Finite Group Databasebeta

← #13076664

Subgroups — #13076664

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×#67000C211yesmaximal, characteristic, complemented
2C2×#66938C211yesmaximal, characteristic, complemented
3C11×#393C211yesmaximal, characteristic, complemented
4#10622844C211yesmaximal, characteristic, complemented
5#10622573C212yesmaximal, complemented
6#10622573C211yesmaximal, characteristic, complemented
7#10622572C212yesmaximal, complemented
8#10622286C212yesmaximal, complemented
9#10622285C212yesmaximal, complemented
10#10622284C211yesmaximal, characteristic, complemented
11#10622263C211yesmaximal, characteristic, complemented
12C22×Q8×C11C2211yescharacteristic
13C22×C22⋊D11C2211yescharacteristic
14C22×C22⋊D11C2212yes—
15C22×D44C2211yescharacteristic
16C22×D44C2212yes—
17C22×Dic22C2211yescharacteristic
18C2×C11×C22⋊C4C2211yescharacteristic
19C2×C11×C22⋊C4C2212yes—
20C2×C22⋊Dic11C2211yescharacteristic
21#67000—24no—
22C2×(C2×D11)⋊C4C2211yescharacteristic
23C2×(C2×D11)⋊C4C2211yescharacteristic
24C2×(C2×D11)⋊C4C2212yes—
25C2×(C2×D11)⋊C4C2212yes—
26C2×(C2×D11)⋊C4C2212yes—
27C2×(C2×D11)⋊C4C2212yes—
28C2×(C2×D11)⋊C4C2212yes—
29C2×Dic11⋊C4C2212yes—
30C2×C4×Dic11C2211yescharacteristic
31#66938—24no—
32C11×#95C2211yescharacteristic
33C11×#95C2212yes—
34C11⋊#95C2212yes—
35C11⋊#95C2211yescharacteristic
36C11⋊#95C2212yes—
37C24×C11C2311yescharacteristic
38C23×D11C2312yes—
39C23×D11C2311yescharacteristic
40C2×Q8×C11—22no—
41C2×Q8×C11—42no—
42C22×C4×C11C2312yes—
43C22×C4×C11C2312yes—
44C22×C4×C11C2311yescharacteristic
45C22×C4×C11C2311yescharacteristic
46C2×C22⋊D11—22no—
47C2×C22⋊D11—42no—
48C2×C22⋊D11—42no—
49C2×C22⋊D11—42no—
50C2×C22⋊D11—42no—
51C22×Dic11C2312yes—
52C22×Dic11C2311yescharacteristic
53C22×Dic11C2311yescharacteristic
54C22×Dic11C2311yescharacteristic
55C2×D44—22no—
56C2×D44—42no—
57C2×D44—42no—
58C2×D44—42no—
59C2×D44—42no—
60C2×Dic22—22no—
61C2×Dic22—42no—
62C11×C22⋊C4—22no—
63C11×C22⋊C4—42no—
64C22⋊Dic11—22no—
65(C2×D11)⋊C4—22no—
66(C2×D11)⋊C4—24no—
67(C2×D11)⋊C4—24no—
68(C2×D11)⋊C4—22no—
69(C2×D11)⋊C4—42no—
70(C2×D11)⋊C4—42no—
71(C2×D11)⋊C4—42no—
72Dic11⋊C4—42no—
73C4×Dic11D414yescomplemented
74#2819—111nomaximal, Sylow
75C23×C11—21no—
76C23×C11—22no—
77C23×C11—22no—
78C23×C11—21no—
79C23×C11—21no—
80C23×C11C2411yescharacteristic
81C22×D11—22no—
82C22×D11—21no—
83C22×D11—22no—
84C22×D11—22no—
85C22×D11—22no—
86C22×D11—22no—
87C22×D11—21no—
88C22×D11—22no—
89C22×D11—22no—
90C22×D11—22no—
91C22×D11—22no—
92C22×D11—21no—
93Q8×C11—44no—
94C2×C4×C11—22no—
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×C11—22no—
102C2×C4×C11—22no—
103C2×C4×C11C2×D412yes—
104C22⋊D11—44no—
105C22⋊D11—48no—
106C2×Dic11—21no—
107C2×Dic11—22no—
108C2×Dic11—21no—
109C2×Dic11—21no—
110C2×Dic11—22no—
111C2×Dic11—22no—
112C2×Dic11—22no—
113C2×Dic11—22no—
114C2×Dic11C2×D412yes—
115C2×Dic11C2×D412yes—
116D44—44no—
117D44—48no—
118Dic22—44no—
119C2×#124—111no—
120C2×#124—111no—
121#394—112no—
122#394—112no—
123#393—111no—
124#393—112no—
125#393D1111yescharacteristic, complemented
126#392—112no—
127#392—111no—
128#392—111no—
129#382—111no—
130C22×C11—41no—
131C22×C11—41no—
132C22×C11—41no—
133C22×C11—42no—
134C22×C11—42no—
135C22×C11C22×D411yescharacteristic
136C22×C11H(5,𝔽2)12yes—
137C22×C11H(5,𝔽2)12yes—
138C22×C11H(5,𝔽2)11yescharacteristic
139C22×C112−1+411yescharacteristic
140C2×D11—41no—
141C2×D11—42no—
142C2×D11—42no—
143C2×D11—41no—
144C2×D11—42no—
145C2×D11—41no—
146C2×D11—42no—
147C2×D11—42no—
148C2×D11—42no—
149C2×D11—42no—
150C2×D11—42no—
151C2×D11—42no—
152C4×C11—22no—
153C4×C11—42no—
154C4×C11—41no—
155C4×C11—42no—
156Dic11—22no—
157Dic11—22no—
158Dic11—41no—
159Dic11—42no—
160C22×Q8—111no—
161C22×Q8C2×D1111yescharacteristic
162C22×D4—111no—
163C22×D4—112no—
164C22×D4—111no—
165C22×D4—112no—
166#124—224no—
167#124—224no—
168C2×C4⋊C4—112no—
169C2×C22⋊C4—111no—
170C2×C22⋊C4—112no—
171C2×C22⋊C4—111no—
172C2×C22⋊C4—112no—
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#95C2×D1111yescharacteristic
184#95C2×D1112yes—
185C2×C11—81no—
186C2×C11#53511yescharacteristic
187C2×C11#53511yescharacteristic
188C2×C11#53711yescharacteristic
189C2×C11H(3,𝔽4)12yes—
190C2×C11#56212yes—
191D11—82no—
192D11—81no—
193C24—111no—
194C24—112no—
195C24C22×D1111yescharacteristic
196C2×Q8—22no—
197C2×Q8—42no—
198C2×Q8—222no—
199C2×Q8—442no—
200C2×D4—222no—
201C2×D4—222no—
202C2×D4—442no—
203C2×D4—442no—
204C2×D4—442no—
205C2×D4—442no—
206C2×D4—442no—
207C2×D4—442no—
208C2×D4—442no—
209C2×D4—442no—
210C22×C4—111no—
211C22×C4—111no—
212C22×C4—112no—
213C22×C4—111no—
214C22×C4C22×D1112yes—
215C22×C4C22×D1112yes—
216C22×C4C22×D1111yescharacteristic
217C22×C4C22×D1111yescharacteristic
218C4⋊C4—442no—
219C22⋊C4—22no—
220C22⋊C4—42no—
221C22⋊C4—222no—
222C22⋊C4—224no—
223C22⋊C4—224no—
224C22⋊C4—222no—
225C22⋊C4—222no—
226C22⋊C4—442no—
227C22⋊C4—442no—
228C22⋊C4—442no—
229C42—114no—
230C11#281911yescharacteristic, complemented, Sylow
231C23—21no—
232C23—22no—
233C23—21no—
234C23—21no—
235C23—22no—
236C23—222no—
237C23—221no—
238C23—222no—
239C23—222no—
240C23—222no—
241C23—221no—
242C23—222no—
243C23—222no—
244C23—222no—
245C23—221no—
246C23—222no—
247C23—222no—
248C23C23×D1111yescharacteristic
249Q8—44no—
250Q8—444no—
251D4—444no—
252D4—448no—
253D4—444no—
254D4—448no—
255C2×C4—22no—
256C2×C4—21no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—22no—
264C2×C4—112no—
265C2×C4—112no—
266C2×C4—221no—
267C2×C4—221no—
268C2×C4—222no—
269C2×C4—221no—
270C2×C4—222no—
271C2×C4—222no—
272C2×C4—222no—
273C2×C4—222no—
274C2×C4D4×D1112yes—
275C22—41no—
276C22—41no—
277C22—42no—
278C22—41no—
279C22—42no—
280C22—442no—
281C22—441no—
282C22—442no—
283C22—441no—
284C22—442no—
285C22—442no—
286C22—442no—
287C22—441no—
288C22—442no—
289C22—442no—
290C22—442no—
291C22—442no—
292C22C2×D4×D1111yescharacteristic
293C22#6703712yes—
294C22#6704011yescharacteristic
295C22#6704211yescharacteristic
296C22#6704212yes—
297C4—22no—
298C4—42no—
299C4—41no—
300C4—42no—
301C4—222no—
302C4—222no—
303C4—441no—
304C4—442no—
305C2—81no—
306C2—882no—
307C2—881no—
308C2#1062312311yescharacteristic
309C2#1062316011yescharacteristic
310C2#1062317812yes—
311C2#1062320511yescharacteristic
312C2#1062321412yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#393C2
hypercenter#393D11
hypocenterC11#2819
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
1. C2×#67000C2semidirect
2. C2×#66938C2semidirect
3. C11×#393C2semidirect
4. #10622844C2semidirect
5. #10622573C2semidirect
6. #10622573C2semidirect
7. #10622572C2semidirect
8. #10622286C2semidirect
9. #10622285C2semidirect
10. #10622284C2semidirect
11. #10622263C2semidirect
73. C4×Dic11D4semidirect
125. #393D11semidirect
230. C11#2819semidirect

Maximal subgroups

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

subgroupindex
C2×#670002
C2×#669382
C11×#3932
#106228442
#106225732
#106225722
#106222862
#106222852
#106222842
#106222632
#281911