Finite Group Databasebeta

← #13073535

Subgroups — #13073535

Order 1408.

620 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×C22⋊Q8C211yesmaximal, characteristic, complemented
2C2×#66999C211yesmaximal, characteristic, complemented
3C2×Q8×Dic11C211yesmaximal, characteristic, complemented
4C2×C4×C22⋊D11C211yesmaximal, characteristic
5#10622825C211yesmaximal, characteristic, complemented
6#10622607C212yesmaximal, complemented
7#10622600C211yesmaximal, characteristic, complemented
8#10622589C211yesmaximal, characteristic, complemented
9#10622585C212yesmaximal, complemented
10#10622570C212yesmaximal
11#10622561C212yesmaximal, complemented
12C22×Q8×C11C2211yescharacteristic
13C23×C4×C11C2211yescharacteristic
14C22×C22⋊D11C2211yescharacteristic
15C22×C4×D11C2211yescharacteristic
16C11×C22⋊Q8—24no—
17C2×C11×C4⋊C4C2212yes—
18C2×C11×C4⋊C4C2211yescharacteristic
19C2×C11×C22⋊C4C2212yes—
20C2×C22⋊Dic11C2211yescharacteristic
21C2×C22⋊Dic11C2212yes—
22#66999—24no—
23Q8×Dic11—24no—
24C4×C22⋊D11—24no—
25C2×(C2×D11)⋊C4C2211yescharacteristic
26C2×(C2×D11)⋊C4C2212yes—
27C2×(C2×D11)⋊C4C2212yes—
28C2×C4⋊Dic11C2212yes—
29C2×C4⋊Dic11C2211yescharacteristic
30C2×C4⋊Dic11C2211yescharacteristic
31C2×Dic11⋊C4C2211yescharacteristic
32C2×Dic11⋊C4C2212yes—
33C2×Dic11⋊C4C2212yes—
34C2×Dic11⋊C4C2212yes—
35C2×C4×Dic11C2212yes—
36C2×C4×Dic11C2211yescharacteristic
37C11⋊#95C2212yes—
38C11⋊#95C2212yes—
39C24×C11C2311yescharacteristic
40C23×D11C2311yescharacteristic
41C2×Q8×C11—22no—
42C2×Q8×C11—22no—
43C2×Q8×C11D414yescomplemented
44C22×C4×C11—22no—
45C22×C4×C11—22no—
46C22×C4×C11—22no—
47C22×C4×C11C2311yescharacteristic
48C22×C4×C11C2312yes—
49C22×C4×C11C2312yes—
50C22×C4×C11C2311yescharacteristic
51C2×C22⋊D11—22no—
52C2×C22⋊D11—22no—
53C2×C22⋊D11Q814yescomplemented
54C22×Dic11C2312yes—
55C22×Dic11C2311yescharacteristic
56C22×Dic11C2312yes—
57C22×Dic11C2311yescharacteristic
58C22×Dic11C2311yescharacteristic
59C2×C4×D11—22no—
60C2×C4×D11—22no—
61C2×C4×D11—22no—
62C11×C4⋊C4—22no—
63C11×C4⋊C4—24no—
64C11×C22⋊C4—24no—
65C22⋊Dic11—22no—
66C22⋊Dic11—42no—
67(C2×D11)⋊C4—22no—
68(C2×D11)⋊C4—24no—
69(C2×D11)⋊C4—42no—
70C4⋊Dic11—24no—
71C4⋊Dic11—22no—
72C4⋊Dic11—22no—
73Dic11⋊C4—22no—
74Dic11⋊C4—24no—
75Dic11⋊C4—24no—
76Dic11⋊C4—42no—
77C4×Dic11—24no—
78C4×Dic11D414yes—
79#2538—111nomaximal, Sylow
80C23×C11—21no—
81C23×C11—21no—
82C23×C11—21no—
83C23×C11—21no—
84C23×C11—21no—
85C23×C11—21no—
86C23×C11C2×Q812yes—
87C23×C11C2411yescharacteristic
88C22×D11—21no—
89C22×D11—21no—
90C22×D11—21no—
91C22×D11—21no—
92C22×D11—21no—
93C22×D11—21no—
94C22×D11C2×Q812yes—
95Q8×C11—28no—
96C2×C4×C11—22no—
97C2×C4×C11—22no—
98C2×C4×C11—21no—
99C2×C4×C11—22no—
100C2×C4×C11—21no—
101C2×C4×C11—22no—
102C2×C4×C11—21no—
103C2×C4×C11—22no—
104C2×C4×C11—44no—
105C2×C4×C11C2×D412yes—
106C2×C4×C11C2×D414yes—
107C2×C4×C11C2×D412yes—
108C2×C4×C11#4112yes—
109C22⋊D11—28no—
110C2×Dic11—21no—
111C2×Dic11—21no—
112C2×Dic11—22no—
113C2×Dic11—21no—
114C2×Dic11—22no—
115C2×Dic11—21no—
116C2×Dic11—22no—
117C2×Dic11—21no—
118C2×Dic11—22no—
119C2×Dic11—22no—
120C2×Dic11—22no—
121C2×Dic11C2×D412yes—
122C2×Dic11C2×D412yes—
123C2×Dic11C2×Q812yes—
124C2×Dic11#4112yes—
125C4×D11—44no—
126C2×C22⋊Q8—111no—
127C2×C22⋊Q8D1111yescharacteristic, complemented
128C2×C4×Q8—111no—
129C2×C4×D4—111no—
130#396—112no—
131#396—112no—
132#390—112no—
133#389—112no—
134#384—111no—
135#380—111no—
136#380—111no—
137C22×C11—22no—
138C22×C11—22no—
139C22×C11—22no—
140C22×C11—41no—
141C22×C11—41no—
142C22×C11—41no—
143C22×C11—41no—
144C22×C11C22×D411yescharacteristic
145C22×C11C22×D411yescharacteristic
146C22×C11C22×Q811yescharacteristic
147C22×C11C2×#4111yescharacteristic
148C22×C11C2×#4111yescharacteristic
149C22×C11H(5,𝔽2)11yescharacteristic
150C22×C112−1+411yescharacteristic
151C2×D11—22no—
152C2×D11—22no—
153C2×D11—22no—
154C2×D11—41no—
155C2×D11—41no—
156C2×D11—41no—
157C2×D11—41no—
158C4×C11—24no—
159C4×C11—41no—
160C4×C11—42no—
161C4×C11#12114yes—
162Dic11—22no—
163Dic11—41no—
164Dic11—42no—
165Dic11—42no—
166Dic11C22⋊Q814yescomplemented
167C22×Q8C2×D1111yescharacteristic
168C22×D4—111no—
169C23×C4—111no—
170C23×C4C2×D1111yescharacteristic
171C22⋊Q8—24no—
172C22⋊Q8—224no—
173C4×Q8—224no—
174C4×D4—224no—
175C2×C4⋊C4—111no—
176C2×C4⋊C4—111no—
177C2×C4⋊C4—112no—
178C2×C4⋊C4—111no—
179C2×C4⋊C4—112no—
180C2×C4⋊C4—112no—
181C2×C4⋊C4—112no—
182C2×C4⋊C4C2×D1111yescharacteristic
183C2×C4⋊C4C2×D1112yes—
184C2×C22⋊C4—111no—
185C2×C22⋊C4—111no—
186C2×C22⋊C4—112no—
187C2×C22⋊C4—112no—
188C2×C22⋊C4—112no—
189C2×C22⋊C4C2×D1112yes—
190C2×C42—111no—
191C2×C42—112no—
192#95—112no—
193#95—112no—
194C2×C11—42no—
195C2×C11C2×#12111yescharacteristic
196C2×C11C2×C22⋊Q811yescharacteristic
197C2×C11#53711yescharacteristic
198C2×C11D4×Q811yescharacteristic
199C2×C11#55011yescharacteristic
200C2×C11#55411yescharacteristic
201C2×C11#55611yescharacteristic
202D11—42no—
203C24—111no—
204C24C22×D1111yescharacteristic
205C2×Q8—22no—
206C2×Q8—22no—
207C2×Q8C22⋊D1114yescomplemented
208C2×D4—114no—
209C2×D4—222no—
210C2×D4—222no—
211C22×C4—22no—
212C22×C4—22no—
213C22×C4—22no—
214C22×C4—111no—
215C22×C4—111no—
216C22×C4—112no—
217C22×C4—111no—
218C22×C4—112no—
219C22×C4—222no—
220C22×C4—222no—
221C22×C4—222no—
222C22×C4C22×D1111yescharacteristic
223C22×C4C22×D1112yes—
224C22×C4C22×D1112yes—
225C22×C4C22×D1111yescharacteristic
226C4⋊C4—22no—
227C4⋊C4—24no—
228C4⋊C4—222no—
229C4⋊C4—224no—
230C4⋊C4—224no—
231C4⋊C4—222no—
232C4⋊C4—224no—
233C4⋊C4—222no—
234C4⋊C4—442no—
235C22⋊C4—24no—
236C22⋊C4—222no—
237C22⋊C4—222no—
238C22⋊C4—224no—
239C22⋊C4—442no—
240C22⋊C4—442no—
241C42—114no—
242C42—224no—
243C11#253811yescharacteristic, complemented, Sylow
244C23—21no—
245C23—21no—
246C23—21no—
247C23—21no—
248C23—21no—
249C23—21no—
250C23—112no—
251C23—221no—
252C23—221no—
253C23—221no—
254C23—221no—
255C23—221no—
256C23—221no—
257C23Q8×D1112yes—
258C23C23×D1111yescharacteristic
259Q8—28no—
260D4—228no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—22no—
266C2×C4—22no—
267C2×C4—22no—
268C2×C4—21no—
269C2×C4—44no—
270C2×C4—112no—
271C2×C4—112no—
272C2×C4—112no—
273C2×C4—112no—
274C2×C4—221no—
275C2×C4—221no—
276C2×C4—222no—
277C2×C4—221no—
278C2×C4—221no—
279C2×C4—222no—
280C2×C4—222no—
281C2×C4—222no—
282C2×C4—222no—
283C2×C4—222no—
284C2×C4—221no—
285C2×C4—444no—
286C2×C4D4×D1112yes—
287C2×C4#434112yes—
288C2×C4C2×C22⋊D1114yes—
289C2×C4C2×C22⋊D1112yes—
290C22—22no—
291C22—22no—
292C22—22no—
293C22—41no—
294C22—41no—
295C22—41no—
296C22—41no—
297C22—222no—
298C22—222no—
299C22—222no—
300C22—441no—
301C22—441no—
302C22—441no—
303C22—441no—
304C22C2×D4×D1111yescharacteristic
305C22C2×#434111yescharacteristic
306C22C2×Q8×D1111yescharacteristic
307C22#6704011yescharacteristic
308C22#41×D1111yescharacteristic
309C22#6704211yescharacteristic
310C22C22×C22⋊D1111yescharacteristic
311C4—24no—
312C4—41no—
313C4—42no—
314C4—114no—
315C4—222no—
316C4—441no—
317C4—442no—
318C4—442no—
319C4#6699214yes—
320C2—42no—
321C2—442no—
322C2D11×C22⋊Q811yescharacteristic
323C2#1062316011yescharacteristic
324C2#1062316611yescharacteristic
325C2#1062317211yescharacteristic
326C2C2×#6699211yescharacteristic
327C2Q8×C22⋊D1111yescharacteristic
328C2#1062336511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC2×C11×C22⋊Q8C2
prime radicalC22×C22⋊D11C22
hypercenterC2×C22⋊Q8D11
hypocenterC11#2538
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×C11×C22⋊Q8C2semidirect
2. C2×#66999C2semidirect
3. C2×Q8×Dic11C2semidirect
5. #10622825C2semidirect
6. #10622607C2semidirect
7. #10622600C2semidirect
8. #10622589C2semidirect
9. #10622585C2semidirect
11. #10622561C2semidirect
43. C2×Q8×C11D4semidirect
53. C2×C22⋊D11Q8semidirect
127. C2×C22⋊Q8D11semidirect
166. Dic11C22⋊Q8semidirect
207. C2×Q8C22⋊D11semidirect
243. C11#2538semidirect

Maximal subgroups

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

subgroupindex
C2×C11×C22⋊Q82
C2×#669992
C2×Q8×Dic112
C2×C4×C22⋊D112
#106228252
#106226072
#106226002
#106225892
#106225852
#106225702
#106225612
#253811