Finite Group Databasebeta

← #14756959

Subgroups — #14756959

Order 2816.

938 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622485C211yesmaximal, characteristic
2#13071255C211yesmaximal, characteristic, complemented
3#13070976C211yesmaximal, characteristic, complemented
4#13069243C211yesmaximal, characteristic, complemented
5#13069241C211yesmaximal, characteristic, complemented
6#13069189C211yesmaximal, characteristic, complemented
7#13068965C211yesmaximal, characteristic
8#13068963C211yesmaximal, characteristic
9#13068878C211yesmaximal, characteristic, complemented
10#13068876C211yesmaximal, characteristic, complemented
11#13068504C211yesmaximal, characteristic, complemented
12#13068440C211yesmaximal, characteristic, complemented
13#13068440C211yesmaximal, characteristic, complemented
14#13068366C211yesmaximal, characteristic, complemented
15C11×#1918C211yesmaximal, characteristic, complemented
16C22×D88C2211yescharacteristic
17C2×#66946C2211yescharacteristic
18C2×#66946C2211yescharacteristic
19C2×#66946C2211yescharacteristic
20C2×C4×D44C2211yescharacteristic
21C2×C11×#107C2211yescharacteristic
22C11×#389C2211yescharacteristic
23C4×C11×C4⋊C4C2211yescharacteristic
24C2×#66885C2211yescharacteristic
25C2×#66885C2211yescharacteristic
26C2×#66879C2211yescharacteristic
27C2×C8×Dic11C2211yescharacteristic
28#10622603—21no—
29#10622601C2211yescharacteristic
30#10622600—21no—
31#10622598C2211yescharacteristic
32C4⋊C4×Dic11C2211yescharacteristic
33C4⋊C4×Dic11C2211yescharacteristic
34C4⋊C4×Dic11C2211yescharacteristic
35C2×#66873C2211yescharacteristic
36C2×#66873C2211yescharacteristic
37C2×#66873C2211yescharacteristic
38C2×#66873C2211yescharacteristic
39C2×#66872C2211yescharacteristic
40C2×#66872C2211yescharacteristic
41#10622552C2211yescharacteristic
42C4×(C2×D11)⋊C4—21no—
43C4×(C2×D11)⋊C4—21no—
44#10622545C2211yescharacteristic
45#10622485C418yescomplemented
46#10622283—21no—
47#10622279—21no—
48#10622277—21no—
49D11×#95—21no—
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52C11×#340C2211yescharacteristic
53C11×#336C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622162C2211yescharacteristic
60C22×D44C2311yescharacteristic
61C22×D44C2311yescharacteristic
62C22×C4×D11—21no—
63C22×C4×D11—21no—
64C22×C4×D11—21no—
65C22×C4×D11—21no—
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C42×C11—21no—
74C2×C42×C11C2311yescharacteristic
75C2×(C2×D11)⋊C4—21no—
76C2×(C2×D11)⋊C4—21no—
77C2×(C2×D11)⋊C4—21no—
78C2×(C2×D11)⋊C4—21no—
79C2×(C2×D11)⋊C4—21no—
80C2×(C2×D11)⋊C4—21no—
81C2×(C2×D11)⋊C4—21no—
82C2×(C2×D11)⋊C4—21no—
83C2×C4⋊Dic11—21no—
84C2×C4⋊Dic11C2311yescharacteristic
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4×Dic11—21no—
87C2×C4×Dic11—21no—
88C2×C4×Dic11—21no—
89C2×C4×Dic11C2311yescharacteristic
90C2×C4×Dic11C2311yescharacteristic
91C22×C11⋊C8C2311yescharacteristic
92C22×C11⋊C8C2311yescharacteristic
93C2×D88—22no—
94C2×D88—22no—
95C2×D88C2×C414yes—
96#66946—22no—
97#66946—22no—
98#66946—22no—
99#66946—22no—
100#66946C2×C414yes—
101#66946C2×C414yescomplemented
102C4×D44—22no—
103C4×D44—22no—
104C11×#107C2×C414yescomplemented
105C11×#95—21no—
106C11×#95—21no—
107C11⋊#95—21no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95D411yescharacteristic
112C11⋊#95D411yescharacteristic
113C11⋊#95D411yescharacteristic
114C11⋊#95D411yescharacteristic
115#66885—22no—
116#66885—22no—
117#66879—22no—
118C8×Dic11C2×C414yescomplemented
119#66873—22no—
120#66873—22no—
121#66873C2×C414yes—
122#66873C2×C414yescomplemented
123#66872—22no—
124#66872—22no—
125#21134—111nomaximal, Sylow
126C23×D11—21no—
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×Dic11C2×D411yescharacteristic
138C22×Dic11C2×D411yescharacteristic
139C22×Dic11C2×D411yescharacteristic
140C22×Dic11C2×D411yescharacteristic
141C2×D44—21no—
142C2×D44—21no—
143C2×D44—21no—
144C2×D44—21no—
145C2×D44—21no—
146C2×D44—21no—
147C2×D44—21no—
148C2×D44—21no—
149C2×D44C22×C412yes—
150C2×D44C22×C412yes—
151C2×D44#4112yes—
152C2×D44#4112yes—
153C2×C4×D11—24no—
154C2×C4×D11—24no—
155C2×C4×D11—24no—
156C2×C4×D11—24no—
157C2×C4×D11—81no—
158C2×C4×D11—81no—
159C2×C4×D11—81no—
160C2×C4×D11—81no—
161C2×C4×D11—81no—
162C2×C4×D11—81no—
163C2×C4×D11—81no—
164C2×C4×D11—81no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11C22×C412yes—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—81no—
177C11×C4⋊C4C22×C412yes—
178C11×C4⋊C4C22×C412yes—
179C11×C4⋊C4#4112yes—
180C42×C11—21no—
181C42×C11—21no—
182C42×C11—81no—
183(C2×D11)⋊C4—24no—
184(C2×D11)⋊C4—24no—
185(C2×D11)⋊C4—24no—
186(C2×D11)⋊C4—24no—
187(C2×D11)⋊C4—81no—
188(C2×D11)⋊C4—81no—
189(C2×D11)⋊C4—81no—
190(C2×D11)⋊C4—81no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—81no—
195C4⋊Dic11#4112yes—
196C4×Dic11—21no—
197C4×Dic11—21no—
198C4×Dic11—81no—
199C4×Dic11—81no—
200C4×Dic11—81no—
201C4×Dic11C22×C412yes—
202C4×Dic11#4112yes—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8C22×C412yes—
209D88—28no—
210C2×C4×D8—111no—
211#2319—111no—
212#2275—111no—
213#1926—111no—
214#1926—111no—
215#1918—111no—
216#1918D1111yescharacteristic, complemented
217#1879—111no—
218#1879—111no—
219#1864—111no—
220#1864—111no—
221C4×#106—111no—
222#1762—111no—
223#1762—111no—
224#1746—111no—
225C23×C11C22×D411yescharacteristic
226C22×D11—22no—
227C22×D11—22no—
228C22×D11—22no—
229C22×D11—22no—
230C22×D11—41no—
231C22×D11—41no—
232C22×D11—41no—
233C22×D11—41no—
234C22×D11—41no—
235C22×D11—41no—
236C22×D11—41no—
237C22×D11—41no—
238C22×D11—41no—
239C22×D11—41no—
240C2×C4×C11—22no—
241C2×C4×C11—22no—
242C2×C4×C11—21no—
243C2×C4×C11—22no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11C23×C411yescharacteristic
259C2×C4×C11C2×#4111yescharacteristic
260C2×C4×C11C2×#4111yescharacteristic
261C2×C4×C11C2×#4111yescharacteristic
262C2×C4×C11C2×#4111yescharacteristic
263C2×C4×C11C2×#4111yescharacteristic
264C2×Dic11—21no—
265C2×Dic11—21no—
266C2×Dic11—21no—
267C2×Dic11—21no—
268C2×Dic11—21no—
269C2×Dic11—21no—
270C2×Dic11—22no—
271C2×Dic11—21no—
272C2×Dic11—21no—
273C2×Dic11—21no—
274C2×Dic11—21no—
275C2×Dic11—41no—
276C2×Dic11—41no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11C4×D412yes—
281C2×Dic11C4×D412yes—
282D44—22no—
283D44—22no—
284D44—22no—
285D44—22no—
286D44—22no—
287D44—41no—
288D44—41no—
289D44#11714yes—
290C4×D11—84no—
291C4×D11—84no—
292C4×D11—84no—
293C4×D11—84no—
294C8×C11—22no—
295C8×C11—41no—
296C11⋊C8—22no—
297C11⋊C8—41no—
298C22×D8—111no—
299C2×C4×D4—111no—
300C2×C4×D4—111no—
301C2×C4×D4—111no—
302C2×C4×D4—111no—
303C4×D8—118no—
304C2×#107C2×D1111yescharacteristic
305C2×#106—111no—
306C2×#106—111no—
307C2×#102—111no—
308C2×#102—111no—
309C2×#102—111no—
310C2×#102—111no—
311C2×#102—111no—
312C2×#102—111no—
313C2×#97—111no—
314C2×C4×C8—111no—
315#390—111no—
316#390—111no—
317#389—111no—
318#389C2×D1111yescharacteristic
319#388—221no—
320#388—221no—
321#381—221no—
322#380—221no—
323C4×C4⋊C4—111no—
324C4×C4⋊C4—111no—
325C4×C4⋊C4—111no—
326C4×C4⋊C4C2×D1111yescharacteristic
327C4×C22⋊C4—221no—
328C4×C22⋊C4—221no—
329C4×C22⋊C4—221no—
330#376—111no—
331C2×#95—221no—
332#340—111no—
333#340—111no—
334#340—111no—
335#340C2×D1111yescharacteristic
336#340C2×D1111yescharacteristic
337#340C2×D1111yescharacteristic
338#336—111no—
339#336—111no—
340#336—111no—
341#336C2×D1111yescharacteristic
342C22×C11C2×C4×D411yescharacteristic
343C22×C11#52511yescharacteristic
344C22×C11#52511yescharacteristic
345C22×C11#57611yescharacteristic
346C22×C11#57611yescharacteristic
347C22×C11#57711yescharacteristic
348C22×C11#57711yescharacteristic
349C2×D11—24no—
350C2×D11—42no—
351C2×D11—42no—
352C2×D11—42no—
353C2×D11—42no—
354C2×D11—42no—
355C2×D11—42no—
356C2×D11—42no—
357C2×D11—42no—
358C2×D11—42no—
359C2×D11—81no—
360C2×D11—81no—
361C2×D11—81no—
362C2×D11—81no—
363C4×C11—41no—
364C4×C11—42no—
365C4×C11—41no—
366C4×C11—42no—
367C4×C11—42no—
368C4×C11—81no—
369C4×C11C2×#11711yescharacteristic
370C4×C11C4×#4111yescharacteristic
371C4×C11#52911yescharacteristic
372C4×C11#52911yescharacteristic
373Dic11—22no—
374Dic11—22no—
375Dic11—41no—
376Dic11—42no—
377Dic11—41no—
378Dic11—81no—
379C22×D4—111no—
380C22×D4—111no—
381C23×C4—221no—
382C23×C4—221no—
383C23×C4—221no—
384C23×C4—221no—
385C2×D8—114no—
386C2×D8—222no—
387C2×D8—222no—
388C22×C8—111no—
389C22×C8—111no—
390C22×C8C22×D1111yescharacteristic
391C22×C8C22×D1111yescharacteristic
392C4×D4—114no—
393C4×D4—114no—
394C4×D4—222no—
395C4×D4—222no—
396C4×D4—222no—
397C4×D4—222no—
398C4×D4—222no—
399C4×D4—222no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—111no—
402C2×C4⋊C4—111no—
403C2×C4⋊C4—221no—
404C2×C4⋊C4C22×D1111yescharacteristic
405C2×C4⋊C4C22×D1111yescharacteristic
406C2×C4⋊C4C22×D1111yescharacteristic
407C2×C4⋊C4C22×D1111yescharacteristic
408C2×C22⋊C4—221no—
409C2×C22⋊C4—221no—
410C2×C22⋊C4—221no—
411C2×C22⋊C4—221no—
412C2×C22⋊C4—221no—
413C2×C22⋊C4—221no—
414C2×C22⋊C4—221no—
415C2×C22⋊C4—221no—
416C2×C42—21no—
417C2×C42—111no—
418C2×C42—111no—
419C2×C42—221no—
420C2×C42—221no—
421C2×C42—221no—
422C2×C42C22×D1111yescharacteristic
423#107C4×D1114yescomplemented
424#106—222no—
425#106—222no—
426#102—114no—
427#102—114no—
428#102—222no—
429#102—222no—
430#102—222no—
431#102—222no—
432#97—222no—
433C4×C8—114no—
434#95—21no—
435#95—21no—
436#95—111no—
437#95—111no—
438#95—111no—
439#95—111no—
440#95—221no—
441#95—221no—
442#95—221no—
443#95—221no—
444C2×C11#229011yescharacteristic
445C2×C11#294811yescharacteristic
446C2×C11#295211yescharacteristic
447C2×C11#311811yescharacteristic
448C2×C11#311811yescharacteristic
449C2×C11#311911yescharacteristic
450C2×C11#311911yescharacteristic
451D11—44no—
452D11—82no—
453C24—221no—
454C24—221no—
455C2×D4—112no—
456C2×D4—112no—
457C2×D4—112no—
458C2×D4—112no—
459C2×D4—221no—
460C2×D4—221no—
461C2×D4—221no—
462C2×D4—221no—
463C2×D4—221no—
464C2×D4—221no—
465C2×D4—221no—
466C2×D4—221no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—111no—
472C22×C4—111no—
473C22×C4—111no—
474C22×C4—111no—
475C22×C4—224no—
476C22×C4—224no—
477C22×C4—224no—
478C22×C4—224no—
479C22×C4—221no—
480C22×C4—221no—
481C22×C4—881no—
482C22×C4—881no—
483C22×C4—881no—
484C22×C4—881no—
485C22×C4—881no—
486C22×C4—881no—
487C22×C4—881no—
488C22×C4—881no—
489C22×C4D4×D1111yescharacteristic
490C22×C4D4×D1111yescharacteristic
491C22×C4C23×D1111yescharacteristic
492D8—228no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—112no—
499C2×C8—221no—
500C2×C8—221no—
501C2×C8—221no—
502C2×C8—221no—
503C2×C8—221no—
504C2×C8C2×C4×D1112yes—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—81no—
511C4⋊C4—112no—
512C4⋊C4—221no—
513C4⋊C4—221no—
514C4⋊C4—221no—
515C4⋊C4—881no—
516C4⋊C4C2×C4×D1112yes—
517C4⋊C4C2×C4×D1112yes—
518C4⋊C4#434312yes—
519C22⋊C4—224no—
520C22⋊C4—224no—
521C22⋊C4—224no—
522C22⋊C4—224no—
523C22⋊C4—881no—
524C22⋊C4—881no—
525C22⋊C4—881no—
526C22⋊C4—881no—
527C42—21no—
528C42—21no—
529C42—81no—
530C42—112no—
531C42—112no—
532C42—221no—
533C42—221no—
534C42—881no—
535C42—881no—
536C42—881no—
537C11#2113411yescharacteristic, complemented, Sylow
538C23—222no—
539C23—222no—
540C23—222no—
541C23—222no—
542C23—441no—
543C23—441no—
544C23—441no—
545C23—441no—
546C23—441no—
547C23—441no—
548C23—441no—
549C23—441no—
550C23—441no—
551C23—441no—
552C23C2×D4×D1111yescharacteristic
553D4—114no—
554D4—222no—
555D4—222no—
556D4—222no—
557D4—222no—
558D4—222no—
559D4—441no—
560D4—441no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—112no—
580C2×C4—112no—
581C2×C4—221no—
582C2×C4—221no—
583C2×C4—221no—
584C2×C4—221no—
585C2×C4—221no—
586C2×C4—221no—
587C2×C4—221no—
588C2×C4—221no—
589C2×C4—221no—
590C2×C4—221no—
591C2×C4—222no—
592C2×C4—441no—
593C2×C4—441no—
594C2×C4—441no—
595C2×C4—441no—
596C2×C4—441no—
597C2×C4—884no—
598C2×C4—884no—
599C2×C4—884no—
600C2×C4—884no—
601C2×C4C22×C4×D1111yescharacteristic
602C2×C4C2×#434311yescharacteristic
603C2×C4#41×D1111yescharacteristic
604C2×C4#41×D1111yescharacteristic
605C2×C4#41×D1111yescharacteristic
606C2×C4#41×D1111yescharacteristic
607C8—22no—
608C8—41no—
609C8—222no—
610C8—441no—
611C22—224no—
612C22—442no—
613C22—442no—
614C22—442no—
615C22—442no—
616C22—442no—
617C22—442no—
618C22—442no—
619C22—442no—
620C22—442no—
621C22—881no—
622C22—881no—
623C22—881no—
624C22—881no—
625C22C4×D4×D1111yescharacteristic
626C22#1062315811yescharacteristic
627C22#1062318711yescharacteristic
628C22#1062328811yescharacteristic
629C22#1062330011yescharacteristic
630C22#1062330911yescharacteristic
631C22#1062330911yescharacteristic
632C4—41no—
633C4—42no—
634C4—41no—
635C4—42no—
636C4—42no—
637C4—81no—
638C4—222no—
639C4—222no—
640C4—442no—
641C4—441no—
642C4—441no—
643C4—881no—
644C4D11×#11711yescharacteristic
645C4C4×#434311yescharacteristic
646C4#1062322211yescharacteristic
647C4#1062323711yescharacteristic
648C2—444no—
649C2—882no—
650C2#1307105411yescharacteristic
651C2#1307746311yescharacteristic
652C2#1307749611yescharacteristic
653C2#1307880311yescharacteristic
654C2#1307880711yescharacteristic
655C2#1307881811yescharacteristic
656C2#1307882211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1918C2
socleC23×C11C22×D4
prime radicalC22×D88C22
cosocleC22×C4×C11C24
hypercenter#1918D11
hypocenterC11#21134
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1918

Complements

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

NH ≅ G/Ntype
2. #13071255C2semidirect
3. #13070976C2semidirect
4. #13069243C2semidirect
5. #13069241C2semidirect
6. #13069189C2semidirect
9. #13068878C2semidirect
10. #13068876C2semidirect
11. #13068504C2semidirect
12. #13068440C2semidirect
13. #13068440C2semidirect
14. #13068366C2semidirect
15. C11×#1918C2semidirect
45. #10622485C4semidirect
101. #66946C2×C4semidirect
104. C11×#107C2×C4semidirect
118. C8×Dic11C2×C4semidirect
122. #66873C2×C4semidirect
216. #1918D11semidirect
423. #107C4×D11semidirect
537. C11#21134semidirect

Maximal subgroups

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

subgroupindex
C2×#106224852
#130712552
#130709762
#130692432
#130692412
#130691892
#130689652
#130689632
#130688782
#130688762
#130685042
#130684402
#130683662
C11×#19182
#2113411