Finite Group Databasebeta

← #35328216

Subgroups — #35328216

Order 21248.

1838 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14581791C211yesmaximal, characteristic
2C2×#19127605C212yesmaximal
3C2×#19127599C211yesmaximal, characteristic
4C2×C4⋊C4×Dic83C211yesmaximal, characteristic
5#24905733C212yesmaximal
6#24905714C212yesmaximal
7#24905694C212yesmaximal
8#24905692C211yesmaximal, characteristic
9#24905692C211yesmaximal, characteristic
10C4×C83⋊#95C211yesmaximal, characteristic
11C83×C4⋊#95C211yesmaximal, characteristic
12C23×Dic166C2212yes—
13C2×#14581791—24no—
14C2×#14581791—24no—
15C2×#14581791C418yescomplemented
16C22×C4⋊Dic83C2211yescharacteristic
17C22×C4⋊Dic83C2211yescharacteristic
18C22×Dic83⋊C4C2212yes—
19C22×Dic83⋊C4C2212yes—
20C22×C4×Dic83C2212yes—
21C22×C4×Dic83C2211yescharacteristic
22C22×C4×Dic83C2211yescharacteristic
23#19127605—28no—
24#19127599—24no—
25C4⋊C4×Dic83—24no—
26C2×C83⋊#95C2211yescharacteristic
27C2×C83⋊#95C2212yes—
28C2×C83⋊#95C2212yes—
29C2×C83⋊#95C2212yes—
30C2×C83⋊#95C2212yes—
31C2×C83⋊#95C2211yescharacteristic
32C2×C83⋊#95C2212yes—
33C2×C83⋊#95C2212yes—
34C2×C83⋊#95C2211yescharacteristic
35C2×C83⋊#95C2211yescharacteristic
36C22×C4⋊C4×C83C2211yescharacteristic
37C22×C4⋊C4×C83C2211yescharacteristic
38C22×C42×C83C2211yescharacteristic
39C2×#95×C83C2212yes—
40C2×#95×C83C2212yes—
41C22×Dic166—24no—
42C22×Dic166—24no—
43C22×Dic166—24no—
44C22×Dic166—24no—
45C22×Dic166—42no—
46C22×Dic166—42no—
47C22×Dic166C2×C418yes—
48C23×Dic83C2312yes—
49C23×Dic83C2311yescharacteristic
50C23×Dic83C2312yes—
51C23×Dic83C2311yescharacteristic
52C23×Dic83C2311yescharacteristic
53C23×Dic83C2311yescharacteristic
54#14581791—232no—
55C2×C4⋊Dic83—22no—
56C2×C4⋊Dic83—22no—
57C2×C4⋊Dic83—22no—
58C2×C4⋊Dic83C2×C414yes—
59C2×C4⋊Dic83D414yes—
60C2×C4⋊Dic83D414yes—
61C2×Dic83⋊C4—24no—
62C2×Dic83⋊C4—24no—
63C2×Dic83⋊C4—24no—
64C2×Dic83⋊C4—24no—
65C2×Dic83⋊C4—42no—
66C2×Dic83⋊C4C2×C418yes—
67C2×C4×Dic83—24no—
68C2×C4×Dic83—24no—
69C2×C4×Dic83—22no—
70C2×C4×Dic83—22no—
71C2×C4×Dic83—22no—
72C2×C4×Dic83—22no—
73C2×C4×Dic83—42no—
74C2×C4×Dic83C2×C414yes—
75C2×C4×Dic83Q814yescomplemented
76C83⋊#95—24no—
77C83⋊#95—24no—
78C83⋊#95—24no—
79C83⋊#95—24no—
80C83⋊#95—22no—
81C83⋊#95—22no—
82C83⋊#95—24no—
83C83⋊#95—42no—
84C83⋊#95D414yes—
85C83⋊#95Q814yescomplemented
86C23×C4×C83C2312yes—
87C23×C4×C83C2311yescharacteristic
88C23×C4×C83C2311yescharacteristic
89C23×C4×C83C2312yes—
90C23×C4×C83C2311yescharacteristic
91C2×C4⋊C4×C83—22no—
92C2×C4⋊C4×C83—22no—
93C2×C4⋊C4×C83—22no—
94C2×C4⋊C4×C83—22no—
95C2×C4⋊C4×C83C2×C414yes—
96C2×C4⋊C4×C83Q814yescomplemented
97C2×C42×C83—22no—
98C2×C42×C83—22no—
99C2×C42×C83—22no—
100#95×C83—24no—
101#95×C83—42no—
102C2×Dic166—216no—
103C2×Dic166—216no—
104C2×Dic166—48no—
105C2×Dic166—48no—
106C2×Dic166—48no—
107C2×Dic166—48no—
108C2×Dic166—48no—
109C22×Dic83—21no—
110C22×Dic83—21no—
111C22×Dic83—22no—
112C22×Dic83—21no—
113C22×Dic83—21no—
114C22×Dic83—21no—
115C22×Dic83—22no—
116C22×Dic83—21no—
117C22×Dic83—21no—
118C22×Dic83—21no—
119C22×Dic83—22no—
120C22×Dic83—22no—
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—21no—
130C22×Dic83—21no—
131C22×Dic83—22no—
132C22×Dic83—22no—
133C22×Dic83—22no—
134C22×Dic83—22no—
135C22×Dic83—22no—
136C22×Dic83—22no—
137C22×Dic83—22no—
138C22×Dic83C22×C414yes—
139C22×Dic83C22×C412yes—
140C22×Dic83C22×C412yes—
141C22×Dic83C2×D414yes—
142C22×Dic83C2×D414yes—
143C22×Dic83C2×D412yes—
144C22×Dic83C2×D412yes—
145C22×Dic83C2×Q812yes—
146C22×Dic83C2×Q812yes—
147C22×Dic83C2×Q812yes—
148C22×Dic83C2×Q812yes—
149C22×Dic83#4112yes—
150C22×Dic83#4112yes—
151C4⋊Dic83—44no—
152C4⋊Dic83C22⋊C4116yes—
153Dic83⋊C4—216no—
154Dic83⋊C4—48no—
155C4×Dic83—28no—
156C4×Dic83—28no—
157C4×Dic83—48no—
158C24×C83C2411yescharacteristic
159C22×C4×C83—22no—
160C22×C4×C83—22no—
161C22×C4×C83—22no—
162C22×C4×C83—22no—
163C22×C4×C83—21no—
164C22×C4×C83—21no—
165C22×C4×C83—22no—
166C22×C4×C83—22no—
167C22×C4×C83—21no—
168C22×C4×C83—21no—
169C22×C4×C83—21no—
170C22×C4×C83—21no—
171C22×C4×C83—22no—
172C22×C4×C83—21no—
173C22×C4×C83—21no—
174C22×C4×C83—22no—
175C22×C4×C83—22no—
176C22×C4×C83—22no—
177C22×C4×C83—21no—
178C22×C4×C83—22no—
179C22×C4×C83—21no—
180C22×C4×C83—22no—
181C22×C4×C83—21no—
182C22×C4×C83—21no—
183C22×C4×C83C22×C414yes—
184C22×C4×C83C22×C412yes—
185C22×C4×C83C2×D412yes—
186C22×C4×C83C2×D412yes—
187C22×C4×C83C2×D412yes—
188C22×C4×C83C2×Q812yes—
189C22×C4×C83C2×Q812yes—
190C22×C4×C83C2×Q814yes—
191C22×C4×C83C2×Q812yes—
192C22×C4×C83#4112yes—
193C22×C4×C83#4112yes—
194C4⋊C4×C83—28no—
195C4⋊C4×C83—28no—
196C42×C83—44no—
197C23×C83C23×C411yescharacteristic
198C23×C83C22×D411yescharacteristic
199C23×C83C22×D411yescharacteristic
200C23×C83C22×D411yescharacteristic
201C23×C83C22×Q811yescharacteristic
202C23×C83C22×Q811yescharacteristic
203C23×C83C22×Q811yescharacteristic
204C23×C83C2×#4111yescharacteristic
205C23×C83C2×#4111yescharacteristic
206C23×C83C2×#4111yescharacteristic
207C23×C83C2×#4111yescharacteristic
208C23×C83H(5,𝔽2)11yescharacteristic
209C23×C83H(5,𝔽2)11yescharacteristic
210C23×C832−1+411yescharacteristic
211C23×C832−1+411yescharacteristic
212C2×C4×C83—24no—
213C2×C4×C83—24no—
214C2×C4×C83—24no—
215C2×C4×C83—24no—
216C2×C4×C83—22no—
217C2×C4×C83—22no—
218C2×C4×C83—22no—
219C2×C4×C83—22no—
220C2×C4×C83—22no—
221C2×C4×C83—24no—
222C2×C4×C83—22no—
223C2×C4×C83—24no—
224C2×C4×C83—41no—
225C2×C4×C83—41no—
226C2×C4×C83—42no—
227C2×C4×C83—41no—
228C2×C4×C83—42no—
229C2×C4×C83—41no—
230C2×C4×C83—42no—
231C2×C4×C83—42no—
232C2×C4×C83—42no—
233C2×C4×C83—41no—
234C2×C4×C83—42no—
235C2×C4×C83—42no—
236C2×C4×C83—42no—
237C2×C4×C83—41no—
238C2×C4×C83—41no—
239C2×C4×C83—41no—
240C2×C4×C83C2×C22⋊C414yes—
241C2×C4×C83C4×Q814yes—
242C2×C4×C83C4×Q814yes—
243C2×C4×C83C22⋊Q814yes—
244C2×C4×C83C22⋊Q814yes—
245C2×C4×C83#12414yes—
246C2×C4×C83C4⋊Q814yes—
247C2×Dic83—22no—
248C2×Dic83—22no—
249C2×Dic83—24no—
250C2×Dic83—24no—
251C2×Dic83—22no—
252C2×Dic83—22no—
253C2×Dic83—22no—
254C2×Dic83—22no—
255C2×Dic83—22no—
256C2×Dic83—24no—
257C2×Dic83—24no—
258C2×Dic83—22no—
259C2×Dic83—22no—
260C2×Dic83—24no—
261C2×Dic83—24no—
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—22no—
271C2×Dic83—22no—
272C2×Dic83—22no—
273C2×Dic83—22no—
274C2×Dic83—41no—
275C2×Dic83—41no—
276C2×Dic83—41no—
277C2×Dic83—41no—
278C2×Dic83—42no—
279C2×Dic83—42no—
280C2×Dic83—42no—
281C2×Dic83—42no—
282C2×Dic83—42no—
283C2×Dic83—42no—
284C2×Dic83—42no—
285C2×Dic83C2×C22⋊C418yes—
286C2×Dic83C4×D414yes—
287C2×Dic83C4×Q814yes—
288C2×Dic83C4⋊Q814yescomplemented
289Dic166—432no—
290C22×C83C22×C22⋊C411yescharacteristic
291C22×C83C2×C4×D411yescharacteristic
292C22×C83C2×C4×Q811yescharacteristic
293C22×C83C2×C4×Q811yescharacteristic
294C22×C83C2×C4×Q811yescharacteristic
295C22×C83#51811yescharacteristic
296C22×C83#51911yescharacteristic
297C22×C83C2×C22⋊Q811yescharacteristic
298C22×C83C2×C22⋊Q811yescharacteristic
299C22×C83C2×#12411yescharacteristic
300C22×C83C2×C4⋊Q811yescharacteristic
301C22×C83C2×C4⋊Q811yescharacteristic
302C22×C83#53211yescharacteristic
303C22×C83#53311yescharacteristic
304C22×C83#53311yescharacteristic
305C22×C83#54211yescharacteristic
306C22×C83#54211yescharacteristic
307C22×C83#54411yescharacteristic
308C22×C83#54411yescharacteristic
309C22×C83D4211yescharacteristic
310C22×C83D4211yescharacteristic
311C22×C83#54611yescharacteristic
312C22×C83#54611yescharacteristic
313C22×C83#54711yescharacteristic
314C22×C83#54811yescharacteristic
315C22×C83#54811yescharacteristic
316C22×C83D4×Q811yescharacteristic
317C22×C83D4×Q811yescharacteristic
318C22×C83D4×Q811yescharacteristic
319C22×C83#55411yescharacteristic
320C22×C83#55411yescharacteristic
321C22×C83#55511yescharacteristic
322C22×C83#55611yescharacteristic
323C22×C83#55711yescharacteristic
324C22×C83Q8211yescharacteristic
325C4×C83—44no—
326C4×C83—44no—
327C4×C83—42no—
328C4×C83—42no—
329C4×C83#39118yescomplemented
330Dic83—24no—
331Dic83—28no—
332Dic83—24no—
333Dic83—24no—
334Dic83—42no—
335Dic83—82no—
336#14053—831nomaximal, Sylow
337C2×C83C2×#39111yescharacteristic
338C2×C83C4×C4⋊Q811yescharacteristic
339C2×C83#233111yescharacteristic
340C2×C83D4×C22⋊C411yescharacteristic
341C2×C83Q8×C22⋊C411yescharacteristic
342C2×C83#236511yescharacteristic
343C2×C83#236911yescharacteristic
344C2×C83#243911yescharacteristic
345C2×C83#244011yescharacteristic
346C2×C83#245111yescharacteristic
347C2×C83#245211yescharacteristic
348C2×C83#249111yescharacteristic
349C2×C83#249211yescharacteristic
350C2×C83#255011yescharacteristic
351C2×C83#255111yescharacteristic
352C22×C4⋊Q8—831no—
353C2×#391—832no—
354C2×#389—831no—
355C2×C4×C4⋊C4—831no—
356#1446—832no—
357#1441—832no—
358#1436—832no—
359C4⋊#95—831no—
360C4⋊#95—831no—
361C4⋊#95D8311yescharacteristic
362C4×#95—831no—
363C83#1405311yescharacteristic, complemented, Sylow
364C23×Q8—832no—
365C2×C4⋊Q8—838no—
366C2×C4⋊Q8—1664no—
367C2×C4⋊Q8—1664no—
368C22×C4⋊C4—832no—
369C22×C4⋊C4—831no—
370C22×C4⋊C4—832no—
371C22×C4⋊C4—831no—
372C22×C4⋊C4C2×D8311yescharacteristic
373C22×C4⋊C4C2×D8311yescharacteristic
374C22×C42—832no—
375C22×C42—831no—
376C22×C42—831no—
377C22×C42C2×D8311yescharacteristic
378#391—1668no—
379#389—1664no—
380C4×C4⋊C4—1664no—
381C2×#95—832no—
382C2×#95—831no—
383C2×#95—831no—
384C2×#95—831no—
385C2×#95—831no—
386C2×#95—832no—
387C2×#95—832no—
388C2×#95—832no—
389C2×#95—832no—
390C2×#95—832no—
391C2×#95C2×D8312yes—
392C2×#95C2×D8312yes—
393C22×Q8—3322no—
394C22×Q8—3322no—
395C22×Q8—838no—
396C22×Q8—1664no—
397C22×Q8—1664no—
398C22×Q8—1664no—
399C22×Q8—1664no—
400C23×C4—832no—
401C23×C4—831no—
402C23×C4—831no—
403C23×C4—831no—
404C23×C4—831no—
405C23×C4—832no—
406C23×C4C22×D8312yes—
407C23×C4C22×D8311yescharacteristic
408C23×C4C22×D8311yescharacteristic
409C23×C4C22×D8312yes—
410C23×C4C22×D8311yescharacteristic
411C4⋊Q8—16632no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—3322no—
417C2×C4⋊C4—834no—
418C2×C4⋊C4—834no—
419C2×C4⋊C4—834no—
420C2×C4⋊C4—838no—
421C2×C4⋊C4—1664no—
422C2×C4⋊C4—1662no—
423C2×C4⋊C4—1664no—
424C2×C4⋊C4—1662no—
425C2×C4⋊C4—1662no—
426C2×C4⋊C4—1664no—
427C2×C4⋊C4—1664no—
428C2×C4⋊C4Dic16614yescomplemented
429C2×C4⋊C4C4×D8314yes—
430C2×C42—22no—
431C2×C42—22no—
432C2×C42—22no—
433C2×C42—3322no—
434C2×C42—834no—
435C2×C42—834no—
436C2×C42—1664no—
437C2×C42—1664no—
438C2×C42—1662no—
439C2×C42—1662no—
440C2×C42—1662no—
441C2×C42—1662no—
442#95—24no—
443#95—42no—
444#95—3322no—
445#95—834no—
446#95—834no—
447#95—1664no—
448#95—1664no—
449#95—1664no—
450#95—1664no—
451#95—1664no—
452#95—1662no—
453#95—1662no—
454C24C23×D8311yescharacteristic
455C2×Q8—3328no—
456C2×Q8—3328no—
457C2×Q8—3328no—
458C2×Q8—3328no—
459C2×Q8—3328no—
460C2×Q8—16616no—
461C2×Q8—16616no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—21no—
465C22×C4—22no—
466C22×C4—21no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—22no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—22no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—22no—
485C22×C4—21no—
486C22×C4—832no—
487C22×C4—832no—
488C22×C4—834no—
489C22×C4—832no—
490C22×C4—832no—
491C22×C4—834no—
492C22×C4—834no—
493C22×C4—832no—
494C22×C4—832no—
495C22×C4—832no—
496C22×C4—832no—
497C22×C4—832no—
498C22×C4—832no—
499C22×C4—1662no—
500C22×C4—1662no—
501C22×C4—1662no—
502C22×C4—1662no—
503C22×C4—1662no—
504C22×C4—1662no—
505C22×C4—1662no—
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—1662no—
516C22×C4—1661no—
517C22×C4—1661no—
518C22×C4—1662no—
519C22×C4—1661no—
520C22×C4—1661no—
521C22×C4—1662no—
522C22×C4—1661no—
523C22×C4—1662no—
524C22×C4—1661no—
525C22×C4—1661no—
526C22×C4—1661no—
527C22×C4—1661no—
528C22×C4C2×C4×D8314yes—
529C22×C4C2×C4×D8312yes—
530C22×C4D4×D8312yes—
531C22×C4D4×D8312yes—
532C22×C4D4×D8312yes—
533C22×C4Q8×D8312yes—
534C22×C4Q8×D8312yes—
535C22×C4C2×Dic16614yes—
536C22×C4C2×Dic16612yes—
537C22×C4#1305058912yes—
538C22×C4#1305059012yes—
539C4⋊C4—28no—
540C4⋊C4—28no—
541C4⋊C4—3328no—
542C4⋊C4—3324no—
543C4⋊C4—8316no—
544C4⋊C4—16616no—
545C42—44no—
546C42—3328no—
547C42—1668no—
548C42—1668no—
549C23C22×C4×D8311yescharacteristic
550C23C2×D4×D8311yescharacteristic
551C23C2×D4×D8311yescharacteristic
552C23C2×D4×D8311yescharacteristic
553C23C2×Q8×D8311yescharacteristic
554C23C2×Q8×D8311yescharacteristic
555C23C22×Dic16611yescharacteristic
556C23#41×D8311yescharacteristic
557C23#41×D8311yescharacteristic
558C23C2×#1305058911yescharacteristic
559C23C2×#1305059011yescharacteristic
560C23#1458183711yescharacteristic
561C23#1458183811yescharacteristic
562C23#1458183911yescharacteristic
563C23#1458184011yescharacteristic
564Q8—33232no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—24no—
569C2×C4—24no—
570C2×C4—22no—
571C2×C4—24no—
572C2×C4—24no—
573C2×C4—24no—
574C2×C4—24no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—41no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—41no—
584C2×C4—42no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—41no—
593C2×C4—3321no—
594C2×C4—3321no—
595C2×C4—3321no—
596C2×C4—3321no—
597C2×C4—3322no—
598C2×C4—3322no—
599C2×C4—3322no—
600C2×C4—3322no—
601C2×C4—3322no—
602C2×C4—3322no—
603C2×C4—3322no—
604C2×C4—838no—
605C2×C4—834no—
606C2×C4—834no—
607C2×C4—834no—
608C2×C4—1662no—
609C2×C4—1662no—
610C2×C4—1662no—
611C2×C4—1662no—
612C2×C4—1664no—
613C2×C4—1662no—
614C2×C4—1662no—
615C2×C4—1664no—
616C2×C4—1662no—
617C2×C4—1662no—
618C2×C4—1664no—
619C2×C4—1662no—
620C2×C4—1664no—
621C2×C4—1662no—
622C2×C4—1662no—
623C2×C4—1662no—
624C2×C4—1662no—
625C2×C4—1662no—
626C2×C4—1662no—
627C2×C4—1662no—
628C2×C4—1662no—
629C2×C4—1662no—
630C2×C4—1664no—
631C2×C4—1662no—
632C2×C4—1664no—
633C2×C4—1662no—
634C2×C4—1662no—
635C2×C4C22⋊C4×D8314yes—
636C2×C4#1458175714yes—
637C2×C4C4×Dic16614yes—
638C2×C4#1458176914yes—
639C2×C4#1458177014yes—
640C2×C4#1458177814yes—
641C2×C4#1458179114yes—
642C22C2×C22⋊C4×D8311yescharacteristic
643C22C4×D4×D8311yescharacteristic
644C22C4×Q8×D8311yescharacteristic
645C22C2×#1458175711yescharacteristic
646C22C2×C4×Dic16611yescharacteristic
647C22#1912817311yescharacteristic
648C22#1912817711yescharacteristic
649C22C2×#1458176911yescharacteristic
650C22C2×#1458177011yescharacteristic
651C22C2×#1458177811yescharacteristic
652C22C4⋊Q8×D8311yescharacteristic
653C22C2×#1458179111yescharacteristic
654C22#1912824611yescharacteristic
655C22#1912825311yescharacteristic
656C22#1912825711yescharacteristic
657C22#1912831811yescharacteristic
658C22#1912832411yescharacteristic
659C22#1912832811yescharacteristic
660C22#1912833111yescharacteristic
661C22#1912833511yescharacteristic
662C22#1912833611yescharacteristic
663C22#1912834411yescharacteristic
664C22#1912834811yescharacteristic
665C22#1912835211yescharacteristic
666C22#1912835911yescharacteristic
667C22#1912836111yescharacteristic
668C22#1912836411yescharacteristic
669C22#1912836611yescharacteristic
670C22D4×Dic16611yescharacteristic
671C22#1912840611yescharacteristic
672C22#1912841011yescharacteristic
673C22#1912841411yescharacteristic
674C22#1912841911yescharacteristic
675C22#1912842711yescharacteristic
676C22Q8×Dic16611yescharacteristic
677C4—44no—
678C4—42no—
679C4—44no—
680C4—42no—
681C4—3322no—
682C4—6642no—
683C4—1664no—
684C4—1664no—
685C4—1668no—
686C4—1664no—
687C4#1912760518yescomplemented
688C2C2×#1912760511yescharacteristic
689C2#2491003411yescharacteristic
690C2#2491021011yescharacteristic
691C2#2491028411yescharacteristic
692C2#2491029711yescharacteristic
693C2#2491052211yescharacteristic
694C2#2491055011yescharacteristic
695C2#2491115711yescharacteristic
696C2#2491116811yescharacteristic
697C2#2491130511yescharacteristic
698C2#2491131611yescharacteristic
699C2#2491182211yescharacteristic
700C2#2491183311yescharacteristic
701C2#2491248711yescharacteristic
702C2#2491249111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D83
commutatorC23×C83C23×C4
FittingC83×C4⋊#95C2
socle, prime radical, cosocleC24×C83C24
hypercenterC4⋊#95D83
hypocenterC83#14053
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
15. C2×#14581791C4semidirect
75. C2×C4×Dic83Q8semidirect
85. C83⋊#95Q8semidirect
96. C2×C4⋊C4×C83Q8semidirect
288. C2×Dic83C4⋊Q8semidirect
329. C4×C83#391semidirect
363. C83#14053semidirect
428. C2×C4⋊C4Dic166semidirect
687. C4#19127605semidirect

Maximal subgroups

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

subgroupindex
C22×#145817912
C2×#191276052
C2×#191275992
C2×C4⋊C4×Dic832
#249057332
#249057142
#249056942
#249056922
C4×C83⋊#952
C83×C4⋊#952
#1405383