Finite Group Databasebeta

← #13078162

Subgroups — #13078162

Order 1408.

472 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 141 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
1C11×#536C211yesmaximal, characteristic, complemented
2C2×#67003C211yesmaximal, characteristic
3C2×#66995C211yesmaximal, characteristic, complemented
4#10623054C211yesmaximal, characteristic, complemented
5#10622845C211yesmaximal, characteristic, complemented
6C2×#66899C211yesmaximal, characteristic, complemented
7#10622703C212yesmaximal, complemented
8#10622696C212yesmaximal, complemented
9#10622670C212yesmaximal, complemented
10#10622667C212yesmaximal, complemented
11#10622612C211yesmaximal, characteristic, complemented
12C2×C11×#41C2211yescharacteristic
13C22×Q8×C11C2211yescharacteristic
14C2×#4339C2211yescharacteristic
15C11×C4⋊Q8C2212yes—
16C11×#124C2212yes—
17C11×#123—22no—
18C11×C22⋊Q8—21no—
19C11×C22⋊Q8—21no—
20C11×#117C2211yescharacteristic
21#67003—24no—
22C2×#4326C2212yes—
23C2×#4326C2211yescharacteristic
24#66995—24no—
25C2×#4325C2212yes—
26C2×#4325C2211yescharacteristic
27C2×#4324C2211yescharacteristic
28C2×#4323C2211yescharacteristic
29C2×C4⋊Dic11C2211yescharacteristic
30C2×#4318C2211yescharacteristic
31C22×C11⋊C8C2211yescharacteristic
32#66945—21no—
33C4⋊C4×D11—21no—
34(C22⋊D11)⋊C4—22no—
35C4×D44C2212yes—
36C4×Dic22C2212yes—
37#66899C2212yes—
38#66899C2212yes—
39#66899C2212yes—
40#66896C2212yes—
41C4⋊(C11⋊C8)C2212yes—
42C4⋊(C11⋊C8)C2212yes—
43C11×#41—22no—
44C11×#41—22no—
45C2×Q8×C11—21no—
46C2×Q8×C11—22no—
47C2×Q8×C11—22no—
48C2×Q8×C11C2312yes—
49C2×Q8×C11C2311yescharacteristic
50C2×D4×C11—21no—
51C2×D4×C11C2311yescharacteristic
52C22×C4×C11—21no—
53C22×C4×C11—21no—
54C22×C4×C11C2311yescharacteristic
55C2×C22⋊D11—21no—
56C22×Dic11—21no—
57#4339—22no—
58#4339D414yes—
59C2×D44C2311yescharacteristic
60C2×C4×D11—21no—
61C2×C4×D11—22no—
62C2×Dic22C2311yescharacteristic
63C11×C4⋊C4—22no—
64C11×C4⋊C4—22no—
65C11×C4⋊C4D411yescharacteristic
66C11×C4⋊C4D411yescharacteristic
67C11×C22⋊C4—22no—
68C11×C22⋊C4—22no—
69C11×C22⋊C4D412yes—
70C42×C11C2312yes—
71#4326—24no—
72#4326—22no—
73#4325—24no—
74#4325—22no—
75#4324—22no—
76#4323—22no—
77(C2×D11)⋊C4—22no—
78C4⋊Dic11—21no—
79C4⋊Dic11C2312yes—
80Dic11⋊C4—22no—
81C4×Dic11—22no—
82#4318—22no—
83C2×C11⋊C8—22no—
84C2×C11⋊C8C2312yes—
85C2×C11⋊C8C2311yescharacteristic
86C2×C11⋊C8C2311yescharacteristic
87#3046—111nomaximal, Sylow
88C23×C11—21no—
89C23×C11C2×D411yescharacteristic
90C22×D11—21no—
91Q8×C11—22no—
92Q8×C11—21no—
93Q8×C11—22no—
94Q8×C11—21no—
95Q8×C11—42no—
96D4×C11—21no—
97D4×C11—21no—
98D4×C11—42no—
99C2×C4×C11—22no—
100C2×C4×C11—21no—
101C2×C4×C11—42no—
102C2×C4×C11—42no—
103C2×C4×C11C2×D412yes—
104C2×C4×C11C2×D412yes—
105C2×C4×C11C2×D412yes—
106C2×C4×C11C2×D411yescharacteristic
107C2×C4×C11#4112yes—
108C2×C4×C11C2411yescharacteristic
109C22⋊D11—24no—
110C2×Dic11—21no—
111C2×Dic11—22no—
112C2×Dic11—81no—
113D44—21no—
114D44C2×D412yes—
115C4×D11—24no—
116C4×D11—82no—
117Dic22—21no—
118Dic22C2×D412yes—
119C11⋊C8—21no—
120C11⋊C8—21no—
121C11⋊C8—22no—
122C2×#137—111no—
123C2×#135—111no—
124#536D1111yescharacteristic, complemented
125#520—111no—
126#464—112no—
127#463—112no—
128#462—112no—
129#461—112no—
130#424—111no—
131#417—111no—
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—22no—
144C4×C11—22no—
145C4×C11—41no—
146C4×C11—42no—
147C4×C11#12112yes—
148C4×C11C22×D411yescharacteristic
149C4×C11C2×#4111yescharacteristic
150Dic11—22no—
151Dic11—42no—
152C2×#41—111no—
153C2×#41C2×D1111yescharacteristic
154C22×Q8C2×D1111yescharacteristic
155#137—224no—
156#135—224no—
157C2×Q16—111no—
158C2×Q16—112no—
159C2×SD16—111no—
160C2×SD16—112no—
161C2×SD16—111no—
162C2×D8—111no—
163C2×M16—111no—
164C22×C8—111no—
165C4⋊Q8C2×D1112yes—
166#124C2×D1112yes—
167#123—22no—
168C22⋊Q8—21no—
169C22⋊Q8—21no—
170C4×Q8—112no—
171C4×D4—112no—
172C4×D4—222no—
173#117—221no—
174#117C2×D1111yescharacteristic
175C2×C4⋊C4—111no—
176C2×C4⋊C4—221no—
177C4⋊C8—112no—
178C4⋊C8—112no—
179#103—112no—
180#103—112no—
181#103—112no—
182#102—112no—
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—21no—
194C2×Q8—22no—
195C2×Q8—22no—
196C2×Q8—111no—
197C2×Q8C22×D1112yes—
198C2×Q8C22×D1111yescharacteristic
199C2×D4—21no—
200C2×D4—111no—
201C2×D4—221no—
202C2×D4C22×D1111yescharacteristic
203C22×C4—21no—
204C22×C4—21no—
205C22×C4—221no—
206C22×C4—221no—
207C22×C4—222no—
208C22×C4C22×D1111yescharacteristic
209Q16—222no—
210Q16—224no—
211SD16—222no—
212SD16—222no—
213SD16—224no—
214D8—222no—
215M16—222no—
216C2×C8—112no—
217C2×C8—111no—
218C2×C8—111no—
219C2×C8—222no—
220C4⋊C4—22no—
221C4⋊C4—22no—
222C4⋊C4—112no—
223C4⋊C4—221no—
224C4⋊C4—222no—
225C4⋊C4C22⋊D1111yescharacteristic
226C4⋊C4C22⋊D1111yescharacteristic
227C22⋊C4—22no—
228C22⋊C4—22no—
229C22⋊C4—222no—
230C22⋊C4C22⋊D1112yes—
231C42—222no—
232C42C22×D1112yes—
233C11#304611yescharacteristic, complemented, Sylow
234C23—21no—
235C23—221no—
236C23C2×C22⋊D1111yescharacteristic
237Q8—22no—
238Q8—21no—
239Q8—22no—
240Q8—21no—
241Q8—42no—
242Q8—112no—
243Q8—221no—
244D4—21no—
245D4—21no—
246D4—42no—
247D4—112no—
248D4—224no—
249D4—221no—
250C2×C4—22no—
251C2×C4—21no—
252C2×C4—42no—
253C2×C4—42no—
254C2×C4—221no—
255C2×C4—224no—
256C2×C4—222no—
257C2×C4—882no—
258C2×C4—881no—
259C2×C4D4×D1112yes—
260C2×C4#434112yes—
261C2×C4C2×C22⋊D1112yes—
262C2×C4C2×C22⋊D1112yes—
263C2×C4C2×C22⋊D1111yescharacteristic
264C2×C4C23×D1111yescharacteristic
265C8—221no—
266C8—221no—
267C8—222no—
268C22—21no—
269C22—21no—
270C22—41no—
271C22—41no—
272C22—41no—
273C22—222no—
274C22—441no—
275C22—441no—
276C22#6699112yes—
277C22C22×C22⋊D1111yescharacteristic
278C4—22no—
279C4—22no—
280C4—41no—
281C4—42no—
282C4—222no—
283C4—442no—
284C4#6699112yes—
285C4C2×D4×D1111yescharacteristic
286C4C2×#434111yescharacteristic
287C2—22no—
288C2—81no—
289C2—442no—
290C2C2×#6699111yescharacteristic
291C2#1062336811yescharacteristic
292C2#1062336911yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#536C2
socleC22×C11C22×D4
prime radicalC2×#67003C2
hypercenter#536D11
hypocenterC11#3046
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #117 ◁ #536

Complements

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

NH ≅ G/Ntype
1. C11×#536C2semidirect
3. C2×#66995C2semidirect
4. #10623054C2semidirect
5. #10622845C2semidirect
6. C2×#66899C2semidirect
7. #10622703C2semidirect
8. #10622696C2semidirect
9. #10622670C2semidirect
10. #10622667C2semidirect
11. #10622612C2semidirect
124. #536D11semidirect
233. C11#3046semidirect

Maximal subgroups

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

subgroupindex
C11×#5362
C2×#670032
C2×#669952
#106230542
#106228452
C2×#668992
#106227032
#106226962
#106226702
#106226672
#106226122
#304611