Finite Group Databasebeta

← #14725528

Subgroups — #14725528

Order 2816.

722 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079192C211yesmaximal, characteristic
2#13077361C211yesmaximal, characteristic, complemented
3#13077355C211yesmaximal, characteristic, complemented
4#13067499C211yesmaximal, characteristic, complemented
5#13067498C211yesmaximal, characteristic, complemented
6#13067447C211yesmaximal, characteristic, complemented
7#13067446C211yesmaximal, characteristic, complemented
8#13067444C211yesmaximal, characteristic, complemented
9C8×#4323C211yesmaximal, characteristic, complemented
10#13067408C211yesmaximal, characteristic, complemented
11D11×#335C211yesmaximal, characteristic, complemented
12#13067013C211yesmaximal, characteristic, complemented
13#13067013C211yesmaximal, characteristic, complemented
14#13066895C211yesmaximal, characteristic, complemented
15C11×#1581C211yesmaximal, characteristic, complemented
16C2×#66960—21no—
17C2×#66954—21no—
18#10623079C2211yescharacteristic
19#10623079C2211yescharacteristic
20C4×C11×D8C2211yescharacteristic
21C11×#436C2211yescharacteristic
22C8×D4×C11C2211yescharacteristic
23#10622770C411yescharacteristic
24#10622764C411yescharacteristic
25#10622740—21no—
26#10622724—21no—
27C4×#4323C2211yescharacteristic
28C4×#4323C2211yescharacteristic
29#10622625C2211yescharacteristic
30D4×C11⋊C8C2211yescharacteristic
31#10622496C411yescharacteristic
32#10622487C411yescharacteristic
33#10622451C2211yescharacteristic
34#10622447C2211yescharacteristic
35D11×C4⋊C8C2211yescharacteristic
36D11×C4⋊C8C2211yescharacteristic
37#10622388C411yescharacteristic
38#10622388C411yescharacteristic
39#10622373C411yescharacteristic
40#10622373C411yescharacteristic
41#10622343—21no—
42#10622341—21no—
43#10622340—21no—
44#10622340—21no—
45C4×D88C2211yescharacteristic
46#10622301C2211yescharacteristic
47C4×#4313C2211yescharacteristic
48C8×D44C2211yescharacteristic
49#10622298C2211yescharacteristic
50C4×C8×D11C2211yescharacteristic
51C11×#335C2211yescharacteristic
52C11×D4⋊C8C2211yescharacteristic
53C11×D4⋊C8C2211yescharacteristic
54C11×#322C2211yescharacteristic
55D4⋊(C11⋊C8)C2211yescharacteristic
56D4⋊(C11⋊C8)C2211yescharacteristic
57#10622121C2211yescharacteristic
58#10622121C2211yescharacteristic
59#10622117C2211yescharacteristic
60#10622117C2211yescharacteristic
61#10622097C2211yescharacteristic
62#10622097C2211yescharacteristic
63#10622096C2211yescharacteristic
64#10622092C2211yescharacteristic
65C8×C11⋊C8C2211yescharacteristic
66C8×C11⋊C8C2211yescharacteristic
67C2×#4339—21no—
68C2×#4339—21no—
69C2×C11×D8C2×C411yescharacteristic
70C2×C11×M16—21no—
71C22×C8×C11—21no—
72C4×D4×C11C2311yescharacteristic
73C4×D4×C11C2311yescharacteristic
74#66993C2×C411yescharacteristic
75#66993C2×C411yescharacteristic
76#66991C2×C411yescharacteristic
77#66991C2×C411yescharacteristic
78C2×#4323C2×C411yescharacteristic
79C2×#4323C2×C411yescharacteristic
80C4×C22⋊D11—21no—
81C4×C22⋊D11—21no—
82C2×#4318—21no—
83C22×C11⋊C8—21no—
84#66960—44no—
85C2×D88C2×C411yescharacteristic
86#66954—44no—
87C2×#4313—21no—
88C2×#4313—21no—
89C2×#4313D411yescharacteristic
90C2×#4313D411yescharacteristic
91C2×C8×D11—21no—
92C2×C8×D11—21no—
93C2×C8×D11—21no—
94C2×C8×D11—21no—
95C2×C8×D11C2×C411yescharacteristic
96C2×C8×D11C2×C411yescharacteristic
97#66948C2×C411yescharacteristic
98#66948C2×C411yescharacteristic
99#66941C2×C411yescharacteristic
100#66941C2×C411yescharacteristic
101#66938—21no—
102#66938—21no—
103#66937—21no—
104#66937—21no—
105C4×D44C2311yescharacteristic
106C4×D44C2311yescharacteristic
107C42×D11C2311yescharacteristic
108C11×#107C2×C411yescharacteristic
109C11×C4⋊C8C2311yescharacteristic
110C11×C4⋊C8C2311yescharacteristic
111C11×#102C2×C411yescharacteristic
112C11×#102C2×C411yescharacteristic
113C11×C22⋊C8—21no—
114C11×C22⋊C8—21no—
115C4×C8×C11C2311yescharacteristic
116C4×C8×C11C2311yescharacteristic
117C4×C8×C11C2311yescharacteristic
118#66896C2×C411yescharacteristic
119#66896C2×C411yescharacteristic
120C22⋊(C11⋊C8)—21no—
121C22⋊(C11⋊C8)—21no—
122#66885C2×C411yescharacteristic
123#66885C2×C411yescharacteristic
124(C2×D11)⋊C8—21no—
125(C2×D11)⋊C8—21no—
126(C2×D11)⋊C8—21no—
127(C2×D11)⋊C8—21no—
128(C2×D11)⋊C8—21no—
129#66882C2×C411yescharacteristic
130#66879D411yescharacteristic
131#66879D411yescharacteristic
132Dic11⋊C8—21no—
133Dic11⋊C8—21no—
134Dic11⋊C8—21no—
135C8×Dic11C2×C411yescharacteristic
136C8×Dic11C2×C411yescharacteristic
137#66873C2×C411yescharacteristic
138#66873C2×C411yescharacteristic
139#66871C2×C411yescharacteristic
140#66871C2×C411yescharacteristic
141C4⋊(C11⋊C8)C2311yescharacteristic
142C4⋊(C11⋊C8)C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144C4×C11⋊C8C2311yescharacteristic
145C4×C11⋊C8C2311yescharacteristic
146#18066—111nomaximal, Sylow
147C2×D4×C11C22×C411yescharacteristic
148C2×D4×C11C22×C411yescharacteristic
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C2×C22⋊D11—21no—
152C2×C22⋊D11—21no—
153C2×C22⋊D11—21no—
154C2×C22⋊D11—21no—
155C2×C22⋊D11—21no—
156C2×C22⋊D11—21no—
157#4339—42no—
158#4339—42no—
159#4339—42no—
160#4339—42no—
161C2×D44—21no—
162C2×D44—21no—
163C2×D44C22×C411yescharacteristic
164C2×D44C22×C411yescharacteristic
165C2×C4×D11—21no—
166C2×C4×D11—21no—
167C2×C4×D11C22×C411yescharacteristic
168C2×C4×D11C2×D411yescharacteristic
169C2×C4×D11#4111yescharacteristic
170C2×Dic22—21no—
171C2×Dic22—21no—
172C11×D8—41no—
173C11×M16—42no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—42no—
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
202#4318—42no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—42no—
207C2×C11⋊C8C22×C411yescharacteristic
208C2×C11⋊C8C22×C411yescharacteristic
209C2×C11⋊C8C2×D411yescharacteristic
210C2×C11⋊C8C2×D411yescharacteristic
211D88—41no—
212#4313—22no—
213#4313—42no—
214#4313—42no—
215#4313D814yescomplemented
216C8×D11—22no—
217C8×D11—41no—
218C8×D11—42no—
219C8×D11—42no—
220C8×D11—42no—
221C8×D11—42no—
222#3169—111no—
223#2935—111no—
224#2935—111no—
225#1589—111no—
226#1589—111no—
227#1581—111no—
228#1581—111no—
229#1581—111no—
230#1581D1111yescharacteristic, complemented
231C8×D8—111no—
232C8×D8—111no—
233C2×#335—111no—
234#1480—111no—
235#1480—111no—
236C8×M16—111no—
237C23×C11—21no—
238C23×C11—21no—
239C22×D11—21no—
240C22×D11—21no—
241C22×D11C4×D411yescharacteristic
242D4×C11—21no—
243D4×C11—21no—
244D4×C11—21no—
245D4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11C23×C411yescharacteristic
253C2×C4×C11C22×D411yescharacteristic
254C2×C4×C11C2×#4111yescharacteristic
255C22⋊D11—42no—
256C22⋊D11—42no—
257C22⋊D11—42no—
258C22⋊D11—42no—
259C22⋊D11—81no—
260C22⋊D11—81no—
261C2×Dic11—21no—
262C2×Dic11—21no—
263C2×Dic11C4×D411yescharacteristic
264C2×Dic11C4×D411yescharacteristic
265C2×Dic11C4×D411yescharacteristic
266D44—21no—
267D44—21no—
268D44—21no—
269D44—21no—
270D44—42no—
271D44—42no—
272C4×D11—21no—
273C4×D11—21no—
274C4×D11—41no—
275C4×D11—41no—
276C4×D11—41no—
277C4×D11—41no—
278C4×D11—41no—
279C4×D11C2×D812yes—
280C4×D11#13512yes—
281Dic22—42no—
282Dic22—42no—
283C8×C11—21no—
284C8×C11—21no—
285C8×C11—21no—
286C8×C11—41no—
287C8×C11—41no—
288C8×C11—41no—
289C8×C11C2×D812yes—
290C11⋊C8—21no—
291C11⋊C8—21no—
292C11⋊C8—41no—
293C11⋊C8—41no—
294C11⋊C8—41no—
295C11⋊C8#13112yescomplemented
296C11⋊C8C2×D812yes—
297C2×#131—221no—
298C2×#131—221no—
299#532—111no—
300#532—111no—
301#500—111no—
302#493—111no—
303#486—111no—
304#486—111no—
305#466—111no—
306#466—111no—
307#466—111no—
308#466—111no—
309C4×D8—111no—
310C4×D8—111no—
311C4×D8—111no—
312C4×D8C2×D1111yescharacteristic
313#436—111no—
314#436—111no—
315#436—111no—
316#436C2×D1111yescharacteristic
317#435—221no—
318#435—221no—
319#435—221no—
320#435—221no—
321C8×D4—111no—
322C8×D4—111no—
323C8×D4—111no—
324C8×D4C2×D1111yescharacteristic
325#431—111no—
326C2×C4⋊C8—111no—
327C2×C4⋊C8—111no—
328#408—221no—
329#408—221no—
330C4×M16—111no—
331C2×C4×C8—111no—
332#335—111no—
333#335—111no—
334#335—111no—
335#335C2×D1111yescharacteristic
336D4⋊C8—111no—
337D4⋊C8—111no—
338D4⋊C8—111no—
339D4⋊C8—111no—
340D4⋊C8—111no—
341D4⋊C8—111no—
342D4⋊C8C2×D1111yescharacteristic
343D4⋊C8C2×D1111yescharacteristic
344#322—111no—
345#322C2×D1111yescharacteristic
346C82—111no—
347C82—111no—
348C22×C11—41no—
349C22×C11—41no—
350C22×C11—41no—
351C22×C11—41no—
352C22×C11—41no—
353C22×C11—41no—
354C22×C11C2×C4×D411yescharacteristic
355C2×D11—21no—
356C2×D11—21no—
357C2×D11—41no—
358C2×D11—41no—
359C2×D11—41no—
360C2×D11—41no—
361C2×D11—41no—
362C2×D11—41no—
363C2×D11C4×D812yes—
364C4×C11—21no—
365C4×C11—41no—
366C4×C11—41no—
367C4×C11C2×#13111yescharacteristic
368C4×C11#56811yescharacteristic
369C4×C11C22×D811yescharacteristic
370C4×C11C2×#13511yescharacteristic
371Dic11—21no—
372Dic11—21no—
373Dic11—41no—
374Dic11—41no—
375Dic11C4×D812yes—
376C2×#41—221no—
377C2×#41—221no—
378C2×D8—111no—
379C2×D8—111no—
380C2×D8—111no—
381C2×D8C4×D1111yescharacteristic
382#131—444no—
383#131—444no—
384C2×M16—21no—
385C2×M16—111no—
386C2×M16—111no—
387C2×M16—221no—
388C2×M16—221no—
389C2×M16—221no—
390C22×C8—21no—
391C22×C8—111no—
392C22×C8—111no—
393C22×C8—221no—
394C22×C8—221no—
395C22×C8—221no—
396C22×C8—221no—
397C22×C8—221no—
398C4⋊Q8—111no—
399C4⋊Q8—111no—
400#127—111no—
401#127—111no—
402#124—221no—
403#124—221no—
404#121—111no—
405#121—111no—
406#121—111no—
407#121—111no—
408#121—221no—
409#121—221no—
410C4×D4—111no—
411C4×D4—111no—
412C4×D4—221no—
413C4×D4—221no—
414C4×D4C22×D1111yescharacteristic
415C4×D4C22×D1111yescharacteristic
416C2×C42—111no—
417#107—111no—
418#107—111no—
419#107—111no—
420#107C4×D1111yescharacteristic
421C4⋊C8—111no—
422C4⋊C8—111no—
423C4⋊C8—221no—
424C4⋊C8—221no—
425C4⋊C8—221no—
426C4⋊C8C22×D1111yescharacteristic
427C4⋊C8C22×D1111yescharacteristic
428#102—111no—
429#102—111no—
430#102—111no—
431#102—111no—
432#102—111no—
433#102—111no—
434#102C4×D1111yescharacteristic
435#102C4×D1111yescharacteristic
436C22⋊C8—21no—
437C22⋊C8—21no—
438C22⋊C8—221no—
439C22⋊C8—221no—
440C22⋊C8—221no—
441C22⋊C8—221no—
442C22⋊C8—221no—
443C22⋊C8—221no—
444C22⋊C8—221no—
445#97—111no—
446#97—111no—
447C4×C8—111no—
448C4×C8—111no—
449C4×C8—111no—
450C4×C8—111no—
451C4×C8—111no—
452C4×C8C22×D1111yescharacteristic
453C4×C8C22×D1111yescharacteristic
454C4×C8C22×D1111yescharacteristic
455C2×C11—81no—
456C2×C11—81no—
457C2×C11#293511yescharacteristic
458C2×C11C2×C4×D811yescharacteristic
459C2×C11#295711yescharacteristic
460D11—22no—
461D11—81no—
462D11—81no—
463#41—442no—
464#41—442no—
465#41—442no—
466#41—442no—
467C2×Q8—221no—
468C2×Q8—221no—
469C2×D4—111no—
470C2×D4—111no—
471C2×D4—221no—
472C2×D4—221no—
473C2×D4—221no—
474C2×D4—221no—
475C2×D4—221no—
476C2×D4—221no—
477C2×D4—221no—
478C2×D4—221no—
479C2×D4C2×C4×D1111yescharacteristic
480C2×D4C2×C4×D1111yescharacteristic
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—111no—
484C22×C4—111no—
485C22×C4—111no—
486C22×C4—221no—
487C22×C4—221no—
488D8—41no—
489D8—222no—
490D8—222no—
491D8—441no—
492M16—42no—
493M16—114no—
494M16—222no—
495M16—442no—
496M16—442no—
497M16—442no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—42no—
502C2×C8—111no—
503C2×C8—111no—
504C2×C8—111no—
505C2×C8—111no—
506C2×C8—222no—
507C2×C8—221no—
508C2×C8—221no—
509C2×C8—221no—
510C2×C8—441no—
511C2×C8—442no—
512C2×C8—442no—
513C2×C8—442no—
514C2×C8—442no—
515C2×C8—442no—
516C2×C8C2×C4×D1111yescharacteristic
517C2×C8C2×C4×D1111yescharacteristic
518C2×C8D4×D1111yescharacteristic
519C2×C8D4×D1111yescharacteristic
520C4⋊C4—111no—
521C4⋊C4—111no—
522C4⋊C4—221no—
523C4⋊C4—221no—
524C4⋊C4C2×C4×D1111yescharacteristic
525C4⋊C4C2×C4×D1111yescharacteristic
526C22⋊C4—21no—
527C22⋊C4—21no—
528C22⋊C4—221no—
529C22⋊C4—221no—
530C22⋊C4—221no—
531C22⋊C4—221no—
532C22⋊C4—221no—
533C22⋊C4—221no—
534C42—111no—
535C42—111no—
536C42—111no—
537C42C23×D1111yescharacteristic
538C11#1806611yescharacteristic, complemented, Sylow
539C23—21no—
540C23—21no—
541C23—111no—
542C23—221no—
543C23—221no—
544Q8—442no—
545Q8—442no—
546D4—21no—
547D4—21no—
548D4—21no—
549D4—21no—
550D4—221no—
551D4—221no—
552D4—221no—
553D4—221no—
554D4—442no—
555D4—442no—
556D4—442no—
557D4—442no—
558D4—442no—
559D4—442no—
560D4—881no—
561D4—881no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—111no—
569C2×C4—112no—
570C2×C4—112no—
571C2×C4—111no—
572C2×C4—111no—
573C2×C4—221no—
574C2×C4—221no—
575C2×C4—221no—
576C2×C4—221no—
577C2×C4—441no—
578C2×C4—441no—
579C2×C4—441no—
580C2×C4—441no—
581C2×C4—441no—
582C2×C4C22×C4×D1111yescharacteristic
583C2×C4C2×D4×D1111yescharacteristic
584C2×C4#41×D1111yescharacteristic
585C8—21no—
586C8—21no—
587C8—21no—
588C8—41no—
589C8—41no—
590C8—41no—
591C8—112no—
592C8—112no—
593C8—221no—
594C8—221no—
595C8—441no—
596C8—441no—
597C8—441no—
598C8D8×D1112yes—
599C22—41no—
600C22—41no—
601C22—41no—
602C22—41no—
603C22—41no—
604C22—41no—
605C22—112no—
606C22—221no—
607C22—221no—
608C22—441no—
609C22—441no—
610C22—441no—
611C22—441no—
612C22—441no—
613C22—441no—
614C22C4×D4×D1111yescharacteristic
615C4—21no—
616C4—41no—
617C4—41no—
618C4—112no—
619C4—221no—
620C4—221no—
621C4—441no—
622C4—441no—
623C4#1062327611yescharacteristic
624C4D11×#13111yescharacteristic
625C4C2×D8×D1111yescharacteristic
626C4D11×#13511yescharacteristic
627C2—81no—
628C2—81no—
629C2—222no—
630C2—881no—
631C2—881no—
632C2#1307735711yescharacteristic
633C2C4×D8×D1111yescharacteristic
634C2#1307753011yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1581C2
socleC22×C11C2×C4×D4
prime radical#13079192C2
cosocleC42×C11C24
hypercenter#1581D11
hypocenterC11#18066
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. #13077361C2semidirect
3. #13077355C2semidirect
4. #13067499C2semidirect
5. #13067498C2semidirect
6. #13067447C2semidirect
7. #13067446C2semidirect
8. #13067444C2semidirect
9. C8×#4323C2semidirect
10. #13067408C2semidirect
11. D11×#335C2semidirect
12. #13067013C2semidirect
13. #13067013C2semidirect
14. #13066895C2semidirect
15. C11×#1581C2semidirect
215. #4313D8semidirect
230. #1581D11semidirect
295. C11⋊C8#131semidirect
538. C11#18066semidirect

Maximal subgroups

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

subgroupindex
#130791922
#130773612
#130773552
#130674992
#130674982
#130674472
#130674462
#130674442
C8×#43232
#130674082
D11×#3352
#130670132
#130668952
C11×#15812
#1806611