Finite Group Databasebeta

← #35327626

Subgroups — #35327626

Order 21248.

1614 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19127599C211yesmaximal, characteristic
2C2×#19127599C211yesmaximal, characteristic
3C2×#19127599C211yesmaximal, characteristic
4C2×#19127598C212yesmaximal
5C2×#19127571C211yesmaximal, characteristic
6C2×C4×C4⋊Dic83C211yesmaximal, characteristic
7#24905727C212yesmaximal
8#24905717C212yesmaximal
9#24905697C212yesmaximal
10#24905693C211yesmaximal, characteristic
11C4×#95×C83C211yesmaximal, characteristic
12C22×C4⋊Dic83C2211yescharacteristic
13C22×C4⋊Dic83C2212yes—
14C22×C4⋊Dic83C2212yes—
15C22×C4⋊Dic83C2211yescharacteristic
16C22×C4⋊Dic83C2211yescharacteristic
17C22×C4⋊Dic83C2211yescharacteristic
18C22×Dic83⋊C4C2212yes—
19C22×Dic83⋊C4C2212yes—
20C22×Dic83⋊C4C2212yes—
21C22×C4×Dic83C2212yes—
22#19127599—24no—
23#19127599—24no—
24#19127599C418yescomplemented
25#19127598—28no—
26#19127571—24no—
27C4×C4⋊Dic83—24no—
28C2×C83⋊#95C2212yes—
29C2×C83⋊#95C2212yes—
30C2×C83⋊#95C2212yes—
31C2×C83⋊#95C2212yes—
32C2×C83⋊#95C2212yes—
33C2×C83⋊#95C2212yes—
34C22×C42×C83C2211yescharacteristic
35C22×C42×C83C2211yescharacteristic
36C22×C42×C83C2211yescharacteristic
37C2×#95×C83C2211yescharacteristic
38C2×#95×C83C2211yescharacteristic
39C2×#95×C83C2211yescharacteristic
40C2×#95×C83C2211yescharacteristic
41C23×Dic83C2312yes—
42C23×Dic83C2312yes—
43C23×Dic83C2312yes—
44C23×Dic83C2312yes—
45C2×C4⋊Dic83—24no—
46C2×C4⋊Dic83—24no—
47C2×C4⋊Dic83—22no—
48C2×C4⋊Dic83—22no—
49C2×C4⋊Dic83—22no—
50C2×C4⋊Dic83—24no—
51C2×C4⋊Dic83—22no—
52C2×C4⋊Dic83—22no—
53C2×C4⋊Dic83—22no—
54C2×C4⋊Dic83—24no—
55C2×C4⋊Dic83—22no—
56C2×C4⋊Dic83—42no—
57C2×C4⋊Dic83—42no—
58C2×C4⋊Dic83C2×C414yes—
59C2×C4⋊Dic83C2×C414yes—
60C2×C4⋊Dic83D414yes—
61C2×C4⋊Dic83D414yes—
62C2×C4⋊Dic83Q814yes—
63C2×Dic83⋊C4—24no—
64C2×Dic83⋊C4—24no—
65C2×Dic83⋊C4—24no—
66C2×Dic83⋊C4—24no—
67C2×Dic83⋊C4—24no—
68C2×Dic83⋊C4—24no—
69C2×Dic83⋊C4—42no—
70C2×Dic83⋊C4—42no—
71C2×Dic83⋊C4C2×C418yes—
72C2×C4×Dic83—24no—
73C2×C4×Dic83—24no—
74C2×C4×Dic83—42no—
75C83⋊#95—24no—
76C83⋊#95—24no—
77C83⋊#95—24no—
78C83⋊#95—24no—
79C83⋊#95—42no—
80C83⋊#95C2×C418yes—
81C23×C4×C83C2311yescharacteristic
82C23×C4×C83C2311yescharacteristic
83C23×C4×C83C2311yescharacteristic
84C23×C4×C83C2311yescharacteristic
85C23×C4×C83C2311yescharacteristic
86C23×C4×C83C2311yescharacteristic
87C23×C4×C83C2311yescharacteristic
88C2×C42×C83—22no—
89C2×C42×C83—22no—
90C2×C42×C83—22no—
91C2×C42×C83—22no—
92C2×C42×C83—22no—
93C2×C42×C83—22no—
94C2×C42×C83—22no—
95C2×C42×C83C2×C414yes—
96C2×C42×C83Q814yes—
97#95×C83—22no—
98#95×C83—22no—
99#95×C83D414yes—
100#95×C83Q814yes—
101C22×Dic83—22no—
102C22×Dic83—22no—
103C22×Dic83—22no—
104C22×Dic83—22no—
105C22×Dic83—22no—
106C22×Dic83—22no—
107C22×Dic83—22no—
108C22×Dic83—22no—
109C22×Dic83—22no—
110C22×Dic83—22no—
111C22×Dic83—22no—
112C22×Dic83—22no—
113C22×Dic83—22no—
114C22×Dic83—22no—
115C22×Dic83—22no—
116C22×Dic83—22no—
117C22×Dic83—22no—
118C22×Dic83—22no—
119C22×Dic83—22no—
120C22×Dic83—22no—
121C22×Dic83—22no—
122C22×Dic83—22no—
123C22×Dic83—22no—
124C22×Dic83C22×C414yes—
125C22×Dic83C22×C414yes—
126C22×Dic83C2×D414yes—
127C22×Dic83C2×D414yes—
128C22×Dic83C2×Q814yes—
129C4⋊Dic83—28no—
130C4⋊Dic83—28no—
131C4⋊Dic83—48no—
132C4⋊Dic83—48no—
133C4⋊Dic83—44no—
134C4⋊Dic83C4⋊C4116yescomplemented
135Dic83⋊C4—216no—
136Dic83⋊C4—48no—
137Dic83⋊C4—48no—
138C4×Dic83—48no—
139C24×C83C2411yescharacteristic
140C22×C4×C83—21no—
141C22×C4×C83—21no—
142C22×C4×C83—21no—
143C22×C4×C83—21no—
144C22×C4×C83—21no—
145C22×C4×C83—21no—
146C22×C4×C83—21no—
147C22×C4×C83—21no—
148C22×C4×C83—21no—
149C22×C4×C83—21no—
150C22×C4×C83—21no—
151C22×C4×C83—21no—
152C22×C4×C83—21no—
153C22×C4×C83—21no—
154C22×C4×C83—21no—
155C22×C4×C83—21no—
156C22×C4×C83—21no—
157C22×C4×C83—21no—
158C22×C4×C83—21no—
159C22×C4×C83—21no—
160C22×C4×C83—21no—
161C22×C4×C83—21no—
162C22×C4×C83—21no—
163C22×C4×C83—21no—
164C22×C4×C83—21no—
165C22×C4×C83—21no—
166C22×C4×C83—21no—
167C22×C4×C83—21no—
168C22×C4×C83—21no—
169C22×C4×C83—21no—
170C22×C4×C83C22×C412yes—
171C22×C4×C83C22×C412yes—
172C22×C4×C83C22×C412yes—
173C22×C4×C83C2×D412yes—
174C22×C4×C83C2×D412yes—
175C22×C4×C83C2×D412yes—
176C22×C4×C83C2×D412yes—
177C22×C4×C83C2×D412yes—
178C22×C4×C83C2×Q812yes—
179C22×C4×C83C2×Q812yes—
180C22×C4×C83C2×Q812yes—
181C22×C4×C83C2×Q812yes—
182C22×C4×C83C2×Q812yes—
183C22×C4×C83C2×Q812yes—
184C22×C4×C83C2×Q812yes—
185C22×C4×C83#4112yes—
186C22×C4×C83#4112yes—
187C22×C4×C83#4112yes—
188C22×C4×C83#4112yes—
189C42×C83—28no—
190C42×C83—28no—
191C42×C83—44no—
192C23×C83C23×C411yescharacteristic
193C23×C83C22×D411yescharacteristic
194C23×C83C22×D411yescharacteristic
195C23×C83C22×D411yescharacteristic
196C23×C83C22×Q811yescharacteristic
197C23×C83C22×Q811yescharacteristic
198C23×C83C22×Q811yescharacteristic
199C23×C83C2×#4111yescharacteristic
200C23×C83C2×#4111yescharacteristic
201C23×C83C2×#4111yescharacteristic
202C23×C83C2×#4111yescharacteristic
203C23×C83H(5,𝔽2)11yescharacteristic
204C23×C83H(5,𝔽2)11yescharacteristic
205C23×C832−1+411yescharacteristic
206C23×C832−1+411yescharacteristic
207C2×C4×C83—22no—
208C2×C4×C83—22no—
209C2×C4×C83—22no—
210C2×C4×C83—22no—
211C2×C4×C83—22no—
212C2×C4×C83—22no—
213C2×C4×C83—22no—
214C2×C4×C83—22no—
215C2×C4×C83—22no—
216C2×C4×C83—22no—
217C2×C4×C83—22no—
218C2×C4×C83—22no—
219C2×C4×C83—22no—
220C2×C4×C83—22no—
221C2×C4×C83—22no—
222C2×C4×C83—22no—
223C2×C4×C83—22no—
224C2×C4×C83—22no—
225C2×C4×C83—22no—
226C2×C4×C83—22no—
227C2×C4×C83—22no—
228C2×C4×C83—22no—
229C2×C4×C83—22no—
230C2×C4×C83—22no—
231C2×C4×C83—22no—
232C2×C4×C83—22no—
233C2×C4×C83—22no—
234C2×C4×C83—41no—
235C2×C4×C83—41no—
236C2×C4×C83—41no—
237C2×C4×C83—41no—
238C2×C4×C83—41no—
239C2×C4×C83—41no—
240C2×C4×C83—41no—
241C2×C4×C83—41no—
242C2×C4×C83—41no—
243C2×C4×C83—41no—
244C2×C4×C83—41no—
245C2×C4×C83—41no—
246C2×C4×C83C2×C4⋊C414yes—
247C2×C4×C83C4×D414yes—
248C2×C4×C83C4×D414yes—
249C2×C4×C83C4×Q814yes—
250C2×C4×C83C4×Q814yes—
251C2×C4×C83#12114yes—
252C2×C4×C83C22⋊Q814yes—
253C2×C4×C83#12514yes—
254C2×C4×C83C4⋊Q814yes—
255C2×C4×C83C4⋊Q814yes—
256C2×Dic83—24no—
257C2×Dic83—24no—
258C2×Dic83—24no—
259C2×Dic83—24no—
260C2×Dic83—24no—
261C2×Dic83—24no—
262C2×Dic83—24no—
263C2×Dic83—24no—
264C2×Dic83—24no—
265C2×Dic83—24no—
266C2×Dic83—24no—
267C2×Dic83—24no—
268C2×Dic83—42no—
269C2×Dic83—42no—
270C2×Dic83—42no—
271C2×Dic83—42no—
272C2×Dic83—42no—
273C2×Dic83—42no—
274C2×Dic83—42no—
275C2×Dic83—42no—
276C2×Dic83—42no—
277C2×Dic83—42no—
278C2×Dic83—42no—
279C2×Dic83—42no—
280C2×Dic83—42no—
281C2×Dic83—42no—
282C2×Dic83—42no—
283C2×Dic83C2×C4⋊C418yes—
284C22×C83C22×C4⋊C411yescharacteristic
285C22×C83C2×C4×D411yescharacteristic
286C22×C83C2×C4×D411yescharacteristic
287C22×C83C2×C4×Q811yescharacteristic
288C22×C83C2×C4×Q811yescharacteristic
289C22×C83#52011yescharacteristic
290C22×C83#52011yescharacteristic
291C22×C83C2×#12111yescharacteristic
292C22×C83C2×C22⋊Q811yescharacteristic
293C22×C83C2×#12511yescharacteristic
294C22×C83C2×C4⋊Q811yescharacteristic
295C22×C83C2×C4⋊Q811yescharacteristic
296C22×C83#53211yescharacteristic
297C22×C83#53311yescharacteristic
298C22×C83#53311yescharacteristic
299C22×C83#54011yescharacteristic
300C22×C83#54111yescharacteristic
301C22×C83#54411yescharacteristic
302C22×C83#54411yescharacteristic
303C22×C83D4211yescharacteristic
304C22×C83D4211yescharacteristic
305C22×C83#54611yescharacteristic
306C22×C83#54711yescharacteristic
307C22×C83#54711yescharacteristic
308C22×C83#54811yescharacteristic
309C22×C83D4×Q811yescharacteristic
310C22×C83D4×Q811yescharacteristic
311C22×C83D4×Q811yescharacteristic
312C22×C83#55011yescharacteristic
313C22×C83#55211yescharacteristic
314C22×C83#55311yescharacteristic
315C22×C83#55411yescharacteristic
316C22×C83#55411yescharacteristic
317C22×C83#55711yescharacteristic
318C22×C83Q8211yescharacteristic
319C4×C83—24no—
320C4×C83—24no—
321C4×C83—24no—
322C4×C83—42no—
323C4×C83—42no—
324C4×C83—42no—
325C4×C83#38918yescomplemented
326Dic83—28no—
327Dic83—44no—
328Dic83—44no—
329Dic83—82no—
330#14005—831nomaximal, Sylow
331C2×C83C2×#38911yescharacteristic
332C2×C83C4×C4⋊Q811yescharacteristic
333C2×C83#233011yescharacteristic
334C2×C83D4×C4⋊C411yescharacteristic
335C2×C83Q8×C4⋊C411yescharacteristic
336C2×C83#236011yescharacteristic
337C2×C83#236111yescharacteristic
338C2×C83#242811yescharacteristic
339C2×C83#242911yescharacteristic
340C2×C83#244011yescharacteristic
341C2×C83#244111yescharacteristic
342C2×C83#250611yescharacteristic
343C2×C83#250711yescharacteristic
344C2×C83#255011yescharacteristic
345C2×C83#255111yescharacteristic
346C2×#389—831no—
347C2×#389—831no—
348C2×#389—831no—
349C2×#389—832no—
350C2×#384—831no—
351C2×C4×C4⋊C4—831no—
352#1444—832no—
353#1441—832no—
354#1436—832no—
355C4⋊#95—831no—
356C4×#95D8311yescharacteristic
357C83#1400511yescharacteristic, complemented, Sylow
358C22×C4⋊C4—832no—
359C22×C4⋊C4—832no—
360C22×C4⋊C4—832no—
361C22×C4⋊C4—832no—
362C22×C4⋊C4—831no—
363C22×C4⋊C4—832no—
364C22×C4⋊C4—831no—
365C22×C4⋊C4—831no—
366C22×C4⋊C4—831no—
367C22×C42—832no—
368C22×C42C2×D8311yescharacteristic
369C22×C42C2×D8311yescharacteristic
370C22×C42C2×D8311yescharacteristic
371#389—838no—
372#389—1664no—
373#389—1664no—
374#389—1668no—
375#384—1664no—
376C4×C4⋊C4—1664no—
377C2×#95—832no—
378C2×#95—832no—
379C2×#95—832no—
380C2×#95—832no—
381C2×#95—832no—
382C2×#95—832no—
383C2×#95C2×D8311yescharacteristic
384C2×#95C2×D8311yescharacteristic
385C2×#95C2×D8311yescharacteristic
386C2×#95C2×D8311yescharacteristic
387C23×C4—832no—
388C23×C4—832no—
389C23×C4—832no—
390C23×C4—832no—
391C23×C4C22×D8311yescharacteristic
392C23×C4C22×D8311yescharacteristic
393C23×C4C22×D8311yescharacteristic
394C23×C4C22×D8311yescharacteristic
395C23×C4C22×D8311yescharacteristic
396C23×C4C22×D8311yescharacteristic
397C23×C4C22×D8311yescharacteristic
398C2×C4⋊C4—3322no—
399C2×C4⋊C4—3322no—
400C2×C4⋊C4—3322no—
401C2×C4⋊C4—3322no—
402C2×C4⋊C4—834no—
403C2×C4⋊C4—834no—
404C2×C4⋊C4—834no—
405C2×C4⋊C4—838no—
406C2×C4⋊C4—834no—
407C2×C4⋊C4—834no—
408C2×C4⋊C4—1664no—
409C2×C4⋊C4—1664no—
410C2×C4⋊C4—1664no—
411C2×C4⋊C4—1664no—
412C2×C4⋊C4—1662no—
413C2×C4⋊C4—1662no—
414C2×C4⋊C4—1664no—
415C2×C4⋊C4—1664no—
416C2×C4⋊C4—1664no—
417C2×C4⋊C4—1664no—
418C2×C4⋊C4—1662no—
419C2×C4⋊C4—1662no—
420C2×C4⋊C4—1662no—
421C2×C4⋊C4—1664no—
422C2×C4⋊C4—1662no—
423C2×C4⋊C4—1664no—
424C2×C4⋊C4—1662no—
425C2×C42—22no—
426C2×C42—22no—
427C2×C42—22no—
428C2×C42—22no—
429C2×C42—22no—
430C2×C42—22no—
431C2×C42—22no—
432C2×C42—3322no—
433C2×C42—1664no—
434C2×C42—1664no—
435C2×C42Dic16614yes—
436C2×C42C4×D8314yes—
437#95—22no—
438#95—22no—
439#95—3322no—
440#95—838no—
441#95—1664no—
442#95—1664no—
443#95—1664no—
444#95—1664no—
445#95Dic16614yes—
446#95D33214yes—
447C24C23×D8311yescharacteristic
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—834no—
479C22×C4—834no—
480C22×C4—834no—
481C22×C4—834no—
482C22×C4—834no—
483C22×C4—1662no—
484C22×C4—1662no—
485C22×C4—1662no—
486C22×C4—1662no—
487C22×C4—1662no—
488C22×C4—1662no—
489C22×C4—1662no—
490C22×C4—1662no—
491C22×C4—1662no—
492C22×C4—1662no—
493C22×C4—1662no—
494C22×C4—1662no—
495C22×C4—1662no—
496C22×C4—1662no—
497C22×C4—1662no—
498C22×C4—1662no—
499C22×C4—1662no—
500C22×C4—1662no—
501C22×C4—1662no—
502C22×C4—1662no—
503C22×C4—1662no—
504C22×C4—1662no—
505C22×C4—1662no—
506C22×C4C2×C4×D8312yes—
507C22×C4C2×C4×D8312yes—
508C22×C4C2×C4×D8312yes—
509C22×C4D4×D8312yes—
510C22×C4D4×D8312yes—
511C22×C4C2×D33212yes—
512C22×C4C2×D33212yes—
513C22×C4C2×D33212yes—
514C22×C4Q8×D8312yes—
515C22×C4C2×Dic16612yes—
516C22×C4C2×Dic16612yes—
517C22×C4C2×Dic16612yes—
518C22×C4C2×Dic16612yes—
519C22×C4C2×Dic16612yes—
520C22×C4C2×Dic16612yes—
521C22×C4#1305058912yes—
522C22×C4#1305059012yes—
523C22×C4#1305059012yes—
524C22×C4#1305059012yes—
525C4⋊C4—3328no—
526C4⋊C4—3328no—
527C4⋊C4—3328no—
528C4⋊C4—3328no—
529C4⋊C4—3324no—
530C4⋊C4—8316no—
531C4⋊C4—1668no—
532C4⋊C4—1668no—
533C4⋊C4—16616no—
534C42—28no—
535C42—28no—
536C42—44no—
537C42—3328no—
538C23C22×C4×D8311yescharacteristic
539C23C2×D4×D8311yescharacteristic
540C23C2×D4×D8311yescharacteristic
541C23C22×D33211yescharacteristic
542C23C2×Q8×D8311yescharacteristic
543C23C22×Dic16611yescharacteristic
544C23C22×Dic16611yescharacteristic
545C23C2×#1305058911yescharacteristic
546C23C2×#1305059011yescharacteristic
547C23C2×#1305059011yescharacteristic
548C23C2×#1305059011yescharacteristic
549C23#1458183811yescharacteristic
550C23#1458183811yescharacteristic
551C23#1458183911yescharacteristic
552C23#1458183911yescharacteristic
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—3322no—
593C2×C4—3322no—
594C2×C4—3322no—
595C2×C4—3322no—
596C2×C4—3322no—
597C2×C4—3322no—
598C2×C4—3322no—
599C2×C4—3322no—
600C2×C4—3322no—
601C2×C4—3322no—
602C2×C4—3322no—
603C2×C4—3322no—
604C2×C4—3322no—
605C2×C4—3322no—
606C2×C4—3322no—
607C2×C4—838no—
608C2×C4—1664no—
609C2×C4—1664no—
610C2×C4—1664no—
611C2×C4—1664no—
612C2×C4—1664no—
613C2×C4—1664no—
614C2×C4—1664no—
615C2×C4—1664no—
616C2×C4—1664no—
617C2×C4—1664no—
618C2×C4—1664no—
619C2×C4—1664no—
620C2×C4C4⋊C4×D8314yes—
621C2×C4(C22⋊D83)⋊C414yes—
622C2×C4C4×D33214yes—
623C2×C4C4×Dic16614yes—
624C2×C4C4×Dic16614yes—
625C2×C4#1458176514yes—
626C2×C4#1458176914yes—
627C2×C4#1458178214yes—
628C2×C4#1458179114yes—
629C2×C4#1458179214yes—
630C22C2×C4⋊C4×D8311yescharacteristic
631C22C2×(C22⋊D83)⋊C411yescharacteristic
632C22C2×C4×D33211yescharacteristic
633C22C2×C4×Dic16611yescharacteristic
634C22C2×C4×Dic16611yescharacteristic
635C22#1912818111yescharacteristic
636C22#1912818111yescharacteristic
637C22C2×#1458176511yescharacteristic
638C22C2×#1458176911yescharacteristic
639C22C2×#1458178211yescharacteristic
640C22C2×#1458179111yescharacteristic
641C22C2×#1458179211yescharacteristic
642C22#1912825111yescharacteristic
643C22#1912825811yescharacteristic
644C22#1912825811yescharacteristic
645C22#1912830611yescharacteristic
646C22#1912831311yescharacteristic
647C22#1912832911yescharacteristic
648C22#1912832911yescharacteristic
649C22D4×D33211yescharacteristic
650C22D4×D33211yescharacteristic
651C22#1912834711yescharacteristic
652C22#1912835511yescharacteristic
653C22#1912835611yescharacteristic
654C22#1912836011yescharacteristic
655C22D4×Dic16611yescharacteristic
656C22D4×Dic16611yescharacteristic
657C22Q8×D33211yescharacteristic
658C22#1912837211yescharacteristic
659C22#1912839111yescharacteristic
660C22#1912839711yescharacteristic
661C22#1912840811yescharacteristic
662C22#1912841111yescharacteristic
663C22#1912842911yescharacteristic
664C22Q8×Dic16611yescharacteristic
665C4—24no—
666C4—24no—
667C4—24no—
668C4—42no—
669C4—42no—
670C4—42no—
671C4—3324no—
672C4—3324no—
673C4—6642no—
674C4—1668no—
675C4#1912759818yescomplemented
676C2C2×#1912759811yescharacteristic
677C2C4×#1458179211yescharacteristic
678C2#2491020411yescharacteristic
679C2C4⋊C4×D33211yescharacteristic
680C2C4⋊C4×Dic16611yescharacteristic
681C2#2491046611yescharacteristic
682C2#2491047711yescharacteristic
683C2#2491105111yescharacteristic
684C2#2491106211yescharacteristic
685C2#2491116511yescharacteristic
686C2#2491117611yescharacteristic
687C2#2491197911yescharacteristic
688C2#2491199011yescharacteristic
689C2#2491248411yescharacteristic
690C2#2491248911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D83
commutatorC23×C83C23×C4
FittingC4×#95×C83C2
socle, prime radical, cosocleC24×C83C24
hypercenterC4×#95D83
hypocenterC83#14005
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ C4×#95

Complements

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

NH ≅ G/Ntype
24. #19127599C4semidirect
134. C4⋊Dic83C4⋊C4semidirect
325. C4×C83#389semidirect
357. C83#14005semidirect
675. C4#19127598semidirect

Maximal subgroups

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

subgroupindex
C2×#191275992
C2×#191275982
C2×#191275712
C2×C4×C4⋊Dic832
#249057272
#249057172
#249056972
#249056932
C4×#95×C832
#1400583