Finite Group Databasebeta

← #14775179

Subgroups — #14775179

Order 2816.

858 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622648C211yesmaximal, characteristic
2#13071499C211yesmaximal, characteristic, complemented
3#13069351C211yesmaximal, characteristic, complemented
4#13069316C211yesmaximal, characteristic, complemented
5#13069240C211yesmaximal, characteristic, complemented
6#13069191C211yesmaximal, characteristic, complemented
7#13069187C211yesmaximal, characteristic, complemented
8#13069045C211yesmaximal, characteristic
9#13068863C211yesmaximal, characteristic, complemented
10#13068815C211yesmaximal, characteristic, complemented
11#13068514C211yesmaximal, characteristic, complemented
12#13068441C211yesmaximal, characteristic, complemented
13#13068394C211yesmaximal, characteristic, complemented
14#13068332C211yesmaximal, characteristic, complemented
15C11×#2363C211yesmaximal, characteristic
16C2×C11×#121C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C2×C11×#117C2211yescharacteristic
19C2×#66979C2211yescharacteristic
20C23×C11⋊C8C2211yescharacteristic
21C11×#390—21no—
22C11×#390C2211yescharacteristic
23C11×#389C2211yescharacteristic
24C11×#388—21no—
25C11×#386—21no—
26C4×C11×C4⋊C4C2211yescharacteristic
27C4×C11×C22⋊C4—21no—
28C4×C11×C22⋊C4C2211yescharacteristic
29C2×#66896C2211yescharacteristic
30C2×#66896C2211yescharacteristic
31C2×#66896C2211yescharacteristic
32C2×#66896C2211yescharacteristic
33#10622825C2211yescharacteristic
34C2×C22⋊(C11⋊C8)C2211yescharacteristic
35#10622648C418yescomplemented
36C2×#66872C2211yescharacteristic
37C2×#66872C2211yescharacteristic
38C2×#66871C2211yescharacteristic
39C2×#66871C2211yescharacteristic
40#10622557—21no—
41#10622557—21no—
42C4×C4⋊Dic11C2211yescharacteristic
43C4×C4⋊Dic11C2211yescharacteristic
44#10622541C2211yescharacteristic
45#10622541C2211yescharacteristic
46C2×#66867C2211yescharacteristic
47C2×#66867C2211yescharacteristic
48#10622263—21no—
49#10622261—21no—
50#10622167C2211yescharacteristic
51#10622167C2211yescharacteristic
52#10622167C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622162C2211yescharacteristic
59#10622162C2211yescharacteristic
60C22×D4×C11—21no—
61C22×D4×C11C2311yescharacteristic
62C23×C4×C11—21no—
63C23×C4×C11C2311yescharacteristic
64C11×#121—22no—
65C11×#121C2×C414yes—
66C4×D4×C11—22no—
67C4×D4×C11—41no—
68C11×#117—22no—
69C11×#117—41no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C22⋊C4—21no—
75C2×C11×C22⋊C4—21no—
76C2×C11×C22⋊C4—21no—
77C2×C11×C22⋊C4—21no—
78C2×C11×C22⋊C4—21no—
79C2×C11×C22⋊C4D411yescharacteristic
80C2×C11×C22⋊C4D411yescharacteristic
81C2×C42×C11—21no—
82C2×C42×C11—21no—
83C2×C42×C11C2311yescharacteristic
84C2×C42×C11C2311yescharacteristic
85C2×C22⋊Dic11—21no—
86C2×C22⋊Dic11—21no—
87#66979—22no—
88#66979C2×C414yescomplemented
89C2×C4⋊Dic11C2311yescharacteristic
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×Dic11⋊C4—21no—
94C2×Dic11⋊C4—21no—
95C2×C4×Dic11—21no—
96C2×C4×Dic11—21no—
97C2×C4×Dic11—21no—
98C22×C11⋊C8—22no—
99C22×C11⋊C8—22no—
100C22×C11⋊C8—41no—
101C22×C11⋊C8C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103C22×C11⋊C8C2311yescharacteristic
104C22×C11⋊C8C2311yescharacteristic
105C11×#95—21no—
106C11×#95—21no—
107C11×#95D411yescharacteristic
108C11×#95D411yescharacteristic
109#66896—22no—
110#66896—41no—
111#66896C2×C414yes—
112#66896C2×C414yes—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C22⋊(C11⋊C8)C2×C414yescomplemented
119#66872—41no—
120#66872C2×C414yescomplemented
121#66871—22no—
122#66871C2×C414yescomplemented
123#66867—22no—
124#66867—41no—
125#22935—111nomaximal, Sylow
126C24×C11—21no—
127C24×C11C2×D411yescharacteristic
128C2×D4×C11—24no—
129C2×D4×C11—21no—
130C2×D4×C11—21no—
131C2×D4×C11—21no—
132C2×D4×C11—21no—
133C2×D4×C11—21no—
134C2×D4×C11—81no—
135C2×D4×C11—81no—
136C2×D4×C11C22×C412yes—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—42no—
145C22×C4×C11—42no—
146C22×C4×C11—81no—
147C22×C4×C11C22×C412yes—
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11#4112yes—
154C22×C4×C11C2411yescharacteristic
155C22×Dic11—21no—
156C22×Dic11—21no—
157C22×Dic11—21no—
158C22×Dic11—21no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—81no—
164C11×C4⋊C4C22×C412yes—
165C11×C4⋊C4#4112yes—
166C11×C22⋊C4—24no—
167C11×C22⋊C4—41no—
168C11×C22⋊C4—41no—
169C11×C22⋊C4—42no—
170C11×C22⋊C4—42no—
171C11×C22⋊C4—42no—
172C11×C22⋊C4—81no—
173C42×C11—21no—
174C42×C11—21no—
175C42×C11—21no—
176C42×C11—21no—
177C42×C11—42no—
178C42×C11—81no—
179C22⋊Dic11—24no—
180C22⋊Dic11—81no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11—21no—
186C4⋊Dic11—21no—
187C4⋊Dic11C22×C412yes—
188C4⋊Dic11C22×C412yes—
189Dic11⋊C4—81no—
190Dic11⋊C4—81no—
191C4×Dic11—24no—
192C4×Dic11—42no—
193C4×Dic11—42no—
194C2×C11⋊C8—21no—
195C2×C11⋊C8—21no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—44no—
204C2×C11⋊C8C22×C412yes—
205C2×C11⋊C8C22×C412yes—
206C2×C11⋊C8#4112yes—
207C2×#482—111no—
208#2363D1111yescharacteristic
209#2346—111no—
210#1943—111no—
211#1936—111no—
212#1926—111no—
213#1919—111no—
214#1918—111no—
215#1893—111no—
216#1862—111no—
217#1854—111no—
218#1776—111no—
219#1762—111no—
220#1752—111no—
221#1735—111no—
222C23×C11—21no—
223C23×C11—21no—
224C23×C11—21no—
225C23×C11—21no—
226C23×C11—21no—
227C23×C11—21no—
228C23×C11—22no—
229C23×C11—41no—
230C23×C11—41no—
231C23×C11—41no—
232C23×C11—41no—
233C23×C11—41no—
234C23×C11—41no—
235C23×C11C4×D412yes—
236C23×C11C22×D411yescharacteristic
237D4×C11—22no—
238D4×C11—22no—
239D4×C11—41no—
240D4×C11—41no—
241D4×C11—84no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—22no—
245C2×C4×C11—22no—
246C2×C4×C11—22no—
247C2×C4×C11—22no—
248C2×C4×C11—22no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—22no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11—84no—
270C2×C4×C11C4×D412yes—
271C2×C4×C11C23×C411yescharacteristic
272C2×C4×C11C2×#4111yescharacteristic
273C2×C4×C11C2×#4111yescharacteristic
274C2×C4×C11C2×#4111yescharacteristic
275C2×C4×C11H(5,𝔽2)11yescharacteristic
276C2×C4×C112−1+411yescharacteristic
277C2×Dic11—22no—
278C2×Dic11—22no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C11⋊C8—22no—
290C11⋊C8—22no—
291C11⋊C8—22no—
292C11⋊C8—41no—
293C23×C8—111no—
294C2×#121C2×D1111yescharacteristic
295C2×C4×D4C2×D1111yescharacteristic
296C2×#117—111no—
297C2×#117C2×D1111yescharacteristic
298#482—118no—
299C2×#107—111no—
300C2×#107—111no—
301C2×#106—111no—
302C2×#106—111no—
303C2×#102—111no—
304C2×#102—111no—
305C2×#102—111no—
306C2×#102—111no—
307C2×C22⋊C8—111no—
308C2×#97—111no—
309C2×#97—111no—
310#390—21no—
311#390C2×D1111yescharacteristic
312#389—111no—
313#389—111no—
314#389C2×D1111yescharacteristic
315#388—21no—
316#388—221no—
317#388—221no—
318#386—21no—
319#382—221no—
320#380—111no—
321C4×C4⋊C4—111no—
322C4×C4⋊C4—111no—
323C4×C4⋊C4C2×D1111yescharacteristic
324C4×C22⋊C4—21no—
325C4×C22⋊C4C2×D1111yescharacteristic
326#376—221no—
327#340—111no—
328#340—111no—
329#340—111no—
330#340—111no—
331#340—111no—
332#340—111no—
333#340—111no—
334#340—111no—
335#336—111no—
336#336—111no—
337C22×C11—22no—
338C22×C11—22no—
339C22×C11—22no—
340C22×C11—41no—
341C22×C11—41no—
342C22×C11—41no—
343C22×C11—41no—
344C22×C11—42no—
345C22×C11—42no—
346C22×C11—42no—
347C22×C11—81no—
348C22×C11—81no—
349C22×C11—81no—
350C22×C11—81no—
351C22×C11C2×C4×D411yescharacteristic
352C22×C11#54611yescharacteristic
353C22×C11#54711yescharacteristic
354C22×C11#57511yescharacteristic
355C22×C11#57511yescharacteristic
356C22×C11#57611yescharacteristic
357C22×C11#57711yescharacteristic
358C4×C11—22no—
359C4×C11—41no—
360C4×C11—41no—
361C4×C11—42no—
362C4×C11—41no—
363C4×C11—41no—
364C4×C11—42no—
365C4×C11—81no—
366C4×C11C4×#4111yescharacteristic
367C4×C11#52011yescharacteristic
368C4×C11#55111yescharacteristic
369C4×C11#55211yescharacteristic
370Dic11—42no—
371Dic11—42no—
372Dic11—81no—
373Dic11—81no—
374C22×D4—21no—
375C22×D4C22×D1111yescharacteristic
376C23×C4—21no—
377C23×C4C22×D1111yescharacteristic
378C22×C8—111no—
379C22×C8—111no—
380C22×C8—111no—
381C22×C8—111no—
382C22×C8—222no—
383C22×C8—222no—
384C22×C8—441no—
385#121—22no—
386#121C4×D1114yes—
387C4×D4—22no—
388C4×D4—41no—
389#117—22no—
390#117—41no—
391#117—114no—
392#117—222no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—111no—
395C2×C4⋊C4—111no—
396C2×C4⋊C4—111no—
397C2×C4⋊C4—111no—
398C2×C4⋊C4—221no—
399C2×C4⋊C4—221no—
400C2×C4⋊C4C22×D1111yescharacteristic
401C2×C4⋊C4C22×D1111yescharacteristic
402C2×C4⋊C4C22×D1111yescharacteristic
403C2×C22⋊C4—21no—
404C2×C22⋊C4—21no—
405C2×C22⋊C4—21no—
406C2×C22⋊C4—21no—
407C2×C22⋊C4—21no—
408C2×C22⋊C4—221no—
409C2×C22⋊C4—221no—
410C2×C22⋊C4C22⋊D1111yescharacteristic
411C2×C22⋊C4C22⋊D1111yescharacteristic
412C2×C42—21no—
413C2×C42—21no—
414C2×C42—221no—
415C2×C42—221no—
416C2×C42—221no—
417C2×C42C22×D1111yescharacteristic
418C2×C42C22×D1111yescharacteristic
419#107—114no—
420#107—222no—
421#106—114no—
422#106—441no—
423#102—114no—
424#102—114no—
425#102—222no—
426#102—441no—
427C22⋊C8—114no—
428#97—222no—
429#97—441no—
430#95—21no—
431#95—21no—
432#95—221no—
433#95—221no—
434#95—221no—
435#95—221no—
436#95—221no—
437#95C22⋊D1111yescharacteristic
438#95C22⋊D1111yescharacteristic
439C2×C11—42no—
440C2×C11—82no—
441C2×C11#235911yescharacteristic
442C2×C11#294311yescharacteristic
443C2×C11#294611yescharacteristic
444C2×C11#331711yescharacteristic
445C2×C11#331911yescharacteristic
446C2×C11#334711yescharacteristic
447C2×C11#334811yescharacteristic
448C24—21no—
449C24C2×C22⋊D1111yescharacteristic
450C2×D4—24no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—81no—
457C2×D4—81no—
458C2×D4C2×C4×D1112yes—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—42no—
467C22×C4—42no—
468C22×C4—81no—
469C22×C4—221no—
470C22×C4—221no—
471C22×C4—221no—
472C22×C4—221no—
473C22×C4C2×C4×D1112yes—
474C22×C4#433912yes—
475C22×C4C2×C22⋊D1111yescharacteristic
476C22×C4C2×C22⋊D1111yescharacteristic
477C22×C4C2×C22⋊D1111yescharacteristic
478C22×C4C2×C22⋊D1111yescharacteristic
479C22×C4C2×C22⋊D1111yescharacteristic
480C22×C4C23×D1111yescharacteristic
481C2×C8—112no—
482C2×C8—112no—
483C2×C8—112no—
484C2×C8—221no—
485C2×C8—221no—
486C2×C8—221no—
487C2×C8—221no—
488C2×C8—221no—
489C2×C8—221no—
490C2×C8—221no—
491C2×C8—221no—
492C2×C8—221no—
493C2×C8—444no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—81no—
499C4⋊C4—112no—
500C4⋊C4—112no—
501C4⋊C4—221no—
502C4⋊C4—221no—
503C4⋊C4—221no—
504C4⋊C4—221no—
505C4⋊C4—221no—
506C4⋊C4—221no—
507C4⋊C4—881no—
508C4⋊C4—881no—
509C4⋊C4C2×C4×D1112yes—
510C4⋊C4#434112yes—
511C22⋊C4—24no—
512C22⋊C4—41no—
513C22⋊C4—41no—
514C22⋊C4—42no—
515C22⋊C4—42no—
516C22⋊C4—42no—
517C22⋊C4—81no—
518C22⋊C4—224no—
519C22⋊C4—881no—
520C42—21no—
521C42—21no—
522C42—21no—
523C42—21no—
524C42—42no—
525C42—81no—
526C42—224no—
527C42—442no—
528C42—442no—
529C11#2293511yescharacteristic, complemented, Sylow
530C23—21no—
531C23—21no—
532C23—21no—
533C23—21no—
534C23—21no—
535C23—21no—
536C23—22no—
537C23—41no—
538C23—41no—
539C23—41no—
540C23—41no—
541C23—41no—
542C23—41no—
543C23C4×C22⋊D1112yes—
544C23C22×C22⋊D1111yescharacteristic
545D4—22no—
546D4—22no—
547D4—41no—
548D4—41no—
549D4—84no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—22no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—84no—
578C2×C4—222no—
579C2×C4—222no—
580C2×C4—441no—
581C2×C4—441no—
582C2×C4—441no—
583C2×C4—441no—
584C2×C4—441no—
585C2×C4—441no—
586C2×C4—441no—
587C2×C4—441no—
588C2×C4—441no—
589C2×C4—441no—
590C2×C4C4×C22⋊D1112yes—
591C2×C4C22×C4×D1111yescharacteristic
592C2×C4C2×#433911yescharacteristic
593C2×C4C2×#434111yescharacteristic
594C2×C4#6703711yescharacteristic
595C2×C4#41×D1111yescharacteristic
596C2×C4#6704311yescharacteristic
597C8—222no—
598C8—222no—
599C8—222no—
600C8—441no—
601C22—22no—
602C22—22no—
603C22—22no—
604C22—41no—
605C22—41no—
606C22—41no—
607C22—41no—
608C22—42no—
609C22—42no—
610C22—42no—
611C22—81no—
612C22—81no—
613C22—81no—
614C22—81no—
615C22C2×C4×C22⋊D1111yescharacteristic
616C22#1062333711yescharacteristic
617C22#1062335311yescharacteristic
618C22#1062335311yescharacteristic
619C22#1062335511yescharacteristic
620C22#1062336611yescharacteristic
621C22#1062336711yescharacteristic
622C4—22no—
623C4—41no—
624C4—41no—
625C4—41no—
626C4—41no—
627C4—42no—
628C4—42no—
629C4—81no—
630C4—442no—
631C4—442no—
632C4—881no—
633C4—881no—
634C4C4×#434111yescharacteristic
635C4#1062307211yescharacteristic
636C4#1062307711yescharacteristic
637C4#1062308711yescharacteristic
638C2—42no—
639C2—82no—
640C2#1307160211yescharacteristic
641C2#1307741411yescharacteristic
642C2#1307744811yescharacteristic
643C2#1308074211yescharacteristic
644C2#1308077211yescharacteristic
645C2#1308111011yescharacteristic
646C2#1308113111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2363C2
socleC23×C11C22×D4
prime radicalC2×C11×#121C22
cosocleC22×C4×C11C24
hypercenter#2363D11
hypocenterC11#22935
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2363

Complements

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

NH ≅ G/Ntype
2. #13071499C2semidirect
3. #13069351C2semidirect
4. #13069316C2semidirect
5. #13069240C2semidirect
6. #13069191C2semidirect
7. #13069187C2semidirect
9. #13068863C2semidirect
10. #13068815C2semidirect
11. #13068514C2semidirect
12. #13068441C2semidirect
13. #13068394C2semidirect
14. #13068332C2semidirect
35. #10622648C4semidirect
88. #66979C2×C4semidirect
118. C22⋊(C11⋊C8)C2×C4semidirect
120. #66872C2×C4semidirect
122. #66871C2×C4semidirect
529. C11#22935semidirect

Maximal subgroups

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

subgroupindex
C2×#106226482
#130714992
#130693512
#130693162
#130692402
#130691912
#130691872
#130690452
#130688632
#130688152
#130685142
#130684412
#130683942
#130683322
C11×#23632
#2293511