Finite Group Databasebeta

← #49157477

Subgroups — #49157477

Order 37504.

252 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 67 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#34036677C211yesmaximal, characteristic
2#34036185C211yesmaximal, characteristic, complemented
3C4⋊C8×D293C211yesmaximal, characteristic, complemented
4#34035877C211yesmaximal, characteristic, complemented
5#34035877C211yesmaximal, characteristic, complemented
6#34035873C211yesmaximal, characteristic, complemented
7#331×C293C211yesmaximal, characteristic, complemented
8C2×#17989801C412yes—
9C2×C8×D293—21no—
10#22627624C2211yescharacteristic
11#22627611C412yes—
12#22627595—21no—
13#22627595—21no—
14D4×Dic293—21no—
15D4×Dic293—21no—
16C42×D293C2211yescharacteristic
17C4⋊#14556873C2211yescharacteristic
18C4⋊#14556873C2211yescharacteristic
19#22627553—21no—
20#22627536—21no—
21#22627534—21no—
22#127×C293C2211yescharacteristic
23C4⋊C8×C293C2211yescharacteristic
24C4⋊C8×C293C2211yescharacteristic
25#17989801—44no—
26C2×Dic586C2×C412yes—
27C2×C22⋊D293—22no—
28C22×Dic293—22no—
29C2×C4×D293C2×C411yescharacteristic
30C2×C4×D293D411yescharacteristic
31C2×C4×D293D411yescharacteristic
32C2×#14556873—21no—
33C2×#14556873—21no—
34C8×D293—42no—
35C4⋊Dic293—21no—
36C4⋊Dic293—21no—
37C22⋊Dic293—22no—
38C22⋊Dic293—22no—
39C4×Dic293C2×C411yescharacteristic
40C4×Dic293D411yescharacteristic
41C4×Dic293D411yescharacteristic
42C2×D4×C293—21no—
43C2×D4×C293—21no—
44C2×D4×C293C2×C412yes—
45C2×C8×C293—21no—
46C2×C8×C293—21no—
47C42×C293C2311yescharacteristic
48C22×D293C22⋊C411yescharacteristic
49Dic586—42no—
50C22⋊D293—44no—
51C2×Dic293—22no—
52C2×Dic293—44no—
53C2×Dic293C22⋊C411yescharacteristic
54C2×Dic293C22⋊C411yescharacteristic
55C2×Dic293C22⋊C411yescharacteristic
56C4×D293—22no—
57C4×D293—21no—
58C4×D293—21no—
59C4×D293—21no—
60C4×D293—21no—
61#14556873—41no—
62#14556873—41no—
63C23×C293—22no—
64D4×C293—42no—
65D4×C293—41no—
66D4×C293—41no—
67D4×C293—41no—
68D4×C293—41no—
69C2×C4×C293C22×C411yescharacteristic
70C2×C4×C293C2×D411yescharacteristic
71C2×C4×C293C2×D411yescharacteristic
72C8×C293—41no—
73C8×C293—41no—
74C22×C293—42no—
75C22×C293—42no—
76C22×C293—42no—
77C22×C293C2×C22⋊C411yescharacteristic
78C2×D293—21no—
79C2×D293—21no—
80C2×D293#10012yes—
81C4×C293—21no—
82C4×C293#13511yescharacteristic
83C4×C293#13511yescharacteristic
84C4×C293AGL(1,ℤ/8)11yescharacteristic
85C4×C293#13711yescharacteristic
86Dic293—21no—
87Dic293—21no—
88Dic293—21no—
89Dic293—42no—
90C2×C293—82no—
91C2×C293C2×#10011yescharacteristic
92C2×C293#41611yescharacteristic
93C2×C293#41711yescharacteristic
94D293—22no—
95C293#155111yescharacteristic, complemented, Sylow
96#1551—2931nomaximal, Sylow
97#532—2931no—
98#432—2931no—
99C2×C4⋊C8—2931no—
100#333—2931no—
101#333—2931no—
102#331—2931no—
103#331D29311yescharacteristic, complemented
104C2×#41—2932no—
105C22×C8—5861no—
106C4⋊Q8—2931no—
107#127C2×D29311yescharacteristic
108#124—2932no—
109#121—5861no—
110#121—5861no—
111C4×D4—5861no—
112C4×D4—5861no—
113C2×C42—2931no—
114C4⋊C8—2931no—
115C4⋊C8—2931no—
116C4⋊C8—5861no—
117C4⋊C8C2×D29311yescharacteristic
118C4⋊C8C2×D29311yescharacteristic
119C22⋊C8—5861no—
120#97—5861no—
121#41—11724no—
122C2×Q8—2932no—
123C2×D4—21no—
124C2×D4—21no—
125C2×D4—5862no—
126C2×D4C4×D29312yes—
127C22×C4—2931no—
128C22×C4—2931no—
129C22×C4—2931no—
130C22×C4—5862no—
131C2×C8—21no—
132C2×C8—21no—
133C2×C8—5861no—
134C2×C8—5861no—
135C2×C8—11722no—
136C4⋊C4—5861no—
137C4⋊C4—5861no—
138C22⋊C4—5862no—
139C22⋊C4—5862no—
140C42—2931no—
141C42—2931no—
142C42—2931no—
143C42C22×D29311yescharacteristic
144C23—22no—
145C23—2931no—
146Q8—11722no—
147D4—42no—
148D4—41no—
149D4—41no—
150D4—41no—
151D4—41no—
152D4—11724no—
153C2×C4—2931no—
154C2×C4—2931no—
155C2×C4—2931no—
156C2×C4—5862no—
157C2×C4—5861no—
158C2×C4—5861no—
159C2×C4—5861no—
160C2×C4—5861no—
161C2×C4—5862no—
162C2×C4—11724no—
163C2×C4C2×C4×D29311yescharacteristic
164C2×C4D4×D29311yescharacteristic
165C2×C4D4×D29311yescharacteristic
166C8—41no—
167C8—41no—
168C8—11721no—
169C8—11721no—
170C22—42no—
171C22—42no—
172C22—42no—
173C22—2932no—
174C22—5861no—
175C22—5861no—
176C22C22⋊C4×D29311yescharacteristic
177C4—21no—
178C4—5861no—
179C4—5861no—
180C4—5861no—
181C4—11722no—
182C4#2262764311yescharacteristic
183C4#2262764511yescharacteristic
184C4#2262764811yescharacteristic
185C4#2262765311yescharacteristic
186C2—82no—
187C2—5862no—
188C2#100×D29311yescharacteristic
189C2#3403612211yescharacteristic
190C2#3403612711yescharacteristic
subgroupG/H
centerC22C22⋊C4×D293
commutatorC2×C4×C293C22×C4
FrattiniC42C22×D293
Fitting#331×C293C2
socleC22×C293C2×C22⋊C4
prime radical#34036677C2
cosocleC42×C293C23
hypercenter#331D293
hypocenterC293#1551
LCSG ▷ C2×C4×C293 ▷ C22×C293 ▷ C293
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
2. #34036185C2semidirect
3. C4⋊C8×D293C2semidirect
4. #34035877C2semidirect
5. #34035877C2semidirect
6. #34035873C2semidirect
7. #331×C293C2semidirect
95. C293#1551semidirect
103. #331D293semidirect

Maximal subgroups

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

subgroupindex
#340366772
#340361852
C4⋊C8×D2932
#340358772
#340358732
#331×C2932
#1551293