Finite Group Databasebeta

← #46835404

Subgroups — #46835404

Order 34688.

202 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 51 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#31774526C211yesmaximal, characteristic
2#31774232C211yesmaximal, characteristic
3#31773835C211yesmaximal, characteristic
4#31773635C211yesmaximal, characteristic
5#31773634C211yesmaximal, characteristic
6#31773622C211yesmaximal, characteristic
7#484×C271C211yesmaximal, characteristic
8#22576159—21no—
9#22576158—21no—
10#22576150—21no—
11#22576150—21no—
12#22576139C2211yescharacteristic
13#22576137—21no—
14#22576116—21no—
15C2×Dic271⋊C4C2211yescharacteristic
16#22576093—21no—
17#22576083—21no—
18C22⋊(C271⋊C8)C2211yescharacteristic
19C271⋊#95—21no—
20C271⋊#95—21no—
21C271⋊#95C2211yescharacteristic
22C22⋊Q8×C271C2211yescharacteristic
23C2×C4⋊C4×C271C2211yescharacteristic
24#107×C271—21no—
25#103×C271—21no—
26C22⋊C8×C271C2211yescharacteristic
27C2×Dic542—21no—
28C2×Dic542D411yescharacteristic
29C22×Dic271—21no—
30C22×Dic271D411yescharacteristic
31C22×Dic271D411yescharacteristic
32C2×C271⋊C8—21no—
33C4⋊Dic271—21no—
34C4⋊Dic271D411yescharacteristic
35Dic271⋊C4—21no—
36Dic271⋊C4—21no—
37Dic271⋊C4—21no—
38Dic271⋊C4—21no—
39Dic271⋊C4—21no—
40Dic271⋊C4—21no—
41Dic271⋊C4—21no—
42C22⋊Dic271—21no—
43C4×Dic271—21no—
44C4×Dic271—21no—
45C2×Q8×C271D411yescharacteristic
46C22×C4×C271—21no—
47C22×C4×C271C2311yescharacteristic
48C2×C8×C271—21no—
49C4⋊C4×C271—21no—
50C4⋊C4×C271—21no—
51C4⋊C4×C271—21no—
52C4⋊C4×C271D411yescharacteristic
53C22⋊C4×C271—21no—
54Dic542—41no—
55Dic542—81no—
56C2×Dic271—21no—
57C2×Dic271—21no—
58C2×Dic271—21no—
59C2×Dic271—21no—
60C2×Dic271—21no—
61C2×Dic271—41no—
62C2×Dic271—41no—
63C2×Dic271—41no—
64C2×Dic271—41no—
65C2×Dic271Q1612yes—
66C271⋊C8—41no—
67C23×C271C2×D411yescharacteristic
68Q8×C271—41no—
69C2×C4×C271—21no—
70C2×C4×C271—21no—
71C2×C4×C271—41no—
72C2×C4×C271—42no—
73C2×C4×C271—41no—
74C2×C4×C271C2×D411yescharacteristic
75C2×C4×C271C2×D411yescharacteristic
76C8×C271—41no—
77C22×C271—21no—
78C22×C271—21no—
79C22×C271#12011yescharacteristic
80C22×C271C2×Q1611yescharacteristic
81C22×C271#13711yescharacteristic
82C4×C271—21no—
83C4×C271—21no—
84C4×C271—41no—
85C4×C271—41no—
86C4×C271—81no—
87Dic271—22no—
88Dic271—41no—
89Dic271—41no—
90Dic271—41no—
91Dic271—81no—
92C2×C271—21no—
93C2×C271—21no—
94C2×C271#45111yescharacteristic
95C2×C271#45411yescharacteristic
96C2×C271#45811yescharacteristic
97C271#161711yescharacteristic, complemented, Sylow
98#1617—2711nomaximal, Sylow
99#544—2711no—
100#484—2711no—
101#484D27111yescharacteristic
102#400—2711no—
103#328—2711no—
104#328—2711no—
105#324—2711no—
106C4⋊Q8—5421no—
107C4⋊Q8—5421no—
108#125—5421no—
109#125—5421no—
110C22⋊Q8—2711no—
111C22⋊Q8—5421no—
112C22⋊Q8C2×D27111yescharacteristic
113#117—5421no—
114C2×C4⋊C4—2711no—
115C2×C4⋊C4C2×D27111yescharacteristic
116#107—21no—
117#107—5421no—
118#103—21no—
119#103—5421no—
120C22⋊C8—2711no—
121C22⋊C8C2×D27111yescharacteristic
122#95—2711no—
123#95—5421no—
124#95—5421no—
125C2×Q8—2711no—
126C2×Q8—5421no—
127C2×Q8C22⋊D27111yescharacteristic
128C22×C4—21no—
129C22×C4—2711no—
130C22×C4—2711no—
131C22×C4—5421no—
132C22×C4C22×D27111yescharacteristic
133C2×C8—21no—
134C2×C8—5421no—
135C4⋊C4—21no—
136C4⋊C4—21no—
137C4⋊C4—21no—
138C4⋊C4—2711no—
139C4⋊C4—5421no—
140C4⋊C4—5421no—
141C4⋊C4—5421no—
142C4⋊C4—5421no—
143C4⋊C4—5421no—
144C4⋊C4—5421no—
145C4⋊C4—5421no—
146C4⋊C4—5421no—
147C4⋊C4C22⋊D27111yescharacteristic
148C22⋊C4—21no—
149C22⋊C4—5421no—
150C42—5421no—
151C42—5421no—
152C23D4×D27111yescharacteristic
153Q8—41no—
154Q8—10841no—
155Q8—21681no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—41no—
159C2×C4—42no—
160C2×C4—41no—
161C2×C4—2712no—
162C2×C4—5421no—
163C2×C4—5421no—
164C2×C4—5421no—
165C2×C4—5421no—
166C2×C4—5421no—
167C2×C4—10841no—
168C2×C4—10841no—
169C2×C4—10841no—
170C2×C4—10841no—
171C2×C4D4×D27111yescharacteristic
172C2×C4C2×C22⋊D27111yescharacteristic
173C8—41no—
174C8—10841no—
175C22—21no—
176C22—21no—
177C22#2257612811yescharacteristic
178C22Q16×D27111yescharacteristic
179C22#2257619211yescharacteristic
180C4—21no—
181C4—21no—
182C4—41no—
183C4—41no—
184C4—81no—
185C4—5422no—
186C4—10841no—
187C4—10841no—
188C4—10841no—
189C4—21681no—
190C2—21no—
191C2—21no—
192C2#3177405111yescharacteristic
193C2#3177406811yescharacteristic
194C2#3177408611yescharacteristic
subgroupG/H
centerC22#22576128
commutator, cosocleC22×C4×C271C23
FrattiniC22×C4C22×D271
Fitting#484×C271C2
socleC22×C271#120
prime radicalC23×C271C2×D4
hypercenter#484D271
hypocenterC271#1617
LCSG ▷ C22×C4×C271 ▷ C22×C271 ▷ C271
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
97. C271#1617semidirect

Maximal subgroups

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

subgroupindex
#317745262
#317742322
#317738352
#317736352
#317736342
#317736222
#484×C2712
#1617271