Finite Group Databasebeta

← #49148515

Subgroups — #49148515

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×#22604418C211yesmaximal, characteristic, complemented
2C2×D4×D577C211yesmaximal, characteristic, complemented
3#32914660C212yesmaximal, complemented
4#32914650C212yesmaximal, complemented
5#32914639C211yesmaximal, characteristic, complemented
6#32914638C211yesmaximal, characteristic, complemented
7#32914635C211yesmaximal, characteristic, complemented
8#32914634C212yesmaximal, complemented
9#32914632C212yesmaximal, complemented
10#32914622C211yesmaximal, characteristic, complemented
11#121×C577C211yesmaximal, characteristic, complemented
12C23×D577C2212yes—
13#22604418—24no—
14C2×Dic1154C2211yescharacteristic, complemented
15C2×D2308C2211yescharacteristic
16C2×D2308C2211yescharacteristic
17C2×D2308C2212yescomplemented
18C2×C22⋊D577C2212yes—
19C2×C22⋊D577C2211yescharacteristic
20C2×C22⋊D577C2211yescharacteristic, complemented
21C2×C22⋊D577C2212yescomplemented
22C2×C22⋊D577C2212yescomplemented
23D4×D577—24no—
24C2×C4×D577C2211yescharacteristic
25C2×C4×D577C2211yescharacteristic, complemented
26C4⋊Dic577C2211yescharacteristic, complemented
27C22⋊Dic577C2212yescomplemented
28#22604395C2212yes—
29#22604395C2212yescomplemented
30#22604395C2212yescomplemented
31C4×Dic577C2212yescomplemented
32C2×D4×C577C2211yescharacteristic
33C2×D4×C577C2212yescomplemented
34C22×C4×C577C2211yescharacteristic, complemented
35C4⋊C4×C577C2211yescharacteristic, complemented
36C22⋊C4×C577C2212yescomplemented
37C22×D577—24no—
38C22×D577—42no—
39C22×D577—42no—
40C22×D577C2312yes—
41C22×D577C2311yescharacteristic
42C22×D577C2311yescharacteristic
43Dic1154—22no—
44D2308—22no—
45D2308—22no—
46D2308—42no—
47C22⋊D577—22no—
48C22⋊D577—24no—
49C22⋊D577—22no—
50C22⋊D577—42no—
51C22⋊D577—42no—
52C2×Dic577C2312yes—
53C2×Dic577C2311yescharacteristic
54C2×Dic577C2311yescharacteristic
55C4×D577—22no—
56C4×D577D414yescomplemented
57C23×C577C2312yes—
58C23×C577C2311yescharacteristic
59D4×C577—22no—
60D4×C577—42no—
61C2×C4×C577—22no—
62C2×C4×C577C2311yescharacteristic
63C2×C4×C577C2312yes—
64C2×C4×C577C2311yescharacteristic
65C22×C577—21no—
66C22×C577—22no—
67C22×C577—21no—
68C22×C577—22no—
69C22×C577—21no—
70C22×C577—22no—
71C22×C577C2411yescharacteristic
72C2×D577—21no—
73C2×D577—21no—
74C2×D577—21no—
75C2×D577—22no—
76C2×D577—21no—
77C2×D577—22no—
78C2×D577—21no—
79C2×D577—22no—
80C2×D577—48no—
81C2×D577C2×D412yes—
82C4×C577—21no—
83C4×C577—22no—
84C4×C577C2×D412yes—
85Dic577—21no—
86Dic577—22no—
87Dic577C2×D412yes—
88C2×C577—42no—
89C2×C577—41no—
90C2×C577C22×D411yescharacteristic
91C2×C577H(5,𝔽2)11yescharacteristic
92C2×C577H(5,𝔽2)11yescharacteristic
93D577—22no—
94D577—41no—
95D577—42no—
96C577#53511yescharacteristic, complemented, Sylow
97#535—5771nomaximal, Sylow
98C2×#41—5771no—
99C22×D4—5771no—
100#127—5772no—
101#124—5772no—
102#121—5771no—
103#121—5771no—
104#121—5771no—
105#121D57711yescharacteristic, complemented
106#120—5772no—
107#120—5772no—
108#117—5771no—
109C24—5772no—
110#41—11544no—
111C2×Q8—5771no—
112C2×D4—5772no—
113C2×D4—5772no—
114C2×D4—5771no—
115C2×D4—5772no—
116C2×D4—5771no—
117C2×D4—5772no—
118C2×D4—5771no—
119C2×D4—5771no—
120C2×D4—11544no—
121C2×D4C2×D57711yescharacteristic
122C2×D4C2×D57712yescomplemented
123C22×C4—5771no—
124C22×C4—5771no—
125C22×C4C2×D57711yescharacteristic, complemented
126C4⋊C4—5771no—
127C4⋊C4C2×D57711yescharacteristic, complemented
128C22⋊C4—5772no—
129C22⋊C4—5772no—
130C22⋊C4—5772no—
131C22⋊C4—5772no—
132C22⋊C4C2×D57712yescomplemented
133C42—5772no—
134C23—23082no—
135C23—23082no—
136C23—5771no—
137C23—5772no—
138C23—5771no—
139C23—11544no—
140C23C22×D57712yes—
141C23C22×D57711yescharacteristic
142Q8—11542no—
143D4—22no—
144D4—42no—
145D4—23082no—
146D4—23082no—
147D4—23082no—
148D4—11542no—
149D4—11544no—
150D4—11542no—
151D4—11542no—
152D4—11542no—
153C2×C4—22no—
154C2×C4—5771no—
155C2×C4—5774no—
156C2×C4—5772no—
157C2×C4—5771no—
158C2×C4—11542no—
159C2×C4C22×D57712yes—
160C2×C4C22×D57711yescharacteristic
161C2×C4C22×D57711yescharacteristic
162C22—21no—
163C22—22no—
164C22—21no—
165C22—22no—
166C22—21no—
167C22—22no—
168C22—23088no—
169C22—5772no—
170C22—11541no—
171C22—11542no—
172C22—11541no—
173C22—11542no—
174C22—11541no—
175C22—11542no—
176C22—11541no—
177C22—11541no—
178C22C23×D57711yescharacteristic
179C4—21no—
180C4—22no—
181C4—5772no—
182C4—11541no—
183C4—11542no—
184C4D4×D57712yes—
185C2—42no—
186C2—41no—
187C2—23082no—
188C2—23081no—
189C2—11542no—
190C2C2×D4×D57711yescharacteristic
191C2#3291470911yescharacteristic
192C2#3291471011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D577
commutator, socle, cosocleC22×C577C24
Fitting#121×C577C2
hypercenter#121D577
hypocenterC577#535
LCSG ▷ C22×C577 ▷ C577
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C2×#22604418C2semidirect
2. C2×D4×D577C2semidirect
3. #32914660C2semidirect
4. #32914650C2semidirect
5. #32914639C2semidirect
6. #32914638C2semidirect
7. #32914635C2semidirect
8. #32914634C2semidirect
9. #32914632C2semidirect
10. #32914622C2semidirect
11. #121×C577C2semidirect
14. C2×Dic1154C22semidirect
17. C2×D2308C22semidirect
20. C2×C22⋊D577C22semidirect
21. C2×C22⋊D577C22semidirect
22. C2×C22⋊D577C22semidirect
25. C2×C4×D577C22semidirect
26. C4⋊Dic577C22semidirect
27. C22⋊Dic577C22semidirect
29. #22604395C22semidirect
30. #22604395C22semidirect
31. C4×Dic577C22semidirect
33. C2×D4×C577C22semidirect
34. C22×C4×C577C22semidirect
35. C4⋊C4×C577C22semidirect
36. C22⋊C4×C577C22semidirect
56. C4×D577D4semidirect
96. C577#535semidirect
105. #121D577semidirect
122. C2×D4C2×D577semidirect
125. C22×C4C2×D577semidirect
127. C4⋊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
C2×#226044182
C2×D4×D5772
#329146602
#329146502
#329146392
#329146382
#329146352
#329146342
#329146322
#329146222
#121×C5772
#535577