Finite Group Databasebeta

← #14760315

Subgroups — #14760315

Order 2816.

954 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622426C211yesmaximal, characteristic
2C2×C4×#4326C211yesmaximal, characteristic, complemented
3C2×#10622321C211yesmaximal, characteristic
4#13071299C211yesmaximal, characteristic
5#13071292C211yesmaximal, characteristic
6#13069474C211yesmaximal, characteristic, complemented
7#13069348C211yesmaximal, characteristic, complemented
8#13069308C211yesmaximal, characteristic, complemented
9#13069304C211yesmaximal, characteristic, complemented
10#13069048C211yesmaximal, characteristic
11#13069046C211yesmaximal, characteristic
12#13068644C211yesmaximal, characteristic
13C4×#66871C211yesmaximal, characteristic, complemented
14#13068447C211yesmaximal, characteristic, complemented
15C11×#1763C211yesmaximal, characteristic, complemented
16C2×C4×Q8×C11C2211yescharacteristic
17C2×#66999C2211yescharacteristic
18C22×#4326C2211yescharacteristic
19C22×#4313C2211yescharacteristic
20C22×C8×D11C2211yescharacteristic
21C2×#66950C2211yescharacteristic
22C2×#66925C2211yescharacteristic
23C2×C4×Dic22C2211yescharacteristic
24C2×C11×#103C2211yescharacteristic
25C2×C11×#103C2211yescharacteristic
26C2×C11×#97C2211yescharacteristic
27C4×C11×C4⋊C4C2211yescharacteristic
28#10622843C2211yescharacteristic
29C2×#66899C2211yescharacteristic
30C2×#66880C2211yescharacteristic
31C2×#66880C2211yescharacteristic
32C2×#66879C2211yescharacteristic
33C2×C8×Dic11C2211yescharacteristic
34C4×#4326—24no—
35#10622603—21no—
36#10622600C2211yescharacteristic
37#10622600C2211yescharacteristic
38#10622598C2211yescharacteristic
39#10622587C2211yescharacteristic
40#10622586C2211yescharacteristic
41#10622585—21no—
42C2×#66874C2211yescharacteristic
43C2×#66871C2211yescharacteristic
44C2×#66871C2211yescharacteristic
45C2×#66871C2211yescharacteristic
46#10622553—21no—
47#10622553—21no—
48C4×C4⋊Dic11C2211yescharacteristic
49#10622546—21no—
50#10622541—21no—
51C2×C4×C11⋊C8C2211yescharacteristic
52#10622426C418yescomplemented
53#10622321—24no—
54#10622283—21no—
55#10622266—21no—
56C11×#340C2211yescharacteristic
57C11×#340C2211yescharacteristic
58#10622189C2211yescharacteristic
59#10622189C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62C22×Q8×C11C2311yescharacteristic
63C22×C4×D11C2311yescharacteristic
64C22×Dic22C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C4×Q8×C11—22no—
68C4×Q8×C11—22no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C42×C11—21no—
74C2×C42×C11—21no—
75C2×C42×C11C2311yescharacteristic
76#66999—22no—
77#66999C2×C414yes—
78C2×#4326—22no—
79C2×#4326—22no—
80C2×#4326C2×C414yes—
81C2×(C2×D11)⋊C4—21no—
82C2×(C2×D11)⋊C4—21no—
83C2×(C2×D11)⋊C4—21no—
84C2×(C2×D11)⋊C4—21no—
85C2×(C2×D11)⋊C4D411yescharacteristic
86C2×(C2×D11)⋊C4D411yescharacteristic
87C2×C4⋊Dic11—21no—
88C2×C4⋊Dic11—21no—
89C2×C4⋊Dic11C2311yescharacteristic
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92C2×Dic11⋊C4—21no—
93C2×Dic11⋊C4—21no—
94C2×Dic11⋊C4—21no—
95C2×Dic11⋊C4D411yescharacteristic
96C2×Dic11⋊C4D411yescharacteristic
97C2×C4×Dic11—21no—
98C2×C4×Dic11—21no—
99C2×C4×Dic11C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101C22×C11⋊C8C2311yescharacteristic
102C2×#4313—22no—
103C2×#4313—22no—
104C2×#4313—22no—
105C2×C8×D11—22no—
106C2×C8×D11—22no—
107C2×C8×D11C2×C414yes—
108#66950—22no—
109#66950C2×C414yes—
110#66925—22no—
111#66925—22no—
112C4×Dic22—22no—
113C4×Dic22—22no—
114C11×#103—22no—
115C11×#103C2×C414yes—
116C11×#97—22no—
117C11×#95—21no—
118#66899—22no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125C11⋊#95—21no—
126C11⋊#95—21no—
127C11⋊#95—21no—
128#66880—22no—
129#66880C2×C414yes—
130#66879—22no—
131C8×Dic11—22no—
132#66874—22no—
133#66871—22no—
134#66871—22no—
135#66871C2×C414yes—
136C4×C11⋊C8D414yes—
137#21525—111nomaximal, Sylow
138C23×D11C2×D411yescharacteristic
139C2×Q8×C11—21no—
140C2×Q8×C11—21no—
141C2×Q8×C11—21no—
142C2×Q8×C11—21no—
143C2×Q8×C11—21no—
144C2×Q8×C11C22×C412yes—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2411yescharacteristic
152C22×Dic11—21no—
153C22×Dic11—21no—
154C22×Dic11—21no—
155C22×Dic11—21no—
156C22×Dic11C2×D411yescharacteristic
157C22×Dic11C2×D411yescharacteristic
158C22×Dic11C2×D411yescharacteristic
159C2×C4×D11—21no—
160C2×C4×D11—21no—
161C2×C4×D11—21no—
162C2×C4×D11—21no—
163C2×C4×D11C22×C412yes—
164C2×C4×D11#4112yes—
165C2×Dic22—21no—
166C2×Dic22—21no—
167C2×Dic22—21no—
168C2×Dic22—21no—
169C2×Dic22—21no—
170C2×Dic22C22×C412yes—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11C22×C412yes—
176C2×C8×C11#4112yes—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—42no—
183C11×C4⋊C4C22×C412yes—
184C42×C11—42no—
185C42×C11—81no—
186C42×C11C2×D412yes—
187C42×C11#4112yes—
188#4326—28no—
189(C2×D11)⋊C4—24no—
190(C2×D11)⋊C4—24no—
191(C2×D11)⋊C4—22no—
192(C2×D11)⋊C4—22no—
193(C2×D11)⋊C4—81no—
194(C2×D11)⋊C4—81no—
195C4⋊Dic11—24no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—81no—
202C4⋊Dic11C22×C412yes—
203Dic11⋊C4—24no—
204Dic11⋊C4—22no—
205Dic11⋊C4—22no—
206Dic11⋊C4—42no—
207Dic11⋊C4—81no—
208C4×Dic11—21no—
209C4×Dic11—21no—
210C4×Dic11—42no—
211C4×Dic11—81no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8C22×C412yes—
215C2×C11⋊C8C2×D412yes—
216C2×C11⋊C8C2×D412yes—
217C2×C11⋊C8#4112yes—
218#4313—28no—
219C8×D11—28no—
220C2×#467—111no—
221C2×C4×Q16—111no—
222C2×#405—111no—
223#2323—111no—
224#2323—111no—
225#1969—111no—
226#1942—111no—
227#1935—111no—
228#1935—111no—
229#1894—111no—
230#1894—111no—
231#1808—111no—
232C4×#107—111no—
233#1763—111no—
234#1763D1111yescharacteristic, complemented
235C23×C11C22×D411yescharacteristic
236C22×D11—21no—
237C22×D11—21no—
238C22×D11—21no—
239C22×D11—21no—
240C22×D11—21no—
241C22×D11—21no—
242C22×D11C4×D412yes—
243Q8×C11—22no—
244Q8×C11—22no—
245Q8×C11—41no—
246Q8×C11—41no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—22no—
252C2×C4×C11—22no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11#12112yes—
264C2×C4×C11#12112yes—
265C2×C4×C11C23×C411yescharacteristic
266C2×C4×C11C22×D411yescharacteristic
267C2×C4×C11C2×#4111yescharacteristic
268C2×C4×C11C2×#4111yescharacteristic
269C2×C4×C11C2×#4111yescharacteristic
270C2×C4×C11C2×#4111yescharacteristic
271C2×Dic11—21no—
272C2×Dic11—21no—
273C2×Dic11—22no—
274C2×Dic11—22no—
275C2×Dic11—21no—
276C2×Dic11—21no—
277C2×Dic11—21no—
278C2×Dic11—21no—
279C2×Dic11—21no—
280C2×Dic11—21no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11C4×D412yes—
292C4×D11—22no—
293C4×D11—22no—
294C4×D11—22no—
295C4×D11—22no—
296Dic22—22no—
297Dic22—22no—
298Dic22—41no—
299Dic22—41no—
300C8×C11—22no—
301C8×C11—22no—
302C11⋊C8—22no—
303C11⋊C8C4×D414yes—
304C22×Q16—111no—
305C22×M16—111no—
306C23×C8—111no—
307C2×C22⋊Q8—111no—
308C2×C22⋊Q8—111no—
309C2×C4×Q8—111no—
310C2×C4×Q8C2×D1111yescharacteristic
311C2×#117—111no—
312#467—118no—
313C4×Q16—224no—
314C2×#107—111no—
315C2×#107—111no—
316C2×#107—111no—
317C2×#103—111no—
318C2×#103—111no—
319C2×#103—111no—
320C2×#103—111no—
321C2×#103C2×D1111yescharacteristic
322C2×#103C2×D1111yescharacteristic
323#405—224no—
324C2×#97—111no—
325C2×#97C2×D1111yescharacteristic
326C2×C4×C8—111no—
327C2×C4×C8—111no—
328#391—111no—
329#391—111no—
330#389—111no—
331#389—111no—
332#389—221no—
333#389—221no—
334#388—221no—
335#388—221no—
336#388—221no—
337#388—221no—
338#387—221no—
339#387—221no—
340#380—111no—
341#380—111no—
342C4×C4⋊C4—111no—
343C4×C4⋊C4C2×D1111yescharacteristic
344#340—111no—
345#340—111no—
346#340—111no—
347#340—111no—
348#340C2×D1111yescharacteristic
349#340C2×D1111yescharacteristic
350C22×C11C2×C4×D411yescharacteristic
351C22×C11C2×#12111yescharacteristic
352C22×C11#53211yescharacteristic
353C22×C11#57611yescharacteristic
354C22×C11#57811yescharacteristic
355C22×C11#57811yescharacteristic
356C22×C11#57811yescharacteristic
357C2×D11—22no—
358C2×D11—22no—
359C2×D11—22no—
360C2×D11—41no—
361C2×D11—41no—
362C2×D11—41no—
363C2×D11—41no—
364C4×C11—22no—
365C4×C11—22no—
366C4×C11—42no—
367C4×C11—42no—
368C4×C11—81no—
369C4×C11—81no—
370C4×C11C2×C4×D411yescharacteristic
371C4×C11C4×#4111yescharacteristic
372C4×C11#52511yescharacteristic
373C4×C11#52911yescharacteristic
374Dic11—22no—
375Dic11—42no—
376Dic11—41no—
377Dic11—41no—
378Dic11—42no—
379Dic11—81no—
380Dic11—81no—
381C22×Q8—111no—
382C22×Q8C22×D1111yescharacteristic
383C23×C4—111no—
384C2×Q16—114no—
385C2×Q16—222no—
386C2×Q16—222no—
387C2×M16—222no—
388C2×M16—222no—
389C2×M16—222no—
390C22×C8—111no—
391C22×C8—111no—
392C22×C8—114no—
393C22×C8—222no—
394C22×C8—222no—
395C22×C8C22×D1111yescharacteristic
396C22×C8C22×D1111yescharacteristic
397C22⋊Q8—114no—
398C22⋊Q8—114no—
399C22⋊Q8—222no—
400C22⋊Q8—222no—
401C4×Q8—22no—
402C4×Q8—22no—
403C4×Q8—222no—
404C4×Q8—222no—
405#117—222no—
406#117—222no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—111no—
409C2×C4⋊C4—111no—
410C2×C4⋊C4—111no—
411C2×C4⋊C4—111no—
412C2×C4⋊C4—111no—
413C2×C4⋊C4—221no—
414C2×C4⋊C4—221no—
415C2×C4⋊C4—221no—
416C2×C4⋊C4—221no—
417C2×C4⋊C4—221no—
418C2×C4⋊C4C22×D1111yescharacteristic
419C2×C4⋊C4C22×D1111yescharacteristic
420C2×C4⋊C4C22×D1111yescharacteristic
421C2×C22⋊C4—111no—
422C2×C22⋊C4—111no—
423C2×C22⋊C4—221no—
424C2×C22⋊C4—221no—
425C2×C22⋊C4—221no—
426C2×C22⋊C4—221no—
427C2×C42—21no—
428C2×C42—21no—
429C2×C42—111no—
430C2×C42—221no—
431C2×C42—221no—
432C2×C42C22×D1111yescharacteristic
433#107—114no—
434#107—222no—
435#107—222no—
436#103—22no—
437#103—114no—
438#103—222no—
439#103—222no—
440#103—222no—
441#103C4×D1114yes—
442#97—22no—
443#97—222no—
444C4×C8—114no—
445C4×C8—222no—
446#95—21no—
447#95—221no—
448#95—221no—
449#95—221no—
450#95—221no—
451#95—221no—
452#95—221no—
453#95—221no—
454#95—221no—
455#95—221no—
456C2×C11C4×#12111yescharacteristic
457C2×C11#295011yescharacteristic
458C2×C11#295111yescharacteristic
459C2×C11#305911yescharacteristic
460C2×C11#306111yescharacteristic
461C2×C11#317511yescharacteristic
462C2×C11#317711yescharacteristic
463D11—42no—
464C24—111no—
465C2×Q8—21no—
466C2×Q8—21no—
467C2×Q8—21no—
468C2×Q8—21no—
469C2×Q8—21no—
470C2×Q8—112no—
471C2×Q8—221no—
472C2×Q8—221no—
473C2×Q8—221no—
474C2×Q8—221no—
475C2×Q8—221no—
476C2×Q8C2×C4×D1112yes—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—111no—
482C22×C4—112no—
483C22×C4—112no—
484C22×C4—111no—
485C22×C4—111no—
486C22×C4—221no—
487C22×C4—221no—
488C22×C4—221no—
489C22×C4—221no—
490C22×C4—221no—
491C22×C4—221no—
492C22×C4—221no—
493C22×C4—221no—
494C22×C4D4×D1111yescharacteristic
495C22×C4D4×D1111yescharacteristic
496C22×C4C23×D1111yescharacteristic
497Q16—228no—
498M16—228no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—112no—
504C2×C8—112no—
505C2×C8—112no—
506C2×C8—112no—
507C2×C8—228no—
508C2×C8—221no—
509C2×C8—221no—
510C2×C8C2×C4×D1112yes—
511C2×C8#433912yes—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—42no—
518C4⋊C4—112no—
519C4⋊C4—224no—
520C4⋊C4—224no—
521C4⋊C4—222no—
522C4⋊C4—222no—
523C4⋊C4—221no—
524C4⋊C4—221no—
525C4⋊C4—221no—
526C4⋊C4—221no—
527C4⋊C4—221no—
528C4⋊C4—442no—
529C4⋊C4—881no—
530C4⋊C4—881no—
531C4⋊C4C2×C4×D1112yes—
532C22⋊C4—224no—
533C22⋊C4—224no—
534C22⋊C4—222no—
535C22⋊C4—222no—
536C22⋊C4—881no—
537C22⋊C4—881no—
538C42—42no—
539C42—81no—
540C42—221no—
541C42—221no—
542C42—442no—
543C42—881no—
544C42#433912yes—
545C42D4×D1112yes—
546C11#2152511yescharacteristic, complemented, Sylow
547C23—112no—
548C23—221no—
549C23—221no—
550C23—221no—
551C23—221no—
552C23—221no—
553C23—221no—
554C23C2×D4×D1111yescharacteristic
555Q8—22no—
556Q8—22no—
557Q8—41no—
558Q8—41no—
559Q8—222no—
560Q8—222no—
561Q8—441no—
562Q8—441no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—112no—
580C2×C4—221no—
581C2×C4—221no—
582C2×C4—222no—
583C2×C4—222no—
584C2×C4—222no—
585C2×C4—222no—
586C2×C4—221no—
587C2×C4—221no—
588C2×C4—221no—
589C2×C4—221no—
590C2×C4—221no—
591C2×C4—221no—
592C2×C4—222no—
593C2×C4—222no—
594C2×C4—441no—
595C2×C4—441no—
596C2×C4—441no—
597C2×C4—441no—
598C2×C4—441no—
599C2×C4—441no—
600C2×C4—441no—
601C2×C4—441no—
602C2×C4—441no—
603C2×C4—441no—
604C2×C4#6693712yes—
605C2×C4#6693712yes—
606C2×C4C22×C4×D1111yescharacteristic
607C2×C4C2×#433911yescharacteristic
608C2×C4C2×#433911yescharacteristic
609C2×C4C2×D4×D1111yescharacteristic
610C2×C4#41×D1111yescharacteristic
611C2×C4#41×D1111yescharacteristic
612C8—22no—
613C8—22no—
614C8—114no—
615C8—222no—
616C22—222no—
617C22—222no—
618C22—222no—
619C22—441no—
620C22—441no—
621C22—441no—
622C22—441no—
623C22C2×#6693711yescharacteristic
624C22C4×D4×D1111yescharacteristic
625C22#1062307911yescharacteristic
626C22#1062330511yescharacteristic
627C22#1062331011yescharacteristic
628C22#1062331011yescharacteristic
629C22#1062331011yescharacteristic
630C4—22no—
631C4—22no—
632C4—42no—
633C4—42no—
634C4—81no—
635C4—81no—
636C4—222no—
637C4—441no—
638C4—442no—
639C4—442no—
640C4—441no—
641C4—881no—
642C4—881no—
643C4C4×#433911yescharacteristic
644C4#1062305911yescharacteristic
645C4C4×D4×D1111yescharacteristic
646C4#1062307811yescharacteristic
647C2—442no—
648C2C4×#6693711yescharacteristic
649C2#1307748111yescharacteristic
650C2#1307748811yescharacteristic
651C2#1307827011yescharacteristic
652C2#1307828511yescharacteristic
653C2#1307925311yescharacteristic
654C2#1307927311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1763C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
cosocleC22×C4×C11C24
hypercenter#1763D11
hypocenterC11#21525
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1763

Complements

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

NH ≅ G/Ntype
2. C2×C4×#4326C2semidirect
6. #13069474C2semidirect
7. #13069348C2semidirect
8. #13069308C2semidirect
9. #13069304C2semidirect
13. C4×#66871C2semidirect
14. #13068447C2semidirect
15. C11×#1763C2semidirect
52. #10622426C4semidirect
234. #1763D11semidirect
546. C11#21525semidirect

Maximal subgroups

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

subgroupindex
C2×#106224262
C2×C4×#43262
C2×#106223212
#130712992
#130712922
#130694742
#130693482
#130693082
#130693042
#130690482
#130690462
#130686442
C4×#668712
#130684472
C11×#17632
#2152511