Finite Group Databasebeta

← #27169826

Subgroups — #27169826

Order 12928.

252 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 67 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#20265728C211yesmaximal, characteristic
2#20265233C211yesmaximal, characteristic, complemented
3C4⋊C8×D101C211yesmaximal, characteristic, complemented
4#20264926C211yesmaximal, characteristic, complemented
5#20264920C211yesmaximal, characteristic, complemented
6#20264920C211yesmaximal, characteristic, complemented
7#333×C101C211yesmaximal, characteristic, complemented
8C2×#13108075C412yes—
9C2×C8×D101—21no—
10#15692252C2211yescharacteristic
11#15692244C412yes—
12#15692230—21no—
13#15692230—21no—
14#15692217—21no—
15#15692217—21no—
16C42×D101C2211yescharacteristic
17C4⋊#11717579C2211yescharacteristic
18C4⋊#11717579C2211yescharacteristic
19#15692184—21no—
20#15692167—21no—
21#15692165—21no—
22C4⋊Q8×C101C2211yescharacteristic
23C4⋊C8×C101C2211yescharacteristic
24C4⋊C8×C101C2211yescharacteristic
25#13108075—44no—
26C2×D404—22no—
27C2×D404—21no—
28C2×D404—21no—
29C2×D404C2×C412yes—
30C2×C4×D101—22no—
31C2×C4×D101C2×C411yescharacteristic
32C2×C4×D101D411yescharacteristic
33C2×C4×D101D411yescharacteristic
34C2×#11717579—21no—
35C2×#11717579—21no—
36C8×D101—42no—
37#13108051—22no—
38#13108051—22no—
39C4×Dic101C2×C411yescharacteristic
40C4×Dic101D411yescharacteristic
41C4×Dic101D411yescharacteristic
42C2×Q8×C101C2×C412yes—
43C2×C8×C101—21no—
44C2×C8×C101—21no—
45C4⋊C4×C101—21no—
46C4⋊C4×C101—21no—
47C42×C101C2311yescharacteristic
48C22×D101—22no—
49C22×D101C22⋊C411yescharacteristic
50Q8×C101—42no—
51C2×C4×C101—22no—
52C2×C4×C101C22×C411yescharacteristic
53C2×C4×C101C2×D411yescharacteristic
54C2×C4×C101C2×D411yescharacteristic
55C2×Dic101C22⋊C411yescharacteristic
56C2×Dic101C22⋊C411yescharacteristic
57C2×Dic101C22⋊C411yescharacteristic
58D404—42no—
59D404—44no—
60D404—41no—
61D404—41no—
62D404—41no—
63D404—41no—
64C4×D101—22no—
65C4×D101—21no—
66C4×D101—21no—
67C4×D101—21no—
68C4×D101—21no—
69C4×D101—44no—
70C8×C101—41no—
71C8×C101—41no—
72#11717579—41no—
73#11717579—41no—
74C22×C101C2×C22⋊C411yescharacteristic
75C2×D101—21no—
76C2×D101—21no—
77C2×D101—42no—
78C2×D101—42no—
79C2×D101—42no—
80C2×D101#10012yes—
81C4×C101—21no—
82C4×C101—42no—
83C4×C101#13511yescharacteristic
84C4×C101#13511yescharacteristic
85C4×C101AGL(1,ℤ/8)11yescharacteristic
86C4×C101#13711yescharacteristic
87Dic101—21no—
88Dic101—21no—
89Dic101—21no—
90C2×C101C2×#10011yescharacteristic
91C2×C101#41611yescharacteristic
92C2×C101#41711yescharacteristic
93D101—22no—
94D101—82no—
95#1551—1011nomaximal, Sylow
96C101#155111yescharacteristic, complemented, Sylow
97#532—1011no—
98#432—1011no—
99C2×C4⋊C8—1011no—
100#333—1011no—
101#333D10111yescharacteristic, complemented
102#331—1011no—
103#331—1011no—
104C2×#41—1012no—
105C22×C8—2021no—
106C4⋊Q8C2×D10111yescharacteristic
107#127—1011no—
108#124—1012no—
109#121—2021no—
110#121—2021no—
111C4×D4—2021no—
112C4×D4—2021no—
113C2×C42—1011no—
114C4⋊C8—1011no—
115C4⋊C8—1011no—
116C4⋊C8—2021no—
117C4⋊C8C2×D10111yescharacteristic
118C4⋊C8C2×D10111yescharacteristic
119C22⋊C8—2021no—
120#97—2021no—
121#41—4044no—
122C2×Q8C4×D10112yes—
123C2×D4—1012no—
124C2×D4—2022no—
125C2×D4—2021no—
126C2×D4—2021no—
127C22×C4—1011no—
128C22×C4—1011no—
129C22×C4—1011no—
130C22×C4—2022no—
131C2×C8—21no—
132C2×C8—21no—
133C2×C8—4042no—
134C2×C8—2021no—
135C2×C8—2021no—
136C4⋊C4—21no—
137C4⋊C4—21no—
138C22⋊C4—2022no—
139C22⋊C4—2022no—
140C42—1011no—
141C42—1011no—
142C42—1011no—
143C42C22×D10111yescharacteristic
144C23—1011no—
145C23—2022no—
146Q8—42no—
147D4—4042no—
148D4—4044no—
149D4—4041no—
150D4—4041no—
151D4—4041no—
152D4—4041no—
153C2×C4—22no—
154C2×C4—1011no—
155C2×C4—1011no—
156C2×C4—1011no—
157C2×C4—4044no—
158C2×C4—2022no—
159C2×C4—2021no—
160C2×C4—2021no—
161C2×C4—2021no—
162C2×C4—2021no—
163C2×C4C2×C4×D10111yescharacteristic
164C2×C4D4×D10111yescharacteristic
165C2×C4D4×D10111yescharacteristic
166C8—41no—
167C8—41no—
168C8—4041no—
169C8—4041no—
170C22—1012no—
171C22—4042no—
172C22—4042no—
173C22—4042no—
174C22—2021no—
175C22—2021no—
176C22C22⋊C4×D10111yescharacteristic
177C4—21no—
178C4—42no—
179C4—2021no—
180C4—2021no—
181C4—2021no—
182C4#1569227611yescharacteristic
183C4#1569227811yescharacteristic
184C4#1569228211yescharacteristic
185C4#1569228711yescharacteristic
186C2—8082no—
187C2—2022no—
188C2#100×D10111yescharacteristic
189C2#2026517211yescharacteristic
190C2#2026517711yescharacteristic
subgroupG/H
centerC22C22⋊C4×D101
commutatorC2×C4×C101C22×C4
FrattiniC42C22×D101
Fitting#333×C101C2
socleC22×C101C2×C22⋊C4
prime radical#20265728C2
cosocleC42×C101C23
hypercenter#333D101
hypocenterC101#1551
LCSG ▷ C2×C4×C101 ▷ C22×C101 ▷ C101
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
2. #20265233C2semidirect
3. C4⋊C8×D101C2semidirect
4. #20264926C2semidirect
5. #20264920C2semidirect
6. #20264920C2semidirect
7. #333×C101C2semidirect
96. C101#1551semidirect
101. #333D101semidirect

Maximal subgroups

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

subgroupindex
#202657282
#202652332
C4⋊C8×D1012
#202649262
#202649202
#333×C1012
#1551101