Finite Group Databasebeta

← #14816830

Subgroups — #14816830

Order 2816.

820 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622442C211yesmaximal, characteristic, complemented
2C2×#10622371C211yesmaximal, characteristic
3#13072490C211yesmaximal, characteristic
4#13071535C211yesmaximal, characteristic, complemented
5#13070139C211yesmaximal, characteristic
6#13070103C211yesmaximal, characteristic, complemented
7#13069954C211yesmaximal, characteristic, complemented
8#13069345C211yesmaximal, characteristic, complemented
9#13069170C211yesmaximal, characteristic, complemented
10#13068974C211yesmaximal, characteristic
11#13068968C211yesmaximal, characteristic
12#13068881C211yesmaximal, characteristic, complemented
13#13068871C211yesmaximal, characteristic, complemented
14#13068865C211yesmaximal, characteristic
15C11×#2065C211yesmaximal, characteristic
16C2×D4×Dic11C2211yescharacteristic
17C22×#4324C2211yescharacteristic
18C2×#66940C2211yescharacteristic
19C2×#66940C2211yescharacteristic
20C2×#66923C2211yescharacteristic
21C2×C4×Dic22C2211yescharacteristic
22C2×C11×#106C2211yescharacteristic
23C2×C11×C4⋊C8C2211yescharacteristic
24C2×C11×#102C2211yescharacteristic
25C2×C11×#102C2211yescharacteristic
26C11×#390C2211yescharacteristic
27C11×#389C2211yescharacteristic
28#10622834C2211yescharacteristic
29C2×#66896C2211yescharacteristic
30C2×#66882C2211yescharacteristic
31C2×#66881C2211yescharacteristic
32C2×#66880C2211yescharacteristic
33C2×#66880C2211yescharacteristic
34C2×C8×Dic11C2211yescharacteristic
35#10622598C2211yescharacteristic
36#10622598C2211yescharacteristic
37#10622590C2211yescharacteristic
38C4⋊C4×Dic11—21no—
39#10622586C2211yescharacteristic
40#10622585—21no—
41C2×#66874C2211yescharacteristic
42C2×#66872C2211yescharacteristic
43C2×#66871C2211yescharacteristic
44#10622562—21no—
45#10622561—21no—
46#10622559—21no—
47#10622555—21no—
48C4×Dic11⋊C4C2211yescharacteristic
49#10622442—24no—
50#10622371—24no—
51#10622263—21no—
52#10622260—21no—
53C11×#340C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×D4×C11C2311yescharacteristic
62C23×Dic11—21no—
63C22×Dic22C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C22⋊C4—21no—
71C2×C11×C22⋊C4—21no—
72C2×C42×C11C2311yescharacteristic
73C2×C22⋊Dic11—21no—
74C2×C22⋊Dic11—21no—
75C2×C22⋊Dic11—21no—
76D4×Dic11—22no—
77D4×Dic11—41no—
78C2×#4324—22no—
79C2×#4324—22no—
80C2×#4324Q814yes—
81C2×C4⋊Dic11—21no—
82C2×C4⋊Dic11—21no—
83C2×C4⋊Dic11C2311yescharacteristic
84C2×C4⋊Dic11C2311yescharacteristic
85C2×C4⋊Dic11C2311yescharacteristic
86C2×Dic11⋊C4—21no—
87C2×Dic11⋊C4—21no—
88C2×Dic11⋊C4—21no—
89C2×Dic11⋊C4—21no—
90C2×Dic11⋊C4—21no—
91C2×Dic11⋊C4—21no—
92C2×Dic11⋊C4D411yescharacteristic
93C2×Dic11⋊C4D411yescharacteristic
94C2×C4×Dic11—21no—
95C2×C4×Dic11—21no—
96C2×C4×Dic11—21no—
97C2×C4×Dic11C2311yescharacteristic
98C2×C4×Dic11C2311yescharacteristic
99C22×C11⋊C8C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101#66940—22no—
102#66940—22no—
103#66940—22no—
104#66940—41no—
105#66923—22no—
106#66923—41no—
107C4×Dic22—22no—
108C4×Dic22—41no—
109C11×#106—22no—
110C11×C4⋊C8—22no—
111C11×#102—22no—
112C11×#102—22no—
113C11×#95—21no—
114#66896—41no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95D411yescharacteristic
121C11⋊#95D411yescharacteristic
122#66882—22no—
123#66881—22no—
124#66880—22no—
125#66880D414yes—
126C8×Dic11—22no—
127#66874—22no—
128#66872—22no—
129#66871—41no—
130#26375—111nomaximal, Sylow
131C24×C11—21no—
132C2×D4×C11—21no—
133C2×D4×C11—21no—
134C2×D4×C11—21no—
135C2×D4×C11—21no—
136C2×D4×C11—21no—
137C2×D4×C11C2×Q812yes—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2411yescharacteristic
144C22×Dic11—21no—
145C22×Dic11—21no—
146C22×Dic11—21no—
147C22×Dic11—21no—
148C22×Dic11—42no—
149C22×Dic11—42no—
150C22×Dic11—81no—
151C22×Dic11C2×D411yescharacteristic
152C22×Dic11C2×D411yescharacteristic
153C22×Dic11C2×D411yescharacteristic
154C22×Dic11C2×D411yescharacteristic
155C2×Dic22—21no—
156C2×Dic22—21no—
157C2×Dic22—21no—
158C2×Dic22C2×D412yes—
159C2×Dic22C2×Q812yes—
160C2×Dic22#4112yes—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11C2×D412yes—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—42no—
173C11×C4⋊C4#4112yes—
174C11×C22⋊C4—81no—
175C11×C22⋊C4—81no—
176C42×C11—21no—
177C42×C11—21no—
178C22⋊Dic11—42no—
179C22⋊Dic11—42no—
180C22⋊Dic11—81no—
181#4324—28no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11—21no—
186C4⋊Dic11—21no—
187C4⋊Dic11—42no—
188C4⋊Dic11—81no—
189C4⋊Dic11C2×D412yes—
190Dic11⋊C4—24no—
191Dic11⋊C4—22no—
192Dic11⋊C4—41no—
193Dic11⋊C4—42no—
194Dic11⋊C4—42no—
195Dic11⋊C4—42no—
196Dic11⋊C4—42no—
197Dic11⋊C4—81no—
198C4×Dic11—24no—
199C4×Dic11—21no—
200C4×Dic11—21no—
201C4×Dic11—21no—
202C4×Dic11—21no—
203C4×Dic11—42no—
204C4×Dic11—42no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8C2×Q812yes—
211C2×#479—111no—
212C2×C4×SD16—111no—
213#2454—111no—
214#2351—111no—
215#2092—111no—
216#2085—111no—
217#2065D1111yescharacteristic
218#2059—111no—
219#1941—111no—
220#1916—111no—
221#1880—111no—
222#1880—111no—
223#1865—111no—
224#1863—111no—
225#1862—111no—
226C23×C11—22no—
227C23×C11—41no—
228C23×C11—41no—
229C23×C11—41no—
230C23×C11—41no—
231C23×C11—41no—
232C23×C11—41no—
233C23×C11C22×D411yescharacteristic
234D4×C11—22no—
235D4×C11—22no—
236D4×C11—41no—
237D4×C11—41no—
238C2×C4×C11—22no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
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×C11C22×D411yescharacteristic
254C2×C4×C11C22×Q811yescharacteristic
255C2×C4×C11C2×#4111yescharacteristic
256C2×C4×C11C2×#4111yescharacteristic
257C2×C4×C11H(5,𝔽2)11yescharacteristic
258C2×C4×C112−1+411yescharacteristic
259C2×Dic11—22no—
260C2×Dic11—21no—
261C2×Dic11—22no—
262C2×Dic11—22no—
263C2×Dic11—21no—
264C2×Dic11—21no—
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—84no—
283C2×Dic11#13512yes—
284Dic22—22no—
285Dic22—22no—
286Dic22—22no—
287Dic22C22⋊Q814yes—
288C8×C11—22no—
289C8×C11—41no—
290C11⋊C8—22no—
291C11⋊C8—41no—
292C22×SD16—111no—
293C2×#125—111no—
294C2×C4×Q8—111no—
295C2×C4×Q8—111no—
296C2×C4×Q8—111no—
297C2×C4×D4—111no—
298#479—224no—
299C4×SD16—224no—
300C2×#107—111no—
301C2×#107—111no—
302C2×#106—111no—
303C2×#106—111no—
304C2×#106C2×D1111yescharacteristic
305C2×C4⋊C8C2×D1111yescharacteristic
306C2×#103—111no—
307C2×#103—111no—
308C2×#103—111no—
309C2×#102—111no—
310C2×#102C2×D1111yescharacteristic
311C2×#102C2×D1111yescharacteristic
312C2×C4×C8—111no—
313#399—221no—
314#396—221no—
315#390—111no—
316#390C2×D1111yescharacteristic
317#389—111no—
318#389—111no—
319#389—111no—
320#389—221no—
321#389—221no—
322#389C2×D1111yescharacteristic
323#385—221no—
324#382—111no—
325#382—221no—
326#380—221no—
327C4×C4⋊C4—111no—
328C4×C4⋊C4—221no—
329#340—111no—
330#340—111no—
331#340—111no—
332#340C2×D1111yescharacteristic
333#336—111no—
334#336—111no—
335#336—111no—
336#336—111no—
337C22×C11—42no—
338C22×C11—42no—
339C22×C11—42no—
340C22×C11—81no—
341C22×C11—81no—
342C22×C11—81no—
343C22×C11—81no—
344C22×C11#52511yescharacteristic
345C22×C11D4211yescharacteristic
346C22×C11D4×Q811yescharacteristic
347C22×C11C2×#13511yescharacteristic
348C22×C11#57511yescharacteristic
349C22×C11#57711yescharacteristic
350C22×C11#57711yescharacteristic
351C4×C11—42no—
352C4×C11—41no—
353C4×C11—41no—
354C4×C11—81no—
355C4×C11—81no—
356C4×C11C2×C22⋊Q811yescharacteristic
357C4×C11#53911yescharacteristic
358C4×C11#54711yescharacteristic
359C4×C11#55411yescharacteristic
360Dic11—24no—
361Dic11—22no—
362Dic11—41no—
363Dic11—41no—
364Dic11—41no—
365Dic11—42no—
366Dic11—81no—
367Dic11—81no—
368C22×Q8—111no—
369C22×D4C22×D1111yescharacteristic
370C23×C4—221no—
371C2×SD16—114no—
372C2×SD16—222no—
373C2×SD16—222no—
374C22×C8—111no—
375C22×C8—111no—
376C22×C8C22×D1111yescharacteristic
377C22×C8C22×D1111yescharacteristic
378#125—222no—
379#125—441no—
380C4×Q8—222no—
381C4×Q8—222no—
382C4×Q8—222no—
383C4×Q8—222no—
384C4×Q8—441no—
385C4×Q8—441no—
386C4×D4—222no—
387C4×D4—441no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—111no—
390C2×C4⋊C4—111no—
391C2×C4⋊C4—111no—
392C2×C4⋊C4—111no—
393C2×C4⋊C4—111no—
394C2×C4⋊C4—221no—
395C2×C4⋊C4—221no—
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×C4⋊C4C22×D1111yescharacteristic
405C2×C22⋊C4—21no—
406C2×C22⋊C4—21no—
407C2×C22⋊C4—221no—
408C2×C22⋊C4—221no—
409C2×C22⋊C4—221no—
410C2×C42—111no—
411C2×C42—111no—
412C2×C42—221no—
413C2×C42—221no—
414C2×C42—221no—
415C2×C42C22×D1111yescharacteristic
416#107—222no—
417#107—441no—
418#106—22no—
419#106—222no—
420#106—222no—
421C4⋊C8—22no—
422#103—114no—
423#103—222no—
424#103—222no—
425#102—22no—
426#102—22no—
427#102—441no—
428C4×C8—222no—
429#95—21no—
430#95—111no—
431#95—111no—
432#95—221no—
433#95—221no—
434#95—221no—
435#95—221no—
436#95—221no—
437C2×C11—82no—
438C2×C11#244911yescharacteristic
439C2×C11#310211yescharacteristic
440C2×C11#312611yescharacteristic
441C2×C11#327111yescharacteristic
442C2×C11#328211yescharacteristic
443C2×C11#338111yescharacteristic
444C2×C11#338811yescharacteristic
445C24—21no—
446C2×Q8—112no—
447C2×Q8—112no—
448C2×Q8—112no—
449C2×Q8—221no—
450C2×Q8—221no—
451C2×Q8—221no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4Q8×D1112yes—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—111no—
462C22×C4—111no—
463C22×C4—111no—
464C22×C4—111no—
465C22×C4—221no—
466C22×C4—221no—
467C22×C4—221no—
468C22×C4—221no—
469C22×C4—442no—
470C22×C4—442no—
471C22×C4—881no—
472C22×C4D4×D1111yescharacteristic
473C22×C4D4×D1111yescharacteristic
474C22×C4C23×D1111yescharacteristic
475SD16—228no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—112no—
482C2×C8—221no—
483C2×C8—221no—
484C2×C8—221no—
485C2×C8—221no—
486C2×C8—221no—
487C2×C8D4×D1112yes—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—42no—
494C4⋊C4—112no—
495C4⋊C4—222no—
496C4⋊C4—224no—
497C4⋊C4—221no—
498C4⋊C4—221no—
499C4⋊C4—221no—
500C4⋊C4—221no—
501C4⋊C4—221no—
502C4⋊C4—441no—
503C4⋊C4—442no—
504C4⋊C4—442no—
505C4⋊C4—442no—
506C4⋊C4—442no—
507C4⋊C4—442no—
508C4⋊C4—881no—
509C4⋊C4—881no—
510C4⋊C4#434112yes—
511C22⋊C4—81no—
512C22⋊C4—81no—
513C22⋊C4—442no—
514C22⋊C4—442no—
515C22⋊C4—881no—
516C42—21no—
517C42—21no—
518C42—224no—
519C42—221no—
520C42—221no—
521C42—221no—
522C42—221no—
523C42—442no—
524C42—442no—
525C11#2637511yescharacteristic, complemented, Sylow
526C23—22no—
527C23—41no—
528C23—41no—
529C23—41no—
530C23—41no—
531C23—41no—
532C23—41no—
533C23C2×D4×D1111yescharacteristic
534Q8—114no—
535Q8—222no—
536Q8—222no—
537Q8—222no—
538D4—22no—
539D4—22no—
540D4—41no—
541D4—41no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—22no—
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—112no—
558C2×C4—221no—
559C2×C4—222no—
560C2×C4—221no—
561C2×C4—222no—
562C2×C4—222no—
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—221no—
572C2×C4—222no—
573C2×C4—441no—
574C2×C4—441no—
575C2×C4—441no—
576C2×C4—441no—
577C2×C4—441no—
578C2×C4—441no—
579C2×C4—441no—
580C2×C4—441no—
581C2×C4—884no—
582C2×C4C2×D4×D1111yescharacteristic
583C2×C4C2×#434111yescharacteristic
584C2×C4C2×Q8×D1111yescharacteristic
585C2×C4#41×D1111yescharacteristic
586C2×C4#6704211yescharacteristic
587C2×C4#6704311yescharacteristic
588C8—22no—
589C8—41no—
590C8—222no—
591C8—441no—
592C22—42no—
593C22—42no—
594C22—42no—
595C22—81no—
596C22—81no—
597C22—81no—
598C22—81no—
599C22#1062313711yescharacteristic
600C22#1062314011yescharacteristic
601C22#1062316311yescharacteristic
602C22#1062329311yescharacteristic
603C22D11×#13511yescharacteristic
604C22#1062330411yescharacteristic
605C22#1062330611yescharacteristic
606C4—41no—
607C4—42no—
608C4—41no—
609C4—81no—
610C4—81no—
611C4—222no—
612C4—224no—
613C4—442no—
614C4—441no—
615C4—441no—
616C4—441no—
617C4—881no—
618C4—881no—
619C4#1062314211yescharacteristic
620C4D11×C22⋊Q811yescharacteristic
621C4#1062316611yescharacteristic
622C4#1062323811yescharacteristic
623C2—82no—
624C2#1307242611yescharacteristic
625C2#1307863111yescharacteristic
626C2#1307890511yescharacteristic
627C2#1308020811yescharacteristic
628C2#1308033011yescharacteristic
629C2#1308148611yescharacteristic
630C2#1308155411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2065C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenter#2065D11
hypocenterC11#26375
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2065

Complements

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

NH ≅ G/Ntype
1. C2×#10622442C2semidirect
4. #13071535C2semidirect
6. #13070103C2semidirect
7. #13069954C2semidirect
8. #13069345C2semidirect
9. #13069170C2semidirect
12. #13068881C2semidirect
13. #13068871C2semidirect
525. C11#26375semidirect

Maximal subgroups

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

subgroupindex
C2×#106224422
C2×#106223712
#130724902
#130715352
#130701392
#130701032
#130699542
#130693452
#130691702
#130689742
#130689682
#130688812
#130688712
#130688652
C11×#20652
#2637511