Finite Group Databasebeta

← #49148514

Subgroups — #49148514

Order 36928.

334 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 103 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×#22604417C211yesmaximal, characteristic, complemented
2C22×C22⋊D577C211yesmaximal, characteristic, complemented
3#32914660C212yesmaximal, complemented
4#32914650C212yesmaximal, complemented
5#32914637C212yesmaximal, complemented
6#32914636C212yesmaximal, complemented
7#32914634C211yesmaximal, characteristic, complemented
8#32914633C211yesmaximal, characteristic, complemented
9#32914632C211yesmaximal, characteristic, complemented
10#32914620C211yesmaximal, characteristic, complemented
11#120×C577C211yesmaximal, characteristic, complemented
12C23×D577C2211yescharacteristic
13#22604417—24no—
14C2×Dic1154C2211yescharacteristic, complemented
15C2×D2308C2212yescomplemented
16C2×C22⋊D577—24no—
17C2×C22⋊D577C2212yes—
18C2×C22⋊D577C2212yes—
19C2×C22⋊D577C2211yescharacteristic
20C2×C22⋊D577C2211yescharacteristic, complemented
21C2×C22⋊D577C2212yescomplemented
22C2×C22⋊D577C2212yescomplemented
23C22×Dic577C2211yescharacteristic
24C22×Dic577C2211yescharacteristic, complemented
25C2×C4×D577C2211yescharacteristic, complemented
26#22604397C2212yescomplemented
27C22⋊Dic577C2211yescharacteristic
28C22⋊Dic577C2212yescomplemented
29#22604395C2212yescomplemented
30#22604395C2212yescomplemented
31C4×Dic577C2212yescomplemented
32C24×C577C2211yescharacteristic
33C2×D4×C577C2211yescharacteristic
34C2×D4×C577C2212yescomplemented
35C22⋊C4×C577C2211yescharacteristic
36C22⋊C4×C577C2212yescomplemented
37C22×D577—22no—
38C22×D577—42no—
39C22×D577C2312yes—
40C22×D577C2311yescharacteristic
41Dic1154—22no—
42D2308—42no—
43C22⋊D577—22no—
44C22⋊D577—24no—
45C22⋊D577—24no—
46C22⋊D577—22no—
47C22⋊D577—42no—
48C22⋊D577—42no—
49C2×Dic577—22no—
50C2×Dic577D414yescomplemented
51C2×Dic577C2312yes—
52C2×Dic577C2311yescharacteristic
53C2×Dic577C2311yescharacteristic
54C2×Dic577C2311yescharacteristic
55C4×D577—22no—
56C23×C577—22no—
57C23×C577—42no—
58C23×C577C2312yes—
59C23×C577C2311yescharacteristic
60C23×C577C2311yescharacteristic
61D4×C577—22no—
62D4×C577—42no—
63C2×C4×C577C2312yes—
64C2×C4×C577C2311yescharacteristic
65C22×C577—22no—
66C22×C577—21no—
67C22×C577—22no—
68C22×C577—22no—
69C22×C577—22no—
70C22×C577—22no—
71C22×C577—44no—
72C22×C577C2×D412yes—
73C22×C577C2411yescharacteristic
74C2×D577—21no—
75C2×D577—22no—
76C2×D577—22no—
77C2×D577—22no—
78C2×D577—22no—
79C2×D577—44no—
80C4×C577—21no—
81C4×C577—22no—
82Dic577—21no—
83Dic577—22no—
84Dic577C2×D412yes—
85Dic577C2×D412yes—
86C2×C577—22no—
87C2×C577—41no—
88C2×C577—42no—
89C2×C577C22×D411yescharacteristic
90C2×C577H(5,𝔽2)12yes—
91D577—41no—
92D577—42no—
93C577#53511yescharacteristic, complemented, Sylow
94#535—5771nomaximal, Sylow
95C2×#41—5771no—
96C22×D4—5771no—
97#127—5772no—
98#124—5772no—
99#121—5772no—
100#121—5772no—
101#120—5771no—
102#120—5771no—
103#120—5771no—
104#120D57711yescharacteristic, complemented
105#117—5771no—
106C24—5771no—
107C24C2×D57711yescharacteristic
108#41—11544no—
109C2×Q8—5771no—
110C2×D4—5772no—
111C2×D4—5772no—
112C2×D4—5771no—
113C2×D4—5772no—
114C2×D4—5772no—
115C2×D4—5771no—
116C2×D4—5772no—
117C2×D4—11544no—
118C2×D4C2×D57711yescharacteristic
119C2×D4C2×D57712yescomplemented
120C22×C4—5771no—
121C22×C4—5771no—
122C22×C4—5771no—
123C4⋊C4—5772no—
124C22⋊C4—5771no—
125C22⋊C4—5772no—
126C22⋊C4—5772no—
127C22⋊C4—5772no—
128C22⋊C4C2×D57711yescharacteristic
129C22⋊C4C2×D57712yescomplemented
130C42—5772no—
131C23—22no—
132C23—42no—
133C23—23082no—
134C23—5772no—
135C23—5771no—
136C23—11542no—
137C23C22×D57712yes—
138C23C22×D57711yescharacteristic
139C23C22×D57711yescharacteristic
140Q8—11542no—
141D4—22no—
142D4—42no—
143D4—23082no—
144D4—23082no—
145D4—23082no—
146D4—11544no—
147D4—11544no—
148D4—11542no—
149D4—11542no—
150C2×C4—5774no—
151C2×C4—5771no—
152C2×C4—5771no—
153C2×C4—5772no—
154C2×C4—5771no—
155C2×C4—11542no—
156C2×C4—11542no—
157C2×C4C22×D57712yes—
158C2×C4C22×D57711yescharacteristic
159C22—22no—
160C22—21no—
161C22—22no—
162C22—22no—
163C22—22no—
164C22—22no—
165C22—44no—
166C22—23084no—
167C22—11541no—
168C22—11542no—
169C22—11542no—
170C22—11542no—
171C22—11542no—
172C22D4×D57712yes—
173C22C23×D57711yescharacteristic
174C4—21no—
175C4—22no—
176C4—5772no—
177C4—5772no—
178C4—11541no—
179C4—11542no—
180C2—22no—
181C2—42no—
182C2—41no—
183C2—23082no—
184C2—23081no—
185C2C2×D4×D57711yescharacteristic
186C2#3291470912yes—
subgroupG/H
center, FrattiniC22C23×D577
commutator, socle, cosocleC22×C577C24
Fitting#120×C577C2
hypercenter#120D577
hypocenterC577#535
LCSG ▷ C22×C577 ▷ C577
UCSC1 ◁ C22 ◁ #120

Complements

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

NH ≅ G/Ntype
1. C2×#22604417C2semidirect
2. C22×C22⋊D577C2semidirect
3. #32914660C2semidirect
4. #32914650C2semidirect
5. #32914637C2semidirect
6. #32914636C2semidirect
7. #32914634C2semidirect
8. #32914633C2semidirect
9. #32914632C2semidirect
10. #32914620C2semidirect
11. #120×C577C2semidirect
14. C2×Dic1154C22semidirect
15. C2×D2308C22semidirect
20. C2×C22⋊D577C22semidirect
21. C2×C22⋊D577C22semidirect
22. C2×C22⋊D577C22semidirect
24. C22×Dic577C22semidirect
25. C2×C4×D577C22semidirect
26. #22604397C22semidirect
28. C22⋊Dic577C22semidirect
29. #22604395C22semidirect
30. #22604395C22semidirect
31. C4×Dic577C22semidirect
34. C2×D4×C577C22semidirect
36. C22⋊C4×C577C22semidirect
50. C2×Dic577D4semidirect
93. C577#535semidirect
104. #120D577semidirect
119. C2×D4C2×D577semidirect
129. C22⋊C4C2×D577semidirect

Maximal subgroups

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

subgroupindex
C2×#226044172
C22×C22⋊D5772
#329146602
#329146502
#329146372
#329146362
#329146342
#329146332
#329146322
#329146202
#120×C5772
#535577