Finite Group Databasebeta

← #35335694

Subgroups — #35335694

Order 21248.

2734 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14581769C211yesmaximal, characteristic
2C23×C4×Dic83C211yesmaximal, characteristic
3C2×#19127605C212yesmaximal, complemented
4C2×#19127559C211yesmaximal, characteristic
5#24905697C212yesmaximal, complemented
6#24905694C212yesmaximal, complemented
7Dic83⋊#95C212yesmaximal, complemented
8#24905686C211yesmaximal, characteristic
9#24905685C211yesmaximal, characteristic
10#24905685C211yesmaximal, characteristic
11C83×C22⋊#95C211yesmaximal, characteristic
12C23×Dic166C2211yescharacteristic
13C24×Dic83C2211yescharacteristic
14C24×Dic83C2211yescharacteristic
15C2×#14581769—24no—
16C2×#14581769—24no—
17C2×#14581769C418yescomplemented
18C22×C4⋊Dic83C2211yescharacteristic
19C22×Dic83⋊C4C2212yes—
20C22×Dic83⋊C4C2211yescharacteristic
21C22×Dic83⋊C4C2211yescharacteristic
22C22×C22⋊Dic83C2211yescharacteristic
23C22×C22⋊Dic83C2211yescharacteristic
24C22×C4×Dic83—28no—
25C22×C4×Dic83—24no—
26C22×C4×Dic83C2212yes—
27C22×C4×Dic83C2212yes—
28#19127605—28no—
29#19127559—24no—
30C2×C83⋊#95C2212yes—
31C2×C83⋊#95C2212yes—
32C2×C83⋊#95C2212yes—
33C2×C83⋊#95C2212yes—
34C2×C83⋊#95C2212yes—
35C2×C83⋊#95C2212yes—
36C2×C83⋊#95C2212yes—
37C24×C4×C83C2211yescharacteristic
38C22×C22⋊C4×C83C2211yescharacteristic
39C22×C22⋊C4×C83C2211yescharacteristic
40C2×#95×C83C2212yes—
41C2×#95×C83C2212yes—
42C22×Dic166—24no—
43C22×Dic166—22no—
44C22×Dic166—22no—
45C22×Dic166—24no—
46C22×Dic166C2×C414yescomplemented
47C23×Dic83—24no—
48C23×Dic83—24no—
49C23×Dic83—24no—
50C23×Dic83—24no—
51C23×Dic83—22no—
52C23×Dic83—22no—
53C23×Dic83C2×C414yes—
54C23×Dic83D414yes—
55C23×Dic83D414yes—
56C23×Dic83Q814yescomplemented
57C23×Dic83C2312yes—
58C23×Dic83C2311yescharacteristic
59C23×Dic83C2311yescharacteristic
60C23×Dic83C2311yescharacteristic
61C23×Dic83C2312yes—
62C23×Dic83C2311yescharacteristic
63#14581769—232no—
64C2×C4⋊Dic83—22no—
65C2×C4⋊Dic83—22no—
66C2×C4⋊Dic83C2×C414yescomplemented
67C2×Dic83⋊C4—22no—
68C2×Dic83⋊C4—22no—
69C2×Dic83⋊C4—22no—
70C2×Dic83⋊C4—22no—
71C2×Dic83⋊C4—24no—
72C2×Dic83⋊C4—24no—
73C2×Dic83⋊C4—24no—
74C2×Dic83⋊C4C2×C414yescomplemented
75C2×Dic83⋊C4C2×C414yescomplemented
76C2×C22⋊Dic83—22no—
77C2×C22⋊Dic83—22no—
78C2×C22⋊Dic83—22no—
79C2×C22⋊Dic83—22no—
80C2×C22⋊Dic83—22no—
81C2×C22⋊Dic83C2×C414yes—
82C2×C4×Dic83—232no—
83C2×C4×Dic83—24no—
84C2×C4×Dic83—24no—
85C2×C4×Dic83—24no—
86C2×C4×Dic83—24no—
87C2×C4×Dic83—24no—
88C2×C4×Dic83D418yes—
89C83⋊#95—24no—
90C83⋊#95—24no—
91C83⋊#95—24no—
92C83⋊#95—24no—
93C83⋊#95—24no—
94C83⋊#95—24no—
95C83⋊#95—24no—
96C25×C83C2311yescharacteristic
97C23×C4×C83—22no—
98C23×C4×C83—22no—
99C23×C4×C83—24no—
100C23×C4×C83—24no—
101C23×C4×C83Q814yescomplemented
102C23×C4×C83C2312yes—
103C23×C4×C83C2311yescharacteristic
104C23×C4×C83C2311yescharacteristic
105C23×C4×C83C2312yes—
106C2×C22⋊C4×C83—22no—
107C2×C22⋊C4×C83—22no—
108C2×C22⋊C4×C83—22no—
109C2×C22⋊C4×C83—22no—
110C2×C22⋊C4×C83—22no—
111C2×C22⋊C4×C83C2×C414yes—
112#95×C83—24no—
113#95×C83—24no—
114C2×Dic166—28no—
115C2×Dic166—216no—
116C2×Dic166—44no—
117C2×Dic166—48no—
118C2×Dic166—44no—
119C22×Dic83—216no—
120C22×Dic83—28no—
121C22×Dic83—28no—
122C22×Dic83—28no—
123C22×Dic83—22no—
124C22×Dic83—22no—
125C22×Dic83—22no—
126C22×Dic83—22no—
127C22×Dic83—22no—
128C22×Dic83—22no—
129C22×Dic83—216no—
130C22×Dic83—28no—
131C22×Dic83—216no—
132C22×Dic83—216no—
133C22×Dic83—28no—
134C22×Dic83—22no—
135C22×Dic83—21no—
136C22×Dic83—21no—
137C22×Dic83—21no—
138C22×Dic83—21no—
139C22×Dic83—22no—
140C22×Dic83—22no—
141C22×Dic83—22no—
142C22×Dic83—22no—
143C22×Dic83—22no—
144C22×Dic83—22no—
145C22×Dic83—22no—
146C22×Dic83—22no—
147C22×Dic83—22no—
148C22×Dic83—22no—
149C22×Dic83C22⋊C4116yes—
150C22×Dic83C22×C412yes—
151C22×Dic83C22×C412yes—
152C22×Dic83C22×C412yes—
153C22×Dic83C22×C412yes—
154C22×Dic83C2×D412yes—
155C22×Dic83C2×D412yes—
156C22×Dic83C2×D414yes—
157C22×Dic83C2×D412yes—
158C22×Dic83C2×D412yes—
159C22×Dic83C2×D414yes—
160C22×Dic83C2×Q814yes—
161C22×Dic83#4114yes—
162C22×Dic83#4114yes—
163C4⋊Dic83—28no—
164Dic83⋊C4—28no—
165Dic83⋊C4—28no—
166Dic83⋊C4—48no—
167C22⋊Dic83—28no—
168C22⋊Dic83—44no—
169C4×Dic83—216no—
170C4×Dic83—216no—
171C24×C83—22no—
172C24×C83—22no—
173C24×C83—22no—
174C24×C83—22no—
175C24×C83C22×C412yes—
176C24×C83C2×D412yes—
177C24×C83C2×D412yes—
178C24×C83C2×Q812yes—
179C24×C83C2×Q812yes—
180C24×C83#4112yes—
181C24×C83#4112yes—
182C24×C83C2411yescharacteristic
183C22×C4×C83—216no—
184C22×C4×C83—28no—
185C22×C4×C83—28no—
186C22×C4×C83—28no—
187C22×C4×C83—22no—
188C22×C4×C83—22no—
189C22×C4×C83—22no—
190C22×C4×C83—22no—
191C22×C4×C83—216no—
192C22×C4×C83—22no—
193C22×C4×C83—21no—
194C22×C4×C83—21no—
195C22×C4×C83—21no—
196C22×C4×C83—21no—
197C22×C4×C83—22no—
198C22×C4×C83—22no—
199C22×C4×C83—22no—
200C22×C4×C83—22no—
201C22×C4×C83—22no—
202C22×C4×C83—22no—
203C22×C4×C83—22no—
204C22×C4×C83—22no—
205C22×C4×C83—22no—
206C22×C4×C83—22no—
207C22×C4×C83C22×C412yes—
208C22×C4×C83C22×C412yes—
209C22×C4×C83C2×D414yes—
210C22×C4×C83C2×Q814yes—
211C22×C4×C83#4114yes—
212C22⋊C4×C83—28no—
213C22⋊C4×C83—44no—
214C23×C83—24no—
215C23×C83—24no—
216C23×C83—22no—
217C23×C83—24no—
218C23×C83—24no—
219C23×C83—24no—
220C23×C83—22no—
221C23×C83—22no—
222C23×C83—24no—
223C23×C83—22no—
224C23×C83—24no—
225C23×C83—24no—
226C23×C83—24no—
227C23×C83—24no—
228C23×C83—24no—
229C23×C83—24no—
230C23×C83C2×C22⋊C414yes—
231C23×C83C4×Q814yes—
232C23×C83C4×Q814yes—
233C23×C83C22⋊Q814yes—
234C23×C83C22⋊Q814yes—
235C23×C83#12414yes—
236C23×C83C4⋊Q814yes—
237C23×C83C23×C411yescharacteristic
238C23×C83C22×D411yescharacteristic
239C23×C83C22×D411yescharacteristic
240C23×C83C22×D412yes—
241C23×C83C22×Q811yescharacteristic
242C23×C83C22×Q811yescharacteristic
243C23×C83C2×#4112yes—
244C23×C83C2×#4112yes—
245C23×C83C2×#4111yescharacteristic
246C23×C83C2×#4112yes—
247C23×C83C2×#4111yescharacteristic
248C2×C4×C83—232no—
249C2×C4×C83—24no—
250C2×C4×C83—24no—
251C2×C4×C83—24no—
252C2×C4×C83—24no—
253C2×C4×C83—24no—
254C2×C4×C83—24no—
255C2×C4×C83—22no—
256C2×C4×C83—22no—
257C2×C4×C83—24no—
258C2×C4×C83—24no—
259C2×C4×C83—41no—
260C2×C4×C83—42no—
261C2×C4×C83—41no—
262C2×C4×C83—41no—
263C2×C4×C83—41no—
264C2×C4×C83—42no—
265C2×C4×C83—42no—
266C2×C4×C83—42no—
267C2×C4×C83—42no—
268C2×C4×C83—42no—
269C2×C4×C83—42no—
270C2×C4×C83—42no—
271C2×C4×C83—42no—
272C2×C4×C83C22⋊Q818yescomplemented
273C2×Dic83—232no—
274C2×Dic83—24no—
275C2×Dic83—24no—
276C2×Dic83—22no—
277C2×Dic83—24no—
278C2×Dic83—24no—
279C2×Dic83—24no—
280C2×Dic83—22no—
281C2×Dic83—24no—
282C2×Dic83—24no—
283C2×Dic83—24no—
284C2×Dic83—232no—
285C2×Dic83—22no—
286C2×Dic83—22no—
287C2×Dic83—24no—
288C2×Dic83—24no—
289C2×Dic83—41no—
290C2×Dic83—42no—
291C2×Dic83—41no—
292C2×Dic83—41no—
293C2×Dic83—41no—
294C2×Dic83—42no—
295C2×Dic83—42no—
296C2×Dic83—42no—
297C2×Dic83—42no—
298C2×Dic83—42no—
299C2×Dic83—42no—
300C2×Dic83—42no—
301C2×Dic83—42no—
302C2×Dic83C2×C22⋊C414yes—
303C2×Dic83C2×C22⋊C414yes—
304C2×Dic83C4×D418yes—
305C2×Dic83#12014yes—
306C2×Dic83#12118yes—
307C2×Dic83C22⋊Q818yescomplemented
308C2×Dic83#12314yes—
309Dic166—416no—
310C22×C83—24no—
311C22×C83—24no—
312C22×C83—28no—
313C22×C83—24no—
314C22×C83—24no—
315C22×C83—28no—
316C22×C83—24no—
317C22×C83—24no—
318C22×C83—28no—
319C22×C83—28no—
320C22×C83#39118yescomplemented
321C22×C83C22×C22⋊C411yescharacteristic
322C22×C83C2×C4×D412yes—
323C22×C83C2×C4×Q811yescharacteristic
324C22×C83C2×C4×Q811yescharacteristic
325C22×C83C4×#4112yes—
326C22×C83C2×#12011yescharacteristic
327C22×C83C2×#12112yes—
328C22×C83C2×C22⋊Q812yes—
329C22×C83C2×C22⋊Q811yescharacteristic
330C22×C83C2×C22⋊Q812yes—
331C22×C83C2×C22⋊Q811yescharacteristic
332C22×C83C2×#12311yescharacteristic
333C22×C83#52512yes—
334C22×C83#52511yescharacteristic
335C22×C83#52511yescharacteristic
336C22×C83#52512yes—
337C22×C83C2×#12411yescharacteristic
338C22×C83#52912yes—
339C22×C83#52912yes—
340C22×C83C2×C4⋊Q811yescharacteristic
341C22×C83#53212yes—
342C22×C83#53312yes—
343C22×C83#53312yes—
344C4×C83—28no—
345C4×C83—42no—
346C4×C83—42no—
347C4×C83—82no—
348Dic83—28no—
349Dic83—24no—
350Dic83—42no—
351Dic83—42no—
352Dic83—82no—
353Dic83#38618yes—
354#14702—831nomaximal, Sylow
355C2×C83—28no—
356C2×C83C2×#38611yescharacteristic
357C2×C83C2×#39111yescharacteristic
358C2×C83#229711yescharacteristic
359C2×C83C4×C22⋊Q812yes—
360C2×C83C4×C22⋊Q812yes—
361C2×C83#284811yescharacteristic
362C2×C83#284811yescharacteristic
363C2×C83#285012yes—
364C2×C83#285511yescharacteristic
365C2×C83#285511yescharacteristic
366C2×C83#285712yes—
367C22×C22⋊Q8—831no—
368C23×C42—831no—
369C2×#391—832no—
370C2×#380—831no—
371#1436—832no—
372#1436—832no—
373C4⋊#95—832no—
374C22⋊#95—831no—
375C22⋊#95—831no—
376C22⋊#95—831no—
377C22⋊#95D8311yescharacteristic
378C83#1470211yescharacteristic, complemented, Sylow
379C23×Q8—831no—
380C24×C4—831no—
381C24×C4—831no—
382C24×C4C2×D8311yescharacteristic
383C2×C22⋊Q8—838no—
384C2×C22⋊Q8—1664no—
385C2×C22⋊Q8—1664no—
386C22×C4⋊C4—831no—
387C22×C4⋊C4—831no—
388C22×C4⋊C4—831no—
389C22×C4⋊C4—832no—
390C22×C22⋊C4—831no—
391C22×C22⋊C4—831no—
392C22×C22⋊C4C2×D8311yescharacteristic
393C22×C22⋊C4C2×D8311yescharacteristic
394C22×C42—832no—
395C22×C42—832no—
396C22×C42—1668no—
397C22×C42—1664no—
398#391—1668no—
399#380—1664no—
400C2×#95—832no—
401C2×#95—832no—
402C2×#95—832no—
403C2×#95—832no—
404C2×#95—832no—
405C2×#95—832no—
406C2×#95—832no—
407C2×#95C2×D8312yes—
408C2×#95C2×D8312yes—
409C25C22×D8311yescharacteristic
410C22×Q8—834no—
411C22×Q8—1662no—
412C22×Q8—1662no—
413C22×Q8—1664no—
414C22×Q8—1664no—
415C23×C4—22no—
416C23×C4—22no—
417C23×C4—24no—
418C23×C4—24no—
419C23×C4—831no—
420C23×C4—834no—
421C23×C4—834no—
422C23×C4—834no—
423C23×C4—831no—
424C23×C4—832no—
425C23×C4—834no—
426C23×C4—831no—
427C23×C4—831no—
428C23×C4—832no—
429C23×C4—1664no—
430C23×C4—1664no—
431C23×C4—1664no—
432C23×C4—1664no—
433C23×C4—1662no—
434C23×C4—1662no—
435C23×C4Dic16614yescomplemented
436C23×C4C22×D8312yes—
437C23×C4C22×D8311yescharacteristic
438C23×C4C22×D8311yescharacteristic
439C23×C4C22×D8312yes—
440C22⋊Q8—16632no—
441C2×C4⋊C4—834no—
442C2×C4⋊C4—834no—
443C2×C4⋊C4—834no—
444C2×C4⋊C4—1664no—
445C2×C4⋊C4—1664no—
446C2×C4⋊C4—1664no—
447C2×C4⋊C4—1662no—
448C2×C4⋊C4—1662no—
449C2×C4⋊C4—1662no—
450C2×C4⋊C4—1662no—
451C2×C4⋊C4—1662no—
452C2×C4⋊C4—1662no—
453C2×C22⋊C4—22no—
454C2×C22⋊C4—22no—
455C2×C22⋊C4—22no—
456C2×C22⋊C4—22no—
457C2×C22⋊C4—22no—
458C2×C22⋊C4—834no—
459C2×C22⋊C4—1662no—
460C2×C22⋊C4—1662no—
461C2×C22⋊C4—1662no—
462C2×C22⋊C4—1662no—
463C2×C22⋊C4—1662no—
464C2×C22⋊C4C4×D8314yes—
465C2×C42—838no—
466C2×C42—1664no—
467C2×C42—1664no—
468C2×C42—1664no—
469C2×C42—1664no—
470C2×C42—16632no—
471C2×C42—1664no—
472#95—24no—
473#95—24no—
474#95—1664no—
475#95—1664no—
476#95—1664no—
477#95—1664no—
478#95—1664no—
479#95—1664no—
480#95—1664no—
481C24—22no—
482C24—22no—
483C24—22no—
484C24—22no—
485C24C2×C4×D8312yes—
486C24D4×D8312yes—
487C24D4×D8312yes—
488C24Q8×D8312yes—
489C24C2×Dic16612yes—
490C24#1305058912yes—
491C24#1305059012yes—
492C24C23×D8311yescharacteristic
493C2×Q8—3324no—
494C2×Q8—3328no—
495C2×Q8—3324no—
496C2×Q8—1668no—
497C2×Q8—16616no—
498C22×C4—28no—
499C22×C4—216no—
500C22×C4—28no—
501C22×C4—28no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—216no—
507C22×C4—22no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—832no—
523C22×C4—834no—
524C22×C4—832no—
525C22×C4—832no—
526C22×C4—834no—
527C22×C4—832no—
528C22×C4—834no—
529C22×C4—832no—
530C22×C4—832no—
531C22×C4—834no—
532C22×C4—834no—
533C22×C4—8316no—
534C22×C4—832no—
535C22×C4—832no—
536C22×C4—1662no—
537C22×C4—1662no—
538C22×C4—1662no—
539C22×C4—1662no—
540C22×C4—1662no—
541C22×C4—1662no—
542C22×C4—1662no—
543C22×C4—1662no—
544C22×C4—1661no—
545C22×C4—1661no—
546C22×C4—1661no—
547C22×C4—1661no—
548C22×C4—1662no—
549C22×C4—1662no—
550C22×C4—1662no—
551C22×C4—1668no—
552C22×C4—16616no—
553C22×C4—16616no—
554C22×C4—1668no—
555C22×C4—16616no—
556C22×C4—1668no—
557C22×C4—1668no—
558C22×C4—16616no—
559C22×C4—1668no—
560C22×C4—1662no—
561C22×C4—1662no—
562C22×C4—1662no—
563C22×C4—1662no—
564C22×C4—1662no—
565C22×C4—1662no—
566C22×C4C2×C4×D8312yes—
567C22×C4C2×C4×D8312yes—
568C22×C4D4×D8314yes—
569C22×C4C2×Dic16614yes—
570C22×C4#1305058914yes—
571C4⋊C4—3328no—
572C4⋊C4—1668no—
573C4⋊C4—1668no—
574C4⋊C4—1668no—
575C22⋊C4—28no—
576C22⋊C4—44no—
577C22⋊C4—3324no—
578C22⋊C4—1668no—
579C42—16616no—
580C42—16616no—
581C23—24no—
582C23—24no—
583C23—22no—
584C23—24no—
585C23—24no—
586C23—24no—
587C23—22no—
588C23—22no—
589C23—24no—
590C23—22no—
591C23—24no—
592C23—24no—
593C23—24no—
594C23—24no—
595C23—24no—
596C23—24no—
597C23C22⋊C4×D8314yes—
598C23#1458175714yes—
599C23C4×Dic16614yes—
600C23#1458176914yes—
601C23#1458177014yes—
602C23#1458177814yes—
603C23#1458179114yes—
604C23C22×C4×D8311yescharacteristic
605C23C2×D4×D8311yescharacteristic
606C23C2×D4×D8311yescharacteristic
607C23C2×D4×D8312yes—
608C23C2×Q8×D8311yescharacteristic
609C23C22×Dic16611yescharacteristic
610C23#41×D8312yes—
611C23#41×D8312yes—
612C23C2×#1305058911yescharacteristic
613C23C2×#1305058912yes—
614C23C2×#1305059011yescharacteristic
615Q8—33216no—
616C2×C4—232no—
617C2×C4—24no—
618C2×C4—24no—
619C2×C4—24no—
620C2×C4—24no—
621C2×C4—24no—
622C2×C4—24no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—24no—
626C2×C4—24no—
627C2×C4—41no—
628C2×C4—42no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—42no—
635C2×C4—42no—
636C2×C4—42no—
637C2×C4—42no—
638C2×C4—42no—
639C2×C4—42no—
640C2×C4—3321no—
641C2×C4—3322no—
642C2×C4—3321no—
643C2×C4—3321no—
644C2×C4—3321no—
645C2×C4—3322no—
646C2×C4—3322no—
647C2×C4—3322no—
648C2×C4—3322no—
649C2×C4—3322no—
650C2×C4—3322no—
651C2×C4—3322no—
652C2×C4—3322no—
653C2×C4—834no—
654C2×C4—838no—
655C2×C4—834no—
656C2×C4—838no—
657C2×C4—834no—
658C2×C4—834no—
659C2×C4—838no—
660C2×C4—1662no—
661C2×C4—1662no—
662C2×C4—1664no—
663C2×C4—1664no—
664C2×C4—16632no—
665C2×C4—16632no—
666C2×C4—1664no—
667C2×C4—1664no—
668C2×C4—1662no—
669C2×C4—1664no—
670C2×C4—1664no—
671C2×C4—1664no—
672C2×C4—1662no—
673C2×C4—1664no—
674C2×C4—1664no—
675C2×C4—1664no—
676C2×C4#1458176918yescomplemented
677C22—24no—
678C22—24no—
679C22—28no—
680C22—24no—
681C22—24no—
682C22—24no—
683C22—28no—
684C22—24no—
685C22—28no—
686C22—28no—
687C22#1912760518yescomplemented
688C22C2×C22⋊C4×D8311yescharacteristic
689C22C4×D4×D8312yes—
690C22C2×#1458175711yescharacteristic
691C22C2×C4×Dic16611yescharacteristic
692C22C4×#1305058912yes—
693C22#120×D8311yescharacteristic
694C22#121×D8312yes—
695C22C22⋊Q8×D8312yes—
696C22C2×#1458176911yescharacteristic
697C22C2×#1458176912yes—
698C22C2×#1458177011yescharacteristic
699C22#123×D8311yescharacteristic
700C22#1912820712yes—
701C22#1912820711yescharacteristic
702C22#1912820911yescharacteristic
703C22#1912821012yes—
704C22C2×#1458177811yescharacteristic
705C22#1912822812yes—
706C22#1912823112yes—
707C22C2×#1458179111yescharacteristic
708C22#1912824612yes—
709C22#1912825312yes—
710C22#1912825412yes—
711C4—28no—
712C4—42no—
713C4—42no—
714C4—82no—
715C4—3322no—
716C4—3322no—
717C4—838no—
718C4—6642no—
719C4—1668no—
720C4—1664no—
721C2—28no—
722C2#386×D8311yescharacteristic
723C2C2×#1912760511yescharacteristic
724C2#2490994811yescharacteristic
725C2C4×#1458176912yes—
726C2#2490999512yes—
727C2#2491574811yescharacteristic
728C2#2491574911yescharacteristic
729C2#2491576012yes—
730C2#2491579911yescharacteristic
731C2#2491580011yescharacteristic
732C2#2491581312yes—
subgroupG/H
center, FrattiniC24C23×D83
commutatorC23×C83C23×C4
FittingC83×C22⋊#95C2
socle, cosocleC24×C83C24
prime radicalC25×C83C23
hypercenterC22⋊#95D83
hypocenterC83#14702
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
3. C2×#19127605C2semidirect
5. #24905697C2semidirect
6. #24905694C2semidirect
7. Dic83⋊#95C2semidirect
17. C2×#14581769C4semidirect
46. C22×Dic166C2×C4semidirect
56. C23×Dic83Q8semidirect
66. C2×C4⋊Dic83C2×C4semidirect
74. C2×Dic83⋊C4C2×C4semidirect
75. C2×Dic83⋊C4C2×C4semidirect
101. C23×C4×C83Q8semidirect
272. C2×C4×C83C22⋊Q8semidirect
307. C2×Dic83C22⋊Q8semidirect
320. C22×C83#391semidirect
378. C83#14702semidirect
435. C23×C4Dic166semidirect
676. C2×C4#14581769semidirect
687. C22#19127605semidirect

Maximal subgroups

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

subgroupindex
C22×#145817692
C23×C4×Dic832
C2×#191276052
C2×#191275592
#249056972
#249056942
Dic83⋊#952
#249056862
#249056852
C83×C22⋊#952
#1470283