Finite Group Databasebeta

← #14760199

Subgroups — #14760199

Order 2816.

932 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622795C211yesmaximal, characteristic
2C2×#10622797C211yesmaximal, characteristic
3C2×#10622403C211yesmaximal, characteristic
4#13071334C211yesmaximal, characteristic
5#13070981C211yesmaximal, characteristic
6#13069537C211yesmaximal, characteristic
7#13069383C211yesmaximal, characteristic
8#13069254C211yesmaximal, characteristic
9#13069251C211yesmaximal, characteristic
10#13068957C211yesmaximal, characteristic
11#13068629C211yesmaximal, characteristic
12#13068472C211yesmaximal, characteristic
13#13068445C211yesmaximal, characteristic
14#103×Dic11C211yesmaximal, characteristic
15C11×#1878C211yesmaximal, characteristic
16C22×C11×Q16C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×Q8×Dic11C2211yescharacteristic
19C2×Q8×Dic11C2211yescharacteristic
20C2×Q8×Dic11C2211yescharacteristic
21C2×#66997C2211yescharacteristic
22C22×#4326C2211yescharacteristic
23C2×#66940C2211yescharacteristic
24C2×C11×#103C2211yescharacteristic
25C2×C11×#103C2211yescharacteristic
26C11×#391C2211yescharacteristic
27C2×#66899C2211yescharacteristic
28C2×#66899C2211yescharacteristic
29C2×#66899C2211yescharacteristic
30#10622797—24no—
31#10622795C418yescomplemented
32C2×#66881C2211yescharacteristic
33C2×#66880C2211yescharacteristic
34C2×#66880C2211yescharacteristic
35C2×#66879C2211yescharacteristic
36C2×Dic11⋊C8C2211yescharacteristic
37C2×Dic11⋊C8C2211yescharacteristic
38C2×C8×Dic11C2211yescharacteristic
39#10622590C2211yescharacteristic
40C4⋊C4×Dic11—21no—
41C4⋊C4×Dic11—21no—
42C4⋊C4×Dic11C2211yescharacteristic
43C4⋊C4×Dic11C2211yescharacteristic
44C2×#66874C2211yescharacteristic
45C2×#66871C2211yescharacteristic
46C4×C4⋊Dic11—21no—
47C4×C4⋊Dic11C2211yescharacteristic
48#10622545—21no—
49#10622545C2211yescharacteristic
50#10622542C2211yescharacteristic
51#10622403—24no—
52#10622268—21no—
53#10622268—21no—
54#10622265—21no—
55#10622265—21no—
56C11×#340C2211yescharacteristic
57C11×#336C2211yescharacteristic
58#10622189C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622162C2211yescharacteristic
62C22×Q8×C11C2311yescharacteristic
63C22×Q8×C11C2311yescharacteristic
64C22×Dic22C2311yescharacteristic
65C2×C11×Q16—22no—
66C2×C11×Q16—22no—
67C2×C11×Q16C2×C414yes—
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C4×Q8×C11—22no—
71C4×Q8×C11—22no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C42×C11—21no—
76C2×C42×C11C2311yescharacteristic
77Q8×Dic11—22no—
78Q8×Dic11—22no—
79Q8×Dic11—22no—
80Q8×Dic11—22no—
81Q8×Dic11C2×C414yes—
82Q8×Dic11D414yes—
83#66997—22no—
84#66997C2×C414yes—
85C2×#4326—22no—
86C2×#4326—22no—
87C2×#4326C2×C414yes—
88C2×C4⋊Dic11—21no—
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11—21no—
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×Dic11⋊C4—21no—
95C2×Dic11⋊C4—21no—
96C2×Dic11⋊C4—21no—
97C2×C4×Dic11—21no—
98C2×C4×Dic11—21no—
99C2×C4×Dic11—21no—
100C2×C4×Dic11—21no—
101C2×C4×Dic11—21no—
102C2×C4×Dic11—21no—
103C2×C4×Dic11—21no—
104C2×C4×Dic11C2311yescharacteristic
105C2×C4×Dic11C2311yescharacteristic
106C22×C11⋊C8C2311yescharacteristic
107C22×C11⋊C8C2311yescharacteristic
108#66940—22no—
109#66940—22no—
110C11×#103—22no—
111C11×#103—22no—
112C11×#95—21no—
113C11×#95—21no—
114#66899—22no—
115#66899—22no—
116#66899C2×C414yes—
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
126C11⋊#95D411yescharacteristic
127C11⋊#95D411yescharacteristic
128#66881—22no—
129#66880—22no—
130#66880C2×C414yes—
131#66879—22no—
132Dic11⋊C8—22no—
133Dic11⋊C8C2×C414yes—
134C8×Dic11—22no—
135#66874—22no—
136#66871—22no—
137#21516—111nomaximal, Sylow
138C2×Q8×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×C11C22×C412yes—
147C2×Q8×C11C22×C412yes—
148C2×Q8×C11C2×D412yes—
149C2×Q8×C11#4112yes—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2411yescharacteristic
157C22×Dic11—21no—
158C22×Dic11—21no—
159C22×Dic11—21no—
160C22×Dic11—21no—
161C22×Dic11C2×D411yescharacteristic
162C22×Dic11C2×D411yescharacteristic
163C22×Dic11C2×D411yescharacteristic
164C22×Dic11C2×D411yescharacteristic
165C2×Dic22—21no—
166C2×Dic22—21no—
167C2×Dic22—21no—
168C2×Dic22—21no—
169C2×Dic22—21no—
170C2×Dic22C22×C412yes—
171C11×Q16—28no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11C22×C412yes—
178C11×C4⋊C4—24no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4#4112yes—
183C42×C11—24no—
184C42×C11—21no—
185C42×C11—21no—
186#4326—28no—
187C4⋊Dic11—24no—
188C4⋊Dic11—24no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—42no—
194C4⋊Dic11C22×C412yes—
195C4⋊Dic11C2×D412yes—
196Dic11⋊C4—24no—
197Dic11⋊C4—24no—
198Dic11⋊C4—42no—
199C4×Dic11—24no—
200C4×Dic11—24no—
201C4×Dic11—42no—
202C4×Dic11—42no—
203C4×Dic11—81no—
204C4×Dic11—81no—
205C4×Dic11—81no—
206C4×Dic11C22×C412yes—
207C4×Dic11C2×D412yes—
208C4×Dic11#4112yes—
209C4×Dic11#4112yes—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8C22×C412yes—
216C2×#462—111no—
217C2×#441—111no—
218C2×C4×Q16—111no—
219#2327—111no—
220#2276—111no—
221#1981—111no—
222#1949—111no—
223#1928—111no—
224#1927—111no—
225#1878—111no—
226#1878D1111yescharacteristic
227#1805—111no—
228#1768—111no—
229#1763—111no—
230C4×#103—111no—
231C23×C11C22×D411yescharacteristic
232Q8×C11—22no—
233Q8×C11—22no—
234Q8×C11—22no—
235Q8×C11—22no—
236Q8×C11—22no—
237Q8×C11—41no—
238Q8×C11—41no—
239Q8×C11C4×D414yes—
240C2×C4×C11—22no—
241C2×C4×C11—22no—
242C2×C4×C11—22no—
243C2×C4×C11—22no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—22no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11C23×C411yescharacteristic
259C2×C4×C11C22×D411yescharacteristic
260C2×C4×C11C2×#4111yescharacteristic
261C2×C4×C11C2×#4111yescharacteristic
262C2×C4×C11C2×#4111yescharacteristic
263C2×C4×C11C2×#4111yescharacteristic
264C2×Dic11—21no—
265C2×Dic11—21no—
266C2×Dic11—21no—
267C2×Dic11—21no—
268C2×Dic11—21no—
269C2×Dic11—21no—
270C2×Dic11—21no—
271C2×Dic11—21no—
272C2×Dic11—22no—
273C2×Dic11—22no—
274C2×Dic11—22no—
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×Dic11C4×D412yes—
285C2×Dic11C4×D412yes—
286C2×Dic11#12112yes—
287C2×Dic11#12112yes—
288Dic22—22no—
289Dic22—22no—
290Dic22—41no—
291Dic22—41no—
292C8×C11—22no—
293C8×C11—41no—
294C11⋊C8—22no—
295C11⋊C8—41no—
296C22×Q16—111no—
297C22×Q16C2×D1111yescharacteristic
298C2×C4⋊Q8—111no—
299C2×C4×Q8—111no—
300C2×C4×Q8—111no—
301C2×C4×Q8—111no—
302C2×C4×Q8—111no—
303C2×C4×Q8C2×D1111yescharacteristic
304#462—118no—
305#441—224no—
306C4×Q16—224no—
307C2×#107—111no—
308C2×#106—111no—
309C2×C4⋊C8—111no—
310C2×C4⋊C8—111no—
311C2×#103—111no—
312C2×#103—111no—
313C2×#103—111no—
314C2×#103—111no—
315C2×#103—111no—
316C2×#103—111no—
317C2×#103C2×D1111yescharacteristic
318C2×#103C2×D1111yescharacteristic
319C2×#97—111no—
320C2×C4×C8—111no—
321#391—111no—
322#391C2×D1111yescharacteristic
323#387—221no—
324#387—221no—
325#387—221no—
326#387—221no—
327#382—111no—
328C4×C4⋊C4—111no—
329C4×C4⋊C4—111no—
330C4×C4⋊C4—111no—
331C4×C4⋊C4—221no—
332C4×C4⋊C4—221no—
333C4×C4⋊C4—221no—
334#376—111no—
335#376—221no—
336#340—111no—
337#340—111no—
338#340—111no—
339#340C2×D1111yescharacteristic
340#336—111no—
341#336C2×D1111yescharacteristic
342C22×C11C2×C4×D411yescharacteristic
343C22×C11C2×#12111yescharacteristic
344C22×C11#52511yescharacteristic
345C22×C11#57711yescharacteristic
346C22×C11#57811yescharacteristic
347C22×C11#57811yescharacteristic
348C22×C11#57811yescharacteristic
349C4×C11—24no—
350C4×C11—41no—
351C4×C11—42no—
352C4×C11—41no—
353C4×C11—42no—
354C4×C11—81no—
355C4×C11C2×C4×D411yescharacteristic
356C4×C11C4×#4111yescharacteristic
357C4×C11#52911yescharacteristic
358C4×C11#53211yescharacteristic
359Dic11—22no—
360Dic11—22no—
361Dic11—22no—
362Dic11—22no—
363Dic11—42no—
364Dic11—42no—
365Dic11—42no—
366Dic11—81no—
367C22×Q8—111no—
368C22×Q8C22×D1111yescharacteristic
369C22×Q8C22×D1111yescharacteristic
370C2×Q16—22no—
371C2×Q16—22no—
372C2×Q16—114no—
373C2×Q16—222no—
374C2×Q16—222no—
375C2×Q16C4×D1114yes—
376C22×C8—111no—
377C22×C8—111no—
378C22×C8C22×D1111yescharacteristic
379C22×C8C22×D1111yescharacteristic
380C4⋊Q8—114no—
381C4⋊Q8—222no—
382C4×Q8—22no—
383C4×Q8—22no—
384C4×Q8—114no—
385C4×Q8—114no—
386C4×Q8—222no—
387C4×Q8—222no—
388C4×Q8—222no—
389C4×Q8—222no—
390C4×Q8—222no—
391C4×Q8—222no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—111no—
394C2×C4⋊C4—111no—
395C2×C4⋊C4—111no—
396C2×C4⋊C4—221no—
397C2×C4⋊C4—221no—
398C2×C4⋊C4—221no—
399C2×C4⋊C4—221no—
400C2×C4⋊C4—221no—
401C2×C4⋊C4—221no—
402C2×C4⋊C4C22×D1111yescharacteristic
403C2×C4⋊C4C22×D1111yescharacteristic
404C2×C42—21no—
405C2×C42—111no—
406C2×C42—111no—
407C2×C42—221no—
408C2×C42—221no—
409C2×C42—221no—
410C2×C42—221no—
411C2×C42—221no—
412C2×C42—221no—
413C2×C42—221no—
414C2×C42C22×D1111yescharacteristic
415#107—222no—
416#106—222no—
417C4⋊C8—114no—
418C4⋊C8—222no—
419#103—22no—
420#103—22no—
421#103—114no—
422#103—114no—
423#103—222no—
424#103—222no—
425#103—222no—
426#103—222no—
427#97—222no—
428C4×C8—222no—
429#95—21no—
430#95—21no—
431#95—111no—
432#95—111no—
433#95—111no—
434#95—111no—
435#95—221no—
436#95—221no—
437#95—221no—
438#95—221no—
439#95—221no—
440#95—221no—
441#95—221no—
442C2×C11C4×#12111yescharacteristic
443C2×C11#294711yescharacteristic
444C2×C11#295011yescharacteristic
445C2×C11#304411yescharacteristic
446C2×C11#304611yescharacteristic
447C2×C11#312011yescharacteristic
448C2×C11#312711yescharacteristic
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8—21no—
452C2×Q8—21no—
453C2×Q8—21no—
454C2×Q8—21no—
455C2×Q8—21no—
456C2×Q8—21no—
457C2×Q8—112no—
458C2×Q8—221no—
459C2×Q8—221no—
460C2×Q8—221no—
461C2×Q8—221no—
462C2×Q8—221no—
463C2×Q8C2×C4×D1112yes—
464C2×Q8C2×C4×D1112yes—
465C2×Q8D4×D1112yes—
466C2×Q8#434112yes—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—111no—
472C22×C4—111no—
473C22×C4—111no—
474C22×C4—111no—
475C22×C4—221no—
476C22×C4—221no—
477C22×C4—221no—
478C22×C4—221no—
479C22×C4D4×D1111yescharacteristic
480C22×C4D4×D1111yescharacteristic
481C22×C4C23×D1111yescharacteristic
482Q16—28no—
483Q16—228no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—112no—
490C2×C8—221no—
491C2×C8—221no—
492C2×C8—221no—
493C2×C8—221no—
494C2×C8—221no—
495C2×C8C2×C4×D1112yes—
496C4⋊C4—24no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—112no—
501C4⋊C4—112no—
502C4⋊C4—224no—
503C4⋊C4—224no—
504C4⋊C4—224no—
505C4⋊C4—224no—
506C4⋊C4—221no—
507C4⋊C4—221no—
508C4⋊C4—221no—
509C4⋊C4—221no—
510C4⋊C4—442no—
511C4⋊C4—442no—
512C4⋊C4#434112yes—
513C42—24no—
514C42—21no—
515C42—21no—
516C42—112no—
517C42—112no—
518C42—112no—
519C42—112no—
520C42—224no—
521C42—224no—
522C42—442no—
523C42—442no—
524C42—881no—
525C42—881no—
526C42—881no—
527C11#2151611yescharacteristic, complemented, Sylow
528C23C2×D4×D1111yescharacteristic
529Q8—22no—
530Q8—22no—
531Q8—22no—
532Q8—22no—
533Q8—22no—
534Q8—41no—
535Q8—41no—
536Q8—222no—
537Q8—222no—
538Q8—441no—
539Q8—441no—
540Q8(C22⋊D11)⋊C414yes—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—22no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—22no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—112no—
560C2×C4—112no—
561C2×C4—112no—
562C2×C4—112no—
563C2×C4—221no—
564C2×C4—221no—
565C2×C4—221no—
566C2×C4—221no—
567C2×C4—221no—
568C2×C4—221no—
569C2×C4—221no—
570C2×C4—221no—
571C2×C4—222no—
572C2×C4—222no—
573C2×C4—222no—
574C2×C4—441no—
575C2×C4—441no—
576C2×C4—441no—
577C2×C4—441no—
578C2×C4—441no—
579C2×C4—441no—
580C2×C4—441no—
581C2×C4—441no—
582C2×C4—441no—
583C2×C4C22×C4×D1111yescharacteristic
584C2×C4C2×D4×D1111yescharacteristic
585C2×C4C2×#434111yescharacteristic
586C2×C4C2×#434111yescharacteristic
587C2×C4#41×D1111yescharacteristic
588C2×C4#41×D1111yescharacteristic
589C8—22no—
590C8—41no—
591C8—222no—
592C8—441no—
593C22C4×D4×D1111yescharacteristic
594C22#1062311711yescharacteristic
595C22D11×#12111yescharacteristic
596C22#1062329711yescharacteristic
597C22#1062330111yescharacteristic
598C22#1062331011yescharacteristic
599C22#1062331011yescharacteristic
600C4—24no—
601C4—42no—
602C4—41no—
603C4—42no—
604C4—41no—
605C4—81no—
606C4—222no—
607C4—222no—
608C4—222no—
609C4—222no—
610C4—442no—
611C4—442no—
612C4—442no—
613C4—881no—
614C4C2×(C22⋊D11)⋊C411yescharacteristic
615C4C4×#434111yescharacteristic
616C4#1062312711yescharacteristic
617C4#1062318011yescharacteristic
618C2#1307112611yescharacteristic
619C2#1307745411yescharacteristic
620C2#1307748111yescharacteristic
621C2#1307814111yescharacteristic
622C2#1307816911yescharacteristic
623C2#1307882311yescharacteristic
624C2#1307891011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1878C2
socle, prime radicalC23×C11C22×D4
cosocleC22×C4×C11C24
hypercenter#1878D11
hypocenterC11#21516
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1878

Complements

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

NH ≅ G/Ntype
31. #10622795C4semidirect
527. C11#21516semidirect

Maximal subgroups

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

subgroupindex
C2×#106227952
C2×#106227972
C2×#106224032
#130713342
#130709812
#130695372
#130693832
#130692542
#130692512
#130689572
#130686292
#130684722
#130684452
#103×Dic112
C11×#18782
#2151611