Finite Group Databasebeta

← #35335668

Subgroups — #35335668

Order 21248.

1566 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19127600C211yesmaximal, characteristic
2C2×#19127597C211yesmaximal, characteristic
3C2×#19127588C212yesmaximal
4C2×C42×Dic83C211yesmaximal, characteristic
5#24905697C212yesmaximal
6#24905694C212yesmaximal
7#24905693C211yesmaximal, characteristic
8#24905692C211yesmaximal, characteristic
9#24905692C211yesmaximal, characteristic
10#24905689C212yesmaximal
11C83×C4⋊#95C211yesmaximal, characteristic
12C22×C4⋊Dic83C2212yes—
13C22×C4⋊Dic83C2211yescharacteristic
14C22×C4⋊Dic83C2211yescharacteristic
15C22×Dic83⋊C4C2212yes—
16C22×C4×Dic83C2211yescharacteristic
17C22×C4×Dic83C2211yescharacteristic
18C22×C4×Dic83C2211yescharacteristic
19C22×C4×Dic83C2211yescharacteristic
20C22×C4×Dic83C2211yescharacteristic
21C22×C4×Dic83C2211yescharacteristic
22#19127600—24no—
23#19127597C418yescomplemented
24#19127588—28no—
25C2×C83⋊#95C2212yes—
26C2×C83⋊#95C2212yes—
27C2×C83⋊#95C2212yes—
28C2×C83⋊#95C2212yes—
29C2×C83⋊#95C2212yes—
30C2×C83⋊#95C2212yes—
31C2×C83⋊#95C2212yes—
32C2×C83⋊#95C2212yes—
33C42×Dic83—24no—
34C22×C4⋊C4×C83C2211yescharacteristic
35C22×C4⋊C4×C83C2211yescharacteristic
36C22×C42×C83C2211yescharacteristic
37C2×#95×C83C2212yes—
38C2×#95×C83C2212yes—
39C23×Dic83C2312yes—
40C23×Dic83C2312yes—
41C23×Dic83C2311yescharacteristic
42C23×Dic83C2311yescharacteristic
43C23×Dic83C2311yescharacteristic
44C23×Dic83C2311yescharacteristic
45C2×C4⋊Dic83—24no—
46C2×C4⋊Dic83—24no—
47C2×C4⋊Dic83—24no—
48C2×C4⋊Dic83—22no—
49C2×C4⋊Dic83—22no—
50C2×C4⋊Dic83—22no—
51C2×C4⋊Dic83—22no—
52C2×C4⋊Dic83—22no—
53C2×C4⋊Dic83C2×C414yes—
54C2×Dic83⋊C4—24no—
55C2×Dic83⋊C4—24no—
56C2×Dic83⋊C4C2×C418yes—
57C2×C4×Dic83—22no—
58C2×C4×Dic83—22no—
59C2×C4×Dic83—22no—
60C2×C4×Dic83—22no—
61C2×C4×Dic83—22no—
62C2×C4×Dic83—22no—
63C2×C4×Dic83—22no—
64C2×C4×Dic83—22no—
65C2×C4×Dic83—22no—
66C2×C4×Dic83—22no—
67C2×C4×Dic83—22no—
68C2×C4×Dic83—22no—
69C2×C4×Dic83—22no—
70C2×C4×Dic83—22no—
71C2×C4×Dic83C2×C414yes—
72C2×C4×Dic83D414yes—
73C2×C4×Dic83D414yes—
74C2×C4×Dic83Q814yes—
75C83⋊#95—24no—
76C83⋊#95—24no—
77C83⋊#95—24no—
78C83⋊#95—24no—
79C83⋊#95—24no—
80C83⋊#95—24no—
81C83⋊#95—24no—
82C83⋊#95C2×C418yes—
83C23×C4×C83C2312yes—
84C23×C4×C83C2312yes—
85C23×C4×C83C2311yescharacteristic
86C23×C4×C83C2311yescharacteristic
87C23×C4×C83C2311yescharacteristic
88C2×C4⋊C4×C83—22no—
89C2×C4⋊C4×C83—22no—
90C2×C4⋊C4×C83—22no—
91C2×C4⋊C4×C83—22no—
92C2×C4⋊C4×C83—22no—
93C2×C4⋊C4×C83C2×C414yes—
94C2×C42×C83—22no—
95C2×C42×C83—22no—
96C2×C42×C83Q814yes—
97#95×C83—24no—
98#95×C83—24no—
99C22×Dic83—21no—
100C22×Dic83—21no—
101C22×Dic83—21no—
102C22×Dic83—21no—
103C22×Dic83—21no—
104C22×Dic83—21no—
105C22×Dic83—21no—
106C22×Dic83—21no—
107C22×Dic83—21no—
108C22×Dic83—21no—
109C22×Dic83—21no—
110C22×Dic83—21no—
111C22×Dic83—21no—
112C22×Dic83—21no—
113C22×Dic83—21no—
114C22×Dic83—21no—
115C22×Dic83—22no—
116C22×Dic83—22no—
117C22×Dic83—22no—
118C22×Dic83—22no—
119C22×Dic83—22no—
120C22×Dic83—22no—
121C22×Dic83—22no—
122C22×Dic83—22no—
123C22×Dic83—22no—
124C22×Dic83—22no—
125C22×Dic83—22no—
126C22×Dic83—22no—
127C22×Dic83—22no—
128C22×Dic83C22×C414yes—
129C22×Dic83C22×C412yes—
130C22×Dic83C22×C412yes—
131C22×Dic83C2×D412yes—
132C22×Dic83C2×D412yes—
133C22×Dic83C2×D412yes—
134C22×Dic83C2×D412yes—
135C22×Dic83C2×Q812yes—
136C22×Dic83C2×Q812yes—
137C22×Dic83#4112yes—
138C22×Dic83#4112yes—
139C22×Dic83#4112yes—
140C22×Dic83#4112yes—
141C4⋊Dic83—28no—
142C4⋊Dic83—44no—
143C4⋊Dic83—48no—
144Dic83⋊C4—216no—
145C4×Dic83—28no—
146C4×Dic83—28no—
147C4×Dic83—28no—
148C4×Dic83—28no—
149C4×Dic83—28no—
150C4×Dic83—28no—
151C24×C83C2411yescharacteristic
152C22×C4×C83—21no—
153C22×C4×C83—21no—
154C22×C4×C83—21no—
155C22×C4×C83—21no—
156C22×C4×C83—21no—
157C22×C4×C83—21no—
158C22×C4×C83—21no—
159C22×C4×C83—21no—
160C22×C4×C83—22no—
161C22×C4×C83—22no—
162C22×C4×C83—22no—
163C22×C4×C83—22no—
164C22×C4×C83—22no—
165C22×C4×C83—22no—
166C22×C4×C83—22no—
167C22×C4×C83—22no—
168C22×C4×C83—22no—
169C22×C4×C83—22no—
170C22×C4×C83—22no—
171C22×C4×C83—22no—
172C22×C4×C83—22no—
173C22×C4×C83C22×C414yes—
174C22×C4×C83C22×C412yes—
175C22×C4×C83C2×D412yes—
176C22×C4×C83C2×D412yes—
177C22×C4×C83C2×Q812yes—
178C22×C4×C83C2×Q812yes—
179C22×C4×C83C2×Q812yes—
180C22×C4×C83C2×Q812yes—
181C22×C4×C83#4112yes—
182C22×C4×C83#4112yes—
183C22×C4×C83#4112yes—
184C22×C4×C83#4112yes—
185C22×C4×C83#4112yes—
186C22×C4×C83#4112yes—
187C4⋊C4×C83—28no—
188C4⋊C4×C83—44no—
189C42×C83—28no—
190C23×C83C23×C411yescharacteristic
191C23×C83C22×D411yescharacteristic
192C23×C83C22×D411yescharacteristic
193C23×C83C22×Q811yescharacteristic
194C23×C83C22×Q811yescharacteristic
195C23×C83C2×#4111yescharacteristic
196C23×C83C2×#4111yescharacteristic
197C23×C83C2×#4111yescharacteristic
198C23×C83C2×#4111yescharacteristic
199C23×C83C2×#4111yescharacteristic
200C23×C83C2×#4111yescharacteristic
201C23×C83C2×#4111yescharacteristic
202C23×C83C2×#4111yescharacteristic
203C23×C83C2×#4111yescharacteristic
204C23×C83C2×#4111yescharacteristic
205C2×C4×C83—22no—
206C2×C4×C83—22no—
207C2×C4×C83—22no—
208C2×C4×C83—22no—
209C2×C4×C83—22no—
210C2×C4×C83—22no—
211C2×C4×C83—22no—
212C2×C4×C83—22no—
213C2×C4×C83—22no—
214C2×C4×C83—22no—
215C2×C4×C83—22no—
216C2×C4×C83—22no—
217C2×C4×C83—24no—
218C2×C4×C83—24no—
219C2×C4×C83—24no—
220C2×C4×C83—42no—
221C2×C4×C83—42no—
222C2×C4×C83—42no—
223C2×C4×C83—42no—
224C2×C4×C83—42no—
225C2×C4×C83—42no—
226C2×C4×C83—42no—
227C2×C4×C83—42no—
228C2×C4×C83—42no—
229C2×C4×C83—42no—
230C2×C4×C83—42no—
231C2×C4×C83#11714yes—
232C2×C4×C83C4×D414yes—
233C2×C4×C83C4×Q814yes—
234C2×C4×C83C22⋊Q814yes—
235C2×C4×C83#12314yes—
236C2×C4×C83#12514yes—
237C2×C4×C83#12514yes—
238C2×C4×C83#12614yes—
239C2×C4×C83C4⋊Q814yes—
240C2×Dic83—22no—
241C2×Dic83—22no—
242C2×Dic83—22no—
243C2×Dic83—22no—
244C2×Dic83—22no—
245C2×Dic83—22no—
246C2×Dic83—22no—
247C2×Dic83—22no—
248C2×Dic83—22no—
249C2×Dic83—22no—
250C2×Dic83—22no—
251C2×Dic83—22no—
252C2×Dic83—22no—
253C2×Dic83—22no—
254C2×Dic83—22no—
255C2×Dic83—22no—
256C2×Dic83—22no—
257C2×Dic83—22no—
258C2×Dic83—22no—
259C2×Dic83—22no—
260C2×Dic83—22no—
261C2×Dic83—22no—
262C2×Dic83—22no—
263C2×Dic83—22no—
264C2×Dic83—24no—
265C2×Dic83—24no—
266C2×Dic83—24no—
267C2×Dic83—42no—
268C2×Dic83—42no—
269C2×Dic83—42no—
270C2×Dic83—42no—
271C2×Dic83—42no—
272C2×Dic83—42no—
273C2×Dic83—42no—
274C2×Dic83—42no—
275C2×Dic83—42no—
276C2×Dic83—42no—
277C2×Dic83—42no—
278C2×Dic83C4×D414yes—
279C2×Dic83C4×Q814yes—
280C2×Dic83#12114yes—
281C2×Dic83C22⋊Q814yes—
282C22×C83C2×#11711yescharacteristic
283C22×C83C2×C4×D411yescharacteristic
284C22×C83C2×C4×D411yescharacteristic
285C22×C83C2×C4×Q811yescharacteristic
286C22×C83C2×C4×Q811yescharacteristic
287C22×C83C4×#4111yescharacteristic
288C22×C83C4×#4111yescharacteristic
289C22×C83C2×#12111yescharacteristic
290C22×C83C2×C22⋊Q811yescharacteristic
291C22×C83C2×C22⋊Q811yescharacteristic
292C22×C83C2×#12311yescharacteristic
293C22×C83#52511yescharacteristic
294C22×C83#52511yescharacteristic
295C22×C83C2×#12511yescharacteristic
296C22×C83C2×#12511yescharacteristic
297C22×C83C2×#12611yescharacteristic
298C22×C83#52911yescharacteristic
299C22×C83#52911yescharacteristic
300C22×C83#52911yescharacteristic
301C22×C83#52911yescharacteristic
302C22×C83#52911yescharacteristic
303C22×C83#52911yescharacteristic
304C22×C83#52911yescharacteristic
305C22×C83#52911yescharacteristic
306C22×C83C2×C4⋊Q811yescharacteristic
307C22×C83#53211yescharacteristic
308C22×C83#53211yescharacteristic
309C22×C83#53211yescharacteristic
310C22×C83#53211yescharacteristic
311C22×C83#53311yescharacteristic
312C22×C83#53311yescharacteristic
313C22×C83#53311yescharacteristic
314C22×C83#53311yescharacteristic
315C22×C83#53311yescharacteristic
316C22×C83#53311yescharacteristic
317C4×C83—24no—
318C4×C83—24no—
319C4×C83—44no—
320C4×C83—82no—
321C4×C83#38718yescomplemented
322Dic83—24no—
323Dic83—24no—
324Dic83—24no—
325Dic83—24no—
326Dic83—44no—
327Dic83—82no—
328#14699—831nomaximal, Sylow
329C2×C83C2×#38711yescharacteristic
330C2×C83#229311yescharacteristic
331C2×C83#229511yescharacteristic
332C2×C83C4×#12111yescharacteristic
333C2×C83C4×C22⋊Q811yescharacteristic
334C2×C83C4×#12511yescharacteristic
335C2×C83C4×C4⋊Q811yescharacteristic
336C2×C83#285111yescharacteristic
337C2×C83#285411yescharacteristic
338C2×C83#285511yescharacteristic
339C2×C83#285711yescharacteristic
340C2×C83#285911yescharacteristic
341C2×C83#286011yescharacteristic
342C2×C83#286311yescharacteristic
343C2×C83#286411yescharacteristic
344C2×#389—831no—
345C2×#389—831no—
346C2×#387—832no—
347C2×C43—831no—
348#1436—832no—
349#1436—832no—
350C4⋊#95—831no—
351C4⋊#95—831no—
352C4⋊#95—831no—
353C4⋊#95D8311yescharacteristic
354#1434—832no—
355C83#1469911yescharacteristic, complemented, Sylow
356C22×C4⋊C4—832no—
357C22×C4⋊C4—831no—
358C22×C4⋊C4—831no—
359C22×C4⋊C4—832no—
360C22×C4⋊C4C2×D8311yescharacteristic
361C22×C4⋊C4C2×D8311yescharacteristic
362C22×C42—831no—
363C22×C42—831no—
364C22×C42—831no—
365C22×C42—831no—
366C22×C42—831no—
367C22×C42—831no—
368C22×C42C2×D8311yescharacteristic
369#389—838no—
370#389—1664no—
371#387—1668no—
372C2×#95—832no—
373C2×#95—832no—
374C2×#95—832no—
375C2×#95—832no—
376C2×#95—832no—
377C2×#95—832no—
378C2×#95—832no—
379C2×#95—832no—
380C2×#95C2×D8312yes—
381C2×#95C2×D8312yes—
382C43—1664no—
383C23×C4—831no—
384C23×C4—831no—
385C23×C4—831no—
386C23×C4—831no—
387C23×C4—832no—
388C23×C4—832no—
389C23×C4C22×D8312yes—
390C23×C4C22×D8312yes—
391C23×C4C22×D8311yescharacteristic
392C23×C4C22×D8311yescharacteristic
393C23×C4C22×D8311yescharacteristic
394C2×C4⋊C4—22no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—838no—
400C2×C4⋊C4—834no—
401C2×C4⋊C4—1664no—
402C2×C4⋊C4—1664no—
403C2×C4⋊C4—1664no—
404C2×C4⋊C4—1662no—
405C2×C4⋊C4—1662no—
406C2×C4⋊C4—1662no—
407C2×C4⋊C4—1664no—
408C2×C4⋊C4—1664no—
409C2×C4⋊C4—1662no—
410C2×C4⋊C4—1662no—
411C2×C4⋊C4C4×D8314yes—
412C2×C42—22no—
413C2×C42—22no—
414C2×C42—834no—
415C2×C42—834no—
416C2×C42—834no—
417C2×C42—834no—
418C2×C42—1662no—
419C2×C42—1662no—
420C2×C42—1662no—
421C2×C42—1662no—
422C2×C42—1662no—
423C2×C42—1662no—
424C2×C42—1662no—
425C2×C42—1662no—
426C2×C42—1662no—
427C2×C42—1662no—
428C2×C42—1662no—
429C2×C42—1662no—
430C2×C42—1662no—
431C2×C42—1662no—
432C2×C42Dic16614yes—
433#95—24no—
434#95—24no—
435#95—838no—
436#95—1664no—
437#95—1664no—
438#95—1664no—
439#95—1664no—
440#95—1664no—
441#95—1664no—
442#95—1664no—
443C24C23×D8311yescharacteristic
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—832no—
466C22×C4—832no—
467C22×C4—832no—
468C22×C4—832no—
469C22×C4—832no—
470C22×C4—832no—
471C22×C4—832no—
472C22×C4—832no—
473C22×C4—832no—
474C22×C4—832no—
475C22×C4—832no—
476C22×C4—832no—
477C22×C4—834no—
478C22×C4—1662no—
479C22×C4—1662no—
480C22×C4—1662no—
481C22×C4—1662no—
482C22×C4—1662no—
483C22×C4—1662no—
484C22×C4—1662no—
485C22×C4—1662no—
486C22×C4—1662no—
487C22×C4—1662no—
488C22×C4—1662no—
489C22×C4—1662no—
490C22×C4—1662no—
491C22×C4—1661no—
492C22×C4—1661no—
493C22×C4—1661no—
494C22×C4—1661no—
495C22×C4—1661no—
496C22×C4—1661no—
497C22×C4—1661no—
498C22×C4—1661no—
499C22×C4—1661no—
500C22×C4—1661no—
501C22×C4—1661no—
502C22×C4—1661no—
503C22×C4—1661no—
504C22×C4—1661no—
505C22×C4—1661no—
506C22×C4—1661no—
507C22×C4C2×C4×D8314yes—
508C22×C4C2×C4×D8312yes—
509C22×C4D4×D8312yes—
510C22×C4D4×D8312yes—
511C22×C4Q8×D8312yes—
512C22×C4C2×Dic16612yes—
513C22×C4C2×Dic16612yes—
514C22×C4C2×Dic16612yes—
515C22×C4#1305058912yes—
516C22×C4#1305058912yes—
517C22×C4#1305058912yes—
518C22×C4#1305059012yes—
519C22×C4#1305059112yes—
520C22×C4#1305059112yes—
521C4⋊C4—28no—
522C4⋊C4—44no—
523C4⋊C4—3328no—
524C4⋊C4—3324no—
525C4⋊C4—16616no—
526C4⋊C4—1668no—
527C42—28no—
528C42—1668no—
529C42—1668no—
530C42—1668no—
531C42—1668no—
532C42—1668no—
533C42—1668no—
534C23C22×C4×D8311yescharacteristic
535C23C2×D4×D8311yescharacteristic
536C23C2×D4×D8311yescharacteristic
537C23C2×Q8×D8311yescharacteristic
538C23C22×Dic16611yescharacteristic
539C23#41×D8311yescharacteristic
540C23#41×D8311yescharacteristic
541C23#41×D8311yescharacteristic
542C23#41×D8311yescharacteristic
543C23C2×#1305058911yescharacteristic
544C23C2×#1305058911yescharacteristic
545C23C2×#1305058911yescharacteristic
546C23C2×#1305059011yescharacteristic
547C23C2×#1305059111yescharacteristic
548C23C2×#1305059111yescharacteristic
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—24no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—3322no—
576C2×C4—3322no—
577C2×C4—3322no—
578C2×C4—3322no—
579C2×C4—3322no—
580C2×C4—3322no—
581C2×C4—3322no—
582C2×C4—3322no—
583C2×C4—3322no—
584C2×C4—3322no—
585C2×C4—3322no—
586C2×C4—834no—
587C2×C4—834no—
588C2×C4—834no—
589C2×C4—834no—
590C2×C4—1664no—
591C2×C4—1664no—
592C2×C4—1664no—
593C2×C4—1662no—
594C2×C4—1662no—
595C2×C4—1662no—
596C2×C4—1662no—
597C2×C4—1662no—
598C2×C4—1662no—
599C2×C4—1662no—
600C2×C4—1662no—
601C2×C4—1662no—
602C2×C4—1662no—
603C2×C4—1662no—
604C2×C4—1662no—
605C2×C4—1662no—
606C2×C4—1662no—
607C2×C4—1662no—
608C2×C4—1662no—
609C2×C4—1662no—
610C2×C4—1662no—
611C2×C4—1662no—
612C2×C4—1662no—
613C2×C4—1662no—
614C2×C4—1662no—
615C2×C4—1662no—
616C2×C4—1662no—
617C2×C4#1458175014yes—
618C2×C4(C22⋊D83)⋊C414yes—
619C2×C4C4×Dic16614yes—
620C2×C4#1458176914yes—
621C2×C4#1458177714yes—
622C2×C4#1458178314yes—
623C2×C4#1458178314yes—
624C2×C4#1458178514yes—
625C2×C4#1458179114yes—
626C22C2×#1458175011yescharacteristic
627C22C4×D4×D8311yescharacteristic
628C22C2×(C22⋊D83)⋊C411yescharacteristic
629C22C4×Q8×D8311yescharacteristic
630C22C2×C4×Dic16611yescharacteristic
631C22C4×#1305058911yescharacteristic
632C22C4×#1305059111yescharacteristic
633C22#121×D8311yescharacteristic
634C22C22⋊Q8×D8311yescharacteristic
635C22C2×#1458176911yescharacteristic
636C22C2×#1458177711yescharacteristic
637C22#1912821111yescharacteristic
638C22#1912821411yescharacteristic
639C22C2×#1458178311yescharacteristic
640C22C2×#1458178311yescharacteristic
641C22C2×#1458178511yescharacteristic
642C22#1912823011yescharacteristic
643C22#1912823011yescharacteristic
644C22#1912823211yescharacteristic
645C22#1912823311yescharacteristic
646C22#1912823611yescharacteristic
647C22#1912823611yescharacteristic
648C22#1912823711yescharacteristic
649C22#1912823811yescharacteristic
650C22C2×#1458179111yescharacteristic
651C22#1912824611yescharacteristic
652C22#1912824811yescharacteristic
653C22#1912824911yescharacteristic
654C22#1912825211yescharacteristic
655C22#1912825311yescharacteristic
656C22#1912825411yescharacteristic
657C22#1912825411yescharacteristic
658C22#1912825511yescharacteristic
659C22#1912825611yescharacteristic
660C22#1912825611yescharacteristic
661C4—24no—
662C4—24no—
663C4—44no—
664C4—82no—
665C4—3324no—
666C4—6642no—
667C4—1664no—
668C4—1664no—
669C4—1664no—
670C4—1664no—
671C4#1912758818yescomplemented
672C2C2×#1912758811yescharacteristic
673C2#2490992111yescharacteristic
674C2#2490993411yescharacteristic
675C2#2490997911yescharacteristic
676C2#2491000111yescharacteristic
677C2C4×#1458178311yescharacteristic
678C2C4×#1458179111yescharacteristic
679C2#2491577111yescharacteristic
680C2#2491579611yescharacteristic
681C2#2491580111yescharacteristic
682C2#2491581311yescharacteristic
683C2#2491582411yescharacteristic
684C2#2491582711yescharacteristic
685C2#2491584211yescharacteristic
686C2#2491584811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D83
commutatorC23×C83C23×C4
FittingC83×C4⋊#95C2
socle, prime radical, cosocleC24×C83C24
hypercenterC4⋊#95D83
hypocenterC83#14699
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
23. #19127597C4semidirect
321. C4×C83#387semidirect
355. C83#14699semidirect
671. C4#19127588semidirect

Maximal subgroups

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

subgroupindex
C2×#191276002
C2×#191275972
C2×#191275882
C2×C42×Dic832
#249056972
#249056942
#249056932
#249056922
#249056892
C83×C4⋊#952
#1469983