Finite Group Databasebeta

← #13080824

Subgroups — #13080824

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#10623207C211yesmaximal, characteristic, complemented
2#10623089C211yesmaximal, characteristic, complemented
3C11×#463C211yesmaximal, characteristic, complemented
4#10622787C211yesmaximal, characteristic, complemented
5#10622785C211yesmaximal, characteristic, complemented
6#10622772C211yesmaximal, characteristic, complemented
7#10622769C211yesmaximal, characteristic, complemented
8#10622669C211yesmaximal, characteristic, complemented
9C4×#4323C211yesmaximal, characteristic, complemented
10#10622460C211yesmaximal, characteristic, complemented
11#10622451C211yesmaximal, characteristic, complemented
12#10622428C211yesmaximal, characteristic, complemented
13#10622416C211yesmaximal, characteristic, complemented
14#10622387C211yesmaximal, characteristic, complemented
15#10622383C211yesmaximal, characteristic, complemented
16C2×#4343C2211yescharacteristic
17C2×D4×D11C2211yescharacteristic
18C2×C11×SD16C2211yescharacteristic, complemented
19C2×C11×D8C2211yescharacteristic
20C11×#124C2211yescharacteristic
21C4×D4×C11C2211yescharacteristic, complemented
22#66999C2211yescharacteristic
23#66991C2211yescharacteristic
24#66991C2211yescharacteristic
25#66991C2211yescharacteristic, complemented
26C2×#4323C2211yescharacteristic
27#66982—21no—
28C4×C22⋊D11—21no—
29C2×#4313C2211yescharacteristic
30C2×#4313C2211yescharacteristic, complemented
31#66945C2211yescharacteristic
32C4⋊C4×D11C2211yescharacteristic, complemented
33#66937—21no—
34#66937—21no—
35#66936—21no—
36#66935—21no—
37C22⋊C4×D11—21no—
38#66932—21no—
39C4×D44C2211yescharacteristic
40C4×D44C2211yescharacteristic
41#66923C2211yescharacteristic, complemented
42C11×C4⋊C8C2211yescharacteristic, complemented
43C11×#103C2211yescharacteristic, complemented
44C11×#102C2211yescharacteristic
45#66899C2211yescharacteristic, complemented
46#66899C2211yescharacteristic, complemented
47#66896C2211yescharacteristic
48#66896C2211yescharacteristic
49#66896C2211yescharacteristic, complemented
50#66885C2211yescharacteristic
51#66885C2211yescharacteristic
52(C2×D11)⋊C8C2211yescharacteristic
53(C2×D11)⋊C8C2211yescharacteristic, complemented
54#66882C2211yescharacteristic, complemented
55#66881C2211yescharacteristic, complemented
56#66873C2211yescharacteristic
57#66871C2211yescharacteristic, complemented
58C4×C11⋊C8C2211yescharacteristic, 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—22no—
69#4343—41no—
70D4×D11—22no—
71D4×D11—41no—
72C2×D44—21no—
73C2×D44D411yescharacteristic
74C2×D44C2311yescharacteristic
75C2×C4×D11—21no—
76C2×C4×D11—21no—
77C2×C4×D11—21no—
78C2×C4×D11C2311yescharacteristic
79C2×C4×D11C2311yescharacteristic
80C11×SD16—41no—
81C11×D8—41no—
82C2×C8×C11C2311yescharacteristic
83C2×C8×C11C2311yescharacteristic
84C11×C4⋊C4C2311yescharacteristic
85C11×C22⋊C4—21no—
86C11×C22⋊C4—21no—
87C11×C22⋊C4—21no—
88C42×C11C2311yescharacteristic
89C22⋊Dic11—21no—
90C22⋊Dic11—21no—
91C22⋊Dic11—21no—
92#4323—22no—
93(C2×D11)⋊C4—21no—
94(C2×D11)⋊C4—21no—
95(C2×D11)⋊C4—21no—
96(C2×D11)⋊C4D411yescharacteristic
97(C2×D11)⋊C4D411yescharacteristic
98C4⋊Dic11D411yescharacteristic
99C4⋊Dic11C2311yescharacteristic
100C4⋊Dic11C2311yescharacteristic
101C4⋊Dic11C2311yescharacteristic
102Dic11⋊C4—21no—
103Dic11⋊C4—21no—
104Dic11⋊C4—21no—
105Dic11⋊C4—21no—
106C4×Dic11—21no—
107C2×C11⋊C8C2311yescharacteristic
108C2×C11⋊C8C2311yescharacteristic
109#4313—41no—
110#4313—41no—
111#3322—111nomaximal, Sylow
112C23×C11—21no—
113C23×C11—21no—
114C22×D11—21no—
115C22×D11—42no—
116C22×D11—42no—
117C22×D11—81no—
118C22×D11C2×D411yescharacteristic
119C22×D11C2×D411yescharacteristic
120Q8×C11—21no—
121Q8×C11—21no—
122D4×C11—21no—
123D4×C11—21no—
124D4×C11—21no—
125D4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—81no—
129C2×C4×C11C2×D411yescharacteristic
130C2×C4×C11C2×D411yescharacteristic
131C2×C4×C11C2411yescharacteristic
132C22⋊D11—42no—
133C22⋊D11—42no—
134C22⋊D11—81no—
135C22⋊D11—81no—
136C2×Dic11—21no—
137C2×Dic11—21no—
138C2×Dic11—21no—
139C2×Dic11C2×D411yescharacteristic
140C2×Dic11C2×D411yescharacteristic
141D44—21no—
142D44—41no—
143D44—42no—
144D44#4112yes—
145C4×D11—21no—
146C4×D11—21no—
147C4×D11—21no—
148C4×D11—21no—
149C4×D11—42no—
150C4×D11—81no—
151C4×D11—81no—
152C8×C11—21no—
153C8×C11—21no—
154C11⋊C8—21no—
155C11⋊C8—21no—
156#553—111no—
157#546—111no—
158#488—111no—
159#485—111no—
160#480—111no—
161#478—111no—
162#469—111no—
163#468—111no—
164#463D1111yescharacteristic, complemented
165#449—111no—
166#447—111no—
167C4×D8—111no—
168#436—111no—
169#418—111no—
170#417—111no—
171C22×C11—41no—
172C22×C11—41no—
173C22×C11—41no—
174C22×C11—41no—
175C22×C11—41no—
176C22×C11—41no—
177C22×C11C22×D411yescharacteristic
178C2×D11—22no—
179C2×D11—21no—
180C2×D11—21no—
181C2×D11—21no—
182C2×D11—21no—
183C2×D11—21no—
184C2×D11—21no—
185C2×D11—41no—
186C2×D11—41no—
187C2×D11—84no—
188C4×C11—21no—
189C4×C11—21no—
190C4×C11—41no—
191C4×C11—41no—
192C4×C11C2×#4111yescharacteristic
193C4×C11H(5,𝔽2)11yescharacteristic
194Dic11—21no—
195Dic11—21no—
196Dic11—41no—
197Dic11—41no—
198Dic11—41no—
199C2×#41—111no—
200C22×D4—111no—
201C2×SD16C2×D1111yescharacteristic, complemented
202C2×D8—111no—
203C2×D8C2×D1111yescharacteristic
204C2×M16—111no—
205C2×M16—111no—
206#126—221no—
207#125—111no—
208#124C2×D1111yescharacteristic
209#123—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×D4—221no—
221C4×D4C2×D1111yescharacteristic, complemented
222#117—111no—
223C2×C4⋊C4—111no—
224C2×C22⋊C4—221no—
225#107—111no—
226#107—111no—
227#106—111no—
228C4⋊C8C2×D1111yescharacteristic, complemented
229#103—111no—
230#103—111no—
231#103C2×D1111yescharacteristic, complemented
232#102—111no—
233#102—111no—
234#102—111no—
235#102—111no—
236#102—111no—
237#102—111no—
238#102C2×D1111yescharacteristic
239C22⋊C8—111no—
240C22⋊C8—111no—
241C4×C8—111no—
242C2×C11—81no—
243C2×C11—81no—
244C2×C11#54611yescharacteristic
245C2×C11#57511yescharacteristic
246C2×C11#57611yescharacteristic
247D11—41no—
248D11—41no—
249D11—42no—
250C24—221no—
251#41—222no—
252#41—441no—
253C2×Q8C22×D1111yescharacteristic
254C2×D4—111no—
255C2×D4—111no—
256C2×D4—221no—
257C2×D4—221no—
258C2×D4—222no—
259C2×D4—221no—
260C2×D4—221no—
261C2×D4—221no—
262C2×D4—441no—
263C2×D4C22×D1111yescharacteristic
264C2×D4C22×D1111yescharacteristic
265C22×C4—21no—
266C22×C4—111no—
267C22×C4—111no—
268C22×C4—221no—
269C22×C4—221no—
270C22×C4—221no—
271SD16—41no—
272D8—41no—
273D8—222no—
274M16—441no—
275M16—441no—
276C2×C8—111no—
277C2×C8—111no—
278C2×C8C22×D1111yescharacteristic
279C2×C8C22×D1111yescharacteristic
280C4⋊C4—111no—
281C4⋊C4—111no—
282C4⋊C4—111no—
283C4⋊C4—111no—
284C4⋊C4—221no—
285C4⋊C4—221no—
286C4⋊C4—221no—
287C4⋊C4—221no—
288C4⋊C4C22×D1111yescharacteristic
289C22⋊C4—21no—
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—111no—
293C22⋊C4—111no—
294C22⋊C4—221no—
295C22⋊C4—221no—
296C22⋊C4—221no—
297C22⋊C4—221no—
298C22⋊C4—221no—
299C22⋊C4—221no—
300C42—221no—
301C42C22×D1111yescharacteristic
302C11#332211yescharacteristic, complemented, Sylow
303C23—21no—
304C23—21no—
305C23—111no—
306C23—111no—
307C23—221no—
308C23—442no—
309C23—442no—
310C23—881no—
311Q8—21no—
312Q8—21no—
313D4—21no—
314D4—21no—
315D4—21no—
316D4—21no—
317D4—112no—
318D4—221no—
319D4—441no—
320D4—442no—
321D4—442no—
322D4—442no—
323D4—881no—
324D4—881no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—81no—
328C2×C4—111no—
329C2×C4—111no—
330C2×C4—221no—
331C2×C4—221no—
332C2×C4—221no—
333C2×C4—221no—
334C2×C4—221no—
335C2×C4—221no—
336C2×C4—221no—
337C2×C4—442no—
338C2×C4—881no—
339C2×C4—881no—
340C2×C4D4×D1111yescharacteristic
341C2×C4D4×D1111yescharacteristic
342C2×C4C23×D1111yescharacteristic
343C8—21no—
344C8—21no—
345C8—221no—
346C8—221no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—221no—
354C22—221no—
355C22—221no—
356C22—221no—
357C22—221no—
358C22—221no—
359C22—222no—
360C22—441no—
361C22—441no—
362C22—884no—
363C22C2×D4×D1111yescharacteristic
364C4—21no—
365C4—21no—
366C4—41no—
367C4—41no—
368C4—221no—
369C4—221no—
370C4—441no—
371C4—441no—
372C4—441no—
373C4#6703711yescharacteristic
374C4#41×D1111yescharacteristic
375C2—81no—
376C2—81no—
377C2—441no—
378C2—441no—
379C2—442no—
380C2#1062314311yescharacteristic
381C2#1062329911yescharacteristic
382C2#1062330511yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#463C2
socleC22×C11C22×D4
hypercenter#463D11
hypocenterC11#3322
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. #10623207C2semidirect
2. #10623089C2semidirect
3. C11×#463C2semidirect
4. #10622787C2semidirect
5. #10622785C2semidirect
6. #10622772C2semidirect
7. #10622769C2semidirect
8. #10622669C2semidirect
9. C4×#4323C2semidirect
10. #10622460C2semidirect
11. #10622451C2semidirect
12. #10622428C2semidirect
13. #10622416C2semidirect
14. #10622387C2semidirect
15. #10622383C2semidirect
18. C2×C11×SD16C22semidirect
21. C4×D4×C11C22semidirect
25. #66991C22semidirect
30. C2×#4313C22semidirect
32. C4⋊C4×D11C22semidirect
41. #66923C22semidirect
42. C11×C4⋊C8C22semidirect
43. C11×#103C22semidirect
45. #66899C22semidirect
46. #66899C22semidirect
49. #66896C22semidirect
53. (C2×D11)⋊C8C22semidirect
54. #66882C22semidirect
55. #66881C22semidirect
57. #66871C22semidirect
58. C4×C11⋊C8C22semidirect
164. #463D11semidirect
201. C2×SD16C2×D11semidirect
221. C4×D4C2×D11semidirect
228. C4⋊C8C2×D11semidirect
231. #103C2×D11semidirect
302. C11#3322semidirect

Maximal subgroups

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

subgroupindex
#106232072
#106230892
C11×#4632
#106227872
#106227852
#106227722
#106227692
#106226692
C4×#43232
#106224602
#106224512
#106224282
#106224162
#106223872
#106223832
#332211