Finite Group Databasebeta

← C83×#22580 #35250404

Subgroups — C83×#22580 #35250404

Order 21248.

1150 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#418×C83C211yesmaximal, characteristic
2C83×#2347C211yesmaximal, characteristic, complemented
3D4×C22⋊C4×C83C211yesmaximal, characteristic
4C83×#1936C211yesmaximal, characteristic, complemented
5C83×#1934C211yesmaximal, characteristic, complemented
6C83×#1926C211yesmaximal, characteristic, complemented
7C83×#1925C211yesmaximal, characteristic, complemented
8C83×#1864C211yesmaximal, characteristic, complemented
9C83×#1862C211yesmaximal, characteristic, complemented
10C83×#1825C211yesmaximal, characteristic, complemented
11C83×#1809C211yesmaximal, characteristic, complemented
12C83×#1786C211yesmaximal, characteristic
13C83×#1762C211yesmaximal, characteristic, complemented
14C4×#102×C83C211yesmaximal, characteristic, complemented
15C83×#1753C211yesmaximal, characteristic, complemented
16C23×D4×C83C2211yescharacteristic
17C22×M16×C83C2211yescharacteristic
18C2×C4×D4×C83C2211yescharacteristic
19C2×C4×D4×C83C2211yescharacteristic
20C2×#117×C83C2211yescharacteristic
21C22×C22⋊C4×C83—21no—
22C2×#107×C83C2211yescharacteristic, complemented
23C2×#106×C83C2211yescharacteristic, complemented
24#418×C83C418yescomplemented
25C2×#102×C83C2211yescharacteristic
26C2×#102×C83C2211yescharacteristic
27C2×#102×C83C2211yescharacteristic
28C2×#102×C83C2211yescharacteristic
29C2×#102×C83C2211yescharacteristic
30C2×#102×C83C2211yescharacteristic
31C2×#102×C83C2211yescharacteristic
32C2×#102×C83C2211yescharacteristic
33C2×C22⋊C8×C83C2211yescharacteristic
34C2×#97×C83C2211yescharacteristic, complemented
35C2×C4×C8×C83C2211yescharacteristic, complemented
36#390×C83C2211yescharacteristic
37#390×C83C2211yescharacteristic
38#389×C83C2211yescharacteristic, complemented
39#389×C83C2211yescharacteristic, complemented
40#388×C83—21no—
41#388×C83—21no—
42#386×C83—21no—
43#386×C83—21no—
44#383×C83—21no—
45#380×C83C2211yescharacteristic
46#380×C83C2211yescharacteristic
47#379×C83—21no—
48C4×C4⋊C4×C83—21no—
49C4×C4⋊C4×C83C2211yescharacteristic, complemented
50C4×C4⋊C4×C83C2211yescharacteristic, complemented
51C4×C22⋊C4×C83C2211yescharacteristic
52#340×C83C2211yescharacteristic, complemented
53#340×C83C2211yescharacteristic, complemented
54#340×C83C2211yescharacteristic, complemented
55#340×C83C2211yescharacteristic, complemented
56#340×C83C2211yescharacteristic, complemented
57#340×C83C2211yescharacteristic, complemented
58#336×C83C2211yescharacteristic, complemented
59#336×C83C2211yescharacteristic, complemented
60C25×C83—21no—
61C22×D4×C83—22no—
62C22×D4×C83—22no—
63C22×D4×C83—21no—
64C22×D4×C83—22no—
65C22×D4×C83—41no—
66C22×D4×C83—41no—
67C22×D4×C83C2×C414yes—
68C22×D4×C83C2311yescharacteristic
69C22×D4×C83C2311yescharacteristic
70C23×C4×C83—21no—
71C23×C4×C83—21no—
72C23×C4×C83C2311yescharacteristic
73C2×M16×C83—41no—
74C2×M16×C83—41no—
75C2×M16×C83C2×C414yescomplemented
76C22×C8×C83C2311yescharacteristic
77C22×C8×C83C2311yescharacteristic
78C22×C8×C83C2311yescharacteristic
79C22×C8×C83C2311yescharacteristic
80C4×D4×C83—22no—
81C4×D4×C83—22no—
82C4×D4×C83—41no—
83C4×D4×C83—41no—
84#117×C83—22no—
85#117×C83C2×C414yescomplemented
86C2×C4⋊C4×C83—21no—
87C2×C4⋊C4×C83—21no—
88C2×C4⋊C4×C83C2311yescharacteristic
89C2×C4⋊C4×C83C2311yescharacteristic
90C2×C4⋊C4×C83C2311yescharacteristic
91C2×C4⋊C4×C83C2311yescharacteristic
92C2×C4⋊C4×C83C2311yescharacteristic
93C2×C4⋊C4×C83C2311yescharacteristic
94C2×C22⋊C4×C83—21no—
95C2×C22⋊C4×C83—21no—
96C2×C22⋊C4×C83—21no—
97C2×C22⋊C4×C83—21no—
98C2×C22⋊C4×C83—21no—
99C2×C22⋊C4×C83—21no—
100C2×C22⋊C4×C83—21no—
101C2×C22⋊C4×C83—21no—
102C2×C22⋊C4×C83—21no—
103C2×C22⋊C4×C83—44no—
104C2×C22⋊C4×C83D411yescharacteristic
105C2×C22⋊C4×C83D411yescharacteristic
106C2×C42×C83—21no—
107C2×C42×C83—21no—
108C2×C42×C83—21no—
109C2×C42×C83C2311yescharacteristic
110C2×C42×C83C2311yescharacteristic
111#107×C83—41no—
112#106×C83—41no—
113#102×C83—22no—
114#102×C83—22no—
115#102×C83—41no—
116#102×C83—41no—
117#102×C83C2×C414yes—
118#102×C83C2×C414yes—
119#102×C83C2×C414yescomplemented
120#102×C83C2×C414yescomplemented
121C22⋊C8×C83—22no—
122#97×C83—41no—
123C4×C8×C83—41no—
124#95×C83—21no—
125#95×C83—21no—
126#95×C83—21no—
127#95×C83—21no—
128#95×C83—21no—
129#95×C83—21no—
130#95×C83D411yescharacteristic
131#95×C83D411yescharacteristic
132C24×C83—21no—
133C24×C83—21no—
134C24×C83—24no—
135C24×C83—42no—
136C24×C83—42no—
137C24×C83—42no—
138C24×C83—42no—
139C24×C83—81no—
140C24×C83—81no—
141C24×C83C2×D411yescharacteristic
142C2×D4×C83—28no—
143C2×D4×C83—24no—
144C2×D4×C83—21no—
145C2×D4×C83—21no—
146C2×D4×C83—21no—
147C2×D4×C83—21no—
148C2×D4×C83—21no—
149C2×D4×C83—21no—
150C2×D4×C83—21no—
151C2×D4×C83—21no—
152C2×D4×C83—44no—
153C2×D4×C83—44no—
154C2×D4×C83—44no—
155C2×D4×C83—42no—
156C2×D4×C83—42no—
157C2×D4×C83C22×C412yes—
158C2×D4×C83C22×C412yes—
159C2×D4×C83#4112yes—
160C2×D4×C83#4112yes—
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—42no—
172C22×C4×C83—42no—
173C22×C4×C83—42no—
174C22×C4×C83—42no—
175C22×C4×C83—81no—
176C22×C4×C83—81no—
177C22×C4×C83C22×C412yes—
178C22×C4×C83C2×D411yescharacteristic
179C22×C4×C83C2×D411yescharacteristic
180C22×C4×C83C2×D411yescharacteristic
181C22×C4×C83C2×D411yescharacteristic
182C22×C4×C83C2×D411yescharacteristic
183C22×C4×C83#4112yes—
184C22×C4×C83C2411yescharacteristic
185M16×C83—44no—
186C2×C8×C83—21no—
187C2×C8×C83—21no—
188C2×C8×C83—21no—
189C2×C8×C83—21no—
190C2×C8×C83—21no—
191C2×C8×C83—21no—
192C2×C8×C83—21no—
193C2×C8×C83—21no—
194C2×C8×C83—21no—
195C2×C8×C83—21no—
196C2×C8×C83C22×C412yes—
197C2×C8×C83C22×C412yes—
198C4⋊C4×C83—21no—
199C4⋊C4×C83—21no—
200C4⋊C4×C83—21no—
201C4⋊C4×C83—21no—
202C4⋊C4×C83—21no—
203C4⋊C4×C83—21no—
204C4⋊C4×C83—21no—
205C4⋊C4×C83—21no—
206C4⋊C4×C83—21no—
207C4⋊C4×C83—21no—
208C4⋊C4×C83—42no—
209C4⋊C4×C83—42no—
210C4⋊C4×C83C22×C412yes—
211C4⋊C4×C83C22×C412yes—
212C22⋊C4×C83—24no—
213C22⋊C4×C83—22no—
214C22⋊C4×C83—41no—
215C22⋊C4×C83—42no—
216C22⋊C4×C83—42no—
217C22⋊C4×C83—42no—
218C22⋊C4×C83—42no—
219C22⋊C4×C83—42no—
220C22⋊C4×C83—81no—
221C22⋊C4×C83—81no—
222C22⋊C4×C83—81no—
223C42×C83—24no—
224C42×C83—21no—
225C42×C83—21no—
226C42×C83—21no—
227C42×C83—21no—
228C42×C83—81no—
229C42×C83—81no—
230C23×C83—22no—
231C23×C83—22no—
232C23×C83—22no—
233C23×C83—21no—
234C23×C83—21no—
235C23×C83—21no—
236C23×C83—21no—
237C23×C83—21no—
238C23×C83—21no—
239C23×C83—22no—
240C23×C83—48no—
241C23×C83—48no—
242C23×C83—41no—
243C23×C83—41no—
244C23×C83—41no—
245C23×C83—41no—
246C23×C83—41no—
247C23×C83—41no—
248C23×C83—41no—
249C23×C83—41no—
250C23×C83—41no—
251C23×C83—41no—
252C23×C83—84no—
253C23×C83—84no—
254C23×C83—84no—
255C23×C83—84no—
256C23×C83—84no—
257C23×C83C4×D412yes—
258C23×C83C22×D411yescharacteristic
259D4×C83—22no—
260D4×C83—22no—
261D4×C83—22no—
262D4×C83—22no—
263D4×C83—22no—
264D4×C83—48no—
265D4×C83—41no—
266D4×C83—41no—
267D4×C83#11714yes—
268C2×C4×C83—21no—
269C2×C4×C83—21no—
270C2×C4×C83—21no—
271C2×C4×C83—21no—
272C2×C4×C83—22no—
273C2×C4×C83—22no—
274C2×C4×C83—22no—
275C2×C4×C83—22no—
276C2×C4×C83—22no—
277C2×C4×C83—22no—
278C2×C4×C83—21no—
279C2×C4×C83—21no—
280C2×C4×C83—21no—
281C2×C4×C83—21no—
282C2×C4×C83—21no—
283C2×C4×C83—21no—
284C2×C4×C83—21no—
285C2×C4×C83—21no—
286C2×C4×C83—21no—
287C2×C4×C83—41no—
288C2×C4×C83—41no—
289C2×C4×C83—41no—
290C2×C4×C83—41no—
291C2×C4×C83—41no—
292C2×C4×C83—41no—
293C2×C4×C83—41no—
294C2×C4×C83—41no—
295C2×C4×C83—41no—
296C2×C4×C83—41no—
297C2×C4×C83—41no—
298C2×C4×C83—41no—
299C2×C4×C83—41no—
300C2×C4×C83—41no—
301C2×C4×C83—41no—
302C2×C4×C83—41no—
303C2×C4×C83—84no—
304C2×C4×C83—84no—
305C2×C4×C83C4×D412yes—
306C2×C4×C83AGL(1,ℤ/8)12yes—
307C2×C4×C83C23×C411yescharacteristic
308C2×C4×C83C2×#4111yescharacteristic
309C2×C4×C83C2×#4111yescharacteristic
310C2×C4×C83C2×#4111yescharacteristic
311C2×C4×C83H(5,𝔽2)11yescharacteristic
312C2×C4×C83H(5,𝔽2)11yescharacteristic
313C8×C83—22no—
314C8×C83—22no—
315C8×C83—41no—
316C8×C83—41no—
317C22×C83—22no—
318C22×C83—24no—
319C22×C83—22no—
320C22×C83—22no—
321C22×C83—42no—
322C22×C83—42no—
323C22×C83—41no—
324C22×C83—42no—
325C22×C83—42no—
326C22×C83—41no—
327C22×C83—41no—
328C22×C83—42no—
329C22×C83—42no—
330C22×C83—41no—
331C22×C83—42no—
332C22×C83—42no—
333C22×C83—42no—
334C22×C83—816no—
335C22×C83—81no—
336C22×C83—81no—
337C22×C83—81no—
338C22×C83—81no—
339C22×C83C2×C4×D411yescharacteristic
340C22×C83#54611yescharacteristic
341C22×C83#54611yescharacteristic
342C22×C83C2×AGL(1,ℤ/8)11yescharacteristic
343C22×C83#57511yescharacteristic
344C22×C83#57611yescharacteristic
345C22×C83#57711yescharacteristic
346C4×C83—22no—
347C4×C83—22no—
348C4×C83—42no—
349C4×C83—42no—
350C4×C83—41no—
351C4×C83—41no—
352C4×C83—41no—
353C4×C83—81no—
354C4×C83—81no—
355C4×C83—81no—
356C4×C83—81no—
357C4×C83C2×#11711yescharacteristic
358C4×C83#51811yescharacteristic
359C4×C83#55111yescharacteristic
360C4×C83#55111yescharacteristic
361#22580C8311yesmaximal, characteristic, direct product factor, Sylow
362C2×C83—42no—
363C2×C83—44no—
364C2×C83—82no—
365C2×C83#234211yescharacteristic
366C2×C83C4×AGL(1,ℤ/8)11yescharacteristic
367C2×C83#294611yescharacteristic
368C2×C83#331111yescharacteristic
369C2×C83#331811yescharacteristic
370C2×C83#332211yescharacteristic
371C2×C83#332411yescharacteristic
372C2×#418C2×C8311yescharacteristic
373#2347C2×C8311yescharacteristic, complemented
374D4×C22⋊C4C2×C8311yescharacteristic
375#1936C2×C8311yescharacteristic, complemented
376#1934C2×C8311yescharacteristic, complemented
377#1926C2×C8311yescharacteristic, complemented
378#1925C2×C8311yescharacteristic, complemented
379#1864C2×C8311yescharacteristic, complemented
380#1862C2×C8311yescharacteristic, complemented
381#1825C2×C8311yescharacteristic, complemented
382#1809C2×C8311yescharacteristic, complemented
383#1786C2×C8311yescharacteristic
384#1762C2×C8311yescharacteristic, complemented
385C4×#102C2×C8311yescharacteristic, complemented
386#1753C2×C8311yescharacteristic, complemented
387C83#2258011yescharacteristic, direct product factor, Sylow
388C23×D4C22×C8311yescharacteristic
389C22×M16C22×C8311yescharacteristic
390C2×C4×D4C22×C8311yescharacteristic
391C2×C4×D4C22×C8311yescharacteristic
392C2×#117C22×C8311yescharacteristic
393C22×C22⋊C4—21no—
394C2×#107C22×C8311yescharacteristic, complemented
395C2×#106C22×C8311yescharacteristic, complemented
396#418C4×C8318yescomplemented
397C2×#102C22×C8311yescharacteristic
398C2×#102C22×C8311yescharacteristic
399C2×#102C22×C8311yescharacteristic
400C2×#102C22×C8311yescharacteristic
401C2×#102C22×C8311yescharacteristic
402C2×#102C22×C8311yescharacteristic
403C2×#102C22×C8311yescharacteristic
404C2×#102C22×C8311yescharacteristic
405C2×C22⋊C8C22×C8311yescharacteristic
406C2×#97C22×C8311yescharacteristic, complemented
407C2×C4×C8C22×C8311yescharacteristic, complemented
408#390C22×C8311yescharacteristic
409#390C22×C8311yescharacteristic
410#389C22×C8311yescharacteristic, complemented
411#389C22×C8311yescharacteristic, complemented
412#388—21no—
413#388—21no—
414#386—21no—
415#386—21no—
416#383—21no—
417#380C22×C8311yescharacteristic
418#380C22×C8311yescharacteristic
419#379—21no—
420C4×C4⋊C4—21no—
421C4×C4⋊C4C22×C8311yescharacteristic, complemented
422C4×C4⋊C4C22×C8311yescharacteristic, complemented
423C4×C22⋊C4C22×C8311yescharacteristic
424#340C22×C8311yescharacteristic, complemented
425#340C22×C8311yescharacteristic, complemented
426#340C22×C8311yescharacteristic, complemented
427#340C22×C8311yescharacteristic, complemented
428#340C22×C8311yescharacteristic, complemented
429#340C22×C8311yescharacteristic, complemented
430#336C22×C8311yescharacteristic, complemented
431#336C22×C8311yescharacteristic, complemented
432C25—21no—
433C22×D4—22no—
434C22×D4—22no—
435C22×D4—21no—
436C22×D4—22no—
437C22×D4—41no—
438C22×D4—41no—
439C22×D4C2×C4×C8314yes—
440C22×D4C23×C8311yescharacteristic
441C22×D4C23×C8311yescharacteristic
442C23×C4—21no—
443C23×C4—21no—
444C23×C4C23×C8311yescharacteristic
445C2×M16—41no—
446C2×M16—41no—
447C2×M16C2×C4×C8314yescomplemented
448C22×C8C23×C8311yescharacteristic
449C22×C8C23×C8311yescharacteristic
450C22×C8C23×C8311yescharacteristic
451C22×C8C23×C8311yescharacteristic
452C4×D4—22no—
453C4×D4—22no—
454C4×D4—41no—
455C4×D4—41no—
456#117—22no—
457#117C2×C4×C8314yescomplemented
458C2×C4⋊C4—21no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4C23×C8311yescharacteristic
461C2×C4⋊C4C23×C8311yescharacteristic
462C2×C4⋊C4C23×C8311yescharacteristic
463C2×C4⋊C4C23×C8311yescharacteristic
464C2×C4⋊C4C23×C8311yescharacteristic
465C2×C4⋊C4C23×C8311yescharacteristic
466C2×C22⋊C4—21no—
467C2×C22⋊C4—21no—
468C2×C22⋊C4—21no—
469C2×C22⋊C4—21no—
470C2×C22⋊C4—21no—
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4—44no—
476C2×C22⋊C4D4×C8311yescharacteristic
477C2×C22⋊C4D4×C8311yescharacteristic
478C2×C42—21no—
479C2×C42—21no—
480C2×C42—21no—
481C2×C42C23×C8311yescharacteristic
482C2×C42C23×C8311yescharacteristic
483#107—41no—
484#106—41no—
485#102—22no—
486#102—22no—
487#102—41no—
488#102—41no—
489#102C2×C4×C8314yes—
490#102C2×C4×C8314yes—
491#102C2×C4×C8314yescomplemented
492#102C2×C4×C8314yescomplemented
493C22⋊C8—22no—
494#97—41no—
495C4×C8—41no—
496#95—21no—
497#95—21no—
498#95—21no—
499#95—21no—
500#95—21no—
501#95—21no—
502#95D4×C8311yescharacteristic
503#95D4×C8311yescharacteristic
504C24—21no—
505C24—21no—
506C24—24no—
507C24—42no—
508C24—42no—
509C24—42no—
510C24—42no—
511C24—81no—
512C24—81no—
513C24C2×D4×C8311yescharacteristic
514C2×D4—28no—
515C2×D4—24no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—44no—
525C2×D4—44no—
526C2×D4—44no—
527C2×D4—42no—
528C2×D4—42no—
529C2×D4C22×C4×C8312yes—
530C2×D4C22×C4×C8312yes—
531C2×D4#41×C8312yes—
532C2×D4#41×C8312yes—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—42no—
544C22×C4—42no—
545C22×C4—42no—
546C22×C4—42no—
547C22×C4—81no—
548C22×C4—81no—
549C22×C4C22×C4×C8312yes—
550C22×C4C2×D4×C8311yescharacteristic
551C22×C4C2×D4×C8311yescharacteristic
552C22×C4C2×D4×C8311yescharacteristic
553C22×C4C2×D4×C8311yescharacteristic
554C22×C4C2×D4×C8311yescharacteristic
555C22×C4#41×C8312yes—
556C22×C4C24×C8311yescharacteristic
557M16—44no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8C22×C4×C8312yes—
569C2×C8C22×C4×C8312yes—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—42no—
581C4⋊C4—42no—
582C4⋊C4C22×C4×C8312yes—
583C4⋊C4C22×C4×C8312yes—
584C22⋊C4—24no—
585C22⋊C4—22no—
586C22⋊C4—41no—
587C22⋊C4—42no—
588C22⋊C4—42no—
589C22⋊C4—42no—
590C22⋊C4—42no—
591C22⋊C4—42no—
592C22⋊C4—81no—
593C22⋊C4—81no—
594C22⋊C4—81no—
595C42—24no—
596C42—21no—
597C42—21no—
598C42—21no—
599C42—21no—
600C42—81no—
601C42—81no—
602C23—22no—
603C23—22no—
604C23—22no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—22no—
612C23—48no—
613C23—48no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—84no—
625C23—84no—
626C23—84no—
627C23—84no—
628C23—84no—
629C23C4×D4×C8312yes—
630C23C22×D4×C8311yescharacteristic
631D4—22no—
632D4—22no—
633D4—22no—
634D4—22no—
635D4—22no—
636D4—48no—
637D4—41no—
638D4—41no—
639D4#117×C8314yes—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—84no—
676C2×C4—84no—
677C2×C4C4×D4×C8312yes—
678C2×C4AGL(1,ℤ/8)×C8312yes—
679C2×C4C23×C4×C8311yescharacteristic
680C2×C4C2×#41×C8311yescharacteristic
681C2×C4C2×#41×C8311yescharacteristic
682C2×C4C2×#41×C8311yescharacteristic
683C2×C4H(5,𝔽2)×C8311yescharacteristic
684C2×C4H(5,𝔽2)×C8311yescharacteristic
685C8—22no—
686C8—22no—
687C8—41no—
688C8—41no—
689C22—22no—
690C22—24no—
691C22—22no—
692C22—22no—
693C22—41no—
694C22—42no—
695C22—42no—
696C22—41no—
697C22—41no—
698C22—42no—
699C22—42no—
700C22—41no—
701C22—42no—
702C22—42no—
703C22—42no—
704C22—42no—
705C22—42no—
706C22—816no—
707C22—81no—
708C22—81no—
709C22—81no—
710C22—81no—
711C22C2×C4×D4×C8311yescharacteristic
712C22#546×C8311yescharacteristic
713C22#546×C8311yescharacteristic
714C22C2×AGL(1,ℤ/8)×C8311yescharacteristic
715C22#575×C8311yescharacteristic
716C22#576×C8311yescharacteristic
717C22#577×C8311yescharacteristic
718C4—22no—
719C4—22no—
720C4—41no—
721C4—41no—
722C4—41no—
723C4—42no—
724C4—42no—
725C4—81no—
726C4—81no—
727C4—81no—
728C4—81no—
729C4C2×#117×C8311yescharacteristic
730C4#518×C8311yescharacteristic
731C4#551×C8311yescharacteristic
732C4#551×C8311yescharacteristic
733C2—42no—
734C2—44no—
735C2—82no—
736C2C83×#234211yescharacteristic
737C2C4×AGL(1,ℤ/8)×C8311yescharacteristic
738C2C83×#294611yescharacteristic
739C2C83×#331111yescharacteristic
740C2C83×#331811yescharacteristic
741C2C83×#332211yescharacteristic
742C2C83×#332411yescharacteristic
subgroupG/H
center, socleC23×C83C22×D4
commutatorC2×C4C23×C4×C83
Frattini, cosocleC22×C4C24×C83
prime radicalC23×D4×C83C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C83 ◁ C4×C22⋊C4×C83 ◁ G

Complements

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

NH ≅ G/Ntype
2. C83×#2347C2semidirect
4. C83×#1936C2semidirect
5. C83×#1934C2semidirect
6. C83×#1926C2semidirect
7. C83×#1925C2semidirect
8. C83×#1864C2semidirect
9. C83×#1862C2semidirect
10. C83×#1825C2semidirect
11. C83×#1809C2semidirect
13. C83×#1762C2semidirect
14. C4×#102×C83C2semidirect
15. C83×#1753C2semidirect
22. C2×#107×C83C22semidirect
23. C2×#106×C83C22semidirect
24. #418×C83C4semidirect
34. C2×#97×C83C22semidirect
35. C2×C4×C8×C83C22semidirect
38. #389×C83C22semidirect
39. #389×C83C22semidirect
49. C4×C4⋊C4×C83C22semidirect
50. C4×C4⋊C4×C83C22semidirect
52. #340×C83C22semidirect
53. #340×C83C22semidirect
54. #340×C83C22semidirect
55. #340×C83C22semidirect
56. #340×C83C22semidirect
57. #340×C83C22semidirect
58. #336×C83C22semidirect
59. #336×C83C22semidirect
75. C2×M16×C83C2×C4semidirect
85. #117×C83C2×C4semidirect
119. #102×C83C2×C4semidirect
120. #102×C83C2×C4semidirect
361. #22580C83direct (N × H)
373. #2347C2×C83semidirect
375. #1936C2×C83semidirect
376. #1934C2×C83semidirect
377. #1926C2×C83semidirect
378. #1925C2×C83semidirect
379. #1864C2×C83semidirect
380. #1862C2×C83semidirect
381. #1825C2×C83semidirect
382. #1809C2×C83semidirect
384. #1762C2×C83semidirect
385. C4×#102C2×C83semidirect
386. #1753C2×C83semidirect
387. C83#22580direct (N × H)
394. C2×#107C22×C83semidirect
395. C2×#106C22×C83semidirect
396. #418C4×C83semidirect
406. C2×#97C22×C83semidirect
407. C2×C4×C8C22×C83semidirect
410. #389C22×C83semidirect
411. #389C22×C83semidirect
421. C4×C4⋊C4C22×C83semidirect
422. C4×C4⋊C4C22×C83semidirect
424. #340C22×C83semidirect
425. #340C22×C83semidirect
426. #340C22×C83semidirect
427. #340C22×C83semidirect
428. #340C22×C83semidirect
429. #340C22×C83semidirect
430. #336C22×C83semidirect
431. #336C22×C83semidirect
447. C2×M16C2×C4×C83semidirect
457. #117C2×C4×C83semidirect
491. #102C2×C4×C83semidirect
492. #102C2×C4×C83semidirect

Maximal subgroups

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

subgroupindex
C2×#418×C832
C83×#23472
D4×C22⋊C4×C832
C83×#19362
C83×#19342
C83×#19262
C83×#19252
C83×#18642
C83×#18622
C83×#18252
C83×#18092
C83×#17862
C83×#17622
C4×#102×C832
C83×#17532
#2258083