Finite Group Databasebeta

← #14725071

Subgroups — #14725071

Order 2816.

656 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078616C211yesmaximal, characteristic
2#13077682C211yesmaximal, characteristic, complemented
3#13077651C211yesmaximal, characteristic, complemented
4#13067527C211yesmaximal, characteristic, complemented
5#13067498C211yesmaximal, characteristic, complemented
6#13067483C211yesmaximal, characteristic, complemented
7#13067477C211yesmaximal, characteristic, complemented
8#13067448C211yesmaximal, characteristic, complemented
9#13067442C211yesmaximal, characteristic, complemented
10#13067437C211yesmaximal, characteristic, complemented
11#13067408C211yesmaximal, characteristic, complemented
12#13067394C211yesmaximal, characteristic, complemented
13#13067086C211yesmaximal, characteristic, complemented
14#13066916C211yesmaximal, characteristic, complemented
15C11×#1478C211yesmaximal, characteristic, complemented
16C2×C4×D4×C11C2211yescharacteristic
17#10623008C2211yescharacteristic
18C11×#431C2211yescharacteristic
19C11×#431C2211yescharacteristic
20#10622830C411yescharacteristic
21#10622830C411yescharacteristic
22#10622820—21no—
23C2×C22⋊(C11⋊C8)—21no—
24#10622628C411yescharacteristic
25#10622628C411yescharacteristic
26C4×#4323C2211yescharacteristic
27C4×#4323C2211yescharacteristic
28C4×#4323C2211yescharacteristic
29C4×#4323C2211yescharacteristic
30#10622625C2211yescharacteristic
31#10622625C2211yescharacteristic
32#10622624—21no—
33#10622624—21no—
34D4×C11⋊C8C2211yescharacteristic
35D4×C11⋊C8C2211yescharacteristic
36#10622620C411yescharacteristic
37#10622620C411yescharacteristic
38#10622580C411yescharacteristic
39#10622580C411yescharacteristic
40#10622539C2211yescharacteristic
41#10622538C2211yescharacteristic
42#10622538C2211yescharacteristic
43#10622451C2211yescharacteristic, complemented
44#10622451C2211yescharacteristic, complemented
45#10622447C2211yescharacteristic, complemented
46#10622447C2211yescharacteristic, complemented
47#10622340—21no—
48#10622340—21no—
49#10622301—21no—
50C8×D44—21no—
51C11×D4⋊C8C2211yescharacteristic
52C11×D4⋊C8C2211yescharacteristic
53C11×D4⋊C8C2211yescharacteristic
54C11×D4⋊C8C2211yescharacteristic
55#10622118C2211yescharacteristic, complemented
56#10622118C2211yescharacteristic, complemented
57#10622117C2211yescharacteristic, complemented
58#10622117C2211yescharacteristic, complemented
59#10622097C2211yescharacteristic, complemented
60#10622097C2211yescharacteristic, complemented
61#10622097C2211yescharacteristic, complemented
62#10622097C2211yescharacteristic, complemented
63#10622093C2211yescharacteristic, complemented
64#10622092C2211yescharacteristic, complemented
65#10622092C2211yescharacteristic, complemented
66C8×C11⋊C8C2211yescharacteristic, complemented
67C22×D4×C11C2×C411yescharacteristic
68C23×C4×C11—21no—
69C2×#4339—21no—
70C4×D4×C11—21no—
71C4×D4×C11—21no—
72C4×D4×C11C2×C411yescharacteristic
73C4×D4×C11C2×C411yescharacteristic
74C4×D4×C11C2311yescharacteristic
75C4×D4×C11C2311yescharacteristic
76C2×C11×C4⋊C4C2×C411yescharacteristic
77C2×C11×C22⋊C4—21no—
78C2×C42×C11C2311yescharacteristic
79C2×#4323C2×C411yescharacteristic
80C2×#4323C2×C411yescharacteristic
81C2×#4323C2×C411yescharacteristic
82C2×#4323C2×C411yescharacteristic
83#66983—21no—
84#66983C2×C411yescharacteristic
85#66983C2×C411yescharacteristic
86C2×#4318—21no—
87C2×#4318—21no—
88C22×C11⋊C8—21no—
89C22×C11⋊C8—21no—
90C2×#4313—21no—
91C2×#4313—21no—
92C2×C8×D11—21no—
93C2×C8×D11—21no—
94#66928—21no—
95#66927C2×C411yescharacteristic
96C4×D44—21no—
97C4×D44C2311yescharacteristic
98C4×D44C2311yescharacteristic
99#66922C2×C411yescharacteristic
100C11×C4⋊C8—21no—
101C11×C4⋊C8C2311yescharacteristic
102C11×C4⋊C8C2311yescharacteristic
103C11×C22⋊C8—21no—
104C11×C22⋊C8—21no—
105C4×C8×C11—21no—
106C4×C8×C11C2311yescharacteristic
107C4×C8×C11C2311yescharacteristic
108#66896C2×C411yescharacteristic
109#66896C2×C411yescharacteristic
110#66896C2×C411yescharacteristic
111#66896C2×C411yescharacteristic
112C22⋊(C11⋊C8)—21no—
113C22⋊(C11⋊C8)—21no—
114C22⋊(C11⋊C8)—21no—
115C22⋊(C11⋊C8)—21no—
116C22⋊(C11⋊C8)—21no—
117C22⋊(C11⋊C8)C2×C411yescharacteristic
118C22⋊(C11⋊C8)C2×C411yescharacteristic
119C22⋊(C11⋊C8)D411yescharacteristic
120C22⋊(C11⋊C8)D411yescharacteristic
121(C2×D11)⋊C8—21no—
122(C2×D11)⋊C8—21no—
123(C2×D11)⋊C8—21no—
124(C2×D11)⋊C8—21no—
125#66873C2×C411yescharacteristic
126#66873C2×C411yescharacteristic
127#66873C2×C411yescharacteristic
128#66873C2×C411yescharacteristic
129#66871C2×C411yescharacteristic
130#66871C2×C411yescharacteristic
131#66871C2×C411yescharacteristic
132#66871C2×C411yescharacteristic
133C4⋊(C11⋊C8)C2×C411yescharacteristic
134C4⋊(C11⋊C8)C2×C411yescharacteristic
135C4⋊(C11⋊C8)D411yescharacteristic
136C4⋊(C11⋊C8)D411yescharacteristic
137C4⋊(C11⋊C8)C2311yescharacteristic
138C4⋊(C11⋊C8)C2311yescharacteristic
139#66867—21no—
140C4×C11⋊C8C2311yescharacteristic
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#18026—111nomaximal, Sylow
145C24×C11—21no—
146C2×D4×C11—22no—
147C2×D4×C11—21no—
148C2×D4×C11—41no—
149C2×D4×C11C22×C411yescharacteristic
150C2×D4×C11C22×C411yescharacteristic
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—81no—
157C22×C4×C11—81no—
158C22×C4×C11C22×C411yescharacteristic
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11#4111yescharacteristic
161C2×C22⋊D11—21no—
162C2×C22⋊D11—21no—
163#4339—81no—
164#4339—81no—
165C2×D44—21no—
166C2×D44—21no—
167C2×D44C22×C411yescharacteristic
168C2×D44C22×C411yescharacteristic
169C2×C4×D11—21no—
170C2×C4×D11—21no—
171C2×Dic22—21no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4C22×C411yescharacteristic
178C11×C4⋊C4C22×C411yescharacteristic
179C11×C22⋊C4—21no—
180C11×C22⋊C4—21no—
181C11×C22⋊C4—21no—
182C11×C22⋊C4—21no—
183C42×C11C22×C411yescharacteristic
184C42×C11C2×D411yescharacteristic
185C42×C11#4111yescharacteristic
186C42×C11C2411yescharacteristic
187#4323—22no—
188#4323—22no—
189#4323—41no—
190#4323—41no—
191(C2×D11)⋊C4—21no—
192(C2×D11)⋊C4—21no—
193(C2×D11)⋊C4—21no—
194(C2×D11)⋊C4—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11C22×C411yescharacteristic
197C4⋊Dic11C22×C411yescharacteristic
198#4318—81no—
199#4318—81no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—81no—
203C2×C11⋊C8—81no—
204C2×C11⋊C8C22×C411yescharacteristic
205C2×C11⋊C8C22×C411yescharacteristic
206C2×C11⋊C8C22×C411yescharacteristic
207C2×C11⋊C8C22×C411yescharacteristic
208C2×C11⋊C8C2×D411yescharacteristic
209C2×C11⋊C8C2×D411yescharacteristic
210C2×C11⋊C8C2×D411yescharacteristic
211C2×C11⋊C8C2×D411yescharacteristic
212#4313—81no—
213#4313—81no—
214C8×D11—81no—
215C8×D11—81no—
216#3100—111no—
217#2979—111no—
218#2974—111no—
219#1594—111no—
220#1589—111no—
221#1586—111no—
222#1586—111no—
223#1581—111no—
224#1581—111no—
225#1580—111no—
226C8×D8—111no—
227#1572—111no—
228#1496—111no—
229#1478D1111yescharacteristic, complemented
230#1454—111no—
231C23×C11—21no—
232C23×C11—21no—
233C23×C11—42no—
234C23×C11—42no—
235C23×C11—81no—
236C23×C11C4×D411yescharacteristic
237C22×D11—21no—
238C22×D11—21no—
239D4×C11—21no—
240D4×C11—21no—
241D4×C11—21no—
242D4×C11—42no—
243D4×C11#13112yes—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—81no—
256C2×C4×C11—81no—
257C2×C4×C11—81no—
258C2×C4×C11C4×D411yescharacteristic
259C2×C4×C11C4×D411yescharacteristic
260C2×C4×C11C4×D411yescharacteristic
261C2×C4×C11C23×C411yescharacteristic
262C2×C4×C11C22×D411yescharacteristic
263C2×C4×C11C2×#4111yescharacteristic
264C22⋊D11—81no—
265C22⋊D11—81no—
266C2×Dic11—21no—
267C2×Dic11—21no—
268D44—21no—
269D44—21no—
270D44—21no—
271D44—21no—
272D44—42no—
273D44—81no—
274C4×D11—41no—
275C4×D11—41no—
276C4×D11—41no—
277C4×D11—41no—
278Dic22—81no—
279C8×C11—41no—
280C8×C11—41no—
281C8×C11—41no—
282C8×C11—41no—
283C11⋊C8—21no—
284C11⋊C8—21no—
285C11⋊C8—21no—
286C11⋊C8—21no—
287C11⋊C8—21no—
288C11⋊C8—21no—
289C11⋊C8—21no—
290C11⋊C8—21no—
291C11⋊C8—41no—
292C11⋊C8—41no—
293#532—111no—
294C2×C4×D4C2×D1111yescharacteristic
295#480—111no—
296#480—111no—
297#474—111no—
298#474—111no—
299#459—111no—
300#459—111no—
301#447—111no—
302#447—111no—
303C4×D8—111no—
304C4×D8—111no—
305C4×D8—111no—
306C4×D8—111no—
307#436—111no—
308#436—111no—
309#436—111no—
310#436—111no—
311#436—221no—
312#435—221no—
313#435—221no—
314C8×D4—111no—
315C8×D4—111no—
316C8×D4—111no—
317C8×D4—111no—
318C8×D4—221no—
319#432—111no—
320#431—111no—
321#431—111no—
322#431C2×D1111yescharacteristic
323#431C2×D1111yescharacteristic
324#408—221no—
325#408—221no—
326#407—221no—
327C2×C22⋊C8—221no—
328#335—111no—
329#335—111no—
330#334—111no—
331#334—111no—
332D4⋊C8—111no—
333D4⋊C8—111no—
334D4⋊C8—111no—
335D4⋊C8—111no—
336D4⋊C8C2×D1111yescharacteristic
337D4⋊C8C2×D1111yescharacteristic
338D4⋊C8C2×D1111yescharacteristic
339D4⋊C8C2×D1111yescharacteristic
340#322—111no—
341#322—111no—
342#322—111no—
343C82—111no—
344C22×C11—21no—
345C22×C11—22no—
346C22×C11—21no—
347C22×C11—21no—
348C22×C11—41no—
349C22×C11—41no—
350C22×C11—41no—
351C22×C11—41no—
352C22×C11—41no—
353C22×C11—84no—
354C22×C11C2×C4×D411yescharacteristic
355C2×D11—41no—
356C2×D11—41no—
357C2×D11—41no—
358C2×D11—41no—
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×C11C2×#13111yescharacteristic
368C4×C11#56811yescharacteristic
369C4×C11#57611yescharacteristic
370C4×C11#57611yescharacteristic
371Dic11—41no—
372Dic11—41no—
373C2×#41—221no—
374C22×D4C4×D1111yescharacteristic
375C23×C4—21no—
376C2×D8—111no—
377C2×D8—111no—
378C2×D8—111no—
379C2×D8—111no—
380C2×M16—221no—
381C2×M16—221no—
382C2×M16—221no—
383C2×M16—221no—
384C22×C8—221no—
385C22×C8—221no—
386C22×C8—221no—
387C22×C8—221no—
388C4⋊Q8—111no—
389#127—111no—
390#124—221no—
391#121—111no—
392#121—111no—
393#121—221no—
394C4×D4—21no—
395C4×D4—21no—
396C4×D4—111no—
397C4×D4—111no—
398C4×D4—221no—
399C4×D4C4×D1111yescharacteristic
400C4×D4C4×D1111yescharacteristic
401C4×D4C22×D1111yescharacteristic
402C4×D4C22×D1111yescharacteristic
403C2×C4⋊C4C4×D1111yescharacteristic
404C2×C22⋊C4—21no—
405C2×C42C22×D1111yescharacteristic
406#107—111no—
407#107—111no—
408#107—111no—
409#107—111no—
410C4⋊C8—21no—
411C4⋊C8—111no—
412C4⋊C8—111no—
413C4⋊C8—111no—
414C4⋊C8—111no—
415C4⋊C8—111no—
416C4⋊C8—111no—
417C4⋊C8C22×D1111yescharacteristic
418C4⋊C8C22×D1111yescharacteristic
419#102—111no—
420#102—111no—
421#102—111no—
422#102—111no—
423#102—111no—
424#102—111no—
425#102—111no—
426#102—111no—
427C22⋊C8—21no—
428C22⋊C8—21no—
429C22⋊C8—111no—
430C22⋊C8—111no—
431C22⋊C8—111no—
432C22⋊C8—111no—
433C22⋊C8—221no—
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—
443C4×C8—21no—
444C4×C8—111no—
445C4×C8—111no—
446C4×C8—111no—
447C4×C8—111no—
448C4×C8C22×D1111yescharacteristic
449C4×C8C22×D1111yescharacteristic
450C2×C11—41no—
451C2×C11—42no—
452C2×C11—81no—
453C2×C11#293311yescharacteristic
454C2×C11#294811yescharacteristic
455C2×C11#295511yescharacteristic
456D11—81no—
457D11—81no—
458C24—21no—
459#41—881no—
460#41—881no—
461C2×Q8—221no—
462C2×D4—22no—
463C2×D4—21no—
464C2×D4—41no—
465C2×D4—111no—
466C2×D4—111no—
467C2×D4—221no—
468C2×D4—221no—
469C2×D4—221no—
470C2×D4—221no—
471C2×D4C2×C4×D1111yescharacteristic
472C2×D4C2×C4×D1111yescharacteristic
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—81no—
479C22×C4—81no—
480C22×C4—221no—
481C22×C4—221no—
482C22×C4C2×C4×D1111yescharacteristic
483C22×C4D4×D1111yescharacteristic
484C22×C4#434111yescharacteristic
485D8—222no—
486D8—222no—
487D8—441no—
488D8—441no—
489M16—881no—
490M16—881no—
491M16—881no—
492M16—881no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—111no—
498C2×C8—111no—
499C2×C8—111no—
500C2×C8—111no—
501C2×C8—111no—
502C2×C8—111no—
503C2×C8—111no—
504C2×C8—111no—
505C2×C8—221no—
506C2×C8—221no—
507C2×C8—881no—
508C2×C8—881no—
509C2×C8—881no—
510C2×C8—881no—
511C4⋊C4—21no—
512C4⋊C4—111no—
513C4⋊C4—111no—
514C4⋊C4—221no—
515C4⋊C4C2×C4×D1111yescharacteristic
516C4⋊C4C2×C4×D1111yescharacteristic
517C22⋊C4—21no—
518C22⋊C4—21no—
519C22⋊C4—21no—
520C22⋊C4—21no—
521C22⋊C4—221no—
522C22⋊C4—221no—
523C22⋊C4—221no—
524C22⋊C4—221no—
525C42C2×C4×D1111yescharacteristic
526C42D4×D1111yescharacteristic
527C42#434111yescharacteristic
528C42C23×D1111yescharacteristic
529C11#1802611yescharacteristic, complemented, Sylow
530C23—21no—
531C23—21no—
532C23—42no—
533C23—42no—
534C23—81no—
535C23—221no—
536C23—221no—
537C23(C22⋊D11)⋊C411yescharacteristic
538Q8—881no—
539D4—21no—
540D4—21no—
541D4—21no—
542D4—42no—
543D4—221no—
544D4—221no—
545D4—221no—
546D4—221no—
547D4—442no—
548D4—881no—
549D4—881no—
550D4—881no—
551D4#6695412yes—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—81no—
564C2×C4—81no—
565C2×C4—81no—
566C2×C4—221no—
567C2×C4—221no—
568C2×C4—441no—
569C2×C4—441no—
570C2×C4—441no—
571C2×C4—441no—
572C2×C4(C22⋊D11)⋊C411yescharacteristic
573C2×C4(C22⋊D11)⋊C411yescharacteristic
574C2×C4(C22⋊D11)⋊C411yescharacteristic
575C2×C4C22×C4×D1111yescharacteristic
576C2×C4C2×D4×D1111yescharacteristic
577C2×C4C2×#434111yescharacteristic
578C8—41no—
579C8—41no—
580C8—41no—
581C8—41no—
582C8—221no—
583C8—221no—
584C8—221no—
585C8—221no—
586C8—221no—
587C8—221no—
588C8—221no—
589C8—221no—
590C8—441no—
591C8—441no—
592C22—21no—
593C22—21no—
594C22—22no—
595C22—21no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—41no—
600C22—41no—
601C22—84no—
602C22—441no—
603C22—441no—
604C22—441no—
605C22—441no—
606C22—441no—
607C22—441no—
608C22C2×(C22⋊D11)⋊C411yescharacteristic
609C4—21no—
610C4—21no—
611C4—21no—
612C4—21no—
613C4—41no—
614C4—41no—
615C4—441no—
616C4—441no—
617C4C2×#6695411yescharacteristic
618C4#1062327611yescharacteristic
619C4#1062330511yescharacteristic
620C4#1062330511yescharacteristic
621C2—41no—
622C2—42no—
623C2—81no—
624C2—881no—
625C2—881no—
626C2#1307733711yescharacteristic
627C2#1307746411yescharacteristic
628C2#1307751511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1478C2
socleC22×C11C2×C4×D4
prime radical#13078616C2
cosocleC42×C11C24
hypercenter#1478D11
hypocenterC11#18026
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1478

Complements

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

NH ≅ G/Ntype
2. #13077682C2semidirect
3. #13077651C2semidirect
4. #13067527C2semidirect
5. #13067498C2semidirect
6. #13067483C2semidirect
7. #13067477C2semidirect
8. #13067448C2semidirect
9. #13067442C2semidirect
10. #13067437C2semidirect
11. #13067408C2semidirect
12. #13067394C2semidirect
13. #13067086C2semidirect
14. #13066916C2semidirect
15. C11×#1478C2semidirect
43. #10622451C22semidirect
44. #10622451C22semidirect
45. #10622447C22semidirect
46. #10622447C22semidirect
55. #10622118C22semidirect
56. #10622118C22semidirect
57. #10622117C22semidirect
58. #10622117C22semidirect
59. #10622097C22semidirect
60. #10622097C22semidirect
61. #10622097C22semidirect
62. #10622097C22semidirect
63. #10622093C22semidirect
64. #10622092C22semidirect
65. #10622092C22semidirect
66. C8×C11⋊C8C22semidirect
229. #1478D11semidirect
529. C11#18026semidirect

Maximal subgroups

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

subgroupindex
#130786162
#130776822
#130776512
#130675272
#130674982
#130674832
#130674772
#130674482
#130674422
#130674372
#130674082
#130673942
#130670862
#130669162
C11×#14782
#1802611