Finite Group Databasebeta

← #27187040

Subgroups — #27187040

Order 12928.

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

normal subgroups only

This group has 306 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#20266148C211yesmaximal, characteristic
2C4×C22⋊#87938C211yesmaximal, characteristic
3#20266047C212yesmaximal, complemented
4#20266047C212yesmaximal, complemented
5#117×D101C211yesmaximal, characteristic
6C2×#13108084C2212yes—
7C2×C22⋊#87938—21no—
8C2×C4×#87938C2212yes—
9#15692312—21no—
10C22⋊#11717581—21no—
11(C2×#87938)⋊C4—21no—
12C22×C4×D101C2211yescharacteristic
13#15692214C411yescharacteristic, complemented
14#15692213C2211yescharacteristic
15#15692213C2211yescharacteristic
16#15692212—21no—
17#15692211—21no—
18C4⋊C4×D101C411yescharacteristic, complemented
19C4⋊C4×D101C411yescharacteristic, complemented
20C22⋊C4×D101—21no—
21C42×D101—21no—
22#117×C101C411yescharacteristic, complemented
23C22×#87938—22no—
24#13108084—24no—
25C2×#11717581—22no—
26C22⋊#87938—24no—
27C4×#87938—24no—
28C23×D101D411yescharacteristic
29C22×Dic101D411yescharacteristic
30C2×C4×D101—24no—
31C2×C4×D101—21no—
32C2×C4×D101—21no—
33C2×C4×D101C2×C411yescharacteristic
34C2×C4×D101D411yescharacteristic
35C2×C4×D101D411yescharacteristic
36C2×C4×D101C2311yescharacteristic
37C4⋊Dic101C2×C411yescharacteristic
38C4⋊Dic101C2×C411yescharacteristic
39#13108053—21no—
40#13108053—21no—
41C22⋊Dic101—21no—
42#13108051—21no—
43#13108051—21no—
44C4×Dic101—21no—
45C4×Dic101—21no—
46C4×Dic101—21no—
47C22×C4×C101C2×C411yescharacteristic
48C4⋊C4×C101C2×C411yescharacteristic
49C4⋊C4×C101C2×C411yescharacteristic
50C22⋊C4×C101—21no—
51C42×C101—21no—
52C23×C101C22⋊C411yescharacteristic
53C22×D101—22no—
54C22×D101—22no—
55C22×D101—41no—
56C22×D101C22⋊C411yescharacteristic
57C22×D101C2×D411yescharacteristic
58C2×#87938—24no—
59C2×#87938—42no—
60C2×#87938—42no—
61C2×C4×C101—22no—
62C2×C4×C101—21no—
63C2×C4×C101—21no—
64C2×C4×C101C22⋊C411yescharacteristic
65C2×C4×C101C22×C411yescharacteristic
66C2×Dic101—22no—
67C2×Dic101—21no—
68C2×Dic101—21no—
69C2×Dic101C22⋊C411yescharacteristic
70C2×Dic101C2×D411yescharacteristic
71C4×D101—22no—
72C4×D101—22no—
73C4×D101—22no—
74C4×D101—42no—
75C4×D101—42no—
76C4×D101#4114yes—
77#11717581—42no—
78C22×C101—21no—
79C22×C101—21no—
80C22×C101—21no—
81C22×C101C2×C22⋊C411yescharacteristic
82C2×D101—21no—
83C2×D101—21no—
84C2×D101—21no—
85C2×D101—21no—
86C2×D101—44no—
87C2×D101#10412yes—
88C2×D101#12312yes—
89#87938—44no—
90C4×C101—21no—
91C4×C101—41no—
92C4×C101—41no—
93C4×C101#11712yes—
94Dic101—21no—
95Dic101—41no—
96Dic101—41no—
97Dic101#12312yes—
98C2×C101—41no—
99C2×C101#38111yescharacteristic
100C2×C101C2×#10411yescharacteristic
101C2×C101#42111yescharacteristic
102D101—22no—
103D101—22no—
104#1826—1011nomaximal, Sylow
105C101#182611yescharacteristic, complemented, Sylow
106C2×#117—1011no—
107#407—1011no—
108C4×C22⋊C4—1011no—
109#339—1012no—
110#339—1012no—
111C23×C4—1011no—
112C2×M16—1012no—
113#117—1011no—
114#117—1011no—
115#117—1011no—
116#117—2021no—
117#117—2021no—
118#117#8793811yescharacteristic, complemented
119C2×C4⋊C4—1011no—
120C2×C4⋊C4—1011no—
121C2×C22⋊C4—2021no—
122C2×C22⋊C4—2021no—
123C2×C42—1012no—
124C2×C42—2021no—
125C22⋊C8—2021no—
126C22⋊C8—2021no—
127#95—2021no—
128C24—1011no—
129C22×C4—1011no—
130C22×C4—1011no—
131C22×C4—1011no—
132C22×C4—1011no—
133C22×C4—1011no—
134C22×C4—2024no—
135C22×C4—2021no—
136C22×C4—2021no—
137C22×C4—2022no—
138C22×C4C2×#8793811yescharacteristic
139M16—2024no—
140C2×C8—2022no—
141C4⋊C4—1011no—
142C4⋊C4—1011no—
143C4⋊C4—2021no—
144C4⋊C4—2021no—
145C4⋊C4C2×#8793811yescharacteristic
146C4⋊C4C2×#8793811yescharacteristic
147C22⋊C4—21no—
148C22⋊C4—2021no—
149C22⋊C4—2021no—
150C22⋊C4—2024no—
151C22⋊C4—2021no—
152C42—21no—
153C42—2021no—
154C42—2021no—
155C42—2024no—
156C42—2021no—
157C23—1011no—
158C23—1011no—
159C23—4041no—
160C23—2022no—
161C23—2022no—
162C23C22⋊#8793811yescharacteristic
163C2×C4—22no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—1011no—
167C2×C4—1014no—
168C2×C4—1011no—
169C2×C4—4042no—
170C2×C4—4042no—
171C2×C4—4042no—
172C2×C4—4042no—
173C2×C4—2022no—
174C2×C4—2022no—
175C2×C4—2022no—
176C2×C4—2024no—
177C2×C4—2021no—
178C2×C4—2021no—
179C2×C4—2022no—
180C2×C4C22⋊#8793811yescharacteristic
181C2×C4C22×#8793811yescharacteristic
182C8—4042no—
183C22—21no—
184C22—21no—
185C22—21no—
186C22—1012no—
187C22—1012no—
188C22—4044no—
189C22—2021no—
190C22—2021no—
191C22—2021no—
192C22—2021no—
193C22C2×C22⋊#8793811yescharacteristic
194C4—21no—
195C4—41no—
196C4—41no—
197C4—1012no—
198C4—4044no—
199C4—4041no—
200C4—4041no—
201C4—2021no—
202C4#1569233412yes—
203C2—41no—
204C2—2022no—
205C2—2022no—
206C2#2026612011yescharacteristic
207C2D101⋊#10411yescharacteristic
208C2#2026617411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#87938
commutatorC2×C4×C101C22×C4
FrattiniC2×C4C22×#87938
Fitting#117×C101C4
socleC22×C101C2×C22⋊C4
prime radicalC23×D101D4
cosocleC2×C4×D101C23
hypercenter#117#87938
hypocenterC101#1826
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
3. #20266047C2semidirect
4. #20266047C2semidirect
13. #15692214C4semidirect
18. C4⋊C4×D101C4semidirect
19. C4⋊C4×D101C4semidirect
22. #117×C101C4semidirect
105. C101#1826semidirect
118. #117#87938semidirect

Maximal subgroups

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

subgroupindex
#202661482
C4×C22⋊#879382
#202660472
#117×D1012
#1826101