Finite Group Databasebeta

← C2×#20257381 #27124475

Subgroups — C2×#20257381 #27124475

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#20257381C2132yesmaximal, direct product factor
2C2×#15689849C211yesmaximal, characteristic, complemented
3C2×#15689845C213yesmaximal, complemented
4C2×#15689828C213yesmaximal, complemented
5C2×#15689821C213yesmaximal, complemented
6C2×#15689814C213yesmaximal, complemented
7C2×Q8×C22⋊D47C211yesmaximal, characteristic, complemented
8C2×#15689785C211yesmaximal, characteristic, complemented
9C2×#15689784C211yesmaximal, characteristic, complemented
10C2×#15689745C213yesmaximal, complemented
11C2×#15689731C213yesmaximal, complemented
12C2×#15689657C213yesmaximal, complemented
13C2×#15689657C213yesmaximal, complemented
14C2×#15689605C211yesmaximal, characteristic, complemented
15C2×#15689599C211yesmaximal, characteristic, complemented
16C22×C4×Q8×C47C211yesmaximal, characteristic, complemented
17C22×#10625354C2211yescharacteristic
18C22×Q8×D47C2211yescharacteristic
19#15689849C22116yescomplemented
20#15689845C22148yescomplemented
21#15689828C22148yescomplemented
22#15689821C22148yescomplemented
23#15689814C22148yescomplemented
24Q8×C22⋊D47C22116yescomplemented
25#15689785C22116yescomplemented
26#15689784C22116yescomplemented
27#15689745C22148yescomplemented
28#15689731C22148yescomplemented
29C2×#13094023C2213yes—
30C2×#13094022C2213yes—
31#15689657C22148yescomplemented
32#15689657C22148yescomplemented
33C2×#13094019C2216yes—
34C2×#13094018C2213yes—
35C2×#13094018C2213yes—
36C2×#13094018C2216yes—
37C2×#13094016C2213yes—
38C2×#13094016C2213yes—
39C2×#13094015C2213yes—
40C2×#13094014C2216yes—
41C2×#13094013C2213yes—
42C2×#13094012C2213yes—
43C2×#13094012C2213yes—
44C2×#13094009C2216yes—
45C2×#13094007C2211yescharacteristic
46C2×#13094007C2213yes—
47C2×#13094004C2213yes—
48C2×#13094003C2213yes—
49C2×#13094003C2213yes—
50C2×#13094002C2216yes—
51C2×#13094000C2213yes—
52C2×#13094000C2213yes—
53C2×#13093999C2213yes—
54C2×#13093998C2213yes—
55C2×#13093998C2213yes—
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—
74C23×Q8×C47C2211yescharacteristic
75C2×C4×Q8×C47C2211yescharacteristic
76C2×C4×Q8×C47C2211yescharacteristic
77C2×C4×Q8×C47C2213yes—
78C2×C4×Q8×C47C2213yes—
79C2×C4×Q8×C47C22116yescomplemented
80C22×C4⋊C4×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⋊D47C2311yescharacteristic
92C22×C4×D47C2313yes—
93C22×C4×D47C2313yes—
94C22×C4×D47C2316yes—
95#13094023C23124yes—
96#13094022C23124yes—
97#13094019C23148yes—
98#13094018C23148yes—
99#13094018C23124yes—
100#13094018C23124yes—
101#13094016C23124yes—
102#13094016C23124yes—
103#13094015C23124yes—
104#13094014C23148yes—
105#13094013C23124yes—
106#13094012C23124yes—
107#13094012C23124yes—
108#13094009C23148yes—
109#13094007C2318yes—
110#13094007C23124yes—
111#13094004C23124yes—
112#13094003C23124yes—
113#13094003C23124yes—
114#13094002C23148yes—
115#13094000C23124yes—
116#13094000C23124yes—
117#13093999C23124yes—
118#13093998C23124yes—
119#13093998C23124yes—
120Q8×Dic47C2318yes—
121Q8×Dic47C2318yes—
122C4×Dic94C23124yes—
123C4×Dic94C23124yes—
124#13093989C23124yes—
125C4×D188C23124yes—
126C4×D188C23124yes—
127#13093986C23124yes—
128C4×C22⋊D47C23124yes—
129C4×C22⋊D47C23124yes—
130C4×C22⋊D47C23148yes—
131#13093982C23124yes—
132#13093981C23124yes—
133#13093981C23124yes—
134#13093981C23148yes—
135C2×C4⋊Dic47C2313yes—
136C2×C4⋊Dic47C2313yes—
137C2×C4⋊Dic47C2313yes—
138C2×C4⋊Dic47C2313yes—
139C2×Dic47⋊C4C2313yes—
140C2×Dic47⋊C4C2311yescharacteristic
141C2×Dic47⋊C4C2313yes—
142C2×Dic47⋊C4C2313yes—
143C2×Dic47⋊C4C2313yes—
144C2×Dic47⋊C4C2316yes—
145C2×Dic47⋊C4C2313yes—
146C2×Dic47⋊C4C2316yes—
147C2×Dic47⋊C4C2313yes—
148C2×Dic47⋊C4C2311yescharacteristic
149C4⋊C4×D47C23124yes—
150C2×C22⋊Dic47C2311yescharacteristic
151C2×C22⋊Dic47C2313yes—
152C2×(C2×D47)⋊C4C2311yescharacteristic
153C2×(C2×D47)⋊C4C2313yes—
154C2×(C2×D47)⋊C4C2313yes—
155C2×(C2×D47)⋊C4C2313yes—
156C2×(C2×D47)⋊C4C2313yes—
157C2×(C2×D47)⋊C4C2316yes—
158C2×(C2×D47)⋊C4C2316yes—
159C2×(C2×D47)⋊C4C2313yes—
160C2×(C2×D47)⋊C4C2313yes—
161C2×(C2×D47)⋊C4C2311yescharacteristic
162C2×C4×Dic47C2316yes—
163C2×C4×Dic47C2313yes—
164C2×C4×Dic47C2313yes—
165C22×Q8×C47—28no—
166C22×Q8×C47C2318yes—
167C22×Q8×C47C2313yes—
168C22×Q8×C47C2311yescharacteristic
169C23×C4×C47C2311yescharacteristic
170C23×C4×C47C2313yes—
171C23×C4×C47C2313yes—
172C4×Q8×C47C23124yes—
173C4×Q8×C47C2318yes—
174C4×Q8×C47C23124yes—
175C4×Q8×C47C2318yes—
176C2×C4⋊C4×C47C2313yes—
177C2×C4⋊C4×C47C2313yes—
178C2×C4⋊C4×C47C2316yes—
179C2×C4⋊C4×C47C23124yes—
180C2×C42×C47C2313yes—
181C2×C42×C47C2313yes—
182C2×C42×C47C2313yes—
183C2×C42×C47C2313yes—
184C2×C42×C47C23124yes—
185C24×C47C2411yescharacteristic
186C23×D47C2411yescharacteristic
187C23×D47C2413yes—
188C2×Q8×C47—232no—
189C2×Q8×C47—212no—
190C2×Q8×C47#4118yes—
191C2×Q8×C47C24112yes—
192C2×Q8×C47C2414yes—
193C22×C4×C47—24no—
194C22×C4×C47—212no—
195C22×C4×C47—46no—
196C22×C4×C47C2411yescharacteristic
197C22×C4×C47C2411yescharacteristic
198C22×C4×C47C2414yes—
199C22×C4×C47C2413yes—
200C22×C4×C47C2413yes—
201C22×C4×C47C2413yes—
202C22×C4×C47C24112yes—
203C22×C4×C47C24112yes—
204C22×C4×C47C2413yes—
205C2×C22⋊D47—212no—
206C2×C22⋊D47—24no—
207C2×C22⋊D47C24112yes—
208C2×C22⋊D47C2414yes—
209C22×Dic47C2411yescharacteristic
210C22×Dic47C2413yes—
211C22×Dic47C2411yescharacteristic
212C22×Dic47C2413yes—
213C22×Dic47C2413yes—
214C22×Dic47C2411yescharacteristic
215#10625354—232no—
216Q8×D47—232no—
217C2×D188—212no—
218C2×D188—46no—
219C2×D188C24112yes—
220C2×D188C24112yes—
221C2×C4×D47—212no—
222C2×C4×D47—212no—
223C2×C4×D47—412no—
224C2×C4×D47C24112yes—
225C2×C4×D47C24112yes—
226C2×C4×D47C24124yes—
227C2×Dic94—212no—
228C2×Dic94—46no—
229C2×Dic94C24112yes—
230C2×Dic94C24112yes—
231C4⋊C4×C47C24112yes—
232C4⋊C4×C47C24112yes—
233C4⋊C4×C47C24124yes—
234C42×C47C24112yes—
235C42×C47C24112yes—
236C42×C47C24112yes—
237C42×C47C24112yes—
238C22⋊Dic47C2414yes—
239C22⋊Dic47C24112yes—
240(C2×D47)⋊C4C2414yes—
241(C2×D47)⋊C4C24112yes—
242(C2×D47)⋊C4C24112yes—
243(C2×D47)⋊C4C24112yes—
244(C2×D47)⋊C4C24112yes—
245(C2×D47)⋊C4C24124yes—
246(C2×D47)⋊C4C24124yes—
247(C2×D47)⋊C4C24112yes—
248(C2×D47)⋊C4C24112yes—
249(C2×D47)⋊C4C2414yes—
250C4⋊Dic47C24112yes—
251C4⋊Dic47C24112yes—
252C4⋊Dic47C24112yes—
253C4⋊Dic47C24112yes—
254Dic47⋊C4C24112yes—
255Dic47⋊C4C2414yes—
256Dic47⋊C4C24112yes—
257Dic47⋊C4C24112yes—
258Dic47⋊C4C24112yes—
259Dic47⋊C4C24124yes—
260Dic47⋊C4C24112yes—
261Dic47⋊C4C24124yes—
262Dic47⋊C4C24112yes—
263Dic47⋊C4C2414yes—
264C4×Dic47C24124yes—
265C4×Dic47C24112yes—
266C4×Dic47C24112yes—
267C23×C47—22no—
268C23×C47—22no—
269C23×C472−1+414yes—
270C23×C47C2512yes—
271C23×C47C2511yescharacteristic
272C22×D47—22no—
273C22×D47—26no—
274C22×D47—22no—
275C22×D47—26no—
276C22×D47—26no—
277C22×D47—22no—
278C22×D47C2512yes—
279C22×D47C2516yes—
280Q8×C47—224no—
281Q8×C47C2×#41116yes—
282C2×C4×C47—26no—
283C2×C4×C47—28no—
284C2×C4×C47—22no—
285C2×C4×C47—22no—
286C2×C4×C47—26no—
287C2×C4×C47—26no—
288C2×C4×C47—224no—
289C2×C4×C47—412no—
290C2×C4×C47C2×#41112yes—
291C2×C4×C47C2516yes—
292C2×C4×C47C2512yes—
293C2×C4×C47C2512yes—
294C2×C4×C47C2516yes—
295C2×C4×C47C2516yes—
296C2×C4×C47C2516yes—
297C22⋊D47—224no—
298C22⋊D47—28no—
299C2×Dic47—26no—
300C2×Dic47—22no—
301C2×Dic47—26no—
302C2×Dic47—22no—
303C2×Dic47—22no—
304C2×Dic47—26no—
305C2×Dic47C2516yes—
306C2×Dic47C2512yes—
307C2×Dic47C2512yes—
308C2×Dic47C2516yes—
309C2×Dic47C2516yes—
310C2×Dic47C2512yes—
311D188—224no—
312D188—412no—
313C4×D47—224no—
314C4×D47—224no—
315C4×D47—424no—
316Dic94—224no—
317Dic94—412no—
318C2×#3516—471nomaximal, Sylow
319C22×C47—22no—
320C22×C47—22no—
321C22×C47—28no—
322C22×C47C22×#4112yes—
323C22×C47C2×2−1+414yes—
324C22×C47C2×2−1+412yes—
325C22×C47#58512yes—
326C22×C47C2611yescharacteristic
327C2×D47—22no—
328C2×D47—26no—
329C2×D47—22no—
330C2×D47—26no—
331C2×D47—26no—
332C2×D47—22no—
333C2×D47—44no—
334C2×D47—412no—
335C4×C47—26no—
336C4×C47—22no—
337C4×C47—22no—
338C4×C47—26no—
339C4×C47—26no—
340C4×C47C22×#41112yes—
341Dic47—26no—
342Dic47—22no—
343Dic47—26no—
344Dic47—22no—
345Dic47—22no—
346Dic47—26no—
347#3516—4732no—
348C2×#557—471no—
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×Q8D4711yescharacteristic, complemented
363C2×C47—24no—
364C2×C47#351614yescomplemented
365C2×C47C23×#4111yescharacteristic
366C2×C47C22×2−1+411yescharacteristic
367C2×C47C2×#58511yescharacteristic
368D47—42no—
369D47—46no—
370C22×#41—471no—
371C23×Q8—471no—
372C23×Q8C2×D4711yescharacteristic
373#557—4716no—
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⋊Q8—473no—
385#529—4748no—
386#529—4748no—
387C2×#126—476no—
388C2×#126—476no—
389C2×#126—473no—
390C2×#126—473no—
391C2×#125—476no—
392C2×#125—473no—
393C2×#125—473no—
394C2×#125—473no—
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—473no—
403C2×C22⋊Q8—473no—
404C2×C22⋊Q8—473no—
405C2×C22⋊Q8—473no—
406C2×C22⋊Q8—476no—
407C2×#121—473no—
408C2×#121—473no—
409C2×#121—473no—
410#520—4716no—
411#519—4716no—
412C2×C4×Q8—471no—
413C2×C4×Q8—471no—
414C2×C4×Q8—473no—
415C2×C4×Q8—473no—
416C2×C4×Q8—473no—
417C2×C4×Q8C2×D4711yescharacteristic
418C2×C4×Q8C2×D4713yes—
419C2×C4×Q8C2×D4711yescharacteristic
420C2×C4×Q8C2×D4713yes—
421C2×C4×Q8C2×D47116yescomplemented
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×#117—473no—
429C2×#117—473no—
430C2×#117—473no—
431C2×#117—476no—
432C22×C4⋊C4—473no—
433C22×C4⋊C4C2×D4713yes—
434C22×C42C2×D4713yes—
435C47C2×#351611yescharacteristic, complemented, Sylow
436C2×#41—478no—
437C2×#41—948no—
438C22×Q8—28no—
439C22×Q8—478no—
440C22×Q8—473no—
441C22×Q8—473no—
442C22×Q8—948no—
443C22×Q8C22×D4713yes—
444C22×Q8C22×D4718yes—
445C22×Q8C22×D4711yescharacteristic
446C22×D4—473no—
447C22×D4—471no—
448C22×D4—473no—
449C22×D4—473no—
450C23×C4—473no—
451C23×C4—473no—
452C23×C4—476no—
453C23×C4C22×D4713yes—
454C23×C4C22×D4711yescharacteristic
455C23×C4C22×D4713yes—
456C4⋊Q8—4724no—
457C4⋊Q8—4724no—
458#126—4748no—
459#126—4748no—
460#126—4724no—
461#126—4724no—
462#125—4748no—
463#125—4724no—
464#125—4724no—
465#125—4724no—
466#124—4724no—
467#124—4724no—
468#124—4724no—
469#123—478no—
470#123—4724no—
471#123—4748no—
472C22⋊Q8—4724no—
473C22⋊Q8—4724no—
474C22⋊Q8—4724no—
475C22⋊Q8—4724no—
476C22⋊Q8—4724no—
477C22⋊Q8—4748no—
478#121—4724no—
479#121—4724no—
480#121—4724no—
481C4×Q8—478no—
482C4×Q8—478no—
483C4×Q8—4724no—
484C4×Q8—4724no—
485C4×Q8—4724no—
486C4×Q8C22×D4718yes—
487C4×Q8C22×D47124yes—
488C4×Q8C22×D4718yes—
489C4×Q8C22×D47124yes—
490C4×D4—4724no—
491C4×D4—4724no—
492C4×D4—4748no—
493C4×D4—4724no—
494C4×D4—4724no—
495C4×D4—4724no—
496#117—4724no—
497#117—4724no—
498#117—4724no—
499#117—4748no—
500C2×C4⋊C4—473no—
501C2×C4⋊C4—473no—
502C2×C4⋊C4—471no—
503C2×C4⋊C4—473no—
504C2×C4⋊C4—473no—
505C2×C4⋊C4—473no—
506C2×C4⋊C4—473no—
507C2×C4⋊C4—476no—
508C2×C4⋊C4—473no—
509C2×C4⋊C4—473no—
510C2×C4⋊C4—476no—
511C2×C4⋊C4—473no—
512C2×C4⋊C4—471no—
513C2×C4⋊C4—473no—
514C2×C4⋊C4—4724no—
515C2×C4⋊C4C22×D4713yes—
516C2×C4⋊C4C22×D4713yes—
517C2×C4⋊C4C22×D4716yes—
518C2×C4⋊C4C22×D47124yes—
519C2×C22⋊C4—471no—
520C2×C22⋊C4—473no—
521C2×C22⋊C4—473no—
522C2×C22⋊C4—471no—
523C2×C22⋊C4—473no—
524C2×C22⋊C4—473no—
525C2×C22⋊C4—473no—
526C2×C22⋊C4—476no—
527C2×C22⋊C4—471no—
528C2×C22⋊C4—476no—
529C2×C22⋊C4—473no—
530C2×C22⋊C4—473no—
531C2×C42—476no—
532C2×C42—473no—
533C2×C42—473no—
534C2×C42C22×D4713yes—
535C2×C42C22×D4713yes—
536C2×C42C22×D4713yes—
537C2×C42C22×D4713yes—
538C2×C42C22×D47124yes—
539C24—471no—
540C24—473no—
541C24C23×D4711yescharacteristic
542#41—9432no—
543C2×Q8—232no—
544C2×Q8—212no—
545C2×Q8—4712no—
546C2×Q8—4712no—
547C2×Q8—9432no—
548C2×Q8—9412no—
549C2×Q8—1886no—
550C2×Q8#1062535018yes—
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—24no—
562C22×C4—212no—
563C22×C4—46no—
564C22×C4—471no—
565C22×C4—473no—
566C22×C4—471no—
567C22×C4—473no—
568C22×C4—473no—
569C22×C4—471no—
570C22×C4—4712no—
571C22×C4—4712no—
572C22×C4—4724no—
573C22×C4—9412no—
574C22×C4—9412no—
575C22×C4—18812no—
576C22×C4C23×D4714yes—
577C22×C4C23×D47112yes—
578C22×C4C23×D4713yes—
579C22×C4C23×D4711yescharacteristic
580C22×C4C23×D4711yescharacteristic
581C22×C4C23×D4713yes—
582C22×C4C23×D4713yes—
583C22×C4C23×D47112yes—
584C22×C4C23×D4713yes—
585C4⋊C4—4712no—
586C4⋊C4—474no—
587C4⋊C4—4712no—
588C4⋊C4—4712no—
589C4⋊C4—4712no—
590C4⋊C4—4724no—
591C4⋊C4—4712no—
592C4⋊C4—4724no—
593C4⋊C4—4712no—
594C4⋊C4—474no—
595C4⋊C4—4712no—
596C4⋊C4—4712no—
597C4⋊C4—4712no—
598C4⋊C4—4712no—
599C4⋊C4C23×D47112yes—
600C4⋊C4C23×D47112yes—
601C4⋊C4C23×D47124yes—
602C22⋊C4—474no—
603C22⋊C4—4712no—
604C22⋊C4—4712no—
605C22⋊C4—474no—
606C22⋊C4—4712no—
607C22⋊C4—4712no—
608C22⋊C4—4712no—
609C22⋊C4—4724no—
610C22⋊C4—474no—
611C22⋊C4—4724no—
612C22⋊C4—4712no—
613C22⋊C4—4712no—
614C42—4724no—
615C42—4712no—
616C42—4712no—
617C42C23×D47112yes—
618C42C23×D47112yes—
619C42C23×D47112yes—
620C42C23×D47112yes—
621C23—22no—
622C23—22no—
623C23—472no—
624C23—476no—
625C23—942no—
626C23—946no—
627C23—942no—
628C23—946no—
629C23—946no—
630C23—942no—
631C23#1309407214yes—
632C23C24×D4712yes—
633C23C24×D4711yescharacteristic
634Q8—224no—
635Q8—9424no—
636Q8—18812no—
637Q8C2×#10625350116yes—
638D4—9424no—
639D4—948no—
640D4—9424no—
641D4—18812no—
642C2×C4—26no—
643C2×C4—28no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—26no—
647C2×C4—26no—
648C2×C4—224no—
649C2×C4—412no—
650C2×C4—472no—
651C2×C4—476no—
652C2×C4—472no—
653C2×C4—476no—
654C2×C4—476no—
655C2×C4—472no—
656C2×C4—942no—
657C2×C4—946no—
658C2×C4—946no—
659C2×C4—942no—
660C2×C4—946no—
661C2×C4—942no—
662C2×C4—9424no—
663C2×C4—9424no—
664C2×C4—18824no—
665C2×C4C2×#10625350112yes—
666C2×C4C24×D4716yes—
667C2×C4C24×D4712yes—
668C2×C4C24×D4712yes—
669C2×C4C24×D4716yes—
670C2×C4C24×D4716yes—
671C2×C4C24×D4716yes—
672C22—28no—
673C22—22no—
674C22—22no—
675C22—942no—
676C22—946no—
677C22—942no—
678C22—946no—
679C22—946no—
680C22—942no—
681C22—1884no—
682C22—18812no—
683C22C22×#1062535012yes—
684C22C2×#1309407214yes—
685C22C2×#1309407212yes—
686C22#1568995912yes—
687C22C25×D4711yescharacteristic
688C4—26no—
689C4—22no—
690C4—22no—
691C4—26no—
692C4—26no—
693C4—942no—
694C4—946no—
695C4—946no—
696C4—942no—
697C4—946no—
698C4—942no—
699C4C22×#10625350112yes—
700C2—24no—
701C2—1882no—
702C2—1886no—
703C2#2025738114yesdirect product factor
704C2C23×#1062535011yescharacteristic
705C2C22×#1309407211yescharacteristic
706C2C2×#1568995911yescharacteristic
subgroupG/H
centerC23C24×D47
commutator, cosocleC22×C47C26
FrattiniC22C25×D47
FittingC22×C4×Q8×C47C2
socleC23×C47C25
hypercenterC22×C4×Q8D47
hypocenterC47C2×#3516
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C4×Q8

Complements

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

NH ≅ G/Ntype
1. #20257381C2direct (N × H)
2. C2×#15689849C2semidirect
3. C2×#15689845C2semidirect
4. C2×#15689828C2semidirect
5. C2×#15689821C2semidirect
6. C2×#15689814C2semidirect
7. C2×Q8×C22⋊D47C2semidirect
8. C2×#15689785C2semidirect
9. C2×#15689784C2semidirect
10. C2×#15689745C2semidirect
11. C2×#15689731C2semidirect
12. C2×#15689657C2semidirect
13. C2×#15689657C2semidirect
14. C2×#15689605C2semidirect
15. C2×#15689599C2semidirect
16. C22×C4×Q8×C47C2semidirect
19. #15689849C22semidirect
20. #15689845C22semidirect
21. #15689828C22semidirect
22. #15689821C22semidirect
23. #15689814C22semidirect
24. Q8×C22⋊D47C22semidirect
25. #15689785C22semidirect
26. #15689784C22semidirect
27. #15689745C22semidirect
28. #15689731C22semidirect
31. #15689657C22semidirect
32. #15689657C22semidirect
56. #15689605C22semidirect
57. #15689599C22semidirect
79. C2×C4×Q8×C47C22semidirect
362. C22×C4×Q8D47semidirect
364. C2×C47#3516semidirect
421. C2×C4×Q8C2×D47semidirect
435. C47C2×#3516semidirect
703. C2#20257381direct (N × H)

Maximal subgroups

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

subgroupindex
#202573812
C2×#156898492
C2×#156898452
C2×#156898282
C2×#156898212
C2×#156898142
C2×Q8×C22⋊D472
C2×#156897852
C2×#156897842
C2×#156897452
C2×#156897312
C2×#156896572
C2×#156896052
C2×#156895992
C22×C4×Q8×C472
C2×#351647