Finite Group Databasebeta

← #14910296

Subgroups — #14910296

Order 2816.

702 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622521C211yesmaximal, characteristic, complemented
2C2×#10622517C211yesmaximal, characteristic, complemented
3#13080376C211yesmaximal, characteristic, complemented
4#13080303C211yesmaximal, characteristic, complemented
5#13070882C211yesmaximal, characteristic, complemented
6#13070729C211yesmaximal, characteristic, complemented
7#13070702C211yesmaximal, characteristic, complemented
8#13070679C211yesmaximal, characteristic, complemented
9#13070652C211yesmaximal, characteristic, complemented
10#13070558C211yesmaximal, characteristic, complemented
11#13070541C211yesmaximal, characteristic, complemented
12#13070541C211yesmaximal, characteristic, complemented
13#13070530C211yesmaximal, characteristic, complemented
14#13070482C211yesmaximal, characteristic, complemented
15C11×#2168C211yesmaximal, characteristic, complemented
16C2×#66957C2211yescharacteristic
17C2×#66957C2211yescharacteristic
18C2×#66957C2211yescharacteristic, complemented
19C22×D88C2211yescharacteristic
20#10623084—21no—
21#10623081—21no—
22C2×C11×M32C2211yescharacteristic
23C22×C11×C16C2211yescharacteristic, complemented
24C8×D4×C11C2211yescharacteristic
25#10622729C2211yescharacteristic
26#10622728C2211yescharacteristic
27#10622728C2211yescharacteristic
28#10622728C2211yescharacteristic, complemented
29#10622521—24no—
30C2×Dic88C2211yescharacteristic, complemented
31#10622517—24no—
32C2×#66864C2211yescharacteristic
33C2×#66864C2211yescharacteristic
34C2×#66864C2211yescharacteristic, complemented
35C2×#66864C2211yescharacteristic, complemented
36C2×D176C2211yescharacteristic
37C2×D176C2211yescharacteristic
38C2×D176C2211yescharacteristic
39C2×D176C2211yescharacteristic
40#10622461—21no—
41#10622457—21no—
42#10622347—21no—
43#10622347—21no—
44#10622347—21no—
45#10622344—21no—
46C4×Dic44C2211yescharacteristic, complemented
47#10622309C2211yescharacteristic
48#10622308C2211yescharacteristic, complemented
49C4×D88C2211yescharacteristic
50C11×C4⋊C16C2211yescharacteristic, complemented
51C11×C22⋊C16C2211yescharacteristic
52C11×C22⋊C16C2211yescharacteristic, complemented
53C11×#346C2211yescharacteristic, complemented
54#10622147C2211yescharacteristic
55#10622147C2211yescharacteristic
56#10622147C2211yescharacteristic, complemented
57#10622147C2211yescharacteristic, complemented
58#10622142C2211yescharacteristic, complemented
59#10622141C2211yescharacteristic, complemented
60#10622141C2211yescharacteristic, complemented
61C2×#4339—21no—
62C2×#4339—21no—
63C2×#4339—21no—
64C22×D44—21no—
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C4×D4×C11D411yescharacteristic
68#66993—41no—
69#66990—41no—
70#66983—21no—
71#66983—21no—
72#66983—21no—
73#66977—21no—
74C2×Dic44C2311yescharacteristic
75C2×Dic44C2311yescharacteristic
76#66957—22no—
77#66957—22no—
78#66957—22no—
79#66957—41no—
80#66957—41no—
81#66957—41no—
82C2×D88—22no—
83C2×D88—21no—
84C2×D88—21no—
85C2×D88—41no—
86C2×D88C2311yescharacteristic
87C2×D88C2311yescharacteristic
88C2×D88C2311yescharacteristic
89C2×D88C2311yescharacteristic
90C2×#4314—21no—
91C2×#4314—21no—
92C2×#4314—21no—
93C2×#4314—21no—
94#66947—41no—
95#66946—41no—
96#66937—41no—
97#66937—41no—
98#66937—41no—
99C22⋊C4×D11—41no—
100#66928—21no—
101#66927—21no—
102C4×D44—21no—
103C4×Dic22—21no—
104C11×M32—22no—
105C2×C11×C16—22no—
106C2×C11×C16C2311yescharacteristic
107C2×C11×C16C2311yescharacteristic
108C2×C11×C16C2311yescharacteristic
109C2×C11×C16C2311yescharacteristic
110C11×C4⋊C8D411yescharacteristic
111C11×C22⋊C8D411yescharacteristic
112C11×C22⋊C8D411yescharacteristic
113C4×C8×C11C2311yescharacteristic
114#66885—21no—
115#66885—21no—
116#66885—21no—
117#66885—21no—
118#66882C2311yescharacteristic
119#66882C2311yescharacteristic
120#66880—21no—
121#66880—21no—
122Dic88—22no—
123#66864—22no—
124#66864—22no—
125#66864—41no—
126#66864D414yescomplemented
127D176—22no—
128D176—22no—
129D176—22no—
130D176—41no—
131#33834—111nomaximal, Sylow
132C23×D11—41no—
133C2×D4×C11D811yescharacteristic
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C2×C22⋊D11—41no—
137C2×C22⋊D11—41no—
138C2×C22⋊D11—41no—
139C2×C22⋊D11—41no—
140C2×C22⋊D11—41no—
141C2×C22⋊D11—41no—
142#4339—42no—
143#4339—42no—
144#4339—42no—
145#4339—81no—
146#4339—81no—
147#4339—81no—
148C2×D44—21no—
149C2×D44—21no—
150C2×D44—21no—
151C2×D44—21no—
152C2×D44—42no—
153C2×D44—41no—
154C2×D44—41no—
155C2×D44—41no—
156C2×D44—81no—
157C2×C4×D11—41no—
158C2×C4×D11—41no—
159C2×C4×D11—41no—
160C2×C4×D11—41no—
161C2×Dic22—21no—
162C2×Dic22—21no—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11C2×D411yescharacteristic
168C2×C8×C11C2×D411yescharacteristic
169C2×C8×C11C2×D411yescharacteristic
170C2×C8×C11C2411yescharacteristic
171C11×C4⋊C4D811yescharacteristic
172C11×C22⋊C4D811yescharacteristic
173C11×C22⋊C4D811yescharacteristic
174C42×C11C2×D411yescharacteristic
175C22⋊Dic11—41no—
176(C2×D11)⋊C4—41no—
177(C2×D11)⋊C4—41no—
178(C2×D11)⋊C4—41no—
179(C2×D11)⋊C4—41no—
180(C2×D11)⋊C4—41no—
181(C2×D11)⋊C4—41no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184Dic11⋊C4—41no—
185Dic11⋊C4—41no—
186C4×Dic11—41no—
187Dic44—21no—
188Dic44—21no—
189Dic44—21no—
190Dic44C2×D412yes—
191D88—21no—
192D88—21no—
193D88—21no—
194D88—21no—
195D88—21no—
196D88—21no—
197D88—21no—
198D88—42no—
199D88—81no—
200D88C2×D412yes—
201#4314—42no—
202#4314—42no—
203#4314—42no—
204#4314—81no—
205C11×C16—21no—
206C11×C16—21no—
207C11×C16—21no—
208C11×C16C2×D412yes—
209C2×#509—111no—
210C2×#508—111no—
211#3287—111no—
212#3280—111no—
213#2250—111no—
214#2220—111no—
215#2215—111no—
216#2211—111no—
217#2206—111no—
218#2189—111no—
219#2186—111no—
220#2186—111no—
221#2184—111no—
222#2175—111no—
223#2168D1111yescharacteristic, complemented
224C23×C11C2×D811yescharacteristic
225C23×C11C2×D811yescharacteristic
226C22×D11—41no—
227C22×D11—41no—
228C22×D11—41no—
229C22×D11—41no—
230C22×D11—82no—
231C22×D11—82no—
232C22×D11—161no—
233D4×C11—41no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11C2×D811yescharacteristic
239C2×C4×C11C2×D811yescharacteristic
240C2×C4×C11C2×D811yescharacteristic
241C2×C4×C11C2×D811yescharacteristic
242C2×C4×C11C22×D411yescharacteristic
243C22⋊D11—82no—
244C22⋊D11—82no—
245C22⋊D11—82no—
246C22⋊D11—161no—
247C22⋊D11—161no—
248C22⋊D11—161no—
249C2×Dic11—41no—
250C2×Dic11—41no—
251C2×Dic11—41no—
252C2×Dic11—41no—
253D44—22no—
254D44—41no—
255D44—41no—
256D44—41no—
257D44—41no—
258D44—41no—
259D44—41no—
260D44—41no—
261D44—82no—
262D44—82no—
263D44—161no—
264C4×D11—82no—
265C4×D11—82no—
266C4×D11—82no—
267C4×D11—161no—
268Dic22—22no—
269Dic22—41no—
270Dic22—41no—
271Dic22—41no—
272C8×C11—21no—
273C8×C11—21no—
274C8×C11—21no—
275C8×C11C22×D411yescharacteristic
276C8×C11H(5,𝔽2)11yescharacteristic
277C2×#135—111no—
278C2×#135—111no—
279C2×#135—111no—
280C22×D8—111no—
281#550—221no—
282#546—221no—
283#509—224no—
284#508—224no—
285C2×Q32—111no—
286C2×SD32—111no—
287C2×SD32—111no—
288C2×SD32—111no—
289C2×SD32—111no—
290C2×D16—111no—
291C2×D16—111no—
292C2×D16—111no—
293C2×D16—111no—
294C2×M32C2×D1111yescharacteristic
295C22×C16C2×D1111yescharacteristic, complemented
296#495—111no—
297#493—111no—
298#467—111no—
299#466—111no—
300#466—111no—
301#466—111no—
302#463—221no—
303#460—221no—
304#450—221no—
305#449—221no—
306#449—221no—
307#449—221no—
308C4×Q16—111no—
309C4×D8—111no—
310C8×D4C2×D1111yescharacteristic
311#366—111no—
312C4⋊C16C2×D1111yescharacteristic, complemented
313#358—111no—
314#358—111no—
315#357—111no—
316#357—111no—
317#357—111no—
318#357—111no—
319C22⋊C16C2×D1111yescharacteristic
320C22⋊C16C2×D1111yescharacteristic, complemented
321#346C2×D1111yescharacteristic, complemented
322C22×C11—21no—
323C22×C11—21no—
324C22×C11—21no—
325C22×C11—21no—
326C22×C11—21no—
327C22×C11—21no—
328C22×C11C22×D811yescharacteristic
329C2×D11—42no—
330C2×D11—81no—
331C2×D11—81no—
332C2×D11—81no—
333C2×D11—81no—
334C2×D11—81no—
335C2×D11—81no—
336C2×D11—81no—
337C2×D11—81no—
338C2×D11—81no—
339C2×D11—81no—
340C2×D11—81no—
341C2×D11—164no—
342C4×C11—21no—
343C4×C11—21no—
344C4×C11—21no—
345C4×C11—21no—
346C4×C11D4211yescharacteristic
347C4×C11#57611yescharacteristic
348Dic11—42no—
349Dic11—81no—
350Dic11—81no—
351Dic11—81no—
352C2×#41—221no—
353C2×#41—221no—
354C2×#41—221no—
355C22×D4—221no—
356#135—222no—
357#135—222no—
358#135—222no—
359#135—441no—
360#135—441no—
361#135—441no—
362C2×Q16—111no—
363C2×Q16—111no—
364C2×SD16—221no—
365C2×SD16—221no—
366C2×SD16—221no—
367C2×SD16—221no—
368C2×D8—111no—
369C2×D8—111no—
370C2×D8—111no—
371C2×D8—111no—
372C2×D8—222no—
373C2×D8—221no—
374C2×D8—221no—
375C2×D8—441no—
376C22×C8C22×D1111yescharacteristic
377C22×C8C22×D1111yescharacteristic
378#127—221no—
379#127—441no—
380#124—221no—
381#123—441no—
382C22⋊Q8—221no—
383#121—221no—
384#121—221no—
385#121—221no—
386#121—441no—
387#121—441no—
388#121—441no—
389#120—441no—
390C4×Q8—221no—
391C4×D4—221no—
392C4×D4—441no—
393C4×D4D4411yescharacteristic
394C2×C22⋊C4—441no—
395Q32—222no—
396SD32—114no—
397SD32—222no—
398SD32—222no—
399SD32—441no—
400D16—222no—
401D16—222no—
402D16—222no—
403D16—441no—
404M32—22no—
405C2×C16—22no—
406C2×C16C22×D1111yescharacteristic
407C2×C16C22×D1111yescharacteristic
408C2×C16C22×D1111yescharacteristic
409C2×C16C22×D1111yescharacteristic
410#107—111no—
411#107—111no—
412C4⋊C8D4411yescharacteristic
413#103—221no—
414#103—221no—
415#102—221no—
416#102—221no—
417#102—221no—
418#102—221no—
419C22⋊C8D4411yescharacteristic
420C22⋊C8D4411yescharacteristic
421C4×C8C22×D1111yescharacteristic
422C2×C11—41no—
423C2×C11—41no—
424C2×C11D4×D811yescharacteristic
425C2×C11#341411yescharacteristic
426C2×C11#341511yescharacteristic
427D11—82no—
428D11—161no—
429D11—161no—
430D11—161no—
431C24—441no—
432#41—442no—
433#41—442no—
434#41—442no—
435#41—881no—
436#41—881no—
437#41—881no—
438C2×Q8—221no—
439C2×Q8—221no—
440C2×D4—221no—
441C2×D4—221no—
442C2×D4—221no—
443C2×D4—221no—
444C2×D4—442no—
445C2×D4—441no—
446C2×D4—441no—
447C2×D4—441no—
448C2×D4—441no—
449C2×D4—441no—
450C2×D4—441no—
451C2×D4—441no—
452C2×D4—441no—
453C2×D4—441no—
454C2×D4—881no—
455C2×D4D8811yescharacteristic
456C22×C4—441no—
457C22×C4—441no—
458C22×C4—441no—
459C22×C4—441no—
460C22×C4C2×D4411yescharacteristic
461C22×C4C2×D4411yescharacteristic
462Q16—112no—
463Q16—221no—
464Q16—221no—
465Q16—221no—
466SD16—442no—
467SD16—442no—
468SD16—442no—
469SD16—881no—
470D8—112no—
471D8—221no—
472D8—221no—
473D8—221no—
474D8—221no—
475D8—221no—
476D8—221no—
477D8—221no—
478D8—442no—
479D8—881no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8C2×D4411yescharacteristic
485C2×C8C2×D4411yescharacteristic
486C2×C8C2×D4411yescharacteristic
487C2×C8C23×D1111yescharacteristic
488C4⋊C4—221no—
489C4⋊C4—221no—
490C4⋊C4—441no—
491C4⋊C4—441no—
492C4⋊C4D8811yescharacteristic
493C22⋊C4—441no—
494C22⋊C4—441no—
495C22⋊C4—441no—
496C22⋊C4—441no—
497C22⋊C4—441no—
498C22⋊C4—441no—
499C22⋊C4—441no—
500C22⋊C4D8811yescharacteristic
501C22⋊C4D8811yescharacteristic
502C42—441no—
503C42C2×D4411yescharacteristic
504C16—21no—
505C16—21no—
506C16—21no—
507C16D4×D1112yes—
508C11#3383411yescharacteristic, complemented, Sylow
509C23—441no—
510C23—441no—
511C23—441no—
512C23—441no—
513C23—882no—
514C23—882no—
515C23—1761no—
516C23C2×D8811yescharacteristic
517C23C2×D8811yescharacteristic
518Q8—222no—
519Q8—441no—
520Q8—441no—
521Q8—441no—
522D4—41no—
523D4—222no—
524D4—441no—
525D4—441no—
526D4—441no—
527D4—441no—
528D4—441no—
529D4—441no—
530D4—441no—
531D4—882no—
532D4—882no—
533D4—882no—
534D4—882no—
535D4—882no—
536D4—1761no—
537D4—1761no—
538D4—1761no—
539D4—1761no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—441no—
545C2×C4—441no—
546C2×C4—441no—
547C2×C4—441no—
548C2×C4—882no—
549C2×C4—882no—
550C2×C4—882no—
551C2×C4—1761no—
552C2×C4C2×D8811yescharacteristic
553C2×C4C2×D8811yescharacteristic
554C2×C4C2×D8811yescharacteristic
555C2×C4C2×D8811yescharacteristic
556C2×C4C22×D4411yescharacteristic
557C8—21no—
558C8—21no—
559C8—21no—
560C8C2×D4×D1111yescharacteristic
561C8#6704211yescharacteristic
562C22—21no—
563C22—21no—
564C22—21no—
565C22—21no—
566C22—21no—
567C22—21no—
568C22—442no—
569C22—881no—
570C22—881no—
571C22—881no—
572C22—881no—
573C22—881no—
574C22—881no—
575C22—881no—
576C22—881no—
577C22—881no—
578C22—881no—
579C22—881no—
580C22—1764no—
581C22C22×D8811yescharacteristic
582C4—21no—
583C4—21no—
584C4—21no—
585C4—21no—
586C4—442no—
587C4—881no—
588C4—881no—
589C4—881no—
590C4D4×D4411yescharacteristic
591C4#1062328311yescharacteristic
592C2—41no—
593C2—41no—
594C2—882no—
595C2—1761no—
596C2—1761no—
597C2—1761no—
598C2D4×D8811yescharacteristic
599C2#1308175211yescharacteristic
600C2#1308175711yescharacteristic
subgroupG/H
centerC22C22×D88
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2168C2
socleC22×C11C22×D8
hypercenter#2168D11
hypocenterC11#33834
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #2168

Complements

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

NH ≅ G/Ntype
1. C2×#10622521C2semidirect
2. C2×#10622517C2semidirect
3. #13080376C2semidirect
4. #13080303C2semidirect
5. #13070882C2semidirect
6. #13070729C2semidirect
7. #13070702C2semidirect
8. #13070679C2semidirect
9. #13070652C2semidirect
10. #13070558C2semidirect
11. #13070541C2semidirect
12. #13070541C2semidirect
13. #13070530C2semidirect
14. #13070482C2semidirect
15. C11×#2168C2semidirect
18. C2×#66957C22semidirect
23. C22×C11×C16C22semidirect
28. #10622728C22semidirect
30. C2×Dic88C22semidirect
34. C2×#66864C22semidirect
35. C2×#66864C22semidirect
46. C4×Dic44C22semidirect
48. #10622308C22semidirect
50. C11×C4⋊C16C22semidirect
52. C11×C22⋊C16C22semidirect
53. C11×#346C22semidirect
56. #10622147C22semidirect
57. #10622147C22semidirect
58. #10622142C22semidirect
59. #10622141C22semidirect
60. #10622141C22semidirect
126. #66864D4semidirect
223. #2168D11semidirect
295. C22×C16C2×D11semidirect
312. C4⋊C16C2×D11semidirect
320. C22⋊C16C2×D11semidirect
321. #346C2×D11semidirect
508. C11#33834semidirect

Maximal subgroups

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

subgroupindex
C2×#106225212
C2×#106225172
#130803762
#130803032
#130708822
#130707292
#130707022
#130706792
#130706522
#130705582
#130705412
#130705302
#130704822
C11×#21682
#3383411