Finite Group Databasebeta

← #14816853

Subgroups — #14816853

Order 2816.

856 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622407C211yesmaximal, characteristic, complemented
2#13072460C211yesmaximal, characteristic
3#13071534C211yesmaximal, characteristic, complemented
4#13070135C211yesmaximal, characteristic
5#13070101C211yesmaximal, characteristic, complemented
6#13070002C211yesmaximal, characteristic
7#13069947C211yesmaximal, characteristic, complemented
8#13069349C211yesmaximal, characteristic, complemented
9#13069173C211yesmaximal, characteristic, complemented
10#13068973C211yesmaximal, characteristic
11#13068973C211yesmaximal, characteristic
12#13068884C211yesmaximal, characteristic, complemented
13#13068872C211yesmaximal, characteristic, complemented
14#13068863C211yesmaximal, characteristic
15C2×C4×C11×SD16C211yesmaximal, characteristic
16C22×C11×SD16C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C2×Q8×Dic11C2211yescharacteristic
20C2×Q8×Dic11C2211yescharacteristic
21C2×#66977—21no—
22C2×#66941C2211yescharacteristic
23C4×C11×SD16—24no—
24C2×C11×#106C2211yescharacteristic
25C2×C11×#103C2211yescharacteristic
26C2×C11×#102C2211yescharacteristic
27C2×C4×C8×C11C2211yescharacteristic
28C2×#66899C2211yescharacteristic
29C2×#66899C2211yescharacteristic
30#10622834C2211yescharacteristic
31#10622834C2211yescharacteristic
32C2×#66896C2211yescharacteristic
33C2×#66896C2211yescharacteristic
34#10622823—21no—
35C2×#66882C2211yescharacteristic
36C2×#66882C2211yescharacteristic
37C2×Dic11⋊C8C2211yescharacteristic
38#10622598C2211yescharacteristic
39#10622590—21no—
40#10622590C2211yescharacteristic
41#10622586—21no—
42#10622586C2211yescharacteristic
43C2×#66872C2211yescharacteristic
44C2×#66871C2211yescharacteristic
45#10622561—21no—
46#10622560—21no—
47C4×Dic11⋊C4—21no—
48C4×Dic11⋊C4C2211yescharacteristic
49#10622541—21no—
50#10622541C2211yescharacteristic
51#10622541C2211yescharacteristic
52#10622407—24no—
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C22×D4×C11C2311yescharacteristic
63C23×C4×C11—21no—
64C22×Dic22—21no—
65C2×C11×SD16—22no—
66C2×C11×SD16—22no—
67C2×C11×SD16Q814yescomplemented
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C4×Q8×C11—22no—
71C4×Q8×C11—41no—
72C4×D4×C11—22no—
73C4×D4×C11—41no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C22⋊C4—21no—
78C2×C42×C11—21no—
79C2×C42×C11C2311yescharacteristic
80C2×C22⋊Dic11—21no—
81C2×C22⋊Dic11—21no—
82C2×C22⋊Dic11—21no—
83C2×C22⋊Dic11—21no—
84Q8×Dic11—22no—
85Q8×Dic11—22no—
86Q8×Dic11—22no—
87Q8×Dic11—41no—
88C2×C4⋊Dic11—21no—
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11—21no—
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95#66977—44no—
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4—21no—
98C2×Dic11⋊C4—21no—
99C2×Dic11⋊C4—21no—
100C2×Dic11⋊C4D411yescharacteristic
101C2×Dic11⋊C4D411yescharacteristic
102C2×C4×Dic11—21no—
103C2×C4×Dic11—21no—
104C2×C4×Dic11C2311yescharacteristic
105C2×C4×Dic11C2311yescharacteristic
106C22×C11⋊C8C2311yescharacteristic
107C22×C11⋊C8C2311yescharacteristic
108#66941—22no—
109#66941—41no—
110C11×#106—22no—
111C11×#103D414yes—
112C11×#102—22no—
113C4×C8×C11—22no—
114#66899—22no—
115#66899—22no—
116#66896—22no—
117#66896—41no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C11⋊#95D411yescharacteristic
125C11⋊#95D411yescharacteristic
126#66882—22no—
127#66882—22no—
128Dic11⋊C8—22no—
129#66872—41no—
130#66871—22no—
131#26377—111nomaximal, Sylow
132C24×C11—21no—
133C2×Q8×C11—21no—
134C2×Q8×C11—21no—
135C2×Q8×C11—21no—
136C2×Q8×C11C2×D412yes—
137C2×Q8×C11C2×Q812yes—
138C2×Q8×C11#4112yes—
139C2×D4×C11—21no—
140C2×D4×C11—21no—
141C2×D4×C11—21no—
142C2×D4×C11—21no—
143C2×D4×C11—21no—
144C2×D4×C11C2×Q812yes—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—42no—
149C22×C4×C11—42no—
150C22×C4×C11—81no—
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2411yescharacteristic
154C22×Dic11—21no—
155C22×Dic11—21no—
156C22×Dic11—21no—
157C22×Dic11—21no—
158C22×Dic11C2×D411yescharacteristic
159C22×Dic11C2×D411yescharacteristic
160C22×Dic11C2×D411yescharacteristic
161C22×Dic11C2×D411yescharacteristic
162C2×Dic22—42no—
163C2×Dic22—42no—
164C2×Dic22—81no—
165C11×SD16—28no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11C2×D412yes—
171C2×C8×C11C2×Q812yes—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—42no—
176C11×C4⋊C4C2×D412yes—
177C11×C22⋊C4—42no—
178C42×C11—21no—
179C42×C11—21no—
180C42×C11—42no—
181C22⋊Dic11—42no—
182C22⋊Dic11—42no—
183C22⋊Dic11—42no—
184C22⋊Dic11—81no—
185C4⋊Dic11—24no—
186C4⋊Dic11—21no—
187C4⋊Dic11—21no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—42no—
194C4⋊Dic11—42no—
195C4⋊Dic11#4112yes—
196Dic11⋊C4—22no—
197Dic11⋊C4—22no—
198Dic11⋊C4—42no—
199Dic11⋊C4—42no—
200Dic11⋊C4—42no—
201Dic11⋊C4—42no—
202C4×Dic11—24no—
203C4×Dic11—21no—
204C4×Dic11—21no—
205C4×Dic11—21no—
206C4×Dic11—21no—
207C4×Dic11—42no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×#477—111no—
215C2×C4×SD16D1111yescharacteristic
216#2452—111no—
217#2351—111no—
218#2092—111no—
219#2085—111no—
220#2067—111no—
221#2058—111no—
222#1942—111no—
223#1916—111no—
224#1880—111no—
225#1880—111no—
226#1865—111no—
227#1863—111no—
228#1862—111no—
229C23×C11—22no—
230C23×C11—41no—
231C23×C11—41no—
232C23×C11—41no—
233C23×C11—41no—
234C23×C11—41no—
235C23×C11—41no—
236C23×C11C22×D411yescharacteristic
237Q8×C11—22no—
238Q8×C11—22no—
239Q8×C11—22no—
240Q8×C11C22⋊Q814yescomplemented
241D4×C11—22no—
242D4×C11—22no—
243D4×C11—41no—
244D4×C11—41no—
245C2×C4×C11—22no—
246C2×C4×C11—22no—
247C2×C4×C11—21no—
248C2×C4×C11—22no—
249C2×C4×C11—21no—
250C2×C4×C11—22no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—84no—
260C2×C4×C11AGL(1,ℤ/8)12yes—
261C2×C4×C11C22×D411yescharacteristic
262C2×C4×C11C22×Q811yescharacteristic
263C2×C4×C11C2×#4111yescharacteristic
264C2×C4×C11C2×#4111yescharacteristic
265C2×C4×C11H(5,𝔽2)11yescharacteristic
266C2×C4×C112−1+411yescharacteristic
267C2×Dic11—21no—
268C2×Dic11—21no—
269C2×Dic11—21no—
270C2×Dic11—21no—
271C2×Dic11—22no—
272C2×Dic11—21no—
273C2×Dic11—21no—
274C2×Dic11—21no—
275C2×Dic11—21no—
276C2×Dic11—21no—
277C2×Dic11—21no—
278C2×Dic11—21no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11#13512yes—
291Dic22—84no—
292C8×C11—22no—
293C8×C11—22no—
294C11⋊C8—41no—
295C11⋊C8—41no—
296C22×SD16C2×D1111yescharacteristic
297C2×C4⋊Q8—111no—
298C2×C22⋊Q8—221no—
299C2×C4×Q8—111no—
300C2×C4×Q8—111no—
301C2×C4×Q8C2×D1111yescharacteristic
302C2×C4×D4C2×D1111yescharacteristic
303#477—224no—
304C4×SD16—24no—
305C2×#107—111no—
306C2×#107—111no—
307C2×#107—111no—
308C2×#106—111no—
309C2×#106C2×D1111yescharacteristic
310C2×C4⋊C8—111no—
311C2×#103—111no—
312C2×#103—111no—
313C2×#103C2×D1111yescharacteristic
314C2×#102—111no—
315C2×#102—111no—
316C2×#102C2×D1111yescharacteristic
317C2×C4×C8C2×D1111yescharacteristic
318#396—221no—
319#393—221no—
320#390—111no—
321#390—111no—
322#389—111no—
323#389—111no—
324#389—111no—
325#389—111no—
326#389—221no—
327#389—221no—
328#385—221no—
329#382—111no—
330#382—221no—
331C4×C4⋊C4—111no—
332C4×C4⋊C4—221no—
333#340—111no—
334#340—111no—
335#340—111no—
336#340—111no—
337#336—111no—
338#336—111no—
339#336—111no—
340#336—111no—
341C22×C11—42no—
342C22×C11—42no—
343C22×C11—42no—
344C22×C11—81no—
345C22×C11—81no—
346C22×C11—81no—
347C22×C11—81no—
348C22×C11#52511yescharacteristic
349C22×C11D4211yescharacteristic
350C22×C11D4×Q811yescharacteristic
351C22×C11C2×#13511yescharacteristic
352C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
353C22×C11#57711yescharacteristic
354C22×C11#57811yescharacteristic
355C4×C11—24no—
356C4×C11—22no—
357C4×C11—42no—
358C4×C11—41no—
359C4×C11—81no—
360C4×C11C2×C22⋊Q811yescharacteristic
361C4×C11#53911yescharacteristic
362C4×C11#54711yescharacteristic
363C4×C11#55411yescharacteristic
364Dic11—22no—
365Dic11—41no—
366Dic11—42no—
367Dic11—41no—
368Dic11—41no—
369Dic11—81no—
370Dic11—81no—
371Dic11—81no—
372C22×Q8—221no—
373C22×Q8C22×D1111yescharacteristic
374C22×D4C22×D1111yescharacteristic
375C23×C4—21no—
376C2×SD16—22no—
377C2×SD16—22no—
378C2×SD16Dic2214yescomplemented
379C22×C8—111no—
380C22×C8—111no—
381C22×C8C22×D1111yescharacteristic
382C22×C8C22×D1111yescharacteristic
383C4⋊Q8—222no—
384C4⋊Q8—441no—
385C22⋊Q8—444no—
386C4×Q8—22no—
387C4×Q8—41no—
388C4×Q8—222no—
389C4×Q8—222no—
390C4×Q8—222no—
391C4×Q8—441no—
392C4×D4—22no—
393C4×D4—41no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—111no—
396C2×C4⋊C4—111no—
397C2×C4⋊C4—111no—
398C2×C4⋊C4—111no—
399C2×C4⋊C4—111no—
400C2×C4⋊C4—111no—
401C2×C4⋊C4—221no—
402C2×C4⋊C4—221no—
403C2×C4⋊C4—221no—
404C2×C4⋊C4—221no—
405C2×C4⋊C4—221no—
406C2×C4⋊C4—221no—
407C2×C4⋊C4—221no—
408C2×C4⋊C4C22×D1111yescharacteristic
409C2×C4⋊C4C22×D1111yescharacteristic
410C2×C22⋊C4—21no—
411C2×C22⋊C4—221no—
412C2×C22⋊C4—221no—
413C2×C22⋊C4—221no—
414C2×C22⋊C4—221no—
415C2×C42—21no—
416C2×C42—111no—
417C2×C42—111no—
418C2×C42—221no—
419C2×C42—221no—
420C2×C42C22×D1111yescharacteristic
421#107—222no—
422#107—222no—
423#107—222no—
424#106—22no—
425#106—441no—
426C4⋊C8—222no—
427#103—222no—
428#103—222no—
429#103C22⋊D1114yes—
430#102—22no—
431#102—222no—
432#102—441no—
433C4×C8—22no—
434#95—111no—
435#95—111no—
436#95—221no—
437#95—221no—
438#95—221no—
439#95—221no—
440#95—221no—
441#95—221no—
442C2×C11—82no—
443C2×C11#244911yescharacteristic
444C2×C11#310611yescharacteristic
445C2×C11#312111yescharacteristic
446C2×C11#326511yescharacteristic
447C2×C11#328511yescharacteristic
448C2×C11#338111yescharacteristic
449C2×C11#338611yescharacteristic
450C24—21no—
451C2×Q8—21no—
452C2×Q8—21no—
453C2×Q8—21no—
454C2×Q8—442no—
455C2×Q8—442no—
456C2×Q8—881no—
457C2×Q8C2×Dic2212yes—
458C2×Q8#433912yes—
459C2×Q8C2×C22⋊D1112yes—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4C2×Dic2212yes—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—42no—
470C22×C4—42no—
471C22×C4—81no—
472C22×C4—111no—
473C22×C4—111no—
474C22×C4—111no—
475C22×C4—111no—
476C22×C4—221no—
477C22×C4—221no—
478C22×C4—221no—
479C22×C4—221no—
480C22×C4D4×D1111yescharacteristic
481C22×C4D4×D1111yescharacteristic
482C22×C4C23×D1111yescharacteristic
483SD16—28no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—221no—
489C2×C8—221no—
490C2×C8—221no—
491C2×C8—221no—
492C2×C8—221no—
493C2×C8—221no—
494C2×C8C2×Dic2212yes—
495C2×C8C2×C22⋊D1112yes—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—42no—
500C4⋊C4—112no—
501C4⋊C4—222no—
502C4⋊C4—224no—
503C4⋊C4—222no—
504C4⋊C4—221no—
505C4⋊C4—221no—
506C4⋊C4—221no—
507C4⋊C4—221no—
508C4⋊C4—221no—
509C4⋊C4—221no—
510C4⋊C4—221no—
511C4⋊C4—442no—
512C4⋊C4—442no—
513C4⋊C4—442no—
514C4⋊C4—442no—
515C4⋊C4—442no—
516C4⋊C4—442no—
517C4⋊C4C2×C22⋊D1112yes—
518C22⋊C4—42no—
519C22⋊C4—442no—
520C22⋊C4—442no—
521C22⋊C4—442no—
522C22⋊C4—881no—
523C42—21no—
524C42—21no—
525C42—42no—
526C42—224no—
527C42—221no—
528C42—221no—
529C42—221no—
530C42—221no—
531C42—442no—
532C11#2637711yescharacteristic, complemented, Sylow
533C23—22no—
534C23—41no—
535C23—41no—
536C23—41no—
537C23—41no—
538C23—41no—
539C23—41no—
540C23C2×D4×D1111yescharacteristic
541Q8—22no—
542Q8—22no—
543Q8—22no—
544Q8—884no—
545Q8#6697714yescomplemented
546D4—22no—
547D4—22no—
548D4—41no—
549D4—41no—
550C2×C4—21no—
551C2×C4—22no—
552C2×C4—21no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—22no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—84no—
565C2×C4—112no—
566C2×C4—221no—
567C2×C4—221no—
568C2×C4—221no—
569C2×C4—221no—
570C2×C4—221no—
571C2×C4—221no—
572C2×C4—221no—
573C2×C4—221no—
574C2×C4—221no—
575C2×C4—221no—
576C2×C4—222no—
577C2×C4—221no—
578C2×C4—441no—
579C2×C4—441no—
580C2×C4—441no—
581C2×C4—441no—
582C2×C4—441no—
583C2×C4—441no—
584C2×C4—441no—
585C2×C4—441no—
586C2×C4—441no—
587C2×C4—441no—
588C2×C4—441no—
589C2×C4#6696712yes—
590C2×C4C22×Dic2211yescharacteristic
591C2×C4C2×#433911yescharacteristic
592C2×C4#6703711yescharacteristic
593C2×C4#41×D1111yescharacteristic
594C2×C4#6704311yescharacteristic
595C2×C4C22×C22⋊D1111yescharacteristic
596C8—22no—
597C8—22no—
598C8—441no—
599C8—441no—
600C22—42no—
601C22—42no—
602C22—42no—
603C22—81no—
604C22—81no—
605C22—81no—
606C22—81no—
607C22D4×Dic2211yescharacteristic
608C22#1062307811yescharacteristic
609C22C2×#6696711yescharacteristic
610C22#1062329311yescharacteristic
611C22D11×#13511yescharacteristic
612C22#1062330211yescharacteristic
613C22D4×C22⋊D1111yescharacteristic
614C4—24no—
615C4—22no—
616C4—41no—
617C4—42no—
618C4—81no—
619C4—222no—
620C4—441no—
621C4—441no—
622C4—441no—
623C4—442no—
624C4—881no—
625C4—881no—
626C4—881no—
627C4#1062307011yescharacteristic
628C4#1062309511yescharacteristic
629C4C2×#6697711yescharacteristic
630C4#1062335511yescharacteristic
631C2—82no—
632C2#1307241911yescharacteristic
633C2#1307867411yescharacteristic
634C2#1307884111yescharacteristic
635C2#1308011111yescharacteristic
636C2#1308035111yescharacteristic
637C2#1308149211yescharacteristic
638C2#1308153511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C4×C11×SD16C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenterC2×C4×SD16D11
hypocenterC11#26377
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#10622407C2semidirect
3. #13071534C2semidirect
5. #13070101C2semidirect
7. #13069947C2semidirect
8. #13069349C2semidirect
9. #13069173C2semidirect
12. #13068884C2semidirect
13. #13068872C2semidirect
67. C2×C11×SD16Q8semidirect
240. Q8×C11C22⋊Q8semidirect
378. C2×SD16Dic22semidirect
532. C11#26377semidirect
545. Q8#66977semidirect

Maximal subgroups

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

subgroupindex
C2×#106224072
#130724602
#130715342
#130701352
#130701012
#130700022
#130699472
#130693492
#130691732
#130689732
#130688842
#130688722
#130688632
C2×C4×C11×SD162
#2637711