Finite Group Databasebeta

← C2×#20249579 #26383029

Subgroups — C2×#20249579 #26383029

Order 12032.

1918 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20249579C2116yesmaximal, direct product factor
2C2×#15689061C211yesmaximal, characteristic
3C2×#15689061C211yesmaximal, characteristic
4C2×#15689056C211yesmaximal, characteristic
5C2×#15689054C211yesmaximal, characteristic
6C2×#15689054C211yesmaximal, characteristic
7C2×#15689053C211yesmaximal, characteristic
8C2×#15689043C211yesmaximal, characteristic
9C2×#15689043C211yesmaximal, characteristic
10C2×#15689027C211yesmaximal, characteristic
11C2×#15689010C211yesmaximal, characteristic
12C2×#15689007C211yesmaximal, characteristic
13C2×#15688990C211yesmaximal, characteristic
14C2×#15688987C211yesmaximal, characteristic
15C2×C4×Dic47⋊C4C211yesmaximal, characteristic
16C2×C47×#389C211yesmaximal, characteristic
17C23×Dic94C2211yescharacteristic
18C22×C4⋊Dic47C2211yescharacteristic
19C22×Dic47⋊C4C2211yescharacteristic
20C22×Dic47⋊C4C2211yescharacteristic
21C22×Dic47⋊C4C2211yescharacteristic
22C22×Dic47⋊C4C2211yescharacteristic
23C22×Dic47⋊C4C2211yescharacteristic
24C22×Dic47⋊C4C2211yescharacteristic
25C22×Dic47⋊C4C2211yescharacteristic
26C22×Dic47⋊C4C2211yescharacteristic
27C22×C4×Dic47C2211yescharacteristic
28C22×C4×Dic47C2211yescharacteristic
29#15689061C2218yes—
30#15689061C2218yes—
31#15689056C2218yes—
32#15689054C2218yes—
33#15689054C2218yes—
34#15689053C2218yes—
35#15689043C2218yes—
36#15689043C2218yes—
37#15689027C2218yes—
38#15689010C2218yes—
39#15689007C2218yes—
40#15688990C2218yes—
41#15688987C2218yes—
42C4×Dic47⋊C4C2218yes—
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
59C22×C4⋊C4×C47C2211yescharacteristic
60C22×C4⋊C4×C47C2211yescharacteristic
61C22×C4⋊C4×C47C2211yescharacteristic
62C22×C4⋊C4×C47C2211yescharacteristic
63C22×C42×C47C2211yescharacteristic
64C47×#389C2218yes—
65C2×#95×C47C2211yescharacteristic
66C2×#95×C47C2211yescharacteristic
67C22×Dic94—24no—
68C22×Dic94—42no—
69C22×Dic94—42no—
70C22×Dic94C2314yes—
71C23×Dic47C2311yescharacteristic
72C23×Dic47C2311yescharacteristic
73C23×Dic47C2311yescharacteristic
74C23×Dic47C2311yescharacteristic
75C23×Dic47C2311yescharacteristic
76C23×Dic47C2311yescharacteristic
77C23×Dic47C2311yescharacteristic
78C23×Dic47C2311yescharacteristic
79C2×C4⋊Dic47—42no—
80C2×C4⋊Dic47C2314yes—
81C2×Dic47⋊C4—24no—
82C2×Dic47⋊C4—24no—
83C2×Dic47⋊C4—24no—
84C2×Dic47⋊C4—24no—
85C2×Dic47⋊C4—42no—
86C2×Dic47⋊C4—42no—
87C2×Dic47⋊C4—42no—
88C2×Dic47⋊C4—42no—
89C2×Dic47⋊C4C2314yes—
90C2×Dic47⋊C4C2314yes—
91C2×Dic47⋊C4C2314yes—
92C2×Dic47⋊C4C2314yes—
93C2×Dic47⋊C4C2314yes—
94C2×Dic47⋊C4C2314yes—
95C2×Dic47⋊C4C2314yes—
96C2×Dic47⋊C4C2314yes—
97C2×C4×Dic47—42no—
98C2×C4×Dic47Q818yescomplemented
99C2×C4×Dic47C2314yes—
100C2×C4×Dic47C2314yes—
101C47⋊#95C2314yes—
102C47⋊#95C2314yes—
103C47⋊#95C2314yes—
104C47⋊#95C2314yes—
105C47⋊#95C2314yes—
106C47⋊#95C2314yes—
107C47⋊#95C2314yes—
108C47⋊#95C2314yes—
109C47⋊#95C2314yes—
110C47⋊#95C2314yes—
111C47⋊#95C2314yes—
112C47⋊#95C2314yes—
113C47⋊#95C2314yes—
114C47⋊#95C2314yes—
115C47⋊#95C2314yes—
116C47⋊#95C2314yes—
117C23×C4×C47C2311yescharacteristic
118C23×C4×C47C2311yescharacteristic
119C23×C4×C47C2311yescharacteristic
120C23×C4×C47C2311yescharacteristic
121C23×C4×C47C2311yescharacteristic
122C23×C4×C47C2311yescharacteristic
123C23×C4×C47C2311yescharacteristic
124C2×C4⋊C4×C47—24no—
125C2×C4⋊C4×C47—42no—
126C2×C4⋊C4×C47—42no—
127C2×C4⋊C4×C47—42no—
128C2×C4⋊C4×C47C2314yes—
129C2×C4⋊C4×C47C2314yes—
130C2×C4⋊C4×C47C2314yes—
131C2×C4⋊C4×C47C2314yes—
132C2×C42×C47—42no—
133C2×C42×C47C2314yes—
134#95×C47C2314yes—
135#95×C47C2314yes—
136C24×C47C2411yescharacteristic
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×C47C2×Q814yes—
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×Dic47C2×Q814yes—
187C22×Dic47C2×Q814yes—
188C22×Dic47#4114yes—
189C22×Dic47C2412yes—
190C22×Dic47C2412yes—
191C22×Dic47C2412yes—
192C22×Dic47C2412yes—
193C22×Dic47C2412yes—
194C22×Dic47C2412yes—
195C22×Dic47C2412yes—
196C22×Dic47C2412yes—
197C2×Dic94—28no—
198C2×Dic94—44no—
199C2×Dic94—44no—
200C2×Dic94—416no—
201C4⋊C4×C47—28no—
202C4⋊C4×C47—44no—
203C4⋊C4×C47—44no—
204C4⋊C4×C47—44no—
205C42×C47—44no—
206C4⋊Dic47—44no—
207Dic47⋊C4—28no—
208Dic47⋊C4—28no—
209Dic47⋊C4—28no—
210Dic47⋊C4—28no—
211Dic47⋊C4—44no—
212Dic47⋊C4—44no—
213Dic47⋊C4—44no—
214Dic47⋊C4—44no—
215C4×Dic47—44no—
216C4×Dic47C2×Q8116yescomplemented
217C23×C47C22×Q812yes—
218C23×C47C2×#4112yes—
219C23×C47C2×#4112yes—
220C23×C47H(5,𝔽2)12yes—
221C23×C47H(5,𝔽2)12yes—
222C23×C472−1+412yes—
223C23×C472−1+412yes—
224C23×C47C2511yescharacteristic
225C2×C4×C47—28no—
226C2×C4×C47—28no—
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—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—44no—
247C2×C4×C47—44no—
248C2×C4×C47—44no—
249C2×C4×C47—44no—
250C2×C4×C47—44no—
251C2×C4×C47C22×Q814yes—
252C2×C4×C47C2×#4114yes—
253C2×Dic47—28no—
254C2×Dic47—28no—
255C2×Dic47—28no—
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—22no—
271C2×Dic47—22no—
272C2×Dic47—22no—
273C2×Dic47—22no—
274C2×Dic47—22no—
275C2×Dic47—22no—
276C2×Dic47—22no—
277C2×Dic47—44no—
278C2×Dic47—44no—
279C2×Dic47—44no—
280C2×Dic47—44no—
281C2×Dic47—44no—
282C2×Dic47C22×Q814yes—
283C2×Dic47C22×Q814yes—
284C2×Dic47C2×#4114yes—
285Dic94—416no—
286C2×#2666—471nomaximal, Sylow
287C22×C47#53314yes—
288C22×C47#53814yes—
289C22×C47#53914yes—
290C22×C47#54114yes—
291C22×C47#54214yes—
292C22×C47#54414yes—
293C22×C47#54414yes—
294C22×C47C23×Q811yescharacteristic
295C22×C47C22×#4111yescharacteristic
296C22×C47C22×#4111yescharacteristic
297C22×C47C2×H(5,𝔽2)11yescharacteristic
298C22×C47C2×H(5,𝔽2)11yescharacteristic
299C22×C47C2×2−1+411yescharacteristic
300C22×C47C2×2−1+411yescharacteristic
301C4×C47—24no—
302C4×C47—24no—
303C4×C47—42no—
304C4×C47—42no—
305C4×C47—42no—
306C4×C47—42no—
307C4×C47—42no—
308Dic47—24no—
309Dic47—24no—
310Dic47—24no—
311Dic47—42no—
312Dic47—42no—
313Dic47—42no—
314Dic47—42no—
315Dic47—42no—
316#2666—4716no—
317C2×#400—471no—
318C2×#400—471no—
319C2×#398—471no—
320C2×#398—471no—
321C2×#398—471no—
322C2×#398—471no—
323C2×#395—471no—
324C2×#395—471no—
325C2×#391—471no—
326C2×#389D4711yescharacteristic
327C2×#387—471no—
328C2×#387—471no—
329C2×#383—471no—
330C2×#382—471no—
331C2×C4×C4⋊C4—471no—
332C2×C47#266618yescomplemented
333C2×C47C2×#53311yescharacteristic
334C2×C47C2×#53811yescharacteristic
335C2×C47C2×#53911yescharacteristic
336C2×C47C2×#54111yescharacteristic
337C2×C47C2×#54211yescharacteristic
338C2×C47C2×#54411yescharacteristic
339C2×C47C2×#54411yescharacteristic
340C23×Q8—471no—
341C22×C4⋊C4—471no—
342C22×C4⋊C4—471no—
343C22×C4⋊C4—471no—
344C22×C4⋊C4—471no—
345C22×C4⋊C4—471no—
346C22×C4⋊C4—471no—
347C22×C4⋊C4—471no—
348C22×C4⋊C4—471no—
349C22×C4⋊C4—471no—
350C22×C4⋊C4C2×D4711yescharacteristic
351C22×C4⋊C4C2×D4711yescharacteristic
352C22×C4⋊C4C2×D4711yescharacteristic
353C22×C4⋊C4C2×D4711yescharacteristic
354C22×C42—471no—
355C22×C42—471no—
356C22×C42C2×D4711yescharacteristic
357#400—478no—
358#400—478no—
359#398—478no—
360#398—478no—
361#398—478no—
362#398—478no—
363#395—478no—
364#395—478no—
365#391—478no—
366#389C2×D4718yes—
367#387—478no—
368#387—478no—
369#383—478no—
370#382—478no—
371C4×C4⋊C4—478no—
372C2×#95—471no—
373C2×#95—471no—
374C2×#95—471no—
375C2×#95—471no—
376C2×#95—471no—
377C2×#95—471no—
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×#95C2×D4711yescharacteristic
389C2×#95C2×D4711yescharacteristic
390C47C2×#266611yescharacteristic, complemented, Sylow
391C22×Q8—474no—
392C22×Q8—944no—
393C22×Q8—1882no—
394C22×Q8—1882no—
395C23×C4—471no—
396C23×C4—471no—
397C23×C4—471no—
398C23×C4—471no—
399C23×C4—471no—
400C23×C4—471no—
401C23×C4—471no—
402C23×C4—471no—
403C23×C4C22×D4711yescharacteristic
404C23×C4C22×D4711yescharacteristic
405C23×C4C22×D4711yescharacteristic
406C23×C4C22×D4711yescharacteristic
407C23×C4C22×D4711yescharacteristic
408C23×C4C22×D4711yescharacteristic
409C23×C4C22×D4711yescharacteristic
410C2×C4⋊C4—24no—
411C2×C4⋊C4—42no—
412C2×C4⋊C4—42no—
413C2×C4⋊C4—42no—
414C2×C4⋊C4—474no—
415C2×C4⋊C4—474no—
416C2×C4⋊C4—474no—
417C2×C4⋊C4—474no—
418C2×C4⋊C4—474no—
419C2×C4⋊C4—474no—
420C2×C4⋊C4—474no—
421C2×C4⋊C4—474no—
422C2×C4⋊C4—474no—
423C2×C4⋊C4—944no—
424C2×C4⋊C4—944no—
425C2×C4⋊C4—944no—
426C2×C4⋊C4—944no—
427C2×C4⋊C4—1882no—
428C2×C4⋊C4—1882no—
429C2×C4⋊C4—1882no—
430C2×C4⋊C4—1882no—
431C2×C4⋊C4—1882no—
432C2×C4⋊C4C22×D4714yes—
433C2×C4⋊C4C22×D4714yes—
434C2×C4⋊C4C22×D4714yes—
435C2×C4⋊C4C22×D4714yes—
436C2×C42—42no—
437C2×C42—478no—
438C2×C42—474no—
439C2×C42—474no—
440C2×C42—1882no—
441C2×C42C22×D4714yes—
442#95—474no—
443#95—474no—
444#95—474no—
445#95—474no—
446#95—474no—
447#95—474no—
448#95—474no—
449#95—474no—
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#95C22×D4714yes—
459#95C22×D4714yes—
460C24C23×D4711yescharacteristic
461C2×Q8—948no—
462C2×Q8—1884no—
463C2×Q8—1884no—
464C2×Q8—18816no—
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—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—474no—
485C22×C4—474no—
486C22×C4—474no—
487C22×C4—472no—
488C22×C4—472no—
489C22×C4—472no—
490C22×C4—472no—
491C22×C4—472no—
492C22×C4—472no—
493C22×C4—472no—
494C22×C4—472no—
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—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#1062535014yes—
517C22×C4Q8×D4714yes—
518C22×C4C23×D4712yes—
519C22×C4C23×D4712yes—
520C22×C4C23×D4712yes—
521C22×C4C23×D4712yes—
522C22×C4C23×D4712yes—
523C22×C4C23×D4712yes—
524C22×C4C23×D4712yes—
525C4⋊C4—28no—
526C4⋊C4—44no—
527C4⋊C4—44no—
528C4⋊C4—44no—
529C4⋊C4—948no—
530C4⋊C4—948no—
531C4⋊C4—948no—
532C4⋊C4—948no—
533C4⋊C4—1884no—
534C4⋊C4—1884no—
535C4⋊C4—1884no—
536C4⋊C4—1884no—
537C4⋊C4—1884no—
538C42—44no—
539C42—4716no—
540C42—1884no—
541C23C2×Q8×D4712yes—
542C23#41×D4712yes—
543C23C2×#1062535012yes—
544C23#1309406912yes—
545C23#1309406912yes—
546C23#1309407112yes—
547C23#1309407212yes—
548C23C24×D4711yescharacteristic
549Q8—18816no—
550C2×C4—28no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—28no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
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—44no—
572C2×C4—44no—
573C2×C4—44no—
574C2×C4—44no—
575C2×C4—44no—
576C2×C4—474no—
577C2×C4—474no—
578C2×C4—474no—
579C2×C4—948no—
580C2×C4—948no—
581C2×C4—942no—
582C2×C4—942no—
583C2×C4—942no—
584C2×C4—942no—
585C2×C4—942no—
586C2×C4—942no—
587C2×C4—948no—
588C2×C4—942no—
589C2×C4—942no—
590C2×C4—942no—
591C2×C4—942no—
592C2×C4—942no—
593C2×C4—942no—
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—1884no—
604C2×C4—1884no—
605C2×C4—1884no—
606C2×C4—1884no—
607C2×C4—1884no—
608C2×C4C2×Q8×D4714yes—
609C2×C4C2×#1062535014yes—
610C22#1568967714yes—
611C22#1568970514yes—
612C22#1568972014yes—
613C22#1568973214yes—
614C22#1568973814yes—
615C22#1568975014yes—
616C22#1568975214yes—
617C22C22×Q8×D4711yescharacteristic
618C22C2×#41×D4711yescharacteristic
619C22C22×#1062535011yescharacteristic
620C22C2×#1309406911yescharacteristic
621C22C2×#1309406911yescharacteristic
622C22C2×#1309407111yescharacteristic
623C22C2×#1309407211yescharacteristic
624C4—24no—
625C4—24no—
626C4—42no—
627C4—42no—
628C4—42no—
629C4—42no—
630C4—42no—
631C4—944no—
632C4—944no—
633C4—944no—
634C4—1882no—
635C4—1882no—
636C4—1882no—
637C4—1882no—
638C4—1882no—
639C2#2024957918yesdirect product factor
640C2C2×#1568967711yescharacteristic
641C2C2×#1568970511yescharacteristic
642C2C2×#1568972011yescharacteristic
643C2C2×#1568973211yescharacteristic
644C2C2×#1568973811yescharacteristic
645C2C2×#1568975011yescharacteristic
646C2C2×#1568975211yescharacteristic
subgroupG/H
centerC24C23×D47
commutator, cosocleC23×C47C25
FrattiniC23C24×D47
FittingC2×C47×#389C2
socle, prime radicalC24×C47C24
hypercenterC2×#389D47
hypocenterC47C2×#2666
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
1. #20249579C2direct (N × H)
98. C2×C4×Dic47Q8semidirect
216. C4×Dic47C2×Q8semidirect
332. C2×C47#2666semidirect
390. C47C2×#2666semidirect
639. C2#20249579direct (N × H)

Maximal subgroups

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

subgroupindex
#202495792
C2×#156890612
C2×#156890562
C2×#156890542
C2×#156890532
C2×#156890432
C2×#156890272
C2×#156890102
C2×#156890072
C2×#156889902
C2×#156889872
C2×C4×Dic47⋊C42
C2×C47×#3892
C2×#266647