Finite Group Databasebeta

← #14814221

Subgroups — #14814221

Order 2816.

812 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622779C211yesmaximal, characteristic
2C2×#10622402C211yesmaximal, characteristic, complemented
3#13072417C211yesmaximal, characteristic
4#13071537C211yesmaximal, characteristic, complemented
5#13070137C211yesmaximal, characteristic
6#13070119C211yesmaximal, characteristic, complemented
7#13070036C211yesmaximal, characteristic, complemented
8#13069856C211yesmaximal, characteristic
9#13069315C211yesmaximal, characteristic
10#13069179C211yesmaximal, characteristic, complemented
11#13068973C211yesmaximal, characteristic
12#13068957C211yesmaximal, characteristic, complemented
13#13068871C211yesmaximal, characteristic, complemented
14#13068868C211yesmaximal, characteristic, complemented
15C11×#1880C211yesmaximal, characteristic
16C22×C11×SD16C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×Q8×Dic11C2211yescharacteristic
19C2×Q8×Dic11C2211yescharacteristic
20C22×#4326C2211yescharacteristic
21C2×#66989C2211yescharacteristic
22C2×#66940C2211yescharacteristic
23C2×C11×#103C2211yescharacteristic
24C2×C11×#102C2211yescharacteristic
25C11×#390C2211yescharacteristic
26C2×#66899C2211yescharacteristic
27#10622834C2211yescharacteristic
28C2×#66896C2211yescharacteristic
29C2×#66896C2211yescharacteristic
30#10622779—24no—
31C2×#66880C2211yescharacteristic
32C2×#66880C2211yescharacteristic
33C2×#66879C2211yescharacteristic
34C2×Dic11⋊C8C2211yescharacteristic
35#10622598—21no—
36#10622598—21no—
37#10622598C2211yescharacteristic
38#10622598C2211yescharacteristic
39#10622586C2211yescharacteristic
40C2×#66874C2211yescharacteristic
41C2×#66872C2211yescharacteristic
42C2×#66871C2211yescharacteristic
43#10622565—21no—
44#10622564—21no—
45#10622562—21no—
46#10622558—21no—
47#10622549—21no—
48#10622549C2211yescharacteristic
49C4×C4⋊Dic11—21no—
50C4×C4⋊Dic11C2211yescharacteristic
51#10622542C2211yescharacteristic
52#10622402—24no—
53C11×#340C2211yescharacteristic
54C11×#336C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C22×D4×C11C2311yescharacteristic
63C22×Dic22C2311yescharacteristic
64C2×C11×SD16—22no—
65C2×C11×SD16—22no—
66C2×C11×SD16—22no—
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C4×Q8×C11—22no—
70C4×Q8×C11—22no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C22⋊C4—21no—
75C2×C11×C22⋊C4—21no—
76C2×C42×C11—21no—
77C2×C42×C11C2311yescharacteristic
78C2×C22⋊Dic11—21no—
79C2×C22⋊Dic11—21no—
80C2×C22⋊Dic11—21no—
81C2×C22⋊Dic11—21no—
82Q8×Dic11—22no—
83Q8×Dic11—22no—
84Q8×Dic11—41no—
85Q8×Dic11—41no—
86C2×#4326—22no—
87C2×#4326—22no—
88C2×#4326D414yes—
89#66989—22no—
90#66989—41no—
91C2×C4⋊Dic11—21no—
92C2×C4⋊Dic11—21no—
93C2×C4⋊Dic11—21no—
94C2×C4⋊Dic11—21no—
95C2×C4⋊Dic11D411yescharacteristic
96C2×C4⋊Dic11D411yescharacteristic
97C2×C4⋊Dic11C2311yescharacteristic
98C2×C4⋊Dic11C2311yescharacteristic
99C2×C4⋊Dic11C2311yescharacteristic
100C2×Dic11⋊C4—21no—
101C2×Dic11⋊C4—21no—
102C2×C4×Dic11—21no—
103C2×C4×Dic11—21no—
104C2×C4×Dic11—21no—
105C2×C4×Dic11C2311yescharacteristic
106C2×C4×Dic11C2311yescharacteristic
107C22×C11⋊C8C2311yescharacteristic
108C22×C11⋊C8C2311yescharacteristic
109#66940—22no—
110#66940—41no—
111C11×#103—22no—
112C11×#102—22no—
113#66899—22no—
114#66896—22no—
115#66896—41no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95D411yescharacteristic
124C11⋊#95D411yescharacteristic
125#66880—22no—
126#66880—22no—
127#66879—22no—
128Dic11⋊C8—22no—
129#66874—22no—
130#66872—22no—
131#66871—41no—
132#26189—111nomaximal, Sylow
133C24×C11—21no—
134C2×Q8×C11—21no—
135C2×Q8×C11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11C2×D412yes—
138C2×Q8×C11#4112yes—
139C2×Q8×C11#4112yes—
140C2×D4×C11—21no—
141C2×D4×C11—21no—
142C2×D4×C11—21no—
143C2×D4×C11—21no—
144C2×D4×C11—21no—
145C2×D4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2411yescharacteristic
152C22×Dic11—21no—
153C22×Dic11—21no—
154C22×Dic11—21no—
155C22×Dic11—21no—
156C22×Dic11C2×D411yescharacteristic
157C22×Dic11C2×D411yescharacteristic
158C22×Dic11C2×D411yescharacteristic
159C22×Dic11C2×D411yescharacteristic
160C2×Dic22—21no—
161C2×Dic22—21no—
162C2×Dic22—21no—
163C2×Dic22—21no—
164C2×Dic22—21no—
165C2×Dic22C2×D412yes—
166C11×SD16—44no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C11×C4⋊C4—24no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4#4112yes—
178C11×C22⋊C4—42no—
179C11×C22⋊C4—81no—
180C42×C11—24no—
181C42×C11—21no—
182C42×C11—21no—
183C22⋊Dic11—42no—
184C22⋊Dic11—42no—
185C22⋊Dic11—42no—
186C22⋊Dic11—81no—
187#4326—28no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—41no—
195C4⋊Dic11—41no—
196C4⋊Dic11—42no—
197C4⋊Dic11—42no—
198C4⋊Dic11—42no—
199C4⋊Dic11—42no—
200Dic11⋊C4—42no—
201Dic11⋊C4—81no—
202C4×Dic11—21no—
203C4×Dic11—21no—
204C4×Dic11—21no—
205C4×Dic11—21no—
206C4×Dic11—42no—
207C4×Dic11—42no—
208C4×Dic11—42no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8C2×D412yes—
215C2×#464—111no—
216C2×#441—111no—
217#2448—111no—
218#2351—111no—
219#2092—111no—
220#2088—111no—
221#2074—111no—
222#2042—111no—
223#1936—111no—
224#1917—111no—
225#1880—111no—
226#1880D1111yescharacteristic
227#1878—111no—
228#1863—111no—
229#1863—111no—
230C23×C11—41no—
231C23×C11—41no—
232C23×C11—41no—
233C23×C11—41no—
234C23×C11—41no—
235C23×C11—41no—
236C23×C11—41no—
237C23×C11C22×D411yescharacteristic
238Q8×C11—22no—
239Q8×C11—22no—
240Q8×C11—22no—
241Q8×C11#12314yes—
242D4×C11—41no—
243D4×C11—41no—
244D4×C11—41no—
245D4×C11—41no—
246C2×C4×C11—22no—
247C2×C4×C11—22no—
248C2×C4×C11—22no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—22no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11C22×D411yescharacteristic
262C2×C4×C11C2×#4111yescharacteristic
263C2×C4×C11C2×#4111yescharacteristic
264C2×C4×C11C2×#4111yescharacteristic
265C2×C4×C11H(5,𝔽2)11yescharacteristic
266C2×C4×C112−1+411yescharacteristic
267C2×Dic11—21no—
268C2×Dic11—21no—
269C2×Dic11—21no—
270C2×Dic11—21no—
271C2×Dic11—22no—
272C2×Dic11—21no—
273C2×Dic11—21no—
274C2×Dic11—21no—
275C2×Dic11—21no—
276C2×Dic11—21no—
277C2×Dic11—21no—
278C2×Dic11—21no—
279C2×Dic11—21no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291Dic22—22no—
292Dic22—22no—
293Dic22—41no—
294Dic22—41no—
295C8×C11—41no—
296C8×C11—41no—
297C11⋊C8—22no—
298C11⋊C8—41no—
299C22×Q16—111no—
300C22×SD16C2×D1111yescharacteristic
301C2×#124—111no—
302C2×C4×Q8—111no—
303C2×C4×Q8—111no—
304C2×C4×Q8—111no—
305C2×C4×Q8C2×D1111yescharacteristic
306#464—224no—
307#441—224no—
308C2×#107—111no—
309C2×#106—111no—
310C2×C4⋊C8—111no—
311C2×#103—111no—
312C2×#103—111no—
313C2×#103—111no—
314C2×#103—111no—
315C2×#103C2×D1111yescharacteristic
316C2×#102—111no—
317C2×#102—111no—
318C2×#102C2×D1111yescharacteristic
319C2×#97—111no—
320#399—221no—
321#397—221no—
322#391—111no—
323#390—111no—
324#390C2×D1111yescharacteristic
325#389—111no—
326#389—111no—
327#389—111no—
328#389—221no—
329#389—221no—
330#388—221no—
331#388—221no—
332#382—111no—
333#382—221no—
334C4×C4⋊C4—111no—
335C4×C4⋊C4—221no—
336#340—111no—
337#340—111no—
338#340—111no—
339#340C2×D1111yescharacteristic
340#336—111no—
341#336—111no—
342#336—111no—
343#336C2×D1111yescharacteristic
344C22×C11—81no—
345C22×C11—81no—
346C22×C11—81no—
347C22×C11—81no—
348C22×C11—81no—
349C22×C11—81no—
350C22×C11—81no—
351C22×C11#52511yescharacteristic
352C22×C11D4211yescharacteristic
353C22×C11#54811yescharacteristic
354C22×C11#57511yescharacteristic
355C22×C11#57511yescharacteristic
356C22×C11#57711yescharacteristic
357C22×C11#57811yescharacteristic
358C4×C11—24no—
359C4×C11—41no—
360C4×C11—42no—
361C4×C11—41no—
362C4×C11—81no—
363C4×C11C2×#12311yescharacteristic
364C4×C11#53911yescharacteristic
365C4×C11#54711yescharacteristic
366C4×C11#55311yescharacteristic
367Dic11—42no—
368Dic11—41no—
369Dic11—41no—
370Dic11—41no—
371Dic11—41no—
372Dic11—81no—
373Dic11—81no—
374Dic11—81no—
375C22×Q8—111no—
376C22×Q8C22×D1111yescharacteristic
377C22×D4C22×D1111yescharacteristic
378C2×Q16—114no—
379C2×Q16—222no—
380C2×Q16—222no—
381C2×SD16—22no—
382C2×SD16—22no—
383C2×SD16—22no—
384C22×C8—111no—
385C22×C8—111no—
386C22×C8C22×D1111yescharacteristic
387C22×C8C22×D1111yescharacteristic
388#124—222no—
389#124—441no—
390C4×Q8—22no—
391C4×Q8—22no—
392C4×Q8—222no—
393C4×Q8—222no—
394C4×Q8—222no—
395C4×Q8—441no—
396C4×Q8—441no—
397C4×Q8—441no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—111no—
400C2×C4⋊C4—111no—
401C2×C4⋊C4—111no—
402C2×C4⋊C4—111no—
403C2×C4⋊C4—111no—
404C2×C4⋊C4—221no—
405C2×C4⋊C4—221no—
406C2×C4⋊C4—221no—
407C2×C4⋊C4—221no—
408C2×C4⋊C4—221no—
409C2×C4⋊C4—221no—
410C2×C4⋊C4C22×D1111yescharacteristic
411C2×C4⋊C4C22×D1111yescharacteristic
412C2×C22⋊C4—21no—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—221no—
415C2×C22⋊C4—221no—
416C2×C22⋊C4—221no—
417C2×C22⋊C4—221no—
418C2×C42—21no—
419C2×C42—111no—
420C2×C42—111no—
421C2×C42—221no—
422C2×C42—221no—
423C2×C42—221no—
424C2×C42C22×D1111yescharacteristic
425#107—441no—
426#106—222no—
427C4⋊C8—222no—
428#103—22no—
429#103—222no—
430#103—222no—
431#103—222no—
432#103—222no—
433#102—22no—
434#102—222no—
435#102—441no—
436#97—222no—
437#95—111no—
438#95—111no—
439#95—221no—
440#95—221no—
441#95—221no—
442#95—221no—
443#95—221no—
444#95—221no—
445#95—221no—
446C2×C11—161no—
447C2×C11#244311yescharacteristic
448C2×C11#311111yescharacteristic
449C2×C11#312111yescharacteristic
450C2×C11#327111yescharacteristic
451C2×C11#327711yescharacteristic
452C2×C11#337111yescharacteristic
453C2×C11#337711yescharacteristic
454C24—21no—
455C2×Q8—21no—
456C2×Q8—21no—
457C2×Q8—21no—
458C2×Q8—112no—
459C2×Q8—221no—
460C2×Q8—221no—
461C2×Q8—221no—
462C2×Q8—221no—
463C2×Q8—221no—
464C2×Q8#433912yes—
465C2×Q8D4×D1112yes—
466C2×Q8#434112yes—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—111no—
477C22×C4—111no—
478C22×C4—111no—
479C22×C4—111no—
480C22×C4—221no—
481C22×C4—221no—
482C22×C4—221no—
483C22×C4—221no—
484C22×C4D4×D1111yescharacteristic
485C22×C4D4×D1111yescharacteristic
486C22×C4C23×D1111yescharacteristic
487Q16—228no—
488SD16—44no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—112no—
496C2×C8—221no—
497C2×C8—221no—
498C2×C8—221no—
499C2×C8—221no—
500C2×C8—221no—
501C4⋊C4—24no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—221no—
506C4⋊C4—221no—
507C4⋊C4—221no—
508C4⋊C4—221no—
509C4⋊C4—221no—
510C4⋊C4—221no—
511C4⋊C4—441no—
512C4⋊C4—441no—
513C4⋊C4—442no—
514C4⋊C4—442no—
515C4⋊C4—442no—
516C4⋊C4—442no—
517C4⋊C4—442no—
518C4⋊C4—881no—
519C4⋊C4#434112yes—
520C22⋊C4—42no—
521C22⋊C4—81no—
522C22⋊C4—442no—
523C22⋊C4—442no—
524C22⋊C4—442no—
525C22⋊C4—881no—
526C42—24no—
527C42—21no—
528C42—21no—
529C42—221no—
530C42—221no—
531C42—221no—
532C42—221no—
533C42—442no—
534C42—442no—
535C42—442no—
536C11#2618911yescharacteristic, complemented, Sylow
537C23—41no—
538C23—41no—
539C23—41no—
540C23—41no—
541C23—41no—
542C23—41no—
543C23—41no—
544C23C2×D4×D1111yescharacteristic
545Q8—22no—
546Q8—22no—
547Q8—22no—
548Q8—222no—
549Q8—222no—
550Q8—441no—
551Q8—441no—
552Q8#6693614yes—
553D4—41no—
554D4—41no—
555D4—41no—
556D4—41no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—22no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—221no—
573C2×C4—221no—
574C2×C4—221no—
575C2×C4—221no—
576C2×C4—221no—
577C2×C4—221no—
578C2×C4—221no—
579C2×C4—221no—
580C2×C4—221no—
581C2×C4—221no—
582C2×C4—221no—
583C2×C4—221no—
584C2×C4—222no—
585C2×C4—441no—
586C2×C4—441no—
587C2×C4—441no—
588C2×C4—441no—
589C2×C4—441no—
590C2×C4—441no—
591C2×C4—441no—
592C2×C4—441no—
593C2×C4—441no—
594C2×C4—441no—
595C2×C4—441no—
596C2×C4C2×#433911yescharacteristic
597C2×C4C2×D4×D1111yescharacteristic
598C2×C4C2×#434111yescharacteristic
599C2×C4C2×#434111yescharacteristic
600C2×C4#6704211yescharacteristic
601C2×C4#6704311yescharacteristic
602C8—41no—
603C8—41no—
604C8—222no—
605C8—441no—
606C22—81no—
607C22—81no—
608C22—81no—
609C22—81no—
610C22—81no—
611C22—81no—
612C22—81no—
613C22#1062308311yescharacteristic
614C22#1062311711yescharacteristic
615C22#1062314011yescharacteristic
616C22#1062329311yescharacteristic
617C22#1062329911yescharacteristic
618C22#1062330411yescharacteristic
619C22#1062331011yescharacteristic
620C4—24no—
621C4—41no—
622C4—41no—
623C4—42no—
624C4—81no—
625C4—441no—
626C4—441no—
627C4—441no—
628C4—441no—
629C4—442no—
630C4—881no—
631C4—881no—
632C4—881no—
633C4C2×#6693611yescharacteristic
634C4#1062309611yescharacteristic
635C4#1062314211yescharacteristic
636C4#1062319611yescharacteristic
637C2—161no—
638C2#1307235711yescharacteristic
639C2#1307871811yescharacteristic
640C2#1307883811yescharacteristic
641C2#1308019611yescharacteristic
642C2#1308026811yescharacteristic
643C2#1308138011yescharacteristic
644C2#1308145911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1880C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenter#1880D11
hypocenterC11#26189
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1880

Complements

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

NH ≅ G/Ntype
2. C2×#10622402C2semidirect
4. #13071537C2semidirect
6. #13070119C2semidirect
7. #13070036C2semidirect
10. #13069179C2semidirect
12. #13068957C2semidirect
13. #13068871C2semidirect
14. #13068868C2semidirect
536. C11#26189semidirect

Maximal subgroups

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

subgroupindex
C2×#106227792
C2×#106224022
#130724172
#130715372
#130701372
#130701192
#130700362
#130698562
#130693152
#130691792
#130689732
#130689572
#130688712
#130688682
C11×#18802
#2618911