Finite Group Databasebeta

← #8094906

Subgroups — #8094906

Order 512.

6414 conjugacy classes of subgroups.

The subgroup lattice has 1145 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53102C214yesmaximal, complemented
2#53096C214yesmaximal, complemented
3#53063C214yesmaximal, complemented
4#52971C214yesmaximal, complemented
5#52397C218yesmaximal, complemented
6#46334C214yesmaximal, complemented
7#46324C214yesmaximal, complemented
8#45716C214yesmaximal, complemented
9#45655C214yesmaximal, complemented
10#45593C214yesmaximal, complemented
11#45483C214yesmaximal, complemented
12#35554C211yesmaximal, characteristic, complemented
13#35527C211yesmaximal, characteristic, complemented
14#35514C212yesmaximal, complemented
15#35512C212yesmaximal, complemented
16#35262C212yesmaximal, complemented
17#35252C212yesmaximal, complemented
18#35160C212yesmaximal, complemented
19C2×#2541C211yesmaximal, characteristic, complemented
20#34737C212yesmaximal, complemented
21C22×H(5,𝔽2)C2211yescharacteristic
22C2×#560C2214yescomplemented
23C2×#535C2212yes—
24C22×#127C2211yescharacteristic
25C22×#127C2212yescomplemented
26C2×#525C2212yes—
27C2×#525C2212yes—
28C22×#121C2212yes—
29C22×#121C2212yescomplemented
30C2×#518C2211yescharacteristic, complemented
31C22×C4×D4C2211yescharacteristic, complemented
32C22×#117C2212yescomplemented
33#2856C2214yescomplemented
34#2854C2214yescomplemented
35#2854C2214yescomplemented
36#2852C2218yescomplemented
37#2850C2214yescomplemented
38#2829C2218yescomplemented
39#2828C2218yescomplemented
40#2828C2218yescomplemented
41#2826C2218yescomplemented
42#2825C2218yescomplemented
43#2825C2218yescomplemented
44#2818C2218yescomplemented
45#2813C2218yescomplemented
46#2813C2218yescomplemented
47#2812C2218yescomplemented
48#2803C2218yescomplemented
49#2778C2218yescomplemented
50#2778C2218yescomplemented
51#2757C2218yescomplemented
52#2756C2218yescomplemented
53#2748C2214yescomplemented
54#2709C2214yescomplemented
55#2709C2218yescomplemented
56#2705C2218yescomplemented
57#2703C2218yescomplemented
58#2703C2218yescomplemented
59#2697C2214yescomplemented
60#2693C2218yescomplemented
61#2685C2218yescomplemented
62#2678C2218yescomplemented
63#2678C2218yescomplemented
64#2673C2218yescomplemented
65#2673C2218yescomplemented
66#2673C2218yescomplemented
67#2669C2218yescomplemented
68#2669C2214yescomplemented
69#2668C2218yescomplemented
70#2643C2218yescomplemented
71#2624C2214yescomplemented
72#2624C2214yescomplemented
73#2620C2214yescomplemented
74#2619C2214yescomplemented
75#2541C2214yescomplemented
76#2541C2214yescomplemented
77#2541C2214yescomplemented
78#2541C2214yescomplemented
79#2537C2214yescomplemented
80#2537C2214yescomplemented
81#2535C2214yescomplemented
82#2535C2214yescomplemented
83#2514C2214yescomplemented
84#2513C2214yescomplemented
85#2512C2214yescomplemented
86#2511C2214yescomplemented
87#2504C2214yescomplemented
88#2501C2214yescomplemented
89#2500C2214yescomplemented
90#2500C2214yescomplemented
91#2497C2214yescomplemented
92#2496C2214yescomplemented
93#2495C2214yescomplemented
94#2494C2214yescomplemented
95#2482C2218yescomplemented
96#2445C2214yescomplemented
97#2445C2214yescomplemented
98#2445C2214yescomplemented
99#2445C2214yescomplemented
100#2433C2214yescomplemented
101#2433C2214yescomplemented
102#2431C2214yescomplemented
103#2431C2214yescomplemented
104#2428C2214yescomplemented
105#2428C2214yescomplemented
106#2427C2214yescomplemented
107#2427C2214yescomplemented
108#2417C2212yescomplemented
109#2417C2212yescomplemented
110#2416C2214yescomplemented
111#2416C2214yescomplemented
112#2416C2212yescomplemented
113#2416C2212yescomplemented
114#2415C2212yescomplemented
115#2415C2212yescomplemented
116#2414C2214yescomplemented
117#2414C2212yescomplemented
118#2414C2212yescomplemented
119#2414C2214yescomplemented
120#2413C2214yescomplemented
121#2412C2214yescomplemented
122#2412C2218yescomplemented
123#2411C2214yescomplemented
124#2411C2218yescomplemented
125#2410C2218yescomplemented
126#2410C2218yescomplemented
127#2410C2214yescomplemented
128#2408C2214yescomplemented
129#2408C2214yescomplemented
130#2408C2214yescomplemented
131#2408C2214yescomplemented
132#2407C2214yescomplemented
133#2407C2214yescomplemented
134#2407C2214yescomplemented
135#2407C2214yescomplemented
136#2405C2218yes—
137#2405C2214yescomplemented
138#2405C2218yescomplemented
139#2405C2214yescomplemented
140#2403C2214yes—
141#2403C2218yes—
142#2403C2214yes—
143#2392C2214yescomplemented
144#2392C2214yescomplemented
145C2×#392C2214yescomplemented
146#2380C2214yescomplemented
147#2376C2214yescomplemented
148#2375C2214yescomplemented
149#2317C2212yescomplemented
150#2317C2212yescomplemented
151#2311C2212yes—
152#2311C2212yes—
153#2309C2212yes—
154#2309C2211yescharacteristic
155#2309C2211yescharacteristic, complemented
156C4×#121C2214yescomplemented
157C4×#121C2214yescomplemented
158#2297C2212yes—
159#2296C2212yescomplemented
160C2×#390C2212yescomplemented
161#2280C2212yescomplemented
162C2×C4×C4⋊C4C2211yescharacteristic, complemented
163C2×H(5,𝔽2)—48no—
164C2×H(5,𝔽2)—44no—
165C22×#41C2312yes—
166C22×#41C2314yes—
167C23×D4C2311yescharacteristic
168C23×D4C2311yescharacteristic
169C23×D4C2311yescharacteristic
170C23×D4C2314yes—
171C23×D4C2314yes—
172C23×D4C2312yes—
173C23×D4C2314yes—
174C23×D4C2314yes—
175C23×D4C2312yes—
176C24×C4C2312yes—
177#560—416no—
178#535—48no—
179C2×#127—44no—
180C2×#127—48no—
181C2×#127C2314yes—
182C2×#127C2314yes—
183C2×#127C2314yes—
184C2×#127C2318yes—
185C2×#127C2314yes—
186C2×#127C2314yes—
187C2×#126C2318yes—
188C2×#124C2314yes—
189#525—48no—
190#525—48no—
191C2×#123C2318yes—
192C2×#123C2314yes—
193C2×#123C2314yes—
194C2×#123C2314yes—
195C2×#123C2314yes—
196C2×#123C2318yes—
197C2×#123C2318yes—
198C2×C22⋊Q8C2312yes—
199C2×C22⋊Q8C2312yes—
200C2×C22⋊Q8C2312yes—
201C2×C22⋊Q8C2312yes—
202C2×#121—48no—
203C2×#121—48no—
204C2×#121C2314yes—
205C2×#121C2314yes—
206C2×#121C2314yes—
207C2×#121C2312yes—
208C2×#121C2318yes—
209C2×#121C2312yes—
210C2×#121C2314yes—
211C2×#121C2314yes—
212C2×#121C2314yes—
213C2×#121C2314yes—
214C2×#121C2312yes—
215C2×#121C2312yes—
216C2×#121C2314yes—
217C2×#121C2314yes—
218C2×#121C2318yes—
219C2×#121C2314yes—
220C2×#121C2314yes—
221C2×#121C2314yes—
222C2×#121C2318yes—
223C2×#121C2318yes—
224C2×#120C2314yes—
225C2×#120C2314yes—
226C2×#120C2314yes—
227C2×#120C2318yes—
228C2×#120C2318yes—
229C2×#120C2314yes—
230C2×#120C2318yes—
231C2×#120C2318yes—
232#518—44no—
233C2×C4×D4—44no—
234C2×C4×D4C2312yes—
235C2×C4×D4C2312yes—
236C2×C4×D4C2314yes—
237C2×C4×D4C2314yes—
238C2×C4×D4C2314yes—
239C2×C4×D4C2312yes—
240C2×C4×D4C2312yes—
241C2×C4×D4C2314yes—
242C2×C4×D4C2314yes—
243C2×C4×D4C2314yes—
244C2×#117—48no—
245C2×#117C2312yes—
246C2×#117C2312yes—
247C2×#117C2312yes—
248C2×#117C2314yes—
249C2×#117C2314yes—
250C2×#117C2312yes—
251C2×#117C2312yes—
252C22×C4⋊C4C2312yes—
253C22×C4⋊C4C2312yes—
254C22×C4⋊C4C2312yes—
255C22×C4⋊C4C2311yescharacteristic
256C22×C22⋊C4C2312yes—
257C22×C22⋊C4C2314yes—
258C22×C22⋊C4C2314yes—
259C22×C22⋊C4C2314yes—
260C22×C22⋊C4C2314yes—
261C22×C42C2311yescharacteristic
262C22×C42C2314yes—
263C22×C42C2312yes—
264#401C2318yes—
265#400C2318yes—
266#400C2318yes—
267#400C2318yes—
268#399C2318yes—
269#399C2318yes—
270#398C2314yes—
271#398C2314yes—
272#397C2314yes—
273#397C2318yes—
274#397C2318yes—
275#397C2318yes—
276#397C2318yes—
277#397C2314yes—
278#397C2318yes—
279#397C2318yes—
280#397C2318yes—
281#396C2314yes—
282#396C2318yes—
283#396C2314yes—
284#396C2318yes—
285#396C2314yes—
286#396C2318yes—
287#396C2314yes—
288#394C2314yes—
289#394C2318yes—
290#394C2318yes—
291#394C2318yes—
292#394C2318yes—
293#394C2318yes—
294#394C2314yes—
295#394C2318yes—
296#394C2318yes—
297#394C2318yes—
298#394C2318yes—
299#394C2318yes—
300#394C2318yes—
301#394C2318yes—
302#394C2314yes—
303#394C2318yes—
304#394C2318yes—
305#394C2318yes—
306#394C2318yes—
307#394C2318yes—
308#394C2318yes—
309#394C2318yes—
310#394C2314yes—
311#394C2314yes—
312#394C2314yes—
313#394C2318yes—
314#392C2314yes—
315#392C2318yes—
316#392C2318yes—
317#392C2318yes—
318#392C2318yes—
319#392C2318yes—
320#392C2318yes—
321#392C2318yes—
322#392C2318yes—
323#392C2318yes—
324#392C2318yes—
325#392C2318yes—
326#392C2318yes—
327#392C2318yes—
328#392C2318yes—
329#392C2318yes—
330#392C2314yes—
331#392C2318yes—
332#391C2314yes—
333#391C2314yes—
334#391C2312yes—
335#391C2312yes—
336#390C2314yes—
337#390C2314yes—
338#390C2314yes—
339#390C2314yes—
340#390C2314yes—
341#390C2314yes—
342#390C2314yes—
343#390C2314yes—
344#390C2314yes—
345#390C2314yes—
346#390C2314yes—
347#390C2318yes—
348#390C2314yes—
349#390C2318yes—
350#390C2314yes—
351#390C2314yes—
352#390C2312yes—
353#390C2312yes—
354#390C2318yes—
355#389C2314yes—
356#389C2314yes—
357#389C2314yes—
358#389C2314yes—
359#389C2314yes—
360#389C2314yes—
361#389C2312yes—
362#389C2312yes—
363#389C2312yes—
364#389C2312yes—
365#388C2314yes—
366#388C2318yes—
367#388C2318yes—
368#388C2318yes—
369#388C2318yes—
370#388C2318yes—
371#388C2318yes—
372#388C2318yes—
373#388C2318yes—
374#388C2318yes—
375#388C2314yes—
376#388C2314yes—
377#388C2314yes—
378#387C2318yes—
379#387C2318yes—
380#387C2318yes—
381#386C2318yes—
382#386C2318yes—
383#386C2314yes—
384#386C2318yes—
385#386C2318yes—
386#386C2318yes—
387#386C2318yes—
388#386C2318yes—
389#386C2318yes—
390#386C2318yes—
391#386C2318yes—
392#386C2314yes—
393#386C2318yes—
394#386C2314yes—
395#386C2318yes—
396#386C2314yes—
397#386C2314yes—
398#386C2318yes—
399#386C2314yes—
400#386C2314yes—
401#386C2318yes—
402#386C2314yes—
403#386C2314yes—
404#386C2314yes—
405#385C2318yes—
406#385C2318yes—
407#385C2318yes—
408#385C2314yes—
409#385C2318yes—
410#385C2314yes—
411#384C2314yes—
412#384C2314yes—
413#383C2318yes—
414#382C2314yes—
415#382C2314yes—
416#381C2314yes—
417#380C2314yes—
418#380C2314yes—
419#380C2314yes—
420#380C2314yes—
421#380C2312yes—
422#380C2312yes—
423#380C2312yes—
424#380C2312yes—
425#380C2318yes—
426#380C2314yes—
427#380C2314yes—
428#380C2318yes—
429#379C2314yes—
430#379C2318yes—
431#379C2314yes—
432#379C2318yes—
433#379C2318yes—
434#379C2314yes—
435C4×C4⋊C4C2314yes—
436C4×C4⋊C4C2314yes—
437C4×C4⋊C4C2314yes—
438C4×C4⋊C4C2314yes—
439C4×C22⋊C4C2314yes—
440C4×C22⋊C4C2314yes—
441C4×C22⋊C4C2314yes—
442C4×C22⋊C4C2314yes—
443C2×#95C2312yes—
444C25C2412yes—
445C25C2412yes—
446C25C2412yes—
447C25C2414yes—
448H(5,𝔽2)—464no—
449C2×#41—28no—
450C2×#41—28no—
451C2×#41—28no—
452C2×#41—48no—
453C2×#41—48no—
454C2×#41—48no—
455C22×Q8C2412yes—
456C22×D4—24no—
457C22×D4—24no—
458C22×D4—28no—
459C22×D4—28no—
460C22×D4—24no—
461C22×D4—42no—
462C22×D4—48no—
463C22×D4—48no—
464C22×D4—48no—
465C22×D4—44no—
466C22×D4—44no—
467C22×D4—42no—
468C22×D4—48no—
469C22×D4—48no—
470C22×D4—44no—
471C22×D4—44no—
472C22×D4—416no—
473C22×D4—48no—
474C22×D4—48no—
475C22×D4—48no—
476C22×D4—84no—
477C22×D4—84no—
478C22×D4—84no—
479C22×D4C2414yes—
480C22×D4C2414yes—
481C22×D4C2414yes—
482C22×D4C2412yes—
483C22×D4C2412yes—
484C22×D4C2411yescharacteristic
485C22×D4C2414yes—
486C22×D4C2414yes—
487C22×D4C2418yes—
488C22×D4C2414yes—
489C22×D4C2414yes—
490C22×D4C2418yes—
491C22×D4C2414yes—
492C22×D4C2414yes—
493C22×D4C2418yes—
494C22×D4C2418yes—
495C22×D4C2418yes—
496C22×D4C2418yes—
497C22×D4C2418yes—
498C22×D4C2418yes—
499C22×D4C2411yescharacteristic
500C23×C4—28no—
501C23×C4—28no—
502C23×C4—28no—
503C23×C4C2412yes—
504C23×C4C2412yes—
505C23×C4C2411yescharacteristic
506C23×C4C2412yes—
507C23×C4C2412yes—
508C23×C4C2412yes—
509C23×C4C2414yes—
510C23×C4C2414yes—
511C23×C4C2411yescharacteristic
512C23×C4C2414yes—
513C23×C4C2414yes—
514C23×C4C2414yes—
515C23×C4C2414yes—
516C23×C4C2414yes—
517C23×C4C2411yescharacteristic
518#127—216no—
519#127—48no—
520#127—48no—
521#127—48no—
522#127—48no—
523#127—416no—
524#126—416no—
525#124—48no—
526#123—48no—
527#123—48no—
528#123—416no—
529#123—48no—
530#123—48no—
531#123—88no—
532#123—88no—
533C22⋊Q8—44no—
534C22⋊Q8—44no—
535C22⋊Q8—44no—
536C22⋊Q8—44no—
537#121—216no—
538#121—48no—
539#121—416no—
540#121—48no—
541#121—48no—
542#121—48no—
543#121—48no—
544#121—48no—
545#121—48no—
546#121—48no—
547#121—48no—
548#121—44no—
549#121—44no—
550#121—44no—
551#121—44no—
552#121—48no—
553#121—48no—
554#121—416no—
555#121—88no—
556#121—88no—
557#120—48no—
558#120—48no—
559#120—48no—
560#120—48no—
561#120—416no—
562#120—416no—
563#120—88no—
564#120—88no—
565C4×D4—48no—
566C4×D4—48no—
567C4×D4—44no—
568C4×D4—44no—
569C4×D4—44no—
570C4×D4—44no—
571C4×D4—48no—
572C4×D4—48no—
573C4×D4—48no—
574C4×D4—48no—
575#117—28no—
576#117—28no—
577#117—28no—
578#117—48no—
579#117—48no—
580#117—44no—
581#117—44no—
582C2×C4⋊C4—28no—
583C2×C4⋊C4—44no—
584C2×C4⋊C4—44no—
585C2×C4⋊C4—42no—
586C2×C4⋊C4C2412yes—
587C2×C4⋊C4C2412yes—
588C2×C4⋊C4C2412yes—
589C2×C4⋊C4C2412yes—
590C2×C4⋊C4C2414yes—
591C2×C4⋊C4C2414yes—
592C2×C4⋊C4C2412yes—
593C2×C4⋊C4C2412yes—
594C2×C4⋊C4C2414yes—
595C2×C4⋊C4C2414yes—
596C2×C4⋊C4C2414yes—
597C2×C4⋊C4C2414yes—
598C2×C4⋊C4C2411yescharacteristic
599C2×C4⋊C4C2412yes—
600C2×C4⋊C4C2411yescharacteristic
601C2×C4⋊C4C2414yes—
602C2×C4⋊C4C2414yes—
603C2×C4⋊C4C2414yes—
604C2×C4⋊C4C2414yes—
605C2×C4⋊C4C2418yes—
606C2×C4⋊C4C2418yes—
607C2×C4⋊C4C2418yes—
608C2×C4⋊C4C2418yes—
609C2×C4⋊C4C2414yes—
610C2×C4⋊C4C2414yes—
611C2×C22⋊C4—48no—
612C2×C22⋊C4—48no—
613C2×C22⋊C4—44no—
614C2×C22⋊C4—48no—
615C2×C22⋊C4—48no—
616C2×C22⋊C4C2414yes—
617C2×C22⋊C4C2414yes—
618C2×C22⋊C4C2414yes—
619C2×C22⋊C4C2414yes—
620C2×C22⋊C4C2414yes—
621C2×C22⋊C4C2414yes—
622C2×C22⋊C4C2414yes—
623C2×C22⋊C4C2414yes—
624C2×C22⋊C4C2412yes—
625C2×C22⋊C4C2412yes—
626C2×C22⋊C4C2412yes—
627C2×C22⋊C4C2412yes—
628C2×C22⋊C4C2418yes—
629C2×C22⋊C4C2418yes—
630C2×C22⋊C4C2418yes—
631C2×C22⋊C4C2418yes—
632C2×C22⋊C4C2418yes—
633C2×C22⋊C4C2414yes—
634C2×C22⋊C4C2414yes—
635C2×C22⋊C4C2414yes—
636C2×C22⋊C4C2414yes—
637C2×C22⋊C4C2414yes—
638C2×C22⋊C4C2414yes—
639C2×C22⋊C4C2414yes—
640C2×C22⋊C4C2414yes—
641C2×C22⋊C4C2414yes—
642C2×C22⋊C4C2414yes—
643C2×C22⋊C4C2418yes—
644C2×C22⋊C4C2418yes—
645C2×C22⋊C4C2418yes—
646C2×C22⋊C4C2418yes—
647C2×C22⋊C4C2418yes—
648C2×C22⋊C4C2418yes—
649C2×C22⋊C4C2418yes—
650C2×C22⋊C4C2414yes—
651C2×C22⋊C4C2418yes—
652C2×C22⋊C4C2418yes—
653C2×C22⋊C4C2414yes—
654C2×C22⋊C4C2414yes—
655C2×C22⋊C4C2414yes—
656C2×C22⋊C4C2418yes—
657C2×C22⋊C4C2414yes—
658C2×C22⋊C4C2414yes—
659C2×C22⋊C4C2418yes—
660C2×C22⋊C4C2418yes—
661C2×C22⋊C4C2414yes—
662C2×C42—24no—
663C2×C42—48no—
664C2×C42—44no—
665C2×C42C2414yes—
666C2×C42C2414yes—
667C2×C42C2414yes—
668C2×C42C2412yes—
669C2×C42C2412yes—
670C2×C42C2414yes—
671C2×C42C2414yes—
672C2×C42C2414yes—
673C2×C42C2414yes—
674#95C2418yes—
675#95C2414yes—
676#95C2414yes—
677#95C2414yes—
678#95C2414yes—
679#95C2414yes—
680#95C2414yes—
681#95C2414yes—
682#95C2414yes—
683#95C2414yes—
684#95C2414yes—
685#95C2414yes—
686#95C2414yes—
687#95C2418yes—
688#95C2418yes—
689#95C2418yes—
690#95C2418yes—
691#95C2418yes—
692#95C2418yes—
693#95C2418yes—
694#95C2418yes—
695C24—24no—
696C24—24no—
697C24—24no—
698C24—24no—
699C24—24no—
700C24—28no—
701C24—28no—
702C24—24no—
703C24—42no—
704C24—42no—
705C24—42no—
706C24—44no—
707C24—48no—
708C24—42no—
709C24—42no—
710C24—42no—
711C24—42no—
712C24—44no—
713C24—44no—
714C24—44no—
715C24—44no—
716C24—48no—
717C24C2514yes—
718C24C2514yes—
719C24C2512yes—
720C24C2514yes—
721C24C2512yes—
722C24C2511yescharacteristic
723#41—464no—
724#41—432no—
725C2×Q8—24no—
726C2×Q8—24no—
727C2×Q8—24no—
728C2×D4—28no—
729C2×D4—28no—
730C2×D4—28no—
731C2×D4—24no—
732C2×D4—28no—
733C2×D4—28no—
734C2×D4—216no—
735C2×D4—216no—
736C2×D4—28no—
737C2×D4—28no—
738C2×D4—28no—
739C2×D4—28no—
740C2×D4—28no—
741C2×D4—24no—
742C2×D4—24no—
743C2×D4—22no—
744C2×D4—28no—
745C2×D4—24no—
746C2×D4—28no—
747C2×D4—24no—
748C2×D4—28no—
749C2×D4—41no—
750C2×D4—42no—
751C2×D4—41no—
752C2×D4—48no—
753C2×D4—48no—
754C2×D4—48no—
755C2×D4—41no—
756C2×D4—41no—
757C2×D4—416no—
758C2×D4—44no—
759C2×D4—44no—
760C2×D4—44no—
761C2×D4—44no—
762C2×D4—44no—
763C2×D4—44no—
764C2×D4—48no—
765C2×D4—48no—
766C2×D4—48no—
767C2×D4—48no—
768C2×D4—48no—
769C2×D4—48no—
770C2×D4—44no—
771C2×D4—44no—
772C2×D4—44no—
773C2×D4—44no—
774C2×D4—48no—
775C2×D4—48no—
776C2×D4—48no—
777C2×D4—48no—
778C2×D4—44no—
779C2×D4—44no—
780C2×D4—44no—
781C2×D4—48no—
782C2×D4—48no—
783C2×D4—48no—
784C2×D4—44no—
785C2×D4—48no—
786C2×D4—48no—
787C2×D4—48no—
788C2×D4—48no—
789C2×D4—48no—
790C2×D4—48no—
791C2×D4—464no—
792C2×D4—464no—
793C2×D4—416no—
794C2×D4—416no—
795C2×D4—816no—
796C2×D4—832no—
797C2×D4—832no—
798C2×D4—816no—
799C2×D4H(5,𝔽2)14yescomplemented
800C22×C4—22no—
801C22×C4—22no—
802C22×C4—22no—
803C22×C4—22no—
804C22×C4—28no—
805C22×C4—24no—
806C22×C4—24no—
807C22×C4—24no—
808C22×C4—28no—
809C22×C4—24no—
810C22×C4—24no—
811C22×C4—24no—
812C22×C4—24no—
813C22×C4—24no—
814C22×C4—24no—
815C22×C4—24no—
816C22×C4—24no—
817C22×C4—24no—
818C22×C4—24no—
819C22×C4—28no—
820C22×C4—28no—
821C22×C4—24no—
822C22×C4—24no—
823C22×C4—28no—
824C22×C4—44no—
825C22×C4—48no—
826C22×C4—44no—
827C22×C4—42no—
828C22×C4—44no—
829C22×C4—44no—
830C22×C4—44no—
831C22×C4—44no—
832C22×C4—44no—
833C22×C4—44no—
834C22×C4—44no—
835C22×C4—44no—
836C22×C4—44no—
837C22×C4—48no—
838C22×C4—44no—
839C22×C4—432no—
840C22×C4H(5,𝔽2)14yes—
841C22×C4H(5,𝔽2)18yes—
842C22×C4C2512yes—
843C22×C4C2514yes—
844C22×C4C2514yes—
845C22×C4C2518yes—
846C22×C4C2514yes—
847C22×C4C2514yes—
848C22×C4C2514yes—
849C22×C4C2514yes—
850C22×C4C2512yes—
851C22×C4C2514yes—
852C22×C4C2512yes—
853C22×C4C2511yescharacteristic
854C22×C4C2511yescharacteristic
855C22×C4C2512yes—
856C4⋊C4—28no—
857C4⋊C4—28no—
858C4⋊C4—24no—
859C4⋊C4—24no—
860C4⋊C4—24no—
861C4⋊C4—24no—
862C4⋊C4—24no—
863C4⋊C4—24no—
864C4⋊C4—28no—
865C4⋊C4—28no—
866C4⋊C4—44no—
867C4⋊C4—44no—
868C4⋊C4—41no—
869C4⋊C4—42no—
870C4⋊C4—41no—
871C4⋊C4—44no—
872C4⋊C4—44no—
873C4⋊C4—44no—
874C4⋊C4—44no—
875C4⋊C4—48no—
876C4⋊C4—48no—
877C4⋊C4—48no—
878C4⋊C4—48no—
879C4⋊C4—44no—
880C4⋊C4—44no—
881C22⋊C4—28no—
882C22⋊C4—28no—
883C22⋊C4—28no—
884C22⋊C4—28no—
885C22⋊C4—28no—
886C22⋊C4—28no—
887C22⋊C4—44no—
888C22⋊C4—44no—
889C22⋊C4—42no—
890C22⋊C4—42no—
891C22⋊C4—42no—
892C22⋊C4—42no—
893C22⋊C4—48no—
894C22⋊C4—48no—
895C22⋊C4—48no—
896C22⋊C4—48no—
897C22⋊C4—48no—
898C22⋊C4—44no—
899C22⋊C4—44no—
900C22⋊C4—44no—
901C22⋊C4—44no—
902C22⋊C4—44no—
903C22⋊C4—44no—
904C22⋊C4—44no—
905C22⋊C4—44no—
906C22⋊C4—44no—
907C22⋊C4—48no—
908C22⋊C4—48no—
909C22⋊C4—48no—
910C22⋊C4—48no—
911C22⋊C4—44no—
912C22⋊C4—48no—
913C22⋊C4—44no—
914C22⋊C4—44no—
915C22⋊C4—48no—
916C22⋊C4—48no—
917C22⋊C4—48no—
918C22⋊C4—48no—
919C22⋊C4—44no—
920C22⋊C4—44no—
921C22⋊C4—44no—
922C22⋊C4—48no—
923C22⋊C4—44no—
924C22⋊C4—48no—
925C22⋊C4—48no—
926C22⋊C4—44no—
927C42—24no—
928C42—24no—
929C42—28no—
930C42—28no—
931C42—28no—
932C42—28no—
933C42—44no—
934C42—44no—
935C42—44no—
936C23—21no—
937C23—21no—
938C23—22no—
939C23—22no—
940C23—22no—
941C23—22no—
942C23—22no—
943C23—22no—
944C23—22no—
945C23—24no—
946C23—22no—
947C23—22no—
948C23—28no—
949C23—24no—
950C23—22no—
951C23—24no—
952C23—24no—
953C23—24no—
954C23—28no—
955C23—24no—
956C23—24no—
957C23—24no—
958C23—22no—
959C23—24no—
960C23—24no—
961C23—22no—
962C23—24no—
963C23—28no—
964C23—24no—
965C23—24no—
966C23—22no—
967C23—28no—
968C23—22no—
969C23—48no—
970C23—48no—
971C23—48no—
972C23—416no—
973C23—48no—
974C23—48no—
975C23—48no—
976C23—84no—
977C23—84no—
978C23—84no—
979C23—84no—
980C23—84no—
981C23—84no—
982C23—84no—
983C23—88no—
984C23—88no—
985C23—88no—
986C23—88no—
987C23—164no—
988C23—164no—
989C23—168no—
990C23—168no—
991C23C2×H(5,𝔽2)14yes—
992C23C2×H(5,𝔽2)12yes—
993C23C2×H(5,𝔽2)14yes—
994C23C2611yescharacteristic
995Q8—48no—
996D4—44no—
997D4—48no—
998D4—44no—
999D4—432no—
1000D4—416no—
1001D4—416no—
1002D4—416no—
1003D4—48no—
1004D4—88no—
1005D4—88no—
1006D4—88no—
1007D4—88no—
1008D4—816no—
1009D4—816no—
1010D4—88no—
1011D4—88no—
1012D4—816no—
1013D4—816no—
1014D4—816no—
1015D4—168no—
1016D4—168no—
1017C2×C4—28no—
1018C2×C4—21no—
1019C2×C4—21no—
1020C2×C4—21no—
1021C2×C4—21no—
1022C2×C4—22no—
1023C2×C4—24no—
1024C2×C4—24no—
1025C2×C4—24no—
1026C2×C4—24no—
1027C2×C4—28no—
1028C2×C4—24no—
1029C2×C4—24no—
1030C2×C4—22no—
1031C2×C4—24no—
1032C2×C4—24no—
1033C2×C4—24no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—28no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—24no—
1041C2×C4—24no—
1042C2×C4—24no—
1043C2×C4—24no—
1044C2×C4—24no—
1045C2×C4—24no—
1046C2×C4—24no—
1047C2×C4—24no—
1048C2×C4—24no—
1049C2×C4—24no—
1050C2×C4—24no—
1051C2×C4—22no—
1052C2×C4—24no—
1053C2×C4—28no—
1054C2×C4—22no—
1055C2×C4—44no—
1056C2×C4—416no—
1057C2×C4—416no—
1058C2×C4—48no—
1059C2×C4—48no—
1060C2×C4—48no—
1061C2×C4—48no—
1062C2×C4—48no—
1063C2×C4—416no—
1064C2×C4—88no—
1065C2×C4—88no—
1066C2×C4—164no—
1067C2×C4—164no—
1068C2×C4#560116yescomplemented
1069C2×C4C2×H(5,𝔽2)12yes—
1070C2×C4C2×H(5,𝔽2)14yes—
1071C2×C4C2×H(5,𝔽2)14yes—
1072C2×C4C2×H(5,𝔽2)14yes—
1073C2×C4#58512yes—
1074C22—22no—
1075C22—22no—
1076C22—24no—
1077C22—24no—
1078C22—24no—
1079C22—24no—
1080C22—24no—
1081C22—42no—
1082C22—42no—
1083C22—42no—
1084C22—42no—
1085C22—44no—
1086C22—42no—
1087C22—44no—
1088C22—44no—
1089C22—44no—
1090C22—42no—
1091C22—44no—
1092C22—44no—
1093C22—42no—
1094C22—42no—
1095C22—48no—
1096C22—48no—
1097C22—44no—
1098C22—44no—
1099C22—42no—
1100C22—44no—
1101C22—44no—
1102C22—44no—
1103C22—42no—
1104C22—44no—
1105C22—44no—
1106C22—48no—
1107C22—42no—
1108C22—48no—
1109C22—816no—
1110C22—168no—
1111C22—168no—
1112C22—1616no—
1113C22C2×#56014yes—
1114C22C22×H(5,𝔽2)11yescharacteristic
1115C22C22×H(5,𝔽2)11yescharacteristic
1116C22C22×H(5,𝔽2)12yes—
1117C22C2×#58511yescharacteristic
1118C22H(7,𝔽2)12yes—
1119C4—22no—
1120C4—22no—
1121C4—44no—
1122C4—42no—
1123C4—44no—
1124C4—48no—
1125C4—44no—
1126C4—44no—
1127C4—42no—
1128C4—42no—
1129C4—44no—
1130C4—44no—
1131C4—44no—
1132C4C2×#56018yes—
1133C2—24no—
1134C2—44no—
1135C2—82no—
1136C2—84no—
1137C2—84no—
1138C2—84no—
1139C2C22×#56011yescharacteristic
1140C2#6281811yescharacteristic
1141C2#6287411yescharacteristic
1142C2#6291212yes—
1143C2#6295512yes—
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. #53102C2semidirect
2. #53096C2semidirect
3. #53063C2semidirect
4. #52971C2semidirect
5. #52397C2semidirect
6. #46334C2semidirect
7. #46324C2semidirect
8. #45716C2semidirect
9. #45655C2semidirect
10. #45593C2semidirect
11. #45483C2semidirect
12. #35554C2semidirect
13. #35527C2semidirect
14. #35514C2semidirect
15. #35512C2semidirect
16. #35262C2semidirect
17. #35252C2semidirect
18. #35160C2semidirect
19. C2×#2541C2semidirect
20. #34737C2semidirect
22. C2×#560C22semidirect
25. C22×#127C22semidirect
29. C22×#121C22semidirect
30. C2×#518C22semidirect
31. C22×C4×D4C22semidirect
32. C22×#117C22semidirect
33. #2856C22semidirect
34. #2854C22semidirect
35. #2854C22semidirect
36. #2852C22semidirect
37. #2850C22semidirect
38. #2829C22semidirect
39. #2828C22semidirect
40. #2828C22semidirect
41. #2826C22semidirect
42. #2825C22semidirect
43. #2825C22semidirect
44. #2818C22semidirect
45. #2813C22semidirect
46. #2813C22semidirect
47. #2812C22semidirect
48. #2803C22semidirect
49. #2778C22semidirect
50. #2778C22semidirect
51. #2757C22semidirect
52. #2756C22semidirect
53. #2748C22semidirect
54. #2709C22semidirect
55. #2709C22semidirect
56. #2705C22semidirect
57. #2703C22semidirect
58. #2703C22semidirect
59. #2697C22semidirect
60. #2693C22semidirect
61. #2685C22semidirect
62. #2678C22semidirect
63. #2678C22semidirect
64. #2673C22semidirect
65. #2673C22semidirect
66. #2673C22semidirect
67. #2669C22semidirect
68. #2669C22semidirect
69. #2668C22semidirect
70. #2643C22semidirect
71. #2624C22semidirect
72. #2624C22semidirect
73. #2620C22semidirect
74. #2619C22semidirect
75. #2541C22semidirect
76. #2541C22semidirect
77. #2541C22semidirect
78. #2541C22semidirect
79. #2537C22semidirect
80. #2537C22semidirect
81. #2535C22semidirect
82. #2535C22semidirect
83. #2514C22semidirect
84. #2513C22semidirect
85. #2512C22semidirect
86. #2511C22semidirect
87. #2504C22semidirect
88. #2501C22semidirect
89. #2500C22semidirect
90. #2500C22semidirect
91. #2497C22semidirect
92. #2496C22semidirect
93. #2495C22semidirect
94. #2494C22semidirect
95. #2482C22semidirect
96. #2445C22semidirect
97. #2445C22semidirect
98. #2445C22semidirect
99. #2445C22semidirect
100. #2433C22semidirect
101. #2433C22semidirect
102. #2431C22semidirect
103. #2431C22semidirect
104. #2428C22semidirect
105. #2428C22semidirect
106. #2427C22semidirect
107. #2427C22semidirect
108. #2417C22semidirect
109. #2417C22semidirect
110. #2416C22semidirect
111. #2416C22semidirect
112. #2416C22semidirect
113. #2416C22semidirect
114. #2415C22semidirect
115. #2415C22semidirect
116. #2414C22semidirect
117. #2414C22semidirect
118. #2414C22semidirect
119. #2414C22semidirect
120. #2413C22semidirect
121. #2412C22semidirect
122. #2412C22semidirect
123. #2411C22semidirect
124. #2411C22semidirect
125. #2410C22semidirect
126. #2410C22semidirect
127. #2410C22semidirect
128. #2408C22semidirect
129. #2408C22semidirect
130. #2408C22semidirect
131. #2408C22semidirect
132. #2407C22semidirect
133. #2407C22semidirect
134. #2407C22semidirect
135. #2407C22semidirect
137. #2405C22semidirect
138. #2405C22semidirect
139. #2405C22semidirect
143. #2392C22semidirect
144. #2392C22semidirect
145. C2×#392C22semidirect
146. #2380C22semidirect
147. #2376C22semidirect
148. #2375C22semidirect
149. #2317C22semidirect
150. #2317C22semidirect
155. #2309C22semidirect
156. C4×#121C22semidirect
157. C4×#121C22semidirect
159. #2296C22semidirect
160. C2×#390C22semidirect
161. #2280C22semidirect
162. C2×C4×C4⋊C4C22semidirect
799. C2×D4H(5,𝔽2)semidirect
1068. C2×C4#560semidirect

Maximal subgroups

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

subgroupindex
#531022
#530962
#530632
#529712
#523972
#463342
#463242
#457162
#456552
#455932
#454832
#355542
#355272
#355142
#355122
#352622
#352522
#351602
C2×#25412
#347372