Finite Group Databasebeta

← #13078719

Subgroups — #13078719

Order 1408.

392 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#529C211yesmaximal, characteristic, complemented
2C4×#4339C211yesmaximal, characteristic, complemented
3#10622679C211yesmaximal, characteristic, complemented
4#10622676C211yesmaximal, characteristic, complemented
5#10622670C211yesmaximal, characteristic, complemented
6#10622667C211yesmaximal, characteristic, complemented
7#10622660C211yesmaximal, characteristic, complemented
8#10622658C211yesmaximal, characteristic, complemented
9#10622650C211yesmaximal, characteristic
10#10622648C211yesmaximal, characteristic, complemented
11#10622643C211yesmaximal, characteristic, complemented
12#10622639C211yesmaximal, characteristic, complemented
13#10622631C211yesmaximal, characteristic, complemented
14#10622627C211yesmaximal, characteristic, complemented
15#10622539C211yesmaximal, characteristic, complemented
16C2×#4339C2211yescharacteristic
17C11×#126—21no—
18C11×#125C2211yescharacteristic
19C11×#124C2211yescharacteristic
20C11×#123—21no—
21C11×C22⋊Q8C2211yescharacteristic
22C11×#121C2211yescharacteristic
23C4×Q8×C11C2211yescharacteristic
24C4×D4×C11—21no—
25C4×D4×C11C2211yescharacteristic
26C11×#117—21no—
27C2×C42×C11C2211yescharacteristic
28C2×#4326C2211yescharacteristic
29C2×#4325C2211yescharacteristic
30C2×#4324C2211yescharacteristic
31C2×#4323C2211yescharacteristic
32C4×C22⋊D11—21no—
33C4×C22⋊D11—21no—
34#66979C2211yescharacteristic
35C4×D44C2211yescharacteristic
36C4×D44C2211yescharacteristic
37#66925—21no—
38C42×D11—21no—
39C4×Dic22C2211yescharacteristic
40C4×Dic22C2211yescharacteristic
41#66899C2211yescharacteristic
42#66899C2211yescharacteristic
43#66896C2211yescharacteristic
44#66896C2211yescharacteristic
45C22⋊(C11⋊C8)C2211yescharacteristic
46C22⋊(C11⋊C8)C2211yescharacteristic
47#66874C2211yescharacteristic
48#66874C2211yescharacteristic
49#66873C2211yescharacteristic
50#66873C2211yescharacteristic
51#66872C2211yescharacteristic
52#66872C2211yescharacteristic
53#66871C2211yescharacteristic
54#66871C2211yescharacteristic
55C4⋊(C11⋊C8)C2211yescharacteristic
56C4⋊(C11⋊C8)C2211yescharacteristic
57#66867C2211yescharacteristic
58#66867C2211yescharacteristic
59C2×Q8×C11C2311yescharacteristic
60C2×D4×C11—21no—
61C2×D4×C11C2311yescharacteristic
62C22×C4×C11—21no—
63C22×C4×C11D411yescharacteristic
64C22×C4×C11D411yescharacteristic
65C22×C4×C11C2311yescharacteristic
66C2×C22⋊D11—21no—
67#4339—22no—
68#4339—22no—
69C2×D44C2311yescharacteristic
70C2×C4×D11—21no—
71C2×C4×D11—21no—
72C2×C4×D11—21no—
73C2×Dic22C2311yescharacteristic
74C11×C4⋊C4—21no—
75C11×C4⋊C4—21no—
76C11×C4⋊C4—21no—
77C11×C4⋊C4—21no—
78C11×C4⋊C4C2311yescharacteristic
79C11×C4⋊C4C2311yescharacteristic
80C11×C22⋊C4—21no—
81C11×C22⋊C4—21no—
82C11×C22⋊C4—21no—
83C11×C22⋊C4—21no—
84C11×C22⋊C4—21no—
85C42×C11—21no—
86C42×C11D411yescharacteristic
87C42×C11D411yescharacteristic
88C42×C11C2311yescharacteristic
89C42×C11C2311yescharacteristic
90C22⋊Dic11—21no—
91#4326—22no—
92#4325—22no—
93#4324—22no—
94#4323—22no—
95(C2×D11)⋊C4—21no—
96(C2×D11)⋊C4—21no—
97C4⋊Dic11C2311yescharacteristic
98C4⋊Dic11C2311yescharacteristic
99Dic11⋊C4—21no—
100Dic11⋊C4—21no—
101C4×Dic11—21no—
102C4×Dic11—21no—
103C4×Dic11—21no—
104C2×C11⋊C8C2311yescharacteristic
105C2×C11⋊C8C2311yescharacteristic
106C2×C11⋊C8C2311yescharacteristic
107C2×C11⋊C8C2311yescharacteristic
108#3111—111nomaximal, Sylow
109C23×C11—21no—
110C23×C11C2×D411yescharacteristic
111C22×D11—21no—
112Q8×C11—21no—
113Q8×C11—21no—
114D4×C11—21no—
115D4×C11—21no—
116D4×C11—42no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—41no—
123C2×C4×C11—41no—
124C2×C4×C11—42no—
125C2×C4×C11C2×D411yescharacteristic
126C2×C4×C11C2×D411yescharacteristic
127C2×C4×C11C2×D411yescharacteristic
128C2×C4×C11C2×D411yescharacteristic
129C2×C4×C11C2×D411yescharacteristic
130C2×C4×C11C2411yescharacteristic
131C22⋊D11—24no—
132C2×Dic11—21no—
133C2×Dic11—21no—
134C2×Dic11—21no—
135D44—21no—
136D44#4112yes—
137C4×D11—24no—
138C4×D11—42no—
139C4×D11—42no—
140Dic22—21no—
141Dic22#4112yes—
142C11⋊C8—21no—
143C11⋊C8—21no—
144C11⋊C8—21no—
145C11⋊C8—21no—
146#529D1111yescharacteristic, complemented
147C4×#41—111no—
148#485—111no—
149#482—111no—
150#479—111no—
151#478—111no—
152#464—111no—
153#463—111no—
154#452—111no—
155#449—111no—
156#442—111no—
157#441—111no—
158#440—111no—
159#440—111no—
160#432—111no—
161C22×C11—21no—
162C22×C11—21no—
163C22×C11—21no—
164C22×C11—41no—
165C22×C11—41no—
166C22×C11—41no—
167C22×C11C22×D411yescharacteristic
168C2×D11—22no—
169C2×D11—41no—
170C2×D11—41no—
171C4×C11—21no—
172C4×C11—21no—
173C4×C11—21no—
174C4×C11—21no—
175C4×C11—21no—
176C4×C11—41no—
177C4×C11—41no—
178C4×C11—41no—
179C4×C11C2×#4111yescharacteristic
180C4×C11C2×#4111yescharacteristic
181Dic11—22no—
182Dic11—41no—
183Dic11—41no—
184C2×#41—111no—
185C2×Q16—111no—
186C2×SD16—111no—
187C2×SD16—111no—
188C2×D8—111no—
189#126—21no—
190#125C2×D1111yescharacteristic
191#124C2×D1111yescharacteristic
192#123—21no—
193C22⋊Q8C2×D1111yescharacteristic
194#121C2×D1111yescharacteristic
195C4×Q8—111no—
196C4×Q8—111no—
197C4×Q8C2×D1111yescharacteristic
198C4×D4—21no—
199C4×D4—111no—
200C4×D4—111no—
201C4×D4—221no—
202C4×D4—221no—
203C4×D4C2×D1111yescharacteristic
204#117—21no—
205#117—111no—
206#117—221no—
207C2×C42—221no—
208C2×C42C2×D1111yescharacteristic
209#107—111no—
210#107—111no—
211#106—111no—
212#106—111no—
213C4⋊C8—111no—
214C4⋊C8—111no—
215#103—111no—
216#103—111no—
217#103—111no—
218#103—111no—
219#102—111no—
220#102—111no—
221#102—111no—
222#102—111no—
223C22⋊C8—111no—
224C22⋊C8—111no—
225#97—111no—
226#97—111no—
227C2×C11—41no—
228C2×C11—81no—
229C2×C11#52511yescharacteristic
230C2×C11#57511yescharacteristic
231C2×C11#57511yescharacteristic
232D11—42no—
233#41—222no—
234#41—222no—
235C2×Q8—111no—
236C2×Q8C22×D1111yescharacteristic
237C2×D4—21no—
238C2×D4—111no—
239C2×D4—221no—
240C2×D4C22×D1111yescharacteristic
241C22×C4—21no—
242C22×C4—221no—
243C22×C4—221no—
244C22×C4—221no—
245C22×C4C22⋊D1111yescharacteristic
246C22×C4C22⋊D1111yescharacteristic
247C22×C4C22×D1111yescharacteristic
248Q16—222no—
249SD16—222no—
250SD16—222no—
251D8—222no—
252C2×C8—111no—
253C2×C8—111no—
254C2×C8—111no—
255C2×C8—111no—
256C4⋊C4—21no—
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4—111no—
261C4⋊C4—111no—
262C4⋊C4—221no—
263C4⋊C4—221no—
264C4⋊C4C22×D1111yescharacteristic
265C4⋊C4C22×D1111yescharacteristic
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—21no—
270C22⋊C4—21no—
271C22⋊C4—221no—
272C22⋊C4—221no—
273C22⋊C4—221no—
274C42—21no—
275C42—221no—
276C42—221no—
277C42—221no—
278C42C22⋊D1111yescharacteristic
279C42C22⋊D1111yescharacteristic
280C42C22×D1111yescharacteristic
281C42C22×D1111yescharacteristic
282C11#311111yescharacteristic, complemented, Sylow
283C23—21no—
284C23—221no—
285C23C2×C22⋊D1111yescharacteristic
286Q8—21no—
287Q8—21no—
288Q8—112no—
289Q8—221no—
290D4—21no—
291D4—21no—
292D4—42no—
293D4—112no—
294D4—224no—
295D4—221no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—42no—
304C2×C4—224no—
305C2×C4—221no—
306C2×C4—221no—
307C2×C4—221no—
308C2×C4—442no—
309C2×C4—442no—
310C2×C4C2×C22⋊D1111yescharacteristic
311C2×C4C2×C22⋊D1111yescharacteristic
312C2×C4C2×C22⋊D1111yescharacteristic
313C2×C4C2×C22⋊D1111yescharacteristic
314C2×C4C2×C22⋊D1111yescharacteristic
315C2×C4C23×D1111yescharacteristic
316C8—221no—
317C8—221no—
318C8—221no—
319C8—221no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—222no—
327C22—441no—
328C22—441no—
329C22C22×C22⋊D1111yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—41no—
336C4—41no—
337C4—41no—
338C4—222no—
339C4—441no—
340C4—441no—
341C4#41×D1111yescharacteristic
342C4#41×D1111yescharacteristic
343C2—41no—
344C2—81no—
345C2—442no—
346C2#1062335311yescharacteristic
347C2#1062335311yescharacteristic
348C2#1062335911yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#529C2
socleC22×C11C22×D4
prime radical#10622650C2
hypercenter#529D11
hypocenterC11#3111
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #529

Complements

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

NH ≅ G/Ntype
1. C11×#529C2semidirect
2. C4×#4339C2semidirect
3. #10622679C2semidirect
4. #10622676C2semidirect
5. #10622670C2semidirect
6. #10622667C2semidirect
7. #10622660C2semidirect
8. #10622658C2semidirect
10. #10622648C2semidirect
11. #10622643C2semidirect
12. #10622639C2semidirect
13. #10622631C2semidirect
14. #10622627C2semidirect
15. #10622539C2semidirect
146. #529D11semidirect
282. C11#3111semidirect

Maximal subgroups

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

subgroupindex
C11×#5292
C4×#43392
#106226792
#106226762
#106226702
#106226672
#106226602
#106226582
#106226502
#106226482
#106226432
#106226392
#106226312
#106226272
#106225392
#311111