Finite Group Databasebeta

← #46830775

Subgroups — #46830775

Order 34624.

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#31772624C211yesmaximal, characteristic, complemented
2#31772618C211yesmaximal, characteristic, complemented
3#31772613C211yesmaximal, characteristic, complemented
4#31772611C211yesmaximal, characteristic, complemented
5#31772610C211yesmaximal, characteristic, complemented
6#31772609C211yesmaximal, characteristic, complemented
7#31772601C211yesmaximal, characteristic, complemented
8#31772600C211yesmaximal, characteristic, complemented
9#31772600C211yesmaximal, characteristic, complemented
10#31772600C211yesmaximal, characteristic, complemented
11#31772599C211yesmaximal, characteristic, complemented
12C4×C22⋊D541C211yesmaximal, characteristic, complemented
13#31772588C211yesmaximal, characteristic, complemented
14#31772584C211yesmaximal, characteristic, complemented
15#121×C541C211yesmaximal, characteristic, complemented
16C2×D2164C2211yescharacteristic
17C2×C22⋊D541C2211yescharacteristic
18C2×C22⋊D541C2211yescharacteristic
19C2×C22⋊D541C2211yescharacteristic
20C2×C22⋊D541C2211yescharacteristic
21C2×C22⋊D541C2211yescharacteristic
22C2×C22⋊D541C2211yescharacteristic
23C22×Dic541C2211yescharacteristic
24C22×Dic541C2211yescharacteristic
25C2×C4×D541C2211yescharacteristic
26C2×C4×D541C2211yescharacteristic
27C4⋊Dic541C2211yescharacteristic
28#22575815C2211yescharacteristic
29#22575815C2211yescharacteristic
30#22575815C2211yescharacteristic
31#22575815C2211yescharacteristic
32#22575815C2211yescharacteristic
33#22575815C2211yescharacteristic
34C22⋊Dic541C2211yescharacteristic
35C22⋊Dic541C2211yescharacteristic
36C22⋊Dic541C2211yescharacteristic
37C22⋊Dic541C2211yescharacteristic
38#22575813C2211yescharacteristic
39#22575813C2211yescharacteristic
40#22575813C2211yescharacteristic
41#22575813C2211yescharacteristic
42C4×Dic541C2211yescharacteristic
43C4×Dic541C2211yescharacteristic
44C2×D4×C541C2211yescharacteristic
45C2×D4×C541C2211yescharacteristic
46C2×D4×C541C2211yescharacteristic
47C22×C4×C541C2211yescharacteristic
48C4⋊C4×C541C2211yescharacteristic
49C22⋊C4×C541C2211yescharacteristic
50C22⋊C4×C541C2211yescharacteristic
51C22×D541C2311yescharacteristic
52C22×D541C2311yescharacteristic
53D2164—41no—
54C22⋊D541—22no—
55C22⋊D541—22no—
56C22⋊D541—41no—
57C22⋊D541—41no—
58C22⋊D541—41no—
59C22⋊D541—41no—
60C2×Dic541—22no—
61C2×Dic541—41no—
62C2×Dic541C2311yescharacteristic
63C2×Dic541C2311yescharacteristic
64C2×Dic541C2311yescharacteristic
65C2×Dic541C2311yescharacteristic
66C2×Dic541C2311yescharacteristic
67C2×Dic541C2311yescharacteristic
68C4×D541—41no—
69C4×D541—41no—
70C23×C541C2311yescharacteristic
71C23×C541C2311yescharacteristic
72C23×C541C2311yescharacteristic
73D4×C541—41no—
74D4×C541—41no—
75D4×C541—41no—
76C2×C4×C541—41no—
77C2×C4×C541C2311yescharacteristic
78C2×C4×C541C2311yescharacteristic
79C2×C4×C541C2311yescharacteristic
80C2×C4×C541C2311yescharacteristic
81C22×C541—21no—
82C22×C541—21no—
83C22×C541—21no—
84C22×C541—21no—
85C22×C541—21no—
86C22×C541—21no—
87C22×C541—21no—
88C22×C541—21no—
89C22×C541—21no—
90C22×C541C2411yescharacteristic
91C2×D541—21no—
92C2×D541—21no—
93C2×D541—21no—
94C2×D541—21no—
95C2×D541—21no—
96C2×D541—21no—
97C4×C541—21no—
98C4×C541—21no—
99C4×C541—21no—
100C4×C541—21no—
101Dic541—21no—
102Dic541—21no—
103Dic541—21no—
104Dic541—21no—
105Dic541—21no—
106Dic541#4112yes—
107C2×C541—41no—
108C2×C541—41no—
109C2×C541—41no—
110C2×C541C2×#4111yescharacteristic
111C2×C541H(5,𝔽2)11yescharacteristic
112C2×C541H(5,𝔽2)11yescharacteristic
113D541—41no—
114D541—41no—
115C541#54011yescharacteristic, complemented, Sylow
116#540—5411nomaximal, Sylow
117#127—5411no—
118#125—5411no—
119#123—5411no—
120#123—5411no—
121#123—5411no—
122#123—5411no—
123#121—5411no—
124#121—5411no—
125#121—5411no—
126#121—5411no—
127#121—5411no—
128#121D54111yescharacteristic, complemented
129C4×D4—5411no—
130C4×D4—5411no—
131#117—5411no—
132C2×D4—5411no—
133C2×D4—5411no—
134C2×D4—5411no—
135C2×D4—5411no—
136C2×D4—5411no—
137C2×D4—5411no—
138C2×D4—5411no—
139C2×D4C2×D54111yescharacteristic
140C2×D4C2×D54111yescharacteristic
141C2×D4C2×D54111yescharacteristic
142C22×C4—5411no—
143C22×C4—5411no—
144C22×C4—5411no—
145C22×C4—5411no—
146C22×C4C2×D54111yescharacteristic
147C4⋊C4—5411no—
148C4⋊C4—5411no—
149C4⋊C4—5411no—
150C4⋊C4—5411no—
151C4⋊C4—5411no—
152C4⋊C4—5411no—
153C4⋊C4—5411no—
154C4⋊C4C2×D54111yescharacteristic
155C22⋊C4—5411no—
156C22⋊C4—5411no—
157C22⋊C4—5411no—
158C22⋊C4—5411no—
159C22⋊C4—5411no—
160C22⋊C4—5411no—
161C22⋊C4—5411no—
162C22⋊C4—5411no—
163C22⋊C4C2×D54111yescharacteristic
164C22⋊C4C2×D54111yescharacteristic
165C42—5411no—
166C42—5411no—
167C23—5411no—
168C23—5411no—
169C23C22×D54111yescharacteristic
170C23C22×D54111yescharacteristic
171C23C22×D54111yescharacteristic
172D4—41no—
173D4—41no—
174D4—41no—
175D4—10822no—
176D4—10822no—
177D4—21641no—
178D4—21641no—
179D4—21641no—
180D4—21641no—
181D4—21641no—
182C2×C4—41no—
183C2×C4—5411no—
184C2×C4—5411no—
185C2×C4—5411no—
186C2×C4—5411no—
187C2×C4—5411no—
188C2×C4—5411no—
189C2×C4—10822no—
190C2×C4—21641no—
191C2×C4—21641no—
192C2×C4—21641no—
193C2×C4C22×D54111yescharacteristic
194C2×C4C22×D54111yescharacteristic
195C2×C4C22×D54111yescharacteristic
196C2×C4C22×D54111yescharacteristic
197C22—21no—
198C22—21no—
199C22—21no—
200C22—21no—
201C22—21no—
202C22—21no—
203C22—21no—
204C22—21no—
205C22—21no—
206C22—10821no—
207C22—10821no—
208C22—10821no—
209C22—10821no—
210C22—10821no—
211C22—10821no—
212C22C23×D54111yescharacteristic
213C4—21no—
214C4—21no—
215C4—21no—
216C4—21no—
217C4—5412no—
218C4—10821no—
219C4—10821no—
220C4—10821no—
221C4—10821no—
222C4—10821no—
223C2—41no—
224C2—41no—
225C2—41no—
226C2—21641no—
227C2—21641no—
228C2#41×D54111yescharacteristic
229C2#3177267311yescharacteristic
230C2#3177267311yescharacteristic
subgroupG/H
center, FrattiniC22C23×D541
commutator, socle, cosocleC22×C541C24
Fitting#121×C541C2
hypercenter#121D541
hypocenterC541#540
LCSG ▷ C22×C541 ▷ C541
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. #31772624C2semidirect
2. #31772618C2semidirect
3. #31772613C2semidirect
4. #31772611C2semidirect
5. #31772610C2semidirect
6. #31772609C2semidirect
7. #31772601C2semidirect
8. #31772600C2semidirect
9. #31772600C2semidirect
10. #31772600C2semidirect
11. #31772599C2semidirect
12. C4×C22⋊D541C2semidirect
13. #31772588C2semidirect
14. #31772584C2semidirect
15. #121×C541C2semidirect
115. C541#540semidirect
128. #121D541semidirect

Maximal subgroups

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

subgroupindex
#317726242
#317726182
#317726132
#317726112
#317726102
#317726092
#317726012
#317726002
#317725992
C4×C22⋊D5412
#317725882
#317725842
#121×C5412
#540541