Finite Group Databasebeta

← #14909668

Subgroups — #14909668

Order 2816.

730 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079192C211yesmaximal, characteristic, complemented
2D11×#493C211yesmaximal, characteristic, complemented
3#13070864C212yesmaximal, complemented
4#13070838C212yesmaximal, complemented
5#13070652C211yesmaximal, characteristic, complemented
6#13070651C211yesmaximal, characteristic, complemented
7#13070648C211yesmaximal, characteristic, complemented
8#13070529C212yesmaximal, complemented
9#13070526C212yesmaximal, complemented
10#13070414C211yesmaximal, characteristic, complemented
11C11×#2206C211yesmaximal, characteristic, complemented
12C2×D8×D11—21no—
13C2×D8×D11C2212yes—
14D11×#127—21no—
15#10623079—21no—
16C2×C11×D16C2212yescomplemented
17C11×#493C2211yescharacteristic
18C4×C11×D8C2211yescharacteristic, complemented
19#10622770C2211yescharacteristic
20#10622764—21no—
21#10622764C2212yes—
22#10622764C2211yescharacteristic, complemented
23C2×#66890C2212yescomplemented
24C2×#66890C2212yescomplemented
25#10622686—21no—
26C4×#4323—21no—
27C2×D176C2212yescomplemented
28#10622496C2211yescharacteristic
29#10622487C2211yescharacteristic, complemented
30#10622388—21no—
31#10622373—21no—
32#10622308C2211yescharacteristic
33C4×D88C2211yescharacteristic, complemented
34C4×C8×D11C2211yescharacteristic
35C11×C4⋊C16C2211yescharacteristic, complemented
36C11×#357C2212yescomplemented
37#10622200C2212yescomplemented
38#10622147C2212yescomplemented
39(C2×D11)⋊C16C2212yes—
40C16×Dic11C2212yescomplemented
41#10622129C2212yescomplemented
42C4⋊(C11⋊C16)C2211yescharacteristic, complemented
43C2×D4×D11—22no—
44C2×D4×D11—41no—
45C2×D4×D11—41no—
46C2×#4339—41no—
47C2×C11×D8—21no—
48C2×C11×D8C2312yes—
49C2×C11×D8C2311yescharacteristic
50C11×#127—21no—
51C4×D4×C11—21no—
52#66993—22no—
53#66993—21no—
54#66993—41no—
55#66993—41no—
56#66991—21no—
57C2×#4323—22no—
58C2×#4323—22no—
59C2×#4323—21no—
60C4×C22⋊D11—41no—
61D8×D11—42no—
62D8×D11—42no—
63D8×D11—44no—
64C2×D88—21no—
65C2×D88C2311yescharacteristic
66C2×D88C2312yes—
67C2×C8×D11D411yescharacteristic
68C2×C8×D11C2311yescharacteristic
69#66948—21no—
70#66941—21no—
71#66938—41no—
72#66937—41no—
73#66927—21no—
74C4×D44—21no—
75C42×D11D411yescharacteristic
76C11×D16—42no—
77C2×C11×C16C2312yes—
78C11×#107C2311yescharacteristic
79C11×#102—21no—
80C4×C8×C11C2311yescharacteristic
81#66896—21no—
82#66890—42no—
83#66890—42no—
84#66885—21no—
85#66882C2311yescharacteristic
86C8×Dic11D411yescharacteristic
87C8×Dic11C2311yescharacteristic
88C2×C11⋊C16C2312yes—
89#66873—21no—
90#66871—21no—
91C4×C11⋊C8D411yescharacteristic
92D176—42no—
93#33771—111nomaximal, Sylow
94C23×D11—42no—
95C2×D4×C11—21no—
96C2×D4×C11—22no—
97C2×D4×C11—41no—
98C2×D4×C11—41no—
99C22×C4×C11—41no—
100C2×C22⋊D11—41no—
101C2×C22⋊D11—41no—
102C2×C22⋊D11—42no—
103C2×C22⋊D11—42no—
104C2×C22⋊D11—42no—
105C2×C22⋊D11—41no—
106D4×D11—44no—
107D4×D11—44no—
108D4×D11—84no—
109D4×D11—84no—
110#4339—84no—
111C2×D44—21no—
112C2×D44—22no—
113C2×D44—41no—
114C2×D44—41no—
115C2×D44—41no—
116C2×C4×D11—41no—
117C2×C4×D11D811yescharacteristic
118C2×C4×D11D811yescharacteristic
119C2×C4×D11C2×D411yescharacteristic
120C2×Dic22—41no—
121C11×D8—21no—
122C11×D8—22no—
123C11×D8—21no—
124C11×D8—22no—
125C11×D8—42no—
126C2×C8×C11C2×D411yescharacteristic
127C2×C8×C11C2411yescharacteristic
128C11×C4⋊C4—21no—
129C11×C22⋊C4—41no—
130C42×C11C2×D411yescharacteristic
131C22⋊Dic11—41no—
132#4323—44no—
133#4323—44no—
134#4323—42no—
135(C2×D11)⋊C4—41no—
136(C2×D11)⋊C4—41no—
137C4⋊Dic11—21no—
138Dic11⋊C4—41no—
139C4×Dic11D811yescharacteristic
140C4×Dic11D811yescharacteristic
141C4×Dic11C2×D411yescharacteristic
142C2×C11⋊C8C2×D411yescharacteristic
143C2×C11⋊C8C2×D411yescharacteristic
144D88—21no—
145D88—22no—
146D88—21no—
147D88—22no—
148D88—42no—
149C8×D11—21no—
150C8×D11—21no—
151C8×D11—22no—
152C11×C16—22no—
153C11⋊C16—22no—
154#3169—111no—
155C2×#493—111no—
156#2246—112no—
157#2240—112no—
158#2206—111no—
159#2206—111no—
160#2206—111no—
161#2206D1111yescharacteristic, complemented
162#2184—112no—
163#2184—112no—
164#2162—111no—
165C23×C11—41no—
166C23×C11—42no—
167C22×D11—41no—
168C22×D11—42no—
169C22×D11—84no—
170C22×D11—84no—
171C22×D11—84no—
172C22×D11C2×D811yescharacteristic
173D4×C11—42no—
174D4×C11—41no—
175D4×C11—42no—
176D4×C11—41no—
177D4×C11—82no—
178D4×C11—82no—
179C2×C4×C11—41no—
180C2×C4×C11—82no—
181C2×C4×C11C2×D811yescharacteristic
182C2×C4×C11C2×D811yescharacteristic
183C2×C4×C11C22×D411yescharacteristic
184C22⋊D11—84no—
185C22⋊D11—82no—
186C22⋊D11—82no—
187C22⋊D11—84no—
188C22⋊D11—84no—
189C22⋊D11—82no—
190C2×Dic11—41no—
191C2×Dic11C2×D811yescharacteristic
192C2×Dic11C2×D811yescharacteristic
193C2×Dic11C2×D811yescharacteristic
194D44—42no—
195D44—41no—
196D44—42no—
197D44—41no—
198D44—82no—
199D44—82no—
200D44—82no—
201C4×D11—21no—
202C4×D11—21no—
203C4×D11—22no—
204C4×D11—82no—
205C4×D11D1614yescomplemented
206Dic22—82no—
207C8×C11—21no—
208C8×C11H(5,𝔽2)11yescharacteristic
209C8×C11H(5,𝔽2)11yescharacteristic
210C11⋊C8—21no—
211C11⋊C8AGL(1,ℤ/8)12yes—
212C22×D8—112no—
213C22×D8—221no—
214#532—221no—
215C2×#127—221no—
216C2×D16—112no—
217C2×D16—112no—
218C2×D16—112no—
219C2×D16C2×D1112yescomplemented
220#500—111no—
221#493—112no—
222#493—111no—
223#493—111no—
224#493—221no—
225#493—221no—
226#493C2×D1111yescharacteristic
227#486—221no—
228#466—111no—
229#466—111no—
230#466—221no—
231C4×D8—111no—
232C4×D8—221no—
233C4×D8C2×D1111yescharacteristic, complemented
234C2×C4×C8—111no—
235C4⋊C16—111no—
236C4⋊C16C2×D1111yescharacteristic, complemented
237#357—112no—
238#357—112no—
239#357—112no—
240#357C2×D1112yescomplemented
241C22⋊C16—112no—
242C4×C16—112no—
243C22×C11—81no—
244C22×C11—82no—
245C22×C11—82no—
246C22×C11—81no—
247C22×C11—82no—
248C22×C11—81no—
249C22×C11C22×D811yescharacteristic
250C2×D11—21no—
251C2×D11—21no—
252C2×D11—82no—
253C2×D11—81no—
254C2×D11—82no—
255C2×D11—81no—
256C2×D11—82no—
257C2×D11—81no—
258C2×D11—168no—
259C2×D11C2×D1612yes—
260C4×C11—21no—
261C4×C11—81no—
262C4×C11C2×D1612yes—
263C4×C11#53511yescharacteristic
264C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
265Dic11—21no—
266Dic11—81no—
267Dic11C2×D1612yes—
268Dic11#50912yes—
269C2×#41—441no—
270C22×D4—222no—
271C22×D4—441no—
272C22×D4—441no—
273C2×D8—21no—
274C2×D8—112no—
275C2×D8—111no—
276C2×D8—222no—
277C2×D8—222no—
278C2×D8—221no—
279C2×D8—221no—
280C2×D8—442no—
281C2×D8—442no—
282C2×D8—444no—
283C2×D8C22×D1112yes—
284C2×D8C22×D1111yescharacteristic
285C22×C8—111no—
286C22×C8—111no—
287C4⋊Q8—221no—
288#127—21no—
289#127—222no—
290#127—221no—
291#127—221no—
292#127—441no—
293#127—441no—
294#124—441no—
295#121—221no—
296#121—221no—
297#121—441no—
298C4×D4—21no—
299C4×D4—221no—
300C4×D4—441no—
301C2×C42—111no—
302D16—42no—
303D16—442no—
304D16—442no—
305D16—442no—
306C2×C16—112no—
307C2×C16C22×D1112yes—
308#107—111no—
309#107—221no—
310#107C22×D1111yescharacteristic
311#102—21no—
312#102—221no—
313#102—221no—
314#102—221no—
315C4×C8—111no—
316C4×C8—111no—
317C4×C8—111no—
318C4×C8C22×D1111yescharacteristic
319C2×C11—162no—
320C2×C11—161no—
321C2×C11#320511yescharacteristic
322C2×C11C22×D1611yescharacteristic
323C2×C11C2×#50911yescharacteristic
324D11—22no—
325D11—161no—
326D11—162no—
327C24—442no—
328#41—884no—
329C2×Q8—441no—
330C2×D4—21no—
331C2×D4—22no—
332C2×D4—41no—
333C2×D4—41no—
334C2×D4—221no—
335C2×D4—222no—
336C2×D4—441no—
337C2×D4—441no—
338C2×D4—441no—
339C2×D4—442no—
340C2×D4—442no—
341C2×D4—442no—
342C2×D4—444no—
343C2×D4—444no—
344C2×D4—441no—
345C2×D4—441no—
346C2×D4—441no—
347C2×D4—884no—
348C2×D4—884no—
349C22×C4—41no—
350C22×C4—111no—
351C22×C4—111no—
352C22×C4—111no—
353C22×C4—441no—
354D8—21no—
355D8—22no—
356D8—21no—
357D8—22no—
358D8—42no—
359D8—221no—
360D8—222no—
361D8—221no—
362D8—222no—
363D8—442no—
364D8—444no—
365D8—442no—
366D8—444no—
367C2×C8—111no—
368C2×C8—111no—
369C2×C8—222no—
370C2×C8—221no—
371C2×C8—221no—
372C2×C8D4×D1111yescharacteristic
373C2×C8C23×D1111yescharacteristic
374C4⋊C4—21no—
375C4⋊C4—221no—
376C4⋊C4—441no—
377C22⋊C4—41no—
378C22⋊C4—441no—
379C22⋊C4—441no—
380C22⋊C4—441no—
381C42—111no—
382C42—111no—
383C42—111no—
384C42D4×D1111yescharacteristic
385C16—22no—
386C16—222no—
387C11#3377111yescharacteristic, complemented, Sylow
388C23—41no—
389C23—42no—
390C23—111no—
391C23—441no—
392C23—442no—
393C23—884no—
394C23—884no—
395C23—884no—
396Q8—882no—
397D4—42no—
398D4—41no—
399D4—42no—
400D4—41no—
401D4—82no—
402D4—82no—
403D4—442no—
404D4—441no—
405D4—442no—
406D4—441no—
407D4—882no—
408D4—882no—
409D4—884no—
410D4—884no—
411D4—882no—
412D4—882no—
413D4—884no—
414D4—882no—
415D4—882no—
416C2×C4—41no—
417C2×C4—82no—
418C2×C4—111no—
419C2×C4—111no—
420C2×C4—114no—
421C2×C4—111no—
422C2×C4—222no—
423C2×C4—221no—
424C2×C4—221no—
425C2×C4—441no—
426C2×C4—882no—
427C2×C4D8×D1111yescharacteristic
428C2×C4D8×D1111yescharacteristic
429C2×C4C2×D4×D1111yescharacteristic
430C8—21no—
431C8—112no—
432C8—221no—
433C8#6703711yescharacteristic
434C8#6704211yescharacteristic
435C22—81no—
436C22—82no—
437C22—82no—
438C22—81no—
439C22—82no—
440C22—81no—
441C22—112no—
442C22—221no—
443C22—221no—
444C22—881no—
445C22—882no—
446C22—882no—
447C22—881no—
448C22—882no—
449C22—881no—
450C22—1768no—
451C22C2×D8×D1111yescharacteristic
452C4—21no—
453C4—81no—
454C4—112no—
455C4—112no—
456C4—221no—
457C4—881no—
458C4D11×D1612yes—
459C4#1062313811yescharacteristic
460C4D11×AGL(1,ℤ/8)11yescharacteristic
461C2—162no—
462C2—161no—
463C2—222no—
464C2—1762no—
465C2—1761no—
466C2#1307953311yescharacteristic
467C2C2×D11×D1611yescharacteristic
468C2D11×#50911yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2206C2
socleC22×C11C22×D8
hypercenter#2206D11
hypocenterC11#33771
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2206

Complements

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

NH ≅ G/Ntype
1. #13079192C2semidirect
2. D11×#493C2semidirect
3. #13070864C2semidirect
4. #13070838C2semidirect
5. #13070652C2semidirect
6. #13070651C2semidirect
7. #13070648C2semidirect
8. #13070529C2semidirect
9. #13070526C2semidirect
10. #13070414C2semidirect
11. C11×#2206C2semidirect
16. C2×C11×D16C22semidirect
18. C4×C11×D8C22semidirect
22. #10622764C22semidirect
23. C2×#66890C22semidirect
24. C2×#66890C22semidirect
27. C2×D176C22semidirect
29. #10622487C22semidirect
33. C4×D88C22semidirect
35. C11×C4⋊C16C22semidirect
36. C11×#357C22semidirect
37. #10622200C22semidirect
38. #10622147C22semidirect
40. C16×Dic11C22semidirect
41. #10622129C22semidirect
42. C4⋊(C11⋊C16)C22semidirect
161. #2206D11semidirect
205. C4×D11D16semidirect
219. C2×D16C2×D11semidirect
233. C4×D8C2×D11semidirect
236. C4⋊C16C2×D11semidirect
240. #357C2×D11semidirect
387. C11#33771semidirect

Maximal subgroups

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

subgroupindex
#130791922
D11×#4932
#130708642
#130708382
#130706522
#130706512
#130706482
#130705292
#130705262
#130704142
C11×#22062
#3377111