Finite Group Databasebeta

← #13078165

Subgroups — #13078165

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#10623356C211yesmaximal, characteristic, complemented
2C2×#67003C211yesmaximal, characteristic
3C2×#66962C211yesmaximal, characteristic, complemented
4#10623035C211yesmaximal, characteristic, complemented
5C11×#417C211yesmaximal, characteristic, complemented
6#10622732C211yesmaximal, characteristic, complemented
7C2×#66874C211yesmaximal, characteristic, complemented
8#10622431C212yesmaximal, complemented
9#10622406C212yesmaximal, complemented
10#10622400C212yesmaximal, complemented
11#10622380C212yesmaximal, complemented
12C2×C11×#41C2211yescharacteristic
13C2×#4339C2211yescharacteristic
14C22×Dic22C2211yescharacteristic
15C2×C11×M16C2211yescharacteristic
16C2×C11×C4⋊C4C2211yescharacteristic
17#67003—24no—
18#66997C2212yes—
19C2×#4326C2211yescharacteristic
20C2×#4325C2211yescharacteristic
21#66989C2212yes—
22#66988—22no—
23C2×#4324C2211yescharacteristic
24C2×#4323C2211yescharacteristic
25C4×C22⋊D11—22no—
26#66979C2211yescharacteristic
27#66977—21no—
28#66977—21no—
29C22×C11⋊C8C2211yescharacteristic
30#66962—24no—
31C2×Dic44C2212yes—
32C2×#4314C2212yes—
33#66946C2212yes—
34#66945—21no—
35C4⋊C4×D11—21no—
36#66940C2212yes—
37C11×#103C2212yes—
38C11×#102C2212yes—
39Dic11⋊C8C2212yes—
40Dic11⋊C8C2212yes—
41#66874C2212yes—
42#66874C2212yes—
43C11×#41—22no—
44C11×#41—22no—
45C2×Q8×C11C2311yescharacteristic
46C2×D4×C11—21no—
47C2×D4×C11C2311yescharacteristic
48C22×C4×C11—21no—
49C22×C4×C11—21no—
50C22×C4×C11C2311yescharacteristic
51C2×C22⋊D11—21no—
52C22×Dic11—21no—
53#4339—22no—
54#4339D414yes—
55C2×D44C2311yescharacteristic
56C2×C4×D11—22no—
57C2×C4×D11—21no—
58C2×Dic22—22no—
59C2×Dic22—21no—
60C2×Dic22—22no—
61C2×Dic22C2312yes—
62C2×Dic22C2311yescharacteristic
63C11×M16—22no—
64C2×C8×C11C2312yes—
65C11×C4⋊C4—21no—
66C11×C4⋊C4C2312yes—
67C22⋊Dic11—22no—
68C22⋊Dic11—22no—
69C22⋊Dic11D412yes—
70#4326—22no—
71#4325—22no—
72#4324—22no—
73#4323—22no—
74(C2×D11)⋊C4—22no—
75C4⋊Dic11D411yescharacteristic
76C4⋊Dic11D411yescharacteristic
77Dic11⋊C4—22no—
78Dic11⋊C4—22no—
79Dic11⋊C4—22no—
80C4×Dic11—22no—
81C4×Dic11C2312yes—
82C2×C11⋊C8—22no—
83C2×C11⋊C8C2311yescharacteristic
84C2×C11⋊C8C2311yescharacteristic
85Dic44—24no—
86#4314—24no—
87#3046—111nomaximal, Sylow
88C23×C11—21no—
89C23×C11C2×D411yescharacteristic
90C22×D11—21no—
91Q8×C11—21no—
92Q8×C11—21no—
93D4×C11—21no—
94D4×C11—21no—
95D4×C11—42no—
96C2×C4×C11—22no—
97C2×C4×C11—21no—
98C2×C4×C11—42no—
99C2×C4×C11—81no—
100C2×C4×C11C2×D411yescharacteristic
101C2×C4×C11C2×D412yes—
102C2×C4×C11#4112yes—
103C2×C4×C11C2411yescharacteristic
104C22⋊D11—24no—
105C2×Dic11—21no—
106C2×Dic11—22no—
107C2×Dic11—42no—
108C2×Dic11C2×D412yes—
109C2×Dic11C2×D412yes—
110D44—21no—
111D44C2×D412yes—
112C4×D11—24no—
113C4×D11—82no—
114Dic22—21no—
115Dic22—22no—
116Dic22—22no—
117Dic22—42no—
118Dic22C2×D412yes—
119C8×C11—22no—
120C11⋊C8—21no—
121C11⋊C8—21no—
122C2×#137—111no—
123C2×#135—111no—
124#536—111no—
125#520—111no—
126#464—112no—
127#463—112no—
128#462—112no—
129#461—112no—
130#424—111no—
131#417D1111yescharacteristic, complemented
132C2×#103—111no—
133C22×C11—21no—
134C22×C11—21no—
135C22×C11—41no—
136C22×C11—41no—
137C22×C11—41no—
138C22×C11#12112yes—
139C22×C11C22×D411yescharacteristic
140C2×D11—22no—
141C2×D11—41no—
142C2×D11—41no—
143C4×C11—41no—
144C4×C11—42no—
145C4×C11#12112yes—
146C4×C11C22×D411yescharacteristic
147C4×C11C2×#4111yescharacteristic
148Dic11—22no—
149Dic11—22no—
150Dic11—22no—
151Dic11—42no—
152C2×#41—111no—
153C2×#41C2×D1111yescharacteristic
154C22×Q8—111no—
155#137—224no—
156#135—224no—
157C2×Q16—111no—
158C2×Q16—112no—
159C2×SD16—111no—
160C2×SD16—111no—
161C2×SD16—112no—
162C2×D8—111no—
163C2×M16C2×D1111yescharacteristic
164C22×C8—111no—
165C4⋊Q8—112no—
166#124—112no—
167#123—222no—
168C22⋊Q8—221no—
169C22⋊Q8—221no—
170C4×Q8—112no—
171C4×D4—112no—
172C4×D4—222no—
173#117—111no—
174#117—221no—
175C2×C4⋊C4—221no—
176C2×C4⋊C4C2×D1111yescharacteristic
177C4⋊C8—112no—
178C4⋊C8—112no—
179#103—112no—
180#103—112no—
181#103C2×D1112yes—
182#102C2×D1112yes—
183C2×C11—22no—
184C2×C11—81no—
185C2×C11C2×#12111yescharacteristic
186C2×C11#57711yescharacteristic
187C2×C11#57811yescharacteristic
188D11—42no—
189#41—22no—
190#41—22no—
191#41—114no—
192#41—222no—
193C2×Q8—111no—
194C2×Q8—112no—
195C2×Q8—221no—
196C2×Q8—222no—
197C2×Q8—222no—
198C2×Q8C22×D1111yescharacteristic
199C2×D4—21no—
200C2×D4—111no—
201C2×D4—221no—
202C2×D4C22×D1111yescharacteristic
203C22×C4—21no—
204C22×C4—21no—
205C22×C4—222no—
206C22×C4—221no—
207C22×C4—221no—
208C22×C4C22×D1111yescharacteristic
209Q16—224no—
210Q16—222no—
211SD16—224no—
212SD16—222no—
213SD16—222no—
214D8—222no—
215M16—22no—
216C2×C8—111no—
217C2×C8—111no—
218C2×C8—222no—
219C2×C8C22×D1112yes—
220C4⋊C4—21no—
221C4⋊C4—111no—
222C4⋊C4—111no—
223C4⋊C4—222no—
224C4⋊C4—222no—
225C4⋊C4—222no—
226C4⋊C4C22×D1112yes—
227C22⋊C4—112no—
228C22⋊C4—222no—
229C22⋊C4—222no—
230C22⋊C4—222no—
231C42—112no—
232C42—222no—
233C11#304611yescharacteristic, complemented, Sylow
234C23—21no—
235C23—221no—
236C23D4×D1111yescharacteristic
237Q8—21no—
238Q8—21no—
239Q8—112no—
240Q8—221no—
241Q8—222no—
242Q8—222no—
243Q8—442no—
244D4—21no—
245D4—21no—
246D4—42no—
247D4—112no—
248D4—224no—
249D4—221no—
250C2×C4—22no—
251C2×C4—21no—
252C2×C4—42no—
253C2×C4—81no—
254C2×C4—112no—
255C2×C4—112no—
256C2×C4—221no—
257C2×C4—224no—
258C2×C4—222no—
259C2×C4—442no—
260C2×C4—882no—
261C2×C4#433912yes—
262C2×C4D4×D1111yescharacteristic
263C2×C4D4×D1112yes—
264C2×C4C23×D1111yescharacteristic
265C8—22no—
266C8—221no—
267C8—221no—
268C22—21no—
269C22—21no—
270C22—41no—
271C22—41no—
272C22—41no—
273C22—222no—
274C22—441no—
275C22—441no—
276C22#6693712yes—
277C22C2×D4×D1111yescharacteristic
278C4—41no—
279C4—42no—
280C4—222no—
281C4—222no—
282C4—222no—
283C4—442no—
284C4#6693712yes—
285C4C2×#433911yescharacteristic
286C4C2×D4×D1111yescharacteristic
287C2—22no—
288C2—81no—
289C2—442no—
290C2C2×#6693711yescharacteristic
291C2#1062330611yescharacteristic
292C2#1062331011yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#417C2
socleC22×C11C22×D4
prime radicalC2×#67003C2
hypercenter#417D11
hypocenterC11#3046
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
1. #10623356C2semidirect
3. C2×#66962C2semidirect
4. #10623035C2semidirect
5. C11×#417C2semidirect
6. #10622732C2semidirect
7. C2×#66874C2semidirect
8. #10622431C2semidirect
9. #10622406C2semidirect
10. #10622400C2semidirect
11. #10622380C2semidirect
131. #417D11semidirect
233. C11#3046semidirect

Maximal subgroups

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

subgroupindex
#106233562
C2×#670032
C2×#669622
#106230352
C11×#4172
#106227322
C2×#668742
#106224312
#106224062
#106224002
#106223802
#304611