Finite Group Databasebeta

← C2×#20257384 #27124478

Subgroups — C2×#20257384 #27124478

Order 12032.

7130 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20257384C2132yesmaximal, direct product factor
2C2×#15689846C213yesmaximal, complemented
3C2×#15689834C213yesmaximal, complemented
4C2×#15689826C213yesmaximal, complemented
5C2×#15689811C213yesmaximal, complemented
6C2×Q8×D188C211yesmaximal, characteristic, complemented
7C2×#15689785C211yesmaximal, characteristic, complemented
8C2×#15689785C211yesmaximal, characteristic, complemented
9C2×#15689747C213yesmaximal, complemented
10C2×#15689736C213yesmaximal, complemented
11C2×#15689660C213yesmaximal, complemented
12C2×#15689658C213yesmaximal, complemented
13C2×#15689605C211yesmaximal, characteristic, complemented
14C2×#15689599C211yesmaximal, characteristic, complemented
15C2×C4×Q8×D47C211yesmaximal, characteristic, complemented
16C2×C47×#557C211yesmaximal, characteristic, complemented
17C22×#10625354C2211yescharacteristic
18C22×Q8×D47C2211yescharacteristic
19C22×Q8×D47C2211yescharacteristic
20#15689846C22148yescomplemented
21#15689834C22148yescomplemented
22#15689826C22148yescomplemented
23#15689811C22148yescomplemented
24Q8×D188C22116yescomplemented
25#15689785C22116yescomplemented
26#15689785C22116yescomplemented
27#15689747C22148yescomplemented
28#15689736C22148yescomplemented
29C2×#13094024C2213yes—
30#15689660C22148yescomplemented
31#15689658C22148yescomplemented
32C2×#13094019C2216yes—
33C2×#13094019C2213yes—
34C2×#13094019C2213yes—
35C2×#13094019C2216yes—
36C2×#13094015C2216yes—
37C2×#13094015C2213yes—
38C2×#13094013C2213yes—
39C2×#13094012C2213yes—
40C2×#13094012C2213yes—
41C2×#13094009C2216yes—
42C2×#13094009C2213yes—
43C2×#13094009C2211yescharacteristic
44C2×#13094004C2213yes—
45C2×#13094004C2213yes—
46C2×#13094004C2213yes—
47C2×#13094004C2213yes—
48C2×#13094000C2216yes—
49C2×#13094000C2213yes—
50C2×#13093999C2213yes—
51C2×#13093999C2213yes—
52C2×#13093999C2213yes—
53#15689605C22116yescomplemented
54#15689599C22116yescomplemented
55C2×Q8×Dic47C2211yescharacteristic
56C2×C4×Dic94C2213yes—
57C2×C4×Dic94C2213yes—
58C2×#13093989C2213yes—
59C2×#13093989C2213yes—
60C4×Q8×D47C22116yescomplemented
61C2×C4×D188C2213yes—
62C2×C4×D188C2213yes—
63C2×C4×D188C2213yes—
64C2×C4×D188C2213yes—
65C2×#13093986C2213yes—
66C2×#13093986C2216yes—
67C2×#13093982C2213yes—
68C2×#13093982C2216yes—
69C2×#13093981C2213yes—
70C2×#13093981C2213yes—
71C2×C4⋊C4×D47C2213yes—
72C2×C4⋊C4×D47C2213yes—
73C2×C42×D47C2213yes—
74C47×#557C22116yescomplemented
75C2×C4⋊Q8×C47C2213yes—
76C2×#125×C47C2213yes—
77C2×#125×C47C2213yes—
78C2×C4×Q8×C47C2211yescharacteristic
79C2×C4×Q8×C47C2211yescharacteristic
80C2×C4×Q8×C47C2211yescharacteristic
81C2×C4×Q8×C47C2213yes—
82C2×#10625354—28no—
83C2×#10625354C2318yes—
84C22×Dic94C2313yes—
85C22×Dic94C2313yes—
86C2×Q8×D47—28no—
87C2×Q8×D47—28no—
88C2×Q8×D47C2318yes—
89C2×Q8×D47C2318yes—
90C22×D188C2313yes—
91C22×D188C2313yes—
92C22×D188C2311yescharacteristic
93C22×D188C2313yes—
94C22×C4×D47C2311yescharacteristic
95C22×C4×D47C2313yes—
96C22×C4×D47C2313yes—
97C22×C4×D47C2313yes—
98C22×C4×D47C2313yes—
99C22×C4×D47C2316yes—
100#13094024C23124yes—
101#13094019C23148yes—
102#13094019C23148yes—
103#13094019C23124yes—
104#13094019C23124yes—
105#13094015C23124yes—
106#13094015C23148yes—
107#13094013C23124yes—
108#13094012C23124yes—
109#13094012C23124yes—
110#13094009C23148yes—
111#13094009C23124yes—
112#13094009C2318yes—
113#13094004C23124yes—
114#13094004C23124yes—
115#13094004C23124yes—
116#13094004C23124yes—
117#13094000C23148yes—
118#13094000C23124yes—
119#13093999C23124yes—
120#13093999C23124yes—
121#13093999C23124yes—
122Q8×Dic47C2318yes—
123C4×Dic94C23124yes—
124C4×Dic94C23124yes—
125#13093989C23124yes—
126#13093989C23124yes—
127C4×D188C23124yes—
128C4×D188C23124yes—
129C4×D188C23124yes—
130C4×D188C23124yes—
131#13093986C23124yes—
132#13093986C23148yes—
133#13093982C23124yes—
134#13093982C23148yes—
135#13093981C23124yes—
136#13093981C23124yes—
137C2×C4⋊Dic47C2313yes—
138C2×C4⋊Dic47C2316yes—
139C2×C4⋊Dic47C2313yes—
140C2×C4⋊Dic47C2313yes—
141C2×C4⋊Dic47C2313yes—
142C2×Dic47⋊C4C2313yes—
143C2×Dic47⋊C4C2316yes—
144C2×Dic47⋊C4C2311yescharacteristic
145C2×Dic47⋊C4C2313yes—
146C2×Dic47⋊C4C2313yes—
147C4⋊C4×D47C23124yes—
148C4⋊C4×D47C23124yes—
149C2×(C2×D47)⋊C4C2311yescharacteristic
150C2×(C2×D47)⋊C4C2313yes—
151C2×(C2×D47)⋊C4C2313yes—
152C2×(C2×D47)⋊C4C2313yes—
153C2×(C2×D47)⋊C4C2313yes—
154C2×(C2×D47)⋊C4C2316yes—
155C2×(C2×D47)⋊C4C2313yes—
156C2×(C2×D47)⋊C4C2316yes—
157C2×(C2×D47)⋊C4C2311yescharacteristic
158C2×(C2×D47)⋊C4C2311yescharacteristic
159C2×(C2×D47)⋊C4C2313yes—
160C2×(C2×D47)⋊C4C2313yes—
161C2×C4×Dic47C2313yes—
162C2×C4×Dic47C2313yes—
163C2×C4×Dic47C2313yes—
164C2×C4×Dic47C2316yes—
165C42×D47C23124yes—
166C22×Q8×C47C2313yes—
167C22×Q8×C47C2311yescharacteristic
168C4⋊Q8×C47C23124yes—
169#125×C47C23124yes—
170#125×C47C23124yes—
171C4×Q8×C47C2318yes—
172C4×Q8×C47C2318yes—
173C4×Q8×C47C2318yes—
174C4×Q8×C47C23124yes—
175C2×C4⋊C4×C47C2311yescharacteristic
176C2×C4⋊C4×C47C2313yes—
177C2×C4⋊C4×C47C2313yes—
178C2×C4⋊C4×C47C2313yes—
179C2×C4⋊C4×C47C2313yes—
180C2×C4⋊C4×C47C2313yes—
181C2×C4⋊C4×C47C2316yes—
182C2×C42×C47C2313yes—
183C2×C42×C47C2313yes—
184C2×C42×C47C2313yes—
185C23×D47C2411yescharacteristic
186C23×D47C2413yes—
187C23×D47C2411yescharacteristic
188C2×Q8×C47—46no—
189C2×Q8×C47#4118yes—
190C2×Q8×C47C24112yes—
191C2×Q8×C47C2414yes—
192C22×C4×C47C2411yescharacteristic
193C22×C4×C47C2411yescharacteristic
194C22×C4×C47C2411yescharacteristic
195C22×C4×C47C2413yes—
196C22×C4×C47C2413yes—
197C22×C4×C47C2413yes—
198C22×C4×C47C2413yes—
199C22×Dic47C2411yescharacteristic
200C22×Dic47C2413yes—
201C22×Dic47C2413yes—
202C22×Dic47C2413yes—
203C22×Dic47C2411yescharacteristic
204#10625354—232no—
205Q8×D47—232no—
206Q8×D47—232no—
207C2×D188—212no—
208C2×D188—24no—
209C2×D188—212no—
210C2×D188—46no—
211C2×D188C24112yes—
212C2×D188C24112yes—
213C2×D188C2414yes—
214C2×D188C24112yes—
215C2×C4×D47—24no—
216C2×C4×D47—212no—
217C2×C4×D47—212no—
218C2×C4×D47—212no—
219C2×C4×D47—412no—
220C2×C4×D47—46no—
221C2×C4×D47C2414yes—
222C2×C4×D47C24112yes—
223C2×C4×D47C24112yes—
224C2×C4×D47C24112yes—
225C2×C4×D47C24112yes—
226C2×C4×D47C24124yes—
227C2×Dic94—212no—
228C2×Dic94—212no—
229C2×Dic94C24112yes—
230C2×Dic94C24112yes—
231C4⋊C4×C47C2414yes—
232C4⋊C4×C47C24112yes—
233C4⋊C4×C47C24112yes—
234C4⋊C4×C47C24112yes—
235C4⋊C4×C47C24112yes—
236C4⋊C4×C47C24112yes—
237C4⋊C4×C47C24124yes—
238C42×C47C24112yes—
239C42×C47C24112yes—
240C42×C47C24112yes—
241(C2×D47)⋊C4C2414yes—
242(C2×D47)⋊C4C24112yes—
243(C2×D47)⋊C4C24112yes—
244(C2×D47)⋊C4C24112yes—
245(C2×D47)⋊C4C24112yes—
246(C2×D47)⋊C4C24124yes—
247(C2×D47)⋊C4C24112yes—
248(C2×D47)⋊C4C24124yes—
249(C2×D47)⋊C4C2414yes—
250(C2×D47)⋊C4C2414yes—
251(C2×D47)⋊C4C24112yes—
252(C2×D47)⋊C4C24112yes—
253C4⋊Dic47C24112yes—
254C4⋊Dic47C24124yes—
255C4⋊Dic47C24112yes—
256C4⋊Dic47C24112yes—
257C4⋊Dic47C24112yes—
258Dic47⋊C4C24112yes—
259Dic47⋊C4C24124yes—
260Dic47⋊C4C2414yes—
261Dic47⋊C4C24112yes—
262Dic47⋊C4C24112yes—
263C4×Dic47C24112yes—
264C4×Dic47C24112yes—
265C4×Dic47C24112yes—
266C4×Dic47C24124yes—
267C23×C47C2511yescharacteristic
268C22×D47—22no—
269C22×D47—22no—
270C22×D47—22no—
271C22×D47—26no—
272C22×D47—22no—
273C22×D47—26no—
274C22×D47—26no—
275C22×D47—22no—
276C22×D472−1+414yes—
277C22×D47C2512yes—
278C22×D47C2516yes—
279C22×D47C2512yes—
280Q8×C47—412no—
281Q8×C47C2×#41116yes—
282C2×C4×C47—22no—
283C2×C4×C47—22no—
284C2×C4×C47—26no—
285C2×C4×C47—26no—
286C2×C4×C47—26no—
287C2×C4×C47—22no—
288C2×C4×C47C2×#41112yes—
289C2×C4×C47C2512yes—
290C2×C4×C47C2516yes—
291C2×C4×C47C2516yes—
292C2×C4×C47C2512yes—
293C2×C4×C47C2512yes—
294C2×C4×C47C2516yes—
295C2×C4×C47C2516yes—
296C2×Dic47—26no—
297C2×Dic47—26no—
298C2×Dic47—22no—
299C2×Dic47—22no—
300C2×Dic47—26no—
301C2×Dic47C2512yes—
302C2×Dic47C2516yes—
303C2×Dic47C2516yes—
304C2×Dic47C2516yes—
305C2×Dic47C2512yes—
306D188—224no—
307D188—28no—
308D188—224no—
309D188—412no—
310C4×D47—28no—
311C4×D47—224no—
312C4×D47—224no—
313C4×D47—224no—
314C4×D47—424no—
315C4×D47—412no—
316Dic94—224no—
317Dic94—224no—
318C2×#3516—471nomaximal, Sylow
319C22×C47C22×#4112yes—
320C22×C47C2×2−1+412yes—
321C22×C47#58512yes—
322C22×C47C2611yescharacteristic
323C2×D47—22no—
324C2×D47—22no—
325C2×D47—28no—
326C2×D47—22no—
327C2×D47—26no—
328C2×D47—22no—
329C2×D47—26no—
330C2×D47—26no—
331C2×D47—22no—
332C2×D47—44no—
333C2×D47—412no—
334C2×D47C2×2−1+414yes—
335C4×C47—22no—
336C4×C47—26no—
337C4×C47—22no—
338C4×C47—26no—
339C4×C47—26no—
340C4×C47—22no—
341C4×C47C22×#41112yes—
342Dic47—26no—
343Dic47—26no—
344Dic47—22no—
345Dic47—22no—
346Dic47—26no—
347#3516—4732no—
348C2×#557D4711yescharacteristic, complemented
349C2×#556—473no—
350C2×#554—473no—
351C2×#553—473no—
352C2×#552—473no—
353C2×D4×Q8—471no—
354C2×#548—471no—
355C2×#548—471no—
356C2×#542—473no—
357C2×#541—473no—
358C2×#529—473no—
359C2×#529—473no—
360C2×#520—471no—
361C2×#519—471no—
362C22×C4×Q8—471no—
363C2×C47#351614yescomplemented
364C2×C47C23×#4111yescharacteristic
365C2×C47C22×2−1+411yescharacteristic
366C2×C47C2×#58511yescharacteristic
367D47—24no—
368D47—42no—
369D47—46no—
370C22×#41—471no—
371C23×Q8—471no—
372C23×Q8—471no—
373#557C2×D47116yescomplemented
374#556—4748no—
375#554—4748no—
376#553—4748no—
377#552—4748no—
378D4×Q8—4716no—
379#548—4716no—
380#548—4716no—
381#542—4748no—
382#541—4748no—
383C2×C4⋊Q8—473no—
384C2×C4⋊Q8C2×D4713yes—
385#529—4748no—
386#529—4748no—
387C2×#126—476no—
388C2×#126—473no—
389C2×#126—473no—
390C2×#126—476no—
391C2×#125—473no—
392C2×#125—476no—
393C2×#125C2×D4713yes—
394C2×#125C2×D4713yes—
395C2×#124—473no—
396C2×#124—473no—
397C2×#124—473no—
398C2×#123—471no—
399C2×#123—473no—
400C2×#123—476no—
401C2×C22⋊Q8—473no—
402C2×C22⋊Q8—476no—
403C2×C22⋊Q8—473no—
404C2×C22⋊Q8—473no—
405C2×C22⋊Q8—473no—
406C2×C22⋊Q8—473no—
407C2×#121—473no—
408C2×#121—473no—
409C2×#121—473no—
410#520—4716no—
411#519—4716no—
412C2×C4×Q8—471no—
413C2×C4×Q8—4716no—
414C2×C4×Q8—473no—
415C2×C4×Q8—473no—
416C2×C4×Q8—473no—
417C2×C4×Q8—473no—
418C2×C4×Q8C2×D4711yescharacteristic
419C2×C4×Q8C2×D4711yescharacteristic
420C2×C4×Q8C2×D4711yescharacteristic
421C2×C4×Q8C2×D4713yes—
422C2×C4×D4—473no—
423C2×C4×D4—476no—
424C2×C4×D4—473no—
425C2×C4×D4—473no—
426C2×C4×D4—473no—
427C2×C4×D4—473no—
428C2×#117—473no—
429C2×#117—476no—
430C2×#117—473no—
431C2×#117—473no—
432C22×C4⋊C4—473no—
433C22×C4⋊C4—473no—
434C22×C42—473no—
435C47C2×#351611yescharacteristic, complemented, Sylow
436C2×#41—478no—
437C2×#41—948no—
438C22×Q8—478no—
439C22×Q8—478no—
440C22×Q8—473no—
441C22×Q8—473no—
442C22×Q8—948no—
443C22×Q8—948no—
444C22×Q8C22×D4713yes—
445C22×Q8C22×D4711yescharacteristic
446C22×D4—473no—
447C22×D4—471no—
448C22×D4—473no—
449C22×D4—473no—
450C23×C4—473no—
451C23×C4—473no—
452C23×C4—473no—
453C23×C4—471no—
454C23×C4—473no—
455C23×C4—476no—
456C4⋊Q8—4724no—
457C4⋊Q8C22×D47124yes—
458#126—4748no—
459#126—4724no—
460#126—4724no—
461#126—4748no—
462#125—4724no—
463#125—4748no—
464#125C22×D47124yes—
465#125C22×D47124yes—
466#124—4724no—
467#124—4724no—
468#124—4724no—
469#123—478no—
470#123—4724no—
471#123—4748no—
472C22⋊Q8—4724no—
473C22⋊Q8—4748no—
474C22⋊Q8—4724no—
475C22⋊Q8—4724no—
476C22⋊Q8—4724no—
477C22⋊Q8—4724no—
478#121—4724no—
479#121—4724no—
480#121—4724no—
481C4×Q8—478no—
482C4×Q8—4724no—
483C4×Q8—4724no—
484C4×Q8—4724no—
485C4×Q8—4724no—
486C4×Q8C22×D4718yes—
487C4×Q8C22×D4718yes—
488C4×Q8C22×D4718yes—
489C4×Q8C22×D47124yes—
490C4×D4—4724no—
491C4×D4—4748no—
492C4×D4—4724no—
493C4×D4—4724no—
494C4×D4—4724no—
495C4×D4—4724no—
496#117—4724no—
497#117—4748no—
498#117—4724no—
499#117—4724no—
500C2×C4⋊C4—473no—
501C2×C4⋊C4—473no—
502C2×C4⋊C4—476no—
503C2×C4⋊C4—471no—
504C2×C4⋊C4—473no—
505C2×C4⋊C4—473no—
506C2×C4⋊C4—476no—
507C2×C4⋊C4—473no—
508C2×C4⋊C4—473no—
509C2×C4⋊C4—473no—
510C2×C4⋊C4—4724no—
511C2×C4⋊C4—4724no—
512C2×C4⋊C4C22×D4713yes—
513C2×C4⋊C4C22×D4713yes—
514C2×C4⋊C4C22×D4713yes—
515C2×C4⋊C4C22×D4713yes—
516C2×C4⋊C4C22×D4716yes—
517C2×C4⋊C4C22×D4711yescharacteristic
518C2×C4⋊C4C22×D4713yes—
519C2×C22⋊C4—473no—
520C2×C22⋊C4—471no—
521C2×C22⋊C4—473no—
522C2×C22⋊C4—473no—
523C2×C22⋊C4—473no—
524C2×C22⋊C4—476no—
525C2×C22⋊C4—473no—
526C2×C22⋊C4—471no—
527C2×C22⋊C4—471no—
528C2×C22⋊C4—476no—
529C2×C22⋊C4—473no—
530C2×C22⋊C4—473no—
531C2×C42—473no—
532C2×C42—476no—
533C2×C42—473no—
534C2×C42—473no—
535C2×C42—4724no—
536C2×C42C22×D4713yes—
537C2×C42C22×D4713yes—
538C2×C42C22×D4713yes—
539C24—471no—
540C24—471no—
541C24—473no—
542#41—9432no—
543C2×Q8—46no—
544C2×Q8—4712no—
545C2×Q8—4712no—
546C2×Q8—9432no—
547C2×Q8—9432no—
548C2×Q8—9412no—
549C2×Q8—9412no—
550C2×Q8#1062535418yes—
551C2×Q8C23×D47112yes—
552C2×Q8C23×D4714yes—
553C2×D4—4712no—
554C2×D4—474no—
555C2×D4—4712no—
556C2×D4—4712no—
557C2×D4—9412no—
558C2×D4—944no—
559C2×D4—9412no—
560C2×D4—1886no—
561C22×C4—471no—
562C22×C4—473no—
563C22×C4—473no—
564C22×C4—473no—
565C22×C4—471no—
566C22×C4—474no—
567C22×C4—4712no—
568C22×C4—4712no—
569C22×C4—4712no—
570C22×C4—4712no—
571C22×C4—4724no—
572C22×C4—944no—
573C22×C4—9412no—
574C22×C4—9412no—
575C22×C4—9412no—
576C22×C4—18812no—
577C22×C4—1886no—
578C22×C4C23×D4711yescharacteristic
579C22×C4C23×D4713yes—
580C22×C4C23×D4713yes—
581C22×C4C23×D4711yescharacteristic
582C22×C4C23×D4711yescharacteristic
583C22×C4C23×D4713yes—
584C22×C4C23×D4713yes—
585C4⋊C4—4712no—
586C4⋊C4—4724no—
587C4⋊C4—474no—
588C4⋊C4—4712no—
589C4⋊C4—4712no—
590C4⋊C4—4712no—
591C4⋊C4—4724no—
592C4⋊C4—4712no—
593C4⋊C4—4712no—
594C4⋊C4—4712no—
595C4⋊C4C23×D47112yes—
596C4⋊C4C23×D47112yes—
597C4⋊C4C23×D47112yes—
598C4⋊C4C23×D47112yes—
599C4⋊C4C23×D47124yes—
600C4⋊C4C23×D4714yes—
601C4⋊C4C23×D47112yes—
602C22⋊C4—4712no—
603C22⋊C4—474no—
604C22⋊C4—4712no—
605C22⋊C4—4712no—
606C22⋊C4—4712no—
607C22⋊C4—4724no—
608C22⋊C4—4712no—
609C22⋊C4—474no—
610C22⋊C4—474no—
611C22⋊C4—4724no—
612C22⋊C4—4712no—
613C22⋊C4—4712no—
614C42—4712no—
615C42—4712no—
616C42—4712no—
617C42—4724no—
618C42C23×D47112yes—
619C42C23×D47112yes—
620C42C23×D47112yes—
621C23—474no—
622C23—472no—
623C23—472no—
624C23—476no—
625C23—942no—
626C23—942no—
627C23—942no—
628C23—946no—
629C23—942no—
630C23—946no—
631C23—946no—
632C23—942no—
633C23C24×D4711yescharacteristic
634Q8—412no—
635Q8—9424no—
636Q8—9424no—
637Q8C2×#10625354116yes—
638D4—9424no—
639D4—948no—
640D4—9424no—
641D4—18812no—
642C2×C4—22no—
643C2×C4—26no—
644C2×C4—22no—
645C2×C4—26no—
646C2×C4—26no—
647C2×C4—22no—
648C2×C4—472no—
649C2×C4—476no—
650C2×C4—476no—
651C2×C4—476no—
652C2×C4—472no—
653C2×C4—948no—
654C2×C4—942no—
655C2×C4—946no—
656C2×C4—946no—
657C2×C4—942no—
658C2×C4—946no—
659C2×C4—9424no—
660C2×C4—9424no—
661C2×C4—9424no—
662C2×C4—18824no—
663C2×C4—18812no—
664C2×C4C2×#10625354112yes—
665C2×C4C24×D4712yes—
666C2×C4C24×D4716yes—
667C2×C4C24×D4716yes—
668C2×C4C24×D4712yes—
669C2×C4C24×D4712yes—
670C2×C4C24×D4716yes—
671C2×C4C24×D4716yes—
672C22—474no—
673C22—948no—
674C22—942no—
675C22—942no—
676C22—942no—
677C22—946no—
678C22—942no—
679C22—946no—
680C22—946no—
681C22—942no—
682C22—1884no—
683C22—18812no—
684C22C22×#1062535412yes—
685C222−1+4×D4712yes—
686C22#1568995912yes—
687C22C25×D4711yescharacteristic
688C4—22no—
689C4—26no—
690C4—22no—
691C4—26no—
692C4—26no—
693C4—22no—
694C4—942no—
695C4—946no—
696C4—946no—
697C4—942no—
698C4—946no—
699C4C22×#10625354112yes—
700C2—944no—
701C2—1882no—
702C2—1886no—
703C2#2025738414yesdirect product factor
704C2C23×#1062535411yescharacteristic
705C2C2×2−1+4×D4711yescharacteristic
706C2C2×#1568995911yescharacteristic
subgroupG/H
centerC23C24×D47
commutator, cosocleC22×C47C26
FrattiniC22C25×D47
FittingC2×C47×#557C2
socleC23×C47C25
hypercenterC2×#557D47
hypocenterC47C2×#3516
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
1. #20257384C2direct (N × H)
2. C2×#15689846C2semidirect
3. C2×#15689834C2semidirect
4. C2×#15689826C2semidirect
5. C2×#15689811C2semidirect
6. C2×Q8×D188C2semidirect
7. C2×#15689785C2semidirect
8. C2×#15689785C2semidirect
9. C2×#15689747C2semidirect
10. C2×#15689736C2semidirect
11. C2×#15689660C2semidirect
12. C2×#15689658C2semidirect
13. C2×#15689605C2semidirect
14. C2×#15689599C2semidirect
15. C2×C4×Q8×D47C2semidirect
16. C2×C47×#557C2semidirect
20. #15689846C22semidirect
21. #15689834C22semidirect
22. #15689826C22semidirect
23. #15689811C22semidirect
24. Q8×D188C22semidirect
25. #15689785C22semidirect
26. #15689785C22semidirect
27. #15689747C22semidirect
28. #15689736C22semidirect
30. #15689660C22semidirect
31. #15689658C22semidirect
53. #15689605C22semidirect
54. #15689599C22semidirect
60. C4×Q8×D47C22semidirect
74. C47×#557C22semidirect
348. C2×#557D47semidirect
363. C2×C47#3516semidirect
373. #557C2×D47semidirect
435. C47C2×#3516semidirect
703. C2#20257384direct (N × H)

Maximal subgroups

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

subgroupindex
#202573842
C2×#156898462
C2×#156898342
C2×#156898262
C2×#156898112
C2×Q8×D1882
C2×#156897852
C2×#156897472
C2×#156897362
C2×#156896602
C2×#156896582
C2×#156896052
C2×#156895992
C2×C4×Q8×D472
C2×C47×#5572
C2×#351647