Finite Group Databasebeta

← C83×#18447 #35246271

Subgroups — C83×#18447 #35246271

Order 21248.

982 conjugacy classes of subgroups.

The subgroup lattice has 970 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C83×#3534C211yesmaximal, characteristic
2C83×#3193C211yesmaximal, characteristic, complemented
3C83×#3190C211yesmaximal, characteristic, complemented
4C83×#2814C211yesmaximal, characteristic, complemented
5C83×#1612C211yesmaximal, characteristic, complemented
6C83×#1610C211yesmaximal, characteristic, complemented
7C83×#1609C211yesmaximal, characteristic, complemented
8C83×#1607C211yesmaximal, characteristic, complemented
9C83×#1606C211yesmaximal, characteristic, complemented
10C83×#1604C211yesmaximal, characteristic, complemented
11C83×#1603C211yesmaximal, characteristic, complemented
12C83×#1601C211yesmaximal, characteristic, complemented
13C83×#1519C211yesmaximal, characteristic, complemented
14C83×#1513C211yesmaximal, characteristic, complemented
15C83×#1468C211yesmaximal, characteristic, complemented
16#562×C83—21no—
17#560×C83—21no—
18#553×C83—21no—
19#551×C83—21no—
20#546×C83—21no—
21#546×C83—21no—
22#546×C83—21no—
23D42×C83—21no—
24#540×C83—21no—
25#539×C83—21no—
26#539×C83C2211yescharacteristic
27#538×C83—21no—
28#538×C83C2211yescharacteristic
29#537×C83C2211yescharacteristic
30#534×C83—21no—
31#534×C83C2211yescharacteristic
32#525×C83C2211yescharacteristic
33C2×#123×C83C2211yescharacteristic
34C2×C22⋊Q8×C83C2211yescharacteristic, complemented
35C2×#121×C83C2211yescharacteristic
36#485×C83—21no—
37#484×C83—21no—
38#483×C83C2211yescharacteristic, complemented
39#480×C83C2211yescharacteristic
40#480×C83C2211yescharacteristic, complemented
41#480×C83C2211yescharacteristic, complemented
42#468×C83—21no—
43#468×C83—21no—
44#467×C83—21no—
45#465×C83—21no—
46#452×C83—21no—
47#451×C83C2211yescharacteristic, complemented
48#450×C83—21no—
49#448×C83C2211yescharacteristic
50#448×C83C2211yescharacteristic, complemented
51#448×C83C2211yescharacteristic, complemented
52#407×C83C2211yescharacteristic, complemented
53C2×C22⋊C8×C83C2211yescharacteristic, complemented
54#398×C83—21no—
55#398×C83C2211yescharacteristic, complemented
56#397×C83—21no—
57#397×C83C2211yescharacteristic, complemented
58#396×C83—21no—
59#395×C83C2211yescharacteristic, complemented
60#394×C83—21no—
61#393×C83C2211yescharacteristic, complemented
62#380×C83C2211yescharacteristic, complemented
63#328×C83C2211yescharacteristic, complemented
64#328×C83C2211yescharacteristic, complemented
65#327×C83C2211yescharacteristic
66#327×C83C2211yescharacteristic
67#327×C83C2211yescharacteristic, complemented
68#327×C83C2211yescharacteristic, complemented
69#327×C83C2211yescharacteristic, complemented
70#327×C83C2211yescharacteristic, complemented
71#324×C83C2211yescharacteristic, complemented
72#324×C83C2211yescharacteristic, complemented
73#323×C83C2211yescharacteristic, complemented
74#323×C83C2211yescharacteristic, complemented
75C2×#41×C83—21no—
76C2×#41×C83D411yescharacteristic
77C22×Q8×C83C2311yescharacteristic
78C22×D4×C83—21no—
79C22×D4×C83—21no—
80C22×D4×C83—21no—
81C22×D4×C83D411yescharacteristic
82C22×D4×C83D411yescharacteristic
83C23×C4×C83C2311yescharacteristic
84C2×Q16×C83—21no—
85C2×SD16×C83—21no—
86C2×SD16×C83—21no—
87C2×SD16×C83—21no—
88C2×M16×C83—21no—
89C22×C8×C83—21no—
90#127×C83—21no—
91#126×C83—21no—
92#126×C83—21no—
93#126×C83—21no—
94#126×C83—21no—
95#125×C83—21no—
96#125×C83—21no—
97#124×C83—21no—
98#124×C83—21no—
99#124×C83—21no—
100#123×C83—21no—
101#123×C83—21no—
102#123×C83—21no—
103#123×C83—21no—
104#123×C83—21no—
105#123×C83—21no—
106#123×C83—21no—
107#123×C83—21no—
108#123×C83—21no—
109#123×C83—21no—
110#123×C83—21no—
111#123×C83—21no—
112#123×C83—21no—
113#123×C83—21no—
114C22⋊Q8×C83—21no—
115C22⋊Q8×C83—21no—
116C22⋊Q8×C83—21no—
117C22⋊Q8×C83—21no—
118C22⋊Q8×C83—21no—
119C22⋊Q8×C83—21no—
120C22⋊Q8×C83—21no—
121C22⋊Q8×C83—21no—
122C22⋊Q8×C83—21no—
123C22⋊Q8×C83D411yescharacteristic
124C22⋊Q8×C83C2311yescharacteristic
125#121×C83—21no—
126#121×C83—21no—
127#121×C83—21no—
128#121×C83—21no—
129#121×C83—21no—
130#121×C83—21no—
131#121×C83—21no—
132#121×C83—21no—
133#121×C83—21no—
134#121×C83—21no—
135#121×C83—21no—
136#121×C83—21no—
137#121×C83—21no—
138#121×C83—21no—
139#121×C83—21no—
140#121×C83D411yescharacteristic
141#121×C83D411yescharacteristic
142#121×C83D411yescharacteristic
143#121×C83C2311yescharacteristic
144#121×C83C2311yescharacteristic
145#121×C83C2311yescharacteristic
146#120×C83—21no—
147#120×C83—21no—
148#120×C83—21no—
149#120×C83—21no—
150#120×C83—21no—
151#120×C83—21no—
152#120×C83—21no—
153#120×C83—21no—
154C4×D4×C83—21no—
155C4×D4×C83—21no—
156C4×D4×C83—21no—
157C4×D4×C83—21no—
158C4×D4×C83—21no—
159C4×D4×C83—21no—
160C4×D4×C83—21no—
161C4×D4×C83—21no—
162#117×C83—21no—
163#117×C83D411yescharacteristic
164C2×C4⋊C4×C83—21no—
165C2×C4⋊C4×C83—21no—
166C2×C4⋊C4×C83—21no—
167C2×C4⋊C4×C83—21no—
168C2×C4⋊C4×C83D411yescharacteristic
169C2×C4⋊C4×C83D411yescharacteristic
170C2×C4⋊C4×C83C2311yescharacteristic
171C2×C4⋊C4×C83C2311yescharacteristic
172C2×C22⋊C4×C83—21no—
173C2×C22⋊C4×C83—21no—
174C2×C22⋊C4×C83—21no—
175C2×C22⋊C4×C83—21no—
176C2×C22⋊C4×C83—21no—
177C2×C22⋊C4×C83—21no—
178C2×C22⋊C4×C83—21no—
179C2×C22⋊C4×C83D411yescharacteristic
180C2×C22⋊C4×C83D411yescharacteristic
181C2×C22⋊C4×C83C2311yescharacteristic
182#107×C83—21no—
183#107×C83—21no—
184#107×C83—21no—
185#106×C83—21no—
186#103×C83—21no—
187#103×C83—21no—
188#103×C83—21no—
189#103×C83—21no—
190#103×C83—21no—
191#102×C83—21no—
192#102×C83—21no—
193#102×C83—21no—
194C22⋊C8×C83—21no—
195C22⋊C8×C83—21no—
196C22⋊C8×C83C2311yescharacteristic
197C22⋊C8×C83C2311yescharacteristic
198C22⋊C8×C83C2311yescharacteristic
199C22⋊C8×C83C2311yescharacteristic
200#95×C83—21no—
201#95×C83—21no—
202#95×C83—21no—
203#95×C83—21no—
204#95×C83C2311yescharacteristic
205#95×C83C2311yescharacteristic
206C24×C83—21no—
207C24×C83—21no—
208C24×C83C2×D411yescharacteristic
209C24×C83C2×D411yescharacteristic
210#41×C83—81no—
211#41×C83—81no—
212#41×C83—81no—
213C2×Q8×C83—21no—
214C2×Q8×C83—21no—
215C2×Q8×C83—21no—
216C2×Q8×C83—81no—
217C2×Q8×C83C2×D411yescharacteristic
218C2×D4×C83—21no—
219C2×D4×C83—21no—
220C2×D4×C83—21no—
221C2×D4×C83—21no—
222C2×D4×C83—21no—
223C2×D4×C83—21no—
224C2×D4×C83—21no—
225C2×D4×C83—21no—
226C2×D4×C83—21no—
227C2×D4×C83—21no—
228C2×D4×C83—21no—
229C2×D4×C83—21no—
230C2×D4×C83—21no—
231C2×D4×C83—21no—
232C2×D4×C83—21no—
233C2×D4×C83—21no—
234C2×D4×C83—21no—
235C2×D4×C83—81no—
236C2×D4×C83—81no—
237C2×D4×C83—81no—
238C2×D4×C83—81no—
239C2×D4×C83—81no—
240C2×D4×C83—81no—
241C2×D4×C83—82no—
242C2×D4×C83C2×D411yescharacteristic
243C2×D4×C83C2×D411yescharacteristic
244C2×D4×C83C2×D411yescharacteristic
245C22×C4×C83—21no—
246C22×C4×C83—21no—
247C22×C4×C83—21no—
248C22×C4×C83—21no—
249C22×C4×C83—21no—
250C22×C4×C83—21no—
251C22×C4×C83—21no—
252C22×C4×C83—21no—
253C22×C4×C83—21no—
254C22×C4×C83—21no—
255C22×C4×C83—21no—
256C22×C4×C83—81no—
257C22×C4×C83C2×D411yescharacteristic
258C22×C4×C83C2×D411yescharacteristic
259C22×C4×C83C2×D411yescharacteristic
260C22×C4×C83C2×D411yescharacteristic
261C22×C4×C83C2×D411yescharacteristic
262C22×C4×C83C2×D411yescharacteristic
263C22×C4×C83C2×D411yescharacteristic
264C22×C4×C83C2×D411yescharacteristic
265C22×C4×C83C2411yescharacteristic
266Q16×C83—81no—
267SD16×C83—81no—
268SD16×C83—81no—
269SD16×C83—81no—
270M16×C83—81no—
271C2×C8×C83—21no—
272C2×C8×C83—21no—
273C2×C8×C83—21no—
274C2×C8×C83—21no—
275C2×C8×C83—81no—
276C4⋊C4×C83—21no—
277C4⋊C4×C83—21no—
278C4⋊C4×C83—21no—
279C4⋊C4×C83—21no—
280C4⋊C4×C83—21no—
281C4⋊C4×C83—21no—
282C4⋊C4×C83—21no—
283C4⋊C4×C83—21no—
284C4⋊C4×C83—21no—
285C4⋊C4×C83—21no—
286C4⋊C4×C83—21no—
287C4⋊C4×C83—21no—
288C4⋊C4×C83—21no—
289C4⋊C4×C83—21no—
290C4⋊C4×C83—21no—
291C4⋊C4×C83—41no—
292C4⋊C4×C83—41no—
293C4⋊C4×C83—81no—
294C4⋊C4×C83—81no—
295C4⋊C4×C83—81no—
296C4⋊C4×C83C2×D411yescharacteristic
297C4⋊C4×C83C2×D411yescharacteristic
298C4⋊C4×C83C2×D411yescharacteristic
299C4⋊C4×C83C2×D411yescharacteristic
300C22⋊C4×C83—21no—
301C22⋊C4×C83—21no—
302C22⋊C4×C83—21no—
303C22⋊C4×C83—21no—
304C22⋊C4×C83—21no—
305C22⋊C4×C83—21no—
306C22⋊C4×C83—21no—
307C22⋊C4×C83—21no—
308C22⋊C4×C83—21no—
309C22⋊C4×C83—21no—
310C22⋊C4×C83—21no—
311C22⋊C4×C83—21no—
312C22⋊C4×C83—21no—
313C22⋊C4×C83—21no—
314C22⋊C4×C83—21no—
315C22⋊C4×C83—21no—
316C22⋊C4×C83—21no—
317C22⋊C4×C83—21no—
318C22⋊C4×C83—21no—
319C22⋊C4×C83—21no—
320C22⋊C4×C83—21no—
321C22⋊C4×C83—21no—
322C22⋊C4×C83—21no—
323C22⋊C4×C83—21no—
324C22⋊C4×C83—21no—
325C22⋊C4×C83—41no—
326C22⋊C4×C83—41no—
327C22⋊C4×C83—81no—
328C22⋊C4×C83—81no—
329C22⋊C4×C83—81no—
330C42×C83—21no—
331C42×C83—21no—
332C42×C83—21no—
333C23×C83—21no—
334C23×C83—21no—
335C23×C83—21no—
336C23×C83—21no—
337C23×C83—21no—
338C23×C83—21no—
339C23×C83—21no—
340C23×C83—21no—
341C23×C83—41no—
342C23×C83—41no—
343C23×C83—42no—
344C23×C83—41no—
345C23×C83—41no—
346C23×C83—81no—
347C23×C83—81no—
348C23×C83—81no—
349C23×C83—81no—
350C23×C83—81no—
351C23×C83#12011yescharacteristic
352C23×C83#12011yescharacteristic
353C23×C83C22×D411yescharacteristic
354Q8×C83—41no—
355Q8×C83—41no—
356Q8×C83—41no—
357Q8×C83—41no—
358Q8×C83—41no—
359Q8×C83—81no—
360D4×C83—41no—
361D4×C83—41no—
362D4×C83—41no—
363D4×C83—42no—
364D4×C83—42no—
365D4×C83—41no—
366D4×C83—41no—
367D4×C83—41no—
368D4×C83—41no—
369D4×C83—41no—
370D4×C83—41no—
371D4×C83—81no—
372D4×C83—81no—
373D4×C83—81no—
374D4×C83—81no—
375D4×C83—81no—
376D4×C83—81no—
377D4×C83—81no—
378D4×C83—81no—
379D4×C83—81no—
380D4×C83—81no—
381D4×C83—81no—
382D4×C83—81no—
383C2×C4×C83—21no—
384C2×C4×C83—21no—
385C2×C4×C83—21no—
386C2×C4×C83—21no—
387C2×C4×C83—21no—
388C2×C4×C83—21no—
389C2×C4×C83—21no—
390C2×C4×C83—21no—
391C2×C4×C83—21no—
392C2×C4×C83—21no—
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—81no—
414C2×C4×C83—81no—
415C2×C4×C83—81no—
416C2×C4×C83—81no—
417C2×C4×C83—81no—
418C2×C4×C83—81no—
419C2×C4×C83—81no—
420C2×C4×C83#12011yescharacteristic
421C2×C4×C83#12011yescharacteristic
422C2×C4×C83C22×D411yescharacteristic
423C2×C4×C83C22×D411yescharacteristic
424C8×C83—41no—
425C8×C83—41no—
426C8×C83—41no—
427C8×C83—41no—
428C22×C83—21no—
429C22×C83—21no—
430C22×C83—21no—
431C22×C83—21no—
432C22×C83—21no—
433C22×C83—21no—
434C22×C83—21no—
435C22×C83—21no—
436C22×C83—41no—
437C22×C83—41no—
438C22×C83—41no—
439C22×C83—41no—
440C22×C83—41no—
441C22×C83—41no—
442C22×C83—41no—
443C22×C83—41no—
444C22×C83—41no—
445C22×C83—41no—
446C22×C83—41no—
447C22×C83—41no—
448C22×C83—81no—
449C22×C83—81no—
450C22×C83—81no—
451C22×C83—81no—
452C22×C83—162no—
453C22×C83—162no—
454C22×C83C2×#12011yescharacteristic
455C22×C83#57611yescharacteristic
456C22×C83#57711yescharacteristic
457C4×C83—21no—
458C4×C83—21no—
459C4×C83—21no—
460C4×C83—21no—
461C4×C83—41no—
462C4×C83—41no—
463C4×C83—41no—
464C4×C83—41no—
465C4×C83—41no—
466C4×C83—41no—
467C4×C83—41no—
468C4×C83—41no—
469C4×C83—81no—
470C4×C83—81no—
471C4×C83—81no—
472C4×C83—81no—
473#18447C8311yesmaximal, characteristic, direct product factor, Sylow
474C2×C83—21no—
475C2×C83—21no—
476C2×C83—41no—
477C2×C83—41no—
478C2×C83—81no—
479C2×C83—81no—
480C2×C83—81no—
481C2×C83—81no—
482C2×C83#301211yescharacteristic
483C2×C83#302211yescharacteristic
484C2×C83#302611yescharacteristic
485#3534C2×C8311yescharacteristic
486#3193C2×C8311yescharacteristic, complemented
487#3190C2×C8311yescharacteristic, complemented
488#2814C2×C8311yescharacteristic, complemented
489#1612C2×C8311yescharacteristic, complemented
490#1610C2×C8311yescharacteristic, complemented
491#1609C2×C8311yescharacteristic, complemented
492#1607C2×C8311yescharacteristic, complemented
493#1606C2×C8311yescharacteristic, complemented
494#1604C2×C8311yescharacteristic, complemented
495#1603C2×C8311yescharacteristic, complemented
496#1601C2×C8311yescharacteristic, complemented
497#1519C2×C8311yescharacteristic, complemented
498#1513C2×C8311yescharacteristic, complemented
499#1468C2×C8311yescharacteristic, complemented
500C83#1844711yescharacteristic, direct product factor, Sylow
501#562—21no—
502#560—21no—
503#553—21no—
504#551—21no—
505#546—21no—
506#546—21no—
507#546—21no—
508D42—21no—
509#540—21no—
510#539—21no—
511#539C22×C8311yescharacteristic
512#538—21no—
513#538C22×C8311yescharacteristic
514#537C22×C8311yescharacteristic
515#534—21no—
516#534C22×C8311yescharacteristic
517#525C22×C8311yescharacteristic
518C2×#123C22×C8311yescharacteristic
519C2×C22⋊Q8C22×C8311yescharacteristic, complemented
520C2×#121C22×C8311yescharacteristic
521#485—21no—
522#484—21no—
523#483C22×C8311yescharacteristic, complemented
524#480C22×C8311yescharacteristic
525#480C22×C8311yescharacteristic, complemented
526#480C22×C8311yescharacteristic, complemented
527#468—21no—
528#468—21no—
529#467—21no—
530#465—21no—
531#452—21no—
532#451C22×C8311yescharacteristic, complemented
533#450—21no—
534#448C22×C8311yescharacteristic
535#448C22×C8311yescharacteristic, complemented
536#448C22×C8311yescharacteristic, complemented
537#407C22×C8311yescharacteristic, complemented
538C2×C22⋊C8C22×C8311yescharacteristic, complemented
539#398—21no—
540#398C22×C8311yescharacteristic, complemented
541#397—21no—
542#397C22×C8311yescharacteristic, complemented
543#396—21no—
544#395C22×C8311yescharacteristic, complemented
545#394—21no—
546#393C22×C8311yescharacteristic, complemented
547#380C22×C8311yescharacteristic, complemented
548#328C22×C8311yescharacteristic, complemented
549#328C22×C8311yescharacteristic, complemented
550#327C22×C8311yescharacteristic
551#327C22×C8311yescharacteristic
552#327C22×C8311yescharacteristic, complemented
553#327C22×C8311yescharacteristic, complemented
554#327C22×C8311yescharacteristic, complemented
555#327C22×C8311yescharacteristic, complemented
556#324C22×C8311yescharacteristic, complemented
557#324C22×C8311yescharacteristic, complemented
558#323C22×C8311yescharacteristic, complemented
559#323C22×C8311yescharacteristic, complemented
560C2×#41—21no—
561C2×#41D4×C8311yescharacteristic
562C22×Q8C23×C8311yescharacteristic
563C22×D4—21no—
564C22×D4—21no—
565C22×D4—21no—
566C22×D4D4×C8311yescharacteristic
567C22×D4D4×C8311yescharacteristic
568C23×C4C23×C8311yescharacteristic
569C2×Q16—21no—
570C2×SD16—21no—
571C2×SD16—21no—
572C2×SD16—21no—
573C2×M16—21no—
574C22×C8—21no—
575#127—21no—
576#126—21no—
577#126—21no—
578#126—21no—
579#126—21no—
580#125—21no—
581#125—21no—
582#124—21no—
583#124—21no—
584#124—21no—
585#123—21no—
586#123—21no—
587#123—21no—
588#123—21no—
589#123—21no—
590#123—21no—
591#123—21no—
592#123—21no—
593#123—21no—
594#123—21no—
595#123—21no—
596#123—21no—
597#123—21no—
598#123—21no—
599C22⋊Q8—21no—
600C22⋊Q8—21no—
601C22⋊Q8—21no—
602C22⋊Q8—21no—
603C22⋊Q8—21no—
604C22⋊Q8—21no—
605C22⋊Q8—21no—
606C22⋊Q8—21no—
607C22⋊Q8—21no—
608C22⋊Q8D4×C8311yescharacteristic
609C22⋊Q8C23×C8311yescharacteristic
610#121—21no—
611#121—21no—
612#121—21no—
613#121—21no—
614#121—21no—
615#121—21no—
616#121—21no—
617#121—21no—
618#121—21no—
619#121—21no—
620#121—21no—
621#121—21no—
622#121—21no—
623#121—21no—
624#121—21no—
625#121D4×C8311yescharacteristic
626#121D4×C8311yescharacteristic
627#121D4×C8311yescharacteristic
628#121C23×C8311yescharacteristic
629#121C23×C8311yescharacteristic
630#121C23×C8311yescharacteristic
631#120—21no—
632#120—21no—
633#120—21no—
634#120—21no—
635#120—21no—
636#120—21no—
637#120—21no—
638#120—21no—
639C4×D4—21no—
640C4×D4—21no—
641C4×D4—21no—
642C4×D4—21no—
643C4×D4—21no—
644C4×D4—21no—
645C4×D4—21no—
646C4×D4—21no—
647#117—21no—
648#117D4×C8311yescharacteristic
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4—21no—
653C2×C4⋊C4D4×C8311yescharacteristic
654C2×C4⋊C4D4×C8311yescharacteristic
655C2×C4⋊C4C23×C8311yescharacteristic
656C2×C4⋊C4C23×C8311yescharacteristic
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4D4×C8311yescharacteristic
665C2×C22⋊C4D4×C8311yescharacteristic
666C2×C22⋊C4C23×C8311yescharacteristic
667#107—21no—
668#107—21no—
669#107—21no—
670#106—21no—
671#103—21no—
672#103—21no—
673#103—21no—
674#103—21no—
675#103—21no—
676#102—21no—
677#102—21no—
678#102—21no—
679C22⋊C8—21no—
680C22⋊C8—21no—
681C22⋊C8C23×C8311yescharacteristic
682C22⋊C8C23×C8311yescharacteristic
683C22⋊C8C23×C8311yescharacteristic
684C22⋊C8C23×C8311yescharacteristic
685#95—21no—
686#95—21no—
687#95—21no—
688#95—21no—
689#95C23×C8311yescharacteristic
690#95C23×C8311yescharacteristic
691C24—21no—
692C24—21no—
693C24C2×D4×C8311yescharacteristic
694C24C2×D4×C8311yescharacteristic
695#41—81no—
696#41—81no—
697#41—81no—
698C2×Q8—21no—
699C2×Q8—21no—
700C2×Q8—21no—
701C2×Q8—81no—
702C2×Q8C2×D4×C8311yescharacteristic
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—21no—
711C2×D4—21no—
712C2×D4—21no—
713C2×D4—21no—
714C2×D4—21no—
715C2×D4—21no—
716C2×D4—21no—
717C2×D4—21no—
718C2×D4—21no—
719C2×D4—21no—
720C2×D4—81no—
721C2×D4—81no—
722C2×D4—81no—
723C2×D4—81no—
724C2×D4—81no—
725C2×D4—81no—
726C2×D4—82no—
727C2×D4C2×D4×C8311yescharacteristic
728C2×D4C2×D4×C8311yescharacteristic
729C2×D4C2×D4×C8311yescharacteristic
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—81no—
742C22×C4C2×D4×C8311yescharacteristic
743C22×C4C2×D4×C8311yescharacteristic
744C22×C4C2×D4×C8311yescharacteristic
745C22×C4C2×D4×C8311yescharacteristic
746C22×C4C2×D4×C8311yescharacteristic
747C22×C4C2×D4×C8311yescharacteristic
748C22×C4C2×D4×C8311yescharacteristic
749C22×C4C2×D4×C8311yescharacteristic
750C22×C4C24×C8311yescharacteristic
751Q16—81no—
752SD16—81no—
753SD16—81no—
754SD16—81no—
755M16—81no—
756C2×C8—21no—
757C2×C8—21no—
758C2×C8—21no—
759C2×C8—21no—
760C2×C8—81no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—21no—
768C4⋊C4—21no—
769C4⋊C4—21no—
770C4⋊C4—21no—
771C4⋊C4—21no—
772C4⋊C4—21no—
773C4⋊C4—21no—
774C4⋊C4—21no—
775C4⋊C4—21no—
776C4⋊C4—41no—
777C4⋊C4—41no—
778C4⋊C4—81no—
779C4⋊C4—81no—
780C4⋊C4—81no—
781C4⋊C4C2×D4×C8311yescharacteristic
782C4⋊C4C2×D4×C8311yescharacteristic
783C4⋊C4C2×D4×C8311yescharacteristic
784C4⋊C4C2×D4×C8311yescharacteristic
785C22⋊C4—21no—
786C22⋊C4—21no—
787C22⋊C4—21no—
788C22⋊C4—21no—
789C22⋊C4—21no—
790C22⋊C4—21no—
791C22⋊C4—21no—
792C22⋊C4—21no—
793C22⋊C4—21no—
794C22⋊C4—21no—
795C22⋊C4—21no—
796C22⋊C4—21no—
797C22⋊C4—21no—
798C22⋊C4—21no—
799C22⋊C4—21no—
800C22⋊C4—21no—
801C22⋊C4—21no—
802C22⋊C4—21no—
803C22⋊C4—21no—
804C22⋊C4—21no—
805C22⋊C4—21no—
806C22⋊C4—21no—
807C22⋊C4—21no—
808C22⋊C4—21no—
809C22⋊C4—21no—
810C22⋊C4—41no—
811C22⋊C4—41no—
812C22⋊C4—81no—
813C22⋊C4—81no—
814C22⋊C4—81no—
815C42—21no—
816C42—21no—
817C42—21no—
818C23—21no—
819C23—21no—
820C23—21no—
821C23—21no—
822C23—21no—
823C23—21no—
824C23—21no—
825C23—21no—
826C23—41no—
827C23—41no—
828C23—42no—
829C23—41no—
830C23—41no—
831C23—81no—
832C23—81no—
833C23—81no—
834C23—81no—
835C23—81no—
836C23#120×C8311yescharacteristic
837C23#120×C8311yescharacteristic
838C23C22×D4×C8311yescharacteristic
839Q8—41no—
840Q8—41no—
841Q8—41no—
842Q8—41no—
843Q8—41no—
844Q8—81no—
845D4—41no—
846D4—41no—
847D4—41no—
848D4—42no—
849D4—42no—
850D4—41no—
851D4—41no—
852D4—41no—
853D4—41no—
854D4—41no—
855D4—41no—
856D4—81no—
857D4—81no—
858D4—81no—
859D4—81no—
860D4—81no—
861D4—81no—
862D4—81no—
863D4—81no—
864D4—81no—
865D4—81no—
866D4—81no—
867D4—81no—
868C2×C4—21no—
869C2×C4—21no—
870C2×C4—21no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
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—81no—
899C2×C4—81no—
900C2×C4—81no—
901C2×C4—81no—
902C2×C4—81no—
903C2×C4—81no—
904C2×C4—81no—
905C2×C4#120×C8311yescharacteristic
906C2×C4#120×C8311yescharacteristic
907C2×C4C22×D4×C8311yescharacteristic
908C2×C4C22×D4×C8311yescharacteristic
909C8—41no—
910C8—41no—
911C8—41no—
912C8—41no—
913C22—21no—
914C22—21no—
915C22—21no—
916C22—21no—
917C22—21no—
918C22—21no—
919C22—21no—
920C22—21no—
921C22—41no—
922C22—41no—
923C22—41no—
924C22—41no—
925C22—41no—
926C22—41no—
927C22—41no—
928C22—41no—
929C22—41no—
930C22—41no—
931C22—41no—
932C22—41no—
933C22—81no—
934C22—81no—
935C22—81no—
936C22—81no—
937C22—162no—
938C22—162no—
939C22C2×#120×C8311yescharacteristic
940C22#576×C8311yescharacteristic
941C22#577×C8311yescharacteristic
942C4—21no—
943C4—21no—
944C4—21no—
945C4—21no—
946C4—41no—
947C4—41no—
948C4—41no—
949C4—41no—
950C4—41no—
951C4—41no—
952C4—41no—
953C4—41no—
954C4—81no—
955C4—81no—
956C4—81no—
957C4—81no—
958C2—21no—
959C2—21no—
960C2—41no—
961C2—41no—
962C2—81no—
963C2—81no—
964C2—81no—
965C2—81no—
966C2C83×#301211yescharacteristic
967C2C83×#302211yescharacteristic
968C2C83×#302611yescharacteristic
subgroupG/H
center, socleC22×C83C2×#120
commutator, Frattini, cosocleC22×C4C24×C83
prime radicalC83×#3534C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C83 ◁ C23×C4×C83 ◁ G

Complements

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

NH ≅ G/Ntype
2. C83×#3193C2semidirect
3. C83×#3190C2semidirect
4. C83×#2814C2semidirect
5. C83×#1612C2semidirect
6. C83×#1610C2semidirect
7. C83×#1609C2semidirect
8. C83×#1607C2semidirect
9. C83×#1606C2semidirect
10. C83×#1604C2semidirect
11. C83×#1603C2semidirect
12. C83×#1601C2semidirect
13. C83×#1519C2semidirect
14. C83×#1513C2semidirect
15. C83×#1468C2semidirect
34. C2×C22⋊Q8×C83C22semidirect
38. #483×C83C22semidirect
40. #480×C83C22semidirect
41. #480×C83C22semidirect
47. #451×C83C22semidirect
50. #448×C83C22semidirect
51. #448×C83C22semidirect
52. #407×C83C22semidirect
53. C2×C22⋊C8×C83C22semidirect
55. #398×C83C22semidirect
57. #397×C83C22semidirect
59. #395×C83C22semidirect
61. #393×C83C22semidirect
62. #380×C83C22semidirect
63. #328×C83C22semidirect
64. #328×C83C22semidirect
67. #327×C83C22semidirect
68. #327×C83C22semidirect
69. #327×C83C22semidirect
70. #327×C83C22semidirect
71. #324×C83C22semidirect
72. #324×C83C22semidirect
73. #323×C83C22semidirect
74. #323×C83C22semidirect
473. #18447C83direct (N × H)
486. #3193C2×C83semidirect
487. #3190C2×C83semidirect
488. #2814C2×C83semidirect
489. #1612C2×C83semidirect
490. #1610C2×C83semidirect
491. #1609C2×C83semidirect
492. #1607C2×C83semidirect
493. #1606C2×C83semidirect
494. #1604C2×C83semidirect
495. #1603C2×C83semidirect
496. #1601C2×C83semidirect
497. #1519C2×C83semidirect
498. #1513C2×C83semidirect
499. #1468C2×C83semidirect
500. C83#18447direct (N × H)
519. C2×C22⋊Q8C22×C83semidirect
523. #483C22×C83semidirect
525. #480C22×C83semidirect
526. #480C22×C83semidirect
532. #451C22×C83semidirect
535. #448C22×C83semidirect
536. #448C22×C83semidirect
537. #407C22×C83semidirect
538. C2×C22⋊C8C22×C83semidirect
540. #398C22×C83semidirect
542. #397C22×C83semidirect
544. #395C22×C83semidirect
546. #393C22×C83semidirect
547. #380C22×C83semidirect
548. #328C22×C83semidirect
549. #328C22×C83semidirect
552. #327C22×C83semidirect
553. #327C22×C83semidirect
554. #327C22×C83semidirect
555. #327C22×C83semidirect
556. #324C22×C83semidirect
557. #324C22×C83semidirect
558. #323C22×C83semidirect
559. #323C22×C83semidirect

Maximal subgroups

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

subgroupindex
C83×#35342
C83×#31932
C83×#31902
C83×#28142
C83×#16122
C83×#16102
C83×#16092
C83×#16072
C83×#16062
C83×#16042
C83×#16032
C83×#16012
C83×#15192
C83×#15132
C83×#14682
#1844783