Finite Group Databasebeta

← #35326906

Subgroups — #35326906

Order 21248.

1794 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Q8×Dic83C211yesmaximal, characteristic
2C2×#19127608C211yesmaximal, characteristic
3C2×#19127599C211yesmaximal, characteristic
4C2×#19127597C211yesmaximal, characteristic
5#24905715C212yesmaximal
6#24905715C212yesmaximal
7#24905692C211yesmaximal, characteristic
8Dic83⋊#95C212yesmaximal
9#24905689C212yesmaximal
10C4×C83⋊#95C211yesmaximal, characteristic
11C2×#391×C83C211yesmaximal, characteristic
12C2×Q8×Dic83—24no—
13C2×Q8×Dic83—24no—
14C2×Q8×Dic83C418yescomplemented
15C22×C4⋊Dic83C2211yescharacteristic
16C22×C4⋊Dic83C2212yes—
17C22×C4⋊Dic83C2211yescharacteristic
18C22×Dic83⋊C4C2212yes—
19C22×Dic83⋊C4C2212yes—
20C22×C4×Dic83C2211yescharacteristic
21C22×C4×Dic83C2211yescharacteristic
22C22×C4×Dic83C2212yes—
23#19127608—24no—
24#19127599—24no—
25#19127597—24no—
26C2×C83⋊#95C2212yes—
27C2×C83⋊#95C2212yes—
28C2×C83⋊#95C2212yes—
29C2×C83⋊#95C2212yes—
30C2×C83⋊#95C2211yescharacteristic
31C2×C83⋊#95C2211yescharacteristic
32C2×C83⋊#95C2211yescharacteristic
33C2×C83⋊#95C2212yes—
34C2×C83⋊#95C2212yes—
35C2×C83⋊#95C2211yescharacteristic
36C23×Q8×C83C2211yescharacteristic
37C22×C4⋊C4×C83C2211yescharacteristic
38C22×C42×C83C2211yescharacteristic
39#391×C83—24no—
40C2×#95×C83C2212yes—
41C2×#95×C83C2212yes—
42C23×Dic83C2312yes—
43C23×Dic83C2311yescharacteristic
44C23×Dic83C2311yescharacteristic
45C23×Dic83C2311yescharacteristic
46C23×Dic83C2312yes—
47C23×Dic83C2311yescharacteristic
48Q8×Dic83—232no—
49C2×C4⋊Dic83—24no—
50C2×C4⋊Dic83—24no—
51C2×C4⋊Dic83—22no—
52C2×C4⋊Dic83—22no—
53C2×C4⋊Dic83—22no—
54C2×C4⋊Dic83C2×C418yes—
55C2×C4⋊Dic83C2×C414yes—
56C2×C4⋊Dic83D414yes—
57C2×C4⋊Dic83D414yes—
58C2×Dic83⋊C4—24no—
59C2×Dic83⋊C4—24no—
60C2×Dic83⋊C4—24no—
61C2×Dic83⋊C4—24no—
62C2×Dic83⋊C4—42no—
63C2×Dic83⋊C4—42no—
64C2×C4×Dic83—24no—
65C2×C4×Dic83—24no—
66C2×C4×Dic83—22no—
67C2×C4×Dic83—22no—
68C2×C4×Dic83—22no—
69C2×C4×Dic83—22no—
70C2×C4×Dic83—22no—
71C2×C4×Dic83C2×C418yes—
72C2×C4×Dic83C2×C414yes—
73C83⋊#95—24no—
74C83⋊#95—24no—
75C83⋊#95—22no—
76C83⋊#95—22no—
77C83⋊#95—24no—
78C83⋊#95—24no—
79C83⋊#95—24no—
80C83⋊#95—22no—
81C83⋊#95—42no—
82C83⋊#95Q814yescomplemented
83C22×Q8×C83—22no—
84C22×Q8×C83—22no—
85C22×Q8×C83—22no—
86C22×Q8×C83—22no—
87C22×Q8×C83C2×C414yes—
88C22×Q8×C83D414yes—
89C22×Q8×C83Q814yes—
90C23×C4×C83C2312yes—
91C23×C4×C83C2311yescharacteristic
92C23×C4×C83C2311yescharacteristic
93C23×C4×C83C2312yes—
94C23×C4×C83C2311yescharacteristic
95C2×C4⋊C4×C83—22no—
96C2×C4⋊C4×C83—22no—
97C2×C4⋊C4×C83—22no—
98C2×C42×C83—22no—
99C2×C42×C83—22no—
100C2×C42×C83—22no—
101#95×C83—24no—
102#95×C83—24no—
103C22×Dic83—21no—
104C22×Dic83—21no—
105C22×Dic83—22no—
106C22×Dic83—22no—
107C22×Dic83—22no—
108C22×Dic83—21no—
109C22×Dic83—21no—
110C22×Dic83—22no—
111C22×Dic83—21no—
112C22×Dic83—21no—
113C22×Dic83—21no—
114C22×Dic83—21no—
115C22×Dic83—21no—
116C22×Dic83—21no—
117C22×Dic83—21no—
118C22×Dic83—21no—
119C22×Dic83—21no—
120C22×Dic83—21no—
121C22×Dic83—21no—
122C22×Dic83—21no—
123C22×Dic83—21no—
124C22×Dic83—21no—
125C22×Dic83—21no—
126C22×Dic83—21no—
127C22×Dic83—21no—
128C22×Dic83—21no—
129C22×Dic83—22no—
130C22×Dic83—22no—
131C22×Dic83—22no—
132C22×Dic83—22no—
133C22×Dic83—22no—
134C22×Dic83—22no—
135C22×Dic83—22no—
136C22×Dic83C22×C412yes—
137C22×Dic83C22×C414yes—
138C22×Dic83C22×C412yes—
139C22×Dic83C2×D414yes—
140C22×Dic83C2×D414yes—
141C22×Dic83C2×Q812yes—
142C22×Dic83C2×Q812yes—
143C22×Dic83#4112yes—
144C22×Dic83#4112yes—
145C4⋊Dic83—216no—
146C4⋊Dic83—44no—
147C4⋊Dic83C22⋊C4116yes—
148Dic83⋊C4—48no—
149Dic83⋊C4—48no—
150C4×Dic83—28no—
151C4×Dic83—216no—
152C4×Dic83—44no—
153C24×C83C2411yescharacteristic
154C2×Q8×C83—28no—
155C2×Q8×C83—28no—
156C2×Q8×C83—28no—
157C2×Q8×C83—28no—
158C2×Q8×C83—28no—
159C2×Q8×C83—28no—
160C2×Q8×C83C4⋊C4116yescomplemented
161C22×C4×C83—22no—
162C22×C4×C83—22no—
163C22×C4×C83—22no—
164C22×C4×C83—22no—
165C22×C4×C83—21no—
166C22×C4×C83—21no—
167C22×C4×C83—21no—
168C22×C4×C83—21no—
169C22×C4×C83—21no—
170C22×C4×C83—21no—
171C22×C4×C83—21no—
172C22×C4×C83—21no—
173C22×C4×C83—21no—
174C22×C4×C83—21no—
175C22×C4×C83—21no—
176C22×C4×C83—21no—
177C22×C4×C83—22no—
178C22×C4×C83—22no—
179C22×C4×C83—22no—
180C22×C4×C83—22no—
181C22×C4×C83—22no—
182C22×C4×C83—22no—
183C22×C4×C83—22no—
184C22×C4×C83C22×C414yes—
185C22×C4×C83C22×C412yes—
186C22×C4×C83C2×D412yes—
187C22×C4×C83C2×D412yes—
188C22×C4×C83C2×D414yes—
189C22×C4×C83C2×D412yes—
190C22×C4×C83C2×Q812yes—
191C22×C4×C83C2×Q814yes—
192C22×C4×C83C2×Q812yes—
193C22×C4×C83#4112yes—
194C22×C4×C83#4112yes—
195C22×C4×C83#4112yes—
196C4⋊C4×C83—44no—
197C42×C83—44no—
198C23×C83C23×C411yescharacteristic
199C23×C83C22×D411yescharacteristic
200C23×C83C22×D411yescharacteristic
201C23×C83C22×D411yescharacteristic
202C23×C83C22×Q811yescharacteristic
203C23×C83C22×Q811yescharacteristic
204C23×C83C2×#4111yescharacteristic
205C23×C83C2×#4111yescharacteristic
206C23×C83C2×#4111yescharacteristic
207C23×C83C2×#4111yescharacteristic
208C23×C83C2×#4111yescharacteristic
209C23×C83H(5,𝔽2)11yescharacteristic
210C23×C832−1+411yescharacteristic
211C23×C832−1+411yescharacteristic
212C23×C832−1+411yescharacteristic
213Q8×C83—232no—
214C2×C4×C83—24no—
215C2×C4×C83—24no—
216C2×C4×C83—24no—
217C2×C4×C83—24no—
218C2×C4×C83—24no—
219C2×C4×C83—24no—
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—41no—
227C2×C4×C83—41no—
228C2×C4×C83—41no—
229C2×C4×C83—41no—
230C2×C4×C83—41no—
231C2×C4×C83—41no—
232C2×C4×C83—41no—
233C2×C4×C83—41no—
234C2×C4×C83—42no—
235C2×C4×C83—42no—
236C2×C4×C83—42no—
237C2×C4×C83—42no—
238C2×C4×C83—42no—
239C2×C4×C83—42no—
240C2×C4×C83—42no—
241C2×C4×C83C2×C22⋊C414yes—
242C2×C4×C83C2×C4⋊C418yes—
243C2×C4×C83C2×C4⋊C414yes—
244C2×C4×C83#11714yes—
245C2×C4×C83#12114yes—
246C2×C4×C83#12114yes—
247C2×C4×C83C22⋊Q814yes—
248C2×C4×C83C22⋊Q814yes—
249C2×Dic83—22no—
250C2×Dic83—24no—
251C2×Dic83—22no—
252C2×Dic83—24no—
253C2×Dic83—24no—
254C2×Dic83—24no—
255C2×Dic83—24no—
256C2×Dic83—24no—
257C2×Dic83—22no—
258C2×Dic83—22no—
259C2×Dic83—22no—
260C2×Dic83—22no—
261C2×Dic83—22no—
262C2×Dic83—22no—
263C2×Dic83—22no—
264C2×Dic83—22no—
265C2×Dic83—22no—
266C2×Dic83—22no—
267C2×Dic83—22no—
268C2×Dic83—22no—
269C2×Dic83—22no—
270C2×Dic83—41no—
271C2×Dic83—41no—
272C2×Dic83—41no—
273C2×Dic83—41no—
274C2×Dic83—41no—
275C2×Dic83—41no—
276C2×Dic83—41no—
277C2×Dic83—41no—
278C2×Dic83—41no—
279C2×Dic83—41no—
280C2×Dic83—41no—
281C2×Dic83—41no—
282C2×Dic83—42no—
283C2×Dic83—42no—
284C2×Dic83—42no—
285C2×Dic83—42no—
286C2×Dic83—42no—
287C2×Dic83—42no—
288C2×Dic83—42no—
289C2×Dic83C2×C22⋊C418yes—
290C2×Dic83C4×Q814yes—
291C22×C83C22×C22⋊C411yescharacteristic
292C22×C83C22×C4⋊C411yescharacteristic
293C22×C83C2×#11711yescharacteristic
294C22×C83C2×C4×Q811yescharacteristic
295C22×C83C4×#4111yescharacteristic
296C22×C83#51911yescharacteristic
297C22×C83#52011yescharacteristic
298C22×C83C2×#12111yescharacteristic
299C22×C83C2×#12111yescharacteristic
300C22×C83C2×C22⋊Q811yescharacteristic
301C22×C83C2×C22⋊Q811yescharacteristic
302C22×C83#52911yescharacteristic
303C22×C83#52911yescharacteristic
304C22×C83#53311yescharacteristic
305C22×C83#53311yescharacteristic
306C22×C83#54111yescharacteristic
307C22×C83#54111yescharacteristic
308C22×C83#54211yescharacteristic
309C22×C83#54211yescharacteristic
310C22×C83#54611yescharacteristic
311C22×C83#54611yescharacteristic
312C22×C83#54711yescharacteristic
313C22×C83#54711yescharacteristic
314C22×C83#54811yescharacteristic
315C22×C83#54811yescharacteristic
316C22×C83#54811yescharacteristic
317C22×C83#54811yescharacteristic
318C22×C83D4×Q811yescharacteristic
319C22×C83D4×Q811yescharacteristic
320C22×C83D4×Q811yescharacteristic
321C22×C83#55011yescharacteristic
322C22×C83#55711yescharacteristic
323C22×C83#55711yescharacteristic
324C22×C83#55711yescharacteristic
325C22×C83Q8211yescharacteristic
326C4×C83—28no—
327C4×C83—42no—
328C4×C83—42no—
329C4×C83—82no—
330C4×C83#38018yes—
331Dic83—28no—
332Dic83—24no—
333Dic83—42no—
334Dic83—42no—
335Dic83—42no—
336Dic83—82no—
337#13935—831nomaximal, Sylow
338C2×C83C2×#38011yescharacteristic
339C2×C83#229511yescharacteristic
340C2×C83#232011yescharacteristic
341C2×C83#233911yescharacteristic
342C2×C83Q8×C22⋊C411yescharacteristic
343C2×C83Q8×C4⋊C411yescharacteristic
344C2×C83#235111yescharacteristic
345C2×C83#242611yescharacteristic
346C2×C83#242611yescharacteristic
347C2×C83#242911yescharacteristic
348C2×C83#242911yescharacteristic
349C2×C83#245111yescharacteristic
350C2×C83#245111yescharacteristic
351C2×C83#245311yescharacteristic
352C2×C83#245311yescharacteristic
353C22×C4×Q8—831no—
354C2×#391—831no—
355C2×#391D8311yescharacteristic
356C2×#389—831no—
357C2×#389—831no—
358#1441—832no—
359#1441—832no—
360C4⋊#95—832no—
361C4⋊#95—831no—
362#1434—832no—
363C4×#95—831no—
364C83#1393511yescharacteristic, complemented, Sylow
365C23×Q8C2×D8311yescharacteristic
366C2×C4×Q8—838no—
367C2×C4×Q8—1664no—
368C2×C4×Q8—1664no—
369C22×C4⋊C4—832no—
370C22×C4⋊C4—832no—
371C22×C4⋊C4—831no—
372C22×C4⋊C4—832no—
373C22×C4⋊C4—831no—
374C22×C4⋊C4C2×D8311yescharacteristic
375C22×C42—831no—
376C22×C42—832no—
377C22×C42—831no—
378C22×C42C2×D8311yescharacteristic
379#391—24no—
380#391—1664no—
381#389—1664no—
382#389—1664no—
383C2×#95—832no—
384C2×#95—831no—
385C2×#95—831no—
386C2×#95—831no—
387C2×#95—831no—
388C2×#95—832no—
389C2×#95—832no—
390C2×#95—832no—
391C2×#95—832no—
392C2×#95—832no—
393C2×#95C2×D8312yes—
394C2×#95C2×D8312yes—
395C22×Q8—22no—
396C22×Q8—22no—
397C22×Q8—22no—
398C22×Q8—22no—
399C22×Q8Dic16614yes—
400C22×Q8C4×D8314yes—
401C22×Q8C22⋊D8314yes—
402C23×C4—832no—
403C23×C4—831no—
404C23×C4—831no—
405C23×C4—831no—
406C23×C4—831no—
407C23×C4—832no—
408C23×C4C22×D8312yes—
409C23×C4C22×D8311yescharacteristic
410C23×C4C22×D8311yescharacteristic
411C23×C4C22×D8312yes—
412C23×C4C22×D8311yescharacteristic
413C4×Q8—16632no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—3322no—
418C2×C4⋊C4—3322no—
419C2×C4⋊C4—834no—
420C2×C4⋊C4—834no—
421C2×C4⋊C4—834no—
422C2×C4⋊C4—838no—
423C2×C4⋊C4—1664no—
424C2×C4⋊C4—1664no—
425C2×C4⋊C4—1664no—
426C2×C4⋊C4—1662no—
427C2×C4⋊C4—1662no—
428C2×C4⋊C4—1662no—
429C2×C4⋊C4—1664no—
430C2×C4⋊C4—1664no—
431C2×C4⋊C4—1664no—
432C2×C42—22no—
433C2×C42—22no—
434C2×C42—22no—
435C2×C42—838no—
436C2×C42—834no—
437C2×C42—1662no—
438C2×C42—1662no—
439C2×C42—1662no—
440C2×C42—1664no—
441C2×C42—1664no—
442C2×C42—1662no—
443C2×C42—1662no—
444#95—24no—
445#95—24no—
446#95—3322no—
447#95—834no—
448#95—1664no—
449#95—1664no—
450#95—1662no—
451#95—1662no—
452#95—1664no—
453#95—1664no—
454#95—1664no—
455#95—1662no—
456C24C23×D8311yescharacteristic
457C2×Q8—28no—
458C2×Q8—28no—
459C2×Q8—28no—
460C2×Q8—28no—
461C2×Q8—28no—
462C2×Q8—28no—
463C2×Q8Dic83⋊C4116yescomplemented
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
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—21no—
479C22×C4—21no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—832no—
488C22×C4—834no—
489C22×C4—834no—
490C22×C4—834no—
491C22×C4—832no—
492C22×C4—832no—
493C22×C4—832no—
494C22×C4—832no—
495C22×C4—832no—
496C22×C4—1662no—
497C22×C4—1662no—
498C22×C4—1662no—
499C22×C4—1662no—
500C22×C4—1662no—
501C22×C4—1662no—
502C22×C4—1662no—
503C22×C4—1661no—
504C22×C4—1661no—
505C22×C4—1661no—
506C22×C4—1661no—
507C22×C4—1661no—
508C22×C4—1661no—
509C22×C4—1661no—
510C22×C4—1661no—
511C22×C4—1661no—
512C22×C4—1661no—
513C22×C4—1661no—
514C22×C4—1661no—
515C22×C4—1661no—
516C22×C4—1661no—
517C22×C4—1661no—
518C22×C4—1661no—
519C22×C4—1661no—
520C22×C4—1661no—
521C22×C4—1661no—
522C22×C4—1661no—
523C22×C4—1662no—
524C22×C4—1662no—
525C22×C4—1662no—
526C22×C4—1661no—
527C22×C4—1662no—
528C22×C4—1661no—
529C22×C4C2×C4×D8314yes—
530C22×C4C2×C4×D8312yes—
531C22×C4D4×D8312yes—
532C22×C4D4×D8312yes—
533C22×C4C2×C22⋊D8314yes—
534C22×C4C2×C22⋊D8312yes—
535C22×C4Q8×D8312yes—
536C22×C4C2×Dic16614yes—
537C22×C4C2×Dic16612yes—
538C22×C4#1305058912yes—
539C22×C4#1305058912yes—
540C22×C4#1305059112yes—
541C4⋊C4—44no—
542C4⋊C4—3328no—
543C4⋊C4—3328no—
544C4⋊C4—3324no—
545C4⋊C4—8316no—
546C4⋊C4—16616no—
547C42—44no—
548C42—3324no—
549C42—16616no—
550C42—1668no—
551C23C22×C4×D8311yescharacteristic
552C23C2×D4×D8311yescharacteristic
553C23C2×D4×D8311yescharacteristic
554C23C22×C22⋊D8311yescharacteristic
555C23C2×Q8×D8311yescharacteristic
556C23C22×Dic16611yescharacteristic
557C23#41×D8311yescharacteristic
558C23#41×D8311yescharacteristic
559C23C2×#1305058911yescharacteristic
560C23C2×#1305058911yescharacteristic
561C23C2×#1305059111yescharacteristic
562C23#1458183811yescharacteristic
563C23#1458183911yescharacteristic
564C23#1458184011yescharacteristic
565C23#1458184011yescharacteristic
566Q8—232no—
567C2×C4—24no—
568C2×C4—24no—
569C2×C4—24no—
570C2×C4—24no—
571C2×C4—24no—
572C2×C4—24no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—3321no—
595C2×C4—3321no—
596C2×C4—3321no—
597C2×C4—3321no—
598C2×C4—3321no—
599C2×C4—3321no—
600C2×C4—3321no—
601C2×C4—3321no—
602C2×C4—3321no—
603C2×C4—3321no—
604C2×C4—3321no—
605C2×C4—3321no—
606C2×C4—3322no—
607C2×C4—3322no—
608C2×C4—3322no—
609C2×C4—3322no—
610C2×C4—3322no—
611C2×C4—3322no—
612C2×C4—3322no—
613C2×C4—838no—
614C2×C4—834no—
615C2×C4—1662no—
616C2×C4—1662no—
617C2×C4—1662no—
618C2×C4—1662no—
619C2×C4—1662no—
620C2×C4—1662no—
621C2×C4—1662no—
622C2×C4—1662no—
623C2×C4—1662no—
624C2×C4—1664no—
625C2×C4—1664no—
626C2×C4—1664no—
627C2×C4—1664no—
628C2×C4—1662no—
629C2×C4—1662no—
630C2×C4—1662no—
631C2×C4—1662no—
632C2×C4—1662no—
633C2×C4—1664no—
634C2×C4—1662no—
635C2×C4—1664no—
636C2×C4C22⋊C4×D8314yes—
637C2×C4C2×Dic83⋊C418yes—
638C2×C4C2×Dic83⋊C414yes—
639C2×C4#1458174814yes—
640C2×C4#1458176414yes—
641C2×C4#1458176414yes—
642C2×C4#1458176914yes—
643C2×C4#1458176914yes—
644C22C2×C22⋊C4×D8311yescharacteristic
645C22C22×Dic83⋊C411yescharacteristic
646C22C2×#1458174811yescharacteristic
647C22C4×Q8×D8311yescharacteristic
648C22C4×#1305059111yescharacteristic
649C22#1912817711yescharacteristic
650C22#1912818311yescharacteristic
651C22C2×#1458176411yescharacteristic
652C22C2×#1458176411yescharacteristic
653C22C2×#1458176911yescharacteristic
654C22C2×#1458176911yescharacteristic
655C22#1912823011yescharacteristic
656C22#1912823711yescharacteristic
657C22#1912825311yescharacteristic
658C22#1912825611yescharacteristic
659C22#1912831111yescharacteristic
660C22#1912831211yescharacteristic
661C22#1912832011yescharacteristic
662C22#1912832411yescharacteristic
663C22#1912834211yescharacteristic
664C22#1912834411yescharacteristic
665C22#1912835311yescharacteristic
666C22#1912835411yescharacteristic
667C22#1912835811yescharacteristic
668C22#1912835911yescharacteristic
669C22#1912836111yescharacteristic
670C22#1912836211yescharacteristic
671C22#1912836411yescharacteristic
672C22Q8×C22⋊D8311yescharacteristic
673C22#1912836611yescharacteristic
674C22#1912837011yescharacteristic
675C22#1912842711yescharacteristic
676C22#1912842711yescharacteristic
677C22#1912843011yescharacteristic
678C22Q8×Dic16611yescharacteristic
679C4—28no—
680C4—42no—
681C4—42no—
682C4—82no—
683C4—3322no—
684C4—3322no—
685C4—3322no—
686C4—6642no—
687C4—1668no—
688C4—1664no—
689C4#1912755918yes—
690C2C2×#1912755911yescharacteristic
691C2#2490993811yescharacteristic
692C2#2491010811yescharacteristic
693C2#2491029211yescharacteristic
694C2#2491029711yescharacteristic
695C2Q8×Dic83⋊C411yescharacteristic
696C2#2491038111yescharacteristic
697C2#2491103111yescharacteristic
698C2#2491103211yescharacteristic
699C2#2491106411yescharacteristic
700C2#2491106511yescharacteristic
701C2#2491130411yescharacteristic
702C2#2491130511yescharacteristic
703C2#2491132611yescharacteristic
704C2#2491132711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D83
commutatorC23×C83C23×C4
FittingC2×#391×C83C2
socle, prime radical, cosocleC24×C83C24
hypercenterC2×#391D83
hypocenterC83#13935
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ C2×#391

Complements

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

NH ≅ G/Ntype
14. C2×Q8×Dic83C4semidirect
82. C83⋊#95Q8semidirect
160. C2×Q8×C83C4⋊C4semidirect
364. C83#13935semidirect
463. C2×Q8Dic83⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×Q8×Dic832
C2×#191276082
C2×#191275992
C2×#191275972
#249057152
#249056922
Dic83⋊#952
#249056892
C4×C83⋊#952
C2×#391×C832
#1393583