Finite Group Databasebeta

← #14908258

Subgroups — #14908258

Order 2816.

686 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622528C211yesmaximal, characteristic, complemented
2C22×#66862C211yesmaximal, characteristic, complemented
3#13078195C211yesmaximal, characteristic
4D11×#467C211yesmaximal, characteristic, complemented
5#13070728C211yesmaximal, characteristic, complemented
6#13070726C211yesmaximal, characteristic, complemented
7#13070725C211yesmaximal, characteristic, complemented
8#13070723C211yesmaximal, characteristic, complemented
9#13070710C211yesmaximal, characteristic, complemented
10#13070707C211yesmaximal, characteristic, complemented
11#13070705C211yesmaximal, characteristic, complemented
12#13070403C211yesmaximal, characteristic, complemented
13#13070334C211yesmaximal, characteristic, complemented
14#13070325C211yesmaximal, characteristic, complemented
15C11×#2217C211yesmaximal, characteristic, complemented
16C2×Q16×D11C2211yescharacteristic
17C2×#66965C2211yescharacteristic
18C22×C8×D11C2211yescharacteristic
19D11×C22⋊Q8—21no—
20#10623137—21no—
21C2×C11×SD32C2211yescharacteristic, complemented
22C22×C11×C16C2211yescharacteristic
23C11×#467C2211yescharacteristic
24C11×#466C2211yescharacteristic
25#10622801C2211yescharacteristic
26C2×#66893C2211yescharacteristic, complemented
27#10622770C2211yescharacteristic
28C2×#66891C2211yescharacteristic, complemented
29#10622729C2211yescharacteristic
30#10622729C2211yescharacteristic
31C22×C11⋊C16C2211yescharacteristic
32#10622664—21no—
33#10622654—21no—
34#10622528—24no—
35C2×Dic88C2211yescharacteristic, complemented
36C2×#66862—24no—
37C2×#66862C2211yescharacteristic
38C2×#66862C2211yescharacteristic
39C2×#66862C2211yescharacteristic
40C2×#66862C2211yescharacteristic
41#10622500C2211yescharacteristic
42#10622500C2211yescharacteristic
43#10622493C2211yescharacteristic
44D11×#107C2211yescharacteristic
45#10622426—21no—
46D11×#103—21no—
47#10622391—21no—
48#10622385—21no—
49C11×#367C2211yescharacteristic, complemented
50C11×#358C2211yescharacteristic, complemented
51C11×#357C2211yescharacteristic, complemented
52#10622202C2211yescharacteristic, complemented
53#10622200C2211yescharacteristic, complemented
54#10622142C2211yescharacteristic, complemented
55#10622141C2211yescharacteristic, complemented
56#10622141C2211yescharacteristic, complemented
57#10622130C2211yescharacteristic, complemented
58#10622130C2211yescharacteristic, complemented
59#10622128C2211yescharacteristic, complemented
60#10622127C2211yescharacteristic, complemented
61C2×Q8×D11—21no—
62C2×#4341—21no—
63C22×C4×D11D411yescharacteristic
64C2×C11×Q16C2311yescharacteristic
65C2×C11×D8C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C11×C22⋊Q8—21no—
68C11×#121—21no—
69#66999—21no—
70C2×#4326—21no—
71#66991—21no—
72#66990—41no—
73D4×Dic11—41no—
74C2×#4324—21no—
75#66977—21no—
76#66977—21no—
77C22×C11⋊C8D411yescharacteristic
78Q16×D11—22no—
79Q16×D11—22no—
80#66965—22no—
81#66965—22no—
82C2×Dic44C2311yescharacteristic
83C2×Dic44C2311yescharacteristic
84C2×C8×D11—22no—
85C2×C8×D11—22no—
86C2×C8×D11D411yescharacteristic
87C2×C8×D11D411yescharacteristic
88C2×C8×D11C2311yescharacteristic
89C2×C8×D11C2311yescharacteristic
90#66950—21no—
91#66950—21no—
92#66949—41no—
93#66945—21no—
94C4⋊C4×D11—21no—
95C4⋊C4×D11—41no—
96#66936—41no—
97(C22⋊D11)⋊C4—41no—
98C22⋊C4×D11—41no—
99#66931—41no—
100C11×SD32—22no—
101C2×C11×C16—22no—
102C2×C11×C16C2311yescharacteristic
103C2×C11×C16C2311yescharacteristic
104C11×#107C2311yescharacteristic
105C11×#107C2311yescharacteristic
106C11×#103—21no—
107C11×#102—21no—
108#66899—21no—
109#66896—21no—
110#66893—22no—
111#66891—22no—
112#66882C2311yescharacteristic
113#66882C2311yescharacteristic
114#66880—21no—
115#66880—21no—
116C2×C11⋊C16—22no—
117C2×C11⋊C16C2311yescharacteristic
118C2×C11⋊C16C2311yescharacteristic
119#66874—21no—
120#66874—21no—
121#66872—21no—
122#66871—21no—
123Dic88—22no—
124#66862—22no—
125#66862—22no—
126#66862—22no—
127#66862D414yescomplemented
128#33606—111nomaximal, Sylow
129C23×D11D811yescharacteristic
130C2×Q8×C11—21no—
131C2×D4×C11—21no—
132C2×D4×C11—41no—
133C22×C4×C11C2×D411yescharacteristic
134C2×C22⋊D11—41no—
135C2×C22⋊D11—41no—
136C22×Dic11—41no—
137C22×Dic11D811yescharacteristic
138Q8×D11—42no—
139Q8×D11—42no—
140#4341—42no—
141#4341—42no—
142C2×C4×D11—22no—
143C2×C4×D11—22no—
144C2×C4×D11—41no—
145C2×C4×D11—41no—
146C2×C4×D11D811yescharacteristic
147C2×C4×D11D811yescharacteristic
148C2×C4×D11C2×D411yescharacteristic
149C2×C4×D11C2×D411yescharacteristic
150C2×Dic22—21no—
151C2×Dic22—21no—
152C2×Dic22—41no—
153C11×Q16—21no—
154C11×Q16—21no—
155C11×D8—21no—
156C11×D8—21no—
157C2×C8×C11—21no—
158C2×C8×C11—21no—
159C2×C8×C11C2×D411yescharacteristic
160C2×C8×C11C2411yescharacteristic
161C11×C4⋊C4—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—41no—
164C11×C22⋊C4—41no—
165C11×C22⋊C4—41no—
166C22⋊Dic11—41no—
167C22⋊Dic11—41no—
168C22⋊Dic11—41no—
169#4326—42no—
170#4324—42no—
171(C2×D11)⋊C4—41no—
172(C2×D11)⋊C4—41no—
173(C2×D11)⋊C4—41no—
174(C2×D11)⋊C4—41no—
175C4⋊Dic11—21no—
176C4⋊Dic11—21no—
177C4⋊Dic11—41no—
178C4⋊Dic11—41no—
179Dic11⋊C4—41no—
180Dic11⋊C4—41no—
181Dic11⋊C4—41no—
182Dic11⋊C4—41no—
183C4×Dic11—41no—
184C2×C11⋊C8—22no—
185C2×C11⋊C8C2×D411yescharacteristic
186C2×C11⋊C8C2×D411yescharacteristic
187Dic44—21no—
188Dic44—21no—
189Dic44—21no—
190Dic44—21no—
191C8×D11—22no—
192C8×D11—21no—
193C8×D11—21no—
194C8×D11—22no—
195C8×D11C2×D412yes—
196C8×D11#4112yes—
197C11×C16—21no—
198C11×C16C2×D412yes—
199C11⋊C16—21no—
200C11⋊C16C2×D412yes—
201C2×#510—111no—
202C22×M32—111no—
203#3050—111no—
204C2×#467—111no—
205#2220—111no—
206#2220—111no—
207#2219—111no—
208#2219—111no—
209#2217—111no—
210#2217D1111yescharacteristic, complemented
211#2216—111no—
212#2216—111no—
213#2159—111no—
214#2141—111no—
215#2139—111no—
216C23×C11—41no—
217C23×C11C2×D811yescharacteristic
218C22×D11—22no—
219C22×D11—22no—
220C22×D11—41no—
221C22×D11C2×D811yescharacteristic
222C22×D11C2×D811yescharacteristic
223Q8×C11—41no—
224Q8×C11—41no—
225D4×C11—41no—
226D4×C11—41no—
227D4×C11—82no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—41no—
231C2×C4×C11—41no—
232C2×C4×C11—41no—
233C2×C4×C11C2×D811yescharacteristic
234C2×C4×C11C22×D411yescharacteristic
235C22⋊D11—82no—
236C22⋊D11—82no—
237C2×Dic11—22no—
238C2×Dic11—41no—
239C2×Dic11—41no—
240C2×Dic11—41no—
241C2×Dic11—41no—
242C2×Dic11—82no—
243C2×Dic11C2×D811yescharacteristic
244C2×Dic11C2×D811yescharacteristic
245C4×D11—22no—
246C4×D11—21no—
247C4×D11—21no—
248C4×D11—22no—
249C4×D11—82no—
250C4×D11—82no—
251C4×D11#12112yes—
252C4×D11#13512yes—
253Dic22—41no—
254Dic22—41no—
255Dic22—41no—
256Dic22—41no—
257Dic22—82no—
258C8×C11—21no—
259C8×C11C22×D411yescharacteristic
260C8×C11C2×#4111yescharacteristic
261C11⋊C8—21no—
262C11⋊C8#12112yes—
263C2×#135—111no—
264C22×Q16—111no—
265C23×C8—111no—
266#525—221no—
267C2×C22⋊Q8—221no—
268#510—224no—
269C2×Q32—111no—
270C2×Q32—111no—
271C2×SD32—111no—
272C2×SD32C2×D1111yescharacteristic, complemented
273C2×M32—111no—
274C2×M32—111no—
275C2×M32—111no—
276C2×M32—111no—
277C2×M32—224no—
278C22×C16—111no—
279C22×C16C2×D1111yescharacteristic
280#467—111no—
281#467—111no—
282#467—111no—
283#467—111no—
284#467—111no—
285#467—221no—
286#467—221no—
287#467C2×D1111yescharacteristic
288#466—111no—
289#466C2×D1111yescharacteristic
290#465—221no—
291#465—221no—
292#427—111no—
293C2×#107—111no—
294#416—221no—
295C2×#103—221no—
296#367—111no—
297#367C2×D1111yescharacteristic, complemented
298#366—111no—
299#366—111no—
300#358—111no—
301#358—111no—
302#358—111no—
303#358—111no—
304#358—111no—
305#358C2×D1111yescharacteristic, complemented
306#357—111no—
307#357C2×D1111yescharacteristic, complemented
308C22×C11—21no—
309C22×C11—21no—
310C22×C11—81no—
311C22×C11—81no—
312C22×C11—81no—
313C22×C11#51012yescomplemented
314C22×C11C22×D811yescharacteristic
315C2×D11—21no—
316C2×D11—21no—
317C2×D11—21no—
318C2×D11—21no—
319C2×D11—21no—
320C2×D11—44no—
321C2×D11#46612yes—
322C4×C11—21no—
323C4×C11—81no—
324C4×C11—81no—
325C4×C11—81no—
326C4×C11C2×#12111yescharacteristic
327C4×C11C2×#13511yescharacteristic
328Dic11—21no—
329Dic11—81no—
330Dic11—81no—
331Dic11—81no—
332Dic11—81no—
333Dic11#46612yes—
334C2×#41—221no—
335C22×Q8—221no—
336C23×C4—111no—
337#135—222no—
338#135—222no—
339C2×Q16—111no—
340C2×Q16—111no—
341C2×Q16—222no—
342C2×Q16—222no—
343C2×Q16—221no—
344C2×Q16C22×D1111yescharacteristic
345C2×SD16—221no—
346C2×D8C22×D1111yescharacteristic
347C22×C8—111no—
348C22×C8—111no—
349C22×C8—111no—
350C22×C8—111no—
351C22×C8—111no—
352C22×C8—222no—
353C22×C8—222no—
354C22×C8C22×D1111yescharacteristic
355#123—441no—
356C22⋊Q8—21no—
357C22⋊Q8—221no—
358C22⋊Q8—221no—
359C22⋊Q8—221no—
360C22⋊Q8—221no—
361C22⋊Q8—221no—
362C22⋊Q8—441no—
363C22⋊Q8—441no—
364#121—21no—
365#121—221no—
366#120—441no—
367C4×D4—441no—
368C4×D4—441no—
369#117—221no—
370C2×C4⋊C4—221no—
371C2×C4⋊C4—441no—
372C2×C22⋊C4—441no—
373Q32—222no—
374Q32—222no—
375SD32—22no—
376SD32—222no—
377M32—114no—
378M32—222no—
379M32—222no—
380M32—222no—
381C2×C16—22no—
382C2×C16—111no—
383C2×C16—111no—
384C2×C16—222no—
385C2×C16C22×D1111yescharacteristic
386C2×C16C22×D1111yescharacteristic
387#107—111no—
388#107—111no—
389#107—221no—
390#107C22×D1111yescharacteristic
391#107C22×D1111yescharacteristic
392#106—221no—
393#103—21no—
394#103—221no—
395#103—221no—
396#103—221no—
397#103—221no—
398#103—221no—
399#102—21no—
400#102—221no—
401C2×C11—22no—
402C2×C11—161no—
403C2×C11C2×#46611yescharacteristic
404C2×C11C2×#51011yescharacteristic
405C2×C11#341411yescharacteristic
406D11—22no—
407D11—41no—
408C24—111no—
409#41—442no—
410#41—442no—
411C2×Q8—21no—
412C2×Q8—221no—
413C2×Q8—221no—
414C2×Q8—441no—
415C2×Q8—442no—
416C2×Q8—442no—
417C2×D4—21no—
418C2×D4—41no—
419C2×D4—441no—
420C2×D4—441no—
421C22×C4—111no—
422C22×C4—111no—
423C22×C4—111no—
424C22×C4—111no—
425C22×C4—111no—
426C22×C4—222no—
427C22×C4—222no—
428C22×C4—441no—
429C22×C4—441no—
430C22×C4—441no—
431C22×C4D4×D1111yescharacteristic
432Q16—21no—
433Q16—21no—
434Q16—221no—
435Q16—221no—
436Q16—221no—
437Q16—221no—
438Q16—442no—
439SD16—442no—
440D8—21no—
441D8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—111no—
445C2×C8—112no—
446C2×C8—112no—
447C2×C8—111no—
448C2×C8—222no—
449C2×C8—222no—
450C2×C8—222no—
451C2×C8—221no—
452C2×C8—221no—
453C2×C8D4×D1111yescharacteristic
454C2×C8C23×D1111yescharacteristic
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—41no—
458C4⋊C4—221no—
459C4⋊C4—221no—
460C4⋊C4—441no—
461C4⋊C4—441no—
462C4⋊C4—441no—
463C4⋊C4—441no—
464C4⋊C4—441no—
465C4⋊C4—441no—
466C22⋊C4—41no—
467C22⋊C4—41no—
468C22⋊C4—441no—
469C22⋊C4—441no—
470C22⋊C4—441no—
471C22⋊C4—441no—
472C22⋊C4—441no—
473C22⋊C4—441no—
474C22⋊C4—441no—
475C42—441no—
476C16—21no—
477C16—112no—
478C16—221no—
479C16D4×D1112yes—
480C11#3360611yescharacteristic, complemented, Sylow
481C23—41no—
482C23—111no—
483C23—111no—
484C23—222no—
485C23—222no—
486C23—441no—
487C23D8×D1111yescharacteristic
488Q8—41no—
489Q8—41no—
490Q8—441no—
491Q8—441no—
492Q8—441no—
493Q8—441no—
494Q8—882no—
495D4—41no—
496D4—41no—
497D4—82no—
498D4—882no—
499D4—882no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—111no—
506C2×C4—112no—
507C2×C4—112no—
508C2×C4—111no—
509C2×C4—222no—
510C2×C4—222no—
511C2×C4—222no—
512C2×C4—221no—
513C2×C4—221no—
514C2×C4—441no—
515C2×C4—441no—
516C2×C4—441no—
517C2×C4—441no—
518C2×C4—882no—
519C2×C4—882no—
520C2×C4—882no—
521C2×C4D8×D1111yescharacteristic
522C2×C4C2×D4×D1111yescharacteristic
523C8—21no—
524C8—112no—
525C8—221no—
526C8C2×D4×D1111yescharacteristic
527C8#41×D1111yescharacteristic
528C22—21no—
529C22—21no—
530C22—81no—
531C22—81no—
532C22—81no—
533C22—112no—
534C22—221no—
535C22—221no—
536C22—221no—
537C22—221no—
538C22—221no—
539C22—444no—
540C22#1062252812yescomplemented
541C22C2×D8×D1111yescharacteristic
542C4—21no—
543C4—81no—
544C4—81no—
545C4—81no—
546C4—112no—
547C4—221no—
548C4—881no—
549C4—881no—
550C4—881no—
551C4—881no—
552C4D11×#12111yescharacteristic
553C4D11×#13511yescharacteristic
554C2—22no—
555C2—161no—
556C2—222no—
557C2—441no—
558C2D11×#46611yescharacteristic
559C2C2×#1062252811yescharacteristic
560C2#1308174911yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2217C2
socleC22×C11C22×D8
prime radical#13078195C2
hypercenter#2217D11
hypocenterC11#33606
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2217

Complements

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

NH ≅ G/Ntype
1. C2×#10622528C2semidirect
2. C22×#66862C2semidirect
4. D11×#467C2semidirect
5. #13070728C2semidirect
6. #13070726C2semidirect
7. #13070725C2semidirect
8. #13070723C2semidirect
9. #13070710C2semidirect
10. #13070707C2semidirect
11. #13070705C2semidirect
12. #13070403C2semidirect
13. #13070334C2semidirect
14. #13070325C2semidirect
15. C11×#2217C2semidirect
21. C2×C11×SD32C22semidirect
26. C2×#66893C22semidirect
28. C2×#66891C22semidirect
35. C2×Dic88C22semidirect
49. C11×#367C22semidirect
50. C11×#358C22semidirect
51. C11×#357C22semidirect
52. #10622202C22semidirect
53. #10622200C22semidirect
54. #10622142C22semidirect
55. #10622141C22semidirect
56. #10622141C22semidirect
57. #10622130C22semidirect
58. #10622130C22semidirect
59. #10622128C22semidirect
60. #10622127C22semidirect
127. #66862D4semidirect
210. #2217D11semidirect
272. C2×SD32C2×D11semidirect
297. #367C2×D11semidirect
305. #358C2×D11semidirect
307. #357C2×D11semidirect
313. C22×C11#510semidirect
480. C11#33606semidirect
540. C22#10622528semidirect

Maximal subgroups

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

subgroupindex
C2×#106225282
C22×#668622
#130781952
D11×#4672
#130707282
#130707262
#130707252
#130707232
#130707102
#130707072
#130707052
#130704032
#130703342
#130703252
C11×#22172
#3360611