Finite Group Databasebeta

← #27170144

Subgroups — #27170144

Order 12928.

232 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 49 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#20265765C211yesmaximal, characteristic
2#20265507C211yesmaximal, characteristic, complemented
3#20265490C211yesmaximal, characteristic, complemented
4#20264913C211yesmaximal, characteristic, complemented
5#20264910C211yesmaximal, characteristic, complemented
6#20264901C211yesmaximal, characteristic, complemented
7#397×C101C211yesmaximal, characteristic, complemented
8#15692248—21no—
9#15692241—21no—
10#15692237—21no—
11#15692234C2211yescharacteristic
12#15692229C2211yescharacteristic
13#15692228—21no—
14#15692224—21no—
15C4×C22⋊D101—21no—
16#15692188—21no—
17#15692186—21no—
18#15692178—21no—
19#15692175—21no—
20C22⋊#11717579C2211yescharacteristic
21C22⋊#11717579C2211yescharacteristic
22C2×C4⋊C4×C101C2211yescharacteristic
23C2×C22⋊C4×C101—21no—
24C2×C22⋊C4×C101C2211yescharacteristic
25#95×C101—21no—
26#95×C101C2211yescharacteristic
27C2×Dic202D411yescharacteristic
28C2×D404D411yescharacteristic
29C2×C22⋊D101—21no—
30C2×C22⋊D101—21no—
31C2×C22⋊D101—21no—
32C2×C4×D101—21no—
33C2×#11717579—21no—
34C2×#11717579—21no—
35C4⋊Dic101D411yescharacteristic
36C4⋊Dic101D411yescharacteristic
37#13108053—21no—
38#13108053—21no—
39C22⋊Dic101—21no—
40C22⋊Dic101—21no—
41C22⋊Dic101—21no—
42#13108051—21no—
43#13108051—21no—
44C4×Dic101—21no—
45C24×C101D411yescharacteristic
46C22×C4×C101—21no—
47C22×C4×C101—21no—
48C22×C4×C101D411yescharacteristic
49C22×C4×C101C2311yescharacteristic
50C4⋊C4×C101—21no—
51C4⋊C4×C101—21no—
52C22⋊C4×C101—21no—
53C22⋊C4×C101—21no—
54C22⋊C4×C101—42no—
55C23×C101—21no—
56C23×C101—21no—
57C23×C101—21no—
58C23×C101—41no—
59C23×C101—41no—
60C23×C101C2×D411yescharacteristic
61C22×D101—21no—
62C2×C4×C101—21no—
63C2×C4×C101—41no—
64C2×C4×C101—41no—
65C2×C4×C101—41no—
66C2×C4×C101—41no—
67C2×C4×C101—41no—
68C2×C4×C101—41no—
69C2×C4×C101—41no—
70C2×C4×C101—41no—
71C2×C4×C101C2×D411yescharacteristic
72C2×C4×C101C2×D411yescharacteristic
73C22⋊D101—41no—
74C22⋊D101—41no—
75C22⋊D101—81no—
76C22⋊D101—81no—
77C2×Dic101—21no—
78C2×Dic101—21no—
79C2×Dic101—21no—
80D404—41no—
81C4×D101—81no—
82Dic202—41no—
83#11717579—41no—
84#11717579—41no—
85C22×C101—21no—
86C22×C101—21no—
87C22×C101—42no—
88C22×C101—41no—
89C22×C101—41no—
90C22×C101—41no—
91C22×C101—81no—
92C22×C101#12011yescharacteristic
93C22×C101#13511yescharacteristic
94C22×C101AGL(1,ℤ/8)11yescharacteristic
95C2×D101—41no—
96C2×D101—41no—
97C2×D101—41no—
98C4×C101—21no—
99C4×C101—21no—
100C4×C101—41no—
101C4×C101—81no—
102C4×C101—81no—
103Dic101—41no—
104Dic101—41no—
105Dic101—41no—
106C2×C101—21no—
107C2×C101—21no—
108C2×C101—81no—
109C2×C101#44911yescharacteristic
110C2×C101#45511yescharacteristic
111C2×C101#45811yescharacteristic
112D101—81no—
113#1612—1011nomaximal, Sylow
114C101#161211yescharacteristic, complemented, Sylow
115#538—1011no—
116#483—1011no—
117#480—1011no—
118#397D10111yescharacteristic, complemented
119#328—1011no—
120#327—1011no—
121#323—1011no—
122#126—2021no—
123#124—2021no—
124#123—2021no—
125C22⋊Q8—1011no—
126#121—1011no—
127#121—2021no—
128#120—2021no—
129C4×D4—2021no—
130C2×C4⋊C4C2×D10111yescharacteristic
131C2×C22⋊C4—21no—
132C2×C22⋊C4C2×D10111yescharacteristic
133#107—2021no—
134#106—2021no—
135#103—2021no—
136#102—2021no—
137C22⋊C8—1011no—
138C22⋊C8—1011no—
139#95—21no—
140#95C2×D10111yescharacteristic
141C24C22⋊D10111yescharacteristic
142C2×Q8—1011no—
143C2×D4—1011no—
144C2×D4—2021no—
145C2×D4—2021no—
146C2×D4—2021no—
147C22×C4—21no—
148C22×C4—21no—
149C22×C4—2021no—
150C22×C4C22⋊D10111yescharacteristic
151C22×C4C22×D10111yescharacteristic
152C2×C8—2021no—
153C2×C8—2021no—
154C4⋊C4—21no—
155C4⋊C4—21no—
156C4⋊C4—1011no—
157C4⋊C4—1011no—
158C4⋊C4—2021no—
159C4⋊C4—2021no—
160C22⋊C4—21no—
161C22⋊C4—21no—
162C22⋊C4—42no—
163C22⋊C4—2021no—
164C22⋊C4—2021no—
165C22⋊C4—2021no—
166C22⋊C4—2021no—
167C22⋊C4—2021no—
168C42—2021no—
169C23—21no—
170C23—21no—
171C23—21no—
172C23—41no—
173C23—41no—
174C23—2021no—
175C23C2×C22⋊D10111yescharacteristic
176Q8—4041no—
177D4—8081no—
178D4—8081no—
179D4—4041no—
180D4—4041no—
181D4—4041no—
182C2×C4—21no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—41no—
191C2×C4—8081no—
192C2×C4—2021no—
193C2×C4—2021no—
194C2×C4—2021no—
195C2×C4D4×D10111yescharacteristic
196C2×C4D4×D10111yescharacteristic
197C8—4041no—
198C8—4041no—
199C22—21no—
200C22—21no—
201C22—42no—
202C22—41no—
203C22—41no—
204C22—41no—
205C22—81no—
206C22—4041no—
207C22—4041no—
208C22—4041no—
209C22#1569222311yescharacteristic
210C22#1569227511yescharacteristic
211C22#1569228111yescharacteristic
212C4—21no—
213C4—21no—
214C4—41no—
215C4—81no—
216C4—81no—
217C4—4041no—
218C4—4041no—
219C4—4041no—
220C2—21no—
221C2—21no—
222C2—81no—
223C2—8081no—
224C2#2026532011yescharacteristic
225C2#2026535411yescharacteristic
226C2#2026536611yescharacteristic
subgroupG/H
centerC22#15692223
commutator, cosocleC22×C4×C101C23
FrattiniC22×C4C22×D101
Fitting#397×C101C2
socleC22×C101#120
prime radical#20265765C2
hypercenter#397D101
hypocenterC101#1612
LCSG ▷ C22×C4×C101 ▷ C22×C101 ▷ C101
UCSC1 ◁ C22 ◁ C22×C4 ◁ #397

Complements

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

NH ≅ G/Ntype
2. #20265507C2semidirect
3. #20265490C2semidirect
4. #20264913C2semidirect
5. #20264910C2semidirect
6. #20264901C2semidirect
7. #397×C101C2semidirect
114. C101#1612semidirect
118. #397D101semidirect

Maximal subgroups

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

subgroupindex
#202657652
#202655072
#202654902
#202649132
#202649102
#202649012
#397×C1012
#1612101