Finite Group Databasebeta

← #14782685

Subgroups — #14782685

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×#10622734C211yesmaximal, characteristic, complemented
2#13077136C211yesmaximal, characteristic
3C2×#10622746C211yesmaximal, characteristic
4#13077060C211yesmaximal, characteristic
5#13070063C214yesmaximal, complemented
6#13070058C214yesmaximal, complemented
7#13068354C211yesmaximal, characteristic, complemented
8C2×#10622192C211yesmaximal, characteristic, complemented
9C11×#1738C211yesmaximal, characteristic, complemented
10C22×#4339C2211yescharacteristic
11C22×C11×M16C2211yescharacteristic
12C22×C11×M16C2211yescharacteristic
13C22×C11×M16C2211yescharacteristic
14C2×#66979C2211yescharacteristic
15C22×C4⋊Dic11C2211yescharacteristic
16C22×#4318C2211yescharacteristic
17#10622746—22no—
18#10622746C2214yes—
19#10622746C2212yes—
20#10622746C2212yes—
21#10622744—21no—
22#10622742—22no—
23#10622739—22no—
24#10622734—22no—
25#10622734—22no—
26#10622733—21no—
27#10622726—22no—
28C2×#66885—21no—
29#10622723C2214yes—
30C2×#66882C2212yescomplemented
31C2×#66881C2212yescomplemented
32C2×#66880—21no—
33C11×#341C2214yescomplemented
34#10622192C2214yescomplemented
35#10622192C2212yescomplemented
36#10622192C2212yescomplemented
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—22no—
52C2×C11×M16—22no—
53C2×C11×M16—21no—
54C2×C11×M16—21no—
55C2×C11×M16—22no—
56C2×C11×M16—22no—
57C2×C11×M16—22no—
58C2×C11×M16—22no—
59C2×C11×M16D412yes—
60C2×C11×M16D412yes—
61C2×C11×M16C2312yes—
62C2×C11×M16C2312yes—
63C22×C8×C11—21no—
64C22×C8×C11—21no—
65C22×C8×C11C2312yes—
66C2×C22⋊Dic11—21no—
67#66979—21no—
68#66979—21no—
69#66979—21no—
70#66979—21no—
71C2×C4⋊Dic11—21no—
72C2×C4⋊Dic11—21no—
73C2×C4⋊Dic11—21no—
74C2×C4⋊Dic11—21no—
75C2×C4⋊Dic11—21no—
76C2×C4⋊Dic11C2312yes—
77C2×C4⋊Dic11C2311yescharacteristic
78C2×C4⋊Dic11C2311yescharacteristic
79C2×C4×Dic11—21no—
80C2×#4318—21no—
81C2×#4318—22no—
82C2×#4318—22no—
83C2×#4318C2312yes—
84C22×C11⋊C8—21no—
85#66885—24no—
86#66885—22no—
87#66885—22no—
88(C2×D11)⋊C8—28no—
89#66882—24no—
90#66881—24no—
91#66880—22no—
92#66880—22no—
93#66880—24no—
94#23647—111nomaximal, Sylow
95C24×C11#4111yescharacteristic
96C23×D11—21no—
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11#4111yescharacteristic
102C22×C4×C11#4112yes—
103C22×C4×C11#4112yes—
104C22×C4×C11#4112yes—
105C22×C4×C11#4112yes—
106C22×C4×C11C2411yescharacteristic
107C2×C22⋊D11—22no—
108C2×C22⋊D11—22no—
109C2×C22⋊D11—42no—
110C2×C22⋊D11—42no—
111C22×Dic11—21no—
112C22×Dic11—21no—
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—24no—
141C11×M16—24no—
142C11×M16—22no—
143C11×M16—22no—
144C11×M16—22no—
145C11×M16—22no—
146C11×M16—42no—
147C11×M16—42no—
148C2×C8×C11—22no—
149C2×C8×C11—22no—
150C2×C8×C11—22no—
151C2×C8×C11—22no—
152C2×C8×C11—42no—
153C2×C8×C11—42no—
154C2×C8×C11C2×D414yes—
155C22⋊Dic11—41no—
156C22⋊Dic11—41no—
157C4⋊Dic11—22no—
158C4⋊Dic11—21no—
159C4⋊Dic11—21no—
160C4⋊Dic11—21no—
161C4⋊Dic11—22no—
162C4⋊Dic11—21no—
163C4⋊Dic11—41no—
164C4⋊Dic11—41no—
165C4×Dic11—41no—
166C4×Dic11—41no—
167#4318—22no—
168#4318—22no—
169#4318—42no—
170C2×C11⋊C8—22no—
171C2×C11⋊C8—42no—
172C2×#428—111no—
173#2896—111no—
174C2×#417—111no—
175#2879—111no—
176#2079—114no—
177#2078—114no—
178#1742—111no—
179C2×#343—111no—
180#1738D1111yescharacteristic, complemented
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#12111yescharacteristic
193C2×C4×C11#12111yescharacteristic
194C2×C4×C11#12312yes—
195C2×C4×C11#12312yes—
196C2×C4×C11#12312yes—
197C2×C4×C11#12312yes—
198C2×C4×C11#12312yes—
199C2×C4×C11#12312yes—
200C2×C4×C11#12412yes—
201C2×C4×C11#12412yes—
202C2×C4×C11#12612yes—
203C2×C4×C11#12612yes—
204C2×C4×C11C22×D411yescharacteristic
205C2×C4×C11C22×D411yescharacteristic
206C2×C4×C11C2×#4111yescharacteristic
207C2×C4×C11C2×#4111yescharacteristic
208C2×C4×C11C2×#4111yescharacteristic
209C2×C4×C11C2×#4111yescharacteristic
210C22⋊D11—42no—
211C22⋊D11—42no—
212C22⋊D11—44no—
213C2×Dic11—22no—
214C2×Dic11—42no—
215C2×Dic11—41no—
216C2×Dic11—41no—
217C2×Dic11—42no—
218C2×Dic11—82no—
219C2×Dic11—82no—
220C2×Dic11—81no—
221C2×Dic11—81no—
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—24no—
233C8×C11—42no—
234C8×C11—42no—
235C11⋊C8—42no—
236C22×#41—111no—
237C22×M16—111no—
238C22×M16C2×D1111yescharacteristic
239C22×M16C2×D1111yescharacteristic
240C22×M16C2×D1111yescharacteristic
241C2×#117—111no—
242C22×C4⋊C4—111no—
243#428—222no—
244#428—222no—
245C2×#107—112no—
246C2×#106—112no—
247#419—221no—
248#418—221no—
249#417—112no—
250#417—114no—
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—112no—
260#343—114no—
261#343—112no—
262#341C2×D1114yescomplemented
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#39712yes—
281C4×C11#39712yes—
282C4×C11C2×#12311yescharacteristic
283C4×C11C2×#12311yescharacteristic
284C4×C11C2×#12311yescharacteristic
285C4×C11C2×#12411yescharacteristic
286Dic11—42no—
287Dic11—81no—
288Dic11—82no—
289Dic11—81no—
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—22no—
305C2×M16—22no—
306C2×M16—21no—
307C2×M16—21no—
308C2×M16—22no—
309C2×M16—22no—
310C2×M16—22no—
311C2×M16—22no—
312C2×M16—112no—
313C2×M16—221no—
314C2×M16—222no—
315C2×M16—222no—
316C2×M16D4412yes—
317C2×M16D4412yes—
318C2×M16C22×D1112yes—
319C2×M16C22×D1112yes—
320C22×C8—21no—
321C22×C8—21no—
322C22×C8—221no—
323C22×C8C22×D1112yes—
324#117—221no—
325#117—221no—
326#117—221no—
327#117—221no—
328C2×C4⋊C4—112no—
329C2×C4⋊C4—111no—
330C2×C4⋊C4—111no—
331C2×C4⋊C4—221no—
332C2×C4⋊C4—221no—
333C2×C4⋊C4—221no—
334C2×C4⋊C4—221no—
335C2×C4⋊C4—221no—
336C2×C22⋊C4—221no—
337C2×C42—221no—
338#107—224no—
339#106—224no—
340#103—224no—
341#103—222no—
342#103—222no—
343#102—224no—
344#102—222no—
345#102—222no—
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#434311yescharacteristic
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—222no—
376C2×D4—221no—
377C2×D4—442no—
378C2×D4—442no—
379C22×C4—221no—
380C22×C4—222no—
381C22×C4—222no—
382C22×C4—221no—
383C22×C4—221no—
384C22×C4—222no—
385C22×C4—442no—
386C22×C4—442no—
387C22×C4—441no—
388C22×C4—441no—
389C22×C4—882no—
390C22×C4C2×D4411yescharacteristic
391C22×C4C2×D4411yescharacteristic
392C22×C4#433912yes—
393C22×C4#433912yes—
394C22×C4D4×D1111yescharacteristic
395C22×C4D4×D1111yescharacteristic
396C22×C4#434112yes—
397C22×C4#434112yes—
398C22×C4#434311yescharacteristic
399C22×C4C23×D1111yescharacteristic
400M16—24no—
401M16—24no—
402M16—22no—
403M16—22no—
404M16—22no—
405M16—22no—
406M16—42no—
407M16—42no—
408M16—222no—
409M16—222no—
410M16—442no—
411C2×C8—22no—
412C2×C8—22no—
413C2×C8—22no—
414C2×C8—22no—
415C2×C8—42no—
416C2×C8—42no—
417C2×C8—222no—
418C2×C8—442no—
419C2×C8C2×D4414yes—
420C4⋊C4—221no—
421C4⋊C4—222no—
422C4⋊C4—221no—
423C4⋊C4—222no—
424C4⋊C4—221no—
425C4⋊C4—221no—
426C4⋊C4—441no—
427C4⋊C4—441no—
428C22⋊C4—441no—
429C22⋊C4—441no—
430C42—441no—
431C42—441no—
432C11#2364711yescharacteristic, complemented, Sylow
433C23—41no—
434C23—41no—
435C23—222no—
436C23—442no—
437C23—881no—
438C23—881no—
439C23#6694811yescharacteristic
440C23#6694811yescharacteristic
441C23#6695112yes—
442C23#6695112yes—
443C23C2×#434311yescharacteristic
444Q8—222no—
445Q8—222no—
446Q8—442no—
447D4—222no—
448D4—222no—
449D4—442no—
450D4—442no—
451D4—444no—
452D4—442no—
453C2×C4—222no—
454C2×C4—442no—
455C2×C4—442no—
456C2×C4—442no—
457C2×C4—444no—
458C2×C4—441no—
459C2×C4—441no—
460C2×C4—442no—
461C2×C4—882no—
462C2×C4—882no—
463C2×C4—882no—
464C2×C4—881no—
465C2×C4—881no—
466C2×C4#6692812yes—
467C2×C4#6692812yes—
468C2×C4#6693612yes—
469C2×C4#6693612yes—
470C2×C4#6693612yes—
471C2×C4#6693612yes—
472C2×C4#6693912yes—
473C2×C4#6693912yes—
474C2×C4#6694811yescharacteristic
475C2×C4#6694811yescharacteristic
476C2×C4#6695112yes—
477C2×C4#6695112yes—
478C2×C4C22×D4411yescharacteristic
479C2×C4C2×#433911yescharacteristic
480C2×C4C2×#433911yescharacteristic
481C2×C4C2×D4×D1111yescharacteristic
482C2×C4C2×#434111yescharacteristic
483C2×C4C2×#434111yescharacteristic
484C8—24no—
485C8—42no—
486C8—42no—
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#1062228712yes—
501C22#1062228712yes—
502C22C2×#6694811yescharacteristic
503C22C2×#6695111yescharacteristic
504C22C2×#6695111yescharacteristic
505C4—442no—
506C4—882no—
507C4—881no—
508C4—881no—
509C4#1062228712yes—
510C4#1062228712yes—
511C4C2×#6692811yescharacteristic
512C4C2×#6693611yescharacteristic
513C4C2×#6693611yescharacteristic
514C4C2×#6693911yescharacteristic
515C2—22no—
516C2—21no—
517C2—21no—
518C2—22no—
519C2—882no—
520C2C2×#1062228711yescharacteristic
521C2#1307834511yescharacteristic
522C2#1307835411yescharacteristic
subgroupG/H
centerC22C2×#66948
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1738C2
socleC22×C11C2×#121
prime radicalC22×#4339C22
hypercenter#1738D11
hypocenterC11#23647
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1738

Complements

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

NH ≅ G/Ntype
1. C2×#10622734C2semidirect
5. #13070063C2semidirect
6. #13070058C2semidirect
7. #13068354C2semidirect
8. C2×#10622192C2semidirect
9. C11×#1738C2semidirect
30. C2×#66882C22semidirect
31. C2×#66881C22semidirect
33. C11×#341C22semidirect
34. #10622192C22semidirect
35. #10622192C22semidirect
36. #10622192C22semidirect
180. #1738D11semidirect
262. #341C2×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×#106227342
#130771362
C2×#106227462
#130770602
#130700632
#130700582
#130683542
C2×#106221922
C11×#17382
#2364711