Finite Group Databasebeta

← #46830819

Subgroups — #46830819

Order 34624.

334 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 115 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
1C2×#22575835C211yesmaximal, characteristic, complemented
2#31772615C211yesmaximal, characteristic, complemented
3#31772609C212yesmaximal, complemented
4#31772607C211yesmaximal, characteristic, complemented
5#31772600C212yesmaximal, complemented
6#31772599C211yesmaximal, characteristic, complemented
7#31772597C212yesmaximal, complemented
8D4×Dic541C211yesmaximal, characteristic, complemented
9C4×C22⋊D541C211yesmaximal, characteristic, complemented
10C2×C22⋊Dic541C212yesmaximal, complemented
11C22×D4×C541C211yesmaximal, characteristic, complemented
12#22575835—24no—
13C2×Dic1082C2211yescharacteristic, complemented
14C2×C22⋊D541C2211yescharacteristic
15C2×C22⋊D541C2212yescomplemented
16C2×C22⋊D541C2212yescomplemented
17C22×Dic541C2212yescomplemented
18C22×Dic541C2212yescomplemented
19C2×C4×D541C2211yescharacteristic, complemented
20C4⋊Dic541C2211yescharacteristic, complemented
21#22575815C2211yescharacteristic, complemented
22#22575815C2212yescomplemented
23C22⋊Dic541C2211yescharacteristic
24C22⋊Dic541C2212yes—
25C22⋊Dic541C2212yescomplemented
26C22⋊Dic541C2212yescomplemented
27C22⋊Dic541C2212yescomplemented
28C22⋊Dic541C2212yescomplemented
29#22575813C2211yescharacteristic, complemented
30C4×Dic541C2211yescharacteristic, complemented
31C24×C541C2212yes—
32C2×D4×C541—24no—
33C2×D4×C541C2211yescharacteristic
34C2×D4×C541C2212yes—
35C2×D4×C541C2211yescharacteristic
36C22×C4×C541C2211yescharacteristic
37C22×D541C2311yescharacteristic
38Dic1082—22no—
39C22⋊D541—24no—
40C22⋊D541—22no—
41C22⋊D541—42no—
42C2×Dic541—24no—
43C2×Dic541—42no—
44C2×Dic541C2311yescharacteristic
45C2×Dic541C2311yescharacteristic
46C2×Dic541C2312yes—
47C2×Dic541C2311yescharacteristic
48C2×Dic541C2312yes—
49C4×D541—22no—
50C23×C541—24no—
51C23×C541—24no—
52C23×C541—42no—
53C23×C541C2312yes—
54C23×C541C2312yes—
55C23×C541C2311yescharacteristic
56D4×C541—24no—
57D4×C541—22no—
58D4×C541D414yescomplemented
59C2×C4×C541—22no—
60C2×C4×C541C2311yescharacteristic
61C2×C4×C541C2311yescharacteristic
62C22×C541—21no—
63C22×C541—22no—
64C22×C541—21no—
65C22×C541—22no—
66C22×C541—22no—
67C22×C541—22no—
68C22×C541—22no—
69C22×C541—48no—
70C22×C541C2×D414yes—
71C22×C541#4112yescomplemented
72C22×C541C2411yescharacteristic
73C2×D541—21no—
74C2×D541—21no—
75C2×D541—21no—
76C4×C541—21no—
77C4×C541C2×D412yes—
78Dic541—21no—
79Dic541—22no—
80Dic541—21no—
81Dic541—21no—
82Dic541—22no—
83C2×C541—22no—
84C2×C541—24no—
85C2×C541—42no—
86C2×C541C22×D411yescharacteristic
87C2×C541C2×#4111yescharacteristic
88C2×C541H(5,𝔽2)11yescharacteristic
89D541—41no—
90C541#54611yescharacteristic, complemented, Sylow
91#546—5411nomaximal, Sylow
92C2×#41—5411no—
93C22×D4D54111yescharacteristic, complemented
94#124—5411no—
95#123—5412no—
96C22⋊Q8—5411no—
97#121—5411no—
98#121—5412no—
99#120—5412no—
100C4×D4—5411no—
101C4×D4—5411no—
102C2×C22⋊C4—5412no—
103C24C2×D54112yes—
104#41—10824no—
105C2×Q8—5411no—
106C2×D4—24no—
107C2×D4—5411no—
108C2×D4—5412no—
109C2×D4—5412no—
110C2×D4C2×D54112yes—
111C2×D4C2×D54111yescharacteristic
112C2×D4C2×D54111yescharacteristic
113C22×C4—5412no—
114C22×C4—5412no—
115C22×C4—5411no—
116C22×C4C2×D54111yescharacteristic
117C4⋊C4—5411no—
118C4⋊C4—5411no—
119C4⋊C4—5412no—
120C22⋊C4—5411no—
121C22⋊C4—5412no—
122C22⋊C4—5412no—
123C22⋊C4—5412no—
124C22⋊C4—5412no—
125C22⋊C4—5412no—
126C22⋊C4—5411no—
127C42—5411no—
128C23—24no—
129C23—24no—
130C23—42no—
131C23—5411no—
132C23C22×D54112yes—
133C23C22×D54112yes—
134C23C22×D54111yescharacteristic
135Q8—10822no—
136D4—24no—
137D4—22no—
138D4—10824no—
139D4—10822no—
140D4—21642no—
141D4C22⋊D54114yescomplemented
142C2×C4—22no—
143C2×C4—5411no—
144C2×C4—5411no—
145C2×C4—5412no—
146C2×C4—5411no—
147C2×C4—5412no—
148C2×C4—10824no—
149C2×C4—10822no—
150C2×C4—21642no—
151C2×C4C22×D54111yescharacteristic
152C2×C4C22×D54111yescharacteristic
153C22—22no—
154C22—21no—
155C22—21no—
156C22—22no—
157C22—22no—
158C22—22no—
159C22—22no—
160C22—48no—
161C22—10821no—
162C22—10821no—
163C22—10821no—
164C22C2×C22⋊D54114yes—
165C22#2257583512yescomplemented
166C22C23×D54111yescharacteristic
167C4—21no—
168C4—10821no—
169C4—10822no—
170C4—10821no—
171C4—10822no—
172C4—10821no—
173C4C2×C22⋊D54112yes—
174C2—22no—
175C2—24no—
176C2—42no—
177C2—21641no—
178C2C22×C22⋊D54111yescharacteristic
179C2C2×#2257583511yescharacteristic
180C2#3177267311yescharacteristic
subgroupG/H
center, FrattiniC22C23×D541
commutator, socle, cosocleC22×C541C24
FittingC22×D4×C541C2
hypercenterC22×D4D541
hypocenterC541#546
LCSG ▷ C22×C541 ▷ C541
UCSC1 ◁ C22 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×#22575835C2semidirect
2. #31772615C2semidirect
3. #31772609C2semidirect
4. #31772607C2semidirect
5. #31772600C2semidirect
6. #31772599C2semidirect
7. #31772597C2semidirect
8. D4×Dic541C2semidirect
9. C4×C22⋊D541C2semidirect
10. C2×C22⋊Dic541C2semidirect
11. C22×D4×C541C2semidirect
13. C2×Dic1082C22semidirect
15. C2×C22⋊D541C22semidirect
16. C2×C22⋊D541C22semidirect
17. C22×Dic541C22semidirect
18. C22×Dic541C22semidirect
19. C2×C4×D541C22semidirect
20. C4⋊Dic541C22semidirect
21. #22575815C22semidirect
22. #22575815C22semidirect
25. C22⋊Dic541C22semidirect
26. C22⋊Dic541C22semidirect
27. C22⋊Dic541C22semidirect
28. C22⋊Dic541C22semidirect
29. #22575813C22semidirect
30. C4×Dic541C22semidirect
58. D4×C541D4semidirect
71. C22×C541#41semidirect
90. C541#546semidirect
93. C22×D4D541semidirect
141. D4C22⋊D541semidirect
165. C22#22575835semidirect

Maximal subgroups

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

subgroupindex
C2×#225758352
#317726152
#317726092
#317726072
#317726002
#317725992
#317725972
D4×Dic5412
C4×C22⋊D5412
C2×C22⋊Dic5412
C22×D4×C5412
#546541