Finite Group Databasebeta

← #14810695

Subgroups — #14810695

Order 2816.

1028 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623098C211yesmaximal, characteristic, complemented
2C2×#10622669C211yesmaximal, characteristic
3C2×#10622667C211yesmaximal, characteristic
4#13069767C211yesmaximal, characteristic, complemented
5#13069762C211yesmaximal, characteristic
6#13069757C211yesmaximal, characteristic, complemented
7#13069752C211yesmaximal, characteristic
8#13069573C211yesmaximal, characteristic, complemented
9#13069553C211yesmaximal, characteristic, complemented
10#13068974C211yesmaximal, characteristic
11#13068974C211yesmaximal, characteristic
12#13068960C211yesmaximal, characteristic, complemented
13#13068960C211yesmaximal, characteristic, complemented
14C4×#66874C211yesmaximal, characteristic, complemented
15C11×#2592C211yesmaximal, characteristic
16C2×C11×#124C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×#66997—21no—
19C22×#4326C2211yescharacteristic
20C22×#4324C2211yescharacteristic
21#10623098—24no—
22#10623098—24no—
23C2×#66942—21no—
24C2×#66942—21no—
25C2×#66940—21no—
26C2×#66923C2211yescharacteristic
27C2×#66923C2211yescharacteristic
28C2×#66922C2211yescharacteristic
29C2×C4×Dic22C2211yescharacteristic
30C2×C4×Dic22C2211yescharacteristic
31C2×C4×Dic22C2211yescharacteristic
32C11×#397—21no—
33C11×#393—21no—
34C11×#391C2211yescharacteristic
35C11×#391C2211yescharacteristic
36C11×#390C2211yescharacteristic
37C11×#390C2211yescharacteristic
38C11×#388—21no—
39C11×#388—21no—
40C4×C11×C4⋊C4C2211yescharacteristic
41C2×#66899C2211yescharacteristic
42C2×#66899C2211yescharacteristic
43C2×#66899C2211yescharacteristic
44C2×#66896C2211yescharacteristic
45C2×#66896C2211yescharacteristic
46C2×#66896C2211yescharacteristic
47#10622669—24no—
48#10622667—24no—
49C2×#66874C2211yescharacteristic
50C2×#66874C2211yescharacteristic
51C2×C4⋊(C11⋊C8)C2211yescharacteristic
52C2×C4×C11⋊C8C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622162C2211yescharacteristic
60#10622162C2211yescharacteristic
61#10622162C2211yescharacteristic
62#10622162C2211yescharacteristic
63C22×Q8×C11D411yescharacteristic
64C22×Q8×C11C2311yescharacteristic
65C22×D4×C11C2311yescharacteristic
66C22×Dic22—21no—
67C22×Dic22C2311yescharacteristic
68C11×#124—22no—
69C11×#124—22no—
70C4×Q8×C11—22no—
71C4×Q8×C11—22no—
72C2×C11×C4⋊C4D411yescharacteristic
73C2×C11×C4⋊C4D411yescharacteristic
74C2×C11×C4⋊C4D411yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C22⋊C4—21no—
78C2×C11×C22⋊C4—21no—
79C2×C11×C22⋊C4—21no—
80C2×C11×C22⋊C4—21no—
81C2×C11×C22⋊C4—21no—
82C2×C11×C22⋊C4—21no—
83C2×C42×C11—21no—
84C2×C42×C11C2311yescharacteristic
85C2×C42×C11C2311yescharacteristic
86C2×C42×C11C2311yescharacteristic
87#66997—28no—
88C2×#4326—22no—
89C2×#4326—22no—
90C2×#4326—22no—
91C2×#4324—22no—
92C2×#4324—22no—
93C2×#4324—22no—
94C2×C4⋊Dic11—21no—
95C2×C4⋊Dic11C2311yescharacteristic
96C2×C4⋊Dic11C2311yescharacteristic
97C2×C4⋊Dic11C2311yescharacteristic
98C2×Dic11⋊C4—21no—
99C2×Dic11⋊C4—21no—
100C2×Dic11⋊C4—21no—
101C2×Dic11⋊C4—21no—
102C2×Dic11⋊C4—21no—
103C2×Dic11⋊C4—21no—
104C2×Dic11⋊C4—21no—
105C2×C4×Dic11—21no—
106C2×C4×Dic11—21no—
107C2×C4×Dic11—21no—
108C22×C11⋊C8C2311yescharacteristic
109C22×C11⋊C8C2311yescharacteristic
110C22×C11⋊C8C2311yescharacteristic
111C22×C11⋊C8C2311yescharacteristic
112#66942—28no—
113#66942—28no—
114#66940—28no—
115#66923—22no—
116#66923—22no—
117#66923—22no—
118#66923D414yes—
119#66922—22no—
120#66922—22no—
121C4×Dic22—22no—
122C4×Dic22—22no—
123C4×Dic22—22no—
124C4×Dic22—22no—
125C4×Dic22—22no—
126C4×Dic22D414yes—
127C11×#95—21no—
128C11×#95—21no—
129C11×#95—21no—
130C11×#95—21no—
131C11×#95—21no—
132#66899—22no—
133#66899—22no—
134#66899—22no—
135#66896—22no—
136#66896—22no—
137#66896—22no—
138#66874—22no—
139#66874—22no—
140C4⋊(C11⋊C8)—22no—
141C4×C11⋊C8—22no—
142#25937—111nomaximal, Sylow
143C24×C11—21no—
144C2×Q8×C11—22no—
145C2×Q8×C11—22no—
146C2×Q8×C11—21no—
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×Q8×C11—21no—
150C2×Q8×C11—21no—
151C2×Q8×C11—21no—
152C2×Q8×C11—41no—
153C2×D4×C11—21no—
154C2×D4×C11—21no—
155C2×D4×C11—21no—
156C2×D4×C11—21no—
157C2×D4×C11—21no—
158C2×D4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11C2×D411yescharacteristic
164C22×C4×C11C2×D411yescharacteristic
165C22×C4×C11C2×D411yescharacteristic
166C22×C4×C11C2×D411yescharacteristic
167C22×C4×C11C2×D411yescharacteristic
168C22×C4×C11C2411yescharacteristic
169C22×Dic11—21no—
170C22×Dic11—21no—
171C22×Dic11—21no—
172C22×Dic11—21no—
173C2×Dic22—24no—
174C2×Dic22—21no—
175C2×Dic22—21no—
176C2×Dic22—21no—
177C2×Dic22—42no—
178C2×Dic22—42no—
179C2×Dic22C2×D412yes—
180C2×Dic22#4112yes—
181C2×Dic22#4112yes—
182C11×C4⋊C4—22no—
183C11×C4⋊C4—22no—
184C11×C4⋊C4—22no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—21no—
189C11×C22⋊C4—42no—
190C11×C22⋊C4—42no—
191C11×C22⋊C4—42no—
192C11×C22⋊C4—42no—
193C11×C22⋊C4—81no—
194C11×C22⋊C4—81no—
195C42×C11—21no—
196C42×C11—21no—
197C42×C11—21no—
198C42×C11—21no—
199C42×C11—81no—
200C42×C11C2×D412yes—
201C42×C11C2×D412yes—
202#4326—44no—
203#4324—44no—
204C4⋊Dic11—24no—
205C4⋊Dic11—21no—
206C4⋊Dic11—21no—
207C4⋊Dic11—21no—
208C4⋊Dic11C2×D412yes—
209C4⋊Dic11C2×D412yes—
210C4⋊Dic11C2×D412yes—
211Dic11⋊C4—24no—
212Dic11⋊C4—24no—
213Dic11⋊C4—24no—
214Dic11⋊C4—24no—
215Dic11⋊C4—24no—
216Dic11⋊C4—24no—
217Dic11⋊C4—24no—
218C4×Dic11—24no—
219C4×Dic11—24no—
220C4×Dic11—24no—
221C2×C11⋊C8—21no—
222C2×C11⋊C8—21no—
223C2×C11⋊C8—21no—
224C2×C11⋊C8—21no—
225C2×C11⋊C8—21no—
226C2×C11⋊C8—21no—
227C2×C11⋊C8—21no—
228C2×C11⋊C8—21no—
229C2×C11⋊C8—21no—
230C2×C11⋊C8—21no—
231C2×C11⋊C8—21no—
232C2×C11⋊C8—21no—
233C2×#557—111no—
234C2×#488—111no—
235C2×#464—111no—
236#2592D1111yescharacteristic
237#2026—111no—
238#2025—111no—
239#2024—111no—
240#2023—111no—
241#1989—111no—
242#1984—111no—
243#1880—111no—
244#1880—111no—
245#1878—111no—
246#1878—111no—
247C4×#103—111no—
248C23×C11—41no—
249C23×C11—41no—
250C23×C11—41no—
251C23×C11—41no—
252C23×C11—41no—
253C23×C11—41no—
254C23×C11—41no—
255C23×C11C22×D411yescharacteristic
256Q8×C11—44no—
257Q8×C11—41no—
258Q8×C11—41no—
259Q8×C11—41no—
260Q8×C11—41no—
261D4×C11—41no—
262D4×C11—41no—
263D4×C11—41no—
264D4×C11—41no—
265C2×C4×C11—21no—
266C2×C4×C11—21no—
267C2×C4×C11—21no—
268C2×C4×C11—21no—
269C2×C4×C11—21no—
270C2×C4×C11—21no—
271C2×C4×C11—21no—
272C2×C4×C11—21no—
273C2×C4×C11—21no—
274C2×C4×C11—21no—
275C2×C4×C11—21no—
276C2×C4×C11—21no—
277C2×C4×C11—21no—
278C2×C4×C11—21no—
279C2×C4×C11—21no—
280C2×C4×C11—41no—
281C2×C4×C11—41no—
282C2×C4×C11—41no—
283C2×C4×C11—41no—
284C2×C4×C11—41no—
285C2×C4×C11—41no—
286C2×C4×C11—41no—
287C2×C4×C11—41no—
288C2×C4×C11—41no—
289C2×C4×C11#12012yes—
290C2×C4×C11#12012yes—
291C2×C4×C11#13512yes—
292C2×C4×C11C22×D411yescharacteristic
293C2×C4×C11C22×D411yescharacteristic
294C2×C4×C11C2×#4111yescharacteristic
295C2×C4×C11C2×#4111yescharacteristic
296C2×C4×C112−1+411yescharacteristic
297C2×C4×C112−1+411yescharacteristic
298C2×Dic11—22no—
299C2×Dic11—22no—
300C2×Dic11—22no—
301C2×Dic11—22no—
302C2×Dic11—22no—
303C2×Dic11—22no—
304C2×Dic11—41no—
305C2×Dic11—41no—
306C2×Dic11—41no—
307C2×Dic11—41no—
308C2×Dic11—41no—
309C2×Dic11—41no—
310Dic22—22no—
311Dic22—22no—
312Dic22—22no—
313Dic22—48no—
314Dic22#12414yes—
315C11⋊C8—41no—
316C11⋊C8—41no—
317C11⋊C8—41no—
318C11⋊C8—41no—
319C22×Q16—111no—
320C22×SD16—111no—
321#557—224no—
322#557—224no—
323C2×C4⋊Q8—111no—
324C2×C4⋊Q8—221no—
325C2×#125—111no—
326C2×#125—111no—
327C2×#125—221no—
328C2×#125—221no—
329C2×#124C2×D1111yescharacteristic
330C2×C4×Q8—111no—
331C2×C4×Q8—111no—
332C2×C4×Q8—111no—
333C2×C4×Q8—221no—
334C2×C4×Q8C2×D1111yescharacteristic
335#488—224no—
336#464—224no—
337C2×C4⋊C8—111no—
338C2×#103—111no—
339C2×#103—111no—
340C2×#103—111no—
341C2×#103—111no—
342C2×#103—111no—
343C2×#102—111no—
344C2×#102—111no—
345C2×#102—111no—
346C2×C4×C8—111no—
347#397—21no—
348#393—21no—
349#391C2×D1111yescharacteristic
350#391C2×D1111yescharacteristic
351#390C2×D1111yescharacteristic
352#390C2×D1111yescharacteristic
353#388—21no—
354#388—21no—
355C4×C4⋊C4C2×D1111yescharacteristic
356#340—111no—
357#340—111no—
358#340—111no—
359#340—111no—
360#340—111no—
361#340—111no—
362#336—111no—
363#336—111no—
364#336—111no—
365#336—111no—
366C22×C11—81no—
367C22×C11—81no—
368C22×C11—81no—
369C22×C11—81no—
370C22×C11—81no—
371C22×C11—81no—
372C22×C11—81no—
373C22×C11C2×#12011yescharacteristic
374C22×C11#54811yescharacteristic
375C22×C11#54811yescharacteristic
376C22×C11C2×#13511yescharacteristic
377C22×C11#57511yescharacteristic
378C22×C11#57711yescharacteristic
379C22×C11#57811yescharacteristic
380C4×C11—22no—
381C4×C11—22no—
382C4×C11—22no—
383C4×C11—41no—
384C4×C11—41no—
385C4×C11—41no—
386C4×C11—81no—
387C4×C11—81no—
388C4×C11—81no—
389C4×C11C2×#12411yescharacteristic
390C4×C11#53611yescharacteristic
391C4×C11#54811yescharacteristic
392C4×C11#54811yescharacteristic
393Dic11—24no—
394Dic11—42no—
395Dic11—42no—
396Dic11—42no—
397C22×Q8—111no—
398C22×Q8—221no—
399C22×Q8C22⋊D1111yescharacteristic
400C22×Q8C22×D1111yescharacteristic
401C22×D4C22×D1111yescharacteristic
402C2×Q16—222no—
403C2×Q16—222no—
404C2×Q16—222no—
405C2×SD16—222no—
406C2×SD16—222no—
407C2×SD16—222no—
408C22×C8—111no—
409C22×C8—111no—
410C22×C8—111no—
411C22×C8—111no—
412C4⋊Q8—222no—
413C4⋊Q8—222no—
414C4⋊Q8—228no—
415#125—114no—
416#125—222no—
417#125—222no—
418#125—228no—
419#125—228no—
420#125—222no—
421#124—22no—
422#124—22no—
423C4×Q8—22no—
424C4×Q8—22no—
425C4×Q8—114no—
426C4×Q8—222no—
427C4×Q8—222no—
428C4×Q8—222no—
429C4×Q8—222no—
430C4×Q8—228no—
431C4×Q8—222no—
432C2×C4⋊C4—111no—
433C2×C4⋊C4—111no—
434C2×C4⋊C4—111no—
435C2×C4⋊C4—221no—
436C2×C4⋊C4—221no—
437C2×C4⋊C4—221no—
438C2×C4⋊C4—221no—
439C2×C4⋊C4—221no—
440C2×C4⋊C4—221no—
441C2×C4⋊C4—221no—
442C2×C4⋊C4—221no—
443C2×C4⋊C4C22⋊D1111yescharacteristic
444C2×C4⋊C4C22⋊D1111yescharacteristic
445C2×C4⋊C4C22⋊D1111yescharacteristic
446C2×C4⋊C4C22×D1111yescharacteristic
447C2×C4⋊C4C22×D1111yescharacteristic
448C2×C22⋊C4—21no—
449C2×C22⋊C4—21no—
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C42—21no—
455C2×C42—221no—
456C2×C42—221no—
457C2×C42—221no—
458C2×C42C22×D1111yescharacteristic
459C2×C42C22×D1111yescharacteristic
460C2×C42C22×D1111yescharacteristic
461C4⋊C8—222no—
462#103—222no—
463#103—222no—
464#103—222no—
465#103—222no—
466#103—222no—
467#102—222no—
468#102—222no—
469#102—222no—
470C4×C8—222no—
471#95—21no—
472#95—21no—
473#95—21no—
474#95—21no—
475#95—21no—
476C2×C11—161no—
477C2×C11#243611yescharacteristic
478C2×C11#300211yescharacteristic
479C2×C11#301311yescharacteristic
480C2×C11#336411yescharacteristic
481C2×C11#336511yescharacteristic
482C2×C11#337111yescharacteristic
483C2×C11#337711yescharacteristic
484C24—21no—
485C2×Q8—22no—
486C2×Q8—22no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—41no—
494C2×Q8—112no—
495C2×Q8—112no—
496C2×Q8—112no—
497C2×Q8—224no—
498C2×Q8—221no—
499C2×Q8—221no—
500C2×Q8—221no—
501C2×Q8—442no—
502C2×Q8—442no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—221no—
513C22×C4—221no—
514C22×C4—221no—
515C22×C4—221no—
516C22×C4C2×C22⋊D1111yescharacteristic
517C22×C4C2×C22⋊D1111yescharacteristic
518C22×C4C2×C22⋊D1111yescharacteristic
519C22×C4C2×C22⋊D1111yescharacteristic
520C22×C4C2×C22⋊D1111yescharacteristic
521C22×C4C2×C22⋊D1111yescharacteristic
522C22×C4C23×D1111yescharacteristic
523Q16—444no—
524SD16—444no—
525C2×C8—221no—
526C2×C8—221no—
527C2×C8—221no—
528C2×C8—221no—
529C2×C8—221no—
530C2×C8—221no—
531C2×C8—221no—
532C2×C8—221no—
533C2×C8—221no—
534C2×C8—221no—
535C2×C8—221no—
536C2×C8—221no—
537C4⋊C4—22no—
538C4⋊C4—22no—
539C4⋊C4—22no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—112no—
545C4⋊C4—112no—
546C4⋊C4—112no—
547C4⋊C4—224no—
548C4⋊C4—224no—
549C4⋊C4—224no—
550C4⋊C4—224no—
551C4⋊C4—224no—
552C4⋊C4—224no—
553C4⋊C4—224no—
554C4⋊C4—224no—
555C4⋊C4—221no—
556C4⋊C4—221no—
557C4⋊C4—221no—
558C22⋊C4—42no—
559C22⋊C4—42no—
560C22⋊C4—42no—
561C22⋊C4—42no—
562C22⋊C4—81no—
563C22⋊C4—81no—
564C42—21no—
565C42—21no—
566C42—21no—
567C42—21no—
568C42—81no—
569C42—224no—
570C42—224no—
571C42—224no—
572C42D4×D1112yes—
573C42D4×D1112yes—
574C11#2593711yescharacteristic, complemented, Sylow
575C23—41no—
576C23—41no—
577C23—41no—
578C23—41no—
579C23—41no—
580C23—41no—
581C23—41no—
582C23C22×C22⋊D1111yescharacteristic
583Q8—44no—
584Q8—41no—
585Q8—41no—
586Q8—41no—
587Q8—41no—
588Q8—114no—
589Q8—222no—
590Q8—222no—
591Q8—222no—
592Q8—448no—
593D4—41no—
594D4—41no—
595D4—41no—
596D4—41no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—222no—
622C2×C4—222no—
623C2×C4—222no—
624C2×C4—222no—
625C2×C4—222no—
626C2×C4—222no—
627C2×C4—441no—
628C2×C4—441no—
629C2×C4—441no—
630C2×C4—441no—
631C2×C4—441no—
632C2×C4—441no—
633C2×C4#6699012yes—
634C2×C4#6699012yes—
635C2×C4#6700312yes—
636C2×C4C2×D4×D1111yescharacteristic
637C2×C4C2×D4×D1111yescharacteristic
638C2×C4#41×D1111yescharacteristic
639C2×C4#41×D1111yescharacteristic
640C2×C4#6704311yescharacteristic
641C2×C4#6704311yescharacteristic
642C8—441no—
643C8—441no—
644C8—441no—
645C8—441no—
646C22—81no—
647C22—81no—
648C22—81no—
649C22—81no—
650C22—81no—
651C22—81no—
652C22—81no—
653C22C2×#6699011yescharacteristic
654C22C2×#6700311yescharacteristic
655C22#1062335311yescharacteristic
656C22#1062336211yescharacteristic
657C22#1062336211yescharacteristic
658C22#1062336711yescharacteristic
659C22#1062336911yescharacteristic
660C4—22no—
661C4—22no—
662C4—22no—
663C4—41no—
664C4—41no—
665C4—41no—
666C4—81no—
667C4—81no—
668C4—81no—
669C4—224no—
670C4—442no—
671C4—442no—
672C4—442no—
673C4D11×#12411yescharacteristic
674C4#1062320611yescharacteristic
675C4#1062320811yescharacteristic
676C4#1062320811yescharacteristic
677C2—161no—
678C2#1307227111yescharacteristic
679C2#1307783211yescharacteristic
680C2#1307792811yescharacteristic
681C2#1308129711yescharacteristic
682C2#1308130811yescharacteristic
683C2#1308137811yescharacteristic
684C2#1308145211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2592C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenter#2592D11
hypocenterC11#25937
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ #2592

Complements

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

NH ≅ G/Ntype
1. C2×#10623098C2semidirect
4. #13069767C2semidirect
6. #13069757C2semidirect
8. #13069573C2semidirect
9. #13069553C2semidirect
12. #13068960C2semidirect
13. #13068960C2semidirect
14. C4×#66874C2semidirect
574. C11#25937semidirect

Maximal subgroups

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

subgroupindex
C2×#106230982
C2×#106226692
C2×#106226672
#130697672
#130697622
#130697572
#130697522
#130695732
#130695532
#130689742
#130689602
C4×#668742
C11×#25922
#2593711