Finite Group Databasebeta

← #46835637

Subgroups — #46835637

Order 34688.

200 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 53 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#31774617C211yesmaximal, characteristic
2#31774295C211yesmaximal, characteristic, complemented
3#31774177C211yesmaximal, characteristic
4#31774108C211yesmaximal, characteristic, complemented
5#31773642C211yesmaximal, characteristic, complemented
6#31773629C211yesmaximal, characteristic, complemented
7D4⋊C8×C271C211yesmaximal, characteristic
8C2×Dic1084—21no—
9#22576160C2211yescharacteristic
10#22576160C2211yescharacteristic
11#22576153—22no—
12#22576147—21no—
13#22576139—21no—
14C4×Dic542C2211yescharacteristic
15#22576125—21no—
16#22576119—21no—
17#22576093—21no—
18#22576092—22no—
19C4⋊(C271⋊C8)C2211yescharacteristic
20#22576085—21no—
21#22576081—21no—
22C4×D4×C271C2211yescharacteristic
23C4⋊C8×C271C2211yescharacteristic
24C4×C8×C271C2211yescharacteristic
25C2×Dic542—21no—
26C2×Dic542—21no—
27C2×Dic542D411yescharacteristic
28Dic1084—42no—
29C2×C271⋊C8—21no—
30C4⋊Dic271—21no—
31C4⋊Dic271—21no—
32C4⋊Dic271—21no—
33C4⋊Dic271D412yes—
34C4⋊Dic271D411yescharacteristic
35Dic271⋊C4—22no—
36Dic271⋊C4—21no—
37C22⋊Dic271—22no—
38C22⋊Dic271—22no—
39C4×Dic271—22no—
40C4×Dic271—21no—
41C2×D4×C271D411yescharacteristic
42C22×C4×C271—21no—
43C2×C8×C271—21no—
44C2×C8×C271—21no—
45C4⋊C4×C271D411yescharacteristic
46C22⋊C4×C271—21no—
47C42×C271C2311yescharacteristic
48Dic542—21no—
49Dic542—21no—
50Dic542—41no—
51Dic542—41no—
52Dic542—41no—
53Dic542—41no—
54C2×Dic271—21no—
55C2×Dic271—21no—
56C2×Dic271—22no—
57C2×Dic271—41no—
58C271⋊C8—41no—
59C23×C271—21no—
60D4×C271—21no—
61D4×C271—21no—
62C2×C4×C271—21no—
63C2×C4×C271—41no—
64C2×C4×C271—41no—
65C2×C4×C271C2×D411yescharacteristic
66C2×C4×C271C2×D411yescharacteristic
67C2×C4×C271C2×D411yescharacteristic
68C8×C271—22no—
69C8×C271—41no—
70C22×C271—41no—
71C22×C271—41no—
72C22×C271—41no—
73C22×C271#12011yescharacteristic
74C4×C271—21no—
75C4×C271—41no—
76C4×C271#13511yescharacteristic
77C4×C271#13511yescharacteristic
78C4×C271AGL(1,ℤ/8)11yescharacteristic
79C4×C271#13711yescharacteristic
80Dic271—41no—
81Dic271—42no—
82Dic271—41no—
83Dic271—81no—
84C2×C271—81no—
85C2×C271#44911yescharacteristic
86C2×C271#45211yescharacteristic
87C2×C271#45611yescharacteristic
88C271#165211yescharacteristic, complemented, Sylow
89#1652—2711nomaximal, Sylow
90#556—2711no—
91#498—2711no—
92#474—2711no—
93#462—2711no—
94#332—2711no—
95Q8⋊C8—2711no—
96D4⋊C8D27111yescharacteristic
97C2×Q16—5421no—
98C4⋊Q8—2711no—
99C4⋊Q8—2711no—
100#126—5422no—
101#124—5421no—
102C22⋊Q8—5421no—
103C4×Q8—2711no—
104C4×Q8—5421no—
105C4×D4C2×D27111yescharacteristic
106#117—5421no—
107#107—5421no—
108#106—5422no—
109C4⋊C8—2711no—
110C4⋊C8C2×D27111yescharacteristic
111#103—5421no—
112#102—5421no—
113C4×C8C2×D27111yescharacteristic
114C2×Q8—2711no—
115C2×Q8—5421no—
116C2×Q8—5421no—
117C2×D4D108411yescharacteristic
118C22×C4—21no—
119Q16—10842no—
120C2×C8—21no—
121C2×C8—21no—
122C2×C8—5421no—
123C4⋊C4—2711no—
124C4⋊C4—2712no—
125C4⋊C4—5422no—
126C4⋊C4—5421no—
127C4⋊C4—5421no—
128C4⋊C4—5421no—
129C4⋊C4—5421no—
130C4⋊C4D108411yescharacteristic
131C22⋊C4—21no—
132C22⋊C4—5422no—
133C22⋊C4—5422no—
134C42—5422no—
135C42—5421no—
136C42C22×D27111yescharacteristic
137C23—21no—
138Q8—5421no—
139Q8—5421no—
140Q8—10841no—
141Q8—10841no—
142Q8—10841no—
143Q8—10841no—
144D4—21no—
145D4—21no—
146C2×C4—21no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—5421no—
150C2×C4—5422no—
151C2×C4—5421no—
152C2×C4—10841no—
153C2×C4D4×D27111yescharacteristic
154C2×C4D4×D27111yescharacteristic
155C2×C4C2×D108411yescharacteristic
156C8—22no—
157C8—41no—
158C8—10841no—
159C22—41no—
160C22—41no—
161C22—41no—
162C22#2257613011yescharacteristic
163C4—21no—
164C4—41no—
165C4—10841no—
166C4—10842no—
167C4—10841no—
168C4—21681no—
169C4#2257618111yescharacteristic
170C4#2257618211yescharacteristic
171C4#2257618411yescharacteristic
172C4#2257619311yescharacteristic
173C2—81no—
174C2#3177404311yescharacteristic
175C2#3177406111yescharacteristic
176C2#3177408111yescharacteristic
subgroupG/H
centerC22#22576130
commutator, cosocleC42×C271C23
FrattiniC42C22×D271
FittingD4⋊C8×C271C2
socleC22×C271#120
prime radicalC2×D4×C271D4
hypercenterD4⋊C8D271
hypocenterC271#1652
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. #31774295C2semidirect
4. #31774108C2semidirect
5. #31773642C2semidirect
6. #31773629C2semidirect
88. C271#1652semidirect

Maximal subgroups

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

subgroupindex
#317746172
#317742952
#317741772
#317741082
#317736422
#317736292
D4⋊C8×C2712
#1652271