Finite Group Databasebeta

← #27186397

Subgroups — #27186397

Order 12928.

280 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 62 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#20266147C211yesmaximal, characteristic, complemented
2C2×C22⋊#11717581C211yesmaximal, characteristic, complemented
3#20266023C212yesmaximal, complemented
4#20266020C212yesmaximal, complemented
5C2×#15692236C211yesmaximal, characteristic
6C2×#13108083—21no—
7C22×#11717581—21no—
8C22⋊#11717581—21no—
9C22⋊#11717581—21no—
10C22⋊#11717581C2212yes—
11C22⋊#11717581C2212yes—
12C23×Dic101C2211yescharacteristic
13#15692236—21no—
14#15692236—21no—
15#15692236—21no—
16#15692236—21no—
17C2×#13108053C411yescharacteristic
18C2×#13108053C2211yescharacteristic
19C2×C22⋊Dic101C411yescharacteristic
20C2×C22⋊Dic101C411yescharacteristic
21C2×C22⋊Dic101C2211yescharacteristic
22C22×D4×C101C411yescharacteristic
23#13108083—42no—
24C2×#11717581—22no—
25C2×#11717581—22no—
26C2×#11717581—42no—
27C22×Dic101—42no—
28C22×Dic101C2×C411yescharacteristic
29C22×Dic101C2×C411yescharacteristic
30C22×Dic101C2×C411yescharacteristic
31C22×Dic101D411yescharacteristic
32C22×Dic101D411yescharacteristic
33C22×Dic101D411yescharacteristic
34C22×Dic101D411yescharacteristic
35C22×Dic101C2311yescharacteristic
36#13108053—21no—
37#13108053—21no—
38#13108053—21no—
39#13108053—21no—
40C22⋊Dic101—21no—
41C22⋊Dic101—21no—
42C22⋊Dic101—21no—
43C22⋊Dic101—21no—
44C22⋊Dic101—21no—
45C22⋊Dic101—21no—
46C24×C101C2×C411yescharacteristic
47C24×C101C2×C411yescharacteristic
48C2×D4×C101—21no—
49C2×D4×C101—21no—
50C2×D4×C101—42no—
51C22×C4×C101C2×C411yescharacteristic
52C23×C101—22no—
53C23×C101—22no—
54C23×C101—21no—
55C23×C101—22no—
56C23×C101—41no—
57C23×C101—41no—
58C23×C101—41no—
59C23×C101C22⋊C411yescharacteristic
60C23×C101C22⋊C411yescharacteristic
61C23×C101C22×C411yescharacteristic
62D4×C101—42no—
63D4×C101—42no—
64C2×C4×C101—21no—
65C2×C4×C101—41no—
66C2×Dic101—22no—
67C2×Dic101—22no—
68C2×Dic101—21no—
69C2×Dic101—21no—
70C2×Dic101—22no—
71C2×Dic101—41no—
72C2×Dic101—41no—
73C2×Dic101—41no—
74C2×Dic101—41no—
75C2×Dic101—41no—
76C2×Dic101C22⋊C411yescharacteristic
77C2×Dic101C22⋊C411yescharacteristic
78C2×Dic101C2×D411yescharacteristic
79C2×Dic101C2×D411yescharacteristic
80#11717581—42no—
81#11717581—42no—
82C22×C101—21no—
83C22×C101—21no—
84C22×C101—21no—
85C22×C101—21no—
86C22×C101—21no—
87C22×C101—21no—
88C22×C101—21no—
89C22×C101—44no—
90C22×C101—41no—
91C22×C101—41no—
92C22×C101—41no—
93C22×C101—82no—
94C22×C101#9912yes—
95C22×C101C2×C22⋊C411yescharacteristic
96C22×C101#13112yes—
97C4×C101—41no—
98Dic101—21no—
99Dic101—21no—
100Dic101—21no—
101Dic101—21no—
102Dic101—41no—
103Dic101—41no—
104C2×C101—22no—
105C2×C101—22no—
106C2×C101—41no—
107C2×C101—81no—
108C2×C101#40811yescharacteristic
109C2×C101C2×#9911yescharacteristic
110C2×C101#41311yescharacteristic
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#8793811yescharacteristic
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—1011no—
128C2×C22⋊C4—1011no—
129C2×C22⋊C4—1011no—
130C2×C22⋊C4—1011no—
131C22⋊C8—1012no—
132C22⋊C8—1012no—
133C22⋊C8—2021no—
134C22⋊C8—2021no—
135C24C2×#8793811yescharacteristic
136C24C2×#8793811yescharacteristic
137C2×D4—21no—
138C2×D4—21no—
139C2×D4—42no—
140C22×C4—1011no—
141C22×C4—1011no—
142C22×C4—1011no—
143C22×C4—1011no—
144C22×C4—1011no—
145C22×C4—1011no—
146C22×C4—1011no—
147C22×C4—1011no—
148C22×C4—4042no—
149C22×C4C2×#8793811yescharacteristic
150M16—4042no—
151C2×C8—4042no—
152C2×C8—2022no—
153C2×C8—2022no—
154C4⋊C4—2021no—
155C4⋊C4—2021no—
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—22no—
165C23—22no—
166C23—21no—
167C23—22no—
168C23—41no—
169C23—41no—
170C23—41no—
171C23C22⋊#8793811yescharacteristic
172C23C22⋊#8793811yescharacteristic
173C23C22×#8793811yescharacteristic
174D4—42no—
175D4—42no—
176C2×C4—21no—
177C2×C4—41no—
178C2×C4—1011no—
179C2×C4—1011no—
180C2×C4—1011no—
181C2×C4—1011no—
182C2×C4—4041no—
183C2×C4—4041no—
184C2×C4—4041no—
185C2×C4—4041no—
186C2×C4—4041no—
187C2×C4—2021no—
188C2×C4—2021no—
189C2×C4—2022no—
190C2×C4—2022no—
191C2×C4—2022no—
192C8—4042no—
193C8—4042no—
194C22—21no—
195C22—21no—
196C22—21no—
197C22—21no—
198C22—21no—
199C22—21no—
200C22—21no—
201C22—44no—
202C22—41no—
203C22—41no—
204C22—41no—
205C22—82no—
206C22#1569231312yes—
207C22C2×C22⋊#8793811yescharacteristic
208C22#1569234212yes—
209C4—41no—
210C4—4041no—
211C4—4041no—
212C4—2021no—
213C4—2021no—
214C4—2021no—
215C4—2021no—
216C2—22no—
217C2—22no—
218C2—41no—
219C2—81no—
220C2#2026615011yescharacteristic
221C2C2×#1569231311yescharacteristic
222C2#2026616411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#87938
commutatorC23×C101C22×C4
FrattiniC23C22×#87938
Fitting, prime radicalC22×D4×C101C4
socleC22×C101C2×C22⋊C4
cosocleC22×Dic101C23
hypercenterC22×D4#87938
hypocenterC101#1468
LCSG ▷ C23×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C24 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. #20266147C2semidirect
2. C2×C22⋊#11717581C2semidirect
3. #20266023C2semidirect
4. #20266020C2semidirect
112. C101#1468semidirect

Maximal subgroups

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

subgroupindex
#202661472
C2×C22⋊#117175812
#202660232
#202660202
C2×#156922362
#1468101