Finite Group Databasebeta

← #46830813

Subgroups — #46830813

Order 34624.

334 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 113 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×D4×D541C211yesmaximal, characteristic, complemented
2#31772617C211yesmaximal, characteristic, complemented
3#31772611C212yesmaximal, complemented
4#31772604C211yesmaximal, characteristic, complemented
5#31772602C211yesmaximal, characteristic, complemented
6#31772600C212yesmaximal, complemented
7#31772596C212yesmaximal, complemented
8D4×Dic541C211yesmaximal, characteristic, complemented
9C4×C22⋊D541C211yesmaximal, characteristic, complemented
10C2×#22575813C212yesmaximal, complemented
11C2×#41×C541C211yesmaximal, characteristic, complemented
12C23×D541C2212yes—
13C2×D2164C2211yescharacteristic
14C2×C22⋊D541C2211yescharacteristic
15C2×C22⋊D541C2212yes—
16C2×C22⋊D541C2212yescomplemented
17D4×D541—24no—
18C22×Dic541C2212yescomplemented
19C2×C4×D541C2211yescharacteristic
20C4⋊Dic541C2211yescharacteristic, complemented
21#22575815C2211yescharacteristic, complemented
22#22575815C2212yescomplemented
23C22⋊Dic541C2211yescharacteristic, complemented
24C22⋊Dic541C2212yescomplemented
25#22575813C2211yescharacteristic
26#22575813C2212yes—
27#22575813C2212yescomplemented
28#22575813C2212yescomplemented
29#22575813C2212yescomplemented
30C4×Dic541C2211yescharacteristic, complemented
31#41×C541—24no—
32C2×Q8×C541C2211yescharacteristic, complemented
33C2×D4×C541C2211yescharacteristic
34C2×D4×C541C2212yescomplemented
35C22×C4×C541C2212yescomplemented
36C22×C4×C541C2211yescharacteristic, complemented
37C22×D541—24no—
38C22×D541—24no—
39C22×D541—42no—
40C22×D541C2312yes—
41C22×D541C2311yescharacteristic
42D2164—22no—
43C22⋊D541—24no—
44C22⋊D541—22no—
45C22⋊D541—42no—
46C2×Dic541—42no—
47C2×Dic541C2311yescharacteristic
48C2×Dic541C2311yescharacteristic
49C2×Dic541C2312yes—
50C2×Dic541C2311yescharacteristic
51C4×D541—22no—
52C23×C541C2311yescharacteristic
53C23×C541C2312yes—
54Q8×C541—22no—
55D4×C541—24no—
56D4×C541D414yescomplemented
57C2×C4×C541—24no—
58C2×C4×C541—22no—
59C2×C4×C541C2311yescharacteristic
60C2×C4×C541C2312yes—
61C2×C4×C541C2311yescharacteristic
62C22×C541—22no—
63C22×C541—22no—
64C22×C541—21no—
65C22×C541—21no—
66C22×C541—21no—
67C22×C541C2×D414yes—
68C22×C541C2411yescharacteristic
69C2×D541—21no—
70C2×D541—21no—
71C2×D541—22no—
72C2×D541—22no—
73C2×D541—22no—
74C2×D541—48no—
75C2×D541#4112yescomplemented
76C4×C541—21no—
77C4×C541—22no—
78C4×C541C2×D412yes—
79Dic541—21no—
80Dic541—21no—
81Dic541—21no—
82Dic541—22no—
83C2×C541—24no—
84C2×C541—41no—
85C2×C541C22×D411yescharacteristic
86C2×C541C2×#4111yescharacteristic
87C2×C541H(5,𝔽2)11yescharacteristic
88D541—22no—
89D541—42no—
90C541#54611yescharacteristic, complemented, Sylow
91#546—5411nomaximal, Sylow
92C2×#41D54111yescharacteristic, complemented
93C22×D4—5411no—
94#124—5411no—
95#123—5412no—
96C22⋊Q8—5411no—
97#121—5412no—
98#121—5411no—
99#120—5412no—
100C4×D4—5411no—
101C4×D4—5411no—
102C2×C22⋊C4—5412no—
103C24—5412no—
104#41—24no—
105C2×Q8C2×D54111yescharacteristic, complemented
106C2×D4—5411no—
107C2×D4—5412no—
108C2×D4—5412no—
109C2×D4—5411no—
110C2×D4—10824no—
111C2×D4C2×D54111yescharacteristic
112C2×D4C2×D54112yescomplemented
113C22×C4—5412no—
114C22×C4—5411no—
115C22×C4C2×D54112yescomplemented
116C22×C4C2×D54111yescharacteristic, complemented
117C4⋊C4—5411no—
118C4⋊C4—5411no—
119C4⋊C4—5412no—
120C22⋊C4—5412no—
121C22⋊C4—5411no—
122C22⋊C4—5411no—
123C22⋊C4—5412no—
124C22⋊C4—5412no—
125C22⋊C4—5412no—
126C22⋊C4—5412no—
127C42—5411no—
128C23—5411no—
129C23—5412no—
130C23—10824no—
131C23—10824no—
132C23—21642no—
133C23C22×D54111yescharacteristic
134C23C22×D54112yes—
135Q8—22no—
136D4—24no—
137D4—10822no—
138D4—10824no—
139D4—10822no—
140D4—21642no—
141D4C22⋊D54114yescomplemented
142C2×C4—24no—
143C2×C4—22no—
144C2×C4—5411no—
145C2×C4—5411no—
146C2×C4—5412no—
147C2×C4—5411no—
148C2×C4—10822no—
149C2×C4—21642no—
150C2×C4C22×D54111yescharacteristic
151C2×C4C22×D54112yes—
152C2×C4C22×D54111yescharacteristic
153C22—22no—
154C22—22no—
155C22—21no—
156C22—21no—
157C22—21no—
158C22—5412no—
159C22—10821no—
160C22—10821no—
161C22—10822no—
162C22—10822no—
163C22—10822no—
164C22—21648no—
165C22C2×C22⋊D54114yes—
166C22C23×D54111yescharacteristic
167C4—21no—
168C4—22no—
169C4—10821no—
170C4—10822no—
171C4—10821no—
172C4—10821no—
173C4C2×C22⋊D54112yes—
174C2—24no—
175C2—41no—
176C2—10822no—
177C2—21642no—
178C2C22×C22⋊D54111yescharacteristic
179C2#41×D54111yescharacteristic
180C2#3177267411yescharacteristic
subgroupG/H
center, FrattiniC22C23×D541
commutator, socle, cosocleC22×C541C24
FittingC2×#41×C541C2
hypercenterC2×#41D541
hypocenterC541#546
LCSG ▷ C22×C541 ▷ C541
UCSC1 ◁ C22 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×D4×D541C2semidirect
2. #31772617C2semidirect
3. #31772611C2semidirect
4. #31772604C2semidirect
5. #31772602C2semidirect
6. #31772600C2semidirect
7. #31772596C2semidirect
8. D4×Dic541C2semidirect
9. C4×C22⋊D541C2semidirect
10. C2×#22575813C2semidirect
11. C2×#41×C541C2semidirect
16. C2×C22⋊D541C22semidirect
18. C22×Dic541C22semidirect
20. C4⋊Dic541C22semidirect
21. #22575815C22semidirect
22. #22575815C22semidirect
23. C22⋊Dic541C22semidirect
24. C22⋊Dic541C22semidirect
27. #22575813C22semidirect
28. #22575813C22semidirect
29. #22575813C22semidirect
30. C4×Dic541C22semidirect
32. C2×Q8×C541C22semidirect
34. C2×D4×C541C22semidirect
35. C22×C4×C541C22semidirect
36. C22×C4×C541C22semidirect
56. D4×C541D4semidirect
75. C2×D541#41semidirect
90. C541#546semidirect
92. C2×#41D541semidirect
105. C2×Q8C2×D541semidirect
112. C2×D4C2×D541semidirect
115. C22×C4C2×D541semidirect
116. C22×C4C2×D541semidirect
141. D4C22⋊D541semidirect

Maximal subgroups

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

subgroupindex
C2×D4×D5412
#317726172
#317726112
#317726042
#317726022
#317726002
#317725962
D4×Dic5412
C4×C22⋊D5412
C2×#225758132
C2×#41×C5412
#546541