Finite Group Databasebeta

← #37583916

Subgroups — #37583916

Order 24448.

354 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#27133197C211yesmaximal, characteristic, complemented
2#27132970C211yesmaximal, characteristic, complemented
3#27132967C211yesmaximal, characteristic, complemented
4#27132963C211yesmaximal, characteristic, complemented
5#27132960C211yesmaximal, characteristic, complemented
6#27132919C211yesmaximal, characteristic, complemented
7#27132914C211yesmaximal, characteristic
8#27132911C211yesmaximal, characteristic, complemented
9#27132907C211yesmaximal, characteristic, complemented
10#27132885C211yesmaximal, characteristic, complemented
11#27132882C211yesmaximal, characteristic, complemented
12#27132878C211yesmaximal, characteristic, complemented
13#27132875C211yesmaximal, characteristic, complemented
14#27132687C211yesmaximal, characteristic, complemented
15#529×C191C211yesmaximal, characteristic, complemented
16C2×#15690277C2211yescharacteristic
17C2×#15690275C2211yescharacteristic
18C2×#15690274C2211yescharacteristic
19C2×#15690272C2211yescharacteristic
20C2×#15690271C2211yescharacteristic
21C2×#15690271C2211yescharacteristic
22#20259316—21no—
23#20259314C2211yescharacteristic
24#20259310C2211yescharacteristic
25#20259305—21no—
26#20259301C2211yescharacteristic
27#20259296C2211yescharacteristic
28C4×Dic382C2211yescharacteristic
29C4×D764C2211yescharacteristic
30C4×C22⋊D191—21no—
31#20259279—21no—
32#20259255C2211yescharacteristic
33#20259255C2211yescharacteristic
34#20259253C2211yescharacteristic
35#20259253C2211yescharacteristic
36C4⋊(C191⋊C8)C2211yescharacteristic
37C4⋊(C191⋊C8)C2211yescharacteristic
38C4⋊(C191⋊C8)C2211yescharacteristic
39C4⋊(C191⋊C8)C2211yescharacteristic
40#20259246C2211yescharacteristic
41#20259246C2211yescharacteristic
42#20259245C2211yescharacteristic
43#20259245C2211yescharacteristic
44#20259243C2211yescharacteristic
45#20259243C2211yescharacteristic
46#20259242C2211yescharacteristic
47#20259242C2211yescharacteristic
48#126×C191—21no—
49#125×C191C2211yescharacteristic
50#124×C191C2211yescharacteristic
51#123×C191—21no—
52C22⋊Q8×C191C2211yescharacteristic
53#121×C191C2211yescharacteristic
54C4×Q8×C191C2211yescharacteristic
55C4×D4×C191—21no—
56C4×D4×C191C2211yescharacteristic
57#117×C191—21no—
58C2×C42×C191C2211yescharacteristic
59C2×Dic382C2311yescharacteristic
60C2×D764C2311yescharacteristic
61C2×C22⋊D191—21no—
62C2×C4×D191—21no—
63#15690277—41no—
64#15690275—41no—
65#15690274—41no—
66#15690272—41no—
67#15690271—41no—
68#15690271—41no—
69C2×C191⋊C8C2311yescharacteristic
70C2×C191⋊C8C2311yescharacteristic
71C2×C191⋊C8C2311yescharacteristic
72C2×C191⋊C8C2311yescharacteristic
73C4⋊Dic191C2311yescharacteristic
74C4⋊Dic191C2311yescharacteristic
75Dic191⋊C4—21no—
76Dic191⋊C4—21no—
77Dic191⋊C4—21no—
78Dic191⋊C4—21no—
79C22⋊Dic191—21no—
80(C2×D191)⋊C4—21no—
81(C2×D191)⋊C4—21no—
82(C2×D191)⋊C4—21no—
83(C2×D191)⋊C4—21no—
84C4×Dic191—21no—
85C2×Q8×C191C2311yescharacteristic
86C2×D4×C191—21no—
87C2×D4×C191C2311yescharacteristic
88C22×C4×C191—21no—
89C22×C4×C191D411yescharacteristic
90C22×C4×C191D411yescharacteristic
91C22×C4×C191C2311yescharacteristic
92C4⋊C4×C191—21no—
93C4⋊C4×C191—21no—
94C4⋊C4×C191—21no—
95C4⋊C4×C191—21no—
96C4⋊C4×C191C2311yescharacteristic
97C4⋊C4×C191C2311yescharacteristic
98C22⋊C4×C191—21no—
99C22⋊C4×C191—21no—
100C22⋊C4×C191—21no—
101C22⋊C4×C191—21no—
102C22⋊C4×C191—21no—
103C42×C191—21no—
104C42×C191D411yescharacteristic
105C42×C191D411yescharacteristic
106C42×C191C2311yescharacteristic
107C42×C191C2311yescharacteristic
108C22×D191—21no—
109Dic382—21no—
110Dic382—21no—
111D764—21no—
112D764—21no—
113C22⋊D191—42no—
114C2×Dic191—21no—
115C2×Dic191—21no—
116C2×Dic191—21no—
117C4×D191—42no—
118C191⋊C8—21no—
119C191⋊C8—21no—
120C191⋊C8—21no—
121C191⋊C8—21no—
122C23×C191—21no—
123C23×C191C2×D411yescharacteristic
124Q8×C191—21no—
125Q8×C191—21no—
126D4×C191—21no—
127D4×C191—21no—
128D4×C191—42no—
129C2×C4×C191—21no—
130C2×C4×C191—21no—
131C2×C4×C191—21no—
132C2×C4×C191—21no—
133C2×C4×C191—21no—
134C2×C4×C191—41no—
135C2×C4×C191—41no—
136C2×C4×C191—42no—
137C2×C4×C191C2×D411yescharacteristic
138C2×C4×C191C2×D411yescharacteristic
139C2×C4×C191C2×D411yescharacteristic
140C2×C4×C191C2×D411yescharacteristic
141C2×C4×C191C2×D411yescharacteristic
142C2×C4×C191C2411yescharacteristic
143C22×C191—21no—
144C22×C191—21no—
145C22×C191—21no—
146C22×C191—41no—
147C22×C191—41no—
148C22×C191—41no—
149C22×C191C22×D411yescharacteristic
150C2×D191—41no—
151C2×D191—41no—
152C2×D191—41no—
153C4×C191—21no—
154C4×C191—21no—
155C4×C191—21no—
156C4×C191—21no—
157C4×C191—21no—
158C4×C191—41no—
159C4×C191—41no—
160C4×C191—41no—
161C4×C191H(5,𝔽2)11yescharacteristic
162C4×C1912−1+411yescharacteristic
163Dic191—41no—
164Dic191—41no—
165Dic191—41no—
166C2×C191—41no—
167C2×C191—81no—
168C2×C191#53711yescharacteristic
169C2×C191#57511yescharacteristic
170C2×C191#57511yescharacteristic
171D191—81no—
172C191#325611yescharacteristic, complemented, Sylow
173#3256—1911nomaximal, Sylow
174#529—1911no—
175#529D19111yescharacteristic, complemented
176#479—1911no—
177#479—1911no—
178#478—1911no—
179#478—1911no—
180#470—1911no—
181#469—1911no—
182#468—1911no—
183#468—1911no—
184#464—1911no—
185#464—1911no—
186#463—1911no—
187#463—1911no—
188#423—1911no—
189C2×Q16—1911no—
190C2×SD16—1911no—
191C2×SD16—1911no—
192C2×D8—1911no—
193C2×M16—1911no—
194C2×M16—1911no—
195#126—21no—
196#126—3821no—
197#125—1911no—
198#125C2×D19111yescharacteristic
199#124—1911no—
200#124C2×D19111yescharacteristic
201#123—21no—
202#123—3821no—
203C22⋊Q8—1911no—
204C22⋊Q8C2×D19111yescharacteristic
205#121—1911no—
206#121C2×D19111yescharacteristic
207C4×Q8—1911no—
208C4×Q8C2×D19111yescharacteristic
209C4×D4—21no—
210C4×D4—3821no—
211C4×D4—1911no—
212C4×D4C2×D19111yescharacteristic
213#117—21no—
214#117—3821no—
215C2×C42C2×D19111yescharacteristic
216#107—1911no—
217#107—1911no—
218#106—1911no—
219#106—1911no—
220C4⋊C8—1911no—
221C4⋊C8—1911no—
222C4⋊C8—1911no—
223C4⋊C8—1911no—
224#103—1911no—
225#103—1911no—
226#103—1911no—
227#103—1911no—
228#102—1911no—
229#102—1911no—
230#102—1911no—
231#102—1911no—
232C2×Q8—1911no—
233C2×Q8C22×D19111yescharacteristic
234C2×D4—21no—
235C2×D4—3821no—
236C2×D4—1911no—
237C2×D4C22×D19111yescharacteristic
238C22×C4—21no—
239C22×C4—3821no—
240C22×C4C22⋊D19111yescharacteristic
241C22×C4C22⋊D19111yescharacteristic
242C22×C4C22×D19111yescharacteristic
243Q16—7641no—
244SD16—7641no—
245SD16—7641no—
246D8—7641no—
247M16—7641no—
248M16—7641no—
249C2×C8—1911no—
250C2×C8—1911no—
251C2×C8—1911no—
252C2×C8—1911no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—21no—
257C4⋊C4—3821no—
258C4⋊C4—3821no—
259C4⋊C4—3821no—
260C4⋊C4—3821no—
261C4⋊C4—1911no—
262C4⋊C4—1911no—
263C4⋊C4C22×D19111yescharacteristic
264C4⋊C4C22×D19111yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—21no—
270C22⋊C4—3821no—
271C22⋊C4—3821no—
272C22⋊C4—3821no—
273C22⋊C4—3821no—
274C22⋊C4—3821no—
275C42—21no—
276C42—3821no—
277C42C22⋊D19111yescharacteristic
278C42C22⋊D19111yescharacteristic
279C42C22×D19111yescharacteristic
280C42C22×D19111yescharacteristic
281C23—21no—
282C23—3821no—
283C23C2×C22⋊D19111yescharacteristic
284Q8—21no—
285Q8—21no—
286Q8—3821no—
287Q8—3821no—
288D4—21no—
289D4—21no—
290D4—42no—
291D4—3821no—
292D4—3821no—
293D4—7642no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—42no—
302C2×C4—3821no—
303C2×C4—3821no—
304C2×C4—3821no—
305C2×C4—7642no—
306C2×C4C2×C22⋊D19111yescharacteristic
307C2×C4C2×C22⋊D19111yescharacteristic
308C2×C4C2×C22⋊D19111yescharacteristic
309C2×C4C2×C22⋊D19111yescharacteristic
310C2×C4C2×C22⋊D19111yescharacteristic
311C2×C4C23×D19111yescharacteristic
312C8—3821no—
313C8—3821no—
314C8—3821no—
315C8—3821no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—41no—
320C22—41no—
321C22—41no—
322C22—7641no—
323C22—7641no—
324C22—7641no—
325C22C22×C22⋊D19111yescharacteristic
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—21no—
331C4—41no—
332C4—41no—
333C4—41no—
334C4—7641no—
335C4—7641no—
336C4—7641no—
337C4#2025936811yescharacteristic
338C4#2025936911yescharacteristic
339C2—41no—
340C2—81no—
341C2—15281no—
342C2#2713324111yescharacteristic
343C2#2713346111yescharacteristic
344C2#2713346111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
Fitting#529×C191C2
socleC22×C191C22×D4
prime radical#27132914C2
hypercenter#529D191
hypocenterC191#3256
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C2×C42 ◁ #529

Complements

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

NH ≅ G/Ntype
1. #27133197C2semidirect
2. #27132970C2semidirect
3. #27132967C2semidirect
4. #27132963C2semidirect
5. #27132960C2semidirect
6. #27132919C2semidirect
8. #27132911C2semidirect
9. #27132907C2semidirect
10. #27132885C2semidirect
11. #27132882C2semidirect
12. #27132878C2semidirect
13. #27132875C2semidirect
14. #27132687C2semidirect
15. #529×C191C2semidirect
172. C191#3256semidirect
175. #529D191semidirect

Maximal subgroups

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

subgroupindex
#271331972
#271329702
#271329672
#271329632
#271329602
#271329192
#271329142
#271329112
#271329072
#271328852
#271328822
#271328782
#271328752
#271326872
#529×C1912
#3256191