Finite Group Databasebeta

← #49148510

Subgroups — #49148510

Order 36928.

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

normal subgroups only

This group has 346 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
1C22×D2308C211yesmaximal, characteristic, complemented
2C2×D4×D577C211yesmaximal, characteristic, complemented
3#32914649C212yesmaximal, complemented
4#32914647C211yesmaximal, characteristic, complemented
5#32914639C212yesmaximal, complemented
6#32914637C212yesmaximal, complemented
7#32914634C211yesmaximal, characteristic, complemented
8#32914634C212yesmaximal, complemented
9#32914632C211yesmaximal, characteristic, complemented
10C22⋊C4×D577C211yesmaximal, characteristic, complemented
11#123×C577C211yesmaximal, characteristic, complemented
12C23×D577C2211yescharacteristic
13C23×D577C2211yescharacteristic, complemented
14C23×D577C2211yescharacteristic, complemented
15C2×D2308—24no—
16C2×D2308C2212yes—
17C2×D2308C2211yescharacteristic, complemented
18C2×D2308C2212yescomplemented
19C2×D2308C2212yescomplemented
20C2×C22⋊D577C2211yescharacteristic
21C2×C22⋊D577C2211yescharacteristic, complemented
22C2×C22⋊D577C2212yescomplemented
23D4×D577—24no—
24C2×C4×D577C2211yescharacteristic, complemented
25C2×C4×D577C2212yescomplemented
26#22604397C2212yescomplemented
27C22⋊Dic577C2211yescharacteristic, complemented
28#22604395C2212yescomplemented
29#22604395C2212yescomplemented
30#22604395C2212yescomplemented
31#22604395C2212yescomplemented
32C2×D4×C577C2211yescharacteristic
33C22×C4×C577C2211yescharacteristic, complemented
34C4⋊C4×C577C2212yescomplemented
35C22⋊C4×C577C2211yescharacteristic, complemented
36C22⋊C4×C577C2212yescomplemented
37C22×D577—22no—
38C22×D577—22no—
39C22×D577—42no—
40C22×D577—42no—
41C22×D577—42no—
42C22×D577D414yescomplemented
43C22×D577C2311yescharacteristic
44C22×D577C2312yes—
45C22×D577C2311yescharacteristic
46C22×D577C2311yescharacteristic
47D2308—22no—
48D2308—24no—
49D2308—24no—
50D2308—42no—
51C22⋊D577—22no—
52C22⋊D577—22no—
53C22⋊D577—42no—
54C2×Dic577C2312yes—
55C2×Dic577C2311yescharacteristic
56C4×D577—22no—
57C4×D577—42no—
58C23×C577C2311yescharacteristic
59C23×C577C2311yescharacteristic
60D4×C577—22no—
61C2×C4×C577—22no—
62C2×C4×C577C2312yes—
63C2×C4×C577C2312yes—
64C2×C4×C577C2311yescharacteristic
65C22×C577—22no—
66C22×C577—21no—
67C22×C577—22no—
68C22×C577C2×D412yes—
69C22×C577C2411yescharacteristic
70C2×D577—22no—
71C2×D577—22no—
72C2×D577—21no—
73C2×D577—22no—
74C2×D577—22no—
75C2×D577—22no—
76C2×D577—22no—
77C2×D577—44no—
78C2×D577—44no—
79C2×D577—44no—
80C2×D577C2×D412yes—
81C2×D577C2×D412yes—
82C4×C577—22no—
83C4×C577—21no—
84C4×C577—22no—
85Dic577—21no—
86Dic577—22no—
87C2×C577—22no—
88C2×C577—41no—
89C2×C577C22×D411yescharacteristic
90C2×C577H(5,𝔽2)12yes—
91D577—22no—
92D577—22no—
93D577—41no—
94D577—42no—
95C577#53411yescharacteristic, complemented, Sylow
96#534—5771nomaximal, Sylow
97C22×D4—5771no—
98C22×D4—5771no—
99#123—5771no—
100#123—5772no—
101#123D57711yescharacteristic, complemented
102#121—5772no—
103#121—5772no—
104#120—5771no—
105#120—5772no—
106#120—5771no—
107C2×C22⋊C4—5771no—
108C24—5771no—
109C24—5771no—
110C24—5771no—
111C2×D4—5772no—
112C2×D4—5771no—
113C2×D4—5771no—
114C2×D4—5772no—
115C2×D4—5772no—
116C2×D4—5771no—
117C2×D4—5772no—
118C2×D4—11544no—
119C2×D4—11544no—
120C2×D4C2×D57711yescharacteristic
121C22×C4—5772no—
122C22×C4—5771no—
123C22×C4C2×D57711yescharacteristic, complemented
124C4⋊C4—5772no—
125C4⋊C4C2×D57712yescomplemented
126C22⋊C4—5771no—
127C22⋊C4—5772no—
128C22⋊C4—5772no—
129C22⋊C4—5772no—
130C22⋊C4—5772no—
131C22⋊C4C2×D57711yescharacteristic, complemented
132C22⋊C4C2×D57712yescomplemented
133C23—23082no—
134C23—23082no—
135C23—23082no—
136C23—5774no—
137C23—5771no—
138C23—5771no—
139C23—5772no—
140C23—5771no—
141C23—11542no—
142C23—11542no—
143C23C22×D57711yescharacteristic
144C23C22×D57711yescharacteristic
145D4—22no—
146D4—23082no—
147D4—23082no—
148D4—11544no—
149D4—11544no—
150D4—11542no—
151D4—11542no—
152D4—11542no—
153C2×C4—22no—
154C2×C4—23082no—
155C2×C4—5772no—
156C2×C4—5771no—
157C2×C4—11542no—
158C2×C4C22×D57712yes—
159C2×C4C22×D57711yescharacteristic
160C2×C4C22×D57712yes—
161C22—22no—
162C22—21no—
163C22—22no—
164C22—23084no—
165C22—23084no—
166C22—23084no—
167C22—5772no—
168C22—5772no—
169C22—11542no—
170C22—11541no—
171C22—11542no—
172C22—11542no—
173C22—11542no—
174C22—11542no—
175C22—11542no—
176C22D4×D57712yes—
177C22C23×D57711yescharacteristic
178C4—22no—
179C4—21no—
180C4—22no—
181C4—11541no—
182C4—11542no—
183C2—22no—
184C2—41no—
185C2—23082no—
186C2—23081no—
187C2—11542no—
188C2—11542no—
189C2C2×D4×D57711yescharacteristic
190C2#3291471012yes—
subgroupG/H
center, FrattiniC22C23×D577
commutator, socle, cosocleC22×C577C24
Fitting#123×C577C2
hypercenter#123D577
hypocenterC577#534
LCSG ▷ C22×C577 ▷ C577
UCSC1 ◁ C22 ◁ #123

Complements

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

NH ≅ G/Ntype
1. C22×D2308C2semidirect
2. C2×D4×D577C2semidirect
3. #32914649C2semidirect
4. #32914647C2semidirect
5. #32914639C2semidirect
6. #32914637C2semidirect
7. #32914634C2semidirect
8. #32914634C2semidirect
9. #32914632C2semidirect
10. C22⋊C4×D577C2semidirect
11. #123×C577C2semidirect
13. C23×D577C22semidirect
14. C23×D577C22semidirect
17. C2×D2308C22semidirect
18. C2×D2308C22semidirect
19. C2×D2308C22semidirect
21. C2×C22⋊D577C22semidirect
22. C2×C22⋊D577C22semidirect
24. C2×C4×D577C22semidirect
25. C2×C4×D577C22semidirect
26. #22604397C22semidirect
27. C22⋊Dic577C22semidirect
28. #22604395C22semidirect
29. #22604395C22semidirect
30. #22604395C22semidirect
31. #22604395C22semidirect
33. C22×C4×C577C22semidirect
34. C4⋊C4×C577C22semidirect
35. C22⋊C4×C577C22semidirect
36. C22⋊C4×C577C22semidirect
42. C22×D577D4semidirect
95. C577#534semidirect
101. #123D577semidirect
123. C22×C4C2×D577semidirect
125. C4⋊C4C2×D577semidirect
131. C22⋊C4C2×D577semidirect
132. C22⋊C4C2×D577semidirect

Maximal subgroups

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

subgroupindex
C22×D23082
C2×D4×D5772
#329146492
#329146472
#329146392
#329146372
#329146342
#329146322
C22⋊C4×D5772
#123×C5772
#534577