Finite Group Databasebeta

← #14826966

Subgroups — #14826966

Order 2816.

762 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#13071672C211yesmaximal, characteristic, complemented
2#13070160C211yesmaximal, characteristic, complemented
3#13069933C211yesmaximal, characteristic
4#13069862C211yesmaximal, characteristic, complemented
5#13069698C211yesmaximal, characteristic
6#13069469C211yesmaximal, characteristic
7#13069250C211yesmaximal, characteristic, complemented
8#13069240C211yesmaximal, characteristic
9#13069191C211yesmaximal, characteristic, complemented
10#13069175C211yesmaximal, characteristic, complemented
11#13068974C211yesmaximal, characteristic
12#13068974C211yesmaximal, characteristic
13#13068618C211yesmaximal, characteristic, complemented
14C4×#66874C211yesmaximal, characteristic, complemented
15C11×#2512C211yesmaximal, characteristic
16C2×C11×#126—21no—
17C22×#4324C2211yescharacteristic
18C22×#4324C2211yescharacteristic
19C2×#66922C2211yescharacteristic
20C2×C4×Dic22C2211yescharacteristic
21C2×C4×Dic22C2211yescharacteristic
22C11×#397—21no—
23C11×#396—21no—
24C11×#390C2211yescharacteristic
25C11×#390C2211yescharacteristic
26C11×#390C2211yescharacteristic
27C11×#389C2211yescharacteristic
28C11×#388—21no—
29C11×#384C2211yescharacteristic
30C4×C11×C4⋊C4C2211yescharacteristic
31C4×C11×C4⋊C4C2211yescharacteristic
32C2×#66896C2211yescharacteristic
33C2×#66896C2211yescharacteristic
34C4⋊C4×Dic11—21no—
35#10622586—21no—
36C2×#66874C2211yescharacteristic
37C2×#66874C2211yescharacteristic
38C2×#66874C2211yescharacteristic
39C2×#66874C2211yescharacteristic
40C2×#66874C2211yescharacteristic
41C2×#66874C2211yescharacteristic
42C2×#66872C2211yescharacteristic
43C2×#66872C2211yescharacteristic
44C4×C4⋊Dic11C2211yescharacteristic
45#10622542C2211yescharacteristic
46#10622542C2211yescharacteristic
47C2×C4⋊(C11⋊C8)C2211yescharacteristic
48C2×C4×C11⋊C8C2211yescharacteristic
49#10622267—21no—
50#10622267—21no—
51#10622167C2211yescharacteristic
52#10622167C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622162C2211yescharacteristic
56#10622162C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×D4×C11C2311yescharacteristic
60C22×Dic22C2311yescharacteristic
61C22×Dic22C2311yescharacteristic
62C11×#126—44no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4D411yescharacteristic
67C2×C11×C4⋊C4D411yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C22⋊C4—21no—
72C2×C11×C22⋊C4—21no—
73C2×C11×C22⋊C4—21no—
74C2×C11×C22⋊C4—21no—
75C2×C11×C22⋊C4—21no—
76C2×C11×C22⋊C4—21no—
77C2×C42×C11—21no—
78C2×C42×C11C2311yescharacteristic
79C2×C42×C11C2311yescharacteristic
80C2×C42×C11C2311yescharacteristic
81C2×#4324—22no—
82C2×#4324—22no—
83C2×#4324—22no—
84C2×#4324—41no—
85C2×#4324—41no—
86C2×#4324—41no—
87C2×C4⋊Dic11—21no—
88C2×C4⋊Dic11—21no—
89C2×C4⋊Dic11C2311yescharacteristic
90C2×C4⋊Dic11C2311yescharacteristic
91C2×Dic11⋊C4—21no—
92C2×Dic11⋊C4—21no—
93C2×C4×Dic11—21no—
94C2×C4×Dic11—21no—
95C2×C4×Dic11—21no—
96C22×C11⋊C8C2311yescharacteristic
97C22×C11⋊C8C2311yescharacteristic
98C22×C11⋊C8C2311yescharacteristic
99C22×C11⋊C8C2311yescharacteristic
100#66922—22no—
101#66922—22no—
102C4×Dic22—22no—
103C4×Dic22—22no—
104C4×Dic22—41no—
105C4×Dic22—41no—
106C11×#95—21no—
107C11×#95—21no—
108C11×#95D411yescharacteristic
109C11×#95D411yescharacteristic
110#66896—22no—
111#66896—41no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117#66874—22no—
118#66874—22no—
119#66874—22no—
120#66874—41no—
121#66874—41no—
122#66874—41no—
123#66872—22no—
124#66872—41no—
125C4⋊(C11⋊C8)—41no—
126C4×C11⋊C8—41no—
127#27066—111nomaximal, Sylow
128C24×C11—21no—
129C2×D4×C11—21no—
130C2×D4×C11—21no—
131C2×D4×C11—21no—
132C2×D4×C11—21no—
133C2×D4×C11—21no—
134C2×D4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2411yescharacteristic
145C22×Dic11—21no—
146C22×Dic11—21no—
147C22×Dic11—21no—
148C22×Dic11—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—21no—
159C2×Dic22#4112yes—
160C2×Dic22#4112yes—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—41no—
168C11×C4⋊C4—42no—
169C11×C4⋊C4—42no—
170C11×C4⋊C4—81no—
171C11×C4⋊C4SD1614yescomplemented
172C11×C22⋊C4—42no—
173C11×C22⋊C4—42no—
174C11×C22⋊C4—42no—
175C11×C22⋊C4—42no—
176C11×C22⋊C4—81no—
177C11×C22⋊C4—81no—
178C42×C11—21no—
179C42×C11—21no—
180C42×C11—21no—
181C42×C11—21no—
182C42×C11—21no—
183C42×C11—21no—
184C42×C11—42no—
185#4324—44no—
186#4324—44no—
187C4⋊Dic11—24no—
188C4⋊Dic11—24no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11#4112yes—
193Dic11⋊C4—42no—
194Dic11⋊C4—42no—
195C4×Dic11—42no—
196C4×Dic11—42no—
197C4×Dic11—42no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8#4112yes—
210#2512D1111yescharacteristic
211#2365—111no—
212#2096—111no—
213#2055—111no—
214#2043—111no—
215#2013—111no—
216#1968—111no—
217#1927—111no—
218#1926—111no—
219#1919—111no—
220#1916—111no—
221#1880—111no—
222#1880—111no—
223#1803—111no—
224C4×#103—111no—
225C23×C11—41no—
226C23×C11—41no—
227C23×C11—41no—
228C23×C11—41no—
229C23×C11—41no—
230C23×C11—41no—
231C23×C11—41no—
232C23×C11C22×D411yescharacteristic
233D4×C11—41no—
234D4×C11—41no—
235D4×C11—41no—
236D4×C11—41no—
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—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11C2×SD1612yes—
262C2×C4×C11C2×SD1612yes—
263C2×C4×C11C2×SD1612yes—
264C2×C4×C11C2×#4111yescharacteristic
265C2×C4×C11C2×#4111yescharacteristic
266C2×C4×C11C2×#4111yescharacteristic
267C2×C4×C11C2×#4111yescharacteristic
268C2×C4×C11H(5,𝔽2)11yescharacteristic
269C2×C4×C11H(5,𝔽2)11yescharacteristic
270C2×Dic11—22no—
271C2×Dic11—22no—
272C2×Dic11—22no—
273C2×Dic11—41no—
274C2×Dic11—41no—
275C2×Dic11—41no—
276C2×Dic11—41no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282Dic22—22no—
283Dic22—22no—
284Dic22—22no—
285Dic22—22no—
286Dic22—41no—
287Dic22—41no—
288Dic22—41no—
289Dic22—41no—
290C11⋊C8—22no—
291C11⋊C8—41no—
292C11⋊C8—41no—
293C11⋊C8—41no—
294C22×SD16—111no—
295C22×SD16—111no—
296C2×C4⋊Q8—111no—
297C2×#126—21no—
298C2×C4×Q8—111no—
299C2×C4×Q8—111no—
300C2×#106—111no—
301C2×#106—111no—
302C2×C4⋊C8—111no—
303C2×#103—111no—
304C2×#103—111no—
305C2×#103—111no—
306C2×#103—111no—
307C2×#103—111no—
308C2×#103—111no—
309C2×#102—111no—
310C2×#102—111no—
311C2×C4×C8—111no—
312#397—21no—
313#396—21no—
314#391—111no—
315#391—111no—
316#390C2×D1111yescharacteristic
317#390C2×D1111yescharacteristic
318#390C2×D1111yescharacteristic
319#389—221no—
320#389C2×D1111yescharacteristic
321#388—21no—
322#387—221no—
323#387—221no—
324#384C2×D1111yescharacteristic
325C4×C4⋊C4—111no—
326C4×C4⋊C4—221no—
327C4×C4⋊C4C2×D1111yescharacteristic
328C4×C4⋊C4C2×D1111yescharacteristic
329#340—111no—
330#340—111no—
331#340—111no—
332#340—111no—
333#336—111no—
334#336—111no—
335#336—111no—
336#336—111no—
337C22×C11—81no—
338C22×C11—81no—
339C22×C11—81no—
340C22×C11—81no—
341C22×C11—81no—
342C22×C11—81no—
343C22×C11—81no—
344C22×C11#52511yescharacteristic
345C22×C11#54611yescharacteristic
346C22×C11#55011yescharacteristic
347C22×C11C22×SD1611yescharacteristic
348C22×C11#57511yescharacteristic
349C22×C11#57711yescharacteristic
350C22×C11#57811yescharacteristic
351C4×C11—22no—
352C4×C11—22no—
353C4×C11—22no—
354C4×C11—41no—
355C4×C11—41no—
356C4×C11—41no—
357C4×C11—81no—
358C4×C11—81no—
359C4×C11—81no—
360C4×C11#52911yescharacteristic
361C4×C11#53811yescharacteristic
362C4×C11#55111yescharacteristic
363C4×C11#55311yescharacteristic
364Dic11—42no—
365Dic11—42no—
366Dic11—42no—
367Dic11—81no—
368C22×Q8—111no—
369C22×Q8—111no—
370C22×D4C22×D1111yescharacteristic
371C2×SD16—222no—
372C2×SD16—222no—
373C2×SD16—222no—
374C2×SD16—441no—
375C2×SD16—441no—
376C2×SD16—441no—
377C22×C8—111no—
378C22×C8—111no—
379C22×C8—111no—
380C22×C8—111no—
381C4⋊Q8—222no—
382C4⋊Q8—222no—
383#126—44no—
384C4×Q8—222no—
385C4×Q8—222no—
386C4×Q8—441no—
387C4×Q8—441no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—111no—
392C2×C4⋊C4—111no—
393C2×C4⋊C4—221no—
394C2×C4⋊C4—221no—
395C2×C4⋊C4—221no—
396C2×C4⋊C4—221no—
397C2×C4⋊C4C22⋊D1111yescharacteristic
398C2×C4⋊C4C22⋊D1111yescharacteristic
399C2×C4⋊C4C22×D1111yescharacteristic
400C2×C4⋊C4C22×D1111yescharacteristic
401C2×C4⋊C4C22×D1111yescharacteristic
402C2×C22⋊C4—21no—
403C2×C22⋊C4—21no—
404C2×C22⋊C4—21no—
405C2×C22⋊C4—21no—
406C2×C22⋊C4—21no—
407C2×C22⋊C4—21no—
408C2×C42—21no—
409C2×C42—221no—
410C2×C42—221no—
411C2×C42—221no—
412C2×C42C22×D1111yescharacteristic
413C2×C42C22×D1111yescharacteristic
414C2×C42C22×D1111yescharacteristic
415#106—222no—
416#106—441no—
417C4⋊C8—441no—
418#103—222no—
419#103—222no—
420#103—222no—
421#103—441no—
422#103—441no—
423#103—441no—
424#102—222no—
425#102—441no—
426C4×C8—441no—
427#95—21no—
428#95—21no—
429#95—221no—
430#95—221no—
431#95—221no—
432#95—221no—
433#95—221no—
434#95C22⋊D1111yescharacteristic
435#95C22⋊D1111yescharacteristic
436C2×C11—161no—
437C2×C11#246711yescharacteristic
438C2×C11#310311yescharacteristic
439C2×C11#312111yescharacteristic
440C2×C11#329811yescharacteristic
441C2×C11#330711yescharacteristic
442C2×C11#339211yescharacteristic
443C2×C11#340211yescharacteristic
444C24—21no—
445C2×Q8—112no—
446C2×Q8—112no—
447C2×Q8—221no—
448C2×Q8—221no—
449C2×Q8—221no—
450C2×Q8—221no—
451C2×Q8—221no—
452C2×Q8—221no—
453C2×Q8—221no—
454C2×Q8—221no—
455C2×Q8—221no—
456C2×Q8—221no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—221no—
467C22×C4—221no—
468C22×C4—221no—
469C22×C4—221no—
470C22×C4C2×C22⋊D1111yescharacteristic
471C22×C4C2×C22⋊D1111yescharacteristic
472C22×C4C2×C22⋊D1111yescharacteristic
473C22×C4C2×C22⋊D1111yescharacteristic
474C22×C4C2×C22⋊D1111yescharacteristic
475C22×C4C2×C22⋊D1111yescharacteristic
476C22×C4C23×D1111yescharacteristic
477SD16—444no—
478SD16—444no—
479C2×C8—112no—
480C2×C8—221no—
481C2×C8—221no—
482C2×C8—221no—
483C2×C8—221no—
484C2×C8—221no—
485C2×C8—221no—
486C2×C8—221no—
487C2×C8—221no—
488C2×C8—221no—
489C2×C8—221no—
490C2×C8—221no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—41no—
498C4⋊C4—42no—
499C4⋊C4—42no—
500C4⋊C4—81no—
501C4⋊C4—112no—
502C4⋊C4—224no—
503C4⋊C4—224no—
504C4⋊C4—221no—
505C4⋊C4—221no—
506C4⋊C4—221no—
507C4⋊C4—442no—
508C4⋊C4—442no—
509C4⋊C4#432414yescomplemented
510C22⋊C4—42no—
511C22⋊C4—42no—
512C22⋊C4—42no—
513C22⋊C4—42no—
514C22⋊C4—81no—
515C22⋊C4—81no—
516C42—21no—
517C42—21no—
518C42—21no—
519C42—21no—
520C42—21no—
521C42—21no—
522C42—42no—
523C42—442no—
524C42—442no—
525C42—442no—
526C11#2706611yescharacteristic, complemented, Sylow
527C23—41no—
528C23—41no—
529C23—41no—
530C23—41no—
531C23—41no—
532C23—41no—
533C23—41no—
534C23C22×C22⋊D1111yescharacteristic
535Q8—222no—
536Q8—222no—
537Q8—222no—
538Q8—222no—
539Q8—441no—
540Q8—441no—
541Q8—441no—
542Q8—441no—
543D4—41no—
544D4—41no—
545D4—41no—
546D4—41no—
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—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—222no—
572C2×C4—222no—
573C2×C4—222no—
574C2×C4—441no—
575C2×C4—441no—
576C2×C4—441no—
577C2×C4—441no—
578C2×C4—441no—
579C2×C4—441no—
580C2×C4—441no—
581C2×C4—441no—
582C2×C4—441no—
583C2×C4C2×#432412yes—
584C2×C4C2×#432412yes—
585C2×C4C2×#432412yes—
586C2×C4#41×D1111yescharacteristic
587C2×C4#41×D1111yescharacteristic
588C2×C4#41×D1111yescharacteristic
589C2×C4#41×D1111yescharacteristic
590C2×C4#6704211yescharacteristic
591C2×C4#6704211yescharacteristic
592C8—222no—
593C8—441no—
594C8—441no—
595C8—441no—
596C22—81no—
597C22—81no—
598C22—81no—
599C22—81no—
600C22—81no—
601C22—81no—
602C22—81no—
603C22C22×#432411yescharacteristic
604C22#1062335311yescharacteristic
605C22#1062335911yescharacteristic
606C22#1062336011yescharacteristic
607C22#1062336511yescharacteristic
608C22#1062336711yescharacteristic
609C22#1062336911yescharacteristic
610C4—22no—
611C4—22no—
612C4—22no—
613C4—41no—
614C4—41no—
615C4—41no—
616C4—81no—
617C4—81no—
618C4—81no—
619C4—442no—
620C4—442no—
621C4—442no—
622C4—881no—
623C4#1062323511yescharacteristic
624C4#1062323611yescharacteristic
625C4#1062323711yescharacteristic
626C4#1062324011yescharacteristic
627C2—161no—
628C2#1307266311yescharacteristic
629C2#1307864311yescharacteristic
630C2#1307883911yescharacteristic
631C2#1308047511yescharacteristic
632C2#1308058611yescharacteristic
633C2#1308159711yescharacteristic
634C2#1308169111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2512C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenter#2512D11
hypocenterC11#27066
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2512

Complements

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

NH ≅ G/Ntype
1. #13071672C2semidirect
2. #13070160C2semidirect
4. #13069862C2semidirect
7. #13069250C2semidirect
9. #13069191C2semidirect
10. #13069175C2semidirect
13. #13068618C2semidirect
14. C4×#66874C2semidirect
171. C11×C4⋊C4SD16semidirect
509. C4⋊C4#4324semidirect
526. C11#27066semidirect

Maximal subgroups

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

subgroupindex
#130716722
#130701602
#130699332
#130698622
#130696982
#130694692
#130692502
#130692402
#130691912
#130691752
#130689742
#130686182
C4×#668742
C11×#25122
#2706611