Finite Group Databasebeta

← #13080769

Subgroups — #13080769

Order 1408.

414 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623265C211yesmaximal, characteristic, complemented
2#10623085C211yesmaximal, characteristic, complemented
3C11×#474C211yesmaximal, characteristic, complemented
4#10622702C211yesmaximal, characteristic, complemented
5#10622627C211yesmaximal, characteristic, complemented
6#10622501C211yesmaximal, characteristic, complemented
7#10622499C211yesmaximal, characteristic, complemented
8#10622498C211yesmaximal, characteristic, complemented
9#10622496C211yesmaximal, characteristic, complemented
10#10622457C211yesmaximal, characteristic, complemented
11#10622449C211yesmaximal, characteristic, complemented
12#10622394C211yesmaximal, characteristic, complemented
13#10622386C211yesmaximal, characteristic, complemented
14#10622385C211yesmaximal, characteristic, complemented
15#10622383C211yesmaximal, characteristic, complemented
16C2×#4341C2211yescharacteristic
17C2×D4×D11C2211yescharacteristic
18C11×C4⋊Q8C2211yescharacteristic, complemented
19C4×D4×C11C2211yescharacteristic
20#67000—21no—
21#67000—21no—
22C2×#4323C2211yescharacteristic
23#66983—21no—
24C2×(C2×D11)⋊C4—21no—
25C2×D88C2211yescharacteristic
26C2×#4314C2211yescharacteristic, complemented
27C2×#4313C2211yescharacteristic
28C2×C8×D11C2211yescharacteristic, complemented
29#66950C2211yescharacteristic
30#66948—21no—
31#66948C2211yescharacteristic
32#66948C2211yescharacteristic
33#66948C2211yescharacteristic, complemented
34#66945—21no—
35#66945C2211yescharacteristic
36#66945C2211yescharacteristic, complemented
37#66939—21no—
38#66935—21no—
39#66928C2211yescharacteristic
40C4×D44C2211yescharacteristic
41C4×D44C2211yescharacteristic, complemented
42C11×#107C2211yescharacteristic, complemented
43C11×#107C2211yescharacteristic, complemented
44C11×C4⋊C8C2211yescharacteristic, complemented
45C11×#102C2211yescharacteristic
46C11×#102C2211yescharacteristic
47#66896C2211yescharacteristic
48#66885C2211yescharacteristic
49(C2×D11)⋊C8C2211yescharacteristic
50(C2×D11)⋊C8C2211yescharacteristic, complemented
51#66880C2211yescharacteristic, complemented
52#66874C2211yescharacteristic, complemented
53#66874C2211yescharacteristic, complemented
54#66873C2211yescharacteristic
55#66873C2211yescharacteristic
56#66873C2211yescharacteristic, complemented
57#66872C2211yescharacteristic, complemented
58#66867C2211yescharacteristic, complemented
59C23×D11—21no—
60C2×Q8×C11—21no—
61C2×D4×C11C2311yescharacteristic
62C22×C4×C11—21no—
63C2×C22⋊D11—21no—
64C2×C22⋊D11—21no—
65C22×Dic11—21no—
66#4341—22no—
67#4341—41no—
68D4×D11—22no—
69D4×D11—41no—
70C2×D44—21no—
71C2×D44—21no—
72C2×D44—21no—
73C2×D44D411yescharacteristic
74C2×D44C2311yescharacteristic
75C2×D44C2311yescharacteristic
76C2×C4×D11—21no—
77C2×C4×D11C2311yescharacteristic
78C2×C4×D11C2311yescharacteristic
79C2×Dic22C2311yescharacteristic
80C2×C8×C11C2311yescharacteristic
81C2×C8×C11C2311yescharacteristic
82C11×C4⋊C4—21no—
83C11×C4⋊C4C2311yescharacteristic
84C11×C4⋊C4C2311yescharacteristic
85C11×C4⋊C4C2311yescharacteristic
86C11×C22⋊C4—21no—
87C42×C11C2311yescharacteristic
88#4323—22no—
89(C2×D11)⋊C4—21no—
90(C2×D11)⋊C4—21no—
91(C2×D11)⋊C4—21no—
92(C2×D11)⋊C4—21no—
93(C2×D11)⋊C4—21no—
94(C2×D11)⋊C4—21no—
95(C2×D11)⋊C4—21no—
96(C2×D11)⋊C4—21no—
97(C2×D11)⋊C4—21no—
98(C2×D11)⋊C4D411yescharacteristic
99(C2×D11)⋊C4D411yescharacteristic
100C4⋊Dic11—21no—
101C4⋊Dic11D411yescharacteristic
102C4⋊Dic11C2311yescharacteristic
103C4×Dic11—21no—
104C4×Dic11—21no—
105C2×C11⋊C8C2311yescharacteristic
106C2×C11⋊C8C2311yescharacteristic
107D88—41no—
108#4314—41no—
109#4313—41no—
110C8×D11—41no—
111#3319—111nomaximal, Sylow
112C23×C11—21no—
113C22×D11—21no—
114C22×D11—21no—
115C22×D11—42no—
116C22×D11—42no—
117C22×D11—81no—
118C22×D11C2×D411yescharacteristic
119C22×D11C2×D411yescharacteristic
120Q8×C11—81no—
121D4×C11—21no—
122D4×C11#4112yes—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—81no—
127C2×C4×C11C2×D411yescharacteristic
128C2×C4×C11C2×D411yescharacteristic
129C2×C4×C11C2411yescharacteristic
130C22⋊D11—42no—
131C22⋊D11—42no—
132C2×Dic11—21no—
133C2×Dic11—21no—
134C2×Dic11—42no—
135C2×Dic11C2×D411yescharacteristic
136C2×Dic11C2×D411yescharacteristic
137D44—21no—
138D44—21no—
139D44—21no—
140D44—21no—
141D44—41no—
142D44—81no—
143D44—81no—
144D44—81no—
145C4×D11—21no—
146C4×D11—21no—
147C4×D11—21no—
148C4×D11—21no—
149C4×D11—42no—
150Dic22—21no—
151Dic22—21no—
152C8×C11—21no—
153C8×C11—21no—
154C11⋊C8—21no—
155C11⋊C8—21no—
156#555—111no—
157#546—111no—
158#489—111no—
159#485—111no—
160#482—111no—
161#474D1111yescharacteristic, complemented
162#468—111no—
163#466—111no—
164#463—111no—
165#449—111no—
166#447—111no—
167#442—111no—
168#435—111no—
169#418—111no—
170#416—111no—
171C22×C11—22no—
172C22×C11—41no—
173C22×C11—41no—
174C22×C11C22×D411yescharacteristic
175C2×D11—21no—
176C2×D11—21no—
177C2×D11—21no—
178C2×D11—21no—
179C2×D11—21no—
180C2×D11—21no—
181C2×D11—41no—
182C2×D11—41no—
183C2×D11—41no—
184C2×D11—41no—
185C2×D11—41no—
186C2×D11—41no—
187C2×D11—84no—
188C4×C11—21no—
189C4×C11—21no—
190C4×C11—41no—
191C4×C11—41no—
192C4×C11—41no—
193C4×C11C2×#4111yescharacteristic
194C4×C11H(5,𝔽2)11yescharacteristic
195Dic11—21no—
196Dic11—21no—
197Dic11—41no—
198Dic11—41no—
199C2×#41—111no—
200C22×D4—111no—
201C2×SD16—111no—
202C2×D8—111no—
203C2×D8—111no—
204C2×M16—111no—
205C22×C8—111no—
206C4⋊Q8C2×D1111yescharacteristic, complemented
207#124—111no—
208#124—221no—
209#124—221no—
210#123—221no—
211C22⋊Q8—111no—
212#121—111no—
213#121—111no—
214#121—111no—
215#121—221no—
216#121—221no—
217#120—221no—
218C4×D4—111no—
219C4×D4—111no—
220C4×D4C2×D1111yescharacteristic
221#117—111no—
222#117—111no—
223#117—221no—
224C2×C22⋊C4—221no—
225#107C2×D1111yescharacteristic, complemented
226#107C2×D1111yescharacteristic, complemented
227#106—111no—
228C4⋊C8C2×D1111yescharacteristic, complemented
229#103—111no—
230#103—111no—
231#103—111no—
232#102—111no—
233#102—111no—
234#102—111no—
235#102—111no—
236#102—111no—
237#102C2×D1111yescharacteristic
238#102C2×D1111yescharacteristic
239C22⋊C8—111no—
240C22⋊C8—111no—
241#97—111no—
242C2×C11—42no—
243C2×C11#54611yescharacteristic
244C2×C11#57511yescharacteristic
245C2×C11#57611yescharacteristic
246D11—41no—
247D11—41no—
248D11—81no—
249D11—81no—
250C24—221no—
251#41—222no—
252#41—441no—
253C2×Q8—21no—
254C2×Q8—111no—
255C2×D4—111no—
256C2×D4—111no—
257C2×D4—111no—
258C2×D4—221no—
259C2×D4—221no—
260C2×D4—221no—
261C2×D4—221no—
262C2×D4—222no—
263C2×D4—221no—
264C2×D4—441no—
265C2×D4C22×D1111yescharacteristic
266C22×C4—21no—
267C22×C4—111no—
268C22×C4—111no—
269C22×C4—221no—
270C22×C4—221no—
271SD16—441no—
272D8—222no—
273D8—441no—
274M16—441no—
275C2×C8—111no—
276C2×C8—111no—
277C2×C8—441no—
278C2×C8C22×D1111yescharacteristic
279C2×C8C22×D1111yescharacteristic
280C4⋊C4—21no—
281C4⋊C4—111no—
282C4⋊C4—111no—
283C4⋊C4—221no—
284C4⋊C4C22×D1111yescharacteristic
285C4⋊C4C22×D1111yescharacteristic
286C4⋊C4C22×D1111yescharacteristic
287C22⋊C4—21no—
288C22⋊C4—111no—
289C22⋊C4—111no—
290C22⋊C4—221no—
291C22⋊C4—221no—
292C22⋊C4—221no—
293C22⋊C4—221no—
294C22⋊C4—221no—
295C22⋊C4—221no—
296C22⋊C4—221no—
297C22⋊C4—221no—
298C22⋊C4—221no—
299C42—221no—
300C42—221no—
301C42C22×D1111yescharacteristic
302C11#331911yescharacteristic, complemented, Sylow
303C23—21no—
304C23—111no—
305C23—111no—
306C23—221no—
307C23—221no—
308C23—442no—
309C23—442no—
310C23—881no—
311Q8—81no—
312Q8—221no—
313Q8—221no—
314D4—21no—
315D4—221no—
316D4—221no—
317D4—221no—
318D4—221no—
319D4—441no—
320D4—442no—
321D4—442no—
322D4—881no—
323D4—881no—
324D4—881no—
325D4#434312yes—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—81no—
330C2×C4—111no—
331C2×C4—111no—
332C2×C4—221no—
333C2×C4—221no—
334C2×C4—221no—
335C2×C4—221no—
336C2×C4—221no—
337C2×C4—221no—
338C2×C4—442no—
339C2×C4—442no—
340C2×C4D4×D1111yescharacteristic
341C2×C4D4×D1111yescharacteristic
342C2×C4C23×D1111yescharacteristic
343C8—21no—
344C8—21no—
345C8—221no—
346C8—221no—
347C22—22no—
348C22—41no—
349C22—41no—
350C22—221no—
351C22—221no—
352C22—221no—
353C22—221no—
354C22—221no—
355C22—221no—
356C22—441no—
357C22—441no—
358C22—441no—
359C22—441no—
360C22—441no—
361C22—441no—
362C22—884no—
363C22C2×D4×D1111yescharacteristic
364C4—21no—
365C4—21no—
366C4—41no—
367C4—41no—
368C4—41no—
369C4—221no—
370C4—221no—
371C4—441no—
372C4—441no—
373C4C2×#434311yescharacteristic
374C4#6704211yescharacteristic
375C2—42no—
376C2—441no—
377C2—441no—
378C2—881no—
379C2—881no—
380C2#1062316111yescharacteristic
381C2#1062328811yescharacteristic
382C2#1062330811yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#474C2
socleC22×C11C22×D4
hypercenter#474D11
hypocenterC11#3319
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #10623265C2semidirect
2. #10623085C2semidirect
3. C11×#474C2semidirect
4. #10622702C2semidirect
5. #10622627C2semidirect
6. #10622501C2semidirect
7. #10622499C2semidirect
8. #10622498C2semidirect
9. #10622496C2semidirect
10. #10622457C2semidirect
11. #10622449C2semidirect
12. #10622394C2semidirect
13. #10622386C2semidirect
14. #10622385C2semidirect
15. #10622383C2semidirect
18. C11×C4⋊Q8C22semidirect
26. C2×#4314C22semidirect
28. C2×C8×D11C22semidirect
33. #66948C22semidirect
36. #66945C22semidirect
41. C4×D44C22semidirect
42. C11×#107C22semidirect
43. C11×#107C22semidirect
44. C11×C4⋊C8C22semidirect
50. (C2×D11)⋊C8C22semidirect
51. #66880C22semidirect
52. #66874C22semidirect
53. #66874C22semidirect
56. #66873C22semidirect
57. #66872C22semidirect
58. #66867C22semidirect
161. #474D11semidirect
206. C4⋊Q8C2×D11semidirect
225. #107C2×D11semidirect
226. #107C2×D11semidirect
228. C4⋊C8C2×D11semidirect
302. C11#3319semidirect

Maximal subgroups

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

subgroupindex
#106232652
#106230852
C11×#4742
#106227022
#106226272
#106225012
#106224992
#106224982
#106224962
#106224572
#106224492
#106223942
#106223862
#106223852
#106223832
#331911