Finite Group Databasebeta

← #14775858

Subgroups — #14775858

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#13078398C211yesmaximal, characteristic
2#13077181C211yesmaximal, characteristic
3#13069598C211yesmaximal, characteristic, complemented
4#13069391C211yesmaximal, characteristic, complemented
5#13069366C211yesmaximal, characteristic, complemented
6#13069361C211yesmaximal, characteristic, complemented
7#13069215C211yesmaximal, characteristic, complemented
8#13069215C211yesmaximal, characteristic, complemented
9#13068890C211yesmaximal, characteristic
10#13068890C211yesmaximal, characteristic
11#13068475C211yesmaximal, characteristic, complemented
12#13068462C211yesmaximal, characteristic
13#13068455C211yesmaximal, characteristic
14#13068429C211yesmaximal, characteristic
15C11×#2962C211yesmaximal, characteristic, complemented
16C11×#533C2211yescharacteristic
17C2×#66954C2211yescharacteristic
18C2×#66954C2211yescharacteristic
19C4×#4339C2211yescharacteristic
20C11×#446—21no—
21C11×#446—21no—
22C11×#446—21no—
23C8×Q8×C11—21no—
24C11×#424C2211yescharacteristic
25C11×#424C2211yescharacteristic
26C2×C11×C4⋊C8C2211yescharacteristic
27C11×#405C2211yescharacteristic
28C11×#405C2211yescharacteristic
29C4×C11×M16C2211yescharacteristic
30C2×#66889C2211yescharacteristic
31C2×#66889C2211yescharacteristic
32C2×#66886C2211yescharacteristic
33C2×#66886C2211yescharacteristic
34#10622715C2211yescharacteristic
35#10622715C2211yescharacteristic
36C2×#66879C2211yescharacteristic
37C2×C8×Dic11C2211yescharacteristic
38#10622707C411yescharacteristic, complemented
39#10622704C411yescharacteristic, complemented
40#10622700C411yescharacteristic, complemented
41#10622697C411yescharacteristic, complemented
42#10622679C411yescharacteristic, complemented
43#10622679C411yescharacteristic, complemented
44#10622676C411yescharacteristic, complemented
45#10622676C411yescharacteristic, complemented
46#10622615C2211yescharacteristic
47#10622615C2211yescharacteristic
48#10622611C2211yescharacteristic
49#10622611C2211yescharacteristic
50#10622545C2211yescharacteristic
51#10622537C2211yescharacteristic
52C2×C4⋊(C11⋊C8)C2211yescharacteristic
53#10622452—21no—
54#10622452—21no—
55#10622450—21no—
56D11×C4⋊C8—21no—
57#10622196C2211yescharacteristic
58#10622196C2211yescharacteristic
59#10622193C2211yescharacteristic
60#10622193C2211yescharacteristic
61#10622188C2211yescharacteristic
62#10622188C2211yescharacteristic
63#10622170C2211yescharacteristic
64#10622170C2211yescharacteristic
65#10622170C2211yescharacteristic
66#10622170C2211yescharacteristic
67C2×#4339C2311yescharacteristic
68C2×C11×M16C2311yescharacteristic
69C2×C11×M16C2311yescharacteristic
70C22×C8×C11C2311yescharacteristic
71C22×C8×C11C2311yescharacteristic
72C11×C4⋊Q8C2×C411yescharacteristic
73C11×C4⋊Q8C2×C411yescharacteristic
74C11×#125C2×C411yescharacteristic
75C11×#125C2×C411yescharacteristic
76C11×C22⋊Q8—21no—
77C11×C22⋊Q8—21no—
78C4×Q8×C11—21no—
79C4×Q8×C11—21no—
80C11×#117C2311yescharacteristic
81C11×#117C2311yescharacteristic
82C2×C42×C11C2311yescharacteristic
83C4×C22⋊D11—21no—
84C4×C22⋊D11—21no—
85#66979C2311yescharacteristic
86C2×C4×Dic11C2311yescharacteristic
87C2×C4×Dic11C2311yescharacteristic
88C2×#4318C2311yescharacteristic
89C2×#4318C2311yescharacteristic
90C22×C11⋊C8C2311yescharacteristic
91C22×C11⋊C8C2311yescharacteristic
92#66954—22no—
93#66954—22no—
94#66954—41no—
95#66954—41no—
96C2×#4313—21no—
97C2×#4313—21no—
98C2×C8×D11—21no—
99C2×C8×D11—21no—
100C4×D44C2×C411yescharacteristic
101C4×D44C2×C411yescharacteristic
102#66925—21no—
103C42×D11—21no—
104C4×Dic22C2×C411yescharacteristic
105C4×Dic22C2×C411yescharacteristic
106C11×C4⋊C8—21no—
107C11×C4⋊C8—21no—
108C11×C4⋊C8—21no—
109C11×C4⋊C8—21no—
110C11×C4⋊C8D411yescharacteristic
111C11×C4⋊C8D411yescharacteristic
112C11×C4⋊C8D411yescharacteristic
113C11×C4⋊C8D411yescharacteristic
114C11×#97—21no—
115C11×#97—21no—
116C11×#97—21no—
117C4×C8×C11—21no—
118C4×C8×C11—21no—
119C4×C8×C11—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122#66889—22no—
123#66889Q814yescomplemented
124#66886—41no—
125#66886—41no—
126#66879—41no—
127Dic11⋊C8—21no—
128Dic11⋊C8—21no—
129Dic11⋊C8—21no—
130Dic11⋊C8—21no—
131C8×Dic11—41no—
132#66874C2×C411yescharacteristic
133#66874C2×C411yescharacteristic
134#66874C2×C411yescharacteristic
135#66874C2×C411yescharacteristic
136#66873C2×C411yescharacteristic
137#66873C2×C411yescharacteristic
138#66873C2×C411yescharacteristic
139#66873C2×C411yescharacteristic
140#66872C2×C411yescharacteristic
141#66872C2×C411yescharacteristic
142#66872C2×C411yescharacteristic
143#66872C2×C411yescharacteristic
144#66871C2×C411yescharacteristic
145#66871C2×C411yescharacteristic
146#66871C2×C411yescharacteristic
147#66871C2×C411yescharacteristic
148C4⋊(C11⋊C8)—21no—
149C4⋊(C11⋊C8)—21no—
150C4⋊(C11⋊C8)C2×C411yescharacteristic
151C4⋊(C11⋊C8)C2×C411yescharacteristic
152C4⋊(C11⋊C8)C2×C411yescharacteristic
153C4⋊(C11⋊C8)C2×C411yescharacteristic
154#22984—111nomaximal, Sylow
155C2×Q8×C11—21no—
156C2×Q8×C11—21no—
157C22×C4×C11#4111yescharacteristic
158C22×C4×C11#4111yescharacteristic
159C22×C4×C11C2411yescharacteristic
160C2×C22⋊D11—21no—
161C22×Dic11—21no—
162C22×Dic11—21no—
163#4339—21no—
164#4339—21no—
165#4339C2×Q812yes—
166#4339#4112yes—
167C2×D44C22×C411yescharacteristic
168C2×C4×D11—21no—
169C2×C4×D11—21no—
170C2×C4×D11—21no—
171C2×Dic22C22×C411yescharacteristic
172C11×M16—21no—
173C11×M16—21no—
174C11×M16—21no—
175C11×M16C2×Q812yes—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11—21no—
181C2×C8×C11—21no—
182C2×C8×C11C2×D411yescharacteristic
183C2×C8×C11C2×D411yescharacteristic
184C2×C8×C11C2×D411yescharacteristic
185C2×C8×C11C2×D411yescharacteristic
186C11×C4⋊C4—21no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—21no—
189C11×C4⋊C4—21no—
190C11×C4⋊C4—21no—
191C11×C4⋊C4—21no—
192C11×C4⋊C4C22×C411yescharacteristic
193C11×C4⋊C4C22×C411yescharacteristic
194C11×C4⋊C4C22×C411yescharacteristic
195C11×C4⋊C4C22×C411yescharacteristic
196C11×C22⋊C4—21no—
197C11×C22⋊C4—21no—
198C42×C11—21no—
199C42×C11—21no—
200C42×C11C22×C411yescharacteristic
201C42×C11C22×C411yescharacteristic
202C42×C11C2×D411yescharacteristic
203C42×C11C2×D411yescharacteristic
204C22⋊Dic11—21no—
205(C2×D11)⋊C4—21no—
206(C2×D11)⋊C4—21no—
207C4⋊Dic11C22×C411yescharacteristic
208C4⋊Dic11C22×C411yescharacteristic
209Dic11⋊C4—21no—
210Dic11⋊C4—21no—
211C4×Dic11—21no—
212C4×Dic11—21no—
213C4×Dic11—21no—
214C4×Dic11—21no—
215C4×Dic11—21no—
216C4×Dic11—21no—
217C4×Dic11C2×Q812yes—
218#4318—21no—
219#4318—21no—
220#4318—21no—
221#4318—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⋊C8C22×C411yescharacteristic
229C2×C11⋊C8C22×C411yescharacteristic
230C2×C11⋊C8C22×C411yescharacteristic
231C2×C11⋊C8C22×C411yescharacteristic
232#4313—42no—
233#4313—42no—
234C8×D11—42no—
235C8×D11—42no—
236#3076—111no—
237#2962D1111yescharacteristic, complemented
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#1866—111no—
247#1768—111no—
248#1765—111no—
249#1764—111no—
250#1759—111no—
251C23×C11C2×#4111yescharacteristic
252C22×D11—21no—
253Q8×C11—42no—
254Q8×C11—81no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11C4×D411yescharacteristic
262C2×C4×C11C4×D411yescharacteristic
263C2×C4×C11C4×D411yescharacteristic
264C2×C4×C11C4×D411yescharacteristic
265C2×C4×C11C23×C411yescharacteristic
266C2×C4×C11C22×D411yescharacteristic
267C2×C4×C11C22×Q811yescharacteristic
268C2×C4×C11C2×#4111yescharacteristic
269C2×C4×C11H(5,𝔽2)11yescharacteristic
270C2×C4×C112−1+411yescharacteristic
271C22⋊D11—22no—
272C22⋊D11—22no—
273C2×Dic11—21no—
274C2×Dic11—21no—
275C2×Dic11—21no—
276C2×Dic11—22no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282D44—21no—
283D44C4×Q812yes—
284C4×D11—22no—
285C4×D11—22no—
286C4×D11—42no—
287C4×D11—81no—
288Dic22—21no—
289Dic22C4×Q812yes—
290C8×C11—21no—
291C8×C11—21no—
292C8×C11—21no—
293C8×C11—21no—
294C8×C11—22no—
295C8×C11—41no—
296C11⋊C8—21no—
297C11⋊C8—21no—
298C11⋊C8—21no—
299C11⋊C8—21no—
300C11⋊C8—41no—
301C11⋊C8—41no—
302C2×#131—111no—
303C2×#131—111no—
304#533C2×D1111yescharacteristic
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—21no—
315#446—21no—
316#446—21no—
317C8×Q8—21no—
318C2×#108—111no—
319C2×#108—111no—
320#427—111no—
321#427—111no—
322#424—111no—
323#424—111no—
324#424—221no—
325#424—221no—
326#424C2×D1111yescharacteristic
327#424C2×D1111yescharacteristic
328#423—111no—
329#423—221no—
330C2×C4⋊C8—111no—
331C2×C4⋊C8—221no—
332C2×C4⋊C8C2×D1111yescharacteristic
333C2×#104—111no—
334C2×#104—111no—
335#416—111no—
336#416—111no—
337#405C2×D1111yescharacteristic
338#405C2×D1111yescharacteristic
339C4×M16C2×D1111yescharacteristic
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#339—111no—
351#336—111no—
352#336—111no—
353C22×C11—21no—
354C22×C11—21no—
355C22×C11C2×C4×D411yescharacteristic
356C22×C11#55211yescharacteristic
357C22×C11#55411yescharacteristic
358C2×D11—22no—
359C2×D11—41no—
360C2×D11—41no—
361C4×C11—21no—
362C4×C11—21no—
363C4×C11—21no—
364C4×C11—21no—
365C4×C11—41no—
366C4×C11—41no—
367C4×C11—41no—
368C4×C11—41no—
369C4×C11C2×C4×Q811yescharacteristic
370C4×C11#52011yescharacteristic
371C4×C11#54611yescharacteristic
372C4×C11D4×Q811yescharacteristic
373Dic11—22no—
374Dic11—42no—
375Dic11—41no—
376Dic11—41no—
377Dic11—81no—
378C2×#41—111no—
379#131—222no—
380#131—222no—
381#131—441no—
382#131—441no—
383C2×M16—111no—
384C2×M16—111no—
385C2×M16—221no—
386C2×M16—221no—
387C2×M16C22×D1111yescharacteristic
388C2×M16C22×D1111yescharacteristic
389C22×C8—111no—
390C22×C8—111no—
391C22×C8—221no—
392C22×C8—221no—
393C22×C8C22×D1111yescharacteristic
394C22×C8C22×D1111yescharacteristic
395C4⋊Q8C4×D1111yescharacteristic
396C4⋊Q8C4×D1111yescharacteristic
397#125C4×D1111yescharacteristic
398#125C4×D1111yescharacteristic
399C22⋊Q8—21no—
400C22⋊Q8—21no—
401C4×Q8—21no—
402C4×Q8—21no—
403C4×Q8—111no—
404C4×Q8—111no—
405C4×D4—111no—
406C4×D4—111no—
407C4×D4—221no—
408C4×D4—221no—
409#117—111no—
410#117—221no—
411#117C22×D1111yescharacteristic
412#117C22×D1111yescharacteristic
413C2×C42—111no—
414C2×C42—111no—
415C2×C42—221no—
416C2×C42C22×D1111yescharacteristic
417#108—441no—
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—21no—
430C4⋊C8—21no—
431C4⋊C8—111no—
432C4⋊C8—111no—
433C4⋊C8—111no—
434C4⋊C8—111no—
435C4⋊C8—221no—
436C4⋊C8—221no—
437C4⋊C8—221no—
438C4⋊C8—221no—
439C4⋊C8—221no—
440C4⋊C8—221no—
441C4⋊C8C22⋊D1111yescharacteristic
442C4⋊C8C22⋊D1111yescharacteristic
443C4⋊C8C22⋊D1111yescharacteristic
444C4⋊C8C22⋊D1111yescharacteristic
445#104—114no—
446#104—222no—
447#103—111no—
448#103—111no—
449#103—111no—
450#103—111no—
451#102—111no—
452#102—111no—
453#102—111no—
454#102—111no—
455#97—21no—
456#97—21no—
457#97—21no—
458#97—441no—
459C4×C8—21no—
460C4×C8—21no—
461C4×C8—21no—
462C4×C8—441no—
463#95—221no—
464#95—221no—
465C2×C11—21no—
466C2×C11—21no—
467C2×C11#236011yescharacteristic
468C2×C11#295511yescharacteristic
469C2×C11#295711yescharacteristic
470D11—42no—
471#41—112no—
472#41—112no—
473#41—221no—
474#41—221no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—111no—
478C2×D4—111no—
479C2×D4—221no—
480C22×C4—221no—
481C22×C4—221no—
482C22×C4—221no—
483C22×C4—221no—
484C22×C4—221no—
485C22×C4#433911yescharacteristic
486C22×C4#433911yescharacteristic
487C22×C4C23×D1111yescharacteristic
488M16—21no—
489M16—21no—
490M16—21no—
491M16—221no—
492M16—221no—
493M16—221no—
494M16—221no—
495M16—442no—
496M16—442no—
497M16Q8×D1112yes—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—111no—
505C2×C8—111no—
506C2×C8—111no—
507C2×C8—111no—
508C2×C8—221no—
509C2×C8—221no—
510C2×C8—221no—
511C2×C8—221no—
512C2×C8—221no—
513C2×C8—221no—
514C2×C8—442no—
515C2×C8—442no—
516C2×C8C2×C22⋊D1111yescharacteristic
517C2×C8C2×C22⋊D1111yescharacteristic
518C2×C8C2×C22⋊D1111yescharacteristic
519C2×C8C2×C22⋊D1111yescharacteristic
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—111no—
527C4⋊C4—111no—
528C4⋊C4—221no—
529C4⋊C4—221no—
530C4⋊C4C2×C4×D1111yescharacteristic
531C4⋊C4C2×C4×D1111yescharacteristic
532C4⋊C4C2×C4×D1111yescharacteristic
533C4⋊C4C2×C4×D1111yescharacteristic
534C22⋊C4—21no—
535C22⋊C4—21no—
536C22⋊C4—221no—
537C22⋊C4—221no—
538C22⋊C4—221no—
539C42—21no—
540C42—21no—
541C42—112no—
542C42—221no—
543C42—221no—
544C42—221no—
545C42—221no—
546C42—221no—
547C42—221no—
548C42C2×C4×D1111yescharacteristic
549C42C2×C4×D1111yescharacteristic
550C42C2×C22⋊D1111yescharacteristic
551C42C2×C22⋊D1111yescharacteristic
552C11#2298411yescharacteristic, complemented, Sylow
553C23—221no—
554C23C2×#433911yescharacteristic
555Q8—42no—
556Q8—81no—
557Q8—112no—
558Q8—221no—
559D4—112no—
560D4—222no—
561D4—222no—
562D4—221no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—221no—
570C2×C4—222no—
571C2×C4—222no—
572C2×C4—221no—
573C2×C4—221no—
574C2×C4—222no—
575C2×C4—442no—
576C2×C4—441no—
577C2×C4—441no—
578C2×C4—441no—
579C2×C4—441no—
580C2×C4—441no—
581C2×C4—881no—
582C2×C4C4×C22⋊D1111yescharacteristic
583C2×C4C4×C22⋊D1111yescharacteristic
584C2×C4C4×C22⋊D1111yescharacteristic
585C2×C4C4×C22⋊D1111yescharacteristic
586C2×C4C22×C4×D1111yescharacteristic
587C2×C4C2×Q8×D1111yescharacteristic
588C2×C4#6704011yescharacteristic
589C2×C4#41×D1111yescharacteristic
590C2×C4#6704211yescharacteristic
591C2×C4C22×C22⋊D1111yescharacteristic
592C8—22no—
593C8—21no—
594C8—21no—
595C8—21no—
596C8—21no—
597C8—41no—
598C8—221no—
599C8—221no—
600C8—221no—
601C8—221no—
602C8—441no—
603C8—441no—
604C22—21no—
605C22—21no—
606C22—222no—
607C22—441no—
608C22—441no—
609C22#1062311011yescharacteristic
610C22#1062311211yescharacteristic
611C22C2×C4×C22⋊D1111yescharacteristic
612C4—21no—
613C4—21no—
614C4—21no—
615C4—21no—
616C4—41no—
617C4—41no—
618C4—41no—
619C4—41no—
620C4—222no—
621C4—442no—
622C4—441no—
623C4—441no—
624C4—881no—
625C4C4×Q8×D1111yescharacteristic
626C4#1062310511yescharacteristic
627C4Q8×C22⋊D1111yescharacteristic
628C4#1062336011yescharacteristic
629C2—21no—
630C2—21no—
631C2—442no—
632C2#1307161711yescharacteristic
633C2#1307751711yescharacteristic
634C2#1307753111yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2962C2
socleC22×C11C2×C4×D4
prime radicalC2×#4339C23
cosocleC22×C4×C11C24
hypercenter#2962D11
hypocenterC11#22984
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C4⋊C8 ◁ #2962

Complements

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

NH ≅ G/Ntype
3. #13069598C2semidirect
4. #13069391C2semidirect
5. #13069366C2semidirect
6. #13069361C2semidirect
7. #13069215C2semidirect
8. #13069215C2semidirect
11. #13068475C2semidirect
15. C11×#2962C2semidirect
38. #10622707C4semidirect
39. #10622704C4semidirect
40. #10622700C4semidirect
41. #10622697C4semidirect
42. #10622679C4semidirect
43. #10622679C4semidirect
44. #10622676C4semidirect
45. #10622676C4semidirect
123. #66889Q8semidirect
237. #2962D11semidirect
552. C11#22984semidirect

Maximal subgroups

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

subgroupindex
#130783982
#130771812
#130695982
#130693912
#130693662
#130693612
#130692152
#130688902
#130684752
#130684622
#130684552
#130684292
C11×#29622
#2298411