Finite Group Databasebeta

← #7672886

Subgroups — #7672886

Order 512.

5680 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#43727C214yesmaximal, complemented
2#43342C214yesmaximal, complemented
3#43307C214yesmaximal, complemented
4#43306C214yesmaximal, complemented
5#38198C218yesmaximal, complemented
6#38197C218yesmaximal, complemented
7#38115C218yesmaximal, complemented
8#38109C218yesmaximal, complemented
9#35455C211yesmaximal, characteristic, complemented
10#35448C212yesmaximal, complemented
11#35446C211yesmaximal, characteristic
12#34995C212yesmaximal, complemented
13#34985C212yesmaximal, complemented
14C2×#2623C211yesmaximal, characteristic, complemented
15#34256C212yesmaximal
16#34251C212yesmaximal, complemented
17C2×#2322C212yesmaximal, complemented
18C22×H(5,𝔽2)C2211yescharacteristic
19C2×#543C2211yescharacteristic, complemented
20C22×#123C2212yes—
21C22×#123C2211yescharacteristic
22C2×#518C2212yes—
23C22×C4×D4C2212yes—
24C23×C4⋊C4C2211yescharacteristic, complemented
25#2855C2214yescomplemented
26#2852C2218yescomplemented
27#2848C2214yescomplemented
28#2799C2214yescomplemented
29#2796C2218yescomplemented
30#2789C2214yescomplemented
31#2786C2218yescomplemented
32#2782C2214yescomplemented
33#2758C2218yescomplemented
34#2757C2218yescomplemented
35#2755C2218yescomplemented
36#2751C2218yescomplemented
37#2750C2218yescomplemented
38#2746C2218yescomplemented
39#2742C2214yescomplemented
40#2740C2218yescomplemented
41#2739C2218yescomplemented
42#2738C2218yescomplemented
43#2736C2214yescomplemented
44#2735C2214yescomplemented
45#2728C2214yescomplemented
46#2723C2218yescomplemented
47#2722C2214yescomplemented
48#2643C2218yescomplemented
49#2627C2214yescomplemented
50#2626C2214yescomplemented
51#2623C2218yescomplemented
52#2623C2218yescomplemented
53#2612C2214yescomplemented
54#2609C2214yescomplemented
55#2586C2214yescomplemented
56#2572C2214yescomplemented
57#2561C2212yescomplemented
58#2561C2212yescomplemented
59#2530C2218yescomplemented
60#2527C2218yescomplemented
61#2526C2218yescomplemented
62#2523C2214yescomplemented
63#2522C2218yescomplemented
64#2517C2214yescomplemented
65#2515C2218yescomplemented
66#2510C2218yescomplemented
67#2505C2218yescomplemented
68#2505C2218yescomplemented
69#2503C2212yescomplemented
70#2503C2212yescomplemented
71#2493C2218yescomplemented
72#2493C2218yescomplemented
73#2488C2218yescomplemented
74#2488C2218yescomplemented
75#2484C2218yescomplemented
76#2483C2214yescomplemented
77#2483C2218yescomplemented
78#2482C2218yescomplemented
79#2481C2218yescomplemented
80#2480C2218yescomplemented
81#2480C2218yescomplemented
82#2479C2218yescomplemented
83#2450C2218yescomplemented
84#2450C2218yescomplemented
85#2449C2218yescomplemented
86#2449C2218yescomplemented
87#2438C2218yescomplemented
88#2437C2214yescomplemented
89#2419C2218yescomplemented
90#2419C2218yescomplemented
91#2419C2218yescomplemented
92#2419C2218yescomplemented
93#2406C2218yes—
94#2406C2212yes—
95#2406C2212yes—
96#2405C2212yes—
97#2405C2212yes—
98#2405C2218yes—
99C2×#400C2212yescomplemented
100C2×#399C2212yescomplemented
101C2×#398C2212yescomplemented
102C2×#397C2212yescomplemented
103#2353C2218yescomplemented
104#2352C2218yescomplemented
105#2343C2218yescomplemented
106#2342C2218yescomplemented
107#2339C2218yes—
108#2339C2218yes—
109D4×C22⋊C4C2218yes—
110D4×C22⋊C4C2218yes—
111#2322C2218yescomplemented
112#2322C2218yescomplemented
113#2322C2218yescomplemented
114#2322C2218yescomplemented
115#2318C2218yescomplemented
116#2315C2212yescomplemented
117#2315C2212yescomplemented
118#2311C2214yes—
119#2308C2214yes—
120#2308C2212yes—
121#2308C2211yescharacteristic
122#2308C2212yes—
123#2308C2212yes—
124#2297C2214yes—
125C2×#389C2214yescomplemented
126#2290C2218yescomplemented
127C2×#388C2214yescomplemented
128C2×#387C2214yescomplemented
129C2×#386C2212yes—
130C2×#386C2212yes—
131C2×#386C2214yes—
132C2×#385C2212yescomplemented
133C2×#385C2214yescomplemented
134C2×#385C2212yescomplemented
135C2×#381C2212yescomplemented
136C2×#381C2211yescharacteristic, complemented
137#2273C2211yescharacteristic, complemented
138C2×C4×C22⋊C4C2212yescomplemented
139C2×H(5,𝔽2)—216no—
140C2×H(5,𝔽2)—44no—
141C22×#41C2314yes—
142C22×#41C2312yes—
143C23×D4C2311yescharacteristic
144C23×D4C2314yes—
145C23×D4C2312yes—
146C23×D4C2312yes—
147C24×C4C2311yescharacteristic
148C24×C4C2312yes—
149C24×C4C2312yes—
150#543—44no—
151C2×#126C2318yes—
152C2×#123—216no—
153C2×#123—44no—
154C2×#123C2314yes—
155C2×#123C2314yes—
156C2×#123C2318yes—
157C2×#123C2318yes—
158C2×C22⋊Q8C2312yes—
159C2×C22⋊Q8C2312yes—
160C2×C22⋊Q8C2314yes—
161C2×C22⋊Q8C2314yes—
162C2×C22⋊Q8C2318yes—
163#518—216no—
164C2×C4×D4—48no—
165C2×C4×D4C2318yes—
166C2×C4×D4C2318yes—
167C2×C4×D4C2318yes—
168C2×C4×D4C2318yes—
169C2×#117C2314yes—
170C2×#117C2318yes—
171C22×C4⋊C4—44no—
172C22×C4⋊C4C2314yes—
173C22×C4⋊C4C2312yes—
174C22×C4⋊C4C2312yes—
175C22×C4⋊C4C2312yes—
176C22×C4⋊C4C2314yes—
177C22×C4⋊C4C2314yes—
178C22×C4⋊C4C2311yescharacteristic
179C22×C4⋊C4C2311yescharacteristic
180C22×C4⋊C4C2314yes—
181C22×C4⋊C4C2314yes—
182C22×C22⋊C4C2312yes—
183C22×C22⋊C4C2312yes—
184C22×C22⋊C4C2311yescharacteristic
185C22×C22⋊C4C2312yes—
186C22×C22⋊C4C2312yes—
187C22×C22⋊C4C2314yes—
188C22×C22⋊C4C2314yes—
189C22×C22⋊C4C2311yescharacteristic
190C22×C22⋊C4C2311yescharacteristic
191C22×C22⋊C4C2312yes—
192C22×C22⋊C4C2314yes—
193C22×C22⋊C4C2314yes—
194C22×C22⋊C4C2318yes—
195C22×C42C2312yes—
196C22×C42C2314yes—
197#401C2318yes—
198#400C2314yes—
199#400C2314yes—
200#400C2318yes—
201#400C2318yes—
202#400C2318yes—
203#400C2318yes—
204#400C2318yes—
205#400C2318yes—
206#400C2318yes—
207#400C2318yes—
208#400C2318yes—
209#399C2314yes—
210#399C2318yes—
211#399C2314yes—
212#399C2318yes—
213#398C2314yes—
214#398C2318yes—
215#398C2318yes—
216#398C2314yes—
217#398C2318yes—
218#398C2318yes—
219#398C2318yes—
220#397C2314yes—
221#397C2314yes—
222#397C2314yes—
223#397C2318yes—
224#397C2314yes—
225#397C2318yes—
226#397C2318yes—
227#397C2318yes—
228#397C2318yes—
229#397C2318yes—
230#397C2318yes—
231#397C2318yes—
232#396C2318yes—
233#396C2318yes—
234#396C2318yes—
235#395C2318yes—
236#395C2314yes—
237#395C2314yes—
238#394C2314yes—
239#394C2314yes—
240#394C2318yes—
241#394C2318yes—
242#393C2314yes—
243#393C2314yes—
244#393C2318yes—
245#391C2318yes—
246#391C2314yes—
247#391C2314yes—
248#391C2318yes—
249#391C2318yes—
250#390C2318yes—
251#390C2318yes—
252#389C2318yes—
253#389C2318yes—
254#389C2318yes—
255#389C2318yes—
256#389C2318yes—
257#388C2318yes—
258#388C2318yes—
259#388C2318yes—
260#388C2318yes—
261#388C2318yes—
262#388C2318yes—
263#388C2318yes—
264#388C2318yes—
265#388C2318yes—
266#388C2318yes—
267#388C2318yes—
268#388C2318yes—
269#388C2318yes—
270#387C2318yes—
271#387C2318yes—
272#387C2318yes—
273#387C2318yes—
274#387C2318yes—
275#387C2318yes—
276#387C2318yes—
277#387C2318yes—
278#387C2318yes—
279#387C2318yes—
280#387C2318yes—
281#387C2318yes—
282#387C2318yes—
283#387C2318yes—
284#387C2318yes—
285#387C2318yes—
286#387C2318yes—
287#386C2314yes—
288#386C2314yes—
289#386C2314yes—
290#386C2314yes—
291#386C2314yes—
292#386C2314yes—
293#386C2318yes—
294#386C2318yes—
295#386C2318yes—
296#386C2318yes—
297#386C2318yes—
298#386C2318yes—
299#386C2314yes—
300#386C2314yes—
301#386C2314yes—
302#386C2318yes—
303#386C2318yes—
304#386C2318yes—
305#386C2318yes—
306#386C2314yes—
307#385C2318yes—
308#385C2318yes—
309#385C2318yes—
310#385C2318yes—
311#385C2314yes—
312#385C2314yes—
313#385C2314yes—
314#385C2318yes—
315#385C2318yes—
316#385C2318yes—
317#385C2318yes—
318#385C2318yes—
319#385C2318yes—
320#385C2318yes—
321#385C2318yes—
322#385C2318yes—
323#385C2314yes—
324#385C2318yes—
325#385C2314yes—
326#385C2318yes—
327#385C2314yes—
328#385C2318yes—
329#383C2318yes—
330#383C2318yes—
331#382C2318yes—
332#382C2314yes—
333#382C2314yes—
334#381C2314yes—
335#381C2314yes—
336#381C2314yes—
337#381C2318yes—
338#381C2314yes—
339#381C2314yes—
340#381C2312yes—
341#381C2318yes—
342#381C2318yes—
343#381C2318yes—
344#381C2318yes—
345#381C2318yes—
346#380C2318yes—
347#380C2318yes—
348#380C2314yes—
349#380C2314yes—
350#380C2318yes—
351#380C2318yes—
352#380C2318yes—
353#379C2314yes—
354#379C2314yes—
355#379C2314yes—
356#379C2318yes—
357#379C2312yes—
358#379C2314yes—
359#379C2314yes—
360C4×C4⋊C4C2318yes—
361C4×C22⋊C4C2312yes—
362C4×C22⋊C4C2312yes—
363C4×C22⋊C4C2318yes—
364C4×C22⋊C4C2318yes—
365C4×C22⋊C4C2318yes—
366C4×C22⋊C4C2318yes—
367C4×C22⋊C4C2318yes—
368C4×C22⋊C4C2318yes—
369#376C2318yes—
370C2×#95C2314yes—
371C2×#95C2314yes—
372C2×#95C2314yes—
373C2×#95C2318yes—
374C2×#95C2314yes—
375C2×#95C2312yes—
376C2×#95C2312yes—
377C2×#95C2314yes—
378C2×#95C2314yes—
379C2×#95C2314yes—
380C25C2411yescharacteristic
381C25C2412yes—
382C25C2412yes—
383C25C2411yescharacteristic
384H(5,𝔽2)—464no—
385C2×#41—216no—
386C2×#41—216no—
387C2×#41—216no—
388C2×#41—48no—
389C2×#41—44no—
390C22×Q8C2412yes—
391C22×Q8C2412yes—
392C22×Q8C2412yes—
393C22×D4—28no—
394C22×D4—28no—
395C22×D4—216no—
396C22×D4—28no—
397C22×D4—24no—
398C22×D4—216no—
399C22×D4—216no—
400C22×D4—44no—
401C22×D4—48no—
402C22×D4#41116yes—
403C22×D4C2414yes—
404C22×D4C2412yes—
405C22×D4C2414yes—
406C22×D4C2414yes—
407C22×D4C2414yes—
408C23×C4—28no—
409C23×C4—24no—
410C23×C4—28no—
411C23×C4—44no—
412C23×C4—84no—
413C23×C4—84no—
414C23×C4C2414yes—
415C23×C4C2411yescharacteristic
416C23×C4C2411yescharacteristic
417C23×C4C2411yescharacteristic
418C23×C4C2414yes—
419C23×C4C2412yes—
420C23×C4C2412yes—
421C23×C4C2411yescharacteristic
422C23×C4C2414yes—
423C23×C4C2414yes—
424C23×C4C2411yescharacteristic
425C23×C4C2418yes—
426C23×C4C2414yes—
427C23×C4C2412yes—
428C23×C4C2414yes—
429C23×C4C2414yes—
430C23×C4C2412yes—
431C23×C4C2412yes—
432C23×C4C2412yes—
433C23×C4C2418yes—
434#126—88no—
435#123—216no—
436#123—216no—
437#123—232no—
438#123—416no—
439C22⋊Q8—44no—
440C22⋊Q8—44no—
441C22⋊Q8—48no—
442C22⋊Q8—48no—
443C22⋊Q8—88no—
444C4×D4—232no—
445C4×D4—232no—
446C4×D4—416no—
447C4×D4—416no—
448#117—216no—
449#117—88no—
450C2×C4⋊C4—216no—
451C2×C4⋊C4—48no—
452C2×C4⋊C4—48no—
453C2×C4⋊C4—44no—
454C2×C4⋊C4—44no—
455C2×C4⋊C4—44no—
456C2×C4⋊C4—42no—
457C2×C4⋊C4—42no—
458C2×C4⋊C4—84no—
459C2×C4⋊C4—84no—
460C2×C4⋊C4C2418yes—
461C2×C4⋊C4C2418yes—
462C2×C4⋊C4C2418yes—
463C2×C4⋊C4C2412yes—
464C2×C4⋊C4C2412yes—
465C2×C4⋊C4C2414yes—
466C2×C4⋊C4C2414yes—
467C2×C4⋊C4C2412yes—
468C2×C4⋊C4C2412yes—
469C2×C4⋊C4C2418yes—
470C2×C4⋊C4C2418yes—
471C2×C4⋊C4C2418yes—
472C2×C4⋊C4C2418yes—
473C2×C4⋊C4C2414yes—
474C2×C4⋊C4C2414yes—
475C2×C4⋊C4C2418yes—
476C2×C4⋊C4C2418yes—
477C2×C4⋊C4C2414yes—
478C2×C4⋊C4C2412yes—
479C2×C4⋊C4C2412yes—
480C2×C4⋊C4C2414yes—
481C2×C4⋊C4C2418yes—
482C2×C4⋊C4C2418yes—
483C2×C4⋊C4C2418yes—
484C2×C22⋊C4—216no—
485C2×C22⋊C4—28no—
486C2×C22⋊C4—28no—
487C2×C22⋊C4—28no—
488C2×C22⋊C4—216no—
489C2×C22⋊C4—28no—
490C2×C22⋊C4—24no—
491C2×C22⋊C4—44no—
492C2×C22⋊C4—42no—
493C2×C22⋊C4—42no—
494C2×C22⋊C4—84no—
495C2×C22⋊C4—88no—
496C2×C22⋊C4—84no—
497C2×C22⋊C4C2414yes—
498C2×C22⋊C4C2414yes—
499C2×C22⋊C4C2414yes—
500C2×C22⋊C4C2414yes—
501C2×C22⋊C4C2414yes—
502C2×C22⋊C4C2414yes—
503C2×C22⋊C4C2418yes—
504C2×C22⋊C4C2414yes—
505C2×C22⋊C4C2414yes—
506C2×C22⋊C4C2414yes—
507C2×C22⋊C4C2418yes—
508C2×C22⋊C4C2418yes—
509C2×C22⋊C4C2418yes—
510C2×C22⋊C4C2418yes—
511C2×C22⋊C4C2418yes—
512C2×C22⋊C4C2418yes—
513C2×C22⋊C4C2418yes—
514C2×C22⋊C4C2414yes—
515C2×C22⋊C4C2414yes—
516C2×C22⋊C4C2418yes—
517C2×C22⋊C4C2418yes—
518C2×C22⋊C4C2418yes—
519C2×C22⋊C4C2414yes—
520C2×C22⋊C4C2418yes—
521C2×C22⋊C4C2418yes—
522C2×C22⋊C4C2418yes—
523C2×C22⋊C4C2414yes—
524C2×C42—44no—
525C2×C42—84no—
526C2×C42C2418yes—
527C2×C42C2414yes—
528C2×C42C2418yes—
529C2×C42C2418yes—
530C2×C42C2418yes—
531C2×C42C2414yes—
532#95C2418yes—
533#95C2418yes—
534#95C2418yes—
535#95C2418yes—
536#95C2418yes—
537#95C2418yes—
538#95C2418yes—
539#95C2418yes—
540#95C2418yes—
541#95C2418yes—
542#95C2418yes—
543#95C2414yes—
544#95C2414yes—
545#95C2418yes—
546#95C2418yes—
547#95C2418yes—
548#95C2418yes—
549#95C2414yes—
550#95C2414yes—
551#95C2418yes—
552#95C2418yes—
553#95C2418yes—
554#95C2414yes—
555#95C2414yes—
556#95C2418yes—
557#95C2418yes—
558#95C2418yes—
559#95C2418yes—
560#95C2418yes—
561#95C2418yes—
562#95C2414yes—
563#95C2414yes—
564C24—24no—
565C24—24no—
566C24—28no—
567C24—24no—
568C24—22no—
569C24—42no—
570C24—42no—
571C24—44no—
572C24—44no—
573C24—42no—
574C24—42no—
575C24—42no—
576C24—44no—
577C24—44no—
578C24C2×#4118yes—
579C24C2×#4118yes—
580C24H(5,𝔽2)14yes—
581C24C2512yes—
582C24C2514yes—
583C24C2511yescharacteristic
584C24C2512yes—
585#41—464no—
586#41—432no—
587C2×Q8—28no—
588C2×Q8—42no—
589C2×Q8—42no—
590C2×Q8—42no—
591C2×Q8—44no—
592C2×Q8—44no—
593C2×D4—264no—
594C2×D4—28no—
595C2×D4—28no—
596C2×D4—28no—
597C2×D4—28no—
598C2×D4—28no—
599C2×D4—28no—
600C2×D4—28no—
601C2×D4—28no—
602C2×D4—28no—
603C2×D4—28no—
604C2×D4—44no—
605C2×D4—42no—
606C2×D4—432no—
607C2×D4—464no—
608C2×D4—416no—
609C2×D4C2×#41116yes—
610C2×D4C2×#41116yes—
611C22×C4—24no—
612C22×C4—24no—
613C22×C4—28no—
614C22×C4—28no—
615C22×C4—28no—
616C22×C4—24no—
617C22×C4—24no—
618C22×C4—28no—
619C22×C4—24no—
620C22×C4—24no—
621C22×C4—24no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—28no—
625C22×C4—22no—
626C22×C4—216no—
627C22×C4—28no—
628C22×C4—28no—
629C22×C4—24no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—24no—
633C22×C4—28no—
634C22×C4—28no—
635C22×C4—28no—
636C22×C4—28no—
637C22×C4—44no—
638C22×C4—44no—
639C22×C4—44no—
640C22×C4—44no—
641C22×C4—42no—
642C22×C4—44no—
643C22×C4—44no—
644C22×C4—44no—
645C22×C4—48no—
646C22×C4—44no—
647C22×C4—44no—
648C22×C4—48no—
649C22×C4—42no—
650C22×C4—44no—
651C22×C4—44no—
652C22×C4—44no—
653C22×C4—48no—
654C22×C4—48no—
655C22×C4—42no—
656C22×C4—44no—
657C22×C4—48no—
658C22×C4—44no—
659C22×C4—44no—
660C22×C4—416no—
661C22×C4—816no—
662C22×C4—816no—
663C22×C4C2×#4118yes—
664C22×C4C2512yes—
665C22×C4C2518yes—
666C22×C4C2514yes—
667C22×C4C2512yes—
668C22×C4C2518yes—
669C22×C4C2518yes—
670C22×C4C2514yes—
671C22×C4C2512yes—
672C22×C4C2512yes—
673C22×C4C2514yes—
674C22×C4C2514yes—
675C22×C4C2512yes—
676C22×C4C2514yes—
677C4⋊C4—216no—
678C4⋊C4—216no—
679C4⋊C4—216no—
680C4⋊C4—42no—
681C4⋊C4—42no—
682C4⋊C4—44no—
683C4⋊C4—44no—
684C4⋊C4—42no—
685C4⋊C4—42no—
686C4⋊C4—48no—
687C4⋊C4—44no—
688C4⋊C4—44no—
689C4⋊C4—48no—
690C4⋊C4—48no—
691C4⋊C4—48no—
692C4⋊C4—48no—
693C4⋊C4—48no—
694C4⋊C4—48no—
695C4⋊C4—48no—
696C4⋊C4—42no—
697C4⋊C4—44no—
698C4⋊C4—44no—
699C4⋊C4—42no—
700C4⋊C4—48no—
701C22⋊C4—28no—
702C22⋊C4—28no—
703C22⋊C4—216no—
704C22⋊C4—28no—
705C22⋊C4—28no—
706C22⋊C4—28no—
707C22⋊C4—28no—
708C22⋊C4—216no—
709C22⋊C4—216no—
710C22⋊C4—28no—
711C22⋊C4—28no—
712C22⋊C4—28no—
713C22⋊C4—48no—
714C22⋊C4—44no—
715C22⋊C4—44no—
716C22⋊C4—48no—
717C22⋊C4—48no—
718C22⋊C4—48no—
719C22⋊C4—48no—
720C22⋊C4—48no—
721C22⋊C4—48no—
722C22⋊C4—48no—
723C22⋊C4—48no—
724C22⋊C4—44no—
725C22⋊C4—48no—
726C22⋊C4—48no—
727C22⋊C4—44no—
728C42—216no—
729C42—48no—
730C42—48no—
731C42—48no—
732C42—44no—
733C42—44no—
734C23—24no—
735C23—22no—
736C23—24no—
737C23—22no—
738C23—24no—
739C23—24no—
740C23—28no—
741C23—28no—
742C23—216no—
743C23—24no—
744C23—22no—
745C23—24no—
746C23—24no—
747C23—44no—
748C23—416no—
749C23—44no—
750C23—416no—
751C23—48no—
752C23—44no—
753C23—84no—
754C23—88no—
755C23—84no—
756C23—88no—
757C23—82no—
758C23—82no—
759C23—816no—
760C23—162no—
761C23—162no—
762C23#551116yes—
763C23C22×#4118yes—
764C23C22×#4114yes—
765C23C22×#4114yes—
766C23C22×#4114yes—
767C23C2×H(5,𝔽2)14yes—
768C23C2×H(5,𝔽2)12yes—
769C23C2611yescharacteristic
770Q8—48no—
771Q8—162no—
772Q8—162no—
773D4—232no—
774D4—232no—
775D4—416no—
776D4—48no—
777D4—416no—
778C2×C4—24no—
779C2×C4—24no—
780C2×C4—216no—
781C2×C4—28no—
782C2×C4—28no—
783C2×C4—28no—
784C2×C4—24no—
785C2×C4—24no—
786C2×C4—24no—
787C2×C4—24no—
788C2×C4—24no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—24no—
792C2×C4—24no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—28no—
797C2×C4—28no—
798C2×C4—24no—
799C2×C4—24no—
800C2×C4—24no—
801C2×C4—24no—
802C2×C4—28no—
803C2×C4—28no—
804C2×C4—24no—
805C2×C4—24no—
806C2×C4—28no—
807C2×C4—28no—
808C2×C4—28no—
809C2×C4—28no—
810C2×C4—48no—
811C2×C4—416no—
812C2×C4—416no—
813C2×C4—48no—
814C2×C4—48no—
815C2×C4—416no—
816C2×C4—44no—
817C2×C4—44no—
818C2×C4—44no—
819C2×C4—88no—
820C2×C4—88no—
821C2×C4—816no—
822C2×C4—82no—
823C2×C4—84no—
824C2×C4—82no—
825C2×C4—88no—
826C2×C4—88no—
827C2×C4—84no—
828C2×C4—816no—
829C2×C4C22×#4118yes—
830C22—28no—
831C22—28no—
832C22—28no—
833C22—24no—
834C22—22no—
835C22—24no—
836C22—22no—
837C22—216no—
838C22—28no—
839C22—416no—
840C22—48no—
841C22—44no—
842C22—44no—
843C22—48no—
844C22—42no—
845C22—42no—
846C22—42no—
847C22—816no—
848C22—164no—
849C22—168no—
850C22C2×#55118yes—
851C22C2×#55114yes—
852C22C23×#4112yes—
853C22C22×H(5,𝔽2)11yescharacteristic
854C22H(7,𝔽2)12yes—
855C222−1+612yes—
856C4—28no—
857C4—48no—
858C4—48no—
859C4—48no—
860C4—44no—
861C4—44no—
862C4—44no—
863C4—42no—
864C4—44no—
865C4—42no—
866C4—42no—
867C4—42no—
868C4—42no—
869C2—28no—
870C2—24no—
871C2—48no—
872C2—82no—
873C2C22×#55111yescharacteristic
874C2#6284714yes—
875C2#6286211yescharacteristic
876C2#6287111yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC22×H(5,𝔽2)C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #43727C2semidirect
2. #43342C2semidirect
3. #43307C2semidirect
4. #43306C2semidirect
5. #38198C2semidirect
6. #38197C2semidirect
7. #38115C2semidirect
8. #38109C2semidirect
9. #35455C2semidirect
10. #35448C2semidirect
12. #34995C2semidirect
13. #34985C2semidirect
14. C2×#2623C2semidirect
16. #34251C2semidirect
17. C2×#2322C2semidirect
19. C2×#543C22semidirect
24. C23×C4⋊C4C22semidirect
25. #2855C22semidirect
26. #2852C22semidirect
27. #2848C22semidirect
28. #2799C22semidirect
29. #2796C22semidirect
30. #2789C22semidirect
31. #2786C22semidirect
32. #2782C22semidirect
33. #2758C22semidirect
34. #2757C22semidirect
35. #2755C22semidirect
36. #2751C22semidirect
37. #2750C22semidirect
38. #2746C22semidirect
39. #2742C22semidirect
40. #2740C22semidirect
41. #2739C22semidirect
42. #2738C22semidirect
43. #2736C22semidirect
44. #2735C22semidirect
45. #2728C22semidirect
46. #2723C22semidirect
47. #2722C22semidirect
48. #2643C22semidirect
49. #2627C22semidirect
50. #2626C22semidirect
51. #2623C22semidirect
52. #2623C22semidirect
53. #2612C22semidirect
54. #2609C22semidirect
55. #2586C22semidirect
56. #2572C22semidirect
57. #2561C22semidirect
58. #2561C22semidirect
59. #2530C22semidirect
60. #2527C22semidirect
61. #2526C22semidirect
62. #2523C22semidirect
63. #2522C22semidirect
64. #2517C22semidirect
65. #2515C22semidirect
66. #2510C22semidirect
67. #2505C22semidirect
68. #2505C22semidirect
69. #2503C22semidirect
70. #2503C22semidirect
71. #2493C22semidirect
72. #2493C22semidirect
73. #2488C22semidirect
74. #2488C22semidirect
75. #2484C22semidirect
76. #2483C22semidirect
77. #2483C22semidirect
78. #2482C22semidirect
79. #2481C22semidirect
80. #2480C22semidirect
81. #2480C22semidirect
82. #2479C22semidirect
83. #2450C22semidirect
84. #2450C22semidirect
85. #2449C22semidirect
86. #2449C22semidirect
87. #2438C22semidirect
88. #2437C22semidirect
89. #2419C22semidirect
90. #2419C22semidirect
91. #2419C22semidirect
92. #2419C22semidirect
99. C2×#400C22semidirect
100. C2×#399C22semidirect
101. C2×#398C22semidirect
102. C2×#397C22semidirect
103. #2353C22semidirect
104. #2352C22semidirect
105. #2343C22semidirect
106. #2342C22semidirect
111. #2322C22semidirect
112. #2322C22semidirect
113. #2322C22semidirect
114. #2322C22semidirect
115. #2318C22semidirect
116. #2315C22semidirect
117. #2315C22semidirect
125. C2×#389C22semidirect
126. #2290C22semidirect
127. C2×#388C22semidirect
128. C2×#387C22semidirect
132. C2×#385C22semidirect
133. C2×#385C22semidirect
134. C2×#385C22semidirect
135. C2×#381C22semidirect
136. C2×#381C22semidirect
137. #2273C22semidirect
138. C2×C4×C22⋊C4C22semidirect

Maximal subgroups

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

subgroupindex
#437272
#433422
#433072
#433062
#381982
#381972
#381152
#381092
#354552
#354482
#354462
#349952
#349852
C2×#26232
#342562
#342512
C2×#23222