Finite Group Databasebeta

← #46825970

Subgroups — #46825970

Order 34432.

234 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 44 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
1C2×#22575513C211yesmaximal, characteristic
2C2×#22575511C211yesmaximal, characteristic
3#31770482C211yesmaximal, characteristic
4C2×#16864411—21no—
5C2×C22⋊#11761640—21no—
6#22575513—21no—
7#22575513C412yescomplemented
8#22575511—21no—
9#22575511C412yescomplemented
10C22×C22⋊D269C2211yescharacteristic
11C23×Dic269C411yescharacteristic, complemented
12C2×#16864379—21no—
13#22575360—21no—
14C2×C22⋊C4×C269C411yescharacteristic, complemented
15C22×#11761640—41no—
16#16864411—22no—
17#16864411—41no—
18C2×#14524137—41no—
19C22⋊#11761640—22no—
20C22⋊#11761640—41no—
21C23×D269D411yescharacteristic
22C2×C22⋊D269—41no—
23C2×C22⋊D269—41no—
24C2×C22⋊D269C2×C411yescharacteristic
25C2×C22⋊D269C2×C411yescharacteristic
26C2×C22⋊D269D411yescharacteristic
27C2×C22⋊D269Q811yescharacteristic
28C22×Dic269—21no—
29C22×Dic269—41no—
30C22×Dic269—42no—
31C22×Dic269D411yescharacteristic
32#16864379—42no—
33C24×C269C2×C411yescharacteristic
34C22×C4×C269—21no—
35C22⋊C4×C269—41no—
36C2×#11761640—42no—
37C2×#11761640—81no—
38C2×#11761640—81no—
39#14524137—42no—
40C22×D269—21no—
41C22×D269—21no—
42C22×D269—41no—
43C22×D269—41no—
44C22×D269C22⋊C411yescharacteristic
45C22×D269C4⋊C411yescharacteristic
46C22⋊D269—41no—
47C22⋊D269—41no—
48C22⋊D269—41no—
49C22⋊D269—41no—
50C2×Dic269—21no—
51C2×Dic269—21no—
52C2×Dic269—22no—
53C2×Dic269—41no—
54C2×Dic269—42no—
55C2×Dic269—41no—
56C2×Dic269—42no—
57C2×Dic269C22⋊C411yescharacteristic
58C2×Dic269C4⋊C411yescharacteristic
59C23×C269—21no—
60C23×C269—21no—
61C23×C269—41no—
62C23×C269—41no—
63C23×C269C4211yescharacteristic
64C23×C269C22⋊C411yescharacteristic
65C23×C269C4⋊C411yescharacteristic
66C2×C4×C269—41no—
67C2×C4×C269—41no—
68C2×C4×C269—41no—
69C22×C269—21no—
70C22×C269—21no—
71C22×C269—21no—
72C22×C269—21no—
73C22×C269—41no—
74C22×C269—41no—
75C22×C269—42no—
76C22×C269—41no—
77C22×C269—41no—
78C22×C269#9511yescharacteristic
79C22×C269#9911yescharacteristic
80C22×C269#9911yescharacteristic
81C2×D269—21no—
82C2×D269—21no—
83C2×D269—41no—
84C2×D269—41no—
85C2×D269—41no—
86C2×D269—41no—
87C2×D269—81no—
88#11761640—82no—
89C4×C269—81no—
90Dic269—21no—
91Dic269—21no—
92Dic269—42no—
93C2×C269—21no—
94C2×C269—21no—
95C2×C269—41no—
96C2×C269—41no—
97C2×C269#34211yescharacteristic
98C2×C269AΣL(1,𝔽16)11yescharacteristic
99C2×C269#35211yescharacteristic
100D269—41no—
101D269—41no—
102C269#139011yescharacteristic, complemented, Sylow
103#1390—2691nomaximal, Sylow
104C2×#100—2691no—
105C2×#99—2691no—
106#386—2691no—
107C22×D4—2691no—
108C23×C4—2691no—
109C2×M16—5381no—
110C2×C22⋊C4—5381no—
111C2×C22⋊C4—5381no—
112C2×C22⋊C4#1176164011yescharacteristic, complemented
113#100—2692no—
114#100—5381no—
115#99—2692no—
116#99—5381no—
117#95—5381no—
118C24—2691no—
119C24C2×#1176164011yescharacteristic
120C2×D4—2691no—
121C2×D4—2691no—
122C2×D4—2691no—
123C2×D4—2691no—
124C2×D4—10761no—
125C2×D4—10761no—
126C22×C4—21no—
127C22×C4—2691no—
128C22×C4—5381no—
129C22×C4—10762no—
130C22×C4—10761no—
131C22×C4—10761no—
132M16—5382no—
133M16—10761no—
134C2×C8—10761no—
135C22⋊C4—41no—
136C22⋊C4—5382no—
137C22⋊C4—10762no—
138C22⋊C4—10761no—
139C23—21no—
140C23—21no—
141C23—41no—
142C23—41no—
143C23—2691no—
144C23—2691no—
145C23—5381no—
146C23—5381no—
147C23—10761no—
148C23—10761no—
149C23C4×#1176164011yescharacteristic
150C23C22⋊#1176164011yescharacteristic
151C23C4⋊#1176164011yescharacteristic
152D4—10761no—
153D4—10761no—
154D4—10761no—
155D4—10761no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—2691no—
160C2×C4—2691no—
161C2×C4—5381no—
162C2×C4—5381no—
163C2×C4—5382no—
164C2×C4—10761no—
165C2×C4—10762no—
166C2×C4—10761no—
167C2×C4—10762no—
168C2×C4—10762no—
169C2×C4—21521no—
170C2×C4—21521no—
171C8—10762no—
172C22—21no—
173C22—21no—
174C22—21no—
175C22—21no—
176C22—41no—
177C22—41no—
178C22—42no—
179C22—41no—
180C22—41no—
181C22—5381no—
182C22—5381no—
183C22—10761no—
184C22—10761no—
185C22—10761no—
186C22—10761no—
187C22—21521no—
188C22(C2×#11761640)⋊C411yescharacteristic
189C22#2257551111yescharacteristic
190C22#2257551211yescharacteristic
191C4—81no—
192C4—5381no—
193C4—5381no—
194C4—10762no—
195C4—21522no—
196C2—21no—
197C2—21no—
198C2—41no—
199C2—41no—
200C2—10761no—
201C2—10761no—
202C2#3177148311yescharacteristic
203C2#3177150611yescharacteristic
204C2#3177150811yescharacteristic
subgroupG/H
centerC22#22575512
commutatorC23×C269C42
FrattiniC24C2×#11761640
FittingC2×C22⋊C4×C269C4
socleC22×C269#99
prime radical, cosocleC22×C22⋊D269C22
hypercenterC2×C22⋊C4#11761640
hypocenterC269#1390
LCSG ▷ C23×C269 ▷ C22×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C23 ◁ C24 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
7. #22575513C4semidirect
9. #22575511C4semidirect
11. C23×Dic269C4semidirect
14. C2×C22⋊C4×C269C4semidirect
102. C269#1390semidirect
112. C2×C22⋊C4#11761640semidirect

Maximal subgroups

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

subgroupindex
C2×#225755132
C2×#225755112
#317704822
#1390269