Finite Group Databasebeta

← #14802043

Subgroups — #14802043

Order 2816.

842 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622418C211yesmaximal, characteristic
2C2×#10622426C211yesmaximal, characteristic
3#13073098C211yesmaximal, characteristic
4#13071617C211yesmaximal, characteristic
5#13070098C211yesmaximal, characteristic, complemented
6#13070037C211yesmaximal, characteristic, complemented
7#13069996C211yesmaximal, characteristic, complemented
8#13069937C211yesmaximal, characteristic, complemented
9#13069383C211yesmaximal, characteristic, complemented
10#13069248C211yesmaximal, characteristic, complemented
11#13068957C211yesmaximal, characteristic, complemented
12#13068922C211yesmaximal, characteristic
13#13068792C211yesmaximal, characteristic
14D11×#340C211yesmaximal, characteristic
15C11×#1805C211yesmaximal, characteristic, complemented
16C2×C4×Q8×C11C2211yescharacteristic
17C2×#66999C2211yescharacteristic
18C22×#4326C2211yescharacteristic
19C22×C8×D11C2211yescharacteristic
20C2×#66950C2211yescharacteristic
21C2×C4⋊C4×D11C2211yescharacteristic
22C2×C4⋊C4×D11C2211yescharacteristic
23C2×C11×C4⋊C8C2211yescharacteristic
24C2×C11×#103C2211yescharacteristic
25C2×C11×#103C2211yescharacteristic
26C11×#382C2211yescharacteristic
27#10622843C2211yescharacteristic
28C2×#66899C2211yescharacteristic
29C2×(C2×D11)⋊C8C2211yescharacteristic
30C2×#66881C2211yescharacteristic
31C2×#66880C2211yescharacteristic
32C2×#66880C2211yescharacteristic
33C2×Dic11⋊C8C2211yescharacteristic
34#10622602—21no—
35#10622590C2211yescharacteristic
36C4⋊C4×Dic11C2211yescharacteristic
37#10622587C2211yescharacteristic
38#10622585—21no—
39C2×#66874C2211yescharacteristic
40C2×#66872C2211yescharacteristic
41C2×#66871C2211yescharacteristic
42C4×(C2×D11)⋊C4—21no—
43C4×(C2×D11)⋊C4C2211yescharacteristic
44#10622546—21no—
45#10622542C2211yescharacteristic
46#10622541C2211yescharacteristic
47#10622426—24no—
48#10622418—24no—
49#10622277—21no—
50#10622277—21no—
51#10622273—21no—
52#10622273—21no—
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C22×C4×D11—21no—
63C22×C4×D11—21no—
64C22×C4×D11C2311yescharacteristic
65C22×Dic22C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C4×Q8×C11—22no—
69C4×Q8×C11—41no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C42×C11—21no—
75C2×C42×C11C2311yescharacteristic
76#66999—22no—
77#66999D414yes—
78C2×#4326—22no—
79C2×#4326—22no—
80C2×#4326—41no—
81C2×(C2×D11)⋊C4—21no—
82C2×(C2×D11)⋊C4—21no—
83C2×(C2×D11)⋊C4D411yescharacteristic
84C2×(C2×D11)⋊C4D411yescharacteristic
85C2×C4⋊Dic11—21no—
86C2×C4⋊Dic11C2311yescharacteristic
87C2×C4⋊Dic11C2311yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89C2×Dic11⋊C4—21no—
90C2×Dic11⋊C4—21no—
91C2×Dic11⋊C4—21no—
92C2×Dic11⋊C4—21no—
93C2×C4×Dic11—21no—
94C2×C4×Dic11C2311yescharacteristic
95C22×C11⋊C8C2311yescharacteristic
96C22×C11⋊C8C2311yescharacteristic
97C2×C8×D11—22no—
98C2×C8×D11—22no—
99C2×C8×D11—41no—
100#66950—22no—
101#66950—22no—
102C4⋊C4×D11—22no—
103C4⋊C4×D11—22no—
104C4⋊C4×D11—22no—
105C4⋊C4×D11—41no—
106C11×C4⋊C8—41no—
107C11×#103—22no—
108C11×#103—22no—
109C11×#95—21no—
110C11×#95—21no—
111#66899—22no—
112C11⋊#95—21no—
113C11⋊#95—21no—
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⋊#95D411yescharacteristic
123C11⋊#95D411yescharacteristic
124(C2×D11)⋊C8—22no—
125#66881—22no—
126#66880—22no—
127#66880—41no—
128Dic11⋊C8—22no—
129#66874—22no—
130#66872—22no—
131#66871—22no—
132#25208—111nomaximal, Sylow
133C23×D11C2×D411yescharacteristic
134C2×Q8×C11—21no—
135C2×Q8×C11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11—21no—
138C2×Q8×C11—21no—
139C2×Q8×C11C2×D412yes—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2411yescharacteristic
147C22×Dic11—21no—
148C22×Dic11—21no—
149C22×Dic11—21no—
150C22×Dic11—21no—
151C22×Dic11C2×D411yescharacteristic
152C22×Dic11C2×D411yescharacteristic
153C22×Dic11C2×D411yescharacteristic
154C2×C4×D11—21no—
155C2×C4×D11—21no—
156C2×C4×D11—21no—
157C2×C4×D11—21no—
158C2×C4×D11—42no—
159C2×C4×D11—42no—
160C2×C4×D11—42no—
161C2×C4×D11—42no—
162C2×C4×D11—42no—
163C2×C4×D11—81no—
164C2×C4×D11C2×D412yes—
165C2×C4×D11#4112yes—
166C2×Dic22—21no—
167C2×Dic22—21no—
168C2×Dic22—21no—
169C2×Dic22—21no—
170C2×Dic22—21no—
171C2×Dic22—21no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—42no—
184C11×C4⋊C4#4112yes—
185C42×C11—21no—
186C42×C11—21no—
187C42×C11—42no—
188#4326—44no—
189(C2×D11)⋊C4—24no—
190(C2×D11)⋊C4—22no—
191(C2×D11)⋊C4—22no—
192(C2×D11)⋊C4—42no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—42no—
199C4⋊Dic11C2×D412yes—
200Dic11⋊C4—24no—
201Dic11⋊C4—42no—
202Dic11⋊C4—42no—
203Dic11⋊C4—81no—
204C4×Dic11—21no—
205C4×Dic11—21no—
206C4×Dic11—81no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8#4112yes—
213C8×D11—44no—
214C2×#483—111no—
215C2×#467—111no—
216#2503—111no—
217#2360—111no—
218#2085—111no—
219#2074—111no—
220#2066—111no—
221#2056—111no—
222#1949—111no—
223#1927—111no—
224#1878—111no—
225#1872—111no—
226#1850—111no—
227#1805D1111yescharacteristic, complemented
228C2×#340—111no—
229C23×C11C22×D411yescharacteristic
230C22×D11—21no—
231C22×D11—21no—
232C22×D11—21no—
233C22×D11—21no—
234C22×D11#12112yes—
235C22×D11#13512yes—
236C22×D11#13712yes—
237Q8×C11—22no—
238Q8×C11—22no—
239Q8×C11—41no—
240Q8×C11—41no—
241C2×C4×C11—22no—
242C2×C4×C11—22no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
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×C11—41no—
259C2×C4×C11C22×D411yescharacteristic
260C2×C4×C11C2×#4111yescharacteristic
261C2×C4×C11C2×#4111yescharacteristic
262C2×C4×C11C2×#4111yescharacteristic
263C2×C4×C11H(5,𝔽2)11yescharacteristic
264C2×C4×C112−1+411yescharacteristic
265C2×Dic11—21no—
266C2×Dic11—21no—
267C2×Dic11—22no—
268C2×Dic11—21no—
269C2×Dic11—21no—
270C2×Dic11—21no—
271C2×Dic11—21no—
272C2×Dic11—21no—
273C2×Dic11—21no—
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#12112yes—
286C4×D11—22no—
287C4×D11—22no—
288C4×D11—22no—
289C4×D11—22no—
290C4×D11—84no—
291C4×D11—84no—
292Dic22—41no—
293Dic22—41no—
294Dic22—41no—
295Dic22—41no—
296C8×C11—41no—
297C8×C11—41no—
298C11⋊C8—22no—
299C11⋊C8—41no—
300C22×Q16—111no—
301C23×C8—111no—
302C2×C22⋊Q8—111no—
303C2×C22⋊Q8—111no—
304C2×C4×Q8C2×D1111yescharacteristic
305C22×C4⋊C4—111no—
306C22×C4⋊C4—111no—
307#483—224no—
308#467—224no—
309C2×#107—111no—
310C2×#106—111no—
311C2×#106—111no—
312C2×C4⋊C8—111no—
313C2×C4⋊C8C2×D1111yescharacteristic
314C2×#103—111no—
315C2×#103—111no—
316C2×#103—111no—
317C2×#103—111no—
318C2×#103C2×D1111yescharacteristic
319C2×#103C2×D1111yescharacteristic
320C2×C22⋊C8—111no—
321#400—221no—
322#400—221no—
323#391—111no—
324#391—111no—
325#391—111no—
326#389—111no—
327#389—221no—
328#387—221no—
329#385—221no—
330#382—111no—
331#382C2×D1111yescharacteristic
332#381—221no—
333#381—221no—
334C4×C4⋊C4—111no—
335C4×C22⋊C4—111no—
336C4×C22⋊C4—221no—
337#340—111no—
338#340—111no—
339#340—111no—
340#340—111no—
341#340C2×D1111yescharacteristic
342#340C2×D1111yescharacteristic
343#336—111no—
344#336—111no—
345C22×C11C2×#12111yescharacteristic
346C22×C11#54611yescharacteristic
347C22×C11#54711yescharacteristic
348C22×C11C2×#13511yescharacteristic
349C22×C11C2×#13711yescharacteristic
350C22×C11#57711yescharacteristic
351C22×C11#57811yescharacteristic
352C2×D11—22no—
353C2×D11—22no—
354C2×D11—22no—
355C2×D11—22no—
356C2×D11—22no—
357C2×D11—22no—
358C2×D11#46414yes—
359C4×C11—42no—
360C4×C11—41no—
361C4×C11—42no—
362C4×C11—41no—
363C4×C11—81no—
364C4×C11—81no—
365C4×C11#52911yescharacteristic
366C4×C11#53911yescharacteristic
367C4×C11#54611yescharacteristic
368C4×C11#54711yescharacteristic
369Dic11—22no—
370Dic11—41no—
371Dic11—41no—
372Dic11—42no—
373Dic11—81no—
374Dic11—81no—
375Dic11—81no—
376C22×Q8—111no—
377C22×Q8C22×D1111yescharacteristic
378C23×C4—111no—
379C23×C4—221no—
380C23×C4—221no—
381C2×Q16—222no—
382C2×Q16—222no—
383C2×Q16—441no—
384C22×C8—111no—
385C22×C8—111no—
386C22×C8—222no—
387C22×C8—222no—
388C22×C8—441no—
389C22×C8C22×D1111yescharacteristic
390C22×C8C22×D1111yescharacteristic
391C22⋊Q8—114no—
392C22⋊Q8—222no—
393C22⋊Q8—222no—
394C22⋊Q8—222no—
395C4×Q8—22no—
396C4×Q8—41no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—111no—
399C2×C4⋊C4—111no—
400C2×C4⋊C4—111no—
401C2×C4⋊C4—222no—
402C2×C4⋊C4—222no—
403C2×C4⋊C4—221no—
404C2×C4⋊C4—222no—
405C2×C4⋊C4—221no—
406C2×C4⋊C4—221no—
407C2×C4⋊C4—221no—
408C2×C4⋊C4—221no—
409C2×C4⋊C4—441no—
410C2×C4⋊C4C22×D1111yescharacteristic
411C2×C4⋊C4C22×D1111yescharacteristic
412C2×C4⋊C4C22×D1111yescharacteristic
413C2×C22⋊C4—111no—
414C2×C22⋊C4—111no—
415C2×C22⋊C4—221no—
416C2×C22⋊C4—221no—
417C2×C42—21no—
418C2×C42—111no—
419C2×C42—221no—
420C2×C42C22×D1111yescharacteristic
421#107—222no—
422#106—222no—
423#106—222no—
424C4⋊C8—41no—
425C4⋊C8—222no—
426#103—22no—
427#103—22no—
428#103—222no—
429#103—222no—
430#103—222no—
431#103—441no—
432C22⋊C8—222no—
433#95—21no—
434#95—21no—
435#95—111no—
436#95—111no—
437#95—221no—
438#95—221no—
439#95—221no—
440#95—221no—
441#95—221no—
442#95—221no—
443#95—221no—
444#95—221no—
445#95—221no—
446#95—221no—
447C2×C11#242511yescharacteristic
448C2×C11C2×#46411yescharacteristic
449C2×C11#304611yescharacteristic
450C2×C11#329611yescharacteristic
451C2×C11#331211yescharacteristic
452C2×C11#333611yescharacteristic
453C2×C11#334411yescharacteristic
454D11—24no—
455C24—111no—
456C2×Q8—21no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8—21no—
461C2×Q8—221no—
462C2×Q8—221no—
463C2×Q8—221no—
464C2×Q8—221no—
465C2×Q8—221no—
466C2×Q8—221no—
467C2×Q8D4×D1112yes—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—111no—
473C22×C4—112no—
474C22×C4—112no—
475C22×C4—111no—
476C22×C4—111no—
477C22×C4—221no—
478C22×C4—221no—
479C22×C4—221no—
480C22×C4—221no—
481C22×C4—221no—
482C22×C4—221no—
483C22×C4—221no—
484C22×C4—221no—
485C22×C4—442no—
486C22×C4—442no—
487C22×C4—442no—
488C22×C4—442no—
489C22×C4—442no—
490C22×C4—881no—
491C22×C4D4×D1111yescharacteristic
492C22×C4D4×D1111yescharacteristic
493C22×C4C23×D1111yescharacteristic
494Q16—444no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—112no—
502C2×C8—221no—
503C2×C8—221no—
504C2×C8—221no—
505C2×C8—221no—
506C2×C8—221no—
507C2×C8—444no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—42no—
514C4⋊C4—112no—
515C4⋊C4—224no—
516C4⋊C4—221no—
517C4⋊C4—221no—
518C4⋊C4—221no—
519C4⋊C4—221no—
520C4⋊C4—221no—
521C4⋊C4—442no—
522C4⋊C4—442no—
523C4⋊C4—442no—
524C4⋊C4—881no—
525C4⋊C4#433912yes—
526C22⋊C4—222no—
527C22⋊C4—222no—
528C22⋊C4—224no—
529C22⋊C4—442no—
530C42—21no—
531C42—21no—
532C42—42no—
533C42—221no—
534C42—221no—
535C42—881no—
536C11#2520811yescharacteristic, complemented, Sylow
537C23—112no—
538C23—112no—
539C23—112no—
540C23—221no—
541C23—221no—
542C23—221no—
543C23—221no—
544C23C2×D4×D1111yescharacteristic
545Q8—22no—
546Q8—22no—
547Q8—41no—
548Q8—41no—
549Q8—441no—
550Q8—441no—
551Q8—441no—
552Q8—441no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—22no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—22no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—112no—
572C2×C4—221no—
573C2×C4—221no—
574C2×C4—222no—
575C2×C4—222no—
576C2×C4—222no—
577C2×C4—222no—
578C2×C4—221no—
579C2×C4—221no—
580C2×C4—221no—
581C2×C4—221no—
582C2×C4—222no—
583C2×C4—221no—
584C2×C4—221no—
585C2×C4—441no—
586C2×C4—441no—
587C2×C4—441no—
588C2×C4—441no—
589C2×C4—441no—
590C2×C4—441no—
591C2×C4—441no—
592C2×C4—441no—
593C2×C4—441no—
594C2×C4—441no—
595C2×C4—441no—
596C2×C4—884no—
597C2×C4—884no—
598C2×C4C2×#433911yescharacteristic
599C2×C4C2×D4×D1111yescharacteristic
600C2×C4#6703711yescharacteristic
601C2×C4#6704011yescharacteristic
602C2×C4#41×D1111yescharacteristic
603C2×C4#41×D1111yescharacteristic
604C8—41no—
605C8—41no—
606C8—222no—
607C8—441no—
608C22—114no—
609C22—222no—
610C22—222no—
611C22—222no—
612C22—222no—
613C22—222no—
614C22—222no—
615C22#1062302111yescharacteristic
616C22D11×#12111yescharacteristic
617C22#1062316211yescharacteristic
618C22D11×#13511yescharacteristic
619C22#1062330111yescharacteristic
620C22D11×#13711yescharacteristic
621C22#1062331011yescharacteristic
622C4—42no—
623C4—41no—
624C4—41no—
625C4—42no—
626C4—81no—
627C4—81no—
628C4—222no—
629C4—441no—
630C4—442no—
631C4—441no—
632C4—881no—
633C4—881no—
634C4—881no—
635C4#1062303811yescharacteristic
636C4#1062305911yescharacteristic
637C4#1062314111yescharacteristic
638C4#1062316911yescharacteristic
639C2—224no—
640C2#1307216411yescharacteristic
641C2D11×#46411yescharacteristic
642C2#1307816911yescharacteristic
643C2#1308045211yescharacteristic
644C2#1308066811yescharacteristic
645C2#1308098111yescharacteristic
646C2#1308107811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1805C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
hypercenter#1805D11
hypocenterC11#25208
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1805

Complements

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

NH ≅ G/Ntype
5. #13070098C2semidirect
6. #13070037C2semidirect
7. #13069996C2semidirect
8. #13069937C2semidirect
9. #13069383C2semidirect
10. #13069248C2semidirect
11. #13068957C2semidirect
15. C11×#1805C2semidirect
227. #1805D11semidirect
536. C11#25208semidirect

Maximal subgroups

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

subgroupindex
C2×#106224182
C2×#106224262
#130730982
#130716172
#130700982
#130700372
#130699962
#130699372
#130693832
#130692482
#130689572
#130689222
#130687922
D11×#3402
C11×#18052
#2520811