Finite Group Databasebeta

← #36312629

Subgroups — #36312629

Order 21248.

7094 conjugacy classes of subgroups.

The subgroup lattice has 944 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24921550C214yesmaximal, complemented
2#24921539C214yesmaximal, complemented
3#24921457C214yesmaximal, complemented
4#24921445C214yesmaximal, complemented
5#24921327C216yesmaximal, complemented
6#24921269C211yesmaximal, characteristic, complemented
7#24921230C211yesmaximal, characteristic, complemented
8#24921169C216yesmaximal, complemented
9#24921114C211yesmaximal, characteristic, complemented
10#24921084C214yesmaximal, complemented
11#24921079C214yesmaximal, complemented
12#24921053C214yesmaximal, complemented
13Q8×#13050589C214yesmaximal, complemented
14#24920887C216yesmaximal, complemented
15#24920755C216yesmaximal, complemented
162−1+4×Dic83C211yesmaximal, characteristic, complemented
17#24920672C211yesmaximal, characteristic, complemented
18C22×Q8×Dic83C211yesmaximal, characteristic, complemented
19C83×#3486C211yesmaximal, characteristic, complemented
20C2×#14581840C2211yescharacteristic
21#19128433C22112yescomplemented
22Q8×Dic166C2214yescomplemented
23#19128430C2214yescomplemented
24#19128427C2214yescomplemented
25#19128427C2214yescomplemented
26#19128426C22112yescomplemented
27#19128425C22112yescomplemented
28#19128422C22112yescomplemented
29#19128420C22112yescomplemented
30#19128409C22112yes—
31#19128409C22112yescomplemented
32#19128408C22112yes—
33#19128403C22112yes—
34#19128397C22112yes—
35#19128393C22112yes—
36#19128393C22112yescomplemented
37#19128391C22112yes—
38#19128385C22112yescomplemented
39#19128370C2214yescomplemented
40Q8×C22⋊D83C2214yes—
41Q8×C22⋊D83C2214yes—
42Q8×C22⋊D83C2214yescomplemented
43#19128362C2214yes—
44#19128362C2214yes—
45#19128362C2214yescomplemented
46#19128358C2214yescomplemented
47#19128355C22112yes—
48#19128351C22112yes—
49#19128329C2216yes—
50#19128324C22112yescomplemented
51#19128320C22112yescomplemented
52#19128312C22112yescomplemented
53#19128311C22112yescomplemented
54#19128295C22124yes—
55#19128279C2216yes—
56#19128275C2216yes—
57#19128256C22112yescomplemented
58#19128254C2216yes—
59#19128253C2216yes—
60#19128253C2216yes—
61#19128253C22112yescomplemented
62#19128247C2216yes—
63#19128246C2216yes—
64#19128246C2216yes—
65#19128237C2216yes—
66#19128237C2216yes—
67#19128237C22112yescomplemented
68#19128232C2216yes—
69#19128232C2216yes—
70#19128231C22112yes—
71#19128231C22112yes—
72#19128230C22112yescomplemented
73#19128228C22112yes—
74#19128228C22112yes—
75#19128212C2216yes—
76#19128207C22112yes—
77#19128207C2214yes—
78#19128184C2216yes—
79#19128184C2214yescomplemented
80#19128183C2214yescomplemented
81#19128181C2216yes—
82#19128179C2211yescharacteristic
83#19128179C2214yescomplemented
84#19128177C2214yescomplemented
85#41×Dic83C2216yes—
86#41×Dic83C2214yescomplemented
87C4×#13050591C2214yescomplemented
88#19128169C2216yes—
89C4×#13050589C22112yes—
90C4×#13050589C22112yes—
91C2×Q8×Dic83C2213yes—
92C2×Q8×Dic83C2211yescharacteristic
93C2×Q8×Dic83C2214yes—
94C2×Q8×Dic83C2211yescharacteristic
95C2×Q8×Dic83C2214yes—
96C2×Q8×Dic83C2214yes—
97C2×Q8×Dic83C2213yes—
98C2×Q8×Dic83C2214yes—
99C2×Q8×Dic83C2214yescomplemented
100C4×Q8×D83C2214yescomplemented
101C22×C4⋊Dic83C2213yes—
102C22×C4×Dic83C2213yes—
103C2×2−1+4×C83C2211yescharacteristic
104C23×Q8×C83C2211yescharacteristic
105D4×Q8×C83C2214yes—
106D4×Q8×C83C2214yes—
107#548×C83C2214yes—
108#548×C83C2214yes—
109#536×C83C2216yes—
110#525×C83C2216yes—
111#519×C83C2211yescharacteristic
112#14581840—28no—
113C2×#13050591C2314yes—
114C2×#13050590C2316yes—
115C2×#13050589C2314yes—
116C2×#13050589C23112yes—
117C2×Q8×D83C2314yes—
118C23×Dic83C2311yescharacteristic
119C23×Dic83C2313yes—
120#14581792C23112yes—
121#14581791C23112yes—
122#14581791C2316yes—
123#14581791C2316yes—
124#14581790C23112yes—
125#14581790C2316yes—
126#14581788C2316yes—
127#14581787C23112yes—
128#14581787C23124yes—
129#14581787C23112yes—
130#14581785C23112yes—
131#14581785C23112yes—
132#14581785C23124yes—
133#14581784C23112yes—
134#14581783C23112yes—
135#14581783C2316yes—
136#14581783C23124yes—
137#14581783C2316yes—
138#14581782C23124yes—
139#14581782C23112yes—
140#14581782C23112yes—
141#14581781C23112yes—
142#14581781C2316yes—
143#14581779C2316yes—
144#14581778C23112yes—
145#14581778C23112yes—
146#14581776C23124yes—
147#14581776C23112yes—
148#14581776C2314yes—
149#14581775C23112yes—
150#14581774C23124yes—
151#14581773C23112yes—
152#14581773C2314yes—
153#14581772C23124yes—
154#14581771C23112yes—
155#14581771C2316yes—
156#14581771C2316yes—
157#14581769C23124yes—
158#14581769C23112yes—
159#14581769C23112yes—
160#14581769C2314yes—
161#14581769C2314yes—
162#14581768C23112yes—
163#14581768C23112yes—
164#14581768C23112yes—
165#14581766C23112yes—
166#14581766C2316yes—
167#14581766C2316yes—
168#14581764C23112yes—
169#14581764C2314yes—
170#14581764C23112yes—
171#14581764C2314yes—
172#14581763C23112yes—
173#14581761C2314yes—
174Q8×Dic83C23112yes—
175Q8×Dic83C2314yes—
176Q8×Dic83C2314yes—
177Q8×Dic83C2314yes—
178Q8×Dic83C2314yes—
179Q8×Dic83C23112yes—
180Q8×Dic83C23112yes—
181Q8×Dic83C23112yes—
182Q8×Dic83C2314yes—
183Q8×Dic83C2314yes—
184Q8×Dic83C23112yes—
185Q8×Dic83C2316yes—
186Q8×Dic83C2316yes—
187C4×Dic166C23112yes—
188C4×Dic166C23112yes—
189C4×Dic166C23112yes—
190#14581757C2316yes—
191#14581757C23112yes—
192#14581757C23112yes—
193#14581757C2316yes—
194C4×D332C23112yes—
195D4×Dic83C2316yes—
196D4×Dic83C23112yes—
197D4×Dic83C23112yes—
198D4×Dic83C2314yes—
199D4×Dic83C2314yes—
200D4×Dic83C2316yes—
201D4×Dic83C23112yes—
202#14581754C2316yes—
203#14581754C2316yes—
204C4×C22⋊D83C23112yes—
205C4×C22⋊D83C23112yes—
206C4×C22⋊D83C23112yes—
207C4×C22⋊D83C23112yes—
208(C22⋊D83)⋊C4C23112yes—
209(C22⋊D83)⋊C4C23112yes—
210(C22⋊D83)⋊C4C2314yes—
211(C22⋊D83)⋊C4C23112yes—
212(C22⋊D83)⋊C4C2314yes—
213(C22⋊D83)⋊C4C23112yes—
214#14581751C23112yes—
215#14581751C2316yes—
216#14581751C23112yes—
217#14581750C23112yes—
218#14581750C23112yes—
219#14581750C23112yes—
220#14581749C23112yes—
221#14581748C23112yes—
222#14581748C23112yes—
223#14581748C2314yes—
224#14581748C23112yes—
225C2×C4⋊Dic83C2313yes—
226C2×C4⋊Dic83C23112yes—
227C2×C4⋊Dic83C23112yes—
228C2×C4⋊Dic83C23112yes—
229C2×C4⋊Dic83C2313yes—
230C2×C4⋊Dic83C2316yes—
231C4⋊C4×D83C23112yes—
232C2×C4×Dic83C2316yes—
233C2×C4×Dic83C2316yes—
234C2×C4×Dic83C2313yes—
235C2×C4×Dic83C2313yes—
236C2×C4×Dic83C2313yes—
237C2×C4×Dic83C2316yes—
238C2×C4×Dic83C2316yes—
239C2×C4×Dic83C2313yes—
240C2×C4×Dic83C23112yes—
241C42×D83C23112yes—
2422−1+4×C83—28no—
243C2×#41×C83C2314yes—
244C2×#41×C83C2316yes—
245C22×Q8×C83—28no—
246C22×Q8×C83C2314yes—
247C22×Q8×C83C2314yes—
248C22×Q8×C83C2314yes—
249C22×Q8×C83C2313yes—
250C22×Q8×C83C2311yescharacteristic
251C23×C4×C83C2313yes—
252C4⋊Q8×C83C23112yes—
253#124×C83C23112yes—
254#123×C83C23112yes—
255C22⋊Q8×C83C23112yes—
256C22⋊Q8×C83C2316yes—
257C22⋊Q8×C83C2316yes—
258C22⋊Q8×C83C23112yes—
259#121×C83C2316yes—
260#121×C83C2316yes—
261#120×C83C2314yes—
262C4×Q8×C83C2314yes—
263C4×Q8×C83C2314yes—
264C4×D4×C83C23112yes—
265C4×D4×C83C23112yes—
266#117×C83C2316yes—
267#13050591—216no—
268#13050590—224no—
269#13050589—216no—
270#13050589—424no—
271C2×Dic166C2414yes—
272C2×Dic166C2416yes—
273C2×Dic166C24112yes—
274Q8×D83—216no—
275C2×D332C2416yes—
276C2×C22⋊D83C2414yes—
277C2×C22⋊D83C2414yes—
278C2×C22⋊D83C2414yes—
279C2×C22⋊D83C2414yes—
280C2×C22⋊D83C24112yes—
281C22×Dic83—24no—
282C22×Dic83—46no—
283C22×Dic83C2411yescharacteristic
284C22×Dic83C2411yescharacteristic
285C22×Dic83C2411yescharacteristic
286C22×Dic83C2416yes—
287C22×Dic83C2411yescharacteristic
288C22×Dic83C2411yescharacteristic
289C22×Dic83C2414yes—
290C22×Dic83C2413yes—
291C22×Dic83C2416yes—
292C22×Dic83C24112yes—
293C22×Dic83C2413yes—
294C22×Dic83C2411yescharacteristic
295C2×C4×D83C24112yes—
296C2×C4×D83C2414yes—
297C2×C4×D83C24112yes—
298C4⋊Dic83C24112yes—
299C4⋊Dic83C2416yes—
300C4⋊Dic83C2416yes—
301C4⋊Dic83C24112yes—
302C4⋊Dic83C24124yes—
303C4⋊Dic83C24112yes—
304C4⋊Dic83C2414yes—
305C4⋊Dic83C2414yes—
306C4⋊Dic83C24112yes—
307Dic83⋊C4C24112yes—
308Dic83⋊C4C2414yes—
309Dic83⋊C4C2414yes—
310Dic83⋊C4C24112yes—
311Dic83⋊C4C24112yes—
312Dic83⋊C4C24112yes—
313Dic83⋊C4C24112yes—
314Dic83⋊C4C24112yes—
315Dic83⋊C4C2414yes—
316Dic83⋊C4C2414yes—
317C22⋊Dic83C2414yes—
318C22⋊Dic83C2414yes—
319C22⋊Dic83C2414yes—
320C22⋊Dic83C24112yes—
321C22⋊Dic83C24112yes—
322C22⋊Dic83C2414yes—
323C22⋊Dic83C2414yes—
324(C2×D83)⋊C4C24112yes—
325(C2×D83)⋊C4C24112yes—
326(C2×D83)⋊C4C2414yes—
327(C2×D83)⋊C4C2414yes—
328(C2×D83)⋊C4C24112yes—
329(C2×D83)⋊C4C24112yes—
330C4×Dic83C2416yes—
331C4×Dic83C2416yes—
332C4×Dic83C2416yes—
333C4×Dic83C24112yes—
334C4×Dic83C24112yes—
335C4×Dic83C24112yes—
336C4×Dic83C2416yes—
337C4×Dic83C2416yes—
338C4×Dic83C2414yes—
339C4×Dic83C2416yes—
340C4×Dic83C2416yes—
341C4×Dic83C2414yes—
342C4×Dic83C2416yes—
343C24×C83C2411yescharacteristic
344#41×C83—216no—
345#41×C83—224no—
346C2×Q8×C83—216no—
347C2×Q8×C83—216no—
348C2×Q8×C83—216no—
349C2×Q8×C83—212no—
350C2×Q8×C83#4118yescomplemented
351C2×Q8×C83C24112yes—
352C2×Q8×C83C2416yes—
353C2×Q8×C83C2414yes—
354C2×D4×C83C2416yes—
355C2×D4×C83C2414yes—
356C2×D4×C83C2414yes—
357C2×D4×C83C2414yes—
358C22×C4×C83—212no—
359C22×C4×C83C2416yes—
360C22×C4×C83C2416yes—
361C22×C4×C83C24112yes—
362C22×C4×C83C2413yes—
363C22×C4×C83C2413yes—
364C4⋊C4×C83C24112yes—
365C4⋊C4×C83C24112yes—
366C4⋊C4×C83C2416yes—
367C4⋊C4×C83C2416yes—
368C22⋊C4×C83C2414yes—
369C22⋊C4×C83C2414yes—
370C22⋊C4×C83C24112yes—
371C22⋊C4×C83C2414yes—
372C22⋊C4×C83C24112yes—
373C42×C83C24112yes—
374C23×C83—22no—
375C23×C83—22no—
376C23×C83—22no—
377C23×C83C2514yes—
378C23×C83C2511yescharacteristic
379C23×C83C2511yescharacteristic
380C23×C83C2511yescharacteristic
381C22×D83C2514yes—
382Q8×C83—224no—
383Q8×C83—212no—
384Q8×C83C2×#41116yes—
385D4×C83—28no—
386D4×C83—28no—
387D4×C83—28no—
388D4×C83—212no—
389C2×C4×C83—26no—
390C2×C4×C83—212no—
391C2×C4×C83—212no—
392C2×C4×C83—224no—
393C2×C4×C83C2×#41112yes—
394C2×C4×C83C2514yes—
395C2×C4×C83C2514yes—
396C2×C4×C83C2516yes—
397C2×C4×C83C2514yes—
398C2×C4×C83C2516yes—
399C22⋊D83—28no—
400C22⋊D83—28no—
401C22⋊D83—28no—
402C22⋊D83—28no—
403C22⋊D83—412no—
404C2×Dic83—22no—
405C2×Dic83—212no—
406C2×Dic83—22no—
407C2×Dic83—22no—
408C2×Dic83—22no—
409C2×Dic83—22no—
410C2×Dic83—28no—
411C2×Dic83—43no—
412C2×Dic83—46no—
413C2×Dic83—43no—
414C2×Dic83—412no—
415C2×Dic832−1+414yescomplemented
416C2×Dic83C2511yescharacteristic
417C2×Dic83C2511yescharacteristic
418C2×Dic83C2516yes—
419C2×Dic83C2514yes—
420C2×Dic83C2514yes—
421C2×Dic83C2516yes—
422C2×Dic83C2514yes—
423C2×Dic83C2511yescharacteristic
424C2×Dic83C2511yescharacteristic
425D332—212no—
426C4×D83—224no—
427C4×D83—28no—
428C4×D83—412no—
429Dic166—212no—
430Dic166—28no—
431Dic166—412no—
432C22×C83—28no—
433C22×C83—21no—
434C22×C83—21no—
435C22×C83—21no—
436C22×C83—21no—
437C22×C83—21no—
438C22×C83—21no—
439C22×C83—24no—
440C22×C83—24no—
441C22×C83—24no—
442C22×C83C22×#4112yes—
443C22×C83C2×2−1+412yes—
444C22×C83#58512yes—
445C22×C83C2611yescharacteristic
446C2×D83—24no—
447C2×D83—24no—
448C2×D83—24no—
449C4×C83—24no—
450C4×C83—26no—
451C4×C83—24no—
452C4×C83—24no—
453C4×C83C22×#41112yes—
454Dic83—24no—
455Dic83—24no—
456Dic83—21no—
457Dic83—21no—
458Dic83—24no—
459Dic83—26no—
460Dic83—26no—
461Dic83C2×2−1+412yes—
462Dic83C2×2−1+412yes—
463#62788—831nomaximal, Sylow
464C2×C83—22no—
465C2×C83—22no—
466C2×C83—22no—
467C2×C83—44no—
468C2×C83C23×#4111yescharacteristic
469C2×C83C22×2−1+411yescharacteristic
470C2×C83C2×#58511yescharacteristic
471D83—44no—
472#3523—834no—
473#3522—834no—
474#3516—834no—
475#3516—834no—
476#3507—836no—
477#3502—831no—
478#3497—831no—
479#3492—836no—
480#3486—831no—
481#3486D8311yescharacteristic, complemented
482#3482—834no—
483#3482—834no—
484#3480—834no—
485Q8×#41—834no—
486#3461—836no—
487#3444—836no—
488C4×2−1+4—831no—
489C4×2−1+4—831no—
490C22×C4×Q8—831no—
491C83#6278811yescharacteristic, complemented, Sylow
492C2×2−1+4—831no—
493C2×2−1+4C2×D8311yescharacteristic
494C23×Q8C2×D8311yescharacteristic
495#559—8312no—
496Q82—834no—
497#557—8312no—
498#557—834no—
499#557—834no—
500#557—834no—
501#556—8312no—
502#556—8312no—
503#556—8312no—
504#554—8312no—
505#554—8312no—
506#554—8312no—
507#553—8312no—
508#553—8312no—
509#552—8312no—
510#552—8312no—
511#552—8312no—
512#552—8312no—
513#550—834no—
514D4×Q8—834no—
515D4×Q8—834no—
516D4×Q8—834no—
517D4×Q8C2×D8314yes—
518D4×Q8C2×D8314yes—
519#548—834no—
520#548—834no—
521#548—834no—
522#548—834no—
523#548C2×D8314yes—
524#548C2×D8314yes—
525#547—8312no—
526#547—8312no—
527#544—836no—
528#542—8312no—
529#542—8312no—
530#541—8312no—
531#541—8312no—
532#539—8324no—
533#537—836no—
534#536—836no—
535#536C2×D8316yes—
536#533—8312no—
537#533—836no—
538#533—836no—
539#533—8312no—
540#533—836no—
541#532—836no—
542#532—836no—
543#532—836no—
544#529—8312no—
545#529—8312no—
546#529—8312no—
547#529—836no—
548#529—836no—
549#529—8312no—
550#529—836no—
551#529—836no—
552#529—8312no—
553#529—8312no—
554#525—836no—
555#525—834no—
556#525—8312no—
557#525C2×D8316yes—
558#520—836no—
559#520—834no—
560#520—834no—
561#520—836no—
562#519—831no—
563#519—834no—
564#519—834no—
565#519C2×D8311yescharacteristic
566C4×#41—836no—
567C4×#41—834no—
568C4×#41—834no—
569C4×#41—8312no—
570C4×#41—8312no—
571C4×#41—836no—
572C2×C4×Q8—831no—
573C2×C4×Q8—833no—
574C2×C4×Q8—834no—
575C2×C4×Q8—834no—
576C2×C4×Q8—831no—
577C2×C4×Q8—833no—
578C2×C4×Q8—834no—
579C2×C4×Q8—834no—
580C2×C4×Q8—834no—
581C2×C4×Q8—834no—
582C22×C4⋊C4—833no—
583C22×C42—833no—
5842−1+4—28no—
5852−1+4—1668no—
586C2×#41—834no—
587C2×#41—8312no—
588C2×#41—834no—
589C2×#41—836no—
590C2×#41C22×D8316yes—
591C2×#41C22×D8314yes—
592C22×Q8—28no—
593C22×Q8—834no—
594C22×Q8C22×D8313yes—
595C22×Q8C22×D8314yes—
596C22×Q8C22×D8314yes—
597C22×Q8C22×D8314yes—
598C22×Q8C22×D8311yescharacteristic
599C23×C4—833no—
600C23×C4—831no—
601C23×C4C22×D8313yes—
602C4⋊Q8—836no—
603C4⋊Q8—8312no—
604C4⋊Q8—836no—
605C4⋊Q8—836no—
606C4⋊Q8—8312no—
607C4⋊Q8—8312no—
608C4⋊Q8C22×D83112yes—
609#127—836no—
610#126—8312no—
611#126—8312no—
612#126—8324no—
613#126—8312no—
614#126—8312no—
615#126—8324no—
616#125—8312no—
617#125—8312no—
618#125—836no—
619#125—836no—
620#125—8312no—
621#125—8324no—
622#125—8324no—
623#125—8312no—
624#124—836no—
625#124—8312no—
626#124—836no—
627#124—8312no—
628#124—8312no—
629#124C22×D83112yes—
630#123—834no—
631#123—8312no—
632#123—8312no—
633#123—834no—
634#123—8312no—
635#123—8324no—
636#123—8324no—
637#123C22×D83112yes—
638C22⋊Q8—8312no—
639C22⋊Q8—8312no—
640C22⋊Q8—8312no—
641C22⋊Q8—836no—
642C22⋊Q8—836no—
643C22⋊Q8—8312no—
644C22⋊Q8—8324no—
645C22⋊Q8—834no—
646C22⋊Q8—834no—
647C22⋊Q8—8312no—
648C22⋊Q8—8312no—
649C22⋊Q8—8324no—
650C22⋊Q8C22×D8316yes—
651C22⋊Q8C22×D8316yes—
652C22⋊Q8C22×D83112yes—
653C22⋊Q8C22×D83112yes—
654#121—8312no—
655#121—834no—
656#121—834no—
657#121—8312no—
658#121—8312no—
659#121—836no—
660#121—836no—
661#121—8312no—
662#121C22×D8316yes—
663#121C22×D8316yes—
664#120—834no—
665#120C22×D8314yes—
666C4×Q8—834no—
667C4×Q8—834no—
668C4×Q8—8312no—
669C4×Q8—8312no—
670C4×Q8—834no—
671C4×Q8—834no—
672C4×Q8—8312no—
673C4×Q8—8312no—
674C4×Q8—836no—
675C4×Q8—834no—
676C4×Q8—8312no—
677C4×Q8—836no—
678C4×Q8—834no—
679C4×Q8—836no—
680C4×Q8—836no—
681C4×Q8—8312no—
682C4×Q8—8312no—
683C4×Q8—8312no—
684C4×Q8—8312no—
685C4×Q8—8312no—
686C4×Q8C22×D8314yes—
687C4×Q8C22×D8314yes—
688C4×D4—834no—
689C4×D4—834no—
690C4×D4—836no—
691C4×D4—8312no—
692C4×D4—836no—
693C4×D4—8312no—
694C4×D4—8312no—
695C4×D4—8312no—
696C4×D4—8312no—
697C4×D4—8312no—
698C4×D4—8312no—
699C4×D4—836no—
700C4×D4—836no—
701C4×D4—834no—
702C4×D4—834no—
703C4×D4—8312no—
704C4×D4—8312no—
705C4×D4—8312no—
706C4×D4—8312no—
707C4×D4—8312no—
708C4×D4C22×D83112yes—
709C4×D4C22×D83112yes—
710#117—836no—
711#117—8312no—
712#117—8312no—
713#117—8312no—
714#117—8312no—
715#117—8312no—
716#117—834no—
717#117—8312no—
718#117—8312no—
719#117—8312no—
720#117—8312no—
721#117C22×D8316yes—
722C2×C4⋊C4—833no—
723C2×C4⋊C4—833no—
724C2×C4⋊C4—836no—
725C2×C4⋊C4—8312no—
726C2×C4⋊C4—8312no—
727C2×C4⋊C4—8312no—
728C2×C4⋊C4—8312no—
729C2×C42—833no—
730C2×C42—836no—
731C2×C42—836no—
732C2×C42—833no—
733C2×C42—836no—
734C2×C42—833no—
735C2×C42—836no—
736C2×C42—833no—
737C2×C42—8312no—
738C2×C42—8312no—
739C24C23×D8311yescharacteristic
740#41—216no—
741#41—224no—
742#41—33224no—
743#41—16616no—
744#41—16616no—
745#41—16624no—
746C2×Q8—216no—
747C2×Q8—216no—
748C2×Q8—216no—
749C2×Q8—212no—
750C2×Q8—8312no—
751C2×Q8—834no—
752C2×Q8—836no—
753C2×Q8—16616no—
754C2×Q8#1305058918yescomplemented
755C2×Q8C23×D83112yes—
756C2×Q8C23×D8316yes—
757C2×Q8C23×D8314yes—
758C2×D4—8312no—
759C2×D4—834no—
760C2×D4—834no—
761C2×D4—834no—
762C2×D4—834no—
763C2×D4—836no—
764C2×D4C23×D8314yes—
765C2×D4C23×D8316yes—
766C2×D4C23×D8314yes—
767C2×D4C23×D8314yes—
768C22×C4—212no—
769C22×C4—3326no—
770C22×C4—833no—
771C22×C4—836no—
772C22×C4—833no—
773C22×C4—8312no—
774C22×C4—8312no—
775C22×C4—831no—
776C22×C4—831no—
777C22×C4—831no—
778C22×C4—831no—
779C22×C4—831no—
780C22×C4—831no—
781C22×C4—834no—
782C22×C4—836no—
783C22×C4—834no—
784C22×C4—8312no—
785C22×C4—1664no—
786C22×C4C23×D8316yes—
787C22×C4C23×D8316yes—
788C22×C4C23×D8313yes—
789C22×C4C23×D83112yes—
790C22×C4C23×D8313yes—
791C4⋊C4—8312no—
792C4⋊C4—8312no—
793C4⋊C4—8324no—
794C4⋊C4—836no—
795C4⋊C4—8312no—
796C4⋊C4—8312no—
797C4⋊C4—836no—
798C4⋊C4—834no—
799C4⋊C4—834no—
800C4⋊C4—834no—
801C4⋊C4—834no—
802C4⋊C4—834no—
803C4⋊C4—834no—
804C4⋊C4—8312no—
805C4⋊C4—8312no—
806C4⋊C4—8312no—
807C4⋊C4—8312no—
808C4⋊C4—8312no—
809C4⋊C4—8312no—
810C4⋊C4C23×D8316yes—
811C4⋊C4C23×D8316yes—
812C4⋊C4C23×D83112yes—
813C4⋊C4C23×D83112yes—
814C22⋊C4—834no—
815C22⋊C4—834no—
816C22⋊C4—8312no—
817C22⋊C4—834no—
818C22⋊C4—834no—
819C22⋊C4—834no—
820C22⋊C4—8312no—
821C22⋊C4—8312no—
822C22⋊C4—834no—
823C22⋊C4—834no—
824C22⋊C4—8312no—
825C22⋊C4—8312no—
826C22⋊C4—8312no—
827C22⋊C4C23×D8314yes—
828C22⋊C4C23×D8314yes—
829C22⋊C4C23×D83112yes—
830C22⋊C4C23×D83112yes—
831C22⋊C4C23×D8314yes—
832C42—836no—
833C42—834no—
834C42—834no—
835C42—836no—
836C42—836no—
837C42—836no—
838C42—836no—
839C42—836no—
840C42—836no—
841C42—836no—
842C42—8312no—
843C42—8312no—
844C42—8312no—
845C42C23×D83112yes—
846C23—22no—
847C23—22no—
848C23—22no—
849C23—834no—
850C23C24×D8314yes—
851C23C24×D8311yescharacteristic
852C23C24×D8311yescharacteristic
853C23C24×D8311yescharacteristic
854Q8—224no—
855Q8—212no—
856Q8—33212no—
857Q8—1668no—
858Q8—16612no—
859Q8C2×#13050589116yes—
860D4—28no—
861D4—28no—
862D4—28no—
863D4—212no—
864D4—33212no—
865D4—1668no—
866D4—1668no—
867D4—1668no—
868D4—1668no—
869D4—16612no—
870C2×C4—26no—
871C2×C4—212no—
872C2×C4—212no—
873C2×C4—224no—
874C2×C4—33212no—
875C2×C4—3323no—
876C2×C4—3326no—
877C2×C4—3323no—
878C2×C4—33212no—
879C2×C4—834no—
880C2×C4—831no—
881C2×C4—831no—
882C2×C4—831no—
883C2×C4—831no—
884C2×C4—836no—
885C2×C4—834no—
886C2×C4—834no—
887C2×C4—834no—
888C2×C4—836no—
889C2×C4—1668no—
890C2×C4—1662no—
891C2×C4—1662no—
892C2×C4—1662no—
893C2×C4—1662no—
894C2×C4—1668no—
895C2×C4—1662no—
896C2×C4—16612no—
897C2×C4—16624no—
898C2×C4C2×#13050589112yes—
899C2×C4C24×D8316yes—
900C2×C4C24×D8314yes—
901C2×C4C24×D8314yes—
902C2×C4C24×D8314yes—
903C2×C4C24×D8316yes—
904C22—28no—
905C22—21no—
906C22—21no—
907C22—21no—
908C22—21no—
909C22—21no—
910C22—21no—
911C22—24no—
912C22—24no—
913C22—24no—
914C22—1664no—
915C22—1664no—
916C22—1664no—
917C22C22×#1305058912yes—
918C222−1+4×D8312yes—
919C22#1912853812yes—
920C22C25×D8311yescharacteristic
921C4—24no—
922C4—26no—
923C4—24no—
924C4—24no—
925C4—832no—
926C4—832no—
927C4—1664no—
928C4—1661no—
929C4—1661no—
930C4—1664no—
931C4—1666no—
932C4—1664no—
933C4—1666no—
934C4C22×#13050589112yes—
935C2—22no—
936C2—22no—
937C2—22no—
938C2—44no—
939C2—3324no—
940C2C23×#1305058911yescharacteristic
941C2C2×2−1+4×D8311yescharacteristic
942C2C2×#1912853811yescharacteristic
subgroupG/H
center, FrattiniC22C25×D83
commutator, socle, cosocleC22×C83C26
FittingC83×#3486C2
hypercenter#3486D83
hypocenterC83#62788
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C22 ◁ #3486

Complements

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

NH ≅ G/Ntype
1. #24921550C2semidirect
2. #24921539C2semidirect
3. #24921457C2semidirect
4. #24921445C2semidirect
5. #24921327C2semidirect
6. #24921269C2semidirect
7. #24921230C2semidirect
8. #24921169C2semidirect
9. #24921114C2semidirect
10. #24921084C2semidirect
11. #24921079C2semidirect
12. #24921053C2semidirect
13. Q8×#13050589C2semidirect
14. #24920887C2semidirect
15. #24920755C2semidirect
16. 2−1+4×Dic83C2semidirect
17. #24920672C2semidirect
18. C22×Q8×Dic83C2semidirect
19. C83×#3486C2semidirect
21. #19128433C22semidirect
22. Q8×Dic166C22semidirect
23. #19128430C22semidirect
24. #19128427C22semidirect
25. #19128427C22semidirect
26. #19128426C22semidirect
27. #19128425C22semidirect
28. #19128422C22semidirect
29. #19128420C22semidirect
31. #19128409C22semidirect
36. #19128393C22semidirect
38. #19128385C22semidirect
39. #19128370C22semidirect
42. Q8×C22⋊D83C22semidirect
45. #19128362C22semidirect
46. #19128358C22semidirect
50. #19128324C22semidirect
51. #19128320C22semidirect
52. #19128312C22semidirect
53. #19128311C22semidirect
57. #19128256C22semidirect
61. #19128253C22semidirect
67. #19128237C22semidirect
72. #19128230C22semidirect
79. #19128184C22semidirect
80. #19128183C22semidirect
83. #19128179C22semidirect
84. #19128177C22semidirect
86. #41×Dic83C22semidirect
87. C4×#13050591C22semidirect
99. C2×Q8×Dic83C22semidirect
100. C4×Q8×D83C22semidirect
350. C2×Q8×C83#41semidirect
415. C2×Dic832−1+4semidirect
481. #3486D83semidirect
491. C83#62788semidirect
754. C2×Q8#13050589semidirect

Maximal subgroups

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

subgroupindex
#249215502
#249215392
#249214572
#249214452
#249213272
#249212692
#249212302
#249211692
#249211142
#249210842
#249210792
#249210532
Q8×#130505892
#249208872
#249207552
2−1+4×Dic832
#249206722
C22×Q8×Dic832
C83×#34862
#6278883