Finite Group Databasebeta

← #37527043

Subgroups — #37527043

Order 22976.

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

normal subgroups only

This group has 240 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#26040011C211yesmaximal, characteristic, complemented
2#26040005C211yesmaximal, characteristic, complemented
3#26040000C211yesmaximal, characteristic, complemented
4#26039998C211yesmaximal, characteristic, complemented
5#26039997C211yesmaximal, characteristic, complemented
6#26039996C211yesmaximal, characteristic, complemented
7#26039988C211yesmaximal, characteristic, complemented
8#26039987C211yesmaximal, characteristic, complemented
9#26039987C211yesmaximal, characteristic, complemented
10#26039987C211yesmaximal, characteristic, complemented
11#26039986C211yesmaximal, characteristic, complemented
12C4×C22⋊D359C211yesmaximal, characteristic, complemented
13(C22⋊D359)⋊C4C211yesmaximal, characteristic, complemented
14#26039971C211yesmaximal, characteristic, complemented
15#121×C359C211yesmaximal, characteristic, complemented
16C2×D1436C2211yescharacteristic
17C2×C22⋊D359C2211yescharacteristic
18C2×C22⋊D359C2211yescharacteristic
19C2×C22⋊D359C2211yescharacteristic
20C2×C22⋊D359C2211yescharacteristic
21C2×C22⋊D359C2211yescharacteristic
22C2×C22⋊D359C2211yescharacteristic
23C22×Dic359C2211yescharacteristic
24C22×Dic359C2211yescharacteristic
25C2×C4×D359C2211yescharacteristic
26C2×C4×D359C2211yescharacteristic
27C4⋊Dic359C2211yescharacteristic
28Dic359⋊C4C2211yescharacteristic
29Dic359⋊C4C2211yescharacteristic
30Dic359⋊C4C2211yescharacteristic
31Dic359⋊C4C2211yescharacteristic
32Dic359⋊C4C2211yescharacteristic
33Dic359⋊C4C2211yescharacteristic
34C22⋊Dic359C2211yescharacteristic
35C22⋊Dic359C2211yescharacteristic
36C22⋊Dic359C2211yescharacteristic
37C22⋊Dic359C2211yescharacteristic
38(C2×D359)⋊C4C2211yescharacteristic
39(C2×D359)⋊C4C2211yescharacteristic
40(C2×D359)⋊C4C2211yescharacteristic
41(C2×D359)⋊C4C2211yescharacteristic
42C4×Dic359C2211yescharacteristic
43C4×Dic359C2211yescharacteristic
44C2×D4×C359C2211yescharacteristic
45C2×D4×C359C2211yescharacteristic
46C2×D4×C359C2211yescharacteristic
47C22×C4×C359C2211yescharacteristic
48C4⋊C4×C359C2211yescharacteristic
49C22⋊C4×C359C2211yescharacteristic
50C22⋊C4×C359C2211yescharacteristic
51C22×D359C2311yescharacteristic
52C22×D359C2311yescharacteristic
53D1436—41no—
54C22⋊D359—22no—
55C22⋊D359—22no—
56C22⋊D359—41no—
57C22⋊D359—41no—
58C22⋊D359—41no—
59C22⋊D359—41no—
60C2×Dic359—22no—
61C2×Dic359—41no—
62C2×Dic359C2311yescharacteristic
63C2×Dic359C2311yescharacteristic
64C2×Dic359C2311yescharacteristic
65C2×Dic359C2311yescharacteristic
66C2×Dic359C2311yescharacteristic
67C2×Dic359C2311yescharacteristic
68C4×D359—41no—
69C4×D359—41no—
70C23×C359C2311yescharacteristic
71C23×C359C2311yescharacteristic
72C23×C359C2311yescharacteristic
73D4×C359—41no—
74D4×C359—41no—
75D4×C359—41no—
76C2×C4×C359—41no—
77C2×C4×C359C2311yescharacteristic
78C2×C4×C359C2311yescharacteristic
79C2×C4×C359C2311yescharacteristic
80C2×C4×C359C2311yescharacteristic
81C22×C359—21no—
82C22×C359—21no—
83C22×C359—21no—
84C22×C359—21no—
85C22×C359—21no—
86C22×C359—21no—
87C22×C359—21no—
88C22×C359—21no—
89C22×C359—21no—
90C22×C359C2411yescharacteristic
91C2×D359—21no—
92C2×D359—21no—
93C2×D359—21no—
94C2×D359—21no—
95C2×D359—21no—
96C2×D359—21no—
97C4×C359—21no—
98C4×C359—21no—
99C4×C359—21no—
100C4×C359—21no—
101Dic359—21no—
102Dic359—21no—
103Dic359—21no—
104Dic359—21no—
105Dic359—21no—
106Dic359#4112yes—
107C2×C359—41no—
108C2×C359—41no—
109C2×C359—41no—
110C2×C359C2×#4111yescharacteristic
111C2×C359H(5,𝔽2)11yescharacteristic
112C2×C359H(5,𝔽2)11yescharacteristic
113D359—41no—
114D359—41no—
115C359#54011yescharacteristic, complemented, Sylow
116#540—3591nomaximal, Sylow
117#127—3591no—
118#125—3591no—
119#123—3591no—
120#123—3591no—
121#123—3591no—
122#123—3591no—
123#121—3591no—
124#121—3591no—
125#121—3591no—
126#121—3591no—
127#121—3591no—
128#121D35911yescharacteristic, complemented
129C4×D4—3591no—
130C4×D4—3591no—
131#117—3591no—
132C2×D4—3591no—
133C2×D4—3591no—
134C2×D4—3591no—
135C2×D4—3591no—
136C2×D4—3591no—
137C2×D4—3591no—
138C2×D4—3591no—
139C2×D4C2×D35911yescharacteristic
140C2×D4C2×D35911yescharacteristic
141C2×D4C2×D35911yescharacteristic
142C22×C4—3591no—
143C22×C4—3591no—
144C22×C4—3591no—
145C22×C4—3591no—
146C22×C4C2×D35911yescharacteristic
147C4⋊C4—3591no—
148C4⋊C4—3591no—
149C4⋊C4—3591no—
150C4⋊C4—3591no—
151C4⋊C4—3591no—
152C4⋊C4—3591no—
153C4⋊C4—3591no—
154C4⋊C4C2×D35911yescharacteristic
155C22⋊C4—3591no—
156C22⋊C4—3591no—
157C22⋊C4—3591no—
158C22⋊C4—3591no—
159C22⋊C4—3591no—
160C22⋊C4—3591no—
161C22⋊C4—3591no—
162C22⋊C4—3591no—
163C22⋊C4C2×D35911yescharacteristic
164C22⋊C4C2×D35911yescharacteristic
165C42—3591no—
166C42—3591no—
167C23—3591no—
168C23—3591no—
169C23C22×D35911yescharacteristic
170C23C22×D35911yescharacteristic
171C23C22×D35911yescharacteristic
172D4—41no—
173D4—41no—
174D4—41no—
175D4—14361no—
176D4—14361no—
177D4—14361no—
178D4—14361no—
179D4—14361no—
180D4—7182no—
181D4—7182no—
182C2×C4—41no—
183C2×C4—3591no—
184C2×C4—3591no—
185C2×C4—3591no—
186C2×C4—3591no—
187C2×C4—3591no—
188C2×C4—3591no—
189C2×C4—14361no—
190C2×C4—14361no—
191C2×C4—14361no—
192C2×C4—7182no—
193C2×C4C22×D35911yescharacteristic
194C2×C4C22×D35911yescharacteristic
195C2×C4C22×D35911yescharacteristic
196C2×C4C22×D35911yescharacteristic
197C22—21no—
198C22—21no—
199C22—21no—
200C22—21no—
201C22—21no—
202C22—21no—
203C22—21no—
204C22—21no—
205C22—21no—
206C22—7181no—
207C22—7181no—
208C22—7181no—
209C22—7181no—
210C22—7181no—
211C22—7181no—
212C22C23×D35911yescharacteristic
213C4—21no—
214C4—21no—
215C4—21no—
216C4—21no—
217C4—3592no—
218C4—7181no—
219C4—7181no—
220C4—7181no—
221C4—7181no—
222C4—7181no—
223C2—41no—
224C2—41no—
225C2—41no—
226C2—14361no—
227C2—14361no—
228C2#41×D35911yescharacteristic
229C2#2604006011yescharacteristic
230C2#2604006011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D359
commutator, socle, cosocleC22×C359C24
Fitting#121×C359C2
hypercenter#121D359
hypocenterC359#540
LCSG ▷ C22×C359 ▷ C359
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. #26040011C2semidirect
2. #26040005C2semidirect
3. #26040000C2semidirect
4. #26039998C2semidirect
5. #26039997C2semidirect
6. #26039996C2semidirect
7. #26039988C2semidirect
8. #26039987C2semidirect
9. #26039987C2semidirect
10. #26039987C2semidirect
11. #26039986C2semidirect
12. C4×C22⋊D359C2semidirect
13. (C22⋊D359)⋊C4C2semidirect
14. #26039971C2semidirect
15. #121×C359C2semidirect
115. C359#540semidirect
128. #121D359semidirect

Maximal subgroups

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

subgroupindex
#260400112
#260400052
#260400002
#260399982
#260399972
#260399962
#260399882
#260399872
#260399862
C4×C22⋊D3592
(C22⋊D359)⋊C42
#260399712
#121×C3592
#540359