Finite Group Databasebeta

← #46811594

Subgroups — #46811594

Order 34432.

222 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 222 conjugacy classes of subgroups — too many to draw. Only its 73 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#31770633C211yesmaximal, characteristic, complemented
2C2×#22575379C211yesmaximal, characteristic
3#31770602C211yesmaximal, characteristic
4#31770573C211yesmaximal, characteristic
5C2×#22575363C211yesmaximal, characteristic, complemented
6#31770366C211yesmaximal, characteristic, complemented
7#341×C269C211yesmaximal, characteristic, complemented
8C2×#16864402C2211yescharacteristic
9C22×#14524130C2211yescharacteristic
10#22575412C2211yescharacteristic
11C2×C4×Dic269C2211yescharacteristic
12#22575382—22no—
13#22575379—22no—
14#22575378C412yescomplemented
15#22575375C412yescomplemented
16#22575365—22no—
17#22575363—22no—
18C2×M16×C269C2211yescharacteristic
19C2×M16×C269C2211yescharacteristic
20C22×C8×C269C2211yescharacteristic
21#16864402—21no—
22#16864402—21no—
23#16864402—21no—
24#16864402—21no—
25C2×Dic538C2×C411yescharacteristic
26C2×D1076C2×C411yescharacteristic
27C2×C22⋊D269—21no—
28C22×Dic269—21no—
29C2×C4×D269—21no—
30C2×#14524130—21no—
31C2×#14524130—21no—
32C2×#14524130D412yes—
33C4⋊Dic269C2×C412yes—
34C22⋊Dic269—21no—
35C4×Dic269—21no—
36C4×Dic269—21no—
37C4×Dic269D412yes—
38C22×C4×C269C2311yescharacteristic
39M16×C269—21no—
40M16×C269—21no—
41M16×C269—21no—
42M16×C269—21no—
43C2×C8×C269—21no—
44C2×C8×C269—21no—
45C2×C8×C269—21no—
46C2×C8×C269—21no—
47C2×C8×C269C2×C412yes—
48C22×D269—21no—
49Dic538—21no—
50Dic538—21no—
51D1076—21no—
52D1076—21no—
53C22⋊D269—41no—
54C22⋊D269—41no—
55C2×Dic269—22no—
56C2×Dic269—21no—
57C2×Dic269—22no—
58C2×Dic269—42no—
59C4×D269—41no—
60C4×D269—41no—
61#14524130—22no—
62C23×C269#4111yescharacteristic
63C2×C4×C269C22×C411yescharacteristic
64C2×C4×C269C2×D411yescharacteristic
65C2×C4×C269C2×D411yescharacteristic
66C2×C4×C269#4111yescharacteristic
67C2×C4×C269#4111yescharacteristic
68C2×C4×C269#4111yescharacteristic
69C8×C269—22no—
70C8×C269—41no—
71C8×C269—41no—
72C22×C269—22no—
73C22×C269C4×D411yescharacteristic
74C22×C269#12311yescharacteristic
75C22×C269#12611yescharacteristic
76C2×D269—41no—
77C2×D269—42no—
78C4×C269#11711yescharacteristic
79C4×C269C4×D411yescharacteristic
80C4×C269#12111yescharacteristic
81C4×C269#12411yescharacteristic
82Dic269—42no—
83Dic269—41no—
84Dic269—42no—
85C2×C269—21no—
86C2×C269—21no—
87C2×C269#38811yescharacteristic
88C2×C269#44412yes—
89D269—81no—
90C269#193811yescharacteristic, complemented, Sylow
91#1938—2691nomaximal, Sylow
92#424—2691no—
93C2×#104—2691no—
94#416—2691no—
95#408—2691no—
96C2×#97—2691no—
97#341D26911yescharacteristic, complemented
98#339—2691no—
99C2×#41—2691no—
100C2×M16C2×D26911yescharacteristic
101C2×M16C2×D26911yescharacteristic
102C22×C8—2691no—
103C22×C8C2×D26911yescharacteristic
104#117—2691no—
105C2×C42—2691no—
106C4⋊C8—5382no—
107#104—5382no—
108#103—2692no—
109#102—2692no—
110C22⋊C8—5382no—
111#97—5382no—
112#41—5381no—
113#41—5381no—
114#41—5381no—
115#41—5381no—
116C2×Q8—2691no—
117C2×D4—2691no—
118C2×D4—5381no—
119C22×C4—5381no—
120C22×C4—5381no—
121C22×C4C22×D26911yescharacteristic
122M16—21no—
123M16—21no—
124M16—21no—
125M16—21no—
126C2×C8—21no—
127C2×C8—21no—
128C2×C8—21no—
129C2×C8—21no—
130C2×C8—2692no—
131C2×C8—5381no—
132C2×C8—5381no—
133C2×C8C4×D26912yes—
134C4⋊C4—2692no—
135C22⋊C4—5381no—
136C42—2692no—
137C42—5381no—
138C42—5381no—
139C23—5381no—
140C23#1686440311yescharacteristic
141Q8—5381no—
142Q8—5381no—
143D4—5381no—
144D4—5381no—
145D4—10761no—
146D4—10761no—
147C2×C4—5382no—
148C2×C4—5381no—
149C2×C4—5382no—
150C2×C4—10762no—
151C2×C4—10761no—
152C2×C4—10761no—
153C2×C4C2×C4×D26911yescharacteristic
154C2×C4D4×D26911yescharacteristic
155C2×C4D4×D26911yescharacteristic
156C2×C4#1686440111yescharacteristic
157C2×C4#1686440211yescharacteristic
158C2×C4#1686440211yescharacteristic
159C8—22no—
160C8—41no—
161C8—41no—
162C8—5382no—
163C22—22no—
164C22—10762no—
165C22—10761no—
166C22#2257541511yescharacteristic
167C22#2257543811yescharacteristic
168C22#2257544811yescharacteristic
169C4—10762no—
170C4—10762no—
171C4—10761no—
172C4#2257541011yescharacteristic
173C4#2257541311yescharacteristic
174C4#2257542611yescharacteristic
175C4#2257543911yescharacteristic
176C2—21no—
177C2—21no—
178C2—21521no—
179C2#3177049411yescharacteristic
180C2#3177072612yes—
subgroupG/H
centerC2×C4D4×D269
commutatorC2×C4×C269C22×C4
FrattiniC22×C4C22×D269
Fitting#341×C269C2
socleC22×C269C4×D4
prime radicalC2×#16864402C22
cosocleC22×C4×C269C23
hypercenter#341D269
hypocenterC269#1938
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #341

Complements

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

NH ≅ G/Ntype
1. #31770633C2semidirect
5. C2×#22575363C2semidirect
6. #31770366C2semidirect
7. #341×C269C2semidirect
14. #22575378C4semidirect
15. #22575375C4semidirect
90. C269#1938semidirect
97. #341D269semidirect

Maximal subgroups

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

subgroupindex
#317706332
C2×#225753792
#317706022
#317705732
C2×#225753632
#317703662
#341×C2692
#1938269