Finite Group Databasebeta

← #27186400

Subgroups — #27186400

Order 12928.

280 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 60 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#20266023C212yesmaximal, complemented
4#20266021C212yesmaximal, complemented
5C2×#15692240C211yesmaximal, characteristic
6C2×#13108084—21no—
7C2×D101⋊C8—21no—
8#15692312—21no—
9#15692312—21no—
10C22⋊#11717581C2212yes—
11C22⋊#11717581C2212yes—
12C22×D404C411yescharacteristic
13C22×C4×D101C2211yescharacteristic
14#15692240—21no—
15#15692240—21no—
16#15692240—21no—
17#15692240—21no—
18C2×#13108053C2211yescharacteristic
19C2×#13108051C411yescharacteristic
20C2×#13108051C411yescharacteristic
21C2×#13108051C2211yescharacteristic
22C2×C4⋊C4×C101C411yescharacteristic
23#13108084—42no—
24D101⋊C8—42no—
25C2×#11717581—22no—
26C2×#11717581—22no—
27C23×D101C2×C411yescharacteristic
28C23×D101C2×C411yescharacteristic
29C2×D404—21no—
30C2×D404—21no—
31C2×D404—42no—
32C22×Dic101C2×C411yescharacteristic
33C22×Dic101C2311yescharacteristic
34C2×C4×D101—42no—
35C2×C4×D101D411yescharacteristic
36C2×C4×D101D411yescharacteristic
37C2×C4×D101D411yescharacteristic
38C2×C4×D101D411yescharacteristic
39#13108053—21no—
40#13108053—21no—
41#13108051—21no—
42#13108051—21no—
43#13108051—21no—
44#13108051—21no—
45#13108051—21no—
46#13108051—21no—
47C22×C4×C101C2×C411yescharacteristic
48C22×C4×C101C2×C411yescharacteristic
49C22×C4×C101C2×C411yescharacteristic
50C4⋊C4×C101—21no—
51C4⋊C4×C101—21no—
52C23×C101C22×C411yescharacteristic
53C22×D101—22no—
54C22×D101—22no—
55C22×D101—21no—
56C22×D101—22no—
57C22×D101—41no—
58C22×D101—41no—
59C22×D101—41no—
60C22×D101C22⋊C411yescharacteristic
61C22×D101C22⋊C411yescharacteristic
62C2×C4×C101—21no—
63C2×C4×C101—21no—
64C2×C4×C101—41no—
65C2×C4×C101—41no—
66C2×C4×C101—41no—
67C2×C4×C101C22⋊C411yescharacteristic
68C2×C4×C101C22⋊C411yescharacteristic
69C2×Dic101—21no—
70C2×Dic101—22no—
71C2×Dic101—41no—
72C2×Dic101C2×D411yescharacteristic
73C2×Dic101C2×D411yescharacteristic
74D404—42no—
75D404—42no—
76C4×D101—22no—
77C4×D101—22no—
78C4×D101—41no—
79C4×D101—41no—
80#11717581—42no—
81#11717581—42no—
82C22×C101—21no—
83C22×C101—21no—
84C22×C101C2×C22⋊C411yescharacteristic
85C22×C101#13112yes—
86C2×D101—21no—
87C2×D101—21no—
88C2×D101—21no—
89C2×D101—21no—
90C2×D101—21no—
91C2×D101—44no—
92C2×D101—41no—
93C2×D101—41no—
94C2×D101—41no—
95C2×D101—82no—
96C2×D101#9912yes—
97C4×C101—21no—
98C4×C101—21no—
99C4×C101—41no—
100C4×C101—41no—
101Dic101—21no—
102Dic101—21no—
103Dic101—41no—
104C2×C101—22no—
105C2×C101#40811yescharacteristic
106C2×C101C2×#9911yescharacteristic
107C2×C101#41311yescharacteristic
108D101—22no—
109D101—41no—
110D101—81no—
111#1468—1011nomaximal, Sylow
112C101#146811yescharacteristic, complemented, Sylow
113C2×#123—1011no—
114#407—1011no—
115C2×C22⋊C8—1011no—
116#324—1012no—
117#323—1012no—
118C22×D4—1011no—
119C23×C4—1011no—
120C2×M16—2021no—
121C22×C8—2021no—
122#123—2021no—
123#123—2021no—
124#123—2021no—
125#123—2021no—
126C2×C4⋊C4—1011no—
127C2×C4⋊C4#8793811yescharacteristic
128C2×C22⋊C4—1011no—
129C2×C22⋊C4—1011no—
130C2×C22⋊C4—1011no—
131C22⋊C8—1012no—
132C22⋊C8—1012no—
133C22⋊C8—2021no—
134C22⋊C8—2021no—
135C24—1011no—
136C24—1011no—
137C2×D4—4042no—
138C2×D4—2021no—
139C2×D4—2021no—
140C22×C4—1011no—
141C22×C4—1011no—
142C22×C4—1011no—
143C22×C4—1011no—
144C22×C4—1011no—
145C22×C4—1011no—
146C22×C4—4042no—
147C22×C4C2×#8793811yescharacteristic
148C22×C4C2×#8793811yescharacteristic
149C22×C4C2×#8793811yescharacteristic
150M16—4042no—
151C2×C8—4042no—
152C2×C8—2022no—
153C2×C8—2022no—
154C4⋊C4—21no—
155C4⋊C4—21no—
156C4⋊C4—2021no—
157C4⋊C4—2021no—
158C22⋊C4—2021no—
159C22⋊C4—2021no—
160C22⋊C4—2021no—
161C22⋊C4—2021no—
162C22⋊C4—2021no—
163C22⋊C4—2021no—
164C23—1011no—
165C23—1011no—
166C23—4041no—
167C23—4041no—
168C23—4041no—
169C23—2022no—
170C23—2022no—
171C23—2021no—
172C23—2022no—
173C23C22×#8793811yescharacteristic
174D4—4042no—
175D4—4042no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—41no—
179C2×C4—41no—
180C2×C4—41no—
181C2×C4—1011no—
182C2×C4—1011no—
183C2×C4—4041no—
184C2×C4—4041no—
185C2×C4—4041no—
186C2×C4—2022no—
187C2×C4—2022no—
188C2×C4—2021no—
189C2×C4—2022no—
190C2×C4C22⋊#8793811yescharacteristic
191C2×C4C22⋊#8793811yescharacteristic
192C8—4042no—
193C8—4042no—
194C22—21no—
195C22—21no—
196C22—8082no—
197C22—1012no—
198C22—4044no—
199C22—4041no—
200C22—4041no—
201C22—4041no—
202C22—2021no—
203C22—2021no—
204C22—2021no—
205C22—2021no—
206C22—2021no—
207C22C2×C22⋊#8793811yescharacteristic
208C22#1569234312yes—
209C4—21no—
210C4—21no—
211C4—41no—
212C4—41no—
213C4—4041no—
214C4—2021no—
215C4—2021no—
216C2—22no—
217C2—8081no—
218C2—4041no—
219C2—2022no—
220C2#2026615211yescharacteristic
221C2D101⋊#9911yescharacteristic
222C2#2026616311yescharacteristic
subgroupG/H
centerC22C2×C22⋊#87938
commutatorC23×C101C22×C4
FrattiniC23C22×#87938
FittingC2×C4⋊C4×C101C4
socleC22×C101C2×C22⋊C4
prime radicalC22×D404C4
cosocleC22×Dic101C23
hypercenterC2×C4⋊C4#87938
hypocenterC101#1468
LCSG ▷ C23×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. #20266148C2semidirect
2. D101⋊(C22⋊C8)C2semidirect
3. #20266023C2semidirect
4. #20266021C2semidirect
112. C101#1468semidirect

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
#202660212
C2×#156922402
#1468101