Finite Group Databasebeta

← #13067598

Subgroups — #13067598

Order 1408.

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

normal subgroups only

This group has 260 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#10623025C211yesmaximal, characteristic
2#10622560C211yesmaximal, characteristic, complemented
3#10622352C211yesmaximal, characteristic, complemented
4#10622351C211yesmaximal, characteristic, complemented
5C11×#323C211yesmaximal, characteristic, complemented
6#10622108C211yesmaximal, characteristic, complemented
7#10622105C211yesmaximal, characteristic, complemented
8C22×Dic22C2211yescharacteristic
9C2×C11×C22⋊C4C2211yescharacteristic
10#67006—21no—
11C2×C22⋊Dic11—21no—
12#66983C2211yescharacteristic
13C4×C22⋊D11—21no—
14#66977C2211yescharacteristic
15C2×Dic44—21no—
16C2×#4314—21no—
17#66938—21no—
18#66937—21no—
19#66936—21no—
20#66932—21no—
21C11×C22⋊C8C2211yescharacteristic
22C11×C22⋊C8C2211yescharacteristic
23C11⋊#95—21no—
24C11⋊#95C2211yescharacteristic
25#66880—21no—
26#66880—21no—
27C24×C11D411yescharacteristic
28C22×C4×C11D411yescharacteristic
29C22×C4×C11C2311yescharacteristic
30C2×C22⋊D11—21no—
31C2×C22⋊D11—21no—
32C2×C22⋊D11—21no—
33C22×Dic11—21no—
34C22×Dic11—21no—
35C2×D44D411yescharacteristic
36C2×C4×D11—21no—
37C2×Dic22—21no—
38C2×Dic22—21no—
39C2×Dic22—42no—
40C2×Dic22D411yescharacteristic
41C2×C8×C11—21no—
42C2×C8×C11—21no—
43C11×C22⋊C4—21no—
44C11×C22⋊C4—21no—
45C22⋊Dic11—21no—
46C22⋊Dic11—21no—
47C22⋊Dic11—21no—
48C22⋊Dic11—42no—
49(C2×D11)⋊C4—21no—
50(C2×D11)⋊C4—21no—
51C4⋊Dic11D411yescharacteristic
52C4⋊Dic11D411yescharacteristic
53Dic11⋊C4—21no—
54Dic11⋊C4—21no—
55C4×Dic11—21no—
56Dic44—42no—
57#4314—42no—
58#1606—111nomaximal, Sylow
59C23×C11—21no—
60C23×C11—21no—
61C23×C11—21no—
62C23×C11—41no—
63C23×C11—41no—
64C23×C11C2×D411yescharacteristic
65C22×D11—21no—
66C2×C4×C11—21no—
67C2×C4×C11—41no—
68C2×C4×C11—41no—
69C2×C4×C11C2×D411yescharacteristic
70C2×C4×C11C2×D411yescharacteristic
71C22⋊D11—41no—
72C22⋊D11—41no—
73C22⋊D11—81no—
74C22⋊D11—81no—
75C2×Dic11—22no—
76C2×Dic11—21no—
77C2×Dic11—21no—
78C2×Dic11—21no—
79C2×Dic11—41no—
80C2×Dic11—41no—
81C2×Dic11—41no—
82C2×Dic11—41no—
83C2×Dic11—41no—
84D44—41no—
85C4×D11—81no—
86Dic22—22no—
87Dic22—22no—
88Dic22—41no—
89Dic22—41no—
90Dic22—41no—
91C8×C11—41no—
92C8×C11—41no—
93#538—111no—
94#451—111no—
95#448—111no—
96#393—111no—
97#328—111no—
98#327—111no—
99#323D1111yescharacteristic, complemented
100C22×C11—21no—
101C22×C11—21no—
102C22×C11—42no—
103C22×C11—41no—
104C22×C11—41no—
105C22×C11—41no—
106C22×C11—81no—
107C22×C11#12011yescharacteristic
108C22×C11#13511yescharacteristic
109C22×C11#13711yescharacteristic
110C2×D11—41no—
111C2×D11—41no—
112C2×D11—41no—
113C4×C11—21no—
114C4×C11—21no—
115C4×C11—41no—
116Dic11—41no—
117Dic11—41no—
118Dic11—42no—
119Dic11—41no—
120Dic11—81no—
121C22×Q8—111no—
122C2×Q16—221no—
123C2×SD16—221no—
124#126—221no—
125#124—221no—
126#123—221no—
127C22⋊Q8—111no—
128#121—111no—
129#121—221no—
130#120—221no—
131C4×D4—221no—
132C2×C22⋊C4—221no—
133C2×C22⋊C4C2×D1111yescharacteristic
134#103—221no—
135#103—221no—
136C22⋊C8C2×D1111yescharacteristic
137C22⋊C8C2×D1111yescharacteristic
138#95—111no—
139#95—221no—
140C2×C11—21no—
141C2×C11—21no—
142C2×C11—81no—
143C2×C11#45211yescharacteristic
144C2×C11#45511yescharacteristic
145C2×C11B(4,𝔽2)11yescharacteristic
146D11—81no—
147C24D4411yescharacteristic
148C2×Q8—111no—
149C2×Q8—221no—
150C2×Q8—221no—
151C2×Q8—442no—
152C2×D4—111no—
153C2×D4—221no—
154C2×D4—221no—
155C2×D4—221no—
156C22×C4—221no—
157C22×C4—221no—
158C22×C4—221no—
159C22×C4D4411yescharacteristic
160C22×C4C22×D1111yescharacteristic
161Q16—442no—
162SD16—442no—
163C2×C8—21no—
164C2×C8—21no—
165C4⋊C4—111no—
166C4⋊C4—111no—
167C4⋊C4—221no—
168C4⋊C4—221no—
169C22⋊C4—21no—
170C22⋊C4—21no—
171C22⋊C4—221no—
172C22⋊C4—221no—
173C22⋊C4—221no—
174C22⋊C4—221no—
175C22⋊C4—221no—
176C22⋊C4—442no—
177C42—221no—
178C11#160611yescharacteristic, complemented, Sylow
179C23—21no—
180C23—21no—
181C23—21no—
182C23—41no—
183C23—41no—
184C23—221no—
185C23C2×D4411yescharacteristic
186Q8—222no—
187Q8—222no—
188Q8—441no—
189Q8—441no—
190Q8—441no—
191D4—441no—
192D4—441no—
193D4—441no—
194D4—881no—
195D4—881no—
196C2×C4—21no—
197C2×C4—41no—
198C2×C4—41no—
199C2×C4—222no—
200C2×C4—221no—
201C2×C4—221no—
202C2×C4—221no—
203C2×C4—441no—
204C2×C4—441no—
205C2×C4—441no—
206C2×C4—441no—
207C2×C4—441no—
208C2×C4—881no—
209C2×C4D4×D1111yescharacteristic
210C2×C4D4×D1111yescharacteristic
211C8—41no—
212C8—41no—
213C22—21no—
214C22—21no—
215C22—42no—
216C22—41no—
217C22—41no—
218C22—41no—
219C22—81no—
220C22—441no—
221C22—441no—
222C22—441no—
223C22#6693511yescharacteristic
224C22#6695711yescharacteristic
225C22#6696211yescharacteristic
226C4—21no—
227C4—21no—
228C4—41no—
229C4—441no—
230C4—442no—
231C4—441no—
232C4—441no—
233C4—881no—
234C2—21no—
235C2—21no—
236C2—81no—
237C2—881no—
238C2#1062234611yescharacteristic
239C2#1062235411yescharacteristic
240C2#1062235911yescharacteristic
subgroupG/H
centerC22#66935
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
FittingC11×#323C2
socleC22×C11#120
prime radical#10623025C2
hypercenter#323D11
hypocenterC11#1606
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #323

Complements

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

NH ≅ G/Ntype
2. #10622560C2semidirect
3. #10622352C2semidirect
4. #10622351C2semidirect
5. C11×#323C2semidirect
6. #10622108C2semidirect
7. #10622105C2semidirect
99. #323D11semidirect
178. C11#1606semidirect

Maximal subgroups

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

subgroupindex
#106230252
#106225602
#106223522
#106223512
C11×#3232
#106221082
#106221052
#160611