Finite Group Databasebeta

← #13070626

Subgroups — #13070626

Order 1408.

260 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 41 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#10623251C211yesmaximal, characteristic, complemented
2#10622690C211yesmaximal, characteristic, complemented
3#10622355C211yesmaximal, characteristic, complemented
4#10622354C211yesmaximal, characteristic, complemented
5C11×#353C211yesmaximal, characteristic, complemented
6#10622110C211yesmaximal, characteristic, complemented
7#10622109C211yesmaximal, characteristic, complemented
8#67037C2211yescharacteristic
9C11×#127C2211yescharacteristic
10#66992—21no—
11#66992—21no—
12#66992—21no—
13#66990—21no—
14#66990C2211yescharacteristic
15#66988—21no—
16#66988C2211yescharacteristic
17#66985—21no—
18#66939—21no—
19#66935—21no—
20#66929—21no—
21C11×#99C2211yescharacteristic
22C11×#99C2211yescharacteristic
23#66897C2211yescharacteristic
24#66870—21no—
25#66870—21no—
26#66869—21no—
27C23×D11D411yescharacteristic
28C2×D4×C11—21no—
29C2×D4×C11—21no—
30C2×D4×C11D411yescharacteristic, complemented
31C2×D4×C11C2311yescharacteristic
32C2×C22⋊D11—21no—
33C2×C22⋊D11—21no—
34C2×C22⋊D11—21no—
35C2×C22⋊D11—21no—
36C2×C22⋊D11—21no—
37C22×Dic11—21no—
38C22×Dic11D411yescharacteristic, complemented
39#4341—41no—
40D4×D11—41no—
41#4339—21no—
42C2×D44—41no—
43C11×C22⋊C4—21no—
44C11×C22⋊C4—21no—
45C42×C11D411yescharacteristic, complemented
46C22⋊Dic11—21no—
47C22⋊Dic11—21no—
48C22⋊Dic11D411yescharacteristic
49C22⋊Dic11D411yescharacteristic, complemented
50#4324—41no—
51#4323—41no—
52(C2×D11)⋊C4—21no—
53(C2×D11)⋊C4—21no—
54(C2×D11)⋊C4—21no—
55(C2×D11)⋊C4—41no—
56(C2×D11)⋊C4—41no—
57C4⋊Dic11—41no—
58Dic11⋊C4—21no—
59Dic11⋊C4—21no—
60Dic11⋊C4—21no—
61#4318—21no—
62#2200—111nomaximal, Sylow
63C23×C11—21no—
64C23×C11C2×D411yescharacteristic
65C23×C11C2×D411yescharacteristic
66C22×D11—21no—
67C22×D11—21no—
68C22×D11—21no—
69C22×D11—41no—
70C22×D11—81no—
71D4×C11—41no—
72D4×C11—41no—
73D4×C11—81no—
74D4×C11—81no—
75C2×C4×C11—21no—
76C2×C4×C11—41no—
77C2×C4×C11—41no—
78C2×C4×C11C2×D411yescharacteristic
79C22⋊D11—41no—
80C22⋊D11—41no—
81C22⋊D11—41no—
82C22⋊D11—81no—
83C22⋊D11—81no—
84C22⋊D11—81no—
85C2×Dic11—21no—
86C2×Dic11—21no—
87C2×Dic11—21no—
88C2×Dic11—21no—
89C2×Dic11—21no—
90C2×Dic11—41no—
91C2×Dic11—81no—
92D44—21no—
93D44—82no—
94C4×D11—41no—
95Dic22—21no—
96C11⋊C8—41no—
97#560—111no—
98#458—111no—
99B(4,𝔽2)—111no—
100#453—111no—
101#353D1111yescharacteristic, complemented
102#352—111no—
103AΣL(1,𝔽16)—111no—
104C22×C11—21no—
105C22×C11—21no—
106C22×C11—41no—
107C22×C11—41no—
108C22×C11—41no—
109C22×C11—41no—
110C22×C11—41no—
111C22×C11#12011yescharacteristic
112C2×D11—41no—
113C2×D11—41no—
114C2×D11—42no—
115C2×D11—41no—
116C2×D11—41no—
117C2×D11—81no—
118C2×D11—81no—
119C2×D11—81no—
120C4×C11—21no—
121C4×C11—41no—
122C4×C11—81no—
123C4×C11—81no—
124Dic11—41no—
125Dic11—41no—
126Dic11—41no—
127Dic11—41no—
128H(5,𝔽2)—111no—
129AGL(1,ℤ/8)—221no—
130#127C2×D1111yescharacteristic
131#126—221no—
132#123—111no—
133#123—221no—
134#123—221no—
135#121—221no—
136#121—221no—
137#121—221no—
138#120—111no—
139#120—221no—
140#120—221no—
141#104—221no—
142#100—111no—
143#99—221no—
144#99—221no—
145#99C2×D1111yescharacteristic
146#99C2×D1111yescharacteristic
147C2×C11—21no—
148C2×C11—41no—
149C2×C11—41no—
150C2×C11—81no—
151C2×C11B(4,𝔽2)11yescharacteristic
152D11—81no—
153D11—81no—
154C24—111no—
155#41—221no—
156#41—441no—
157C2×D4—21no—
158C2×D4—21no—
159C2×D4—221no—
160C2×D4—221no—
161C2×D4—221no—
162C2×D4—221no—
163C2×D4—221no—
164C2×D4—441no—
165C2×D4—441no—
166C2×D4D4411yescharacteristic, complemented
167C2×D4C22×D1111yescharacteristic
168C22×C4—111no—
169C22×C4—221no—
170SD16—441no—
171D8—441no—
172M16—221no—
173C4⋊C4—221no—
174C4⋊C4—221no—
175C4⋊C4—221no—
176C4⋊C4—441no—
177C22⋊C4—21no—
178C22⋊C4—21no—
179C22⋊C4—111no—
180C22⋊C4—111no—
181C22⋊C4—221no—
182C22⋊C4—221no—
183C22⋊C4—221no—
184C22⋊C4—221no—
185C22⋊C4—221no—
186C22⋊C4—441no—
187C22⋊C4—441no—
188C42D4411yescharacteristic, complemented
189C11#220011yescharacteristic, complemented, Sylow
190C23—21no—
191C23—221no—
192C23—221no—
193C23—221no—
194C23—441no—
195C23—881no—
196C23D4×D1111yescharacteristic
197C23D4×D1111yescharacteristic
198Q8—221no—
199D4—41no—
200D4—41no—
201D4—81no—
202D4—81no—
203D4—221no—
204D4—441no—
205D4—441no—
206D4—441no—
207D4—882no—
208D4—881no—
209D4—881no—
210D4—881no—
211C2×C4—21no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—221no—
215C2×C4—221no—
216C2×C4—221no—
217C2×C4—221no—
218C2×C4—221no—
219C2×C4—441no—
220C2×C4—441no—
221C2×C4—881no—
222C2×C4C2×D4411yescharacteristic
223C8—441no—
224C22—21no—
225C22—21no—
226C22—41no—
227C22—41no—
228C22—41no—
229C22—41no—
230C22—41no—
231C22—441no—
232C22—441no—
233C22—442no—
234C22—441no—
235C22—441no—
236C22—881no—
237C22—881no—
238C22—881no—
239C22#6693511yescharacteristic
240C4—21no—
241C4—41no—
242C4—81no—
243C4—81no—
244C4—441no—
245C4—441no—
246C4—441no—
247C4—441no—
248C2—21no—
249C2—41no—
250C2—41no—
251C2—81no—
252C2—881no—
253C2—881no—
254C2#1062235411yescharacteristic
subgroupG/H
centerC2#10622354
commutator, cosocleC2×D4×C11C23
FrattiniC2×D4C22×D11
FittingC11×#353C2
socleC2×C11B(4,𝔽2)
hypercenter#353D11
hypocenterC11#2200
LCSG ▷ C2×D4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #353

Complements

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

NH ≅ G/Ntype
1. #10623251C2semidirect
2. #10622690C2semidirect
3. #10622355C2semidirect
4. #10622354C2semidirect
5. C11×#353C2semidirect
6. #10622110C2semidirect
7. #10622109C2semidirect
30. C2×D4×C11D4semidirect
38. C22×Dic11D4semidirect
45. C42×C11D4semidirect
49. C22⋊Dic11D4semidirect
101. #353D11semidirect
166. C2×D4D44semidirect
188. C42D44semidirect
189. C11#2200semidirect

Maximal subgroups

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

subgroupindex
#106232512
#106226902
#106223552
#106223542
C11×#3532
#106221102
#106221092
#220011