Finite Group Databasebeta

← #45687945

Subgroups — #45687945

Order 33344.

330 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 109 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×#22552365C211yesmaximal, characteristic, complemented
2C22×C4×D521C211yesmaximal, characteristic, complemented
3#30659693C212yesmaximal, complemented
4#30659684C211yesmaximal, characteristic, complemented
5#30659683C211yesmaximal, characteristic, complemented
6#30659682C211yesmaximal, characteristic, complemented
7#30659678C212yesmaximal, complemented
8#30659670C212yesmaximal, complemented
9#30659668C212yesmaximal, complemented
10#30659666C211yesmaximal, characteristic, complemented
11C22⋊Q8×C521C211yesmaximal, characteristic, complemented
12C23×D521C2211yescharacteristic
13#22552365—24no—
14C2×D2084C2212yes—
15C2×D2084C2212yes—
16C2×D2084C2211yescharacteristic, complemented
17C2×C22⋊D521C2212yes—
18C22×Dic521C2211yescharacteristic
19C2×C4×D521—24no—
20C2×C4×D521C2211yescharacteristic
21C2×C4×D521C2211yescharacteristic
22C2×C4×D521C2211yescharacteristic
23C2×C4×D521C2211yescharacteristic
24C2×C4×D521C2212yescomplemented
25C4⋊Dic521C2211yescharacteristic, complemented
26#22552343C2212yescomplemented
27#22552341C2212yes—
28#22552341C2212yes—
29#22552341C2212yescomplemented
30#22552341C2212yescomplemented
31C4×Dic521C2212yescomplemented
32C2×Q8×C521C2211yescharacteristic, complemented
33C22×C4×C521C2211yescharacteristic
34C4⋊C4×C521C2211yescharacteristic, complemented
35C4⋊C4×C521C2212yescomplemented
36C22⋊C4×C521C2212yes—
37C22×D521—22no—
38C22×D521—22no—
39C22×D521—22no—
40C22×D521C2312yes—
41C22×D521C2311yescharacteristic
42C22×D521C2311yescharacteristic
43D2084—24no—
44D2084—24no—
45D2084—22no—
46C22⋊D521—24no—
47C2×Dic521—22no—
48C2×Dic521C2312yes—
49C2×Dic521C2311yescharacteristic
50C2×Dic521C2311yescharacteristic
51C4×D521—22no—
52C4×D521—22no—
53C4×D521—22no—
54C4×D521—24no—
55C4×D521D414yescomplemented
56C23×C521C2311yescharacteristic
57Q8×C521—22no—
58C2×C4×C521—22no—
59C2×C4×C521C2312yes—
60C2×C4×C521C2312yes—
61C2×C4×C521C2311yescharacteristic
62C2×C4×C521C2311yescharacteristic
63C22×C521—21no—
64C22×C521—21no—
65C22×C521#4112yescomplemented
66C22×C521C2411yescharacteristic
67C2×D521—28no—
68C2×D521—21no—
69C2×D521—21no—
70C2×D521—21no—
71C2×D521—21no—
72C2×D521—22no—
73C2×D521—22no—
74C2×D521—22no—
75C2×D521C2×D412yes—
76C2×D521#4112yescomplemented
77C4×C521—21no—
78C4×C521—22no—
79C4×C521—22no—
80C4×C521C2×D412yes—
81Dic521—21no—
82Dic521—22no—
83Dic521C2×D412yes—
84C2×C521—22no—
85C2×C521C22×D411yescharacteristic
86C2×C521C2×#4111yescharacteristic
87C2×C521C2×#4111yescharacteristic
88D521—22no—
89D521—22no—
90D521—42no—
91C521#52511yescharacteristic, complemented, Sylow
92#525—5211nomaximal, Sylow
93C2×#41—5211no—
94C23×C4—5211no—
95#123—5212no—
96C22⋊Q8—5211no—
97C22⋊Q8D52111yescharacteristic, complemented
98#121—5211no—
99#121—5211no—
100#120—5212no—
101C4×D4—5212no—
102C4×D4—5212no—
103#117—5211no—
104C24—5211no—
105#41—10424no—
106C2×Q8C2×D52111yescharacteristic, complemented
107C2×D4—5212no—
108C2×D4—5212no—
109C2×D4—5212no—
110C2×D4—5211no—
111C22×C4—5211no—
112C22×C4—5211no—
113C22×C4—5211no—
114C22×C4—5211no—
115C22×C4—5211no—
116C22×C4—5212no—
117C22×C4—10424no—
118C22×C4C2×D52111yescharacteristic
119C4⋊C4—5212no—
120C4⋊C4—5211no—
121C4⋊C4C2×D52111yescharacteristic, complemented
122C4⋊C4C2×D52112yescomplemented
123C22⋊C4—5212no—
124C22⋊C4—5212no—
125C22⋊C4—5212no—
126C22⋊C4—5212no—
127C22⋊C4C2×D52112yes—
128C42—5212no—
129C23—5211no—
130C23—5211no—
131C23—5212no—
132C23—10422no—
133C23—10422no—
134C23—10422no—
135C23C22×D52111yescharacteristic
136Q8—22no—
137D4—10424no—
138D4—10424no—
139D4—10424no—
140D4—10422no—
141C2×C4—22no—
142C2×C4—5211no—
143C2×C4—5214no—
144C2×C4—5212no—
145C2×C4—5211no—
146C2×C4—10422no—
147C2×C4—10424no—
148C2×C4—10422no—
149C2×C4—10422no—
150C2×C4—10422no—
151C2×C4C22×D52112yes—
152C2×C4C22×D52111yescharacteristic
153C2×C4C22×D52112yes—
154C2×C4C22×D52111yescharacteristic
155C22—21no—
156C22—21no—
157C22—5212no—
158C22—5212no—
159C22—10428no—
160C22—10421no—
161C22—10421no—
162C22—10421no—
163C22—10421no—
164C22—10422no—
165C22—10422no—
166C22—10422no—
167C22#2255236512yescomplemented
168C22C23×D52111yescharacteristic
169C4—21no—
170C4—22no—
171C4—22no—
172C4—5212no—
173C4—10421no—
174C4—10422no—
175C4D4×D52112yes—
176C2—22no—
177C2—10422no—
178C2—10422no—
179C2—20842no—
180C2C2×D4×D52111yescharacteristic
181C2#41×D52111yescharacteristic
182C2C2×#2255236511yescharacteristic
subgroupG/H
center, FrattiniC22C23×D521
commutator, socle, cosocleC22×C521C24
FittingC22⋊Q8×C521C2
hypercenterC22⋊Q8D521
hypocenterC521#525
LCSG ▷ C22×C521 ▷ C521
UCSC1 ◁ C22 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×#22552365C2semidirect
2. C22×C4×D521C2semidirect
3. #30659693C2semidirect
4. #30659684C2semidirect
5. #30659683C2semidirect
6. #30659682C2semidirect
7. #30659678C2semidirect
8. #30659670C2semidirect
9. #30659668C2semidirect
10. #30659666C2semidirect
11. C22⋊Q8×C521C2semidirect
16. C2×D2084C22semidirect
24. C2×C4×D521C22semidirect
25. C4⋊Dic521C22semidirect
26. #22552343C22semidirect
29. #22552341C22semidirect
30. #22552341C22semidirect
31. C4×Dic521C22semidirect
32. C2×Q8×C521C22semidirect
34. C4⋊C4×C521C22semidirect
35. C4⋊C4×C521C22semidirect
55. C4×D521D4semidirect
65. C22×C521#41semidirect
76. C2×D521#41semidirect
91. C521#525semidirect
97. C22⋊Q8D521semidirect
106. C2×Q8C2×D521semidirect
121. C4⋊C4C2×D521semidirect
122. C4⋊C4C2×D521semidirect
167. C22#22552365semidirect

Maximal subgroups

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

subgroupindex
C2×#225523652
C22×C4×D5212
#306596932
#306596842
#306596832
#306596822
#306596782
#306596702
#306596682
#306596662
C22⋊Q8×C5212
#525521