Finite Group Databasebeta

← #14909667

Subgroups — #14909667

Order 2816.

730 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079190C211yesmaximal, characteristic, complemented
2C2×#10622764C211yesmaximal, characteristic, complemented
3#13070864C212yesmaximal, complemented
4#13070838C212yesmaximal, complemented
5#13070650C212yesmaximal, complemented
6#13070649C212yesmaximal, complemented
7#13070530C211yesmaximal, characteristic, complemented
8#13070528C211yesmaximal, characteristic, complemented
9#13070527C211yesmaximal, characteristic, complemented
10#13070412C211yesmaximal, characteristic, complemented
11C11×#2184C211yesmaximal, characteristic, complemented
12C22×C11×D8C2211yescharacteristic
13C2×#66993—21no—
14C22×#4323—21no—
15C22×D88C2211yescharacteristic
16#10623127—21no—
17C2×C11×D16C2212yescomplemented
18C11×#466C2211yescharacteristic
19#10622764—21no—
20#10622764—21no—
21#10622764C2212yes—
22#10622764C2212yes—
23#10622764C2211yescharacteristic, complemented
24D8×Dic11C2211yescharacteristic, complemented
25C2×#66890C2212yescomplemented
26C2×#66890C2212yescomplemented
27#10622728C2211yescharacteristic
28C2×C8×Dic11C2211yescharacteristic
29#10622651—21no—
30C2×D176C2212yescomplemented
31#10622487C2211yescharacteristic, complemented
32#10622485C2211yescharacteristic, complemented
33#10622373—21no—
34#10622369—21no—
35C11×#357C2212yescomplemented
36C11×C22⋊C16C2211yescharacteristic
37#10622200C2212yescomplemented
38C22⋊(C11⋊C16)C2211yescharacteristic
39#10622147C2212yescomplemented
40Dic11⋊C16C2212yescomplemented
41C16×Dic11C2212yescomplemented
42#10622129C2212yescomplemented
43C22×D4×C11—21no—
44C22×C22⋊D11—41no—
45C22×C22⋊D11—41no—
46C2×#4341—41no—
47C22×D44—21no—
48C2×C11×D8—21no—
49C2×C11×D8—42no—
50C2×C11×D8C2311yescharacteristic
51C2×C11×D8C2312yes—
52C22×C8×C11C2311yescharacteristic
53C11×#121—21no—
54#66993—22no—
55#66993—22no—
56#66993—21no—
57#66993—41no—
58#66993—41no—
59#66992—41no—
60D4×Dic11—21no—
61C2×#4323—22no—
62C2×#4323—22no—
63C2×#4323—21no—
64C2×#4323—44no—
65#66983—21no—
66C2×C4×Dic11D411yescharacteristic
67C22×C11⋊C8D411yescharacteristic
68C2×D88—21no—
69C2×D88—42no—
70C2×D88C2311yescharacteristic
71C2×D88C2312yes—
72#66946—21no—
73#66941—21no—
74#66938—41no—
75(C22⋊D11)⋊C4—41no—
76C11×D16—42no—
77C2×C11×C16C2312yes—
78C11×#107C2311yescharacteristic
79C11×#102—21no—
80#66896—21no—
81#66890—42no—
82#66890—42no—
83#66885—21no—
84#66882C2311yescharacteristic
85C8×Dic11D411yescharacteristic
86C8×Dic11D411yescharacteristic
87C8×Dic11C2311yescharacteristic
88C8×Dic11C2311yescharacteristic
89C2×C11⋊C16C2312yes—
90#66873—21no—
91#66871—21no—
92D176—42no—
93#33771—111nomaximal, Sylow
94C24×C11—41no—
95C23×D11—41no—
96C2×D4×C11—21no—
97C2×D4×C11—22no—
98C2×D4×C11—42no—
99C2×D4×C11—42no—
100C2×D4×C11—41no—
101C2×D4×C11—41no—
102C22×C4×C11C2×D411yescharacteristic
103C2×C22⋊D11—41no—
104C2×C22⋊D11—41no—
105C2×C22⋊D11—42no—
106C2×C22⋊D11—42no—
107C2×C22⋊D11—42no—
108C2×C22⋊D11—42no—
109C2×C22⋊D11—41no—
110C2×C22⋊D11—84no—
111C2×C22⋊D11—84no—
112C22×Dic11—41no—
113C22×Dic11D811yescharacteristic
114C22×Dic11D811yescharacteristic
115#4341—84no—
116C2×D44—21no—
117C2×D44—22no—
118C2×D44—42no—
119C2×D44—42no—
120C2×D44—41no—
121C2×C4×D11—41no—
122C2×Dic22—41no—
123C11×D8—22no—
124C11×D8—22no—
125C11×D8—22no—
126C11×D8—42no—
127C2×C8×C11—22no—
128C2×C8×C11C2×D411yescharacteristic
129C2×C8×C11C2411yescharacteristic
130C11×C4⋊C4—21no—
131C11×C22⋊C4—41no—
132C22⋊Dic11—41no—
133#4323—44no—
134#4323—42no—
135#4323—44no—
136(C2×D11)⋊C4—41no—
137(C2×D11)⋊C4—41no—
138C4⋊Dic11—21no—
139Dic11⋊C4—41no—
140C4×Dic11D811yescharacteristic
141C4×Dic11D811yescharacteristic
142C4×Dic11C2×D411yescharacteristic
143C4×Dic11C2×D411yescharacteristic
144C2×C11⋊C8—22no—
145C2×C11⋊C8C2×D411yescharacteristic
146C2×C11⋊C8C2×D411yescharacteristic
147D88—22no—
148D88—22no—
149D88—22no—
150D88—42no—
151C11×C16—22no—
152C11⋊C16—22no—
153#3169—111no—
154C2×#493—111no—
155#2246—112no—
156#2240—112no—
157#2206—112no—
158#2206—112no—
159#2184—111no—
160#2184—111no—
161#2184—111no—
162#2184D1111yescharacteristic, complemented
163#2162—111no—
164C23×C11—41no—
165C23×C11—42no—
166C23×C11—82no—
167C23×C11—82no—
168C23×C11—82no—
169C23×C11C2×D811yescharacteristic
170C22×D11—41no—
171C22×D11—42no—
172C22×D11—82no—
173C22×D11—82no—
174C22×D11—82no—
175D4×C11—42no—
176D4×C11—41no—
177D4×C11—42no—
178D4×C11—41no—
179D4×C11—82no—
180D4×C11—82no—
181C2×C4×C11—21no—
182C2×C4×C11—21no—
183C2×C4×C11—41no—
184C2×C4×C11C2×D811yescharacteristic
185C2×C4×C11C22×D411yescharacteristic
186C22⋊D11—84no—
187C22⋊D11—82no—
188C22⋊D11—82no—
189C22⋊D11—84no—
190C22⋊D11—84no—
191C22⋊D11—82no—
192C22⋊D11—84no—
193C2×Dic11—22no—
194C2×Dic11—41no—
195C2×Dic11—82no—
196C2×Dic11D1614yescomplemented
197C2×Dic11C2×D811yescharacteristic
198C2×Dic11C2×D811yescharacteristic
199C2×Dic11C2×D811yescharacteristic
200C2×Dic11C2×D811yescharacteristic
201D44—42no—
202D44—41no—
203D44—42no—
204D44—41no—
205D44—82no—
206C4×D11—82no—
207Dic22—82no—
208C8×C11—21no—
209C8×C11H(5,𝔽2)12yes—
210C11⋊C8—21no—
211C11⋊C8AGL(1,ℤ/8)12yes—
212C22×D8—111no—
213C22×D8—221no—
214C22×D8C2×D1111yescharacteristic
215#532—221no—
216C2×#127—221no—
217C2×D16—112no—
218C2×D16—112no—
219C2×D16—112no—
220C2×D16C2×D1112yescomplemented
221#500—111no—
222#493—112no—
223#493—112no—
224#493—111no—
225#493—221no—
226#493—221no—
227#486—221no—
228#466—111no—
229#466—221no—
230#466C2×D1111yescharacteristic
231C4×D8—111no—
232C4×D8—111no—
233C4×D8—221no—
234C2×C4×C8—111no—
235C4⋊C16—112no—
236#357—112no—
237#357—112no—
238#357—112no—
239#357C2×D1112yescomplemented
240C22⋊C16—111no—
241C22⋊C16C2×D1111yescharacteristic
242C4×C16—112no—
243C22×C11—21no—
244C22×C11—21no—
245C22×C11—81no—
246C22×C11—82no—
247C22×C11—82no—
248C22×C11—81no—
249C22×C11—82no—
250C22×C11—81no—
251C22×C11—164no—
252C22×C11C2×D1612yes—
253C22×C11C22×D811yescharacteristic
254C2×D11—82no—
255C2×D11—81no—
256C2×D11—82no—
257C2×D11—81no—
258C2×D11—82no—
259C2×D11—81no—
260C2×D11—164no—
261C4×C11—21no—
262C4×C11—81no—
263C4×C11#53511yescharacteristic
264C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
265Dic11—21no—
266Dic11—81no—
267Dic11C2×D1612yes—
268Dic11C2×D1612yes—
269Dic11#50912yes—
270C2×#41—441no—
271C22×D4—21no—
272C22×D4—221no—
273C22×D4—441no—
274C22×D4—441no—
275C2×D8—21no—
276C2×D8—42no—
277C2×D8—112no—
278C2×D8—111no—
279C2×D8—222no—
280C2×D8—222no—
281C2×D8—221no—
282C2×D8—221no—
283C2×D8—442no—
284C2×D8—444no—
285C2×D8C22×D1112yes—
286C2×D8C22×D1111yescharacteristic
287C22×C8—111no—
288C22×C8C22×D1111yescharacteristic
289C4⋊Q8—221no—
290#127—222no—
291#127—222no—
292#127—221no—
293#127—441no—
294#127—441no—
295#124—441no—
296#121—21no—
297#121—221no—
298#121—441no—
299C4×D4—221no—
300C4×D4—221no—
301C4×D4—441no—
302C2×C42—111no—
303D16—42no—
304D16—442no—
305D16—442no—
306D16—442no—
307C2×C16—112no—
308C2×C16C22×D1112yes—
309#107—111no—
310#107—221no—
311#107C22×D1111yescharacteristic
312#102—21no—
313#102—221no—
314#102—221no—
315#102—221no—
316C4×C8—111no—
317C4×C8—111no—
318C4×C8—111no—
319C4×C8—111no—
320C2×C11—22no—
321C2×C11—161no—
322C2×C11—162no—
323C2×C11#320511yescharacteristic
324C2×C11C22×D1611yescharacteristic
325C2×C11C2×#50911yescharacteristic
326D11—161no—
327D11—162no—
328C24—41no—
329C24—441no—
330#41—884no—
331C2×Q8—441no—
332C2×D4—21no—
333C2×D4—22no—
334C2×D4—42no—
335C2×D4—42no—
336C2×D4—41no—
337C2×D4—41no—
338C2×D4—221no—
339C2×D4—222no—
340C2×D4—442no—
341C2×D4—442no—
342C2×D4—441no—
343C2×D4—441no—
344C2×D4—442no—
345C2×D4—442no—
346C2×D4—442no—
347C2×D4—442no—
348C2×D4—441no—
349C2×D4—441no—
350C2×D4—884no—
351C2×D4—884no—
352C22×C4—111no—
353C22×C4—111no—
354C22×C4—441no—
355C22×C4—441no—
356C22×C4D4×D1111yescharacteristic
357D8—22no—
358D8—22no—
359D8—22no—
360D8—42no—
361D8—222no—
362D8—222no—
363D8—222no—
364D8—442no—
365D8—444no—
366D8—442no—
367D8—444no—
368C2×C8—22no—
369C2×C8—111no—
370C2×C8—111no—
371C2×C8—222no—
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—
384C42—111no—
385C16—22no—
386C16—222no—
387C11#3377111yescharacteristic, complemented, Sylow
388C23—41no—
389C23—42no—
390C23—82no—
391C23—82no—
392C23—82no—
393C23—441no—
394C23—442no—
395C23—882no—
396C23—882no—
397C23—882no—
398C23D8×D1111yescharacteristic
399Q8—882no—
400D4—42no—
401D4—41no—
402D4—42no—
403D4—41no—
404D4—82no—
405D4—82no—
406D4—442no—
407D4—441no—
408D4—442no—
409D4—441no—
410D4—882no—
411D4—884no—
412D4—884no—
413D4—884no—
414D4—882no—
415D4—882no—
416D4—884no—
417D4—882no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—41no—
421C2×C4—111no—
422C2×C4—111no—
423C2×C4—111no—
424C2×C4—114no—
425C2×C4—111no—
426C2×C4—222no—
427C2×C4—441no—
428C2×C4—882no—
429C2×C4—882no—
430C2×C4D8×D1111yescharacteristic
431C2×C4C2×D4×D1111yescharacteristic
432C8—21no—
433C8—112no—
434C8—221no—
435C8#6703712yes—
436C22—21no—
437C22—21no—
438C22—81no—
439C22—82no—
440C22—82no—
441C22—81no—
442C22—82no—
443C22—81no—
444C22—164no—
445C22—881no—
446C22—882no—
447C22—882no—
448C22—881no—
449C22—882no—
450C22—881no—
451C22—1764no—
452C22D11×D1612yes—
453C22C2×D8×D1111yescharacteristic
454C4—21no—
455C4—81no—
456C4—112no—
457C4—112no—
458C4—112no—
459C4—221no—
460C4—881no—
461C4#1062312311yescharacteristic
462C4D11×AGL(1,ℤ/8)11yescharacteristic
463C2—22no—
464C2—162no—
465C2—161no—
466C2—1762no—
467C2—1761no—
468C2#1307953211yescharacteristic
469C2C2×D11×D1611yescharacteristic
470C2D11×#50911yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2184C2
socleC22×C11C22×D8
hypercenter#2184D11
hypocenterC11#33771
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2184

Complements

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

NH ≅ G/Ntype
1. #13079190C2semidirect
2. C2×#10622764C2semidirect
3. #13070864C2semidirect
4. #13070838C2semidirect
5. #13070650C2semidirect
6. #13070649C2semidirect
7. #13070530C2semidirect
8. #13070528C2semidirect
9. #13070527C2semidirect
10. #13070412C2semidirect
11. C11×#2184C2semidirect
17. C2×C11×D16C22semidirect
23. #10622764C22semidirect
24. D8×Dic11C22semidirect
25. C2×#66890C22semidirect
26. C2×#66890C22semidirect
30. C2×D176C22semidirect
31. #10622487C22semidirect
32. #10622485C22semidirect
35. C11×#357C22semidirect
37. #10622200C22semidirect
39. #10622147C22semidirect
40. Dic11⋊C16C22semidirect
41. C16×Dic11C22semidirect
42. #10622129C22semidirect
162. #2184D11semidirect
196. C2×Dic11D16semidirect
220. C2×D16C2×D11semidirect
239. #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
#130791902
C2×#106227642
#130708642
#130708382
#130706502
#130706492
#130705302
#130705282
#130705272
#130704122
C11×#21842
#3377111