Finite Group Databasebeta

← #14773540

Subgroups — #14773540

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×#10622369C211yesmaximal, characteristic
2#13071588C211yesmaximal, characteristic, complemented
3#13071585C211yesmaximal, characteristic, complemented
4#13069481C211yesmaximal, characteristic
5#13069479C211yesmaximal, characteristic
6#13069245C211yesmaximal, characteristic, complemented
7#13069244C211yesmaximal, characteristic, complemented
8#13069242C211yesmaximal, characteristic, complemented
9#13068777C211yesmaximal, characteristic, complemented
10#13068625C211yesmaximal, characteristic, complemented
11#13068624C211yesmaximal, characteristic, complemented
12C4×#66871C211yesmaximal, characteristic, complemented
13#13068508C211yesmaximal, characteristic, complemented
14#13068477C211yesmaximal, characteristic, complemented
15C11×#1926C211yesmaximal, characteristic, complemented
16C2×D4×Dic11C2211yescharacteristic
17C22×#4323C2211yescharacteristic
18C2×#66946C2211yescharacteristic
19C2×C11×#106C2211yescharacteristic
20C2×C11×#102C2211yescharacteristic
21C2×C11×#102C2211yescharacteristic
22C11×#390C2211yescharacteristic
23C4×C11×C4⋊C4C2211yescharacteristic
24#10622834C2211yescharacteristic
25C2×#66896C2211yescharacteristic
26C2×#66885C2211yescharacteristic
27C2×#66885C2211yescharacteristic
28C2×#66881C2211yescharacteristic
29C2×Dic11⋊C8C2211yescharacteristic
30C2×C8×Dic11C2211yescharacteristic
31C2×C8×Dic11C2211yescharacteristic
32#10622601C2211yescharacteristic
33#10622590C2211yescharacteristic
34#10622590C2211yescharacteristic
35C4⋊C4×Dic11C2211yescharacteristic
36C4⋊C4×Dic11C2211yescharacteristic
37C2×#66873C2211yescharacteristic
38C2×#66871C2211yescharacteristic
39C2×#66871C2211yescharacteristic
40C2×#66871C2211yescharacteristic
41#10622558—21no—
42#10622557—21no—
43#10622556—21no—
44C22⋊C4×Dic11—21no—
45#10622553—21no—
46#10622552C2211yescharacteristic
47C4×(C2×D11)⋊C4—21no—
48C4×C4⋊Dic11C2211yescharacteristic
49C4×Dic11⋊C4C2211yescharacteristic
50C2×C4×C11⋊C8C2211yescharacteristic
51#10622369C418yescomplemented
52#10622282—21no—
53#10622277—21no—
54C11×#340C2211yescharacteristic
55C11×#336C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60C22×D4×C11C2311yescharacteristic
61C23×Dic11—21no—
62C22×D44C2311yescharacteristic
63C22×C4×D11—21no—
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C22⋊C4—21no—
70C2×C11×C22⋊C4—21no—
71C2×C42×C11—21no—
72C2×C42×C11C2311yescharacteristic
73C2×C22⋊Dic11—21no—
74C2×C22⋊Dic11—21no—
75C2×C22⋊Dic11—21no—
76D4×Dic11—22no—
77D4×Dic11C2×C414yes—
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⋊Dic11C2311yescharacteristic
87C2×C4⋊Dic11C2311yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89C2×Dic11⋊C4D411yescharacteristic
90C2×Dic11⋊C4D411yescharacteristic
91C2×C4×Dic11—21no—
92C2×C4×Dic11—21no—
93C2×C4×Dic11—21no—
94C2×C4×Dic11C2311yescharacteristic
95C2×C4×Dic11C2311yescharacteristic
96C22×C11⋊C8C2311yescharacteristic
97C22×C11⋊C8C2311yescharacteristic
98#66946—22no—
99#66946C2×C414yes—
100C11×#106—41no—
101C11×#102—41no—
102C11×#102C2×C414yes—
103C11×#95—21no—
104#66896—41no—
105C11⋊#95—21no—
106C11⋊#95—21no—
107C11⋊#95—21no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95D411yescharacteristic
113C11⋊#95D411yescharacteristic
114#66885—41no—
115#66885C2×C414yes—
116#66881—41no—
117Dic11⋊C8—22no—
118C8×Dic11—22no—
119C8×Dic11C2×C414yes—
120#66873—41no—
121#66871—22no—
122#66871—22no—
123#66871C2×C414yes—
124C4×C11⋊C8—22no—
125#22810—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—21no—
136C22×C4×C11—21no—
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2411yescharacteristic
140C22×Dic11—24no—
141C22×Dic11—21no—
142C22×Dic11—21no—
143C22×Dic11—21no—
144C22×Dic11—81no—
145C22×Dic11—81no—
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—21no—
164C2×C8×C11C22×C412yes—
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—42no—
172C11×C22⋊C4—81no—
173C42×C11—21no—
174C42×C11—21no—
175C42×C11—81no—
176C22⋊Dic11—24no—
177C22⋊Dic11—42no—
178C22⋊Dic11—81no—
179#4323—28no—
180(C2×D11)⋊C4—24no—
181(C2×D11)⋊C4—42no—
182(C2×D11)⋊C4—42no—
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⋊Dic11C22×C412yes—
191Dic11⋊C4—22no—
192Dic11⋊C4—22no—
193C4×Dic11—21no—
194C4×Dic11—21no—
195C4×Dic11—81no—
196C4×Dic11—81no—
197C4×Dic11—81no—
198C4×Dic11C22×C412yes—
199C4×Dic11#4112yes—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8C22×C412yes—
204C2×C11⋊C8#4112yes—
205C2×C11⋊C8#4112yes—
206C2×C4×D8—111no—
207#2357—111no—
208#2357—111no—
209#1970—111no—
210#1970—111no—
211#1926—111no—
212#1926—111no—
213#1926—111no—
214#1926D1111yescharacteristic, complemented
215#1846—111no—
216#1804—111no—
217#1804—111no—
218C4×#107—111no—
219C4×#107—111no—
220C8×C4⋊C4—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—22no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
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—41no—
254C2×C4×C11#13512yes—
255C2×C4×C11C23×C411yescharacteristic
256C2×C4×C11C2×#4111yescharacteristic
257C2×C4×C11C2×#4111yescharacteristic
258C2×C4×C11C2×#4111yescharacteristic
259C2×C4×C11H(5,𝔽2)11yescharacteristic
260C2×C4×C112−1+411yescharacteristic
261C2×Dic11—21no—
262C2×Dic11—21no—
263C2×Dic11—21no—
264C2×Dic11—21no—
265C2×Dic11—21no—
266C2×Dic11—21no—
267C2×Dic11—22no—
268C2×Dic11—21no—
269C2×Dic11—21no—
270C2×Dic11—21no—
271C2×Dic11—41no—
272C2×Dic11—41no—
273C2×Dic11—41no—
274C2×Dic11—41no—
275C2×Dic11—41no—
276C2×Dic11—41no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—84no—
280C2×Dic11C4×D412yes—
281C2×Dic11C4×D412yes—
282C2×Dic11#13512yes—
283D44—22no—
284D44—22no—
285D44—41no—
286D44—41no—
287C4×D11—84no—
288C8×C11—22no—
289C8×C11—41no—
290C11⋊C8—41no—
291C11⋊C8#11714yes—
292C22×D8—111no—
293C2×C4×D4—111no—
294C2×C4×D4—111no—
295C4×D8—118no—
296C2×#107—111no—
297C2×#107—111no—
298C2×#107—111no—
299C2×#106—111no—
300C2×#106C2×D1111yescharacteristic
301C2×C4⋊C8—111no—
302C2×#102—111no—
303C2×#102—111no—
304C2×#102—111no—
305C2×#102—111no—
306C2×#102C2×D1111yescharacteristic
307C2×#102C2×D1111yescharacteristic
308C2×C4×C8—111no—
309C2×C4×C8—111no—
310C2×C4×C8—111no—
311#390—111no—
312#390—111no—
313#390—111no—
314#390C2×D1111yescharacteristic
315#388—221no—
316#388—221no—
317#388—221no—
318#388—221no—
319#382—111no—
320#382—111no—
321#381—221no—
322#381—221no—
323C4×C4⋊C4—111no—
324C4×C4⋊C4—111no—
325C4×C4⋊C4—111no—
326C4×C4⋊C4—111no—
327C4×C4⋊C4C2×D1111yescharacteristic
328C4×C22⋊C4—221no—
329C4×C22⋊C4—221no—
330#340—111no—
331#340—111no—
332#340—111no—
333#340C2×D1111yescharacteristic
334#336—111no—
335#336C2×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#54711yescharacteristic
345C22×C11#55011yescharacteristic
346C22×C11C2×#13511yescharacteristic
347C22×C11C2×#13511yescharacteristic
348C22×C11#57611yescharacteristic
349C22×C11#57611yescharacteristic
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—41no—
359C4×C11—42no—
360C4×C11—81no—
361C4×C11—81no—
362C4×C11C2×#11711yescharacteristic
363C4×C11#52011yescharacteristic
364C4×C11#55511yescharacteristic
365C4×C11#55611yescharacteristic
366Dic11—22no—
367Dic11—22no—
368Dic11—22no—
369Dic11—41no—
370Dic11—42no—
371Dic11—81no—
372Dic11—81no—
373C22×D4—111no—
374C22×D4C22×D1111yescharacteristic
375C23×C4—221no—
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—114no—
385C4×D4—114no—
386C4×D4—222no—
387C4×D4—222no—
388C2×C4⋊C4—111no—
389C2×C4⋊C4—111no—
390C2×C4⋊C4—111no—
391C2×C4⋊C4—111no—
392C2×C4⋊C4—111no—
393C2×C4⋊C4C22×D1111yescharacteristic
394C2×C4⋊C4C22×D1111yescharacteristic
395C2×C4⋊C4C22×D1111yescharacteristic
396C2×C22⋊C4—21no—
397C2×C22⋊C4—21no—
398C2×C22⋊C4—221no—
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×C42—21no—
407C2×C42—111no—
408C2×C42—111no—
409C2×C42—221no—
410C2×C42—221no—
411C2×C42—221no—
412C2×C42C22×D1111yescharacteristic
413#107—114no—
414#107—222no—
415#107—222no—
416#106—41no—
417#106—441no—
418C4⋊C8—222no—
419#102—41no—
420#102—114no—
421#102—441no—
422#102—441no—
423#102—441no—
424#102C4×D1114yes—
425C4×C8—114no—
426C4×C8—222no—
427C4×C8—222no—
428#95—21no—
429#95—111no—
430#95—111no—
431#95—221no—
432#95—221no—
433#95—221no—
434#95—221no—
435#95—221no—
436#95—221no—
437#95—221no—
438C2×C11—82no—
439C2×C11#235411yescharacteristic
440C2×C11C4×#13511yescharacteristic
441C2×C11#294811yescharacteristic
442C2×C11#333911yescharacteristic
443C2×C11#333911yescharacteristic
444C2×C11#339611yescharacteristic
445C2×C11#339611yescharacteristic
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—21no—
463C22×C4—21no—
464C22×C4—111no—
465C22×C4—111no—
466C22×C4—111no—
467C22×C4—111no—
468C22×C4—224no—
469C22×C4—224no—
470C22×C4—221no—
471C22×C4—221no—
472C22×C4—221no—
473C22×C4—881no—
474C22×C4—881no—
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—21no—
486C2×C8—112no—
487C2×C8—112no—
488C2×C8—112no—
489C2×C8—221no—
490C2×C8—221no—
491C2×C8—221no—
492C2×C8C2×C4×D1112yes—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—112no—
499C4⋊C4—222no—
500C4⋊C4—222no—
501C4⋊C4—221no—
502C4⋊C4—221no—
503C4⋊C4—221no—
504C4⋊C4—221no—
505C4⋊C4—221no—
506C4⋊C4C2×C4×D1112yes—
507C22⋊C4—42no—
508C22⋊C4—81no—
509C22⋊C4—224no—
510C22⋊C4—224no—
511C22⋊C4—442no—
512C22⋊C4—442no—
513C22⋊C4—442no—
514C22⋊C4—881no—
515C22⋊C4—881no—
516C22⋊C4—881no—
517C42—21no—
518C42—21no—
519C42—81no—
520C42—112no—
521C42—112no—
522C42—221no—
523C42—221no—
524C42—881no—
525C42—881no—
526C42—881no—
527C11#2281011yescharacteristic, 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—21no—
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—112no—
566C2×C4—112no—
567C2×C4—112no—
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—222no—
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—884no—
588C2×C4#6696912yes—
589C2×C4C22×C4×D1111yescharacteristic
590C2×C4#6703711yescharacteristic
591C2×C4#41×D1111yescharacteristic
592C2×C4#41×D1111yescharacteristic
593C2×C4#41×D1111yescharacteristic
594C2×C4#6704311yescharacteristic
595C8—22no—
596C8—41no—
597C8—114no—
598C8—441no—
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—
613C22C4×D4×D1111yescharacteristic
614C22#1062313011yescharacteristic
615C22#1062318611yescharacteristic
616C22C2×#6696911yescharacteristic
617C22D11×#13511yescharacteristic
618C22#1062330511yescharacteristic
619C22#1062330511yescharacteristic
620C4—22no—
621C4—41no—
622C4—42no—
623C4—81no—
624C4—81no—
625C4—222no—
626C4—222no—
627C4—222no—
628C4—441no—
629C4—442no—
630C4—881no—
631C4—881no—
632C4D11×#11711yescharacteristic
633C4#1062307711yescharacteristic
634C4#1062320111yescharacteristic
635C4#1062323311yescharacteristic
636C2—82no—
637C2—882no—
638C2#1307156211yescharacteristic
639C2C4×#6696911yescharacteristic
640C2#1307746511yescharacteristic
641C2#1308101111yescharacteristic
642C2#1308101611yescharacteristic
643C2#1308162311yescharacteristic
644C2#1308162711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1926C2
socleC23×C11C22×D4
prime radicalC22×#4323C22
cosocleC22×C4×C11C24
hypercenter#1926D11
hypocenterC11#22810
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1926

Complements

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

NH ≅ G/Ntype
2. #13071588C2semidirect
3. #13071585C2semidirect
6. #13069245C2semidirect
7. #13069244C2semidirect
8. #13069242C2semidirect
9. #13068777C2semidirect
10. #13068625C2semidirect
11. #13068624C2semidirect
12. C4×#66871C2semidirect
13. #13068508C2semidirect
14. #13068477C2semidirect
15. C11×#1926C2semidirect
51. #10622369C4semidirect
214. #1926D11semidirect
527. C11#22810semidirect

Maximal subgroups

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

subgroupindex
C2×#106223692
#130715882
#130715852
#130694812
#130694792
#130692452
#130692442
#130692422
#130687772
#130686252
#130686242
C4×#668712
#130685082
#130684772
C11×#19262
#2281011