Finite Group Databasebeta

← #15624566

Subgroups — #15624566

Order 2816.

2130 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623356C211yesmaximal, characteristic, complemented
2#13079507C214yesmaximal, complemented
3#13079492C218yesmaximal, complemented
4#13079488C214yesmaximal, complemented
5#13078564C212yesmaximal, complemented
6#13078545C212yesmaximal, complemented
7#13078248C214yesmaximal, complemented
8#13077876C212yesmaximal, complemented
9#13077849C212yesmaximal, complemented
10#13077061C211yesmaximal, characteristic, complemented
11C11×#3449C211yesmaximal, characteristic
12C22×C11×#41C2211yescharacteristic
13C22×C11×#41C2211yescharacteristic
14C23×Dic22C2211yescharacteristic, complemented
15C11×#537C2214yes—
16C11×#536—21no—
17C11×#536C2212yes—
18C11×#535—21no—
19C11×#535C2212yes—
20C11×#534—21no—
21C11×#534—21no—
22C11×#532—22no—
23C11×#525—22no—
24C11×#525C2212yes—
25C11×#525C2212yes—
26C2×C11×#117C2211yescharacteristic
27#10623356—22no—
28#10623356—22no—
29#10623356C2214yes—
30#10623356C2214yescomplemented
31C2×#67004C2214yes—
32C2×#66997—21no—
33C2×#66989—21no—
34C2×#66988—21no—
35C2×#66988—21no—
36C2×#66979C2211yescharacteristic, complemented
37C2×#66977C2212yes—
38C2×#66977C2212yescomplemented
39C22×#4318C2212yescomplemented
40#10622852C2218yescomplemented
41#10622847C2214yes—
42#10622847C2214yescomplemented
43#10622845C2214yes—
44#10622841C2214yescomplemented
45#10622831C2214yescomplemented
46#10622820C2212yes—
47#10622820C2212yescomplemented
48#10622665C2218yescomplemented
49#10622664C2218yescomplemented
50#10622663C2218yescomplemented
51#10622658C2218yescomplemented
52#10622655C2218yescomplemented
53#10622654C2218yescomplemented
54#10622653C2218yescomplemented
55#10622648C2218yescomplemented
56#10622617C2214yescomplemented
57#10622609C2218yescomplemented
58#10622608C2214yescomplemented
59#10622584C2214yescomplemented
60#10622583C2214yescomplemented
61C2×C11×#41—21no—
62C2×C11×#41—21no—
63C2×C11×#41—44no—
64C2×C11×#41—44no—
65C2×C11×#41D412yes—
66C2×C11×#41D412yes—
67C2×C11×#41C2312yes—
68C2×C11×#41C2312yes—
69C2×C11×#41C2312yes—
70C2×C11×#41C2312yes—
71C22×Q8×C11D411yescharacteristic
72C22×Q8×C11C2311yescharacteristic
73C22×D4×C11—21no—
74C22×D4×C11D411yescharacteristic
75C22×D4×C11D411yescharacteristic
76C22×D4×C11D411yescharacteristic
77C22×D4×C11C2311yescharacteristic
78C23×C4×C11—21no—
79C23×C4×C11C2311yescharacteristic
80C23×C4×C11C2311yescharacteristic
81C23×C4×C11C2311yescharacteristic
82C23×Dic11—21no—
83C22×Dic22—21no—
84C22×Dic22—22no—
85C22×Dic22—44no—
86C22×Dic22C2312yes—
87C22×Dic22C2314yes—
88C11×C4⋊Q8—22no—
89C11×#127—22no—
90C11×#124—22no—
91C11×#124—22no—
92C11×#123—22no—
93C11×#123—22no—
94C11×#123—22no—
95C11×#123—22no—
96C11×C22⋊Q8—24no—
97C11×C22⋊Q8C2314yes—
98C11×C22⋊Q8C2314yes—
99C11×#121—24no—
100C11×#121—24no—
101C11×#121—24no—
102C11×#121C2314yes—
103C11×#121C2314yes—
104C11×#120—22no—
105C11×#120—22no—
106C11×#120—22no—
107C11×#120—22no—
108C4×D4×C11—24no—
109C4×D4×C11—24no—
110C11×#117—21no—
111C11×#117—21no—
112C11×#117C2312yes—
113C11×#117C2312yes—
114C2×C11×C4⋊C4C2312yes—
115C2×C11×C22⋊C4—21no—
116C2×C42×C11—21no—
117C2×C22⋊Dic11—22no—
118C2×C22⋊Dic11—22no—
119C2×C22⋊Dic11—21no—
120#67004—48no—
121#66997—24no—
122#66997—24no—
123C2×#4326C2318yes—
124#66989—24no—
125#66989—24no—
126#66988—24no—
127#66988—24no—
128#66988—24no—
129#66988—24no—
130C2×#4324C2318yes—
131#66979—22no—
132#66979C2314yes—
133C2×C4⋊Dic11C2312yes—
134#66977—22no—
135#66977—22no—
136#66977—24no—
137#66977C2314yes—
138#66977C2314yes—
139#66977C2318yes—
140C2×Dic11⋊C4—22no—
141C2×Dic11⋊C4—22no—
142C2×C4×Dic11—21no—
143C2×#4318—44no—
144C2×#4318C2314yes—
145C2×#4318C2314yes—
146C22×C11⋊C8C2314yes—
147#66899C2318yes—
148#66896C2318yes—
149C22⋊(C11⋊C8)C2314yes—
150C22⋊(C11⋊C8)C2314yes—
151C22⋊(C11⋊C8)C2318yes—
152#66874C2318yes—
153#66874C2318yes—
154#66872C2318yes—
155#66871C2318yes—
156#60754—111nomaximal, Sylow
157C24×C11—21no—
158C24×C11C2×D411yescharacteristic
159C24×C11C2×D411yescharacteristic
160C24×C11C2×D411yescharacteristic
161C11×#41—28no—
162C11×#41—44no—
163C11×#41—44no—
164C11×#41—42no—
165C11×#41—42no—
166C11×#41—42no—
167C11×#41—42no—
168C11×#41—44no—
169C11×#41—44no—
170C11×#41—44no—
171C2×Q8×C11—21no—
172C2×Q8×C11—42no—
173C2×Q8×C11—42no—
174C2×Q8×C11C2×D412yes—
175C2×Q8×C11C2×D412yes—
176C2×Q8×C11C2412yes—
177C2×D4×C11—22no—
178C2×D4×C11—22no—
179C2×D4×C11—24no—
180C2×D4×C11—24no—
181C2×D4×C11—21no—
182C2×D4×C11—42no—
183C2×D4×C11—42no—
184C2×D4×C11—42no—
185C2×D4×C11—42no—
186C2×D4×C11—44no—
187C2×D4×C11C2×D412yes—
188C2×D4×C11C2×D412yes—
189C2×D4×C11C2×D412yes—
190C2×D4×C11C2×D412yes—
191C2×D4×C11C2×D412yes—
192C2×D4×C11C2×D412yes—
193C2×D4×C11C2412yes—
194C22×C4×C11—24no—
195C22×C4×C11—24no—
196C22×C4×C11—24no—
197C22×C4×C11—21no—
198C22×C4×C11—22no—
199C22×C4×C11—22no—
200C22×C4×C11—22no—
201C22×C4×C11—44no—
202C22×C4×C11C2×D411yescharacteristic
203C22×C4×C11C2×D411yescharacteristic
204C22×C4×C11C2×D411yescharacteristic
205C22×C4×C11C2×D411yescharacteristic
206C22×C4×C11C2×D411yescharacteristic
207C22×C4×C11C2×D412yes—
208C22×C4×C11C2×D412yes—
209C22×C4×C11C2411yescharacteristic
210C22×C4×C11C2411yescharacteristic
211C22×C4×C11C2412yes—
212C22×C4×C11C2412yes—
213C22×C4×C11C2411yescharacteristic
214C22×Dic11—22no—
215C22×Dic11—22no—
216C22×Dic11—24no—
217C22×Dic11—44no—
218C2×Dic22—22no—
219C2×Dic22—24no—
220C2×Dic22—28no—
221C2×Dic22—44no—
222C2×Dic22—44no—
223C2×Dic22—44no—
224C2×Dic22—48no—
225C2×Dic22C2414yes—
226C11×C4⋊C4—22no—
227C11×C4⋊C4—24no—
228C11×C4⋊C4—24no—
229C11×C4⋊C4C2414yes—
230C11×C22⋊C4—22no—
231C11×C22⋊C4—22no—
232C11×C22⋊C4—24no—
233C11×C22⋊C4—24no—
234C11×C22⋊C4—24no—
235C11×C22⋊C4—24no—
236C42×C11—22no—
237C42×C11—22no—
238C22⋊Dic11—24no—
239C22⋊Dic11—28no—
240C22⋊Dic11—24no—
241C22⋊Dic11—24no—
242#4326—48no—
243#4324—48no—
244C4⋊Dic11—22no—
245C4⋊Dic11C2414yes—
246Dic11⋊C4—24no—
247Dic11⋊C4—28no—
248Dic11⋊C4—24no—
249C4×Dic11—24no—
250#4318—28no—
251#4318—44no—
252C2×C11⋊C8—44no—
253C2×C11⋊C8C2418yes—
254#3449D1111yescharacteristic
255C2×#536—111no—
256#3202—114no—
257#3201—118no—
258#3200—114no—
259#3095—112no—
260#3093—112no—
261#3056—114no—
262#3007—112no—
263#3004—112no—
264#2879—111no—
265C23×C11—22no—
266C23×C11—22no—
267C23×C11—22no—
268C23×C11—22no—
269C23×C11—42no—
270C23×C11—42no—
271C23×C11—42no—
272C23×C11—42no—
273C23×C11—82no—
274C23×C11C22×D411yescharacteristic
275C23×C11C22×D412yes—
276C23×C11C22×D411yescharacteristic
277C23×C11C22×D412yes—
278C23×C11C22×D411yescharacteristic
279Q8×C11—24no—
280Q8×C11—42no—
281Q8×C11—42no—
282Q8×C11—42no—
283D4×C11—24no—
284D4×C11—42no—
285D4×C11—42no—
286D4×C11—42no—
287D4×C11—42no—
288D4×C11—42no—
289D4×C11—42no—
290D4×C11—42no—
291D4×C11—44no—
292D4×C11—44no—
293D4×C11—84no—
294D4×C11—84no—
295C2×C4×C11—22no—
296C2×C4×C11—22no—
297C2×C4×C11—22no—
298C2×C4×C11—24no—
299C2×C4×C11—22no—
300C2×C4×C11—24no—
301C2×C4×C11—22no—
302C2×C4×C11—22no—
303C2×C4×C11—22no—
304C2×C4×C11—22no—
305C2×C4×C11—22no—
306C2×C4×C11—22no—
307C2×C4×C11—22no—
308C2×C4×C11—24no—
309C2×C4×C11—22no—
310C2×C4×C11—44no—
311C2×C4×C11—42no—
312C2×C4×C11—44no—
313C2×C4×C11—82no—
314C2×C4×C11C22×D412yes—
315C2×C4×C11C22×D411yescharacteristic
316C2×C4×C11C22×D412yes—
317C2×C4×C11C22×D411yescharacteristic
318C2×C4×C11C22×D411yescharacteristic
319C2×C4×C11H(5,𝔽2)14yes—
320C2×C4×C11C2511yescharacteristic
321C2×Dic11—24no—
322C2×Dic11—24no—
323C2×Dic11—48no—
324C2×Dic11—44no—
325C2×Dic11—44no—
326Dic22—28no—
327Dic22—48no—
328Dic22—44no—
329C11⋊C8—28no—
330C22×#41C2×D1111yescharacteristic
331C22×#41C2×D1111yescharacteristic
332C23×Q8—111no—
333C2×#137—114no—
334C22×M16—112no—
335#537C2×D1114yes—
336#536—21no—
337#536—114no—
338#536—114no—
339#536—222no—
340#536—222no—
341#536C2×D1112yes—
342#535—21no—
343#535C2×D1112yes—
344#534—21no—
345#534—21no—
346#532—22no—
347C2×C4⋊Q8—221no—
348C2×#124—221no—
349#525—22no—
350#525C2×D1112yes—
351#525C2×D1112yes—
352C2×#123—221no—
353C2×#123—221no—
354C2×C22⋊Q8—112no—
355C2×C22⋊Q8—112no—
356C2×#117—111no—
357C2×#117C2×D1111yescharacteristic
358#485—118no—
359#485—118no—
360#484—114no—
361#483—114no—
362#482—118no—
363#470—118no—
364#468—118no—
365#467—118no—
366#465—118no—
367#452—118no—
368#451—114no—
369#451—118no—
370#450—114no—
371#448—118no—
372#428—114no—
373#419—114no—
374#417—114no—
375#408—114no—
376#408—114no—
377#407—112no—
378#407—112no—
379C22×C11—22no—
380C22×C11—22no—
381C22×C11—24no—
382C22×C11—24no—
383C22×C11—22no—
384C22×C11—21no—
385C22×C11—21no—
386C22×C11—22no—
387C22×C11—22no—
388C22×C11—44no—
389C22×C11—44no—
390C22×C11—42no—
391C22×C11—82no—
392C22×C11—82no—
393C22×C11—84no—
394C22×C11#53412yes—
395C22×C11C23×D411yescharacteristic
396C4×C11—21no—
397C4×C11—21no—
398C4×C11—22no—
399C4×C11—22no—
400C4×C11—44no—
401C4×C11—42no—
402C4×C11#53412yes—
403C4×C11C2×H(5,𝔽2)12yes—
404Dic11—44no—
405Dic11—44no—
406C2×#41—21no—
407C2×#41—21no—
408C2×#41—44no—
409C2×#41—44no—
410C2×#41C22⋊D1112yes—
411C2×#41C22⋊D1112yes—
412C2×#41C22×D1112yes—
413C2×#41C22×D1112yes—
414C2×#41C22×D1112yes—
415C2×#41C22×D1112yes—
416C22×Q8—112no—
417C22×Q8—114no—
418C22×Q8—221no—
419C22×Q8—222no—
420C22×Q8—444no—
421C22×Q8C22⋊D1111yescharacteristic
422C22×Q8C22×D1111yescharacteristic
423C22×D4—21no—
424C22×D4C22⋊D1111yescharacteristic
425C22×D4C22⋊D1111yescharacteristic
426C22×D4C22⋊D1111yescharacteristic
427C22×D4C22×D1111yescharacteristic
428C23×C4—21no—
429C23×C4—221no—
430C23×C4C22×D1111yescharacteristic
431C23×C4C22×D1111yescharacteristic
432C23×C4C22×D1111yescharacteristic
433#137—448no—
434C2×Q16—118no—
435C2×SD16—118no—
436C2×M16—114no—
437C2×M16—114no—
438C2×M16—444no—
439C22×C8—114no—
440C4⋊Q8—22no—
441C4⋊Q8—224no—
442C4⋊Q8—224no—
443#127—22no—
444#124—22no—
445#124—22no—
446#124—224no—
447#124—224no—
448#123—22no—
449#123—22no—
450#123—22no—
451#123—22no—
452#123—224no—
453#123—224no—
454#123—224no—
455#123—224no—
456C22⋊Q8—24no—
457C22⋊Q8—114no—
458C22⋊Q8—114no—
459C22⋊Q8—118no—
460C22⋊Q8—222no—
461C22⋊Q8—222no—
462C22⋊Q8—224no—
463C22⋊Q8C22×D1114yes—
464C22⋊Q8C22×D1114yes—
465#121—24no—
466#121—24no—
467#121—24no—
468#121C22×D1114yes—
469#121C22×D1114yes—
470#120—22no—
471#120—22no—
472#120—22no—
473#120—22no—
474C4×D4—24no—
475C4×D4—24no—
476#117—21no—
477#117—21no—
478#117—114no—
479#117—222no—
480#117C22×D1112yes—
481#117C22×D1112yes—
482C2×C4⋊C4—112no—
483C2×C4⋊C4—222no—
484C2×C4⋊C4—222no—
485C2×C4⋊C4C22×D1112yes—
486C2×C22⋊C4—21no—
487C2×C22⋊C4—221no—
488C2×C22⋊C4—222no—
489C2×C22⋊C4—222no—
490C2×C42—21no—
491C2×C42—221no—
492#107—118no—
493#106—118no—
494#103—118no—
495#103—118no—
496#103—118no—
497#102—118no—
498C22⋊C8—118no—
499C22⋊C8—114no—
500C22⋊C8—114no—
501C2×C11—22no—
502C2×C11—42no—
503C2×C11—41no—
504C2×C11—42no—
505C2×C11—41no—
506C2×C11—82no—
507C2×C11C2×#53411yescharacteristic
508C2×C11#358612yes—
509C24—21no—
510C24C2×C22⋊D1111yescharacteristic
511C24C2×C22⋊D1111yescharacteristic
512C24C2×C22⋊D1111yescharacteristic
513#41—28no—
514#41—42no—
515#41—42no—
516#41—42no—
517#41—42no—
518#41—44no—
519#41—44no—
520#41—44no—
521#41—44no—
522#41—44no—
523C2×Q8—21no—
524C2×Q8—42no—
525C2×Q8—42no—
526C2×Q8—114no—
527C2×Q8—222no—
528C2×Q8—224no—
529C2×Q8—228no—
530C2×Q8—444no—
531C2×Q8—444no—
532C2×Q8—444no—
533C2×Q8—448no—
534C2×Q8C2×C22⋊D1112yes—
535C2×Q8C2×C22⋊D1112yes—
536C2×Q8C23×D1112yes—
537C2×D4—22no—
538C2×D4—22no—
539C2×D4—24no—
540C2×D4—24no—
541C2×D4—21no—
542C2×D4—42no—
543C2×D4—42no—
544C2×D4—42no—
545C2×D4—42no—
546C2×D4—44no—
547C2×D4C2×C22⋊D1112yes—
548C2×D4C2×C22⋊D1112yes—
549C2×D4C2×C22⋊D1112yes—
550C2×D4C2×C22⋊D1112yes—
551C2×D4C2×C22⋊D1112yes—
552C2×D4C2×C22⋊D1112yes—
553C2×D4C23×D1112yes—
554C22×C4—24no—
555C22×C4—24no—
556C22×C4—24no—
557C22×C4—21no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—44no—
562C22×C4—222no—
563C22×C4—222no—
564C22×C4—224no—
565C22×C4—444no—
566C22×C4C2×C22⋊D1111yescharacteristic
567C22×C4C2×C22⋊D1111yescharacteristic
568C22×C4C2×C22⋊D1111yescharacteristic
569C22×C4C2×C22⋊D1111yescharacteristic
570C22×C4C2×C22⋊D1111yescharacteristic
571C22×C4C2×C22⋊D1112yes—
572C22×C4C2×C22⋊D1112yes—
573C22×C4C23×D1111yescharacteristic
574C22×C4C23×D1112yes—
575C22×C4C23×D1111yescharacteristic
576C22×C4C23×D1112yes—
577C22×C4C23×D1111yescharacteristic
578Q16—448no—
579SD16—448no—
580M16—228no—
581M16—444no—
582C2×C8—118no—
583C2×C8—444no—
584C4⋊C4—22no—
585C4⋊C4—24no—
586C4⋊C4—24no—
587C4⋊C4—114no—
588C4⋊C4—222no—
589C4⋊C4—224no—
590C4⋊C4—228no—
591C4⋊C4—224no—
592C4⋊C4C23×D1114yes—
593C22⋊C4—22no—
594C22⋊C4—22no—
595C22⋊C4—24no—
596C22⋊C4—24no—
597C22⋊C4—24no—
598C22⋊C4—24no—
599C22⋊C4—224no—
600C22⋊C4—224no—
601C22⋊C4—228no—
602C22⋊C4—224no—
603C42—22no—
604C42—22no—
605C42—224no—
606C11#6075411yescharacteristic, complemented, Sylow
607C23—22no—
608C23—22no—
609C23—22no—
610C23—22no—
611C23—42no—
612C23—42no—
613C23—42no—
614C23—42no—
615C23—82no—
616C23C22×C22⋊D1111yescharacteristic
617C23C22×C22⋊D1112yes—
618C23C22×C22⋊D1112yes—
619C23C22×C22⋊D1111yescharacteristic
620C23C22×C22⋊D1111yescharacteristic
621Q8—24no—
622Q8—42no—
623Q8—42no—
624Q8—42no—
625Q8—228no—
626Q8—448no—
627Q8—444no—
628D4—24no—
629D4—42no—
630D4—42no—
631D4—42no—
632D4—42no—
633D4—42no—
634D4—42no—
635D4—42no—
636D4—44no—
637D4—44no—
638D4—84no—
639D4—84no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—24no—
645C2×C4—24no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—24no—
654C2×C4—22no—
655C2×C4—44no—
656C2×C4—42no—
657C2×C4—44no—
658C2×C4—82no—
659C2×C4—224no—
660C2×C4—224no—
661C2×C4—448no—
662C2×C4—444no—
663C2×C4—444no—
664C2×C4#6703714yes—
665C2×C4C22×C22⋊D1111yescharacteristic
666C2×C4C22×C22⋊D1112yes—
667C2×C4C22×C22⋊D1112yes—
668C2×C4C22×C22⋊D1111yescharacteristic
669C2×C4C22×C22⋊D1111yescharacteristic
670C2×C4C24×D1111yescharacteristic
671C8—228no—
672C22—22no—
673C22—22no—
674C22—24no—
675C22—24no—
676C22—22no—
677C22—21no—
678C22—22no—
679C22—21no—
680C22—22no—
681C22—44no—
682C22—44no—
683C22—42no—
684C22—82no—
685C22—82no—
686C22—84no—
687C22#1062333512yes—
688C22C23×C22⋊D1111yescharacteristic
689C4—21no—
690C4—21no—
691C4—22no—
692C4—22no—
693C4—44no—
694C4—42no—
695C4—444no—
696C4—444no—
697C4#1062333512yes—
698C4C2×#6703712yes—
699C2—22no—
700C2—42no—
701C2—41no—
702C2—41no—
703C2—42no—
704C2—82no—
705C2C2×#1062333511yescharacteristic
706C2#1308340212yes—
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
Fitting, prime radicalC11×#3449C2
socleC22×C11C23×D4
hypercenter#3449D11
hypocenterC11#60754
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×#41 ◁ #3449

Complements

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

NH ≅ G/Ntype
1. C2×#10623356C2semidirect
2. #13079507C2semidirect
3. #13079492C2semidirect
4. #13079488C2semidirect
5. #13078564C2semidirect
6. #13078545C2semidirect
7. #13078248C2semidirect
8. #13077876C2semidirect
9. #13077849C2semidirect
10. #13077061C2semidirect
14. C23×Dic22C22semidirect
30. #10623356C22semidirect
36. C2×#66979C22semidirect
38. C2×#66977C22semidirect
39. C22×#4318C22semidirect
40. #10622852C22semidirect
42. #10622847C22semidirect
44. #10622841C22semidirect
45. #10622831C22semidirect
47. #10622820C22semidirect
48. #10622665C22semidirect
49. #10622664C22semidirect
50. #10622663C22semidirect
51. #10622658C22semidirect
52. #10622655C22semidirect
53. #10622654C22semidirect
54. #10622653C22semidirect
55. #10622648C22semidirect
56. #10622617C22semidirect
57. #10622609C22semidirect
58. #10622608C22semidirect
59. #10622584C22semidirect
60. #10622583C22semidirect
606. C11#60754semidirect

Maximal subgroups

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

subgroupindex
C2×#106233562
#130795072
#130794922
#130794882
#130785642
#130785452
#130782482
#130778762
#130778492
#130770612
C11×#34492
#6075411