Finite Group Databasebeta

← C83×#22062 #35249886

Subgroups — C83×#22062 #35249886

Order 21248.

900 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C83×#3002C211yesmaximal, characteristic
2C83×#2930C211yesmaximal, characteristic, complemented
3C83×#2879C211yesmaximal, characteristic, complemented
4C83×#1975C211yesmaximal, characteristic, complemented
5C83×#1974C211yesmaximal, characteristic, complemented
6C83×#1938C211yesmaximal, characteristic, complemented
7C83×#1937C211yesmaximal, characteristic, complemented
8C83×#1929C211yesmaximal, characteristic, complemented
9C83×#1929C211yesmaximal, characteristic, complemented
10C83×#1876C211yesmaximal, characteristic, complemented
11C83×#1876C211yesmaximal, characteristic, complemented
12C83×#1871C211yesmaximal, characteristic, complemented
13C83×#1855C211yesmaximal, characteristic, complemented
14C83×#1789C211yesmaximal, characteristic, complemented
15C83×#1753C211yesmaximal, characteristic, complemented
16C22×#41×C83C2211yescharacteristic
17C2×#135×C83C2211yescharacteristic
18C2×#135×C83C2211yescharacteristic
19C2×#131×C83C2211yescharacteristic, complemented
20C22×M16×C83C2211yescharacteristic
21C22×M16×C83C2211yescharacteristic
22#525×C83C2211yescharacteristic
23#452×C83C411yescharacteristic, complemented
24#452×C83C411yescharacteristic, complemented
25#451×C83C411yescharacteristic, complemented
26#450×C83C411yescharacteristic, complemented
27#449×C83C411yescharacteristic, complemented
28#449×C83C411yescharacteristic, complemented
29#448×C83C411yescharacteristic, complemented
30#447×C83C411yescharacteristic, complemented
31#436×C83—21no—
32#436×C83—21no—
33#435×C83—21no—
34#435×C83—21no—
35C2×#108×C83C2211yescharacteristic, complemented
36C2×#108×C83C2211yescharacteristic, complemented
37#424×C83C2211yescharacteristic, complemented
38C2×#104×C83C2211yescharacteristic
39C2×#104×C83C2211yescharacteristic
40C2×#104×C83C2211yescharacteristic
41C2×#104×C83C2211yescharacteristic
42C2×#104×C83C2211yescharacteristic, complemented
43C2×#104×C83C2211yescharacteristic, complemented
44#416×C83C2211yescharacteristic
45#416×C83C2211yescharacteristic
46#408×C83—21no—
47#408×C83—21no—
48#408×C83C2211yescharacteristic
49#408×C83C2211yescharacteristic
50#408×C83C2211yescharacteristic
51#408×C83C2211yescharacteristic
52#408×C83C2211yescharacteristic, complemented
53#407×C83—21no—
54#407×C83—21no—
55#407×C83C2211yescharacteristic
56C2×C22⋊C8×C83C2211yescharacteristic
57#405×C83C2211yescharacteristic, complemented
58C2×#97×C83C2211yescharacteristic, complemented
59C2×C4×C8×C83C2211yescharacteristic, complemented
60C4×C22⋊C4×C83C2211yescharacteristic
61#341×C83C2211yescharacteristic, complemented
62#341×C83C2211yescharacteristic, complemented
63#339×C83C2211yescharacteristic, complemented
64#339×C83C2211yescharacteristic, complemented
65#336×C83C2211yescharacteristic, complemented
66#336×C83C2211yescharacteristic, complemented
67C2×#41×C83—21no—
68C2×#41×C83—21no—
69C2×#41×C83—41no—
70C2×#41×C83—41no—
71C2×#41×C83—41no—
72C2×#41×C83—41no—
73C2×#41×C83C2×C411yescharacteristic
74C2×#41×C83C2×C411yescharacteristic
75C2×#41×C83C2311yescharacteristic
76C2×#41×C83C2311yescharacteristic
77C2×#41×C83C2311yescharacteristic
78C22×Q8×C83C2×C411yescharacteristic
79C22×D4×C83—21no—
80C22×D4×C83C2×C411yescharacteristic
81C23×C4×C83—21no—
82C23×C4×C83C2311yescharacteristic
83#135×C83—41no—
84#135×C83—41no—
85#135×C83—41no—
86#135×C83—41no—
87C2×Q16×C83C2×C411yescharacteristic
88C2×Q16×C83C2×C411yescharacteristic
89C2×SD16×C83C2×C411yescharacteristic
90C2×SD16×C83C2×C411yescharacteristic
91C2×SD16×C83C2×C411yescharacteristic
92C2×SD16×C83C2×C411yescharacteristic
93C2×D8×C83C2×C411yescharacteristic
94C2×D8×C83C2×C411yescharacteristic
95#131×C83—41no—
96#131×C83—41no—
97C2×M16×C83—21no—
98C2×M16×C83—21no—
99C2×M16×C83—41no—
100C2×M16×C83—41no—
101C2×M16×C83—41no—
102C2×M16×C83—41no—
103C2×M16×C83D411yescharacteristic
104C2×M16×C83D411yescharacteristic
105C2×M16×C83D411yescharacteristic
106C2×M16×C83D411yescharacteristic
107C2×M16×C83C2311yescharacteristic
108C2×M16×C83C2311yescharacteristic
109C2×M16×C83C2311yescharacteristic
110C2×M16×C83C2311yescharacteristic
111C22×C8×C83—21no—
112C22×C8×C83—21no—
113C22×C8×C83C2311yescharacteristic
114C22×C8×C83C2311yescharacteristic
115C22×C8×C83C2311yescharacteristic
116C22×C8×C83C2311yescharacteristic
117#123×C83—21no—
118C22⋊Q8×C83C2×C411yescharacteristic
119C22⋊Q8×C83C2×C411yescharacteristic
120#121×C83C2×C411yescharacteristic
121#121×C83C2×C411yescharacteristic
122#120×C83—21no—
123C4×D4×C83—21no—
124C4×D4×C83—21no—
125#117×C83C2311yescharacteristic
126C2×C22⋊C4×C83—21no—
127C2×C42×C83C2311yescharacteristic
128C2×C42×C83C2311yescharacteristic
129#108×C83—41no—
130#108×C83—41no—
131C4⋊C8×C83—21no—
132C4⋊C8×C83—21no—
133#104×C83—41no—
134#104×C83—41no—
135#104×C83—41no—
136#104×C83—41no—
137#104×C83—41no—
138#104×C83—41no—
139#103×C83C2×C411yescharacteristic
140#103×C83C2×C411yescharacteristic
141#103×C83C2×C411yescharacteristic
142#103×C83C2×C411yescharacteristic
143#102×C83C2×C411yescharacteristic
144#102×C83C2×C411yescharacteristic
145#102×C83C2×C411yescharacteristic
146#102×C83C2×C411yescharacteristic
147C22⋊C8×C83—21no—
148C22⋊C8×C83—21no—
149C22⋊C8×C83—21no—
150C22⋊C8×C83—21no—
151C22⋊C8×C83—21no—
152C22⋊C8×C83—21no—
153C22⋊C8×C83—21no—
154C22⋊C8×C83—21no—
155C22⋊C8×C83—21no—
156C22⋊C8×C83—21no—
157C22⋊C8×C83—21no—
158C22⋊C8×C83—21no—
159C22⋊C8×C83C2×C411yescharacteristic
160C22⋊C8×C83C2×C411yescharacteristic
161C22⋊C8×C83C2×C411yescharacteristic
162C22⋊C8×C83C2×C411yescharacteristic
163#97×C83—21no—
164#97×C83—41no—
165C4×C8×C83—21no—
166C4×C8×C83—41no—
167#95×C83—21no—
168C24×C83—21no—
169C24×C83#4111yescharacteristic
170#41×C83—21no—
171#41×C83—21no—
172#41×C83—21no—
173#41×C83—21no—
174#41×C83—21no—
175#41×C83—21no—
176#41×C83—21no—
177#41×C83—21no—
178#41×C83—21no—
179#41×C83—21no—
180#41×C83—21no—
181#41×C83—21no—
182#41×C83—41no—
183#41×C83—41no—
184#41×C83—41no—
185#41×C83—41no—
186#41×C83—42no—
187#41×C83—42no—
188#41×C83—42no—
189#41×C83—42no—
190C2×Q8×C83—21no—
191C2×Q8×C83—41no—
192C2×Q8×C83—41no—
193C2×Q8×C83C22×C411yescharacteristic
194C2×Q8×C83C22×C411yescharacteristic
195C2×Q8×C83C22×C411yescharacteristic
196C2×D4×C83—21no—
197C2×D4×C83—21no—
198C2×D4×C83—21no—
199C2×D4×C83—21no—
200C2×D4×C83—21no—
201C2×D4×C83—21no—
202C2×D4×C83—21no—
203C2×D4×C83—21no—
204C2×D4×C83—41no—
205C2×D4×C83—41no—
206C2×D4×C83—42no—
207C2×D4×C83—42no—
208C2×D4×C83C22×C411yescharacteristic
209C2×D4×C83C22×C411yescharacteristic
210C2×D4×C83C22×C411yescharacteristic
211C22×C4×C83—21no—
212C22×C4×C83—21no—
213C22×C4×C83—21no—
214C22×C4×C83—21no—
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—42no—
224C22×C4×C83—42no—
225C22×C4×C83C22×C411yescharacteristic
226C22×C4×C83C22×C411yescharacteristic
227C22×C4×C83C2×D411yescharacteristic
228C22×C4×C83C2×D411yescharacteristic
229C22×C4×C83#4111yescharacteristic
230C22×C4×C83C2411yescharacteristic
231Q16×C83—41no—
232Q16×C83—41no—
233SD16×C83—41no—
234SD16×C83—41no—
235SD16×C83—41no—
236SD16×C83—41no—
237D8×C83—41no—
238D8×C83—41no—
239M16×C83—21no—
240M16×C83—21no—
241M16×C83—21no—
242M16×C83—21no—
243M16×C83—21no—
244M16×C83—21no—
245M16×C83—21no—
246M16×C83—21no—
247M16×C83—41no—
248M16×C83—41no—
249M16×C83—41no—
250M16×C83—41no—
251M16×C83—42no—
252M16×C83—42no—
253C2×C8×C83—21no—
254C2×C8×C83—21no—
255C2×C8×C83—21no—
256C2×C8×C83—21no—
257C2×C8×C83—21no—
258C2×C8×C83—21no—
259C2×C8×C83—21no—
260C2×C8×C83—21no—
261C2×C8×C83—21no—
262C2×C8×C83—21no—
263C2×C8×C83—21no—
264C2×C8×C83—21no—
265C2×C8×C83—42no—
266C2×C8×C83—42no—
267C2×C8×C83C22×C411yescharacteristic
268C2×C8×C83C22×C411yescharacteristic
269C2×C8×C83C22×C411yescharacteristic
270C2×C8×C83C22×C411yescharacteristic
271C2×C8×C83C2×D411yescharacteristic
272C2×C8×C83C2×D411yescharacteristic
273C2×C8×C83C2×D411yescharacteristic
274C2×C8×C83C2×D411yescharacteristic
275C4⋊C4×C83—21no—
276C4⋊C4×C83—21no—
277C4⋊C4×C83C22×C411yescharacteristic
278C4⋊C4×C83C22×C411yescharacteristic
279C22⋊C4×C83—21no—
280C22⋊C4×C83—21no—
281C22⋊C4×C83—21no—
282C22⋊C4×C83—21no—
283C22⋊C4×C83—21no—
284C22⋊C4×C83—42no—
285C42×C83—21no—
286C42×C83—21no—
287C42×C83—21no—
288C42×C83—21no—
289C42×C83—21no—
290C23×C83—21no—
291C23×C83—21no—
292C23×C83—21no—
293C23×C83—21no—
294C23×C83—21no—
295C23×C83—41no—
296C23×C83—41no—
297C23×C83—42no—
298C23×C83—81no—
299C23×C83—81no—
300C23×C83C4×D411yescharacteristic
301C23×C83C4×D411yescharacteristic
302C23×C83C2×#4111yescharacteristic
303Q8×C83—21no—
304Q8×C83—21no—
305Q8×C83—21no—
306Q8×C83—21no—
307Q8×C83—21no—
308Q8×C83—21no—
309Q8×C83—42no—
310D4×C83—21no—
311D4×C83—21no—
312D4×C83—21no—
313D4×C83—21no—
314D4×C83—21no—
315D4×C83—21no—
316D4×C83—42no—
317D4×C83—42no—
318D4×C83—42no—
319D4×C83—41no—
320D4×C83—41no—
321D4×C83—41no—
322D4×C83—41no—
323D4×C83—41no—
324D4×C83—41no—
325D4×C83—81no—
326D4×C83—81no—
327C2×C4×C83—21no—
328C2×C4×C83—21no—
329C2×C4×C83—21no—
330C2×C4×C83—21no—
331C2×C4×C83—21no—
332C2×C4×C83—21no—
333C2×C4×C83—21no—
334C2×C4×C83—21no—
335C2×C4×C83—21no—
336C2×C4×C83—21no—
337C2×C4×C83—22no—
338C2×C4×C83—21no—
339C2×C4×C83—21no—
340C2×C4×C83—21no—
341C2×C4×C83—21no—
342C2×C4×C83—21no—
343C2×C4×C83—42no—
344C2×C4×C83—42no—
345C2×C4×C83—41no—
346C2×C4×C83—42no—
347C2×C4×C83—41no—
348C2×C4×C83—41no—
349C2×C4×C83—41no—
350C2×C4×C83—41no—
351C2×C4×C83—41no—
352C2×C4×C83—41no—
353C2×C4×C83—41no—
354C2×C4×C83—41no—
355C2×C4×C83—41no—
356C2×C4×C83—41no—
357C2×C4×C83C4×D411yescharacteristic
358C2×C4×C83C4×D411yescharacteristic
359C2×C4×C83C23×C411yescharacteristic
360C2×C4×C83C22×D411yescharacteristic
361C2×C4×C83H(5,𝔽2)11yescharacteristic
362C2×C4×C83H(5,𝔽2)11yescharacteristic
363C2×C4×C83H(5,𝔽2)11yescharacteristic
364C2×C4×C83H(5,𝔽2)11yescharacteristic
365C8×C83—21no—
366C8×C83—21no—
367C8×C83—21no—
368C8×C83—21no—
369C8×C83—21no—
370C8×C83—21no—
371C8×C83—21no—
372C8×C83—21no—
373C8×C83—41no—
374C8×C83—41no—
375C8×C83—41no—
376C8×C83—41no—
377C22×C83—21no—
378C22×C83—21no—
379C22×C83—21no—
380C22×C83—21no—
381C22×C83—21no—
382C22×C83—21no—
383C22×C83—21no—
384C22×C83—21no—
385C22×C83—41no—
386C22×C83—41no—
387C22×C83—41no—
388C22×C83—41no—
389C22×C83—41no—
390C22×C83—41no—
391C22×C83—41no—
392C22×C83—41no—
393C22×C83—41no—
394C22×C83—81no—
395C22×C83—81no—
396C22×C83—84no—
397C22×C83C2×C4×D411yescharacteristic
398C22×C83#53811yescharacteristic
399C22×C83#53811yescharacteristic
400C4×C83—21no—
401C4×C83—21no—
402C4×C83—42no—
403C4×C83—41no—
404C4×C83—41no—
405C4×C83—41no—
406C4×C83—41no—
407C4×C83—41no—
408C4×C83—81no—
409C4×C83#51811yescharacteristic
410C4×C83#51811yescharacteristic
411C4×C83#53411yescharacteristic
412C4×C83#53511yescharacteristic
413#22062C8311yesmaximal, characteristic, direct product factor, Sylow
414C2×C83—21no—
415C2×C83—21no—
416C2×C83—41no—
417C2×C83—41no—
418C2×C83—81no—
419C2×C83—81no—
420C2×C83—81no—
421C2×C83#232111yescharacteristic
422C2×C83#295611yescharacteristic
423C2×C83#295711yescharacteristic
424#3002C2×C8311yescharacteristic
425#2930C2×C8311yescharacteristic, complemented
426#2879C2×C8311yescharacteristic, complemented
427#1975C2×C8311yescharacteristic, complemented
428#1974C2×C8311yescharacteristic, complemented
429#1938C2×C8311yescharacteristic, complemented
430#1937C2×C8311yescharacteristic, complemented
431#1929C2×C8311yescharacteristic, complemented
432#1929C2×C8311yescharacteristic, complemented
433#1876C2×C8311yescharacteristic, complemented
434#1876C2×C8311yescharacteristic, complemented
435#1871C2×C8311yescharacteristic, complemented
436#1855C2×C8311yescharacteristic, complemented
437#1789C2×C8311yescharacteristic, complemented
438#1753C2×C8311yescharacteristic, complemented
439C83#2206211yescharacteristic, direct product factor, Sylow
440C22×#41C22×C8311yescharacteristic
441C2×#135C22×C8311yescharacteristic
442C2×#135C22×C8311yescharacteristic
443C2×#131C22×C8311yescharacteristic, complemented
444C22×M16C22×C8311yescharacteristic
445C22×M16C22×C8311yescharacteristic
446#525C22×C8311yescharacteristic
447#452C4×C8311yescharacteristic, complemented
448#452C4×C8311yescharacteristic, complemented
449#451C4×C8311yescharacteristic, complemented
450#450C4×C8311yescharacteristic, complemented
451#449C4×C8311yescharacteristic, complemented
452#449C4×C8311yescharacteristic, complemented
453#448C4×C8311yescharacteristic, complemented
454#447C4×C8311yescharacteristic, complemented
455#436—21no—
456#436—21no—
457#435—21no—
458#435—21no—
459C2×#108C22×C8311yescharacteristic, complemented
460C2×#108C22×C8311yescharacteristic, complemented
461#424C22×C8311yescharacteristic, complemented
462C2×#104C22×C8311yescharacteristic
463C2×#104C22×C8311yescharacteristic
464C2×#104C22×C8311yescharacteristic
465C2×#104C22×C8311yescharacteristic
466C2×#104C22×C8311yescharacteristic, complemented
467C2×#104C22×C8311yescharacteristic, complemented
468#416C22×C8311yescharacteristic
469#416C22×C8311yescharacteristic
470#408—21no—
471#408—21no—
472#408C22×C8311yescharacteristic
473#408C22×C8311yescharacteristic
474#408C22×C8311yescharacteristic
475#408C22×C8311yescharacteristic
476#408C22×C8311yescharacteristic, complemented
477#407—21no—
478#407—21no—
479#407C22×C8311yescharacteristic
480C2×C22⋊C8C22×C8311yescharacteristic
481#405C22×C8311yescharacteristic, complemented
482C2×#97C22×C8311yescharacteristic, complemented
483C2×C4×C8C22×C8311yescharacteristic, complemented
484C4×C22⋊C4C22×C8311yescharacteristic
485#341C22×C8311yescharacteristic, complemented
486#341C22×C8311yescharacteristic, complemented
487#339C22×C8311yescharacteristic, complemented
488#339C22×C8311yescharacteristic, complemented
489#336C22×C8311yescharacteristic, complemented
490#336C22×C8311yescharacteristic, complemented
491C2×#41—21no—
492C2×#41—21no—
493C2×#41—41no—
494C2×#41—41no—
495C2×#41—41no—
496C2×#41—41no—
497C2×#41C2×C4×C8311yescharacteristic
498C2×#41C2×C4×C8311yescharacteristic
499C2×#41C23×C8311yescharacteristic
500C2×#41C23×C8311yescharacteristic
501C2×#41C23×C8311yescharacteristic
502C22×Q8C2×C4×C8311yescharacteristic
503C22×D4—21no—
504C22×D4C2×C4×C8311yescharacteristic
505C23×C4—21no—
506C23×C4C23×C8311yescharacteristic
507#135—41no—
508#135—41no—
509#135—41no—
510#135—41no—
511C2×Q16C2×C4×C8311yescharacteristic
512C2×Q16C2×C4×C8311yescharacteristic
513C2×SD16C2×C4×C8311yescharacteristic
514C2×SD16C2×C4×C8311yescharacteristic
515C2×SD16C2×C4×C8311yescharacteristic
516C2×SD16C2×C4×C8311yescharacteristic
517C2×D8C2×C4×C8311yescharacteristic
518C2×D8C2×C4×C8311yescharacteristic
519#131—41no—
520#131—41no—
521C2×M16—21no—
522C2×M16—21no—
523C2×M16—41no—
524C2×M16—41no—
525C2×M16—41no—
526C2×M16—41no—
527C2×M16D4×C8311yescharacteristic
528C2×M16D4×C8311yescharacteristic
529C2×M16D4×C8311yescharacteristic
530C2×M16D4×C8311yescharacteristic
531C2×M16C23×C8311yescharacteristic
532C2×M16C23×C8311yescharacteristic
533C2×M16C23×C8311yescharacteristic
534C2×M16C23×C8311yescharacteristic
535C22×C8—21no—
536C22×C8—21no—
537C22×C8C23×C8311yescharacteristic
538C22×C8C23×C8311yescharacteristic
539C22×C8C23×C8311yescharacteristic
540C22×C8C23×C8311yescharacteristic
541#123—21no—
542C22⋊Q8C2×C4×C8311yescharacteristic
543C22⋊Q8C2×C4×C8311yescharacteristic
544#121C2×C4×C8311yescharacteristic
545#121C2×C4×C8311yescharacteristic
546#120—21no—
547C4×D4—21no—
548C4×D4—21no—
549#117C23×C8311yescharacteristic
550C2×C22⋊C4—21no—
551C2×C42C23×C8311yescharacteristic
552C2×C42C23×C8311yescharacteristic
553#108—41no—
554#108—41no—
555C4⋊C8—21no—
556C4⋊C8—21no—
557#104—41no—
558#104—41no—
559#104—41no—
560#104—41no—
561#104—41no—
562#104—41no—
563#103C2×C4×C8311yescharacteristic
564#103C2×C4×C8311yescharacteristic
565#103C2×C4×C8311yescharacteristic
566#103C2×C4×C8311yescharacteristic
567#102C2×C4×C8311yescharacteristic
568#102C2×C4×C8311yescharacteristic
569#102C2×C4×C8311yescharacteristic
570#102C2×C4×C8311yescharacteristic
571C22⋊C8—21no—
572C22⋊C8—21no—
573C22⋊C8—21no—
574C22⋊C8—21no—
575C22⋊C8—21no—
576C22⋊C8—21no—
577C22⋊C8—21no—
578C22⋊C8—21no—
579C22⋊C8—21no—
580C22⋊C8—21no—
581C22⋊C8—21no—
582C22⋊C8—21no—
583C22⋊C8C2×C4×C8311yescharacteristic
584C22⋊C8C2×C4×C8311yescharacteristic
585C22⋊C8C2×C4×C8311yescharacteristic
586C22⋊C8C2×C4×C8311yescharacteristic
587#97—21no—
588#97—41no—
589C4×C8—21no—
590C4×C8—41no—
591#95—21no—
592C24—21no—
593C24#41×C8311yescharacteristic
594#41—21no—
595#41—21no—
596#41—21no—
597#41—21no—
598#41—21no—
599#41—21no—
600#41—21no—
601#41—21no—
602#41—21no—
603#41—21no—
604#41—21no—
605#41—21no—
606#41—41no—
607#41—41no—
608#41—41no—
609#41—41no—
610#41—42no—
611#41—42no—
612#41—42no—
613#41—42no—
614C2×Q8—21no—
615C2×Q8—41no—
616C2×Q8—41no—
617C2×Q8C22×C4×C8311yescharacteristic
618C2×Q8C22×C4×C8311yescharacteristic
619C2×Q8C22×C4×C8311yescharacteristic
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—41no—
629C2×D4—41no—
630C2×D4—42no—
631C2×D4—42no—
632C2×D4C22×C4×C8311yescharacteristic
633C2×D4C22×C4×C8311yescharacteristic
634C2×D4C22×C4×C8311yescharacteristic
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—42no—
648C22×C4—42no—
649C22×C4C22×C4×C8311yescharacteristic
650C22×C4C22×C4×C8311yescharacteristic
651C22×C4C2×D4×C8311yescharacteristic
652C22×C4C2×D4×C8311yescharacteristic
653C22×C4#41×C8311yescharacteristic
654C22×C4C24×C8311yescharacteristic
655Q16—41no—
656Q16—41no—
657SD16—41no—
658SD16—41no—
659SD16—41no—
660SD16—41no—
661D8—41no—
662D8—41no—
663M16—21no—
664M16—21no—
665M16—21no—
666M16—21no—
667M16—21no—
668M16—21no—
669M16—21no—
670M16—21no—
671M16—41no—
672M16—41no—
673M16—41no—
674M16—41no—
675M16—42no—
676M16—42no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—42no—
690C2×C8—42no—
691C2×C8C22×C4×C8311yescharacteristic
692C2×C8C22×C4×C8311yescharacteristic
693C2×C8C22×C4×C8311yescharacteristic
694C2×C8C22×C4×C8311yescharacteristic
695C2×C8C2×D4×C8311yescharacteristic
696C2×C8C2×D4×C8311yescharacteristic
697C2×C8C2×D4×C8311yescharacteristic
698C2×C8C2×D4×C8311yescharacteristic
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4C22×C4×C8311yescharacteristic
702C4⋊C4C22×C4×C8311yescharacteristic
703C22⋊C4—21no—
704C22⋊C4—21no—
705C22⋊C4—21no—
706C22⋊C4—21no—
707C22⋊C4—21no—
708C22⋊C4—42no—
709C42—21no—
710C42—21no—
711C42—21no—
712C42—21no—
713C42—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—41no—
720C23—41no—
721C23—42no—
722C23—81no—
723C23—81no—
724C23C4×D4×C8311yescharacteristic
725C23C4×D4×C8311yescharacteristic
726C23C2×#41×C8311yescharacteristic
727Q8—21no—
728Q8—21no—
729Q8—21no—
730Q8—21no—
731Q8—21no—
732Q8—21no—
733Q8—42no—
734D4—21no—
735D4—21no—
736D4—21no—
737D4—21no—
738D4—21no—
739D4—21no—
740D4—42no—
741D4—42no—
742D4—42no—
743D4—41no—
744D4—41no—
745D4—41no—
746D4—41no—
747D4—41no—
748D4—41no—
749D4—81no—
750D4—81no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—22no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4C4×D4×C8311yescharacteristic
782C2×C4C4×D4×C8311yescharacteristic
783C2×C4C23×C4×C8311yescharacteristic
784C2×C4C22×D4×C8311yescharacteristic
785C2×C4H(5,𝔽2)×C8311yescharacteristic
786C2×C4H(5,𝔽2)×C8311yescharacteristic
787C2×C4H(5,𝔽2)×C8311yescharacteristic
788C2×C4H(5,𝔽2)×C8311yescharacteristic
789C8—21no—
790C8—21no—
791C8—21no—
792C8—21no—
793C8—21no—
794C8—21no—
795C8—21no—
796C8—21no—
797C8—41no—
798C8—41no—
799C8—41no—
800C8—41no—
801C22—21no—
802C22—21no—
803C22—21no—
804C22—21no—
805C22—21no—
806C22—21no—
807C22—21no—
808C22—21no—
809C22—41no—
810C22—41no—
811C22—41no—
812C22—41no—
813C22—41no—
814C22—41no—
815C22—41no—
816C22—41no—
817C22—41no—
818C22—81no—
819C22—81no—
820C22—84no—
821C22C2×C4×D4×C8311yescharacteristic
822C22#538×C8311yescharacteristic
823C22#538×C8311yescharacteristic
824C4—21no—
825C4—21no—
826C4—42no—
827C4—41no—
828C4—41no—
829C4—41no—
830C4—41no—
831C4—41no—
832C4—81no—
833C4#518×C8311yescharacteristic
834C4#518×C8311yescharacteristic
835C4#534×C8311yescharacteristic
836C4#535×C8311yescharacteristic
837C2—21no—
838C2—21no—
839C2—41no—
840C2—41no—
841C2—81no—
842C2—81no—
843C2—81no—
844C2C83×#232111yescharacteristic
845C2C83×#295611yescharacteristic
846C2C83×#295711yescharacteristic
subgroupG/H
centerC2×C4×C83C22×D4
commutatorC2×C4C23×C4×C83
Frattini, cosocleC22×C4C24×C83
socleC22×C83C2×C4×D4
prime radicalC83×#3002C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C83 ◁ C22×M16×C83 ◁ G

Complements

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

NH ≅ G/Ntype
2. C83×#2930C2semidirect
3. C83×#2879C2semidirect
4. C83×#1975C2semidirect
5. C83×#1974C2semidirect
6. C83×#1938C2semidirect
7. C83×#1937C2semidirect
8. C83×#1929C2semidirect
9. C83×#1929C2semidirect
10. C83×#1876C2semidirect
11. C83×#1876C2semidirect
12. C83×#1871C2semidirect
13. C83×#1855C2semidirect
14. C83×#1789C2semidirect
15. C83×#1753C2semidirect
19. C2×#131×C83C22semidirect
23. #452×C83C4semidirect
24. #452×C83C4semidirect
25. #451×C83C4semidirect
26. #450×C83C4semidirect
27. #449×C83C4semidirect
28. #449×C83C4semidirect
29. #448×C83C4semidirect
30. #447×C83C4semidirect
35. C2×#108×C83C22semidirect
36. C2×#108×C83C22semidirect
37. #424×C83C22semidirect
42. C2×#104×C83C22semidirect
43. C2×#104×C83C22semidirect
52. #408×C83C22semidirect
57. #405×C83C22semidirect
58. C2×#97×C83C22semidirect
59. C2×C4×C8×C83C22semidirect
61. #341×C83C22semidirect
62. #341×C83C22semidirect
63. #339×C83C22semidirect
64. #339×C83C22semidirect
65. #336×C83C22semidirect
66. #336×C83C22semidirect
413. #22062C83direct (N × H)
425. #2930C2×C83semidirect
426. #2879C2×C83semidirect
427. #1975C2×C83semidirect
428. #1974C2×C83semidirect
429. #1938C2×C83semidirect
430. #1937C2×C83semidirect
431. #1929C2×C83semidirect
432. #1929C2×C83semidirect
433. #1876C2×C83semidirect
434. #1876C2×C83semidirect
435. #1871C2×C83semidirect
436. #1855C2×C83semidirect
437. #1789C2×C83semidirect
438. #1753C2×C83semidirect
439. C83#22062direct (N × H)
443. C2×#131C22×C83semidirect
447. #452C4×C83semidirect
448. #452C4×C83semidirect
449. #451C4×C83semidirect
450. #450C4×C83semidirect
451. #449C4×C83semidirect
452. #449C4×C83semidirect
453. #448C4×C83semidirect
454. #447C4×C83semidirect
459. C2×#108C22×C83semidirect
460. C2×#108C22×C83semidirect
461. #424C22×C83semidirect
466. C2×#104C22×C83semidirect
467. C2×#104C22×C83semidirect
476. #408C22×C83semidirect
481. #405C22×C83semidirect
482. C2×#97C22×C83semidirect
483. C2×C4×C8C22×C83semidirect
485. #341C22×C83semidirect
486. #341C22×C83semidirect
487. #339C22×C83semidirect
488. #339C22×C83semidirect
489. #336C22×C83semidirect
490. #336C22×C83semidirect

Maximal subgroups

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

subgroupindex
C83×#30022
C83×#29302
C83×#28792
C83×#19752
C83×#19742
C83×#19382
C83×#19372
C83×#19292
C83×#18762
C83×#18712
C83×#18552
C83×#17892
C83×#17532
#2206283