Finite Group Databasebeta

← #14775857

Subgroups — #14775857

Order 2816.

692 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078400C211yesmaximal, characteristic
2#13077562C211yesmaximal, characteristic, complemented
3#13077182C211yesmaximal, characteristic
4#13069595C211yesmaximal, characteristic, complemented
5#13069388C211yesmaximal, characteristic, complemented
6#13069367C211yesmaximal, characteristic, complemented
7#13069361C211yesmaximal, characteristic, complemented
8#13069216C211yesmaximal, characteristic, complemented
9#13069213C211yesmaximal, characteristic, complemented
10#13068889C211yesmaximal, characteristic
11#13068472C211yesmaximal, characteristic, complemented
12#13068463C211yesmaximal, characteristic
13#13068451C211yesmaximal, characteristic
14#13068428C211yesmaximal, characteristic
15C11×#1866C211yesmaximal, characteristic
16C2×C11×#131C2211yescharacteristic
17#41×Dic11C2211yescharacteristic
18C2×#67001C2211yescharacteristic
19#10623048C2211yescharacteristic
20C2×C11×#108C2211yescharacteristic
21C11×#424C2211yescharacteristic
22C2×C11×#104C2211yescharacteristic
23C11×#416C2211yescharacteristic
24C2×#66901C2211yescharacteristic
25#10622846C2211yescharacteristic
26C2×#66886C2211yescharacteristic
27#10622732—21no—
28#10622732C2211yescharacteristic
29#10622732C2211yescharacteristic
30#10622731—21no—
31#10622731C2211yescharacteristic
32M16×Dic11C2211yescharacteristic
33#10622719C2211yescharacteristic
34#10622715—21no—
35#10622715C2211yescharacteristic
36#10622714C2211yescharacteristic
37C2×#66879C2211yescharacteristic
38C2×Dic11⋊C8—21no—
39C2×Dic11⋊C8C2211yescharacteristic
40C2×Dic11⋊C8C2211yescharacteristic
41C2×C8×Dic11C2211yescharacteristic
42#10622611C2211yescharacteristic
43#10622610C2211yescharacteristic
44#10622545C2211yescharacteristic
45#10622444—21no—
46#10622443—21no—
47#10622441—21no—
48#10622441—21no—
49#10622412C411yescharacteristic, complemented
50#10622409C411yescharacteristic, complemented
51#10622407C411yescharacteristic, complemented
52#10622404C411yescharacteristic, complemented
53#10622379C411yescharacteristic, complemented
54#10622376C411yescharacteristic, complemented
55#10622374C411yescharacteristic, complemented
56#10622372C411yescharacteristic, complemented
57C11×#339C2211yescharacteristic
58C11×#336C2211yescharacteristic
59#10622196C2211yescharacteristic
60#10622193C2211yescharacteristic
61#10622193C2211yescharacteristic
62#10622190C2211yescharacteristic
63#10622170C2211yescharacteristic
64#10622162C2211yescharacteristic
65#10622161C2211yescharacteristic
66#10622161C2211yescharacteristic
67C2×C11×#41C2311yescharacteristic
68C11×#131—22no—
69C11×#131—41no—
70C2×C11×M16—21no—
71C2×C11×M16C2311yescharacteristic
72C2×C11×M16C2311yescharacteristic
73C22×C8×C11—21no—
74C22×C8×C11C2311yescharacteristic
75C22×C8×C11C2311yescharacteristic
76C11×#117C2311yescharacteristic
77C2×C42×C11C2311yescharacteristic
78#67001—22no—
79#67001—41no—
80Q8×Dic11C2×C411yescharacteristic
81Q8×Dic11C2×C411yescharacteristic
82D4×Dic11—21no—
83D4×Dic11—21no—
84D4×Dic11C2×C411yescharacteristic
85D4×Dic11C2×C411yescharacteristic
86#66979—21no—
87#66979C2311yescharacteristic
88#66979C2311yescharacteristic
89C2×C4×Dic11—21no—
90C2×C4×Dic11C2311yescharacteristic
91C2×C4×Dic11C2311yescharacteristic
92C2×#4318—21no—
93C2×#4318C2311yescharacteristic
94C2×#4318C2311yescharacteristic
95C22×C11⋊C8—21no—
96C22×C11⋊C8C2311yescharacteristic
97C22×C11⋊C8C2311yescharacteristic
98#66943C2×C411yescharacteristic
99#66943C2×C411yescharacteristic
100#66941C2×C411yescharacteristic
101#66941C2×C411yescharacteristic
102#66931—21no—
103#66931—21no—
104C4×Dic22—21no—
105C4×Dic22—21no—
106C11×#108—41no—
107C11×C4⋊C8—21no—
108C11×C4⋊C8—21no—
109C11×#104—22no—
110C11×#103C2×C411yescharacteristic
111C11×#103C2×C411yescharacteristic
112C11×#102C2×C411yescharacteristic
113C11×#102C2×C411yescharacteristic
114#66901Q814yescomplemented
115#66899C2×C411yescharacteristic
116#66899C2×C411yescharacteristic
117#66896C2×C411yescharacteristic
118#66896C2×C411yescharacteristic
119C11⋊#95—21no—
120C11⋊#95—21no—
121#66886—41no—
122#66882C2×C411yescharacteristic
123#66882C2×C411yescharacteristic
124#66881C2×C411yescharacteristic
125#66881C2×C411yescharacteristic
126#66879—21no—
127#66879—21no—
128#66879—41no—
129Dic11⋊C8—21no—
130Dic11⋊C8—21no—
131Dic11⋊C8—21no—
132Dic11⋊C8—21no—
133Dic11⋊C8—21no—
134Dic11⋊C8—21no—
135Dic11⋊C8—21no—
136Dic11⋊C8—21no—
137Dic11⋊C8C2×C411yescharacteristic
138Dic11⋊C8C2×C411yescharacteristic
139Dic11⋊C8C2×C411yescharacteristic
140Dic11⋊C8C2×C411yescharacteristic
141Dic11⋊C8D411yescharacteristic
142Dic11⋊C8D411yescharacteristic
143Dic11⋊C8D411yescharacteristic
144Dic11⋊C8D411yescharacteristic
145C8×Dic11—21no—
146C8×Dic11—21no—
147C8×Dic11—41no—
148#66872C2×C411yescharacteristic
149#66872C2×C411yescharacteristic
150#66871C2×C411yescharacteristic
151#66871C2×C411yescharacteristic
152#66867—21no—
153C4×C11⋊C8—21no—
154#22984—111nomaximal, Sylow
155C11×#41—21no—
156C11×#41—21no—
157C11×#41C2×Q812yes—
158C11×#41#4112yes—
159C2×Q8×C11C22×C411yescharacteristic
160C2×D4×C11—21no—
161C2×D4×C11C22×C411yescharacteristic
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11C2411yescharacteristic
165C22×Dic11—21no—
166C22×Dic11—21no—
167C22×Dic11—21no—
168C22×Dic11#4111yescharacteristic
169C22×Dic11#4111yescharacteristic
170C2×Dic22—21no—
171C2×Dic22—21no—
172C11×M16—21no—
173C11×M16—21no—
174C11×M16—21no—
175C11×M16—21no—
176C11×M16—42no—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11—21no—
181C2×C8×C11—21no—
182C2×C8×C11—21no—
183C2×C8×C11—42no—
184C2×C8×C11C22×C411yescharacteristic
185C2×C8×C11C22×C411yescharacteristic
186C2×C8×C11C2×D411yescharacteristic
187C2×C8×C11C2×D411yescharacteristic
188C11×C4⋊C4C22×C411yescharacteristic
189C11×C4⋊C4C22×C411yescharacteristic
190C11×C22⋊C4—21no—
191C42×C11—21no—
192C42×C11—21no—
193C42×C11—21no—
194C22⋊Dic11—21no—
195C22⋊Dic11—21no—
196C22⋊Dic11—21no—
197C22⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11C22×C411yescharacteristic
203C4⋊Dic11C22×C411yescharacteristic
204C4⋊Dic11C22×C411yescharacteristic
205C4⋊Dic11C22×C411yescharacteristic
206Dic11⋊C4—21no—
207Dic11⋊C4—21no—
208Dic11⋊C4—21no—
209Dic11⋊C4—21no—
210C4×Dic11—21no—
211C4×Dic11—21no—
212C4×Dic11—21no—
213C4×Dic11—21no—
214C4×Dic11—21no—
215C4×Dic11C22×C411yescharacteristic
216C4×Dic11C22×C411yescharacteristic
217C4×Dic11C2×D411yescharacteristic
218C4×Dic11C2×D411yescharacteristic
219C4×Dic11C2×Q812yes—
220#4318—21no—
221#4318—21no—
222#4318—21no—
223#4318—42no—
224#4318C2×Q812yes—
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—42no—
232C2×C11⋊C8C22×C411yescharacteristic
233C2×C11⋊C8C22×C411yescharacteristic
234C2×C11⋊C8C2×D411yescharacteristic
235C2×C11⋊C8C2×D411yescharacteristic
236#3076—111no—
237#2962—111no—
238#2906—111no—
239#1995—111no—
240#1950—111no—
241#1946—111no—
242#1945—111no—
243#1922—111no—
244#1922—111no—
245#1866—111no—
246#1866D1111yescharacteristic
247#1768—111no—
248#1765—111no—
249#1764—111no—
250#1759—111no—
251C23×C11—21no—
252C23×C11C2×#4111yescharacteristic
253Q8×C11—21no—
254Q8×C11C4×Q812yes—
255D4×C11—22no—
256D4×C11—22no—
257D4×C11—21no—
258D4×C11C4×Q812yes—
259C2×C4×C11—21no—
260C2×C4×C11—22no—
261C2×C4×C11—22no—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11C23×C411yescharacteristic
268C2×C4×C11C22×D411yescharacteristic
269C2×C4×C11C22×Q811yescharacteristic
270C2×C4×C11C2×#4111yescharacteristic
271C2×C4×C11H(5,𝔽2)11yescharacteristic
272C2×C4×C112−1+411yescharacteristic
273C2×Dic11—21no—
274C2×Dic11—21no—
275C2×Dic11—21no—
276C2×Dic11—21no—
277C2×Dic11—22no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—42no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11—81no—
284C2×Dic11C4×D411yescharacteristic
285C2×Dic11C4×D411yescharacteristic
286C2×Dic11C4×D411yescharacteristic
287C2×Dic11C4×D411yescharacteristic
288Dic22—42no—
289Dic22—81no—
290C8×C11—21no—
291C8×C11—21no—
292C8×C11—21no—
293C8×C11—21no—
294C8×C11—41no—
295C8×C11—41no—
296C11⋊C8—21no—
297C11⋊C8—21no—
298C11⋊C8—21no—
299C11⋊C8—21no—
300C11⋊C8—22no—
301C11⋊C8—41no—
302C2×#131—111no—
303C2×#131C2×D1111yescharacteristic
304#533—111no—
305C4×#41—111no—
306#479—111no—
307#479—111no—
308#478—111no—
309#478—111no—
310#477—111no—
311#476—111no—
312#475—111no—
313#474—111no—
314#446—221no—
315#446—221no—
316#446—221no—
317C8×Q8—221no—
318C2×#108—111no—
319C2×#108C2×D1111yescharacteristic
320#427—111no—
321#427—111no—
322#424—111no—
323#424—111no—
324#424—111no—
325#424—221no—
326#424—221no—
327#424C2×D1111yescharacteristic
328#423—111no—
329#423—221no—
330C2×C4⋊C8—111no—
331C2×C4⋊C8—111no—
332C2×C4⋊C8—221no—
333C2×#104—111no—
334C2×#104C2×D1111yescharacteristic
335#416—111no—
336#416C2×D1111yescharacteristic
337#405—111no—
338#405—111no—
339C4×M16—111no—
340C2×#97—111no—
341C2×C4×C8—111no—
342#376—111no—
343#341—111no—
344#341—111no—
345#339—111no—
346#339—111no—
347#339—111no—
348#339—111no—
349#339—111no—
350#339C2×D1111yescharacteristic
351#336—111no—
352#336C2×D1111yescharacteristic
353C22×C11—21no—
354C22×C11—21no—
355C22×C11—22no—
356C22×C11—41no—
357C22×C11—41no—
358C22×C11C2×C4×D411yescharacteristic
359C22×C11#55211yescharacteristic
360C22×C11#55411yescharacteristic
361C4×C11—22no—
362C4×C11—41no—
363C4×C11—41no—
364C4×C11—81no—
365C4×C11C2×C4×Q811yescharacteristic
366C4×C11#52011yescharacteristic
367C4×C11#54611yescharacteristic
368C4×C11D4×Q811yescharacteristic
369Dic11—21no—
370Dic11—21no—
371Dic11—21no—
372Dic11—21no—
373Dic11—42no—
374Dic11—41no—
375Dic11—41no—
376Dic11—41no—
377Dic11—41no—
378C2×#41C22×D1111yescharacteristic
379#131—22no—
380#131—41no—
381#131—222no—
382#131—441no—
383C2×M16—21no—
384C2×M16—111no—
385C2×M16—111no—
386C2×M16—221no—
387C2×M16C22×D1111yescharacteristic
388C2×M16C22×D1111yescharacteristic
389C22×C8—21no—
390C22×C8—111no—
391C22×C8—111no—
392C22×C8—221no—
393C22×C8C22×D1111yescharacteristic
394C22×C8C22×D1111yescharacteristic
395C4⋊Q8—111no—
396C4⋊Q8—111no—
397#125—111no—
398#125—111no—
399C22⋊Q8—221no—
400C22⋊Q8—221no—
401C4×Q8—111no—
402C4×Q8—111no—
403C4×Q8—221no—
404C4×Q8—221no—
405C4×D4—111no—
406C4×D4—111no—
407C4×D4—221no—
408C4×D4—221no—
409#117—111no—
410#117—111no—
411#117—221no—
412#117C22×D1111yescharacteristic
413C2×C42—111no—
414C2×C42—111no—
415C2×C42—221no—
416C2×C42C22×D1111yescharacteristic
417#108—41no—
418#108—441no—
419#107—111no—
420#107—111no—
421#107—111no—
422#107—111no—
423#106—111no—
424#106—111no—
425#106—111no—
426#106—111no—
427C4⋊C8—21no—
428C4⋊C8—21no—
429C4⋊C8—111no—
430C4⋊C8—111no—
431C4⋊C8—111no—
432C4⋊C8—111no—
433C4⋊C8—111no—
434C4⋊C8—111no—
435C4⋊C8—111no—
436C4⋊C8—111no—
437C4⋊C8—221no—
438C4⋊C8—221no—
439C4⋊C8—221no—
440C4⋊C8—221no—
441C4⋊C8—221no—
442C4⋊C8—221no—
443C4⋊C8—221no—
444C4⋊C8—221no—
445#104—22no—
446#104—114no—
447#103—111no—
448#103—111no—
449#103C4×D1111yescharacteristic
450#103C4×D1111yescharacteristic
451#102—111no—
452#102—111no—
453#102C4×D1111yescharacteristic
454#102C4×D1111yescharacteristic
455#97—221no—
456#97—221no—
457#97—221no—
458#97—441no—
459C4×C8—221no—
460C4×C8—221no—
461C4×C8—221no—
462C4×C8—441no—
463#95—221no—
464#95—221no—
465C2×C11—21no—
466C2×C11—21no—
467C2×C11—42no—
468C2×C11#236011yescharacteristic
469C2×C11#295511yescharacteristic
470C2×C11#295711yescharacteristic
471#41—21no—
472#41—21no—
473#41#434112yes—
474#41Q8×D1112yes—
475C2×Q8—221no—
476C2×Q8—221no—
477C2×Q8C2×C4×D1111yescharacteristic
478C2×D4—21no—
479C2×D4C2×C4×D1111yescharacteristic
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—111no—
483C22×C4—111no—
484C22×C4—221no—
485C22×C4—221no—
486C22×C4—221no—
487C22×C4C23×D1111yescharacteristic
488M16—21no—
489M16—21no—
490M16—21no—
491M16—21no—
492M16—42no—
493M16—112no—
494M16—221no—
495M16—221no—
496M16—221no—
497M16—442no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—42no—
505C2×C8—111no—
506C2×C8—111no—
507C2×C8—111no—
508C2×C8—111no—
509C2×C8—221no—
510C2×C8—221no—
511C2×C8—221no—
512C2×C8—221no—
513C2×C8—221no—
514C2×C8—221no—
515C2×C8—442no—
516C2×C8C2×C4×D1111yescharacteristic
517C2×C8C2×C4×D1111yescharacteristic
518C2×C8D4×D1111yescharacteristic
519C2×C8D4×D1111yescharacteristic
520C4⋊C4—111no—
521C4⋊C4—111no—
522C4⋊C4—111no—
523C4⋊C4—111no—
524C4⋊C4—221no—
525C4⋊C4—221no—
526C4⋊C4—221no—
527C4⋊C4—221no—
528C4⋊C4—221no—
529C4⋊C4—221no—
530C4⋊C4—221no—
531C4⋊C4—221no—
532C4⋊C4C2×C4×D1111yescharacteristic
533C4⋊C4C2×C4×D1111yescharacteristic
534C22⋊C4—21no—
535C22⋊C4—221no—
536C22⋊C4—221no—
537C22⋊C4—221no—
538C22⋊C4—221no—
539C42—21no—
540C42—21no—
541C42—21no—
542C42—111no—
543C42—111no—
544C42—111no—
545C42—111no—
546C42—112no—
547C42—221no—
548C42—221no—
549C42—221no—
550C42—221no—
551C42—221no—
552C11#2298411yescharacteristic, complemented, Sylow
553C23—21no—
554C23#41×D1111yescharacteristic
555Q8—21no—
556Q8—442no—
557Q8—881no—
558Q8#6694012yes—
559D4—22no—
560D4—22no—
561D4—21no—
562D4#6694012yes—
563C2×C4—21no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—111no—
572C2×C4—111no—
573C2×C4—111no—
574C2×C4—111no—
575C2×C4—221no—
576C2×C4—221no—
577C2×C4—221no—
578C2×C4—221no—
579C2×C4—222no—
580C2×C4—441no—
581C2×C4—441no—
582C2×C4—442no—
583C2×C4—441no—
584C2×C4—441no—
585C2×C4—881no—
586C2×C4C22×C4×D1111yescharacteristic
587C2×C4C2×D4×D1111yescharacteristic
588C2×C4C2×#434111yescharacteristic
589C2×C4#6703711yescharacteristic
590C2×C4C2×Q8×D1111yescharacteristic
591C2×C4#6704311yescharacteristic
592C8—21no—
593C8—21no—
594C8—21no—
595C8—21no—
596C8—41no—
597C8—41no—
598C8—221no—
599C8—221no—
600C8—221no—
601C8—221no—
602C8—222no—
603C8—441no—
604C22—21no—
605C22—21no—
606C22—22no—
607C22—41no—
608C22—41no—
609C22C4×D4×D1111yescharacteristic
610C22#1062316711yescharacteristic
611C22#1062318111yescharacteristic
612C4—22no—
613C4—41no—
614C4—41no—
615C4—81no—
616C4—221no—
617C4—221no—
618C4—221no—
619C4—221no—
620C4—442no—
621C4—441no—
622C4—441no—
623C4—441no—
624C4—441no—
625C4C2×#6694011yescharacteristic
626C4#1062307711yescharacteristic
627C4#1062312211yescharacteristic
628C4#1062316311yescharacteristic
629C2—21no—
630C2—21no—
631C2—42no—
632C2#1307161611yescharacteristic
633C2#1307751411yescharacteristic
634C2#1307753011yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1866C2
socleC22×C11C2×C4×D4
prime radicalC2×C11×#41C23
cosocleC22×C4×C11C24
hypercenter#1866D11
hypocenterC11#22984
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1866

Complements

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

NH ≅ G/Ntype
2. #13077562C2semidirect
4. #13069595C2semidirect
5. #13069388C2semidirect
6. #13069367C2semidirect
7. #13069361C2semidirect
8. #13069216C2semidirect
9. #13069213C2semidirect
11. #13068472C2semidirect
49. #10622412C4semidirect
50. #10622409C4semidirect
51. #10622407C4semidirect
52. #10622404C4semidirect
53. #10622379C4semidirect
54. #10622376C4semidirect
55. #10622374C4semidirect
56. #10622372C4semidirect
114. #66901Q8semidirect
552. C11#22984semidirect

Maximal subgroups

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

subgroupindex
#130784002
#130775622
#130771822
#130695952
#130693882
#130693672
#130693612
#130692162
#130692132
#130688892
#130684722
#130684632
#130684512
#130684282
C11×#18662
#2298411