Finite Group Databasebeta

← #14764432

Subgroups — #14764432

Order 2816.

800 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071057C211yesmaximal, characteristic
2#13069222C211yesmaximal, characteristic, complemented
3#13069220C211yesmaximal, characteristic, complemented
4#13069175C211yesmaximal, characteristic, complemented
5#13068907C211yesmaximal, characteristic
6#13068907C211yesmaximal, characteristic
7#13068795C211yesmaximal, characteristic, complemented
8#13068792C211yesmaximal, characteristic, complemented
9#13068760C211yesmaximal, characteristic, complemented
10#13068734C211yesmaximal, characteristic, complemented
11#13068686C211yesmaximal, characteristic, complemented
12#13068597C211yesmaximal, characteristic, complemented
13C4×(C2×D11)⋊C8C211yesmaximal, characteristic, complemented
14D11×#336C211yesmaximal, characteristic, complemented
15C11×#1916C211yesmaximal, characteristic, complemented
16C22×C8×D11C2211yescharacteristic
17C22×C8×D11C2211yescharacteristic
18C2×C4×D44C2211yescharacteristic
19C2×#66925C2211yescharacteristic
20C2×C42×D11C2211yescharacteristic
21C2×C11×C4⋊C8C2211yescharacteristic
22C2×C4×C8×C11C2211yescharacteristic
23C4×C11×C4⋊C4C2211yescharacteristic
24C2×(C2×D11)⋊C8C2211yescharacteristic
25C2×(C2×D11)⋊C8C2211yescharacteristic
26C2×(C2×D11)⋊C8C2211yescharacteristic
27C2×(C2×D11)⋊C8C2211yescharacteristic
28C2×(C2×D11)⋊C8C2211yescharacteristic
29C2×(C2×D11)⋊C8C2211yescharacteristic
30C2×Dic11⋊C8C2211yescharacteristic
31C2×Dic11⋊C8C2211yescharacteristic
32#10622603C411yescharacteristic
33#10622603C411yescharacteristic
34#10622602C411yescharacteristic
35#10622602C411yescharacteristic
36C4×(C2×D11)⋊C4C2211yescharacteristic
37C4×(C2×D11)⋊C4C2211yescharacteristic
38#10622545C2211yescharacteristic
39C2×C4⋊(C11⋊C8)C2211yescharacteristic
40C2×C4×C11⋊C8C2211yescharacteristic
41#10622278C411yescharacteristic
42#10622278C411yescharacteristic
43#10622267C411yescharacteristic
44#10622267C411yescharacteristic
45C11×#336C2211yescharacteristic
46C11×#336C2211yescharacteristic
47C11×#336C2211yescharacteristic
48C11×#336C2211yescharacteristic
49#10622188C2211yescharacteristic
50#10622188C2211yescharacteristic
51#10622188C2211yescharacteristic
52#10622188C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622162C2211yescharacteristic
56#10622162C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×D44C2×C411yescharacteristic
60C22×C4×D11C2×C411yescharacteristic
61C22×C4×D11C2×C411yescharacteristic
62C22×C4×D11C2311yescharacteristic
63C22×C4×D11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C2×C11×C4⋊C4C2×C411yescharacteristic
69C2×C11×C4⋊C4C2×C411yescharacteristic
70C2×C42×C11C2311yescharacteristic
71C2×C42×C11C2311yescharacteristic
72C2×C42×C11C2311yescharacteristic
73C2×(C2×D11)⋊C4C2×C411yescharacteristic
74C2×(C2×D11)⋊C4C2×C411yescharacteristic
75C2×(C2×D11)⋊C4C2×C411yescharacteristic
76C2×(C2×D11)⋊C4C2×C411yescharacteristic
77C2×(C2×D11)⋊C4C2×C411yescharacteristic
78C2×(C2×D11)⋊C4C2×C411yescharacteristic
79C2×(C2×D11)⋊C4C2×C411yescharacteristic
80C2×(C2×D11)⋊C4C2×C411yescharacteristic
81C2×C4⋊Dic11C2×C411yescharacteristic
82C2×Dic11⋊C4C2×C411yescharacteristic
83C2×Dic11⋊C4C2×C411yescharacteristic
84C2×C4×Dic11C2×C411yescharacteristic
85C2×C4×Dic11C2×C411yescharacteristic
86C2×C4×Dic11C2311yescharacteristic
87C2×C4×Dic11C2311yescharacteristic
88C22×C11⋊C8C2311yescharacteristic
89C22×C11⋊C8C2311yescharacteristic
90C22×C11⋊C8C2311yescharacteristic
91C22×C11⋊C8C2311yescharacteristic
92C2×C8×D11—22no—
93C2×C8×D11—22no—
94C2×C8×D11—41no—
95C2×C8×D11—41no—
96C2×C8×D11—41no—
97C2×C8×D11—41no—
98C4×D44—22no—
99C4×D44—22no—
100#66925—41no—
101#66925—41no—
102C42×D11—41no—
103C42×D11—41no—
104C11×C4⋊C8—41no—
105C4×C8×C11—41no—
106C11×#95C2×C411yescharacteristic
107C11×#95C2×C411yescharacteristic
108C11⋊#95C2×C411yescharacteristic
109C11⋊#95C2×C411yescharacteristic
110C11⋊#95C2×C411yescharacteristic
111C11⋊#95C2×C411yescharacteristic
112C11⋊#95C2×C411yescharacteristic
113C11⋊#95C2×C411yescharacteristic
114C11⋊#95C2×C411yescharacteristic
115C11⋊#95C2×C411yescharacteristic
116(C2×D11)⋊C8—22no—
117(C2×D11)⋊C8—22no—
118(C2×D11)⋊C8—41no—
119(C2×D11)⋊C8—41no—
120(C2×D11)⋊C8—41no—
121(C2×D11)⋊C8—41no—
122Dic11⋊C8—41no—
123Dic11⋊C8—41no—
124C4⋊(C11⋊C8)—41no—
125C4×C11⋊C8—41no—
126#21997—111nomaximal, Sylow
127C23×D11C22×C411yescharacteristic
128C23×D11C22×C411yescharacteristic
129C22×C4×C11C22×C411yescharacteristic
130C22×C4×C11C22×C411yescharacteristic
131C22×C4×C11C22×C411yescharacteristic
132C22×C4×C11C22×C411yescharacteristic
133C22×C4×C11C22×C411yescharacteristic
134C22×C4×C11C22×C411yescharacteristic
135C22×C4×C11C2411yescharacteristic
136C22×Dic11C22×C411yescharacteristic
137C22×Dic11C22×C411yescharacteristic
138C22×Dic11C22×C411yescharacteristic
139C22×Dic11C22×C411yescharacteristic
140C22×Dic11C22×C411yescharacteristic
141C22×Dic11C22×C411yescharacteristic
142C2×D44—22no—
143C2×D44—22no—
144C2×D44—22no—
145C2×C4×D11—22no—
146C2×C4×D11—22no—
147C2×C4×D11—22no—
148C2×C4×D11—22no—
149C2×C4×D11—21no—
150C2×C4×D11—21no—
151C2×C4×D11—21no—
152C2×C4×D11—21no—
153C2×C4×D11—21no—
154C2×C4×D11—21no—
155C2×C4×D11—21no—
156C2×C4×D11—21no—
157C2×C4×D11—21no—
158C2×C4×D11—21no—
159C2×C4×D11—41no—
160C2×C4×D11—41no—
161C2×C4×D11#4112yes—
162C2×C4×D11#4112yes—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C11×C4⋊C4—22no—
176C11×C4⋊C4—22no—
177C42×C11—21no—
178C42×C11—21no—
179C42×C11—21no—
180C42×C11—21no—
181C42×C11—21no—
182C42×C11—21no—
183(C2×D11)⋊C4—22no—
184(C2×D11)⋊C4—22no—
185(C2×D11)⋊C4—22no—
186(C2×D11)⋊C4—22no—
187(C2×D11)⋊C4—22no—
188(C2×D11)⋊C4—22no—
189(C2×D11)⋊C4—41no—
190(C2×D11)⋊C4—41no—
191C4⋊Dic11—22no—
192Dic11⋊C4—41no—
193Dic11⋊C4—41no—
194C4×Dic11—21no—
195C4×Dic11—21no—
196C4×Dic11—21no—
197C4×Dic11—21no—
198C4×Dic11—41no—
199C4×Dic11—41no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C8×D11—44no—
213C8×D11—44no—
214#2290—111no—
215#1923—111no—
216#1923—111no—
217#1916—111no—
218#1916D1111yescharacteristic, complemented
219#1869—111no—
220#1869—111no—
221#1850—111no—
222#1850—111no—
223#1840—111no—
224#1832—111no—
225#1818—111no—
226#1798—111no—
227C4×C22⋊C8—111no—
228C2×#336—111no—
229C23×C11C23×C411yescharacteristic
230C22×D11—21no—
231C22×D11—21no—
232C22×D11—21no—
233C22×D11—21no—
234C22×D11—21no—
235C22×D11—21no—
236C22×D11—21no—
237C22×D11—21no—
238C22×D11—21no—
239C22×D11—21no—
240C22×D11—21no—
241C22×D11#11712yes—
242C22×D11#13112yes—
243C22×D11#13112yes—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11#13112yes—
261C2×C4×C11#13112yes—
262C2×C4×C11C2×#4111yescharacteristic
263C2×C4×C11C2×#4111yescharacteristic
264C2×C4×C11H(5,𝔽2)11yescharacteristic
265C2×C4×C11H(5,𝔽2)11yescharacteristic
266C2×C4×C11H(5,𝔽2)11yescharacteristic
267C2×C4×C112−1+411yescharacteristic
268C2×Dic11—21no—
269C2×Dic11—21no—
270C2×Dic11—21no—
271C2×Dic11—21no—
272C2×Dic11—21no—
273C2×Dic11—21no—
274C2×Dic11—21no—
275C2×Dic11—21no—
276C2×Dic11—21no—
277C2×Dic11—21no—
278C2×Dic11—21no—
279C2×Dic11—21no—
280C2×Dic11—21no—
281C2×Dic11—21no—
282C2×Dic11—21no—
283C2×Dic11—21no—
284C2×Dic11—21no—
285C2×Dic11#11712yes—
286D44—44no—
287C4×D11—22no—
288C4×D11—22no—
289C4×D11—22no—
290C4×D11—22no—
291C4×D11—44no—
292C4×D11—44no—
293C4×D11—41no—
294C4×D11—41no—
295C4×D11—41no—
296C4×D11—41no—
297C8×C11—41no—
298C8×C11—41no—
299C8×C11—41no—
300C8×C11—41no—
301C11⋊C8—41no—
302C11⋊C8—41no—
303C11⋊C8—41no—
304C11⋊C8—41no—
305C23×C8—111no—
306C23×C8—111no—
307C2×C4×D4—111no—
308C2×#117—111no—
309C22×C42—111no—
310C2×C4⋊C8—111no—
311C2×C4⋊C8—111no—
312C2×C4⋊C8—111no—
313C2×C4⋊C8C2×D1111yescharacteristic
314C2×C22⋊C8—111no—
315C2×C22⋊C8—111no—
316C2×C22⋊C8—111no—
317C2×C22⋊C8—111no—
318C2×C22⋊C8—111no—
319C2×C22⋊C8—111no—
320C2×C4×C8—111no—
321C2×C4×C8C2×D1111yescharacteristic
322#388—111no—
323#388—111no—
324#387—111no—
325#387—111no—
326#386—111no—
327#386—111no—
328#385—111no—
329#385—111no—
330C4×C4⋊C4C2×D1111yescharacteristic
331C4×C22⋊C4—111no—
332C4×C22⋊C4—111no—
333#376—111no—
334#336—111no—
335#336—111no—
336#336—111no—
337#336—111no—
338#336—111no—
339#336—111no—
340#336—111no—
341#336—111no—
342#336—111no—
343#336—111no—
344#336C2×D1111yescharacteristic
345#336C2×D1111yescharacteristic
346#336C2×D1111yescharacteristic
347#336C2×D1111yescharacteristic
348C22×C11C2×#11711yescharacteristic
349C22×C11#51811yescharacteristic
350C22×C11#52011yescharacteristic
351C22×C11C2×#13111yescharacteristic
352C22×C11C2×#13111yescharacteristic
353C22×C11C2×#13111yescharacteristic
354C22×C11C2×#13111yescharacteristic
355C2×D11—22no—
356C2×D11—22no—
357C2×D11—22no—
358C2×D11—22no—
359C2×D11—22no—
360C2×D11—22no—
361C2×D11—41no—
362C2×D11—41no—
363C2×D11—41no—
364C2×D11—41no—
365C2×D11—41no—
366C2×D11—41no—
367C2×D11—41no—
368C2×D11#43314yes—
369C4×C11—22no—
370C4×C11—22no—
371C4×C11—41no—
372C4×C11—41no—
373C4×C11—41no—
374C4×C11—41no—
375C4×C11#53811yescharacteristic
376C4×C11#53811yescharacteristic
377C4×C11#53911yescharacteristic
378C4×C11#53911yescharacteristic
379Dic11—22no—
380Dic11—41no—
381Dic11—41no—
382Dic11—41no—
383Dic11—41no—
384Dic11—41no—
385C22×D4—111no—
386C23×C4—111no—
387C23×C4—111no—
388C23×C4—111no—
389C23×C4—111no—
390C22×C8—111no—
391C22×C8—111no—
392C22×C8—111no—
393C22×C8—111no—
394C22×C8—222no—
395C22×C8—222no—
396C22×C8—441no—
397C22×C8—441no—
398C22×C8—441no—
399C22×C8—441no—
400C22×C8C22×D1111yescharacteristic
401C22×C8C22×D1111yescharacteristic
402C22×C8C22×D1111yescharacteristic
403C22×C8C22×D1111yescharacteristic
404C4×D4—222no—
405C4×D4—222no—
406#117—441no—
407#117—441no—
408C2×C4⋊C4—111no—
409C2×C4⋊C4—111no—
410C2×C4⋊C4—111no—
411C2×C4⋊C4C4×D1111yescharacteristic
412C2×C4⋊C4C4×D1111yescharacteristic
413C2×C22⋊C4—111no—
414C2×C22⋊C4—111no—
415C2×C22⋊C4—111no—
416C2×C22⋊C4—111no—
417C2×C22⋊C4—111no—
418C2×C22⋊C4—111no—
419C2×C22⋊C4—111no—
420C2×C22⋊C4—111no—
421C2×C42—111no—
422C2×C42—111no—
423C2×C42—111no—
424C2×C42—111no—
425C2×C42—441no—
426C2×C42—441no—
427C2×C42C22×D1111yescharacteristic
428C2×C42C22×D1111yescharacteristic
429C2×C42C22×D1111yescharacteristic
430C4⋊C8—41no—
431C4⋊C8—441no—
432C4⋊C8—441no—
433C4⋊C8—441no—
434C22⋊C8—222no—
435C22⋊C8—222no—
436C22⋊C8—441no—
437C22⋊C8—441no—
438C22⋊C8—441no—
439C22⋊C8—441no—
440C4×C8—41no—
441C4×C8—441no—
442#95—111no—
443#95—111no—
444#95—111no—
445#95—111no—
446#95—111no—
447#95—111no—
448#95—111no—
449#95—111no—
450#95C4×D1111yescharacteristic
451#95C4×D1111yescharacteristic
452C2×C11#231811yescharacteristic
453C2×C11C2×#43311yescharacteristic
454C2×C11#292211yescharacteristic
455C2×C11#297711yescharacteristic
456C2×C11#297711yescharacteristic
457C2×C11#299411yescharacteristic
458C2×C11#299411yescharacteristic
459D11—24no—
460D11—81no—
461C24—111no—
462C24—111no—
463C2×D4—222no—
464C2×D4—222no—
465C2×D4—222no—
466C22×C4—111no—
467C22×C4—112no—
468C22×C4—112no—
469C22×C4—111no—
470C22×C4—111no—
471C22×C4—111no—
472C22×C4—111no—
473C22×C4—111no—
474C22×C4—222no—
475C22×C4—222no—
476C22×C4—221no—
477C22×C4—221no—
478C22×C4—221no—
479C22×C4—221no—
480C22×C4—222no—
481C22×C4—222no—
482C22×C4—221no—
483C22×C4—221no—
484C22×C4—221no—
485C22×C4—221no—
486C22×C4—221no—
487C22×C4—221no—
488C22×C4—441no—
489C22×C4—441no—
490C22×C4C2×C4×D1111yescharacteristic
491C22×C4C2×C4×D1111yescharacteristic
492C22×C4C2×C4×D1111yescharacteristic
493C22×C4C2×C4×D1111yescharacteristic
494C22×C4C2×C4×D1111yescharacteristic
495C22×C4C2×C4×D1111yescharacteristic
496C22×C4C23×D1111yescharacteristic
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—221no—
510C2×C8—221no—
511C2×C8—221no—
512C2×C8—221no—
513C2×C8—221no—
514C2×C8—221no—
515C2×C8—221no—
516C2×C8—221no—
517C2×C8—221no—
518C2×C8—221no—
519C2×C8—221no—
520C2×C8—221no—
521C2×C8—444no—
522C2×C8—444no—
523C4⋊C4—22no—
524C4⋊C4—22no—
525C4⋊C4—222no—
526C4⋊C4—441no—
527C4⋊C4—441no—
528C22⋊C4—222no—
529C22⋊C4—222no—
530C22⋊C4—222no—
531C22⋊C4—222no—
532C22⋊C4—222no—
533C22⋊C4—222no—
534C22⋊C4—441no—
535C22⋊C4—441no—
536C42—21no—
537C42—21no—
538C42—21no—
539C42—21no—
540C42—21no—
541C42—21no—
542C42—221no—
543C42—221no—
544C42—221no—
545C42—221no—
546C42—441no—
547C42—441no—
548C11#2199711yescharacteristic, complemented, Sylow
549C23—112no—
550C23—112no—
551C23—112no—
552C23—221no—
553C23—221no—
554C23—221no—
555C23—221no—
556C23—221no—
557C23—221no—
558C23—221no—
559C23—221no—
560C23—221no—
561C23—221no—
562C23—221no—
563C23C22×C4×D1111yescharacteristic
564D4—444no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—112no—
582C2×C4—221no—
583C2×C4—221no—
584C2×C4—222no—
585C2×C4—222no—
586C2×C4—222no—
587C2×C4—222no—
588C2×C4—221no—
589C2×C4—221no—
590C2×C4—221no—
591C2×C4—221no—
592C2×C4—221no—
593C2×C4—221no—
594C2×C4—221no—
595C2×C4—221no—
596C2×C4—221no—
597C2×C4—221no—
598C2×C4—221no—
599C2×C4—221no—
600C2×C4—221no—
601C2×C4—221no—
602C2×C4—221no—
603C2×C4—444no—
604C2×C4—444no—
605C2×C4—441no—
606C2×C4—441no—
607C2×C4—441no—
608C2×C4—441no—
609C2×C4#6695412yes—
610C2×C4#6696012yes—
611C2×C4#6703711yescharacteristic
612C2×C4#6704011yescharacteristic
613C2×C4#41×D1111yescharacteristic
614C2×C4#41×D1111yescharacteristic
615C2×C4#6704211yescharacteristic
616C2×C4#6704211yescharacteristic
617C8—41no—
618C8—41no—
619C8—41no—
620C8—41no—
621C8—441no—
622C8—441no—
623C8—441no—
624C8—441no—
625C22—114no—
626C22—222no—
627C22—222no—
628C22—222no—
629C22—222no—
630C22—222no—
631C22—222no—
632C22—441no—
633C22—441no—
634C22—441no—
635C22—441no—
636C22—441no—
637C22—441no—
638C22—441no—
639C22D11×#11711yescharacteristic
640C22#1062307611yescharacteristic
641C22#1062310511yescharacteristic
642C22C2×#6695411yescharacteristic
643C22C2×#6696011yescharacteristic
644C22D11×#13111yescharacteristic
645C22D11×#13111yescharacteristic
646C4—22no—
647C4—22no—
648C4—41no—
649C4—41no—
650C4—41no—
651C4—41no—
652C4—222no—
653C4—441no—
654C4—441no—
655C4—441no—
656C4—441no—
657C4—441no—
658C4#1062316911yescharacteristic
659C4#1062318811yescharacteristic
660C4#1062322311yescharacteristic
661C4#1062323511yescharacteristic
662C2—224no—
663C2—881no—
664C2#1307124811yescharacteristic
665C2D11×#43311yescharacteristic
666C2#1307725511yescharacteristic
667C2#1307766711yescharacteristic
668C2#1307766911yescharacteristic
669C2#1307777511yescharacteristic
670C2#1307777911yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1916C2
prime radicalC22×D44C2×C4
cosocleC22×C4×C11C24
hypercenter#1916D11
hypocenterC11#21997
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1916

Complements

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

NH ≅ G/Ntype
2. #13069222C2semidirect
3. #13069220C2semidirect
4. #13069175C2semidirect
7. #13068795C2semidirect
8. #13068792C2semidirect
9. #13068760C2semidirect
10. #13068734C2semidirect
11. #13068686C2semidirect
12. #13068597C2semidirect
13. C4×(C2×D11)⋊C8C2semidirect
14. D11×#336C2semidirect
15. C11×#1916C2semidirect
218. #1916D11semidirect
548. C11#21997semidirect

Maximal subgroups

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

subgroupindex
#130710572
#130692222
#130692202
#130691752
#130689072
#130687952
#130687922
#130687602
#130687342
#130686862
#130685972
C4×(C2×D11)⋊C82
D11×#3362
C11×#19162
#2199711