Finite Group Databasebeta

← #27169806

Subgroups — #27169806

Order 12928.

260 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 73 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#20265725C211yesmaximal, characteristic
2#20265199C211yesmaximal, characteristic, complemented
3C4⋊C8×D101C211yesmaximal, characteristic, complemented
4#20264924C211yesmaximal, characteristic, complemented
5#20264922C211yesmaximal, characteristic, complemented
6#20264921C211yesmaximal, characteristic, complemented
7#331×C101C211yesmaximal, characteristic, complemented
8C2×#13108073—21no—
9C2×#13108057—21no—
10C2×C8×D101—21no—
11#15692255C2211yescharacteristic
12#15692242—21no—
13#15692226—21no—
14#15692226C412yes—
15D4×Dic101—21no—
16D4×Dic101C412yes—
17C42×D101C2211yescharacteristic
18C4⋊#11717579C2211yescharacteristic
19C4⋊#11717579C2211yescharacteristic
20#15692184—21no—
21#15692184—21no—
22#127×C101C2211yescharacteristic
23C4⋊C8×C101C2211yescharacteristic
24C4⋊C8×C101C2211yescharacteristic
25#13108073—42no—
26#13108073—42no—
27C2×Dic202—21no—
28C2×C22⋊D101—22no—
29C22×Dic101—22no—
30C2×C4×D101C2×C411yescharacteristic
31C2×C4×D101D411yescharacteristic
32C2×C4×D101D411yescharacteristic
33#13108057—42no—
34C2×#11717579—21no—
35C2×#11717579—21no—
36C8×D101—42no—
37C4⋊Dic101—21no—
38C4⋊Dic101C2×C412yes—
39C22⋊Dic101—22no—
40C22⋊Dic101—22no—
41C4×Dic101C2×C411yescharacteristic
42C4×Dic101D411yescharacteristic
43C4×Dic101D411yescharacteristic
44C2×D4×C101—21no—
45C2×D4×C101—21no—
46C2×D4×C101C2×C412yes—
47C2×C8×C101—21no—
48C2×C8×C101—21no—
49C42×C101C2311yescharacteristic
50C23×C101—22no—
51C22×D101C22⋊C411yescharacteristic
52D4×C101—42no—
53D4×C101—41no—
54D4×C101—41no—
55D4×C101—41no—
56D4×C101—41no—
57C2×C4×C101C22×C411yescharacteristic
58C2×C4×C101C2×D411yescharacteristic
59C2×C4×C101C2×D411yescharacteristic
60C22⋊D101—44no—
61C2×Dic101—22no—
62C2×Dic101—44no—
63C2×Dic101C22⋊C411yescharacteristic
64C2×Dic101C22⋊C411yescharacteristic
65C2×Dic101C22⋊C411yescharacteristic
66C4×D101—21no—
67C4×D101—21no—
68C4×D101—41no—
69C4×D101D812yes—
70C4×D101SD1612yes—
71Dic202—41no—
72Dic202—41no—
73C8×C101—41no—
74C8×C101—41no—
75#11717579—41no—
76#11717579—41no—
77C22×C101—42no—
78C22×C101—42no—
79C22×C101—42no—
80C22×C101C2×C22⋊C411yescharacteristic
81C2×D101—21no—
82C2×D101—21no—
83C2×D101#10212yes—
84C4×C101—21no—
85C4×C101C2×D811yescharacteristic
86C4×C101C2×SD1611yescharacteristic
87C4×C101AGL(1,ℤ/8)11yescharacteristic
88C4×C101#13711yescharacteristic
89Dic101—21no—
90Dic101—21no—
91Dic101—42no—
92Dic101#10212yes—
93C2×C101—82no—
94C2×C101#41311yescharacteristic
95C2×C101C2×#10211yescharacteristic
96C2×C101#41711yescharacteristic
97D101—22no—
98#1547—1011nomaximal, Sylow
99C101#154711yescharacteristic, complemented, Sylow
100#532—1011no—
101#423—1011no—
102C2×C4⋊C8—1011no—
103#332—1011no—
104#332—1011no—
105#331—1011no—
106#331D10111yescharacteristic, complemented
107C2×#41—2021no—
108C2×M16—2021no—
109C22×C8—2021no—
110C4⋊Q8—1011no—
111#127C2×D10111yescharacteristic
112#124—2021no—
113#121—1012no—
114#121—2021no—
115C4×D4—1012no—
116C4×D4—2021no—
117C2×C42—1011no—
118C4⋊C8—1011no—
119C4⋊C8—1011no—
120C4⋊C8—2021no—
121C4⋊C8—2021no—
122C4⋊C8C2×D10111yescharacteristic
123C4⋊C8C2×D10111yescharacteristic
124#41—4042no—
125#41—4042no—
126C2×Q8—2021no—
127C2×D4—21no—
128C2×D4—21no—
129C2×D4—2022no—
130C2×D4C4×D10112yes—
131C22×C4—1011no—
132C22×C4—1011no—
133C22×C4—1011no—
134C22×C4—2022no—
135M16—4042no—
136C2×C8—21no—
137C2×C8—21no—
138C2×C8—4042no—
139C2×C8—2021no—
140C2×C8—2021no—
141C4⋊C4—1012no—
142C4⋊C4—2021no—
143C22⋊C4—2022no—
144C22⋊C4—2022no—
145C42—1011no—
146C42—1011no—
147C42—1011no—
148C42C22×D10111yescharacteristic
149C23—22no—
150C23—1011no—
151Q8—4041no—
152Q8—4041no—
153D4—42no—
154D4—41no—
155D4—41no—
156D4—41no—
157D4—41no—
158D4—4044no—
159C2×C4—1011no—
160C2×C4—1012no—
161C2×C4—1012no—
162C2×C4—1011no—
163C2×C4—1011no—
164C2×C4—4041no—
165C2×C4—4044no—
166C2×C4—2022no—
167C2×C4—2021no—
168C2×C4—2021no—
169C2×C4C2×C4×D10111yescharacteristic
170C2×C4D4×D10111yescharacteristic
171C2×C4D4×D10111yescharacteristic
172C8—41no—
173C8—41no—
174C8—4041no—
175C8—4041no—
176C22—42no—
177C22—42no—
178C22—42no—
179C22—1012no—
180C22—2021no—
181C22—2021no—
182C22C22⋊C4×D10111yescharacteristic
183C4—21no—
184C4—1012no—
185C4—4042no—
186C4—2021no—
187C4—2021no—
188C4D8×D10111yescharacteristic
189C4SD16×D10111yescharacteristic
190C4#1569227911yescharacteristic
191C4#1569228411yescharacteristic
192C2—82no—
193C2—2022no—
194C2#2026515811yescharacteristic
195C2#102×D10111yescharacteristic
196C2#2026517511yescharacteristic
subgroupG/H
centerC22C22⋊C4×D101
commutatorC2×C4×C101C22×C4
FrattiniC42C22×D101
Fitting#331×C101C2
socleC22×C101C2×C22⋊C4
prime radical#20265725C2
cosocleC42×C101C23
hypercenter#331D101
hypocenterC101#1547
LCSG ▷ C2×C4×C101 ▷ C22×C101 ▷ C101
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
2. #20265199C2semidirect
3. C4⋊C8×D101C2semidirect
4. #20264924C2semidirect
5. #20264922C2semidirect
6. #20264921C2semidirect
7. #331×C101C2semidirect
99. C101#1547semidirect
106. #331D101semidirect

Maximal subgroups

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

subgroupindex
#202657252
#202651992
C4⋊C8×D1012
#202649242
#202649222
#202649212
#331×C1012
#1547101