Finite Group Databasebeta

← #7649073

Subgroups — #7649073

Order 512.

5612 conjugacy classes of subgroups.

The subgroup lattice has 914 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42191C214yesmaximal, complemented
2#41532C218yesmaximal, complemented
3#41427C214yesmaximal, complemented
4#40888C218yesmaximal, complemented
5#38605C218yesmaximal, complemented
6#38467C214yesmaximal, complemented
7#38178C218yesmaximal, complemented
8#37881C214yesmaximal, complemented
9#35455C212yesmaximal, complemented
10#35446C212yesmaximal
11#35370C212yesmaximal, complemented
12#35097C212yesmaximal, complemented
13#34985C211yesmaximal, characteristic, complemented
14C2×#2486C211yesmaximal, characteristic, complemented
15C2×#2413C212yesmaximal, complemented
16#34256C211yesmaximal, characteristic
17#34199C212yesmaximal, complemented
18C22×H(5,𝔽2)C2211yescharacteristic
19C2×#543C2211yescharacteristic, complemented
20C22×#123C2212yes—
21C22×#123C2212yes—
22C22×#123C2212yes—
23C2×#518C2211yescharacteristic
24C22×C4×D4C2211yescharacteristic
25C22×#117C2212yescomplemented
26C23×C4⋊C4C2211yescharacteristic, complemented
27#2855C2212yescomplemented
28#2853C2218yescomplemented
29#2848C2212yescomplemented
30#2833C2214yescomplemented
31#2830C2214yescomplemented
32#2827C2218yescomplemented
33#2808C2214yescomplemented
34#2806C2214yescomplemented
35#2805C2214yescomplemented
36#2800C2218yescomplemented
37#2788C2218yescomplemented
38#2787C2218yescomplemented
39#2781C2218yescomplemented
40#2779C2218yescomplemented
41#2774C2218yescomplemented
42#2771C2214yescomplemented
43#2770C2218yescomplemented
44#2768C2218yescomplemented
45#2765C2218yescomplemented
46#2764C2214yescomplemented
47#2741C2218yescomplemented
48#2736C2214yescomplemented
49#2735C2218yescomplemented
50#2735C2214yescomplemented
51#2727C2214yescomplemented
52#2702C2218yescomplemented
53#2666C2218yescomplemented
54#2653C2218yescomplemented
55#2652C2218yescomplemented
56#2651C2218yescomplemented
57#2649C2218yescomplemented
58#2646C2214yescomplemented
59#2627C2212yescomplemented
60#2626C2212yescomplemented
61#2626C2214yescomplemented
62#2623C2218yescomplemented
63#2593C2214yescomplemented
64#2589C2218yescomplemented
65#2587C2218yescomplemented
66#2586C2214yescomplemented
67#2561C2214yescomplemented
68#2561C2214yescomplemented
69#2518C2218yescomplemented
70#2510C2218yescomplemented
71#2510C2218yescomplemented
72#2505C2218yescomplemented
73#2503C2214yescomplemented
74#2503C2214yescomplemented
75#2498C2218yescomplemented
76#2498C2218yescomplemented
77#2493C2218yescomplemented
78#2488C2218yescomplemented
79#2488C2218yescomplemented
80#2488C2218yescomplemented
81#2488C2218yescomplemented
82#2486C2218yescomplemented
83#2486C2218yescomplemented
84#2484C2218yescomplemented
85#2482C2218yescomplemented
86#2481C2218yescomplemented
87#2481C2218yescomplemented
88#2480C2218yescomplemented
89#2480C2218yescomplemented
90#2450C2218yescomplemented
91#2449C2218yescomplemented
92#2413C2218yescomplemented
93#2413C2218yescomplemented
94#2413C2218yescomplemented
95#2413C2218yescomplemented
96#2406C2214yes—
97#2406C2218yes—
98#2406C2218yes—
99#2406C2214yes—
100#2405C2214yes—
101#2405C2218yes—
102#2405C2214yes—
103#2405C2218yes—
104C2×#398C2214yescomplemented
105C2×#398C2212yescomplemented
106C2×#397C2212yescomplemented
107C2×#396C2214yescomplemented
108#2359C2218yescomplemented
109#2359C2218yescomplemented
110#2344C2218yescomplemented
111#2342C2218yescomplemented
112#2339C2218yes—
113D4×C22⋊C4C2218yes—
114#2334C2218yescomplemented
115#2329C2214yescomplemented
116#2322C2218yescomplemented
117#2315C2211yescharacteristic, complemented
118#2315C2212yescomplemented
119#2312C2214yescomplemented
120#2311C2212yes—
121#2308C2212yes—
122#2308C2212yes—
123#2308C2212yes—
124#2308C2212yes—
125#2308C2212yes—
126C4×#123C2218yescomplemented
127#2297C2212yes—
128C2×#389C2212yescomplemented
129C2×#389C2214yescomplemented
130C2×#388C2214yescomplemented
131C2×#386C2212yes—
132C2×#386C2212yes—
133C2×#385C2212yescomplemented
134C2×#381C2212yescomplemented
135C2×#381C2212yescomplemented
136C2×#380C2211yescharacteristic, complemented
137C2×#380C2212yescomplemented
138#2273C2212yescomplemented
139C2×H(5,𝔽2)—28no—
140C2×H(5,𝔽2)—44no—
141C2×H(5,𝔽2)—44no—
142C22×#41C2312yes—
143C22×#41C2314yes—
144C23×D4C2312yes—
145C23×D4C2311yescharacteristic
146C23×D4C2312yes—
147C23×D4C2314yes—
148C24×C4C2312yes—
149C24×C4C2311yescharacteristic
150C24×C4C2311yescharacteristic
151#543—44no—
152C2×#126C2318yes—
153C2×#123—216no—
154C2×#123—48no—
155C2×#123—48no—
156C2×#123C2314yes—
157C2×#123C2318yes—
158C2×#123C2314yes—
159C2×#123C2314yes—
160C2×#123C2314yes—
161C2×#123C2318yes—
162C2×#123C2318yes—
163C2×#123C2318yes—
164C2×C22⋊Q8C2314yes—
165C2×C22⋊Q8C2314yes—
166C2×C22⋊Q8C2314yes—
167C2×C22⋊Q8C2312yes—
168C2×C22⋊Q8C2312yes—
169#518—44no—
170C2×C4×D4—44no—
171C2×C4×D4C2318yes—
172C2×C4×D4C2318yes—
173C2×#117—48no—
174C2×#117C2312yes—
175C2×#117C2318yes—
176C2×#117C2318yes—
177C22×C4⋊C4—44no—
178C22×C4⋊C4C2314yes—
179C22×C4⋊C4C2311yescharacteristic
180C22×C4⋊C4C2314yes—
181C22×C4⋊C4C2314yes—
182C22×C4⋊C4C2314yes—
183C22×C4⋊C4C2312yes—
184C22×C4⋊C4C2312yes—
185C22×C4⋊C4C2314yes—
186C22×C4⋊C4C2312yes—
187C22×C4⋊C4C2314yes—
188C22×C4⋊C4C2312yes—
189C22×C4⋊C4C2312yes—
190C22×C22⋊C4C2312yes—
191C22×C22⋊C4C2311yescharacteristic
192C22×C22⋊C4C2312yes—
193C22×C22⋊C4C2312yes—
194C22×C22⋊C4C2312yes—
195C22×C22⋊C4C2314yes—
196C22×C22⋊C4C2312yes—
197C22×C22⋊C4C2312yes—
198C22×C22⋊C4C2311yescharacteristic
199C22×C22⋊C4C2312yes—
200C22×C22⋊C4C2314yes—
201C22×C22⋊C4C2314yes—
202C22×C22⋊C4C2314yes—
203C22×C42C2314yes—
204C22×C42C2311yescharacteristic
205#401C2318yes—
206#400C2318yes—
207#400C2318yes—
208#400C2314yes—
209#400C2318yes—
210#400C2318yes—
211#400C2318yes—
212#400C2318yes—
213#400C2318yes—
214#400C2318yes—
215#400C2318yes—
216#399C2318yes—
217#399C2318yes—
218#399C2314yes—
219#398C2318yes—
220#398C2318yes—
221#398C2314yes—
222#398C2314yes—
223#398C2318yes—
224#398C2318yes—
225#398C2318yes—
226#398C2318yes—
227#398C2318yes—
228#398C2318yes—
229#397C2318yes—
230#397C2318yes—
231#397C2314yes—
232#397C2318yes—
233#397C2318yes—
234#397C2318yes—
235#397C2318yes—
236#397C2318yes—
237#397C2314yes—
238#397C2318yes—
239#396C2318yes—
240#396C2318yes—
241#396C2318yes—
242#396C2318yes—
243#396C2318yes—
244#396C2318yes—
245#395C2314yes—
246#395C2318yes—
247#395C2318yes—
248#394C2318yes—
249#394C2318yes—
250#394C2318yes—
251#394C2318yes—
252#394C2318yes—
253#394C2318yes—
254#393C2318yes—
255#393C2318yes—
256#393C2314yes—
257#391C2314yes—
258#391C2318yes—
259#391C2314yes—
260#391C2318yes—
261#391C2314yes—
262#390C2314yes—
263#390C2314yes—
264#389C2318yes—
265#389C2318yes—
266#389C2318yes—
267#389C2318yes—
268#389C2314yes—
269#389C2318yes—
270#389C2318yes—
271#389C2314yes—
272#389C2318yes—
273#389C2314yes—
274#388C2318yes—
275#388C2318yes—
276#388C2318yes—
277#388C2318yes—
278#388C2318yes—
279#388C2318yes—
280#388C2318yes—
281#388C2318yes—
282#388C2318yes—
283#388C2318yes—
284#388C2318yes—
285#388C2318yes—
286#388C2318yes—
287#388C2318yes—
288#388C2318yes—
289#388C2318yes—
290#388C2318yes—
291#388C2318yes—
292#388C2318yes—
293#387C2318yes—
294#387C2318yes—
295#387C2318yes—
296#387C2318yes—
297#387C2318yes—
298#387C2318yes—
299#387C2318yes—
300#387C2318yes—
301#387C2318yes—
302#387C2318yes—
303#387C2318yes—
304#387C2318yes—
305#386C2314yes—
306#386C2314yes—
307#386C2314yes—
308#386C2318yes—
309#386C2318yes—
310#386C2318yes—
311#386C2318yes—
312#386C2314yes—
313#386C2314yes—
314#386C2314yes—
315#386C2318yes—
316#386C2318yes—
317#386C2314yes—
318#386C2318yes—
319#386C2318yes—
320#386C2314yes—
321#385C2318yes—
322#385C2318yes—
323#385C2318yes—
324#385C2318yes—
325#385C2318yes—
326#385C2318yes—
327#385C2318yes—
328#385C2318yes—
329#385C2318yes—
330#385C2318yes—
331#385C2314yes—
332#385C2318yes—
333#385C2314yes—
334#385C2318yes—
335#385C2318yes—
336#383C2318yes—
337#382C2318yes—
338#382C2318yes—
339#381C2314yes—
340#381C2314yes—
341#381C2314yes—
342#381C2314yes—
343#381C2314yes—
344#381C2314yes—
345#381C2314yes—
346#381C2314yes—
347#381C2314yes—
348#381C2318yes—
349#381C2318yes—
350#380C2318yes—
351#380C2314yes—
352#380C2314yes—
353#380C2312yes—
354#380C2318yes—
355#380C2312yes—
356#380C2314yes—
357#380C2318yes—
358#380C2318yes—
359#379C2314yes—
360#379C2314yes—
361#379C2314yes—
362#379C2314yes—
363#379C2314yes—
364#379C2318yes—
365#379C2318yes—
366C4×C4⋊C4C2318yes—
367C4×C4⋊C4C2318yes—
368C4×C22⋊C4C2314yes—
369C4×C22⋊C4C2314yes—
370C4×C22⋊C4C2318yes—
371C4×C22⋊C4C2318yes—
372C4×C22⋊C4C2318yes—
373C4×C22⋊C4C2318yes—
374C4×C22⋊C4C2318yes—
375C2×#95C2314yes—
376C2×#95C2314yes—
377C2×#95C2314yes—
378C2×#95C2314yes—
379C2×#95C2312yes—
380C2×#95C2314yes—
381C2×#95C2314yes—
382C2×#95C2314yes—
383C25C2412yes—
384C25C2411yescharacteristic
385C25C2412yes—
386C25C2411yescharacteristic
387H(5,𝔽2)—464no—
388C2×#41—216no—
389C2×#41—28no—
390C2×#41—44no—
391C2×#41—44no—
392C2×#41—48no—
393C2×#41—48no—
394C22×Q8C2412yes—
395C22×Q8C2412yes—
396C22×Q8C2412yes—
397C22×D4—24no—
398C22×D4—24no—
399C22×D4—28no—
400C22×D4—28no—
401C22×D4—28no—
402C22×D4—28no—
403C22×D4—216no—
404C22×D4—48no—
405C22×D4—48no—
406C22×D4—44no—
407C22×D4—44no—
408C22×D4#4118yes—
409C22×D4C2414yes—
410C22×D4C2414yes—
411C22×D4C2414yes—
412C22×D4C2414yes—
413C22×D4C2412yes—
414C23×C4—28no—
415C23×C4—24no—
416C23×C4—28no—
417C23×C4—28no—
418C23×C4—44no—
419C23×C4—44no—
420C23×C4—42no—
421C23×C4C2412yes—
422C23×C4C2414yes—
423C23×C4C2414yes—
424C23×C4C2412yes—
425C23×C4C2411yescharacteristic
426C23×C4C2412yes—
427C23×C4C2414yes—
428C23×C4C2411yescharacteristic
429C23×C4C2412yes—
430C23×C4C2414yes—
431C23×C4C2414yes—
432C23×C4C2414yes—
433C23×C4C2412yes—
434C23×C4C2411yescharacteristic
435C23×C4C2411yescharacteristic
436C23×C4C2411yescharacteristic
437C23×C4C2414yes—
438C23×C4C2412yes—
439C23×C4C2414yes—
440C23×C4C2414yes—
441#126—416no—
442#123—216no—
443#123—232no—
444#123—216no—
445#123—48no—
446#123—48no—
447#123—416no—
448#123—416no—
449#123—416no—
450C22⋊Q8—48no—
451C22⋊Q8—48no—
452C22⋊Q8—44no—
453C22⋊Q8—44no—
454C22⋊Q8—48no—
455C4×D4—416no—
456C4×D4—416no—
457#117—416no—
458#117—416no—
459#117—44no—
460C2×C4⋊C4—216no—
461C2×C4⋊C4—48no—
462C2×C4⋊C4—44no—
463C2×C4⋊C4—44no—
464C2×C4⋊C4—48no—
465C2×C4⋊C4—48no—
466C2×C4⋊C4—44no—
467C2×C4⋊C4—48no—
468C2×C4⋊C4—42no—
469C2×C4⋊C4—48no—
470C2×C4⋊C4—44no—
471C2×C4⋊C4—44no—
472C2×C4⋊C4C2418yes—
473C2×C4⋊C4C2418yes—
474C2×C4⋊C4C2418yes—
475C2×C4⋊C4C2414yes—
476C2×C4⋊C4C2412yes—
477C2×C4⋊C4C2414yes—
478C2×C4⋊C4C2412yes—
479C2×C4⋊C4C2412yes—
480C2×C4⋊C4C2414yes—
481C2×C4⋊C4C2412yes—
482C2×C4⋊C4C2418yes—
483C2×C4⋊C4C2418yes—
484C2×C4⋊C4C2414yes—
485C2×C4⋊C4C2418yes—
486C2×C4⋊C4C2418yes—
487C2×C4⋊C4C2418yes—
488C2×C4⋊C4C2418yes—
489C2×C4⋊C4C2414yes—
490C2×C4⋊C4C2418yes—
491C2×C4⋊C4C2414yes—
492C2×C4⋊C4C2412yes—
493C2×C4⋊C4C2414yes—
494C2×C4⋊C4C2414yes—
495C2×C4⋊C4C2412yes—
496C2×C4⋊C4C2414yes—
497C2×C4⋊C4C2418yes—
498C2×C4⋊C4C2418yes—
499C2×C4⋊C4C2414yes—
500C2×C22⋊C4—216no—
501C2×C22⋊C4—28no—
502C2×C22⋊C4—28no—
503C2×C22⋊C4—28no—
504C2×C22⋊C4—24no—
505C2×C22⋊C4—28no—
506C2×C22⋊C4—48no—
507C2×C22⋊C4—48no—
508C2×C22⋊C4—44no—
509C2×C22⋊C4—42no—
510C2×C22⋊C4—48no—
511C2×C22⋊C4—44no—
512C2×C22⋊C4—44no—
513C2×C22⋊C4C2414yes—
514C2×C22⋊C4C2418yes—
515C2×C22⋊C4C2414yes—
516C2×C22⋊C4C2414yes—
517C2×C22⋊C4C2414yes—
518C2×C22⋊C4C2414yes—
519C2×C22⋊C4C2414yes—
520C2×C22⋊C4C2414yes—
521C2×C22⋊C4C2414yes—
522C2×C22⋊C4C2414yes—
523C2×C22⋊C4C2418yes—
524C2×C22⋊C4C2418yes—
525C2×C22⋊C4C2414yes—
526C2×C22⋊C4C2414yes—
527C2×C22⋊C4C2418yes—
528C2×C22⋊C4C2418yes—
529C2×C22⋊C4C2418yes—
530C2×C22⋊C4C2418yes—
531C2×C22⋊C4C2418yes—
532C2×C22⋊C4C2418yes—
533C2×C22⋊C4C2418yes—
534C2×C22⋊C4C2418yes—
535C2×C22⋊C4C2418yes—
536C2×C22⋊C4C2418yes—
537C2×C22⋊C4C2418yes—
538C2×C22⋊C4C2418yes—
539C2×C22⋊C4C2418yes—
540C2×C42—48no—
541C2×C42—42no—
542C2×C42C2418yes—
543C2×C42C2418yes—
544C2×C42C2414yes—
545C2×C42C2414yes—
546C2×C42C2418yes—
547C2×C42C2418yes—
548#95C2418yes—
549#95C2418yes—
550#95C2418yes—
551#95C2418yes—
552#95C2418yes—
553#95C2414yes—
554#95C2414yes—
555#95C2418yes—
556#95C2418yes—
557#95C2418yes—
558#95C2418yes—
559#95C2418yes—
560#95C2418yes—
561#95C2418yes—
562#95C2418yes—
563#95C2418yes—
564#95C2418yes—
565#95C2418yes—
566#95C2418yes—
567#95C2418yes—
568#95C2418yes—
569#95C2418yes—
570#95C2414yes—
571#95C2414yes—
572#95C2418yes—
573#95C2418yes—
574#95C2418yes—
575#95C2418yes—
576C24—22no—
577C24—22no—
578C24—24no—
579C24—24no—
580C24—24no—
581C24—24no—
582C24—42no—
583C24—42no—
584C24—42no—
585C24—42no—
586C24—42no—
587C24—42no—
588C24—44no—
589C24—44no—
590C24—44no—
591C24—44no—
592C24C2×#4114yes—
593C24C2×#4114yes—
594C24H(5,𝔽2)14yes—
595C24H(5,𝔽2)14yes—
596C24C2514yes—
597C24C2512yes—
598C24C2512yes—
599C24C2511yescharacteristic
600#41—432no—
601#41—464no—
602C2×Q8—24no—
603C2×Q8—42no—
604C2×Q8—42no—
605C2×Q8—42no—
606C2×Q8—42no—
607C2×Q8—44no—
608C2×Q8—44no—
609C2×D4—232no—
610C2×D4—28no—
611C2×D4—28no—
612C2×D4—28no—
613C2×D4—28no—
614C2×D4—28no—
615C2×D4—28no—
616C2×D4—28no—
617C2×D4—28no—
618C2×D4—28no—
619C2×D4—24no—
620C2×D4—42no—
621C2×D4—42no—
622C2×D4—44no—
623C2×D4—44no—
624C2×D4—464no—
625C2×D4—432no—
626C2×D4—432no—
627C2×D4C2×#41116yes—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—24no—
632C22×C4—28no—
633C22×C4—24no—
634C22×C4—28no—
635C22×C4—24no—
636C22×C4—24no—
637C22×C4—24no—
638C22×C4—24no—
639C22×C4—28no—
640C22×C4—22no—
641C22×C4—24no—
642C22×C4—24no—
643C22×C4—28no—
644C22×C4—28no—
645C22×C4—28no—
646C22×C4—28no—
647C22×C4—24no—
648C22×C4—24no—
649C22×C4—24no—
650C22×C4—28no—
651C22×C4—28no—
652C22×C4—22no—
653C22×C4—28no—
654C22×C4—24no—
655C22×C4—24no—
656C22×C4—22no—
657C22×C4—28no—
658C22×C4—28no—
659C22×C4—28no—
660C22×C4—44no—
661C22×C4—44no—
662C22×C4—42no—
663C22×C4—44no—
664C22×C4—44no—
665C22×C4—44no—
666C22×C4—42no—
667C22×C4—42no—
668C22×C4—44no—
669C22×C4—44no—
670C22×C4—44no—
671C22×C4—44no—
672C22×C4—44no—
673C22×C4—42no—
674C22×C4—44no—
675C22×C4—44no—
676C22×C4—44no—
677C22×C4—42no—
678C22×C4—44no—
679C22×C4—44no—
680C22×C4—44no—
681C22×C4—416no—
682C22×C4—432no—
683C22×C4—88no—
684C22×C4C2×#4114yes—
685C22×C4C2514yes—
686C22×C4C2518yes—
687C22×C4C2512yes—
688C22×C4C2514yes—
689C22×C4C2512yes—
690C22×C4C2518yes—
691C22×C4C2512yes—
692C22×C4C2518yes—
693C22×C4C2514yes—
694C22×C4C2514yes—
695C22×C4C2514yes—
696C22×C4C2512yes—
697C22×C4C2512yes—
698C4⋊C4—216no—
699C4⋊C4—216no—
700C4⋊C4—216no—
701C4⋊C4—28no—
702C4⋊C4—42no—
703C4⋊C4—44no—
704C4⋊C4—42no—
705C4⋊C4—42no—
706C4⋊C4—44no—
707C4⋊C4—42no—
708C4⋊C4—44no—
709C4⋊C4—48no—
710C4⋊C4—48no—
711C4⋊C4—48no—
712C4⋊C4—44no—
713C4⋊C4—48no—
714C4⋊C4—48no—
715C4⋊C4—48no—
716C4⋊C4—48no—
717C4⋊C4—48no—
718C4⋊C4—44no—
719C4⋊C4—44no—
720C4⋊C4—44no—
721C4⋊C4—44no—
722C4⋊C4—42no—
723C4⋊C4—42no—
724C4⋊C4—44no—
725C4⋊C4—48no—
726C22⋊C4—28no—
727C22⋊C4—28no—
728C22⋊C4—216no—
729C22⋊C4—216no—
730C22⋊C4—28no—
731C22⋊C4—28no—
732C22⋊C4—28no—
733C22⋊C4—28no—
734C22⋊C4—28no—
735C22⋊C4—28no—
736C22⋊C4—28no—
737C22⋊C4—216no—
738C22⋊C4—48no—
739C22⋊C4—48no—
740C22⋊C4—44no—
741C22⋊C4—44no—
742C22⋊C4—48no—
743C22⋊C4—48no—
744C22⋊C4—48no—
745C22⋊C4—48no—
746C22⋊C4—48no—
747C22⋊C4—48no—
748C22⋊C4—48no—
749C22⋊C4—48no—
750C22⋊C4—48no—
751C22⋊C4—48no—
752C22⋊C4—48no—
753C42—48no—
754C42—48no—
755C42—44no—
756C42—48no—
757C42—44no—
758C42—48no—
759C23—22no—
760C23—24no—
761C23—22no—
762C23—24no—
763C23—22no—
764C23—22no—
765C23—24no—
766C23—24no—
767C23—28no—
768C23—24no—
769C23—24no—
770C23—24no—
771C23—28no—
772C23—28no—
773C23—44no—
774C23—48no—
775C23—44no—
776C23—48no—
777C23—48no—
778C23—48no—
779C23—48no—
780C23—82no—
781C23—82no—
782C23—84no—
783C23—88no—
784C23—84no—
785C23—84no—
786C23—88no—
787C23—88no—
788C23—162no—
789C23—162no—
790C23—164no—
791C23#538116yes—
792C23C22×#4114yes—
793C23C22×#4114yes—
794C23C22×#4112yes—
795C23C2×H(5,𝔽2)12yes—
796C23C2×H(5,𝔽2)12yes—
797C23C2×H(5,𝔽2)14yes—
798C23C2×H(5,𝔽2)14yes—
799C23C2611yescharacteristic
800Q8—48no—
801Q8—162no—
802Q8—162no—
803D4—232no—
804D4—48no—
805D4—416no—
806D4—416no—
807D4—416no—
808C2×C4—28no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—28no—
814C2×C4—28no—
815C2×C4—24no—
816C2×C4—24no—
817C2×C4—24no—
818C2×C4—24no—
819C2×C4—28no—
820C2×C4—28no—
821C2×C4—22no—
822C2×C4—24no—
823C2×C4—24no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—24no—
827C2×C4—24no—
828C2×C4—24no—
829C2×C4—24no—
830C2×C4—24no—
831C2×C4—28no—
832C2×C4—28no—
833C2×C4—28no—
834C2×C4—28no—
835C2×C4—24no—
836C2×C4—24no—
837C2×C4—28no—
838C2×C4—28no—
839C2×C4—28no—
840C2×C4—28no—
841C2×C4—24no—
842C2×C4—416no—
843C2×C4—416no—
844C2×C4—416no—
845C2×C4—44no—
846C2×C4—48no—
847C2×C4—416no—
848C2×C4—48no—
849C2×C4—48no—
850C2×C4—416no—
851C2×C4—48no—
852C2×C4—88no—
853C2×C4—88no—
854C2×C4—84no—
855C2×C4—82no—
856C2×C4—84no—
857C2×C4—88no—
858C2×C4—82no—
859C2×C4—164no—
860C2×C4C22×#4114yes—
861C2×C4#58514yes—
862C22—24no—
863C22—28no—
864C22—22no—
865C22—24no—
866C22—22no—
867C22—24no—
868C22—28no—
869C22—24no—
870C22—28no—
871C22—24no—
872C22—416no—
873C22—42no—
874C22—42no—
875C22—44no—
876C22—48no—
877C22—44no—
878C22—44no—
879C22—48no—
880C22—44no—
881C22—88no—
882C22—168no—
883C22—168no—
884C22C2×#53814yes—
885C22C2×#53818yes—
886C22C23×#4111yescharacteristic
887C22C22×H(5,𝔽2)11yescharacteristic
888C22C22×H(5,𝔽2)11yescharacteristic
889C22C2×#58512yes—
890C222−1+612yes—
891C4—24no—
892C4—24no—
893C4—48no—
894C4—42no—
895C4—42no—
896C4—44no—
897C4—42no—
898C4—44no—
899C4—48no—
900C4—48no—
901C4—44no—
902C4—44no—
903C4—44no—
904C2—24no—
905C2—28no—
906C2—44no—
907C2—84no—
908C2C22×#53811yescharacteristic
909C2#6282011yescharacteristic
910C2#6287111yescharacteristic
911C2#6290112yes—
912C2#6299112yes—
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. #42191C2semidirect
2. #41532C2semidirect
3. #41427C2semidirect
4. #40888C2semidirect
5. #38605C2semidirect
6. #38467C2semidirect
7. #38178C2semidirect
8. #37881C2semidirect
9. #35455C2semidirect
11. #35370C2semidirect
12. #35097C2semidirect
13. #34985C2semidirect
14. C2×#2486C2semidirect
15. C2×#2413C2semidirect
17. #34199C2semidirect
19. C2×#543C22semidirect
25. C22×#117C22semidirect
26. C23×C4⋊C4C22semidirect
27. #2855C22semidirect
28. #2853C22semidirect
29. #2848C22semidirect
30. #2833C22semidirect
31. #2830C22semidirect
32. #2827C22semidirect
33. #2808C22semidirect
34. #2806C22semidirect
35. #2805C22semidirect
36. #2800C22semidirect
37. #2788C22semidirect
38. #2787C22semidirect
39. #2781C22semidirect
40. #2779C22semidirect
41. #2774C22semidirect
42. #2771C22semidirect
43. #2770C22semidirect
44. #2768C22semidirect
45. #2765C22semidirect
46. #2764C22semidirect
47. #2741C22semidirect
48. #2736C22semidirect
49. #2735C22semidirect
50. #2735C22semidirect
51. #2727C22semidirect
52. #2702C22semidirect
53. #2666C22semidirect
54. #2653C22semidirect
55. #2652C22semidirect
56. #2651C22semidirect
57. #2649C22semidirect
58. #2646C22semidirect
59. #2627C22semidirect
60. #2626C22semidirect
61. #2626C22semidirect
62. #2623C22semidirect
63. #2593C22semidirect
64. #2589C22semidirect
65. #2587C22semidirect
66. #2586C22semidirect
67. #2561C22semidirect
68. #2561C22semidirect
69. #2518C22semidirect
70. #2510C22semidirect
71. #2510C22semidirect
72. #2505C22semidirect
73. #2503C22semidirect
74. #2503C22semidirect
75. #2498C22semidirect
76. #2498C22semidirect
77. #2493C22semidirect
78. #2488C22semidirect
79. #2488C22semidirect
80. #2488C22semidirect
81. #2488C22semidirect
82. #2486C22semidirect
83. #2486C22semidirect
84. #2484C22semidirect
85. #2482C22semidirect
86. #2481C22semidirect
87. #2481C22semidirect
88. #2480C22semidirect
89. #2480C22semidirect
90. #2450C22semidirect
91. #2449C22semidirect
92. #2413C22semidirect
93. #2413C22semidirect
94. #2413C22semidirect
95. #2413C22semidirect
104. C2×#398C22semidirect
105. C2×#398C22semidirect
106. C2×#397C22semidirect
107. C2×#396C22semidirect
108. #2359C22semidirect
109. #2359C22semidirect
110. #2344C22semidirect
111. #2342C22semidirect
114. #2334C22semidirect
115. #2329C22semidirect
116. #2322C22semidirect
117. #2315C22semidirect
118. #2315C22semidirect
119. #2312C22semidirect
126. C4×#123C22semidirect
128. C2×#389C22semidirect
129. C2×#389C22semidirect
130. C2×#388C22semidirect
133. C2×#385C22semidirect
134. C2×#381C22semidirect
135. C2×#381C22semidirect
136. C2×#380C22semidirect
137. C2×#380C22semidirect
138. #2273C22semidirect

Maximal subgroups

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

subgroupindex
#421912
#415322
#414272
#408882
#386052
#384672
#381782
#378812
#354552
#354462
#353702
#350972
#349852
C2×#24862
C2×#24132
#342562
#341992