Finite Group Databasebeta

← #13080817

Subgroups — #13080817

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
1C11×#546C211yesmaximal, characteristic, complemented
2#10623096C211yesmaximal, characteristic, complemented
3#10622851C211yesmaximal, characteristic, complemented
4#10622845C211yesmaximal, characteristic, complemented
5#10622830C211yesmaximal, characteristic, complemented
6#10622828C211yesmaximal, characteristic, complemented
7#10622670C211yesmaximal, characteristic, complemented
8#10622669C211yesmaximal, characteristic, complemented
9#10622662C211yesmaximal, characteristic, complemented
10#10622658C211yesmaximal, characteristic, complemented
11#10622652C211yesmaximal, characteristic, complemented
12#10622646C211yesmaximal, characteristic, complemented
13C4×#4323C211yesmaximal, characteristic, complemented
14#10622625C211yesmaximal, characteristic, complemented
15#10622622C211yesmaximal, characteristic, complemented
16C2×C11×#41C2211yescharacteristic
17C22×D4×C11C2211yescharacteristic
18C11×#124C2211yescharacteristic
19C11×#123—21no—
20C11×C22⋊Q8C2211yescharacteristic
21C11×#121—21no—
22C11×#121C2211yescharacteristic
23C11×#120—21no—
24C4×D4×C11C2211yescharacteristic
25C4×D4×C11C2211yescharacteristic
26C2×C11×C22⋊C4—21no—
27C2×#4325C2211yescharacteristic, complemented
28#66992—21no—
29C2×#4323C2211yescharacteristic
30C2×#4323C2211yescharacteristic
31#66983C2211yescharacteristic
32#66983C2211yescharacteristic, complemented
33#66979C2211yescharacteristic
34C2×C4⋊Dic11C2211yescharacteristic, complemented
35C2×#4318C2211yescharacteristic
36C2×#4318C2211yescharacteristic, complemented
37#66951—21no—
38#66936—21no—
39(C22⋊D11)⋊C4—21no—
40C4×D44C2211yescharacteristic, complemented
41#66923C2211yescharacteristic, complemented
42#66899C2211yescharacteristic, complemented
43#66899C2211yescharacteristic, complemented
44#66899C2211yescharacteristic, complemented
45#66896C2211yescharacteristic
46#66896C2211yescharacteristic
47#66896C2211yescharacteristic
48#66896C2211yescharacteristic
49#66896C2211yescharacteristic
50#66896C2211yescharacteristic
51C22⋊(C11⋊C8)C2211yescharacteristic
52C22⋊(C11⋊C8)C2211yescharacteristic, complemented
53#66873C2211yescharacteristic, complemented
54#66872C2211yescharacteristic, complemented
55#66871C2211yescharacteristic, complemented
56#66871C2211yescharacteristic, complemented
57C4⋊(C11⋊C8)C2211yescharacteristic, complemented
58C4×C11⋊C8C2211yescharacteristic, complemented
59C24×C11—21no—
60C11×#41—22no—
61C11×#41—41no—
62C2×Q8×C11C2311yescharacteristic
63C2×D4×C11—22no—
64C2×D4×C11—21no—
65C2×D4×C11—21no—
66C2×D4×C11—21no—
67C2×D4×C11—41no—
68C2×D4×C11D411yescharacteristic
69C2×D4×C11C2311yescharacteristic
70C2×D4×C11C2311yescharacteristic
71C22×C4×C11—21no—
72C22×C4×C11—21no—
73C22×C4×C11C2311yescharacteristic
74C22×C4×C11C2311yescharacteristic
75C2×C22⋊D11—21no—
76C2×C22⋊D11—21no—
77C22×Dic11—21no—
78C2×D44C2311yescharacteristic
79C2×C4×D11—21no—
80C11×C4⋊C4—21no—
81C11×C4⋊C4D411yescharacteristic
82C11×C4⋊C4C2311yescharacteristic
83C11×C22⋊C4—21no—
84C11×C22⋊C4—21no—
85C11×C22⋊C4—21no—
86C11×C22⋊C4—21no—
87C11×C22⋊C4—21no—
88C11×C22⋊C4D411yescharacteristic
89C11×C22⋊C4D411yescharacteristic
90C42×C11C2311yescharacteristic
91C22⋊Dic11—21no—
92#4325—41no—
93#4323—22no—
94#4323—41no—
95(C2×D11)⋊C4—21no—
96(C2×D11)⋊C4—21no—
97(C2×D11)⋊C4—21no—
98C4⋊Dic11—21no—
99C4⋊Dic11C2311yescharacteristic
100C4⋊Dic11C2311yescharacteristic
101C4⋊Dic11C2311yescharacteristic
102Dic11⋊C4—21no—
103Dic11⋊C4—21no—
104C4×Dic11—21no—
105#4318—41no—
106#4318—41no—
107C2×C11⋊C8C2311yescharacteristic
108C2×C11⋊C8C2311yescharacteristic
109C2×C11⋊C8C2311yescharacteristic
110C2×C11⋊C8C2311yescharacteristic
111#3322—111nomaximal, Sylow
112C23×C11—21no—
113C23×C11—21no—
114C23×C11—42no—
115C23×C11—42no—
116C23×C11—81no—
117C23×C11C2×D411yescharacteristic
118C23×C11C2×D411yescharacteristic
119C22×D11—21no—
120Q8×C11—21no—
121Q8×C11—21no—
122D4×C11—21no—
123D4×C11—21no—
124D4×C11—21no—
125D4×C11—41no—
126D4×C11—42no—
127D4×C11—42no—
128D4×C11—81no—
129D4×C11#4112yes—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—42no—
137C2×C4×C11—81no—
138C2×C4×C11C2×D411yescharacteristic
139C2×C4×C11C2×D411yescharacteristic
140C2×C4×C11C2×D411yescharacteristic
141C2×C4×C11C2×D411yescharacteristic
142C2×C4×C11C2411yescharacteristic
143C22⋊D11—42no—
144C22⋊D11—81no—
145C2×Dic11—21no—
146C2×Dic11—21no—
147C2×Dic11—21no—
148C2×Dic11—81no—
149D44—21no—
150D44—21no—
151C4×D11—81no—
152C11⋊C8—21no—
153C11⋊C8—21no—
154C11⋊C8—21no—
155C11⋊C8—21no—
156#553—111no—
157#546D1111yescharacteristic, complemented
158#488—111no—
159#485—111no—
160#480—111no—
161#478—111no—
162#469—111no—
163#468—111no—
164#463—111no—
165#449—111no—
166#447—111no—
167C4×D8—111no—
168#436—111no—
169#418—111no—
170#417—111no—
171C22×C11—21no—
172C22×C11—21no—
173C22×C11—22no—
174C22×C11—21no—
175C22×C11—21no—
176C22×C11—21no—
177C22×C11—21no—
178C22×C11—41no—
179C22×C11—41no—
180C22×C11—41no—
181C22×C11—41no—
182C22×C11—41no—
183C22×C11—84no—
184C22×C11C22×D411yescharacteristic
185C2×D11—41no—
186C2×D11—41no—
187C2×D11—41no—
188C4×C11—21no—
189C4×C11—21no—
190C4×C11—21no—
191C4×C11—21no—
192C4×C11—41no—
193C4×C11—41no—
194C4×C11C2×#4111yescharacteristic
195C4×C11H(5,𝔽2)11yescharacteristic
196Dic11—41no—
197Dic11—41no—
198Dic11—41no—
199C2×#41C2×D1111yescharacteristic
200C22×D4C2×D1111yescharacteristic
201C2×SD16—111no—
202C2×D8—111no—
203C2×D8—111no—
204C2×M16—111no—
205C2×M16—111no—
206#126—221no—
207#125—111no—
208#124C2×D1111yescharacteristic
209#123—21no—
210#123—221no—
211C22⋊Q8C2×D1111yescharacteristic
212#121—21no—
213#121—111no—
214#121—111no—
215#121—221no—
216#121C2×D1111yescharacteristic
217#120—21no—
218C4×D4—111no—
219C4×D4—221no—
220C4×D4C2×D1111yescharacteristic
221C4×D4C2×D1111yescharacteristic
222#117—111no—
223C2×C4⋊C4—111no—
224C2×C22⋊C4—21no—
225#107—111no—
226#107—111no—
227#106—111no—
228C4⋊C8—111no—
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#102—111no—
238#102—111no—
239C22⋊C8—111no—
240C22⋊C8—111no—
241C4×C8—111no—
242C2×C11—41no—
243C2×C11—41no—
244C2×C11—42no—
245C2×C11—81no—
246C2×C11#54611yescharacteristic
247C2×C11#57511yescharacteristic
248C2×C11#57611yescharacteristic
249D11—81no—
250C24—21no—
251#41—22no—
252#41—41no—
253C2×Q8C22×D1111yescharacteristic
254C2×D4—22no—
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—41no—
259C2×D4—111no—
260C2×D4—221no—
261C2×D4—221no—
262C2×D4C22⋊D1111yescharacteristic
263C2×D4C22×D1111yescharacteristic
264C2×D4C22×D1111yescharacteristic
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—221no—
268C22×C4—221no—
269C22×C4C22×D1111yescharacteristic
270C22×C4C22×D1111yescharacteristic
271SD16—441no—
272D8—222no—
273D8—441no—
274M16—441no—
275M16—441no—
276C2×C8—111no—
277C2×C8—111no—
278C2×C8—111no—
279C2×C8—111no—
280C4⋊C4—21no—
281C4⋊C4—111no—
282C4⋊C4—111no—
283C4⋊C4—111no—
284C4⋊C4—221no—
285C4⋊C4—221no—
286C4⋊C4—221no—
287C4⋊C4C22⋊D1111yescharacteristic
288C4⋊C4C22×D1111yescharacteristic
289C22⋊C4—21no—
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—21no—
293C22⋊C4—21no—
294C22⋊C4—221no—
295C22⋊C4—221no—
296C22⋊C4—221no—
297C22⋊C4—221no—
298C22⋊C4C22⋊D1111yescharacteristic
299C22⋊C4C22⋊D1111yescharacteristic
300C42—221no—
301C42C22×D1111yescharacteristic
302C11#332211yescharacteristic, complemented, Sylow
303C23—21no—
304C23—21no—
305C23—42no—
306C23—42no—
307C23—81no—
308C23—221no—
309C23C2×C22⋊D1111yescharacteristic
310C23C2×C22⋊D1111yescharacteristic
311Q8—21no—
312Q8—21no—
313D4—21no—
314D4—21no—
315D4—21no—
316D4—41no—
317D4—42no—
318D4—42no—
319D4—81no—
320D4—221no—
321D4—221no—
322D4—442no—
323D4—881no—
324D4#434112yes—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—42no—
332C2×C4—81no—
333C2×C4—221no—
334C2×C4—221no—
335C2×C4—221no—
336C2×C4—881no—
337C2×C4—881no—
338C2×C4C2×C22⋊D1111yescharacteristic
339C2×C4C2×C22⋊D1111yescharacteristic
340C2×C4C2×C22⋊D1111yescharacteristic
341C2×C4C2×C22⋊D1111yescharacteristic
342C2×C4C23×D1111yescharacteristic
343C8—221no—
344C8—221no—
345C8—221no—
346C8—221no—
347C22—21no—
348C22—21no—
349C22—22no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—84no—
360C22—441no—
361C22—441no—
362C22—441no—
363C22C22×C22⋊D1111yescharacteristic
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—41no—
369C4—41no—
370C4—441no—
371C4—441no—
372C4—441no—
373C4C2×#434111yescharacteristic
374C4#6703711yescharacteristic
375C2—41no—
376C2—41no—
377C2—42no—
378C2—81no—
379C2—881no—
380C2#1062333711yescharacteristic
381C2#1062335311yescharacteristic
382C2#1062336611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#546C2
socleC22×C11C22×D4
hypercenter#546D11
hypocenterC11#3322
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ #546

Complements

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

NH ≅ G/Ntype
1. C11×#546C2semidirect
2. #10623096C2semidirect
3. #10622851C2semidirect
4. #10622845C2semidirect
5. #10622830C2semidirect
6. #10622828C2semidirect
7. #10622670C2semidirect
8. #10622669C2semidirect
9. #10622662C2semidirect
10. #10622658C2semidirect
11. #10622652C2semidirect
12. #10622646C2semidirect
13. C4×#4323C2semidirect
14. #10622625C2semidirect
15. #10622622C2semidirect
27. C2×#4325C22semidirect
32. #66983C22semidirect
34. C2×C4⋊Dic11C22semidirect
36. C2×#4318C22semidirect
40. C4×D44C22semidirect
41. #66923C22semidirect
42. #66899C22semidirect
43. #66899C22semidirect
44. #66899C22semidirect
52. C22⋊(C11⋊C8)C22semidirect
53. #66873C22semidirect
54. #66872C22semidirect
55. #66871C22semidirect
56. #66871C22semidirect
57. C4⋊(C11⋊C8)C22semidirect
58. C4×C11⋊C8C22semidirect
157. #546D11semidirect
302. C11#3322semidirect

Maximal subgroups

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

subgroupindex
C11×#5462
#106230962
#106228512
#106228452
#106228302
#106228282
#106226702
#106226692
#106226622
#106226582
#106226522
#106226462
C4×#43232
#106226252
#106226222
#332211