Finite Group Databasebeta

← #7623713

Subgroups — #7623713

Order 512.

1545 conjugacy classes of subgroups.

The subgroup lattice has 869 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#61234C211yesmaximal, characteristic, complemented
2D4×#135C211yesmaximal, characteristic, complemented
3#33900C211yesmaximal, characteristic, complemented
4#33899C211yesmaximal, characteristic, complemented
5#33898C211yesmaximal, characteristic, complemented
6#33897C211yesmaximal, characteristic, complemented
7#33896C211yesmaximal, characteristic, complemented
8#33895C211yesmaximal, characteristic, complemented
9#33894C212yesmaximal, complemented
10#33893C212yesmaximal, complemented
11#33892C211yesmaximal, characteristic, complemented
12#33891C211yesmaximal, characteristic, complemented
13#33890C212yesmaximal, complemented
14#33889C212yesmaximal, complemented
15#33697C211yesmaximal, characteristic, complemented
16#33645C212yesmaximal, complemented
17#33626C211yesmaximal, characteristic, complemented
18#33604C212yesmaximal, complemented
19#33579C211yesmaximal, characteristic, complemented
20#33516C212yesmaximal, complemented
21C4×#508C211yesmaximal, characteristic, complemented
22C2×#2169C211yesmaximal, characteristic, complemented
23#33380C212yesmaximal, complemented
24C22×#135C2212yes—
25#3475—21no—
26D4×#41—21no—
27C2×#508C2211yescharacteristic
28C2×#508C2212yescomplemented
29C22×M32C2212yescomplemented
30#3342C2211yescharacteristic
31#3341C2211yescharacteristic
32#3340—21no—
33#3339C2212yescomplemented
34#3338C2211yescharacteristic, complemented
35#3337—22no—
36#3336C2212yescomplemented
37#3335—21no—
38#3334C2211yescharacteristic, complemented
39#3287C2211yescharacteristic
40D4×Q16C2211yescharacteristic
41#3285C2212yes—
42#3284—21no—
43#3283C2211yescharacteristic
44#3282—22no—
45D4×SD16—21no—
46#3280C2212yes—
47D4×D8C2211yescharacteristic
48#3160C2211yescharacteristic, complemented
49#3147C2211yescharacteristic
50#3091—22no—
51#3076—21no—
52#3050C2212yes—
53#3050C2212yescomplemented
54#3035—21no—
55#3002—22no—
56C4×#135C2211yescharacteristic
57C4×#135C2211yescharacteristic, complemented
58C2×C8×D4C2211yescharacteristic
59C2×#427C2212yescomplemented
60#2242C2212yescomplemented
61#2242C2212yescomplemented
62#2241C2211yescharacteristic, complemented
63#2241C2211yescharacteristic, complemented
64#2240C2211yescharacteristic, complemented
65#2240C2211yescharacteristic, complemented
66#2237C2212yescomplemented
67#2237C2212yescomplemented
68#2236C2212yescomplemented
69#2235C2212yescomplemented
70#2234C2212yescomplemented
71#2234C2212yescomplemented
72#2233C2212yescomplemented
73#2232C2212yescomplemented
74#2229C2212yescomplemented
75#2228C2212yescomplemented
76#2227C2211yescharacteristic, complemented
77#2226C2211yescharacteristic, complemented
78#2225C2211yescharacteristic, complemented
79#2224C2211yescharacteristic, complemented
80#2220C2212yescomplemented
81#2220C2212yescomplemented
82#2220C2212yescomplemented
83#2220C2212yescomplemented
84#2219C2212yescomplemented
85#2219C2212yescomplemented
86#2218C2212yescomplemented
87#2218C2212yescomplemented
88#2211C2212yescomplemented
89#2210C2212yescomplemented
90#2209C2211yescharacteristic, complemented
91#2208C2211yescharacteristic, complemented
92#2207C2211yescharacteristic, complemented
93#2206C2211yescharacteristic, complemented
94#2189C2212yescomplemented
95#2189C2212yescomplemented
96#2188C2212yescomplemented
97#2187C2212yescomplemented
98#2186C2212yescomplemented
99#2186C2212yescomplemented
100#2185C2212yescomplemented
101#2184C2212yescomplemented
102C4×Q32C2211yescharacteristic, complemented
103C4×Q32C2211yescharacteristic, complemented
104C4×SD32C2211yescharacteristic, complemented
105C4×SD32C2211yescharacteristic, complemented
106C4×SD32C2211yescharacteristic, complemented
107C4×SD32C2211yescharacteristic, complemented
108C4×D16C2211yescharacteristic, complemented
109C4×D16C2211yescharacteristic, complemented
110#2169C2211yescharacteristic
111#2169C2211yescharacteristic
112#2169C2212yescomplemented
113#2169C2212yescomplemented
114#2169C2211yescharacteristic, complemented
115#2169C2211yescharacteristic, complemented
116#2158C2212yescomplemented
117#2158C2211yescharacteristic, complemented
118C2×C4⋊C16C2211yescharacteristic, complemented
119#2141C2212yescomplemented
120#2141C2212yescomplemented
121#2140C2212yescomplemented
122#2140C2212yescomplemented
123#2139C2212yescomplemented
124#2139C2212yescomplemented
125#2139C2212yescomplemented
126#2139C2212yescomplemented
127#2138C2212yes—
128#2138C2211yescharacteristic
129#2138C2212yescomplemented
130#2138C2211yescharacteristic, complemented
131#2138C2212yescomplemented
132#2138C2212yescomplemented
133C2×C22⋊C16C2212yescomplemented
134C2×C4×C16C2211yescharacteristic, complemented
135C22×#41—22no—
136C2×#135—28no—
137C2×#135—22no—
138C2×#135—22no—
139C2×#135—21no—
140C2×#135—44no—
141C2×#135C2312yes—
142C2×#135C2311yescharacteristic
143C2×#135C2312yes—
144C2×#135C2312yes—
145C2×#135C2311yescharacteristic
146C22×Q16C2312yes—
147C22×SD16—22no—
148C22×D8C2312yes—
149C23×C8C2312yes—
150#556—21no—
151#555—21no—
152#554—21no—
153#553—22no—
154#552—22no—
155#552—41no—
156#551—42no—
157#550—21no—
158D4×Q8—21no—
159#548—22no—
160#547—21no—
161#547—21no—
162#547—41no—
163#546—22no—
164#546—41no—
165#546—42no—
166D42—21no—
167D42—41no—
168#533—21no—
169#532—21no—
170#532—41no—
171#529—42no—
172#529—41no—
173#525—22no—
174#525—22no—
175#525—42no—
176C4×#41—21no—
177C4×#41—21no—
178C4×#41—41no—
179C2×C4×D4—41no—
180C2×C4×D4D411yescharacteristic
181C2×#117—22no—
182#508—24no—
183#508—44no—
184C2×Q32C2311yescharacteristic
185C2×Q32C2312yes—
186C2×SD32C2311yescharacteristic
187C2×SD32C2311yescharacteristic
188C2×SD32C2312yes—
189C2×SD32C2312yes—
190C2×D16C2311yescharacteristic
191C2×D16C2312yes—
192C2×M32—44no—
193C2×M32C2312yes—
194C2×M32C2312yes—
195C2×M32C2312yes—
196C2×M32C2312yes—
197C22×C16C2311yescharacteristic
198C22×C16C2311yescharacteristic
199C22×C16C2312yes—
200#500C2311yescharacteristic
201#500C2311yescharacteristic
202#499—21no—
203#499C2312yes—
204#498—21no—
205#495—21no—
206#495C2312yes—
207#494C2311yescharacteristic
208#493C2311yescharacteristic
209#492—21no—
210#485—22no—
211#485—22no—
212#484—22no—
213#483—22no—
214#482—22no—
215#482—22no—
216#481—22no—
217#480—22no—
218#479—22no—
219#478—22no—
220#477—21no—
221#476—21no—
222#475—21no—
223#474—21no—
224#467C2312yes—
225#467C2312yes—
226#467C2312yes—
227#467C2312yes—
228#466C2312yes—
229#466C2312yes—
230#466C2312yes—
231#466C2312yes—
232#465—22no—
233#465—22no—
234#465—22no—
235#465—22no—
236#464—22no—
237#463—22no—
238#462—21no—
239#461—21no—
240#460—21no—
241#459—21no—
242#452—22no—
243#452—22no—
244#451—22no—
245#450—22no—
246#449—22no—
247#449—22no—
248#448—22no—
249#447—22no—
250C4×Q16C2311yescharacteristic
251C4×Q16C2311yescharacteristic
252C4×Q16C2311yescharacteristic
253C4×Q16C2311yescharacteristic
254C4×SD16—21no—
255C4×SD16—21no—
256C4×SD16—21no—
257C4×SD16—21no—
258C4×D8C2311yescharacteristic
259C4×D8C2311yescharacteristic
260C4×D8C2311yescharacteristic
261C4×D8C2311yescharacteristic
262C8×D4D411yescharacteristic
263C8×D4D412yes—
264C8×D4D411yescharacteristic
265C8×D4C2311yescharacteristic
266C8×D4C2312yes—
267C8×D4C2311yescharacteristic
268#427—22no—
269#427—22no—
270#427—21no—
271#427C2312yes—
272#427C2312yes—
273#427C2312yes—
274#427C2311yescharacteristic
275#427C2311yescharacteristic
276C2×#107C2312yes—
277C2×#107C2312yes—
278C2×#106—22no—
279C2×C4⋊C8D411yescharacteristic
280#416—22no—
281#416—21no—
282#416—21no—
283#416—22no—
284C2×C22⋊C8D412yes—
285C2×C4×C8C2311yescharacteristic
286#367C2311yescharacteristic
287#367C2311yescharacteristic
288#367C2312yes—
289#367C2312yes—
290#366C2311yescharacteristic
291#366C2311yescharacteristic
292#366C2312yes—
293#366C2312yes—
294C4⋊C16C2311yescharacteristic
295C4⋊C16C2311yescharacteristic
296C4⋊C16C2312yes—
297#358C2311yescharacteristic
298#358C2311yescharacteristic
299#358C2312yes—
300#358C2312yes—
301#358C2312yes—
302#358C2312yes—
303#358C2312yes—
304#358C2312yes—
305#358C2311yescharacteristic
306#358C2311yescharacteristic
307#358C2312yes—
308#358C2312yes—
309#357C2311yescharacteristic
310#357C2311yescharacteristic
311#357C2312yes—
312#357C2312yes—
313#357C2312yes—
314#357C2312yes—
315#357C2312yes—
316#357C2312yes—
317#357C2311yescharacteristic
318#357C2311yescharacteristic
319#357C2312yes—
320#357C2312yes—
321C22⋊C16C2312yes—
322C22⋊C16C2312yes—
323C22⋊C16C2312yes—
324C22⋊C16C2312yes—
325C4×C16C2311yescharacteristic
326C4×C16C2311yescharacteristic
327C4×C16C2311yescharacteristic
328C4×C16C2311yescharacteristic
329C2×#41—21no—
330C2×#41—21no—
331C2×#41—22no—
332C2×#41—22no—
333C2×#41—22no—
334C2×#41—48no—
335C2×#41—41no—
336C2×#41—42no—
337C2×#41—42no—
338C2×#41—84no—
339C22×Q8—22no—
340C22×D4—22no—
341C22×D4—42no—
342C22×D4—41no—
343C22×D4D811yescharacteristic
344C23×C4—42no—
345C23×C4C2×D412yes—
346#135—24no—
347#135—24no—
348#135—24no—
349#135—22no—
350#135—22no—
351#135—24no—
352#135—22no—
353#135—42no—
354#135—42no—
355#135—48no—
356#135—48no—
357#135—82no—
358#135#4114yescomplemented
359C2×Q16—24no—
360C2×Q16—22no—
361C2×Q16—21no—
362C2×Q16—42no—
363C2×Q16C2412yes—
364C2×Q16C2411yescharacteristic
365C2×Q16C2411yescharacteristic
366C2×SD16—21no—
367C2×SD16—22no—
368C2×SD16—22no—
369C2×SD16—22no—
370C2×SD16—21no—
371C2×SD16—22no—
372C2×SD16—48no—
373C2×D8—24no—
374C2×D8—22no—
375C2×D8—21no—
376C2×D8—42no—
377C2×D8C2412yes—
378C2×D8C2411yescharacteristic
379C2×D8C2411yescharacteristic
380C22×C8—24no—
381C22×C8—24no—
382C22×C8C2×D412yes—
383C22×C8C2×D412yes—
384C22×C8C2×D412yes—
385C22×C8C2×D411yescharacteristic
386C22×C8C2412yes—
387C22×C8C2412yes—
388C22×C8C2411yescharacteristic
389C4⋊Q8—21no—
390C4⋊Q8—21no—
391C4⋊Q8—21no—
392C4⋊Q8—41no—
393#127—21no—
394#127—41no—
395#126—42no—
396#126—42no—
397#126—42no—
398#125—22no—
399#125—42no—
400#125—41no—
401#124—22no—
402#124—41no—
403#124—42no—
404#124—42no—
405#123—42no—
406#123—42no—
407#123—42no—
408#123—42no—
409#123—42no—
410#123—42no—
411#123—42no—
412C22⋊Q8—22no—
413C22⋊Q8—22no—
414C22⋊Q8—22no—
415C22⋊Q8—22no—
416C22⋊Q8—41no—
417C22⋊Q8—41no—
418C22⋊Q8—42no—
419C22⋊Q8—41no—
420C22⋊Q8—42no—
421C22⋊Q8—42no—
422#121—22no—
423#121—22no—
424#121—22no—
425#121—22no—
426#121—42no—
427#121—42no—
428#121—41no—
429#121—41no—
430#121—41no—
431#121—41no—
432#121—41no—
433#121—42no—
434#121—42no—
435#120—42no—
436#120—42no—
437#120—42no—
438#120—42no—
439C4×Q8—21no—
440C4×Q8—21no—
441C4×Q8—21no—
442C4×Q8—21no—
443C4×Q8—41no—
444C4×Q8—41no—
445C4×Q8—41no—
446C4×D4—21no—
447C4×D4—21no—
448C4×D4—21no—
449C4×D4—21no—
450C4×D4—41no—
451C4×D4—41no—
452C4×D4—42no—
453C4×D4—41no—
454C4×D4—41no—
455C4×D4—41no—
456C4×D4—41no—
457C4×D4—42no—
458C4×D4—42no—
459C4×D4—42no—
460C4×D4—41no—
461C4×D4—42no—
462C4×D4—42no—
463C4×D4—41no—
464C4×D4—41no—
465C4×D4D811yescharacteristic
466C4×D4D811yescharacteristic
467C4×D4D812yes—
468C4×D4C2×D411yescharacteristic
469C4×D4C2×D412yes—
470C4×D4C2×D411yescharacteristic
471#117—21no—
472#117—22no—
473#117—22no—
474#117—22no—
475#117—21no—
476#117—42no—
477#117—42no—
478#117—41no—
479#117—42no—
480#117—41no—
481#117—41no—
482C2×C4⋊C4—22no—
483C2×C4⋊C4—22no—
484C2×C4⋊C4—41no—
485C2×C4⋊C4D811yescharacteristic
486C2×C22⋊C4—42no—
487C2×C22⋊C4—42no—
488C2×C22⋊C4D812yes—
489C2×C42—42no—
490C2×C42—41no—
491C2×C42—41no—
492C2×C42C2×D411yescharacteristic
493Q32—22no—
494Q32—42no—
495SD32—22no—
496SD32—22no—
497SD32—42no—
498SD32—42no—
499D16—22no—
500D16—42no—
501M32—42no—
502M32—42no—
503M32—42no—
504M32—42no—
505C2×C16—22no—
506C2×C16—22no—
507C2×C16—24no—
508C2×C16C2411yescharacteristic
509C2×C16C2411yescharacteristic
510C2×C16C2411yescharacteristic
511C2×C16C2411yescharacteristic
512C2×C16C2412yes—
513C2×C16C2412yes—
514#107—22no—
515#107—22no—
516#107—21no—
517#107—21no—
518#107C2411yescharacteristic
519#107C2411yescharacteristic
520#107C2412yes—
521#107C2412yes—
522#107C2411yescharacteristic
523#107C2411yescharacteristic
524#106—21no—
525#106—22no—
526#106—22no—
527#106—22no—
528#106—22no—
529#106—21no—
530C4⋊C8C2×D411yescharacteristic
531C4⋊C8C2×D411yescharacteristic
532C4⋊C8C2×D412yes—
533#103—21no—
534#103—21no—
535#103—21no—
536#103—21no—
537#103—22no—
538#103—22no—
539#103—22no—
540#103—22no—
541#102—21no—
542#102—21no—
543#102—21no—
544#102—21no—
545#102—22no—
546#102—22no—
547#102—22no—
548#102—22no—
549C22⋊C8C2×D412yes—
550C22⋊C8C2×D412yes—
551C22⋊C8C2×D412yes—
552C22⋊C8C2×D412yes—
553C4×C8C2×D411yescharacteristic
554C4×C8C2×D411yescharacteristic
555C4×C8C2411yescharacteristic
556C4×C8C2411yescharacteristic
557C24—42no—
558C24C2×D812yes—
559#41—24no—
560#41—44no—
561#41—44no—
562#41—42no—
563#41—44no—
564#41—42no—
565#41—44no—
566#41—42no—
567#41—88no—
568#41—82no—
569#41—82no—
570#41—88no—
571#41—84no—
572C2×Q8—21no—
573C2×Q8—21no—
574C2×Q8—22no—
575C2×Q8—44no—
576C2×Q8—41no—
577C2×Q8—42no—
578C2×Q8—41no—
579C2×Q8—82no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—22no—
583C2×D4—42no—
584C2×D4—44no—
585C2×D4—41no—
586C2×D4—42no—
587C2×D4—41no—
588C2×D4—42no—
589C2×D4—42no—
590C2×D4—42no—
591C2×D4—42no—
592C2×D4—42no—
593C2×D4—42no—
594C2×D4—41no—
595C2×D4—42no—
596C2×D4—41no—
597C2×D4—82no—
598C2×D4—84no—
599C2×D4—88no—
600C2×D4C2×D811yescharacteristic
601C2×D4C2×D811yescharacteristic
602C2×D4C2×D812yes—
603C22×C4—24no—
604C22×C4—24no—
605C22×C4—41no—
606C22×C4—42no—
607C22×C4—42no—
608C22×C4—42no—
609C22×C4—41no—
610C22×C4—41no—
611C22×C4—42no—
612C22×C4—42no—
613C22×C4—41no—
614C22×C4—42no—
615C22×C4—41no—
616C22×C4—41no—
617C22×C4—88no—
618C22×C4C2×D811yescharacteristic
619C22×C4C2×D812yes—
620C22×C4C2×D812yes—
621C22×C4C2×D812yes—
622C22×C4C2×D811yescharacteristic
623C22×C4C22×D412yes—
624C22×C4C22×D412yes—
625C22×C4C22×D411yescharacteristic
626Q16—21no—
627Q16—22no—
628Q16—21no—
629Q16—21no—
630Q16—22no—
631Q16—44no—
632Q16—81no—
633Q16C2×#4112yes—
634SD16—24no—
635SD16—44no—
636SD16—44no—
637SD16—44no—
638SD16—42no—
639SD16—82no—
640D8—21no—
641D8—22no—
642D8—21no—
643D8—21no—
644D8—22no—
645D8—44no—
646D8—81no—
647D8C2×#4112yes—
648C2×C8—24no—
649C2×C8—22no—
650C2×C8—24no—
651C2×C8—24no—
652C2×C8—22no—
653C2×C8—22no—
654C2×C8—22no—
655C2×C8—22no—
656C2×C8C22×D411yescharacteristic
657C2×C8C22×D411yescharacteristic
658C2×C8C22×D412yes—
659C2×C8C22×D412yes—
660C2×C8C22×D411yescharacteristic
661C2×C8C2×#4112yes—
662C2×C8H(5,𝔽2)12yes—
663C2×C8C2511yescharacteristic
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—22no—
669C4⋊C4—22no—
670C4⋊C4—42no—
671C4⋊C4—42no—
672C4⋊C4—41no—
673C4⋊C4—42no—
674C4⋊C4—41no—
675C4⋊C4—41no—
676C4⋊C4—41no—
677C4⋊C4—41no—
678C4⋊C4—41no—
679C4⋊C4—42no—
680C4⋊C4—42no—
681C4⋊C4—42no—
682C4⋊C4—41no—
683C4⋊C4—42no—
684C4⋊C4—42no—
685C4⋊C4—41no—
686C4⋊C4C2×D811yescharacteristic
687C4⋊C4C2×D811yescharacteristic
688C4⋊C4C2×D812yes—
689C22⋊C4—41no—
690C22⋊C4—42no—
691C22⋊C4—42no—
692C22⋊C4—42no—
693C22⋊C4—42no—
694C22⋊C4—41no—
695C22⋊C4—42no—
696C22⋊C4—42no—
697C22⋊C4—42no—
698C22⋊C4—42no—
699C22⋊C4—42no—
700C22⋊C4—41no—
701C22⋊C4—41no—
702C22⋊C4—41no—
703C22⋊C4—41no—
704C22⋊C4—42no—
705C22⋊C4—42no—
706C22⋊C4—42no—
707C22⋊C4—42no—
708C22⋊C4C2×D812yes—
709C22⋊C4C2×D812yes—
710C22⋊C4C2×D812yes—
711C22⋊C4C2×D812yes—
712C42—42no—
713C42—42no—
714C42—41no—
715C42—41no—
716C42—41no—
717C42—41no—
718C42—41no—
719C42—41no—
720C42—42no—
721C42C2×D811yescharacteristic
722C42C2×D811yescharacteristic
723C42C22×D411yescharacteristic
724C42C22×D411yescharacteristic
725C16—21no—
726C16—21no—
727C16—21no—
728C16—21no—
729C16—22no—
730C16—22no—
731C23—24no—
732C23—42no—
733C23—42no—
734C23—41no—
735C23—41no—
736C23—42no—
737C23—84no—
738C23—84no—
739C23—162no—
740C23C22×D812yes—
741C23C22×D812yes—
742C23C22×D811yescharacteristic
743Q8—22no—
744Q8—41no—
745Q8—42no—
746Q8—41no—
747Q8—42no—
748Q8—41no—
749Q8—84no—
750Q8—82no—
751Q8—161no—
752D4—22no—
753D4—22no—
754D4—22no—
755D4—42no—
756D4—44no—
757D4—42no—
758D4—41no—
759D4—41no—
760D4—42no—
761D4—41no—
762D4—84no—
763D4—84no—
764D4—84no—
765D4—84no—
766D4—84no—
767D4—84no—
768D4—82no—
769D4—82no—
770D4—161no—
771D4—162no—
772D4—162no—
773C2×C4—24no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—24no—
778C2×C4—24no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—44no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—41no—
791C2×C4—42no—
792C2×C4—84no—
793C2×C4—84no—
794C2×C4—84no—
795C2×C4—84no—
796C2×C4—82no—
797C2×C4—82no—
798C2×C4—84no—
799C2×C4—82no—
800C2×C4—161no—
801C2×C4—161no—
802C2×C4—162no—
803C2×C4#54612yes—
804C2×C4C22×D811yescharacteristic
805C2×C4C22×D812yes—
806C2×C4C22×D811yescharacteristic
807C2×C4C22×D811yescharacteristic
808C2×C4C22×D812yes—
809C2×C4C22×D811yescharacteristic
810C2×C4C22×D811yescharacteristic
811C2×C4#57712yes—
812C2×C4C23×D411yescharacteristic
813C8—22no—
814C8—22no—
815C8—21no—
816C8—21no—
817C8#54612yes—
818C8C22×#4111yescharacteristic
819C8C2×H(5,𝔽2)11yescharacteristic
820C22—21no—
821C22—21no—
822C22—22no—
823C22—22no—
824C22—22no—
825C22—22no—
826C22—22no—
827C22—22no—
828C22—42no—
829C22—84no—
830C22—81no—
831C22—81no—
832C22—81no—
833C22—82no—
834C22—81no—
835C22—82no—
836C22—82no—
837C22—81no—
838C22—168no—
839C22#329412yes—
840C22C23×D811yescharacteristic
841C4—21no—
842C4—21no—
843C4—21no—
844C4—22no—
845C4—22no—
846C4—42no—
847C4—81no—
848C4—81no—
849C4—82no—
850C4—81no—
851C4—81no—
852C4—82no—
853C4—82no—
854C4—81no—
855C4#329412yes—
856C4#341412yes—
857C4C2×#54611yescharacteristic
858C4C2×#57711yescharacteristic
859C2—22no—
860C2—42no—
861C2—42no—
862C2—82no—
863C2—161no—
864C2—162no—
865C2C2×#329411yescharacteristic
866C2C2×#341411yescharacteristic
867C2#6263511yescharacteristic
subgroupG/H
centerC2×C4C22×D8
commutator, Frattini, cosocleC2×C8C25
socleC22C23×D8
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4 ◁ C2×C4×D4 ◁ C2×C8×D4 ◁ G
LECSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #61234C2semidirect
2. D4×#135C2semidirect
3. #33900C2semidirect
4. #33899C2semidirect
5. #33898C2semidirect
6. #33897C2semidirect
7. #33896C2semidirect
8. #33895C2semidirect
9. #33894C2semidirect
10. #33893C2semidirect
11. #33892C2semidirect
12. #33891C2semidirect
13. #33890C2semidirect
14. #33889C2semidirect
15. #33697C2semidirect
16. #33645C2semidirect
17. #33626C2semidirect
18. #33604C2semidirect
19. #33579C2semidirect
20. #33516C2semidirect
21. C4×#508C2semidirect
22. C2×#2169C2semidirect
23. #33380C2semidirect
28. C2×#508C22semidirect
29. C22×M32C22semidirect
33. #3339C22semidirect
34. #3338C22semidirect
36. #3336C22semidirect
38. #3334C22semidirect
48. #3160C22semidirect
53. #3050C22semidirect
57. C4×#135C22semidirect
59. C2×#427C22semidirect
60. #2242C22semidirect
61. #2242C22semidirect
62. #2241C22semidirect
63. #2241C22semidirect
64. #2240C22semidirect
65. #2240C22semidirect
66. #2237C22semidirect
67. #2237C22semidirect
68. #2236C22semidirect
69. #2235C22semidirect
70. #2234C22semidirect
71. #2234C22semidirect
72. #2233C22semidirect
73. #2232C22semidirect
74. #2229C22semidirect
75. #2228C22semidirect
76. #2227C22semidirect
77. #2226C22semidirect
78. #2225C22semidirect
79. #2224C22semidirect
80. #2220C22semidirect
81. #2220C22semidirect
82. #2220C22semidirect
83. #2220C22semidirect
84. #2219C22semidirect
85. #2219C22semidirect
86. #2218C22semidirect
87. #2218C22semidirect
88. #2211C22semidirect
89. #2210C22semidirect
90. #2209C22semidirect
91. #2208C22semidirect
92. #2207C22semidirect
93. #2206C22semidirect
94. #2189C22semidirect
95. #2189C22semidirect
96. #2188C22semidirect
97. #2187C22semidirect
98. #2186C22semidirect
99. #2186C22semidirect
100. #2185C22semidirect
101. #2184C22semidirect
102. C4×Q32C22semidirect
103. C4×Q32C22semidirect
104. C4×SD32C22semidirect
105. C4×SD32C22semidirect
106. C4×SD32C22semidirect
107. C4×SD32C22semidirect
108. C4×D16C22semidirect
109. C4×D16C22semidirect
112. #2169C22semidirect
113. #2169C22semidirect
114. #2169C22semidirect
115. #2169C22semidirect
116. #2158C22semidirect
117. #2158C22semidirect
118. C2×C4⋊C16C22semidirect
119. #2141C22semidirect
120. #2141C22semidirect
121. #2140C22semidirect
122. #2140C22semidirect
123. #2139C22semidirect
124. #2139C22semidirect
125. #2139C22semidirect
126. #2139C22semidirect
129. #2138C22semidirect
130. #2138C22semidirect
131. #2138C22semidirect
132. #2138C22semidirect
133. C2×C22⋊C16C22semidirect
134. C2×C4×C16C22semidirect
358. #135#41semidirect

Maximal subgroups

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

subgroupindex
#612342
D4×#1352
#339002
#338992
#338982
#338972
#338962
#338952
#338942
#338932
#338922
#338912
#338902
#338892
#336972
#336452
#336262
#336042
#335792
#335162
C4×#5082
C2×#21692
#333802