Finite Group Databasebeta

← #46835532

Subgroups — #46835532

Order 34688.

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

normal subgroups only

This group has 228 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#31774248C211yesmaximal, characteristic, complemented
3#31774193C211yesmaximal, characteristic, complemented
4#31774187C211yesmaximal, characteristic
5#31773644C211yesmaximal, characteristic, complemented
6#31773629C211yesmaximal, characteristic, complemented
7D4⋊C8×C271C211yesmaximal, characteristic
8C22×Dic542—21no—
9#22576160C2211yescharacteristic
10#22576160C2211yescharacteristic
11#22576159—21no—
12#22576139—21no—
13#22576137—22no—
14C4×Dic542C2211yescharacteristic
15D4×Dic271—21no—
16#22576094—21no—
17#22576091—21no—
18C4⋊(C271⋊C8)C2211yescharacteristic
19#22576085—21no—
20#22576085—22no—
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—
32C2×C271⋊C8—21no—
33C4⋊Dic271—21no—
34C4⋊Dic271—21no—
35C4⋊Dic271—21no—
36C4⋊Dic271D412yes—
37C4⋊Dic271D411yescharacteristic
38Dic271⋊C4—22no—
39Dic271⋊C4—21no—
40C22⋊Dic271—22no—
41C4×Dic271—21no—
42C2×D4×C271D411yescharacteristic
43C22×C4×C271—21no—
44C2×C8×C271—21no—
45C2×C8×C271—21no—
46C4⋊C4×C271D411yescharacteristic
47C22⋊C4×C271—21no—
48C42×C271C2311yescharacteristic
49Dic542—21no—
50Dic542—44no—
51Dic542—41no—
52Dic542—41no—
53Dic542—42no—
54Dic542SD1612yes—
55C2×Dic271—21no—
56C2×Dic271—21no—
57C2×Dic271—22no—
58C2×Dic271—44no—
59C2×Dic271—41no—
60C271⋊C8—41no—
61C23×C271—21no—
62D4×C271—21no—
63D4×C271Q1612yes—
64C2×C4×C271—21no—
65C2×C4×C271—41no—
66C2×C4×C271—41no—
67C2×C4×C271C2×D411yescharacteristic
68C2×C4×C271C2×D411yescharacteristic
69C2×C4×C271C2×D411yescharacteristic
70C8×C271—41no—
71C8×C271—41no—
72C22×C271—22no—
73C22×C271—41no—
74C22×C271—41no—
75C22×C271#12011yescharacteristic
76C4×C271—21no—
77C4×C271—41no—
78C4×C271C2×SD1611yescharacteristic
79C4×C271C2×Q1611yescharacteristic
80C4×C271AGL(1,ℤ/8)11yescharacteristic
81C4×C271#13711yescharacteristic
82Dic271—22no—
83Dic271—42no—
84Dic271—41no—
85Dic271—81no—
86C2×C271—42no—
87C2×C271#45011yescharacteristic
88C2×C271#45111yescharacteristic
89C2×C271#45411yescharacteristic
90C271#163711yescharacteristic, complemented, Sylow
91#1637—2711nomaximal, Sylow
92D4×Q8—2711no—
93#487—2711no—
94#477—2711no—
95#476—2711no—
96#332—2711no—
97Q8⋊C8—2711no—
98D4⋊C8D27111yescharacteristic
99C22×Q8—5421no—
100C4⋊Q8—2711no—
101C4⋊Q8—2711no—
102C4⋊Q8—5421no—
103C22⋊Q8—5422no—
104C22⋊Q8—5421no—
105C4×Q8—2711no—
106C4×D4—5421no—
107C4×D4C2×D27111yescharacteristic
108#107—5421no—
109#106—5421no—
110C4⋊C8—2711no—
111C4⋊C8C2×D27111yescharacteristic
112#103—5422no—
113#103—5421no—
114#102—5421no—
115C4×C8C2×D27111yescharacteristic
116C2×Q8—2711no—
117C2×Q8—5422no—
118C2×Q8—5421no—
119C2×Q8—5421no—
120C2×Q8—10842no—
121C2×Q8—10842no—
122C2×D4D108411yescharacteristic
123C22×C4—21no—
124C22×C4—5422no—
125C2×C8—21no—
126C2×C8—21no—
127C2×C8—5421no—
128C4⋊C4—2712no—
129C4⋊C4—2711no—
130C4⋊C4—5422no—
131C4⋊C4—5421no—
132C4⋊C4—5421no—
133C4⋊C4—5421no—
134C4⋊C4—5421no—
135C4⋊C4D108411yescharacteristic
136C22⋊C4—21no—
137C22⋊C4—5422no—
138C42—5421no—
139C42C22×D27111yescharacteristic
140C23—21no—
141Q8—2712no—
142Q8—5421no—
143Q8—10842no—
144Q8—10844no—
145Q8—10841no—
146Q8—10841no—
147D4—21no—
148D4Dic108412yes—
149C2×C4—21no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4—5421no—
153C2×C4—5421no—
154C2×C4—5422no—
155C2×C4—10844no—
156C2×C4—10841no—
157C2×C4D4×D27111yescharacteristic
158C2×C4D4×D27111yescharacteristic
159C2×C4C2×D108411yescharacteristic
160C8—41no—
161C8—41no—
162C8—10841no—
163C22—22no—
164C22—41no—
165C22—41no—
166C22#2257613011yescharacteristic
167C4—21no—
168C4—41no—
169C4—5422no—
170C4—10842no—
171C4—10841no—
172C4—21681no—
173C4SD16×D27111yescharacteristic
174C4C2×Dic108411yescharacteristic
175C4#2257618411yescharacteristic
176C4#2257619311yescharacteristic
177C2—42no—
178C2#3177404911yescharacteristic
179C2#3177405511yescharacteristic
180C2#3177407111yescharacteristic
subgroupG/H
centerC22#22576130
commutator, cosocleC42×C271C23
FrattiniC42C22×D271
FittingD4⋊C8×C271C2
socleC22×C271#120
prime radicalC2×D4×C271D4
hypercenterD4⋊C8D271
hypocenterC271#1637
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. #31774248C2semidirect
3. #31774193C2semidirect
5. #31773644C2semidirect
6. #31773629C2semidirect
90. C271#1637semidirect

Maximal subgroups

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

subgroupindex
D4×Dic5422
#317742482
#317741932
#317741872
#317736442
#317736292
D4⋊C8×C2712
#1637271