Finite Group Databasebeta

← #14826459

Subgroups — #14826459

Order 2816.

792 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073045C211yesmaximal, characteristic, complemented
2#13071632C211yesmaximal, characteristic
3#13070023C211yesmaximal, characteristic, complemented
4#13069991C211yesmaximal, characteristic, complemented
5#13069806C211yesmaximal, characteristic
6#13069805C211yesmaximal, characteristic
7#13069378C211yesmaximal, characteristic, complemented
8#13069343C211yesmaximal, characteristic, complemented
9#13069219C211yesmaximal, characteristic, complemented
10#13069199C211yesmaximal, characteristic, complemented
11#13069193C211yesmaximal, characteristic, complemented
12#13068878C211yesmaximal, characteristic, complemented
13#13068809C211yesmaximal, characteristic, complemented
14#13068430C211yesmaximal, characteristic, complemented
15C11×#1823C211yesmaximal, characteristic, complemented
16C22×C11×C4⋊C4C2211yescharacteristic
17C2×#66983C2211yescharacteristic
18C2×C4×C22⋊D11—21no—
19C2×#66946C2211yescharacteristic
20C2×C11×C22⋊C8C2211yescharacteristic
21C11×#380C2211yescharacteristic
22#10622826—21no—
23#10622825C2211yescharacteristic
24C4×C22⋊Dic11C2211yescharacteristic
25C2×C22⋊(C11⋊C8)C2211yescharacteristic
26C2×#66885C2211yescharacteristic
27C2×#66885C2211yescharacteristic
28C2×#66881C2211yescharacteristic
29C2×Dic11⋊C8C2211yescharacteristic
30C2×C8×Dic11C2211yescharacteristic
31#10622603—21no—
32#10622602—21no—
33#10622601C2211yescharacteristic
34#10622598C2211yescharacteristic
35#10622589C2211yescharacteristic
36C4⋊C4×Dic11C2211yescharacteristic
37C4⋊C4×Dic11C2211yescharacteristic
38#10622586C2211yescharacteristic
39#10622586C2211yescharacteristic
40C2×#66873C2211yescharacteristic
41C2×#66873C2211yescharacteristic
42C2×#66872C2211yescharacteristic
43C2×#66872C2211yescharacteristic
44C2×#66872C2211yescharacteristic
45#10622561—21no—
46#10622557—21no—
47#10622272—21no—
48#10622265—21no—
49C11×#340C2211yescharacteristic
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52C11×#340C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59C23×C4×C11—21no—
60C23×C4×C11C2311yescharacteristic
61C22×C22⋊D11—21no—
62C22×D44C2311yescharacteristic
63C22×C4×D11—21no—
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C2×C11×C4⋊C4—22no—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4—41no—
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C22⋊C4—21no—
74C2×C22⋊Dic11—21no—
75C2×C22⋊Dic11D411yescharacteristic
76C2×C22⋊Dic11D411yescharacteristic
77#66983—22no—
78#66983—22no—
79C4×C22⋊D11—44no—
80C2×(C2×D11)⋊C4—21no—
81C2×(C2×D11)⋊C4—21no—
82C2×(C2×D11)⋊C4—21no—
83C2×(C2×D11)⋊C4—21no—
84C2×C4⋊Dic11—21no—
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4⋊Dic11C2311yescharacteristic
87C2×C4⋊Dic11C2311yescharacteristic
88C2×Dic11⋊C4—21no—
89C2×Dic11⋊C4—21no—
90C2×Dic11⋊C4—21no—
91C2×Dic11⋊C4—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#66946—41no—
100C11×C22⋊C8—41no—
101C11×#95—21no—
102C11⋊#95—21no—
103C11⋊#95—21no—
104C11⋊#95—21no—
105C11⋊#95—21no—
106C11⋊#95—21no—
107C11⋊#95—21no—
108C11⋊#95D411yescharacteristic
109C11⋊#95D411yescharacteristic
110C22⋊(C11⋊C8)—22no—
111#66885—22no—
112#66885—41no—
113#66881—22no—
114Dic11⋊C8—22no—
115C8×Dic11—41no—
116#66873—22no—
117#66873—22no—
118#66872—22no—
119#66872—22no—
120#66872—41no—
121#27032—111nomaximal, Sylow
122C24×C11C2×D411yescharacteristic
123C23×D11—21no—
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—42no—
135C22×C4×C11—42no—
136C22×C4×C11—81no—
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2411yescharacteristic
139C2×C22⋊D11—24no—
140C2×C22⋊D11—42no—
141C2×C22⋊D11—42no—
142C22×Dic11—21no—
143C22×Dic11—21no—
144C22×Dic11—21no—
145C22×Dic11C2×D411yescharacteristic
146C22×Dic11C2×D411yescharacteristic
147C22×Dic11C2×D411yescharacteristic
148C22×Dic11C2×D411yescharacteristic
149C2×D44—21no—
150C2×D44—21no—
151C2×D44—21no—
152C2×D44—21no—
153C2×D44—21no—
154C2×D44#4112yes—
155C2×C4×D11—42no—
156C2×C4×D11—42no—
157C2×C4×D11—81no—
158C2×C8×C11—21no—
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—42no—
172C11×C4⋊C4#4112yes—
173C11×C22⋊C4—81no—
174C22⋊Dic11—41no—
175C22⋊Dic11—81no—
176C22⋊Dic11SD1614yes—
177(C2×D11)⋊C4—24no—
178(C2×D11)⋊C4—42no—
179(C2×D11)⋊C4—42no—
180(C2×D11)⋊C4—81no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11—21no—
186C4⋊Dic11—81no—
187C4⋊Dic11#4112yes—
188Dic11⋊C4—42no—
189Dic11⋊C4—42no—
190Dic11⋊C4—81no—
191Dic11⋊C4—81no—
192C4×Dic11—21no—
193C4×Dic11—21no—
194C4×Dic11—21no—
195C4×Dic11—21no—
196C4×Dic11—42no—
197C4×Dic11—81no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8#4112yes—
204#2497—111no—
205#2361—111no—
206#2071—111no—
207#2065—111no—
208#2034—111no—
209#2034—111no—
210#1948—111no—
211#1941—111no—
212#1923—111no—
213#1920—111no—
214#1919—111no—
215#1864—111no—
216#1853—111no—
217#1823D1111yescharacteristic, complemented
218C4×#102—111no—
219C23×C11—21no—
220C23×C11—21no—
221C23×C11—21no—
222C23×C11—21no—
223C23×C11—21no—
224C23×C11—21no—
225C23×C11C2×SD1612yes—
226C23×C11C22×D411yescharacteristic
227C22×D11—22no—
228C22×D11—41no—
229C22×D11—41no—
230C22×D11—41no—
231C22×D11—41no—
232C22×D11—41no—
233C22×D11—41no—
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×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—84no—
254C2×C4×C11C2×#4111yescharacteristic
255C2×C4×C11C2×#4111yescharacteristic
256C2×C4×C11C2×#4111yescharacteristic
257C2×C4×C11C2×#4111yescharacteristic
258C2×C4×C11H(5,𝔽2)11yescharacteristic
259C2×C4×C112−1+411yescharacteristic
260C22⋊D11—48no—
261C2×Dic11—21no—
262C2×Dic11—21no—
263C2×Dic11—21no—
264C2×Dic11—21no—
265C2×Dic11—22no—
266C2×Dic11—21no—
267C2×Dic11—21no—
268C2×Dic11—21no—
269C2×Dic11—21no—
270C2×Dic11—21no—
271C2×Dic11—21no—
272C2×Dic11—41no—
273C2×Dic11—41no—
274C2×Dic11—41no—
275C2×Dic11—41no—
276C2×Dic11—41no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11C2×SD1612yes—
281C2×Dic11C2×SD1612yes—
282D44—22no—
283D44—22no—
284D44—41no—
285D44—41no—
286C4×D11—84no—
287C8×C11—41no—
288C8×C11—41no—
289C11⋊C8—22no—
290C11⋊C8—41no—
291C2×#121—111no—
292C2×C4×D4—111no—
293C2×C4×D4—221no—
294C22×C4⋊C4C2×D1111yescharacteristic
295C2×#106—111no—
296C2×#106—111no—
297C2×#106—111no—
298C2×#106—111no—
299C2×C4⋊C8—111no—
300C2×#102—111no—
301C2×#102—111no—
302C2×#102—111no—
303C2×#102—111no—
304C2×C22⋊C8—111no—
305C2×C22⋊C8C2×D1111yescharacteristic
306C2×C4×C8—111no—
307#400—221no—
308#396—221no—
309#390—111no—
310#389—111no—
311#389—111no—
312#389—111no—
313#388—221no—
314#388—221no—
315#387—221no—
316#386—221no—
317#385—221no—
318#384—111no—
319#380—111no—
320#380C2×D1111yescharacteristic
321C4×C4⋊C4—111no—
322C4×C4⋊C4—111no—
323C4×C22⋊C4—111no—
324#340—111no—
325#340—111no—
326#340—111no—
327#340—111no—
328#340C2×D1111yescharacteristic
329#340C2×D1111yescharacteristic
330#340C2×D1111yescharacteristic
331#340C2×D1111yescharacteristic
332#336—111no—
333#336—111no—
334C22×C11—22no—
335C22×C11—22no—
336C22×C11—22no—
337C22×C11—41no—
338C22×C11—41no—
339C22×C11—41no—
340C22×C11—41no—
341C22×C11#52511yescharacteristic
342C22×C11#54611yescharacteristic
343C22×C11#54711yescharacteristic
344C22×C11C22×SD1611yescharacteristic
345C22×C11#57511yescharacteristic
346C22×C11#57611yescharacteristic
347C22×C11#57711yescharacteristic
348C2×D11—42no—
349C2×D11—42no—
350C2×D11—42no—
351C2×D11—81no—
352C2×D11—81no—
353C2×D11—81no—
354C2×D11—81no—
355C4×C11—41no—
356C4×C11—42no—
357C4×C11—81no—
358C4×C11—81no—
359C4×C11—81no—
360C4×C11#52911yescharacteristic
361C4×C11#53911yescharacteristic
362C4×C11#55311yescharacteristic
363C4×C11#55611yescharacteristic
364Dic11—22no—
365Dic11—22no—
366Dic11—41no—
367Dic11—42no—
368Dic11—41no—
369Dic11—81no—
370Dic11—81no—
371C22×D4—111no—
372C22×D4—221no—
373C23×C4—21no—
374C23×C4—221no—
375C23×C4C22×D1111yescharacteristic
376C22×C8—111no—
377C22×C8—111no—
378C22×C8C22×D1111yescharacteristic
379C22×C8C22×D1111yescharacteristic
380#121—222no—
381#121—222no—
382C4×D4—222no—
383C4×D4—441no—
384C4×D4—444no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—41no—
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⋊C4—221no—
396C2×C4⋊C4C22×D1111yescharacteristic
397C2×C4⋊C4C22×D1111yescharacteristic
398C2×C4⋊C4C22×D1111yescharacteristic
399C2×C4⋊C4C22×D1111yescharacteristic
400C2×C22⋊C4—21no—
401C2×C22⋊C4—111no—
402C2×C22⋊C4—111no—
403C2×C22⋊C4—221no—
404C2×C22⋊C4—221no—
405C2×C22⋊C4—221no—
406C2×C22⋊C4—221no—
407C2×C22⋊C4—221no—
408C2×C42—111no—
409C2×C42—111no—
410C2×C42—221no—
411C2×C42—221no—
412#106—222no—
413#106—222no—
414#106—222no—
415#106—441no—
416C4⋊C8—222no—
417#102—222no—
418#102—222no—
419#102—222no—
420#102—441no—
421C22⋊C8—41no—
422C22⋊C8—222no—
423C4×C8—441no—
424#95—21no—
425#95—111no—
426#95—111no—
427#95—221no—
428#95—221no—
429#95—221no—
430#95—221no—
431#95—221no—
432#95—221no—
433C2×C11—42no—
434C2×C11#246611yescharacteristic
435C2×C11#310111yescharacteristic
436C2×C11#311911yescharacteristic
437C2×C11#329511yescharacteristic
438C2×C11#332111yescharacteristic
439C2×C11#333511yescharacteristic
440C2×C11#335511yescharacteristic
441D11—82no—
442C24—221no—
443C24D4×D1111yescharacteristic
444C2×D4—112no—
445C2×D4—224no—
446C2×D4—221no—
447C2×D4—221no—
448C2×D4—221no—
449C2×D4—221no—
450C2×D4—221no—
451C2×D4—442no—
452C2×D4—442no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—42no—
464C22×C4—42no—
465C22×C4—81no—
466C22×C4—111no—
467C22×C4—111no—
468C22×C4—111no—
469C22×C4—111no—
470C22×C4—221no—
471C22×C4—221no—
472C22×C4—221no—
473C22×C4—442no—
474C22×C4—442no—
475C22×C4—881no—
476C22×C4D4×D1111yescharacteristic
477C22×C4C23×D1111yescharacteristic
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—112no—
485C2×C8—221no—
486C2×C8—221no—
487C2×C8—221no—
488C2×C8—221no—
489C2×C8—221no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—42no—
498C4⋊C4—112no—
499C4⋊C4—221no—
500C4⋊C4—221no—
501C4⋊C4—221no—
502C4⋊C4—221no—
503C4⋊C4—221no—
504C4⋊C4—442no—
505C4⋊C4—442no—
506C4⋊C4—881no—
507C4⋊C4—881no—
508C4⋊C4—881no—
509C4⋊C4#433912yes—
510C22⋊C4—81no—
511C22⋊C4—114no—
512C22⋊C4—224no—
513C22⋊C4—442no—
514C22⋊C4—442no—
515C22⋊C4—441no—
516C22⋊C4—881no—
517C22⋊C4—881no—
518C42—221no—
519C42—221no—
520C42—221no—
521C42—221no—
522C42—442no—
523C42—881no—
524C11#2703211yescharacteristic, complemented, Sylow
525C23—21no—
526C23—21no—
527C23—21no—
528C23—21no—
529C23—21no—
530C23—21no—
531C23—222no—
532C23—441no—
533C23—441no—
534C23—441no—
535C23—441no—
536C23—441no—
537C23—441no—
538C23SD16×D1112yes—
539C23C2×D4×D1111yescharacteristic
540D4—222no—
541D4—222no—
542D4—448no—
543D4—441no—
544D4—441no—
545C2×C4—22no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
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—112no—
566C2×C4—112no—
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—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×C4C2×#433911yescharacteristic
588C2×C4#6703711yescharacteristic
589C2×C4#41×D1111yescharacteristic
590C2×C4#41×D1111yescharacteristic
591C2×C4#41×D1111yescharacteristic
592C2×C4#6704311yescharacteristic
593C8—41no—
594C8—41no—
595C8—222no—
596C8—441no—
597C22—22no—
598C22—22no—
599C22—22no—
600C22—41no—
601C22—41no—
602C22—41no—
603C22—41no—
604C22—442no—
605C22—442no—
606C22—442no—
607C22—881no—
608C22—881no—
609C22—881no—
610C22—881no—
611C22#1062302111yescharacteristic
612C22#1062318611yescharacteristic
613C22#1062318711yescharacteristic
614C22#1062328811yescharacteristic
615C22C2×SD16×D1111yescharacteristic
616C22#1062330811yescharacteristic
617C22#1062330911yescharacteristic
618C4—41no—
619C4—42no—
620C4—81no—
621C4—81no—
622C4—81no—
623C4—222no—
624C4—222no—
625C4—442no—
626C4—441no—
627C4—441no—
628C4—881no—
629C4—881no—
630C4#1062305911yescharacteristic
631C4#1062306411yescharacteristic
632C4#1062319111yescharacteristic
633C4#1062319211yescharacteristic
634C2—42no—
635C2—882no—
636C2#1307265111yescharacteristic
637C2#1307862111yescharacteristic
638C2#1307881811yescharacteristic
639C2#1308043611yescharacteristic
640C2#1308080311yescharacteristic
641C2#1308096611yescharacteristic
642C2#1308122211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1823C2
socleC23×C11C22×D4
prime radicalC2×#66983C22
hypercenter#1823D11
hypocenterC11#27032
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1823

Complements

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

NH ≅ G/Ntype
1. #13073045C2semidirect
3. #13070023C2semidirect
4. #13069991C2semidirect
7. #13069378C2semidirect
8. #13069343C2semidirect
9. #13069219C2semidirect
10. #13069199C2semidirect
11. #13069193C2semidirect
12. #13068878C2semidirect
13. #13068809C2semidirect
14. #13068430C2semidirect
15. C11×#1823C2semidirect
217. #1823D11semidirect
524. C11#27032semidirect

Maximal subgroups

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

subgroupindex
#130730452
#130716322
#130700232
#130699912
#130698062
#130698052
#130693782
#130693432
#130692192
#130691992
#130691932
#130688782
#130688092
#130684302
C11×#18232
#2703211