Finite Group Databasebeta

← #27186539

Subgroups — #27186539

Order 12928.

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

normal subgroups only

This group has 326 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#20266149C211yesmaximal, characteristic, complemented
2#20266120C211yesmaximal, characteristic, complemented
3#20266029C214yesmaximal, complemented
4C2×#15692230C211yesmaximal, characteristic
5C2×#13108083—21no—
6C2×C22⋊#87938—21no—
7#15692312—21no—
8#15692312C2212yescomplemented
9(C2×#87938)⋊C4—21no—
10(C2×#87938)⋊C4C2212yescomplemented
11C22×D404—21no—
12C22×D404C411yescharacteristic, complemented
13C22×C4×D101C2211yescharacteristic
14#15692230—21no—
15#15692230—21no—
16#15692230C412yescomplemented
17#15692230C2212yes—
18C2×#13108051—21no—
19C2×C4⋊C4×C101C411yescharacteristic, complemented
20C22×#87938—22no—
21#13108083—42no—
22C2×#11717581—22no—
23C22⋊#87938—42no—
24C23×D101—21no—
25C23×D101D411yescharacteristic
26C2×D404—22no—
27C2×D404—22no—
28C2×D404—21no—
29C2×D404—42no—
30C2×D404—44no—
31C2×D404C2×C412yes—
32C22×Dic101D411yescharacteristic
33C2×C4×D101—42no—
34C2×C4×D101C2×C411yescharacteristic
35C2×C4×D101D411yescharacteristic
36C2×C4×D101D411yescharacteristic
37C2×C4×D101C2311yescharacteristic
38#13108051—22no—
39#13108051—22no—
40C22×C4×C101—21no—
41C22×C4×C101C2×C411yescharacteristic
42C4⋊C4×C101—21no—
43C4⋊C4×C101C2×C412yes—
44C23×C101C22⋊C411yescharacteristic
45C22×D101—22no—
46C22×D101—22no—
47C22×D101—22no—
48C22×D101—41no—
49C22×D101—42no—
50C22×D101—42no—
51C22×D101—42no—
52C22×D101C22⋊C411yescharacteristic
53C22×D101C2×D411yescharacteristic
54C2×#87938—42no—
55C2×#87938—42no—
56C2×#87938—42no—
57C2×C4×C101—22no—
58C2×C4×C101—22no—
59C2×C4×C101—42no—
60C2×C4×C101C22⋊C411yescharacteristic
61C2×C4×C101C22×C411yescharacteristic
62C2×Dic101—22no—
63C2×Dic101C22⋊C411yescharacteristic
64C2×Dic101C2×D411yescharacteristic
65D404—42no—
66D404—42no—
67D404—44no—
68D404—44no—
69C4×D101—41no—
70C4×D101—41no—
71C4×D101—41no—
72C4×D101—41no—
73#11717581—42no—
74C22×C101—21no—
75C22×C101—21no—
76C22×C101#9912yes—
77C22×C101C2×C22⋊C411yescharacteristic
78C2×D101—21no—
79C2×D101—21no—
80C2×D101—21no—
81C2×D101—21no—
82C2×D101—21no—
83C2×D101—44no—
84C2×D101—42no—
85C2×D101—42no—
86C2×D101—42no—
87C2×D101—84no—
88C2×D101AGL(1,ℤ/8)12yes—
89#87938—82no—
90C4×C101—21no—
91C4×C101—21no—
92C4×C101—42no—
93Dic101—21no—
94Dic101—21no—
95C2×C101—22no—
96C2×C101C2×#9911yescharacteristic
97C2×C101#41811yescharacteristic
98C2×C101#42111yescharacteristic
99D101—22no—
100D101—41no—
101D101—82no—
102#1510—1011nomaximal, Sylow
103C101#151011yescharacteristic, complemented, Sylow
104C2×#121—1011no—
105#407—1011no—
106#381—1011no—
107#327—1014no—
108C22×D4—1011no—
109C22×D4—2021no—
110C23×C4—1011no—
111C2×M16—2021no—
112#121—1012no—
113#121—1012no—
114#121—2021no—
115#121—2021no—
116C2×C4⋊C4#8793811yescharacteristic, complemented
117C2×C22⋊C4—2021no—
118C2×C22⋊C4—2021no—
119C22⋊C8—1012no—
120C22⋊C8—2021no—
121#95—1012no—
122#95—2021no—
123C24—1011no—
124C24—2021no—
125C2×D4—1012no—
126C2×D4—4042no—
127C2×D4—4044no—
128C2×D4—2022no—
129C2×D4—2022no—
130C2×D4—2021no—
131C22×C4—21no—
132C22×C4—1011no—
133C22×C4—1011no—
134C22×C4—1011no—
135C22×C4—1011no—
136C22×C4—1011no—
137C22×C4—4042no—
138C22×C4—2022no—
139C22×C4C2×#8793811yescharacteristic
140M16—4042no—
141C2×C8—2022no—
142C4⋊C4—21no—
143C4⋊C4C2×#8793812yes—
144C22⋊C4—4042no—
145C22⋊C4—2022no—
146C22⋊C4—2022no—
147C23—1011no—
148C23—1011no—
149C23—4042no—
150C23—4042no—
151C23—4041no—
152C23—4042no—
153C23—2022no—
154C23—2022no—
155C23—2022no—
156C23C22⋊#8793811yescharacteristic
157D4—4042no—
158D4—4042no—
159D4—4044no—
160D4—4044no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—42no—
164C2×C4—1011no—
165C2×C4—1011no—
166C2×C4—4041no—
167C2×C4—4041no—
168C2×C4—4041no—
169C2×C4—4041no—
170C2×C4—4042no—
171C2×C4—4042no—
172C2×C4—4042no—
173C2×C4—2022no—
174C2×C4C22⋊#8793811yescharacteristic
175C2×C4C22×#8793811yescharacteristic
176C8—4042no—
177C22—21no—
178C22—21no—
179C22—8084no—
180C22—1012no—
181C22—4044no—
182C22—4042no—
183C22—4042no—
184C22—4042no—
185C22—2021no—
186C22—2021no—
187C22—2021no—
188C22—2021no—
189C22—2021no—
190C22#1569231412yes—
191C22C2×C22⋊#8793811yescharacteristic
192C4—21no—
193C4—21no—
194C4—42no—
195C4—8082no—
196C4—2021no—
197C4—2021no—
198C2—22no—
199C2—8082no—
200C2—4041no—
201C2—2022no—
202C2C2×#1569231411yescharacteristic
203C2#2026616911yescharacteristic
204C2#2026617611yescharacteristic
subgroupG/H
centerC22C2×C22⋊#87938
commutatorC2×C4×C101C22×C4
FrattiniC2×C4C22×#87938
FittingC2×C4⋊C4×C101C4
socleC22×C101C2×C22⋊C4
prime radicalC2×#15692230C2
cosocleC2×C4×D101C23
hypercenterC2×C4⋊C4#87938
hypocenterC101#1510
LCSG ▷ C2×C4×C101 ▷ C22×C101 ▷ C101
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #20266149C2semidirect
2. #20266120C2semidirect
3. #20266029C2semidirect
8. #15692312C22semidirect
10. (C2×#87938)⋊C4C22semidirect
12. C22×D404C4semidirect
16. #15692230C4semidirect
19. C2×C4⋊C4×C101C4semidirect
103. C101#1510semidirect
116. C2×C4⋊C4#87938semidirect

Maximal subgroups

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

subgroupindex
#202661492
#202661202
#202660292
C2×#156922302
#1510101