Finite Group Databasebeta

← #13077684

Subgroups — #13077684

Order 1408.

394 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623079C211yesmaximal, characteristic
2C11×#435C211yesmaximal, characteristic, complemented
3#10622742C211yesmaximal, characteristic, complemented
4#10622740C211yesmaximal, characteristic, complemented
5#10622724C211yesmaximal, characteristic, complemented
6#10622723C211yesmaximal, characteristic, complemented
7#10622624C211yesmaximal, characteristic, complemented
8#10622449C211yesmaximal, characteristic, complemented
9#10622448C211yesmaximal, characteristic, complemented
10#10622343C211yesmaximal, characteristic, complemented
11#10622341C211yesmaximal, characteristic, complemented
12#10622340C211yesmaximal, characteristic, complemented
13#10622340C211yesmaximal, characteristic, complemented
14#10622319C211yesmaximal, characteristic, complemented
15#10622318C211yesmaximal, characteristic, complemented
16C2×#4339C2211yescharacteristic
17C2×#4339C2211yescharacteristic
18C2×C11×M16C2211yescharacteristic
19C22×C8×C11C2211yescharacteristic
20C4×D4×C11C2211yescharacteristic
21#66993C411yescharacteristic
22#66991C411yescharacteristic
23C4×C22⋊D11C2211yescharacteristic
24C4×C22⋊D11C2211yescharacteristic
25C2×#4318C2211yescharacteristic
26C22×C11⋊C8C2211yescharacteristic
27C2×#4313C2211yescharacteristic
28C2×#4313C2211yescharacteristic
29C2×C8×D11C2211yescharacteristic
30C2×C8×D11C2211yescharacteristic
31#66948C411yescharacteristic
32#66941C411yescharacteristic
33#66938C411yescharacteristic
34#66938C411yescharacteristic
35#66937C411yescharacteristic
36#66937C411yescharacteristic
37C4×D44C2211yescharacteristic
38C42×D11C2211yescharacteristic
39C11×C4⋊C8C2211yescharacteristic
40C11×C22⋊C8C2211yescharacteristic
41C11×C22⋊C8C2211yescharacteristic
42C11×#97C2211yescharacteristic
43C22⋊(C11⋊C8)C2211yescharacteristic
44C22⋊(C11⋊C8)C2211yescharacteristic
45(C2×D11)⋊C8C2211yescharacteristic
46(C2×D11)⋊C8C2211yescharacteristic
47(C2×D11)⋊C8C2211yescharacteristic
48(C2×D11)⋊C8C2211yescharacteristic
49(C2×D11)⋊C8C2211yescharacteristic
50(C2×D11)⋊C8C2211yescharacteristic
51(C2×D11)⋊C8C2211yescharacteristic
52(C2×D11)⋊C8C2211yescharacteristic
53#66879C2211yescharacteristic
54#66879C2211yescharacteristic
55Dic11⋊C8C2211yescharacteristic
56Dic11⋊C8C2211yescharacteristic
57C4⋊(C11⋊C8)C2211yescharacteristic
58#66867C2211yescharacteristic
59C2×D4×C11C2×C411yescharacteristic
60C22×C4×C11C2311yescharacteristic
61C22×C4×C11C2311yescharacteristic
62C2×C22⋊D11C2×C411yescharacteristic
63C2×C22⋊D11C2×C411yescharacteristic
64C2×C22⋊D11C2×C411yescharacteristic
65C2×C22⋊D11C2×C411yescharacteristic
66C2×C22⋊D11C2×C411yescharacteristic
67C2×C22⋊D11C2×C411yescharacteristic
68#4339—41no—
69#4339—41no—
70#4339—41no—
71#4339—41no—
72C2×D44C2×C411yescharacteristic
73C2×D44C2×C411yescharacteristic
74C2×D44C2×C411yescharacteristic
75C2×C4×D11C2×C411yescharacteristic
76C2×C4×D11C2×C411yescharacteristic
77C2×C4×D11C2311yescharacteristic
78C2×C4×D11C2311yescharacteristic
79C2×C4×D11C2311yescharacteristic
80C2×Dic22C2×C411yescharacteristic
81C2×Dic22C2×C411yescharacteristic
82C11×M16—41no—
83C2×C8×C11—41no—
84C2×C8×C11C2311yescharacteristic
85C2×C8×C11C2311yescharacteristic
86C2×C8×C11C2311yescharacteristic
87C2×C8×C11C2311yescharacteristic
88C11×C4⋊C4C2×C411yescharacteristic
89C11×C22⋊C4C2×C411yescharacteristic
90C11×C22⋊C4C2×C411yescharacteristic
91C42×C11C2311yescharacteristic
92C22⋊Dic11C2×C411yescharacteristic
93C22⋊Dic11C2×C411yescharacteristic
94(C2×D11)⋊C4C2×C411yescharacteristic
95(C2×D11)⋊C4C2×C411yescharacteristic
96(C2×D11)⋊C4C2×C411yescharacteristic
97(C2×D11)⋊C4C2×C411yescharacteristic
98C4⋊Dic11C2×C411yescharacteristic
99Dic11⋊C4C2×C411yescharacteristic
100Dic11⋊C4C2×C411yescharacteristic
101C4×Dic11C2×C411yescharacteristic
102C4×Dic11C2×C411yescharacteristic
103C4×Dic11C2311yescharacteristic
104#4318—41no—
105C2×C11⋊C8—41no—
106C2×C11⋊C8C2311yescharacteristic
107C2×C11⋊C8C2311yescharacteristic
108C2×C11⋊C8C2311yescharacteristic
109C2×C11⋊C8C2311yescharacteristic
110#4313—41no—
111#4313—41no—
112C8×D11—41no—
113C8×D11—41no—
114#2980—111nomaximal, Sylow
115C23×C11C22×C411yescharacteristic
116C23×C11C22×C411yescharacteristic
117C22×D11C22×C411yescharacteristic
118C22×D11C22×C411yescharacteristic
119C22×D11C22×C411yescharacteristic
120D4×C11—41no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11C22×C411yescharacteristic
126C2×C4×C11C22×C411yescharacteristic
127C2×C4×C11C22×C411yescharacteristic
128C2×C4×C11C22×C411yescharacteristic
129C2×C4×C11C2411yescharacteristic
130C22⋊D11—41no—
131C22⋊D11—41no—
132C22⋊D11—41no—
133C22⋊D11—41no—
134C22⋊D11—41no—
135C22⋊D11—41no—
136C2×Dic11C22×C411yescharacteristic
137C2×Dic11C22×C411yescharacteristic
138C2×Dic11C22×C411yescharacteristic
139C2×Dic11C22×C411yescharacteristic
140C2×Dic11C22×C411yescharacteristic
141D44—41no—
142D44—41no—
143D44—41no—
144C4×D11—21no—
145C4×D11—21no—
146C4×D11—21no—
147C4×D11—21no—
148C4×D11—21no—
149C4×D11—21no—
150C4×D11—41no—
151C4×D11—41no—
152Dic22—41no—
153Dic22—41no—
154C8×C11—21no—
155C8×C11—21no—
156C8×C11—21no—
157C8×C11—21no—
158C11⋊C8—21no—
159C11⋊C8—21no—
160C11⋊C8—21no—
161C11⋊C8—21no—
162#532—111no—
163#435—111no—
164#435—111no—
165#435—111no—
166#435—111no—
167#435—111no—
168#435—111no—
169#435—111no—
170#435D1111yescharacteristic, complemented
171#432—111no—
172#432—111no—
173#408—111no—
174#408—111no—
175#408—111no—
176#408—111no—
177C22×C11—21no—
178C22×C11—21no—
179C22×C11—21no—
180C22×C11—21no—
181C22×C11—21no—
182C22×C11—21no—
183C22×C11C23×C411yescharacteristic
184C2×D11—21no—
185C2×D11—21no—
186C2×D11—21no—
187C2×D11—21no—
188C2×D11—21no—
189C2×D11—21no—
190C2×D11—21no—
191C2×D11—21no—
192C2×D11—21no—
193C4×C11—21no—
194C4×C11—21no—
195C4×C11—21no—
196C4×C11—21no—
197C4×C11H(5,𝔽2)11yescharacteristic
198C4×C11H(5,𝔽2)11yescharacteristic
199Dic11—21no—
200Dic11—21no—
201Dic11—21no—
202Dic11—21no—
203Dic11—21no—
204C2×#41—111no—
205C2×#41—111no—
206C2×M16—111no—
207C2×M16—111no—
208C2×M16—111no—
209C2×M16C2×D1111yescharacteristic
210C22×C8—111no—
211C22×C8—111no—
212C22×C8—111no—
213C22×C8C2×D1111yescharacteristic
214C4⋊Q8—111no—
215#127—111no—
216#124—111no—
217#124—111no—
218#121—111no—
219#121—111no—
220#121—111no—
221#121—111no—
222C4×D4—111no—
223C4×D4—111no—
224C4×D4—111no—
225C4×D4C2×D1111yescharacteristic
226C2×C42—111no—
227C4⋊C8—111no—
228C4⋊C8—111no—
229C4⋊C8—111no—
230C4⋊C8C2×D1111yescharacteristic
231C22⋊C8—111no—
232C22⋊C8—111no—
233C22⋊C8—111no—
234C22⋊C8—111no—
235C22⋊C8—111no—
236C22⋊C8—111no—
237C22⋊C8—111no—
238C22⋊C8—111no—
239C22⋊C8—111no—
240C22⋊C8—111no—
241C22⋊C8C2×D1111yescharacteristic
242C22⋊C8C2×D1111yescharacteristic
243#97—111no—
244#97—111no—
245#97—111no—
246#97C2×D1111yescharacteristic
247C2×C11—41no—
248C2×C11—41no—
249C2×C11#51811yescharacteristic
250C2×C11#56811yescharacteristic
251C2×C11#56811yescharacteristic
252D11—41no—
253D11—41no—
254D11—41no—
255#41—441no—
256#41—441no—
257#41—441no—
258#41—441no—
259C2×Q8—111no—
260C2×Q8—111no—
261C2×D4—111no—
262C2×D4—111no—
263C2×D4—111no—
264C2×D4—111no—
265C2×D4—111no—
266C2×D4—111no—
267C2×D4—111no—
268C2×D4—111no—
269C2×D4—111no—
270C2×D4C4×D1111yescharacteristic
271C22×C4—111no—
272C22×C4—111no—
273C22×C4—111no—
274C22×C4—111no—
275C22×C4—111no—
276C22×C4C22×D1111yescharacteristic
277C22×C4C22×D1111yescharacteristic
278M16—41no—
279M16—441no—
280M16—441no—
281M16—441no—
282C2×C8—41no—
283C2×C8—111no—
284C2×C8—111no—
285C2×C8—111no—
286C2×C8—111no—
287C2×C8—441no—
288C2×C8—441no—
289C2×C8—441no—
290C2×C8C22×D1111yescharacteristic
291C2×C8C22×D1111yescharacteristic
292C2×C8C22×D1111yescharacteristic
293C2×C8C22×D1111yescharacteristic
294C4⋊C4—111no—
295C4⋊C4—111no—
296C4⋊C4—111no—
297C4⋊C4C4×D1111yescharacteristic
298C22⋊C4—111no—
299C22⋊C4—111no—
300C22⋊C4—111no—
301C22⋊C4—111no—
302C22⋊C4—111no—
303C22⋊C4—111no—
304C22⋊C4C4×D1111yescharacteristic
305C22⋊C4C4×D1111yescharacteristic
306C42—111no—
307C42—111no—
308C42—111no—
309C42C22×D1111yescharacteristic
310C11#298011yescharacteristic, complemented, Sylow
311C23—111no—
312C23—111no—
313C23—111no—
314C23C2×C4×D1111yescharacteristic
315C23C2×C4×D1111yescharacteristic
316Q8—441no—
317Q8—441no—
318D4—41no—
319D4—441no—
320D4—441no—
321D4—441no—
322D4—441no—
323D4—441no—
324D4—441no—
325D4—441no—
326D4—441no—
327D4—441no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—111no—
333C2×C4—111no—
334C2×C4—111no—
335C2×C4—111no—
336C2×C4—111no—
337C2×C4—221no—
338C2×C4—221no—
339C2×C4—221no—
340C2×C4—221no—
341C2×C4—221no—
342C2×C4—221no—
343C2×C4—441no—
344C2×C4—441no—
345C2×C4C2×C4×D1111yescharacteristic
346C2×C4C2×C4×D1111yescharacteristic
347C2×C4C2×C4×D1111yescharacteristic
348C2×C4C2×C4×D1111yescharacteristic
349C2×C4C23×D1111yescharacteristic
350C8—21no—
351C8—21no—
352C8—21no—
353C8—21no—
354C8—221no—
355C8—221no—
356C8—221no—
357C8—221no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—221no—
365C22—221no—
366C22—221no—
367C22—221no—
368C22—221no—
369C22—221no—
370C22—221no—
371C22—221no—
372C22—221no—
373C22C22×C4×D1111yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—21no—
378C4—221no—
379C4—221no—
380C4—221no—
381C4—221no—
382C4—221no—
383C4#6703711yescharacteristic
384C4#6704211yescharacteristic
385C2—41no—
386C2—41no—
387C2—441no—
388C2—441no—
389C2—441no—
390C2#1062307611yescharacteristic
391C2#1062327611yescharacteristic
392C2#1062328111yescharacteristic
subgroupG/H
center, FrattiniC2×C4C23×D11
commutator, socleC22×C11C23×C4
FittingC11×#435C2
prime radical#10623079C2
cosocleC2×C4×C11C24
hypercenter#435D11
hypocenterC11#2980
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ #435

Complements

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

NH ≅ G/Ntype
2. C11×#435C2semidirect
3. #10622742C2semidirect
4. #10622740C2semidirect
5. #10622724C2semidirect
6. #10622723C2semidirect
7. #10622624C2semidirect
8. #10622449C2semidirect
9. #10622448C2semidirect
10. #10622343C2semidirect
11. #10622341C2semidirect
12. #10622340C2semidirect
13. #10622340C2semidirect
14. #10622319C2semidirect
15. #10622318C2semidirect
170. #435D11semidirect
310. C11#2980semidirect

Maximal subgroups

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

subgroupindex
#106230792
C11×#4352
#106227422
#106227402
#106227242
#106227232
#106226242
#106224492
#106224482
#106223432
#106223412
#106223402
#106223192
#106223182
#298011