Finite Group Databasebeta

← #46810039

Subgroups — #46810039

Order 34432.

234 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 55 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#31771260C211yesmaximal, characteristic
2#31770956C211yesmaximal, characteristic, complemented
3#31770896C211yesmaximal, characteristic, complemented
4#31770895C211yesmaximal, characteristic, complemented
5#31770352C211yesmaximal, characteristic, complemented
6#31770334C211yesmaximal, characteristic, complemented
7D4⋊C8×C269C211yesmaximal, characteristic, complemented
8C2×#16864402—21no—
9#22575453C2211yescharacteristic
10#22575453C2211yescharacteristic
11#22575435—22no—
12#22575432—21no—
13#22575424—21no—
14C4×D1076C2211yescharacteristic
15C4⋊C4×D269—21no—
16#22575385—21no—
17#22575384—21no—
18C4⋊#14524130C2211yescharacteristic
19#22575378—22no—
20#22575375—21no—
21#22575374—21no—
22C4×D4×C269C2211yescharacteristic
23C4⋊C8×C269C2211yescharacteristic
24C4×C8×C269C2211yescharacteristic
25#16864402—42no—
26#16864402—42no—
27C2×Dic538—21no—
28C2×Dic538—21no—
29C2×D1076D411yescharacteristic
30C2×C22⋊D269—22no—
31C2×C4×D269—22no—
32C2×C4×D269—21no—
33C2×#14524130—21no—
34C4⋊Dic269—21no—
35C4⋊Dic269—21no—
36C4⋊Dic269—21no—
37C4⋊Dic269D412yes—
38C4⋊Dic269D411yescharacteristic
39#16864381—22no—
40C22⋊Dic269—22no—
41#16864379—21no—
42C2×D4×C269D411yescharacteristic
43C22×C4×C269—21no—
44C2×C8×C269—21no—
45C2×C8×C269—21no—
46C4⋊C4×C269D411yescharacteristic
47C22⋊C4×C269—21no—
48C42×C269C2311yescharacteristic
49C22×D269—21no—
50Dic538—41no—
51Dic538—41no—
52Dic538—42no—
53D1076—21no—
54D1076SD1612yes—
55C22⋊D269—44no—
56C2×Dic269—21no—
57C2×Dic269—22no—
58C2×Dic269—41no—
59C4×D269—44no—
60C4×D269—41no—
61C4×D269—41no—
62#14524130—41no—
63C23×C269—21no—
64D4×C269—21no—
65D4×C269—21no—
66C2×C4×C269—21no—
67C2×C4×C269—41no—
68C2×C4×C269—41no—
69C2×C4×C269C2×D411yescharacteristic
70C2×C4×C269C2×D411yescharacteristic
71C2×C4×C269C2×D411yescharacteristic
72C8×C269—41no—
73C8×C269—41no—
74C22×C269—41no—
75C22×C269—41no—
76C22×C269—41no—
77C22×C269#12011yescharacteristic
78C2×D269—22no—
79C2×D269—41no—
80C2×D269—41no—
81C4×C269—21no—
82C4×C269—41no—
83C4×C269C2×SD1611yescharacteristic
84C4×C269#13511yescharacteristic
85C4×C269AGL(1,ℤ/8)11yescharacteristic
86C4×C269#13711yescharacteristic
87Dic269—42no—
88Dic269—41no—
89Dic269—81no—
90C2×C269—81no—
91C2×C269#45011yescharacteristic
92C2×C269#45211yescharacteristic
93C2×C269#45411yescharacteristic
94D269—42no—
95C269#163511yescharacteristic, complemented, Sylow
96#1635—2691nomaximal, Sylow
97#547—2691no—
98#487—2691no—
99#476—2691no—
100#476—2691no—
101#332—2691no—
102D4⋊C8—2691no—
103D4⋊C8D26911yescharacteristic, complemented
104C2×#41—5381no—
105C4⋊Q8—2691no—
106C4⋊Q8—2691no—
107#123—5382no—
108C22⋊Q8—5381no—
109#121—5381no—
110C4×D4—2691no—
111C4×D4C2×D26911yescharacteristic
112C2×C4⋊C4—5381no—
113#106—5381no—
114#106—5381no—
115C4⋊C8—2691no—
116C4⋊C8C2×D26911yescharacteristic
117#103—5382no—
118#102—5381no—
119#102—5381no—
120C4×C8C2×D26911yescharacteristic
121#41—10762no—
122#41—10762no—
123C2×Q8—5381no—
124C2×Q8—5381no—
125C2×D4—2691no—
126C2×D4—5382no—
127C2×D4D107611yescharacteristic
128C22×C4—21no—
129C22×C4—5382no—
130C22×C4—5381no—
131C2×C8—21no—
132C2×C8—21no—
133C2×C8—5381no—
134C4⋊C4—2692no—
135C4⋊C4—2691no—
136C4⋊C4—5382no—
137C4⋊C4—5381no—
138C4⋊C4—5381no—
139C4⋊C4—5381no—
140C4⋊C4D107611yescharacteristic
141C22⋊C4—21no—
142C22⋊C4—5382no—
143C22⋊C4—5381no—
144C42C22×D26911yescharacteristic
145C23—21no—
146C23—5381no—
147Q8—10762no—
148Q8—10761no—
149Q8—10761no—
150D4—21no—
151D4—21no—
152D4—2692no—
153D4—5381no—
154D4—10764no—
155C2×C4—21no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—5381no—
159C2×C4—5382no—
160C2×C4—10764no—
161C2×C4—10761no—
162C2×C4—10761no—
163C2×C4—10761no—
164C2×C4D4×D26911yescharacteristic
165C2×C4D4×D26911yescharacteristic
166C2×C4C2×D107611yescharacteristic
167C8—41no—
168C8—41no—
169C8—10761no—
170C22—41no—
171C22—41no—
172C22—41no—
173C22—5382no—
174C22—10761no—
175C22—10761no—
176C22#2257542311yescharacteristic
177C4—21no—
178C4—41no—
179C4—10762no—
180C4—10761no—
181C4—21521no—
182C4SD16×D26911yescharacteristic
183C4#2257547511yescharacteristic
184C4#2257547711yescharacteristic
185C4#2257548611yescharacteristic
186C2—81no—
187C2—10762no—
188C2#3177075711yescharacteristic
189C2#3177076911yescharacteristic
190C2#3177077911yescharacteristic
subgroupG/H
centerC22#22575423
commutator, cosocleC42×C269C23
FrattiniC42C22×D269
FittingD4⋊C8×C269C2
socleC22×C269#120
prime radical#31771260C2
hypercenterD4⋊C8D269
hypocenterC269#1635
LCSG ▷ C42×C269 ▷ C22×C269 ▷ C269
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #31770956C2semidirect
3. #31770896C2semidirect
4. #31770895C2semidirect
5. #31770352C2semidirect
6. #31770334C2semidirect
7. D4⋊C8×C269C2semidirect
95. C269#1635semidirect
103. D4⋊C8D269semidirect

Maximal subgroups

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

subgroupindex
#317712602
#317709562
#317708962
#317708952
#317703522
#317703342
D4⋊C8×C2692
#1635269