Finite Group Databasebeta

← #49183221

Subgroups — #49183221

Order 37952.

330 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 111 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×#23748732C211yesmaximal, characteristic, complemented
2C23×Dic593C211yesmaximal, characteristic, complemented
3#34039269C211yesmaximal, characteristic, complemented
4#34039266C211yesmaximal, characteristic, complemented
5#34039262C212yesmaximal, complemented
6#34039257C212yesmaximal, complemented
7#34039254C211yesmaximal, characteristic, complemented
8D4×Dic593C212yesmaximal, complemented
9#34039245C212yesmaximal, complemented
10#34039241C211yesmaximal, characteristic, complemented
11#120×C593C211yesmaximal, characteristic, complemented
12#23748732—24no—
13C2×Dic1186C2211yescharacteristic, complemented
14C2×C22⋊D593C2211yescharacteristic
15C2×C22⋊D593C2212yes—
16C2×C22⋊D593C2211yescharacteristic, complemented
17C22×Dic593—24no—
18C22×Dic593C2212yes—
19C22×Dic593C2212yes—
20C22×Dic593C2211yescharacteristic
21C22×Dic593C2211yescharacteristic
22C22×Dic593C2211yescharacteristic, complemented
23C2×C4×D593C2211yescharacteristic, complemented
24C4⋊Dic593C2212yescomplemented
25#23748712C2212yescomplemented
26#23748712C2212yescomplemented
27C22⋊Dic593C2211yescharacteristic
28C22⋊Dic593C2212yes—
29C22⋊Dic593C2212yescomplemented
30#23748710C2212yescomplemented
31C4×Dic593C2212yescomplemented
32C24×C593C2211yescharacteristic
33C2×D4×C593C2211yescharacteristic
34C2×D4×C593C2212yes—
35C22⋊C4×C593C2211yescharacteristic
36C22⋊C4×C593C2212yes—
37C22×D593C2311yescharacteristic
38Dic1186—22no—
39C22⋊D593—22no—
40C22⋊D593—24no—
41C22⋊D593—22no—
42C2×Dic593—22no—
43C2×Dic593—24no—
44C2×Dic593—24no—
45C2×Dic593—22no—
46C2×Dic593D414yescomplemented
47C2×Dic593C2312yes—
48C2×Dic593C2312yes—
49C2×Dic593C2311yescharacteristic
50C2×Dic593C2311yescharacteristic
51C2×Dic593C2311yescharacteristic
52C4×D593—22no—
53C23×C593—22no—
54C23×C593—24no—
55C23×C593C2311yescharacteristic
56C23×C593C2311yescharacteristic
57C23×C593C2312yes—
58D4×C593—22no—
59D4×C593—24no—
60C2×C4×C593C2312yes—
61C2×C4×C593C2311yescharacteristic
62C22×C593—28no—
63C22×C593—22no—
64C22×C593—22no—
65C22×C593—22no—
66C22×C593—21no—
67C22×C593—22no—
68C22×C593C2×D412yes—
69C22×C593#4114yescomplemented
70C22×C593C2411yescharacteristic
71C2×D593—21no—
72C2×D593—22no—
73C4×C593—21no—
74C4×C593—22no—
75Dic593—22no—
76Dic593—21no—
77Dic593—22no—
78Dic593C2×D412yes—
79Dic593C2×D412yes—
80C2×C593—22no—
81C2×C593—24no—
82C2×C593—41no—
83C2×C593C22×D411yescharacteristic
84C2×C593C2×#4112yes—
85D593—41no—
86C593#52511yescharacteristic, complemented, Sylow
87#525—5931nomaximal, Sylow
88C2×#41—5931no—
89C23×C4—5931no—
90#123—5931no—
91#123—5931no—
92C22⋊Q8—5932no—
93#121—5932no—
94#120—5931no—
95#120D59311yescharacteristic, complemented
96C4×D4—5932no—
97C4×D4—5932no—
98#117—5931no—
99C24C2×D59311yescharacteristic
100#41—11864no—
101C2×Q8—5931no—
102C2×D4—5932no—
103C2×D4—5931no—
104C2×D4—5931no—
105C2×D4C2×D59312yes—
106C2×D4C2×D59311yescharacteristic
107C22×C4—5931no—
108C22×C4—5932no—
109C22×C4—5931no—
110C22×C4—5932no—
111C22×C4—5931no—
112C22×C4—5931no—
113C22×C4—11864no—
114C4⋊C4—5932no—
115C4⋊C4—5932no—
116C4⋊C4—5932no—
117C22⋊C4—5931no—
118C22⋊C4—5932no—
119C22⋊C4—5932no—
120C22⋊C4—5932no—
121C22⋊C4C2×D59311yescharacteristic
122C22⋊C4C2×D59312yes—
123C42—5932no—
124C23—22no—
125C23—24no—
126C23—5931no—
127C23C22×D59311yescharacteristic
128C23C22×D59311yescharacteristic
129C23C22×D59312yes—
130Q8—11862no—
131D4—22no—
132D4—24no—
133D4—11862no—
134D4—11862no—
135D4—11864no—
136C2×C4—5934no—
137C2×C4—5931no—
138C2×C4—5931no—
139C2×C4—5932no—
140C2×C4—5932no—
141C2×C4—5931no—
142C2×C4—11862no—
143C2×C4—11864no—
144C2×C4—11864no—
145C2×C4—11862no—
146C2×C4—11862no—
147C2×C4C22×D59312yes—
148C2×C4C22×D59311yescharacteristic
149C22—28no—
150C22—22no—
151C22—22no—
152C22—22no—
153C22—21no—
154C22—22no—
155C22—11861no—
156C22—11862no—
157C22D4×D59312yes—
158C22#2374873214yescomplemented
159C22C23×D59311yescharacteristic
160C4—21no—
161C4—22no—
162C4—5932no—
163C4—5932no—
164C4—11862no—
165C4—11861no—
166C4—11862no—
167C2—22no—
168C2—24no—
169C2—41no—
170C2—23721no—
171C2C2×D4×D59311yescharacteristic
172C2C2×#2374873212yes—
subgroupG/H
center, FrattiniC22C23×D593
commutator, socle, cosocleC22×C593C24
Fitting#120×C593C2
hypercenter#120D593
hypocenterC593#525
LCSG ▷ C22×C593 ▷ C593
UCSC1 ◁ C22 ◁ #120

Complements

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

NH ≅ G/Ntype
1. C2×#23748732C2semidirect
2. C23×Dic593C2semidirect
3. #34039269C2semidirect
4. #34039266C2semidirect
5. #34039262C2semidirect
6. #34039257C2semidirect
7. #34039254C2semidirect
8. D4×Dic593C2semidirect
9. #34039245C2semidirect
10. #34039241C2semidirect
11. #120×C593C2semidirect
13. C2×Dic1186C22semidirect
16. C2×C22⋊D593C22semidirect
22. C22×Dic593C22semidirect
23. C2×C4×D593C22semidirect
24. C4⋊Dic593C22semidirect
25. #23748712C22semidirect
26. #23748712C22semidirect
29. C22⋊Dic593C22semidirect
30. #23748710C22semidirect
31. C4×Dic593C22semidirect
46. C2×Dic593D4semidirect
69. C22×C593#41semidirect
86. C593#525semidirect
95. #120D593semidirect
158. C22#23748732semidirect

Maximal subgroups

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

subgroupindex
C2×#237487322
C23×Dic5932
#340392692
#340392662
#340392622
#340392572
#340392542
D4×Dic5932
#340392452
#340392412
#120×C5932
#525593