Finite Group Databasebeta

← #46835616

Subgroups — #46835616

Order 34688.

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×Dic542C211yesmaximal, characteristic
2#31774302C211yesmaximal, characteristic, complemented
3#31774177C211yesmaximal, characteristic
4#31774108C211yesmaximal, characteristic, complemented
5#31773644C211yesmaximal, characteristic, complemented
6#31773629C211yesmaximal, characteristic, complemented
7D4⋊C8×C271C211yesmaximal, characteristic
8C22×Dic542—21no—
9C2×Dic1084—21no—
10#22576160C2211yescharacteristic
11#22576160C2211yescharacteristic
12#22576159—21no—
13#22576139—21no—
14#22576137—22no—
15C4×Dic542C2211yescharacteristic
16D4×Dic271—21no—
17#22576094—22no—
18#22576093—21no—
19C4⋊(C271⋊C8)C2211yescharacteristic
20#22576085—21no—
21#22576081—21no—
22C4×D4×C271C2211yescharacteristic
23C4⋊C8×C271C2211yescharacteristic
24C4×C8×C271C2211yescharacteristic
25C2×Dic542—22no—
26C2×Dic542—21no—
27C2×Dic542—21no—
28C2×Dic542—42no—
29C2×Dic542—42no—
30C2×Dic542D411yescharacteristic
31C22×Dic271—22no—
32Dic1084—42no—
33C2×C271⋊C8—21no—
34C4⋊Dic271—21no—
35C4⋊Dic271—21no—
36C4⋊Dic271—21no—
37C4⋊Dic271D412yes—
38C4⋊Dic271D411yescharacteristic
39Dic271⋊C4—22no—
40Dic271⋊C4—21no—
41C22⋊Dic271—22no—
42C4×Dic271—21no—
43C2×D4×C271D411yescharacteristic
44C22×C4×C271—21no—
45C2×C8×C271—21no—
46C2×C8×C271—21no—
47C4⋊C4×C271D411yescharacteristic
48C22⋊C4×C271—21no—
49C42×C271C2311yescharacteristic
50Dic542—21no—
51Dic542—44no—
52Dic542—41no—
53Dic542—41no—
54Dic542—41no—
55Dic542—41no—
56Dic542D812yes—
57C2×Dic271—21no—
58C2×Dic271—21no—
59C2×Dic271—22no—
60C2×Dic271—44no—
61C2×Dic271—41no—
62C271⋊C8—41no—
63C23×C271—21no—
64D4×C271—21no—
65D4×C271Q1612yescomplemented
66C2×C4×C271—21no—
67C2×C4×C271—41no—
68C2×C4×C271—41no—
69C2×C4×C271C2×D411yescharacteristic
70C2×C4×C271C2×D411yescharacteristic
71C2×C4×C271C2×D411yescharacteristic
72C8×C271—22no—
73C8×C271—41no—
74C22×C271—22no—
75C22×C271—41no—
76C22×C271—41no—
77C22×C271#12011yescharacteristic
78C4×C271—21no—
79C4×C271—41no—
80C4×C271C2×D811yescharacteristic
81C4×C271C2×Q1611yescharacteristic
82C4×C271AGL(1,ℤ/8)11yescharacteristic
83C4×C271#13711yescharacteristic
84Dic271—22no—
85Dic271—42no—
86Dic271—41no—
87Dic271—81no—
88C2×C271—42no—
89C2×C271#44711yescharacteristic
90C2×C271#45111yescharacteristic
91C2×C271#45611yescharacteristic
92C271#164911yescharacteristic, complemented, Sylow
93#1649—2711nomaximal, Sylow
94D4×Q8—2711no—
95#500—2711no—
96#474—2711no—
97#462—2711no—
98#332—2711no—
99Q8⋊C8—2711no—
100D4⋊C8D27111yescharacteristic
101C22×Q8—5421no—
102C2×Q16—5421no—
103C4⋊Q8—2711no—
104C4⋊Q8—2711no—
105C4⋊Q8—5421no—
106C22⋊Q8—5422no—
107C22⋊Q8—5421no—
108C4×Q8—2711no—
109C4×D4—5421no—
110C4×D4C2×D27111yescharacteristic
111#107—5422no—
112#107—5421no—
113C4⋊C8—2711no—
114C4⋊C8C2×D27111yescharacteristic
115#103—5421no—
116#102—5421no—
117C4×C8C2×D27111yescharacteristic
118C2×Q8—2711no—
119C2×Q8—5422no—
120C2×Q8—5421no—
121C2×Q8—5421no—
122C2×Q8—10842no—
123C2×Q8—10842no—
124C2×D4D108411yescharacteristic
125C22×C4—21no—
126C22×C4—5422no—
127Q16—10842no—
128C2×C8—21no—
129C2×C8—21no—
130C2×C8—5421no—
131C4⋊C4—2711no—
132C4⋊C4—2712no—
133C4⋊C4—5422no—
134C4⋊C4—5421no—
135C4⋊C4—5421no—
136C4⋊C4—5421no—
137C4⋊C4—5421no—
138C4⋊C4D108411yescharacteristic
139C22⋊C4—21no—
140C22⋊C4—5422no—
141C42—5421no—
142C42C22×D27111yescharacteristic
143C23—21no—
144Q8—2712no—
145Q8—5421no—
146Q8—10844no—
147Q8—10841no—
148Q8—10841no—
149Q8—10841no—
150Q8—10841no—
151D4—21no—
152D4Dic108412yescomplemented
153C2×C4—21no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—5421no—
157C2×C4—5421no—
158C2×C4—5422no—
159C2×C4—10844no—
160C2×C4—10841no—
161C2×C4D4×D27111yescharacteristic
162C2×C4D4×D27111yescharacteristic
163C2×C4C2×D108411yescharacteristic
164C8—22no—
165C8—41no—
166C8—10841no—
167C22—22no—
168C22—41no—
169C22—41no—
170C22#2257613011yescharacteristic
171C4—21no—
172C4—41no—
173C4—5422no—
174C4—10842no—
175C4—10841no—
176C4—21681no—
177C4D8×D27111yescharacteristic
178C4C2×Dic108411yescharacteristic
179C4#2257618711yescharacteristic
180C4#2257619311yescharacteristic
181C2—42no—
182C2#3177403211yescharacteristic
183C2#3177405511yescharacteristic
184C2#3177408111yescharacteristic
subgroupG/H
centerC22#22576130
commutator, cosocleC42×C271C23
FrattiniC42C22×D271
FittingD4⋊C8×C271C2
socleC22×C271#120
prime radicalC2×D4×C271D4
hypercenterD4⋊C8D271
hypocenterC271#1649
LCSG ▷ C42×C271 ▷ C22×C271 ▷ C271
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #31774302C2semidirect
4. #31774108C2semidirect
5. #31773644C2semidirect
6. #31773629C2semidirect
65. D4×C271Q16semidirect
92. C271#1649semidirect
152. D4Dic1084semidirect

Maximal subgroups

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

subgroupindex
D4×Dic5422
#317743022
#317741772
#317741082
#317736442
#317736292
D4⋊C8×C2712
#1649271