Finite Group Databasebeta

← #27187432

Subgroups — #27187432

Order 12928.

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

normal subgroups only

This group has 262 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#20266164C212yesmaximal, complemented
2#20266086C212yesmaximal, complemented
3#20266085C212yesmaximal, complemented
4#20265740C211yesmaximal, characteristic
5C2×#13108083—22no—
6#15692316C2214yescomplemented
7#15692315—22no—
8C2×#13108073C2211yescharacteristic
9C2×D4×D101C411yescharacteristic
10#15692251C411yescharacteristic
11#15692243C2211yescharacteristic
12#15692242C2211yescharacteristic
13#15692227—22no—
14#15692223—22no—
15#15692212C411yescharacteristic
16#127×C101C411yescharacteristic
17#13108083—24no—
18#13108083—42no—
19C2×#11717581—42no—
20C23×D101—21no—
21#13108073—42no—
22C2×Dic202C2311yescharacteristic
23C2×D404C2×C411yescharacteristic
24C2×C22⋊D101—22no—
25C2×C22⋊D101—21no—
26C2×C22⋊D101D412yes—
27D4×D101—42no—
28C22×Dic101D412yes—
29C2×C4×D101C2×C411yescharacteristic
30#13108053—21no—
31C22⋊Dic101—22no—
32#13108051—21no—
33#13108051—22no—
34C4×Dic101C2×C411yescharacteristic
35C2×D4×C101—22no—
36C2×D4×C101C2×C411yescharacteristic
37C2×D4×C101C2×C411yescharacteristic
38C42×C101C2×C411yescharacteristic
39C23×C101—21no—
40C23×C101C22⋊C412yes—
41C22×D101—21no—
42C22×D101—42no—
43C22×D101—82no—
44C22×D101C22⋊C411yescharacteristic
45D4×C101—41no—
46D4×C101—41no—
47D4×C101—82no—
48C2×C4×C101—21no—
49C2×C4×C101C22×C411yescharacteristic
50C22⋊D101—42no—
51C22⋊D101—42no—
52C22⋊D101—82no—
53C2×Dic101—22no—
54C2×Dic101—22no—
55C2×Dic101—21no—
56C2×Dic101C22⋊C411yescharacteristic
57C2×Dic101C2×D412yes—
58D404—41no—
59C4×D101—22no—
60Dic202—41no—
61#11717581—44no—
62C22×C101—22no—
63C22×C101—42no—
64C22×C101—42no—
65C22×C101—41no—
66C22×C101C2×C22⋊C411yescharacteristic
67C2×D101—21no—
68C2×D101—41no—
69C2×D101—42no—
70C2×D101—41no—
71C2×D101—84no—
72C4×C101—21no—
73C4×C101—41no—
74Dic101—22no—
75Dic101—41no—
76Dic101#9912yes—
77C2×C101—21no—
78C2×C101—42no—
79C2×C101—81no—
80C2×C101C2×#9911yescharacteristic
81D101—41no—
82D101—81no—
83#2134—1011nomaximal, Sylow
84C101#213411yescharacteristic, complemented, Sylow
85#535—1011no—
86#413—1012no—
87#355—1012no—
88#355—1012no—
89C2×#41—1011no—
90C22×D4—1011no—
91C2×M16—2022no—
92#127—1011no—
93#127#8793811yescharacteristic
94#124—1011no—
95#124—1011no—
96#121—2022no—
97#120—2022no—
98#117—1011no—
99#101—1014no—
100#100—2022no—
101C24—2021no—
102#41—4042no—
103C2×Q8—1011no—
104C2×D4—22no—
105C2×D4—1012no—
106C2×D4—1011no—
107C2×D4—4042no—
108C2×D4—2021no—
109C2×D4—2022no—
110C2×D4C2×#8793811yescharacteristic
111C2×D4C2×#8793811yescharacteristic
112C22×C4—1012no—
113C22×C4—1011no—
114M16—4042no—
115M16—2024no—
116C2×C8—4042no—
117C4⋊C4—2021no—
118C22⋊C4—2022no—
119C22⋊C4—2021no—
120C22⋊C4—2022no—
121C42—1011no—
122C42C2×#8793811yescharacteristic
123C23—21no—
124C23—8082no—
125C23—1011no—
126C23—4042no—
127C23—2021no—
128C23C22⋊#8793812yes—
129Q8—4041no—
130D4—41no—
131D4—41no—
132D4—82no—
133D4—8082no—
134D4—4041no—
135D4—4042no—
136D4—4042no—
137C2×C4—21no—
138C2×C4—1011no—
139C2×C4—1012no—
140C2×C4—2022no—
141C2×C4—2022no—
142C2×C4—2022no—
143C2×C4—2021no—
144C2×C4C22×#8793811yescharacteristic
145C8—4044no—
146C22—22no—
147C22—42no—
148C22—42no—
149C22—41no—
150C22—8084no—
151C22—4042no—
152C22—4041no—
153C22—4041no—
154C22—2021no—
155C22C2×C22⋊#8793811yescharacteristic
156C4—21no—
157C4—41no—
158C4—1012no—
159C4—4041no—
160C4—2022no—
161C2—21no—
162C2—42no—
163C2—81no—
164C2—8081no—
165C2—4041no—
166C2D101⋊#9911yescharacteristic
subgroupG/H
centerC2D101⋊#99
commutatorC2×C4×C101C22×C4
FrattiniC2×C4C22×#87938
Fitting#127×C101C4
socleC2×C101C2×#99
prime radical#20265740C2
cosocleC2×Dic202C23
hypercenter#127#87938
hypocenterC101#2134
LCSG ▷ C2×C4×C101 ▷ C22×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #127

Complements

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

NH ≅ G/Ntype
1. #20266164C2semidirect
2. #20266086C2semidirect
3. #20266085C2semidirect
6. #15692316C22semidirect
84. C101#2134semidirect

Maximal subgroups

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

subgroupindex
#202661642
#202660862
#202660852
#202657402
#2134101