Finite Group Databasebeta

← #37583356

Subgroups — #37583356

Order 24448.

418 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 109 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#27133173C212yesmaximal, complemented
2#27133007C212yesmaximal, complemented
3#27132986C212yesmaximal, complemented
4#27132921C211yesmaximal, characteristic, complemented
5#27132907C212yesmaximal, complemented
6#27132826C212yesmaximal, complemented
7#27132805C212yesmaximal, complemented
8#27132626C211yesmaximal, characteristic, complemented
9#469×C191C211yesmaximal, characteristic, complemented
10C2×#15690286C2212yes—
11C22×C4×D191C2211yescharacteristic
12C2×Dic764C2211yescharacteristic, complemented
13C2×#15690275C2212yescomplemented
14C2×#15690271C2211yescharacteristic
15#20259304—22no—
16#20259302C2212yes—
17#20259301C2212yes—
18#20259293C2212yes—
19#20259290—22no—
20D4×Dic191—22no—
21(C22⋊D191)⋊C4—22no—
22#20259280C2212yes—
23#20259255C2212yescomplemented
24#20259254C2211yescharacteristic, complemented
25#20259247C2212yescomplemented
26#20259245C2212yescomplemented
27#20259243C2212yescomplemented
28(C2×D191)⋊C8C2212yes—
29(C2×D191)⋊C8C2212yes—
30C2×D8×C191C2211yescharacteristic, complemented
31C2×M16×C191C2211yescharacteristic
32#121×C191C2212yes—
33#106×C191C2211yescharacteristic, complemented
34#102×C191C2212yescomplemented
35C23×D191D411yescharacteristic
36#15690286—42no—
37#15690286—42no—
38C2×Dic382C2312yes—
39C2×C22⋊D191—22no—
40C2×C22⋊D191—22no—
41C22×Dic191—22no—
42C22×Dic191D411yescharacteristic
43C2×C4×D191—41no—
44C2×C4×D191—41no—
45C2×C4×D191D412yes—
46C2×C4×D191C2312yes—
47Dic764—41no—
48#15690275—42no—
49#15690271—41no—
50C2×C191⋊C8C2312yes—
51C4⋊Dic191—22no—
52C4⋊Dic191C2312yes—
53Dic191⋊C4—22no—
54C22⋊Dic191—22no—
55C22⋊Dic191—22no—
56(C2×D191)⋊C4—22no—
57(C2×D191)⋊C4—22no—
58C4×Dic191—22no—
59C2×D4×C191—22no—
60C2×D4×C191C2312yes—
61C22×C4×C191C2311yescharacteristic
62D8×C191—41no—
63M16×C191—41no—
64C2×C8×C191C2311yescharacteristic
65C2×C8×C191C2311yescharacteristic
66C4⋊C4×C191C2312yes—
67C22⋊C4×C191—22no—
68C22×D191—41no—
69C22×D191—42no—
70C22×D191C2×D412yes—
71Dic382—22no—
72Dic382—22no—
73C22⋊D191—44no—
74C22⋊D191—44no—
75C2×Dic191—22no—
76C2×Dic191—22no—
77C2×Dic191—41no—
78C2×Dic191—44no—
79C2×Dic191C2×D412yes—
80C4×D191—22no—
81C4×D191—22no—
82C4×D191—42no—
83C191⋊C8—22no—
84C23×C191—22no—
85C23×C191C2×D411yescharacteristic
86D4×C191—22no—
87D4×C191—22no—
88D4×C191—44no—
89C2×C4×C191—21no—
90C2×C4×C191—21no—
91C2×C4×C191—22no—
92C2×C4×C191C2×D411yescharacteristic
93C2×C4×C191C2411yescharacteristic
94C8×C191—21no—
95C8×C191—21no—
96C22×C191—21no—
97C22×C191—22no—
98C22×C191—42no—
99C22×C191—42no—
100C22×C191—42no—
101C22×C191C22×D411yescharacteristic
102C2×D191—22no—
103C2×D191—22no—
104C2×D191—22no—
105C2×D191—44no—
106C4×C191—21no—
107C4×C191—42no—
108C4×C191H(5,𝔽2)11yescharacteristic
109C4×C191H(5,𝔽2)11yescharacteristic
110Dic191—22no—
111Dic191—42no—
112Dic191—42no—
113C2×C191—41no—
114C2×C191—82no—
115C2×C191#53411yescharacteristic
116C2×C191#57512yes—
117D191—42no—
118C191#319711yescharacteristic, complemented, Sylow
119#3197—1911nomaximal, Sylow
120#525—1912no—
121#485—1912no—
122#482—1912no—
123#470—1911no—
124#469D19111yescharacteristic, complemented
125#468—1912no—
126#452—1912no—
127#449—1912no—
128#407—1911no—
129C2×#41—1912no—
130C23×C4—1911no—
131C2×Q16—1911no—
132C2×SD16—1912no—
133C2×D8C2×D19111yescharacteristic, complemented
134C2×M16—1911no—
135C2×M16C2×D19111yescharacteristic
136#123—3822no—
137C22⋊Q8—1912no—
138C22⋊Q8—1912no—
139#121—1912no—
140#121C2×D19112yes—
141#120—3822no—
142C4×D4—3822no—
143C4×D4—3822no—
144#117—1912no—
145#107—1912no—
146#106—1911no—
147#106C2×D19111yescharacteristic, complemented
148#103—1912no—
149#103—1912no—
150#102—1912no—
151#102C2×D19112yescomplemented
152C22⋊C8—1912no—
153C22⋊C8—1912no—
154C24—1911no—
155#41—7642no—
156#41—7642no—
157C2×Q8—1912no—
158C2×D4—22no—
159C2×D4—3822no—
160C2×D4—3822no—
161C2×D4C22×D19112yes—
162C22×C4—3822no—
163C22×C4—1912no—
164C22×C4—1911no—
165C22×C4—1912no—
166C22×C4—7641no—
167C22×C4—7641no—
168C22×C4C22×D19111yescharacteristic
169Q16—7641no—
170SD16—7642no—
171D8—41no—
172M16—41no—
173M16—7641no—
174C2×C8—1912no—
175C2×C8C22×D19111yescharacteristic
176C2×C8C22×D19111yescharacteristic
177C4⋊C4—3822no—
178C4⋊C4—3822no—
179C4⋊C4—1912no—
180C4⋊C4C22×D19112yes—
181C22⋊C4—22no—
182C22⋊C4—3822no—
183C22⋊C4—3822no—
184C22⋊C4—3822no—
185C22⋊C4—3822no—
186C42—3822no—
187C23—22no—
188C23—1912no—
189C23—7641no—
190C23—7642no—
191C23D4×D19111yescharacteristic
192Q8—3822no—
193Q8—3822no—
194D4—22no—
195D4—22no—
196D4—44no—
197D4—7644no—
198D4—7644no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—22no—
202C2×C4—3822no—
203C2×C4—3822no—
204C2×C4—3822no—
205C2×C4—3822no—
206C2×C4—1912no—
207C2×C4—7642no—
208C2×C4—7641no—
209C2×C4—7644no—
210C2×C4D4×D19111yescharacteristic
211C2×C4C23×D19111yescharacteristic
212C8—21no—
213C8—21no—
214C8—3822no—
215C22—22no—
216C22—21no—
217C22—42no—
218C22—42no—
219C22—42no—
220C22—3822no—
221C22—3822no—
222C22—3822no—
223C22—7644no—
224C22C2×D4×D19111yescharacteristic
225C4—21no—
226C4—42no—
227C4—3822no—
228C4—7642no—
229C4—7642no—
230C4#2025936711yescharacteristic
231C4#2025936811yescharacteristic
232C2—41no—
233C2—82no—
234C2—7642no—
235C2#2713322111yescharacteristic
236C2#2713345912yes—
subgroupG/H
centerC22C2×D4×D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
Fitting#469×C191C2
socleC22×C191C22×D4
hypercenter#469D191
hypocenterC191#3197
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. #27133173C2semidirect
2. #27133007C2semidirect
3. #27132986C2semidirect
4. #27132921C2semidirect
5. #27132907C2semidirect
6. #27132826C2semidirect
7. #27132805C2semidirect
8. #27132626C2semidirect
9. #469×C191C2semidirect
12. C2×Dic764C22semidirect
13. C2×#15690275C22semidirect
23. #20259255C22semidirect
24. #20259254C22semidirect
25. #20259247C22semidirect
26. #20259245C22semidirect
27. #20259243C22semidirect
30. C2×D8×C191C22semidirect
33. #106×C191C22semidirect
34. #102×C191C22semidirect
118. C191#3197semidirect
124. #469D191semidirect
133. C2×D8C2×D191semidirect
147. #106C2×D191semidirect
151. #102C2×D191semidirect

Maximal subgroups

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

subgroupindex
#271331732
#271330072
#271329862
#271329212
#271329072
#271328262
#271328052
#271326262
#469×C1912
#3197191