Finite Group Databasebeta

← #14743961

Subgroups — #14743961

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
1#13081515C211yesmaximal, characteristic
2Q8×#4323C211yesmaximal, characteristic
3Q16×D44C211yesmaximal, characteristic, complemented
4#13068295C211yesmaximal, characteristic, complemented
5#13068132C211yesmaximal, characteristic, complemented
6#13068064C211yesmaximal, characteristic, complemented
7#13068000C211yesmaximal, characteristic, complemented
8#13067981C211yesmaximal, characteristic, complemented
9#13067865C211yesmaximal, characteristic, complemented
10#13067863C211yesmaximal, characteristic, complemented
11#13067830C211yesmaximal, characteristic, complemented
12#13067779C211yesmaximal, characteristic, complemented
13#13067467C211yesmaximal, characteristic, complemented
14#13067438C211yesmaximal, characteristic
15C11×#3299C211yesmaximal, characteristic, complemented
16C11×#554C2211yescharacteristic
17D4×Q8×C11C2211yescharacteristic
18C2×Q16×D11—21no—
19Q8×D44C2211yescharacteristic
20Q8×D44C2211yescharacteristic
21C11×#487C2211yescharacteristic
22C11×#484—21no—
23C11×#477C2211yescharacteristic
24C11×#467—21no—
25C11×#462C2211yescharacteristic
26C11×#451—21no—
27C4×C11×Q16C2211yescharacteristic
28C8×D4×C11C2211yescharacteristic
29C2×C11×#103—21no—
30#10622700—21no—
31#10622700C2211yescharacteristic
32#10622697C2211yescharacteristic
33#10622694C2211yescharacteristic
34#10622692C2211yescharacteristic
35#10622691—21no—
36#10622691C2211yescharacteristic
37#10622691C2211yescharacteristic
38#10622679—21no—
39#10622678—21no—
40#10622644C2211yescharacteristic
41#10622644C2211yescharacteristic
42#10622637C2211yescharacteristic
43Q8×C11⋊C8C2211yescharacteristic
44#10622627—21no—
45C4×#4323—21no—
46C4×#4323C2211yescharacteristic
47#10622621—21no—
48#10622620—21no—
49#10622620C2211yescharacteristic
50#10622620C2211yescharacteristic
51#10622500—21no—
52#10622421—21no—
53#10622421—21no—
54#10622312C2211yescharacteristic
55C8×D44C2211yescharacteristic
56#10622185C2211yescharacteristic
57#10622184C2211yescharacteristic
58Q8⋊(C11⋊C8)C2211yescharacteristic
59Q8⋊(C11⋊C8)C2211yescharacteristic
60D4⋊(C11⋊C8)C2211yescharacteristic
61#10622121C2211yescharacteristic
62#10622120C2211yescharacteristic
63#10622120C2211yescharacteristic
64#10622118C2211yescharacteristic
65#10622096C2211yescharacteristic
66#10622092C2211yescharacteristic
67C22×Q8×C11—21no—
68C2×Q8×D11—21no—
69C2×Q8×D11—21no—
70C2×C11×Q16—21no—
71C2×C11×Q16D411yescharacteristic
72C22×C8×C11—21no—
73C11×C4⋊Q8—21no—
74C11×C4⋊Q8C2311yescharacteristic
75C11×C4⋊Q8C2311yescharacteristic
76C11×#125—21no—
77C11×C22⋊Q8—21no—
78C11×C22⋊Q8—21no—
79C11×C22⋊Q8—41no—
80C11×C22⋊Q8—41no—
81C4×Q8×C11C2311yescharacteristic
82C4×Q8×C11C2311yescharacteristic
83C4×D4×C11—21no—
84C4×D4×C11—21no—
85C4×D4×C11C2311yescharacteristic
86C2×C11×C4⋊C4—21no—
87C2×#4326—21no—
88C2×#4326—21no—
89C2×#4323D411yescharacteristic
90Q16×D11—44no—
91C2×Dic44—21no—
92C2×Dic44—21no—
93C2×C8×D11—21no—
94#66950—21no—
95#66950—21no—
96#66950—41no—
97#66950—41no—
98C4×D44—21no—
99C4×D44—21no—
100C4×D44C2311yescharacteristic
101#66922—21no—
102#66922—21no—
103#66922C2311yescharacteristic
104#66922C2311yescharacteristic
105C11×#107—21no—
106C11×#107D411yescharacteristic
107C11×C4⋊C8C2311yescharacteristic
108C11×#103—21no—
109C11×#103—21no—
110C11×#103—21no—
111C11×#103—21no—
112C11×#103D411yescharacteristic
113C11×#103D411yescharacteristic
114C11×C22⋊C8—21no—
115C4×C8×C11C2311yescharacteristic
116#66899—41no—
117#66896—21no—
118#66896—21no—
119#66896D411yescharacteristic
120(C2×D11)⋊C8—21no—
121#66874—21no—
122#66874—21no—
123#66873—21no—
124#66873—21no—
125#66873D411yescharacteristic
126#66872—21no—
127#66872—21no—
128#66872—21no—
129#66871—21no—
130#66871—21no—
131#66871—21no—
132#66871—21no—
133#66871—21no—
134#66871—41no—
135#66871D411yescharacteristic
136C4⋊(C11⋊C8)—21no—
137C4⋊(C11⋊C8)—21no—
138C4⋊(C11⋊C8)C2311yescharacteristic
139C4⋊(C11⋊C8)C2311yescharacteristic
140C4⋊(C11⋊C8)C2311yescharacteristic
141#66867—21no—
142C4×C11⋊C8—21no—
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×Q8×C11C2×D411yescharacteristic
153C2×D4×C11C2×D411yescharacteristic
154C22×C4×C11—21no—
155C22×C4×C11—41no—
156C22×C4×C11—41no—
157Q8×D11—42no—
158Q8×D11—42no—
159Q8×D11—81no—
160Q8×D11—81no—
161C2×D44C2×D411yescharacteristic
162C2×C4×D11—21no—
163C2×C4×D11—41no—
164C2×C4×D11—41no—
165C2×Dic22—21no—
166C2×Dic22—21no—
167C2×Dic22—41no—
168C2×Dic22—41no—
169C11×Q16—22no—
170C11×Q16—81no—
171C2×C8×C11—21no—
172C2×C8×C11—81no—
173C2×C8×C11C2×D411yescharacteristic
174C2×C8×C11C2×D411yescharacteristic
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—41no—
182C11×C4⋊C4—41no—
183C11×C4⋊C4—41no—
184C11×C4⋊C4C2×D411yescharacteristic
185C11×C4⋊C4C2×D411yescharacteristic
186C11×C4⋊C4C2×D411yescharacteristic
187C11×C22⋊C4—21no—
188C11×C22⋊C4—41no—
189C11×C22⋊C4—41no—
190C42×C11—21no—
191C42×C11—21no—
192C42×C11C2411yescharacteristic
193#4326—42no—
194#4326—42no—
195#4323Q1614yescomplemented
196(C2×D11)⋊C4—21no—
197(C2×D11)⋊C4—41no—
198(C2×D11)⋊C4—41no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11—41no—
204C4⋊Dic11—41no—
205C4⋊Dic11C2×D411yescharacteristic
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8C2×D411yescharacteristic
211C2×C11⋊C8C2×D411yescharacteristic
212Dic44—42no—
213Dic44—81no—
214C8×D11—42no—
215#3384—111no—
216Q8×D8—111no—
217#3299D1111yescharacteristic, complemented
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—
231C22×D11—21no—
232Q8×C11—21no—
233Q8×C11—21no—
234Q8×C11—21no—
235Q8×C11—41no—
236Q8×C11—41no—
237Q8×C11—82no—
238Q8×C11—81no—
239Q8×C11AGL(1,ℤ/8)12yes—
240D4×C11—21no—
241D4×C11C2×Q1612yescomplemented
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—82no—
252C2×C4×C11—161no—
253C2×C4×C11C22×D411yescharacteristic
254C2×C4×C11C22×D411yescharacteristic
255C2×C4×C11H(5,𝔽2)11yescharacteristic
256C2×Dic11—21no—
257C2×Dic11—41no—
258C2×Dic11—41no—
259D44—21no—
260D44C2×Q1612yes—
261C4×D11—41no—
262C4×D11—41no—
263C4×D11—82no—
264C4×D11—82no—
265Dic22—41no—
266Dic22—41no—
267Dic22—41no—
268Dic22—41no—
269Dic22—82no—
270Dic22—82no—
271C8×C11—21no—
272C8×C11—21no—
273C8×C11—41no—
274C11⋊C8—21no—
275C11⋊C8—41no—
276C11⋊C8—41no—
277C11⋊C8—41no—
278C11⋊C8—41no—
279C11⋊C8C2×Q1612yescomplemented
280C22×Q16—221no—
281#554C2×D1111yescharacteristic
282D4×Q8—111no—
283D4×Q8—111no—
284D4×Q8C2×D1111yescharacteristic
285#501—221no—
286#500—111no—
287#500—111no—
288#500—221no—
289#498—111no—
290#494—111no—
291#487—111no—
292#487C2×D1111yescharacteristic
293#484—21no—
294#478—221no—
295#477C2×D1111yescharacteristic
296#476—111no—
297#476—221no—
298#474—111no—
299#474—111no—
300#474—111no—
301#474—221no—
302#474—221no—
303#467—21no—
304#467—221no—
305#462—111no—
306#462—111no—
307#462C2×D1111yescharacteristic
308#451—21no—
309#451—221no—
310#451—221no—
311#446—111no—
312C8×Q8—111no—
313#442—221no—
314C4×Q16C2×D1111yescharacteristic
315C4×D8—111no—
316C4×D8—221no—
317C8×D4—111no—
318C8×D4C2×D1111yescharacteristic
319C2×#103—21no—
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—41no—
333C22×C11—41no—
334C22×C11D4211yescharacteristic
335C2×D11—22no—
336C2×D11—41no—
337C2×D11—41no—
338C4×C11—22no—
339C4×C11—21no—
340C4×C11—41no—
341C4×C11—41no—
342C4×C11—41no—
343C4×C11—41no—
344C4×C11—81no—
345C4×C11—81no—
346C4×C11C22×Q1611yescharacteristic
347C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
348C4×C11#57611yescharacteristic
349C4×C11#57811yescharacteristic
350Dic11—41no—
351Dic11—81no—
352Dic11—81no—
353C22×Q8—21no—
354C22×Q8—221no—
355C22×Q8—221no—
356C2×Q16—21no—
357C2×Q16—221no—
358C2×Q16—221no—
359C2×Q16—221no—
360C2×Q16—221no—
361C2×Q16—444no—
362C2×Q16C22⋊D1111yescharacteristic
363C2×D8—111no—
364C22×C8—21no—
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×Q8C22×D1111yescharacteristic
383C4×Q8C22×D1111yescharacteristic
384C4×D4—21no—
385C4×D4—21no—
386C4×D4—111no—
387C4×D4—221no—
388C4×D4—221no—
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—221no—
401#106—221no—
402#106—221no—
403C4⋊C8—111no—
404C4⋊C8—111no—
405C4⋊C8—111no—
406C4⋊C8—221no—
407C4⋊C8—221no—
408C4⋊C8C22×D1111yescharacteristic
409#103—21no—
410#103—21no—
411#103—21no—
412#103—21no—
413#103—221no—
414#103—221no—
415#103—441no—
416#103C22⋊D1111yescharacteristic
417#103C22⋊D1111yescharacteristic
418#102—111no—
419#102—111no—
420#102—221no—
421#102—221no—
422#102—221no—
423#102—221no—
424C22⋊C8—21no—
425C22⋊C8—221no—
426#97—221no—
427C4×C8—111no—
428C4×C8—111no—
429C4×C8—221no—
430C4×C8C22×D1111yescharacteristic
431C2×C11—42no—
432C2×C11#326411yescharacteristic
433C2×C11D4×Q1611yescharacteristic
434C2×C11#328911yescharacteristic
435D11—42no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8—41no—
439C2×Q8—42no—
440C2×Q8—81no—
441C2×Q8—221no—
442C2×Q8—221no—
443C2×Q8—441no—
444C2×Q8—441no—
445C2×Q8—442no—
446C2×Q8—442no—
447C2×Q8—881no—
448C2×Q8—881no—
449C2×Q8C2×C22⋊D1111yescharacteristic
450C2×Q8C2×C22⋊D1111yescharacteristic
451C2×D4—111no—
452C2×D4D4×D1111yescharacteristic
453C22×C4—21no—
454C22×C4—41no—
455C22×C4—41no—
456C22×C4—221no—
457C22×C4—441no—
458C22×C4—441no—
459Q16—22no—
460Q16—81no—
461Q16—442no—
462Q16—442no—
463Q16—442no—
464Q16—881no—
465D8—114no—
466C2×C8—21no—
467C2×C8—81no—
468C2×C8—111no—
469C2×C8—111no—
470C2×C8—221no—
471C2×C8—221no—
472C2×C8—221no—
473C2×C8—221no—
474C2×C8—442no—
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—21no—
483C4⋊C4—41no—
484C4⋊C4—41no—
485C4⋊C4—41no—
486C4⋊C4—111no—
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—41no—
498C22⋊C4—41no—
499C22⋊C4—221no—
500C22⋊C4—441no—
501C22⋊C4—441no—
502C42—21no—
503C42—21no—
504C42C23×D1111yescharacteristic
505C11#1981111yescharacteristic, complemented, Sylow
506C23—21no—
507C23—221no—
508Q8—21no—
509Q8—21no—
510Q8—21no—
511Q8—41no—
512Q8—41no—
513Q8—82no—
514Q8—81no—
515Q8—441no—
516Q8—441no—
517Q8—441no—
518Q8—441no—
519Q8—882no—
520Q8—882no—
521Q8#6700212yes—
522D4—21no—
523D4—112no—
524D4—221no—
525D4Q16×D1112yescomplemented
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—82no—
536C2×C4—161no—
537C2×C4—221no—
538C2×C4—441no—
539C2×C4—441no—
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—21no—
549C8—41no—
550C8—112no—
551C8—221no—
552C8—441no—
553C8—441no—
554C8—441no—
555C8—441no—
556C22—22no—
557C22—41no—
558C22—41no—
559C22—222no—
560C22—441no—
561C22—441no—
562C22D4×C22⋊D1111yescharacteristic
563C4—22no—
564C4—21no—
565C4—41no—
566C4—41no—
567C4—41no—
568C4—41no—
569C4—81no—
570C4—81no—
571C4—441no—
572C4—881no—
573C4—881no—
574C4C2×Q16×D1111yescharacteristic
575C4#1062329711yescharacteristic
576C4C2×#6700211yescharacteristic
577C4#1062336611yescharacteristic
578C2—42no—
579C2—442no—
580C2#1308009711yescharacteristic
581C2Q16×C22⋊D1111yescharacteristic
582C2#1308038911yescharacteristic
subgroupG/H
centerC22D4×C22⋊D11
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3299C2
socleC22×C11D42
prime radicalC2×#4323D4
hypercenter#3299D11
hypocenterC11#19811
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #3299

Complements

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

NH ≅ G/Ntype
3. Q16×D44C2semidirect
4. #13068295C2semidirect
5. #13068132C2semidirect
6. #13068064C2semidirect
7. #13068000C2semidirect
8. #13067981C2semidirect
9. #13067865C2semidirect
10. #13067863C2semidirect
11. #13067830C2semidirect
12. #13067779C2semidirect
13. #13067467C2semidirect
15. C11×#3299C2semidirect
195. #4323Q16semidirect
217. #3299D11semidirect
241. D4×C11C2×Q16semidirect
279. C11⋊C8C2×Q16semidirect
505. C11#19811semidirect
525. D4Q16×D11semidirect

Maximal subgroups

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

subgroupindex
#130815152
Q8×#43232
Q16×D442
#130682952
#130681322
#130680642
#130680002
#130679812
#130678652
#130678632
#130678302
#130677792
#130674672
#130674382
C11×#32992
#1981111