Finite Group Databasebeta

← #27186879

Subgroups — #27186879

Order 12928.

412 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 94 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
1C2×#15692313C212yesmaximal
2C4×C22⋊#87938C212yesmaximal, complemented
3#20266055C212yesmaximal, complemented
4C2×#15692215C211yesmaximal, characteristic
5C2×C22⋊#87938C2214yes—
6C2×C4×#87938—22no—
7#15692313C418yescomplemented
8(C2×#87938)⋊C4—22no—
9C22×C22⋊D101C2211yescharacteristic
10C23×Dic101C411yescharacteristic, complemented
11C22×C4×D101C2211yescharacteristic
12#15692215—22no—
13#15692215—22no—
14C2×#13108053C411yescharacteristic, complemented
15C2×#13108051C2211yescharacteristic
16C2×C4×Dic101C411yescharacteristic, complemented
17C2×C22⋊C4×C101C411yescharacteristic, complemented
18C22×#87938—24no—
19C22⋊#87938—24no—
20C22⋊#87938C2×C418yescomplemented
21C4×#87938—44no—
22C23×D101C2311yescharacteristic
23C2×C22⋊D101—22no—
24C2×C22⋊D101—22no—
25C2×C22⋊D101C2×C414yes—
26C22×Dic101—21no—
27C22×Dic101—21no—
28C22×Dic101—42no—
29C22×Dic101C2×C411yescharacteristic
30C22×Dic101C2×C411yescharacteristic
31C22×Dic101C2×C411yescharacteristic
32C2×C4×D101—42no—
33C2×C4×D101D412yes—
34C2×C4×D101D412yes—
35#13108053—22no—
36#13108051—22no—
37C4×Dic101—21no—
38C4×Dic101—21no—
39C24×C101C2×C411yescharacteristic
40C22×C4×C101C2×C411yescharacteristic
41C22×C4×C101C2×C411yescharacteristic
42C22⋊C4×C101—22no—
43C23×C101—21no—
44C23×C101—21no—
45C23×C101—41no—
46C23×C101—41no—
47C23×C101C4212yescomplemented
48C23×C101C22×C411yescharacteristic
49C22×D101—41no—
50C22×D101—41no—
51C22×D101C22×C412yes—
52C22×D101C2×D412yes—
53C22×D101#4112yes—
54C2×#87938—28no—
55C2×#87938—44no—
56C2×#87938—44no—
57C2×C4×C101—21no—
58C2×C4×C101—41no—
59C2×C4×C101—41no—
60C2×C4×C101C22⋊C412yes—
61C22⋊D101—28no—
62C2×Dic101—21no—
63C2×Dic101—21no—
64C2×Dic101—22no—
65C2×Dic101—21no—
66C2×Dic101—42no—
67C2×Dic101—42no—
68C2×Dic101—41no—
69C2×Dic101C4212yescomplemented
70C2×Dic101C22⋊C411yescharacteristic
71C2×Dic101C22⋊C411yescharacteristic
72C4×D101—24no—
73C4×D101—42no—
74C22×C101—21no—
75C22×C101—21no—
76C22×C101—22no—
77C22×C101—42no—
78C22×C101—42no—
79C22×C101—41no—
80C22×C101—41no—
81C22×C101C2×C4211yescharacteristic
82C22×C101C2×C22⋊C411yescharacteristic
83C22×C101#11711yescharacteristic
84C2×D101—22no—
85C2×D101—22no—
86C2×D101—42no—
87C2×D101—42no—
88C2×D101C4×D414yes—
89#87938—48no—
90C4×C101—22no—
91C4×C101—41no—
92Dic101—22no—
93Dic101—21no—
94Dic101—41no—
95Dic101#9912yescomplemented
96C2×C101—21no—
97C2×C101—21no—
98C2×C101—42no—
99C2×C101C4×C22⋊C411yescharacteristic
100C2×C101C2×#9911yescharacteristic
101C2×C101#41011yescharacteristic
102D101—24no—
103C4×#99—1011nomaximal, Sylow
104C101C4×#9911yescharacteristic, complemented, Sylow
105C2×C4×D4—1011no—
106C2×#99—1012no—
107C4×C22⋊C4—1012no—
108#342—1012no—
109C22×D4—1011no—
110C23×C4—1011no—
111C23×C4—1011no—
112C4×D4—2022no—
113C4×D4—2022no—
114C2×C4⋊C4—1011no—
115C2×C22⋊C4—1014no—
116C2×C22⋊C4—1011no—
117C2×C22⋊C4#8793811yescharacteristic, complemented
118C2×C42—1011no—
119C2×C42—2022no—
120#99—1018no—
121#95—2022no—
122C24—1011no—
123C24C2×#8793811yescharacteristic
124C2×D4—1014no—
125C2×D4—2022no—
126C2×D4—2022no—
127C22×C4—1011no—
128C22×C4—1011no—
129C22×C4—1012no—
130C22×C4—1012no—
131C22×C4—1011no—
132C22×C4—4042no—
133C22×C4—4042no—
134C22×C4—2021no—
135C22×C4—2021no—
136C22×C4—2024no—
137C22×C4C2×#8793811yescharacteristic
138C22×C4C2×#8793811yescharacteristic
139C4⋊C4—2022no—
140C22⋊C4—22no—
141C22⋊C4—1018no—
142C22⋊C4—2022no—
143C22⋊C4—2024no—
144C42—4044no—
145C42—2021no—
146C42—2021no—
147C23—21no—
148C23—21no—
149C23—41no—
150C23—41no—
151C23—1012no—
152C23—1012no—
153C23—1012no—
154C23—4041no—
155C23—4041no—
156C23C4×#8793812yescomplemented
157C23C22×#8793811yescharacteristic
158D4—2028no—
159C2×C4—21no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—1011no—
163C2×C4—1012no—
164C2×C4—1011no—
165C2×C4—4042no—
166C2×C4—4042no—
167C2×C4—4044no—
168C2×C4—4044no—
169C2×C4—4042no—
170C2×C4—4041no—
171C2×C4—2024no—
172C2×C4—2022no—
173C2×C4—2028no—
174C2×C4—2021no—
175C2×C4—2021no—
176C2×C4—2021no—
177C2×C4C22⋊#8793812yes—
178C22—21no—
179C22—21no—
180C22—22no—
181C22—42no—
182C22—42no—
183C22—41no—
184C22—41no—
185C22—1014no—
186C22—4042no—
187C22—4042no—
188C22—2022no—
189C22—2022no—
190C22C2×C4×#8793811yescharacteristic
191C22C2×C22⋊#8793811yescharacteristic
192C22#1569233411yescharacteristic
193C4—22no—
194C4—41no—
195C4—1012no—
196C4—4048no—
197C4—4041no—
198C4—2022no—
199C4—2021no—
200C2—21no—
201C2—21no—
202C2—42no—
203C2—2024no—
204C2C4×C22⋊#8793811yescharacteristic
205C2D101⋊#9911yescharacteristic
206C2#2026615711yescharacteristic
subgroupG/H
centerC22C2×C22⋊#87938
commutatorC22×C101C2×C42
FrattiniC23C22×#87938
FittingC2×C22⋊C4×C101C4
socleC22×C101C2×C22⋊C4
prime radicalC22×C22⋊D101C22
cosocleC23×D101C23
hypercenterC2×C22⋊C4#87938
hypocenterC101C4×#99
LCSG ▷ C22×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
2. C4×C22⋊#87938C2semidirect
3. #20266055C2semidirect
7. #15692313C4semidirect
10. C23×Dic101C4semidirect
14. C2×#13108053C4semidirect
16. C2×C4×Dic101C4semidirect
17. C2×C22⋊C4×C101C4semidirect
20. C22⋊#87938C2×C4semidirect
47. C23×C101C42semidirect
69. C2×Dic101C42semidirect
95. Dic101#99semidirect
104. C101C4×#99semidirect
117. C2×C22⋊C4#87938semidirect
156. C23C4×#87938semidirect

Maximal subgroups

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

subgroupindex
C2×#156923132
C4×C22⋊#879382
#202660552
C2×#156922152
C4×#99101