Finite Group Databasebeta

← #14756841

Subgroups — #14756841

Order 2816.

922 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622502C211yesmaximal, characteristic
2#13071074C211yesmaximal, characteristic
3C4×#66940C211yesmaximal, characteristic, complemented
4#13069243C211yesmaximal, characteristic
5#13069234C211yesmaximal, characteristic
6#13069189C211yesmaximal, characteristic, complemented
7#13068972C211yesmaximal, characteristic
8#13068970C211yesmaximal, characteristic
9#13068885C211yesmaximal, characteristic, complemented
10#13068869C211yesmaximal, characteristic, complemented
11#13068512C211yesmaximal, characteristic, complemented
12#13068445C211yesmaximal, characteristic, complemented
13#13068440C211yesmaximal, characteristic
14#13068363C211yesmaximal, characteristic, complemented
15C11×#1921C211yesmaximal, characteristic, complemented
16C22×#4314C2211yescharacteristic
17C2×#66946C2211yescharacteristic
18C2×#66945—21no—
19C2×#66940C2211yescharacteristic
20C2×#66940C2211yescharacteristic
21C2×C4×Dic22C2211yescharacteristic
22C2×C11×#107C2211yescharacteristic
23C11×#389C2211yescharacteristic
24C4×C11×C4⋊C4C2211yescharacteristic
25C2×#66885C2211yescharacteristic
26C2×#66880C2211yescharacteristic
27C2×#66879C2211yescharacteristic
28C2×#66879C2211yescharacteristic
29#10622603—21no—
30#10622601C2211yescharacteristic
31#10622598C2211yescharacteristic
32C4⋊C4×Dic11C2211yescharacteristic
33C4⋊C4×Dic11C2211yescharacteristic
34C4⋊C4×Dic11C2211yescharacteristic
35C2×#66874C2211yescharacteristic
36C2×#66874C2211yescharacteristic
37C2×#66873C2211yescharacteristic
38C2×#66873C2211yescharacteristic
39C2×#66872C2211yescharacteristic
40C2×#66871C2211yescharacteristic
41#10622552C2211yescharacteristic
42C4×Dic11⋊C4—21no—
43C42×Dic11—21no—
44C42×Dic11C2211yescharacteristic
45#10622502C418yescomplemented
46#10622283—21no—
47#10622279—21no—
48#10622262—21no—
49#10622262—21no—
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52C11×#340C2211yescharacteristic
53C11×#336C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622162C2211yescharacteristic
60C22×D44C2311yescharacteristic
61C22×C4×D11—21no—
62C22×Dic22C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C42×C11—21no—
71C2×C42×C11C2311yescharacteristic
72C2×(C2×D11)⋊C4—21no—
73C2×(C2×D11)⋊C4—21no—
74C2×(C2×D11)⋊C4—21no—
75C2×(C2×D11)⋊C4—21no—
76C2×(C2×D11)⋊C4—21no—
77C2×C4⋊Dic11—21no—
78C2×C4⋊Dic11C2311yescharacteristic
79C2×C4⋊Dic11C2311yescharacteristic
80C2×Dic11⋊C4—21no—
81C2×Dic11⋊C4—21no—
82C2×Dic11⋊C4—21no—
83C2×C4×Dic11—21no—
84C2×C4×Dic11—21no—
85C2×C4×Dic11—21no—
86C2×C4×Dic11—21no—
87C2×C4×Dic11—21no—
88C2×C4×Dic11—21no—
89C2×C4×Dic11D411yescharacteristic
90C2×C4×Dic11D411yescharacteristic
91C2×C4×Dic11D411yescharacteristic
92C2×C4×Dic11D411yescharacteristic
93C2×C4×Dic11C2311yescharacteristic
94C2×C4×Dic11C2311yescharacteristic
95C22×C11⋊C8C2311yescharacteristic
96C22×C11⋊C8C2311yescharacteristic
97C2×#4314—22no—
98C2×#4314—22no—
99C2×#4314C2×C414yes—
100#66946—22no—
101#66946C2×C414yes—
102#66945—44no—
103#66940—22no—
104#66940—22no—
105#66940—22no—
106#66940C2×C414yes—
107C4×Dic22—22no—
108C4×Dic22—22no—
109C11×#107C2×C414yes—
110C11×#95—21no—
111C11×#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116#66885—22no—
117#66880—22no—
118#66879—22no—
119#66879C2×C414yes—
120#66874—22no—
121#66874C2×C414yes—
122#66873—22no—
123#66873C2×C414yes—
124#66872—22no—
125#66871—22no—
126#21124—111nomaximal, Sylow
127C23×D11—21no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2411yescharacteristic
135C22×Dic11—21no—
136C22×Dic11—21no—
137C22×Dic11—21no—
138C22×Dic11C2×D411yescharacteristic
139C22×Dic11C2×D411yescharacteristic
140C22×Dic11C2×D411yescharacteristic
141C22×Dic11C2×D411yescharacteristic
142C2×D44—21no—
143C2×D44—21no—
144C2×D44—21no—
145C2×D44—21no—
146C2×D44—21no—
147C2×D44C22×C412yes—
148C2×C4×D11—24no—
149C2×C4×D11—42no—
150C2×C4×D11—42no—
151C2×Dic22—21no—
152C2×Dic22—21no—
153C2×Dic22—21no—
154C2×Dic22C22×C412yes—
155C2×Dic22#4112yes—
156C2×Dic22#4112yes—
157C2×C8×C11—21no—
158C2×C8×C11—21no—
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11C22×C412yes—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—42no—
169C11×C4⋊C4C22×C412yes—
170C11×C4⋊C4C22×C412yes—
171C11×C4⋊C4#4112yes—
172C42×C11—21no—
173C42×C11—21no—
174C42×C11—42no—
175(C2×D11)⋊C4—24no—
176(C2×D11)⋊C4—42no—
177(C2×D11)⋊C4—42no—
178(C2×D11)⋊C4—42no—
179(C2×D11)⋊C4—42no—
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—42no—
184C4⋊Dic11#4112yes—
185Dic11⋊C4—24no—
186Dic11⋊C4—24no—
187Dic11⋊C4—24no—
188C4×Dic11—24no—
189C4×Dic11—24no—
190C4×Dic11—24no—
191C4×Dic11—22no—
192C4×Dic11—22no—
193C4×Dic11—21no—
194C4×Dic11—21no—
195C4×Dic11—41no—
196C4×Dic11—41no—
197C4×Dic11—42no—
198C4×Dic11—42no—
199C4×Dic11—42no—
200C4×Dic11C22×C412yes—
201C4×Dic11#4112yes—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8C22×C412yes—
208#4314—28no—
209C2×#440—111no—
210#2293—111no—
211C42×Q8—111no—
212#1926—111no—
213#1925—111no—
214#1921D1111yescharacteristic, complemented
215#1918—111no—
216#1880—111no—
217#1880—111no—
218#1865—111no—
219#1863—111no—
220#1776—111no—
221#1763—111no—
222#1762—111no—
223#1745—111no—
224C23×C11C22×D411yescharacteristic
225C22×D11—22no—
226C22×D11—41no—
227C22×D11—41no—
228C22×D11—41no—
229C22×D11—41no—
230C22×D11—41no—
231C22×D11—41no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—22no—
235C2×C4×C11—22no—
236C2×C4×C11—22no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11#13712yes—
250C2×C4×C11C23×C411yescharacteristic
251C2×C4×C11C2×#4111yescharacteristic
252C2×C4×C11C2×#4111yescharacteristic
253C2×C4×C11C2×#4111yescharacteristic
254C2×C4×C11C2×#4111yescharacteristic
255C2×C4×C11C2×#4111yescharacteristic
256C2×Dic11—22no—
257C2×Dic11—21no—
258C2×Dic11—22no—
259C2×Dic11—22no—
260C2×Dic11—21no—
261C2×Dic11—21no—
262C2×Dic11—21no—
263C2×Dic11—21no—
264C2×Dic11—21no—
265C2×Dic11—21no—
266C2×Dic11—22no—
267C2×Dic11—21no—
268C2×Dic11—21no—
269C2×Dic11—41no—
270C2×Dic11—41no—
271C2×Dic11—41no—
272C2×Dic11—41no—
273C2×Dic11—41no—
274C2×Dic11C4×D412yes—
275C2×Dic11C4×D412yes—
276C2×Dic11AGL(1,ℤ/8)12yes—
277D44—22no—
278D44—22no—
279D44—41no—
280D44—41no—
281C4×D11—48no—
282Dic22—22no—
283Dic22—22no—
284Dic22—22no—
285Dic22#11714yescomplemented
286C8×C11—22no—
287C8×C11—41no—
288C11⋊C8—22no—
289C11⋊C8—41no—
290C22×SD16—111no—
291C2×C4×Q8—111no—
292C2×C4×Q8—111no—
293C2×C4×Q8—111no—
294C2×C4×D4—111no—
295C2×#117—221no—
296#440—118no—
297C2×#107—111no—
298C2×#107C2×D1111yescharacteristic
299C2×#106—111no—
300C2×#103—111no—
301C2×#103—111no—
302C2×#103—111no—
303C2×#102—111no—
304C2×#102—111no—
305C2×#102—111no—
306C2×#97—111no—
307C2×#97—111no—
308#390—111no—
309#390—111no—
310#389—111no—
311#389C2×D1111yescharacteristic
312#388—221no—
313#388—221no—
314C4×C4⋊C4—111no—
315C4×C4⋊C4—111no—
316C4×C4⋊C4—111no—
317C4×C4⋊C4—221no—
318C4×C4⋊C4—221no—
319C4×C4⋊C4—221no—
320C4×C4⋊C4C2×D1111yescharacteristic
321C4×C22⋊C4—221no—
322C43—111no—
323C43—221no—
324#340—111no—
325#340—111no—
326#340—111no—
327#340C2×D1111yescharacteristic
328#340C2×D1111yescharacteristic
329#340C2×D1111yescharacteristic
330#336—111no—
331#336—111no—
332#336—111no—
333#336C2×D1111yescharacteristic
334C22×C11C2×C4×D411yescharacteristic
335C22×C11#52511yescharacteristic
336C22×C11#52511yescharacteristic
337C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
338C22×C11C2×#13711yescharacteristic
339C22×C11#57511yescharacteristic
340C22×C11#57511yescharacteristic
341C2×D11—42no—
342C2×D11—42no—
343C2×D11—42no—
344C2×D11—81no—
345C2×D11—81no—
346C2×D11—81no—
347C2×D11—81no—
348C4×C11—22no—
349C4×C11—42no—
350C4×C11—41no—
351C4×C11—42no—
352C4×C11—42no—
353C4×C11—81no—
354C4×C11C2×#11711yescharacteristic
355C4×C11C4×#4111yescharacteristic
356C4×C11#52911yescharacteristic
357C4×C11#52911yescharacteristic
358Dic11—22no—
359Dic11—22no—
360Dic11—22no—
361Dic11—24no—
362Dic11—41no—
363Dic11—42no—
364Dic11—81no—
365C22×Q8—111no—
366C22×D4—111no—
367C23×C4—221no—
368C2×SD16—114no—
369C2×SD16—222no—
370C2×SD16—222no—
371C22×C8—111no—
372C22×C8—111no—
373C22×C8C22×D1111yescharacteristic
374C22×C8C22×D1111yescharacteristic
375C4×Q8—114no—
376C4×Q8—222no—
377C4×Q8—222no—
378C4×Q8—222no—
379C4×Q8—222no—
380C4×Q8—222no—
381C4×D4—114no—
382C4×D4—222no—
383#117—444no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—111no—
386C2×C4⋊C4—111no—
387C2×C4⋊C4—221no—
388C2×C4⋊C4—221no—
389C2×C4⋊C4—221no—
390C2×C4⋊C4—221no—
391C2×C4⋊C4C22×D1111yescharacteristic
392C2×C4⋊C4C22×D1111yescharacteristic
393C2×C4⋊C4C22×D1111yescharacteristic
394C2×C4⋊C4C22×D1111yescharacteristic
395C2×C22⋊C4—221no—
396C2×C22⋊C4—221no—
397C2×C22⋊C4—221no—
398C2×C22⋊C4—221no—
399C2×C22⋊C4—221no—
400C2×C42—21no—
401C2×C42—111no—
402C2×C42—111no—
403C2×C42—111no—
404C2×C42—111no—
405C2×C42—111no—
406C2×C42—111no—
407C2×C42—221no—
408C2×C42—221no—
409C2×C42—221no—
410C2×C42—221no—
411C2×C42—221no—
412C2×C42—221no—
413C2×C42C22×D1111yescharacteristic
414#107—222no—
415#107C4×D1114yes—
416#106—222no—
417#103—114no—
418#103—222no—
419#103—222no—
420#102—114no—
421#102—222no—
422#102—222no—
423#97—114no—
424#97—222no—
425#95—21no—
426#95—21no—
427#95—221no—
428#95—221no—
429#95—221no—
430#95—221no—
431C2×C11#229011yescharacteristic
432C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
433C2×C11C4×#13711yescharacteristic
434C2×C11#311111yescharacteristic
435C2×C11#311211yescharacteristic
436C2×C11#311511yescharacteristic
437C2×C11#311711yescharacteristic
438D11—82no—
439C24—221no—
440C2×Q8—112no—
441C2×Q8—112no—
442C2×Q8—112no—
443C2×Q8—221no—
444C2×Q8—221no—
445C2×Q8—221no—
446C2×D4—112no—
447C2×D4—221no—
448C2×D4—221no—
449C2×D4—221no—
450C2×D4—221no—
451C2×D4—221no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—111no—
457C22×C4—111no—
458C22×C4—111no—
459C22×C4—111no—
460C22×C4—224no—
461C22×C4—221no—
462C22×C4—221no—
463C22×C4—221no—
464C22×C4—442no—
465C22×C4—442no—
466C22×C4D4×D1111yescharacteristic
467C22×C4D4×D1111yescharacteristic
468C22×C4C23×D1111yescharacteristic
469SD16—228no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—112no—
476C2×C8—221no—
477C2×C8—221no—
478C2×C8—221no—
479C2×C8—221no—
480C2×C8—221no—
481C2×C8C2×C4×D1112yes—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—42no—
488C4⋊C4—112no—
489C4⋊C4—224no—
490C4⋊C4—224no—
491C4⋊C4—224no—
492C4⋊C4—221no—
493C4⋊C4—221no—
494C4⋊C4—221no—
495C4⋊C4—442no—
496C4⋊C4C2×C4×D1112yes—
497C4⋊C4C2×C4×D1112yes—
498C4⋊C4#434312yes—
499C22⋊C4—224no—
500C22⋊C4—442no—
501C22⋊C4—442no—
502C22⋊C4—442no—
503C22⋊C4—442no—
504C42—21no—
505C42—21no—
506C42—42no—
507C42—112no—
508C42—112no—
509C42—222no—
510C42—224no—
511C42—224no—
512C42—224no—
513C42—222no—
514C42—221no—
515C42—221no—
516C42—441no—
517C42—441no—
518C42—442no—
519C42—442no—
520C42—442no—
521C11#2112411yescharacteristic, complemented, Sylow
522C23—222no—
523C23—441no—
524C23—441no—
525C23—441no—
526C23—441no—
527C23—441no—
528C23—441no—
529C23C2×D4×D1111yescharacteristic
530Q8—114no—
531Q8—222no—
532Q8—222no—
533Q8—222no—
534D4—222no—
535D4—222no—
536D4—441no—
537D4—441no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—21no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—112no—
556C2×C4—112no—
557C2×C4—112no—
558C2×C4—221no—
559C2×C4—221no—
560C2×C4—221no—
561C2×C4—221no—
562C2×C4—221no—
563C2×C4—222no—
564C2×C4—221no—
565C2×C4—222no—
566C2×C4—222no—
567C2×C4—221no—
568C2×C4—221no—
569C2×C4—221no—
570C2×C4—222no—
571C2×C4—448no—
572C2×C4—441no—
573C2×C4—441no—
574C2×C4—441no—
575C2×C4—441no—
576C2×C4—441no—
577C2×C4#6697112yes—
578C2×C4C22×C4×D1111yescharacteristic
579C2×C4C2×#434311yescharacteristic
580C2×C4#41×D1111yescharacteristic
581C2×C4#41×D1111yescharacteristic
582C2×C4#41×D1111yescharacteristic
583C2×C4#41×D1111yescharacteristic
584C8—22no—
585C8—41no—
586C8—222no—
587C8—441no—
588C22—442no—
589C22—442no—
590C22—442no—
591C22—881no—
592C22—881no—
593C22—881no—
594C22—881no—
595C22C4×D4×D1111yescharacteristic
596C22#1062315811yescharacteristic
597C22#1062318711yescharacteristic
598C22C2×#6697111yescharacteristic
599C22#1062329911yescharacteristic
600C22D11×AGL(1,ℤ/8)11yescharacteristic
601C22#1062330411yescharacteristic
602C4—22no—
603C4—42no—
604C4—42no—
605C4—42no—
606C4—41no—
607C4—81no—
608C4—222no—
609C4—222no—
610C4—224no—
611C4—222no—
612C4—441no—
613C4—442no—
614C4—881no—
615C4D11×#11711yescharacteristic
616C4C4×#434311yescharacteristic
617C4#1062322211yescharacteristic
618C4#1062323711yescharacteristic
619C2—882no—
620C2#1307105411yescharacteristic
621C2#1307742711yescharacteristic
622C2C4×#6697111yescharacteristic
623C2#1307873011yescharacteristic
624C2#1307874011yescharacteristic
625C2#1307876211yescharacteristic
626C2#1307879011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1921C2
socleC23×C11C22×D4
prime radicalC22×D44C23
cosocleC22×C4×C11C24
hypercenter#1921D11
hypocenterC11#21124
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1921

Complements

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

NH ≅ G/Ntype
3. C4×#66940C2semidirect
6. #13069189C2semidirect
9. #13068885C2semidirect
10. #13068869C2semidirect
11. #13068512C2semidirect
12. #13068445C2semidirect
14. #13068363C2semidirect
15. C11×#1921C2semidirect
45. #10622502C4semidirect
214. #1921D11semidirect
285. Dic22#117semidirect
521. C11#21124semidirect

Maximal subgroups

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

subgroupindex
C2×#106225022
#130710742
C4×#669402
#130692432
#130692342
#130691892
#130689722
#130689702
#130688852
#130688692
#130685122
#130684452
#130684402
#130683632
C11×#19212
#2112411