Finite Group Databasebeta

← #37527142

Subgroups — #37527142

Order 22976.

238 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 97 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#26040009C211yesmaximal, characteristic, complemented
2#26040008C211yesmaximal, characteristic, complemented
3#26040005C211yesmaximal, characteristic, complemented
4#26040000C211yesmaximal, characteristic, complemented
5#26039998C211yesmaximal, characteristic, complemented
6#26039989C211yesmaximal, characteristic, complemented
7#26039988C211yesmaximal, characteristic, complemented
8#26039987C211yesmaximal, characteristic, complemented
9#26039987C211yesmaximal, characteristic, complemented
10C4×C22⋊D359C211yesmaximal, characteristic, complemented
11(C22⋊D359)⋊C4C211yesmaximal, characteristic, complemented
12(C22⋊D359)⋊C4C211yesmaximal, characteristic, complemented
13#26039972C211yesmaximal, characteristic, complemented
14C2×Dic359⋊C4C211yesmaximal, characteristic, complemented
15C4×D4×C359C211yesmaximal, characteristic, complemented
16C2×D1436C2211yescharacteristic
17C2×C22⋊D359C2211yescharacteristic
18C2×C22⋊D359C2211yescharacteristic
19C2×C22⋊D359C2211yescharacteristic
20C2×C22⋊D359C2211yescharacteristic
21C22×Dic359C2211yescharacteristic
22C22×Dic359C2211yescharacteristic
23C2×C4×D359C2211yescharacteristic
24C2×C4×D359C2211yescharacteristic
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×D4×C359C2211yescharacteristic
45C22×C4×C359C2211yescharacteristic
46C22×C4×C359C2211yescharacteristic
47C4⋊C4×C359C2211yescharacteristic
48C22⋊C4×C359C2211yescharacteristic
49C22⋊C4×C359C2211yescharacteristic
50C42×C359C2211yescharacteristic
51C22×D359C2311yescharacteristic
52C22×D359C2311yescharacteristic
53D1436—41no—
54C22⋊D359—22no—
55C22⋊D359—22no—
56C22⋊D359—22no—
57C22⋊D359—41no—
58C2×Dic359—22no—
59C2×Dic359—41no—
60C2×Dic359C2311yescharacteristic
61C2×Dic359C2311yescharacteristic
62C2×Dic359C2311yescharacteristic
63C2×Dic359C2311yescharacteristic
64C2×Dic359C2311yescharacteristic
65C2×Dic359C2311yescharacteristic
66C4×D359—22no—
67C4×D359—41no—
68C23×C359C2311yescharacteristic
69C23×C359C2311yescharacteristic
70D4×C359—22no—
71C2×C4×C359—41no—
72C2×C4×C359—41no—
73C2×C4×C359C2311yescharacteristic
74C2×C4×C359C2311yescharacteristic
75C2×C4×C359C2311yescharacteristic
76C2×C4×C359C2311yescharacteristic
77C2×C4×C359C2311yescharacteristic
78C22×C359—21no—
79C22×C359—21no—
80C22×C359—21no—
81C22×C359—21no—
82C22×C359—21no—
83C22×C359#4112yes—
84C22×C359C2411yescharacteristic
85C2×D359—21no—
86C2×D359—21no—
87C2×D359—21no—
88C2×D359—21no—
89C2×D359—21no—
90C2×D359—21no—
91C4×C359—21no—
92C4×C359—21no—
93C4×C359—21no—
94C4×C359—21no—
95C4×C359—21no—
96Dic359—21no—
97Dic359—21no—
98Dic359—21no—
99Dic359—21no—
100Dic359—21no—
101Dic359#4112yes—
102C2×C359—22no—
103C2×C359—41no—
104C2×C359C2×#4111yescharacteristic
105C2×C359C2×#4111yescharacteristic
106C2×C359H(5,𝔽2)11yescharacteristic
107D359—41no—
108D359—41no—
109C359#55311yescharacteristic, complemented, Sylow
110#553—3591nomaximal, Sylow
111#126—3591no—
112#126—3591no—
113#125—3591no—
114#123—3591no—
115#123—3591no—
116#121—3591no—
117#121—3591no—
118#121—3591no—
119#121—3591no—
120C4×D4—3591no—
121C4×D4—3591no—
122C4×D4—3591no—
123C4×D4D35911yescharacteristic, complemented
124#117—3591no—
125C2×C4⋊C4—3591no—
126C2×D4—3591no—
127C2×D4—3591no—
128C2×D4—3591no—
129C2×D4—3591no—
130C2×D4—3591no—
131C2×D4C2×D35911yescharacteristic
132C22×C4—3591no—
133C22×C4—3591no—
134C22×C4—3591no—
135C22×C4—3591no—
136C22×C4C2×D35911yescharacteristic
137C22×C4C2×D35911yescharacteristic
138C4⋊C4—3591no—
139C4⋊C4—3591no—
140C4⋊C4—3591no—
141C4⋊C4—3591no—
142C4⋊C4—3591no—
143C4⋊C4—3591no—
144C4⋊C4—3591no—
145C4⋊C4—3591no—
146C4⋊C4—3591no—
147C4⋊C4C2×D35911yescharacteristic
148C22⋊C4—3591no—
149C22⋊C4—3591no—
150C22⋊C4—3591no—
151C22⋊C4—3591no—
152C22⋊C4—3591no—
153C22⋊C4—3591no—
154C22⋊C4—3591no—
155C22⋊C4—3591no—
156C22⋊C4C2×D35911yescharacteristic
157C22⋊C4C2×D35911yescharacteristic
158C42—3591no—
159C42—3591no—
160C42C2×D35911yescharacteristic
161C23—3591no—
162C23—3591no—
163C23C22×D35911yescharacteristic
164C23C22×D35911yescharacteristic
165D4—22no—
166D4—14361no—
167D4—14361no—
168D4—7182no—
169D4—7182no—
170D4—7182no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—3591no—
174C2×C4—3591no—
175C2×C4—3591no—
176C2×C4—3591no—
177C2×C4—3591no—
178C2×C4—3591no—
179C2×C4—14361no—
180C2×C4—14361no—
181C2×C4—7182no—
182C2×C4—7182no—
183C2×C4C22×D35911yescharacteristic
184C2×C4C22×D35911yescharacteristic
185C2×C4C22×D35911yescharacteristic
186C2×C4C22×D35911yescharacteristic
187C2×C4C22×D35911yescharacteristic
188C22—21no—
189C22—21no—
190C22—21no—
191C22—21no—
192C22—21no—
193C22—7181no—
194C22—7181no—
195C22—7181no—
196C22—7181no—
197C22—7181no—
198C22—7181no—
199C22#1915334112yes—
200C22C23×D35911yescharacteristic
201C4—21no—
202C4—21no—
203C4—21no—
204C4—21no—
205C4—21no—
206C4—3592no—
207C4—7181no—
208C4—7181no—
209C4—7181no—
210C4—7181no—
211C4—7181no—
212C2—22no—
213C2—41no—
214C2—14361no—
215C2—14361no—
216C2#41×D35911yescharacteristic
217C2C2×#1915334111yescharacteristic
218C2#2604006011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D359
commutator, socle, cosocleC22×C359C24
FittingC4×D4×C359C2
hypercenterC4×D4D359
hypocenterC359#553
LCSG ▷ C22×C359 ▷ C359
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #26040009C2semidirect
2. #26040008C2semidirect
3. #26040005C2semidirect
4. #26040000C2semidirect
5. #26039998C2semidirect
6. #26039989C2semidirect
7. #26039988C2semidirect
8. #26039987C2semidirect
9. #26039987C2semidirect
10. C4×C22⋊D359C2semidirect
11. (C22⋊D359)⋊C4C2semidirect
12. (C22⋊D359)⋊C4C2semidirect
13. #26039972C2semidirect
14. C2×Dic359⋊C4C2semidirect
15. C4×D4×C359C2semidirect
109. C359#553semidirect
123. C4×D4D359semidirect

Maximal subgroups

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

subgroupindex
#260400092
#260400082
#260400052
#260400002
#260399982
#260399892
#260399882
#260399872
C4×C22⋊D3592
(C22⋊D359)⋊C42
#260399722
C2×Dic359⋊C42
C4×D4×C3592
#553359