Finite Group Databasebeta

← #3497×D83 #36312573

Subgroups — #3497×D83 #36312573

Order 21248.

11210 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×2−1+4×D83C212yesmaximal, complemented
2#24921234C211yesmaximal, characteristic, complemented
3#24921233C214yesmaximal, complemented
4#24921232C216yesmaximal, complemented
5#24921231C218yesmaximal, complemented
6#24921230C212yesmaximal, complemented
7#24921229C216yesmaximal, complemented
8#24921228C214yesmaximal, complemented
9#550×D83C214yesmaximal, complemented
10D4×Q8×D83C214yesmaximal, complemented
11#548×D83C218yesmaximal, complemented
12#537×D83C216yesmaximal, complemented
13#532×D83C216yesmaximal, complemented
14C2×C4×Q8×D83C211yesmaximal, characteristic, complemented
15C83×#3497C211yesmaximal, characteristic, complemented
16C2×#14581840C2212yescomplemented
17C2×#14581840C2218yescomplemented
18C2×#14581839C2218yescomplemented
19C2×#14581839C22112yescomplemented
202−1+4×D83—232no—
21C2×#41×D83C2218yes—
22C2×#41×D83C22112yes—
23C22×Q8×D83C2218yes—
24C22×Q8×D83C2211yescharacteristic
25#19128373C2214yescomplemented
26#19128372C22112yescomplemented
27#19128371C22112yescomplemented
28#19128370C2218yescomplemented
29#19128369C22124yescomplemented
30Q8×D332C2214yescomplemented
31D4×Dic166C22112yescomplemented
32#19128366C22112yescomplemented
33Q8×C22⋊D83C2218yescomplemented
34#19128364C22124yescomplemented
35#19128363C2218yescomplemented
36#19128362C2218yescomplemented
37#19128361C22124yescomplemented
38#19128360C22124yescomplemented
39#19128359C22124yescomplemented
40#19128358C2218yescomplemented
41#19128357C22124yescomplemented
42#19128282C2216yescomplemented
43#19128281C22124yescomplemented
44#19128280C22124yescomplemented
45#19128279C22112yescomplemented
46#19128278C22124yescomplemented
47#19128252C2216yescomplemented
48#19128251C2216yescomplemented
49#19128250C22112yescomplemented
50#19128249C2216yescomplemented
51#19128248C22112yescomplemented
52#19128248C22112yescomplemented
53#19128247C22112yescomplemented
54#19128246C22112yescomplemented
55#19128246C22112yescomplemented
56C4⋊Q8×D83C2216yes—
57#127×D83C2216yes—
58#124×D83C22112yes—
59C22⋊Q8×D83C22124yes—
60#121×D83C22124yes—
61#121×D83C2214yes—
62#121×D83C22112yes—
63C2×Q8×Dic83C2211yescharacteristic, complemented
64C2×C4×Dic166C2213yescomplemented
65C2×#14581757C2213yescomplemented
66C4×Q8×D83C2214yes—
67C4×Q8×D83C2214yes—
68C4×Q8×D83C2214yescomplemented
69C4×Q8×D83C2214yescomplemented
70C4×D4×D83C22112yes—
71C4×D4×D83C22112yes—
72C2×C4⋊C4×D83C2213yes—
73C2×C42×D83C2213yes—
74C2×2−1+4×C83C2212yescomplemented
75#550×C83C2214yescomplemented
76D4×Q8×C83C2214yescomplemented
77#548×C83C2218yescomplemented
78#537×C83C2216yescomplemented
79#532×C83C2216yescomplemented
80C2×C4×Q8×C83C2211yescharacteristic, complemented
81#14581840—264no—
82#14581840—216no—
83#14581839—296no—
84#14581839—264no—
85C2×#13050591C2318yes—
86C2×#13050591C23112yes—
87C2×#13050590C23124yes—
88C2×#13050590C23112yes—
89C2×#13050590C23124yes—
90C2×#13050589C23124yes—
91C2×#13050589C23124yes—
92C2×#13050589C23112yes—
93#41×D83—264no—
94#41×D83—296no—
95C22×Dic166C23124yes—
96C22×Dic166C2313yes—
97C2×Q8×D83—264no—
98C2×Q8×D83D4116yescomplemented
99C2×Q8×D83C2318yes—
100C2×Q8×D83C23124yes—
101C2×Q8×D83C23112yes—
102C2×Q8×D83C2314yes—
103C2×Q8×D83C2314yes—
104C2×D4×D83C2314yes—
105C2×D4×D83C2318yes—
106C2×D4×D83C23112yes—
107C2×D4×D83C23112yes—
108C22×C4×D83C2311yescharacteristic
109C22×C4×D83C23124yes—
110C22×C4×D83C2313yes—
111C22×C4×D83C2313yes—
112#14581792C2316yes—
113#14581791C23112yes—
114#14581791C23112yes—
115#14581790C23112yes—
116#14581789C2316yes—
117#14581788C23112yes—
118#14581788C23112yes—
119#14581788C23112yes—
120#14581781C23112yes—
121#14581780C23112yes—
122#14581779C23112yes—
123#14581778C23124yes—
124#14581778C23124yes—
125#14581772C23124yes—
126#14581771C23124yes—
127#14581770C23148yes—
128#14581769C23148yes—
129#14581768C23124yes—
130#14581767C23124yes—
131#14581767C2314yes—
132#14581767C23112yes—
133#14581766C23124yes—
134#14581766C2314yes—
135#14581766C23112yes—
136#14581765C23148yes—
137#14581765C2318yes—
138#14581765C23124yes—
139#14581764C23148yes—
140#14581764C2318yes—
141#14581764C23124yes—
142#14581763C23124yes—
143#14581763C2314yes—
144#14581763C23112yes—
145Q8×Dic83C2314yes—
146Q8×Dic83C2314yes—
147C4×Dic166C23112yes—
148C4×Dic166C23112yes—
149#14581757C23112yes—
150#14581757C23112yes—
151C4×D332C23112yes—
152C4×D332C23112yes—
153D4×Dic83C23112yes—
154D4×Dic83C23112yes—
155#14581754C23112yes—
156#14581754C23112yes—
157C4×C22⋊D83C23124yes—
158C4×C22⋊D83C23124yes—
159(C22⋊D83)⋊C4C23124yes—
160(C22⋊D83)⋊C4C23124yes—
161C2×C4⋊Dic83C2313yes—
162C2×Dic83⋊C4C2316yes—
163C4⋊C4×D83C23112yes—
164C4⋊C4×D83C23112yes—
165C4⋊C4×D83C2314yes—
166C4⋊C4×D83C23112yes—
167C22⋊C4×D83C2318yes—
168C22⋊C4×D83C23124yes—
169C2×C4×Dic83C2313yes—
170C2×C4×Dic83C2313yes—
171C2×C4×Dic83C2313yes—
172C42×D83C2316yes—
173C42×D83C2316yes—
174C42×D83C2316yes—
175C42×D83C2316yes—
1762−1+4×C83—216no—
177C2×#41×C83C2318yes—
178C2×#41×C83C23112yes—
179C22×Q8×C83C2318yes—
180C22×Q8×C83C2311yescharacteristic
181C4⋊Q8×C83C2316yes—
182#127×C83C2316yes—
183#124×C83C23112yes—
184C22⋊Q8×C83C23124yes—
185#121×C83C23124yes—
186#121×C83C2314yes—
187#121×C83C23112yes—
188C4×Q8×C83C2314yes—
189C4×Q8×C83C2314yes—
190C4×D4×C83C23112yes—
191C4×D4×C83C23112yes—
192C2×C4⋊C4×C83C2313yes—
193C2×C42×C83C2313yes—
194C23×D83C2418yes—
195C23×D83C2411yescharacteristic
196#13050591—232no—
197#13050591—248no—
198#13050590—248no—
199#13050590—296no—
200#13050590—296no—
201#13050589—296no—
202#13050589—248no—
203#13050589—296no—
204C2×Dic166—296no—
205C2×Dic166C2×D4124yescomplemented
206C2×Dic166C24124yes—
207C2×Dic166C24112yes—
208C2×Dic166C24112yes—
209Q8×D83—232no—
210Q8×D83—248no—
211Q8×D83—296no—
212Q8×D83C2×D4132yes—
213Q8×D83C2×D4132yescomplemented
214C2×D332C2418yes—
215C2×D332C24112yes—
216C2×D332C2414yes—
217C2×D332C24112yes—
218C2×C22⋊D83C2418yes—
219C2×C22⋊D83C2418yes—
220C2×C22⋊D83C24124yes—
221C2×C22⋊D83C2418yes—
222C2×C22⋊D83C24124yes—
223D4×D83—232no—
224D4×D83—248no—
225D4×D83—216no—
226D4×D83—424no—
227C22×Dic83C2411yescharacteristic
228C22×Dic83C24124yes—
229C22×Dic83C2413yes—
230C22×Dic83C2413yes—
231C2×C4×D83—296no—
232C2×C4×D83—24no—
233C2×C4×D83—46no—
234C2×C4×D83C2×D4124yes—
235C2×C4×D83C2411yescharacteristic
236C2×C4×D83C24124yes—
237C2×C4×D83C2411yescharacteristic
238C2×C4×D83C24124yes—
239C2×C4×D83C2418yes—
240C2×C4×D83C2416yes—
241C2×C4×D83C2411yescharacteristic
242C2×C4×D83C2416yes—
243C2×C4×D83C2416yes—
244C2×C4×D83C2416yes—
245C2×C4×D83C2411yescharacteristic
246C4⋊Dic83C24112yes—
247C4⋊Dic83C24112yes—
248C4⋊Dic83C2414yes—
249Dic83⋊C4C24124yes—
250Dic83⋊C4C24124yes—
251Dic83⋊C4C2418yes—
252C22⋊Dic83C24124yes—
253C22⋊Dic83C2418yes—
254(C2×D83)⋊C4C24124yes—
255(C2×D83)⋊C4C24124yes—
256(C2×D83)⋊C4C2418yes—
257(C2×D83)⋊C4C2418yes—
258C4×Dic83C2416yes—
259C4×Dic83C2416yes—
260C4×Dic83C2416yes—
261C4×Dic83C2416yes—
262C4×Dic83C2416yes—
263C4×Dic83C2416yes—
264#41×C83—232no—
265#41×C83—248no—
266C2×Q8×C83—232no—
267C2×Q8×C83C2×D418yescomplemented
268C2×Q8×C83C24112yes—
269C2×Q8×C83C2414yes—
270C2×D4×C83C24112yes—
271C2×D4×C83C2414yes—
272C2×D4×C83C2418yes—
273C2×D4×C83C24112yes—
274C22×C4×C83C2411yescharacteristic
275C22×C4×C83C24124yes—
276C22×C4×C83C2413yes—
277C22×C4×C83C2413yes—
278C4⋊C4×C83C24112yes—
279C4⋊C4×C83C24112yes—
280C4⋊C4×C83C2414yes—
281C22⋊C4×C83C24124yes—
282C22⋊C4×C83C2418yes—
283C42×C83C2416yes—
284C42×C83C2416yes—
285C23×C83C2518yes—
286C23×C83C2511yescharacteristic
287C22×D83—22no—
288C22×D83—22no—
289C22×D83—216no—
290C22×D83—216no—
291C22×D83—216no—
292C22×D83C22×D414yes—
293C22×D83C2518yes—
294C22×D83C2511yescharacteristic
295C22×D83C2511yescharacteristic
296Q8×C83—224no—
297Q8×C83C22×D4116yes—
298D4×C83—216no—
299D4×C83—224no—
300D4×C83—28no—
301D4×C83—412no—
302C2×C4×C83—248no—
303C2×C4×C83—22no—
304C2×C4×C83—43no—
305C2×C4×C83C22×D4112yes—
306C2×C4×C83C2511yescharacteristic
307C2×C4×C83C2516yes—
308C2×C4×C83C2518yes—
309C2×C4×C83C2516yes—
310C2×C4×C83C2511yescharacteristic
311C22⋊D83—216no—
312C22⋊D83—216no—
313C22⋊D83—248no—
314C22⋊D83—216no—
315C22⋊D83—424no—
316C2×Dic83—248no—
317C2×Dic83—22no—
318C2×Dic83—43no—
319C2×Dic83C22×D4112yes—
320C2×Dic83C2511yescharacteristic
321C2×Dic83C2516yes—
322C2×Dic83C2518yes—
323C2×Dic83C2516yes—
324C2×Dic83C2511yescharacteristic
325D332—216no—
326D332—224no—
327D332—28no—
328D332—412no—
329C4×D83—216no—
330C4×D83—22no—
331C4×D83—212no—
332C4×D83—248no—
333C4×D83—22no—
334C4×D83—248no—
335C4×D83—22no—
336C4×D83—46no—
337C4×D83C22×D4124yes—
338C4×D83C22×D4124yes—
339C4×D832−1+414yescomplemented
340Dic166—224no—
341Dic166—248no—
342Dic166C22×D4148yes—
343C22×C83—21no—
344C22×C83—21no—
345C22×C83—28no—
346C22×C83—28no—
347C22×C83—28no—
348C22×C83C23×D412yes—
349C22×C83C2611yescharacteristic
350C2×D83—21no—
351C2×D83—21no—
352C2×D83—28no—
353C2×D83—28no—
354C2×D83—28no—
355C2×D83—28no—
356C2×D83—432no—
357C2×D83C23×D412yes—
358C2×D83C23×D412yes—
359C2×D83C2×2−1+412yes—
360C2×D83#58512yes—
361C4×C83—28no—
362C4×C83—21no—
363C4×C83—26no—
364C4×C83C23×D4112yes—
365C4×C83C2×2−1+412yescomplemented
366Dic83—28no—
367Dic83—21no—
368Dic83—26no—
369Dic83C23×D4112yes—
370Dic83C2×2−1+412yescomplemented
371C2×#3497—831nomaximal, Sylow
372C2×C83—22no—
373C2×C83—48no—
374C2×C83C24×D411yescharacteristic
375C2×C83C22×2−1+411yescharacteristic
376C2×C83C2×#58511yescharacteristic
377D83—22no—
378D83—48no—
379D83#349714yesdirect product factor
380C22×2−1+4—832no—
381#3497—832no—
382#3497—834no—
383#3497—834no—
384#3497—838no—
385#3497—836no—
386#3497—836no—
387#3497—831no—
388#3497D8311yescharacteristic, direct product factor
389C2×#550—834no—
390C2×D4×Q8—834no—
391C2×#548—838no—
392C2×#537—836no—
393C2×#532—836no—
394C22×C4×Q8—831no—
395C83C2×#349711yescharacteristic, complemented, Sylow
396C2×2−1+4—838no—
397C2×2−1+4—8312no—
398C2×2−1+4—838no—
399C2×2−1+4—832no—
400C2×2−1+4—16632no—
401C2×2−1+4C2×D8312yescomplemented
402C22×#41—8312no—
403C22×#41—838no—
404C23×Q8—831no—
405C23×Q8—838no—
406#550—838no—
407#550—8312no—
408#550—8324no—
409#550—834no—
410#550—8312no—
411#550C2×D8314yescomplemented
412D4×Q8—838no—
413D4×Q8—8312no—
414D4×Q8—8324no—
415D4×Q8—834no—
416D4×Q8—8312no—
417D4×Q8C2×D8314yescomplemented
418#548—838no—
419#548—838no—
420#548—8324no—
421#548—8324no—
422#548—8324no—
423#548—838no—
424#548—8324no—
425#548C2×D8318yescomplemented
426#537—8312no—
427#537—8324no—
428#537—8324no—
429#537—8324no—
430#537—836no—
431#537C2×D8316yescomplemented
432#532—8312no—
433#532—836no—
434#532—836no—
435#532—8312no—
436#532—8312no—
437#532—8312no—
438#532—8312no—
439#532—8312no—
440#532—836no—
441#532C2×D8316yescomplemented
442C2×C4⋊Q8—836no—
443C2×#127—836no—
444C2×#124—8312no—
445C2×C22⋊Q8—8324no—
446C2×#121—834no—
447C2×#121—8312no—
448C2×#121—8324no—
449C2×C4×Q8—831no—
450C2×C4×Q8—834no—
451C2×C4×Q8—834no—
452C2×C4×Q8—834no—
453C2×C4×Q8—834no—
454C2×C4×Q8—833no—
455C2×C4×Q8—833no—
456C2×C4×Q8C2×D8311yescharacteristic, complemented
457C2×C4×D4—8312no—
458C2×C4×D4—8312no—
459C22×C4⋊C4—833no—
460C22×C42—833no—
4612−1+4—216no—
4622−1+4—16664no—
4632−1+4—16664no—
4642−1+4—16696no—
4652−1+4—16616no—
466C2×#41—8312no—
467C2×#41—838no—
468C2×#41—8324no—
469C2×#41—8312no—
470C2×#41—8324no—
471C2×#41—8324no—
472C2×#41—8312no—
473C2×#41—8324no—
474C2×#41—16696no—
475C2×#41—16664no—
476C2×#41C22×D83112yes—
477C2×#41C22×D8318yes—
478C22×Q8—8316no—
479C22×Q8—834no—
480C22×Q8—834no—
481C22×Q8—8312no—
482C22×Q8—8324no—
483C22×Q8—838no—
484C22×Q8—833no—
485C22×Q8—8324no—
486C22×Q8—16664no—
487C22×Q8C22×D8318yes—
488C22×Q8C22×D8311yescharacteristic
489C22×D4—8312no—
490C22×D4—834no—
491C22×D4—838no—
492C22×D4—8312no—
493C23×C4—833no—
494C23×C4—833no—
495C23×C4—8324no—
496C23×C4—831no—
497C4⋊Q8—8312no—
498C4⋊Q8—8312no—
499C4⋊Q8—8312no—
500C4⋊Q8—836no—
501C4⋊Q8C22×D8316yes—
502#127—8312no—
503#127—8312no—
504#127—8312no—
505#127—836no—
506#127C22×D8316yes—
507#124—8312no—
508#124—8312no—
509#124—8324no—
510#124—8324no—
511#124—8312no—
512#124C22×D83112yes—
513C22⋊Q8—8324no—
514C22⋊Q8—8324no—
515C22⋊Q8—8348no—
516C22⋊Q8—8324no—
517C22⋊Q8—8348no—
518C22⋊Q8C22×D83124yes—
519#121—834no—
520#121—8312no—
521#121—8324no—
522#121—838no—
523#121—8324no—
524#121—8348no—
525#121—834no—
526#121—8312no—
527#121—8324no—
528#121—834no—
529#121—8312no—
530#121—8324no—
531#121—838no—
532#121—8324no—
533#121—8348no—
534#121C22×D8314yes—
535#121C22×D83112yes—
536#121C22×D83124yes—
537C4×Q8—834no—
538C4×Q8—834no—
539C4×Q8—8312no—
540C4×Q8—8312no—
541C4×Q8—8312no—
542C4×Q8—8312no—
543C4×Q8C22×D8314yes—
544C4×Q8C22×D8314yes—
545C4×D4—8312no—
546C4×D4—8312no—
547C4×D4—8324no—
548C4×D4—8324no—
549C4×D4—8312no—
550C4×D4—8312no—
551C4×D4—8324no—
552C4×D4—8324no—
553C4×D4—8312no—
554C4×D4—8312no—
555C4×D4C22×D83112yes—
556C4×D4C22×D83112yes—
557C2×C4⋊C4—836no—
558C2×C4⋊C4—833no—
559C2×C4⋊C4—8312no—
560C2×C4⋊C4—8312no—
561C2×C4⋊C4—834no—
562C2×C4⋊C4—8312no—
563C2×C4⋊C4C22×D8313yes—
564C2×C22⋊C4—838no—
565C2×C22⋊C4—8324no—
566C2×C42—833no—
567C2×C42—833no—
568C2×C42—833no—
569C2×C42—836no—
570C2×C42—836no—
571C2×C42—836no—
572C2×C42—836no—
573C2×C42C22×D8313yes—
574C24—831no—
575C24—838no—
576#41—232no—
577#41—248no—
578#41—16696no—
579#41—16696no—
580#41—16696no—
581#41—16648no—
582#41—16648no—
583#41—16696no—
584#41—16632no—
585#41—16648no—
586C2×Q8—232no—
587C2×Q8—8332no—
588C2×Q8—8332no—
589C2×Q8—8324no—
590C2×Q8—8312no—
591C2×Q8—8324no—
592C2×Q8—8312no—
593C2×Q8—16696no—
594C2×Q8—16648no—
595C2×Q8—16696no—
596C2×Q8—16632no—
597C2×Q8D4×D8318yescomplemented
598C2×Q8C23×D83112yes—
599C2×Q8C23×D8314yes—
600C2×D4—33224no—
601C2×D4—8324no—
602C2×D4—838no—
603C2×D4—838no—
604C2×D4—838no—
605C2×D4—8324no—
606C2×D4—8312no—
607C2×D4—834no—
608C2×D4—838no—
609C2×D4—8312no—
610C2×D4—16648no—
611C2×D4—16616no—
612C2×D4—16632no—
613C2×D4C23×D8314yes—
614C2×D4C23×D8318yes—
615C2×D4C23×D83112yes—
616C2×D4C23×D83112yes—
617C22×C4—3326no—
618C22×C4—833no—
619C22×C4—836no—
620C22×C4—833no—
621C22×C4—8324no—
622C22×C4—831no—
623C22×C4—836no—
624C22×C4—836no—
625C22×C4—831no—
626C22×C4—8324no—
627C22×C4—831no—
628C22×C4—831no—
629C22×C4—831no—
630C22×C4—836no—
631C22×C4—838no—
632C22×C4—8324no—
633C22×C4—8324no—
634C22×C4—16696no—
635C22×C4—1664no—
636C22×C4C23×D8311yescharacteristic
637C22×C4C23×D83124yes—
638C22×C4C23×D8313yes—
639C22×C4C23×D8313yes—
640C4⋊C4—8324no—
641C4⋊C4—8312no—
642C4⋊C4—838no—
643C4⋊C4—834no—
644C4⋊C4—8324no—
645C4⋊C4—8312no—
646C4⋊C4C23×D83112yes—
647C4⋊C4C23×D8314yes—
648C4⋊C4C23×D83112yes—
649C22⋊C4—838no—
650C22⋊C4—8324no—
651C22⋊C4—838no—
652C22⋊C4—838no—
653C22⋊C4—8324no—
654C22⋊C4—8324no—
655C22⋊C4C23×D8318yes—
656C22⋊C4C23×D83124yes—
657C42—836no—
658C42—836no—
659C42—836no—
660C42—836no—
661C42—836no—
662C42—836no—
663C42C23×D8316yes—
664C42C23×D8316yes—
665C23—831no—
666C23—834no—
667C23—831no—
668C23—838no—
669C23—16616no—
670C23—16616no—
671C23—16616no—
672C23—1662no—
673C23—1662no—
674C23C24×D8318yes—
675C23C24×D8311yescharacteristic
676Q8—224no—
677Q8—8348no—
678Q8—16648no—
679Q8—16624no—
680Q8C2×D4×D83116yes—
681D4—216no—
682D4—224no—
683D4—28no—
684D4—412no—
685D4—33212no—
686D4—33224no—
687D4—16616no—
688D4—16648no—
689D4—16616no—
690D4—16616no—
691D4—16616no—
692D4—16624no—
693D4—1668no—
694C2×C4—248no—
695C2×C4—22no—
696C2×C4—43no—
697C2×C4—3326no—
698C2×C4—3323no—
699C2×C4—8312no—
700C2×C4—831no—
701C2×C4—836no—
702C2×C4—8324no—
703C2×C4—8324no—
704C2×C4—834no—
705C2×C4—831no—
706C2×C4—836no—
707C2×C4—838no—
708C2×C4—16648no—
709C2×C4—1662no—
710C2×C4—16612no—
711C2×C4—16616no—
712C2×C4—1662no—
713C2×C4—16648no—
714C2×C4—1662no—
715C2×C4—16648no—
716C2×C4—1662no—
717C2×C4C2×D4×D83112yes—
718C2×C4C24×D8311yescharacteristic
719C2×C4C24×D8316yes—
720C2×C4C24×D8318yes—
721C2×C4C24×D8316yes—
722C2×C4C24×D8311yescharacteristic
723C22—21no—
724C22—21no—
725C22—28no—
726C22—28no—
727C22—28no—
728C22—33232no—
729C22—832no—
730C22—832no—
731C22—832no—
732C22—832no—
733C22—1668no—
734C22—1668no—
735C22—1668no—
736C22—1668no—
737C22—1661no—
738C22—1661no—
739C22C22×D4×D8312yes—
740C22C25×D8311yescharacteristic
741C4—28no—
742C4—21no—
743C4—26no—
744C4—8312no—
745C4—832no—
746C4—1668no—
747C4—1661no—
748C4—1666no—
749C4C22×D4×D83112yes—
750C42−1+4×D8312yescomplemented
751C2—22no—
752C2—48no—
753C2—3328no—
754C2—834no—
755C2—1662no—
756C2C23×D4×D8311yescharacteristic
757C2C2×2−1+4×D8311yescharacteristic
758C2#585×D8311yescharacteristic
subgroupG/H
center, FrattiniC22C25×D83
commutator, socle, cosocleC22×C83C26
FittingC83×#3497C2
hypercenter#3497D83
hypocenterC83C2×#3497
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C22 ◁ #3497

Complements

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

NH ≅ G/Ntype
1. C2×2−1+4×D83C2semidirect
2. #24921234C2semidirect
3. #24921233C2semidirect
4. #24921232C2semidirect
5. #24921231C2semidirect
6. #24921230C2semidirect
7. #24921229C2semidirect
8. #24921228C2semidirect
9. #550×D83C2semidirect
10. D4×Q8×D83C2semidirect
11. #548×D83C2semidirect
12. #537×D83C2semidirect
13. #532×D83C2semidirect
14. C2×C4×Q8×D83C2semidirect
15. C83×#3497C2semidirect
16. C2×#14581840C22semidirect
17. C2×#14581840C22semidirect
18. C2×#14581839C22semidirect
19. C2×#14581839C22semidirect
25. #19128373C22semidirect
26. #19128372C22semidirect
27. #19128371C22semidirect
28. #19128370C22semidirect
29. #19128369C22semidirect
30. Q8×D332C22semidirect
31. D4×Dic166C22semidirect
32. #19128366C22semidirect
33. Q8×C22⋊D83C22semidirect
34. #19128364C22semidirect
35. #19128363C22semidirect
36. #19128362C22semidirect
37. #19128361C22semidirect
38. #19128360C22semidirect
39. #19128359C22semidirect
40. #19128358C22semidirect
41. #19128357C22semidirect
42. #19128282C22semidirect
43. #19128281C22semidirect
44. #19128280C22semidirect
45. #19128279C22semidirect
46. #19128278C22semidirect
47. #19128252C22semidirect
48. #19128251C22semidirect
49. #19128250C22semidirect
50. #19128249C22semidirect
51. #19128248C22semidirect
52. #19128248C22semidirect
53. #19128247C22semidirect
54. #19128246C22semidirect
55. #19128246C22semidirect
63. C2×Q8×Dic83C22semidirect
64. C2×C4×Dic166C22semidirect
65. C2×#14581757C22semidirect
68. C4×Q8×D83C22semidirect
69. C4×Q8×D83C22semidirect
74. C2×2−1+4×C83C22semidirect
75. #550×C83C22semidirect
76. D4×Q8×C83C22semidirect
77. #548×C83C22semidirect
78. #537×C83C22semidirect
79. #532×C83C22semidirect
80. C2×C4×Q8×C83C22semidirect
98. C2×Q8×D83D4semidirect
205. C2×Dic166C2×D4semidirect
213. Q8×D83C2×D4semidirect
267. C2×Q8×C83C2×D4semidirect
339. C4×D832−1+4semidirect
365. C4×C83C2×2−1+4semidirect
370. Dic83C2×2−1+4semidirect
379. D83#3497direct (N × H)
388. #3497D83direct (N × H)
395. C83C2×#3497semidirect
401. C2×2−1+4C2×D83semidirect
411. #550C2×D83semidirect
417. D4×Q8C2×D83semidirect
425. #548C2×D83semidirect
431. #537C2×D83semidirect
441. #532C2×D83semidirect
456. C2×C4×Q8C2×D83semidirect
597. C2×Q8D4×D83semidirect
750. C42−1+4×D83semidirect

Maximal subgroups

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

subgroupindex
C2×2−1+4×D832
#249212342
#249212332
#249212322
#249212312
#249212302
#249212292
#249212282
#550×D832
D4×Q8×D832
#548×D832
#537×D832
#532×D832
C2×C4×Q8×D832
C83×#34972
C2×#349783