Finite Group Databasebeta

← #27186574

Subgroups — #27186574

Order 12928.

218 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 56 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#20266195C211yesmaximal, characteristic, complemented
2#20266122C211yesmaximal, characteristic, complemented
3#20266030C212yesmaximal, complemented
4#20266028C212yesmaximal
5#20265709C211yesmaximal, characteristic
6#15692322—21no—
7#15692312C2212yes—
8C4×#11717581—21no—
9(C2×#87938)⋊C4—21no—
10(C2×#87938)⋊C4—21no—
11(C2×#87938)⋊C4C2212yes—
12#15692248—21no—
13#15692246C411yescharacteristic, complemented
14#15692242C411yescharacteristic, complemented
15#15692237—21no—
16#15692235C2211yescharacteristic
17#15692226C2211yescharacteristic
18C4×Dic202C411yescharacteristic, complemented
19C4×C22⋊D101—21no—
20#15692214—21no—
21C42×D101C2211yescharacteristic
22C4×D4×C101C411yescharacteristic, complemented
23C22×#87938—22no—
24C2×#11717581—22no—
25C2×Dic202C2×C411yescharacteristic
26C2×C22⋊D101—21no—
27C2×C4×D101D411yescharacteristic
28C2×C4×D101D411yescharacteristic
29C2×C4×D101C2311yescharacteristic
30C4⋊Dic101—21no—
31C4⋊Dic101—21no—
32C4⋊Dic101C2×C411yescharacteristic
33#13108053—21no—
34#13108053—21no—
35C22⋊Dic101—21no—
36C22⋊Dic101—21no—
37C22⋊Dic101—21no—
38#13108051—21no—
39C4×Dic101—21no—
40C4×Dic101C2×C411yescharacteristic
41C4×Dic101D411yescharacteristic
42C4×Dic101D411yescharacteristic
43C2×D4×C101C2×C411yescharacteristic
44C22×C4×C101—21no—
45C4⋊C4×C101C2×C411yescharacteristic
46C22⋊C4×C101—21no—
47C42×C101C2×C411yescharacteristic
48C23×C101—21no—
49C22×D101C2×D411yescharacteristic
50C2×#87938—42no—
51C2×#87938—42no—
52C2×#87938—42no—
53D4×C101—41no—
54C2×C4×C101—21no—
55C2×C4×C101—42no—
56C2×C4×C101C22⋊C411yescharacteristic
57C2×C4×C101C22⋊C411yescharacteristic
58C2×C4×C101C22×C411yescharacteristic
59C22⋊D101—42no—
60C2×Dic101—21no—
61C2×Dic101—21no—
62C2×Dic101C22⋊C411yescharacteristic
63C2×Dic101C22⋊C411yescharacteristic
64C2×Dic101C2×D411yescharacteristic
65C4×D101—22no—
66C4×D101—41no—
67C4×D101—41no—
68Dic202—41no—
69#11717581—42no—
70C22×C101—41no—
71C22×C101—41no—
72C22×C101—41no—
73C22×C101C2×C22⋊C411yescharacteristic
74C2×D101—21no—
75C2×D101—21no—
76C2×D101#13512yes—
77#87938—82no—
78C4×C101—21no—
79C4×C101—21no—
80C4×C101—21no—
81C4×C101—41no—
82Dic101—21no—
83Dic101—21no—
84Dic101—21no—
85Dic101—41no—
86Dic101—41no—
87C2×C101—81no—
88C2×C101#41011yescharacteristic
89C2×C101#41611yescharacteristic
90C2×C101#42111yescharacteristic
91D101—22no—
92#1521—1011nomaximal, Sylow
93C101#152111yescharacteristic, complemented, Sylow
94#529—1011no—
95#431—1011no—
96#383—1011no—
97#328—1012no—
98#327—1012no—
99#126—2021no—
100#125—1011no—
101#124—1011no—
102#123—2021no—
103C22⋊Q8—1011no—
104#121—1011no—
105C4×Q8—1011no—
106C4×D4—2021no—
107C4×D4#8793811yescharacteristic, complemented
108#117—2021no—
109C2×C42—1011no—
110C4⋊C8—2021no—
111C22⋊C8—1012no—
112C4×C8—2021no—
113#95—1012no—
114#95—2021no—
115#95—2021no—
116C2×Q8—1011no—
117C2×D4—2021no—
118C2×D4C2×#8793811yescharacteristic
119C22×C4—21no—
120C22×C4—1011no—
121C22×C4—1011no—
122C22×C4—1011no—
123C22×C4—2022no—
124C2×C8—2022no—
125C4⋊C4—1011no—
126C4⋊C4—2021no—
127C4⋊C4—2021no—
128C4⋊C4—2021no—
129C4⋊C4—2021no—
130C4⋊C4C2×#8793811yescharacteristic
131C22⋊C4—21no—
132C22⋊C4—2021no—
133C22⋊C4—2021no—
134C22⋊C4—2021no—
135C22⋊C4—2021no—
136C42—1011no—
137C42—1011no—
138C42—1011no—
139C42—2021no—
140C42C2×#8793811yescharacteristic
141C23—21no—
142C23—1011no—
143Q8—4041no—
144D4—41no—
145D4—4042no—
146C2×C4—21no—
147C2×C4—42no—
148C2×C4—1011no—
149C2×C4—1011no—
150C2×C4—1011no—
151C2×C4—4041no—
152C2×C4—4041no—
153C2×C4—4042no—
154C2×C4—4042no—
155C2×C4—4042no—
156C2×C4—2022no—
157C2×C4—2021no—
158C2×C4—2021no—
159C2×C4C22⋊#8793811yescharacteristic
160C2×C4C22⋊#8793811yescharacteristic
161C2×C4C22×#8793811yescharacteristic
162C8—4042no—
163C22—41no—
164C22—41no—
165C22—41no—
166C22—1012no—
167C22—2021no—
168C22—2021no—
169C22C2×C22⋊#8793811yescharacteristic
170C4—21no—
171C4—21no—
172C4—21no—
173C4—41no—
174C4—8082no—
175C4—4041no—
176C4—4041no—
177C4—2021no—
178C4—2021no—
179C4—2021no—
180C2—81no—
181C2—2022no—
182C2#2026615611yescharacteristic
183C2#2026616711yescharacteristic
184C2#2026617511yescharacteristic
subgroupG/H
centerC22C2×C22⋊#87938
commutatorC2×C4×C101C22×C4
FrattiniC2×C4C22×#87938
FittingC4×D4×C101C4
socleC22×C101C2×C22⋊C4
prime radical#15692226C22
cosocleC2×C4×D101C23
hypercenterC4×D4#87938
hypocenterC101#1521
LCSG ▷ C2×C4×C101 ▷ C22×C101 ▷ C101
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #20266195C2semidirect
2. #20266122C2semidirect
3. #20266030C2semidirect
13. #15692246C4semidirect
14. #15692242C4semidirect
18. C4×Dic202C4semidirect
22. C4×D4×C101C4semidirect
93. C101#1521semidirect
107. C4×D4#87938semidirect

Maximal subgroups

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

subgroupindex
#202661952
#202661222
#202660302
#202660282
#202657092
#1521101