Finite Group Databasebeta

← #27186494

Subgroups — #27186494

Order 12928.

202 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 60 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#20266198C211yesmaximal, characteristic
2#20266193C211yesmaximal, characteristic
3#20266027C212yesmaximal, complemented
4Q8⋊#11717581C212yesmaximal, complemented
5#20265729C211yesmaximal, characteristic
6C4⋊#11717581—21no—
7C4⋊#11717581C2212yes—
8C22⋊#11717581—21no—
9C22⋊#11717581—21no—
10#15692310—21no—
11C4×#11717581C2212yes—
12#15692254C411yescharacteristic
13#15692253C411yescharacteristic
14#15692245—21no—
15#15692234C411yescharacteristic
16#15692232—21no—
17Q8×Dic101C2211yescharacteristic
18#15692220—21no—
19#15692220C2211yescharacteristic
20#15692211—21no—
21C2×C4×Dic101C2211yescharacteristic
22C22⋊Q8×C101C411yescharacteristic
23C2×#11717581—22no—
24C2×#11717581—22no—
25C2×Dic202—21no—
26C2×Dic202C2×C411yescharacteristic
27C22×Dic101D411yescharacteristic
28C22×Dic101D411yescharacteristic
29C4⋊Dic101—21no—
30C4⋊Dic101C2×C411yescharacteristic
31#13108053—21no—
32#13108053—21no—
33#13108053—21no—
34#13108053—21no—
35#13108053—21no—
36C22⋊Dic101—21no—
37C4×Dic101—21no—
38C4×Dic101—21no—
39C4×Dic101C2×C411yescharacteristic
40C4×Dic101D411yescharacteristic
41C4×Dic101D411yescharacteristic
42C4×Dic101C2311yescharacteristic
43C2×Q8×C101C2×C411yescharacteristic
44C22×C4×C101C2×C411yescharacteristic
45C4⋊C4×C101—21no—
46C4⋊C4×C101C2×C411yescharacteristic
47C22⋊C4×C101—21no—
48C23×C101C22⋊C411yescharacteristic
49Q8×C101—22no—
50C2×C4×C101—22no—
51C2×C4×C101—21no—
52C2×C4×C101—21no—
53C2×C4×C101C22⋊C411yescharacteristic
54C2×C4×C101C22×C411yescharacteristic
55C2×Dic101—22no—
56C2×Dic101—21no—
57C2×Dic101—21no—
58C2×Dic101—41no—
59C2×Dic101C22⋊C411yescharacteristic
60C2×Dic101C22⋊C411yescharacteristic
61C2×Dic101C2×D411yescharacteristic
62C2×Dic101C2×D411yescharacteristic
63Dic202—22no—
64Dic202—42no—
65#11717581—42no—
66#11717581—42no—
67C22×C101—21no—
68C22×C101—21no—
69C22×C101—21no—
70C22×C101C2×C22⋊C411yescharacteristic
71C4×C101—21no—
72C4×C101—41no—
73C4×C101—41no—
74C4×C101#13112yes—
75Dic101—21no—
76Dic101—21no—
77Dic101—21no—
78Dic101—41no—
79Dic101—41no—
80Dic101#13712yes—
81C2×C101—41no—
82C2×C101#40811yescharacteristic
83C2×C101#41911yescharacteristic
84C2×C101#42111yescharacteristic
85#1497—1011nomaximal, Sylow
86C101#149711yescharacteristic, complemented, Sylow
87#533—1011no—
88#432—1011no—
89#431—1011no—
90Q8⋊C8—1012no—
91Q8⋊C8—1012no—
92C4⋊Q8—1011no—
93C4⋊Q8—1011no—
94#125—2021no—
95C22⋊Q8—1011no—
96C22⋊Q8—2021no—
97C22⋊Q8#8793811yescharacteristic
98C4×Q8—1011no—
99C4×Q8—1011no—
100C4×Q8—2021no—
101#117—2021no—
102C2×C42—1011no—
103C4⋊C8—1012no—
104C4⋊C8—2021no—
105C22⋊C8—2021no—
106C22⋊C8—2021no—
107#97—2021no—
108C4×C8—1012no—
109C2×Q8—1011no—
110C2×Q8—2021no—
111C2×Q8C2×#8793811yescharacteristic
112C22×C4—1011no—
113C22×C4—1011no—
114C22×C4C2×#8793811yescharacteristic
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—21no—
127C22⋊C4—2021no—
128C42—1011no—
129C42—1011no—
130C42—1011no—
131C42—1011no—
132C42—2021no—
133C42—2021no—
134C23C22⋊#8793811yescharacteristic
135Q8—22no—
136Q8—4042no—
137Q8—2022no—
138C2×C4—22no—
139C2×C4—21no—
140C2×C4—21no—
141C2×C4—1011no—
142C2×C4—1011no—
143C2×C4—1011no—
144C2×C4—1011no—
145C2×C4—4041no—
146C2×C4—2022no—
147C2×C4—2021no—
148C2×C4—2021no—
149C2×C4C22⋊#8793811yescharacteristic
150C2×C4C22×#8793811yescharacteristic
151C8—4042no—
152C8—4042no—
153C22—21no—
154C22—21no—
155C22—21no—
156C22C2×C22⋊#8793811yescharacteristic
157C4—21no—
158C4—41no—
159C4—41no—
160C4—1012no—
161C4—4041no—
162C4—4041no—
163C4—2021no—
164C4—2021no—
165C4—2021no—
166C4#1569234212yes—
167C2—41no—
168C2#2026615011yescharacteristic
169C2#2026617011yescharacteristic
170C2#2026617411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#87938
commutatorC2×C4×C101C22×C4
FrattiniC2×C4C22×#87938
FittingC22⋊Q8×C101C4
socleC22×C101C2×C22⋊C4
prime radicalC23×C101C22⋊C4
cosocleC4×Dic101C23
hypercenterC22⋊Q8#87938
hypocenterC101#1497
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
3. #20266027C2semidirect
4. Q8⋊#11717581C2semidirect
86. C101#1497semidirect

Maximal subgroups

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

subgroupindex
#202661982
#202661932
#202660272
Q8⋊#117175812
#202657292
#1497101