Finite Group Databasebeta

← C83×#26336 #35254160

Subgroups — C83×#26336 #35254160

Order 21248.

966 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#474×C83C211yesmaximal, characteristic, complemented
2C22×#107×C83C211yesmaximal, characteristic, complemented
3C83×#2440C211yesmaximal, characteristic, complemented
4C83×#2361C211yesmaximal, characteristic
5C83×#2093C211yesmaximal, characteristic, complemented
6C83×#2086C211yesmaximal, characteristic, complemented
7C83×#2067C211yesmaximal, characteristic, complemented
8C83×#2057C211yesmaximal, characteristic, complemented
9C83×#1947C211yesmaximal, characteristic, complemented
10C83×#1918C211yesmaximal, characteristic, complemented
11C83×#1893C211yesmaximal, characteristic
12C83×#1874C211yesmaximal, characteristic
13C83×#1862C211yesmaximal, characteristic, complemented
14C83×#1852C211yesmaximal, characteristic, complemented
15C83×#1850C211yesmaximal, characteristic, complemented
16C23×C8×C83C2211yescharacteristic
17C2×C4⋊Q8×C83C2211yescharacteristic
18C2×C22⋊Q8×C83—21no—
19C2×#121×C83C2211yescharacteristic
20C2×C4×D4×C83—21no—
21C2×C4×D4×C83C2211yescharacteristic
22C22×C4⋊C4×C83C2211yescharacteristic
23C22×C4⋊C4×C83C2211yescharacteristic
24#474×C83—24no—
25C2×#107×C83—24no—
26C2×#107×C83C2211yescharacteristic
27C2×#107×C83C2211yescharacteristic
28C2×#107×C83C2211yescharacteristic
29C2×#107×C83C2211yescharacteristic
30C2×#107×C83C2211yescharacteristic
31C2×#107×C83C2211yescharacteristic
32C2×C4⋊C8×C83C2211yescharacteristic
33C2×C4⋊C8×C83C2211yescharacteristic
34C2×#102×C83C2211yescharacteristic
35C2×#102×C83C2211yescharacteristic
36C2×#102×C83C2211yescharacteristic
37C2×#102×C83C2211yescharacteristic
38C2×C22⋊C8×C83C2211yescharacteristic
39#398×C83—21no—
40#395×C83—21no—
41#390×C83C2211yescharacteristic
42#389×C83C2211yescharacteristic
43#389×C83C2211yescharacteristic
44#389×C83C2211yescharacteristic
45#388×C83—21no—
46#386×C83—21no—
47#385×C83—21no—
48#385×C83—21no—
49#384×C83C2211yescharacteristic
50#380×C83C2211yescharacteristic
51C4×C4⋊C4×C83C2211yescharacteristic
52C4×C22⋊C4×C83C2211yescharacteristic
53#340×C83C2211yescharacteristic
54#340×C83C2211yescharacteristic
55#340×C83C2211yescharacteristic
56#340×C83C2211yescharacteristic
57#340×C83C2211yescharacteristic
58#340×C83C2211yescharacteristic
59#336×C83C2211yescharacteristic
60#336×C83C2211yescharacteristic
61C22×Q8×C83—21no—
62C22×D4×C83—21no—
63C22×D4×C83C2311yescharacteristic
64C23×C4×C83—21no—
65C23×C4×C83—21no—
66C23×C4×C83—21no—
67C23×C4×C83C2311yescharacteristic
68C22×C8×C83—22no—
69C22×C8×C83—22no—
70C22×C8×C83—22no—
71C22×C8×C83C2311yescharacteristic
72C22×C8×C83C2311yescharacteristic
73C22×C8×C83C2311yescharacteristic
74C22×C8×C83C2311yescharacteristic
75C4⋊Q8×C83—22no—
76C4⋊Q8×C83—41no—
77C22⋊Q8×C83—44no—
78#121×C83—22no—
79#121×C83Q814yescomplemented
80C4×D4×C83—22no—
81C4×D4×C83—41no—
82C4×D4×C83—44no—
83C2×C4⋊C4×C83—22no—
84C2×C4⋊C4×C83—22no—
85C2×C4⋊C4×C83—21no—
86C2×C4⋊C4×C83—21no—
87C2×C4⋊C4×C83—21no—
88C2×C4⋊C4×C83—21no—
89C2×C4⋊C4×C83—21no—
90C2×C4⋊C4×C83—21no—
91C2×C4⋊C4×C83—21no—
92C2×C4⋊C4×C83—21no—
93C2×C4⋊C4×C83—41no—
94C2×C4⋊C4×C83—41no—
95C2×C4⋊C4×C83C2311yescharacteristic
96C2×C4⋊C4×C83C2311yescharacteristic
97C2×C4⋊C4×C83C2311yescharacteristic
98C2×C4⋊C4×C83C2311yescharacteristic
99C2×C4⋊C4×C83C2311yescharacteristic
100C2×C4⋊C4×C83C2311yescharacteristic
101C2×C4⋊C4×C83C2311yescharacteristic
102C2×C22⋊C4×C83—21no—
103C2×C22⋊C4×C83—21no—
104C2×C22⋊C4×C83—21no—
105C2×C22⋊C4×C83—21no—
106C2×C22⋊C4×C83—21no—
107C2×C22⋊C4×C83D411yescharacteristic
108C2×C22⋊C4×C83D411yescharacteristic
109C2×C42×C83—21no—
110C2×C42×C83C2311yescharacteristic
111C2×C42×C83C2311yescharacteristic
112#107×C83—22no—
113#107×C83—22no—
114#107×C83—22no—
115#107×C83—22no—
116#107×C83—41no—
117#107×C83D414yescomplemented
118C4⋊C8×C83—22no—
119C4⋊C8×C83—22no—
120#102×C83—22no—
121#102×C83—22no—
122#102×C83—22no—
123#102×C83—41no—
124C22⋊C8×C83—22no—
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×C83C2×D411yescharacteristic
134C2×Q8×C83—42no—
135C2×Q8×C83—42no—
136C2×Q8×C83—81no—
137C2×D4×C83—24no—
138C2×D4×C83—21no—
139C2×D4×C83—21no—
140C2×D4×C83—21no—
141C2×D4×C83—21no—
142C2×D4×C83—21no—
143C2×D4×C83—42no—
144C2×D4×C83—42no—
145C2×D4×C83C2×Q812yes—
146C22×C4×C83—21no—
147C22×C4×C83—21no—
148C22×C4×C83—21no—
149C22×C4×C83—21no—
150C22×C4×C83—21no—
151C22×C4×C83—21no—
152C22×C4×C83—21no—
153C22×C4×C83—21no—
154C22×C4×C83—21no—
155C22×C4×C83—21no—
156C22×C4×C83—21no—
157C22×C4×C83—42no—
158C22×C4×C83—42no—
159C22×C4×C83—42no—
160C22×C4×C83—42no—
161C22×C4×C83—42no—
162C22×C4×C83—42no—
163C22×C4×C83—81no—
164C22×C4×C83—81no—
165C22×C4×C83—81no—
166C22×C4×C83C2×D411yescharacteristic
167C22×C4×C83C2×D411yescharacteristic
168C22×C4×C83C2×D411yescharacteristic
169C22×C4×C83C2×D411yescharacteristic
170C22×C4×C83C2×D411yescharacteristic
171C22×C4×C83C2×Q812yes—
172C22×C4×C83#4112yes—
173C22×C4×C83C2411yescharacteristic
174C2×C8×C83—28no—
175C2×C8×C83—21no—
176C2×C8×C83—21no—
177C2×C8×C83—21no—
178C2×C8×C83—21no—
179C2×C8×C83—21no—
180C2×C8×C83—21no—
181C2×C8×C83—21no—
182C2×C8×C83—21no—
183C2×C8×C83—21no—
184C2×C8×C83—21no—
185C2×C8×C83C2×D412yes—
186C2×C8×C83#4112yes—
187C4⋊C4×C83—21no—
188C4⋊C4×C83—21no—
189C4⋊C4×C83—21no—
190C4⋊C4×C83—21no—
191C4⋊C4×C83—21no—
192C4⋊C4×C83—21no—
193C4⋊C4×C83—21no—
194C4⋊C4×C83—21no—
195C4⋊C4×C83—21no—
196C4⋊C4×C83—21no—
197C4⋊C4×C83—21no—
198C4⋊C4×C83—42no—
199C4⋊C4×C83—42no—
200C4⋊C4×C83—42no—
201C4⋊C4×C83—42no—
202C4⋊C4×C83—42no—
203C4⋊C4×C83—42no—
204C4⋊C4×C83—42no—
205C4⋊C4×C83—81no—
206C4⋊C4×C83C2×D412yes—
207C4⋊C4×C83C2×D412yes—
208C4⋊C4×C83C2×Q812yes—
209C22⋊C4×C83—22no—
210C22⋊C4×C83—24no—
211C22⋊C4×C83—42no—
212C22⋊C4×C83—42no—
213C22⋊C4×C83—42no—
214C22⋊C4×C83—81no—
215C22⋊C4×C83D814yes—
216C42×C83—21no—
217C42×C83—21no—
218C42×C83—21no—
219C42×C83—21no—
220C42×C83—42no—
221C23×C83—21no—
222C23×C83—21no—
223C23×C83—21no—
224C23×C83—21no—
225C23×C83—22no—
226C23×C83—41no—
227C23×C83—41no—
228C23×C83—41no—
229C23×C83—41no—
230C23×C83—41no—
231C23×C83—41no—
232C23×C83C22⋊Q812yes—
233C23×C83C2×D812yes—
234C23×C83#13712yes—
235C23×C83C22×D411yescharacteristic
236Q8×C83—84no—
237D4×C83—22no—
238D4×C83—22no—
239D4×C83—48no—
240D4×C83—41no—
241D4×C83—41no—
242C2×C4×C83—21no—
243C2×C4×C83—21no—
244C2×C4×C83—21no—
245C2×C4×C83—21no—
246C2×C4×C83—21no—
247C2×C4×C83—21no—
248C2×C4×C83—22no—
249C2×C4×C83—22no—
250C2×C4×C83—22no—
251C2×C4×C83—22no—
252C2×C4×C83—22no—
253C2×C4×C83—21no—
254C2×C4×C83—22no—
255C2×C4×C83—22no—
256C2×C4×C83—21no—
257C2×C4×C83—21no—
258C2×C4×C83—21no—
259C2×C4×C83—21no—
260C2×C4×C83—21no—
261C2×C4×C83—41no—
262C2×C4×C83—41no—
263C2×C4×C83—41no—
264C2×C4×C83—41no—
265C2×C4×C83—41no—
266C2×C4×C83—41no—
267C2×C4×C83—41no—
268C2×C4×C83—41no—
269C2×C4×C83—41no—
270C2×C4×C83—41no—
271C2×C4×C83—41no—
272C2×C4×C83—41no—
273C2×C4×C83—41no—
274C2×C4×C83—41no—
275C2×C4×C83—41no—
276C2×C4×C83—41no—
277C2×C4×C83—41no—
278C2×C4×C83—41no—
279C2×C4×C83—84no—
280C2×C4×C83—84no—
281C2×C4×C83—84no—
282C2×C4×C83C22⋊Q812yes—
283C2×C4×C83C2×D812yes—
284C2×C4×C83C2×D812yes—
285C2×C4×C83C22×D411yescharacteristic
286C2×C4×C83C22×Q811yescharacteristic
287C2×C4×C83C2×#4111yescharacteristic
288C2×C4×C83C2×#4111yescharacteristic
289C2×C4×C83H(5,𝔽2)11yescharacteristic
290C2×C4×C832−1+411yescharacteristic
291C8×C83—22no—
292C8×C83—22no—
293C8×C83—41no—
294C8×C83—41no—
295C22×C83—22no—
296C22×C83—22no—
297C22×C83—22no—
298C22×C83—22no—
299C22×C83—22no—
300C22×C83—22no—
301C22×C83—42no—
302C22×C83—42no—
303C22×C83—42no—
304C22×C83—81no—
305C22×C83—81no—
306C22×C83—81no—
307C22×C83—81no—
308C22×C83#47414yescomplemented
309C22×C83C2×C22⋊Q811yescharacteristic
310C22×C83D4211yescharacteristic
311C22×C83#54711yescharacteristic
312C22×C83C22×D811yescharacteristic
313C22×C83C2×#13711yescharacteristic
314C22×C83#57611yescharacteristic
315C22×C83#57811yescharacteristic
316C4×C83—22no—
317C4×C83—22no—
318C4×C83—22no—
319C4×C83—41no—
320C4×C83—41no—
321C4×C83—42no—
322C4×C83—42no—
323C4×C83—42no—
324C4×C83—81no—
325C4×C83—81no—
326C4×C83—81no—
327C4×C83—81no—
328C4×C83#52511yescharacteristic
329C4×C83#53911yescharacteristic
330C4×C83D4×Q811yescharacteristic
331C4×C83#55411yescharacteristic
332#26336C8311yesmaximal, characteristic, direct product factor, Sylow
333C2×C83—24no—
334C2×C83—82no—
335C2×C83#244911yescharacteristic
336C2×C83C2×#47411yescharacteristic
337C2×C83#308311yescharacteristic
338C2×C83#327011yescharacteristic
339C2×C83D4×D811yescharacteristic
340C2×C83#333411yescharacteristic
341C2×C83#334611yescharacteristic
342C2×#474C2×C8311yescharacteristic, complemented
343C22×#107C2×C8311yescharacteristic, complemented
344#2440C2×C8311yescharacteristic, complemented
345#2361C2×C8311yescharacteristic
346#2093C2×C8311yescharacteristic, complemented
347#2086C2×C8311yescharacteristic, complemented
348#2067C2×C8311yescharacteristic, complemented
349#2057C2×C8311yescharacteristic, complemented
350#1947C2×C8311yescharacteristic, complemented
351#1918C2×C8311yescharacteristic, complemented
352#1893C2×C8311yescharacteristic
353#1874C2×C8311yescharacteristic
354#1862C2×C8311yescharacteristic, complemented
355#1852C2×C8311yescharacteristic, complemented
356#1850C2×C8311yescharacteristic, complemented
357C83#2633611yescharacteristic, direct product factor, Sylow
358C23×C8C22×C8311yescharacteristic
359C2×C4⋊Q8C22×C8311yescharacteristic
360C2×C22⋊Q8—21no—
361C2×#121C22×C8311yescharacteristic
362C2×C4×D4—21no—
363C2×C4×D4C22×C8311yescharacteristic
364C22×C4⋊C4C22×C8311yescharacteristic
365C22×C4⋊C4C22×C8311yescharacteristic
366#474—24no—
367C2×#107—24no—
368C2×#107C22×C8311yescharacteristic
369C2×#107C22×C8311yescharacteristic
370C2×#107C22×C8311yescharacteristic
371C2×#107C22×C8311yescharacteristic
372C2×#107C22×C8311yescharacteristic
373C2×#107C22×C8311yescharacteristic
374C2×C4⋊C8C22×C8311yescharacteristic
375C2×C4⋊C8C22×C8311yescharacteristic
376C2×#102C22×C8311yescharacteristic
377C2×#102C22×C8311yescharacteristic
378C2×#102C22×C8311yescharacteristic
379C2×#102C22×C8311yescharacteristic
380C2×C22⋊C8C22×C8311yescharacteristic
381#398—21no—
382#395—21no—
383#390C22×C8311yescharacteristic
384#389C22×C8311yescharacteristic
385#389C22×C8311yescharacteristic
386#389C22×C8311yescharacteristic
387#388—21no—
388#386—21no—
389#385—21no—
390#385—21no—
391#384C22×C8311yescharacteristic
392#380C22×C8311yescharacteristic
393C4×C4⋊C4C22×C8311yescharacteristic
394C4×C22⋊C4C22×C8311yescharacteristic
395#340C22×C8311yescharacteristic
396#340C22×C8311yescharacteristic
397#340C22×C8311yescharacteristic
398#340C22×C8311yescharacteristic
399#340C22×C8311yescharacteristic
400#340C22×C8311yescharacteristic
401#336C22×C8311yescharacteristic
402#336C22×C8311yescharacteristic
403C22×Q8—21no—
404C22×D4—21no—
405C22×D4C23×C8311yescharacteristic
406C23×C4—21no—
407C23×C4—21no—
408C23×C4—21no—
409C23×C4C23×C8311yescharacteristic
410C22×C8—22no—
411C22×C8—22no—
412C22×C8—22no—
413C22×C8C23×C8311yescharacteristic
414C22×C8C23×C8311yescharacteristic
415C22×C8C23×C8311yescharacteristic
416C22×C8C23×C8311yescharacteristic
417C4⋊Q8—22no—
418C4⋊Q8—41no—
419C22⋊Q8—44no—
420#121—22no—
421#121Q8×C8314yescomplemented
422C4×D4—22no—
423C4×D4—41no—
424C4×D4—44no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4—41no—
436C2×C4⋊C4—41no—
437C2×C4⋊C4C23×C8311yescharacteristic
438C2×C4⋊C4C23×C8311yescharacteristic
439C2×C4⋊C4C23×C8311yescharacteristic
440C2×C4⋊C4C23×C8311yescharacteristic
441C2×C4⋊C4C23×C8311yescharacteristic
442C2×C4⋊C4C23×C8311yescharacteristic
443C2×C4⋊C4C23×C8311yescharacteristic
444C2×C22⋊C4—21no—
445C2×C22⋊C4—21no—
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4D4×C8311yescharacteristic
450C2×C22⋊C4D4×C8311yescharacteristic
451C2×C42—21no—
452C2×C42C23×C8311yescharacteristic
453C2×C42C23×C8311yescharacteristic
454#107—22no—
455#107—22no—
456#107—22no—
457#107—22no—
458#107—41no—
459#107D4×C8314yescomplemented
460C4⋊C8—22no—
461C4⋊C8—22no—
462#102—22no—
463#102—22no—
464#102—22no—
465#102—41no—
466C22⋊C8—22no—
467#95—21no—
468#95—21no—
469#95—21no—
470#95—21no—
471#95—21no—
472#95D4×C8311yescharacteristic
473#95D4×C8311yescharacteristic
474C24—21no—
475C24C2×D4×C8311yescharacteristic
476C2×Q8—42no—
477C2×Q8—42no—
478C2×Q8—81no—
479C2×D4—24no—
480C2×D4—21no—
481C2×D4—21no—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—42no—
486C2×D4—42no—
487C2×D4C2×Q8×C8312yes—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—42no—
500C22×C4—42no—
501C22×C4—42no—
502C22×C4—42no—
503C22×C4—42no—
504C22×C4—42no—
505C22×C4—81no—
506C22×C4—81no—
507C22×C4—81no—
508C22×C4C2×D4×C8311yescharacteristic
509C22×C4C2×D4×C8311yescharacteristic
510C22×C4C2×D4×C8311yescharacteristic
511C22×C4C2×D4×C8311yescharacteristic
512C22×C4C2×D4×C8311yescharacteristic
513C22×C4C2×Q8×C8312yes—
514C22×C4#41×C8312yes—
515C22×C4C24×C8311yescharacteristic
516C2×C8—28no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8C2×D4×C8312yes—
528C2×C8#41×C8312yes—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—42no—
541C4⋊C4—42no—
542C4⋊C4—42no—
543C4⋊C4—42no—
544C4⋊C4—42no—
545C4⋊C4—42no—
546C4⋊C4—42no—
547C4⋊C4—81no—
548C4⋊C4C2×D4×C8312yes—
549C4⋊C4C2×D4×C8312yes—
550C4⋊C4C2×Q8×C8312yes—
551C22⋊C4—22no—
552C22⋊C4—24no—
553C22⋊C4—42no—
554C22⋊C4—42no—
555C22⋊C4—42no—
556C22⋊C4—81no—
557C22⋊C4D8×C8314yes—
558C42—21no—
559C42—21no—
560C42—21no—
561C42—21no—
562C42—42no—
563C23—21no—
564C23—21no—
565C23—21no—
566C23—21no—
567C23—22no—
568C23—41no—
569C23—41no—
570C23—41no—
571C23—41no—
572C23—41no—
573C23—41no—
574C23C22⋊Q8×C8312yes—
575C23C2×D8×C8312yes—
576C23#137×C8312yes—
577C23C22×D4×C8311yescharacteristic
578Q8—84no—
579D4—22no—
580D4—22no—
581D4—48no—
582D4—41no—
583D4—41no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—21no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—84no—
622C2×C4—84no—
623C2×C4—84no—
624C2×C4C22⋊Q8×C8312yes—
625C2×C4C2×D8×C8312yes—
626C2×C4C2×D8×C8312yes—
627C2×C4C22×D4×C8311yescharacteristic
628C2×C4C22×Q8×C8311yescharacteristic
629C2×C4C2×#41×C8311yescharacteristic
630C2×C4C2×#41×C8311yescharacteristic
631C2×C4H(5,𝔽2)×C8311yescharacteristic
632C2×C42−1+4×C8311yescharacteristic
633C8—22no—
634C8—22no—
635C8—41no—
636C8—41no—
637C22—22no—
638C22—22no—
639C22—22no—
640C22—22no—
641C22—22no—
642C22—22no—
643C22—42no—
644C22—42no—
645C22—42no—
646C22—81no—
647C22—81no—
648C22—81no—
649C22—81no—
650C22#474×C8314yescomplemented
651C22C2×C22⋊Q8×C8311yescharacteristic
652C22D42×C8311yescharacteristic
653C22#547×C8311yescharacteristic
654C22C22×D8×C8311yescharacteristic
655C22C2×#137×C8311yescharacteristic
656C22#576×C8311yescharacteristic
657C22#578×C8311yescharacteristic
658C4—22no—
659C4—22no—
660C4—22no—
661C4—42no—
662C4—42no—
663C4—42no—
664C4—41no—
665C4—41no—
666C4—81no—
667C4—81no—
668C4—81no—
669C4—81no—
670C4#525×C8311yescharacteristic
671C4#539×C8311yescharacteristic
672C4D4×Q8×C8311yescharacteristic
673C4#554×C8311yescharacteristic
674C2—24no—
675C2—82no—
676C2C83×#244911yescharacteristic
677C2C2×#474×C8311yescharacteristic
678C2C83×#308311yescharacteristic
679C2C83×#327011yescharacteristic
680C2D4×D8×C8311yescharacteristic
681C2C83×#333411yescharacteristic
682C2C83×#334611yescharacteristic
subgroupG/H
center, socleC23×C83C22×D4
commutator, Frattini, cosocleC22×C4C24×C83
prime radicalC2×#121×C83C22
LCSG ▷ C22×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
1. C2×#474×C83C2semidirect
2. C22×#107×C83C2semidirect
3. C83×#2440C2semidirect
5. C83×#2093C2semidirect
6. C83×#2086C2semidirect
7. C83×#2067C2semidirect
8. C83×#2057C2semidirect
9. C83×#1947C2semidirect
10. C83×#1918C2semidirect
13. C83×#1862C2semidirect
14. C83×#1852C2semidirect
15. C83×#1850C2semidirect
79. #121×C83Q8semidirect
117. #107×C83D4semidirect
308. C22×C83#474semidirect
332. #26336C83direct (N × H)
342. C2×#474C2×C83semidirect
343. C22×#107C2×C83semidirect
344. #2440C2×C83semidirect
346. #2093C2×C83semidirect
347. #2086C2×C83semidirect
348. #2067C2×C83semidirect
349. #2057C2×C83semidirect
350. #1947C2×C83semidirect
351. #1918C2×C83semidirect
354. #1862C2×C83semidirect
355. #1852C2×C83semidirect
356. #1850C2×C83semidirect
357. C83#26336direct (N × H)
421. #121Q8×C83semidirect
459. #107D4×C83semidirect
650. C22#474×C83semidirect

Maximal subgroups

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

subgroupindex
C2×#474×C832
C22×#107×C832
C83×#24402
C83×#23612
C83×#20932
C83×#20862
C83×#20672
C83×#20572
C83×#19472
C83×#19182
C83×#18932
C83×#18742
C83×#18622
C83×#18522
C83×#18502
#2633683