Finite Group Databasebeta

← #14803255

Subgroups — #14803255

Order 2816.

828 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622684C211yesmaximal, characteristic
2C2×#10622635C211yesmaximal, characteristic, complemented
3#13071710C211yesmaximal, characteristic, complemented
4#13070004C211yesmaximal, characteristic, complemented
5#13069990C211yesmaximal, characteristic, complemented
6#13069852C211yesmaximal, characteristic, complemented
7#13069852C211yesmaximal, characteristic, complemented
8#13069549C211yesmaximal, characteristic, complemented
9#13069549C211yesmaximal, characteristic, complemented
10#13069544C211yesmaximal, characteristic
11#13069340C211yesmaximal, characteristic, complemented
12#13069240C211yesmaximal, characteristic, complemented
13#13069233C211yesmaximal, characteristic, complemented
14#13068446C211yesmaximal, characteristic, complemented
15C11×#2548C211yesmaximal, characteristic
16C2×C11×#127C2211yescharacteristic
17C2×C11×#124C2211yescharacteristic
18C2×C11×#124C2211yescharacteristic
19C2×C4×Q8×C11C2211yescharacteristic
20C2×#66923C2211yescharacteristic
21C11×#394—21no—
22C11×#394—21no—
23C11×#390—21no—
24C11×#390—21no—
25C11×#390C2211yescharacteristic
26C11×#390C2211yescharacteristic
27C4×C11×C4⋊C4C2211yescharacteristic
28C2×#66899C2211yescharacteristic
29C2×#66899C2211yescharacteristic
30C2×#66899C2211yescharacteristic
31C2×#66899C2211yescharacteristic
32C2×#66896C2211yescharacteristic
33C2×#66896C2211yescharacteristic
34C2×#66896C2211yescharacteristic
35C2×#66896C2211yescharacteristic
36C2×#66896C2211yescharacteristic
37C2×#66896C2211yescharacteristic
38C2×#66896C2211yescharacteristic
39C2×#66896C2211yescharacteristic
40#10622684—24no—
41#10622635—24no—
42#10622591—21no—
43#10622585—21no—
44C2×#66872C2211yescharacteristic
45C2×#66871C2211yescharacteristic
46C4×C4⋊Dic11C2211yescharacteristic
47C4×C4⋊Dic11C2211yescharacteristic
48C4×C4⋊Dic11C2211yescharacteristic
49#10622541C2211yescharacteristic
50#10622541C2211yescharacteristic
51C2×C4⋊(C11⋊C8)C2211yescharacteristic
52C2×C4⋊(C11⋊C8)C2211yescharacteristic
53C2×C4⋊(C11⋊C8)C2211yescharacteristic
54C2×#66867C2211yescharacteristic
55#10622265—21no—
56#10622262—21no—
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622162C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C22×D4×C11—21no—
63C22×D4×C11—21no—
64C22×D4×C11C2311yescharacteristic
65C22×D4×C11C2311yescharacteristic
66C11×#127—22no—
67C11×#127—22no—
68C11×#124—22no—
69C11×#124—22no—
70C11×#124—41no—
71C11×#124—41no—
72C4×Q8×C11—22no—
73C4×Q8×C11—22no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4D411yescharacteristic
76C2×C11×C4⋊C4D411yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
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×C11×C22⋊C4—21no—
84C2×C11×C22⋊C4—21no—
85C2×C11×C22⋊C4—21no—
86C2×C42×C11—21no—
87C2×C42×C11C2311yescharacteristic
88C2×C42×C11C2311yescharacteristic
89C2×C42×C11C2311yescharacteristic
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×Dic11⋊C4—21no—
95C2×Dic11⋊C4—21no—
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4—21no—
98C2×C4×Dic11—21no—
99C2×C4×Dic11—21no—
100C2×C4×Dic11—21no—
101C22×C11⋊C8C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103C22×C11⋊C8C2311yescharacteristic
104C22×C11⋊C8C2311yescharacteristic
105#66923—22no—
106#66923D414yes—
107C11×#95D411yescharacteristic
108C11×#95D411yescharacteristic
109#66899—22no—
110#66899—22no—
111#66899—22no—
112#66899—22no—
113#66896—22no—
114#66896—22no—
115#66896—22no—
116#66896—22no—
117#66896—22no—
118#66896—22no—
119#66896—41no—
120#66896—41no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125C11⋊#95—21no—
126#66872—22no—
127#66871—22no—
128C4⋊(C11⋊C8)—22no—
129C4⋊(C11⋊C8)—41no—
130C4⋊(C11⋊C8)—41no—
131#66867—22no—
132#25291—111nomaximal, Sylow
133C24×C11—21no—
134C24×C11—21no—
135C2×Q8×C11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11—21no—
138C2×Q8×C11—21no—
139C2×Q8×C11—21no—
140C2×Q8×C11#4112yes—
141C2×D4×C11—21no—
142C2×D4×C11—21no—
143C2×D4×C11—21no—
144C2×D4×C11—21no—
145C2×D4×C11—21no—
146C2×D4×C11—21no—
147C2×D4×C11—21no—
148C2×D4×C11—21no—
149C2×D4×C11—21no—
150C2×D4×C11—21no—
151C2×D4×C11—21no—
152C2×D4×C11—21no—
153C2×D4×C11—42no—
154C2×D4×C11—42no—
155C2×D4×C11—42no—
156C2×D4×C11—42no—
157C2×D4×C11—81no—
158C2×D4×C11—81no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11C2×D411yescharacteristic
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11C2×D411yescharacteristic
164C22×C4×C11C2×D411yescharacteristic
165C22×C4×C11C2×D411yescharacteristic
166C22×C4×C11C2×D411yescharacteristic
167C22×C4×C11C2411yescharacteristic
168C22×Dic11—21no—
169C22×Dic11—21no—
170C22×Dic11—21no—
171C22×Dic11—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—41no—
175C11×C4⋊C4—41no—
176C11×C4⋊C4—42no—
177C11×C22⋊C4—42no—
178C11×C22⋊C4—42no—
179C11×C22⋊C4—42no—
180C11×C22⋊C4—42no—
181C11×C22⋊C4—81no—
182C11×C22⋊C4—81no—
183C11×C22⋊C4—81no—
184C11×C22⋊C4—81no—
185C42×C11—21no—
186C42×C11—21no—
187C42×C11—21no—
188C42×C11—21no—
189C42×C11—42no—
190C42×C11C2×D412yes—
191C42×C11#4112yes—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11C2×D412yes—
198C4⋊Dic11C2×D412yes—
199C4⋊Dic11#4112yes—
200Dic11⋊C4—24no—
201Dic11⋊C4—24no—
202Dic11⋊C4—42no—
203Dic11⋊C4—81no—
204C4×Dic11—42no—
205C4×Dic11—81no—
206C4×Dic11—81no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8—21no—
217C2×C11⋊C8—21no—
218C2×C11⋊C8—21no—
219C2×#490—111no—
220C2×#479—111no—
221#2548D1111yescharacteristic
222#2370—111no—
223#2067—111no—
224#2065—111no—
225#2042—111no—
226#2042—111no—
227#1983—111no—
228#1983—111no—
229#1982—111no—
230#1940—111no—
231#1926—111no—
232#1925—111no—
233#1763—111no—
234C23×C11—41no—
235C23×C11—41no—
236C23×C11—41no—
237C23×C11—41no—
238C23×C11—41no—
239C23×C11—41no—
240C23×C11—41no—
241C23×C11—41no—
242C23×C11—41no—
243C23×C11—41no—
244C23×C11—41no—
245C23×C11—41no—
246C23×C11—41no—
247C23×C11—41no—
248C23×C11C22×D411yescharacteristic
249Q8×C11—22no—
250Q8×C11—22no—
251Q8×C11—41no—
252Q8×C11—41no—
253D4×C11—41no—
254D4×C11—41no—
255D4×C11—41no—
256D4×C11—41no—
257D4×C11—41no—
258D4×C11—41no—
259D4×C11—41no—
260D4×C11—41no—
261D4×C11—84no—
262D4×C11—84no—
263C2×C4×C11—21no—
264C2×C4×C11—21no—
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—22no—
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#12112yes—
286C2×C4×C11#12112yes—
287C2×C4×C11C22×D411yescharacteristic
288C2×C4×C11C2×#4111yescharacteristic
289C2×C4×C11C2×#4111yescharacteristic
290C2×C4×C11C2×#4111yescharacteristic
291C2×C4×C11H(5,𝔽2)11yescharacteristic
292C2×C4×C112−1+411yescharacteristic
293C2×Dic11—22no—
294C2×Dic11—22no—
295C2×Dic11—22no—
296C2×Dic11—41no—
297C2×Dic11—41no—
298C2×Dic11—41no—
299C2×Dic11—41no—
300C2×Dic11—41no—
301C2×Dic11—41no—
302C2×Dic11—41no—
303C2×Dic11—41no—
304C2×Dic11—41no—
305C11⋊C8—41no—
306C11⋊C8—41no—
307C11⋊C8—41no—
308C11⋊C8—41no—
309C2×#127C2×D1111yescharacteristic
310C2×#125—111no—
311C2×#124C2×D1111yescharacteristic
312C2×#124C2×D1111yescharacteristic
313C2×C4×Q8C2×D1111yescharacteristic
314#490—224no—
315#479—224no—
316C2×#107—111no—
317C2×#106—111no—
318C2×C4⋊C8—111no—
319C2×C4⋊C8—111no—
320C2×C4⋊C8—111no—
321C2×#103—111no—
322C2×#103—111no—
323C2×#103—111no—
324C2×#103—111no—
325C2×#102—111no—
326C2×#102—111no—
327C2×#102—111no—
328C2×#102—111no—
329C2×#102—111no—
330C2×#102—111no—
331C2×#102—111no—
332C2×#102—111no—
333C2×#97—111no—
334#394—21no—
335#394—21no—
336#390—21no—
337#390—21no—
338#390C2×D1111yescharacteristic
339#390C2×D1111yescharacteristic
340#389—111no—
341#389—111no—
342#389—221no—
343#387—221no—
344#387—221no—
345C4×C4⋊C4—111no—
346C4×C4⋊C4—111no—
347C4×C4⋊C4—111no—
348C4×C4⋊C4—221no—
349C4×C4⋊C4C2×D1111yescharacteristic
350#340—111no—
351#340—111no—
352#336—111no—
353#336—111no—
354C22×C11—81no—
355C22×C11—81no—
356C22×C11—81no—
357C22×C11—81no—
358C22×C11—81no—
359C22×C11—81no—
360C22×C11—81no—
361C22×C11—81no—
362C22×C11—81no—
363C22×C11—81no—
364C22×C11—81no—
365C22×C11—81no—
366C22×C11—81no—
367C22×C11—81no—
368C22×C11C2×#12111yescharacteristic
369C22×C11#54611yescharacteristic
370C22×C11#54811yescharacteristic
371C22×C11#57511yescharacteristic
372C22×C11#57511yescharacteristic
373C22×C11#57611yescharacteristic
374C22×C11#57711yescharacteristic
375C4×C11—22no—
376C4×C11—22no—
377C4×C11—42no—
378C4×C11—41no—
379C4×C11—41no—
380C4×C11—41no—
381C4×C11—41no—
382C4×C11—81no—
383C4×C11#52911yescharacteristic
384C4×C11#54211yescharacteristic
385C4×C11#54811yescharacteristic
386C4×C11#55011yescharacteristic
387Dic11—42no—
388Dic11—42no—
389Dic11—42no—
390Dic11—81no—
391C22×Q8C22×D1111yescharacteristic
392C22×D4—21no—
393C22×D4—21no—
394C22×D4C22×D1111yescharacteristic
395C22×D4C22×D1111yescharacteristic
396C22×C8—111no—
397C22×C8—111no—
398C22×C8—111no—
399C22×C8—111no—
400#127—22no—
401#127—22no—
402#125—114no—
403#125—222no—
404#124—22no—
405#124—22no—
406#124—41no—
407#124—41no—
408C4×Q8—22no—
409C4×Q8—22no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—111no—
412C2×C4⋊C4—111no—
413C2×C4⋊C4—111no—
414C2×C4⋊C4—111no—
415C2×C4⋊C4—221no—
416C2×C4⋊C4—221no—
417C2×C4⋊C4—221no—
418C2×C4⋊C4—221no—
419C2×C4⋊C4C22⋊D1111yescharacteristic
420C2×C4⋊C4C22⋊D1111yescharacteristic
421C2×C4⋊C4C22×D1111yescharacteristic
422C2×C22⋊C4—21no—
423C2×C22⋊C4—21no—
424C2×C22⋊C4—21no—
425C2×C22⋊C4—21no—
426C2×C22⋊C4—21no—
427C2×C22⋊C4—21no—
428C2×C22⋊C4—21no—
429C2×C22⋊C4—21no—
430C2×C42—21no—
431C2×C42—221no—
432C2×C42—221no—
433C2×C42—221no—
434C2×C42C22×D1111yescharacteristic
435C2×C42C22×D1111yescharacteristic
436C2×C42C22×D1111yescharacteristic
437#107—222no—
438#106—222no—
439C4⋊C8—222no—
440C4⋊C8—441no—
441C4⋊C8—441no—
442#103—222no—
443#103—222no—
444#103—222no—
445#103—222no—
446#102—222no—
447#102—222no—
448#102—222no—
449#102—222no—
450#102—222no—
451#102—222no—
452#102—441no—
453#102—441no—
454#97—222no—
455#95—221no—
456#95—221no—
457#95—221no—
458#95—221no—
459#95—221no—
460#95C22⋊D1111yescharacteristic
461#95C22⋊D1111yescharacteristic
462C2×C11—161no—
463C2×C11—161no—
464C2×C11#242611yescharacteristic
465C2×C11#304011yescharacteristic
466C2×C11#304511yescharacteristic
467C2×C11#330911yescharacteristic
468C2×C11#331711yescharacteristic
469C2×C11#337011yescharacteristic
470C2×C11#337111yescharacteristic
471C24—21no—
472C24—21no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8#434112yes—
479C2×D4—21no—
480C2×D4—21no—
481C2×D4—21no—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—42no—
492C2×D4—42no—
493C2×D4—42no—
494C2×D4—42no—
495C2×D4—81no—
496C2×D4—81no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—221no—
500C22×C4—221no—
501C22×C4—221no—
502C22×C4—221no—
503C22×C4C2×C22⋊D1111yescharacteristic
504C22×C4C2×C22⋊D1111yescharacteristic
505C22×C4C2×C22⋊D1111yescharacteristic
506C22×C4C2×C22⋊D1111yescharacteristic
507C22×C4C2×C22⋊D1111yescharacteristic
508C22×C4C2×C22⋊D1111yescharacteristic
509C22×C4C23×D1111yescharacteristic
510C2×C8—221no—
511C2×C8—221no—
512C2×C8—221no—
513C2×C8—221no—
514C2×C8—221no—
515C2×C8—221no—
516C2×C8—221no—
517C2×C8—221no—
518C2×C8—221no—
519C2×C8—221no—
520C2×C8—221no—
521C2×C8—221no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—41no—
525C4⋊C4—41no—
526C4⋊C4—42no—
527C4⋊C4—112no—
528C4⋊C4—112no—
529C4⋊C4—112no—
530C4⋊C4—224no—
531C4⋊C4—224no—
532C4⋊C4—221no—
533C4⋊C4—221no—
534C4⋊C4—221no—
535C4⋊C4—221no—
536C4⋊C4—221no—
537C4⋊C4—442no—
538C4⋊C4—881no—
539C22⋊C4—42no—
540C22⋊C4—42no—
541C22⋊C4—42no—
542C22⋊C4—42no—
543C22⋊C4—81no—
544C22⋊C4—81no—
545C22⋊C4—81no—
546C22⋊C4—81no—
547C42—21no—
548C42—21no—
549C42—21no—
550C42—21no—
551C42—42no—
552C42—442no—
553C42—881no—
554C42—881no—
555C42D4×D1112yes—
556C42#434112yes—
557C11#2529111yescharacteristic, complemented, Sylow
558C23—41no—
559C23—41no—
560C23—41no—
561C23—41no—
562C23—41no—
563C23—41no—
564C23—41no—
565C23—41no—
566C23—41no—
567C23—41no—
568C23—41no—
569C23—41no—
570C23—41no—
571C23—41no—
572C23C22×C22⋊D1111yescharacteristic
573Q8—22no—
574Q8—22no—
575Q8—41no—
576Q8—41no—
577D4—41no—
578D4—41no—
579D4—41no—
580D4—41no—
581D4—41no—
582D4—41no—
583D4—41no—
584D4—41no—
585D4—84no—
586D4—84no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—22no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—222no—
610C2×C4—222no—
611C2×C4—222no—
612C2×C4—441no—
613C2×C4—441no—
614C2×C4—441no—
615C2×C4—441no—
616C2×C4—441no—
617C2×C4—441no—
618C2×C4—441no—
619C2×C4—441no—
620C2×C4—441no—
621C2×C4#6699112yes—
622C2×C4#6699112yes—
623C2×C4C2×D4×D1111yescharacteristic
624C2×C4C2×#434111yescharacteristic
625C2×C4C2×#434111yescharacteristic
626C2×C4#6703711yescharacteristic
627C2×C4#41×D1111yescharacteristic
628C2×C4#6704311yescharacteristic
629C8—441no—
630C8—441no—
631C8—441no—
632C8—441no—
633C22—81no—
634C22—81no—
635C22—81no—
636C22—81no—
637C22—81no—
638C22—81no—
639C22—81no—
640C22—81no—
641C22—81no—
642C22—81no—
643C22—81no—
644C22—81no—
645C22—81no—
646C22—81no—
647C22C2×#6699111yescharacteristic
648C22#1062333711yescharacteristic
649C22#1062335311yescharacteristic
650C22#1062335311yescharacteristic
651C22#1062336211yescharacteristic
652C22#1062336611yescharacteristic
653C22#1062336711yescharacteristic
654C4—22no—
655C4—22no—
656C4—41no—
657C4—41no—
658C4—42no—
659C4—41no—
660C4—41no—
661C4—81no—
662C4—442no—
663C4—442no—
664C4—442no—
665C4—881no—
666C4#1062312911yescharacteristic
667C4#1062313011yescharacteristic
668C4#1062313111yescharacteristic
669C4#1062313411yescharacteristic
670C2—161no—
671C2—161no—
672C2#1307217811yescharacteristic
673C2#1307810611yescharacteristic
674C2#1307815111yescharacteristic
675C2#1308062211yescharacteristic
676C2#1308074211yescharacteristic
677C2#1308136311yescharacteristic
678C2#1308137811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2548C2
socleC23×C11C22×D4
prime radicalC2×C11×#127C22
hypercenter#2548D11
hypocenterC11#25291
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2548

Complements

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

NH ≅ G/Ntype
2. C2×#10622635C2semidirect
3. #13071710C2semidirect
4. #13070004C2semidirect
5. #13069990C2semidirect
6. #13069852C2semidirect
7. #13069852C2semidirect
8. #13069549C2semidirect
9. #13069549C2semidirect
11. #13069340C2semidirect
12. #13069240C2semidirect
13. #13069233C2semidirect
14. #13068446C2semidirect
557. C11#25291semidirect

Maximal subgroups

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

subgroupindex
C2×#106226842
C2×#106226352
#130717102
#130700042
#130699902
#130698522
#130695492
#130695442
#130693402
#130692402
#130692332
#130684462
C11×#25482
#2529111