Finite Group Databasebeta

← C83×#14408 #35242232

Subgroups — C83×#14408 #35242232

Order 21248.

1650 conjugacy classes of subgroups.

The subgroup lattice has 1022 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#389×C83C211yesmaximal, characteristic, complemented
2C2×#388×C83C211yesmaximal, characteristic
3C2×#388×C83C211yesmaximal, characteristic
4C2×#385×C83C211yesmaximal, characteristic
5C2×#380×C83C211yesmaximal, characteristic
6C83×#1444C211yesmaximal, characteristic, complemented
7C83×#1442C211yesmaximal, characteristic, complemented
8C83×#1441C211yesmaximal, characteristic, complemented
9C83×#1441C211yesmaximal, characteristic, complemented
10C83×#1439C211yesmaximal, characteristic
11C83×#1439C211yesmaximal, characteristic
12C83×#1436C211yesmaximal, characteristic, complemented
13C83×#1436C211yesmaximal, characteristic, complemented
14C83×C4⋊#95C211yesmaximal, characteristic, complemented
15C83×C22⋊#95C211yesmaximal, characteristic
16C24×C4×C83C2211yescharacteristic
17C22×C4⋊C4×C83C2211yescharacteristic
18C22×C4⋊C4×C83C2211yescharacteristic
19C22×C4⋊C4×C83C2211yescharacteristic
20C22×C4⋊C4×C83C2211yescharacteristic
21C22×C4⋊C4×C83C2211yescharacteristic
22C22×C4⋊C4×C83C2211yescharacteristic
23C22×C4⋊C4×C83C2211yescharacteristic
24C22×C4⋊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×C42×C83C2211yescharacteristic
32C22×C42×C83C2211yescharacteristic
33#389×C83—24no—
34#388×C83—24no—
35#388×C83—24no—
36#385×C83C418yescomplemented
37#380×C83—24no—
38C2×#95×C83C2211yescharacteristic
39C2×#95×C83C2211yescharacteristic
40C2×#95×C83C2211yescharacteristic
41C2×#95×C83C2211yescharacteristic
42C2×#95×C83C2211yescharacteristic
43C2×#95×C83C2211yescharacteristic
44C2×#95×C83C2211yescharacteristic
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
56C25×C83C2311yescharacteristic
57C23×C4×C83—22no—
58C23×C4×C83—22no—
59C23×C4×C83—41no—
60C23×C4×C83—41no—
61C23×C4×C83—41no—
62C23×C4×C83—41no—
63C23×C4×C83C2×C414yes—
64C23×C4×C83C2311yescharacteristic
65C23×C4×C83C2311yescharacteristic
66C23×C4×C83C2311yescharacteristic
67C23×C4×C83C2311yescharacteristic
68C23×C4×C83C2311yescharacteristic
69C23×C4×C83C2311yescharacteristic
70C23×C4×C83C2311yescharacteristic
71C23×C4×C83C2311yescharacteristic
72C23×C4×C83C2311yescharacteristic
73C23×C4×C83C2311yescharacteristic
74C23×C4×C83C2311yescharacteristic
75C23×C4×C83C2311yescharacteristic
76C23×C4×C83C2311yescharacteristic
77C23×C4×C83C2311yescharacteristic
78C2×C4⋊C4×C83—22no—
79C2×C4⋊C4×C83—22no—
80C2×C4⋊C4×C83—22no—
81C2×C4⋊C4×C83—22no—
82C2×C4⋊C4×C83—22no—
83C2×C4⋊C4×C83—22no—
84C2×C4⋊C4×C83—22no—
85C2×C4⋊C4×C83—22no—
86C2×C4⋊C4×C83—22no—
87C2×C4⋊C4×C83—41no—
88C2×C4⋊C4×C83—41no—
89C2×C4⋊C4×C83—41no—
90C2×C4⋊C4×C83—41no—
91C2×C4⋊C4×C83—41no—
92C2×C4⋊C4×C83—41no—
93C2×C4⋊C4×C83—41no—
94C2×C4⋊C4×C83—41no—
95C2×C4⋊C4×C83—41no—
96C2×C4⋊C4×C83—41no—
97C2×C4⋊C4×C83—41no—
98C2×C4⋊C4×C83—41no—
99C2×C4⋊C4×C83C2×C414yes—
100C2×C4⋊C4×C83C2×C414yes—
101C2×C4⋊C4×C83D414yes—
102C2×C22⋊C4×C83—22no—
103C2×C22⋊C4×C83—22no—
104C2×C22⋊C4×C83—22no—
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—41no—
111C2×C22⋊C4×C83—41no—
112C2×C22⋊C4×C83—41no—
113C2×C22⋊C4×C83—41no—
114C2×C22⋊C4×C83—41no—
115C2×C22⋊C4×C83—41no—
116C2×C22⋊C4×C83C2×C414yes—
117C2×C22⋊C4×C83C2×C414yes—
118C2×C22⋊C4×C83D414yes—
119C2×C22⋊C4×C83Q814yes—
120C2×C42×C83—22no—
121C2×C42×C83—22no—
122C2×C42×C83—22no—
123C2×C42×C83—22no—
124C2×C42×C83—41no—
125C2×C42×C83—41no—
126#95×C83—22no—
127#95×C83—22no—
128#95×C83—22no—
129#95×C83—22no—
130#95×C83—22no—
131#95×C83—22no—
132#95×C83—22no—
133#95×C83—22no—
134#95×C83—22no—
135#95×C83—22no—
136#95×C83—41no—
137#95×C83—41no—
138#95×C83—41no—
139#95×C83—41no—
140#95×C83—41no—
141#95×C83—41no—
142#95×C83C2×C414yes—
143#95×C83C2×C414yes—
144C24×C83—21no—
145C24×C83—21no—
146C24×C83—21no—
147C24×C83—21no—
148C24×C83—21no—
149C24×C83—21no—
150C24×C83—21no—
151C24×C83—21no—
152C24×C83—21no—
153C24×C83—21no—
154C24×C83—21no—
155C24×C83—21no—
156C24×C83C22×C412yes—
157C24×C83C2×D412yes—
158C24×C83C2×Q812yes—
159C24×C83C2411yescharacteristic
160C22×C4×C83—21no—
161C22×C4×C83—21no—
162C22×C4×C83—21no—
163C22×C4×C83—21no—
164C22×C4×C83—21no—
165C22×C4×C83—21no—
166C22×C4×C83—21no—
167C22×C4×C83—21no—
168C22×C4×C83—21no—
169C22×C4×C83—21no—
170C22×C4×C83—21no—
171C22×C4×C83—21no—
172C22×C4×C83—21no—
173C22×C4×C83—21no—
174C22×C4×C83—21no—
175C22×C4×C83—21no—
176C22×C4×C83—21no—
177C22×C4×C83—21no—
178C22×C4×C83—21no—
179C22×C4×C83—21no—
180C22×C4×C83—21no—
181C22×C4×C83—21no—
182C22×C4×C83—21no—
183C22×C4×C83—21no—
184C22×C4×C83—21no—
185C22×C4×C83—21no—
186C22×C4×C83—21no—
187C22×C4×C83—21no—
188C22×C4×C83—21no—
189C22×C4×C83—21no—
190C22×C4×C83—21no—
191C22×C4×C83—21no—
192C22×C4×C83—21no—
193C22×C4×C83—21no—
194C22×C4×C83—21no—
195C22×C4×C83—21no—
196C22×C4×C83—21no—
197C22×C4×C83—21no—
198C22×C4×C83—21no—
199C22×C4×C83—21no—
200C22×C4×C83—21no—
201C22×C4×C83—21no—
202C22×C4×C83—21no—
203C22×C4×C83—21no—
204C22×C4×C83—21no—
205C22×C4×C83—21no—
206C22×C4×C83—21no—
207C22×C4×C83—21no—
208C22×C4×C83—21no—
209C22×C4×C83—21no—
210C22×C4×C83—21no—
211C22×C4×C83—21no—
212C22×C4×C83—21no—
213C22×C4×C83—21no—
214C22×C4×C83—28no—
215C22×C4×C83—21no—
216C22×C4×C83—21no—
217C22×C4×C83—21no—
218C22×C4×C83—21no—
219C22×C4×C83—21no—
220C22×C4×C83—21no—
221C22×C4×C83—21no—
222C22×C4×C83—21no—
223C22×C4×C83—21no—
224C22×C4×C83—21no—
225C22×C4×C83—21no—
226C22×C4×C83—21no—
227C22×C4×C83—21no—
228C22×C4×C83—21no—
229C22×C4×C83—21no—
230C22×C4×C83—21no—
231C22×C4×C83—21no—
232C22×C4×C83—21no—
233C22×C4×C83—21no—
234C22×C4×C83—21no—
235C22×C4×C83—21no—
236C22×C4×C83—21no—
237C22×C4×C83—21no—
238C22×C4×C83—21no—
239C22×C4×C83—21no—
240C22×C4×C83—21no—
241C22×C4×C83—21no—
242C22×C4×C83—21no—
243C22×C4×C83—44no—
244C22×C4×C83—44no—
245C22×C4×C83—44no—
246C22×C4×C83—44no—
247C22×C4×C83—44no—
248C22×C4×C83—44no—
249C22×C4×C83C22×C412yes—
250C22×C4×C83C22×C412yes—
251C22×C4×C83C22×C412yes—
252C22×C4×C83C22×C412yes—
253C22×C4×C83C22×C412yes—
254C22×C4×C83C22×C412yes—
255C22×C4×C83C2×D412yes—
256C22×C4×C83C2×D412yes—
257C22×C4×C83C2×D412yes—
258C22×C4×C83C2×D412yes—
259C22×C4×C83C2×D412yes—
260C22×C4×C83C2×Q812yes—
261C22×C4×C83C2×Q812yes—
262C22×C4×C83#4112yes—
263C22×C4×C83#4112yes—
264C22×C4×C83#4112yes—
265C4⋊C4×C83—28no—
266C4⋊C4×C83—44no—
267C4⋊C4×C83—44no—
268C4⋊C4×C83—44no—
269C4⋊C4×C83—44no—
270C4⋊C4×C83—44no—
271C4⋊C4×C83—44no—
272C4⋊C4×C83—44no—
273C22⋊C4×C83—44no—
274C22⋊C4×C83—44no—
275C22⋊C4×C83—44no—
276C22⋊C4×C83—44no—
277C22⋊C4×C83—44no—
278C22⋊C4×C83C4⋊C4116yescomplemented
279C42×C83—44no—
280C42×C83—44no—
281C23×C83—22no—
282C23×C83—22no—
283C23×C83—22no—
284C23×C83—22no—
285C23×C83—22no—
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—41no—
300C23×C83—41no—
301C23×C83—41no—
302C23×C83—41no—
303C23×C83—41no—
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×C83C2×C4⋊C414yes—
316C23×C83C23×C411yescharacteristic
317C23×C83C22×D411yescharacteristic
318C23×C83C22×D411yescharacteristic
319C23×C83C22×Q811yescharacteristic
320C23×C83C2×#4111yescharacteristic
321C23×C83C2×#4111yescharacteristic
322C23×C83C2×#4111yescharacteristic
323C23×C83H(5,𝔽2)11yescharacteristic
324C23×C83H(5,𝔽2)11yescharacteristic
325C23×C83H(5,𝔽2)11yescharacteristic
326C23×C83H(5,𝔽2)11yescharacteristic
327C23×C83H(5,𝔽2)11yescharacteristic
328C23×C832−1+411yescharacteristic
329C23×C832−1+411yescharacteristic
330C23×C832−1+411yescharacteristic
331C2×C4×C83—22no—
332C2×C4×C83—22no—
333C2×C4×C83—22no—
334C2×C4×C83—22no—
335C2×C4×C83—22no—
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—22no—
355C2×C4×C83—22no—
356C2×C4×C83—22no—
357C2×C4×C83—22no—
358C2×C4×C83—22no—
359C2×C4×C83—22no—
360C2×C4×C83—22no—
361C2×C4×C83—22no—
362C2×C4×C83—22no—
363C2×C4×C83—22no—
364C2×C4×C83—22no—
365C2×C4×C83—22no—
366C2×C4×C83—22no—
367C2×C4×C83—22no—
368C2×C4×C83—22no—
369C2×C4×C83—22no—
370C2×C4×C83—416no—
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×C83—41no—
381C2×C4×C83—41no—
382C2×C4×C83—41no—
383C2×C4×C83—41no—
384C2×C4×C83—41no—
385C2×C4×C83—41no—
386C2×C4×C83—41no—
387C2×C4×C83—41no—
388C2×C4×C83—41no—
389C2×C4×C83—41no—
390C2×C4×C83—41no—
391C2×C4×C83—41no—
392C2×C4×C83—41no—
393C2×C4×C83—41no—
394C2×C4×C83—41no—
395C2×C4×C83—41no—
396C2×C4×C83—41no—
397C2×C4×C83—41no—
398C2×C4×C83—41no—
399C2×C4×C83—41no—
400C2×C4×C83—41no—
401C2×C4×C83—41no—
402C2×C4×C83—41no—
403C2×C4×C83—41no—
404C2×C4×C83—41no—
405C2×C4×C83—41no—
406C2×C4×C83—41no—
407C2×C4×C83—41no—
408C2×C4×C83—41no—
409C2×C4×C83—41no—
410C2×C4×C83—41no—
411C2×C4×C83—41no—
412C2×C4×C83—41no—
413C2×C4×C83—41no—
414C2×C4×C83—41no—
415C2×C4×C83—41no—
416C2×C4×C83—41no—
417C2×C4×C83—41no—
418C2×C4×C83—41no—
419C2×C4×C83—41no—
420C2×C4×C83—41no—
421C2×C4×C83—41no—
422C2×C4×C83—41no—
423C2×C4×C83—41no—
424C2×C4×C83—41no—
425C2×C4×C83—41no—
426C2×C4×C83—41no—
427C2×C4×C83C2×C4⋊C414yes—
428C2×C4×C83C2×C4⋊C414yes—
429C2×C4×C83C4×D414yes—
430C22×C83—24no—
431C22×C83—24no—
432C22×C83—24no—
433C22×C83—42no—
434C22×C83—42no—
435C22×C83—42no—
436C22×C83—42no—
437C22×C83—42no—
438C22×C83—42no—
439C22×C83—42no—
440C22×C83—42no—
441C22×C83—42no—
442C22×C83—42no—
443C22×C83—42no—
444C22×C83—42no—
445C22×C83C22×C4⋊C411yescharacteristic
446C22×C83C2×C4×D411yescharacteristic
447C22×C83C4×#4111yescharacteristic
448C22×C83#51811yescharacteristic
449C22×C83#51811yescharacteristic
450C22×C83#51911yescharacteristic
451C22×C83#52011yescharacteristic
452C22×C83#53411yescharacteristic
453C22×C83#53511yescharacteristic
454C22×C83#53711yescharacteristic
455C22×C83#53711yescharacteristic
456C22×C83#53811yescharacteristic
457C22×C83#53811yescharacteristic
458C22×C83#53811yescharacteristic
459C22×C83#53911yescharacteristic
460C22×C83#54011yescharacteristic
461C22×C83#54211yescharacteristic
462C22×C83#54411yescharacteristic
463C22×C83#54411yescharacteristic
464C22×C83D4211yescharacteristic
465C22×C83#54611yescharacteristic
466C22×C83#54611yescharacteristic
467C22×C83#54711yescharacteristic
468C22×C83#54711yescharacteristic
469C22×C83#54811yescharacteristic
470C22×C83D4×Q811yescharacteristic
471C22×C83#55211yescharacteristic
472C22×C83#55411yescharacteristic
473C22×C83#55411yescharacteristic
474C22×C83#55411yescharacteristic
475C22×C83#55611yescharacteristic
476C22×C83#56211yescharacteristic
477C22×C83#56211yescharacteristic
478C22×C83#56311yescharacteristic
479C22×C83#56311yescharacteristic
480C4×C83—24no—
481C4×C83—24no—
482C4×C83—24no—
483C4×C83—42no—
484C4×C83—42no—
485C4×C83—42no—
486C4×C83—42no—
487C4×C83—42no—
488C4×C83—42no—
489C4×C83—42no—
490C4×C83—81no—
491C4×C83—81no—
492C4×C83—81no—
493C4×C83—81no—
494#14408C8311yesmaximal, characteristic, direct product factor, Sylow
495C2×C83—44no—
496C2×C83#231611yescharacteristic
497C2×C83#232111yescharacteristic
498C2×C83#233511yescharacteristic
499C2×C83D4×C4⋊C411yescharacteristic
500C2×C83#234911yescharacteristic
501C2×C83#236211yescharacteristic
502C2×C83#237811yescharacteristic
503C2×C83#267111yescharacteristic
504C2×C83#267611yescharacteristic
505C2×C83#269511yescharacteristic
506C2×C83#271511yescharacteristic
507C2×C83#272011yescharacteristic
508C2×C83#272911yescharacteristic
509C2×C83#276811yescharacteristic
510C2×C83#278811yescharacteristic
511C2×#389C2×C8311yescharacteristic, complemented
512C2×#388C2×C8311yescharacteristic
513C2×#388C2×C8311yescharacteristic
514C2×#385C2×C8311yescharacteristic
515C2×#380C2×C8311yescharacteristic
516#1444C2×C8311yescharacteristic, complemented
517#1442C2×C8311yescharacteristic, complemented
518#1441C2×C8311yescharacteristic, complemented
519#1441C2×C8311yescharacteristic, complemented
520#1439C2×C8311yescharacteristic
521#1439C2×C8311yescharacteristic
522#1436C2×C8311yescharacteristic, complemented
523#1436C2×C8311yescharacteristic, complemented
524C4⋊#95C2×C8311yescharacteristic, complemented
525C22⋊#95C2×C8311yescharacteristic
526C83#1440811yescharacteristic, direct product factor, Sylow
527C24×C4C22×C8311yescharacteristic
528C22×C4⋊C4C22×C8311yescharacteristic
529C22×C4⋊C4C22×C8311yescharacteristic
530C22×C4⋊C4C22×C8311yescharacteristic
531C22×C4⋊C4C22×C8311yescharacteristic
532C22×C4⋊C4C22×C8311yescharacteristic
533C22×C4⋊C4C22×C8311yescharacteristic
534C22×C4⋊C4C22×C8311yescharacteristic
535C22×C4⋊C4C22×C8311yescharacteristic
536C22×C22⋊C4C22×C8311yescharacteristic
537C22×C22⋊C4C22×C8311yescharacteristic
538C22×C22⋊C4C22×C8311yescharacteristic
539C22×C22⋊C4C22×C8311yescharacteristic
540C22×C22⋊C4C22×C8311yescharacteristic
541C22×C22⋊C4C22×C8311yescharacteristic
542C22×C42C22×C8311yescharacteristic
543C22×C42C22×C8311yescharacteristic
544#389—24no—
545#388—24no—
546#388—24no—
547#385C4×C8318yescomplemented
548#380—24no—
549C2×#95C22×C8311yescharacteristic
550C2×#95C22×C8311yescharacteristic
551C2×#95C22×C8311yescharacteristic
552C2×#95C22×C8311yescharacteristic
553C2×#95C22×C8311yescharacteristic
554C2×#95C22×C8311yescharacteristic
555C2×#95C22×C8311yescharacteristic
556C2×#95C22×C8311yescharacteristic
557C2×#95C22×C8311yescharacteristic
558C2×#95C22×C8311yescharacteristic
559C2×#95C22×C8311yescharacteristic
560C2×#95C22×C8311yescharacteristic
561C2×#95C22×C8311yescharacteristic
562C2×#95C22×C8311yescharacteristic
563C2×#95C22×C8311yescharacteristic
564C2×#95C22×C8311yescharacteristic
565C2×#95C22×C8311yescharacteristic
566C2×#95C22×C8311yescharacteristic
567C25C23×C8311yescharacteristic
568C23×C4—22no—
569C23×C4—22no—
570C23×C4—41no—
571C23×C4—41no—
572C23×C4—41no—
573C23×C4—41no—
574C23×C4C2×C4×C8314yes—
575C23×C4C23×C8311yescharacteristic
576C23×C4C23×C8311yescharacteristic
577C23×C4C23×C8311yescharacteristic
578C23×C4C23×C8311yescharacteristic
579C23×C4C23×C8311yescharacteristic
580C23×C4C23×C8311yescharacteristic
581C23×C4C23×C8311yescharacteristic
582C23×C4C23×C8311yescharacteristic
583C23×C4C23×C8311yescharacteristic
584C23×C4C23×C8311yescharacteristic
585C23×C4C23×C8311yescharacteristic
586C23×C4C23×C8311yescharacteristic
587C23×C4C23×C8311yescharacteristic
588C23×C4C23×C8311yescharacteristic
589C2×C4⋊C4—22no—
590C2×C4⋊C4—22no—
591C2×C4⋊C4—22no—
592C2×C4⋊C4—22no—
593C2×C4⋊C4—22no—
594C2×C4⋊C4—22no—
595C2×C4⋊C4—22no—
596C2×C4⋊C4—22no—
597C2×C4⋊C4—22no—
598C2×C4⋊C4—41no—
599C2×C4⋊C4—41no—
600C2×C4⋊C4—41no—
601C2×C4⋊C4—41no—
602C2×C4⋊C4—41no—
603C2×C4⋊C4—41no—
604C2×C4⋊C4—41no—
605C2×C4⋊C4—41no—
606C2×C4⋊C4—41no—
607C2×C4⋊C4—41no—
608C2×C4⋊C4—41no—
609C2×C4⋊C4—41no—
610C2×C4⋊C4C2×C4×C8314yes—
611C2×C4⋊C4C2×C4×C8314yes—
612C2×C4⋊C4D4×C8314yes—
613C2×C22⋊C4—22no—
614C2×C22⋊C4—22no—
615C2×C22⋊C4—22no—
616C2×C22⋊C4—22no—
617C2×C22⋊C4—22no—
618C2×C22⋊C4—22no—
619C2×C22⋊C4—22no—
620C2×C22⋊C4—22no—
621C2×C22⋊C4—41no—
622C2×C22⋊C4—41no—
623C2×C22⋊C4—41no—
624C2×C22⋊C4—41no—
625C2×C22⋊C4—41no—
626C2×C22⋊C4—41no—
627C2×C22⋊C4C2×C4×C8314yes—
628C2×C22⋊C4C2×C4×C8314yes—
629C2×C22⋊C4D4×C8314yes—
630C2×C22⋊C4Q8×C8314yes—
631C2×C42—22no—
632C2×C42—22no—
633C2×C42—22no—
634C2×C42—22no—
635C2×C42—41no—
636C2×C42—41no—
637#95—22no—
638#95—22no—
639#95—22no—
640#95—22no—
641#95—22no—
642#95—22no—
643#95—22no—
644#95—22no—
645#95—22no—
646#95—22no—
647#95—41no—
648#95—41no—
649#95—41no—
650#95—41no—
651#95—41no—
652#95—41no—
653#95C2×C4×C8314yes—
654#95C2×C4×C8314yes—
655C24—21no—
656C24—21no—
657C24—21no—
658C24—21no—
659C24—21no—
660C24—21no—
661C24—21no—
662C24—21no—
663C24—21no—
664C24—21no—
665C24—21no—
666C24—21no—
667C24C22×C4×C8312yes—
668C24C2×D4×C8312yes—
669C24C2×Q8×C8312yes—
670C24C24×C8311yescharacteristic
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
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—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—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—28no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—44no—
755C22×C4—44no—
756C22×C4—44no—
757C22×C4—44no—
758C22×C4—44no—
759C22×C4—44no—
760C22×C4C22×C4×C8312yes—
761C22×C4C22×C4×C8312yes—
762C22×C4C22×C4×C8312yes—
763C22×C4C22×C4×C8312yes—
764C22×C4C22×C4×C8312yes—
765C22×C4C22×C4×C8312yes—
766C22×C4C2×D4×C8312yes—
767C22×C4C2×D4×C8312yes—
768C22×C4C2×D4×C8312yes—
769C22×C4C2×D4×C8312yes—
770C22×C4C2×D4×C8312yes—
771C22×C4C2×Q8×C8312yes—
772C22×C4C2×Q8×C8312yes—
773C22×C4#41×C8312yes—
774C22×C4#41×C8312yes—
775C22×C4#41×C8312yes—
776C4⋊C4—28no—
777C4⋊C4—44no—
778C4⋊C4—44no—
779C4⋊C4—44no—
780C4⋊C4—44no—
781C4⋊C4—44no—
782C4⋊C4—44no—
783C4⋊C4—44no—
784C22⋊C4—44no—
785C22⋊C4—44no—
786C22⋊C4—44no—
787C22⋊C4—44no—
788C22⋊C4—44no—
789C22⋊C4C4⋊C4×C83116yescomplemented
790C42—44no—
791C42—44no—
792C23—22no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—22no—
799C23—22no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23C2×C4⋊C4×C8314yes—
827C23C23×C4×C8311yescharacteristic
828C23C22×D4×C8311yescharacteristic
829C23C22×D4×C8311yescharacteristic
830C23C22×Q8×C8311yescharacteristic
831C23C2×#41×C8311yescharacteristic
832C23C2×#41×C8311yescharacteristic
833C23C2×#41×C8311yescharacteristic
834C23H(5,𝔽2)×C8311yescharacteristic
835C23H(5,𝔽2)×C8311yescharacteristic
836C23H(5,𝔽2)×C8311yescharacteristic
837C23H(5,𝔽2)×C8311yescharacteristic
838C23H(5,𝔽2)×C8311yescharacteristic
839C232−1+4×C8311yescharacteristic
840C232−1+4×C8311yescharacteristic
841C232−1+4×C8311yescharacteristic
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
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—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—416no—
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—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4C2×C4⋊C4×C8314yes—
939C2×C4C2×C4⋊C4×C8314yes—
940C2×C4C4×D4×C8314yes—
941C22—24no—
942C22—24no—
943C22—24no—
944C22—42no—
945C22—42no—
946C22—42no—
947C22—42no—
948C22—42no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22—42no—
953C22—42no—
954C22—42no—
955C22—42no—
956C22C22×C4⋊C4×C8311yescharacteristic
957C22C2×C4×D4×C8311yescharacteristic
958C22C4×#41×C8311yescharacteristic
959C22#518×C8311yescharacteristic
960C22#518×C8311yescharacteristic
961C22#519×C8311yescharacteristic
962C22#520×C8311yescharacteristic
963C22#534×C8311yescharacteristic
964C22#535×C8311yescharacteristic
965C22#537×C8311yescharacteristic
966C22#537×C8311yescharacteristic
967C22#538×C8311yescharacteristic
968C22#538×C8311yescharacteristic
969C22#538×C8311yescharacteristic
970C22#539×C8311yescharacteristic
971C22#540×C8311yescharacteristic
972C22#542×C8311yescharacteristic
973C22#544×C8311yescharacteristic
974C22#544×C8311yescharacteristic
975C22D42×C8311yescharacteristic
976C22#546×C8311yescharacteristic
977C22#546×C8311yescharacteristic
978C22#547×C8311yescharacteristic
979C22#547×C8311yescharacteristic
980C22#548×C8311yescharacteristic
981C22D4×Q8×C8311yescharacteristic
982C22#552×C8311yescharacteristic
983C22#554×C8311yescharacteristic
984C22#554×C8311yescharacteristic
985C22#554×C8311yescharacteristic
986C22#556×C8311yescharacteristic
987C22#562×C8311yescharacteristic
988C22#562×C8311yescharacteristic
989C22#563×C8311yescharacteristic
990C22#563×C8311yescharacteristic
991C4—24no—
992C4—24no—
993C4—24no—
994C4—42no—
995C4—42no—
996C4—42no—
997C4—42no—
998C4—42no—
999C4—42no—
1000C4—42no—
1001C4—81no—
1002C4—81no—
1003C4—81no—
1004C4—81no—
1005C2—44no—
1006C2C83×#231611yescharacteristic
1007C2C83×#232111yescharacteristic
1008C2C83×#233511yescharacteristic
1009C2D4×C4⋊C4×C8311yescharacteristic
1010C2C83×#234911yescharacteristic
1011C2C83×#236211yescharacteristic
1012C2C83×#237811yescharacteristic
1013C2C83×#267111yescharacteristic
1014C2C83×#267611yescharacteristic
1015C2C83×#269511yescharacteristic
1016C2C83×#271511yescharacteristic
1017C2C83×#272011yescharacteristic
1018C2C83×#272911yescharacteristic
1019C2C83×#276811yescharacteristic
1020C2C83×#278811yescharacteristic
subgroupG/H
center, socleC24×C83C24
commutatorC23C23×C4×C83
Frattini, cosocleC24C24×C83
prime radicalC25×C83C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C83 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#389×C83C2semidirect
6. C83×#1444C2semidirect
7. C83×#1442C2semidirect
8. C83×#1441C2semidirect
9. C83×#1441C2semidirect
12. C83×#1436C2semidirect
13. C83×#1436C2semidirect
14. C83×C4⋊#95C2semidirect
36. #385×C83C4semidirect
278. C22⋊C4×C83C4⋊C4semidirect
494. #14408C83direct (N × H)
511. C2×#389C2×C83semidirect
516. #1444C2×C83semidirect
517. #1442C2×C83semidirect
518. #1441C2×C83semidirect
519. #1441C2×C83semidirect
522. #1436C2×C83semidirect
523. #1436C2×C83semidirect
524. C4⋊#95C2×C83semidirect
526. C83#14408direct (N × H)
547. #385C4×C83semidirect
789. C22⋊C4C4⋊C4×C83semidirect

Maximal subgroups

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

subgroupindex
C2×#389×C832
C2×#388×C832
C2×#385×C832
C2×#380×C832
C83×#14442
C83×#14422
C83×#14412
C83×#14392
C83×#14362
C83×C4⋊#952
C83×C22⋊#952
#1440883