Finite Group Databasebeta

← C2×#20257497 #27124562

Subgroups — C2×#20257497 #27124562

Order 12032.

7226 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20257497C2132yesmaximal, direct product factor
2C2×#15689856C213yesmaximal, complemented
3C2×#15689849C211yesmaximal, characteristic, complemented
4C2×#15689836C213yesmaximal, complemented
5C2×#15689823C213yesmaximal, complemented
6C2×#15689812C213yesmaximal, complemented
7C2×#15689792C211yesmaximal, characteristic, complemented
8C2×#15689785C211yesmaximal, characteristic, complemented
9C2×#15689780C211yesmaximal, characteristic, complemented
10C2×#15689738C213yesmaximal, complemented
11C2×#15689724C213yesmaximal, complemented
12C2×#15689657C213yesmaximal, complemented
13C2×#15689657C213yesmaximal, complemented
14C2×#15689605C211yesmaximal, characteristic, complemented
15C2×#15689599C211yesmaximal, characteristic, complemented
16C2×C4×#41×C47C211yesmaximal, characteristic, complemented
17C22×#10625354C2211yescharacteristic
18C22×Q8×D47C2211yescharacteristic
19#15689856C22148yescomplemented
20#15689849C22116yescomplemented
21#15689836C22148yescomplemented
22#15689823C22148yescomplemented
23#15689812C22148yescomplemented
24#15689792C22116yescomplemented
25#15689785C22116yescomplemented
26#15689780C22116yescomplemented
27#15689738C22148yescomplemented
28#15689724C22148yescomplemented
29C2×#13094023C2213yes—
30C2×#13094020C2213yes—
31#15689657C22148yescomplemented
32#15689657C22148yescomplemented
33C2×#13094018C2211yescharacteristic
34C2×#13094018C2213yes—
35C2×#13094017C2216yes—
36C2×#13094016C2213yes—
37C2×#13094016C2213yes—
38C2×#13094015C2213yes—
39C2×#13094012C2213yes—
40C2×#13094012C2213yes—
41C2×#13094011C2213yes—
42C2×#13094010C2216yes—
43C2×#13094007C2213yes—
44C2×#13094007C2213yes—
45C2×#13094007C2216yes—
46C2×#13094006C2216yes—
47C2×#13094004C2213yes—
48C2×#13094003C2213yes—
49C2×#13094003C2213yes—
50C2×#13093999C2213yes—
51C2×#13093998C2213yes—
52C2×#13093998C2213yes—
53C2×#13093997C2216yes—
54C2×#13093995C2213yes—
55C2×#13093995C2213yes—
56#15689605C22116yescomplemented
57#15689599C22116yescomplemented
58C2×Q8×Dic47C2211yescharacteristic
59C2×Q8×Dic47C2211yescharacteristic
60C2×C4×Dic94C2213yes—
61C2×C4×Dic94C2213yes—
62C2×#13093989C2213yes—
63C2×C4×D188C2213yes—
64C2×C4×D188C2213yes—
65C2×#13093986C2213yes—
66C2×C4×C22⋊D47C2213yes—
67C2×C4×C22⋊D47C2213yes—
68C2×C4×C22⋊D47C2216yes—
69C2×#13093982C2213yes—
70C2×#13093981C2213yes—
71C2×#13093981C2213yes—
72C2×#13093981C2216yes—
73C2×C4⋊C4×D47C2213yes—
74C22×#41×C47C2211yescharacteristic
75C4×#41×C47C22116yescomplemented
76C2×C4×Q8×C47C2211yescharacteristic
77C2×C4×Q8×C47C2211yescharacteristic
78C2×C4×D4×C47C2213yes—
79C2×C4×D4×C47C2213yes—
80C2×#117×C47C2213yes—
81C22×C42×C47C2213yes—
82C2×#10625354—28no—
83C2×#10625354C2318yes—
84C22×Dic94C2313yes—
85C22×Dic94C2313yes—
86C2×Q8×D47—28no—
87C2×Q8×D47C2318yes—
88C22×D188C2313yes—
89C22×D188C2313yes—
90C22×C22⋊D47C2313yes—
91C22×C22⋊D47C2316yes—
92C22×C22⋊D47C2313yes—
93C22×C4×D47C2313yes—
94C22×C4×D47C2313yes—
95C22×C4×D47C2316yes—
96#13094023C23124yes—
97#13094020C23124yes—
98#13094018C2318yes—
99#13094018C23124yes—
100#13094017C23148yes—
101#13094016C23124yes—
102#13094016C23124yes—
103#13094015C23124yes—
104#13094012C23124yes—
105#13094012C23124yes—
106#13094011C23124yes—
107#13094010C23148yes—
108#13094007C23148yes—
109#13094007C23124yes—
110#13094007C23124yes—
111#13094006C23148yes—
112#13094004C23124yes—
113#13094003C23124yes—
114#13094003C23124yes—
115#13093999C23124yes—
116#13093998C23124yes—
117#13093998C23124yes—
118#13093997C23148yes—
119#13093995C23124yes—
120#13093995C23124yes—
121Q8×Dic47C2318yes—
122Q8×Dic47C2318yes—
123C4×Dic94C23124yes—
124C4×Dic94C23124yes—
125#13093989C23124yes—
126C4×D188C23124yes—
127C4×D188C23124yes—
128#13093986C23124yes—
129C4×C22⋊D47C23124yes—
130C4×C22⋊D47C23124yes—
131C4×C22⋊D47C23148yes—
132#13093982C23124yes—
133#13093981C23124yes—
134#13093981C23148yes—
135#13093981C23124yes—
136C2×C4⋊Dic47C2313yes—
137C2×C4⋊Dic47C2313yes—
138C2×C4⋊Dic47C2313yes—
139C2×C4⋊Dic47C2313yes—
140C2×Dic47⋊C4C2313yes—
141C2×Dic47⋊C4C2311yescharacteristic
142C2×Dic47⋊C4C2313yes—
143C2×Dic47⋊C4C2313yes—
144C2×Dic47⋊C4C2313yes—
145C2×Dic47⋊C4C2316yes—
146C2×Dic47⋊C4C2311yescharacteristic
147C2×Dic47⋊C4C2313yes—
148C2×Dic47⋊C4C2311yescharacteristic
149C4⋊C4×D47C23124yes—
150C2×C22⋊Dic47C2313yes—
151C2×C22⋊Dic47C2316yes—
152C2×C22⋊Dic47C2313yes—
153C2×(C2×D47)⋊C4C2311yescharacteristic
154C2×(C2×D47)⋊C4C2313yes—
155C2×(C2×D47)⋊C4C2313yes—
156C2×(C2×D47)⋊C4C2313yes—
157C2×(C2×D47)⋊C4C2313yes—
158C2×(C2×D47)⋊C4C2316yes—
159C2×(C2×D47)⋊C4C2311yescharacteristic
160C2×(C2×D47)⋊C4C2313yes—
161C2×(C2×D47)⋊C4C2311yescharacteristic
162C2×C4×Dic47C2316yes—
163C2×C4×Dic47C2313yes—
164C2×C4×Dic47C2313yes—
165C2×#41×C47—28no—
166C2×#41×C47C2318yes—
167C22×Q8×C47C2311yescharacteristic
168C22×D4×C47C2313yes—
169C23×C4×C47C2313yes—
170C23×C4×C47C2313yes—
171C23×C4×C47C2313yes—
172C4×Q8×C47C2318yes—
173C4×Q8×C47C2318yes—
174C4×D4×C47C23124yes—
175C4×D4×C47C23124yes—
176#117×C47C23124yes—
177C2×C4⋊C4×C47C2313yes—
178C2×C4⋊C4×C47C2313yes—
179C2×C22⋊C4×C47C2316yes—
180C2×C42×C47C2311yescharacteristic
181C2×C42×C47C2313yes—
182C2×C42×C47C2313yes—
183C2×C42×C47C2313yes—
184C2×C42×C47C23124yes—
185C24×C47C2413yes—
186C23×D47C2411yescharacteristic
187C23×D47C2413yes—
188#41×C47—232no—
189C2×Q8×C47#4118yes—
190C2×Q8×C47C2414yes—
191C2×D4×C47—212no—
192C2×D4×C47C24112yes—
193C22×C4×C47—212no—
194C22×C4×C47—46no—
195C22×C4×C47—46no—
196C22×C4×C47C2411yescharacteristic
197C22×C4×C47C2411yescharacteristic
198C22×C4×C47C2411yescharacteristic
199C22×C4×C47C2413yes—
200C22×C4×C47C2413yes—
201C22×C4×C47C24112yes—
202C22×C4×C47C24112yes—
203C22×C4×C47C24112yes—
204C22×C4×C47C2413yes—
205C2×C22⋊D47—412no—
206C2×C22⋊D47—46no—
207C2×C22⋊D47—46no—
208C2×C22⋊D47C24112yes—
209C2×C22⋊D47C24124yes—
210C2×C22⋊D47C24112yes—
211C22×Dic47C2411yescharacteristic
212C22×Dic47C2413yes—
213C22×Dic47C2411yescharacteristic
214C22×Dic47C2413yes—
215C22×Dic47C2413yes—
216C22×Dic47C2411yescharacteristic
217#10625354—232no—
218Q8×D47—232no—
219C2×D188—212no—
220C2×D188—46no—
221C2×D188C24112yes—
222C2×D188C24112yes—
223C2×C4×D47—212no—
224C2×C4×D47—212no—
225C2×C4×D47—412no—
226C2×C4×D47C24112yes—
227C2×C4×D47C24112yes—
228C2×C4×D47C24124yes—
229C2×Dic94—212no—
230C2×Dic94—46no—
231C2×Dic94C24112yes—
232C2×Dic94C24112yes—
233C4⋊C4×C47C24112yes—
234C4⋊C4×C47C24112yes—
235C22⋊C4×C47C24124yes—
236C42×C47C2414yes—
237C42×C47C24112yes—
238C42×C47C24112yes—
239C42×C47C24112yes—
240C22⋊Dic47C24112yes—
241C22⋊Dic47C24124yes—
242C22⋊Dic47C24112yes—
243(C2×D47)⋊C4C2414yes—
244(C2×D47)⋊C4C24112yes—
245(C2×D47)⋊C4C24112yes—
246(C2×D47)⋊C4C24112yes—
247(C2×D47)⋊C4C24112yes—
248(C2×D47)⋊C4C24124yes—
249(C2×D47)⋊C4C2414yes—
250(C2×D47)⋊C4C24112yes—
251(C2×D47)⋊C4C2414yes—
252C4⋊Dic47C24112yes—
253C4⋊Dic47C24112yes—
254C4⋊Dic47C24112yes—
255C4⋊Dic47C24112yes—
256Dic47⋊C4C24112yes—
257Dic47⋊C4C2414yes—
258Dic47⋊C4C24112yes—
259Dic47⋊C4C24112yes—
260Dic47⋊C4C24112yes—
261Dic47⋊C4C24124yes—
262Dic47⋊C4C2414yes—
263Dic47⋊C4C24112yes—
264Dic47⋊C4C2414yes—
265C4×Dic47C24124yes—
266C4×Dic47C24112yes—
267C4×Dic47C24112yes—
268C23×C47—26no—
269C23×C47—26no—
270C23×C47—26no—
271C23×C47C2516yes—
272C23×C47C2511yescharacteristic
273C22×D47—22no—
274C22×D47—26no—
275C22×D47—26no—
276C22×D47—22no—
277C22×D47—26no—
278C22×D47—22no—
279C22×D47C2512yes—
280C22×D47C2516yes—
281Q8×C47C2×#41116yes—
282D4×C47—224no—
283C2×C4×C47—22no—
284C2×C4×C47—26no—
285C2×C4×C47—26no—
286C2×C4×C47—22no—
287C2×C4×C47—22no—
288C2×C4×C47—224no—
289C2×C4×C47—412no—
290C2×C4×C47—412no—
291C2×C4×C47C2×#41112yes—
292C2×C4×C47C2516yes—
293C2×C4×C47C2512yes—
294C2×C4×C47C2512yes—
295C2×C4×C47C2512yes—
296C2×C4×C47C2516yes—
297C2×C4×C47C2516yes—
298C22⋊D47—424no—
299C22⋊D47—412no—
300C22⋊D47—412no—
301C2×Dic47—26no—
302C2×Dic47—22no—
303C2×Dic47—22no—
304C2×Dic47—26no—
305C2×Dic47—26no—
306C2×Dic47—22no—
307C2×Dic47C2512yes—
308C2×Dic47C2516yes—
309C2×Dic47C2512yes—
310C2×Dic47C2516yes—
311C2×Dic47C2516yes—
312C2×Dic47C2512yes—
313D188—224no—
314D188—412no—
315C4×D47—224no—
316C4×D47—224no—
317C4×D47—424no—
318Dic94—224no—
319Dic94—412no—
320C2×#3524—471nomaximal, Sylow
321C22×C47—26no—
322C22×C47—26no—
323C22×C47—26no—
324C22×C47—412no—
325C22×C47C22×#4112yes—
326C22×C47#58512yes—
327C22×C47#58512yes—
328C22×C47C2611yescharacteristic
329C2×D47—22no—
330C2×D47—26no—
331C2×D47—26no—
332C2×D47—22no—
333C2×D47—26no—
334C2×D47—22no—
335C2×D47—44no—
336C2×D47—412no—
337C4×C47—22no—
338C4×C47—26no—
339C4×C47—26no—
340C4×C47—22no—
341C4×C47—22no—
342C4×C47C22×#41112yes—
343Dic47—26no—
344Dic47—22no—
345Dic47—22no—
346Dic47—26no—
347Dic47—26no—
348Dic47—22no—
349#3524—4732no—
350C2×#559—473no—
351C2×#557—471no—
352C2×#555—473no—
353C2×#553—473no—
354C2×#552—473no—
355C2×#550—471no—
356C2×#548—471no—
357C2×#548—471no—
358C2×#542—473no—
359C2×#540—473no—
360C2×#529—473no—
361C2×#529—473no—
362C2×#520—471no—
363C2×#519—471no—
364C2×C4×#41D4711yescharacteristic, complemented
365C2×C47—46no—
366C2×C47#352414yescomplemented
367C2×C47C23×#4111yescharacteristic
368C2×C47C2×#58511yescharacteristic
369C2×C47C2×#58511yescharacteristic
370D47—42no—
371D47—46no—
372C22×#41—471no—
373C22×#41C2×D4711yescharacteristic
374C23×Q8—471no—
375#559—4748no—
376#557—4716no—
377#555—4748no—
378#553—4748no—
379#552—4748no—
380#550—4716no—
381#548—4716no—
382#548—4716no—
383#542—4748no—
384#540—4748no—
385C2×C4⋊Q8—473no—
386C2×#127—473no—
387#529—4748no—
388#529—4748no—
389C2×#126—476no—
390C2×#126—471no—
391C2×#126—473no—
392C2×#125—473no—
393C2×#125—473no—
394C2×#125—473no—
395C2×#124—473no—
396C2×#124—476no—
397C2×#124—473no—
398C2×#124—473no—
399C2×#123—476no—
400C2×#123—473no—
401C2×#123—473no—
402C2×#123—476no—
403C2×C22⋊Q8—473no—
404C2×C22⋊Q8—473no—
405C2×C22⋊Q8—473no—
406C2×#121—473no—
407C2×#121—473no—
408C2×#121—473no—
409C2×#121—473no—
410C2×#121—473no—
411C2×#121—476no—
412#520—4716no—
413#519—4716no—
414C4×#41C2×D47116yescomplemented
415C2×C4×Q8—471no—
416C2×C4×Q8—471no—
417C2×C4×Q8—473no—
418C2×C4×Q8—473no—
419C2×C4×Q8—473no—
420C2×C4×Q8C2×D4711yescharacteristic
421C2×C4×Q8C2×D4711yescharacteristic
422C2×C4×D4—473no—
423C2×C4×D4—473no—
424C2×C4×D4—476no—
425C2×C4×D4—473no—
426C2×C4×D4—473no—
427C2×C4×D4—473no—
428C2×C4×D4C2×D4713yes—
429C2×C4×D4C2×D4713yes—
430C2×#117—473no—
431C2×#117—473no—
432C2×#117—473no—
433C2×#117—476no—
434C2×#117C2×D4713yes—
435C22×C4⋊C4—473no—
436C22×C42C2×D4713yes—
437C47C2×#352411yescharacteristic, complemented, Sylow
438C2×#41—28no—
439C2×#41—478no—
440C2×#41—948no—
441C2×#41C22×D4718yes—
442C22×Q8—478no—
443C22×Q8—473no—
444C22×Q8—473no—
445C22×Q8—948no—
446C22×Q8C22×D4711yescharacteristic
447C22×D4—473no—
448C22×D4—476no—
449C22×D4—473no—
450C22×D4—473no—
451C22×D4—473no—
452C22×D4C22×D4713yes—
453C23×C4—473no—
454C23×C4—473no—
455C23×C4—476no—
456C23×C4C22×D4713yes—
457C23×C4C22×D4713yes—
458C23×C4C22×D4713yes—
459C4⋊Q8—4724no—
460#127—4724no—
461#126—4748no—
462#126—478no—
463#126—4724no—
464#125—4724no—
465#125—4724no—
466#125—4724no—
467#124—4724no—
468#124—4748no—
469#124—4724no—
470#124—4724no—
471#123—4748no—
472#123—4724no—
473#123—4724no—
474#123—4748no—
475C22⋊Q8—4724no—
476C22⋊Q8—4724no—
477C22⋊Q8—4724no—
478#121—4724no—
479#121—4724no—
480#121—4724no—
481#121—4724no—
482#121—4724no—
483#121—4748no—
484C4×Q8—478no—
485C4×Q8—478no—
486C4×Q8—4724no—
487C4×Q8—4724no—
488C4×Q8—4724no—
489C4×Q8C22×D4718yes—
490C4×Q8C22×D4718yes—
491C4×D4—4724no—
492C4×D4—4724no—
493C4×D4—4748no—
494C4×D4—4724no—
495C4×D4—4724no—
496C4×D4—4724no—
497C4×D4C22×D47124yes—
498C4×D4C22×D47124yes—
499#117—4724no—
500#117—4724no—
501#117—4724no—
502#117—4748no—
503#117C22×D47124yes—
504C2×C4⋊C4—473no—
505C2×C4⋊C4—473no—
506C2×C4⋊C4—471no—
507C2×C4⋊C4—473no—
508C2×C4⋊C4—473no—
509C2×C4⋊C4—473no—
510C2×C4⋊C4—473no—
511C2×C4⋊C4—476no—
512C2×C4⋊C4—471no—
513C2×C4⋊C4—473no—
514C2×C4⋊C4—473no—
515C2×C4⋊C4—471no—
516C2×C4⋊C4—473no—
517C2×C4⋊C4—4724no—
518C2×C4⋊C4C22×D4713yes—
519C2×C4⋊C4C22×D4713yes—
520C2×C22⋊C4—473no—
521C2×C22⋊C4—476no—
522C2×C22⋊C4—473no—
523C2×C22⋊C4—471no—
524C2×C22⋊C4—473no—
525C2×C22⋊C4—473no—
526C2×C22⋊C4—473no—
527C2×C22⋊C4—473no—
528C2×C22⋊C4—476no—
529C2×C22⋊C4—471no—
530C2×C22⋊C4—473no—
531C2×C22⋊C4—471no—
532C2×C22⋊C4C22×D4716yes—
533C2×C42—476no—
534C2×C42—473no—
535C2×C42—473no—
536C2×C42C22×D4713yes—
537C2×C42C22×D4713yes—
538C2×C42C22×D4713yes—
539C2×C42C22×D47124yes—
540C2×C42C22×D4711yescharacteristic
541C24—471no—
542C24—473no—
543C24C23×D4713yes—
544#41—232no—
545#41—9432no—
546C2×Q8—4712no—
547C2×Q8—4712no—
548C2×Q8—9432no—
549C2×Q8—9412no—
550C2×Q8—1886no—
551C2×Q8#1062535018yes—
552C2×Q8C23×D4714yes—
553C2×D4—212no—
554C2×D4—4712no—
555C2×D4—4724no—
556C2×D4—4712no—
557C2×D4—4712no—
558C2×D4—4712no—
559C2×D4—9412no—
560C2×D4—1886no—
561C2×D4—1886no—
562C2×D4—1886no—
563C2×D4—18812no—
564C2×D4C23×D47112yes—
565C22×C4—212no—
566C22×C4—46no—
567C22×C4—46no—
568C22×C4—471no—
569C22×C4—473no—
570C22×C4—471no—
571C22×C4—473no—
572C22×C4—473no—
573C22×C4—471no—
574C22×C4—4712no—
575C22×C4—4712no—
576C22×C4—4724no—
577C22×C4—9412no—
578C22×C4—9412no—
579C22×C4—18812no—
580C22×C4C23×D47112yes—
581C22×C4C23×D4713yes—
582C22×C4C23×D4711yescharacteristic
583C22×C4C23×D4711yescharacteristic
584C22×C4C23×D4711yescharacteristic
585C22×C4C23×D4713yes—
586C22×C4C23×D47112yes—
587C22×C4C23×D47112yes—
588C22×C4C23×D4713yes—
589C4⋊C4—4712no—
590C4⋊C4—474no—
591C4⋊C4—4712no—
592C4⋊C4—4712no—
593C4⋊C4—4712no—
594C4⋊C4—4724no—
595C4⋊C4—474no—
596C4⋊C4—4712no—
597C4⋊C4—474no—
598C4⋊C4—4712no—
599C4⋊C4—4712no—
600C4⋊C4—4712no—
601C4⋊C4—4712no—
602C4⋊C4C23×D47112yes—
603C4⋊C4C23×D47112yes—
604C22⋊C4—4712no—
605C22⋊C4—4724no—
606C22⋊C4—4712no—
607C22⋊C4—474no—
608C22⋊C4—4712no—
609C22⋊C4—4712no—
610C22⋊C4—4712no—
611C22⋊C4—4712no—
612C22⋊C4—4724no—
613C22⋊C4—474no—
614C22⋊C4—4712no—
615C22⋊C4—474no—
616C22⋊C4C23×D47124yes—
617C42—4724no—
618C42—4712no—
619C42—4712no—
620C42C23×D4714yes—
621C42C23×D47112yes—
622C42C23×D47112yes—
623C42C23×D47112yes—
624C23—26no—
625C23—26no—
626C23—26no—
627C23—472no—
628C23—476no—
629C23—942no—
630C23—946no—
631C23—946no—
632C23—942no—
633C23—946no—
634C23—942no—
635C23C24×D4716yes—
636C23C24×D4711yescharacteristic
637Q8—9424no—
638Q8—18812no—
639Q8C2×#10625350116yes—
640D4—224no—
641D4—9424no—
642D4—18812no—
643D4—18812no—
644D4—18812no—
645D4—18824no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—26no—
650C2×C4—26no—
651C2×C4—224no—
652C2×C4—412no—
653C2×C4—412no—
654C2×C4—472no—
655C2×C4—476no—
656C2×C4—472no—
657C2×C4—476no—
658C2×C4—476no—
659C2×C4—472no—
660C2×C4—942no—
661C2×C4—946no—
662C2×C4—946no—
663C2×C4—942no—
664C2×C4—946no—
665C2×C4—942no—
666C2×C4—9424no—
667C2×C4—9424no—
668C2×C4—18824no—
669C2×C4C2×#10625350112yes—
670C2×C4C24×D4716yes—
671C2×C4C24×D4712yes—
672C2×C4C24×D4712yes—
673C2×C4C24×D4712yes—
674C2×C4C24×D4716yes—
675C2×C4C24×D4716yes—
676C22—26no—
677C22—26no—
678C22—26no—
679C22—412no—
680C22—942no—
681C22—946no—
682C22—946no—
683C22—942no—
684C22—946no—
685C22—942no—
686C22—1884no—
687C22—18812no—
688C22C22×#1062535012yes—
689C22#1568995912yes—
690C22#1568995912yes—
691C22C25×D4711yescharacteristic
692C4—22no—
693C4—22no—
694C4—22no—
695C4—26no—
696C4—26no—
697C4—942no—
698C4—946no—
699C4—946no—
700C4—942no—
701C4—946no—
702C4—942no—
703C4C22×#10625350112yes—
704C2—46no—
705C2—1882no—
706C2—1886no—
707C2#2025749714yesdirect product factor
708C2C23×#1062535011yescharacteristic
709C2C2×#1568995911yescharacteristic
710C2C2×#1568995911yescharacteristic
subgroupG/H
centerC23C24×D47
commutator, cosocleC22×C47C26
FrattiniC22C25×D47
FittingC2×C4×#41×C47C2
socleC23×C47C25
hypercenterC2×C4×#41D47
hypocenterC47C2×#3524
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C4×#41

Complements

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

NH ≅ G/Ntype
1. #20257497C2direct (N × H)
2. C2×#15689856C2semidirect
3. C2×#15689849C2semidirect
4. C2×#15689836C2semidirect
5. C2×#15689823C2semidirect
6. C2×#15689812C2semidirect
7. C2×#15689792C2semidirect
8. C2×#15689785C2semidirect
9. C2×#15689780C2semidirect
10. C2×#15689738C2semidirect
11. C2×#15689724C2semidirect
12. C2×#15689657C2semidirect
13. C2×#15689657C2semidirect
14. C2×#15689605C2semidirect
15. C2×#15689599C2semidirect
16. C2×C4×#41×C47C2semidirect
19. #15689856C22semidirect
20. #15689849C22semidirect
21. #15689836C22semidirect
22. #15689823C22semidirect
23. #15689812C22semidirect
24. #15689792C22semidirect
25. #15689785C22semidirect
26. #15689780C22semidirect
27. #15689738C22semidirect
28. #15689724C22semidirect
31. #15689657C22semidirect
32. #15689657C22semidirect
56. #15689605C22semidirect
57. #15689599C22semidirect
75. C4×#41×C47C22semidirect
364. C2×C4×#41D47semidirect
366. C2×C47#3524semidirect
414. C4×#41C2×D47semidirect
437. C47C2×#3524semidirect
707. C2#20257497direct (N × H)

Maximal subgroups

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

subgroupindex
#202574972
C2×#156898562
C2×#156898492
C2×#156898362
C2×#156898232
C2×#156898122
C2×#156897922
C2×#156897852
C2×#156897802
C2×#156897382
C2×#156897242
C2×#156896572
C2×#156896052
C2×#156895992
C2×C4×#41×C472
C2×#352447