Finite Group Databasebeta

← #35332895

Subgroups — #35332895

Order 21248.

1810 conjugacy classes of subgroups.

The subgroup lattice has 1034 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14581769C211yesmaximal, characteristic
2C2×#19127588C211yesmaximal, characteristic, complemented
3C2×#19127585C211yesmaximal, characteristic, complemented
4#24905733C211yesmaximal, characteristic, complemented
5#24905733C211yesmaximal, characteristic, complemented
6#24905732C211yesmaximal, characteristic, complemented
7#24905729C211yesmaximal, characteristic, complemented
8#24905708C211yesmaximal, characteristic
9#24905706C211yesmaximal, characteristic
10#24905700C211yesmaximal, characteristic
11#24905693C211yesmaximal, characteristic, complemented
12Dic83⋊#95C211yesmaximal, characteristic, complemented
13#24905685C211yesmaximal, characteristic
14#24905685C211yesmaximal, characteristic
15C83×#1437C211yesmaximal, characteristic
16C23×Dic166C2211yescharacteristic
17C24×Dic83C2211yescharacteristic
18C2×#14581769—24no—
19C2×#14581769—24no—
20C2×#14581769C418yescomplemented
21C22×C4⋊Dic83C2211yescharacteristic
22C22×C4⋊Dic83C2211yescharacteristic
23C22×Dic83⋊C4C2211yescharacteristic
24C22×Dic83⋊C4C2211yescharacteristic
25C22×Dic83⋊C4C2211yescharacteristic
26C22×C22⋊Dic83C2211yescharacteristic
27C22×C22⋊Dic83C2211yescharacteristic
28C22×C22⋊Dic83C2211yescharacteristic
29C22×C4×Dic83C2211yescharacteristic
30#19127588—24no—
31#19127585—24no—
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
47C2×C83⋊#95C2211yescharacteristic
48C2×C83⋊#95C2211yescharacteristic
49C22×C22⋊C4×C83C2211yescharacteristic
50C22×C22⋊C4×C83C2211yescharacteristic
51C22×C22⋊C4×C83C2211yescharacteristic
52C22×C42×C83C2211yescharacteristic
53C2×#95×C83C2211yescharacteristic
54C2×#95×C83C2211yescharacteristic
55C2×#95×C83C2211yescharacteristic
56C22×Dic166—22no—
57C22×Dic166—22no—
58C22×Dic166—41no—
59C22×Dic166—41no—
60C22×Dic166—41no—
61C22×Dic166—41no—
62C22×Dic166C2×C414yes—
63C23×Dic83—22no—
64C23×Dic83—22no—
65C23×Dic83—41no—
66C23×Dic83—41no—
67C23×Dic83—41no—
68C23×Dic83—41no—
69C23×Dic83C2×C414yes—
70C23×Dic83C2311yescharacteristic
71C23×Dic83C2311yescharacteristic
72C23×Dic83C2311yescharacteristic
73C23×Dic83C2311yescharacteristic
74C23×Dic83C2311yescharacteristic
75C23×Dic83C2311yescharacteristic
76C23×Dic83C2311yescharacteristic
77C23×Dic83C2311yescharacteristic
78#14581769—232no—
79C2×C4⋊Dic83—22no—
80C2×C4⋊Dic83—22no—
81C2×C4⋊Dic83—22no—
82C2×C4⋊Dic83—22no—
83C2×C4⋊Dic83—41no—
84C2×C4⋊Dic83C2×C414yes—
85C2×Dic83⋊C4—22no—
86C2×Dic83⋊C4—22no—
87C2×Dic83⋊C4—22no—
88C2×Dic83⋊C4—22no—
89C2×Dic83⋊C4—41no—
90C2×Dic83⋊C4C2×C414yes—
91C2×Dic83⋊C4C2×C414yes—
92C2×Dic83⋊C4D414yes—
93C2×Dic83⋊C4D414yes—
94C2×C22⋊Dic83—22no—
95C2×C22⋊Dic83—22no—
96C2×C22⋊Dic83—22no—
97C2×C22⋊Dic83—22no—
98C2×C22⋊Dic83—22no—
99C2×C22⋊Dic83—41no—
100C2×C22⋊Dic83—41no—
101C2×C22⋊Dic83—41no—
102C2×C22⋊Dic83C2×C414yes—
103C2×C4×Dic83—22no—
104C2×C4×Dic83—22no—
105C2×C4×Dic83—41no—
106C83⋊#95—22no—
107C83⋊#95—22no—
108C83⋊#95—22no—
109C83⋊#95—22no—
110C83⋊#95—22no—
111C83⋊#95—22no—
112C83⋊#95—22no—
113C83⋊#95—41no—
114C83⋊#95—41no—
115C83⋊#95—41no—
116C83⋊#95—41no—
117C83⋊#95—41no—
118C83⋊#95—41no—
119C83⋊#95—41no—
120C83⋊#95—41no—
121C83⋊#95—41no—
122C83⋊#95—41no—
123C25×C83C2311yescharacteristic
124C23×C4×C83C2311yescharacteristic
125C23×C4×C83C2311yescharacteristic
126C23×C4×C83C2311yescharacteristic
127C23×C4×C83C2311yescharacteristic
128C23×C4×C83C2311yescharacteristic
129C23×C4×C83C2311yescharacteristic
130C2×C22⋊C4×C83—22no—
131C2×C22⋊C4×C83—22no—
132C2×C22⋊C4×C83—22no—
133C2×C22⋊C4×C83—22no—
134C2×C22⋊C4×C83—41no—
135C2×C22⋊C4×C83—41no—
136C2×C22⋊C4×C83—41no—
137C2×C22⋊C4×C83C2×C414yes—
138C2×C22⋊C4×C83Q814yescomplemented
139C2×C42×C83—22no—
140C2×C42×C83—22no—
141C2×C42×C83—41no—
142#95×C83—22no—
143#95×C83—41no—
144#95×C83—41no—
145C2×Dic166—28no—
146C2×Dic166—44no—
147C2×Dic166—44no—
148C2×Dic166—44no—
149C2×Dic166—44no—
150C2×Dic166—44no—
151C2×Dic166—44no—
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—28no—
179C22×Dic83—21no—
180C22×Dic83—21no—
181C22×Dic83—21no—
182C22×Dic83—21no—
183C22×Dic83—21no—
184C22×Dic83—21no—
185C22×Dic83—21no—
186C22×Dic83—21no—
187C22×Dic83—21no—
188C22×Dic83—21no—
189C22×Dic83—21no—
190C22×Dic83—21no—
191C22×Dic83—21no—
192C22×Dic83—21no—
193C22×Dic83—21no—
194C22×Dic83—21no—
195C22×Dic83—21no—
196C22×Dic83—21no—
197C22×Dic83—21no—
198C22×Dic83—21no—
199C22×Dic83—21no—
200C22×Dic83—44no—
201C22×Dic83—44no—
202C22×Dic83—44no—
203C22×Dic83—44no—
204C22×Dic83—44no—
205C22×Dic83—44no—
206C22×Dic83C22×C412yes—
207C22×Dic83C22×C412yes—
208C22×Dic83C22×C412yes—
209C22×Dic83C22×C412yes—
210C22×Dic83C2×D412yes—
211C22×Dic83C2×D412yes—
212C22×Dic83C2×D412yes—
213C22×Dic83C2×D412yes—
214C22×Dic83#4112yes—
215C4⋊Dic83—28no—
216C4⋊Dic83—44no—
217Dic83⋊C4—28no—
218Dic83⋊C4—44no—
219Dic83⋊C4C22⋊C4116yescomplemented
220C22⋊Dic83—28no—
221C22⋊Dic83—44no—
222C22⋊Dic83—44no—
223C4×Dic83—44no—
224C24×C83—21no—
225C24×C83—21no—
226C24×C83—21no—
227C24×C83—21no—
228C24×C83—21no—
229C24×C83—21no—
230C24×C83—21no—
231C24×C83—21no—
232C24×C83—21no—
233C24×C83—21no—
234C24×C83—21no—
235C24×C83—21no—
236C24×C83C22×C412yes—
237C24×C83C2×Q812yes—
238C24×C83#4112yes—
239C24×C83C2411yescharacteristic
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×C83—21no—
251C22×C4×C83—21no—
252C22×C4×C83—21no—
253C22×C4×C83—21no—
254C22×C4×C83—21no—
255C22×C4×C83—21no—
256C22×C4×C83—21no—
257C22×C4×C83—21no—
258C22×C4×C83—21no—
259C22×C4×C83—21no—
260C22×C4×C83—21no—
261C22×C4×C83—21no—
262C22×C4×C83—21no—
263C22×C4×C83—21no—
264C22×C4×C83—21no—
265C22×C4×C83—21no—
266C22×C4×C83—21no—
267C22×C4×C83—21no—
268C22×C4×C83—21no—
269C22×C4×C83—21no—
270C22×C4×C83—21no—
271C22×C4×C83—21no—
272C22×C4×C83—21no—
273C22×C4×C83—21no—
274C22×C4×C83—21no—
275C22×C4×C83C22×C412yes—
276C22×C4×C83C22×C412yes—
277C22×C4×C83C2×D412yes—
278C22×C4×C83C2×D412yes—
279C22×C4×C83C2×Q812yes—
280C22×C4×C83C2×Q812yes—
281C22×C4×C83#4112yes—
282C22⋊C4×C83—28no—
283C22⋊C4×C83—44no—
284C22⋊C4×C83—44no—
285C42×C83—44no—
286C23×C83—22no—
287C23×C83—22no—
288C23×C83—22no—
289C23×C83—22no—
290C23×C83—22no—
291C23×C83—22no—
292C23×C83—22no—
293C23×C83—22no—
294C23×C83—22no—
295C23×C83—22no—
296C23×C83—22no—
297C23×C83—22no—
298C23×C83—22no—
299C23×C83—22no—
300C23×C83—22no—
301C23×C83—22no—
302C23×C83—22no—
303C23×C83—22no—
304C23×C83—41no—
305C23×C83—41no—
306C23×C83—41no—
307C23×C83—41no—
308C23×C83—41no—
309C23×C83—41no—
310C23×C83—41no—
311C23×C83—41no—
312C23×C83—41no—
313C23×C83—41no—
314C23×C83—41no—
315C23×C83—41no—
316C23×C83—41no—
317C23×C83—41no—
318C23×C83—41no—
319C23×C83—41no—
320C23×C83C4×Q814yes—
321C23×C83C23×C411yescharacteristic
322C23×C83C22×D411yescharacteristic
323C23×C83C22×D411yescharacteristic
324C23×C83C22×Q811yescharacteristic
325C23×C83C2×#4111yescharacteristic
326C23×C83C2×#4111yescharacteristic
327C23×C83C2×#4111yescharacteristic
328C23×C83H(5,𝔽2)11yescharacteristic
329C23×C83H(5,𝔽2)11yescharacteristic
330C23×C83H(5,𝔽2)11yescharacteristic
331C23×C83H(5,𝔽2)11yescharacteristic
332C23×C83H(5,𝔽2)11yescharacteristic
333C23×C832−1+411yescharacteristic
334C23×C832−1+411yescharacteristic
335C23×C832−1+411yescharacteristic
336C2×C4×C83—22no—
337C2×C4×C83—22no—
338C2×C4×C83—22no—
339C2×C4×C83—22no—
340C2×C4×C83—22no—
341C2×C4×C83—22no—
342C2×C4×C83—22no—
343C2×C4×C83—22no—
344C2×C4×C83—22no—
345C2×C4×C83—22no—
346C2×C4×C83—22no—
347C2×C4×C83—22no—
348C2×C4×C83—22no—
349C2×C4×C83—22no—
350C2×C4×C83—22no—
351C2×C4×C83—22no—
352C2×C4×C83—22no—
353C2×C4×C83—22no—
354C2×C4×C83—41no—
355C2×C4×C83—41no—
356C2×C4×C83—41no—
357C2×C4×C83—41no—
358C2×C4×C83—41no—
359C2×C4×C83—41no—
360C2×C4×C83—41no—
361C2×C4×C83—41no—
362C2×C4×C83—41no—
363C2×C4×C83—41no—
364C2×C4×C83—41no—
365C2×C4×C83—41no—
366C2×C4×C83—41no—
367C2×C4×C83—41no—
368C2×C4×C83—41no—
369C2×C4×C83—41no—
370C2×C4×C83—41no—
371C2×C4×C83—41no—
372C2×C4×C83—41no—
373C2×C4×C83—41no—
374C2×C4×C83—41no—
375C2×C4×C83—41no—
376C2×C4×C83—41no—
377C2×C4×C83C2×C22⋊C414yes—
378C2×Dic83—22no—
379C2×Dic83—22no—
380C2×Dic83—22no—
381C2×Dic83—22no—
382C2×Dic83—22no—
383C2×Dic83—22no—
384C2×Dic83—22no—
385C2×Dic83—22no—
386C2×Dic83—22no—
387C2×Dic83—22no—
388C2×Dic83—22no—
389C2×Dic83—22no—
390C2×Dic83—22no—
391C2×Dic83—22no—
392C2×Dic83—22no—
393C2×Dic83—22no—
394C2×Dic83—22no—
395C2×Dic83—22no—
396C2×Dic83—22no—
397C2×Dic83—22no—
398C2×Dic83—22no—
399C2×Dic83—416no—
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—41no—
411C2×Dic83—41no—
412C2×Dic83—41no—
413C2×Dic83—41no—
414C2×Dic83—41no—
415C2×Dic83—41no—
416C2×Dic83—41no—
417C2×Dic83—41no—
418C2×Dic83—41no—
419C2×Dic83—41no—
420C2×Dic83—41no—
421C2×Dic83—41no—
422C2×Dic83—41no—
423C2×Dic83—41no—
424C2×Dic83—41no—
425C2×Dic83—41no—
426C2×Dic83—41no—
427C2×Dic83—41no—
428C2×Dic83—41no—
429C2×Dic83—41no—
430C2×Dic83—41no—
431C2×Dic83—41no—
432C2×Dic83—41no—
433C2×Dic83C2×C22⋊C414yes—
434C2×Dic83C2×C22⋊C414yes—
435Dic166—416no—
436C22×C83—24no—
437C22×C83—24no—
438C22×C83—24no—
439C22×C83—42no—
440C22×C83—42no—
441C22×C83—42no—
442C22×C83—42no—
443C22×C83—42no—
444C22×C83—42no—
445C22×C83—42no—
446C22×C83—42no—
447C22×C83—42no—
448C22×C83—42no—
449C22×C83—42no—
450C22×C83—42no—
451C22×C83C22×C22⋊C411yescharacteristic
452C22×C83C2×C4×Q811yescharacteristic
453C22×C83C4×#4111yescharacteristic
454C22×C83#51811yescharacteristic
455C22×C83#51811yescharacteristic
456C22×C83#51911yescharacteristic
457C22×C83#52011yescharacteristic
458C22×C83#53511yescharacteristic
459C22×C83#53511yescharacteristic
460C22×C83#53511yescharacteristic
461C22×C83#53511yescharacteristic
462C22×C83#53811yescharacteristic
463C22×C83#53911yescharacteristic
464C22×C83#53911yescharacteristic
465C22×C83#53911yescharacteristic
466C22×C83#54211yescharacteristic
467C22×C83#54211yescharacteristic
468C22×C83#54311yescharacteristic
469C22×C83#54411yescharacteristic
470C22×C83#54611yescharacteristic
471C22×C83#54611yescharacteristic
472C22×C83#54711yescharacteristic
473C22×C83#54711yescharacteristic
474C22×C83#54811yescharacteristic
475C22×C83#54811yescharacteristic
476C22×C83D4×Q811yescharacteristic
477C22×C83D4×Q811yescharacteristic
478C22×C83#55111yescharacteristic
479C22×C83#55111yescharacteristic
480C22×C83#55411yescharacteristic
481C22×C83#55411yescharacteristic
482C22×C83#56211yescharacteristic
483C22×C83#56211yescharacteristic
484C22×C83#56311yescharacteristic
485C22×C83#56311yescharacteristic
486C4×C83—24no—
487C4×C83—42no—
488C4×C83—42no—
489C4×C83—42no—
490C4×C83—42no—
491C4×C83—81no—
492Dic83—24no—
493Dic83—24no—
494Dic83—42no—
495Dic83—42no—
496Dic83—42no—
497Dic83—81no—
498Dic83—81no—
499Dic83—81no—
500#14448—831nomaximal, Sylow
501C2×C83—44no—
502C2×C83#230911yescharacteristic
503C2×C83#232911yescharacteristic
504C2×C83#233211yescharacteristic
505C2×C83#233911yescharacteristic
506C2×C83Q8×C22⋊C411yescharacteristic
507C2×C83#236811yescharacteristic
508C2×C83#237811yescharacteristic
509C2×C83#269211yescharacteristic
510C2×C83#269211yescharacteristic
511C2×C83#269611yescharacteristic
512C2×C83#269611yescharacteristic
513C2×C83#272011yescharacteristic
514C2×C83#272011yescharacteristic
515C2×C83#272311yescharacteristic
516C2×C83#272311yescharacteristic
517C22×C22⋊Q8—831no—
518C2×#387—831no—
519C2×#387—831no—
520#1446—831no—
521#1446—831no—
522#1445—831no—
523#1445—831no—
524#1439—831no—
525#1439—831no—
526#1437—831no—
527#1437D8311yescharacteristic
528C4⋊#95—831no—
529C4⋊#95—831no—
530C22⋊#95—831no—
531C22⋊#95—831no—
532C83#1444811yescharacteristic, complemented, Sylow
533C23×Q8—831no—
534C24×C4—831no—
535C2×C22⋊Q8—838no—
536C2×C22⋊Q8—1664no—
537C2×C22⋊Q8—1664no—
538C22×C4⋊C4—831no—
539C22×C4⋊C4—831no—
540C22×C4⋊C4—831no—
541C22×C4⋊C4—831no—
542C22×C4⋊C4—831no—
543C22×C22⋊C4—831no—
544C22×C22⋊C4—831no—
545C22×C22⋊C4—831no—
546C22×C22⋊C4C2×D8311yescharacteristic
547C22×C22⋊C4C2×D8311yescharacteristic
548C22×C22⋊C4C2×D8311yescharacteristic
549C22×C42—831no—
550C22×C42C2×D8311yescharacteristic
551#387—1664no—
552#387—1664no—
553C2×#95—831no—
554C2×#95—831no—
555C2×#95—831no—
556C2×#95—831no—
557C2×#95—831no—
558C2×#95—831no—
559C2×#95—831no—
560C2×#95—831no—
561C2×#95—831no—
562C2×#95—831no—
563C2×#95—831no—
564C2×#95—831no—
565C2×#95—831no—
566C2×#95—831no—
567C2×#95—831no—
568C2×#95—831no—
569C2×#95—831no—
570C2×#95C2×D8311yescharacteristic
571C2×#95C2×D8311yescharacteristic
572C2×#95C2×D8311yescharacteristic
573C25C22×D8311yescharacteristic
574C22×Q8—3321no—
575C22×Q8—3321no—
576C22×Q8—3321no—
577C22×Q8—3321no—
578C22×Q8—834no—
579C22×Q8—1662no—
580C22×Q8—1662no—
581C23×C4—3321no—
582C23×C4—3321no—
583C23×C4—3321no—
584C23×C4—3321no—
585C23×C4—834no—
586C23×C4—831no—
587C23×C4—831no—
588C23×C4—831no—
589C23×C4—831no—
590C23×C4—831no—
591C23×C4—831no—
592C23×C4—831no—
593C23×C4—831no—
594C23×C4—1662no—
595C23×C4—1662no—
596C23×C4C22×D8311yescharacteristic
597C23×C4C22×D8311yescharacteristic
598C23×C4C22×D8311yescharacteristic
599C23×C4C22×D8311yescharacteristic
600C23×C4C22×D8311yescharacteristic
601C23×C4C22×D8311yescharacteristic
602C22⋊Q8—16632no—
603C2×C4⋊C4—3321no—
604C2×C4⋊C4—3321no—
605C2×C4⋊C4—834no—
606C2×C4⋊C4—834no—
607C2×C4⋊C4—834no—
608C2×C4⋊C4—834no—
609C2×C4⋊C4—834no—
610C2×C4⋊C4—1662no—
611C2×C4⋊C4—1662no—
612C2×C4⋊C4—1662no—
613C2×C4⋊C4—1662no—
614C2×C4⋊C4—1662no—
615C2×C4⋊C4—1662no—
616C2×C4⋊C4—1662no—
617C2×C4⋊C4—1662no—
618C2×C22⋊C4—22no—
619C2×C22⋊C4—22no—
620C2×C22⋊C4—22no—
621C2×C22⋊C4—22no—
622C2×C22⋊C4—41no—
623C2×C22⋊C4—41no—
624C2×C22⋊C4—41no—
625C2×C22⋊C4—3321no—
626C2×C22⋊C4—3321no—
627C2×C22⋊C4—3321no—
628C2×C22⋊C4—834no—
629C2×C22⋊C4—1662no—
630C2×C22⋊C4—1662no—
631C2×C22⋊C4—1662no—
632C2×C22⋊C4—1662no—
633C2×C22⋊C4—1662no—
634C2×C22⋊C4Dic16614yescomplemented
635C2×C22⋊C4C4×D8314yes—
636C2×C42—22no—
637C2×C42—22no—
638C2×C42—41no—
639C2×C42—3321no—
640C2×C42—1662no—
641C2×C42—1662no—
642#95—22no—
643#95—41no—
644#95—41no—
645#95—3321no—
646#95—3321no—
647#95—3321no—
648#95—3321no—
649#95—3321no—
650#95—3321no—
651#95—3321no—
652#95—3321no—
653#95—3321no—
654#95—3321no—
655#95—1662no—
656#95—1662no—
657#95—1662no—
658#95—1662no—
659#95—1662no—
660#95—1662no—
661#95—1662no—
662C24—21no—
663C24—21no—
664C24—21no—
665C24—21no—
666C24—21no—
667C24—21no—
668C24—21no—
669C24—21no—
670C24—21no—
671C24—21no—
672C24—21no—
673C24—21no—
674C24C2×C4×D8312yes—
675C24C2×Dic16612yes—
676C24#1305059012yes—
677C24C23×D8311yescharacteristic
678C2×Q8—3324no—
679C2×Q8—3324no—
680C2×Q8—3324no—
681C2×Q8—3324no—
682C2×Q8—3324no—
683C2×Q8—3324no—
684C2×Q8—1668no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—3324no—
721C22×C4—3324no—
722C22×C4—3324no—
723C22×C4—3324no—
724C22×C4—3324no—
725C22×C4—3324no—
726C22×C4—832no—
727C22×C4—832no—
728C22×C4—832no—
729C22×C4—832no—
730C22×C4—832no—
731C22×C4—832no—
732C22×C4—832no—
733C22×C4—832no—
734C22×C4—832no—
735C22×C4—1661no—
736C22×C4—1661no—
737C22×C4—1661no—
738C22×C4—1661no—
739C22×C4—1661no—
740C22×C4—1661no—
741C22×C4—1661no—
742C22×C4—1661no—
743C22×C4—1661no—
744C22×C4—1661no—
745C22×C4—1661no—
746C22×C4—1661no—
747C22×C4—1661no—
748C22×C4—1661no—
749C22×C4—1661no—
750C22×C4—1661no—
751C22×C4—1661no—
752C22×C4—1661no—
753C22×C4—1661no—
754C22×C4—1661no—
755C22×C4—1661no—
756C22×C4—1668no—
757C22×C4—1661no—
758C22×C4—1661no—
759C22×C4—1661no—
760C22×C4—1661no—
761C22×C4—1661no—
762C22×C4—1661no—
763C22×C4—1661no—
764C22×C4—1661no—
765C22×C4—1661no—
766C22×C4—1661no—
767C22×C4—1661no—
768C22×C4—1661no—
769C22×C4—1661no—
770C22×C4—1661no—
771C22×C4—1661no—
772C22×C4—1661no—
773C22×C4—1661no—
774C22×C4—1661no—
775C22×C4—1661no—
776C22×C4—1661no—
777C22×C4—1661no—
778C22×C4—1661no—
779C22×C4—1661no—
780C22×C4—1661no—
781C22×C4—1661no—
782C22×C4—1661no—
783C22×C4C2×C4×D8312yes—
784C22×C4C2×C4×D8312yes—
785C22×C4D4×D8312yes—
786C22×C4D4×D8312yes—
787C22×C4C2×Dic16612yes—
788C22×C4C2×Dic16612yes—
789C22×C4#1305058912yes—
790C4⋊C4—3324no—
791C4⋊C4—3324no—
792C4⋊C4—8316no—
793C4⋊C4—1668no—
794C4⋊C4—1668no—
795C22⋊C4—28no—
796C22⋊C4—44no—
797C22⋊C4—44no—
798C22⋊C4—3324no—
799C22⋊C4—3324no—
800C22⋊C4—1668no—
801C42—44no—
802C42—3324no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—22no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—22no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23—41no—
836C23—41no—
837C23C4×Dic16614yes—
838C23C22×C4×D8311yescharacteristic
839C23C2×D4×D8311yescharacteristic
840C23C2×D4×D8311yescharacteristic
841C23C22×Dic16611yescharacteristic
842C23#41×D8311yescharacteristic
843C23C2×#1305058911yescharacteristic
844C23C2×#1305059011yescharacteristic
845C23#1458183711yescharacteristic
846C23#1458183711yescharacteristic
847C23#1458183711yescharacteristic
848C23#1458183811yescharacteristic
849C23#1458183811yescharacteristic
850C23#1458183911yescharacteristic
851C23#1458183911yescharacteristic
852C23#1458183911yescharacteristic
853Q8—33216no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—3321no—
896C2×C4—3321no—
897C2×C4—3321no—
898C2×C4—3321no—
899C2×C4—3321no—
900C2×C4—3321no—
901C2×C4—3321no—
902C2×C4—3321no—
903C2×C4—3321no—
904C2×C4—3321no—
905C2×C4—3321no—
906C2×C4—3321no—
907C2×C4—33216no—
908C2×C4—3321no—
909C2×C4—3321no—
910C2×C4—3321no—
911C2×C4—3321no—
912C2×C4—3321no—
913C2×C4—3321no—
914C2×C4—3321no—
915C2×C4—3321no—
916C2×C4—3321no—
917C2×C4—3321no—
918C2×C4—3321no—
919C2×C4—3321no—
920C2×C4—3321no—
921C2×C4—3321no—
922C2×C4—3321no—
923C2×C4—3321no—
924C2×C4—3321no—
925C2×C4—3321no—
926C2×C4—3321no—
927C2×C4—3321no—
928C2×C4—3321no—
929C2×C4—834no—
930C2×C4—834no—
931C2×C4—1662no—
932C2×C4—1662no—
933C2×C4—1662no—
934C2×C4—1662no—
935C2×C4—1662no—
936C2×C4—1662no—
937C2×C4—1662no—
938C2×C4—1662no—
939C2×C4—1662no—
940C2×C4—1662no—
941C2×C4—1662no—
942C2×C4—1662no—
943C2×C4—1662no—
944C2×C4—1662no—
945C2×C4—1662no—
946C2×C4—1662no—
947C2×C4—1662no—
948C2×C4—1662no—
949C2×C4—1662no—
950C2×C4—1662no—
951C2×C4—1662no—
952C2×C4C22⋊C4×D8314yes—
953C22—24no—
954C22—24no—
955C22—24no—
956C22—42no—
957C22—42no—
958C22—42no—
959C22—42no—
960C22—42no—
961C22—42no—
962C22—42no—
963C22—42no—
964C22—42no—
965C22—42no—
966C22—42no—
967C22—42no—
968C22C2×C22⋊C4×D8311yescharacteristic
969C22C2×C4×Dic16611yescharacteristic
970C22C4×#1305058911yescharacteristic
971C22#1912817311yescharacteristic
972C22#1912817311yescharacteristic
973C22#1912817811yescharacteristic
974C22#1912818011yescharacteristic
975C22#1912826411yescharacteristic
976C22#1912826711yescharacteristic
977C22#1912826711yescharacteristic
978C22#1912826911yescharacteristic
979C22#1912828411yescharacteristic
980C22#1912829211yescharacteristic
981C22#1912829311yescharacteristic
982C22#1912829511yescharacteristic
983C22#1912831511yescharacteristic
984C22#1912831811yescharacteristic
985C22#1912832711yescharacteristic
986C22#1912832911yescharacteristic
987C22#1912833811yescharacteristic
988C22#1912834011yescharacteristic
989C22#1912834911yescharacteristic
990C22#1912835111yescharacteristic
991C22#1912836011yescharacteristic
992C22#1912836011yescharacteristic
993C22D4×Dic16611yescharacteristic
994C22D4×Dic16611yescharacteristic
995C22#1912837511yescharacteristic
996C22#1912837711yescharacteristic
997C22#1912840811yescharacteristic
998C22#1912841011yescharacteristic
999C22#1912844611yescharacteristic
1000C22#1912844811yescharacteristic
1001C22#1912845111yescharacteristic
1002C22#1912845311yescharacteristic
1003C4—24no—
1004C4—42no—
1005C4—42no—
1006C4—42no—
1007C4—42no—
1008C4—81no—
1009C4—3322no—
1010C4—3322no—
1011C4—3322no—
1012C4—6641no—
1013C4—6641no—
1014C4—6641no—
1015C4—1664no—
1016C4—1664no—
1017C2—44no—
1018C2#2491004211yescharacteristic
1019C2#2491019111yescharacteristic
1020C2#2491022011yescharacteristic
1021C2#2491028911yescharacteristic
1022C2C22⋊C4×Dic16611yescharacteristic
1023C2#2491054111yescharacteristic
1024C2#2491062311yescharacteristic
1025C2#2491395611yescharacteristic
1026C2#2491396311yescharacteristic
1027C2#2491401011yescharacteristic
1028C2#2491401711yescharacteristic
1029C2#2491434011yescharacteristic
1030C2#2491434711yescharacteristic
1031C2#2491437911yescharacteristic
1032C2#2491438611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D83
commutatorC23×C83C23×C4
FittingC83×#1437C2
socle, cosocleC24×C83C24
prime radicalC25×C83C23
hypercenter#1437D83
hypocenterC83#14448
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ #1437

Complements

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

NH ≅ G/Ntype
2. C2×#19127588C2semidirect
3. C2×#19127585C2semidirect
4. #24905733C2semidirect
5. #24905733C2semidirect
6. #24905732C2semidirect
7. #24905729C2semidirect
11. #24905693C2semidirect
12. Dic83⋊#95C2semidirect
20. C2×#14581769C4semidirect
138. C2×C22⋊C4×C83Q8semidirect
219. Dic83⋊C4C22⋊C4semidirect
532. C83#14448semidirect
634. C2×C22⋊C4Dic166semidirect

Maximal subgroups

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

subgroupindex
C22×#145817692
C2×#191275882
C2×#191275852
#249057332
#249057322
#249057292
#249057082
#249057062
#249057002
#249056932
Dic83⋊#952
#249056852
C83×#14372
#1444883