Finite Group Databasebeta

← #13080819

Subgroups — #13080819

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#10623096C211yesmaximal, characteristic, complemented
2#10623081C211yesmaximal, characteristic, complemented
3C11×#436C211yesmaximal, characteristic, complemented
4#10622748C211yesmaximal, characteristic, complemented
5#10622747C211yesmaximal, characteristic, complemented
6#10622746C211yesmaximal, characteristic, complemented
7#10622744C211yesmaximal, characteristic, complemented
8#10622460C211yesmaximal, characteristic, complemented
9#10622457C211yesmaximal, characteristic, complemented
10#10622349C211yesmaximal, characteristic, complemented
11#10622347C211yesmaximal, characteristic, complemented
12#10622345C211yesmaximal, characteristic, complemented
13#10622336C211yesmaximal, characteristic, complemented
14#10622310C211yesmaximal, characteristic, complemented
15C4×D88C211yesmaximal, characteristic, complemented
16C2×#4339C2211yescharacteristic
17C22×D44C2211yescharacteristic
18C2×C11×M16C2211yescharacteristic
19C2×C11×M16C2211yescharacteristic, complemented
20C4×D4×C11C2211yescharacteristic
21#66992—21no—
22#66990—21no—
23#66983C2211yescharacteristic
24#66983C2211yescharacteristic
25#66983C2211yescharacteristic, complemented
26#66979C2211yescharacteristic
27C2×C4⋊Dic11C2211yescharacteristic, complemented
28#66977C2211yescharacteristic
29C2×D88C2211yescharacteristic
30C2×D88C2211yescharacteristic
31C2×#4314C2211yescharacteristic, complemented
32#66951—21no—
33#66947—21no—
34#66937—21no—
35#66936—21no—
36(C22⋊D11)⋊C4—21no—
37C22⋊C4×D11—21no—
38#66928C2211yescharacteristic
39C4×D44C2211yescharacteristic
40C4×D44C2211yescharacteristic, complemented
41#66923C2211yescharacteristic, complemented
42C11×C4⋊C8C2211yescharacteristic, complemented
43C11×C22⋊C8C2211yescharacteristic
44C11×C22⋊C8C2211yescharacteristic, complemented
45C4×C8×C11C2211yescharacteristic, complemented
46#66885C2211yescharacteristic
47#66885C2211yescharacteristic
48#66885C2211yescharacteristic
49#66885C2211yescharacteristic
50#66885C2211yescharacteristic
51#66885C2211yescharacteristic
52#66885C2211yescharacteristic, complemented
53#66882C2211yescharacteristic, complemented
54#66882C2211yescharacteristic, complemented
55#66881C2211yescharacteristic, complemented
56#66880C2211yescharacteristic, complemented
57#66880C2211yescharacteristic, complemented
58#66880C2211yescharacteristic, complemented
59C23×D11—21no—
60C2×D4×C11D411yescharacteristic
61C22×C4×C11C2311yescharacteristic
62C22×C4×C11C2311yescharacteristic
63C2×C22⋊D11—21no—
64C2×C22⋊D11—21no—
65C2×C22⋊D11—21no—
66C2×C22⋊D11—21no—
67C22×Dic11—21no—
68#4339—22no—
69#4339—41no—
70C2×D44—22no—
71C2×D44—21no—
72C2×D44—41no—
73C2×D44C2311yescharacteristic
74C2×D44C2311yescharacteristic
75C2×D44C2311yescharacteristic
76C2×C4×D11—21no—
77C2×C4×D11—21no—
78C2×C4×D11—21no—
79C2×Dic22C2311yescharacteristic
80C11×M16—41no—
81C11×M16—41no—
82C2×C8×C11C2311yescharacteristic
83C2×C8×C11C2311yescharacteristic
84C2×C8×C11C2311yescharacteristic
85C2×C8×C11C2311yescharacteristic
86C11×C4⋊C4D411yescharacteristic
87C11×C22⋊C4D411yescharacteristic
88C11×C22⋊C4D411yescharacteristic
89C42×C11C2311yescharacteristic
90C22⋊Dic11—21no—
91C22⋊Dic11—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)⋊C4—21no—
99C4⋊Dic11—21no—
100C4⋊Dic11C2311yescharacteristic
101C4⋊Dic11C2311yescharacteristic
102C4⋊Dic11C2311yescharacteristic
103C4⋊Dic11C2311yescharacteristic
104Dic11⋊C4—21no—
105Dic11⋊C4—21no—
106Dic11⋊C4—21no—
107C4×Dic11—21no—
108D88—22no—
109D88—41no—
110#4314—41no—
111#3322—111nomaximal, Sylow
112C23×C11C2×D411yescharacteristic
113C23×C11C2×D411yescharacteristic
114C22×D11—21no—
115C22×D11—21no—
116C22×D11—21no—
117C22×D11—42no—
118C22×D11—42no—
119C22×D11—81no—
120D4×C11—41no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11C2×D411yescharacteristic
126C2×C4×C11C2×D411yescharacteristic
127C2×C4×C11C2×D411yescharacteristic
128C2×C4×C11C2×D411yescharacteristic
129C2×C4×C11C2411yescharacteristic
130C22⋊D11—42no—
131C22⋊D11—42no—
132C22⋊D11—81no—
133C22⋊D11—81no—
134C2×Dic11—21no—
135C2×Dic11—21no—
136C2×Dic11—21no—
137C2×Dic11—21no—
138C2×Dic11—21no—
139C2×Dic11—81no—
140D44—21no—
141D44—21no—
142D44—21no—
143D44—21no—
144D44—21no—
145D44—42no—
146D44#4112yes—
147C4×D11—42no—
148C4×D11—81no—
149C4×D11—81no—
150Dic22—21no—
151Dic22—21no—
152C8×C11—21no—
153C8×C11—21no—
154C8×C11—21no—
155C8×C11—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#463—111no—
165#449—111no—
166#447—111no—
167C4×D8—111no—
168#436D1111yescharacteristic, complemented
169#418—111no—
170#417—111no—
171C22×C11—21no—
172C22×C11—21no—
173C22×C11—21no—
174C22×C11—21no—
175C22×C11—21no—
176C22×C11—21no—
177C22×C11C22×D411yescharacteristic
178C2×D11—22no—
179C2×D11—41no—
180C2×D11—41no—
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—21no—
191C4×C11—21no—
192C4×C11C2×#4111yescharacteristic
193C4×C11H(5,𝔽2)11yescharacteristic
194Dic11—41no—
195Dic11—41no—
196Dic11—41no—
197Dic11—41no—
198Dic11—41no—
199C2×#41—111no—
200C22×D4—111no—
201C2×SD16—111no—
202C2×D8—111no—
203C2×D8—111no—
204C2×M16C2×D1111yescharacteristic
205C2×M16C2×D1111yescharacteristic, complemented
206#126—221no—
207#125—111no—
208#124—111no—
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
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#103—111no—
232#102—111no—
233#102—111no—
234#102—111no—
235#102—111no—
236#102—111no—
237#102—111no—
238#102—111no—
239C22⋊C8C2×D1111yescharacteristic
240C22⋊C8C2×D1111yescharacteristic, complemented
241C4×C8C2×D1111yescharacteristic, complemented
242C2×C11—41no—
243C2×C11—41no—
244C2×C11#54611yescharacteristic
245C2×C11#57511yescharacteristic
246C2×C11#57611yescharacteristic
247D11—42no—
248D11—81no—
249D11—81no—
250C24—221no—
251#41—222no—
252#41—441no—
253C2×Q8—111no—
254C2×D4—111no—
255C2×D4—111no—
256C2×D4—111no—
257C2×D4—222no—
258C2×D4—221no—
259C2×D4—221no—
260C2×D4—221no—
261C2×D4—221no—
262C2×D4—221no—
263C2×D4—441no—
264C2×D4D4411yescharacteristic
265C22×C4—221no—
266C22×C4—221no—
267C22×C4—221no—
268C22×C4—221no—
269C22×C4C22×D1111yescharacteristic
270C22×C4C22×D1111yescharacteristic
271SD16—441no—
272D8—222no—
273D8—441no—
274M16—41no—
275M16—41no—
276C2×C8C22×D1111yescharacteristic
277C2×C8C22×D1111yescharacteristic
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⋊C4D4411yescharacteristic
289C22⋊C4—221no—
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⋊C4D4411yescharacteristic
299C22⋊C4D4411yescharacteristic
300C42—221no—
301C42C22×D1111yescharacteristic
302C11#332211yescharacteristic, complemented, Sylow
303C23—221no—
304C23—221no—
305C23—221no—
306C23—442no—
307C23—442no—
308C23—881no—
309C23C2×D4411yescharacteristic
310C23C2×D4411yescharacteristic
311Q8—221no—
312Q8—221no—
313D4—41no—
314D4—112no—
315D4—221no—
316D4—221no—
317D4—221no—
318D4—221no—
319D4—221no—
320D4—442no—
321D4—442no—
322D4—442no—
323D4—881no—
324D4—881no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—221no—
330C2×C4—221no—
331C2×C4—221no—
332C2×C4—221no—
333C2×C4—221no—
334C2×C4—442no—
335C2×C4—881no—
336C2×C4—881no—
337C2×C4—881no—
338C2×C4C2×D4411yescharacteristic
339C2×C4C2×D4411yescharacteristic
340C2×C4C2×D4411yescharacteristic
341C2×C4C2×D4411yescharacteristic
342C2×C4C23×D1111yescharacteristic
343C8—21no—
344C8—21no—
345C8—21no—
346C8—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—222no—
354C22—441no—
355C22—441no—
356C22—441no—
357C22—441no—
358C22—441no—
359C22—441no—
360C22—441no—
361C22—441no—
362C22—884no—
363C22C22×D4411yescharacteristic
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—441no—
369C4—441no—
370C4—441no—
371C4—441no—
372C4—441no—
373C4#6703711yescharacteristic
374C4#41×D1111yescharacteristic
375C2—41no—
376C2—41no—
377C2—442no—
378C2—881no—
379C2—881no—
380C2#1062308511yescharacteristic
381C2#1062327911yescharacteristic
382C2#1062328311yescharacteristic
subgroupG/H
centerC22C22×D44
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#436C2
socleC22×C11C22×D4
hypercenter#436D11
hypocenterC11#3322
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ #436

Complements

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

NH ≅ G/Ntype
1. #10623096C2semidirect
2. #10623081C2semidirect
3. C11×#436C2semidirect
4. #10622748C2semidirect
5. #10622747C2semidirect
6. #10622746C2semidirect
7. #10622744C2semidirect
8. #10622460C2semidirect
9. #10622457C2semidirect
10. #10622349C2semidirect
11. #10622347C2semidirect
12. #10622345C2semidirect
13. #10622336C2semidirect
14. #10622310C2semidirect
15. C4×D88C2semidirect
19. C2×C11×M16C22semidirect
25. #66983C22semidirect
27. C2×C4⋊Dic11C22semidirect
31. C2×#4314C22semidirect
40. C4×D44C22semidirect
41. #66923C22semidirect
42. C11×C4⋊C8C22semidirect
44. C11×C22⋊C8C22semidirect
45. C4×C8×C11C22semidirect
52. #66885C22semidirect
53. #66882C22semidirect
54. #66882C22semidirect
55. #66881C22semidirect
56. #66880C22semidirect
57. #66880C22semidirect
58. #66880C22semidirect
168. #436D11semidirect
205. C2×M16C2×D11semidirect
228. C4⋊C8C2×D11semidirect
240. C22⋊C8C2×D11semidirect
241. C4×C8C2×D11semidirect
302. C11#3322semidirect

Maximal subgroups

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

subgroupindex
#106230962
#106230812
C11×#4362
#106227482
#106227472
#106227462
#106227442
#106224602
#106224572
#106223492
#106223472
#106223452
#106223362
#106223102
C4×D882
#332211