Finite Group Databasebeta

← #14909847

Subgroups — #14909847

Order 2816.

606 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079255C211yesmaximal, characteristic, complemented
2#13079102C211yesmaximal, characteristic, complemented
3#13070882C211yesmaximal, characteristic, complemented
4#13070877C211yesmaximal, characteristic, complemented
5#13070853C211yesmaximal, characteristic, complemented
6#13070840C211yesmaximal, characteristic, complemented
7#13070679C211yesmaximal, characteristic, complemented
8#13070672C211yesmaximal, characteristic, complemented
9#13070657C211yesmaximal, characteristic, complemented
10#13070652C211yesmaximal, characteristic, complemented
11#13070558C211yesmaximal, characteristic, complemented
12#13070547C211yesmaximal, characteristic, complemented
13#13070541C211yesmaximal, characteristic, complemented
14#13070530C211yesmaximal, characteristic, complemented
15C11×#2164C211yesmaximal, characteristic, complemented
16C2×#66961—21no—
17C2×#66957C2211yescharacteristic
18C22×D88C2211yescharacteristic
19#10623065—21no—
20#10623056—21no—
21C11×#405C2211yescharacteristic
22#10622747—21no—
23#10622729C2211yescharacteristic
24#10622728C2211yescharacteristic
25C2×Dic88C2211yescharacteristic, complemented
26C2×#66864C2211yescharacteristic
27C2×#66864C2211yescharacteristic
28C2×#66864C2211yescharacteristic, complemented
29C2×#66864C2211yescharacteristic, complemented
30C2×D176C2211yescharacteristic
31C2×D176C2211yescharacteristic
32C2×D176C2211yescharacteristic, complemented
33#10622327—21no—
34#10622325—21no—
35#10622325—21no—
36#10622323—21no—
37C4×Dic44C2211yescharacteristic, complemented
38#10622309C2211yescharacteristic
39#10622309C2211yescharacteristic
40#10622309C2211yescharacteristic, complemented
41#10622308C2211yescharacteristic
42#10622308C2211yescharacteristic
43C4×D88C2211yescharacteristic, complemented
44#10622295C2211yescharacteristic, complemented
45C11×C4⋊C16C2211yescharacteristic, complemented
46C11×C4⋊C16C2211yescharacteristic, complemented
47C11×C22⋊C16C2211yescharacteristic
48C11×C22⋊C16C2211yescharacteristic
49C11×#346C2211yescharacteristic, complemented
50C4×C11×C16C2211yescharacteristic, complemented
51#10622147C2211yescharacteristic
52#10622147C2211yescharacteristic
53#10622147C2211yescharacteristic
54#10622147C2211yescharacteristic
55#10622147C2211yescharacteristic, complemented
56#10622147C2211yescharacteristic, complemented
57#10622141C2211yescharacteristic, complemented
58#10622141C2211yescharacteristic, complemented
59C2×#4339—21no—
60C22×D44—21no—
61C2×C11×M16D411yescharacteristic
62C22×C8×C11C2311yescharacteristic
63C11×#117D411yescharacteristic
64#66983—21no—
65#66977—21no—
66#66961—44no—
67C2×Dic44C2311yescharacteristic
68C2×Dic44C2311yescharacteristic
69#66957—41no—
70#66957—41no—
71C2×D88—21no—
72C2×D88—21no—
73C2×D88—21no—
74C2×D88—41no—
75C2×D88—41no—
76C2×D88C2311yescharacteristic
77C2×D88C2311yescharacteristic
78C2×D88C2311yescharacteristic
79C2×D88C2311yescharacteristic
80C2×#4314—21no—
81C2×#4314—21no—
82C2×#4314—21no—
83C2×#4314—21no—
84#66951—41no—
85#66949—41no—
86#66948—41no—
87#66948—41no—
88#66938—41no—
89#66936—41no—
90#66935—41no—
91#66935—41no—
92#66928—21no—
93#66928—21no—
94#66928—21no—
95#66927—21no—
96#66927—21no—
97C4×D44—21no—
98#66922—21no—
99C4×Dic22—21no—
100C2×C11×C16C2311yescharacteristic
101C2×C11×C16C2311yescharacteristic
102C2×C11×C16C2311yescharacteristic
103C2×C11×C16C2311yescharacteristic
104C11×#97D411yescharacteristic
105C11×#97D411yescharacteristic
106C4×C8×C11C2311yescharacteristic
107C4×C8×C11C2311yescharacteristic
108#66885—21no—
109#66885—21no—
110#66882—21no—
111#66882C2311yescharacteristic
112#66882C2311yescharacteristic
113#66880—21no—
114#66880—21no—
115Dic88—41no—
116#66864—41no—
117#66864—41no—
118#66864—41no—
119#66864—41no—
120D176—41no—
121D176—41no—
122D176—41no—
123#33790—111nomaximal, Sylow
124C23×D11—41no—
125C22×C4×C11C2×D411yescharacteristic
126C2×C22⋊D11—41no—
127C2×C22⋊D11—41no—
128#4339—42no—
129#4339—42no—
130C2×D44—21no—
131C2×D44—21no—
132C2×D44—21no—
133C2×D44—21no—
134C2×D44—42no—
135C2×D44—42no—
136C2×D44—41no—
137C2×D44—41no—
138C2×D44—41no—
139C2×D44—41no—
140C2×D44—41no—
141C2×C4×D11—41no—
142C2×C4×D11—41no—
143C2×Dic22—21no—
144C2×Dic22—21no—
145C2×Dic22—41no—
146C11×M16—22no—
147C2×C8×C11—21no—
148C2×C8×C11—21no—
149C2×C8×C11C2×D411yescharacteristic
150C2×C8×C11C2×D411yescharacteristic
151C2×C8×C11C2×D411yescharacteristic
152C2×C8×C11C2411yescharacteristic
153C11×C4⋊C4D811yescharacteristic
154C11×C4⋊C4D811yescharacteristic
155C11×C22⋊C4D811yescharacteristic
156C11×C22⋊C4D811yescharacteristic
157C42×C11C2×D411yescharacteristic
158C42×C11C2×D411yescharacteristic
159C22⋊Dic11—41no—
160(C2×D11)⋊C4—41no—
161(C2×D11)⋊C4—41no—
162(C2×D11)⋊C4—41no—
163(C2×D11)⋊C4—41no—
164(C2×D11)⋊C4—41no—
165(C2×D11)⋊C4—41no—
166(C2×D11)⋊C4—41no—
167(C2×D11)⋊C4—41no—
168C4⋊Dic11—21no—
169C4⋊Dic11—21no—
170C4⋊Dic11—41no—
171Dic11⋊C4—41no—
172Dic11⋊C4—41no—
173C4×Dic11—41no—
174Dic44—21no—
175Dic44—21no—
176Dic44—21no—
177Dic44—21no—
178D88—21no—
179D88—21no—
180D88—21no—
181D88—21no—
182D88—21no—
183D88—21no—
184D88—21no—
185D88—21no—
186D88—42no—
187D88—42no—
188D88—42no—
189#4314—42no—
190#4314—42no—
191#4314—42no—
192#4314—42no—
193C11×C16—21no—
194C11×C16—21no—
195C11×C16—21no—
196C11×C16—21no—
197#3175—111no—
198#3155—111no—
199#2250—111no—
200#2249—111no—
201#2243—111no—
202#2240—111no—
203#2211—111no—
204#2210—111no—
205#2207—111no—
206#2206—111no—
207#2189—111no—
208#2187—111no—
209#2186—111no—
210#2184—111no—
211#2164D1111yescharacteristic, complemented
212C23×C11C2×D811yescharacteristic
213C22×D11—41no—
214C22×D11—41no—
215C22×D11—41no—
216C22×D11—41no—
217C22×D11—82no—
218C22×D11—161no—
219C22×D11—161no—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11C2×D811yescharacteristic
223C2×C4×C11C2×D811yescharacteristic
224C2×C4×C11C2×D811yescharacteristic
225C2×C4×C11C2×D811yescharacteristic
226C2×C4×C11C2×D811yescharacteristic
227C2×C4×C11C22×D411yescharacteristic
228C22⋊D11—82no—
229C22⋊D11—161no—
230C2×Dic11—41no—
231C2×Dic11—41no—
232C2×Dic11—41no—
233C2×Dic11—41no—
234D44—41no—
235D44—41no—
236D44—41no—
237D44—41no—
238D44—41no—
239D44—41no—
240D44—41no—
241D44—41no—
242D44—82no—
243D44—161no—
244D44—161no—
245D44—161no—
246D44—161no—
247C4×D11—82no—
248C4×D11—161no—
249Dic22—41no—
250Dic22—41no—
251Dic22—41no—
252Dic22—41no—
253Dic22—161no—
254C8×C11—21no—
255C8×C11—21no—
256C8×C11AGL(1,ℤ/8)12yes—
257C8×C11H(5,𝔽2)11yescharacteristic
258C8×C11H(5,𝔽2)11yescharacteristic
259C2×AGL(1,ℤ/8)—221no—
260C2×#135—111no—
261C22×D8—111no—
262#542—221no—
263#535—221no—
264C2×Q32—111no—
265C2×SD32—111no—
266C2×SD32—111no—
267C2×SD32—111no—
268C2×SD32—111no—
269C2×D16—111no—
270C2×D16—111no—
271C2×D16—111no—
272#500—111no—
273#496—221no—
274#496—221no—
275#495—111no—
276#495—111no—
277#495—111no—
278#493—111no—
279#493—111no—
280#489—221no—
281#468—221no—
282#467—111no—
283#466—111no—
284#440—221no—
285C4×Q16—111no—
286C4×D8—111no—
287#405C2×D1111yescharacteristic
288C4⋊C16C2×D1111yescharacteristic, complemented
289C4⋊C16C2×D1111yescharacteristic, complemented
290#358—111no—
291#358—111no—
292#357—111no—
293#357—111no—
294#357—111no—
295#357—111no—
296#357—111no—
297#357—111no—
298C22⋊C16C2×D1111yescharacteristic
299C22⋊C16C2×D1111yescharacteristic
300#346C2×D1111yescharacteristic, complemented
301C4×C16C2×D1111yescharacteristic, complemented
302C22×C11—21no—
303C22×C11—21no—
304C22×C11—21no—
305C22×C11C22×D811yescharacteristic
306C2×D11—81no—
307C2×D11—81no—
308C2×D11—81no—
309C2×D11—81no—
310C2×D11—81no—
311C2×D11—81no—
312C2×D11—81no—
313C2×D11—81no—
314C2×D11—81no—
315C2×D11—81no—
316C2×D11—81no—
317C2×D11—81no—
318C2×D11—164no—
319C4×C11—21no—
320C4×C11—21no—
321C4×C11—21no—
322C4×C11—21no—
323C4×C11—21no—
324C4×C11#53511yescharacteristic
325C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
326Dic11—81no—
327Dic11—81no—
328Dic11—81no—
329Dic11—81no—
330C2×#41—221no—
331C22×D4—221no—
332AGL(1,ℤ/8)—444no—
333#135—441no—
334#135—441no—
335C2×Q16—111no—
336C2×Q16—111no—
337C2×SD16—221no—
338C2×SD16—221no—
339C2×SD16—221no—
340C2×SD16—221no—
341C2×D8—111no—
342C2×D8—111no—
343C2×D8—111no—
344C2×D8—111no—
345C2×D8—221no—
346C2×D8—221no—
347C2×D8—221no—
348C2×D8—441no—
349C2×D8—441no—
350C2×M16D4411yescharacteristic
351C22×C8C22×D1111yescharacteristic
352C4⋊Q8—221no—
353#127—221no—
354#127—221no—
355#126—441no—
356#124—221no—
357#124—221no—
358#124—221no—
359#124—441no—
360#123—441no—
361C22⋊Q8—221no—
362C22⋊Q8—441no—
363#121—221no—
364#121—441no—
365#121—441no—
366#120—441no—
367#120—441no—
368C4×Q8—221no—
369C4×D4—221no—
370#117D4411yescharacteristic
371Q32—441no—
372SD32—441no—
373SD32—441no—
374SD32—441no—
375SD32—441no—
376D16—441no—
377D16—441no—
378D16—441no—
379C2×C16C22×D1111yescharacteristic
380C2×C16C22×D1111yescharacteristic
381C2×C16C22×D1111yescharacteristic
382C2×C16C22×D1111yescharacteristic
383#107—111no—
384#107—111no—
385#107—221no—
386#103—221no—
387#103—221no—
388#102—221no—
389#102—221no—
390#97D4411yescharacteristic
391#97D4411yescharacteristic
392C4×C8C22×D1111yescharacteristic
393C4×C8C22×D1111yescharacteristic
394C2×C11—41no—
395C2×C11#320511yescharacteristic
396C2×C11#341511yescharacteristic
397C2×C11#341611yescharacteristic
398D11—161no—
399D11—161no—
400D11—161no—
401D11—161no—
402C24—441no—
403#41—442no—
404#41—442no—
405C2×Q8—221no—
406C2×Q8—221no—
407C2×Q8—441no—
408C2×D4—221no—
409C2×D4—221no—
410C2×D4—221no—
411C2×D4—221no—
412C2×D4—442no—
413C2×D4—442no—
414C2×D4—441no—
415C2×D4—441no—
416C2×D4—441no—
417C2×D4—441no—
418C2×D4—441no—
419C2×D4—441no—
420C2×D4—441no—
421C22×C4—441no—
422C22×C4—441no—
423C22×C4C2×D4411yescharacteristic
424Q16—221no—
425Q16—221no—
426Q16—221no—
427Q16—221no—
428SD16—442no—
429SD16—442no—
430SD16—442no—
431SD16—442no—
432D8—221no—
433D8—221no—
434D8—221no—
435D8—221no—
436D8—221no—
437D8—221no—
438D8—221no—
439D8—221no—
440D8—442no—
441D8—442no—
442D8—442no—
443M16—22no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8C2×D4411yescharacteristic
447C2×C8C2×D4411yescharacteristic
448C2×C8C2×D4411yescharacteristic
449C2×C8C23×D1111yescharacteristic
450C4⋊C4—221no—
451C4⋊C4—221no—
452C4⋊C4—441no—
453C4⋊C4—441no—
454C4⋊C4—441no—
455C4⋊C4D8811yescharacteristic
456C4⋊C4D8811yescharacteristic
457C22⋊C4—441no—
458C22⋊C4—441no—
459C22⋊C4—441no—
460C22⋊C4—441no—
461C22⋊C4—441no—
462C22⋊C4—441no—
463C22⋊C4—441no—
464C22⋊C4—441no—
465C22⋊C4—441no—
466C22⋊C4D8811yescharacteristic
467C22⋊C4D8811yescharacteristic
468C42—441no—
469C42C2×D4411yescharacteristic
470C42C2×D4411yescharacteristic
471C16—21no—
472C16—21no—
473C16—21no—
474C16—21no—
475C11#3379011yescharacteristic, complemented, Sylow
476C23—441no—
477C23—441no—
478C23—441no—
479C23—441no—
480C23—882no—
481C23—1761no—
482C23—1761no—
483C23C2×D8811yescharacteristic
484Q8—441no—
485Q8—441no—
486Q8—441no—
487Q8—441no—
488Q8—1761no—
489D4—441no—
490D4—441no—
491D4—441no—
492D4—441no—
493D4—441no—
494D4—441no—
495D4—441no—
496D4—441no—
497D4—882no—
498D4—882no—
499D4—1761no—
500D4—1761no—
501D4—1761no—
502D4—1761no—
503D4—1761no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—441no—
507C2×C4—441no—
508C2×C4—441no—
509C2×C4—441no—
510C2×C4—882no—
511C2×C4—1761no—
512C2×C4C2×D8811yescharacteristic
513C2×C4C2×D8811yescharacteristic
514C2×C4C2×D8811yescharacteristic
515C2×C4C2×D8811yescharacteristic
516C2×C4C2×D8811yescharacteristic
517C2×C4C22×D4411yescharacteristic
518C8—21no—
519C8—21no—
520C8#6696112yes—
521C8#6704211yescharacteristic
522C8#6704211yescharacteristic
523C22—21no—
524C22—21no—
525C22—21no—
526C22—881no—
527C22—881no—
528C22—881no—
529C22—881no—
530C22—881no—
531C22—881no—
532C22—881no—
533C22—881no—
534C22—881no—
535C22—881no—
536C22—881no—
537C22—881no—
538C22—1764no—
539C22C22×D8811yescharacteristic
540C4—21no—
541C4—21no—
542C4—21no—
543C4—21no—
544C4—21no—
545C4—881no—
546C4—881no—
547C4—881no—
548C4—881no—
549C4#1062305611yescharacteristic
550C4C2×#6696111yescharacteristic
551C2—41no—
552C2—1761no—
553C2—1761no—
554C2—1761no—
555C2—1761no—
556C2#1307953611yescharacteristic
557C2#1308175711yescharacteristic
558C2#1308176411yescharacteristic
subgroupG/H
centerC22C22×D88
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2164C2
socleC22×C11C22×D8
hypercenter#2164D11
hypocenterC11#33790
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #117 ◁ #405 ◁ #2164

Complements

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

NH ≅ G/Ntype
1. #13079255C2semidirect
2. #13079102C2semidirect
3. #13070882C2semidirect
4. #13070877C2semidirect
5. #13070853C2semidirect
6. #13070840C2semidirect
7. #13070679C2semidirect
8. #13070672C2semidirect
9. #13070657C2semidirect
10. #13070652C2semidirect
11. #13070558C2semidirect
12. #13070547C2semidirect
13. #13070541C2semidirect
14. #13070530C2semidirect
15. C11×#2164C2semidirect
25. C2×Dic88C22semidirect
28. C2×#66864C22semidirect
29. C2×#66864C22semidirect
32. C2×D176C22semidirect
37. C4×Dic44C22semidirect
40. #10622309C22semidirect
43. C4×D88C22semidirect
44. #10622295C22semidirect
45. C11×C4⋊C16C22semidirect
46. C11×C4⋊C16C22semidirect
49. C11×#346C22semidirect
50. C4×C11×C16C22semidirect
55. #10622147C22semidirect
56. #10622147C22semidirect
57. #10622141C22semidirect
58. #10622141C22semidirect
211. #2164D11semidirect
288. C4⋊C16C2×D11semidirect
289. C4⋊C16C2×D11semidirect
300. #346C2×D11semidirect
301. C4×C16C2×D11semidirect
475. C11#33790semidirect

Maximal subgroups

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

subgroupindex
#130792552
#130791022
#130708822
#130708772
#130708532
#130708402
#130706792
#130706722
#130706572
#130706522
#130705582
#130705472
#130705412
#130705302
C11×#21642
#3379011