Finite Group Databasebeta

← #13073576

Subgroups — #13073576

Order 1408.

724 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66983C212yesmaximal, complemented
2C2×#66983C211yesmaximal, characteristic, complemented
3C2×C4×C22⋊D11C211yesmaximal, characteristic, complemented
4C2×C11×#95C211yesmaximal, characteristic, complemented
5#10622826C212yesmaximal, complemented
6#10622287C211yesmaximal, characteristic, complemented
7#10622285C211yesmaximal, characteristic, complemented
8#10622284C211yesmaximal, characteristic, complemented
9#10622283C212yesmaximal, complemented
10#10622278C212yesmaximal, complemented
11#10622274C211yesmaximal, characteristic, complemented
12C23×C4×C11C2212yes—
13C23×C4×C11C2211yescharacteristic
14C22×C22⋊D11C2212yes—
15C22×C22⋊D11C2211yescharacteristic
16C22×D44C2212yes—
17C22×D44C2211yescharacteristic
18C22×C4×D11C2211yescharacteristic
19C2×C22⋊Dic11C2211yescharacteristic
20#66983—24no—
21#66983—28no—
22C4×C22⋊D11—24no—
23C2×(C2×D11)⋊C4C2212yes—
24C2×(C2×D11)⋊C4C2212yes—
25C2×(C2×D11)⋊C4C2212yes—
26C2×(C2×D11)⋊C4C2212yes—
27C2×(C2×D11)⋊C4C2211yescharacteristic
28C2×(C2×D11)⋊C4C2212yes—
29C2×C4⋊Dic11C2212yes—
30C2×C4⋊Dic11C2211yescharacteristic
31C2×Dic11⋊C4C2211yescharacteristic
32C2×C4×Dic11C2211yescharacteristic
33C11×#95C2211yescharacteristic
34C11×#95C2212yes—
35C11×#95C2211yescharacteristic
36C11⋊#95C2212yes—
37C11⋊#95C2212yes—
38C24×C11C2311yescharacteristic
39C23×D11C2312yes—
40C23×D11C2311yescharacteristic
41C22×C4×C11—24no—
42C22×C4×C11—24no—
43C22×C4×C11—42no—
44C22×C4×C11—42no—
45C22×C4×C11D414yescomplemented
46C22×C4×C11C2312yes—
47C22×C4×C11C2311yescharacteristic
48C22×C4×C11C2311yescharacteristic
49C22×C4×C11C2312yes—
50C2×C22⋊D11—22no—
51C2×C22⋊D11—24no—
52C2×C22⋊D11—24no—
53C2×C22⋊D11—22no—
54C2×C22⋊D11—24no—
55C2×C22⋊D11D414yescomplemented
56C22×Dic11C2311yescharacteristic
57C22×Dic11C2311yescharacteristic
58C22×Dic11C2312yes—
59C22×Dic11C2311yescharacteristic
60C2×D44—24no—
61C2×D44—22no—
62C2×D44—24no—
63C2×D44—42no—
64C2×D44—42no—
65C2×C4×D11—22no—
66C2×C4×D11—42no—
67C22⋊Dic11—22no—
68(C2×D11)⋊C4—24no—
69(C2×D11)⋊C4—24no—
70(C2×D11)⋊C4—22no—
71(C2×D11)⋊C4—24no—
72(C2×D11)⋊C4—24no—
73(C2×D11)⋊C4—42no—
74C4⋊Dic11—24no—
75C4⋊Dic11—22no—
76Dic11⋊C4—22no—
77C4×Dic11—22no—
78#2543—111nomaximal, Sylow
79C23×C11—22no—
80C23×C11—22no—
81C23×C11C2×D412yes—
82C23×C11C2×D412yes—
83C23×C11#4112yes—
84C23×C11C2411yescharacteristic
85C22×D11—21no—
86C22×D11—22no—
87C22×D11—21no—
88C22×D11—22no—
89C22×D11—22no—
90C22×D11—22no—
91C22×D11—22no—
92C22×D11—22no—
93C22×D11—22no—
94C22×D11—22no—
95C22×D11—22no—
96C22×D11C2×D412yes—
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×C11—22no—
104C2×C4×C11—44no—
105C2×C4×C11—48no—
106C2×C4×C11C2×D412yes—
107C2×C4×C11C2×D412yes—
108C2×C4×C11#4114yes—
109C22⋊D11—28no—
110C22⋊D11—48no—
111C2×Dic11—21no—
112C2×Dic11—21no—
113C2×Dic11—21no—
114C2×Dic11—21no—
115C2×Dic11—22no—
116C2×Dic11—22no—
117C2×Dic11—22no—
118C2×Dic11—22no—
119C2×Dic11—22no—
120C2×Dic11C2×D412yes—
121D44—48no—
122D44—44no—
123C4×D11—44no—
124C2×#121—111no—
125C2×#121—112no—
126C2×C4×D4—111no—
127#398—111no—
128#397—111no—
129#394—111no—
130#392—111no—
131#388—112no—
132#386—112no—
133#386—112no—
134C2×#95D1111yescharacteristic, complemented
135C22×C11—22no—
136C22×C11—22no—
137C22×C11—24no—
138C22×C11—24no—
139C22×C11#12114yes—
140C22×C11C22×D411yescharacteristic
141C22×C11C22×D411yescharacteristic
142C22×C11C2×#4112yes—
143C22×C11C2×#4111yescharacteristic
144C22×C11H(5,𝔽2)12yes—
145C2×D11—22no—
146C2×D11—24no—
147C2×D11—41no—
148C2×D11—41no—
149C2×D11—42no—
150C2×D11—42no—
151C2×D11—42no—
152C2×D11—42no—
153C2×D11—42no—
154C2×D11—42no—
155C2×D11—42no—
156C2×D11—42no—
157C4×C11—22no—
158C4×C11—22no—
159C4×C11—24no—
160C4×C11—42no—
161Dic11—22no—
162Dic11—42no—
163Dic11—41no—
164Dic11—41no—
165C22×D4—111no—
166C22×D4—112no—
167C22×D4—112no—
168C22×D4—111no—
169C23×C4—111no—
170C23×C4C2×D1112yes—
171C23×C4C2×D1111yescharacteristic
172#121—228no—
173#121—224no—
174C4×D4—224no—
175C2×C4⋊C4—111no—
176C2×C4⋊C4—112no—
177C2×C4⋊C4—111no—
178C2×C22⋊C4—111no—
179C2×C22⋊C4—111no—
180C2×C22⋊C4—112no—
181C2×C22⋊C4—112no—
182C2×C22⋊C4—112no—
183C2×C22⋊C4—112no—
184C2×C22⋊C4—112no—
185C2×C42—111no—
186#95—112no—
187#95—112no—
188#95C2×D1112yes—
189#95C2×D1111yescharacteristic
190#95C2×D1111yescharacteristic
191C2×C11—24no—
192C2×C11C2×#12111yescharacteristic
193C2×C11#53211yescharacteristic
194C2×C11#53411yescharacteristic
195C2×C11#54612yes—
196C2×C11#55312yes—
197D11—42no—
198D11—82no—
199C24—111no—
200C24—112no—
201C24C22×D1111yescharacteristic
202C2×D4—114no—
203C2×D4—224no—
204C2×D4—222no—
205C2×D4—222no—
206C2×D4—224no—
207C2×D4—224no—
208C2×D4—224no—
209C2×D4—222no—
210C2×D4—224no—
211C2×D4—442no—
212C2×D4—442no—
213C22×C4—24no—
214C22×C4—24no—
215C22×C4—42no—
216C22×C4—42no—
217C22×C4—111no—
218C22×C4—111no—
219C22×C4—111no—
220C22×C4—112no—
221C22×C4—222no—
222C22×C4—442no—
223C22×C4D4414yescomplemented
224C22×C4C22×D1112yes—
225C22×C4C22×D1111yescharacteristic
226C22×C4C22×D1111yescharacteristic
227C22×C4C22×D1112yes—
228C4⋊C4—224no—
229C4⋊C4—222no—
230C4⋊C4—222no—
231C22⋊C4—224no—
232C22⋊C4—224no—
233C22⋊C4—222no—
234C22⋊C4—222no—
235C22⋊C4—224no—
236C22⋊C4—224no—
237C22⋊C4—442no—
238C42—222no—
239C11#254311yescharacteristic, complemented, Sylow
240C23—22no—
241C23—22no—
242C23—112no—
243C23—221no—
244C23—222no—
245C23—222no—
246C23—221no—
247C23—222no—
248C23—222no—
249C23—222no—
250C23—222no—
251C23—222no—
252C23—222no—
253C23—222no—
254C23C2×D4412yes—
255C23D4×D1112yes—
256C23#434312yes—
257C23C23×D1111yescharacteristic
258D4—228no—
259D4—448no—
260D4—444no—
261D4—448no—
262C2×C4—22no—
263C2×C4—22no—
264C2×C4—22no—
265C2×C4—22no—
266C2×C4—22no—
267C2×C4—22no—
268C2×C4—22no—
269C2×C4—44no—
270C2×C4—48no—
271C2×C4—112no—
272C2×C4—221no—
273C2×C4—221no—
274C2×C4—221no—
275C2×C4—221no—
276C2×C4—222no—
277C2×C4—222no—
278C2×C4—222no—
279C2×C4—222no—
280C2×C4—222no—
281C2×C4—444no—
282C2×C4C2×D4412yes—
283C2×C4C2×D4412yes—
284C2×C4#433914yes—
285C22—22no—
286C22—24no—
287C22—22no—
288C22—24no—
289C22—224no—
290C22—222no—
291C22—441no—
292C22—441no—
293C22—442no—
294C22—442no—
295C22—442no—
296C22—442no—
297C22—442no—
298C22—442no—
299C22—442no—
300C22—442no—
301C22#6694814yes—
302C22C22×D4411yescharacteristic
303C22C2×#433912yes—
304C22C2×D4×D1111yescharacteristic
305C22#6703712yes—
306C22C2×#434311yescharacteristic
307C4—24no—
308C4—22no—
309C4—22no—
310C4—42no—
311C4—222no—
312C4—441no—
313C4—441no—
314C4—442no—
315C2—24no—
316C2—442no—
317C2—882no—
318C2#1062300811yescharacteristic
319C2#1062302112yes—
320C2#1062302411yescharacteristic
321C2C2×#6694811yescharacteristic
322C2#1062304512yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC2×C11×#95C2
hypercenterC2×#95D11
hypocenterC11#2543
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
1. C2×#66983C2semidirect
2. C2×#66983C2semidirect
3. C2×C4×C22⋊D11C2semidirect
4. C2×C11×#95C2semidirect
5. #10622826C2semidirect
6. #10622287C2semidirect
7. #10622285C2semidirect
8. #10622284C2semidirect
9. #10622283C2semidirect
10. #10622278C2semidirect
11. #10622274C2semidirect
45. C22×C4×C11D4semidirect
55. C2×C22⋊D11D4semidirect
134. C2×#95D11semidirect
223. C22×C4D44semidirect
239. C11#2543semidirect

Maximal subgroups

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

subgroupindex
C2×#669832
C2×C4×C22⋊D112
C2×C11×#952
#106228262
#106222872
#106222852
#106222842
#106222832
#106222782
#106222742
#254311