Finite Group Databasebeta

← #14816876

Subgroups — #14816876

Order 2816.

848 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622379C211yesmaximal, characteristic
2C2×C4×#4324C211yesmaximal, characteristic
3#13072478C211yesmaximal, characteristic, complemented
4#13071521C211yesmaximal, characteristic
5#13070161C211yesmaximal, characteristic, complemented
6#13070103C211yesmaximal, characteristic, complemented
7#13069998C211yesmaximal, characteristic, complemented
8#13069952C211yesmaximal, characteristic, complemented
9#13069341C211yesmaximal, characteristic, complemented
10#13069171C211yesmaximal, characteristic, complemented
11#13068948C211yesmaximal, characteristic
12#13068948C211yesmaximal, characteristic
13#13068875C211yesmaximal, characteristic
14#13068873C211yesmaximal, characteristic, complemented
15C11×#1862C211yesmaximal, characteristic
16C2×C4×D4×C11C2211yescharacteristic
17C2×D4×Dic11C2211yescharacteristic
18C2×D4×Dic11C2211yescharacteristic
19C22×#4324C2211yescharacteristic
20C2×#66943C2211yescharacteristic
21C2×C4×Dic22C2211yescharacteristic
22C2×C11×#107C2211yescharacteristic
23C2×C11×#102C2211yescharacteristic
24C2×C11×#102C2211yescharacteristic
25C11×#389C2211yescharacteristic
26C2×#66896C2211yescharacteristic
27#10622823—21no—
28C2×C11⋊#95—21no—
29C2×#66882C2211yescharacteristic
30C2×#66880C2211yescharacteristic
31C2×#66880C2211yescharacteristic
32C2×Dic11⋊C8C2211yescharacteristic
33C4×#4324—24no—
34#10622594—21no—
35#10622590C2211yescharacteristic
36#10622587C2211yescharacteristic
37#10622587C2211yescharacteristic
38#10622586C2211yescharacteristic
39#10622586C2211yescharacteristic
40#10622585—21no—
41C2×#66874C2211yescharacteristic
42C2×#66872C2211yescharacteristic
43C2×#66872C2211yescharacteristic
44C2×#66872C2211yescharacteristic
45#10622559—21no—
46#10622555—21no—
47C4×Dic11⋊C4C2211yescharacteristic
48#10622541C2211yescharacteristic
49C2×C4×C11⋊C8C2211yescharacteristic
50#10622379—24no—
51#10622271—21no—
52#10622270—21no—
53C11×#340C2211yescharacteristic
54C11×#336C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×D4×C11C2311yescharacteristic
62C23×C4×C11—21no—
63C23×Dic11—21no—
64C23×Dic11—21no—
65C22×Dic22C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C4×D4×C11—22no—
69C4×D4×C11—41no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C22⋊C4—21no—
75C2×C42×C11C2311yescharacteristic
76C2×C22⋊Dic11—21no—
77C2×C22⋊Dic11—21no—
78D4×Dic11—22no—
79D4×Dic11—22no—
80D4×Dic11—22no—
81D4×Dic11—41no—
82C2×#4324—22no—
83C2×#4324—22no—
84C2×#4324Q814yes—
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×Dic11⋊C4—21no—
94C2×Dic11⋊C4D411yescharacteristic
95C2×Dic11⋊C4D411yescharacteristic
96C2×C4×Dic11—21no—
97C2×C4×Dic11C2311yescharacteristic
98C2×C4×Dic11C2311yescharacteristic
99C22×C11⋊C8C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101#66943—22no—
102#66943—41no—
103C4×Dic22—22no—
104C4×Dic22—41no—
105C11×#107—41no—
106C11×#102—22no—
107C11×#102—22no—
108C11×#95—21no—
109#66896D414yes—
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⋊#95D411yescharacteristic
120C11⋊#95D411yescharacteristic
121#66882—22no—
122#66880—22no—
123#66880—41no—
124Dic11⋊C8—22no—
125#66874—22no—
126#66872—22no—
127#66872—22no—
128#66872—22no—
129C4×C11⋊C8—22no—
130#26378—111nomaximal, Sylow
131C24×C11—21no—
132C2×D4×C11—21no—
133C2×D4×C11—21no—
134C2×D4×C11—21no—
135C2×D4×C11C2×D412yes—
136C2×D4×C11C2×Q812yes—
137C2×D4×C11#4112yes—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—42no—
142C22×C4×C11—42no—
143C22×C4×C11—81no—
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2411yescharacteristic
147C22×Dic11—24no—
148C22×Dic11—21no—
149C22×Dic11—21no—
150C22×Dic11—21no—
151C22×Dic11—21no—
152C22×Dic11—42no—
153C22×Dic11—42no—
154C22×Dic11—81no—
155C22×Dic11—81no—
156C22×Dic11—81no—
157C22×Dic11C2×D411yescharacteristic
158C22×Dic11C2×D411yescharacteristic
159C22×Dic11C2×D411yescharacteristic
160C22×Dic11C2×D411yescharacteristic
161C2×Dic22—21no—
162C2×Dic22—21no—
163C2×Dic22—21no—
164C2×Dic22—21no—
165C2×Dic22—21no—
166C2×Dic22C2×Q812yes—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—42no—
180C11×C22⋊C4—42no—
181C42×C11—21no—
182C42×C11—21no—
183C22⋊Dic11—24no—
184C22⋊Dic11—42no—
185#4324—28no—
186C4⋊Dic11—21no—
187C4⋊Dic11—21no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11—42no—
191C4⋊Dic11C2×D412yes—
192C4⋊Dic11#4112yes—
193Dic11⋊C4—22no—
194Dic11⋊C4—41no—
195Dic11⋊C4—42no—
196Dic11⋊C4—42no—
197Dic11⋊C4—42no—
198Dic11⋊C4—81no—
199Dic11⋊C4—81no—
200C4×Dic11—21no—
201C4×Dic11—21no—
202C4×Dic11—21no—
203C4×Dic11—21no—
204C4×Dic11—42no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8C2×D412yes—
210C2×C11⋊C8C2×Q812yes—
211C2×#478—111no—
212C2×C4×SD16—111no—
213#2453—111no—
214#2349—111no—
215#2097—111no—
216#2085—111no—
217#2066—111no—
218#2059—111no—
219#1941—111no—
220#1916—111no—
221#1877—111no—
222#1877—111no—
223#1864—111no—
224#1863—111no—
225#1862D1111yescharacteristic
226C23×C11—22no—
227C23×C11—22no—
228C23×C11—22no—
229C23×C11—41no—
230C23×C11—41no—
231C23×C11—41no—
232C23×C11—41no—
233C23×C11C22×D411yescharacteristic
234D4×C11—22no—
235D4×C11—22no—
236D4×C11—22no—
237D4×C11C22⋊Q814yes—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—41no—
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—84no—
253C2×C4×C11#13512yes—
254C2×C4×C11C22×D411yescharacteristic
255C2×C4×C11C22×Q811yescharacteristic
256C2×C4×C11C2×#4111yescharacteristic
257C2×C4×C11C2×#4111yescharacteristic
258C2×C4×C11H(5,𝔽2)11yescharacteristic
259C2×C4×C112−1+411yescharacteristic
260C2×Dic11—21no—
261C2×Dic11—21no—
262C2×Dic11—22no—
263C2×Dic11—21no—
264C2×Dic11—21no—
265C2×Dic11—22no—
266C2×Dic11—22no—
267C2×Dic11—21no—
268C2×Dic11—21no—
269C2×Dic11—21no—
270C2×Dic11—21no—
271C2×Dic11—21no—
272C2×Dic11—21no—
273C2×Dic11—21no—
274C2×Dic11—21no—
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—84no—
285C2×Dic11—84no—
286Dic22—22no—
287Dic22—22no—
288Dic22—41no—
289Dic22—41no—
290C8×C11—41no—
291C8×C11—41no—
292C11⋊C8—22no—
293C11⋊C8—22no—
294C22×SD16—111no—
295C2×#125—111no—
296C2×C4×Q8—111no—
297C2×C4×D4—111no—
298C2×C4×D4—111no—
299C2×C4×D4C2×D1111yescharacteristic
300#478—224no—
301C4×SD16—224no—
302C2×#107—111no—
303C2×#107C2×D1111yescharacteristic
304C2×#106—111no—
305C2×#106—111no—
306C2×#106—111no—
307C2×C4⋊C8—111no—
308C2×#103—111no—
309C2×#103—111no—
310C2×#103—111no—
311C2×#102—111no—
312C2×#102C2×D1111yescharacteristic
313C2×#102C2×D1111yescharacteristic
314C2×C4×C8—111no—
315#400—221no—
316#398—221no—
317#391—111no—
318#391—111no—
319#389—111no—
320#389—111no—
321#389—111no—
322#389—221no—
323#389C2×D1111yescharacteristic
324#387—221no—
325#385—221no—
326#385—221no—
327#382—111no—
328#380—221no—
329C4×C4⋊C4—111no—
330C2×#95—221no—
331#340—111no—
332#340—111no—
333#340—111no—
334#340C2×D1111yescharacteristic
335#336—111no—
336#336—111no—
337#336—111no—
338#336C2×D1111yescharacteristic
339C22×C11—24no—
340C22×C11—42no—
341C22×C11—42no—
342C22×C11—42no—
343C22×C11—42no—
344C22×C11—42no—
345C22×C11—42no—
346C22×C11#52511yescharacteristic
347C22×C11D4211yescharacteristic
348C22×C11D4×Q811yescharacteristic
349C22×C11C2×#13511yescharacteristic
350C22×C11#57511yescharacteristic
351C22×C11#57711yescharacteristic
352C22×C11#57711yescharacteristic
353C4×C11—22no—
354C4×C11—41no—
355C4×C11—81no—
356C4×C11—81no—
357C4×C11—81no—
358C4×C11C2×C22⋊Q811yescharacteristic
359C4×C11#53911yescharacteristic
360C4×C11#54711yescharacteristic
361C4×C11#55411yescharacteristic
362Dic11—41no—
363Dic11—41no—
364Dic11—42no—
365Dic11—42no—
366Dic11—41no—
367Dic11—42no—
368Dic11—41no—
369Dic11—81no—
370C22×Q8—111no—
371C22×D4C22×D1111yescharacteristic
372C23×C4—21no—
373C23×C4—221no—
374C23×C4—221no—
375C2×SD16—114no—
376C2×SD16—222no—
377C2×SD16—222no—
378C22×C8—111no—
379C22×C8—111no—
380C22×C8C22×D1111yescharacteristic
381C22×C8C22×D1111yescharacteristic
382#125—222no—
383#125—441no—
384C4×Q8—222no—
385C4×Q8—441no—
386C4×D4—22no—
387C4×D4—41no—
388C4×D4—222no—
389C4×D4—222no—
390C4×D4—222no—
391C4×D4—441no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—111no—
394C2×C4⋊C4—111no—
395C2×C4⋊C4—111no—
396C2×C4⋊C4—111no—
397C2×C4⋊C4—111no—
398C2×C4⋊C4—221no—
399C2×C4⋊C4—221no—
400C2×C4⋊C4—221no—
401C2×C4⋊C4—221no—
402C2×C4⋊C4—221no—
403C2×C4⋊C4—221no—
404C2×C4⋊C4C22×D1111yescharacteristic
405C2×C4⋊C4C22×D1111yescharacteristic
406C2×C4⋊C4C22×D1111yescharacteristic
407C2×C22⋊C4—21no—
408C2×C22⋊C4—221no—
409C2×C22⋊C4—221no—
410C2×C42—111no—
411C2×C42—111no—
412C2×C42—221no—
413C2×C42C22×D1111yescharacteristic
414#107—41no—
415#107—222no—
416#106—222no—
417#106—222no—
418#106—222no—
419C4⋊C8—222no—
420#103—222no—
421#103—222no—
422#103—441no—
423#102—22no—
424#102—22no—
425#102—114no—
426C4×C8—222no—
427#95—21no—
428#95—111no—
429#95—111no—
430#95—221no—
431#95—221no—
432#95—221no—
433#95—221no—
434#95—221no—
435#95—221no—
436#95—221no—
437#95—221no—
438#95—221no—
439C2×C11—44no—
440C2×C11#244911yescharacteristic
441C2×C11#310211yescharacteristic
442C2×C11#312311yescharacteristic
443C2×C11#326711yescharacteristic
444C2×C11#328211yescharacteristic
445C2×C11#338111yescharacteristic
446C2×C11#338811yescharacteristic
447C24—21no—
448C2×Q8—112no—
449C2×Q8—221no—
450C2×Q8—221no—
451C2×Q8—221no—
452C2×Q8—221no—
453C2×Q8—221no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4#433912yes—
458C2×D4D4×D1112yes—
459C2×D4Q8×D1112yes—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—42no—
464C22×C4—42no—
465C22×C4—81no—
466C22×C4—111no—
467C22×C4—111no—
468C22×C4—111no—
469C22×C4—111no—
470C22×C4—221no—
471C22×C4—221no—
472C22×C4—221no—
473C22×C4—224no—
474C22×C4—221no—
475C22×C4—442no—
476C22×C4—442no—
477C22×C4—881no—
478C22×C4—881no—
479C22×C4—881no—
480C22×C4D4×D1111yescharacteristic
481C22×C4D4×D1111yescharacteristic
482C22×C4C23×D1111yescharacteristic
483SD16—228no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—112no—
491C2×C8—112no—
492C2×C8—221no—
493C2×C8—221no—
494C2×C8—221no—
495C2×C8—221no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—42no—
503C4⋊C4—112no—
504C4⋊C4—112no—
505C4⋊C4—222no—
506C4⋊C4—221no—
507C4⋊C4—221no—
508C4⋊C4—221no—
509C4⋊C4—221no—
510C4⋊C4—441no—
511C4⋊C4—442no—
512C4⋊C4—442no—
513C4⋊C4—442no—
514C4⋊C4—442no—
515C4⋊C4—881no—
516C4⋊C4—881no—
517C22⋊C4—42no—
518C22⋊C4—224no—
519C22⋊C4—442no—
520C42—21no—
521C42—21no—
522C42—221no—
523C42—221no—
524C42—221no—
525C42—221no—
526C42—442no—
527C11#2637811yescharacteristic, complemented, Sylow
528C23—22no—
529C23—22no—
530C23—22no—
531C23—41no—
532C23—41no—
533C23—41no—
534C23—41no—
535C23C2×D4×D1111yescharacteristic
536Q8—222no—
537Q8—222no—
538Q8—441no—
539Q8—441no—
540D4—22no—
541D4—22no—
542D4—22no—
543D4#6694914yes—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—84no—
559C2×C4—221no—
560C2×C4—221no—
561C2×C4—221no—
562C2×C4—221no—
563C2×C4—221no—
564C2×C4—221no—
565C2×C4—221no—
566C2×C4—221no—
567C2×C4—221no—
568C2×C4—221no—
569C2×C4—222no—
570C2×C4—221no—
571C2×C4—221no—
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×C4—884no—
584C2×C4—884no—
585C2×C4#6696512yes—
586C2×C4C2×#433911yescharacteristic
587C2×C4C2×D4×D1111yescharacteristic
588C2×C4#6703711yescharacteristic
589C2×C4C2×Q8×D1111yescharacteristic
590C2×C4#41×D1111yescharacteristic
591C2×C4#6704311yescharacteristic
592C8—41no—
593C8—41no—
594C8—222no—
595C8—222no—
596C22—24no—
597C22—42no—
598C22—42no—
599C22—42no—
600C22—42no—
601C22—42no—
602C22—42no—
603C22#1062307811yescharacteristic
604C22#1062312111yescharacteristic
605C22#1062316311yescharacteristic
606C22C2×#6696511yescharacteristic
607C22#1062329911yescharacteristic
608C22#1062330611yescharacteristic
609C22#1062330911yescharacteristic
610C4—22no—
611C4—41no—
612C4—81no—
613C4—81no—
614C4—81no—
615C4—441no—
616C4—442no—
617C4—441no—
618C4—442no—
619C4—441no—
620C4—442no—
621C4—441no—
622C4—881no—
623C4C2×#6694911yescharacteristic
624C4#1062309511yescharacteristic
625C4#1062316711yescharacteristic
626C4#1062318611yescharacteristic
627C2—44no—
628C2#1307242711yescharacteristic
629C2#1307863011yescharacteristic
630C2#1307886711yescharacteristic
631C2#1308014511yescharacteristic
632C2#1308032711yescharacteristic
633C2#1308149511yescharacteristic
634C2#1308156511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1862C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenter#1862D11
hypocenterC11#26378
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1862

Complements

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

NH ≅ G/Ntype
3. #13072478C2semidirect
5. #13070161C2semidirect
6. #13070103C2semidirect
7. #13069998C2semidirect
8. #13069952C2semidirect
9. #13069341C2semidirect
10. #13069171C2semidirect
14. #13068873C2semidirect
527. C11#26378semidirect

Maximal subgroups

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

subgroupindex
C2×#106223792
C2×C4×#43242
#130724782
#130715212
#130701612
#130701032
#130699982
#130699522
#130693412
#130691712
#130689482
#130688752
#130688732
C11×#18622
#2637811