Finite Group Databasebeta

← #13078085

Subgroups — #13078085

Order 1408.

484 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 143 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
1C2×C11×#137C211yesmaximal, characteristic, complemented
2#10623363C211yesmaximal, characteristic
3C2×Q8×Dic11C211yesmaximal, characteristic, complemented
4C2×#66995C211yesmaximal, characteristic, complemented
5#10622845C211yesmaximal, characteristic, complemented
6#10622798C212yesmaximal, complemented
7#10622795C212yesmaximal, complemented
8#10622779C212yesmaximal, complemented
9#10622776C212yesmaximal, complemented
10#10622746C211yesmaximal, characteristic, complemented
11#10622731C211yesmaximal, characteristic, complemented
12C2×C11×#41C2211yescharacteristic
13C22×Q8×C11C2211yescharacteristic
14C2×#4339C2211yescharacteristic
15C11×#137—24no—
16C2×C11×Q16C2212yes—
17C2×C11×SD16C2212yes—
18C2×C11×M16C2211yescharacteristic
19#67000C2211yescharacteristic
20Q8×Dic11—21no—
21Q8×Dic11—21no—
22Q8×Dic11C2212yes—
23Q8×Dic11C2212yes—
24#66997C2211yescharacteristic
25C2×#4326C2212yes—
26#66995—24no—
27C2×#4325C2212yes—
28#66993C2211yescharacteristic
29#66992—21no—
30#66992—21no—
31#66989C2211yescharacteristic
32C4×C22⋊D11—21no—
33C4×C22⋊D11—21no—
34C2×C4⋊Dic11—21no—
35C2×C4⋊Dic11C2211yescharacteristic
36C2×C4×Dic11—21no—
37C2×C4×Dic11C2211yescharacteristic
38C2×#4318C2211yescharacteristic
39#66899C2212yes—
40#66896C2212yes—
41#66885C2212yes—
42#66880C2212yes—
43Dic11⋊C8C2212yes—
44Dic11⋊C8C2212yes—
45C11×#41—22no—
46C11×#41—22no—
47C2×Q8×C11—21no—
48C2×Q8×C11—22no—
49C2×Q8×C11D414yescomplemented
50C2×Q8×C11C2311yescharacteristic
51C2×Q8×C11C2312yes—
52C2×D4×C11—21no—
53C2×D4×C11C2311yescharacteristic
54C22×C4×C11—21no—
55C22×C4×C11—21no—
56C22×C4×C11C2311yescharacteristic
57C2×C22⋊D11—21no—
58C2×C22⋊D11—21no—
59C2×C22⋊D11—21no—
60C22×Dic11—21no—
61C22×Dic11D411yescharacteristic
62C22×Dic11D411yescharacteristic
63#4339—22no—
64#4339—22no—
65C2×D44C2311yescharacteristic
66C2×C4×D11—21no—
67C2×Dic22C2311yescharacteristic
68C11×Q16—24no—
69C11×SD16—24no—
70C11×M16—22no—
71C2×C8×C11C2312yes—
72C22⋊Dic11—21no—
73C22⋊Dic11—21no—
74#4326—24no—
75#4325—24no—
76(C2×D11)⋊C4—21no—
77(C2×D11)⋊C4—21no—
78C4⋊Dic11—22no—
79C4⋊Dic11—22no—
80C4⋊Dic11—21no—
81C4⋊Dic11C2312yes—
82Dic11⋊C4—21no—
83Dic11⋊C4—21no—
84C4×Dic11—22no—
85C4×Dic11—22no—
86C4×Dic11D411yescharacteristic
87C4×Dic11D411yescharacteristic
88C4×Dic11C2311yescharacteristic
89C4×Dic11C2311yescharacteristic
90#4318—22no—
91C2×C11⋊C8C2312yes—
92#3037—111nomaximal, Sylow
93C23×C11—21no—
94C23×C11C2×D411yescharacteristic
95C22×D11—21no—
96Q8×C11—24no—
97Q8×C11—22no—
98Q8×C11—21no—
99Q8×C11—21no—
100Q8×C11C2×D414yes—
101D4×C11—21no—
102D4×C11—21no—
103D4×C11—42no—
104C2×C4×C11—24no—
105C2×C4×C11—22no—
106C2×C4×C11—21no—
107C2×C4×C11—42no—
108C2×C4×C11C2×D411yescharacteristic
109C2×C4×C11C2×D412yes—
110C2×C4×C11#4112yes—
111C2×C4×C11C2411yescharacteristic
112C22⋊D11—42no—
113C22⋊D11—42no—
114C22⋊D11—42no—
115C2×Dic11—22no—
116C2×Dic11—22no—
117C2×Dic11—21no—
118C2×Dic11—41no—
119C2×Dic11—42no—
120C2×Dic11C2×D411yescharacteristic
121C2×Dic11C2×D411yescharacteristic
122C2×Dic11C2×D411yescharacteristic
123C2×Dic11C2×D411yescharacteristic
124D44—21no—
125D44—21no—
126C4×D11—42no—
127Dic22—21no—
128Dic22—21no—
129C8×C11—22no—
130C11⋊C8—22no—
131C2×#137—111no—
132C2×#137D1111yescharacteristic, complemented
133#532—111no—
134C2×C4×Q8—111no—
135#464—112no—
136#464—112no—
137#462—112no—
138#460—112no—
139#423—111no—
140#417—111no—
141#417—111no—
142C22×C11—21no—
143C22×C11—21no—
144C22×C11—41no—
145C22×C11—41no—
146C22×C11—41no—
147C22×C11#12112yes—
148C22×C11C22×D411yescharacteristic
149C2×D11—41no—
150C2×D11—41no—
151C2×D11—41no—
152C4×C11—24no—
153C4×C11—41no—
154C4×C11#12112yes—
155C4×C11C22×D411yescharacteristic
156C4×C11C2×#4111yescharacteristic
157Dic11—21no—
158Dic11—21no—
159Dic11—21no—
160Dic11—41no—
161Dic11—42no—
162Dic11#13712yescomplemented
163C2×#41—111no—
164C2×#41C2×D1111yescharacteristic
165C22×Q8C2×D1111yescharacteristic
166#137—24no—
167#137—224no—
168C2×Q16—112no—
169C2×Q16C2×D1112yes—
170C2×SD16—112no—
171C2×SD16C2×D1112yes—
172C2×M16—111no—
173C2×M16C2×D1111yescharacteristic
174C4⋊Q8—111no—
175#127—111no—
176#124—111no—
177#124—111no—
178#121—221no—
179#121—221no—
180C4×Q8—112no—
181C4×Q8—112no—
182C4×Q8—221no—
183C4×Q8—221no—
184C4×D4—221no—
185C4×D4—221no—
186C2×C4⋊C4—111no—
187C2×C4⋊C4—221no—
188C2×C42—111no—
189C2×C42—221no—
190C4⋊C8—112no—
191C4⋊C8—112no—
192#103—112no—
193#103—112no—
194#102—112no—
195#102—112no—
196C2×C11—22no—
197C2×C11—81no—
198C2×C11C2×#12111yescharacteristic
199C2×C11C2×#13711yescharacteristic
200C2×C11#57511yescharacteristic
201D11—81no—
202#41—22no—
203#41—22no—
204#41—222no—
205#41—222no—
206C2×Q8—21no—
207C2×Q8—22no—
208C2×Q8—111no—
209C2×Q8C22⋊D1114yescomplemented
210C2×Q8C22×D1111yescharacteristic
211C2×Q8C22×D1112yes—
212C2×D4—21no—
213C2×D4—111no—
214C2×D4—221no—
215C2×D4—221no—
216C2×D4—221no—
217C2×D4C22×D1111yescharacteristic
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—111no—
221C22×C4—111no—
222C22×C4—221no—
223C22×C4—221no—
224C22×C4C22×D1111yescharacteristic
225Q16—24no—
226Q16—224no—
227SD16—24no—
228SD16—224no—
229M16—22no—
230M16—222no—
231C2×C8—112no—
232C2×C8C22×D1112yes—
233C4⋊C4—112no—
234C4⋊C4—222no—
235C4⋊C4—222no—
236C4⋊C4—221no—
237C4⋊C4—221no—
238C4⋊C4—221no—
239C22⋊C4—221no—
240C22⋊C4—221no—
241C22⋊C4—221no—
242C22⋊C4—221no—
243C42—111no—
244C42—111no—
245C42—111no—
246C42—111no—
247C42—222no—
248C42—222no—
249C11#303711yescharacteristic, complemented, Sylow
250C23—21no—
251C23—221no—
252C23D4×D1111yescharacteristic
253Q8—24no—
254Q8—22no—
255Q8—21no—
256Q8—21no—
257Q8—221no—
258Q8—221no—
259Q8C2×C22⋊D1114yes—
260D4—21no—
261D4—21no—
262D4—42no—
263D4—221no—
264D4—221no—
265D4—442no—
266D4—442no—
267D4—442no—
268C2×C4—24no—
269C2×C4—22no—
270C2×C4—21no—
271C2×C4—42no—
272C2×C4—111no—
273C2×C4—111no—
274C2×C4—111no—
275C2×C4—111no—
276C2×C4—222no—
277C2×C4—222no—
278C2×C4—221no—
279C2×C4—441no—
280C2×C4—442no—
281C2×C4—442no—
282C2×C4D4×D1111yescharacteristic
283C2×C4#434112yes—
284C2×C4C2×C22⋊D1112yes—
285C2×C4C23×D1111yescharacteristic
286C8—22no—
287C8—222no—
288C22—21no—
289C22—21no—
290C22—41no—
291C22—41no—
292C22—41no—
293C22—441no—
294C22—441no—
295C22—441no—
296C22#6699212yes—
297C22C2×D4×D1111yescharacteristic
298C4—24no—
299C4—41no—
300C4—112no—
301C4—221no—
302C4—221no—
303C4—221no—
304C4—442no—
305C4—441no—
306C4#6699212yes—
307C4C2×#434111yescharacteristic
308C4C22×C22⋊D1111yescharacteristic
309C2—22no—
310C2—81no—
311C2—881no—
312C2D11×#13711yescharacteristic
313C2#1062330811yescharacteristic
314C2C2×#6699211yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC2×C11×#137C2
socleC22×C11C22×D4
prime radical#10623363C2
hypercenterC2×#137D11
hypocenterC11#3037
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
1. C2×C11×#137C2semidirect
3. C2×Q8×Dic11C2semidirect
4. C2×#66995C2semidirect
5. #10622845C2semidirect
6. #10622798C2semidirect
7. #10622795C2semidirect
8. #10622779C2semidirect
9. #10622776C2semidirect
10. #10622746C2semidirect
11. #10622731C2semidirect
49. C2×Q8×C11D4semidirect
132. C2×#137D11semidirect
162. Dic11#137semidirect
209. C2×Q8C22⋊D11semidirect
249. C11#3037semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#1372
#106233632
C2×Q8×Dic112
C2×#669952
#106228452
#106227982
#106227952
#106227792
#106227762
#106227462
#106227312
#303711