Finite Group Databasebeta

← #27186514

Subgroups — #27186514

Order 12928.

240 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 68 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#20266195C211yesmaximal, characteristic
2C4×C4⋊#87938C211yesmaximal, characteristic
3#20266031C212yesmaximal
4#20266030C212yesmaximal
5#20265731C211yesmaximal, characteristic
6C2×C4⋊#87938—21no—
7C2×C4×#87938—21no—
8#15692322—21no—
9#15692312C2212yes—
10C4×#11717581—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—24no—
26C4×#87938—42no—
27C2×Dic202—21no—
28C2×Dic202C2×C411yescharacteristic
29C2×C4×D101D411yescharacteristic
30C2×C4×D101D411yescharacteristic
31C2×C4×D101C2311yescharacteristic
32C4⋊Dic101—21no—
33C4⋊Dic101C2×C411yescharacteristic
34#13108053—21no—
35#13108053—21no—
36#13108053—21no—
37#13108053—21no—
38#13108053—21no—
39#13108051—21no—
40#13108051—21no—
41C4×Dic101—21no—
42C4×Dic101C2×C411yescharacteristic
43C4×Dic101D411yescharacteristic
44C4×Dic101D411yescharacteristic
45C2×Q8×C101C2×C411yescharacteristic
46C4⋊C4×C101—21no—
47C4⋊C4×C101C2×C411yescharacteristic
48C42×C101—21no—
49C42×C101C2×C411yescharacteristic
50C22×D101C2×D411yescharacteristic
51C2×#87938—24no—
52C2×#87938—42no—
53C2×#87938—42no—
54Q8×C101—41no—
55C2×C4×C101—21no—
56C2×C4×C101—21no—
57C2×C4×C101C22⋊C411yescharacteristic
58C2×C4×C101C22⋊C411yescharacteristic
59C2×C4×C101C22×C411yescharacteristic
60C2×Dic101—21no—
61C2×Dic101—21no—
62C2×Dic101C22⋊C411yescharacteristic
63C2×Dic101C22⋊C411yescharacteristic
64C2×Dic101C2×D411yescharacteristic
65C4×D101—22no—
66C4×D101—41no—
67C4×D101SD1612yes—
68C4×D101Q1612yes—
69Dic202—42no—
70Dic202—41no—
71#11717581—42no—
72C22×C101C2×C22⋊C411yescharacteristic
73C2×D101—21no—
74C2×D101—21no—
75C2×D101C2×SD1611yescharacteristic
76C2×D101C2×Q1611yescharacteristic
77#87938—44no—
78C4×C101—21no—
79C4×C101—21no—
80C4×C101—41no—
81C4×C101—41no—
82C4×C101#10312yes—
83Dic101—21no—
84Dic101—41no—
85Dic101—41no—
86Dic101#10312yes—
87Dic101#10412yes—
88C2×C101#41011yescharacteristic
89C2×C101C2×#10311yescharacteristic
90C2×C101C2×#10411yescharacteristic
91D101—21no—
92D101—21no—
93#1503—1011nomaximal, Sylow
94C101#150311yescharacteristic, complemented, Sylow
95#533—1011no—
96#431—1011no—
97C4×C4⋊C4—1011no—
98#328—1012no—
99#328—1012no—
100C4⋊Q8—1011no—
101C4⋊Q8—1011no—
102#125—2021no—
103C22⋊Q8—1011no—
104C22⋊Q8—1011no—
105C22⋊Q8—2021no—
106C4×Q8—1011no—
107C4×Q8—2021no—
108C4×Q8#8793811yescharacteristic, complemented
109#117—2021no—
110C2×C4⋊C4—2021no—
111C2×C42—1011no—
112C2×C42—2021no—
113C4⋊C8—2021no—
114C22⋊C8—1012no—
115C4×C8—2021no—
116#95—1012no—
117C2×Q8—1011no—
118C2×Q8—2021no—
119C2×Q8C2×#8793811yescharacteristic
120C22×C4—1011no—
121C22×C4—1011no—
122C22×C4—1011no—
123C22×C4—2022no—
124C2×C8—2022no—
125C4⋊C4—21no—
126C4⋊C4—1011no—
127C4⋊C4—2021no—
128C4⋊C4—2021no—
129C4⋊C4—2021no—
130C4⋊C4—2021no—
131C4⋊C4—2021no—
132C4⋊C4—2024no—
133C4⋊C4—2021no—
134C4⋊C4C2×#8793811yescharacteristic
135C22⋊C4—2021no—
136C22⋊C4—2021no—
137C42—21no—
138C42—1011no—
139C42—1011no—
140C42—1011no—
141C42—4042no—
142C42—2021no—
143C42C2×#8793811yescharacteristic
144C23—1011no—
145Q8—41no—
146Q8—4041no—
147Q8—4042no—
148C2×C4—21no—
149C2×C4—21no—
150C2×C4—1011no—
151C2×C4—1011no—
152C2×C4—1012no—
153C2×C4—1012no—
154C2×C4—1011no—
155C2×C4—4041no—
156C2×C4—4042no—
157C2×C4—4042no—
158C2×C4—2022no—
159C2×C4—2024no—
160C2×C4—2021no—
161C2×C4—2021no—
162C2×C4C22⋊#8793811yescharacteristic
163C2×C4C22⋊#8793811yescharacteristic
164C2×C4C22×#8793811yescharacteristic
165C8—4042no—
166C22—1011no—
167C22—1011no—
168C22—2021no—
169C22—2021no—
170C22C2×C22⋊#8793811yescharacteristic
171C4—21no—
172C4—21no—
173C4—41no—
174C4—41no—
175C4—1012no—
176C4—1012no—
177C4—4044no—
178C4—4041no—
179C4—4041no—
180C4—2021no—
181C4#1569231812yes—
182C2—2021no—
183C2—2021no—
184C2#2026615611yescharacteristic
185C2C2×#1569231811yescharacteristic
186C2D101⋊#10411yescharacteristic
subgroupG/H
centerC2×C4C22⋊#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#1503
LCSG ▷ C2×C4×C101 ▷ C22×C101 ▷ C101
UCSC1 ◁ C2×C4 ◁ 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
94. C101#1503semidirect
108. C4×Q8#87938semidirect

Maximal subgroups

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

subgroupindex
#202661952
C4×C4⋊#879382
#202660312
#202660302
#202657312
#1503101