Finite Group Databasebeta

← #27186401

Subgroups — #27186401

Order 12928.

256 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 60 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#20266197C211yesmaximal, characteristic, complemented
2#20266193C211yesmaximal, characteristic, complemented
3#20266021C212yesmaximal, complemented
4#20266020C212yesmaximal, complemented
5C2×#15692241C211yesmaximal, characteristic
6#15692322—21no—
7C4⋊#11717581—21no—
8C22⋊#11717581C2212yes—
9C22⋊#11717581C2212yes—
10#15692310—21no—
11C4×#11717581—21no—
12C22×Dic202C411yescharacteristic
13C22×C22⋊D101C411yescharacteristic
14#15692241—21no—
15#15692241—21no—
16#15692241—21no—
17#15692241—21no—
18C2×C22⋊Dic101C2211yescharacteristic
19C2×#13108051C411yescharacteristic
20C2×#13108051C2211yescharacteristic
21C2×C4×Dic101C2211yescharacteristic
22C2×C22⋊C4×C101C411yescharacteristic
23C2×#11717581—22no—
24C2×#11717581—22no—
25C23×D101C2×C411yescharacteristic
26C2×Dic202—21no—
27C2×Dic202—21no—
28C2×Dic202—42no—
29C2×C22⋊D101—21no—
30C2×C22⋊D101—21no—
31C2×C22⋊D101—42no—
32C22×Dic101C2×C411yescharacteristic
33C22×Dic101C2×C411yescharacteristic
34C22×Dic101C2311yescharacteristic
35C22⋊Dic101—21no—
36C22⋊Dic101—21no—
37#13108051—21no—
38#13108051—21no—
39#13108051—21no—
40#13108051—21no—
41C4×Dic101D411yescharacteristic
42C4×Dic101D411yescharacteristic
43C4×Dic101D411yescharacteristic
44C4×Dic101D411yescharacteristic
45C24×C101C2×C411yescharacteristic
46C22×C4×C101C2×C411yescharacteristic
47C22×C4×C101C2×C411yescharacteristic
48C22⋊C4×C101—21no—
49C22⋊C4×C101—21no—
50C23×C101—21no—
51C23×C101—22no—
52C23×C101—41no—
53C23×C101—41no—
54C23×C101C22×C411yescharacteristic
55C22×D101—21no—
56C22×D101—22no—
57C22×D101—41no—
58C22×D101—41no—
59C2×C4×C101—22no—
60C2×C4×C101—21no—
61C2×C4×C101—41no—
62C2×C4×C101C22⋊C411yescharacteristic
63C2×C4×C101C22⋊C411yescharacteristic
64C22⋊D101—42no—
65C22⋊D101—42no—
66C2×Dic101—22no—
67C2×Dic101—21no—
68C2×Dic101—41no—
69C2×Dic101—41no—
70C2×Dic101C22⋊C411yescharacteristic
71C2×Dic101C22⋊C411yescharacteristic
72C2×Dic101C2×D411yescharacteristic
73C2×Dic101C2×D411yescharacteristic
74Dic202—42no—
75Dic202—42no—
76#11717581—42no—
77#11717581—42no—
78C22×C101—21no—
79C22×C101—21no—
80C22×C101—41no—
81C22×C101—41no—
82C22×C101—41no—
83C22×C101—82no—
84C22×C101C2×C22⋊C411yescharacteristic
85C22×C101#13112yes—
86C2×D101—41no—
87C2×D101—41no—
88C2×D101—41no—
89C2×D101—82no—
90C4×C101—21no—
91C4×C101—21no—
92C4×C101—41no—
93Dic101—21no—
94Dic101—21no—
95Dic101—21no—
96Dic101—41no—
97Dic101#10012yes—
98C2×C101—22no—
99C2×C101—81no—
100C2×C101#40811yescharacteristic
101C2×C101#41011yescharacteristic
102C2×C101C2×#10011yescharacteristic
103D101—81no—
104#1469—1011nomaximal, Sylow
105C101#146911yescharacteristic, complemented, Sylow
106C2×#124—1011no—
107#432—1011no—
108#431—1011no—
109#323—1012no—
110#323—1012no—
111C22×Q8—1011no—
112C22×D4—1011no—
113#124—2021no—
114#124—2021no—
115#124—2021no—
116#124—2021no—
117C2×C22⋊C4—1011no—
118C2×C22⋊C4—1011no—
119C2×C22⋊C4—1011no—
120C2×C22⋊C4#8793811yescharacteristic
121C2×C42—1011no—
122C4⋊C8—2021no—
123C4⋊C8—2021no—
124C22⋊C8—1012no—
125C22⋊C8—1012no—
126#97—2021no—
127C4×C8—2021no—
128C24—1011no—
129C24C2×#8793811yescharacteristic
130C2×Q8—4042no—
131C2×Q8—2021no—
132C2×Q8—2021no—
133C2×D4—4042no—
134C2×D4—2021no—
135C2×D4—2021no—
136C22×C4—1011no—
137C22×C4—1011no—
138C22×C4—1011no—
139C22×C4C2×#8793811yescharacteristic
140C22×C4C2×#8793811yescharacteristic
141C2×C8—2022no—
142C2×C8—2022no—
143C22⋊C4—21no—
144C22⋊C4—21no—
145C22⋊C4—2021no—
146C22⋊C4—2021no—
147C22⋊C4—2021no—
148C22⋊C4—2021no—
149C22⋊C4—2021no—
150C22⋊C4—2021no—
151C42—1011no—
152C42—1011no—
153C42—1011no—
154C42—1011no—
155C23—21no—
156C23—22no—
157C23—41no—
158C23—41no—
159C23—4041no—
160C23—4041no—
161C23—2022no—
162C23—2021no—
163C23C22×#8793811yescharacteristic
164Q8—4042no—
165Q8—4042no—
166D4—4042no—
167D4—4042no—
168C2×C4—22no—
169C2×C4—21no—
170C2×C4—41no—
171C2×C4—1011no—
172C2×C4—1011no—
173C2×C4—1011no—
174C2×C4—1011no—
175C2×C4—4041no—
176C2×C4—4041no—
177C2×C4—2022no—
178C2×C4—2021no—
179C2×C4C22⋊#8793811yescharacteristic
180C2×C4C22⋊#8793811yescharacteristic
181C8—4042no—
182C8—4042no—
183C22—21no—
184C22—21no—
185C22—41no—
186C22—41no—
187C22—41no—
188C22—82no—
189C22—8082no—
190C22—4041no—
191C22—4041no—
192C22—4041no—
193C22C2×C22⋊#8793811yescharacteristic
194C22#1569234212yes—
195C4—21no—
196C4—21no—
197C4—41no—
198C4—1012no—
199C4—4041no—
200C4—2021no—
201C4—2021no—
202C4—2021no—
203C2—22no—
204C2—81no—
205C2—8081no—
206C2#2026615011yescharacteristic
207C2#2026615611yescharacteristic
208C2D101⋊#10011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#87938
commutatorC23×C101C22×C4
FrattiniC23C22×#87938
FittingC2×C22⋊C4×C101C4
socleC22×C101C2×C22⋊C4
prime radicalC22×C22⋊D101C4
cosocleC22×Dic101C23
hypercenterC2×C22⋊C4#87938
hypocenterC101#1469
LCSG ▷ C23×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #20266197C2semidirect
2. #20266193C2semidirect
3. #20266021C2semidirect
4. #20266020C2semidirect
105. C101#1469semidirect

Maximal subgroups

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

subgroupindex
#202661972
#202661932
#202660212
#202660202
C2×#156922412
#1469101