Finite Group Databasebeta

← #37582699

Subgroups — #37582699

Order 24448.

406 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#27133280C211yesmaximal, characteristic, complemented
2#27133137C211yesmaximal, characteristic, complemented
3#27133004C211yesmaximal, characteristic, complemented
4#27132952C211yesmaximal, characteristic, complemented
5#27132942C211yesmaximal, characteristic, complemented
6#27132877C211yesmaximal, characteristic, complemented
7#27132877C211yesmaximal, characteristic, complemented
8#27132816C211yesmaximal, characteristic, complemented
9#27132796C211yesmaximal, characteristic
10#27132772C211yesmaximal, characteristic, complemented
11#27132762C211yesmaximal, characteristic, complemented
12#27132750C211yesmaximal, characteristic, complemented
13#27132743C211yesmaximal, characteristic, complemented
14#27132721C211yesmaximal, characteristic, complemented
15#482×C191C211yesmaximal, characteristic, complemented
16C22×D764C2211yescharacteristic
17C2×#15690276C2211yescharacteristic
18C2×#15690276C2211yescharacteristic
19C2×#15690272C2211yescharacteristic
20C2×#15690272C2211yescharacteristic
21#20259321C2211yescharacteristic, complemented
22#20259315—21no—
23#20259309—21no—
24#20259309C2211yescharacteristic, complemented
25#20259303—21no—
26#20259301C2211yescharacteristic
27#20259299—21no—
28#20259287C2211yescharacteristic, complemented
29C4×D764—21no—
30C4×D764—21no—
31D4×Dic191C2211yescharacteristic, complemented
32#20259284C2211yescharacteristic
33#20259284C2211yescharacteristic
34#20259284C2211yescharacteristic
35#20259284C2211yescharacteristic
36#20259281C2211yescharacteristic
37C22⋊C4×D191—21no—
38C22⋊C4×D191—21no—
39#20259255C2211yescharacteristic, complemented
40#20259253C2211yescharacteristic, complemented
41Dic191⋊C8C2211yescharacteristic, complemented
42Dic191⋊C8C2211yescharacteristic, complemented
43#20259245C2211yescharacteristic, complemented
44#20259245C2211yescharacteristic, complemented
45#20259244C2211yescharacteristic
46#20259244C2211yescharacteristic
47#20259242C2211yescharacteristic
48#20259242C2211yescharacteristic
49C22⋊(C191⋊C8)C2211yescharacteristic
50#20259232C2211yescharacteristic, complemented
51C8×Dic191C2211yescharacteristic, complemented
52#121×C191C2211yescharacteristic
53#117×C191C2211yescharacteristic
54#107×C191C2211yescharacteristic, complemented
55#106×C191C2211yescharacteristic, complemented
56#102×C191C2211yescharacteristic, complemented
57#102×C191C2211yescharacteristic, complemented
58C22⋊C8×C191C2211yescharacteristic
59C23×D191—21no—
60C2×Dic382—21no—
61C2×Dic382C2311yescharacteristic
62C2×D764—22no—
63C2×D764—22no—
64C2×D764—21no—
65C2×D764C2311yescharacteristic
66C2×D764C2311yescharacteristic
67C22×Dic191—21no—
68C2×C4×D191—21no—
69C2×C4×D191—21no—
70C2×C4×D191—21no—
71C2×C4×D191—21no—
72#15690276—22no—
73#15690276—22no—
74#15690272—22no—
75#15690272—22no—
76C2×C191⋊C8C2311yescharacteristic
77C2×C191⋊C8C2311yescharacteristic
78C4⋊Dic191D411yescharacteristic
79C4⋊Dic191D411yescharacteristic
80C4⋊Dic191C2311yescharacteristic
81Dic191⋊C4—21no—
82Dic191⋊C4—21no—
83Dic191⋊C4—21no—
84C22⋊Dic191—21no—
85C22⋊Dic191—21no—
86C22⋊Dic191—21no—
87C22⋊Dic191—21no—
88C22⋊Dic191D411yescharacteristic
89C22⋊Dic191D411yescharacteristic
90(C2×D191)⋊C4—21no—
91(C2×D191)⋊C4—21no—
92(C2×D191)⋊C4—21no—
93(C2×D191)⋊C4—21no—
94C4×Dic191—21no—
95C4×Dic191C2311yescharacteristic
96C4×Dic191C2311yescharacteristic
97C2×D4×C191—21no—
98C2×D4×C191C2311yescharacteristic
99C22×C4×C191C2311yescharacteristic
100C2×C8×C191C2311yescharacteristic
101C2×C8×C191C2311yescharacteristic
102C4⋊C4×C191C2311yescharacteristic
103C4⋊C4×C191C2311yescharacteristic
104C4⋊C4×C191C2311yescharacteristic
105C22⋊C4×C191—21no—
106C22⋊C4×C191—21no—
107C42×C191—21no—
108C22×D191—21no—
109C22×D191—21no—
110C22×D191—24no—
111C22×D191—81no—
112C22×D191—81no—
113Dic382—21no—
114Dic382—21no—
115Dic382—81no—
116D764—24no—
117D764—21no—
118D764—21no—
119D764#4112yes—
120D764#4112yes—
121C2×Dic191—21no—
122C2×Dic191—21no—
123C2×Dic191—81no—
124C2×Dic191C2×D411yescharacteristic
125C2×Dic191C2×D411yescharacteristic
126C2×Dic191C2×D411yescharacteristic
127C2×Dic191C2×D411yescharacteristic
128C4×D191—81no—
129C4×D191—81no—
130C4×D191—81no—
131C4×D191—81no—
132C191⋊C8—21no—
133C191⋊C8—21no—
134C23×C191—21no—
135C23×C191C2×D411yescharacteristic
136D4×C191—21no—
137D4×C191—21no—
138D4×C191—81no—
139C2×C4×C191—21no—
140C2×C4×C191—21no—
141C2×C4×C191—21no—
142C2×C4×C191—21no—
143C2×C4×C191—21no—
144C2×C4×C191C2×D411yescharacteristic
145C2×C4×C191C2411yescharacteristic
146C8×C191—21no—
147C8×C191—21no—
148C22×C191—21no—
149C22×C191—21no—
150C22×C191—21no—
151C22×C191—41no—
152C22×C191—41no—
153C22×C191—41no—
154C22×C191C22×D411yescharacteristic
155C2×D191—22no—
156C2×D191—22no—
157C2×D191—41no—
158C2×D191—41no—
159C2×D191—41no—
160C2×D191—41no—
161C2×D191—84no—
162C4×C191—21no—
163C4×C191—41no—
164C4×C191—41no—
165C4×C191—41no—
166C4×C191C2×#4111yescharacteristic
167C4×C191C2×#4111yescharacteristic
168Dic191—21no—
169Dic191—21no—
170Dic191—21no—
171Dic191—21no—
172Dic191—41no—
173Dic191—41no—
174C2×C191—41no—
175C2×C191—81no—
176C2×C191#52511yescharacteristic
177C2×C191#57611yescharacteristic
178C2×C191#57711yescharacteristic
179D191—42no—
180D191—42no—
181C191#311811yescharacteristic, complemented, Sylow
182#3118—1911nomaximal, Sylow
183#542—1911no—
184#518—1911no—
185#485—1911no—
186#482D19111yescharacteristic, complemented
187#476—1911no—
188#474—1911no—
189#463—1911no—
190#463—1911no—
191#450—1911no—
192#447—1911no—
193#442—1911no—
194#440—1911no—
195C4×SD16—1911no—
196C4×D8—1911no—
197#433—1911no—
198C22×D4—1911no—
199C2×SD16—1911no—
200C2×SD16—1911no—
201C2×D8—1911no—
202C2×D8—1911no—
203C4⋊Q8—1911no—
204#126—3821no—
205#124—3821no—
206#124—1911no—
207#123—3821no—
208C22⋊Q8—3821no—
209C22⋊Q8—1911no—
210#121C2×D19111yescharacteristic
211C4×Q8—1911no—
212C4×D4—3821no—
213C4×D4—3821no—
214C4×D4—1911no—
215C4×D4—1911no—
216C4×D4—1911no—
217C4×D4—1911no—
218C4×D4—1911no—
219#117—1911no—
220#117C2×D19111yescharacteristic
221C2×C22⋊C4—3821no—
222C2×C22⋊C4—3821no—
223#107—1911no—
224#107C2×D19111yescharacteristic, complemented
225#106—1911no—
226#106C2×D19111yescharacteristic, complemented
227C4⋊C8—1911no—
228C4⋊C8—1911no—
229#103—1911no—
230#103—1911no—
231#102—1911no—
232#102—1911no—
233#102—1911no—
234#102—1911no—
235#102C2×D19111yescharacteristic, complemented
236#102C2×D19111yescharacteristic, complemented
237C22⋊C8—1911no—
238C22⋊C8C2×D19111yescharacteristic
239#97—1911no—
240C4×C8—1911no—
241C24—3821no—
242C2×Q8—3821no—
243C2×Q8—1911no—
244C2×D4—21no—
245C2×D4—3822no—
246C2×D4—3822no—
247C2×D4—3821no—
248C2×D4—1911no—
249C2×D4—1911no—
250C2×D4C22×D19111yescharacteristic
251C22×C4—3821no—
252C22×C4—3821no—
253C22×C4—3821no—
254C22×C4—3821no—
255C22×C4—3821no—
256C22×C4C22×D19111yescharacteristic
257SD16—3822no—
258SD16—3822no—
259D8—3822no—
260D8—3822no—
261C2×C8—1911no—
262C2×C8—1911no—
263C2×C8C22×D19111yescharacteristic
264C2×C8C22×D19111yescharacteristic
265C4⋊C4—3821no—
266C4⋊C4—3821no—
267C4⋊C4—3821no—
268C4⋊C4—1911no—
269C4⋊C4—1911no—
270C4⋊C4—1911no—
271C4⋊C4C22×D19111yescharacteristic
272C4⋊C4C22×D19111yescharacteristic
273C4⋊C4C22×D19111yescharacteristic
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—3821no—
277C22⋊C4—3821no—
278C22⋊C4—3821no—
279C22⋊C4—3821no—
280C22⋊C4—3821no—
281C22⋊C4—3821no—
282C22⋊C4—3821no—
283C22⋊C4—3821no—
284C22⋊C4—1911no—
285C22⋊C4—1911no—
286C42—21no—
287C42—3821no—
288C42—1911no—
289C42—1911no—
290C23—21no—
291C23—3824no—
292C23—3821no—
293C23—3821no—
294C23—15281no—
295C23—15281no—
296C23D4×D19111yescharacteristic
297Q8—3821no—
298Q8—3821no—
299Q8—15281no—
300D4—21no—
301D4—21no—
302D4—81no—
303D4—3824no—
304D4—3821no—
305D4—3821no—
306D4—1912no—
307D4—1912no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—3821no—
314C2×C4—3821no—
315C2×C4—1911no—
316C2×C4—1911no—
317C2×C4—1911no—
318C2×C4—1911no—
319C2×C4—15281no—
320C2×C4—15281no—
321C2×C4—15281no—
322C2×C4—15281no—
323C2×C4—15281no—
324C2×C4D4×D19111yescharacteristic
325C2×C4C23×D19111yescharacteristic
326C8—21no—
327C8—21no—
328C8—3821no—
329C8—3821no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—3822no—
337C22—3822no—
338C22—15284no—
339C22—7641no—
340C22—7641no—
341C22—7641no—
342C22—7641no—
343C22C2×D4×D19111yescharacteristic
344C4—21no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—3821no—
349C4—3821no—
350C4—3821no—
351C4—3821no—
352C4—7641no—
353C4—7641no—
354C4#41×D19111yescharacteristic
355C4#41×D19111yescharacteristic
356C2—41no—
357C2—81no—
358C2—7642no—
359C2—7642no—
360C2#2713317111yescharacteristic
361C2#2713346711yescharacteristic
362C2#2713347011yescharacteristic
subgroupG/H
centerC22C2×D4×D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
Fitting#482×C191C2
socleC22×C191C22×D4
prime radical#27132796C2
hypercenter#482D191
hypocenterC191#3118
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
1. #27133280C2semidirect
2. #27133137C2semidirect
3. #27133004C2semidirect
4. #27132952C2semidirect
5. #27132942C2semidirect
6. #27132877C2semidirect
7. #27132877C2semidirect
8. #27132816C2semidirect
10. #27132772C2semidirect
11. #27132762C2semidirect
12. #27132750C2semidirect
13. #27132743C2semidirect
14. #27132721C2semidirect
15. #482×C191C2semidirect
21. #20259321C22semidirect
24. #20259309C22semidirect
28. #20259287C22semidirect
31. D4×Dic191C22semidirect
39. #20259255C22semidirect
40. #20259253C22semidirect
41. Dic191⋊C8C22semidirect
42. Dic191⋊C8C22semidirect
43. #20259245C22semidirect
44. #20259245C22semidirect
50. #20259232C22semidirect
51. C8×Dic191C22semidirect
54. #107×C191C22semidirect
55. #106×C191C22semidirect
56. #102×C191C22semidirect
57. #102×C191C22semidirect
181. C191#3118semidirect
186. #482D191semidirect
224. #107C2×D191semidirect
226. #106C2×D191semidirect
235. #102C2×D191semidirect
236. #102C2×D191semidirect

Maximal subgroups

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

subgroupindex
#271332802
#271331372
#271330042
#271329522
#271329422
#271328772
#271328162
#271327962
#271327722
#271327622
#271327502
#271327432
#271327212
#482×C1912
#3118191