Finite Group Databasebeta

← #35328527

Subgroups — #35328527

Order 21248.

1478 conjugacy classes of subgroups.

The subgroup lattice has 984 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19127589C211yesmaximal, characteristic
2C2×#19127547C211yesmaximal, characteristic, complemented
3#24905722C211yesmaximal, characteristic, complemented
4#24905713C211yesmaximal, characteristic, complemented
5#24905710C211yesmaximal, characteristic
6#24905706C211yesmaximal, characteristic
7#24905700C211yesmaximal, characteristic
8#24905700C211yesmaximal, characteristic
9#24905700C211yesmaximal, characteristic
10#24905694C211yesmaximal, characteristic, complemented
11Dic83⋊#95C211yesmaximal, characteristic, complemented
12#24905689C211yesmaximal, characteristic, complemented
13#24905687C211yesmaximal, characteristic, complemented
14C4×C83⋊#95C211yesmaximal, characteristic, complemented
15C2×#388×C83C211yesmaximal, characteristic
16C22×Dic83⋊C4C2211yescharacteristic
17C22×Dic83⋊C4C2211yescharacteristic
18C22×C22⋊Dic83C2211yescharacteristic
19C22×C22⋊Dic83C2211yescharacteristic
20C22×C22⋊Dic83C2211yescharacteristic
21C22×C22⋊Dic83C2211yescharacteristic
22C22×C4×Dic83C2211yescharacteristic
23C22×C4×Dic83C2211yescharacteristic
24C22×C4×Dic83C2211yescharacteristic
25C22×C4×Dic83C2211yescharacteristic
26#19127589C418yescomplemented
27#19127547—24no—
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
46C22×C4⋊C4×C83C2211yescharacteristic
47C22×C22⋊C4×C83C2211yescharacteristic
48C22×C22⋊C4×C83C2211yescharacteristic
49C22×C22⋊C4×C83C2211yescharacteristic
50C22×C42×C83C2211yescharacteristic
51#388×C83—24no—
52C2×#95×C83C2211yescharacteristic
53C2×#95×C83C2211yescharacteristic
54C23×Dic83C2311yescharacteristic
55C23×Dic83C2311yescharacteristic
56C23×Dic83C2311yescharacteristic
57C23×Dic83C2311yescharacteristic
58C23×Dic83C2311yescharacteristic
59C23×Dic83C2311yescharacteristic
60C23×Dic83C2311yescharacteristic
61C23×Dic83C2311yescharacteristic
62C2×Dic83⋊C4—22no—
63C2×Dic83⋊C4—22no—
64C2×Dic83⋊C4—41no—
65C2×Dic83⋊C4—41no—
66C2×Dic83⋊C4—41no—
67C2×Dic83⋊C4C2×C414yes—
68C2×C22⋊Dic83—22no—
69C2×C22⋊Dic83—22no—
70C2×C22⋊Dic83—22no—
71C2×C22⋊Dic83—22no—
72C2×C22⋊Dic83—22no—
73C2×C22⋊Dic83—22no—
74C2×C22⋊Dic83—41no—
75C2×C22⋊Dic83—41no—
76C2×C22⋊Dic83—41no—
77C2×C22⋊Dic83—41no—
78C2×C22⋊Dic83C2×C414yes—
79C2×C22⋊Dic83C2×C414yes—
80C2×C4×Dic83—22no—
81C2×C4×Dic83—22no—
82C2×C4×Dic83—22no—
83C2×C4×Dic83—22no—
84C2×C4×Dic83—22no—
85C2×C4×Dic83—22no—
86C2×C4×Dic83—22no—
87C2×C4×Dic83—22no—
88C2×C4×Dic83—22no—
89C2×C4×Dic83—41no—
90C2×C4×Dic83—41no—
91C2×C4×Dic83C2×C414yes—
92C83⋊#95—22no—
93C83⋊#95—22no—
94C83⋊#95—22no—
95C83⋊#95—22no—
96C83⋊#95—22no—
97C83⋊#95—22no—
98C83⋊#95—22no—
99C83⋊#95—22no—
100C83⋊#95—22no—
101C83⋊#95—22no—
102C83⋊#95—22no—
103C83⋊#95—41no—
104C83⋊#95—41no—
105C83⋊#95—41no—
106C83⋊#95—41no—
107C83⋊#95—41no—
108C83⋊#95C2×C414yes—
109C83⋊#95C2×C414yes—
110C25×C83C2311yescharacteristic
111C23×C4×C83C2311yescharacteristic
112C23×C4×C83C2311yescharacteristic
113C23×C4×C83C2311yescharacteristic
114C23×C4×C83C2311yescharacteristic
115C23×C4×C83C2311yescharacteristic
116C23×C4×C83C2311yescharacteristic
117C2×C4⋊C4×C83—22no—
118C2×C4⋊C4×C83—41no—
119C2×C4⋊C4×C83—41no—
120C2×C22⋊C4×C83—22no—
121C2×C22⋊C4×C83—22no—
122C2×C22⋊C4×C83—22no—
123C2×C22⋊C4×C83—22no—
124C2×C22⋊C4×C83—22no—
125C2×C22⋊C4×C83—22no—
126C2×C22⋊C4×C83—41no—
127C2×C22⋊C4×C83—41no—
128C2×C22⋊C4×C83C2×C414yes—
129C2×C42×C83—22no—
130C2×C42×C83—22no—
131C2×C42×C83D414yes—
132#95×C83—22no—
133#95×C83—22no—
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×Dic83—21no—
168C22×Dic83—21no—
169C22×Dic83—21no—
170C22×Dic83—21no—
171C22×Dic83—21no—
172C22×Dic83—21no—
173C22×Dic83—21no—
174C22×Dic83—21no—
175C22×Dic83—21no—
176C22×Dic83—21no—
177C22×Dic83—21no—
178C22×Dic83—21no—
179C22×Dic83—21no—
180C22×Dic83C22×C412yes—
181C22×Dic83C22×C412yes—
182C22×Dic83C22×C412yes—
183C22×Dic83C22×C412yes—
184C22×Dic83#4112yes—
185C22×Dic83#4112yes—
186C22×Dic83#4112yes—
187C22×Dic83#4112yes—
188C22×Dic83#4112yes—
189C22×Dic83#4112yes—
190Dic83⋊C4—44no—
191Dic83⋊C4—44no—
192C22⋊Dic83—28no—
193C22⋊Dic83—44no—
194C22⋊Dic83—44no—
195C22⋊Dic83—44no—
196C4×Dic83—28no—
197C4×Dic83—28no—
198C4×Dic83—44no—
199C4×Dic83—44no—
200C24×C83—21no—
201C24×C83—21no—
202C24×C83—21no—
203C24×C83—21no—
204C24×C83—21no—
205C24×C83—21no—
206C24×C83—21no—
207C24×C83—21no—
208C24×C83—21no—
209C24×C83—21no—
210C24×C83—21no—
211C24×C83—21no—
212C24×C83—21no—
213C24×C83—21no—
214C24×C83C22×C412yes—
215C24×C83C2411yescharacteristic
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×C83—21no—
228C22×C4×C83—21no—
229C22×C4×C83—21no—
230C22×C4×C83—21no—
231C22×C4×C83—21no—
232C22×C4×C83—21no—
233C22×C4×C83—21no—
234C22×C4×C83—21no—
235C22×C4×C83—21no—
236C22×C4×C83—21no—
237C22×C4×C83—21no—
238C22×C4×C83—21no—
239C22×C4×C83—21no—
240C22×C4×C83—21no—
241C22×C4×C83—21no—
242C22×C4×C83—21no—
243C22×C4×C83—21no—
244C22×C4×C83—21no—
245C22×C4×C83—21no—
246C22×C4×C83—21no—
247C22×C4×C83—21no—
248C22×C4×C83—21no—
249C22×C4×C83—21no—
250C22×C4×C83C22×C412yes—
251C22×C4×C83C22×C412yes—
252C22×C4×C83C2×D412yes—
253C22×C4×C83C2×D412yes—
254C22×C4×C83C2×D412yes—
255C22×C4×C83#4112yes—
256C22×C4×C83#4112yes—
257C22×C4×C83#4112yes—
258C4⋊C4×C83—44no—
259C22⋊C4×C83—28no—
260C22⋊C4×C83—44no—
261C22⋊C4×C83—44no—
262C42×C83—28no—
263C23×C83—22no—
264C23×C83—22no—
265C23×C83—22no—
266C23×C83—22no—
267C23×C83—22no—
268C23×C83—22no—
269C23×C83—22no—
270C23×C83—41no—
271C23×C83—41no—
272C23×C83—41no—
273C23×C83—41no—
274C23×C83—41no—
275C23×C83—41no—
276C23×C83—41no—
277C23×C83—41no—
278C23×C83—41no—
279C23×C83—41no—
280C23×C83—41no—
281C23×C83—41no—
282C23×C83—41no—
283C23×C83—41no—
284C23×C83—41no—
285C23×C83—41no—
286C23×C83—41no—
287C23×C83—41no—
288C23×C83—41no—
289C23×C83—41no—
290C23×C83—41no—
291C23×C83—41no—
292C23×C83—41no—
293C23×C83—41no—
294C23×C83—41no—
295C23×C83—41no—
296C23×C83—41no—
297C23×C83—41no—
298C23×C83C23×C411yescharacteristic
299C23×C83C22×D411yescharacteristic
300C23×C83C2×#4111yescharacteristic
301C23×C83C2×#4111yescharacteristic
302C23×C83C2×#4111yescharacteristic
303C23×C83C2×#4111yescharacteristic
304C23×C83C2×#4111yescharacteristic
305C23×C83C2×#4111yescharacteristic
306C23×C83C2×#4111yescharacteristic
307C23×C83C2×#4111yescharacteristic
308C23×C83C2×#4111yescharacteristic
309C23×C83H(5,𝔽2)11yescharacteristic
310C23×C83H(5,𝔽2)11yescharacteristic
311C23×C83H(5,𝔽2)11yescharacteristic
312C23×C832−1+411yescharacteristic
313C2×C4×C83—22no—
314C2×C4×C83—22no—
315C2×C4×C83—22no—
316C2×C4×C83—22no—
317C2×C4×C83—22no—
318C2×C4×C83—22no—
319C2×C4×C83—22no—
320C2×C4×C83—22no—
321C2×C4×C83—22no—
322C2×C4×C83—22no—
323C2×C4×C83—22no—
324C2×C4×C83—22no—
325C2×C4×C83—22no—
326C2×C4×C83—22no—
327C2×C4×C83—22no—
328C2×C4×C83—22no—
329C2×C4×C83—22no—
330C2×C4×C83—22no—
331C2×C4×C83—41no—
332C2×C4×C83—41no—
333C2×C4×C83—41no—
334C2×C4×C83—41no—
335C2×C4×C83—41no—
336C2×C4×C83—41no—
337C2×C4×C83—41no—
338C2×C4×C83—41no—
339C2×C4×C83—41no—
340C2×C4×C83—41no—
341C2×C4×C83—41no—
342C2×C4×C83—41no—
343C2×C4×C83—41no—
344C2×C4×C83—41no—
345C2×C4×C83—41no—
346C2×C4×C83—41no—
347C2×C4×C83—41no—
348C2×C4×C83—41no—
349C2×C4×C83—41no—
350C2×C4×C83—41no—
351C2×C4×C83—41no—
352C2×C4×C83—41no—
353C2×C4×C83C4×D414yes—
354C2×C4×C83#12314yes—
355C2×Dic83—22no—
356C2×Dic83—22no—
357C2×Dic83—22no—
358C2×Dic83—22no—
359C2×Dic83—22no—
360C2×Dic83—22no—
361C2×Dic83—22no—
362C2×Dic83—22no—
363C2×Dic83—22no—
364C2×Dic83—22no—
365C2×Dic83—22no—
366C2×Dic83—22no—
367C2×Dic83—22no—
368C2×Dic83—22no—
369C2×Dic83—22no—
370C2×Dic83—22no—
371C2×Dic83—22no—
372C2×Dic83—22no—
373C2×Dic83—22no—
374C2×Dic83—22no—
375C2×Dic83—22no—
376C2×Dic83—22no—
377C2×Dic83—22no—
378C2×Dic83—22no—
379C2×Dic83—22no—
380C2×Dic83—22no—
381C2×Dic83—22no—
382C2×Dic83—41no—
383C2×Dic83—41no—
384C2×Dic83—41no—
385C2×Dic83—41no—
386C2×Dic83—41no—
387C2×Dic83—41no—
388C2×Dic83—41no—
389C2×Dic83—41no—
390C2×Dic83—41no—
391C2×Dic83—41no—
392C2×Dic83—41no—
393C2×Dic83—41no—
394C2×Dic83—41no—
395C2×Dic83—41no—
396C2×Dic83—41no—
397C2×Dic83—41no—
398C2×Dic83—41no—
399C2×Dic83—41no—
400C2×Dic83—41no—
401C2×Dic83—41no—
402C2×Dic83—41no—
403C2×Dic83—41no—
404C2×Dic83—41no—
405C2×Dic83—41no—
406C2×Dic83—41no—
407C2×Dic83—41no—
408C2×Dic83—41no—
409C2×Dic83—41no—
410C2×Dic83#11714yes—
411C22×C83—42no—
412C22×C83—42no—
413C22×C83—42no—
414C22×C83—42no—
415C22×C83—42no—
416C22×C83—42no—
417C22×C83—42no—
418C22×C83—81no—
419C22×C83—81no—
420C22×C83—81no—
421C22×C83—81no—
422C22×C83—81no—
423C22×C83—81no—
424C22×C83—81no—
425C22×C83—81no—
426C22×C83C2×#11711yescharacteristic
427C22×C83C2×C4×D411yescharacteristic
428C22×C83C4×#4111yescharacteristic
429C22×C83C4×#4111yescharacteristic
430C22×C83C4×#4111yescharacteristic
431C22×C83#51811yescharacteristic
432C22×C83#52011yescharacteristic
433C22×C83C2×#12311yescharacteristic
434C22×C83#52511yescharacteristic
435C22×C83#52911yescharacteristic
436C22×C83#52911yescharacteristic
437C22×C83#52911yescharacteristic
438C22×C83#52911yescharacteristic
439C22×C83#53211yescharacteristic
440C22×C83#53211yescharacteristic
441C22×C83#53511yescharacteristic
442C22×C83#53711yescharacteristic
443C22×C83#54011yescharacteristic
444C22×C83#54211yescharacteristic
445C22×C83#55111yescharacteristic
446C22×C83#55111yescharacteristic
447C22×C83#55111yescharacteristic
448C22×C83#55111yescharacteristic
449C22×C83#55111yescharacteristic
450C22×C83#55211yescharacteristic
451C22×C83#55211yescharacteristic
452C22×C83#55211yescharacteristic
453C22×C83#55311yescharacteristic
454C22×C83#55311yescharacteristic
455C22×C83#55311yescharacteristic
456C22×C83#55511yescharacteristic
457C22×C83#55511yescharacteristic
458C22×C83#55511yescharacteristic
459C22×C83#55511yescharacteristic
460C22×C83#55611yescharacteristic
461C4×C83—24no—
462C4×C83—24no—
463C4×C83—42no—
464C4×C83—42no—
465C4×C83—81no—
466C4×C83—81no—
467Dic83—24no—
468Dic83—42no—
469Dic83—42no—
470Dic83—42no—
471Dic83—42no—
472Dic83—42no—
473Dic83—42no—
474Dic83—42no—
475#14074—831nomaximal, Sylow
476C2×C83—82no—
477C2×C83#229311yescharacteristic
478C2×C83C4×#12311yescharacteristic
479C2×C83#232411yescharacteristic
480C2×C83#234611yescharacteristic
481C2×C83#235311yescharacteristic
482C2×C83#237211yescharacteristic
483C2×C83#237311yescharacteristic
484C2×C83#249811yescharacteristic
485C2×C83#250011yescharacteristic
486C2×C83#252611yescharacteristic
487C2×C83#252911yescharacteristic
488C2×C83#253111yescharacteristic
489C2×C83#253211yescharacteristic
490C2×C83#260111yescharacteristic
491C2×C83#261011yescharacteristic
492C2×#388—831no—
493C2×#388D8311yescharacteristic
494C2×#376—831no—
495#1442—831no—
496#1441—831no—
497#1440—831no—
498#1439—831no—
499#1437—831no—
500#1437—831no—
501#1437—831no—
502#1436—831no—
503C4⋊#95—831no—
504#1434—831no—
505#1434—831no—
506C4×#95—831no—
507C83#1407411yescharacteristic, complemented, Sylow
508C22×C4⋊C4—831no—
509C22×C4⋊C4—831no—
510C22×C4⋊C4C2×D8311yescharacteristic
511C22×C22⋊C4—831no—
512C22×C22⋊C4—831no—
513C22×C22⋊C4—831no—
514C22×C22⋊C4—831no—
515C22×C22⋊C4C2×D8311yescharacteristic
516C22×C22⋊C4C2×D8311yescharacteristic
517C22×C22⋊C4C2×D8311yescharacteristic
518C22×C42—831no—
519C22×C42—831no—
520C22×C42—831no—
521C22×C42—831no—
522C22×C42C2×D8311yescharacteristic
523#388—24no—
524#388—838no—
525#376—1664no—
526C2×#95—831no—
527C2×#95—831no—
528C2×#95—831no—
529C2×#95—831no—
530C2×#95—831no—
531C2×#95—831no—
532C2×#95—831no—
533C2×#95—831no—
534C2×#95—831no—
535C2×#95—831no—
536C2×#95—831no—
537C2×#95—831no—
538C2×#95—831no—
539C2×#95—831no—
540C2×#95—831no—
541C2×#95—831no—
542C2×#95—831no—
543C2×#95—831no—
544C2×#95C2×D8311yescharacteristic
545C2×#95C2×D8311yescharacteristic
546C25C22×D8311yescharacteristic
547C23×C4—831no—
548C23×C4—831no—
549C23×C4—831no—
550C23×C4—831no—
551C23×C4—831no—
552C23×C4—831no—
553C23×C4—831no—
554C23×C4—831no—
555C23×C4C22×D8311yescharacteristic
556C23×C4C22×D8311yescharacteristic
557C23×C4C22×D8311yescharacteristic
558C23×C4C22×D8311yescharacteristic
559C23×C4C22×D8311yescharacteristic
560C23×C4C22×D8311yescharacteristic
561C2×C4⋊C4—22no—
562C2×C4⋊C4—41no—
563C2×C4⋊C4—41no—
564C2×C4⋊C4—3321no—
565C2×C4⋊C4—3321no—
566C2×C4⋊C4—3321no—
567C2×C4⋊C4—834no—
568C2×C4⋊C4—1662no—
569C2×C4⋊C4—1662no—
570C2×C22⋊C4—22no—
571C2×C22⋊C4—22no—
572C2×C22⋊C4—22no—
573C2×C22⋊C4—22no—
574C2×C22⋊C4—22no—
575C2×C22⋊C4—22no—
576C2×C22⋊C4—41no—
577C2×C22⋊C4—41no—
578C2×C22⋊C4—3321no—
579C2×C22⋊C4—3321no—
580C2×C22⋊C4—3321no—
581C2×C22⋊C4—3321no—
582C2×C22⋊C4—834no—
583C2×C22⋊C4—834no—
584C2×C22⋊C4—1662no—
585C2×C22⋊C4—1662no—
586C2×C22⋊C4—1662no—
587C2×C22⋊C4—1662no—
588C2×C22⋊C4—1662no—
589C2×C22⋊C4—1662no—
590C2×C22⋊C4C4×D8314yes—
591C2×C42—22no—
592C2×C42—22no—
593C2×C42—3321no—
594C2×C42—3321no—
595C2×C42—834no—
596C2×C42—1662no—
597C2×C42—1662no—
598C2×C42—1662no—
599C2×C42—1662no—
600C2×C42—1662no—
601C2×C42—1662no—
602C2×C42—1662no—
603C2×C42—1662no—
604C2×C42—1662no—
605C2×C42C22⋊D8314yes—
606#95—22no—
607#95—22no—
608#95—3321no—
609#95—3321no—
610#95—3321no—
611#95—3321no—
612#95—3321no—
613#95—834no—
614#95—834no—
615#95—1662no—
616#95—1662no—
617#95—1662no—
618#95—1662no—
619#95—1662no—
620#95—1662no—
621#95—1662no—
622#95—1662no—
623#95—1662no—
624#95—1662no—
625#95—1662no—
626C24—21no—
627C24—21no—
628C24—21no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24—21no—
640C24C2×C4×D8312yes—
641C24C23×D8311yescharacteristic
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—832no—
677C22×C4—832no—
678C22×C4—832no—
679C22×C4—832no—
680C22×C4—832no—
681C22×C4—832no—
682C22×C4—832no—
683C22×C4—832no—
684C22×C4—832no—
685C22×C4—832no—
686C22×C4—1661no—
687C22×C4—1661no—
688C22×C4—1661no—
689C22×C4—1661no—
690C22×C4—1661no—
691C22×C4—1661no—
692C22×C4—1661no—
693C22×C4—1661no—
694C22×C4—1661no—
695C22×C4—1661no—
696C22×C4—1661no—
697C22×C4—1661no—
698C22×C4—1661no—
699C22×C4—1661no—
700C22×C4—1661no—
701C22×C4—1661no—
702C22×C4—1661no—
703C22×C4—1661no—
704C22×C4—1661no—
705C22×C4—1661no—
706C22×C4—1661no—
707C22×C4—1661no—
708C22×C4—1661no—
709C22×C4—1661no—
710C22×C4—1661no—
711C22×C4—1661no—
712C22×C4—1661no—
713C22×C4—1661no—
714C22×C4—1661no—
715C22×C4—1661no—
716C22×C4—1661no—
717C22×C4—1661no—
718C22×C4—1661no—
719C22×C4—1661no—
720C22×C4—1661no—
721C22×C4—1661no—
722C22×C4—1661no—
723C22×C4—1661no—
724C22×C4—1661no—
725C22×C4—1661no—
726C22×C4—1661no—
727C22×C4—1661no—
728C22×C4—1661no—
729C22×C4—1661no—
730C22×C4—1661no—
731C22×C4—1661no—
732C22×C4C2×C4×D8312yes—
733C22×C4C2×C4×D8312yes—
734C22×C4C2×C22⋊D8312yes—
735C22×C4C2×C22⋊D8312yes—
736C22×C4C2×C22⋊D8312yes—
737C22×C4#1305058912yes—
738C22×C4#1305058912yes—
739C22×C4#1305059012yes—
740C4⋊C4—44no—
741C4⋊C4—3324no—
742C4⋊C4—3324no—
743C22⋊C4—28no—
744C22⋊C4—44no—
745C22⋊C4—44no—
746C22⋊C4—3324no—
747C22⋊C4—3324no—
748C22⋊C4—3324no—
749C22⋊C4—1668no—
750C42—28no—
751C42—3324no—
752C42—3324no—
753C42—1668no—
754C42—1668no—
755C23—22no—
756C23—22no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—41no—
763C23—41no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23C22×C4×D8311yescharacteristic
791C23C22×C22⋊D8311yescharacteristic
792C23#41×D8311yescharacteristic
793C23#41×D8311yescharacteristic
794C23#41×D8311yescharacteristic
795C23#41×D8311yescharacteristic
796C23#41×D8311yescharacteristic
797C23#41×D8311yescharacteristic
798C23C2×#1305058911yescharacteristic
799C23C2×#1305058911yescharacteristic
800C23C2×#1305059011yescharacteristic
801C23#1458183711yescharacteristic
802C23#1458183711yescharacteristic
803C23#1458183811yescharacteristic
804C23#1458183911yescharacteristic
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—3321no—
846C2×C4—3321no—
847C2×C4—3321no—
848C2×C4—3321no—
849C2×C4—3321no—
850C2×C4—3321no—
851C2×C4—3321no—
852C2×C4—3321no—
853C2×C4—3321no—
854C2×C4—3321no—
855C2×C4—3321no—
856C2×C4—3321no—
857C2×C4—3321no—
858C2×C4—3321no—
859C2×C4—3321no—
860C2×C4—3321no—
861C2×C4—3321no—
862C2×C4—3321no—
863C2×C4—3321no—
864C2×C4—3321no—
865C2×C4—3321no—
866C2×C4—3321no—
867C2×C4—3321no—
868C2×C4—3321no—
869C2×C4—3321no—
870C2×C4—3321no—
871C2×C4—3321no—
872C2×C4—3321no—
873C2×C4—834no—
874C2×C4—1662no—
875C2×C4—1662no—
876C2×C4—1662no—
877C2×C4—1662no—
878C2×C4—1662no—
879C2×C4—1662no—
880C2×C4—1662no—
881C2×C4—1662no—
882C2×C4—1662no—
883C2×C4—1662no—
884C2×C4—1662no—
885C2×C4—1662no—
886C2×C4—1662no—
887C2×C4—1662no—
888C2×C4—1662no—
889C2×C4—1662no—
890C2×C4—1662no—
891C2×C4—1662no—
892C2×C4—1662no—
893C2×C4—1662no—
894C2×C4—1662no—
895C2×C4—1662no—
896C2×C4—1662no—
897C2×C4—1662no—
898C2×C4—1662no—
899C2×C4—1662no—
900C2×C4—1662no—
901C2×C4C4×C22⋊D8314yes—
902C2×C4#1458177314yes—
903C22—42no—
904C22—42no—
905C22—42no—
906C22—42no—
907C22—42no—
908C22—42no—
909C22—42no—
910C22—81no—
911C22—81no—
912C22—81no—
913C22—81no—
914C22—81no—
915C22—81no—
916C22—81no—
917C22—81no—
918C22#117×D8311yescharacteristic
919C22C2×C4×C22⋊D8311yescharacteristic
920C22C4×#1305058911yescharacteristic
921C22C4×#1305058911yescharacteristic
922C22#1912816911yescharacteristic
923C22#1912817311yescharacteristic
924C22#1912818011yescharacteristic
925C22C2×#1458177311yescharacteristic
926C22#1912820811yescharacteristic
927C22#1912822911yescharacteristic
928C22#1912822911yescharacteristic
929C22#1912823111yescharacteristic
930C22#1912823111yescharacteristic
931C22#1912824711yescharacteristic
932C22#1912824711yescharacteristic
933C22#1912826811yescharacteristic
934C22#1912827911yescharacteristic
935C22#1912830211yescharacteristic
936C22#1912831611yescharacteristic
937C22#1912837411yescharacteristic
938C22#1912837411yescharacteristic
939C22#1912837611yescharacteristic
940C22#1912838111yescharacteristic
941C22#1912838111yescharacteristic
942C22#1912838711yescharacteristic
943C22#1912838811yescharacteristic
944C22#1912838811yescharacteristic
945C22#1912839811yescharacteristic
946C22#1912839811yescharacteristic
947C22#1912840211yescharacteristic
948C22#1912841311yescharacteristic
949C22#1912841311yescharacteristic
950C22#1912841511yescharacteristic
951C22#1912841511yescharacteristic
952C22#1912841811yescharacteristic
953C4—24no—
954C4—24no—
955C4—42no—
956C4—42no—
957C4—81no—
958C4—81no—
959C4—3322no—
960C4—3322no—
961C4—3322no—
962C4—3322no—
963C4—3322no—
964C4—3322no—
965C4—3322no—
966C4—1664no—
967C2—82no—
968C2#2490992211yescharacteristic
969C2C4×#1458177311yescharacteristic
970C2#2491015011yescharacteristic
971C2#2491034511yescharacteristic
972C2#2491039811yescharacteristic
973C2#2491057011yescharacteristic
974C2#2491058011yescharacteristic
975C2#2491190911yescharacteristic
976C2#2491192611yescharacteristic
977C2#2491223711yescharacteristic
978C2#2491228211yescharacteristic
979C2#2491231211yescharacteristic
980C2#2491232711yescharacteristic
981C2#2491306211yescharacteristic
982C2#2491315211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D83
commutatorC23×C83C23×C4
FittingC2×#388×C83C2
socle, cosocleC24×C83C24
prime radicalC25×C83C23
hypercenterC2×#388D83
hypocenterC83#14074
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C2×#19127547C2semidirect
3. #24905722C2semidirect
4. #24905713C2semidirect
10. #24905694C2semidirect
11. Dic83⋊#95C2semidirect
12. #24905689C2semidirect
13. #24905687C2semidirect
14. C4×C83⋊#95C2semidirect
26. #19127589C4semidirect
507. C83#14074semidirect

Maximal subgroups

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

subgroupindex
C2×#191275892
C2×#191275472
#249057222
#249057132
#249057102
#249057062
#249057002
#249056942
Dic83⋊#952
#249056892
#249056872
C4×C83⋊#952
C2×#388×C832
#1407483