Finite Group Databasebeta

← #37527160

Subgroups — #37527160

Order 22976.

212 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 95 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, complemented
3#26040010C211yesmaximal, characteristic, complemented
4#26040008C211yesmaximal, characteristic, complemented
5#26040001C211yesmaximal, characteristic
6#26040001C211yesmaximal, characteristic
7#26039993C211yesmaximal, characteristic, complemented
8#26039992C211yesmaximal, characteristic, complemented
9C4×Dic718C211yesmaximal, characteristic, complemented
10#26039980C211yesmaximal, characteristic, complemented
11#26039980C211yesmaximal, characteristic, complemented
12(C22⋊D359)⋊C4C211yesmaximal, characteristic
13#26039972C211yesmaximal, characteristic, complemented
14#26039971C211yesmaximal, characteristic, complemented
15#126×C359C211yesmaximal, characteristic, complemented
16C2×Dic718C2211yescharacteristic
17C2×Dic718C2211yescharacteristic
18C2×Dic718C2211yescharacteristic
19C2×C22⋊D359C2211yescharacteristic
20C22×Dic359C2211yescharacteristic
21C2×C4×D359C2211yescharacteristic
22C4⋊Dic359C2211yescharacteristic
23C4⋊Dic359C2211yescharacteristic
24Dic359⋊C4C2211yescharacteristic
25Dic359⋊C4C2211yescharacteristic
26Dic359⋊C4C2211yescharacteristic
27Dic359⋊C4C2211yescharacteristic
28Dic359⋊C4C2211yescharacteristic
29Dic359⋊C4C2211yescharacteristic
30Dic359⋊C4C2211yescharacteristic
31C22⋊Dic359C2211yescharacteristic
32C22⋊Dic359C2211yescharacteristic
33(C2×D359)⋊C4C2211yescharacteristic
34(C2×D359)⋊C4C2211yescharacteristic
35(C2×D359)⋊C4C2211yescharacteristic
36(C2×D359)⋊C4C2211yescharacteristic
37(C2×D359)⋊C4C2211yescharacteristic
38C4×Dic359C2211yescharacteristic
39C4×Dic359C2211yescharacteristic
40C4×Dic359C2211yescharacteristic
41C4×Dic359C2211yescharacteristic
42C4×Dic359C2211yescharacteristic
43C4×Dic359C2211yescharacteristic
44C4⋊C4×C359C2211yescharacteristic
45C4⋊C4×C359C2211yescharacteristic
46C4⋊C4×C359C2211yescharacteristic
47C22⋊C4×C359C2211yescharacteristic
48C22⋊C4×C359C2211yescharacteristic
49C22⋊C4×C359C2211yescharacteristic
50C42×C359C2211yescharacteristic
51C22×D359C2311yescharacteristic
52Dic718—22no—
53Dic718—22no—
54Dic718—22no—
55C22⋊D359—22no—
56C2×Dic359—22no—
57C2×Dic359C2311yescharacteristic
58C2×Dic359C2311yescharacteristic
59C2×Dic359C2311yescharacteristic
60C2×Dic359C2311yescharacteristic
61C2×Dic359C2311yescharacteristic
62C2×Dic359C2311yescharacteristic
63C2×Dic359C2311yescharacteristic
64C4×D359—22no—
65C23×C359C2311yescharacteristic
66C2×C4×C359C2311yescharacteristic
67C2×C4×C359C2311yescharacteristic
68C2×C4×C359C2311yescharacteristic
69C2×C4×C359C2311yescharacteristic
70C2×C4×C359C2311yescharacteristic
71C2×C4×C359C2311yescharacteristic
72C22×C359—21no—
73C22×C359—21no—
74C22×C359—21no—
75C22×C359C2411yescharacteristic
76C2×D359—21no—
77C2×D359—21no—
78C2×D359—21no—
79C4×C359—21no—
80C4×C359—21no—
81C4×C359—21no—
82C4×C359—21no—
83C4×C359—21no—
84C4×C359—21no—
85Dic359—21no—
86Dic359—21no—
87Dic359—21no—
88Dic359—21no—
89Dic359—21no—
90Dic359#4112yes—
91Dic359#4112yes—
92C2×C359—41no—
93C2×C359C2×#4111yescharacteristic
94C2×C359C2×#4111yescharacteristic
95C2×C3592−1+411yescharacteristic
96D359—41no—
97C359#55611yescharacteristic, complemented, Sylow
98#556—3591nomaximal, Sylow
99C4⋊Q8—3591no—
100#126—3591no—
101#126—3591no—
102#126—3591no—
103#126D35911yescharacteristic, complemented
104#124—3591no—
105#124—3591no—
106C22⋊Q8—3591no—
107C22⋊Q8—3591no—
108C4×Q8—3591no—
109C4×Q8—3591no—
110C4×Q8—3591no—
111C4×D4—3591no—
112#117—3591no—
113#117—3591no—
114C2×Q8—3591no—
115C2×Q8—3591no—
116C2×Q8—3591no—
117C2×D4—3591no—
118C22×C4—3591no—
119C22×C4—3591no—
120C4⋊C4—3591no—
121C4⋊C4—3591no—
122C4⋊C4—3591no—
123C4⋊C4—3591no—
124C4⋊C4—3591no—
125C4⋊C4—3591no—
126C4⋊C4—3591no—
127C4⋊C4—3591no—
128C4⋊C4—3591no—
129C4⋊C4C2×D35911yescharacteristic
130C4⋊C4C2×D35911yescharacteristic
131C4⋊C4C2×D35911yescharacteristic
132C22⋊C4—3591no—
133C22⋊C4—3591no—
134C22⋊C4—3591no—
135C22⋊C4—3591no—
136C22⋊C4—3591no—
137C22⋊C4—3591no—
138C22⋊C4—3591no—
139C22⋊C4C2×D35911yescharacteristic
140C22⋊C4C2×D35911yescharacteristic
141C22⋊C4C2×D35911yescharacteristic
142C42—3591no—
143C42—3591no—
144C42—3591no—
145C42—3591no—
146C42—3591no—
147C42—3591no—
148C42C2×D35911yescharacteristic
149C23—3591no—
150C23C22×D35911yescharacteristic
151Q8—7182no—
152Q8—7182no—
153Q8—7182no—
154D4—7182no—
155C2×C4—3591no—
156C2×C4—3591no—
157C2×C4—3591no—
158C2×C4—3591no—
159C2×C4—3591no—
160C2×C4—3591no—
161C2×C4—3591no—
162C2×C4—7182no—
163C2×C4—7182no—
164C2×C4C22×D35911yescharacteristic
165C2×C4C22×D35911yescharacteristic
166C2×C4C22×D35911yescharacteristic
167C2×C4C22×D35911yescharacteristic
168C2×C4C22×D35911yescharacteristic
169C2×C4C22×D35911yescharacteristic
170C22—21no—
171C22—21no—
172C22—21no—
173C22—7181no—
174C22—7181no—
175C22—7181no—
176C22C23×D35911yescharacteristic
177C4—21no—
178C4—21no—
179C4—21no—
180C4—21no—
181C4—21no—
182C4—21no—
183C4—3592no—
184C4—3592no—
185C4—7181no—
186C4—7181no—
187C4—7181no—
188C4—7181no—
189C4—7181no—
190C2—41no—
191C2—14361no—
192C2#41×D35911yescharacteristic
193C2#41×D35911yescharacteristic
194C2#2604006211yescharacteristic
subgroupG/H
center, FrattiniC22C23×D359
commutator, socle, cosocleC22×C359C24
Fitting#126×C359C2
prime radicalC2×C22⋊D359C22
hypercenter#126D359
hypocenterC359#556
LCSG ▷ C22×C359 ▷ C359
UCSC1 ◁ C22 ◁ #126

Complements

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

NH ≅ G/Ntype
1. #26040014C2semidirect
2. #26040010C2semidirect
3. #26040010C2semidirect
4. #26040008C2semidirect
7. #26039993C2semidirect
8. #26039992C2semidirect
9. C4×Dic718C2semidirect
10. #26039980C2semidirect
11. #26039980C2semidirect
13. #26039972C2semidirect
14. #26039971C2semidirect
15. #126×C359C2semidirect
97. C359#556semidirect
103. #126D359semidirect

Maximal subgroups

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

subgroupindex
#260400142
#260400102
#260400082
#260400012
#260399932
#260399922
C4×Dic7182
#260399802
(C22⋊D359)⋊C42
#260399722
#260399712
#126×C3592
#556359