Finite Group Databasebeta

← #50306398

Subgroups — #50306398

Order 38336.

330 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 107 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×#23751077C211yesmaximal, characteristic, complemented
2C22×C4×D599C211yesmaximal, characteristic, complemented
3#34062698C211yesmaximal, characteristic, complemented
4#34062693C212yesmaximal, complemented
5#34062688C212yesmaximal, complemented
6#34062685C211yesmaximal, characteristic, complemented
7#34062683C211yesmaximal, characteristic, complemented
8#34062677C212yesmaximal, complemented
9(C22⋊D599)⋊C4C212yesmaximal, complemented
10#34062671C211yesmaximal, characteristic, complemented
11#123×C599C211yesmaximal, characteristic, complemented
12C23×D599C2211yescharacteristic
13#23751077—24no—
14C2×Dic1198C2211yescharacteristic, complemented
15C2×D2396C2212yes—
16C2×C22⋊D599C2212yes—
17C2×C22⋊D599C2211yescharacteristic
18C2×C22⋊D599C2211yescharacteristic, complemented
19C22×Dic599C2211yescharacteristic
20C22×Dic599C2211yescharacteristic, complemented
21C2×C4×D599—24no—
22C2×C4×D599C2212yes—
23C2×C4×D599C2212yes—
24C2×C4×D599C2211yescharacteristic, complemented
25Dic599⋊C4C2212yescomplemented
26Dic599⋊C4C2212yescomplemented
27C22⋊Dic599C2211yescharacteristic
28(C2×D599)⋊C4C2212yes—
29(C2×D599)⋊C4C2212yes—
30(C2×D599)⋊C4C2212yescomplemented
31C4×Dic599C2212yescomplemented
32C2×D4×C599C2211yescharacteristic
33C22×C4×C599C2211yescharacteristic
34C4⋊C4×C599C2212yescomplemented
35C22⋊C4×C599C2211yescharacteristic
36C22⋊C4×C599C2212yescomplemented
37C22×D599—22no—
38C22×D599—24no—
39C22×D599C2311yescharacteristic
40C22×D599C2312yes—
41Dic1198—22no—
42D2396—24no—
43C22⋊D599—22no—
44C22⋊D599—24no—
45C22⋊D599—22no—
46C2×Dic599—22no—
47C2×Dic599D414yescomplemented
48C2×Dic599C2312yes—
49C2×Dic599C2311yescharacteristic
50C2×Dic599C2311yescharacteristic
51C2×Dic599C2311yescharacteristic
52C4×D599—24no—
53C4×D599—24no—
54C4×D599—22no—
55C23×C599C2311yescharacteristic
56C23×C599C2311yescharacteristic
57D4×C599—22no—
58C2×C4×C599—22no—
59C2×C4×C599C2312yes—
60C2×C4×C599C2312yes—
61C2×C4×C599C2311yescharacteristic
62C22×C599—22no—
63C22×C599—21no—
64C22×C599—22no—
65C22×C599C2×D412yes—
66C22×C599C2411yescharacteristic
67C2×D599—28no—
68C2×D599—22no—
69C2×D599—22no—
70C2×D599—21no—
71C2×D599—22no—
72C2×D599#4114yescomplemented
73C4×C599—22no—
74C4×C599—21no—
75C4×C599—22no—
76Dic599—21no—
77Dic599—22no—
78Dic599C2×D412yes—
79Dic599C2×D412yes—
80C2×C599—22no—
81C2×C599—41no—
82C2×C599C22×D411yescharacteristic
83C2×C599C2×#4112yes—
84D599—24no—
85D599—41no—
86C599#52511yescharacteristic, complemented, Sylow
87#525—5991nomaximal, Sylow
88C2×#41—5991no—
89C23×C4—5991no—
90#123—5991no—
91#123D59911yescharacteristic, complemented
92C22⋊Q8—5992no—
93#121—5992no—
94#120—5991no—
95#120—5991no—
96C4×D4—5992no—
97C4×D4—5992no—
98#117—5991no—
99C24—5991no—
100#41—11984no—
101C2×Q8—5991no—
102C2×D4—5992no—
103C2×D4—5991no—
104C2×D4—5991no—
105C2×D4—5992no—
106C2×D4C2×D59911yescharacteristic
107C22×C4—5991no—
108C22×C4—5991no—
109C22×C4—5992no—
110C22×C4—5991no—
111C22×C4—5992no—
112C22×C4—11984no—
113C22×C4C2×D59911yescharacteristic
114C4⋊C4—5992no—
115C4⋊C4—5992no—
116C4⋊C4C2×D59912yescomplemented
117C22⋊C4—5991no—
118C22⋊C4—5992no—
119C22⋊C4—5992no—
120C22⋊C4—5992no—
121C22⋊C4C2×D59911yescharacteristic
122C22⋊C4C2×D59912yescomplemented
123C42—5992no—
124C23—5992no—
125C23—5991no—
126C23—11984no—
127C23—11982no—
128C23C22×D59911yescharacteristic
129C23C22×D59911yescharacteristic
130Q8—11982no—
131D4—22no—
132D4—11984no—
133D4—11982no—
134D4—11984no—
135D4—11982no—
136C2×C4—22no—
137C2×C4—5994no—
138C2×C4—5991no—
139C2×C4—5991no—
140C2×C4—5992no—
141C2×C4—5991no—
142C2×C4—11984no—
143C2×C4—11984no—
144C2×C4—11982no—
145C2×C4—11982no—
146C2×C4C22×D59912yes—
147C2×C4C22×D59911yescharacteristic
148C2×C4C22×D59912yes—
149C22—22no—
150C22—21no—
151C22—22no—
152C22—5994no—
153C22—11988no—
154C22—11981no—
155C22—11982no—
156C22—11982no—
157C22—11982no—
158C22D4×D59912yes—
159C22C23×D59911yescharacteristic
160C4—22no—
161C4—21no—
162C4—22no—
163C4—5992no—
164C4—5992no—
165C4—11981no—
166C4—11982no—
167C2—22no—
168C2—41no—
169C2—23961no—
170C2—11984no—
171C2C2×D4×D59911yescharacteristic
172C2#41×D59912yes—
subgroupG/H
center, FrattiniC22C23×D599
commutator, socle, cosocleC22×C599C24
Fitting#123×C599C2
hypercenter#123D599
hypocenterC599#525
LCSG ▷ C22×C599 ▷ C599
UCSC1 ◁ C22 ◁ #123

Complements

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

NH ≅ G/Ntype
1. C2×#23751077C2semidirect
2. C22×C4×D599C2semidirect
3. #34062698C2semidirect
4. #34062693C2semidirect
5. #34062688C2semidirect
6. #34062685C2semidirect
7. #34062683C2semidirect
8. #34062677C2semidirect
9. (C22⋊D599)⋊C4C2semidirect
10. #34062671C2semidirect
11. #123×C599C2semidirect
14. C2×Dic1198C22semidirect
18. C2×C22⋊D599C22semidirect
20. C22×Dic599C22semidirect
24. C2×C4×D599C22semidirect
25. Dic599⋊C4C22semidirect
26. Dic599⋊C4C22semidirect
30. (C2×D599)⋊C4C22semidirect
31. C4×Dic599C22semidirect
34. C4⋊C4×C599C22semidirect
36. C22⋊C4×C599C22semidirect
47. C2×Dic599D4semidirect
72. C2×D599#41semidirect
86. C599#525semidirect
91. #123D599semidirect
116. C4⋊C4C2×D599semidirect
122. C22⋊C4C2×D599semidirect

Maximal subgroups

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

subgroupindex
C2×#237510772
C22×C4×D5992
#340626982
#340626932
#340626882
#340626852
#340626832
#340626772
(C22⋊D599)⋊C42
#340626712
#123×C5992
#525599