Finite Group Databasebeta

← C2×#20256217 #27096045

Subgroups — C2×#20256217 #27096045

Order 12032.

1886 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689846C211yesmaximal, characteristic, complemented
2C2×#15689833C211yesmaximal, characteristic, complemented
3#20256217C2116yesmaximal, direct product factor
4C2×#15689492C211yesmaximal, characteristic, complemented
5C2×#15689483C211yesmaximal, characteristic, complemented
6C2×#15689478C211yesmaximal, characteristic, complemented
7C2×#15689431C211yesmaximal, characteristic, complemented
8C2×#15689409C211yesmaximal, characteristic, complemented
9C2×#15689424C211yesmaximal, characteristic, complemented
10C2×#15689339C211yesmaximal, characteristic
11C2×#15689339C211yesmaximal, characteristic
12C2×#15689329C211yesmaximal, characteristic, complemented
13C2×#15689236C211yesmaximal, characteristic
14C2×#15689225C211yesmaximal, characteristic, complemented
15C2×C4×#10625325C211yesmaximal, characteristic, complemented
16C2×C47×#446C211yesmaximal, characteristic, complemented
17C22×#10625325C2211yescharacteristic
18C22×#10625325C2211yescharacteristic
19C22×D376C2211yescharacteristic
20#15689846—24no—
21#15689846C2218yescomplemented
22#15689833—24no—
23#15689833C2218yescomplemented
24C2×#13094024C2211yescharacteristic
25C2×#13094024C2211yescharacteristic
26C2×#13094019—21no—
27C2×#13094019—21no—
28C2×#13094016C2211yescharacteristic
29C2×#13094016C2211yescharacteristic
30C2×#13094012C2211yescharacteristic
31C2×#13094012C2211yescharacteristic
32C2×#13094002—21no—
33C2×#13094002—21no—
34C2×#13094000—21no—
35C2×#13094000—21no—
36C2×C4×Dic94C2211yescharacteristic
37C2×C4×Dic94C2211yescharacteristic
38C2×C4×D188C2211yescharacteristic
39C2×C4×D188C2211yescharacteristic
40C2×C4×D188C2211yescharacteristic
41C2×C4×D188C2211yescharacteristic
42C2×#13093982—21no—
43C2×C4⋊C4×D47—21no—
44#15689492C2218yescomplemented
45#15689483C2218yescomplemented
46#15689478C2218yescomplemented
47#15689431C2218yescomplemented
48#15689424C2218yescomplemented
49#15689409C2218yescomplemented
50#15689339C2218yes—
51#15689339C2218yes—
52#15689329C2218yescomplemented
53#15689236C2218yes—
54#15689225C2218yescomplemented
55C4×#10625325C2218yescomplemented
56C2×#13093958C2211yescharacteristic
57C2×#13093956C2211yescharacteristic
58C2×#13093956C2211yescharacteristic
59C2×#13093949C2211yescharacteristic
60C2×#13093949C2211yescharacteristic
61C2×#13093949C2211yescharacteristic
62C2×#13093949C2211yescharacteristic
63C2×#13093949C2211yescharacteristic
64C2×#13093949C2211yescharacteristic
65C2×#13093946C2211yescharacteristic
66C2×#13093946C2211yescharacteristic
67C2×#13093946C2211yescharacteristic
68C2×#13093946C2211yescharacteristic
69C2×C4×Q8×C47C2211yescharacteristic
70C47×#446C2218yescomplemented
71C2×C4⋊C8×C47C2211yescharacteristic
72C2×C4⋊C8×C47C2211yescharacteristic
73C2×C4⋊C8×C47C2211yescharacteristic
74C2×#97×C47C2211yescharacteristic
75C2×#97×C47C2211yescharacteristic
76C2×C4×C8×C47C2211yescharacteristic
77C22×Dic94—21no—
78C22×Dic94C2311yescharacteristic
79C22×Dic94C2311yescharacteristic
80C22×D188C2311yescharacteristic
81C22×D188C2311yescharacteristic
82C22×C4×D47—21no—
83C22×C4×D47—21no—
84C22×C4×D47—21no—
85C22×C4×D47—21no—
86C2×#10625325—24no—
87C2×#10625325—24no—
88C2×#10625325C2314yes—
89C2×#10625325C2314yes—
90C2×D376—24no—
91C2×D376C2314yes—
92#13094024—22no—
93#13094024—22no—
94#13094024C2314yes—
95#13094024C2314yes—
96#13094019—28no—
97#13094019—28no—
98#13094016—22no—
99#13094016—22no—
100#13094016C2314yes—
101#13094016C2314yes—
102#13094012—22no—
103#13094012—22no—
104#13094012C2314yes—
105#13094012C2314yes—
106#13094002—28no—
107#13094002—28no—
108#13094000—28no—
109#13094000—28no—
110C4×Dic94—22no—
111C4×Dic94—22no—
112C4×Dic94C2314yes—
113C4×Dic94C2314yes—
114C4×D188—22no—
115C4×D188—22no—
116C4×D188—22no—
117C4×D188—22no—
118C4×D188C2314yes—
119C4×D188C2314yes—
120C4×D188C2314yes—
121C4×D188C2314yes—
122#13093982—28no—
123C2×C4⋊Dic47—21no—
124C2×C4⋊Dic47—21no—
125C2×C4⋊Dic47—21no—
126C2×C4⋊Dic47C2311yescharacteristic
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—
136C4⋊C4×D47—28no—
137C2×(C2×D47)⋊C4—21no—
138C2×(C2×D47)⋊C4—21no—
139C2×(C2×D47)⋊C4—21no—
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×C4×Dic47—21no—
146C2×C4×Dic47—21no—
147#13093958C2314yes—
148#13093956C2314yes—
149#13093956C2314yes—
150#13093949C2314yes—
151#13093949C2314yes—
152#13093949C2314yes—
153#13093949C2314yes—
154#13093949C2314yes—
155#13093949C2314yes—
156#13093946C2314yes—
157#13093946C2314yes—
158#13093946C2314yes—
159#13093946C2314yes—
160C22×Q8×C47D411yescharacteristic
161C22×C8×C47C2311yescharacteristic
162C22×C8×C47C2311yescharacteristic
163C22×C8×C47C2311yescharacteristic
164C22×C8×C47C2311yescharacteristic
165C4×Q8×C47D414yes—
166C4×Q8×C47C2314yes—
167C2×C4⋊C4×C47D411yescharacteristic
168C2×C4⋊C4×C47D411yescharacteristic
169C2×C4⋊C4×C47D411yescharacteristic
170C2×C42×C47C2311yescharacteristic
171C2×C42×C47C2311yescharacteristic
172C2×C42×C47C2311yescharacteristic
173C4⋊C8×C47C2314yes—
174C4⋊C8×C47C2314yes—
175C4⋊C8×C47C2314yes—
176#97×C47C2314yes—
177#97×C47C2314yes—
178C4×C8×C47C2314yes—
179C23×D47—21no—
180C23×D47—21no—
181C2×Q8×C47—42no—
182C2×Q8×C47C2×D414yes—
183C22×C4×C47C2×D411yescharacteristic
184C22×C4×C47C2×D411yescharacteristic
185C22×C4×C47C2×D411yescharacteristic
186C22×C4×C47C2×D411yescharacteristic
187C22×C4×C47C2×D411yescharacteristic
188C22×C4×C47C2×D411yescharacteristic
189C22×C4×C47C2411yescharacteristic
190C22×Dic47—21no—
191C22×Dic47—21no—
192C22×Dic47—21no—
193C22×Dic47—21no—
194C22×Dic47—21no—
195C22×Dic47—21no—
196C2×D188—21no—
197C2×D188—22no—
198C2×D188—22no—
199C2×D188—22no—
200C2×D188—21no—
201C2×D188#4114yes—
202C2×D188C2412yes—
203C2×D188C2412yes—
204C2×C4×D47—24no—
205C2×C4×D47—24no—
206C2×C4×D47—24no—
207C2×C4×D47—24no—
208C2×C4×D47—44no—
209C2×C4×D47—44no—
210C2×C4×D47—82no—
211C2×C4×D47—82no—
212C2×Dic94—22no—
213C2×Dic94—22no—
214C2×Dic94—22no—
215C2×Dic94—22no—
216C2×Dic94—21no—
217C2×Dic94—21no—
218C2×Dic94—24no—
219C2×Dic94—82no—
220C2×Dic94C2412yes—
221C2×Dic94C2412yes—
222C2×C8×C47—22no—
223C2×C8×C47—22no—
224C2×C8×C47—22no—
225C2×C8×C47—22no—
226C2×C8×C47C2412yes—
227C2×C8×C47C2412yes—
228C2×C8×C47C2412yes—
229C2×C8×C47C2412yes—
230C4⋊C4×C47C2×D414yes—
231C4⋊C4×C47C2×D414yes—
232C4⋊C4×C47C2×D414yes—
233C42×C47C2×D412yes—
234C42×C47C2×D412yes—
235C42×C47C2×D412yes—
236C42×C47C2412yes—
237C42×C47C2412yes—
238C42×C47C2412yes—
239(C2×D47)⋊C4—24no—
240(C2×D47)⋊C4—24no—
241(C2×D47)⋊C4—24no—
242(C2×D47)⋊C4—24no—
243(C2×D47)⋊C4—24no—
244(C2×D47)⋊C4—24no—
245(C2×D47)⋊C4—24no—
246(C2×D47)⋊C4—24no—
247C4⋊Dic47—24no—
248C4⋊Dic47—24no—
249C4⋊Dic47—24no—
250C4⋊Dic47—21no—
251C4⋊Dic47—21no—
252C4⋊Dic47—21no—
253C4⋊Dic47—21no—
254C4⋊Dic47C2412yes—
255C4⋊Dic47C2412yes—
256C4⋊Dic47C2412yes—
257C4⋊Dic47C2412yes—
258Dic47⋊C4—24no—
259Dic47⋊C4—24no—
260Dic47⋊C4—24no—
261Dic47⋊C4—24no—
262Dic47⋊C4—24no—
263Dic47⋊C4—24no—
264C4×Dic47—24no—
265C4×Dic47—24no—
266D376—28no—
267#10625325—28no—
268#10625325—28no—
269C23×C47C22×D411yescharacteristic
270C22×D47—24no—
271C22×D47—22no—
272C22×D47—22no—
273C22×D47—42no—
274C22×D47—42no—
275C22×D47—42no—
276C22×D47—42no—
277C22×D47—42no—
278Q8×C47—44no—
279C2×C4×C47—22no—
280C2×C4×C47—22no—
281C2×C4×C47—22no—
282C2×C4×C47—22no—
283C2×C4×C47—22no—
284C2×C4×C47—22no—
285C2×C4×C47C22×D412yes—
286C2×C4×C47C22×D412yes—
287C2×C4×C47C22×D412yes—
288C2×C4×C47C22×D412yes—
289C2×C4×C47C22×D412yes—
290C2×C4×C47C22×D412yes—
291C2×C4×C47C22×D411yescharacteristic
292C2×C4×C47C2×#4112yes—
293C2×C4×C472−1+412yes—
294C2×C4×C47C2511yescharacteristic
295C2×Dic47—22no—
296C2×Dic47—22no—
297C2×Dic47—22no—
298C2×Dic47—22no—
299C2×Dic47—22no—
300C2×Dic47—22no—
301C2×Dic47—42no—
302C2×Dic47—42no—
303C2×Dic47—42no—
304C2×Dic47—42no—
305C2×Dic47—42no—
306C2×Dic47—42no—
307D188—24no—
308D188—22no—
309D188—22no—
310D188—22no—
311D188—42no—
312D188C2×#4114yes—
313C4×D47—48no—
314C4×D47—48no—
315C4×D47—84no—
316C4×D47—84no—
317Dic94—22no—
318Dic94—22no—
319Dic94—22no—
320Dic94—22no—
321Dic94—42no—
322Dic94—42no—
323Dic94—84no—
324C8×C47—22no—
325C8×C47—22no—
326C8×C47—22no—
327C8×C47—22no—
328C2×#3376—471nomaximal, Sylow
329C22×C47#54812yes—
330C22×C47#57512yes—
331C22×C47#57712yes—
332C22×C47C23×D411yescharacteristic
333C2×D47—24no—
334C2×D47—48no—
335C2×D47—42no—
336C2×D47—42no—
337C2×D47—42no—
338C2×D47—42no—
339C2×D47—42no—
340C2×D47—84no—
341C4×C47—22no—
342C4×C47—22no—
343C4×C47—22no—
344C4×C47—22no—
345C4×C47—22no—
346C4×C47—22no—
347C4×C47#54812yes—
348C4×C47C22×#4111yescharacteristic
349C4×C47C2×2−1+411yescharacteristic
350Dic47—42no—
351Dic47—42no—
352Dic47—42no—
353Dic47—42no—
354Dic47—42no—
355Dic47—42no—
356C2×#556—471no—
357C2×#554—471no—
358#3376—4716no—
359C2×#491—471no—
360C2×#489—471no—
361C2×#488—471no—
362C2×#479—471no—
363C2×#475—471no—
364C2×#478—471no—
365C2×#463—471no—
366C2×#463—471no—
367C2×#461—471no—
368C2×#446D4711yescharacteristic, complemented
369C2×#442—471no—
370C2×#440—471no—
371C2×C4×SD16—471no—
372C2×C47#337614yescomplemented
373C2×C47C2×#54811yescharacteristic
374C2×C47C2×#57511yescharacteristic
375C2×C47C2×#57711yescharacteristic
376D47—44no—
377D47—82no—
378C22×SD16—471no—
379C22×SD16—471no—
380C22×D8—471no—
381#556—478no—
382#556—944no—
383#554—478no—
384#554—944no—
385C2×C4⋊Q8—471no—
386C2×C4⋊Q8—471no—
387C2×#126—941no—
388C2×#126—941no—
389C2×#125—471no—
390C2×#125—471no—
391C2×#124—471no—
392C2×#124—471no—
393C2×C22⋊Q8—941no—
394C2×C22⋊Q8—941no—
395C2×C22⋊Q8—941no—
396C2×C22⋊Q8—941no—
397C2×C4×Q8—471no—
398C2×C4×Q8—471no—
399C2×C4×Q8C2×D4711yescharacteristic
400C2×C4×D4—471no—
401C2×C4×D4—471no—
402C2×C4×D4—471no—
403C2×C4×D4—471no—
404C2×#117—941no—
405C22×C4⋊C4—941no—
406#491—478no—
407#489—478no—
408#488—478no—
409#479—478no—
410#478—478no—
411#475—478no—
412#463—478no—
413#463—478no—
414#461—478no—
415#446C2×D4718yescomplemented
416#442—478no—
417#440—478no—
418C4×SD16—478no—
419C2×#107—471no—
420C2×#106—471no—
421C2×#106—471no—
422C2×C4⋊C8C2×D4711yescharacteristic
423C2×C4⋊C8C2×D4711yescharacteristic
424C2×C4⋊C8C2×D4711yescharacteristic
425C2×#103—471no—
426C2×#103—471no—
427C2×#103—471no—
428C2×#103—471no—
429C2×#103—471no—
430C2×#103—471no—
431C2×#102—471no—
432C2×#102—471no—
433C2×#102—471no—
434C2×#102—471no—
435C2×#97C2×D4711yescharacteristic
436C2×#97C2×D4711yescharacteristic
437C2×C4×C8C2×D4711yescharacteristic
438C47C2×#337611yescharacteristic, complemented, Sylow
439C22×Q8—471no—
440C22×Q8—471no—
441C22×Q8—941no—
442C22×Q8D18811yescharacteristic
443C22×D4—471no—
444C22×D4—471no—
445C23×C4—941no—
446C23×C4—941no—
447C23×C4—941no—
448C23×C4—941no—
449C2×SD16—474no—
450C2×SD16—474no—
451C2×SD16—944no—
452C2×SD16—944no—
453C2×D8—474no—
454C2×D8—944no—
455C22×C8C22×D4711yescharacteristic
456C22×C8C22×D4711yescharacteristic
457C22×C8C22×D4711yescharacteristic
458C22×C8C22×D4711yescharacteristic
459C4⋊Q8—474no—
460C4⋊Q8—474no—
461C4⋊Q8—942no—
462C4⋊Q8—942no—
463#126—948no—
464#126—948no—
465#125—474no—
466#125—474no—
467#125—942no—
468#125—942no—
469#124—474no—
470#124—474no—
471#124—942no—
472#124—942no—
473C22⋊Q8—948no—
474C22⋊Q8—948no—
475C22⋊Q8—948no—
476C22⋊Q8—948no—
477C4×Q8—474no—
478C4×Q8—474no—
479C4×Q8—942no—
480C4×Q8—942no—
481C4×Q8D18814yes—
482C4×Q8C22×D4714yes—
483C4×D4—474no—
484C4×D4—474no—
485C4×D4—474no—
486C4×D4—474no—
487C4×D4—942no—
488C4×D4—942no—
489C4×D4—942no—
490C4×D4—942no—
491#117—948no—
492C2×C4⋊C4—471no—
493C2×C4⋊C4—471no—
494C2×C4⋊C4—471no—
495C2×C4⋊C4—471no—
496C2×C4⋊C4—941no—
497C2×C4⋊C4—941no—
498C2×C4⋊C4—941no—
499C2×C4⋊C4—941no—
500C2×C4⋊C4—941no—
501C2×C4⋊C4—941no—
502C2×C4⋊C4—941no—
503C2×C4⋊C4—941no—
504C2×C4⋊C4—941no—
505C2×C4⋊C4—948no—
506C2×C4⋊C4D18811yescharacteristic
507C2×C4⋊C4D18811yescharacteristic
508C2×C4⋊C4D18811yescharacteristic
509C2×C22⋊C4—941no—
510C2×C22⋊C4—941no—
511C2×C22⋊C4—941no—
512C2×C22⋊C4—941no—
513C2×C22⋊C4—941no—
514C2×C22⋊C4—941no—
515C2×C22⋊C4—941no—
516C2×C22⋊C4—941no—
517C2×C42—941no—
518C2×C42—941no—
519C2×C42C22×D4711yescharacteristic
520C2×C42C22×D4711yescharacteristic
521C2×C42C22×D4711yescharacteristic
522#107—474no—
523#106—474no—
524#106—474no—
525C4⋊C8C22×D4714yes—
526C4⋊C8C22×D4714yes—
527C4⋊C8C22×D4714yes—
528#103—474no—
529#103—474no—
530#103—474no—
531#103—474no—
532#103—474no—
533#103—474no—
534#102—474no—
535#102—474no—
536#102—474no—
537#102—474no—
538#97C22×D4714yes—
539#97C22×D4714yes—
540C4×C8C22×D4714yes—
541C24—941no—
542C24—941no—
543C2×Q8—42no—
544C2×Q8—472no—
545C2×Q8—472no—
546C2×Q8—944no—
547C2×Q8—941no—
548C2×Q8—941no—
549C2×Q8—942no—
550C2×Q8—942no—
551C2×Q8—942no—
552C2×Q8—942no—
553C2×Q8—3762no—
554C2×Q8C2×D18814yes—
555C2×D4—474no—
556C2×D4—472no—
557C2×D4—472no—
558C2×D4—941no—
559C2×D4—941no—
560C2×D4—942no—
561C2×D4—942no—
562C2×D4—942no—
563C22×C4—941no—
564C22×C4—941no—
565C22×C4—941no—
566C22×C4—941no—
567C22×C4—941no—
568C22×C4—941no—
569C22×C4—944no—
570C22×C4—944no—
571C22×C4—944no—
572C22×C4—944no—
573C22×C4—3762no—
574C22×C4—3762no—
575C22×C4—1884no—
576C22×C4—1884no—
577C22×C4C2×D18811yescharacteristic
578C22×C4C2×D18811yescharacteristic
579C22×C4C2×D18811yescharacteristic
580C22×C4C2×D18811yescharacteristic
581C22×C4C2×D18811yescharacteristic
582C22×C4C2×D18811yescharacteristic
583C22×C4C23×D4711yescharacteristic
584SD16—948no—
585SD16—948no—
586D8—948no—
587C2×C8—22no—
588C2×C8—22no—
589C2×C8—22no—
590C2×C8—22no—
591C2×C8C23×D4712yes—
592C2×C8C23×D4712yes—
593C2×C8C23×D4712yes—
594C2×C8C23×D4712yes—
595C4⋊C4—472no—
596C4⋊C4—472no—
597C4⋊C4—472no—
598C4⋊C4—472no—
599C4⋊C4—944no—
600C4⋊C4—944no—
601C4⋊C4—944no—
602C4⋊C4—944no—
603C4⋊C4—944no—
604C4⋊C4—944no—
605C4⋊C4—941no—
606C4⋊C4—941no—
607C4⋊C4—941no—
608C4⋊C4—941no—
609C4⋊C4—944no—
610C4⋊C4—944no—
611C4⋊C4—944no—
612C4⋊C4C2×D18814yes—
613C4⋊C4C2×D18814yes—
614C4⋊C4C2×D18814yes—
615C22⋊C4—944no—
616C22⋊C4—944no—
617C22⋊C4—944no—
618C22⋊C4—944no—
619C22⋊C4—944no—
620C22⋊C4—944no—
621C22⋊C4—944no—
622C22⋊C4—944no—
623C42—944no—
624C42—944no—
625C42C2×D18812yes—
626C42C2×D18812yes—
627C42C2×D18812yes—
628C42C23×D4712yes—
629C42C23×D4712yes—
630C42C23×D4712yes—
631C23—944no—
632C23—942no—
633C23—942no—
634C23—1882no—
635C23—1882no—
636C23—1882no—
637C23—1882no—
638C23—1882no—
639C23C22×D18811yescharacteristic
640Q8—44no—
641Q8—942no—
642Q8—942no—
643Q8—942no—
644Q8—942no—
645Q8—3764no—
646Q8—1882no—
647Q8—1882no—
648D4—474no—
649D4—944no—
650D4—942no—
651D4—942no—
652D4—942no—
653D4—1882no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—942no—
661C2×C4—942no—
662C2×C4—942no—
663C2×C4—942no—
664C2×C4—942no—
665C2×C4—942no—
666C2×C4—3764no—
667C2×C4—3764no—
668C2×C4—1888no—
669C2×C4—1888no—
670C2×C4—1882no—
671C2×C4—1882no—
672C2×C4—1882no—
673C2×C4—1882no—
674C2×C4—1882no—
675C2×C4—1882no—
676C2×C4C22×D18812yes—
677C2×C4C22×D18812yes—
678C2×C4C22×D18812yes—
679C2×C4C22×D18812yes—
680C2×C4C22×D18812yes—
681C2×C4C22×D18812yes—
682C2×C4C22×D18811yescharacteristic
683C2×C4#41×D4712yes—
684C2×C4#1309407212yes—
685C2×C4C24×D4711yescharacteristic
686C8—22no—
687C8—22no—
688C8—22no—
689C8—22no—
690C22—944no—
691C22—3764no—
692C22—1882no—
693C22—1882no—
694C22—1882no—
695C22—1882no—
696C22—1882no—
697C22—1888no—
698C22#1568978512yes—
699C22#1568992312yes—
700C22#1568993512yes—
701C22C23×D18811yescharacteristic
702C4—22no—
703C4—22no—
704C4—22no—
705C4—22no—
706C4—22no—
707C4—22no—
708C4—1882no—
709C4—1882no—
710C4—1882no—
711C4—1882no—
712C4—1882no—
713C4—1882no—
714C4#1568978512yes—
715C4C2×#41×D4711yescharacteristic
716C4C2×#1309407211yescharacteristic
717C2—3762no—
718C2—1884no—
719C2#2025621714yesdirect product factor
720C2C2×#1568978511yescharacteristic
721C2C2×#1568992311yescharacteristic
722C2C2×#1568993511yescharacteristic
subgroupG/H
centerC23C22×D188
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#446C2
socleC23×C47C22×D4
prime radicalC22×D376C22
hypercenterC2×#446D47
hypocenterC47C2×#3376
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#446

Complements

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

NH ≅ G/Ntype
1. C2×#15689846C2semidirect
2. C2×#15689833C2semidirect
3. #20256217C2direct (N × H)
4. C2×#15689492C2semidirect
5. C2×#15689483C2semidirect
6. C2×#15689478C2semidirect
7. C2×#15689431C2semidirect
8. C2×#15689409C2semidirect
9. C2×#15689424C2semidirect
12. C2×#15689329C2semidirect
14. C2×#15689225C2semidirect
15. C2×C4×#10625325C2semidirect
16. C2×C47×#446C2semidirect
21. #15689846C22semidirect
23. #15689833C22semidirect
44. #15689492C22semidirect
45. #15689483C22semidirect
46. #15689478C22semidirect
47. #15689431C22semidirect
48. #15689424C22semidirect
49. #15689409C22semidirect
52. #15689329C22semidirect
54. #15689225C22semidirect
55. C4×#10625325C22semidirect
70. C47×#446C22semidirect
368. C2×#446D47semidirect
372. C2×C47#3376semidirect
415. #446C2×D47semidirect
438. C47C2×#3376semidirect
719. C2#20256217direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156898462
C2×#156898332
#202562172
C2×#156894922
C2×#156894832
C2×#156894782
C2×#156894312
C2×#156894092
C2×#156894242
C2×#156893392
C2×#156893292
C2×#156892362
C2×#156892252
C2×C4×#106253252
C2×C47×#4462
C2×#337647