Finite Group Databasebeta

← #35326558

Subgroups — #35326558

Order 21248.

1962 conjugacy classes of subgroups.

The subgroup lattice has 1042 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19127576C211yesmaximal, characteristic
2C2×#19127566C211yesmaximal, characteristic, complemented
3C2×C22⋊C4×Dic83C211yesmaximal, characteristic
4C22×C83⋊#95C211yesmaximal, characteristic
5#24905722C211yesmaximal, characteristic, complemented
6#24905722C211yesmaximal, characteristic, complemented
7#24905719C211yesmaximal, characteristic, complemented
8#24905719C211yesmaximal, characteristic, complemented
9#24905692C211yesmaximal, characteristic, complemented
10#24905689C211yesmaximal, characteristic, complemented
11#24905689C211yesmaximal, characteristic, complemented
12#24905686C211yesmaximal, characteristic
13#24905685C211yesmaximal, characteristic
14#24905685C211yesmaximal, characteristic
15C2×#385×C83C211yesmaximal, characteristic
16C24×Dic83C2211yescharacteristic
17C24×Dic83C2211yescharacteristic
18C22×C4⋊Dic83C2211yescharacteristic
19C22×C4⋊Dic83C2211yescharacteristic
20C22×C22⋊Dic83C2211yescharacteristic
21C22×C22⋊Dic83C2211yescharacteristic
22C22×C4×Dic83C2211yescharacteristic
23C22×C4×Dic83C2211yescharacteristic
24#19127576—24no—
25#19127566—24no—
26C22⋊C4×Dic83C418yescomplemented
27C2×C83⋊#95—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
46C2×C83⋊#95C2211yescharacteristic
47C2×C83⋊#95C2211yescharacteristic
48C24×C4×C83C2211yescharacteristic
49C22×C4⋊C4×C83C2211yescharacteristic
50C22×C4⋊C4×C83C2211yescharacteristic
51C22×C22⋊C4×C83C2211yescharacteristic
52C22×C22⋊C4×C83C2211yescharacteristic
53#385×C83—24no—
54C2×#95×C83C2211yescharacteristic
55C2×#95×C83C2211yescharacteristic
56C23×Dic83—22no—
57C23×Dic83—22no—
58C23×Dic83—22no—
59C23×Dic83—22no—
60C23×Dic83—22no—
61C23×Dic83—22no—
62C23×Dic83—22no—
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
78C2×C4⋊Dic83—22no—
79C2×C4⋊Dic83—22no—
80C2×C4⋊Dic83—22no—
81C2×C4⋊Dic83—22no—
82C2×C4⋊Dic83—41no—
83C2×C4⋊Dic83—41no—
84C2×C22⋊Dic83—22no—
85C2×C22⋊Dic83—22no—
86C2×C22⋊Dic83—22no—
87C2×C22⋊Dic83—22no—
88C2×C22⋊Dic83—22no—
89C2×C22⋊Dic83C2×C414yes—
90C2×C4×Dic83—22no—
91C2×C4×Dic83—22no—
92C2×C4×Dic83—41no—
93C2×C4×Dic83—41no—
94C2×C4×Dic83C2×C414yescomplemented
95C2×C4×Dic83C2×C414yescomplemented
96C83⋊#95—22no—
97C83⋊#95—22no—
98C83⋊#95—22no—
99C83⋊#95—22no—
100C83⋊#95—22no—
101C83⋊#95—22no—
102C83⋊#95—22no—
103C83⋊#95—22no—
104C83⋊#95—22no—
105C83⋊#95—22no—
106C83⋊#95—22no—
107C83⋊#95—41no—
108C83⋊#95—41no—
109C83⋊#95—41no—
110C83⋊#95—41no—
111C83⋊#95—41no—
112C83⋊#95—41no—
113C83⋊#95C2×C414yescomplemented
114C83⋊#95C2×C414yescomplemented
115C83⋊#95D414yes—
116C25×C83C2311yescharacteristic
117C23×C4×C83—22no—
118C23×C4×C83—22no—
119C23×C4×C83—22no—
120C23×C4×C83—22no—
121C23×C4×C83—22no—
122C23×C4×C83—41no—
123C23×C4×C83—41no—
124C23×C4×C83C2311yescharacteristic
125C23×C4×C83C2311yescharacteristic
126C23×C4×C83C2311yescharacteristic
127C23×C4×C83C2311yescharacteristic
128C23×C4×C83C2311yescharacteristic
129C23×C4×C83C2311yescharacteristic
130C2×C4⋊C4×C83—22no—
131C2×C4⋊C4×C83—22no—
132C2×C4⋊C4×C83—22no—
133C2×C4⋊C4×C83—22no—
134C2×C4⋊C4×C83—41no—
135C2×C4⋊C4×C83—41no—
136C2×C22⋊C4×C83—22no—
137C2×C22⋊C4×C83—22no—
138C2×C22⋊C4×C83—22no—
139C2×C22⋊C4×C83C2×C414yes—
140C2×C22⋊C4×C83D414yes—
141C2×C22⋊C4×C83Q814yes—
142#95×C83—22no—
143#95×C83—22no—
144C22×Dic83—21no—
145C22×Dic83—21no—
146C22×Dic83—21no—
147C22×Dic83—21no—
148C22×Dic83—28no—
149C22×Dic83—28no—
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×Dic83—28no—
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—44no—
196C22×Dic83—44no—
197C22×Dic83—44no—
198C22×Dic83—44no—
199C22×Dic83—44no—
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×Dic83#4112yes—
213C22×Dic83#4112yes—
214C4⋊Dic83—44no—
215C4⋊Dic83—44no—
216C22⋊Dic83—28no—
217C22⋊Dic83—44no—
218C4×Dic83—28no—
219C4×Dic83—44no—
220C24×C83—21no—
221C24×C83—21no—
222C24×C83—21no—
223C24×C83—21no—
224C24×C83—21no—
225C24×C83—21no—
226C24×C83—21no—
227C24×C83—21no—
228C24×C83C22×C412yes—
229C24×C83C2×D412yes—
230C24×C83C2×Q812yes—
231C24×C83#4112yes—
232C24×C83#4112yes—
233C24×C83#4112yes—
234C24×C83#4112yes—
235C24×C83C2411yescharacteristic
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—28no—
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—44no—
272C22×C4×C83—44no—
273C22×C4×C83—44no—
274C22×C4×C83—44no—
275C22×C4×C83—44no—
276C22×C4×C83—44no—
277C22×C4×C83C22×C412yes—
278C22×C4×C83C22×C412yes—
279C22×C4×C83C2×D412yes—
280C22×C4×C83C2×D412yes—
281C22×C4×C83C2×D412yes—
282C22×C4×C83C2×Q812yes—
283C22×C4×C83C2×Q812yes—
284C22×C4×C83#4112yes—
285C4⋊C4×C83—44no—
286C4⋊C4×C83—44no—
287C22⋊C4×C83—44no—
288C22⋊C4×C83C4⋊C4116yes—
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—22no—
305C23×C83—22no—
306C23×C83—22no—
307C23×C83—22no—
308C23×C83—22no—
309C23×C83—22no—
310C23×C83—22no—
311C23×C83—22no—
312C23×C83—22no—
313C23×C83—22no—
314C23×C83—22no—
315C23×C83—22no—
316C23×C83—22no—
317C23×C83C2×C4⋊C414yes—
318C23×C83#11714yes—
319C23×C83#11714yes—
320C23×C83#12414yes—
321C23×C83#12414yes—
322C23×C83#12514yes—
323C23×C83#12514yes—
324C23×C83C23×C411yescharacteristic
325C23×C83C22×D411yescharacteristic
326C23×C83C22×D411yescharacteristic
327C23×C83C22×Q811yescharacteristic
328C23×C83C2×#4111yescharacteristic
329C23×C83C2×#4111yescharacteristic
330C23×C83C2×#4111yescharacteristic
331C23×C83C2×#4111yescharacteristic
332C23×C83C2×#4111yescharacteristic
333C23×C83C2×#4111yescharacteristic
334C23×C83C2×#4111yescharacteristic
335C23×C83H(5,𝔽2)11yescharacteristic
336C23×C83H(5,𝔽2)11yescharacteristic
337C23×C83H(5,𝔽2)11yescharacteristic
338C23×C832−1+411yescharacteristic
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—22no—
355C2×C4×C83—22no—
356C2×C4×C83—22no—
357C2×C4×C83—416no—
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×C83—41no—
378C2×C4×C83—41no—
379C2×C4×C83—41no—
380C2×C4×C83C2×C4⋊C414yes—
381C2×C4×C83C2×C4⋊C414yes—
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—22no—
400C2×Dic83—22no—
401C2×Dic83—22no—
402C2×Dic83—22no—
403C2×Dic83—416no—
404C2×Dic83—416no—
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×Dic83—41no—
434C2×Dic83—41no—
435C2×Dic83—41no—
436C2×Dic83—41no—
437C2×Dic83—41no—
438C2×Dic83—41no—
439C2×Dic83C4×D414yes—
440C22×C83—24no—
441C22×C83—24no—
442C22×C83—24no—
443C22×C83—24no—
444C22×C83—24no—
445C22×C83—24no—
446C22×C83—24no—
447C22×C83—24no—
448C22×C83—24no—
449C22×C83—24no—
450C22×C83—24no—
451C22×C83—24no—
452C22×C83—24no—
453C22×C83—24no—
454C22×C83#38218yescomplemented
455C22×C83C22×C4⋊C411yescharacteristic
456C22×C83C2×#11711yescharacteristic
457C22×C83C2×#11711yescharacteristic
458C22×C83C2×C4×D411yescharacteristic
459C22×C83C4×#4111yescharacteristic
460C22×C83#51811yescharacteristic
461C22×C83#52011yescharacteristic
462C22×C83#52511yescharacteristic
463C22×C83#52511yescharacteristic
464C22×C83C2×#12411yescharacteristic
465C22×C83C2×#12411yescharacteristic
466C22×C83C2×#12511yescharacteristic
467C22×C83C2×#12511yescharacteristic
468C22×C83#52911yescharacteristic
469C22×C83#52911yescharacteristic
470C22×C83#53811yescharacteristic
471C22×C83#53811yescharacteristic
472C22×C83#53911yescharacteristic
473C22×C83#53911yescharacteristic
474C22×C83D4211yescharacteristic
475C22×C83#54611yescharacteristic
476C22×C83#54611yescharacteristic
477C22×C83#54611yescharacteristic
478C22×C83#54611yescharacteristic
479C22×C83#54711yescharacteristic
480C22×C83D4×Q811yescharacteristic
481C22×C83#55111yescharacteristic
482C22×C83#55111yescharacteristic
483C22×C83#55111yescharacteristic
484C22×C83#55111yescharacteristic
485C22×C83#55211yescharacteristic
486C22×C83#55211yescharacteristic
487C22×C83#55411yescharacteristic
488C22×C83#55411yescharacteristic
489C22×C83#55411yescharacteristic
490C4×C83—24no—
491C4×C83—24no—
492C4×C83—42no—
493C4×C83—42no—
494C4×C83—81no—
495C4×C83—81no—
496Dic83—24no—
497Dic83—42no—
498Dic83—42no—
499Dic83—42no—
500Dic83—42no—
501Dic83—42no—
502Dic83—81no—
503Dic83—81no—
504#13896—831nomaximal, Sylow
505C2×C83—28no—
506C2×C83C2×#38211yescharacteristic
507C2×C83#229011yescharacteristic
508C2×C83#231811yescharacteristic
509C2×C83#234211yescharacteristic
510C2×C83#234311yescharacteristic
511C2×C83D4×C4⋊C411yescharacteristic
512C2×C83#234911yescharacteristic
513C2×C83#247211yescharacteristic
514C2×C83#247211yescharacteristic
515C2×C83#247311yescharacteristic
516C2×C83#247311yescharacteristic
517C2×C83#248811yescharacteristic
518C2×C83#248811yescharacteristic
519C2×C83#250511yescharacteristic
520C2×C83#250511yescharacteristic
521C2×#385—831no—
522C2×#385D8311yescharacteristic
523C2×#382—831no—
524C2×C4×C22⋊C4—831no—
525C22×#95—831no—
526#1442—831no—
527#1442—831no—
528#1442—831no—
529#1442—831no—
530C4⋊#95—831no—
531#1434—831no—
532#1434—831no—
533C22⋊#95—831no—
534C22⋊#95—831no—
535C22⋊#95—831no—
536C83#1389611yescharacteristic, complemented, Sylow
537C24×C4—831no—
538C24×C4—831no—
539C24×C4C2×D8311yescharacteristic
540C22×C4⋊C4—831no—
541C22×C4⋊C4—831no—
542C22×C4⋊C4C2×D8311yescharacteristic
543C22×C4⋊C4C2×D8311yescharacteristic
544C22×C22⋊C4—831no—
545C22×C22⋊C4—831no—
546C22×C22⋊C4C2×D8311yescharacteristic
547C22×C22⋊C4C2×D8311yescharacteristic
548C22×C42—831no—
549C22×C42—831no—
550#385—24no—
551#385—1664no—
552#382—1664no—
553C4×C22⋊C4—838no—
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×#95—831no—
571C2×#95—831no—
572C2×#95—831no—
573C2×#95—831no—
574C2×#95—1664no—
575C2×#95C2×D8311yescharacteristic
576C2×#95C2×D8311yescharacteristic
577C25C22×D8311yescharacteristic
578C23×C4—22no—
579C23×C4—22no—
580C23×C4—22no—
581C23×C4—22no—
582C23×C4—22no—
583C23×C4—41no—
584C23×C4—41no—
585C23×C4—3321no—
586C23×C4—3321no—
587C23×C4—3321no—
588C23×C4—3321no—
589C23×C4—834no—
590C23×C4—831no—
591C23×C4—831no—
592C23×C4—831no—
593C23×C4—831no—
594C23×C4—831no—
595C23×C4—831no—
596C23×C4—831no—
597C23×C4—831no—
598C23×C4—1662no—
599C23×C4—1662no—
600C23×C4—1662no—
601C23×C4—1662no—
602C23×C4—1662no—
603C23×C4—1662no—
604C23×C4—1662no—
605C23×C4—1662no—
606C23×C4—1662no—
607C23×C4C22×D8311yescharacteristic
608C23×C4C22×D8311yescharacteristic
609C23×C4C22×D8311yescharacteristic
610C23×C4C22×D8311yescharacteristic
611C23×C4C22×D8311yescharacteristic
612C23×C4C22×D8311yescharacteristic
613C2×C4⋊C4—22no—
614C2×C4⋊C4—22no—
615C2×C4⋊C4—22no—
616C2×C4⋊C4—22no—
617C2×C4⋊C4—41no—
618C2×C4⋊C4—41no—
619C2×C4⋊C4—3321no—
620C2×C4⋊C4—3321no—
621C2×C4⋊C4—1662no—
622C2×C4⋊C4—1662no—
623C2×C4⋊C4—1662no—
624C2×C4⋊C4—1662no—
625C2×C22⋊C4—22no—
626C2×C22⋊C4—22no—
627C2×C22⋊C4—22no—
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⋊C4Dic16614yes—
635C2×C22⋊C4C4×D8314yes—
636C2×C22⋊C4C22⋊D8314yes—
637C2×C42—3321no—
638C2×C42—3321no—
639C2×C42—834no—
640C2×C42—834no—
641C2×C42—1662no—
642C2×C42—1662no—
643#95—22no—
644#95—22no—
645#95—3321no—
646#95—3321no—
647#95—3321no—
648#95—3321no—
649#95—3321no—
650#95—3321no—
651#95—834no—
652#95—834no—
653#95—834no—
654#95—1662no—
655#95—1662no—
656#95—1662no—
657#95—1662no—
658#95—1662no—
659#95—1662no—
660#95—1662no—
661#95—1662no—
662#95—1662no—
663#95—1662no—
664#95—1662no—
665C24—21no—
666C24—21no—
667C24—21no—
668C24—21no—
669C24—21no—
670C24—21no—
671C24—21no—
672C24—21no—
673C24C2×C4×D8312yes—
674C24C2×C22⋊D8312yes—
675C24C2×Dic16612yes—
676C24#1305058912yes—
677C24#1305058912yes—
678C24#1305059112yes—
679C24#1305059112yes—
680C24C23×D8311yescharacteristic
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—28no—
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—44no—
717C22×C4—44no—
718C22×C4—44no—
719C22×C4—44no—
720C22×C4—44no—
721C22×C4—44no—
722C22×C4—3324no—
723C22×C4—3324no—
724C22×C4—3324no—
725C22×C4—3324no—
726C22×C4—3324no—
727C22×C4—3324no—
728C22×C4—3324no—
729C22×C4—3324no—
730C22×C4—3324no—
731C22×C4—3324no—
732C22×C4—3324no—
733C22×C4—832no—
734C22×C4—832no—
735C22×C4—832no—
736C22×C4—832no—
737C22×C4—832no—
738C22×C4—832no—
739C22×C4—832no—
740C22×C4—832no—
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—1668no—
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×C4—1661no—
784C22×C4—1661no—
785C22×C4—1661no—
786C22×C4—1661no—
787C22×C4—1668no—
788C22×C4—1661no—
789C22×C4—1661no—
790C22×C4—1661no—
791C22×C4—1661no—
792C22×C4C2×C4×D8312yes—
793C22×C4C2×C4×D8312yes—
794C22×C4D4×D8312yes—
795C22×C4C2×C22⋊D8312yes—
796C22×C4C2×C22⋊D8312yes—
797C22×C4C2×Dic16612yes—
798C22×C4C2×Dic16612yes—
799C22×C4#1305058912yes—
800C4⋊C4—44no—
801C4⋊C4—44no—
802C4⋊C4—3324no—
803C4⋊C4—3324no—
804C22⋊C4—44no—
805C22⋊C4—3324no—
806C22⋊C4—1668no—
807C22⋊C4Dic83⋊C4116yes—
808C42—3324no—
809C42—1668no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—22no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—22no—
821C23—22no—
822C23—22no—
823C23—22no—
824C23—22no—
825C23—22no—
826C23—22no—
827C23—22no—
828C23—22no—
829C23—22no—
830C23—22no—
831C23—22no—
832C23—22no—
833C23—22no—
834C23—22no—
835C23—22no—
836C23—22no—
837C23—22no—
838C23C2×Dic83⋊C414yes—
839C23#1458175014yes—
840C23#1458175014yes—
841C23#1458177914yes—
842C23#1458178114yes—
843C23#1458178314yes—
844C23#1458178314yes—
845C23C22×C4×D8311yescharacteristic
846C23C2×D4×D8311yescharacteristic
847C23C22×C22⋊D8311yescharacteristic
848C23C22×Dic16611yescharacteristic
849C23#41×D8311yescharacteristic
850C23#41×D8311yescharacteristic
851C23C2×#1305058911yescharacteristic
852C23C2×#1305058911yescharacteristic
853C23C2×#1305058911yescharacteristic
854C23C2×#1305059111yescharacteristic
855C23C2×#1305059111yescharacteristic
856C23#1458183711yescharacteristic
857C23#1458183711yescharacteristic
858C23#1458183811yescharacteristic
859C23#1458183911yescharacteristic
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—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—416no—
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—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—33216no—
902C2×C4—3321no—
903C2×C4—3321no—
904C2×C4—3321no—
905C2×C4—3321no—
906C2×C4—3321no—
907C2×C4—3321no—
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—33216no—
923C2×C4—3321no—
924C2×C4—3321no—
925C2×C4—3321no—
926C2×C4—3321no—
927C2×C4—3321no—
928C2×C4—3321no—
929C2×C4—3321no—
930C2×C4—3321no—
931C2×C4—3321no—
932C2×C4—3321no—
933C2×C4—3321no—
934C2×C4—3321no—
935C2×C4—3321no—
936C2×C4—3321no—
937C2×C4—834no—
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×C4—1662no—
953C2×C4—1662no—
954C2×C4—1662no—
955C2×C4—1662no—
956C2×C4—1662no—
957C2×C4—1662no—
958C2×C4—1662no—
959C2×C4C2×Dic83⋊C414yes—
960C2×C4C2×Dic83⋊C414yes—
961C22—24no—
962C22—24no—
963C22—24no—
964C22—24no—
965C22—24no—
966C22—24no—
967C22—24no—
968C22—24no—
969C22—24no—
970C22—24no—
971C22—24no—
972C22—24no—
973C22—24no—
974C22—24no—
975C22#1912756618yescomplemented
976C22C22×Dic83⋊C411yescharacteristic
977C22C2×#1458175011yescharacteristic
978C22C2×#1458175011yescharacteristic
979C22C4×D4×D8311yescharacteristic
980C22C4×#1305058911yescharacteristic
981C22#1912817311yescharacteristic
982C22#1912818011yescharacteristic
983C22#1912820711yescharacteristic
984C22#1912821411yescharacteristic
985C22C2×#1458177911yescharacteristic
986C22C2×#1458178111yescharacteristic
987C22C2×#1458178311yescharacteristic
988C22C2×#1458178311yescharacteristic
989C22#1912822811yescharacteristic
990C22#1912823711yescharacteristic
991C22#1912828611yescharacteristic
992C22#1912829111yescharacteristic
993C22#1912829511yescharacteristic
994C22#1912830011yescharacteristic
995C22D4×C22⋊D8311yescharacteristic
996C22#1912833811yescharacteristic
997C22#1912833911yescharacteristic
998C22#1912834211yescharacteristic
999C22#1912834511yescharacteristic
1000C22#1912835011yescharacteristic
1001C22D4×Dic16611yescharacteristic
1002C22#1912837411yescharacteristic
1003C22#1912837811yescharacteristic
1004C22#1912837811yescharacteristic
1005C22#1912838211yescharacteristic
1006C22#1912838811yescharacteristic
1007C22#1912839311yescharacteristic
1008C22#1912840811yescharacteristic
1009C22#1912841011yescharacteristic
1010C22#1912841011yescharacteristic
1011C4—24no—
1012C4—24no—
1013C4—42no—
1014C4—42no—
1015C4—81no—
1016C4—81no—
1017C4—3322no—
1018C4—3322no—
1019C4—3322no—
1020C4—3322no—
1021C4—3322no—
1022C4—6641no—
1023C4—6641no—
1024C4—1664no—
1025C2—28no—
1026C2C2×#1912756611yescharacteristic
1027C2#2490989911yescharacteristic
1028C2#2491009111yescharacteristic
1029C2#2491031011yescharacteristic
1030C2#2491032111yescharacteristic
1031C2D4×Dic83⋊C411yescharacteristic
1032C2#2491036811yescharacteristic
1033C2#2491158811yescharacteristic
1034C2#2491159611yescharacteristic
1035C2#2491160311yescharacteristic
1036C2#2491161111yescharacteristic
1037C2#2491179311yescharacteristic
1038C2#2491179511yescharacteristic
1039C2#2491196811yescharacteristic
1040C2#2491197011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D83
commutatorC23×C83C23×C4
FittingC2×#385×C83C2
socle, cosocleC24×C83C24
prime radicalC25×C83C23
hypercenterC2×#385D83
hypocenterC83#13896
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
2. C2×#19127566C2semidirect
5. #24905722C2semidirect
6. #24905722C2semidirect
7. #24905719C2semidirect
8. #24905719C2semidirect
9. #24905692C2semidirect
10. #24905689C2semidirect
11. #24905689C2semidirect
26. C22⋊C4×Dic83C4semidirect
94. C2×C4×Dic83C2×C4semidirect
95. C2×C4×Dic83C2×C4semidirect
113. C83⋊#95C2×C4semidirect
114. C83⋊#95C2×C4semidirect
454. C22×C83#382semidirect
536. C83#13896semidirect
975. C22#19127566semidirect

Maximal subgroups

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

subgroupindex
C2×#191275762
C2×#191275662
C2×C22⋊C4×Dic832
C22×C83⋊#952
#249057222
#249057192
#249056922
#249056892
#249056862
#249056852
C2×#385×C832
#1389683