Finite Group Databasebeta

← #27186407

Subgroups — #27186407

Order 12928.

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

normal subgroups only

This group has 322 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, complemented
2D101⋊(C22⋊C8)C211yesmaximal, characteristic, complemented
3#20266020C214yesmaximal, complemented
4C2×#15692226C211yesmaximal, characteristic
5C2×#13108084—21no—
6C2×D101⋊C8—21no—
7#15692312—21no—
8#15692312—21no—
9C22⋊#11717581C2212yes—
10C22⋊#11717581C2212yes—
11C22×C22⋊D101C412yes—
12C22×C4×D101C2211yescharacteristic
13#15692226—21no—
14#15692226—21no—
15#15692226—21no—
16#15692226—21no—
17C2×C4⋊Dic101C411yescharacteristic
18C2×C22⋊Dic101C2212yes—
19C22×D4×C101C411yescharacteristic
20#13108084—42no—
21D101⋊C8—42no—
22C2×#11717581—22no—
23C2×#11717581—22no—
24C23×D101C2×C411yescharacteristic
25C2×C22⋊D101—22no—
26C2×C22⋊D101—22no—
27C2×C22⋊D101—44no—
28C22×Dic101C2×C412yes—
29C22×Dic101C2311yescharacteristic
30C2×C4×D101—42no—
31C2×C4×D101D411yescharacteristic
32C2×C4×D101D411yescharacteristic
33C2×C4×D101D411yescharacteristic
34C2×C4×D101D411yescharacteristic
35C4⋊Dic101—21no—
36C4⋊Dic101—21no—
37C22⋊Dic101—22no—
38C22⋊Dic101—22no—
39C24×C101C2×C412yes—
40C2×D4×C101—21no—
41C2×D4×C101—21no—
42C2×D4×C101—42no—
43C22×C4×C101C2×C411yescharacteristic
44C23×C101—22no—
45C23×C101—24no—
46C23×C101—42no—
47C23×C101—42no—
48C23×C101C22×C411yescharacteristic
49C22×D101—22no—
50C22×D101—22no—
51C22×D101—41no—
52C22×D101C22⋊C411yescharacteristic
53C22×D101C22⋊C411yescharacteristic
54D4×C101—42no—
55D4×C101—42no—
56C2×C4×C101—22no—
57C2×C4×C101C22⋊C411yescharacteristic
58C2×C4×C101C22⋊C411yescharacteristic
59C22⋊D101—44no—
60C22⋊D101—44no—
61C2×Dic101—22no—
62C2×Dic101—41no—
63C2×Dic101—42no—
64C2×Dic101C2×D411yescharacteristic
65C2×Dic101C2×D411yescharacteristic
66C4×D101—22no—
67C4×D101—22no—
68C4×D101—41no—
69C4×D101—41no—
70#11717581—42no—
71#11717581—42no—
72C22×C101—21no—
73C22×C101—21no—
74C22×C101—42no—
75C22×C101—42no—
76C22×C101—42no—
77C22×C101—84no—
78C22×C101C2×C22⋊C411yescharacteristic
79C22×C101#13112yes—
80C2×D101—21no—
81C2×D101—21no—
82C2×D101—21no—
83C2×D101—21no—
84C2×D101—21no—
85C2×D101—44no—
86C2×D101#10012yes—
87C4×C101—21no—
88C4×C101#9912yes—
89Dic101—21no—
90Dic101—21no—
91Dic101—42no—
92C2×C101—22no—
93C2×C101—82no—
94C2×C101#40811yescharacteristic
95C2×C101C2×#9911yescharacteristic
96C2×C101C2×#10011yescharacteristic
97D101—22no—
98D101—41no—
99#1471—1011nomaximal, Sylow
100C101#147111yescharacteristic, complemented, Sylow
101C2×#121—1011no—
102#407—1011no—
103C2×C22⋊C8—1011no—
104#323—1014no—
105C22×D4—1012no—
106C22×D4#8793811yescharacteristic
107C23×C4—1011no—
108C2×M16—2021no—
109C22×C8—2021no—
110#121—2021no—
111#121—2021no—
112#121—2021no—
113#121—2021no—
114C2×C4⋊C4—1011no—
115C2×C22⋊C4—1012no—
116C22⋊C8—1012no—
117C22⋊C8—1012no—
118C22⋊C8—2021no—
119C22⋊C8—2021no—
120C24—1011no—
121C24C2×#8793812yes—
122C2×D4—21no—
123C2×D4—21no—
124C2×D4—42no—
125C2×D4—4044no—
126C2×D4—2022no—
127C2×D4—2022no—
128C22×C4—1011no—
129C22×C4—1011no—
130C22×C4—1011no—
131C22×C4—1011no—
132C22×C4—1011no—
133C22×C4—1012no—
134C22×C4—4042no—
135C22×C4C2×#8793811yescharacteristic
136M16—4042no—
137C2×C8—4042no—
138C2×C8—2022no—
139C2×C8—2022no—
140C4⋊C4—2021no—
141C4⋊C4—2021no—
142C22⋊C4—2022no—
143C22⋊C4—2022no—
144C23—22no—
145C23—24no—
146C23—42no—
147C23—42no—
148C23—1011no—
149C23—1011no—
150C23—4041no—
151C23—2022no—
152C23—2022no—
153C23C22×#8793811yescharacteristic
154D4—42no—
155D4—42no—
156D4—4044no—
157D4—4044no—
158C2×C4—22no—
159C2×C4—1011no—
160C2×C4—1011no—
161C2×C4—4041no—
162C2×C4—4041no—
163C2×C4—4042no—
164C2×C4—4041no—
165C2×C4—2022no—
166C2×C4—2022no—
167C2×C4—2022no—
168C2×C4C22⋊#8793811yescharacteristic
169C2×C4C22⋊#8793811yescharacteristic
170C8—4042no—
171C8—4042no—
172C22—21no—
173C22—21no—
174C22—42no—
175C22—42no—
176C22—42no—
177C22—84no—
178C22—1012no—
179C22—4044no—
180C22—2021no—
181C22—2021no—
182C22—2021no—
183C22—2021no—
184C22—2021no—
185C22C2×C22⋊#8793811yescharacteristic
186C22#1569234212yes—
187C4—21no—
188C4—4042no—
189C4—2021no—
190C4—2021no—
191C4#1569231312yes—
192C2—22no—
193C2—82no—
194C2—4041no—
195C2—2022no—
196C2#2026615111yescharacteristic
197C2C2×#1569231311yescharacteristic
198C2D101⋊#10011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#87938
commutatorC23×C101C22×C4
FrattiniC23C22×#87938
FittingC22×D4×C101C4
socleC22×C101C2×C22⋊C4
prime radicalC2×#15692226C2
cosocleC22×Dic101C23
hypercenterC22×D4#87938
hypocenterC101#1471
LCSG ▷ C23×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. #20266148C2semidirect
2. D101⋊(C22⋊C8)C2semidirect
3. #20266020C2semidirect
100. C101#1471semidirect

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
#202660202
C2×#156922262
#1471101