Finite Group Databasebeta

← C2×#20251567 #26422649

Subgroups — C2×#20251567 #26422649

Order 12032.

1718 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20251567C2116yesmaximal, direct product factor
2C2×C47⋊#401C211yesmaximal, characteristic
3C2×C47⋊#401C211yesmaximal, characteristic
4C2×#15689065C211yesmaximal, characteristic
5C2×#15689064C211yesmaximal, characteristic
6C2×#15689064C211yesmaximal, characteristic
7C2×#15689062C211yesmaximal, characteristic
8C2×#15689061C211yesmaximal, characteristic
9C2×#15689056C211yesmaximal, characteristic
10C2×#15689056C211yesmaximal, characteristic
11C2×#15689054C211yesmaximal, characteristic
12C2×#15689042C211yesmaximal, characteristic
13C2×#15689030C211yesmaximal, characteristic
14C2×#15689009C211yesmaximal, characteristic
15C2×#15689005C211yesmaximal, characteristic
16C2×C47×#395C211yesmaximal, characteristic
17C22×C4⋊Dic47C2211yescharacteristic
18C22×C4⋊Dic47C2211yescharacteristic
19C22×Dic47⋊C4C2211yescharacteristic
20C22×Dic47⋊C4C2211yescharacteristic
21C22×Dic47⋊C4C2211yescharacteristic
22C22×Dic47⋊C4C2211yescharacteristic
23C22×Dic47⋊C4C2211yescharacteristic
24C22×Dic47⋊C4C2211yescharacteristic
25C22×C4×Dic47C2211yescharacteristic
26C47⋊#401C2218yes—
27C47⋊#401C2218yes—
28#15689065C2218yes—
29#15689064C2218yes—
30#15689064C2218yes—
31#15689062C2218yes—
32#15689061C2218yes—
33#15689056C2218yes—
34#15689056C2218yes—
35#15689054C2218yes—
36#15689042C2218yes—
37#15689030C2218yes—
38#15689009C2218yes—
39#15689005C2218yes—
40C2×C47⋊#95C2211yescharacteristic
41C2×C47⋊#95C2211yescharacteristic
42C2×C47⋊#95C2211yescharacteristic
43C2×C47⋊#95C2211yescharacteristic
44C2×C47⋊#95C2211yescharacteristic
45C2×C47⋊#95C2211yescharacteristic
46C2×C47⋊#95C2211yescharacteristic
47C2×C47⋊#95C2211yescharacteristic
48C2×C47⋊#95C2211yescharacteristic
49C2×C47⋊#95C2211yescharacteristic
50C2×C47⋊#95C2211yescharacteristic
51C2×C47⋊#95C2211yescharacteristic
52C2×C47⋊#95C2211yescharacteristic
53C2×C47⋊#95C2211yescharacteristic
54C2×C47⋊#95C2211yescharacteristic
55C2×C47⋊#95C2211yescharacteristic
56C2×C47⋊#95C2211yescharacteristic
57C2×C47⋊#95C2211yescharacteristic
58C2×C47⋊#95C2211yescharacteristic
59C23×Q8×C47C2211yescharacteristic
60C22×C4⋊C4×C47C2211yescharacteristic
61C22×C4⋊C4×C47C2211yescharacteristic
62C22×C4⋊C4×C47C2211yescharacteristic
63C47×#395C2218yes—
64C2×#95×C47C2211yescharacteristic
65C2×#95×C47C2211yescharacteristic
66C2×#95×C47C2211yescharacteristic
67C23×Dic47C2311yescharacteristic
68C23×Dic47C2311yescharacteristic
69C23×Dic47C2311yescharacteristic
70C23×Dic47C2311yescharacteristic
71C23×Dic47C2311yescharacteristic
72C23×Dic47C2311yescharacteristic
73C23×Dic47C2311yescharacteristic
74C23×Dic47C2311yescharacteristic
75C2×C4⋊Dic47—42no—
76C2×C4⋊Dic47—42no—
77C2×C4⋊Dic47C2314yes—
78C2×C4⋊Dic47C2314yes—
79C2×Dic47⋊C4—24no—
80C2×Dic47⋊C4—42no—
81C2×Dic47⋊C4—42no—
82C2×Dic47⋊C4—42no—
83C2×Dic47⋊C4—42no—
84C2×Dic47⋊C4—42no—
85C2×Dic47⋊C4C2314yes—
86C2×Dic47⋊C4C2314yes—
87C2×Dic47⋊C4C2314yes—
88C2×Dic47⋊C4C2314yes—
89C2×Dic47⋊C4C2314yes—
90C2×Dic47⋊C4C2314yes—
91C2×C4×Dic47—42no—
92C2×C4×Dic47C2314yes—
93C47⋊#95C2314yes—
94C47⋊#95C2314yes—
95C47⋊#95C2314yes—
96C47⋊#95C2314yes—
97C47⋊#95C2314yes—
98C47⋊#95C2314yes—
99C47⋊#95C2314yes—
100C47⋊#95C2314yes—
101C47⋊#95C2314yes—
102C47⋊#95C2314yes—
103C47⋊#95C2314yes—
104C47⋊#95C2314yes—
105C47⋊#95C2314yes—
106C47⋊#95C2314yes—
107C47⋊#95C2314yes—
108C47⋊#95C2314yes—
109C47⋊#95C2314yes—
110C47⋊#95C2314yes—
111C47⋊#95C2314yes—
112C22×Q8×C47—24no—
113C22×Q8×C47—42no—
114C22×Q8×C47—42no—
115C22×Q8×C47C2314yes—
116C23×C4×C47C2311yescharacteristic
117C23×C4×C47C2311yescharacteristic
118C23×C4×C47C2311yescharacteristic
119C23×C4×C47C2311yescharacteristic
120C23×C4×C47C2311yescharacteristic
121C23×C4×C47C2311yescharacteristic
122C23×C4×C47C2311yescharacteristic
123C2×C4⋊C4×C47—24no—
124C2×C4⋊C4×C47—42no—
125C2×C4⋊C4×C47—42no—
126C2×C4⋊C4×C47C2314yes—
127C2×C4⋊C4×C47C2314yes—
128C2×C4⋊C4×C47C2314yes—
129#95×C47C2314yes—
130#95×C47C2314yes—
131#95×C47C2314yes—
132C24×C47C2411yescharacteristic
133C2×Q8×C47—28no—
134C2×Q8×C47—44no—
135C2×Q8×C47—44no—
136C2×Q8×C47—416no—
137C22×C4×C47—22no—
138C22×C4×C47—22no—
139C22×C4×C47—22no—
140C22×C4×C47—22no—
141C22×C4×C47—22no—
142C22×C4×C47—22no—
143C22×C4×C47—22no—
144C22×C4×C47—22no—
145C22×C4×C47—22no—
146C22×C4×C47—22no—
147C22×C4×C47—22no—
148C22×C4×C47—22no—
149C22×C4×C47—22no—
150C22×C4×C47—22no—
151C22×C4×C47—22no—
152C22×C4×C47—22no—
153C22×C4×C47—22no—
154C22×C4×C47—22no—
155C22×C4×C47—22no—
156C22×C4×C47—22no—
157C22×C4×C47#4114yes—
158C22×C4×C47C2412yes—
159C22×C4×C47C2412yes—
160C22×C4×C47C2412yes—
161C22×C4×C47C2412yes—
162C22×C4×C47C2412yes—
163C22×C4×C47C2412yes—
164C22×C4×C47C2412yes—
165C22×Dic47—22no—
166C22×Dic47—22no—
167C22×Dic47—22no—
168C22×Dic47—22no—
169C22×Dic47—22no—
170C22×Dic47—22no—
171C22×Dic47—22no—
172C22×Dic47—22no—
173C22×Dic47—22no—
174C22×Dic47—22no—
175C22×Dic47—22no—
176C22×Dic47—22no—
177C22×Dic47—22no—
178C22×Dic47—22no—
179C22×Dic47—22no—
180C22×Dic47—22no—
181C22×Dic47—22no—
182C22×Dic47—22no—
183C22×Dic47—22no—
184C22×Dic47—22no—
185C22×Dic47—22no—
186C22×Dic47—22no—
187C22×Dic47—22no—
188C22×Dic47—22no—
189C22×Dic47C2412yes—
190C22×Dic47C2412yes—
191C22×Dic47C2412yes—
192C22×Dic47C2412yes—
193C22×Dic47C2412yes—
194C22×Dic47C2412yes—
195C22×Dic47C2412yes—
196C22×Dic47C2412yes—
197C4⋊C4×C47—28no—
198C4⋊C4×C47—44no—
199C4⋊C4×C47—44no—
200C4⋊Dic47—44no—
201C4⋊Dic47—44no—
202Dic47⋊C4—28no—
203Dic47⋊C4—44no—
204Dic47⋊C4—44no—
205Dic47⋊C4—44no—
206Dic47⋊C4—44no—
207Dic47⋊C4—44no—
208C4×Dic47—44no—
209C23×C47C2×#4112yes—
210C23×C47H(5,𝔽2)12yes—
211C23×C47H(5,𝔽2)12yes—
212C23×C472−1+412yes—
213C23×C472−1+412yes—
214C23×C472−1+412yes—
215C23×C472−1+412yes—
216C23×C47C2511yescharacteristic
217Q8×C47—416no—
218C2×C4×C47—28no—
219C2×C4×C47—22no—
220C2×C4×C47—22no—
221C2×C4×C47—22no—
222C2×C4×C47—22no—
223C2×C4×C47—22no—
224C2×C4×C47—22no—
225C2×C4×C47—22no—
226C2×C4×C47—22no—
227C2×C4×C47—22no—
228C2×C4×C47—22no—
229C2×C4×C47—22no—
230C2×C4×C47—22no—
231C2×C4×C47—22no—
232C2×C4×C47—22no—
233C2×C4×C47—22no—
234C2×C4×C47—22no—
235C2×C4×C47—22no—
236C2×C4×C47—22no—
237C2×C4×C47—22no—
238C2×C4×C47—22no—
239C2×C4×C47—44no—
240C2×C4×C47—44no—
241C2×C4×C47—44no—
242C2×C4×C47—44no—
243C2×C4×C47—44no—
244C2×C4×C47—44no—
245C2×C4×C47C2×#4114yes—
246C2×Dic47—22no—
247C2×Dic47—22no—
248C2×Dic47—22no—
249C2×Dic47—22no—
250C2×Dic47—22no—
251C2×Dic47—22no—
252C2×Dic47—22no—
253C2×Dic47—22no—
254C2×Dic47—22no—
255C2×Dic47—22no—
256C2×Dic47—22no—
257C2×Dic47—22no—
258C2×Dic47—22no—
259C2×Dic47—22no—
260C2×Dic47—22no—
261C2×Dic47—22no—
262C2×Dic47—22no—
263C2×Dic47—22no—
264C2×Dic47—22no—
265C2×Dic47—22no—
266C2×Dic47—22no—
267C2×Dic47—22no—
268C2×Dic47—22no—
269C2×Dic47—22no—
270C2×Dic47—44no—
271C2×Dic47—44no—
272C2×Dic47—44no—
273C2×Dic47—44no—
274C2×Dic47—44no—
275C2×Dic47—44no—
276C2×Dic47—44no—
277C2×Dic47—44no—
278C2×#2833—471nomaximal, Sylow
279C22×C47#53814yes—
280C22×C47#54114yes—
281C22×C47#54114yes—
282C22×C47#56314yes—
283C22×C47#56314yes—
284C22×C47#56314yes—
285C22×C47#56314yes—
286C22×C47C22×#4111yescharacteristic
287C22×C47C2×H(5,𝔽2)11yescharacteristic
288C22×C47C2×H(5,𝔽2)11yescharacteristic
289C22×C47C2×2−1+411yescharacteristic
290C22×C47C2×2−1+411yescharacteristic
291C22×C47C2×2−1+411yescharacteristic
292C22×C47C2×2−1+411yescharacteristic
293C4×C47—24no—
294C4×C47—42no—
295C4×C47—42no—
296C4×C47—42no—
297C4×C47—42no—
298C4×C47—42no—
299C4×C47—42no—
300Dic47—42no—
301Dic47—42no—
302Dic47—42no—
303Dic47—42no—
304Dic47—42no—
305Dic47—42no—
306Dic47—42no—
307Dic47—42no—
308#2833—4716no—
309C2×#401—471no—
310C2×#401—471no—
311C2×#400—471no—
312C2×#400—471no—
313C2×#400—471no—
314C2×#400—471no—
315C2×#400—471no—
316C2×#398—471no—
317C2×#398—471no—
318C2×#398—471no—
319C2×#395—471no—
320C2×#395D4711yescharacteristic
321C2×#391—471no—
322C2×#387—471no—
323C2×#387—471no—
324C2×C47#283318yescomplemented
325C2×C47C2×#53811yescharacteristic
326C2×C47C2×#54111yescharacteristic
327C2×C47C2×#54111yescharacteristic
328C2×C47C2×#56311yescharacteristic
329C2×C47C2×#56311yescharacteristic
330C2×C47C2×#56311yescharacteristic
331C2×C47C2×#56311yescharacteristic
332C23×Q8C2×D4711yescharacteristic
333C22×C4⋊C4—471no—
334C22×C4⋊C4—471no—
335C22×C4⋊C4—471no—
336C22×C4⋊C4—471no—
337C22×C4⋊C4—471no—
338C22×C4⋊C4—471no—
339C22×C4⋊C4—471no—
340C22×C4⋊C4—471no—
341C22×C4⋊C4C2×D4711yescharacteristic
342C22×C4⋊C4C2×D4711yescharacteristic
343C22×C4⋊C4C2×D4711yescharacteristic
344C22×C42—471no—
345#401—478no—
346#401—478no—
347#400—478no—
348#400—478no—
349#400—478no—
350#400—478no—
351#400—478no—
352#398—478no—
353#398—478no—
354#398—478no—
355#395—478no—
356#395C2×D4718yes—
357#391—478no—
358#387—478no—
359#387—478no—
360C2×#95—471no—
361C2×#95—471no—
362C2×#95—471no—
363C2×#95—471no—
364C2×#95—471no—
365C2×#95—471no—
366C2×#95—471no—
367C2×#95—471no—
368C2×#95—471no—
369C2×#95—471no—
370C2×#95—471no—
371C2×#95—471no—
372C2×#95—471no—
373C2×#95—471no—
374C2×#95—471no—
375C2×#95—471no—
376C2×#95—471no—
377C2×#95—471no—
378C2×#95—471no—
379C2×#95C2×D4711yescharacteristic
380C2×#95C2×D4711yescharacteristic
381C2×#95C2×D4711yescharacteristic
382C47C2×#283311yescharacteristic, complemented, Sylow
383C22×Q8—24no—
384C22×Q8—42no—
385C22×Q8—42no—
386C22×Q8C22×D4714yes—
387C23×C4—471no—
388C23×C4—471no—
389C23×C4—471no—
390C23×C4—471no—
391C23×C4—471no—
392C23×C4—471no—
393C23×C4—471no—
394C23×C4—471no—
395C23×C4C22×D4711yescharacteristic
396C23×C4C22×D4711yescharacteristic
397C23×C4C22×D4711yescharacteristic
398C23×C4C22×D4711yescharacteristic
399C23×C4C22×D4711yescharacteristic
400C23×C4C22×D4711yescharacteristic
401C23×C4C22×D4711yescharacteristic
402C2×C4⋊C4—24no—
403C2×C4⋊C4—42no—
404C2×C4⋊C4—42no—
405C2×C4⋊C4—474no—
406C2×C4⋊C4—474no—
407C2×C4⋊C4—474no—
408C2×C4⋊C4—474no—
409C2×C4⋊C4—474no—
410C2×C4⋊C4—474no—
411C2×C4⋊C4—474no—
412C2×C4⋊C4—474no—
413C2×C4⋊C4—944no—
414C2×C4⋊C4—1882no—
415C2×C4⋊C4—1882no—
416C2×C4⋊C4—1882no—
417C2×C4⋊C4—1882no—
418C2×C4⋊C4—1882no—
419C2×C4⋊C4—1882no—
420C2×C4⋊C4—1882no—
421C2×C4⋊C4C22×D4714yes—
422C2×C4⋊C4C22×D4714yes—
423C2×C4⋊C4C22×D4714yes—
424C2×C42—474no—
425C2×C42—1882no—
426#95—474no—
427#95—474no—
428#95—474no—
429#95—474no—
430#95—474no—
431#95—474no—
432#95—474no—
433#95—474no—
434#95—474no—
435#95—474no—
436#95—474no—
437#95—474no—
438#95—474no—
439#95—474no—
440#95—474no—
441#95—474no—
442#95—474no—
443#95—474no—
444#95—474no—
445#95C22×D4714yes—
446#95C22×D4714yes—
447#95C22×D4714yes—
448C24C23×D4711yescharacteristic
449C2×Q8—28no—
450C2×Q8—44no—
451C2×Q8—44no—
452C2×Q8—416no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—472no—
474C22×C4—472no—
475C22×C4—472no—
476C22×C4—472no—
477C22×C4—472no—
478C22×C4—472no—
479C22×C4—472no—
480C22×C4—472no—
481C22×C4—942no—
482C22×C4—942no—
483C22×C4—942no—
484C22×C4—942no—
485C22×C4—942no—
486C22×C4—942no—
487C22×C4—942no—
488C22×C4—942no—
489C22×C4—942no—
490C22×C4—942no—
491C22×C4—942no—
492C22×C4—942no—
493C22×C4—942no—
494C22×C4—942no—
495C22×C4—942no—
496C22×C4—942no—
497C22×C4—942no—
498C22×C4—942no—
499C22×C4—942no—
500C22×C4—942no—
501C22×C4—942no—
502C22×C4—942no—
503C22×C4—942no—
504C22×C4—942no—
505C22×C4#1062535214yes—
506C22×C4C23×D4712yes—
507C22×C4C23×D4712yes—
508C22×C4C23×D4712yes—
509C22×C4C23×D4712yes—
510C22×C4C23×D4712yes—
511C22×C4C23×D4712yes—
512C22×C4C23×D4712yes—
513C4⋊C4—28no—
514C4⋊C4—44no—
515C4⋊C4—44no—
516C4⋊C4—948no—
517C4⋊C4—1884no—
518C4⋊C4—1884no—
519C4⋊C4—1884no—
520C4⋊C4—1884no—
521C4⋊C4—1884no—
522C4⋊C4—1884no—
523C4⋊C4—1884no—
524C42—1884no—
525C23C2×#1062535212yes—
526C23#1309406912yes—
527C23#1309406912yes—
528C23#1309407112yes—
529C23#1309407212yes—
530C23#1309407212yes—
531C23#1309407212yes—
532C23C24×D4711yescharacteristic
533Q8—416no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—28no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—44no—
556C2×C4—44no—
557C2×C4—44no—
558C2×C4—44no—
559C2×C4—44no—
560C2×C4—44no—
561C2×C4—942no—
562C2×C4—942no—
563C2×C4—942no—
564C2×C4—942no—
565C2×C4—942no—
566C2×C4—942no—
567C2×C4—942no—
568C2×C4—942no—
569C2×C4—942no—
570C2×C4—942no—
571C2×C4—942no—
572C2×C4—942no—
573C2×C4—942no—
574C2×C4—942no—
575C2×C4—942no—
576C2×C4—942no—
577C2×C4—942no—
578C2×C4—942no—
579C2×C4—942no—
580C2×C4—942no—
581C2×C4—942no—
582C2×C4—942no—
583C2×C4—942no—
584C2×C4—942no—
585C2×C4—1884no—
586C2×C4—1884no—
587C2×C4—1884no—
588C2×C4—1884no—
589C2×C4—1884no—
590C2×C4—1884no—
591C2×C4—1884no—
592C2×C4—1884no—
593C2×C4C2×#1062535214yes—
594C22#1568970814yes—
595C22#1568973314yes—
596C22#1568973414yes—
597C22#1568987214yes—
598C22#1568987214yes—
599C22#1568987414yes—
600C22#1568987414yes—
601C22C22×#1062535211yescharacteristic
602C22C2×#1309406911yescharacteristic
603C22C2×#1309406911yescharacteristic
604C22C2×#1309407111yescharacteristic
605C22C2×#1309407211yescharacteristic
606C22C2×#1309407211yescharacteristic
607C22C2×#1309407211yescharacteristic
608C4—24no—
609C4—42no—
610C4—42no—
611C4—42no—
612C4—42no—
613C4—42no—
614C4—42no—
615C4—1882no—
616C4—1882no—
617C4—1882no—
618C4—1882no—
619C4—1882no—
620C4—1882no—
621C4—1882no—
622C4—1882no—
623C2#2025156718yesdirect product factor
624C2C2×#1568970811yescharacteristic
625C2C2×#1568973311yescharacteristic
626C2C2×#1568973411yescharacteristic
627C2C2×#1568987211yescharacteristic
628C2C2×#1568987211yescharacteristic
629C2C2×#1568987411yescharacteristic
630C2C2×#1568987411yescharacteristic
subgroupG/H
centerC24C23×D47
commutator, cosocleC23×C47C25
FrattiniC23C24×D47
FittingC2×C47×#395C2
socle, prime radicalC24×C47C24
hypercenterC2×#395D47
hypocenterC47C2×#2833
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#395

Complements

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

NH ≅ G/Ntype
1. #20251567C2direct (N × H)
324. C2×C47#2833semidirect
382. C47C2×#2833semidirect
623. C2#20251567direct (N × H)

Maximal subgroups

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

subgroupindex
#202515672
C2×C47⋊#4012
C2×#156890652
C2×#156890642
C2×#156890622
C2×#156890612
C2×#156890562
C2×#156890542
C2×#156890422
C2×#156890302
C2×#156890092
C2×#156890052
C2×C47×#3952
C2×#283347