Finite Group Databasebeta

← #14760173

Subgroups — #14760173

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×#10622777C211yesmaximal, characteristic
2C2×SD16×Dic11C211yesmaximal, characteristic
3#13071336C211yesmaximal, characteristic, complemented
4#13070977C211yesmaximal, characteristic
5#13069540C211yesmaximal, characteristic, complemented
6#13069386C211yesmaximal, characteristic, complemented
7#13069259C211yesmaximal, characteristic, complemented
8#13069252C211yesmaximal, characteristic, complemented
9#13068952C211yesmaximal, characteristic
10#13068952C211yesmaximal, characteristic
11#13068626C211yesmaximal, characteristic
12#13068475C211yesmaximal, characteristic, complemented
13#13068448C211yesmaximal, characteristic, complemented
14#103×Dic11C211yesmaximal, characteristic, complemented
15C2×C11×#461C211yesmaximal, characteristic
16C22×C11×SD16C2211yescharacteristic
17C22×C11×SD16C2211yescharacteristic
18C2×C11×C4⋊Q8C2211yescharacteristic
19C2×C4×D4×C11C2211yescharacteristic
20C2×Q8×Dic11C2211yescharacteristic
21C2×Q8×Dic11C2211yescharacteristic
22C2×D4×Dic11C2211yescharacteristic
23C2×D4×Dic11C2211yescharacteristic
24C11×#461C418yescomplemented
25C2×C11×C4⋊C8C2211yescharacteristic
26C2×C11×#103C2211yescharacteristic
27C2×C11×#103C2211yescharacteristic
28#10622843C2211yescharacteristic
29#10622843C2211yescharacteristic
30C2×#66899C2211yescharacteristic
31C2×#66899C2211yescharacteristic
32C2×#66899C2211yescharacteristic
33C2×#66899C2211yescharacteristic
34C2×#66896C2211yescharacteristic
35C2×#66896C2211yescharacteristic
36C4×C22⋊Dic11—21no—
37C2×C11⋊#95—21no—
38#10622777—24no—
39SD16×Dic11—24no—
40C2×#66882C2211yescharacteristic
41C2×#66881C2211yescharacteristic
42C2×#66879C2211yescharacteristic
43C2×C8×Dic11C2211yescharacteristic
44#10622594—21no—
45#10622594—21no—
46#10622594—21no—
47#10622594—21no—
48C4⋊C4×Dic11C2211yescharacteristic
49C4⋊C4×Dic11C2211yescharacteristic
50C22⋊C4×Dic11—21no—
51C22⋊C4×Dic11—21no—
52#10622549C2211yescharacteristic
53C4×C4⋊Dic11C2211yescharacteristic
54#10622545C2211yescharacteristic
55C2×C4⋊(C11⋊C8)C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622188C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62C22×Q8×C11C2311yescharacteristic
63C22×Q8×C11C2311yescharacteristic
64C22×D4×C11C2311yescharacteristic
65C23×C4×C11—21no—
66C23×Dic11—21no—
67C23×Dic11—21no—
68C2×C11×SD16—22no—
69C2×C11×SD16—22no—
70C2×C11×SD16—22no—
71C2×C11×SD16—22no—
72C2×C11×SD16C2×C414yes—
73C2×C11×SD16C2×C414yes—
74C22×C8×C11C2311yescharacteristic
75C22×C8×C11C2311yescharacteristic
76C11×C4⋊Q8—22no—
77C11×C4⋊Q8C2×C414yescomplemented
78C4×D4×C11—22no—
79C4×D4×C11C2×C414yes—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4—21no—
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C22⋊C4—21no—
84C2×C42×C11C2311yescharacteristic
85C2×C22⋊Dic11—21no—
86C2×C22⋊Dic11—21no—
87Q8×Dic11—22no—
88Q8×Dic11—22no—
89Q8×Dic11—22no—
90Q8×Dic11—22no—
91D4×Dic11—22no—
92D4×Dic11—22no—
93D4×Dic11—22no—
94D4×Dic11D414yes—
95C2×C4⋊Dic11—21no—
96C2×C4⋊Dic11—21no—
97C2×C4⋊Dic11C2311yescharacteristic
98C2×C4⋊Dic11C2311yescharacteristic
99C2×C4⋊Dic11C2311yescharacteristic
100C2×C4⋊Dic11C2311yescharacteristic
101C2×C4×Dic11—21no—
102C2×C4×Dic11—21no—
103C2×C4×Dic11—21no—
104C2×C4×Dic11—21no—
105C2×C4×Dic11—21no—
106C2×C4×Dic11C2311yescharacteristic
107C2×C4×Dic11C2311yescharacteristic
108C22×C11⋊C8C2311yescharacteristic
109C22×C11⋊C8C2311yescharacteristic
110C11×C4⋊C8C2×C414yescomplemented
111C11×#103C2×C414yescomplemented
112C11×#103C2×C414yescomplemented
113#66899—22no—
114#66899—22no—
115#66899—22no—
116#66899—22no—
117#66896—22no—
118#66896—22no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125C11⋊#95—21no—
126C11⋊#95—21no—
127C11⋊#95—21no—
128C11⋊#95D411yescharacteristic
129C11⋊#95D411yescharacteristic
130C11⋊#95D411yescharacteristic
131C11⋊#95D411yescharacteristic
132#66882—22no—
133#66881—22no—
134#66879—22no—
135C8×Dic11—22no—
136C4⋊(C11⋊C8)—22no—
137#21514—111nomaximal, Sylow
138C24×C11—21no—
139C2×Q8×C11—21no—
140C2×Q8×C11—21no—
141C2×Q8×C11—21no—
142C2×Q8×C11—21no—
143C2×Q8×C11—21no—
144C2×Q8×C11—21no—
145C2×Q8×C11—21no—
146C2×Q8×C11—21no—
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×Q8×C11C22×C412yes—
150C2×Q8×C11C22×C412yes—
151C2×D4×C11—21no—
152C2×D4×C11—21no—
153C2×D4×C11—21no—
154C2×D4×C11C22×C412yes—
155C2×D4×C11C2×D412yes—
156C2×D4×C11#4112yes—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—24no—
161C22×C4×C11—81no—
162C22×C4×C11—81no—
163C22×C4×C11C2×D411yescharacteristic
164C22×C4×C11C2×D411yescharacteristic
165C22×C4×C11C2411yescharacteristic
166C22×Dic11—24no—
167C22×Dic11—24no—
168C22×Dic11—21no—
169C22×Dic11—21no—
170C22×Dic11—21no—
171C22×Dic11—21no—
172C22×Dic11—81no—
173C22×Dic11—81no—
174C22×Dic11—81no—
175C22×Dic11—81no—
176C22×Dic11C2×D411yescharacteristic
177C22×Dic11C2×D411yescharacteristic
178C22×Dic11C2×D411yescharacteristic
179C22×Dic11C2×D411yescharacteristic
180C11×SD16—28no—
181C11×SD16—28no—
182C2×C8×C11—21no—
183C2×C8×C11—21no—
184C2×C8×C11—21no—
185C2×C8×C11—21no—
186C2×C8×C11C22×C412yes—
187C2×C8×C11C22×C412yes—
188C11×C4⋊C4—24no—
189C11×C4⋊C4—24no—
190C11×C4⋊C4—21no—
191C11×C4⋊C4C22×C412yes—
192C11×C22⋊C4—24no—
193C42×C11C22×C412yes—
194C42×C11#4112yes—
195C22⋊Dic11—24no—
196C22⋊Dic11—24no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11—42no—
204C4⋊Dic11—42no—
205C4⋊Dic11C2×D412yes—
206C4⋊Dic11#4112yes—
207C4×Dic11—21no—
208C4×Dic11—21no—
209C4×Dic11—42no—
210C4×Dic11—42no—
211C4×Dic11—81no—
212C4×Dic11—81no—
213C4×Dic11—81no—
214C4×Dic11C2×D412yes—
215C4×Dic11#4112yes—
216C2×C11⋊C8—21no—
217C2×C11⋊C8—21no—
218C2×C11⋊C8—21no—
219C2×C11⋊C8—21no—
220C2×C11⋊C8—21no—
221C2×C11⋊C8—21no—
222C2×#461D1111yescharacteristic
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#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
245Q8×C11—22no—
246Q8×C11—22no—
247Q8×C11—22no—
248Q8×C11—22no—
249Q8×C11—41no—
250Q8×C11—41no—
251Q8×C11—41no—
252Q8×C11—41no—
253D4×C11—22no—
254D4×C11—22no—
255D4×C11—22no—
256D4×C11C4×D414yes—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—22no—
262C2×C4×C11—22no—
263C2×C4×C11—22no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11—41no—
270C2×C4×C11—84no—
271C2×C4×C11C4×D412yes—
272C2×C4×C11C4×D412yes—
273C2×C4×C11C23×C411yescharacteristic
274C2×C4×C11C22×D411yescharacteristic
275C2×C4×C11C2×#4111yescharacteristic
276C2×C4×C11C2×#4111yescharacteristic
277C2×C4×C11C2×#4111yescharacteristic
278C2×C4×C11C2×#4111yescharacteristic
279C2×Dic11—21no—
280C2×Dic11—21no—
281C2×Dic11—21no—
282C2×Dic11—21no—
283C2×Dic11—22no—
284C2×Dic11—21no—
285C2×Dic11—21no—
286C2×Dic11—22no—
287C2×Dic11—21no—
288C2×Dic11—21no—
289C2×Dic11—21no—
290C2×Dic11—21no—
291C2×Dic11—41no—
292C2×Dic11—41no—
293C2×Dic11—41no—
294C2×Dic11—41no—
295C2×Dic11—41no—
296C2×Dic11—41no—
297C2×Dic11—41no—
298C2×Dic11—41no—
299C2×Dic11—41no—
300C2×Dic11—41no—
301C2×Dic11—84no—
302C2×Dic11—84no—
303C2×Dic11#12112yes—
304C2×Dic11#12112yes—
305C8×C11—22no—
306C8×C11—22no—
307C11⋊C8—41no—
308C11⋊C8—41no—
309C22×SD16C2×D1111yescharacteristic
310C22×SD16C2×D1111yescharacteristic
311C2×C4⋊Q8C2×D1111yescharacteristic
312C2×C4×Q8—111no—
313C2×C4×Q8—111no—
314C2×C4×D4—111no—
315C2×C4×D4—111no—
316C2×C4×D4C2×D1111yescharacteristic
317#461Dic1118yescomplemented
318#440—224no—
319C4×SD16—224no—
320C2×#107—111no—
321C2×#106—111no—
322C2×C4⋊C8—111no—
323C2×C4⋊C8C2×D1111yescharacteristic
324C2×#103—111no—
325C2×#103—111no—
326C2×#103—111no—
327C2×#103—111no—
328C2×#103C2×D1111yescharacteristic
329C2×#103C2×D1111yescharacteristic
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⋊C4—111no—
342C4×C4⋊C4—111no—
343C4×C4⋊C4—111no—
344C4×C22⋊C4—221no—
345C4×C22⋊C4—221no—
346C4×C22⋊C4—221no—
347#376—111no—
348C2×#95—221no—
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—42no—
372C4×C11—42no—
373C4×C11—42no—
374C4×C11C2×C4×D411yescharacteristic
375C4×C11C4×#4111yescharacteristic
376C4×C11#52911yescharacteristic
377C4×C11#53211yescharacteristic
378Dic11—22no—
379Dic11—22no—
380Dic11—41no—
381Dic11—41no—
382Dic11—42no—
383Dic11—42no—
384Dic11—81no—
385Dic11—81no—
386C22×Q8C22×D1111yescharacteristic
387C22×Q8C22×D1111yescharacteristic
388C22×D4C22×D1111yescharacteristic
389C23×C4—21no—
390C23×C4—221no—
391C23×C4—221no—
392C2×SD16—22no—
393C2×SD16—22no—
394C2×SD16—22no—
395C2×SD16—22no—
396C2×SD16C2×Dic1114yes—
397C2×SD16C2×Dic1114yes—
398C22×C8—111no—
399C22×C8—111no—
400C22×C8C22×D1111yescharacteristic
401C22×C8C22×D1111yescharacteristic
402C4⋊Q8—22no—
403C4⋊Q8C2×Dic1114yescomplemented
404C4×Q8—222no—
405C4×Q8—222no—
406C4×Q8—222no—
407C4×Q8—222no—
408C4×D4—22no—
409C4×D4—114no—
410C4×D4—222no—
411C4×D4—222no—
412C4×D4—222no—
413C4×D4C2×Dic1114yes—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—111no—
417C2×C4⋊C4—111no—
418C2×C4⋊C4—111no—
419C2×C4⋊C4—111no—
420C2×C4⋊C4—221no—
421C2×C4⋊C4—221no—
422C2×C4⋊C4C22×D1111yescharacteristic
423C2×C22⋊C4—21no—
424C2×C22⋊C4—221no—
425C2×C22⋊C4—221no—
426C2×C42—111no—
427C2×C42—111no—
428C2×C42—221no—
429C2×C42—221no—
430C2×C42—221no—
431C2×C42—221no—
432C2×C42—221no—
433C2×C42C22×D1111yescharacteristic
434#107—222no—
435#106—222no—
436C4⋊C8—222no—
437C4⋊C8C2×Dic1114yescomplemented
438#103—222no—
439#103—222no—
440#103—222no—
441#103—222no—
442#103C2×Dic1114yescomplemented
443#103C2×Dic1114yescomplemented
444#102—222no—
445#102—222no—
446#97—222no—
447C4×C8—222no—
448#95—111no—
449#95—111no—
450#95—111no—
451#95—111no—
452#95—221no—
453#95—221no—
454#95—221no—
455#95—221no—
456#95—221no—
457#95—221no—
458#95—221no—
459#95—221no—
460#95—221no—
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—21no—
471C2×Q8—21no—
472C2×Q8—21no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8C22×Dic1112yes—
481C2×Q8C22×Dic1112yes—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4D4×D1112yes—
486C2×D4#434112yes—
487C2×D4C22×Dic1112yes—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—24no—
492C22×C4—81no—
493C22×C4—81no—
494C22×C4—111no—
495C22×C4—111no—
496C22×C4—111no—
497C22×C4—111no—
498C22×C4—224no—
499C22×C4—221no—
500C22×C4—221no—
501C22×C4—224no—
502C22×C4—221no—
503C22×C4—221no—
504C22×C4—881no—
505C22×C4—881no—
506C22×C4—881no—
507C22×C4—881no—
508C22×C4D4×D1111yescharacteristic
509C22×C4D4×D1111yescharacteristic
510C22×C4C23×D1111yescharacteristic
511SD16—28no—
512SD16—28no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—221no—
518C2×C8—221no—
519C2×C8—221no—
520C2×C8—221no—
521C2×C8—221no—
522C2×C8—221no—
523C2×C8C22×Dic1112yes—
524C2×C8C22×Dic1112yes—
525C4⋊C4—24no—
526C4⋊C4—24no—
527C4⋊C4—21no—
528C4⋊C4—112no—
529C4⋊C4—112no—
530C4⋊C4—221no—
531C4⋊C4—221no—
532C4⋊C4—221no—
533C4⋊C4—221no—
534C4⋊C4—221no—
535C4⋊C4—221no—
536C4⋊C4—442no—
537C4⋊C4—442no—
538C4⋊C4C22×Dic1112yes—
539C22⋊C4—24no—
540C22⋊C4—224no—
541C22⋊C4—224no—
542C42—112no—
543C42—112no—
544C42—221no—
545C42—221no—
546C42—442no—
547C42—442no—
548C42—881no—
549C42—881no—
550C42—881no—
551C42#434112yes—
552C42C22×Dic1112yes—
553C11#2151411yescharacteristic, complemented, Sylow
554C23—22no—
555C23—22no—
556C23—22no—
557C23—41no—
558C23—41no—
559C23—41no—
560C23—41no—
561C23C2×D4×D1111yescharacteristic
562Q8—22no—
563Q8—22no—
564Q8—22no—
565Q8—22no—
566Q8—41no—
567Q8—41no—
568Q8—41no—
569Q8—41no—
570D4—22no—
571D4—22no—
572D4—22no—
573D4D4×Dic1114yes—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—84no—
588C2×C4—112no—
589C2×C4—112no—
590C2×C4—221no—
591C2×C4—221no—
592C2×C4—221no—
593C2×C4—221no—
594C2×C4—221no—
595C2×C4—221no—
596C2×C4—221no—
597C2×C4—221no—
598C2×C4—222no—
599C2×C4—221no—
600C2×C4—221no—
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×C4—884no—
613C2×C4—884no—
614C2×C4D4×Dic1112yes—
615C2×C4D4×Dic1112yes—
616C2×C4C2×D4×D1111yescharacteristic
617C2×C4C2×#434111yescharacteristic
618C2×C4C2×#434111yescharacteristic
619C2×C4#41×D1111yescharacteristic
620C2×C4#41×D1111yescharacteristic
621C2×C4C23×Dic1111yescharacteristic
622C8—22no—
623C8—22no—
624C8—441no—
625C8—441no—
626C22—24no—
627C22—42no—
628C22—42no—
629C22—42no—
630C22—42no—
631C22—42no—
632C22—42no—
633C22D11×#12111yescharacteristic
634C22#1062313711yescharacteristic
635C22#1062329311yescharacteristic
636C22#1062329311yescharacteristic
637C22#1062330911yescharacteristic
638C22#1062331011yescharacteristic
639C22C2×D4×Dic1111yescharacteristic
640C4—22no—
641C4—22no—
642C4—42no—
643C4—42no—
644C4—42no—
645C4—222no—
646C4—222no—
647C4—441no—
648C4—441no—
649C4—442no—
650C4—442no—
651C4—881no—
652C4—881no—
653C4#1062312711yescharacteristic
654C4#1062313111yescharacteristic
655C4C2×D4×Dic1111yescharacteristic
656C4#41×Dic1111yescharacteristic
657C2—44no—
658C2#121×Dic1111yescharacteristic
659C2#1307746011yescharacteristic
660C2#1307747611yescharacteristic
661C2#1307812311yescharacteristic
662C2#1307816111yescharacteristic
663C2#1307882711yescharacteristic
664C2#1307886611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#461C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
cosocleC22×C4×C11C24
hypercenterC2×#461D11
hypocenterC11#21514
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#461

Complements

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

NH ≅ G/Ntype
3. #13071336C2semidirect
5. #13069540C2semidirect
6. #13069386C2semidirect
7. #13069259C2semidirect
8. #13069252C2semidirect
12. #13068475C2semidirect
13. #13068448C2semidirect
14. #103×Dic11C2semidirect
24. C11×#461C4semidirect
77. C11×C4⋊Q8C2×C4semidirect
110. C11×C4⋊C8C2×C4semidirect
111. C11×#103C2×C4semidirect
112. C11×#103C2×C4semidirect
317. #461Dic11semidirect
403. C4⋊Q8C2×Dic11semidirect
437. C4⋊C8C2×Dic11semidirect
442. #103C2×Dic11semidirect
443. #103C2×Dic11semidirect
553. C11#21514semidirect

Maximal subgroups

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

subgroupindex
C2×#106227772
C2×SD16×Dic112
#130713362
#130709772
#130695402
#130693862
#130692592
#130692522
#130689522
#130686262
#130684752
#130684482
#103×Dic112
C2×C11×#4612
#2151411