Finite Group Databasebeta

← #14827013

Subgroups — #14827013

Order 2816.

734 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#13073213C211yesmaximal, characteristic
2#13071672C211yesmaximal, characteristic, complemented
3#13070163C211yesmaximal, characteristic, complemented
4#13069934C211yesmaximal, characteristic
5#13069863C211yesmaximal, characteristic, complemented
6#13069701C211yesmaximal, characteristic
7#13069470C211yesmaximal, characteristic
8#13069258C211yesmaximal, characteristic, complemented
9#13069237C211yesmaximal, characteristic
10#13069202C211yesmaximal, characteristic, complemented
11#13068970C211yesmaximal, characteristic
12#13068970C211yesmaximal, characteristic
13#13068632C211yesmaximal, characteristic, complemented
14C4×#66880C211yesmaximal, characteristic, complemented
15C11×#1916C211yesmaximal, characteristic, complemented
16C22×#4314C2211yescharacteristic
17C22×#4314C2211yescharacteristic
18C2×#66922C2211yescharacteristic
19C2×C4×Dic22C2211yescharacteristic
20C2×C4×Dic22C2211yescharacteristic
21C2×C11×C4⋊C8C2211yescharacteristic
22C2×C4×C8×C11C2211yescharacteristic
23C4×C11×C4⋊C4C2211yescharacteristic
24C2×#66885C2211yescharacteristic
25C2×#66885C2211yescharacteristic
26C2×#66882C2211yescharacteristic
27C2×#66881C2211yescharacteristic
28C2×#66880C2211yescharacteristic
29C2×#66880C2211yescharacteristic
30C2×#66880C2211yescharacteristic
31C2×#66880C2211yescharacteristic
32C2×#66880C2211yescharacteristic
33C2×#66880C2211yescharacteristic
34#10622606—21no—
35#10622603—21no—
36C4⋊C4×Dic11—21no—
37#10622586—21no—
38#10622552C2211yescharacteristic
39#10622552C2211yescharacteristic
40#10622552C2211yescharacteristic
41#10622549C2211yescharacteristic
42C4×C4⋊Dic11C2211yescharacteristic
43C4×C4⋊Dic11C2211yescharacteristic
44#10622542C2211yescharacteristic
45#10622542C2211yescharacteristic
46#10622541C2211yescharacteristic
47#10622288—21no—
48#10622282—21no—
49#10622267—21no—
50#10622267—21no—
51C11×#336C2211yescharacteristic
52C11×#336C2211yescharacteristic
53C11×#336C2211yescharacteristic
54C11×#336C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622189C2211yescharacteristic
59C22×D44C2311yescharacteristic
60C22×Dic22C2311yescharacteristic
61C22×Dic22C2311yescharacteristic
62C22×C8×C11C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C2×C11×C4⋊C4D411yescharacteristic
67C2×C11×C4⋊C4D411yescharacteristic
68C2×C42×C11C2311yescharacteristic
69C2×C42×C11C2311yescharacteristic
70C2×C42×C11C2311yescharacteristic
71C2×(C2×D11)⋊C4—21no—
72C2×(C2×D11)⋊C4—21no—
73C2×(C2×D11)⋊C4—21no—
74C2×(C2×D11)⋊C4—21no—
75C2×(C2×D11)⋊C4—21no—
76C2×(C2×D11)⋊C4—21no—
77C2×C4⋊Dic11—21no—
78C2×C4⋊Dic11—21no—
79C2×C4⋊Dic11C2311yescharacteristic
80C2×C4⋊Dic11C2311yescharacteristic
81C2×C4⋊Dic11C2311yescharacteristic
82C2×C4⋊Dic11C2311yescharacteristic
83C2×C4⋊Dic11C2311yescharacteristic
84C2×Dic11⋊C4—21no—
85C2×Dic11⋊C4—21no—
86C2×Dic11⋊C4—21no—
87C2×C4×Dic11—21no—
88C2×C4×Dic11—21no—
89C2×C4×Dic11—21no—
90C2×C4×Dic11—21no—
91C2×#4314—22no—
92C2×#4314—22no—
93C2×#4314—22no—
94C2×#4314—41no—
95C2×#4314—41no—
96C2×#4314—41no—
97#66922—22no—
98#66922—22no—
99C4×Dic22—22no—
100C4×Dic22—22no—
101C4×Dic22—41no—
102C4×Dic22—41no—
103C11×C4⋊C8—41no—
104C4×C8×C11—41no—
105C11×#95D411yescharacteristic
106C11×#95D411yescharacteristic
107C11⋊#95—21no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116#66885—22no—
117#66885—41no—
118#66882—41no—
119#66881—22no—
120#66880—22no—
121#66880—22no—
122#66880—22no—
123#66880—41no—
124#66880—41no—
125#66880—41no—
126#27069—111nomaximal, Sylow
127C23×D11—21no—
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2411yescharacteristic
135C22×Dic11—21no—
136C22×Dic11—21no—
137C22×Dic11—21no—
138C22×Dic11—21no—
139C22×Dic11—21no—
140C22×Dic11—21no—
141C22×Dic11—21no—
142C2×D44—21no—
143C2×D44—21no—
144C2×D44—21no—
145C2×D44—21no—
146C2×D44—21no—
147C2×D44—21no—
148C2×Dic22—21no—
149C2×Dic22—21no—
150C2×Dic22—21no—
151C2×Dic22—21no—
152C2×Dic22—21no—
153C2×Dic22—21no—
154C2×Dic22—21no—
155C2×Dic22—21no—
156C2×Dic22—21no—
157C2×Dic22—21no—
158C2×Dic22#4112yes—
159C2×Dic22#4112yes—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11#4112yes—
172C11×C4⋊C4—22no—
173C11×C4⋊C4—22no—
174C42×C11—21no—
175C42×C11—21no—
176C42×C11—21no—
177C42×C11—21no—
178C42×C11—21no—
179C42×C11—21no—
180(C2×D11)⋊C4—42no—
181(C2×D11)⋊C4—42no—
182(C2×D11)⋊C4—81no—
183(C2×D11)⋊C4—81no—
184(C2×D11)⋊C4—81no—
185(C2×D11)⋊C4—81no—
186C4⋊Dic11—24no—
187C4⋊Dic11—24no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11#4112yes—
198Dic11⋊C4—42no—
199Dic11⋊C4—42no—
200Dic11⋊C4—81no—
201C4×Dic11—42no—
202C4×Dic11—42no—
203C4×Dic11—42no—
204C4×Dic11—81no—
205#4314—44no—
206#4314—44no—
207#2513—111no—
208#2365—111no—
209#2097—111no—
210#2055—111no—
211#2043—111no—
212#2013—111no—
213#1968—111no—
214#1928—111no—
215#1925—111no—
216#1920—111no—
217#1916D1111yescharacteristic, complemented
218#1880—111no—
219#1880—111no—
220#1805—111no—
221C4×#103—111no—
222C23×C11C22×D411yescharacteristic
223C22×D11—41no—
224C22×D11—41no—
225C22×D11—41no—
226C22×D11—41no—
227C22×D11—41no—
228C22×D11—41no—
229C22×D11—41no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11#13512yes—
247C2×C4×C11#13712yes—
248C2×C4×C11C2×#4111yescharacteristic
249C2×C4×C11C2×#4111yescharacteristic
250C2×C4×C11C2×#4111yescharacteristic
251C2×C4×C11C2×#4111yescharacteristic
252C2×C4×C11H(5,𝔽2)11yescharacteristic
253C2×C4×C11H(5,𝔽2)11yescharacteristic
254C2×Dic11—22no—
255C2×Dic11—22no—
256C2×Dic11—22no—
257C2×Dic11—41no—
258C2×Dic11—41no—
259C2×Dic11—41no—
260C2×Dic11—41no—
261C2×Dic11—41no—
262C2×Dic11—41no—
263C2×Dic11—41no—
264C2×Dic11—41no—
265C2×Dic11—41no—
266C2×Dic11—41no—
267C2×Dic11—41no—
268C2×Dic11—41no—
269C2×Dic11—41no—
270C2×Dic11—41no—
271C2×Dic11—41no—
272C2×Dic11—41no—
273C2×Dic11—41no—
274C2×Dic11—41no—
275D44—41no—
276D44—41no—
277D44—41no—
278D44—41no—
279Dic22—22no—
280Dic22—22no—
281Dic22—22no—
282Dic22—22no—
283Dic22—41no—
284Dic22—41no—
285Dic22—41no—
286Dic22—41no—
287C8×C11—22no—
288C8×C11—41no—
289C8×C11—41no—
290C8×C11—41no—
291C22×SD16—111no—
292C22×SD16—111no—
293C2×C4⋊Q8—111no—
294C2×C4×Q8—111no—
295C2×C4×Q8—111no—
296C2×#107—111no—
297C2×#106—111no—
298C2×C4⋊C8C2×D1111yescharacteristic
299C2×#103—111no—
300C2×#103—111no—
301C2×#103—111no—
302C2×#103—111no—
303C2×#103—111no—
304C2×#103—111no—
305C2×#102—111no—
306C2×#102—111no—
307C2×C4×C8C2×D1111yescharacteristic
308#397—221no—
309#397—221no—
310#391—111no—
311#391—111no—
312#390—111no—
313#390—111no—
314#390—111no—
315#389—111no—
316#389—221no—
317#388—221no—
318#388—221no—
319#387—221no—
320#387—221no—
321#382—111no—
322C4×C4⋊C4—111no—
323C4×C4⋊C4—111no—
324C4×C4⋊C4—221no—
325C4×C4⋊C4C2×D1111yescharacteristic
326#340—111no—
327#340—111no—
328#340—111no—
329#340—111no—
330#336C2×D1111yescharacteristic
331#336C2×D1111yescharacteristic
332#336C2×D1111yescharacteristic
333#336C2×D1111yescharacteristic
334C22×C11#52511yescharacteristic
335C22×C11#54611yescharacteristic
336C22×C11#55011yescharacteristic
337C22×C11C2×#13511yescharacteristic
338C22×C11C2×#13711yescharacteristic
339C22×C11#57711yescharacteristic
340C22×C11#57711yescharacteristic
341C2×D11—81no—
342C2×D11—81no—
343C2×D11—81no—
344C2×D11—81no—
345C2×D11—81no—
346C2×D11—81no—
347C2×D11—81no—
348C4×C11—22no—
349C4×C11—22no—
350C4×C11—41no—
351C4×C11—41no—
352C4×C11—41no—
353C4×C11—41no—
354C4×C11#52911yescharacteristic
355C4×C11#53811yescharacteristic
356C4×C11#55111yescharacteristic
357C4×C11#55311yescharacteristic
358Dic11—42no—
359Dic11—42no—
360Dic11—42no—
361Dic11—81no—
362Dic11—81no—
363Dic11—81no—
364Dic11—81no—
365C22×Q8—111no—
366C22×Q8—111no—
367C22×D4—111no—
368C2×SD16—222no—
369C2×SD16—222no—
370C2×SD16—222no—
371C2×SD16—441no—
372C2×SD16—441no—
373C2×SD16—441no—
374C22×C8C22×D1111yescharacteristic
375C22×C8C22×D1111yescharacteristic
376C22×C8C22×D1111yescharacteristic
377C22×C8C22×D1111yescharacteristic
378C4⋊Q8—222no—
379C4⋊Q8—222no—
380C4×Q8—222no—
381C4×Q8—222no—
382C4×Q8—441no—
383C4×Q8—441no—
384C2×C4⋊C4—111no—
385C2×C4⋊C4—111no—
386C2×C4⋊C4—111no—
387C2×C4⋊C4—111no—
388C2×C4⋊C4—111no—
389C2×C4⋊C4—221no—
390C2×C4⋊C4—221no—
391C2×C4⋊C4—221no—
392C2×C4⋊C4—221no—
393C2×C4⋊C4—221no—
394C2×C4⋊C4D4411yescharacteristic
395C2×C4⋊C4D4411yescharacteristic
396C2×C22⋊C4—221no—
397C2×C22⋊C4—221no—
398C2×C22⋊C4—221no—
399C2×C22⋊C4—221no—
400C2×C22⋊C4—221no—
401C2×C22⋊C4—221no—
402C2×C42—221no—
403C2×C42—221no—
404C2×C42—221no—
405C2×C42—221no—
406C2×C42C22×D1111yescharacteristic
407C2×C42C22×D1111yescharacteristic
408C2×C42C22×D1111yescharacteristic
409#107—441no—
410#106—222no—
411C4⋊C8—41no—
412#103—222no—
413#103—222no—
414#103—222no—
415#103—441no—
416#103—441no—
417#103—441no—
418#102—222no—
419#102—441no—
420C4×C8—41no—
421#95—221no—
422#95—221no—
423#95—221no—
424#95—221no—
425#95—221no—
426#95—221no—
427#95—221no—
428#95—221no—
429#95—221no—
430#95D4411yescharacteristic
431#95D4411yescharacteristic
432C2×C11#246711yescharacteristic
433C2×C11#310811yescharacteristic
434C2×C11#312611yescharacteristic
435C2×C11#330311yescharacteristic
436C2×C11#332011yescharacteristic
437C2×C11#339411yescharacteristic
438C2×C11#340011yescharacteristic
439D11—161no—
440C24—221no—
441C2×Q8—112no—
442C2×Q8—112no—
443C2×Q8—221no—
444C2×Q8—221no—
445C2×Q8—221no—
446C2×Q8—221no—
447C2×Q8—221no—
448C2×Q8—221no—
449C2×Q8—221no—
450C2×Q8—221no—
451C2×Q8—221no—
452C2×Q8—221no—
453C2×D4—221no—
454C2×D4—221no—
455C2×D4—221no—
456C2×D4—221no—
457C2×D4—221no—
458C2×D4—221no—
459C22×C4—221no—
460C22×C4—221no—
461C22×C4—221no—
462C22×C4—221no—
463C22×C4—221no—
464C22×C4—221no—
465C22×C4—221no—
466C22×C4C2×D4411yescharacteristic
467C22×C4C2×D4411yescharacteristic
468C22×C4C2×D4411yescharacteristic
469C22×C4C2×D4411yescharacteristic
470C22×C4C2×D4411yescharacteristic
471C22×C4C2×D4411yescharacteristic
472C22×C4C23×D1111yescharacteristic
473SD16—444no—
474SD16—444no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8#434312yes—
487C4⋊C4—22no—
488C4⋊C4—22no—
489C4⋊C4—112no—
490C4⋊C4—224no—
491C4⋊C4—224no—
492C4⋊C4—221no—
493C4⋊C4—221no—
494C4⋊C4—221no—
495C4⋊C4—221no—
496C4⋊C4—221no—
497C4⋊C4—221no—
498C4⋊C4—221no—
499C4⋊C4—221no—
500C4⋊C4—221no—
501C4⋊C4—442no—
502C4⋊C4—442no—
503C4⋊C4—881no—
504C22⋊C4—442no—
505C22⋊C4—442no—
506C22⋊C4—881no—
507C22⋊C4—881no—
508C22⋊C4—881no—
509C22⋊C4—881no—
510C42—21no—
511C42—21no—
512C42—21no—
513C42—21no—
514C42—21no—
515C42—21no—
516C42—442no—
517C42—442no—
518C42—442no—
519C42—881no—
520C11#2706911yescharacteristic, complemented, Sylow
521C23—441no—
522C23—441no—
523C23—441no—
524C23—441no—
525C23—441no—
526C23—441no—
527C23—441no—
528C23C22×D4411yescharacteristic
529Q8—222no—
530Q8—222no—
531Q8—222no—
532Q8—222no—
533Q8—441no—
534Q8—441no—
535Q8—441no—
536Q8—441no—
537D4—441no—
538D4—441no—
539D4—441no—
540D4—441no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—222no—
558C2×C4—222no—
559C2×C4—222no—
560C2×C4—441no—
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—441no—
570C2×C4—441no—
571C2×C4—441no—
572C2×C4—441no—
573C2×C4—441no—
574C2×C4—441no—
575C2×C4—441no—
576C2×C4—441no—
577C2×C4—441no—
578C2×C4#6695712yes—
579C2×C4#6696212yes—
580C2×C4#6703711yescharacteristic
581C2×C4C2×#434311yescharacteristic
582C2×C4#41×D1111yescharacteristic
583C2×C4#41×D1111yescharacteristic
584C2×C4#41×D1111yescharacteristic
585C2×C4#6704211yescharacteristic
586C8—22no—
587C8—41no—
588C8—41no—
589C8—41no—
590C22—881no—
591C22—881no—
592C22—881no—
593C22—881no—
594C22—881no—
595C22—881no—
596C22—881no—
597C22#1062305511yescharacteristic
598C22#1062308511yescharacteristic
599C22#1062310811yescharacteristic
600C22C2×#6695711yescharacteristic
601C22C2×#6696211yescharacteristic
602C22#1062328211yescharacteristic
603C22#1062328211yescharacteristic
604C4—22no—
605C4—22no—
606C4—41no—
607C4—41no—
608C4—41no—
609C4—41no—
610C4—442no—
611C4—442no—
612C4—442no—
613C4—881no—
614C4—881no—
615C4—881no—
616C4—881no—
617C4#1062316811yescharacteristic
618C4#1062318811yescharacteristic
619C4#1062322211yescharacteristic
620C4#1062324011yescharacteristic
621C2—1761no—
622C2#1307266511yescharacteristic
623C2#1307869811yescharacteristic
624C2#1307890811yescharacteristic
625C2#1308054511yescharacteristic
626C2#1308078911yescharacteristic
627C2#1308161411yescharacteristic
628C2#1308167111yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1916C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#1916D11
hypocenterC11#27069
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #1916

Complements

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

NH ≅ G/Ntype
2. #13071672C2semidirect
3. #13070163C2semidirect
5. #13069863C2semidirect
8. #13069258C2semidirect
10. #13069202C2semidirect
13. #13068632C2semidirect
14. C4×#66880C2semidirect
15. C11×#1916C2semidirect
217. #1916D11semidirect
520. C11#27069semidirect

Maximal subgroups

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

subgroupindex
#130732132
#130716722
#130701632
#130699342
#130698632
#130697012
#130694702
#130692582
#130692372
#130692022
#130689702
#130686322
C4×#668802
C11×#19162
#2706911