Finite Group Databasebeta

← #14821888

Subgroups — #14821888

Order 2816.

764 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13072990C211yesmaximal, characteristic
2#13069938C211yesmaximal, characteristic, complemented
3#13069816C211yesmaximal, characteristic
4#13069757C211yesmaximal, characteristic, complemented
5#13069624C211yesmaximal, characteristic
6#13069564C211yesmaximal, characteristic, complemented
7#13069291C211yesmaximal, characteristic, complemented
8#13069257C211yesmaximal, characteristic, complemented
9#13069224C211yesmaximal, characteristic
10#13069205C211yesmaximal, characteristic, complemented
11#13068957C211yesmaximal, characteristic, complemented
12#13068923C211yesmaximal, characteristic
13#13068706C211yesmaximal, characteristic
14C4×#66899C211yesmaximal, characteristic, complemented
15C11×#2360C211yesmaximal, characteristic
16C2×C11×C22⋊Q8C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×#4326C2211yescharacteristic
20C2×#66977C2211yescharacteristic
21C2×#66922C2211yescharacteristic
22C11×#391C2211yescharacteristic
23C11×#389—21no—
24C11×#389C2211yescharacteristic
25C11×#387—21no—
26C11×#385—21no—
27C4×C11×C4⋊C4C2211yescharacteristic
28C4×C11×C22⋊C4—21no—
29C4×C11×C22⋊C4C2211yescharacteristic
30C2×#66899C2211yescharacteristic
31C2×#66899C2211yescharacteristic
32C2×#66899C2211yescharacteristic
33#10622825C2211yescharacteristic
34C2×C22⋊(C11⋊C8)C2211yescharacteristic
35C2×C22⋊(C11⋊C8)C2211yescharacteristic
36C2×#66874C2211yescharacteristic
37C2×#66874C2211yescharacteristic
38C2×#66874C2211yescharacteristic
39C2×#66871C2211yescharacteristic
40#10622564—21no—
41#10622560—21no—
42C4×C4⋊Dic11C2211yescharacteristic
43#10622542C2211yescharacteristic
44#10622542C2211yescharacteristic
45C2×C4⋊(C11⋊C8)C2211yescharacteristic
46C2×C4×C11⋊C8C2211yescharacteristic
47#10622273—21no—
48#10622259—21no—
49#10622167C2211yescharacteristic
50#10622167C2211yescharacteristic
51#10622167C2211yescharacteristic
52#10622167C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×Q8×C11C2311yescharacteristic
60C23×C4×C11—21no—
61C23×C4×C11C2311yescharacteristic
62C22×Dic22—21no—
63C22×Dic22C2311yescharacteristic
64C11×C22⋊Q8—22no—
65C11×C22⋊Q8—22no—
66C4×Q8×C11—22no—
67C4×Q8×C11—41no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—22no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—41no—
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C22⋊C4—21no—
78C2×C11×C22⋊C4D411yescharacteristic
79C2×C11×C22⋊C4D411yescharacteristic
80C2×C42×C11—21no—
81C2×C42×C11—21no—
82C2×C42×C11C2311yescharacteristic
83C2×C42×C11C2311yescharacteristic
84C2×C22⋊Dic11—21no—
85C2×C22⋊Dic11—21no—
86C2×#4326—22no—
87C2×#4326—41no—
88C2×#4326—41no—
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93#66977—22no—
94#66977—41no—
95C2×Dic11⋊C4—21no—
96C2×C4×Dic11—21no—
97C22×C11⋊C8C2311yescharacteristic
98C22×C11⋊C8C2311yescharacteristic
99C22×C11⋊C8C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101#66922—22no—
102#66922—41no—
103C11×#95—21no—
104C11×#95—21no—
105C11×#95—21no—
106C11×#95—21no—
107C11×#95D411yescharacteristic
108C11×#95D411yescharacteristic
109#66899—22no—
110#66899—22no—
111#66899—41no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C22⋊(C11⋊C8)—41no—
119C22⋊(C11⋊C8)—41no—
120#66874—22no—
121#66874—22no—
122#66874—41no—
123#66871—22no—
124C4⋊(C11⋊C8)—41no—
125C4×C11⋊C8—41no—
126#26726—111nomaximal, Sylow
127C24×C11C2×D411yescharacteristic
128C2×Q8×C11—21no—
129C2×Q8×C11—21no—
130C2×Q8×C11—21no—
131C2×Q8×C11—21no—
132C2×Q8×C11—21no—
133C2×Q8×C11#4112yes—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—42no—
145C22×C4×C11—42no—
146C22×C4×C11—81no—
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2411yescharacteristic
153C22×Dic11—21no—
154C22×Dic11—21no—
155C22×Dic11—21no—
156C22×Dic11—21no—
157C2×Dic22—21no—
158C2×Dic22—21no—
159C2×Dic22—21no—
160C2×Dic22—21no—
161C2×Dic22—21no—
162C2×Dic22—21no—
163C2×Dic22—42no—
164C2×Dic22—42no—
165C2×Dic22—81no—
166C11×C4⋊C4—24no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—42no—
172C11×C4⋊C4—42no—
173C11×C4⋊C4—81no—
174C11×C4⋊C4#4112yes—
175C11×C4⋊C4#4112yes—
176C11×C22⋊C4—24no—
177C11×C22⋊C4—41no—
178C11×C22⋊C4Q1614yescomplemented
179C42×C11—21no—
180C42×C11—21no—
181C42×C11—21no—
182C42×C11—21no—
183C42×C11—42no—
184C42×C11—81no—
185C22⋊Dic11—42no—
186C22⋊Dic11—81no—
187#4326—44no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—42no—
194C4⋊Dic11#4112yes—
195Dic11⋊C4—42no—
196C4×Dic11—81no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209#2492—111no—
210#2360D1111yescharacteristic
211#2056—111no—
212#2036—111no—
213#2024—111no—
214#2001—111no—
215#1987—111no—
216#1933—111no—
217#1928—111no—
218#1923—111no—
219#1921—111no—
220#1878—111no—
221#1872—111no—
222#1824—111no—
223C4×#103—111no—
224C23×C11—21no—
225C23×C11—21no—
226C23×C11—21no—
227C23×C11—21no—
228C23×C11—21no—
229C23×C11—21no—
230C23×C11C2×Q1612yes—
231C23×C11C22×D411yescharacteristic
232Q8×C11—22no—
233Q8×C11—22no—
234Q8×C11—41no—
235Q8×C11—41no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—22no—
241C2×C4×C11—22no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—22no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—84no—
266C2×C4×C11C2×Q1612yes—
267C2×C4×C11C2×Q1612yes—
268C2×C4×C11C2×#4111yescharacteristic
269C2×C4×C11C2×#4111yescharacteristic
270C2×C4×C11C2×#4111yescharacteristic
271C2×C4×C11C2×#4111yescharacteristic
272C2×C4×C11H(5,𝔽2)11yescharacteristic
273C2×C4×C11H(5,𝔽2)11yescharacteristic
274C2×Dic11—22no—
275C2×Dic11—41no—
276C2×Dic11—41no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286Dic22—41no—
287Dic22—41no—
288Dic22—41no—
289Dic22—41no—
290Dic22—84no—
291C11⋊C8—41no—
292C11⋊C8—41no—
293C11⋊C8—41no—
294C11⋊C8—41no—
295C22×Q16—111no—
296C2×C4⋊Q8—111no—
297C2×C22⋊Q8—111no—
298C2×C22⋊Q8C2×D1111yescharacteristic
299C2×C4×Q8C2×D1111yescharacteristic
300C22×C4⋊C4C2×D1111yescharacteristic
301C2×#107—111no—
302C2×C4⋊C8—111no—
303C2×#103—111no—
304C2×#103—111no—
305C2×#103—111no—
306C2×#103—111no—
307C2×#103—111no—
308C2×#103—111no—
309C2×C22⋊C8—111no—
310C2×C22⋊C8—111no—
311C2×C4×C8—111no—
312#400—221no—
313#393—221no—
314#391—111no—
315#391—111no—
316#391—221no—
317#391C2×D1111yescharacteristic
318#389—21no—
319#389C2×D1111yescharacteristic
320#388—221no—
321#387—21no—
322#385—21no—
323#380—111no—
324C4×C4⋊C4—111no—
325C4×C4⋊C4C2×D1111yescharacteristic
326C4×C22⋊C4—21no—
327C4×C22⋊C4C2×D1111yescharacteristic
328#340—111no—
329#340—111no—
330#340—111no—
331#340—111no—
332#340—111no—
333#340—111no—
334#340—111no—
335#340—111no—
336#336—111no—
337#336—111no—
338C22×C11—22no—
339C22×C11—22no—
340C22×C11—22no—
341C22×C11—41no—
342C22×C11—41no—
343C22×C11—41no—
344C22×C11—41no—
345C22×C11#52511yescharacteristic
346C22×C11#54611yescharacteristic
347C22×C11#54611yescharacteristic
348C22×C11C22×Q1611yescharacteristic
349C22×C11#57511yescharacteristic
350C22×C11#57711yescharacteristic
351C22×C11#57711yescharacteristic
352C4×C11—22no—
353C4×C11—22no—
354C4×C11—42no—
355C4×C11—41no—
356C4×C11—42no—
357C4×C11—41no—
358C4×C11—42no—
359C4×C11—41no—
360C4×C11—81no—
361C4×C11#52911yescharacteristic
362C4×C11#53811yescharacteristic
363C4×C11#55511yescharacteristic
364C4×C11#55911yescharacteristic
365Dic11—42no—
366Dic11—81no—
367Dic11—81no—
368Dic11—81no—
369C22×Q8—111no—
370C22×Q8—221no—
371C22×Q8C22×D1111yescharacteristic
372C23×C4—21no—
373C23×C4C22×D1111yescharacteristic
374C2×Q16—222no—
375C2×Q16—441no—
376C2×Q16—441no—
377C22×C8—111no—
378C22×C8—111no—
379C22×C8—111no—
380C22×C8—111no—
381C4⋊Q8—222no—
382C4⋊Q8—441no—
383C22⋊Q8—22no—
384C22⋊Q8—22no—
385C22⋊Q8—222no—
386C22⋊Q8—441no—
387C4×Q8—22no—
388C4×Q8—41no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—41no—
395C2×C4⋊C4—111no—
396C2×C4⋊C4—111no—
397C2×C4⋊C4—111no—
398C2×C4⋊C4—221no—
399C2×C4⋊C4—221no—
400C2×C4⋊C4C22×D1111yescharacteristic
401C2×C4⋊C4C22×D1111yescharacteristic
402C2×C4⋊C4C22×D1111yescharacteristic
403C2×C22⋊C4—21no—
404C2×C22⋊C4—221no—
405C2×C22⋊C4—221no—
406C2×C22⋊C4C22⋊D1111yescharacteristic
407C2×C22⋊C4C22⋊D1111yescharacteristic
408C2×C42—21no—
409C2×C42—21no—
410C2×C42—221no—
411C2×C42C22×D1111yescharacteristic
412C2×C42C22×D1111yescharacteristic
413#107—222no—
414C4⋊C8—441no—
415#103—222no—
416#103—222no—
417#103—222no—
418#103—222no—
419#103—441no—
420#103—441no—
421C22⋊C8—441no—
422C22⋊C8—441no—
423C4×C8—441no—
424#95—21no—
425#95—21no—
426#95—21no—
427#95—21no—
428#95—221no—
429#95—221no—
430#95—221no—
431#95—221no—
432#95—221no—
433#95—221no—
434#95C22⋊D1111yescharacteristic
435#95C22⋊D1111yescharacteristic
436C2×C11—42no—
437C2×C11#245911yescharacteristic
438C2×C11#310411yescharacteristic
439C2×C11#312511yescharacteristic
440C2×C11#329911yescharacteristic
441C2×C11#329911yescharacteristic
442C2×C11#331111yescharacteristic
443C2×C11#332311yescharacteristic
444C24C2×C22⋊D1111yescharacteristic
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—221no—
451C2×Q8—221no—
452C2×Q8—221no—
453C2×Q8—221no—
454C2×Q8—221no—
455C2×Q8—221no—
456C2×Q8—442no—
457C2×Q8—442no—
458C2×Q8—881no—
459C2×Q8#433912yes—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—42no—
471C22×C4—42no—
472C22×C4—81no—
473C22×C4—221no—
474C22×C4—221no—
475C22×C4—221no—
476C22×C4—221no—
477C22×C4C2×C22⋊D1111yescharacteristic
478C22×C4C2×C22⋊D1111yescharacteristic
479C22×C4C2×C22⋊D1111yescharacteristic
480C22×C4C2×C22⋊D1111yescharacteristic
481C22×C4C2×C22⋊D1111yescharacteristic
482C22×C4C23×D1111yescharacteristic
483Q16—444no—
484C2×C8—221no—
485C2×C8—221no—
486C2×C8—221no—
487C2×C8—221no—
488C2×C8—221no—
489C2×C8—221no—
490C2×C8—221no—
491C2×C8—221no—
492C2×C8—221no—
493C2×C8—221no—
494C2×C8—221no—
495C2×C8—221no—
496C4⋊C4—24no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—42no—
502C4⋊C4—42no—
503C4⋊C4—81no—
504C4⋊C4—112no—
505C4⋊C4—221no—
506C4⋊C4—221no—
507C4⋊C4—221no—
508C4⋊C4—221no—
509C4⋊C4—221no—
510C4⋊C4—442no—
511C4⋊C4—442no—
512C4⋊C4#433912yes—
513C4⋊C4#434112yes—
514C22⋊C4—24no—
515C22⋊C4—41no—
516C22⋊C4—442no—
517C22⋊C4—881no—
518C22⋊C4#432614yescomplemented
519C42—21no—
520C42—21no—
521C42—21no—
522C42—21no—
523C42—42no—
524C42—81no—
525C42—881no—
526C11#2672611yescharacteristic, complemented, Sylow
527C23—21no—
528C23—21no—
529C23—21no—
530C23—21no—
531C23—21no—
532C23—21no—
533C23C2×#432612yes—
534C23C22×C22⋊D1111yescharacteristic
535Q8—22no—
536Q8—22no—
537Q8—41no—
538Q8—41no—
539Q8—441no—
540Q8—441no—
541Q8—441no—
542Q8—441no—
543Q8—884no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—22no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—84no—
574C2×C4—222no—
575C2×C4—441no—
576C2×C4—441no—
577C2×C4—441no—
578C2×C4—441no—
579C2×C4—441no—
580C2×C4—441no—
581C2×C4—441no—
582C2×C4—441no—
583C2×C4—441no—
584C2×C4—441no—
585C2×C4—441no—
586C2×C4C2×#432612yes—
587C2×C4C2×#432612yes—
588C2×C4C2×#433911yescharacteristic
589C2×C4C2×#433911yescharacteristic
590C2×C4C2×#434111yescharacteristic
591C2×C4#6703711yescharacteristic
592C2×C4#41×D1111yescharacteristic
593C2×C4#6704211yescharacteristic
594C8—441no—
595C8—441no—
596C8—441no—
597C8—441no—
598C22—22no—
599C22—22no—
600C22—22no—
601C22—41no—
602C22—41no—
603C22—41no—
604C22—41no—
605C22#1062332211yescharacteristic
606C22#1062333711yescharacteristic
607C22C22×#432611yescharacteristic
608C22#1062335311yescharacteristic
609C22#1062336011yescharacteristic
610C22#1062336711yescharacteristic
611C22#1062336811yescharacteristic
612C4—22no—
613C4—22no—
614C4—41no—
615C4—42no—
616C4—42no—
617C4—41no—
618C4—42no—
619C4—41no—
620C4—81no—
621C4—442no—
622C4—881no—
623C4—881no—
624C4—881no—
625C4#1062306911yescharacteristic
626C4#1062309011yescharacteristic
627C4#1062309111yescharacteristic
628C4#1062309411yescharacteristic
629C2—42no—
630C2#1307254711yescharacteristic
631C2#1307865511yescharacteristic
632C2#1307889311yescharacteristic
633C2#1308048611yescharacteristic
634C2#1308049211yescharacteristic
635C2#1308065211yescharacteristic
636C2#1308082611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2360C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenter#2360D11
hypocenterC11#26726
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2360

Complements

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

NH ≅ G/Ntype
2. #13069938C2semidirect
4. #13069757C2semidirect
6. #13069564C2semidirect
7. #13069291C2semidirect
8. #13069257C2semidirect
10. #13069205C2semidirect
11. #13068957C2semidirect
14. C4×#66899C2semidirect
178. C11×C22⋊C4Q16semidirect
518. C22⋊C4#4326semidirect
526. C11#26726semidirect

Maximal subgroups

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

subgroupindex
#130729902
#130699382
#130698162
#130697572
#130696242
#130695642
#130692912
#130692572
#130692242
#130692052
#130689572
#130689232
#130687062
C4×#668992
C11×#23602
#2672611