Finite Group Databasebeta

← #13079709

Subgroups — #13079709

Order 1408.

408 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#10623205C211yesmaximal, characteristic, complemented
2#10623092C211yesmaximal, characteristic, complemented
3C11×#463C211yesmaximal, characteristic, complemented
4#10622785C211yesmaximal, characteristic, complemented
5#10622781C211yesmaximal, characteristic, complemented
6#10622769C211yesmaximal, characteristic, complemented
7#10622767C211yesmaximal, characteristic, complemented
8#10622667C211yesmaximal, characteristic, complemented
9#10622628C211yesmaximal, characteristic, complemented
10#10622461C211yesmaximal, characteristic, complemented
11#10622453C211yesmaximal, characteristic, complemented
12#10622423C211yesmaximal, characteristic, complemented
13#10622408C211yesmaximal, characteristic, complemented
14#10622389C211yesmaximal, characteristic, complemented
15#10622373C211yesmaximal, characteristic, complemented
16C2×#4343C2211yescharacteristic
17C2×D4×D11C2211yescharacteristic
18C2×C11×SD16C2211yescharacteristic, complemented
19C2×C11×D8C2211yescharacteristic
20C11×#124C2211yescharacteristic
21C4×D4×C11C2211yescharacteristic, complemented
22#67000C2211yescharacteristic
23C2×#4326C2211yescharacteristic, complemented
24#66993C2211yescharacteristic
25#66991C2211yescharacteristic
26#66989C2211yescharacteristic, complemented
27C2×#4324C2211yescharacteristic
28C2×#4323C2211yescharacteristic
29C2×#4323C2211yescharacteristic, complemented
30#66982—21no—
31#66977—21no—
32C2×#4314C2211yescharacteristic
33C2×#4314C2211yescharacteristic, complemented
34#66950C2211yescharacteristic
35#66941C2211yescharacteristic, complemented
36#66938—21no—
37#66937—21no—
38#66937—21no—
39#66935—21no—
40#66935—21no—
41#66932—21no—
42#66927C2211yescharacteristic
43#66925C2211yescharacteristic
44C4×Dic22C2211yescharacteristic, complemented
45C11×C4⋊C8C2211yescharacteristic, complemented
46C11×#103C2211yescharacteristic, complemented
47C11×#102C2211yescharacteristic
48#66899C2211yescharacteristic, complemented
49#66896C2211yescharacteristic
50#66885C2211yescharacteristic
51#66885C2211yescharacteristic, complemented
52(C2×D11)⋊C8C2211yescharacteristic
53(C2×D11)⋊C8C2211yescharacteristic
54#66879C2211yescharacteristic, complemented
55C8×Dic11C2211yescharacteristic, complemented
56#66873C2211yescharacteristic
57#66873C2211yescharacteristic, complemented
58C4⋊(C11⋊C8)C2211yescharacteristic, complemented
59C23×D11—21no—
60C2×Q8×C11C2311yescharacteristic
61C2×D4×C11C2311yescharacteristic
62C2×D4×C11C2311yescharacteristic
63C22×C4×C11—21no—
64C2×C22⋊D11—21no—
65C2×C22⋊D11—21no—
66C2×C22⋊D11—21no—
67C2×C22⋊D11—21no—
68#4343—41no—
69#4343—41no—
70D4×D11—41no—
71D4×D11—41no—
72C2×D44—21no—
73C2×D44—21no—
74C2×D44—21no—
75C2×D44C2311yescharacteristic
76C2×D44C2311yescharacteristic
77C2×C4×D11—21no—
78C2×C4×D11C2311yescharacteristic
79C2×Dic22—21no—
80C2×Dic22C2311yescharacteristic
81C11×SD16—41no—
82C11×D8—41no—
83C2×C8×C11C2311yescharacteristic
84C2×C8×C11C2311yescharacteristic
85C11×C4⋊C4C2311yescharacteristic
86C11×C22⋊C4—21no—
87C11×C22⋊C4—21no—
88C11×C22⋊C4—21no—
89C42×C11C2311yescharacteristic
90C22⋊Dic11—21no—
91C22⋊Dic11—21no—
92C22⋊Dic11—21no—
93#4326—41no—
94#4324—41no—
95#4323—41no—
96#4323—41no—
97(C2×D11)⋊C4—21no—
98(C2×D11)⋊C4—21no—
99(C2×D11)⋊C4—21no—
100(C2×D11)⋊C4D411yescharacteristic
101(C2×D11)⋊C4D411yescharacteristic
102C4⋊Dic11—21no—
103C4⋊Dic11C2311yescharacteristic
104Dic11⋊C4—21no—
105Dic11⋊C4—21no—
106Dic11⋊C4D411yescharacteristic
107Dic11⋊C4D411yescharacteristic
108C4×Dic11—21no—
109C4×Dic11C2311yescharacteristic
110C2×C11⋊C8C2311yescharacteristic
111C2×C11⋊C8C2311yescharacteristic
112#4314—41no—
113#4314—41no—
114#3224—111nomaximal, Sylow
115C23×C11—21no—
116C23×C11—21no—
117C22×D11—21no—
118C22×D11—21no—
119C22×D11—42no—
120C22×D11—81no—
121C22×D11—81no—
122C22×D11C2×D411yescharacteristic
123Q8×C11—21no—
124Q8×C11—21no—
125D4×C11—21no—
126D4×C11—21no—
127D4×C11—21no—
128D4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—81no—
132C2×C4×C11C2×D411yescharacteristic
133C2×C4×C11C2×D411yescharacteristic
134C2×C4×C11C2411yescharacteristic
135C22⋊D11—42no—
136C22⋊D11—81no—
137C22⋊D11—81no—
138C22⋊D11—81no—
139C2×Dic11—21no—
140C2×Dic11—21no—
141C2×Dic11C2×D411yescharacteristic
142C2×Dic11C2×D411yescharacteristic
143C2×Dic11C2×D411yescharacteristic
144D44—21no—
145D44—21no—
146D44—21no—
147D44—21no—
148D44—42no—
149D44—81no—
150D44—81no—
151C4×D11—21no—
152C4×D11—21no—
153C4×D11—42no—
154Dic22—21no—
155Dic22—21no—
156Dic22—81no—
157C8×C11—21no—
158C8×C11—21no—
159C11⋊C8—21no—
160C11⋊C8—21no—
161#542—111no—
162#535—111no—
163#496—111no—
164#495—111no—
165#489—111no—
166#486—111no—
167#464—111no—
168#463D1111yescharacteristic, complemented
169#460—111no—
170#459—111no—
171#452—111no—
172#450—111no—
173#449—111no—
174#447—111no—
175#433—111no—
176C22×C11—41no—
177C22×C11—41no—
178C22×C11—41no—
179C22×C11—41no—
180C22×C11—41no—
181C22×C11—41no—
182C22×C11C22×D411yescharacteristic
183C2×D11—21no—
184C2×D11—21no—
185C2×D11—21no—
186C2×D11—41no—
187C2×D11—41no—
188C2×D11—41no—
189C2×D11—41no—
190C2×D11—41no—
191C2×D11—41no—
192C2×D11—84no—
193C4×C11—21no—
194C4×C11—21no—
195C4×C11—41no—
196C4×C11—41no—
197C4×C11H(5,𝔽2)11yescharacteristic
198C4×C11H(5,𝔽2)11yescharacteristic
199Dic11—21no—
200Dic11—21no—
201Dic11—21no—
202Dic11—41no—
203Dic11—41no—
204C2×#41—111no—
205C22×D4—111no—
206C2×Q16—111no—
207C2×SD16—111no—
208C2×SD16—111no—
209C2×SD16—111no—
210C2×SD16C2×D1111yescharacteristic, complemented
211C2×D8—111no—
212C2×D8—111no—
213C2×D8C2×D1111yescharacteristic
214C4⋊Q8—111no—
215#127—111no—
216#127—111no—
217#126—221no—
218#124—111no—
219#124—111no—
220#124—221no—
221#124C2×D1111yescharacteristic
222#123—221no—
223C22⋊Q8—111no—
224C22⋊Q8—221no—
225#121—111no—
226#121—221no—
227#121—221no—
228#120—221no—
229#120—221no—
230C4×Q8—111no—
231C4×D4C2×D1111yescharacteristic, complemented
232#117—111no—
233C4⋊C8—111no—
234C4⋊C8C2×D1111yescharacteristic, complemented
235#103—111no—
236#103C2×D1111yescharacteristic, complemented
237#102—111no—
238#102—111no—
239#102—111no—
240#102—111no—
241#102—111no—
242#102C2×D1111yescharacteristic
243C22⋊C8—111no—
244C22⋊C8—111no—
245#97—111no—
246C4×C8—111no—
247C2×C11—81no—
248C2×C11—81no—
249C2×C11#53511yescharacteristic
250C2×C11#57611yescharacteristic
251C2×C11#57711yescharacteristic
252D11—41no—
253D11—81no—
254D11—81no—
255C24—221no—
256#41—441no—
257#41—441no—
258C2×Q8—111no—
259C2×Q8—221no—
260C2×Q8C22×D1111yescharacteristic
261C2×D4—111no—
262C2×D4—111no—
263C2×D4—221no—
264C2×D4—221no—
265C2×D4—221no—
266C2×D4—221no—
267C2×D4—221no—
268C2×D4—221no—
269C2×D4—221no—
270C2×D4—441no—
271C2×D4—441no—
272C2×D4C22×D1111yescharacteristic
273C2×D4C22×D1111yescharacteristic
274C22×C4—21no—
275C22×C4—111no—
276C22×C4—221no—
277Q16—441no—
278SD16—41no—
279SD16—441no—
280SD16—441no—
281SD16—441no—
282D8—41no—
283D8—441no—
284D8—441no—
285C2×C8—111no—
286C2×C8—111no—
287C2×C8C22×D1111yescharacteristic
288C2×C8C22×D1111yescharacteristic
289C4⋊C4—111no—
290C4⋊C4—111no—
291C4⋊C4—111no—
292C4⋊C4—221no—
293C4⋊C4—221no—
294C4⋊C4—221no—
295C4⋊C4C22×D1111yescharacteristic
296C22⋊C4—21no—
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—111no—
300C22⋊C4—111no—
301C22⋊C4—221no—
302C22⋊C4—221no—
303C22⋊C4—221no—
304C22⋊C4—221no—
305C22⋊C4—221no—
306C22⋊C4—221no—
307C42—111no—
308C42—221no—
309C42C22×D1111yescharacteristic
310C11#322411yescharacteristic, complemented, Sylow
311C23—21no—
312C23—21no—
313C23—111no—
314C23—221no—
315C23—221no—
316C23—442no—
317C23—881no—
318C23—881no—
319Q8—21no—
320Q8—21no—
321Q8—221no—
322Q8—221no—
323Q8—881no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—21no—
328D4—221no—
329D4—221no—
330D4—221no—
331D4—221no—
332D4—442no—
333D4—442no—
334D4—881no—
335D4—881no—
336D4—881no—
337D4—881no—
338D4—881no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—81no—
342C2×C4—111no—
343C2×C4—111no—
344C2×C4—111no—
345C2×C4—221no—
346C2×C4—221no—
347C2×C4—221no—
348C2×C4—221no—
349C2×C4—442no—
350C2×C4D4×D1111yescharacteristic
351C2×C4D4×D1111yescharacteristic
352C2×C4C23×D1111yescharacteristic
353C8—21no—
354C8—21no—
355C8—221no—
356C8—221no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—221no—
364C22—221no—
365C22—221no—
366C22—441no—
367C22—441no—
368C22—441no—
369C22—441no—
370C22—441no—
371C22—441no—
372C22—884no—
373C22C2×D4×D1111yescharacteristic
374C4—21no—
375C4—21no—
376C4—41no—
377C4—41no—
378C4—221no—
379C4—221no—
380C4—221no—
381C4—441no—
382C4—441no—
383C4#6703711yescharacteristic
384C4#6704211yescharacteristic
385C2—81no—
386C2—81no—
387C2—441no—
388C2—881no—
389C2—881no—
390C2#1062313811yescharacteristic
391C2#1062330111yescharacteristic
392C2#1062330511yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#463C2
socleC22×C11C22×D4
hypercenter#463D11
hypocenterC11#3224
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. #10623205C2semidirect
2. #10623092C2semidirect
3. C11×#463C2semidirect
4. #10622785C2semidirect
5. #10622781C2semidirect
6. #10622769C2semidirect
7. #10622767C2semidirect
8. #10622667C2semidirect
9. #10622628C2semidirect
10. #10622461C2semidirect
11. #10622453C2semidirect
12. #10622423C2semidirect
13. #10622408C2semidirect
14. #10622389C2semidirect
15. #10622373C2semidirect
18. C2×C11×SD16C22semidirect
21. C4×D4×C11C22semidirect
23. C2×#4326C22semidirect
26. #66989C22semidirect
29. C2×#4323C22semidirect
33. C2×#4314C22semidirect
35. #66941C22semidirect
44. C4×Dic22C22semidirect
45. C11×C4⋊C8C22semidirect
46. C11×#103C22semidirect
48. #66899C22semidirect
51. #66885C22semidirect
54. #66879C22semidirect
55. C8×Dic11C22semidirect
57. #66873C22semidirect
58. C4⋊(C11⋊C8)C22semidirect
168. #463D11semidirect
210. C2×SD16C2×D11semidirect
231. C4×D4C2×D11semidirect
234. C4⋊C8C2×D11semidirect
236. #103C2×D11semidirect
310. C11#3224semidirect

Maximal subgroups

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

subgroupindex
#106232052
#106230922
C11×#4632
#106227852
#106227812
#106227692
#106227672
#106226672
#106226282
#106224612
#106224532
#106224232
#106224082
#106223892
#106223732
#322411