Finite Group Databasebeta

← #46809577

Subgroups — #46809577

Order 34432.

252 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 67 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#31771153C211yesmaximal, characteristic
2#31770661C211yesmaximal, characteristic, complemented
3C4⋊C8×D269C211yesmaximal, characteristic, complemented
4#31770353C211yesmaximal, characteristic, complemented
5#31770353C211yesmaximal, characteristic, complemented
6#31770349C211yesmaximal, characteristic, complemented
7#331×C269C211yesmaximal, characteristic, complemented
8C2×#16864401C412yes—
9C2×C8×D269—21no—
10#22575453C2211yescharacteristic
11#22575440C412yes—
12#22575424—21no—
13#22575424—21no—
14D4×Dic269—21no—
15D4×Dic269—21no—
16C42×D269C2211yescharacteristic
17C4⋊#14524130C2211yescharacteristic
18C4⋊#14524130C2211yescharacteristic
19#22575382—21no—
20#22575365—21no—
21#22575363—21no—
22#127×C269C2211yescharacteristic
23C4⋊C8×C269C2211yescharacteristic
24C4⋊C8×C269C2211yescharacteristic
25#16864401—44no—
26C2×Dic538C2×C412yes—
27C2×C22⋊D269—22no—
28C22×Dic269—22no—
29C2×C4×D269C2×C411yescharacteristic
30C2×C4×D269D411yescharacteristic
31C2×C4×D269D411yescharacteristic
32C2×#14524130—21no—
33C2×#14524130—21no—
34C8×D269—42no—
35C4⋊Dic269—21no—
36C4⋊Dic269—21no—
37C22⋊Dic269—22no—
38C22⋊Dic269—22no—
39C4×Dic269C2×C411yescharacteristic
40C4×Dic269D411yescharacteristic
41C4×Dic269D411yescharacteristic
42C2×D4×C269—21no—
43C2×D4×C269—21no—
44C2×D4×C269C2×C412yes—
45C2×C8×C269—21no—
46C2×C8×C269—21no—
47C42×C269C2311yescharacteristic
48C22×D269C22⋊C411yescharacteristic
49Dic538—42no—
50C22⋊D269—44no—
51C2×Dic269—22no—
52C2×Dic269—44no—
53C2×Dic269C22⋊C411yescharacteristic
54C2×Dic269C22⋊C411yescharacteristic
55C2×Dic269C22⋊C411yescharacteristic
56C4×D269—22no—
57C4×D269—21no—
58C4×D269—21no—
59C4×D269—21no—
60C4×D269—21no—
61#14524130—41no—
62#14524130—41no—
63C23×C269—22no—
64D4×C269—42no—
65D4×C269—41no—
66D4×C269—41no—
67D4×C269—41no—
68D4×C269—41no—
69C2×C4×C269C22×C411yescharacteristic
70C2×C4×C269C2×D411yescharacteristic
71C2×C4×C269C2×D411yescharacteristic
72C8×C269—41no—
73C8×C269—41no—
74C22×C269—42no—
75C22×C269—42no—
76C22×C269—42no—
77C22×C269C2×C22⋊C411yescharacteristic
78C2×D269—21no—
79C2×D269—21no—
80C2×D269#10012yes—
81C4×C269—21no—
82C4×C269#13511yescharacteristic
83C4×C269#13511yescharacteristic
84C4×C269AGL(1,ℤ/8)11yescharacteristic
85C4×C269#13711yescharacteristic
86Dic269—21no—
87Dic269—21no—
88Dic269—21no—
89Dic269—42no—
90C2×C269—82no—
91C2×C269C2×#10011yescharacteristic
92C2×C269#41611yescharacteristic
93C2×C269#41711yescharacteristic
94D269—22no—
95C269#155111yescharacteristic, complemented, Sylow
96#1551—2691nomaximal, Sylow
97#532—2691no—
98#432—2691no—
99C2×C4⋊C8—2691no—
100#333—2691no—
101#333—2691no—
102#331—2691no—
103#331D26911yescharacteristic, complemented
104C2×#41—2692no—
105C22×C8—5381no—
106C4⋊Q8—2691no—
107#127C2×D26911yescharacteristic
108#124—2692no—
109#121—5381no—
110#121—5381no—
111C4×D4—5381no—
112C4×D4—5381no—
113C2×C42—2691no—
114C4⋊C8—2691no—
115C4⋊C8—2691no—
116C4⋊C8—5381no—
117C4⋊C8C2×D26911yescharacteristic
118C4⋊C8C2×D26911yescharacteristic
119C22⋊C8—5381no—
120#97—5381no—
121#41—10764no—
122C2×Q8—2692no—
123C2×D4—21no—
124C2×D4—21no—
125C2×D4—5382no—
126C2×D4C4×D26912yes—
127C22×C4—2691no—
128C22×C4—2691no—
129C22×C4—2691no—
130C22×C4—5382no—
131C2×C8—21no—
132C2×C8—21no—
133C2×C8—5381no—
134C2×C8—5381no—
135C2×C8—10762no—
136C4⋊C4—5381no—
137C4⋊C4—5381no—
138C22⋊C4—5382no—
139C22⋊C4—5382no—
140C42—2691no—
141C42—2691no—
142C42—2691no—
143C42C22×D26911yescharacteristic
144C23—22no—
145C23—2691no—
146Q8—10762no—
147D4—42no—
148D4—41no—
149D4—41no—
150D4—41no—
151D4—41no—
152D4—10764no—
153C2×C4—2691no—
154C2×C4—2691no—
155C2×C4—2691no—
156C2×C4—5382no—
157C2×C4—5381no—
158C2×C4—5381no—
159C2×C4—5381no—
160C2×C4—5381no—
161C2×C4—5382no—
162C2×C4—10764no—
163C2×C4C2×C4×D26911yescharacteristic
164C2×C4D4×D26911yescharacteristic
165C2×C4D4×D26911yescharacteristic
166C8—41no—
167C8—41no—
168C8—10761no—
169C8—10761no—
170C22—42no—
171C22—42no—
172C22—42no—
173C22—2692no—
174C22—5381no—
175C22—5381no—
176C22C22⋊C4×D26911yescharacteristic
177C4—21no—
178C4—5381no—
179C4—5381no—
180C4—5381no—
181C4—10762no—
182C4#2257547211yescharacteristic
183C4#2257547411yescharacteristic
184C4#2257547711yescharacteristic
185C4#2257548211yescharacteristic
186C2—82no—
187C2—5382no—
188C2#100×D26911yescharacteristic
189C2#3177059811yescharacteristic
190C2#3177060311yescharacteristic
subgroupG/H
centerC22C22⋊C4×D269
commutatorC2×C4×C269C22×C4
FrattiniC42C22×D269
Fitting#331×C269C2
socleC22×C269C2×C22⋊C4
prime radical#31771153C2
cosocleC42×C269C23
hypercenter#331D269
hypocenterC269#1551
LCSG ▷ C2×C4×C269 ▷ C22×C269 ▷ C269
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
2. #31770661C2semidirect
3. C4⋊C8×D269C2semidirect
4. #31770353C2semidirect
5. #31770353C2semidirect
6. #31770349C2semidirect
7. #331×C269C2semidirect
95. C269#1551semidirect
103. #331D269semidirect

Maximal subgroups

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

subgroupindex
#317711532
#317706612
C4⋊C8×D2692
#317703532
#317703492
#331×C2692
#1551269