Finite Group Databasebeta

← #27186544

Subgroups — #27186544

Order 12928.

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

normal subgroups only

This group has 222 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#20266199C211yesmaximal, characteristic, complemented
2#20266121C211yesmaximal, characteristic, complemented
3#20266031C212yesmaximal, complemented
4#20266028C212yesmaximal
5#20265706C211yesmaximal, characteristic
6C2×C4⋊#87938—21no—
7C4⋊#11717581—21no—
8#15692312C2212yes—
9#15692310—21no—
10(C2×#87938)⋊C4—21no—
11(C2×#87938)⋊C4C2212yes—
12#15692248—21no—
13#15692247C411yescharacteristic, complemented
14#15692237—21no—
15#15692231C2211yescharacteristic
16#15692226C2211yescharacteristic
17Q8×Dic101C411yescharacteristic, complemented
18D4×Dic101C411yescharacteristic, complemented
19#15692215—21no—
20#15692211—21no—
21C42×D101C2211yescharacteristic
22#124×C101C411yescharacteristic, complemented
23C22×#87938—22no—
24C2×#11717581—22no—
25C4⋊#87938—42no—
26C2×C22⋊D101—21no—
27C22×Dic101—21no—
28C2×C4×D101D411yescharacteristic
29C2×C4×D101D411yescharacteristic
30C2×C4×D101C2311yescharacteristic
31C4⋊Dic101—21no—
32C4⋊Dic101C2×C411yescharacteristic
33C4⋊Dic101C2×C411yescharacteristic
34#13108053—21no—
35#13108053—21no—
36#13108053—21no—
37C22⋊Dic101—21no—
38C22⋊Dic101—21no—
39#13108051—21no—
40C4×Dic101—21no—
41C4×Dic101C2×C411yescharacteristic
42C4×Dic101D411yescharacteristic
43C4×Dic101D411yescharacteristic
44C2×Q8×C101C2×C411yescharacteristic
45C2×D4×C101C2×C411yescharacteristic
46C22⋊C4×C101—21no—
47C22⋊C4×C101—21no—
48C42×C101C2×C411yescharacteristic
49C23×C101—21no—
50C22×D101C2×D411yescharacteristic
51C2×#87938—42no—
52C2×#87938—42no—
53C2×#87938—42no—
54Q8×C101—41no—
55D4×C101—41no—
56C2×C4×C101—21no—
57C2×C4×C101C22⋊C411yescharacteristic
58C2×C4×C101C22⋊C411yescharacteristic
59C2×C4×C101C22×C411yescharacteristic
60C22⋊D101—41no—
61C22⋊D101—41no—
62C2×Dic101—21no—
63C2×Dic101—21no—
64C2×Dic101—42no—
65C2×Dic101C22⋊C411yescharacteristic
66C2×Dic101C22⋊C411yescharacteristic
67C2×Dic101C2×D411yescharacteristic
68C4×D101—21no—
69C4×D101—21no—
70C4×D101—41no—
71C4×D101—41no—
72#11717581—42no—
73C22×C101—41no—
74C22×C101—41no—
75C22×C101—41no—
76C22×C101C2×C22⋊C411yescharacteristic
77C2×D101—21no—
78C2×D101—21no—
79C2×D101AGL(1,ℤ/8)11yescharacteristic
80C2×D101#13711yescharacteristic
81#87938—82no—
82C4×C101—21no—
83C4×C101—21no—
84C4×C101—21no—
85C4×C101—41no—
86Dic101—21no—
87Dic101—21no—
88Dic101—21no—
89Dic101—41no—
90Dic101—41no—
91C2×C101—81no—
92C2×C101#41011yescharacteristic
93C2×C101#41711yescharacteristic
94C2×C101#42111yescharacteristic
95D101—21no—
96D101—21no—
97#1512—1011nomaximal, Sylow
98C101#151211yescharacteristic, complemented, Sylow
99#529—1011no—
100#432—1011no—
101#382—1011no—
102#328—1012no—
103#327—1012no—
104#126—2021no—
105#125—1011no—
106#124#8793811yescharacteristic, complemented
107#123—2021no—
108C22⋊Q8—1011no—
109#121—1011no—
110C4×Q8—1011no—
111C4×D4—1011no—
112C4×D4—2021no—
113#117—2021no—
114C2×C4⋊C4—2021no—
115C2×C42—1011no—
116C4⋊C8—2021no—
117C22⋊C8—1012no—
118#97—2021no—
119#95—1012no—
120#95—2021no—
121C2×Q8C2×#8793811yescharacteristic
122C2×D4—2021no—
123C2×D4C2×#8793811yescharacteristic
124C22×C4—1011no—
125C22×C4—1011no—
126C22×C4—1011no—
127C22×C4—2021no—
128C22×C4—2022no—
129C2×C8—2022no—
130C4⋊C4—1011no—
131C4⋊C4—1011no—
132C4⋊C4—4042no—
133C4⋊C4—2021no—
134C4⋊C4—2021no—
135C4⋊C4—2021no—
136C4⋊C4—2021no—
137C22⋊C4—21no—
138C22⋊C4—21no—
139C22⋊C4—2021no—
140C22⋊C4—2021no—
141C22⋊C4—2021no—
142C42—1011no—
143C42—1011no—
144C42—1011no—
145C42—2021no—
146C42C2×#8793811yescharacteristic
147C23—21no—
148C23—1011no—
149Q8—41no—
150D4—41no—
151D4—4041no—
152D4—4041no—
153C2×C4—21no—
154C2×C4—1011no—
155C2×C4—1011no—
156C2×C4—1011no—
157C2×C4—4041no—
158C2×C4—4041no—
159C2×C4—4042no—
160C2×C4—4042no—
161C2×C4—4042no—
162C2×C4—4042no—
163C2×C4—2021no—
164C2×C4—2021no—
165C2×C4—2021no—
166C2×C4—2021no—
167C2×C4C22⋊#8793811yescharacteristic
168C2×C4C22⋊#8793811yescharacteristic
169C2×C4C22×#8793811yescharacteristic
170C8—4042no—
171C22—41no—
172C22—41no—
173C22—41no—
174C22—1011no—
175C22—1011no—
176C22—2021no—
177C22—2021no—
178C22C2×C22⋊#8793811yescharacteristic
179C4—21no—
180C4—21no—
181C4—21no—
182C4—41no—
183C4—8082no—
184C4—4041no—
185C4—4041no—
186C4—2021no—
187C4—2021no—
188C4—2021no—
189C2—81no—
190C2—2021no—
191C2—2021no—
192C2#2026615711yescharacteristic
193C2#2026616811yescharacteristic
194C2#2026617411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#87938
commutatorC2×C4×C101C22×C4
FrattiniC2×C4C22×#87938
Fitting#124×C101C4
socleC22×C101C2×C22⋊C4
prime radical#15692226C22
cosocleC2×C4×D101C23
hypercenter#124#87938
hypocenterC101#1512
LCSG ▷ C2×C4×C101 ▷ C22×C101 ▷ C101
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
1. #20266199C2semidirect
2. #20266121C2semidirect
3. #20266031C2semidirect
13. #15692247C4semidirect
17. Q8×Dic101C4semidirect
18. D4×Dic101C4semidirect
22. #124×C101C4semidirect
98. C101#1512semidirect
106. #124#87938semidirect

Maximal subgroups

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

subgroupindex
#202661992
#202661212
#202660312
#202660282
#202657062
#1512101