Finite Group Databasebeta

← #14775191

Subgroups — #14775191

Order 2816.

858 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622648C211yesmaximal, characteristic
2#13071658C211yesmaximal, characteristic
3#13071503C211yesmaximal, characteristic, complemented
4#13069353C211yesmaximal, characteristic, complemented
5#13069310C211yesmaximal, characteristic, complemented
6#13069246C211yesmaximal, characteristic, complemented
7#13069197C211yesmaximal, characteristic, complemented
8#13069185C211yesmaximal, characteristic, complemented
9#13068861C211yesmaximal, characteristic, complemented
10#13068813C211yesmaximal, characteristic, complemented
11#13068512C211yesmaximal, characteristic, complemented
12#13068443C211yesmaximal, characteristic, complemented
13#13068392C211yesmaximal, characteristic, complemented
14#13068333C211yesmaximal, characteristic, complemented
15C11×#1893C211yesmaximal, characteristic
16C23×C8×C11C2211yescharacteristic
17C2×C11×#121C2211yescharacteristic
18C2×D4×Dic11C2211yescharacteristic
19C2×#66979C2211yescharacteristic
20C2×#66979C2211yescharacteristic
21C2×C11×#102C2211yescharacteristic
22C2×C11×#102C2211yescharacteristic
23C11×#380C2211yescharacteristic
24#10622834—21no—
25#10622834C2211yescharacteristic
26#10622833—21no—
27C2×#66896C2211yescharacteristic
28C2×#66896C2211yescharacteristic
29C4×C22⋊Dic11C2211yescharacteristic
30C2×C22⋊(C11⋊C8)C2211yescharacteristic
31C2×#66879C2211yescharacteristic
32C2×#66879C2211yescharacteristic
33#10622648C418yescomplemented
34#10622598C2211yescharacteristic
35C4⋊C4×Dic11C2211yescharacteristic
36C4⋊C4×Dic11C2211yescharacteristic
37C4⋊C4×Dic11C2211yescharacteristic
38#10622586C2211yescharacteristic
39#10622586C2211yescharacteristic
40C2×#66872C2211yescharacteristic
41C2×#66872C2211yescharacteristic
42C2×#66871C2211yescharacteristic
43C2×#66871C2211yescharacteristic
44#10622564—21no—
45#10622558—21no—
46#10622558—21no—
47C22⋊C4×Dic11—21no—
48#10622263—21no—
49#10622261—21no—
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60C22×D4×C11—21no—
61C22×D4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×Dic11—21no—
64C22×C8×C11—22no—
65C22×C8×C11—22no—
66C22×C8×C11—41no—
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C11×#121—22no—
70C11×#121C2×C414yes—
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C22⋊C4—21no—
75C2×C11×C22⋊C4—21no—
76C2×C22⋊Dic11—21no—
77C2×C22⋊Dic11—21no—
78C2×C22⋊Dic11—21no—
79C2×C22⋊Dic11—21no—
80C2×C22⋊Dic11—21no—
81C2×C22⋊Dic11D411yescharacteristic
82C2×C22⋊Dic11D411yescharacteristic
83D4×Dic11—22no—
84D4×Dic11—41no—
85#66979—22no—
86#66979—22no—
87#66979—41no—
88#66979C2×C414yescomplemented
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×Dic11⋊C4—21no—
95C2×Dic11⋊C4—21no—
96C2×C4×Dic11—21no—
97C2×C4×Dic11—21no—
98C2×C4×Dic11—21no—
99C2×C4×Dic11—21no—
100C2×C4×Dic11—21no—
101C2×C4×Dic11C2311yescharacteristic
102C2×C4×Dic11C2311yescharacteristic
103C22×C11⋊C8C2311yescharacteristic
104C22×C11⋊C8C2311yescharacteristic
105C11×#102—22no—
106C11×#102—41no—
107C11×#95—21no—
108#66896C2×C414yes—
109#66896C2×C414yes—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95D411yescharacteristic
117C11⋊#95D411yescharacteristic
118C22⋊(C11⋊C8)C2×C414yescomplemented
119#66879—22no—
120#66879—41no—
121#66872—41no—
122#66872C2×C414yescomplemented
123#66871—22no—
124#66871C2×C414yescomplemented
125#22935—111nomaximal, Sylow
126C24×C11—21no—
127C24×C11C2×D411yescharacteristic
128C2×D4×C11—24no—
129C2×D4×C11—21no—
130C2×D4×C11—21no—
131C2×D4×C11—21no—
132C2×D4×C11—21no—
133C2×D4×C11—21no—
134C2×D4×C11—81no—
135C2×D4×C11—81no—
136C2×D4×C11C22×C412yes—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11C22×C412yes—
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11#4112yes—
147C22×C4×C11C2411yescharacteristic
148C22×Dic11—21no—
149C22×Dic11—21no—
150C22×Dic11—21no—
151C22×Dic11—21no—
152C22×Dic11—42no—
153C22×Dic11—42no—
154C22×Dic11—81no—
155C22×Dic11C2×D411yescharacteristic
156C22×Dic11C2×D411yescharacteristic
157C22×Dic11C2×D411yescharacteristic
158C22×Dic11C2×D411yescharacteristic
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C2×C8×C11—44no—
165C2×C8×C11#4112yes—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4C22×C412yes—
172C11×C22⋊C4—24no—
173C11×C22⋊C4—81no—
174C22⋊Dic11—24no—
175C22⋊Dic11—41no—
176C22⋊Dic11—41no—
177C22⋊Dic11—42no—
178C22⋊Dic11—42no—
179C22⋊Dic11—42no—
180C22⋊Dic11—81no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11—21no—
186C4⋊Dic11—81no—
187C4⋊Dic11C22×C412yes—
188C4⋊Dic11C22×C412yes—
189C4⋊Dic11#4112yes—
190Dic11⋊C4—81no—
191Dic11⋊C4—81no—
192C4×Dic11—24no—
193C4×Dic11—21no—
194C4×Dic11—21no—
195C4×Dic11—21no—
196C4×Dic11—21no—
197C4×Dic11—42no—
198C4×Dic11—42no—
199C4×Dic11—42no—
200C4×Dic11—81no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8C22×C412yes—
206C2×C11⋊C8C22×C412yes—
207C2×#482—111no—
208#2363—111no—
209#2346—111no—
210#1943—111no—
211#1936—111no—
212#1926—111no—
213#1919—111no—
214#1918—111no—
215#1893D1111yescharacteristic
216#1862—111no—
217#1854—111no—
218#1776—111no—
219#1762—111no—
220#1752—111no—
221#1735—111no—
222C23×C11—21no—
223C23×C11—21no—
224C23×C11—21no—
225C23×C11—21no—
226C23×C11—21no—
227C23×C11—21no—
228C23×C11—22no—
229C23×C11—41no—
230C23×C11—41no—
231C23×C11—41no—
232C23×C11—41no—
233C23×C11—41no—
234C23×C11—41no—
235C23×C11C4×D412yes—
236C23×C11C22×D411yescharacteristic
237D4×C11—22no—
238D4×C11—22no—
239D4×C11—41no—
240D4×C11—41no—
241D4×C11—84no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—22no—
245C2×C4×C11—22no—
246C2×C4×C11—22no—
247C2×C4×C11—22no—
248C2×C4×C11—22no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11C4×D412yes—
258C2×C4×C11C23×C411yescharacteristic
259C2×C4×C11C2×#4111yescharacteristic
260C2×C4×C11C2×#4111yescharacteristic
261C2×C4×C11C2×#4111yescharacteristic
262C2×C4×C11H(5,𝔽2)11yescharacteristic
263C2×C4×C112−1+411yescharacteristic
264C2×Dic11—22no—
265C2×Dic11—22no—
266C2×Dic11—21no—
267C2×Dic11—21no—
268C2×Dic11—22no—
269C2×Dic11—21no—
270C2×Dic11—21no—
271C2×Dic11—21no—
272C2×Dic11—21no—
273C2×Dic11—21no—
274C2×Dic11—21no—
275C2×Dic11—21no—
276C2×Dic11—21no—
277C2×Dic11—21no—
278C2×Dic11—21no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11—84no—
289C8×C11—22no—
290C8×C11—41no—
291C11⋊C8—22no—
292C11⋊C8—22no—
293C23×C8C2×D1111yescharacteristic
294C2×#121C2×D1111yescharacteristic
295C2×C4×D4—111no—
296C2×#117—111no—
297C2×#117—111no—
298#482—118no—
299C2×#107—111no—
300C2×#107—111no—
301C2×#106—111no—
302C2×#106—111no—
303C2×#102—111no—
304C2×#102—111no—
305C2×#102C2×D1111yescharacteristic
306C2×#102C2×D1111yescharacteristic
307C2×C22⋊C8—111no—
308C2×#97—111no—
309C2×#97—111no—
310#390—111no—
311#390—221no—
312#389—111no—
313#389—111no—
314#389—111no—
315#388—221no—
316#388—221no—
317#388—221no—
318#386—221no—
319#382—221no—
320#380C2×D1111yescharacteristic
321C4×C4⋊C4—111no—
322C4×C4⋊C4—111no—
323C4×C4⋊C4—111no—
324C4×C22⋊C4—111no—
325C4×C22⋊C4—221no—
326#376—221no—
327#340—111no—
328#340—111no—
329#340—111no—
330#340—111no—
331#340—111no—
332#340—111no—
333#340C2×D1111yescharacteristic
334#340C2×D1111yescharacteristic
335#336—111no—
336#336—111no—
337C22×C11—22no—
338C22×C11—22no—
339C22×C11—22no—
340C22×C11—41no—
341C22×C11—41no—
342C22×C11—41no—
343C22×C11—41no—
344C22×C11—42no—
345C22×C11—42no—
346C22×C11—42no—
347C22×C11—81no—
348C22×C11—81no—
349C22×C11—81no—
350C22×C11—81no—
351C22×C11C2×C4×D411yescharacteristic
352C22×C11#54611yescharacteristic
353C22×C11#54711yescharacteristic
354C22×C11#57511yescharacteristic
355C22×C11#57511yescharacteristic
356C22×C11#57611yescharacteristic
357C22×C11#57711yescharacteristic
358C4×C11—22no—
359C4×C11—42no—
360C4×C11—81no—
361C4×C11—81no—
362C4×C11C4×#4111yescharacteristic
363C4×C11#52011yescharacteristic
364C4×C11#55111yescharacteristic
365C4×C11#55211yescharacteristic
366Dic11—41no—
367Dic11—41no—
368Dic11—42no—
369Dic11—42no—
370Dic11—41no—
371Dic11—41no—
372Dic11—42no—
373Dic11—81no—
374C22×D4—21no—
375C22×D4C22×D1111yescharacteristic
376C23×C4—221no—
377C23×C4C22×D1111yescharacteristic
378C22×C8—22no—
379C22×C8—22no—
380C22×C8—41no—
381C22×C8—111no—
382C22×C8—111no—
383C22×C8C22×D1111yescharacteristic
384C22×C8C22×D1111yescharacteristic
385#121—22no—
386#121C4×D1114yes—
387C4×D4—222no—
388C4×D4—441no—
389#117—114no—
390#117—222no—
391#117—222no—
392#117—441no—
393C2×C4⋊C4—111no—
394C2×C4⋊C4—111no—
395C2×C4⋊C4—111no—
396C2×C4⋊C4—111no—
397C2×C4⋊C4—221no—
398C2×C4⋊C4—221no—
399C2×C4⋊C4—221no—
400C2×C4⋊C4C22×D1111yescharacteristic
401C2×C4⋊C4C22×D1111yescharacteristic
402C2×C4⋊C4C22×D1111yescharacteristic
403C2×C22⋊C4—21no—
404C2×C22⋊C4—21no—
405C2×C22⋊C4—111no—
406C2×C22⋊C4—111no—
407C2×C22⋊C4—221no—
408C2×C22⋊C4—221no—
409C2×C22⋊C4—221no—
410C2×C22⋊C4—221no—
411C2×C22⋊C4—221no—
412C2×C42—111no—
413C2×C42—111no—
414C2×C42—221no—
415C2×C42—221no—
416C2×C42—221no—
417C2×C42—221no—
418C2×C42—221no—
419#107—114no—
420#107—222no—
421#106—114no—
422#106—441no—
423#102—22no—
424#102—41no—
425#102—114no—
426#102—114no—
427C22⋊C8—114no—
428#97—222no—
429#97—441no—
430#95—21no—
431#95—111no—
432#95—111no—
433#95—221no—
434#95—221no—
435#95—221no—
436#95—221no—
437#95—221no—
438#95—221no—
439C2×C11—42no—
440C2×C11—82no—
441C2×C11#235911yescharacteristic
442C2×C11#294311yescharacteristic
443C2×C11#294611yescharacteristic
444C2×C11#331711yescharacteristic
445C2×C11#331911yescharacteristic
446C2×C11#334711yescharacteristic
447C2×C11#334811yescharacteristic
448C24—21no—
449C24D4×D1111yescharacteristic
450C2×D4—24no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—81no—
457C2×D4—81no—
458C2×D4C2×C4×D1112yes—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—111no—
467C22×C4—111no—
468C22×C4—111no—
469C22×C4—111no—
470C22×C4—221no—
471C22×C4—221no—
472C22×C4—221no—
473C22×C4—221no—
474C22×C4—442no—
475C22×C4—442no—
476C22×C4—881no—
477C22×C4C2×C4×D1112yes—
478C22×C4D4×D1111yescharacteristic
479C22×C4#434112yes—
480C22×C4C23×D1111yescharacteristic
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—44no—
487C2×C8—112no—
488C2×C8—112no—
489C2×C8—221no—
490C2×C8—221no—
491C2×C8—221no—
492C2×C8—221no—
493C2×C8#434112yes—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—112no—
500C4⋊C4—112no—
501C4⋊C4—112no—
502C4⋊C4—221no—
503C4⋊C4—221no—
504C4⋊C4—221no—
505C4⋊C4—221no—
506C4⋊C4—221no—
507C4⋊C4—881no—
508C4⋊C4—881no—
509C4⋊C4—881no—
510C4⋊C4C2×C4×D1112yes—
511C22⋊C4—24no—
512C22⋊C4—81no—
513C22⋊C4—224no—
514C22⋊C4—441no—
515C22⋊C4—441no—
516C22⋊C4—442no—
517C22⋊C4—442no—
518C22⋊C4—442no—
519C22⋊C4—881no—
520C42—224no—
521C42—221no—
522C42—221no—
523C42—221no—
524C42—221no—
525C42—442no—
526C42—442no—
527C42—442no—
528C42—881no—
529C11#2293511yescharacteristic, complemented, Sylow
530C23—21no—
531C23—21no—
532C23—21no—
533C23—21no—
534C23—21no—
535C23—21no—
536C23—22no—
537C23—41no—
538C23—41no—
539C23—41no—
540C23—41no—
541C23—41no—
542C23—41no—
543C23(C22⋊D11)⋊C412yes—
544C23C2×D4×D1111yescharacteristic
545D4—22no—
546D4—22no—
547D4—41no—
548D4—41no—
549D4—84no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—222no—
566C2×C4—222no—
567C2×C4—221no—
568C2×C4—221no—
569C2×C4—221no—
570C2×C4—221no—
571C2×C4—221no—
572C2×C4—221no—
573C2×C4—221no—
574C2×C4—221no—
575C2×C4—221no—
576C2×C4—221no—
577C2×C4—222no—
578C2×C4—221no—
579C2×C4—221no—
580C2×C4—441no—
581C2×C4—441no—
582C2×C4—441no—
583C2×C4—441no—
584C2×C4—441no—
585C2×C4—441no—
586C2×C4—441no—
587C2×C4—441no—
588C2×C4—441no—
589C2×C4—884no—
590C2×C4(C22⋊D11)⋊C412yes—
591C2×C4C22×C4×D1111yescharacteristic
592C2×C4C2×#434111yescharacteristic
593C2×C4C2×#434111yescharacteristic
594C2×C4#6703711yescharacteristic
595C2×C4#41×D1111yescharacteristic
596C2×C4#6704311yescharacteristic
597C8—22no—
598C8—41no—
599C8—222no—
600C8—222no—
601C22—22no—
602C22—22no—
603C22—22no—
604C22—41no—
605C22—41no—
606C22—41no—
607C22—41no—
608C22—42no—
609C22—42no—
610C22—42no—
611C22—81no—
612C22—81no—
613C22—81no—
614C22—81no—
615C22C2×(C22⋊D11)⋊C411yescharacteristic
616C22#1062314111yescharacteristic
617C22#1062314211yescharacteristic
618C22#1062328811yescharacteristic
619C22#1062329311yescharacteristic
620C22#1062329911yescharacteristic
621C22#1062329911yescharacteristic
622C4—22no—
623C4—42no—
624C4—81no—
625C4—81no—
626C4—441no—
627C4—441no—
628C4—442no—
629C4—441no—
630C4—442no—
631C4—441no—
632C4—442no—
633C4—881no—
634C4C4×#434111yescharacteristic
635C4#1062307711yescharacteristic
636C4#1062311811yescharacteristic
637C4#1062318111yescharacteristic
638C2—42no—
639C2—82no—
640C2#1307161411yescharacteristic
641C2#1307741211yescharacteristic
642C2#1307744211yescharacteristic
643C2#1308074811yescharacteristic
644C2#1308077811yescharacteristic
645C2#1308112211yescharacteristic
646C2#1308113711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1893C2
socleC23×C11C22×D4
prime radicalC2×C11×#121C22
cosocleC22×C4×C11C24
hypercenter#1893D11
hypocenterC11#22935
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1893

Complements

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

NH ≅ G/Ntype
3. #13071503C2semidirect
4. #13069353C2semidirect
5. #13069310C2semidirect
6. #13069246C2semidirect
7. #13069197C2semidirect
8. #13069185C2semidirect
9. #13068861C2semidirect
10. #13068813C2semidirect
11. #13068512C2semidirect
12. #13068443C2semidirect
13. #13068392C2semidirect
14. #13068333C2semidirect
33. #10622648C4semidirect
88. #66979C2×C4semidirect
118. C22⋊(C11⋊C8)C2×C4semidirect
122. #66872C2×C4semidirect
124. #66871C2×C4semidirect
529. C11#22935semidirect

Maximal subgroups

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

subgroupindex
C2×#106226482
#130716582
#130715032
#130693532
#130693102
#130692462
#130691972
#130691852
#130688612
#130688132
#130685122
#130684432
#130683922
#130683332
C11×#18932
#2293511