Finite Group Databasebeta

← #14725512

Subgroups — #14725512

Order 2816.

718 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077649C211yesmaximal, characteristic, complemented
2#13077648C211yesmaximal, characteristic, complemented
3C4×D8×D11C211yesmaximal, characteristic
4#13067528C211yesmaximal, characteristic, complemented
5#13067527C211yesmaximal, characteristic, complemented
6#13067447C211yesmaximal, characteristic, complemented
7#13067446C211yesmaximal, characteristic, complemented
8#13067444C211yesmaximal, characteristic, complemented
9#13067438C211yesmaximal, characteristic, complemented
10#13067437C211yesmaximal, characteristic, complemented
11#13067378C211yesmaximal, characteristic, complemented
12#13067057C211yesmaximal, characteristic, complemented
13#13067057C211yesmaximal, characteristic, complemented
14#13066904C211yesmaximal, characteristic, complemented
15C11×#1581C211yesmaximal, characteristic, complemented
16C2×D8×D11C411yescharacteristic
17C4×D4×D11C2211yescharacteristic
18C4×D4×D11C2211yescharacteristic
19C4×C11×D8C2211yescharacteristic
20C11×#436C2211yescharacteristic, complemented
21C8×D4×C11C2211yescharacteristic, complemented
22D8×Dic11C411yescharacteristic
23#10622740—21no—
24#10622739—21no—
25#10622724—21no—
26C2×(C2×D11)⋊C8—21no—
27C4×#4323C2211yescharacteristic
28C4×#4323C2211yescharacteristic
29#10622625C2211yescharacteristic, complemented
30D4×C11⋊C8C2211yescharacteristic, complemented
31D11×#107C411yescharacteristic
32#10622485C411yescharacteristic
33#10622451C2211yescharacteristic, complemented
34#10622448C2211yescharacteristic
35#10622448C2211yescharacteristic
36#10622447C2211yescharacteristic, complemented
37D11×#102C411yescharacteristic
38D11×#102C411yescharacteristic
39#10622369C411yescharacteristic
40#10622369C411yescharacteristic
41#10622343—21no—
42#10622341—21no—
43#10622339—21no—
44D11×C22⋊C8—21no—
45C4×D88C2211yescharacteristic
46#10622301C2211yescharacteristic, complemented
47C4×#4313C2211yescharacteristic
48C8×D44C2211yescharacteristic, complemented
49#10622298C2211yescharacteristic
50C4×C8×D11C2211yescharacteristic
51C11×#335C2211yescharacteristic, complemented
52C11×D4⋊C8C2211yescharacteristic, complemented
53C11×D4⋊C8C2211yescharacteristic, complemented
54C11×#322C2211yescharacteristic, complemented
55D4⋊(C11⋊C8)C2211yescharacteristic, complemented
56D4⋊(C11⋊C8)C2211yescharacteristic, complemented
57#10622121C2211yescharacteristic, complemented
58#10622121C2211yescharacteristic, complemented
59#10622118C2211yescharacteristic, complemented
60#10622118C2211yescharacteristic, complemented
61#10622097C2211yescharacteristic, complemented
62#10622097C2211yescharacteristic, complemented
63#10622096C2211yescharacteristic, complemented
64#10622092C2211yescharacteristic, complemented
65#10622092C2211yescharacteristic, complemented
66#10622092C2211yescharacteristic, complemented
67C2×D4×D11C2×C411yescharacteristic
68C2×D4×D11C2×C411yescharacteristic
69C22×C4×D11—21no—
70C22×C4×D11—21no—
71C2×C11×D8C2×C411yescharacteristic
72C2×C11×M16—21no—
73C22×C8×C11—21no—
74C4×D4×C11C2311yescharacteristic
75C4×D4×C11C2311yescharacteristic
76D4×Dic11C2×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—
84D8×D11—24no—
85C2×D88C2×C411yescharacteristic
86C2×#4313—21no—
87C2×#4313—21no—
88C2×#4313—21no—
89C2×C8×D11—21no—
90C2×C8×D11—21no—
91C2×C8×D11C2×C411yescharacteristic
92C2×C8×D11C2×C411yescharacteristic
93#66946C2×C411yescharacteristic
94#66946C2×C411yescharacteristic
95C4⋊C4×D11C2×C411yescharacteristic
96C4⋊C4×D11C2×C411yescharacteristic
97(C22⋊D11)⋊C4—21no—
98(C22⋊D11)⋊C4—21no—
99C22⋊C4×D11—21no—
100C22⋊C4×D11—21no—
101C4×D44C2311yescharacteristic
102C4×D44C2311yescharacteristic
103C42×D11C2311yescharacteristic
104C11×#107C2×C411yescharacteristic
105C11×C4⋊C8C2311yescharacteristic
106C11×C4⋊C8C2311yescharacteristic
107C11×#102C2×C411yescharacteristic
108C11×#102C2×C411yescharacteristic
109C11×C22⋊C8—21no—
110C11×C22⋊C8—21no—
111C4×C8×C11C2311yescharacteristic
112C4×C8×C11C2311yescharacteristic
113C4×C8×C11C2311yescharacteristic
114#66896C2×C411yescharacteristic
115#66896C2×C411yescharacteristic
116C22⋊(C11⋊C8)—21no—
117C22⋊(C11⋊C8)—21no—
118#66885C2×C411yescharacteristic
119#66885C2×C411yescharacteristic
120(C2×D11)⋊C8—21no—
121(C2×D11)⋊C8—21no—
122(C2×D11)⋊C8—21no—
123(C2×D11)⋊C8—21no—
124(C2×D11)⋊C8—21no—
125(C2×D11)⋊C8—21no—
126(C2×D11)⋊C8D411yescharacteristic
127(C2×D11)⋊C8D411yescharacteristic
128#66882C2×C411yescharacteristic
129#66879—21no—
130#66879—21no—
131#66879—21no—
132Dic11⋊C8D411yescharacteristic
133Dic11⋊C8D411yescharacteristic
134C8×Dic11C2×C411yescharacteristic
135C8×Dic11C2×C411yescharacteristic
136#66873C2×C411yescharacteristic
137#66873C2×C411yescharacteristic
138#66871C2×C411yescharacteristic
139#66871C2×C411yescharacteristic
140C4⋊(C11⋊C8)C2311yescharacteristic
141C4⋊(C11⋊C8)C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144C4×C11⋊C8C2311yescharacteristic
145#18064—111nomaximal, Sylow
146C23×D11—21no—
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—
154C22×Dic11—21no—
155C22×Dic11—21no—
156D4×D11—22no—
157D4×D11—22no—
158D4×D11—41no—
159D4×D11—41no—
160C2×D44C22×C411yescharacteristic
161C2×D44C22×C411yescharacteristic
162C2×C4×D11—21no—
163C2×C4×D11—21no—
164C2×C4×D11—21no—
165C2×C4×D11—21no—
166C2×C4×D11—21no—
167C2×C4×D11—21no—
168C2×C4×D11—81no—
169C2×C4×D11—81no—
170C2×C4×D11—81no—
171C2×C4×D11—81no—
172C2×C4×D11C22×C411yescharacteristic
173C2×C4×D11C2×D411yescharacteristic
174C2×C4×D11#4111yescharacteristic
175C11×D8—22no—
176C11×M16—81no—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11—81no—
181C2×C8×C11C22×C411yescharacteristic
182C2×C8×C11C22×C411yescharacteristic
183C2×C8×C11C2×D411yescharacteristic
184C2×C8×C11C2×D411yescharacteristic
185C11×C4⋊C4C22×C411yescharacteristic
186C11×C4⋊C4C22×C411yescharacteristic
187C11×C22⋊C4—21no—
188C11×C22⋊C4—21no—
189C42×C11C2411yescharacteristic
190C22⋊Dic11—21no—
191C22⋊Dic11—21no—
192#4323—22no—
193#4323M1614yescomplemented
194(C2×D11)⋊C4—21no—
195(C2×D11)⋊C4—21no—
196(C2×D11)⋊C4—21no—
197(C2×D11)⋊C4—21no—
198C4⋊Dic11C22×C411yescharacteristic
199C4⋊Dic11C22×C411yescharacteristic
200Dic11⋊C4—21no—
201Dic11⋊C4—21no—
202C4×Dic11C22×C411yescharacteristic
203C4×Dic11C2×D411yescharacteristic
204C4×Dic11#4111yescharacteristic
205#4318—81no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—81no—
210C2×C11⋊C8C22×C411yescharacteristic
211C2×C11⋊C8C22×C411yescharacteristic
212C2×C11⋊C8C2×D411yescharacteristic
213C2×C11⋊C8C2×D411yescharacteristic
214D88—22no—
215#4313—42no—
216#4313—81no—
217#4313—81no—
218C8×D11—22no—
219C8×D11—41no—
220C8×D11—81no—
221C8×D11—81no—
222#2974—111no—
223#2974—111no—
224C2×C4×D8—111no—
225#1594—111no—
226#1594—111no—
227#1581—111no—
228#1581—111no—
229#1581—111no—
230#1581D1111yescharacteristic, complemented
231#1580—111no—
232#1580—111no—
233#1568—111no—
234#1490—111no—
235#1490—111no—
236#1451—111no—
237C23×C11—21no—
238C23×C11—21no—
239C22×D11—21no—
240C22×D11—21no—
241C22×D11—42no—
242C22×D11—42no—
243C22×D11—42no—
244C22×D11—42no—
245C22×D11—81no—
246C22×D11—81no—
247C22×D11C4×D411yescharacteristic
248D4×C11—21no—
249D4×C11—21no—
250D4×C11—21no—
251D4×C11C2×M1612yes—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11C23×C411yescharacteristic
259C2×C4×C11C22×D411yescharacteristic
260C2×C4×C11C2×#4111yescharacteristic
261C22⋊D11—42no—
262C22⋊D11—42no—
263C2×Dic11—21no—
264C2×Dic11—21no—
265C2×Dic11—81no—
266C2×Dic11—81no—
267C2×Dic11C4×D411yescharacteristic
268C2×Dic11C4×D411yescharacteristic
269C2×Dic11C4×D411yescharacteristic
270D44—21no—
271D44—21no—
272D44—21no—
273D44C2×M1612yes—
274C4×D11—22no—
275C4×D11—21no—
276C4×D11—21no—
277C4×D11—21no—
278C4×D11—21no—
279C4×D11—41no—
280C4×D11—41no—
281C4×D11—41no—
282C4×D11—41no—
283C4×D11—81no—
284C4×D11—81no—
285C4×D11—81no—
286C4×D11—81no—
287C8×C11—21no—
288C8×C11—21no—
289C8×C11—21no—
290C8×C11—21no—
291C8×C11—41no—
292C8×C11—41no—
293C8×C11—41no—
294C11⋊C8—21no—
295C11⋊C8—21no—
296C11⋊C8—21no—
297C11⋊C8—41no—
298C11⋊C8—41no—
299C11⋊C8—41no—
300C11⋊C8C2×M1612yes—
301C22×D8—111no—
302C2×C4×D4—111no—
303C2×C4×D4—111no—
304C4×D8—111no—
305C4×D8—111no—
306C4×D8—111no—
307C4×D8—111no—
308C4×D8—111no—
309C4×D8—111no—
310C4×D8—111no—
311C4×D8C2×D1111yescharacteristic
312#436—111no—
313#436—111no—
314#436—111no—
315#436C2×D1111yescharacteristic, complemented
316#435—221no—
317#435—221no—
318#435—221no—
319#435—221no—
320C8×D4—111no—
321C8×D4—111no—
322C8×D4—111no—
323C8×D4C2×D1111yescharacteristic, complemented
324#432—111no—
325#432—111no—
326#431—111no—
327C2×#107—111no—
328C2×#102—111no—
329C2×#102—111no—
330#407—221no—
331#407—221no—
332C2×C22⋊C8—221no—
333C2×C22⋊C8—221no—
334C4×M16—111no—
335C2×C4×C8—111no—
336#335—111no—
337#335C2×D1111yescharacteristic, complemented
338#334—111no—
339#334—111no—
340D4⋊C8—111no—
341D4⋊C8—111no—
342D4⋊C8—111no—
343D4⋊C8—111no—
344D4⋊C8—111no—
345D4⋊C8—111no—
346D4⋊C8C2×D1111yescharacteristic, complemented
347D4⋊C8C2×D1111yescharacteristic, complemented
348#322—111no—
349#322—111no—
350#322—111no—
351#322C2×D1111yescharacteristic, complemented
352C22×C11—22no—
353C22×C11—41no—
354C22×C11—41no—
355C22×C11—41no—
356C22×C11—41no—
357C22×C11—41no—
358C22×C11C2×C4×D411yescharacteristic
359C2×D11—21no—
360C2×D11—21no—
361C2×D11—22no—
362C2×D11—41no—
363C2×D11—41no—
364C2×D11—41no—
365C2×D11—41no—
366C2×D11—41no—
367C2×D11—84no—
368C2×D11—84no—
369C2×D11#44412yes—
370C4×C11—21no—
371C4×C11—41no—
372C4×C11—41no—
373C4×C11C22×M1611yescharacteristic
374C4×C11#56811yescharacteristic
375C4×C11#57611yescharacteristic
376C4×C11#57611yescharacteristic
377Dic11—21no—
378Dic11—21no—
379Dic11—21no—
380Dic11—41no—
381Dic11—41no—
382C22×D4—111no—
383C22×D4—111no—
384C23×C4—221no—
385C23×C4—221no—
386C2×D8—111no—
387C2×D8—111no—
388C2×D8—111no—
389C2×D8—224no—
390C2×D8C4×D1111yescharacteristic
391C2×M16—21no—
392C2×M16—221no—
393C2×M16—221no—
394C2×M16—221no—
395C2×M16—221no—
396C22×C8—21no—
397C22×C8—111no—
398C22×C8—111no—
399C22×C8—221no—
400C22×C8—221no—
401C22×C8—221no—
402C4×D4—111no—
403C4×D4—111no—
404C4×D4—111no—
405C4×D4—111no—
406C4×D4—111no—
407C4×D4—111no—
408C4×D4—221no—
409C4×D4—221no—
410C4×D4—221no—
411C4×D4—221no—
412C4×D4C22×D1111yescharacteristic
413C4×D4C22×D1111yescharacteristic
414C2×C4⋊C4—111no—
415C2×C4⋊C4—111no—
416C2×C22⋊C4—221no—
417C2×C22⋊C4—221no—
418C2×C42—111no—
419#107—111no—
420#107—111no—
421#107—111no—
422#107C4×D1111yescharacteristic
423C4⋊C8—111no—
424C4⋊C8—111no—
425C4⋊C8—111no—
426C4⋊C8—111no—
427C4⋊C8C22×D1111yescharacteristic
428C4⋊C8C22×D1111yescharacteristic
429#102—111no—
430#102—111no—
431#102—111no—
432#102—111no—
433#102—111no—
434#102—111no—
435#102C4×D1111yescharacteristic
436#102C4×D1111yescharacteristic
437C22⋊C8—21no—
438C22⋊C8—21no—
439C22⋊C8—111no—
440C22⋊C8—111no—
441C22⋊C8—221no—
442C22⋊C8—221no—
443C22⋊C8—221no—
444C22⋊C8—221no—
445C22⋊C8—221no—
446C22⋊C8—221no—
447C22⋊C8—221no—
448C22⋊C8—221no—
449#97—221no—
450#97—221no—
451#97—221no—
452C4×C8—111no—
453C4×C8—111no—
454C4×C8—111no—
455C4×C8—111no—
456C4×C8—111no—
457C4×C8C22×D1111yescharacteristic
458C4×C8C22×D1111yescharacteristic
459C4×C8C22×D1111yescharacteristic
460C2×C11—42no—
461C2×C11—81no—
462C2×C11D4×M1611yescharacteristic
463C2×C11#294811yescharacteristic
464C2×C11C2×#44411yescharacteristic
465D11—22no—
466D11—42no—
467D11—81no—
468C24—221no—
469C24—221no—
470C2×D4—111no—
471C2×D4—111no—
472C2×D4—221no—
473C2×D4—221no—
474C2×D4—222no—
475C2×D4—222no—
476C2×D4—441no—
477C2×D4—441no—
478C2×D4C2×C4×D1111yescharacteristic
479C2×D4C2×C4×D1111yescharacteristic
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—111no—
483C22×C4—111no—
484C22×C4—111no—
485C22×C4—221no—
486C22×C4—221no—
487C22×C4—221no—
488C22×C4—221no—
489C22×C4—221no—
490C22×C4—221no—
491C22×C4—221no—
492C22×C4—221no—
493C22×C4—881no—
494C22×C4—881no—
495C22×C4—881no—
496C22×C4—881no—
497D8—22no—
498D8—114no—
499D8—222no—
500D8—222no—
501M16—81no—
502M16—442no—
503M16—881no—
504M16—881no—
505M16—881no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—81no—
510C2×C8—111no—
511C2×C8—111no—
512C2×C8—111no—
513C2×C8—111no—
514C2×C8—222no—
515C2×C8—221no—
516C2×C8—221no—
517C2×C8—221no—
518C2×C8—441no—
519C2×C8—881no—
520C2×C8—881no—
521C2×C8—881no—
522C2×C8C2×C4×D1111yescharacteristic
523C2×C8C2×C4×D1111yescharacteristic
524C2×C8D4×D1111yescharacteristic
525C2×C8D4×D1111yescharacteristic
526C4⋊C4—111no—
527C4⋊C4—111no—
528C4⋊C4—221no—
529C4⋊C4—221no—
530C4⋊C4C2×C4×D1111yescharacteristic
531C4⋊C4C2×C4×D1111yescharacteristic
532C22⋊C4—21no—
533C22⋊C4—21no—
534C22⋊C4—221no—
535C22⋊C4—221no—
536C22⋊C4—221no—
537C22⋊C4—221no—
538C22⋊C4—221no—
539C22⋊C4—221no—
540C42—111no—
541C42—111no—
542C42—111no—
543C42C23×D1111yescharacteristic
544C11#1806411yescharacteristic, complemented, Sylow
545C23—21no—
546C23—21no—
547C23—111no—
548C23—221no—
549C23—221no—
550C23—442no—
551C23—442no—
552C23—442no—
553C23—442no—
554C23—881no—
555C23—881no—
556D4—21no—
557D4—21no—
558D4—21no—
559D4—112no—
560D4—221no—
561D4—221no—
562D4—221no—
563D4—442no—
564D4—442no—
565D4M16×D1112yes—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—111no—
573C2×C4—111no—
574C2×C4—111no—
575C2×C4—222no—
576C2×C4—221no—
577C2×C4—221no—
578C2×C4—221no—
579C2×C4—221no—
580C2×C4—221no—
581C2×C4—221no—
582C2×C4—441no—
583C2×C4—441no—
584C2×C4—441no—
585C2×C4—441no—
586C2×C4—881no—
587C2×C4—881no—
588C2×C4—881no—
589C2×C4—881no—
590C2×C4—881no—
591C2×C4—881no—
592C2×C4C22×C4×D1111yescharacteristic
593C2×C4C2×D4×D1111yescharacteristic
594C2×C4#41×D1111yescharacteristic
595C8—21no—
596C8—21no—
597C8—21no—
598C8—21no—
599C8—41no—
600C8—41no—
601C8—41no—
602C8—112no—
603C8—221no—
604C8—221no—
605C8—221no—
606C8—441no—
607C8—441no—
608C8—441no—
609C22—22no—
610C22—41no—
611C22—41no—
612C22—41no—
613C22—41no—
614C22—41no—
615C22—112no—
616C22—221no—
617C22—221no—
618C22—222no—
619C22—441no—
620C22—441no—
621C22—441no—
622C22—441no—
623C22—441no—
624C22—884no—
625C22—884no—
626C22C4×D4×D1111yescharacteristic
627C4—21no—
628C4—41no—
629C4—41no—
630C4—221no—
631C4—221no—
632C4—221no—
633C4—441no—
634C4—441no—
635C4C2×M16×D1111yescharacteristic
636C4#1062328111yescharacteristic
637C4#1062328811yescharacteristic
638C4#1062330011yescharacteristic
639C2—42no—
640C2—81no—
641C2—222no—
642C2—442no—
643C2—881no—
644C2#1307734911yescharacteristic
645C2#1307746311yescharacteristic
646C2D11×#44411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1581C2
socleC22×C11C2×C4×D4
prime radicalC2×D8×D11C4
cosocleC42×C11C24
hypercenter#1581D11
hypocenterC11#18064
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1581

Complements

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

NH ≅ G/Ntype
1. #13077649C2semidirect
2. #13077648C2semidirect
4. #13067528C2semidirect
5. #13067527C2semidirect
6. #13067447C2semidirect
7. #13067446C2semidirect
8. #13067444C2semidirect
9. #13067438C2semidirect
10. #13067437C2semidirect
11. #13067378C2semidirect
12. #13067057C2semidirect
13. #13067057C2semidirect
14. #13066904C2semidirect
15. C11×#1581C2semidirect
20. C11×#436C22semidirect
21. C8×D4×C11C22semidirect
29. #10622625C22semidirect
30. D4×C11⋊C8C22semidirect
33. #10622451C22semidirect
36. #10622447C22semidirect
46. #10622301C22semidirect
48. C8×D44C22semidirect
51. C11×#335C22semidirect
52. C11×D4⋊C8C22semidirect
53. C11×D4⋊C8C22semidirect
54. C11×#322C22semidirect
55. D4⋊(C11⋊C8)C22semidirect
56. D4⋊(C11⋊C8)C22semidirect
57. #10622121C22semidirect
58. #10622121C22semidirect
59. #10622118C22semidirect
60. #10622118C22semidirect
61. #10622097C22semidirect
62. #10622097C22semidirect
63. #10622096C22semidirect
64. #10622092C22semidirect
65. #10622092C22semidirect
66. #10622092C22semidirect
193. #4323M16semidirect
230. #1581D11semidirect
315. #436C2×D11semidirect
323. C8×D4C2×D11semidirect
337. #335C2×D11semidirect
346. D4⋊C8C2×D11semidirect
347. D4⋊C8C2×D11semidirect
351. #322C2×D11semidirect
544. C11#18064semidirect

Maximal subgroups

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

subgroupindex
#130776492
#130776482
C4×D8×D112
#130675282
#130675272
#130674472
#130674462
#130674442
#130674382
#130674372
#130673782
#130670572
#130669042
C11×#15812
#1806411