Finite Group Databasebeta

← #13076663

Subgroups — #13076663

Order 1408.

580 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 580 conjugacy classes of subgroups — too many to draw. Only its 125 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×#66989C211yesmaximal, characteristic, complemented
2C2×#66938C211yesmaximal, characteristic, complemented
3C11×#392C211yesmaximal, characteristic, complemented
4#10622836C211yesmaximal, characteristic, complemented
5#10622836C212yesmaximal, complemented
6#10622835C212yesmaximal, complemented
7#10622572C212yesmaximal, complemented
8#10622560C212yesmaximal, complemented
9#10622560C211yesmaximal, characteristic, complemented
10#10622286C211yesmaximal, characteristic, complemented
11#10622263C211yesmaximal, characteristic, complemented
12C22×D4×C11C2211yescharacteristic
13C22×D4×C11C2212yes—
14C22×C22⋊D11C2211yescharacteristic
15C22×C22⋊D11C2212yes—
16C22×Dic22C2211yescharacteristic
17C22×Dic22C2211yescharacteristic
18C2×C11×C22⋊C4C2211yescharacteristic
19C2×C11×C22⋊C4C2212yes—
20C2×C22⋊Dic11C2211yescharacteristic
21C2×C22⋊Dic11C2212yes—
22C2×C22⋊Dic11C2212yes—
23C2×C22⋊Dic11C2212yes—
24C2×C22⋊Dic11C2212yes—
25#66989—24no—
26C2×(C2×D11)⋊C4C2211yescharacteristic
27C2×(C2×D11)⋊C4C2211yescharacteristic
28C2×(C2×D11)⋊C4C2212yes—
29C2×Dic11⋊C4C2212yes—
30C2×C4×Dic11C2211yescharacteristic
31#66938—24no—
32C11×#95C2211yescharacteristic
33C11⋊#95C2211yescharacteristic
34C11⋊#95C2212yes—
35C11⋊#95C2212yes—
36C11⋊#95C2212yes—
37C24×C11C2312yes—
38C24×C11C2311yescharacteristic
39C23×D11C2311yescharacteristic
40C2×D4×C11—22no—
41C2×D4×C11—42no—
42C2×D4×C11—42no—
43C2×D4×C11—42no—
44C2×D4×C11—42no—
45C22×C4×C11C2312yes—
46C22×C4×C11C2311yescharacteristic
47C22×C4×C11C2311yescharacteristic
48C2×C22⋊D11—22no—
49C2×C22⋊D11—42no—
50C2×C22⋊D11—42no—
51C2×C22⋊D11—42no—
52C2×C22⋊D11—42no—
53C22×Dic11C2312yes—
54C22×Dic11C2311yescharacteristic
55C22×Dic11C2312yes—
56C22×Dic11C2311yescharacteristic
57C22×Dic11C2311yescharacteristic
58C2×Dic22—22no—
59C2×Dic22—22no—
60C2×Dic22—42no—
61C2×Dic22—42no—
62C11×C22⋊C4—22no—
63C11×C22⋊C4—42no—
64C22⋊Dic11—22no—
65C22⋊Dic11—24no—
66C22⋊Dic11—24no—
67C22⋊Dic11—42no—
68C22⋊Dic11—42no—
69(C2×D11)⋊C4—22no—
70(C2×D11)⋊C4—22no—
71(C2×D11)⋊C4—42no—
72Dic11⋊C4—42no—
73C4×Dic11D414yescomplemented
74#2819—111nomaximal, Sylow
75C23×C11—22no—
76C23×C11—21no—
77C23×C11—22no—
78C23×C11—22no—
79C23×C11—22no—
80C23×C11—22no—
81C23×C11—22no—
82C23×C11—22no—
83C23×C11—22no—
84C23×C11—21no—
85C23×C11—22no—
86C23×C11—21no—
87C23×C11C2411yescharacteristic
88C22×D11—21no—
89C22×D11—22no—
90C22×D11—22no—
91C22×D11—21no—
92C22×D11—21no—
93D4×C11—44no—
94D4×C11—48no—
95C2×C4×C11—22no—
96C2×C4×C11—21no—
97C2×C4×C11—22no—
98C2×C4×C11—22no—
99C2×C4×C11—22no—
100C2×C4×C11—22no—
101C2×C4×C11C2×D412yes—
102C22⋊D11—44no—
103C22⋊D11—48no—
104C2×Dic11—21no—
105C2×Dic11—22no—
106C2×Dic11—21no—
107C2×Dic11—21no—
108C2×Dic11—22no—
109C2×Dic11—22no—
110C2×Dic11—22no—
111C2×Dic11—22no—
112C2×Dic11—22no—
113C2×Dic11—22no—
114C2×Dic11—22no—
115C2×Dic11C2×D412yes—
116C2×Dic11C2×D412yes—
117Dic22—44no—
118Dic22—44no—
119C2×#124—111no—
120C2×#124—111no—
121#394—112no—
122#394—112no—
123#393—112no—
124#393—111no—
125#393—111no—
126#392—112no—
127#392—111no—
128#392D1111yescharacteristic, complemented
129#382—111no—
130C22×C11—42no—
131C22×C11—42no—
132C22×C11—41no—
133C22×C11—41no—
134C22×C11—42no—
135C22×C11—41no—
136C22×C11—42no—
137C22×C11—42no—
138C22×C11—42no—
139C22×C11—42no—
140C22×C11—42no—
141C22×C11—42no—
142C22×C11C22×D411yescharacteristic
143C22×C11H(5,𝔽2)12yes—
144C22×C11H(5,𝔽2)12yes—
145C22×C11H(5,𝔽2)11yescharacteristic
146C22×C112−1+411yescharacteristic
147C2×D11—41no—
148C2×D11—41no—
149C2×D11—41no—
150C2×D11—42no—
151C2×D11—42no—
152C4×C11—22no—
153C4×C11—41no—
154C4×C11—42no—
155Dic11—22no—
156Dic11—22no—
157Dic11—41no—
158Dic11—42no—
159Dic11—42no—
160C22×Q8—111no—
161C22×Q8—111no—
162C22×D4—111no—
163C22×D4—112no—
164C22×D4C2×D1111yescharacteristic
165C22×D4C2×D1112yes—
166#124—224no—
167#124—224no—
168C2×C4⋊C4—112no—
169C2×C22⋊C4—112no—
170C2×C22⋊C4—112no—
171C2×C22⋊C4—111no—
172C2×C22⋊C4—111no—
173C2×C22⋊C4—111no—
174C2×C22⋊C4—112no—
175C2×C22⋊C4—112no—
176C2×C22⋊C4—112no—
177C2×C22⋊C4C2×D1111yescharacteristic
178C2×C22⋊C4C2×D1112yes—
179C2×C42—111no—
180#95—112no—
181#95—111no—
182#95—112no—
183#95—112no—
184#95C2×D1111yescharacteristic
185C2×C11—82no—
186C2×C11—81no—
187C2×C11#53511yescharacteristic
188C2×C11#53511yescharacteristic
189C2×C11#53711yescharacteristic
190C2×C11H(3,𝔽4)12yes—
191C2×C11#56212yes—
192D11—81no—
193C24—111no—
194C24C22×D1111yescharacteristic
195C24C22×D1112yes—
196C2×Q8—222no—
197C2×Q8—222no—
198C2×Q8—442no—
199C2×Q8—442no—
200C2×D4—22no—
201C2×D4—42no—
202C2×D4—42no—
203C2×D4—42no—
204C2×D4—42no—
205C2×D4—222no—
206C2×D4—442no—
207C2×D4—442no—
208C2×D4—442no—
209C2×D4—442no—
210C22×C4—111no—
211C22×C4—111no—
212C22×C4—112no—
213C22×C4—112no—
214C22×C4—111no—
215C22×C4C22×D1112yes—
216C22×C4C22×D1111yescharacteristic
217C22×C4C22×D1111yescharacteristic
218C4⋊C4—442no—
219C22⋊C4—22no—
220C22⋊C4—42no—
221C22⋊C4—222no—
222C22⋊C4—222no—
223C22⋊C4—224no—
224C22⋊C4—224no—
225C22⋊C4—222no—
226C22⋊C4—442no—
227C22⋊C4—442no—
228C22⋊C4—442no—
229C42—114no—
230C11#281911yescharacteristic, complemented, Sylow
231C23—21no—
232C23—22no—
233C23—22no—
234C23—22no—
235C23—22no—
236C23—22no—
237C23—21no—
238C23—22no—
239C23—22no—
240C23—22no—
241C23—21no—
242C23—22no—
243C23—221no—
244C23—222no—
245C23—222no—
246C23—221no—
247C23—221no—
248C23C23×D1111yescharacteristic
249Q8—444no—
250Q8—444no—
251D4—44no—
252D4—48no—
253D4—444no—
254D4—448no—
255C2×C4—22no—
256C2×C4—21no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—112no—
262C2×C4—112no—
263C2×C4—221no—
264C2×C4—222no—
265C2×C4—221no—
266C2×C4—221no—
267C2×C4—222no—
268C2×C4—222no—
269C2×C4—222no—
270C2×C4—222no—
271C2×C4—222no—
272C2×C4—222no—
273C2×C4—222no—
274C2×C4D4×D1112yes—
275C22—41no—
276C22—42no—
277C22—42no—
278C22—41no—
279C22—42no—
280C22—42no—
281C22—42no—
282C22—41no—
283C22—42no—
284C22—42no—
285C22—42no—
286C22—42no—
287C22—441no—
288C22—441no—
289C22—442no—
290C22—441no—
291C22—442no—
292C22C2×D4×D1111yescharacteristic
293C22#6703712yes—
294C22#6703712yes—
295C22#6703711yescharacteristic
296C22#6704311yescharacteristic
297C4—22no—
298C4—41no—
299C4—42no—
300C4—222no—
301C4—222no—
302C4—441no—
303C4—442no—
304C4—442no—
305C2—81no—
306C2—82no—
307C2—881no—
308C2#1062312311yescharacteristic
309C2#1062312512yes—
310C2#1062313911yescharacteristic
311C2#1062315212yes—
312C2#1062324611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#392C2
hypercenter#392D11
hypocenterC11#2819
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C2×#66989C2semidirect
2. C2×#66938C2semidirect
3. C11×#392C2semidirect
4. #10622836C2semidirect
5. #10622836C2semidirect
6. #10622835C2semidirect
7. #10622572C2semidirect
8. #10622560C2semidirect
9. #10622560C2semidirect
10. #10622286C2semidirect
11. #10622263C2semidirect
73. C4×Dic11D4semidirect
128. #392D11semidirect
230. C11#2819semidirect

Maximal subgroups

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

subgroupindex
C2×#669892
C2×#669382
C11×#3922
#106228362
#106228352
#106225722
#106225602
#106222862
#106222632
#281911