Finite Group Databasebeta

← #14816788

Subgroups — #14816788

Order 2816.

864 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622620C211yesmaximal, characteristic
2C2×SD16×Dic11C211yesmaximal, characteristic
3#13072457C211yesmaximal, characteristic, complemented
4#13071521C211yesmaximal, characteristic
5#13070166C211yesmaximal, characteristic, complemented
6#13070102C211yesmaximal, characteristic, complemented
7#13070011C211yesmaximal, characteristic, complemented
8#13069950C211yesmaximal, characteristic, complemented
9#13069348C211yesmaximal, characteristic, complemented
10#13069176C211yesmaximal, characteristic, complemented
11#13068952C211yesmaximal, characteristic
12#13068879C211yesmaximal, characteristic
13#13068868C211yesmaximal, characteristic, complemented
14#13068861C211yesmaximal, characteristic
15C11×#1877C211yesmaximal, characteristic
16C22×C11×SD16C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C2×Q8×Dic11C2211yescharacteristic
19C2×D4×Dic11C2211yescharacteristic
20C2×D4×Dic11C2211yescharacteristic
21C2×#66922C2211yescharacteristic
22C2×C11×#103C2211yescharacteristic
23C2×C11×#102C2211yescharacteristic
24C11×#391C2211yescharacteristic
25#10622843C2211yescharacteristic
26C2×#66899C2211yescharacteristic
27C2×#66899C2211yescharacteristic
28C2×#66896C2211yescharacteristic
29C2×#66896C2211yescharacteristic
30#10622823—21no—
31C2×C11⋊#95—21no—
32SD16×Dic11—24no—
33C2×#66881C2211yescharacteristic
34C2×#66881C2211yescharacteristic
35C2×C8×Dic11C2211yescharacteristic
36#10622620—24no—
37#10622598C2211yescharacteristic
38#10622590C2211yescharacteristic
39#10622586C2211yescharacteristic
40#10622586C2211yescharacteristic
41C2×#66871C2211yescharacteristic
42C2×#66871C2211yescharacteristic
43C2×#66871C2211yescharacteristic
44#10622559—21no—
45#10622555—21no—
46C4×Dic11⋊C4C2211yescharacteristic
47#10622541C2211yescharacteristic
48C2×C4⋊(C11⋊C8)C2211yescharacteristic
49#10622274—21no—
50#10622269—21no—
51#10622268—21no—
52#10622259—21no—
53C11×#340C2211yescharacteristic
54C11×#336C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622188C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C22×D4×C11C2311yescharacteristic
63C23×C4×C11—21no—
64C23×Dic11—21no—
65C23×Dic11—21no—
66C22×Dic22—21no—
67C2×C11×SD16—22no—
68C2×C11×SD16—22no—
69C2×C11×SD16Q814yescomplemented
70C22×C8×C11C2311yescharacteristic
71C22×C8×C11C2311yescharacteristic
72C4×D4×C11—22no—
73C4×D4×C11—41no—
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C22⋊C4—21no—
77C2×C42×C11C2311yescharacteristic
78C2×C22⋊Dic11—21no—
79C2×C22⋊Dic11—21no—
80Q8×Dic11—22no—
81Q8×Dic11—41no—
82D4×Dic11—22no—
83D4×Dic11—22no—
84D4×Dic11—22no—
85D4×Dic11—41no—
86C2×C4⋊Dic11—21no—
87C2×C4⋊Dic11—21no—
88C2×C4⋊Dic11—21no—
89C2×C4⋊Dic11C2311yescharacteristic
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×Dic11⋊C4—21no—
94C2×Dic11⋊C4—21no—
95C2×Dic11⋊C4—21no—
96C2×Dic11⋊C4D411yescharacteristic
97C2×Dic11⋊C4D411yescharacteristic
98C2×C4×Dic11—21no—
99C2×C4×Dic11C2311yescharacteristic
100C2×C4×Dic11C2311yescharacteristic
101C22×C11⋊C8C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103#66922—22no—
104#66922—41no—
105C11×#103—41no—
106C11×#102—22no—
107C11×#95—21no—
108C11×#95—21no—
109#66899—22no—
110#66899—22no—
111#66896—22no—
112#66896D414yes—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95D411yescharacteristic
122C11⋊#95D411yescharacteristic
123#66881—22no—
124#66881—41no—
125C8×Dic11—22no—
126#66871—22no—
127#66871—22no—
128#66871—22no—
129C4⋊(C11⋊C8)—22no—
130#26372—111nomaximal, Sylow
131C24×C11—21no—
132C2×Q8×C11—21no—
133C2×Q8×C11—21no—
134C2×Q8×C11—21no—
135C2×Q8×C11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11C2×Q812yes—
138C2×D4×C11—21no—
139C2×D4×C11—21no—
140C2×D4×C11—21no—
141C2×D4×C11C2×D412yes—
142C2×D4×C11C2×Q812yes—
143C2×D4×C11#4112yes—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—42no—
148C22×C4×C11—42no—
149C22×C4×C11—81no—
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2411yescharacteristic
153C22×Dic11—24no—
154C22×Dic11—21no—
155C22×Dic11—21no—
156C22×Dic11—21no—
157C22×Dic11—21no—
158C22×Dic11—42no—
159C22×Dic11—42no—
160C22×Dic11—81no—
161C22×Dic11—81no—
162C22×Dic11—81no—
163C22×Dic11C2×D411yescharacteristic
164C22×Dic11C2×D411yescharacteristic
165C22×Dic11C2×D411yescharacteristic
166C22×Dic11C2×D411yescharacteristic
167C2×Dic22—42no—
168C2×Dic22—42no—
169C2×Dic22—81no—
170C11×SD16—28no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11C2×Q812yes—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C22⋊C4—42no—
182C42×C11—21no—
183C42×C11—21no—
184C22⋊Dic11—24no—
185C22⋊Dic11—42no—
186C4⋊Dic11—21no—
187C4⋊Dic11—21no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—42no—
193C4⋊Dic11—42no—
194C4⋊Dic11—81no—
195C4⋊Dic11C2×D412yes—
196C4⋊Dic11#4112yes—
197Dic11⋊C4—22no—
198Dic11⋊C4—22no—
199Dic11⋊C4—81no—
200Dic11⋊C4—81no—
201Dic11⋊C4—81no—
202C4×Dic11—21no—
203C4×Dic11—21no—
204C4×Dic11—21no—
205C4×Dic11—21no—
206C4×Dic11—42no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8C2×D412yes—
213C2×#474—111no—
214C2×C4×SD16—111no—
215#2451—111no—
216#2349—111no—
217#2097—111no—
218#2085—111no—
219#2068—111no—
220#2058—111no—
221#1942—111no—
222#1916—111no—
223#1877—111no—
224#1877D1111yescharacteristic
225#1864—111no—
226#1863—111no—
227#1862—111no—
228C23×C11—22no—
229C23×C11—22no—
230C23×C11—22no—
231C23×C11—41no—
232C23×C11—41no—
233C23×C11—41no—
234C23×C11—41no—
235C23×C11C22×D411yescharacteristic
236Q8×C11—22no—
237Q8×C11—22no—
238Q8×C11—41no—
239Q8×C11—41no—
240D4×C11—22no—
241D4×C11—22no—
242D4×C11—22no—
243D4×C11C22⋊Q814yes—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—22no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—84no—
259C2×C4×C11#13512yes—
260C2×C4×C11C22×D411yescharacteristic
261C2×C4×C11C22×Q811yescharacteristic
262C2×C4×C11C2×#4111yescharacteristic
263C2×C4×C11C2×#4111yescharacteristic
264C2×C4×C11H(5,𝔽2)11yescharacteristic
265C2×C4×C112−1+411yescharacteristic
266C2×Dic11—21no—
267C2×Dic11—21no—
268C2×Dic11—21no—
269C2×Dic11—21no—
270C2×Dic11—22no—
271C2×Dic11—21no—
272C2×Dic11—22no—
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—84no—
290C2×Dic11—84no—
291C2×Dic11#13712yes—
292Dic22—84no—
293C8×C11—22no—
294C8×C11—41no—
295C11⋊C8—22no—
296C11⋊C8—41no—
297C22×SD16C2×D1111yescharacteristic
298C2×C4⋊Q8—111no—
299C2×C4×Q8—111no—
300C2×C4×D4—111no—
301C2×C4×D4—111no—
302C2×C4×D4C2×D1111yescharacteristic
303#474—224no—
304C4×SD16—224no—
305C2×#107—111no—
306C2×#107—111no—
307C2×#107—111no—
308C2×#106—111no—
309C2×#106—111no—
310C2×C4⋊C8—111no—
311C2×#103—111no—
312C2×#103—111no—
313C2×#103C2×D1111yescharacteristic
314C2×#102—111no—
315C2×#102—111no—
316C2×#102C2×D1111yescharacteristic
317C2×C4×C8—111no—
318#398—221no—
319#395—221no—
320#391—111no—
321#391—221no—
322#391C2×D1111yescharacteristic
323#389—111no—
324#389—111no—
325#389—111no—
326#389—111no—
327#387—221no—
328#385—221no—
329#385—221no—
330#382—111no—
331#380—221no—
332C4×C4⋊C4—111no—
333C2×#95—221no—
334#340—111no—
335#340—111no—
336#340—111no—
337#340C2×D1111yescharacteristic
338#336—111no—
339#336—111no—
340#336—111no—
341#336C2×D1111yescharacteristic
342C22×C11—24no—
343C22×C11—42no—
344C22×C11—42no—
345C22×C11—42no—
346C22×C11—42no—
347C22×C11—42no—
348C22×C11—42no—
349C22×C11#52511yescharacteristic
350C22×C11D4211yescharacteristic
351C22×C11D4×Q811yescharacteristic
352C22×C11C2×#13511yescharacteristic
353C22×C11C2×#13711yescharacteristic
354C22×C11#57611yescharacteristic
355C22×C11#57711yescharacteristic
356C4×C11—22no—
357C4×C11—42no—
358C4×C11—41no—
359C4×C11—81no—
360C4×C11—81no—
361C4×C11C2×C22⋊Q811yescharacteristic
362C4×C11#53911yescharacteristic
363C4×C11#54711yescharacteristic
364C4×C11#55411yescharacteristic
365Dic11—22no—
366Dic11—41no—
367Dic11—41no—
368Dic11—42no—
369Dic11—42no—
370Dic11—41no—
371Dic11—81no—
372Dic11—81no—
373C22×Q8—221no—
374C22×Q8C22×D1111yescharacteristic
375C22×D4C22×D1111yescharacteristic
376C23×C4—21no—
377C23×C4—221no—
378C23×C4—221no—
379C2×SD16—22no—
380C2×SD16—22no—
381C2×SD16Dic2214yescomplemented
382C22×C8—111no—
383C22×C8—111no—
384C22×C8C22×D1111yescharacteristic
385C22×C8C22×D1111yescharacteristic
386C4⋊Q8—222no—
387C4⋊Q8—441no—
388C4×Q8—222no—
389C4×Q8—441no—
390C4×D4—22no—
391C4×D4—41no—
392C4×D4—222no—
393C4×D4—222no—
394C4×D4—222no—
395C4×D4—441no—
396C2×C4⋊C4—111no—
397C2×C4⋊C4—111no—
398C2×C4⋊C4—111no—
399C2×C4⋊C4—111no—
400C2×C4⋊C4—111no—
401C2×C4⋊C4—111no—
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×C42—111no—
414C2×C42—111no—
415C2×C42—221no—
416C2×C42C22×D1111yescharacteristic
417#107—222no—
418#107—222no—
419#107—222no—
420#106—222no—
421#106—441no—
422C4⋊C8—222no—
423#103—41no—
424#103—222no—
425#103—222no—
426#102—22no—
427#102—114no—
428#102—222no—
429C4×C8—222no—
430#95—21no—
431#95—21no—
432#95—111no—
433#95—111no—
434#95—221no—
435#95—221no—
436#95—221no—
437#95—221no—
438#95—221no—
439#95—221no—
440#95—221no—
441#95—221no—
442C2×C11—44no—
443C2×C11#244911yescharacteristic
444C2×C11#310711yescharacteristic
445C2×C11#311811yescharacteristic
446C2×C11#326611yescharacteristic
447C2×C11#328011yescharacteristic
448C2×C11#338111yescharacteristic
449C2×C11#338511yescharacteristic
450C24—21no—
451C2×Q8—21no—
452C2×Q8—21no—
453C2×Q8—21no—
454C2×Q8—21no—
455C2×Q8—21no—
456C2×Q8—442no—
457C2×Q8—442no—
458C2×Q8—881no—
459C2×Q8C2×Dic2212yes—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4C2×Dic2212yes—
464C2×D4D4×D1112yes—
465C2×D4#434112yes—
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—224no—
479C22×C4—221no—
480C22×C4—221no—
481C22×C4—442no—
482C22×C4—442no—
483C22×C4—881no—
484C22×C4—881no—
485C22×C4—881no—
486C22×C4D4×D1111yescharacteristic
487C22×C4D4×D1111yescharacteristic
488C22×C4C23×D1111yescharacteristic
489SD16—28no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—112no—
496C2×C8—221no—
497C2×C8—221no—
498C2×C8—221no—
499C2×C8—221no—
500C2×C8—221no—
501C2×C8C2×Dic2212yes—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—112no—
507C4⋊C4—112no—
508C4⋊C4—222no—
509C4⋊C4—222no—
510C4⋊C4—221no—
511C4⋊C4—221no—
512C4⋊C4—221no—
513C4⋊C4—221no—
514C4⋊C4—221no—
515C4⋊C4—221no—
516C4⋊C4—442no—
517C4⋊C4—442no—
518C4⋊C4—881no—
519C4⋊C4—881no—
520C4⋊C4—881no—
521C4⋊C4—881no—
522C22⋊C4—42no—
523C22⋊C4—224no—
524C22⋊C4—442no—
525C42—21no—
526C42—21no—
527C42—221no—
528C42—221no—
529C42—221no—
530C42—221no—
531C42—442no—
532C11#2637211yescharacteristic, complemented, Sylow
533C23—22no—
534C23—22no—
535C23—22no—
536C23—41no—
537C23—41no—
538C23—41no—
539C23—41no—
540C23C2×D4×D1111yescharacteristic
541Q8—22no—
542Q8—22no—
543Q8—41no—
544Q8—41no—
545Q8—884no—
546D4—22no—
547D4—22no—
548D4—22no—
549D4#6693114yes—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—22no—
555C2×C4—21no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
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—222no—
576C2×C4—221no—
577C2×C4—221no—
578C2×C4—222no—
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—884no—
590C2×C4—884no—
591C2×C4#6696912yes—
592C2×C4C22×Dic2211yescharacteristic
593C2×C4C2×D4×D1111yescharacteristic
594C2×C4C2×#434111yescharacteristic
595C2×C4#6703711yescharacteristic
596C2×C4#41×D1111yescharacteristic
597C2×C4#6704311yescharacteristic
598C8—22no—
599C8—41no—
600C8—222no—
601C8—441no—
602C22—24no—
603C22—42no—
604C22—42no—
605C22—42no—
606C22—42no—
607C22—42no—
608C22—42no—
609C22D4×Dic2211yescharacteristic
610C22#1062312111yescharacteristic
611C22#1062313711yescharacteristic
612C22C2×#6696911yescharacteristic
613C22#1062330111yescharacteristic
614C22#1062330511yescharacteristic
615C22D11×#13711yescharacteristic
616C4—22no—
617C4—42no—
618C4—41no—
619C4—81no—
620C4—81no—
621C4—222no—
622C4—441no—
623C4—442no—
624C4—441no—
625C4—441no—
626C4—442no—
627C4—881no—
628C4—881no—
629C4C2×#6693111yescharacteristic
630C4#1062307011yescharacteristic
631C4#1062313311yescharacteristic
632C4#1062318611yescharacteristic
633C2—44no—
634C2#1307242911yescharacteristic
635C2#1307868411yescharacteristic
636C2#1307879911yescharacteristic
637C2#1308012411yescharacteristic
638C2#1308029411yescharacteristic
639C2#1308148911yescharacteristic
640C2#1308152711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1877C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenter#1877D11
hypocenterC11#26372
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1877

Complements

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

NH ≅ G/Ntype
3. #13072457C2semidirect
5. #13070166C2semidirect
6. #13070102C2semidirect
7. #13070011C2semidirect
8. #13069950C2semidirect
9. #13069348C2semidirect
10. #13069176C2semidirect
13. #13068868C2semidirect
69. C2×C11×SD16Q8semidirect
381. C2×SD16Dic22semidirect
532. C11#26372semidirect

Maximal subgroups

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

subgroupindex
C2×#106226202
C2×SD16×Dic112
#130724572
#130715212
#130701662
#130701022
#130700112
#130699502
#130693482
#130691762
#130689522
#130688792
#130688682
#130688612
C11×#18772
#2637211