Finite Group Databasebeta

← #27169839

Subgroups — #27169839

Order 12928.

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

normal subgroups only

This group has 198 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#20265229C211yesmaximal, characteristic
4#20264925C211yesmaximal, characteristic, complemented
5#20264925C211yesmaximal, characteristic, complemented
6#20264923C211yesmaximal, characteristic, complemented
7#332×C101C211yesmaximal, characteristic, complemented
8#15692255C2211yescharacteristic
9#15692246—21no—
10#15692235C412yes—
11#15692231—21no—
12Q8×Dic101—21no—
13#15692220C412yes—
14#15692213—21no—
15C42×D101C2211yescharacteristic
16C4⋊#11717579C2211yescharacteristic
17C4⋊#11717579C2211yescharacteristic
18#15692167—21no—
19#15692167—21no—
20#15692165—21no—
21C8×Dic101—21no—
22C4⋊Q8×C101C2211yescharacteristic
23C4⋊C8×C101C2211yescharacteristic
24C4⋊C8×C101C2211yescharacteristic
25C2×Dic202C2×C412yes—
26C2×C4×D101C2×C411yescharacteristic
27C2×C4×D101D411yescharacteristic
28C2×C4×D101D411yescharacteristic
29C2×#11717579—21no—
30C2×#11717579—21no—
31C4⋊Dic101—21no—
32C4⋊Dic101—21no—
33C4⋊Dic101—22no—
34#13108053—22no—
35#13108051—22no—
36C4×Dic101—22no—
37C4×Dic101C2×C411yescharacteristic
38C4×Dic101D411yescharacteristic
39C4×Dic101D411yescharacteristic
40C2×Q8×C101—21no—
41C2×C8×C101—21no—
42C2×C8×C101—21no—
43C4⋊C4×C101—21no—
44C4⋊C4×C101C2×C412yes—
45C42×C101C2311yescharacteristic
46C22×D101C22⋊C411yescharacteristic
47Q8×C101—41no—
48Q8×C101—41no—
49C2×C4×C101—22no—
50C2×C4×C101C22×C411yescharacteristic
51C2×C4×C101C2×D411yescharacteristic
52C2×C4×C101C2×D411yescharacteristic
53C2×Dic101—22no—
54C2×Dic101C22⋊C411yescharacteristic
55C2×Dic101C22⋊C411yescharacteristic
56C2×Dic101C22⋊C411yescharacteristic
57C4×D101—21no—
58C4×D101—21no—
59C4×D101—21no—
60C4×D101—21no—
61C4×D101—41no—
62Dic202—42no—
63C8×C101—41no—
64C8×C101—41no—
65#11717579—41no—
66#11717579—41no—
67C22×C101C2×C22⋊C411yescharacteristic
68C2×D101—21no—
69C2×D101—21no—
70C2×D101—21no—
71C4×C101—21no—
72C4×C101—42no—
73C4×C101#13511yescharacteristic
74C4×C101#13511yescharacteristic
75C4×C101#13711yescharacteristic
76C4×C101#13711yescharacteristic
77Dic101—21no—
78Dic101—21no—
79Dic101—21no—
80Dic101—42no—
81C2×C101#41311yescharacteristic
82C2×C101#41611yescharacteristic
83C2×C101#41911yescharacteristic
84D101—41no—
85#1554—1011nomaximal, Sylow
86C101#155411yescharacteristic, complemented, Sylow
87#533—1011no—
88#432—1011no—
89#431—1011no—
90#333—1011no—
91#333—1011no—
92#332—1011no—
93#332D10111yescharacteristic, complemented
94C4⋊Q8—1011no—
95C4⋊Q8C2×D10111yescharacteristic
96#125—2021no—
97C22⋊Q8—1012no—
98C22⋊Q8—2021no—
99C4×Q8—1012no—
100C4×Q8—2021no—
101#117—2021no—
102C2×C42—1011no—
103C4⋊C8—1011no—
104C4⋊C8—1011no—
105C4⋊C8C2×D10111yescharacteristic
106C4⋊C8C2×D10111yescharacteristic
107C22⋊C8—2021no—
108C22⋊C8—2021no—
109#97—2021no—
110C4×C8—2021no—
111C2×Q8—21no—
112C2×Q8—1012no—
113C22×C4—1011no—
114C22×C4—1011no—
115C22×C4—1011no—
116C2×C8—21no—
117C2×C8—21no—
118C2×C8—2021no—
119C2×C8—2021no—
120C4⋊C4—21no—
121C4⋊C4—2022no—
122C4⋊C4—2022no—
123C4⋊C4—2021no—
124C4⋊C4—2021no—
125C4⋊C4C4×D10112yes—
126C22⋊C4—2022no—
127C42—1011no—
128C42—1011no—
129C42—1011no—
130C42—2022no—
131C42C22×D10111yescharacteristic
132C23—1011no—
133Q8—41no—
134Q8—41no—
135Q8—4042no—
136C2×C4—22no—
137C2×C4—1011no—
138C2×C4—1011no—
139C2×C4—1011no—
140C2×C4—4041no—
141C2×C4—2022no—
142C2×C4—2021no—
143C2×C4—2021no—
144C2×C4—2021no—
145C2×C4—2021no—
146C2×C4C2×C4×D10111yescharacteristic
147C2×C4D4×D10111yescharacteristic
148C2×C4D4×D10111yescharacteristic
149C8—41no—
150C8—41no—
151C8—4041no—
152C8—4041no—
153C22—2021no—
154C22—2021no—
155C22—2021no—
156C22C22⋊C4×D10111yescharacteristic
157C4—21no—
158C4—42no—
159C4—4042no—
160C4—2021no—
161C4—2021no—
162C4—2021no—
163C4#1569227411yescharacteristic
164C4#1569227611yescharacteristic
165C4#1569228411yescharacteristic
166C4#1569228711yescharacteristic
167C2—4041no—
168C2#2026516011yescharacteristic
169C2#2026517011yescharacteristic
170C2#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#1554
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
86. C101#1554semidirect
93. #332D101semidirect

Maximal subgroups

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

subgroupindex
#202657322
#202652332
#202652292
#202649252
#202649232
#332×C1012
#1554101