Finite Group Databasebeta

← #49183324

Subgroups — #49183324

Order 37952.

192 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 192 conjugacy classes of subgroups — too many to draw. Only its 93 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
1#34039284C211yesmaximal, characteristic, complemented
2#34039280C211yesmaximal, characteristic
3#34039280C211yesmaximal, characteristic
4#34039280C211yesmaximal, characteristic
5#34039279C211yesmaximal, characteristic
6#34039276C211yesmaximal, characteristic, complemented
7#34039275C211yesmaximal, characteristic, complemented
8#34039275C211yesmaximal, characteristic, complemented
9#34039275C211yesmaximal, characteristic, complemented
10#34039263C211yesmaximal, characteristic
11#34039263C211yesmaximal, characteristic
12C4×Dic1186C211yesmaximal, characteristic, complemented
13#34039250C211yesmaximal, characteristic, complemented
14#34039243C211yesmaximal, characteristic
15#125×C593C211yesmaximal, characteristic, complemented
16C2×Dic1186C2211yescharacteristic
17C2×Dic1186C2211yescharacteristic
18C2×C4×D593C2211yescharacteristic
19C4⋊Dic593C2211yescharacteristic
20C4⋊Dic593C2211yescharacteristic
21C4⋊Dic593C2211yescharacteristic
22C4⋊Dic593C2211yescharacteristic
23#23748712C2211yescharacteristic
24#23748712C2211yescharacteristic
25#23748712C2211yescharacteristic
26#23748712C2211yescharacteristic
27#23748712C2211yescharacteristic
28#23748712C2211yescharacteristic
29#23748712C2211yescharacteristic
30#23748712C2211yescharacteristic
31#23748712C2211yescharacteristic
32#23748712C2211yescharacteristic
33#23748710C2211yescharacteristic
34#23748710C2211yescharacteristic
35#23748710C2211yescharacteristic
36#23748710C2211yescharacteristic
37#23748710C2211yescharacteristic
38#23748710C2211yescharacteristic
39C4×Dic593C2211yescharacteristic
40C4×Dic593C2211yescharacteristic
41C4×Dic593C2211yescharacteristic
42C4×Dic593C2211yescharacteristic
43C4×Dic593C2211yescharacteristic
44C4⋊C4×C593C2211yescharacteristic
45C4⋊C4×C593C2211yescharacteristic
46C4⋊C4×C593C2211yescharacteristic
47C4⋊C4×C593C2211yescharacteristic
48C4⋊C4×C593C2211yescharacteristic
49C4⋊C4×C593C2211yescharacteristic
50C42×C593C2211yescharacteristic
51C22×D593C2311yescharacteristic
52Dic1186—22no—
53Dic1186—22no—
54C2×Dic593C2311yescharacteristic
55C2×Dic593C2311yescharacteristic
56C2×Dic593C2311yescharacteristic
57C2×Dic593C2311yescharacteristic
58C2×Dic593C2311yescharacteristic
59C2×Dic593C2311yescharacteristic
60C2×Dic593C2311yescharacteristic
61C4×D593—22no—
62C2×C4×C593C2311yescharacteristic
63C2×C4×C593C2311yescharacteristic
64C2×C4×C593C2311yescharacteristic
65C2×C4×C593C2311yescharacteristic
66C2×C4×C593C2311yescharacteristic
67C2×C4×C593C2311yescharacteristic
68C2×C4×C593C2311yescharacteristic
69C22×C593C2411yescharacteristic
70C2×D593—21no—
71C2×D593—21no—
72C2×D593—21no—
73C4×C593—21no—
74C4×C593—21no—
75C4×C593—21no—
76C4×C593—21no—
77C4×C593—21no—
78C4×C593—21no—
79C4×C593—21no—
80Dic593—21no—
81Dic593—21no—
82Dic593—21no—
83Dic593—21no—
84Dic593—21no—
85Dic593—21no—
86Dic593#4112yes—
87C2×C593C2×#4111yescharacteristic
88C2×C5932−1+411yescharacteristic
89C2×C5932−1+411yescharacteristic
90D593—41no—
91C593#54111yescharacteristic, complemented, Sylow
92#541—5931nomaximal, Sylow
93C4⋊Q8—5931no—
94#126—5931no—
95#126—5931no—
96#126—5931no—
97#126—5931no—
98#125—5931no—
99#125—5931no—
100#125—5931no—
101#125—5931no—
102#125D59311yescharacteristic, complemented
103C22⋊Q8—5931no—
104C22⋊Q8—5931no—
105C4×Q8—5931no—
106C4×Q8—5931no—
107#117—5931no—
108C2×Q8—5931no—
109C2×Q8—5931no—
110C22×C4—5931no—
111C4⋊C4—5931no—
112C4⋊C4—5931no—
113C4⋊C4—5931no—
114C4⋊C4—5931no—
115C4⋊C4—5931no—
116C4⋊C4—5931no—
117C4⋊C4—5931no—
118C4⋊C4—5931no—
119C4⋊C4—5931no—
120C4⋊C4—5931no—
121C4⋊C4—5931no—
122C4⋊C4—5931no—
123C4⋊C4—5931no—
124C4⋊C4—5931no—
125C4⋊C4C2×D59311yescharacteristic
126C4⋊C4C2×D59311yescharacteristic
127C4⋊C4C2×D59311yescharacteristic
128C4⋊C4C2×D59311yescharacteristic
129C4⋊C4C2×D59311yescharacteristic
130C4⋊C4C2×D59311yescharacteristic
131C22⋊C4—5931no—
132C22⋊C4—5931no—
133C22⋊C4—5931no—
134C22⋊C4—5931no—
135C22⋊C4—5931no—
136C22⋊C4—5931no—
137C42—5931no—
138C42—5931no—
139C42—5931no—
140C42—5931no—
141C42—5931no—
142C42C2×D59311yescharacteristic
143C23—5931no—
144Q8—11862no—
145Q8—11862no—
146C2×C4—5931no—
147C2×C4—5931no—
148C2×C4—5931no—
149C2×C4—5931no—
150C2×C4—5931no—
151C2×C4—5931no—
152C2×C4—5931no—
153C2×C4—11862no—
154C2×C4C22×D59311yescharacteristic
155C2×C4C22×D59311yescharacteristic
156C2×C4C22×D59311yescharacteristic
157C2×C4C22×D59311yescharacteristic
158C2×C4C22×D59311yescharacteristic
159C2×C4C22×D59311yescharacteristic
160C2×C4C22×D59311yescharacteristic
161C22—11861no—
162C22—11861no—
163C22—11861no—
164C22C23×D59311yescharacteristic
165C4—21no—
166C4—21no—
167C4—21no—
168C4—21no—
169C4—21no—
170C4—21no—
171C4—21no—
172C4—5932no—
173C4—11861no—
174C4—11861no—
175C4—11861no—
176C4—11861no—
177C4—11861no—
178C4—11861no—
179C2—23721no—
180C2#41×D59311yescharacteristic
181C2#3403933211yescharacteristic
182C2#3403933311yescharacteristic
subgroupG/H
center, FrattiniC22C23×D593
commutator, socle, cosocleC22×C593C24
Fitting#125×C593C2
prime radicalC22×D593C23
hypercenter#125D593
hypocenterC593#541
LCSG ▷ C22×C593 ▷ C593
UCSC1 ◁ C22 ◁ #125

Complements

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

NH ≅ G/Ntype
1. #34039284C2semidirect
6. #34039276C2semidirect
7. #34039275C2semidirect
8. #34039275C2semidirect
9. #34039275C2semidirect
12. C4×Dic1186C2semidirect
13. #34039250C2semidirect
15. #125×C593C2semidirect
91. C593#541semidirect
102. #125D593semidirect

Maximal subgroups

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

subgroupindex
#340392842
#340392802
#340392792
#340392762
#340392752
#340392632
C4×Dic11862
#340392502
#340392432
#125×C5932
#541593