Finite Group Databasebeta

← C83×#25174 #35252998

Subgroups — C83×#25174 #35252998

Order 21248.

1234 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#459×C83C211yesmaximal, characteristic, complemented
2C2×#449×C83C211yesmaximal, characteristic, complemented
3C2×#449×C83C211yesmaximal, characteristic, complemented
4C2×#442×C83C211yesmaximal, characteristic, complemented
5C83×#2428C211yesmaximal, characteristic, complemented
6C83×#2339C211yesmaximal, characteristic, complemented
7C83×#2066C211yesmaximal, characteristic, complemented
8C83×#2034C211yesmaximal, characteristic, complemented
9C83×#2033C211yesmaximal, characteristic, complemented
10C83×#2014C211yesmaximal, characteristic, complemented
11C83×#1973C211yesmaximal, characteristic, complemented
12C83×#1924C211yesmaximal, characteristic, complemented
13C83×#1879C211yesmaximal, characteristic, complemented
14C83×#1877C211yesmaximal, characteristic, complemented
15C83×#1862C211yesmaximal, characteristic, complemented
16C22×#41×C83C2211yescharacteristic
17C22×SD16×C83C2211yescharacteristic
18C22×SD16×C83C2211yescharacteristic
19C22×D8×C83C2211yescharacteristic
20C22×D8×C83C2211yescharacteristic
21C2×#127×C83C2211yescharacteristic
22C2×#121×C83—21no—
23C2×#121×C83C2211yescharacteristic
24C2×#121×C83C2211yescharacteristic
25C2×C4×D4×C83C2211yescharacteristic
26C2×C4×D4×C83C2211yescharacteristic
27C2×C4×D4×C83C2211yescharacteristic
28#459×C83—24no—
29#449×C83—24no—
30#449×C83—24no—
31#442×C83—24no—
32C2×#107×C83C2211yescharacteristic
33C2×#106×C83C2211yescharacteristic
34C2×C4⋊C8×C83C2211yescharacteristic
35C2×#103×C83C2211yescharacteristic
36C2×#103×C83C2211yescharacteristic
37C2×#102×C83C2211yescharacteristic
38C2×#102×C83C2211yescharacteristic
39C2×#102×C83C2211yescharacteristic
40C2×#102×C83C2211yescharacteristic
41C2×#102×C83C2211yescharacteristic
42C2×#102×C83C2211yescharacteristic
43C2×C22⋊C8×C83C2211yescharacteristic
44C2×C22⋊C8×C83C2211yescharacteristic
45C2×#97×C83C2211yescharacteristic
46#394×C83—21no—
47#392×C83—21no—
48#391×C83C2211yescharacteristic
49#391×C83C2211yescharacteristic
50#390×C83C2211yescharacteristic
51#389×C83C2211yescharacteristic
52#386×C83—21no—
53#386×C83—21no—
54#386×C83—21no—
55#381×C83—21no—
56#380×C83C2211yescharacteristic
57C4×C22⋊C4×C83C2211yescharacteristic
58C2×#95×C83—21no—
59#340×C83C2211yescharacteristic
60#340×C83C2211yescharacteristic
61#336×C83C2211yescharacteristic
62#336×C83C2211yescharacteristic
63C2×#41×C83—22no—
64C2×#41×C83—22no—
65C2×#41×C83—22no—
66C2×#41×C83—22no—
67C2×#41×C83—41no—
68C2×#41×C83—41no—
69C22×Q8×C83C2311yescharacteristic
70C22×D4×C83—21no—
71C22×D4×C83—21no—
72C22×D4×C83—21no—
73C22×D4×C83—21no—
74C22×D4×C83—21no—
75C22×D4×C83C2311yescharacteristic
76C22×D4×C83C2311yescharacteristic
77C22×D4×C83C2311yescharacteristic
78C23×C4×C83—21no—
79C23×C4×C83—21no—
80C23×C4×C83—21no—
81C23×C4×C83—21no—
82C23×C4×C83C2311yescharacteristic
83C2×SD16×C83—22no—
84C2×SD16×C83—22no—
85C2×SD16×C83—22no—
86C2×SD16×C83—22no—
87C2×SD16×C83—41no—
88C2×SD16×C83—41no—
89C2×D8×C83—22no—
90C2×D8×C83—22no—
91C2×D8×C83—22no—
92C2×D8×C83—22no—
93C2×D8×C83—22no—
94C2×D8×C83D414yescomplemented
95C22×C8×C83C2311yescharacteristic
96C22×C8×C83C2311yescharacteristic
97C22×C8×C83C2311yescharacteristic
98C22×C8×C83C2311yescharacteristic
99#127×C83—22no—
100#127×C83—41no—
101#121×C83—22no—
102#121×C83—22no—
103#121×C83—44no—
104#121×C83—41no—
105#121×C83—41no—
106C4×D4×C83—22no—
107C4×D4×C83—22no—
108C4×D4×C83—22no—
109C4×D4×C83—41no—
110C4×D4×C83—41no—
111C4×D4×C83—41no—
112C2×C4⋊C4×C83—21no—
113C2×C4⋊C4×C83C2311yescharacteristic
114C2×C4⋊C4×C83C2311yescharacteristic
115C2×C4⋊C4×C83C2311yescharacteristic
116C2×C4⋊C4×C83C2311yescharacteristic
117C2×C22⋊C4×C83—21no—
118C2×C22⋊C4×C83—21no—
119C2×C22⋊C4×C83—21no—
120C2×C22⋊C4×C83—21no—
121C2×C22⋊C4×C83—21no—
122C2×C22⋊C4×C83—21no—
123C2×C22⋊C4×C83—21no—
124C2×C22⋊C4×C83—21no—
125C2×C22⋊C4×C83D411yescharacteristic
126C2×C22⋊C4×C83D411yescharacteristic
127C2×C42×C83C2311yescharacteristic
128C2×C42×C83C2311yescharacteristic
129#107×C83—41no—
130#106×C83—22no—
131C4⋊C8×C83—22no—
132#103×C83—22no—
133#103×C83—22no—
134#102×C83—22no—
135#102×C83—22no—
136#102×C83—22no—
137#102×C83—22no—
138#102×C83—41no—
139#102×C83D414yescomplemented
140C22⋊C8×C83—22no—
141C22⋊C8×C83—22no—
142#97×C83—22no—
143#95×C83—21no—
144#95×C83—21no—
145#95×C83—21no—
146#95×C83—21no—
147#95×C83—21no—
148#95×C83—21no—
149#95×C83D411yescharacteristic
150#95×C83D411yescharacteristic
151C24×C83—21no—
152C24×C83—21no—
153C24×C83—21no—
154C24×C83C2×D411yescharacteristic
155#41×C83—44no—
156#41×C83—44no—
157#41×C83—44no—
158#41×C83—44no—
159C2×Q8×C83—21no—
160C2×Q8×C83—21no—
161C2×Q8×C83—21no—
162C2×Q8×C83—21no—
163C2×Q8×C83—21no—
164C2×Q8×C83#4112yes—
165C2×D4×C83—24no—
166C2×D4×C83—21no—
167C2×D4×C83—21no—
168C2×D4×C83—21no—
169C2×D4×C83—21no—
170C2×D4×C83—21no—
171C2×D4×C83—21no—
172C2×D4×C83—21no—
173C2×D4×C83—21no—
174C2×D4×C83—21no—
175C2×D4×C83—21no—
176C2×D4×C83—21no—
177C2×D4×C83—21no—
178C2×D4×C83—21no—
179C2×D4×C83—21no—
180C2×D4×C83—42no—
181C2×D4×C83—42no—
182C2×D4×C83—42no—
183C2×D4×C83—42no—
184C2×D4×C83—42no—
185C2×D4×C83—42no—
186C2×D4×C83—42no—
187C2×D4×C83—42no—
188C2×D4×C83—42no—
189C2×D4×C83—42no—
190C2×D4×C83—81no—
191C2×D4×C83—81no—
192C2×D4×C83—81no—
193C2×D4×C83—81no—
194C2×D4×C83C2×D412yes—
195C2×D4×C83C2×D412yes—
196C2×D4×C83C2×D412yes—
197C2×D4×C83#4112yes—
198C22×C4×C83—24no—
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—42no—
211C22×C4×C83—42no—
212C22×C4×C83—42no—
213C22×C4×C83—42no—
214C22×C4×C83—42no—
215C22×C4×C83—42no—
216C22×C4×C83—42no—
217C22×C4×C83—42no—
218C22×C4×C83—81no—
219C22×C4×C83—81no—
220C22×C4×C83—81no—
221C22×C4×C83C2×D411yescharacteristic
222C22×C4×C83C2×D411yescharacteristic
223C22×C4×C83C2×D411yescharacteristic
224C22×C4×C83C2×D411yescharacteristic
225C22×C4×C83C2×D411yescharacteristic
226C22×C4×C83C2411yescharacteristic
227SD16×C83—44no—
228SD16×C83—44no—
229D8×C83—28no—
230D8×C83—44no—
231C2×C8×C83—21no—
232C2×C8×C83—21no—
233C2×C8×C83—21no—
234C2×C8×C83—21no—
235C2×C8×C83—21no—
236C2×C8×C83—21no—
237C2×C8×C83—21no—
238C2×C8×C83—21no—
239C2×C8×C83—21no—
240C2×C8×C83—21no—
241C2×C8×C83C2×D412yes—
242C2×C8×C83C2×D412yes—
243C4⋊C4×C83—21no—
244C4⋊C4×C83—21no—
245C4⋊C4×C83—21no—
246C4⋊C4×C83—21no—
247C4⋊C4×C83—21no—
248C4⋊C4×C83—21no—
249C4⋊C4×C83—21no—
250C4⋊C4×C83—42no—
251C4⋊C4×C83C2×D412yes—
252C22⋊C4×C83—22no—
253C22⋊C4×C83—41no—
254C22⋊C4×C83—42no—
255C22⋊C4×C83—42no—
256C22⋊C4×C83—42no—
257C22⋊C4×C83—42no—
258C22⋊C4×C83—42no—
259C22⋊C4×C83—42no—
260C22⋊C4×C83—81no—
261C22⋊C4×C83—81no—
262C42×C83—21no—
263C42×C83—21no—
264C42×C83—21no—
265C42×C83—21no—
266C23×C83—22no—
267C23×C83—22no—
268C23×C83—22no—
269C23×C83—21no—
270C23×C83—22no—
271C23×C83—21no—
272C23×C83—21no—
273C23×C83—21no—
274C23×C83—21no—
275C23×C83—21no—
276C23×C83—21no—
277C23×C83—41no—
278C23×C83—41no—
279C23×C83—41no—
280C23×C83—41no—
281C23×C83—41no—
282C23×C83—41no—
283C23×C83—41no—
284C23×C83—41no—
285C23×C83—41no—
286C23×C83—41no—
287C23×C83—41no—
288C23×C83—41no—
289C23×C83—41no—
290C23×C83—41no—
291C23×C83—41no—
292C23×C83—41no—
293C23×C83—41no—
294C23×C83C22×D411yescharacteristic
295Q8×C83—22no—
296Q8×C83—22no—
297Q8×C83—41no—
298Q8×C83—41no—
299D4×C83—22no—
300D4×C83—22no—
301D4×C83—22no—
302D4×C83—22no—
303D4×C83—22no—
304D4×C83—48no—
305D4×C83—41no—
306D4×C83—41no—
307D4×C83—41no—
308D4×C83—41no—
309D4×C83—41no—
310D4×C83—41no—
311D4×C83—84no—
312D4×C83—84no—
313D4×C83—84no—
314D4×C83—84no—
315D4×C83#12114yescomplemented
316C2×C4×C83—21no—
317C2×C4×C83—21no—
318C2×C4×C83—21no—
319C2×C4×C83—22no—
320C2×C4×C83—21no—
321C2×C4×C83—21no—
322C2×C4×C83—21no—
323C2×C4×C83—22no—
324C2×C4×C83—21no—
325C2×C4×C83—21no—
326C2×C4×C83—21no—
327C2×C4×C83—21no—
328C2×C4×C83—21no—
329C2×C4×C83—21no—
330C2×C4×C83—21no—
331C2×C4×C83—21no—
332C2×C4×C83—48no—
333C2×C4×C83—41no—
334C2×C4×C83—41no—
335C2×C4×C83—41no—
336C2×C4×C83—41no—
337C2×C4×C83—41no—
338C2×C4×C83—41no—
339C2×C4×C83—41no—
340C2×C4×C83—41no—
341C2×C4×C83—41no—
342C2×C4×C83—41no—
343C2×C4×C83—41no—
344C2×C4×C83—41no—
345C2×C4×C83—41no—
346C2×C4×C83—41no—
347C2×C4×C83—41no—
348C2×C4×C83—41no—
349C2×C4×C83—41no—
350C2×C4×C83—84no—
351C2×C4×C83—84no—
352C2×C4×C83—84no—
353C2×C4×C83AGL(1,ℤ/8)12yes—
354C2×C4×C83C22×D411yescharacteristic
355C2×C4×C83C22×D411yescharacteristic
356C2×C4×C83C2×#4111yescharacteristic
357C2×C4×C83C2×#4111yescharacteristic
358C2×C4×C83H(5,𝔽2)11yescharacteristic
359C2×C4×C83H(5,𝔽2)11yescharacteristic
360C8×C83—22no—
361C8×C83—22no—
362C8×C83—41no—
363C8×C83—41no—
364C22×C83—24no—
365C22×C83—42no—
366C22×C83—42no—
367C22×C83—42no—
368C22×C83—42no—
369C22×C83—42no—
370C22×C83—42no—
371C22×C83—41no—
372C22×C83—41no—
373C22×C83—41no—
374C22×C83—42no—
375C22×C83—41no—
376C22×C83—42no—
377C22×C83—42no—
378C22×C83—41no—
379C22×C83—41no—
380C22×C83—41no—
381C22×C83—81no—
382C22×C83—81no—
383C22×C83—81no—
384C22×C83—81no—
385C22×C83—81no—
386C22×C83—81no—
387C22×C83—81no—
388C22×C83—81no—
389C22×C83—81no—
390C22×C83—81no—
391C22×C83—81no—
392C22×C83#52511yescharacteristic
393C22×C83D4211yescharacteristic
394C22×C83D4211yescharacteristic
395C22×C83C2×AGL(1,ℤ/8)11yescharacteristic
396C22×C83#57511yescharacteristic
397C22×C83#57611yescharacteristic
398C22×C83#57711yescharacteristic
399C4×C83—22no—
400C4×C83—41no—
401C4×C83—42no—
402C4×C83—41no—
403C4×C83—41no—
404C4×C83—41no—
405C4×C83—42no—
406C4×C83—81no—
407C4×C83—81no—
408C4×C83—81no—
409C4×C83C2×#12111yescharacteristic
410C4×C83#53811yescharacteristic
411C4×C83#54611yescharacteristic
412C4×C83#54611yescharacteristic
413#25174C8311yesmaximal, characteristic, direct product factor, Sylow
414C2×C83—44no—
415C2×C83—81no—
416C2×C83—82no—
417C2×C83—161no—
418C2×C83#242411yescharacteristic
419C2×C83#311511yescharacteristic
420C2×C83#311911yescharacteristic
421C2×C83#326411yescharacteristic
422C2×C83#326711yescharacteristic
423C2×C83#326811yescharacteristic
424C2×C83#327211yescharacteristic
425C2×#459C2×C8311yescharacteristic, complemented
426C2×#449C2×C8311yescharacteristic, complemented
427C2×#449C2×C8311yescharacteristic, complemented
428C2×#442C2×C8311yescharacteristic, complemented
429#2428C2×C8311yescharacteristic, complemented
430#2339C2×C8311yescharacteristic, complemented
431#2066C2×C8311yescharacteristic, complemented
432#2034C2×C8311yescharacteristic, complemented
433#2033C2×C8311yescharacteristic, complemented
434#2014C2×C8311yescharacteristic, complemented
435#1973C2×C8311yescharacteristic, complemented
436#1924C2×C8311yescharacteristic, complemented
437#1879C2×C8311yescharacteristic, complemented
438#1877C2×C8311yescharacteristic, complemented
439#1862C2×C8311yescharacteristic, complemented
440C83#2517411yescharacteristic, direct product factor, Sylow
441C22×#41C22×C8311yescharacteristic
442C22×SD16C22×C8311yescharacteristic
443C22×SD16C22×C8311yescharacteristic
444C22×D8C22×C8311yescharacteristic
445C22×D8C22×C8311yescharacteristic
446C2×#127C22×C8311yescharacteristic
447C2×#121—21no—
448C2×#121C22×C8311yescharacteristic
449C2×#121C22×C8311yescharacteristic
450C2×C4×D4C22×C8311yescharacteristic
451C2×C4×D4C22×C8311yescharacteristic
452C2×C4×D4C22×C8311yescharacteristic
453#459—24no—
454#449—24no—
455#449—24no—
456#442—24no—
457C2×#107C22×C8311yescharacteristic
458C2×#106C22×C8311yescharacteristic
459C2×C4⋊C8C22×C8311yescharacteristic
460C2×#103C22×C8311yescharacteristic
461C2×#103C22×C8311yescharacteristic
462C2×#102C22×C8311yescharacteristic
463C2×#102C22×C8311yescharacteristic
464C2×#102C22×C8311yescharacteristic
465C2×#102C22×C8311yescharacteristic
466C2×#102C22×C8311yescharacteristic
467C2×#102C22×C8311yescharacteristic
468C2×C22⋊C8C22×C8311yescharacteristic
469C2×C22⋊C8C22×C8311yescharacteristic
470C2×#97C22×C8311yescharacteristic
471#394—21no—
472#392—21no—
473#391C22×C8311yescharacteristic
474#391C22×C8311yescharacteristic
475#390C22×C8311yescharacteristic
476#389C22×C8311yescharacteristic
477#386—21no—
478#386—21no—
479#386—21no—
480#381—21no—
481#380C22×C8311yescharacteristic
482C4×C22⋊C4C22×C8311yescharacteristic
483C2×#95—21no—
484#340C22×C8311yescharacteristic
485#340C22×C8311yescharacteristic
486#336C22×C8311yescharacteristic
487#336C22×C8311yescharacteristic
488C2×#41—22no—
489C2×#41—22no—
490C2×#41—22no—
491C2×#41—22no—
492C2×#41—41no—
493C2×#41—41no—
494C22×Q8C23×C8311yescharacteristic
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4C23×C8311yescharacteristic
501C22×D4C23×C8311yescharacteristic
502C22×D4C23×C8311yescharacteristic
503C23×C4—21no—
504C23×C4—21no—
505C23×C4—21no—
506C23×C4—21no—
507C23×C4C23×C8311yescharacteristic
508C2×SD16—22no—
509C2×SD16—22no—
510C2×SD16—22no—
511C2×SD16—22no—
512C2×SD16—41no—
513C2×SD16—41no—
514C2×D8—22no—
515C2×D8—22no—
516C2×D8—22no—
517C2×D8—22no—
518C2×D8—22no—
519C2×D8D4×C8314yescomplemented
520C22×C8C23×C8311yescharacteristic
521C22×C8C23×C8311yescharacteristic
522C22×C8C23×C8311yescharacteristic
523C22×C8C23×C8311yescharacteristic
524#127—22no—
525#127—41no—
526#121—22no—
527#121—22no—
528#121—44no—
529#121—41no—
530#121—41no—
531C4×D4—22no—
532C4×D4—22no—
533C4×D4—22no—
534C4×D4—41no—
535C4×D4—41no—
536C4×D4—41no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4C23×C8311yescharacteristic
539C2×C4⋊C4C23×C8311yescharacteristic
540C2×C4⋊C4C23×C8311yescharacteristic
541C2×C4⋊C4C23×C8311yescharacteristic
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4D4×C8311yescharacteristic
551C2×C22⋊C4D4×C8311yescharacteristic
552C2×C42C23×C8311yescharacteristic
553C2×C42C23×C8311yescharacteristic
554#107—41no—
555#106—22no—
556C4⋊C8—22no—
557#103—22no—
558#103—22no—
559#102—22no—
560#102—22no—
561#102—22no—
562#102—22no—
563#102—41no—
564#102D4×C8314yescomplemented
565C22⋊C8—22no—
566C22⋊C8—22no—
567#97—22no—
568#95—21no—
569#95—21no—
570#95—21no—
571#95—21no—
572#95—21no—
573#95—21no—
574#95D4×C8311yescharacteristic
575#95D4×C8311yescharacteristic
576C24—21no—
577C24—21no—
578C24—21no—
579C24C2×D4×C8311yescharacteristic
580#41—44no—
581#41—44no—
582#41—44no—
583#41—44no—
584C2×Q8—21no—
585C2×Q8—21no—
586C2×Q8—21no—
587C2×Q8—21no—
588C2×Q8—21no—
589C2×Q8#41×C8312yes—
590C2×D4—24no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—42no—
606C2×D4—42no—
607C2×D4—42no—
608C2×D4—42no—
609C2×D4—42no—
610C2×D4—42no—
611C2×D4—42no—
612C2×D4—42no—
613C2×D4—42no—
614C2×D4—42no—
615C2×D4—81no—
616C2×D4—81no—
617C2×D4—81no—
618C2×D4—81no—
619C2×D4C2×D4×C8312yes—
620C2×D4C2×D4×C8312yes—
621C2×D4C2×D4×C8312yes—
622C2×D4#41×C8312yes—
623C22×C4—24no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—42no—
636C22×C4—42no—
637C22×C4—42no—
638C22×C4—42no—
639C22×C4—42no—
640C22×C4—42no—
641C22×C4—42no—
642C22×C4—42no—
643C22×C4—81no—
644C22×C4—81no—
645C22×C4—81no—
646C22×C4C2×D4×C8311yescharacteristic
647C22×C4C2×D4×C8311yescharacteristic
648C22×C4C2×D4×C8311yescharacteristic
649C22×C4C2×D4×C8311yescharacteristic
650C22×C4C2×D4×C8311yescharacteristic
651C22×C4C24×C8311yescharacteristic
652SD16—44no—
653SD16—44no—
654D8—28no—
655D8—44no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—21no—
662C2×C8—21no—
663C2×C8—21no—
664C2×C8—21no—
665C2×C8—21no—
666C2×C8C2×D4×C8312yes—
667C2×C8C2×D4×C8312yes—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—21no—
675C4⋊C4—42no—
676C4⋊C4C2×D4×C8312yes—
677C22⋊C4—22no—
678C22⋊C4—41no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—42no—
683C22⋊C4—42no—
684C22⋊C4—42no—
685C22⋊C4—81no—
686C22⋊C4—81no—
687C42—21no—
688C42—21no—
689C42—21no—
690C42—21no—
691C23—22no—
692C23—22no—
693C23—22no—
694C23—21no—
695C23—22no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23C22×D4×C8311yescharacteristic
720Q8—22no—
721Q8—22no—
722Q8—41no—
723Q8—41no—
724D4—22no—
725D4—22no—
726D4—22no—
727D4—22no—
728D4—22no—
729D4—48no—
730D4—41no—
731D4—41no—
732D4—41no—
733D4—41no—
734D4—41no—
735D4—41no—
736D4—84no—
737D4—84no—
738D4—84no—
739D4—84no—
740D4#121×C8314yescomplemented
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—22no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—22no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—48no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—84no—
776C2×C4—84no—
777C2×C4—84no—
778C2×C4AGL(1,ℤ/8)×C8312yes—
779C2×C4C22×D4×C8311yescharacteristic
780C2×C4C22×D4×C8311yescharacteristic
781C2×C4C2×#41×C8311yescharacteristic
782C2×C4C2×#41×C8311yescharacteristic
783C2×C4H(5,𝔽2)×C8311yescharacteristic
784C2×C4H(5,𝔽2)×C8311yescharacteristic
785C8—22no—
786C8—22no—
787C8—41no—
788C8—41no—
789C22—24no—
790C22—42no—
791C22—42no—
792C22—42no—
793C22—42no—
794C22—42no—
795C22—42no—
796C22—41no—
797C22—41no—
798C22—41no—
799C22—42no—
800C22—41no—
801C22—42no—
802C22—42no—
803C22—41no—
804C22—41no—
805C22—41no—
806C22—81no—
807C22—81no—
808C22—81no—
809C22—81no—
810C22—81no—
811C22—81no—
812C22—81no—
813C22—81no—
814C22—81no—
815C22—81no—
816C22—81no—
817C22#525×C8311yescharacteristic
818C22D42×C8311yescharacteristic
819C22D42×C8311yescharacteristic
820C22C2×AGL(1,ℤ/8)×C8311yescharacteristic
821C22#575×C8311yescharacteristic
822C22#576×C8311yescharacteristic
823C22#577×C8311yescharacteristic
824C4—22no—
825C4—41no—
826C4—42no—
827C4—41no—
828C4—41no—
829C4—41no—
830C4—42no—
831C4—81no—
832C4—81no—
833C4—81no—
834C4C2×#121×C8311yescharacteristic
835C4#538×C8311yescharacteristic
836C4#546×C8311yescharacteristic
837C4#546×C8311yescharacteristic
838C2—44no—
839C2—81no—
840C2—82no—
841C2—161no—
842C2C83×#242411yescharacteristic
843C2C83×#311511yescharacteristic
844C2C83×#311911yescharacteristic
845C2C83×#326411yescharacteristic
846C2C83×#326711yescharacteristic
847C2C83×#326811yescharacteristic
848C2C83×#327211yescharacteristic
subgroupG/H
center, socleC23×C83C22×D4
commutator, Frattini, cosocleC22×C4C24×C83
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×#459×C83C2semidirect
2. C2×#449×C83C2semidirect
3. C2×#449×C83C2semidirect
4. C2×#442×C83C2semidirect
5. C83×#2428C2semidirect
6. C83×#2339C2semidirect
7. C83×#2066C2semidirect
8. C83×#2034C2semidirect
9. C83×#2033C2semidirect
10. C83×#2014C2semidirect
11. C83×#1973C2semidirect
12. C83×#1924C2semidirect
13. C83×#1879C2semidirect
14. C83×#1877C2semidirect
15. C83×#1862C2semidirect
94. C2×D8×C83D4semidirect
139. #102×C83D4semidirect
315. D4×C83#121semidirect
413. #25174C83direct (N × H)
425. C2×#459C2×C83semidirect
426. C2×#449C2×C83semidirect
427. C2×#449C2×C83semidirect
428. C2×#442C2×C83semidirect
429. #2428C2×C83semidirect
430. #2339C2×C83semidirect
431. #2066C2×C83semidirect
432. #2034C2×C83semidirect
433. #2033C2×C83semidirect
434. #2014C2×C83semidirect
435. #1973C2×C83semidirect
436. #1924C2×C83semidirect
437. #1879C2×C83semidirect
438. #1877C2×C83semidirect
439. #1862C2×C83semidirect
440. C83#25174direct (N × H)
519. C2×D8D4×C83semidirect
564. #102D4×C83semidirect
740. D4#121×C83semidirect

Maximal subgroups

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

subgroupindex
C2×#459×C832
C2×#449×C832
C2×#442×C832
C83×#24282
C83×#23392
C83×#20662
C83×#20342
C83×#20332
C83×#20142
C83×#19732
C83×#19242
C83×#18792
C83×#18772
C83×#18622
#2517483