Finite Group Databasebeta

← #14826573

Subgroups — #14826573

Order 2816.

734 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073018C211yesmaximal, characteristic, complemented
2#13071658C211yesmaximal, characteristic
3#13070032C211yesmaximal, characteristic, complemented
4#13069986C211yesmaximal, characteristic, complemented
5#13069802C211yesmaximal, characteristic
6#13069381C211yesmaximal, characteristic, complemented
7#13069343C211yesmaximal, characteristic, complemented
8#13069219C211yesmaximal, characteristic, complemented
9#13069210C211yesmaximal, characteristic, complemented
10#13069190C211yesmaximal, characteristic, complemented
11#13068861C211yesmaximal, characteristic, complemented
12#13068813C211yesmaximal, characteristic, complemented
13#13068712C211yesmaximal, characteristic, complemented
14#102×Dic11C211yesmaximal, characteristic, complemented
15C11×#2033C211yesmaximal, characteristic
16C2×C11×#121C2211yescharacteristic
17C2×D4×Dic11C2211yescharacteristic
18C2×#66979C2211yescharacteristic
19C2×C11×#107C2211yescharacteristic
20C2×C11×#102C2211yescharacteristic
21C2×C11×#102C2211yescharacteristic
22C2×C11×C22⋊C8C2211yescharacteristic
23C11×#380C2211yescharacteristic
24#10622834—21no—
25#10622834C2211yescharacteristic
26#10622833—21no—
27C2×#66896C2211yescharacteristic
28C2×#66896C2211yescharacteristic
29#10622825C2211yescharacteristic
30C4×C22⋊Dic11C2211yescharacteristic
31C2×C22⋊(C11⋊C8)C2211yescharacteristic
32C2×Dic11⋊C8C2211yescharacteristic
33C2×C8×Dic11C2211yescharacteristic
34#10622598C2211yescharacteristic
35#10622598C2211yescharacteristic
36#10622590C2211yescharacteristic
37C4⋊C4×Dic11C2211yescharacteristic
38C4⋊C4×Dic11C2211yescharacteristic
39#10622586C2211yescharacteristic
40C2×#66872C2211yescharacteristic
41C2×#66872C2211yescharacteristic
42C2×#66871C2211yescharacteristic
43#10622566—21no—
44#10622564—21no—
45#10622557—21no—
46C22⋊C4×Dic11—21no—
47C11⋊#401—21no—
48#10622268—21no—
49C11×#340C2211yescharacteristic
50#10622189C2211yescharacteristic
51#10622189C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59C22×D4×C11—21no—
60C22×D4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×Dic11—21no—
63C22×C8×C11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C11×#121—22no—
66C11×#121—22no—
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C22⋊C4—21no—
71C2×C11×C22⋊C4—21no—
72C2×C22⋊Dic11—21no—
73C2×C22⋊Dic11—21no—
74C2×C22⋊Dic11—21no—
75C2×C22⋊Dic11—21no—
76C2×C22⋊Dic11—21no—
77C2×C22⋊Dic11D411yescharacteristic
78C2×C22⋊Dic11D411yescharacteristic
79D4×Dic11—22no—
80D4×Dic11—41no—
81#66979—22no—
82#66979—41no—
83C2×C4⋊Dic11—21no—
84C2×C4⋊Dic11—21no—
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4⋊Dic11C2311yescharacteristic
87C2×C4⋊Dic11C2311yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89C2×Dic11⋊C4—21no—
90C2×C4×Dic11—21no—
91C2×C4×Dic11—21no—
92C2×C4×Dic11—21no—
93C2×C4×Dic11C2311yescharacteristic
94C2×C4×Dic11C2311yescharacteristic
95C22×C11⋊C8C2311yescharacteristic
96C22×C11⋊C8C2311yescharacteristic
97C11×#107—22no—
98C11×#102—22no—
99C11×#102—41no—
100C11×C22⋊C8—41no—
101C11×#95—21no—
102#66896—22no—
103#66896—22no—
104C11⋊#95—21no—
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
114C22⋊(C11⋊C8)—22no—
115Dic11⋊C8—22no—
116C8×Dic11—41no—
117#66872—22no—
118#66872—41no—
119#66871—22no—
120#27040—111nomaximal, Sylow
121C24×C11—21no—
122C24×C11C2×D411yescharacteristic
123C2×D4×C11—24no—
124C2×D4×C11—21no—
125C2×D4×C11—21no—
126C2×D4×C11—21no—
127C2×D4×C11—21no—
128C2×D4×C11—21no—
129C2×D4×C11—81no—
130C2×D4×C11—81no—
131C2×D4×C11#4112yes—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2411yescharacteristic
143C22×Dic11—21no—
144C22×Dic11—21no—
145C22×Dic11—21no—
146C22×Dic11—21no—
147C22×Dic11—42no—
148C22×Dic11—42no—
149C22×Dic11—81no—
150C22×Dic11C2×D411yescharacteristic
151C22×Dic11C2×D411yescharacteristic
152C22×Dic11C2×D411yescharacteristic
153C22×Dic11C2×D411yescharacteristic
154C2×C8×C11—21no—
155C2×C8×C11—21no—
156C2×C8×C11—21no—
157C2×C8×C11—21no—
158C2×C8×C11—21no—
159C2×C8×C11—21no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4#4112yes—
166C11×C22⋊C4—24no—
167C11×C22⋊C4—81no—
168C22⋊Dic11—22no—
169C22⋊Dic11—41no—
170C22⋊Dic11—42no—
171C22⋊Dic11—42no—
172C22⋊Dic11—42no—
173C22⋊Dic11—42no—
174C22⋊Dic11—81no—
175C4⋊Dic11—21no—
176C4⋊Dic11—21no—
177C4⋊Dic11—21no—
178C4⋊Dic11—21no—
179C4⋊Dic11—21no—
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182C4⋊Dic11—81no—
183C4⋊Dic11—81no—
184C4⋊Dic11#4112yes—
185Dic11⋊C4—42no—
186C4×Dic11—21no—
187C4×Dic11—21no—
188C4×Dic11—21no—
189C4×Dic11—21no—
190C4×Dic11—42no—
191C4×Dic11—81no—
192C4×Dic11—81no—
193C2×C11⋊C8—21no—
194C2×C11⋊C8—21no—
195C2×C11⋊C8—21no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8#4112yes—
199#2494—111no—
200#2363—111no—
201#2073—111no—
202#2065—111no—
203#2034—111no—
204#2033D1111yescharacteristic
205#1949—111no—
206#1941—111no—
207#1923—111no—
208#1921—111no—
209#1918—111no—
210#1862—111no—
211#1854—111no—
212#1825—111no—
213C4×#102—111no—
214C23×C11—22no—
215C23×C11—21no—
216C23×C11—21no—
217C23×C11—21no—
218C23×C11—21no—
219C23×C11—21no—
220C23×C11—21no—
221C23×C11—21no—
222C23×C11—41no—
223C23×C11—41no—
224C23×C11—41no—
225C23×C11—41no—
226C23×C11—41no—
227C23×C11—41no—
228C23×C11C22×D411yescharacteristic
229D4×C11—22no—
230D4×C11—22no—
231D4×C11—41no—
232D4×C11—41no—
233D4×C11—84no—
234C2×C4×C11—21no—
235C2×C4×C11—22no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11C2×#4111yescharacteristic
251C2×C4×C11C2×#4111yescharacteristic
252C2×C4×C11C2×#4111yescharacteristic
253C2×C4×C11C2×#4111yescharacteristic
254C2×C4×C11H(5,𝔽2)11yescharacteristic
255C2×C4×C112−1+411yescharacteristic
256C2×Dic11—21no—
257C2×Dic11—21no—
258C2×Dic11—21no—
259C2×Dic11—22no—
260C2×Dic11—21no—
261C2×Dic11—21no—
262C2×Dic11—21no—
263C2×Dic11—21no—
264C2×Dic11—21no—
265C2×Dic11—21no—
266C2×Dic11—21no—
267C2×Dic11—21no—
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—41no—
278C2×Dic11—41no—
279C2×Dic11—84no—
280C2×Dic11#13512yes—
281C8×C11—41no—
282C8×C11—41no—
283C11⋊C8—22no—
284C11⋊C8—41no—
285C2×#121C2×D1111yescharacteristic
286C2×C4×D4—111no—
287C2×#117—111no—
288C2×#107—111no—
289C2×#107C2×D1111yescharacteristic
290C2×#106—111no—
291C2×#106—111no—
292C2×C4⋊C8—111no—
293C2×#102—111no—
294C2×#102—111no—
295C2×#102C2×D1111yescharacteristic
296C2×#102C2×D1111yescharacteristic
297C2×C22⋊C8—111no—
298C2×C22⋊C8C2×D1111yescharacteristic
299C2×C4×C8—111no—
300#401—221no—
301#397—221no—
302#390—111no—
303#390—221no—
304#389—111no—
305#389—111no—
306#389—111no—
307#388—221no—
308#388—221no—
309#387—221no—
310#386—221no—
311#382—111no—
312#380—111no—
313#380C2×D1111yescharacteristic
314C4×C4⋊C4—111no—
315C4×C4⋊C4—111no—
316C4×C22⋊C4—111no—
317C4×C22⋊C4—221no—
318#340—111no—
319#340—111no—
320#340—111no—
321#340—111no—
322#340—111no—
323#340—111no—
324#340—111no—
325#340C2×D1111yescharacteristic
326#336—111no—
327#336—111no—
328C22×C11—41no—
329C22×C11—41no—
330C22×C11—41no—
331C22×C11—42no—
332C22×C11—41no—
333C22×C11—42no—
334C22×C11—41no—
335C22×C11—42no—
336C22×C11—41no—
337C22×C11—41no—
338C22×C11—81no—
339C22×C11—81no—
340C22×C11—81no—
341C22×C11—81no—
342C22×C11#52511yescharacteristic
343C22×C11#54611yescharacteristic
344C22×C11#54711yescharacteristic
345C22×C11C2×#13511yescharacteristic
346C22×C11#57511yescharacteristic
347C22×C11#57611yescharacteristic
348C22×C11#57711yescharacteristic
349C4×C11—42no—
350C4×C11—41no—
351C4×C11—81no—
352C4×C11—81no—
353C4×C11#52911yescharacteristic
354C4×C11#53911yescharacteristic
355C4×C11#55311yescharacteristic
356C4×C11#55611yescharacteristic
357Dic11—22no—
358Dic11—41no—
359Dic11—41no—
360Dic11—42no—
361Dic11—41no—
362Dic11—81no—
363Dic11—81no—
364Dic11—81no—
365C22×D4—21no—
366C22×D4C22×D1111yescharacteristic
367C23×C4—221no—
368C23×C4C22×D1111yescharacteristic
369C22×C8—111no—
370C22×C8—111no—
371C22×C8C22×D1111yescharacteristic
372C22×C8C22×D1111yescharacteristic
373#121—22no—
374#121—22no—
375C4×D4—222no—
376C4×D4—441no—
377#117—222no—
378#117—441no—
379C2×C4⋊C4—111no—
380C2×C4⋊C4—111no—
381C2×C4⋊C4—111no—
382C2×C4⋊C4—111no—
383C2×C4⋊C4—221no—
384C2×C4⋊C4—221no—
385C2×C4⋊C4—221no—
386C2×C4⋊C4C22×D1111yescharacteristic
387C2×C4⋊C4C22×D1111yescharacteristic
388C2×C4⋊C4C22×D1111yescharacteristic
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
391C2×C22⋊C4—111no—
392C2×C22⋊C4—111no—
393C2×C22⋊C4—221no—
394C2×C22⋊C4—221no—
395C2×C22⋊C4—221no—
396C2×C22⋊C4—221no—
397C2×C22⋊C4—221no—
398C2×C42—111no—
399C2×C42—111no—
400C2×C42—221no—
401C2×C42—221no—
402C2×C42—221no—
403#107—22no—
404#107—222no—
405#106—222no—
406#106—441no—
407C4⋊C8—222no—
408#102—22no—
409#102—41no—
410#102—222no—
411#102—222no—
412C22⋊C8—41no—
413C22⋊C8—222no—
414C4×C8—441no—
415#95—21no—
416#95—111no—
417#95—111no—
418#95—221no—
419#95—221no—
420#95—221no—
421#95—221no—
422#95—221no—
423#95—221no—
424#95—221no—
425#95—221no—
426C2×C11—81no—
427C2×C11—82no—
428C2×C11#246611yescharacteristic
429C2×C11#310211yescharacteristic
430C2×C11#311811yescharacteristic
431C2×C11#329711yescharacteristic
432C2×C11#331711yescharacteristic
433C2×C11#334011yescharacteristic
434C2×C11#335511yescharacteristic
435C24—21no—
436C24D4×D1111yescharacteristic
437C2×D4—24no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—81no—
444C2×D4—81no—
445C2×D4#434112yes—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—111no—
456C22×C4—111no—
457C22×C4—111no—
458C22×C4—111no—
459C22×C4—221no—
460C22×C4—221no—
461C22×C4—221no—
462C22×C4—221no—
463C22×C4—442no—
464C22×C4—442no—
465C22×C4—881no—
466C22×C4D4×D1111yescharacteristic
467C22×C4C23×D1111yescharacteristic
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—112no—
475C2×C8—221no—
476C2×C8—221no—
477C2×C8—221no—
478C2×C8—221no—
479C2×C8—221no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—112no—
486C4⋊C4—221no—
487C4⋊C4—221no—
488C4⋊C4—221no—
489C4⋊C4—221no—
490C4⋊C4—221no—
491C4⋊C4—221no—
492C4⋊C4—221no—
493C4⋊C4—442no—
494C4⋊C4—881no—
495C4⋊C4—881no—
496C4⋊C4#434112yes—
497C22⋊C4—24no—
498C22⋊C4—81no—
499C22⋊C4—222no—
500C22⋊C4—441no—
501C22⋊C4—442no—
502C22⋊C4—442no—
503C22⋊C4—442no—
504C22⋊C4—442no—
505C22⋊C4—881no—
506C42—221no—
507C42—221no—
508C42—221no—
509C42—221no—
510C42—442no—
511C42—881no—
512C42—881no—
513C11#2704011yescharacteristic, complemented, Sylow
514C23—21no—
515C23—21no—
516C23—21no—
517C23—21no—
518C23—22no—
519C23—21no—
520C23—21no—
521C23—21no—
522C23—41no—
523C23—41no—
524C23—41no—
525C23—41no—
526C23—41no—
527C23—41no—
528C23C2×D4×D1111yescharacteristic
529D4—22no—
530D4—22no—
531D4—41no—
532D4—41no—
533D4—84no—
534C2×C4—21no—
535C2×C4—22no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—112no—
551C2×C4—221no—
552C2×C4—221no—
553C2×C4—221no—
554C2×C4—221no—
555C2×C4—221no—
556C2×C4—221no—
557C2×C4—221no—
558C2×C4—221no—
559C2×C4—221no—
560C2×C4—222no—
561C2×C4—221no—
562C2×C4—221no—
563C2×C4—441no—
564C2×C4—441no—
565C2×C4—441no—
566C2×C4—441no—
567C2×C4—441no—
568C2×C4—441no—
569C2×C4—441no—
570C2×C4—441no—
571C2×C4—441no—
572C2×C4—441no—
573C2×C4—441no—
574C2×C4—884no—
575C2×C4C2×#434111yescharacteristic
576C2×C4C2×#434111yescharacteristic
577C2×C4#6703711yescharacteristic
578C2×C4#41×D1111yescharacteristic
579C2×C4#41×D1111yescharacteristic
580C2×C4#6704311yescharacteristic
581C8—41no—
582C8—41no—
583C8—222no—
584C8—441no—
585C22—41no—
586C22—42no—
587C22—41no—
588C22—42no—
589C22—41no—
590C22—42no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22—81no—
596C22—81no—
597C22—81no—
598C22—81no—
599C22#1062311711yescharacteristic
600C22#1062314111yescharacteristic
601C22#1062318611yescharacteristic
602C22#1062328811yescharacteristic
603C22D11×#13511yescharacteristic
604C22#1062330611yescharacteristic
605C22#1062330811yescharacteristic
606C4—41no—
607C4—42no—
608C4—81no—
609C4—81no—
610C4—222no—
611C4—441no—
612C4—442no—
613C4—441no—
614C4—441no—
615C4—881no—
616C4—881no—
617C4—881no—
618C4#1062313311yescharacteristic
619C4#1062314511yescharacteristic
620C4#1062318011yescharacteristic
621C4#1062320211yescharacteristic
622C2—81no—
623C2—82no—
624C2#1307264511yescharacteristic
625C2#1307863511yescharacteristic
626C2#1307879311yescharacteristic
627C2#1308046111yescharacteristic
628C2#1308073711yescharacteristic
629C2#1308102711yescharacteristic
630C2#1308122211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2033C2
socleC23×C11C22×D4
prime radicalC2×C11×#121C22
hypercenter#2033D11
hypocenterC11#27040
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2033

Complements

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

NH ≅ G/Ntype
1. #13073018C2semidirect
3. #13070032C2semidirect
4. #13069986C2semidirect
6. #13069381C2semidirect
7. #13069343C2semidirect
8. #13069219C2semidirect
9. #13069210C2semidirect
10. #13069190C2semidirect
11. #13068861C2semidirect
12. #13068813C2semidirect
13. #13068712C2semidirect
14. #102×Dic11C2semidirect
513. C11#27040semidirect

Maximal subgroups

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

subgroupindex
#130730182
#130716582
#130700322
#130699862
#130698022
#130693812
#130693432
#130692192
#130692102
#130691902
#130688612
#130688132
#130687122
#102×Dic112
C11×#20332
#2704011