Finite Group Databasebeta

← #37527052

Subgroups — #37527052

Order 22976.

192 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 192 conjugacy classes of subgroups — too many to draw. Only its 93 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#26040014C211yesmaximal, characteristic, complemented
2#26040010C211yesmaximal, characteristic
3#26040010C211yesmaximal, characteristic
4#26040010C211yesmaximal, characteristic
5#26040009C211yesmaximal, characteristic
6#26040006C211yesmaximal, characteristic, complemented
7#26040005C211yesmaximal, characteristic, complemented
8#26040005C211yesmaximal, characteristic, complemented
9#26040005C211yesmaximal, characteristic, complemented
10#26039993C211yesmaximal, characteristic
11#26039993C211yesmaximal, characteristic
12C4×Dic718C211yesmaximal, characteristic, complemented
13#26039980C211yesmaximal, characteristic, complemented
14#26039973C211yesmaximal, characteristic
15#125×C359C211yesmaximal, characteristic, complemented
16C2×Dic718C2211yescharacteristic
17C2×Dic718C2211yescharacteristic
18C2×C4×D359C2211yescharacteristic
19C4⋊Dic359C2211yescharacteristic
20C4⋊Dic359C2211yescharacteristic
21C4⋊Dic359C2211yescharacteristic
22C4⋊Dic359C2211yescharacteristic
23Dic359⋊C4C2211yescharacteristic
24Dic359⋊C4C2211yescharacteristic
25Dic359⋊C4C2211yescharacteristic
26Dic359⋊C4C2211yescharacteristic
27Dic359⋊C4C2211yescharacteristic
28Dic359⋊C4C2211yescharacteristic
29Dic359⋊C4C2211yescharacteristic
30Dic359⋊C4C2211yescharacteristic
31Dic359⋊C4C2211yescharacteristic
32Dic359⋊C4C2211yescharacteristic
33(C2×D359)⋊C4C2211yescharacteristic
34(C2×D359)⋊C4C2211yescharacteristic
35(C2×D359)⋊C4C2211yescharacteristic
36(C2×D359)⋊C4C2211yescharacteristic
37(C2×D359)⋊C4C2211yescharacteristic
38(C2×D359)⋊C4C2211yescharacteristic
39C4×Dic359C2211yescharacteristic
40C4×Dic359C2211yescharacteristic
41C4×Dic359C2211yescharacteristic
42C4×Dic359C2211yescharacteristic
43C4×Dic359C2211yescharacteristic
44C4⋊C4×C359C2211yescharacteristic
45C4⋊C4×C359C2211yescharacteristic
46C4⋊C4×C359C2211yescharacteristic
47C4⋊C4×C359C2211yescharacteristic
48C4⋊C4×C359C2211yescharacteristic
49C4⋊C4×C359C2211yescharacteristic
50C42×C359C2211yescharacteristic
51C22×D359C2311yescharacteristic
52Dic718—22no—
53Dic718—22no—
54C2×Dic359C2311yescharacteristic
55C2×Dic359C2311yescharacteristic
56C2×Dic359C2311yescharacteristic
57C2×Dic359C2311yescharacteristic
58C2×Dic359C2311yescharacteristic
59C2×Dic359C2311yescharacteristic
60C2×Dic359C2311yescharacteristic
61C4×D359—22no—
62C2×C4×C359C2311yescharacteristic
63C2×C4×C359C2311yescharacteristic
64C2×C4×C359C2311yescharacteristic
65C2×C4×C359C2311yescharacteristic
66C2×C4×C359C2311yescharacteristic
67C2×C4×C359C2311yescharacteristic
68C2×C4×C359C2311yescharacteristic
69C22×C359C2411yescharacteristic
70C2×D359—21no—
71C2×D359—21no—
72C2×D359—21no—
73C4×C359—21no—
74C4×C359—21no—
75C4×C359—21no—
76C4×C359—21no—
77C4×C359—21no—
78C4×C359—21no—
79C4×C359—21no—
80Dic359—21no—
81Dic359—21no—
82Dic359—21no—
83Dic359—21no—
84Dic359—21no—
85Dic359—21no—
86Dic359#4112yes—
87C2×C359C2×#4111yescharacteristic
88C2×C3592−1+411yescharacteristic
89C2×C3592−1+411yescharacteristic
90D359—41no—
91C359#54111yescharacteristic, complemented, Sylow
92#541—3591nomaximal, Sylow
93C4⋊Q8—3591no—
94#126—3591no—
95#126—3591no—
96#126—3591no—
97#126—3591no—
98#125—3591no—
99#125—3591no—
100#125—3591no—
101#125—3591no—
102#125D35911yescharacteristic, complemented
103C22⋊Q8—3591no—
104C22⋊Q8—3591no—
105C4×Q8—3591no—
106C4×Q8—3591no—
107#117—3591no—
108C2×Q8—3591no—
109C2×Q8—3591no—
110C22×C4—3591no—
111C4⋊C4—3591no—
112C4⋊C4—3591no—
113C4⋊C4—3591no—
114C4⋊C4—3591no—
115C4⋊C4—3591no—
116C4⋊C4—3591no—
117C4⋊C4—3591no—
118C4⋊C4—3591no—
119C4⋊C4—3591no—
120C4⋊C4—3591no—
121C4⋊C4—3591no—
122C4⋊C4—3591no—
123C4⋊C4—3591no—
124C4⋊C4—3591no—
125C4⋊C4C2×D35911yescharacteristic
126C4⋊C4C2×D35911yescharacteristic
127C4⋊C4C2×D35911yescharacteristic
128C4⋊C4C2×D35911yescharacteristic
129C4⋊C4C2×D35911yescharacteristic
130C4⋊C4C2×D35911yescharacteristic
131C22⋊C4—3591no—
132C22⋊C4—3591no—
133C22⋊C4—3591no—
134C22⋊C4—3591no—
135C22⋊C4—3591no—
136C22⋊C4—3591no—
137C42—3591no—
138C42—3591no—
139C42—3591no—
140C42—3591no—
141C42—3591no—
142C42C2×D35911yescharacteristic
143C23—3591no—
144Q8—7182no—
145Q8—7182no—
146C2×C4—3591no—
147C2×C4—3591no—
148C2×C4—3591no—
149C2×C4—3591no—
150C2×C4—3591no—
151C2×C4—3591no—
152C2×C4—3591no—
153C2×C4—7182no—
154C2×C4C22×D35911yescharacteristic
155C2×C4C22×D35911yescharacteristic
156C2×C4C22×D35911yescharacteristic
157C2×C4C22×D35911yescharacteristic
158C2×C4C22×D35911yescharacteristic
159C2×C4C22×D35911yescharacteristic
160C2×C4C22×D35911yescharacteristic
161C22—7181no—
162C22—7181no—
163C22—7181no—
164C22C23×D35911yescharacteristic
165C4—21no—
166C4—21no—
167C4—21no—
168C4—21no—
169C4—21no—
170C4—21no—
171C4—21no—
172C4—3592no—
173C4—7181no—
174C4—7181no—
175C4—7181no—
176C4—7181no—
177C4—7181no—
178C4—7181no—
179C2—14361no—
180C2#41×D35911yescharacteristic
181C2#2604006211yescharacteristic
182C2#2604006311yescharacteristic
subgroupG/H
center, FrattiniC22C23×D359
commutator, socle, cosocleC22×C359C24
Fitting#125×C359C2
prime radicalC22×D359C23
hypercenter#125D359
hypocenterC359#541
LCSG ▷ C22×C359 ▷ C359
UCSC1 ◁ C22 ◁ #125

Complements

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

NH ≅ G/Ntype
1. #26040014C2semidirect
6. #26040006C2semidirect
7. #26040005C2semidirect
8. #26040005C2semidirect
9. #26040005C2semidirect
12. C4×Dic718C2semidirect
13. #26039980C2semidirect
15. #125×C359C2semidirect
91. C359#541semidirect
102. #125D359semidirect

Maximal subgroups

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

subgroupindex
#260400142
#260400102
#260400092
#260400062
#260400052
#260399932
C4×Dic7182
#260399802
#260399732
#125×C3592
#541359