C2×C22⋊Dic47—21no—
148C2×C4×Dic47—21no—
149C2×C4×Dic47—21no—
150C2×C4×Dic47—21no—
151#13093958C2314yes—
152#13093956C2314yes—
153#13093956C2314yes—
154#13093949C2314yes—
155#13093949C2314yes—
156#13093949C2314yes—
157#13093949C2314yes—
158#13093949C2314yes—
159#13093949C2314yes—
160#13093949C2314yes—
161#13093949C2314yes—
162#13093949C2314yes—
163#13093949C2314yes—
164C22×D4×C47D411yescharacteristic
165C23×C4×C47C2311yescharacteristic
166C23×C4×C47C2311yescharacteristic
167C2×M16×C47—42no—
168C2×M16×C47C2314yes—
169C22×C8×C47—42no—
170C22×C8×C47C2311yescharacteristic
171C22×C8×C47C2311yescharacteristic
172C22×C8×C47C2311yescharacteristic
173C22×C8×C47C2311yescharacteristic
174C22×C8×C47C2314yes—
175C4×D4×C47D414yes—
176C4×D4×C47C2314yes—
177C2×C4⋊C4×C47D411yescharacteristic
178C2×C22⋊C4×C47D411yescharacteristic
179C2×C22⋊C4×C47D411yescharacteristic
180C2×C42×C47C2311yescharacteristic
181C4⋊C8×C47C2314yes—
182C22⋊C8×C47C2314yes—
183C22⋊C8×C47C2314yes—
184#97×C47C2314yes—
185C24×C47C2×D411yescharacteristic
186C24×C47C2×D411yescharacteristic
187C2×D4×C47—24no—
188C2×D4×C47C2×D414yes—
189C22×C4×C47—22no—
190C22×C4×C47—22no—
191C22×C4×C47—22no—
192C22×C4×C47—22no—
193C22×C4×C47C2×D411yescharacteristic
194C22×C4×C47C2×D411yescharacteristic
195C22×C4×C47C2×D411yescharacteristic
196C22×C4×C47C2×D411yescharacteristic
197C22×C4×C47C2×D412yes—
198C22×C4×C47C2×D412yes—
199C22×C4×C47C2412yes—
200C22×C4×C47C2412yes—
201C22×C4×C47C2411yescharacteristic
202C22×Dic47—21no—
203C22×Dic47—21no—
204C22×Dic47—21no—
205C22×Dic47—21no—
206C22×Dic47—21no—
207C22×Dic47—21no—
208C22×Dic47—21no—
209C22×Dic47—21no—
210C22×Dic47—24no—
211C22×Dic47—24no—
212C22×Dic47—24no—
213C22×Dic47—44no—
214C22×Dic47—44no—
215C22×Dic47—44no—
216C2×Dic94—21no—
217C2×Dic94—22no—
218C2×Dic94—22no—
219C2×Dic94—22no—
220C2×Dic94—22no—
221C2×Dic94—22no—
222C2×Dic94—22no—
223C2×Dic94—22no—
224C2×Dic94—28no—
225C2×Dic94—28no—
226C2×Dic94—21no—
227C2×Dic94—24no—
228C2×Dic94—24no—
229C2×Dic94—21no—
230C2×Dic94—21no—
231C2×Dic94—44no—
232C2×Dic94—44no—
233C2×Dic94—48no—
234C2×Dic94—48no—
235C2×Dic94—44no—
236C2×Dic94—44no—
237C2×Dic94#4114yes—
238C2×Dic94C2412yes—
239C2×Dic94C2412yes—
240C2×Dic94C2412yes—
241C2×Dic94C2412yes—
242M16×C47—44no—
243C2×C8×C47—22no—
244C2×C8×C47—22no—
245C2×C8×C47—22no—
246C2×C8×C47—22no—
247C2×C8×C47—44no—
248C2×C8×C47C2412yes—
249C2×C8×C47C2412yes—
250C2×C8×C47C2412yes—
251C2×C8×C47C2412yes—
252C4⋊C4×C47C2×D414yes—
253C22⋊C4×C47C2×D414yes—
254C22⋊C4×C47C2×D414yes—
255C42×C47C2×D412yes—
256C42×C47C2412yes—
257C22⋊Dic47—24no—
258C22⋊Dic47—24no—
259C22⋊Dic47—24no—
260C22⋊Dic47—24no—
261C22⋊Dic47—24no—
262C4⋊Dic47—21no—
263C4⋊Dic47—21no—
264C4⋊Dic47—24no—
265C4⋊Dic47—24no—
266C4⋊Dic47—24no—
267C4⋊Dic47—21no—
268C4⋊Dic47—21no—
269C4⋊Dic47C2412yes—
270C4⋊Dic47C2412yes—
271C4⋊Dic47C2412yes—
272C4⋊Dic47C2412yes—
273Dic47⋊C4—24no—
274Dic47⋊C4—24no—
275Dic47⋊C4—24no—
276Dic47⋊C4—24no—
277Dic47⋊C4—24no—
278Dic47⋊C4—24no—
279Dic47⋊C4—24no—
280Dic47⋊C4—24no—
281C4×Dic47—24no—
282C4×Dic47—24no—
283C4×Dic47—24no—
284Dic188—28no—
285Dic188—44no—
286Dic188—44no—
287C23×C47—22no—
288C23×C47—22no—
289C23×C47—22no—
290C23×C47—22no—
291C23×C47—22no—
292C23×C47#13714yes—
293C23×C47C22×D412yes—
294C23×C47C22×D412yes—
295C23×C47C22×D411yescharacteristic
296D4×C47—28no—
297C2×C4×C47—22no—
298C2×C4×C47—22no—
299C2×C4×C47—22no—
300C2×C4×C47—22no—
301C2×C4×C47—24no—
302C2×C4×C47—24no—
303C2×C4×C47—22no—
304C2×C4×C47—22no—
305C2×C4×C47—22no—
306C2×C4×C47—22no—
307C2×C4×C47C22×D412yes—
308C2×C4×C47C22×D412yes—
309C2×C4×C47C22×D412yes—
310C2×C4×C47C22×D412yes—
311C2×C4×C47C22×D411yescharacteristic
312C2×C4×C47C2×#4112yes—
313C2×C4×C47H(5,𝔽2)12yes—
314C2×C4×C47C2511yescharacteristic
315C2×Dic47—24no—
316C2×Dic47—22no—
317C2×Dic47—22no—
318C2×Dic47—22no—
319C2×Dic47—22no—
320C2×Dic47—22no—
321C2×Dic47—22no—
322C2×Dic47—22no—
323C2×Dic47—22no—
324C2×Dic47—48no—
325C2×Dic47—48no—
326C2×Dic47—42no—
327C2×Dic47—42no—
328C2×Dic47—42no—
329C2×Dic47—48no—
330C2×Dic47—42no—
331C2×Dic47—42no—
332C2×Dic47—42no—
333C2×Dic47—42no—
334Dic94—24no—
335Dic94—22no—
336Dic94—22no—
337Dic94—22no—
338Dic94—22no—
339Dic94—22no—
340Dic94—22no—
341Dic94—22no—
342Dic94—48no—
343Dic94—48no—
344Dic94—42no—
345Dic94—42no—
346Dic94—42no—
347Dic94C2×#4114yes—
348C8×C47—22no—
349C8×C47—22no—
350C8×C47—22no—
351C8×C47—22no—
352C2×#3312—471nomaximal, Sylow
353C22×C47—22no—
354C22×C47—28no—
355C22×C47—22no—
356C22×C47—22no—
357C22×C47—22no—
358C22×C47—22no—
359C22×C47—44no—
360C22×C47#54612yes—
361C22×C47C2×#13714yes—
362C22×C47C2×#13712yes—
363C22×C47#57812yes—
364C22×C47C23×D411yescharacteristic
365C4×C47—22no—
366C4×C47—22no—
367C4×C47—22no—
368C4×C47—22no—
369C4×C47#54612yes—
370C4×C47C22×#4111yescharacteristic
371C4×C47C2×H(5,𝔽2)11yescharacteristic
372Dic47—24no—
373Dic47—42no—
374Dic47—42no—
375Dic47—42no—
376Dic47—42no—
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×#462—471no—
390C2×#451—471no—
391C2×#451—471no—
392C2×#441—471no—
393C2×#435D4711yescharacteristic
394C2×#419—471no—
395C22×#103—471no—
396C2×C47—24no—
397C2×C47—42no—
398C2×C47#331214yescomplemented
399C2×C47C2×#54611yescharacteristic
400C2×C47C22×#13711yescharacteristic
401C2×C47C2×#57811yescharacteristic
402C23×Q8—471no—
403C23×Q8—471no—
404C22×Q16—471no—
405C22×Q16—471no—
406C22×Q16—471no—
407C22×M16C2×D4711yescharacteristic
408C23×C8C2×D4711yescharacteristic
409#552—478no—
410#552—944no—
411D4×Q8—478no—
412D4×Q8—944no—
413C2×C4⋊Q8—471no—
414C2×C4⋊Q8—941no—
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×Q8—471no—
427C2×C4×D4—941no—
428C2×C4×D4C2×D4711yescharacteristic
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#462—478no—
439#451—478no—
440#451—478no—
441#441—478no—
442#435C2×D4718yes—
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—471no—
457C2×#103—478no—
458C2×#103—471no—
459C2×C22⋊C8C2×D4711yescharacteristic
460C2×C22⋊C8C2×D4711yescharacteristic
461C2×#97C2×D4711yescharacteristic
462C47C2×#331211yescharacteristic, complemented, Sylow
463C22×Q8—471no—
464C22×Q8—471no—
465C22×Q8—471no—
466C22×Q8—471no—
467C22×Q8—474no—
468C22×Q8—474no—
469C22×Q8—944no—
470C22×Q8—944no—
471C22×Q8—941no—
472C22×Q8—941no—
473C22×Q8—942no—
474C22×Q8—942no—
475C22×Q8—1882no—
476C22×Q8—1882no—
477C22×D4D18811yescharacteristic
478C23×C4—941no—
479C23×C4—941no—
480C23×C4—941no—
481C23×C4C22×D4711yescharacteristic
482C23×C4C22×D4711yescharacteristic
483C2×Q16—474no—
484C2×Q16—474no—
485C2×Q16—474no—
486C2×Q16—944no—
487C2×Q16—1882no—
488C2×Q16—1882no—
489C2×M16—42no—
490C2×M16C22×D4714yes—
491C22×C8—42no—
492C22×C8C22×D4711yescharacteristic
493C22×C8C22×D4711yescharacteristic
494C22×C8C22×D4711yescharacteristic
495C22×C8C22×D4711yescharacteristic
496C22×C8C22×D4714yes—
497C4⋊Q8—474no—
498C4⋊Q8—948no—
499C4⋊Q8—942no—
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—942no—
510C22⋊Q8—942no—
511C22⋊Q8—942no—
512C22⋊Q8—942no—
513C22⋊Q8—948no—
514C22⋊Q8—948no—
515C4×Q8—474no—
516C4×Q8—474no—
517C4×Q8—942no—
518C4×Q8—942no—
519C4×D4—948no—
520C4×D4D18814yes—
521C4×D4C22×D4714yes—
522#117—474no—
523#117—942no—
524#117—948no—
525C2×C4⋊C4—471no—
526C2×C4⋊C4—471no—
527C2×C4⋊C4—474no—
528C2×C4⋊C4—471no—
529C2×C4⋊C4—471no—
530C2×C4⋊C4—941no—
531C2×C4⋊C4—942no—
532C2×C4⋊C4—941no—
533C2×C4⋊C4—941no—
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⋊C4D18811yescharacteristic
543C2×C22⋊C4—941no—
544C2×C22⋊C4—941no—
545C2×C22⋊C4—941no—
546C2×C22⋊C4—941no—
547C2×C22⋊C4—941no—
548C2×C22⋊C4D18811yescharacteristic
549C2×C22⋊C4D18811yescharacteristic
550C2×C42—941no—
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#103—474no—
567#103—474no—
568C22⋊C8C22×D4714yes—
569C22⋊C8C22×D4714yes—
570#97C22×D4714yes—
571C24C2×D18811yescharacteristic
572C24C2×D18811yescharacteristic
573C2×Q8—474no—
574C2×Q8—472no—
575C2×Q8—472no—
576C2×Q8—472no—
577C2×Q8—472no—
578C2×Q8—948no—
579C2×Q8—948no—
580C2×Q8—941no—
581C2×Q8—941no—
582C2×Q8—944no—
583C2×Q8—944no—
584C2×Q8—941no—
585C2×Q8—941no—
586C2×Q8—942no—
587C2×Q8—942no—
588C2×Q8—942no—
589C2×Q8—942no—
590C2×Q8—942no—
591C2×Q8—942no—
592C2×Q8—942no—
593C2×Q8—1884no—
594C2×Q8—1884no—
595C2×Q8—1884no—
596C2×Q8—1884no—
597C2×Q8—1888no—
598C2×Q8—1888no—
599C2×D4—24no—
600C2×D4C2×D18814yes—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—941no—
606C22×C4—944no—
607C22×C4—944no—
608C22×C4—944no—
609C22×C4—941no—
610C22×C4—941no—
611C22×C4—941no—
612C22×C4—941no—
613C22×C4—941no—
614C22×C4—941no—
615C22×C4—941no—
616C22×C4—1884no—
617C22×C4—1884no—
618C22×C4—1884no—
619C22×C4C2×D18812yes—
620C22×C4C2×D18812yes—
621C22×C4C2×D18811yescharacteristic
622C22×C4C2×D18811yescharacteristic
623C22×C4C2×D18811yescharacteristic
624C22×C4C2×D18811yescharacteristic
625C22×C4C23×D4712yes—
626C22×C4C23×D4712yes—
627C22×C4C23×D4711yescharacteristic
628Q16—948no—
629Q16—1884no—
630Q16—1884no—
631M16—44no—
632C2×C8—22no—
633C2×C8—22no—
634C2×C8—22no—
635C2×C8—22no—
636C2×C8—44no—
637C2×C8C23×D4712yes—
638C2×C8C23×D4712yes—
639C2×C8C23×D4712yes—
640C2×C8C23×D4712yes—
641C4⋊C4—472no—
642C4⋊C4—472no—
643C4⋊C4—472no—
644C4⋊C4—472no—
645C4⋊C4—944no—
646C4⋊C4—944no—
647C4⋊C4—944no—
648C4⋊C4—944no—
649C4⋊C4—944no—
650C4⋊C4—944no—
651C4⋊C4—944no—
652C4⋊C4—944no—
653C4⋊C4—941no—
654C4⋊C4—941no—
655C4⋊C4—944no—
656C4⋊C4—941no—
657C4⋊C4—941no—
658C4⋊C4—944no—
659C4⋊C4—944no—
660C4⋊C4C2×D18814yes—
661C22⋊C4—944no—
662C22⋊C4—944no—
663C22⋊C4—944no—
664C22⋊C4—944no—
665C22⋊C4—944no—
666C22⋊C4C2×D18814yes—
667C22⋊C4C2×D18814yes—
668C42—944no—
669C42—944no—
670C42—944no—
671C42C2×D18812yes—
672C42C23×D4712yes—
673C23—22no—
674C23—22no—
675C23—22no—
676C23—22no—
677C23—22no—
678C23#1309405714yes—
679C23C22×D18812yes—
680C23C22×D18812yes—
681C23C22×D18811yescharacteristic
682Q8—474no—
683Q8—944no—
684Q8—942no—
685Q8—942no—
686Q8—942no—
687Q8—942no—
688Q8—942no—
689Q8—942no—
690Q8—942no—
691Q8—1888no—
692Q8—1888no—
693Q8—1882no—
694Q8—1882no—
695Q8—1882no—
696D4—28no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—944no—
708C2×C4—942no—
709C2×C4—942no—
710C2×C4—942no—
711C2×C4—942no—
712C2×C4—942no—
713C2×C4—942no—
714C2×C4—942no—
715C2×C4—942no—
716C2×C4—1888no—
717C2×C4—1888no—
718C2×C4—1882no—
719C2×C4—1882no—
720C2×C4—1882no—
721C2×C4—1888no—
722C2×C4—1882no—
723C2×C4—1882no—
724C2×C4—1882no—
725C2×C4—1882no—
726C2×C4C22×D18812yes—
727C2×C4C22×D18812yes—
728C2×C4C22×D18812yes—
729C2×C4C22×D18812yes—
730C2×C4C22×D18811yescharacteristic
731C2×C4#41×D4712yes—
732C2×C4#1309406912yes—
733C2×C4C24×D4711yescharacteristic
734C8—22no—
735C8—22no—
736C8—22no—
737C8—22no—
738C22—22no—
739C22—22no—
740C22—28no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—44no—
745C22#1568976812yes—
746C22C2×#1309405714yes—
747C22C2×#1309405712yes—
748C22#1568994012yes—
749C22C23×D18811yescharacteristic
750C4—22no—
751C4—22no—
752C4—22no—
753C4—22no—
754C4—944no—
755C4—1882no—
756C4—1882no—
757C4—1882no—
758C4—1882no—
759C4—1882no—
760C4—1882no—
761C4—1882no—
762C4#1568976812yes—
763C4C2×#41×D4711yescharacteristic
764C4C2×#1309406911yescharacteristic
765C2—24no—
766C2—42no—
767C2#2025544114yesdirect product factor
768C2C2×#1568976811yescharacteristic
769C2C22×#1309405711yescharacteristic
770C2C2×#1568994011yescharacteristic
subgroupG/H
centerC23C22×D188
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#435C2
socleC23×C47C22×D4
prime radicalC22×D4×C47D4
hypercenterC2×#435D47
hypocenterC47C2×#3312
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
3. #20255441C2direct (N × H)
4. C2×#15689492C2semidirect
5. C2×#15689465C2semidirect
6. C2×#15689454C2semidirect
7. C2×#15689431C2semidirect
8. C2×#15689381C2semidirect
9. C2×#15689364C2semidirect
10. C2×#15689334C2semidirect
11. C2×#15689281C2semidirect
12. C2×#15689281C2semidirect
13. C2×#15689231C2semidirect
14. C2×#15689133C2semidirect
15. C22×#13093949C2semidirect
44. #15689492C22semidirect
45. #15689465C22semidirect
46. #15689454C22semidirect
47. #15689431C22semidirect
48. #15689381C22semidirect
49. #15689364C22semidirect
50. #15689334C22semidirect
51. #15689281C22semidirect
52. #15689281C22semidirect
53. #15689231C22semidirect
57. #15689133C22semidirect
68. C2×#13093949C22semidirect
398. C2×C47#3312semidirect
462. C47C2×#3312semidirect
767. C2#20255441direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156898132
C2×D4×Dic942
#202554412
C2×#156894922
C2×#156894652
C2×#156894542
C2×#156894312
C2×#156893812
C2×#156893642
C2×#156893342
C2×#156892812
C2×#156892312
C2×#156891332
C22×#130939492
C2×C47×#4352
C2×#331247