Finite Group Databasebeta

← C2×#20249268 #26383207

Subgroups — C2×#20249268 #26383207

Order 12032.

2286 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094014C211yesmaximal, characteristic
2C22×C4×Dic94C211yesmaximal, characteristic
3#20249268C2116yesmaximal, direct product factor
4C2×#15689065C211yesmaximal, characteristic
5C2×#15689065C211yesmaximal, characteristic
6C2×#15689064C211yesmaximal, characteristic
7C2×#15689064C211yesmaximal, characteristic
8C2×#15689057C211yesmaximal, characteristic
9C2×#15689056C211yesmaximal, characteristic
10C2×#15689044C211yesmaximal, characteristic
11C2×#15689043C211yesmaximal, characteristic
12C2×#15689008C211yesmaximal, characteristic
13C2×#15689007C211yesmaximal, characteristic
14C2×#15689004C211yesmaximal, characteristic
15C2×#15688990C211yesmaximal, characteristic
16C2×C47×#387C211yesmaximal, characteristic
17C23×Dic94C2211yescharacteristic
18C2×#13094014—28no—
19C2×#13094014C2218yes—
20C2×C4×Dic94—28no—
21C2×C4×Dic94C2218yes—
22C22×C4⋊Dic47C2211yescharacteristic
23C22×C4⋊Dic47C2211yescharacteristic
24C22×C4⋊Dic47C2211yescharacteristic
25C22×Dic47⋊C4C2211yescharacteristic
26C22×Dic47⋊C4C2211yescharacteristic
27C22×Dic47⋊C4C2211yescharacteristic
28C22×Dic47⋊C4C2211yescharacteristic
29C22×Dic47⋊C4C2211yescharacteristic
30C22×Dic47⋊C4C2211yescharacteristic
31C22×Dic47⋊C4C2211yescharacteristic
32C22×Dic47⋊C4C2211yescharacteristic
33C22×C4×Dic47C2211yescharacteristic
34C22×C4×Dic47C2211yescharacteristic
35#15689065C2218yes—
36#15689065C2218yes—
37#15689064C2218yes—
38#15689064C2218yes—
39#15689057C2218yes—
40#15689056C2218yes—
41#15689044C2218yes—
42#15689043C2218yes—
43#15689008C2218yes—
44#15689007C2218yes—
45#15689004C2218yes—
46#15688990C2218yes—
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
59C2×C47⋊#95C2211yescharacteristic
60C2×C47⋊#95C2211yescharacteristic
61C22×C4⋊C4×C47C2211yescharacteristic
62C22×C4⋊C4×C47C2211yescharacteristic
63C22×C42×C47C2211yescharacteristic
64C47×#387C2218yes—
65C2×#95×C47C2211yescharacteristic
66C2×#95×C47C2211yescharacteristic
67C2×#95×C47C2211yescharacteristic
68C2×#95×C47C2211yescharacteristic
69C22×Dic94—24no—
70C22×Dic94—24no—
71C22×Dic94—24no—
72C22×Dic94C2314yes—
73C23×Dic47C2311yescharacteristic
74C23×Dic47C2311yescharacteristic
75C23×Dic47C2311yescharacteristic
76C23×Dic47C2311yescharacteristic
77C23×Dic47C2311yescharacteristic
78C23×Dic47C2311yescharacteristic
79C23×Dic47C2311yescharacteristic
80C23×Dic47C2311yescharacteristic
81#13094014—232no—
82C4×Dic94—232no—
83C2×C4⋊Dic47—24no—
84C2×C4⋊Dic47—24no—
85C2×C4⋊Dic47—24no—
86C2×C4⋊Dic47C2314yes—
87C2×C4⋊Dic47C2314yes—
88C2×C4⋊Dic47C2314yes—
89C2×Dic47⋊C4—24no—
90C2×Dic47⋊C4—24no—
91C2×Dic47⋊C4—24no—
92C2×Dic47⋊C4—24no—
93C2×Dic47⋊C4—24no—
94C2×Dic47⋊C4—24no—
95C2×Dic47⋊C4—24no—
96C2×Dic47⋊C4—24no—
97C2×Dic47⋊C4C2314yes—
98C2×Dic47⋊C4C2314yes—
99C2×Dic47⋊C4C2314yes—
100C2×Dic47⋊C4C2314yes—
101C2×Dic47⋊C4C2314yes—
102C2×Dic47⋊C4C2314yes—
103C2×Dic47⋊C4C2314yes—
104C2×Dic47⋊C4C2314yes—
105C2×C4×Dic47—24no—
106C2×C4×Dic47D418yes—
107C2×C4×Dic47C2314yes—
108C2×C4×Dic47C2314yes—
109C47⋊#95C2314yes—
110C47⋊#95C2314yes—
111C47⋊#95C2314yes—
112C47⋊#95C2314yes—
113C47⋊#95C2314yes—
114C47⋊#95C2314yes—
115C47⋊#95C2314yes—
116C47⋊#95C2314yes—
117C47⋊#95C2314yes—
118C47⋊#95C2314yes—
119C47⋊#95C2314yes—
120C47⋊#95C2314yes—
121C47⋊#95C2314yes—
122C47⋊#95C2314yes—
123C23×C4×C47C2311yescharacteristic
124C23×C4×C47C2311yescharacteristic
125C23×C4×C47C2311yescharacteristic
126C23×C4×C47C2311yescharacteristic
127C23×C4×C47C2311yescharacteristic
128C23×C4×C47C2311yescharacteristic
129C23×C4×C47C2311yescharacteristic
130C2×C4⋊C4×C47—24no—
131C2×C4⋊C4×C47—24no—
132C2×C4⋊C4×C47C2314yes—
133C2×C4⋊C4×C47C2314yes—
134C2×C42×C47—24no—
135C2×C42×C47C2314yes—
136#95×C47C2314yes—
137#95×C47C2314yes—
138#95×C47C2314yes—
139#95×C47C2314yes—
140C24×C47C2411yescharacteristic
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—22no—
158C22×C4×C47—22no—
159C22×C4×C47—22no—
160C22×C4×C47C2×D414yes—
161C22×C4×C47#4114yes—
162C22×C4×C47C2412yes—
163C22×C4×C47C2412yes—
164C22×C4×C47C2412yes—
165C22×C4×C47C2412yes—
166C22×C4×C47C2412yes—
167C22×C4×C47C2412yes—
168C22×C4×C47C2412yes—
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×Dic47—22no—
190C22×Dic47C2×D414yes—
191C22×Dic47C2×D414yes—
192C22×Dic47#4114yes—
193C22×Dic47C2412yes—
194C22×Dic47C2412yes—
195C22×Dic47C2412yes—
196C22×Dic47C2412yes—
197C22×Dic47C2412yes—
198C22×Dic47C2412yes—
199C22×Dic47C2412yes—
200C22×Dic47C2412yes—
201C2×Dic94—232no—
202C2×Dic94—28no—
203C2×Dic94—28no—
204C2×Dic94—28no—
205C4⋊C4×C47—28no—
206C4⋊C4×C47—28no—
207C42×C47—28no—
208C4⋊Dic47—28no—
209C4⋊Dic47—28no—
210C4⋊Dic47—28no—
211Dic47⋊C4—28no—
212Dic47⋊C4—28no—
213Dic47⋊C4—28no—
214Dic47⋊C4—28no—
215Dic47⋊C4—28no—
216Dic47⋊C4—28no—
217Dic47⋊C4—28no—
218Dic47⋊C4—28no—
219C4×Dic47—28no—
220C4×Dic47C2×D4116yes—
221C23×C47C22×D412yes—
222C23×C47C2×#4112yes—
223C23×C47C2×#4112yes—
224C23×C472−1+412yes—
225C23×C472−1+412yes—
226C23×C472−1+412yes—
227C23×C472−1+412yes—
228C23×C47C2511yescharacteristic
229C2×C4×C47—28no—
230C2×C4×C47—28no—
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—22no—
240C2×C4×C47—22no—
241C2×C4×C47—22no—
242C2×C4×C47—22no—
243C2×C4×C47—22no—
244C2×C4×C47—22no—
245C2×C4×C47—22no—
246C2×C4×C47—22no—
247C2×C4×C47—22no—
248C2×C4×C47—22no—
249C2×C4×C47—22no—
250C2×C4×C47—44no—
251C2×C4×C47—44no—
252C2×C4×C47—44no—
253C2×C4×C47—44no—
254C2×C4×C47—44no—
255C2×C4×C47C22×D414yes—
256C2×C4×C47C2×#4114yes—
257C2×Dic47—28no—
258C2×Dic47—28no—
259C2×Dic47—28no—
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—22no—
271C2×Dic47—22no—
272C2×Dic47—22no—
273C2×Dic47—22no—
274C2×Dic47—22no—
275C2×Dic47—22no—
276C2×Dic47—22no—
277C2×Dic47—22no—
278C2×Dic47—22no—
279C2×Dic47—22no—
280C2×Dic47—22no—
281C2×Dic47—44no—
282C2×Dic47—44no—
283C2×Dic47—44no—
284C2×Dic47—44no—
285C2×Dic47—44no—
286C2×Dic47C22×D414yes—
287C2×Dic47C22×D414yes—
288C2×Dic47C2×#4114yes—
289Dic94—232no—
290C2×#2634—471nomaximal, Sylow
291C22×C47#52514yes—
292C22×C47#53614yes—
293C22×C47#53614yes—
294C22×C47#54114yes—
295C22×C47#54114yes—
296C22×C47#54114yes—
297C22×C47#54114yes—
298C22×C47C23×D411yescharacteristic
299C22×C47C22×#4111yescharacteristic
300C22×C47C22×#4111yescharacteristic
301C22×C47C2×2−1+411yescharacteristic
302C22×C47C2×2−1+411yescharacteristic
303C22×C47C2×2−1+411yescharacteristic
304C22×C47C2×2−1+411yescharacteristic
305C4×C47—24no—
306C4×C47—24no—
307C4×C47—42no—
308C4×C47—42no—
309C4×C47—42no—
310C4×C47—42no—
311C4×C47—42no—
312Dic47—24no—
313Dic47—24no—
314Dic47—24no—
315Dic47—42no—
316Dic47—42no—
317Dic47—42no—
318Dic47—42no—
319Dic47—42no—
320C22×#125—471no—
321C22×C4×Q8—471no—
322#2634—4716no—
323C2×#400—471no—
324C2×#400—471no—
325C2×#400—471no—
326C2×#400—471no—
327C2×#398—471no—
328C2×#398—471no—
329C2×#395—471no—
330C2×#395—471no—
331C2×#387—471no—
332C2×#387—471no—
333C2×#387—471no—
334C2×#387D4711yescharacteristic
335C2×#383—471no—
336C2×C47#263418yescomplemented
337C2×C47C2×#52511yescharacteristic
338C2×C47C2×#53611yescharacteristic
339C2×C47C2×#53611yescharacteristic
340C2×C47C2×#54111yescharacteristic
341C2×C47C2×#54111yescharacteristic
342C2×C47C2×#54111yescharacteristic
343C2×C47C2×#54111yescharacteristic
344C23×Q8—471no—
345C2×#125—478no—
346C2×#125—948no—
347C2×C4×Q8—478no—
348C2×C4×Q8—948no—
349C22×C4⋊C4—471no—
350C22×C4⋊C4—471no—
351C22×C4⋊C4—471no—
352C22×C4⋊C4—471no—
353C22×C4⋊C4—471no—
354C22×C4⋊C4—471no—
355C22×C4⋊C4—471no—
356C22×C4⋊C4—471no—
357C22×C4⋊C4—471no—
358C22×C4⋊C4—471no—
359C22×C4⋊C4—471no—
360C22×C4⋊C4C2×D4711yescharacteristic
361C22×C4⋊C4C2×D4711yescharacteristic
362C22×C42—471no—
363C22×C42—471no—
364C22×C42C2×D4711yescharacteristic
365#400—478no—
366#400—478no—
367#400—478no—
368#400—478no—
369#398—478no—
370#398—478no—
371#395—478no—
372#395—478no—
373#387—478no—
374#387—478no—
375#387—478no—
376#387C2×D4718yes—
377#383—478no—
378C2×#95—471no—
379C2×#95—471no—
380C2×#95—471no—
381C2×#95—471no—
382C2×#95—471no—
383C2×#95—471no—
384C2×#95—471no—
385C2×#95—471no—
386C2×#95—471no—
387C2×#95—471no—
388C2×#95—471no—
389C2×#95—471no—
390C2×#95—471no—
391C2×#95—471no—
392C2×#95C2×D4711yescharacteristic
393C2×#95C2×D4711yescharacteristic
394C2×#95C2×D4711yescharacteristic
395C2×#95C2×D4711yescharacteristic
396C47C2×#263411yescharacteristic, complemented, Sylow
397C22×Q8—474no—
398C22×Q8—944no—
399C22×Q8—944no—
400C22×Q8—944no—
401C23×C4—471no—
402C23×C4—471no—
403C23×C4—471no—
404C23×C4—471no—
405C23×C4—471no—
406C23×C4—471no—
407C23×C4—471no—
408C23×C4—471no—
409C23×C4C22×D4711yescharacteristic
410C23×C4C22×D4711yescharacteristic
411C23×C4C22×D4711yescharacteristic
412C23×C4C22×D4711yescharacteristic
413C23×C4C22×D4711yescharacteristic
414C23×C4C22×D4711yescharacteristic
415C23×C4C22×D4711yescharacteristic
416#125—9432no—
417C4×Q8—9432no—
418C2×C4⋊C4—24no—
419C2×C4⋊C4—24no—
420C2×C4⋊C4—474no—
421C2×C4⋊C4—474no—
422C2×C4⋊C4—474no—
423C2×C4⋊C4—474no—
424C2×C4⋊C4—474no—
425C2×C4⋊C4—474no—
426C2×C4⋊C4—474no—
427C2×C4⋊C4—474no—
428C2×C4⋊C4—474no—
429C2×C4⋊C4—474no—
430C2×C4⋊C4—474no—
431C2×C4⋊C4—944no—
432C2×C4⋊C4—944no—
433C2×C4⋊C4—944no—
434C2×C4⋊C4—944no—
435C2×C4⋊C4—944no—
436C2×C4⋊C4—944no—
437C2×C4⋊C4—944no—
438C2×C4⋊C4—944no—
439C2×C4⋊C4—944no—
440C2×C4⋊C4—944no—
441C2×C4⋊C4—944no—
442C2×C4⋊C4C22×D4714yes—
443C2×C4⋊C4C22×D4714yes—
444C2×C42—24no—
445C2×C42—478no—
446C2×C42—474no—
447C2×C42—474no—
448C2×C42—944no—
449C2×C42C22×D4714yes—
450#95—474no—
451#95—474no—
452#95—474no—
453#95—474no—
454#95—474no—
455#95—474no—
456#95—474no—
457#95—474no—
458#95—474no—
459#95—474no—
460#95—474no—
461#95—474no—
462#95—474no—
463#95—474no—
464#95C22×D4714yes—
465#95C22×D4714yes—
466#95C22×D4714yes—
467#95C22×D4714yes—
468C24C23×D4711yescharacteristic
469C2×Q8—948no—
470C2×Q8—948no—
471C2×Q8—9432no—
472C2×Q8—948no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—474no—
493C22×C4—474no—
494C22×C4—474no—
495C22×C4—472no—
496C22×C4—472no—
497C22×C4—472no—
498C22×C4—472no—
499C22×C4—472no—
500C22×C4—472no—
501C22×C4—472no—
502C22×C4—472no—
503C22×C4—942no—
504C22×C4—942no—
505C22×C4—942no—
506C22×C4—942no—
507C22×C4—942no—
508C22×C4—942no—
509C22×C4—942no—
510C22×C4—942no—
511C22×C4—942no—
512C22×C4—942no—
513C22×C4—942no—
514C22×C4—942no—
515C22×C4—942no—
516C22×C4—942no—
517C22×C4—942no—
518C22×C4—942no—
519C22×C4—942no—
520C22×C4—942no—
521C22×C4—942no—
522C22×C4—942no—
523C22×C4—942no—
524C22×C4#1062535014yes—
525C22×C4D4×D4714yes—
526C22×C4C23×D4712yes—
527C22×C4C23×D4712yes—
528C22×C4C23×D4712yes—
529C22×C4C23×D4712yes—
530C22×C4C23×D4712yes—
531C22×C4C23×D4712yes—
532C22×C4C23×D4712yes—
533C4⋊C4—28no—
534C4⋊C4—28no—
535C4⋊C4—948no—
536C4⋊C4—948no—
537C4⋊C4—948no—
538C4⋊C4—948no—
539C4⋊C4—948no—
540C4⋊C4—948no—
541C4⋊C4—948no—
542C4⋊C4—948no—
543C4⋊C4—948no—
544C4⋊C4—948no—
545C4⋊C4—948no—
546C42—28no—
547C42—4716no—
548C42—948no—
549C23C2×D4×D4712yes—
550C23#41×D4712yes—
551C23C2×#1062535012yes—
552C23#1309407112yes—
553C23#1309407112yes—
554C23#1309407112yes—
555C23#1309407212yes—
556C23C24×D4711yescharacteristic
557Q8—9432no—
558C2×C4—28no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—28no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—44no—
580C2×C4—44no—
581C2×C4—44no—
582C2×C4—44no—
583C2×C4—44no—
584C2×C4—474no—
585C2×C4—474no—
586C2×C4—474no—
587C2×C4—948no—
588C2×C4—948no—
589C2×C4—942no—
590C2×C4—942no—
591C2×C4—942no—
592C2×C4—942no—
593C2×C4—948no—
594C2×C4—942no—
595C2×C4—942no—
596C2×C4—942no—
597C2×C4—942no—
598C2×C4—942no—
599C2×C4—942no—
600C2×C4—942no—
601C2×C4—942no—
602C2×C4—942no—
603C2×C4—942no—
604C2×C4—942no—
605C2×C4—942no—
606C2×C4—942no—
607C2×C4—942no—
608C2×C4—942no—
609C2×C4—942no—
610C2×C4—942no—
611C2×C4—1884no—
612C2×C4—1884no—
613C2×C4—1884no—
614C2×C4—1884no—
615C2×C4—1884no—
616C2×C4C2×D4×D4714yes—
617C2×C4C2×#1062535014yes—
618C22#1568963214yes—
619C22#1568969514yes—
620C22#1568969614yes—
621C22#1568973014yes—
622C22#1568973114yes—
623C22#1568973214yes—
624C22#1568973514yes—
625C22C22×D4×D4711yescharacteristic
626C22C2×#41×D4711yescharacteristic
627C22C22×#1062535011yescharacteristic
628C22C2×#1309407111yescharacteristic
629C22C2×#1309407111yescharacteristic
630C22C2×#1309407111yescharacteristic
631C22C2×#1309407211yescharacteristic
632C4—24no—
633C4—24no—
634C4—42no—
635C4—42no—
636C4—42no—
637C4—42no—
638C4—42no—
639C4—944no—
640C4—944no—
641C4—944no—
642C4—1882no—
643C4—1882no—
644C4—1882no—
645C4—1882no—
646C4—1882no—
647C2#2024926818yesdirect product factor
648C2C2×#1568963211yescharacteristic
649C2C2×#1568969511yescharacteristic
650C2C2×#1568969611yescharacteristic
651C2C2×#1568973011yescharacteristic
652C2C2×#1568973111yescharacteristic
653C2C2×#1568973211yescharacteristic
654C2C2×#1568973511yescharacteristic
subgroupG/H
centerC24C23×D47
commutator, cosocleC23×C47C25
FrattiniC23C24×D47
FittingC2×C47×#387C2
socle, prime radicalC24×C47C24
hypercenterC2×#387D47
hypocenterC47C2×#2634
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
3. #20249268C2direct (N × H)
336. C2×C47#2634semidirect
396. C47C2×#2634semidirect
647. C2#20249268direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940142
C22×C4×Dic942
#202492682
C2×#156890652
C2×#156890642
C2×#156890572
C2×#156890562
C2×#156890442
C2×#156890432
C2×#156890082
C2×#156890072
C2×#156890042
C2×#156889902
C2×C47×#3872
C2×#263447