Finite Group Databasebeta

← #14758136

Subgroups — #14758136

Order 2816.

862 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622627C211yesmaximal, characteristic
2#13071259C211yesmaximal, characteristic, complemented
3#13071254C211yesmaximal, characteristic, complemented
4#13069489C211yesmaximal, characteristic
5#13069479C211yesmaximal, characteristic
6#13069358C211yesmaximal, characteristic, complemented
7#13069343C211yesmaximal, characteristic, complemented
8#13069314C211yesmaximal, characteristic, complemented
9#13069310C211yesmaximal, characteristic, complemented
10#13069300C211yesmaximal, characteristic, complemented
11#13069296C211yesmaximal, characteristic, complemented
12#13068514C211yesmaximal, characteristic, complemented
13C4×#66885C211yesmaximal, characteristic, complemented
14#13068302C211yesmaximal, characteristic, complemented
15C4×C11×#102C211yesmaximal, characteristic, complemented
16C2×C4×D4×C11C2211yescharacteristic
17C22×#4323C2211yescharacteristic
18C2×C4×D44C2211yescharacteristic
19C2×C11×#102C2211yescharacteristic
20C2×C11×#102C2211yescharacteristic
21C2×C4×C8×C11C2211yescharacteristic
22C4×C11×C4⋊C4C2211yescharacteristic
23#10622834C2211yescharacteristic
24#10622834C2211yescharacteristic
25C2×#66896C2211yescharacteristic
26#10622825—21no—
27#10622824—21no—
28C2×#66885C2211yescharacteristic
29C2×#66885C2211yescharacteristic
30C2×#66879C2211yescharacteristic
31C2×#66879C2211yescharacteristic
32C2×C8×Dic11C2211yescharacteristic
33C2×C8×Dic11C2211yescharacteristic
34#10622627C418yescomplemented
35#10622601C2211yescharacteristic
36#10622601C2211yescharacteristic
37#10622598C2211yescharacteristic
38#10622598C2211yescharacteristic
39#10622586C2211yescharacteristic
40#10622586C2211yescharacteristic
41C2×#66873C2211yescharacteristic
42C2×#66872C2211yescharacteristic
43C2×#66872C2211yescharacteristic
44C2×#66871C2211yescharacteristic
45#10622564—21no—
46#10622564—21no—
47#10622553—21no—
48#10622553—21no—
49C4×C4⋊Dic11C2211yescharacteristic
50#10622545C2211yescharacteristic
51C2×#66867C2211yescharacteristic
52#10622280—21no—
53#10622277—21no—
54C11×#340C2211yescharacteristic
55C11×#340C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60C22×D4×C11C2311yescharacteristic
61C23×C4×C11—21no—
62C22×D44C2311yescharacteristic
63C22×C4×D11—21no—
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C4×D4×C11—22no—
67C4×D4×C11C2×C414yes—
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C22⋊C4—21no—
72C2×C42×C11—21no—
73C2×C42×C11C2311yescharacteristic
74C2×C22⋊Dic11—21no—
75C2×C22⋊Dic11—21no—
76C2×C22⋊Dic11—21no—
77C2×C22⋊Dic11—21no—
78C2×#4323—22no—
79C2×#4323—22no—
80C2×#4323C2×C414yes—
81C2×(C2×D11)⋊C4—21no—
82C2×(C2×D11)⋊C4—21no—
83C2×(C2×D11)⋊C4—21no—
84C2×(C2×D11)⋊C4—21no—
85C2×(C2×D11)⋊C4—21no—
86C2×C4⋊Dic11—21no—
87C2×C4⋊Dic11—21no—
88C2×C4⋊Dic11C2311yescharacteristic
89C2×C4⋊Dic11C2311yescharacteristic
90C2×C4⋊Dic11C2311yescharacteristic
91C2×Dic11⋊C4—21no—
92C2×Dic11⋊C4—21no—
93C2×C4×Dic11—21no—
94C2×C4×Dic11C2311yescharacteristic
95C2×C4×Dic11C2311yescharacteristic
96C22×C11⋊C8C2311yescharacteristic
97C22×C11⋊C8C2311yescharacteristic
98C4×D44—22no—
99C4×D44C2×C414yes—
100C11×#102—22no—
101C11×#102—22no—
102C4×C8×C11—22no—
103C11×#95—21no—
104#66896C2×C414yes—
105C11⋊#95—21no—
106C11⋊#95—21no—
107C11⋊#95—21no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95D411yescharacteristic
111C11⋊#95D411yescharacteristic
112C11⋊#95D411yescharacteristic
113C11⋊#95D411yescharacteristic
114#66885—22no—
115#66885—22no—
116#66879—22no—
117#66879—22no—
118C8×Dic11—22no—
119C8×Dic11—22no—
120#66873C2×C414yes—
121#66872—22no—
122#66872C2×C414yes—
123#66871—22no—
124#66867C2×C414yes—
125#21290—111nomaximal, Sylow
126C24×C11—21no—
127C23×D11—21no—
128C2×D4×C11—21no—
129C2×D4×C11—21no—
130C2×D4×C11—21no—
131C2×D4×C11—21no—
132C2×D4×C11—21no—
133C2×D4×C11C22×C412yes—
134C22×C4×C11—21no—
135C22×C4×C11—24no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—81no—
139C22×C4×C11—81no—
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2411yescharacteristic
143C22×Dic11—21no—
144C22×Dic11—21no—
145C22×Dic11—21no—
146C22×Dic11C2×D411yescharacteristic
147C22×Dic11C2×D411yescharacteristic
148C22×Dic11C2×D411yescharacteristic
149C22×Dic11C2×D411yescharacteristic
150C2×D44—21no—
151C2×D44—21no—
152C2×D44—21no—
153C2×D44—21no—
154C2×D44—21no—
155C2×D44C22×C412yes—
156C2×C4×D11—24no—
157C2×C4×D11—81no—
158C2×C4×D11—81no—
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11#4112yes—
164C2×C8×C11#4112yes—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4C22×C412yes—
171C11×C22⋊C4—24no—
172C42×C11—81no—
173C42×C11C22×C412yes—
174C42×C11#4112yes—
175C22⋊Dic11—81no—
176C22⋊Dic11—81no—
177C22⋊Dic11—81no—
178C22⋊Dic11—81no—
179#4323—28no—
180(C2×D11)⋊C4—24no—
181(C2×D11)⋊C4—81no—
182(C2×D11)⋊C4—81no—
183(C2×D11)⋊C4—81no—
184(C2×D11)⋊C4—81no—
185C4⋊Dic11—21no—
186C4⋊Dic11—21no—
187C4⋊Dic11—21no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11—81no—
191C4⋊Dic11—81no—
192C4⋊Dic11C22×C412yes—
193Dic11⋊C4—81no—
194Dic11⋊C4—81no—
195C4×Dic11—21no—
196C4×Dic11—21no—
197C4×Dic11—21no—
198C4×Dic11—21no—
199C4×Dic11—81no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8C22×C412yes—
203C2×C11⋊C8C22×C412yes—
204C2×C11⋊C8#4112yes—
205C2×C11⋊C8#4112yes—
206C2×#442—111no—
207#2319—111no—
208#2319—111no—
209#1972—111no—
210#1970—111no—
211#1944—111no—
212#1941—111no—
213#1936—111no—
214#1936—111no—
215#1934—111no—
216#1934—111no—
217#1776—111no—
218C4×#102—111no—
219C4×#102D1111yescharacteristic, complemented
220#1726—111no—
221C23×C11—22no—
222C23×C11—41no—
223C23×C11—41no—
224C23×C11—41no—
225C23×C11—41no—
226C23×C11—41no—
227C23×C11—41no—
228C23×C11C22×D411yescharacteristic
229C22×D11—22no—
230C22×D11—41no—
231C22×D11—41no—
232C22×D11—41no—
233C22×D11—41no—
234C22×D11—41no—
235C22×D11—41no—
236D4×C11—22no—
237D4×C11—22no—
238D4×C11—41no—
239D4×C11—41no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—22no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—84no—
254C2×C4×C11C4×D412yes—
255C2×C4×C11C4×D412yes—
256C2×C4×C11C23×C411yescharacteristic
257C2×C4×C11C2×#4111yescharacteristic
258C2×C4×C11C2×#4111yescharacteristic
259C2×C4×C11C2×#4111yescharacteristic
260C2×C4×C11C2×#4111yescharacteristic
261C2×C4×C11C2×#4111yescharacteristic
262C2×Dic11—22no—
263C2×Dic11—21no—
264C2×Dic11—21no—
265C2×Dic11—21no—
266C2×Dic11—21no—
267C2×Dic11—21no—
268C2×Dic11—21no—
269C2×Dic11—21no—
270C2×Dic11—21no—
271C2×Dic11—21no—
272C2×Dic11—21no—
273C2×Dic11—21no—
274C2×Dic11—21no—
275C2×Dic11—41no—
276C2×Dic11—41no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283D44—22no—
284D44—22no—
285D44—41no—
286D44—41no—
287C4×D11—84no—
288C8×C11—22no—
289C8×C11—22no—
290C11⋊C8—22no—
291C11⋊C8#11714yes—
292C22×D8—111no—
293C2×C4×D4—111no—
294C2×C4×D4C2×D1111yescharacteristic
295#442—118no—
296C2×#107—111no—
297C2×#106—111no—
298C2×#106—111no—
299C2×#102—111no—
300C2×#102—111no—
301C2×#102—111no—
302C2×#102—111no—
303C2×#102C2×D1111yescharacteristic
304C2×#102C2×D1111yescharacteristic
305C2×#97—111no—
306C2×#97—111no—
307C2×#97—111no—
308C2×C4×C8—111no—
309C2×C4×C8—111no—
310C2×C4×C8C2×D1111yescharacteristic
311#390—111no—
312#390—111no—
313#390—111no—
314#390—111no—
315#389—111no—
316#389—111no—
317#389—111no—
318#389—111no—
319#388—221no—
320#388—221no—
321#388—221no—
322#388—221no—
323#381—221no—
324#381—221no—
325#380—221no—
326#380—221no—
327C4×C4⋊C4—111no—
328C4×C4⋊C4C2×D1111yescharacteristic
329#376—111no—
330#340—111no—
331#340—111no—
332#340—111no—
333#340—111no—
334#340C2×D1111yescharacteristic
335#340C2×D1111yescharacteristic
336C22×C11—42no—
337C22×C11—42no—
338C22×C11—42no—
339C22×C11—81no—
340C22×C11—81no—
341C22×C11—81no—
342C22×C11—81no—
343C22×C11C2×C4×D411yescharacteristic
344C22×C11#53211yescharacteristic
345C22×C11#53211yescharacteristic
346C22×C11#57611yescharacteristic
347C22×C11#57611yescharacteristic
348C22×C11#57711yescharacteristic
349C22×C11#57711yescharacteristic
350C2×D11—42no—
351C2×D11—42no—
352C2×D11—42no—
353C2×D11—81no—
354C2×D11—81no—
355C2×D11—81no—
356C2×D11—81no—
357C4×C11—22no—
358C4×C11—22no—
359C4×C11—42no—
360C4×C11—81no—
361C4×C11—81no—
362C4×C11C2×#11711yescharacteristic
363C4×C11C4×#4111yescharacteristic
364C4×C11#52911yescharacteristic
365C4×C11#52911yescharacteristic
366Dic11—41no—
367Dic11—41no—
368Dic11—41no—
369Dic11—41no—
370Dic11—42no—
371Dic11—81no—
372Dic11—81no—
373C22×D4—111no—
374C22×D4C22×D1111yescharacteristic
375C23×C4—21no—
376C23×C4—221no—
377C2×D8—114no—
378C2×D8—222no—
379C2×D8—222no—
380C22×C8—111no—
381C22×C8—111no—
382C22×C8C22×D1111yescharacteristic
383C22×C8C22×D1111yescharacteristic
384C4×D4—22no—
385C4×D4—114no—
386C4×D4—222no—
387C4×D4C4×D1114yes—
388C2×C4⋊C4—111no—
389C2×C4⋊C4—111no—
390C2×C4⋊C4—111no—
391C2×C4⋊C4—221no—
392C2×C4⋊C4—221no—
393C2×C4⋊C4—221no—
394C2×C4⋊C4—221no—
395C2×C4⋊C4C22×D1111yescharacteristic
396C2×C4⋊C4C22×D1111yescharacteristic
397C2×C4⋊C4C22×D1111yescharacteristic
398C2×C22⋊C4—21no—
399C2×C22⋊C4—221no—
400C2×C22⋊C4—221no—
401C2×C22⋊C4—221no—
402C2×C22⋊C4—221no—
403C2×C22⋊C4—221no—
404C2×C22⋊C4—221no—
405C2×C22⋊C4—221no—
406C2×C22⋊C4—221no—
407C2×C22⋊C4—221no—
408C2×C42—21no—
409C2×C42—111no—
410C2×C42—111no—
411C2×C42—221no—
412C2×C42C22×D1111yescharacteristic
413#107—222no—
414#106—114no—
415#106—222no—
416#102—22no—
417#102—22no—
418#102—114no—
419#102—114no—
420#102—222no—
421#102—222no—
422#97—114no—
423#97—222no—
424#97—222no—
425C4×C8—22no—
426C4×C8—222no—
427C4×C8—222no—
428#95—21no—
429#95—111no—
430#95—111no—
431#95—111no—
432#95—111no—
433#95—221no—
434#95—221no—
435#95—221no—
436#95—221no—
437#95—221no—
438C2×C11—82no—
439C2×C11#229311yescharacteristic
440C2×C11#294611yescharacteristic
441C2×C11#294611yescharacteristic
442C2×C11#317311yescharacteristic
443C2×C11#317611yescharacteristic
444C2×C11#317911yescharacteristic
445C2×C11#317911yescharacteristic
446D11—82no—
447C24—21no—
448C24—221no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—112no—
455C2×D4—221no—
456C2×D4—221no—
457C2×D4—221no—
458C2×D4—221no—
459C2×D4—221no—
460C2×D4C2×C4×D1112yes—
461C22×C4—21no—
462C22×C4—24no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—81no—
466C22×C4—81no—
467C22×C4—111no—
468C22×C4—111no—
469C22×C4—111no—
470C22×C4—111no—
471C22×C4—221no—
472C22×C4—224no—
473C22×C4—221no—
474C22×C4—221no—
475C22×C4—881no—
476C22×C4—881no—
477C22×C4D4×D1111yescharacteristic
478C22×C4D4×D1111yescharacteristic
479C22×C4C23×D1111yescharacteristic
480D8—228no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—112no—
486C2×C8—112no—
487C2×C8—112no—
488C2×C8—112no—
489C2×C8—221no—
490C2×C8—221no—
491C2×C8#433912yes—
492C2×C8#433912yes—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—112no—
499C4⋊C4—221no—
500C4⋊C4—221no—
501C4⋊C4—221no—
502C4⋊C4—221no—
503C4⋊C4—221no—
504C4⋊C4—881no—
505C4⋊C4—881no—
506C4⋊C4—881no—
507C4⋊C4—881no—
508C4⋊C4C2×C4×D1112yes—
509C22⋊C4—24no—
510C22⋊C4—224no—
511C22⋊C4—881no—
512C22⋊C4—881no—
513C22⋊C4—881no—
514C22⋊C4—881no—
515C22⋊C4—881no—
516C22⋊C4—881no—
517C22⋊C4—881no—
518C22⋊C4—881no—
519C42—81no—
520C42—221no—
521C42—221no—
522C42—221no—
523C42—221no—
524C42—881no—
525C42C2×C4×D1112yes—
526C42#434112yes—
527C11#2129011yescharacteristic, complemented, Sylow
528C23—22no—
529C23—41no—
530C23—41no—
531C23—41no—
532C23—41no—
533C23—41no—
534C23—41no—
535C23—222no—
536C23—441no—
537C23—441no—
538C23—441no—
539C23—441no—
540C23—441no—
541C23—441no—
542C23C2×D4×D1111yescharacteristic
543D4—22no—
544D4—22no—
545D4—41no—
546D4—41no—
547D4—222no—
548D4—222no—
549D4—441no—
550D4—441no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—22no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—84no—
565C2×C4—222no—
566C2×C4—221no—
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—221no—
578C2×C4—441no—
579C2×C4—441no—
580C2×C4—441no—
581C2×C4—441no—
582C2×C4—441no—
583C2×C4—441no—
584C2×C4—441no—
585C2×C4—441no—
586C2×C4—884no—
587C2×C4(C22⋊D11)⋊C412yes—
588C2×C4(C22⋊D11)⋊C412yes—
589C2×C4C22×C4×D1111yescharacteristic
590C2×C4C2×#433911yescharacteristic
591C2×C4C2×#433911yescharacteristic
592C2×C4C2×#434111yescharacteristic
593C2×C4#41×D1111yescharacteristic
594C2×C4#41×D1111yescharacteristic
595C8—22no—
596C8—22no—
597C8—114no—
598C8—222no—
599C22—42no—
600C22—42no—
601C22—42no—
602C22—81no—
603C22—81no—
604C22—81no—
605C22—81no—
606C22—442no—
607C22—442no—
608C22—442no—
609C22—881no—
610C22—881no—
611C22—881no—
612C22—881no—
613C22C2×(C22⋊D11)⋊C411yescharacteristic
614C22#1062307911yescharacteristic
615C22#1062307911yescharacteristic
616C22#1062328811yescharacteristic
617C22#1062329311yescharacteristic
618C22#1062330011yescharacteristic
619C22#1062330111yescharacteristic
620C4—22no—
621C4—22no—
622C4—42no—
623C4—81no—
624C4—81no—
625C4—441no—
626C4—441no—
627C4—442no—
628C4—441no—
629C4—441no—
630C4—881no—
631C4—881no—
632C4C4×#433911yescharacteristic
633C4D11×#11711yescharacteristic
634C4#1062306911yescharacteristic
635C4#1062306911yescharacteristic
636C2—82no—
637C2—882no—
638C2#1307107911yescharacteristic
639C2#1307744211yescharacteristic
640C2#1307745111yescharacteristic
641C2#1307922911yescharacteristic
642C2#1307926211yescharacteristic
643C2#1307929511yescharacteristic
644C2#1307930311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC4×C11×#102C2
socleC23×C11C22×D4
prime radicalC22×#4323C22
cosocleC22×C4×C11C24
hypercenterC4×#102D11
hypocenterC11#21290
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×#102

Complements

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

NH ≅ G/Ntype
2. #13071259C2semidirect
3. #13071254C2semidirect
6. #13069358C2semidirect
7. #13069343C2semidirect
8. #13069314C2semidirect
9. #13069310C2semidirect
10. #13069300C2semidirect
11. #13069296C2semidirect
12. #13068514C2semidirect
13. C4×#66885C2semidirect
14. #13068302C2semidirect
15. C4×C11×#102C2semidirect
34. #10622627C4semidirect
219. C4×#102D11semidirect
527. C11#21290semidirect

Maximal subgroups

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

subgroupindex
C2×#106226272
#130712592
#130712542
#130694892
#130694792
#130693582
#130693432
#130693142
#130693102
#130693002
#130692962
#130685142
C4×#668852
#130683022
C4×C11×#1022
#2129011