Finite Group Databasebeta

← #14813951

Subgroups — #14813951

Order 2816.

800 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622795C211yesmaximal, characteristic
2C2×#10622403C211yesmaximal, characteristic
3#13072395C211yesmaximal, characteristic
4Q8×C4⋊Dic11C211yesmaximal, characteristic
5#13070154C211yesmaximal, characteristic
6#13070113C211yesmaximal, characteristic
7#13070026C211yesmaximal, characteristic
8#13069861C211yesmaximal, characteristic
9#13069294C211yesmaximal, characteristic
10#13069172C211yesmaximal, characteristic
11#13068959C211yesmaximal, characteristic
12#13068957C211yesmaximal, characteristic
13#13068871C211yesmaximal, characteristic
14#13068868C211yesmaximal, characteristic
15C11×#1878C211yesmaximal, characteristic
16C22×C11×Q16C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×Q8×Dic11C2211yescharacteristic
19C2×Q8×Dic11C2211yescharacteristic
20C2×#66997C2211yescharacteristic
21C22×#4326C2211yescharacteristic
22C2×#66940C2211yescharacteristic
23C2×C11×#103C2211yescharacteristic
24C2×C11×#103C2211yescharacteristic
25C11×#391C2211yescharacteristic
26#10622843C2211yescharacteristic
27C2×#66899C2211yescharacteristic
28C2×#66899C2211yescharacteristic
29C2×#66899C2211yescharacteristic
30#10622795—24no—
31C2×#66880C2211yescharacteristic
32C2×#66880C2211yescharacteristic
33C2×Dic11⋊C8C2211yescharacteristic
34C2×C8×Dic11C2211yescharacteristic
35#10622598—21no—
36#10622598—21no—
37#10622598C2211yescharacteristic
38#10622598C2211yescharacteristic
39#10622586C2211yescharacteristic
40C2×#66874C2211yescharacteristic
41C2×#66871C2211yescharacteristic
42C2×#66871C2211yescharacteristic
43#10622548—21no—
44#10622548C2211yescharacteristic
45C4×C4⋊Dic11—21no—
46C4×C4⋊Dic11C2211yescharacteristic
47#10622542C2211yescharacteristic
48#10622403—24no—
49#10622271—21no—
50#10622270—21no—
51#10622267—21no—
52#10622265—21no—
53C11×#340C2211yescharacteristic
54C11×#336C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C22×Q8×C11C2311yescharacteristic
63C22×Dic22C2311yescharacteristic
64C2×C11×Q16—22no—
65C2×C11×Q16—22no—
66C2×C11×Q16—22no—
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C4×Q8×C11—22no—
70C4×Q8×C11—22no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C42×C11—21no—
75C2×C42×C11C2311yescharacteristic
76Q8×Dic11—22no—
77Q8×Dic11—22no—
78Q8×Dic11—41no—
79Q8×Dic11—41no—
80#66997—22no—
81#66997—41no—
82C2×#4326—22no—
83C2×#4326—22no—
84C2×#4326D414yes—
85C2×C4⋊Dic11—21no—
86C2×C4⋊Dic11—21no—
87C2×C4⋊Dic11—21no—
88C2×C4⋊Dic11—21no—
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11—21no—
91C2×C4⋊Dic11D411yescharacteristic
92C2×C4⋊Dic11D411yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×C4⋊Dic11C2311yescharacteristic
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4—21no—
98C2×Dic11⋊C4—21no—
99C2×Dic11⋊C4—21no—
100C2×C4×Dic11—21no—
101C2×C4×Dic11—21no—
102C2×C4×Dic11—21no—
103C2×C4×Dic11C2311yescharacteristic
104C2×C4×Dic11C2311yescharacteristic
105C22×C11⋊C8C2311yescharacteristic
106C22×C11⋊C8C2311yescharacteristic
107#66940—22no—
108#66940—41no—
109C11×#103—22no—
110C11×#103—22no—
111C11×#95—21no—
112C11×#95—21no—
113#66899—22no—
114#66899—22no—
115#66899—41no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95D411yescharacteristic
124C11⋊#95D411yescharacteristic
125#66880—22no—
126#66880—22no—
127Dic11⋊C8—22no—
128C8×Dic11—22no—
129#66874—22no—
130#66871—22no—
131#66871—41no—
132#26171—111nomaximal, Sylow
133C2×Q8×C11—21no—
134C2×Q8×C11—21no—
135C2×Q8×C11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11—21no—
138C2×Q8×C11—21no—
139C2×Q8×C11—21no—
140C2×Q8×C11—21no—
141C2×Q8×C11—21no—
142C2×Q8×C11C2×D412yes—
143C2×Q8×C11#4112yes—
144C2×Q8×C11#4112yes—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2411yescharacteristic
152C22×Dic11—21no—
153C22×Dic11—21no—
154C22×Dic11—21no—
155C22×Dic11—21no—
156C22×Dic11C2×D411yescharacteristic
157C22×Dic11C2×D411yescharacteristic
158C22×Dic11C2×D411yescharacteristic
159C22×Dic11C2×D411yescharacteristic
160C2×Dic22—21no—
161C2×Dic22—21no—
162C2×Dic22—21no—
163C2×Dic22—21no—
164C2×Dic22—21no—
165C2×Dic22C2×D412yes—
166C11×Q16—44no—
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—24no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4#4112yes—
178C42×C11—24no—
179C42×C11—21no—
180C42×C11—21no—
181#4326—28no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11—21no—
186C4⋊Dic11—21no—
187C4⋊Dic11—21no—
188C4⋊Dic11—41no—
189C4⋊Dic11—42no—
190C4⋊Dic11—42no—
191C4⋊Dic11—42no—
192C4⋊Dic11—81no—
193C4⋊Dic11—81no—
194C4⋊Dic11—81no—
195C4⋊Dic11Q1614yescomplemented
196Dic11⋊C4—42no—
197Dic11⋊C4—42no—
198Dic11⋊C4—42no—
199Dic11⋊C4—42no—
200C4×Dic11—21no—
201C4×Dic11—21no—
202C4×Dic11—21no—
203C4×Dic11—21no—
204C4×Dic11—42no—
205C4×Dic11—42no—
206C4×Dic11—42no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8C2×D412yes—
213C2×#462—111no—
214C2×C4×Q16—111no—
215#2446—111no—
216Q8×C4⋊C4—111no—
217#2095—111no—
218#2087—111no—
219#2072—111no—
220#2043—111no—
221#1933—111no—
222#1916—111no—
223#1878—111no—
224#1878—111no—
225#1878D1111yescharacteristic
226#1863—111no—
227#1863—111no—
228C23×C11C22×D411yescharacteristic
229Q8×C11—22no—
230Q8×C11—22no—
231Q8×C11—22no—
232Q8×C11—41no—
233Q8×C11—41no—
234Q8×C11—41no—
235Q8×C11—41no—
236Q8×C11#12314yes—
237C2×C4×C11—21no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—22no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
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×C11C2×Q1612yes—
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—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—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—41no—
282C2×Dic11—41no—
283C2×Dic11C2×Q1612yes—
284C2×Dic11C2×Q1612yes—
285Dic22—22no—
286Dic22—22no—
287Dic22—41no—
288Dic22—41no—
289C8×C11—41no—
290C8×C11—41no—
291C11⋊C8—22no—
292C11⋊C8—41no—
293C22×Q16—111no—
294C22×Q16C2×D1111yescharacteristic
295C2×C4⋊Q8—111no—
296C2×C4×Q8—111no—
297C2×C4×Q8—111no—
298C2×C4×Q8—111no—
299C2×C4×Q8C2×D1111yescharacteristic
300#462—224no—
301C4×Q16—224no—
302C2×#107—111no—
303C2×#107—111no—
304C2×C4⋊C8—111no—
305C2×#103—111no—
306C2×#103—111no—
307C2×#103—111no—
308C2×#103—111no—
309C2×#103—111no—
310C2×#103—111no—
311C2×#103C2×D1111yescharacteristic
312C2×#103C2×D1111yescharacteristic
313C2×C4×C8—111no—
314#400—221no—
315#398—221no—
316#391—111no—
317#391—111no—
318#391C2×D1111yescharacteristic
319#389—111no—
320#389—111no—
321#389—111no—
322#389—221no—
323#389—221no—
324#387—221no—
325#387—221no—
326#384—111no—
327#384—221no—
328C4×C4⋊C4—111no—
329C4×C4⋊C4—221no—
330#340—111no—
331#340—111no—
332#340—111no—
333#340C2×D1111yescharacteristic
334#336—111no—
335#336—111no—
336#336—111no—
337#336C2×D1111yescharacteristic
338C22×C11#52511yescharacteristic
339C22×C11D4211yescharacteristic
340C22×C11#54811yescharacteristic
341C22×C11C22×Q1611yescharacteristic
342C22×C11#57511yescharacteristic
343C22×C11#57711yescharacteristic
344C22×C11#57811yescharacteristic
345C4×C11—22no—
346C4×C11—24no—
347C4×C11—41no—
348C4×C11—42no—
349C4×C11—81no—
350C4×C11—81no—
351C4×C11C2×#12311yescharacteristic
352C4×C11#53911yescharacteristic
353C4×C11#54711yescharacteristic
354C4×C11#55311yescharacteristic
355Dic11—22no—
356Dic11—22no—
357Dic11—42no—
358Dic11—41no—
359Dic11—41no—
360Dic11—81no—
361Dic11—81no—
362Dic11—81no—
363C22×Q8—111no—
364C22×Q8C22×D1111yescharacteristic
365C22×Q8C22×D1111yescharacteristic
366C2×Q16—22no—
367C2×Q16—22no—
368C2×Q16—22no—
369C2×Q16—114no—
370C2×Q16—222no—
371C2×Q16—222no—
372C22×C8—111no—
373C22×C8—111no—
374C22×C8C22×D1111yescharacteristic
375C22×C8C22×D1111yescharacteristic
376C4⋊Q8—222no—
377C4⋊Q8—441no—
378C4×Q8—22no—
379C4×Q8—22no—
380C4×Q8—222no—
381C4×Q8—222no—
382C4×Q8—222no—
383C4×Q8—441no—
384C4×Q8—441no—
385C4×Q8—441no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—111no—
388C2×C4⋊C4—111no—
389C2×C4⋊C4—111no—
390C2×C4⋊C4—111no—
391C2×C4⋊C4—111no—
392C2×C4⋊C4—221no—
393C2×C4⋊C4—221no—
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×C42—21no—
405C2×C42—111no—
406C2×C42—111no—
407C2×C42—221no—
408C2×C42—221no—
409C2×C42—221no—
410C2×C42C22×D1111yescharacteristic
411#107—222no—
412#107—441no—
413C4⋊C8—222no—
414#103—22no—
415#103—22no—
416#103—222no—
417#103—222no—
418#103—222no—
419#103—222no—
420#103—222no—
421#103—441no—
422C4×C8—222no—
423#95—21no—
424#95—21no—
425#95—111no—
426#95—111no—
427#95—221no—
428#95—221no—
429#95—221no—
430#95—221no—
431#95—221no—
432#95—221no—
433#95—221no—
434C2×C11#244311yescharacteristic
435C2×C11#310411yescharacteristic
436C2×C11#312011yescharacteristic
437C2×C11#327111yescharacteristic
438C2×C11D4×Q1611yescharacteristic
439C2×C11#336311yescharacteristic
440C2×C11#337711yescharacteristic
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—112no—
451C2×Q8—221no—
452C2×Q8—221no—
453C2×Q8—221no—
454C2×Q8—221no—
455C2×Q8—221no—
456C2×Q8#433912yes—
457C2×Q8D4×D1112yes—
458C2×Q8#434112yes—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—111no—
464C22×C4—111no—
465C22×C4—111no—
466C22×C4—111no—
467C22×C4—221no—
468C22×C4—221no—
469C22×C4—221no—
470C22×C4—221no—
471C22×C4D4×D1111yescharacteristic
472C22×C4D4×D1111yescharacteristic
473C22×C4C23×D1111yescharacteristic
474Q16—44no—
475Q16—228no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—112no—
483C2×C8—221no—
484C2×C8—221no—
485C2×C8—221no—
486C2×C8—221no—
487C2×C8—221no—
488C4⋊C4—24no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—114no—
493C4⋊C4—221no—
494C4⋊C4—221no—
495C4⋊C4—221no—
496C4⋊C4—221no—
497C4⋊C4—221no—
498C4⋊C4—221no—
499C4⋊C4—441no—
500C4⋊C4—442no—
501C4⋊C4—442no—
502C4⋊C4—442no—
503C4⋊C4—442no—
504C4⋊C4—442no—
505C4⋊C4—442no—
506C4⋊C4—442no—
507C4⋊C4—881no—
508C4⋊C4—881no—
509C4⋊C4—881no—
510C4⋊C4#434112yes—
511C42—24no—
512C42—21no—
513C42—21no—
514C42—221no—
515C42—221no—
516C42—221no—
517C42—221no—
518C42—442no—
519C42—442no—
520C42—442no—
521C11#2617111yescharacteristic, complemented, Sylow
522C23C2×D4×D1111yescharacteristic
523Q8—22no—
524Q8—22no—
525Q8—22no—
526Q8—41no—
527Q8—41no—
528Q8—41no—
529Q8—41no—
530Q8—222no—
531Q8—222no—
532Q8—441no—
533Q8—441no—
534Q8#6693614yes—
535C2×C4—21no—
536C2×C4—22no—
537C2×C4—21no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—22no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—112no—
553C2×C4—112no—
554C2×C4—221no—
555C2×C4—221no—
556C2×C4—221no—
557C2×C4—221no—
558C2×C4—221no—
559C2×C4—221no—
560C2×C4—221no—
561C2×C4—221no—
562C2×C4—221no—
563C2×C4—221no—
564C2×C4—222no—
565C2×C4—441no—
566C2×C4—441no—
567C2×C4—441no—
568C2×C4—441no—
569C2×C4—441no—
570C2×C4—441no—
571C2×C4—441no—
572C2×C4—441no—
573C2×C4—441no—
574C2×C4—441no—
575C2×C4—441no—
576C2×C4Q16×D1112yes—
577C2×C4C2×#433911yescharacteristic
578C2×C4C2×D4×D1111yescharacteristic
579C2×C4C2×#434111yescharacteristic
580C2×C4C2×#434111yescharacteristic
581C2×C4#6704211yescharacteristic
582C2×C4#6704311yescharacteristic
583C8—41no—
584C8—41no—
585C8—222no—
586C8—441no—
587C22#1062308311yescharacteristic
588C22#1062311711yescharacteristic
589C22#1062314011yescharacteristic
590C22C2×Q16×D1111yescharacteristic
591C22#1062330111yescharacteristic
592C22#1062330811yescharacteristic
593C22#1062331011yescharacteristic
594C4—22no—
595C4—24no—
596C4—41no—
597C4—42no—
598C4—81no—
599C4—81no—
600C4—222no—
601C4—222no—
602C4—441no—
603C4—441no—
604C4—442no—
605C4—881no—
606C4—881no—
607C4—881no—
608C4C2×#6693611yescharacteristic
609C4#1062309611yescharacteristic
610C4#1062314211yescharacteristic
611C4#1062319611yescharacteristic
612C2#1307235711yescharacteristic
613C2#1307865011yescharacteristic
614C2#1307882311yescharacteristic
615C2#1308020711yescharacteristic
616C2#1308036311yescharacteristic
617C2#1308129211yescharacteristic
618C2#1308146311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1878C2
socle, prime radicalC23×C11C22×D4
hypercenter#1878D11
hypocenterC11#26171
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1878

Complements

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

NH ≅ G/Ntype
195. C4⋊Dic11Q16semidirect
521. C11#26171semidirect

Maximal subgroups

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

subgroupindex
C2×#106227952
C2×#106224032
#130723952
Q8×C4⋊Dic112
#130701542
#130701132
#130700262
#130698612
#130692942
#130691722
#130689592
#130689572
#130688712
#130688682
C11×#18782
#2617111