Finite Group Databasebeta

← #14760144

Subgroups — #14760144

Order 2816.

980 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622458C211yesmaximal, characteristic
2C2×#10622323C211yesmaximal, characteristic
3C2×C4×Dic44C211yesmaximal, characteristic, complemented
4#13071327C211yesmaximal, characteristic
5#13070979C211yesmaximal, characteristic, complemented
6#13069546C211yesmaximal, characteristic
7#13069375C211yesmaximal, characteristic, complemented
8#13069258C211yesmaximal, characteristic, complemented
9#13069237C211yesmaximal, characteristic
10#13068970C211yesmaximal, characteristic
11#13068956C211yesmaximal, characteristic, complemented
12#13068622C211yesmaximal, characteristic, complemented
13#13068447C211yesmaximal, characteristic, complemented
14C4×#66885C211yesmaximal, characteristic
15C11×#1768C211yesmaximal, characteristic, complemented
16C22×Dic44C2211yescharacteristic
17C22×#4314C2211yescharacteristic
18C2×#66928C2211yescharacteristic
19C2×C4×D44C2211yescharacteristic
20C2×C4×Dic22C2211yescharacteristic
21C2×C4×Dic22C2211yescharacteristic
22C2×C4×Dic22C2211yescharacteristic
23C2×C4×Dic22C2211yescharacteristic
24C2×C11×C4⋊C8C2211yescharacteristic
25C2×C11×C4⋊C8C2211yescharacteristic
26C2×C11×#97C2211yescharacteristic
27C2×C4×C8×C11C2211yescharacteristic
28C11×#376C2211yescharacteristic
29C2×#66885C2211yescharacteristic
30C2×#66885C2211yescharacteristic
31C2×#66885C2211yescharacteristic
32C2×#66882C2211yescharacteristic
33C2×#66882C2211yescharacteristic
34C2×#66880C2211yescharacteristic
35C2×#66880C2211yescharacteristic
36C2×#66880C2211yescharacteristic
37C2×#66880C2211yescharacteristic
38C2×#66880C2211yescharacteristic
39#10622552C2211yescharacteristic
40#10622548C2211yescharacteristic
41C4×C4⋊Dic11C2211yescharacteristic
42C4×C4⋊Dic11C2211yescharacteristic
43C4×C4⋊Dic11C2211yescharacteristic
44#10622542C2211yescharacteristic
45#10622458C418yescomplemented
46#10622323—24no—
47C4×Dic44—24no—
48#10622283—21no—
49#10622283—21no—
50#10622281—21no—
51#10622281—21no—
52#10622262—21no—
53#10622262—21no—
54#10622262—21no—
55#10622261—21no—
56C11×#336C2211yescharacteristic
57C11×#336C2211yescharacteristic
58#10622189C2211yescharacteristic
59#10622189C2211yescharacteristic
60#10622189C2211yescharacteristic
61#10622189C2211yescharacteristic
62C22×D44C2311yescharacteristic
63C22×C4×D11—21no—
64C22×Dic22C2311yescharacteristic
65C22×Dic22C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C2×C42×C11C2311yescharacteristic
71C2×C42×C11C2311yescharacteristic
72C2×C42×C11C2311yescharacteristic
73C2×(C2×D11)⋊C4—21no—
74C2×(C2×D11)⋊C4—21no—
75C2×(C2×D11)⋊C4—21no—
76C2×(C2×D11)⋊C4—21no—
77C2×(C2×D11)⋊C4—21no—
78C2×C4⋊Dic11—21no—
79C2×C4⋊Dic11—21no—
80C2×C4⋊Dic11C2311yescharacteristic
81C2×C4⋊Dic11C2311yescharacteristic
82C2×C4⋊Dic11C2311yescharacteristic
83C2×C4⋊Dic11C2311yescharacteristic
84C2×C4⋊Dic11C2311yescharacteristic
85C2×Dic11⋊C4—21no—
86C2×Dic11⋊C4—21no—
87C2×Dic11⋊C4—21no—
88C2×Dic11⋊C4—21no—
89C2×C4×Dic11—21no—
90C2×C4×Dic11—21no—
91C2×C4×Dic11—21no—
92C2×C4×Dic11—21no—
93C2×C4×Dic11—21no—
94C2×C4×Dic11—21no—
95C2×C4×Dic11—21no—
96C2×Dic44—22no—
97C2×Dic44—22no—
98C2×Dic44C2×C414yescomplemented
99C2×#4314—22no—
100C2×#4314—22no—
101C2×#4314C2×C414yes—
102#66928—22no—
103#66928C2×C414yes—
104C4×D44—22no—
105C4×D44—22no—
106C4×Dic22—22no—
107C4×Dic22—22no—
108C4×Dic22—22no—
109C4×Dic22—22no—
110C4×Dic22—22no—
111C4×Dic22—22no—
112C4×Dic22C2×C414yescomplemented
113C4×Dic22D414yes—
114C11×C4⋊C8—22no—
115C11×C4⋊C8C2×C414yescomplemented
116C11×#97—22no—
117C4×C8×C11—22no—
118C11×#95D411yescharacteristic
119C11×#95D411yescharacteristic
120C11×#95D411yescharacteristic
121C11×#95D411yescharacteristic
122C11⋊#95—21no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125C11⋊#95—21no—
126C11⋊#95—21no—
127#66885—22no—
128#66885—22no—
129#66885C2×C414yes—
130#66882—22no—
131#66882—22no—
132#66880—22no—
133#66880—22no—
134#66880—22no—
135#66880—22no—
136#66880C2×C414yescomplemented
137#21512—111nomaximal, Sylow
138C23×D11—21no—
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2411yescharacteristic
146C22×Dic11—21no—
147C22×Dic11—21no—
148C22×Dic11—21no—
149C22×Dic11—21no—
150C22×Dic11—21no—
151C22×Dic11—21no—
152C22×Dic11—21no—
153C2×D44—21no—
154C2×D44—21no—
155C2×D44—21no—
156C2×D44—21no—
157C2×D44—21no—
158C2×D44C22×C412yes—
159C2×C4×D11—42no—
160C2×C4×D11—81no—
161C2×C4×D11—81no—
162C2×Dic22—21no—
163C2×Dic22—21no—
164C2×Dic22—21no—
165C2×Dic22—21no—
166C2×Dic22—21no—
167C2×Dic22—21no—
168C2×Dic22—21no—
169C2×Dic22—21no—
170C2×Dic22C22×C412yes—
171C2×Dic22C22×C412yes—
172C2×Dic22C2×D412yes—
173C2×Dic22#4112yes—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11—21no—
181C2×C8×C11—21no—
182C2×C8×C11—21no—
183C2×C8×C11—21no—
184C2×C8×C11C22×C412yes—
185C2×C8×C11C22×C412yes—
186C42×C11—21no—
187C42×C11—21no—
188C42×C11C22×C412yes—
189C42×C11C2×D412yes—
190C42×C11#4112yes—
191C42×C11#4112yes—
192(C2×D11)⋊C4—24no—
193(C2×D11)⋊C4—24no—
194(C2×D11)⋊C4—42no—
195(C2×D11)⋊C4—81no—
196(C2×D11)⋊C4—81no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11—81no—
205C4⋊Dic11—81no—
206C4⋊Dic11C22×C412yes—
207C4⋊Dic11C2×D412yes—
208C4⋊Dic11#4112yes—
209Dic11⋊C4—24no—
210Dic11⋊C4—24no—
211Dic11⋊C4—24no—
212Dic11⋊C4—42no—
213C4×Dic11—24no—
214C4×Dic11—24no—
215C4×Dic11—24no—
216C4×Dic11—42no—
217C4×Dic11—81no—
218C4×Dic11—81no—
219C4×Dic11—81no—
220Dic44—28no—
221#4314—28no—
222C2×#464—111no—
223C2×#440—111no—
224C2×C4×Q16—111no—
225#2326—111no—
226#2276—111no—
227#1983—111no—
228#1947—111no—
229#1928—111no—
230#1925—111no—
231#1880—111no—
232#1878—111no—
233#1803—111no—
234#1768D1111yescharacteristic, complemented
235#1763—111no—
236C4×#102—111no—
237C23×C11C22×D411yescharacteristic
238C22×D11—22no—
239C22×D11—41no—
240C22×D11—41no—
241C22×D11—41no—
242C22×D11—41no—
243C22×D11—41no—
244C22×D11—41no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
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—21no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11C4×D412yes—
260C2×C4×C11C4×D412yes—
261C2×C4×C11#12112yes—
262C2×C4×C11#12112yes—
263C2×C4×C11C23×C411yescharacteristic
264C2×C4×C11C22×D411yescharacteristic
265C2×C4×C11C2×#4111yescharacteristic
266C2×C4×C11C2×#4111yescharacteristic
267C2×C4×C11C2×#4111yescharacteristic
268C2×C4×C11C2×#4111yescharacteristic
269C2×Dic11—22no—
270C2×Dic11—22no—
271C2×Dic11—22no—
272C2×Dic11—22no—
273C2×Dic11—22no—
274C2×Dic11—22no—
275C2×Dic11—22no—
276C2×Dic11—41no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—41no—
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—
290D44—22no—
291D44—22no—
292D44—41no—
293D44—41no—
294C4×D11—84no—
295Dic22—22no—
296Dic22—22no—
297Dic22—22no—
298Dic22—22no—
299Dic22—22no—
300Dic22—41no—
301Dic22—41no—
302Dic22C4×D414yes—
303C8×C11—22no—
304C8×C11—22no—
305C8×C11—41no—
306C8×C11—41no—
307C22×Q16—111no—
308C22×SD16—111no—
309C2×#124—111no—
310C2×C4×Q8—111no—
311C2×C4×Q8—111no—
312C2×C4×Q8—111no—
313C2×C4×Q8—111no—
314C2×C4×D4—111no—
315#464—118no—
316#440—224no—
317C4×Q16—224no—
318C2×#107—111no—
319C2×#107—111no—
320C2×C4⋊C8C2×D1111yescharacteristic
321C2×C4⋊C8C2×D1111yescharacteristic
322C2×#103—111no—
323C2×#103—111no—
324C2×#103—111no—
325C2×#103—111no—
326C2×#103—111no—
327C2×#102—111no—
328C2×#102—111no—
329C2×#102—111no—
330C2×#97C2×D1111yescharacteristic
331C2×C4×C8C2×D1111yescharacteristic
332#391—111no—
333#390—111no—
334#388—221no—
335#388—221no—
336#385—221no—
337#385—221no—
338#384—111no—
339C4×C4⋊C4—111no—
340C4×C4⋊C4—111no—
341C4×C4⋊C4—111no—
342C4×C4⋊C4—221no—
343C4×C4⋊C4—221no—
344C4×C4⋊C4—221no—
345#376—221no—
346#376C2×D1111yescharacteristic
347#340—111no—
348#340—111no—
349#340—111no—
350#340—111no—
351#336C2×D1111yescharacteristic
352#336C2×D1111yescharacteristic
353C22×C11C2×C4×D411yescharacteristic
354C22×C11C2×#12111yescharacteristic
355C22×C11#52511yescharacteristic
356C22×C11#57611yescharacteristic
357C22×C11#57711yescharacteristic
358C22×C11#57811yescharacteristic
359C22×C11#57811yescharacteristic
360C2×D11—42no—
361C2×D11—42no—
362C2×D11—42no—
363C2×D11—81no—
364C2×D11—81no—
365C2×D11—81no—
366C2×D11—81no—
367C4×C11—22no—
368C4×C11—22no—
369C4×C11—22no—
370C4×C11—22no—
371C4×C11—41no—
372C4×C11—41no—
373C4×C11C2×C4×D411yescharacteristic
374C4×C11C4×#4111yescharacteristic
375C4×C11#52911yescharacteristic
376C4×C11#53211yescharacteristic
377Dic11—24no—
378Dic11—42no—
379Dic11—42no—
380Dic11—42no—
381Dic11—42no—
382Dic11—81no—
383Dic11—81no—
384C22×Q8—111no—
385C22×Q8—111no—
386C22×D4—111no—
387C23×C4—221no—
388C2×Q16—114no—
389C2×Q16—222no—
390C2×Q16—222no—
391C2×SD16—114no—
392C2×SD16—222no—
393C2×SD16—222no—
394C22×C8C22×D1111yescharacteristic
395C22×C8C22×D1111yescharacteristic
396C22×C8C22×D1111yescharacteristic
397C22×C8C22×D1111yescharacteristic
398#124—114no—
399#124—222no—
400C4×Q8—114no—
401C4×Q8—114no—
402C4×Q8—222no—
403C4×Q8—222no—
404C4×Q8—222no—
405C4×Q8—222no—
406C4×Q8—222no—
407C4×Q8—222no—
408C4×D4—222no—
409C4×D4—222no—
410C2×C4⋊C4—111no—
411C2×C4⋊C4—111no—
412C2×C4⋊C4—111no—
413C2×C4⋊C4—111no—
414C2×C4⋊C4—111no—
415C2×C4⋊C4—221no—
416C2×C4⋊C4—221no—
417C2×C4⋊C4—221no—
418C2×C4⋊C4—221no—
419C2×C4⋊C4—221no—
420C2×C4⋊C4—221no—
421C2×C22⋊C4—221no—
422C2×C22⋊C4—221no—
423C2×C22⋊C4—221no—
424C2×C22⋊C4—221no—
425C2×C22⋊C4—221no—
426C2×C42—221no—
427C2×C42—221no—
428C2×C42—221no—
429C2×C42—221no—
430C2×C42—221no—
431C2×C42—221no—
432C2×C42—221no—
433C2×C42C22×D1111yescharacteristic
434C2×C42C22×D1111yescharacteristic
435C2×C42C22×D1111yescharacteristic
436#107—222no—
437#107—222no—
438C4⋊C8—22no—
439C4⋊C8C4×D1114yescomplemented
440#103—114no—
441#103—222no—
442#103—222no—
443#103—222no—
444#103—222no—
445#102—114no—
446#102—222no—
447#102—222no—
448#97—22no—
449C4×C8—22no—
450#95—221no—
451#95—221no—
452#95—221no—
453#95—221no—
454#95—221no—
455#95D4411yescharacteristic
456#95D4411yescharacteristic
457#95D4411yescharacteristic
458#95D4411yescharacteristic
459C2×C11C4×#12111yescharacteristic
460C2×C11#294711yescharacteristic
461C2×C11#295111yescharacteristic
462C2×C11#304411yescharacteristic
463C2×C11#304511yescharacteristic
464C2×C11#312111yescharacteristic
465C2×C11#312411yescharacteristic
466D11—82no—
467C24—221no—
468C2×Q8—112no—
469C2×Q8—112no—
470C2×Q8—112no—
471C2×Q8—112no—
472C2×Q8—221no—
473C2×Q8—221no—
474C2×Q8—221no—
475C2×Q8—221no—
476C2×Q8—221no—
477C2×Q8—221no—
478C2×Q8—221no—
479C2×Q8—221no—
480C2×D4—112no—
481C2×D4—221no—
482C2×D4—221no—
483C2×D4—221no—
484C2×D4—221no—
485C2×D4—221no—
486C22×C4—221no—
487C22×C4—221no—
488C22×C4—221no—
489C22×C4—221no—
490C22×C4—221no—
491C22×C4—221no—
492C22×C4—221no—
493C22×C4—442no—
494C22×C4—881no—
495C22×C4—881no—
496C22×C4C2×D4411yescharacteristic
497C22×C4C2×D4411yescharacteristic
498C22×C4C2×D4411yescharacteristic
499C22×C4C2×D4411yescharacteristic
500C22×C4C2×D4411yescharacteristic
501C22×C4C2×D4411yescharacteristic
502C22×C4C23×D1111yescharacteristic
503Q16—228no—
504SD16—228no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8C2×C4×D1112yes—
516C2×C8C2×C4×D1112yes—
517C4⋊C4—112no—
518C4⋊C4—112no—
519C4⋊C4—112no—
520C4⋊C4—224no—
521C4⋊C4—224no—
522C4⋊C4—224no—
523C4⋊C4—221no—
524C4⋊C4—221no—
525C4⋊C4—221no—
526C4⋊C4—221no—
527C4⋊C4—221no—
528C4⋊C4—221no—
529C4⋊C4—221no—
530C4⋊C4—442no—
531C4⋊C4—881no—
532C4⋊C4—881no—
533C22⋊C4—224no—
534C22⋊C4—224no—
535C22⋊C4—442no—
536C22⋊C4—881no—
537C22⋊C4—881no—
538C42—21no—
539C42—21no—
540C42—224no—
541C42—224no—
542C42—224no—
543C42—442no—
544C42—881no—
545C42—881no—
546C42—881no—
547C42C2×C4×D1112yes—
548C42#433912yes—
549C42D4×D1112yes—
550C42#434312yes—
551C11#2151211yescharacteristic, complemented, Sylow
552C23—222no—
553C23—441no—
554C23—441no—
555C23—441no—
556C23—441no—
557C23—441no—
558C23—441no—
559C23C22×D4411yescharacteristic
560Q8—114no—
561Q8—222no—
562Q8—222no—
563Q8—222no—
564Q8—222no—
565Q8—222no—
566Q8—441no—
567Q8—441no—
568D4—222no—
569D4—222no—
570D4—441no—
571D4—441no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—222no—
587C2×C4—222no—
588C2×C4—222no—
589C2×C4—222no—
590C2×C4—222no—
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×C4—441no—
604C2×C4—441no—
605C2×C4—441no—
606C2×C4—441no—
607C2×C4—884no—
608C2×C4C4×D4412yes—
609C2×C4C4×D4412yes—
610C2×C4#6694812yes—
611C2×C4#6694812yes—
612C2×C4C22×C4×D1111yescharacteristic
613C2×C4C2×#433911yescharacteristic
614C2×C4C2×D4×D1111yescharacteristic
615C2×C4C2×#434311yescharacteristic
616C2×C4#41×D1111yescharacteristic
617C2×C4#41×D1111yescharacteristic
618C8—22no—
619C8—22no—
620C8—41no—
621C8—41no—
622C22—442no—
623C22—442no—
624C22—442no—
625C22—881no—
626C22—881no—
627C22—881no—
628C22—881no—
629C22C2×C4×D4411yescharacteristic
630C22C2×#6694811yescharacteristic
631C22#1062305511yescharacteristic
632C22#1062328211yescharacteristic
633C22#1062328311yescharacteristic
634C22#1062328411yescharacteristic
635C22#1062328411yescharacteristic
636C4—22no—
637C4—22no—
638C4—22no—
639C4—22no—
640C4—41no—
641C4—41no—
642C4—224no—
643C4—442no—
644C4—442no—
645C4—442no—
646C4—442no—
647C4—881no—
648C4—881no—
649C4C4×D4×D1111yescharacteristic
650C4#1062307911yescharacteristic
651C4C4×#434311yescharacteristic
652C4#1062311111yescharacteristic
653C2—882no—
654C2C4×#6694811yescharacteristic
655C2#1307746111yescharacteristic
656C2#1307749311yescharacteristic
657C2#1307814711yescharacteristic
658C2#1307815711yescharacteristic
659C2#1307884711yescharacteristic
660C2#1307888011yescharacteristic
subgroupG/H
centerC23C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1768C2
socleC23×C11C22×D4
prime radicalC22×D44C23
cosocleC22×C4×C11C24
hypercenter#1768D11
hypocenterC11#21512
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ #376 ◁ #1768

Complements

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

NH ≅ G/Ntype
3. C2×C4×Dic44C2semidirect
5. #13070979C2semidirect
7. #13069375C2semidirect
8. #13069258C2semidirect
11. #13068956C2semidirect
12. #13068622C2semidirect
13. #13068447C2semidirect
15. C11×#1768C2semidirect
45. #10622458C4semidirect
98. C2×Dic44C2×C4semidirect
112. C4×Dic22C2×C4semidirect
115. C11×C4⋊C8C2×C4semidirect
136. #66880C2×C4semidirect
234. #1768D11semidirect
439. C4⋊C8C4×D11semidirect
551. C11#21512semidirect

Maximal subgroups

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

subgroupindex
C2×#106224582
C2×#106223232
C2×C4×Dic442
#130713272
#130709792
#130695462
#130693752
#130692582
#130692372
#130689702
#130689562
#130686222
#130684472
C4×#668852
C11×#17682
#2151211