Finite Group Databasebeta

← #49174269

Subgroups — #49174269

Order 37504.

200 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 54 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#34037152C211yesmaximal, characteristic, complemented
2#34037151C211yesmaximal, characteristic, complemented
3#34036986C212yesmaximal, complemented
4#34036984C212yesmaximal, complemented
5#34036661C211yesmaximal, characteristic
6#22627691—21no—
7C4⋊#14556880—21no—
8#22627681—21no—
9#22627681—21no—
10#22627679C2212yes—
11#22627679C2212yes—
12#22627617—21no—
13#22627615C2211yescharacteristic
14#22627611C2211yescharacteristic
15#22627606—21no—
16#22627604C411yescharacteristic
17#22627595C411yescharacteristic
18C4×Dic586C411yescharacteristic
19C4×C22⋊D293—21no—
20#22627583—21no—
21C42×D293C2211yescharacteristic
22C4×D4×C293C411yescharacteristic
23C2×#14556880—22no—
24C2×#14556880—22no—
25C2×Dic586C2×C411yescharacteristic
26C2×C22⋊D293—21no—
27C2×C4×D293C2×C411yescharacteristic
28C2×C4×D293D411yescharacteristic
29C2×C4×D293D411yescharacteristic
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×Dic293D411yescharacteristic
41C4×Dic293D411yescharacteristic
42C4×Dic293C2311yescharacteristic
43C2×D4×C293C2×C411yescharacteristic
44C22×C4×C293—21no—
45C4⋊C4×C293C2×C411yescharacteristic
46C22⋊C4×C293—21no—
47C42×C293C2×C411yescharacteristic
48#14556880—42no—
49#14556880—42no—
50C22×D293C22⋊C411yescharacteristic
51Dic586—41no—
52C22⋊D293—42no—
53C2×Dic293—21no—
54C2×Dic293—21no—
55C2×Dic293C22⋊C411yescharacteristic
56C2×Dic293C2×D411yescharacteristic
57C2×Dic293C2×D411yescharacteristic
58C4×D293—41no—
59C4×D293—41no—
60C4×D293—41no—
61C23×C293—21no—
62D4×C293—41no—
63C2×C4×C293—21no—
64C2×C4×C293—42no—
65C2×C4×C293C22⋊C411yescharacteristic
66C2×C4×C293C22⋊C411yescharacteristic
67C2×C4×C293C22×C411yescharacteristic
68C22×C293—41no—
69C22×C293—41no—
70C22×C293—41no—
71C22×C293C2×C22⋊C411yescharacteristic
72C2×D293—21no—
73C2×D293—21no—
74C2×D293—21no—
75C4×C293—21no—
76C4×C293—21no—
77C4×C293—21no—
78C4×C293—41no—
79Dic293—21no—
80Dic293—21no—
81Dic293—21no—
82Dic293—41no—
83Dic293—41no—
84C2×C293—81no—
85C2×C293#41311yescharacteristic
86C2×C293#42111yescharacteristic
87C2×C293#42111yescharacteristic
88D293—41no—
89C293#153511yescharacteristic, complemented, Sylow
90#1535—2931nomaximal, Sylow
91#529—2931no—
92#432—2931no—
93#432—2931no—
94#330—2932no—
95#329—2932no—
96#126—5861no—
97#125—2931no—
98#124—2931no—
99#123—5861no—
100C22⋊Q8—2931no—
101#121—2931no—
102C4×Q8—2931no—
103C4×D4—5861no—
104C4×D4#1192407811yescharacteristic
105#117—5861no—
106C2×C42—2931no—
107C4⋊C8—5861no—
108C4⋊C8—5861no—
109C22⋊C8—5861no—
110C22⋊C8—5861no—
111#97—2932no—
112#97—2932no—
113C2×Q8—2931no—
114C2×D4—5861no—
115C2×D4C2×#1192407811yescharacteristic
116C22×C4—21no—
117C22×C4—2931no—
118C22×C4—2931no—
119C22×C4—2931no—
120C2×C8—5862no—
121C2×C8—5862no—
122C4⋊C4—2931no—
123C4⋊C4—5861no—
124C4⋊C4—5861no—
125C4⋊C4—5861no—
126C4⋊C4—5861no—
127C4⋊C4C2×#1192407811yescharacteristic
128C22⋊C4—21no—
129C22⋊C4—5861no—
130C22⋊C4—5861no—
131C22⋊C4—5861no—
132C22⋊C4—5861no—
133C42—2931no—
134C42—2931no—
135C42—2931no—
136C42—5861no—
137C42C2×#1192407811yescharacteristic
138C23—21no—
139C23—2931no—
140Q8—11721no—
141D4—41no—
142D4—11722no—
143C2×C4—21no—
144C2×C4—42no—
145C2×C4—2931no—
146C2×C4—2931no—
147C2×C4—2931no—
148C2×C4—5861no—
149C2×C4—5861no—
150C2×C4—11721no—
151C2×C4—11721no—
152C2×C4—11721no—
153C2×C4C22⋊#1192407811yescharacteristic
154C2×C4C22⋊#1192407811yescharacteristic
155C2×C4C22×#1192407811yescharacteristic
156C8—11722no—
157C8—11722no—
158C22—41no—
159C22—41no—
160C22—41no—
161C22—5861no—
162C22—5861no—
163C22—5861no—
164C22C2×C22⋊#1192407811yescharacteristic
165C4—21no—
166C4—21no—
167C4—21no—
168C4—41no—
169C4—5861no—
170C4—5861no—
171C4—5861no—
172C4—11721no—
173C4—11721no—
174C2—81no—
175C2—11721no—
176C2#3403711511yescharacteristic
177C2#3403712611yescharacteristic
178C2#3403712711yescharacteristic
subgroupG/H
centerC22C2×C22⋊#11924078
commutatorC2×C4×C293C22×C4
FrattiniC2×C4C22×#11924078
FittingC4×D4×C293C4
socleC22×C293C2×C22⋊C4
prime radical#22627595C4
cosocleC4×Dic293C23
hypercenterC4×D4#11924078
hypocenterC293#1535
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. #34037152C2semidirect
2. #34037151C2semidirect
3. #34036986C2semidirect
4. #34036984C2semidirect
89. C293#1535semidirect

Maximal subgroups

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

subgroupindex
#340371522
#340371512
#340369862
#340369842
#340366612
#1535293