Finite Group Databasebeta

← #35326344

Subgroups — #35326344

Order 21248.

1702 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19127567C211yesmaximal, characteristic, complemented
2C2×#19127561C211yesmaximal, characteristic
3C2×#19127561C211yesmaximal, characteristic
4C2×C4×C4⋊Dic83C211yesmaximal, characteristic, complemented
5#24905725C212yesmaximal, complemented
6#24905712C212yesmaximal
7#24905700C212yesmaximal
8#24905693C211yesmaximal, characteristic, complemented
9#24905693C211yesmaximal, characteristic, complemented
10#24905688C212yesmaximal, complemented
11C2×C4×C22⋊C4×C83C211yesmaximal, characteristic
12C22×C4⋊Dic83C2211yescharacteristic
13C22×C4⋊Dic83C2211yescharacteristic
14C22×C4⋊Dic83C2211yescharacteristic
15C22×C4⋊Dic83C2211yescharacteristic
16C22×C22⋊Dic83C2212yes—
17C22×C22⋊Dic83C2212yes—
18C22×C4×Dic83C2212yes—
19#19127567—24no—
20#19127561—24no—
21#19127561—24no—
22C4×C4⋊Dic83—24no—
23C2×C83⋊#95C2212yes—
24C2×C83⋊#95C2212yes—
25C2×C83⋊#95C2212yes—
26C2×C83⋊#95C2212yes—
27C2×C83⋊#95C2212yes—
28C2×C83⋊#95C2212yes—
29C2×C83⋊#95C2212yes—
30C2×C83⋊#95C2212yes—
31C2×C83⋊#95C2212yes—
32C24×C4×C83C2211yescharacteristic
33C22×C22⋊C4×C83C2211yescharacteristic
34C22×C22⋊C4×C83C2211yescharacteristic
35C22×C42×C83C2211yescharacteristic
36C22×C42×C83C2211yescharacteristic
37C4×C22⋊C4×C83C418yescomplemented
38C2×#95×C83C2211yescharacteristic
39C2×#95×C83C2211yescharacteristic
40C23×Dic83C2312yes—
41C23×Dic83C2312yes—
42C23×Dic83C2312yes—
43C23×Dic83C2312yes—
44C2×C4⋊Dic83—22no—
45C2×C4⋊Dic83—22no—
46C2×C4⋊Dic83—22no—
47C2×C4⋊Dic83—22no—
48C2×C4⋊Dic83—22no—
49C2×C4⋊Dic83—22no—
50C2×C4⋊Dic83—22no—
51C2×C4⋊Dic83—22no—
52C2×C4⋊Dic83—22no—
53C2×C4⋊Dic83—22no—
54C2×C4⋊Dic83D414yes—
55C2×C4⋊Dic83D414yes—
56C2×C22⋊Dic83—24no—
57C2×C22⋊Dic83—24no—
58C2×C22⋊Dic83—24no—
59C2×C22⋊Dic83—24no—
60C2×C22⋊Dic83—42no—
61C2×C22⋊Dic83—42no—
62C2×C4×Dic83—24no—
63C2×C4×Dic83—24no—
64C2×C4×Dic83—42no—
65C83⋊#95—24no—
66C83⋊#95—24no—
67C83⋊#95—24no—
68C83⋊#95—24no—
69C83⋊#95—24no—
70C83⋊#95—24no—
71C83⋊#95—42no—
72C83⋊#95—42no—
73C83⋊#95—42no—
74C25×C83C2311yescharacteristic
75C23×C4×C83—22no—
76C23×C4×C83—22no—
77C23×C4×C83—22no—
78C23×C4×C83—22no—
79C23×C4×C83—22no—
80C23×C4×C83—22no—
81C23×C4×C83C2×C414yes—
82C23×C4×C83C2311yescharacteristic
83C23×C4×C83C2311yescharacteristic
84C23×C4×C83C2311yescharacteristic
85C23×C4×C83C2311yescharacteristic
86C23×C4×C83C2311yescharacteristic
87C23×C4×C83C2311yescharacteristic
88C2×C22⋊C4×C83—22no—
89C2×C22⋊C4×C83—22no—
90C2×C22⋊C4×C83—22no—
91C2×C22⋊C4×C83—22no—
92C2×C22⋊C4×C83C2×C414yes—
93C2×C22⋊C4×C83C2×C414yes—
94C2×C42×C83—22no—
95C2×C42×C83—22no—
96C2×C42×C83—22no—
97C2×C42×C83—22no—
98C2×C42×C83C2×C414yes—
99C2×C42×C83C2×C414yes—
100#95×C83C2×C414yes—
101#95×C83C2×C414yes—
102C22×Dic83—22no—
103C22×Dic83—22no—
104C22×Dic83—22no—
105C22×Dic83—22no—
106C22×Dic83—22no—
107C22×Dic83—22no—
108C22×Dic83—22no—
109C22×Dic83—22no—
110C22×Dic83—22no—
111C22×Dic83—22no—
112C22×Dic83—22no—
113C22×Dic83—22no—
114C22×Dic83—22no—
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×Dic83C2×D414yes—
129C22×Dic83C2×D414yes—
130C4⋊Dic83—28no—
131C4⋊Dic83—28no—
132C4⋊Dic83—44no—
133C4⋊Dic83—44no—
134C22⋊Dic83—48no—
135C22⋊Dic83—48no—
136C4×Dic83—48no—
137C24×C83—21no—
138C24×C83—21no—
139C24×C83—21no—
140C24×C83—21no—
141C24×C83—21no—
142C24×C83—21no—
143C24×C83—21no—
144C24×C83—21no—
145C24×C83—21no—
146C24×C83—21no—
147C24×C83—21no—
148C24×C83—21no—
149C24×C83C22×C412yes—
150C24×C83#4112yes—
151C24×C83#4112yes—
152C24×C83C2411yescharacteristic
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—21no—
161C22×C4×C83—21no—
162C22×C4×C83—21no—
163C22×C4×C83—21no—
164C22×C4×C83—21no—
165C22×C4×C83—21no—
166C22×C4×C83—21no—
167C22×C4×C83—21no—
168C22×C4×C83—21no—
169C22×C4×C83—21no—
170C22×C4×C83—21no—
171C22×C4×C83—21no—
172C22×C4×C83—21no—
173C22×C4×C83—21no—
174C22×C4×C83—21no—
175C22×C4×C83—21no—
176C22×C4×C83—21no—
177C22×C4×C83—21no—
178C22×C4×C83—21no—
179C22×C4×C83—21no—
180C22×C4×C83—21no—
181C22×C4×C83—28no—
182C22×C4×C83—28no—
183C22×C4×C83—28no—
184C22×C4×C83—44no—
185C22×C4×C83—44no—
186C22×C4×C83—44no—
187C22×C4×C83—44no—
188C22×C4×C83C22×C412yes—
189C22×C4×C83C22×C412yes—
190C22×C4×C83C22×C412yes—
191C22×C4×C83C22×C412yes—
192C22×C4×C83C22×C412yes—
193C22×C4×C83C22×C412yes—
194C22×C4×C83C2×D412yes—
195C22×C4×C83C2×D412yes—
196C22×C4×C83#4112yes—
197C22×C4×C83#4112yes—
198C22×C4×C83#4112yes—
199C22×C4×C83#4112yes—
200C22×C4×C83#4112yes—
201C22×C4×C83#4112yes—
202C22⋊C4×C83—28no—
203C22⋊C4×C83—28no—
204C42×C83—28no—
205C42×C83—28no—
206C23×C83—22no—
207C23×C83—22no—
208C23×C83—22no—
209C23×C83—22no—
210C23×C83—22no—
211C23×C83—22no—
212C23×C83—22no—
213C23×C83—22no—
214C23×C83—22no—
215C23×C83—22no—
216C23×C83—22no—
217C23×C83—22no—
218C23×C83—22no—
219C23×C83—22no—
220C23×C83—22no—
221C23×C83—22no—
222C23×C83—22no—
223C23×C83—22no—
224C23×C83—41no—
225C23×C83—41no—
226C23×C83—41no—
227C23×C83—41no—
228C23×C83—41no—
229C23×C83—41no—
230C23×C83—41no—
231C23×C83—41no—
232C23×C83—41no—
233C23×C83—41no—
234C23×C83—41no—
235C23×C83—41no—
236C23×C83—41no—
237C23×C83—41no—
238C23×C83—41no—
239C23×C83—41no—
240C23×C83#11714yes—
241C23×C83C23×C411yescharacteristic
242C23×C83C22×D411yescharacteristic
243C23×C83C22×D411yescharacteristic
244C23×C83C2×#4111yescharacteristic
245C23×C83C2×#4111yescharacteristic
246C23×C83C2×#4111yescharacteristic
247C23×C83C2×#4111yescharacteristic
248C23×C83C2×#4111yescharacteristic
249C23×C83C2×#4111yescharacteristic
250C23×C83C2×#4111yescharacteristic
251C23×C83C2×#4111yescharacteristic
252C23×C83H(5,𝔽2)11yescharacteristic
253C23×C83H(5,𝔽2)11yescharacteristic
254C23×C832−1+411yescharacteristic
255C23×C832−1+411yescharacteristic
256C2×C4×C83—22no—
257C2×C4×C83—22no—
258C2×C4×C83—22no—
259C2×C4×C83—22no—
260C2×C4×C83—22no—
261C2×C4×C83—22no—
262C2×C4×C83—22no—
263C2×C4×C83—22no—
264C2×C4×C83—22no—
265C2×C4×C83—22no—
266C2×C4×C83—22no—
267C2×C4×C83—22no—
268C2×C4×C83—22no—
269C2×C4×C83—22no—
270C2×C4×C83—22no—
271C2×C4×C83—22no—
272C2×C4×C83—22no—
273C2×C4×C83—22no—
274C2×C4×C83—41no—
275C2×C4×C83—41no—
276C2×C4×C83—41no—
277C2×C4×C83—41no—
278C2×C4×C83—41no—
279C2×C4×C83—41no—
280C2×C4×C83—41no—
281C2×C4×C83—41no—
282C2×C4×C83—41no—
283C2×C4×C83—41no—
284C2×C4×C83—41no—
285C2×C4×C83—41no—
286C2×C4×C83—41no—
287C2×C4×C83—41no—
288C2×C4×C83—41no—
289C2×C4×C83—41no—
290C2×C4×C83—416no—
291C2×C4×C83#11714yes—
292C2×C4×C83#11714yes—
293C2×C4×C83C4×D414yes—
294C2×C4×C83C4×D414yes—
295C2×C4×C83#12114yes—
296C2×C4×C83#12314yes—
297C2×C4×C83#12414yes—
298C2×C4×C83#12614yes—
299C2×Dic83—24no—
300C2×Dic83—24no—
301C2×Dic83—24no—
302C2×Dic83—24no—
303C2×Dic83—24no—
304C2×Dic83—24no—
305C2×Dic83—42no—
306C2×Dic83—42no—
307C2×Dic83—42no—
308C2×Dic83—42no—
309C2×Dic83—42no—
310C2×Dic83—42no—
311C2×Dic83—42no—
312C2×Dic83—42no—
313C2×Dic83—42no—
314C2×Dic83—42no—
315C2×Dic83—42no—
316C2×Dic83—42no—
317C2×Dic83—42no—
318C2×Dic83—42no—
319C2×Dic83—42no—
320C2×Dic83—42no—
321C2×Dic83—42no—
322C2×Dic83—42no—
323C2×Dic83—42no—
324C2×Dic83—42no—
325C2×Dic83—42no—
326C2×Dic83—42no—
327C22×C83—24no—
328C22×C83—24no—
329C22×C83—24no—
330C22×C83—42no—
331C22×C83—42no—
332C22×C83—42no—
333C22×C83—42no—
334C22×C83—42no—
335C22×C83—42no—
336C22×C83—42no—
337C22×C83—42no—
338C22×C83—42no—
339C22×C83—42no—
340C22×C83—42no—
341C22×C83—42no—
342C22×C83C2×#11711yescharacteristic
343C22×C83C2×#11711yescharacteristic
344C22×C83C2×#11711yescharacteristic
345C22×C83C2×C4×D411yescharacteristic
346C22×C83C2×C4×D411yescharacteristic
347C22×C83#52011yescharacteristic
348C22×C83#52011yescharacteristic
349C22×C83C2×#12111yescharacteristic
350C22×C83C2×#12311yescharacteristic
351C22×C83C2×#12411yescharacteristic
352C22×C83C2×#12611yescharacteristic
353C22×C83#52911yescharacteristic
354C22×C83#52911yescharacteristic
355C22×C83#52911yescharacteristic
356C22×C83#52911yescharacteristic
357C22×C83#54011yescharacteristic
358C22×C83#54111yescharacteristic
359C22×C83#54211yescharacteristic
360C22×C83#54211yescharacteristic
361C22×C83#54611yescharacteristic
362C22×C83#54611yescharacteristic
363C22×C83#54611yescharacteristic
364C22×C83#54711yescharacteristic
365C22×C83#54811yescharacteristic
366C22×C83#54811yescharacteristic
367C22×C83#54811yescharacteristic
368C22×C83#55011yescharacteristic
369C22×C83#55211yescharacteristic
370C22×C83#55211yescharacteristic
371C22×C83#55211yescharacteristic
372C22×C83#55311yescharacteristic
373C22×C83#55311yescharacteristic
374C22×C83#55311yescharacteristic
375C22×C83#55511yescharacteristic
376C22×C83#55611yescharacteristic
377C4×C83—24no—
378C4×C83—42no—
379C4×C83—42no—
380C4×C83—42no—
381C4×C83—42no—
382C4×C83#38818yes—
383Dic83—44no—
384Dic83—44no—
385Dic83—82no—
386Dic83—82no—
387#13875—831nomaximal, Sylow
388C2×C83—44no—
389C2×C83#228311yescharacteristic
390C2×C83C2×#38811yescharacteristic
391C2×C83#231411yescharacteristic
392C2×C83#235211yescharacteristic
393C2×C83#235211yescharacteristic
394C2×C83#235211yescharacteristic
395C2×C83#235411yescharacteristic
396C2×C83#242011yescharacteristic
397C2×C83#242111yescharacteristic
398C2×C83#242611yescharacteristic
399C2×C83#242711yescharacteristic
400C2×C83#248911yescharacteristic
401C2×C83#249011yescharacteristic
402C2×C83#249411yescharacteristic
403C2×C83#249511yescharacteristic
404C2×#382—831no—
405C2×#380—831no—
406C2×#380—831no—
407C2×C4×C4⋊C4—831no—
408C2×C4×C22⋊C4D8311yescharacteristic
409#1443—832no—
410#1440—832no—
411#1437—832no—
412C4⋊#95—831no—
413C4⋊#95—831no—
414#1434—832no—
415C83#1387511yescharacteristic, complemented, Sylow
416C24×C4C2×D8311yescharacteristic
417C22×C4⋊C4—831no—
418C22×C4⋊C4—831no—
419C22×C4⋊C4—831no—
420C22×C4⋊C4—831no—
421C22×C22⋊C4—832no—
422C22×C22⋊C4—832no—
423C22×C22⋊C4C2×D8311yescharacteristic
424C22×C22⋊C4C2×D8311yescharacteristic
425C22×C42—832no—
426C22×C42C2×D8311yescharacteristic
427C22×C42C2×D8311yescharacteristic
428#382—1664no—
429#380—1664no—
430#380—1664no—
431C4×C4⋊C4—1664no—
432C4×C22⋊C4Dic8318yescomplemented
433C2×#95—832no—
434C2×#95—832no—
435C2×#95—832no—
436C2×#95—832no—
437C2×#95—832no—
438C2×#95—832no—
439C2×#95—832no—
440C2×#95—832no—
441C2×#95—832no—
442C2×#95C2×D8311yescharacteristic
443C2×#95C2×D8311yescharacteristic
444C25C22×D8311yescharacteristic
445C23×C4—22no—
446C23×C4—22no—
447C23×C4—22no—
448C23×C4—22no—
449C23×C4—22no—
450C23×C4—22no—
451C23×C4—832no—
452C23×C4—832no—
453C23×C4—832no—
454C23×C4—832no—
455C23×C4C2×Dic8314yes—
456C23×C4C22×D8311yescharacteristic
457C23×C4C22×D8311yescharacteristic
458C23×C4C22×D8311yescharacteristic
459C23×C4C22×D8311yescharacteristic
460C23×C4C22×D8311yescharacteristic
461C23×C4C22×D8311yescharacteristic
462C2×C4⋊C4—834no—
463C2×C4⋊C4—834no—
464C2×C4⋊C4—1662no—
465C2×C4⋊C4—1662no—
466C2×C4⋊C4—1662no—
467C2×C4⋊C4—1662no—
468C2×C4⋊C4—1662no—
469C2×C4⋊C4—1662no—
470C2×C4⋊C4—1662no—
471C2×C4⋊C4—1662no—
472C2×C4⋊C4—1662no—
473C2×C4⋊C4—1662no—
474C2×C22⋊C4—22no—
475C2×C22⋊C4—22no—
476C2×C22⋊C4—22no—
477C2×C22⋊C4—22no—
478C2×C22⋊C4—3322no—
479C2×C22⋊C4—3322no—
480C2×C22⋊C4—1664no—
481C2×C22⋊C4—1664no—
482C2×C22⋊C4—1664no—
483C2×C22⋊C4—1664no—
484C2×C22⋊C4C2×Dic8314yes—
485C2×C22⋊C4C2×Dic8314yes—
486C2×C42—22no—
487C2×C42—22no—
488C2×C42—22no—
489C2×C42—22no—
490C2×C42—3322no—
491C2×C42—1664no—
492C2×C42—1664no—
493C2×C42C2×Dic8314yes—
494C2×C42C2×Dic8314yes—
495#95—3322no—
496#95—3322no—
497#95—3322no—
498#95—1664no—
499#95—1664no—
500#95—1664no—
501#95—1664no—
502#95—1664no—
503#95—1664no—
504#95C2×Dic8314yes—
505#95C2×Dic8314yes—
506C24—21no—
507C24—21no—
508C24—21no—
509C24—21no—
510C24—21no—
511C24—21no—
512C24—21no—
513C24—21no—
514C24—21no—
515C24—21no—
516C24—21no—
517C24—21no—
518C24C22×Dic8312yes—
519C24#1305059012yes—
520C24#1305059012yes—
521C24C23×D8311yescharacteristic
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—28no—
551C22×C4—28no—
552C22×C4—28no—
553C22×C4—44no—
554C22×C4—44no—
555C22×C4—44no—
556C22×C4—44no—
557C22×C4—834no—
558C22×C4—834no—
559C22×C4—1662no—
560C22×C4—1662no—
561C22×C4—1662no—
562C22×C4—1662no—
563C22×C4—1662no—
564C22×C4—1662no—
565C22×C4—1662no—
566C22×C4—1662no—
567C22×C4—1662no—
568C22×C4—1662no—
569C22×C4—1662no—
570C22×C4—1662no—
571C22×C4—1662no—
572C22×C4—1662no—
573C22×C4—1662no—
574C22×C4—1662no—
575C22×C4—1662no—
576C22×C4—1662no—
577C22×C4—1662no—
578C22×C4—1662no—
579C22×C4—1662no—
580C22×C4—1662no—
581C22×C4—1662no—
582C22×C4—1662no—
583C22×C4—1662no—
584C22×C4—1662no—
585C22×C4C22×Dic8312yes—
586C22×C4C22×Dic8312yes—
587C22×C4C22×Dic8312yes—
588C22×C4C22×Dic8312yes—
589C22×C4C22×Dic8312yes—
590C22×C4C22×Dic8312yes—
591C22×C4D4×D8312yes—
592C22×C4D4×D8312yes—
593C22×C4#1305058912yes—
594C22×C4#1305058912yes—
595C22×C4#1305059012yes—
596C22×C4#1305059012yes—
597C22×C4#1305059012yes—
598C22×C4#1305059012yes—
599C4⋊C4—3324no—
600C4⋊C4—3324no—
601C4⋊C4—1668no—
602C4⋊C4—1668no—
603C22⋊C4—28no—
604C22⋊C4—28no—
605C22⋊C4—3328no—
606C22⋊C4—3328no—
607C42—28no—
608C42—28no—
609C42—3328no—
610C23—22no—
611C23—22no—
612C23—22no—
613C23—22no—
614C23—22no—
615C23—22no—
616C23—22no—
617C23—22no—
618C23—22no—
619C23—22no—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23#1458175114yes—
645C23C23×Dic8311yescharacteristic
646C23C2×D4×D8311yescharacteristic
647C23C2×D4×D8311yescharacteristic
648C23C2×#1305058911yescharacteristic
649C23C2×#1305058911yescharacteristic
650C23C2×#1305059011yescharacteristic
651C23C2×#1305059011yescharacteristic
652C23C2×#1305059011yescharacteristic
653C23C2×#1305059011yescharacteristic
654C23C2×#1305059011yescharacteristic
655C23C2×#1305059011yescharacteristic
656C23#1458183811yescharacteristic
657C23#1458183811yescharacteristic
658C23#1458183911yescharacteristic
659C23#1458183911yescharacteristic
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—416no—
695C2×C4—3322no—
696C2×C4—3322no—
697C2×C4—3322no—
698C2×C4—3322no—
699C2×C4—3322no—
700C2×C4—3322no—
701C2×C4—3322no—
702C2×C4—3322no—
703C2×C4—3322no—
704C2×C4—3322no—
705C2×C4—3322no—
706C2×C4—3322no—
707C2×C4—3322no—
708C2×C4—3322no—
709C2×C4—3322no—
710C2×C4—3322no—
711C2×C4—3322no—
712C2×C4—3322no—
713C2×C4—3322no—
714C2×C4—3322no—
715C2×C4—3322no—
716C2×C4—3322no—
717C2×C4—1664no—
718C2×C4—1664no—
719C2×C4—1664no—
720C2×C4—1664no—
721C2×C4—1664no—
722C2×C4—1664no—
723C2×C4#1458175114yes—
724C2×C4#1458175114yes—
725C2×C4D4×Dic8314yes—
726C2×C4D4×Dic8314yes—
727C2×C4#1458176514yes—
728C2×C4#1458177414yes—
729C2×C4#1458177814yes—
730C2×C4#1458178514yes—
731C22—24no—
732C22—24no—
733C22—24no—
734C22—42no—
735C22—42no—
736C22—42no—
737C22—42no—
738C22—42no—
739C22—42no—
740C22—42no—
741C22—42no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22C2×#1458175111yescharacteristic
747C22C2×#1458175111yescharacteristic
748C22C2×#1458175111yescharacteristic
749C22C2×D4×Dic8311yescharacteristic
750C22C2×D4×Dic8311yescharacteristic
751C22#1912818411yescharacteristic
752C22#1912818411yescharacteristic
753C22C2×#1458176511yescharacteristic
754C22C2×#1458177411yescharacteristic
755C22C2×#1458177811yescharacteristic
756C22C2×#1458178511yescharacteristic
757C22#1912823511yescharacteristic
758C22#1912823511yescharacteristic
759C22#1912823511yescharacteristic
760C22#1912823511yescharacteristic
761C22#1912830611yescharacteristic
762C22#1912831311yescharacteristic
763C22#1912832211yescharacteristic
764C22#1912832211yescharacteristic
765C22#1912834711yescharacteristic
766C22#1912834711yescharacteristic
767C22#1912834711yescharacteristic
768C22#1912835611yescharacteristic
769C22#1912836011yescharacteristic
770C22#1912836011yescharacteristic
771C22#1912836011yescharacteristic
772C22#1912837211yescharacteristic
773C22#1912839111yescharacteristic
774C22#1912839111yescharacteristic
775C22#1912839111yescharacteristic
776C22#1912839711yescharacteristic
777C22#1912839711yescharacteristic
778C22#1912839711yescharacteristic
779C22#1912841611yescharacteristic
780C22#1912842111yescharacteristic
781C4—24no—
782C4—42no—
783C4—42no—
784C4—42no—
785C4—42no—
786C4—3324no—
787C4—3324no—
788C4—6642no—
789C4—6642no—
790C4#1912759418yes—
791C2—44no—
792C2#2490986111yescharacteristic
793C2C2×#1912759411yescharacteristic
794C2#2491007211yescharacteristic
795C2#2491039211yescharacteristic
796C2#2491039211yescharacteristic
797C2#2491039211yescharacteristic
798C2#2491041211yescharacteristic
799C2#2491095511yescharacteristic
800C2#2491096611yescharacteristic
801C2#2491102911yescharacteristic
802C2#2491104011yescharacteristic
803C2#2491180411yescharacteristic
804C2#2491181511yescharacteristic
805C2#2491186311yescharacteristic
806C2#2491187411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D83
commutatorC23×C83C23×C4
FittingC2×C4×C22⋊C4×C83C2
socle, cosocleC24×C83C24
prime radicalC25×C83C23
hypercenterC2×C4×C22⋊C4D83
hypocenterC83#13875
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#19127567C2semidirect
4. C2×C4×C4⋊Dic83C2semidirect
5. #24905725C2semidirect
8. #24905693C2semidirect
9. #24905693C2semidirect
10. #24905688C2semidirect
37. C4×C22⋊C4×C83C4semidirect
415. C83#13875semidirect
432. C4×C22⋊C4Dic83semidirect

Maximal subgroups

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

subgroupindex
C2×#191275672
C2×#191275612
C2×C4×C4⋊Dic832
#249057252
#249057122
#249057002
#249056932
#249056882
C2×C4×C22⋊C4×C832
#1387583