Finite Group Databasebeta

← #14775142

Subgroups — #14775142

Order 2816.

846 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622335C211yesmaximal, characteristic
2#13071619C211yesmaximal, characteristic
3#13071491C211yesmaximal, characteristic
4#13069354C211yesmaximal, characteristic, complemented
5#13069306C211yesmaximal, characteristic, complemented
6#13069251C211yesmaximal, characteristic, complemented
7#13069188C211yesmaximal, characteristic, complemented
8#13069188C211yesmaximal, characteristic, complemented
9#13069039C211yesmaximal, characteristic
10#13068887C211yesmaximal, characteristic, complemented
11#13068811C211yesmaximal, characteristic
12#13068513C211yesmaximal, characteristic, complemented
13#13068447C211yesmaximal, characteristic, complemented
14C2×#10622189C211yesmaximal, characteristic
15C11×#1752C211yesmaximal, characteristic
16C23×C8×C11C2211yescharacteristic
17C22×C4⋊Dic11C2211yescharacteristic
18C22×C4⋊Dic11C2211yescharacteristic
19C2×#66977C2211yescharacteristic
20C2×C4×Dic22C2211yescharacteristic
21C2×C11×C22⋊C8C2211yescharacteristic
22C2×C11×#97C2211yescharacteristic
23C2×C11×#97C2211yescharacteristic
24C4×C11×C22⋊C4C2211yescharacteristic
25#10622825C2211yescharacteristic
26C2×#66882C2211yescharacteristic
27C2×#66882C2211yescharacteristic
28C2×#66881C2211yescharacteristic
29C2×#66881C2211yescharacteristic
30C2×#66880C2211yescharacteristic
31C2×#66880C2211yescharacteristic
32C2×#66880C2211yescharacteristic
33C2×#66880C2211yescharacteristic
34#10622559—21no—
35#10622555—21no—
36C22⋊C4×Dic11—21no—
37C22⋊C4×Dic11—21no—
38C4×C4⋊Dic11C2211yescharacteristic
39C4×C4⋊Dic11C2211yescharacteristic
40C4×C4⋊Dic11C2211yescharacteristic
41#10622542C2211yescharacteristic
42#10622541C2211yescharacteristic
43#10622541C2211yescharacteristic
44#10622541C2211yescharacteristic
45#10622335C418yescomplemented
46#10622268—21no—
47#10622267—21no—
48#10622267—21no—
49#10622260—21no—
50C11×#336C2211yescharacteristic
51C11×#336C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622189C2211yescharacteristic
59#10622189C2211yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×Dic11—21no—
62C23×Dic11—21no—
63C22×Dic22C2311yescharacteristic
64C22×C8×C11—22no—
65C22×C8×C11—22no—
66C22×C8×C11—41no—
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C22×C8×C11C2311yescharacteristic
71C2×C11×C22⋊C4D411yescharacteristic
72C2×C11×C22⋊C4D411yescharacteristic
73C2×C42×C11C2311yescharacteristic
74C2×C42×C11C2311yescharacteristic
75C2×C22⋊Dic11—21no—
76C2×C22⋊Dic11—21no—
77C2×C4⋊Dic11—21no—
78C2×C4⋊Dic11—22no—
79C2×C4⋊Dic11—22no—
80C2×C4⋊Dic11—21no—
81C2×C4⋊Dic11—41no—
82C2×C4⋊Dic11C2×C414yes—
83C2×C4⋊Dic11C2311yescharacteristic
84C2×C4⋊Dic11C2311yescharacteristic
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4⋊Dic11C2311yescharacteristic
87C2×C4⋊Dic11C2311yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89C2×C4⋊Dic11C2311yescharacteristic
90#66977—22no—
91#66977C2×C414yes—
92C2×Dic11⋊C4—21no—
93C2×Dic11⋊C4—21no—
94C2×Dic11⋊C4—21no—
95C2×Dic11⋊C4—21no—
96C2×Dic11⋊C4—21no—
97C2×C4×Dic11—21no—
98C2×C4×Dic11—21no—
99C2×C4×Dic11—21no—
100C2×C4×Dic11—21no—
101C4×Dic22—22no—
102C4×Dic22—41no—
103C11×C22⋊C8C2×C414yes—
104C11×#97—22no—
105C11×#97—41no—
106C11×#95D411yescharacteristic
107C11×#95D411yescharacteristic
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117#66882C2×C414yescomplemented
118#66882C2×C414yescomplemented
119#66881—22no—
120#66881—41no—
121#66880—22no—
122#66880—41no—
123#66880C2×C414yescomplemented
124#66880C2×C414yescomplemented
125#22932—111nomaximal, Sylow
126C24×C11C2×D411yescharacteristic
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11C22×C412yes—
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11#4112yes—
138C22×C4×C11C2411yescharacteristic
139C22×Dic11—24no—
140C22×Dic11—21no—
141C22×Dic11—21no—
142C22×Dic11—21no—
143C22×Dic11—21no—
144C22×Dic11—21no—
145C22×Dic11—21no—
146C22×Dic11—21no—
147C22×Dic11—21no—
148C22×Dic11—42no—
149C22×Dic11—42no—
150C22×Dic11—81no—
151C22×Dic11—81no—
152C22×Dic11—81no—
153C2×Dic22—21no—
154C2×Dic22—21no—
155C2×Dic22—21no—
156C2×Dic22—21no—
157C2×Dic22—21no—
158C2×Dic22C22×C412yes—
159C2×C8×C11—21no—
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—44no—
169C2×C8×C11C22×C412yes—
170C2×C8×C11C22×C412yes—
171C2×C8×C11#4112yes—
172C11×C22⋊C4—22no—
173C11×C22⋊C4—22no—
174C42×C11—21no—
175C42×C11—21no—
176C42×C11—21no—
177C42×C11—21no—
178C22⋊Dic11—24no—
179C22⋊Dic11—42no—
180C4⋊Dic11—24no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11—21no—
186C4⋊Dic11—21no—
187C4⋊Dic11—21no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—42no—
192C4⋊Dic11C22×C412yes—
193C4⋊Dic11C22×C412yes—
194C4⋊Dic11C22×C412yes—
195C4⋊Dic11#4112yes—
196Dic11⋊C4—24no—
197Dic11⋊C4—42no—
198Dic11⋊C4—81no—
199Dic11⋊C4—81no—
200Dic11⋊C4—81no—
201C4×Dic11—42no—
202C4×Dic11—81no—
203C4×Dic11—81no—
204C4×Dic11—81no—
205C2×#484—111no—
206#2360—111no—
207#2345—111no—
208#1943—111no—
209#1935—111no—
210#1927—111no—
211#1918—111no—
212#1918—111no—
213#1892—111no—
214#1865—111no—
215#1853—111no—
216#1776—111no—
217#1763—111no—
218#1752D1111yescharacteristic
219C2×#340—111no—
220C23×C11—21no—
221C23×C11—21no—
222C23×C11—21no—
223C23×C11—21no—
224C23×C11C4×D412yes—
225C23×C11#13712yes—
226C23×C11#13712yes—
227C23×C11C22×D411yescharacteristic
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—22no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—22no—
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×C11C4×D412yes—
247C2×C4×C11C23×C411yescharacteristic
248C2×C4×C11C2×#4111yescharacteristic
249C2×C4×C11C2×#4111yescharacteristic
250C2×C4×C11C2×#4111yescharacteristic
251C2×C4×C11H(5,𝔽2)11yescharacteristic
252C2×C4×C112−1+411yescharacteristic
253C2×Dic11—22no—
254C2×Dic11—22no—
255C2×Dic11—22no—
256C2×Dic11—22no—
257C2×Dic11—22no—
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—
275C2×Dic11—41no—
276C2×Dic11—41no—
277C2×Dic11—84no—
278C2×Dic11—84no—
279Dic22—22no—
280Dic22—22no—
281Dic22—41no—
282Dic22—41no—
283C8×C11—22no—
284C8×C11—22no—
285C8×C11—22no—
286C8×C11—41no—
287C23×C8C2×D1111yescharacteristic
288C2×C22⋊Q8—111no—
289C2×C4×Q8—111no—
290C22×C4⋊C4—111no—
291C22×C4⋊C4—111no—
292#484—118no—
293C2×#107—111no—
294C2×#107—111no—
295C2×#106—111no—
296C2×#106—111no—
297C2×#103—111no—
298C2×#103—111no—
299C2×#103—111no—
300C2×#103—111no—
301C2×C22⋊C8C2×D1111yescharacteristic
302C2×#97C2×D1111yescharacteristic
303C2×#97C2×D1111yescharacteristic
304#391—111no—
305#389—111no—
306#389—111no—
307#389—111no—
308#389—221no—
309#387—221no—
310#387—221no—
311#387—221no—
312#385—221no—
313#380—111no—
314#380—221no—
315C4×C4⋊C4—111no—
316C4×C4⋊C4—111no—
317C4×C4⋊C4—111no—
318C4×C22⋊C4—221no—
319C4×C22⋊C4—221no—
320C4×C22⋊C4C2×D1111yescharacteristic
321#340—111no—
322#340—111no—
323#340—111no—
324#340—111no—
325#340—111no—
326#340—111no—
327#340—111no—
328#340—111no—
329#336C2×D1111yescharacteristic
330#336C2×D1111yescharacteristic
331C22×C11—22no—
332C22×C11—22no—
333C22×C11—22no—
334C22×C11—22no—
335C22×C11—22no—
336C22×C11—22no—
337C22×C11#44114yes—
338C22×C11C2×C4×D411yescharacteristic
339C22×C11#54611yescharacteristic
340C22×C11#54711yescharacteristic
341C22×C11C2×#13711yescharacteristic
342C22×C11C2×#13711yescharacteristic
343C22×C11#57611yescharacteristic
344C22×C11#57711yescharacteristic
345C4×C11—22no—
346C4×C11—41no—
347C4×C11—41no—
348C4×C11—41no—
349C4×C11—41no—
350C4×C11C4×#4111yescharacteristic
351C4×C11#52011yescharacteristic
352C4×C11#55111yescharacteristic
353C4×C11#55211yescharacteristic
354Dic11—42no—
355Dic11—42no—
356Dic11—42no—
357Dic11—42no—
358Dic11—42no—
359Dic11—81no—
360Dic11—81no—
361Dic11—81no—
362C22×Q8—111no—
363C23×C4—221no—
364C23×C4—221no—
365C23×C4C22×D1111yescharacteristic
366C22×C8—22no—
367C22×C8—22no—
368C22×C8—41no—
369C22×C8C22×D1111yescharacteristic
370C22×C8C22×D1111yescharacteristic
371C22×C8C22×D1111yescharacteristic
372C22×C8C22×D1111yescharacteristic
373C22⋊Q8—114no—
374C22⋊Q8—222no—
375C4×Q8—222no—
376C4×Q8—441no—
377C2×C4⋊C4—114no—
378C2×C4⋊C4—111no—
379C2×C4⋊C4—111no—
380C2×C4⋊C4—111no—
381C2×C4⋊C4—111no—
382C2×C4⋊C4—111no—
383C2×C4⋊C4—111no—
384C2×C4⋊C4—111no—
385C2×C4⋊C4—222no—
386C2×C4⋊C4—221no—
387C2×C4⋊C4—221no—
388C2×C4⋊C4—222no—
389C2×C4⋊C4—221no—
390C2×C4⋊C4—221no—
391C2×C4⋊C4—221no—
392C2×C4⋊C4—221no—
393C2×C4⋊C4—221no—
394C2×C4⋊C4—441no—
395C2×C22⋊C4—221no—
396C2×C22⋊C4—221no—
397C2×C22⋊C4D4411yescharacteristic
398C2×C22⋊C4D4411yescharacteristic
399C2×C42—221no—
400C2×C42—221no—
401C2×C42—221no—
402C2×C42—221no—
403C2×C42C22×D1111yescharacteristic
404C2×C42C22×D1111yescharacteristic
405#107—114no—
406#107—114no—
407#106—222no—
408#106—441no—
409#103—114no—
410#103—114no—
411#103—222no—
412#103—441no—
413C22⋊C8C4×D1114yes—
414#97—22no—
415#97—41no—
416#95—221no—
417#95—221no—
418#95—221no—
419#95—221no—
420#95—221no—
421#95—221no—
422#95—221no—
423#95—221no—
424#95—221no—
425#95D4411yescharacteristic
426#95D4411yescharacteristic
427C2×C11—24no—
428C2×C11#235911yescharacteristic
429C2×C11C2×#44111yescharacteristic
430C2×C11#294611yescharacteristic
431C2×C11#331411yescharacteristic
432C2×C11#332011yescharacteristic
433C2×C11#334411yescharacteristic
434C2×C11#334611yescharacteristic
435C24C2×D4411yescharacteristic
436C2×Q8—112no—
437C2×Q8—221no—
438C2×Q8—221no—
439C2×Q8—221no—
440C2×Q8—221no—
441C2×Q8—221no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—221no—
447C22×C4—221no—
448C22×C4—221no—
449C22×C4—221no—
450C22×C4—221no—
451C22×C4—224no—
452C22×C4—221no—
453C22×C4—221no—
454C22×C4—221no—
455C22×C4—442no—
456C22×C4—442no—
457C22×C4—881no—
458C22×C4—881no—
459C22×C4—881no—
460C22×C4C2×C4×D1112yes—
461C22×C4C2×D4411yescharacteristic
462C22×C4C2×D4411yescharacteristic
463C22×C4C2×D4411yescharacteristic
464C22×C4C2×D4411yescharacteristic
465C22×C4C2×D4411yescharacteristic
466C22×C4#433912yes—
467C22×C4C23×D1111yescharacteristic
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—44no—
478C2×C8C2×C4×D1112yes—
479C2×C8C2×C4×D1112yes—
480C2×C8#434112yes—
481C4⋊C4—112no—
482C4⋊C4—112no—
483C4⋊C4—112no—
484C4⋊C4—112no—
485C4⋊C4—224no—
486C4⋊C4—224no—
487C4⋊C4—221no—
488C4⋊C4—221no—
489C4⋊C4—221no—
490C4⋊C4—221no—
491C4⋊C4—221no—
492C4⋊C4—221no—
493C4⋊C4—221no—
494C4⋊C4—221no—
495C4⋊C4—221no—
496C4⋊C4—221no—
497C4⋊C4—442no—
498C4⋊C4—442no—
499C4⋊C4—881no—
500C4⋊C4—881no—
501C4⋊C4—881no—
502C22⋊C4—22no—
503C22⋊C4—22no—
504C22⋊C4—224no—
505C22⋊C4—442no—
506C42—21no—
507C42—21no—
508C42—21no—
509C42—21no—
510C42—442no—
511C42—881no—
512C42—881no—
513C42—881no—
514C11#2293211yescharacteristic, complemented, Sylow
515C23—21no—
516C23—21no—
517C23—21no—
518C23—21no—
519C23C4×D4412yes—
520C23#6696212yes—
521C23#6696212yes—
522C23C22×D4411yescharacteristic
523Q8—222no—
524Q8—222no—
525Q8—441no—
526Q8—441no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—222no—
546C2×C4—222no—
547C2×C4—222no—
548C2×C4—222no—
549C2×C4—222no—
550C2×C4—441no—
551C2×C4—441no—
552C2×C4—441no—
553C2×C4—441no—
554C2×C4—441no—
555C2×C4—441no—
556C2×C4—441no—
557C2×C4—441no—
558C2×C4—441no—
559C2×C4—441no—
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—884no—
570C2×C4—884no—
571C2×C4C4×D4412yes—
572C2×C4C22×C4×D1111yescharacteristic
573C2×C4C2×#433911yescharacteristic
574C2×C4C2×#434111yescharacteristic
575C2×C4#6703711yescharacteristic
576C2×C4#41×D1111yescharacteristic
577C2×C4#6704311yescharacteristic
578C8—22no—
579C8—22no—
580C8—22no—
581C8—41no—
582C22—22no—
583C22—22no—
584C22—22no—
585C22—22no—
586C22—22no—
587C22—22no—
588C22#1062232914yes—
589C22C2×C4×D4411yescharacteristic
590C22#1062308511yescharacteristic
591C22#1062308611yescharacteristic
592C22C2×#6696211yescharacteristic
593C22C2×#6696211yescharacteristic
594C22#1062328211yescharacteristic
595C22#1062328311yescharacteristic
596C4—22no—
597C4—41no—
598C4—41no—
599C4—41no—
600C4—41no—
601C4—442no—
602C4—442no—
603C4—442no—
604C4—442no—
605C4—442no—
606C4—881no—
607C4—881no—
608C4—881no—
609C4#1062302611yescharacteristic
610C4#1062306211yescharacteristic
611C4C4×#434111yescharacteristic
612C4#1062307711yescharacteristic
613C2—24no—
614C2#1307161011yescharacteristic
615C2C2×#1062232911yescharacteristic
616C2#1307745011yescharacteristic
617C2#1308069911yescharacteristic
618C2#1308078911yescharacteristic
619C2#1308107311yescharacteristic
620C2#1308110311yescharacteristic
subgroupG/H
centerC23C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1752C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenter#1752D11
hypocenterC11#22932
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #1752

Complements

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

NH ≅ G/Ntype
4. #13069354C2semidirect
5. #13069306C2semidirect
6. #13069251C2semidirect
7. #13069188C2semidirect
8. #13069188C2semidirect
10. #13068887C2semidirect
12. #13068513C2semidirect
13. #13068447C2semidirect
45. #10622335C4semidirect
117. #66882C2×C4semidirect
118. #66882C2×C4semidirect
123. #66880C2×C4semidirect
124. #66880C2×C4semidirect
514. C11#22932semidirect

Maximal subgroups

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

subgroupindex
C2×#106223352
#130716192
#130714912
#130693542
#130693062
#130692512
#130691882
#130690392
#130688872
#130688112
#130685132
#130684472
C2×#106221892
C11×#17522
#2293211