Finite Group Databasebeta

← #35409370

Subgroups — #35409370

Order 21248.

1226 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128231C211yesmaximal, characteristic
2C2×#19127755C211yesmaximal, characteristic, complemented
3C22×C8×Dic83C211yesmaximal, characteristic, complemented
4#24908397C212yesmaximal, complemented
5#24908255C212yesmaximal, complemented
6#24907756C211yesmaximal, characteristic, complemented
7#24907755C211yesmaximal, characteristic, complemented
8#24907753C211yesmaximal, characteristic, complemented
9#24907231C212yesmaximal, complemented
10#24907228C212yesmaximal, complemented
11C83×#1869C211yesmaximal, characteristic, complemented
12C23×C83⋊C8C2211yescharacteristic
13#19128231—24no—
14#19128231—24no—
15C2×#14581787C411yescharacteristic
16C2×#14581785C411yescharacteristic
17C2×#14581782C411yescharacteristic
18C2×#14581778C411yescharacteristic
19C2×#14581776C411yescharacteristic
20C2×#14581773C411yescharacteristic
21C2×#14581769C411yescharacteristic
22C2×#14581764C411yescharacteristic
23C2×C4×Dic166C2211yescharacteristic
24C2×C4×C22⋊D83C2211yescharacteristic
25C2×C4×C22⋊D83C2211yescharacteristic
26C2×#14581751C2211yescharacteristic
27C2×#14581749C2211yescharacteristic
28C22×C4×Dic83C2211yescharacteristic
29#19127755—24no—
30C2×Dic83⋊C8C2212yes—
31C2×C22⋊(C83⋊C8)C2211yescharacteristic
32C2×C22⋊(C83⋊C8)C2212yes—
33C2×(C2×D83)⋊C8C2212yes—
34C2×(C2×D83)⋊C8C2212yes—
35C2×#14581702C2212yes—
36C2×C8×Dic83—24no—
37C2×C8×Dic83C2212yes—
38C2×C8×Dic83C2212yes—
39#19127456C2212yes—
40#19127455C2212yes—
41#19127455C2212yes—
42C23×C8×C83C2211yescharacteristic
43C2×C4×D4×C83C2211yescharacteristic
44C2×C22⋊C8×C83C2211yescharacteristic
45C2×C22⋊C8×C83C2212yes—
46#336×C83C2212yes—
47C22×Dic166C2×C411yescharacteristic
48C22×C22⋊D83C2×C411yescharacteristic
49C22×C22⋊D83C2×C411yescharacteristic
50C23×Dic83C2×C411yescharacteristic
51C23×Dic83C2×C411yescharacteristic
52C22×C4×D83C2311yescharacteristic
53C22×C83⋊C8—24no—
54C22×C83⋊C8—22no—
55C22×C83⋊C8C2312yes—
56C22×C83⋊C8C2312yes—
57#14581787—24no—
58#14581785—24no—
59#14581782—24no—
60#14581778—24no—
61#14581776—24no—
62#14581773—24no—
63#14581769—24no—
64#14581764—24no—
65C4×Dic166—22no—
66C4×Dic166—22no—
67C4×C22⋊D83—22no—
68C4×C22⋊D83—22no—
69C4×C22⋊D83—22no—
70C4×C22⋊D83—22no—
71#14581751—22no—
72#14581751—22no—
73#14581749—22no—
74#14581749—22no—
75C2×C4⋊Dic83C2×C411yescharacteristic
76C2×C4⋊Dic83C2×C411yescharacteristic
77C2×C4⋊Dic83C2×C411yescharacteristic
78C2×Dic83⋊C4C2×C411yescharacteristic
79C2×Dic83⋊C4C2×C411yescharacteristic
80C2×Dic83⋊C4C2×C411yescharacteristic
81C2×Dic83⋊C4C2×C411yescharacteristic
82C2×Dic83⋊C4C2×C411yescharacteristic
83C2×Dic83⋊C4C2×C411yescharacteristic
84C2×C22⋊Dic83C2×C411yescharacteristic
85C2×C22⋊Dic83C2×C411yescharacteristic
86C2×C22⋊Dic83C2×C411yescharacteristic
87C2×C22⋊Dic83C2×C411yescharacteristic
88C2×(C2×D83)⋊C4C2×C411yescharacteristic
89C2×(C2×D83)⋊C4C2×C411yescharacteristic
90C2×(C2×D83)⋊C4C2×C411yescharacteristic
91C2×(C2×D83)⋊C4C2×C411yescharacteristic
92C2×C4×Dic83C2×C411yescharacteristic
93C2×C4×Dic83C2×C411yescharacteristic
94C2×C4×Dic83D414yes—
95C2×C4×Dic83D414yes—
96C2×C4×Dic83C2311yescharacteristic
97C2×C4×Dic83C2311yescharacteristic
98C2×C4×Dic83C2311yescharacteristic
99Dic83⋊C8—24no—
100C22⋊(C83⋊C8)—24no—
101C22⋊(C83⋊C8)—22no—
102(C2×D83)⋊C8—24no—
103(C2×D83)⋊C8—24no—
104#14581702—24no—
105C8×Dic83—24no—
106C8×Dic83—24no—
107C22×D4×C83C2×C411yescharacteristic
108C23×C4×C83C2311yescharacteristic
109C23×C4×C83C2311yescharacteristic
110C22×C8×C83—22no—
111C22×C8×C83—24no—
112C22×C8×C83C2312yes—
113C22×C8×C83C2312yes—
114C4×D4×C83—22no—
115C4×D4×C83—22no—
116C2×C4⋊C4×C83C2×C411yescharacteristic
117C2×C22⋊C4×C83C2×C411yescharacteristic
118C2×C22⋊C4×C83C2×C411yescharacteristic
119C2×C42×C83C2311yescharacteristic
120C22⋊C8×C83—22no—
121C22⋊C8×C83—24no—
122C23×D83C22×C411yescharacteristic
123C2×Dic166—22no—
124C2×Dic166—24no—
125C2×C22⋊D83—22no—
126C2×C22⋊D83—22no—
127C2×C22⋊D83—22no—
128C2×C22⋊D83—22no—
129C2×C22⋊D83—24no—
130C22×Dic83—22no—
131C22×Dic83—22no—
132C22×Dic83—24no—
133C22×Dic83C22⋊C414yes—
134C22×Dic83C22⋊C414yes—
135C22×Dic83C22×C411yescharacteristic
136C22×Dic83C22×C411yescharacteristic
137C22×Dic83C22×C411yescharacteristic
138C22×Dic83C22×C411yescharacteristic
139C22×Dic83C22×C411yescharacteristic
140C22×Dic83C22×C411yescharacteristic
141C22×Dic83C22×C411yescharacteristic
142C2×C4×D83—21no—
143C2×C4×D83—21no—
144C2×C4×D83—22no—
145C2×C4×D83—22no—
146C2×C83⋊C8—28no—
147C2×C83⋊C8—22no—
148C2×C83⋊C8—22no—
149C2×C83⋊C8—22no—
150C2×C83⋊C8—22no—
151C2×C83⋊C8—22no—
152C2×C83⋊C8#4114yes—
153C4⋊Dic83—22no—
154C4⋊Dic83—22no—
155C4⋊Dic83—22no—
156Dic83⋊C4—22no—
157Dic83⋊C4—22no—
158Dic83⋊C4—22no—
159Dic83⋊C4—22no—
160Dic83⋊C4—22no—
161Dic83⋊C4—22no—
162C22⋊Dic83—22no—
163C22⋊Dic83—22no—
164C22⋊Dic83—22no—
165C22⋊Dic83—22no—
166(C2×D83)⋊C4—22no—
167(C2×D83)⋊C4—22no—
168(C2×D83)⋊C4—22no—
169(C2×D83)⋊C4—22no—
170C4×Dic83—21no—
171C4×Dic83—21no—
172C4×Dic83C22⋊C414yes—
173C4×Dic83C22⋊C414yes—
174C4×Dic83C2×D412yes—
175C4×Dic83C2×D412yes—
176C4×Dic83C2×D412yes—
177C4×Dic83C2×D412yes—
178C24×C83C22×C411yescharacteristic
179C24×C83C22×C411yescharacteristic
180C2×D4×C83—22no—
181C2×D4×C83—22no—
182C2×D4×C83—22no—
183C22×C4×C83—22no—
184C22×C4×C83—22no—
185C22×C4×C83—21no—
186C22×C4×C83—21no—
187C22×C4×C83—22no—
188C22×C4×C83—22no—
189C22×C4×C83C22×C411yescharacteristic
190C22×C4×C83C22×C411yescharacteristic
191C22×C4×C83C22×C411yescharacteristic
192C22×C4×C83C22×C411yescharacteristic
193C22×C4×C83C2×D412yes—
194C22×C4×C83C2×D412yes—
195C22×C4×C83C2411yescharacteristic
196C2×C8×C83—28no—
197C2×C8×C83—22no—
198C2×C8×C83—22no—
199C2×C8×C83—22no—
200C2×C8×C83—22no—
201C2×C8×C83—22no—
202C2×C8×C83#4114yes—
203C4⋊C4×C83—22no—
204C22⋊C4×C83—22no—
205C22⋊C4×C83—22no—
206C42×C83—21no—
207C42×C83—21no—
208C23×C83—22no—
209C23×C83—22no—
210C23×C83—21no—
211C23×C83—22no—
212C23×C83—21no—
213C23×C83—21no—
214C23×C83—22no—
215C23×C83C2×C22⋊C412yes—
216C23×C83#13112yes—
217C23×C83#13112yes—
218C23×C83C23×C411yescharacteristic
219C22×D83—21no—
220C22×D83—22no—
221C22×D83—22no—
222C22×D83—21no—
223C22×D83—21no—
224D4×C83—44no—
225C2×C4×C83—22no—
226C2×C4×C83—22no—
227C2×C4×C83—22no—
228C2×C4×C83—24no—
229C2×C4×C83—21no—
230C2×C4×C83—21no—
231C2×C4×C83—21no—
232C2×C4×C83—22no—
233C2×C4×C83—21no—
234C2×C4×C83—21no—
235C2×C4×C83—22no—
236C2×C4×C83—41no—
237C2×C4×C83—41no—
238C2×C4×C83—42no—
239C2×C4×C83C2×C22⋊C412yes—
240C2×C4×C83C22×D411yescharacteristic
241C2×C4×C83C22×D411yescharacteristic
242C2×C4×C83C2×#4112yes—
243C2×C4×C83C2×#4112yes—
244C22⋊D83—44no—
245C22⋊D83—44no—
246C2×Dic83—22no—
247C2×Dic83—21no—
248C2×Dic83—21no—
249C2×Dic83—21no—
250C2×Dic83—21no—
251C2×Dic83—28no—
252C2×Dic83—28no—
253C2×Dic83—21no—
254C2×Dic83—21no—
255C2×Dic83—21no—
256C2×Dic83—22no—
257C2×Dic83—21no—
258C2×Dic83—21no—
259C2×Dic83—22no—
260C2×Dic83C2×C22⋊C412yes—
261C2×Dic83C2×C22⋊C412yes—
262C2×Dic83C2×C22⋊C412yes—
263C2×Dic83C2×C22⋊C412yes—
264C2×Dic83#13114yes—
265C4×D83—41no—
266C4×D83—41no—
267C4×D83—42no—
268Dic166—44no—
269C8×C83—24no—
270C8×C83—42no—
271C83⋊C8—24no—
272C83⋊C8—42no—
273C22×C83—22no—
274C22×C83—24no—
275C22×C83—24no—
276C22×C83—22no—
277C22×C83—41no—
278C22×C83—41no—
279C22×C83—42no—
280C22×C83—42no—
281C22×C83—41no—
282C22×C83#40814yes—
283C22×C83C22×C22⋊C411yescharacteristic
284C22×C83C4×#4112yes—
285C22×C83C2×#13112yes—
286C22×C83C2×#13111yescharacteristic
287C22×C83C2×#13111yescharacteristic
288C2×D83—41no—
289C2×D83—41no—
290C2×D83—42no—
291C2×D83—42no—
292C2×D83—41no—
293C4×C83—22no—
294C4×C83—41no—
295C4×C83—41no—
296C4×C83—41no—
297C4×C83#52511yescharacteristic
298C4×C83#52511yescharacteristic
299C4×C83#53212yes—
300Dic83—22no—
301Dic83—22no—
302Dic83—22no—
303Dic83—41no—
304Dic83—41no—
305Dic83—41no—
306Dic83#40814yes—
307#21375—831nomaximal, Sylow
308C2×C83—24no—
309C2×C83—81no—
310C2×C83#229711yescharacteristic
311C2×C83C2×#40811yescharacteristic
312C2×C83C2×#40811yescharacteristic
313C2×C83#296612yes—
314C2×C83#296612yes—
315D83—81no—
316C2×#529—831no—
317C2×#432—831no—
318C22×C4×C8—831no—
319#1984—832no—
320#1954—832no—
321#1869—831no—
322#1869—831no—
323#1869—831no—
324#1869D8311yescharacteristic, complemented
325#1750—832no—
326#1750—832no—
327C83#2137511yescharacteristic, complemented, Sylow
328C23×C8—831no—
329C23×C8C2×D8311yescharacteristic
330#529—1664no—
331#529—1664no—
332C2×#126—831no—
333C2×#126—831no—
334C2×#125—831no—
335C2×#124—831no—
336C2×#123—831no—
337C2×#123—831no—
338C2×C22⋊Q8—831no—
339C2×#121—831no—
340C2×C4×Q8—831no—
341C2×C4×D4—831no—
342C2×C4×D4—831no—
343C2×C4×D4C2×D8311yescharacteristic
344C2×#117—831no—
345C2×#117—831no—
346C22×C42—831no—
347#432—1664no—
348C2×C4⋊C8—832no—
349C2×C22⋊C8—831no—
350C2×C22⋊C8—832no—
351C2×C22⋊C8—832no—
352C2×C22⋊C8—832no—
353C2×C22⋊C8C2×D8311yescharacteristic
354C2×C22⋊C8C2×D8312yes—
355C2×#97—832no—
356C2×C4×C8—832no—
357C2×C4×C8—832no—
358C2×C4×C8—1664no—
359#336—832no—
360#336—832no—
361#336—832no—
362#336C2×D8312yes—
363C22×Q8—831no—
364C22×D4—831no—
365C22×D4—831no—
366C22×D4C4×D8311yescharacteristic
367C23×C4—831no—
368C23×C4—831no—
369C23×C4—831no—
370C23×C4C22×D8311yescharacteristic
371C23×C4C22×D8311yescharacteristic
372C22×C8—22no—
373C22×C8—24no—
374C22×C8—832no—
375C22×C8—832no—
376C22×C8—1664no—
377C22×C8—1662no—
378C22×C8C22×D8312yes—
379C22×C8C22×D8312yes—
380#126—1664no—
381#126—1664no—
382#125—1664no—
383#124—1664no—
384#123—1664no—
385#123—1664no—
386C22⋊Q8—1664no—
387#121—1664no—
388C4×Q8—1662no—
389C4×Q8—1662no—
390C4×D4—22no—
391C4×D4—22no—
392C4×D4—1662no—
393C4×D4—1662no—
394C4×D4—1662no—
395C4×D4—1662no—
396#117—1662no—
397#117—1662no—
398#117—1662no—
399#117—1662no—
400C2×C4⋊C4—831no—
401C2×C4⋊C4—831no—
402C2×C4⋊C4—831no—
403C2×C4⋊C4—831no—
404C2×C4⋊C4—831no—
405C2×C4⋊C4—831no—
406C2×C4⋊C4—831no—
407C2×C4⋊C4—831no—
408C2×C4⋊C4—831no—
409C2×C4⋊C4C4×D8311yescharacteristic
410C2×C22⋊C4—831no—
411C2×C22⋊C4—831no—
412C2×C22⋊C4—831no—
413C2×C22⋊C4—831no—
414C2×C22⋊C4—831no—
415C2×C22⋊C4—831no—
416C2×C22⋊C4—831no—
417C2×C22⋊C4—831no—
418C2×C22⋊C4C4×D8311yescharacteristic
419C2×C22⋊C4C4×D8311yescharacteristic
420C2×C42—831no—
421C2×C42—831no—
422C2×C42—834no—
423C2×C42—834no—
424C2×C42—831no—
425C2×C42—831no—
426C2×C42—831no—
427C2×C42C22×D8311yescharacteristic
428C4⋊C8—1664no—
429C22⋊C8—22no—
430C22⋊C8—24no—
431C22⋊C8—1664no—
432C22⋊C8—1664no—
433C22⋊C8—1662no—
434C22⋊C8—1664no—
435#97—1664no—
436C4×C8—1664no—
437C4×C8—1664no—
438C24—831no—
439C24C2×C4×D8311yescharacteristic
440C24C2×C4×D8311yescharacteristic
441C2×Q8—1662no—
442C2×Q8—1664no—
443C2×D4—22no—
444C2×D4—22no—
445C2×D4—22no—
446C2×D4—1662no—
447C2×D4—1664no—
448C2×D4—1662no—
449C2×D4—1662no—
450C2×D4—1662no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—831no—
458C22×C4—831no—
459C22×C4—831no—
460C22×C4—831no—
461C22×C4—834no—
462C22×C4—834no—
463C22×C4—831no—
464C22×C4—831no—
465C22×C4—831no—
466C22×C4—1661no—
467C22×C4—1661no—
468C22×C4—1662no—
469C22×C4—1662no—
470C22×C4—1664no—
471C22×C4—1662no—
472C22×C4—1662no—
473C22×C4C2×C4×D8311yescharacteristic
474C22×C4C2×C4×D8311yescharacteristic
475C22×C4C2×C4×D8311yescharacteristic
476C22×C4C2×C4×D8311yescharacteristic
477C22×C4D4×D8312yes—
478C22×C4D4×D8312yes—
479C22×C4C23×D8311yescharacteristic
480C2×C8—28no—
481C2×C8—22no—
482C2×C8—22no—
483C2×C8—22no—
484C2×C8—22no—
485C2×C8—22no—
486C2×C8—834no—
487C2×C8—1662no—
488C2×C8—1662no—
489C2×C8—1662no—
490C2×C8—1668no—
491C2×C8—1662no—
492C2×C8—1662no—
493C2×C8#1305058914yes—
494C4⋊C4—22no—
495C4⋊C4—1662no—
496C4⋊C4—1662no—
497C4⋊C4—1662no—
498C4⋊C4—1662no—
499C4⋊C4—1662no—
500C4⋊C4—1662no—
501C4⋊C4—1662no—
502C4⋊C4—1662no—
503C4⋊C4—1662no—
504C22⋊C4—22no—
505C22⋊C4—22no—
506C22⋊C4—1662no—
507C22⋊C4—1662no—
508C22⋊C4—1662no—
509C22⋊C4—1662no—
510C22⋊C4—1662no—
511C22⋊C4—1662no—
512C22⋊C4—1662no—
513C22⋊C4—1662no—
514C42—21no—
515C42—21no—
516C42—832no—
517C42—832no—
518C42—832no—
519C42—832no—
520C42—834no—
521C42—834no—
522C42—1661no—
523C42—1661no—
524C23—22no—
525C23—22no—
526C23—21no—
527C23—22no—
528C23—22no—
529C23—21no—
530C23—21no—
531C23—1661no—
532C23—1662no—
533C23—1662no—
534C23—1661no—
535C23—1661no—
536C23C22⋊C4×D8312yes—
537C23#1458179812yes—
538C23#1458180012yes—
539C23C22×C4×D8311yescharacteristic
540Q8—3324no—
541D4—44no—
542D4—3324no—
543D4—3324no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—24no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—42no—
558C2×C4—3321no—
559C2×C4—3321no—
560C2×C4—3322no—
561C2×C4—832no—
562C2×C4—834no—
563C2×C4—832no—
564C2×C4—832no—
565C2×C4—832no—
566C2×C4—1661no—
567C2×C4—1661no—
568C2×C4—1661no—
569C2×C4—1662no—
570C2×C4—1662no—
571C2×C4—1661no—
572C2×C4—1661no—
573C2×C4—1668no—
574C2×C4—1668no—
575C2×C4—1662no—
576C2×C4—1661no—
577C2×C4—1661no—
578C2×C4—1661no—
579C2×C4—1661no—
580C2×C4C22⋊C4×D8312yes—
581C2×C4C2×D4×D8311yescharacteristic
582C2×C4C2×D4×D8311yescharacteristic
583C2×C4#41×D8312yes—
584C2×C4C2×#1305058912yes—
585C8—24no—
586C8—42no—
587C8—3322no—
588C8—1664no—
589C22—22no—
590C22—22no—
591C22—24no—
592C22—24no—
593C22—41no—
594C22—41no—
595C22—41no—
596C22—42no—
597C22—42no—
598C22—3321no—
599C22—3321no—
600C22—3321no—
601C22—3322no—
602C22—3322no—
603C22#1912766614yes—
604C22C2×C22⋊C4×D8311yescharacteristic
605C22C4×#1305058912yes—
606C22#131×D8312yes—
607C22C2×#1458179811yescharacteristic
608C22C2×#1458180011yescharacteristic
609C4—22no—
610C4—41no—
611C4—41no—
612C4—41no—
613C4—3321no—
614C4—3321no—
615C4—3321no—
616C4—834no—
617C4—1662no—
618C4—1662no—
619C4—1662no—
620C4#1912820711yescharacteristic
621C4#1912820911yescharacteristic
622C4#1912824612yes—
623C2—24no—
624C2—81no—
625C2—6641no—
626C2#2490994811yescharacteristic
627C2#408×D8311yescharacteristic
628C2C2×#1912766611yescharacteristic
629C2#2491643112yes—
630C2#2491643312yes—
subgroupG/H
center, FrattiniC22×C4C23×D83
commutator, socleC23×C83C23×C4
FittingC83×#1869C2
prime radicalC2×#14581764C4
cosocleC22×C4×C83C24
hypercenter#1869D83
hypocenterC83#21375
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C22×C4 ◁ #1869

Complements

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

NH ≅ G/Ntype
2. C2×#19127755C2semidirect
3. C22×C8×Dic83C2semidirect
4. #24908397C2semidirect
5. #24908255C2semidirect
6. #24907756C2semidirect
7. #24907755C2semidirect
8. #24907753C2semidirect
9. #24907231C2semidirect
10. #24907228C2semidirect
11. C83×#1869C2semidirect
324. #1869D83semidirect
327. C83#21375semidirect

Maximal subgroups

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

subgroupindex
C2×#191282312
C2×#191277552
C22×C8×Dic832
#249083972
#249082552
#249077562
#249077552
#249077532
#249072312
#249072282
C83×#18692
#2137583