Finite Group Databasebeta

← #13079513

Subgroups — #13079513

Order 1408.

402 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
1C11×#537C211yesmaximal, characteristic, complemented
2#10623364C211yesmaximal, characteristic, complemented
3#10622852C211yesmaximal, characteristic, complemented
4#10622851C211yesmaximal, characteristic, complemented
5#10622847C211yesmaximal, characteristic, complemented
6#10622664C211yesmaximal, characteristic, complemented
7#10622662C211yesmaximal, characteristic, complemented
8#10622660C211yesmaximal, characteristic, complemented
9#10622657C211yesmaximal, characteristic, complemented
10#10622655C211yesmaximal, characteristic, complemented
11#10622651C211yesmaximal, characteristic, complemented
12#10622650C211yesmaximal, characteristic, complemented
13#10622646C211yesmaximal, characteristic, complemented
14#10622583C211yesmaximal, characteristic, complemented
15#10622580C211yesmaximal, characteristic, complemented
16C2×C11×#41C2211yescharacteristic
17C2×C11×#41C2211yescharacteristic
18C2×#4339C2211yescharacteristic
19C11×C22⋊Q8—21no—
20C11×C22⋊Q8C2211yescharacteristic
21C11×C22⋊Q8C2211yescharacteristic
22C11×#121—21no—
23C11×#121—21no—
24C11×#121—21no—
25C11×#121C2211yescharacteristic
26C11×#121C2211yescharacteristic
27C2×C11×C4⋊C4C2211yescharacteristic
28#66999—21no—
29C2×#4326C2211yescharacteristic
30C2×#4325C2211yescharacteristic
31#66992—21no—
32#66992—21no—
33#66991—21no—
34C2×#4324C2211yescharacteristic
35C2×#4323C2211yescharacteristic
36#66983C2211yescharacteristic
37#66983C2211yescharacteristic
38C2×C4⋊Dic11C2211yescharacteristic
39#66977C2211yescharacteristic
40#66977C2211yescharacteristic
41C2×#4318C2211yescharacteristic
42C22×C11⋊C8C2211yescharacteristic
43#66899C2211yescharacteristic
44#66899C2211yescharacteristic
45#66896C2211yescharacteristic
46#66896C2211yescharacteristic
47C22⋊(C11⋊C8)C2211yescharacteristic
48C22⋊(C11⋊C8)C2211yescharacteristic
49C22⋊(C11⋊C8)C2211yescharacteristic
50C22⋊(C11⋊C8)C2211yescharacteristic
51#66874C2211yescharacteristic
52#66874C2211yescharacteristic
53#66873C2211yescharacteristic
54#66873C2211yescharacteristic
55#66871C2211yescharacteristic
56#66871C2211yescharacteristic
57#66871C2211yescharacteristic
58#66871C2211yescharacteristic
59C11×#41—41no—
60C11×#41—41no—
61C11×#41—41no—
62C11×#41—41no—
63C2×Q8×C11D411yescharacteristic
64C2×Q8×C11C2311yescharacteristic
65C2×D4×C11—21no—
66C2×D4×C11—21no—
67C2×D4×C11—21no—
68C2×D4×C11D411yescharacteristic
69C2×D4×C11D411yescharacteristic
70C2×D4×C11D411yescharacteristic
71C2×D4×C11C2311yescharacteristic
72C22×C4×C11—21no—
73C22×C4×C11—21no—
74C22×C4×C11C2311yescharacteristic
75C22×C4×C11C2311yescharacteristic
76C22×C4×C11C2311yescharacteristic
77C2×C22⋊D11—21no—
78C2×C22⋊D11—21no—
79C2×C22⋊D11—21no—
80C22×Dic11—21no—
81#4339—41no—
82#4339—41no—
83C2×D44C2311yescharacteristic
84C2×C4×D11—21no—
85C2×Dic22C2311yescharacteristic
86C11×C4⋊C4—21no—
87C11×C4⋊C4—21no—
88C11×C4⋊C4—21no—
89C11×C4⋊C4C2311yescharacteristic
90C11×C4⋊C4C2311yescharacteristic
91C11×C22⋊C4—21no—
92C11×C22⋊C4—21no—
93C11×C22⋊C4—21no—
94C11×C22⋊C4—21no—
95C22⋊Dic11—21no—
96C22⋊Dic11—21no—
97#4326—41no—
98#4325—41no—
99#4324—41no—
100#4323—41no—
101(C2×D11)⋊C4—21no—
102(C2×D11)⋊C4—21no—
103C4⋊Dic11—21no—
104C4⋊Dic11C2311yescharacteristic
105C4⋊Dic11C2311yescharacteristic
106Dic11⋊C4—21no—
107Dic11⋊C4—21no—
108#4318—41no—
109C2×C11⋊C8—41no—
110C2×C11⋊C8C2311yescharacteristic
111C2×C11⋊C8C2311yescharacteristic
112C2×C11⋊C8C2311yescharacteristic
113C2×C11⋊C8C2311yescharacteristic
114#3203—111nomaximal, Sylow
115C23×C11—21no—
116C23×C11C2×D411yescharacteristic
117C23×C11C2×D411yescharacteristic
118C23×C11C2×D411yescharacteristic
119C22×D11—21no—
120Q8×C11—21no—
121Q8×C11—21no—
122Q8×C11—41no—
123D4×C11—21no—
124D4×C11—21no—
125D4×C11—41no—
126D4×C11—41no—
127D4×C11—41no—
128D4×C11—42no—
129D4×C11—81no—
130D4×C11—81no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—21no—
140C2×C4×C11—42no—
141C2×C4×C11—81no—
142C2×C4×C11C2×D411yescharacteristic
143C2×C4×C11C2×D411yescharacteristic
144C2×C4×C11C2×D411yescharacteristic
145C2×C4×C11C2411yescharacteristic
146C22⋊D11—42no—
147C22⋊D11—81no—
148C22⋊D11—81no—
149C2×Dic11—21no—
150C2×Dic11—21no—
151C2×Dic11—21no—
152C2×Dic11—81no—
153D44—21no—
154D44—21no—
155C4×D11—42no—
156Dic22—21no—
157Dic22—21no—
158C11⋊C8—21no—
159C11⋊C8—21no—
160C11⋊C8—21no—
161C11⋊C8—21no—
162#537—111no—
163#537D1111yescharacteristic, complemented
164#484—111no—
165#484—111no—
166#480—111no—
167#480—111no—
168#468—111no—
169#468—111no—
170#467—111no—
171#466—111no—
172#452—111no—
173#452—111no—
174#449—111no—
175#449—111no—
176#408—111no—
177C22×C11—21no—
178C22×C11—21no—
179C22×C11—21no—
180C22×C11—21no—
181C22×C11—21no—
182C22×C11—21no—
183C22×C11—21no—
184C22×C11—21no—
185C22×C11—21no—
186C22×C11—41no—
187C22×C11—41no—
188C22×C11—41no—
189C22×C11C22×D411yescharacteristic
190C2×D11—41no—
191C2×D11—41no—
192C2×D11—41no—
193C4×C11—21no—
194C4×C11—21no—
195C4×C11—21no—
196C4×C11—41no—
197C4×C11—41no—
198C4×C11—41no—
199C4×C11H(5,𝔽2)11yescharacteristic
200C4×C11H(5,𝔽2)11yescharacteristic
201Dic11—41no—
202Dic11—41no—
203Dic11—41no—
204C2×#41—111no—
205C2×#41C2×D1111yescharacteristic
206C2×#41C2×D1111yescharacteristic
207C2×Q16—111no—
208C2×SD16—111no—
209C2×SD16—111no—
210C2×D8—111no—
211C2×M16—111no—
212C22×C8—111no—
213C22⋊Q8—21no—
214C22⋊Q8—111no—
215C22⋊Q8—111no—
216C22⋊Q8—221no—
217C22⋊Q8C2×D1111yescharacteristic
218C22⋊Q8C2×D1111yescharacteristic
219#121—21no—
220#121—21no—
221#121—21no—
222#121—111no—
223#121—111no—
224#121—221no—
225#121—221no—
226#121—221no—
227#121C2×D1111yescharacteristic
228#121C2×D1111yescharacteristic
229C2×C4⋊C4—111no—
230C2×C4⋊C4C2×D1111yescharacteristic
231#107—111no—
232#107—111no—
233#107—111no—
234#107—111no—
235#103—111no—
236#103—111no—
237#103—111no—
238#103—111no—
239#102—111no—
240#102—111no—
241#102—111no—
242#102—111no—
243C22⋊C8—111no—
244C22⋊C8—111no—
245C22⋊C8—111no—
246C22⋊C8—111no—
247C2×C11—41no—
248C2×C11—41no—
249C2×C11—41no—
250C2×C11—81no—
251C2×C11#53411yescharacteristic
252C2×C11#57611yescharacteristic
253C2×C11#57811yescharacteristic
254D11—81no—
255#41—41no—
256#41—41no—
257#41—41no—
258#41—41no—
259#41—441no—
260#41—441no—
261C2×Q8—111no—
262C2×Q8C22⋊D1111yescharacteristic
263C2×Q8C22×D1111yescharacteristic
264C2×D4—21no—
265C2×D4—21no—
266C2×D4—21no—
267C2×D4—111no—
268C2×D4—221no—
269C2×D4—221no—
270C2×D4—221no—
271C2×D4C22⋊D1111yescharacteristic
272C2×D4C22⋊D1111yescharacteristic
273C2×D4C22⋊D1111yescharacteristic
274C2×D4C22×D1111yescharacteristic
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—221no—
278C22×C4—221no—
279C22×C4C22×D1111yescharacteristic
280C22×C4C22×D1111yescharacteristic
281C22×C4C22×D1111yescharacteristic
282Q16—441no—
283SD16—441no—
284SD16—441no—
285D8—441no—
286M16—441no—
287C2×C8—111no—
288C2×C8—111no—
289C2×C8—111no—
290C2×C8—111no—
291C2×C8—441no—
292C4⋊C4—21no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—111no—
296C4⋊C4—111no—
297C4⋊C4—221no—
298C4⋊C4—221no—
299C4⋊C4—221no—
300C4⋊C4C22×D1111yescharacteristic
301C4⋊C4C22×D1111yescharacteristic
302C22⋊C4—21no—
303C22⋊C4—21no—
304C22⋊C4—21no—
305C22⋊C4—21no—
306C22⋊C4—221no—
307C22⋊C4—221no—
308C22⋊C4—221no—
309C22⋊C4—221no—
310C11#320311yescharacteristic, complemented, Sylow
311C23—21no—
312C23—221no—
313C23C2×C22⋊D1111yescharacteristic
314C23C2×C22⋊D1111yescharacteristic
315C23C2×C22⋊D1111yescharacteristic
316Q8—21no—
317Q8—21no—
318Q8—41no—
319Q8—221no—
320Q8—221no—
321D4—21no—
322D4—21no—
323D4—41no—
324D4—41no—
325D4—41no—
326D4—42no—
327D4—81no—
328D4—81no—
329D4—221no—
330D4—221no—
331D4—442no—
332D4—881no—
333D4—881no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—42no—
344C2×C4—81no—
345C2×C4—221no—
346C2×C4—221no—
347C2×C4—221no—
348C2×C4—442no—
349C2×C4—881no—
350C2×C4C2×C22⋊D1111yescharacteristic
351C2×C4C2×C22⋊D1111yescharacteristic
352C2×C4C2×C22⋊D1111yescharacteristic
353C2×C4C23×D1111yescharacteristic
354C8—221no—
355C8—221no—
356C8—221no—
357C8—221no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—441no—
371C22—441no—
372C22—441no—
373C22C22×C22⋊D1111yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—441no—
381C4—441no—
382C4—441no—
383C4#6703711yescharacteristic
384C4#6703711yescharacteristic
385C2—41no—
386C2—41no—
387C2—41no—
388C2—81no—
389C2—881no—
390C2#1062333511yescharacteristic
391C2#1062336611yescharacteristic
392C2#1062336911yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#537C2
socleC22×C11C22×D4
hypercenter#537D11
hypocenterC11#3203
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×#41 ◁ #537

Complements

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

NH ≅ G/Ntype
1. C11×#537C2semidirect
2. #10623364C2semidirect
3. #10622852C2semidirect
4. #10622851C2semidirect
5. #10622847C2semidirect
6. #10622664C2semidirect
7. #10622662C2semidirect
8. #10622660C2semidirect
9. #10622657C2semidirect
10. #10622655C2semidirect
11. #10622651C2semidirect
12. #10622650C2semidirect
13. #10622646C2semidirect
14. #10622583C2semidirect
15. #10622580C2semidirect
163. #537D11semidirect
310. C11#3203semidirect

Maximal subgroups

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

subgroupindex
C11×#5372
#106233642
#106228522
#106228512
#106228472
#106226642
#106226622
#106226602
#106226572
#106226552
#106226512
#106226502
#106226462
#106225832
#106225802
#320311