Finite Group Databasebeta

← #37576054

Subgroups — #37576054

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×#20259296C211yesmaximal, characteristic, complemented
3C2×#20259292C211yesmaximal, characteristic, complemented
4C2×#20259292C211yesmaximal, characteristic, complemented
5C2×(C22⋊D191)⋊C4C211yesmaximal, characteristic, complemented
6C22×(C2×D191)⋊C4C211yesmaximal, characteristic, complemented
7#27132585C211yesmaximal, characteristic, complemented
8#27132581C211yesmaximal, characteristic, complemented
9#27132580C211yesmaximal, characteristic, complemented
10#27132573C211yesmaximal, characteristic, complemented
11#27132564C211yesmaximal, characteristic, complemented
12#27132555C211yesmaximal, characteristic, complemented
13#27132541C211yesmaximal, characteristic, complemented
14#27132540C211yesmaximal, characteristic, complemented
15#385×C191C211yesmaximal, characteristic, complemented
16C24×D191C2211yescharacteristic
17C22×D764C2211yescharacteristic
18C22×D764C2211yescharacteristic
19C22×D764C2211yescharacteristic
20C22×D764C2211yescharacteristic
21C22×D764C2211yescharacteristic, complemented
22C22×C22⋊D191C2211yescharacteristic
23C22×C22⋊D191C2211yescharacteristic
24C23×Dic191C2211yescharacteristic
25C22×C4×D191C2211yescharacteristic, complemented
26#20259297—24no—
27#20259296—24no—
28#20259292—24no—
29#20259292—24no—
30(C22⋊D191)⋊C4—24no—
31C2×C4⋊Dic191C2211yescharacteristic, complemented
32C2×Dic191⋊C4C2211yescharacteristic, complemented
33C2×(C2×D191)⋊C4—24no—
34C2×(C2×D191)⋊C4C2211yescharacteristic
35C2×(C2×D191)⋊C4C2211yescharacteristic
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
47C2×C4×Dic191C2211yescharacteristic, complemented
48C191⋊#95C2211yescharacteristic, complemented
49C191⋊#95C2211yescharacteristic, complemented
50C23×C4×C191C2211yescharacteristic
51C2×C4⋊C4×C191C2211yescharacteristic, complemented
52C2×C4⋊C4×C191C2211yescharacteristic, complemented
53C2×C22⋊C4×C191C2211yescharacteristic
54C2×C22⋊C4×C191C2211yescharacteristic
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—41no—
79C2×D764—41no—
80C2×D764—41no—
81C2×D764—41no—
82C2×D764—41no—
83C2×C22⋊D191—22no—
84C2×C22⋊D191—22no—
85C2×C22⋊D191—22no—
86C2×C22⋊D191—22no—
87C2×C22⋊D191—22no—
88C2×C22⋊D191D414yescomplemented
89C22×Dic191—22no—
90C22×Dic191—22no—
91C22×Dic191—41no—
92C22×Dic191C2311yescharacteristic
93C22×Dic191C2311yescharacteristic
94C22×Dic191C2311yescharacteristic
95C22×Dic191C2311yescharacteristic
96C2×C4×D191—22no—
97C2×C4×D191—22no—
98C2×C4×D191—41no—
99C4⋊Dic191—22no—
100Dic191⋊C4—22no—
101(C2×D191)⋊C4—22no—
102(C2×D191)⋊C4—22no—
103(C2×D191)⋊C4—22no—
104(C2×D191)⋊C4—22no—
105(C2×D191)⋊C4—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—41no—
113(C2×D191)⋊C4D414yescomplemented
114C4×Dic191—22no—
115C24×C191C2311yescharacteristic
116C22×C4×C191—22no—
117C22×C4×C191—22no—
118C22×C4×C191—41no—
119C22×C4×C191C2311yescharacteristic
120C22×C4×C191C2311yescharacteristic
121C22×C4×C191C2311yescharacteristic
122C22×C4×C191C2311yescharacteristic
123C22×C4×C191C2311yescharacteristic
124C22×C4×C191C2311yescharacteristic
125C4⋊C4×C191—22no—
126C4⋊C4×C191—41no—
127C22⋊C4×C191—22no—
128C22⋊C4×C191D414yescomplemented
129C22×D191—28no—
130C22×D191—21no—
131C22×D191—21no—
132C22×D191—21no—
133C22×D191—21no—
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—21no—
154C22×D191—21no—
155C22×D191—44no—
156C22×D191—44no—
157C22×D191—44no—
158C22×D191—44no—
159C22×D191—44no—
160C22×D191—44no—
161C22×D191C2×D412yes—
162C22×D191C2×D412yes—
163C22×D191#4112yes—
164D764—44no—
165D764—44no—
166D764—44no—
167D764—44no—
168D764—44no—
169C22⋊D191—28no—
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—44no—
182C2×Dic191C2×D412yes—
183C2×Dic191C2×D412yes—
184C4×D191—44no—
185C23×C191—21no—
186C23×C191—21no—
187C23×C191—21no—
188C23×C191—21no—
189C23×C191C2×D412yes—
190C23×C191C2×D412yes—
191C23×C191#4112yes—
192C23×C191C2411yescharacteristic
193C2×C4×C191—21no—
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×C191—44no—
209C2×C4×C191C2×D412yes—
210C2×C4×C191C2×D412yes—
211C2×C4×C191C2×D412yes—
212C22×C191—22no—
213C22×C191—22no—
214C22×C191—22no—
215C22×C191—22no—
216C22×C191—22no—
217C22×C191—22no—
218C22×C191#12114yescomplemented
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—416no—
236C2×D191—41no—
237C2×D191—41no—
238C2×D191—41no—
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—41no—
255C4×C191—22no—
256C4×C191—22no—
257C4×C191—22no—
258C4×C191—41no—
259C4×C191—41no—
260C4×C191—41no—
261Dic191—22no—
262Dic191—22no—
263Dic191—41no—
264Dic191—41no—
265C2×C191—24no—
266C2×C191C2×#12111yescharacteristic
267C2×C191#52511yescharacteristic
268C2×C191#53811yescharacteristic
269C2×C191D4211yescharacteristic
270C2×C191D4211yescharacteristic
271C2×C191#54611yescharacteristic
272C2×C191#54611yescharacteristic
273D191—42no—
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#388—1911no—
291#386—1911no—
292#386—1911no—
293#385D19111yescharacteristic, complemented
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×C4C2×D19111yescharacteristic
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⋊C4C2×D19111yescharacteristic, complemented
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⋊C4—1911no—
328C2×C22⋊C4C2×D19111yescharacteristic
329C2×C22⋊C4C2×D19111yescharacteristic
330C2×C42—1911no—
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—22no—
369C22×C4—22no—
370C22×C4—41no—
371C22×C4—3822no—
372C22×C4—3822no—
373C22×C4—3822no—
374C22×C4—3822no—
375C22×C4—1911no—
376C22×C4—1911no—
377C22×C4—1911no—
378C22×C4—1911no—
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—41no—
389C4⋊C4—3822no—
390C4⋊C4—3822no—
391C22⋊C4—22no—
392C22⋊C4—3822no—
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—3822no—
407C23—21no—
408C23—21no—
409C23—21no—
410C23—21no—
411C23—3828no—
412C23—3821no—
413C23—3821no—
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—7644no—
441C23—7644no—
442C23—7644no—
443C23—7644no—
444C23—7644no—
445C23—7644no—
446C23D4×D19112yes—
447C23C2×D76412yes—
448C23#1569028812yes—
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—21no—
472C2×C4—44no—
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—3821no—
483C2×C4—1912no—
484C2×C4—1912no—
485C2×C4—7644no—
486C2×C4—7644no—
487C2×C4D4×D19112yes—
488C2×C4C2×D76412yes—
489C2×C4C2×D76412yes—
490C22—22no—
491C22—22no—
492C22—22no—
493C22—22no—
494C22—22no—
495C22—22no—
496C22—3822no—
497C22—3822no—
498C22—3822no—
499C22—3822no—
500C22—3822no—
501C22—3822no—
502C22—3822no—
503C22—3822no—
504C22—3822no—
505C22—76416no—
506C22—7641no—
507C22—7641no—
508C22—7641no—
509C22—7641no—
510C22—7641no—
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#2025929714yescomplemented
526C22C2×D4×D19111yescharacteristic
527C22C2×D4×D19111yescharacteristic
528C22C22×D76411yescharacteristic
529C22#41×D19111yescharacteristic
530C22C2×#1569028811yescharacteristic
531C22#2025936711yescharacteristic
532C22#2025936811yescharacteristic
533C4—22no—
534C4—22no—
535C4—22no—
536C4—41no—
537C4—41no—
538C4—41no—
539C4—3822no—
540C4—3822no—
541C4—7641no—
542C4—7641no—
543C2—24no—
544C2—15281no—
545C2—7642no—
546C2—7642no—
547C2—7642no—
548C2C2×#2025929711yescharacteristic
549C2#2713317611yescharacteristic
550C2#2713325311yescharacteristic
551C2#2713329511yescharacteristic
552C2D4×D76411yescharacteristic
553C2#2713330511yescharacteristic
554C2#2713330811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D191
commutator, socle, cosocleC23×C191C24
Fitting#385×C191C2
hypercenter#385D191
hypocenterC191#2424
LCSG ▷ C23×C191 ▷ C191
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
1. C2×#20259297C2semidirect
2. C2×#20259296C2semidirect
3. C2×#20259292C2semidirect
4. C2×#20259292C2semidirect
5. C2×(C22⋊D191)⋊C4C2semidirect
6. C22×(C2×D191)⋊C4C2semidirect
7. #27132585C2semidirect
8. #27132581C2semidirect
9. #27132580C2semidirect
10. #27132573C2semidirect
11. #27132564C2semidirect
12. #27132555C2semidirect
13. #27132541C2semidirect
14. #27132540C2semidirect
15. #385×C191C2semidirect
21. C22×D764C22semidirect
25. C22×C4×D191C22semidirect
31. C2×C4⋊Dic191C22semidirect
32. 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
47. C2×C4×Dic191C22semidirect
48. C191⋊#95C22semidirect
49. C191⋊#95C22semidirect
51. C2×C4⋊C4×C191C22semidirect
52. C2×C4⋊C4×C191C22semidirect
55. #95×C191C22semidirect
56. #95×C191C22semidirect
88. C2×C22⋊D191D4semidirect
113. (C2×D191)⋊C4D4semidirect
128. C22⋊C4×C191D4semidirect
218. C22×C191#121semidirect
277. C191#2424semidirect
293. #385D191semidirect
312. C2×C4⋊C4C2×D191semidirect
313. C2×C4⋊C4C2×D191semidirect
333. #95C2×D191semidirect
334. #95C2×D191semidirect
405. C22⋊C4D764semidirect
525. C22#20259297semidirect

Maximal subgroups

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

subgroupindex
C2×#202592972
C2×#202592962
C2×#202592922
C2×(C22⋊D191)⋊C42
C22×(C2×D191)⋊C42
#271325852
#271325812
#271325802
#271325732
#271325642
#271325552
#271325412
#271325402
#385×C1912
#2424191