Finite Group Databasebeta

← #14781145

Subgroups — #14781145

Order 2816.

1222 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082021C211yesmaximal, characteristic, complemented
2#13077136C211yesmaximal, characteristic
3#13077133C211yesmaximal, characteristic
4#13071106C211yesmaximal, characteristic
5#13069776C214yesmaximal, complemented
6#13069771C214yesmaximal, complemented
7#13068354C211yesmaximal, characteristic, complemented
8C2×#10622161C211yesmaximal, characteristic, complemented
9C2×C11×#339C211yesmaximal, characteristic, complemented
10C22×#4339C2211yescharacteristic
11C22×C11×M16C2211yescharacteristic
12C2×C11×#117C2211yescharacteristic
13C22×C42×C11C2211yescharacteristic
14C2×#66979C2211yescharacteristic
15C2×#66979C2211yescharacteristic
16C22×#4318C2211yescharacteristic
17#10623050—22no—
18#10623050C2214yes—
19#10623048—22no—
20#10623048—22no—
21#10623031—22no—
22#10623014—22no—
23#10623001—22no—
24#10622826—22no—
25#10622746—22no—
26#10622744C2212yes—
27#10622733C2212yes—
28#10622726—22no—
29#10622617C2212yes—
30#10622615—22no—
31#10622614C2212yes—
32#10622579—22no—
33#10622552C2212yes—
34C4×(C2×D11)⋊C4—22no—
35#10622542C2212yes—
36C11×#339C2214yes—
37#10622192C2214yes—
38#10622161C2214yes—
39C23×C4×C11—21no—
40C23×C4×C11C2311yescharacteristic
41C22×C22⋊D11—21no—
42C2×#4339—22no—
43C2×#4339—21no—
44C2×#4339—21no—
45C2×#4339—21no—
46C2×#4339—21no—
47C2×#4339—22no—
48C2×#4339—22no—
49C2×#4339Q814yescomplemented
50C22×D44C2311yescharacteristic
51C22×C4×D11—21no—
52C22×Dic22C2311yescharacteristic
53C2×C11×M16—21no—
54C2×C11×M16—22no—
55C2×C11×M16—22no—
56C2×C11×M16C2312yes—
57C22×C8×C11—21no—
58C11×#117—21no—
59C11×#117—21no—
60C11×#117D412yes—
61C11×#117C2312yes—
62C2×C11×C4⋊C4D412yes—
63C2×C11×C22⋊C4—21no—
64C2×C42×C11—21no—
65C2×C42×C11—22no—
66C2×C42×C11—22no—
67C2×C42×C11—21no—
68C2×C42×C11C2312yes—
69C2×C22⋊Dic11—21no—
70C2×C22⋊Dic11D412yes—
71C2×(C2×D11)⋊C4—24no—
72#66979—21no—
73#66979—21no—
74#66979—21no—
75#66979—21no—
76#66979—21no—
77#66979—21no—
78#66979D412yes—
79#66979C2312yes—
80C2×C4⋊Dic11D412yes—
81C2×C4⋊Dic11C2312yes—
82#66977—28no—
83C2×C4×Dic11—21no—
84C2×C4×Dic11D412yes—
85C2×#4318—21no—
86C2×#4318—22no—
87C2×#4318—22no—
88C2×#4318C2312yes—
89C22×C11⋊C8—21no—
90#66943—24no—
91#66943—24no—
92#66941—24no—
93#66941—24no—
94#66931—28no—
95#66931—28no—
96#66923—24no—
97#66922—24no—
98C4×Dic22—28no—
99C11⋊#95—24no—
100#66885—24no—
101#66880—24no—
102#66874—24no—
103#66873—24no—
104#23461—111nomaximal, Sylow
105C24×C11C2×D411yescharacteristic
106C23×D11—21no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—44no—
110C22×C4×C11—42no—
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2×Q812yes—
117C22×C4×C11#4112yes—
118C22×C4×C11#4112yes—
119C22×C4×C11#4112yes—
120C22×C4×C11C2411yescharacteristic
121C2×C22⋊D11—24no—
122C2×C22⋊D11—41no—
123C2×C22⋊D11—41no—
124C2×C22⋊D11—42no—
125C22×Dic11—22no—
126C22×Dic11—21no—
127C22×Dic11C2×D414yes—
128#4339—24no—
129#4339—24no—
130#4339—24no—
131#4339—24no—
132#4339—42no—
133#4339—42no—
134#4339—42no—
135#4339—42no—
136C2×D44—21no—
137C2×D44—21no—
138C2×D44—21no—
139C2×D44—21no—
140C2×D44—21no—
141C2×D44C2×Q812yes—
142C2×C4×D11—24no—
143C2×C4×D11—41no—
144C2×C4×D11—41no—
145C2×C4×D11—42no—
146C2×Dic22—28no—
147C2×Dic22—21no—
148C2×Dic22—21no—
149C2×Dic22—21no—
150C2×Dic22—21no—
151C2×Dic22—21no—
152C2×Dic22C2×Q812yes—
153C11×M16—22no—
154C11×M16—22no—
155C11×M16—42no—
156C2×C8×C11—22no—
157C2×C8×C11—42no—
158C11×C4⋊C4—22no—
159C11×C4⋊C4C2×D414yes—
160C11×C22⋊C4—22no—
161C11×C22⋊C4—22no—
162C42×C11—22no—
163C42×C11—22no—
164C42×C11—22no—
165C42×C11—22no—
166C42×C11—42no—
167C22⋊Dic11—22no—
168C22⋊Dic11—22no—
169C22⋊Dic11—22no—
170C22⋊Dic11—22no—
171(C2×D11)⋊C4—48no—
172C4⋊Dic11—28no—
173C4⋊Dic11—22no—
174C4⋊Dic11—22no—
175C4⋊Dic11—22no—
176C4⋊Dic11C2×D414yes—
177Dic11⋊C4—28no—
178Dic11⋊C4—28no—
179C4×Dic11—22no—
180C4×Dic11—22no—
181C4×Dic11—22no—
182C4×Dic11—22no—
183#4318—22no—
184#4318—22no—
185#4318—42no—
186C2×C11⋊C8—22no—
187C2×C11⋊C8—42no—
188#3458—111no—
189#2896—111no—
190#2896—111no—
191#2297—111no—
192#2028—114no—
193#2027—114no—
194#1742—111no—
195C2×#339—111no—
196C2×#339D1111yescharacteristic, complemented
197C23×C11—42no—
198C23×C11#12011yescharacteristic
199C23×C11#12011yescharacteristic
200C23×C11C22⋊Q812yes—
201C23×C11#12412yes—
202C23×C11C22×D411yescharacteristic
203C22×D11—22no—
204C22×D11—44no—
205C22×D11—41no—
206C22×D11—41no—
207C2×C4×C11—24no—
208C2×C4×C11—24no—
209C2×C4×C11—42no—
210C2×C4×C11—48no—
211C2×C4×C11—42no—
212C2×C4×C11—82no—
213C2×C4×C11#12011yescharacteristic
214C2×C4×C11#12011yescharacteristic
215C2×C4×C11C22⋊Q812yes—
216C2×C4×C11C22⋊Q812yes—
217C2×C4×C11C22⋊Q812yes—
218C2×C4×C11C22⋊Q812yes—
219C2×C4×C11C22⋊Q812yes—
220C2×C4×C11#12412yes—
221C2×C4×C11#12412yes—
222C2×C4×C11#12412yes—
223C2×C4×C11#12412yes—
224C2×C4×C11#12412yes—
225C2×C4×C11C22×D411yescharacteristic
226C2×C4×C11C22×D411yescharacteristic
227C2×C4×C11C22×Q811yescharacteristic
228C2×C4×C11C2×#4111yescharacteristic
229C2×C4×C11C2×#4111yescharacteristic
230C2×C4×C11C2×#4111yescharacteristic
231C22⋊D11—44no—
232C22⋊D11—44no—
233C2×Dic11—24no—
234C2×Dic11—24no—
235C2×Dic11—22no—
236C2×Dic11—41no—
237C2×Dic11—41no—
238C2×Dic11—44no—
239C2×Dic11—82no—
240D44—22no—
241D44—22no—
242D44—41no—
243D44—41no—
244C4×D11—44no—
245C4×D11—44no—
246Dic22—22no—
247Dic22—22no—
248Dic22—41no—
249Dic22—41no—
250Dic22—88no—
251C8×C11—42no—
252C11⋊C8—42no—
253C22×#41—111no—
254C22×M16—111no—
255C22×M16C2×D1111yescharacteristic
256#544—114no—
257#544—222no—
258#544—222no—
259#543—222no—
260#533—222no—
261#533—222no—
262#533—222no—
263C2×#117—111no—
264C2×#117—111no—
265C2×#117C2×D1111yescharacteristic
266C22×C42C2×D1111yescharacteristic
267#419—112no—
268#419—112no—
269#418—112no—
270#418—112no—
271#417—222no—
272#417—222no—
273#416—222no—
274#416—222no—
275#391—112no—
276#390—112no—
277#386—222no—
278C4×C22⋊C4—222no—
279#343—114no—
280#339—114no—
281#339C2×D1114yes—
282C22×C11—22no—
283C22×C11—22no—
284C22×C11—22no—
285C22×C11—42no—
286C22×C11—42no—
287C22×C11#39312yes—
288C22×C11#39312yes—
289C22×C11C2×#12011yescharacteristic
290C22×C11C2×C22⋊Q811yescharacteristic
291C22×C11C2×#12411yescharacteristic
292C2×D11—44no—
293C2×D11—42no—
294C2×D11—82no—
295C2×D11—82no—
296C4×C11—44no—
297C4×C11—44no—
298C4×C11#39312yes—
299C4×C11#39312yes—
300C4×C11C2×C22⋊Q811yescharacteristic
301C4×C11C2×C22⋊Q811yescharacteristic
302C4×C11C2×#12411yescharacteristic
303C4×C11C2×#12411yescharacteristic
304Dic11—42no—
305Dic11—44no—
306Dic11—44no—
307C2×#41—114no—
308C2×#41—222no—
309C2×#41—221no—
310C2×#41—221no—
311C2×#41—222no—
312C2×#41—221no—
313C2×#41—221no—
314C2×#41—222no—
315C22×Q8—111no—
316C22×D4—111no—
317C22×D4—221no—
318C23×C4—21no—
319C23×C4—221no—
320C23×C4C22×D1111yescharacteristic
321C2×M16—21no—
322C2×M16—22no—
323C2×M16—22no—
324C2×M16—112no—
325C2×M16—221no—
326C2×M16—222no—
327C2×M16—222no—
328C2×M16C22×D1112yes—
329C22×C8—21no—
330C22×C8—221no—
331C4⋊Q8—224no—
332C4⋊Q8—224no—
333C4⋊Q8—224no—
334#125—224no—
335#125—224no—
336#125—224no—
337C22⋊Q8—228no—
338C22⋊Q8—228no—
339C22⋊Q8—228no—
340C4×Q8—228no—
341#117—21no—
342#117—21no—
343#117—112no—
344#117—112no—
345#117—221no—
346#117—221no—
347#117—221no—
348#117—221no—
349#117—221no—
350#117—221no—
351#117D4412yes—
352#117C22×D1112yes—
353C2×C4⋊C4—112no—
354C2×C4⋊C4—112no—
355C2×C4⋊C4D4412yes—
356C2×C22⋊C4—21no—
357C2×C22⋊C4—112no—
358C2×C22⋊C4—221no—
359C2×C22⋊C4—224no—
360C2×C42—21no—
361C2×C42—22no—
362C2×C42—22no—
363C2×C42—21no—
364C2×C42—112no—
365C2×C42—221no—
366C2×C42C22×D1112yes—
367#103—224no—
368#103—224no—
369#102—224no—
370#102—224no—
371#95—224no—
372C2×C11—21no—
373C2×C11—21no—
374C2×C11—22no—
375C2×C11—22no—
376C2×C11C2×#39311yescharacteristic
377C2×C11#301812yes—
378D11—82no—
379C24—221no—
380C24D4×D1111yescharacteristic
381#41—224no—
382#41—224no—
383#41—224no—
384#41—224no—
385#41—442no—
386#41—442no—
387#41—442no—
388#41—442no—
389C2×Q8—112no—
390C2×Q8—228no—
391C2×Q8—221no—
392C2×Q8—221no—
393C2×Q8—221no—
394C2×Q8—221no—
395C2×Q8—221no—
396C2×D4—112no—
397C2×D4—224no—
398C2×D4—221no—
399C2×D4—221no—
400C2×D4—221no—
401C2×D4—221no—
402C2×D4—221no—
403C2×D4—441no—
404C2×D4—441no—
405C2×D4—442no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—44no—
409C22×C4—42no—
410C22×C4—114no—
411C22×C4—221no—
412C22×C4—222no—
413C22×C4—224no—
414C22×C4—441no—
415C22×C4—441no—
416C22×C4—442no—
417C22×C4C2×D4411yescharacteristic
418C22×C4C2×D4411yescharacteristic
419C22×C4#433912yes—
420C22×C4#433912yes—
421C22×C4D4×D1111yescharacteristic
422C22×C4D4×D1111yescharacteristic
423C22×C4D4×D1111yescharacteristic
424C22×C4#434112yes—
425C22×C4Q8×D1112yes—
426C22×C4C23×D1111yescharacteristic
427M16—22no—
428M16—22no—
429M16—42no—
430M16—222no—
431M16—222no—
432M16—442no—
433C2×C8—22no—
434C2×C8—42no—
435C2×C8—222no—
436C2×C8—442no—
437C4⋊C4—22no—
438C4⋊C4—114no—
439C4⋊C4—228no—
440C4⋊C4—228no—
441C4⋊C4—228no—
442C4⋊C4—222no—
443C4⋊C4—222no—
444C4⋊C4—222no—
445C4⋊C4C2×D4414yes—
446C22⋊C4—22no—
447C22⋊C4—22no—
448C22⋊C4—222no—
449C22⋊C4—222no—
450C22⋊C4—222no—
451C22⋊C4—222no—
452C22⋊C4—448no—
453C42—22no—
454C42—22no—
455C42—22no—
456C42—22no—
457C42—42no—
458C42—222no—
459C42—222no—
460C42—222no—
461C42—222no—
462C11#2346111yescharacteristic, complemented, Sylow
463C23—42no—
464C23—222no—
465C23—444no—
466C23—441no—
467C23—441no—
468C23#6693511yescharacteristic
469C23#6693511yescharacteristic
470C23#6693812yes—
471C23#6694912yes—
472C23C2×D4×D1111yescharacteristic
473Q8—222no—
474Q8—222no—
475Q8—441no—
476Q8—441no—
477Q8—888no—
478D4—222no—
479D4—222no—
480D4—444no—
481D4—444no—
482D4—441no—
483D4—441no—
484C2×C4—24no—
485C2×C4—24no—
486C2×C4—42no—
487C2×C4—48no—
488C2×C4—42no—
489C2×C4—82no—
490C2×C4—224no—
491C2×C4—224no—
492C2×C4—222no—
493C2×C4—441no—
494C2×C4—441no—
495C2×C4—444no—
496C2×C4—444no—
497C2×C4—444no—
498C2×C4—882no—
499C2×C4#6692812yes—
500C2×C4#6692812yes—
501C2×C4#6693511yescharacteristic
502C2×C4#6693511yescharacteristic
503C2×C4#6693812yes—
504C2×C4#6693812yes—
505C2×C4#6693812yes—
506C2×C4#6694912yes—
507C2×C4#6694912yes—
508C2×C4#6694912yes—
509C2×C4#6695012yes—
510C2×C4#6695012yes—
511C2×C4C22×D4411yescharacteristic
512C2×C4C2×#433911yescharacteristic
513C2×C4C2×#433911yescharacteristic
514C2×C4C2×D4×D1111yescharacteristic
515C2×C4C2×#434111yescharacteristic
516C2×C4C2×Q8×D1111yescharacteristic
517C8—42no—
518C8—442no—
519C22—22no—
520C22—22no—
521C22—22no—
522C22—42no—
523C22—42no—
524C22—444no—
525C22—442no—
526C22—882no—
527C22—882no—
528C22#1062228612yes—
529C22#1062228612yes—
530C22C2×#6693511yescharacteristic
531C22C2×#6693811yescharacteristic
532C22C2×#6694911yescharacteristic
533C4—44no—
534C4—44no—
535C4—442no—
536C4—444no—
537C4—444no—
538C4#1062228612yes—
539C4#1062228612yes—
540C4C2×#6692811yescharacteristic
541C4C2×#6693811yescharacteristic
542C4C2×#6694911yescharacteristic
543C4C2×#6695011yescharacteristic
544C2—21no—
545C2—21no—
546C2—22no—
547C2—22no—
548C2—882no—
549C2C2×#1062228611yescharacteristic
550C2#1307796712yes—
subgroupG/H
centerC2×C4#66935
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#339C2
socleC22×C11C2×#120
prime radicalC22×#4339C22
hypercenterC2×#339D11
hypocenterC11#23461
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#339

Complements

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

NH ≅ G/Ntype
1. #13082021C2semidirect
5. #13069776C2semidirect
6. #13069771C2semidirect
7. #13068354C2semidirect
8. C2×#10622161C2semidirect
9. C2×C11×#339C2semidirect
49. C2×#4339Q8semidirect
196. C2×#339D11semidirect
462. C11#23461semidirect

Maximal subgroups

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

subgroupindex
#130820212
#130771362
#130771332
#130711062
#130697762
#130697712
#130683542
C2×#106221612
C2×C11×#3392
#2346111