Finite Group Databasebeta

← #14775359

Subgroups — #14775359

Order 2816.

846 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622657C211yesmaximal, characteristic
2#13071483C211yesmaximal, characteristic
3#13069351C211yesmaximal, characteristic, complemented
4#13069295C211yesmaximal, characteristic, complemented
5#13069247C211yesmaximal, characteristic, complemented
6#13069205C211yesmaximal, characteristic, complemented
7#13069187C211yesmaximal, characteristic, complemented
8#13069050C211yesmaximal, characteristic
9#13068870C211yesmaximal, characteristic, complemented
10#13068815C211yesmaximal, characteristic
11C4×#66871C211yesmaximal, characteristic, complemented
12#13068446C211yesmaximal, characteristic, complemented
13#13068400C211yesmaximal, characteristic
14#13068337C211yesmaximal, characteristic
15C11×#2362C211yesmaximal, characteristic
16C2×C11×C22⋊Q8C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×C11×#117C2211yescharacteristic
19C22×C4⋊Dic11C2211yescharacteristic
20C22×#4318C2211yescharacteristic
21C2×#66930—21no—
22C11×#391C2211yescharacteristic
23C11×#389C2211yescharacteristic
24C11×#388—21no—
25C11×#388—21no—
26C11×#387—21no—
27C4×C11×C4⋊C4—21no—
28C4×C11×C4⋊C4C2211yescharacteristic
29C4×C11×C22⋊C4C2211yescharacteristic
30C2×#66899C2211yescharacteristic
31C2×#66899C2211yescharacteristic
32C2×#66899C2211yescharacteristic
33C2×#66899C2211yescharacteristic
34#10622825C2211yescharacteristic
35C2×C22⋊(C11⋊C8)C2211yescharacteristic
36#10622657C418yescomplemented
37C2×#66872C2211yescharacteristic
38C2×#66871C2211yescharacteristic
39C2×#66871C2211yescharacteristic
40C2×#66871C2211yescharacteristic
41#10622556—21no—
42C4×C4⋊Dic11C2211yescharacteristic
43C4×C4⋊Dic11C2211yescharacteristic
44#10622541C2211yescharacteristic
45#10622541C2211yescharacteristic
46C2×#66867C2211yescharacteristic
47C2×C4×C11⋊C8C2211yescharacteristic
48#10622266—21no—
49#10622266—21no—
50#10622167C2211yescharacteristic
51#10622167C2211yescharacteristic
52#10622167C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622162C2211yescharacteristic
59#10622162C2211yescharacteristic
60C22×Q8×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×Dic11—21no—
63C11×C22⋊Q8—22no—
64C11×C22⋊Q8C2×C414yes—
65C4×Q8×C11—22no—
66C4×Q8×C11—41no—
67C11×#117—22no—
68C11×#117—41no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C22⋊C4—21no—
76C2×C11×C22⋊C4—21no—
77C2×C11×C22⋊C4D411yescharacteristic
78C2×C11×C22⋊C4D411yescharacteristic
79C2×C42×C11—21no—
80C2×C42×C11—21no—
81C2×C42×C11—21no—
82C2×C42×C11C2311yescharacteristic
83C2×C42×C11C2311yescharacteristic
84C2×C22⋊Dic11—21no—
85C2×C4⋊Dic11—21no—
86C2×C4⋊Dic11—22no—
87C2×C4⋊Dic11C2×C414yes—
88C2×C4⋊Dic11C2311yescharacteristic
89C2×C4⋊Dic11C2311yescharacteristic
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92C2×Dic11⋊C4—21no—
93C2×Dic11⋊C4—21no—
94C2×C4×Dic11—21no—
95C2×C4×Dic11—21no—
96C2×#4318—22no—
97C2×#4318—22no—
98C2×#4318—41no—
99C22×C11⋊C8C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101C22×C11⋊C8C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103#66930—44no—
104C11×#95—21no—
105C11×#95—21no—
106C11×#95—21no—
107C11×#95—21no—
108C11×#95D411yescharacteristic
109C11×#95D411yescharacteristic
110#66899—22no—
111#66899—41no—
112#66899C2×C414yes—
113#66899C2×C414yes—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C22⋊(C11⋊C8)C2×C414yes—
120#66872—41no—
121#66871—22no—
122#66871C2×C414yes—
123#66871C2×C414yes—
124#66867—41no—
125C4×C11⋊C8—22no—
126#22947—111nomaximal, Sylow
127C24×C11C2×D411yescharacteristic
128C2×Q8×C11—21no—
129C2×Q8×C11—21no—
130C2×Q8×C11—21no—
131C2×Q8×C11—21no—
132C2×Q8×C11—21no—
133C2×Q8×C11C22×C412yes—
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×C11—21no—
142C22×C4×C11C22×C412yes—
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11#4112yes—
149C22×C4×C11C2411yescharacteristic
150C22×Dic11—24no—
151C22×Dic11—21no—
152C22×Dic11—21no—
153C22×Dic11—21no—
154C22×Dic11—21no—
155C22×Dic11—42no—
156C22×Dic11—42no—
157C11×C4⋊C4—24no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—42no—
163C11×C4⋊C4—42no—
164C11×C4⋊C4C22×C412yes—
165C11×C4⋊C4#4112yes—
166C11×C22⋊C4—24no—
167C11×C22⋊C4—22no—
168C11×C22⋊C4—41no—
169C11×C22⋊C4—42no—
170C42×C11—21no—
171C42×C11—21no—
172C42×C11—21no—
173C42×C11—21no—
174C42×C11—42no—
175C42×C11—42no—
176C42×C11—42no—
177C22⋊Dic11—42no—
178C4⋊Dic11—24no—
179C4⋊Dic11—21no—
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11C22×C412yes—
186C4⋊Dic11C22×C412yes—
187Dic11⋊C4—42no—
188Dic11⋊C4—42no—
189C4×Dic11—42no—
190C4×Dic11—42no—
191#4318—44no—
192C2×C11⋊C8—21no—
193C2×C11⋊C8—21no—
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⋊C8C22×C412yes—
202C2×C11⋊C8C22×C412yes—
203C2×C11⋊C8#4112yes—
204C2×#484—111no—
205#2362D1111yescharacteristic
206#2344—111no—
207#1943—111no—
208#1933—111no—
209#1927—111no—
210#1921—111no—
211#1918—111no—
212#1894—111no—
213#1863—111no—
214#1854—111no—
215C4×#107—111no—
216#1763—111no—
217#1753—111no—
218#1736—111no—
219C23×C11—21no—
220C23×C11—21no—
221C23×C11—21no—
222C23×C11—21no—
223C23×C11—21no—
224C23×C11—21no—
225C23×C11C4×D412yes—
226C23×C11C22×D411yescharacteristic
227Q8×C11—22no—
228Q8×C11—22no—
229Q8×C11—41no—
230Q8×C11—41no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—22no—
236C2×C4×C11—22no—
237C2×C4×C11—22no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—22no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11C4×D412yes—
261C2×C4×C11AGL(1,ℤ/8)12yes—
262C2×C4×C11C23×C411yescharacteristic
263C2×C4×C11C2×#4111yescharacteristic
264C2×C4×C11C2×#4111yescharacteristic
265C2×C4×C11C2×#4111yescharacteristic
266C2×C4×C11H(5,𝔽2)11yescharacteristic
267C2×C4×C112−1+411yescharacteristic
268C2×Dic11—22no—
269C2×Dic11—22no—
270C2×Dic11—48no—
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—41no—
280C2×Dic11—41no—
281C11⋊C8—22no—
282C11⋊C8—22no—
283C11⋊C8—22no—
284C11⋊C8—41no—
285C22×M16—111no—
286C2×C22⋊Q8C2×D1111yescharacteristic
287C2×C4×Q8C2×D1111yescharacteristic
288C2×#117—221no—
289C2×#117C2×D1111yescharacteristic
290C22×C4⋊C4—111no—
291#484—118no—
292C2×#107—111no—
293C2×#107—111no—
294C2×#107—111no—
295C2×#106—111no—
296C2×#103—111no—
297C2×#103—111no—
298C2×#103—111no—
299C2×#103—111no—
300C2×C22⋊C8—111no—
301C2×#97—111no—
302C2×C4×C8—111no—
303#391C2×D1111yescharacteristic
304#389—111no—
305#389—111no—
306#389C2×D1111yescharacteristic
307#388—21no—
308#388—21no—
309#387—21no—
310#387—221no—
311#387—221no—
312#381—221no—
313#380—111no—
314C4×C4⋊C4—21no—
315C4×C4⋊C4—111no—
316C4×C4⋊C4—111no—
317C4×C4⋊C4C2×D1111yescharacteristic
318C4×C22⋊C4C2×D1111yescharacteristic
319#340—111no—
320#340—111no—
321#340—111no—
322#340—111no—
323#340—111no—
324#340—111no—
325#340—111no—
326#340—111no—
327#336—111no—
328#336—111no—
329C22×C11—22no—
330C22×C11—22no—
331C22×C11—22no—
332C22×C11—41no—
333C22×C11—41no—
334C22×C11—41no—
335C22×C11—41no—
336C22×C11C2×C4×D411yescharacteristic
337C22×C11#54611yescharacteristic
338C22×C11#54711yescharacteristic
339C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
340C22×C11#57511yescharacteristic
341C22×C11#57811yescharacteristic
342C22×C11#57811yescharacteristic
343C4×C11—22no—
344C4×C11—22no—
345C4×C11—41no—
346C4×C11—42no—
347C4×C11—41no—
348C4×C11—42no—
349C4×C11—42no—
350C4×C11—41no—
351C4×C11—81no—
352C4×C11C4×#4111yescharacteristic
353C4×C11#52011yescharacteristic
354C4×C11#55111yescharacteristic
355C4×C11#55211yescharacteristic
356Dic11—42no—
357Dic11—42no—
358Dic11—81no—
359Dic11—81no—
360C22×Q8C22×D1111yescharacteristic
361C23×C4—221no—
362C23×C4C22×D1111yescharacteristic
363C2×M16—222no—
364C2×M16—222no—
365C2×M16—441no—
366C22×C8—111no—
367C22×C8—111no—
368C22×C8—111no—
369C22×C8—111no—
370C22⋊Q8—22no—
371C22⋊Q8C4×D1114yes—
372C4×Q8—22no—
373C4×Q8—41no—
374#117—22no—
375#117—41no—
376#117—444no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—114no—
381C2×C4⋊C4—111no—
382C2×C4⋊C4—111no—
383C2×C4⋊C4—111no—
384C2×C4⋊C4—111no—
385C2×C4⋊C4—222no—
386C2×C4⋊C4—221no—
387C2×C4⋊C4—221no—
388C2×C4⋊C4—221no—
389C2×C4⋊C4C22×D1111yescharacteristic
390C2×C4⋊C4C22×D1111yescharacteristic
391C2×C4⋊C4C22×D1111yescharacteristic
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4—221no—
395C2×C22⋊C4C22⋊D1111yescharacteristic
396C2×C22⋊C4C22⋊D1111yescharacteristic
397C2×C42—21no—
398C2×C42—21no—
399C2×C42—21no—
400C2×C42—221no—
401C2×C42—221no—
402C2×C42C22×D1111yescharacteristic
403C2×C42C22×D1111yescharacteristic
404#107—114no—
405#107—114no—
406#107—222no—
407#106—441no—
408#103—114no—
409#103—114no—
410#103—222no—
411#103—441no—
412C22⋊C8—114no—
413#97—441no—
414C4×C8—222no—
415#95—21no—
416#95—21no—
417#95—21no—
418#95—21no—
419#95—221no—
420#95—221no—
421#95—221no—
422#95—221no—
423#95—221no—
424#95C22⋊D1111yescharacteristic
425#95C22⋊D1111yescharacteristic
426C2×C11—42no—
427C2×C11#235911yescharacteristic
428C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
429C2×C11#295011yescharacteristic
430C2×C11#332711yescharacteristic
431C2×C11#333011yescharacteristic
432C2×C11#334311yescharacteristic
433C2×C11#334911yescharacteristic
434C24C2×C22⋊D1111yescharacteristic
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8C2×C4×D1112yes—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—224no—
450C22×C4—221no—
451C22×C4—221no—
452C22×C4—221no—
453C22×C4—221no—
454C22×C4—442no—
455C22×C4—442no—
456C22×C4C2×C4×D1112yes—
457C22×C4#433912yes—
458C22×C4C2×C22⋊D1111yescharacteristic
459C22×C4C2×C22⋊D1111yescharacteristic
460C22×C4C2×C22⋊D1111yescharacteristic
461C22×C4C2×C22⋊D1111yescharacteristic
462C22×C4C2×C22⋊D1111yescharacteristic
463C22×C4C23×D1111yescharacteristic
464M16—444no—
465C2×C8—112no—
466C2×C8—112no—
467C2×C8—112no—
468C2×C8—221no—
469C2×C8—221no—
470C2×C8—221no—
471C2×C8—221no—
472C2×C8—221no—
473C2×C8—221no—
474C2×C8—221no—
475C2×C8—221no—
476C2×C8—221no—
477C4⋊C4—24no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—42no—
483C4⋊C4—42no—
484C4⋊C4—112no—
485C4⋊C4—112no—
486C4⋊C4—224no—
487C4⋊C4—221no—
488C4⋊C4—221no—
489C4⋊C4—221no—
490C4⋊C4—221no—
491C4⋊C4—221no—
492C4⋊C4—221no—
493C4⋊C4—442no—
494C4⋊C4—442no—
495C4⋊C4C2×C4×D1112yes—
496C4⋊C4#434112yes—
497C22⋊C4—24no—
498C22⋊C4—22no—
499C22⋊C4—41no—
500C22⋊C4—42no—
501C22⋊C4—442no—
502C42—21no—
503C42—21no—
504C42—21no—
505C42—21no—
506C42—42no—
507C42—42no—
508C42—42no—
509C42—442no—
510C42—442no—
511C11#2294711yescharacteristic, complemented, Sylow
512C23—21no—
513C23—21no—
514C23—21no—
515C23—21no—
516C23—21no—
517C23—21no—
518C23C4×C22⋊D1112yes—
519C23C22×C22⋊D1111yescharacteristic
520Q8—22no—
521Q8—22no—
522Q8—41no—
523Q8—41no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—22no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—222no—
554C2×C4—222no—
555C2×C4—448no—
556C2×C4—441no—
557C2×C4—441no—
558C2×C4—441no—
559C2×C4—441no—
560C2×C4—441no—
561C2×C4—441no—
562C2×C4—441no—
563C2×C4—441no—
564C2×C4—441no—
565C2×C4—441no—
566C2×C4C4×C22⋊D1112yes—
567C2×C4#6700212yes—
568C2×C4C22×C4×D1111yescharacteristic
569C2×C4C2×#433911yescharacteristic
570C2×C4C2×#434111yescharacteristic
571C2×C4#6703711yescharacteristic
572C2×C4#41×D1111yescharacteristic
573C2×C4#6704311yescharacteristic
574C8—222no—
575C8—222no—
576C8—222no—
577C8—441no—
578C22—22no—
579C22—22no—
580C22—22no—
581C22—41no—
582C22—41no—
583C22—41no—
584C22—41no—
585C22C2×C4×C22⋊D1111yescharacteristic
586C22#1062333711yescharacteristic
587C22C2×#6700211yescharacteristic
588C22#1062335311yescharacteristic
589C22#1062335511yescharacteristic
590C22#1062336911yescharacteristic
591C22#1062336911yescharacteristic
592C4—22no—
593C4—22no—
594C4—41no—
595C4—41no—
596C4—41no—
597C4—42no—
598C4—42no—
599C4—42no—
600C4—81no—
601C4—442no—
602C4—442no—
603C4—881no—
604C4—881no—
605C4C4×#434111yescharacteristic
606C4#1062307211yescharacteristic
607C4#1062307711yescharacteristic
608C4#1062308711yescharacteristic
609C2—42no—
610C2#1307160211yescharacteristic
611C2C4×#6700211yescharacteristic
612C2#1307748211yescharacteristic
613C2#1308088411yescharacteristic
614C2#1308092111yescharacteristic
615C2#1308105611yescharacteristic
616C2#1308114011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2362C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenter#2362D11
hypocenterC11#22947
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2362

Complements

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

NH ≅ G/Ntype
3. #13069351C2semidirect
4. #13069295C2semidirect
5. #13069247C2semidirect
6. #13069205C2semidirect
7. #13069187C2semidirect
9. #13068870C2semidirect
11. C4×#66871C2semidirect
12. #13068446C2semidirect
36. #10622657C4semidirect
511. C11#22947semidirect

Maximal subgroups

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

subgroupindex
C2×#106226572
#130714832
#130693512
#130692952
#130692472
#130692052
#130691872
#130690502
#130688702
#130688152
C4×#668712
#130684462
#130684002
#130683372
C11×#23622
#2294711