Finite Group Databasebeta

← #27186531

Subgroups — #27186531

Order 12928.

294 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 294 conjugacy classes of subgroups — too many to draw. Only its 64 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#20266148C211yesmaximal, characteristic
2C4×C22⋊#87938C211yesmaximal, characteristic
3#20266030C214yesmaximal, complemented
4C2×#15692235C211yesmaximal, characteristic
5C2×#13108084—21no—
6C2×C22⋊#87938—21no—
7C2×C4×#87938—21no—
8#15692312C2212yes—
9C22⋊#11717581—21no—
10(C2×#87938)⋊C4C2212yes—
11C22×Dic202C411yescharacteristic, complemented
12C22×C4×D101C2211yescharacteristic
13#15692235—21no—
14#15692235—21no—
15#15692235C412yescomplemented
16#15692235C2212yes—
17C2×C4⋊Dic101—21no—
18C2×#13108051—21no—
19C2×C4⋊C4×C101C411yescharacteristic, complemented
20C22×#87938—22no—
21#13108084—42no—
22C2×#11717581—22no—
23C22⋊#87938—24no—
24C4×#87938—42no—
25C23×D101D411yescharacteristic
26C2×Dic202—21no—
27C2×Dic202—42no—
28C2×Dic202C2×C412yes—
29C22×Dic101—21no—
30C22×Dic101D411yescharacteristic
31C2×C4×D101—42no—
32C2×C4×D101C2×C411yescharacteristic
33C2×C4×D101D411yescharacteristic
34C2×C4×D101D411yescharacteristic
35C2×C4×D101C2311yescharacteristic
36C4⋊Dic101—22no—
37C4⋊Dic101—22no—
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—41no—
48C22×D101C22⋊C411yescharacteristic
49C22×D101C2×D411yescharacteristic
50C2×#87938—24no—
51C2×#87938—42no—
52C2×#87938—42no—
53C2×C4×C101—22no—
54C2×C4×C101—22no—
55C2×C4×C101—42no—
56C2×C4×C101C22⋊C411yescharacteristic
57C2×C4×C101C22×C411yescharacteristic
58C2×Dic101—22no—
59C2×Dic101—41no—
60C2×Dic101—42no—
61C2×Dic101C22⋊C411yescharacteristic
62C2×Dic101C2×D411yescharacteristic
63C4×D101—22no—
64C4×D101—22no—
65C4×D101—41no—
66C4×D101—41no—
67Dic202—42no—
68Dic202—42no—
69#11717581—42no—
70C22×C101—21no—
71C22×C101—21no—
72C22×C101#10412yes—
73C22×C101C2×C22⋊C411yescharacteristic
74C2×D101—21no—
75C2×D101—21no—
76C2×D101—21no—
77C2×D101—21no—
78C2×D101—21no—
79C2×D101—44no—
80C2×D101#13712yes—
81#87938—44no—
82C4×C101—21no—
83C4×C101—42no—
84C4×C101#9912yes—
85Dic101—21no—
86Dic101—21no—
87Dic101—42no—
88C2×C101—22no—
89C2×C101C2×#9911yescharacteristic
90C2×C101#41911yescharacteristic
91C2×C101C2×#10411yescharacteristic
92D101—22no—
93D101—41no—
94#1508—1011nomaximal, Sylow
95C101#150811yescharacteristic, complemented, Sylow
96C2×C22⋊Q8—1011no—
97#407—1011no—
98C4×C22⋊C4—1011no—
99#328—1014no—
100C22×Q8—1011no—
101C23×C4—1011no—
102C2×M16—2021no—
103C22⋊Q8—1012no—
104C22⋊Q8—1012no—
105C22⋊Q8—2021no—
106C22⋊Q8—2021no—
107C2×C4⋊C4—2021no—
108C2×C4⋊C4#8793811yescharacteristic, complemented
109C2×C22⋊C4—2021no—
110C2×C22⋊C4—2021no—
111C2×C42—2021no—
112C22⋊C8—1012no—
113C22⋊C8—2021no—
114#95—1012no—
115C24—1011no—
116C2×Q8—1012no—
117C2×Q8—4042no—
118C2×Q8—2021no—
119C22×C4—21no—
120C22×C4—1011no—
121C22×C4—1011no—
122C22×C4—1011no—
123C22×C4—1011no—
124C22×C4—1011no—
125C22×C4—4042no—
126C22×C4—2022no—
127C22×C4—2021no—
128C22×C4C2×#8793811yescharacteristic
129M16—4042no—
130C2×C8—2022no—
131C4⋊C4—21no—
132C4⋊C4—2022no—
133C4⋊C4—2022no—
134C4⋊C4C2×#8793812yes—
135C22⋊C4—2022no—
136C22⋊C4—2022no—
137C22⋊C4—2024no—
138C42—4042no—
139C23—1011no—
140C23—1011no—
141C23—4041no—
142C23—2022no—
143C23—2022no—
144C23C22⋊#8793811yescharacteristic
145Q8—4042no—
146Q8—4042no—
147C2×C4—22no—
148C2×C4—22no—
149C2×C4—42no—
150C2×C4—1011no—
151C2×C4—1011no—
152C2×C4—4041no—
153C2×C4—4041no—
154C2×C4—4042no—
155C2×C4—4042no—
156C2×C4—4042no—
157C2×C4—4041no—
158C2×C4—2024no—
159C2×C4—2022no—
160C2×C4—2022no—
161C2×C4—2022no—
162C2×C4C22⋊#8793811yescharacteristic
163C2×C4C22×#8793811yescharacteristic
164C8—4042no—
165C22—21no—
166C22—21no—
167C22—1012no—
168C22—4044no—
169C22—2021no—
170C22—2021no—
171C22—2021no—
172C22—2021no—
173C22—2021no—
174C22#1569231912yes—
175C22C2×C22⋊#8793811yescharacteristic
176C4—21no—
177C4—42no—
178C4—4044no—
179C4—4042no—
180C4—2021no—
181C4—2021no—
182C4#1569231412yes—
183C2—22no—
184C2—4041no—
185C2—2022no—
186C2C2×#1569231411yescharacteristic
187C2#2026617011yescharacteristic
188C2C2×#1569231911yescharacteristic
subgroupG/H
centerC22C2×C22⋊#87938
commutatorC2×C4×C101C22×C4
FrattiniC2×C4C22×#87938
FittingC2×C4⋊C4×C101C4
socleC22×C101C2×C22⋊C4
prime radicalC23×D101D4
cosocleC2×C4×D101C23
hypercenterC2×C4⋊C4#87938
hypocenterC101#1508
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
3. #20266030C2semidirect
11. C22×Dic202C4semidirect
15. #15692235C4semidirect
19. C2×C4⋊C4×C101C4semidirect
95. C101#1508semidirect
108. C2×C4⋊C4#87938semidirect

Maximal subgroups

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

subgroupindex
#202661482
C4×C22⋊#879382
#202660302
C2×#156922352
#1508101