Finite Group Databasebeta

← #27186513

Subgroups — #27186513

Order 12928.

284 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 70 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#20266196C211yesmaximal, characteristic, complemented
2C4×C4⋊#87938C211yesmaximal, characteristic, complemented
3#20266029C214yesmaximal, complemented
4#20265728C211yesmaximal, characteristic
5C2×C4⋊#87938—21no—
6C2×C4×#87938—21no—
7C4⋊#11717581—21no—
8#15692312C2212yes—
9C4×#11717581—21no—
10(C2×#87938)⋊C4C2212yes—
11C2×#13108075—21no—
12#15692252C411yescharacteristic, complemented
13#15692244—21no—
14#15692230—21no—
15#15692230C2212yes—
16#15692217—21no—
17#15692217C412yescomplemented
18C42×D101C2211yescharacteristic
19C4⋊Q8×C101C411yescharacteristic, complemented
20C22×#87938—22no—
21C2×#11717581—22no—
22C4⋊#87938—24no—
23C4×#87938—42no—
24#13108075—42no—
25#13108075—42no—
26C2×D404—22no—
27C2×D404—21no—
28C2×D404—21no—
29C2×D404C2×C412yes—
30C2×C4×D101—22no—
31C2×C4×D101D411yescharacteristic
32C2×C4×D101D411yescharacteristic
33C2×C4×D101C2311yescharacteristic
34#13108051—22no—
35#13108051—22no—
36C4×Dic101C2×C411yescharacteristic
37C4×Dic101D411yescharacteristic
38C4×Dic101D411yescharacteristic
39C2×Q8×C101—21no—
40C4⋊C4×C101—21no—
41C4⋊C4×C101C2×C412yes—
42C42×C101C2×C411yescharacteristic
43C22×D101—22no—
44C22×D101C2×D411yescharacteristic
45C2×#87938—24no—
46C2×#87938—42no—
47C2×#87938—42no—
48Q8×C101—42no—
49C2×C4×C101—22no—
50C2×C4×C101C22⋊C411yescharacteristic
51C2×C4×C101C22⋊C411yescharacteristic
52C2×C4×C101C22×C411yescharacteristic
53C2×Dic101C22⋊C411yescharacteristic
54C2×Dic101C22⋊C411yescharacteristic
55C2×Dic101C2×D411yescharacteristic
56D404—42no—
57D404—42no—
58D404—42no—
59D404—42no—
60D404—42no—
61C4×D101—22no—
62C4×D101—41no—
63C4×D101—44no—
64C4×D101D812yes—
65C4×D101SD1612yes—
66#11717581—42no—
67C22×C101C2×C22⋊C411yescharacteristic
68C2×D101—21no—
69C2×D101—21no—
70C2×D101—42no—
71C2×D101—42no—
72C2×D101—42no—
73C2×D101C2×D811yescharacteristic
74C2×D101C2×SD1611yescharacteristic
75#87938—44no—
76C4×C101—21no—
77C4×C101—42no—
78C4×C101#10212yes—
79C4×C101#10412yes—
80Dic101—21no—
81Dic101—21no—
82Dic101#10212yes—
83C2×C101#41011yescharacteristic
84C2×C101C2×#10211yescharacteristic
85C2×C101C2×#10411yescharacteristic
86D101—21no—
87D101—21no—
88D101—82no—
89#1502—1011nomaximal, Sylow
90C101#150211yescharacteristic, complemented, Sylow
91#532—1011no—
92#431—1011no—
93C4×C4⋊C4—1011no—
94#327—1014no—
95C2×#41—2021no—
96C4⋊Q8#8793811yescharacteristic, complemented
97#127—1011no—
98#124—2021no—
99#121—1012no—
100#121—2021no—
101C4×D4—1012no—
102C4×D4—2021no—
103C2×C4⋊C4—2021no—
104C2×C42—1011no—
105C2×C42—2021no—
106C4⋊C8—2021no—
107C22⋊C8—1012no—
108C4×C8—2021no—
109#95—1012no—
110#41—4042no—
111#41—4042no—
112C2×Q8—21no—
113C2×D4—1012no—
114C2×D4—2022no—
115C2×D4—2021no—
116C2×D4—2021no—
117C22×C4—1011no—
118C22×C4—1011no—
119C22×C4—1011no—
120C22×C4—2022no—
121C22×C4—2022no—
122C2×C8—2022no—
123C4⋊C4—21no—
124C4⋊C4—2024no—
125C4⋊C4C2×#8793812yes—
126C22⋊C4—2022no—
127C22⋊C4—2022no—
128C42—1011no—
129C42—1011no—
130C42—1011no—
131C42—4042no—
132C42C2×#8793811yescharacteristic
133C23—1011no—
134C23—2022no—
135Q8—42no—
136D4—4042no—
137D4—4042no—
138D4—4042no—
139D4—4042no—
140D4—4042no—
141C2×C4—22no—
142C2×C4—1011no—
143C2×C4—1012no—
144C2×C4—1012no—
145C2×C4—1011no—
146C2×C4—1011no—
147C2×C4—4041no—
148C2×C4—4044no—
149C2×C4—4042no—
150C2×C4—4042no—
151C2×C4—2024no—
152C2×C4—2022no—
153C2×C4C22⋊#8793811yescharacteristic
154C2×C4C22⋊#8793811yescharacteristic
155C2×C4C22×#8793811yescharacteristic
156C8—4042no—
157C22—1011no—
158C22—1011no—
159C22—4042no—
160C22—4042no—
161C22—4042no—
162C22—2021no—
163C22—2021no—
164C22C2×C22⋊#8793811yescharacteristic
165C4—21no—
166C4—42no—
167C4—1012no—
168C4—4044no—
169C4—2021no—
170C4—2021no—
171C4#1569231712yes—
172C4#1569232012yes—
173C2—8082no—
174C2—2021no—
175C2—2021no—
176C2#2026615811yescharacteristic
177C2C2×#1569231711yescharacteristic
178C2C2×#1569232011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#87938
commutatorC2×C4×C101C22×C4
FrattiniC2×C4C22×#87938
FittingC4⋊Q8×C101C4
socleC22×C101C2×C22⋊C4
prime radical#20265728C2
cosocleC2×C4×D101C23
hypercenterC4⋊Q8#87938
hypocenterC101#1502
LCSG ▷ C2×C4×C101 ▷ C22×C101 ▷ C101
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. #20266196C2semidirect
2. C4×C4⋊#87938C2semidirect
3. #20266029C2semidirect
12. #15692252C4semidirect
17. #15692217C4semidirect
19. C4⋊Q8×C101C4semidirect
90. C101#1502semidirect
96. C4⋊Q8#87938semidirect

Maximal subgroups

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

subgroupindex
#202661962
C4×C4⋊#879382
#202660292
#202657282
#1502101