Finite Group Databasebeta

← #13069696

Subgroups — #13069696

Order 1408.

426 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 426 conjugacy classes of subgroups — too many to draw. Only its 91 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
1C22×D88C211yesmaximal, characteristic
2C22×#4314C211yesmaximal, characteristic, complemented
3C2×#66928C211yesmaximal, characteristic, complemented
4C2×#66885C211yesmaximal, characteristic, complemented
5C2×#66880C211yesmaximal, characteristic, complemented
6#10622552C211yesmaximal, characteristic, complemented
7C11×#336C211yesmaximal, characteristic, complemented
8C22×D44C2211yescharacteristic
9C22×D44C2211yescharacteristic
10C22×Dic22C2211yescharacteristic
11C22×C8×C11C2211yescharacteristic
12C22×C8×C11C2211yescharacteristic
13C2×C42×C11C2211yescharacteristic
14C2×(C2×D11)⋊C4—22no—
15C2×(C2×D11)⋊C4—22no—
16C2×C4⋊Dic11C2211yescharacteristic
17C2×D88—22no—
18C2×D88—22no—
19C2×D88—22no—
20C2×#4314—22no—
21C2×#4314—22no—
22C2×#4314—22no—
23#66928—22no—
24#66928—22no—
25#66885—22no—
26#66880—22no—
27C23×D11—21no—
28C23×D11—21no—
29C22×C4×C11D412yes—
30C22×C4×C11C2311yescharacteristic
31C22×Dic11—21no—
32C22×Dic11—21no—
33C2×D44—21no—
34C2×D44—21no—
35C2×D44—21no—
36C2×D44—21no—
37C2×D44—21no—
38C2×D44—21no—
39C2×D44—21no—
40C2×D44—21no—
41C2×D44—21no—
42C2×D44—21no—
43C2×D44D412yes—
44C2×D44D412yes—
45C2×Dic22—21no—
46C2×Dic22—21no—
47C2×Dic22—21no—
48C2×Dic22—21no—
49C2×Dic22—21no—
50C2×Dic22D412yes—
51C2×C8×C11—21no—
52C2×C8×C11—21no—
53C2×C8×C11—21no—
54C2×C8×C11—21no—
55C2×C8×C11D412yes—
56C2×C8×C11D412yes—
57C42×C11—21no—
58C42×C11—21no—
59(C2×D11)⋊C4—28no—
60(C2×D11)⋊C4—44no—
61C4⋊Dic11—21no—
62C4⋊Dic11—21no—
63D88—28no—
64#4314—28no—
65#2012—111nomaximal, Sylow
66C23×C11C2×D411yescharacteristic
67C22×D11—22no—
68C22×D11—22no—
69C22×D11—41no—
70C22×D11—41no—
71C22×D11—41no—
72C22×D11—41no—
73C22×D11—42no—
74C22×D11—42no—
75C22×D11—42no—
76C22×D11—42no—
77C2×C4×C11—22no—
78C2×C4×C11—22no—
79C2×C4×C11—22no—
80C2×C4×C11C2×D411yescharacteristic
81C2×C4×C11C2×D411yescharacteristic
82C2×C4×C11C2×D411yescharacteristic
83C2×C4×C11C2×D411yescharacteristic
84C2×C4×C11C2×D411yescharacteristic
85C2×C4×C11#4111yescharacteristic
86C2×Dic11—22no—
87C2×Dic11—41no—
88C2×Dic11—41no—
89C2×Dic11—41no—
90C2×Dic11—42no—
91D44—22no—
92D44—22no—
93D44—22no—
94D44—22no—
95D44—41no—
96D44—41no—
97D44—41no—
98D44—41no—
99Dic22—22no—
100Dic22—22no—
101Dic22—41no—
102Dic22—41no—
103C8×C11—22no—
104C8×C11—22no—
105C22×SD16—111no—
106C22×D8—111no—
107C2×#124—111no—
108C2×#103—111no—
109C2×#102—111no—
110#390—111no—
111#336D1111yescharacteristic, complemented
112C22×C11#12011yescharacteristic
113C22×C11#12111yescharacteristic
114C22×C11#12711yescharacteristic
115C22×C11#13512yes—
116C22×C11AGL(1,ℤ/8)12yes—
117C2×D11—42no—
118C2×D11—42no—
119C2×D11—44no—
120C2×D11—44no—
121C2×D11—82no—
122C2×D11—82no—
123C2×D11—81no—
124C2×D11—81no—
125C2×D11—81no—
126C2×D11—81no—
127C4×C11—42no—
128C4×C11#12011yescharacteristic
129C4×C11#12011yescharacteristic
130C4×C11#12111yescharacteristic
131C4×C11#12111yescharacteristic
132Dic11—42no—
133Dic11—81no—
134C22×Q8—111no—
135C22×D4—111no—
136C22×D4—111no—
137C2×SD16—222no—
138C2×SD16—222no—
139C2×SD16—222no—
140C2×D8—222no—
141C2×D8—222no—
142C2×D8—222no—
143C22×C8C2×D1111yescharacteristic
144C22×C8C2×D1111yescharacteristic
145#124—222no—
146#124—222no—
147C2×C4⋊C4—111no—
148C2×C22⋊C4—222no—
149C2×C22⋊C4—222no—
150C2×C42C2×D1111yescharacteristic
151#103—222no—
152#102—222no—
153C2×C11#39211yescharacteristic
154C2×C11#44912yes—
155C2×C11#46312yes—
156C2×C11#49511yescharacteristic
157C2×C11#49611yescharacteristic
158D11—82no—
159D11—82no—
160C24—221no—
161C24—221no—
162C2×Q8—112no—
163C2×Q8—221no—
164C2×Q8—221no—
165C2×Q8—221no—
166C2×Q8—221no—
167C2×Q8—221no—
168C2×D4—112no—
169C2×D4—112no—
170C2×D4—221no—
171C2×D4—221no—
172C2×D4—221no—
173C2×D4—221no—
174C2×D4—221no—
175C2×D4—221no—
176C2×D4—221no—
177C2×D4—221no—
178C2×D4—221no—
179C2×D4—221no—
180C22×C4—221no—
181C22×C4—221no—
182C22×C4D4412yes—
183C22×C4C22×D1111yescharacteristic
184SD16—228no—
185D8—228no—
186C2×C8—21no—
187C2×C8—21no—
188C2×C8—21no—
189C2×C8—21no—
190C2×C8D4412yes—
191C2×C8D4412yes—
192C4⋊C4—221no—
193C4⋊C4—221no—
194C22⋊C4—228no—
195C22⋊C4—444no—
196C42—21no—
197C42—21no—
198C11#201211yescharacteristic, complemented, Sylow
199C23—222no—
200C23—222no—
201C23—441no—
202C23—441no—
203C23—441no—
204C23—441no—
205C23—442no—
206C23—442no—
207C23—442no—
208C23—442no—
209C23C2×D4411yescharacteristic
210Q8—222no—
211Q8—222no—
212Q8—441no—
213Q8—441no—
214D4—222no—
215D4—222no—
216D4—222no—
217D4—222no—
218D4—441no—
219D4—441no—
220D4—441no—
221D4—441no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—222no—
226C2×C4—441no—
227C2×C4—441no—
228C2×C4—441no—
229C2×C4—442no—
230C2×C4C2×D4411yescharacteristic
231C2×C4C2×D4411yescharacteristic
232C2×C4D4×D1111yescharacteristic
233C2×C4D4×D1111yescharacteristic
234C2×C4D4×D1111yescharacteristic
235C2×C4#434311yescharacteristic
236C8—22no—
237C8—22no—
238C22—442no—
239C22—442no—
240C22—444no—
241C22—444no—
242C22—881no—
243C22—881no—
244C22—881no—
245C22—881no—
246C22—882no—
247C22—882no—
248C22#6692711yescharacteristic
249C22#6693511yescharacteristic
250C22#6694811yescharacteristic
251C22#6695712yes—
252C22#6696112yes—
253C4—42no—
254C4—442no—
255C4—881no—
256C4#6693511yescharacteristic
257C4#6693511yescharacteristic
258C4#6694811yescharacteristic
259C4#6694811yescharacteristic
260C2—882no—
261C2—882no—
262C2#1062228411yescharacteristic
263C2#1062230911yescharacteristic
264C2#1062232511yescharacteristic
265C2#1062234712yes—
266C2#1062245712yes—
subgroupG/H
centerC23C2×D44
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
FittingC11×#336C2
socleC23×C11C2×D4
prime radicalC22×D88C2
hypercenter#336D11
hypocenterC11#2012
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #336

Complements

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

NH ≅ G/Ntype
2. C22×#4314C2semidirect
3. C2×#66928C2semidirect
4. C2×#66885C2semidirect
5. C2×#66880C2semidirect
6. #10622552C2semidirect
7. C11×#336C2semidirect
111. #336D11semidirect
198. C11#2012semidirect

Maximal subgroups

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

subgroupindex
C22×D882
C22×#43142
C2×#669282
C2×#668852
C2×#668802
#106225522
C11×#3362
#201211