Finite Group Databasebeta

← #8933820

Subgroups — #8933820

Order 512.

5830 conjugacy classes of subgroups.

The subgroup lattice has 859 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59799C214yesmaximal, complemented
2#59074C218yesmaximal, complemented
3#52071C214yesmaximal, complemented
4#51986C218yesmaximal, complemented
5#49489C218yesmaximal, complemented
6#48583C218yesmaximal, complemented
7#48149C218yesmaximal, complemented
8#46998C211yesmaximal, characteristic, complemented
9#46390C212yesmaximal, complemented
10#46385C212yesmaximal, complemented
11#46384C211yesmaximal, characteristic, complemented
12#35616C211yesmaximal, characteristic, complemented
13#35512C212yesmaximal, complemented
14#35451C212yesmaximal, complemented
15#35355C212yesmaximal, complemented
16#35351C212yesmaximal, complemented
17C22×H(5,𝔽2)C2211yescharacteristic
18C2×#554C2214yescomplemented
19C2×#536C2212yescomplemented
20C22×#124C2211yescharacteristic
21C2×#525C2214yescomplemented
22C22×#121C2212yes—
23C2×#518C2212yescomplemented
24#2842C2211yescharacteristic, complemented
25#2840C2211yescharacteristic, complemented
26#2808C2218yescomplemented
27#2799C2214yescomplemented
28#2797C2218yescomplemented
29#2797C2218yescomplemented
30#2751C2218yescomplemented
31#2749C2218yescomplemented
32#2747C2218yescomplemented
33#2740C2218yescomplemented
34#2737C2218yescomplemented
35#2736C2214yescomplemented
36#2735C2218yescomplemented
37#2735C2218yescomplemented
38#2730C2218yescomplemented
39#2729C2218yescomplemented
40#2728C2214yescomplemented
41#2711C2218yescomplemented
42#2696C2218yescomplemented
43#2694C2218yescomplemented
44#2692C2218yescomplemented
45#2690C2218yescomplemented
46#2684C2218yescomplemented
47#2684C2218yescomplemented
48#2676C2218yescomplemented
49#2668C2218yescomplemented
50#2668C2214yescomplemented
51#2651C2218yescomplemented
52#2648C2218yescomplemented
53#2632C2214yescomplemented
54#2631C2214yescomplemented
55#2599C2214yescomplemented
56#2598C2214yescomplemented
57#2593C2214yescomplemented
58#2591C2218yescomplemented
59#2579C2214yescomplemented
60#2578C2218yescomplemented
61#2577C2218yescomplemented
62#2558C2218yescomplemented
63#2557C2218yescomplemented
64#2555C2214yescomplemented
65#2543C2218yescomplemented
66#2534C2214yescomplemented
67#2516C2218yescomplemented
68#2484C2214yescomplemented
69#2483C2211yescharacteristic, complemented
70#2483C2212yescomplemented
71#2482C2214yescomplemented
72#2477C2218yescomplemented
73#2476C2218yescomplemented
74#2475C2218yescomplemented
75#2474C2218yescomplemented
76#2472C2218yescomplemented
77#2472C2218yescomplemented
78#2464C2218yescomplemented
79#2463C2218yescomplemented
80#2461C2218yescomplemented
81#2460C2218yescomplemented
82#2459C2218yescomplemented
83#2458C2218yescomplemented
84#2456C2218yescomplemented
85#2450C2218yescomplemented
86#2449C2218yescomplemented
87#2444C2218yescomplemented
88#2444C2218yescomplemented
89#2443C2218yescomplemented
90#2443C2218yescomplemented
91#2435C2218yescomplemented
92#2432C2218yescomplemented
93#2424C2218yescomplemented
94#2424C2218yescomplemented
95#2409C2214yescomplemented
96#2408C2218yes—
97#2408C2214yescomplemented
98#2408C2218yescomplemented
99#2407C2218yes—
100#2407C2218yescomplemented
101#2405C2212yes—
102#2405C2212yes—
103#2405C2212yes—
104#2405C2212yes—
105#2405C2212yescomplemented
106#2405C2214yescomplemented
107#2405C2214yescomplemented
108#2403C2212yes—
109#2403C2212yes—
110#2403C2214yescomplemented
111#2403C2211yescharacteristic, complemented
112#2381C2214yescomplemented
113#2375C2218yescomplemented
114#2368C2218yescomplemented
115#2367C2218yescomplemented
116#2364C2218yescomplemented
117#2361C2218yescomplemented
118#2321C2214yescomplemented
119#2321C2214yescomplemented
120#2312C2212yescomplemented
121#2312C2212yescomplemented
122#2311C2214yescomplemented
123#2309C2211yescharacteristic
124#2309C2212yes—
125#2308C2214yescomplemented
126#2308C2212yescomplemented
127C4×#123C2214yescomplemented
128C4×#120C2214yescomplemented
129#2297C2212yescomplemented
130C2×#385C2214yescomplemented
131C2×H(5,𝔽2)—44no—
132C2×H(5,𝔽2)—48no—
133C22×#41C2314yes—
134C22×#41C2312yes—
135C23×Q8C2311yescharacteristic
136C23×D4C2312yes—
137C23×D4C2311yescharacteristic
138C23×D4C2312yes—
139C23×D4C2312yes—
140C23×D4C2314yes—
141C23×D4C2312yes—
142C24×C4C2312yes—
143#554—416no—
144#536—48no—
145C2×C4⋊Q8C2314yes—
146C2×#125C2318yes—
147C2×#124—44no—
148C2×#124C2318yes—
149C2×#124C2314yes—
150C2×#124C2318yes—
151#525—416no—
152C2×#123C2314yes—
153C2×#123C2314yes—
154C2×#123C2314yes—
155C2×#123C2314yes—
156C2×#123C2314yes—
157C2×C22⋊Q8C2318yes—
158C2×C22⋊Q8C2318yes—
159C2×C22⋊Q8C2318yes—
160C2×C22⋊Q8C2318yes—
161C2×#121—48no—
162C2×#121C2318yes—
163C2×#121C2318yes—
164C2×#121C2318yes—
165C2×#121C2318yes—
166C2×#121C2318yes—
167C2×#120C2314yes—
168C2×#120C2314yes—
169C2×#120C2318yes—
170C2×#120C2314yes—
171C2×#120C2314yes—
172C2×#120C2314yes—
173#518—48no—
174C2×C4×Q8C2314yes—
175C2×C4×D4C2314yes—
176C2×C4×D4C2314yes—
177C2×C4×D4C2314yes—
178C2×C4×D4C2314yes—
179C2×C4×D4C2318yes—
180C2×C4×D4C2318yes—
181C2×C4×D4C2318yes—
182C2×C4×D4C2314yes—
183C2×#117C2314yes—
184C2×#117C2312yes—
185C2×#117C2314yes—
186C22×C4⋊C4C2312yes—
187C22×C4⋊C4C2318yes—
188C22×C22⋊C4C2312yes—
189C22×C22⋊C4C2312yes—
190C22×C22⋊C4C2314yes—
191C22×C22⋊C4C2314yes—
192C22×C22⋊C4C2312yes—
193C22×C22⋊C4C2312yes—
194C22×C42C2311yescharacteristic
195#400C2318yes—
196#400C2318yes—
197#400C2318yes—
198#400C2314yes—
199#399C2314yes—
200#399C2318yes—
201#399C2318yes—
202#398C2318yes—
203#398C2314yes—
204#398C2318yes—
205#398C2318yes—
206#397C2318yes—
207#397C2318yes—
208#397C2318yes—
209#397C2318yes—
210#397C2314yes—
211#397C2318yes—
212#397C2318yes—
213#397C2318yes—
214#397C2318yes—
215#397C2318yes—
216#396C2318yes—
217#396C2318yes—
218#396C2318yes—
219#396C2318yes—
220#395C2314yes—
221#395C2318yes—
222#394C2318yes—
223#394C2318yes—
224#394C2318yes—
225#394C2318yes—
226#394C2314yes—
227#394C2318yes—
228#394C2318yes—
229#394C2318yes—
230#394C2318yes—
231#394C2318yes—
232#394C2318yes—
233#394C2318yes—
234#394C2318yes—
235#394C2318yes—
236#393C2314yes—
237#393C2318yes—
238#393C2318yes—
239#393C2318yes—
240#393C2318yes—
241#392C2314yes—
242#392C2318yes—
243#392C2318yes—
244#392C2318yes—
245#392C2318yes—
246#392C2318yes—
247#391C2318yes—
248#391C2318yes—
249#391C2314yes—
250#391C2318yes—
251#390C2318yes—
252#390C2318yes—
253#390C2318yes—
254#390C2318yes—
255#390C2318yes—
256#390C2318yes—
257#390C2314yes—
258#390C2318yes—
259#389C2318yes—
260#388C2318yes—
261#388C2318yes—
262#388C2318yes—
263#388C2318yes—
264#388C2318yes—
265#388C2318yes—
266#388C2318yes—
267#388C2318yes—
268#388C2318yes—
269#388C2318yes—
270#388C2318yes—
271#388C2318yes—
272#388C2318yes—
273#388C2318yes—
274#388C2318yes—
275#388C2318yes—
276#388C2318yes—
277#388C2318yes—
278#388C2318yes—
279#388C2318yes—
280#388C2318yes—
281#387C2318yes—
282#387C2318yes—
283#387C2318yes—
284#387C2318yes—
285#387C2318yes—
286#387C2318yes—
287#387C2318yes—
288#387C2318yes—
289#387C2318yes—
290#387C2318yes—
291#387C2318yes—
292#386C2318yes—
293#386C2318yes—
294#386C2318yes—
295#386C2318yes—
296#386C2318yes—
297#386C2318yes—
298#386C2314yes—
299#386C2314yes—
300#386C2314yes—
301#386C2314yes—
302#386C2314yes—
303#386C2318yes—
304#386C2314yes—
305#386C2318yes—
306#386C2318yes—
307#386C2314yes—
308#386C2318yes—
309#386C2318yes—
310#386C2318yes—
311#386C2314yes—
312#386C2318yes—
313#386C2318yes—
314#386C2314yes—
315#386C2314yes—
316#385C2314yes—
317#385C2314yes—
318#385C2318yes—
319#385C2318yes—
320#385C2314yes—
321#385C2318yes—
322#385C2314yes—
323#385C2318yes—
324#385C2318yes—
325#385C2314yes—
326#385C2314yes—
327#385C2318yes—
328#385C2314yes—
329#385C2318yes—
330#385C2314yes—
331#383C2314yes—
332#383C2314yes—
333#381C2314yes—
334#381C2314yes—
335#381C2314yes—
336#381C2314yes—
337#380C2318yes—
338#380C2318yes—
339#380C2314yes—
340#380C2314yes—
341#379C2311yescharacteristic
342#379C2312yes—
343#379C2314yes—
344#379C2314yes—
345#379C2312yes—
346#379C2311yescharacteristic
347#379C2314yes—
348#379C2312yes—
349#379C2314yes—
350#379C2314yes—
351#379C2318yes—
352#379C2318yes—
353#379C2314yes—
354C4×C4⋊C4C2318yes—
355C4×C4⋊C4C2318yes—
356C4×C22⋊C4C2314yes—
357C4×C22⋊C4C2314yes—
358C4×C22⋊C4C2318yes—
359C4×C22⋊C4C2318yes—
360C4×C22⋊C4C2318yes—
361C4×C22⋊C4C2318yes—
362C2×#95C2318yes—
363C25C2412yes—
364C25C2411yescharacteristic
365C25C2412yes—
366C25C2412yes—
367C25C2411yescharacteristic
368H(5,𝔽2)—464no—
369C2×#41—216no—
370C2×#41—28no—
371C2×#41—48no—
372C2×#41—44no—
373C2×#41—44no—
374C2×#41—48no—
375C22×Q8—42no—
376C22×Q8—44no—
377C22×Q8C2414yes—
378C22×Q8C2414yes—
379C22×Q8C2412yes—
380C22×D4—28no—
381C22×D4—28no—
382C22×D4—24no—
383C22×D4—48no—
384C22×D4—44no—
385C22×D4—48no—
386C22×D4—48no—
387C22×D4—48no—
388C22×D4—44no—
389C22×D4—48no—
390C22×D4—44no—
391C22×D4—48no—
392C22×D4—48no—
393C22×D4C2414yes—
394C22×D4C2414yes—
395C22×D4C2414yes—
396C22×D4C2414yes—
397C22×D4C2414yes—
398C22×D4C2414yes—
399C22×D4C2418yes—
400C22×D4C2418yes—
401C22×D4C2418yes—
402C22×D4C2414yes—
403C22×D4C2412yes—
404C23×C4—48no—
405C23×C4—44no—
406C23×C4C2412yes—
407C23×C4C2411yescharacteristic
408C23×C4C2412yes—
409C23×C4C2414yes—
410C23×C4C2412yes—
411C23×C4C2412yes—
412C23×C4C2412yes—
413C23×C4C2412yes—
414C23×C4C2412yes—
415C23×C4C2418yes—
416C23×C4C2414yes—
417C23×C4C2418yes—
418C23×C4C2414yes—
419C4⋊Q8—216no—
420#125—416no—
421#124—48no—
422#124—416no—
423#124—416no—
424#123—48no—
425#123—48no—
426#123—48no—
427#123—48no—
428#123—48no—
429C22⋊Q8—232no—
430C22⋊Q8—416no—
431C22⋊Q8—416no—
432C22⋊Q8—416no—
433#121—416no—
434#121—416no—
435#121—416no—
436#121—416no—
437#121—416no—
438#120—48no—
439#120—48no—
440#120—48no—
441#120—48no—
442#120—48no—
443#120—416no—
444C4×Q8—48no—
445C4×D4—48no—
446C4×D4—416no—
447C4×D4—416no—
448C4×D4—416no—
449C4×D4—48no—
450C4×D4—48no—
451C4×D4—48no—
452C4×D4—48no—
453#117—44no—
454#117—48no—
455#117—48no—
456C2×C4⋊C4—416no—
457C2×C4⋊C4—44no—
458C2×C4⋊C4C2418yes—
459C2×C4⋊C4C2418yes—
460C2×C4⋊C4C2418yes—
461C2×C4⋊C4C2418yes—
462C2×C4⋊C4C2418yes—
463C2×C4⋊C4C2414yes—
464C2×C4⋊C4C2418yes—
465C2×C4⋊C4C2418yes—
466C2×C4⋊C4C2414yes—
467C2×C4⋊C4C2414yes—
468C2×C4⋊C4C2414yes—
469C2×C4⋊C4C2414yes—
470C2×C4⋊C4C2418yes—
471C2×C4⋊C4C2418yes—
472C2×C4⋊C4C2418yes—
473C2×C4⋊C4C2418yes—
474C2×C22⋊C4—28no—
475C2×C22⋊C4—28no—
476C2×C22⋊C4—48no—
477C2×C22⋊C4—48no—
478C2×C22⋊C4—44no—
479C2×C22⋊C4—44no—
480C2×C22⋊C4C2414yes—
481C2×C22⋊C4C2414yes—
482C2×C22⋊C4C2414yes—
483C2×C22⋊C4C2414yes—
484C2×C22⋊C4C2418yes—
485C2×C22⋊C4C2418yes—
486C2×C22⋊C4C2418yes—
487C2×C22⋊C4C2418yes—
488C2×C22⋊C4C2414yes—
489C2×C22⋊C4C2414yes—
490C2×C22⋊C4C2418yes—
491C2×C22⋊C4C2418yes—
492C2×C22⋊C4C2414yes—
493C2×C22⋊C4C2414yes—
494C2×C22⋊C4C2414yes—
495C2×C22⋊C4C2414yes—
496C2×C22⋊C4C2412yes—
497C2×C22⋊C4C2412yes—
498C2×C22⋊C4C2418yes—
499C2×C22⋊C4C2418yes—
500C2×C22⋊C4C2418yes—
501C2×C22⋊C4C2414yes—
502C2×C22⋊C4C2414yes—
503C2×C22⋊C4C2414yes—
504C2×C22⋊C4C2418yes—
505C2×C22⋊C4C2418yes—
506C2×C22⋊C4C2418yes—
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⋊C4C2418yes—
516C2×C22⋊C4C2418yes—
517C2×C42—42no—
518C2×C42C2414yes—
519C2×C42C2414yes—
520C2×C42C2418yes—
521C2×C42C2414yes—
522C2×C42C2418yes—
523C2×C42C2414yes—
524C2×C42C2418yes—
525#95C2418yes—
526#95C2418yes—
527#95C2418yes—
528#95C2418yes—
529#95C2418yes—
530#95C2418yes—
531#95C2418yes—
532#95C2418yes—
533#95C2418yes—
534#95C2418yes—
535#95C2418yes—
536#95C2418yes—
537#95C2418yes—
538#95C2418yes—
539#95C2414yes—
540#95C2418yes—
541#95C2418yes—
542#95C2418yes—
543#95C2414yes—
544#95C2414yes—
545#95C2414yes—
546#95C2418yes—
547C24—24no—
548C24—28no—
549C24—22no—
550C24—24no—
551C24—42no—
552C24—42no—
553C24—44no—
554C24—44no—
555C24—42no—
556C24—44no—
557C24—44no—
558C24—44no—
559C24—44no—
560C24—44no—
561C24—44no—
562C24—48no—
563C24H(5,𝔽2)14yes—
564C24C2514yes—
565C24C2512yes—
566C24C2512yes—
567C24C2511yescharacteristic
568C24C2514yes—
569#41—464no—
570#41—432no—
571C2×Q8—28no—
572C2×Q8—42no—
573C2×Q8—42no—
574C2×Q8—44no—
575C2×Q8—44no—
576C2×Q8—44no—
577C2×Q8—48no—
578C2×Q8—88no—
579C2×Q8H(5,𝔽2)18yes—
580C2×D4—28no—
581C2×D4—28no—
582C2×D4—28no—
583C2×D4—28no—
584C2×D4—28no—
585C2×D4—28no—
586C2×D4—216no—
587C2×D4—28no—
588C2×D4—216no—
589C2×D4—216no—
590C2×D4—216no—
591C2×D4—28no—
592C2×D4—28no—
593C2×D4—28no—
594C2×D4—28no—
595C2×D4—24no—
596C2×D4—44no—
597C2×D4—44no—
598C2×D4—44no—
599C2×D4—44no—
600C2×D4—42no—
601C2×D4—44no—
602C2×D4—42no—
603C2×D4—44no—
604C2×D4—44no—
605C2×D4—44no—
606C2×D4—432no—
607C2×D4—416no—
608C2×D4—48no—
609C2×D4—48no—
610C2×D4—48no—
611C2×D4—48no—
612C2×D4—48no—
613C2×D4—48no—
614C2×D4—432no—
615C2×D4—432no—
616C2×D4—464no—
617C2×D4—816no—
618C22×C4—22no—
619C22×C4—24no—
620C22×C4—28no—
621C22×C4—24no—
622C22×C4—24no—
623C22×C4—24no—
624C22×C4—24no—
625C22×C4—24no—
626C22×C4—24no—
627C22×C4—28no—
628C22×C4—28no—
629C22×C4—28no—
630C22×C4—216no—
631C22×C4—44no—
632C22×C4—44no—
633C22×C4—42no—
634C22×C4—48no—
635C22×C4—48no—
636C22×C4—48no—
637C22×C4—48no—
638C22×C4—48no—
639C22×C4—44no—
640C22×C4—44no—
641C22×C4—44no—
642C22×C4—44no—
643C22×C4—44no—
644C22×C4—44no—
645C22×C4—48no—
646C22×C4—48no—
647C22×C4—816no—
648C22×C4C2514yes—
649C22×C4C2514yes—
650C22×C4C2514yes—
651C22×C4C2514yes—
652C22×C4C2518yes—
653C22×C4C2518yes—
654C22×C4C2514yes—
655C22×C4C2514yes—
656C22×C4C2514yes—
657C22×C4C2512yes—
658C22×C4C2514yes—
659C4⋊C4—216no—
660C4⋊C4—216no—
661C4⋊C4—216no—
662C4⋊C4—216no—
663C4⋊C4—216no—
664C4⋊C4—44no—
665C4⋊C4—48no—
666C4⋊C4—48no—
667C4⋊C4—44no—
668C4⋊C4—44no—
669C4⋊C4—44no—
670C4⋊C4—44no—
671C4⋊C4—48no—
672C4⋊C4—48no—
673C4⋊C4—48no—
674C4⋊C4—48no—
675C22⋊C4—28no—
676C22⋊C4—28no—
677C22⋊C4—28no—
678C22⋊C4—28no—
679C22⋊C4—216no—
680C22⋊C4—216no—
681C22⋊C4—216no—
682C22⋊C4—216no—
683C22⋊C4—44no—
684C22⋊C4—44no—
685C22⋊C4—44no—
686C22⋊C4—44no—
687C22⋊C4—48no—
688C22⋊C4—48no—
689C22⋊C4—44no—
690C22⋊C4—44no—
691C22⋊C4—42no—
692C22⋊C4—42no—
693C22⋊C4—48no—
694C22⋊C4—48no—
695C22⋊C4—48no—
696C22⋊C4—44no—
697C22⋊C4—48no—
698C22⋊C4—48no—
699C22⋊C4—48no—
700C22⋊C4—44no—
701C22⋊C4—48no—
702C22⋊C4—44no—
703C22⋊C4—48no—
704C22⋊C4—48no—
705C22⋊C4—48no—
706C22⋊C4—48no—
707C22⋊C4—48no—
708C22⋊C4—48no—
709C22⋊C4—44no—
710C22⋊C4—48no—
711C22⋊C4—48no—
712C42—28no—
713C42—44no—
714C42—48no—
715C42—44no—
716C42—44no—
717C42—48no—
718C42—48no—
719C23—216no—
720C23—28no—
721C23—22no—
722C23—24no—
723C23—24no—
724C23—24no—
725C23—24no—
726C23—24no—
727C23—28no—
728C23—24no—
729C23—24no—
730C23—22no—
731C23—24no—
732C23—24no—
733C23—24no—
734C23—28no—
735C23—28no—
736C23—28no—
737C23—44no—
738C23—48no—
739C23—44no—
740C23—48no—
741C23—48no—
742C23—84no—
743C23—816no—
744C23—84no—
745C23—84no—
746C23—84no—
747C23—84no—
748C23—164no—
749C23—168no—
750C23—164no—
751C23—168no—
752C23—164no—
753C23C2×H(5,𝔽2)14yes—
754C23C2×H(5,𝔽2)12yes—
755C23#58518yes—
756C23C2611yescharacteristic
757Q8—48no—
758Q8—88no—
759Q8—88no—
760D4—416no—
761D4—416no—
762D4—416no—
763D4—416no—
764D4—48no—
765D4—416no—
766D4—416no—
767D4—416no—
768D4—816no—
769D4—816no—
770D4—816no—
771C2×C4—216no—
772C2×C4—28no—
773C2×C4—24no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—24no—
777C2×C4—24no—
778C2×C4—24no—
779C2×C4—24no—
780C2×C4—28no—
781C2×C4—24no—
782C2×C4—24no—
783C2×C4—24no—
784C2×C4—24no—
785C2×C4—28no—
786C2×C4—28no—
787C2×C4—28no—
788C2×C4—28no—
789C2×C4—28no—
790C2×C4—28no—
791C2×C4—28no—
792C2×C4—28no—
793C2×C4—28no—
794C2×C4—28no—
795C2×C4—24no—
796C2×C4—24no—
797C2×C4—28no—
798C2×C4—48no—
799C2×C4—416no—
800C2×C4—48no—
801C2×C4—816no—
802C2×C4—84no—
803C2×C4—84no—
804C2×C4—84no—
805C2×C4—84no—
806C2×C4—816no—
807C2×C4—164no—
808C2×C4—164no—
809C2×C4C2×H(5,𝔽2)14yes—
810C2×C4C2×H(5,𝔽2)18yes—
811C22—216no—
812C22—22no—
813C22—24no—
814C22—24no—
815C22—24no—
816C22—28no—
817C22—24no—
818C22—48no—
819C22—48no—
820C22—44no—
821C22—44no—
822C22—44no—
823C22—48no—
824C22—48no—
825C22—48no—
826C22—44no—
827C22—42no—
828C22—44no—
829C22—44no—
830C22—44no—
831C22—816no—
832C22—164no—
833C22—168no—
834C22—164no—
835C22—168no—
836C22C22×H(5,𝔽2)12yes—
837C22C22×H(5,𝔽2)11yescharacteristic
838C22C2×#58514yes—
839C4—28no—
840C4—24no—
841C4—44no—
842C4—48no—
843C4—44no—
844C4—48no—
845C4—44no—
846C4—44no—
847C4—44no—
848C4—44no—
849C4—44no—
850C2—48no—
851C2—44no—
852C2—42no—
853C2—82no—
854C2—84no—
855C2#6281711yescharacteristic
856C2#6282012yes—
857C2#6302014yes—
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. #59799C2semidirect
2. #59074C2semidirect
3. #52071C2semidirect
4. #51986C2semidirect
5. #49489C2semidirect
6. #48583C2semidirect
7. #48149C2semidirect
8. #46998C2semidirect
9. #46390C2semidirect
10. #46385C2semidirect
11. #46384C2semidirect
12. #35616C2semidirect
13. #35512C2semidirect
14. #35451C2semidirect
15. #35355C2semidirect
16. #35351C2semidirect
18. C2×#554C22semidirect
19. C2×#536C22semidirect
21. C2×#525C22semidirect
23. C2×#518C22semidirect
24. #2842C22semidirect
25. #2840C22semidirect
26. #2808C22semidirect
27. #2799C22semidirect
28. #2797C22semidirect
29. #2797C22semidirect
30. #2751C22semidirect
31. #2749C22semidirect
32. #2747C22semidirect
33. #2740C22semidirect
34. #2737C22semidirect
35. #2736C22semidirect
36. #2735C22semidirect
37. #2735C22semidirect
38. #2730C22semidirect
39. #2729C22semidirect
40. #2728C22semidirect
41. #2711C22semidirect
42. #2696C22semidirect
43. #2694C22semidirect
44. #2692C22semidirect
45. #2690C22semidirect
46. #2684C22semidirect
47. #2684C22semidirect
48. #2676C22semidirect
49. #2668C22semidirect
50. #2668C22semidirect
51. #2651C22semidirect
52. #2648C22semidirect
53. #2632C22semidirect
54. #2631C22semidirect
55. #2599C22semidirect
56. #2598C22semidirect
57. #2593C22semidirect
58. #2591C22semidirect
59. #2579C22semidirect
60. #2578C22semidirect
61. #2577C22semidirect
62. #2558C22semidirect
63. #2557C22semidirect
64. #2555C22semidirect
65. #2543C22semidirect
66. #2534C22semidirect
67. #2516C22semidirect
68. #2484C22semidirect
69. #2483C22semidirect
70. #2483C22semidirect
71. #2482C22semidirect
72. #2477C22semidirect
73. #2476C22semidirect
74. #2475C22semidirect
75. #2474C22semidirect
76. #2472C22semidirect
77. #2472C22semidirect
78. #2464C22semidirect
79. #2463C22semidirect
80. #2461C22semidirect
81. #2460C22semidirect
82. #2459C22semidirect
83. #2458C22semidirect
84. #2456C22semidirect
85. #2450C22semidirect
86. #2449C22semidirect
87. #2444C22semidirect
88. #2444C22semidirect
89. #2443C22semidirect
90. #2443C22semidirect
91. #2435C22semidirect
92. #2432C22semidirect
93. #2424C22semidirect
94. #2424C22semidirect
95. #2409C22semidirect
97. #2408C22semidirect
98. #2408C22semidirect
100. #2407C22semidirect
105. #2405C22semidirect
106. #2405C22semidirect
107. #2405C22semidirect
110. #2403C22semidirect
111. #2403C22semidirect
112. #2381C22semidirect
113. #2375C22semidirect
114. #2368C22semidirect
115. #2367C22semidirect
116. #2364C22semidirect
117. #2361C22semidirect
118. #2321C22semidirect
119. #2321C22semidirect
120. #2312C22semidirect
121. #2312C22semidirect
122. #2311C22semidirect
125. #2308C22semidirect
126. #2308C22semidirect
127. C4×#123C22semidirect
128. C4×#120C22semidirect
129. #2297C22semidirect
130. C2×#385C22semidirect

Maximal subgroups

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

subgroupindex
#597992
#590742
#520712
#519862
#494892
#485832
#481492
#469982
#463902
#463852
#463842
#356162
#355122
#354512
#353552
#353512