Finite Group Databasebeta

← #35313189

Subgroups — #35313189

Order 21248.

886 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
1C2×#19127570C211yesmaximal, characteristic
2C2×#19127464C211yesmaximal, characteristic
3C2×#19127463C211yesmaximal, characteristic
4C2×#19127463C211yesmaximal, characteristic
5C2×#19127455C211yesmaximal, characteristic
6#24905692C211yesmaximal, characteristic
7C2×#340×C83C211yesmaximal, characteristic
8C23×C83⋊C8C2211yescharacteristic
9C22×C4⋊Dic83C2211yescharacteristic
10C22×C4⋊Dic83C2211yescharacteristic
11C22×Dic83⋊C4—21no—
12C22×Dic83⋊C4—21no—
13C22×C4×Dic83C2211yescharacteristic
14#19127570—22no—
15#19127570C414yescomplemented
16C2×C83⋊#95—21no—
17C2×C83⋊#95—21no—
18#19127464—22no—
19#19127463—22no—
20#19127463—22no—
21#19127455—22no—
22C23×C8×C83C2211yescharacteristic
23C22×C4⋊C4×C83C2211yescharacteristic
24C22×C4⋊C4×C83C2211yescharacteristic
25#340×C83—22no—
26C23×Dic83—21no—
27C23×Dic83—21no—
28C23×Dic83D411yescharacteristic
29C23×Dic83D411yescharacteristic
30C22×C83⋊C8—21no—
31C22×C83⋊C8—21no—
32C22×C83⋊C8—21no—
33C22×C83⋊C8—21no—
34C22×C83⋊C8—21no—
35C22×C83⋊C8—21no—
36C22×C83⋊C8Q812yes—
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⋊Dic83C2×C412yes—
48C2×C4⋊Dic83D412yes—
49C2×Dic83⋊C4—24no—
50C2×Dic83⋊C4—24no—
51C2×Dic83⋊C4—42no—
52C2×Dic83⋊C4—42no—
53C2×Dic83⋊C4—42no—
54C2×Dic83⋊C4—42no—
55C2×C4×Dic83—21no—
56C2×C4×Dic83—21no—
57C2×C4×Dic83—21no—
58C2×C4×Dic83—21no—
59C2×C4×Dic83C2×C412yes—
60C2×C4×Dic83D412yes—
61C83⋊#95—42no—
62C83⋊#95—42no—
63C23×C4×C83—21no—
64C23×C4×C83—21no—
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×C83Q812yes—
73C2×C4⋊C4×C83—21no—
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×C83—21no—
83C2×C4⋊C4×C83C2×C412yes—
84C2×C4⋊C4×C83D412yes—
85C22×Dic83—21no—
86C22×Dic83—21no—
87C22×Dic83—21no—
88C22×Dic83—21no—
89C22×Dic83—21no—
90C22×Dic83—21no—
91C22×Dic83—21no—
92C22×Dic83—21no—
93C22×Dic83—22no—
94C22×Dic83—22no—
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×Dic83C22⋊C412yes—
108C22×Dic83C22⋊C412yes—
109C22×Dic83D812yes—
110C22×Dic83SD1612yes—
111C22×Dic83SD1612yes—
112C22×Dic83Q1612yes—
113C2×C83⋊C8—22no—
114C2×C83⋊C8—22no—
115C2×C83⋊C8—22no—
116C2×C83⋊C8—41no—
117C2×C83⋊C8—41no—
118C2×C83⋊C8—41no—
119C2×C83⋊C8—41no—
120C4⋊Dic83—22no—
121C4⋊Dic83—22no—
122C4⋊Dic83—22no—
123C4⋊Dic83—22no—
124C4⋊Dic83—41no—
125C4⋊Dic83—41no—
126C4⋊Dic83—41no—
127C4⋊Dic83—41no—
128Dic83⋊C4—48no—
129Dic83⋊C4—48no—
130C4×Dic83—22no—
131C4×Dic83—22no—
132C4×Dic83—22no—
133C4×Dic83—22no—
134C24×C83C2×D411yescharacteristic
135C22×C4×C83—22no—
136C22×C4×C83—22no—
137C22×C4×C83—41no—
138C22×C4×C83—41no—
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×C83C2×D411yescharacteristic
151C22×C4×C83C2×D411yescharacteristic
152C22×C4×C83C2×D411yescharacteristic
153C22×C4×C83C2×Q811yescharacteristic
154C22×C4×C83C2×Q811yescharacteristic
155C22×C4×C83#4111yescharacteristic
156C22×C4×C83#4111yescharacteristic
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—41no—
175C4⋊C4×C83—41no—
176C4⋊C4×C83—41no—
177C4⋊C4×C83—41no—
178C23×C83C2×C22⋊C411yescharacteristic
179C23×C83#12111yescharacteristic
180C23×C83#12111yescharacteristic
181C23×C83#12311yescharacteristic
182C23×C83#12311yescharacteristic
183C23×C83#12411yescharacteristic
184C23×C83C4⋊Q811yescharacteristic
185C23×C83C2×D811yescharacteristic
186C23×C83C2×SD1611yescharacteristic
187C23×C83C2×SD1611yescharacteristic
188C23×C83C2×Q1611yescharacteristic
189C23×C83AGL(1,ℤ/8)11yescharacteristic
190C23×C83AGL(1,ℤ/8)11yescharacteristic
191C23×C83#13711yescharacteristic
192C23×C83#13711yescharacteristic
193C2×C4×C83—42no—
194C2×C4×C83—42no—
195C2×C4×C83—42no—
196C2×C4×C83—42no—
197C2×C4×C83—42no—
198C2×C4×C83—42no—
199C2×C4×C83—81no—
200C2×C4×C83—81no—
201C2×C4×C83—81no—
202C2×C4×C83—81no—
203C2×C4×C83—81no—
204C2×C4×C83—81no—
205C2×C4×C83—81no—
206C2×C4×C83—81no—
207C2×C4×C83#11711yescharacteristic
208C2×C4×C83#11711yescharacteristic
209C2×C4×C83C4×D411yescharacteristic
210C2×C4×C83C4×D411yescharacteristic
211C2×C4×C83C4×Q811yescharacteristic
212C2×C4×C83C4×Q811yescharacteristic
213C2×C4×C83C22⋊Q811yescharacteristic
214C2×C4×C83C22⋊Q811yescharacteristic
215C2×C4×C83C22⋊Q811yescharacteristic
216C2×C4×C83C22⋊Q811yescharacteristic
217C2×C4×C83C22⋊Q811yescharacteristic
218C2×C4×C83C22⋊Q811yescharacteristic
219C2×C4×C83#12311yescharacteristic
220C2×C4×C83#12311yescharacteristic
221C2×C4×C83#12311yescharacteristic
222C2×C4×C83#12311yescharacteristic
223C2×C4×C83#12311yescharacteristic
224C2×C4×C83#12311yescharacteristic
225C2×C4×C83#12411yescharacteristic
226C2×C4×C83#12511yescharacteristic
227C2×C4×C83#12511yescharacteristic
228C2×C4×C83#12511yescharacteristic
229C2×C4×C83#12511yescharacteristic
230C2×C4×C83#12611yescharacteristic
231C2×C4×C83#12611yescharacteristic
232C2×C4×C83#12611yescharacteristic
233C2×C4×C83#12611yescharacteristic
234C2×C4×C83#12711yescharacteristic
235C2×Dic83—22no—
236C2×Dic83—22no—
237C2×Dic83—22no—
238C2×Dic83—22no—
239C2×Dic83—22no—
240C2×Dic83—22no—
241C2×Dic83—22no—
242C2×Dic83—22no—
243C2×Dic83—22no—
244C2×Dic83—22no—
245C2×Dic83—22no—
246C2×Dic83—22no—
247C2×Dic83—42no—
248C2×Dic83—42no—
249C2×Dic83—42no—
250C2×Dic83—42no—
251C2×Dic83—42no—
252C2×Dic83—42no—
253C2×Dic83—81no—
254C2×Dic83—81no—
255C2×Dic83—81no—
256C2×Dic83—81no—
257C2×Dic83—81no—
258C2×Dic83—81no—
259C2×Dic83—81no—
260C2×Dic83—81no—
261C2×Dic83#10214yes—
262C2×Dic83#10314yes—
263C8×C83—42no—
264C83⋊C8—42no—
265C22×C83#38111yescharacteristic
266C22×C83#39011yescharacteristic
267C22×C83#39111yescharacteristic
268C22×C83#39711yescharacteristic
269C22×C83#39711yescharacteristic
270C22×C83#39811yescharacteristic
271C22×C83#39811yescharacteristic
272C22×C83C2×#10211yescharacteristic
273C22×C83C2×#10311yescharacteristic
274C22×C83#41811yescharacteristic
275C22×C83#41911yescharacteristic
276C22×C83#45911yescharacteristic
277C22×C83#45911yescharacteristic
278C22×C83#46011yescharacteristic
279C22×C83#46011yescharacteristic
280C22×C83#46111yescharacteristic
281C22×C83#46111yescharacteristic
282C22×C83#46211yescharacteristic
283C22×C83#46211yescharacteristic
284C22×C83#48011yescharacteristic
285C22×C83#48011yescharacteristic
286C22×C83#48111yescharacteristic
287C22×C83#48111yescharacteristic
288C22×C83#48311yescharacteristic
289C22×C83#48311yescharacteristic
290C22×C83#48411yescharacteristic
291C22×C83#48411yescharacteristic
292C22×C83#48611yescharacteristic
293C22×C83#48711yescharacteristic
294C22×C83#48911yescharacteristic
295C22×C83#48911yescharacteristic
296C22×C83#49811yescharacteristic
297C22×C83#50011yescharacteristic
298C22×C83#50111yescharacteristic
299C22×C83#50111yescharacteristic
300C4×C83—82no—
301C4×C83—82no—
302C4×C83#38711yescharacteristic
303C4×C83#38711yescharacteristic
304C4×C83#38711yescharacteristic
305C4×C83#38711yescharacteristic
306C4×C83#39911yescharacteristic
307C4×C83#39911yescharacteristic
308C4×C83#40011yescharacteristic
309C4×C83#40011yescharacteristic
310Dic83—24no—
311Dic83—24no—
312Dic83—82no—
313Dic83—82no—
314#11357—831nomaximal, Sylow
315C2×C83#144511yescharacteristic
316C2×C83#182311yescharacteristic
317C2×C83#182411yescharacteristic
318C2×C83#198111yescharacteristic
319C2×C83#198211yescharacteristic
320C2×C83#199011yescharacteristic
321C2×C83#199311yescharacteristic
322C2×C83#207111yescharacteristic
323C2×C83#207111yescharacteristic
324C2×C83#207211yescharacteristic
325C2×C83#207211yescharacteristic
326C2×C83#208311yescharacteristic
327C2×C83#208311yescharacteristic
328C2×C83#208411yescharacteristic
329C2×C83#208411yescharacteristic
330C2×#384—831no—
331C2×#340—831no—
332C2×#340—831no—
333C2×#340—831no—
334C2×#340D8311yescharacteristic
335C2×#336—831no—
336C4⋊#95—831no—
337C83#1135711yescharacteristic, complemented, Sylow
338C23×C8—831no—
339C23×C8C2×D8311yescharacteristic
340C22×C4⋊C4—831no—
341C22×C4⋊C4—831no—
342C22×C4⋊C4—1661no—
343C22×C4⋊C4—1661no—
344C22×C4⋊C4C2×D8311yescharacteristic
345C22×C4⋊C4C2×D8311yescharacteristic
346C22×C42—831no—
347#384—834no—
348#384—1662no—
349C2×#95—1661no—
350C2×#95—1661no—
351#340—22no—
352#340—1662no—
353#340—1662no—
354#340—1662no—
355#336—1662no—
356C23×C4—21no—
357C23×C4—21no—
358C23×C4—831no—
359C23×C4—831no—
360C23×C4—1661no—
361C23×C4—1661no—
362C23×C4C22×D8311yescharacteristic
363C22×C8—21no—
364C22×C8—21no—
365C22×C8—21no—
366C22×C8—21no—
367C22×C8—21no—
368C22×C8—21no—
369C22×C8—832no—
370C22×C8—1661no—
371C22×C8—1661no—
372C22×C8—1661no—
373C22×C8—1661no—
374C22×C8—1661no—
375C22×C8—1661no—
376C22×C8Dic16612yes—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
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—3322no—
388C2×C4⋊C4—3322no—
389C2×C4⋊C4—3322no—
390C2×C4⋊C4—3322no—
391C2×C4⋊C4—832no—
392C2×C4⋊C4—832no—
393C2×C4⋊C4—1664no—
394C2×C4⋊C4—1664no—
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×C4⋊C4—1661no—
404C2×C4⋊C4—1661no—
405C2×C4⋊C4C4×D8312yes—
406C2×C4⋊C4C22⋊D8312yes—
407C2×C42—832no—
408C2×C42—832no—
409C2×C42—1661no—
410C2×C42—1661no—
411C2×C42—1661no—
412C2×C42—1661no—
413#95—3322no—
414#95—3322no—
415C24D4×D8311yescharacteristic
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—41no—
419C22×C4—41no—
420C22×C4—41no—
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—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—832no—
443C22×C4—832no—
444C22×C4—832no—
445C22×C4—832no—
446C22×C4—832no—
447C22×C4—832no—
448C22×C4—1662no—
449C22×C4—1662no—
450C22×C4—1661no—
451C22×C4—1661no—
452C22×C4—1661no—
453C22×C4—1661no—
454C22×C4—1661no—
455C22×C4—1661no—
456C22×C4—1661no—
457C22×C4—1661no—
458C22×C4C2×C4×D8311yescharacteristic
459C22×C4D4×D8311yescharacteristic
460C22×C4D4×D8311yescharacteristic
461C22×C4C2×C22⋊D8311yescharacteristic
462C22×C4Q8×D8311yescharacteristic
463C22×C4C2×Dic16611yescharacteristic
464C22×C4#1305058911yescharacteristic
465C22×C4#1305058911yescharacteristic
466C22×C4#1305058911yescharacteristic
467C22×C4#1305059011yescharacteristic
468C22×C4#1305059011yescharacteristic
469C22×C4#1305059011yescharacteristic
470C22×C4#1305059011yescharacteristic
471C22×C4#1305059111yescharacteristic
472C2×C8—22no—
473C2×C8—22no—
474C2×C8—22no—
475C2×C8—41no—
476C2×C8—41no—
477C2×C8—41no—
478C2×C8—41no—
479C2×C8—3321no—
480C2×C8—3321no—
481C2×C8—3321no—
482C2×C8—3321no—
483C2×C8—1662no—
484C2×C8—1662no—
485C2×C8—1662no—
486C4⋊C4—22no—
487C4⋊C4—22no—
488C4⋊C4—22no—
489C4⋊C4—22no—
490C4⋊C4—41no—
491C4⋊C4—41no—
492C4⋊C4—41no—
493C4⋊C4—41no—
494C4⋊C4—3328no—
495C4⋊C4—3328no—
496C4⋊C4—3321no—
497C4⋊C4—3321no—
498C4⋊C4—3321no—
499C4⋊C4—3321no—
500C4⋊C4—1662no—
501C4⋊C4—1662no—
502C4⋊C4—1662no—
503C4⋊C4—1662no—
504C42—1662no—
505C42—1662no—
506C42—1662no—
507C42—1662no—
508C23C22⋊C4×D8311yescharacteristic
509C23#1458176411yescharacteristic
510C23#1458176511yescharacteristic
511C23#1458177411yescharacteristic
512C23#1458177711yescharacteristic
513C23#1458177811yescharacteristic
514C23#1458179111yescharacteristic
515C23D8×D8311yescharacteristic
516C23SD16×D8311yescharacteristic
517C23SD16×D8311yescharacteristic
518C23Q16×D8311yescharacteristic
519C23#1458181611yescharacteristic
520C23#1458181911yescharacteristic
521C23#1458182111yescharacteristic
522C23#1458182411yescharacteristic
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—81no—
530C2×C4—81no—
531C2×C4—81no—
532C2×C4—81no—
533C2×C4—81no—
534C2×C4—81no—
535C2×C4—81no—
536C2×C4—81no—
537C2×C4—3322no—
538C2×C4—3322no—
539C2×C4—3322no—
540C2×C4—3322no—
541C2×C4—3322no—
542C2×C4—3322no—
543C2×C4—834no—
544C2×C4—834no—
545C2×C4—6641no—
546C2×C4—6641no—
547C2×C4—6641no—
548C2×C4—6641no—
549C2×C4—6641no—
550C2×C4—6641no—
551C2×C4—6641no—
552C2×C4—6641no—
553C2×C4—1662no—
554C2×C4—1662no—
555C2×C4—1662no—
556C2×C4—1662no—
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×C4#1458174911yescharacteristic
566C2×C4#1458175011yescharacteristic
567C2×C4(C22⋊D83)⋊C411yescharacteristic
568C2×C4C4×C22⋊D8311yescharacteristic
569C2×C4#1458175711yescharacteristic
570C2×C4C4×Dic16611yescharacteristic
571C2×C4#1458176811yescharacteristic
572C2×C4#1458176911yescharacteristic
573C2×C4#1458176911yescharacteristic
574C2×C4#1458177011yescharacteristic
575C2×C4#1458177011yescharacteristic
576C2×C4#1458177111yescharacteristic
577C2×C4#1458177311yescharacteristic
578C2×C4#1458177411yescharacteristic
579C2×C4#1458177411yescharacteristic
580C2×C4#1458177511yescharacteristic
581C2×C4#1458177711yescharacteristic
582C2×C4#1458177711yescharacteristic
583C2×C4#1458177811yescharacteristic
584C2×C4#1458178211yescharacteristic
585C2×C4#1458178211yescharacteristic
586C2×C4#1458178311yescharacteristic
587C2×C4#1458178411yescharacteristic
588C2×C4#1458178511yescharacteristic
589C2×C4#1458178511yescharacteristic
590C2×C4#1458178611yescharacteristic
591C2×C4#1458178711yescharacteristic
592C2×C4#1458178811yescharacteristic
593C8—42no—
594C8—3322no—
595C22#1912756311yescharacteristic
596C22#1912760111yescharacteristic
597C22#1912760511yescharacteristic
598C22#1912762911yescharacteristic
599C22#1912763011yescharacteristic
600C22#1912763411yescharacteristic
601C22#1912763511yescharacteristic
602C22#102×D8311yescharacteristic
603C22#103×D8311yescharacteristic
604C22#1912770411yescharacteristic
605C22#1912770811yescharacteristic
606C22#1912789411yescharacteristic
607C22#1912789511yescharacteristic
608C22#1912789911yescharacteristic
609C22#1912790011yescharacteristic
610C22#1912790411yescharacteristic
611C22#1912790511yescharacteristic
612C22#1912790911yescharacteristic
613C22#1912791011yescharacteristic
614C22#1912801311yescharacteristic
615C22#1912801611yescharacteristic
616C22#1912801811yescharacteristic
617C22#1912802111yescharacteristic
618C22#1912803011yescharacteristic
619C22#1912803311yescharacteristic
620C22#1912803511yescharacteristic
621C22#1912803811yescharacteristic
622C22#1912804611yescharacteristic
623C22#1912805011yescharacteristic
624C22#1912805911yescharacteristic
625C22#1912806211yescharacteristic
626C22#1912809811yescharacteristic
627C22#1912810511yescharacteristic
628C22#1912810811yescharacteristic
629C22#1912810911yescharacteristic
630C4—82no—
631C4—82no—
632C4—6642no—
633C4—6642no—
634C4—1664no—
635C4—1664no—
636C4#1912758211yescharacteristic
637C4#1912758311yescharacteristic
638C4#1912758511yescharacteristic
639C4#1912758811yescharacteristic
640C4#1912763611yescharacteristic
641C4#1912763711yescharacteristic
642C4#1912764211yescharacteristic
643C4#1912764311yescharacteristic
644C2#2490572911yescharacteristic
645C2#2490754811yescharacteristic
646C2#2490755211yescharacteristic
647C2#2490838411yescharacteristic
648C2#2490838811yescharacteristic
649C2#2490842211yescharacteristic
650C2#2490843411yescharacteristic
651C2#2490886911yescharacteristic
652C2#2490887011yescharacteristic
653C2#2490887411yescharacteristic
654C2#2490887511yescharacteristic
655C2#2490893711yescharacteristic
656C2#2490893811yescharacteristic
657C2#2490894211yescharacteristic
658C2#2490894311yescharacteristic
subgroupG/H
centerC24D4×D83
commutatorC22×C4×C83C22×C4
FrattiniC23×C4C22×D83
FittingC2×#340×C83C2
socle, prime radicalC24×C83C2×D4
cosocleC23×C4×C83C23
hypercenterC2×#340D83
hypocenterC83#11357
LCSG ▷ C22×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. #19127570C4semidirect
337. C83#11357semidirect

Maximal subgroups

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

subgroupindex
C2×#191275702
C2×#191274642
C2×#191274632
C2×#191274552
#249056922
C2×#340×C832
#1135783