Finite Group Databasebeta

← #14725070

Subgroups — #14725070

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#13078614C211yesmaximal, characteristic
2#13077679C211yesmaximal, characteristic, complemented
3#13077649C211yesmaximal, characteristic, complemented
4#13067527C211yesmaximal, characteristic, complemented
5#13067502C211yesmaximal, characteristic, complemented
6#13067480C211yesmaximal, characteristic, complemented
7#13067480C211yesmaximal, characteristic, complemented
8#13067446C211yesmaximal, characteristic, complemented
9#13067444C211yesmaximal, characteristic, complemented
10#13067437C211yesmaximal, characteristic, complemented
11#13067395C211yesmaximal, characteristic, complemented
12#13067083C211yesmaximal, characteristic, complemented
13#13067005C211yesmaximal, characteristic, complemented
14#13066915C211yesmaximal, characteristic, complemented
15C8×C11×D8C211yesmaximal, characteristic, complemented
16#10623079C2211yescharacteristic
17C4×D4×D11C2211yescharacteristic
18C4×C11×D8C2211yescharacteristic
19C8×D4×C11C2211yescharacteristic
20C8×D4×C11C2211yescharacteristic, complemented
21#10622769C411yescharacteristic
22#10622763C411yescharacteristic
23#10622724—21no—
24#10622723—21no—
25C8×C22⋊D11—21no—
26C2×(C2×D11)⋊C8—21no—
27C4×#4323C2211yescharacteristic
28C4×#4323C2211yescharacteristic
29#10622625C2211yescharacteristic, complemented
30D4×C11⋊C8C2211yescharacteristic
31#10622503C411yescharacteristic
32#10622495C411yescharacteristic
33#10622451C2211yescharacteristic
34#10622448C2211yescharacteristic
35#10622447C2211yescharacteristic, complemented
36#10622446C2211yescharacteristic
37#10622399C411yescharacteristic
38#10622387C411yescharacteristic
39#10622386C411yescharacteristic
40#10622372C411yescharacteristic
41#10622343—21no—
42#10622342—21no—
43#10622340—21no—
44#10622339—21no—
45C4×D88C2211yescharacteristic
46#10622301C2211yescharacteristic
47#10622301C2211yescharacteristic, complemented
48#10622298C2211yescharacteristic
49#10622298C2211yescharacteristic
50#10622298C2211yescharacteristic
51C11×#335C2211yescharacteristic, complemented
52C11×D4⋊C8C2211yescharacteristic
53C11×D4⋊C8C2211yescharacteristic, complemented
54C82×C11C2211yescharacteristic, 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
66#10622092C2211yescharacteristic, complemented
67C2×D4×D11C2×C411yescharacteristic
68C2×#4339—21no—
69C22×C4×D11—21no—
70C2×C11×D8C2×C411yescharacteristic
71C22×C8×C11—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—
82C2×#4318—21no—
83C22×C11⋊C8—21no—
84C2×D88C2×C411yescharacteristic
85C2×#4313—21no—
86C2×#4313—21no—
87C2×#4313—21no—
88C2×C8×D11—21no—
89#66948C2×C411yescharacteristic
90#66946C2×C411yescharacteristic
91C4⋊C4×D11C2×C411yescharacteristic
92#66941C2×C411yescharacteristic
93#66938—21no—
94#66937—21no—
95(C22⋊D11)⋊C4—21no—
96C22⋊C4×D11—21no—
97C4×D44C2311yescharacteristic
98C4×D44C2311yescharacteristic
99C42×D11C2311yescharacteristic
100C11×#107C2×C411yescharacteristic
101C11×C4⋊C8C2311yescharacteristic
102C11×C4⋊C8C2311yescharacteristic
103C11×#102C2×C411yescharacteristic
104C11×#102C2×C411yescharacteristic
105C11×C22⋊C8—21no—
106C11×C22⋊C8—21no—
107C4×C8×C11C2311yescharacteristic
108C4×C8×C11C2311yescharacteristic
109C4×C8×C11C2311yescharacteristic
110#66896C2×C411yescharacteristic
111#66896C2×C411yescharacteristic
112C22⋊(C11⋊C8)—21no—
113C22⋊(C11⋊C8)—21no—
114#66885C2×C411yescharacteristic
115#66885C2×C411yescharacteristic
116(C2×D11)⋊C8—21no—
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—
129Dic11⋊C8—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#18026—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—41no—
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—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—81no—
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—41no—
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
202#4318—81no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—81no—
207C2×C11⋊C8C22×C411yescharacteristic
208C2×C11⋊C8C22×C411yescharacteristic
209C2×C11⋊C8C2×D411yescharacteristic
210C2×C11⋊C8C2×D411yescharacteristic
211D88—41no—
212#4313—81no—
213#4313—81no—
214#4313—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×D8D1111yescharacteristic, complemented
227#1572—111no—
228#1496—111no—
229#1478—111no—
230#1454—111no—
231C23×C11—21no—
232C23×C11—21no—
233C22×D11—21no—
234C22×D11—21no—
235C22×D11—42no—
236C22×D11—42no—
237C22×D11—81no—
238C22×D11C4×D411yescharacteristic
239D4×C11—21no—
240D4×C11—21no—
241D4×C11—21no—
242D4×C11#13112yes—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11C23×C411yescharacteristic
250C2×C4×C11C22×D411yescharacteristic
251C2×C4×C11C2×#4111yescharacteristic
252C22⋊D11—42no—
253C22⋊D11—42no—
254C22⋊D11—81no—
255C22⋊D11—81no—
256C2×Dic11—21no—
257C2×Dic11—21no—
258C2×Dic11—81no—
259C2×Dic11C4×D411yescharacteristic
260C2×Dic11C4×D411yescharacteristic
261C2×Dic11C4×D411yescharacteristic
262D44—21no—
263D44—21no—
264D44—21no—
265D44—21no—
266D44—81no—
267C4×D11—21no—
268C4×D11—21no—
269C4×D11—21no—
270C4×D11—21no—
271C4×D11—41no—
272C4×D11—41no—
273C4×D11—41no—
274C4×D11—41no—
275C4×D11—41no—
276C4×D11—81no—
277C4×D11—81no—
278Dic22—81no—
279C8×C11—21no—
280C8×C11—21no—
281C8×C11—21no—
282C8×C11—21no—
283C8×C11—41no—
284C8×C11—41no—
285C8×C11—41no—
286C11⋊C8—21no—
287C11⋊C8—21no—
288C11⋊C8—21no—
289C11⋊C8—21no—
290C11⋊C8—41no—
291C11⋊C8—41no—
292C11⋊C8—41no—
293#532—111no—
294C2×C4×D4—111no—
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×D8C2×D1111yescharacteristic
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—221no—
317C8×D4C2×D1111yescharacteristic
318C8×D4C2×D1111yescharacteristic, complemented
319#432—111no—
320#431—111no—
321#431—111no—
322#431—111no—
323#431—111no—
324#408—221no—
325#408—221no—
326#407—221no—
327C2×C22⋊C8—221no—
328#335—111no—
329#335C2×D1111yescharacteristic, complemented
330#334—111no—
331#334—111no—
332D4⋊C8—111no—
333D4⋊C8—111no—
334D4⋊C8—111no—
335D4⋊C8—111no—
336D4⋊C8—111no—
337D4⋊C8—111no—
338D4⋊C8C2×D1111yescharacteristic
339D4⋊C8C2×D1111yescharacteristic, complemented
340#322—111no—
341#322—111no—
342#322—111no—
343C82C2×D1111yescharacteristic, complemented
344C22×C11—22no—
345C22×C11—41no—
346C22×C11—41no—
347C22×C11—41no—
348C22×C11—41no—
349C22×C11—41no—
350C22×C11C2×C4×D411yescharacteristic
351C2×D11—21no—
352C2×D11—21no—
353C2×D11—21no—
354C2×D11—41no—
355C2×D11—41no—
356C2×D11—41no—
357C2×D11—41no—
358C2×D11—41no—
359C2×D11—41no—
360C2×D11—84no—
361C4×C11—21no—
362C4×C11—41no—
363C4×C11—41no—
364C4×C11C2×#13111yescharacteristic
365C4×C11#56811yescharacteristic
366C4×C11#57611yescharacteristic
367C4×C11#57611yescharacteristic
368Dic11—21no—
369Dic11—21no—
370Dic11—21no—
371Dic11—41no—
372Dic11—41no—
373C2×#41—221no—
374C22×D4—111no—
375C23×C4—221no—
376C2×D8—111no—
377C2×D8—111no—
378C2×D8—111no—
379C2×D8C4×D1111yescharacteristic
380C2×M16—221no—
381C2×M16—221no—
382C2×M16—221no—
383C2×M16—221no—
384C22×C8—21no—
385C22×C8—21no—
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—111no—
395C4×D4—111no—
396C4×D4—111no—
397C4×D4—111no—
398C4×D4—221no—
399C4×D4—221no—
400C4×D4—221no—
401C4×D4C22×D1111yescharacteristic
402C4×D4C22×D1111yescharacteristic
403C2×C4⋊C4—111no—
404C2×C22⋊C4—221no—
405C2×C42—111no—
406#107—111no—
407#107—111no—
408#107—111no—
409#107C4×D1111yescharacteristic
410C4⋊C8—111no—
411C4⋊C8—111no—
412C4⋊C8—111no—
413C4⋊C8—111no—
414C4⋊C8—111no—
415C4⋊C8—111no—
416C4⋊C8—221no—
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#102C4×D1111yescharacteristic
426#102C4×D1111yescharacteristic
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—111no—
444C4×C8—111no—
445C4×C8—111no—
446C4×C8—221no—
447C4×C8C22×D1111yescharacteristic
448C4×C8C22×D1111yescharacteristic
449C4×C8C22×D1111yescharacteristic
450C2×C11—42no—
451C2×C11—81no—
452C2×C11#293311yescharacteristic
453C2×C11#294811yescharacteristic
454C2×C11#295511yescharacteristic
455D11—41no—
456D11—81no—
457D11—81no—
458C24—221no—
459#41—881no—
460#41—881no—
461C2×Q8—221no—
462C2×D4—111no—
463C2×D4—111no—
464C2×D4—221no—
465C2×D4—221no—
466C2×D4—221no—
467C2×D4—221no—
468C2×D4—222no—
469C2×D4—221no—
470C2×D4—441no—
471C2×D4C2×C4×D1111yescharacteristic
472C2×D4C2×C4×D1111yescharacteristic
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—111no—
476C22×C4—111no—
477C22×C4—111no—
478C22×C4—221no—
479C22×C4—221no—
480C22×C4—221no—
481C22×C4—221no—
482C22×C4—221no—
483C22×C4—881no—
484C22×C4—881no—
485D8—22no—
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—81no—
497C2×C8—81no—
498C2×C8—111no—
499C2×C8—111no—
500C2×C8—111no—
501C2×C8—111no—
502C2×C8—221no—
503C2×C8—221no—
504C2×C8—221no—
505C2×C8—881no—
506C2×C8—881no—
507C2×C8C2×C4×D1111yescharacteristic
508C2×C8C2×C4×D1111yescharacteristic
509C2×C8D4×D1111yescharacteristic
510C2×C8D4×D1111yescharacteristic
511C4⋊C4—111no—
512C4⋊C4—111no—
513C4⋊C4—221no—
514C4⋊C4—221no—
515C4⋊C4C2×C4×D1111yescharacteristic
516C4⋊C4C2×C4×D1111yescharacteristic
517C22⋊C4—21no—
518C22⋊C4—21no—
519C22⋊C4—221no—
520C22⋊C4—221no—
521C22⋊C4—221no—
522C22⋊C4—221no—
523C22⋊C4—221no—
524C22⋊C4—221no—
525C42—111no—
526C42—111no—
527C42—111no—
528C42C23×D1111yescharacteristic
529C11#1802611yescharacteristic, complemented, Sylow
530C23—21no—
531C23—21no—
532C23—111no—
533C23—221no—
534C23—221no—
535C23—442no—
536C23—442no—
537C23—881no—
538Q8—881no—
539D4—21no—
540D4—21no—
541D4—21no—
542D4—221no—
543D4—221no—
544D4—221no—
545D4—221no—
546D4—442no—
547D4—442no—
548D4—881no—
549D4—881no—
550D4—881no—
551D4#6695412yes—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—111no—
559C2×C4—111no—
560C2×C4—111no—
561C2×C4—221no—
562C2×C4—221no—
563C2×C4—221no—
564C2×C4—221no—
565C2×C4—221no—
566C2×C4—221no—
567C2×C4—441no—
568C2×C4—441no—
569C2×C4—441no—
570C2×C4—441no—
571C2×C4—441no—
572C2×C4—881no—
573C2×C4—881no—
574C2×C4—881no—
575C2×C4C22×C4×D1111yescharacteristic
576C2×C4C2×D4×D1111yescharacteristic
577C2×C4#41×D1111yescharacteristic
578C8—21no—
579C8—21no—
580C8—21no—
581C8—21no—
582C8—41no—
583C8—41no—
584C8—41no—
585C8—221no—
586C8—221no—
587C8—221no—
588C8—221no—
589C8—441no—
590C8—441no—
591C8—441no—
592C22—22no—
593C22—41no—
594C22—41no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—221no—
599C22—221no—
600C22—221no—
601C22—441no—
602C22—441no—
603C22—441no—
604C22—441no—
605C22—441no—
606C22—441no—
607C22—884no—
608C22C4×D4×D1111yescharacteristic
609C4—21no—
610C4—41no—
611C4—41no—
612C4—221no—
613C4—221no—
614C4—221no—
615C4—441no—
616C4—441no—
617C4C2×#6695411yescharacteristic
618C4#1062328111yescharacteristic
619C4#1062328811yescharacteristic
620C4#1062330011yescharacteristic
621C2—42no—
622C2—81no—
623C2—441no—
624C2—881no—
625C2—881no—
626C2#1307733611yescharacteristic
627C2#1307746311yescharacteristic
628C2#1307751411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC8×C11×D8C2
socleC22×C11C2×C4×D4
prime radical#13078614C2
cosocleC42×C11C24
hypercenterC8×D8D11
hypocenterC11#18026
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ C8×D8

Complements

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

NH ≅ G/Ntype
2. #13077679C2semidirect
3. #13077649C2semidirect
4. #13067527C2semidirect
5. #13067502C2semidirect
6. #13067480C2semidirect
7. #13067480C2semidirect
8. #13067446C2semidirect
9. #13067444C2semidirect
10. #13067437C2semidirect
11. #13067395C2semidirect
12. #13067083C2semidirect
13. #13067005C2semidirect
14. #13066915C2semidirect
15. C8×C11×D8C2semidirect
20. C8×D4×C11C22semidirect
29. #10622625C22semidirect
35. #10622447C22semidirect
47. #10622301C22semidirect
51. C11×#335C22semidirect
53. C11×D4⋊C8C22semidirect
54. C82×C11C22semidirect
56. D4⋊(C11⋊C8)C22semidirect
58. #10622121C22semidirect
59. #10622118C22semidirect
60. #10622118C22semidirect
62. #10622097C22semidirect
63. #10622096C22semidirect
64. #10622092C22semidirect
65. #10622092C22semidirect
66. #10622092C22semidirect
226. C8×D8D11semidirect
318. C8×D4C2×D11semidirect
329. #335C2×D11semidirect
339. D4⋊C8C2×D11semidirect
343. C82C2×D11semidirect
529. C11#18026semidirect

Maximal subgroups

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

subgroupindex
#130786142
#130776792
#130776492
#130675272
#130675022
#130674802
#130674462
#130674442
#130674372
#130673952
#130670832
#130670052
#130669152
C8×C11×D82
#1802611