Finite Group Databasebeta

← #27187138

Subgroups — #27187138

Order 12928.

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

normal subgroups only

This group has 324 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#20266245C211yesmaximal, characteristic
2#20266170C212yesmaximal
3D101⋊#101C211yesmaximal, characteristic
4#20266048C212yesmaximal
5C4⋊Q8×D101C211yesmaximal, characteristic
6D101⋊M16C2212yes—
7Q8×#87938—24no—
8#15692334—22no—
9#15692334C2212yes—
10#15692318—24no—
11#15692316—22no—
12C2×Q8×D101C2211yescharacteristic
13C2×Q8×D101C2211yescharacteristic
14#15692255C411yescharacteristic, complemented
15#15692254—22no—
16#15692253C411yescharacteristic, complemented
17#15692253C411yescharacteristic, complemented
18C4⋊C4×D101—22no—
19C42×D101C2211yescharacteristic
20C4⋊Q8×C101C411yescharacteristic, complemented
21#13108084—22no—
22#13108083—22no—
23D101⋊C8—22no—
24C4⋊#87938—24no—
25C4⋊#87938D414yes—
26C22⋊#87938—22no—
27C4×#87938—24no—
28C4×#87938—22no—
29C2×Dic202—21no—
30C2×Dic202C2×C411yescharacteristic
31C2×Dic202C2×C411yescharacteristic
32C2×Dic202D412yes—
33Q8×D101—22no—
34Q8×D101—22no—
35Q8×D101—22no—
36Q8×D101—22no—
37C2×C4×D101—21no—
38C2×C4×D101—21no—
39C2×C4×D101D412yes—
40C2×C4×D101C2311yescharacteristic
41C4⋊Dic101—22no—
42#13108053—22no—
43#13108053—22no—
44C4×Dic101—21no—
45C4×Dic101C2×C411yescharacteristic
46C2×Q8×C101C2×C411yescharacteristic
47C2×Q8×C101C2×C411yescharacteristic
48C4⋊C4×C101—22no—
49C42×C101C2×C411yescharacteristic
50C22×D101C2×D411yescharacteristic
51C2×#87938—24no—
52Q8×C101—22no—
53Q8×C101—22no—
54C2×C4×C101—21no—
55C2×C4×C101—21no—
56C2×C4×C101C22⋊C412yes—
57C2×C4×C101C22×C411yescharacteristic
58C2×Dic101—21no—
59C2×Dic101—21no—
60C2×Dic101C22⋊C412yes—
61C2×Dic101C2×D411yescharacteristic
62C4×D101—24no—
63C4×D101—22no—
64C4×D101—22no—
65C4×D101—41no—
66C4×D101—41no—
67C4×D101C2×D412yes—
68C4×D101#4112yes—
69Dic202—22no—
70Dic202—24no—
71Dic202—22no—
72Dic202—42no—
73#11717581—42no—
74C22×C101C2×C22⋊C411yescharacteristic
75C2×D101—22no—
76C2×D101#12011yescharacteristic
77C2×D101#12311yescharacteristic
78#87938—44no—
79C4×C101—22no—
80C4×C101—22no—
81C4×C101—41no—
82C4×C101C4×D412yes—
83Dic101—22no—
84Dic101—22no—
85Dic101—41no—
86Dic101#12112yes—
87C2×C101—21no—
88C2×C101#38611yescharacteristic
89D101—21no—
90D101#45612yes—
91#1886—1011nomaximal, Sylow
92C101#188611yescharacteristic, complemented, Sylow
93C2×C4⋊Q8—1011no—
94#519—1011no—
95#419—1012no—
96C2×#101—1011no—
97#339—1012no—
98C22×Q8—1011no—
99C22×Q8—1011no—
100C2×M16—1012no—
101C4⋊Q8—1011no—
102C4⋊Q8—1011no—
103C4⋊Q8—1011no—
104C4⋊Q8—2022no—
105C4⋊Q8#8793811yescharacteristic, complemented
106C4×Q8—2024no—
107#117—1012no—
108#117—2022no—
109C2×C4⋊C4—2022no—
110C2×C42—1011no—
111#103—2024no—
112#101—2022no—
113C2×Q8—1012no—
114C2×Q8—1011no—
115C2×Q8—1011no—
116C2×Q8—2021no—
117C2×Q8—2022no—
118C2×Q8—2022no—
119C2×Q8—2022no—
120C2×Q8—2022no—
121C2×Q8C2×#8793811yescharacteristic
122C2×Q8C2×#8793811yescharacteristic
123C22×C4—1011no—
124C22×C4—1012no—
125C22×C4—2021no—
126C22×C4—2021no—
127M16—2022no—
128M16—2022no—
129C2×C8—2022no—
130C4⋊C4—22no—
131C4⋊C4—1014no—
132C4⋊C4—2022no—
133C4⋊C4—2022no—
134C4⋊C4—2024no—
135C4⋊C4—2022no—
136C22⋊C4—2022no—
137C42—1011no—
138C42—2021no—
139C42—2022no—
140C42—2024no—
141C42C2×#8793811yescharacteristic
142C23—1011no—
143Q8—22no—
144Q8—22no—
145Q8—4042no—
146Q8—2024no—
147Q8—2022no—
148Q8—2022no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—1011no—
152C2×C4—1012no—
153C2×C4—1012no—
154C2×C4—1012no—
155C2×C4—4041no—
156C2×C4—4041no—
157C2×C4—2022no—
158C2×C4—2022no—
159C2×C4—2024no—
160C2×C4—2024no—
161C2×C4—2021no—
162C2×C4—2021no—
163C2×C4C22⋊#8793812yes—
164C2×C4C22×#8793811yescharacteristic
165C8—4042no—
166C22—1011no—
167C22—1011no—
168C22—2022no—
169C22C2×C22⋊#8793811yescharacteristic
170C4—22no—
171C4—22no—
172C4—41no—
173C4—1012no—
174C4—4044no—
175C4—4041no—
176C4—2022no—
177C4—2022no—
178C4D4×#8793812yes—
179C2—21no—
180C2—1012no—
181C2—2021no—
182C2#2026612511yescharacteristic
subgroupG/H
centerC2#20266125
commutatorC2×C4×C101C22×C4
FrattiniC2×C4C22×#87938
FittingC4⋊Q8×C101C4
socleC2×C101#386
prime radicalC22×D101C2×D4
cosocleC2×C4×D101C23
hypercenterC4⋊Q8#87938
hypocenterC101#1886
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
14. #15692255C4semidirect
16. #15692253C4semidirect
17. #15692253C4semidirect
20. C4⋊Q8×C101C4semidirect
92. C101#1886semidirect
105. C4⋊Q8#87938semidirect

Maximal subgroups

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

subgroupindex
#202662452
#202661702
D101⋊#1012
#202660482
C4⋊Q8×D1012
#1886101