Finite Group Databasebeta

← #27187405

Subgroups — #27187405

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#20266084C212yesmaximal, complemented
3#20266082C212yesmaximal, complemented
4#20265727C211yesmaximal, characteristic
5#15692334—22no—
6#15692314C2214yes—
7#15692313—22no—
8C2×#13108074C411yescharacteristic, complemented
9C2×#13108074C2211yescharacteristic
10#15692255C411yescharacteristic, complemented
11#15692252C2211yescharacteristic
12#15692243C411yescharacteristic, complemented
13#15692243C2211yescharacteristic
14#15692229—22no—
15C4×D404—22no—
16C2×C42×C101C411yescharacteristic, complemented
17C4⋊#87938—42no—
18C22⋊#87938—24no—
19C4×#87938—42no—
20#13108074—41no—
21#13108074—41no—
22#13108074—41no—
23#13108074—41no—
24C2×Dic202C2×C411yescharacteristic
25C2×Dic202C2×C411yescharacteristic
26C2×D404—22no—
27C2×D404C2×C411yescharacteristic
28C2×D404C2311yescharacteristic
29C2×C22⋊D101—21no—
30C2×C22⋊D101D412yes—
31C2×C4×D101—21no—
32C2×C4×D101D412yes—
33C4⋊Dic101—22no—
34#13108051—22no—
35#13108051—22no—
36C22×C4×C101—21no—
37C22×C4×C101C2×C411yescharacteristic
38C42×C101—21no—
39C42×C101C2×C411yescharacteristic
40C42×C101C2×C411yescharacteristic
41C23×C101C22⋊C411yescharacteristic
42C22×D101—21no—
43C22×D101C2×D412yes—
44C2×#87938—44no—
45C2×C4×C101—21no—
46C2×C4×C101—21no—
47C2×C4×C101—21no—
48C2×C4×C101—21no—
49C2×C4×C101—42no—
50C2×C4×C101C22⋊C411yescharacteristic
51C2×C4×C101C22×C411yescharacteristic
52C22⋊D101—42no—
53C22⋊D101—42no—
54C2×Dic101—21no—
55C2×Dic101C22⋊C412yes—
56D404—41no—
57D404—41no—
58D404—44no—
59C4×D101—22no—
60C4×D101—22no—
61C4×D101—41no—
62C4×D101—41no—
63Dic202—41no—
64Dic202—41no—
65C22×C101—21no—
66C22×C101—41no—
67C22×C101C2×C22⋊C411yescharacteristic
68C2×D101—22no—
69C2×D101—42no—
70C2×D101—42no—
71C2×D101—41no—
72#87938—84no—
73C4×C101—22no—
74C4×C101—21no—
75C4×C101—41no—
76C4×C101#9911yescharacteristic
77C4×C101#9911yescharacteristic
78Dic101—22no—
79Dic101—41no—
80C2×C101—21no—
81C2×C101—41no—
82C2×C101C2×#9911yescharacteristic
83D101—42no—
84D101—81no—
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—1011no—
97#121—2022no—
98C4×D4—2022no—
99#117—2022no—
100C2×C42#8793811yescharacteristic, complemented
101#99—1014no—
102#99—2022no—
103#41—4041no—
104#41—4041no—
105#41—4041no—
106#41—4041no—
107C2×Q8—1011no—
108C2×Q8—1011no—
109C2×D4—1012no—
110C2×D4—1011no—
111C2×D4—1011no—
112C2×D4—2022no—
113C2×D4—2021no—
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—21no—
124C42—4042no—
125C42C2×#8793811yescharacteristic
126C42C2×#8793811yescharacteristic
127C23—1012no—
128C23—2021no—
129C23C22⋊#8793811yescharacteristic
130Q8—4041no—
131Q8—4041no—
132D4—4041no—
133D4—4044no—
134D4—4041no—
135D4—4042no—
136D4—4042no—
137C2×C4—21no—
138C2×C4—21no—
139C2×C4—21no—
140C2×C4—21no—
141C2×C4—42no—
142C2×C4—1012no—
143C2×C4—4044no—
144C2×C4—4041no—
145C2×C4—4041no—
146C2×C4—2021no—
147C2×C4—2022no—
148C2×C4—2022no—
149C2×C4C22⋊#8793811yescharacteristic
150C2×C4C22×#8793811yescharacteristic
151C22—21no—
152C22—41no—
153C22—4042no—
154C22—4042no—
155C22—4041no—
156C22—2022no—
157C22C2×C22⋊#8793811yescharacteristic
158C4—22no—
159C4—21no—
160C4—41no—
161C4—8084no—
162C4—4041no—
163C4—2022no—
164C4#1569231411yescharacteristic
165C4#1569231411yescharacteristic
166C2—21no—
167C2—41no—
168C2—8081no—
169C2—4042no—
170C2C2×#1569231411yescharacteristic
subgroupG/H
centerC4#15692314
commutatorC2×C4×C101C22×C4
FrattiniC2×C4C22×#87938
FittingC2×C42×C101C4
socleC2×C101C2×#99
prime radical#20265727C2
cosocleC2×D404C23
hypercenterC2×C42#87938
hypocenterC101#2126
LCSG ▷ C2×C4×C101 ▷ C22×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. #20266156C2semidirect
2. #20266084C2semidirect
3. #20266082C2semidirect
8. C2×#13108074C4semidirect
10. #15692255C4semidirect
12. #15692243C4semidirect
16. C2×C42×C101C4semidirect
86. C101#2126semidirect
100. C2×C42#87938semidirect

Maximal subgroups

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

subgroupindex
#202661562
#202660842
#202660822
#202657272
#2126101