Finite Group Databasebeta

← C83×#14732 #35242556

Subgroups — C83×#14732 #35242556

Order 21248.

2662 conjugacy classes of subgroups.

The subgroup lattice has 1362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D4×C83C211yesmaximal, characteristic, complemented
2C2×#396×C83C211yesmaximal, characteristic, complemented
3C2×#394×C83C211yesmaximal, characteristic, complemented
4C2×#394×C83C211yesmaximal, characteristic, complemented
5C2×#392×C83C211yesmaximal, characteristic
6C2×#386×C83C211yesmaximal, characteristic, complemented
7C2×#386×C83C211yesmaximal, characteristic, complemented
8C2×#380×C83C211yesmaximal, characteristic, complemented
9C83×#1441C211yesmaximal, characteristic, complemented
10C83×#1440C211yesmaximal, characteristic, complemented
11C83×#1439C211yesmaximal, characteristic, complemented
12C83×#1438C211yesmaximal, characteristic, complemented
13C83×#1437C211yesmaximal, characteristic, complemented
14C83×#1436C211yesmaximal, characteristic, complemented
15C83×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C83C2211yescharacteristic
17C23×D4×C83C2211yescharacteristic
18C23×D4×C83C2211yescharacteristic
19C24×C4×C83C2211yescharacteristic
20C24×C4×C83C2211yescharacteristic
21C2×C4×D4×C83—24no—
22C2×C4×D4×C83—24no—
23C2×C4×D4×C83—24no—
24C22×C4⋊C4×C83C2211yescharacteristic
25C22×C4⋊C4×C83C2211yescharacteristic
26C22×C4⋊C4×C83C2211yescharacteristic
27C22×C4⋊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×C22⋊C4×C83C2211yescharacteristic
39C22×C22⋊C4×C83C2211yescharacteristic
40C22×C22⋊C4×C83C2211yescharacteristic
41C22×C42×C83C2211yescharacteristic
42#396×C83—24no—
43#394×C83—24no—
44#394×C83—24no—
45#392×C83—24no—
46#386×C83—24no—
47#386×C83—24no—
48#380×C83—24no—
49C2×#95×C83C2211yescharacteristic
50C2×#95×C83C2211yescharacteristic
51C2×#95×C83C2211yescharacteristic
52C2×#95×C83C2211yescharacteristic
53C2×#95×C83C2211yescharacteristic
54C2×#95×C83C2211yescharacteristic
55C2×#95×C83C2211yescharacteristic
56C2×#95×C83C2211yescharacteristic
57C2×#95×C83C2211yescharacteristic
58C2×#95×C83C2211yescharacteristic
59C2×#95×C83C2211yescharacteristic
60C2×#95×C83C2211yescharacteristic
61C25×C83C2311yescharacteristic
62C25×C83C2311yescharacteristic
63C25×C83C2311yescharacteristic
64C22×D4×C83—22no—
65C22×D4×C83—22no—
66C22×D4×C83—22no—
67C22×D4×C83—22no—
68C22×D4×C83—22no—
69C22×D4×C83—22no—
70C22×D4×C83—22no—
71C22×D4×C83—22no—
72C22×D4×C83—22no—
73C22×D4×C83—22no—
74C22×D4×C83—22no—
75C22×D4×C83—22no—
76C22×D4×C83—22no—
77C22×D4×C83—22no—
78C22×D4×C83—22no—
79C22×D4×C83—22no—
80C22×D4×C83—41no—
81C22×D4×C83—41no—
82C22×D4×C83—41no—
83C22×D4×C83—41no—
84C22×D4×C83D414yes—
85C23×C4×C83—22no—
86C23×C4×C83—22no—
87C23×C4×C83—22no—
88C23×C4×C83—22no—
89C23×C4×C83—22no—
90C23×C4×C83—22no—
91C23×C4×C83—22no—
92C23×C4×C83—22no—
93C23×C4×C83—22no—
94C23×C4×C83—41no—
95C23×C4×C83—41no—
96C23×C4×C83—41no—
97C23×C4×C83—41no—
98C23×C4×C83D414yescomplemented
99C23×C4×C83C2311yescharacteristic
100C23×C4×C83C2311yescharacteristic
101C23×C4×C83C2311yescharacteristic
102C23×C4×C83C2311yescharacteristic
103C23×C4×C83C2311yescharacteristic
104C23×C4×C83C2311yescharacteristic
105C23×C4×C83C2311yescharacteristic
106C23×C4×C83C2311yescharacteristic
107C23×C4×C83C2311yescharacteristic
108C23×C4×C83C2311yescharacteristic
109C23×C4×C83C2311yescharacteristic
110C23×C4×C83C2311yescharacteristic
111C4×D4×C83—232no—
112C2×C4⋊C4×C83—22no—
113C2×C4⋊C4×C83—22no—
114C2×C4⋊C4×C83—22no—
115C2×C4⋊C4×C83—22no—
116C2×C4⋊C4×C83—22no—
117C2×C4⋊C4×C83—22no—
118C2×C4⋊C4×C83—22no—
119C2×C4⋊C4×C83—22no—
120C2×C4⋊C4×C83—22no—
121C2×C4⋊C4×C83—41no—
122C2×C4⋊C4×C83—41no—
123C2×C4⋊C4×C83D414yescomplemented
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—22no—
133C2×C22⋊C4×C83—22no—
134C2×C22⋊C4×C83—22no—
135C2×C22⋊C4×C83—22no—
136C2×C22⋊C4×C83—22no—
137C2×C22⋊C4×C83—22no—
138C2×C22⋊C4×C83—22no—
139C2×C22⋊C4×C83—22no—
140C2×C22⋊C4×C83—22no—
141C2×C22⋊C4×C83—22no—
142C2×C22⋊C4×C83—22no—
143C2×C22⋊C4×C83—22no—
144C2×C22⋊C4×C83—22no—
145C2×C22⋊C4×C83—22no—
146C2×C22⋊C4×C83—22no—
147C2×C22⋊C4×C83—22no—
148C2×C22⋊C4×C83—22no—
149C2×C22⋊C4×C83—22no—
150C2×C22⋊C4×C83—22no—
151C2×C22⋊C4×C83—22no—
152C2×C22⋊C4×C83—22no—
153C2×C22⋊C4×C83—22no—
154C2×C22⋊C4×C83—22no—
155C2×C22⋊C4×C83—22no—
156C2×C22⋊C4×C83—41no—
157C2×C22⋊C4×C83—41no—
158C2×C22⋊C4×C83—41no—
159C2×C22⋊C4×C83—41no—
160C2×C22⋊C4×C83—41no—
161C2×C22⋊C4×C83—41no—
162C2×C22⋊C4×C83D414yescomplemented
163C2×C42×C83—22no—
164C2×C42×C83—22no—
165C2×C42×C83—22no—
166#95×C83—22no—
167#95×C83—22no—
168#95×C83—22no—
169#95×C83—22no—
170#95×C83—22no—
171#95×C83—22no—
172#95×C83—22no—
173#95×C83—22no—
174#95×C83—22no—
175#95×C83—41no—
176#95×C83—41no—
177#95×C83D414yescomplemented
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×C83—21no—
208C24×C83—21no—
209C24×C83—21no—
210C24×C83—21no—
211C24×C83—21no—
212C24×C83—21no—
213C24×C83—21no—
214C24×C83—21no—
215C24×C83—21no—
216C24×C83C2×D412yes—
217C24×C83C2×D412yes—
218C24×C83C2×D412yes—
219C24×C83C2×D412yes—
220C24×C83#4112yes—
221C24×C83#4112yes—
222C24×C83#4112yes—
223C24×C83C2411yescharacteristic
224C2×D4×C83—28no—
225C2×D4×C83—28no—
226C2×D4×C83—28no—
227C2×D4×C83—28no—
228C2×D4×C83—28no—
229C2×D4×C83—28no—
230C2×D4×C83—28no—
231C2×D4×C83—28no—
232C2×D4×C83—28no—
233C2×D4×C83—44no—
234C2×D4×C83—44no—
235C2×D4×C83—44no—
236C2×D4×C83—44no—
237C2×D4×C83—44no—
238C2×D4×C83—44no—
239C2×D4×C83—44no—
240C2×D4×C83—44no—
241C2×D4×C83—44no—
242C2×D4×C83—44no—
243C2×D4×C83—44no—
244C2×D4×C83—44no—
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—28no—
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—28no—
289C22×C4×C83—28no—
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×C83—21no—
307C22×C4×C83—21no—
308C22×C4×C83—21no—
309C22×C4×C83—21no—
310C22×C4×C83—21no—
311C22×C4×C83—21no—
312C22×C4×C83—21no—
313C22×C4×C83—21no—
314C22×C4×C83—21no—
315C22×C4×C83—21no—
316C22×C4×C83—21no—
317C22×C4×C83—21no—
318C22×C4×C83—44no—
319C22×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×C83C2×D412yes—
330C22×C4×C83C2×D412yes—
331C22×C4×C83C2×D412yes—
332C22×C4×C83C2×D412yes—
333C22×C4×C83C2×D412yes—
334C22×C4×C83C2×D412yes—
335C22×C4×C83C2×D412yes—
336C22×C4×C83C2×D412yes—
337C22×C4×C83C2×D412yes—
338C22×C4×C83C2×D412yes—
339C22×C4×C83C2×D412yes—
340C22×C4×C83#4112yes—
341C22×C4×C83#4112yes—
342C22×C4×C83#4112yes—
343C4⋊C4×C83—28no—
344C4⋊C4×C83—44no—
345C4⋊C4×C83—44no—
346C4⋊C4×C83—44no—
347C22⋊C4×C83—28no—
348C22⋊C4×C83—28no—
349C22⋊C4×C83—44no—
350C22⋊C4×C83—44no—
351C22⋊C4×C83—44no—
352C22⋊C4×C83—44no—
353C22⋊C4×C83—44no—
354C22⋊C4×C83—44no—
355C22⋊C4×C83—44no—
356C22⋊C4×C83—44no—
357C22⋊C4×C83—44no—
358C22⋊C4×C83—44no—
359C22⋊C4×C83—44no—
360C42×C83—28no—
361C23×C83—22no—
362C23×C83—22no—
363C23×C83—22no—
364C23×C83—22no—
365C23×C83—22no—
366C23×C83—22no—
367C23×C83—22no—
368C23×C83—22no—
369C23×C83—22no—
370C23×C83—22no—
371C23×C83—22no—
372C23×C83—22no—
373C23×C83—22no—
374C23×C83—22no—
375C23×C83—22no—
376C23×C83—22no—
377C23×C83—22no—
378C23×C83—22no—
379C23×C83—22no—
380C23×C83—22no—
381C23×C83—22no—
382C23×C83—22no—
383C23×C83—22no—
384C23×C83—22no—
385C23×C83—22no—
386C23×C83—22no—
387C23×C83—22no—
388C23×C83—22no—
389C23×C83—22no—
390C23×C83—22no—
391C23×C83—22no—
392C23×C83—22no—
393C23×C83—22no—
394C23×C83—22no—
395C23×C83—22no—
396C23×C83—22no—
397C23×C83—22no—
398C23×C83—22no—
399C23×C83—22no—
400C23×C83—22no—
401C23×C83—22no—
402C23×C83—22no—
403C23×C83—22no—
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×C83—41no—
442C23×C83—41no—
443C23×C83—41no—
444C23×C83—41no—
445C23×C83—41no—
446C23×C83—41no—
447C23×C83—41no—
448C23×C83—41no—
449C23×C83—41no—
450C23×C83—41no—
451C23×C83—41no—
452C23×C83—41no—
453C23×C83—41no—
454C23×C83—41no—
455C23×C83—41no—
456C23×C83—41no—
457C23×C83—41no—
458C23×C83—41no—
459C23×C83—41no—
460C23×C83—41no—
461C23×C83—41no—
462C23×C83—41no—
463C23×C83—41no—
464C23×C83#12114yes—
465C23×C83#12114yes—
466C23×C83C22×D411yescharacteristic
467C23×C83C22×D411yescharacteristic
468C23×C83C22×D411yescharacteristic
469C23×C83C22×D411yescharacteristic
470C23×C83C22×D411yescharacteristic
471C23×C83C2×#4111yescharacteristic
472C23×C83C2×#4111yescharacteristic
473C23×C83C2×#4111yescharacteristic
474C23×C83C2×#4111yescharacteristic
475C23×C83C2×#4111yescharacteristic
476C23×C83C2×#4111yescharacteristic
477C23×C83H(5,𝔽2)11yescharacteristic
478C23×C83H(5,𝔽2)11yescharacteristic
479C23×C83H(5,𝔽2)11yescharacteristic
480C23×C832−1+411yescharacteristic
481D4×C83—232no—
482D4×C83—416no—
483D4×C83—416no—
484C2×C4×C83—22no—
485C2×C4×C83—22no—
486C2×C4×C83—22no—
487C2×C4×C83—22no—
488C2×C4×C83—22no—
489C2×C4×C83—22no—
490C2×C4×C83—22no—
491C2×C4×C83—22no—
492C2×C4×C83—22no—
493C2×C4×C83—22no—
494C2×C4×C83—22no—
495C2×C4×C83—22no—
496C2×C4×C83—22no—
497C2×C4×C83—22no—
498C2×C4×C83—22no—
499C2×C4×C83—22no—
500C2×C4×C83—22no—
501C2×C4×C83—22no—
502C2×C4×C83—22no—
503C2×C4×C83—22no—
504C2×C4×C83—22no—
505C2×C4×C83—22no—
506C2×C4×C83—22no—
507C2×C4×C83—22no—
508C2×C4×C83—22no—
509C2×C4×C83—22no—
510C2×C4×C83—22no—
511C2×C4×C83—22no—
512C2×C4×C83—22no—
513C2×C4×C83—22no—
514C2×C4×C83—22no—
515C2×C4×C83—22no—
516C2×C4×C83—22no—
517C2×C4×C83—416no—
518C2×C4×C83—416no—
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—41no—
543C2×C4×C83—41no—
544C2×C4×C83—41no—
545C2×C4×C83—41no—
546C2×C4×C83—41no—
547C2×C4×C83—41no—
548C2×C4×C83—41no—
549C2×C4×C83—41no—
550C2×C4×C83—41no—
551C2×C4×C83—41no—
552C2×C4×C83—41no—
553C2×C4×C83—41no—
554C2×C4×C83—41no—
555C2×C4×C83—41no—
556C2×C4×C83—41no—
557C2×C4×C83—41no—
558C2×C4×C83—41no—
559C2×C4×C83—41no—
560C2×C4×C83—41no—
561C2×C4×C83—41no—
562C2×C4×C83—41no—
563C2×C4×C83—41no—
564C2×C4×C83—41no—
565C2×C4×C83—41no—
566C2×C4×C83—41no—
567C2×C4×C83#12014yes—
568C2×C4×C83#12114yes—
569C2×C4×C83#12114yes—
570C22×C83—24no—
571C22×C83—24no—
572C22×C83—24no—
573C22×C83—24no—
574C22×C83—24no—
575C22×C83—24no—
576C22×C83—42no—
577C22×C83—42no—
578C22×C83—42no—
579C22×C83—42no—
580C22×C83—42no—
581C22×C83—42no—
582C22×C83—42no—
583C22×C83—42no—
584C22×C83—42no—
585C22×C83—42no—
586C22×C83—42no—
587C22×C83—42no—
588C22×C83—42no—
589C22×C83—42no—
590C22×C83—42no—
591C22×C83—42no—
592C22×C83—42no—
593C22×C83—42no—
594C22×C83—42no—
595C22×C83—42no—
596C22×C83—42no—
597C22×C83—42no—
598C22×C83—42no—
599C22×C83—42no—
600C22×C83—42no—
601C22×C83—42no—
602C22×C83—42no—
603C22×C83—42no—
604C22×C83—42no—
605C22×C83—42no—
606C22×C83—42no—
607C22×C83—81no—
608C22×C83—81no—
609C22×C83—81no—
610C22×C83—81no—
611C22×C83—81no—
612C22×C83—81no—
613C22×C83—81no—
614C22×C83—81no—
615C22×C83C2×#12011yescharacteristic
616C22×C83C2×#12111yescharacteristic
617C22×C83C2×#12111yescharacteristic
618C22×C83C2×#12111yescharacteristic
619C22×C83C2×#12111yescharacteristic
620C22×C83#52511yescharacteristic
621C22×C83#52511yescharacteristic
622C22×C83#52511yescharacteristic
623C22×C83#52511yescharacteristic
624C22×C83#52511yescharacteristic
625C22×C83#52911yescharacteristic
626C22×C83#52911yescharacteristic
627C22×C83#53211yescharacteristic
628C22×C83#53411yescharacteristic
629C22×C83#53711yescharacteristic
630C22×C83#53811yescharacteristic
631C22×C83#53911yescharacteristic
632C22×C83#54011yescharacteristic
633C22×C83#54211yescharacteristic
634C22×C83D4211yescharacteristic
635C22×C83D4211yescharacteristic
636C22×C83D4211yescharacteristic
637C22×C83#54611yescharacteristic
638C22×C83#54611yescharacteristic
639C22×C83#54611yescharacteristic
640C22×C83#54611yescharacteristic
641C22×C83#54611yescharacteristic
642C22×C83#54711yescharacteristic
643C22×C83#54711yescharacteristic
644C22×C83#54811yescharacteristic
645C22×C83#54811yescharacteristic
646C22×C83#55011yescharacteristic
647C22×C83#55111yescharacteristic
648C22×C83#55111yescharacteristic
649C22×C83#55311yescharacteristic
650C4×C83—24no—
651C4×C83—24no—
652C4×C83—24no—
653C4×C83—42no—
654C4×C83—42no—
655C4×C83—42no—
656C4×C83—42no—
657C4×C83—42no—
658C4×C83—81no—
659C4×C83—81no—
660C4×C83—81no—
661C4×C83—81no—
662#14732C8311yesmaximal, characteristic, direct product factor, Sylow
663C2×C83—44no—
664C2×C83—44no—
665C2×C83—82no—
666C2×C83#239211yescharacteristic
667C2×C83#240711yescharacteristic
668C2×C83#241011yescharacteristic
669C2×C83#241611yescharacteristic
670C2×C83#242411yescharacteristic
671C2×C83#242511yescharacteristic
672C2×C83#242711yescharacteristic
673C2×C83#242811yescharacteristic
674C2×C83#245711yescharacteristic
675C2×C83#246111yescharacteristic
676C2×C83#246311yescharacteristic
677C2×C83#246711yescharacteristic
678C2×C83#253411yescharacteristic
679C2×C83#263011yescharacteristic
680C2×C83#284711yescharacteristic
681C22×C4×D4C2×C8311yescharacteristic, complemented
682C2×#396C2×C8311yescharacteristic, complemented
683C2×#394C2×C8311yescharacteristic, complemented
684C2×#394C2×C8311yescharacteristic, complemented
685C2×#392C2×C8311yescharacteristic
686C2×#386C2×C8311yescharacteristic, complemented
687C2×#386C2×C8311yescharacteristic, complemented
688C2×#380C2×C8311yescharacteristic, complemented
689#1441C2×C8311yescharacteristic, complemented
690#1440C2×C8311yescharacteristic, complemented
691#1439C2×C8311yescharacteristic, complemented
692#1438C2×C8311yescharacteristic, complemented
693#1437C2×C8311yescharacteristic, complemented
694#1436C2×C8311yescharacteristic, complemented
695C22⋊#95C2×C8311yescharacteristic, complemented
696C83#1473211yescharacteristic, direct product factor, Sylow
697C23×D4C22×C8311yescharacteristic
698C23×D4C22×C8311yescharacteristic
699C23×D4C22×C8311yescharacteristic
700C24×C4C22×C8311yescharacteristic
701C24×C4C22×C8311yescharacteristic
702C2×C4×D4—24no—
703C2×C4×D4—24no—
704C2×C4×D4—24no—
705C22×C4⋊C4C22×C8311yescharacteristic
706C22×C4⋊C4C22×C8311yescharacteristic
707C22×C4⋊C4C22×C8311yescharacteristic
708C22×C4⋊C4C22×C8311yescharacteristic
709C22×C22⋊C4C22×C8311yescharacteristic
710C22×C22⋊C4C22×C8311yescharacteristic
711C22×C22⋊C4C22×C8311yescharacteristic
712C22×C22⋊C4C22×C8311yescharacteristic
713C22×C22⋊C4C22×C8311yescharacteristic
714C22×C22⋊C4C22×C8311yescharacteristic
715C22×C22⋊C4C22×C8311yescharacteristic
716C22×C22⋊C4C22×C8311yescharacteristic
717C22×C22⋊C4C22×C8311yescharacteristic
718C22×C22⋊C4C22×C8311yescharacteristic
719C22×C22⋊C4C22×C8311yescharacteristic
720C22×C22⋊C4C22×C8311yescharacteristic
721C22×C22⋊C4C22×C8311yescharacteristic
722C22×C42C22×C8311yescharacteristic
723#396—24no—
724#394—24no—
725#394—24no—
726#392—24no—
727#386—24no—
728#386—24no—
729#380—24no—
730C2×#95C22×C8311yescharacteristic
731C2×#95C22×C8311yescharacteristic
732C2×#95C22×C8311yescharacteristic
733C2×#95C22×C8311yescharacteristic
734C2×#95C22×C8311yescharacteristic
735C2×#95C22×C8311yescharacteristic
736C2×#95C22×C8311yescharacteristic
737C2×#95C22×C8311yescharacteristic
738C2×#95C22×C8311yescharacteristic
739C2×#95C22×C8311yescharacteristic
740C2×#95C22×C8311yescharacteristic
741C2×#95C22×C8311yescharacteristic
742C25C23×C8311yescharacteristic
743C25C23×C8311yescharacteristic
744C25C23×C8311yescharacteristic
745C22×D4—22no—
746C22×D4—22no—
747C22×D4—22no—
748C22×D4—22no—
749C22×D4—22no—
750C22×D4—22no—
751C22×D4—22no—
752C22×D4—22no—
753C22×D4—22no—
754C22×D4—22no—
755C22×D4—22no—
756C22×D4—22no—
757C22×D4—22no—
758C22×D4—22no—
759C22×D4—22no—
760C22×D4—22no—
761C22×D4—41no—
762C22×D4—41no—
763C22×D4—41no—
764C22×D4—41no—
765C22×D4D4×C8314yes—
766C23×C4—22no—
767C23×C4—22no—
768C23×C4—22no—
769C23×C4—22no—
770C23×C4—22no—
771C23×C4—22no—
772C23×C4—22no—
773C23×C4—22no—
774C23×C4—22no—
775C23×C4—41no—
776C23×C4—41no—
777C23×C4—41no—
778C23×C4—41no—
779C23×C4D4×C8314yescomplemented
780C23×C4C23×C8311yescharacteristic
781C23×C4C23×C8311yescharacteristic
782C23×C4C23×C8311yescharacteristic
783C23×C4C23×C8311yescharacteristic
784C23×C4C23×C8311yescharacteristic
785C23×C4C23×C8311yescharacteristic
786C23×C4C23×C8311yescharacteristic
787C23×C4C23×C8311yescharacteristic
788C23×C4C23×C8311yescharacteristic
789C23×C4C23×C8311yescharacteristic
790C23×C4C23×C8311yescharacteristic
791C23×C4C23×C8311yescharacteristic
792C4×D4—232no—
793C2×C4⋊C4—22no—
794C2×C4⋊C4—22no—
795C2×C4⋊C4—22no—
796C2×C4⋊C4—22no—
797C2×C4⋊C4—22no—
798C2×C4⋊C4—22no—
799C2×C4⋊C4—22no—
800C2×C4⋊C4—22no—
801C2×C4⋊C4—22no—
802C2×C4⋊C4—41no—
803C2×C4⋊C4—41no—
804C2×C4⋊C4D4×C8314yescomplemented
805C2×C22⋊C4—22no—
806C2×C22⋊C4—22no—
807C2×C22⋊C4—22no—
808C2×C22⋊C4—22no—
809C2×C22⋊C4—22no—
810C2×C22⋊C4—22no—
811C2×C22⋊C4—22no—
812C2×C22⋊C4—22no—
813C2×C22⋊C4—22no—
814C2×C22⋊C4—22no—
815C2×C22⋊C4—22no—
816C2×C22⋊C4—22no—
817C2×C22⋊C4—22no—
818C2×C22⋊C4—22no—
819C2×C22⋊C4—22no—
820C2×C22⋊C4—22no—
821C2×C22⋊C4—22no—
822C2×C22⋊C4—22no—
823C2×C22⋊C4—22no—
824C2×C22⋊C4—22no—
825C2×C22⋊C4—22no—
826C2×C22⋊C4—22no—
827C2×C22⋊C4—22no—
828C2×C22⋊C4—22no—
829C2×C22⋊C4—22no—
830C2×C22⋊C4—22no—
831C2×C22⋊C4—22no—
832C2×C22⋊C4—22no—
833C2×C22⋊C4—22no—
834C2×C22⋊C4—22no—
835C2×C22⋊C4—22no—
836C2×C22⋊C4—22no—
837C2×C22⋊C4—41no—
838C2×C22⋊C4—41no—
839C2×C22⋊C4—41no—
840C2×C22⋊C4—41no—
841C2×C22⋊C4—41no—
842C2×C22⋊C4—41no—
843C2×C22⋊C4D4×C8314yescomplemented
844C2×C42—22no—
845C2×C42—22no—
846C2×C42—22no—
847#95—22no—
848#95—22no—
849#95—22no—
850#95—22no—
851#95—22no—
852#95—22no—
853#95—22no—
854#95—22no—
855#95—22no—
856#95—41no—
857#95—41no—
858#95D4×C8314yescomplemented
859C24—21no—
860C24—21no—
861C24—21no—
862C24—21no—
863C24—21no—
864C24—21no—
865C24—21no—
866C24—21no—
867C24—21no—
868C24—21no—
869C24—21no—
870C24—21no—
871C24—21no—
872C24—21no—
873C24—21no—
874C24—21no—
875C24—21no—
876C24—21no—
877C24—21no—
878C24—21no—
879C24—21no—
880C24—21no—
881C24—21no—
882C24—21no—
883C24—21no—
884C24—21no—
885C24—21no—
886C24—21no—
887C24—21no—
888C24—21no—
889C24—21no—
890C24—21no—
891C24—21no—
892C24—21no—
893C24—21no—
894C24—21no—
895C24—21no—
896C24—21no—
897C24C2×D4×C8312yes—
898C24C2×D4×C8312yes—
899C24C2×D4×C8312yes—
900C24C2×D4×C8312yes—
901C24#41×C8312yes—
902C24#41×C8312yes—
903C24#41×C8312yes—
904C24C24×C8311yescharacteristic
905C2×D4—28no—
906C2×D4—28no—
907C2×D4—28no—
908C2×D4—28no—
909C2×D4—28no—
910C2×D4—28no—
911C2×D4—28no—
912C2×D4—28no—
913C2×D4—28no—
914C2×D4—44no—
915C2×D4—44no—
916C2×D4—44no—
917C2×D4—44no—
918C2×D4—44no—
919C2×D4—44no—
920C2×D4—44no—
921C2×D4—44no—
922C2×D4—44no—
923C2×D4—44no—
924C2×D4—44no—
925C2×D4—44no—
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—28no—
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×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—21no—
969C22×C4—28no—
970C22×C4—28no—
971C22×C4—21no—
972C22×C4—21no—
973C22×C4—21no—
974C22×C4—21no—
975C22×C4—21no—
976C22×C4—21no—
977C22×C4—21no—
978C22×C4—21no—
979C22×C4—21no—
980C22×C4—21no—
981C22×C4—21no—
982C22×C4—21no—
983C22×C4—21no—
984C22×C4—21no—
985C22×C4—21no—
986C22×C4—21no—
987C22×C4—21no—
988C22×C4—21no—
989C22×C4—21no—
990C22×C4—21no—
991C22×C4—21no—
992C22×C4—21no—
993C22×C4—21no—
994C22×C4—21no—
995C22×C4—21no—
996C22×C4—21no—
997C22×C4—21no—
998C22×C4—21no—
999C22×C4—44no—
1000C22×C4—44no—
1001C22×C4—44no—
1002C22×C4—44no—
1003C22×C4—44no—
1004C22×C4—44no—
1005C22×C4—44no—
1006C22×C4—44no—
1007C22×C4—44no—
1008C22×C4—44no—
1009C22×C4—44no—
1010C22×C4C2×D4×C8312yes—
1011C22×C4C2×D4×C8312yes—
1012C22×C4C2×D4×C8312yes—
1013C22×C4C2×D4×C8312yes—
1014C22×C4C2×D4×C8312yes—
1015C22×C4C2×D4×C8312yes—
1016C22×C4C2×D4×C8312yes—
1017C22×C4C2×D4×C8312yes—
1018C22×C4C2×D4×C8312yes—
1019C22×C4C2×D4×C8312yes—
1020C22×C4C2×D4×C8312yes—
1021C22×C4#41×C8312yes—
1022C22×C4#41×C8312yes—
1023C22×C4#41×C8312yes—
1024C4⋊C4—28no—
1025C4⋊C4—44no—
1026C4⋊C4—44no—
1027C4⋊C4—44no—
1028C22⋊C4—28no—
1029C22⋊C4—28no—
1030C22⋊C4—44no—
1031C22⋊C4—44no—
1032C22⋊C4—44no—
1033C22⋊C4—44no—
1034C22⋊C4—44no—
1035C22⋊C4—44no—
1036C22⋊C4—44no—
1037C22⋊C4—44no—
1038C22⋊C4—44no—
1039C22⋊C4—44no—
1040C22⋊C4—44no—
1041C42—28no—
1042C23—22no—
1043C23—22no—
1044C23—22no—
1045C23—22no—
1046C23—22no—
1047C23—22no—
1048C23—22no—
1049C23—22no—
1050C23—22no—
1051C23—22no—
1052C23—22no—
1053C23—22no—
1054C23—22no—
1055C23—22no—
1056C23—22no—
1057C23—22no—
1058C23—22no—
1059C23—22no—
1060C23—22no—
1061C23—22no—
1062C23—22no—
1063C23—22no—
1064C23—22no—
1065C23—22no—
1066C23—22no—
1067C23—22no—
1068C23—22no—
1069C23—22no—
1070C23—22no—
1071C23—22no—
1072C23—22no—
1073C23—22no—
1074C23—22no—
1075C23—22no—
1076C23—22no—
1077C23—22no—
1078C23—22no—
1079C23—22no—
1080C23—22no—
1081C23—22no—
1082C23—22no—
1083C23—22no—
1084C23—22no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—41no—
1126C23—41no—
1127C23—41no—
1128C23—41no—
1129C23—41no—
1130C23—41no—
1131C23—41no—
1132C23—41no—
1133C23—41no—
1134C23—41no—
1135C23—41no—
1136C23—41no—
1137C23—41no—
1138C23—41no—
1139C23—41no—
1140C23—41no—
1141C23—41no—
1142C23—41no—
1143C23—41no—
1144C23—41no—
1145C23#121×C8314yes—
1146C23#121×C8314yes—
1147C23C22×D4×C8311yescharacteristic
1148C23C22×D4×C8311yescharacteristic
1149C23C22×D4×C8311yescharacteristic
1150C23C22×D4×C8311yescharacteristic
1151C23C22×D4×C8311yescharacteristic
1152C23C2×#41×C8311yescharacteristic
1153C23C2×#41×C8311yescharacteristic
1154C23C2×#41×C8311yescharacteristic
1155C23C2×#41×C8311yescharacteristic
1156C23C2×#41×C8311yescharacteristic
1157C23C2×#41×C8311yescharacteristic
1158C23H(5,𝔽2)×C8311yescharacteristic
1159C23H(5,𝔽2)×C8311yescharacteristic
1160C23H(5,𝔽2)×C8311yescharacteristic
1161C232−1+4×C8311yescharacteristic
1162D4—232no—
1163D4—416no—
1164D4—416no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—22no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—22no—
1188C2×C4—22no—
1189C2×C4—22no—
1190C2×C4—22no—
1191C2×C4—22no—
1192C2×C4—22no—
1193C2×C4—22no—
1194C2×C4—22no—
1195C2×C4—22no—
1196C2×C4—22no—
1197C2×C4—22no—
1198C2×C4—416no—
1199C2×C4—416no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4—41no—
1247C2×C4—41no—
1248C2×C4#120×C8314yes—
1249C2×C4#121×C8314yes—
1250C2×C4#121×C8314yes—
1251C22—24no—
1252C22—24no—
1253C22—24no—
1254C22—24no—
1255C22—24no—
1256C22—24no—
1257C22—42no—
1258C22—42no—
1259C22—42no—
1260C22—42no—
1261C22—42no—
1262C22—42no—
1263C22—42no—
1264C22—42no—
1265C22—42no—
1266C22—42no—
1267C22—42no—
1268C22—42no—
1269C22—42no—
1270C22—42no—
1271C22—42no—
1272C22—42no—
1273C22—42no—
1274C22—42no—
1275C22—42no—
1276C22—42no—
1277C22—42no—
1278C22—42no—
1279C22—42no—
1280C22—42no—
1281C22—42no—
1282C22—42no—
1283C22—42no—
1284C22—42no—
1285C22—42no—
1286C22—42no—
1287C22—42no—
1288C22—81no—
1289C22—81no—
1290C22—81no—
1291C22—81no—
1292C22—81no—
1293C22—81no—
1294C22—81no—
1295C22—81no—
1296C22C2×#120×C8311yescharacteristic
1297C22C2×#121×C8311yescharacteristic
1298C22C2×#121×C8311yescharacteristic
1299C22C2×#121×C8311yescharacteristic
1300C22C2×#121×C8311yescharacteristic
1301C22#525×C8311yescharacteristic
1302C22#525×C8311yescharacteristic
1303C22#525×C8311yescharacteristic
1304C22#525×C8311yescharacteristic
1305C22#525×C8311yescharacteristic
1306C22#529×C8311yescharacteristic
1307C22#529×C8311yescharacteristic
1308C22#532×C8311yescharacteristic
1309C22#534×C8311yescharacteristic
1310C22#537×C8311yescharacteristic
1311C22#538×C8311yescharacteristic
1312C22#539×C8311yescharacteristic
1313C22#540×C8311yescharacteristic
1314C22#542×C8311yescharacteristic
1315C22D42×C8311yescharacteristic
1316C22D42×C8311yescharacteristic
1317C22D42×C8311yescharacteristic
1318C22#546×C8311yescharacteristic
1319C22#546×C8311yescharacteristic
1320C22#546×C8311yescharacteristic
1321C22#546×C8311yescharacteristic
1322C22#546×C8311yescharacteristic
1323C22#547×C8311yescharacteristic
1324C22#547×C8311yescharacteristic
1325C22#548×C8311yescharacteristic
1326C22#548×C8311yescharacteristic
1327C22#550×C8311yescharacteristic
1328C22#551×C8311yescharacteristic
1329C22#551×C8311yescharacteristic
1330C22#553×C8311yescharacteristic
1331C4—24no—
1332C4—24no—
1333C4—24no—
1334C4—42no—
1335C4—42no—
1336C4—42no—
1337C4—42no—
1338C4—42no—
1339C4—81no—
1340C4—81no—
1341C4—81no—
1342C4—81no—
1343C2—44no—
1344C2—44no—
1345C2—82no—
1346C2C83×#239211yescharacteristic
1347C2C83×#240711yescharacteristic
1348C2C83×#241011yescharacteristic
1349C2C83×#241611yescharacteristic
1350C2C83×#242411yescharacteristic
1351C2C83×#242511yescharacteristic
1352C2C83×#242711yescharacteristic
1353C2C83×#242811yescharacteristic
1354C2C83×#245711yescharacteristic
1355C2C83×#246111yescharacteristic
1356C2C83×#246311yescharacteristic
1357C2C83×#246711yescharacteristic
1358C2C83×#253411yescharacteristic
1359C2C83×#263011yescharacteristic
1360C2C83×#284711yescharacteristic
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. C22×C4×D4×C83C2semidirect
2. C2×#396×C83C2semidirect
3. C2×#394×C83C2semidirect
4. C2×#394×C83C2semidirect
6. C2×#386×C83C2semidirect
7. C2×#386×C83C2semidirect
8. C2×#380×C83C2semidirect
9. C83×#1441C2semidirect
10. C83×#1440C2semidirect
11. C83×#1439C2semidirect
12. C83×#1438C2semidirect
13. C83×#1437C2semidirect
14. C83×#1436C2semidirect
15. C83×C22⋊#95C2semidirect
98. C23×C4×C83D4semidirect
123. C2×C4⋊C4×C83D4semidirect
162. C2×C22⋊C4×C83D4semidirect
177. #95×C83D4semidirect
662. #14732C83direct (N × H)
681. C22×C4×D4C2×C83semidirect
682. C2×#396C2×C83semidirect
683. C2×#394C2×C83semidirect
684. C2×#394C2×C83semidirect
686. C2×#386C2×C83semidirect
687. C2×#386C2×C83semidirect
688. C2×#380C2×C83semidirect
689. #1441C2×C83semidirect
690. #1440C2×C83semidirect
691. #1439C2×C83semidirect
692. #1438C2×C83semidirect
693. #1437C2×C83semidirect
694. #1436C2×C83semidirect
695. C22⋊#95C2×C83semidirect
696. C83#14732direct (N × H)
779. C23×C4D4×C83semidirect
804. C2×C4⋊C4D4×C83semidirect
843. C2×C22⋊C4D4×C83semidirect
858. #95D4×C83semidirect

Maximal subgroups

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

subgroupindex
C22×C4×D4×C832
C2×#396×C832
C2×#394×C832
C2×#392×C832
C2×#386×C832
C2×#380×C832
C83×#14412
C83×#14402
C83×#14392
C83×#14382
C83×#14372
C83×#14362
C83×C22⋊#952
#1473283