Finite Group Databasebeta

← #14723892

Subgroups — #14723892

Order 2816.

678 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078614C211yesmaximal, characteristic
2#13077693C211yesmaximal, characteristic, complemented
3#13077637C211yesmaximal, characteristic, complemented
4#13067480C211yesmaximal, characteristic, complemented
5#13067478C211yesmaximal, characteristic, complemented
6#13067447C211yesmaximal, characteristic, complemented
7#13067437C211yesmaximal, characteristic, complemented
8#13067437C211yesmaximal, characteristic, complemented
9D8×C11⋊C8C211yesmaximal, characteristic, complemented
10#13067410C211yesmaximal, characteristic, complemented
11#13067395C211yesmaximal, characteristic, complemented
12#13067057C211yesmaximal, characteristic, complemented
13#13067031C211yesmaximal, characteristic, complemented
14#13066912C211yesmaximal, characteristic, complemented
15C11×#1581C211yesmaximal, characteristic, complemented
16#10623079C2211yescharacteristic
17C4×D4×D11C2211yescharacteristic
18C4×C11×D8C2211yescharacteristic
19C11×#436C2211yescharacteristic, complemented
20C8×D4×C11C2211yescharacteristic
21#10622769C411yescharacteristic
22#10622763C411yescharacteristic
23#10622742—21no—
24#10622740—21no—
25C8×C22⋊D11—21no—
26C2×(C2×D11)⋊C8—21no—
27C4×#4323C2211yescharacteristic
28C4×#4323C2211yescharacteristic
29D4×C11⋊C8C2211yescharacteristic
30D4×C11⋊C8C2211yescharacteristic, complemented
31#10622503C411yescharacteristic
32#10622495C411yescharacteristic
33#10622448C2211yescharacteristic
34#10622447C2211yescharacteristic
35#10622447C2211yescharacteristic, complemented
36#10622446C2211yescharacteristic
37#10622399C411yescharacteristic
38#10622387C411yescharacteristic
39#10622386C411yescharacteristic
40#10622372C411yescharacteristic
41#10622343—21no—
42#10622340—21no—
43(C22⋊D11)⋊C8—21no—
44D11×C22⋊C8—21no—
45C4×D88C2211yescharacteristic
46#10622301C2211yescharacteristic, complemented
47C4×#4313C2211yescharacteristic
48C8×D44C2211yescharacteristic
49#10622298C2211yescharacteristic
50#10622298C2211yescharacteristic
51C11×#335C2211yescharacteristic, complemented
52C11×D4⋊C8C2211yescharacteristic
53C11×D4⋊C8C2211yescharacteristic, complemented
54C11×#322C2211yescharacteristic, complemented
55D4⋊(C11⋊C8)C2211yescharacteristic
56D4⋊(C11⋊C8)C2211yescharacteristic, complemented
57#10622121C2211yescharacteristic
58#10622121C2211yescharacteristic, complemented
59#10622118C2211yescharacteristic, complemented
60#10622118C2211yescharacteristic, complemented
61#10622097C2211yescharacteristic
62#10622097C2211yescharacteristic, complemented
63#10622096C2211yescharacteristic, complemented
64#10622092C2211yescharacteristic, complemented
65#10622092C2211yescharacteristic, complemented
66C8×C11⋊C8C2211yescharacteristic, complemented
67C2×D4×D11C2×C411yescharacteristic
68C2×#4339—21no—
69C22×C4×D11—21no—
70C2×C11×D8C2×C411yescharacteristic
71C2×C11×M16—21no—
72C22×C8×C11—21no—
73C4×D4×C11C2311yescharacteristic
74C4×D4×C11C2311yescharacteristic
75#66993C2×C411yescharacteristic
76#66991C2×C411yescharacteristic
77D4×Dic11C2×C411yescharacteristic
78C2×#4323C2×C411yescharacteristic
79C2×#4323C2×C411yescharacteristic
80C4×C22⋊D11—21no—
81C4×C22⋊D11—21no—
82C22×C11⋊C8—21no—
83C22×C11⋊C8—21no—
84C2×D88C2×C411yescharacteristic
85C2×#4313—21no—
86C2×#4313—21no—
87C2×C8×D11—21no—
88C2×C8×D11—21no—
89C2×C8×D11—21no—
90#66948C2×C411yescharacteristic
91#66946C2×C411yescharacteristic
92C4⋊C4×D11C2×C411yescharacteristic
93#66941C2×C411yescharacteristic
94#66938—21no—
95#66937—21no—
96(C22⋊D11)⋊C4—21no—
97C22⋊C4×D11—21no—
98C4×D44C2311yescharacteristic
99C4×D44C2311yescharacteristic
100C42×D11C2311yescharacteristic
101C11×#107C2×C411yescharacteristic
102C11×C4⋊C8C2311yescharacteristic
103C11×C4⋊C8C2311yescharacteristic
104C11×#102C2×C411yescharacteristic
105C11×#102C2×C411yescharacteristic
106C11×C22⋊C8—21no—
107C11×C22⋊C8—21no—
108C4×C8×C11C2311yescharacteristic
109C4×C8×C11C2311yescharacteristic
110C4×C8×C11C2311yescharacteristic
111#66896C2×C411yescharacteristic
112#66896C2×C411yescharacteristic
113C22⋊(C11⋊C8)—21no—
114C22⋊(C11⋊C8)—21no—
115#66885C2×C411yescharacteristic
116#66885C2×C411yescharacteristic
117(C2×D11)⋊C8—21no—
118(C2×D11)⋊C8—21no—
119(C2×D11)⋊C8—21no—
120(C2×D11)⋊C8—21no—
121(C2×D11)⋊C8—21no—
122(C2×D11)⋊C8—21no—
123(C2×D11)⋊C8C2×C411yescharacteristic
124(C2×D11)⋊C8C2×C411yescharacteristic
125(C2×D11)⋊C8D411yescharacteristic
126(C2×D11)⋊C8D411yescharacteristic
127#66882C2×C411yescharacteristic
128#66879—21no—
129#66879—21no—
130Dic11⋊C8C2×C411yescharacteristic
131Dic11⋊C8C2×C411yescharacteristic
132Dic11⋊C8D411yescharacteristic
133Dic11⋊C8D411yescharacteristic
134C8×Dic11—21no—
135#66873C2×C411yescharacteristic
136#66873C2×C411yescharacteristic
137#66871C2×C411yescharacteristic
138#66871C2×C411yescharacteristic
139C4⋊(C11⋊C8)C2311yescharacteristic
140C4⋊(C11⋊C8)C2311yescharacteristic
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#17922—111nomaximal, Sylow
145C23×D11—21no—
146C2×D4×C11C22×C411yescharacteristic
147C2×D4×C11C22×C411yescharacteristic
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C2×C22⋊D11—21no—
151C2×C22⋊D11—21no—
152C2×C22⋊D11—21no—
153C2×C22⋊D11—21no—
154C22×Dic11—21no—
155D4×D11—22no—
156D4×D11—22no—
157#4339—81no—
158#4339—81no—
159C2×D44—21no—
160C2×D44C22×C411yescharacteristic
161C2×D44C22×C411yescharacteristic
162C2×C4×D11—21no—
163C2×C4×D11—21no—
164C2×C4×D11—21no—
165C2×C4×D11—21no—
166C2×C4×D11—81no—
167C2×C4×D11—81no—
168C2×C4×D11C22×C411yescharacteristic
169C2×C4×D11C2×D411yescharacteristic
170C2×C4×D11#4111yescharacteristic
171C2×Dic22—21no—
172C11×D8—22no—
173C11×M16—81no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—81no—
178C2×C8×C11C22×C411yescharacteristic
179C2×C8×C11C22×C411yescharacteristic
180C2×C8×C11C2×D411yescharacteristic
181C2×C8×C11C2×D411yescharacteristic
182C11×C4⋊C4C22×C411yescharacteristic
183C11×C4⋊C4C22×C411yescharacteristic
184C11×C22⋊C4—21no—
185C11×C22⋊C4—21no—
186C42×C11C2411yescharacteristic
187C22⋊Dic11—21no—
188C22⋊Dic11—21no—
189#4323—22no—
190#4323—22no—
191(C2×D11)⋊C4—21no—
192(C2×D11)⋊C4—21no—
193(C2×D11)⋊C4—21no—
194(C2×D11)⋊C4—21no—
195C4⋊Dic11C22×C411yescharacteristic
196C4⋊Dic11C22×C411yescharacteristic
197Dic11⋊C4—21no—
198Dic11⋊C4—21no—
199C4×Dic11C22×C411yescharacteristic
200C4×Dic11C2×D411yescharacteristic
201C4×Dic11#4111yescharacteristic
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—81no—
206C2×C11⋊C8—81no—
207C2×C11⋊C8C22×C411yescharacteristic
208C2×C11⋊C8C22×C411yescharacteristic
209C2×C11⋊C8C2×D411yescharacteristic
210C2×C11⋊C8C2×D411yescharacteristic
211D88—22no—
212#4313—42no—
213#4313—81no—
214C8×D11—81no—
215C8×D11—81no—
216C8×D11—81no—
217#3100—111no—
218#2981—111no—
219#2972—111no—
220#1586—111no—
221#1586—111no—
222#1581—111no—
223#1581D1111yescharacteristic, complemented
224#1580—111no—
225#1580—111no—
226C8×D8—111no—
227C8×D8—111no—
228#1572—111no—
229#1490—111no—
230#1484—111no—
231#1453—111no—
232C23×C11—21no—
233C23×C11—21no—
234C22×D11—21no—
235C22×D11—24no—
236C22×D11—21no—
237C22×D11—81no—
238C22×D11—81no—
239C22×D11C4×D411yescharacteristic
240D4×C11—21no—
241D4×C11—21no—
242D4×C11—21no—
243D4×C11#13112yes—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11C23×C411yescharacteristic
251C2×C4×C11C22×D411yescharacteristic
252C2×C4×C11C2×#4111yescharacteristic
253C22⋊D11—24no—
254C22⋊D11—81no—
255C22⋊D11—81no—
256C22⋊D11—81no—
257C2×Dic11—21no—
258C2×Dic11—21no—
259C2×Dic11—81no—
260C2×Dic11C4×D411yescharacteristic
261C2×Dic11C4×D411yescharacteristic
262C2×Dic11C4×D411yescharacteristic
263D44—21no—
264D44—21no—
265D44—21no—
266D44—81no—
267D44#13112yes—
268C4×D11—21no—
269C4×D11—21no—
270C4×D11—21no—
271C4×D11—21no—
272C4×D11—41no—
273C4×D11—41no—
274C4×D11—41no—
275C4×D11—41no—
276C4×D11—41no—
277C4×D11—81no—
278C4×D11—81no—
279Dic22—81no—
280C8×C11—21no—
281C8×C11—21no—
282C8×C11—21no—
283C8×C11—21no—
284C8×C11—41no—
285C8×C11—41no—
286C8×C11—41no—
287C11⋊C8—22no—
288C11⋊C8—21no—
289C11⋊C8—21no—
290C11⋊C8—21no—
291C11⋊C8—21no—
292C11⋊C8—41no—
293C11⋊C8—41no—
294#532—111no—
295C2×C4×D4—111no—
296#480—111no—
297#480—111no—
298#474—111no—
299#474—111no—
300#459—111no—
301#459—111no—
302#447—111no—
303#447—111no—
304C4×D8—111no—
305C4×D8—111no—
306C4×D8—111no—
307C4×D8C2×D1111yescharacteristic
308#436—111no—
309#436C2×D1111yescharacteristic, complemented
310#435—221no—
311#435—221no—
312C8×D4—111no—
313C8×D4—111no—
314C8×D4—111no—
315C8×D4—111no—
316C8×D4—111no—
317C8×D4—221no—
318C8×D4—221no—
319C8×D4C2×D1111yescharacteristic
320#432—111no—
321#431—111no—
322#431—111no—
323#431—111no—
324#408—221no—
325#408—221no—
326C2×C22⋊C8—221no—
327C2×C22⋊C8—221no—
328C4×M16—111no—
329#335—111no—
330#335C2×D1111yescharacteristic, complemented
331#334—111no—
332#334—111no—
333D4⋊C8—111no—
334D4⋊C8—111no—
335D4⋊C8—111no—
336D4⋊C8—111no—
337D4⋊C8—111no—
338D4⋊C8—111no—
339D4⋊C8C2×D1111yescharacteristic
340D4⋊C8C2×D1111yescharacteristic, complemented
341#322—111no—
342#322—111no—
343#322C2×D1111yescharacteristic, complemented
344C82—111no—
345C22×C11—22no—
346C22×C11—41no—
347C22×C11—41no—
348C22×C11—41no—
349C22×C11—41no—
350C22×C11—41no—
351C22×C11C2×C4×D411yescharacteristic
352C2×D11—21no—
353C2×D11—22no—
354C2×D11—21no—
355C2×D11—21no—
356C2×D11—41no—
357C2×D11—41no—
358C2×D11—41no—
359C2×D11—41no—
360C2×D11—41no—
361C2×D11—84no—
362C4×C11—21no—
363C4×C11—41no—
364C4×C11—41no—
365C4×C11C2×#13111yescharacteristic
366C4×C11C2×#13111yescharacteristic
367C4×C11#57611yescharacteristic
368C4×C11#57611yescharacteristic
369Dic11—21no—
370Dic11—21no—
371Dic11—21no—
372Dic11—41no—
373Dic11—41no—
374C2×#41—221no—
375C22×D4—111no—
376C23×C4—221no—
377C2×D8—111no—
378C2×D8—111no—
379C2×D8—111no—
380C2×D8C4×D1111yescharacteristic
381C2×M16—21no—
382C2×M16—221no—
383C2×M16—221no—
384C22×C8—21no—
385C22×C8—221no—
386C22×C8—221no—
387C22×C8—221no—
388C22×C8—221no—
389C22×C8—221no—
390C4⋊Q8—111no—
391#127—111no—
392#124—221no—
393#121—111no—
394#121—111no—
395#121—221no—
396C4×D4—111no—
397C4×D4—111no—
398C4×D4—111no—
399C4×D4—111no—
400C4×D4—221no—
401C4×D4—221no—
402C4×D4—221no—
403C4×D4C22×D1111yescharacteristic
404C4×D4C22×D1111yescharacteristic
405C2×C4⋊C4—111no—
406C2×C22⋊C4—221no—
407C2×C42—111no—
408#107—111no—
409#107—111no—
410#107—111no—
411#107C4×D1111yescharacteristic
412C4⋊C8—111no—
413C4⋊C8—111no—
414C4⋊C8—111no—
415C4⋊C8—111no—
416C4⋊C8—111no—
417C4⋊C8—111no—
418C4⋊C8C22×D1111yescharacteristic
419C4⋊C8C22×D1111yescharacteristic
420#102—111no—
421#102—111no—
422#102—111no—
423#102—111no—
424#102—111no—
425#102—111no—
426#102C4×D1111yescharacteristic
427#102C4×D1111yescharacteristic
428C22⋊C8—21no—
429C22⋊C8—21no—
430C22⋊C8—111no—
431C22⋊C8—111no—
432C22⋊C8—111no—
433C22⋊C8—111no—
434C22⋊C8—221no—
435C22⋊C8—221no—
436C22⋊C8—221no—
437C22⋊C8—221no—
438C22⋊C8—221no—
439C22⋊C8—221no—
440C22⋊C8—221no—
441C22⋊C8—221no—
442#97—221no—
443#97—221no—
444C4×C8—111no—
445C4×C8—111no—
446C4×C8—111no—
447C4×C8—221no—
448C4×C8C22×D1111yescharacteristic
449C4×C8C22×D1111yescharacteristic
450C4×C8C22×D1111yescharacteristic
451C2×C11—42no—
452C2×C11—81no—
453C2×C11#292911yescharacteristic
454C2×C11#294811yescharacteristic
455C2×C11#295611yescharacteristic
456D11—41no—
457D11—42no—
458D11—81no—
459C24—221no—
460#41—881no—
461#41—881no—
462C2×Q8—221no—
463C2×D4—111no—
464C2×D4—111no—
465C2×D4—221no—
466C2×D4—221no—
467C2×D4—221no—
468C2×D4—221no—
469C2×D4—222no—
470C2×D4—222no—
471C2×D4—221no—
472C2×D4C2×C4×D1111yescharacteristic
473C2×D4C2×C4×D1111yescharacteristic
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—111no—
477C22×C4—111no—
478C22×C4—111no—
479C22×C4—221no—
480C22×C4—221no—
481C22×C4—221no—
482C22×C4—221no—
483C22×C4—221no—
484C22×C4—881no—
485C22×C4—881no—
486D8—22no—
487D8—222no—
488D8—222no—
489D8—222no—
490M16—81no—
491M16—442no—
492M16—881no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—81no—
497C2×C8—111no—
498C2×C8—111no—
499C2×C8—111no—
500C2×C8—111no—
501C2×C8—221no—
502C2×C8—221no—
503C2×C8—221no—
504C2×C8—881no—
505C2×C8—881no—
506C2×C8—881no—
507C2×C8—881no—
508C2×C8—881no—
509C2×C8C2×C4×D1111yescharacteristic
510C2×C8C2×C4×D1111yescharacteristic
511C2×C8D4×D1111yescharacteristic
512C2×C8D4×D1111yescharacteristic
513C4⋊C4—111no—
514C4⋊C4—111no—
515C4⋊C4—221no—
516C4⋊C4—221no—
517C4⋊C4C2×C4×D1111yescharacteristic
518C4⋊C4C2×C4×D1111yescharacteristic
519C22⋊C4—21no—
520C22⋊C4—21no—
521C22⋊C4—221no—
522C22⋊C4—221no—
523C22⋊C4—221no—
524C22⋊C4—221no—
525C22⋊C4—221no—
526C22⋊C4—221no—
527C42—111no—
528C42—111no—
529C42—111no—
530C42C23×D1111yescharacteristic
531C11#1792211yescharacteristic, complemented, Sylow
532C23—21no—
533C23—21no—
534C23—111no—
535C23—224no—
536C23—221no—
537C23—221no—
538C23—881no—
539C23—881no—
540Q8—881no—
541D4—21no—
542D4—21no—
543D4—21no—
544D4—112no—
545D4—224no—
546D4—221no—
547D4—221no—
548D4—221no—
549D4—881no—
550D4—881no—
551D4—881no—
552D4—881no—
553D4#6696012yes—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—111no—
561C2×C4—111no—
562C2×C4—111no—
563C2×C4—221no—
564C2×C4—221no—
565C2×C4—221no—
566C2×C4—221no—
567C2×C4—221no—
568C2×C4—221no—
569C2×C4—441no—
570C2×C4—441no—
571C2×C4—441no—
572C2×C4—441no—
573C2×C4—441no—
574C2×C4—881no—
575C2×C4—881no—
576C2×C4—881no—
577C2×C4C22×C4×D1111yescharacteristic
578C2×C4C2×D4×D1111yescharacteristic
579C2×C4#41×D1111yescharacteristic
580C8—21no—
581C8—21no—
582C8—21no—
583C8—21no—
584C8—41no—
585C8—41no—
586C8—41no—
587C8—222no—
588C8—221no—
589C8—221no—
590C8—221no—
591C8—221no—
592C8—441no—
593C8—441no—
594C22—22no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—41no—
600C22—221no—
601C22—221no—
602C22—222no—
603C22—221no—
604C22—441no—
605C22—441no—
606C22—441no—
607C22—441no—
608C22—441no—
609C22—884no—
610C22C4×D4×D1111yescharacteristic
611C4—21no—
612C4—41no—
613C4—41no—
614C4—221no—
615C4—221no—
616C4—221no—
617C4—441no—
618C4—441no—
619C4C2×#6696011yescharacteristic
620C4D11×#13111yescharacteristic
621C4#1062328811yescharacteristic
622C4#1062330011yescharacteristic
623C2—42no—
624C2—81no—
625C2—441no—
626C2—442no—
627C2—881no—
628C2#1307730711yescharacteristic
629C2#1307746311yescharacteristic
630C2#1307752411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1581C2
socleC22×C11C2×C4×D4
prime radical#13078614C2
cosocleC42×C11C24
hypercenter#1581D11
hypocenterC11#17922
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1581

Complements

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

NH ≅ G/Ntype
2. #13077693C2semidirect
3. #13077637C2semidirect
4. #13067480C2semidirect
5. #13067478C2semidirect
6. #13067447C2semidirect
7. #13067437C2semidirect
8. #13067437C2semidirect
9. D8×C11⋊C8C2semidirect
10. #13067410C2semidirect
11. #13067395C2semidirect
12. #13067057C2semidirect
13. #13067031C2semidirect
14. #13066912C2semidirect
15. C11×#1581C2semidirect
19. C11×#436C22semidirect
30. D4×C11⋊C8C22semidirect
35. #10622447C22semidirect
46. #10622301C22semidirect
51. C11×#335C22semidirect
53. C11×D4⋊C8C22semidirect
54. C11×#322C22semidirect
56. D4⋊(C11⋊C8)C22semidirect
58. #10622121C22semidirect
59. #10622118C22semidirect
60. #10622118C22semidirect
62. #10622097C22semidirect
63. #10622096C22semidirect
64. #10622092C22semidirect
65. #10622092C22semidirect
66. C8×C11⋊C8C22semidirect
223. #1581D11semidirect
309. #436C2×D11semidirect
330. #335C2×D11semidirect
340. D4⋊C8C2×D11semidirect
343. #322C2×D11semidirect
531. C11#17922semidirect

Maximal subgroups

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

subgroupindex
#130786142
#130776932
#130776372
#130674802
#130674782
#130674472
#130674372
D8×C11⋊C82
#130674102
#130673952
#130670572
#130670312
#130669122
C11×#15812
#1792211