Finite Group Databasebeta

← #27186446

Subgroups — #27186446

Order 12928.

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

normal subgroups only

This group has 212 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#20266196C211yesmaximal, characteristic, complemented
2#20266196C211yesmaximal, characteristic, complemented
3#20266027C212yesmaximal, complemented
4#20266025C212yesmaximal, complemented
5#20265712C211yesmaximal, characteristic
6C4⋊#11717581—21no—
7C4⋊#11717581C2212yes—
8#15692312—21no—
9#15692312—21no—
10C4×#11717581—21no—
11C4×#11717581C2212yes—
12#15692250—21no—
13#15692243C411yescharacteristic
14#15692240—21no—
15#15692235C411yescharacteristic
16#15692230C411yescharacteristic
17#15692220C2211yescharacteristic
18#15692217—21no—
19#15692217C2211yescharacteristic
20#15692213—21no—
21C42×D101C2211yescharacteristic
22#125×C101C411yescharacteristic
23C2×#11717581—22no—
24C2×#11717581—22no—
25C2×Dic202C2×C411yescharacteristic
26C2×D404—21no—
27C2×D404C2×C411yescharacteristic
28C2×C4×D101—21no—
29C2×C4×D101C2×C411yescharacteristic
30C2×C4×D101D411yescharacteristic
31C2×C4×D101D411yescharacteristic
32C4⋊Dic101—21no—
33#13108053—21no—
34#13108051—21no—
35#13108051—21no—
36#13108051—21no—
37#13108051—21no—
38#13108051—21no—
39C4×Dic101—21no—
40C4×Dic101D411yescharacteristic
41C4×Dic101D411yescharacteristic
42C4×Dic101C2311yescharacteristic
43C4⋊C4×C101—21no—
44C4⋊C4×C101—21no—
45C4⋊C4×C101C2×C411yescharacteristic
46C4⋊C4×C101C2×C411yescharacteristic
47C42×C101C2×C411yescharacteristic
48C22×D101—21no—
49C22×D101C22⋊C411yescharacteristic
50C2×C4×C101—21no—
51C2×C4×C101—21no—
52C2×C4×C101C22⋊C411yescharacteristic
53C2×C4×C101C22⋊C411yescharacteristic
54C2×C4×C101C22×C411yescharacteristic
55C2×Dic101—21no—
56C2×Dic101C22⋊C411yescharacteristic
57C2×Dic101C2×D411yescharacteristic
58C2×Dic101C2×D411yescharacteristic
59D404—22no—
60D404—42no—
61C4×D101—22no—
62C4×D101—22no—
63C4×D101—41no—
64C4×D101—42no—
65Dic202—22no—
66#11717581—42no—
67#11717581—42no—
68C22×C101C2×C22⋊C411yescharacteristic
69C2×D101—21no—
70C2×D101—21no—
71C2×D101—21no—
72C2×D101—41no—
73C2×D101—41no—
74C2×D101—41no—
75C4×C101—21no—
76C4×C101—21no—
77C4×C101—41no—
78C4×C101—41no—
79C4×C101#13112yes—
80Dic101—21no—
81Dic101—21no—
82Dic101—41no—
83Dic101#13512yes—
84C2×C101#40811yescharacteristic
85C2×C101#41611yescharacteristic
86C2×C101#42111yescharacteristic
87D101—41no—
88D101—81no—
89#1482—1011nomaximal, Sylow
90C101#148211yescharacteristic, complemented, Sylow
91#529—1011no—
92#431—1011no—
93#431—1011no—
94Q8⋊C8—1012no—
95D4⋊C8—1012no—
96#126—2021no—
97#125#8793811yescharacteristic
98#124—1011no—
99#123—2021no—
100C22⋊Q8—1011no—
101#121—1011no—
102C4×Q8—1011no—
103C4×D4—1011no—
104C4×D4—2021no—
105#117—2021no—
106C2×C42—1011no—
107C4⋊C8—1012no—
108C4⋊C8—2021no—
109C22⋊C8—2021no—
110C22⋊C8—2021no—
111C4×C8—1012no—
112C4×C8—2021no—
113C2×Q8—1011no—
114C2×D4—1011no—
115C2×D4—2021no—
116C22×C4—1011no—
117C22×C4—1011no—
118C22×C4—1011no—
119C22×C4—2021no—
120C2×C8—2022no—
121C2×C8—2022no—
122C4⋊C4—21no—
123C4⋊C4—21no—
124C4⋊C4—2021no—
125C4⋊C4—2021no—
126C4⋊C4C2×#8793811yescharacteristic
127C4⋊C4C2×#8793811yescharacteristic
128C22⋊C4—2021no—
129C22⋊C4—2021no—
130C22⋊C4—2021no—
131C22⋊C4—2021no—
132C22⋊C4—2021no—
133C42—1011no—
134C42—1011no—
135C42—1011no—
136C42—2021no—
137C42C2×#8793811yescharacteristic
138C23—1011no—
139C23—2021no—
140Q8—2022no—
141D4—4042no—
142D4—2022no—
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—1011no—
146C2×C4—1011no—
147C2×C4—1011no—
148C2×C4—4041no—
149C2×C4—4042no—
150C2×C4—2022no—
151C2×C4—2021no—
152C2×C4—2022no—
153C2×C4C22⋊#8793811yescharacteristic
154C2×C4C22⋊#8793811yescharacteristic
155C2×C4C22×#8793811yescharacteristic
156C8—4042no—
157C8—4042no—
158C22—4041no—
159C22—4041no—
160C22—4041no—
161C22—2021no—
162C22—2021no—
163C22—2021no—
164C22C2×C22⋊#8793811yescharacteristic
165C4—21no—
166C4—21no—
167C4—41no—
168C4—41no—
169C4—1012no—
170C4—4041no—
171C4—2021no—
172C4—2021no—
173C4#1569234312yes—
174C2—8081no—
175C2—4041no—
176C2#2026615211yescharacteristic
177C2#2026616711yescharacteristic
178C2#2026617411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#87938
commutatorC2×C4×C101C22×C4
FrattiniC2×C4C22×#87938
Fitting#125×C101C4
socleC22×C101C2×C22⋊C4
prime radical#15692230C4
cosocleC4×Dic101C23
hypercenter#125#87938
hypocenterC101#1482
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
1. #20266196C2semidirect
2. #20266196C2semidirect
3. #20266027C2semidirect
4. #20266025C2semidirect
90. C101#1482semidirect

Maximal subgroups

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

subgroupindex
#202661962
#202660272
#202660252
#202657122
#1482101