Finite Group Databasebeta

← #46810137

Subgroups — #46810137

Order 34432.

234 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 59 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
1D4×Dic538C211yesmaximal, characteristic
2#31771010C211yesmaximal, characteristic, complemented
3#31770885C211yesmaximal, characteristic
4#31770816C211yesmaximal, characteristic, complemented
5#31770352C211yesmaximal, characteristic, complemented
6#31770337C211yesmaximal, characteristic, complemented
7D4⋊C8×C269C211yesmaximal, characteristic
8C22×Dic538—21no—
9C2×Dic1076—21no—
10#22575453C2211yescharacteristic
11#22575453C2211yescharacteristic
12#22575452—21no—
13#22575432—21no—
14#22575430—22no—
15C4×Dic538C2211yescharacteristic
16D4×Dic269—21no—
17#22575387—22no—
18#22575386—21no—
19C4⋊#14524130C2211yescharacteristic
20#22575378—21no—
21#22575374—21no—
22C4×D4×C269C2211yescharacteristic
23C4⋊C8×C269C2211yescharacteristic
24C4×C8×C269C2211yescharacteristic
25C2×Dic538—22no—
26C2×Dic538—21no—
27C2×Dic538—21no—
28C2×Dic538—42no—
29C2×Dic538—42no—
30C2×Dic538D411yescharacteristic
31C22×Dic269—22no—
32Dic1076—42no—
33C2×#14524130—21no—
34C4⋊Dic269—21no—
35C4⋊Dic269—21no—
36C4⋊Dic269—21no—
37C4⋊Dic269D411yescharacteristic
38C4⋊Dic269D412yes—
39#16864381—22no—
40#16864381—21no—
41C22⋊Dic269—22no—
42C4×Dic269—21no—
43C2×D4×C269D411yescharacteristic
44C22×C4×C269—21no—
45C2×C8×C269—21no—
46C2×C8×C269—21no—
47C4⋊C4×C269D411yescharacteristic
48C22⋊C4×C269—21no—
49C42×C269C2311yescharacteristic
50Dic538—21no—
51Dic538—44no—
52Dic538—41no—
53Dic538—41no—
54Dic538—41no—
55Dic538—41no—
56Dic538D812yes—
57C2×Dic269—21no—
58C2×Dic269—21no—
59C2×Dic269—22no—
60C2×Dic269—44no—
61C2×Dic269—41no—
62#14524130—41no—
63C23×C269—21no—
64D4×C269—21no—
65D4×C269Q1612yescomplemented
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—22no—
73C8×C269—41no—
74C22×C269—22no—
75C22×C269—41no—
76C22×C269—41no—
77C22×C269#12011yescharacteristic
78C4×C269—21no—
79C4×C269—41no—
80C4×C269C2×D811yescharacteristic
81C4×C269C2×Q1611yescharacteristic
82C4×C269AGL(1,ℤ/8)11yescharacteristic
83C4×C269#13711yescharacteristic
84Dic269—22no—
85Dic269—42no—
86Dic269—41no—
87Dic269—81no—
88C2×C269—42no—
89C2×C269#44711yescharacteristic
90C2×C269#45111yescharacteristic
91C2×C269#45611yescharacteristic
92C269#164911yescharacteristic, complemented, Sylow
93#1649—2691nomaximal, Sylow
94D4×Q8—2691no—
95#500—2691no—
96#474—2691no—
97#462—2691no—
98#332—2691no—
99Q8⋊C8—2691no—
100D4⋊C8D26911yescharacteristic
101C22×Q8—5381no—
102C2×Q16—5381no—
103C4⋊Q8—2691no—
104C4⋊Q8—2691no—
105C4⋊Q8—5381no—
106C22⋊Q8—5382no—
107C22⋊Q8—5381no—
108C4×Q8—2691no—
109C4×D4—5381no—
110C4×D4C2×D26911yescharacteristic
111#107—5382no—
112#107—5381no—
113C4⋊C8—2691no—
114C4⋊C8C2×D26911yescharacteristic
115#103—5381no—
116#102—5381no—
117C4×C8C2×D26911yescharacteristic
118C2×Q8—2691no—
119C2×Q8—5382no—
120C2×Q8—5381no—
121C2×Q8—5381no—
122C2×Q8—10762no—
123C2×Q8—10762no—
124C2×D4D107611yescharacteristic
125C22×C4—21no—
126C22×C4—5382no—
127Q16—10762no—
128C2×C8—21no—
129C2×C8—21no—
130C2×C8—5381no—
131C4⋊C4—2691no—
132C4⋊C4—2692no—
133C4⋊C4—5382no—
134C4⋊C4—5381no—
135C4⋊C4—5381no—
136C4⋊C4—5381no—
137C4⋊C4—5381no—
138C4⋊C4D107611yescharacteristic
139C22⋊C4—21no—
140C22⋊C4—5382no—
141C42—5381no—
142C42C22×D26911yescharacteristic
143C23—21no—
144Q8—2692no—
145Q8—5381no—
146Q8—10764no—
147Q8—10761no—
148Q8—10761no—
149Q8—10761no—
150Q8—10761no—
151D4—21no—
152D4Dic107612yescomplemented
153C2×C4—21no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—5381no—
157C2×C4—5381no—
158C2×C4—5382no—
159C2×C4—10764no—
160C2×C4—10761no—
161C2×C4D4×D26911yescharacteristic
162C2×C4D4×D26911yescharacteristic
163C2×C4C2×D107611yescharacteristic
164C8—22no—
165C8—41no—
166C8—10761no—
167C22—22no—
168C22—41no—
169C22—41no—
170C22#2257542311yescharacteristic
171C4—21no—
172C4—41no—
173C4—5382no—
174C4—10762no—
175C4—10761no—
176C4—21521no—
177C4D8×D26911yescharacteristic
178C4C2×Dic107611yescharacteristic
179C4#2257548011yescharacteristic
180C4#2257548611yescharacteristic
181C2—42no—
182C2#3177074011yescharacteristic
183C2#3177076311yescharacteristic
184C2#3177078911yescharacteristic
subgroupG/H
centerC22#22575423
commutator, cosocleC42×C269C23
FrattiniC42C22×D269
FittingD4⋊C8×C269C2
socleC22×C269#120
prime radicalC2×D4×C269D4
hypercenterD4⋊C8D269
hypocenterC269#1649
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. #31771010C2semidirect
4. #31770816C2semidirect
5. #31770352C2semidirect
6. #31770337C2semidirect
65. D4×C269Q16semidirect
92. C269#1649semidirect
152. D4Dic1076semidirect

Maximal subgroups

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

subgroupindex
D4×Dic5382
#317710102
#317708852
#317708162
#317703522
#317703372
D4⋊C8×C2692
#1649269