Finite Group Databasebeta

← #35310571

Subgroups — #35310571

Order 21248.

958 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14581723C211yesmaximal, characteristic
2C2×C4⋊C4×Dic83C211yesmaximal, characteristic
3C2×#19127464C211yesmaximal, characteristic
4C2×#19127463C211yesmaximal, characteristic
5C2×#19127455C211yesmaximal, characteristic
6#24905692C211yesmaximal, characteristic
7C2×#340×C83C211yesmaximal, characteristic
8C23×C83⋊C8C2211yescharacteristic
9C22×C4⋊Dic83C2211yescharacteristic
10C22×C4⋊Dic83C2211yescharacteristic
11C22×C4×Dic83—21no—
12C22×C4×Dic83C2211yescharacteristic
13C2×#14581723—22no—
14C2×#14581723—22no—
15C2×#14581723C414yescomplemented
16C4⋊C4×Dic83—22no—
17C4⋊C4×Dic83—22no—
18C2×C83⋊#95—21no—
19C2×C83⋊#95—21no—
20C2×C83⋊#95—21no—
21#19127464—22no—
22#19127463C414yescomplemented
23#19127455C414yescomplemented
24C23×C8×C83C2211yescharacteristic
25C22×C4⋊C4×C83C2211yescharacteristic
26C22×C4⋊C4×C83C2211yescharacteristic
27#340×C83—22no—
28C23×Dic83—21no—
29C23×Dic83—21no—
30C23×Dic83D411yescharacteristic
31C23×Dic83D411yescharacteristic
32C22×C83⋊C8—21no—
33C22×C83⋊C8—21no—
34C22×C83⋊C8—21no—
35C22×C83⋊C8—21no—
36C22×C83⋊C8C2×C412yes—
37C22×C83⋊C8C2×C412yes—
38C22×C83⋊C8C2×C412yes—
39C2×C4⋊Dic83—21no—
40C2×C4⋊Dic83—21no—
41C2×C4⋊Dic83—21no—
42C2×C4⋊Dic83—21no—
43C2×C4⋊Dic83—21no—
44C2×C4⋊Dic83—21no—
45C2×C4⋊Dic83—21no—
46C2×C4⋊Dic83—21no—
47C2×C4⋊Dic83C2×C412yes—
48C2×C4⋊Dic83C2×C412yes—
49C2×C4⋊Dic83D412yes—
50C2×C4⋊Dic83Q812yes—
51C2×C4×Dic83—24no—
52C2×C4×Dic83—21no—
53C2×C4×Dic83—21no—
54C2×C4×Dic83—21no—
55C2×C4×Dic83—21no—
56C2×C4×Dic83—42no—
57C2×C4×Dic83—42no—
58C2×C4×Dic83C2×C412yes—
59C2×C4×Dic83Q812yes—
60#14581723—28no—
61C83⋊#95—24no—
62C83⋊#95—42no—
63C83⋊#95—42no—
64C23×C4×C83—21no—
65C23×C4×C83—21no—
66C23×C4×C83C2311yescharacteristic
67C22×C8×C83—21no—
68C22×C8×C83—21no—
69C22×C8×C83—21no—
70C22×C8×C83—21no—
71C22×C8×C83—21no—
72C22×C8×C83—21no—
73C22×C8×C83C2×C412yes—
74C2×C4⋊C4×C83—21no—
75C2×C4⋊C4×C83—21no—
76C2×C4⋊C4×C83—21no—
77C2×C4⋊C4×C83—21no—
78C2×C4⋊C4×C83—21no—
79C2×C4⋊C4×C83—21no—
80C2×C4⋊C4×C83—21no—
81C2×C4⋊C4×C83—21no—
82C2×C4⋊C4×C83C2×C412yes—
83C2×C4⋊C4×C83C2×C412yes—
84C2×C4⋊C4×C83D412yes—
85C2×C4⋊C4×C83D412yes—
86C22×Dic83—21no—
87C22×Dic83—21no—
88C22×Dic83—21no—
89C22×Dic83—21no—
90C22×Dic83—22no—
91C22×Dic83—22no—
92C22×Dic83—21no—
93C22×Dic83—22no—
94C22×Dic83—21no—
95C22×Dic83—21no—
96C22×Dic83—21no—
97C22×Dic83—21no—
98C22×Dic83—21no—
99C22×Dic83—22no—
100C22×Dic83—41no—
101C22×Dic83—41no—
102C22×Dic83—41no—
103C22×Dic83—41no—
104C22×Dic83—41no—
105C22×Dic83—41no—
106C22×Dic83—41no—
107C22×Dic83—41no—
108C22×Dic83—41no—
109C22×Dic83—41no—
110C22×Dic83C4⋊C412yes—
111C22×Dic83C4⋊C412yes—
112C22×Dic83SD1612yes—
113C22×Dic83SD1612yes—
114C2×C83⋊C8—22no—
115C2×C83⋊C8—22no—
116C2×C83⋊C8—22no—
117C2×C83⋊C8—22no—
118C2×C83⋊C8—22no—
119C2×C83⋊C8—22no—
120C2×C83⋊C8C4214yescomplemented
121C4⋊Dic83—22no—
122C4⋊Dic83—22no—
123C4⋊Dic83—22no—
124C4⋊Dic83—22no—
125C4⋊Dic83—22no—
126C4⋊Dic83—41no—
127C4⋊Dic83—41no—
128C4⋊Dic83C4⋊C414yes—
129C4×Dic83—22no—
130C4×Dic83—22no—
131C4×Dic83—22no—
132C4×Dic83—22no—
133C4×Dic83—48no—
134C24×C83C2×D411yescharacteristic
135C22×C4×C83—22no—
136C22×C4×C83—22no—
137C22×C4×C83—22no—
138C22×C4×C83—22no—
139C22×C4×C83—41no—
140C22×C4×C83—41no—
141C22×C4×C83—41no—
142C22×C4×C83—41no—
143C22×C4×C83—41no—
144C22×C4×C83—41no—
145C22×C4×C83—41no—
146C22×C4×C83—41no—
147C22×C4×C83—41no—
148C22×C4×C83—41no—
149C22×C4×C83C22×C411yescharacteristic
150C22×C4×C83C22×C411yescharacteristic
151C22×C4×C83C22×C411yescharacteristic
152C22×C4×C83C2×D411yescharacteristic
153C22×C4×C83C2×D411yescharacteristic
154C22×C4×C83C2×D411yescharacteristic
155C22×C4×C83C2×Q811yescharacteristic
156C22×C4×C83C2×Q811yescharacteristic
157C22×C4×C83#4111yescharacteristic
158C22×C4×C83#4111yescharacteristic
159C22×C4×C83#4111yescharacteristic
160C22×C4×C83#4111yescharacteristic
161C22×C4×C83#4111yescharacteristic
162C22×C4×C83#4111yescharacteristic
163C2×C8×C83—22no—
164C2×C8×C83—22no—
165C2×C8×C83—22no—
166C2×C8×C83—41no—
167C2×C8×C83—41no—
168C2×C8×C83—41no—
169C2×C8×C83—41no—
170C4⋊C4×C83—22no—
171C4⋊C4×C83—22no—
172C4⋊C4×C83—22no—
173C4⋊C4×C83—22no—
174C4⋊C4×C83—22no—
175C4⋊C4×C83—41no—
176C4⋊C4×C83—41no—
177C4⋊C4×C83C22⋊C414yes—
178C23×C83C2×C4⋊C411yescharacteristic
179C23×C83C4×D411yescharacteristic
180C23×C83C4×D411yescharacteristic
181C23×C83#12011yescharacteristic
182C23×C83#12111yescharacteristic
183C23×C83C22⋊Q811yescharacteristic
184C23×C83#12311yescharacteristic
185C23×C83C2×SD1611yescharacteristic
186C23×C83C2×SD1611yescharacteristic
187C23×C83#13511yescharacteristic
188C23×C83#13511yescharacteristic
189C23×C83AGL(1,ℤ/8)11yescharacteristic
190C23×C83AGL(1,ℤ/8)11yescharacteristic
191C23×C83#13711yescharacteristic
192C23×C83#13711yescharacteristic
193C2×C4×C83—24no—
194C2×C4×C83—42no—
195C2×C4×C83—42no—
196C2×C4×C83—42no—
197C2×C4×C83—42no—
198C2×C4×C83—42no—
199C2×C4×C83—42no—
200C2×C4×C83—42no—
201C2×C4×C83—42no—
202C2×C4×C83—42no—
203C2×C4×C83—81no—
204C2×C4×C83—81no—
205C2×C4×C83—81no—
206C2×C4×C83—81no—
207C2×C4×C83C2×C4211yescharacteristic
208C2×C4×C83C2×C22⋊C411yescharacteristic
209C2×C4×C83C2×C4⋊C411yescharacteristic
210C2×C4×C83#11711yescharacteristic
211C2×C4×C83#11711yescharacteristic
212C2×C4×C83#11711yescharacteristic
213C2×C4×C83C4×D411yescharacteristic
214C2×C4×C83C4×D411yescharacteristic
215C2×C4×C83C4×D411yescharacteristic
216C2×C4×C83C4×D411yescharacteristic
217C2×C4×C83C4×D411yescharacteristic
218C2×C4×C83C4×D411yescharacteristic
219C2×C4×C83C4×Q811yescharacteristic
220C2×C4×C83C4×Q811yescharacteristic
221C2×C4×C83C4×Q811yescharacteristic
222C2×C4×C83C4×Q811yescharacteristic
223C2×C4×C83#12111yescharacteristic
224C2×C4×C83C22⋊Q811yescharacteristic
225C2×C4×C83C22⋊Q811yescharacteristic
226C2×C4×C83C22⋊Q811yescharacteristic
227C2×C4×C83#12311yescharacteristic
228C2×C4×C83#12311yescharacteristic
229C2×C4×C83#12411yescharacteristic
230C2×C4×C83#12511yescharacteristic
231C2×C4×C83#12511yescharacteristic
232C2×C4×C83#12611yescharacteristic
233C2×C4×C83#12611yescharacteristic
234C2×C4×C83C4⋊Q811yescharacteristic
235C2×Dic83—22no—
236C2×Dic83—22no—
237C2×Dic83—22no—
238C2×Dic83—22no—
239C2×Dic83—22no—
240C2×Dic83—22no—
241C2×Dic83—22no—
242C2×Dic83—24no—
243C2×Dic83—22no—
244C2×Dic83—22no—
245C2×Dic83—42no—
246C2×Dic83—42no—
247C2×Dic83—41no—
248C2×Dic83—42no—
249C2×Dic83—42no—
250C2×Dic83—41no—
251C2×Dic83—42no—
252C2×Dic83—42no—
253C2×Dic83—41no—
254C2×Dic83—41no—
255C2×Dic83—42no—
256C2×Dic83—42no—
257C2×Dic83—42no—
258C2×Dic83—81no—
259C2×Dic83—81no—
260C2×Dic83—81no—
261C2×Dic83—81no—
262C2×Dic83#10614yescomplemented
263C8×C83—42no—
264C83⋊C8—24no—
265C22×C83C4×C4⋊C411yescharacteristic
266C22×C83#38511yescharacteristic
267C22×C83#38511yescharacteristic
268C22×C83#38611yescharacteristic
269C22×C83#38711yescharacteristic
270C22×C83#38811yescharacteristic
271C22×C83#38911yescharacteristic
272C22×C83C2×#10611yescharacteristic
273C22×C83#42711yescharacteristic
274C22×C83#42811yescharacteristic
275C22×C83#42811yescharacteristic
276C22×C83C4×SD1611yescharacteristic
277C22×C83C4×SD1611yescharacteristic
278C22×C83C4×SD1611yescharacteristic
279C22×C83C4×SD1611yescharacteristic
280C22×C83#44011yescharacteristic
281C22×C83#44011yescharacteristic
282C22×C83#44111yescharacteristic
283C22×C83#44211yescharacteristic
284C22×C83#44811yescharacteristic
285C22×C83#44911yescharacteristic
286C22×C83#45011yescharacteristic
287C22×C83#45211yescharacteristic
288C22×C83#46011yescharacteristic
289C22×C83#46111yescharacteristic
290C22×C83#46311yescharacteristic
291C22×C83#46411yescharacteristic
292C22×C83#47511yescharacteristic
293C22×C83#47611yescharacteristic
294C22×C83#47811yescharacteristic
295C22×C83#47911yescharacteristic
296C22×C83#48111yescharacteristic
297C22×C83#48211yescharacteristic
298C22×C83#48311yescharacteristic
299C22×C83#48511yescharacteristic
300C4×C83—44no—
301C4×C83—82no—
302C4×C83C4×C22⋊C411yescharacteristic
303C4×C83C4×C4⋊C411yescharacteristic
304C4×C83#38711yescharacteristic
305C4×C83#38711yescharacteristic
306C4×C83#38711yescharacteristic
307C4×C83#38811yescharacteristic
308C4×C83#38911yescharacteristic
309C4×C83#39111yescharacteristic
310Dic83—24no—
311Dic83—42no—
312Dic83—44no—
313Dic83—82no—
314#10908—831nomaximal, Sylow
315C2×C83#143611yescharacteristic
316C2×C83C4×#10611yescharacteristic
317C2×C83#177611yescharacteristic
318C2×C83#185311yescharacteristic
319C2×C83#185411yescharacteristic
320C2×C83#186411yescharacteristic
321C2×C83#186511yescharacteristic
322C2×C83#187711yescharacteristic
323C2×C83#188011yescharacteristic
324C2×C83#191911yescharacteristic
325C2×C83#192011yescharacteristic
326C2×C83#192611yescharacteristic
327C2×C83#192711yescharacteristic
328C2×C83#194811yescharacteristic
329C2×C83#194911yescharacteristic
330C22×#106—831no—
331C2×C4×C4⋊C4—831no—
332C2×#340—831no—
333C2×#340—831no—
334C2×#340D8311yescharacteristic
335C2×#336—831no—
336C4⋊#95—831no—
337C83#1090811yescharacteristic, complemented, Sylow
338C23×C8—831no—
339C23×C8C2×D8311yescharacteristic
340C22×C4⋊C4—831no—
341C22×C4⋊C4—831no—
342C22×C4⋊C4C2×D8311yescharacteristic
343C22×C4⋊C4C2×D8311yescharacteristic
344C22×C42—831no—
345C22×C42—1661no—
346C2×#106—834no—
347C2×#106—1662no—
348C2×#106—1662no—
349C4×C4⋊C4—1662no—
350C4×C4⋊C4—1662no—
351C2×#95—1661no—
352C2×#95—1661no—
353C2×#95—1661no—
354#340—22no—
355#340—834no—
356#340—1662no—
357#336—834no—
358C23×C4—21no—
359C23×C4—21no—
360C23×C4—831no—
361C23×C4—831no—
362C23×C4—1661no—
363C23×C4—1661no—
364C23×C4C22×D8311yescharacteristic
365C22×C8—21no—
366C22×C8—21no—
367C22×C8—21no—
368C22×C8—21no—
369C22×C8—21no—
370C22×C8—21no—
371C22×C8—832no—
372C22×C8—832no—
373C22×C8—832no—
374C22×C8—1661no—
375C22×C8—1661no—
376C22×C8—1661no—
377C22×C8—1661no—
378C22×C8C4×D8312yes—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—832no—
388C2×C4⋊C4—832no—
389C2×C4⋊C4—832no—
390C2×C4⋊C4—832no—
391C2×C4⋊C4—1661no—
392C2×C4⋊C4—1661no—
393C2×C4⋊C4—1661no—
394C2×C4⋊C4—1661no—
395C2×C4⋊C4—1661no—
396C2×C4⋊C4—1661no—
397C2×C4⋊C4—1661no—
398C2×C4⋊C4—1661no—
399C2×C4⋊C4C4×D8312yes—
400C2×C4⋊C4C4×D8312yes—
401C2×C4⋊C4D33212yes—
402C2×C4⋊C4C22⋊D8312yes—
403C2×C42—3322no—
404C2×C42—3322no—
405C2×C42—832no—
406C2×C42—832no—
407C2×C42—1664no—
408C2×C42—1661no—
409C2×C42—1661no—
410C2×C42—1661no—
411C2×C42—1661no—
412#106—1668no—
413#95—3322no—
414#95—3322no—
415#95—1664no—
416C24D4×D8311yescharacteristic
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—41no—
422C22×C4—41no—
423C22×C4—41no—
424C22×C4—41no—
425C22×C4—41no—
426C22×C4—41no—
427C22×C4—41no—
428C22×C4—41no—
429C22×C4—41no—
430C22×C4—41no—
431C22×C4—3321no—
432C22×C4—3321no—
433C22×C4—3321no—
434C22×C4—3321no—
435C22×C4—3321no—
436C22×C4—3321no—
437C22×C4—3321no—
438C22×C4—3321no—
439C22×C4—3321no—
440C22×C4—3321no—
441C22×C4—832no—
442C22×C4—832no—
443C22×C4—832no—
444C22×C4—832no—
445C22×C4—1662no—
446C22×C4—1661no—
447C22×C4—1662no—
448C22×C4—1662no—
449C22×C4—1661no—
450C22×C4—1661no—
451C22×C4—1661no—
452C22×C4—1661no—
453C22×C4—1661no—
454C22×C4—1662no—
455C22×C4—1661no—
456C22×C4—1661no—
457C22×C4—1661no—
458C22×C4—1661no—
459C22×C4C2×C4×D8311yescharacteristic
460C22×C4C2×C4×D8311yescharacteristic
461C22×C4C2×C4×D8311yescharacteristic
462C22×C4D4×D8311yescharacteristic
463C22×C4C2×C22⋊D8311yescharacteristic
464C22×C4C2×D33211yescharacteristic
465C22×C4Q8×D8311yescharacteristic
466C22×C4Q8×D8311yescharacteristic
467C22×C4#1305058911yescharacteristic
468C22×C4#1305058911yescharacteristic
469C22×C4#1305058911yescharacteristic
470C22×C4#1305058911yescharacteristic
471C22×C4#1305059011yescharacteristic
472C22×C4#1305059011yescharacteristic
473C2×C8—22no—
474C2×C8—22no—
475C2×C8—22no—
476C2×C8—41no—
477C2×C8—41no—
478C2×C8—41no—
479C2×C8—41no—
480C2×C8—834no—
481C2×C8—1662no—
482C2×C8—1662no—
483C2×C8—1662no—
484C2×C8—1662no—
485C2×C8—1662no—
486C2×C8—1662no—
487C4⋊C4—22no—
488C4⋊C4—22no—
489C4⋊C4—22no—
490C4⋊C4—22no—
491C4⋊C4—22no—
492C4⋊C4—41no—
493C4⋊C4—41no—
494C4⋊C4—3321no—
495C4⋊C4—3321no—
496C4⋊C4—834no—
497C4⋊C4—1662no—
498C4⋊C4—1662no—
499C4⋊C4—1662no—
500C4⋊C4—1662no—
501C4⋊C4—1662no—
502C4⋊C4(C2×D83)⋊C414yes—
503C42—3328no—
504C42—1662no—
505C42—1662no—
506C42—1662no—
507C42—1662no—
508C23C4⋊C4×D8311yescharacteristic
509C23(C22⋊D83)⋊C411yescharacteristic
510C23(C22⋊D83)⋊C411yescharacteristic
511C23#1458176211yescharacteristic
512C23#1458176411yescharacteristic
513C23#1458177011yescharacteristic
514C23#1458177411yescharacteristic
515C23SD16×D8311yescharacteristic
516C23SD16×D8311yescharacteristic
517C23#1458181111yescharacteristic
518C23#1458181511yescharacteristic
519C23#1458181611yescharacteristic
520C23#1458181911yescharacteristic
521C23#1458182111yescharacteristic
522C23#1458182411yescharacteristic
523C2×C4—24no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—81no—
534C2×C4—81no—
535C2×C4—81no—
536C2×C4—81no—
537C2×C4—3322no—
538C2×C4—3322no—
539C2×C4—3321no—
540C2×C4—3322no—
541C2×C4—3321no—
542C2×C4—3322no—
543C2×C4—3322no—
544C2×C4—3321no—
545C2×C4—3321no—
546C2×C4—3322no—
547C2×C4—3322no—
548C2×C4—3322no—
549C2×C4—3322no—
550C2×C4—834no—
551C2×C4—6641no—
552C2×C4—6641no—
553C2×C4—6641no—
554C2×C4—6641no—
555C2×C4—1662no—
556C2×C4—1664no—
557C2×C4—1662no—
558C2×C4—1662no—
559C2×C4—1662no—
560C2×C4—1662no—
561C2×C4—1662no—
562C2×C4—1662no—
563C2×C4—1662no—
564C2×C4—1662no—
565C2×C4C42×D8311yescharacteristic
566C2×C4C2×(C2×D83)⋊C411yescharacteristic
567C2×C4C4⋊C4×D8311yescharacteristic
568C2×C4#1458174811yescharacteristic
569C2×C4#1458174811yescharacteristic
570C2×C4#1458174911yescharacteristic
571C2×C4(C22⋊D83)⋊C411yescharacteristic
572C2×C4(C22⋊D83)⋊C411yescharacteristic
573C2×C4C4×C22⋊D8311yescharacteristic
574C2×C4C4×C22⋊D8311yescharacteristic
575C2×C4C4×D33211yescharacteristic
576C2×C4C4×D33211yescharacteristic
577C2×C4#1458175711yescharacteristic
578C2×C4#1458175711yescharacteristic
579C2×C4#1458175711yescharacteristic
580C2×C4#1458175711yescharacteristic
581C2×C4#1458176411yescharacteristic
582C2×C4#1458177011yescharacteristic
583C2×C4#1458177211yescharacteristic
584C2×C4#1458177211yescharacteristic
585C2×C4#1458177411yescharacteristic
586C2×C4#1458177611yescharacteristic
587C2×C4#1458177911yescharacteristic
588C2×C4#1458178211yescharacteristic
589C2×C4#1458178211yescharacteristic
590C2×C4#1458178511yescharacteristic
591C2×C4#1458178511yescharacteristic
592C2×C4#1458179011yescharacteristic
593C8—42no—
594C8—1664no—
595C22#1912755211yescharacteristic
596C22#1912757511yescharacteristic
597C22#1912757511yescharacteristic
598C22#1912757811yescharacteristic
599C22#1912758311yescharacteristic
600C22#1912759511yescharacteristic
601C22#1912759611yescharacteristic
602C22#106×D8311yescharacteristic
603C22#1912773811yescharacteristic
604C22#1912774011yescharacteristic
605C22#1912774211yescharacteristic
606C22#1912778611yescharacteristic
607C22#1912778611yescharacteristic
608C22#1912779211yescharacteristic
609C22#1912779211yescharacteristic
610C22#1912779811yescharacteristic
611C22#1912780411yescharacteristic
612C22#1912780511yescharacteristic
613C22#1912781011yescharacteristic
614C22#1912784111yescharacteristic
615C22#1912784911yescharacteristic
616C22#1912785311yescharacteristic
617C22#1912786411yescharacteristic
618C22#1912789911yescharacteristic
619C22#1912790411yescharacteristic
620C22#1912791411yescharacteristic
621C22#1912792511yescharacteristic
622C22#1912798511yescharacteristic
623C22#1912799011yescharacteristic
624C22#1912800411yescharacteristic
625C22#1912800711yescharacteristic
626C22#1912801811yescharacteristic
627C22#1912802311yescharacteristic
628C22#1912803011yescharacteristic
629C22#1912804111yescharacteristic
630C4—44no—
631C4—82no—
632C4—3322no—
633C4—3324no—
634C4—6642no—
635C4—1664no—
636C4C4×(C2×D83)⋊C411yescharacteristic
637C4#1912755211yescharacteristic
638C4#1912758311yescharacteristic
639C4#1912758611yescharacteristic
640C4#1912758611yescharacteristic
641C4#1912759511yescharacteristic
642C4#1912759611yescharacteristic
643C4#1912760611yescharacteristic
644C2#2490569811yescharacteristic
645C2#2490735111yescharacteristic
646C2#2490735911yescharacteristic
647C2#2490765711yescharacteristic
648C2#2490766511yescharacteristic
649C2#2490772511yescharacteristic
650C2#2490773211yescharacteristic
651C2#2490779511yescharacteristic
652C2#2490781611yescharacteristic
653C2#2490803911yescharacteristic
654C2#2490804611yescharacteristic
655C2#2490809311yescharacteristic
656C2#2490810011yescharacteristic
657C2#2490822311yescharacteristic
658C2#2490822811yescharacteristic
subgroupG/H
centerC24D4×D83
commutatorC2×C4×C83C2×C42
FrattiniC23×C4C22×D83
FittingC2×#340×C83C2
socle, prime radicalC24×C83C2×D4
cosocleC23×C4×C83C23
hypercenterC2×#340D83
hypocenterC83#10908
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C24 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
15. C2×#14581723C4semidirect
22. #19127463C4semidirect
23. #19127455C4semidirect
120. C2×C83⋊C8C42semidirect
262. C2×Dic83#106semidirect
337. C83#10908semidirect

Maximal subgroups

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

subgroupindex
C22×#145817232
C2×C4⋊C4×Dic832
C2×#191274642
C2×#191274632
C2×#191274552
#249056922
C2×#340×C832
#1090883