Finite Group Databasebeta

← #13073610

Subgroups — #13073610

Order 1408.

604 conjugacy classes of subgroups.

The subgroup lattice has 322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C22⋊D11C211yesmaximal, characteristic
2C2×#66941C211yesmaximal, characteristic, complemented
3C2×#66938C212yesmaximal
4C11×#380C211yesmaximal, characteristic, complemented
5#10622825C211yesmaximal, characteristic, complemented
6#10622600C211yesmaximal, characteristic, complemented
7#10622600C211yesmaximal, characteristic, complemented
8C4⋊C4×Dic11C211yesmaximal, characteristic, complemented
9#10622565C212yesmaximal, complemented
10#10622288C212yesmaximal, complemented
11#10622259C212yesmaximal, complemented
12C23×C4×C11C2211yescharacteristic
13C22×C22⋊D11C2211yescharacteristic
14C22×C4×D11C2211yescharacteristic
15C22×Dic22C2212yes—
16C2×C11×C4⋊C4C2211yescharacteristic
17C2×C11×C4⋊C4C2211yescharacteristic
18C2×C11×C22⋊C4C2212yes—
19C2×C22⋊Dic11C2212yes—
20C2×C22⋊Dic11C2211yescharacteristic
21C4×C22⋊D11—24no—
22C2×(C2×D11)⋊C4C2212yes—
23C2×(C2×D11)⋊C4C2212yes—
24C2×(C2×D11)⋊C4C2211yescharacteristic
25C2×C4⋊Dic11C2211yescharacteristic
26C2×C4⋊Dic11C2211yescharacteristic
27C2×Dic11⋊C4C2211yescharacteristic
28C2×Dic11⋊C4C2212yes—
29C2×C4×Dic11C2212yes—
30C2×C4×Dic11C2211yescharacteristic
31#66941—24no—
32#66938—28no—
33C11×#95C2212yes—
34C11⋊#95C2212yes—
35C11⋊#95C2212yes—
36C11⋊#95C2212yes—
37C11⋊#95C2212yes—
38C24×C11C2311yescharacteristic
39C23×D11C2311yescharacteristic
40C22×C4×C11—22no—
41C22×C4×C11—22no—
42C22×C4×C11—22no—
43C22×C4×C11C2311yescharacteristic
44C22×C4×C11C2312yes—
45C22×C4×C11C2312yes—
46C22×C4×C11C2311yescharacteristic
47C2×C22⋊D11—22no—
48C2×C22⋊D11—22no—
49C2×C22⋊D11D414yes—
50C22×Dic11C2311yescharacteristic
51C22×Dic11C2312yes—
52C22×Dic11C2312yes—
53C22×Dic11C2311yescharacteristic
54C22×Dic11C2311yescharacteristic
55C2×C4×D11—22no—
56C2×C4×D11—22no—
57C2×C4×D11—22no—
58C2×Dic22—24no—
59C2×Dic22—24no—
60C2×Dic22—24no—
61C11×C4⋊C4—22no—
62C11×C4⋊C4—22no—
63C11×C22⋊C4—24no—
64C22⋊Dic11—22no—
65C22⋊Dic11—24no—
66(C2×D11)⋊C4—22no—
67(C2×D11)⋊C4—24no—
68(C2×D11)⋊C4—24no—
69C4⋊Dic11—22no—
70C4⋊Dic11—22no—
71Dic11⋊C4—24no—
72Dic11⋊C4—22no—
73C4×Dic11—24no—
74C4×Dic11D414yes—
75#2547—111nomaximal, Sylow
76C23×C11—21no—
77C23×C11—21no—
78C23×C11—21no—
79C23×C11—21no—
80C23×C11—21no—
81C23×C11—21no—
82C23×C11C2×D412yes—
83C23×C11C2411yescharacteristic
84C22×D11—21no—
85C22×D11—21no—
86C22×D11—21no—
87C22×D11—21no—
88C22×D11—21no—
89C22×D11—21no—
90C22×D11C2×D412yes—
91C2×C4×C11—22no—
92C2×C4×C11—21no—
93C2×C4×C11—22no—
94C2×C4×C11—22no—
95C2×C4×C11—22no—
96C2×C4×C11—22no—
97C2×C4×C11—21no—
98C2×C4×C11—21no—
99C2×C4×C11—22no—
100C2×C4×C11—44no—
101C2×C4×C11C2×D412yes—
102C2×C4×C11#4112yes—
103C2×C4×C11#4112yes—
104C22⋊D11—28no—
105C2×Dic11—21no—
106C2×Dic11—21no—
107C2×Dic11—22no—
108C2×Dic11—22no—
109C2×Dic11—21no—
110C2×Dic11—22no—
111C2×Dic11—22no—
112C2×Dic11—22no—
113C2×Dic11—21no—
114C2×Dic11—21no—
115C2×Dic11—22no—
116C2×Dic11C2×D412yes—
117C2×Dic11C2×D412yes—
118C2×Dic11C2×D412yes—
119C2×Dic11#4112yes—
120C4×D11—44no—
121Dic22—48no—
122C2×C4⋊Q8—111no—
123C2×#124—112no—
124C2×C4×D4—111no—
125#397—112no—
126#397—112no—
127#391—112no—
128#380—111no—
129#380—111no—
130#380—111no—
131#380D1111yescharacteristic, complemented
132C4×C4⋊C4—111no—
133C22×C11—22no—
134C22×C11—22no—
135C22×C11—22no—
136C22×C11—41no—
137C22×C11—41no—
138C22×C11—41no—
139C22×C11—41no—
140C22×C11C22×D411yescharacteristic
141C22×C11C22×D411yescharacteristic
142C22×C11C2×#4111yescharacteristic
143C22×C11C2×#4111yescharacteristic
144C22×C11C2×#4111yescharacteristic
145C22×C112−1+411yescharacteristic
146C22×C112−1+411yescharacteristic
147C2×D11—22no—
148C2×D11—22no—
149C2×D11—22no—
150C2×D11—41no—
151C2×D11—41no—
152C2×D11—41no—
153C2×D11—41no—
154C4×C11—42no—
155C4×C11—41no—
156C4×C11—42no—
157C4×C11#12414yescomplemented
158Dic11—22no—
159Dic11—42no—
160Dic11—41no—
161Dic11—42no—
162Dic11#12114yes—
163C22×Q8—112no—
164C22×D4—111no—
165C23×C4—111no—
166C23×C4C2×D1111yescharacteristic
167C4⋊Q8—224no—
168#124—228no—
169C4×D4—224no—
170C2×C4⋊C4—111no—
171C2×C4⋊C4—111no—
172C2×C4⋊C4—112no—
173C2×C4⋊C4—111no—
174C2×C4⋊C4C2×D1111yescharacteristic
175C2×C4⋊C4C2×D1111yescharacteristic
176C2×C22⋊C4—111no—
177C2×C22⋊C4—112no—
178C2×C22⋊C4—111no—
179C2×C22⋊C4—112no—
180C2×C22⋊C4—112no—
181C2×C22⋊C4C2×D1112yes—
182C2×C42—111no—
183C2×C42—112no—
184#95—112no—
185#95—112no—
186#95—112no—
187#95—112no—
188#95C2×D1112yes—
189C2×C11—42no—
190C2×C11C2×#12111yescharacteristic
191C2×C11C2×#12411yescharacteristic
192C2×C11#53611yescharacteristic
193C2×C11#54711yescharacteristic
194C2×C11#54711yescharacteristic
195C2×C11#55611yescharacteristic
196C2×C11#55611yescharacteristic
197D11—42no—
198C24—111no—
199C24C22×D1111yescharacteristic
200C2×Q8—224no—
201C2×Q8—224no—
202C2×Q8—224no—
203C2×D4—114no—
204C2×D4—222no—
205C2×D4—222no—
206C22×C4—22no—
207C22×C4—22no—
208C22×C4—22no—
209C22×C4—111no—
210C22×C4—111no—
211C22×C4—111no—
212C22×C4—112no—
213C22×C4—112no—
214C22×C4—222no—
215C22×C4—222no—
216C22×C4—222no—
217C22×C4C22×D1111yescharacteristic
218C22×C4C22×D1112yes—
219C22×C4C22×D1112yes—
220C22×C4C22×D1111yescharacteristic
221C4⋊C4—22no—
222C4⋊C4—22no—
223C4⋊C4—222no—
224C4⋊C4—224no—
225C4⋊C4—222no—
226C4⋊C4—222no—
227C22⋊C4—24no—
228C22⋊C4—222no—
229C22⋊C4—224no—
230C22⋊C4—224no—
231C22⋊C4—222no—
232C22⋊C4—224no—
233C42—114no—
234C42—224no—
235C11#254711yescharacteristic, complemented, Sylow
236C23—21no—
237C23—21no—
238C23—21no—
239C23—21no—
240C23—21no—
241C23—21no—
242C23—112no—
243C23—221no—
244C23—221no—
245C23—221no—
246C23—221no—
247C23—221no—
248C23—221no—
249C23D4×D1112yes—
250C23C23×D1111yescharacteristic
251Q8—448no—
252D4—228no—
253C2×C4—21no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—21no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—21no—
260C2×C4—22no—
261C2×C4—22no—
262C2×C4—44no—
263C2×C4—112no—
264C2×C4—112no—
265C2×C4—112no—
266C2×C4—112no—
267C2×C4—221no—
268C2×C4—221no—
269C2×C4—222no—
270C2×C4—221no—
271C2×C4—222no—
272C2×C4—222no—
273C2×C4—221no—
274C2×C4—222no—
275C2×C4—221no—
276C2×C4—222no—
277C2×C4—222no—
278C2×C4—444no—
279C2×C4#433912yes—
280C2×C4D4×D1112yes—
281C2×C4#434112yes—
282C22—22no—
283C22—22no—
284C22—22no—
285C22—41no—
286C22—41no—
287C22—41no—
288C22—41no—
289C22—222no—
290C22—222no—
291C22—222no—
292C22—441no—
293C22—441no—
294C22—441no—
295C22—441no—
296C22C2×#433911yescharacteristic
297C22C2×D4×D1111yescharacteristic
298C22C2×D4×D1111yescharacteristic
299C22C2×#434111yescharacteristic
300C22#6704011yescharacteristic
301C22#41×D1111yescharacteristic
302C22#6704311yescharacteristic
303C4—41no—
304C4—42no—
305C4—42no—
306C4—114no—
307C4—222no—
308C4—441no—
309C4—442no—
310C4—442no—
311C4#6693814yescomplemented
312C2—42no—
313C2—442no—
314C2C2×#6693811yescharacteristic
315C2#1062303811yescharacteristic
316C2#1062306411yescharacteristic
317C2D11×#12111yescharacteristic
318C2#1062314211yescharacteristic
319C2#1062315911yescharacteristic
320C2#1062317211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#380C2
prime radicalC22×C22⋊D11C22
hypercenter#380D11
hypocenterC11#2547
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #380

Complements

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

NH ≅ G/Ntype
2. C2×#66941C2semidirect
4. C11×#380C2semidirect
5. #10622825C2semidirect
6. #10622600C2semidirect
7. #10622600C2semidirect
8. C4⋊C4×Dic11C2semidirect
9. #10622565C2semidirect
10. #10622288C2semidirect
11. #10622259C2semidirect
131. #380D11semidirect
157. C4×C11#124semidirect
235. C11#2547semidirect
311. C4#66938semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C22⋊D112
C2×#669412
C2×#669382
C11×#3802
#106228252
#106226002
C4⋊C4×Dic112
#106225652
#106222882
#106222592
#254711