Finite Group Databasebeta

← #14802039

Subgroups — #14802039

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×#10622475C211yesmaximal, characteristic
2C2×#10622500C211yesmaximal, characteristic
3#13073098C211yesmaximal, characteristic
4#13071620C211yesmaximal, characteristic
5#13070038C211yesmaximal, characteristic, complemented
6#13069994C211yesmaximal, characteristic, complemented
7#13069940C211yesmaximal, characteristic, complemented
8#13069381C211yesmaximal, characteristic, complemented
9#13069249C211yesmaximal, characteristic, complemented
10#13068956C211yesmaximal, characteristic, complemented
11#13068922C211yesmaximal, characteristic
12#13068795C211yesmaximal, characteristic
13#13068628C211yesmaximal, characteristic, complemented
14D11×#340C211yesmaximal, characteristic
15C11×#2085C211yesmaximal, characteristic, complemented
16C22×Dic44C2211yescharacteristic
17C22×C8×D11C2211yescharacteristic
18C2×#66950C2211yescharacteristic
19C2×#66950C2211yescharacteristic
20C2×C4⋊C4×D11C2211yescharacteristic
21C2×C4⋊C4×D11C2211yescharacteristic
22C2×C4×Dic22C2211yescharacteristic
23C2×C11×#107C2211yescharacteristic
24C2×C11×#106C2211yescharacteristic
25C11×#389C2211yescharacteristic
26C11×#382C2211yescharacteristic
27C2×(C2×D11)⋊C8C2211yescharacteristic
28C2×#66880C2211yescharacteristic
29C2×#66880C2211yescharacteristic
30C2×Dic11⋊C8C2211yescharacteristic
31#10622602—21no—
32#10622590C2211yescharacteristic
33C4⋊C4×Dic11C2211yescharacteristic
34#10622587C2211yescharacteristic
35#10622587C2211yescharacteristic
36#10622586—21no—
37C2×#66874C2211yescharacteristic
38C2×#66874C2211yescharacteristic
39C2×#66874C2211yescharacteristic
40C2×#66874C2211yescharacteristic
41C2×#66872C2211yescharacteristic
42C4×(C2×D11)⋊C4C2211yescharacteristic
43#10622542C2211yescharacteristic
44C2×C4⋊(C11⋊C8)C2211yescharacteristic
45#10622500—24no—
46#10622475—24no—
47#10622279—21no—
48#10622277—21no—
49#10622277—21no—
50#10622273—21no—
51#10622273—21no—
52#10622267—21no—
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55C11×#336C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×C4×D11—21no—
62C22×C4×D11—21no—
63C22×C4×D11C2311yescharacteristic
64C22×Dic22C2311yescharacteristic
65C22×Dic22C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C42×C11C2311yescharacteristic
74C2×(C2×D11)⋊C4—21no—
75C2×(C2×D11)⋊C4—21no—
76C2×(C2×D11)⋊C4D411yescharacteristic
77C2×(C2×D11)⋊C4D411yescharacteristic
78C2×C4⋊Dic11—21no—
79C2×C4⋊Dic11—21no—
80C2×C4⋊Dic11C2311yescharacteristic
81C2×C4⋊Dic11C2311yescharacteristic
82C2×Dic11⋊C4—21no—
83C2×Dic11⋊C4—21no—
84C2×Dic11⋊C4—21no—
85C2×C4×Dic11—21no—
86C2×C4×Dic11—21no—
87C2×C4×Dic11C2311yescharacteristic
88C22×C11⋊C8C2311yescharacteristic
89C22×C11⋊C8C2311yescharacteristic
90C2×Dic44—22no—
91C2×Dic44—22no—
92C2×Dic44—41no—
93C2×C8×D11—22no—
94C2×C8×D11—22no—
95C2×C8×D11—41no—
96#66950—22no—
97#66950—22no—
98#66950—22no—
99#66950D414yes—
100C4⋊C4×D11—22no—
101C4⋊C4×D11—22no—
102C4⋊C4×D11—22no—
103C4⋊C4×D11—41no—
104C4×Dic22—22no—
105C4×Dic22—41no—
106C11×#107—22no—
107C11×#106—22no—
108C11×#95—21no—
109C11×#95—21no—
110C11×#95—21no—
111C11⋊#95—21no—
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⋊#95D411yescharacteristic
121C11⋊#95D411yescharacteristic
122(C2×D11)⋊C8—22no—
123#66880—22no—
124#66880—22no—
125Dic11⋊C8—22no—
126#66874—22no—
127#66874—22no—
128#66874—22no—
129#66874—41no—
130#66872—22no—
131C4⋊(C11⋊C8)—41no—
132#25208—111nomaximal, Sylow
133C23×D11C2×D411yescharacteristic
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2411yescharacteristic
141C22×Dic11—21no—
142C22×Dic11—21no—
143C22×Dic11—21no—
144C22×Dic11—21no—
145C22×Dic11C2×D411yescharacteristic
146C22×Dic11C2×D411yescharacteristic
147C22×Dic11C2×D411yescharacteristic
148C2×C4×D11—21no—
149C2×C4×D11—21no—
150C2×C4×D11—21no—
151C2×C4×D11—21no—
152C2×C4×D11—42no—
153C2×C4×D11—42no—
154C2×C4×D11—42no—
155C2×C4×D11—42no—
156C2×C4×D11—42no—
157C2×C4×D11—81no—
158C2×C4×D11C2×D412yes—
159C2×C4×D11#4112yes—
160C2×Dic22—21no—
161C2×Dic22—21no—
162C2×Dic22—21no—
163C2×Dic22—21no—
164C2×Dic22—21no—
165C2×Dic22—21no—
166C2×Dic22—21no—
167C2×Dic22—21no—
168C2×Dic22—21no—
169C2×Dic22—21no—
170C2×Dic22—21no—
171C2×Dic22C2×D412yes—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11#4112yes—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—81no—
186C11×C4⋊C4C2×D412yes—
187C42×C11—21no—
188C42×C11—21no—
189(C2×D11)⋊C4—24no—
190(C2×D11)⋊C4—22no—
191(C2×D11)⋊C4—22no—
192(C2×D11)⋊C4—42no—
193C4⋊Dic11—24no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—42no—
198C4⋊Dic11#4112yes—
199Dic11⋊C4—42no—
200Dic11⋊C4—42no—
201Dic11⋊C4—42no—
202C4×Dic11—21no—
203C4×Dic11—21no—
204C4×Dic11—42no—
205C4×Dic11—81no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212Dic44—44no—
213C8×D11—44no—
214C2×#483—111no—
215C2×#467—111no—
216#2503—111no—
217#2360—111no—
218#2085D1111yescharacteristic, complemented
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#1805—111no—
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—
237C2×C4×C11—22no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
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×C11C22×D411yescharacteristic
256C2×C4×C11C2×#4111yescharacteristic
257C2×C4×C11C2×#4111yescharacteristic
258C2×C4×C11C2×#4111yescharacteristic
259C2×C4×C11H(5,𝔽2)11yescharacteristic
260C2×C4×C112−1+411yescharacteristic
261C2×Dic11—21no—
262C2×Dic11—21no—
263C2×Dic11—22no—
264C2×Dic11—22no—
265C2×Dic11—21no—
266C2×Dic11—21no—
267C2×Dic11—21no—
268C2×Dic11—21no—
269C2×Dic11—21no—
270C2×Dic11—21no—
271C2×Dic11—41no—
272C2×Dic11—41no—
273C2×Dic11—41no—
274C2×Dic11—41no—
275C2×Dic11—41no—
276C2×Dic11—41no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11#12112yes—
282C4×D11—22no—
283C4×D11—22no—
284C4×D11—22no—
285C4×D11—22no—
286C4×D11—84no—
287C4×D11—84no—
288Dic22—22no—
289Dic22—22no—
290Dic22—41no—
291Dic22—41no—
292Dic22—41no—
293Dic22—41no—
294Dic22—41no—
295Dic22—41no—
296C8×C11—22no—
297C8×C11—41no—
298C11⋊C8—41no—
299C11⋊C8—41no—
300C22×Q16—111no—
301C23×C8—111no—
302C2×C22⋊Q8—111no—
303C2×C22⋊Q8—111no—
304C2×C4×Q8—111no—
305C22×C4⋊C4—111no—
306C22×C4⋊C4—111no—
307#483—224no—
308#467—224no—
309C2×#107C2×D1111yescharacteristic
310C2×#106—111no—
311C2×#106C2×D1111yescharacteristic
312C2×C4⋊C8—111no—
313C2×C4⋊C8—111no—
314C2×#103—111no—
315C2×#103—111no—
316C2×#103—111no—
317C2×#103—111no—
318C2×#103—111no—
319C2×#103—111no—
320C2×C22⋊C8—111no—
321#400—221no—
322#400—221no—
323#391—111no—
324#391—111no—
325#391—111no—
326#389—221no—
327#389C2×D1111yescharacteristic
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#336C2×D1111yescharacteristic
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—41no—
360C4×C11—42no—
361C4×C11—41no—
362C4×C11—81no—
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—42no—
374Dic11—81no—
375Dic11—81no—
376C22×Q8—111no—
377C22×Q8—111no—
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—222no—
396C4×Q8—441no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—111no—
399C2×C4⋊C4—111no—
400C2×C4⋊C4—222no—
401C2×C4⋊C4—222no—
402C2×C4⋊C4—222no—
403C2×C4⋊C4—221no—
404C2×C4⋊C4—221no—
405C2×C4⋊C4—221no—
406C2×C4⋊C4—221no—
407C2×C4⋊C4—221no—
408C2×C4⋊C4—441no—
409C2×C4⋊C4C22×D1111yescharacteristic
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—111no—
418C2×C42—221no—
419C2×C42—221no—
420C2×C42C22×D1111yescharacteristic
421#107—22no—
422#106—22no—
423#106—222no—
424C4⋊C8—222no—
425C4⋊C8—441no—
426#103—222no—
427#103—222no—
428#103—222no—
429#103—222no—
430#103—222no—
431#103—441no—
432C22⋊C8—222no—
433#95—21no—
434#95—21no—
435#95—21no—
436#95—111no—
437#95—111no—
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—112no—
457C2×Q8—221no—
458C2×Q8—221no—
459C2×Q8—221no—
460C2×Q8—221no—
461C2×Q8—221no—
462C2×Q8—221no—
463C2×Q8—221no—
464C2×Q8—221no—
465C2×Q8—221no—
466C2×Q8—221no—
467C2×Q8—221no—
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—221no—
501C2×C8—221no—
502C2×C8—221no—
503C2×C8—221no—
504C2×C8—221no—
505C2×C8—221no—
506C2×C8—444no—
507C2×C8#434312yes—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—81no—
516C4⋊C4—112no—
517C4⋊C4—224no—
518C4⋊C4—221no—
519C4⋊C4—221no—
520C4⋊C4—221no—
521C4⋊C4—442no—
522C4⋊C4—442no—
523C4⋊C4—442no—
524C4⋊C4—442no—
525C4⋊C4D4×D1112yes—
526C22⋊C4—222no—
527C22⋊C4—222no—
528C22⋊C4—224no—
529C22⋊C4—442no—
530C42—21no—
531C42—21no—
532C42—221no—
533C42—221no—
534C42—442no—
535C42—881no—
536C11#2520811yescharacteristic, complemented, Sylow
537C23—112no—
538C23—112no—
539C23—112no—
540C23—221no—
541C23—221no—
542C23—221no—
543C23—221no—
544C23C2×D4×D1111yescharacteristic
545Q8—222no—
546Q8—222no—
547Q8—441no—
548Q8—441no—
549Q8—441no—
550Q8—441no—
551Q8—441no—
552Q8—441no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—22no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—41no—
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—221no—
583C2×C4—221no—
584C2×C4—222no—
585C2×C4—222no—
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×D4×D1111yescharacteristic
599C2×C4C2×#434311yescharacteristic
600C2×C4#6704011yescharacteristic
601C2×C4#41×D1111yescharacteristic
602C2×C4#41×D1111yescharacteristic
603C2×C4#6704211yescharacteristic
604C8—22no—
605C8—41no—
606C8—441no—
607C8—441no—
608C22—114no—
609C22—222no—
610C22—222no—
611C22—222no—
612C22—222no—
613C22—222no—
614C22—222no—
615C22D11×#12111yescharacteristic
616C22#1062318511yescharacteristic
617C22#1062325711yescharacteristic
618C22D11×#13511yescharacteristic
619C22#1062330211yescharacteristic
620C22#1062330611yescharacteristic
621C22D11×#13711yescharacteristic
622C4—41no—
623C4—41no—
624C4—42no—
625C4—81no—
626C4—81no—
627C4—81no—
628C4—222no—
629C4—442no—
630C4—442no—
631C4—441no—
632C4—441no—
633C4—881no—
634C4—881no—
635C4#1062316111yescharacteristic
636C4#1062316211yescharacteristic
637C4#1062322211yescharacteristic
638C4#1062322311yescharacteristic
639C2—224no—
640C2#1307216011yescharacteristic
641C2D11×#46411yescharacteristic
642C2#1307816711yescharacteristic
643C2#1308045411yescharacteristic
644C2#1308067011yescharacteristic
645C2#1308098311yescharacteristic
646C2#1308107011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2085C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
hypercenter#2085D11
hypocenterC11#25208
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2085

Complements

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

NH ≅ G/Ntype
5. #13070038C2semidirect
6. #13069994C2semidirect
7. #13069940C2semidirect
8. #13069381C2semidirect
9. #13069249C2semidirect
10. #13068956C2semidirect
13. #13068628C2semidirect
15. C11×#2085C2semidirect
218. #2085D11semidirect
536. C11#25208semidirect

Maximal subgroups

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

subgroupindex
C2×#106224752
C2×#106225002
#130730982
#130716202
#130700382
#130699942
#130699402
#130693812
#130692492
#130689562
#130689222
#130687952
#130686282
D11×#3402
C11×#20852
#2520811