Finite Group Databasebeta

← #49174193

Subgroups — #49174193

Order 37504.

274 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 60 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#34037101C211yesmaximal, characteristic
2#34037072C211yesmaximal, characteristic
3#34036982C214yesmaximal, complemented
4C2×#22627604C211yesmaximal, characteristic
5C2×#17989811—21no—
6C2×C22⋊#11924078—21no—
7#22627681—21no—
8#22627681C2212yes—
9(C2×#11924078)⋊C4—21no—
10(C2×#11924078)⋊C4C2212yes—
11C22×Dic586C411yescharacteristic, complemented
12C22×C4×D293C2211yescharacteristic
13#22627604—21no—
14#22627604—21no—
15#22627604C412yescomplemented
16#22627604C2212yes—
17C2×C4⋊Dic293—21no—
18C2×#17989779—21no—
19C2×C4⋊C4×C293C411yescharacteristic, complemented
20C22×#11924078—22no—
21#17989811—42no—
22C2×#14556880—22no—
23C22⋊#11924078—42no—
24C23×D293D411yescharacteristic
25C2×Dic586—21no—
26C2×Dic586—42no—
27C2×Dic586C2×C412yes—
28C22×Dic293—21no—
29C22×Dic293D411yescharacteristic
30C2×C4×D293—42no—
31C2×C4×D293C2×C411yescharacteristic
32C2×C4×D293D411yescharacteristic
33C2×C4×D293D411yescharacteristic
34C2×C4×D293C2311yescharacteristic
35C4⋊Dic293—22no—
36C4⋊Dic293—22no—
37#17989779—22no—
38#17989779—22no—
39C22×C4×C293—21no—
40C22×C4×C293C2×C411yescharacteristic
41C4⋊C4×C293—21no—
42C4⋊C4×C293C2×C412yes—
43C2×#11924078—42no—
44C2×#11924078—42no—
45C2×#11924078—42no—
46#14556880—42no—
47C22×D293—22no—
48C22×D293—22no—
49C22×D293—41no—
50C22×D293C22⋊C411yescharacteristic
51C22×D293C2×D411yescharacteristic
52Dic586—42no—
53Dic586—42no—
54C2×Dic293—22no—
55C2×Dic293—22no—
56C2×Dic293—42no—
57C2×Dic293C22⋊C411yescharacteristic
58C2×Dic293C2×D411yescharacteristic
59C4×D293—41no—
60C4×D293—41no—
61C4×D293—41no—
62C4×D293—41no—
63C23×C293C22⋊C411yescharacteristic
64C2×C4×C293—22no—
65C2×C4×C293—22no—
66C2×C4×C293—42no—
67C2×C4×C293C22⋊C411yescharacteristic
68C2×C4×C293C22×C411yescharacteristic
69C22×C293—21no—
70C22×C293—21no—
71C22×C293#9912yes—
72C22×C293C2×C22⋊C411yescharacteristic
73C2×D293—21no—
74C2×D293—21no—
75C2×D293—21no—
76C2×D293—21no—
77C2×D293—21no—
78C2×D293—44no—
79C2×D293#13712yes—
80#11924078—82no—
81C4×C293—21no—
82C4×C293—21no—
83C4×C293—42no—
84Dic293—21no—
85Dic293—21no—
86Dic293—42no—
87C2×C293—22no—
88C2×C293C2×#9911yescharacteristic
89C2×C293#41911yescharacteristic
90C2×C293#42111yescharacteristic
91D293—22no—
92D293—41no—
93C293#151111yescharacteristic, complemented, Sylow
94#1511—2931nomaximal, Sylow
95C2×C22⋊Q8—2931no—
96#407—2931no—
97#381—2931no—
98#328—2934no—
99C22×Q8—2931no—
100C23×C4—2931no—
101C2×M16—5861no—
102C22⋊Q8—2932no—
103C22⋊Q8—2932no—
104C22⋊Q8—5861no—
105C22⋊Q8—5861no—
106C2×C4⋊C4—5861no—
107C2×C4⋊C4#1192407811yescharacteristic, complemented
108C2×C22⋊C4—5861no—
109C2×C22⋊C4—5861no—
110C22⋊C8—2932no—
111C22⋊C8—5861no—
112#95—2932no—
113#95—5861no—
114C24—2931no—
115C2×Q8—2932no—
116C2×Q8—5861no—
117C2×Q8—11722no—
118C22×C4—21no—
119C22×C4—2931no—
120C22×C4—2931no—
121C22×C4—2931no—
122C22×C4—2931no—
123C22×C4—2931no—
124C22×C4—5861no—
125C22×C4—5862no—
126C22×C4—11722no—
127C22×C4C2×#1192407811yescharacteristic
128M16—11722no—
129C2×C8—5862no—
130C4⋊C4—21no—
131C4⋊C4—5862no—
132C4⋊C4—5862no—
133C4⋊C4C2×#1192407812yes—
134C22⋊C4—5862no—
135C22⋊C4—5862no—
136C22⋊C4—11722no—
137C23—2931no—
138C23—2931no—
139C23—5862no—
140C23—5862no—
141C23—11721no—
142C23C22⋊#1192407811yescharacteristic
143Q8—11722no—
144Q8—11722no—
145C2×C4—22no—
146C2×C4—22no—
147C2×C4—42no—
148C2×C4—2931no—
149C2×C4—2931no—
150C2×C4—5862no—
151C2×C4—5862no—
152C2×C4—11721no—
153C2×C4—11721no—
154C2×C4—11721no—
155C2×C4—11721no—
156C2×C4—11722no—
157C2×C4—11722no—
158C2×C4—11722no—
159C2×C4—11722no—
160C2×C4C22⋊#1192407811yescharacteristic
161C2×C4C22×#1192407811yescharacteristic
162C8—11722no—
163C22—21no—
164C22—21no—
165C22—2932no—
166C22—5861no—
167C22—5861no—
168C22—5861no—
169C22—5861no—
170C22—5861no—
171C22—11724no—
172C22#2262768312yes—
173C22C2×C22⋊#1192407811yescharacteristic
174C4—21no—
175C4—21no—
176C4—42no—
177C4—23442no—
178C4—5861no—
179C4—5861no—
180C4—11722no—
181C2—22no—
182C2—5862no—
183C2—11721no—
184C2C2×#2262768311yescharacteristic
185C2#3403712211yescharacteristic
186C2#3403712711yescharacteristic
subgroupG/H
centerC22C2×C22⋊#11924078
commutatorC2×C4×C293C22×C4
FrattiniC2×C4C22×#11924078
FittingC2×C4⋊C4×C293C4
socleC22×C293C2×C22⋊C4
prime radicalC23×D293D4
cosocleC2×C4×D293C23
hypercenterC2×C4⋊C4#11924078
hypocenterC293#1511
LCSG ▷ C2×C4×C293 ▷ C22×C293 ▷ C293
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #34036982C2semidirect
11. C22×Dic586C4semidirect
15. #22627604C4semidirect
19. C2×C4⋊C4×C293C4semidirect
93. C293#1511semidirect
107. C2×C4⋊C4#11924078semidirect

Maximal subgroups

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

subgroupindex
#340371012
#340370722
#340369822
C2×#226276042
#1511293