Finite Group Databasebeta

← C83×#18434 #35246258

Subgroups — C83×#18434 #35246258

Order 21248.

982 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C83×#3560C211yesmaximal, characteristic, complemented
2C83×#3213C211yesmaximal, characteristic, complemented
3C83×#3211C211yesmaximal, characteristic, complemented
4C83×#2662C211yesmaximal, characteristic, complemented
5C83×#1606C211yesmaximal, characteristic, complemented
6C83×#1604C211yesmaximal, characteristic, complemented
7C83×#1603C211yesmaximal, characteristic, complemented
8C83×#1601C211yesmaximal, characteristic, complemented
9C83×#1600C211yesmaximal, characteristic, complemented
10C83×#1598C211yesmaximal, characteristic, complemented
11C83×#1597C211yesmaximal, characteristic, complemented
12C83×#1595C211yesmaximal, characteristic, complemented
13C83×#1509C211yesmaximal, characteristic, complemented
14C83×#1502C211yesmaximal, characteristic, complemented
15C83×#1473C211yesmaximal, characteristic, complemented
16#563×C83—21no—
17#560×C83—21no—
18#553×C83—21no—
19#553×C83—21no—
20#551×C83—21no—
21#547×C83—21no—
22#546×C83—21no—
23#546×C83—21no—
24#542×C83—21no—
25#539×C83—21no—
26#539×C83C2211yescharacteristic
27#538×C83—21no—
28#538×C83—21no—
29#538×C83C2211yescharacteristic
30#537×C83C2211yescharacteristic
31#534×C83C2211yescharacteristic
32#532×C83C2211yescharacteristic
33#529×C83C2211yescharacteristic
34C2×#126×C83C2211yescharacteristic
35C2×#124×C83C2211yescharacteristic, complemented
36#496×C83—21no—
37#495×C83—21no—
38#489×C83—21no—
39#488×C83—21no—
40#464×C83—21no—
41#463×C83—21no—
42#463×C83—21no—
43#463×C83—21no—
44#451×C83C2211yescharacteristic, complemented
45#450×C83C2211yescharacteristic, complemented
46#448×C83C2211yescharacteristic
47#448×C83C2211yescharacteristic
48#448×C83C2211yescharacteristic, complemented
49#447×C83C2211yescharacteristic
50#447×C83C2211yescharacteristic
51#447×C83C2211yescharacteristic, complemented
52#432×C83C2211yescharacteristic, complemented
53#431×C83C2211yescharacteristic, complemented
54#396×C83—21no—
55#395×C83C2211yescharacteristic, complemented
56#394×C83—21no—
57#394×C83C2211yescharacteristic, complemented
58#393×C83C2211yescharacteristic
59#392×C83C2211yescharacteristic
60#390×C83—21no—
61#388×C83—21no—
62C4×C4⋊C4×C83C2211yescharacteristic, complemented
63#328×C83C2211yescharacteristic, complemented
64#328×C83C2211yescharacteristic, complemented
65#327×C83C2211yescharacteristic
66#327×C83C2211yescharacteristic
67#327×C83C2211yescharacteristic
68#327×C83C2211yescharacteristic
69#327×C83C2211yescharacteristic, complemented
70#327×C83C2211yescharacteristic, complemented
71#324×C83C2211yescharacteristic, complemented
72#324×C83C2211yescharacteristic, complemented
73#323×C83C2211yescharacteristic
74#323×C83C2211yescharacteristic
75C2×#41×C83—21no—
76C2×#41×C83—21no—
77C22×Q8×C83C2311yescharacteristic
78C22×D4×C83—21no—
79C22×D4×C83—21no—
80C22×D4×C83C2311yescharacteristic
81C2×Q16×C83—21no—
82C2×SD16×C83—21no—
83C2×SD16×C83—21no—
84C2×SD16×C83—21no—
85C2×SD16×C83—21no—
86C2×D8×C83—21no—
87C2×D8×C83—21no—
88C2×D8×C83—21no—
89C4⋊Q8×C83—21no—
90C4⋊Q8×C83D411yescharacteristic, complemented
91#127×C83D411yescharacteristic, complemented
92#126×C83—21no—
93#126×C83—21no—
94#126×C83—21no—
95#126×C83—21no—
96#126×C83—21no—
97#126×C83—21no—
98#126×C83—21no—
99#126×C83—21no—
100#126×C83—21no—
101#125×C83—21no—
102#125×C83—21no—
103#125×C83D411yescharacteristic, complemented
104#124×C83—21no—
105#124×C83—21no—
106#124×C83—21no—
107#124×C83—21no—
108#124×C83—21no—
109#124×C83—21no—
110#124×C83—21no—
111#124×C83—21no—
112#124×C83D411yescharacteristic, complemented
113#123×C83—21no—
114#123×C83—21no—
115#123×C83—21no—
116#123×C83—21no—
117#123×C83—21no—
118#123×C83—21no—
119#123×C83—21no—
120#123×C83—21no—
121#123×C83—21no—
122#123×C83—21no—
123#123×C83—21no—
124#123×C83—21no—
125C22⋊Q8×C83—21no—
126C22⋊Q8×C83—21no—
127C22⋊Q8×C83—21no—
128C22⋊Q8×C83—21no—
129C22⋊Q8×C83—21no—
130C22⋊Q8×C83—21no—
131C22⋊Q8×C83—21no—
132C22⋊Q8×C83C2311yescharacteristic
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×C83—21no—
141#121×C83—21no—
142#121×C83—21no—
143#121×C83—21no—
144#121×C83—21no—
145#121×C83C2311yescharacteristic
146#121×C83C2311yescharacteristic
147#121×C83C2311yescharacteristic
148#120×C83—21no—
149#120×C83—21no—
150#120×C83—21no—
151#120×C83—21no—
152#120×C83—21no—
153C4×Q8×C83D411yescharacteristic, complemented
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—
162C4×D4×C83D411yescharacteristic, complemented
163C4×D4×C83D411yescharacteristic, complemented
164C4×D4×C83D411yescharacteristic, complemented
165#117×C83—21no—
166#117×C83—21no—
167C2×C4⋊C4×C83—21no—
168C2×C4⋊C4×C83—21no—
169C2×C4⋊C4×C83—21no—
170C2×C4⋊C4×C83D411yescharacteristic
171C2×C4⋊C4×C83D411yescharacteristic
172C2×C4⋊C4×C83C2311yescharacteristic
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×C83—21no—
180C2×C22⋊C4×C83—21no—
181C2×C22⋊C4×C83D411yescharacteristic
182C2×C22⋊C4×C83D411yescharacteristic
183C2×C22⋊C4×C83C2311yescharacteristic
184C2×C42×C83—21no—
185C2×C42×C83C2311yescharacteristic
186C4⋊C8×C83—21no—
187C4⋊C8×C83—21no—
188#103×C83—21no—
189#103×C83—21no—
190#103×C83—21no—
191#103×C83—21no—
192#102×C83—21no—
193#102×C83—21no—
194#102×C83—21no—
195#102×C83—21no—
196C22⋊C8×C83C2311yescharacteristic
197C22⋊C8×C83C2311yescharacteristic
198C22⋊C8×C83C2311yescharacteristic
199C22⋊C8×C83C2311yescharacteristic
200#97×C83—21no—
201C4×C8×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
209#41×C83—81no—
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—21no—
217C2×Q8×C83—81no—
218C2×Q8×C83C2×D411yescharacteristic
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—42no—
234C2×D4×C83—81no—
235C2×D4×C83—81no—
236C2×D4×C83—81no—
237C2×D4×C83—81no—
238C2×D4×C83—81no—
239C2×D4×C83C2×D411yescharacteristic
240C2×D4×C83C2×D411yescharacteristic
241C2×D4×C83C2×D411yescharacteristic
242C22×C4×C83—21no—
243C22×C4×C83—21no—
244C22×C4×C83—21no—
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×C83C2×D411yescharacteristic
254C22×C4×C83C2×D411yescharacteristic
255C22×C4×C83C2×D411yescharacteristic
256C22×C4×C83C2×D411yescharacteristic
257C22×C4×C83C2×D411yescharacteristic
258C22×C4×C83C2411yescharacteristic
259Q16×C83—81no—
260SD16×C83—81no—
261SD16×C83—81no—
262SD16×C83—81no—
263SD16×C83—81no—
264D8×C83—81no—
265D8×C83—81no—
266D8×C83—81no—
267C2×C8×C83—21no—
268C2×C8×C83—21no—
269C2×C8×C83—21no—
270C2×C8×C83—21no—
271C4⋊C4×C83—21no—
272C4⋊C4×C83—21no—
273C4⋊C4×C83—21no—
274C4⋊C4×C83—21no—
275C4⋊C4×C83—21no—
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—42no—
289C4⋊C4×C83—81no—
290C4⋊C4×C83C2×D411yescharacteristic
291C4⋊C4×C83C2×D411yescharacteristic
292C4⋊C4×C83C2×D411yescharacteristic
293C4⋊C4×C83C2×D411yescharacteristic
294C22⋊C4×C83—21no—
295C22⋊C4×C83—21no—
296C22⋊C4×C83—21no—
297C22⋊C4×C83—21no—
298C22⋊C4×C83—21no—
299C22⋊C4×C83—21no—
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—42no—
320C22⋊C4×C83—41no—
321C22⋊C4×C83—41no—
322C22⋊C4×C83—41no—
323C22⋊C4×C83—41no—
324C22⋊C4×C83—81no—
325C22⋊C4×C83—81no—
326C22⋊C4×C83—81no—
327C42×C83—21no—
328C42×C83—21no—
329C42×C83—21no—
330C42×C83—81no—
331C42×C83C2×D411yescharacteristic
332C42×C83C2×D411yescharacteristic
333C42×C83C2×D411yescharacteristic
334C42×C83C2×D411yescharacteristic
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—41no—
344C23×C83—41no—
345C23×C83—41no—
346C23×C83—41no—
347C23×C83—41no—
348C23×C83—41no—
349C23×C83—41no—
350C23×C83—81no—
351C23×C83—81no—
352C23×C83—81no—
353C23×C83C22×D411yescharacteristic
354Q8×C83—41no—
355Q8×C83—41no—
356Q8×C83—41no—
357Q8×C83—41no—
358Q8×C83—41no—
359Q8×C83—81no—
360Q8×C83—81no—
361D4×C83—41no—
362D4×C83—41no—
363D4×C83—41no—
364D4×C83—41no—
365D4×C83—41no—
366D4×C83—41no—
367D4×C83—41no—
368D4×C83—41no—
369D4×C83—41no—
370D4×C83—41no—
371D4×C83—41no—
372D4×C83—41no—
373D4×C83—41no—
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—
383D4×C83—84no—
384C2×C4×C83—21no—
385C2×C4×C83—21no—
386C2×C4×C83—22no—
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—21no—
394C2×C4×C83—21no—
395C2×C4×C83—21no—
396C2×C4×C83—21no—
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—81no—
410C2×C4×C83—81no—
411C2×C4×C83—81no—
412C2×C4×C83—81no—
413C2×C4×C83—81no—
414C2×C4×C83—81no—
415C2×C4×C83—81no—
416C2×C4×C83—81no—
417C2×C4×C83#12011yescharacteristic
418C2×C4×C83#12011yescharacteristic
419C2×C4×C83#12011yescharacteristic
420C2×C4×C83#12011yescharacteristic
421C2×C4×C83C22×D411yescharacteristic
422C2×C4×C83C22×D411yescharacteristic
423C8×C83—41no—
424C8×C83—41no—
425C8×C83—41no—
426C8×C83—41no—
427C22×C83—21no—
428C22×C83—21no—
429C22×C83—41no—
430C22×C83—41no—
431C22×C83—41no—
432C22×C83—41no—
433C22×C83—41no—
434C22×C83—41no—
435C22×C83—41no—
436C22×C83—41no—
437C22×C83—41no—
438C22×C83—41no—
439C22×C83—41no—
440C22×C83—41no—
441C22×C83—81no—
442C22×C83—81no—
443C22×C83—81no—
444C22×C83—81no—
445C22×C83—81no—
446C22×C83—81no—
447C22×C83—81no—
448C22×C83—81no—
449C22×C83—81no—
450C22×C83—162no—
451C22×C83C2×#12011yescharacteristic
452C22×C83#57611yescharacteristic
453C22×C83#57711yescharacteristic
454C4×C83—21no—
455C4×C83—21no—
456C4×C83—21no—
457C4×C83—21no—
458C4×C83—21no—
459C4×C83—21no—
460C4×C83—42no—
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—
471#18434C8311yesmaximal, characteristic, direct product factor, Sylow
472C2×C83—21no—
473C2×C83—21no—
474C2×C83—81no—
475C2×C83—81no—
476C2×C83—81no—
477C2×C83—81no—
478C2×C83—161no—
479C2×C83#301211yescharacteristic
480C2×C83#301811yescharacteristic
481C2×C83#302711yescharacteristic
482#3560C2×C8311yescharacteristic, complemented
483#3213C2×C8311yescharacteristic, complemented
484#3211C2×C8311yescharacteristic, complemented
485#2662C2×C8311yescharacteristic, complemented
486#1606C2×C8311yescharacteristic, complemented
487#1604C2×C8311yescharacteristic, complemented
488#1603C2×C8311yescharacteristic, complemented
489#1601C2×C8311yescharacteristic, complemented
490#1600C2×C8311yescharacteristic, complemented
491#1598C2×C8311yescharacteristic, complemented
492#1597C2×C8311yescharacteristic, complemented
493#1595C2×C8311yescharacteristic, complemented
494#1509C2×C8311yescharacteristic, complemented
495#1502C2×C8311yescharacteristic, complemented
496#1473C2×C8311yescharacteristic, complemented
497C83#1843411yescharacteristic, direct product factor, Sylow
498#563—21no—
499#560—21no—
500#553—21no—
501#553—21no—
502#551—21no—
503#547—21no—
504#546—21no—
505#546—21no—
506#542—21no—
507#539—21no—
508#539C22×C8311yescharacteristic
509#538—21no—
510#538—21no—
511#538C22×C8311yescharacteristic
512#537C22×C8311yescharacteristic
513#534C22×C8311yescharacteristic
514#532C22×C8311yescharacteristic
515#529C22×C8311yescharacteristic
516C2×#126C22×C8311yescharacteristic
517C2×#124C22×C8311yescharacteristic, complemented
518#496—21no—
519#495—21no—
520#489—21no—
521#488—21no—
522#464—21no—
523#463—21no—
524#463—21no—
525#463—21no—
526#451C22×C8311yescharacteristic, complemented
527#450C22×C8311yescharacteristic, complemented
528#448C22×C8311yescharacteristic
529#448C22×C8311yescharacteristic
530#448C22×C8311yescharacteristic, complemented
531#447C22×C8311yescharacteristic
532#447C22×C8311yescharacteristic
533#447C22×C8311yescharacteristic, complemented
534#432C22×C8311yescharacteristic, complemented
535#431C22×C8311yescharacteristic, complemented
536#396—21no—
537#395C22×C8311yescharacteristic, complemented
538#394—21no—
539#394C22×C8311yescharacteristic, complemented
540#393C22×C8311yescharacteristic
541#392C22×C8311yescharacteristic
542#390—21no—
543#388—21no—
544C4×C4⋊C4C22×C8311yescharacteristic, complemented
545#328C22×C8311yescharacteristic, complemented
546#328C22×C8311yescharacteristic, complemented
547#327C22×C8311yescharacteristic
548#327C22×C8311yescharacteristic
549#327C22×C8311yescharacteristic
550#327C22×C8311yescharacteristic
551#327C22×C8311yescharacteristic, complemented
552#327C22×C8311yescharacteristic, complemented
553#324C22×C8311yescharacteristic, complemented
554#324C22×C8311yescharacteristic, complemented
555#323C22×C8311yescharacteristic
556#323C22×C8311yescharacteristic
557C2×#41—21no—
558C2×#41—21no—
559C22×Q8C23×C8311yescharacteristic
560C22×D4—21no—
561C22×D4—21no—
562C22×D4C23×C8311yescharacteristic
563C2×Q16—21no—
564C2×SD16—21no—
565C2×SD16—21no—
566C2×SD16—21no—
567C2×SD16—21no—
568C2×D8—21no—
569C2×D8—21no—
570C2×D8—21no—
571C4⋊Q8—21no—
572C4⋊Q8D4×C8311yescharacteristic, complemented
573#127D4×C8311yescharacteristic, complemented
574#126—21no—
575#126—21no—
576#126—21no—
577#126—21no—
578#126—21no—
579#126—21no—
580#126—21no—
581#126—21no—
582#126—21no—
583#125—21no—
584#125—21no—
585#125D4×C8311yescharacteristic, complemented
586#124—21no—
587#124—21no—
588#124—21no—
589#124—21no—
590#124—21no—
591#124—21no—
592#124—21no—
593#124—21no—
594#124D4×C8311yescharacteristic, complemented
595#123—21no—
596#123—21no—
597#123—21no—
598#123—21no—
599#123—21no—
600#123—21no—
601#123—21no—
602#123—21no—
603#123—21no—
604#123—21no—
605#123—21no—
606#123—21no—
607C22⋊Q8—21no—
608C22⋊Q8—21no—
609C22⋊Q8—21no—
610C22⋊Q8—21no—
611C22⋊Q8—21no—
612C22⋊Q8—21no—
613C22⋊Q8—21no—
614C22⋊Q8C23×C8311yescharacteristic
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#121—21no—
626#121—21no—
627#121C23×C8311yescharacteristic
628#121C23×C8311yescharacteristic
629#121C23×C8311yescharacteristic
630#120—21no—
631#120—21no—
632#120—21no—
633#120—21no—
634#120—21no—
635C4×Q8D4×C8311yescharacteristic, complemented
636C4×D4—21no—
637C4×D4—21no—
638C4×D4—21no—
639C4×D4—21no—
640C4×D4—21no—
641C4×D4—21no—
642C4×D4—21no—
643C4×D4—21no—
644C4×D4D4×C8311yescharacteristic, complemented
645C4×D4D4×C8311yescharacteristic, complemented
646C4×D4D4×C8311yescharacteristic, complemented
647#117—21no—
648#117—21no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4D4×C8311yescharacteristic
653C2×C4⋊C4D4×C8311yescharacteristic
654C2×C4⋊C4C23×C8311yescharacteristic
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
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⋊C4D4×C8311yescharacteristic
664C2×C22⋊C4D4×C8311yescharacteristic
665C2×C22⋊C4C23×C8311yescharacteristic
666C2×C42—21no—
667C2×C42C23×C8311yescharacteristic
668C4⋊C8—21no—
669C4⋊C8—21no—
670#103—21no—
671#103—21no—
672#103—21no—
673#103—21no—
674#102—21no—
675#102—21no—
676#102—21no—
677#102—21no—
678C22⋊C8C23×C8311yescharacteristic
679C22⋊C8C23×C8311yescharacteristic
680C22⋊C8C23×C8311yescharacteristic
681C22⋊C8C23×C8311yescharacteristic
682#97—21no—
683C4×C8—21no—
684#95—21no—
685#95—21no—
686#95C23×C8311yescharacteristic
687#95C23×C8311yescharacteristic
688C24—21no—
689C24—21no—
690C24C2×D4×C8311yescharacteristic
691#41—81no—
692#41—81no—
693#41—81no—
694#41—81no—
695C2×Q8—21no—
696C2×Q8—21no—
697C2×Q8—21no—
698C2×Q8—21no—
699C2×Q8—81no—
700C2×Q8C2×D4×C8311yescharacteristic
701C2×D4—21no—
702C2×D4—21no—
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—42no—
716C2×D4—81no—
717C2×D4—81no—
718C2×D4—81no—
719C2×D4—81no—
720C2×D4—81no—
721C2×D4C2×D4×C8311yescharacteristic
722C2×D4C2×D4×C8311yescharacteristic
723C2×D4C2×D4×C8311yescharacteristic
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4C2×D4×C8311yescharacteristic
736C22×C4C2×D4×C8311yescharacteristic
737C22×C4C2×D4×C8311yescharacteristic
738C22×C4C2×D4×C8311yescharacteristic
739C22×C4C2×D4×C8311yescharacteristic
740C22×C4C24×C8311yescharacteristic
741Q16—81no—
742SD16—81no—
743SD16—81no—
744SD16—81no—
745SD16—81no—
746D8—81no—
747D8—81no—
748D8—81no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8—21no—
752C2×C8—21no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—21no—
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—42no—
771C4⋊C4—81no—
772C4⋊C4C2×D4×C8311yescharacteristic
773C4⋊C4C2×D4×C8311yescharacteristic
774C4⋊C4C2×D4×C8311yescharacteristic
775C4⋊C4C2×D4×C8311yescharacteristic
776C22⋊C4—21no—
777C22⋊C4—21no—
778C22⋊C4—21no—
779C22⋊C4—21no—
780C22⋊C4—21no—
781C22⋊C4—21no—
782C22⋊C4—21no—
783C22⋊C4—21no—
784C22⋊C4—21no—
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—42no—
802C22⋊C4—41no—
803C22⋊C4—41no—
804C22⋊C4—41no—
805C22⋊C4—41no—
806C22⋊C4—81no—
807C22⋊C4—81no—
808C22⋊C4—81no—
809C42—21no—
810C42—21no—
811C42—21no—
812C42—81no—
813C42C2×D4×C8311yescharacteristic
814C42C2×D4×C8311yescharacteristic
815C42C2×D4×C8311yescharacteristic
816C42C2×D4×C8311yescharacteristic
817C23—21no—
818C23—21no—
819C23—21no—
820C23—21no—
821C23—21no—
822C23—21no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—81no—
833C23—81no—
834C23—81no—
835C23C22×D4×C8311yescharacteristic
836Q8—41no—
837Q8—41no—
838Q8—41no—
839Q8—41no—
840Q8—41no—
841Q8—81no—
842Q8—81no—
843D4—41no—
844D4—41no—
845D4—41no—
846D4—41no—
847D4—41no—
848D4—41no—
849D4—41no—
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—84no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—22no—
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—21no—
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—81no—
892C2×C4—81no—
893C2×C4—81no—
894C2×C4—81no—
895C2×C4—81no—
896C2×C4—81no—
897C2×C4—81no—
898C2×C4—81no—
899C2×C4#120×C8311yescharacteristic
900C2×C4#120×C8311yescharacteristic
901C2×C4#120×C8311yescharacteristic
902C2×C4#120×C8311yescharacteristic
903C2×C4C22×D4×C8311yescharacteristic
904C2×C4C22×D4×C8311yescharacteristic
905C8—41no—
906C8—41no—
907C8—41no—
908C8—41no—
909C22—21no—
910C22—21no—
911C22—41no—
912C22—41no—
913C22—41no—
914C22—41no—
915C22—41no—
916C22—41no—
917C22—41no—
918C22—41no—
919C22—41no—
920C22—41no—
921C22—41no—
922C22—41no—
923C22—81no—
924C22—81no—
925C22—81no—
926C22—81no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22—81no—
931C22—81no—
932C22—162no—
933C22C2×#120×C8311yescharacteristic
934C22#576×C8311yescharacteristic
935C22#577×C8311yescharacteristic
936C4—21no—
937C4—21no—
938C4—21no—
939C4—21no—
940C4—21no—
941C4—21no—
942C4—42no—
943C4—41no—
944C4—41no—
945C4—41no—
946C4—41no—
947C4—41no—
948C4—41no—
949C4—41no—
950C4—41no—
951C4—81no—
952C4—81no—
953C2—21no—
954C2—21no—
955C2—81no—
956C2—81no—
957C2—81no—
958C2—81no—
959C2—161no—
960C2C83×#301211yescharacteristic
961C2C83×#301811yescharacteristic
962C2C83×#302711yescharacteristic
subgroupG/H
center, socleC22×C83C2×#120
commutator, Frattini, cosocleC22×C4C24×C83
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C83 ◁ C2×C42×C83 ◁ G

Complements

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

NH ≅ G/Ntype
1. C83×#3560C2semidirect
2. C83×#3213C2semidirect
3. C83×#3211C2semidirect
4. C83×#2662C2semidirect
5. C83×#1606C2semidirect
6. C83×#1604C2semidirect
7. C83×#1603C2semidirect
8. C83×#1601C2semidirect
9. C83×#1600C2semidirect
10. C83×#1598C2semidirect
11. C83×#1597C2semidirect
12. C83×#1595C2semidirect
13. C83×#1509C2semidirect
14. C83×#1502C2semidirect
15. C83×#1473C2semidirect
35. C2×#124×C83C22semidirect
44. #451×C83C22semidirect
45. #450×C83C22semidirect
48. #448×C83C22semidirect
51. #447×C83C22semidirect
52. #432×C83C22semidirect
53. #431×C83C22semidirect
55. #395×C83C22semidirect
57. #394×C83C22semidirect
62. C4×C4⋊C4×C83C22semidirect
63. #328×C83C22semidirect
64. #328×C83C22semidirect
69. #327×C83C22semidirect
70. #327×C83C22semidirect
71. #324×C83C22semidirect
72. #324×C83C22semidirect
90. C4⋊Q8×C83D4semidirect
91. #127×C83D4semidirect
103. #125×C83D4semidirect
112. #124×C83D4semidirect
153. C4×Q8×C83D4semidirect
162. C4×D4×C83D4semidirect
163. C4×D4×C83D4semidirect
164. C4×D4×C83D4semidirect
471. #18434C83direct (N × H)
482. #3560C2×C83semidirect
483. #3213C2×C83semidirect
484. #3211C2×C83semidirect
485. #2662C2×C83semidirect
486. #1606C2×C83semidirect
487. #1604C2×C83semidirect
488. #1603C2×C83semidirect
489. #1601C2×C83semidirect
490. #1600C2×C83semidirect
491. #1598C2×C83semidirect
492. #1597C2×C83semidirect
493. #1595C2×C83semidirect
494. #1509C2×C83semidirect
495. #1502C2×C83semidirect
496. #1473C2×C83semidirect
497. C83#18434direct (N × H)
517. C2×#124C22×C83semidirect
526. #451C22×C83semidirect
527. #450C22×C83semidirect
530. #448C22×C83semidirect
533. #447C22×C83semidirect
534. #432C22×C83semidirect
535. #431C22×C83semidirect
537. #395C22×C83semidirect
539. #394C22×C83semidirect
544. C4×C4⋊C4C22×C83semidirect
545. #328C22×C83semidirect
546. #328C22×C83semidirect
551. #327C22×C83semidirect
552. #327C22×C83semidirect
553. #324C22×C83semidirect
554. #324C22×C83semidirect
572. C4⋊Q8D4×C83semidirect
573. #127D4×C83semidirect
585. #125D4×C83semidirect
594. #124D4×C83semidirect
635. C4×Q8D4×C83semidirect
644. C4×D4D4×C83semidirect
645. C4×D4D4×C83semidirect
646. C4×D4D4×C83semidirect

Maximal subgroups

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

subgroupindex
C83×#35602
C83×#32132
C83×#32112
C83×#26622
C83×#16062
C83×#16042
C83×#16032
C83×#16012
C83×#16002
C83×#15982
C83×#15972
C83×#15952
C83×#15092
C83×#15022
C83×#14732
#1843483