Finite Group Databasebeta

← #7660949

Subgroups — #7660949

Order 512.

8442 conjugacy classes of subgroups.

The subgroup lattice has 987 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3487C211yesmaximal, characteristic, complemented
2C2×#3486C211yesmaximal, characteristic, complemented
3#52163C213yesmaximal, complemented
4#42979C216yesmaximal, complemented
5#42913C216yesmaximal, complemented
6#42806C216yesmaximal, complemented
7#39861C216yesmaximal, complemented
8#39860C216yesmaximal, complemented
9#39166C216yesmaximal, complemented
10#37419C213yesmaximal, complemented
11#37374C213yesmaximal, complemented
12#37269C213yesmaximal, complemented
13#36575C212yesmaximal, complemented
14#36430C212yesmaximal, complemented
15#36428C212yesmaximal, complemented
16#35831C212yesmaximal, complemented
17#35801C212yesmaximal, complemented
18#35723C212yesmaximal, complemented
19#34259C211yesmaximal, characteristic, complemented
20C22×2−1+4C2211yescharacteristic
21C23×#41C2211yescharacteristic, complemented
22C24×Q8C2211yescharacteristic, complemented
23#3487—216no—
24#3486—216no—
25C2×#550C2216yes—
26C2×#550C2212yescomplemented
27C2×D4×Q8C2212yes—
28C2×D4×Q8C2216yescomplemented
29C2×#548C2216yes—
30C2×#548C2212yes—
31C2×#548C2212yes—
32C2×#548C2212yes—
33C2×#548C2216yescomplemented
34C2×#548C2212yescomplemented
35C2×#536C2213yes—
36C2×#536C2213yescomplemented
37C2×#535C2213yes—
38C2×#535C2213yescomplemented
39C2×#525C2213yes—
40C2×#525C2213yes—
41C2×#525C2213yescomplemented
42C2×#525C2213yescomplemented
43C2×#520C2211yescharacteristic, complemented
44C2×#519C2211yescharacteristic, complemented
45C2×#519C2211yescharacteristic, complemented
46C2×C4×#41C2211yescharacteristic, complemented
47#2850C2216yescomplemented
48#2848C2216yescomplemented
49#2847C2216yescomplemented
50#2816C22112yescomplemented
51#2732C2216yescomplemented
52#2731C2216yescomplemented
53#2731C2216yescomplemented
54#2730C22112yescomplemented
55#2729C22112yescomplemented
56#2728C2216yescomplemented
57#2724C2213yes—
58#2717C2216yescomplemented
59#2709C22112yescomplemented
60#2709C2216yescomplemented
61#2708C2216yes—
62#2708C2216yescomplemented
63#2708C22112yescomplemented
64#2697C2213yes—
65#2697C2216yes—
66#2697C2211yescharacteristic
67#2684C22112yescomplemented
68#2684C2216yescomplemented
69#2679C2213yes—
70#2669C2216yescomplemented
71#2668C22112yes—
72#2668C2216yes—
73#2668C2216yescomplemented
74#2639C22112yescomplemented
75#2638C22112yescomplemented
76#2635C22112yescomplemented
77#2625C2216yescomplemented
78#2624C2216yescomplemented
79#2620C2216yescomplemented
80#2600C22112yescomplemented
81#2564C22112yescomplemented
82#2544C2216yescomplemented
83#2544C2216yescomplemented
84#2543C22112yescomplemented
85#2537C2216yescomplemented
86#2535C2216yescomplemented
87#2500C2216yescomplemented
88#2499C2216yescomplemented
89#2485C2216yes—
90#2485C2216yescomplemented
91#2448C2216yescomplemented
92#2448C2216yescomplemented
93#2446C2216yescomplemented
94#2446C2216yescomplemented
95#2436C2216yescomplemented
96#2436C2216yescomplemented
97#2436C2216yescomplemented
98#2435C2216yescomplemented
99#2432C2216yescomplemented
100#2432C2216yescomplemented
101#2428C2216yescomplemented
102#2428C2216yescomplemented
103#2427C2216yescomplemented
104#2427C2216yescomplemented
105#2423C2216yescomplemented
106#2423C2216yescomplemented
107#2421C2216yescomplemented
108#2421C2216yescomplemented
109#2417C2216yescomplemented
110#2416C2216yescomplemented
111#2415C2216yescomplemented
112#2414C2216yescomplemented
113#2409C2216yescomplemented
114#2409C2216yescomplemented
115#2409C2216yescomplemented
116#2408C2216yes—
117#2407C2216yes—
118#2407C2216yes—
119#2395C2216yes—
120#2395C2216yescomplemented
121#2392C2216yescomplemented
122#2351C2212yescomplemented
123Q8×C4⋊C4C2212yescomplemented
124#2341C2212yescomplemented
125#2341C2212yescomplemented
126Q8×C22⋊C4C2212yescomplemented
127Q8×C22⋊C4C2212yescomplemented
128Q8×C22⋊C4C2212yescomplemented
129Q8×C22⋊C4C2212yescomplemented
130#2339C2216yescomplemented
131#2339C2216yescomplemented
132#2325C22112yescomplemented
133#2311C2213yes—
134#2310C2213yescomplemented
135C4×#121C2216yescomplemented
136C4×#120C2216yes—
137C4×#120C2216yescomplemented
138#2297C2213yes—
139C2×#391C2213yescomplemented
140C2×2−1+4—44no—
141C2×2−1+4—44no—
142C2×2−1+4D4116yescomplemented
143C22×#41—28no—
144C22×#41—44no—
145C22×#41—44no—
146C22×#41C2312yes—
147C22×#41C2311yescharacteristic
148C22×#41C2316yes—
149C22×#41C2313yes—
150C22×#41C2313yes—
151C22×#41C2313yes—
152C23×Q8—28no—
153C23×Q8—44no—
154C23×Q8—44no—
155C23×Q8C2312yes—
156C23×Q8C2311yescharacteristic
157C23×Q8C2311yescharacteristic
158C23×Q8C2313yes—
159C23×Q8C2316yes—
160C23×Q8C2313yes—
161C23×D4C2313yes—
162C24×C4C2313yes—
163C24×C4C2313yes—
164#550—248no—
165#550—216no—
166D4×Q8—216no—
167D4×Q8—248no—
168#548—248no—
169#548—216no—
170#548—216no—
171#548—248no—
172#548—48no—
173#548—48no—
174#536—224no—
175#536—224no—
176#535—224no—
177#535—224no—
178C2×C4⋊Q8C2316yes—
179C2×C4⋊Q8C2316yes—
180C2×#127C2316yes—
181C2×#127C2316yes—
182C2×#124C2316yes—
183C2×#124C2316yes—
184C2×#124C2316yes—
185C2×#124C2316yes—
186C2×#124C2316yes—
187C2×#124C2316yes—
188#525—224no—
189#525—224no—
190#525—224no—
191#525—224no—
192C2×#123C2311yescharacteristic
193C2×#123C2313yes—
194C2×#123C2313yes—
195C2×#123C2313yes—
196C2×#123C2316yes—
197C2×C22⋊Q8C23112yes—
198C2×C22⋊Q8C2316yes—
199C2×C22⋊Q8C2316yes—
200C2×C22⋊Q8C2316yes—
201C2×C22⋊Q8C2316yes—
202C2×C22⋊Q8C2316yes—
203C2×C22⋊Q8C2316yes—
204C2×C22⋊Q8C2316yes—
205C2×C22⋊Q8C2316yes—
206C2×#121C23112yes—
207C2×#121C2316yes—
208C2×#121C2316yes—
209C2×#121C2316yes—
210C2×#121C2316yes—
211C2×#121C2316yes—
212C2×#121C2316yes—
213C2×#121C23112yes—
214C2×#121C2316yes—
215C2×#121C2316yes—
216C2×#121C2316yes—
217C2×#120C2311yescharacteristic
218C2×#120C2313yes—
219C2×#120C2313yes—
220C2×#120C2313yes—
221C2×#120C2316yes—
222C2×#120C2316yes—
223C2×#120C2316yes—
224#520—44no—
225#519—28no—
226#519—28no—
227C4×#41—44no—
228C2×C4×Q8C2312yes—
229C2×C4×Q8C2312yes—
230C2×C4×Q8C2312yes—
231C2×C4×Q8C2312yes—
232C2×C4×Q8C2316yes—
233C2×C4×Q8C2316yes—
234C2×C4×D4C23112yes—
235C2×C4×D4C23112yes—
236C2×C4×D4C2316yes—
237C2×C4×D4C2316yes—
238C2×C4×D4C2316yes—
239C2×C4×D4C2316yes—
240C2×C4×D4C2316yes—
241C2×C4×D4C2316yes—
242C2×C4×D4C2316yes—
243C2×C4×D4C2316yes—
244C2×#117C2313yes—
245C2×#117C2313yes—
246C2×#117C2313yes—
247C2×#117C2313yes—
248C2×#117C2313yes—
249C2×#117C2313yes—
250C22×C4⋊C4C2313yes—
251C22×C42C2313yes—
252#400C2316yes—
253#400C23112yes—
254#400C2316yes—
255#399C2316yes—
256#399C23112yes—
257#399C2316yes—
258#398C2316yes—
259#398C23112yes—
260#398C2316yes—
261#398C2316yes—
262#397C23112yes—
263#397C23112yes—
264#397C2316yes—
265#397C23112yes—
266#397C2316yes—
267#397C2316yes—
268#397C2316yes—
269#397C2316yes—
270#397C2312yes—
271#397C2316yes—
272#396C2316yes—
273#396C23112yes—
274#396C2312yes—
275#395C23112yes—
276#394C2316yes—
277#394C23112yes—
278#394C23112yes—
279#394C23112yes—
280#394C23112yes—
281#394C23112yes—
282#394C2316yes—
283#394C23112yes—
284#394C2316yes—
285#394C23112yes—
286#394C23112yes—
287#394C2316yes—
288#394C2312yes—
289#394C2316yes—
290#394C2316yes—
291#393C23112yes—
292#393C23112yes—
293#393C23112yes—
294#392C23112yes—
295#392C2316yes—
296#392C23112yes—
297#391C2313yes—
298#391C2316yes—
299#391C2316yes—
300#391C2316yes—
301#391C2316yes—
302#391C2316yes—
303#391C2316yes—
304#391C2316yes—
305#391C2316yes—
306#391C2316yes—
307#391C2313yes—
308#390C2313yes—
309#390C2316yes—
310#390C2316yes—
311#390C2316yes—
312#390C2316yes—
313#390C2316yes—
314#390C2311yescharacteristic
315#389C2316yes—
316#389C2316yes—
317#389C2316yes—
318#389C2316yes—
319#389C2316yes—
320#388C23112yes—
321#388C23112yes—
322#388C2316yes—
323#388C23112yes—
324#388C23112yes—
325#388C23112yes—
326#388C2312yes—
327#387C23112yes—
328#387C23112yes—
329#387C23112yes—
330#387C23112yes—
331#386C23112yes—
332#386C23112yes—
333#386C2316yes—
334#386C2316yes—
335#386C2316yes—
336#386C2316yes—
337#386C23112yes—
338#386C23112yes—
339#386C23112yes—
340#386C23112yes—
341#386C2316yes—
342#386C2316yes—
343#386C2316yes—
344#386C2316yes—
345#386C2316yes—
346#386C23112yes—
347#386C2316yes—
348#386C2316yes—
349#386C2312yes—
350#385C2316yes—
351#385C23112yes—
352#385C2316yes—
353#385C23112yes—
354#385C2316yes—
355#385C2316yes—
356#385C2316yes—
357#385C2316yes—
358#384C2316yes—
359#382C2316yes—
360#381C23112yes—
361#380C2316yes—
362#380C23112yes—
363#380C2316yes—
364#380C2316yes—
365#380C2316yes—
366#380C2316yes—
367#380C2316yes—
368#380C2316yes—
369#379C23112yes—
370#379C2316yes—
371#379C2312yes—
372C4×C4⋊C4C2316yes—
373C4×C4⋊C4C2316yes—
374C4×C22⋊C4C2316yes—
375C4×C22⋊C4C2316yes—
376C4×C22⋊C4C2316yes—
377C4×C22⋊C4C2316yes—
378C4×C22⋊C4C2316yes—
379C4×C22⋊C4C2316yes—
380C2×#95C23112yes—
381C25C2411yescharacteristic
382C25C2413yes—
3832−1+4—464no—
384C2×#41—224no—
385C2×#41—28no—
386C2×#41—24no—
387C2×#41—24no—
388C2×#41—28no—
389C2×#41—28no—
390C2×#41—46no—
391C2×#41—46no—
392C2×#41—412no—
393C2×#41—412no—
394C2×#41—46no—
395C2×#41—46no—
396C2×#41—46no—
397C2×#41—46no—
398C2×#41—464no—
399C2×#41C2×D418yes—
400C2×#41C2×D4124yes—
401C2×#41C2×D4124yes—
402C2×#41C2×D4124yes—
403C22×Q8—24no—
404C22×Q8—24no—
405C22×Q8—24no—
406C22×Q8—24no—
407C22×Q8—224no—
408C22×Q8—28no—
409C22×Q8—28no—
410C22×Q8—28no—
411C22×Q8—212no—
412C22×Q8—46no—
413C22×Q8—46no—
414C22×Q8—412no—
415C22×Q8—412no—
416C22×Q8—46no—
417C22×Q8—46no—
418C22×Q8—464no—
419C22×Q8C2×D418yes—
420C22×Q8C2×D418yes—
421C22×Q8C2×D4124yes—
422C22×Q8C2416yes—
423C22×Q8C2413yes—
424C22×Q8C2413yes—
425C22×Q8C2416yes—
426C22×Q8C2413yes—
427C22×Q8C2411yescharacteristic
428C22×D4—212no—
429C22×D4—46no—
430C22×D4—46no—
431C22×D4C2416yes—
432C22×D4C2412yes—
433C22×D4C2416yes—
434C22×D4C2413yes—
435C22×D4C2416yes—
436C22×D4C2416yes—
437C22×D4C2416yes—
438C22×D4C24112yes—
439C22×D4C2416yes—
440C22×D4C2416yes—
441C22×D4C2411yescharacteristic
442C22×D4C2413yes—
443C22×D4C2413yes—
444C23×C4—212no—
445C23×C4—212no—
446C23×C4—46no—
447C23×C4—46no—
448C23×C4—46no—
449C23×C4—46no—
450C23×C4C2416yes—
451C23×C4C2416yes—
452C23×C4C2413yes—
453C23×C4C2413yes—
454C23×C4C2413yes—
455C23×C4C2416yes—
456C23×C4C2416yes—
457C23×C4C2411yescharacteristic
458C23×C4C2413yes—
459C23×C4C2416yes—
460C23×C4C2416yes—
461C23×C4C2416yes—
462C4⋊Q8—224no—
463C4⋊Q8—224no—
464#127—224no—
465#127—224no—
466#124—224no—
467#124—224no—
468#124—224no—
469#124—224no—
470#124—412no—
471#124—412no—
472#123—24no—
473#123—212no—
474#123—212no—
475#123—212no—
476#123—224no—
477C22⋊Q8—224no—
478C22⋊Q8—224no—
479C22⋊Q8—224no—
480C22⋊Q8—224no—
481C22⋊Q8—224no—
482C22⋊Q8—224no—
483C22⋊Q8—248no—
484C22⋊Q8—412no—
485C22⋊Q8—412no—
486#121—224no—
487#121—224no—
488#121—224no—
489#121—224no—
490#121—224no—
491#121—224no—
492#121—248no—
493#121—424no—
494#121—412no—
495#121—412no—
496#121—412no—
497#120—24no—
498#120—212no—
499#120—212no—
500#120—212no—
501#120—224no—
502#120—412no—
503#120—412no—
504C4×Q8—224no—
505C4×Q8—28no—
506C4×Q8—224no—
507C4×Q8—28no—
508C4×Q8—28no—
509C4×Q8—28no—
510C4×D4—224no—
511C4×D4—224no—
512C4×D4—248no—
513C4×D4—224no—
514C4×D4—224no—
515C4×D4—248no—
516C4×D4—412no—
517C4×D4—412no—
518C4×D4—412no—
519C4×D4—412no—
520#117—212no—
521#117—212no—
522#117—212no—
523#117—212no—
524#117—46no—
525#117—46no—
526C2×C4⋊C4—46no—
527C2×C4⋊C4C2416yes—
528C2×C4⋊C4C2416yes—
529C2×C4⋊C4C2416yes—
530C2×C4⋊C4C2416yes—
531C2×C4⋊C4C2416yes—
532C2×C4⋊C4C2416yes—
533C2×C4⋊C4C2416yes—
534C2×C4⋊C4C2412yes—
535C2×C4⋊C4C24112yes—
536C2×C4⋊C4C2416yes—
537C2×C4⋊C4C2416yes—
538C2×C4⋊C4C2413yes—
539C2×C4⋊C4C2411yescharacteristic
540C2×C4⋊C4C2416yes—
541C2×C4⋊C4C2416yes—
542C2×C4⋊C4C2416yes—
543C2×C4⋊C4C24112yes—
544C2×C4⋊C4C2412yes—
545C2×C4⋊C4C2416yes—
546C2×C4⋊C4C2416yes—
547C2×C22⋊C4C2411yescharacteristic
548C2×C22⋊C4C2413yes—
549C2×C22⋊C4C2411yescharacteristic
550C2×C22⋊C4C2413yes—
551C2×C22⋊C4C2416yes—
552C2×C22⋊C4C2412yes—
553C2×C22⋊C4C2412yes—
554C2×C22⋊C4C2416yes—
555C2×C22⋊C4C24112yes—
556C2×C22⋊C4C2416yes—
557C2×C22⋊C4C2416yes—
558C2×C22⋊C4C2416yes—
559C2×C22⋊C4C24112yes—
560C2×C22⋊C4C2416yes—
561C2×C22⋊C4C2416yes—
562C2×C22⋊C4C2412yes—
563C2×C22⋊C4C2416yes—
564C2×C22⋊C4C2416yes—
565C2×C22⋊C4C2412yes—
566C2×C22⋊C4C2412yes—
567C2×C22⋊C4C2416yes—
568C2×C22⋊C4C2416yes—
569C2×C22⋊C4C2416yes—
570C2×C22⋊C4C2416yes—
571C2×C22⋊C4C2416yes—
572C2×C22⋊C4C2416yes—
573C2×C22⋊C4C2416yes—
574C2×C22⋊C4C24112yes—
575C2×C22⋊C4C24112yes—
576C2×C22⋊C4C2416yes—
577C2×C22⋊C4C24112yes—
578C2×C22⋊C4C2412yes—
579C2×C22⋊C4C2412yes—
580C2×C22⋊C4C2412yes—
581C2×C22⋊C4C2416yes—
582C2×C22⋊C4C24112yes—
583C2×C42—46no—
584C2×C42C2416yes—
585C2×C42C2416yes—
586C2×C42C2416yes—
587C2×C42C2416yes—
588C2×C42C2416yes—
589C2×C42C2416yes—
590C2×C42C2413yes—
591C2×C42C2411yescharacteristic
592#95C2416yes—
593#95C2416yes—
594#95C24112yes—
595#95C24112yes—
596#95C2412yes—
597#95C2412yes—
598#95C2416yes—
599#95C2416yes—
600#95C2416yes—
601#95C2416yes—
602#95C2416yes—
603#95C2416yes—
604#95C2416yes—
605#95C2416yes—
606#95C2412yes—
607#95C2416yes—
608#95C2416yes—
609#95C2416yes—
610#95C24112yes—
611#95C24112yes—
612#95C24112yes—
613C24—22no—
614C24—24no—
615C24—26no—
616C24—41no—
617C24—41no—
618C24—42no—
619C24—43no—
620C24—43no—
621C24—46no—
622C24—46no—
623C24C2516yes—
624C24C2511yescharacteristic
625C24C2511yescharacteristic
626C24C2513yes—
627C24C2512yes—
628#41—232no—
629#41—448no—
630#41—448no—
631#41—448no—
632#41—496no—
633#41—432no—
634C2×Q8—232no—
635C2×Q8—232no—
636C2×Q8—212no—
637C2×Q8—212no—
638C2×Q8—26no—
639C2×Q8—26no—
640C2×Q8—26no—
641C2×Q8—26no—
642C2×Q8—212no—
643C2×Q8—212no—
644C2×Q8—46no—
645C2×Q8—46no—
646C2×Q8—43no—
647C2×Q8—43no—
648C2×Q8—448no—
649C2×Q8—448no—
650C2×Q8—496no—
651C2×Q8—432no—
652C2×Q8C22×D4112yes—
653C2×Q8C22×D4112yes—
654C2×Q8C22×D4112yes—
655C2×Q8C22×D414yes—
656C2×Q8H(5,𝔽2)14yes—
657C2×Q8H(5,𝔽2)14yes—
658C2×D4—24no—
659C2×D4—212no—
660C2×D4—24no—
661C2×D4—212no—
662C2×D4—212no—
663C2×D4—224no—
664C2×D4—212no—
665C2×D4—212no—
666C2×D4—212no—
667C2×D4—212no—
668C2×D4—212no—
669C2×D4—26no—
670C2×D4—26no—
671C2×D4—212no—
672C2×D4—212no—
673C2×D4—46no—
674C2×D4—46no—
675C2×D4—46no—
676C2×D4—42no—
677C2×D4—41no—
678C2×D4—41no—
679C2×D4—43no—
680C2×D4—43no—
681C2×D4—43no—
682C2×D4—43no—
683C2×D4—448no—
684C2×D4—46no—
685C2×D4—46no—
686C2×D4—46no—
687C2×D4—46no—
688C2×D4—412no—
689C2×D4—46no—
690C2×D4—46no—
691C2×D4—46no—
692C2×D4—46no—
693C2×D4—412no—
694C2×D4C22×D4112yes—
695C2×D4C22×D414yes—
696C2×D4C22×D4112yes—
697C2×D4C22×D4112yes—
698C22×C4—26no—
699C22×C4—26no—
700C22×C4—26no—
701C22×C4—26no—
702C22×C4—26no—
703C22×C4—26no—
704C22×C4—22no—
705C22×C4—26no—
706C22×C4—212no—
707C22×C4—212no—
708C22×C4—212no—
709C22×C4—212no—
710C22×C4—212no—
711C22×C4—212no—
712C22×C4—212no—
713C22×C4—212no—
714C22×C4—41no—
715C22×C4—41no—
716C22×C4—46no—
717C22×C4—46no—
718C22×C4—43no—
719C22×C4—43no—
720C22×C4—46no—
721C22×C4—46no—
722C22×C4—46no—
723C22×C4—46no—
724C22×C4—46no—
725C22×C4—46no—
726C22×C4—46no—
727C22×C4—46no—
728C22×C4—412no—
729C22×C4—448no—
730C22×C4—448no—
731C22×C4C22×D4112yes—
732C22×C4C22×D4112yes—
733C22×C4C22×D4112yes—
734C22×C4C22×D4124yes—
735C22×C4C2512yes—
736C22×C4C2516yes—
737C22×C4C2516yes—
738C22×C4C2512yes—
739C22×C4C2516yes—
740C22×C4C2512yes—
741C22×C4C2516yes—
742C22×C4C2512yes—
743C22×C4C2512yes—
744C22×C4C2516yes—
745C22×C4C2513yes—
746C22×C4C2513yes—
747C22×C4C2511yescharacteristic
748C22×C4C2513yes—
749C4⋊C4—212no—
750C4⋊C4—212no—
751C4⋊C4—212no—
752C4⋊C4—212no—
753C4⋊C4—212no—
754C4⋊C4—24no—
755C4⋊C4—224no—
756C4⋊C4—212no—
757C4⋊C4—212no—
758C4⋊C4—212no—
759C4⋊C4—212no—
760C4⋊C4—43no—
761C4⋊C4—42no—
762C4⋊C4—46no—
763C4⋊C4—46no—
764C4⋊C4—41no—
765C4⋊C4—46no—
766C4⋊C4—46no—
767C4⋊C4—412no—
768C4⋊C4—46no—
769C22⋊C4—22no—
770C22⋊C4—26no—
771C22⋊C4—22no—
772C22⋊C4—26no—
773C22⋊C4—212no—
774C22⋊C4—24no—
775C22⋊C4—212no—
776C22⋊C4—224no—
777C22⋊C4—212no—
778C22⋊C4—212no—
779C22⋊C4—24no—
780C22⋊C4—212no—
781C22⋊C4—24no—
782C22⋊C4—224no—
783C22⋊C4—212no—
784C22⋊C4—212no—
785C22⋊C4—46no—
786C22⋊C4—42no—
787C22⋊C4—412no—
788C22⋊C4—42no—
789C22⋊C4—42no—
790C22⋊C4—46no—
791C22⋊C4—46no—
792C22⋊C4—42no—
793C22⋊C4—42no—
794C22⋊C4—46no—
795C22⋊C4—46no—
796C22⋊C4—46no—
797C22⋊C4—46no—
798C22⋊C4—46no—
799C22⋊C4—46no—
800C22⋊C4—46no—
801C22⋊C4—46no—
802C22⋊C4—412no—
803C22⋊C4—412no—
804C22⋊C4—412no—
805C42—212no—
806C42—212no—
807C42—212no—
808C42—212no—
809C42—212no—
810C42—212no—
811C42—41no—
812C42—43no—
813C23—22no—
814C23—23no—
815C23—23no—
816C23—22no—
817C23—22no—
818C23—21no—
819C23—21no—
820C23—21no—
821C23—21no—
822C23—22no—
823C23—22no—
824C23—22no—
825C23—26no—
826C23—22no—
827C23—22no—
828C23—22no—
829C23—26no—
830C23—22no—
831C23—26no—
832C23—26no—
833C23—26no—
834C23—26no—
835C23—26no—
836C23—26no—
837C23—26no—
838C23—48no—
839C23—44no—
840C23—44no—
841C23—48no—
842C23—412no—
843C23—44no—
844C23—812no—
845C23—86no—
846C23—86no—
847C23—812no—
848C23C23×D412yes—
849C23C23×D416yes—
850C23C23×D412yes—
851C23#58514yes—
852C23C2611yescharacteristic
853Q8—224no—
854Q8—224no—
855Q8—412no—
856Q8—424no—
857Q8—424no—
858Q8#534116yes—
859D4—224no—
860D4—44no—
861D4—412no—
862D4—412no—
863D4—424no—
864D4—424no—
865D4—48no—
866D4—424no—
867D4—824no—
868D4—812no—
869D4—812no—
870D4—812no—
871D4—812no—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—23no—
875C2×C4—23no—
876C2×C4—23no—
877C2×C4—23no—
878C2×C4—224no—
879C2×C4—224no—
880C2×C4—224no—
881C2×C4—22no—
882C2×C4—26no—
883C2×C4—26no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—26no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—26no—
890C2×C4—26no—
891C2×C4—26no—
892C2×C4—26no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—26no—
897C2×C4—26no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—26no—
901C2×C4—26no—
902C2×C4—26no—
903C2×C4—22no—
904C2×C4—26no—
905C2×C4—22no—
906C2×C4—26no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—26no—
911C2×C4—424no—
912C2×C4—424no—
913C2×C4—424no—
914C2×C4—44no—
915C2×C4—412no—
916C2×C4—424no—
917C2×C4—424no—
918C2×C4—812no—
919C2×C4—166no—
920C2×C4C23×D416yes—
921C2×C4C23×D416yes—
922C2×C4C23×D412yes—
923C2×C4C23×D416yes—
924C2×C4C2×H(5,𝔽2)16yes—
925C2×C4C2×H(5,𝔽2)16yes—
926C22—24no—
927C22—212no—
928C22—24no—
929C22—24no—
930C22—24no—
931C22—24no—
932C22—22no—
933C22—22no—
934C22—26no—
935C22—416no—
936C22—42no—
937C22—43no—
938C22—41no—
939C22—41no—
940C22—43no—
941C22—42no—
942C22—41no—
943C22—41no—
944C22—46no—
945C22—42no—
946C22—42no—
947C22—42no—
948C22—42no—
949C22—46no—
950C22—46no—
951C22—46no—
952C22—46no—
953C22—46no—
954C22—46no—
955C22—46no—
956C22—824no—
957C22C24×D411yescharacteristic
958C22C22×H(5,𝔽2)11yescharacteristic
959C22C22×H(5,𝔽2)11yescharacteristic
960C22C2×#58512yes—
961C222−1+612yes—
962C4—22no—
963C4—26no—
964C4—26no—
965C4—42no—
966C4—46no—
967C4—46no—
968C4—42no—
969C4—46no—
970C4—42no—
971C4—42no—
972C4—46no—
973C4—42no—
974C4—46no—
975C4C2×#534112yes—
976C2—46no—
977C2—44no—
978C2—42no—
979C2—42no—
980C2—86no—
981C2C22×#53411yescharacteristic
982C2#6289712yes—
983C2#6300212yes—
984C2#6302011yescharacteristic
985C2#6304411yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3487C2semidirect
2. C2×#3486C2semidirect
3. #52163C2semidirect
4. #42979C2semidirect
5. #42913C2semidirect
6. #42806C2semidirect
7. #39861C2semidirect
8. #39860C2semidirect
9. #39166C2semidirect
10. #37419C2semidirect
11. #37374C2semidirect
12. #37269C2semidirect
13. #36575C2semidirect
14. #36430C2semidirect
15. #36428C2semidirect
16. #35831C2semidirect
17. #35801C2semidirect
18. #35723C2semidirect
19. #34259C2semidirect
21. C23×#41C22semidirect
22. C24×Q8C22semidirect
26. C2×#550C22semidirect
28. C2×D4×Q8C22semidirect
33. C2×#548C22semidirect
34. C2×#548C22semidirect
36. C2×#536C22semidirect
38. C2×#535C22semidirect
41. C2×#525C22semidirect
42. C2×#525C22semidirect
43. C2×#520C22semidirect
44. C2×#519C22semidirect
45. C2×#519C22semidirect
46. C2×C4×#41C22semidirect
47. #2850C22semidirect
48. #2848C22semidirect
49. #2847C22semidirect
50. #2816C22semidirect
51. #2732C22semidirect
52. #2731C22semidirect
53. #2731C22semidirect
54. #2730C22semidirect
55. #2729C22semidirect
56. #2728C22semidirect
58. #2717C22semidirect
59. #2709C22semidirect
60. #2709C22semidirect
62. #2708C22semidirect
63. #2708C22semidirect
67. #2684C22semidirect
68. #2684C22semidirect
70. #2669C22semidirect
73. #2668C22semidirect
74. #2639C22semidirect
75. #2638C22semidirect
76. #2635C22semidirect
77. #2625C22semidirect
78. #2624C22semidirect
79. #2620C22semidirect
80. #2600C22semidirect
81. #2564C22semidirect
82. #2544C22semidirect
83. #2544C22semidirect
84. #2543C22semidirect
85. #2537C22semidirect
86. #2535C22semidirect
87. #2500C22semidirect
88. #2499C22semidirect
90. #2485C22semidirect
91. #2448C22semidirect
92. #2448C22semidirect
93. #2446C22semidirect
94. #2446C22semidirect
95. #2436C22semidirect
96. #2436C22semidirect
97. #2436C22semidirect
98. #2435C22semidirect
99. #2432C22semidirect
100. #2432C22semidirect
101. #2428C22semidirect
102. #2428C22semidirect
103. #2427C22semidirect
104. #2427C22semidirect
105. #2423C22semidirect
106. #2423C22semidirect
107. #2421C22semidirect
108. #2421C22semidirect
109. #2417C22semidirect
110. #2416C22semidirect
111. #2415C22semidirect
112. #2414C22semidirect
113. #2409C22semidirect
114. #2409C22semidirect
115. #2409C22semidirect
120. #2395C22semidirect
121. #2392C22semidirect
122. #2351C22semidirect
123. Q8×C4⋊C4C22semidirect
124. #2341C22semidirect
125. #2341C22semidirect
126. Q8×C22⋊C4C22semidirect
127. Q8×C22⋊C4C22semidirect
128. Q8×C22⋊C4C22semidirect
129. Q8×C22⋊C4C22semidirect
130. #2339C22semidirect
131. #2339C22semidirect
132. #2325C22semidirect
134. #2310C22semidirect
135. C4×#121C22semidirect
137. C4×#120C22semidirect
139. C2×#391C22semidirect
142. C2×2−1+4D4semidirect

Maximal subgroups

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

subgroupindex
C2×#34872
C2×#34862
#521632
#429792
#429132
#428062
#398612
#398602
#391662
#374192
#373742
#372692
#365752
#364302
#364282
#358312
#358012
#357232
#342592