Finite Group Databasebeta

← #14760172

Subgroups — #14760172

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×#10622632C211yesmaximal, characteristic
2C2×#10622631C211yesmaximal, characteristic
3C2×C4×#4324C211yesmaximal, characteristic
4#13071335C211yesmaximal, characteristic, complemented
5#13069539C211yesmaximal, characteristic, complemented
6#13069384C211yesmaximal, characteristic, complemented
7#13069257C211yesmaximal, characteristic, complemented
8#13069250C211yesmaximal, characteristic, complemented
9#13068950C211yesmaximal, characteristic
10#13068950C211yesmaximal, characteristic
11#13068626C211yesmaximal, characteristic
12#13068473C211yesmaximal, characteristic, complemented
13#13068449C211yesmaximal, characteristic, complemented
14C4×#66874C211yesmaximal, characteristic, complemented
15C11×#2275C211yesmaximal, characteristic
16C2×C4×D4×C11C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C22×#4324C2211yescharacteristic
20C22×#4324C2211yescharacteristic
21C2×#66922C2211yescharacteristic
22C2×C4×Dic22C2211yescharacteristic
23C2×C4×Dic22C2211yescharacteristic
24C4×C11×C4⋊C4C2211yescharacteristic
25C4×C11×C4⋊C4C2211yescharacteristic
26C4×C11×C4⋊C4C2211yescharacteristic
27C4×C11×C22⋊C4—21no—
28C4×C11×C22⋊C4—21no—
29C4×C11×C22⋊C4—21no—
30C11×#376C2211yescharacteristic
31C2×C11×#95—21no—
32C2×#66896C2211yescharacteristic
33C2×#66896C2211yescharacteristic
34#10622632C418yescomplemented
35#10622631—24no—
36C4×#4324—24no—
37C2×#66874C2211yescharacteristic
38C2×#66874C2211yescharacteristic
39C2×#66874C2211yescharacteristic
40C2×#66874C2211yescharacteristic
41C2×#66874C2211yescharacteristic
42C2×#66874C2211yescharacteristic
43C2×#66872C2211yescharacteristic
44C2×#66871C2211yescharacteristic
45#10622549C2211yescharacteristic
46#10622542C2211yescharacteristic
47#10622542C2211yescharacteristic
48C2×C4⋊(C11⋊C8)C2211yescharacteristic
49C2×C4⋊(C11⋊C8)C2211yescharacteristic
50C2×#66867C2211yescharacteristic
51C2×C4×C11⋊C8C2211yescharacteristic
52#10622266—21no—
53#10622266—21no—
54#10622266—21no—
55#10622266—21no—
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622162C2211yescharacteristic
61#10622162C2211yescharacteristic
62C22×D4×C11C2311yescharacteristic
63C23×C4×C11—21no—
64C23×C4×C11—21no—
65C23×C4×C11—21no—
66C22×Dic22C2311yescharacteristic
67C22×Dic22C2311yescharacteristic
68C4×D4×C11—22no—
69C4×D4×C11—22no—
70C4×D4×C11—22no—
71C4×D4×C11—22no—
72C4×D4×C11C2×C414yes—
73C4×D4×C11D414yes—
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C22⋊C4—21no—
78C2×C11×C22⋊C4—21no—
79C2×C11×C22⋊C4—21no—
80C2×C42×C11—21no—
81C2×C42×C11—21no—
82C2×C42×C11—21no—
83C2×C42×C11C2311yescharacteristic
84C2×C42×C11C2311yescharacteristic
85C2×C42×C11C2311yescharacteristic
86C2×#4324—22no—
87C2×#4324—22no—
88C2×#4324—22no—
89C2×#4324—22no—
90C2×#4324C2×C414yes—
91C2×#4324C2×C414yes—
92C2×C4⋊Dic11—21no—
93C2×C4⋊Dic11—21no—
94C2×C4⋊Dic11C2311yescharacteristic
95C2×C4⋊Dic11C2311yescharacteristic
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4—21no—
98C2×C4×Dic11—21no—
99C2×C4×Dic11—21no—
100C22×C11⋊C8C2311yescharacteristic
101C22×C11⋊C8C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103C22×C11⋊C8C2311yescharacteristic
104#66922—22no—
105#66922C2×C414yescomplemented
106C4×Dic22—22no—
107C4×Dic22—22no—
108C4×Dic22—22no—
109C4×Dic22—22no—
110C11×#95—21no—
111C11×#95—21no—
112C11×#95—21no—
113C11×#95D411yescharacteristic
114C11×#95D411yescharacteristic
115C11×#95D411yescharacteristic
116C11×#95D411yescharacteristic
117#66896—22no—
118#66896—22no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125#66874—22no—
126#66874—22no—
127#66874—22no—
128#66874—22no—
129#66874C2×C414yescomplemented
130#66874C2×C414yescomplemented
131#66872—22no—
132#66871—22no—
133C4⋊(C11⋊C8)—22no—
134C4⋊(C11⋊C8)C2×C414yescomplemented
135#66867—22no—
136C4×C11⋊C8—22no—
137#21514—111nomaximal, Sylow
138C24×C11—21no—
139C2×D4×C11—21no—
140C2×D4×C11—21no—
141C2×D4×C11—21no—
142C2×D4×C11C22×C412yes—
143C2×D4×C11C2×D412yes—
144C2×D4×C11#4112yes—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—24no—
149C22×C4×C11—24no—
150C22×C4×C11—24no—
151C22×C4×C11—81no—
152C22×C4×C11—81no—
153C22×C4×C11—81no—
154C22×C4×C11—81no—
155C22×C4×C11—81no—
156C22×C4×C11—81no—
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11C2×D411yescharacteristic
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11C2411yescharacteristic
164C22×Dic11—21no—
165C22×Dic11—21no—
166C22×Dic11—21no—
167C22×Dic11—21no—
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—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4C22×C412yes—
184C11×C4⋊C4C2×D412yes—
185C11×C4⋊C4#4112yes—
186C11×C22⋊C4—24no—
187C11×C22⋊C4—24no—
188C11×C22⋊C4—24no—
189C42×C11—21no—
190C42×C11—21no—
191C42×C11—81no—
192C42×C11—81no—
193C42×C11—81no—
194C42×C11C22×C412yes—
195C42×C11C2×D412yes—
196C42×C11#4112yes—
197C42×C11#4112yes—
198#4324—28no—
199#4324—28no—
200C4⋊Dic11—24no—
201C4⋊Dic11—24no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11—21no—
205C4⋊Dic11—21no—
206Dic11⋊C4—42no—
207Dic11⋊C4—42no—
208C4×Dic11—42no—
209C4×Dic11—42no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8—21no—
217C2×C11⋊C8—21no—
218C2×C11⋊C8—21no—
219C2×C11⋊C8—21no—
220C2×C11⋊C8C22×C412yes—
221C2×C11⋊C8C22×C412yes—
222C2×#461—111no—
223C2×#440—111no—
224C2×C4×SD16—111no—
225#2327—111no—
226#2275D1111yescharacteristic
227#1981—111no—
228#1949—111no—
229#1928—111no—
230#1927—111no—
231#1877—111no—
232#1877—111no—
233#1804—111no—
234#1768—111no—
235#1763—111no—
236C4×#103—111no—
237C23×C11—22no—
238C23×C11—22no—
239C23×C11—22no—
240C23×C11—41no—
241C23×C11—41no—
242C23×C11—41no—
243C23×C11—41no—
244C23×C11C22×D411yescharacteristic
245D4×C11—22no—
246D4×C11—22no—
247D4×C11—22no—
248D4×C11C4×D414yes—
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—22no—
258C2×C4×C11—22no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—22no—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
264C2×C4×C11—21no—
265C2×C4×C11—21no—
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—84no—
273C2×C4×C11—84no—
274C2×C4×C11—84no—
275C2×C4×C11C4×D412yes—
276C2×C4×C11C4×D412yes—
277C2×C4×C11#12112yes—
278C2×C4×C11#12112yes—
279C2×C4×C11C23×C411yescharacteristic
280C2×C4×C11C22×D411yescharacteristic
281C2×C4×C11C2×#4111yescharacteristic
282C2×C4×C11C2×#4111yescharacteristic
283C2×C4×C11C2×#4111yescharacteristic
284C2×C4×C11C2×#4111yescharacteristic
285C2×Dic11—22no—
286C2×Dic11—22no—
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—
296C2×Dic11—41no—
297Dic22—22no—
298Dic22—22no—
299Dic22—22no—
300Dic22—22no—
301Dic22—41no—
302Dic22—41no—
303Dic22—41no—
304Dic22—41no—
305C11⋊C8—22no—
306C11⋊C8—22no—
307C11⋊C8—41no—
308C11⋊C8—41no—
309C22×SD16—111no—
310C22×SD16—111no—
311C2×C4⋊Q8—111no—
312C2×C4×Q8—111no—
313C2×C4×Q8—111no—
314C2×C4×D4C2×D1111yescharacteristic
315C2×C4×D4C2×D1111yescharacteristic
316C2×C4×D4C2×D1111yescharacteristic
317#461—118no—
318#440—224no—
319C4×SD16—224no—
320C2×#107—111no—
321C2×#106—111no—
322C2×C4⋊C8—111no—
323C2×C4⋊C8—111no—
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×#97—111no—
333C2×C4×C8—111no—
334#391—111no—
335#391—111no—
336#387—221no—
337#387—221no—
338#387—221no—
339#387—221no—
340#382—111no—
341C4×C4⋊C4C2×D1111yescharacteristic
342C4×C4⋊C4C2×D1111yescharacteristic
343C4×C4⋊C4C2×D1111yescharacteristic
344C4×C22⋊C4—21no—
345C4×C22⋊C4—21no—
346C4×C22⋊C4—21no—
347#376C2×D1111yescharacteristic
348C2×#95—21no—
349#340—111no—
350#340—111no—
351#340—111no—
352#340—111no—
353#336—111no—
354#336—111no—
355C22×C11—24no—
356C22×C11—42no—
357C22×C11—42no—
358C22×C11—42no—
359C22×C11—42no—
360C22×C11—42no—
361C22×C11—42no—
362C22×C11C2×C4×D411yescharacteristic
363C22×C11C2×#12111yescharacteristic
364C22×C11#52511yescharacteristic
365C22×C11#57711yescharacteristic
366C22×C11#57711yescharacteristic
367C22×C11#57711yescharacteristic
368C22×C11#57811yescharacteristic
369C4×C11—22no—
370C4×C11—22no—
371C4×C11—22no—
372C4×C11—22no—
373C4×C11—41no—
374C4×C11—41no—
375C4×C11—42no—
376C4×C11—42no—
377C4×C11—42no—
378C4×C11C2×C4×D411yescharacteristic
379C4×C11C4×#4111yescharacteristic
380C4×C11#52911yescharacteristic
381C4×C11#53211yescharacteristic
382Dic11—42no—
383Dic11—42no—
384Dic11—81no—
385Dic11—81no—
386C22×Q8—111no—
387C22×Q8—111no—
388C22×D4C22×D1111yescharacteristic
389C23×C4—21no—
390C23×C4—21no—
391C23×C4—21no—
392C2×SD16—114no—
393C2×SD16—114no—
394C2×SD16—222no—
395C2×SD16—222no—
396C2×SD16—222no—
397C2×SD16—222no—
398C22×C8—111no—
399C22×C8—111no—
400C22×C8—111no—
401C22×C8—111no—
402C4⋊Q8—114no—
403C4⋊Q8—222no—
404C4×Q8—222no—
405C4×Q8—222no—
406C4×Q8—222no—
407C4×Q8—222no—
408C4×D4—22no—
409C4×D4—22no—
410C4×D4—22no—
411C4×D4—22no—
412C4×D4C4×D1114yes—
413C4×D4D4414yes—
414C2×C4⋊C4—111no—
415C2×C4⋊C4—111no—
416C2×C4⋊C4—221no—
417C2×C4⋊C4—221no—
418C2×C4⋊C4—221no—
419C2×C4⋊C4—221no—
420C2×C4⋊C4C22×D1111yescharacteristic
421C2×C4⋊C4C22×D1111yescharacteristic
422C2×C4⋊C4C22×D1111yescharacteristic
423C2×C22⋊C4—21no—
424C2×C22⋊C4—21no—
425C2×C22⋊C4—21no—
426C2×C42—21no—
427C2×C42—21no—
428C2×C42—21no—
429C2×C42—221no—
430C2×C42—221no—
431C2×C42C22×D1111yescharacteristic
432C2×C42C22×D1111yescharacteristic
433C2×C42C22×D1111yescharacteristic
434#107—222no—
435#106—222no—
436C4⋊C8—114no—
437C4⋊C8—222no—
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—222no—
447C4×C8—222no—
448#95—21no—
449#95—21no—
450#95—21no—
451#95—221no—
452#95—221no—
453#95—221no—
454#95—221no—
455#95—221no—
456#95—221no—
457#95C22⋊D1111yescharacteristic
458#95C22⋊D1111yescharacteristic
459#95C22⋊D1111yescharacteristic
460#95C22⋊D1111yescharacteristic
461C2×C11—44no—
462C2×C11C4×#12111yescharacteristic
463C2×C11#294711yescharacteristic
464C2×C11#294911yescharacteristic
465C2×C11#304211yescharacteristic
466C2×C11#304611yescharacteristic
467C2×C11#312011yescharacteristic
468C2×C11#312311yescharacteristic
469C24—21no—
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—21no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4C2×C4×D1112yes—
486C2×D4C2×D4412yes—
487C2×D4#433912yes—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—24no—
492C22×C4—24no—
493C22×C4—24no—
494C22×C4—81no—
495C22×C4—81no—
496C22×C4—81no—
497C22×C4—81no—
498C22×C4—81no—
499C22×C4—81no—
500C22×C4—221no—
501C22×C4—221no—
502C22×C4—221no—
503C22×C4—221no—
504C22×C4C2×C22⋊D1111yescharacteristic
505C22×C4C2×C22⋊D1111yescharacteristic
506C22×C4C2×C22⋊D1111yescharacteristic
507C22×C4C2×C22⋊D1111yescharacteristic
508C22×C4C2×C22⋊D1111yescharacteristic
509C22×C4C2×C22⋊D1111yescharacteristic
510C22×C4C23×D1111yescharacteristic
511SD16—228no—
512SD16—228no—
513C2×C8—112no—
514C2×C8—112no—
515C2×C8—221no—
516C2×C8—221no—
517C2×C8—221no—
518C2×C8—221no—
519C2×C8—221no—
520C2×C8—221no—
521C2×C8—221no—
522C2×C8—221no—
523C2×C8—221no—
524C2×C8—221no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—224no—
529C4⋊C4—224no—
530C4⋊C4—221no—
531C4⋊C4—221no—
532C4⋊C4—221no—
533C4⋊C4—221no—
534C4⋊C4—442no—
535C4⋊C4—442no—
536C4⋊C4C2×C4×D1112yes—
537C4⋊C4C2×D4412yes—
538C4⋊C4#433912yes—
539C22⋊C4—24no—
540C22⋊C4—24no—
541C22⋊C4—24no—
542C42—21no—
543C42—21no—
544C42—81no—
545C42—81no—
546C42—81no—
547C42—442no—
548C42—442no—
549C42C2×C4×D1112yes—
550C42C2×D4412yes—
551C42#433912yes—
552C42#433912yes—
553C11#2151411yescharacteristic, complemented, Sylow
554C23—22no—
555C23—22no—
556C23—22no—
557C23—41no—
558C23—41no—
559C23—41no—
560C23—41no—
561C23C22×C22⋊D1111yescharacteristic
562Q8—222no—
563Q8—222no—
564Q8—222no—
565Q8—222no—
566Q8—441no—
567Q8—441no—
568Q8—441no—
569Q8—441no—
570D4—22no—
571D4—22no—
572D4—22no—
573D4C4×D4414yes—
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—22no—
583C2×C4—22no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—22no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—84no—
598C2×C4—84no—
599C2×C4—84no—
600C2×C4—222no—
601C2×C4—222no—
602C2×C4—441no—
603C2×C4—441no—
604C2×C4—441no—
605C2×C4—441no—
606C2×C4—441no—
607C2×C4—441no—
608C2×C4—441no—
609C2×C4—441no—
610C2×C4—441no—
611C2×C4—441no—
612C2×C4C4×C22⋊D1112yes—
613C2×C4C4×C22⋊D1112yes—
614C2×C4#6698312yes—
615C2×C4#6698312yes—
616C2×C4C22×C4×D1111yescharacteristic
617C2×C4C22×D4411yescharacteristic
618C2×C4C2×#433911yescharacteristic
619C2×C4C2×#433911yescharacteristic
620C2×C4C2×#433911yescharacteristic
621C2×C4C2×#433911yescharacteristic
622C8—222no—
623C8—222no—
624C8—441no—
625C8—441no—
626C22—24no—
627C22—42no—
628C22—42no—
629C22—42no—
630C22—42no—
631C22—42no—
632C22—42no—
633C22C2×C4×C22⋊D1111yescharacteristic
634C22C2×#6698311yescharacteristic
635C22#1062332211yescharacteristic
636C22#1062336711yescharacteristic
637C22#1062336711yescharacteristic
638C22#1062336711yescharacteristic
639C22#1062336911yescharacteristic
640C4—22no—
641C4—22no—
642C4—22no—
643C4—22no—
644C4—41no—
645C4—41no—
646C4—42no—
647C4—42no—
648C4—42no—
649C4—442no—
650C4—442no—
651C4—881no—
652C4—881no—
653C4C2×C4×D4411yescharacteristic
654C4C4×#433911yescharacteristic
655C4#1062300811yescharacteristic
656C4#1062301011yescharacteristic
657C2—44no—
658C2C4×#6698311yescharacteristic
659C2#1307745511yescharacteristic
660C2#1307747311yescharacteristic
661C2#1307812811yescharacteristic
662C2#1307816611yescharacteristic
663C2#1307883011yescharacteristic
664C2#1307886811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2275C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
cosocleC22×C4×C11C24
hypercenter#2275D11
hypocenterC11#21514
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ #376 ◁ #2275

Complements

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

NH ≅ G/Ntype
4. #13071335C2semidirect
5. #13069539C2semidirect
6. #13069384C2semidirect
7. #13069257C2semidirect
8. #13069250C2semidirect
12. #13068473C2semidirect
13. #13068449C2semidirect
14. C4×#66874C2semidirect
34. #10622632C4semidirect
105. #66922C2×C4semidirect
129. #66874C2×C4semidirect
130. #66874C2×C4semidirect
134. C4⋊(C11⋊C8)C2×C4semidirect
553. C11#21514semidirect

Maximal subgroups

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

subgroupindex
C2×#106226322
C2×#106226312
C2×C4×#43242
#130713352
#130695392
#130693842
#130692572
#130692502
#130689502
#130686262
#130684732
#130684492
C4×#668742
C11×#22752
#2151411