Finite Group Databasebeta

← #27186459

Subgroups — #27186459

Order 12928.

312 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 74 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#20266194C211yesmaximal, characteristic, complemented
2#20266180C211yesmaximal, characteristic, complemented
3#20266025C214yesmaximal, complemented
4C2×#15692217C211yesmaximal, characteristic
5C2×#13108083—21no—
6#15692322—21no—
7#15692322—21no—
8C4⋊#11717581C2212yescomplemented
9C22⋊#11717581—21no—
10C4×#11717581C2212yescomplemented
11C22×D404C411yescharacteristic
12C22×C4×D101—21no—
13#15692217—21no—
14#15692217—21no—
15#15692217C412yes—
16#15692217C2212yes—
17C2×#13108051—21no—
18C2×C4×Dic101C2211yescharacteristic
19C2×C4⋊C4×C101C411yescharacteristic
20#13108083—42no—
21C2×#11717581—22no—
22C2×#11717581—22no—
23C23×D101—21no—
24C2×D404—21no—
25C2×D404—24no—
26C2×D404C2×C412yes—
27C22×Dic101D411yescharacteristic
28C22×Dic101D411yescharacteristic
29C2×C4×D101—22no—
30C2×C4×D101—22no—
31C2×C4×D101—42no—
32C2×C4×D101—42no—
33#13108051—22no—
34#13108051—22no—
35C4×Dic101C2×C411yescharacteristic
36C4×Dic101D411yescharacteristic
37C4×Dic101D411yescharacteristic
38C4×Dic101C2311yescharacteristic
39C22×C4×C101—21no—
40C22×C4×C101C2×C411yescharacteristic
41C4⋊C4×C101—21no—
42C4⋊C4×C101C2×C412yes—
43C23×C101C22⋊C411yescharacteristic
44C22×D101—24no—
45C22×D101—22no—
46C22×D101—42no—
47C22×D101—42no—
48C2×C4×C101—22no—
49C2×C4×C101—22no—
50C2×C4×C101—42no—
51C2×C4×C101C22⋊C411yescharacteristic
52C2×C4×C101C22×C411yescharacteristic
53C2×Dic101—41no—
54C2×Dic101C22⋊C411yescharacteristic
55C2×Dic101C22⋊C411yescharacteristic
56C2×Dic101D812yes—
57C2×Dic101SD1612yes—
58C2×Dic101C2×D411yescharacteristic
59C2×Dic101C2×D411yescharacteristic
60D404—24no—
61D404—22no—
62D404M1614yescomplemented
63C4×D101—44no—
64C4×D101—42no—
65C4×D101—42no—
66#11717581—42no—
67#11717581—42no—
68C22×C101—21no—
69C22×C101—21no—
70C22×C101#10212yes—
71C22×C101C2×C22⋊C411yescharacteristic
72C2×D101—24no—
73C2×D101—48no—
74C2×D101—42no—
75C2×D101—42no—
76C4×C101—21no—
77C4×C101—42no—
78C4×C101C2×M1612yes—
79Dic101—21no—
80Dic101—21no—
81Dic101#10212yes—
82Dic101C2×D811yescharacteristic
83Dic101C2×SD1611yescharacteristic
84C2×C101—22no—
85C2×C101#40711yescharacteristic
86C2×C101C2×#10211yescharacteristic
87C2×C101#42111yescharacteristic
88D101—44no—
89#1486—1011nomaximal, Sylow
90C101#148611yescharacteristic, complemented, Sylow
91C2×C4×D4—1011no—
92#431—1011no—
93#423—1011no—
94D4⋊C8—1014no—
95C22×D4—1011no—
96C23×C4—2021no—
97C2×M16—2021no—
98C4×D4—1012no—
99C4×D4—1012no—
100C4×D4—2021no—
101C4×D4—2021no—
102C2×C4⋊C4#8793811yescharacteristic
103C2×C22⋊C4—2021no—
104C2×C42—1011no—
105C4⋊C8—1012no—
106C4⋊C8—2021no—
107C4⋊C8—2021no—
108C22⋊C8—2021no—
109C4×C8—1012no—
110C24—2021no—
111C2×D4—1012no—
112C2×D4—2024no—
113C2×D4—2021no—
114C22×C4—21no—
115C22×C4—1011no—
116C22×C4—1011no—
117C22×C4—4042no—
118C22×C4—4042no—
119C22×C4—2022no—
120C22×C4—2022no—
121C22×C4C2×#8793811yescharacteristic
122M16—4042no—
123C2×C8—2022no—
124C2×C8—2022no—
125C4⋊C4—21no—
126C4⋊C4C2×#8793812yes—
127C22⋊C4—2022no—
128C22⋊C4—2022no—
129C42—1011no—
130C42—1011no—
131C42—1011no—
132C42—1011no—
133C23—4042no—
134C23—4042no—
135C23—2024no—
136C23—2022no—
137C23C22⋊#8793811yescharacteristic
138D4—1014no—
139D4—2024no—
140D4—2022no—
141C2×C4—22no—
142C2×C4—22no—
143C2×C4—42no—
144C2×C4—1012no—
145C2×C4—1012no—
146C2×C4—1011no—
147C2×C4—1011no—
148C2×C4—1011no—
149C2×C4—1011no—
150C2×C4—4042no—
151C2×C4—4044no—
152C2×C4—4042no—
153C2×C4—4041no—
154C2×C4C22⋊#8793811yescharacteristic
155C2×C4C22×#8793811yescharacteristic
156C8—4042no—
157C8—4042no—
158C22—21no—
159C22—21no—
160C22—4048no—
161C22—4042no—
162C22—4042no—
163C22—2024no—
164C22#1569231712yes—
165C22C2×C22⋊#8793811yescharacteristic
166C4—21no—
167C4—42no—
168C4—1011no—
169C4—1012no—
170C4—1011no—
171C4—2021no—
172C4—2021no—
173C4D101⋊M1612yes—
174C2—22no—
175C2—4044no—
176C2#2026614911yescharacteristic
177C2C2×#1569231711yescharacteristic
178C2#2026617611yescharacteristic
subgroupG/H
centerC22C2×C22⋊#87938
commutatorC2×C4×C101C22×C4
FrattiniC2×C4C22×#87938
FittingC2×C4⋊C4×C101C4
socleC22×C101C2×C22⋊C4
prime radicalC22×D404C4
cosocleC4×Dic101C23
hypercenterC2×C4⋊C4#87938
hypocenterC101#1486
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #20266194C2semidirect
2. #20266180C2semidirect
3. #20266025C2semidirect
8. C4⋊#11717581C22semidirect
10. C4×#11717581C22semidirect
62. D404M16semidirect
90. C101#1486semidirect

Maximal subgroups

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

subgroupindex
#202661942
#202661802
#202660252
C2×#156922172
#1486101