Finite Group Databasebeta

← #27186657

Subgroups — #27186657

Order 12928.

198 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 198 conjugacy classes of subgroups — too many to draw. Only its 58 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#20266200C211yesmaximal, characteristic
2#20266195C211yesmaximal, characteristic
3#20266037C212yesmaximal, complemented
4#20266036C212yesmaximal, complemented
5#20265731C211yesmaximal, characteristic
6#15692322C2212yes—
7#15692322C2212yes—
8#15692312—21no—
9#15692312—21no—
10#15692310—21no—
11C4×#11717581—21no—
12#15692254C2211yescharacteristic
13#15692253C2211yescharacteristic
14#15692245—21no—
15#15692235C411yescharacteristic
16#15692233—21no—
17#15692231C411yescharacteristic
18C4×Dic202—21no—
19C4×Dic202C411yescharacteristic
20#15692212—21no—
21C42×D101C2211yescharacteristic
22C4×Q8×C101C411yescharacteristic
23C2×#11717581—22no—
24C2×#11717581—22no—
25C2×Dic202—21no—
26C2×Dic202C2×C411yescharacteristic
27C2×C4×D101C2×C411yescharacteristic
28C2×C4×D101D411yescharacteristic
29C2×C4×D101D411yescharacteristic
30C4⋊Dic101—21no—
31C4⋊Dic101C2×C411yescharacteristic
32#13108053—21no—
33#13108053—21no—
34#13108053—21no—
35#13108053—21no—
36#13108053—21no—
37#13108051—21no—
38#13108051—21no—
39C4×Dic101—21no—
40C4×Dic101D411yescharacteristic
41C4×Dic101D411yescharacteristic
42C4×Dic101C2311yescharacteristic
43C2×Q8×C101C2×C411yescharacteristic
44C4⋊C4×C101—21no—
45C4⋊C4×C101C2×C411yescharacteristic
46C42×C101—21no—
47C42×C101C2×C411yescharacteristic
48C22×D101C22⋊C411yescharacteristic
49Q8×C101—41no—
50C2×C4×C101—21no—
51C2×C4×C101—21no—
52C2×C4×C101C22⋊C411yescharacteristic
53C2×C4×C101C22⋊C411yescharacteristic
54C2×C4×C101C22×C411yescharacteristic
55C2×Dic101—21no—
56C2×Dic101—21no—
57C2×Dic101C22⋊C411yescharacteristic
58C2×Dic101C2×D411yescharacteristic
59C2×Dic101C2×D411yescharacteristic
60C4×D101—22no—
61C4×D101—22no—
62C4×D101—41no—
63Dic202—42no—
64Dic202—41no—
65#11717581—42no—
66#11717581—42no—
67C22×C101C2×C22⋊C411yescharacteristic
68C2×D101—21no—
69C2×D101—21no—
70C2×D101—21no—
71C4×C101—21no—
72C4×C101—21no—
73C4×C101—21no—
74C4×C101—41no—
75C4×C101—41no—
76Dic101—21no—
77Dic101—41no—
78Dic101—41no—
79Dic101#13512yes—
80Dic101#13712yes—
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—1012no—
91#332—1012no—
92C4⋊Q8—1011no—
93C4⋊Q8—1011no—
94#125—2021no—
95C22⋊Q8—1011no—
96C22⋊Q8—1011no—
97C22⋊Q8—2021no—
98C4×Q8—1011no—
99C4×Q8—2021no—
100C4×Q8#8793811yescharacteristic
101#117—2021no—
102C2×C42—1011no—
103C4⋊C8—1012no—
104C4⋊C8—1012no—
105C22⋊C8—2021no—
106C22⋊C8—2021no—
107#97—2021no—
108C4×C8—2021no—
109C2×Q8—1011no—
110C2×Q8—2021no—
111C2×Q8C2×#8793811yescharacteristic
112C22×C4—1011no—
113C22×C4—1011no—
114C22×C4—1011no—
115C2×C8—2022no—
116C2×C8—2022no—
117C4⋊C4—21no—
118C4⋊C4—1011no—
119C4⋊C4—2021no—
120C4⋊C4—2021no—
121C4⋊C4—2021no—
122C4⋊C4—2021no—
123C4⋊C4—2021no—
124C4⋊C4—2021no—
125C4⋊C4C2×#8793811yescharacteristic
126C22⋊C4—2021no—
127C22⋊C4—2021no—
128C42—21no—
129C42—1011no—
130C42—1011no—
131C42—1011no—
132C42—2021no—
133C42C2×#8793811yescharacteristic
134C23—1011no—
135Q8—41no—
136Q8—4041no—
137Q8—4042no—
138C2×C4—21no—
139C2×C4—21no—
140C2×C4—1011no—
141C2×C4—1011no—
142C2×C4—1011no—
143C2×C4—4041no—
144C2×C4—2022no—
145C2×C4—2022no—
146C2×C4—2021no—
147C2×C4—2021no—
148C2×C4C22⋊#8793811yescharacteristic
149C2×C4C22⋊#8793811yescharacteristic
150C2×C4C22×#8793811yescharacteristic
151C8—4042no—
152C8—4042no—
153C22—2021no—
154C22—2021no—
155C22—2021no—
156C22C2×C22⋊#8793811yescharacteristic
157C4—21no—
158C4—21no—
159C4—21no—
160C4—41no—
161C4—41no—
162C4—1012no—
163C4—1012no—
164C4—4041no—
165C4—4041no—
166C4—2021no—
167C2—4041no—
168C2#2026616311yescharacteristic
169C2#2026616711yescharacteristic
170C2#2026617011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#87938
commutatorC2×C4×C101C22×C4
FrattiniC2×C4C22×#87938
FittingC4×Q8×C101C4
socleC22×C101C2×C22⋊C4
prime radicalC22×D101C22⋊C4
cosocleC4×Dic101C23
hypercenterC4×Q8#87938
hypocenterC101#1554
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
3. #20266037C2semidirect
4. #20266036C2semidirect
86. C101#1554semidirect

Maximal subgroups

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

subgroupindex
#202662002
#202661952
#202660372
#202660362
#202657312
#1554101