Finite Group Databasebeta

← #49175264

Subgroups — #49175264

Order 37504.

816 conjugacy classes of subgroups; only the 210 normal subgroups are shown.

normal subgroups only

This group has 816 conjugacy classes of subgroups — too many to draw. Only its 210 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
1C22×C22⋊#11924078C212yesmaximal
2#34037076C218yesmaximal, complemented
3#34037071C214yesmaximal, complemented
4C2×C22⋊C4×D293C211yesmaximal, characteristic
5C23×#11924078C2214yes—
6C2×C4⋊#11924078C2218yescomplemented
7C2×C22⋊#11924078—28no—
8C2×C22⋊#11924078C2214yes—
9C2×C22⋊#11924078C2214yes—
10(C2×#11924078)⋊C4C2218yescomplemented
11C24×D293C2211yescharacteristic
12C22×C4×D293C2212yes—
13C2×C22⋊Dic293C411yescharacteristic, complemented
14C2×#17989779C412yescomplemented
15C22⋊C4×D293C414yescomplemented
16C22⋊C4×D293C2214yes—
17C2×C22⋊C4×C293C411yescharacteristic, complemented
18C22×#11924078—28no—
19C22×#11924078—48no—
20C22×#11924078C2318yes—
21C4⋊#11924078—48no—
22C22⋊#11924078—28no—
23C22⋊#11924078—28no—
24C23×D293—44no—
25C23×D293C2×C412yes—
26C23×D293C2×C411yescharacteristic
27C23×D293D414yes—
28C23×D293Q814yes—
29C23×D293C2311yescharacteristic
30C23×D293C2312yes—
31C22×Dic293C2×C412yescomplemented
32C2×C4×D293—44no—
33C2×C4×D293C2×C414yescomplemented
34C2×C4×D293C2314yes—
35C22⋊Dic293C2×C414yescomplemented
36#17989779C2×C418yescomplemented
37C24×C293C2×C411yescharacteristic
38C22×C4×C293C2×C412yescomplemented
39C22⋊C4×C293C2×C414yescomplemented
40C2×#11924078—28no—
41C2×#11924078—216no—
42C2×#11924078—416no—
43C22×D293—24no—
44C22×D293—28no—
45C22×D293—48no—
46C22×D293—48no—
47C22×D293—44no—
48C22×D293—42no—
49C22×D293C4⋊C418yescomplemented
50C22×D293C4⋊C414yescomplemented
51C22×D293C22×C412yes—
52C22×D293C22×C411yescharacteristic
53C22×D293C2×D412yes—
54C22×D293C2×D414yes—
55C22×D293C2×Q812yes—
56C22×D293C2×Q814yes—
57C22×D293C2411yescharacteristic
58C2×Dic293—42no—
59C2×Dic293C22×C414yes—
60C4×D293—28no—
61C4×D293—44no—
62C23×C293—42no—
63C23×C293C4⋊C414yescomplemented
64C23×C293C22×C412yes—
65C23×C293C22×C411yescharacteristic
66C2×C4×C293—42no—
67C2×C4×C293C22×C414yes—
68C22×C293—22no—
69C22×C293—24no—
70C22×C293—44no—
71C22×C293C2×C4⋊C414yes—
72C22×C293C2×C4⋊C412yes—
73C22×C293C23×C411yescharacteristic
74C2×D293—22no—
75C2×D293—24no—
76C2×D293—24no—
77C2×D293—28no—
78C2×D293—24no—
79C2×D293—28no—
80C2×D293—48no—
81C2×D293—44no—
82C2×D293C2×C4⋊C414yes—
83C2×D293C2×C4⋊C412yes—
84C2×D293C22×D411yescharacteristic
85C2×D293C22×Q811yescharacteristic
86C2×D293H(5,𝔽2)14yes—
87#11924078—48no—
88C4×C293—24no—
89Dic293—24no—
90C2×C293—22no—
91C2×C293—24no—
92C2×C293C22×C4⋊C411yescharacteristic
93C2×C293#51812yes—
94D293—22no—
95D293—24no—
96D293#53412yes—
97D293#54312yes—
98C293#231511yescharacteristic, complemented, Sylow
99#2315—2931nomaximal, Sylow
100C22×C22⋊C4—2931no—
101C22×C22⋊C4—2932no—
102#385—2938no—
103#380—2934no—
104C25—2931no—
105C23×C4—2932no—
106C23×C4—2934no—
107C2×C4⋊C4—2938no—
108C2×C22⋊C4—2931no—
109C2×C22⋊C4—2932no—
110C2×C22⋊C4—2934no—
111C2×C22⋊C4—2934no—
112C2×C22⋊C4—2934no—
113C2×C22⋊C4—2934no—
114C2×C22⋊C4—5868no—
115C2×C22⋊C4#1192407811yescharacteristic, complemented
116#95—2938no—
117C24—2931no—
118C24—2932no—
119C24—2934no—
120C24—2934no—
121C24—2931no—
122C24—2932no—
123C24—11724no—
124C24C2×#1192407811yescharacteristic
125C22×C4—2932no—
126C22×C4—2934no—
127C22×C4—2934no—
128C22×C4—2938no—
129C22×C4—5868no—
130C22×C4—11724no—
131C22×C4—11728no—
132C22×C4C2×#1192407812yescomplemented
133C4⋊C4—11728no—
134C22⋊C4—2934no—
135C22⋊C4—2938no—
136C22⋊C4—5868no—
137C22⋊C4—5868no—
138C22⋊C4C2×#1192407814yescomplemented
139C23—42no—
140C23—2931no—
141C23—2932no—
142C23—2934no—
143C23—2932no—
144C23—2934no—
145C23—2932no—
146C23—2931no—
147C23—2938no—
148C23—2934no—
149C23—5864no—
150C23—5868no—
151C23—11722no—
152C23—11724no—
153C23—11728no—
154C23—11728no—
155C23C4⋊#1192407814yescomplemented
156C23C22×#1192407812yes—
157C23C22×#1192407811yescharacteristic
158C2×C4—42no—
159C2×C4—2934no—
160C2×C4—5868no—
161C2×C4—5868no—
162C2×C4—58616no—
163C2×C4—11724no—
164C2×C4—11722no—
165C2×C4—117216no—
166C2×C4C22×#1192407814yes—
167C22—22no—
168C22—24no—
169C22—44no—
170C22—2931no—
171C22—2931no—
172C22—2934no—
173C22—2932no—
174C22—2934no—
175C22—5868no—
176C22—5864no—
177C22—5864no—
178C22—5868no—
179C22—5862no—
180C22—5864no—
181C22—11724no—
182C22—11728no—
183C22C2×C4⋊#1192407812yes—
184C22C2×C4⋊#1192407814yes—
185C22C23×#1192407811yescharacteristic
186C4—24no—
187C4—5864no—
188C4—11728no—
189C2—22no—
190C2—24no—
191C2—2932no—
192C2—2932no—
193C2—5864no—
194C2—5862no—
195C2C22×C4⋊#1192407811yescharacteristic
196C2#3403719612yes—
subgroupG/H
center, FrattiniC22C23×#11924078
commutator, socleC22×C293C23×C4
FittingC2×C22⋊C4×C293C4
prime radicalC24×D293C22
cosocleC22×D293C24
hypercenterC2×C22⋊C4#11924078
hypocenterC293#2315
LCSG ▷ C22×C293 ▷ C293
UCSC1 ◁ C22 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #34037076C2semidirect
3. #34037071C2semidirect
6. C2×C4⋊#11924078C22semidirect
10. (C2×#11924078)⋊C4C22semidirect
13. C2×C22⋊Dic293C4semidirect
14. C2×#17989779C4semidirect
15. C22⋊C4×D293C4semidirect
17. C2×C22⋊C4×C293C4semidirect
31. C22×Dic293C2×C4semidirect
33. C2×C4×D293C2×C4semidirect
35. C22⋊Dic293C2×C4semidirect
36. #17989779C2×C4semidirect
38. C22×C4×C293C2×C4semidirect
39. C22⋊C4×C293C2×C4semidirect
49. C22×D293C4⋊C4semidirect
50. C22×D293C4⋊C4semidirect
63. C23×C293C4⋊C4semidirect
98. C293#2315semidirect
115. C2×C22⋊C4#11924078semidirect
132. C22×C4C2×#11924078semidirect
138. C22⋊C4C2×#11924078semidirect
155. C23C4⋊#11924078semidirect

Maximal subgroups

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

subgroupindex
C22×C22⋊#119240782
#340370762
#340370712
C2×C22⋊C4×D2932
#2315293