Finite Group Databasebeta

← #27187039

Subgroups — #27187039

Order 12928.

306 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 70 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#20266047C214yesmaximal, complemented
4C2×#15692213C211yesmaximal, characteristic
5C2×#13108084C2212yes—
6C2×C22⋊#87938—21no—
7C2×C4×#87938C2212yes—
8#15692312—21no—
9C22⋊#11717581—21no—
10(C2×#87938)⋊C4—21no—
11C22×C4×D101C2211yescharacteristic
12#15692213—21no—
13#15692213—21no—
14#15692213C412yescomplemented
15#15692213C2212yes—
16C2×C4⋊Dic101C411yescharacteristic, complemented
17C2×#13108051—21no—
18C2×C4×Dic101—21no—
19C2×C4⋊C4×C101C411yescharacteristic, complemented
20C22×#87938—22no—
21#13108084—24no—
22C2×#11717581—22no—
23C22⋊#87938—24no—
24C4×#87938—24no—
25C23×D101D411yescharacteristic
26C22×Dic101—21no—
27C22×Dic101D411yescharacteristic
28C2×C4×D101—24no—
29C2×C4×D101C2×C411yescharacteristic
30C2×C4×D101D411yescharacteristic
31C2×C4×D101D411yescharacteristic
32C2×C4×D101C2311yescharacteristic
33C4⋊Dic101—21no—
34C4⋊Dic101C2×C412yes—
35#13108051—22no—
36#13108051—22no—
37C4×Dic101—22no—
38C4×Dic101—22no—
39C22×C4×C101—21no—
40C22×C4×C101C2×C411yescharacteristic
41C4⋊C4×C101—21no—
42C4⋊C4×C101C2×C412yes—
43C23×C101C22⋊C411yescharacteristic
44C22×D101—22no—
45C22×D101—22no—
46C22×D101—41no—
47C22×D101C22⋊C411yescharacteristic
48C22×D101C2×D411yescharacteristic
49C2×#87938—24no—
50C2×#87938—42no—
51C2×#87938—42no—
52C2×C4×C101—22no—
53C2×C4×C101—22no—
54C2×C4×C101—42no—
55C2×C4×C101C22⋊C411yescharacteristic
56C2×C4×C101C22×C411yescharacteristic
57C2×Dic101—22no—
58C2×Dic101—22no—
59C2×Dic101—42no—
60C2×Dic101C22⋊C411yescharacteristic
61C2×Dic101C2×D411yescharacteristic
62C4×D101—22no—
63C4×D101—22no—
64C4×D101—22no—
65C4×D101#4114yes—
66#11717581—42no—
67C22×C101—21no—
68C22×C101—21no—
69C22×C101#10412yes—
70C22×C101C2×C22⋊C411yescharacteristic
71C2×D101—21no—
72C2×D101—21no—
73C2×D101—21no—
74C2×D101—21no—
75C2×D101—21no—
76C2×D101—44no—
77C2×D101#12312yes—
78#87938—44no—
79C4×C101—21no—
80C4×C101—42no—
81C4×C101#11712yes—
82Dic101—21no—
83Dic101—42no—
84Dic101#12312yes—
85C2×C101—22no—
86C2×C101#38111yescharacteristic
87C2×C101C2×#10411yescharacteristic
88C2×C101#42111yescharacteristic
89D101—22no—
90D101—41no—
91#1826—1011nomaximal, Sylow
92C101#182611yescharacteristic, complemented, Sylow
93C2×#117—1011no—
94#407—1011no—
95C4×C22⋊C4—1011no—
96#339—1014no—
97C23×C4—1011no—
98C2×M16—1012no—
99#117—1012no—
100#117—1012no—
101#117—2021no—
102#117—2021no—
103C2×C4⋊C4—1011no—
104C2×C4⋊C4#8793811yescharacteristic, complemented
105C2×C22⋊C4—2021no—
106C2×C22⋊C4—2021no—
107C2×C42—1012no—
108C2×C42—2021no—
109C22⋊C8—2021no—
110C22⋊C8—2021no—
111#95—2021no—
112C24—1011no—
113C22×C4—21no—
114C22×C4—1011no—
115C22×C4—1011no—
116C22×C4—1011no—
117C22×C4—1011no—
118C22×C4—1011no—
119C22×C4—2024no—
120C22×C4—2022no—
121C22×C4—2021no—
122C22×C4C2×#8793811yescharacteristic
123M16—2024no—
124C2×C8—2022no—
125C4⋊C4—21no—
126C4⋊C4—1012no—
127C4⋊C4—2021no—
128C4⋊C4C2×#8793812yes—
129C22⋊C4—2022no—
130C22⋊C4—2022no—
131C22⋊C4—2024no—
132C42—2022no—
133C42—2022no—
134C42—2024no—
135C23—1011no—
136C23—1011no—
137C23—4041no—
138C23—2022no—
139C23—2022no—
140C23C22⋊#8793811yescharacteristic
141C2×C4—22no—
142C2×C4—22no—
143C2×C4—42no—
144C2×C4—1011no—
145C2×C4—1014no—
146C2×C4—1011no—
147C2×C4—4042no—
148C2×C4—4042no—
149C2×C4—4042no—
150C2×C4—2022no—
151C2×C4—2022no—
152C2×C4—2022no—
153C2×C4—2024no—
154C2×C4—2022no—
155C2×C4—2022no—
156C2×C4C22⋊#8793811yescharacteristic
157C2×C4C22×#8793811yescharacteristic
158C8—4042no—
159C22—21no—
160C22—21no—
161C22—1012no—
162C22—4044no—
163C22—2021no—
164C22—2021no—
165C22—2021no—
166C22—2021no—
167C22—2021no—
168C22#1569232012yes—
169C22C2×C22⋊#8793811yescharacteristic
170C4—21no—
171C4—42no—
172C4—1012no—
173C4—4044no—
174C4—4042no—
175C4—2021no—
176C4#1569233412yes—
177C2—22no—
178C2—4041no—
179C2—2022no—
180C2#2026612011yescharacteristic
181C2C2×#1569232011yescharacteristic
182C2#2026617511yescharacteristic
subgroupG/H
centerC22C2×C22⋊#87938
commutatorC2×C4×C101C22×C4
FrattiniC2×C4C22×#87938
FittingC2×C4⋊C4×C101C4
socleC22×C101C2×C22⋊C4
prime radicalC23×D101D4
cosocleC2×C4×D101C23
hypercenterC2×C4⋊C4#87938
hypocenterC101#1826
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #20266047C2semidirect
14. #15692213C4semidirect
16. C2×C4⋊Dic101C4semidirect
19. C2×C4⋊C4×C101C4semidirect
92. C101#1826semidirect
104. C2×C4⋊C4#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
C2×#156922132
#1826101