Finite Group Databasebeta

← #35327435

Subgroups — #35327435

Order 21248.

1282 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19127587C211yesmaximal, characteristic
2C2×#19127568C211yesmaximal, characteristic
3C2×C4⋊C4×Dic83C211yesmaximal, characteristic
4#24905724C211yesmaximal, characteristic
5#24905723C211yesmaximal, characteristic
6#24905722C211yesmaximal, characteristic
7#24905697C211yesmaximal, characteristic
8#24905695C211yesmaximal, characteristic
9#24905694C211yesmaximal, characteristic
10#24905694C211yesmaximal, characteristic
11#24905694C211yesmaximal, characteristic
12#24905687C211yesmaximal, characteristic
13#24905687C211yesmaximal, characteristic
14#95×Dic83C211yesmaximal, characteristic
15C83×#1441C211yesmaximal, characteristic
16C22×C4⋊Dic83C2211yescharacteristic
17C22×Dic83⋊C4C2211yescharacteristic
18C22×C4×Dic83C2211yescharacteristic
19C22×C4×Dic83C2211yescharacteristic
20C22×C4×Dic83C2211yescharacteristic
21C22×C4×Dic83C2211yescharacteristic
22C22×C4×Dic83C2211yescharacteristic
23#19127587C418yescomplemented
24#19127568—24no—
25C4⋊C4×Dic83—24no—
26C2×C83⋊#95C2211yescharacteristic
27C2×C83⋊#95C2211yescharacteristic
28C2×C83⋊#95C2211yescharacteristic
29C2×C83⋊#95C2211yescharacteristic
30C2×C83⋊#95C2211yescharacteristic
31C2×C83⋊#95C2211yescharacteristic
32C2×C83⋊#95C2211yescharacteristic
33C2×C83⋊#95C2211yescharacteristic
34C2×C83⋊#95C2211yescharacteristic
35C2×C83⋊#95C2211yescharacteristic
36C2×C83⋊#95C2211yescharacteristic
37C2×C83⋊#95C2211yescharacteristic
38C2×C83⋊#95C2211yescharacteristic
39C2×C83⋊#95C2211yescharacteristic
40C2×C83⋊#95C2211yescharacteristic
41C2×C83⋊#95C2211yescharacteristic
42C2×C83⋊#95C2211yescharacteristic
43C2×C83⋊#95C2211yescharacteristic
44C2×C83⋊#95C2211yescharacteristic
45C2×C83⋊#95C2211yescharacteristic
46C2×C83⋊#95C2211yescharacteristic
47C22×C4⋊C4×C83C2211yescharacteristic
48C22×C4⋊C4×C83C2211yescharacteristic
49C2×#95×C83C2211yescharacteristic
50C2×#95×C83C2211yescharacteristic
51C2×#95×C83C2211yescharacteristic
52C2×#95×C83C2211yescharacteristic
53C2×#95×C83C2211yescharacteristic
54C23×Dic83C2311yescharacteristic
55C23×Dic83C2311yescharacteristic
56C23×Dic83C2311yescharacteristic
57C23×Dic83C2311yescharacteristic
58C23×Dic83C2311yescharacteristic
59C23×Dic83C2311yescharacteristic
60C23×Dic83C2311yescharacteristic
61C23×Dic83C2311yescharacteristic
62C2×C4⋊Dic83—22no—
63C2×C4⋊Dic83—22no—
64C2×C4⋊Dic83C2×C414yes—
65C2×Dic83⋊C4—22no—
66C2×Dic83⋊C4—22no—
67C2×Dic83⋊C4—22no—
68C2×C4×Dic83—22no—
69C2×C4×Dic83—22no—
70C2×C4×Dic83—22no—
71C2×C4×Dic83—22no—
72C2×C4×Dic83—22no—
73C2×C4×Dic83—22no—
74C2×C4×Dic83—22no—
75C2×C4×Dic83—22no—
76C2×C4×Dic83—22no—
77C2×C4×Dic83—22no—
78C2×C4×Dic83—22no—
79C2×C4×Dic83—41no—
80C2×C4×Dic83—41no—
81C2×C4×Dic83—41no—
82C2×C4×Dic83C2×C414yes—
83C83⋊#95—22no—
84C83⋊#95—22no—
85C83⋊#95—22no—
86C83⋊#95—22no—
87C83⋊#95—22no—
88C83⋊#95—22no—
89C83⋊#95—22no—
90C83⋊#95—22no—
91C83⋊#95—22no—
92C83⋊#95—22no—
93C83⋊#95—22no—
94C83⋊#95—22no—
95C83⋊#95—22no—
96C83⋊#95—22no—
97C83⋊#95—22no—
98C83⋊#95—41no—
99C83⋊#95C2×C414yes—
100C83⋊#95C2×C414yes—
101C83⋊#95C2×C414yes—
102C83⋊#95C2×C414yes—
103C83⋊#95D414yes—
104C23×C4×C83C2311yescharacteristic
105C23×C4×C83C2311yescharacteristic
106C23×C4×C83C2311yescharacteristic
107C23×C4×C83C2311yescharacteristic
108C23×C4×C83C2311yescharacteristic
109C23×C4×C83C2311yescharacteristic
110C23×C4×C83C2311yescharacteristic
111C2×C4⋊C4×C83—22no—
112C2×C4⋊C4×C83—22no—
113C2×C4⋊C4×C83—22no—
114C2×C4⋊C4×C83—22no—
115C2×C4⋊C4×C83—22no—
116C2×C4⋊C4×C83C2×C414yes—
117#95×C83—22no—
118#95×C83—22no—
119#95×C83—22no—
120#95×C83—41no—
121#95×C83—41no—
122C22×Dic83—21no—
123C22×Dic83—21no—
124C22×Dic83—21no—
125C22×Dic83—21no—
126C22×Dic83—21no—
127C22×Dic83—21no—
128C22×Dic83—21no—
129C22×Dic83—21no—
130C22×Dic83—21no—
131C22×Dic83—21no—
132C22×Dic83—21no—
133C22×Dic83—21no—
134C22×Dic83—21no—
135C22×Dic83—21no—
136C22×Dic83—21no—
137C22×Dic83—21no—
138C22×Dic83—21no—
139C22×Dic83—21no—
140C22×Dic83—21no—
141C22×Dic83—21no—
142C22×Dic83—21no—
143C22×Dic83—21no—
144C22×Dic83—21no—
145C22×Dic83—21no—
146C22×Dic83—21no—
147C22×Dic83—21no—
148C22×Dic83—21no—
149C22×Dic83—21no—
150C22×Dic83—21no—
151C22×Dic83—21no—
152C22×Dic83—21no—
153C22×Dic83—21no—
154C22×Dic83—21no—
155C22×Dic83—21no—
156C22×Dic83—21no—
157C22×Dic83—21no—
158C22×Dic83—21no—
159C22×Dic83—21no—
160C22×Dic83—21no—
161C22×Dic83—21no—
162C22×Dic83—21no—
163C22×Dic83—21no—
164C22×Dic83—21no—
165C22×Dic83—21no—
166C22×Dic83—21no—
167C22×Dic83C22×C412yes—
168C22×Dic83C22×C412yes—
169C22×Dic83C22×C412yes—
170C22×Dic83C22×C412yes—
171C22×Dic83C2×D412yes—
172C22×Dic83C2×D412yes—
173C22×Dic83#4112yes—
174C22×Dic83#4112yes—
175C22×Dic83#4112yes—
176C22×Dic83#4112yes—
177C22×Dic83#4112yes—
178C4⋊Dic83—28no—
179Dic83⋊C4—44no—
180C4×Dic83—28no—
181C4×Dic83—28no—
182C4×Dic83—44no—
183C4×Dic83—44no—
184C4×Dic83—44no—
185C24×C83C2411yescharacteristic
186C22×C4×C83—21no—
187C22×C4×C83—21no—
188C22×C4×C83—21no—
189C22×C4×C83—21no—
190C22×C4×C83—21no—
191C22×C4×C83—21no—
192C22×C4×C83—21no—
193C22×C4×C83—21no—
194C22×C4×C83—21no—
195C22×C4×C83—21no—
196C22×C4×C83—21no—
197C22×C4×C83—21no—
198C22×C4×C83—21no—
199C22×C4×C83—21no—
200C22×C4×C83—21no—
201C22×C4×C83—21no—
202C22×C4×C83—21no—
203C22×C4×C83—21no—
204C22×C4×C83—21no—
205C22×C4×C83—21no—
206C22×C4×C83—21no—
207C22×C4×C83—21no—
208C22×C4×C83—21no—
209C22×C4×C83—21no—
210C22×C4×C83—21no—
211C22×C4×C83—21no—
212C22×C4×C83—21no—
213C22×C4×C83—21no—
214C22×C4×C83—21no—
215C22×C4×C83—21no—
216C22×C4×C83—21no—
217C22×C4×C83—21no—
218C22×C4×C83—21no—
219C22×C4×C83—21no—
220C22×C4×C83—21no—
221C22×C4×C83—21no—
222C22×C4×C83—21no—
223C22×C4×C83—21no—
224C22×C4×C83—21no—
225C22×C4×C83—21no—
226C22×C4×C83—21no—
227C22×C4×C83C22×C412yes—
228C22×C4×C83C22×C412yes—
229C22×C4×C83C22×C412yes—
230C22×C4×C83C2×D412yes—
231C22×C4×C83#4112yes—
232C22×C4×C83#4112yes—
233C22×C4×C83#4112yes—
234C22×C4×C83#4112yes—
235C4⋊C4×C83—28no—
236C4⋊C4×C83—28no—
237C23×C83C23×C411yescharacteristic
238C23×C83C22×D411yescharacteristic
239C23×C83C2×#4111yescharacteristic
240C23×C83C2×#4111yescharacteristic
241C23×C83C2×#4111yescharacteristic
242C23×C83C2×#4111yescharacteristic
243C23×C83C2×#4111yescharacteristic
244C23×C83C2×#4111yescharacteristic
245C23×C83C2×#4111yescharacteristic
246C23×C83C2×#4111yescharacteristic
247C23×C83C2×#4111yescharacteristic
248C23×C83H(5,𝔽2)11yescharacteristic
249C23×C832−1+411yescharacteristic
250C23×C832−1+411yescharacteristic
251C23×C832−1+411yescharacteristic
252C2×C4×C83—22no—
253C2×C4×C83—22no—
254C2×C4×C83—22no—
255C2×C4×C83—22no—
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—41no—
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—41no—
291C2×C4×C83—41no—
292C2×C4×C83—41no—
293C2×C4×C83—41no—
294C2×C4×C83—41no—
295C2×C4×C83—41no—
296C2×C4×C83—41no—
297C2×C4×C83—41no—
298C2×C4×C83—41no—
299C2×C4×C83—41no—
300C2×C4×C83#11714yes—
301C2×Dic83—22no—
302C2×Dic83—22no—
303C2×Dic83—22no—
304C2×Dic83—22no—
305C2×Dic83—22no—
306C2×Dic83—22no—
307C2×Dic83—22no—
308C2×Dic83—22no—
309C2×Dic83—22no—
310C2×Dic83—22no—
311C2×Dic83—22no—
312C2×Dic83—22no—
313C2×Dic83—22no—
314C2×Dic83—22no—
315C2×Dic83—22no—
316C2×Dic83—22no—
317C2×Dic83—22no—
318C2×Dic83—22no—
319C2×Dic83—22no—
320C2×Dic83—22no—
321C2×Dic83—22no—
322C2×Dic83—22no—
323C2×Dic83—22no—
324C2×Dic83—22no—
325C2×Dic83—22no—
326C2×Dic83—22no—
327C2×Dic83—22no—
328C2×Dic83—41no—
329C2×Dic83—41no—
330C2×Dic83—41no—
331C2×Dic83—41no—
332C2×Dic83—41no—
333C2×Dic83—41no—
334C2×Dic83—41no—
335C2×Dic83—41no—
336C2×Dic83—41no—
337C2×Dic83—41no—
338C2×Dic83—41no—
339C2×Dic83—41no—
340C2×Dic83—41no—
341C2×Dic83—41no—
342C2×Dic83—41no—
343C2×Dic83—41no—
344C2×Dic83—41no—
345C2×Dic83—41no—
346C2×Dic83—41no—
347C2×Dic83—41no—
348C2×Dic83—41no—
349C2×Dic83—41no—
350C2×Dic83—41no—
351C2×Dic83—41no—
352C2×Dic83—41no—
353C2×Dic83—41no—
354C2×Dic83—41no—
355C2×Dic83C4×D414yes—
356C2×Dic83#12614yes—
357C22×C83C2×#11711yescharacteristic
358C22×C83C2×C4×D411yescharacteristic
359C22×C83C4×#4111yescharacteristic
360C22×C83C4×#4111yescharacteristic
361C22×C83C4×#4111yescharacteristic
362C22×C83#51911yescharacteristic
363C22×C83#52011yescharacteristic
364C22×C83#52511yescharacteristic
365C22×C83#52511yescharacteristic
366C22×C83C2×#12611yescharacteristic
367C22×C83#52911yescharacteristic
368C22×C83#52911yescharacteristic
369C22×C83#52911yescharacteristic
370C22×C83#52911yescharacteristic
371C22×C83#52911yescharacteristic
372C22×C83#53911yescharacteristic
373C22×C83#53911yescharacteristic
374C22×C83#54111yescharacteristic
375C22×C83#54111yescharacteristic
376C22×C83#54611yescharacteristic
377C22×C83#54711yescharacteristic
378C22×C83#54711yescharacteristic
379C22×C83#54811yescharacteristic
380C22×C83#55111yescharacteristic
381C22×C83#55211yescharacteristic
382C22×C83#55211yescharacteristic
383C22×C83#55211yescharacteristic
384C22×C83#55211yescharacteristic
385C22×C83#55311yescharacteristic
386C22×C83#55311yescharacteristic
387C22×C83#55611yescharacteristic
388C22×C83#55611yescharacteristic
389C22×C83#55611yescharacteristic
390C22×C83#55611yescharacteristic
391C22×C83#55611yescharacteristic
392C4×C83—24no—
393C4×C83—42no—
394C4×C83—42no—
395C4×C83—42no—
396C4×C83—42no—
397C4×C83—42no—
398C4×C83—81no—
399Dic83—24no—
400Dic83—24no—
401Dic83—42no—
402Dic83—42no—
403Dic83—42no—
404Dic83—42no—
405Dic83—42no—
406Dic83—81no—
407#13989—831nomaximal, Sylow
408C2×C83#229011yescharacteristic
409C2×C83C4×#12611yescharacteristic
410C2×C83#233611yescharacteristic
411C2×C83#234711yescharacteristic
412C2×C83#235611yescharacteristic
413C2×C83#235911yescharacteristic
414C2×C83#236211yescharacteristic
415C2×C83#246611yescharacteristic
416C2×C83#246911yescharacteristic
417C2×C83#247811yescharacteristic
418C2×C83#248111yescharacteristic
419C2×C83#251411yescharacteristic
420C2×C83#252411yescharacteristic
421C2×C83#257311yescharacteristic
422C2×C83#257711yescharacteristic
423C2×#387—831no—
424C2×#383—831no—
425C2×C4×C4⋊C4—831no—
426#1443—831no—
427#1443—831no—
428#1442—831no—
429#1441D8311yescharacteristic
430#1436—831no—
431#1436—831no—
432#1436—831no—
433#1436—831no—
434#1436—831no—
435#1434—831no—
436#1434—831no—
437C4×#95—831no—
438C83#1398911yescharacteristic, complemented, Sylow
439C22×C4⋊C4—831no—
440C22×C4⋊C4—831no—
441C22×C4⋊C4C2×D8311yescharacteristic
442C22×C4⋊C4C2×D8311yescharacteristic
443C22×C42—831no—
444C22×C42—831no—
445C22×C42—831no—
446C22×C42—831no—
447C22×C42—831no—
448#387—838no—
449#383—1664no—
450C4×C4⋊C4—1664no—
451C2×#95—831no—
452C2×#95—831no—
453C2×#95—831no—
454C2×#95—831no—
455C2×#95—831no—
456C2×#95—831no—
457C2×#95—831no—
458C2×#95—831no—
459C2×#95—831no—
460C2×#95—831no—
461C2×#95—831no—
462C2×#95—831no—
463C2×#95—831no—
464C2×#95—831no—
465C2×#95—831no—
466C2×#95—831no—
467C2×#95—831no—
468C2×#95—831no—
469C2×#95—831no—
470C2×#95—831no—
471C2×#95—831no—
472C2×#95C2×D8311yescharacteristic
473C2×#95C2×D8311yescharacteristic
474C2×#95C2×D8311yescharacteristic
475C2×#95C2×D8311yescharacteristic
476C2×#95C2×D8311yescharacteristic
477C23×C4—831no—
478C23×C4—831no—
479C23×C4—831no—
480C23×C4—831no—
481C23×C4—831no—
482C23×C4—831no—
483C23×C4—831no—
484C23×C4—831no—
485C23×C4C22×D8311yescharacteristic
486C23×C4C22×D8311yescharacteristic
487C23×C4C22×D8311yescharacteristic
488C23×C4C22×D8311yescharacteristic
489C23×C4C22×D8311yescharacteristic
490C23×C4C22×D8311yescharacteristic
491C23×C4C22×D8311yescharacteristic
492C2×C4⋊C4—22no—
493C2×C4⋊C4—22no—
494C2×C4⋊C4—22no—
495C2×C4⋊C4—22no—
496C2×C4⋊C4—22no—
497C2×C4⋊C4—834no—
498C2×C4⋊C4—1662no—
499C2×C4⋊C4—1662no—
500C2×C4⋊C4—1662no—
501C2×C4⋊C4—1662no—
502C2×C4⋊C4—1662no—
503C2×C4⋊C4C4×D8314yes—
504C2×C42—3321no—
505C2×C42—3321no—
506C2×C42—3321no—
507C2×C42—834no—
508C2×C42—1662no—
509C2×C42—1662no—
510C2×C42—1662no—
511C2×C42—1662no—
512C2×C42—1662no—
513C2×C42—1662no—
514C2×C42—1662no—
515C2×C42—1662no—
516C2×C42—1662no—
517C2×C42—1662no—
518C2×C42—1662no—
519#95—22no—
520#95—22no—
521#95—22no—
522#95—41no—
523#95—41no—
524#95—3321no—
525#95—834no—
526#95—834no—
527#95—834no—
528#95—834no—
529#95—834no—
530#95—1662no—
531#95—1662no—
532#95—1662no—
533#95—1662no—
534#95—1662no—
535#95—1662no—
536#95—1662no—
537#95—1662no—
538#95—1662no—
539#95—1662no—
540#95—1662no—
541#95—1662no—
542#95—1662no—
543#95—1662no—
544#95—1662no—
545C24C23×D8311yescharacteristic
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—832no—
588C22×C4—832no—
589C22×C4—832no—
590C22×C4—832no—
591C22×C4—832no—
592C22×C4—832no—
593C22×C4—832no—
594C22×C4—832no—
595C22×C4—832no—
596C22×C4—832no—
597C22×C4—832no—
598C22×C4—1661no—
599C22×C4—1661no—
600C22×C4—1661no—
601C22×C4—1661no—
602C22×C4—1661no—
603C22×C4—1661no—
604C22×C4—1661no—
605C22×C4—1661no—
606C22×C4—1661no—
607C22×C4—1661no—
608C22×C4—1661no—
609C22×C4—1661no—
610C22×C4—1661no—
611C22×C4—1661no—
612C22×C4—1661no—
613C22×C4—1661no—
614C22×C4—1661no—
615C22×C4—1661no—
616C22×C4—1661no—
617C22×C4—1661no—
618C22×C4—1661no—
619C22×C4—1661no—
620C22×C4—1661no—
621C22×C4—1661no—
622C22×C4—1661no—
623C22×C4—1661no—
624C22×C4—1661no—
625C22×C4—1661no—
626C22×C4—1661no—
627C22×C4—1661no—
628C22×C4—1661no—
629C22×C4—1661no—
630C22×C4—1661no—
631C22×C4—1661no—
632C22×C4—1661no—
633C22×C4—1661no—
634C22×C4—1661no—
635C22×C4—1661no—
636C22×C4—1661no—
637C22×C4—1661no—
638C22×C4—1661no—
639C22×C4—1661no—
640C22×C4—1661no—
641C22×C4—1661no—
642C22×C4—1661no—
643C22×C4C2×C4×D8312yes—
644C22×C4C2×C4×D8312yes—
645C22×C4C2×C4×D8312yes—
646C22×C4D4×D8312yes—
647C22×C4#1305058912yes—
648C22×C4#1305058912yes—
649C22×C4#1305058912yes—
650C22×C4#1305059112yes—
651C4⋊C4—28no—
652C4⋊C4—28no—
653C4⋊C4—3324no—
654C4⋊C4—1668no—
655C42—3324no—
656C42—3324no—
657C42—3324no—
658C42—1668no—
659C42—1668no—
660C23C22×C4×D8311yescharacteristic
661C23C2×D4×D8311yescharacteristic
662C23#41×D8311yescharacteristic
663C23#41×D8311yescharacteristic
664C23#41×D8311yescharacteristic
665C23#41×D8311yescharacteristic
666C23#41×D8311yescharacteristic
667C23C2×#1305058911yescharacteristic
668C23C2×#1305058911yescharacteristic
669C23C2×#1305058911yescharacteristic
670C23C2×#1305059111yescharacteristic
671C23#1458183711yescharacteristic
672C23#1458183911yescharacteristic
673C23#1458184011yescharacteristic
674C23#1458184011yescharacteristic
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—3321no—
724C2×C4—3321no—
725C2×C4—3321no—
726C2×C4—3321no—
727C2×C4—3321no—
728C2×C4—3321no—
729C2×C4—3321no—
730C2×C4—3321no—
731C2×C4—3321no—
732C2×C4—3321no—
733C2×C4—3321no—
734C2×C4—3321no—
735C2×C4—3321no—
736C2×C4—3321no—
737C2×C4—3321no—
738C2×C4—3321no—
739C2×C4—3321no—
740C2×C4—3321no—
741C2×C4—3321no—
742C2×C4—3321no—
743C2×C4—3321no—
744C2×C4—3321no—
745C2×C4—3321no—
746C2×C4—3321no—
747C2×C4—3321no—
748C2×C4—3321no—
749C2×C4—3321no—
750C2×C4—834no—
751C2×C4—834no—
752C2×C4—1662no—
753C2×C4—1662no—
754C2×C4—1662no—
755C2×C4—1662no—
756C2×C4—1662no—
757C2×C4—1662no—
758C2×C4—1662no—
759C2×C4—1662no—
760C2×C4—1662no—
761C2×C4—1662no—
762C2×C4—1662no—
763C2×C4—1662no—
764C2×C4—1662no—
765C2×C4—1662no—
766C2×C4—1662no—
767C2×C4—1662no—
768C2×C4—1662no—
769C2×C4—1662no—
770C2×C4—1662no—
771C2×C4—1662no—
772C2×C4—1662no—
773C2×C4—1662no—
774C2×C4—1662no—
775C2×C4—1662no—
776C2×C4—1662no—
777C2×C4—1662no—
778C2×C4—1662no—
779C2×C4#1458174814yes—
780C22C2×#1458174811yescharacteristic
781C22C4×D4×D8311yescharacteristic
782C22C4×#1305058911yescharacteristic
783C22#1912816911yescharacteristic
784C22C4×#1305059111yescharacteristic
785C22#1912817711yescharacteristic
786C22#1912818211yescharacteristic
787C22#1912820711yescharacteristic
788C22#1912821111yescharacteristic
789C22#126×D8311yescharacteristic
790C22#1912822811yescharacteristic
791C22#1912822811yescharacteristic
792C22#1912823211yescharacteristic
793C22#1912823611yescharacteristic
794C22#1912823711yescharacteristic
795C22#1912829611yescharacteristic
796C22#1912829711yescharacteristic
797C22#1912831011yescharacteristic
798C22#1912831211yescharacteristic
799C22#1912834011yescharacteristic
800C22#1912834911yescharacteristic
801C22#1912835411yescharacteristic
802C22#1912836111yescharacteristic
803C22#1912837811yescharacteristic
804C22#1912838311yescharacteristic
805C22#1912838311yescharacteristic
806C22#1912838511yescharacteristic
807C22#1912839311yescharacteristic
808C22#1912839811yescharacteristic
809C22#1912839811yescharacteristic
810C22#1912841811yescharacteristic
811C22#1912842011yescharacteristic
812C22#1912842211yescharacteristic
813C22#1912842211yescharacteristic
814C22#1912842511yescharacteristic
815C4—24no—
816C4—42no—
817C4—42no—
818C4—42no—
819C4—42no—
820C4—42no—
821C4—81no—
822C4—3322no—
823C4—3322no—
824C4—3322no—
825C4—3322no—
826C4—3322no—
827C4—6641no—
828C4—1664no—
829C4—1664no—
830C2#2490990311yescharacteristic
831C2#2491001311yescharacteristic
832C2#2491026111yescharacteristic
833C2#2491035811yescharacteristic
834C2#2491042711yescharacteristic
835C2#2491045011yescharacteristic
836C2#2491048511yescharacteristic
837C2#2491149211yescharacteristic
838C2#2491153711yescharacteristic
839C2#2491168011yescharacteristic
840C2#2491172511yescharacteristic
841C2#2491206611yescharacteristic
842C2#2491219811yescharacteristic
843C2#2491271511yescharacteristic
844C2#2491278511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D83
commutatorC23×C83C23×C4
FittingC83×#1441C2
socle, prime radical, cosocleC24×C83C24
hypercenter#1441D83
hypocenterC83#13989
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ #1441

Complements

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

NH ≅ G/Ntype
23. #19127587C4semidirect
438. C83#13989semidirect

Maximal subgroups

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

subgroupindex
C2×#191275872
C2×#191275682
C2×C4⋊C4×Dic832
#249057242
#249057232
#249057222
#249056972
#249056952
#249056942
#249056872
#95×Dic832
C83×#14412
#1398983