Finite Group Databasebeta

← #35328131

Subgroups — #35328131

Order 21248.

1530 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19127597C211yesmaximal, characteristic
2C2×#19127597C211yesmaximal, characteristic
3C2×C4×Dic83⋊C4C211yesmaximal, characteristic
4C2×C4×C4⋊Dic83C211yesmaximal, characteristic
5#24905726C212yesmaximal
6#24905713C212yesmaximal
7#24905698C212yesmaximal
8#24905692C211yesmaximal, characteristic
9#24905692C211yesmaximal, characteristic
10Dic83⋊#95C212yesmaximal
11C2×#389×C83C211yesmaximal, characteristic
12C22×C4⋊Dic83C2211yescharacteristic
13C22×C4⋊Dic83C2211yescharacteristic
14C22×Dic83⋊C4C2211yescharacteristic
15C22×Dic83⋊C4C2212yes—
16C22×Dic83⋊C4C2211yescharacteristic
17C22×Dic83⋊C4C2212yes—
18C22×C4×Dic83C2211yescharacteristic
19C22×C4×Dic83C2212yes—
20C22×C4×Dic83C2211yescharacteristic
21#19127597—24no—
22#19127597C418yescomplemented
23C4×Dic83⋊C4—24no—
24C4×C4⋊Dic83—24no—
25C2×C83⋊#95C2212yes—
26C2×C83⋊#95C2211yescharacteristic
27C2×C83⋊#95C2212yes—
28C2×C83⋊#95C2212yes—
29C2×C83⋊#95C2211yescharacteristic
30C2×C83⋊#95C2212yes—
31C2×C83⋊#95C2212yes—
32C2×C83⋊#95C2212yes—
33C2×C83⋊#95C2212yes—
34C22×C4⋊C4×C83C2211yescharacteristic
35C22×C4⋊C4×C83C2211yescharacteristic
36C22×C4⋊C4×C83C2212yes—
37C22×C42×C83C2211yescharacteristic
38#389×C83—24no—
39C2×#95×C83C2212yes—
40C23×Dic83C2311yescharacteristic
41C23×Dic83C2311yescharacteristic
42C23×Dic83C2312yes—
43C23×Dic83C2311yescharacteristic
44C23×Dic83C2312yes—
45C23×Dic83C2311yescharacteristic
46C2×C4⋊Dic83—22no—
47C2×C4⋊Dic83—22no—
48C2×C4⋊Dic83C2×C414yes—
49C2×C4⋊Dic83D414yes—
50C2×C4⋊Dic83Q814yes—
51C2×C4⋊Dic83Q814yes—
52C2×Dic83⋊C4—22no—
53C2×Dic83⋊C4—22no—
54C2×Dic83⋊C4—24no—
55C2×Dic83⋊C4—24no—
56C2×Dic83⋊C4—22no—
57C2×Dic83⋊C4—22no—
58C2×Dic83⋊C4—22no—
59C2×Dic83⋊C4—42no—
60C2×Dic83⋊C4—42no—
61C2×Dic83⋊C4—42no—
62C2×Dic83⋊C4C2×C418yes—
63C2×Dic83⋊C4Q814yes—
64C2×C4×Dic83—24no—
65C2×C4×Dic83—22no—
66C2×C4×Dic83—22no—
67C2×C4×Dic83—22no—
68C2×C4×Dic83—22no—
69C2×C4×Dic83—22no—
70C2×C4×Dic83—24no—
71C2×C4×Dic83—42no—
72C2×C4×Dic83C2×C414yes—
73C83⋊#95—24no—
74C83⋊#95—24no—
75C83⋊#95—24no—
76C83⋊#95—22no—
77C83⋊#95—22no—
78C83⋊#95—42no—
79C83⋊#95—42no—
80C83⋊#95—42no—
81C83⋊#95C2×C418yes—
82C23×C4×C83C2312yes—
83C23×C4×C83C2312yes—
84C23×C4×C83C2311yescharacteristic
85C23×C4×C83C2311yescharacteristic
86C23×C4×C83C2311yescharacteristic
87C2×C4⋊C4×C83—22no—
88C2×C4⋊C4×C83—22no—
89C2×C4⋊C4×C83—22no—
90C2×C4⋊C4×C83—24no—
91C2×C4⋊C4×C83—22no—
92C2×C4⋊C4×C83—22no—
93C2×C4⋊C4×C83—42no—
94C2×C4⋊C4×C83—42no—
95C2×C4⋊C4×C83C2×C414yes—
96C2×C42×C83—22no—
97C2×C42×C83—22no—
98C2×C42×C83D414yes—
99#95×C83—24no—
100C22×Dic83—21no—
101C22×Dic83—21no—
102C22×Dic83—22no—
103C22×Dic83—21no—
104C22×Dic83—22no—
105C22×Dic83—21no—
106C22×Dic83—22no—
107C22×Dic83—22no—
108C22×Dic83—21no—
109C22×Dic83—21no—
110C22×Dic83—21no—
111C22×Dic83—21no—
112C22×Dic83—22no—
113C22×Dic83—21no—
114C22×Dic83—22no—
115C22×Dic83—21no—
116C22×Dic83—21no—
117C22×Dic83—21no—
118C22×Dic83—22no—
119C22×Dic83—21no—
120C22×Dic83—21no—
121C22×Dic83—22no—
122C22×Dic83—21no—
123C22×Dic83—21no—
124C22×Dic83—22no—
125C22×Dic83—21no—
126C22×Dic83—22no—
127C22×Dic83—21no—
128C22×Dic83—21no—
129C22×Dic83—21no—
130C22×Dic83—21no—
131C22×Dic83—21no—
132C22×Dic83C22×C412yes—
133C22×Dic83C22×C414yes—
134C22×Dic83C22×C412yes—
135C22×Dic83C2×D414yes—
136C22×Dic83C2×Q812yes—
137C22×Dic83C2×Q814yes—
138C22×Dic83C2×Q814yes—
139C22×Dic83C2×Q812yes—
140C22×Dic83#4112yes—
141C22×Dic83#4112yes—
142C4⋊Dic83—28no—
143C4⋊Dic83C4⋊C4116yescomplemented
144Dic83⋊C4—28no—
145Dic83⋊C4—28no—
146Dic83⋊C4—48no—
147Dic83⋊C4—48no—
148C4×Dic83—28no—
149C4×Dic83—48no—
150C4×Dic83—44no—
151C24×C83C2411yescharacteristic
152C22×C4×C83—21no—
153C22×C4×C83—21no—
154C22×C4×C83—21no—
155C22×C4×C83—21no—
156C22×C4×C83—22no—
157C22×C4×C83—21no—
158C22×C4×C83—21no—
159C22×C4×C83—22no—
160C22×C4×C83—21no—
161C22×C4×C83—21no—
162C22×C4×C83—21no—
163C22×C4×C83—21no—
164C22×C4×C83—22no—
165C22×C4×C83—22no—
166C22×C4×C83—22no—
167C22×C4×C83—22no—
168C22×C4×C83—22no—
169C22×C4×C83—22no—
170C22×C4×C83—22no—
171C22×C4×C83—22no—
172C22×C4×C83—22no—
173C22×C4×C83—22no—
174C22×C4×C83—22no—
175C22×C4×C83C22×C414yes—
176C22×C4×C83C22×C412yes—
177C22×C4×C83C2×D412yes—
178C22×C4×C83C2×D412yes—
179C22×C4×C83C2×D412yes—
180C22×C4×C83C2×D412yes—
181C22×C4×C83C2×Q812yes—
182C22×C4×C83C2×Q812yes—
183C22×C4×C83C2×Q812yes—
184C22×C4×C83#4112yes—
185C22×C4×C83#4112yes—
186C22×C4×C83#4112yes—
187C4⋊C4×C83—28no—
188C4⋊C4×C83—48no—
189C4⋊C4×C83—44no—
190C42×C83—28no—
191C23×C83C23×C411yescharacteristic
192C23×C83C22×D411yescharacteristic
193C23×C83C22×D411yescharacteristic
194C23×C83C22×Q811yescharacteristic
195C23×C83C22×Q811yescharacteristic
196C23×C83C22×Q811yescharacteristic
197C23×C83C2×#4111yescharacteristic
198C23×C83C2×#4111yescharacteristic
199C23×C83C2×#4111yescharacteristic
200C23×C83C2×#4111yescharacteristic
201C23×C83C2×#4111yescharacteristic
202C23×C83H(5,𝔽2)11yescharacteristic
203C23×C83H(5,𝔽2)11yescharacteristic
204C23×C83H(5,𝔽2)11yescharacteristic
205C23×C832−1+411yescharacteristic
206C2×C4×C83—22no—
207C2×C4×C83—22no—
208C2×C4×C83—22no—
209C2×C4×C83—22no—
210C2×C4×C83—22no—
211C2×C4×C83—22no—
212C2×C4×C83—24no—
213C2×C4×C83—24no—
214C2×C4×C83—24no—
215C2×C4×C83—22no—
216C2×C4×C83—22no—
217C2×C4×C83—22no—
218C2×C4×C83—42no—
219C2×C4×C83—42no—
220C2×C4×C83—42no—
221C2×C4×C83—42no—
222C2×C4×C83—41no—
223C2×C4×C83—41no—
224C2×C4×C83—41no—
225C2×C4×C83—41no—
226C2×C4×C83—42no—
227C2×C4×C83—42no—
228C2×C4×C83—42no—
229C2×C4×C83—42no—
230C2×C4×C83—42no—
231C2×C4×C83—42no—
232C2×C4×C83—42no—
233C2×C4×C83C2×C4⋊C414yes—
234C2×C4×C83C4×D414yes—
235C2×C4×C83C4×Q814yes—
236C2×C4×C83#12114yes—
237C2×C4×C83C22⋊Q814yes—
238C2×C4×C83C22⋊Q814yes—
239C2×C4×C83#12514yes—
240C2×C4×C83C4⋊Q814yes—
241C2×Dic83—22no—
242C2×Dic83—24no—
243C2×Dic83—22no—
244C2×Dic83—24no—
245C2×Dic83—22no—
246C2×Dic83—22no—
247C2×Dic83—22no—
248C2×Dic83—22no—
249C2×Dic83—24no—
250C2×Dic83—24no—
251C2×Dic83—24no—
252C2×Dic83—24no—
253C2×Dic83—22no—
254C2×Dic83—22no—
255C2×Dic83—22no—
256C2×Dic83—22no—
257C2×Dic83—24no—
258C2×Dic83—22no—
259C2×Dic83—22no—
260C2×Dic83—22no—
261C2×Dic83—22no—
262C2×Dic83—24no—
263C2×Dic83—22no—
264C2×Dic83—24no—
265C2×Dic83—41no—
266C2×Dic83—41no—
267C2×Dic83—42no—
268C2×Dic83—41no—
269C2×Dic83—41no—
270C2×Dic83—41no—
271C2×Dic83—41no—
272C2×Dic83—41no—
273C2×Dic83—42no—
274C2×Dic83—41no—
275C2×Dic83—42no—
276C2×Dic83—41no—
277C2×Dic83—41no—
278C2×Dic83—42no—
279C2×Dic83—41no—
280C2×Dic83—41no—
281C2×Dic83C2×C4⋊C418yes—
282C2×Dic83C4×Q814yes—
283C22×C83C22×C4⋊C411yescharacteristic
284C22×C83C2×C4×D411yescharacteristic
285C22×C83C2×C4×Q811yescharacteristic
286C22×C83C2×C4×Q811yescharacteristic
287C22×C83C4×#4111yescharacteristic
288C22×C83#51811yescharacteristic
289C22×C83#52011yescharacteristic
290C22×C83C2×#12111yescharacteristic
291C22×C83C2×C22⋊Q811yescharacteristic
292C22×C83C2×C22⋊Q811yescharacteristic
293C22×C83#52511yescharacteristic
294C22×C83C2×#12511yescharacteristic
295C22×C83#52911yescharacteristic
296C22×C83C2×C4⋊Q811yescharacteristic
297C22×C83#53311yescharacteristic
298C22×C83#53511yescharacteristic
299C22×C83#53711yescharacteristic
300C22×C83#54011yescharacteristic
301C22×C83#54211yescharacteristic
302C22×C83#54611yescharacteristic
303C22×C83#54611yescharacteristic
304C22×C83D4×Q811yescharacteristic
305C22×C83#55011yescharacteristic
306C22×C83#55211yescharacteristic
307C22×C83#55311yescharacteristic
308C22×C83#55411yescharacteristic
309C22×C83#55411yescharacteristic
310C22×C83#55411yescharacteristic
311C22×C83#55411yescharacteristic
312C22×C83#55411yescharacteristic
313C22×C83#55511yescharacteristic
314C22×C83#55711yescharacteristic
315C22×C83#55711yescharacteristic
316C22×C83Q8211yescharacteristic
317C22×C83Q8211yescharacteristic
318C4×C83—24no—
319C4×C83—44no—
320C4×C83—42no—
321C4×C83—82no—
322C4×C83#38918yes—
323Dic83—28no—
324Dic83—24no—
325Dic83—42no—
326Dic83—42no—
327Dic83—42no—
328Dic83—44no—
329#14045—831nomaximal, Sylow
330C2×C83C2×#38911yescharacteristic
331C2×C83C4×C22⋊Q811yescharacteristic
332C2×C83#232411yescharacteristic
333C2×C83#234911yescharacteristic
334C2×C83Q8×C4⋊C411yescharacteristic
335C2×C83#236911yescharacteristic
336C2×C83#237011yescharacteristic
337C2×C83#241411yescharacteristic
338C2×C83#241711yescharacteristic
339C2×C83#245111yescharacteristic
340C2×C83#245411yescharacteristic
341C2×C83#250711yescharacteristic
342C2×C83#250811yescharacteristic
343C2×C83#256711yescharacteristic
344C2×C83#258411yescharacteristic
345C2×#389—831no—
346C2×#389—831no—
347C2×#389D8311yescharacteristic
348C2×C4×C4⋊C4—831no—
349C2×C4×C4⋊C4—831no—
350#1444—832no—
351#1441—832no—
352#1436—832no—
353C4⋊#95—832no—
354C4⋊#95—831no—
355C4⋊#95—831no—
356C83#1404511yescharacteristic, complemented, Sylow
357C22×C4⋊C4—832no—
358C22×C4⋊C4—832no—
359C22×C4⋊C4—831no—
360C22×C4⋊C4—831no—
361C22×C4⋊C4—831no—
362C22×C4⋊C4—831no—
363C22×C4⋊C4C2×D8311yescharacteristic
364C22×C4⋊C4C2×D8311yescharacteristic
365C22×C4⋊C4C2×D8312yes—
366C22×C42—832no—
367C22×C42—831no—
368C22×C42—831no—
369C22×C42C2×D8311yescharacteristic
370#389—24no—
371#389—838no—
372#389—1664no—
373C4×C4⋊C4—1664no—
374C4×C4⋊C4—1664no—
375C2×#95—832no—
376C2×#95—832no—
377C2×#95—832no—
378C2×#95—832no—
379C2×#95—831no—
380C2×#95—832no—
381C2×#95—832no—
382C2×#95—831no—
383C2×#95—832no—
384C2×#95C2×D8312yes—
385C23×C4—832no—
386C23×C4—831no—
387C23×C4—831no—
388C23×C4—831no—
389C23×C4—831no—
390C23×C4—832no—
391C23×C4C22×D8312yes—
392C23×C4C22×D8312yes—
393C23×C4C22×D8311yescharacteristic
394C23×C4C22×D8311yescharacteristic
395C23×C4C22×D8311yescharacteristic
396C2×C4⋊C4—22no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—24no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—42no—
403C2×C4⋊C4—42no—
404C2×C4⋊C4—3322no—
405C2×C4⋊C4—3322no—
406C2×C4⋊C4—3322no—
407C2×C4⋊C4—838no—
408C2×C4⋊C4—834no—
409C2×C4⋊C4—834no—
410C2×C4⋊C4—834no—
411C2×C4⋊C4—834no—
412C2×C4⋊C4—834no—
413C2×C4⋊C4—1664no—
414C2×C4⋊C4—1664no—
415C2×C4⋊C4—1662no—
416C2×C4⋊C4—1662no—
417C2×C4⋊C4—1662no—
418C2×C4⋊C4—1662no—
419C2×C4⋊C4—1662no—
420C2×C4⋊C4—1662no—
421C2×C4⋊C4—1662no—
422C2×C4⋊C4C4×D8314yes—
423C2×C42—22no—
424C2×C42—22no—
425C2×C42—3322no—
426C2×C42—834no—
427C2×C42—1664no—
428C2×C42—1662no—
429C2×C42—1662no—
430C2×C42—1662no—
431C2×C42—1664no—
432C2×C42—1662no—
433C2×C42—1662no—
434C2×C42C22⋊D8314yes—
435#95—24no—
436#95—3322no—
437#95—3322no—
438#95—3322no—
439#95—838no—
440#95—1664no—
441#95—1664no—
442#95—1664no—
443#95—1662no—
444#95—1662no—
445C24C23×D8311yescharacteristic
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—22no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—832no—
470C22×C4—834no—
471C22×C4—834no—
472C22×C4—834no—
473C22×C4—832no—
474C22×C4—832no—
475C22×C4—832no—
476C22×C4—832no—
477C22×C4—834no—
478C22×C4—832no—
479C22×C4—1661no—
480C22×C4—1662no—
481C22×C4—1661no—
482C22×C4—1661no—
483C22×C4—1661no—
484C22×C4—1661no—
485C22×C4—1662no—
486C22×C4—1661no—
487C22×C4—1661no—
488C22×C4—1661no—
489C22×C4—1661no—
490C22×C4—1662no—
491C22×C4—1662no—
492C22×C4—1661no—
493C22×C4—1661no—
494C22×C4—1662no—
495C22×C4—1661no—
496C22×C4—1661no—
497C22×C4—1661no—
498C22×C4—1661no—
499C22×C4—1662no—
500C22×C4—1661no—
501C22×C4—1661no—
502C22×C4—1661no—
503C22×C4—1661no—
504C22×C4—1662no—
505C22×C4—1661no—
506C22×C4—1661no—
507C22×C4—1662no—
508C22×C4—1661no—
509C22×C4—1662no—
510C22×C4—1662no—
511C22×C4C2×C4×D8314yes—
512C22×C4C2×C4×D8312yes—
513C22×C4D4×D8312yes—
514C22×C4C2×C22⋊D8312yes—
515C22×C4C2×C22⋊D8312yes—
516C22×C4C2×C22⋊D8312yes—
517C22×C4Q8×D8312yes—
518C22×C4Q8×D8312yes—
519C22×C4Q8×D8312yes—
520C22×C4#1305058912yes—
521C22×C4#1305059012yes—
522C22×C4#1305059112yes—
523C4⋊C4—28no—
524C4⋊C4—48no—
525C4⋊C4—44no—
526C4⋊C4—3328no—
527C4⋊C4—3328no—
528C4⋊C4—8316no—
529C4⋊C4—1668no—
530C4⋊C4—1668no—
531C4⋊C4—1668no—
532C42—28no—
533C42—3328no—
534C42—3324no—
535C42—1668no—
536C23C22×C4×D8311yescharacteristic
537C23C2×D4×D8311yescharacteristic
538C23C22×C22⋊D8311yescharacteristic
539C23C2×Q8×D8311yescharacteristic
540C23C2×Q8×D8311yescharacteristic
541C23C2×Q8×D8311yescharacteristic
542C23#41×D8311yescharacteristic
543C23#41×D8311yescharacteristic
544C23C2×#1305058911yescharacteristic
545C23C2×#1305059011yescharacteristic
546C23C2×#1305059111yescharacteristic
547C23#1458183711yescharacteristic
548C23#1458183711yescharacteristic
549C23#1458183811yescharacteristic
550C23#1458183911yescharacteristic
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—24no—
558C2×C4—24no—
559C2×C4—24no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—3322no—
579C2×C4—3321no—
580C2×C4—3321no—
581C2×C4—3322no—
582C2×C4—3321no—
583C2×C4—3321no—
584C2×C4—3321no—
585C2×C4—3321no—
586C2×C4—3322no—
587C2×C4—3321no—
588C2×C4—3321no—
589C2×C4—3321no—
590C2×C4—3321no—
591C2×C4—3321no—
592C2×C4—3322no—
593C2×C4—3321no—
594C2×C4—838no—
595C2×C4—834no—
596C2×C4—1662no—
597C2×C4—1662no—
598C2×C4—1662no—
599C2×C4—1664no—
600C2×C4—1662no—
601C2×C4—1664no—
602C2×C4—1662no—
603C2×C4—1662no—
604C2×C4—1662no—
605C2×C4—1662no—
606C2×C4—1664no—
607C2×C4—1662no—
608C2×C4—1664no—
609C2×C4—1664no—
610C2×C4—1664no—
611C2×C4—1664no—
612C2×C4—1662no—
613C2×C4—1664no—
614C2×C4—1662no—
615C2×C4—1664no—
616C2×C4—1662no—
617C2×C4—1662no—
618C2×C4—1662no—
619C2×C4—1662no—
620C2×C4C4⋊C4×D8314yes—
621C2×C4C4×C22⋊D8314yes—
622C2×C4#1458175714yes—
623C2×C4#1458176414yes—
624C2×C4#1458176814yes—
625C2×C4#1458177014yes—
626C2×C4#1458178214yes—
627C2×C4#1458179014yes—
628C22C2×C4⋊C4×D8311yescharacteristic
629C22C2×C4×C22⋊D8311yescharacteristic
630C22C4×Q8×D8311yescharacteristic
631C22C2×#1458175711yescharacteristic
632C22C4×#1305059111yescharacteristic
633C22#1912817311yescharacteristic
634C22#1912818011yescharacteristic
635C22C2×#1458176411yescharacteristic
636C22C2×#1458176811yescharacteristic
637C22C2×#1458177011yescharacteristic
638C22#1912820811yescharacteristic
639C22C2×#1458178211yescharacteristic
640C22#1912823811yescharacteristic
641C22C2×#1458179011yescharacteristic
642C22#1912825511yescharacteristic
643C22#1912826811yescharacteristic
644C22#1912827911yescharacteristic
645C22#1912830211yescharacteristic
646C22#1912831611yescharacteristic
647C22#1912834211yescharacteristic
648C22#1912834811yescharacteristic
649C22#1912836411yescharacteristic
650C22#1912836911yescharacteristic
651C22#1912839311yescharacteristic
652C22#1912839811yescharacteristic
653C22#1912840711yescharacteristic
654C22#1912840711yescharacteristic
655C22#1912840911yescharacteristic
656C22#1912841211yescharacteristic
657C22#1912841211yescharacteristic
658C22#1912841511yescharacteristic
659C22#1912842811yescharacteristic
660C22#1912842811yescharacteristic
661C22#1912843111yescharacteristic
662C22#1912843111yescharacteristic
663C4—24no—
664C4—42no—
665C4—44no—
666C4—82no—
667C4—3322no—
668C4—3322no—
669C4—3322no—
670C4—3324no—
671C4—1668no—
672C4—1664no—
673C4#1912759618yes—
674C2C2×#1912759611yescharacteristic
675C2C4×#1458176811yescharacteristic
676C2#2491015011yescharacteristic
677C2#2491037211yescharacteristic
678C2#2491037711yescharacteristic
679C2#2491054911yescharacteristic
680C2#2491056411yescharacteristic
681C2#2491088211yescharacteristic
682C2#2491091511yescharacteristic
683C2#2491130311yescharacteristic
684C2#2491133611yescharacteristic
685C2#2491199111yescharacteristic
686C2#2491200211yescharacteristic
687C2#2491267211yescharacteristic
688C2#2491285211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D83
commutatorC23×C83C23×C4
FittingC2×#389×C83C2
socle, prime radical, cosocleC24×C83C24
hypercenterC2×#389D83
hypocenterC83#14045
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
22. #19127597C4semidirect
143. C4⋊Dic83C4⋊C4semidirect
356. C83#14045semidirect

Maximal subgroups

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

subgroupindex
C2×#191275972
C2×C4×Dic83⋊C42
C2×C4×C4⋊Dic832
#249057262
#249057132
#249056982
#249056922
Dic83⋊#952
C2×#389×C832
#1404583