Finite Group Databasebeta

← C83×#16552 #35244376

Subgroups — C83×#16552 #35244376

Order 21248.

1998 conjugacy classes of subgroups.

The subgroup lattice has 1308 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#397×C83C211yesmaximal, characteristic, complemented
2C2×#396×C83C211yesmaximal, characteristic, complemented
3C2×#394×C83C211yesmaximal, characteristic, complemented
4C2×#394×C83C211yesmaximal, characteristic, complemented
5C2×#392×C83C211yesmaximal, characteristic
6C2×#390×C83C211yesmaximal, characteristic, complemented
7C83×#1441C211yesmaximal, characteristic, complemented
8C83×#1440C211yesmaximal, characteristic, complemented
9C83×#1439C211yesmaximal, characteristic, complemented
10C83×#1439C211yesmaximal, characteristic, complemented
11C83×#1438C211yesmaximal, characteristic, complemented
12C83×#1438C211yesmaximal, characteristic, complemented
13C83×#1438C211yesmaximal, characteristic, complemented
14C83×#1437C211yesmaximal, characteristic, complemented
15C83×#1436C211yesmaximal, characteristic, complemented
16C23×D4×C83C2211yescharacteristic
17C23×D4×C83C2211yescharacteristic
18C23×D4×C83C2211yescharacteristic
19C22×C4⋊C4×C83C2211yescharacteristic
20C22×C4⋊C4×C83C2211yescharacteristic
21C22×C4⋊C4×C83C2211yescharacteristic
22C22×C4⋊C4×C83C2211yescharacteristic
23C22×C22⋊C4×C83C2211yescharacteristic
24C22×C22⋊C4×C83C2211yescharacteristic
25C22×C22⋊C4×C83C2211yescharacteristic
26C22×C22⋊C4×C83C2211yescharacteristic
27C22×C22⋊C4×C83C2211yescharacteristic
28C22×C22⋊C4×C83C2211yescharacteristic
29C22×C22⋊C4×C83C2211yescharacteristic
30C22×C22⋊C4×C83C2211yescharacteristic
31C22×C22⋊C4×C83C2211yescharacteristic
32C22×C22⋊C4×C83C2211yescharacteristic
33C22×C22⋊C4×C83C2211yescharacteristic
34C22×C22⋊C4×C83C2211yescharacteristic
35C22×C22⋊C4×C83C2211yescharacteristic
36C22×C22⋊C4×C83C2211yescharacteristic
37C22×C22⋊C4×C83C2211yescharacteristic
38C22×C42×C83C2211yescharacteristic
39#397×C83—24no—
40#396×C83—24no—
41#394×C83—24no—
42#394×C83—24no—
43#392×C83—24no—
44#390×C83—24no—
45C2×#95×C83C2211yescharacteristic
46C2×#95×C83C2211yescharacteristic
47C2×#95×C83C2211yescharacteristic
48C2×#95×C83C2211yescharacteristic
49C2×#95×C83C2211yescharacteristic
50C2×#95×C83C2211yescharacteristic
51C2×#95×C83C2211yescharacteristic
52C2×#95×C83C2211yescharacteristic
53C2×#95×C83C2211yescharacteristic
54C2×#95×C83C2211yescharacteristic
55C2×#95×C83C2211yescharacteristic
56C2×#95×C83C2211yescharacteristic
57C25×C83C2311yescharacteristic
58C25×C83C2311yescharacteristic
59C25×C83C2311yescharacteristic
60C22×D4×C83—22no—
61C22×D4×C83—22no—
62C22×D4×C83—22no—
63C22×D4×C83—22no—
64C22×D4×C83—22no—
65C22×D4×C83—22no—
66C22×D4×C83—22no—
67C22×D4×C83—22no—
68C22×D4×C83—41no—
69C22×D4×C83—41no—
70C22×D4×C83—41no—
71C22×D4×C83—41no—
72C22×D4×C83—41no—
73C22×D4×C83—41no—
74C22×D4×C83—41no—
75C22×D4×C83—41no—
76C22×D4×C83—41no—
77C22×D4×C83—41no—
78C22×D4×C83—41no—
79C22×D4×C83—41no—
80C22×D4×C83D414yes—
81C23×C4×C83C2311yescharacteristic
82C23×C4×C83C2311yescharacteristic
83C23×C4×C83C2311yescharacteristic
84C23×C4×C83C2311yescharacteristic
85C23×C4×C83C2311yescharacteristic
86C23×C4×C83C2311yescharacteristic
87C23×C4×C83C2311yescharacteristic
88C23×C4×C83C2311yescharacteristic
89C23×C4×C83C2311yescharacteristic
90C23×C4×C83C2311yescharacteristic
91C23×C4×C83C2311yescharacteristic
92C23×C4×C83C2311yescharacteristic
93C2×C4⋊C4×C83—22no—
94C2×C4⋊C4×C83—22no—
95C2×C4⋊C4×C83—22no—
96C2×C4⋊C4×C83—22no—
97C2×C4⋊C4×C83—22no—
98C2×C4⋊C4×C83—22no—
99C2×C4⋊C4×C83—41no—
100C2×C4⋊C4×C83—41no—
101C2×C4⋊C4×C83—41no—
102C2×C4⋊C4×C83—41no—
103C2×C4⋊C4×C83—41no—
104C2×C4⋊C4×C83D414yescomplemented
105C2×C22⋊C4×C83—22no—
106C2×C22⋊C4×C83—22no—
107C2×C22⋊C4×C83—22no—
108C2×C22⋊C4×C83—22no—
109C2×C22⋊C4×C83—22no—
110C2×C22⋊C4×C83—22no—
111C2×C22⋊C4×C83—22no—
112C2×C22⋊C4×C83—22no—
113C2×C22⋊C4×C83—22no—
114C2×C22⋊C4×C83—22no—
115C2×C22⋊C4×C83—22no—
116C2×C22⋊C4×C83—22no—
117C2×C22⋊C4×C83—22no—
118C2×C22⋊C4×C83—22no—
119C2×C22⋊C4×C83—22no—
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—22no—
127C2×C22⋊C4×C83—22no—
128C2×C22⋊C4×C83—22no—
129C2×C22⋊C4×C83—22no—
130C2×C22⋊C4×C83—22no—
131C2×C22⋊C4×C83—22no—
132C2×C22⋊C4×C83—41no—
133C2×C22⋊C4×C83—41no—
134C2×C22⋊C4×C83—41no—
135C2×C22⋊C4×C83—41no—
136C2×C22⋊C4×C83—41no—
137C2×C22⋊C4×C83—41no—
138C2×C22⋊C4×C83—41no—
139C2×C22⋊C4×C83—41no—
140C2×C22⋊C4×C83—41no—
141C2×C22⋊C4×C83—41no—
142C2×C22⋊C4×C83—41no—
143C2×C22⋊C4×C83—41no—
144C2×C22⋊C4×C83—41no—
145C2×C22⋊C4×C83—41no—
146C2×C22⋊C4×C83—41no—
147C2×C22⋊C4×C83—41no—
148C2×C22⋊C4×C83—41no—
149C2×C22⋊C4×C83—41no—
150C2×C42×C83—22no—
151C2×C42×C83—41no—
152C2×C42×C83—41no—
153#95×C83—22no—
154#95×C83—22no—
155#95×C83—22no—
156#95×C83—22no—
157#95×C83—22no—
158#95×C83—22no—
159#95×C83—41no—
160#95×C83—41no—
161#95×C83—41no—
162#95×C83—41no—
163#95×C83—41no—
164#95×C83D414yescomplemented
165C24×C83—21no—
166C24×C83—21no—
167C24×C83—21no—
168C24×C83—21no—
169C24×C83—21no—
170C24×C83—21no—
171C24×C83—21no—
172C24×C83—21no—
173C24×C83—21no—
174C24×C83—21no—
175C24×C83—21no—
176C24×C83—21no—
177C24×C83—21no—
178C24×C83—21no—
179C24×C83—21no—
180C24×C83—21no—
181C24×C83—21no—
182C24×C83—21no—
183C24×C83—21no—
184C24×C83—21no—
185C24×C83—21no—
186C24×C83—21no—
187C24×C83—21no—
188C24×C83—21no—
189C24×C83—21no—
190C24×C83—21no—
191C24×C83—21no—
192C24×C83—21no—
193C24×C83—21no—
194C24×C83—21no—
195C24×C83—21no—
196C24×C83—21no—
197C24×C83—21no—
198C24×C83—21no—
199C24×C83—21no—
200C24×C83—21no—
201C24×C83—21no—
202C24×C83—21no—
203C24×C83—21no—
204C24×C83—21no—
205C24×C83—21no—
206C24×C83—21no—
207C24×C83C2×D412yes—
208C24×C83C2×D412yes—
209C24×C83#4112yes—
210C24×C83C2411yescharacteristic
211C2×D4×C83—28no—
212C2×D4×C83—44no—
213C2×D4×C83—44no—
214C2×D4×C83—44no—
215C2×D4×C83—44no—
216C2×D4×C83—44no—
217C2×D4×C83—44no—
218C2×D4×C83—44no—
219C2×D4×C83—44no—
220C2×D4×C83—44no—
221C2×D4×C83—44no—
222C2×D4×C83—44no—
223C2×D4×C83—44no—
224C2×D4×C83—44no—
225C2×D4×C83—44no—
226C2×D4×C83—44no—
227C2×D4×C83—44no—
228C2×D4×C83—44no—
229C2×D4×C83—44no—
230C2×D4×C83—44no—
231C2×D4×C83—44no—
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×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×C83—21no—
276C22×C4×C83—21no—
277C22×C4×C83—21no—
278C22×C4×C83—21no—
279C22×C4×C83—21no—
280C22×C4×C83—21no—
281C22×C4×C83—21no—
282C22×C4×C83—21no—
283C22×C4×C83—21no—
284C22×C4×C83—21no—
285C22×C4×C83—21no—
286C22×C4×C83—21no—
287C22×C4×C83—21no—
288C22×C4×C83—21no—
289C22×C4×C83—21no—
290C22×C4×C83—21no—
291C22×C4×C83—21no—
292C22×C4×C83—21no—
293C22×C4×C83—21no—
294C22×C4×C83—21no—
295C22×C4×C83—21no—
296C22×C4×C83—21no—
297C22×C4×C83—21no—
298C22×C4×C83—21no—
299C22×C4×C83—21no—
300C22×C4×C83—21no—
301C22×C4×C83—21no—
302C22×C4×C83—21no—
303C22×C4×C83—21no—
304C22×C4×C83—21no—
305C22×C4×C83—21no—
306C22×C4×C83C2×D412yes—
307C22×C4×C83C2×D412yes—
308C22×C4×C83C2×D412yes—
309C22×C4×C83C2×D412yes—
310C22×C4×C83C2×D412yes—
311C22×C4×C83C2×D412yes—
312C22×C4×C83C2×D412yes—
313C22×C4×C83#4112yes—
314C22×C4×C83#4112yes—
315C22×C4×C83#4112yes—
316C4⋊C4×C83—44no—
317C4⋊C4×C83—44no—
318C4⋊C4×C83—44no—
319C4⋊C4×C83—44no—
320C22⋊C4×C83—44no—
321C22⋊C4×C83—44no—
322C22⋊C4×C83—44no—
323C22⋊C4×C83—44no—
324C22⋊C4×C83—44no—
325C22⋊C4×C83—44no—
326C22⋊C4×C83—44no—
327C22⋊C4×C83—44no—
328C22⋊C4×C83—44no—
329C22⋊C4×C83—44no—
330C22⋊C4×C83—44no—
331C22⋊C4×C83—44no—
332C22⋊C4×C83—44no—
333C22⋊C4×C83—44no—
334C22⋊C4×C83—44no—
335C42×C83—44no—
336C23×C83—22no—
337C23×C83—22no—
338C23×C83—22no—
339C23×C83—22no—
340C23×C83—22no—
341C23×C83—22no—
342C23×C83—22no—
343C23×C83—22no—
344C23×C83—22no—
345C23×C83—22no—
346C23×C83—22no—
347C23×C83—22no—
348C23×C83—22no—
349C23×C83—22no—
350C23×C83—22no—
351C23×C83—22no—
352C23×C83—22no—
353C23×C83—22no—
354C23×C83—22no—
355C23×C83—22no—
356C23×C83—22no—
357C23×C83—41no—
358C23×C83—41no—
359C23×C83—41no—
360C23×C83—41no—
361C23×C83—41no—
362C23×C83—41no—
363C23×C83—41no—
364C23×C83—41no—
365C23×C83—41no—
366C23×C83—41no—
367C23×C83—41no—
368C23×C83—41no—
369C23×C83—41no—
370C23×C83—41no—
371C23×C83—41no—
372C23×C83—41no—
373C23×C83—41no—
374C23×C83—41no—
375C23×C83—41no—
376C23×C83—41no—
377C23×C83—41no—
378C23×C83—41no—
379C23×C83—41no—
380C23×C83—41no—
381C23×C83—41no—
382C23×C83—41no—
383C23×C83—41no—
384C23×C83—41no—
385C23×C83—41no—
386C23×C83—41no—
387C23×C83—41no—
388C23×C83—41no—
389C23×C83—41no—
390C23×C83—41no—
391C23×C83—41no—
392C23×C83—41no—
393C23×C83—41no—
394C23×C83—41no—
395C23×C83—41no—
396C23×C83—41no—
397C23×C83—41no—
398C23×C83—41no—
399C23×C83—41no—
400C23×C83—41no—
401C23×C83—41no—
402C23×C83—41no—
403C23×C83—41no—
404C23×C83—41no—
405C23×C83—41no—
406C23×C83—41no—
407C23×C83—41no—
408C23×C83—41no—
409C23×C83—41no—
410C23×C83—41no—
411C23×C83—41no—
412C23×C83—41no—
413C23×C83—41no—
414C23×C83—41no—
415C23×C83—41no—
416C23×C83—41no—
417C23×C83—41no—
418C23×C83—41no—
419C23×C83—41no—
420C23×C83—41no—
421C23×C83—41no—
422C23×C83—41no—
423C23×C83—41no—
424C23×C83—41no—
425C23×C83—41no—
426C23×C83—41no—
427C23×C83—41no—
428C23×C83—41no—
429C23×C83—41no—
430C23×C83—41no—
431C23×C83—41no—
432C23×C83—41no—
433C23×C83—41no—
434C23×C83—41no—
435C23×C83—41no—
436C23×C83—41no—
437C23×C83—41no—
438C23×C83—41no—
439C23×C83—41no—
440C23×C83—41no—
441C23×C83C22×D411yescharacteristic
442C23×C83C22×D411yescharacteristic
443C23×C83C22×D411yescharacteristic
444C23×C83C2×#4111yescharacteristic
445C23×C83C2×#4111yescharacteristic
446C23×C83C2×#4111yescharacteristic
447C23×C83C2×#4111yescharacteristic
448C23×C83H(5,𝔽2)11yescharacteristic
449C23×C83H(5,𝔽2)11yescharacteristic
450C23×C83H(5,𝔽2)11yescharacteristic
451C23×C83H(5,𝔽2)11yescharacteristic
452C23×C83H(5,𝔽2)11yescharacteristic
453C23×C83H(5,𝔽2)11yescharacteristic
454C23×C83H(5,𝔽2)11yescharacteristic
455C23×C832−1+411yescharacteristic
456D4×C83—416no—
457D4×C83—416no—
458D4×C83—416no—
459C2×C4×C83—22no—
460C2×C4×C83—22no—
461C2×C4×C83—22no—
462C2×C4×C83—22no—
463C2×C4×C83—22no—
464C2×C4×C83—22no—
465C2×C4×C83—22no—
466C2×C4×C83—22no—
467C2×C4×C83—22no—
468C2×C4×C83—22no—
469C2×C4×C83—22no—
470C2×C4×C83—22no—
471C2×C4×C83—22no—
472C2×C4×C83—22no—
473C2×C4×C83—22no—
474C2×C4×C83—22no—
475C2×C4×C83—22no—
476C2×C4×C83—22no—
477C2×C4×C83—22no—
478C2×C4×C83—22no—
479C2×C4×C83—22no—
480C2×C4×C83—22no—
481C2×C4×C83—22no—
482C2×C4×C83—22no—
483C2×C4×C83—22no—
484C2×C4×C83—22no—
485C2×C4×C83—22no—
486C2×C4×C83—41no—
487C2×C4×C83—41no—
488C2×C4×C83—41no—
489C2×C4×C83—41no—
490C2×C4×C83—41no—
491C2×C4×C83—41no—
492C2×C4×C83—41no—
493C2×C4×C83—41no—
494C2×C4×C83—41no—
495C2×C4×C83—41no—
496C2×C4×C83—41no—
497C2×C4×C83—41no—
498C2×C4×C83—41no—
499C2×C4×C83—41no—
500C2×C4×C83—41no—
501C2×C4×C83—41no—
502C2×C4×C83—41no—
503C2×C4×C83—41no—
504C2×C4×C83—41no—
505C2×C4×C83—41no—
506C2×C4×C83—41no—
507C2×C4×C83—41no—
508C2×C4×C83—41no—
509C2×C4×C83—41no—
510C2×C4×C83—41no—
511C2×C4×C83—41no—
512C2×C4×C83—41no—
513C2×C4×C83—41no—
514C2×C4×C83—41no—
515C2×C4×C83—41no—
516C2×C4×C83—41no—
517C2×C4×C83—41no—
518C2×C4×C83—41no—
519C2×C4×C83—41no—
520C2×C4×C83—41no—
521C2×C4×C83—41no—
522C2×C4×C83—41no—
523C2×C4×C83—41no—
524C2×C4×C83—41no—
525C2×C4×C83—41no—
526C2×C4×C83—41no—
527C2×C4×C83—41no—
528C2×C4×C83—41no—
529C2×C4×C83—41no—
530C2×C4×C83—41no—
531C2×C4×C83—41no—
532C2×C4×C83—41no—
533C2×C4×C83—41no—
534C2×C4×C83—41no—
535C2×C4×C83—41no—
536C2×C4×C83—41no—
537C2×C4×C83—41no—
538C2×C4×C83—41no—
539C2×C4×C83—41no—
540C2×C4×C83—41no—
541C2×C4×C83—41no—
542C2×C4×C83#12114yes—
543C22×C83—42no—
544C22×C83—42no—
545C22×C83—42no—
546C22×C83—42no—
547C22×C83—42no—
548C22×C83—42no—
549C22×C83—42no—
550C22×C83—42no—
551C22×C83—42no—
552C22×C83—42no—
553C22×C83—42no—
554C22×C83—42no—
555C22×C83—42no—
556C22×C83—42no—
557C22×C83—42no—
558C22×C83—42no—
559C22×C83—42no—
560C22×C83—42no—
561C22×C83—42no—
562C22×C83—42no—
563C22×C83—42no—
564C22×C83—81no—
565C22×C83—81no—
566C22×C83—81no—
567C22×C83—81no—
568C22×C83—81no—
569C22×C83—81no—
570C22×C83—81no—
571C22×C83—81no—
572C22×C83—81no—
573C22×C83—81no—
574C22×C83—81no—
575C22×C83—81no—
576C22×C83—81no—
577C22×C83—81no—
578C22×C83—81no—
579C22×C83—81no—
580C22×C83—81no—
581C22×C83—81no—
582C22×C83—81no—
583C22×C83—81no—
584C22×C83—81no—
585C22×C83—81no—
586C22×C83—81no—
587C22×C83—81no—
588C22×C83C2×#12111yescharacteristic
589C22×C83#52911yescharacteristic
590C22×C83#53211yescharacteristic
591C22×C83#53411yescharacteristic
592C22×C83#53411yescharacteristic
593C22×C83#53411yescharacteristic
594C22×C83#53511yescharacteristic
595C22×C83#53511yescharacteristic
596C22×C83#53711yescharacteristic
597C22×C83#53811yescharacteristic
598C22×C83#53811yescharacteristic
599C22×C83#53811yescharacteristic
600C22×C83#53811yescharacteristic
601C22×C83#53811yescharacteristic
602C22×C83#53811yescharacteristic
603C22×C83#54011yescharacteristic
604C22×C83#54011yescharacteristic
605C22×C83#54211yescharacteristic
606C22×C83#54211yescharacteristic
607C22×C83D4211yescharacteristic
608C22×C83D4211yescharacteristic
609C22×C83#54611yescharacteristic
610C22×C83#54611yescharacteristic
611C22×C83#54611yescharacteristic
612C22×C83#54611yescharacteristic
613C22×C83#54711yescharacteristic
614C22×C83#54811yescharacteristic
615C22×C83#55011yescharacteristic
616C22×C83#55011yescharacteristic
617C22×C83#55111yescharacteristic
618C22×C83#55311yescharacteristic
619C22×C83#56011yescharacteristic
620C22×C83#56011yescharacteristic
621C22×C83#56211yescharacteristic
622C22×C83#56211yescharacteristic
623C4×C83—24no—
624C4×C83—42no—
625C4×C83—42no—
626C4×C83—42no—
627C4×C83—42no—
628C4×C83—42no—
629C4×C83—42no—
630C4×C83—42no—
631C4×C83—81no—
632C4×C83—81no—
633C4×C83—81no—
634C4×C83—81no—
635#16552C8311yesmaximal, characteristic, direct product factor, Sylow
636C2×C83—82no—
637C2×C83—82no—
638C2×C83—82no—
639C2×C83#242711yescharacteristic
640C2×C83#242811yescharacteristic
641C2×C83#255411yescharacteristic
642C2×C83#261711yescharacteristic
643C2×C83#264811yescharacteristic
644C2×C83#266211yescharacteristic
645C2×C83#267311yescharacteristic
646C2×C83#267611yescharacteristic
647C2×C83#267811yescharacteristic
648C2×C83#268211yescharacteristic
649C2×C83#269711yescharacteristic
650C2×C83#270111yescharacteristic
651C2×C83#271411yescharacteristic
652C2×C83#273011yescharacteristic
653C2×C83#282911yescharacteristic
654C2×#397C2×C8311yescharacteristic, complemented
655C2×#396C2×C8311yescharacteristic, complemented
656C2×#394C2×C8311yescharacteristic, complemented
657C2×#394C2×C8311yescharacteristic, complemented
658C2×#392C2×C8311yescharacteristic
659C2×#390C2×C8311yescharacteristic, complemented
660#1441C2×C8311yescharacteristic, complemented
661#1440C2×C8311yescharacteristic, complemented
662#1439C2×C8311yescharacteristic, complemented
663#1439C2×C8311yescharacteristic, complemented
664#1438C2×C8311yescharacteristic, complemented
665#1438C2×C8311yescharacteristic, complemented
666#1438C2×C8311yescharacteristic, complemented
667#1437C2×C8311yescharacteristic, complemented
668#1436C2×C8311yescharacteristic, complemented
669C83#1655211yescharacteristic, direct product factor, Sylow
670C23×D4C22×C8311yescharacteristic
671C23×D4C22×C8311yescharacteristic
672C23×D4C22×C8311yescharacteristic
673C22×C4⋊C4C22×C8311yescharacteristic
674C22×C4⋊C4C22×C8311yescharacteristic
675C22×C4⋊C4C22×C8311yescharacteristic
676C22×C4⋊C4C22×C8311yescharacteristic
677C22×C22⋊C4C22×C8311yescharacteristic
678C22×C22⋊C4C22×C8311yescharacteristic
679C22×C22⋊C4C22×C8311yescharacteristic
680C22×C22⋊C4C22×C8311yescharacteristic
681C22×C22⋊C4C22×C8311yescharacteristic
682C22×C22⋊C4C22×C8311yescharacteristic
683C22×C22⋊C4C22×C8311yescharacteristic
684C22×C22⋊C4C22×C8311yescharacteristic
685C22×C22⋊C4C22×C8311yescharacteristic
686C22×C22⋊C4C22×C8311yescharacteristic
687C22×C22⋊C4C22×C8311yescharacteristic
688C22×C22⋊C4C22×C8311yescharacteristic
689C22×C22⋊C4C22×C8311yescharacteristic
690C22×C22⋊C4C22×C8311yescharacteristic
691C22×C22⋊C4C22×C8311yescharacteristic
692C22×C42C22×C8311yescharacteristic
693#397—24no—
694#396—24no—
695#394—24no—
696#394—24no—
697#392—24no—
698#390—24no—
699C2×#95C22×C8311yescharacteristic
700C2×#95C22×C8311yescharacteristic
701C2×#95C22×C8311yescharacteristic
702C2×#95C22×C8311yescharacteristic
703C2×#95C22×C8311yescharacteristic
704C2×#95C22×C8311yescharacteristic
705C2×#95C22×C8311yescharacteristic
706C2×#95C22×C8311yescharacteristic
707C2×#95C22×C8311yescharacteristic
708C2×#95C22×C8311yescharacteristic
709C2×#95C22×C8311yescharacteristic
710C2×#95C22×C8311yescharacteristic
711C25C23×C8311yescharacteristic
712C25C23×C8311yescharacteristic
713C25C23×C8311yescharacteristic
714C22×D4—22no—
715C22×D4—22no—
716C22×D4—22no—
717C22×D4—22no—
718C22×D4—22no—
719C22×D4—22no—
720C22×D4—22no—
721C22×D4—22no—
722C22×D4—41no—
723C22×D4—41no—
724C22×D4—41no—
725C22×D4—41no—
726C22×D4—41no—
727C22×D4—41no—
728C22×D4—41no—
729C22×D4—41no—
730C22×D4—41no—
731C22×D4—41no—
732C22×D4—41no—
733C22×D4—41no—
734C22×D4D4×C8314yes—
735C23×C4C23×C8311yescharacteristic
736C23×C4C23×C8311yescharacteristic
737C23×C4C23×C8311yescharacteristic
738C23×C4C23×C8311yescharacteristic
739C23×C4C23×C8311yescharacteristic
740C23×C4C23×C8311yescharacteristic
741C23×C4C23×C8311yescharacteristic
742C23×C4C23×C8311yescharacteristic
743C23×C4C23×C8311yescharacteristic
744C23×C4C23×C8311yescharacteristic
745C23×C4C23×C8311yescharacteristic
746C23×C4C23×C8311yescharacteristic
747C2×C4⋊C4—22no—
748C2×C4⋊C4—22no—
749C2×C4⋊C4—22no—
750C2×C4⋊C4—22no—
751C2×C4⋊C4—22no—
752C2×C4⋊C4—22no—
753C2×C4⋊C4—41no—
754C2×C4⋊C4—41no—
755C2×C4⋊C4—41no—
756C2×C4⋊C4—41no—
757C2×C4⋊C4—41no—
758C2×C4⋊C4D4×C8314yescomplemented
759C2×C22⋊C4—22no—
760C2×C22⋊C4—22no—
761C2×C22⋊C4—22no—
762C2×C22⋊C4—22no—
763C2×C22⋊C4—22no—
764C2×C22⋊C4—22no—
765C2×C22⋊C4—22no—
766C2×C22⋊C4—22no—
767C2×C22⋊C4—22no—
768C2×C22⋊C4—22no—
769C2×C22⋊C4—22no—
770C2×C22⋊C4—22no—
771C2×C22⋊C4—22no—
772C2×C22⋊C4—22no—
773C2×C22⋊C4—22no—
774C2×C22⋊C4—22no—
775C2×C22⋊C4—22no—
776C2×C22⋊C4—22no—
777C2×C22⋊C4—22no—
778C2×C22⋊C4—22no—
779C2×C22⋊C4—22no—
780C2×C22⋊C4—22no—
781C2×C22⋊C4—22no—
782C2×C22⋊C4—22no—
783C2×C22⋊C4—22no—
784C2×C22⋊C4—22no—
785C2×C22⋊C4—22no—
786C2×C22⋊C4—41no—
787C2×C22⋊C4—41no—
788C2×C22⋊C4—41no—
789C2×C22⋊C4—41no—
790C2×C22⋊C4—41no—
791C2×C22⋊C4—41no—
792C2×C22⋊C4—41no—
793C2×C22⋊C4—41no—
794C2×C22⋊C4—41no—
795C2×C22⋊C4—41no—
796C2×C22⋊C4—41no—
797C2×C22⋊C4—41no—
798C2×C22⋊C4—41no—
799C2×C22⋊C4—41no—
800C2×C22⋊C4—41no—
801C2×C22⋊C4—41no—
802C2×C22⋊C4—41no—
803C2×C22⋊C4—41no—
804C2×C42—22no—
805C2×C42—41no—
806C2×C42—41no—
807#95—22no—
808#95—22no—
809#95—22no—
810#95—22no—
811#95—22no—
812#95—22no—
813#95—41no—
814#95—41no—
815#95—41no—
816#95—41no—
817#95—41no—
818#95D4×C8314yescomplemented
819C24—21no—
820C24—21no—
821C24—21no—
822C24—21no—
823C24—21no—
824C24—21no—
825C24—21no—
826C24—21no—
827C24—21no—
828C24—21no—
829C24—21no—
830C24—21no—
831C24—21no—
832C24—21no—
833C24—21no—
834C24—21no—
835C24—21no—
836C24—21no—
837C24—21no—
838C24—21no—
839C24—21no—
840C24—21no—
841C24—21no—
842C24—21no—
843C24—21no—
844C24—21no—
845C24—21no—
846C24—21no—
847C24—21no—
848C24—21no—
849C24—21no—
850C24—21no—
851C24—21no—
852C24—21no—
853C24—21no—
854C24—21no—
855C24—21no—
856C24—21no—
857C24—21no—
858C24—21no—
859C24—21no—
860C24—21no—
861C24C2×D4×C8312yes—
862C24C2×D4×C8312yes—
863C24#41×C8312yes—
864C24C24×C8311yescharacteristic
865C2×D4—28no—
866C2×D4—44no—
867C2×D4—44no—
868C2×D4—44no—
869C2×D4—44no—
870C2×D4—44no—
871C2×D4—44no—
872C2×D4—44no—
873C2×D4—44no—
874C2×D4—44no—
875C2×D4—44no—
876C2×D4—44no—
877C2×D4—44no—
878C2×D4—44no—
879C2×D4—44no—
880C2×D4—44no—
881C2×D4—44no—
882C2×D4—44no—
883C2×D4—44no—
884C2×D4—44no—
885C2×D4—44no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4C2×D4×C8312yes—
961C22×C4C2×D4×C8312yes—
962C22×C4C2×D4×C8312yes—
963C22×C4C2×D4×C8312yes—
964C22×C4C2×D4×C8312yes—
965C22×C4C2×D4×C8312yes—
966C22×C4C2×D4×C8312yes—
967C22×C4#41×C8312yes—
968C22×C4#41×C8312yes—
969C22×C4#41×C8312yes—
970C4⋊C4—44no—
971C4⋊C4—44no—
972C4⋊C4—44no—
973C4⋊C4—44no—
974C22⋊C4—44no—
975C22⋊C4—44no—
976C22⋊C4—44no—
977C22⋊C4—44no—
978C22⋊C4—44no—
979C22⋊C4—44no—
980C22⋊C4—44no—
981C22⋊C4—44no—
982C22⋊C4—44no—
983C22⋊C4—44no—
984C22⋊C4—44no—
985C22⋊C4—44no—
986C22⋊C4—44no—
987C22⋊C4—44no—
988C22⋊C4—44no—
989C42—44no—
990C23—22no—
991C23—22no—
992C23—22no—
993C23—22no—
994C23—22no—
995C23—22no—
996C23—22no—
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—22no—
1003C23—22no—
1004C23—22no—
1005C23—22no—
1006C23—22no—
1007C23—22no—
1008C23—22no—
1009C23—22no—
1010C23—22no—
1011C23—41no—
1012C23—41no—
1013C23—41no—
1014C23—41no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23—41no—
1020C23—41no—
1021C23—41no—
1022C23—41no—
1023C23—41no—
1024C23—41no—
1025C23—41no—
1026C23—41no—
1027C23—41no—
1028C23—41no—
1029C23—41no—
1030C23—41no—
1031C23—41no—
1032C23—41no—
1033C23—41no—
1034C23—41no—
1035C23—41no—
1036C23—41no—
1037C23—41no—
1038C23—41no—
1039C23—41no—
1040C23—41no—
1041C23—41no—
1042C23—41no—
1043C23—41no—
1044C23—41no—
1045C23—41no—
1046C23—41no—
1047C23—41no—
1048C23—41no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23C22×D4×C8311yescharacteristic
1096C23C22×D4×C8311yescharacteristic
1097C23C22×D4×C8311yescharacteristic
1098C23C2×#41×C8311yescharacteristic
1099C23C2×#41×C8311yescharacteristic
1100C23C2×#41×C8311yescharacteristic
1101C23C2×#41×C8311yescharacteristic
1102C23H(5,𝔽2)×C8311yescharacteristic
1103C23H(5,𝔽2)×C8311yescharacteristic
1104C23H(5,𝔽2)×C8311yescharacteristic
1105C23H(5,𝔽2)×C8311yescharacteristic
1106C23H(5,𝔽2)×C8311yescharacteristic
1107C23H(5,𝔽2)×C8311yescharacteristic
1108C23H(5,𝔽2)×C8311yescharacteristic
1109C232−1+4×C8311yescharacteristic
1110D4—416no—
1111D4—416no—
1112D4—416no—
1113C2×C4—22no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—22no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4#121×C8314yes—
1197C22—42no—
1198C22—42no—
1199C22—42no—
1200C22—42no—
1201C22—42no—
1202C22—42no—
1203C22—42no—
1204C22—42no—
1205C22—42no—
1206C22—42no—
1207C22—42no—
1208C22—42no—
1209C22—42no—
1210C22—42no—
1211C22—42no—
1212C22—42no—
1213C22—42no—
1214C22—42no—
1215C22—42no—
1216C22—42no—
1217C22—42no—
1218C22—81no—
1219C22—81no—
1220C22—81no—
1221C22—81no—
1222C22—81no—
1223C22—81no—
1224C22—81no—
1225C22—81no—
1226C22—81no—
1227C22—81no—
1228C22—81no—
1229C22—81no—
1230C22—81no—
1231C22—81no—
1232C22—81no—
1233C22—81no—
1234C22—81no—
1235C22—81no—
1236C22—81no—
1237C22—81no—
1238C22—81no—
1239C22—81no—
1240C22—81no—
1241C22—81no—
1242C22C2×#121×C8311yescharacteristic
1243C22#529×C8311yescharacteristic
1244C22#532×C8311yescharacteristic
1245C22#534×C8311yescharacteristic
1246C22#534×C8311yescharacteristic
1247C22#534×C8311yescharacteristic
1248C22#535×C8311yescharacteristic
1249C22#535×C8311yescharacteristic
1250C22#537×C8311yescharacteristic
1251C22#538×C8311yescharacteristic
1252C22#538×C8311yescharacteristic
1253C22#538×C8311yescharacteristic
1254C22#538×C8311yescharacteristic
1255C22#538×C8311yescharacteristic
1256C22#538×C8311yescharacteristic
1257C22#540×C8311yescharacteristic
1258C22#540×C8311yescharacteristic
1259C22#542×C8311yescharacteristic
1260C22#542×C8311yescharacteristic
1261C22D42×C8311yescharacteristic
1262C22D42×C8311yescharacteristic
1263C22#546×C8311yescharacteristic
1264C22#546×C8311yescharacteristic
1265C22#546×C8311yescharacteristic
1266C22#546×C8311yescharacteristic
1267C22#547×C8311yescharacteristic
1268C22#548×C8311yescharacteristic
1269C22#550×C8311yescharacteristic
1270C22#550×C8311yescharacteristic
1271C22#551×C8311yescharacteristic
1272C22#553×C8311yescharacteristic
1273C22#560×C8311yescharacteristic
1274C22#560×C8311yescharacteristic
1275C22#562×C8311yescharacteristic
1276C22#562×C8311yescharacteristic
1277C4—24no—
1278C4—42no—
1279C4—42no—
1280C4—42no—
1281C4—42no—
1282C4—42no—
1283C4—42no—
1284C4—42no—
1285C4—81no—
1286C4—81no—
1287C4—81no—
1288C4—81no—
1289C2—82no—
1290C2—82no—
1291C2—82no—
1292C2C83×#242711yescharacteristic
1293C2C83×#242811yescharacteristic
1294C2C83×#255411yescharacteristic
1295C2C83×#261711yescharacteristic
1296C2C83×#264811yescharacteristic
1297C2C83×#266211yescharacteristic
1298C2C83×#267311yescharacteristic
1299C2C83×#267611yescharacteristic
1300C2C83×#267811yescharacteristic
1301C2C83×#268211yescharacteristic
1302C2C83×#269711yescharacteristic
1303C2C83×#270111yescharacteristic
1304C2C83×#271411yescharacteristic
1305C2C83×#273011yescharacteristic
1306C2C83×#282911yescharacteristic
subgroupG/H
center, socleC24×C83C24
commutator, Frattini, cosocleC24C24×C83
prime radicalC2×#392×C83C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C83 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#397×C83C2semidirect
2. C2×#396×C83C2semidirect
3. C2×#394×C83C2semidirect
4. C2×#394×C83C2semidirect
6. C2×#390×C83C2semidirect
7. C83×#1441C2semidirect
8. C83×#1440C2semidirect
9. C83×#1439C2semidirect
10. C83×#1439C2semidirect
11. C83×#1438C2semidirect
12. C83×#1438C2semidirect
13. C83×#1438C2semidirect
14. C83×#1437C2semidirect
15. C83×#1436C2semidirect
104. C2×C4⋊C4×C83D4semidirect
164. #95×C83D4semidirect
635. #16552C83direct (N × H)
654. C2×#397C2×C83semidirect
655. C2×#396C2×C83semidirect
656. C2×#394C2×C83semidirect
657. C2×#394C2×C83semidirect
659. C2×#390C2×C83semidirect
660. #1441C2×C83semidirect
661. #1440C2×C83semidirect
662. #1439C2×C83semidirect
663. #1439C2×C83semidirect
664. #1438C2×C83semidirect
665. #1438C2×C83semidirect
666. #1438C2×C83semidirect
667. #1437C2×C83semidirect
668. #1436C2×C83semidirect
669. C83#16552direct (N × H)
758. C2×C4⋊C4D4×C83semidirect
818. #95D4×C83semidirect

Maximal subgroups

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

subgroupindex
C2×#397×C832
C2×#396×C832
C2×#394×C832
C2×#392×C832
C2×#390×C832
C83×#14412
C83×#14402
C83×#14392
C83×#14382
C83×#14372
C83×#14362
#1655283