Finite Group Databasebeta

← #14775567

Subgroups — #14775567

Order 2816.

926 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622372C211yesmaximal, characteristic
2#13071669C211yesmaximal, characteristic, complemented
3D4×Dic11⋊C4C211yesmaximal, characteristic
4#13069575C211yesmaximal, characteristic, complemented
5#13069371C211yesmaximal, characteristic, complemented
6#13069347C211yesmaximal, characteristic, complemented
7#13069346C211yesmaximal, characteristic, complemented
8#13069188C211yesmaximal, characteristic, complemented
9#13069185C211yesmaximal, characteristic, complemented
10#13068861C211yesmaximal, characteristic
11#13068477C211yesmaximal, characteristic, complemented
12#102×Dic11C211yesmaximal, characteristic
13#102×Dic11C211yesmaximal, characteristic
14C4×#66896C211yesmaximal, characteristic
15C11×#1862C211yesmaximal, characteristic
16C2×C4×D4×C11C2211yescharacteristic
17C2×D4×Dic11C2211yescharacteristic
18C2×D4×Dic11C2211yescharacteristic
19C22×Dic11⋊C4—21no—
20C2×#66941C2211yescharacteristic
21C2×#66940—21no—
22C2×C11×#107C2211yescharacteristic
23C2×C11×#102C2211yescharacteristic
24C2×C11×#102C2211yescharacteristic
25C11×#389C2211yescharacteristic
26C2×#66896C2211yescharacteristic
27C2×#66896C2211yescharacteristic
28#10622823—21no—
29C2×#66882C2211yescharacteristic
30C2×Dic11⋊C8C2211yescharacteristic
31C2×C8×Dic11C2211yescharacteristic
32C2×C8×Dic11C2211yescharacteristic
33#10622591—21no—
34#10622589C2211yescharacteristic
35C4⋊C4×Dic11C2211yescharacteristic
36C4⋊C4×Dic11C2211yescharacteristic
37#10622586C2211yescharacteristic
38#10622586C2211yescharacteristic
39C2×#66871C2211yescharacteristic
40C2×#66871C2211yescharacteristic
41#10622559—21no—
42#10622555—21no—
43C4×C4⋊Dic11C2211yescharacteristic
44C4×Dic11⋊C4C2211yescharacteristic
45#10622541C2211yescharacteristic
46C2×C4×C11⋊C8C2211yescharacteristic
47#10622372C418yescomplemented
48#10622265—21no—
49#10622259—21no—
50C11×#340C2211yescharacteristic
51C11×#336C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60C22×D4×C11C2311yescharacteristic
61C23×C4×C11—21no—
62C23×Dic11—21no—
63C23×Dic11—21no—
64C22×Dic22—21no—
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C4×D4×C11—22no—
68C4×D4×C11—41no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C22⋊C4—21no—
74C2×C42×C11C2311yescharacteristic
75C2×C22⋊Dic11—21no—
76C2×C22⋊Dic11—21no—
77D4×Dic11—22no—
78D4×Dic11—22no—
79D4×Dic11—41no—
80D4×Dic11C2×C414yes—
81C2×C4⋊Dic11C2311yescharacteristic
82C2×C4⋊Dic11C2311yescharacteristic
83C2×C4⋊Dic11C2311yescharacteristic
84C2×C4⋊Dic11C2311yescharacteristic
85C2×Dic11⋊C4—21no—
86C2×Dic11⋊C4—21no—
87C2×Dic11⋊C4—21no—
88C2×Dic11⋊C4—21no—
89C2×Dic11⋊C4—21no—
90C2×Dic11⋊C4—21no—
91C2×Dic11⋊C4—44no—
92C2×Dic11⋊C4D411yescharacteristic
93C2×Dic11⋊C4D411yescharacteristic
94C2×C4×Dic11—21no—
95C2×C4×Dic11—21no—
96C2×C4×Dic11—21no—
97C2×C4×Dic11C2311yescharacteristic
98C2×C4×Dic11C2311yescharacteristic
99C22×C11⋊C8C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101#66941—22no—
102#66941C2×C414yescomplemented
103#66940—44no—
104C11×#107—41no—
105C11×#102—22no—
106C11×#102C2×C414yes—
107C11×#95—21no—
108#66896C2×C414yes—
109#66896Q814yescomplemented
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95D411yescharacteristic
117C11⋊#95D411yescharacteristic
118#66882C2×C414yescomplemented
119Dic11⋊C8C2×C414yescomplemented
120C8×Dic11—22no—
121C8×Dic11—41no—
122#66871—41no—
123#66871C2×C414yescomplemented
124C4×C11⋊C8—41no—
125#22962—111nomaximal, Sylow
126C24×C11—21no—
127C2×D4×C11—21no—
128C2×D4×C11—21no—
129C2×D4×C11—21no—
130C2×D4×C11C22×C412yes—
131C2×D4×C11C2×Q812yes—
132C2×D4×C11#4112yes—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—42no—
137C22×C4×C11—42no—
138C22×C4×C11—81no—
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2411yescharacteristic
142C22×Dic11—24no—
143C22×Dic11—21no—
144C22×Dic11—21no—
145C22×Dic11—21no—
146C22×Dic11—21no—
147C22×Dic11—42no—
148C22×Dic11—42no—
149C22×Dic11—42no—
150C22×Dic11—42no—
151C22×Dic11—81no—
152C22×Dic11C2×D411yescharacteristic
153C22×Dic11C2×D411yescharacteristic
154C22×Dic11C2×D411yescharacteristic
155C22×Dic11C2×D411yescharacteristic
156C2×Dic22—24no—
157C2×Dic22—42no—
158C2×Dic22—42no—
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C2×C8×C11C22×C412yes—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—42no—
171C11×C4⋊C4C22×C412yes—
172C11×C22⋊C4—42no—
173C42×C11—21no—
174C42×C11—21no—
175C22⋊Dic11—24no—
176C22⋊Dic11—42no—
177C4⋊Dic11—21no—
178C4⋊Dic11—21no—
179C4⋊Dic11—21no—
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182C4⋊Dic11C22×C412yes—
183C4⋊Dic11C22×C412yes—
184C4⋊Dic11C2×Q812yes—
185Dic11⋊C4—24no—
186Dic11⋊C4—22no—
187Dic11⋊C4—42no—
188Dic11⋊C4—42no—
189Dic11⋊C4—42no—
190Dic11⋊C4—42no—
191Dic11⋊C4—81no—
192Dic11⋊C4D814yes—
193C4×Dic11—21no—
194C4×Dic11—21no—
195C4×Dic11—42no—
196C4×Dic11—42no—
197C4×Dic11—42no—
198C4×Dic11C22×C412yes—
199C4×Dic11#4112yes—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8C22×C412yes—
205C2×C11⋊C8C2×Q812yes—
206C2×#474—111no—
207#2365—111no—
208D4×C4⋊C4—111no—
209#1990—111no—
210#1947—111no—
211#1942—111no—
212#1942—111no—
213#1918—111no—
214#1918—111no—
215#1862—111no—
216#1862D1111yescharacteristic
217C8×C4⋊C4—111no—
218C4×#102—111no—
219C4×#102—111no—
220C4×#102—111no—
221C23×C11—22no—
222C23×C11—22no—
223C23×C11—22no—
224C23×C11—41no—
225C23×C11—41no—
226C23×C11—41no—
227C23×C11—41no—
228C23×C11C22×D411yescharacteristic
229D4×C11—22no—
230D4×C11—22no—
231D4×C11—22no—
232D4×C11C4×Q814yescomplemented
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—22no—
236C2×C4×C11—21no—
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×C11—84no—
248C2×C4×C11C2×D812yes—
249C2×C4×C11C23×C411yescharacteristic
250C2×C4×C11C22×Q811yescharacteristic
251C2×C4×C11C2×#4111yescharacteristic
252C2×C4×C11C2×#4111yescharacteristic
253C2×C4×C11H(5,𝔽2)11yescharacteristic
254C2×C4×C112−1+411yescharacteristic
255C2×Dic11—21no—
256C2×Dic11—21no—
257C2×Dic11—21no—
258C2×Dic11—21no—
259C2×Dic11—22no—
260C2×Dic11—22no—
261C2×Dic11—21no—
262C2×Dic11—22no—
263C2×Dic11—21no—
264C2×Dic11—21no—
265C2×Dic11—41no—
266C2×Dic11—41no—
267C2×Dic11—41no—
268C2×Dic11—41no—
269C2×Dic11—41no—
270C2×Dic11—41no—
271C2×Dic11—48no—
272C2×Dic11—41no—
273C2×Dic11—41no—
274C2×Dic11—41no—
275C2×Dic11—84no—
276C2×Dic11C4×D412yes—
277C2×Dic11C4×D412yes—
278C2×Dic11C2×D812yes—
279C2×Dic11C2×D812yes—
280C2×Dic11#13512yes—
281Dic22—48no—
282C8×C11—22no—
283C8×C11—41no—
284C11⋊C8—22no—
285C11⋊C8—22no—
286C2×C4⋊Q8—111no—
287C2×C4×Q8—221no—
288C2×C4×D4—111no—
289C2×C4×D4—111no—
290C2×C4×D4C2×D1111yescharacteristic
291C22×C4⋊C4—221no—
292#474—118no—
293C2×#107—111no—
294C2×#107—111no—
295C2×#107—111no—
296C2×#107C2×D1111yescharacteristic
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×C8—111no—
305#391—221no—
306#389—111no—
307#389—111no—
308#389—111no—
309#389C2×D1111yescharacteristic
310#387—221no—
311#387—221no—
312#385—221no—
313#385—221no—
314#384—111no—
315#380—221no—
316C4×C4⋊C4—111no—
317C4×C4⋊C4—111no—
318C4×C4⋊C4—111no—
319C4×C4⋊C4—111no—
320#340—111no—
321#340—111no—
322#340—111no—
323#340—111no—
324#340—111no—
325#340—111no—
326#340—111no—
327#340C2×D1111yescharacteristic
328#336—111no—
329#336C2×D1111yescharacteristic
330C22×C11—24no—
331C22×C11—42no—
332C22×C11—42no—
333C22×C11—42no—
334C22×C11—42no—
335C22×C11—42no—
336C22×C11—42no—
337C22×C11C2×C4×D411yescharacteristic
338C22×C11#54611yescharacteristic
339C22×C11D4×Q811yescharacteristic
340C22×C11C22×D811yescharacteristic
341C22×C11C2×#13511yescharacteristic
342C22×C11#57711yescharacteristic
343C22×C11#57811yescharacteristic
344C4×C11—22no—
345C4×C11—42no—
346C4×C11—41no—
347C4×C11—81no—
348C4×C11—81no—
349C4×C11C2×C4×Q811yescharacteristic
350C4×C11#52011yescharacteristic
351C4×C11#55211yescharacteristic
352C4×C11#55411yescharacteristic
353Dic11—22no—
354Dic11—22no—
355Dic11—42no—
356Dic11—42no—
357Dic11—42no—
358Dic11—41no—
359Dic11—81no—
360Dic11C4×D814yes—
361C22×Q8—221no—
362C22×D4C22×D1111yescharacteristic
363C23×C4—21no—
364C23×C4—221no—
365C23×C4—221no—
366C22×C8—111no—
367C22×C8—111no—
368C22×C8C22×D1111yescharacteristic
369C22×C8C22×D1111yescharacteristic
370C4⋊Q8—114no—
371C4⋊Q8—222no—
372C4×Q8—444no—
373C4×D4—22no—
374C4×D4—41no—
375C4×D4—114no—
376C4×D4—222no—
377C4×D4—222no—
378C4×D4—441no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—111no—
381C2×C4⋊C4—111no—
382C2×C4⋊C4—111no—
383C2×C4⋊C4—111no—
384C2×C4⋊C4—111no—
385C2×C4⋊C4—111no—
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⋊C4—444no—
393C2×C4⋊C4C22×D1111yescharacteristic
394C2×C4⋊C4C22×D1111yescharacteristic
395C2×C4⋊C4C22×D1111yescharacteristic
396C2×C22⋊C4—21no—
397C2×C22⋊C4—221no—
398C2×C22⋊C4—221no—
399C2×C42—111no—
400C2×C42—111no—
401C2×C42—221no—
402C2×C42—221no—
403C2×C42—221no—
404C2×C42C22×D1111yescharacteristic
405#107—41no—
406#107—114no—
407#107—114no—
408#107—441no—
409C4⋊C8—114no—
410#102—22no—
411#102—114no—
412#102—114no—
413#102C4×D1114yes—
414C4×C8—222no—
415C4×C8—441no—
416C4×C8—441no—
417#95—21no—
418#95—111no—
419#95—111no—
420#95—221no—
421#95—221no—
422#95—221no—
423#95—221no—
424#95—221no—
425#95—221no—
426C2×C11—44no—
427C2×C11#236011yescharacteristic
428C2×C11C2×C4×D811yescharacteristic
429C2×C11#294711yescharacteristic
430C2×C11#329411yescharacteristic
431C2×C11#330211yescharacteristic
432C2×C11Q8×D811yescharacteristic
433C2×C11#338111yescharacteristic
434C24—21no—
435C2×Q8—224no—
436C2×Q8—442no—
437C2×Q8—442no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4C2×C4×D1112yes—
442C2×D4#434112yes—
443C2×D4Q8×D1112yes—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—42no—
448C22×C4—42no—
449C22×C4—81no—
450C22×C4—111no—
451C22×C4—111no—
452C22×C4—111no—
453C22×C4—111no—
454C22×C4—224no—
455C22×C4—221no—
456C22×C4—221no—
457C22×C4—221no—
458C22×C4—221no—
459C22×C4—442no—
460C22×C4—442no—
461C22×C4—442no—
462C22×C4—442no—
463C22×C4—881no—
464C22×C4D4×D1111yescharacteristic
465C22×C4D4×D1111yescharacteristic
466C22×C4C23×D1111yescharacteristic
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—112no—
473C2×C8—112no—
474C2×C8—221no—
475C2×C8—221no—
476C2×C8—221no—
477C2×C8—221no—
478C2×C8C2×C4×D1112yes—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—42no—
485C4⋊C4—114no—
486C4⋊C4—112no—
487C4⋊C4—112no—
488C4⋊C4—112no—
489C4⋊C4—222no—
490C4⋊C4—224no—
491C4⋊C4—221no—
492C4⋊C4—221no—
493C4⋊C4—221no—
494C4⋊C4—221no—
495C4⋊C4—221no—
496C4⋊C4—442no—
497C4⋊C4—442no—
498C4⋊C4—442no—
499C4⋊C4—442no—
500C4⋊C4—881no—
501C4⋊C4C2×C4×D1112yes—
502C22⋊C4—42no—
503C22⋊C4—224no—
504C22⋊C4—442no—
505C42—21no—
506C42—21no—
507C42—112no—
508C42—112no—
509C42—221no—
510C42—221no—
511C42—442no—
512C42—442no—
513C42—442no—
514C11#2296211yescharacteristic, complemented, Sylow
515C23—22no—
516C23—22no—
517C23—22no—
518C23—41no—
519C23—41no—
520C23—41no—
521C23—41no—
522C23C2×D4×D1111yescharacteristic
523Q8—448no—
524D4—22no—
525D4—22no—
526D4—22no—
527D4#6694014yescomplemented
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—84no—
543C2×C4—112no—
544C2×C4—112no—
545C2×C4—112no—
546C2×C4—112no—
547C2×C4—112no—
548C2×C4—221no—
549C2×C4—221no—
550C2×C4—221no—
551C2×C4—221no—
552C2×C4—221no—
553C2×C4—221no—
554C2×C4—222no—
555C2×C4—222no—
556C2×C4—221no—
557C2×C4—222no—
558C2×C4—448no—
559C2×C4—441no—
560C2×C4—441no—
561C2×C4—441no—
562C2×C4—441no—
563C2×C4—441no—
564C2×C4—441no—
565C2×C4—441no—
566C2×C4—441no—
567C2×C4—441no—
568C2×C4—884no—
569C2×C4D8×D1112yes—
570C2×C4C22×C4×D1111yescharacteristic
571C2×C4C2×#434111yescharacteristic
572C2×C4#6703711yescharacteristic
573C2×C4C2×Q8×D1111yescharacteristic
574C2×C4#41×D1111yescharacteristic
575C2×C4#6704311yescharacteristic
576C8—22no—
577C8—41no—
578C8—222no—
579C8—222no—
580C22—24no—
581C22—42no—
582C22—42no—
583C22—42no—
584C22—42no—
585C22—42no—
586C22—42no—
587C22C4×D4×D1111yescharacteristic
588C22#1062312211yescharacteristic
589C22#1062316311yescharacteristic
590C22C2×D8×D1111yescharacteristic
591C22D11×#13511yescharacteristic
592C22#1062330611yescharacteristic
593C22#1062331011yescharacteristic
594C4—22no—
595C4—42no—
596C4—41no—
597C4—81no—
598C4—81no—
599C4—114no—
600C4—222no—
601C4—222no—
602C4—442no—
603C4—442no—
604C4—442no—
605C4—441no—
606C4—881no—
607C4C2×#6694011yescharacteristic
608C4#1062307711yescharacteristic
609C4#1062316711yescharacteristic
610C4#1062318111yescharacteristic
611C2—44no—
612C2#1307161611yescharacteristic
613C2C4×D8×D1111yescharacteristic
614C2#1307745611yescharacteristic
615C2#1308042211yescharacteristic
616C2#1308052611yescharacteristic
617C2#1308146611yescharacteristic
618C2#1308148611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1862C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
cosocleC22×C4×C11C24
hypercenter#1862D11
hypocenterC11#22962
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1862

Complements

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

NH ≅ G/Ntype
2. #13071669C2semidirect
4. #13069575C2semidirect
5. #13069371C2semidirect
6. #13069347C2semidirect
7. #13069346C2semidirect
8. #13069188C2semidirect
9. #13069185C2semidirect
11. #13068477C2semidirect
47. #10622372C4semidirect
102. #66941C2×C4semidirect
109. #66896Q8semidirect
118. #66882C2×C4semidirect
119. Dic11⋊C8C2×C4semidirect
123. #66871C2×C4semidirect
232. D4×C11C4×Q8semidirect
514. C11#22962semidirect
527. D4#66940semidirect

Maximal subgroups

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

subgroupindex
C2×#106223722
#130716692
D4×Dic11⋊C42
#130695752
#130693712
#130693472
#130693462
#130691882
#130691852
#130688612
#130684772
#102×Dic112
C4×#668962
C11×#18622
#2296211