Finite Group Databasebeta

← #14723705

Subgroups — #14723705

Order 2816.

766 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078614C211yesmaximal, characteristic
2#13077323C211yesmaximal, characteristic, complemented
3C8×D4×D11C211yesmaximal, characteristic, complemented
4#13067483C211yesmaximal, characteristic, complemented
5#13067481C211yesmaximal, characteristic, complemented
6#13067479C211yesmaximal, characteristic, complemented
7#13067477C211yesmaximal, characteristic, complemented
8#13067441C211yesmaximal, characteristic, complemented
9#13067438C211yesmaximal, characteristic, complemented
10#13067438C211yesmaximal, characteristic, complemented
11#13067385C211yesmaximal, characteristic, complemented
12#13067039C211yesmaximal, characteristic, complemented
13#13067013C211yesmaximal, characteristic, complemented
14#13066907C211yesmaximal, characteristic, complemented
15C11×#1580C211yesmaximal, characteristic, complemented
16C2×#66954—21no—
17C22×C8×D11—21no—
18#10623079C2211yescharacteristic
19C4×D4×D11C2211yescharacteristic
20C4×C11×D8C2211yescharacteristic
21C8×D4×C11C2211yescharacteristic
22C8×D4×C11C2211yescharacteristic, complemented
23#10622769C411yescharacteristic
24#10622763C411yescharacteristic
25C8×C22⋊D11—21no—
26C8×C22⋊D11—21no—
27C4×#4323C2211yescharacteristic
28C4×#4323C2211yescharacteristic
29#10622625C2211yescharacteristic, complemented
30D4×C11⋊C8C2211yescharacteristic
31#10622503C411yescharacteristic
32#10622495C411yescharacteristic
33#10622451C2211yescharacteristic, complemented
34#10622450C2211yescharacteristic
35#10622447C2211yescharacteristic
36D11×C4⋊C8C2211yescharacteristic
37#10622399C411yescharacteristic
38#10622387C411yescharacteristic
39#10622386C411yescharacteristic
40#10622372C411yescharacteristic
41#10622342—21no—
42#10622340—21no—
43(C22⋊D11)⋊C8—21no—
44D11×C22⋊C8—21no—
45C4×D88C2211yescharacteristic
46C8×D44C2211yescharacteristic
47C8×D44C2211yescharacteristic, complemented
48#10622298C2211yescharacteristic
49#10622298C2211yescharacteristic
50C4×C8×D11C2211yescharacteristic
51C11×#334C2211yescharacteristic, complemented
52C11×D4⋊C8C2211yescharacteristic
53C11×D4⋊C8C2211yescharacteristic, complemented
54C11×#322C2211yescharacteristic, complemented
55D4⋊(C11⋊C8)C2211yescharacteristic
56D4⋊(C11⋊C8)C2211yescharacteristic, complemented
57#10622121C2211yescharacteristic
58#10622121C2211yescharacteristic, complemented
59#10622118C2211yescharacteristic, complemented
60#10622118C2211yescharacteristic, complemented
61#10622097C2211yescharacteristic
62#10622097C2211yescharacteristic, complemented
63#10622095C2211yescharacteristic, complemented
64#10622093C2211yescharacteristic, complemented
65#10622092C2211yescharacteristic, complemented
66#10622092C2211yescharacteristic, complemented
67C2×D4×D11C2×C411yescharacteristic
68C2×#4339—21no—
69C22×C4×D11—21no—
70C2×C11×D8C2×C411yescharacteristic
71C22×C8×C11—21no—
72C22×C8×C11—21no—
73C4×D4×C11C2311yescharacteristic
74C4×D4×C11C2311yescharacteristic
75#66993C2×C411yescharacteristic
76#66991C2×C411yescharacteristic
77D4×Dic11C2×C411yescharacteristic
78C2×#4323C2×C411yescharacteristic
79C2×#4323C2×C411yescharacteristic
80C4×C22⋊D11—21no—
81C4×C22⋊D11—21no—
82C2×#4318—21no—
83C22×C11⋊C8—21no—
84C2×D88C2×C411yescharacteristic
85#66954—44no—
86C2×#4313—21no—
87C2×#4313—21no—
88C2×C8×D11—21no—
89C2×C8×D11—21no—
90C2×C8×D11—21no—
91C2×C8×D11—21no—
92C2×C8×D11—44no—
93C2×C8×D11D411yescharacteristic
94C2×C8×D11D411yescharacteristic
95#66948C2×C411yescharacteristic
96#66946C2×C411yescharacteristic
97C4⋊C4×D11C2×C411yescharacteristic
98#66941C2×C411yescharacteristic
99#66938—21no—
100#66937—21no—
101(C22⋊D11)⋊C4—21no—
102C22⋊C4×D11—21no—
103C4×D44C2311yescharacteristic
104C4×D44C2311yescharacteristic
105C42×D11C2311yescharacteristic
106C11×#107C2×C411yescharacteristic
107C11×C4⋊C8C2311yescharacteristic
108C11×C4⋊C8C2311yescharacteristic
109C11×#102C2×C411yescharacteristic
110C11×#102C2×C411yescharacteristic
111C11×C22⋊C8—21no—
112C11×C22⋊C8—21no—
113C4×C8×C11C2311yescharacteristic
114C4×C8×C11C2311yescharacteristic
115C4×C8×C11C2311yescharacteristic
116#66896C2×C411yescharacteristic
117#66896C2×C411yescharacteristic
118C22⋊(C11⋊C8)—21no—
119C22⋊(C11⋊C8)—21no—
120#66885C2×C411yescharacteristic
121#66885C2×C411yescharacteristic
122(C2×D11)⋊C8—21no—
123(C2×D11)⋊C8—21no—
124(C2×D11)⋊C8—21no—
125(C2×D11)⋊C8—21no—
126(C2×D11)⋊C8—21no—
127(C2×D11)⋊C8C2×C411yescharacteristic
128(C2×D11)⋊C8C2×C411yescharacteristic
129#66882C2×C411yescharacteristic
130Dic11⋊C8—21no—
131Dic11⋊C8—21no—
132Dic11⋊C8—21no—
133Dic11⋊C8C2×C411yescharacteristic
134Dic11⋊C8C2×C411yescharacteristic
135C8×Dic11D411yescharacteristic
136C8×Dic11D411yescharacteristic
137#66873C2×C411yescharacteristic
138#66873C2×C411yescharacteristic
139#66871C2×C411yescharacteristic
140#66871C2×C411yescharacteristic
141C4⋊(C11⋊C8)C2311yescharacteristic
142C4⋊(C11⋊C8)C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144C4×C11⋊C8C2311yescharacteristic
145C4×C11⋊C8C2311yescharacteristic
146#17907—111nomaximal, Sylow
147C23×D11—21no—
148C2×D4×C11C22×C411yescharacteristic
149C2×D4×C11C22×C411yescharacteristic
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C2×C22⋊D11—21no—
153C2×C22⋊D11—21no—
154C2×C22⋊D11—21no—
155C2×C22⋊D11—21no—
156C22×Dic11—21no—
157D4×D11—22no—
158D4×D11—22no—
159#4339—42no—
160#4339—42no—
161C2×D44—21no—
162C2×D44C22×C411yescharacteristic
163C2×D44C22×C411yescharacteristic
164C2×C4×D11—21no—
165C2×C4×D11—21no—
166C2×C4×D11—21no—
167C2×C4×D11—21no—
168C2×C4×D11—42no—
169C2×C4×D11—42no—
170C2×C4×D11C22×C411yescharacteristic
171C2×C4×D11C2×D411yescharacteristic
172C2×C4×D11#4111yescharacteristic
173C2×Dic22—21no—
174C11×D8—22no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—42no—
179C2×C8×C11—42no—
180C2×C8×C11C22×C411yescharacteristic
181C2×C8×C11C22×C411yescharacteristic
182C2×C8×C11C2×D411yescharacteristic
183C2×C8×C11C2×D411yescharacteristic
184C11×C4⋊C4C22×C411yescharacteristic
185C11×C4⋊C4C22×C411yescharacteristic
186C11×C22⋊C4—21no—
187C11×C22⋊C4—21no—
188C42×C11C2411yescharacteristic
189C22⋊Dic11—21no—
190C22⋊Dic11—21no—
191#4323—22no—
192#4323—22no—
193(C2×D11)⋊C4—21no—
194(C2×D11)⋊C4—21no—
195(C2×D11)⋊C4—21no—
196(C2×D11)⋊C4—21no—
197C4⋊Dic11C22×C411yescharacteristic
198C4⋊Dic11C22×C411yescharacteristic
199Dic11⋊C4—21no—
200Dic11⋊C4—21no—
201C4×Dic11C22×C411yescharacteristic
202C4×Dic11C2×D411yescharacteristic
203C4×Dic11#4111yescharacteristic
204#4318—42no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—42no—
209C2×C11⋊C8C22×C411yescharacteristic
210C2×C11⋊C8C22×C411yescharacteristic
211C2×C11⋊C8C2×D411yescharacteristic
212C2×C11⋊C8C2×D411yescharacteristic
213D88—22no—
214#4313—42no—
215#4313—42no—
216C8×D11—22no—
217C8×D11—22no—
218C8×D11—42no—
219C8×D11—42no—
220C8×D11—42no—
221C8×D11—42no—
222#3100—111no—
223#2931—111no—
224C2×C8×D4—111no—
225#1586—111no—
226#1586—111no—
227#1586—111no—
228#1586—111no—
229#1580—111no—
230#1580—111no—
231#1580—111no—
232#1580D1111yescharacteristic, complemented
233#1570—111no—
234#1486—111no—
235#1480—111no—
236#1452—111no—
237C23×C11—21no—
238C23×C11—21no—
239C22×D11—24no—
240C22×D11—21no—
241C22×D11—21no—
242C22×D11—42no—
243C22×D11—42no—
244C22×D11C4×D411yescharacteristic
245D4×C11—21no—
246D4×C11—21no—
247D4×C11—21no—
248D4×C11#13112yescomplemented
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11C23×C411yescharacteristic
256C2×C4×C11C22×D411yescharacteristic
257C2×C4×C11C2×#4111yescharacteristic
258C22⋊D11—24no—
259C22⋊D11—42no—
260C22⋊D11—42no—
261C22⋊D11—42no—
262C2×Dic11—21no—
263C2×Dic11—21no—
264C2×Dic11—42no—
265C2×Dic11C4×D411yescharacteristic
266C2×Dic11C4×D411yescharacteristic
267C2×Dic11C4×D411yescharacteristic
268D44—21no—
269D44—21no—
270D44—21no—
271D44—42no—
272D44#13112yescomplemented
273C4×D11—21no—
274C4×D11—21no—
275C4×D11—41no—
276C4×D11—42no—
277C4×D11—41no—
278C4×D11—41no—
279C4×D11—41no—
280C4×D11—41no—
281C4×D11—42no—
282C4×D11AGL(1,ℤ/8)12yes—
283C4×D11AGL(1,ℤ/8)12yes—
284Dic22—42no—
285C8×C11—21no—
286C8×C11—21no—
287C8×C11—21no—
288C8×C11—21no—
289C8×C11—41no—
290C8×C11—41no—
291C8×C11—41no—
292C11⋊C8—21no—
293C11⋊C8—21no—
294C11⋊C8—21no—
295C11⋊C8—21no—
296C11⋊C8—41no—
297C11⋊C8—41no—
298C11⋊C8—41no—
299C2×#131—221no—
300C23×C8—221no—
301#532—111no—
302C2×C4×D4—111no—
303#480—111no—
304#480—111no—
305#474—111no—
306#474—111no—
307#459—111no—
308#459—111no—
309#447—111no—
310#447—111no—
311C4×D8—111no—
312C4×D8—111no—
313C4×D8—111no—
314C4×D8C2×D1111yescharacteristic
315#436—111no—
316#436—111no—
317#436—221no—
318C8×D4—111no—
319C8×D4—111no—
320C8×D4—111no—
321C8×D4—111no—
322C8×D4—221no—
323C8×D4—221no—
324C8×D4—221no—
325C8×D4C2×D1111yescharacteristic
326C8×D4C2×D1111yescharacteristic, complemented
327#431—111no—
328#431—111no—
329#423—111no—
330C2×C4⋊C8—111no—
331#408—221no—
332C2×C22⋊C8—221no—
333C2×C4×C8—111no—
334#334—111no—
335#334—111no—
336#334—111no—
337#334C2×D1111yescharacteristic, complemented
338D4⋊C8—111no—
339D4⋊C8—111no—
340D4⋊C8—111no—
341D4⋊C8—111no—
342D4⋊C8—111no—
343D4⋊C8—111no—
344D4⋊C8C2×D1111yescharacteristic
345D4⋊C8C2×D1111yescharacteristic, complemented
346#322—111no—
347#322—111no—
348#322—111no—
349#322C2×D1111yescharacteristic, complemented
350C22×C11—22no—
351C22×C11—41no—
352C22×C11—41no—
353C22×C11—41no—
354C22×C11—41no—
355C22×C11—41no—
356C22×C11C2×C4×D411yescharacteristic
357C2×D11—21no—
358C2×D11—21no—
359C2×D11—22no—
360C2×D11—48no—
361C2×D11—41no—
362C2×D11—41no—
363C2×D11—41no—
364C2×D11—41no—
365C2×D11—41no—
366C2×D11#44212yes—
367C4×C11—21no—
368C4×C11—41no—
369C4×C11—41no—
370C4×C11C2×#13111yescharacteristic
371C4×C11C2×#13111yescharacteristic
372C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
373C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
374Dic11—21no—
375Dic11—21no—
376Dic11—41no—
377Dic11—41no—
378Dic11#44212yes—
379C2×#41—221no—
380C22×D4—111no—
381C23×C4—221no—
382C2×D8—111no—
383C2×D8—111no—
384C2×D8—111no—
385C2×D8C4×D1111yescharacteristic
386#131—444no—
387C2×M16—221no—
388C2×M16—221no—
389C2×M16—221no—
390C22×C8—21no—
391C22×C8—21no—
392C22×C8—111no—
393C22×C8—111no—
394C22×C8—221no—
395C22×C8—221no—
396C22×C8—221no—
397C22×C8—221no—
398C22×C8—221no—
399C22×C8—444no—
400C4⋊Q8—111no—
401#127—111no—
402#124—221no—
403#121—111no—
404#121—111no—
405#121—221no—
406C4×D4—111no—
407C4×D4—111no—
408C4×D4—111no—
409C4×D4—111no—
410C4×D4—221no—
411C4×D4—221no—
412C4×D4—221no—
413C4×D4C22×D1111yescharacteristic
414C4×D4C22×D1111yescharacteristic
415C2×C4⋊C4—111no—
416C2×C22⋊C4—221no—
417C2×C42—111no—
418#107—111no—
419#107—111no—
420#107—111no—
421#107C4×D1111yescharacteristic
422C4⋊C8—111no—
423C4⋊C8—111no—
424C4⋊C8—111no—
425C4⋊C8—111no—
426C4⋊C8—221no—
427C4⋊C8—221no—
428C4⋊C8—221no—
429C4⋊C8C22×D1111yescharacteristic
430C4⋊C8C22×D1111yescharacteristic
431#102—111no—
432#102—111no—
433#102—111no—
434#102—111no—
435#102—111no—
436#102—111no—
437#102C4×D1111yescharacteristic
438#102C4×D1111yescharacteristic
439C22⋊C8—21no—
440C22⋊C8—21no—
441C22⋊C8—111no—
442C22⋊C8—111no—
443C22⋊C8—221no—
444C22⋊C8—221no—
445C22⋊C8—221no—
446C22⋊C8—221no—
447C22⋊C8—221no—
448C22⋊C8—221no—
449C22⋊C8—221no—
450C4×C8—111no—
451C4×C8—111no—
452C4×C8—111no—
453C4×C8—111no—
454C4×C8—111no—
455C4×C8C22×D1111yescharacteristic
456C4×C8C22×D1111yescharacteristic
457C4×C8C22×D1111yescharacteristic
458C2×C11—42no—
459C2×C11—81no—
460C2×C11#292911yescharacteristic
461C2×C11C2×#44211yescharacteristic
462C2×C11#295511yescharacteristic
463D11—22no—
464D11—42no—
465D11—81no—
466C24—221no—
467#41—442no—
468#41—442no—
469C2×Q8—221no—
470C2×D4—111no—
471C2×D4—111no—
472C2×D4—221no—
473C2×D4—221no—
474C2×D4—221no—
475C2×D4—221no—
476C2×D4—222no—
477C2×D4—222no—
478C2×D4—221no—
479C2×D4C2×C4×D1111yescharacteristic
480C2×D4C2×C4×D1111yescharacteristic
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—111no—
484C22×C4—111no—
485C22×C4—111no—
486C22×C4—221no—
487C22×C4—221no—
488C22×C4—221no—
489C22×C4—221no—
490C22×C4—221no—
491C22×C4—442no—
492C22×C4—442no—
493D8—22no—
494D8—222no—
495D8—222no—
496D8—222no—
497M16—442no—
498M16—442no—
499M16—442no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—42no—
504C2×C8—42no—
505C2×C8—111no—
506C2×C8—111no—
507C2×C8—111no—
508C2×C8—111no—
509C2×C8—222no—
510C2×C8—222no—
511C2×C8—221no—
512C2×C8—221no—
513C2×C8—221no—
514C2×C8—442no—
515C2×C8—442no—
516C2×C8—442no—
517C2×C8—442no—
518C2×C8—442no—
519C2×C8C2×C4×D1111yescharacteristic
520C2×C8C2×C4×D1111yescharacteristic
521C2×C8D4×D1111yescharacteristic
522C2×C8D4×D1111yescharacteristic
523C4⋊C4—111no—
524C4⋊C4—111no—
525C4⋊C4—221no—
526C4⋊C4—221no—
527C4⋊C4C2×C4×D1111yescharacteristic
528C4⋊C4C2×C4×D1111yescharacteristic
529C22⋊C4—21no—
530C22⋊C4—21no—
531C22⋊C4—221no—
532C22⋊C4—221no—
533C22⋊C4—221no—
534C22⋊C4—221no—
535C22⋊C4—221no—
536C22⋊C4—221no—
537C42—111no—
538C42—111no—
539C42—111no—
540C42C23×D1111yescharacteristic
541C11#1790711yescharacteristic, complemented, Sylow
542C23—21no—
543C23—21no—
544C23—111no—
545C23—224no—
546C23—221no—
547C23—221no—
548C23—442no—
549C23—442no—
550Q8—442no—
551D4—21no—
552D4—21no—
553D4—21no—
554D4—112no—
555D4—224no—
556D4—221no—
557D4—221no—
558D4—221no—
559D4—442no—
560D4—442no—
561D4—442no—
562D4—442no—
563D4#6695412yescomplemented
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—111no—
571C2×C4—112no—
572C2×C4—112no—
573C2×C4—111no—
574C2×C4—111no—
575C2×C4—221no—
576C2×C4—221no—
577C2×C4—221no—
578C2×C4—221no—
579C2×C4—441no—
580C2×C4—442no—
581C2×C4—442no—
582C2×C4—442no—
583C2×C4—441no—
584C2×C4—441no—
585C2×C4—441no—
586C2×C4—441no—
587C2×C4C22×C4×D1111yescharacteristic
588C2×C4C2×D4×D1111yescharacteristic
589C2×C4#41×D1111yescharacteristic
590C8—21no—
591C8—21no—
592C8—21no—
593C8—21no—
594C8—41no—
595C8—41no—
596C8—41no—
597C8—221no—
598C8—221no—
599C8—221no—
600C8—221no—
601C8—441no—
602C8—441no—
603C8—441no—
604C22—22no—
605C22—41no—
606C22—41no—
607C22—41no—
608C22—41no—
609C22—41no—
610C22—112no—
611C22—221no—
612C22—221no—
613C22—222no—
614C22—448no—
615C22—441no—
616C22—441no—
617C22—441no—
618C22—441no—
619C22—441no—
620C22C4×D4×D1111yescharacteristic
621C4—21no—
622C4—41no—
623C4—41no—
624C4—112no—
625C4—221no—
626C4—221no—
627C4—441no—
628C4—441no—
629C4C2×#6695411yescharacteristic
630C4D11×#13111yescharacteristic
631C4D11×AGL(1,ℤ/8)11yescharacteristic
632C4D11×AGL(1,ℤ/8)11yescharacteristic
633C2—42no—
634C2—81no—
635C2—222no—
636C2—442no—
637C2—881no—
638C2#1307730511yescharacteristic
639C2D11×#44211yescharacteristic
640C2#1307751611yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1580C2
socleC22×C11C2×C4×D4
prime radical#13078614C2
cosocleC42×C11C24
hypercenter#1580D11
hypocenterC11#17907
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1580

Complements

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

NH ≅ G/Ntype
2. #13077323C2semidirect
3. C8×D4×D11C2semidirect
4. #13067483C2semidirect
5. #13067481C2semidirect
6. #13067479C2semidirect
7. #13067477C2semidirect
8. #13067441C2semidirect
9. #13067438C2semidirect
10. #13067438C2semidirect
11. #13067385C2semidirect
12. #13067039C2semidirect
13. #13067013C2semidirect
14. #13066907C2semidirect
15. C11×#1580C2semidirect
22. C8×D4×C11C22semidirect
29. #10622625C22semidirect
33. #10622451C22semidirect
47. C8×D44C22semidirect
51. C11×#334C22semidirect
53. C11×D4⋊C8C22semidirect
54. C11×#322C22semidirect
56. D4⋊(C11⋊C8)C22semidirect
58. #10622121C22semidirect
59. #10622118C22semidirect
60. #10622118C22semidirect
62. #10622097C22semidirect
63. #10622095C22semidirect
64. #10622093C22semidirect
65. #10622092C22semidirect
66. #10622092C22semidirect
232. #1580D11semidirect
248. D4×C11#131semidirect
272. D44#131semidirect
326. C8×D4C2×D11semidirect
337. #334C2×D11semidirect
345. D4⋊C8C2×D11semidirect
349. #322C2×D11semidirect
541. C11#17907semidirect
563. D4#66954semidirect

Maximal subgroups

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

subgroupindex
#130786142
#130773232
C8×D4×D112
#130674832
#130674812
#130674792
#130674772
#130674412
#130674382
#130673852
#130670392
#130670132
#130669072
C11×#15802
#1790711