Finite Group Databasebeta

← #37582873

Subgroups — #37582873

Order 24448.

404 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#27133293C211yesmaximal, characteristic, complemented
2#27133231C211yesmaximal, characteristic
3#27133029C211yesmaximal, characteristic, complemented
4#27133026C211yesmaximal, characteristic, complemented
5#27133024C211yesmaximal, characteristic, complemented
6#27133022C211yesmaximal, characteristic, complemented
7#27133019C211yesmaximal, characteristic, complemented
8#27133010C211yesmaximal, characteristic, complemented
9#27133008C211yesmaximal, characteristic, complemented
10#27132666C211yesmaximal, characteristic, complemented
11#27132663C211yesmaximal, characteristic, complemented
12#27132658C211yesmaximal, characteristic, complemented
13#102×D191C211yesmaximal, characteristic, complemented
14#27132617C211yesmaximal, characteristic, complemented
15#488×C191C211yesmaximal, characteristic, complemented
16C2×#15690288C2211yescharacteristic
17C2×D4×D191C2211yescharacteristic
18C2×#15690270C2211yescharacteristic
19C2×C8×D191C2211yescharacteristic
20#20259322C2211yescharacteristic, complemented
21#20259321—21no—
22#20259321C2211yescharacteristic, complemented
23#20259319C2211yescharacteristic
24#20259318C2211yescharacteristic
25#20259313C2211yescharacteristic, complemented
26#20259312—21no—
27#20259311C2211yescharacteristic
28#20259302—21no—
29#20259300—21no—
30#20259295—21no—
31#20259295—21no—
32#20259292—21no—
33#20259292—21no—
34#20259280C2211yescharacteristic
35#20259279C2211yescharacteristic
36C4⋊C4×D191C2211yescharacteristic
37#20259246C2211yescharacteristic, complemented
38#20259246C2211yescharacteristic, complemented
39#20259244C2211yescharacteristic
40#20259244C2211yescharacteristic
41#20259244C2211yescharacteristic, complemented
42#20259244C2211yescharacteristic, complemented
43#20259243C2211yescharacteristic
44#20259243C2211yescharacteristic
45#20259242C2211yescharacteristic
46#20259242C2211yescharacteristic
47#20259242C2211yescharacteristic, complemented
48#20259242C2211yescharacteristic, complemented
49#20259233C2211yescharacteristic, complemented
50#20259232C2211yescharacteristic, complemented
51C8×Dic191C2211yescharacteristic, 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—
60#15690288—22no—
61#15690288—22no—
62C2×Dic382—21no—
63C2×Dic382—21no—
64C2×D764—21no—
65C2×D764—21no—
66C2×D764—21no—
67C2×D764C2311yescharacteristic
68C2×D764C2311yescharacteristic
69C2×C22⋊D191—21no—
70C2×C22⋊D191—21no—
71C2×C22⋊D191—21no—
72D4×D191—22no—
73D4×D191—22no—
74C2×C4×D191—21no—
75C2×C4×D191—21no—
76C2×C4×D191C2311yescharacteristic
77#15690270—22no—
78C2×C191⋊C8C2311yescharacteristic
79C2×C191⋊C8C2311yescharacteristic
80C8×D191—22no—
81C4⋊Dic191—21no—
82C4⋊Dic191—21no—
83C4⋊Dic191C2311yescharacteristic
84C4⋊Dic191C2311yescharacteristic
85Dic191⋊C4—21no—
86Dic191⋊C4—21no—
87Dic191⋊C4—21no—
88Dic191⋊C4D411yescharacteristic
89Dic191⋊C4D411yescharacteristic
90(C2×D191)⋊C4—21no—
91(C2×D191)⋊C4—21no—
92(C2×D191)⋊C4—21no—
93(C2×D191)⋊C4D411yescharacteristic
94(C2×D191)⋊C4D411yescharacteristic
95C4×Dic191—21no—
96C4×Dic191C2311yescharacteristic
97C2×Q8×C191C2311yescharacteristic
98C2×D4×C191C2311yescharacteristic
99C2×C8×C191C2311yescharacteristic
100C2×C8×C191C2311yescharacteristic
101C4⋊C4×C191—21no—
102C4⋊C4×C191—21no—
103C4⋊C4×C191C2311yescharacteristic
104C4⋊C4×C191C2311yescharacteristic
105C22⋊C4×C191—21no—
106C22⋊C4×C191—21no—
107C42×C191C2311yescharacteristic
108C22×D191—21no—
109C22×D191—21no—
110C22×D191—42no—
111C22×D191—81no—
112C22×D191—81no—
113C22×D191C2×D411yescharacteristic
114Dic382—81no—
115Dic382—81no—
116D764—21no—
117D764—21no—
118D764—21no—
119D764—21no—
120D764—42no—
121D764—81no—
122D764—81no—
123C22⋊D191—42no—
124C22⋊D191—81no—
125C22⋊D191—81no—
126C2×Dic191—21no—
127C2×Dic191—21no—
128C2×Dic191C2×D411yescharacteristic
129C2×Dic191C2×D411yescharacteristic
130C2×Dic191C2×D411yescharacteristic
131C4×D191—42no—
132C4×D191—81no—
133C4×D191#4112yes—
134C4×D191#4112yes—
135C191⋊C8—21no—
136C191⋊C8—21no—
137C23×C191—21no—
138Q8×C191—21no—
139Q8×C191—21no—
140D4×C191—21no—
141D4×C191—21no—
142C2×C4×C191—21no—
143C2×C4×C191—21no—
144C2×C4×C191—21no—
145C2×C4×C191C2×D411yescharacteristic
146C2×C4×C191C2×D411yescharacteristic
147C2×C4×C191C2411yescharacteristic
148C8×C191—21no—
149C8×C191—21no—
150C22×C191—41no—
151C22×C191—41no—
152C22×C191—41no—
153C22×C191C22×D411yescharacteristic
154C2×D191—21no—
155C2×D191—21no—
156C2×D191—41no—
157C2×D191—41no—
158C2×D191—41no—
159C2×D191—41no—
160C2×D191—41no—
161C2×D191—41no—
162C2×D191—84no—
163C2×D191#12412yes—
164C4×C191—21no—
165C4×C191—21no—
166C4×C191—41no—
167C4×C191—41no—
168C4×C191—41no—
169C4×C191C2×#4111yescharacteristic
170C4×C191C2×#4111yescharacteristic
171Dic191—21no—
172Dic191—21no—
173Dic191—41no—
174Dic191—41no—
175Dic191#12412yes—
176C2×C191—81no—
177C2×C191C2×#12411yescharacteristic
178C2×C191#57611yescharacteristic
179C2×C191#57711yescharacteristic
180D191—22no—
181D191—81no—
182D191—81no—
183C191#313611yescharacteristic, complemented, Sylow
184#3136—1911nomaximal, Sylow
185#544—1911no—
186#535—1911no—
187#490—1911no—
188#490—1911no—
189#489—1911no—
190#489—1911no—
191#488—1911no—
192#488D19111yescharacteristic, complemented
193#486—1911no—
194#486—1911no—
195#418—1911no—
196#417—1911no—
197#416—1911no—
198C2×#102—1911no—
199#405—1911no—
200C2×#41—1911no—
201C22×D4—1911no—
202C2×M16—1911no—
203C22×C8—1911no—
204C4⋊Q8—3821no—
205C4⋊Q8—1911no—
206C4⋊Q8—1911no—
207#127—1911no—
208#127—1911no—
209#125—3821no—
210#125—1911no—
211#125C2×D19111yescharacteristic, complemented
212#124—1911no—
213#124C2×D19111yescharacteristic
214C22⋊Q8—3821no—
215C22⋊Q8—3821no—
216#121—3821no—
217#121—3821no—
218#120—3821no—
219#120—3821no—
220#117—1911no—
221#117—1911no—
222C2×C4⋊C4—1911no—
223#103—1911no—
224#103—1911no—
225#103C2×D19111yescharacteristic, complemented
226#103C2×D19111yescharacteristic, complemented
227#102—1911no—
228#102—1911no—
229#102—1911no—
230#102—1911no—
231#102—1911no—
232#102—1911no—
233#102—1911no—
234#102—1911no—
235#102—1911no—
236#102—1911no—
237#102C2×D19111yescharacteristic
238#102C2×D19111yescharacteristic
239#97—1911no—
240#97—1911no—
241C4×C8—1911no—
242C4×C8C2×D19111yescharacteristic, complemented
243C24—3821no—
244#41—3822no—
245#41—3822no—
246C2×Q8—3821no—
247C2×Q8—3821no—
248C2×Q8C22×D19111yescharacteristic
249C2×D4—3821no—
250C2×D4—3822no—
251C2×D4—3822no—
252C2×D4—3821no—
253C2×D4—3821no—
254C2×D4—3821no—
255C2×D4—3821no—
256C2×D4—3821no—
257C2×D4—1911no—
258C2×D4—1911no—
259C2×D4C22×D19111yescharacteristic
260C22×C4—3821no—
261C22×C4—3821no—
262C22×C4—1911no—
263M16—3822no—
264C2×C8—3822no—
265C2×C8—1911no—
266C2×C8—1911no—
267C2×C8C22×D19111yescharacteristic
268C2×C8C22×D19111yescharacteristic
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—3821no—
272C4⋊C4—3821no—
273C4⋊C4—3821no—
274C4⋊C4—3821no—
275C4⋊C4—3821no—
276C4⋊C4—1911no—
277C4⋊C4—1911no—
278C4⋊C4—1911no—
279C4⋊C4—1911no—
280C4⋊C4C22×D19111yescharacteristic
281C4⋊C4C22×D19111yescharacteristic
282C22⋊C4—21no—
283C22⋊C4—21no—
284C22⋊C4—3821no—
285C22⋊C4—3821no—
286C22⋊C4—3821no—
287C22⋊C4—1911no—
288C22⋊C4—1911no—
289C42—3821no—
290C42—1911no—
291C42C22×D19111yescharacteristic
292C23—21no—
293C23—3821no—
294C23—3821no—
295C23—1911no—
296C23—15281no—
297C23—15281no—
298C23—7642no—
299Q8—21no—
300Q8—21no—
301Q8—15281no—
302Q8—15281no—
303D4—21no—
304D4—21no—
305D4—3821no—
306D4—3821no—
307D4—3821no—
308D4—3821no—
309D4—15281no—
310D4—15281no—
311D4—15281no—
312D4—15281no—
313D4—7642no—
314D4—7642no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—3821no—
319C2×C4—3821no—
320C2×C4—1911no—
321C2×C4—1911no—
322C2×C4—1911no—
323C2×C4—1912no—
324C2×C4—1912no—
325C2×C4—15281no—
326C2×C4—7642no—
327C2×C4D4×D19111yescharacteristic
328C2×C4D4×D19111yescharacteristic
329C2×C4C23×D19111yescharacteristic
330C8—21no—
331C8—21no—
332C8—3821no—
333C8—3821no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—3821no—
338C22—3821no—
339C22—1912no—
340C22—15284no—
341C22—7641no—
342C22—7641no—
343C22—7641no—
344C22—7641no—
345C22—7641no—
346C22—7641no—
347C22C2×D4×D19111yescharacteristic
348C4—21no—
349C4—21no—
350C4—41no—
351C4—41no—
352C4—41no—
353C4—3821no—
354C4—3821no—
355C4—1912no—
356C4—7641no—
357C4—7641no—
358C4#41×D19111yescharacteristic
359C4#41×D19111yescharacteristic
360C2—81no—
361C2—3822no—
362C2—15281no—
363C2—15281no—
364C2#124×D19111yescharacteristic
365C2#2713346511yescharacteristic
366C2#2713347011yescharacteristic
subgroupG/H
centerC22C2×D4×D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
Fitting#488×C191C2
socleC22×C191C22×D4
prime radical#27133231C2
hypercenter#488D191
hypocenterC191#3136
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. #27133293C2semidirect
3. #27133029C2semidirect
4. #27133026C2semidirect
5. #27133024C2semidirect
6. #27133022C2semidirect
7. #27133019C2semidirect
8. #27133010C2semidirect
9. #27133008C2semidirect
10. #27132666C2semidirect
11. #27132663C2semidirect
12. #27132658C2semidirect
13. #102×D191C2semidirect
14. #27132617C2semidirect
15. #488×C191C2semidirect
20. #20259322C22semidirect
22. #20259321C22semidirect
25. #20259313C22semidirect
37. #20259246C22semidirect
38. #20259246C22semidirect
41. #20259244C22semidirect
42. #20259244C22semidirect
47. #20259242C22semidirect
48. #20259242C22semidirect
49. #20259233C22semidirect
50. #20259232C22semidirect
51. C8×Dic191C22semidirect
52. #125×C191C22semidirect
54. #103×C191C22semidirect
55. #103×C191C22semidirect
58. C4×C8×C191C22semidirect
183. C191#3136semidirect
192. #488D191semidirect
211. #125C2×D191semidirect
225. #103C2×D191semidirect
226. #103C2×D191semidirect
242. C4×C8C2×D191semidirect

Maximal subgroups

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

subgroupindex
#271332932
#271332312
#271330292
#271330262
#271330242
#271330222
#271330192
#271330102
#271330082
#271326662
#271326632
#271326582
#102×D1912
#271326172
#488×C1912
#3136191