Finite Group Databasebeta

← #37576061

Subgroups — #37576061

Order 24448.

922 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#20259297C211yesmaximal, characteristic, complemented
2C2×#20259295C211yesmaximal, characteristic, complemented
3C2×#20259292C211yesmaximal, characteristic, complemented
4C2×#20259292C211yesmaximal, characteristic, complemented
5C2×C4×D764C211yesmaximal, characteristic, complemented
6C2×C22⋊C4×D191C211yesmaximal, characteristic, complemented
7#27132585C211yesmaximal, characteristic, complemented
8#27132579C211yesmaximal, characteristic, complemented
9#27132579C211yesmaximal, characteristic, complemented
10#27132573C211yesmaximal, characteristic, complemented
11#27132565C211yesmaximal, characteristic, complemented
12#27132541C211yesmaximal, characteristic, complemented
13#27132541C211yesmaximal, characteristic, complemented
14#27132537C211yesmaximal, characteristic, complemented
15#388×C191C211yesmaximal, characteristic, complemented
16C24×D191C2211yescharacteristic
17C22×D764C2211yescharacteristic
18C22×D764C2211yescharacteristic
19C22×D764C2211yescharacteristic
20C22×D764C2211yescharacteristic
21C22×D764C2211yescharacteristic, complemented
22C22×C22⋊D191C2211yescharacteristic
23C22×C22⋊D191C2211yescharacteristic
24C22×C4×D191C2211yescharacteristic
25C22×C4×D191C2211yescharacteristic
26C22×C4×D191C2211yescharacteristic, complemented
27#20259297—24no—
28#20259295—24no—
29#20259292—24no—
30#20259292—24no—
31C4×D764—24no—
32C2×C4⋊Dic191C2211yescharacteristic, complemented
33C2×C4⋊Dic191C2211yescharacteristic, complemented
34C2×Dic191⋊C4C2211yescharacteristic, complemented
35C2×C22⋊Dic191C2211yescharacteristic
36C2×(C2×D191)⋊C4C2211yescharacteristic
37C2×(C2×D191)⋊C4C2211yescharacteristic
38C2×(C2×D191)⋊C4C2211yescharacteristic
39C2×(C2×D191)⋊C4C2211yescharacteristic
40C2×(C2×D191)⋊C4C2211yescharacteristic
41C2×(C2×D191)⋊C4C2211yescharacteristic
42C2×(C2×D191)⋊C4C2211yescharacteristic, complemented
43C2×(C2×D191)⋊C4C2211yescharacteristic, complemented
44C2×(C2×D191)⋊C4C2211yescharacteristic, complemented
45C2×(C2×D191)⋊C4C2211yescharacteristic, complemented
46C2×(C2×D191)⋊C4C2211yescharacteristic, complemented
47C22⋊C4×D191—24no—
48C191⋊#95C2211yescharacteristic, complemented
49C191⋊#95C2211yescharacteristic, complemented
50C2×C4⋊C4×C191C2211yescharacteristic, complemented
51C2×C22⋊C4×C191C2211yescharacteristic
52C2×C22⋊C4×C191C2211yescharacteristic
53C2×C22⋊C4×C191C2211yescharacteristic
54C2×C42×C191C2211yescharacteristic, complemented
55#95×C191C2211yescharacteristic, complemented
56#95×C191C2211yescharacteristic, complemented
57C23×D191—22no—
58C23×D191—22no—
59C23×D191—22no—
60C23×D191—22no—
61C23×D191—22no—
62C23×D191—41no—
63C23×D191—41no—
64C23×D191C2311yescharacteristic
65C23×D191C2311yescharacteristic
66C23×D191C2311yescharacteristic
67C23×D191C2311yescharacteristic
68C2×D764—22no—
69C2×D764—22no—
70C2×D764—22no—
71C2×D764—22no—
72C2×D764—22no—
73C2×D764—22no—
74C2×D764—22no—
75C2×D764—22no—
76C2×D764—22no—
77C2×D764—22no—
78C2×D764—22no—
79C2×D764—41no—
80C2×D764—41no—
81C2×D764—41no—
82C2×D764D414yescomplemented
83C2×C22⋊D191—22no—
84C2×C22⋊D191—22no—
85C2×C22⋊D191—22no—
86C2×C22⋊D191—22no—
87C2×C22⋊D191—41no—
88C2×C22⋊D191—41no—
89C22×Dic191C2311yescharacteristic
90C22×Dic191C2311yescharacteristic
91C22×Dic191C2311yescharacteristic
92C22×Dic191C2311yescharacteristic
93C2×C4×D191—22no—
94C2×C4×D191—22no—
95C2×C4×D191—22no—
96C2×C4×D191—22no—
97C2×C4×D191—22no—
98C2×C4×D191—22no—
99C2×C4×D191—41no—
100C2×C4×D191—41no—
101C2×C4×D191—41no—
102C4⋊Dic191—22no—
103C4⋊Dic191—41no—
104Dic191⋊C4—22no—
105C22⋊Dic191—22no—
106(C2×D191)⋊C4—22no—
107(C2×D191)⋊C4—22no—
108(C2×D191)⋊C4—22no—
109(C2×D191)⋊C4—22no—
110(C2×D191)⋊C4—22no—
111(C2×D191)⋊C4—22no—
112(C2×D191)⋊C4—22no—
113(C2×D191)⋊C4—22no—
114(C2×D191)⋊C4—22no—
115(C2×D191)⋊C4—41no—
116(C2×D191)⋊C4D414yescomplemented
117C24×C191C2311yescharacteristic
118C22×C4×C191C2311yescharacteristic
119C22×C4×C191C2311yescharacteristic
120C22×C4×C191C2311yescharacteristic
121C22×C4×C191C2311yescharacteristic
122C22×C4×C191C2311yescharacteristic
123C22×C4×C191C2311yescharacteristic
124C4⋊C4×C191—22no—
125C22⋊C4×C191—22no—
126C22⋊C4×C191—22no—
127C22⋊C4×C191D414yescomplemented
128C42×C191—22no—
129C22×D191—21no—
130C22×D191—21no—
131C22×D191—21no—
132C22×D191—21no—
133C22×D191—28no—
134C22×D191—21no—
135C22×D191—21no—
136C22×D191—21no—
137C22×D191—21no—
138C22×D191—21no—
139C22×D191—21no—
140C22×D191—21no—
141C22×D191—21no—
142C22×D191—21no—
143C22×D191—21no—
144C22×D191—21no—
145C22×D191—21no—
146C22×D191—21no—
147C22×D191—21no—
148C22×D191—21no—
149C22×D191—21no—
150C22×D191—21no—
151C22×D191—21no—
152C22×D191—21no—
153C22×D191—44no—
154C22×D191—44no—
155C22×D191—44no—
156C22×D191—44no—
157C22×D191—44no—
158C22×D191—44no—
159C22×D191C2×D412yes—
160C22×D191C2×D412yes—
161C22×D191C2×D412yes—
162C22×D191#4112yes—
163C22×D191#4112yes—
164D764—28no—
165D764—44no—
166D764—44no—
167D764—44no—
168D764—44no—
169C22⋊D191—44no—
170C22⋊D191—44no—
171C2×Dic191—21no—
172C2×Dic191—21no—
173C2×Dic191—21no—
174C2×Dic191—21no—
175C2×Dic191—21no—
176C2×Dic191—21no—
177C2×Dic191—21no—
178C2×Dic191—21no—
179C2×Dic191—21no—
180C2×Dic191—21no—
181C2×Dic191—21no—
182C2×Dic191C2×D412yes—
183C4×D191—44no—
184C4×D191—44no—
185C4×D191—44no—
186C23×C191—21no—
187C23×C191—21no—
188C23×C191—21no—
189C23×C191—21no—
190C23×C191—21no—
191C23×C191—21no—
192C23×C191C2×D412yes—
193C23×C191C2411yescharacteristic
194C2×C4×C191—21no—
195C2×C4×C191—21no—
196C2×C4×C191—21no—
197C2×C4×C191—21no—
198C2×C4×C191—21no—
199C2×C4×C191—21no—
200C2×C4×C191—21no—
201C2×C4×C191—21no—
202C2×C4×C191—21no—
203C2×C4×C191—21no—
204C2×C4×C191—21no—
205C2×C4×C191—21no—
206C2×C4×C191—21no—
207C2×C4×C191—21no—
208C2×C4×C191C2×D412yes—
209C2×C4×C191C2×D412yes—
210C2×C4×C191C2×D412yes—
211C2×C4×C191C2×D412yes—
212C22×C191—22no—
213C22×C191—22no—
214C22×C191—22no—
215C22×C191—41no—
216C22×C191—41no—
217C22×C191—41no—
218C22×C191—41no—
219C22×C191C22×D411yescharacteristic
220C22×C191C22×D411yescharacteristic
221C22×C191C22×D411yescharacteristic
222C22×C191C2×#4111yescharacteristic
223C22×C191C2×#4111yescharacteristic
224C22×C191H(5,𝔽2)11yescharacteristic
225C22×C191H(5,𝔽2)11yescharacteristic
226C2×D191—22no—
227C2×D191—22no—
228C2×D191—22no—
229C2×D191—22no—
230C2×D191—22no—
231C2×D191—22no—
232C2×D191—22no—
233C2×D191—22no—
234C2×D191—22no—
235C2×D191—22no—
236C2×D191—22no—
237C2×D191—22no—
238C2×D191—416no—
239C2×D191—41no—
240C2×D191—41no—
241C2×D191—41no—
242C2×D191—41no—
243C2×D191—41no—
244C2×D191—41no—
245C2×D191—41no—
246C2×D191—41no—
247C2×D191—41no—
248C2×D191—41no—
249C2×D191—41no—
250C2×D191—41no—
251C2×D191—41no—
252C2×D191—41no—
253C2×D191—41no—
254C2×D191#12114yescomplemented
255C4×C191—22no—
256C4×C191—22no—
257C4×C191—22no—
258C4×C191—22no—
259C4×C191—41no—
260C4×C191—41no—
261Dic191—22no—
262Dic191—41no—
263Dic191—41no—
264Dic191—41no—
265C2×C191—42no—
266C2×C191C2×#12111yescharacteristic
267C2×C191#52511yescharacteristic
268C2×C191#53811yescharacteristic
269C2×C191D4211yescharacteristic
270C2×C191D4211yescharacteristic
271C2×C191#54611yescharacteristic
272C2×C191#54611yescharacteristic
273D191—24no—
274D191—42no—
275D191—42no—
276D191—81no—
277C191#242411yescharacteristic, complemented, Sylow
278#2424—1911nomaximal, Sylow
279C2×#121—1911no—
280C2×#121—1911no—
281C2×#120—1911no—
282C2×#120—1911no—
283C2×C4×D4—1911no—
284C22×C22⋊C4—1911no—
285#396—1911no—
286#394—1911no—
287#394—1911no—
288#392—1911no—
289#390—1911no—
290#388D19111yescharacteristic, complemented
291#386—1911no—
292#386—1911no—
293#385—1911no—
294C25—1911no—
295C22×D4—1911no—
296C22×D4—1911no—
297C22×D4—1911no—
298C22×D4—1911no—
299C22×D4—1911no—
300C22×D4—1911no—
301C22×D4—1911no—
302C23×C4—1911no—
303C23×C4—1911no—
304C23×C4—1911no—
305#121—3824no—
306#121—3824no—
307#120—3824no—
308#120—3824no—
309C4×D4—3824no—
310C2×C4⋊C4—1911no—
311C2×C4⋊C4—1911no—
312C2×C4⋊C4—1911no—
313C2×C4⋊C4C2×D19111yescharacteristic, complemented
314C2×C22⋊C4—3824no—
315C2×C22⋊C4—1911no—
316C2×C22⋊C4—1911no—
317C2×C22⋊C4—1911no—
318C2×C22⋊C4—1911no—
319C2×C22⋊C4—1911no—
320C2×C22⋊C4—1911no—
321C2×C22⋊C4—1911no—
322C2×C22⋊C4—1911no—
323C2×C22⋊C4—1911no—
324C2×C22⋊C4—1911no—
325C2×C22⋊C4—1911no—
326C2×C22⋊C4—1911no—
327C2×C22⋊C4C2×D19111yescharacteristic
328C2×C22⋊C4C2×D19111yescharacteristic
329C2×C22⋊C4C2×D19111yescharacteristic
330C2×C42C2×D19111yescharacteristic, complemented
331#95—1911no—
332#95—1911no—
333#95C2×D19111yescharacteristic, complemented
334#95C2×D19111yescharacteristic, complemented
335C24—3822no—
336C24—3822no—
337C24—3822no—
338C24—3822no—
339C24—3822no—
340C24—1911no—
341C24—1911no—
342C24—1911no—
343C24—1911no—
344C24—7641no—
345C24—7641no—
346C24C22×D19111yescharacteristic
347C2×D4—3822no—
348C2×D4—3822no—
349C2×D4—3822no—
350C2×D4—3822no—
351C2×D4—3822no—
352C2×D4—3822no—
353C2×D4—3822no—
354C2×D4—3822no—
355C2×D4—3822no—
356C2×D4—3822no—
357C2×D4—3822no—
358C2×D4—3822no—
359C2×D4—3822no—
360C2×D4—3822no—
361C2×D4—3822no—
362C2×D4—1914no—
363C2×D4—7641no—
364C2×D4—7641no—
365C2×D4—7641no—
366C2×D4—7641no—
367C2×D4—7641no—
368C22×C4—3822no—
369C22×C4—3822no—
370C22×C4—3822no—
371C22×C4—3822no—
372C22×C4—3822no—
373C22×C4—3822no—
374C22×C4—1911no—
375C22×C4—1911no—
376C22×C4—1911no—
377C22×C4—1911no—
378C22×C4—7641no—
379C22×C4—7641no—
380C22×C4—7641no—
381C22×C4C22×D19111yescharacteristic
382C22×C4C22×D19111yescharacteristic
383C22×C4C22×D19111yescharacteristic
384C22×C4C22×D19111yescharacteristic
385C22×C4C22×D19111yescharacteristic
386C22×C4C22×D19111yescharacteristic
387C4⋊C4—22no—
388C4⋊C4—3822no—
389C4⋊C4—3822no—
390C4⋊C4—7641no—
391C22⋊C4—22no—
392C22⋊C4—22no—
393C22⋊C4—3822no—
394C22⋊C4—3822no—
395C22⋊C4—3822no—
396C22⋊C4—3822no—
397C22⋊C4—3822no—
398C22⋊C4—3822no—
399C22⋊C4—3822no—
400C22⋊C4—3822no—
401C22⋊C4—3822no—
402C22⋊C4—3822no—
403C22⋊C4—1914no—
404C22⋊C4—7641no—
405C22⋊C4D76414yescomplemented
406C42—22no—
407C23—21no—
408C23—21no—
409C23—21no—
410C23—21no—
411C23—21no—
412C23—21no—
413C23—3828no—
414C23—3821no—
415C23—3821no—
416C23—3821no—
417C23—3821no—
418C23—3821no—
419C23—3821no—
420C23—3821no—
421C23—3821no—
422C23—3821no—
423C23—3821no—
424C23—3821no—
425C23—3821no—
426C23—3821no—
427C23—3821no—
428C23—3821no—
429C23—3821no—
430C23—3821no—
431C23—3821no—
432C23—3821no—
433C23—3821no—
434C23—3821no—
435C23—3821no—
436C23—3821no—
437C23—1912no—
438C23—1912no—
439C23—1912no—
440C23—1912no—
441C23—1912no—
442C23—7644no—
443C23—7644no—
444C23—7644no—
445C23—7644no—
446C23—7644no—
447C23—7644no—
448C23C2×D76412yes—
449C23C23×D19111yescharacteristic
450D4—3828no—
451D4—7644no—
452D4—7644no—
453D4—7644no—
454D4—7644no—
455D4—7644no—
456D4—7644no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—3821no—
472C2×C4—3821no—
473C2×C4—3821no—
474C2×C4—3821no—
475C2×C4—3821no—
476C2×C4—3821no—
477C2×C4—3821no—
478C2×C4—3821no—
479C2×C4—3821no—
480C2×C4—3821no—
481C2×C4—3821no—
482C2×C4—1912no—
483C2×C4—7644no—
484C2×C4—7644no—
485C2×C4—7644no—
486C2×C4D4×D19112yes—
487C2×C4D4×D19112yes—
488C2×C4C2×D76412yes—
489C2×C4C2×D76412yes—
490C22—22no—
491C22—22no—
492C22—22no—
493C22—41no—
494C22—41no—
495C22—41no—
496C22—41no—
497C22—3822no—
498C22—3822no—
499C22—3822no—
500C22—3822no—
501C22—3822no—
502C22—3822no—
503C22—3822no—
504C22—3822no—
505C22—3822no—
506C22—3822no—
507C22—3822no—
508C22—3822no—
509C22—1914no—
510C22—76416no—
511C22—7641no—
512C22—7641no—
513C22—7641no—
514C22—7641no—
515C22—7641no—
516C22—7641no—
517C22—7641no—
518C22—7641no—
519C22—7641no—
520C22—7641no—
521C22—7641no—
522C22—7641no—
523C22—7641no—
524C22—7641no—
525C22—7641no—
526C22C2×D4×D19111yescharacteristic
527C22C2×D4×D19111yescharacteristic
528C22C22×D76411yescharacteristic
529C22#41×D19111yescharacteristic
530C22#41×D19111yescharacteristic
531C22#2025936811yescharacteristic
532C22#2025936811yescharacteristic
533C4—22no—
534C4—22no—
535C4—22no—
536C4—22no—
537C4—41no—
538C4—41no—
539C4—3822no—
540C4—7641no—
541C4—7641no—
542C4—7641no—
543C2—42no—
544C2—3824no—
545C2—15281no—
546C2—7642no—
547C2—7642no—
548C2#121×D19111yescharacteristic
549C2#2713317511yescharacteristic
550C2#2713325211yescharacteristic
551C2D4×D76411yescharacteristic
552C2D4×D76411yescharacteristic
553C2#2713330511yescharacteristic
554C2#2713330611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D191
commutator, socle, cosocleC23×C191C24
Fitting#388×C191C2
hypercenter#388D191
hypocenterC191#2424
LCSG ▷ C23×C191 ▷ C191
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. C2×#20259297C2semidirect
2. C2×#20259295C2semidirect
3. C2×#20259292C2semidirect
4. C2×#20259292C2semidirect
5. C2×C4×D764C2semidirect
6. C2×C22⋊C4×D191C2semidirect
7. #27132585C2semidirect
8. #27132579C2semidirect
9. #27132579C2semidirect
10. #27132573C2semidirect
11. #27132565C2semidirect
12. #27132541C2semidirect
13. #27132541C2semidirect
14. #27132537C2semidirect
15. #388×C191C2semidirect
21. C22×D764C22semidirect
26. C22×C4×D191C22semidirect
32. C2×C4⋊Dic191C22semidirect
33. C2×C4⋊Dic191C22semidirect
34. C2×Dic191⋊C4C22semidirect
42. C2×(C2×D191)⋊C4C22semidirect
43. C2×(C2×D191)⋊C4C22semidirect
44. C2×(C2×D191)⋊C4C22semidirect
45. C2×(C2×D191)⋊C4C22semidirect
46. C2×(C2×D191)⋊C4C22semidirect
48. C191⋊#95C22semidirect
49. C191⋊#95C22semidirect
50. C2×C4⋊C4×C191C22semidirect
54. C2×C42×C191C22semidirect
55. #95×C191C22semidirect
56. #95×C191C22semidirect
82. C2×D764D4semidirect
116. (C2×D191)⋊C4D4semidirect
127. C22⋊C4×C191D4semidirect
254. C2×D191#121semidirect
277. C191#2424semidirect
290. #388D191semidirect
313. C2×C4⋊C4C2×D191semidirect
330. C2×C42C2×D191semidirect
333. #95C2×D191semidirect
334. #95C2×D191semidirect
405. C22⋊C4D764semidirect

Maximal subgroups

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

subgroupindex
C2×#202592972
C2×#202592952
C2×#202592922
C2×C4×D7642
C2×C22⋊C4×D1912
#271325852
#271325792
#271325732
#271325652
#271325412
#271325372
#388×C1912
#2424191