Finite Group Databasebeta

← #46830820

Subgroups — #46830820

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×#22575835C211yesmaximal, characteristic, complemented
2C2×D4×D541C211yesmaximal, characteristic, complemented
3#31772616C211yesmaximal, characteristic, complemented
4#31772612C212yesmaximal, complemented
5#31772608C211yesmaximal, characteristic, complemented
6#31772603C211yesmaximal, characteristic, complemented
7#31772602C212yesmaximal, complemented
8#31772598C212yesmaximal, complemented
9C4×D2164C211yesmaximal, characteristic, complemented
10C2×#22575813C212yesmaximal, complemented
11C4×D4×C541C211yesmaximal, characteristic, complemented
12C23×D541C2212yes—
13#22575835—24no—
14C2×Dic1082C2211yescharacteristic, complemented
15C2×D2164C2211yescharacteristic
16C2×D2164C2211yescharacteristic
17C2×D2164C2212yescomplemented
18C2×C22⋊D541C2212yes—
19C2×C22⋊D541C2212yescomplemented
20D4×D541—24no—
21C22×Dic541C2212yescomplemented
22C2×C4×D541C2211yescharacteristic
23C2×C4×D541C2211yescharacteristic, complemented
24C4⋊Dic541C2211yescharacteristic, complemented
25C4⋊Dic541C2212yescomplemented
26#22575813C2211yescharacteristic
27#22575813C2212yes—
28#22575813C2212yescomplemented
29#22575813C2212yescomplemented
30#22575813C2211yescharacteristic, complemented
31#22575813C2212yescomplemented
32C2×D4×C541C2211yescharacteristic
33C22×C4×C541C2212yescomplemented
34C4⋊C4×C541C2211yescharacteristic, complemented
35C22⋊C4×C541C2212yescomplemented
36C42×C541C2211yescharacteristic, complemented
37C22×D541—24no—
38C22×D541—24no—
39C22×D541—42no—
40C22×D541C2312yes—
41C22×D541C2311yescharacteristic
42C22×D541C2311yescharacteristic
43Dic1082—22no—
44D2164—22no—
45D2164—22no—
46D2164—42no—
47C22⋊D541—24no—
48C22⋊D541—24no—
49C2×Dic541—24no—
50C2×Dic541C2311yescharacteristic
51C2×Dic541C2312yes—
52C2×Dic541C2311yescharacteristic
53C4×D541—22no—
54C4×D541—22no—
55C23×C541C2312yes—
56D4×C541D414yescomplemented
57C2×C4×C541—42no—
58C2×C4×C541C2311yescharacteristic
59C2×C4×C541C2311yescharacteristic
60C2×C4×C541C2312yes—
61C2×C4×C541C2311yescharacteristic
62C22×C541—22no—
63C22×C541—22no—
64C22×C541C2×D414yes—
65C22×C541C2411yescharacteristic
66C2×D541—21no—
67C2×D541—21no—
68C2×D541—21no—
69C2×D541—22no—
70C2×D541—21no—
71C2×D541—22no—
72C2×D541—21no—
73C2×D541—22no—
74C2×D541—48no—
75C2×D541#4112yescomplemented
76C4×C541—21no—
77C4×C541—22no—
78C4×C541—21no—
79C4×C541C2×D412yes—
80Dic541—21no—
81Dic541—21no—
82Dic541—22no—
83C2×C541—24no—
84C2×C541C22×D411yescharacteristic
85C2×C541C2×#4111yescharacteristic
86C2×C541H(5,𝔽2)11yescharacteristic
87D541—22no—
88D541—41no—
89D541—42no—
90C541#54611yescharacteristic, complemented, Sylow
91#546—5411nomaximal, Sylow
92C2×#41—5411no—
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×D4D54111yescharacteristic, complemented
102C2×C22⋊C4—5412no—
103C24—5412no—
104#41—10824no—
105C2×Q8—5411no—
106C2×D4—5412no—
107C2×D4—5412no—
108C2×D4—5411no—
109C2×D4—5411no—
110C2×D4—5412no—
111C2×D4—10824no—
112C2×D4C2×D54111yescharacteristic
113C22×C4—5412no—
114C22×C4—5411no—
115C22×C4—5411no—
116C22×C4C2×D54112yescomplemented
117C4⋊C4—5411no—
118C4⋊C4—5412no—
119C4⋊C4C2×D54111yescharacteristic, complemented
120C22⋊C4—5411no—
121C22⋊C4—5412no—
122C22⋊C4—5412no—
123C22⋊C4—5412no—
124C22⋊C4—5411no—
125C22⋊C4—5412no—
126C22⋊C4C2×D54112yescomplemented
127C42C2×D54111yescharacteristic, complemented
128C23—5411no—
129C23—5412no—
130C23—5411no—
131C23—10824no—
132C23—10824no—
133C23—21642no—
134C23C22×D54112yes—
135Q8—10822no—
136D4—10822no—
137D4—10824no—
138D4—10824no—
139D4—10822no—
140D4—21642no—
141D4D216414yescomplemented
142C2×C4—42no—
143C2×C4—5411no—
144C2×C4—5412no—
145C2×C4—5411no—
146C2×C4—10824no—
147C2×C4—10822no—
148C2×C4—10822no—
149C2×C4C22×D54111yescharacteristic
150C2×C4C22×D54111yescharacteristic
151C2×C4C22×D54112yes—
152C2×C4C22×D54111yescharacteristic
153C22—22no—
154C22—22no—
155C22—5412no—
156C22—10821no—
157C22—10821no—
158C22—10821no—
159C22—10822no—
160C22—10821no—
161C22—10822no—
162C22—10821no—
163C22—10822no—
164C22—21648no—
165C22C2×D216414yes—
166C22C23×D54111yescharacteristic
167C4—21no—
168C4—22no—
169C4—21no—
170C4—10821no—
171C4—10821no—
172C4—10822no—
173C4C2×D216412yes—
174C2—24no—
175C2—10822no—
176C2—21642no—
177C2—21641no—
178C2C22×D216411yescharacteristic
179C2#41×D54111yescharacteristic
180C2#3177267311yescharacteristic
subgroupG/H
center, FrattiniC22C23×D541
commutator, socle, cosocleC22×C541C24
FittingC4×D4×C541C2
hypercenterC4×D4D541
hypocenterC541#546
LCSG ▷ C22×C541 ▷ C541
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×#22575835C2semidirect
2. C2×D4×D541C2semidirect
3. #31772616C2semidirect
4. #31772612C2semidirect
5. #31772608C2semidirect
6. #31772603C2semidirect
7. #31772602C2semidirect
8. #31772598C2semidirect
9. C4×D2164C2semidirect
10. C2×#22575813C2semidirect
11. C4×D4×C541C2semidirect
14. C2×Dic1082C22semidirect
17. C2×D2164C22semidirect
19. C2×C22⋊D541C22semidirect
21. C22×Dic541C22semidirect
23. C2×C4×D541C22semidirect
24. C4⋊Dic541C22semidirect
25. C4⋊Dic541C22semidirect
28. #22575813C22semidirect
29. #22575813C22semidirect
30. #22575813C22semidirect
31. #22575813C22semidirect
33. C22×C4×C541C22semidirect
34. C4⋊C4×C541C22semidirect
35. C22⋊C4×C541C22semidirect
36. C42×C541C22semidirect
56. D4×C541D4semidirect
75. C2×D541#41semidirect
90. C541#546semidirect
101. C4×D4D541semidirect
116. C22×C4C2×D541semidirect
119. C4⋊C4C2×D541semidirect
126. C22⋊C4C2×D541semidirect
127. C42C2×D541semidirect
141. D4D2164semidirect

Maximal subgroups

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

subgroupindex
C2×#225758352
C2×D4×D5412
#317726162
#317726122
#317726082
#317726032
#317726022
#317725982
C4×D21642
C2×#225758132
C4×D4×C5412
#546541