Finite Group Databasebeta

← #14725594

Subgroups — #14725594

Order 2816.

714 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#13067528C211yesmaximal, characteristic, complemented
5#13067527C211yesmaximal, characteristic, complemented
6#13067482C211yesmaximal, characteristic, complemented
7#13067481C211yesmaximal, characteristic, complemented
8#13067479C211yesmaximal, characteristic, complemented
9#13067438C211yesmaximal, characteristic, complemented
10#13067437C211yesmaximal, characteristic, complemented
11D11×#334C211yesmaximal, characteristic, complemented
12#13067013C211yesmaximal, characteristic, complemented
13#13067013C211yesmaximal, characteristic, complemented
14#13066904C211yesmaximal, characteristic, complemented
15C11×#1586C211yesmaximal, 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×#334C2211yescharacteristic
52C11×D4⋊C8C2211yescharacteristic
53C11×D4⋊C8C2211yescharacteristic
54C11×#322C2211yescharacteristic
55D4⋊(C11⋊C8)C2211yescharacteristic
56D4⋊(C11⋊C8)C2211yescharacteristic
57#10622121C2211yescharacteristic
58#10622121C2211yescharacteristic
59#10622118C2211yescharacteristic
60#10622118C2211yescharacteristic
61#10622097C2211yescharacteristic
62#10622097C2211yescharacteristic
63#10622095C2211yescharacteristic
64#10622092C2211yescharacteristic
65#10622092C2211yescharacteristic
66#10622092C2211yescharacteristic
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#18073—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—22no—
214#4313—42no—
215#4313—42no—
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#1594—111no—
226#1594—111no—
227#1586—111no—
228#1586—111no—
229#1586—111no—
230#1586D1111yescharacteristic, complemented
231#1580—111no—
232#1580—111no—
233C2×#334—111no—
234#1480—111no—
235#1480—111no—
236#1451—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×D11AGL(1,ℤ/8)12yes—
280C4×D11AGL(1,ℤ/8)12yes—
281Dic22—42no—
282Dic22—42no—
283C8×C11—21no—
284C8×C11—21no—
285C8×C11—21no—
286C8×C11—21no—
287C8×C11—41no—
288C8×C11—41no—
289C8×C11—41no—
290C11⋊C8—21no—
291C11⋊C8—21no—
292C11⋊C8—21no—
293C11⋊C8—41no—
294C11⋊C8—41no—
295C11⋊C8—41no—
296C11⋊C8#13112yescomplemented
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#334—111no—
333#334—111no—
334#334—111no—
335#334C2×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#322—111no—
346#322—111no—
347#322C2×D1111yescharacteristic
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×D11#44212yes—
364C4×C11—21no—
365C4×C11—41no—
366C4×C11—41no—
367C4×C11C2×#13111yescharacteristic
368C4×C11#56811yescharacteristic
369C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
370C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
371Dic11—21no—
372Dic11—21no—
373Dic11—41no—
374Dic11—41no—
375Dic11#44212yes—
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×#44211yescharacteristic
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—222no—
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#1807311yescharacteristic, 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—21no—
589C8—41no—
590C8—41no—
591C8—41no—
592C8—112no—
593C8—221no—
594C8—221no—
595C8—221no—
596C8—441no—
597C8—441no—
598C8—441no—
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
625C4D11×AGL(1,ℤ/8)11yescharacteristic
626C4D11×AGL(1,ℤ/8)11yescharacteristic
627C2—81no—
628C2—81no—
629C2—222no—
630C2—881no—
631C2—881no—
632C2#1307735711yescharacteristic
633C2D11×#44211yescharacteristic
634C2#1307752811yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1586C2
socleC22×C11C2×C4×D4
prime radical#13079192C2
cosocleC42×C11C24
hypercenter#1586D11
hypocenterC11#18073
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1586

Complements

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

NH ≅ G/Ntype
2. #13077361C2semidirect
3. #13077355C2semidirect
4. #13067528C2semidirect
5. #13067527C2semidirect
6. #13067482C2semidirect
7. #13067481C2semidirect
8. #13067479C2semidirect
9. #13067438C2semidirect
10. #13067437C2semidirect
11. D11×#334C2semidirect
12. #13067013C2semidirect
13. #13067013C2semidirect
14. #13066904C2semidirect
15. C11×#1586C2semidirect
230. #1586D11semidirect
296. C11⋊C8#131semidirect
538. C11#18073semidirect

Maximal subgroups

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

subgroupindex
#130791922
#130773612
#130773552
#130675282
#130675272
#130674822
#130674812
#130674792
#130674382
#130674372
D11×#3342
#130670132
#130669042
C11×#15862
#1807311