Finite Group Databasebeta

← #8898345

Subgroups — #8898345

Order 512.

5592 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#57721C218yesmaximal, complemented
2#57595C214yesmaximal, complemented
3#48773C214yesmaximal, complemented
4#47898C218yesmaximal, complemented
5#47802C214yesmaximal, complemented
6#47142C218yesmaximal, complemented
7#46999C212yesmaximal, complemented
8#46997C212yesmaximal, complemented
9#46388C212yesmaximal, complemented
10#38912C218yesmaximal, complemented
11#37932C214yesmaximal, complemented
12#36720C212yesmaximal, complemented
13#36718C211yesmaximal, characteristic, complemented
14#35540C211yesmaximal, characteristic, complemented
15#35446C212yesmaximal, complemented
16#35354C212yesmaximal, complemented
17#35347C211yesmaximal, characteristic
18C22×H(5,𝔽2)C2211yescharacteristic
19C2×#551C2214yescomplemented
20C2×#543C2211yescharacteristic, complemented
21C2×#534C2212yes—
22C22×#123C2212yes—
23C22×#123C2214yescomplemented
24C22×#121C2211yescharacteristic
25C2×#518C2211yescharacteristic, complemented
26#2848C2214yescomplemented
27#2848C2212yescomplemented
28#2844C2214yescomplemented
29#2842C2212yescomplemented
30#2841C2214yescomplemented
31#2838C2218yescomplemented
32#2792C2214yescomplemented
33#2792C2218yescomplemented
34#2771C2218yescomplemented
35#2765C2218yescomplemented
36#2765C2218yescomplemented
37#2765C2218yescomplemented
38#2763C2214yescomplemented
39#2761C2218yescomplemented
40#2760C2214yescomplemented
41#2751C2218yescomplemented
42#2750C2218yescomplemented
43#2746C2218yescomplemented
44#2743C2218yescomplemented
45#2743C2218yescomplemented
46#2743C2218yescomplemented
47#2724C2214yescomplemented
48#2718C2218yescomplemented
49#2717C2214yescomplemented
50#2708C2218yescomplemented
51#2706C2218yescomplemented
52#2706C2218yescomplemented
53#2697C2218yescomplemented
54#2695C2218yescomplemented
55#2695C2218yescomplemented
56#2687C2218yescomplemented
57#2687C2218yescomplemented
58#2681C2218yescomplemented
59#2680C2214yescomplemented
60#2680C2218yescomplemented
61#2680C2218yescomplemented
62#2672C2218yescomplemented
63#2672C2218yescomplemented
64#2646C2214yescomplemented
65#2627C2214yescomplemented
66#2626C2214yescomplemented
67#2626C2212yescomplemented
68#2623C2218yescomplemented
69#2622C2218yescomplemented
70#2609C2214yescomplemented
71#2609C2218yescomplemented
72#2583C2218yescomplemented
73#2583C2212yescomplemented
74#2579C2218yescomplemented
75#2576C2218yescomplemented
76#2561C2214yescomplemented
77#2553C2218yescomplemented
78#2553C2218yescomplemented
79#2534C2214yescomplemented
80#2505C2218yescomplemented
81#2502C2214yescomplemented
82#2487C2214yescomplemented
83#2483C2212yescomplemented
84#2483C2212yescomplemented
85#2483C2212yescomplemented
86#2482C2218yescomplemented
87#2480C2218yescomplemented
88#2477C2218yescomplemented
89#2476C2218yescomplemented
90#2471C2218yescomplemented
91#2470C2218yescomplemented
92#2470C2218yescomplemented
93#2470C2218yescomplemented
94#2470C2218yescomplemented
95#2457C2218yescomplemented
96#2455C2214yescomplemented
97#2455C2218yescomplemented
98#2435C2212yescomplemented
99#2430C2218yes—
100#2422C2218yescomplemented
101#2422C2218yescomplemented
102#2420C2218yescomplemented
103#2418C2218yescomplemented
104#2411C2218yescomplemented
105#2410C2218yes—
106#2406C2212yes—
107#2406C2218yes—
108#2406C2214yescomplemented
109#2406C2218yescomplemented
110#2406C2214yescomplemented
111#2405C2212yes—
112#2405C2212yes—
113#2405C2218yes—
114#2405C2212yes—
115#2405C2212yes—
116#2405C2212yes—
117#2405C2218yescomplemented
118#2405C2212yescomplemented
119#2405C2212yescomplemented
120#2404C2212yes—
121#2403C2212yes—
122#2375C2214yescomplemented
123#2342C2218yescomplemented
124#2329C2214yescomplemented
125#2322C2214yescomplemented
126#2317C2218yescomplemented
127#2317C2212yescomplemented
128#2315C2214yescomplemented
129#2312C2212yescomplemented
130#2312C2212yescomplemented
131#2312C2211yescharacteristic, complemented
132#2309C2211yescharacteristic, complemented
133#2308C2211yescharacteristic
134#2308C2212yes—
135#2308C2214yescomplemented
136C4×#120C2214yescomplemented
137C2×#386C2212yes—
138#2280C2212yescomplemented
139C2×H(5,𝔽2)—44no—
140C2×H(5,𝔽2)—48no—
141C22×#41C2312yes—
142C22×#41C2314yes—
143C23×D4C2312yes—
144C23×D4C2311yescharacteristic
145C23×D4C2314yes—
146C23×D4C2311yescharacteristic
147C23×D4C2312yes—
148C23×D4C2311yescharacteristic
149C24×C4C2311yescharacteristic
150C24×C4C2312yes—
151#551—416no—
152#543—44no—
153#534—48no—
154C2×#126C2318yes—
155C2×#124C2314yes—
156C2×#123—48no—
157C2×#123—416no—
158C2×#123C2314yes—
159C2×#123C2318yes—
160C2×#123C2318yes—
161C2×#123C2314yes—
162C2×#123C2314yes—
163C2×#123C2318yes—
164C2×#123C2314yes—
165C2×#123C2314yes—
166C2×#123C2314yes—
167C2×#123C2318yes—
168C2×#123C2318yes—
169C2×#123C2314yes—
170C2×#123C2314yes—
171C2×C22⋊Q8C2314yes—
172C2×C22⋊Q8C2318yes—
173C2×C22⋊Q8C2312yes—
174C2×C22⋊Q8C2314yes—
175C2×C22⋊Q8C2312yes—
176C2×C22⋊Q8C2314yes—
177C2×#121—44no—
178C2×#121C2318yes—
179C2×#121C2318yes—
180C2×#120C2314yes—
181C2×#120C2314yes—
182C2×#120C2314yes—
183#518—44no—
184C2×C4×D4C2314yes—
185C2×C4×D4C2318yes—
186C2×C4×D4C2314yes—
187C2×#117C2312yes—
188C2×#117C2318yes—
189C2×#117C2312yes—
190C2×#117C2318yes—
191C22×C4⋊C4C2311yescharacteristic
192C22×C4⋊C4C2318yes—
193C22×C4⋊C4C2312yes—
194C22×C4⋊C4C2312yes—
195C22×C22⋊C4C2312yes—
196C22×C22⋊C4C2312yes—
197C22×C22⋊C4C2311yescharacteristic
198C22×C22⋊C4C2318yes—
199C22×C22⋊C4C2312yes—
200C22×C22⋊C4C2314yes—
201C22×C22⋊C4C2312yes—
202C22×C22⋊C4C2314yes—
203C22×C22⋊C4C2311yescharacteristic
204C22×C22⋊C4C2312yes—
205#401C2318yes—
206#400C2318yes—
207#400C2318yes—
208#400C2318yes—
209#400C2318yes—
210#400C2318yes—
211#400C2318yes—
212#400C2318yes—
213#399C2318yes—
214#399C2314yes—
215#399C2318yes—
216#399C2318yes—
217#398C2318yes—
218#398C2318yes—
219#398C2318yes—
220#398C2318yes—
221#398C2314yes—
222#398C2318yes—
223#398C2318yes—
224#398C2318yes—
225#397C2318yes—
226#397C2318yes—
227#397C2318yes—
228#397C2318yes—
229#397C2318yes—
230#397C2318yes—
231#397C2318yes—
232#397C2318yes—
233#397C2318yes—
234#396C2318yes—
235#396C2318yes—
236#396C2318yes—
237#396C2318yes—
238#396C2318yes—
239#396C2318yes—
240#395C2318yes—
241#395C2318yes—
242#395C2314yes—
243#395C2318yes—
244#395C2314yes—
245#394C2318yes—
246#394C2318yes—
247#394C2314yes—
248#394C2318yes—
249#394C2318yes—
250#394C2318yes—
251#394C2318yes—
252#394C2318yes—
253#394C2318yes—
254#394C2318yes—
255#394C2318yes—
256#394C2318yes—
257#394C2318yes—
258#393C2318yes—
259#393C2314yes—
260#393C2314yes—
261#392C2318yes—
262#392C2314yes—
263#391C2318yes—
264#390C2318yes—
265#390C2318yes—
266#390C2314yes—
267#389C2318yes—
268#389C2318yes—
269#389C2318yes—
270#389C2318yes—
271#389C2318yes—
272#389C2318yes—
273#389C2318yes—
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#387C2318yes—
289#387C2318yes—
290#387C2318yes—
291#387C2318yes—
292#387C2318yes—
293#387C2318yes—
294#387C2318yes—
295#386C2318yes—
296#386C2318yes—
297#386C2318yes—
298#386C2314yes—
299#386C2318yes—
300#386C2314yes—
301#386C2314yes—
302#386C2318yes—
303#386C2314yes—
304#386C2314yes—
305#386C2318yes—
306#386C2318yes—
307#386C2314yes—
308#386C2318yes—
309#386C2314yes—
310#386C2318yes—
311#386C2314yes—
312#386C2314yes—
313#386C2318yes—
314#385C2318yes—
315#385C2318yes—
316#385C2318yes—
317#385C2318yes—
318#385C2318yes—
319#385C2318yes—
320#385C2318yes—
321#385C2314yes—
322#385C2314yes—
323#385C2318yes—
324#385C2318yes—
325#385C2314yes—
326#385C2314yes—
327#385C2314yes—
328#385C2318yes—
329#385C2318yes—
330#385C2314yes—
331#385C2318yes—
332#385C2318yes—
333#385C2314yes—
334#385C2314yes—
335#385C2318yes—
336#385C2314yes—
337#385C2314yes—
338#385C2318yes—
339#385C2314yes—
340#384C2314yes—
341#384C2318yes—
342#382C2318yes—
343#382C2314yes—
344#382C2318yes—
345#381C2314yes—
346#381C2314yes—
347#381C2312yes—
348#381C2314yes—
349#381C2318yes—
350#381C2314yes—
351#381C2314yes—
352#381C2318yes—
353#381C2314yes—
354#380C2312yes—
355#380C2314yes—
356#380C2314yes—
357#380C2314yes—
358#380C2314yes—
359#380C2318yes—
360#380C2318yes—
361#380C2318yes—
362#380C2314yes—
363#379C2314yes—
364#379C2314yes—
365#379C2312yes—
366#379C2312yes—
367#379C2312yes—
368#379C2318yes—
369#379C2312yes—
370#379C2314yes—
371#379C2314yes—
372#379C2314yes—
373#379C2314yes—
374C4×C22⋊C4C2314yes—
375C4×C22⋊C4C2314yes—
376C4×C22⋊C4C2312yes—
377C4×C22⋊C4C2318yes—
378C4×C22⋊C4C2318yes—
379C4×C22⋊C4C2318yes—
380C2×#95C2314yes—
381C25C2412yes—
382C25C2411yescharacteristic
383C25C2411yescharacteristic
384C25C2412yes—
385C25C2411yescharacteristic
386H(5,𝔽2)—464no—
387C2×#41—44no—
388C2×#41—48no—
389C2×#41—48no—
390C2×#41—48no—
391C2×#41—48no—
392C22×Q8C2412yes—
393C22×Q8C2412yes—
394C22×Q8C2412yes—
395C22×D4—24no—
396C22×D4—24no—
397C22×D4—28no—
398C22×D4—216no—
399C22×D4—28no—
400C22×D4—44no—
401C22×D4—42no—
402C22×D4—48no—
403C22×D4—48no—
404C22×D4—48no—
405C22×D4—44no—
406C22×D4—44no—
407C22×D4—44no—
408C22×D4—44no—
409C22×D4C2414yes—
410C22×D4C2414yes—
411C22×D4C2414yes—
412C22×D4C2414yes—
413C22×D4C2414yes—
414C22×D4C2412yes—
415C22×D4C2418yes—
416C22×D4C2414yes—
417C23×C4—44no—
418C23×C4—42no—
419C23×C4—44no—
420C23×C4—48no—
421C23×C4C2411yescharacteristic
422C23×C4C2418yes—
423C23×C4C2412yes—
424C23×C4C2412yes—
425C23×C4C2411yescharacteristic
426C23×C4C2412yes—
427C23×C4C2418yes—
428C23×C4C2412yes—
429C23×C4C2411yescharacteristic
430C23×C4C2411yescharacteristic
431C23×C4C2414yes—
432C23×C4C2414yes—
433C23×C4C2412yes—
434C23×C4C2412yes—
435C23×C4C2414yes—
436C23×C4C2412yes—
437C23×C4C2412yes—
438#126—416no—
439#124—48no—
440#123—416no—
441#123—48no—
442#123—416no—
443#123—416no—
444#123—48no—
445#123—48no—
446#123—416no—
447#123—48no—
448#123—48no—
449#123—48no—
450#123—48no—
451#123—416no—
452#123—48no—
453C22⋊Q8—48no—
454C22⋊Q8—48no—
455C22⋊Q8—44no—
456C22⋊Q8—44no—
457C22⋊Q8—416no—
458C22⋊Q8—48no—
459#121—416no—
460#121—416no—
461#120—216no—
462#120—48no—
463#120—48no—
464C4×D4—48no—
465C4×D4—48no—
466C4×D4—416no—
467#117—44no—
468#117—416no—
469#117—44no—
470#117—416no—
471C2×C4⋊C4—42no—
472C2×C4⋊C4—416no—
473C2×C4⋊C4—44no—
474C2×C4⋊C4—44no—
475C2×C4⋊C4C2418yes—
476C2×C4⋊C4C2414yes—
477C2×C4⋊C4C2418yes—
478C2×C4⋊C4C2418yes—
479C2×C4⋊C4C2418yes—
480C2×C4⋊C4C2418yes—
481C2×C4⋊C4C2418yes—
482C2×C4⋊C4C2418yes—
483C2×C4⋊C4C2412yes—
484C2×C4⋊C4C2412yes—
485C2×C4⋊C4C2418yes—
486C2×C4⋊C4C2418yes—
487C2×C4⋊C4C2414yes—
488C2×C4⋊C4C2418yes—
489C2×C4⋊C4C2418yes—
490C2×C4⋊C4C2418yes—
491C2×C4⋊C4C2412yes—
492C2×C4⋊C4C2414yes—
493C2×C4⋊C4C2414yes—
494C2×C4⋊C4C2412yes—
495C2×C4⋊C4C2418yes—
496C2×C4⋊C4C2414yes—
497C2×C4⋊C4C2418yes—
498C2×C4⋊C4C2418yes—
499C2×C22⋊C4—28no—
500C2×C22⋊C4—24no—
501C2×C22⋊C4—28no—
502C2×C22⋊C4—232no—
503C2×C22⋊C4—48no—
504C2×C22⋊C4—44no—
505C2×C22⋊C4—44no—
506C2×C22⋊C4—42no—
507C2×C22⋊C4—48no—
508C2×C22⋊C4—44no—
509C2×C22⋊C4C2414yes—
510C2×C22⋊C4C2418yes—
511C2×C22⋊C4C2418yes—
512C2×C22⋊C4C2414yes—
513C2×C22⋊C4C2414yes—
514C2×C22⋊C4C2414yes—
515C2×C22⋊C4C2414yes—
516C2×C22⋊C4C2414yes—
517C2×C22⋊C4C2418yes—
518C2×C22⋊C4C2418yes—
519C2×C22⋊C4C2418yes—
520C2×C22⋊C4C2418yes—
521C2×C22⋊C4C2414yes—
522C2×C22⋊C4C2414yes—
523C2×C22⋊C4C2414yes—
524C2×C22⋊C4C2418yes—
525C2×C22⋊C4C2414yes—
526C2×C22⋊C4C2418yes—
527C2×C22⋊C4C2414yes—
528C2×C22⋊C4C2418yes—
529C2×C22⋊C4C2414yes—
530C2×C22⋊C4C2418yes—
531C2×C22⋊C4C2418yes—
532C2×C22⋊C4C2418yes—
533C2×C22⋊C4C2414yes—
534C2×C22⋊C4C2418yes—
535C2×C22⋊C4C2414yes—
536C2×C22⋊C4C2414yes—
537C2×C22⋊C4C2418yes—
538C2×C22⋊C4C2414yes—
539C2×C22⋊C4C2414yes—
540C2×C22⋊C4C2414yes—
541C2×C22⋊C4C2418yes—
542C2×C22⋊C4C2418yes—
543C2×C22⋊C4C2414yes—
544C2×C42C2414yes—
545C2×C42C2414yes—
546C2×C42C2414yes—
547C2×C42C2418yes—
548C2×C42C2418yes—
549#95C2418yes—
550#95C2418yes—
551#95C2418yes—
552#95C2418yes—
553#95C2418yes—
554#95C2418yes—
555#95C2418yes—
556#95C2418yes—
557#95C2418yes—
558#95C2414yes—
559#95C2418yes—
560#95C2418yes—
561#95C2414yes—
562#95C2418yes—
563#95C2418yes—
564#95C2418yes—
565#95C2418yes—
566#95C2414yes—
567#95C2418yes—
568#95C2418yes—
569#95C2418yes—
570#95C2418yes—
571#95C2418yes—
572#95C2414yes—
573C24—24no—
574C24—28no—
575C24—24no—
576C24—22no—
577C24—22no—
578C24—44no—
579C24—42no—
580C24—42no—
581C24—42no—
582C24—42no—
583C24—42no—
584C24—42no—
585C24—44no—
586C24—44no—
587C24—42no—
588C24—42no—
589C24—44no—
590C24—42no—
591C24—42no—
592C24H(5,𝔽2)14yes—
593C24H(5,𝔽2)18yes—
594C24C2512yes—
595C24C2511yescharacteristic
596C24C2514yes—
597C24C2512yes—
598C24C2512yes—
599#41—432no—
600#41—464no—
601C2×Q8—42no—
602C2×Q8—44no—
603C2×Q8—42no—
604C2×Q8—42no—
605C2×Q8—44no—
606C2×Q8—44no—
607C2×D4—28no—
608C2×D4—28no—
609C2×D4—28no—
610C2×D4—28no—
611C2×D4—28no—
612C2×D4—28no—
613C2×D4—28no—
614C2×D4—28no—
615C2×D4—28no—
616C2×D4—28no—
617C2×D4—216no—
618C2×D4—28no—
619C2×D4—28no—
620C2×D4—42no—
621C2×D4—44no—
622C2×D4—44no—
623C2×D4—44no—
624C2×D4—44no—
625C2×D4—44no—
626C2×D4—416no—
627C2×D4—48no—
628C2×D4—44no—
629C2×D4—44no—
630C2×D4—48no—
631C2×D4—432no—
632C2×D4—464no—
633C2×D4—416no—
634C2×D4—432no—
635C2×D4—88no—
636C22×C4—22no—
637C22×C4—24no—
638C22×C4—216no—
639C22×C4—22no—
640C22×C4—24no—
641C22×C4—28no—
642C22×C4—24no—
643C22×C4—24no—
644C22×C4—24no—
645C22×C4—22no—
646C22×C4—24no—
647C22×C4—216no—
648C22×C4—24no—
649C22×C4—22no—
650C22×C4—28no—
651C22×C4—48no—
652C22×C4—48no—
653C22×C4—44no—
654C22×C4—44no—
655C22×C4—44no—
656C22×C4—42no—
657C22×C4—42no—
658C22×C4—42no—
659C22×C4—44no—
660C22×C4—48no—
661C22×C4—44no—
662C22×C4—48no—
663C22×C4—44no—
664C22×C4—42no—
665C22×C4—44no—
666C22×C4—44no—
667C22×C4—42no—
668C22×C4—44no—
669C22×C4—42no—
670C22×C4—42no—
671C22×C4—44no—
672C22×C4—44no—
673C22×C4—44no—
674C22×C4—44no—
675C22×C4—44no—
676C22×C4—88no—
677C22×C4—816no—
678C22×C4C2514yes—
679C22×C4C2512yes—
680C22×C4C2518yes—
681C22×C4C2514yes—
682C22×C4C2512yes—
683C22×C4C2518yes—
684C22×C4C2518yes—
685C22×C4C2514yes—
686C22×C4C2514yes—
687C22×C4C2512yes—
688C22×C4C2514yes—
689C22×C4C2512yes—
690C4⋊C4—216no—
691C4⋊C4—44no—
692C4⋊C4—48no—
693C4⋊C4—48no—
694C4⋊C4—48no—
695C4⋊C4—48no—
696C4⋊C4—48no—
697C4⋊C4—48no—
698C4⋊C4—48no—
699C4⋊C4—48no—
700C4⋊C4—44no—
701C4⋊C4—48no—
702C4⋊C4—42no—
703C4⋊C4—42no—
704C4⋊C4—48no—
705C4⋊C4—48no—
706C4⋊C4—48no—
707C4⋊C4—48no—
708C4⋊C4—44no—
709C4⋊C4—42no—
710C4⋊C4—44no—
711C4⋊C4—44no—
712C4⋊C4—42no—
713C4⋊C4—48no—
714C22⋊C4—28no—
715C22⋊C4—216no—
716C22⋊C4—28no—
717C22⋊C4—28no—
718C22⋊C4—28no—
719C22⋊C4—28no—
720C22⋊C4—216no—
721C22⋊C4—216no—
722C22⋊C4—216no—
723C22⋊C4—28no—
724C22⋊C4—216no—
725C22⋊C4—216no—
726C22⋊C4—48no—
727C22⋊C4—44no—
728C22⋊C4—44no—
729C22⋊C4—44no—
730C22⋊C4—44no—
731C22⋊C4—48no—
732C22⋊C4—48no—
733C22⋊C4—44no—
734C22⋊C4—44no—
735C22⋊C4—44no—
736C22⋊C4—48no—
737C22⋊C4—44no—
738C22⋊C4—48no—
739C22⋊C4—44no—
740C22⋊C4—44no—
741C22⋊C4—48no—
742C22⋊C4—48no—
743C22⋊C4—44no—
744C22⋊C4—48no—
745C22⋊C4—48no—
746C22⋊C4—48no—
747C22⋊C4—44no—
748C22⋊C4—44no—
749C42—28no—
750C42—48no—
751C42—44no—
752C42—44no—
753C42—48no—
754C23—216no—
755C23—28no—
756C23—24no—
757C23—24no—
758C23—24no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—28no—
763C23—24no—
764C23—22no—
765C23—24no—
766C23—24no—
767C23—24no—
768C23—22no—
769C23—28no—
770C23—24no—
771C23—22no—
772C23—24no—
773C23—24no—
774C23—44no—
775C23—48no—
776C23—44no—
777C23—44no—
778C23—416no—
779C23—44no—
780C23—82no—
781C23—84no—
782C23—84no—
783C23—82no—
784C23—816no—
785C23—88no—
786C23—82no—
787C23—82no—
788C23—162no—
789C23—162no—
790C23—164no—
791C23—164no—
792C23—164no—
793C23C2×H(5,𝔽2)14yes—
794C23C2×H(5,𝔽2)12yes—
795C23C2×H(5,𝔽2)14yes—
796C23C2×H(5,𝔽2)18yes—
797C23C2611yescharacteristic
798Q8—48no—
799Q8—162no—
800Q8—162no—
801D4—416no—
802D4—48no—
803D4—416no—
804D4—416no—
805D4—416no—
806D4—416no—
807D4—816no—
808D4—88no—
809C2×C4—28no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—28no—
813C2×C4—24no—
814C2×C4—28no—
815C2×C4—24no—
816C2×C4—28no—
817C2×C4—24no—
818C2×C4—28no—
819C2×C4—24no—
820C2×C4—22no—
821C2×C4—28no—
822C2×C4—24no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—24no—
826C2×C4—24no—
827C2×C4—24no—
828C2×C4—24no—
829C2×C4—28no—
830C2×C4—28no—
831C2×C4—28no—
832C2×C4—28no—
833C2×C4—24no—
834C2×C4—28no—
835C2×C4—28no—
836C2×C4—28no—
837C2×C4—28no—
838C2×C4—432no—
839C2×C4—416no—
840C2×C4—48no—
841C2×C4—44no—
842C2×C4—48no—
843C2×C4—88no—
844C2×C4—84no—
845C2×C4—84no—
846C2×C4—84no—
847C2×C4—816no—
848C2×C4—84no—
849C2×C4—82no—
850C2×C4—82no—
851C2×C4—162no—
852C2×C4—162no—
853C2×C4—164no—
854C2×C4#58514yes—
855C22—24no—
856C22—28no—
857C22—22no—
858C22—24no—
859C22—22no—
860C22—24no—
861C22—24no—
862C22—22no—
863C22—216no—
864C22—28no—
865C22—42no—
866C22—44no—
867C22—44no—
868C22—42no—
869C22—44no—
870C22—48no—
871C22—48no—
872C22—44no—
873C22—42no—
874C22—42no—
875C22—42no—
876C22—48no—
877C22—816no—
878C22—88no—
879C22—168no—
880C22—164no—
881C22—164no—
882C22C22×H(5,𝔽2)11yescharacteristic
883C22C22×H(5,𝔽2)12yes—
884C22C2×#58512yes—
885C222−1+612yes—
886C4—24no—
887C4—42no—
888C4—44no—
889C4—44no—
890C4—44no—
891C4—42no—
892C4—42no—
893C4—44no—
894C4—44no—
895C4—48no—
896C4—48no—
897C4—48no—
898C2—44no—
899C2—48no—
900C2—44no—
901C2—42no—
902C2—82no—
903C2#6281711yescharacteristic
904C2#6282011yescharacteristic
905C2#6287111yescharacteristic
906C2#6290114yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35347C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #57721C2semidirect
2. #57595C2semidirect
3. #48773C2semidirect
4. #47898C2semidirect
5. #47802C2semidirect
6. #47142C2semidirect
7. #46999C2semidirect
8. #46997C2semidirect
9. #46388C2semidirect
10. #38912C2semidirect
11. #37932C2semidirect
12. #36720C2semidirect
13. #36718C2semidirect
14. #35540C2semidirect
15. #35446C2semidirect
16. #35354C2semidirect
19. C2×#551C22semidirect
20. C2×#543C22semidirect
23. C22×#123C22semidirect
25. C2×#518C22semidirect
26. #2848C22semidirect
27. #2848C22semidirect
28. #2844C22semidirect
29. #2842C22semidirect
30. #2841C22semidirect
31. #2838C22semidirect
32. #2792C22semidirect
33. #2792C22semidirect
34. #2771C22semidirect
35. #2765C22semidirect
36. #2765C22semidirect
37. #2765C22semidirect
38. #2763C22semidirect
39. #2761C22semidirect
40. #2760C22semidirect
41. #2751C22semidirect
42. #2750C22semidirect
43. #2746C22semidirect
44. #2743C22semidirect
45. #2743C22semidirect
46. #2743C22semidirect
47. #2724C22semidirect
48. #2718C22semidirect
49. #2717C22semidirect
50. #2708C22semidirect
51. #2706C22semidirect
52. #2706C22semidirect
53. #2697C22semidirect
54. #2695C22semidirect
55. #2695C22semidirect
56. #2687C22semidirect
57. #2687C22semidirect
58. #2681C22semidirect
59. #2680C22semidirect
60. #2680C22semidirect
61. #2680C22semidirect
62. #2672C22semidirect
63. #2672C22semidirect
64. #2646C22semidirect
65. #2627C22semidirect
66. #2626C22semidirect
67. #2626C22semidirect
68. #2623C22semidirect
69. #2622C22semidirect
70. #2609C22semidirect
71. #2609C22semidirect
72. #2583C22semidirect
73. #2583C22semidirect
74. #2579C22semidirect
75. #2576C22semidirect
76. #2561C22semidirect
77. #2553C22semidirect
78. #2553C22semidirect
79. #2534C22semidirect
80. #2505C22semidirect
81. #2502C22semidirect
82. #2487C22semidirect
83. #2483C22semidirect
84. #2483C22semidirect
85. #2483C22semidirect
86. #2482C22semidirect
87. #2480C22semidirect
88. #2477C22semidirect
89. #2476C22semidirect
90. #2471C22semidirect
91. #2470C22semidirect
92. #2470C22semidirect
93. #2470C22semidirect
94. #2470C22semidirect
95. #2457C22semidirect
96. #2455C22semidirect
97. #2455C22semidirect
98. #2435C22semidirect
100. #2422C22semidirect
101. #2422C22semidirect
102. #2420C22semidirect
103. #2418C22semidirect
104. #2411C22semidirect
108. #2406C22semidirect
109. #2406C22semidirect
110. #2406C22semidirect
117. #2405C22semidirect
118. #2405C22semidirect
119. #2405C22semidirect
122. #2375C22semidirect
123. #2342C22semidirect
124. #2329C22semidirect
125. #2322C22semidirect
126. #2317C22semidirect
127. #2317C22semidirect
128. #2315C22semidirect
129. #2312C22semidirect
130. #2312C22semidirect
131. #2312C22semidirect
132. #2309C22semidirect
135. #2308C22semidirect
136. C4×#120C22semidirect
138. #2280C22semidirect

Maximal subgroups

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

subgroupindex
#577212
#575952
#487732
#478982
#478022
#471422
#469992
#469972
#463882
#389122
#379322
#367202
#367182
#355402
#354462
#353542
#353472