Finite Group Databasebeta

← #36289236

Subgroups — #36289236

Order 21248.

2234 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×#19128347C211yesmaximal, characteristic
2#24919538C218yesmaximal, complemented
3#24918974C218yesmaximal, complemented
4#24918462C212yesmaximal, complemented
5#24918265C212yesmaximal, complemented
6#24918235C212yesmaximal, complemented
7#24917558C212yesmaximal, complemented
8#24916721C212yesmaximal, complemented
9C2×#19127851C212yesmaximal, complemented
10#24916492C211yesmaximal, characteristic, complemented
11C83×#3501C211yesmaximal, characteristic, complemented
12C22×#13050590C2211yescharacteristic
13C23×D332C2211yescharacteristic
14C2×#14581823C2214yescomplemented
15C22×#13050577C2214yescomplemented
16#19128347—24no—
17#19128347C2218yes—
18C2×#14581780C2211yescharacteristic
19C2×#14581777—21no—
20C2×#14581771C2211yescharacteristic
21C2×#14581766C2211yescharacteristic
22C2×#14581765—21no—
23C2×#14581760—21no—
24C2×C4×D332C2211yescharacteristic
25C2×C22⋊C4×D83—21no—
26#19128093C2214yescomplemented
27#19128063C2214yescomplemented
28#19128036C2214yescomplemented
29#19128034C2214yescomplemented
30#19128014C2214yescomplemented
31#19127978C2214yescomplemented
32#19127949C2218yescomplemented
33#19127940C2218yescomplemented
34#19127923C2218yescomplemented
35#19127903C2214yescomplemented
36#19127861C2218yescomplemented
37#19127857C2214yescomplemented
38#19127856C2214yescomplemented
39#19127851C2214yes—
40#19127851C2214yes—
41#19127851C2218yescomplemented
42#19127840C2214yescomplemented
43#19127799C2218yescomplemented
44#19127773C2218yescomplemented
45#19127758C2212yescomplemented
46#19127700C2214yescomplemented
47C2×#14581712C2214yescomplemented
48#19127665C2212yescomplemented
49C2×C22⋊(C83⋊C8)C2212yes—
50#554×C83—24no—
51#554×C83C2214yescomplemented
52D4×Q8×C83C2214yescomplemented
53#544×C83—21no—
54#543×C83—21no—
55#543×C83—21no—
56#533×C83C2212yescomplemented
57C2×C22⋊Q8×C83C2212yes—
58C2×C22⋊Q8×C83C2212yescomplemented
59#518×C83—21no—
60C2×C4×D4×C83C2211yescharacteristic
61C24×D83—21no—
62C2×#13050590—22no—
63C2×#13050590—44no—
64C2×#13050590C2314yes—
65C22×Dic166C2311yescharacteristic
66C22×D332—22no—
67C22×D332—21no—
68C22×D332—44no—
69C22×D332C2311yescharacteristic
70C22×D332C2314yes—
71C22×D332C2311yescharacteristic
72C22×C22⋊D83—21no—
73C22×C22⋊D83—21no—
74C22×C4×D83—21no—
75C22×C4×D83—21no—
76#14581823—48no—
77C2×#13050580C2318yescomplemented
78C2×#13050577—48no—
79C2×#13050577C2318yes—
80C2×#13050577C2318yes—
81C2×#13050574C2314yescomplemented
82C22×C83⋊C8C2314yes—
83#14581780—22no—
84#14581780C2314yes—
85#14581777—28no—
86#14581771—22no—
87#14581771C2314yes—
88#14581766—22no—
89#14581766C2314yes—
90#14581765—28no—
91#14581760—28no—
92C4×D332—22no—
93C4×D332C2314yes—
94C2×C4⋊Dic83C2311yescharacteristic
95C2×Dic83⋊C4—21no—
96C2×C22⋊Dic83—21no—
97C2×(C2×D83)⋊C4—21no—
98C2×(C2×D83)⋊C4—21no—
99C2×(C2×D83)⋊C4—21no—
100C2×(C2×D83)⋊C4—21no—
101C22⋊C4×D83—28no—
102#14581725C2318yescomplemented
103C4⋊(C83⋊C8)C2314yescomplemented
104#14581716C2318yescomplemented
105#14581715C2318yescomplemented
106#14581712C2318yes—
107#14581712C2318yes—
108C22⋊(C83⋊C8)C2314yes—
109C22⋊(C83⋊C8)C2314yes—
110C22⋊(C83⋊C8)C2314yescomplemented
111#14581703C2314yescomplemented
112C22×Q8×C83C2312yes—
113C22×Q8×C83C2312yescomplemented
114C22×D4×C83D411yescharacteristic
115C23×C4×C83C2311yescharacteristic
116C23×C4×C83C2311yescharacteristic
117C4⋊Q8×C83—24no—
118C4⋊Q8×C83C2312yescomplemented
119C4⋊Q8×C83C2312yescomplemented
120#125×C83—24no—
121#125×C83—22no—
122C22⋊Q8×C83—22no—
123C22⋊Q8×C83—22no—
124C22⋊Q8×C83—22no—
125C22⋊Q8×C83—22no—
126C22⋊Q8×C83—22no—
127C22⋊Q8×C83—24no—
128C22⋊Q8×C83—24no—
129C22⋊Q8×C83—24no—
130C22⋊Q8×C83—24no—
131C22⋊Q8×C83C2314yes—
132C22⋊Q8×C83C2314yes—
133C22⋊Q8×C83C2314yescomplemented
134C4×Q8×C83—22no—
135C4×Q8×C83C2314yescomplemented
136C4×D4×C83—24no—
137C4×D4×C83—24no—
138C4×D4×C83D414yes—
139C4×D4×C83C2314yes—
140#117×C83—22no—
141C2×C4⋊C4×C83—22no—
142C2×C4⋊C4×C83—22no—
143C2×C4⋊C4×C83D411yescharacteristic
144C2×C4⋊C4×C83C2312yes—
145C2×C4⋊C4×C83C2312yescomplemented
146C2×C22⋊C4×C83—22no—
147C2×C22⋊C4×C83—22no—
148C2×C22⋊C4×C83D411yescharacteristic
149C2×C22⋊C4×C83D411yescharacteristic
150C2×C42×C83C2311yescharacteristic
151C23×D83—21no—
152C23×D83—21no—
153C23×D83—24no—
154C23×D83—44no—
155C23×D83—44no—
156C23×D83—82no—
157#13050590—28no—
158#13050590—44no—
159#13050590—48no—
160C2×Dic166—21no—
161C2×Dic166—42no—
162C2×Dic166C2412yes—
163C2×D332—21no—
164C2×D332—24no—
165C2×D332—28no—
166C2×D332—24no—
167C2×D332—21no—
168C2×D332—44no—
169C2×D332—42no—
170C2×D332—48no—
171C2×D332—44no—
172C2×D332C2412yes—
173C2×D332C2412yes—
174C2×C22⋊D83—24no—
175C2×C22⋊D83—24no—
176C2×C22⋊D83—44no—
177C2×C22⋊D83—82no—
178C22×Dic83—21no—
179C22×Dic83—21no—
180C2×C4×D83—24no—
181C2×C4×D83—24no—
182C2×C4×D83—44no—
183C2×C4×D83—82no—
184#13050580—48no—
185#13050577—216no—
186#13050577—48no—
187#13050574—44no—
188C2×C83⋊C8—44no—
189C2×C83⋊C8C2418yes—
190C4⋊Dic83—21no—
191C4⋊Dic83C2412yes—
192Dic83⋊C4—24no—
193C22⋊Dic83—24no—
194(C2×D83)⋊C4—24no—
195(C2×D83)⋊C4—24no—
196(C2×D83)⋊C4—24no—
197(C2×D83)⋊C4—24no—
198C24×C83C2×D411yescharacteristic
199C24×C83C2×D411yescharacteristic
200C2×Q8×C83—22no—
201C2×Q8×C83—22no—
202C2×Q8×C83—22no—
203C2×Q8×C83—44no—
204C2×Q8×C83—44no—
205C2×Q8×C83C2414yes—
206C2×D4×C83—24no—
207C2×D4×C83C2×D414yes—
208C22×C4×C83—22no—
209C22×C4×C83—22no—
210C22×C4×C83—22no—
211C22×C4×C83—22no—
212C22×C4×C83—42no—
213C22×C4×C83—42no—
214C22×C4×C83C2×D411yescharacteristic
215C22×C4×C83C2×D412yes—
216C22×C4×C83C2×D412yes—
217C22×C4×C83C2×D411yescharacteristic
218C22×C4×C83C2×D411yescharacteristic
219C22×C4×C83C2×D411yescharacteristic
220C22×C4×C83C2412yes—
221C22×C4×C83C2412yes—
222C22×C4×C83C2411yescharacteristic
223C4⋊C4×C83—24no—
224C4⋊C4×C83—24no—
225C4⋊C4×C83—24no—
226C4⋊C4×C83—22no—
227C4⋊C4×C83—22no—
228C4⋊C4×C83—22no—
229C4⋊C4×C83—22no—
230C4⋊C4×C83—22no—
231C4⋊C4×C83—24no—
232C4⋊C4×C83C2×D414yes—
233C4⋊C4×C83C2414yes—
234C22⋊C4×C83—24no—
235C22⋊C4×C83—24no—
236C22⋊C4×C83—24no—
237C22⋊C4×C83C2×D414yes—
238C22⋊C4×C83C2×D414yes—
239C42×C83—24no—
240C42×C83C2×D412yes—
241C42×C83C2412yes—
242C23×C83—22no—
243C23×C83—41no—
244C23×C83—41no—
245C23×C83—41no—
246C23×C83—41no—
247C23×C83#13714yescomplemented
248C23×C83C22×D412yes—
249C23×C83C22×D411yescharacteristic
250C23×C83C22×D412yes—
251C22×D83—24no—
252C22×D83—22no—
253C22×D83—22no—
254C22×D83—48no—
255C22×D83—42no—
256C22×D83—42no—
257C22×D83—42no—
258C22×D83—42no—
259C22×D83—48no—
260C22×D83—42no—
261C22×D83—84no—
262C22×D83—816no—
263Q8×C83—28no—
264Q8×C83—82no—
265Q8×C83—82no—
266Q8×C83—82no—
267D4×C83—28no—
268C2×C4×C83—22no—
269C2×C4×C83—22no—
270C2×C4×C83—24no—
271C2×C4×C83—24no—
272C2×C4×C83—24no—
273C2×C4×C83—24no—
274C2×C4×C83—41no—
275C2×C4×C83—42no—
276C2×C4×C83—41no—
277C2×C4×C83—42no—
278C2×C4×C83—41no—
279C2×C4×C83—82no—
280C2×C4×C83—82no—
281C2×C4×C83—82no—
282C2×C4×C83—82no—
283C2×C4×C83C22×D412yes—
284C2×C4×C83C22×D411yescharacteristic
285C2×C4×C83C22×D412yes—
286C2×C4×C83C22×D412yes—
287C2×C4×C83C22×D412yes—
288C2×C4×C83C2511yescharacteristic
289C22⋊D83—48no—
290C22⋊D83—84no—
291C2×Dic83—22no—
292C2×Dic83—22no—
293C2×Dic83—42no—
294C2×Dic83—42no—
295D332—24no—
296D332—22no—
297D332—24no—
298D332—48no—
299D332—42no—
300D332H(5,𝔽2)14yes—
301C4×D83—48no—
302C4×D83—84no—
303Dic166—24no—
304Dic166—42no—
305C83⋊C8—28no—
306C22×C83—21no—
307C22×C83—22no—
308C22×C83—21no—
309C22×C83—22no—
310C22×C83—22no—
311C22×C83—22no—
312C22×C83—22no—
313C22×C83—44no—
314C22×C83—82no—
315C22×C83C2×#13712yes—
316C22×C83C2×#13714yes—
317C22×C83C23×D411yescharacteristic
318C2×D83—24no—
319C2×D83—48no—
320C2×D83—42no—
321C2×D83—42no—
322C2×D83—42no—
323C2×D83—42no—
324C2×D83—42no—
325C2×D83—816no—
326C2×D83—84no—
327C4×C83—22no—
328C4×C83—21no—
329C4×C83—22no—
330C4×C83—22no—
331C4×C83—22no—
332C4×C83—44no—
333C4×C83—44no—
334C4×C83C2×H(5,𝔽2)12yes—
335Dic83—42no—
336Dic83—42no—
337#61570—831nomaximal, Sylow
338C2×C83—22no—
339C2×C83—24no—
340C2×C83—42no—
341C2×C83#348411yescharacteristic
342C2×C83C22×#13711yescharacteristic
343C2×C83#358511yescharacteristic
344D83—44no—
345D83—82no—
346#3501D8311yescharacteristic, complemented
347C2×#546—831no—
348#3314—838no—
349#3266—838no—
350#3215—832no—
351#3193—832no—
352#3189—832no—
353#3110—832no—
354#3007—832no—
355C2×#450—832no—
356#2973—831no—
357C83#6157011yescharacteristic, complemented, Sylow
358C22×#41—831no—
359C23×D4—831no—
360C2×#137—834no—
361C22×SD16—834no—
362#554—24no—
363#554C2×D8314yescomplemented
364D4×Q8C2×D8314yescomplemented
365#546—838no—
366#546—1664no—
367#544—21no—
368#543—21no—
369#543—21no—
370#533C2×D8312yescomplemented
371C2×#124—831no—
372C2×#123—1661no—
373C2×C22⋊Q8—831no—
374C2×C22⋊Q8C2×D8312yes—
375C2×C22⋊Q8C2×D8312yescomplemented
376C2×#121—831no—
377C2×#121—1661no—
378C2×#120—1661no—
379#518—21no—
380C2×C4×D4—831no—
381C2×C4×D4C2×D8311yescharacteristic
382C22×C22⋊C4—1661no—
383#497—834no—
384#489—834no—
385#484—834no—
386#484—834no—
387#480—834no—
388#474—834no—
389#468—838no—
390#467—838no—
391#464—838no—
392#461—834no—
393#452—838no—
394#451—834no—
395#451—834no—
396#450—834no—
397#450—834no—
398#450—838no—
399#448—834no—
400#440—838no—
401#435—838no—
402#432—832no—
403#417—834no—
404C2×#102—834no—
405#407—832no—
406C2×C22⋊C8—832no—
407C25—1661no—
408C2×#41—3324no—
409C2×#41—834no—
410C2×#41—1662no—
411C22×Q8—831no—
412C22×Q8C22×D8312yes—
413C22×Q8C22×D8312yescomplemented
414C22×D4—3324no—
415C22×D4—831no—
416C22×D4—834no—
417C22×D4—831no—
418C22×D4—1661no—
419C22×D4—1661no—
420C22×D4—1661no—
421C22×D4—1662no—
422C22×D4C22⋊D8311yescharacteristic
423C23×C4—1661no—
424C23×C4—1661no—
425C23×C4C22×D8311yescharacteristic
426C23×C4C22×D8311yescharacteristic
427#137—3328no—
428C2×Q16—838no—
429C2×SD16—3328no—
430C2×SD16—838no—
431C2×SD16—838no—
432C2×M16—834no—
433C22×C8—834no—
434C4⋊Q8—24no—
435C4⋊Q8C22×D8312yescomplemented
436C4⋊Q8C22×D8312yescomplemented
437#125—24no—
438#125—22no—
439#124—834no—
440#124—1662no—
441#123—1668no—
442C22⋊Q8—22no—
443C22⋊Q8—22no—
444C22⋊Q8—22no—
445C22⋊Q8—22no—
446C22⋊Q8—22no—
447C22⋊Q8—24no—
448C22⋊Q8—24no—
449C22⋊Q8—24no—
450C22⋊Q8—24no—
451C22⋊Q8—834no—
452C22⋊Q8—1662no—
453C22⋊Q8C22×D8314yes—
454C22⋊Q8C22×D8314yes—
455C22⋊Q8C22×D8314yescomplemented
456#121—834no—
457#121—1662no—
458#121—1668no—
459#120—1668no—
460C4×Q8—22no—
461C4×Q8C22×D8314yescomplemented
462C4×D4—24no—
463C4×D4—24no—
464C4×D4—834no—
465C4×D4—1662no—
466C4×D4C22⋊D8314yes—
467C4×D4C22×D8314yes—
468#117—22no—
469C2×C4⋊C4—22no—
470C2×C4⋊C4—22no—
471C2×C4⋊C4—831no—
472C2×C4⋊C4—1661no—
473C2×C4⋊C4C22⋊D8311yescharacteristic
474C2×C4⋊C4C22×D8312yes—
475C2×C4⋊C4C22×D8312yescomplemented
476C2×C22⋊C4—22no—
477C2×C22⋊C4—22no—
478C2×C22⋊C4—1661no—
479C2×C22⋊C4—1661no—
480C2×C22⋊C4—1661no—
481C2×C22⋊C4—1661no—
482C2×C22⋊C4—1661no—
483C2×C22⋊C4—1668no—
484C2×C22⋊C4C22⋊D8311yescharacteristic
485C2×C22⋊C4C22⋊D8311yescharacteristic
486C2×C42C22×D8311yescharacteristic
487#107—838no—
488C4⋊C8—834no—
489#103—838no—
490#103—838no—
491#102—838no—
492#102—838no—
493C22⋊C8—834no—
494C22⋊C8—834no—
495C22⋊C8—834no—
496#97—834no—
497C24—3324no—
498C24—3324no—
499C24—6642no—
500C24—1661no—
501C24—1664no—
502C24—1661no—
503C24C2×C22⋊D8311yescharacteristic
504C24C2×C22⋊D8311yescharacteristic
505#41—3324no—
506#41—3328no—
507#41—1668no—
508C2×Q8—22no—
509C2×Q8—22no—
510C2×Q8—22no—
511C2×Q8—44no—
512C2×Q8—44no—
513C2×Q8—3322no—
514C2×Q8—832no—
515C2×Q8—1661no—
516C2×Q8C23×D8314yes—
517C2×D4—24no—
518C2×D4—3324no—
519C2×D4—3322no—
520C2×D4—3324no—
521C2×D4—3328no—
522C2×D4—3324no—
523C2×D4—832no—
524C2×D4—832no—
525C2×D4—6642no—
526C2×D4—1668no—
527C2×D4—1664no—
528C2×D4—1664no—
529C2×D4—1664no—
530C2×D4—1664no—
531C2×D4—1661no—
532C2×D4—1661no—
533C2×D4C2×C22⋊D8314yes—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—42no—
539C22×C4—42no—
540C22×C4—3324no—
541C22×C4—6642no—
542C22×C4—1661no—
543C22×C4—1661no—
544C22×C4—1664no—
545C22×C4—1664no—
546C22×C4C2×C22⋊D8311yescharacteristic
547C22×C4C2×C22⋊D8311yescharacteristic
548C22×C4C2×C22⋊D8311yescharacteristic
549C22×C4C2×C22⋊D8311yescharacteristic
550C22×C4C2×C22⋊D8312yes—
551C22×C4C2×C22⋊D8312yes—
552C22×C4C23×D8311yescharacteristic
553C22×C4C23×D8312yes—
554C22×C4C23×D8312yes—
555Q16—3328no—
556SD16—3328no—
557SD16—16616no—
558M16—3324no—
559C2×C8—3324no—
560C2×C8—838no—
561C4⋊C4—24no—
562C4⋊C4—24no—
563C4⋊C4—24no—
564C4⋊C4—22no—
565C4⋊C4—22no—
566C4⋊C4—22no—
567C4⋊C4—22no—
568C4⋊C4—22no—
569C4⋊C4—24no—
570C4⋊C4—832no—
571C4⋊C4—1661no—
572C4⋊C4—1664no—
573C4⋊C4C2×C22⋊D8314yes—
574C4⋊C4C23×D8314yes—
575C22⋊C4—24no—
576C22⋊C4—24no—
577C22⋊C4—24no—
578C22⋊C4—1664no—
579C22⋊C4—1664no—
580C22⋊C4—1664no—
581C22⋊C4—1664no—
582C22⋊C4—1664no—
583C22⋊C4C2×C22⋊D8314yes—
584C22⋊C4C2×C22⋊D8314yes—
585C42—24no—
586C42C2×C22⋊D8312yes—
587C42C23×D8312yes—
588C23—22no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23—3322no—
594C23—3322no—
595C23—3322no—
596C23—3328no—
597C23—3322no—
598C23—3328no—
599C23—3322no—
600C23—6644no—
601C23—66416no—
602C23—1664no—
603C23—1662no—
604C23—1662no—
605C23#1458182314yescomplemented
606C23C22×C22⋊D8312yes—
607C23C22×C22⋊D8311yescharacteristic
608C23C22×C22⋊D8312yes—
609Q8—28no—
610Q8—82no—
611Q8—82no—
612Q8—82no—
613Q8—3322no—
614Q8—1664no—
615D4—28no—
616D4—3322no—
617D4—3328no—
618D4—3328no—
619D4—834no—
620D4—6644no—
621D4—1664no—
622D4—1664no—
623D4—1662no—
624C2×C4—22no—
625C2×C4—24no—
626C2×C4—24no—
627C2×C4—22no—
628C2×C4—24no—
629C2×C4—24no—
630C2×C4—41no—
631C2×C4—42no—
632C2×C4—41no—
633C2×C4—42no—
634C2×C4—41no—
635C2×C4—82no—
636C2×C4—82no—
637C2×C4—82no—
638C2×C4—82no—
639C2×C4—3328no—
640C2×C4—3322no—
641C2×C4—3322no—
642C2×C4—6644no—
643C2×C4—1662no—
644C2×C4—1662no—
645C2×C4C22×C22⋊D8312yes—
646C2×C4C22×C22⋊D8311yescharacteristic
647C2×C4C22×C22⋊D8312yes—
648C2×C4C22×C22⋊D8312yes—
649C2×C4C22×C22⋊D8312yes—
650C2×C4C24×D8311yescharacteristic
651C8—1668no—
652C22—21no—
653C22—22no—
654C22—21no—
655C22—22no—
656C22—22no—
657C22—22no—
658C22—22no—
659C22—44no—
660C22—82no—
661C22—3328no—
662C22—3322no—
663C22—3322no—
664C22—3322no—
665C22—3322no—
666C22—3322no—
667C22—66416no—
668C22—6644no—
669C22—1664no—
670C22C2×#1458182312yes—
671C22C2×#1458182314yes—
672C22C23×C22⋊D8311yescharacteristic
673C4—21no—
674C4—22no—
675C4—22no—
676C4—22no—
677C4—22no—
678C4—44no—
679C4—44no—
680C4—3322no—
681C4—3322no—
682C4H(5,𝔽2)×D8312yes—
683C2—22no—
684C2—24no—
685C2—42no—
686C2—3324no—
687C2—6642no—
688C2#2492109411yescharacteristic
689C2C22×#1458182311yescharacteristic
690C2#2492224211yescharacteristic
subgroupG/H
centerC22C23×C22⋊D83
commutator, cosocleC2×C4×C83C25
FrattiniC2×C4C24×D83
FittingC83×#3501C2
socleC22×C83C23×D4
prime radicalC2×#19128347C2
hypercenter#3501D83
hypocenterC83#61570
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #3501

Complements

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

NH ≅ G/Ntype
2. #24919538C2semidirect
3. #24918974C2semidirect
4. #24918462C2semidirect
5. #24918265C2semidirect
6. #24918235C2semidirect
7. #24917558C2semidirect
8. #24916721C2semidirect
9. C2×#19127851C2semidirect
10. #24916492C2semidirect
11. C83×#3501C2semidirect
14. C2×#14581823C22semidirect
15. C22×#13050577C22semidirect
26. #19128093C22semidirect
27. #19128063C22semidirect
28. #19128036C22semidirect
29. #19128034C22semidirect
30. #19128014C22semidirect
31. #19127978C22semidirect
32. #19127949C22semidirect
33. #19127940C22semidirect
34. #19127923C22semidirect
35. #19127903C22semidirect
36. #19127861C22semidirect
37. #19127857C22semidirect
38. #19127856C22semidirect
41. #19127851C22semidirect
42. #19127840C22semidirect
43. #19127799C22semidirect
44. #19127773C22semidirect
45. #19127758C22semidirect
46. #19127700C22semidirect
47. C2×#14581712C22semidirect
48. #19127665C22semidirect
51. #554×C83C22semidirect
52. D4×Q8×C83C22semidirect
56. #533×C83C22semidirect
58. C2×C22⋊Q8×C83C22semidirect
77. C2×#13050580C23semidirect
81. C2×#13050574C23semidirect
102. #14581725C23semidirect
103. C4⋊(C83⋊C8)C23semidirect
104. #14581716C23semidirect
105. #14581715C23semidirect
110. C22⋊(C83⋊C8)C23semidirect
111. #14581703C23semidirect
113. C22×Q8×C83C23semidirect
118. C4⋊Q8×C83C23semidirect
119. C4⋊Q8×C83C23semidirect
133. C22⋊Q8×C83C23semidirect
135. C4×Q8×C83C23semidirect
145. C2×C4⋊C4×C83C23semidirect
247. C23×C83#137semidirect
346. #3501D83semidirect
357. C83#61570semidirect
363. #554C2×D83semidirect
364. D4×Q8C2×D83semidirect
370. #533C2×D83semidirect
375. C2×C22⋊Q8C2×D83semidirect
413. C22×Q8C22×D83semidirect
435. C4⋊Q8C22×D83semidirect
436. C4⋊Q8C22×D83semidirect
455. C22⋊Q8C22×D83semidirect
461. C4×Q8C22×D83semidirect
475. C2×C4⋊C4C22×D83semidirect
605. C23#14581823semidirect

Maximal subgroups

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

subgroupindex
C2×#191283472
#249195382
#249189742
#249184622
#249182652
#249182352
#249175582
#249167212
C2×#191278512
#249164922
C83×#35012
#6157083