Finite Group Databasebeta

← #49148462

Subgroups — #49148462

Order 36928.

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×#22604419C211yesmaximal, characteristic, complemented
2C22×C4×D577C211yesmaximal, characteristic, complemented
3#32914649C212yesmaximal, complemented
4#32914640C211yesmaximal, characteristic, complemented
5#32914639C211yesmaximal, characteristic, complemented
6#32914638C211yesmaximal, characteristic, complemented
7#32914634C212yesmaximal, complemented
8#32914626C212yesmaximal, complemented
9#32914624C212yesmaximal, complemented
10#32914622C211yesmaximal, characteristic, complemented
11C22⋊Q8×C577C211yesmaximal, characteristic, complemented
12C23×D577C2211yescharacteristic
13#22604419—24no—
14C2×D2308C2212yes—
15C2×D2308C2212yes—
16C2×D2308C2211yescharacteristic, complemented
17C2×C22⋊D577C2212yes—
18C22×Dic577C2211yescharacteristic
19C2×C4×D577—24no—
20C2×C4×D577C2211yescharacteristic
21C2×C4×D577C2211yescharacteristic
22C2×C4×D577C2211yescharacteristic
23C2×C4×D577C2211yescharacteristic
24C2×C4×D577C2212yescomplemented
25C4⋊Dic577C2211yescharacteristic, complemented
26#22604397C2212yescomplemented
27#22604395C2212yes—
28#22604395C2212yes—
29#22604395C2212yescomplemented
30#22604395C2212yescomplemented
31C4×Dic577C2212yescomplemented
32C2×Q8×C577C2211yescharacteristic, complemented
33C22×C4×C577C2211yescharacteristic
34C4⋊C4×C577C2211yescharacteristic, complemented
35C4⋊C4×C577C2212yescomplemented
36C22⋊C4×C577C2212yes—
37C22×D577—22no—
38C22×D577—22no—
39C22×D577—22no—
40C22×D577C2312yes—
41C22×D577C2311yescharacteristic
42C22×D577C2311yescharacteristic
43D2308—24no—
44D2308—24no—
45D2308—22no—
46C22⋊D577—24no—
47C2×Dic577—22no—
48C2×Dic577C2312yes—
49C2×Dic577C2311yescharacteristic
50C2×Dic577C2311yescharacteristic
51C4×D577—22no—
52C4×D577—22no—
53C4×D577—22no—
54C4×D577—24no—
55C4×D577D414yescomplemented
56C23×C577C2311yescharacteristic
57Q8×C577—22no—
58C2×C4×C577—22no—
59C2×C4×C577C2312yes—
60C2×C4×C577C2312yes—
61C2×C4×C577C2311yescharacteristic
62C2×C4×C577C2311yescharacteristic
63C22×C577—21no—
64C22×C577—21no—
65C22×C577#4112yescomplemented
66C22×C577C2411yescharacteristic
67C2×D577—28no—
68C2×D577—21no—
69C2×D577—21no—
70C2×D577—21no—
71C2×D577—21no—
72C2×D577—22no—
73C2×D577—22no—
74C2×D577—22no—
75C2×D577C2×D412yes—
76C2×D577#4112yescomplemented
77C4×C577—21no—
78C4×C577—22no—
79C4×C577—22no—
80C4×C577C2×D412yes—
81Dic577—21no—
82Dic577—22no—
83Dic577C2×D412yes—
84C2×C577—22no—
85C2×C577C22×D411yescharacteristic
86C2×C577C2×#4111yescharacteristic
87C2×C577C2×#4111yescharacteristic
88D577—22no—
89D577—22no—
90D577—42no—
91C577#52511yescharacteristic, complemented, Sylow
92#525—5771nomaximal, Sylow
93C2×#41—5771no—
94C23×C4—5771no—
95#123—5772no—
96C22⋊Q8—5771no—
97C22⋊Q8D57711yescharacteristic, complemented
98#121—5771no—
99#121—5771no—
100#120—5772no—
101C4×D4—5772no—
102C4×D4—5772no—
103#117—5771no—
104C24—5771no—
105#41—11544no—
106C2×Q8C2×D57711yescharacteristic, complemented
107C2×D4—5772no—
108C2×D4—5772no—
109C2×D4—5772no—
110C2×D4—5771no—
111C22×C4—5771no—
112C22×C4—5771no—
113C22×C4—5771no—
114C22×C4—5772no—
115C22×C4—5771no—
116C22×C4—5771no—
117C22×C4—11544no—
118C22×C4C2×D57711yescharacteristic
119C4⋊C4—5772no—
120C4⋊C4—5771no—
121C4⋊C4C2×D57711yescharacteristic, complemented
122C4⋊C4C2×D57712yescomplemented
123C22⋊C4—5772no—
124C22⋊C4—5772no—
125C22⋊C4—5772no—
126C22⋊C4—5772no—
127C22⋊C4C2×D57712yes—
128C42—5772no—
129C23—5771no—
130C23—5771no—
131C23—5772no—
132C23—11542no—
133C23—11542no—
134C23—11542no—
135C23C22×D57711yescharacteristic
136Q8—22no—
137D4—11544no—
138D4—11544no—
139D4—11544no—
140D4—11542no—
141C2×C4—22no—
142C2×C4—5771no—
143C2×C4—5774no—
144C2×C4—5772no—
145C2×C4—5771no—
146C2×C4—11542no—
147C2×C4—11544no—
148C2×C4—11542no—
149C2×C4—11542no—
150C2×C4—11542no—
151C2×C4C22×D57712yes—
152C2×C4C22×D57711yescharacteristic
153C2×C4C22×D57712yes—
154C2×C4C22×D57711yescharacteristic
155C22—21no—
156C22—21no—
157C22—5772no—
158C22—5772no—
159C22—11548no—
160C22—11542no—
161C22—11542no—
162C22—11542no—
163C22—11541no—
164C22—11541no—
165C22—11541no—
166C22—11541no—
167C22#2260441912yescomplemented
168C22C23×D57711yescharacteristic
169C4—21no—
170C4—22no—
171C4—22no—
172C4—5772no—
173C4—11541no—
174C4—11542no—
175C4D4×D57712yes—
176C2—22no—
177C2—23082no—
178C2—11542no—
179C2—11542no—
180C2C2×D4×D57711yescharacteristic
181C2#41×D57711yescharacteristic
182C2C2×#2260441911yescharacteristic
subgroupG/H
center, FrattiniC22C23×D577
commutator, socle, cosocleC22×C577C24
FittingC22⋊Q8×C577C2
hypercenterC22⋊Q8D577
hypocenterC577#525
LCSG ▷ C22×C577 ▷ C577
UCSC1 ◁ C22 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×#22604419C2semidirect
2. C22×C4×D577C2semidirect
3. #32914649C2semidirect
4. #32914640C2semidirect
5. #32914639C2semidirect
6. #32914638C2semidirect
7. #32914634C2semidirect
8. #32914626C2semidirect
9. #32914624C2semidirect
10. #32914622C2semidirect
11. C22⋊Q8×C577C2semidirect
16. C2×D2308C22semidirect
24. C2×C4×D577C22semidirect
25. C4⋊Dic577C22semidirect
26. #22604397C22semidirect
29. #22604395C22semidirect
30. #22604395C22semidirect
31. C4×Dic577C22semidirect
32. C2×Q8×C577C22semidirect
34. C4⋊C4×C577C22semidirect
35. C4⋊C4×C577C22semidirect
55. C4×D577D4semidirect
65. C22×C577#41semidirect
76. C2×D577#41semidirect
91. C577#525semidirect
97. C22⋊Q8D577semidirect
106. C2×Q8C2×D577semidirect
121. C4⋊C4C2×D577semidirect
122. C4⋊C4C2×D577semidirect
167. C22#22604419semidirect

Maximal subgroups

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

subgroupindex
C2×#226044192
C22×C4×D5772
#329146492
#329146402
#329146392
#329146382
#329146342
#329146262
#329146242
#329146222
C22⋊Q8×C5772
#525577