Finite Group Databasebeta

← #50306403

Subgroups — #50306403

Order 38336.

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×#23751079C211yesmaximal, characteristic, complemented
2C22×C4×D599C211yesmaximal, characteristic, complemented
3#34062700C212yesmaximal, complemented
4#34062691C211yesmaximal, characteristic, complemented
5#34062690C211yesmaximal, characteristic, complemented
6#34062689C211yesmaximal, characteristic, complemented
7#34062685C212yesmaximal, complemented
8#34062677C212yesmaximal, complemented
9(C22⋊D599)⋊C4C212yesmaximal, complemented
10#34062673C211yesmaximal, characteristic, complemented
11C22⋊Q8×C599C211yesmaximal, characteristic, complemented
12C23×D599C2211yescharacteristic
13#23751079—24no—
14C2×D2396C2212yes—
15C2×D2396C2212yes—
16C2×D2396C2211yescharacteristic, complemented
17C2×C22⋊D599C2212yes—
18C22×Dic599C2211yescharacteristic
19C2×C4×D599—24no—
20C2×C4×D599C2211yescharacteristic
21C2×C4×D599C2211yescharacteristic
22C2×C4×D599C2211yescharacteristic
23C2×C4×D599C2211yescharacteristic
24C2×C4×D599C2212yescomplemented
25C4⋊Dic599C2211yescharacteristic, complemented
26Dic599⋊C4C2212yescomplemented
27(C2×D599)⋊C4C2212yes—
28(C2×D599)⋊C4C2212yes—
29(C2×D599)⋊C4C2212yescomplemented
30(C2×D599)⋊C4C2212yescomplemented
31C4×Dic599C2212yescomplemented
32C2×Q8×C599C2211yescharacteristic, complemented
33C22×C4×C599C2211yescharacteristic
34C4⋊C4×C599C2211yescharacteristic, complemented
35C4⋊C4×C599C2212yescomplemented
36C22⋊C4×C599C2212yes—
37C22×D599—22no—
38C22×D599—22no—
39C22×D599—22no—
40C22×D599C2312yes—
41C22×D599C2311yescharacteristic
42C22×D599C2311yescharacteristic
43D2396—24no—
44D2396—24no—
45D2396—22no—
46C22⋊D599—24no—
47C2×Dic599—22no—
48C2×Dic599C2312yes—
49C2×Dic599C2311yescharacteristic
50C2×Dic599C2311yescharacteristic
51C4×D599—22no—
52C4×D599—22no—
53C4×D599—22no—
54C4×D599—24no—
55C4×D599D414yescomplemented
56C23×C599C2311yescharacteristic
57Q8×C599—22no—
58C2×C4×C599—22no—
59C2×C4×C599C2312yes—
60C2×C4×C599C2312yes—
61C2×C4×C599C2311yescharacteristic
62C2×C4×C599C2311yescharacteristic
63C22×C599—21no—
64C22×C599—21no—
65C22×C599#4112yescomplemented
66C22×C599C2411yescharacteristic
67C2×D599—28no—
68C2×D599—21no—
69C2×D599—21no—
70C2×D599—21no—
71C2×D599—21no—
72C2×D599—22no—
73C2×D599—22no—
74C2×D599—22no—
75C2×D599C2×D412yes—
76C2×D599#4112yescomplemented
77C4×C599—21no—
78C4×C599—22no—
79C4×C599—22no—
80C4×C599C2×D412yes—
81Dic599—21no—
82Dic599—22no—
83Dic599C2×D412yes—
84C2×C599—22no—
85C2×C599C22×D411yescharacteristic
86C2×C599C2×#4111yescharacteristic
87C2×C599C2×#4111yescharacteristic
88D599—22no—
89D599—22no—
90D599—42no—
91C599#52511yescharacteristic, complemented, Sylow
92#525—5991nomaximal, Sylow
93C2×#41—5991no—
94C23×C4—5991no—
95#123—5992no—
96C22⋊Q8—5991no—
97C22⋊Q8D59911yescharacteristic, complemented
98#121—5991no—
99#121—5991no—
100#120—5992no—
101C4×D4—5992no—
102C4×D4—5992no—
103#117—5991no—
104C24—5991no—
105#41—11984no—
106C2×Q8C2×D59911yescharacteristic, complemented
107C2×D4—5992no—
108C2×D4—5992no—
109C2×D4—5992no—
110C2×D4—5991no—
111C22×C4—5991no—
112C22×C4—5991no—
113C22×C4—5991no—
114C22×C4—5992no—
115C22×C4—5991no—
116C22×C4—5991no—
117C22×C4—11984no—
118C22×C4C2×D59911yescharacteristic
119C4⋊C4—5991no—
120C4⋊C4—5992no—
121C4⋊C4C2×D59911yescharacteristic, complemented
122C4⋊C4C2×D59912yescomplemented
123C22⋊C4—5992no—
124C22⋊C4—5992no—
125C22⋊C4—5992no—
126C22⋊C4—5992no—
127C22⋊C4C2×D59912yes—
128C42—5992no—
129C23—5991no—
130C23—5991no—
131C23—5992no—
132C23—11982no—
133C23—11982no—
134C23—11982no—
135C23C22×D59911yescharacteristic
136Q8—22no—
137D4—11984no—
138D4—11984no—
139D4—11984no—
140D4—11982no—
141C2×C4—22no—
142C2×C4—5991no—
143C2×C4—5994no—
144C2×C4—5992no—
145C2×C4—5991no—
146C2×C4—11982no—
147C2×C4—11984no—
148C2×C4—11982no—
149C2×C4—11982no—
150C2×C4—11982no—
151C2×C4C22×D59912yes—
152C2×C4C22×D59911yescharacteristic
153C2×C4C22×D59912yes—
154C2×C4C22×D59911yescharacteristic
155C22—21no—
156C22—21no—
157C22—5992no—
158C22—5992no—
159C22—11988no—
160C22—11982no—
161C22—11982no—
162C22—11982no—
163C22—11981no—
164C22—11981no—
165C22—11981no—
166C22—11981no—
167C22#2375107912yescomplemented
168C22C23×D59911yescharacteristic
169C4—21no—
170C4—22no—
171C4—22no—
172C4—5992no—
173C4—11981no—
174C4—11982no—
175C4D4×D59912yes—
176C2—22no—
177C2—23962no—
178C2—11982no—
179C2—11982no—
180C2C2×D4×D59911yescharacteristic
181C2#41×D59911yescharacteristic
182C2C2×#2375107911yescharacteristic
subgroupG/H
center, FrattiniC22C23×D599
commutator, socle, cosocleC22×C599C24
FittingC22⋊Q8×C599C2
hypercenterC22⋊Q8D599
hypocenterC599#525
LCSG ▷ C22×C599 ▷ C599
UCSC1 ◁ C22 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×#23751079C2semidirect
2. C22×C4×D599C2semidirect
3. #34062700C2semidirect
4. #34062691C2semidirect
5. #34062690C2semidirect
6. #34062689C2semidirect
7. #34062685C2semidirect
8. #34062677C2semidirect
9. (C22⋊D599)⋊C4C2semidirect
10. #34062673C2semidirect
11. C22⋊Q8×C599C2semidirect
16. C2×D2396C22semidirect
24. C2×C4×D599C22semidirect
25. C4⋊Dic599C22semidirect
26. Dic599⋊C4C22semidirect
29. (C2×D599)⋊C4C22semidirect
30. (C2×D599)⋊C4C22semidirect
31. C4×Dic599C22semidirect
32. C2×Q8×C599C22semidirect
34. C4⋊C4×C599C22semidirect
35. C4⋊C4×C599C22semidirect
55. C4×D599D4semidirect
65. C22×C599#41semidirect
76. C2×D599#41semidirect
91. C599#525semidirect
97. C22⋊Q8D599semidirect
106. C2×Q8C2×D599semidirect
121. C4⋊C4C2×D599semidirect
122. C4⋊C4C2×D599semidirect
167. C22#23751079semidirect

Maximal subgroups

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

subgroupindex
C2×#237510792
C22×C4×D5992
#340627002
#340626912
#340626902
#340626892
#340626852
#340626772
(C22⋊D599)⋊C42
#340626732
C22⋊Q8×C5992
#525599