Finite Group Databasebeta

← #46809604

Subgroups — #46809604

Order 34432.

246 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 65 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
3#31770627C211yesmaximal, characteristic, complemented
4#31770352C211yesmaximal, characteristic, complemented
5#31770350C211yesmaximal, characteristic, complemented
6#31770349C211yesmaximal, characteristic, complemented
7#331×C269C211yesmaximal, characteristic, complemented
8C2×#16864401—21no—
9C2×#16864385—21no—
10#22575453C2211yescharacteristic
11#22575440—21no—
12#22575424—21no—
13#22575424C412yes—
14D4×Dic269—21no—
15D4×Dic269C412yes—
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—42no—
26#16864401—42no—
27C2×Dic538—21no—
28C2×C22⋊D269—22no—
29C22×Dic269—22no—
30C2×C4×D269C2×C411yescharacteristic
31C2×C4×D269D411yescharacteristic
32C2×C4×D269D411yescharacteristic
33#16864385—42no—
34C2×#14524130—21no—
35C2×#14524130—21no—
36C4⋊Dic269—21no—
37C4⋊Dic269C2×C412yes—
38C22⋊Dic269—22no—
39C22⋊Dic269—22no—
40C4×Dic269C2×C411yescharacteristic
41C4×Dic269D411yescharacteristic
42C4×Dic269D411yescharacteristic
43C2×D4×C269—21no—
44C2×D4×C269—21no—
45C2×D4×C269C2×C412yes—
46C2×C8×C269—21no—
47C2×C8×C269—21no—
48C42×C269C2311yescharacteristic
49C22×D269C22⋊C411yescharacteristic
50Dic538—41no—
51Dic538—41no—
52C22⋊D269—44no—
53C2×Dic269—22no—
54C2×Dic269—44no—
55C2×Dic269C22⋊C411yescharacteristic
56C2×Dic269C22⋊C411yescharacteristic
57C2×Dic269C22⋊C411yescharacteristic
58C4×D269—21no—
59C4×D269—21no—
60C4×D269—21no—
61C4×D269—21no—
62C4×D269—41no—
63#14524130—41no—
64#14524130—41no—
65C23×C269—22no—
66D4×C269—42no—
67D4×C269—41no—
68D4×C269—41no—
69D4×C269—41no—
70D4×C269—41no—
71C2×C4×C269C22×C411yescharacteristic
72C2×C4×C269C2×D411yescharacteristic
73C2×C4×C269C2×D411yescharacteristic
74C8×C269—41no—
75C8×C269—41no—
76C22×C269—42no—
77C22×C269—42no—
78C22×C269—42no—
79C22×C269C2×C22⋊C411yescharacteristic
80C2×D269—21no—
81C2×D269—21no—
82C2×D269—21no—
83C4×C269—21no—
84C4×C269AGL(1,ℤ/8)11yescharacteristic
85C4×C269AGL(1,ℤ/8)11yescharacteristic
86C4×C269AGL(1,ℤ/8)11yescharacteristic
87C4×C269#13711yescharacteristic
88Dic269—21no—
89Dic269—21no—
90Dic269—21no—
91Dic269—42no—
92C2×C269—82no—
93C2×C269#41311yescharacteristic
94C2×C269#41711yescharacteristic
95C2×C269#41811yescharacteristic
96D269—41no—
97C269#155711yescharacteristic, complemented, Sylow
98#1557—2691nomaximal, Sylow
99#532—2691no—
100#432—2691no—
101#423—2691no—
102#332—2691no—
103#332—2691no—
104#331—2691no—
105#331D26911yescharacteristic, complemented
106C2×#41—5381no—
107C2×M16—5381no—
108C4⋊Q8—2691no—
109#127C2×D26911yescharacteristic
110#124—5381no—
111#121—2692no—
112#121—5381no—
113C4×D4—2692no—
114C4×D4—5381no—
115C2×C42—2691no—
116C4⋊C8—2691no—
117C4⋊C8—2691no—
118C4⋊C8—5381no—
119C4⋊C8C2×D26911yescharacteristic
120C4⋊C8C2×D26911yescharacteristic
121C22⋊C8—5381no—
122#97—5381no—
123#41—10762no—
124#41—10762no—
125C2×Q8—5381no—
126C2×D4—21no—
127C2×D4—21no—
128C2×D4—5382no—
129C2×D4C4×D26912yes—
130C22×C4—2691no—
131C22×C4—2691no—
132C22×C4—2691no—
133C22×C4—5382no—
134M16—10762no—
135C2×C8—21no—
136C2×C8—21no—
137C2×C8—5381no—
138C2×C8—5381no—
139C4⋊C4—2692no—
140C4⋊C4—5381no—
141C22⋊C4—5382no—
142C22⋊C4—5382no—
143C42—2691no—
144C42—2691no—
145C42—2691no—
146C42C22×D26911yescharacteristic
147C23—22no—
148C23—2691no—
149Q8—10761no—
150Q8—10761no—
151D4—42no—
152D4—41no—
153D4—41no—
154D4—41no—
155D4—41no—
156D4—10764no—
157C2×C4—2691no—
158C2×C4—2691no—
159C2×C4—2691no—
160C2×C4—5381no—
161C2×C4—5381no—
162C2×C4—5381no—
163C2×C4—5381no—
164C2×C4—5382no—
165C2×C4—10761no—
166C2×C4—10764no—
167C2×C4C2×C4×D26911yescharacteristic
168C2×C4D4×D26911yescharacteristic
169C2×C4D4×D26911yescharacteristic
170C8—41no—
171C8—41no—
172C8—10761no—
173C8—10761no—
174C22—42no—
175C22—42no—
176C22—42no—
177C22—5381no—
178C22—5381no—
179C22—5381no—
180C22C22⋊C4×D26911yescharacteristic
181C4—21no—
182C4—5381no—
183C4—5381no—
184C4—5381no—
185C4—10762no—
186C4#2257547711yescharacteristic
187C4#2257547711yescharacteristic
188C4#2257548011yescharacteristic
189C4#2257548211yescharacteristic
190C2—82no—
191C2—10761no—
192C2#3177058611yescharacteristic
193C2#3177060311yescharacteristic
194C2#3177060811yescharacteristic
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#1557
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. #31770627C2semidirect
4. #31770352C2semidirect
5. #31770350C2semidirect
6. #31770349C2semidirect
7. #331×C269C2semidirect
97. C269#1557semidirect
105. #331D269semidirect

Maximal subgroups

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

subgroupindex
#317711532
#317706612
#317706272
#317703522
#317703502
#317703492
#331×C2692
#1557269