Finite Group Databasebeta

← #46811304

Subgroups — #46811304

Order 34432.

342 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 93 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#31771372C211yesmaximal, characteristic, complemented
2#31770589C211yesmaximal, characteristic, complemented
3#31770569C212yesmaximal, complemented
4#31770375C212yesmaximal, complemented
5#525×C269C211yesmaximal, characteristic
6#22575460—24no—
7C2×#16864386—22no—
8C2×#16864386C2212yes—
9C2×#16864386C2212yes—
10#22575372—21no—
11#22575370—21no—
12C22⋊#14524130—24no—
13C2×#41×C269C2211yescharacteristic
14C23×C4×C269C2211yescharacteristic
15#123×C269C412yes—
16C22⋊Q8×C269—21no—
17#121×C269—21no—
18#120×C269C412yes—
19C4×D4×C269—22no—
20#117×C269C2211yescharacteristic
21#16864386—24no—
22#16864386—22no—
23#16864386—22no—
24#16864386—22no—
25#16864386—22no—
26C2×#14524130—24no—
27C2×#14524130—22no—
28C2×#14524130D414yescomplemented
29C24×C269C2×C411yescharacteristic
30#41×C269—22no—
31#41×C269—22no—
32C2×Q8×C269D411yescharacteristic
33C2×D4×C269—22no—
34C2×D4×C269C2×C412yes—
35C2×D4×C269D411yescharacteristic
36C22×C4×C269—22no—
37C22×C4×C269—21no—
38C22×C4×C269—21no—
39C22×C4×C269—22no—
40C22×C4×C269C2×C411yescharacteristic
41C22×C4×C269D412yes—
42C22×C4×C269C2311yescharacteristic
43C4⋊C4×C269—22no—
44C4⋊C4×C269—21no—
45C22⋊C4×C269—22no—
46C22⋊C4×C269—22no—
47C22⋊C4×C269C2×C412yes—
48C42×C269—21no—
49#14524130—24no—
50#14524130—42no—
51C23×C269—21no—
52C23×C269—22no—
53C23×C269—42no—
54C23×C269C22⋊C412yes—
55C23×C269C22×C411yescharacteristic
56Q8×C269—22no—
57D4×C269—24no—
58D4×C269—22no—
59D4×C269—44no—
60C2×C4×C269—22no—
61C2×C4×C269—22no—
62C2×C4×C269—22no—
63C2×C4×C269—21no—
64C2×C4×C269—22no—
65C2×C4×C269—41no—
66C2×C4×C269—42no—
67C2×C4×C269—41no—
68C2×C4×C269C22⋊C412yes—
69C2×C4×C269C2×D412yes—
70C2×C4×C269C2×D411yescharacteristic
71C2×C4×C269C2×D411yescharacteristic
72C2×C4×C269#4112yes—
73C22×C269—22no—
74C22×C269—24no—
75C22×C269—22no—
76C22×C269—41no—
77C22×C269—42no—
78C22×C269—41no—
79C22×C269—42no—
80C22×C269—41no—
81C22×C269C2×C22⋊C411yescharacteristic
82C22×C269C4×D412yes—
83C4×C269—22no—
84C4×C269—42no—
85C4×C269—41no—
86C4×C269#12011yescharacteristic
87C4×C269#12112yes—
88C4×C269#12311yescharacteristic
89C2×C269—21no—
90C2×C269—22no—
91C2×C269—42no—
92C2×C269—42no—
93C2×C269#38611yescharacteristic
94C269#189111yescharacteristic, complemented, Sylow
95#1891—2691nomaximal, Sylow
96#568—2691no—
97#525D26911yescharacteristic
98#413—2691no—
99#407—2692no—
100#344—2692no—
101C2×#41C2×D26911yescharacteristic
102C23×C4C2×D26911yescharacteristic
103#131—5384no—
104C2×M16—2692no—
105C2×M16—2692no—
106C2×M16—5382no—
107#123Dic26912yes—
108C22⋊Q8—21no—
109#121—21no—
110#120Dic26912yes—
111C4×D4—22no—
112#117C2×D26911yescharacteristic
113#101—5381no—
114#100—5381no—
115C22⋊C8—5384no—
116C24C2×Dic26911yescharacteristic
117#41—22no—
118#41—22no—
119C2×Q8C22⋊D26911yescharacteristic
120C2×D4—22no—
121C2×D4C2×Dic26912yes—
122C2×D4C22⋊D26911yescharacteristic
123C22×C4—22no—
124C22×C4—21no—
125C22×C4—21no—
126C22×C4—22no—
127C22×C4C2×Dic26911yescharacteristic
128C22×C4C22⋊D26912yes—
129C22×C4C22×D26911yescharacteristic
130M16—5384no—
131M16—5382no—
132M16—5382no—
133M16—5382no—
134M16—5382no—
135C2×C8—2694no—
136C2×C8—5384no—
137C2×C8—5382no—
138C4⋊C4—22no—
139C4⋊C4—21no—
140C22⋊C4—22no—
141C22⋊C4—22no—
142C22⋊C4C2×Dic26912yes—
143C42—21no—
144C23—21no—
145C23—22no—
146C23—42no—
147C23C22⋊Dic26912yes—
148C23C22×Dic26911yescharacteristic
149Q8—22no—
150D4—24no—
151D4—22no—
152D4—44no—
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—22no—
156C2×C4—21no—
157C2×C4—22no—
158C2×C4—41no—
159C2×C4—42no—
160C2×C4—41no—
161C2×C4C22⋊Dic26912yes—
162C2×C4D4×D26912yes—
163C2×C4C2×C22⋊D26911yescharacteristic
164C2×C4C2×C22⋊D26911yescharacteristic
165C2×C4#1686440112yes—
166C8—5384no—
167C8—10762no—
168C22—22no—
169C22—24no—
170C22—22no—
171C22—41no—
172C22—42no—
173C22—41no—
174C22—42no—
175C22—41no—
176C22C2×C22⋊Dic26911yescharacteristic
177C22D4×Dic26912yes—
178C4—22no—
179C4—42no—
180C4—41no—
181C4#2257542111yescharacteristic
182C4#2257542512yes—
183C4#2257543411yescharacteristic
184C2—21no—
185C2—22no—
186C2—42no—
187C2—42no—
188C2#3177048511yescharacteristic
subgroupG/H
centerC4#22575421
commutatorC23×C269C22×C4
FrattiniC22×C4C22×D269
Fitting, prime radical#525×C269C2
socleC2×C269#386
cosocleC22×C4×C269C23
hypercenter#525D269
hypocenterC269#1891
LCSG ▷ C23×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C4 ◁ C22×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. #31771372C2semidirect
2. #31770589C2semidirect
3. #31770569C2semidirect
4. #31770375C2semidirect
28. C2×#14524130D4semidirect
94. C269#1891semidirect

Maximal subgroups

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

subgroupindex
#317713722
#317705892
#317705692
#317703752
#525×C2692
#1891269