Finite Group Databasebeta

← #35310572

Subgroups — #35310572

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×#14581724C211yesmaximal, characteristic
2C2×C4×C4⋊Dic83C211yesmaximal, characteristic
3C2×#19127464C211yesmaximal, characteristic
4C2×#19127464C211yesmaximal, characteristic
5C2×#19127464C211yesmaximal, characteristic
6#24905693C211yesmaximal, characteristic
7C2×#336×C83C211yesmaximal, characteristic
8C22×C4⋊Dic83C2211yescharacteristic
9C22×C4⋊Dic83C2211yescharacteristic
10C22×C4⋊Dic83C2211yescharacteristic
11C22×C4⋊Dic83C2211yescharacteristic
12C22×C4×Dic83—21no—
13C2×#14581724—22no—
14C2×#14581724—22no—
15C2×#14581724C414yescomplemented
16C4×C4⋊Dic83—22no—
17C4×C4⋊Dic83—22no—
18C2×C83⋊#95—21no—
19C2×C83⋊#95—21no—
20C2×C83⋊#95—21no—
21#19127464—22no—
22#19127464—22no—
23#19127464C414yescomplemented
24C23×C8×C83C2211yescharacteristic
25C23×C8×C83C2211yescharacteristic
26C22×C42×C83C2211yescharacteristic
27#336×C83C414yescomplemented
28C23×Dic83—21no—
29C23×Dic83—21no—
30C23×Dic83—21no—
31C23×Dic83—21no—
32C2×C4⋊Dic83—21no—
33C2×C4⋊Dic83—21no—
34C2×C4⋊Dic83—21no—
35C2×C4⋊Dic83—21no—
36C2×C4⋊Dic83—21no—
37C2×C4⋊Dic83—21no—
38C2×C4⋊Dic83—21no—
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⋊Dic83—21no—
48C2×C4⋊Dic83C2×C412yes—
49C2×C4⋊Dic83C2×C412yes—
50C2×C4⋊Dic83C2×C412yes—
51C2×C4⋊Dic83C2×C412yes—
52C2×C4⋊Dic83D412yes—
53C2×C4⋊Dic83D412yes—
54C2×C4⋊Dic83D412yes—
55C2×C4⋊Dic83Q812yes—
56C2×C4×Dic83—24no—
57C2×C4×Dic83—42no—
58C2×C4×Dic83—42no—
59#14581724—28no—
60C83⋊#95—24no—
61C83⋊#95—42no—
62C83⋊#95—42no—
63C23×C4×C83D411yescharacteristic
64C23×C4×C83D411yescharacteristic
65C23×C4×C83C2311yescharacteristic
66C22×C8×C83—21no—
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×C83—21no—
74C22×C8×C83—21no—
75C22×C8×C83—21no—
76C22×C8×C83C2×C412yes—
77C22×C8×C83C2×C412yes—
78C22×C8×C83C2×C412yes—
79C22×C8×C83C2×C412yes—
80C2×C42×C83—21no—
81C2×C42×C83—21no—
82C2×C42×C83—21no—
83C2×C42×C83—21no—
84C2×C42×C83C2×C412yes—
85C2×C42×C83Q812yes—
86C22×Dic83—22no—
87C22×Dic83—22no—
88C22×Dic83—22no—
89C22×Dic83—22no—
90C22×Dic83—22no—
91C22×Dic83—22no—
92C22×Dic83—22no—
93C22×Dic83—22no—
94C22×Dic83—41no—
95C22×Dic83—41no—
96C22×Dic83—41no—
97C22×Dic83—41no—
98C22×Dic83—41no—
99C22×Dic83—41no—
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×Dic83—41no—
111C22×Dic83—41no—
112C22×Dic83—41no—
113C22×Dic83—41no—
114C4⋊Dic83—22no—
115C4⋊Dic83—22no—
116C4⋊Dic83—22no—
117C4⋊Dic83—22no—
118C4⋊Dic83—22no—
119C4⋊Dic83—22no—
120C4⋊Dic83—22no—
121C4⋊Dic83—22no—
122C4⋊Dic83—22no—
123C4⋊Dic83—22no—
124C4⋊Dic83—41no—
125C4⋊Dic83—41no—
126C4⋊Dic83—41no—
127C4⋊Dic83—41no—
128C4⋊Dic83C22⋊C414yes—
129C4⋊Dic83C4⋊C414yes—
130C4×Dic83—48no—
131C24×C83C2×D411yescharacteristic
132C22×C4×C83—21no—
133C22×C4×C83—21no—
134C22×C4×C83—21no—
135C22×C4×C83—21no—
136C22×C4×C83—21no—
137C22×C4×C83—21no—
138C22×C4×C83—21no—
139C22×C4×C83—21no—
140C22×C4×C83—21no—
141C22×C4×C83—21no—
142C22×C4×C83C4⋊C412yes—
143C22×C4×C83C4⋊C412yes—
144C22×C4×C83SD1612yes—
145C22×C4×C83SD1612yes—
146C22×C4×C83C22×C411yescharacteristic
147C22×C4×C83C22×C411yescharacteristic
148C22×C4×C83C22×C411yescharacteristic
149C22×C4×C83C2×D411yescharacteristic
150C22×C4×C83C2×D411yescharacteristic
151C22×C4×C83C2×D411yescharacteristic
152C22×C4×C83C2×Q811yescharacteristic
153C22×C4×C83C2×Q811yescharacteristic
154C22×C4×C83#4111yescharacteristic
155C22×C4×C83#4111yescharacteristic
156C22×C4×C83#4111yescharacteristic
157C22×C4×C83#4111yescharacteristic
158C22×C4×C83#4111yescharacteristic
159C22×C4×C83#4111yescharacteristic
160C2×C8×C83—22no—
161C2×C8×C83—22no—
162C2×C8×C83—22no—
163C2×C8×C83—22no—
164C2×C8×C83—22no—
165C2×C8×C83—22no—
166C2×C8×C83—22no—
167C2×C8×C83—22no—
168C2×C8×C83—22no—
169C2×C8×C83—41no—
170C2×C8×C83—41no—
171C2×C8×C83—41no—
172C2×C8×C83—41no—
173C2×C8×C83C4214yescomplemented
174C42×C83—22no—
175C42×C83—22no—
176C42×C83—22no—
177C42×C83—22no—
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—22no—
194C2×C4×C83—22no—
195C2×C4×C83—22no—
196C2×C4×C83—22no—
197C2×C4×C83—22no—
198C2×C4×C83—22no—
199C2×C4×C83—22no—
200C2×C4×C83—22no—
201C2×C4×C83—22no—
202C2×C4×C83—41no—
203C2×C4×C83—41no—
204C2×C4×C83—41no—
205C2×C4×C83—41no—
206C2×C4×C83#10614yescomplemented
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—24no—
236C2×Dic83—24no—
237C2×Dic83—42no—
238C2×Dic83—42no—
239C2×Dic83—42no—
240C2×Dic83—42no—
241C2×Dic83—42no—
242C2×Dic83—42no—
243C2×Dic83—42no—
244C2×Dic83—42no—
245C2×Dic83—42no—
246C2×Dic83—42no—
247C2×Dic83—42no—
248C2×Dic83—42no—
249C2×Dic83—42no—
250C2×Dic83—42no—
251C2×Dic83—42no—
252C2×Dic83—42no—
253C2×Dic83—42no—
254C2×Dic83—42no—
255C2×Dic83—81no—
256C2×Dic83—81no—
257C2×Dic83—81no—
258C2×Dic83—81no—
259C2×Dic83—81no—
260C2×Dic83—81no—
261C2×Dic83—81no—
262C2×Dic83—81no—
263C8×C83—24no—
264C8×C83—42no—
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—24no—
301C4×C83—42no—
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—44no—
311Dic83—44no—
312Dic83—82no—
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×#340—831no—
335C2×#336D8311yescharacteristic
336C4⋊#95—831no—
337C83#1090811yescharacteristic, complemented, Sylow
338C23×C8C2×D8311yescharacteristic
339C23×C8C2×D8311yescharacteristic
340C22×C4⋊C4—831no—
341C22×C4⋊C4—831no—
342C22×C4⋊C4—831no—
343C22×C4⋊C4—831no—
344C22×C42—1661no—
345C22×C42C2×D8311yescharacteristic
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—834no—
355#340—1662no—
356#340—1662no—
357#336Dic8314yescomplemented
358C23×C4—1661no—
359C23×C4—1661no—
360C23×C4—1661no—
361C23×C4—1661no—
362C23×C4D33211yescharacteristic
363C23×C4D33211yescharacteristic
364C23×C4C22×D8311yescharacteristic
365C22×C8—21no—
366C22×C8—21no—
367C22×C8—21no—
368C22×C8—21no—
369C22×C8—21no—
370C22×C8—21no—
371C22×C8—21no—
372C22×C8—21no—
373C22×C8—21no—
374C22×C8—21no—
375C22×C8C4×D8312yes—
376C22×C8C4×D8312yes—
377C22×C8C2×Dic8312yes—
378C22×C8C2×Dic8312yes—
379C2×C4⋊C4—832no—
380C2×C4⋊C4—832no—
381C2×C4⋊C4—832no—
382C2×C4⋊C4—832no—
383C2×C4⋊C4—832no—
384C2×C4⋊C4—832no—
385C2×C4⋊C4—832no—
386C2×C4⋊C4—832no—
387C2×C4⋊C4—1661no—
388C2×C4⋊C4—1661no—
389C2×C4⋊C4—1661no—
390C2×C4⋊C4—1661no—
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⋊C4—1661no—
400C2×C4⋊C4—1661no—
401C2×C4⋊C4—1661no—
402C2×C4⋊C4—1661no—
403C2×C42—21no—
404C2×C42—21no—
405C2×C42—21no—
406C2×C42—21no—
407C2×C42—3322no—
408C2×C42—3322no—
409C2×C42—1664no—
410C2×C42Dic16612yes—
411C2×C42C2×Dic8312yes—
412#106—1668no—
413#95—3322no—
414#95—3322no—
415#95—1664no—
416C24C2×D33211yescharacteristic
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—3321no—
428C22×C4—3321no—
429C22×C4—3321no—
430C22×C4—3321no—
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—3321no—
442C22×C4—3321no—
443C22×C4—3321no—
444C22×C4—3321no—
445C22×C4—3321no—
446C22×C4—3321no—
447C22×C4—1662no—
448C22×C4—1662no—
449C22×C4—1662no—
450C22×C4—1662no—
451C22×C4—1662no—
452C22×C4—1662no—
453C22×C4—1662no—
454C22×C4—1662no—
455C22×C4C4⋊Dic8312yes—
456C22×C4C4⋊Dic8312yes—
457C22×C4#1305057912yes—
458C22×C4#1305057912yes—
459C22×C4C2×C4×D8311yescharacteristic
460C22×C4C2×C4×D8311yescharacteristic
461C22×C4C22×Dic8311yescharacteristic
462C22×C4D4×D8311yescharacteristic
463C22×C4D4×D8311yescharacteristic
464C22×C4D4×D8311yescharacteristic
465C22×C4Q8×D8311yescharacteristic
466C22×C4C2×Dic16611yescharacteristic
467C22×C4#1305058911yescharacteristic
468C22×C4#1305058911yescharacteristic
469C22×C4#1305058911yescharacteristic
470C22×C4#1305059011yescharacteristic
471C22×C4#1305059011yescharacteristic
472C22×C4#1305059111yescharacteristic
473C2×C8—22no—
474C2×C8—22no—
475C2×C8—22no—
476C2×C8—22no—
477C2×C8—22no—
478C2×C8—22no—
479C2×C8—22no—
480C2×C8—22no—
481C2×C8—22no—
482C2×C8—41no—
483C2×C8—41no—
484C2×C8—41no—
485C2×C8—41no—
486C2×C8C4×Dic8314yescomplemented
487C4⋊C4—3321no—
488C4⋊C4—3321no—
489C4⋊C4—3321no—
490C4⋊C4—3321no—
491C4⋊C4—834no—
492C4⋊C4—834no—
493C4⋊C4—1662no—
494C4⋊C4—1662no—
495C4⋊C4—1662no—
496C4⋊C4—1662no—
497C4⋊C4—1662no—
498C4⋊C4—1662no—
499C4⋊C4—1662no—
500C4⋊C4—1662no—
501C4⋊C4—1662no—
502C4⋊C4—1662no—
503C42—22no—
504C42—22no—
505C42—22no—
506C42—22no—
507C42—3328no—
508C23C2×C4⋊Dic8311yescharacteristic
509C23C4×D33211yescharacteristic
510C23C4×D33211yescharacteristic
511C23#1458176211yescharacteristic
512C23#1458176711yescharacteristic
513C23#1458177211yescharacteristic
514C23#1458177611yescharacteristic
515C23C2×#1305057911yescharacteristic
516C23C2×#1305057911yescharacteristic
517C23#1458181411yescharacteristic
518C23#1458181411yescharacteristic
519C23#1458182011yescharacteristic
520C23#1458182011yescharacteristic
521C23#1458182511yescharacteristic
522C23#1458182511yescharacteristic
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—3322no—
537C2×C4—3322no—
538C2×C4—3322no—
539C2×C4—3322no—
540C2×C4—3322no—
541C2×C4—3322no—
542C2×C4—3322no—
543C2×C4—3322no—
544C2×C4—3322no—
545C2×C4—3322no—
546C2×C4—3322no—
547C2×C4—3322no—
548C2×C4—3322no—
549C2×C4—3322no—
550C2×C4—3322no—
551C2×C4—3322no—
552C2×C4—3322no—
553C2×C4—3322no—
554C2×C4—6641no—
555C2×C4—6641no—
556C2×C4—6641no—
557C2×C4—6641no—
558C2×C4—6641no—
559C2×C4—6641no—
560C2×C4—6641no—
561C2×C4—6641no—
562C2×C4—1664no—
563C2×C4—1664no—
564C2×C4#1458172414yescomplemented
565C2×C4C2×C4×Dic8311yescharacteristic
566C2×C4C22⋊C4×D8311yescharacteristic
567C2×C4C4⋊C4×D8311yescharacteristic
568C2×C4#1458174811yescharacteristic
569C2×C4#1458175011yescharacteristic
570C2×C4#1458175111yescharacteristic
571C2×C4(C22⋊D83)⋊C411yescharacteristic
572C2×C4(C22⋊D83)⋊C411yescharacteristic
573C2×C4#1458175411yescharacteristic
574C2×C4D4×Dic8311yescharacteristic
575C2×C4D4×Dic8311yescharacteristic
576C2×C4D4×Dic8311yescharacteristic
577C2×C4#1458175711yescharacteristic
578C2×C4C4×Dic16611yescharacteristic
579C2×C4C4×Dic16611yescharacteristic
580C2×C4Q8×Dic8311yescharacteristic
581C2×C4#1458176511yescharacteristic
582C2×C4#1458176911yescharacteristic
583C2×C4#1458176911yescharacteristic
584C2×C4#1458177011yescharacteristic
585C2×C4#1458177411yescharacteristic
586C2×C4#1458177711yescharacteristic
587C2×C4#1458177811yescharacteristic
588C2×C4#1458178211yescharacteristic
589C2×C4#1458178311yescharacteristic
590C2×C4#1458178511yescharacteristic
591C2×C4#1458178711yescharacteristic
592C2×C4#1458179111yescharacteristic
593C8—24no—
594C8—42no—
595C22C4×C4⋊Dic8311yescharacteristic
596C22#1912757511yescharacteristic
597C22#1912757611yescharacteristic
598C22#1912757911yescharacteristic
599C22#1912758611yescharacteristic
600C22#1912759311yescharacteristic
601C22#1912760011yescharacteristic
602C22C2×#1458172411yescharacteristic
603C22#1912773911yescharacteristic
604C22#1912774311yescharacteristic
605C22#1912774311yescharacteristic
606C22C4×#1305057911yescharacteristic
607C22C4×#1305057911yescharacteristic
608C22C4×#1305057911yescharacteristic
609C22C4×#1305057911yescharacteristic
610C22#1912780311yescharacteristic
611C22#1912780311yescharacteristic
612C22#1912780911yescharacteristic
613C22#1912781411yescharacteristic
614C22#1912784211yescharacteristic
615C22#1912784811yescharacteristic
616C22#1912785411yescharacteristic
617C22#1912786511yescharacteristic
618C22#1912790211yescharacteristic
619C22#1912790711yescharacteristic
620C22#1912791711yescharacteristic
621C22#1912792411yescharacteristic
622C22#1912798711yescharacteristic
623C22#1912799211yescharacteristic
624C22#1912800211yescharacteristic
625C22#1912800911yescharacteristic
626C22#1912802011yescharacteristic
627C22#1912802611yescharacteristic
628C22#1912803211yescharacteristic
629C22#1912804311yescharacteristic
630C4—24no—
631C4—42no—
632C4—3324no—
633C4—3324no—
634C4—6642no—
635C4—6642no—
636C4C22⋊C4×Dic8311yescharacteristic
637C4C4⋊C4×Dic8311yescharacteristic
638C4#1912758411yescharacteristic
639C4#1912758711yescharacteristic
640C4#1912758811yescharacteristic
641C4#1912759411yescharacteristic
642C4#1912759811yescharacteristic
643C4#1912760511yescharacteristic
644C2#2490569711yescharacteristic
645C2C4×#1458172411yescharacteristic
646C2#2490736011yescharacteristic
647C2#2490765811yescharacteristic
648C2#2490766411yescharacteristic
649C2#2490772711yescharacteristic
650C2#2490773411yescharacteristic
651C2#2490779611yescharacteristic
652C2#2490781711yescharacteristic
653C2#2490804211yescharacteristic
654C2#2490804911yescharacteristic
655C2#2490809111yescharacteristic
656C2#2490809811yescharacteristic
657C2#2490822711yescharacteristic
658C2#2490823311yescharacteristic
subgroupG/H
centerC24C2×D332
commutatorC2×C4×C83C2×C42
FrattiniC23×C4C22×D83
FittingC2×#336×C83C2
socle, prime radicalC24×C83C2×D4
cosocleC23×C4×C83C23
hypercenterC2×#336D83
hypocenterC83#10908
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C24 ◁ C22×C42 ◁ C2×#336

Complements

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

NH ≅ G/Ntype
15. C2×#14581724C4semidirect
23. #19127464C4semidirect
27. #336×C83C4semidirect
173. C2×C8×C83C42semidirect
206. C2×C4×C83#106semidirect
337. C83#10908semidirect
357. #336Dic83semidirect
486. C2×C8C4×Dic83semidirect
564. C2×C4#14581724semidirect

Maximal subgroups

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

subgroupindex
C22×#145817242
C2×C4×C4⋊Dic832
C2×#191274642
#249056932
C2×#336×C832
#1090883