Finite Group Databasebeta

← #49157939

Subgroups — #49157939

Order 37504.

234 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 55 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#34036784C211yesmaximal, characteristic
2#34036480C211yesmaximal, characteristic, complemented
3#34036420C211yesmaximal, characteristic, complemented
4#34036419C211yesmaximal, characteristic, complemented
5#34035876C211yesmaximal, characteristic, complemented
6#34035858C211yesmaximal, characteristic, complemented
7D4⋊C8×C293C211yesmaximal, characteristic, complemented
8C2×#17989802—21no—
9#22627624C2211yescharacteristic
10#22627624C2211yescharacteristic
11#22627606—22no—
12#22627603—21no—
13#22627595—21no—
14C4×D1172C2211yescharacteristic
15C4⋊C4×D293—21no—
16#22627556—21no—
17#22627555—21no—
18C4⋊#14556873C2211yescharacteristic
19#22627549—22no—
20#22627546—21no—
21#22627545—21no—
22C4×D4×C293C2211yescharacteristic
23C4⋊C8×C293C2211yescharacteristic
24C4×C8×C293C2211yescharacteristic
25#17989802—42no—
26#17989802—42no—
27C2×Dic586—21no—
28C2×Dic586—21no—
29C2×D1172D411yescharacteristic
30C2×C22⋊D293—22no—
31C2×C4×D293—22no—
32C2×C4×D293—21no—
33C2×#14556873—21no—
34C4⋊Dic293—21no—
35C4⋊Dic293—21no—
36C4⋊Dic293—21no—
37C4⋊Dic293D411yescharacteristic
38C4⋊Dic293D412yes—
39#17989781—22no—
40C22⋊Dic293—22no—
41#17989779—21no—
42C2×D4×C293D411yescharacteristic
43C22×C4×C293—21no—
44C2×C8×C293—21no—
45C2×C8×C293—21no—
46C4⋊C4×C293D411yescharacteristic
47C22⋊C4×C293—21no—
48C42×C293C2311yescharacteristic
49C22×D293—21no—
50Dic586—41no—
51Dic586—41no—
52Dic586—42no—
53D1172—21no—
54D1172SD1612yes—
55C22⋊D293—44no—
56C2×Dic293—21no—
57C2×Dic293—22no—
58C2×Dic293—41no—
59C4×D293—44no—
60C4×D293—41no—
61C4×D293—41no—
62#14556873—41no—
63C23×C293—21no—
64D4×C293—21no—
65D4×C293—21no—
66C2×C4×C293—21no—
67C2×C4×C293—41no—
68C2×C4×C293—41no—
69C2×C4×C293C2×D411yescharacteristic
70C2×C4×C293C2×D411yescharacteristic
71C2×C4×C293C2×D411yescharacteristic
72C8×C293—41no—
73C8×C293—41no—
74C22×C293—41no—
75C22×C293—41no—
76C22×C293—41no—
77C22×C293#12011yescharacteristic
78C2×D293—22no—
79C2×D293—41no—
80C2×D293—41no—
81C4×C293—21no—
82C4×C293—41no—
83C4×C293C2×SD1611yescharacteristic
84C4×C293#13511yescharacteristic
85C4×C293AGL(1,ℤ/8)11yescharacteristic
86C4×C293#13711yescharacteristic
87Dic293—42no—
88Dic293—41no—
89Dic293—81no—
90C2×C293—81no—
91C2×C293#45011yescharacteristic
92C2×C293#45211yescharacteristic
93C2×C293#45411yescharacteristic
94D293—42no—
95C293#163511yescharacteristic, complemented, Sylow
96#1635—2931nomaximal, Sylow
97#547—2931no—
98#487—2931no—
99#476—2931no—
100#476—2931no—
101#332—2931no—
102D4⋊C8—2931no—
103D4⋊C8D29311yescharacteristic, complemented
104C2×#41—5861no—
105C4⋊Q8—2931no—
106C4⋊Q8—2931no—
107#123—5862no—
108C22⋊Q8—5861no—
109#121—5861no—
110C4×D4—2931no—
111C4×D4C2×D29311yescharacteristic
112C2×C4⋊C4—5861no—
113#106—5861no—
114#106—5861no—
115C4⋊C8—2931no—
116C4⋊C8C2×D29311yescharacteristic
117#103—5862no—
118#102—5861no—
119#102—5861no—
120C4×C8C2×D29311yescharacteristic
121#41—11722no—
122#41—11722no—
123C2×Q8—5861no—
124C2×Q8—5861no—
125C2×D4—2931no—
126C2×D4—5862no—
127C2×D4D117211yescharacteristic
128C22×C4—21no—
129C22×C4—5862no—
130C22×C4—5861no—
131C2×C8—21no—
132C2×C8—21no—
133C2×C8—5861no—
134C4⋊C4—2932no—
135C4⋊C4—2931no—
136C4⋊C4—5862no—
137C4⋊C4—5861no—
138C4⋊C4—5861no—
139C4⋊C4—5861no—
140C4⋊C4D117211yescharacteristic
141C22⋊C4—21no—
142C22⋊C4—5862no—
143C22⋊C4—5861no—
144C42C22×D29311yescharacteristic
145C23—21no—
146C23—5861no—
147Q8—11722no—
148Q8—11721no—
149Q8—11721no—
150D4—21no—
151D4—21no—
152D4—2932no—
153D4—5861no—
154D4—11724no—
155C2×C4—21no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—5861no—
159C2×C4—5862no—
160C2×C4—11724no—
161C2×C4—11721no—
162C2×C4—11721no—
163C2×C4—11721no—
164C2×C4D4×D29311yescharacteristic
165C2×C4D4×D29311yescharacteristic
166C2×C4C2×D117211yescharacteristic
167C8—41no—
168C8—41no—
169C8—11721no—
170C22—41no—
171C22—41no—
172C22—41no—
173C22—5862no—
174C22—11721no—
175C22—11721no—
176C22#2262759411yescharacteristic
177C4—21no—
178C4—41no—
179C4—23441no—
180C4—11722no—
181C4—11721no—
182C4SD16×D29311yescharacteristic
183C4#2262764611yescharacteristic
184C4#2262764811yescharacteristic
185C4#2262765711yescharacteristic
186C2—81no—
187C2—11722no—
188C2#3403628111yescharacteristic
189C2#3403629311yescharacteristic
190C2#3403630311yescharacteristic
subgroupG/H
centerC22#22627594
commutator, cosocleC42×C293C23
FrattiniC42C22×D293
FittingD4⋊C8×C293C2
socleC22×C293#120
prime radical#34036784C2
hypercenterD4⋊C8D293
hypocenterC293#1635
LCSG ▷ C42×C293 ▷ C22×C293 ▷ C293
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #34036480C2semidirect
3. #34036420C2semidirect
4. #34036419C2semidirect
5. #34035876C2semidirect
6. #34035858C2semidirect
7. D4⋊C8×C293C2semidirect
95. C293#1635semidirect
103. D4⋊C8D293semidirect

Maximal subgroups

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

subgroupindex
#340367842
#340364802
#340364202
#340364192
#340358762
#340358582
D4⋊C8×C2932
#1635293