Finite Group Databasebeta

← #14805627

Subgroups — #14805627

Order 2816.

818 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×#10622483C211yesmaximal, characteristic
2C2×C8×Dic22C211yesmaximal, characteristic, complemented
3#13073823C211yesmaximal, characteristic, complemented
4#13073537C211yesmaximal, characteristic
5#13070117C211yesmaximal, characteristic, complemented
6#13070115C211yesmaximal, characteristic, complemented
7#13069987C211yesmaximal, characteristic
8#13069985C211yesmaximal, characteristic
9#13069575C211yesmaximal, characteristic, complemented
10#13069376C211yesmaximal, characteristic, complemented
11#13069343C211yesmaximal, characteristic, complemented
12#13069299C211yesmaximal, characteristic
13#13069297C211yesmaximal, characteristic
14#13068430C211yesmaximal, characteristic
15C11×#1941C211yesmaximal, characteristic, complemented
16C2×#66949—21no—
17C2×#66946C2211yescharacteristic
18C2×#66941C2211yescharacteristic
19C2×C4×Dic22C2211yescharacteristic
20C2×C11×#106C2211yescharacteristic
21C2×C11×#106C2211yescharacteristic
22C2×C4×C8×C11C2211yescharacteristic
23C11×#389C2211yescharacteristic
24C11×#389C2211yescharacteristic
25C2×#66885C2211yescharacteristic
26C2×#66885C2211yescharacteristic
27C2×Dic11⋊C8C2211yescharacteristic
28C2×Dic11⋊C8C2211yescharacteristic
29C2×C8×Dic11C2211yescharacteristic
30C2×C8×Dic11C2211yescharacteristic
31#10622607—21no—
32#10622601C2211yescharacteristic
33#10622598C2211yescharacteristic
34#10622592—21no—
35#10622589—21no—
36#10622589C2211yescharacteristic
37C4⋊C4×Dic11C2211yescharacteristic
38#10622586C2211yescharacteristic
39#10622586C2211yescharacteristic
40C2×#66873C2211yescharacteristic
41C2×#66873C2211yescharacteristic
42C2×#66872C2211yescharacteristic
43C2×#66872C2211yescharacteristic
44#10622552C2211yescharacteristic
45#10622541C2211yescharacteristic
46C2×C4⋊(C11⋊C8)C2211yescharacteristic
47#10622483—24no—
48C8×Dic22—24no—
49#10622289—21no—
50#10622280—21no—
51#10622269—21no—
52#10622259—21no—
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×D44C2311yescharacteristic
62C22×C4×D11—21no—
63C22×Dic22—21no—
64C22×Dic22D411yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C42×C11C2311yescharacteristic
74C2×(C2×D11)⋊C4—21no—
75C2×(C2×D11)⋊C4—21no—
76C2×(C2×D11)⋊C4—21no—
77C2×(C2×D11)⋊C4—21no—
78C2×(C2×D11)⋊C4—21no—
79C2×C4⋊Dic11—21no—
80C2×C4⋊Dic11D411yescharacteristic
81C2×C4⋊Dic11C2311yescharacteristic
82C2×C4⋊Dic11C2311yescharacteristic
83C2×C4⋊Dic11C2311yescharacteristic
84C2×Dic11⋊C4—21no—
85C2×Dic11⋊C4—21no—
86C2×Dic11⋊C4—21no—
87C2×Dic11⋊C4—21no—
88C2×Dic11⋊C4—21no—
89C2×Dic11⋊C4—21no—
90C2×Dic11⋊C4D411yescharacteristic
91C2×Dic11⋊C4D411yescharacteristic
92C2×C4×Dic11—21no—
93C2×C4×Dic11C2311yescharacteristic
94C2×C4×Dic11C2311yescharacteristic
95C22×C11⋊C8C2311yescharacteristic
96C22×C11⋊C8C2311yescharacteristic
97#66949—44no—
98#66946—22no—
99#66946—22no—
100#66941—22no—
101#66941—22no—
102C4×Dic22—22no—
103C4×Dic22—22no—
104C11×#106—22no—
105C11×#106—22no—
106C4×C8×C11—22no—
107C11×#95—21no—
108C11×#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114#66885—22no—
115#66885Q814yescomplemented
116Dic11⋊C8—22no—
117Dic11⋊C8D414yes—
118C8×Dic11—22no—
119C8×Dic11—22no—
120#66873—22no—
121#66873—22no—
122#66872—22no—
123#66872—22no—
124C4⋊(C11⋊C8)—22no—
125#25470—111nomaximal, Sylow
126C23×D11—21no—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2411yescharacteristic
134C22×Dic11—21no—
135C22×Dic11—21no—
136C22×Dic11—21no—
137C22×Dic11C2×D411yescharacteristic
138C22×Dic11C2×D411yescharacteristic
139C22×Dic11C2×D411yescharacteristic
140C22×Dic11C2×D411yescharacteristic
141C2×D44—21no—
142C2×D44—21no—
143C2×D44—21no—
144C2×D44—21no—
145C2×D44—21no—
146C2×D44C2×Q812yes—
147C2×C4×D11—42no—
148C2×C4×D11—42no—
149C2×C4×D11—42no—
150C2×Dic22—22no—
151C2×Dic22—22no—
152C2×Dic22—42no—
153C2×Dic22—81no—
154C2×Dic22—81no—
155C2×Dic22SD1614yes—
156C2×C8×C11—21no—
157C2×C8×C11—21no—
158C2×C8×C11—21no—
159C2×C8×C11—21no—
160C2×C8×C11C2×D412yes—
161C2×C8×C11C2×Q812yes—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—42no—
170C11×C4⋊C4—81no—
171C11×C4⋊C4#4112yes—
172C42×C11—21no—
173C42×C11—21no—
174(C2×D11)⋊C4—42no—
175(C2×D11)⋊C4—42no—
176(C2×D11)⋊C4—42no—
177(C2×D11)⋊C4—81no—
178(C2×D11)⋊C4—81no—
179C4⋊Dic11—22no—
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11—81no—
186C4⋊Dic11C2×Q812yes—
187Dic11⋊C4—22no—
188Dic11⋊C4—22no—
189Dic11⋊C4—42no—
190Dic11⋊C4—42no—
191Dic11⋊C4—42no—
192Dic11⋊C4—81no—
193Dic11⋊C4—81no—
194Dic11⋊C4—81no—
195C4×Dic11—21no—
196C4×Dic11—21no—
197C4×Dic11—42no—
198C4×Dic11C2×D412yes—
199C4×Dic11#4112yes—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8C2×D412yes—
206C2×#476—111no—
207C2×C8×Q8—111no—
208#2567—111no—
209#2538—111no—
210#2088—111no—
211#2088—111no—
212#2065—111no—
213#2065—111no—
214#1990—111no—
215#1948—111no—
216#1941—111no—
217#1941D1111yescharacteristic, complemented
218#1934—111no—
219#1934—111no—
220C4×#102—111no—
221C23×C11C22×D411yescharacteristic
222C22×D11—22no—
223C22×D11—41no—
224C22×D11—41no—
225C22×D11—41no—
226C22×D11—41no—
227C22×D11—41no—
228C22×D11—41no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—22no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—41no—
236C2×C4×C11—41no—
237C2×C4×C11—41no—
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×C11C2×SD1612yes—
247C2×C4×C11C22×D411yescharacteristic
248C2×C4×C11C22×Q811yescharacteristic
249C2×C4×C11C2×#4111yescharacteristic
250C2×C4×C11C2×#4111yescharacteristic
251C2×C4×C112−1+411yescharacteristic
252C2×C4×C112−1+411yescharacteristic
253C2×Dic11—21no—
254C2×Dic11—21no—
255C2×Dic11—21no—
256C2×Dic11—21no—
257C2×Dic11—21no—
258C2×Dic11—22no—
259C2×Dic11—21no—
260C2×Dic11—21no—
261C2×Dic11—41no—
262C2×Dic11—41no—
263C2×Dic11—41no—
264C2×Dic11—41no—
265C2×Dic11—41no—
266C2×Dic11—41no—
267C2×Dic11—41no—
268C2×Dic11—41no—
269C2×Dic11#12112yes—
270C2×Dic11#12112yes—
271C2×Dic11C2×SD1612yes—
272C2×Dic11C2×SD1612yes—
273C2×Dic11#13512yes—
274D44—22no—
275D44—22no—
276D44—41no—
277D44—41no—
278C4×D11—84no—
279Dic22—28no—
280Dic22—84no—
281C8×C11—22no—
282C8×C11—22no—
283C11⋊C8—22no—
284C11⋊C8—41no—
285C2×C4⋊Q8—111no—
286C2×C22⋊Q8—221no—
287C2×C4×Q8—111no—
288C2×C4×D4—111no—
289#476—224no—
290C8×Q8—224no—
291C2×#106—111no—
292C2×#106—111no—
293C2×#106C2×D1111yescharacteristic
294C2×#106C2×D1111yescharacteristic
295C2×C4⋊C8—111no—
296C2×C4⋊C8—111no—
297C2×C4⋊C8—111no—
298C2×#102—111no—
299C2×#102—111no—
300C2×#102—111no—
301C2×#102—111no—
302C2×C4×C8—111no—
303C2×C4×C8—111no—
304C2×C4×C8C2×D1111yescharacteristic
305#396—221no—
306#396—221no—
307#395—221no—
308#395—221no—
309#391—221no—
310#390—111no—
311#390—111no—
312#389—111no—
313#389—111no—
314#389—111no—
315#389—111no—
316#389C2×D1111yescharacteristic
317#389C2×D1111yescharacteristic
318#384—111no—
319#384—221no—
320#380—221no—
321C4×C4⋊C4—111no—
322#340—111no—
323#340—111no—
324#340—111no—
325#340—111no—
326#340—111no—
327#340—111no—
328#340C2×D1111yescharacteristic
329#340C2×D1111yescharacteristic
330C22×C11C2×#12111yescharacteristic
331C22×C11#54811yescharacteristic
332C22×C11D4×Q811yescharacteristic
333C22×C11C22×SD1611yescharacteristic
334C22×C11C2×#13511yescharacteristic
335C22×C11#57611yescharacteristic
336C22×C11#57711yescharacteristic
337C2×D11—42no—
338C2×D11—42no—
339C2×D11—42no—
340C2×D11—81no—
341C2×D11—81no—
342C2×D11—81no—
343C2×D11—81no—
344C4×C11—22no—
345C4×C11—42no—
346C4×C11—41no—
347C4×C11—81no—
348C4×C11—81no—
349C4×C11—81no—
350C4×C11#53311yescharacteristic
351C4×C11#54111yescharacteristic
352C4×C11#54711yescharacteristic
353C4×C11D4×Q811yescharacteristic
354Dic11—22no—
355Dic11—22no—
356Dic11—42no—
357Dic11—41no—
358Dic11—81no—
359Dic11—81no—
360Dic11#46514yes—
361C22×Q8—111no—
362C22×Q8—221no—
363C22×D4—111no—
364C23×C4—221no—
365C22×C8—111no—
366C22×C8—111no—
367C22×C8C22×D1111yescharacteristic
368C22×C8C22×D1111yescharacteristic
369C4⋊Q8—222no—
370C4⋊Q8—222no—
371C22⋊Q8—444no—
372C4×Q8—222no—
373C4×Q8—222no—
374C4×D4—222no—
375C4×D4—222no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—111no—
379C2×C4⋊C4—111no—
380C2×C4⋊C4—111no—
381C2×C4⋊C4—111no—
382C2×C4⋊C4—111no—
383C2×C4⋊C4—111no—
384C2×C4⋊C4—221no—
385C2×C4⋊C4—221no—
386C2×C4⋊C4—221no—
387C2×C4⋊C4—221no—
388C2×C4⋊C4—221no—
389C2×C4⋊C4—221no—
390C2×C4⋊C4—221no—
391C2×C4⋊C4C22×D1111yescharacteristic
392C2×C4⋊C4C22×D1111yescharacteristic
393C2×C4⋊C4C22×D1111yescharacteristic
394C2×C4⋊C4C22×D1111yescharacteristic
395C2×C22⋊C4—221no—
396C2×C22⋊C4—221no—
397C2×C22⋊C4—221no—
398C2×C22⋊C4—221no—
399C2×C22⋊C4—221no—
400C2×C42—111no—
401C2×C42—111no—
402C2×C42—221no—
403C2×C42C22×D1111yescharacteristic
404#106—22no—
405#106—22no—
406#106—222no—
407#106—222no—
408C4⋊C8—114no—
409C4⋊C8—222no—
410C4⋊C8—222no—
411#102—114no—
412#102—222no—
413#102—222no—
414#102—222no—
415C4×C8—22no—
416C4×C8—222no—
417C4×C8—222no—
418#95—21no—
419#95—21no—
420#95—221no—
421#95—221no—
422#95—221no—
423#95—221no—
424#95—221no—
425C2×C11#242911yescharacteristic
426C2×C11C2×#46511yescharacteristic
427C2×C11#306211yescharacteristic
428C2×C11#336011yescharacteristic
429C2×C11#336211yescharacteristic
430C2×C11Q8×SD1611yescharacteristic
431C2×C11#338011yescharacteristic
432D11—82no—
433C24—221no—
434C2×Q8—114no—
435C2×Q8—222no—
436C2×Q8—222no—
437C2×Q8—442no—
438C2×Q8—881no—
439C2×Q8—881no—
440C2×D4—112no—
441C2×D4—221no—
442C2×D4—221no—
443C2×D4—221no—
444C2×D4—221no—
445C2×D4—221no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—111no—
451C22×C4—111no—
452C22×C4—111no—
453C22×C4—111no—
454C22×C4—221no—
455C22×C4—221no—
456C22×C4—221no—
457C22×C4—442no—
458C22×C4—442no—
459C22×C4—442no—
460C22×C4D4×D1111yescharacteristic
461C22×C4D4×D1111yescharacteristic
462C22×C4C23×D1111yescharacteristic
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—112no—
468C2×C8—221no—
469C2×C8—221no—
470C2×C8—221no—
471C2×C8—221no—
472C2×C8—221no—
473C2×C8D4×D1112yes—
474C2×C8Q8×D1112yes—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—42no—
483C4⋊C4—81no—
484C4⋊C4—112no—
485C4⋊C4—222no—
486C4⋊C4—222no—
487C4⋊C4—222no—
488C4⋊C4—221no—
489C4⋊C4—221no—
490C4⋊C4—221no—
491C4⋊C4—221no—
492C4⋊C4—221no—
493C4⋊C4—442no—
494C4⋊C4—442no—
495C4⋊C4—442no—
496C4⋊C4—881no—
497C4⋊C4—881no—
498C4⋊C4—881no—
499C4⋊C4—881no—
500C4⋊C4#433912yes—
501C22⋊C4—442no—
502C22⋊C4—442no—
503C22⋊C4—442no—
504C22⋊C4—881no—
505C22⋊C4—881no—
506C42—21no—
507C42—21no—
508C42—112no—
509C42—112no—
510C42—221no—
511C42—221no—
512C42—442no—
513C11#2547011yescharacteristic, complemented, Sylow
514C23—222no—
515C23—441no—
516C23—441no—
517C23—441no—
518C23—441no—
519C23—441no—
520C23—441no—
521C23C2×D4×D1111yescharacteristic
522Q8—228no—
523Q8—884no—
524D4—222no—
525D4—222no—
526D4—441no—
527D4—441no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—22no—
533C2×C4—21no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—112no—
546C2×C4—112no—
547C2×C4—112no—
548C2×C4—112no—
549C2×C4—112no—
550C2×C4—221no—
551C2×C4—221no—
552C2×C4—221no—
553C2×C4—221no—
554C2×C4—222no—
555C2×C4—221no—
556C2×C4—221no—
557C2×C4—221no—
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×C4—884no—
567C2×C4SD16×D1112yes—
568C2×C4C2×#433911yescharacteristic
569C2×C4C2×D4×D1111yescharacteristic
570C2×C4C2×Q8×D1111yescharacteristic
571C2×C4#6704011yescharacteristic
572C2×C4#41×D1111yescharacteristic
573C2×C4#6704311yescharacteristic
574C8—22no—
575C8—22no—
576C8—222no—
577C8—441no—
578C22—442no—
579C22—442no—
580C22—442no—
581C22—881no—
582C22—881no—
583C22—881no—
584C22—881no—
585C22#1062308311yescharacteristic
586C22D11×#12111yescharacteristic
587C22#1062325811yescharacteristic
588C22C2×SD16×D1111yescharacteristic
589C22#1062329311yescharacteristic
590C22D11×#13511yescharacteristic
591C22#1062330011yescharacteristic
592C4—22no—
593C4—41no—
594C4—42no—
595C4—81no—
596C4—81no—
597C4—81no—
598C4—114no—
599C4—222no—
600C4—222no—
601C4—441no—
602C4—442no—
603C4—881no—
604C4—881no—
605C4#1062303811yescharacteristic
606C4#1062310911yescharacteristic
607C4#1062316311yescharacteristic
608C4#1062322711yescharacteristic
609C2—882no—
610C2#1307221411yescharacteristic
611C2D11×#46511yescharacteristic
612C2#1307828911yescharacteristic
613C2#1308126611yescharacteristic
614C2#1308128511yescharacteristic
615C2#1308147311yescharacteristic
616C2#1308148011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1941C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#1941D11
hypocenterC11#25470
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1941

Complements

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

NH ≅ G/Ntype
2. C2×C8×Dic22C2semidirect
3. #13073823C2semidirect
5. #13070117C2semidirect
6. #13070115C2semidirect
9. #13069575C2semidirect
10. #13069376C2semidirect
11. #13069343C2semidirect
15. C11×#1941C2semidirect
115. #66885Q8semidirect
217. #1941D11semidirect
513. C11#25470semidirect

Maximal subgroups

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

subgroupindex
C2×#106224832
C2×C8×Dic222
#130738232
#130735372
#130701172
#130701152
#130699872
#130699852
#130695752
#130693762
#130693432
#130692992
#130692972
#130684302
C11×#19412
#2547011