Finite Group Databasebeta

← #13072176

Subgroups — #13072176

Order 1408.

632 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×Q8×C11C211yesmaximal, characteristic, complemented
2C2×#67000C211yesmaximal, characteristic, complemented
3C2×#66999C211yesmaximal, characteristic, complemented
4C2×#66948C211yesmaximal, characteristic
5#10622607C212yesmaximal, complemented
6#10622604C212yesmaximal, complemented
7#10622598C211yesmaximal, characteristic, complemented
8#10622553C212yesmaximal, complemented
9#10622552C211yesmaximal, characteristic, complemented
10#10622552C212yesmaximal, complemented
11C4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
12C22×Q8×C11C2211yescharacteristic
13C22×D44C2211yescharacteristic
14C22×D44C2212yes—
15C22×C4×D11C2211yescharacteristic
16C4×Q8×C11—24no—
17C2×C11×C4⋊C4C2212yes—
18C2×C11×C4⋊C4C2211yescharacteristic
19C2×C42×C11C2211yescharacteristic
20C2×C42×C11C2212yes—
21#67000—24no—
22#66999—24no—
23C2×(C2×D11)⋊C4C2212yes—
24C2×(C2×D11)⋊C4C2211yescharacteristic
25C2×(C2×D11)⋊C4C2211yescharacteristic
26C2×(C2×D11)⋊C4C2212yes—
27C2×(C2×D11)⋊C4C2212yes—
28C2×(C2×D11)⋊C4C2212yes—
29C2×(C2×D11)⋊C4C2212yes—
30C2×(C2×D11)⋊C4C2212yes—
31C2×C4⋊Dic11C2211yescharacteristic
32C2×C4⋊Dic11C2212yes—
33C2×Dic11⋊C4C2212yes—
34C2×C4×Dic11C2211yescharacteristic
35#66948—24no—
36C11⋊#95C2211yescharacteristic
37C11⋊#95C2211yescharacteristic
38C11⋊#95C2212yes—
39C23×D11C2312yes—
40C23×D11C2311yescharacteristic
41C2×Q8×C11—22no—
42C2×Q8×C11—22no—
43C2×Q8×C11D414yescomplemented
44C22×C4×C11C2311yescharacteristic
45C22×C4×C11C2312yes—
46C22×C4×C11C2312yes—
47C22×C4×C11C2311yescharacteristic
48C22×C4×C11C2311yescharacteristic
49C22×Dic11C2311yescharacteristic
50C22×Dic11C2311yescharacteristic
51C22×Dic11C2311yescharacteristic
52C22×Dic11C2312yes—
53C2×D44—24no—
54C2×D44—24no—
55C2×D44—22no—
56C2×D44—22no—
57C2×D44—22no—
58C2×D44—42no—
59C2×C4×D11—22no—
60C2×C4×D11—22no—
61C2×C4×D11—22no—
62C11×C4⋊C4—24no—
63C11×C4⋊C4D414yes—
64C42×C11—24no—
65C42×C11—22no—
66(C2×D11)⋊C4—22no—
67(C2×D11)⋊C4—24no—
68(C2×D11)⋊C4—24no—
69(C2×D11)⋊C4—24no—
70(C2×D11)⋊C4—24no—
71(C2×D11)⋊C4—22no—
72(C2×D11)⋊C4—24no—
73(C2×D11)⋊C4—42no—
74C4⋊Dic11—22no—
75C4⋊Dic11—42no—
76Dic11⋊C4—24no—
77C4×Dic11—22no—
78#2426—111nomaximal, Sylow
79C23×C11C2411yescharacteristic
80C22×D11—21no—
81C22×D11—21no—
82C22×D11—21no—
83C22×D11—21no—
84C22×D11—21no—
85C22×D11—21no—
86C22×D11—22no—
87C22×D11—22no—
88C22×D11—22no—
89C22×D11—22no—
90C22×D11—22no—
91C22×D11—22no—
92C22×D11—22no—
93C22×D11#4112yes—
94Q8×C11—28no—
95C2×C4×C11—21no—
96C2×C4×C11—22no—
97C2×C4×C11—22no—
98C2×C4×C11—22no—
99C2×C4×C11—22no—
100C2×C4×C11—21no—
101C2×C4×C11—21no—
102C2×C4×C11—21no—
103C2×C4×C11—21no—
104C2×C4×C11C2×D414yes—
105C2×C4×C11C2×D412yes—
106C2×C4×C11C2×D414yes—
107C2×C4×C11C2×D412yes—
108C2×C4×C11#4112yes—
109C2×C4×C11#4112yes—
110C2×Dic11—21no—
111C2×Dic11—21no—
112C2×Dic11—21no—
113C2×Dic11—22no—
114C2×Dic11—21no—
115C2×Dic11—21no—
116C2×Dic11—22no—
117C2×Dic11—21no—
118C2×Dic11—21no—
119C2×Dic11—21no—
120C2×Dic11—22no—
121C2×Dic11—21no—
122D44—48no—
123D44—44no—
124C4×D11—44no—
125C2×#124—111no—
126C2×C22⋊Q8—111no—
127C2×#121—111no—
128C2×C4×Q8D1111yescharacteristic, complemented
129#396—112no—
130#394—112no—
131#390—111no—
132#390—112no—
133#389—111no—
134#388—112no—
135C4×C22⋊C4—111no—
136C22×C11C22×D411yescharacteristic
137C22×C11C22×D411yescharacteristic
138C22×C11C2×#4111yescharacteristic
139C22×C11C2×#4111yescharacteristic
140C22×C11C2×#4111yescharacteristic
141C22×C11H(5,𝔽2)11yescharacteristic
142C22×C112−1+411yescharacteristic
143C2×D11—22no—
144C2×D11—22no—
145C2×D11—22no—
146C2×D11—41no—
147C2×D11—41no—
148C2×D11—41no—
149C2×D11—41no—
150C2×D11—42no—
151C2×D11—42no—
152C2×D11—42no—
153C2×D11—42no—
154C2×D11—42no—
155C2×D11—42no—
156C2×D11—42no—
157C4×C11—24no—
158C4×C11—24no—
159C4×C11—22no—
160C4×C11—41no—
161C4×C11#12114yes—
162Dic11—41no—
163Dic11—41no—
164Dic11—41no—
165Dic11—42no—
166C22×Q8C2×D1111yescharacteristic
167C22×D4—111no—
168C22×D4—112no—
169C23×C4—111no—
170#124—224no—
171C22⋊Q8—224no—
172#121—224no—
173C4×Q8—24no—
174C2×C4⋊C4—112no—
175C2×C4⋊C4—111no—
176C2×C4⋊C4—112no—
177C2×C4⋊C4C2×D1112yes—
178C2×C4⋊C4C2×D1111yescharacteristic
179C2×C22⋊C4—112no—
180C2×C22⋊C4—112no—
181C2×C22⋊C4—112no—
182C2×C22⋊C4—112no—
183C2×C22⋊C4—111no—
184C2×C22⋊C4—111no—
185C2×C22⋊C4—112no—
186C2×C22⋊C4—112no—
187C2×C42—111no—
188C2×C42C2×D1111yescharacteristic
189C2×C42C2×D1112yes—
190#95—111no—
191#95—111no—
192#95—112no—
193C2×C11C2×#12111yescharacteristic
194C2×C11#52911yescharacteristic
195C2×C11#54211yescharacteristic
196C2×C11#54611yescharacteristic
197C2×C11#54811yescharacteristic
198C2×C11#54811yescharacteristic
199C2×C11#55011yescharacteristic
200D11—42no—
201D11—82no—
202C24—111no—
203C24—112no—
204C2×Q8—22no—
205C2×Q8—22no—
206C2×Q8D4414yescomplemented
207C2×D4—224no—
208C2×D4—222no—
209C2×D4—222no—
210C2×D4—224no—
211C2×D4—222no—
212C2×D4—442no—
213C22×C4—111no—
214C22×C4—111no—
215C22×C4—111no—
216C22×C4—112no—
217C22×C4—222no—
218C22×C4—222no—
219C22×C4—222no—
220C22×C4C22×D1111yescharacteristic
221C22×C4C22×D1112yes—
222C22×C4C22×D1111yescharacteristic
223C22×C4C22×D1112yes—
224C22×C4C22×D1111yescharacteristic
225C4⋊C4—24no—
226C4⋊C4—224no—
227C4⋊C4—222no—
228C4⋊C4—442no—
229C4⋊C4C22⋊D1114yes—
230C22⋊C4—222no—
231C22⋊C4—224no—
232C22⋊C4—224no—
233C22⋊C4—224no—
234C22⋊C4—222no—
235C22⋊C4—224no—
236C22⋊C4—224no—
237C22⋊C4—442no—
238C42—24no—
239C42—22no—
240C42—222no—
241C11#242611yescharacteristic, complemented, Sylow
242C23—112no—
243C23—221no—
244C23—221no—
245C23—221no—
246C23—221no—
247C23—221no—
248C23—221no—
249C23—222no—
250C23—222no—
251C23—222no—
252C23—222no—
253C23—222no—
254C23—222no—
255C23—222no—
256C23C23×D1111yescharacteristic
257Q8—28no—
258D4—448no—
259D4—444no—
260C2×C4—22no—
261C2×C4—21no—
262C2×C4—22no—
263C2×C4—22no—
264C2×C4—21no—
265C2×C4—22no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—221no—
270C2×C4—221no—
271C2×C4—222no—
272C2×C4—221no—
273C2×C4—221no—
274C2×C4—221no—
275C2×C4—222no—
276C2×C4—221no—
277C2×C4—221no—
278C2×C4—222no—
279C2×C4—221no—
280C2×C4—221no—
281C2×C4—444no—
282C2×C4C2×D4414yes—
283C2×C4C2×D4412yes—
284C2×C4#433912yes—
285C2×C4#434312yes—
286C2×C4C2×C22⋊D1114yes—
287C2×C4C2×C22⋊D1112yes—
288C22—222no—
289C22—222no—
290C22—222no—
291C22—441no—
292C22—441no—
293C22—441no—
294C22—441no—
295C22—442no—
296C22—442no—
297C22—442no—
298C22—442no—
299C22—442no—
300C22—442no—
301C22—442no—
302C22C22×D4411yescharacteristic
303C22C2×#433911yescharacteristic
304C22C2×#434311yescharacteristic
305C22#6704011yescharacteristic
306C22#41×D1111yescharacteristic
307C22#6704211yescharacteristic
308C22C22×C22⋊D1111yescharacteristic
309C4—24no—
310C4—22no—
311C4—24no—
312C4—41no—
313C4—441no—
314C4—441no—
315C4—441no—
316C4—442no—
317C4#6698314yes—
318C2—442no—
319C2—882no—
320C2#1062310711yescharacteristic
321C2#1062310811yescharacteristic
322C2#1062311111yescharacteristic
323C2#1062311311yescharacteristic
324C2C2×#6698311yescharacteristic
325C2#1062334811yescharacteristic
326C2#1062336011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC2×C4×Q8×C11C2
prime radicalC2×#66948C2
hypercenterC2×C4×Q8D11
hypocenterC11#2426
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
1. C2×C4×Q8×C11C2semidirect
2. C2×#67000C2semidirect
3. C2×#66999C2semidirect
5. #10622607C2semidirect
6. #10622604C2semidirect
7. #10622598C2semidirect
8. #10622553C2semidirect
9. #10622552C2semidirect
10. #10622552C2semidirect
11. C4×(C2×D11)⋊C4C2semidirect
43. C2×Q8×C11D4semidirect
128. C2×C4×Q8D11semidirect
206. C2×Q8D44semidirect
241. C11#2426semidirect

Maximal subgroups

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

subgroupindex
C2×C4×Q8×C112
C2×#670002
C2×#669992
C2×#669482
#106226072
#106226042
#106225982
#106225532
#106225522
C4×(C2×D11)⋊C42
#242611