Finite Group Databasebeta

← #14725075

Subgroups — #14725075

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#13078617C211yesmaximal, characteristic
2#13077682C211yesmaximal, characteristic, complemented
3#13077653C211yesmaximal, characteristic, complemented
4#13067529C211yesmaximal, characteristic, complemented
5#13067500C211yesmaximal, characteristic, complemented
6#13067479C211yesmaximal, characteristic, complemented
7#13067479C211yesmaximal, characteristic, complemented
8#13067444C211yesmaximal, characteristic, complemented
9#13067444C211yesmaximal, characteristic, complemented
10#13067439C211yesmaximal, characteristic, complemented
11#13067410C211yesmaximal, characteristic, complemented
12#13067084C211yesmaximal, characteristic, complemented
13#13067006C211yesmaximal, characteristic, complemented
14#13066916C211yesmaximal, characteristic, complemented
15C11×#1572C211yesmaximal, characteristic, complemented
16#10623008C2211yescharacteristic
17C2×C4×D44C2211yescharacteristic
18C11×#432C2211yescharacteristic
19C11×#431C2211yescharacteristic
20C11×#431C2211yescharacteristic
21#10622538C2211yescharacteristic
22#10622538C2211yescharacteristic
23#10622459C411yescharacteristic
24#10622459C411yescharacteristic
25#10622456C411yescharacteristic
26#10622456C411yescharacteristic
27#10622451C2211yescharacteristic
28#10622451C2211yescharacteristic
29#10622451C2211yescharacteristic, complemented
30#10622451C2211yescharacteristic, complemented
31#10622447C2211yescharacteristic
32#10622447C2211yescharacteristic
33#10622447C2211yescharacteristic, complemented
34#10622447C2211yescharacteristic, complemented
35#10622349C411yescharacteristic
36#10622349C411yescharacteristic
37#10622345C411yescharacteristic
38#10622345C411yescharacteristic
39#10622340—21no—
40#10622340—21no—
41#10622339—21no—
42D11×C22⋊C8—21no—
43#10622319—21no—
44#10622319—21no—
45C4×D88C2211yescharacteristic
46C4×D88C2211yescharacteristic
47C4×D88C2211yescharacteristic
48C4×D88C2211yescharacteristic
49#10622301—21no—
50C8×D44—21no—
51C11×#335C2211yescharacteristic, complemented
52C11×#335C2211yescharacteristic, complemented
53C11×#334C2211yescharacteristic, complemented
54C11×#334C2211yescharacteristic, complemented
55#10622121C2211yescharacteristic
56#10622121C2211yescharacteristic
57#10622121C2211yescharacteristic
58#10622121C2211yescharacteristic
59#10622121C2211yescharacteristic, complemented
60#10622121C2211yescharacteristic, complemented
61#10622121C2211yescharacteristic, complemented
62#10622121C2211yescharacteristic, complemented
63#10622093C2211yescharacteristic, complemented
64#10622092C2211yescharacteristic, complemented
65#10622092C2211yescharacteristic, complemented
66C8×C11⋊C8C2211yescharacteristic, complemented
67C2×#4339—21no—
68C22×D44C2×C411yescharacteristic
69C22×C4×D11—21no—
70C2×C42×C11C2311yescharacteristic
71#66983—21no—
72#66983C2×C411yescharacteristic
73#66983C2×C411yescharacteristic
74C2×(C2×D11)⋊C4—21no—
75C2×C4⋊Dic11C2×C411yescharacteristic
76C2×D88C2×C411yescharacteristic
77C2×D88C2×C411yescharacteristic
78C2×D88C2×C411yescharacteristic
79C2×D88C2×C411yescharacteristic
80C2×#4313—21no—
81C2×#4313—21no—
82C2×#4313—21no—
83C2×#4313—21no—
84C2×C8×D11—21no—
85C2×C8×D11—21no—
86C2×C8×D11—21no—
87C2×C8×D11—21no—
88#66928—21no—
89#66927C2×C411yescharacteristic
90C4×D44—21no—
91C4×D44—21no—
92C4×D44—21no—
93C4×D44C2×C411yescharacteristic
94C4×D44C2×C411yescharacteristic
95C4×D44C2311yescharacteristic
96C4×D44C2311yescharacteristic
97C4×D44C2311yescharacteristic
98C4×D44C2311yescharacteristic
99#66922C2×C411yescharacteristic
100C11×C4⋊C8C2×C411yescharacteristic
101C11×C4⋊C8C2×C411yescharacteristic
102C11×C4⋊C8C2311yescharacteristic
103C11×C4⋊C8C2311yescharacteristic
104C11×C4⋊C8C2311yescharacteristic
105C11×C4⋊C8C2311yescharacteristic
106C11×C22⋊C8—21no—
107C11×C22⋊C8—21no—
108C11×C22⋊C8C2×C411yescharacteristic
109C11×C22⋊C8C2×C411yescharacteristic
110C11×#97—21no—
111C4×C8×C11—21no—
112C4×C8×C11C2311yescharacteristic
113C4×C8×C11C2311yescharacteristic
114C22⋊(C11⋊C8)—21no—
115C22⋊(C11⋊C8)D411yescharacteristic
116C22⋊(C11⋊C8)D411yescharacteristic
117#66885C2×C411yescharacteristic
118#66885C2×C411yescharacteristic
119#66885C2×C411yescharacteristic
120#66885C2×C411yescharacteristic
121#66885C2×C411yescharacteristic
122#66885C2×C411yescharacteristic
123#66885C2×C411yescharacteristic
124#66885C2×C411yescharacteristic
125(C2×D11)⋊C8—21no—
126(C2×D11)⋊C8—21no—
127(C2×D11)⋊C8—21no—
128(C2×D11)⋊C8—21no—
129(C2×D11)⋊C8—21no—
130(C2×D11)⋊C8—21no—
131(C2×D11)⋊C8—21no—
132(C2×D11)⋊C8—21no—
133#66882C2×C411yescharacteristic
134#66882C2×C411yescharacteristic
135#66882C2×C411yescharacteristic
136#66882C2×C411yescharacteristic
137C4⋊(C11⋊C8)—21no—
138C4⋊(C11⋊C8)D411yescharacteristic
139C4⋊(C11⋊C8)D411yescharacteristic
140C4×C11⋊C8C2311yescharacteristic
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#18026—111nomaximal, Sylow
145C23×D11—21no—
146C22×C4×C11C22×C411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11#4111yescharacteristic
149C2×C22⋊D11—21no—
150C2×C22⋊D11—21no—
151C22×Dic11—21no—
152#4339—81no—
153#4339—81no—
154C2×D44—22no—
155C2×D44—21no—
156C2×D44—21no—
157C2×D44—21no—
158C2×D44—41no—
159C2×D44C22×C411yescharacteristic
160C2×D44C22×C411yescharacteristic
161C2×D44C22×C411yescharacteristic
162C2×D44C22×C411yescharacteristic
163C2×C4×D11—21no—
164C2×C4×D11—21no—
165C2×C4×D11—21no—
166C2×C4×D11—21no—
167C2×C4×D11—21no—
168C2×C4×D11—21no—
169C2×C4×D11—81no—
170C2×C4×D11—81no—
171C2×Dic22—21no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11C22×C411yescharacteristic
177C2×C8×C11C22×C411yescharacteristic
178C2×C8×C11C22×C411yescharacteristic
179C2×C8×C11C22×C411yescharacteristic
180C42×C11C22×C411yescharacteristic
181C42×C11C2×D411yescharacteristic
182C42×C11#4111yescharacteristic
183C42×C11C2411yescharacteristic
184(C2×D11)⋊C4—21no—
185(C2×D11)⋊C4—21no—
186(C2×D11)⋊C4—21no—
187(C2×D11)⋊C4—21no—
188(C2×D11)⋊C4—21no—
189(C2×D11)⋊C4—21no—
190(C2×D11)⋊C4—21no—
191(C2×D11)⋊C4—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11C22×C411yescharacteristic
195C4⋊Dic11C22×C411yescharacteristic
196C4⋊Dic11C22×C411yescharacteristic
197C4⋊Dic11C22×C411yescharacteristic
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8C2×D411yescharacteristic
201C2×C11⋊C8C2×D411yescharacteristic
202C2×C11⋊C8C2×D411yescharacteristic
203C2×C11⋊C8C2×D411yescharacteristic
204D88—22no—
205D88—22no—
206D88—41no—
207D88—41no—
208#4313—81no—
209#4313—81no—
210#4313—81no—
211#4313—81no—
212C8×D11—81no—
213C8×D11—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#1572D1111yescharacteristic, complemented
228#1496—111no—
229#1478—111no—
230#1454—111no—
231C23×C11C4×D411yescharacteristic
232C22×D11—21no—
233C22×D11—21no—
234C22×D11—21no—
235C22×D11—21no—
236C22×D11—42no—
237C22×D11—42no—
238C22×D11—81no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—41no—
244C2×C4×C11C4×D411yescharacteristic
245C2×C4×C11C4×D411yescharacteristic
246C2×C4×C11C4×D411yescharacteristic
247C2×C4×C11C23×C411yescharacteristic
248C2×C4×C11C22×D411yescharacteristic
249C2×C4×C11C2×#4111yescharacteristic
250C22⋊D11—81no—
251C22⋊D11—81no—
252C2×Dic11—21no—
253C2×Dic11—21no—
254C2×Dic11—21no—
255C2×Dic11—21no—
256C2×Dic11—81no—
257D44—21no—
258D44—21no—
259D44—21no—
260D44—21no—
261D44—21no—
262D44—21no—
263D44—21no—
264D44—42no—
265D44—42no—
266D44—81no—
267D44#13112yes—
268C4×D11—41no—
269C4×D11—41no—
270C4×D11—41no—
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—
286C8×C11—41no—
287C11⋊C8—21no—
288C11⋊C8—21no—
289C11⋊C8—21no—
290C11⋊C8—21no—
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×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#432C2×D1111yescharacteristic
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#335C2×D1111yescharacteristic, complemented
329#335C2×D1111yescharacteristic, complemented
330#334C2×D1111yescharacteristic, complemented
331#334C2×D1111yescharacteristic, complemented
332D4⋊C8—111no—
333D4⋊C8—111no—
334D4⋊C8—111no—
335D4⋊C8—111no—
336D4⋊C8—111no—
337D4⋊C8—111no—
338D4⋊C8—111no—
339D4⋊C8—111no—
340#322—111no—
341#322—111no—
342#322—111no—
343C82—111no—
344C22×C11—21no—
345C22×C11—21no—
346C22×C11—21no—
347C22×C11C2×C4×D411yescharacteristic
348C2×D11—22no—
349C2×D11—41no—
350C2×D11—41no—
351C2×D11—41no—
352C2×D11—41no—
353C2×D11—41no—
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—21no—
363C4×C11—21no—
364C4×C11—21no—
365C4×C11C2×#13111yescharacteristic
366C4×C11#56811yescharacteristic
367C4×C11#57611yescharacteristic
368C4×C11#57611yescharacteristic
369Dic11—41no—
370Dic11—41no—
371Dic11—41no—
372Dic11—41no—
373C2×#41—221no—
374C22×D4—111no—
375C23×C4—221no—
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—111no—
395C4×D4—111no—
396C4×D4—111no—
397C4×D4—111no—
398C4×D4—111no—
399C4×D4—111no—
400C4×D4—221no—
401C4×D4—221no—
402C4×D4—221no—
403C2×C4⋊C4—111no—
404C2×C22⋊C4—221no—
405C2×C42C22×D1111yescharacteristic
406#107—111no—
407#107—111no—
408#107—111no—
409#107—111no—
410C4⋊C8—111no—
411C4⋊C8—111no—
412C4⋊C8—221no—
413C4⋊C8C4×D1111yescharacteristic
414C4⋊C8C4×D1111yescharacteristic
415C4⋊C8C22×D1111yescharacteristic
416C4⋊C8C22×D1111yescharacteristic
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—221no—
432C22⋊C8—221no—
433C22⋊C8—221no—
434C22⋊C8—221no—
435C22⋊C8—221no—
436C22⋊C8—221no—
437C22⋊C8—221no—
438C22⋊C8—221no—
439C22⋊C8—221no—
440C22⋊C8C4×D1111yescharacteristic
441C22⋊C8C4×D1111yescharacteristic
442#97—21no—
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#293311yescharacteristic
452C2×C11#294811yescharacteristic
453C2×C11#295511yescharacteristic
454D11—42no—
455D11—81no—
456D11—81no—
457D11—81no—
458C24—221no—
459#41—881no—
460#41—881no—
461C2×Q8—221no—
462C2×D4—111no—
463C2×D4—111no—
464C2×D4—111no—
465C2×D4—111no—
466C2×D4—222no—
467C2×D4—221no—
468C2×D4—221no—
469C2×D4—221no—
470C2×D4—221no—
471C2×D4—221no—
472C2×D4—441no—
473C22×C4—221no—
474C22×C4—221no—
475C22×C4—221no—
476C22×C4—221no—
477C22×C4—221no—
478C22×C4—221no—
479C22×C4—221no—
480C22×C4—881no—
481C22×C4—881no—
482C22×C4C2×C4×D1111yescharacteristic
483C22×C4D4×D1111yescharacteristic
484C22×C4#434311yescharacteristic
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—221no—
502C2×C8—221no—
503C2×C8—881no—
504C2×C8—881no—
505C2×C8—881no—
506C2×C8—881no—
507C2×C8C2×C4×D1111yescharacteristic
508C2×C8C2×C4×D1111yescharacteristic
509C2×C8C2×C4×D1111yescharacteristic
510C2×C8C2×C4×D1111yescharacteristic
511C4⋊C4—111no—
512C4⋊C4—111no—
513C4⋊C4—111no—
514C4⋊C4—111no—
515C4⋊C4—221no—
516C4⋊C4—221no—
517C22⋊C4—221no—
518C22⋊C4—221no—
519C22⋊C4—221no—
520C22⋊C4—221no—
521C22⋊C4—221no—
522C22⋊C4—221no—
523C22⋊C4—221no—
524C22⋊C4—221no—
525C42C2×C4×D1111yescharacteristic
526C42D4×D1111yescharacteristic
527C42#434311yescharacteristic
528C42C23×D1111yescharacteristic
529C11#1802611yescharacteristic, complemented, Sylow
530C23—221no—
531C23—221no—
532C23—221no—
533C23—221no—
534C23—442no—
535C23—442no—
536C23—881no—
537C23#6694611yescharacteristic
538Q8—881no—
539D4—112no—
540D4—221no—
541D4—221no—
542D4—221no—
543D4—221no—
544D4—221no—
545D4—221no—
546D4—221no—
547D4—442no—
548D4—442no—
549D4—881no—
550D4—881no—
551D4—881no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—41no—
557C2×C4—221no—
558C2×C4—221no—
559C2×C4—221no—
560C2×C4—221no—
561C2×C4—441no—
562C2×C4—441no—
563C2×C4—441no—
564C2×C4—441no—
565C2×C4—441no—
566C2×C4—441no—
567C2×C4—441no—
568C2×C4—441no—
569C2×C4—881no—
570C2×C4—881no—
571C2×C4—881no—
572C2×C4#6694611yescharacteristic
573C2×C4#6694611yescharacteristic
574C2×C4#6694611yescharacteristic
575C2×C4C22×C4×D1111yescharacteristic
576C2×C4C2×D4×D1111yescharacteristic
577C2×C4C2×#434311yescharacteristic
578C8—21no—
579C8—21no—
580C8—21no—
581C8—21no—
582C8—41no—
583C8—41no—
584C8—41no—
585C8—41no—
586C8—221no—
587C8—221no—
588C8—221no—
589C8—221no—
590C8—441no—
591C8—441no—
592C22—21no—
593C22—21no—
594C22—21no—
595C22—222no—
596C22—441no—
597C22—441no—
598C22—441no—
599C22—441no—
600C22—441no—
601C22—441no—
602C22—441no—
603C22—441no—
604C22—441no—
605C22—441no—
606C22—441no—
607C22—884no—
608C22C2×#6694611yescharacteristic
609C4—21no—
610C4—21no—
611C4—21no—
612C4—21no—
613C4—441no—
614C4—441no—
615C4—441no—
616C4—441no—
617C4D11×#13111yescharacteristic
618C4#1062328111yescharacteristic
619C4#1062330011yescharacteristic
620C4#1062330011yescharacteristic
621C2—41no—
622C2—442no—
623C2—881no—
624C2—881no—
625C2—881no—
626C2#1307734011yescharacteristic
627C2#1307746711yescharacteristic
628C2#1307751811yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1572C2
socleC22×C11C2×C4×D4
prime radical#13078617C2
cosocleC42×C11C24
hypercenter#1572D11
hypocenterC11#18026
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1572

Complements

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

NH ≅ G/Ntype
2. #13077682C2semidirect
3. #13077653C2semidirect
4. #13067529C2semidirect
5. #13067500C2semidirect
6. #13067479C2semidirect
7. #13067479C2semidirect
8. #13067444C2semidirect
9. #13067444C2semidirect
10. #13067439C2semidirect
11. #13067410C2semidirect
12. #13067084C2semidirect
13. #13067006C2semidirect
14. #13066916C2semidirect
15. C11×#1572C2semidirect
29. #10622451C22semidirect
30. #10622451C22semidirect
33. #10622447C22semidirect
34. #10622447C22semidirect
51. C11×#335C22semidirect
52. C11×#335C22semidirect
53. C11×#334C22semidirect
54. C11×#334C22semidirect
59. #10622121C22semidirect
60. #10622121C22semidirect
61. #10622121C22semidirect
62. #10622121C22semidirect
63. #10622093C22semidirect
64. #10622092C22semidirect
65. #10622092C22semidirect
66. C8×C11⋊C8C22semidirect
227. #1572D11semidirect
328. #335C2×D11semidirect
329. #335C2×D11semidirect
330. #334C2×D11semidirect
331. #334C2×D11semidirect
529. C11#18026semidirect

Maximal subgroups

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

subgroupindex
#130786172
#130776822
#130776532
#130675292
#130675002
#130674792
#130674442
#130674392
#130674102
#130670842
#130670062
#130669162
C11×#15722
#1802611