Finite Group Databasebeta

← #13078305

Subgroups — #13078305

Order 1408.

472 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 133 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#10623347C211yesmaximal, characteristic, complemented
2C2×#66995C211yesmaximal, characteristic, complemented
3C2×#66954C211yesmaximal, characteristic, complemented
4#10623041C211yesmaximal, characteristic
5C2×C11×#103C211yesmaximal, characteristic, complemented
6#10622726C211yesmaximal, characteristic, complemented
7#10622577C211yesmaximal, characteristic, complemented
8#10622429C212yesmaximal, complemented
9#10622426C212yesmaximal, complemented
10#10622425C212yesmaximal, complemented
11#10622420C212yesmaximal, complemented
12C22×Q8×C11C2211yescharacteristic
13C2×#4339C2211yescharacteristic
14C2×#4339C2211yescharacteristic
15C22×C8×C11C2211yescharacteristic
16C2×C11×C4⋊C4C2211yescharacteristic
17#67000—21no—
18#66999C2212yes—
19#66999C2212yes—
20#66997—21no—
21C2×#4326C2212yes—
22#66995—24no—
23C2×#4325C2212yes—
24#66983—22no—
25#66982—22no—
26#66979C2211yescharacteristic
27C2×#4318C2211yescharacteristic
28#66954—24no—
29C2×#4313C2212yes—
30C2×C8×D11C2212yes—
31#66950—21no—
32#66950C2212yes—
33#66948—21no—
34#66948C2212yes—
35C11×#103C2212yes—
36C11×#103C2212yes—
37#66885C2211yescharacteristic
38#66885C2211yescharacteristic
39#66880C2211yescharacteristic
40#66880C2211yescharacteristic
41#66872C2212yes—
42#66871C2212yes—
43C2×Q8×C11—21no—
44C2×Q8×C11—22no—
45C2×Q8×C11—22no—
46C2×Q8×C11C2312yes—
47C22×C4×C11—21no—
48C22×C4×C11—21no—
49C22×C4×C11C2311yescharacteristic
50C2×C22⋊D11—21no—
51C2×C22⋊D11D412yes—
52#4339—22no—
53#4339—22no—
54#4339—22no—
55#4339—22no—
56C2×D44—22no—
57C2×D44D411yescharacteristic
58C2×D44C2311yescharacteristic
59C2×C4×D11—21no—
60C2×C4×D11C2312yes—
61C2×Dic22D411yescharacteristic
62C2×Dic22C2311yescharacteristic
63C2×C8×C11—22no—
64C2×C8×C11C2311yescharacteristic
65C2×C8×C11C2311yescharacteristic
66C11×C4⋊C4—21no—
67C11×C4⋊C4C2312yes—
68C22⋊Dic11—21no—
69#4326—24no—
70#4325—24no—
71(C2×D11)⋊C4—22no—
72(C2×D11)⋊C4—22no—
73(C2×D11)⋊C4—22no—
74(C2×D11)⋊C4—22no—
75C4⋊Dic11—22no—
76C4⋊Dic11C2311yescharacteristic
77C4⋊Dic11C2311yescharacteristic
78Dic11⋊C4—22no—
79Dic11⋊C4—22no—
80C4×Dic11—21no—
81#4318D414yescomplemented
82C2×C11⋊C8C2312yes—
83#4313—24no—
84C8×D11—24no—
85#3063—111nomaximal, Sylow
86C23×C11C2×D411yescharacteristic
87C22×D11—21no—
88C22×D11C2×D412yes—
89Q8×C11—22no—
90Q8×C11—22no—
91Q8×C11—42no—
92C2×C4×C11—22no—
93C2×C4×C11—22no—
94C2×C4×C11—42no—
95C2×C4×C11—81no—
96C2×C4×C11C2×D411yescharacteristic
97C2×C4×C11C2×D412yes—
98C2×C4×C11#4112yes—
99C2×C4×C11C2411yescharacteristic
100C22⋊D11—24no—
101C22⋊D11—42no—
102C2×Dic11—21no—
103C2×Dic11—21no—
104C2×Dic11—21no—
105C2×Dic11C2×D412yes—
106D44—22no—
107D44—21no—
108D44—21no—
109D44—82no—
110C4×D11—22no—
111C4×D11—22no—
112C4×D11—42no—
113Dic22—22no—
114Dic22—21no—
115Dic22—21no—
116C8×C11—21no—
117C8×C11—21no—
118C11⋊C8C2×D414yes—
119C2×#137—111no—
120C2×#131—111no—
121#537—111no—
122#536—111no—
123#470—112no—
124#468—112no—
125#467—112no—
126#465—112no—
127#428—111no—
128#416—111no—
129C2×#103D1111yescharacteristic, complemented
130C22×C11—21no—
131C22×C11—21no—
132C22×C11#12112yes—
133C22×C11C22×D411yescharacteristic
134C2×D11—22no—
135C2×D11—22no—
136C2×D11—22no—
137C2×D11—41no—
138C2×D11—41no—
139C2×D11—41no—
140C4×C11—42no—
141C4×C11—42no—
142C4×C11#12112yes—
143C4×C11C22×D411yescharacteristic
144C4×C11C2×#4111yescharacteristic
145Dic11—22no—
146Dic11—41no—
147Dic11—41no—
148Dic11—41no—
149C2×#41—111no—
150C2×#41—111no—
151C22×Q8C2×D1111yescharacteristic
152#137—224no—
153C2×Q16—112no—
154C2×SD16—112no—
155#131—224no—
156C2×M16—111no—
157C2×M16—112no—
158C22×C8—112no—
159C22×C8C2×D1111yescharacteristic
160C4⋊Q8—221no—
161#124—221no—
162#123—222no—
163C22⋊Q8—112no—
164C22⋊Q8—112no—
165C22⋊Q8—112no—
166C22⋊Q8—221no—
167#121—112no—
168#121—221no—
169#121—222no—
170#117—111no—
171C2×C4⋊C4C2×D1111yescharacteristic
172#107—112no—
173#106—112no—
174#103—111no—
175#103—111no—
176#103C2×D1112yes—
177#103C2×D1112yes—
178#102—111no—
179#102—111no—
180C2×C11—22no—
181C2×C11C2×#12111yescharacteristic
182C2×C11#57711yescharacteristic
183C2×C11#57811yescharacteristic
184D11—42no—
185D11—81no—
186#41—222no—
187#41—222no—
188#41—222no—
189#41—222no—
190C2×Q8—21no—
191C2×Q8—22no—
192C2×Q8—22no—
193C2×Q8—111no—
194C2×Q8—111no—
195C2×Q8C22×D1112yes—
196C2×D4—112no—
197C2×D4—111no—
198C2×D4—111no—
199C2×D4—222no—
200C2×D4—221no—
201C22×C4—21no—
202C22×C4—21no—
203C22×C4—112no—
204C22×C4—221no—
205C22×C4C22×D1111yescharacteristic
206Q16—224no—
207SD16—224no—
208M16—114no—
209M16—224no—
210C2×C8—22no—
211C2×C8—112no—
212C2×C8—224no—
213C2×C8C22×D1111yescharacteristic
214C2×C8C22×D1111yescharacteristic
215C4⋊C4—21no—
216C4⋊C4—111no—
217C4⋊C4—111no—
218C4⋊C4—222no—
219C4⋊C4—222no—
220C4⋊C4—222no—
221C4⋊C4C22×D1112yes—
222C22⋊C4—222no—
223C22⋊C4—222no—
224C22⋊C4—222no—
225C22⋊C4—222no—
226C22⋊C4—221no—
227C42—221no—
228C11#306311yescharacteristic, complemented, Sylow
229C23—112no—
230C23—221no—
231C23D4×D1111yescharacteristic
232Q8—22no—
233Q8—22no—
234Q8—42no—
235Q8—222no—
236Q8—221no—
237Q8—221no—
238D4—224no—
239D4—222no—
240D4—221no—
241D4—221no—
242D4—442no—
243D4—882no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—42no—
247C2×C4—81no—
248C2×C4—112no—
249C2×C4—222no—
250C2×C4—222no—
251C2×C4—221no—
252C2×C4—221no—
253C2×C4—221no—
254C2×C4—442no—
255C2×C4#433912yes—
256C2×C4D4×D1111yescharacteristic
257C2×C4D4×D1112yes—
258C2×C4C23×D1111yescharacteristic
259C8—21no—
260C8—21no—
261C8—114no—
262C22—21no—
263C22—21no—
264C22—222no—
265C22—222no—
266C22—222no—
267C22—441no—
268C22—441no—
269C22—441no—
270C22#6693712yes—
271C22C2×D4×D1111yescharacteristic
272C4—42no—
273C4—42no—
274C4—222no—
275C4—441no—
276C4—441no—
277C4—441no—
278C4#6693712yes—
279C4C2×#433911yescharacteristic
280C4C2×D4×D1111yescharacteristic
281C2—22no—
282C2—442no—
283C2—881no—
284C2C2×#6693711yescharacteristic
285C2#1062329311yescharacteristic
286C2#1062329711yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC2×C11×#103C2
socleC22×C11C22×D4
prime radical#10623041C2
hypercenterC2×#103D11
hypocenterC11#3063
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
1. #10623347C2semidirect
2. C2×#66995C2semidirect
3. C2×#66954C2semidirect
5. C2×C11×#103C2semidirect
6. #10622726C2semidirect
7. #10622577C2semidirect
8. #10622429C2semidirect
9. #10622426C2semidirect
10. #10622425C2semidirect
11. #10622420C2semidirect
81. #4318D4semidirect
129. C2×#103D11semidirect
228. C11#3063semidirect

Maximal subgroups

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

subgroupindex
#106233472
C2×#669952
C2×#669542
#106230412
C2×C11×#1032
#106227262
#106225772
#106224292
#106224262
#106224252
#106224202
#306311