Finite Group Databasebeta

← #14805625

Subgroups — #14805625

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×#10622374C211yesmaximal, characteristic
2C2×C8×Dic22C211yesmaximal, characteristic, complemented
3#13073823C211yesmaximal, characteristic, complemented
4#13073536C211yesmaximal, characteristic
5#13070118C211yesmaximal, characteristic, complemented
6#13070116C211yesmaximal, characteristic, complemented
7#13069990C211yesmaximal, characteristic
8#13069988C211yesmaximal, characteristic
9#13069575C211yesmaximal, characteristic, complemented
10#13069378C211yesmaximal, characteristic, complemented
11#13069344C211yesmaximal, characteristic, complemented
12#13069343C211yesmaximal, characteristic, complemented
13#13069301C211yesmaximal, characteristic
14#102×Dic11C211yesmaximal, characteristic
15C11×#1934C211yesmaximal, characteristic
16C2×D4×Dic11C2211yescharacteristic
17C2×#66941C2211yescharacteristic
18C2×#66931—21no—
19C2×C4×Dic22C2211yescharacteristic
20C2×C11×#102C2211yescharacteristic
21C2×C11×#102C2211yescharacteristic
22C2×C4×C8×C11C2211yescharacteristic
23C11×#390C2211yescharacteristic
24C11×#389C2211yescharacteristic
25#10622834C2211yescharacteristic
26C2×#66896C2211yescharacteristic
27C2×#66896C2211yescharacteristic
28C2×#66881C2211yescharacteristic
29C2×#66881C2211yescharacteristic
30C2×Dic11⋊C8C2211yescharacteristic
31C2×Dic11⋊C8C2211yescharacteristic
32C2×C8×Dic11C2211yescharacteristic
33C2×C8×Dic11C2211yescharacteristic
34#10622598C2211yescharacteristic
35#10622598C2211yescharacteristic
36#10622592—21no—
37#10622589—21no—
38#10622589C2211yescharacteristic
39C4⋊C4×Dic11C2211yescharacteristic
40#10622586C2211yescharacteristic
41C2×#66872C2211yescharacteristic
42C2×#66872C2211yescharacteristic
43#10622561—21no—
44#10622561—21no—
45#10622555—21no—
46#10622541C2211yescharacteristic
47#10622541C2211yescharacteristic
48C2×C4⋊(C11⋊C8)C2211yescharacteristic
49#10622374—24no—
50C8×Dic22—24no—
51#10622269—21no—
52#10622259—21no—
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×D4×C11C2311yescharacteristic
62C23×Dic11—21no—
63C22×Dic22—21no—
64C22×Dic22D411yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C22⋊C4—21no—
72C2×C11×C22⋊C4—21no—
73C2×C42×C11C2311yescharacteristic
74C2×C22⋊Dic11—21no—
75C2×C22⋊Dic11—21no—
76C2×C22⋊Dic11—21no—
77D4×Dic11—22no—
78D4×Dic11—22no—
79C2×C4⋊Dic11—21no—
80C2×C4⋊Dic11—21no—
81C2×C4⋊Dic11D411yescharacteristic
82C2×C4⋊Dic11C2311yescharacteristic
83C2×C4⋊Dic11C2311yescharacteristic
84C2×C4⋊Dic11C2311yescharacteristic
85C2×C4⋊Dic11C2311yescharacteristic
86C2×Dic11⋊C4—21no—
87C2×Dic11⋊C4—21no—
88C2×Dic11⋊C4—21no—
89C2×Dic11⋊C4—21no—
90C2×Dic11⋊C4—21no—
91C2×Dic11⋊C4—21no—
92C2×Dic11⋊C4D411yescharacteristic
93C2×Dic11⋊C4D411yescharacteristic
94C2×C4×Dic11—21no—
95C2×C4×Dic11C2311yescharacteristic
96C2×C4×Dic11C2311yescharacteristic
97C22×C11⋊C8C2311yescharacteristic
98C22×C11⋊C8C2311yescharacteristic
99#66941—22no—
100#66941—22no—
101#66931—44no—
102C4×Dic22—22no—
103C4×Dic22—22no—
104C11×#102—22no—
105C11×#102Q814yescomplemented
106C4×C8×C11—22no—
107C11×#95—21no—
108#66896—22no—
109#66896—22no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116#66881—22no—
117#66881—22no—
118Dic11⋊C8—22no—
119Dic11⋊C8D414yes—
120C8×Dic11—22no—
121C8×Dic11—22no—
122#66872—22no—
123#66872—22no—
124C4⋊(C11⋊C8)—22no—
125#25470—111nomaximal, Sylow
126C24×C11—21no—
127C2×D4×C11—21no—
128C2×D4×C11—21no—
129C2×D4×C11—21no—
130C2×D4×C11—21no—
131C2×D4×C11—21no—
132C2×D4×C11C2×Q812yes—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2411yescharacteristic
139C22×Dic11—21no—
140C22×Dic11—21no—
141C22×Dic11—21no—
142C22×Dic11—21no—
143C22×Dic11—42no—
144C22×Dic11—42no—
145C22×Dic11—42no—
146C22×Dic11C2×D411yescharacteristic
147C22×Dic11C2×D411yescharacteristic
148C22×Dic11C2×D411yescharacteristic
149C22×Dic11C2×D411yescharacteristic
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—81no—
168C11×C4⋊C4C2×Q812yes—
169C11×C22⋊C4—42no—
170C11×C22⋊C4—81no—
171C42×C11—21no—
172C42×C11—21no—
173C22⋊Dic11—42no—
174C22⋊Dic11—42no—
175C22⋊Dic11—81no—
176C4⋊Dic11—22no—
177C4⋊Dic11—21no—
178C4⋊Dic11—21no—
179C4⋊Dic11—21no—
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—42no—
185C4⋊Dic11—81no—
186C4⋊Dic11#4112yes—
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#1941—111no—
218#1934—111no—
219#1934D1111yescharacteristic
220C4×#102—111no—
221C23×C11—22no—
222C23×C11—41no—
223C23×C11—41no—
224C23×C11—41no—
225C23×C11—41no—
226C23×C11—41no—
227C23×C11—41no—
228C23×C11C22×D411yescharacteristic
229D4×C11—22no—
230D4×C11—22no—
231D4×C11—41no—
232D4×C11—41no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—22no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
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×C11—41no—
247C2×C4×C11C2×SD1612yes—
248C2×C4×C11C22×D411yescharacteristic
249C2×C4×C11C22×Q811yescharacteristic
250C2×C4×C11C2×#4111yescharacteristic
251C2×C4×C11C2×#4111yescharacteristic
252C2×C4×C112−1+411yescharacteristic
253C2×C4×C112−1+411yescharacteristic
254C2×Dic11—21no—
255C2×Dic11—21no—
256C2×Dic11—21no—
257C2×Dic11—21no—
258C2×Dic11—21no—
259C2×Dic11—22no—
260C2×Dic11—21no—
261C2×Dic11—21no—
262C2×Dic11—41no—
263C2×Dic11—41no—
264C2×Dic11—41no—
265C2×Dic11—41no—
266C2×Dic11—41no—
267C2×Dic11—41no—
268C2×Dic11—41no—
269C2×Dic11—41no—
270C2×Dic11—41no—
271C2×Dic11—41no—
272C2×Dic11—41no—
273C2×Dic11—84no—
274C2×Dic11#12112yes—
275C2×Dic11#12112yes—
276C2×Dic11C2×SD1612yes—
277C2×Dic11C2×SD1612yes—
278C2×Dic11#13512yes—
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×#106—111no—
294C2×#106—111no—
295C2×C4⋊C8—111no—
296C2×C4⋊C8—111no—
297C2×C4⋊C8—111no—
298C2×#102—111no—
299C2×#102—111no—
300C2×#102C2×D1111yescharacteristic
301C2×#102C2×D1111yescharacteristic
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#390C2×D1111yescharacteristic
312#389—111no—
313#389—111no—
314#389—111no—
315#389—111no—
316#389—111no—
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×C11—42no—
331C22×C11—42no—
332C22×C11—42no—
333C22×C11—81no—
334C22×C11—81no—
335C22×C11—81no—
336C22×C11—81no—
337C22×C11C2×#12111yescharacteristic
338C22×C11#54811yescharacteristic
339C22×C11D4×Q811yescharacteristic
340C22×C11C22×SD1611yescharacteristic
341C22×C11C2×#13511yescharacteristic
342C22×C11#57611yescharacteristic
343C22×C11#57711yescharacteristic
344C4×C11—22no—
345C4×C11—42no—
346C4×C11—41no—
347C4×C11—81no—
348C4×C11—81no—
349C4×C11#53311yescharacteristic
350C4×C11#54111yescharacteristic
351C4×C11#54711yescharacteristic
352C4×C11D4×Q811yescharacteristic
353Dic11—22no—
354Dic11—22no—
355Dic11—42no—
356Dic11—41no—
357Dic11—81no—
358Dic11—81no—
359Dic11—81no—
360Dic11#46514yes—
361C22×Q8—111no—
362C22×Q8—221no—
363C22×D4C22×D1111yescharacteristic
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—111no—
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⋊C4—221no—
392C2×C4⋊C4C22×D1111yescharacteristic
393C2×C4⋊C4C22×D1111yescharacteristic
394C2×C4⋊C4C22×D1111yescharacteristic
395C2×C22⋊C4—21no—
396C2×C22⋊C4—21no—
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—222no—
405#106—222no—
406#106—222no—
407#106—222no—
408C4⋊C8—114no—
409C4⋊C8—222no—
410C4⋊C8—222no—
411#102—22no—
412#102—222no—
413#102—222no—
414#102Dic2214yescomplemented
415C4×C8—22no—
416C4×C8—222no—
417C4×C8—222no—
418#95—21no—
419#95—221no—
420#95—221no—
421#95—221no—
422#95—221no—
423#95—221no—
424#95—221no—
425C2×C11—82no—
426C2×C11#242911yescharacteristic
427C2×C11C2×#46511yescharacteristic
428C2×C11#306211yescharacteristic
429C2×C11#336011yescharacteristic
430C2×C11#336211yescharacteristic
431C2×C11Q8×SD1611yescharacteristic
432C2×C11#338011yescharacteristic
433C24—21no—
434C2×Q8—114no—
435C2×Q8—222no—
436C2×Q8—222no—
437C2×Q8—442no—
438C2×Q8—881no—
439C2×Q8—881no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4C2×Dic2212yes—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—111no—
450C22×C4—111no—
451C22×C4—111no—
452C22×C4—111no—
453C22×C4—221no—
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×C8C2×Dic2212yes—
474C2×C8D4×D1112yes—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—81no—
481C4⋊C4—112no—
482C4⋊C4—222no—
483C4⋊C4—222no—
484C4⋊C4—222no—
485C4⋊C4—221no—
486C4⋊C4—221no—
487C4⋊C4—221no—
488C4⋊C4—221no—
489C4⋊C4—221no—
490C4⋊C4—221no—
491C4⋊C4—221no—
492C4⋊C4—442no—
493C4⋊C4—442no—
494C4⋊C4—442no—
495C4⋊C4—442no—
496C4⋊C4—881no—
497C4⋊C4—881no—
498C4⋊C4—881no—
499C4⋊C4—881no—
500C4⋊C4C2×Dic2212yes—
501C22⋊C4—42no—
502C22⋊C4—81no—
503C22⋊C4—442no—
504C22⋊C4—442no—
505C22⋊C4—881no—
506C42—21no—
507C42—21no—
508C42—112no—
509C42—112no—
510C42—221no—
511C42—221no—
512C42—442no—
513C11#2547011yescharacteristic, complemented, Sylow
514C23—22no—
515C23—41no—
516C23—41no—
517C23—41no—
518C23—41no—
519C23—41no—
520C23—41no—
521C23C2×D4×D1111yescharacteristic
522Q8—228no—
523Q8—884no—
524D4—22no—
525D4—22no—
526D4—41no—
527D4—41no—
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—112no—
543C2×C4—112no—
544C2×C4—112no—
545C2×C4—112no—
546C2×C4—112no—
547C2×C4—221no—
548C2×C4—221no—
549C2×C4—221no—
550C2×C4—221no—
551C2×C4—221no—
552C2×C4—221no—
553C2×C4—221no—
554C2×C4—222no—
555C2×C4—441no—
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×C4—884no—
567C2×C4SD16×D1112yes—
568C2×C4C22×Dic2211yescharacteristic
569C2×C4C2×D4×D1111yescharacteristic
570C2×C4#41×D1111yescharacteristic
571C2×C4#41×D1111yescharacteristic
572C2×C4#6704311yescharacteristic
573C2×C4#6704311yescharacteristic
574C8—22no—
575C8—22no—
576C8—222no—
577C8—441no—
578C22—42no—
579C22—42no—
580C22—42no—
581C22—81no—
582C22—81no—
583C22—81no—
584C22—81no—
585C22D4×Dic2211yescharacteristic
586C22D11×#12111yescharacteristic
587C22#1062320811yescharacteristic
588C22#1062328811yescharacteristic
589C22C2×SD16×D1111yescharacteristic
590C22D11×#13511yescharacteristic
591C22#1062330111yescharacteristic
592C4—22no—
593C4—41no—
594C4—42no—
595C4—81no—
596C4—81no—
597C4—114no—
598C4—222no—
599C4—222no—
600C4—441no—
601C4—442no—
602C4—881no—
603C4—881no—
604C4—881no—
605C4#1062304811yescharacteristic
606C4D4×Dic2211yescharacteristic
607C4#1062318611yescharacteristic
608C4#1062323211yescharacteristic
609C2—82no—
610C2#1307221211yescharacteristic
611C2D11×#46511yescharacteristic
612C2#1307829511yescharacteristic
613C2#1308126211yescharacteristic
614C2#1308128411yescharacteristic
615C2SD16×Dic2211yescharacteristic
616C2#1308148311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1934C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenter#1934D11
hypocenterC11#25470
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1934

Complements

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

NH ≅ G/Ntype
2. C2×C8×Dic22C2semidirect
3. #13073823C2semidirect
5. #13070118C2semidirect
6. #13070116C2semidirect
9. #13069575C2semidirect
10. #13069378C2semidirect
11. #13069344C2semidirect
12. #13069343C2semidirect
105. C11×#102Q8semidirect
414. #102Dic22semidirect
513. C11#25470semidirect

Maximal subgroups

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

subgroupindex
C2×#106223742
C2×C8×Dic222
#130738232
#130735362
#130701182
#130701162
#130699902
#130699882
#130695752
#130693782
#130693442
#130693432
#130693012
#102×Dic112
C11×#19342
#2547011