Finite Group Databasebeta

← #14760174

Subgroups — #14760174

Order 2816.

1008 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622454C211yesmaximal, characteristic
2C2×#10622323C211yesmaximal, characteristic
3C2×C4×#4314C211yesmaximal, characteristic
4#13071335C211yesmaximal, characteristic, complemented
5#13070978C211yesmaximal, characteristic
6#13069538C211yesmaximal, characteristic, complemented
7#13069386C211yesmaximal, characteristic, complemented
8#13069258C211yesmaximal, characteristic, complemented
9#13069251C211yesmaximal, characteristic, complemented
10#13068949C211yesmaximal, characteristic
11#13068949C211yesmaximal, characteristic
12#13068627C211yesmaximal, characteristic
13#13068447C211yesmaximal, characteristic, complemented
14C4×#66880C211yesmaximal, characteristic, complemented
15C11×#1768C211yesmaximal, characteristic, complemented
16C22×#4314C2211yescharacteristic
17C22×#4314C2211yescharacteristic
18C2×C4×D44C2211yescharacteristic
19C2×C4×D44C2211yescharacteristic
20C2×C4×D44C2211yescharacteristic
21C2×#66922C2211yescharacteristic
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×#66882C2211yescharacteristic
32C2×#66881C2211yescharacteristic
33C2×#66880C2211yescharacteristic
34C2×#66880C2211yescharacteristic
35C2×#66880C2211yescharacteristic
36C2×#66880C2211yescharacteristic
37C2×#66880C2211yescharacteristic
38C2×#66880C2211yescharacteristic
39#10622549C2211yescharacteristic
40C4×C4⋊Dic11C2211yescharacteristic
41C4×C4⋊Dic11C2211yescharacteristic
42C4×C4⋊Dic11C2211yescharacteristic
43#10622542C2211yescharacteristic
44#10622542C2211yescharacteristic
45#10622454C418yescomplemented
46#10622323—24no—
47C4×#4314—24no—
48#10622279—21no—
49#10622279—21no—
50#10622279—21no—
51D11×#95—21no—
52#10622266—21no—
53#10622266—21no—
54#10622266—21no—
55#10622266—21no—
56C11×#336C2211yescharacteristic
57C11×#336C2211yescharacteristic
58#10622189C2211yescharacteristic
59#10622189C2211yescharacteristic
60#10622189C2211yescharacteristic
61#10622189C2211yescharacteristic
62C22×D44C2311yescharacteristic
63C22×C4×D11—21no—
64C22×C4×D11—21no—
65C22×C4×D11—21no—
66C22×Dic22C2311yescharacteristic
67C22×Dic22C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C22×C8×C11C2311yescharacteristic
71C22×C8×C11C2311yescharacteristic
72C2×C42×C11C2311yescharacteristic
73C2×C42×C11C2311yescharacteristic
74C2×C42×C11C2311yescharacteristic
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×C4×Dic11—21no—
88C2×C4×Dic11—21no—
89C2×C4×Dic11—21no—
90C2×C4×Dic11—21no—
91C2×C4×Dic11—21no—
92C2×#4314—22no—
93C2×#4314—22no—
94C2×#4314—22no—
95C2×#4314—22no—
96C2×#4314C2×C414yes—
97C2×#4314C2×C414yes—
98C4×D44—22no—
99C4×D44—22no—
100C4×D44—22no—
101C4×D44—22no—
102C4×D44C2×C414yes—
103C4×D44D414yes—
104#66922—22no—
105#66922C2×C414yescomplemented
106C4×Dic22—22no—
107C4×Dic22—22no—
108C4×Dic22—22no—
109C4×Dic22—22no—
110C11×C4⋊C8—22no—
111C11×C4⋊C8C2×C414yescomplemented
112C11×#97—22no—
113C4×C8×C11—22no—
114C11×#95D411yescharacteristic
115C11×#95D411yescharacteristic
116C11×#95D411yescharacteristic
117C11×#95D411yescharacteristic
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125C11⋊#95—21no—
126C11⋊#95—21no—
127#66885—22no—
128#66885—22no—
129#66882—22no—
130#66881—22no—
131#66880—22no—
132#66880—22no—
133#66880—22no—
134#66880—22no—
135#66880C2×C414yescomplemented
136#66880C2×C414yescomplemented
137#21514—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×D44C22×C412yes—
157C2×D44C2×D412yes—
158C2×D44#4112yes—
159C2×C4×D11—24no—
160C2×C4×D11—24no—
161C2×C4×D11—24no—
162C2×C4×D11—81no—
163C2×C4×D11—81no—
164C2×C4×D11—81no—
165C2×C4×D11—81no—
166C2×C4×D11—81no—
167C2×C4×D11—81no—
168C2×Dic22—21no—
169C2×Dic22—21no—
170C2×Dic22—21no—
171C2×Dic22—21no—
172C2×Dic22—21no—
173C2×Dic22—21no—
174C2×Dic22—21no—
175C2×Dic22—21no—
176C2×Dic22—21no—
177C2×Dic22—21no—
178C2×Dic22C22×C412yes—
179C2×Dic22C22×C412yes—
180C2×C8×C11—21no—
181C2×C8×C11—21no—
182C2×C8×C11—21no—
183C2×C8×C11—21no—
184C2×C8×C11—21no—
185C2×C8×C11—21no—
186C2×C8×C11—21no—
187C2×C8×C11—21no—
188C2×C8×C11—21no—
189C2×C8×C11—21no—
190C2×C8×C11C22×C412yes—
191C2×C8×C11C22×C412yes—
192C42×C11—21no—
193C42×C11—21no—
194C42×C11C22×C412yes—
195C42×C11C2×D412yes—
196C42×C11#4112yes—
197C42×C11#4112yes—
198(C2×D11)⋊C4—24no—
199(C2×D11)⋊C4—24no—
200(C2×D11)⋊C4—24no—
201C4⋊Dic11—24no—
202C4⋊Dic11—24no—
203C4⋊Dic11—21no—
204C4⋊Dic11—21no—
205C4⋊Dic11—21no—
206C4⋊Dic11—21no—
207C4⋊Dic11—21no—
208C4⋊Dic11—21no—
209C4⋊Dic11—21no—
210C4⋊Dic11C22×C412yes—
211C4⋊Dic11C2×D412yes—
212C4⋊Dic11#4112yes—
213Dic11⋊C4—42no—
214Dic11⋊C4—42no—
215C4×Dic11—42no—
216C4×Dic11—42no—
217C4×Dic11—81no—
218C4×Dic11—81no—
219C4×Dic11—81no—
220#4314—28no—
221#4314—28no—
222C2×#461—111no—
223C2×#440—111no—
224C2×C4×SD16—111no—
225#2327—111no—
226#2275—111no—
227#1981—111no—
228#1949—111no—
229#1928—111no—
230#1927—111no—
231#1877—111no—
232#1877—111no—
233#1804—111no—
234#1768D1111yescharacteristic, complemented
235#1763—111no—
236C4×#103—111no—
237C23×C11C22×D411yescharacteristic
238C22×D11—22no—
239C22×D11—22no—
240C22×D11—22no—
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—41no—
275C2×Dic11—41no—
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—22no—
293D44C4×D414yes—
294C4×D11—84no—
295C4×D11—84no—
296C4×D11—84no—
297Dic22—22no—
298Dic22—22no—
299Dic22—22no—
300Dic22—22no—
301Dic22—41no—
302Dic22—41no—
303Dic22—41no—
304Dic22—41no—
305C8×C11—22no—
306C8×C11—22no—
307C8×C11—41no—
308C8×C11—41no—
309C22×SD16—111no—
310C22×SD16—111no—
311C2×C4⋊Q8—111no—
312C2×C4×Q8—111no—
313C2×C4×Q8—111no—
314C2×C4×D4—111no—
315C2×C4×D4—111no—
316C2×C4×D4—111no—
317#461—118no—
318#440—224no—
319C4×SD16—224no—
320C2×#107—111no—
321C2×#106—111no—
322C2×C4⋊C8C2×D1111yescharacteristic
323C2×C4⋊C8C2×D1111yescharacteristic
324C2×#103—111no—
325C2×#103—111no—
326C2×#103—111no—
327C2×#103—111no—
328C2×#103—111no—
329C2×#103—111no—
330C2×#102—111no—
331C2×#102—111no—
332C2×#97C2×D1111yescharacteristic
333C2×C4×C8C2×D1111yescharacteristic
334#391—111no—
335#391—111no—
336#387—221no—
337#387—221no—
338#387—221no—
339#387—221no—
340#382—111no—
341C4×C4⋊C4—111no—
342C4×C4⋊C4—111no—
343C4×C4⋊C4—111no—
344C4×C22⋊C4—221no—
345C4×C22⋊C4—221no—
346C4×C22⋊C4—221no—
347#376C2×D1111yescharacteristic
348C2×#95—221no—
349#340—111no—
350#340—111no—
351#340—111no—
352#340—111no—
353#336C2×D1111yescharacteristic
354#336C2×D1111yescharacteristic
355C22×C11C2×C4×D411yescharacteristic
356C22×C11C2×#12111yescharacteristic
357C22×C11#52511yescharacteristic
358C22×C11#57711yescharacteristic
359C22×C11#57711yescharacteristic
360C22×C11#57711yescharacteristic
361C22×C11#57811yescharacteristic
362C2×D11—24no—
363C2×D11—42no—
364C2×D11—42no—
365C2×D11—42no—
366C2×D11—42no—
367C2×D11—42no—
368C2×D11—42no—
369C4×C11—22no—
370C4×C11—22no—
371C4×C11—22no—
372C4×C11—22no—
373C4×C11—41no—
374C4×C11—41no—
375C4×C11C2×C4×D411yescharacteristic
376C4×C11C4×#4111yescharacteristic
377C4×C11#52911yescharacteristic
378C4×C11#53211yescharacteristic
379Dic11—42no—
380Dic11—42no—
381Dic11—42no—
382Dic11—42no—
383Dic11—42no—
384Dic11—81no—
385Dic11—81no—
386C22×Q8—111no—
387C22×Q8—111no—
388C22×D4—111no—
389C23×C4—221no—
390C23×C4—221no—
391C23×C4—221no—
392C2×SD16—114no—
393C2×SD16—114no—
394C2×SD16—222no—
395C2×SD16—222no—
396C2×SD16—222no—
397C2×SD16—222no—
398C22×C8C22×D1111yescharacteristic
399C22×C8C22×D1111yescharacteristic
400C22×C8C22×D1111yescharacteristic
401C22×C8C22×D1111yescharacteristic
402C4⋊Q8—114no—
403C4⋊Q8—222no—
404C4×Q8—222no—
405C4×Q8—222no—
406C4×Q8—222no—
407C4×Q8—222no—
408C4×D4—114no—
409C4×D4—114no—
410C4×D4—222no—
411C4×D4—222no—
412C4×D4—222no—
413C4×D4—222no—
414C2×C4⋊C4—111no—
415C2×C4⋊C4—111no—
416C2×C4⋊C4—111no—
417C2×C4⋊C4—111no—
418C2×C4⋊C4—111no—
419C2×C4⋊C4—221no—
420C2×C4⋊C4—221no—
421C2×C4⋊C4—221no—
422C2×C4⋊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×C42C22×D1111yescharacteristic
432C2×C42C22×D1111yescharacteristic
433C2×C42C22×D1111yescharacteristic
434#107—222no—
435#106—222no—
436C4⋊C8—22no—
437C4⋊C8C4×D1114yescomplemented
438#103—114no—
439#103—114no—
440#103—222no—
441#103—222no—
442#103—222no—
443#103—222no—
444#102—222no—
445#102—222no—
446#97—22no—
447C4×C8—22no—
448#95—221no—
449#95—221no—
450#95—221no—
451#95—221no—
452#95—221no—
453#95—221no—
454#95—221no—
455#95—221no—
456#95—221no—
457#95D4411yescharacteristic
458#95D4411yescharacteristic
459#95D4411yescharacteristic
460#95D4411yescharacteristic
461C2×C11C4×#12111yescharacteristic
462C2×C11#294711yescharacteristic
463C2×C11#294911yescharacteristic
464C2×C11#304211yescharacteristic
465C2×C11#304611yescharacteristic
466C2×C11#312011yescharacteristic
467C2×C11#312311yescharacteristic
468D11—44no—
469C24—221no—
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×Q8—221no—
481C2×Q8—221no—
482C2×D4—112no—
483C2×D4—112no—
484C2×D4—112no—
485C2×D4—221no—
486C2×D4—221no—
487C2×D4—221no—
488C22×C4—224no—
489C22×C4—221no—
490C22×C4—221no—
491C22×C4—221no—
492C22×C4—221no—
493C22×C4—221no—
494C22×C4—224no—
495C22×C4—224no—
496C22×C4—221no—
497C22×C4—221no—
498C22×C4—881no—
499C22×C4—881no—
500C22×C4—881no—
501C22×C4—881no—
502C22×C4—881no—
503C22×C4—881no—
504C22×C4C2×D4411yescharacteristic
505C22×C4C2×D4411yescharacteristic
506C22×C4C2×D4411yescharacteristic
507C22×C4C2×D4411yescharacteristic
508C22×C4C2×D4411yescharacteristic
509C22×C4C2×D4411yescharacteristic
510C22×C4C23×D1111yescharacteristic
511SD16—228no—
512SD16—228no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8C2×C4×D1112yes—
524C2×C8C2×C4×D1112yes—
525C4⋊C4—112no—
526C4⋊C4—112no—
527C4⋊C4—112no—
528C4⋊C4—224no—
529C4⋊C4—224no—
530C4⋊C4—221no—
531C4⋊C4—221no—
532C4⋊C4—221no—
533C4⋊C4—221no—
534C4⋊C4—221no—
535C4⋊C4—221no—
536C4⋊C4—221no—
537C4⋊C4—442no—
538C4⋊C4—442no—
539C22⋊C4—224no—
540C22⋊C4—224no—
541C22⋊C4—224no—
542C42—21no—
543C42—21no—
544C42—442no—
545C42—442no—
546C42—881no—
547C42—881no—
548C42—881no—
549C42C2×C4×D1112yes—
550C42#433912yes—
551C42D4×D1112yes—
552C42#434312yes—
553C11#2151411yescharacteristic, complemented, Sylow
554C23—222no—
555C23—222no—
556C23—222no—
557C23—441no—
558C23—441no—
559C23—441no—
560C23—441no—
561C23C22×D4411yescharacteristic
562Q8—222no—
563Q8—222no—
564Q8—222no—
565Q8—222no—
566Q8—441no—
567Q8—441no—
568Q8—441no—
569Q8—441no—
570D4—114no—
571D4—222no—
572D4—222no—
573D4—222no—
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—21no—
587C2×C4—21no—
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—441no—
608C2×C4—441no—
609C2×C4—884no—
610C2×C4—884no—
611C2×C4—884no—
612C2×C4C4×D4412yes—
613C2×C4C4×D4412yes—
614C2×C4#6694812yes—
615C2×C4#6694812yes—
616C2×C4C22×C4×D1111yescharacteristic
617C2×C4C2×#433911yescharacteristic
618C2×C4C2×D4×D1111yescharacteristic
619C2×C4C2×#434311yescharacteristic
620C2×C4#41×D1111yescharacteristic
621C2×C4#41×D1111yescharacteristic
622C8—22no—
623C8—22no—
624C8—41no—
625C8—41no—
626C22—224no—
627C22—442no—
628C22—442no—
629C22—442no—
630C22—442no—
631C22—442no—
632C22—442no—
633C22C2×C4×D4411yescharacteristic
634C22C2×#6694811yescharacteristic
635C22#1062305511yescharacteristic
636C22#1062328211yescharacteristic
637C22#1062328211yescharacteristic
638C22#1062328211yescharacteristic
639C22#1062328411yescharacteristic
640C4—22no—
641C4—22no—
642C4—22no—
643C4—22no—
644C4—41no—
645C4—41no—
646C4—442no—
647C4—442no—
648C4—442no—
649C4—442no—
650C4—442no—
651C4—881no—
652C4—881no—
653C4C4×D4×D1111yescharacteristic
654C4#1062307911yescharacteristic
655C4C4×#434311yescharacteristic
656C4#1062311111yescharacteristic
657C2—444no—
658C2C4×#6694811yescharacteristic
659C2#1307746111yescharacteristic
660C2#1307747711yescharacteristic
661C2#1307812911yescharacteristic
662C2#1307816811yescharacteristic
663C2#1307883211yescharacteristic
664C2#1307886911yescharacteristic
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#21514
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
4. #13071335C2semidirect
6. #13069538C2semidirect
7. #13069386C2semidirect
8. #13069258C2semidirect
9. #13069251C2semidirect
13. #13068447C2semidirect
14. C4×#66880C2semidirect
15. C11×#1768C2semidirect
45. #10622454C4semidirect
105. #66922C2×C4semidirect
111. C11×C4⋊C8C2×C4semidirect
135. #66880C2×C4semidirect
136. #66880C2×C4semidirect
234. #1768D11semidirect
437. C4⋊C8C4×D11semidirect
553. C11#21514semidirect

Maximal subgroups

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

subgroupindex
C2×#106224542
C2×#106223232
C2×C4×#43142
#130713352
#130709782
#130695382
#130693862
#130692582
#130692512
#130689492
#130686272
#130684472
C4×#668802
C11×#17682
#2151411