Finite Group Databasebeta

← #13076946

Subgroups — #13076946

Order 1408.

688 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66991C211yesmaximal, characteristic
2C2×#66936C212yesmaximal, complemented
3C2×C42×D11C211yesmaximal, characteristic, complemented
4C11×#390C211yesmaximal, characteristic, complemented
5#10622834C211yesmaximal, characteristic, complemented
6#10622600C211yesmaximal, characteristic, complemented
7#10622598C211yesmaximal, characteristic, complemented
8#10622569C212yesmaximal, complemented
9#10622564C212yesmaximal, complemented
10#10622558C212yesmaximal, complemented
11#10622541C211yesmaximal, characteristic, complemented
12C22×D4×C11C2211yescharacteristic
13C22×C22⋊D11C2212yes—
14C22×C4×D11C2211yescharacteristic
15C22×C4×D11C2211yescharacteristic
16C22×C4×D11C2211yescharacteristic
17C2×C11×C4⋊C4C2211yescharacteristic
18C2×C11×C22⋊C4C2212yes—
19C2×C11×C22⋊C4C2212yes—
20C2×C42×C11C2211yescharacteristic
21C2×C22⋊Dic11C2212yes—
22C2×C22⋊Dic11C2212yes—
23C2×C22⋊Dic11C2212yes—
24#66991—24no—
25C2×(C2×D11)⋊C4C2212yes—
26C2×C4⋊Dic11C2212yes—
27C2×C4⋊Dic11C2211yescharacteristic
28C2×C4⋊Dic11C2211yescharacteristic
29C2×Dic11⋊C4C2212yes—
30C2×C4×Dic11C2211yescharacteristic
31C2×C4×Dic11C2211yescharacteristic
32C2×C4×Dic11C2211yescharacteristic
33#66936—28no—
34C42×D11—24no—
35C11⋊#95C2212yes—
36C11⋊#95C2212yes—
37C11⋊#95C2212yes—
38C24×C11C2312yes—
39C23×D11C2311yescharacteristic
40C2×D4×C11—22no—
41C2×D4×C11—22no—
42C2×D4×C11—22no—
43C22×C4×C11C2312yes—
44C22×C4×C11C2311yescharacteristic
45C22×C4×C11C2311yescharacteristic
46C22×C4×C11C2311yescharacteristic
47C2×C22⋊D11—24no—
48C2×C22⋊D11—24no—
49C2×C22⋊D11—24no—
50C22×Dic11C2312yes—
51C22×Dic11C2312yes—
52C22×Dic11C2311yescharacteristic
53C22×Dic11C2311yescharacteristic
54C22×Dic11C2311yescharacteristic
55C2×C4×D11—22no—
56C2×C4×D11—22no—
57C2×C4×D11—22no—
58C2×C4×D11—22no—
59C2×C4×D11—22no—
60C2×C4×D11—22no—
61C2×C4×D11—22no—
62C2×C4×D11D414yes—
63C2×C4×D11D414yescomplemented
64C11×C4⋊C4—22no—
65C11×C22⋊C4—24no—
66C11×C22⋊C4—24no—
67C42×C11—22no—
68C22⋊Dic11—24no—
69C22⋊Dic11—24no—
70C22⋊Dic11—24no—
71(C2×D11)⋊C4—24no—
72C4⋊Dic11—24no—
73C4⋊Dic11—22no—
74C4⋊Dic11—22no—
75Dic11⋊C4—24no—
76C4×Dic11—22no—
77C4×Dic11—22no—
78C4×Dic11—22no—
79#2854—111nomaximal, Sylow
80C23×C11—22no—
81C23×C11—22no—
82C23×C11—22no—
83C23×C11—22no—
84C23×C11—22no—
85C23×C11—22no—
86C23×C11—22no—
87C23×C11C2411yescharacteristic
88C22×D11—21no—
89C22×D11—21no—
90C22×D11—21no—
91C22×D11—21no—
92C22×D11C2×D412yes—
93C22×D11C2×D412yes—
94C22×D11#4112yes—
95D4×C11—44no—
96C2×C4×C11—21no—
97C2×C4×C11—21no—
98C2×C4×C11—21no—
99C2×C4×C11—21no—
100C2×C4×C11—22no—
101C2×C4×C11—22no—
102C2×C4×C11—22no—
103C2×C4×C11C2×D412yes—
104C2×C4×C11C2×D412yes—
105C2×C4×C11#4112yes—
106C2×C4×C11#4112yes—
107C2×C4×C11#4112yes—
108C22⋊D11—48no—
109C2×Dic11—21no—
110C2×Dic11—21no—
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×Dic11—22no—
121C2×Dic11C2×D412yes—
122C2×Dic11C2×D412yes—
123C2×Dic11#4112yes—
124C4×D11—28no—
125C4×D11—28no—
126C4×D11—28no—
127C2×#123—112no—
128C2×#121—111no—
129C22×C42—111no—
130#390—111no—
131#390D1111yescharacteristic, complemented
132#389—111no—
133#389—111no—
134#388—112no—
135#388—112no—
136#386—112no—
137#380—111no—
138C22×C11—42no—
139C22×C11—42no—
140C22×C11—42no—
141C22×C11—42no—
142C22×C11—42no—
143C22×C11—42no—
144C22×C11—42no—
145C22×C11C22×D411yescharacteristic
146C22×C11C22×D411yescharacteristic
147C22×C11C2×#4111yescharacteristic
148C22×C11C2×#4111yescharacteristic
149C22×C11C2×#4111yescharacteristic
150C22×C11C2×#4111yescharacteristic
151C22×C11C2×#4111yescharacteristic
152C2×D11—22no—
153C2×D11—22no—
154C2×D11—22no—
155C2×D11—22no—
156C2×D11—22no—
157C2×D11—22no—
158C2×D11#12114yes—
159C4×C11—22no—
160C4×C11—22no—
161C4×C11—42no—
162C4×C11#12314yescomplemented
163Dic11—22no—
164Dic11—22no—
165Dic11—22no—
166Dic11—42no—
167Dic11—42no—
168C22×D4—112no—
169C22×D4C2×D1111yescharacteristic
170C23×C4—111no—
171C23×C4—111no—
172C23×C4—111no—
173#123—228no—
174#121—224no—
175C2×C4⋊C4—111no—
176C2×C4⋊C4—112no—
177C2×C4⋊C4—112no—
178C2×C4⋊C4—111no—
179C2×C4⋊C4C2×D1111yescharacteristic
180C2×C22⋊C4—112no—
181C2×C22⋊C4—112no—
182C2×C22⋊C4—112no—
183C2×C22⋊C4—112no—
184C2×C22⋊C4C2×D1112yes—
185C2×C22⋊C4C2×D1112yes—
186C2×C42—111no—
187C2×C42—111no—
188C2×C42—111no—
189C2×C42—224no—
190C2×C42C2×D1111yescharacteristic
191#95—112no—
192#95—112no—
193#95—112no—
194C2×C11—82no—
195C2×C11C2×#12111yescharacteristic
196C2×C11C2×#12311yescharacteristic
197C2×C11#52511yescharacteristic
198C2×C11#52911yescharacteristic
199C2×C11#52911yescharacteristic
200C2×C11#53211yescharacteristic
201C2×C11#53211yescharacteristic
202D11—24no—
203C24—111no—
204C24C22×D1112yes—
205C2×D4—22no—
206C2×D4—22no—
207C2×D4—22no—
208C2×D4—224no—
209C2×D4—224no—
210C2×D4—224no—
211C22×C4—111no—
212C22×C4—111no—
213C22×C4—111no—
214C22×C4—114no—
215C22×C4—114no—
216C22×C4—112no—
217C22×C4—112no—
218C22×C4—222no—
219C22×C4—222no—
220C22×C4—222no—
221C22×C4—222no—
222C22×C4—222no—
223C22×C4—222no—
224C22×C4—222no—
225C22×C4C22×D1112yes—
226C22×C4C22×D1111yescharacteristic
227C22×C4C22×D1111yescharacteristic
228C22×C4C22×D1111yescharacteristic
229C4⋊C4—22no—
230C4⋊C4—224no—
231C4⋊C4—222no—
232C4⋊C4—222no—
233C4⋊C4—224no—
234C22⋊C4—24no—
235C22⋊C4—24no—
236C22⋊C4—224no—
237C22⋊C4—224no—
238C22⋊C4—224no—
239C22⋊C4—224no—
240C42—22no—
241C42—222no—
242C42—222no—
243C42—222no—
244C11#285411yescharacteristic, complemented, Sylow
245C23—22no—
246C23—22no—
247C23—22no—
248C23—22no—
249C23—22no—
250C23—22no—
251C23—22no—
252C23—112no—
253C23—112no—
254C23—112no—
255C23—221no—
256C23—221no—
257C23—221no—
258C23—221no—
259C23C23×D1111yescharacteristic
260D4—44no—
261D4—448no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—22no—
267C2×C4—22no—
268C2×C4—22no—
269C2×C4—112no—
270C2×C4—112no—
271C2×C4—112no—
272C2×C4—228no—
273C2×C4—228no—
274C2×C4—221no—
275C2×C4—221no—
276C2×C4—221no—
277C2×C4—221no—
278C2×C4—221no—
279C2×C4—221no—
280C2×C4—228no—
281C2×C4—222no—
282C2×C4—222no—
283C2×C4—222no—
284C2×C4—222no—
285C2×C4—222no—
286C2×C4—222no—
287C2×C4#433912yes—
288C2×C4D4×D1112yes—
289C2×C4D4×D1112yes—
290C2×C4#434112yes—
291C2×C4#434112yes—
292C22—42no—
293C22—42no—
294C22—42no—
295C22—42no—
296C22—42no—
297C22—42no—
298C22—42no—
299C22—114no—
300C22—222no—
301C22—222no—
302C22—222no—
303C22—222no—
304C22—222no—
305C22—222no—
306C22C2×#433911yescharacteristic
307C22C2×D4×D1111yescharacteristic
308C22C2×D4×D1111yescharacteristic
309C22C2×#434111yescharacteristic
310C22C2×#434111yescharacteristic
311C22#41×D1111yescharacteristic
312C22#41×D1111yescharacteristic
313C4—22no—
314C4—22no—
315C4—42no—
316C4—222no—
317C4—222no—
318C4—222no—
319C4—442no—
320C4—442no—
321C4#6693614yescomplemented
322C2—82no—
323C2—224no—
324C2C2×#6693611yescharacteristic
325C2#1062307911yescharacteristic
326C2#1062308811yescharacteristic
327C2D11×#12111yescharacteristic
328C2#1062313711yescharacteristic
329C2#1062321111yescharacteristic
330C2#1062324711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#390C2
prime radicalC2×#66991C2
hypercenter#390D11
hypocenterC11#2854
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
2. C2×#66936C2semidirect
3. C2×C42×D11C2semidirect
4. C11×#390C2semidirect
5. #10622834C2semidirect
6. #10622600C2semidirect
7. #10622598C2semidirect
8. #10622569C2semidirect
9. #10622564C2semidirect
10. #10622558C2semidirect
11. #10622541C2semidirect
63. C2×C4×D11D4semidirect
131. #390D11semidirect
162. C4×C11#123semidirect
244. C11#2854semidirect
321. C4#66936semidirect

Maximal subgroups

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

subgroupindex
C2×#669912
C2×#669362
C2×C42×D112
C11×#3902
#106228342
#106226002
#106225982
#106225692
#106225642
#106225582
#106225412
#285411