Finite Group Databasebeta

← #27187312

Subgroups — #27187312

Order 12928.

260 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 78 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
1D101⋊(C4⋊C8)C211yesmaximal, characteristic
2C4×C4⋊#87938C211yesmaximal, characteristic
3#20266050C212yesmaximal
4#20266050C212yesmaximal
5#125×D101C211yesmaximal, characteristic
6C2×D101⋊C8C2212yes—
7C2×C4⋊#87938C2212yes—
8C2×C4×#87938—21no—
9#15692322—21no—
10C4⋊#11717581—21no—
11(C2×#87938)⋊C4—21no—
12#15692247C411yescharacteristic, complemented
13#15692246C411yescharacteristic, complemented
14#15692246C411yescharacteristic, complemented
15#15692245—21no—
16#15692245—21no—
17C4⋊C4×D101—21no—
18C4⋊C4×D101—21no—
19C4⋊C4×D101C2211yescharacteristic
20C4⋊C4×D101C2211yescharacteristic
21C42×D101C2211yescharacteristic
22#125×C101C411yescharacteristic, complemented
23C22×#87938—22no—
24D101⋊C8—24no—
25C2×#11717581—22no—
26C4⋊#87938—22no—
27C4⋊#87938Q814yes—
28C4×#87938—42no—
29C2×C4×D101—21no—
30C2×C4×D101—21no—
31C2×C4×D101D411yescharacteristic
32C2×C4×D101D411yescharacteristic
33C2×C4×D101C2311yescharacteristic
34C4⋊Dic101—21no—
35C4⋊Dic101—21no—
36C4⋊Dic101C2×C411yescharacteristic
37C4⋊Dic101C2×C411yescharacteristic
38#13108053—21no—
39#13108053—21no—
40#13108053—21no—
41#13108053—21no—
42#13108053—21no—
43#13108053—21no—
44C4×Dic101C2×C411yescharacteristic
45C4×Dic101D411yescharacteristic
46C4×Dic101D411yescharacteristic
47C4⋊C4×C101—21no—
48C4⋊C4×C101—21no—
49C4⋊C4×C101C2×C411yescharacteristic
50C4⋊C4×C101C2×C411yescharacteristic
51C42×C101C2×C411yescharacteristic
52C22×D101C2×D411yescharacteristic
53C2×#87938—24no—
54C2×#87938—42no—
55C2×#87938—42no—
56C2×C4×C101—21no—
57C2×C4×C101—21no—
58C2×C4×C101C22⋊C411yescharacteristic
59C2×C4×C101C22⋊C411yescharacteristic
60C2×C4×C101C22×C411yescharacteristic
61C2×Dic101—21no—
62C2×Dic101—21no—
63C2×Dic101C22⋊C411yescharacteristic
64C2×Dic101C22⋊C411yescharacteristic
65C2×Dic101C2×D411yescharacteristic
66C4×D101—22no—
67C4×D101—21no—
68C4×D101—21no—
69C4×D101—42no—
70C4×D101—41no—
71C4×D101—41no—
72C4×D101C2×Q812yes—
73C4×D101#4112yes—
74#11717581—42no—
75C22×C101C2×C22⋊C411yescharacteristic
76C2×D101C22⋊Q812yes—
77C2×D101#13512yes—
78C2×D101AGL(1,ℤ/8)11yescharacteristic
79C2×D101#13711yescharacteristic
80#87938—44no—
81C4×C101—21no—
82C4×C101—21no—
83C4×C101—41no—
84C4×C101—41no—
85C4×C101C4×Q812yes—
86Dic101—21no—
87Dic101—21no—
88Dic101—41no—
89Dic101—41no—
90Dic101#12411yescharacteristic
91Dic101C4⋊Q811yescharacteristic
92C2×C101#39111yescharacteristic
93C2×C101#41611yescharacteristic
94C2×C101#41711yescharacteristic
95D101#47812yes—
96D101#47912yes—
97#1989—1011nomaximal, Sylow
98C101#198911yescharacteristic, complemented, Sylow
99C2×#125—1011no—
100C2×C4⋊C8—1011no—
101C4×C4⋊C4—1011no—
102#340—1012no—
103#340—1012no—
104C22×C8—1012no—
105#125—1011no—
106#125—1011no—
107#125—1011no—
108#125—2021no—
109#125—2021no—
110#125#8793811yescharacteristic, complemented
111C2×C4⋊C4—1012no—
112C2×C4⋊C4—1011no—
113C2×C4⋊C4—1011no—
114C2×C4⋊C4—2021no—
115C2×C4⋊C4—2021no—
116C2×C42—1011no—
117C2×C42—2021no—
118C4⋊C8—2021no—
119C4⋊C8—2021no—
120#95—2021no—
121C22×C4—1011no—
122C22×C4—1011no—
123C22×C4—1011no—
124C22×C4—2021no—
125C22×C4—2021no—
126C22×C4—2022no—
127C2×C8—2022no—
128C2×C8—2024no—
129C4⋊C4—21no—
130C4⋊C4—21no—
131C4⋊C4—1014no—
132C4⋊C4—1011no—
133C4⋊C4—1011no—
134C4⋊C4—2021no—
135C4⋊C4—2021no—
136C4⋊C4—2021no—
137C4⋊C4—2021no—
138C4⋊C4—2021no—
139C4⋊C4—2021no—
140C4⋊C4—2022no—
141C4⋊C4—2021no—
142C4⋊C4—2021no—
143C4⋊C4C2×#8793811yescharacteristic
144C4⋊C4C2×#8793811yescharacteristic
145C42—1011no—
146C42—1011no—
147C42—1011no—
148C42—4042no—
149C42C2×#8793811yescharacteristic
150C23—1011no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—1011no—
154C2×C4—1012no—
155C2×C4—1012no—
156C2×C4—1011no—
157C2×C4—1011no—
158C2×C4—4042no—
159C2×C4—4041no—
160C2×C4—4041no—
161C2×C4—4042no—
162C2×C4—4042no—
163C2×C4—2021no—
164C2×C4—2022no—
165C2×C4—2021no—
166C2×C4—2024no—
167C2×C4—2021no—
168C2×C4—2021no—
169C2×C4C22⋊#8793811yescharacteristic
170C2×C4C22⋊#8793811yescharacteristic
171C2×C4C22×#8793811yescharacteristic
172C8—4042no—
173C22—1012no—
174C22—1012no—
175C22—1011no—
176C22—1011no—
177C22C2×C22⋊#8793811yescharacteristic
178C4—21no—
179C4—21no—
180C4—41no—
181C4—41no—
182C4—1011no—
183C4—1011no—
184C4—4044no—
185C4—4041no—
186C4—4041no—
187C4—2021no—
188C4—2021no—
189C4Q8×#8793812yes—
190C2—1012no—
191C2—1012no—
192C2(C2×#87938)⋊Q811yescharacteristic
193C2#2026616711yescharacteristic
194C2#2026616811yescharacteristic
subgroupG/H
centerC22C2×C22⋊#87938
commutatorC2×C4×C101C22×C4
FrattiniC2×C4C22×#87938
Fitting#125×C101C4
socleC22×C101C2×C22⋊C4
prime radicalC22×D101C2×D4
cosocleC2×C4×D101C23
hypercenter#125#87938
hypocenterC101#1989
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
12. #15692247C4semidirect
13. #15692246C4semidirect
14. #15692246C4semidirect
22. #125×C101C4semidirect
98. C101#1989semidirect
110. #125#87938semidirect

Maximal subgroups

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

subgroupindex
D101⋊(C4⋊C8)2
C4×C4⋊#879382
#202660502
#125×D1012
#1989101