Finite Group Databasebeta

← #27186412

Subgroups — #27186412

Order 12928.

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

normal subgroups only

This group has 270 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
2D101⋊(C22⋊C8)C211yesmaximal, characteristic
3#20266023C214yesmaximal, complemented
4C2×#15692231C211yesmaximal, characteristic
5C2×#13108084—21no—
6C2×D101⋊C8—21no—
7#15692312—21no—
8#15692312—21no—
9C22⋊#11717581C2212yes—
10C22⋊#11717581C2212yes—
11C22×C4×D101C2211yescharacteristic
12#15692231—21no—
13#15692231—21no—
14#15692231—21no—
15#15692231—21no—
16C2×C4⋊Dic101C411yescharacteristic
17C2×#13108053C2212yes—
18C2×#13108051C412yes—
19C22×Q8×C101C411yescharacteristic
20#13108084—42no—
21D101⋊C8—42no—
22C2×#11717581—22no—
23C2×#11717581—22no—
24C23×D101C2×C411yescharacteristic
25C22×Dic101C2×C412yes—
26C22×Dic101C2311yescharacteristic
27C2×C4×D101—42no—
28C2×C4×D101D411yescharacteristic
29C2×C4×D101D411yescharacteristic
30C2×C4×D101D411yescharacteristic
31C2×C4×D101D411yescharacteristic
32C4⋊Dic101—21no—
33C4⋊Dic101—21no—
34#13108053—22no—
35#13108053—22no—
36#13108051—22no—
37#13108051—22no—
38C2×Q8×C101—21no—
39C2×Q8×C101—21no—
40C2×Q8×C101—42no—
41C22×C4×C101C2×C412yes—
42C22×C4×C101C2×C411yescharacteristic
43C23×C101C22×C411yescharacteristic
44C22×D101—22no—
45C22×D101—22no—
46C22×D101—41no—
47C22×D101C22⋊C411yescharacteristic
48C22×D101C22⋊C411yescharacteristic
49Q8×C101—42no—
50Q8×C101—42no—
51C2×C4×C101—22no—
52C2×C4×C101—22no—
53C2×C4×C101—42no—
54C2×C4×C101C22⋊C411yescharacteristic
55C2×C4×C101C22⋊C411yescharacteristic
56C2×Dic101—22no—
57C2×Dic101—24no—
58C2×Dic101—41no—
59C2×Dic101C2×D411yescharacteristic
60C2×Dic101C2×D411yescharacteristic
61C4×D101—22no—
62C4×D101—22no—
63C4×D101—41no—
64C4×D101—41no—
65#11717581—42no—
66#11717581—42no—
67C22×C101—21no—
68C22×C101—21no—
69C22×C101C2×C22⋊C411yescharacteristic
70C22×C101#13112yes—
71C2×D101—21no—
72C2×D101—21no—
73C2×D101—21no—
74C2×D101—21no—
75C2×D101—21no—
76C2×D101—44no—
77C2×D101#10112yes—
78C4×C101—21no—
79C4×C101—42no—
80C4×C101#9912yes—
81Dic101—21no—
82Dic101—21no—
83Dic101—42no—
84C2×C101—22no—
85C2×C101#40811yescharacteristic
86C2×C101C2×#9911yescharacteristic
87C2×C101C2×#10111yescharacteristic
88D101—22no—
89D101—41no—
90#1472—1011nomaximal, Sylow
91C101#147211yescharacteristic, complemented, Sylow
92C2×C22⋊Q8—1011no—
93#407—1011no—
94C2×C22⋊C8—1011no—
95#324—1014no—
96C22×Q8#8793811yescharacteristic
97C23×C4—1011no—
98C2×M16—2021no—
99C22×C8—2021no—
100C22⋊Q8—2021no—
101C22⋊Q8—2021no—
102C22⋊Q8—2021no—
103C22⋊Q8—2021no—
104C2×C4⋊C4—1012no—
105C2×C4⋊C4—1011no—
106C2×C22⋊C4—1012no—
107C22⋊C8—1012no—
108C22⋊C8—1012no—
109C22⋊C8—2021no—
110C22⋊C8—2021no—
111C24—1011no—
112C2×Q8—21no—
113C2×Q8—21no—
114C2×Q8—42no—
115C22×C4—1011no—
116C22×C4—1011no—
117C22×C4—1011no—
118C22×C4—1011no—
119C22×C4—1011no—
120C22×C4—1012no—
121C22×C4—4042no—
122C22×C4C2×#8793812yes—
123C22×C4C2×#8793811yescharacteristic
124M16—4042no—
125C2×C8—4042no—
126C2×C8—2022no—
127C2×C8—2022no—
128C4⋊C4—2022no—
129C4⋊C4—2022no—
130C4⋊C4—2021no—
131C4⋊C4—2021no—
132C22⋊C4—2022no—
133C22⋊C4—2022no—
134C23—1011no—
135C23—1011no—
136C23—4041no—
137C23—2022no—
138C23—2022no—
139C23C22×#8793811yescharacteristic
140Q8—42no—
141Q8—42no—
142C2×C4—22no—
143C2×C4—22no—
144C2×C4—42no—
145C2×C4—1011no—
146C2×C4—1011no—
147C2×C4—4041no—
148C2×C4—4041no—
149C2×C4—4041no—
150C2×C4—2022no—
151C2×C4—2024no—
152C2×C4—2022no—
153C2×C4—2022no—
154C2×C4C22⋊#8793811yescharacteristic
155C2×C4C22⋊#8793811yescharacteristic
156C8—4042no—
157C8—4042no—
158C22—21no—
159C22—21no—
160C22—1012no—
161C22—4044no—
162C22—2021no—
163C22—2021no—
164C22—2021no—
165C22—2021no—
166C22—2021no—
167C22C2×C22⋊#8793811yescharacteristic
168C22#1569234312yes—
169C4—21no—
170C4—42no—
171C4—4042no—
172C4—2021no—
173C4—2021no—
174C4#1569231312yes—
175C2—22no—
176C2—4041no—
177C2—2022no—
178C2#2026615211yescharacteristic
179C2C2×#1569231311yescharacteristic
180C2D101⋊#10111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#87938
commutatorC23×C101C22×C4
FrattiniC23C22×#87938
FittingC22×Q8×C101C4
socleC22×C101C2×C22⋊C4
prime radicalC23×D101C2×C4
cosocleC22×Dic101C23
hypercenterC22×Q8#87938
hypocenterC101#1472
LCSG ▷ C23×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
3. #20266023C2semidirect
91. C101#1472semidirect

Maximal subgroups

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

subgroupindex
#202661482
D101⋊(C22⋊C8)2
#202660232
C2×#156922312
#1472101