Finite Group Databasebeta

← #14771047

Subgroups — #14771047

Order 2816.

934 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071509C211yesmaximal, characteristic
2Q8×C22⋊Dic11C211yesmaximal, characteristic
3#13069308C211yesmaximal, characteristic, complemented
4#13069294C211yesmaximal, characteristic, complemented
5#13069259C211yesmaximal, characteristic, complemented
6#13069252C211yesmaximal, characteristic, complemented
7#13068886C211yesmaximal, characteristic, complemented
8#13068872C211yesmaximal, characteristic, complemented
9#13068711C211yesmaximal, characteristic
10#13068649C211yesmaximal, characteristic
11#13068551C211yesmaximal, characteristic
12#13068448C211yesmaximal, characteristic, complemented
13#103×Dic11C211yesmaximal, characteristic, complemented
14#13068397C211yesmaximal, characteristic
15C2×C11×#419C211yesmaximal, characteristic
16C23×Q8×C11C2211yescharacteristic
17C22×C11×M16C2211yescharacteristic
18C2×C11×#117C2211yescharacteristic
19C2×Q8×Dic11C2211yescharacteristic
20C2×Q8×Dic11C2211yescharacteristic
21C11×#419C418yescomplemented
22C2×C11×#103C2211yescharacteristic
23C2×C11×#103C2211yescharacteristic
24C2×C11×#103C2211yescharacteristic
25C2×C11×#103C2211yescharacteristic
26#10622843—21no—
27#10622843—21no—
28#10622843C2211yescharacteristic
29#10622843C2211yescharacteristic
30C2×#66899C2211yescharacteristic
31C2×#66899C2211yescharacteristic
32C2×#66899C2211yescharacteristic
33C2×#66899C2211yescharacteristic
34#10622825—21no—
35#10622825C2211yescharacteristic
36#10622825C2211yescharacteristic
37C4×C22⋊Dic11—21no—
38C4×C22⋊Dic11C2211yescharacteristic
39C2×C22⋊(C11⋊C8)C2211yescharacteristic
40C2×#66882C2211yescharacteristic
41C2×#66881C2211yescharacteristic
42C2×#66879C2211yescharacteristic
43C2×C8×Dic11C2211yescharacteristic
44#10622598C2211yescharacteristic
45#10622598C2211yescharacteristic
46C4⋊C4×Dic11C2211yescharacteristic
47C4⋊C4×Dic11C2211yescharacteristic
48#10622564—21no—
49#10622564—21no—
50#10622550—21no—
51C4×C4⋊Dic11—21no—
52#10622189C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60C22×Q8×C11—21no—
61C22×Q8×C11—22no—
62C22×Q8×C11—22no—
63C22×Q8×C11—22no—
64C22×Q8×C11—41no—
65C22×Q8×C11—41no—
66C22×Q8×C11C2×C414yes—
67C22×Q8×C11C2311yescharacteristic
68C22×Q8×C11C2311yescharacteristic
69C23×C4×C11—21no—
70C23×C4×C11C2311yescharacteristic
71C2×C11×M16—41no—
72C2×C11×M16—41no—
73C2×C11×M16C2×C414yes—
74C22×C8×C11C2311yescharacteristic
75C22×C8×C11C2311yescharacteristic
76C11×#117—22no—
77C11×#117C2×C414yes—
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C22⋊C4—21no—
81C2×C42×C11—21no—
82C2×C22⋊Dic11—21no—
83C2×C22⋊Dic11—21no—
84C2×C22⋊Dic11D411yescharacteristic
85C2×C22⋊Dic11D411yescharacteristic
86Q8×Dic11—22no—
87Q8×Dic11—22no—
88Q8×Dic11—41no—
89Q8×Dic11—41no—
90C2×C4⋊Dic11—21no—
91C2×C4⋊Dic11—21no—
92C2×C4⋊Dic11—21no—
93C2×C4⋊Dic11—21no—
94C2×C4⋊Dic11C2311yescharacteristic
95C2×C4⋊Dic11C2311yescharacteristic
96C2×C4⋊Dic11C2311yescharacteristic
97C2×C4⋊Dic11C2311yescharacteristic
98C2×C4×Dic11—21no—
99C2×C4×Dic11—21no—
100C2×C4×Dic11—21no—
101C2×C4×Dic11—21no—
102C2×C4×Dic11C2311yescharacteristic
103C2×C4×Dic11C2311yescharacteristic
104C22×C11⋊C8C2311yescharacteristic
105C22×C11⋊C8C2311yescharacteristic
106C11×#103C2×C414yes—
107C11×#103C2×C414yes—
108C11×#103C2×C414yes—
109C11×#103C2×C414yes—
110#66899—22no—
111#66899—22no—
112#66899—41no—
113#66899—41no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C11⋊#95D411yescharacteristic
125C11⋊#95D411yescharacteristic
126C22⋊(C11⋊C8)—22no—
127#66882—41no—
128#66881—41no—
129#66879—41no—
130C8×Dic11—41no—
131#22581—111nomaximal, Sylow
132C24×C11C2×D411yescharacteristic
133C2×Q8×C11—24no—
134C2×Q8×C11—21no—
135C2×Q8×C11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11—21no—
138C2×Q8×C11—28no—
139C2×Q8×C11—21no—
140C2×Q8×C11—21no—
141C2×Q8×C11—21no—
142C2×Q8×C11—21no—
143C2×Q8×C11—42no—
144C2×Q8×C11—42no—
145C2×Q8×C11—44no—
146C2×Q8×C11—44no—
147C2×Q8×C11—44no—
148C2×Q8×C11C22×C412yes—
149C2×Q8×C11C22×C412yes—
150C2×Q8×C11#4112yes—
151C2×Q8×C11#4112yes—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—24no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—42no—
162C22×C4×C11—42no—
163C22×C4×C11C22×C412yes—
164C22×C4×C11C2×D411yescharacteristic
165C22×C4×C11#4112yes—
166C22×C4×C11C2411yescharacteristic
167C22×Dic11—21no—
168C22×Dic11—21no—
169C22×Dic11—21no—
170C22×Dic11—21no—
171C22×Dic11C2×D411yescharacteristic
172C22×Dic11C2×D411yescharacteristic
173C22×Dic11C2×D411yescharacteristic
174C22×Dic11C2×D411yescharacteristic
175C11×M16—44no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11C22×C412yes—
181C2×C8×C11C22×C412yes—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4C22×C412yes—
185C11×C4⋊C4C22×C412yes—
186C11×C22⋊C4—24no—
187C42×C11—24no—
188C22⋊Dic11—22no—
189C22⋊Dic11—41no—
190C22⋊Dic11—42no—
191C22⋊Dic11—81no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—42no—
201C4⋊Dic11—42no—
202C4⋊Dic11—42no—
203C4⋊Dic11—42no—
204C4×Dic11—21no—
205C4×Dic11—21no—
206C4×Dic11—21no—
207C4×Dic11—21no—
208C4×Dic11—42no—
209C4×Dic11—42no—
210C4×Dic11—81no—
211C4×Dic11—81no—
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×#419D1111yescharacteristic
219#2347—111no—
220Q8×C22⋊C4—111no—
221#1935—111no—
222#1933—111no—
223#1928—111no—
224#1927—111no—
225#1865—111no—
226#1863—111no—
227#1825—111no—
228#1809—111no—
229#1787—111no—
230#1763—111no—
231C4×#103—111no—
232#1753—111no—
233C23×C11—21no—
234C23×C11—21no—
235C23×C11—21no—
236C23×C11—21no—
237C23×C11—21no—
238C23×C11—21no—
239C23×C11C4×D412yes—
240C23×C11C22×D411yescharacteristic
241Q8×C11—22no—
242Q8×C11—22no—
243Q8×C11—22no—
244Q8×C11—22no—
245Q8×C11—22no—
246Q8×C11—48no—
247Q8×C11—41no—
248Q8×C11—41no—
249Q8×C11#11714yes—
250C2×C4×C11—22no—
251C2×C4×C11—22no—
252C2×C4×C11—22no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—22no—
256C2×C4×C11—22no—
257C2×C4×C11—22no—
258C2×C4×C11—22no—
259C2×C4×C11—22no—
260C2×C4×C11—22no—
261C2×C4×C11—22no—
262C2×C4×C11—48no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11C4×D412yes—
270C2×C4×C11C23×C411yescharacteristic
271C2×C4×C11C2×#4111yescharacteristic
272C2×C4×C11C2×#4111yescharacteristic
273C2×C4×C11C2×#4111yescharacteristic
274C2×C4×C11H(5,𝔽2)11yescharacteristic
275C2×C4×C11H(5,𝔽2)11yescharacteristic
276C2×Dic11—21no—
277C2×Dic11—21no—
278C2×Dic11—21no—
279C2×Dic11—21no—
280C2×Dic11—21no—
281C2×Dic11—21no—
282C2×Dic11—21no—
283C2×Dic11—21no—
284C2×Dic11—21no—
285C2×Dic11—21no—
286C2×Dic11—21no—
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—
297C2×Dic11—41no—
298C2×Dic11—41no—
299C2×Dic11#13712yes—
300C8×C11—22no—
301C8×C11—22no—
302C11⋊C8—41no—
303C11⋊C8—41no—
304C23×Q8C2×D1111yescharacteristic
305C22×M16C2×D1111yescharacteristic
306C2×C4×Q8—111no—
307C2×C4×Q8—111no—
308C2×#117C2×D1111yescharacteristic
309C2×#107—111no—
310C2×#106—111no—
311#419Dic1118yescomplemented
312C2×#103—111no—
313C2×#103—111no—
314C2×#103—111no—
315C2×#103—111no—
316C2×#103C2×D1111yescharacteristic
317C2×#103C2×D1111yescharacteristic
318C2×#103C2×D1111yescharacteristic
319C2×#103C2×D1111yescharacteristic
320C2×C22⋊C8—111no—
321C2×#97—111no—
322C2×C4×C8—111no—
323#391—111no—
324#391—111no—
325#391—221no—
326#391—221no—
327#389—111no—
328#389—111no—
329#388—221no—
330#388—221no—
331#383—221no—
332#380—111no—
333#380—111no—
334#380—221no—
335C4×C4⋊C4—111no—
336C4×C4⋊C4—111no—
337C4×C4⋊C4—221no—
338C4×C22⋊C4—111no—
339C4×C22⋊C4—221no—
340#340—111no—
341#340—111no—
342#340—111no—
343#340—111no—
344#340—111no—
345#340—111no—
346#336—111no—
347#336—111no—
348C22×C11—22no—
349C22×C11—22no—
350C22×C11—22no—
351C22×C11—41no—
352C22×C11—41no—
353C22×C11—41no—
354C22×C11—41no—
355C22×C11C2×C4×D411yescharacteristic
356C22×C11#54611yescharacteristic
357C22×C11#54611yescharacteristic
358C22×C11C2×#13711yescharacteristic
359C22×C11#57511yescharacteristic
360C22×C11#57711yescharacteristic
361C22×C11#57811yescharacteristic
362C4×C11—22no—
363C4×C11—24no—
364C4×C11—42no—
365C4×C11—42no—
366C4×C11—42no—
367C4×C11C2×#11711yescharacteristic
368C4×C11#51811yescharacteristic
369C4×C11#55111yescharacteristic
370C4×C11#55111yescharacteristic
371Dic11—22no—
372Dic11—41no—
373Dic11—41no—
374Dic11—41no—
375Dic11—81no—
376Dic11—81no—
377Dic11—81no—
378Dic11—81no—
379C22×Q8—21no—
380C22×Q8—22no—
381C22×Q8—22no—
382C22×Q8—22no—
383C22×Q8—41no—
384C22×Q8—41no—
385C22×Q8C2×Dic1114yes—
386C22×Q8C22×D1111yescharacteristic
387C22×Q8C22×D1111yescharacteristic
388C23×C4—21no—
389C23×C4C22×D1111yescharacteristic
390C2×M16—41no—
391C2×M16—41no—
392C2×M16C2×Dic1114yes—
393C22×C8—111no—
394C22×C8—111no—
395C22×C8C22×D1111yescharacteristic
396C22×C8C22×D1111yescharacteristic
397C4×Q8—222no—
398C4×Q8—222no—
399C4×Q8—441no—
400C4×Q8—441no—
401#117—22no—
402#117C2×Dic1114yes—
403C2×C4⋊C4—111no—
404C2×C4⋊C4—111no—
405C2×C4⋊C4—111no—
406C2×C4⋊C4—111no—
407C2×C4⋊C4—221no—
408C2×C4⋊C4—221no—
409C2×C4⋊C4—221no—
410C2×C4⋊C4—221no—
411C2×C4⋊C4C22×D1111yescharacteristic
412C2×C4⋊C4C22×D1111yescharacteristic
413C2×C22⋊C4—21no—
414C2×C22⋊C4—111no—
415C2×C22⋊C4—111no—
416C2×C22⋊C4—221no—
417C2×C22⋊C4—221no—
418C2×C42—21no—
419C2×C42—111no—
420C2×C42—111no—
421C2×C42—221no—
422C2×C42—221no—
423C2×C42—221no—
424C2×C42—221no—
425#107—441no—
426#106—441no—
427#103—222no—
428#103—222no—
429#103—441no—
430#103—441no—
431#103C2×Dic1114yes—
432#103C2×Dic1114yes—
433#103C2×Dic1114yes—
434#103C2×Dic1114yes—
435C22⋊C8—222no—
436#97—441no—
437C4×C8—441no—
438#95—111no—
439#95—111no—
440#95—221no—
441#95—221no—
442#95—221no—
443#95—221no—
444#95—221no—
445#95—221no—
446#95—221no—
447#95—221no—
448#95—221no—
449#95—221no—
450C2×C11—42no—
451C2×C11#234211yescharacteristic
452C2×C11C4×#13711yescharacteristic
453C2×C11#294711yescharacteristic
454C2×C11#331311yescharacteristic
455C2×C11#332011yescharacteristic
456C2×C11#332611yescharacteristic
457C2×C11#332811yescharacteristic
458C24D4×D1111yescharacteristic
459C2×Q8—24no—
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8—21no—
463C2×Q8—21no—
464C2×Q8—28no—
465C2×Q8—21no—
466C2×Q8—21no—
467C2×Q8—21no—
468C2×Q8—21no—
469C2×Q8—42no—
470C2×Q8—42no—
471C2×Q8—44no—
472C2×Q8—44no—
473C2×Q8—44no—
474C2×Q8#433912yes—
475C2×Q8#433912yes—
476C2×Q8C22×Dic1112yes—
477C2×Q8C22×Dic1112yes—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—24no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—42no—
488C22×C4—42no—
489C22×C4—111no—
490C22×C4—111no—
491C22×C4—111no—
492C22×C4—111no—
493C22×C4—221no—
494C22×C4—221no—
495C22×C4—221no—
496C22×C4—221no—
497C22×C4D4×D1111yescharacteristic
498C22×C4#434112yes—
499C22×C4C22×Dic1112yes—
500C22×C4C23×D1111yescharacteristic
501M16—44no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—221no—
507C2×C8—221no—
508C2×C8—221no—
509C2×C8—221no—
510C2×C8—221no—
511C2×C8—221no—
512C2×C8C22×Dic1112yes—
513C2×C8C22×Dic1112yes—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—221no—
517C4⋊C4—221no—
518C4⋊C4—221no—
519C4⋊C4—221no—
520C4⋊C4—221no—
521C4⋊C4—221no—
522C4⋊C4—221no—
523C4⋊C4—221no—
524C4⋊C4—442no—
525C4⋊C4—442no—
526C4⋊C4—442no—
527C4⋊C4—442no—
528C4⋊C4C22×Dic1112yes—
529C4⋊C4C22×Dic1112yes—
530C22⋊C4—24no—
531C22⋊C4—222no—
532C22⋊C4—441no—
533C22⋊C4—442no—
534C22⋊C4—881no—
535C42—24no—
536C42—221no—
537C42—221no—
538C42—221no—
539C42—221no—
540C42—442no—
541C42—442no—
542C42—881no—
543C42—881no—
544C11#2258111yescharacteristic, complemented, Sylow
545C23—21no—
546C23—21no—
547C23—21no—
548C23—21no—
549C23—21no—
550C23—21no—
551C23D4×Dic1112yes—
552C23C2×D4×D1111yescharacteristic
553Q8—22no—
554Q8—22no—
555Q8—22no—
556Q8—22no—
557Q8—22no—
558Q8—48no—
559Q8—41no—
560Q8—41no—
561Q8#6697914yes—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—48no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—112no—
582C2×C4—221no—
583C2×C4—221no—
584C2×C4—221no—
585C2×C4—221no—
586C2×C4—221no—
587C2×C4—221no—
588C2×C4—221no—
589C2×C4—221no—
590C2×C4—221no—
591C2×C4—221no—
592C2×C4—221no—
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×C4D4×Dic1112yes—
606C2×C4C2×#433911yescharacteristic
607C2×C4C2×#433911yescharacteristic
608C2×C4C2×#434111yescharacteristic
609C2×C4#6703711yescharacteristic
610C2×C4#6703711yescharacteristic
611C2×C4C23×Dic1111yescharacteristic
612C8—22no—
613C8—22no—
614C8—441no—
615C8—441no—
616C22—22no—
617C22—22no—
618C22—22no—
619C22—41no—
620C22—41no—
621C22—41no—
622C22—41no—
623C22#1062302111yescharacteristic
624C22#1062302111yescharacteristic
625C22D11×#13711yescharacteristic
626C22#1062330811yescharacteristic
627C22#1062330911yescharacteristic
628C22#1062331011yescharacteristic
629C22C2×D4×Dic1111yescharacteristic
630C4—22no—
631C4—24no—
632C4—42no—
633C4—42no—
634C4—42no—
635C4—222no—
636C4—441no—
637C4—441no—
638C4—441no—
639C4—881no—
640C4—881no—
641C4—881no—
642C4—881no—
643C4#1062302611yescharacteristic
644C4#1062302611yescharacteristic
645C4C2×#6697911yescharacteristic
646C4#1062332911yescharacteristic
647C2—42no—
648C2#1307146511yescharacteristic
649C2#137×Dic1111yescharacteristic
650C2#1307746011yescharacteristic
651C2#1308068311yescharacteristic
652C2#1308078811yescharacteristic
653C2#1308086511yescharacteristic
654C2#1308089511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#419C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenterC2×#419D11
hypocenterC11#22581
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#419

Complements

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

NH ≅ G/Ntype
3. #13069308C2semidirect
4. #13069294C2semidirect
5. #13069259C2semidirect
6. #13069252C2semidirect
7. #13068886C2semidirect
8. #13068872C2semidirect
12. #13068448C2semidirect
13. #103×Dic11C2semidirect
21. C11×#419C4semidirect
311. #419Dic11semidirect
544. C11#22581semidirect

Maximal subgroups

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

subgroupindex
#130715092
Q8×C22⋊Dic112
#130693082
#130692942
#130692592
#130692522
#130688862
#130688722
#130687112
#130686492
#130685512
#130684482
#103×Dic112
#130683972
C2×C11×#4192
#2258111