Finite Group Databasebeta

← #27187425

Subgroups — #27187425

Order 12928.

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

normal subgroups only

This group has 250 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#20266163C212yesmaximal, complemented
2#20266088C212yesmaximal, complemented
3#20266086C212yesmaximal, complemented
4#20265727C211yesmaximal, characteristic
5D101⋊M16—22no—
6#15692316C2214yes—
7#15692315—22no—
8C2×#13108074C411yescharacteristic
9C2×#13108074C2211yescharacteristic
10#15692255C2211yescharacteristic
11#15692252C411yescharacteristic
12#15692243C411yescharacteristic
13#15692243C2211yescharacteristic
14#15692229—22no—
15C4×D404—22no—
16C2×C42×C101C411yescharacteristic
17#13108084—42no—
18#13108083—24no—
19D101⋊C8—42no—
20#13108074—41no—
21#13108074—41no—
22#13108074—41no—
23#13108074—41no—
24C2×Dic202C2×C411yescharacteristic
25C2×Dic202C2311yescharacteristic
26C2×D404—22no—
27C2×D404C2×C411yescharacteristic
28C2×D404C2×C411yescharacteristic
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×D101C22⋊C412yes—
44C2×C4×C101—21no—
45C2×C4×C101—21no—
46C2×C4×C101—21no—
47C2×C4×C101—21no—
48C2×C4×C101—42no—
49C2×C4×C101C22⋊C411yescharacteristic
50C2×C4×C101C22×C411yescharacteristic
51C22⋊D101—42no—
52C22⋊D101—42no—
53C2×Dic101—21no—
54C2×Dic101C2×D412yes—
55D404—41no—
56D404—41no—
57D404—44no—
58C4×D101—22no—
59C4×D101—22no—
60C4×D101—41no—
61C4×D101—41no—
62Dic202—41no—
63Dic202—41no—
64#11717581—44no—
65C22×C101—21no—
66C22×C101—41no—
67C22×C101C2×C22⋊C411yescharacteristic
68C2×D101—22no—
69C2×D101—42no—
70C2×D101—42no—
71C2×D101—41no—
72C4×C101—22no—
73C4×C101—21no—
74C4×C101—41no—
75C4×C101#9911yescharacteristic
76C4×C101#9911yescharacteristic
77Dic101—22no—
78Dic101—41no—
79C2×C101—21no—
80C2×C101—41no—
81C2×C101C2×#9911yescharacteristic
82D101—42no—
83D101—81no—
84#2132—1011nomaximal, Sylow
85C101#213211yescharacteristic, complemented, Sylow
86#532—1011no—
87#413—1012no—
88#356—1012no—
89#355—1012no—
90C2×#41—1011no—
91C2×#41—1011no—
92C2×M16—2022no—
93C4⋊Q8—1011no—
94#127—1011no—
95#124—1011no—
96#124—1011no—
97#121—2022no—
98C4×D4—2022no—
99C2×C42#8793811yescharacteristic
100#101—1014no—
101#100—2022no—
102#41—4041no—
103#41—4041no—
104#41—4041no—
105#41—4041no—
106C2×Q8—1011no—
107C2×Q8—1011no—
108C2×D4—1012no—
109C2×D4—1011no—
110C2×D4—1011no—
111C2×D4—2022no—
112C2×D4—2021no—
113C22×C4—21no—
114C22×C4—1012no—
115C22×C4—2021no—
116C22×C4C2×#8793811yescharacteristic
117M16—4042no—
118M16—2024no—
119C2×C8—4042no—
120C4⋊C4—2022no—
121C22⋊C4—2022no—
122C22⋊C4—2022no—
123C42—21no—
124C42C2×#8793811yescharacteristic
125C42C2×#8793811yescharacteristic
126C23—1012no—
127C23—2021no—
128C23C22⋊#8793811yescharacteristic
129Q8—4041no—
130Q8—4041no—
131D4—4041no—
132D4—4044no—
133D4—4041no—
134D4—4042no—
135D4—4042no—
136C2×C4—21no—
137C2×C4—21no—
138C2×C4—21no—
139C2×C4—21no—
140C2×C4—42no—
141C2×C4—1012no—
142C2×C4—4041no—
143C2×C4—4041no—
144C2×C4—2021no—
145C2×C4—2022no—
146C2×C4—2022no—
147C2×C4C22⋊#8793811yescharacteristic
148C2×C4C22×#8793811yescharacteristic
149C8—4044no—
150C22—21no—
151C22—41no—
152C22—4042no—
153C22—4042no—
154C22—4041no—
155C22—2022no—
156C22C2×C22⋊#8793811yescharacteristic
157C4—22no—
158C4—21no—
159C4—41no—
160C4—4041no—
161C4—2022no—
162C4#1569231411yescharacteristic
163C4#1569231411yescharacteristic
164C2—21no—
165C2—41no—
166C2—8081no—
167C2—4042no—
168C2C2×#1569231411yescharacteristic
subgroupG/H
centerC4#15692314
commutatorC2×C4×C101C22×C4
FrattiniC2×C4C22×#87938
FittingC2×C42×C101C4
socleC2×C101C2×#99
prime radical#20265727C2
cosocleC2×Dic202C23
hypercenterC2×C42#87938
hypocenterC101#2132
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. #20266163C2semidirect
2. #20266088C2semidirect
3. #20266086C2semidirect
85. C101#2132semidirect

Maximal subgroups

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

subgroupindex
#202661632
#202660882
#202660862
#202657272
#2132101