Finite Group Databasebeta

← #27186565

Subgroups — #27186565

Order 12928.

220 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 66 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#20266196C211yesmaximal, characteristic
2#20266121C211yesmaximal, characteristic
3#20266031C212yesmaximal
4#20266030C212yesmaximal
5#20265731C211yesmaximal, characteristic
6C2×C4⋊#87938—21no—
7C4⋊#11717581—21no—
8#15692312C2212yes—
9C4×#11717581—21no—
10(C2×#87938)⋊C4—21no—
11(C2×#87938)⋊C4C2212yes—
12#15692254C411yescharacteristic, complemented
13#15692253C411yescharacteristic, complemented
14#15692245—21no—
15#15692235C2211yescharacteristic
16#15692233—21no—
17#15692231C2211yescharacteristic
18C4×Dic202—21no—
19C4×Dic202C411yescharacteristic, complemented
20#15692212—21no—
21C42×D101C2211yescharacteristic
22C4×Q8×C101C411yescharacteristic, complemented
23C22×#87938—22no—
24C2×#11717581—22no—
25C4⋊#87938—42no—
26C2×Dic202—21no—
27C2×Dic202C2×C411yescharacteristic
28C2×C4×D101D411yescharacteristic
29C2×C4×D101D411yescharacteristic
30C2×C4×D101C2311yescharacteristic
31C4⋊Dic101—21no—
32C4⋊Dic101C2×C411yescharacteristic
33#13108053—21no—
34#13108053—21no—
35#13108053—21no—
36#13108053—21no—
37#13108053—21no—
38#13108051—21no—
39#13108051—21no—
40C4×Dic101—21no—
41C4×Dic101C2×C411yescharacteristic
42C4×Dic101D411yescharacteristic
43C4×Dic101D411yescharacteristic
44C2×Q8×C101C2×C411yescharacteristic
45C4⋊C4×C101—21no—
46C4⋊C4×C101C2×C411yescharacteristic
47C42×C101—21no—
48C42×C101C2×C411yescharacteristic
49C22×D101C2×D411yescharacteristic
50C2×#87938—42no—
51C2×#87938—42no—
52C2×#87938—42no—
53Q8×C101—41no—
54C2×C4×C101—21no—
55C2×C4×C101—21no—
56C2×C4×C101C22⋊C411yescharacteristic
57C2×C4×C101C22⋊C411yescharacteristic
58C2×C4×C101C22×C411yescharacteristic
59C2×Dic101—21no—
60C2×Dic101—21no—
61C2×Dic101C22⋊C411yescharacteristic
62C2×Dic101C22⋊C411yescharacteristic
63C2×Dic101C2×D411yescharacteristic
64C4×D101—41no—
65C4×D101—41no—
66C4×D101SD1612yes—
67C4×D101Q1612yes—
68Dic202—42no—
69Dic202—41no—
70#11717581—42no—
71C22×C101C2×C22⋊C411yescharacteristic
72C2×D101—21no—
73C2×D101—21no—
74C2×D101C2×SD1611yescharacteristic
75C2×D101C2×Q1611yescharacteristic
76#87938—82no—
77C4×C101—21no—
78C4×C101—21no—
79C4×C101—41no—
80C4×C101—41no—
81C4×C101#10312yes—
82Dic101—21no—
83Dic101—21no—
84Dic101—41no—
85Dic101—41no—
86Dic101#10312yes—
87C2×C101#41011yescharacteristic
88C2×C101C2×#10311yescharacteristic
89C2×C101#42111yescharacteristic
90D101—21no—
91D101—21no—
92#1518—1011nomaximal, Sylow
93C101#151811yescharacteristic, complemented, Sylow
94#533—1011no—
95#431—1011no—
96#382—1011no—
97#328—1012no—
98#328—1012no—
99C4⋊Q8—1011no—
100C4⋊Q8—1011no—
101#125—2021no—
102C22⋊Q8—1011no—
103C22⋊Q8—1011no—
104C22⋊Q8—2021no—
105C4×Q8—1011no—
106C4×Q8—2021no—
107C4×Q8#8793811yescharacteristic, complemented
108#117—2021no—
109C2×C4⋊C4—2021no—
110C2×C42—1011no—
111C4⋊C8—2021no—
112C22⋊C8—1012no—
113C4×C8—2021no—
114#95—1012no—
115#95—2021no—
116C2×Q8—1011no—
117C2×Q8—2021no—
118C2×Q8C2×#8793811yescharacteristic
119C22×C4—1011no—
120C22×C4—1011no—
121C22×C4—1011no—
122C22×C4—2022no—
123C2×C8—2022no—
124C4⋊C4—21no—
125C4⋊C4—1011no—
126C4⋊C4—4042no—
127C4⋊C4—2021no—
128C4⋊C4—2021no—
129C4⋊C4—2021no—
130C4⋊C4—2021no—
131C4⋊C4—2021no—
132C4⋊C4—2021no—
133C4⋊C4C2×#8793811yescharacteristic
134C22⋊C4—2021no—
135C22⋊C4—2021no—
136C42—21no—
137C42—1011no—
138C42—1011no—
139C42—1011no—
140C42—2021no—
141C42C2×#8793811yescharacteristic
142C23—1011no—
143Q8—41no—
144Q8—4041no—
145Q8—4042no—
146C2×C4—21no—
147C2×C4—21no—
148C2×C4—1011no—
149C2×C4—1012no—
150C2×C4—1012no—
151C2×C4—1011no—
152C2×C4—1011no—
153C2×C4—4041no—
154C2×C4—4041no—
155C2×C4—4042no—
156C2×C4—4042no—
157C2×C4—4042no—
158C2×C4—2021no—
159C2×C4—2021no—
160C2×C4C22⋊#8793811yescharacteristic
161C2×C4C22⋊#8793811yescharacteristic
162C2×C4C22×#8793811yescharacteristic
163C8—4042no—
164C22—1011no—
165C22—1011no—
166C22—2021no—
167C22—2021no—
168C22C2×C22⋊#8793811yescharacteristic
169C4—21no—
170C4—21no—
171C4—41no—
172C4—41no—
173C4—8082no—
174C4—1012no—
175C4—4041no—
176C4—4041no—
177C4—2021no—
178C4—2021no—
179C4#1569231812yes—
180C2—2021no—
181C2—2021no—
182C2#2026615611yescharacteristic
183C2C2×#1569231811yescharacteristic
184C2#2026617411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#87938
commutatorC2×C4×C101C22×C4
FrattiniC2×C4C22×#87938
FittingC4×Q8×C101C4
socleC22×C101C2×C22⋊C4
prime radicalC22×D101C2×D4
cosocleC2×C4×D101C23
hypercenterC4×Q8#87938
hypocenterC101#1518
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
12. #15692254C4semidirect
13. #15692253C4semidirect
19. C4×Dic202C4semidirect
22. C4×Q8×C101C4semidirect
93. C101#1518semidirect
107. C4×Q8#87938semidirect

Maximal subgroups

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

subgroupindex
#202661962
#202661212
#202660312
#202660302
#202657312
#1518101