Finite Group Databasebeta

← #14782689

Subgroups — #14782689

Order 2816.

914 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622608C211yesmaximal, characteristic, complemented
2#13077133C211yesmaximal, characteristic
3C2×#10622746C211yesmaximal, characteristic
4#13077060C211yesmaximal, characteristic
5#13070065C214yesmaximal, complemented
6#13070060C214yesmaximal, complemented
7C2×#10622192C211yesmaximal, characteristic, complemented
8#13068342C211yesmaximal, characteristic, complemented
9C11×#1742C211yesmaximal, characteristic, complemented
10C22×#4339C2211yescharacteristic
11C22×C11×M16C2211yescharacteristic
12C22×C11×M16C2211yescharacteristic
13C2×C11×#117C2211yescharacteristic
14C22×C4⋊Dic11C2211yescharacteristic
15C22×#4318C2211yescharacteristic
16C22×#4318C2211yescharacteristic
17#10622746—22no—
18#10622746C2214yes—
19#10622742C2214yes—
20#10622739—22no—
21C2×#66885—21no—
22#10622723—22no—
23C2×#66880—21no—
24#10622617—21no—
25#10622615—22no—
26#10622614—21no—
27#10622608—22no—
28#10622608—22no—
29#10622579C2212yes—
30#10622579C2212yes—
31C2×#66872C2212yescomplemented
32C2×#66871C2212yescomplemented
33C11×#343C2212yescomplemented
34C11×#343C2212yescomplemented
35#10622196C2214yescomplemented
36#10622192C2214yescomplemented
37C23×C4×C11C2311yescharacteristic
38C22×C22⋊D11—21no—
39C23×Dic11—21no—
40C2×#4339—21no—
41C2×#4339—21no—
42C2×#4339—22no—
43C2×#4339—22no—
44C2×#4339—22no—
45C2×#4339—22no—
46C2×#4339D412yes—
47C2×#4339C2312yes—
48C22×D44D411yescharacteristic
49C22×C4×D11—21no—
50C22×Dic22D411yescharacteristic
51C2×C11×M16—21no—
52C2×C11×M16—21no—
53C2×C11×M16—22no—
54C2×C11×M16—22no—
55C2×C11×M16—22no—
56C2×C11×M16—22no—
57C2×C11×M16C2312yes—
58C2×C11×M16C2312yes—
59C22×C8×C11—21no—
60C22×C8×C11—21no—
61C11×#117—21no—
62C11×#117—21no—
63C11×#117—21no—
64C11×#117—21no—
65C2×C11×C4⋊C4C2311yescharacteristic
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C22⋊C4—21no—
68C2×C42×C11—21no—
69C2×C4⋊Dic11—21no—
70C2×C4⋊Dic11—21no—
71C2×C4⋊Dic11—21no—
72C2×C4⋊Dic11—21no—
73C2×C4⋊Dic11—21no—
74C2×C4⋊Dic11C2312yes—
75C2×#4318—22no—
76C2×#4318—22no—
77C2×#4318—21no—
78C2×#4318—22no—
79C2×#4318—22no—
80C2×#4318D412yes—
81C2×#4318D412yes—
82C2×#4318C2312yes—
83C22×C11⋊C8—21no—
84C22×C11⋊C8C2312yes—
85#66885—24no—
86(C2×D11)⋊C8—28no—
87#66880—24no—
88#66874—22no—
89#66874—22no—
90#66873—22no—
91#66873—22no—
92#66872—24no—
93#66871—24no—
94#23647—111nomaximal, Sylow
95C24×C11#4111yescharacteristic
96C23×D11—21no—
97C22×C4×C11—21no—
98C22×C4×C11—21no—
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11#4111yescharacteristic
104C22×C4×C11#4112yes—
105C22×C4×C11#4112yes—
106C22×C4×C11#4112yes—
107C22×C4×C11#4112yes—
108C22×C4×C11C2411yescharacteristic
109C2×C22⋊D11—22no—
110C2×C22⋊D11—22no—
111C2×C22⋊D11—42no—
112C2×C22⋊D11—42no—
113C22×Dic11—21no—
114C22×Dic11—22no—
115C22×Dic11—41no—
116C22×Dic11—41no—
117C22×Dic11—82no—
118#4339—24no—
119#4339—24no—
120#4339—22no—
121#4339—22no—
122#4339—22no—
123#4339—22no—
124#4339—42no—
125#4339—42no—
126#4339—42no—
127#4339—42no—
128C2×D44—21no—
129C2×D44—22no—
130C2×D44—22no—
131C2×D44C2×D412yes—
132C2×C4×D11—22no—
133C2×C4×D11—22no—
134C2×C4×D11—42no—
135C2×C4×D11—42no—
136C2×Dic22—21no—
137C2×Dic22—22no—
138C2×Dic22—22no—
139C2×Dic22C2×D412yes—
140C11×M16—22no—
141C11×M16—22no—
142C11×M16—22no—
143C11×M16—22no—
144C11×M16—42no—
145C11×M16—42no—
146C2×C8×C11—22no—
147C2×C8×C11—22no—
148C2×C8×C11—42no—
149C2×C8×C11—42no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—21no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—21no—
154C11×C22⋊C4—41no—
155C11×C22⋊C4—41no—
156C42×C11—41no—
157C42×C11—41no—
158C4⋊Dic11—22no—
159C4⋊Dic11—22no—
160C4⋊Dic11—41no—
161C4⋊Dic11—41no—
162#4318—24no—
163#4318—24no—
164#4318—22no—
165#4318—22no—
166#4318—42no—
167C2×C11⋊C8—22no—
168C2×C11⋊C8—22no—
169C2×C11⋊C8—22no—
170C2×C11⋊C8—42no—
171C2×C11⋊C8C2×D414yes—
172C2×#428—111no—
173#2896—111no—
174C2×#417—111no—
175#2879—111no—
176#2079—114no—
177#2078—114no—
178#1742D1111yescharacteristic, complemented
179C2×#343—111no—
180#1738—111no—
181C23×C11—41no—
182C23×C11—41no—
183C23×C11#12111yescharacteristic
184C23×C11#12111yescharacteristic
185C23×C11#12612yes—
186C23×C11#12612yes—
187C23×C11C2×#4111yescharacteristic
188C22×D11—22no—
189C22×D11—42no—
190C22×D11—81no—
191C22×D11—81no—
192C2×C4×C11—41no—
193C2×C4×C11—41no—
194C2×C4×C11—81no—
195C2×C4×C11—81no—
196C2×C4×C11#12111yescharacteristic
197C2×C4×C11#12111yescharacteristic
198C2×C4×C11#12312yes—
199C2×C4×C11#12312yes—
200C2×C4×C11#12312yes—
201C2×C4×C11#12312yes—
202C2×C4×C11#12312yes—
203C2×C4×C11#12312yes—
204C2×C4×C11#12412yes—
205C2×C4×C11#12412yes—
206C2×C4×C11#12612yes—
207C2×C4×C11#12612yes—
208C2×C4×C11C22×D411yescharacteristic
209C2×C4×C11C22×D411yescharacteristic
210C2×C4×C11C2×#4111yescharacteristic
211C2×C4×C11C2×#4111yescharacteristic
212C2×C4×C11C2×#4111yescharacteristic
213C2×C4×C11C2×#4111yescharacteristic
214C22⋊D11—42no—
215C22⋊D11—42no—
216C22⋊D11—44no—
217C2×Dic11—22no—
218C2×Dic11—42no—
219C2×Dic11—42no—
220C2×Dic11—82no—
221C2×Dic11—82no—
222C2×Dic11—82no—
223D44—22no—
224D44—22no—
225D44—42no—
226C4×D11—42no—
227C4×D11—42no—
228C4×D11—44no—
229Dic22—22no—
230Dic22—22no—
231Dic22—42no—
232C8×C11—42no—
233C8×C11—42no—
234C11⋊C8—24no—
235C11⋊C8—42no—
236C22×#41—111no—
237C22×M16—111no—
238C22×M16—111no—
239C22×M16C2×D1111yescharacteristic
240C22×M16C2×D1111yescharacteristic
241C2×#117C2×D1111yescharacteristic
242C22×C4⋊C4—111no—
243#428—222no—
244#428—222no—
245C2×#107—112no—
246C2×#106—112no—
247#419—221no—
248#418—221no—
249#417—114no—
250#417—112no—
251#417—112no—
252#417—222no—
253#416—222no—
254C2×#103—221no—
255C2×#102—221no—
256#408—114no—
257#408—222no—
258#407—222no—
259#343—114no—
260#343C2×D1112yescomplemented
261#343C2×D1112yescomplemented
262#341—114no—
263C22×C11—21no—
264C22×C11—21no—
265C22×C11—21no—
266C22×C11—21no—
267C22×C11—21no—
268C22×C11—21no—
269C22×C11—42no—
270C22×C11—42no—
271C22×C11#39712yes—
272C22×C11#39712yes—
273C22×C11C2×#12111yescharacteristic
274C22×C11C2×#12611yescharacteristic
275C22×C11C2×#12611yescharacteristic
276C2×D11—42no—
277C2×D11—42no—
278C2×D11—42no—
279C2×D11—84no—
280C4×C11—81no—
281C4×C11—81no—
282C4×C11#39712yes—
283C4×C11#39712yes—
284C4×C11C2×#12311yescharacteristic
285C4×C11C2×#12311yescharacteristic
286C4×C11C2×#12311yescharacteristic
287C4×C11C2×#12411yescharacteristic
288Dic11—42no—
289Dic11—82no—
290C2×#41—112no—
291C2×#41—112no—
292C2×#41—221no—
293C2×#41—221no—
294C2×#41—222no—
295C2×#41—222no—
296C2×#41—222no—
297C2×#41—222no—
298C22×Q8—111no—
299C22×D4—111no—
300C22×D4—221no—
301C23×C4—221no—
302C23×C4—221no—
303C23×C4C22×D1111yescharacteristic
304C2×M16—21no—
305C2×M16—21no—
306C2×M16—22no—
307C2×M16—22no—
308C2×M16—22no—
309C2×M16—22no—
310C2×M16—112no—
311C2×M16—112no—
312C2×M16—112no—
313C2×M16—222no—
314C2×M16—222no—
315C2×M16—221no—
316C2×M16—222no—
317C2×M16—222no—
318C2×M16C22×D1112yes—
319C2×M16C22×D1112yes—
320C22×C8—21no—
321C22×C8—21no—
322C22×C8—112no—
323C22×C8—221no—
324#117—21no—
325#117—21no—
326#117—21no—
327#117—21no—
328C2×C4⋊C4—112no—
329C2×C4⋊C4—221no—
330C2×C4⋊C4—221no—
331C2×C4⋊C4—221no—
332C2×C4⋊C4—221no—
333C2×C4⋊C4—221no—
334C2×C4⋊C4C22×D1111yescharacteristic
335C2×C4⋊C4C22×D1111yescharacteristic
336C2×C22⋊C4—21no—
337C2×C42—21no—
338#107—224no—
339#106—224no—
340#103—222no—
341#103—222no—
342#103—224no—
343#102—222no—
344#102—222no—
345#102—224no—
346C22⋊C8—228no—
347C2×C11—22no—
348C2×C11—21no—
349C2×C11—21no—
350C2×C11—22no—
351C2×C11C2×#39711yescharacteristic
352C2×C11#306811yescharacteristic
353C2×C11#306911yescharacteristic
354D11—82no—
355C24—221no—
356C24#433911yescharacteristic
357#41—224no—
358#41—224no—
359#41—222no—
360#41—222no—
361#41—222no—
362#41—222no—
363#41—442no—
364#41—442no—
365#41—442no—
366#41—442no—
367C2×Q8—112no—
368C2×Q8—221no—
369C2×Q8—222no—
370C2×Q8—222no—
371C2×D4—112no—
372C2×D4—222no—
373C2×D4—222no—
374C2×D4—222no—
375C2×D4—221no—
376C2×D4—222no—
377C2×D4—442no—
378C2×D4—442no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—221no—
382C22×C4—222no—
383C22×C4—222no—
384C22×C4—222no—
385C22×C4—442no—
386C22×C4—442no—
387C22×C4—441no—
388C22×C4—441no—
389C22×C4—882no—
390C22×C4#433911yescharacteristic
391C22×C4#433912yes—
392C22×C4#433912yes—
393C22×C4D4×D1111yescharacteristic
394C22×C4D4×D1111yescharacteristic
395C22×C4D4×D1111yescharacteristic
396C22×C4D4×D1111yescharacteristic
397C22×C4#434112yes—
398C22×C4#434312yes—
399C22×C4C23×D1111yescharacteristic
400M16—22no—
401M16—22no—
402M16—22no—
403M16—22no—
404M16—42no—
405M16—42no—
406M16—224no—
407M16—224no—
408M16—222no—
409M16—222no—
410M16—442no—
411C2×C8—22no—
412C2×C8—22no—
413C2×C8—42no—
414C2×C8—42no—
415C2×C8—114no—
416C2×C8—222no—
417C2×C8—222no—
418C2×C8—222no—
419C2×C8—442no—
420C4⋊C4—21no—
421C4⋊C4—21no—
422C4⋊C4—21no—
423C4⋊C4—21no—
424C4⋊C4—222no—
425C4⋊C4—222no—
426C4⋊C4—441no—
427C4⋊C4—441no—
428C22⋊C4—41no—
429C22⋊C4—41no—
430C42—41no—
431C42—41no—
432C11#2364711yescharacteristic, complemented, Sylow
433C23—41no—
434C23—41no—
435C23—222no—
436C23—442no—
437C23—881no—
438C23—881no—
439C23#6692912yes—
440C23#6693711yescharacteristic
441C23#6693711yescharacteristic
442C23#6695112yes—
443C23C2×#433911yescharacteristic
444Q8—222no—
445Q8—222no—
446Q8—442no—
447D4—222no—
448D4—222no—
449D4—442no—
450D4—442no—
451D4—444no—
452D4—442no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—81no—
456C2×C4—81no—
457C2×C4—222no—
458C2×C4—442no—
459C2×C4—442no—
460C2×C4—442no—
461C2×C4—444no—
462C2×C4—442no—
463C2×C4—882no—
464C2×C4—882no—
465C2×C4—882no—
466C2×C4#6692912yes—
467C2×C4#6693612yes—
468C2×C4#6693612yes—
469C2×C4#6693711yescharacteristic
470C2×C4#6693711yescharacteristic
471C2×C4#6693812yes—
472C2×C4#6693812yes—
473C2×C4#6694712yes—
474C2×C4#6694712yes—
475C2×C4#6694712yes—
476C2×C4#6694712yes—
477C2×C4#6695112yes—
478C2×C4C2×#433911yescharacteristic
479C2×C4C2×#433911yescharacteristic
480C2×C4C2×D4×D1111yescharacteristic
481C2×C4C2×D4×D1111yescharacteristic
482C2×C4C2×#434111yescharacteristic
483C2×C4C2×#434311yescharacteristic
484C8—42no—
485C8—42no—
486C8—224no—
487C8—442no—
488C22—21no—
489C22—21no—
490C22—21no—
491C22—21no—
492C22—21no—
493C22—21no—
494C22—42no—
495C22—42no—
496C22—442no—
497C22—442no—
498C22—442no—
499C22—884no—
500C22#1062228812yes—
501C22#1062228812yes—
502C22C2×#6692911yescharacteristic
503C22C2×#6693711yescharacteristic
504C22C2×#6695111yescharacteristic
505C4—81no—
506C4—81no—
507C4—442no—
508C4—882no—
509C4#1062228812yes—
510C4#1062228812yes—
511C4C2×#6693611yescharacteristic
512C4C2×#6693811yescharacteristic
513C4C2×#6694711yescharacteristic
514C4C2×#6694711yescharacteristic
515C2—22no—
516C2—21no—
517C2—21no—
518C2—22no—
519C2—882no—
520C2C2×#1062228811yescharacteristic
521C2#1307834711yescharacteristic
522C2#1307835611yescharacteristic
subgroupG/H
centerC22C2×#66937
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1742C2
socleC22×C11C2×#121
prime radicalC22×#4339C22
hypercenter#1742D11
hypocenterC11#23647
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1742

Complements

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

NH ≅ G/Ntype
1. C2×#10622608C2semidirect
5. #13070065C2semidirect
6. #13070060C2semidirect
7. C2×#10622192C2semidirect
8. #13068342C2semidirect
9. C11×#1742C2semidirect
31. C2×#66872C22semidirect
32. C2×#66871C22semidirect
33. C11×#343C22semidirect
34. C11×#343C22semidirect
35. #10622196C22semidirect
36. #10622192C22semidirect
178. #1742D11semidirect
260. #343C2×D11semidirect
261. #343C2×D11semidirect
432. C11#23647semidirect

Maximal subgroups

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

subgroupindex
C2×#106226082
#130771332
C2×#106227462
#130770602
#130700652
#130700602
C2×#106221922
#130683422
C11×#17422
#2364711