Finite Group Databasebeta

← #14743954

Subgroups — #14743954

Order 2816.

642 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D8×Dic22C211yesmaximal, characteristic
2#13080486C211yesmaximal, characteristic, complemented
3D4×#4326C211yesmaximal, characteristic, complemented
4#13068290C211yesmaximal, characteristic, complemented
5#13068134C211yesmaximal, characteristic, complemented
6#13068069C211yesmaximal, characteristic, complemented
7#13067995C211yesmaximal, characteristic, complemented
8#13067979C211yesmaximal, characteristic, complemented
9#13067865C211yesmaximal, characteristic, complemented
10#13067864C211yesmaximal, characteristic, complemented
11#13067830C211yesmaximal, characteristic, complemented
12#13067780C211yesmaximal, characteristic, complemented
13#13067464C211yesmaximal, characteristic, complemented
14#13067440C211yesmaximal, characteristic
15C11×#3384C211yesmaximal, characteristic
16C11×#554C2211yescharacteristic
17D4×Q8×C11C2211yescharacteristic
18C22×#4326—21no—
19D4×Dic22C2211yescharacteristic
20D4×Dic22C2211yescharacteristic
21C11×#501—21no—
22C11×#498C2211yescharacteristic
23C11×#478—21no—
24C11×#476—21no—
25C11×#476C2211yescharacteristic
26C11×#474C2211yescharacteristic
27C11×#446C2211yescharacteristic
28C11×#442—21no—
29C4×C11×D8C2211yescharacteristic
30#10622841—21no—
31D8×Dic11—21no—
32#10622706C2211yescharacteristic
33#10622705C2211yescharacteristic
34#10622704C2211yescharacteristic
35#10622703C2211yescharacteristic
36#10622694C2211yescharacteristic
37#10622691C2211yescharacteristic
38#10622664—21no—
39#10622664—21no—
40#10622663—21no—
41#10622663—21no—
42#10622644C2211yescharacteristic
43#10622644C2211yescharacteristic
44C4×#4326C2211yescharacteristic
45D4×C11⋊C8C2211yescharacteristic
46D4×C11⋊C8C2211yescharacteristic
47#10622620C2211yescharacteristic
48#10622620C2211yescharacteristic
49#10622583—21no—
50C2×#66874—21no—
51#10622487—21no—
52#10622372—21no—
53#10622372—21no—
54#10622295C2211yescharacteristic
55C8×Dic22C2211yescharacteristic
56#10622185C2211yescharacteristic
57#10622184C2211yescharacteristic
58Q8⋊(C11⋊C8)C2211yescharacteristic
59D4⋊(C11⋊C8)C2211yescharacteristic
60D4⋊(C11⋊C8)C2211yescharacteristic
61#10622124C2211yescharacteristic
62#10622124C2211yescharacteristic
63#10622122C2211yescharacteristic
64#10622117C2211yescharacteristic
65#10622095C2211yescharacteristic
66#10622093C2211yescharacteristic
67C22×Q8×C11—21no—
68C22×Dic22—21no—
69C22×Dic22—21no—
70C2×C11×D8D411yescharacteristic
71C11×C4⋊Q8—21no—
72C11×C4⋊Q8C2311yescharacteristic
73C11×C4⋊Q8C2311yescharacteristic
74C11×#125—21no—
75C11×C22⋊Q8—21no—
76C11×C22⋊Q8—21no—
77C11×C22⋊Q8—41no—
78C11×C22⋊Q8—41no—
79C4×Q8×C11C2311yescharacteristic
80C4×D4×C11—21no—
81C4×D4×C11—21no—
82C4×D4×C11C2311yescharacteristic
83C4×D4×C11C2311yescharacteristic
84C2×C11×C4⋊C4—21no—
85C2×#4326—21no—
86C2×#4326—21no—
87C2×#4326—21no—
88C2×#4326—21no—
89C2×#4326—21no—
90C2×#4326—44no—
91C2×#4326D411yescharacteristic
92D4×Dic11—21no—
93D4×Dic11—21no—
94#66977—21no—
95#66977—21no—
96C22×C11⋊C8—21no—
97C22×C11⋊C8—21no—
98#66941—21no—
99#66941—21no—
100#66931—41no—
101#66931—41no—
102#66922C2311yescharacteristic
103#66922C2311yescharacteristic
104C4×Dic22C2311yescharacteristic
105C11×#107—21no—
106C11×#107D411yescharacteristic
107C11×#106—21no—
108C11×#106—21no—
109C11×#106—21no—
110C11×C4⋊C8—21no—
111C11×C4⋊C8C2311yescharacteristic
112C11×#102—21no—
113C11×#102—21no—
114C11×#102D411yescharacteristic
115C11×#102D411yescharacteristic
116C11×#97—21no—
117C4×C8×C11C2311yescharacteristic
118#66899—21no—
119#66899—41no—
120#66899D411yescharacteristic
121#66896—21no—
122#66896—21no—
123C22⋊(C11⋊C8)—21no—
124C22⋊(C11⋊C8)—21no—
125#66882—21no—
126#66882—21no—
127Dic11⋊C8—21no—
128C8×Dic11—21no—
129#66874—21no—
130#66874—21no—
131#66874—21no—
132#66874—21no—
133#66874—21no—
134#66874D411yescharacteristic
135#66871—21no—
136#66871—21no—
137#66871—21no—
138#66871—41no—
139#66871D411yescharacteristic
140C4⋊(C11⋊C8)C2311yescharacteristic
141C4⋊(C11⋊C8)C2311yescharacteristic
142C4⋊(C11⋊C8)C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144C4×C11⋊C8C2311yescharacteristic
145#19811—111nomaximal, Sylow
146C2×Q8×C11—21no—
147C2×Q8×C11—21no—
148C2×Q8×C11—41no—
149C2×Q8×C11—42no—
150C2×Q8×C11—81no—
151C2×Q8×C11C2×D411yescharacteristic
152C2×D4×C11C2×D411yescharacteristic
153C2×D4×C11C2×D411yescharacteristic
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—41no—
157C22×C4×C11—41no—
158C22×Dic11—41no—
159C22×Dic11—41no—
160C2×Dic22—21no—
161C2×Dic22—21no—
162C2×Dic22—41no—
163C2×Dic22—41no—
164C2×Dic22—42no—
165C2×Dic22—42no—
166C2×Dic22—81no—
167C2×Dic22—81no—
168C2×Dic22C2×D411yescharacteristic
169C11×D8Q1614yescomplemented
170C2×C8×C11—21no—
171C2×C8×C11C2×D411yescharacteristic
172C2×C8×C11C2×D411yescharacteristic
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—41no—
179C11×C4⋊C4—41no—
180C11×C4⋊C4—41no—
181C11×C4⋊C4C2×D411yescharacteristic
182C11×C4⋊C4C2×D411yescharacteristic
183C11×C4⋊C4C2×D411yescharacteristic
184C11×C22⋊C4—21no—
185C11×C22⋊C4—21no—
186C11×C22⋊C4—41no—
187C11×C22⋊C4—41no—
188C42×C11—21no—
189C42×C11C2411yescharacteristic
190C22⋊Dic11—41no—
191C22⋊Dic11—41no—
192#4326—22no—
193#4326—42no—
194#4326—42no—
195#4326—42no—
196#4326—81no—
197#4326—81no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11C2×D411yescharacteristic
203Dic11⋊C4—21no—
204Dic11⋊C4—41no—
205Dic11⋊C4—41no—
206C4×Dic11—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—42no—
212C2×C11⋊C8—81no—
213C2×C11⋊C8C2×D411yescharacteristic
214C2×C11⋊C8C2×D411yescharacteristic
215#3384D1111yescharacteristic
216Q8×D8—111no—
217#3299—111no—
218D4×Q16—111no—
219#1723—111no—
220#1694—111no—
221#1683—111no—
222#1672—111no—
223#1669—111no—
224#1649—111no—
225#1649—111no—
226#1644—111no—
227#1637—111no—
228#1584—111no—
229#1580—111no—
230C23×C11—21no—
231C23×C11—21no—
232Q8×C11—21no—
233Q8×C11—21no—
234Q8×C11—41no—
235Q8×C11—41no—
236Q8×C11—81no—
237Q8×C11—82no—
238D4×C11—21no—
239D4×C11—21no—
240D4×C11C2×Q1612yes—
241D4×C11C2×Q1612yescomplemented
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—82no—
253C2×C4×C11—161no—
254C2×C4×C11C22×D411yescharacteristic
255C2×C4×C11C22×D411yescharacteristic
256C2×C4×C11H(5,𝔽2)11yescharacteristic
257C2×Dic11—21no—
258C2×Dic11—21no—
259C2×Dic11—41no—
260C2×Dic11—41no—
261C2×Dic11—82no—
262C2×Dic11—82no—
263Dic22—21no—
264Dic22—41no—
265Dic22—41no—
266Dic22—41no—
267Dic22—41no—
268Dic22—82no—
269Dic22—82no—
270Dic22AGL(1,ℤ/8)12yes—
271C8×C11—21no—
272C8×C11—41no—
273C8×C11C2×Q1612yescomplemented
274C11⋊C8—21no—
275C11⋊C8—21no—
276C11⋊C8—41no—
277C11⋊C8—41no—
278C11⋊C8—41no—
279C11⋊C8—41no—
280C22×Q16—221no—
281#554C2×D1111yescharacteristic
282D4×Q8—111no—
283D4×Q8—111no—
284D4×Q8C2×D1111yescharacteristic
285#501—21no—
286#500—111no—
287#500—111no—
288#500—221no—
289#498C2×D1111yescharacteristic
290#494—111no—
291#487—111no—
292#487—111no—
293#484—221no—
294#478—21no—
295#477—111no—
296#476—21no—
297#476C2×D1111yescharacteristic
298#474—111no—
299#474—111no—
300#474—221no—
301#474—221no—
302#474C2×D1111yescharacteristic
303#467—221no—
304#467—221no—
305#462—111no—
306#462—111no—
307#462—111no—
308#451—221no—
309#451—221no—
310#451—221no—
311#446C2×D1111yescharacteristic
312C8×Q8—111no—
313#442—21no—
314C4×Q16—111no—
315C4×D8—221no—
316C4×D8C2×D1111yescharacteristic
317C8×D4—111no—
318C8×D4—111no—
319C2×#103—221no—
320#335—111no—
321#334—111no—
322#333—111no—
323#332—111no—
324#332—111no—
325#332—111no—
326Q8⋊C8—111no—
327Q8⋊C8—111no—
328D4⋊C8—111no—
329D4⋊C8—111no—
330#322—111no—
331C22×C11—22no—
332C22×C11—22no—
333C22×C11—41no—
334C22×C11—41no—
335C22×C11—41no—
336C22×C11—41no—
337C22×C11D4211yescharacteristic
338C4×C11—21no—
339C4×C11—41no—
340C4×C11—41no—
341C4×C11—41no—
342C4×C11—41no—
343C4×C11—81no—
344C4×C11—81no—
345C4×C11C22×Q1611yescharacteristic
346C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
347C4×C11#57611yescharacteristic
348C4×C11#57811yescharacteristic
349Dic11—22no—
350Dic11—41no—
351Dic11—81no—
352Dic11—81no—
353C22×Q8—21no—
354C22×Q8—221no—
355C22×Q8—221no—
356C2×Q16—111no—
357C2×Q16—221no—
358C2×Q16—221no—
359C2×Q16—221no—
360C2×Q16—221no—
361C2×Q16—221no—
362C2×Q16—444no—
363C2×D8C22⋊D1111yescharacteristic
364C22×C8—221no—
365C22×C8—221no—
366C4⋊Q8—21no—
367C4⋊Q8—111no—
368C4⋊Q8—111no—
369C4⋊Q8—221no—
370C4⋊Q8—221no—
371C4⋊Q8C22×D1111yescharacteristic
372C4⋊Q8C22×D1111yescharacteristic
373#125—21no—
374C22⋊Q8—21no—
375C22⋊Q8—21no—
376C22⋊Q8—41no—
377C22⋊Q8—41no—
378C22⋊Q8—221no—
379C22⋊Q8—221no—
380C22⋊Q8—441no—
381C22⋊Q8—441no—
382C4×Q8—111no—
383C4×Q8C22×D1111yescharacteristic
384C4×D4—21no—
385C4×D4—21no—
386C4×D4—221no—
387C4×D4—221no—
388C4×D4C22×D1111yescharacteristic
389C4×D4C22×D1111yescharacteristic
390C2×C4⋊C4—21no—
391#107—21no—
392#107—111no—
393#107—221no—
394#107—221no—
395#107—221no—
396#107—221no—
397#107—221no—
398#107—441no—
399#107C22⋊D1111yescharacteristic
400#106—21no—
401#106—21no—
402#106—21no—
403C4⋊C8—21no—
404C4⋊C8—111no—
405C4⋊C8—111no—
406C4⋊C8—111no—
407C4⋊C8—221no—
408C4⋊C8C22×D1111yescharacteristic
409#103—111no—
410#103—111no—
411#103—221no—
412#103—221no—
413#103—221no—
414#103—221no—
415#103—221no—
416#103—221no—
417#103—441no—
418#102—21no—
419#102—21no—
420#102—221no—
421#102—221no—
422#102C22⋊D1111yescharacteristic
423#102C22⋊D1111yescharacteristic
424C22⋊C8—221no—
425C22⋊C8—221no—
426#97—21no—
427C4×C8—111no—
428C4×C8—111no—
429C4×C8—221no—
430C4×C8C22×D1111yescharacteristic
431C2×C11—42no—
432C2×C11—42no—
433C2×C11#326411yescharacteristic
434C2×C11D4×Q1611yescharacteristic
435C2×C11#328911yescharacteristic
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8—41no—
439C2×Q8—42no—
440C2×Q8—81no—
441C2×Q8—111no—
442C2×Q8—221no—
443C2×Q8—221no—
444C2×Q8—441no—
445C2×Q8—441no—
446C2×Q8—442no—
447C2×Q8—442no—
448C2×Q8—881no—
449C2×Q8—881no—
450C2×Q8D4×D1111yescharacteristic
451C2×D4C2×C22⋊D1111yescharacteristic
452C2×D4C2×C22⋊D1111yescharacteristic
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—41no—
456C22×C4—41no—
457C22×C4—441no—
458C22×C4—441no—
459Q16—222no—
460Q16—442no—
461Q16—442no—
462Q16—442no—
463Q16—881no—
464Q16—881no—
465D8#432614yescomplemented
466C2×C8—21no—
467C2×C8—111no—
468C2×C8—111no—
469C2×C8—221no—
470C2×C8—221no—
471C2×C8—221no—
472C2×C8—221no—
473C2×C8—442no—
474C2×C8—881no—
475C2×C8C2×C22⋊D1111yescharacteristic
476C2×C8C2×C22⋊D1111yescharacteristic
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—41no—
483C4⋊C4—41no—
484C4⋊C4—41no—
485C4⋊C4—111no—
486C4⋊C4—221no—
487C4⋊C4—221no—
488C4⋊C4—221no—
489C4⋊C4—221no—
490C4⋊C4—221no—
491C4⋊C4—441no—
492C4⋊C4—441no—
493C4⋊C4D4×D1111yescharacteristic
494C4⋊C4C2×C22⋊D1111yescharacteristic
495C4⋊C4C2×C22⋊D1111yescharacteristic
496C22⋊C4—21no—
497C22⋊C4—21no—
498C22⋊C4—41no—
499C22⋊C4—41no—
500C22⋊C4—441no—
501C22⋊C4—441no—
502C42—21no—
503C42—221no—
504C42C23×D1111yescharacteristic
505C11#1981111yescharacteristic, complemented, Sylow
506C23—21no—
507C23—21no—
508Q8—21no—
509Q8—21no—
510Q8—41no—
511Q8—41no—
512Q8—81no—
513Q8—82no—
514Q8—112no—
515Q8—221no—
516Q8—441no—
517Q8—441no—
518Q8—441no—
519Q8—441no—
520Q8—882no—
521Q8—882no—
522D4—21no—
523D4—21no—
524D4C2×#432612yes—
525D4C2×#432612yescomplemented
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—82no—
537C2×C4—161no—
538C2×C4—221no—
539C2×C4—221no—
540C2×C4—441no—
541C2×C4—441no—
542C2×C4—882no—
543C2×C4—882no—
544C2×C4C2×D4×D1111yescharacteristic
545C2×C4#6703711yescharacteristic
546C2×C4C22×C22⋊D1111yescharacteristic
547C8—21no—
548C8—41no—
549C8—221no—
550C8—221no—
551C8—441no—
552C8—441no—
553C8—441no—
554C8—441no—
555C8C2×#432612yescomplemented
556C22—22no—
557C22—22no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22D4×C22⋊D1111yescharacteristic
563C4—21no—
564C4—41no—
565C4—41no—
566C4—41no—
567C4—41no—
568C4—81no—
569C4—81no—
570C4—222no—
571C4—441no—
572C4—881no—
573C4—881no—
574C4D11×AGL(1,ℤ/8)11yescharacteristic
575C4#1062330511yescharacteristic
576C4C22×#432611yescharacteristic
577C4#1062336911yescharacteristic
578C2—42no—
579C2—42no—
580C2#1308009011yescharacteristic
581C2D4×#432611yescharacteristic
582C2#1308038911yescharacteristic
subgroupG/H
centerC22D4×C22⋊D11
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3384C2
socleC22×C11D42
prime radicalC2×C11×D8D4
hypercenter#3384D11
hypocenterC11#19811
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #3384

Complements

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

NH ≅ G/Ntype
2. #13080486C2semidirect
3. D4×#4326C2semidirect
4. #13068290C2semidirect
5. #13068134C2semidirect
6. #13068069C2semidirect
7. #13067995C2semidirect
8. #13067979C2semidirect
9. #13067865C2semidirect
10. #13067864C2semidirect
11. #13067830C2semidirect
12. #13067780C2semidirect
13. #13067464C2semidirect
169. C11×D8Q16semidirect
241. D4×C11C2×Q16semidirect
273. C8×C11C2×Q16semidirect
465. D8#4326semidirect
505. C11#19811semidirect
525. D4C2×#4326semidirect
555. C8C2×#4326semidirect

Maximal subgroups

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

subgroupindex
D8×Dic222
#130804862
D4×#43262
#130682902
#130681342
#130680692
#130679952
#130679792
#130678652
#130678642
#130678302
#130677802
#130674642
#130674402
C11×#33842
#1981111