Finite Group Databasebeta

← #27187403

Subgroups — #27187403

Order 12928.

258 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 54 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#20266156C212yesmaximal, complemented
2#20266083C212yesmaximal, complemented
3#20266081C212yesmaximal, complemented
4#20265723C211yesmaximal, characteristic
5#15692334—22no—
6#15692314C2214yes—
7#15692313—22no—
8C2×#13108074C2211yescharacteristic
9#15692253C411yescharacteristic, complemented
10#15692251C2211yescharacteristic
11#15692244C2211yescharacteristic
12#15692242C411yescharacteristic, complemented
13#15692227—22no—
14C4×C22⋊D101—22no—
15C2×C4×Dic101C411yescharacteristic, complemented
16C2×#41×C101C411yescharacteristic, complemented
17C4⋊#87938—42no—
18C22⋊#87938—24no—
19C4×#87938—42no—
20#13108074—41no—
21#13108074—41no—
22C2×Dic202C2×C411yescharacteristic
23C2×D404C2311yescharacteristic
24C2×C22⋊D101—22no—
25C2×C22⋊D101D412yes—
26C22×Dic101—21no—
27C2×C4×D101D412yes—
28#13108053—22no—
29C22⋊Dic101—22no—
30#13108051—22no—
31C4×Dic101—21no—
32C4×Dic101C2×C411yescharacteristic
33C4×Dic101C2×C411yescharacteristic
34#41×C101—41no—
35#41×C101—41no—
36C2×Q8×C101C2×C411yescharacteristic
37C2×D4×C101—21no—
38C2×D4×C101C2×C411yescharacteristic
39C22×C4×C101—21no—
40C22×C4×C101C2×C411yescharacteristic
41C23×C101—21no—
42C23×C101C22⋊C411yescharacteristic
43C22×D101C2×D412yes—
44C2×#87938—44no—
45Q8×C101—41no—
46D4×C101—41no—
47D4×C101—42no—
48C2×C4×C101—21no—
49C2×C4×C101—21no—
50C2×C4×C101—21no—
51C2×C4×C101—41no—
52C2×C4×C101—41no—
53C2×C4×C101C22⋊C411yescharacteristic
54C2×C4×C101C22×C411yescharacteristic
55C22⋊D101—42no—
56C22⋊D101—44no—
57C2×Dic101—21no—
58C2×Dic101—21no—
59C2×Dic101—42no—
60C2×Dic101C22⋊C412yes—
61D404—41no—
62C4×D101—22no—
63C4×D101—22no—
64Dic202—41no—
65C22×C101—21no—
66C22×C101—41no—
67C22×C101—42no—
68C22×C101—41no—
69C22×C101C2×C22⋊C411yescharacteristic
70C2×D101—22no—
71C2×D101—42no—
72#87938—84no—
73C4×C101—21no—
74C4×C101—41no—
75C4×C101#9911yescharacteristic
76C4×C101#9911yescharacteristic
77Dic101—22no—
78Dic101—22no—
79Dic101—41no—
80C2×C101—21no—
81C2×C101—41no—
82C2×C101—81no—
83C2×C101C2×#9911yescharacteristic
84D101—42no—
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#8793811yescharacteristic, complemented
93C4⋊Q8—1011no—
94#127—1011no—
95#124—1011no—
96#124—1011no—
97#121—2022no—
98C4×D4—2022no—
99#117—2022no—
100C2×C42—1011no—
101#99—1014no—
102#99—2022no—
103#41—41no—
104#41—41no—
105#41—4041no—
106#41—4041no—
107C2×Q8—1011no—
108C2×Q8C2×#8793811yescharacteristic
109C2×D4—21no—
110C2×D4—1012no—
111C2×D4—1011no—
112C2×D4—2022no—
113C2×D4C2×#8793811yescharacteristic
114C22×C4—21no—
115C22×C4—1012no—
116C22×C4—2021no—
117C22×C4C2×#8793811yescharacteristic
118C4⋊C4—4042no—
119C4⋊C4—2022no—
120C22⋊C4—2022no—
121C22⋊C4—2022no—
122C22⋊C4—2024no—
123C42—1011no—
124C42—1011no—
125C42—4042no—
126C42—2021no—
127C23—21no—
128C23—1012no—
129C23C22⋊#8793811yescharacteristic
130Q8—41no—
131Q8—4041no—
132D4—41no—
133D4—42no—
134D4—4041no—
135D4—4042no—
136D4—4044no—
137C2×C4—21no—
138C2×C4—21no—
139C2×C4—21no—
140C2×C4—41no—
141C2×C4—41no—
142C2×C4—1012no—
143C2×C4—4044no—
144C2×C4—4042no—
145C2×C4—2021no—
146C2×C4—2021no—
147C2×C4—2022no—
148C2×C4—2022no—
149C2×C4C22⋊#8793811yescharacteristic
150C2×C4C22×#8793811yescharacteristic
151C22—21no—
152C22—41no—
153C22—42no—
154C22—41no—
155C22—4042no—
156C22—2022no—
157C22C2×C22⋊#8793811yescharacteristic
158C4—21no—
159C4—41no—
160C4—8084no—
161C4—4041no—
162C4—2022no—
163C4—2022no—
164C4#1569231311yescharacteristic
165C4#1569231311yescharacteristic
166C2—21no—
167C2—41no—
168C2—81no—
169C2—4042no—
170C2C2×#1569231311yescharacteristic
subgroupG/H
centerC4#15692313
commutatorC2×C4×C101C22×C4
FrattiniC2×C4C22×#87938
FittingC2×#41×C101C4
socleC2×C101C2×#99
prime radical#20265723C2
cosocleC2×D404C23
hypercenterC2×#41#87938
hypocenterC101#2126
LCSG ▷ C2×C4×C101 ▷ C22×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #20266156C2semidirect
2. #20266083C2semidirect
3. #20266081C2semidirect
9. #15692253C4semidirect
12. #15692242C4semidirect
15. C2×C4×Dic101C4semidirect
16. C2×#41×C101C4semidirect
86. C101#2126semidirect
92. C2×#41#87938semidirect

Maximal subgroups

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

subgroupindex
#202661562
#202660832
#202660812
#202657232
#2126101