Finite Group Databasebeta

← #27186371

Subgroups — #27186371

Order 12928.

312 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 80 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#20266194C212yesmaximal, complemented
2#20266021C212yesmaximal, complemented
3#20266020C212yesmaximal, complemented
4C2×C4×C22⋊D101C211yesmaximal, characteristic
5#15692322—22no—
6C22⋊#11717581C2214yes—
7C4×#11717581—22no—
8C22×C22⋊D101C411yescharacteristic
9C22×C4×D101C411yescharacteristic
10C4×C22⋊D101—22no—
11C4×C22⋊D101—22no—
12C2×#13108053C411yescharacteristic
13C2×C22⋊Dic101C2211yescharacteristic
14C2×#13108051C2211yescharacteristic
15C2×C4×Dic101C2211yescharacteristic
16C23×C4×C101C411yescharacteristic
17C2×#11717581—24no—
18C23×D101C2×C411yescharacteristic
19C2×C22⋊D101—22no—
20C2×C22⋊D101—22no—
21C2×C22⋊D101C814yescomplemented
22C22×Dic101C2×C411yescharacteristic
23C22×Dic101C2×C411yescharacteristic
24C22×Dic101C2311yescharacteristic
25C2×C4×D101—21no—
26C2×C4×D101—21no—
27C2×C4×D101—42no—
28#13108053—22no—
29C22⋊Dic101—22no—
30#13108051—22no—
31C4×Dic101D412yes—
32C4×Dic101D412yes—
33C24×C101C2×C411yescharacteristic
34C22×C4×C101—21no—
35C22×C4×C101—21no—
36C22×C4×C101—42no—
37C22×C4×C101C2×C411yescharacteristic
38C22×C4×C101C2×C411yescharacteristic
39C23×C101—21no—
40C23×C101—21no—
41C23×C101—41no—
42C23×C101—41no—
43C23×C101C2×C812yes—
44C23×C101C22×C411yescharacteristic
45C22×D101—21no—
46C22×D101—21no—
47C22×D101—41no—
48C22×D101—41no—
49C22×D101C2×C812yes—
50C2×C4×C101—22no—
51C2×C4×C101—21no—
52C2×C4×C101—42no—
53C2×C4×C101—42no—
54C2×C4×C101—41no—
55C2×C4×C101C22⋊C411yescharacteristic
56C2×C4×C101C22⋊C411yescharacteristic
57C22⋊D101—28no—
58C2×Dic101—21no—
59C2×Dic101—41no—
60C2×Dic101—41no—
61C2×Dic101C22⋊C412yes—
62C2×Dic101C2×C812yes—
63C2×Dic101M1612yes—
64C2×Dic101C2×D412yes—
65C4×D101—42no—
66C4×D101—42no—
67#11717581—44no—
68C22×C101—21no—
69C22×C101—21no—
70C22×C101—22no—
71C22×C101—42no—
72C22×C101—42no—
73C22×C101—41no—
74C22×C101—41no—
75C22×C101C2×C22⋊C411yescharacteristic
76C22×C101C22×C811yescharacteristic
77C22×C101C2×M1611yescharacteristic
78C2×D101—22no—
79C2×D101—42no—
80C2×D101—41no—
81C2×D101—41no—
82C2×D101—42no—
83C4×C101—21no—
84C4×C101—41no—
85C4×C101#10012yes—
86Dic101—22no—
87Dic101—41no—
88Dic101C22⋊C814yes—
89C2×C101—21no—
90C2×C101—21no—
91C2×C101—42no—
92C2×C101C2×C22⋊C811yescharacteristic
93C2×C101#41011yescharacteristic
94C2×C101C2×#10011yescharacteristic
95D101—42no—
96#1460—1011nomaximal, Sylow
97C101#146011yescharacteristic, complemented, Sylow
98C2×C4×D4—1011no—
99#431—1012no—
100#323—1012no—
101#323—1012no—
102C22×D4—1011no—
103C23×C4—1011no—
104C23×C4#8793811yescharacteristic
105C4×D4—2022no—
106C4×D4—2022no—
107C2×C4⋊C4—1011no—
108C2×C22⋊C4—1011no—
109C2×C22⋊C4—1011no—
110C2×C42—1011no—
111C4⋊C8—2022no—
112C22⋊C8—1014no—
113C4×C8—2022no—
114C24—1011no—
115C24C2×#8793811yescharacteristic
116C2×D4—1014no—
117C2×D4—2022no—
118C2×D4—2022no—
119C22×C4—21no—
120C22×C4—21no—
121C22×C4—42no—
122C22×C4—1011no—
123C22×C4—1011no—
124C22×C4—1011no—
125C22×C4—4042no—
126C22×C4—2021no—
127C22×C4—2021no—
128C22×C4C2×#8793811yescharacteristic
129C22×C4C2×#8793811yescharacteristic
130C2×C8—2024no—
131C4⋊C4—2022no—
132C22⋊C4—2022no—
133C22⋊C4—2022no—
134C42—1012no—
135C42—1012no—
136C23—21no—
137C23—21no—
138C23—41no—
139C23—41no—
140C23—1012no—
141C23—4041no—
142C23—4041no—
143C23—2021no—
144C23—2021no—
145C23D101⋊C812yes—
146C23C22×#8793811yescharacteristic
147D4—2028no—
148C2×C4—22no—
149C2×C4—21no—
150C2×C4—42no—
151C2×C4—42no—
152C2×C4—41no—
153C2×C4—1012no—
154C2×C4—1012no—
155C2×C4—1012no—
156C2×C4—1012no—
157C2×C4—4042no—
158C2×C4—4042no—
159C2×C4—4041no—
160C2×C4—4041no—
161C2×C4—2021no—
162C2×C4C22⋊#8793811yescharacteristic
163C2×C4C22⋊#8793811yescharacteristic
164C8—4044no—
165C22—21no—
166C22—21no—
167C22—22no—
168C22—42no—
169C22—42no—
170C22—41no—
171C22—41no—
172C22—4042no—
173C22—4042no—
174C22—4041no—
175C22—4041no—
176C22—2022no—
177C22C2×C22⋊#8793811yescharacteristic
178C22C2×D101⋊C811yescharacteristic
179C22D101⋊M1611yescharacteristic
180C4—21no—
181C4—41no—
182C4—1014no—
183C4—4041no—
184C4—2022no—
185C4#1569231512yes—
186C2—21no—
187C2—21no—
188C2—42no—
189C2—4042no—
190C2D101⋊(C22⋊C8)11yescharacteristic
191C2#2026615611yescharacteristic
192C2C2×#1569231511yescharacteristic
subgroupG/H
centerC2×C4C22⋊#87938
commutatorC22×C101C22×C8
FrattiniC23C22×#87938
FittingC23×C4×C101C4
socleC22×C101C2×C22⋊C4
prime radicalC22×C22⋊D101C4
cosocleC22×Dic101C23
hypercenterC23×C4#87938
hypocenterC101#1460
LCSG ▷ C22×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. #20266194C2semidirect
2. #20266021C2semidirect
3. #20266020C2semidirect
21. C2×C22⋊D101C8semidirect
97. C101#1460semidirect

Maximal subgroups

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

subgroupindex
#202661942
#202660212
#202660202
C2×C4×C22⋊D1012
#1460101