Finite Group Databasebeta

← #14760461

Subgroups — #14760461

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×#10622665C211yesmaximal, characteristic
2C2×C4×#4326C211yesmaximal, characteristic, complemented
3C2×#10622610C211yesmaximal, characteristic
4#13071298C211yesmaximal, characteristic
5#13069486C211yesmaximal, characteristic, complemented
6#13069356C211yesmaximal, characteristic, complemented
7#13069295C211yesmaximal, characteristic, complemented
8#13069291C211yesmaximal, characteristic, complemented
9#13069040C211yesmaximal, characteristic
10#13069037C211yesmaximal, characteristic
11#13068647C211yesmaximal, characteristic
12C4×#66872C211yesmaximal, characteristic, complemented
13#13068449C211yesmaximal, characteristic, complemented
14#13068446C211yesmaximal, characteristic, complemented
15C11×#2323C211yesmaximal, characteristic
16C2×C11×C22⋊Q8C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×C11×#117C2211yescharacteristic
19C22×#4326C2211yescharacteristic
20C2×#66977C2211yescharacteristic
21C22×#4318C2211yescharacteristic
22C23×C11⋊C8C2211yescharacteristic
23C2×C4×Dic22C2211yescharacteristic
24C11×#391C2211yescharacteristic
25C11×#389—21no—
26C11×#389C2211yescharacteristic
27C11×#388—21no—
28C11×#388—21no—
29C11×#387—21no—
30C11×#380C2211yescharacteristic
31C4×C11×C4⋊C4C2211yescharacteristic
32C2×#66899C2211yescharacteristic
33C2×#66899C2211yescharacteristic
34C2×#66899C2211yescharacteristic
35#10622825C2211yescharacteristic
36#10622665C418yescomplemented
37C4×#4326—24no—
38#10622610—24no—
39#10622591—21no—
40#10622585—21no—
41C2×#66874C2211yescharacteristic
42C2×#66874C2211yescharacteristic
43C2×#66874C2211yescharacteristic
44C2×#66872C2211yescharacteristic
45C2×#66872C2211yescharacteristic
46C2×#66871C2211yescharacteristic
47#10622558—21no—
48#10622557—21no—
49C4×C4⋊Dic11C2211yescharacteristic
50#10622542C2211yescharacteristic
51#10622541C2211yescharacteristic
52C2×#66867C2211yescharacteristic
53C2×#66867C2211yescharacteristic
54C2×C4×C11⋊C8C2211yescharacteristic
55C2×C4×C11⋊C8C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62C22×Q8×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C22×Dic22C2311yescharacteristic
65C11×C22⋊Q8—22no—
66C11×C22⋊Q8C2×C414yes—
67C4×Q8×C11—22no—
68C4×Q8×C11—22no—
69C11×#117—22no—
70C11×#117—22no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4D411yescharacteristic
75C2×C11×C4⋊C4D411yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C22⋊C4—21no—
80C2×C11×C22⋊C4—21no—
81C2×C11×C22⋊C4D411yescharacteristic
82C2×C11×C22⋊C4D411yescharacteristic
83C2×C42×C11—21no—
84C2×C42×C11—21no—
85C2×C42×C11C2311yescharacteristic
86C2×C42×C11C2311yescharacteristic
87C2×C22⋊Dic11—21no—
88C2×C22⋊Dic11—21no—
89C2×#4326—22no—
90C2×#4326—22no—
91C2×#4326C2×C414yes—
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95#66977—22no—
96#66977C2×C414yes—
97C2×Dic11⋊C4—21no—
98C2×Dic11⋊C4—21no—
99C2×Dic11⋊C4—21no—
100C2×C4×Dic11—21no—
101C2×C4×Dic11—21no—
102C2×#4318—22no—
103C2×#4318—22no—
104C2×#4318C2×C414yes—
105C22×C11⋊C8—22no—
106C22×C11⋊C8—22no—
107C22×C11⋊C8—22no—
108C22×C11⋊C8C2311yescharacteristic
109C22×C11⋊C8C2311yescharacteristic
110C22×C11⋊C8C2311yescharacteristic
111C22×C11⋊C8C2311yescharacteristic
112C4×Dic22—22no—
113C4×Dic22—22no—
114C11×#95—21no—
115C11×#95—21no—
116C11×#95—21no—
117C11×#95—21no—
118C11×#95—21no—
119#66899—22no—
120#66899—22no—
121#66899C2×C414yes—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125C11⋊#95—21no—
126C11⋊#95—21no—
127#66874—22no—
128#66874—22no—
129#66874C2×C414yes—
130#66872—22no—
131#66872C2×C414yes—
132#66871—22no—
133#66867—22no—
134#66867—22no—
135C4×C11⋊C8—22no—
136C4×C11⋊C8D414yes—
137#21537—111nomaximal, Sylow
138C24×C11C2×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×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11C22×C412yes—
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11#4112yes—
160C22×C4×C11C2411yescharacteristic
161C22×Dic11—21no—
162C22×Dic11—21no—
163C22×Dic11—21no—
164C22×Dic11—21no—
165C2×Dic22—21no—
166C2×Dic22—21no—
167C2×Dic22—21no—
168C2×Dic22—21no—
169C2×Dic22—21no—
170C2×Dic22C22×C412yes—
171C11×C4⋊C4—24no—
172C11×C4⋊C4—22no—
173C11×C4⋊C4—22no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—42no—
180C11×C4⋊C4—81no—
181C11×C4⋊C4C22×C412yes—
182C11×C22⋊C4—24no—
183C11×C22⋊C4—22no—
184C11×C22⋊C4—22no—
185C11×C22⋊C4—81no—
186C42×C11—21no—
187C42×C11—21no—
188C42×C11—42no—
189C42×C11—81no—
190C42×C11C2×D412yes—
191C42×C11#4112yes—
192C22⋊Dic11—24no—
193C22⋊Dic11—81no—
194#4326—28no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11C22×C412yes—
201Dic11⋊C4—24no—
202Dic11⋊C4—42no—
203Dic11⋊C4—81no—
204C4×Dic11—42no—
205C4×Dic11—81no—
206#4318—28no—
207C2×C11⋊C8—28no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8C22×C412yes—
215C2×C11⋊C8C22×C412yes—
216C2×C11⋊C8C2×D412yes—
217C2×C11⋊C8C2×D412yes—
218C2×C11⋊C8#4112yes—
219C2×C11⋊C8#4112yes—
220C2×#470—111no—
221C2×C4×Q16—111no—
222C2×#405—111no—
223#2323—111no—
224#2323D1111yescharacteristic
225#1971—111no—
226#1944—111no—
227#1933—111no—
228#1933—111no—
229#1892—111no—
230#1892—111no—
231#1809—111no—
232C4×#106—111no—
233#1763—111no—
234#1763—111no—
235C23×C11—21no—
236C23×C11—21no—
237C23×C11—21no—
238C23×C11—21no—
239C23×C11—21no—
240C23×C11—21no—
241C23×C11C4×D412yes—
242C23×C11C22×D411yescharacteristic
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—21no—
252C2×C4×C11—21no—
253C2×C4×C11—22no—
254C2×C4×C11—22no—
255C2×C4×C11—22no—
256C2×C4×C11—22no—
257C2×C4×C11—22no—
258C2×C4×C11—22no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
264C2×C4×C11—21no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11—41no—
270C2×C4×C11—41no—
271C2×C4×C11—41no—
272C2×C4×C11—41no—
273C2×C4×C11—41no—
274C2×C4×C11—41no—
275C2×C4×C11C4×D412yes—
276C2×C4×C11#12112yes—
277C2×C4×C11#12112yes—
278C2×C4×C11C23×C411yescharacteristic
279C2×C4×C11C22×D411yescharacteristic
280C2×C4×C11C2×#4111yescharacteristic
281C2×C4×C11C2×#4111yescharacteristic
282C2×C4×C11C2×#4111yescharacteristic
283C2×C4×C11C2×#4111yescharacteristic
284C2×Dic11—22no—
285C2×Dic11—22no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11—41no—
292C2×Dic11—41no—
293C2×Dic11—41no—
294C2×Dic11—41no—
295C2×Dic11—41no—
296Dic22—22no—
297Dic22—22no—
298Dic22—41no—
299Dic22—41no—
300C11⋊C8—22no—
301C11⋊C8—22no—
302C11⋊C8—22no—
303C11⋊C8C4×D414yes—
304C22×Q16—111no—
305C22×M16—111no—
306C23×C8—111no—
307C2×C22⋊Q8—111no—
308C2×C22⋊Q8C2×D1111yescharacteristic
309C2×C4×Q8—111no—
310C2×C4×Q8C2×D1111yescharacteristic
311C2×#117C2×D1111yescharacteristic
312#470—118no—
313C4×Q16—224no—
314C2×#107—111no—
315C2×#106—111no—
316C2×#106—111no—
317C2×#103—111no—
318C2×#103—111no—
319C2×#103—111no—
320C2×#103—111no—
321C2×#103—111no—
322C2×#103—111no—
323#405—224no—
324C2×#97—111no—
325C2×#97—111no—
326C2×C4×C8—111no—
327C2×C4×C8—111no—
328#391—111no—
329#391C2×D1111yescharacteristic
330#389—21no—
331#389—111no—
332#389—221no—
333#389C2×D1111yescharacteristic
334#388—21no—
335#388—21no—
336#388—221no—
337#388—221no—
338#387—21no—
339#387—221no—
340#380—111no—
341#380C2×D1111yescharacteristic
342C4×C4⋊C4—111no—
343C4×C4⋊C4C2×D1111yescharacteristic
344#340—111no—
345#340—111no—
346#340—111no—
347#340—111no—
348#340—111no—
349#340—111no—
350C22×C11—22no—
351C22×C11—22no—
352C22×C11—22no—
353C22×C11—41no—
354C22×C11—41no—
355C22×C11—41no—
356C22×C11—41no—
357C22×C11C2×C4×D411yescharacteristic
358C22×C11C2×#12111yescharacteristic
359C22×C11#53211yescharacteristic
360C22×C11#57711yescharacteristic
361C22×C11#57711yescharacteristic
362C22×C11#57811yescharacteristic
363C22×C11#57811yescharacteristic
364C4×C11—22no—
365C4×C11—22no—
366C4×C11—22no—
367C4×C11—42no—
368C4×C11—41no—
369C4×C11—41no—
370C4×C11—42no—
371C4×C11—81no—
372C4×C11—81no—
373C4×C11C2×C4×D411yescharacteristic
374C4×C11C4×#4111yescharacteristic
375C4×C11#52511yescharacteristic
376C4×C11#52911yescharacteristic
377Dic11—42no—
378Dic11—42no—
379Dic11—81no—
380Dic11—81no—
381C22×Q8—111no—
382C22×Q8C22×D1111yescharacteristic
383C23×C4C22×D1111yescharacteristic
384C2×Q16—114no—
385C2×Q16—222no—
386C2×Q16—222no—
387C2×M16—114no—
388C2×M16—222no—
389C2×M16—222no—
390C22×C8—111no—
391C22×C8—111no—
392C22×C8—111no—
393C22×C8—111no—
394C22×C8—222no—
395C22×C8—222no—
396C22×C8—222no—
397C22⋊Q8—22no—
398C22⋊Q8—114no—
399C22⋊Q8—222no—
400C22⋊Q8C4×D1114yes—
401C4×Q8—22no—
402C4×Q8—22no—
403C4×Q8—222no—
404C4×Q8—222no—
405#117—22no—
406#117—22no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
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⋊C4C22⋊D1111yescharacteristic
417C2×C4⋊C4C22⋊D1111yescharacteristic
418C2×C4⋊C4C22×D1111yescharacteristic
419C2×C4⋊C4C22×D1111yescharacteristic
420C2×C4⋊C4C22×D1111yescharacteristic
421C2×C22⋊C4—21no—
422C2×C22⋊C4—21no—
423C2×C22⋊C4—221no—
424C2×C22⋊C4—221no—
425C2×C22⋊C4C22⋊D1111yescharacteristic
426C2×C22⋊C4C22⋊D1111yescharacteristic
427C2×C42—21no—
428C2×C42—21no—
429C2×C42—221no—
430C2×C42—221no—
431C2×C42C22×D1111yescharacteristic
432C2×C42C22×D1111yescharacteristic
433#107—222no—
434#106—114no—
435#106—222no—
436#103—114no—
437#103—114no—
438#103—222no—
439#103—222no—
440#103—222no—
441#103—222no—
442#97—222no—
443#97—222no—
444C4×C8—114no—
445C4×C8—222no—
446#95—21no—
447#95—21no—
448#95—21no—
449#95—21no—
450#95—21no—
451#95—221no—
452#95—221no—
453#95—221no—
454#95—221no—
455#95—221no—
456C2×C11—42no—
457C2×C11C4×#12111yescharacteristic
458C2×C11#294711yescharacteristic
459C2×C11#294711yescharacteristic
460C2×C11#305911yescharacteristic
461C2×C11#306011yescharacteristic
462C2×C11#317811yescharacteristic
463C2×C11#317811yescharacteristic
464C24C2×C22⋊D1111yescharacteristic
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—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—221no—
486C22×C4—221no—
487C22×C4—221no—
488C22×C4—221no—
489C22×C4C2×C4×D1112yes—
490C22×C4#433912yes—
491C22×C4C2×C22⋊D1111yescharacteristic
492C22×C4C2×C22⋊D1111yescharacteristic
493C22×C4C2×C22⋊D1111yescharacteristic
494C22×C4C2×C22⋊D1111yescharacteristic
495C22×C4C2×C22⋊D1111yescharacteristic
496C22×C4C23×D1111yescharacteristic
497Q16—228no—
498M16—228no—
499C2×C8—112no—
500C2×C8—112no—
501C2×C8—112no—
502C2×C8—112no—
503C2×C8—112no—
504C2×C8—112no—
505C2×C8—228no—
506C2×C8—221no—
507C2×C8—221no—
508C2×C8—221no—
509C2×C8—221no—
510C2×C8—221no—
511C2×C8—221no—
512C4⋊C4—24no—
513C4⋊C4—22no—
514C4⋊C4—22no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—42no—
521C4⋊C4—81no—
522C4⋊C4—112no—
523C4⋊C4—224no—
524C4⋊C4—221no—
525C4⋊C4—221no—
526C4⋊C4—221no—
527C4⋊C4—221no—
528C4⋊C4—221no—
529C4⋊C4—442no—
530C4⋊C4—881no—
531C4⋊C4C2×C4×D1112yes—
532C22⋊C4—24no—
533C22⋊C4—22no—
534C22⋊C4—22no—
535C22⋊C4—81no—
536C22⋊C4—224no—
537C22⋊C4—881no—
538C42—21no—
539C42—21no—
540C42—42no—
541C42—81no—
542C42—442no—
543C42—881no—
544C42D4×D1112yes—
545C42#434112yes—
546C11#2153711yescharacteristic, complemented, Sylow
547C23—21no—
548C23—21no—
549C23—21no—
550C23—21no—
551C23—21no—
552C23—21no—
553C23C4×C22⋊D1112yes—
554C23C22×C22⋊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—21no—
568C2×C4—21no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—222no—
592C2×C4—222no—
593C2×C4—441no—
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×C4C4×C22⋊D1112yes—
604C2×C4#6699212yes—
605C2×C4#6699212yes—
606C2×C4C22×C4×D1111yescharacteristic
607C2×C4C2×#433911yescharacteristic
608C2×C4C2×D4×D1111yescharacteristic
609C2×C4C2×#434111yescharacteristic
610C2×C4#41×D1111yescharacteristic
611C2×C4#41×D1111yescharacteristic
612C8—114no—
613C8—222no—
614C8—222no—
615C8—222no—
616C22—22no—
617C22—22no—
618C22—22no—
619C22—41no—
620C22—41no—
621C22—41no—
622C22—41no—
623C22C2×C4×C22⋊D1111yescharacteristic
624C22C2×#6699211yescharacteristic
625C22#1062336311yescharacteristic
626C22#1062336711yescharacteristic
627C22#1062336811yescharacteristic
628C22#1062336911yescharacteristic
629C22#1062336911yescharacteristic
630C4—22no—
631C4—22no—
632C4—22no—
633C4—41no—
634C4—42no—
635C4—42no—
636C4—41no—
637C4—81no—
638C4—81no—
639C4—442no—
640C4—442no—
641C4—881no—
642C4—881no—
643C4C4×#434111yescharacteristic
644C4#1062306911yescharacteristic
645C4C4×D4×D1111yescharacteristic
646C4#1062307811yescharacteristic
647C2—42no—
648C2C4×#6699211yescharacteristic
649C2#1307745511yescharacteristic
650C2#1307745911yescharacteristic
651C2#1307826811yescharacteristic
652C2#1307827511yescharacteristic
653C2#1307927811yescharacteristic
654C2#1307928611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2323C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenter#2323D11
hypocenterC11#21537
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2323

Complements

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

NH ≅ G/Ntype
2. C2×C4×#4326C2semidirect
5. #13069486C2semidirect
6. #13069356C2semidirect
7. #13069295C2semidirect
8. #13069291C2semidirect
12. C4×#66872C2semidirect
13. #13068449C2semidirect
14. #13068446C2semidirect
36. #10622665C4semidirect
546. C11#21537semidirect

Maximal subgroups

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

subgroupindex
C2×#106226652
C2×C4×#43262
C2×#106226102
#130712982
#130694862
#130693562
#130692952
#130692912
#130690402
#130690372
#130686472
C4×#668722
#130684492
#130684462
C11×#23232
#2153711