Finite Group Databasebeta

← #27187404

Subgroups — #27187404

Order 12928.

258 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 52 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#20266158C212yesmaximal, complemented
2#20266084C212yesmaximal, complemented
3#20266081C212yesmaximal, complemented
4#20265726C211yesmaximal, characteristic
5#15692334—22no—
6#15692314—22no—
7#15692314C2214yes—
8C2×#13108075C2211yescharacteristic
9C2×#13108073C411yescharacteristic, complemented
10#15692253C411yescharacteristic, complemented
11#15692251C2211yescharacteristic
12#15692243C2211yescharacteristic
13#15692228—22no—
14#15692215—22no—
15C42×D101C411yescharacteristic, complemented
16#124×C101C411yescharacteristic, complemented
17C4⋊#87938—42no—
18C22⋊#87938—24no—
19C4×#87938—42no—
20#13108075—41no—
21#13108075—41no—
22#13108073—41no—
23#13108073—41no—
24C2×Dic202C2×C411yescharacteristic
25C2×D404D412yes—
26C2×D404C2311yescharacteristic
27C2×C22⋊D101—21no—
28C2×C22⋊D101—22no—
29C22×Dic101—21no—
30C2×C4×D101—21no—
31C2×C4×D101C2×C411yescharacteristic
32C2×C4×D101D412yes—
33#13108053—22no—
34#13108051—22no—
35C4×Dic101—21no—
36C4×Dic101C2×C411yescharacteristic
37C2×Q8×C101C2×C411yescharacteristic
38C2×D4×C101C2×C411yescharacteristic
39C22⋊C4×C101—22no—
40C42×C101C2×C411yescharacteristic
41C23×C101—21no—
42C22×D101C22⋊C411yescharacteristic
43C22×D101C2×D412yes—
44C2×#87938—44no—
45Q8×C101—41no—
46D4×C101—41no—
47C2×C4×C101—21no—
48C2×C4×C101C22⋊C412yes—
49C2×C4×C101C22×C411yescharacteristic
50C22⋊D101—44no—
51C22⋊D101—42no—
52C2×Dic101—21no—
53C2×Dic101—21no—
54C2×Dic101—41no—
55C2×Dic101—41no—
56C2×Dic101C22⋊C411yescharacteristic
57D404—42no—
58D404—41no—
59C4×D101—21no—
60C4×D101—21no—
61C4×D101—22no—
62C4×D101—22no—
63C4×D101—42no—
64Dic202—41no—
65C22×C101—42no—
66C22×C101—41no—
67C22×C101C2×C22⋊C411yescharacteristic
68C2×D101—21no—
69C2×D101—22no—
70C2×D101—41no—
71C2×D101—42no—
72#87938—84no—
73C4×C101—21no—
74C4×C101—22no—
75C4×C101—41no—
76Dic101—22no—
77Dic101—41no—
78Dic101#9911yescharacteristic
79Dic101#9911yescharacteristic
80C2×C101—21no—
81C2×C101—81no—
82C2×C101C2×#9911yescharacteristic
83D101—42no—
84D101—41no—
85#2126—1011nomaximal, Sylow
86C101#212611yescharacteristic, complemented, Sylow
87#532—1011no—
88#410—1012no—
89#354—1012no—
90#353—1012no—
91C2×#41—1011no—
92C2×#41—1011no—
93C4⋊Q8—1011no—
94#127—1011no—
95#124—1011no—
96#124#8793811yescharacteristic, complemented
97#121—2022no—
98C4×D4—2022no—
99#117—2022no—
100C2×C42—1011no—
101#99—1014no—
102#99—2022no—
103#41—4041no—
104#41—4041no—
105#41—4041no—
106#41—4041no—
107C2×Q8—1011no—
108C2×Q8C2×#8793811yescharacteristic
109C2×D4—1012no—
110C2×D4—1011no—
111C2×D4—2022no—
112C2×D4—2021no—
113C2×D4C2×#8793811yescharacteristic
114C22×C4—1012no—
115C22×C4—1011no—
116C22×C4—2021no—
117C22×C4—2021no—
118C4⋊C4—4042no—
119C4⋊C4—2022no—
120C22⋊C4—22no—
121C22⋊C4—2022no—
122C22⋊C4—2024no—
123C42—1011no—
124C42—4042no—
125C42—2021no—
126C42C2×#8793811yescharacteristic
127C23—21no—
128C23—1012no—
129C23—1011no—
130Q8—41no—
131Q8—4041no—
132D4—41no—
133D4—4042no—
134D4—4041no—
135D4—4042no—
136D4—4044no—
137C2×C4—21no—
138C2×C4—1011no—
139C2×C4—4042no—
140C2×C4—4044no—
141C2×C4—4041no—
142C2×C4—4041no—
143C2×C4—2022no—
144C2×C4—2022no—
145C2×C4—2021no—
146C2×C4—2021no—
147C2×C4—2021no—
148C2×C4—2021no—
149C2×C4C22⋊#8793812yes—
150C2×C4C22×#8793811yescharacteristic
151C22—42no—
152C22—41no—
153C22—4041no—
154C22—4042no—
155C22—2022no—
156C22—2021no—
157C22C2×C22⋊#8793811yescharacteristic
158C4—22no—
159C4—21no—
160C4—41no—
161C4—8084no—
162C4—1011no—
163C4—1011no—
164C4—4041no—
165C4—2022no—
166C2—21no—
167C2—81no—
168C2—4042no—
169C2—4041no—
170C2D101⋊#9911yescharacteristic
subgroupG/H
centerC2D101⋊#99
commutatorC2×C4×C101C22×C4
FrattiniC2×C4C22×#87938
Fitting#124×C101C4
socleC2×C101C2×#99
prime radical#20265726C2
cosocleC2×D404C23
hypercenter#124#87938
hypocenterC101#2126
LCSG ▷ C2×C4×C101 ▷ C22×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #124

Complements

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

NH ≅ G/Ntype
1. #20266158C2semidirect
2. #20266084C2semidirect
3. #20266081C2semidirect
9. C2×#13108073C4semidirect
10. #15692253C4semidirect
15. C42×D101C4semidirect
16. #124×C101C4semidirect
86. C101#2126semidirect
96. #124#87938semidirect

Maximal subgroups

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

subgroupindex
#202661582
#202660842
#202660812
#202657262
#2126101