Finite Group Databasebeta

← #37527039

Subgroups — #37527039

Order 22976.

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

normal subgroups only

This group has 218 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#26040010C211yesmaximal, characteristic, complemented
2#26040008C211yesmaximal, characteristic, complemented
3#26040005C211yesmaximal, characteristic, complemented
4#26040005C211yesmaximal, characteristic, complemented
5#26040000C211yesmaximal, characteristic, complemented
6#26039998C211yesmaximal, characteristic, complemented
7#26039997C211yesmaximal, characteristic, complemented
8#26039997C211yesmaximal, characteristic, complemented
9#26039991C211yesmaximal, characteristic, complemented
10#26039991C211yesmaximal, characteristic, complemented
11#26039988C211yesmaximal, characteristic
12#26039977C211yesmaximal, characteristic, complemented
13C4×C22⋊D359C211yesmaximal, characteristic, complemented
14C4⋊C4×D359C211yesmaximal, characteristic, complemented
15C22⋊Q8×C359C211yesmaximal, characteristic, complemented
16C2×D1436C2211yescharacteristic
17C2×C22⋊D359C2211yescharacteristic
18C2×C22⋊D359C2211yescharacteristic
19C2×C4×D359C2211yescharacteristic
20C2×C4×D359C2211yescharacteristic
21C2×C4×D359C2211yescharacteristic
22C2×C4×D359C2211yescharacteristic
23C4⋊Dic359C2211yescharacteristic
24C4⋊Dic359C2211yescharacteristic
25C4⋊Dic359C2211yescharacteristic
26Dic359⋊C4C2211yescharacteristic
27Dic359⋊C4C2211yescharacteristic
28Dic359⋊C4C2211yescharacteristic
29Dic359⋊C4C2211yescharacteristic
30Dic359⋊C4C2211yescharacteristic
31Dic359⋊C4C2211yescharacteristic
32Dic359⋊C4C2211yescharacteristic
33Dic359⋊C4C2211yescharacteristic
34C22⋊Dic359C2211yescharacteristic
35C22⋊Dic359C2211yescharacteristic
36(C2×D359)⋊C4C2211yescharacteristic
37(C2×D359)⋊C4C2211yescharacteristic
38(C2×D359)⋊C4C2211yescharacteristic
39(C2×D359)⋊C4C2211yescharacteristic
40(C2×D359)⋊C4C2211yescharacteristic
41(C2×D359)⋊C4C2211yescharacteristic
42C4×Dic359C2211yescharacteristic
43C4×Dic359C2211yescharacteristic
44C2×Q8×C359C2211yescharacteristic
45C22×C4×C359C2211yescharacteristic
46C4⋊C4×C359C2211yescharacteristic
47C4⋊C4×C359C2211yescharacteristic
48C4⋊C4×C359C2211yescharacteristic
49C22⋊C4×C359C2211yescharacteristic
50C22⋊C4×C359C2211yescharacteristic
51C22×D359C2311yescharacteristic
52C22×D359C2311yescharacteristic
53D1436—22no—
54C22⋊D359—22no—
55C22⋊D359—41no—
56C2×Dic359C2311yescharacteristic
57C2×Dic359C2311yescharacteristic
58C2×Dic359C2311yescharacteristic
59C2×Dic359C2311yescharacteristic
60C2×Dic359C2311yescharacteristic
61C2×Dic359C2311yescharacteristic
62C4×D359—22no—
63C4×D359—41no—
64C4×D359—41no—
65C4×D359—41no—
66C23×C359C2311yescharacteristic
67Q8×C359—41no—
68C2×C4×C359—41no—
69C2×C4×C359C2311yescharacteristic
70C2×C4×C359C2311yescharacteristic
71C2×C4×C359C2311yescharacteristic
72C2×C4×C359C2311yescharacteristic
73C2×C4×C359C2311yescharacteristic
74C2×C4×C359C2311yescharacteristic
75C22×C359—21no—
76C22×C359—21no—
77C22×C359—21no—
78C22×C359C2411yescharacteristic
79C2×D359—21no—
80C2×D359—21no—
81C2×D359—21no—
82C2×D359—21no—
83C2×D359—21no—
84C2×D359#4112yes—
85C4×C359—21no—
86C4×C359—21no—
87C4×C359—21no—
88C4×C359—21no—
89C4×C359—21no—
90C4×C359—21no—
91Dic359—21no—
92Dic359—21no—
93Dic359—21no—
94Dic359—21no—
95Dic359—21no—
96Dic359—21no—
97C2×C359—41no—
98C2×C359C2×#4111yescharacteristic
99C2×C359H(5,𝔽2)11yescharacteristic
100C2×C3592−1+411yescharacteristic
101D359—22no—
102D359—41no—
103C359#53911yescharacteristic, complemented, Sylow
104#539—3591nomaximal, Sylow
105#126—3591no—
106#126—3591no—
107#125—3591no—
108#125—3591no—
109#123—3591no—
110#123—3591no—
111#123—3591no—
112#123—3591no—
113C22⋊Q8—3591no—
114C22⋊Q8—3591no—
115C22⋊Q8D35911yescharacteristic, complemented
116#121—3591no—
117C4×D4—3591no—
118C4×D4—3591no—
119C2×C4⋊C4—3591no—
120C2×Q8C2×D35911yescharacteristic
121C2×D4—3591no—
122C2×D4—3591no—
123C2×D4—3591no—
124C22×C4—3591no—
125C22×C4—3591no—
126C22×C4—3591no—
127C22×C4—3591no—
128C22×C4C2×D35911yescharacteristic
129C4⋊C4—3591no—
130C4⋊C4—3591no—
131C4⋊C4—3591no—
132C4⋊C4—3591no—
133C4⋊C4—3591no—
134C4⋊C4—3591no—
135C4⋊C4—3591no—
136C4⋊C4—3591no—
137C4⋊C4—3591no—
138C4⋊C4—3591no—
139C4⋊C4—3591no—
140C4⋊C4C2×D35911yescharacteristic
141C4⋊C4C2×D35911yescharacteristic
142C4⋊C4C2×D35911yescharacteristic
143C22⋊C4—3591no—
144C22⋊C4—3591no—
145C22⋊C4—3591no—
146C22⋊C4—3591no—
147C22⋊C4—3591no—
148C22⋊C4—3591no—
149C22⋊C4—3591no—
150C22⋊C4—3591no—
151C22⋊C4C2×D35911yescharacteristic
152C22⋊C4C2×D35911yescharacteristic
153C42—3591no—
154C42—3591no—
155C23—3591no—
156C23—3591no—
157C23C22×D35911yescharacteristic
158Q8—41no—
159D4—14361no—
160D4—7182no—
161D4—7182no—
162C2×C4—41no—
163C2×C4—3591no—
164C2×C4—3591no—
165C2×C4—3591no—
166C2×C4—3591no—
167C2×C4—3591no—
168C2×C4—3591no—
169C2×C4—14361no—
170C2×C4—14361no—
171C2×C4—14361no—
172C2×C4—7182no—
173C2×C4C22×D35911yescharacteristic
174C2×C4C22×D35911yescharacteristic
175C2×C4C22×D35911yescharacteristic
176C2×C4C22×D35911yescharacteristic
177C2×C4C22×D35911yescharacteristic
178C2×C4C22×D35911yescharacteristic
179C22—21no—
180C22—21no—
181C22—21no—
182C22—3592no—
183C22—7181no—
184C22—7181no—
185C22—7181no—
186C22—7181no—
187C22—7181no—
188C22C23×D35911yescharacteristic
189C4—21no—
190C4—21no—
191C4—21no—
192C4—21no—
193C4—21no—
194C4—21no—
195C4—7181no—
196C4—7181no—
197C4—7181no—
198C4—7181no—
199C4—7181no—
200C4—7181no—
201C2—41no—
202C2—14361no—
203C2—7182no—
204C2#41×D35911yescharacteristic
205C2#2604006011yescharacteristic
206C2#2604006311yescharacteristic
subgroupG/H
center, FrattiniC22C23×D359
commutator, socle, cosocleC22×C359C24
FittingC22⋊Q8×C359C2
prime radical#26039988C2
hypercenterC22⋊Q8D359
hypocenterC359#539
LCSG ▷ C22×C359 ▷ C359
UCSC1 ◁ C22 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. #26040010C2semidirect
2. #26040008C2semidirect
3. #26040005C2semidirect
4. #26040005C2semidirect
5. #26040000C2semidirect
6. #26039998C2semidirect
7. #26039997C2semidirect
8. #26039997C2semidirect
9. #26039991C2semidirect
10. #26039991C2semidirect
12. #26039977C2semidirect
13. C4×C22⋊D359C2semidirect
14. C4⋊C4×D359C2semidirect
15. C22⋊Q8×C359C2semidirect
103. C359#539semidirect
115. C22⋊Q8D359semidirect

Maximal subgroups

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

subgroupindex
#260400102
#260400082
#260400052
#260400002
#260399982
#260399972
#260399912
#260399882
#260399772
C4×C22⋊D3592
C4⋊C4×D3592
C22⋊Q8×C3592
#539359