Finite Group Databasebeta

← #27169861

Subgroups — #27169861

Order 12928.

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

normal subgroups only

This group has 202 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#20265732C211yesmaximal, characteristic
2#20265233C211yesmaximal, characteristic
3#20265199C211yesmaximal, characteristic
4#20264925C211yesmaximal, characteristic, complemented
5#20264925C211yesmaximal, characteristic, complemented
6#20264923C211yesmaximal, characteristic, complemented
7#332×C101C211yesmaximal, characteristic, complemented
8C2×#13108057—21no—
9#15692255C2211yescharacteristic
10#15692246—21no—
11#15692235C412yes—
12#15692231—21no—
13Q8×Dic101—21no—
14#15692220C412yes—
15#15692213—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
25C2×Dic202C2×C412yes—
26C2×C4×D101C2×C411yescharacteristic
27C2×C4×D101D411yescharacteristic
28C2×C4×D101D411yescharacteristic
29#13108057—42no—
30C2×#11717579—21no—
31C2×#11717579—21no—
32C4⋊Dic101—21no—
33C4⋊Dic101—21no—
34C4⋊Dic101—22no—
35#13108053—22no—
36#13108051—22no—
37C4×Dic101—22no—
38C4×Dic101C2×C411yescharacteristic
39C4×Dic101D411yescharacteristic
40C4×Dic101D411yescharacteristic
41C2×Q8×C101—21no—
42C2×C8×C101—21no—
43C2×C8×C101—21no—
44C4⋊C4×C101—21no—
45C4⋊C4×C101C2×C412yes—
46C42×C101C2311yescharacteristic
47C22×D101C22⋊C411yescharacteristic
48Q8×C101—41no—
49Q8×C101—41no—
50C2×C4×C101—22no—
51C2×C4×C101C22×C411yescharacteristic
52C2×C4×C101C2×D411yescharacteristic
53C2×C4×C101C2×D411yescharacteristic
54C2×Dic101—22no—
55C2×Dic101C22⋊C411yescharacteristic
56C2×Dic101C22⋊C411yescharacteristic
57C2×Dic101C22⋊C411yescharacteristic
58C4×D101—21no—
59C4×D101—21no—
60C4×D101—21no—
61C4×D101—21no—
62C4×D101—41no—
63Dic202—42no—
64C8×C101—41no—
65C8×C101—41no—
66#11717579—41no—
67#11717579—41no—
68C22×C101C2×C22⋊C411yescharacteristic
69C2×D101—21no—
70C2×D101—21no—
71C2×D101—21no—
72C4×C101—21no—
73C4×C101—42no—
74C4×C101AGL(1,ℤ/8)11yescharacteristic
75C4×C101#13711yescharacteristic
76C4×C101#13711yescharacteristic
77C4×C101#13711yescharacteristic
78Dic101—21no—
79Dic101—21no—
80Dic101—21no—
81Dic101—42no—
82C2×C101#41311yescharacteristic
83C2×C101#41711yescharacteristic
84C2×C101#41911yescharacteristic
85D101—41no—
86#1559—1011nomaximal, Sylow
87C101#155911yescharacteristic, complemented, Sylow
88#533—1011no—
89#432—1011no—
90#423—1011no—
91#333—1011no—
92#333—1011no—
93#332—1011no—
94#332D10111yescharacteristic, complemented
95C2×M16—2021no—
96C4⋊Q8—1011no—
97C4⋊Q8C2×D10111yescharacteristic
98#125—2021no—
99C22⋊Q8—1012no—
100C22⋊Q8—2021no—
101C4×Q8—1012no—
102C4×Q8—2021no—
103#117—2021no—
104C2×C42—1011no—
105C4⋊C8—1011no—
106C4⋊C8—1011no—
107C4⋊C8—2021no—
108C4⋊C8C2×D10111yescharacteristic
109C4⋊C8C2×D10111yescharacteristic
110C22⋊C8—2021no—
111#97—2021no—
112C2×Q8—21no—
113C2×Q8—1012no—
114C22×C4—1011no—
115C22×C4—1011no—
116C22×C4—1011no—
117M16—4042no—
118C2×C8—21no—
119C2×C8—21no—
120C2×C8—2021no—
121C2×C8—2021no—
122C4⋊C4—21no—
123C4⋊C4—2022no—
124C4⋊C4—2022no—
125C4⋊C4—2021no—
126C4⋊C4—2021no—
127C4⋊C4C4×D10112yes—
128C22⋊C4—2022no—
129C42—1011no—
130C42—1011no—
131C42—1011no—
132C42—2022no—
133C42C22×D10111yescharacteristic
134C23—1011no—
135Q8—41no—
136Q8—41no—
137Q8—4042no—
138C2×C4—22no—
139C2×C4—1011no—
140C2×C4—1011no—
141C2×C4—1011no—
142C2×C4—4041no—
143C2×C4—2022no—
144C2×C4—2021no—
145C2×C4—2021no—
146C2×C4—2021no—
147C2×C4—2021no—
148C2×C4C2×C4×D10111yescharacteristic
149C2×C4D4×D10111yescharacteristic
150C2×C4D4×D10111yescharacteristic
151C8—41no—
152C8—41no—
153C8—4041no—
154C8—4041no—
155C22—2021no—
156C22—2021no—
157C22—2021no—
158C22C22⋊C4×D10111yescharacteristic
159C4—21no—
160C4—42no—
161C4—4042no—
162C4—2021no—
163C4—2021no—
164C4—2021no—
165C4#1569227911yescharacteristic
166C4#1569228411yescharacteristic
167C4#1569228411yescharacteristic
168C4#1569228711yescharacteristic
169C2—4041no—
170C2#2026516011yescharacteristic
171C2#2026517511yescharacteristic
172C2#2026518411yescharacteristic
subgroupG/H
centerC22C22⋊C4×D101
commutatorC2×C4×C101C22×C4
FrattiniC42C22×D101
Fitting#332×C101C2
socleC22×C101C2×C22⋊C4
prime radicalC22×D101C22⋊C4
cosocleC42×C101C23
hypercenter#332D101
hypocenterC101#1559
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
4. #20264925C2semidirect
5. #20264925C2semidirect
6. #20264923C2semidirect
7. #332×C101C2semidirect
87. C101#1559semidirect
94. #332D101semidirect

Maximal subgroups

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

subgroupindex
#202657322
#202652332
#202651992
#202649252
#202649232
#332×C1012
#1559101