Finite Group Databasebeta

← #26218070

Subgroups — #26218070

Order 12032.

1994 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689634C211yesmaximal, characteristic
2C22×#13093983C211yesmaximal, characteristic, complemented
3C2×#15689096C212yesmaximal, complemented
4#20243844C214yesmaximal, complemented
5#20243839C214yesmaximal, complemented
6#20243120C212yesmaximal, complemented
7C47×#2280C211yesmaximal, characteristic, complemented
8C22×#10625350C2211yescharacteristic
9#15689634—21no—
10#15689634—21no—
11#15689634—21no—
12#15689634—21no—
13#15689634—22no—
14#15689634—22no—
15C2×#13094007C2212yes—
16C2×#13094003C412yescomplemented
17C2×#13093998C412yescomplemented
18C2×#13093993C2212yes—
19C2×C4×C22⋊D47C414yescomplemented
20C2×#13093983—28no—
21C2×#13093983—21no—
22C2×#13093983—21no—
23C2×#13093983C2212yes—
24C2×#13093983C2212yes—
25C2×#13093983C2211yescharacteristic
26C22×C4⋊Dic47—21no—
27C22×C22⋊Dic47C2212yes—
28C22×C4×Dic47—21no—
29#15689096—28no—
30C2×#13093938C2218yes—
31#15688889C2218yes—
32C24×C4×C47C2211yescharacteristic
33C2×#117×C47C2212yes—
34C47×#381C2212yes—
35C47×#380—22no—
36C47×#379C2212yes—
37C4×C22⋊C4×C47—22no—
38C2×#10625350—24no—
39C2×#10625350—21no—
40C2×#10625350—21no—
41C2×#10625350—21no—
42C2×#10625350—21no—
43C2×#10625350—24no—
44C22×Dic94C2×C411yescharacteristic, complemented
45C22×D188C2×C411yescharacteristic, complemented
46C22×C22⋊D47C2×C414yes—
47C22×C22⋊D47C2312yes—
48C23×Dic47—22no—
49C22×C4×D47C2×C412yescomplemented
50#13094007—22no—
51#13094007—22no—
52#13094007—24no—
53#13094003—22no—
54#13094003—22no—
55#13094003—22no—
56#13094003—22no—
57#13093998—22no—
58#13093998—22no—
59#13093998—22no—
60#13093998—22no—
61#13093993—22no—
62#13093993—24no—
63#13093993—22no—
64C4×C22⋊D47—24no—
65C4×C22⋊D47—24no—
66C4×C22⋊D47—24no—
67C4×C22⋊D47—24no—
68#13093983—28no—
69#13093983—28no—
70#13093983—24no—
71#13093983—21no—
72#13093983—21no—
73#13093983—21no—
74#13093983—21no—
75#13093983—28no—
76#13093983D418yescomplemented
77C2×C4⋊Dic47—28no—
78C2×C4⋊Dic47—22no—
79C2×C4⋊Dic47—22no—
80C2×C4⋊Dic47C2×C412yescomplemented
81C2×Dic47⋊C4C2×C414yescomplemented
82C2×C22⋊Dic47—22no—
83C2×C22⋊Dic47—28no—
84C2×C22⋊Dic47C2×C414yes—
85C2×C22⋊Dic47C2312yes—
86C2×C22⋊Dic47C2314yes—
87C2×(C2×D47)⋊C4C2×C414yescomplemented
88C2×C4×Dic47—28no—
89C2×C4×Dic47—22no—
90C2×C4×Dic47—22no—
91C2×C4×Dic47C2×C412yescomplemented
92#13093938—216no—
93C25×C47C2311yescharacteristic
94C23×C4×C47—24no—
95C23×C4×C47—24no—
96C23×C4×C47C2×C412yes—
97C23×C4×C47C2×C412yes—
98C23×C4×C47D411yescharacteristic
99C23×C4×C47D411yescharacteristic
100C23×C4×C47D411yescharacteristic
101C23×C4×C47D411yescharacteristic
102C23×C4×C47D412yes—
103C23×C4×C47D412yes—
104C23×C4×C47C2311yescharacteristic
105C23×C4×C47C2311yescharacteristic
106#117×C47—24no—
107#117×C47—24no—
108C2×C4⋊C4×C47—22no—
109C2×C22⋊C4×C47—24no—
110C2×C22⋊C4×C47C2314yes—
111C2×C42×C47—22no—
112#95×C47—24no—
113C24×C47—22no—
114C24×C47—22no—
115C24×C47—44no—
116C24×C47C22×C412yes—
117C24×C47C2×D411yescharacteristic
118C24×C47C2×D412yes—
119C24×C47C2×D411yescharacteristic
120C24×C47C2411yescharacteristic
121C23×D47C22×C412yes—
122C22×C4×C47—22no—
123C22×C4×C47—22no—
124C22×C4×C47—28no—
125C22×C4×C47—28no—
126C22×C4×C47—22no—
127C22×C4×C47—22no—
128C22×C4×C47—22no—
129C22×C4×C47—22no—
130C22×C4×C47—28no—
131C22×C4×C47—28no—
132C22×C4×C47—22no—
133C22×C4×C47—22no—
134C22×C4×C47—22no—
135C22×C4×C47—22no—
136C22×C4×C47—24no—
137C22×C4×C47C22⋊C412yes—
138C22×C4×C47C22⋊C412yes—
139C22×C4×C47C22⋊C412yes—
140C22×C4×C47C22⋊C412yes—
141C22×C4×C47C22⋊C412yes—
142C22×C4×C47C22⋊C412yes—
143C22×C4×C47C22⋊C412yes—
144C22×C4×C47C22⋊C412yes—
145C22×C4×C47C22×C412yes—
146C22×C4×C47C22×C411yescharacteristic
147C22×C4×C47C22×C411yescharacteristic
148C22×C4×C47C2×D411yescharacteristic
149C22×C4×C47C2×D411yescharacteristic
150C22×C4×C47C2×D412yes—
151C22×C4×C47C2×D411yescharacteristic
152C22×C4×C47C2×D411yescharacteristic
153C22×C4×C47C2×D411yescharacteristic
154C22×C4×C47C2×D411yescharacteristic
155C22×C4×C47C2×D414yes—
156C22×C4×C47#4114yes—
157C2×C22⋊D47—24no—
158C2×C22⋊D47—24no—
159C2×C22⋊D47—24no—
160C2×C22⋊D47—22no—
161C2×C22⋊D47—22no—
162C2×C22⋊D47—24no—
163C2×C22⋊D47—48no—
164C22×Dic47—28no—
165C22×Dic47—24no—
166C22×Dic47—48no—
167C22×Dic47C22×C412yes—
168C22×Dic47C22×C414yes—
169#10625350—42no—
170#10625350—42no—
171#10625350—44no—
172#10625350—44no—
173#10625350—42no—
174#10625350—42no—
175C2×D188—21no—
176C2×D188—21no—
177C2×D188—24no—
178C2×C4×D47—22no—
179C2×C4×D47—22no—
180C2×C4×D47—28no—
181C2×Dic94—21no—
182C2×Dic94—21no—
183C2×Dic94—24no—
184C4⋊C4×C47—44no—
185C22⋊C4×C47—24no—
186C22⋊C4×C47—24no—
187C22⋊C4×C47—48no—
188C42×C47—44no—
189C22⋊Dic47—28no—
190C22⋊Dic47—24no—
191C22⋊Dic47—24no—
192C22⋊Dic47—24no—
193C22⋊Dic47—22no—
194C22⋊Dic47—22no—
195C22⋊Dic47C2×D418yes—
196(C2×D47)⋊C4—24no—
197(C2×D47)⋊C4—24no—
198C4⋊Dic47—28no—
199C4⋊Dic47—22no—
200C4⋊Dic47—22no—
201C4⋊Dic47—28no—
202Dic47⋊C4—24no—
203Dic47⋊C4—24no—
204C4×Dic47—28no—
205C4×Dic47—22no—
206C4×Dic47—22no—
207C4×Dic47—28no—
208C23×C47—21no—
209C23×C47—21no—
210C23×C47—24no—
211C23×C47—24no—
212C23×C47—21no—
213C23×C47—24no—
214C23×C47—21no—
215C23×C47—24no—
216C23×C47—24no—
217C23×C47—42no—
218C23×C47—42no—
219C23×C47—42no—
220C23×C47—42no—
221C23×C47—48no—
222C23×C47—48no—
223C23×C47C2×C22⋊C412yes—
224C23×C47C2×C22⋊C412yes—
225C23×C47C23×C411yescharacteristic
226C23×C47C22×D412yes—
227C23×C47C22×D411yescharacteristic
228C23×C47C22×D411yescharacteristic
229C23×C47C2×#4112yes—
230C22×D47—22no—
231C22×D47—24no—
232C22×D47—44no—
233C2×C4×C47—24no—
234C2×C4×C47—21no—
235C2×C4×C47—21no—
236C2×C4×C47—24no—
237C2×C4×C47—21no—
238C2×C4×C47—21no—
239C2×C4×C47—24no—
240C2×C4×C47—24no—
241C2×C4×C47—24no—
242C2×C4×C47—24no—
243C2×C4×C47—24no—
244C2×C4×C47—24no—
245C2×C4×C47—24no—
246C2×C4×C47—24no—
247C2×C4×C47—48no—
248C2×C4×C47—44no—
249C2×C4×C47C2×C22⋊C412yes—
250C2×C4×C47C2×C22⋊C412yes—
251C2×C4×C47C2×C22⋊C411yescharacteristic
252C2×C4×C47C2×C22⋊C411yescharacteristic
253C2×C4×C47C2×C22⋊C411yescharacteristic
254C2×C4×C47C2×C22⋊C411yescharacteristic
255C2×C4×C47C4×D414yes—
256C2×C4×C47C4×D414yes—
257C2×C4×C47#12012yes—
258C2×C4×C47#12012yes—
259C2×C4×C47#12114yes—
260C2×C4×C47#12114yes—
261C2×C4×C47#12312yes—
262C2×C4×C47#12312yes—
263C22⋊D47—48no—
264C22⋊D47—42no—
265C22⋊D47—44no—
266C22⋊D47—42no—
267C22⋊D47—48no—
268C2×Dic47—24no—
269C2×Dic47—22no—
270C2×Dic47—24no—
271C2×Dic47—28no—
272C2×Dic47—416no—
273C2×Dic47—48no—
274C2×Dic47—44no—
275D188—42no—
276D188—42no—
277C4×D47—44no—
278C4×D47—44no—
279Dic94—42no—
280Dic94—42no—
281#20983—471nomaximal, Sylow
282C22×C47—24no—
283C22×C47—24no—
284C22×C47—22no—
285C22×C47—22no—
286C22×C47—22no—
287C22×C47—22no—
288C22×C47—22no—
289C22×C47—22no—
290C22×C47—22no—
291C22×C47—22no—
292C22×C47—42no—
293C22×C47—42no—
294C22×C47—48no—
295C22×C47—48no—
296C22×C47—42no—
297C22×C47—42no—
298C22×C47#41014yescomplemented
299C22×C47C22×C22⋊C411yescharacteristic
300C22×C47C2×C4×D412yes—
301C22×C47C2×#12011yescharacteristic
302C22×C47C2×#12112yes—
303C22×C47C2×#12311yescharacteristic
304C2×D47—44no—
305C2×D47—42no—
306C2×D47—84no—
307C4×C47—22no—
308C4×C47—22no—
309C4×C47—84no—
310C4×C47#38612yes—
311C4×C47#38612yes—
312C4×C47#38612yes—
313C4×C47#38612yes—
314Dic47—48no—
315Dic47—44no—
316Dic47—42no—
317C2×#525—471no—
318C22×#117—471no—
319C2×#410—472no—
320#2280D4711yescharacteristic, complemented
321#1899—474no—
322#1898—474no—
323#1740—472no—
324C2×C47—21no—
325C2×C47—22no—
326C2×C47—22no—
327C2×C47—21no—
328C2×C47—24no—
329C2×C47—42no—
330C2×C47C2×#38611yescharacteristic
331C2×C47C2×#41012yes—
332D47—82no—
333C22×#41—471no—
334C24×C4C2×D4711yescharacteristic
335#525—941no—
336#525—941no—
337#525—941no—
338#525—941no—
339#525—942no—
340#525—942no—
341C2×#123—472no—
342C2×C22⋊Q8—472no—
343C2×#121—472no—
344C2×#120—472no—
345C2×C4×D4—474no—
346C2×#117—471no—
347C2×#117—472no—
348C2×#117—472no—
349C2×#117—948no—
350C2×#117—941no—
351C2×#117—941no—
352C2×#117C2×D4712yes—
353C22×C4⋊C4—941no—
354C22×C22⋊C4—472no—
355C22×C42—941no—
356#410—948no—
357C2×#99—478no—
358#381C2×D4712yes—
359#380—22no—
360#379C2×D4712yes—
361C4×C22⋊C4—22no—
362#342—478no—
363C47#2098311yescharacteristic, complemented, Sylow
364C25C22×D4711yescharacteristic
365C2×#41—941no—
366C2×#41—941no—
367C2×#41—944no—
368C2×#41—944no—
369C2×#41—941no—
370C2×#41—941no—
371C22×Q8—471no—
372C22×D4—472no—
373C22×D4—474no—
374C22×D4—471no—
375C23×C4—24no—
376C23×C4—24no—
377C23×C4—472no—
378C23×C4—942no—
379C23×C4C4×D4712yes—
380C23×C4C4×D4712yes—
381C23×C4D18811yescharacteristic
382C23×C4D18811yescharacteristic
383C23×C4D18811yescharacteristic
384C23×C4D18811yescharacteristic
385C23×C4C22⋊D4712yes—
386C23×C4C22⋊D4712yes—
387C23×C4C22×D4711yescharacteristic
388C23×C4C22×D4711yescharacteristic
389#123—942no—
390#123—942no—
391#123—944no—
392C22⋊Q8—942no—
393C22⋊Q8—942no—
394C22⋊Q8—942no—
395C22⋊Q8—942no—
396#121—942no—
397#121—942no—
398#121—942no—
399#121—942no—
400#120—942no—
401#120—942no—
402#120—944no—
403C4×D4—944no—
404C4×D4—944no—
405C4×D4—944no—
406C4×D4—944no—
407#117—24no—
408#117—24no—
409#117—478no—
410#117—948no—
411#117—948no—
412#117—948no—
413#117—941no—
414#117—941no—
415#117—944no—
416#117—941no—
417#117—941no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—472no—
420C2×C4⋊C4—474no—
421C2×C4⋊C4—948no—
422C2×C4⋊C4—942no—
423C2×C4⋊C4—942no—
424C2×C22⋊C4—24no—
425C2×C22⋊C4—474no—
426C2×C22⋊C4—474no—
427C2×C22⋊C4—472no—
428C2×C22⋊C4—474no—
429C2×C22⋊C4—948no—
430C2×C22⋊C4—942no—
431C2×C22⋊C4C22×D4714yes—
432C2×C42—22no—
433C2×C42—472no—
434C2×C42—948no—
435C2×C42—942no—
436C2×C42—942no—
437#99—9416no—
438#95—24no—
439C24—22no—
440C24—22no—
441C24—44no—
442C24—472no—
443C24C2×C4×D4712yes—
444C24C2×D18811yescharacteristic
445C24C2×D18811yescharacteristic
446C24C2×C22⋊D4712yes—
447C24C23×D4711yescharacteristic
448#41—1882no—
449#41—1882no—
450#41—1884no—
451#41—1884no—
452#41—1882no—
453#41—1882no—
454C2×Q8—941no—
455C2×Q8—941no—
456C2×Q8—944no—
457C2×D4—944no—
458C2×D4—944no—
459C2×D4—944no—
460C2×D4—942no—
461C2×D4—942no—
462C2×D4—944no—
463C2×D4—941no—
464C2×D4—941no—
465C2×D4—944no—
466C2×D4—1888no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—28no—
470C22×C4—28no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—28no—
476C22×C4—28no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—24no—
482C22×C4—472no—
483C22×C4—474no—
484C22×C4—948no—
485C22×C4—944no—
486C22×C4—942no—
487C22×C4—942no—
488C22×C4—948no—
489C22×C4—1888no—
490C22×C4(C2×D47)⋊C412yes—
491C22×C4(C2×D47)⋊C412yes—
492C22×C4(C2×D47)⋊C412yes—
493C22×C4(C2×D47)⋊C412yes—
494C22×C4(C2×D47)⋊C412yes—
495C22×C4(C2×D47)⋊C412yes—
496C22×C4(C2×D47)⋊C412yes—
497C22×C4(C2×D47)⋊C412yes—
498C22×C4C2×C4×D4712yes—
499C22×C4C2×C4×D4711yescharacteristic
500C22×C4C2×C4×D4711yescharacteristic
501C22×C4C2×D18811yescharacteristic
502C22×C4C2×D18811yescharacteristic
503C22×C4C2×D18811yescharacteristic
504C22×C4C2×D18811yescharacteristic
505C22×C4D4×D4714yes—
506C22×C4#1062535214yes—
507C22×C4C2×C22⋊D4712yes—
508C22×C4C2×C22⋊D4711yescharacteristic
509C22×C4C2×C22⋊D4711yescharacteristic
510C4⋊C4—44no—
511C4⋊C4—948no—
512C4⋊C4—944no—
513C4⋊C4—944no—
514C4⋊C4—942no—
515C4⋊C4—942no—
516C4⋊C4—948no—
517C22⋊C4—24no—
518C22⋊C4—24no—
519C22⋊C4—48no—
520C22⋊C4—478no—
521C22⋊C4—948no—
522C22⋊C4—944no—
523C22⋊C4—944no—
524C22⋊C4—944no—
525C22⋊C4—942no—
526C22⋊C4—942no—
527C22⋊C4—944no—
528C22⋊C4—944no—
529C42—44no—
530C42—948no—
531C42—942no—
532C42—942no—
533C42—948no—
534C23—24no—
535C23—21no—
536C23—21no—
537C23—24no—
538C23—24no—
539C23—24no—
540C23—21no—
541C23—24no—
542C23—21no—
543C23—42no—
544C23—42no—
545C23—42no—
546C23—42no—
547C23—48no—
548C23—48no—
549C23—944no—
550C23—942no—
551C23—1884no—
552C23C2×(C2×D47)⋊C412yes—
553C23C2×(C2×D47)⋊C412yes—
554C23C22×C4×D4711yescharacteristic
555C23C2×D4×D4712yes—
556C23C22×C22⋊D4711yescharacteristic
557C23C22×D18811yescharacteristic
558C23C2×#1062535212yes—
559Q8—1882no—
560Q8—1882no—
561D4—1888no—
562D4—1888no—
563D4—1882no—
564D4—1884no—
565D4—1882no—
566D4—1882no—
567D4—1882no—
568C2×C4—24no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—24no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—24no—
575C2×C4—24no—
576C2×C4—24no—
577C2×C4—24no—
578C2×C4—24no—
579C2×C4—24no—
580C2×C4—24no—
581C2×C4—24no—
582C2×C4—48no—
583C2×C4—44no—
584C2×C4—944no—
585C2×C4—942no—
586C2×C4—944no—
587C2×C4—948no—
588C2×C4—18816no—
589C2×C4—1888no—
590C2×C4—1884no—
591C2×C4—1884no—
592C2×C4—1884no—
593C2×C4C2×(C2×D47)⋊C412yes—
594C2×C4C2×(C2×D47)⋊C412yes—
595C2×C4C2×(C2×D47)⋊C411yescharacteristic
596C2×C4C2×(C2×D47)⋊C411yescharacteristic
597C2×C4C2×(C2×D47)⋊C411yescharacteristic
598C2×C4C2×(C2×D47)⋊C411yescharacteristic
599C2×C4(C22⋊D47)⋊C414yes—
600C2×C4(C22⋊D47)⋊C414yes—
601C2×C4#1309399412yes—
602C2×C4#1309399412yes—
603C2×C4#1309399614yes—
604C2×C4#1309399614yes—
605C2×C4#1309400812yes—
606C2×C4#1309400812yes—
607C22—24no—
608C22—24no—
609C22—22no—
610C22—22no—
611C22—22no—
612C22—22no—
613C22—22no—
614C22—22no—
615C22—22no—
616C22—22no—
617C22—42no—
618C22—42no—
619C22—48no—
620C22—48no—
621C22—42no—
622C22—42no—
623C22—3764no—
624C22—1882no—
625C22—1884no—
626C22#1568909614yescomplemented
627C22C22×(C2×D47)⋊C411yescharacteristic
628C22C2×(C22⋊D47)⋊C412yes—
629C22C2×#1309399411yescharacteristic
630C22C2×#1309399612yes—
631C22C2×#1309400811yescharacteristic
632C4—22no—
633C4—22no—
634C4—84no—
635C4—1888no—
636C4—1882no—
637C4—1884no—
638C4#1568900012yes—
639C4#1568900012yes—
640C4#1568900012yes—
641C4#1568900012yes—
642C2—22no—
643C2—21no—
644C2—24no—
645C2—21no—
646C2—22no—
647C2—42no—
648C2—3762no—
649C2C2×#1568900011yescharacteristic
650C2C2×#1568909612yes—
subgroupG/H
centerC2×C4C2×(C2×D47)⋊C4
commutatorC23×C47C23×C4
FrattiniC24C23×D47
FittingC47×#2280C2
socleC22×C47C22×C22⋊C4
prime radicalC2×#15689634C2
cosocleC24×C47C24
hypercenter#2280D47
hypocenterC47#20983
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C24×C4 ◁ #2280

Complements

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

NH ≅ G/Ntype
2. C22×#13093983C2semidirect
3. C2×#15689096C2semidirect
4. #20243844C2semidirect
5. #20243839C2semidirect
6. #20243120C2semidirect
7. C47×#2280C2semidirect
16. C2×#13094003C4semidirect
17. C2×#13093998C4semidirect
19. C2×C4×C22⋊D47C4semidirect
44. C22×Dic94C2×C4semidirect
45. C22×D188C2×C4semidirect
49. C22×C4×D47C2×C4semidirect
76. #13093983D4semidirect
80. C2×C4⋊Dic47C2×C4semidirect
81. C2×Dic47⋊C4C2×C4semidirect
87. C2×(C2×D47)⋊C4C2×C4semidirect
91. C2×C4×Dic47C2×C4semidirect
298. C22×C47#410semidirect
320. #2280D47semidirect
363. C47#20983semidirect
626. C22#15689096semidirect

Maximal subgroups

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

subgroupindex
C2×#156896342
C22×#130939832
C2×#156890962
#202438442
#202438392
#202431202
C47×#22802
#2098347