Finite Group Databasebeta

← #14724925

Subgroups — #14724925

Order 2816.

650 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078659C211yesmaximal, characteristic
2#13077650C211yesmaximal, characteristic, complemented
3#13067506C211yesmaximal, characteristic, complemented
4#13067499C211yesmaximal, characteristic, complemented
5#13067494C211yesmaximal, characteristic, complemented
6#13067480C211yesmaximal, characteristic, complemented
7#13067478C211yesmaximal, characteristic, complemented
8#13067471C211yesmaximal, characteristic, complemented
9C8×#4325C211yesmaximal, characteristic, complemented
10C8×#4323C211yesmaximal, characteristic, complemented
11#13067399C211yesmaximal, characteristic, complemented
12#13067076C211yesmaximal, characteristic, complemented
13C2×#10622121C211yesmaximal, characteristic, complemented
14#13066900C211yesmaximal, characteristic, complemented
15C11×#2994C211yesmaximal, characteristic, complemented
16C11×#529C2211yescharacteristic
17C2×C4×D44C2211yescharacteristic
18C11×#446C2211yescharacteristic, complemented
19C8×Q8×C11C2211yescharacteristic, complemented
20C11×#436C2211yescharacteristic, complemented
21C11×#435—21no—
22C8×D4×C11—21no—
23C8×D4×C11C2211yescharacteristic, complemented
24C11×#433—21no—
25C11×#431C2211yescharacteristic
26C11×#424—21no—
27C2×C11×C4⋊C8C2211yescharacteristic
28#10622679C411yescharacteristic
29#10622679C411yescharacteristic
30#10622670C411yescharacteristic
31#10622670C411yescharacteristic
32#10622659C411yescharacteristic
33#10622657C411yescharacteristic
34#10622649C411yescharacteristic
35#10622647C411yescharacteristic
36C4×#4325C2211yescharacteristic
37C4×#4325C2211yescharacteristic
38C4×#4323C2211yescharacteristic
39C4×#4323C2211yescharacteristic
40#10622539C2211yescharacteristic
41#10622538C2211yescharacteristic
42C2×C4×C11⋊C8C2211yescharacteristic
43#10622449—21no—
44#10622449—21no—
45#10622339—21no—
46D11×C22⋊C8—21no—
47#10622301C2211yescharacteristic
48#10622301C2211yescharacteristic
49C8×D44C2211yescharacteristic
50C8×D44C2211yescharacteristic
51Q8⋊(C11⋊C8)C2211yescharacteristic, complemented
52Q8⋊(C11⋊C8)C2211yescharacteristic, complemented
53D4⋊(C11⋊C8)C2211yescharacteristic, complemented
54D4⋊(C11⋊C8)C2211yescharacteristic, complemented
55#10622121C2211yescharacteristic
56#10622121C2211yescharacteristic
57#10622121C2211yescharacteristic
58#10622121C2211yescharacteristic
59#10622118C2211yescharacteristic, complemented
60#10622118C2211yescharacteristic, complemented
61#10622117C2211yescharacteristic, complemented
62#10622117C2211yescharacteristic, complemented
63#10622092C2211yescharacteristic, complemented
64#10622092C2211yescharacteristic, complemented
65C8×C11⋊C8C2211yescharacteristic, complemented
66C8×C11⋊C8C2211yescharacteristic, complemented
67C22×D44C2×C411yescharacteristic
68C22×C4×D11—21no—
69C2×C11×M16—21no—
70C22×C8×C11—21no—
71C22×C8×C11—21no—
72C11×#126—21no—
73C11×#125C2×C411yescharacteristic
74C11×#124C2×C411yescharacteristic
75C11×#123—21no—
76C11×C22⋊Q8C2×C411yescharacteristic
77C11×#121C2×C411yescharacteristic
78C4×Q8×C11C2311yescharacteristic
79C4×D4×C11—21no—
80C4×D4×C11C2311yescharacteristic
81C11×#117—21no—
82C2×C42×C11C2311yescharacteristic
83C2×#4325C2×C411yescharacteristic
84C2×#4325C2×C411yescharacteristic
85C2×#4323C2×C411yescharacteristic
86C2×#4323C2×C411yescharacteristic
87C2×(C2×D11)⋊C4—21no—
88C2×C4⋊Dic11C2×C411yescharacteristic
89C22×C11⋊C8—21no—
90C2×#4313—21no—
91C2×#4313—21no—
92C2×C8×D11—21no—
93C2×C8×D11—21no—
94C4×D44—21no—
95C4×D44—21no—
96C4×D44C2×C411yescharacteristic
97C4×D44C2×C411yescharacteristic
98C4×D44C2311yescharacteristic
99C4×D44C2311yescharacteristic
100C11×C4⋊C8—21no—
101C11×C4⋊C8—21no—
102C11×C4⋊C8—21no—
103C11×C4⋊C8D411yescharacteristic
104C11×C4⋊C8D411yescharacteristic
105C11×C4⋊C8C2311yescharacteristic
106C11×C4⋊C8C2311yescharacteristic
107C11×C22⋊C8—21no—
108C11×C22⋊C8—21no—
109C11×C22⋊C8D411yescharacteristic
110C11×C22⋊C8D411yescharacteristic
111C11×#97—21no—
112C4×C8×C11—21no—
113C4×C8×C11C2311yescharacteristic
114C4×C8×C11C2311yescharacteristic
115#66899C2×C411yescharacteristic
116#66899C2×C411yescharacteristic
117#66896C2×C411yescharacteristic
118#66896C2×C411yescharacteristic
119C22⋊(C11⋊C8)—21no—
120C22⋊(C11⋊C8)C2×C411yescharacteristic
121C22⋊(C11⋊C8)C2×C411yescharacteristic
122(C2×D11)⋊C8—21no—
123(C2×D11)⋊C8—21no—
124(C2×D11)⋊C8—21no—
125(C2×D11)⋊C8—21no—
126#66873C2×C411yescharacteristic
127#66873C2×C411yescharacteristic
128#66873C2×C411yescharacteristic
129#66873C2×C411yescharacteristic
130#66872C2×C411yescharacteristic
131#66872C2×C411yescharacteristic
132#66871C2×C411yescharacteristic
133#66871C2×C411yescharacteristic
134C4⋊(C11⋊C8)C2×C411yescharacteristic
135C4⋊(C11⋊C8)C2×C411yescharacteristic
136C4⋊(C11⋊C8)C2311yescharacteristic
137C4⋊(C11⋊C8)C2311yescharacteristic
138#66867—21no—
139C4×C11⋊C8—21no—
140C4×C11⋊C8C2311yescharacteristic
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#18014—111nomaximal, Sylow
145C23×D11—21no—
146C2×Q8×C11C22×C411yescharacteristic
147C2×D4×C11—21no—
148C2×D4×C11C22×C411yescharacteristic
149C22×C4×C11—21no—
150C22×C4×C11C22×C411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11#4111yescharacteristic
153C22×Dic11—21no—
154C2×D44—22no—
155C2×D44—21no—
156C2×D44—41no—
157C2×D44C22×C411yescharacteristic
158C2×D44C22×C411yescharacteristic
159C2×C4×D11—21no—
160C2×C4×D11—21no—
161C2×C4×D11—21no—
162C2×C4×D11—21no—
163C2×C4×D11—81no—
164C2×C4×D11—81no—
165C11×M16—81no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—81no—
169C2×C8×C11—81no—
170C2×C8×C11C2×D411yescharacteristic
171C2×C8×C11C2×D411yescharacteristic
172C2×C8×C11C2×D411yescharacteristic
173C2×C8×C11C2×D411yescharacteristic
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4C22×C411yescharacteristic
179C11×C4⋊C4C22×C411yescharacteristic
180C11×C22⋊C4—21no—
181C11×C22⋊C4—21no—
182C11×C22⋊C4—21no—
183C11×C22⋊C4—21no—
184C11×C22⋊C4—21no—
185C42×C11—21no—
186C42×C11C22×C411yescharacteristic
187C42×C11C2×D411yescharacteristic
188C42×C11#4111yescharacteristic
189C42×C11C2411yescharacteristic
190#4325—22no—
191#4325—41no—
192#4323—22no—
193#4323—41no—
194(C2×D11)⋊C4—21no—
195(C2×D11)⋊C4—21no—
196(C2×D11)⋊C4—21no—
197(C2×D11)⋊C4—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11C22×C411yescharacteristic
200C4⋊Dic11C22×C411yescharacteristic
201C2×C11⋊C8—24no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8C22×C411yescharacteristic
207C2×C11⋊C8C22×C411yescharacteristic
208C2×C11⋊C8C22×C411yescharacteristic
209C2×C11⋊C8C22×C411yescharacteristic
210#4313—81no—
211#4313—81no—
212C8×D11—81no—
213C8×D11—81no—
214#3105—111no—
215#2994D1111yescharacteristic, complemented
216#2974—111no—
217#1590—111no—
218#1589—111no—
219#1588—111no—
220#1586—111no—
221#1586—111no—
222#1585—111no—
223C8×SD16—111no—
224C8×D8—111no—
225#1573—111no—
226#1494—111no—
227C2×D4⋊C8—111no—
228#1450—111no—
229C23×C11—21no—
230C23×C11C4×D411yescharacteristic
231C22×D11—21no—
232C22×D11—21no—
233C22×D11—42no—
234C22×D11—42no—
235C22×D11—81no—
236Q8×C11—21no—
237Q8×C11—21no—
238D4×C11—21no—
239D4×C11—21no—
240D4×C11—42no—
241C2×C4×C11—22no—
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×C11C4×D411yescharacteristic
252C2×C4×C11C4×D411yescharacteristic
253C2×C4×C11C4×D411yescharacteristic
254C2×C4×C11C23×C411yescharacteristic
255C2×C4×C11C22×D411yescharacteristic
256C2×C4×C11C2×#4111yescharacteristic
257C2×Dic11—21no—
258C2×Dic11—21no—
259C2×Dic11—81no—
260D44—21no—
261D44—21no—
262D44—21no—
263D44—42no—
264D44#13112yes—
265C4×D11—41no—
266C4×D11—41no—
267C4×D11—41no—
268C4×D11—41no—
269C4×D11—81no—
270C4×D11—81no—
271C8×C11—21no—
272C8×C11—21no—
273C8×C11—21no—
274C8×C11—21no—
275C8×C11—41no—
276C8×C11—41no—
277C11⋊C8—22no—
278C11⋊C8—22no—
279C11⋊C8—21no—
280C11⋊C8—21no—
281C11⋊C8—21no—
282C11⋊C8—21no—
283C11⋊C8—41no—
284C11⋊C8—41no—
285#529C2×D1111yescharacteristic
286C2×C4×D4—111no—
287#484—111no—
288#481—111no—
289#478—111no—
290#478—111no—
291#463—111no—
292#463—111no—
293#450—111no—
294#447—111no—
295#446C2×D1111yescharacteristic, complemented
296C8×Q8C2×D1111yescharacteristic, complemented
297C4×SD16—111no—
298C4×SD16—111no—
299C4×D8—111no—
300C4×D8—111no—
301#436—111no—
302#436—111no—
303#436C2×D1111yescharacteristic, complemented
304#435—21no—
305#435—221no—
306#435—221no—
307C8×D4—21no—
308C8×D4—111no—
309C8×D4—111no—
310C8×D4C2×D1111yescharacteristic, complemented
311#433—21no—
312#432—111no—
313#431—111no—
314#431C2×D1111yescharacteristic
315#424—21no—
316C2×C4⋊C8C2×D1111yescharacteristic
317#407—221no—
318C2×C22⋊C8—221no—
319C2×C4×C8—111no—
320#335—111no—
321#335—111no—
322#334—111no—
323#334—111no—
324Q8⋊C8—111no—
325Q8⋊C8—111no—
326D4⋊C8—111no—
327D4⋊C8—111no—
328D4⋊C8—111no—
329D4⋊C8—111no—
330D4⋊C8—111no—
331D4⋊C8—111no—
332#322—111no—
333#322—111no—
334C82—111no—
335C82—111no—
336C22×C11—21no—
337C22×C11—21no—
338C22×C11—41no—
339C22×C11—41no—
340C22×C11—41no—
341C22×C11#44312yes—
342C22×C11C2×C4×D411yescharacteristic
343C2×D11—22no—
344C2×D11—41no—
345C2×D11—41no—
346C2×D11—41no—
347C2×D11—41no—
348C2×D11—41no—
349C2×D11—84no—
350C4×C11—21no—
351C4×C11—21no—
352C4×C11—21no—
353C4×C11—21no—
354C4×C11—41no—
355C4×C11—41no—
356C4×C11—41no—
357C4×C11C2×#13111yescharacteristic
358C4×C11#56811yescharacteristic
359C4×C11#57611yescharacteristic
360C4×C11#57711yescharacteristic
361Dic11—41no—
362Dic11—41no—
363C22×D4—111no—
364C23×C4—221no—
365C2×SD16—111no—
366C2×SD16—111no—
367C2×D8—111no—
368C2×D8—111no—
369C2×M16—21no—
370C2×M16—221no—
371C2×M16—221no—
372C22×C8—21no—
373C22×C8—21no—
374C22×C8—221no—
375C22×C8—221no—
376C22×C8—221no—
377#126—21no—
378#125C4×D1111yescharacteristic
379#124C4×D1111yescharacteristic
380#123—21no—
381C22⋊Q8C4×D1111yescharacteristic
382#121C4×D1111yescharacteristic
383C4×Q8C22×D1111yescharacteristic
384C4×D4—21no—
385C4×D4—111no—
386C4×D4—111no—
387C4×D4—111no—
388C4×D4—111no—
389C4×D4—221no—
390C4×D4—221no—
391C4×D4C22×D1111yescharacteristic
392#117—21no—
393C2×C4⋊C4—111no—
394C2×C22⋊C4—221no—
395C2×C42C22×D1111yescharacteristic
396#107—111no—
397#107—111no—
398#106—111no—
399#106—111no—
400C4⋊C8—21no—
401C4⋊C8—21no—
402C4⋊C8—21no—
403C4⋊C8—111no—
404C4⋊C8—111no—
405C4⋊C8—111no—
406C4⋊C8—111no—
407C4⋊C8C22⋊D1111yescharacteristic
408C4⋊C8C22⋊D1111yescharacteristic
409C4⋊C8C22×D1111yescharacteristic
410C4⋊C8C22×D1111yescharacteristic
411#103—111no—
412#103—111no—
413#102—111no—
414#102—111no—
415#102—111no—
416#102—111no—
417#102—111no—
418#102—111no—
419C22⋊C8—21no—
420C22⋊C8—21no—
421C22⋊C8—111no—
422C22⋊C8—111no—
423C22⋊C8—221no—
424C22⋊C8—221no—
425C22⋊C8—221no—
426C22⋊C8—221no—
427C22⋊C8—221no—
428C22⋊C8C22⋊D1111yescharacteristic
429C22⋊C8C22⋊D1111yescharacteristic
430#97—21no—
431#97—221no—
432C4×C8—21no—
433C4×C8—111no—
434C4×C8—111no—
435C4×C8—111no—
436C4×C8—111no—
437C4×C8—221no—
438C4×C8C22×D1111yescharacteristic
439C4×C8C22×D1111yescharacteristic
440C2×C11—22no—
441C2×C11—81no—
442C2×C11#293311yescharacteristic
443C2×C11#294611yescharacteristic
444C2×C11C2×#44311yescharacteristic
445D11—42no—
446D11—81no—
447C24—221no—
448C2×Q8C2×C4×D1111yescharacteristic
449C2×D4—21no—
450C2×D4—111no—
451C2×D4—111no—
452C2×D4—222no—
453C2×D4—221no—
454C2×D4—441no—
455C2×D4C2×C4×D1111yescharacteristic
456C22×C4—21no—
457C22×C4—221no—
458C22×C4—221no—
459C22×C4—221no—
460C22×C4—221no—
461C22×C4—221no—
462C22×C4—881no—
463C22×C4—881no—
464C22×C4C2×C4×D1111yescharacteristic
465C22×C4#433911yescharacteristic
466C22×C4C2×C22⋊D1111yescharacteristic
467SD16—222no—
468SD16—441no—
469D8—222no—
470D8—441no—
471M16—81no—
472M16—881no—
473M16—881no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—81no—
477C2×C8—81no—
478C2×C8—111no—
479C2×C8—111no—
480C2×C8—111no—
481C2×C8—111no—
482C2×C8—224no—
483C2×C8—221no—
484C2×C8—221no—
485C2×C8—221no—
486C2×C8—221no—
487C2×C8—881no—
488C2×C8—881no—
489C2×C8C2×C22⋊D1111yescharacteristic
490C2×C8C2×C22⋊D1111yescharacteristic
491C2×C8C2×C22⋊D1111yescharacteristic
492C2×C8C2×C22⋊D1111yescharacteristic
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—111no—
498C4⋊C4—111no—
499C4⋊C4—221no—
500C4⋊C4C2×C4×D1111yescharacteristic
501C4⋊C4C2×C4×D1111yescharacteristic
502C22⋊C4—21no—
503C22⋊C4—21no—
504C22⋊C4—21no—
505C22⋊C4—21no—
506C22⋊C4—21no—
507C22⋊C4—221no—
508C22⋊C4—221no—
509C22⋊C4—221no—
510C22⋊C4—221no—
511C42—21no—
512C42C2×C4×D1111yescharacteristic
513C42#433911yescharacteristic
514C42C2×C22⋊D1111yescharacteristic
515C42C23×D1111yescharacteristic
516C11#1801411yescharacteristic, complemented, Sylow
517C23—21no—
518C23—221no—
519C23—221no—
520C23—442no—
521C23—442no—
522C23—881no—
523C23C4×C22⋊D1111yescharacteristic
524Q8—21no—
525Q8—21no—
526D4—21no—
527D4—21no—
528D4—42no—
529D4—112no—
530D4—221no—
531D4—221no—
532D4—221no—
533D4—442no—
534C2×C4—22no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—221no—
545C2×C4—221no—
546C2×C4—441no—
547C2×C4—441no—
548C2×C4—441no—
549C2×C4—441no—
550C2×C4—881no—
551C2×C4—881no—
552C2×C4—881no—
553C2×C4C4×C22⋊D1111yescharacteristic
554C2×C4C4×C22⋊D1111yescharacteristic
555C2×C4C4×C22⋊D1111yescharacteristic
556C2×C4C22×C4×D1111yescharacteristic
557C2×C4C2×#433911yescharacteristic
558C2×C4C22×C22⋊D1111yescharacteristic
559C8—21no—
560C8—21no—
561C8—21no—
562C8—21no—
563C8—41no—
564C8—41no—
565C8—222no—
566C8—222no—
567C8—221no—
568C8—221no—
569C8—221no—
570C8—221no—
571C8—441no—
572C8—441no—
573C22—21no—
574C22—21no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—222no—
579C22—441no—
580C22—441no—
581C22—441no—
582C22—441no—
583C22—441no—
584C22—884no—
585C22#1062275712yes—
586C22C2×C4×C22⋊D1111yescharacteristic
587C4—21no—
588C4—21no—
589C4—21no—
590C4—21no—
591C4—41no—
592C4—41no—
593C4—41no—
594C4—441no—
595C4—441no—
596C4D11×#13111yescharacteristic
597C4#1062328111yescharacteristic
598C4#1062336611yescharacteristic
599C4#1062336811yescharacteristic
600C2—22no—
601C2—81no—
602C2—442no—
603C2—881no—
604C2#1307733811yescharacteristic
605C2#1307744411yescharacteristic
606C2C2×#1062275711yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#2994C2
socleC22×C11C2×C4×D4
prime radical#10622649C4
cosocleC42×C11C24
hypercenter#2994D11
hypocenterC11#18014
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2994

Complements

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

NH ≅ G/Ntype
2. #13077650C2semidirect
3. #13067506C2semidirect
4. #13067499C2semidirect
5. #13067494C2semidirect
6. #13067480C2semidirect
7. #13067478C2semidirect
8. #13067471C2semidirect
9. C8×#4325C2semidirect
10. C8×#4323C2semidirect
11. #13067399C2semidirect
12. #13067076C2semidirect
13. C2×#10622121C2semidirect
14. #13066900C2semidirect
15. C11×#2994C2semidirect
18. C11×#446C22semidirect
19. C8×Q8×C11C22semidirect
20. C11×#436C22semidirect
23. C8×D4×C11C22semidirect
51. Q8⋊(C11⋊C8)C22semidirect
52. Q8⋊(C11⋊C8)C22semidirect
53. D4⋊(C11⋊C8)C22semidirect
54. D4⋊(C11⋊C8)C22semidirect
59. #10622118C22semidirect
60. #10622118C22semidirect
61. #10622117C22semidirect
62. #10622117C22semidirect
63. #10622092C22semidirect
64. #10622092C22semidirect
65. C8×C11⋊C8C22semidirect
66. C8×C11⋊C8C22semidirect
215. #2994D11semidirect
295. #446C2×D11semidirect
296. C8×Q8C2×D11semidirect
303. #436C2×D11semidirect
310. C8×D4C2×D11semidirect
516. C11#18014semidirect

Maximal subgroups

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

subgroupindex
#130786592
#130776502
#130675062
#130674992
#130674942
#130674802
#130674782
#130674712
C8×#43252
C8×#43232
#130673992
#130670762
C2×#106221212
#130669002
C11×#29942
#1801411