Finite Group Databasebeta

← #37583486

Subgroups — #37583486

Order 24448.

410 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#27133198C211yesmaximal, characteristic, complemented
2#124×D191C211yesmaximal, characteristic, complemented
3#27133047C211yesmaximal, characteristic, complemented
4#27133045C211yesmaximal, characteristic, complemented
5#27133020C211yesmaximal, characteristic, complemented
6#27132888C211yesmaximal, characteristic, complemented
7#27132884C211yesmaximal, characteristic, complemented
8#27132881C211yesmaximal, characteristic, complemented
9#27132877C211yesmaximal, characteristic, complemented
10#27132820C211yesmaximal, characteristic, complemented
11#27132815C211yesmaximal, characteristic, complemented
12#27132803C211yesmaximal, characteristic, complemented
13#27132798C211yesmaximal, characteristic
14#27132714C211yesmaximal, characteristic, complemented
15#488×C191C211yesmaximal, characteristic, complemented
16C2×Q8×D191C2211yescharacteristic
17C2×D4×D191C2211yescharacteristic
18C2×Dic764C2211yescharacteristic, complemented
19C2×#15690277C2211yescharacteristic, complemented
20C2×#15690276C2211yescharacteristic
21C2×#15690276C2211yescharacteristic, complemented
22C2×#15690275C2211yescharacteristic
23C2×#15690274C2211yescharacteristic, complemented
24C2×D1528C2211yescharacteristic
25C2×#15690272C2211yescharacteristic
26#20259317—21no—
27#20259311C2211yescharacteristic
28#20259310C2211yescharacteristic
29#20259310C2211yescharacteristic, complemented
30#20259309C2211yescharacteristic
31#20259308—21no—
32#20259308—21no—
33#20259307—21no—
34#20259302C2211yescharacteristic
35#20259297C2211yescharacteristic
36#20259287C2211yescharacteristic, complemented
37#20259284—21no—
38#20259284C2211yescharacteristic, complemented
39#20259280—21no—
40C22⋊C4×D191—21no—
41C22⋊C4×D191—21no—
42C42×D191C2211yescharacteristic
43Dic191⋊C8C2211yescharacteristic, complemented
44Dic191⋊C8C2211yescharacteristic, complemented
45#20259245C2211yescharacteristic, complemented
46#20259245C2211yescharacteristic, complemented
47#20259242C2211yescharacteristic
48#20259242C2211yescharacteristic
49(C2×D191)⋊C8C2211yescharacteristic
50(C2×D191)⋊C8C2211yescharacteristic
51C4×C191⋊C8C2211yescharacteristic, complemented
52#125×C191C2211yescharacteristic, complemented
53#124×C191C2211yescharacteristic
54#103×C191C2211yescharacteristic, complemented
55#103×C191C2211yescharacteristic, complemented
56#102×C191C2211yescharacteristic
57#102×C191C2211yescharacteristic
58C4×C8×C191C2211yescharacteristic, complemented
59C23×D191—21no—
60C2×Dic382—21no—
61C2×Dic382C2311yescharacteristic
62C2×Dic382C2311yescharacteristic
63Q8×D191—41no—
64Q8×D191—41no—
65C2×D764—21no—
66C2×D764C2311yescharacteristic
67C2×D764C2311yescharacteristic
68C2×C22⋊D191—21no—
69D4×D191—41no—
70D4×D191—41no—
71C2×C4×D191—21no—
72C2×C4×D191—21no—
73C2×C4×D191D411yescharacteristic
74C2×C4×D191D411yescharacteristic
75C2×C4×D191C2311yescharacteristic
76Dic764—41no—
77#15690277—41no—
78#15690276—41no—
79#15690276—41no—
80#15690275—41no—
81#15690274—41no—
82D1528—41no—
83#15690272—41no—
84C2×C191⋊C8C2311yescharacteristic
85C2×C191⋊C8C2311yescharacteristic
86C4⋊Dic191—21no—
87Dic191⋊C4—21no—
88C22⋊Dic191—21no—
89C22⋊Dic191—21no—
90(C2×D191)⋊C4—21no—
91(C2×D191)⋊C4—21no—
92(C2×D191)⋊C4—21no—
93(C2×D191)⋊C4—21no—
94(C2×D191)⋊C4—21no—
95(C2×D191)⋊C4—21no—
96(C2×D191)⋊C4—21no—
97(C2×D191)⋊C4—21no—
98(C2×D191)⋊C4—21no—
99C4×Dic191—21no—
100C4×Dic191D411yescharacteristic
101C4×Dic191D411yescharacteristic
102C4×Dic191C2311yescharacteristic
103C2×Q8×C191C2311yescharacteristic
104C2×D4×C191C2311yescharacteristic
105C2×C8×C191C2311yescharacteristic
106C2×C8×C191C2311yescharacteristic
107C4⋊C4×C191—21no—
108C4⋊C4×C191—21no—
109C4⋊C4×C191C2311yescharacteristic
110C4⋊C4×C191C2311yescharacteristic
111C22⋊C4×C191—21no—
112C22⋊C4×C191—21no—
113C42×C191C2311yescharacteristic
114C22×D191—21no—
115C22×D191—21no—
116C22×D191—42no—
117C22×D191—42no—
118C22×D191—42no—
119C22×D191C2×D411yescharacteristic
120Dic382—21no—
121Dic382—21no—
122Dic382—21no—
123Dic382—21no—
124Dic382—42no—
125D764—21no—
126D764—21no—
127D764—21no—
128D764—21no—
129D764—42no—
130C22⋊D191—42no—
131C2×Dic191—21no—
132C2×Dic191—21no—
133C2×Dic191C2×D411yescharacteristic
134C2×Dic191C2×D411yescharacteristic
135C2×Dic191C2×D411yescharacteristic
136C4×D191—22no—
137C4×D191—21no—
138C4×D191—21no—
139C4×D191—41no—
140C4×D191—42no—
141C4×D191—42no—
142C191⋊C8—21no—
143C191⋊C8—21no—
144C23×C191—21no—
145Q8×C191—21no—
146Q8×C191—21no—
147D4×C191—21no—
148D4×C191—21no—
149C2×C4×C191—21no—
150C2×C4×C191—21no—
151C2×C4×C191—21no—
152C2×C4×C191C2×D411yescharacteristic
153C2×C4×C191C2×D411yescharacteristic
154C2×C4×C191C2411yescharacteristic
155C8×C191—21no—
156C8×C191—21no—
157C22×C191—41no—
158C22×C191—41no—
159C22×C191—41no—
160C22×C191C22×D411yescharacteristic
161C2×D191—21no—
162C2×D191—21no—
163C2×D191—41no—
164C2×D191—41no—
165C2×D191—41no—
166C2×D191—41no—
167C2×D191—41no—
168C2×D191—41no—
169C2×D191—84no—
170C2×D191#13512yes—
171C4×C191—21no—
172C4×C191—21no—
173C4×C191—41no—
174C4×C191—41no—
175C4×C191—41no—
176C4×C191H(5,𝔽2)11yescharacteristic
177C4×C191H(5,𝔽2)11yescharacteristic
178Dic191—21no—
179Dic191—21no—
180Dic191—21no—
181Dic191—41no—
182Dic191—41no—
183C2×C191—81no—
184C2×C191#53511yescharacteristic
185C2×C191C2×#13511yescharacteristic
186C2×C191#57511yescharacteristic
187D191—22no—
188D191—81no—
189D191—81no—
190C191#321111yescharacteristic, complemented, Sylow
191#3211—1911nomaximal, Sylow
192#529—1911no—
193C2×#124—1911no—
194#495—1911no—
195#495—1911no—
196#488—1911no—
197#488D19111yescharacteristic, complemented
198#464—1911no—
199#464—1911no—
200#463—1911no—
201#463—1911no—
202#451—1911no—
203#450—1911no—
204#448—1911no—
205#447—1911no—
206#431—1911no—
207C22×Q8—1911no—
208C22×D4—1911no—
209C2×Q16—1911no—
210C2×Q16—1911no—
211C2×SD16—1911no—
212C2×SD16—1911no—
213C2×SD16—1911no—
214C2×SD16—1911no—
215C2×D8—1911no—
216C2×D8—1911no—
217#126—3821no—
218#125C2×D19111yescharacteristic, complemented
219#124—3821no—
220#124—3821no—
221#124—1911no—
222#124—1911no—
223#124—1911no—
224#124—1911no—
225#124C2×D19111yescharacteristic
226#123—3821no—
227C22⋊Q8—1911no—
228#121—1911no—
229C4×Q8—1911no—
230C4×D4—3821no—
231C4×D4—1911no—
232#117—3821no—
233C2×C22⋊C4—3821no—
234C2×C22⋊C4—3821no—
235C2×C42—1911no—
236C4⋊C8—1911no—
237C4⋊C8—1911no—
238#103—1911no—
239#103—1911no—
240#103C2×D19111yescharacteristic, complemented
241#103C2×D19111yescharacteristic, complemented
242#102—1911no—
243#102—1911no—
244#102C2×D19111yescharacteristic
245#102C2×D19111yescharacteristic
246C22⋊C8—1911no—
247C22⋊C8—1911no—
248C4×C8—1911no—
249C4×C8C2×D19111yescharacteristic, complemented
250C24—3821no—
251C2×Q8—3821no—
252C2×Q8—1911no—
253C2×Q8—1911no—
254C2×Q8—7641no—
255C2×Q8—7641no—
256C2×Q8C22×D19111yescharacteristic
257C2×D4—3821no—
258C2×D4—3821no—
259C2×D4—1911no—
260C2×D4—1911no—
261C2×D4—7641no—
262C2×D4—7641no—
263C2×D4C22×D19111yescharacteristic
264C22×C4—3821no—
265C22×C4—3821no—
266C22×C4—1911no—
267C22×C4—1911no—
268C22×C4—1911no—
269Q16—7641no—
270Q16—7641no—
271SD16—7641no—
272SD16—7641no—
273SD16—7641no—
274SD16—7641no—
275D8—7641no—
276D8—7641no—
277C2×C8—1911no—
278C2×C8—1911no—
279C2×C8C22×D19111yescharacteristic
280C2×C8C22×D19111yescharacteristic
281C4⋊C4—21no—
282C4⋊C4—21no—
283C4⋊C4—3821no—
284C4⋊C4—3821no—
285C4⋊C4C22×D19111yescharacteristic
286C4⋊C4C22×D19111yescharacteristic
287C22⋊C4—21no—
288C22⋊C4—21no—
289C22⋊C4—3821no—
290C22⋊C4—3821no—
291C22⋊C4—3821no—
292C22⋊C4—3821no—
293C22⋊C4—3821no—
294C22⋊C4—3821no—
295C22⋊C4—3821no—
296C22⋊C4—3821no—
297C22⋊C4—3821no—
298C22⋊C4—3821no—
299C22⋊C4—3821no—
300C42—3821no—
301C42—1911no—
302C42—1911no—
303C42—1911no—
304C42C22×D19111yescharacteristic
305C23—21no—
306C23—3821no—
307C23—3821no—
308C23—1911no—
309C23—7642no—
310C23—7642no—
311C23—7642no—
312Q8—21no—
313Q8—21no—
314Q8—3821no—
315Q8—3821no—
316Q8—3821no—
317Q8—3821no—
318Q8—7642no—
319D4—21no—
320D4—21no—
321D4—3821no—
322D4—3821no—
323D4—3821no—
324D4—3821no—
325D4—7642no—
326D4—7642no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—3822no—
331C2×C4—3821no—
332C2×C4—3821no—
333C2×C4—3821no—
334C2×C4—3821no—
335C2×C4—1911no—
336C2×C4—1911no—
337C2×C4—1911no—
338C2×C4—7641no—
339C2×C4—7642no—
340C2×C4—7642no—
341C2×C4D4×D19111yescharacteristic
342C2×C4D4×D19111yescharacteristic
343C2×C4C23×D19111yescharacteristic
344C8—21no—
345C8—21no—
346C8—3821no—
347C8—3821no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—3821no—
352C22—3821no—
353C22—1912no—
354C22—15284no—
355C22—7641no—
356C22—7641no—
357C22—7641no—
358C22—7641no—
359C22—7641no—
360C22—7641no—
361C22C2×D4×D19111yescharacteristic
362C4—21no—
363C4—21no—
364C4—41no—
365C4—41no—
366C4—41no—
367C4—3821no—
368C4—3821no—
369C4—3821no—
370C4—7641no—
371C4—7641no—
372C4#2025936811yescharacteristic
373C4#2025936811yescharacteristic
374C2—81no—
375C2—3822no—
376C2—15281no—
377C2—15281no—
378C2#2713323111yescharacteristic
379C2#135×D19111yescharacteristic
380C2#2713346011yescharacteristic
subgroupG/H
centerC22C2×D4×D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
Fitting#488×C191C2
socleC22×C191C22×D4
prime radical#27132798C2
hypercenter#488D191
hypocenterC191#3211
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C42 ◁ #488

Complements

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

NH ≅ G/Ntype
1. #27133198C2semidirect
2. #124×D191C2semidirect
3. #27133047C2semidirect
4. #27133045C2semidirect
5. #27133020C2semidirect
6. #27132888C2semidirect
7. #27132884C2semidirect
8. #27132881C2semidirect
9. #27132877C2semidirect
10. #27132820C2semidirect
11. #27132815C2semidirect
12. #27132803C2semidirect
14. #27132714C2semidirect
15. #488×C191C2semidirect
18. C2×Dic764C22semidirect
19. C2×#15690277C22semidirect
21. C2×#15690276C22semidirect
23. C2×#15690274C22semidirect
29. #20259310C22semidirect
36. #20259287C22semidirect
38. #20259284C22semidirect
43. Dic191⋊C8C22semidirect
44. Dic191⋊C8C22semidirect
45. #20259245C22semidirect
46. #20259245C22semidirect
51. C4×C191⋊C8C22semidirect
52. #125×C191C22semidirect
54. #103×C191C22semidirect
55. #103×C191C22semidirect
58. C4×C8×C191C22semidirect
190. C191#3211semidirect
197. #488D191semidirect
218. #125C2×D191semidirect
240. #103C2×D191semidirect
241. #103C2×D191semidirect
249. C4×C8C2×D191semidirect

Maximal subgroups

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

subgroupindex
#271331982
#124×D1912
#271330472
#271330452
#271330202
#271328882
#271328842
#271328812
#271328772
#271328202
#271328152
#271328032
#271327982
#271327142
#488×C1912
#3211191