Finite Group Databasebeta

← #14775239

Subgroups — #14775239

Order 2816.

802 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622658C211yesmaximal, characteristic
2#13071499C211yesmaximal, characteristic
3#13069356C211yesmaximal, characteristic, complemented
4#13069309C211yesmaximal, characteristic, complemented
5#13069254C211yesmaximal, characteristic, complemented
6#13069205C211yesmaximal, characteristic, complemented
7#13069194C211yesmaximal, characteristic, complemented
8#13069040C211yesmaximal, characteristic
9#13068884C211yesmaximal, characteristic, complemented
10#13068815C211yesmaximal, characteristic
11#13068514C211yesmaximal, characteristic, complemented
12#13068446C211yesmaximal, characteristic, complemented
13#13068394C211yesmaximal, characteristic
14#13068332C211yesmaximal, characteristic
15C11×#2362C211yesmaximal, characteristic
16C2×C11×C22⋊Q8C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×C11×#117C2211yescharacteristic
19C2×#66979C2211yescharacteristic
20C23×C11⋊C8C2211yescharacteristic
21C11×#391C2211yescharacteristic
22C11×#389C2211yescharacteristic
23C11×#388—21no—
24C11×#388—21no—
25C11×#387—21no—
26C4×C11×C4⋊C4—21no—
27C4×C11×C4⋊C4C2211yescharacteristic
28C4×C11×C22⋊C4C2211yescharacteristic
29C2×#66899C2211yescharacteristic
30C2×#66899C2211yescharacteristic
31C2×#66899C2211yescharacteristic
32C2×#66899C2211yescharacteristic
33#10622825C2211yescharacteristic
34C2×C22⋊(C11⋊C8)C2211yescharacteristic
35#10622658C418yescomplemented
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×Q8×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C11×C22⋊Q8—22no—
63C11×C22⋊Q8C2×C414yes—
64C4×Q8×C11—22no—
65C4×Q8×C11—41no—
66C11×#117—22no—
67C11×#117—41no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—21no—
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⋊C4D411yescharacteristic
77C2×C11×C22⋊C4D411yescharacteristic
78C2×C42×C11—21no—
79C2×C42×C11—21no—
80C2×C42×C11—21no—
81C2×C42×C11C2311yescharacteristic
82C2×C42×C11C2311yescharacteristic
83C2×C22⋊Dic11—21no—
84C2×C22⋊Dic11—21no—
85#66979—22no—
86#66979C2×C414yes—
87C2×C4⋊Dic11C2311yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89C2×C4⋊Dic11C2311yescharacteristic
90C2×C4⋊Dic11C2311yescharacteristic
91C2×Dic11⋊C4—21no—
92C2×Dic11⋊C4—21no—
93C2×C4×Dic11—21no—
94C2×C4×Dic11—21no—
95C2×C4×Dic11—21no—
96C22×C11⋊C8—22no—
97C22×C11⋊C8—22no—
98C22×C11⋊C8—41no—
99C22×C11⋊C8C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101C22×C11⋊C8C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103C11×#95—21no—
104C11×#95—21no—
105C11×#95—21no—
106C11×#95—21no—
107C11×#95D411yescharacteristic
108C11×#95D411yescharacteristic
109#66899—22no—
110#66899—41no—
111#66899C2×C414yes—
112#66899C2×C414yes—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C22⋊(C11⋊C8)C2×C414yes—
119#66872—22no—
120#66872C2×C414yes—
121#66871—41no—
122#66871C2×C414yes—
123#66867—22no—
124#66867—41no—
125#22939—111nomaximal, Sylow
126C24×C11C2×D411yescharacteristic
127C2×Q8×C11—21no—
128C2×Q8×C11—21no—
129C2×Q8×C11—21no—
130C2×Q8×C11—21no—
131C2×Q8×C11—21no—
132C2×Q8×C11C22×C412yes—
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×C11C22×C412yes—
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11#4112yes—
148C22×C4×C11C2411yescharacteristic
149C22×Dic11—21no—
150C22×Dic11—21no—
151C22×Dic11—21no—
152C22×Dic11—21no—
153C11×C4⋊C4—24no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—42no—
159C11×C4⋊C4—42no—
160C11×C4⋊C4C22×C412yes—
161C11×C4⋊C4#4112yes—
162C11×C22⋊C4—24no—
163C11×C22⋊C4—41no—
164C11×C22⋊C4—41no—
165C11×C22⋊C4—42no—
166C42×C11—21no—
167C42×C11—21no—
168C42×C11—21no—
169C42×C11—21no—
170C42×C11—42no—
171C42×C11—42no—
172C42×C11—42no—
173C22⋊Dic11—24no—
174C22⋊Dic11—81no—
175C4⋊Dic11—21no—
176C4⋊Dic11—21no—
177C4⋊Dic11—21no—
178C4⋊Dic11—21no—
179C4⋊Dic11—21no—
180C4⋊Dic11—21no—
181C4⋊Dic11C22×C412yes—
182C4⋊Dic11C22×C412yes—
183Dic11⋊C4—81no—
184Dic11⋊C4—81no—
185C4×Dic11—24no—
186C4×Dic11—42no—
187C4×Dic11—42no—
188C2×C11⋊C8—21no—
189C2×C11⋊C8—21no—
190C2×C11⋊C8—21no—
191C2×C11⋊C8—21no—
192C2×C11⋊C8—21no—
193C2×C11⋊C8—21no—
194C2×C11⋊C8—21no—
195C2×C11⋊C8—21no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8—44no—
198C2×C11⋊C8C22×C412yes—
199C2×C11⋊C8C22×C412yes—
200C2×C11⋊C8#4112yes—
201C2×#485—111no—
202#2362D1111yescharacteristic
203#2346—111no—
204#1944—111no—
205#1935—111no—
206#1928—111no—
207#1921—111no—
208#1919—111no—
209#1892—111no—
210#1865—111no—
211#1854—111no—
212#1776—111no—
213#1763—111no—
214#1752—111no—
215#1735—111no—
216C23×C11—21no—
217C23×C11—21no—
218C23×C11—21no—
219C23×C11—21no—
220C23×C11—21no—
221C23×C11—21no—
222C23×C11C4×D412yes—
223C23×C11C22×D411yescharacteristic
224Q8×C11—22no—
225Q8×C11—22no—
226Q8×C11—41no—
227Q8×C11—41no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—22no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—22no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—22no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
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×C11C4×D412yes—
259C2×C4×C11C23×C411yescharacteristic
260C2×C4×C11C2×#4111yescharacteristic
261C2×C4×C11C2×#4111yescharacteristic
262C2×C4×C11C2×#4111yescharacteristic
263C2×C4×C11H(5,𝔽2)11yescharacteristic
264C2×C4×C112−1+411yescharacteristic
265C2×Dic11—22no—
266C2×Dic11—22no—
267C2×Dic11—41no—
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—
277C11⋊C8—22no—
278C11⋊C8—22no—
279C11⋊C8—22no—
280C11⋊C8—41no—
281C23×C8—111no—
282C2×C22⋊Q8C2×D1111yescharacteristic
283C2×C4×Q8C2×D1111yescharacteristic
284C2×#117—111no—
285C2×#117C2×D1111yescharacteristic
286#485—118no—
287C2×#107—111no—
288C2×#107—111no—
289C2×#106—111no—
290C2×#106—111no—
291C2×#103—111no—
292C2×#103—111no—
293C2×#103—111no—
294C2×#103—111no—
295C2×C22⋊C8—111no—
296C2×#97—111no—
297C2×#97—111no—
298#391C2×D1111yescharacteristic
299#389—111no—
300#389—111no—
301#389C2×D1111yescharacteristic
302#388—21no—
303#388—21no—
304#388—221no—
305#388—221no—
306#387—21no—
307#382—221no—
308#380—111no—
309C4×C4⋊C4—21no—
310C4×C4⋊C4—111no—
311C4×C4⋊C4—111no—
312C4×C4⋊C4C2×D1111yescharacteristic
313C4×C22⋊C4C2×D1111yescharacteristic
314#376—221no—
315#340—111no—
316#340—111no—
317#340—111no—
318#340—111no—
319#340—111no—
320#340—111no—
321#340—111no—
322#340—111no—
323#336—111no—
324#336—111no—
325C22×C11—22no—
326C22×C11—22no—
327C22×C11—22no—
328C22×C11—41no—
329C22×C11—41no—
330C22×C11—41no—
331C22×C11—41no—
332C22×C11C2×C4×D411yescharacteristic
333C22×C11#54611yescharacteristic
334C22×C11#54711yescharacteristic
335C22×C11#57511yescharacteristic
336C22×C11#57511yescharacteristic
337C22×C11#57711yescharacteristic
338C22×C11#57811yescharacteristic
339C4×C11—22no—
340C4×C11—41no—
341C4×C11—41no—
342C4×C11—42no—
343C4×C11—42no—
344C4×C11—41no—
345C4×C11—42no—
346C4×C11—41no—
347C4×C11—81no—
348C4×C11C4×#4111yescharacteristic
349C4×C11#52011yescharacteristic
350C4×C11#55111yescharacteristic
351C4×C11#55211yescharacteristic
352Dic11—42no—
353Dic11—42no—
354Dic11—81no—
355Dic11—81no—
356C22×Q8C22×D1111yescharacteristic
357C23×C4C22×D1111yescharacteristic
358C22×C8—111no—
359C22×C8—111no—
360C22×C8—111no—
361C22×C8—111no—
362C22×C8—222no—
363C22×C8—222no—
364C22×C8—441no—
365C22⋊Q8—22no—
366C22⋊Q8C4×D1114yes—
367C4×Q8—22no—
368C4×Q8—41no—
369#117—22no—
370#117—41no—
371#117—114no—
372#117—222no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—111no—
377C2×C4⋊C4—111no—
378C2×C4⋊C4—111no—
379C2×C4⋊C4—111no—
380C2×C4⋊C4—221no—
381C2×C4⋊C4—221no—
382C2×C4⋊C4C22×D1111yescharacteristic
383C2×C4⋊C4C22×D1111yescharacteristic
384C2×C4⋊C4C22×D1111yescharacteristic
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—221no—
388C2×C22⋊C4—221no—
389C2×C22⋊C4C22⋊D1111yescharacteristic
390C2×C22⋊C4C22⋊D1111yescharacteristic
391C2×C42—21no—
392C2×C42—21no—
393C2×C42—21no—
394C2×C42—221no—
395C2×C42—221no—
396C2×C42—221no—
397C2×C42C22×D1111yescharacteristic
398C2×C42C22×D1111yescharacteristic
399#107—114no—
400#107—441no—
401#106—114no—
402#106—222no—
403#103—114no—
404#103—114no—
405#103—222no—
406#103—441no—
407C22⋊C8—114no—
408#97—222no—
409#97—441no—
410#95—21no—
411#95—21no—
412#95—21no—
413#95—21no—
414#95—221no—
415#95—221no—
416#95—221no—
417#95—221no—
418#95—221no—
419#95C22⋊D1111yescharacteristic
420#95C22⋊D1111yescharacteristic
421C2×C11—42no—
422C2×C11#235911yescharacteristic
423C2×C11#294311yescharacteristic
424C2×C11#294711yescharacteristic
425C2×C11#331511yescharacteristic
426C2×C11#332111yescharacteristic
427C2×C11#334811yescharacteristic
428C2×C11#334911yescharacteristic
429C24C2×C22⋊D1111yescharacteristic
430C2×Q8—21no—
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8C2×C4×D1112yes—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—221no—
445C22×C4—221no—
446C22×C4—221no—
447C22×C4—221no—
448C22×C4C2×C4×D1112yes—
449C22×C4#433912yes—
450C22×C4C2×C22⋊D1111yescharacteristic
451C22×C4C2×C22⋊D1111yescharacteristic
452C22×C4C2×C22⋊D1111yescharacteristic
453C22×C4C2×C22⋊D1111yescharacteristic
454C22×C4C2×C22⋊D1111yescharacteristic
455C22×C4C23×D1111yescharacteristic
456C2×C8—112no—
457C2×C8—112no—
458C2×C8—112no—
459C2×C8—221no—
460C2×C8—221no—
461C2×C8—221no—
462C2×C8—221no—
463C2×C8—221no—
464C2×C8—221no—
465C2×C8—221no—
466C2×C8—221no—
467C2×C8—221no—
468C2×C8—444no—
469C4⋊C4—24no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—42no—
475C4⋊C4—42no—
476C4⋊C4—112no—
477C4⋊C4—112no—
478C4⋊C4—221no—
479C4⋊C4—221no—
480C4⋊C4—221no—
481C4⋊C4—221no—
482C4⋊C4—221no—
483C4⋊C4—221no—
484C4⋊C4—881no—
485C4⋊C4—881no—
486C4⋊C4C2×C4×D1112yes—
487C4⋊C4#434112yes—
488C22⋊C4—24no—
489C22⋊C4—41no—
490C22⋊C4—41no—
491C22⋊C4—42no—
492C22⋊C4—224no—
493C22⋊C4—881no—
494C42—21no—
495C42—21no—
496C42—21no—
497C42—21no—
498C42—42no—
499C42—42no—
500C42—42no—
501C42—224no—
502C42—442no—
503C42—442no—
504C11#2293911yescharacteristic, complemented, Sylow
505C23—21no—
506C23—21no—
507C23—21no—
508C23—21no—
509C23—21no—
510C23—21no—
511C23C4×C22⋊D1112yes—
512C23C22×C22⋊D1111yescharacteristic
513Q8—22no—
514Q8—22no—
515Q8—41no—
516Q8—41no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—22no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
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—222no—
548C2×C4—222no—
549C2×C4—441no—
550C2×C4—441no—
551C2×C4—441no—
552C2×C4—441no—
553C2×C4—441no—
554C2×C4—441no—
555C2×C4—441no—
556C2×C4—441no—
557C2×C4—441no—
558C2×C4—441no—
559C2×C4C4×C22⋊D1112yes—
560C2×C4C22×C4×D1111yescharacteristic
561C2×C4C2×#433911yescharacteristic
562C2×C4C2×#434111yescharacteristic
563C2×C4#6703711yescharacteristic
564C2×C4#41×D1111yescharacteristic
565C2×C4#6704311yescharacteristic
566C8—222no—
567C8—222no—
568C8—222no—
569C8—441no—
570C22—22no—
571C22—22no—
572C22—22no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22C2×C4×C22⋊D1111yescharacteristic
578C22#1062333711yescharacteristic
579C22#1062335311yescharacteristic
580C22#1062335311yescharacteristic
581C22#1062335511yescharacteristic
582C22#1062336811yescharacteristic
583C22#1062336911yescharacteristic
584C4—22no—
585C4—41no—
586C4—41no—
587C4—41no—
588C4—42no—
589C4—42no—
590C4—41no—
591C4—42no—
592C4—81no—
593C4—442no—
594C4—442no—
595C4—881no—
596C4—881no—
597C4C4×#434111yescharacteristic
598C4#1062307211yescharacteristic
599C4#1062307711yescharacteristic
600C4#1062308711yescharacteristic
601C2—42no—
602C2#1307160211yescharacteristic
603C2#1307741411yescharacteristic
604C2#1307745911yescharacteristic
605C2#1308071211yescharacteristic
606C2#1308080211yescharacteristic
607C2#1308112511yescharacteristic
608C2#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#22939
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. #13069356C2semidirect
4. #13069309C2semidirect
5. #13069254C2semidirect
6. #13069205C2semidirect
7. #13069194C2semidirect
9. #13068884C2semidirect
11. #13068514C2semidirect
12. #13068446C2semidirect
35. #10622658C4semidirect
504. C11#22939semidirect

Maximal subgroups

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

subgroupindex
C2×#106226582
#130714992
#130693562
#130693092
#130692542
#130692052
#130691942
#130690402
#130688842
#130688152
#130685142
#130684462
#130683942
#130683322
C11×#23622
#2293911