Finite Group Databasebeta

← #49174227

Subgroups — #49174227

Order 37504.

218 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 56 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#34037147C211yesmaximal, characteristic, complemented
2#34037074C211yesmaximal, characteristic, complemented
3#34036982C212yesmaximal, complemented
4#34036980C212yesmaximal
5#34036661C211yesmaximal, characteristic
6#22627691—21no—
7#22627681C2212yes—
8C4×#14556880—21no—
9(C2×#11924078)⋊C4—21no—
10(C2×#11924078)⋊C4—21no—
11(C2×#11924078)⋊C4C2212yes—
12#22627617—21no—
13#22627615C411yescharacteristic, complemented
14#22627611C411yescharacteristic, complemented
15#22627606—21no—
16#22627604C2211yescharacteristic
17#22627595C2211yescharacteristic
18C4×Dic586C411yescharacteristic, complemented
19C4×C22⋊D293—21no—
20#22627583—21no—
21C42×D293C2211yescharacteristic
22C4×D4×C293C411yescharacteristic, complemented
23C22×#11924078—22no—
24C2×#14556880—22no—
25C2×Dic586C2×C411yescharacteristic
26C2×C22⋊D293—21no—
27C2×C4×D293D411yescharacteristic
28C2×C4×D293D411yescharacteristic
29C2×C4×D293C2311yescharacteristic
30C4⋊Dic293—21no—
31C4⋊Dic293—21no—
32C4⋊Dic293C2×C411yescharacteristic
33#17989781—21no—
34#17989781—21no—
35C22⋊Dic293—21no—
36C22⋊Dic293—21no—
37C22⋊Dic293—21no—
38#17989779—21no—
39C4×Dic293—21no—
40C4×Dic293C2×C411yescharacteristic
41C4×Dic293D411yescharacteristic
42C4×Dic293D411yescharacteristic
43C2×D4×C293C2×C411yescharacteristic
44C22×C4×C293—21no—
45C4⋊C4×C293C2×C411yescharacteristic
46C22⋊C4×C293—21no—
47C42×C293C2×C411yescharacteristic
48C2×#11924078—42no—
49C2×#11924078—42no—
50C2×#11924078—42no—
51#14556880—42no—
52C22×D293C2×D411yescharacteristic
53Dic586—41no—
54C22⋊D293—42no—
55C2×Dic293—21no—
56C2×Dic293—21no—
57C2×Dic293C22⋊C411yescharacteristic
58C2×Dic293C22⋊C411yescharacteristic
59C2×Dic293C2×D411yescharacteristic
60C4×D293—22no—
61C4×D293—41no—
62C4×D293—41no—
63C23×C293—21no—
64D4×C293—41no—
65C2×C4×C293—21no—
66C2×C4×C293—42no—
67C2×C4×C293C22⋊C411yescharacteristic
68C2×C4×C293C22⋊C411yescharacteristic
69C2×C4×C293C22×C411yescharacteristic
70C22×C293—41no—
71C22×C293—41no—
72C22×C293—41no—
73C22×C293C2×C22⋊C411yescharacteristic
74C2×D293—21no—
75C2×D293—21no—
76C2×D293#13512yes—
77#11924078—82no—
78C4×C293—21no—
79C4×C293—21no—
80C4×C293—21no—
81C4×C293—41no—
82Dic293—21no—
83Dic293—21no—
84Dic293—21no—
85Dic293—41no—
86Dic293—41no—
87C2×C293—81no—
88C2×C293#41011yescharacteristic
89C2×C293#41611yescharacteristic
90C2×C293#42111yescharacteristic
91D293—22no—
92C293#152111yescharacteristic, complemented, Sylow
93#1521—2931nomaximal, Sylow
94#529—2931no—
95#431—2931no—
96#383—2931no—
97#328—2932no—
98#327—2932no—
99#126—5861no—
100#125—2931no—
101#124—2931no—
102#123—5861no—
103C22⋊Q8—2931no—
104#121—2931no—
105C4×Q8—2931no—
106C4×D4—5861no—
107C4×D4#1192407811yescharacteristic, complemented
108#117—5861no—
109C2×C42—2931no—
110C4⋊C8—5861no—
111C22⋊C8—2932no—
112C4×C8—5861no—
113#95—2932no—
114#95—5861no—
115#95—5861no—
116C2×Q8—2931no—
117C2×D4—5861no—
118C2×D4C2×#1192407811yescharacteristic
119C22×C4—21no—
120C22×C4—2931no—
121C22×C4—2931no—
122C22×C4—2931no—
123C22×C4—5862no—
124C2×C8—5862no—
125C4⋊C4—2931no—
126C4⋊C4—5861no—
127C4⋊C4—5861no—
128C4⋊C4—5861no—
129C4⋊C4—5861no—
130C4⋊C4C2×#1192407811yescharacteristic
131C22⋊C4—21no—
132C22⋊C4—5861no—
133C22⋊C4—5861no—
134C22⋊C4—5861no—
135C22⋊C4—5861no—
136C42—2931no—
137C42—2931no—
138C42—2931no—
139C42—5861no—
140C42C2×#1192407811yescharacteristic
141C23—21no—
142C23—2931no—
143Q8—11721no—
144D4—41no—
145D4—11722no—
146C2×C4—21no—
147C2×C4—42no—
148C2×C4—2931no—
149C2×C4—2931no—
150C2×C4—2931no—
151C2×C4—5862no—
152C2×C4—5861no—
153C2×C4—5861no—
154C2×C4—11721no—
155C2×C4—11721no—
156C2×C4—11722no—
157C2×C4—11722no—
158C2×C4—11722no—
159C2×C4C22⋊#1192407811yescharacteristic
160C2×C4C22⋊#1192407811yescharacteristic
161C2×C4C22×#1192407811yescharacteristic
162C8—11722no—
163C22—41no—
164C22—41no—
165C22—41no—
166C22—2932no—
167C22—5861no—
168C22—5861no—
169C22C2×C22⋊#1192407811yescharacteristic
170C4—21no—
171C4—21no—
172C4—21no—
173C4—41no—
174C4—23442no—
175C4—5861no—
176C4—5861no—
177C4—5861no—
178C4—11721no—
179C4—11721no—
180C2—81no—
181C2—5862no—
182C2#3403710811yescharacteristic
183C2#3403711911yescharacteristic
184C2#3403712711yescharacteristic
subgroupG/H
centerC22C2×C22⋊#11924078
commutatorC2×C4×C293C22×C4
FrattiniC2×C4C22×#11924078
FittingC4×D4×C293C4
socleC22×C293C2×C22⋊C4
prime radical#22627595C22
cosocleC2×C4×D293C23
hypercenterC4×D4#11924078
hypocenterC293#1521
LCSG ▷ C2×C4×C293 ▷ C22×C293 ▷ C293
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #34037147C2semidirect
2. #34037074C2semidirect
3. #34036982C2semidirect
13. #22627615C4semidirect
14. #22627611C4semidirect
18. C4×Dic586C4semidirect
22. C4×D4×C293C4semidirect
92. C293#1521semidirect
107. C4×D4#11924078semidirect

Maximal subgroups

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

subgroupindex
#340371472
#340370742
#340369822
#340369802
#340366612
#1521293