Finite Group Databasebeta

← #46835393

Subgroups — #46835393

Order 34688.

208 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 49 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#31774494C211yesmaximal, characteristic
2#31774232C211yesmaximal, characteristic, complemented
3#31774215C211yesmaximal, characteristic
4#31773633C211yesmaximal, characteristic, complemented
5#31773630C211yesmaximal, characteristic
6#31773623C211yesmaximal, characteristic, complemented
7#400×C271C211yesmaximal, characteristic, complemented
8#22576155—21no—
9#22576150—21no—
10#22576145—21no—
11#22576143—21no—
12#22576139C2211yescharacteristic
13#22576138—21no—
14#22576134C2211yescharacteristic
15C4×C22⋊D271—21no—
16#22576093—21no—
17#22576091—21no—
18#22576083—21no—
19#22576080—21no—
20C22⋊(C271⋊C8)C2211yescharacteristic
21C22⋊(C271⋊C8)C2211yescharacteristic
22C2×C4⋊C4×C271C2211yescharacteristic
23C2×C4⋊C4×C271C2211yescharacteristic
24#95×C271—21no—
25#95×C271—21no—
26#95×C271C2211yescharacteristic
27C2×Dic542D411yescharacteristic
28C2×D1084D411yescharacteristic
29C2×C22⋊D271—21no—
30C2×C4×D271—21no—
31C2×C271⋊C8—21no—
32C2×C271⋊C8—21no—
33C4⋊Dic271D411yescharacteristic
34C4⋊Dic271D411yescharacteristic
35Dic271⋊C4—21no—
36Dic271⋊C4—21no—
37Dic271⋊C4—21no—
38Dic271⋊C4—21no—
39C22⋊Dic271—21no—
40(C2×D271)⋊C4—21no—
41(C2×D271)⋊C4—21no—
42(C2×D271)⋊C4—21no—
43(C2×D271)⋊C4—21no—
44C4×Dic271—21no—
45C22×C4×C271—21no—
46C22×C4×C271—21no—
47C22×C4×C271D411yescharacteristic
48C22×C4×C271D411yescharacteristic
49C22×C4×C271C2311yescharacteristic
50C4⋊C4×C271—21no—
51C4⋊C4×C271—21no—
52C4⋊C4×C271—21no—
53C4⋊C4×C271—21no—
54C22×D271—21no—
55Dic542—41no—
56D1084—41no—
57C22⋊D271—41no—
58C22⋊D271—41no—
59C2×Dic271—21no—
60C2×Dic271—21no—
61C2×Dic271—21no—
62C4×D271—81no—
63C271⋊C8—41no—
64C271⋊C8—41no—
65C23×C271C2×D411yescharacteristic
66C2×C4×C271—21no—
67C2×C4×C271—21no—
68C2×C4×C271—21no—
69C2×C4×C271—21no—
70C2×C4×C271—41no—
71C2×C4×C271—41no—
72C2×C4×C271—41no—
73C2×C4×C271—41no—
74C2×C4×C271—42no—
75C2×C4×C271—41no—
76C2×C4×C271—41no—
77C2×C4×C271C2×D411yescharacteristic
78C2×C4×C271C2×D411yescharacteristic
79C22×C271—21no—
80C22×C271—21no—
81C22×C271#12011yescharacteristic
82C22×C271#13511yescharacteristic
83C22×C271#13711yescharacteristic
84C2×D271—41no—
85C2×D271—41no—
86C2×D271—41no—
87C4×C271—21no—
88C4×C271—21no—
89C4×C271—41no—
90C4×C271—41no—
91C4×C271—81no—
92C4×C271—81no—
93Dic271—41no—
94Dic271—41no—
95Dic271—41no—
96C2×C271—21no—
97C2×C271—21no—
98C2×C271#45211yescharacteristic
99C2×C271#45411yescharacteristic
100C2×C271#45811yescharacteristic
101D271—81no—
102C271#161511yescharacteristic, complemented, Sylow
103#1615—2711nomaximal, Sylow
104#539—2711no—
105#484—2711no—
106#481—2711no—
107#400D27111yescharacteristic, complemented
108#328—2711no—
109#327—2711no—
110#324—2711no—
111#126—5421no—
112#125—5421no—
113#123—5421no—
114#123—5421no—
115C22⋊Q8—2711no—
116C22⋊Q8—5421no—
117#121—2711no—
118C4×D4—5421no—
119C2×C4⋊C4C2×D27111yescharacteristic
120C2×C4⋊C4C2×D27111yescharacteristic
121#107—5421no—
122#106—5421no—
123#103—5421no—
124#102—5421no—
125C22⋊C8—2711no—
126C22⋊C8—2711no—
127#95—21no—
128#95—21no—
129#95C2×D27111yescharacteristic
130C2×Q8—2711no—
131C2×D4—2711no—
132C2×D4—5421no—
133C22×C4—21no—
134C22×C4—21no—
135C22×C4—5421no—
136C22×C4C22⋊D27111yescharacteristic
137C22×C4C22⋊D27111yescharacteristic
138C22×C4C22×D27111yescharacteristic
139C2×C8—5421no—
140C2×C8—5421no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—21no—
144C4⋊C4—21no—
145C4⋊C4—2711no—
146C4⋊C4—2711no—
147C4⋊C4—5421no—
148C4⋊C4—5421no—
149C4⋊C4—5421no—
150C4⋊C4—5421no—
151C22⋊C4—5421no—
152C22⋊C4—5421no—
153C22⋊C4—5421no—
154C22⋊C4—5421no—
155C22⋊C4—5421no—
156C42—5421no—
157C23—5421no—
158C23C2×C22⋊D27111yescharacteristic
159Q8—10841no—
160D4—10841no—
161D4—10841no—
162D4—10841no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—42no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—5421no—
175C2×C4—5421no—
176C2×C4—5421no—
177C2×C4—21681no—
178C2×C4D4×D27111yescharacteristic
179C2×C4D4×D27111yescharacteristic
180C8—10841no—
181C8—10841no—
182C22—21no—
183C22—21no—
184C22—10841no—
185C22—10841no—
186C22—10841no—
187C22#2257612811yescharacteristic
188C22#2257618011yescharacteristic
189C22#2257619111yescharacteristic
190C4—21no—
191C4—21no—
192C4—41no—
193C4—41no—
194C4—81no—
195C4—81no—
196C4—10841no—
197C4—10841no—
198C4—10841no—
199C2—21no—
200C2—21no—
201C2—21681no—
202C2#3177405711yescharacteristic
203C2#3177406911yescharacteristic
204C2#3177408611yescharacteristic
subgroupG/H
centerC22#22576128
commutator, cosocleC22×C4×C271C23
FrattiniC22×C4C22×D271
Fitting#400×C271C2
socleC22×C271#120
prime radical#22576134C22
hypercenter#400D271
hypocenterC271#1615
LCSG ▷ C22×C4×C271 ▷ C22×C271 ▷ C271
UCSC1 ◁ C22 ◁ C22×C4 ◁ #400

Complements

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

NH ≅ G/Ntype
2. #31774232C2semidirect
4. #31773633C2semidirect
6. #31773623C2semidirect
7. #400×C271C2semidirect
102. C271#1615semidirect
107. #400D271semidirect

Maximal subgroups

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

subgroupindex
#317744942
#317742322
#317742152
#317736332
#317736302
#317736232
#400×C2712
#1615271