Finite Group Databasebeta

← #27186472

Subgroups — #27186472

Order 12928.

316 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 68 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#20266199C211yesmaximal, characteristic, complemented
2C4×#13108084C211yesmaximal, characteristic, complemented
3#20266025C212yesmaximal, complemented
4D4⋊#11717581C212yesmaximal, complemented
5C4×D4×D101C211yesmaximal, characteristic
6C2×#13108084—21no—
7C4⋊#11717581C2212yescomplemented
8#15692312—21no—
9#15692310—21no—
10#15692310—21no—
11C4×#11717581C2212yescomplemented
12C2×D4×D101C411yescharacteristic
13C22×C4×D101—21no—
14C4×D404C411yescharacteristic
15D4×Dic101C2211yescharacteristic
16#15692217C2211yescharacteristic
17C4×C22⋊D101—21no—
18#15692215—21no—
19C4⋊C4×D101C411yescharacteristic
20C22⋊C4×D101—21no—
21C42×D101C2211yescharacteristic
22C4×D4×C101C411yescharacteristic
23#13108084—24no—
24C2×#11717581—22no—
25C2×#11717581—22no—
26C23×D101—21no—
27C2×D404C2×C411yescharacteristic
28C2×C22⋊D101—21no—
29D4×D101—22no—
30D4×D101—22no—
31C22×Dic101—21no—
32C2×C4×D101—21no—
33C2×C4×D101—21no—
34C2×C4×D101—21no—
35C2×C4×D101—44no—
36C2×C4×D101C2×C411yescharacteristic
37C2×C4×D101D411yescharacteristic
38C2×C4×D101D411yescharacteristic
39C4⋊Dic101C2×C411yescharacteristic
40#13108053—21no—
41C22⋊Dic101—21no—
42#13108051—21no—
43#13108051—21no—
44C4×Dic101D411yescharacteristic
45C4×Dic101D411yescharacteristic
46C4×Dic101C2311yescharacteristic
47C2×D4×C101C2×C411yescharacteristic
48C22×C4×C101—21no—
49C4⋊C4×C101C2×C411yescharacteristic
50C22⋊C4×C101—21no—
51C42×C101C2×C411yescharacteristic
52C23×C101—21no—
53C22×D101—24no—
54C22×D101—21no—
55C22×D101—42no—
56C22×D101—42no—
57C22×D101C22⋊C411yescharacteristic
58D4×C101—21no—
59D4×C101M1612yescomplemented
60C2×C4×C101—21no—
61C2×C4×C101—42no—
62C2×C4×C101C22⋊C411yescharacteristic
63C2×C4×C101C22⋊C411yescharacteristic
64C2×C4×C101C22×C411yescharacteristic
65C22⋊D101—24no—
66C2×Dic101—21no—
67C2×Dic101—42no—
68C2×Dic101C22⋊C411yescharacteristic
69C2×Dic101C2×D411yescharacteristic
70C2×Dic101C2×D411yescharacteristic
71D404—21no—
72D404M1612yescomplemented
73C4×D101—22no—
74C4×D101—21no—
75C4×D101—21no—
76C4×D101—22no—
77C4×D101—42no—
78C4×D101—42no—
79C4×D101—42no—
80#11717581—24no—
81#11717581—42no—
82C22×C101—22no—
83C22×C101—41no—
84C22×C101—41no—
85C22×C101C2×C22⋊C411yescharacteristic
86C2×D101—21no—
87C2×D101—21no—
88C2×D101—22no—
89C2×D101—48no—
90C2×D101—41no—
91C2×D101—41no—
92C2×D101#10412yes—
93C4×C101—21no—
94C4×C101—21no—
95C4×C101—41no—
96C4×C101C2×M1611yescharacteristic
97C4×C101C2×M1611yescharacteristic
98Dic101—21no—
99Dic101—21no—
100Dic101—41no—
101Dic101AGL(1,ℤ/8)12yes—
102C2×C101—42no—
103C2×C101#40711yescharacteristic
104C2×C101#41811yescharacteristic
105C2×C101C2×#10411yescharacteristic
106D101—22no—
107D101—42no—
108#1490—1011nomaximal, Sylow
109C101#149011yescharacteristic, complemented, Sylow
110C2×C4×D4—1011no—
111#432—1011no—
112C4×M16—1011no—
113D4⋊C8—1012no—
114D4⋊C8—1012no—
115C22×D4—1011no—
116C23×C4—2021no—
117C2×M16—2021no—
118C4×D4—1011no—
119C4×D4—1011no—
120C4×D4—1011no—
121C4×D4—2021no—
122C4×D4—2021no—
123C4×D4#8793811yescharacteristic
124C2×C4⋊C4—1011no—
125C2×C22⋊C4—2021no—
126C2×C42—1011no—
127C4⋊C8—1012no—
128C22⋊C8—2021no—
129#97—2021no—
130#97—2021no—
131C4×C8—1012no—
132C24—2021no—
133C2×D4—1011no—
134C2×D4—2021no—
135C2×D4—2022no—
136C2×D4—2022no—
137C2×D4C2×#8793811yescharacteristic
138C22×C4—21no—
139C22×C4—1011no—
140C22×C4—1011no—
141C22×C4—1011no—
142C22×C4—4044no—
143C22×C4—2021no—
144C22×C4—2021no—
145C22×C4—2021no—
146C22×C4—2021no—
147M16—2024no—
148C2×C8—2022no—
149C2×C8—2022no—
150C4⋊C4—1011no—
151C4⋊C4—2021no—
152C4⋊C4C2×#8793811yescharacteristic
153C22⋊C4—21no—
154C22⋊C4—2021no—
155C22⋊C4—2021no—
156C22⋊C4—2021no—
157C42—1011no—
158C42—1011no—
159C42—1011no—
160C42C2×#8793811yescharacteristic
161C23—21no—
162C23—1011no—
163C23—4042no—
164C23—4042no—
165C23—2024no—
166C23—2021no—
167D4—21no—
168D4—1012no—
169D4—2024no—
170D4—2021no—
171D4#1310808412yescomplemented
172C2×C4—21no—
173C2×C4—42no—
174C2×C4—1011no—
175C2×C4—1011no—
176C2×C4—1011no—
177C2×C4—4042no—
178C2×C4—4042no—
179C2×C4—4042no—
180C2×C4—4042no—
181C2×C4—2022no—
182C2×C4—2022no—
183C2×C4—2021no—
184C2×C4—2021no—
185C2×C4—2021no—
186C2×C4C22⋊#8793811yescharacteristic
187C2×C4C22⋊#8793811yescharacteristic
188C2×C4C22×#8793811yescharacteristic
189C8—4042no—
190C8—2024no—
191C22—22no—
192C22—41no—
193C22—41no—
194C22—1012no—
195C22—4048no—
196C22—4041no—
197C22—4041no—
198C22—2022no—
199C22—2021no—
200C22—2021no—
201C22C2×C22⋊#8793811yescharacteristic
202C4—21no—
203C4—21no—
204C4—41no—
205C4—1012no—
206C4—4041no—
207C4—2021no—
208C4—2021no—
209C4D101⋊M1611yescharacteristic
210C4C2×#1310808411yescharacteristic
211C2—42no—
212C2—4042no—
213C2—2022no—
214C2#2026614811yescharacteristic
215C2#2026616911yescharacteristic
216C2D101⋊#10411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#87938
commutatorC2×C4×C101C22×C4
FrattiniC2×C4C22×#87938
FittingC4×D4×C101C4
socleC22×C101C2×C22⋊C4
prime radicalC2×D4×D101C4
cosocleC4×Dic101C23
hypercenterC4×D4#87938
hypocenterC101#1490
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #20266199C2semidirect
2. C4×#13108084C2semidirect
3. #20266025C2semidirect
4. D4⋊#11717581C2semidirect
7. C4⋊#11717581C22semidirect
11. C4×#11717581C22semidirect
59. D4×C101M16semidirect
72. D404M16semidirect
109. C101#1490semidirect
171. D4#13108084semidirect

Maximal subgroups

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

subgroupindex
#202661992
C4×#131080842
#202660252
D4⋊#117175812
C4×D4×D1012
#1490101