Finite Group Databasebeta

← #49157504

Subgroups — #49157504

Order 37504.

246 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 65 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
3#34036151C211yesmaximal, characteristic, complemented
4#34035876C211yesmaximal, characteristic, complemented
5#34035874C211yesmaximal, characteristic, complemented
6#34035873C211yesmaximal, characteristic, complemented
7#331×C293C211yesmaximal, characteristic, complemented
8C2×#17989801—21no—
9C2×#17989785—21no—
10#22627624C2211yescharacteristic
11#22627611—21no—
12#22627595—21no—
13#22627595C412yes—
14D4×Dic293—21no—
15D4×Dic293C412yes—
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—42no—
26#17989801—42no—
27C2×Dic586—21no—
28C2×C22⋊D293—22no—
29C22×Dic293—22no—
30C2×C4×D293C2×C411yescharacteristic
31C2×C4×D293D411yescharacteristic
32C2×C4×D293D411yescharacteristic
33#17989785—42no—
34C2×#14556873—21no—
35C2×#14556873—21no—
36C4⋊Dic293—21no—
37C4⋊Dic293C2×C412yes—
38C22⋊Dic293—22no—
39C22⋊Dic293—22no—
40C4×Dic293C2×C411yescharacteristic
41C4×Dic293D411yescharacteristic
42C4×Dic293D411yescharacteristic
43C2×D4×C293—21no—
44C2×D4×C293—21no—
45C2×D4×C293C2×C412yes—
46C2×C8×C293—21no—
47C2×C8×C293—21no—
48C42×C293C2311yescharacteristic
49C22×D293C22⋊C411yescharacteristic
50Dic586—41no—
51Dic586—41no—
52C22⋊D293—44no—
53C2×Dic293—22no—
54C2×Dic293—44no—
55C2×Dic293C22⋊C411yescharacteristic
56C2×Dic293C22⋊C411yescharacteristic
57C2×Dic293C22⋊C411yescharacteristic
58C4×D293—21no—
59C4×D293—21no—
60C4×D293—21no—
61C4×D293—21no—
62C4×D293—41no—
63#14556873—41no—
64#14556873—41no—
65C23×C293—22no—
66D4×C293—42no—
67D4×C293—41no—
68D4×C293—41no—
69D4×C293—41no—
70D4×C293—41no—
71C2×C4×C293C22×C411yescharacteristic
72C2×C4×C293C2×D411yescharacteristic
73C2×C4×C293C2×D411yescharacteristic
74C8×C293—41no—
75C8×C293—41no—
76C22×C293—42no—
77C22×C293—42no—
78C22×C293—42no—
79C22×C293C2×C22⋊C411yescharacteristic
80C2×D293—21no—
81C2×D293—21no—
82C2×D293—21no—
83C4×C293—21no—
84C4×C293AGL(1,ℤ/8)11yescharacteristic
85C4×C293AGL(1,ℤ/8)11yescharacteristic
86C4×C293AGL(1,ℤ/8)11yescharacteristic
87C4×C293#13711yescharacteristic
88Dic293—21no—
89Dic293—21no—
90Dic293—21no—
91Dic293—42no—
92C2×C293—82no—
93C2×C293#41311yescharacteristic
94C2×C293#41711yescharacteristic
95C2×C293#41811yescharacteristic
96D293—41no—
97C293#155711yescharacteristic, complemented, Sylow
98#1557—2931nomaximal, Sylow
99#532—2931no—
100#432—2931no—
101#423—2931no—
102#332—2931no—
103#332—2931no—
104#331—2931no—
105#331D29311yescharacteristic, complemented
106C2×#41—5861no—
107C2×M16—5861no—
108C4⋊Q8—2931no—
109#127C2×D29311yescharacteristic
110#124—5861no—
111#121—2932no—
112#121—5861no—
113C4×D4—2932no—
114C4×D4—5861no—
115C2×C42—2931no—
116C4⋊C8—2931no—
117C4⋊C8—2931no—
118C4⋊C8—5861no—
119C4⋊C8C2×D29311yescharacteristic
120C4⋊C8C2×D29311yescharacteristic
121C22⋊C8—5861no—
122#97—5861no—
123#41—11722no—
124#41—11722no—
125C2×Q8—5861no—
126C2×D4—21no—
127C2×D4—21no—
128C2×D4—5862no—
129C2×D4C4×D29312yes—
130C22×C4—2931no—
131C22×C4—2931no—
132C22×C4—2931no—
133C22×C4—5862no—
134M16—11722no—
135C2×C8—21no—
136C2×C8—21no—
137C2×C8—5861no—
138C2×C8—5861no—
139C4⋊C4—2932no—
140C4⋊C4—5861no—
141C22⋊C4—5862no—
142C22⋊C4—5862no—
143C42—2931no—
144C42—2931no—
145C42—2931no—
146C42C22×D29311yescharacteristic
147C23—22no—
148C23—2931no—
149Q8—11721no—
150Q8—11721no—
151D4—42no—
152D4—41no—
153D4—41no—
154D4—41no—
155D4—41no—
156D4—11724no—
157C2×C4—2931no—
158C2×C4—2931no—
159C2×C4—2931no—
160C2×C4—5861no—
161C2×C4—5861no—
162C2×C4—5861no—
163C2×C4—5861no—
164C2×C4—5862no—
165C2×C4—11721no—
166C2×C4—11724no—
167C2×C4C2×C4×D29311yescharacteristic
168C2×C4D4×D29311yescharacteristic
169C2×C4D4×D29311yescharacteristic
170C8—41no—
171C8—41no—
172C8—11721no—
173C8—11721no—
174C22—42no—
175C22—42no—
176C22—42no—
177C22—5861no—
178C22—5861no—
179C22—5861no—
180C22C22⋊C4×D29311yescharacteristic
181C4—21no—
182C4—5861no—
183C4—5861no—
184C4—5861no—
185C4—11722no—
186C4#2262764811yescharacteristic
187C4#2262764811yescharacteristic
188C4#2262765111yescharacteristic
189C4#2262765311yescharacteristic
190C2—82no—
191C2—11721no—
192C2#3403611011yescharacteristic
193C2#3403612711yescharacteristic
194C2#3403613211yescharacteristic
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#1557
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. #34036151C2semidirect
4. #34035876C2semidirect
5. #34035874C2semidirect
6. #34035873C2semidirect
7. #331×C293C2semidirect
97. C293#1557semidirect
105. #331D293semidirect

Maximal subgroups

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

subgroupindex
#340366772
#340361852
#340361512
#340358762
#340358742
#340358732
#331×C2932
#1557293