Finite Group Databasebeta

← C83×#22056 #35249880

Subgroups — C83×#22056 #35249880

Order 21248.

1136 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#447×C83C211yesmaximal, characteristic
2C83×#2324C211yesmaximal, characteristic, complemented
3C83×#2309C211yesmaximal, characteristic, complemented
4C83×#1972C211yesmaximal, characteristic, complemented
5C83×#1970C211yesmaximal, characteristic, complemented
6C83×#1936C211yesmaximal, characteristic, complemented
7C83×#1934C211yesmaximal, characteristic, complemented
8C83×#1926C211yesmaximal, characteristic, complemented
9C83×#1925C211yesmaximal, characteristic, complemented
10C83×#1879C211yesmaximal, characteristic, complemented
11C83×#1879C211yesmaximal, characteristic, complemented
12C83×#1875C211yesmaximal, characteristic, complemented
13C83×#1854C211yesmaximal, characteristic, complemented
14C83×#1786C211yesmaximal, characteristic, complemented
15C83×#1750C211yesmaximal, characteristic, complemented
16C23×D4×C83C2211yescharacteristic
17C22×D8×C83C2211yescharacteristic
18C22×D8×C83C2211yescharacteristic
19C2×#121×C83C2211yescharacteristic
20C2×C4×D4×C83C2211yescharacteristic, complemented
21C2×#117×C83C2211yescharacteristic
22C2×#117×C83C2211yescharacteristic
23#447×C83C418yescomplemented
24C2×#107×C83C2211yescharacteristic, complemented
25C2×#106×C83C2211yescharacteristic, complemented
26C2×#102×C83C2211yescharacteristic
27C2×#102×C83C2211yescharacteristic
28C2×#102×C83C2211yescharacteristic
29C2×#102×C83C2211yescharacteristic
30C2×#102×C83C2211yescharacteristic
31C2×#102×C83C2211yescharacteristic
32C2×#102×C83C2211yescharacteristic, complemented
33C2×#102×C83C2211yescharacteristic, complemented
34C2×C22⋊C8×C83C2211yescharacteristic
35C2×C22⋊C8×C83C2211yescharacteristic
36C2×#97×C83C2211yescharacteristic, complemented
37C2×C4×C8×C83C2211yescharacteristic, complemented
38#390×C83—21no—
39#390×C83—21no—
40#390×C83—21no—
41#390×C83C2211yescharacteristic
42#390×C83C2211yescharacteristic
43#390×C83C2211yescharacteristic
44#390×C83C2211yescharacteristic
45#390×C83C2211yescharacteristic, complemented
46#389×C83C2211yescharacteristic, complemented
47#388×C83—21no—
48#386×C83—21no—
49#385×C83—21no—
50#380×C83C2211yescharacteristic
51#379×C83—21no—
52#379×C83—21no—
53C4×C4⋊C4×C83C2211yescharacteristic, complemented
54#340×C83C2211yescharacteristic, complemented
55#340×C83C2211yescharacteristic, complemented
56#340×C83C2211yescharacteristic, complemented
57#340×C83C2211yescharacteristic, complemented
58#336×C83C2211yescharacteristic, complemented
59#336×C83C2211yescharacteristic, complemented
60C25×C83—21no—
61C22×D4×C83—21no—
62C22×D4×C83—21no—
63C22×D4×C83—22no—
64C22×D4×C83—41no—
65C22×D4×C83—41no—
66C22×D4×C83—41no—
67C22×D4×C83—41no—
68C22×D4×C83C2×C414yescomplemented
69C22×D4×C83C2311yescharacteristic
70C22×D4×C83C2311yescharacteristic
71C22×D4×C83C2311yescharacteristic
72C23×C4×C83—21no—
73C23×C4×C83C2311yescharacteristic
74C2×D8×C83—41no—
75C2×D8×C83—41no—
76C2×D8×C83—41no—
77C2×D8×C83—41no—
78C2×D8×C83C2×C414yes—
79C2×D8×C83C2×C414yes—
80C22×C8×C83C2311yescharacteristic
81C22×C8×C83C2311yescharacteristic
82C22×C8×C83C2311yescharacteristic
83C22×C8×C83C2311yescharacteristic
84#121×C83—22no—
85#121×C83C2×C414yes—
86C4×D4×C83—41no—
87C4×D4×C83—41no—
88#117×C83—41no—
89#117×C83—41no—
90#117×C83—41no—
91#117×C83—41no—
92C2×C4⋊C4×C83—21no—
93C2×C4⋊C4×C83D411yescharacteristic
94C2×C4⋊C4×C83D411yescharacteristic
95C2×C4⋊C4×C83C2311yescharacteristic
96C2×C4⋊C4×C83C2311yescharacteristic
97C2×C4⋊C4×C83C2311yescharacteristic
98C2×C4⋊C4×C83C2311yescharacteristic
99C2×C4⋊C4×C83C2311yescharacteristic
100C2×C22⋊C4×C83—21no—
101C2×C22⋊C4×C83—21no—
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×C83—21no—
108C2×C22⋊C4×C83—21no—
109C2×C22⋊C4×C83—21no—
110C2×C22⋊C4×C83—21no—
111C2×C22⋊C4×C83—21no—
112C2×C22⋊C4×C83—21no—
113C2×C22⋊C4×C83—21no—
114C2×C22⋊C4×C83D411yescharacteristic
115C2×C22⋊C4×C83D411yescharacteristic
116C2×C42×C83—21no—
117C2×C42×C83—21no—
118C2×C42×C83C2311yescharacteristic
119C2×C42×C83C2311yescharacteristic
120#107×C83—41no—
121#106×C83—41no—
122#102×C83—41no—
123#102×C83—41no—
124#102×C83—41no—
125#102×C83—41no—
126#102×C83—41no—
127#102×C83—41no—
128#102×C83C2×C414yescomplemented
129#102×C83C2×C414yescomplemented
130C22⋊C8×C83—22no—
131C22⋊C8×C83C2×C414yescomplemented
132#97×C83—41no—
133C4×C8×C83—41no—
134#95×C83—21no—
135#95×C83—21no—
136#95×C83—21no—
137C24×C83—21no—
138C24×C83—21no—
139C24×C83—21no—
140C24×C83—24no—
141C24×C83—42no—
142C24×C83—42no—
143C24×C83—81no—
144C24×C83—81no—
145C24×C83—81no—
146C24×C83—81no—
147C24×C83C2×D411yescharacteristic
148C2×D4×C83—24no—
149C2×D4×C83—24no—
150C2×D4×C83—21no—
151C2×D4×C83—21no—
152C2×D4×C83—21no—
153C2×D4×C83—21no—
154C2×D4×C83—21no—
155C2×D4×C83—21no—
156C2×D4×C83—21no—
157C2×D4×C83—21no—
158C2×D4×C83—21no—
159C2×D4×C83—21no—
160C2×D4×C83—21no—
161C2×D4×C83—21no—
162C2×D4×C83—21no—
163C2×D4×C83—21no—
164C2×D4×C83—21no—
165C2×D4×C83—44no—
166C2×D4×C83—44no—
167C2×D4×C83—42no—
168C2×D4×C83—42no—
169C2×D4×C83—44no—
170C2×D4×C83—44no—
171C2×D4×C83—81no—
172C2×D4×C83—81no—
173C2×D4×C83C22×C412yes—
174C2×D4×C83C22×C412yes—
175C2×D4×C83C22×C412yes—
176C22×C4×C83—21no—
177C22×C4×C83—21no—
178C22×C4×C83—21no—
179C22×C4×C83—21no—
180C22×C4×C83—21no—
181C22×C4×C83—21no—
182C22×C4×C83—21no—
183C22×C4×C83—21no—
184C22×C4×C83—21no—
185C22×C4×C83—42no—
186C22×C4×C83—81no—
187C22×C4×C83—81no—
188C22×C4×C83C22×C412yes—
189C22×C4×C83C2×D411yescharacteristic
190C22×C4×C83C2×D411yescharacteristic
191C22×C4×C83C2×D411yescharacteristic
192C22×C4×C83C2×D411yescharacteristic
193C22×C4×C83C2×D411yescharacteristic
194C22×C4×C83#4112yes—
195C22×C4×C83C2411yescharacteristic
196D8×C83—44no—
197D8×C83—44no—
198C2×C8×C83—21no—
199C2×C8×C83—21no—
200C2×C8×C83—21no—
201C2×C8×C83—21no—
202C2×C8×C83—21no—
203C2×C8×C83—21no—
204C2×C8×C83—21no—
205C2×C8×C83—21no—
206C2×C8×C83—21no—
207C2×C8×C83—21no—
208C2×C8×C83C22×C412yes—
209C2×C8×C83C22×C412yes—
210C4⋊C4×C83—21no—
211C4⋊C4×C83—21no—
212C4⋊C4×C83—21no—
213C4⋊C4×C83—21no—
214C4⋊C4×C83—21no—
215C4⋊C4×C83—21no—
216C4⋊C4×C83—21no—
217C4⋊C4×C83—21no—
218C4⋊C4×C83—21no—
219C4⋊C4×C83—41no—
220C4⋊C4×C83—41no—
221C4⋊C4×C83—81no—
222C4⋊C4×C83C22×C412yes—
223C22⋊C4×C83—24no—
224C22⋊C4×C83—41no—
225C22⋊C4×C83—41no—
226C22⋊C4×C83—42no—
227C22⋊C4×C83—42no—
228C22⋊C4×C83—81no—
229C22⋊C4×C83—81no—
230C22⋊C4×C83—81no—
231C22⋊C4×C83—81no—
232C22⋊C4×C83—81no—
233C22⋊C4×C83—81no—
234C22⋊C4×C83—81no—
235C22⋊C4×C83—81no—
236C22⋊C4×C83—81no—
237C22⋊C4×C83—81no—
238C22⋊C4×C83—81no—
239C42×C83—21no—
240C42×C83—21no—
241C42×C83—21no—
242C42×C83—21no—
243C42×C83—42no—
244C42×C83—81no—
245C23×C83—21no—
246C23×C83—21no—
247C23×C83—21no—
248C23×C83—21no—
249C23×C83—21no—
250C23×C83—21no—
251C23×C83—22no—
252C23×C83—22no—
253C23×C83—22no—
254C23×C83—48no—
255C23×C83—41no—
256C23×C83—41no—
257C23×C83—41no—
258C23×C83—41no—
259C23×C83—41no—
260C23×C83—41no—
261C23×C83—41no—
262C23×C83—41no—
263C23×C83—41no—
264C23×C83—41no—
265C23×C83—41no—
266C23×C83—41no—
267C23×C83—41no—
268C23×C83—41no—
269C23×C83—41no—
270C23×C83—41no—
271C23×C83—41no—
272C23×C83—41no—
273C23×C83—84no—
274C23×C83—84no—
275C23×C83—84no—
276C23×C83—84no—
277C23×C83—84no—
278C23×C83—84no—
279C23×C83C4×D412yes—
280C23×C83C22×D411yescharacteristic
281D4×C83—22no—
282D4×C83—22no—
283D4×C83—22no—
284D4×C83—22no—
285D4×C83—22no—
286D4×C83—22no—
287D4×C83—48no—
288D4×C83—41no—
289D4×C83—41no—
290D4×C83—41no—
291D4×C83—41no—
292D4×C83—41no—
293D4×C83—41no—
294D4×C83—84no—
295C2×C4×C83—21no—
296C2×C4×C83—21no—
297C2×C4×C83—22no—
298C2×C4×C83—22no—
299C2×C4×C83—22no—
300C2×C4×C83—22no—
301C2×C4×C83—22no—
302C2×C4×C83—21no—
303C2×C4×C83—21no—
304C2×C4×C83—21no—
305C2×C4×C83—21no—
306C2×C4×C83—21no—
307C2×C4×C83—21no—
308C2×C4×C83—21no—
309C2×C4×C83—21no—
310C2×C4×C83—21no—
311C2×C4×C83—21no—
312C2×C4×C83—21no—
313C2×C4×C83—21no—
314C2×C4×C83—41no—
315C2×C4×C83—41no—
316C2×C4×C83—41no—
317C2×C4×C83—41no—
318C2×C4×C83—41no—
319C2×C4×C83—41no—
320C2×C4×C83—41no—
321C2×C4×C83—41no—
322C2×C4×C83—41no—
323C2×C4×C83—41no—
324C2×C4×C83—41no—
325C2×C4×C83—41no—
326C2×C4×C83—41no—
327C2×C4×C83—41no—
328C2×C4×C83—84no—
329C2×C4×C83C4×D412yes—
330C2×C4×C83C23×C411yescharacteristic
331C2×C4×C83C2×#4111yescharacteristic
332C2×C4×C83H(5,𝔽2)11yescharacteristic
333C2×C4×C83H(5,𝔽2)11yescharacteristic
334C2×C4×C83H(5,𝔽2)11yescharacteristic
335C2×C4×C83H(5,𝔽2)11yescharacteristic
336C8×C83—22no—
337C8×C83—22no—
338C8×C83—41no—
339C8×C83—41no—
340C22×C83—22no—
341C22×C83—22no—
342C22×C83—22no—
343C22×C83—41no—
344C22×C83—41no—
345C22×C83—41no—
346C22×C83—41no—
347C22×C83—42no—
348C22×C83—42no—
349C22×C83—42no—
350C22×C83—42no—
351C22×C83—42no—
352C22×C83—42no—
353C22×C83—42no—
354C22×C83—42no—
355C22×C83—42no—
356C22×C83—816no—
357C22×C83—81no—
358C22×C83—81no—
359C22×C83—81no—
360C22×C83—81no—
361C22×C83—81no—
362C22×C83—81no—
363C22×C83—81no—
364C22×C83—81no—
365C22×C83—81no—
366C22×C83—81no—
367C22×C83—81no—
368C22×C83—81no—
369C22×C83C2×C4×D411yescharacteristic
370C22×C83#53411yescharacteristic
371C22×C83#53511yescharacteristic
372C22×C83#57611yescharacteristic
373C22×C83#57611yescharacteristic
374C22×C83#57611yescharacteristic
375C22×C83#57711yescharacteristic
376C4×C83—22no—
377C4×C83—41no—
378C4×C83—41no—
379C4×C83—41no—
380C4×C83—41no—
381C4×C83—42no—
382C4×C83—81no—
383C4×C83—81no—
384C4×C83—81no—
385C4×C83—81no—
386C4×C83#51811yescharacteristic
387C4×C83#51811yescharacteristic
388C4×C83#53811yescharacteristic
389C4×C83#53811yescharacteristic
390#22056C8311yesmaximal, characteristic, direct product factor, Sylow
391C2×C83—42no—
392C2×C83—82no—
393C2×C83—82no—
394C2×C83—82no—
395C2×C83#232111yescharacteristic
396C2×C83#294611yescharacteristic
397C2×C83#294811yescharacteristic
398C2×C83#319811yescharacteristic
399C2×C83#319911yescharacteristic
400C2×C83#322011yescharacteristic
401C2×C83#322411yescharacteristic
402C2×#447C2×C8311yescharacteristic
403#2324C2×C8311yescharacteristic, complemented
404#2309C2×C8311yescharacteristic, complemented
405#1972C2×C8311yescharacteristic, complemented
406#1970C2×C8311yescharacteristic, complemented
407#1936C2×C8311yescharacteristic, complemented
408#1934C2×C8311yescharacteristic, complemented
409#1926C2×C8311yescharacteristic, complemented
410#1925C2×C8311yescharacteristic, complemented
411#1879C2×C8311yescharacteristic, complemented
412#1879C2×C8311yescharacteristic, complemented
413#1875C2×C8311yescharacteristic, complemented
414#1854C2×C8311yescharacteristic, complemented
415#1786C2×C8311yescharacteristic, complemented
416#1750C2×C8311yescharacteristic, complemented
417C83#2205611yescharacteristic, direct product factor, Sylow
418C23×D4C22×C8311yescharacteristic
419C22×D8C22×C8311yescharacteristic
420C22×D8C22×C8311yescharacteristic
421C2×#121C22×C8311yescharacteristic
422C2×C4×D4C22×C8311yescharacteristic, complemented
423C2×#117C22×C8311yescharacteristic
424C2×#117C22×C8311yescharacteristic
425#447C4×C8318yescomplemented
426C2×#107C22×C8311yescharacteristic, complemented
427C2×#106C22×C8311yescharacteristic, complemented
428C2×#102C22×C8311yescharacteristic
429C2×#102C22×C8311yescharacteristic
430C2×#102C22×C8311yescharacteristic
431C2×#102C22×C8311yescharacteristic
432C2×#102C22×C8311yescharacteristic
433C2×#102C22×C8311yescharacteristic
434C2×#102C22×C8311yescharacteristic, complemented
435C2×#102C22×C8311yescharacteristic, complemented
436C2×C22⋊C8C22×C8311yescharacteristic
437C2×C22⋊C8C22×C8311yescharacteristic
438C2×#97C22×C8311yescharacteristic, complemented
439C2×C4×C8C22×C8311yescharacteristic, complemented
440#390—21no—
441#390—21no—
442#390—21no—
443#390C22×C8311yescharacteristic
444#390C22×C8311yescharacteristic
445#390C22×C8311yescharacteristic
446#390C22×C8311yescharacteristic
447#390C22×C8311yescharacteristic, complemented
448#389C22×C8311yescharacteristic, complemented
449#388—21no—
450#386—21no—
451#385—21no—
452#380C22×C8311yescharacteristic
453#379—21no—
454#379—21no—
455C4×C4⋊C4C22×C8311yescharacteristic, complemented
456#340C22×C8311yescharacteristic, complemented
457#340C22×C8311yescharacteristic, complemented
458#340C22×C8311yescharacteristic, complemented
459#340C22×C8311yescharacteristic, complemented
460#336C22×C8311yescharacteristic, complemented
461#336C22×C8311yescharacteristic, complemented
462C25—21no—
463C22×D4—21no—
464C22×D4—21no—
465C22×D4—22no—
466C22×D4—41no—
467C22×D4—41no—
468C22×D4—41no—
469C22×D4—41no—
470C22×D4C2×C4×C8314yescomplemented
471C22×D4C23×C8311yescharacteristic
472C22×D4C23×C8311yescharacteristic
473C22×D4C23×C8311yescharacteristic
474C23×C4—21no—
475C23×C4C23×C8311yescharacteristic
476C2×D8—41no—
477C2×D8—41no—
478C2×D8—41no—
479C2×D8—41no—
480C2×D8C2×C4×C8314yes—
481C2×D8C2×C4×C8314yes—
482C22×C8C23×C8311yescharacteristic
483C22×C8C23×C8311yescharacteristic
484C22×C8C23×C8311yescharacteristic
485C22×C8C23×C8311yescharacteristic
486#121—22no—
487#121C2×C4×C8314yes—
488C4×D4—41no—
489C4×D4—41no—
490#117—41no—
491#117—41no—
492#117—41no—
493#117—41no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4D4×C8311yescharacteristic
496C2×C4⋊C4D4×C8311yescharacteristic
497C2×C4⋊C4C23×C8311yescharacteristic
498C2×C4⋊C4C23×C8311yescharacteristic
499C2×C4⋊C4C23×C8311yescharacteristic
500C2×C4⋊C4C23×C8311yescharacteristic
501C2×C4⋊C4C23×C8311yescharacteristic
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—21no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4D4×C8311yescharacteristic
517C2×C22⋊C4D4×C8311yescharacteristic
518C2×C42—21no—
519C2×C42—21no—
520C2×C42C23×C8311yescharacteristic
521C2×C42C23×C8311yescharacteristic
522#107—41no—
523#106—41no—
524#102—41no—
525#102—41no—
526#102—41no—
527#102—41no—
528#102—41no—
529#102—41no—
530#102C2×C4×C8314yescomplemented
531#102C2×C4×C8314yescomplemented
532C22⋊C8—22no—
533C22⋊C8C2×C4×C8314yescomplemented
534#97—41no—
535C4×C8—41no—
536#95—21no—
537#95—21no—
538#95—21no—
539C24—21no—
540C24—21no—
541C24—21no—
542C24—24no—
543C24—42no—
544C24—42no—
545C24—81no—
546C24—81no—
547C24—81no—
548C24—81no—
549C24C2×D4×C8311yescharacteristic
550C2×D4—24no—
551C2×D4—24no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—44no—
568C2×D4—44no—
569C2×D4—42no—
570C2×D4—42no—
571C2×D4—44no—
572C2×D4—44no—
573C2×D4—81no—
574C2×D4—81no—
575C2×D4C22×C4×C8312yes—
576C2×D4C22×C4×C8312yes—
577C2×D4C22×C4×C8312yes—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—42no—
588C22×C4—81no—
589C22×C4—81no—
590C22×C4C22×C4×C8312yes—
591C22×C4C2×D4×C8311yescharacteristic
592C22×C4C2×D4×C8311yescharacteristic
593C22×C4C2×D4×C8311yescharacteristic
594C22×C4C2×D4×C8311yescharacteristic
595C22×C4C2×D4×C8311yescharacteristic
596C22×C4#41×C8312yes—
597C22×C4C24×C8311yescharacteristic
598D8—44no—
599D8—44no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8C22×C4×C8312yes—
611C2×C8C22×C4×C8312yes—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—41no—
622C4⋊C4—41no—
623C4⋊C4—81no—
624C4⋊C4C22×C4×C8312yes—
625C22⋊C4—24no—
626C22⋊C4—41no—
627C22⋊C4—41no—
628C22⋊C4—42no—
629C22⋊C4—42no—
630C22⋊C4—81no—
631C22⋊C4—81no—
632C22⋊C4—81no—
633C22⋊C4—81no—
634C22⋊C4—81no—
635C22⋊C4—81no—
636C22⋊C4—81no—
637C22⋊C4—81no—
638C22⋊C4—81no—
639C22⋊C4—81no—
640C22⋊C4—81no—
641C42—21no—
642C42—21no—
643C42—21no—
644C42—21no—
645C42—42no—
646C42—81no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—48no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—84no—
676C23—84no—
677C23—84no—
678C23—84no—
679C23—84no—
680C23—84no—
681C23C4×D4×C8312yes—
682C23C22×D4×C8311yescharacteristic
683D4—22no—
684D4—22no—
685D4—22no—
686D4—22no—
687D4—22no—
688D4—22no—
689D4—48no—
690D4—41no—
691D4—41no—
692D4—41no—
693D4—41no—
694D4—41no—
695D4—41no—
696D4—84no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—84no—
731C2×C4C4×D4×C8312yes—
732C2×C4C23×C4×C8311yescharacteristic
733C2×C4C2×#41×C8311yescharacteristic
734C2×C4H(5,𝔽2)×C8311yescharacteristic
735C2×C4H(5,𝔽2)×C8311yescharacteristic
736C2×C4H(5,𝔽2)×C8311yescharacteristic
737C2×C4H(5,𝔽2)×C8311yescharacteristic
738C8—22no—
739C8—22no—
740C8—41no—
741C8—41no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—42no—
758C22—816no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22—81no—
763C22—81no—
764C22—81no—
765C22—81no—
766C22—81no—
767C22—81no—
768C22—81no—
769C22—81no—
770C22—81no—
771C22C2×C4×D4×C8311yescharacteristic
772C22#534×C8311yescharacteristic
773C22#535×C8311yescharacteristic
774C22#576×C8311yescharacteristic
775C22#576×C8311yescharacteristic
776C22#576×C8311yescharacteristic
777C22#577×C8311yescharacteristic
778C4—22no—
779C4—41no—
780C4—41no—
781C4—41no—
782C4—41no—
783C4—42no—
784C4—81no—
785C4—81no—
786C4—81no—
787C4—81no—
788C4#518×C8311yescharacteristic
789C4#518×C8311yescharacteristic
790C4#538×C8311yescharacteristic
791C4#538×C8311yescharacteristic
792C2—42no—
793C2—82no—
794C2—82no—
795C2—82no—
796C2C83×#232111yescharacteristic
797C2C83×#294611yescharacteristic
798C2C83×#294811yescharacteristic
799C2C83×#319811yescharacteristic
800C2C83×#319911yescharacteristic
801C2C83×#322011yescharacteristic
802C2C83×#322411yescharacteristic
subgroupG/H
center, socleC23×C83C22×D4
commutatorC2×C4C23×C4×C83
Frattini, cosocleC22×C4C24×C83
prime radicalC2×#447×C83C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C83 ◁ C2×#117×C83 ◁ G

Complements

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

NH ≅ G/Ntype
2. C83×#2324C2semidirect
3. C83×#2309C2semidirect
4. C83×#1972C2semidirect
5. C83×#1970C2semidirect
6. C83×#1936C2semidirect
7. C83×#1934C2semidirect
8. C83×#1926C2semidirect
9. C83×#1925C2semidirect
10. C83×#1879C2semidirect
11. C83×#1879C2semidirect
12. C83×#1875C2semidirect
13. C83×#1854C2semidirect
14. C83×#1786C2semidirect
15. C83×#1750C2semidirect
20. C2×C4×D4×C83C22semidirect
23. #447×C83C4semidirect
24. C2×#107×C83C22semidirect
25. C2×#106×C83C22semidirect
32. C2×#102×C83C22semidirect
33. C2×#102×C83C22semidirect
36. C2×#97×C83C22semidirect
37. C2×C4×C8×C83C22semidirect
45. #390×C83C22semidirect
46. #389×C83C22semidirect
53. C4×C4⋊C4×C83C22semidirect
54. #340×C83C22semidirect
55. #340×C83C22semidirect
56. #340×C83C22semidirect
57. #340×C83C22semidirect
58. #336×C83C22semidirect
59. #336×C83C22semidirect
68. C22×D4×C83C2×C4semidirect
128. #102×C83C2×C4semidirect
129. #102×C83C2×C4semidirect
131. C22⋊C8×C83C2×C4semidirect
390. #22056C83direct (N × H)
403. #2324C2×C83semidirect
404. #2309C2×C83semidirect
405. #1972C2×C83semidirect
406. #1970C2×C83semidirect
407. #1936C2×C83semidirect
408. #1934C2×C83semidirect
409. #1926C2×C83semidirect
410. #1925C2×C83semidirect
411. #1879C2×C83semidirect
412. #1879C2×C83semidirect
413. #1875C2×C83semidirect
414. #1854C2×C83semidirect
415. #1786C2×C83semidirect
416. #1750C2×C83semidirect
417. C83#22056direct (N × H)
422. C2×C4×D4C22×C83semidirect
425. #447C4×C83semidirect
426. C2×#107C22×C83semidirect
427. C2×#106C22×C83semidirect
434. C2×#102C22×C83semidirect
435. C2×#102C22×C83semidirect
438. C2×#97C22×C83semidirect
439. C2×C4×C8C22×C83semidirect
447. #390C22×C83semidirect
448. #389C22×C83semidirect
455. C4×C4⋊C4C22×C83semidirect
456. #340C22×C83semidirect
457. #340C22×C83semidirect
458. #340C22×C83semidirect
459. #340C22×C83semidirect
460. #336C22×C83semidirect
461. #336C22×C83semidirect
470. C22×D4C2×C4×C83semidirect
530. #102C2×C4×C83semidirect
531. #102C2×C4×C83semidirect
533. C22⋊C8C2×C4×C83semidirect

Maximal subgroups

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

subgroupindex
C2×#447×C832
C83×#23242
C83×#23092
C83×#19722
C83×#19702
C83×#19362
C83×#19342
C83×#19262
C83×#19252
C83×#18792
C83×#18752
C83×#18542
C83×#17862
C83×#17502
#2205683