Finite Group Databasebeta

← #27169853

Subgroups — #27169853

Order 12928.

246 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 65 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
3#20265199C211yesmaximal, characteristic, complemented
4#20264923C211yesmaximal, characteristic, complemented
5#20264920C211yesmaximal, characteristic, complemented
6#20264920C211yesmaximal, characteristic, complemented
7#332×C101C211yesmaximal, characteristic, complemented
8C2×#13108075—21no—
9C2×#13108057—21no—
10#15692252C2211yescharacteristic
11#15692244—21no—
12#15692230—21no—
13#15692230C412yes—
14#15692217—21no—
15#15692217C412yes—
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—42no—
26#13108075—42no—
27C2×D404—22no—
28C2×D404—21no—
29C2×D404—21no—
30C2×D404C2×C412yes—
31C2×C4×D101—22no—
32C2×C4×D101C2×C411yescharacteristic
33C2×C4×D101D411yescharacteristic
34C2×C4×D101D411yescharacteristic
35#13108057—42no—
36C2×#11717579—21no—
37C2×#11717579—21no—
38#13108051—22no—
39#13108051—22no—
40C4×Dic101C2×C411yescharacteristic
41C4×Dic101D411yescharacteristic
42C4×Dic101D411yescharacteristic
43C2×Q8×C101—21no—
44C2×C8×C101—21no—
45C2×C8×C101—21no—
46C4⋊C4×C101—21no—
47C4⋊C4×C101C2×C412yes—
48C42×C101C2311yescharacteristic
49C22×D101—22no—
50C22×D101C22⋊C411yescharacteristic
51Q8×C101—41no—
52Q8×C101—41no—
53C2×C4×C101—22no—
54C2×C4×C101C22×C411yescharacteristic
55C2×C4×C101C2×D411yescharacteristic
56C2×C4×C101C2×D411yescharacteristic
57C2×Dic101C22⋊C411yescharacteristic
58C2×Dic101C22⋊C411yescharacteristic
59C2×Dic101C22⋊C411yescharacteristic
60D404—42no—
61D404—44no—
62D404—41no—
63D404—41no—
64D404—41no—
65D404—41no—
66C4×D101—21no—
67C4×D101—21no—
68C4×D101—21no—
69C4×D101—21no—
70C4×D101—41no—
71C4×D101—44no—
72C8×C101—41no—
73C8×C101—41no—
74#11717579—41no—
75#11717579—41no—
76C22×C101C2×C22⋊C411yescharacteristic
77C2×D101—21no—
78C2×D101—21no—
79C2×D101—21no—
80C2×D101—42no—
81C2×D101—42no—
82C2×D101—42no—
83C4×C101—21no—
84C4×C101—42no—
85C4×C101AGL(1,ℤ/8)11yescharacteristic
86C4×C101AGL(1,ℤ/8)11yescharacteristic
87C4×C101AGL(1,ℤ/8)11yescharacteristic
88C4×C101#13711yescharacteristic
89Dic101—21no—
90Dic101—21no—
91Dic101—21no—
92C2×C101#41311yescharacteristic
93C2×C101#41711yescharacteristic
94C2×C101#41811yescharacteristic
95D101—41no—
96D101—82no—
97#1557—1011nomaximal, Sylow
98C101#155711yescharacteristic, complemented, Sylow
99#532—1011no—
100#432—1011no—
101#423—1011no—
102#332—1011no—
103#332D10111yescharacteristic, complemented
104#331—1011no—
105#331—1011no—
106C2×#41—2021no—
107C2×M16—2021no—
108C4⋊Q8C2×D10111yescharacteristic
109#127—1011no—
110#124—2021no—
111#121—1012no—
112#121—2021no—
113C4×D4—1012no—
114C4×D4—2021no—
115C2×C42—1011no—
116C4⋊C8—1011no—
117C4⋊C8—1011no—
118C4⋊C8—2021no—
119C4⋊C8C2×D10111yescharacteristic
120C4⋊C8C2×D10111yescharacteristic
121C22⋊C8—2021no—
122#97—2021no—
123#41—4042no—
124#41—4042no—
125C2×Q8—21no—
126C2×D4—1012no—
127C2×D4—2022no—
128C2×D4—2021no—
129C2×D4—2021no—
130C22×C4—1011no—
131C22×C4—1011no—
132C22×C4—1011no—
133C22×C4—2022no—
134M16—4042no—
135C2×C8—21no—
136C2×C8—21no—
137C2×C8—2021no—
138C2×C8—2021no—
139C4⋊C4—21no—
140C4⋊C4C4×D10112yes—
141C22⋊C4—2022no—
142C22⋊C4—2022no—
143C42—1011no—
144C42—1011no—
145C42—1011no—
146C42C22×D10111yescharacteristic
147C23—1011no—
148C23—2022no—
149Q8—41no—
150Q8—41no—
151D4—4042no—
152D4—4044no—
153D4—4041no—
154D4—4041no—
155D4—4041no—
156D4—4041no—
157C2×C4—22no—
158C2×C4—1011no—
159C2×C4—1011no—
160C2×C4—1011no—
161C2×C4—4041no—
162C2×C4—4044no—
163C2×C4—2021no—
164C2×C4—2021no—
165C2×C4—2021no—
166C2×C4—2021no—
167C2×C4C2×C4×D10111yescharacteristic
168C2×C4D4×D10111yescharacteristic
169C2×C4D4×D10111yescharacteristic
170C8—41no—
171C8—41no—
172C8—4041no—
173C8—4041no—
174C22—4042no—
175C22—4042no—
176C22—4042no—
177C22—2021no—
178C22—2021no—
179C22—2021no—
180C22C22⋊C4×D10111yescharacteristic
181C4—21no—
182C4—42no—
183C4—2021no—
184C4—2021no—
185C4—2021no—
186C4#1569227911yescharacteristic
187C4#1569228211yescharacteristic
188C4#1569228211yescharacteristic
189C4#1569228711yescharacteristic
190C2—8082no—
191C2—4041no—
192C2#2026516011yescharacteristic
193C2#2026517711yescharacteristic
194C2#2026518011yescharacteristic
subgroupG/H
centerC22C22⋊C4×D101
commutatorC2×C4×C101C22×C4
FrattiniC42C22×D101
Fitting#332×C101C2
socleC22×C101C2×C22⋊C4
prime radical#20265728C2
cosocleC42×C101C23
hypercenter#332D101
hypocenterC101#1557
LCSG ▷ C2×C4×C101 ▷ C22×C101 ▷ C101
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
2. #20265233C2semidirect
3. #20265199C2semidirect
4. #20264923C2semidirect
5. #20264920C2semidirect
6. #20264920C2semidirect
7. #332×C101C2semidirect
98. C101#1557semidirect
103. #332D101semidirect

Maximal subgroups

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

subgroupindex
#202657282
#202652332
#202651992
#202649232
#202649202
#332×C1012
#1557101