Finite Group Databasebeta

← #7672928

Subgroups — #7672928

Order 512.

5260 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#43710C214yesmaximal, complemented
2#43325C214yesmaximal, complemented
3#43289C214yesmaximal, complemented
4#43288C214yesmaximal, complemented
5#39266C218yesmaximal, complemented
6#39265C218yesmaximal, complemented
7#39199C218yesmaximal, complemented
8#39195C218yesmaximal, complemented
9#35463C211yesmaximal, characteristic
10#35455C212yesmaximal, complemented
11#35448C211yesmaximal, characteristic, complemented
12#34993C212yesmaximal, complemented
13#34983C212yesmaximal, complemented
14C2×#2623C211yesmaximal, characteristic, complemented
15#34270C212yesmaximal, complemented
16#34264C212yesmaximal, complemented
17C2×#2322C212yesmaximal, complemented
18C2×#543C2212yes—
19C2×#534C2212yes—
20C2×#534C2211yescharacteristic
21C22×#123C2212yes—
22C22×#123C2211yescharacteristic
23C2×#518C2211yescharacteristic
24C22×C4×D4C2212yes—
25C23×C4⋊C4C2211yescharacteristic
26#2853C2214yescomplemented
27#2850C2218yes—
28#2849C2214yescomplemented
29#2807C2214yescomplemented
30#2807C2218yescomplemented
31#2804C2214yescomplemented
32#2798C2218yescomplemented
33#2798C2218yescomplemented
34#2797C2218yescomplemented
35#2796C2218yescomplemented
36#2794C2214yescomplemented
37#2794C2214yescomplemented
38#2773C2218yescomplemented
39#2773C2218yescomplemented
40#2771C2214yescomplemented
41#2771C2218yescomplemented
42#2754C2218yescomplemented
43#2754C2218yescomplemented
44#2752C2214yescomplemented
45#2751C2218yescomplemented
46#2724C2214yescomplemented
47#2712C2214yescomplemented
48#2710C2218yescomplemented
49#2639C2218yes—
50#2623C2218yescomplemented
51#2623C2218yescomplemented
52#2623C2214yescomplemented
53#2622C2214yescomplemented
54#2607C2214yescomplemented
55#2600C2214yescomplemented
56#2597C2218yescomplemented
57#2595C2218yescomplemented
58#2593C2214yescomplemented
59#2593C2214yescomplemented
60#2589C2218yescomplemented
61#2582C2214yescomplemented
62#2580C2218yescomplemented
63#2575C2218yescomplemented
64#2571C2214yescomplemented
65#2570C2218yescomplemented
66#2561C2218yescomplemented
67#2539C2212yes—
68#2539C2218yes—
69#2539C2212yes—
70#2517C2214yescomplemented
71#2516C2218yescomplemented
72#2513C2218yescomplemented
73#2511C2218yescomplemented
74#2503C2218yescomplemented
75#2501C2212yes—
76#2501C2218yes—
77#2501C2212yes—
78#2488C2218yescomplemented
79#2488C2218yescomplemented
80#2488C2218yescomplemented
81#2488C2218yescomplemented
82#2488C2218yescomplemented
83#2488C2218yescomplemented
84#2484C2212yescomplemented
85#2484C2212yescomplemented
86#2483C2212yescomplemented
87#2483C2212yescomplemented
88#2472C2218yescomplemented
89#2472C2218yescomplemented
90#2458C2218yescomplemented
91#2455C2214yescomplemented
92#2448C2218yescomplemented
93#2447C2218yescomplemented
94#2444C2218yes—
95#2443C2218yes—
96#2419C2218yescomplemented
97#2419C2218yescomplemented
98#2419C2218yescomplemented
99#2418C2218yescomplemented
100C2×#400C2212yescomplemented
101C2×#399C2212yescomplemented
102C2×#398C2212yescomplemented
103C2×#397C2212yescomplemented
104#2368C2218yescomplemented
105#2368C2218yescomplemented
106#2364C2218yes—
107#2361C2218yes—
108#2360C2218yescomplemented
109#2360C2218yescomplemented
110#2359C2218yescomplemented
111#2358C2218yescomplemented
112#2329C2218yescomplemented
113#2322C2218yescomplemented
114#2322C2218yescomplemented
115#2322C2218yescomplemented
116#2322C2218yescomplemented
117#2322C2214yescomplemented
118#2321C2214yescomplemented
119#2315C2212yes—
120#2308C2211yescharacteristic
121#2308C2212yes—
122#2308C2212yes—
123C4×C22⋊Q8C2218yescomplemented
124C4×#123C2214yescomplemented
125C4×#120C2214yescomplemented
126C2×#389C2214yescomplemented
127C2×#388C2214yescomplemented
128C2×#387C2214yescomplemented
129C2×#386C2212yes—
130C2×#386C2212yes—
131C2×#385C2212yes—
132C2×#385C2212yes—
133C2×#385C2214yescomplemented
134C2×#381C2212yes—
135C2×#381C2211yescharacteristic
136#2273C2212yes—
137#2273C2211yescharacteristic
138C2×C4×C22⋊C4C2212yes—
139C23×D4C2312yes—
140C23×D4C2311yescharacteristic
141C24×C4C2311yescharacteristic
142C24×C4C2312yes—
143C24×C4C2312yes—
144#543—216no—
145#534—216no—
146#534—44no—
147C2×#124C2318yes—
148C2×#123—216no—
149C2×#123—44no—
150C2×#123C2314yes—
151C2×#123C2314yes—
152C2×#123C2318yes—
153C2×#123C2314yes—
154C2×#123C2314yes—
155C2×#123C2314yes—
156C2×#123C2318yes—
157C2×#123C2318yes—
158C2×C22⋊Q8C2318yes—
159C2×C22⋊Q8C2318yes—
160C2×C22⋊Q8C2318yes—
161C2×#121C2318yes—
162C2×#121C2312yes—
163C2×#121C2312yes—
164C2×#120C2314yes—
165C2×#120C2314yes—
166C2×#120C2314yes—
167#518—44no—
168C2×C4×Q8C2318yes—
169C2×C4×D4—48no—
170C2×C4×D4C2314yes—
171C2×C4×D4C2318yes—
172C2×C4×D4C2318yes—
173C2×C4×D4C2314yes—
174C2×C4×D4C2318yes—
175C2×#117C2312yes—
176C22×C4⋊C4—44no—
177C22×C4⋊C4C2314yes—
178C22×C4⋊C4C2312yes—
179C22×C4⋊C4C2312yes—
180C22×C4⋊C4C2314yes—
181C22×C4⋊C4C2314yes—
182C22×C4⋊C4C2312yes—
183C22×C4⋊C4C2311yescharacteristic
184C22×C4⋊C4C2311yescharacteristic
185C22×C4⋊C4C2314yes—
186C22×C4⋊C4C2314yes—
187C22×C22⋊C4C2314yes—
188C22×C22⋊C4C2312yes—
189C22×C22⋊C4C2312yes—
190C22×C22⋊C4C2312yes—
191C22×C22⋊C4C2311yescharacteristic
192C22×C22⋊C4C2312yes—
193C22×C22⋊C4C2312yes—
194C22×C22⋊C4C2311yescharacteristic
195C22×C22⋊C4C2311yescharacteristic
196C22×C22⋊C4C2314yes—
197C22×C22⋊C4C2314yes—
198C22×C22⋊C4C2312yes—
199C22×C42C2312yes—
200C22×C42C2314yes—
201#400C2318yes—
202#400C2318yes—
203#400C2314yes—
204#400C2318yes—
205#400C2314yes—
206#400C2314yes—
207#400C2318yes—
208#400C2314yes—
209#400C2318yes—
210#400C2318yes—
211#400C2318yes—
212#400C2318yes—
213#399C2318yes—
214#399C2318yes—
215#399C2318yes—
216#399C2318yes—
217#399C2314yes—
218#399C2314yes—
219#399C2314yes—
220#399C2314yes—
221#398C2318yes—
222#398C2318yes—
223#398C2314yes—
224#398C2314yes—
225#398C2314yes—
226#398C2314yes—
227#397C2318yes—
228#397C2318yes—
229#397C2318yes—
230#397C2318yes—
231#397C2318yes—
232#397C2314yes—
233#397C2318yes—
234#397C2314yes—
235#397C2318yes—
236#397C2318yes—
237#397C2318yes—
238#397C2318yes—
239#394C2318yes—
240#394C2318yes—
241#394C2318yes—
242#394C2318yes—
243#393C2318yes—
244#393C2318yes—
245#393C2318yes—
246#393C2318yes—
247#392C2314yes—
248#392C2314yes—
249#391C2318yes—
250#391C2318yes—
251#391C2318yes—
252#391C2318yes—
253#391C2318yes—
254#391C2318yes—
255#390C2318yes—
256#390C2318yes—
257#390C2318yes—
258#390C2314yes—
259#390C2314yes—
260#390C2318yes—
261#389C2318yes—
262#389C2318yes—
263#389C2318yes—
264#389C2318yes—
265#389C2318yes—
266#389C2318yes—
267#389C2318yes—
268#389C2318yes—
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#388C2318yes—
282#388C2318yes—
283#388C2318yes—
284#388C2318yes—
285#388C2318yes—
286#388C2318yes—
287#387C2318yes—
288#387C2318yes—
289#387C2318yes—
290#387C2318yes—
291#387C2318yes—
292#387C2318yes—
293#387C2318yes—
294#387C2318yes—
295#387C2318yes—
296#387C2318yes—
297#387C2318yes—
298#387C2318yes—
299#387C2318yes—
300#387C2318yes—
301#387C2318yes—
302#387C2318yes—
303#386C2314yes—
304#386C2318yes—
305#386C2318yes—
306#386C2314yes—
307#386C2318yes—
308#386C2318yes—
309#386C2314yes—
310#386C2318yes—
311#386C2314yes—
312#386C2314yes—
313#386C2318yes—
314#386C2318yes—
315#386C2318yes—
316#386C2318yes—
317#386C2314yes—
318#385C2314yes—
319#385C2314yes—
320#385C2314yes—
321#385C2314yes—
322#385C2318yes—
323#385C2314yes—
324#385C2318yes—
325#385C2314yes—
326#385C2318yes—
327#385C2318yes—
328#385C2318yes—
329#385C2318yes—
330#385C2314yes—
331#385C2318yes—
332#385C2314yes—
333#385C2314yes—
334#385C2318yes—
335#385C2318yes—
336#385C2314yes—
337#384C2314yes—
338#384C2314yes—
339#382C2318yes—
340#382C2318yes—
341#382C2318yes—
342#381C2318yes—
343#381C2318yes—
344#381C2314yes—
345#381C2314yes—
346#381C2312yes—
347#381C2318yes—
348#381C2314yes—
349#381C2314yes—
350#381C2314yes—
351#381C2314yes—
352#380C2318yes—
353#379C2314yes—
354#379C2314yes—
355#379C2312yes—
356C4×C4⋊C4C2318yes—
357C4×C4⋊C4C2318yes—
358C4×C4⋊C4C2318yes—
359C4×C4⋊C4C2318yes—
360C4×C22⋊C4C2318yes—
361C4×C22⋊C4C2318yes—
362C4×C22⋊C4C2314yes—
363C4×C22⋊C4C2318yes—
364C4×C22⋊C4C2318yes—
365C4×C22⋊C4C2314yes—
366C4×C22⋊C4C2318yes—
367C4×C22⋊C4C2318yes—
368C4×C22⋊C4C2318yes—
369C4×C22⋊C4C2312yes—
370C4×C22⋊C4C2312yes—
371C2×#95C2314yes—
372C2×#95C2314yes—
373C2×#95C2314yes—
374C2×#95C2314yes—
375C2×#95C2312yes—
376C2×#95C2312yes—
377C2×#95C2314yes—
378C2×#95C2314yes—
379C2×#95C2314yes—
380C25C2411yescharacteristic
381C25C2412yes—
382C25C2411yescharacteristic
383C22×Q8C2418yes—
384C22×D4—28no—
385C22×D4—28no—
386C22×D4—28no—
387C22×D4—28no—
388C22×D4—24no—
389C22×D4C2414yes—
390C22×D4C2414yes—
391C22×D4C2414yes—
392C22×D4C2418yes—
393C22×D4C2412yes—
394C22×D4C2412yes—
395C23×C4—28no—
396C23×C4—24no—
397C23×C4—28no—
398C23×C4—44no—
399C23×C4—84no—
400C23×C4—84no—
401C23×C4C2414yes—
402C23×C4C2411yescharacteristic
403C23×C4C2411yescharacteristic
404C23×C4C2412yes—
405C23×C4C2411yescharacteristic
406C23×C4C2411yescharacteristic
407C23×C4C2411yescharacteristic
408C23×C4C2414yes—
409C23×C4C2412yes—
410C23×C4C2414yes—
411C23×C4C2412yes—
412C23×C4C2414yes—
413C23×C4C2414yes—
414C23×C4C2412yes—
415C23×C4C2412yes—
416C23×C4C2412yes—
417C23×C4C2412yes—
418C23×C4C2418yes—
419C23×C4C2414yes—
420#124—88no—
421#123—216no—
422#123—216no—
423#123—232no—
424#123—216no—
425#123—216no—
426#123—416no—
427#123—48no—
428#123—88no—
429C22⋊Q8—232no—
430C22⋊Q8—232no—
431C22⋊Q8—232no—
432#121—232no—
433#121—44no—
434#121—44no—
435#120—216no—
436#120—216no—
437#120—48no—
438C4×Q8—88no—
439C4×D4—416no—
440C4×D4—416no—
441C4×D4—48no—
442C4×D4—48no—
443C4×D4—88no—
444#117—44no—
445C2×C4⋊C4—216no—
446C2×C4⋊C4—48no—
447C2×C4⋊C4—48no—
448C2×C4⋊C4—44no—
449C2×C4⋊C4—44no—
450C2×C4⋊C4—44no—
451C2×C4⋊C4—42no—
452C2×C4⋊C4—42no—
453C2×C4⋊C4—84no—
454C2×C4⋊C4—84no—
455C2×C4⋊C4C2418yes—
456C2×C4⋊C4C2418yes—
457C2×C4⋊C4C2418yes—
458C2×C4⋊C4C2418yes—
459C2×C4⋊C4C2418yes—
460C2×C4⋊C4C2418yes—
461C2×C4⋊C4C2412yes—
462C2×C4⋊C4C2412yes—
463C2×C4⋊C4C2414yes—
464C2×C4⋊C4C2414yes—
465C2×C4⋊C4C2412yes—
466C2×C4⋊C4C2412yes—
467C2×C4⋊C4C2418yes—
468C2×C4⋊C4C2418yes—
469C2×C4⋊C4C2418yes—
470C2×C4⋊C4C2418yes—
471C2×C4⋊C4C2414yes—
472C2×C4⋊C4C2414yes—
473C2×C4⋊C4C2418yes—
474C2×C4⋊C4C2412yes—
475C2×C4⋊C4C2412yes—
476C2×C4⋊C4C2418yes—
477C2×C4⋊C4C2412yes—
478C2×C4⋊C4C2412yes—
479C2×C4⋊C4C2418yes—
480C2×C22⋊C4—28no—
481C2×C22⋊C4—28no—
482C2×C22⋊C4—28no—
483C2×C22⋊C4—24no—
484C2×C22⋊C4—216no—
485C2×C22⋊C4—44no—
486C2×C22⋊C4—44no—
487C2×C22⋊C4—42no—
488C2×C22⋊C4—42no—
489C2×C22⋊C4—84no—
490C2×C22⋊C4—84no—
491C2×C22⋊C4#41116yes—
492C2×C22⋊C4C2414yes—
493C2×C22⋊C4C2414yes—
494C2×C22⋊C4C2414yes—
495C2×C22⋊C4C2414yes—
496C2×C22⋊C4C2414yes—
497C2×C22⋊C4C2414yes—
498C2×C22⋊C4C2414yes—
499C2×C22⋊C4C2418yes—
500C2×C22⋊C4C2418yes—
501C2×C22⋊C4C2418yes—
502C2×C22⋊C4C2418yes—
503C2×C22⋊C4C2414yes—
504C2×C22⋊C4C2418yes—
505C2×C22⋊C4C2418yes—
506C2×C22⋊C4C2414yes—
507C2×C22⋊C4C2414yes—
508C2×C22⋊C4C2418yes—
509C2×C22⋊C4C2418yes—
510C2×C22⋊C4C2418yes—
511C2×C22⋊C4C2418yes—
512C2×C22⋊C4C2414yes—
513C2×C22⋊C4C2414yes—
514C2×C22⋊C4C2418yes—
515C2×C22⋊C4C2414yes—
516C2×C22⋊C4C2418yes—
517C2×C22⋊C4C2414yes—
518C2×C22⋊C4C2418yes—
519C2×C22⋊C4C2414yes—
520C2×C22⋊C4C2414yes—
521C2×C42—44no—
522C2×C42—84no—
523C2×C42C2414yes—
524C2×C42C2418yes—
525C2×C42C2418yes—
526C2×C42C2414yes—
527C2×C42C2418yes—
528C2×C42C2418yes—
529C2×C42C2418yes—
530C2×C42C2414yes—
531#95C2418yes—
532#95C2418yes—
533#95C2418yes—
534#95C2418yes—
535#95C2418yes—
536#95C2418yes—
537#95C2418yes—
538#95C2418yes—
539#95C2414yes—
540#95C2414yes—
541#95C2418yes—
542#95C2418yes—
543#95C2414yes—
544#95C2414yes—
545#95C2418yes—
546#95C2418yes—
547#95C2418yes—
548#95C2418yes—
549#95C2418yes—
550#95C2418yes—
551#95C2414yes—
552#95C2414yes—
553#95C2418yes—
554#95C2418yes—
555#95C2418yes—
556#95C2418yes—
557#95C2414yes—
558#95C2418yes—
559#95C2418yes—
560#95C2414yes—
561C24—24no—
562C24—24no—
563C24—24no—
564C24—22no—
565C24—24no—
566C24—42no—
567C24—42no—
568C24—44no—
569C24—44no—
570C24—42no—
571C24—42no—
572C24C2×#4118yes—
573C24H(5,𝔽2)14yes—
574C24C2514yes—
575C24C2512yes—
576C24C2512yes—
577C24C2511yescharacteristic
578C2×Q8—216no—
579C2×Q8—48no—
580C2×Q8—48no—
581C2×D4—28no—
582C2×D4—28no—
583C2×D4—28no—
584C2×D4—28no—
585C2×D4—28no—
586C2×D4—28no—
587C2×D4—28no—
588C2×D4—28no—
589C2×D4—28no—
590C2×D4—216no—
591C2×D4—48no—
592C2×D4—48no—
593C2×D4—42no—
594C2×D4—42no—
595C2×D4—44no—
596C2×D4—44no—
597C2×D4—432no—
598C2×D4—416no—
599C22×C4—28no—
600C22×C4—24no—
601C22×C4—28no—
602C22×C4—24no—
603C22×C4—24no—
604C22×C4—24no—
605C22×C4—24no—
606C22×C4—24no—
607C22×C4—24no—
608C22×C4—24no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—28no—
613C22×C4—28no—
614C22×C4—28no—
615C22×C4—24no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—24no—
619C22×C4—28no—
620C22×C4—28no—
621C22×C4—44no—
622C22×C4—44no—
623C22×C4—44no—
624C22×C4—44no—
625C22×C4—44no—
626C22×C4—44no—
627C22×C4—44no—
628C22×C4—44no—
629C22×C4—42no—
630C22×C4—44no—
631C22×C4—44no—
632C22×C4—44no—
633C22×C4—48no—
634C22×C4—48no—
635C22×C4—48no—
636C22×C4—44no—
637C22×C4—44no—
638C22×C4—42no—
639C22×C4—44no—
640C22×C4—42no—
641C22×C4—42no—
642C22×C4—44no—
643C22×C4—44no—
644C22×C4—416no—
645C22×C4—816no—
646C22×C4—816no—
647C22×C4C2×#41116yes—
648C22×C4C2514yes—
649C22×C4C2518yes—
650C22×C4C2518yes—
651C22×C4C2512yes—
652C22×C4C2512yes—
653C22×C4C2514yes—
654C22×C4C2514yes—
655C22×C4C2512yes—
656C22×C4C2512yes—
657C22×C4C2514yes—
658C22×C4C2514yes—
659C22×C4C2512yes—
660C22×C4C2518yes—
661C4⋊C4—216no—
662C4⋊C4—216no—
663C4⋊C4—216no—
664C4⋊C4—216no—
665C4⋊C4—216no—
666C4⋊C4—216no—
667C4⋊C4—42no—
668C4⋊C4—42no—
669C4⋊C4—44no—
670C4⋊C4—44no—
671C4⋊C4—42no—
672C4⋊C4—42no—
673C4⋊C4—48no—
674C4⋊C4—44no—
675C4⋊C4—44no—
676C4⋊C4—48no—
677C4⋊C4—48no—
678C4⋊C4—48no—
679C4⋊C4—48no—
680C4⋊C4—48no—
681C4⋊C4—42no—
682C4⋊C4—42no—
683C4⋊C4—48no—
684C4⋊C4—42no—
685C4⋊C4—42no—
686C22⋊C4—28no—
687C22⋊C4—28no—
688C22⋊C4—28no—
689C22⋊C4—28no—
690C22⋊C4—28no—
691C22⋊C4—28no—
692C22⋊C4—28no—
693C22⋊C4—216no—
694C22⋊C4—216no—
695C22⋊C4—216no—
696C22⋊C4—216no—
697C22⋊C4—44no—
698C22⋊C4—48no—
699C22⋊C4—44no—
700C22⋊C4—44no—
701C22⋊C4—48no—
702C22⋊C4—48no—
703C22⋊C4—48no—
704C22⋊C4—48no—
705C22⋊C4—48no—
706C22⋊C4—48no—
707C22⋊C4—44no—
708C22⋊C4—48no—
709C22⋊C4—44no—
710C22⋊C4—44no—
711C22⋊C4—48no—
712C22⋊C4—44no—
713C22⋊C4C2×#41116yes—
714C22⋊C4C2×#41116yes—
715C42—48no—
716C42—48no—
717C42—48no—
718C42—44no—
719C42—48no—
720C42—44no—
721C42—48no—
722C42—44no—
723C23—24no—
724C23—22no—
725C23—24no—
726C23—22no—
727C23—24no—
728C23—24no—
729C23—24no—
730C23—22no—
731C23—24no—
732C23—24no—
733C23—28no—
734C23—28no—
735C23—24no—
736C23—44no—
737C23—416no—
738C23—44no—
739C23—416no—
740C23—48no—
741C23—44no—
742C23—84no—
743C23—88no—
744C23—84no—
745C23—88no—
746C23—82no—
747C23—82no—
748C23#559116yes—
749C23C22×#4114yes—
750C23C22×#4114yes—
751C23C22×#4114yes—
752C23C2×H(5,𝔽2)14yes—
753C23C2×H(5,𝔽2)12yes—
754C23C2611yescharacteristic
755Q8—816no—
756D4—416no—
757D4—416no—
758D4—416no—
759D4—816no—
760D4—162no—
761D4—162no—
762C2×C4—28no—
763C2×C4—28no—
764C2×C4—28no—
765C2×C4—28no—
766C2×C4—24no—
767C2×C4—24no—
768C2×C4—24no—
769C2×C4—24no—
770C2×C4—24no—
771C2×C4—24no—
772C2×C4—24no—
773C2×C4—22no—
774C2×C4—24no—
775C2×C4—24no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—24no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—28no—
782C2×C4—24no—
783C2×C4—24no—
784C2×C4—28no—
785C2×C4—28no—
786C2×C4—24no—
787C2×C4—24no—
788C2×C4—24no—
789C2×C4—28no—
790C2×C4—28no—
791C2×C4—24no—
792C2×C4—28no—
793C2×C4—416no—
794C2×C4—48no—
795C2×C4—48no—
796C2×C4—416no—
797C2×C4—44no—
798C2×C4—44no—
799C2×C4—48no—
800C2×C4—44no—
801C2×C4—88no—
802C2×C4—88no—
803C2×C4—82no—
804C2×C4—84no—
805C2×C4—82no—
806C2×C4—88no—
807C2×C4—88no—
808C2×C4—84no—
809C2×C4—816no—
810C2×C4—162no—
811C2×C4—162no—
812C2×C4C22×#41116yes—
813C22—28no—
814C22—28no—
815C22—28no—
816C22—24no—
817C22—22no—
818C22—24no—
819C22—22no—
820C22—416no—
821C22—48no—
822C22—48no—
823C22—48no—
824C22—44no—
825C22—42no—
826C22—42no—
827C22—44no—
828C22—44no—
829C22—42no—
830C22—816no—
831C22—164no—
832C22C2×#55918yes—
833C22C2×#55914yes—
834C22C23×#4112yes—
835C22C22×H(5,𝔽2)11yescharacteristic
836C22H(7,𝔽2)12yes—
837C222−1+612yes—
838C4—216no—
839C4—48no—
840C4—48no—
841C4—44no—
842C4—44no—
843C4—44no—
844C4—42no—
845C4—44no—
846C4—42no—
847C4—42no—
848C4—42no—
849C4—42no—
850C4—44no—
851C2—28no—
852C2—24no—
853C2—84no—
854C2—82no—
855C2C22×#55911yescharacteristic
856C2#6284714yes—
857C2#6286211yescharacteristic
858C2#6287111yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35463C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #43710C2semidirect
2. #43325C2semidirect
3. #43289C2semidirect
4. #43288C2semidirect
5. #39266C2semidirect
6. #39265C2semidirect
7. #39199C2semidirect
8. #39195C2semidirect
10. #35455C2semidirect
11. #35448C2semidirect
12. #34993C2semidirect
13. #34983C2semidirect
14. C2×#2623C2semidirect
15. #34270C2semidirect
16. #34264C2semidirect
17. C2×#2322C2semidirect
26. #2853C22semidirect
28. #2849C22semidirect
29. #2807C22semidirect
30. #2807C22semidirect
31. #2804C22semidirect
32. #2798C22semidirect
33. #2798C22semidirect
34. #2797C22semidirect
35. #2796C22semidirect
36. #2794C22semidirect
37. #2794C22semidirect
38. #2773C22semidirect
39. #2773C22semidirect
40. #2771C22semidirect
41. #2771C22semidirect
42. #2754C22semidirect
43. #2754C22semidirect
44. #2752C22semidirect
45. #2751C22semidirect
46. #2724C22semidirect
47. #2712C22semidirect
48. #2710C22semidirect
50. #2623C22semidirect
51. #2623C22semidirect
52. #2623C22semidirect
53. #2622C22semidirect
54. #2607C22semidirect
55. #2600C22semidirect
56. #2597C22semidirect
57. #2595C22semidirect
58. #2593C22semidirect
59. #2593C22semidirect
60. #2589C22semidirect
61. #2582C22semidirect
62. #2580C22semidirect
63. #2575C22semidirect
64. #2571C22semidirect
65. #2570C22semidirect
66. #2561C22semidirect
70. #2517C22semidirect
71. #2516C22semidirect
72. #2513C22semidirect
73. #2511C22semidirect
74. #2503C22semidirect
78. #2488C22semidirect
79. #2488C22semidirect
80. #2488C22semidirect
81. #2488C22semidirect
82. #2488C22semidirect
83. #2488C22semidirect
84. #2484C22semidirect
85. #2484C22semidirect
86. #2483C22semidirect
87. #2483C22semidirect
88. #2472C22semidirect
89. #2472C22semidirect
90. #2458C22semidirect
91. #2455C22semidirect
92. #2448C22semidirect
93. #2447C22semidirect
96. #2419C22semidirect
97. #2419C22semidirect
98. #2419C22semidirect
99. #2418C22semidirect
100. C2×#400C22semidirect
101. C2×#399C22semidirect
102. C2×#398C22semidirect
103. C2×#397C22semidirect
104. #2368C22semidirect
105. #2368C22semidirect
108. #2360C22semidirect
109. #2360C22semidirect
110. #2359C22semidirect
111. #2358C22semidirect
112. #2329C22semidirect
113. #2322C22semidirect
114. #2322C22semidirect
115. #2322C22semidirect
116. #2322C22semidirect
117. #2322C22semidirect
118. #2321C22semidirect
123. C4×C22⋊Q8C22semidirect
124. C4×#123C22semidirect
125. C4×#120C22semidirect
126. C2×#389C22semidirect
127. C2×#388C22semidirect
128. C2×#387C22semidirect
133. C2×#385C22semidirect

Maximal subgroups

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

subgroupindex
#437102
#433252
#432892
#432882
#392662
#392652
#391992
#391952
#354632
#354552
#354482
#349932
#349832
C2×#26232
#342702
#342642
C2×#23222