Finite Group Databasebeta

← #13072269

Subgroups — #13072269

Order 1408.

852 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 852 conjugacy classes of subgroups — too many to draw. Only its 161 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×Q8×D11C211yesmaximal, characteristic, complemented
2C2×#66938C212yesmaximal, complemented
3C2×#66937C211yesmaximal, characteristic
4C11×#393C211yesmaximal, characteristic, complemented
5#10622844C211yesmaximal, characteristic, complemented
6#10622569C212yesmaximal, complemented
7#10622560C211yesmaximal, characteristic, complemented
8#10622286C211yesmaximal, characteristic, complemented
9#10622279C211yesmaximal, characteristic, complemented
10#10622278C212yesmaximal, complemented
11#10622259C212yesmaximal, complemented
12C22×Q8×C11C2211yescharacteristic
13C22×C22⋊D11C2211yescharacteristic
14C22×C22⋊D11C2211yescharacteristic
15C2×Q8×D11—24no—
16C2×Q8×D11—28no—
17C22×D44C2211yescharacteristic
18C22×C4×D11C2212yes—
19C22×C4×D11C2211yescharacteristic
20C22×Dic22C2211yescharacteristic
21C22×Dic22C2212yes—
22C2×C11×C22⋊C4C2211yescharacteristic
23C2×C11×C22⋊C4C2212yes—
24C2×C22⋊Dic11C2212yes—
25C2×(C2×D11)⋊C4C2211yescharacteristic
26C2×(C2×D11)⋊C4C2212yes—
27C2×(C2×D11)⋊C4C2212yes—
28C2×(C2×D11)⋊C4C2212yes—
29C2×Dic11⋊C4C2211yescharacteristic
30C2×C4×Dic11C2212yes—
31#66938—28no—
32#66937—24no—
33C11×#95C2212yes—
34C11×#95C2211yescharacteristic
35C11⋊#95C2212yes—
36C11⋊#95C2212yes—
37C11⋊#95C2212yes—
38C11⋊#95C2211yescharacteristic
39C24×C11C2311yescharacteristic
40C23×D11C2311yescharacteristic
41C23×D11C2311yescharacteristic
42C2×Q8×C11—22no—
43C2×Q8×C11—24no—
44C22×C4×C11C2311yescharacteristic
45C22×C4×C11C2312yes—
46C22×C4×C11C2311yescharacteristic
47C22×C4×C11C2312yes—
48C2×C22⋊D11—22no—
49C2×C22⋊D11—24no—
50C2×C22⋊D11—22no—
51C2×C22⋊D11—24no—
52C22×Dic11C2311yescharacteristic
53C22×Dic11C2312yes—
54C22×Dic11C2312yes—
55C22×Dic11C2311yescharacteristic
56Q8×D11—232no—
57C2×D44—22no—
58C2×D44—24no—
59C2×C4×D11—24no—
60C2×C4×D11—24no—
61C2×C4×D11—24no—
62C2×C4×D11—24no—
63C2×C4×D11D414yes—
64C2×Dic22—24no—
65C2×Dic22—24no—
66C2×Dic22—24no—
67C2×Dic22—22no—
68C2×Dic22D418yescomplemented
69C11×C22⋊C4—22no—
70C11×C22⋊C4—24no—
71C22⋊Dic11—24no—
72(C2×D11)⋊C4—24no—
73(C2×D11)⋊C4—24no—
74(C2×D11)⋊C4—22no—
75(C2×D11)⋊C4—24no—
76Dic11⋊C4—22no—
77C4×Dic11—24no—
78#2436—111nomaximal, Sylow
79C23×C11—22no—
80C23×C11—21no—
81C23×C11—22no—
82C23×C11—21no—
83C23×C11—21no—
84C23×C11C2411yescharacteristic
85C22×D11—22no—
86C22×D11—21no—
87C22×D11—21no—
88C22×D11—22no—
89C22×D11—21no—
90C22×D11—22no—
91C22×D11—21no—
92C22×D11—21no—
93C22×D11C2×D412yes—
94C22×D11#4114yes—
95Q8×C11—28no—
96C2×C4×C11—22no—
97C2×C4×C11—22no—
98C2×C4×C11—22no—
99C2×C4×C11—22no—
100C2×C4×C11—21no—
101C2×C4×C11—22no—
102C2×C4×C11—22no—
103C2×C4×C11—22no—
104C2×C4×C11C2×D412yes—
105C2×C4×C11C2×D414yes—
106C22⋊D11—44no—
107C22⋊D11—44no—
108C2×Dic11—22no—
109C2×Dic11—22no—
110C2×Dic11—22no—
111C2×Dic11—21no—
112C2×Dic11—22no—
113C2×Dic11—22no—
114C2×Dic11—22no—
115C2×Dic11C2×D414yes—
116C2×Dic11C2×D414yes—
117C2×Dic11C2×D412yes—
118D44—44no—
119C4×D11—216no—
120C4×D11—28no—
121Dic22—28no—
122Dic22—216no—
123C23×Q8—111no—
124C2×#124—112no—
125C2×#121—111no—
126#393—111no—
127#393—111no—
128#393—111no—
129#393D1111yescharacteristic, complemented
130#391—112no—
131#386—112no—
132#386—112no—
133C4×C22⋊C4—111no—
134C22×C11—41no—
135C22×C11—41no—
136C22×C11—41no—
137C22×C11—42no—
138C22×C11—42no—
139C22×C11C22×D411yescharacteristic
140C22×C11C22×D412yes—
141C22×C11C2×#4112yes—
142C22×C112−1+411yescharacteristic
143C22×C112−1+411yescharacteristic
144C2×D11—22no—
145C2×D11—22no—
146C2×D11—24no—
147C2×D11—24no—
148C2×D11—41no—
149C2×D11—41no—
150C2×D11—41no—
151C2×D11—42no—
152C2×D11—42no—
153C2×D11#12414yescomplemented
154C4×C11—22no—
155C4×C11—24no—
156C4×C11—41no—
157C4×C11—42no—
158Dic11—24no—
159Dic11—41no—
160Dic11—42no—
161Dic11#12014yes—
162C22×Q8—112no—
163C22×Q8—111no—
164C22×Q8—224no—
165C22×Q8—228no—
166C22×Q8C2×D1111yescharacteristic
167C22×D4—111no—
168C22×D4—111no—
169C22×D4—111no—
170C23×C4—111no—
171C23×C4—112no—
172#124—228no—
173#121—224no—
174C2×C4⋊C4—111no—
175C2×C22⋊C4—112no—
176C2×C22⋊C4—111no—
177C2×C22⋊C4—112no—
178C2×C22⋊C4—112no—
179C2×C22⋊C4—112no—
180C2×C22⋊C4C2×D1111yescharacteristic
181C2×C22⋊C4C2×D1112yes—
182C2×C42—112no—
183#95—111no—
184#95—112no—
185#95—112no—
186#95—112no—
187#95C2×D1111yescharacteristic
188#95C2×D1112yes—
189C2×C11—81no—
190C2×C11C2×#12011yescharacteristic
191C2×C11C2×#12411yescharacteristic
192C2×C11#53611yescharacteristic
193C2×C11#54812yes—
194C2×C11#54812yes—
195D11—24no—
196D11—81no—
197C24—111no—
198C24—111no—
199C24C22×D1111yescharacteristic
200C2×Q8—22no—
201C2×Q8—24no—
202C2×Q8—118no—
203C2×Q8—224no—
204C2×Q8—224no—
205C2×Q8—224no—
206C2×Q8—2232no—
207C2×Q8—222no—
208C2×D4—222no—
209C2×D4—224no—
210C2×D4—222no—
211C2×D4—224no—
212C2×D4—222no—
213C2×D4—224no—
214C22×C4—111no—
215C22×C4—112no—
216C22×C4—114no—
217C22×C4—111no—
218C22×C4—112no—
219C22×C4—224no—
220C22×C4—224no—
221C22×C4—224no—
222C22×C4—224no—
223C22×C4C22×D1111yescharacteristic
224C22×C4C22×D1112yes—
225C22×C4C22×D1111yescharacteristic
226C22×C4C22×D1112yes—
227C4⋊C4—222no—
228C22⋊C4—22no—
229C22⋊C4—24no—
230C22⋊C4—224no—
231C22⋊C4—224no—
232C22⋊C4—224no—
233C22⋊C4—222no—
234C22⋊C4—224no—
235C42—224no—
236C11#243611yescharacteristic, complemented, Sylow
237C23—22no—
238C23—21no—
239C23—21no—
240C23—22no—
241C23—21no—
242C23—112no—
243C23—114no—
244C23—222no—
245C23—221no—
246C23—221no—
247C23—222no—
248C23—221no—
249C23—221no—
250C23—222no—
251C23—221no—
252C23C23×D1111yescharacteristic
253Q8—28no—
254Q8—2216no—
255Q8—228no—
256D4—444no—
257D4—444no—
258D4—444no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—21no—
264C2×C4—22no—
265C2×C4—22no—
266C2×C4—22no—
267C2×C4—114no—
268C2×C4—112no—
269C2×C4—114no—
270C2×C4—228no—
271C2×C4—2216no—
272C2×C4—222no—
273C2×C4—222no—
274C2×C4—222no—
275C2×C4—221no—
276C2×C4—222no—
277C2×C4—222no—
278C2×C4—222no—
279C2×C4D4×D1112yes—
280C2×C4D4×D1114yes—
281C22—41no—
282C22—41no—
283C22—42no—
284C22—41no—
285C22—42no—
286C22—114no—
287C22—222no—
288C22—222no—
289C22—224no—
290C22—224no—
291C22—441no—
292C22—441no—
293C22—442no—
294C22—441no—
295C22—442no—
296C22C2×D4×D1111yescharacteristic
297C22C2×D4×D1112yes—
298C22#6704011yescharacteristic
299C22#41×D1112yes—
300C22#6704311yescharacteristic
301C4—22no—
302C4—24no—
303C4—41no—
304C4—42no—
305C4—114no—
306C4—224no—
307C4—442no—
308C4—441no—
309C2—81no—
310C2—224no—
311C2—881no—
312C2D11×#12011yescharacteristic
313C2#1062315911yescharacteristic
314C2#1062316412yes—
315C2D11×#12411yescharacteristic
316C2#1062320812yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#393C2
prime radicalC2×#66937C2
hypercenter#393D11
hypocenterC11#2436
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
1. C22×Q8×D11C2semidirect
2. C2×#66938C2semidirect
4. C11×#393C2semidirect
5. #10622844C2semidirect
6. #10622569C2semidirect
7. #10622560C2semidirect
8. #10622286C2semidirect
9. #10622279C2semidirect
10. #10622278C2semidirect
11. #10622259C2semidirect
68. C2×Dic22D4semidirect
129. #393D11semidirect
153. C2×D11#124semidirect
236. C11#2436semidirect

Maximal subgroups

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

subgroupindex
C22×Q8×D112
C2×#669382
C2×#669372
C11×#3932
#106228442
#106225692
#106225602
#106222862
#106222792
#106222782
#106222592
#243611