Finite Group Databasebeta

← #14765085

Subgroups — #14765085

Order 2816.

920 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622799C211yesmaximal, characteristic
2#13071301C211yesmaximal, characteristic
3#13071199C211yesmaximal, characteristic
4#13069476C211yesmaximal, characteristic, complemented
5#13069306C211yesmaximal, characteristic, complemented
6#13069295C211yesmaximal, characteristic, complemented
7#13069260C211yesmaximal, characteristic, complemented
8#13069249C211yesmaximal, characteristic, complemented
9#13068959C211yesmaximal, characteristic, complemented
10#13068955C211yesmaximal, characteristic, complemented
11#13068925C211yesmaximal, characteristic
12#13068814C211yesmaximal, characteristic
13#13068549C211yesmaximal, characteristic
14#13068385C211yesmaximal, characteristic
15C11×#1971C211yesmaximal, characteristic, complemented
16C22×Q8×D11C2211yescharacteristic
17C22×C11×Q16C2211yescharacteristic
18C2×#66999C2211yescharacteristic
19C2×Q8×Dic11C2211yescharacteristic
20C22×#4326C2211yescharacteristic
21C2×#66945C2211yescharacteristic
22C2×#66925C2211yescharacteristic
23C2×C11×#106C2211yescharacteristic
24C2×C11×#103C2211yescharacteristic
25C2×C11×#103C2211yescharacteristic
26C2×C11×#97C2211yescharacteristic
27C11×#391C2211yescharacteristic
28C11×#391C2211yescharacteristic
29#10622843C2211yescharacteristic
30C2×#66899C2211yescharacteristic
31C2×#66899C2211yescharacteristic
32C2×#66899C2211yescharacteristic
33#10622799C418yescomplemented
34C2×(C2×D11)⋊C8C2211yescharacteristic
35C2×(C2×D11)⋊C8C2211yescharacteristic
36C2×#66880C2211yescharacteristic
37C2×#66880C2211yescharacteristic
38#10622600C2211yescharacteristic
39C4⋊C4×Dic11C2211yescharacteristic
40#10622587C2211yescharacteristic
41C2×#66874C2211yescharacteristic
42C2×#66871C2211yescharacteristic
43#10622542C2211yescharacteristic
44#10622541C2211yescharacteristic
45C2×C4×C11⋊C8C2211yescharacteristic
46#10622283—21no—
47#10622282—21no—
48#10622277—21no—
49#10622277—21no—
50#10622265—21no—
51#10622260—21no—
52#10622259—21no—
53#10622259—21no—
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60C22×Q8×C11C2311yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C2×Q8×D11—22no—
63C2×Q8×D11—41no—
64C2×Q8×D11—41no—
65C2×Q8×D11—41no—
66C2×Q8×D11—41no—
67C2×Q8×D11C2×C414yes—
68C22×C4×D11—21no—
69C22×C4×D11C2311yescharacteristic
70C22×Dic22—21no—
71C22×Dic22C2311yescharacteristic
72C2×C11×Q16—41no—
73C2×C11×Q16—41no—
74C2×C11×Q16C2×C414yes—
75C22×C8×C11C2311yescharacteristic
76C22×C8×C11C2311yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C42×C11C2311yescharacteristic
80#66999—22no—
81#66999C2×C414yes—
82Q8×Dic11—41no—
83Q8×Dic11—41no—
84C2×#4326—41no—
85C2×#4326—41no—
86C2×#4326C2×C414yes—
87C2×(C2×D11)⋊C4—21no—
88C2×(C2×D11)⋊C4—21no—
89C2×(C2×D11)⋊C4—21no—
90C2×(C2×D11)⋊C4D411yescharacteristic
91C2×(C2×D11)⋊C4D411yescharacteristic
92C2×C4⋊Dic11—21no—
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×C4⋊Dic11C2311yescharacteristic
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4—21no—
98C2×Dic11⋊C4D411yescharacteristic
99C2×Dic11⋊C4D411yescharacteristic
100C2×C4×Dic11—21no—
101C2×C4×Dic11—21no—
102C2×C4×Dic11—21no—
103C2×C4×Dic11C2311yescharacteristic
104C22×C11⋊C8C2311yescharacteristic
105C22×C11⋊C8C2311yescharacteristic
106#66945—41no—
107#66945—41no—
108#66925—41no—
109#66925—41no—
110C11×#106—41no—
111C11×#103—41no—
112C11×#103—41no—
113C11×#97—41no—
114C11×#95—21no—
115C11×#95—21no—
116C11×#95—21no—
117C11×#95—21no—
118#66899—41no—
119#66899—41no—
120#66899C2×C414yes—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125C11⋊#95—21no—
126C11⋊#95—21no—
127C11⋊#95—21no—
128C11⋊#95—21no—
129C11⋊#95—21no—
130(C2×D11)⋊C8—22no—
131(C2×D11)⋊C8C2×C414yes—
132#66880—41no—
133#66880C2×C414yes—
134#66874—41no—
135#66871—41no—
136C4×C11⋊C8—41no—
137#22054—111nomaximal, Sylow
138C23×D11C2×D411yescharacteristic
139C2×Q8×C11—21no—
140C2×Q8×C11—21no—
141C2×Q8×C11—21no—
142C2×Q8×C11—21no—
143C2×Q8×C11—21no—
144C2×Q8×C11—21no—
145C2×Q8×C11—21no—
146C2×Q8×C11—21no—
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×Q8×C11C22×C412yes—
150C2×Q8×C11C22×C412yes—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2411yescharacteristic
158C22×Dic11—21no—
159C22×Dic11—21no—
160C22×Dic11—21no—
161C22×Dic11—21no—
162C22×Dic11C2×D411yescharacteristic
163C22×Dic11C2×D411yescharacteristic
164C22×Dic11C2×D411yescharacteristic
165Q8×D11—44no—
166Q8×D11—44no—
167Q8×D11—44no—
168Q8×D11—44no—
169C2×C4×D11—24no—
170C2×C4×D11—21no—
171C2×C4×D11—21no—
172C2×C4×D11—21no—
173C2×C4×D11—21no—
174C2×C4×D11—42no—
175C2×C4×D11—42no—
176C2×C4×D11C22×C412yes—
177C2×C4×D11#4112yes—
178C2×Dic22—24no—
179C2×Dic22—21no—
180C2×Dic22—21no—
181C2×Dic22—21no—
182C2×Dic22—21no—
183C2×Dic22—21no—
184C2×Dic22—42no—
185C2×Dic22—42no—
186C2×Dic22C22×C412yes—
187C11×Q16—44no—
188C2×C8×C11—21no—
189C2×C8×C11—21no—
190C2×C8×C11—21no—
191C2×C8×C11—21no—
192C2×C8×C11—21no—
193C2×C8×C11C22×C412yes—
194C11×C4⋊C4—21no—
195C11×C4⋊C4—21no—
196C11×C4⋊C4—21no—
197C11×C4⋊C4—21no—
198C42×C11—21no—
199C42×C11—21no—
200#4326—44no—
201(C2×D11)⋊C4—24no—
202(C2×D11)⋊C4—41no—
203(C2×D11)⋊C4—41no—
204(C2×D11)⋊C4—42no—
205(C2×D11)⋊C4—81no—
206C4⋊Dic11—21no—
207C4⋊Dic11—21no—
208C4⋊Dic11—21no—
209C4⋊Dic11—21no—
210C4⋊Dic11—21no—
211C4⋊Dic11—42no—
212C4⋊Dic11C22×C412yes—
213Dic11⋊C4—24no—
214Dic11⋊C4—41no—
215Dic11⋊C4—41no—
216Dic11⋊C4—81no—
217C4×Dic11—21no—
218C4×Dic11—21no—
219C4×Dic11—42no—
220C4×Dic11—42no—
221C4×Dic11—81no—
222C2×C11⋊C8—21no—
223C2×C11⋊C8—21no—
224C2×C11⋊C8—21no—
225C2×C11⋊C8—21no—
226C2×C11⋊C8—21no—
227C2×C11⋊C8C22×C412yes—
228C2×#451—111no—
229#2323—111no—
230#2310—111no—
231#1971D1111yescharacteristic, complemented
232#1969—111no—
233#1935—111no—
234#1933—111no—
235#1928—111no—
236#1927—111no—
237#1878—111no—
238#1878—111no—
239#1873—111no—
240#1854—111no—
241#1787—111no—
242#1750—111no—
243C23×C11C22×D411yescharacteristic
244C22×D11—21no—
245C22×D11—21no—
246C22×D11—21no—
247C22×D11—21no—
248C22×D11—21no—
249C22×D11—21no—
250C22×D11C4×D412yes—
251Q8×C11—22no—
252Q8×C11—22no—
253Q8×C11—22no—
254Q8×C11—22no—
255Q8×C11—41no—
256Q8×C11—41no—
257Q8×C11—41no—
258Q8×C11—41no—
259C2×C4×C11—22no—
260C2×C4×C11—22no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
264C2×C4×C11—21no—
265C2×C4×C11—21no—
266C2×C4×C11—21no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11—41no—
270C2×C4×C11—41no—
271C2×C4×C11—41no—
272C2×C4×C11—41no—
273C2×C4×C11—41no—
274C2×C4×C11—41no—
275C2×C4×C11—41no—
276C2×C4×C11—41no—
277C2×C4×C11C23×C411yescharacteristic
278C2×C4×C11C2×#4111yescharacteristic
279C2×C4×C11H(5,𝔽2)11yescharacteristic
280C2×C4×C11H(5,𝔽2)11yescharacteristic
281C2×C4×C11H(5,𝔽2)11yescharacteristic
282C2×C4×C11H(5,𝔽2)11yescharacteristic
283C2×Dic11—21no—
284C2×Dic11—21no—
285C2×Dic11—22no—
286C2×Dic11—22no—
287C2×Dic11—21no—
288C2×Dic11—21no—
289C2×Dic11—21no—
290C2×Dic11—21no—
291C2×Dic11—21no—
292C2×Dic11—21no—
293C2×Dic11—41no—
294C2×Dic11—41no—
295C2×Dic11—41no—
296C2×Dic11—41no—
297C2×Dic11—41no—
298C2×Dic11—41no—
299C2×Dic11—41no—
300C2×Dic11—41no—
301C2×Dic11—41no—
302C2×Dic11—41no—
303C2×Dic11C4×D412yes—
304C4×D11—22no—
305C4×D11—22no—
306C4×D11—22no—
307C4×D11—22no—
308C4×D11—48no—
309Dic22—22no—
310Dic22—22no—
311Dic22—48no—
312Dic22—41no—
313Dic22—41no—
314C8×C11—22no—
315C8×C11—41no—
316C11⋊C8—22no—
317C11⋊C8—41no—
318C23×Q8—111no—
319C22×Q16—111no—
320C22×Q16C2×D1111yescharacteristic
321C2×C22⋊Q8—111no—
322C2×C4×Q8—111no—
323C2×#117—111no—
324C2×#117—111no—
325#451—118no—
326C2×#107—111no—
327C2×#106C2×D1111yescharacteristic
328C2×#103—111no—
329C2×#103—111no—
330C2×#103—111no—
331C2×#103—111no—
332C2×#103—111no—
333C2×#103—111no—
334C2×#103C2×D1111yescharacteristic
335C2×#103C2×D1111yescharacteristic
336C2×C22⋊C8—111no—
337C2×C22⋊C8—111no—
338C2×#97C2×D1111yescharacteristic
339C2×C4×C8—111no—
340#391—111no—
341#391—111no—
342#391—111no—
343#391—221no—
344#391—221no—
345#391C2×D1111yescharacteristic
346#391C2×D1111yescharacteristic
347#389—111no—
348#389—221no—
349#388—221no—
350#388—221no—
351#387—221no—
352#381—221no—
353#381—221no—
354#380—111no—
355C4×C4⋊C4—111no—
356#340—111no—
357#340—111no—
358#340—111no—
359#340—111no—
360#336—111no—
361#336—111no—
362C22×C11C2×C4×D411yescharacteristic
363C22×C11#53411yescharacteristic
364C22×C11#53511yescharacteristic
365C22×C11#57711yescharacteristic
366C22×C11#57811yescharacteristic
367C22×C11#57811yescharacteristic
368C22×C11#57811yescharacteristic
369C2×D11—22no—
370C2×D11—22no—
371C2×D11—22no—
372C2×D11—41no—
373C2×D11—41no—
374C2×D11—41no—
375C2×D11—41no—
376C4×C11—42no—
377C4×C11—42no—
378C4×C11—41no—
379C4×C11—41no—
380C4×C11—81no—
381C4×C11—81no—
382C4×C11#51811yescharacteristic
383C4×C11#51811yescharacteristic
384C4×C11#53811yescharacteristic
385C4×C11#53811yescharacteristic
386Dic11—22no—
387Dic11—42no—
388Dic11—41no—
389Dic11—41no—
390Dic11—42no—
391Dic11—81no—
392Dic11—81no—
393C22×Q8—114no—
394C22×Q8—111no—
395C22×Q8—221no—
396C22×Q8—222no—
397C22×Q8—441no—
398C22×Q8—441no—
399C22×Q8—441no—
400C22×Q8—441no—
401C22×Q8C22×D1111yescharacteristic
402C22×Q8C22×D1111yescharacteristic
403C23×C4—111no—
404C23×C4—221no—
405C2×Q16—41no—
406C2×Q16—41no—
407C2×Q16—114no—
408C2×Q16—441no—
409C2×Q16—441no—
410C2×Q16C4×D1114yes—
411C22×C8—111no—
412C22×C8—111no—
413C22×C8C22×D1111yescharacteristic
414C22×C8C22×D1111yescharacteristic
415C22⋊Q8—114no—
416C22⋊Q8—222no—
417C4×Q8—441no—
418C4×Q8—441no—
419#117—441no—
420#117—441no—
421#117—441no—
422#117—441no—
423C2×C4⋊C4—111no—
424C2×C4⋊C4—111no—
425C2×C4⋊C4—111no—
426C2×C4⋊C4—111no—
427C2×C4⋊C4—111no—
428C2×C4⋊C4—221no—
429C2×C4⋊C4—221no—
430C2×C4⋊C4—221no—
431C2×C4⋊C4C22×D1111yescharacteristic
432C2×C4⋊C4C22×D1111yescharacteristic
433C2×C22⋊C4—111no—
434C2×C22⋊C4—111no—
435C2×C22⋊C4—221no—
436C2×C22⋊C4—221no—
437C2×C22⋊C4—221no—
438C2×C42—111no—
439C2×C42—221no—
440C2×C42—221no—
441C2×C42—221no—
442C2×C42C22×D1111yescharacteristic
443#107—441no—
444#106—41no—
445#103—41no—
446#103—41no—
447#103—114no—
448#103—114no—
449#103—441no—
450#103—441no—
451#103—441no—
452#103—441no—
453C22⋊C8—114no—
454C22⋊C8—222no—
455#97—41no—
456C4×C8—441no—
457#95—21no—
458#95—21no—
459#95—21no—
460#95—21no—
461#95—221no—
462#95—221no—
463#95—221no—
464#95—221no—
465#95—221no—
466#95—221no—
467#95—221no—
468#95—221no—
469#95—221no—
470C2×C11#232111yescharacteristic
471C2×C11#294711yescharacteristic
472C2×C11#295011yescharacteristic
473C2×C11#320111yescharacteristic
474C2×C11#320211yescharacteristic
475C2×C11#322311yescharacteristic
476C2×C11#322511yescharacteristic
477D11—42no—
478C24—111no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—112no—
490C2×Q8—224no—
491C2×Q8—221no—
492C2×Q8—221no—
493C2×Q8—221no—
494C2×Q8—221no—
495C2×Q8—221no—
496C2×Q8—442no—
497C2×Q8—442no—
498C2×Q8—444no—
499C2×Q8—444no—
500C2×Q8—444no—
501C2×Q8—444no—
502C2×Q8C2×C4×D1112yes—
503C2×Q8C2×C4×D1112yes—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—111no—
509C22×C4—112no—
510C22×C4—112no—
511C22×C4—111no—
512C22×C4—111no—
513C22×C4—224no—
514C22×C4—221no—
515C22×C4—221no—
516C22×C4—221no—
517C22×C4—221no—
518C22×C4—221no—
519C22×C4—221no—
520C22×C4—221no—
521C22×C4—221no—
522C22×C4—442no—
523C22×C4—442no—
524C22×C4D4×D1111yescharacteristic
525C22×C4D4×D1111yescharacteristic
526C22×C4C23×D1111yescharacteristic
527Q16—44no—
528Q16—444no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—112no—
535C2×C8—221no—
536C2×C8—221no—
537C2×C8—221no—
538C2×C8—221no—
539C2×C8—221no—
540C2×C8C2×C4×D1112yes—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—112no—
546C4⋊C4—224no—
547C4⋊C4—221no—
548C4⋊C4—221no—
549C4⋊C4—221no—
550C4⋊C4—221no—
551C4⋊C4—221no—
552C4⋊C4—441no—
553C4⋊C4—441no—
554C4⋊C4—442no—
555C4⋊C4—881no—
556C22⋊C4—224no—
557C22⋊C4—441no—
558C22⋊C4—441no—
559C22⋊C4—442no—
560C22⋊C4—881no—
561C42—21no—
562C42—21no—
563C42—221no—
564C42—221no—
565C42—442no—
566C42—442no—
567C42—881no—
568C11#2205411yescharacteristic, complemented, Sylow
569C23—112no—
570C23—221no—
571C23—221no—
572C23—221no—
573C23—221no—
574C23—221no—
575C23—221no—
576C23C2×D4×D1111yescharacteristic
577Q8—22no—
578Q8—22no—
579Q8—22no—
580Q8—22no—
581Q8—41no—
582Q8—41no—
583Q8—41no—
584Q8—41no—
585Q8—222no—
586Q8—222no—
587Q8—448no—
588Q8—441no—
589Q8—441no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—112no—
609C2×C4—221no—
610C2×C4—221no—
611C2×C4—222no—
612C2×C4—222no—
613C2×C4—222no—
614C2×C4—222no—
615C2×C4—221no—
616C2×C4—221no—
617C2×C4—221no—
618C2×C4—221no—
619C2×C4—222no—
620C2×C4—222no—
621C2×C4—221no—
622C2×C4—221no—
623C2×C4—448no—
624C2×C4—441no—
625C2×C4—441no—
626C2×C4—441no—
627C2×C4—441no—
628C2×C4—441no—
629C2×C4—441no—
630C2×C4—441no—
631C2×C4—441no—
632C2×C4—441no—
633C2×C4—441no—
634C2×C4C22×C4×D1111yescharacteristic
635C2×C4#6703711yescharacteristic
636C2×C4#6703711yescharacteristic
637C2×C4#6703711yescharacteristic
638C2×C4#41×D1111yescharacteristic
639C2×C4#6704211yescharacteristic
640C8—22no—
641C8—41no—
642C8—222no—
643C8—441no—
644C22—222no—
645C22—222no—
646C22—222no—
647C22—441no—
648C22—441no—
649C22—441no—
650C22—441no—
651C22C4×D4×D1111yescharacteristic
652C22#1062313611yescharacteristic
653C22#1062324611yescharacteristic
654C22#1062330911yescharacteristic
655C22#1062331011yescharacteristic
656C22#1062331011yescharacteristic
657C22#1062331011yescharacteristic
658C4—42no—
659C4—42no—
660C4—41no—
661C4—41no—
662C4—81no—
663C4—81no—
664C4—222no—
665C4—442no—
666C4—441no—
667C4—442no—
668C4—441no—
669C4—881no—
670C4—881no—
671C4#1062301711yescharacteristic
672C4#1062307611yescharacteristic
673C4#1062314411yescharacteristic
674C4#1062320911yescharacteristic
675C2—442no—
676C2#1307127511yescharacteristic
677C2#1307745811yescharacteristic
678C2#1307748111yescharacteristic
679C2#1307949911yescharacteristic
680C2#1307950811yescharacteristic
681C2#1307969411yescharacteristic
682C2#1307972011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1971C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
cosocleC22×C4×C11C24
hypercenter#1971D11
hypocenterC11#22054
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1971

Complements

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

NH ≅ G/Ntype
4. #13069476C2semidirect
5. #13069306C2semidirect
6. #13069295C2semidirect
7. #13069260C2semidirect
8. #13069249C2semidirect
9. #13068959C2semidirect
10. #13068955C2semidirect
15. C11×#1971C2semidirect
33. #10622799C4semidirect
231. #1971D11semidirect
568. C11#22054semidirect

Maximal subgroups

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

subgroupindex
C2×#106227992
#130713012
#130711992
#130694762
#130693062
#130692952
#130692602
#130692492
#130689592
#130689552
#130689252
#130688142
#130685492
#130683852
C11×#19712
#2205411