Finite Group Databasebeta

← #6763516

Subgroups — #6763516

Order 512.

1884 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#37870C211yesmaximal, characteristic, complemented
2#37694C211yesmaximal, characteristic, complemented
3#33050C211yesmaximal, characteristic, complemented
4#31855C212yesmaximal, complemented
5#31850C212yesmaximal, complemented
6#31665C212yesmaximal, complemented
7#31662C212yesmaximal, complemented
8#30209C211yesmaximal, characteristic, complemented
9#29816C211yesmaximal, characteristic, complemented
10#29152C211yesmaximal, characteristic, complemented
11#28630C211yesmaximal, characteristic, complemented
12#27986C211yesmaximal, characteristic, complemented
13#27967C211yesmaximal, characteristic, complemented
14#25725C211yesmaximal, characteristic, complemented
15#25611C211yesmaximal, characteristic, complemented
16#24539C212yesmaximal, complemented
17#24538C212yesmaximal, complemented
18#23979C212yesmaximal, complemented
19#23973C212yesmaximal, complemented
20#22279C211yesmaximal, characteristic, complemented
21#21872C211yesmaximal, characteristic, complemented
22#21203C211yesmaximal, characteristic, complemented
23#21104C211yesmaximal, characteristic, complemented
24C2×#556C2211yescharacteristic
25C2×#553C2211yescharacteristic
26C2×#540C2211yescharacteristic
27C22×#127C2211yescharacteristic
28C2×#496C2211yescharacteristic
29C2×#496C2211yescharacteristic
30C2×#488C2211yescharacteristic, complemented
31C2×#450C2212yes—
32C2×#447C2212yes—
33C2×#433C2211yescharacteristic, complemented
34C2×#418C2212yes—
35C2×#418C2212yes—
36C2×C4×M16C2211yescharacteristic
37#2851C2211yescharacteristic
38#2850C2211yescharacteristic
39#2709—22no—
40#2695—22no—
41#2686—22no—
42#2673—22no—
43#2660C2211yescharacteristic, complemented
44#2641C2211yescharacteristic
45#2620C2211yescharacteristic, complemented
46#2619C2211yescharacteristic
47#2565C2211yescharacteristic, complemented
48#2563C2211yescharacteristic, complemented
49#2503C2211yescharacteristic, complemented
50#2500C2211yescharacteristic
51#2500C2211yescharacteristic, complemented
52#2499C2211yescharacteristic
53#2469—22no—
54#2468—22no—
55#2445C2212yes—
56#2428C2212yes—
57#2410—22no—
58#2408C2212yes—
59#2405—22no—
60D4×C22⋊C4C2212yes—
61#2328C2211yescharacteristic
62#2326C2211yescharacteristic, complemented
63#2317C2211yescharacteristic, complemented
64#2290C2211yescharacteristic
65#2285C2211yescharacteristic
66#2101C2212yescomplemented
67#2101C2212yescomplemented
68#2073C2212yescomplemented
69#2073C2212yescomplemented
70#2071C2212yescomplemented
71#2071C2212yescomplemented
72#2055C2212yescomplemented
73#2055C2212yescomplemented
74#2054C2212yescomplemented
75#2054C2212yescomplemented
76#2025C2212yescomplemented
77#2025C2212yescomplemented
78#2023C2212yescomplemented
79#2023C2212yescomplemented
80#2014C2212yes—
81#2011C2212yes—
82#2000C2212yescomplemented
83#2000C2212yescomplemented
84#1999C2212yescomplemented
85#1999C2212yescomplemented
86#1992C2211yescharacteristic, complemented
87#1992C2211yescharacteristic, complemented
88#1991C2211yescharacteristic, complemented
89#1961C2211yescharacteristic
90#1961C2212yes—
91#1961C2212yes—
92#1961C2211yescharacteristic
93#1958C2211yescharacteristic, complemented
94#1957C2211yescharacteristic
95#1957C2211yescharacteristic
96#1957C2211yescharacteristic
97#1957C2211yescharacteristic
98#1936C2212yescomplemented
99#1935C2212yescomplemented
100#1924C2212yescomplemented
101#1917C2212yescomplemented
102#1895C2212yes—
103#1894C2212yes—
104#1880C2212yescomplemented
105#1880C2212yescomplemented
106#1879C2212yescomplemented
107#1879C2212yescomplemented
108#1879C2212yescomplemented
109#1879C2212yescomplemented
110#1877C2212yescomplemented
111#1877C2212yescomplemented
112#1875C2212yescomplemented
113#1875C2212yescomplemented
114#1874C2212yescomplemented
115#1874C2212yescomplemented
116#1870C2212yes—
117#1851C2212yes—
118#1836C2211yescharacteristic, complemented
119#1836C2211yescharacteristic, complemented
120#1835C2211yescharacteristic, complemented
121#1825C2212yes—
122#1825C2212yes—
123#1804C2212yescomplemented
124#1804C2212yescomplemented
125#1802C2212yescomplemented
126#1802C2212yescomplemented
127#1768C2211yescharacteristic, complemented
128#1750C2211yescharacteristic, complemented
129#1749C2211yescharacteristic
130#1746C2211yescharacteristic, complemented
131C23×D4—22no—
132C23×D4C2312yes—
133C22×SD16C2312yes—
134C22×SD16C2312yes—
135C22×D8C2312yes—
136C22×D8C2312yes—
137C22×M16C2312yes—
138#556—44no—
139#553—44no—
140#540—24no—
141#540—42no—
142C2×C4⋊Q8C2311yescharacteristic
143C2×#127—24no—
144C2×#127—22no—
145C2×#127—42no—
146C2×#127C2311yescharacteristic
147C2×#127C2312yes—
148C2×#127C2311yescharacteristic
149C2×#126—21no—
150C2×#126—21no—
151C2×#126—21no—
152C2×#125C2311yescharacteristic
153C2×#125C2311yescharacteristic
154C2×#124—21no—
155C2×#124C2311yescharacteristic
156C2×#123—22no—
157C2×#123—22no—
158C2×#123—21no—
159C2×C22⋊Q8C2311yescharacteristic
160C2×C22⋊Q8C2311yescharacteristic
161C2×#121—21no—
162C2×#121—22no—
163C2×#121—22no—
164C2×#121C2311yescharacteristic
165C2×#121C2312yes—
166C2×#121C2312yes—
167C2×#121C2311yescharacteristic
168C2×#120—22no—
169C2×C4×Q8—21no—
170C2×C4×Q8C2311yescharacteristic
171C2×C4×D4—21no—
172C2×C4×D4C2312yes—
173C2×C4×D4C2311yescharacteristic
174C2×C4×D4C2312yes—
175C2×C4×D4C2311yescharacteristic
176C2×#117C2311yescharacteristic
177C2×#117C2311yescharacteristic
178C2×#117C2311yescharacteristic
179C2×#117C2311yescharacteristic
180C22×C4⋊C4C2311yescharacteristic
181C22×C22⋊C4—22no—
182C22×C42C2311yescharacteristic
183#496—24no—
184#496—42no—
185#488—42no—
186#450—44no—
187#447—44no—
188#433—42no—
189C2×C4⋊C8C2312yes—
190C2×C4⋊C8C2312yes—
191#418—44no—
192#418—44no—
193C2×#103C2312yes—
194C2×#103C2312yes—
195C2×#102C2312yes—
196C2×#102C2312yes—
197C2×#102C2312yes—
198C2×#102C2312yes—
199C2×#102C2312yes—
200C2×#102C2312yes—
201C2×#102C2312yes—
202C2×#102C2312yes—
203C2×#102C2312yes—
204C2×#102C2312yes—
205C2×#102C2312yes—
206C2×#102C2312yes—
207C2×#102C2312yes—
208C2×#102C2312yes—
209C2×C22⋊C8C2312yes—
210C2×C22⋊C8C2312yes—
211C2×C22⋊C8C2312yes—
212C4×M16—42no—
213C2×#97C2311yescharacteristic
214C2×#97C2311yescharacteristic
215C2×#97C2312yes—
216C2×C4×C8C2311yescharacteristic
217C2×C4×C8C2311yescharacteristic
218#400—22no—
219#398—22no—
220#398—22no—
221#397—22no—
222#396—22no—
223#395—22no—
224#394—22no—
225#394—22no—
226#394—22no—
227#394—22no—
228#394—22no—
229#394—22no—
230#394—22no—
231#394—22no—
232#394—22no—
233#394—22no—
234#393—22no—
235#392—22no—
236#392—22no—
237#392—22no—
238#391C2311yescharacteristic
239#391C2311yescharacteristic
240#391C2311yescharacteristic
241#390C2311yescharacteristic
242#390C2311yescharacteristic
243#390C2311yescharacteristic
244#390C2312yes—
245#390C2312yes—
246#390C2312yes—
247#390C2312yes—
248#389—22no—
249#389C2312yes—
250#388—22no—
251#388—22no—
252#388—22no—
253#388—22no—
254#388D412yes—
255#387—22no—
256#387—22no—
257#387—22no—
258#387D412yes—
259#386—22no—
260#386—22no—
261#386—22no—
262#386—22no—
263#386—22no—
264#386—22no—
265#386—22no—
266#386D412yes—
267#385—22no—
268#385—22no—
269#385—22no—
270#385D412yes—
271#384C2311yescharacteristic
272#384C2311yescharacteristic
273#384C2311yescharacteristic
274#384C2311yescharacteristic
275#382C2311yescharacteristic
276#382C2311yescharacteristic
277#382C2311yescharacteristic
278#382C2311yescharacteristic
279#382C2311yescharacteristic
280#382C2311yescharacteristic
281#381—22no—
282#380—22no—
283#380—22no—
284#380C2312yes—
285#379—22no—
286#379—22no—
287C4×C4⋊C4—22no—
288C4×C4⋊C4C2311yescharacteristic
289C4×C22⋊C4C2311yescharacteristic
290C4×C22⋊C4C2311yescharacteristic
291#376C2311yescharacteristic
292#340C2312yes—
293#340C2312yes—
294#340C2312yes—
295#340C2312yes—
296#340C2312yes—
297#340C2312yes—
298#340C2312yes—
299#340C2312yes—
300#340C2312yes—
301#340C2312yes—
302#340C2312yes—
303#340C2312yes—
304#336C2312yes—
305#336C2312yes—
306#336C2312yes—
307#336C2312yes—
308#336C2312yes—
309C25—22no—
310C22×Q8—21no—
311C22×Q8C2411yescharacteristic
312C22×D4—24no—
313C22×D4—21no—
314C22×D4—22no—
315C22×D4—21no—
316C22×D4—22no—
317C22×D4—22no—
318C22×D4—22no—
319C22×D4—22no—
320C22×D4—22no—
321C22×D4—22no—
322C22×D4—24no—
323C22×D4—24no—
324C22×D4—42no—
325C22×D4—42no—
326C22×D4—42no—
327C22×D4—48no—
328C22×D4—84no—
329C22×D4—84no—
330C22×D4C2×D411yescharacteristic
331C22×D4C2411yescharacteristic
332C22×D4C2412yes—
333C22×D4C2412yes—
334C23×C4—21no—
335C23×C4—22no—
336C23×C4—21no—
337C23×C4—22no—
338C23×C4C2×D412yes—
339C23×C4C2411yescharacteristic
340C23×C4C2411yescharacteristic
341C2×SD16—24no—
342C2×SD16—42no—
343C2×SD16—42no—
344C2×SD16—42no—
345C2×SD16—42no—
346C2×SD16—42no—
347C2×D8—24no—
348C2×D8—42no—
349C2×D8—42no—
350C2×D8—42no—
351C2×D8—42no—
352C2×D8—42no—
353C2×M16—24no—
354C2×M16—42no—
355C2×M16—42no—
356C22×C8C2412yes—
357C22×C8C2412yes—
358C22×C8C2412yes—
359C22×C8C2412yes—
360C4⋊Q8—42no—
361#127—24no—
362#127—22no—
363#127—22no—
364#127—22no—
365#127—42no—
366#127—48no—
367#127#4114yes—
368#126—44no—
369#126—44no—
370#126—44no—
371#125—22no—
372#125—22no—
373#125—42no—
374#124—22no—
375#124—22no—
376#124—44no—
377#123—44no—
378#123—48no—
379#123—84no—
380C22⋊Q8—24no—
381C22⋊Q8—42no—
382#121—24no—
383#121—24no—
384#121—48no—
385#121—42no—
386#121—42no—
387#121—44no—
388#121—42no—
389#121—42no—
390#121—84no—
391#120—84no—
392C4×Q8—42no—
393C4×Q8—44no—
394C4×D4—24no—
395C4×D4—24no—
396C4×D4—42no—
397C4×D4—42no—
398C4×D4—42no—
399C4×D4—42no—
400C4×D4—44no—
401#117—22no—
402#117—22no—
403#117—24no—
404#117—24no—
405#117—42no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—42no—
420C2×C4⋊C4C2×D412yes—
421C2×C4⋊C4C2×D411yescharacteristic
422C2×C4⋊C4C2×D412yes—
423C2×C4⋊C4C2411yescharacteristic
424C2×C4⋊C4C2411yescharacteristic
425C2×C4⋊C4C2411yescharacteristic
426C2×C4⋊C4C2411yescharacteristic
427C2×C4⋊C4C2411yescharacteristic
428C2×C4⋊C4C2411yescharacteristic
429C2×C4⋊C4C2412yes—
430C2×C4⋊C4C2412yes—
431C2×C22⋊C4—22no—
432C2×C22⋊C4—21no—
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—22no—
439C2×C22⋊C4—21no—
440C2×C22⋊C4—22no—
441C2×C22⋊C4—21no—
442C2×C22⋊C4—22no—
443C2×C22⋊C4—22no—
444C2×C22⋊C4—22no—
445C2×C22⋊C4—22no—
446C2×C22⋊C4—22no—
447C2×C22⋊C4—22no—
448C2×C22⋊C4—22no—
449C2×C22⋊C4—22no—
450C2×C22⋊C4—22no—
451C2×C22⋊C4—22no—
452C2×C22⋊C4—22no—
453C2×C22⋊C4—22no—
454C2×C22⋊C4—22no—
455C2×C22⋊C4—22no—
456C2×C22⋊C4—84no—
457C2×C22⋊C4C2×D412yes—
458C2×C22⋊C4C2×D411yescharacteristic
459C2×C22⋊C4C2×D411yescharacteristic
460C2×C22⋊C4C2×D412yes—
461C2×C22⋊C4C2×D412yes—
462C2×C42—22no—
463C2×C42—22no—
464C2×C42—21no—
465C2×C42—21no—
466C2×C42—21no—
467C2×C42—21no—
468C2×C42C2×D412yes—
469C2×C42C2411yescharacteristic
470C2×C42C2411yescharacteristic
471C2×C42C2411yescharacteristic
472C2×C42C2411yescharacteristic
473C2×C42C2411yescharacteristic
474C4⋊C8—42no—
475C4⋊C8—42no—
476#103—42no—
477#103—42no—
478#102—42no—
479#102—42no—
480#102—42no—
481#102—42no—
482#102—42no—
483#102—42no—
484#102—42no—
485#102—42no—
486#102—42no—
487#102—42no—
488#102—42no—
489#102—42no—
490#102—42no—
491#102—42no—
492C22⋊C8—24no—
493C22⋊C8—42no—
494C22⋊C8—42no—
495#97—22no—
496#97—22no—
497#97—42no—
498C4×C8—22no—
499C4×C8—22no—
500#95—22no—
501#95—22no—
502#95—22no—
503#95—22no—
504#95—22no—
505#95—22no—
506#95—22no—
507#95—22no—
508#95—22no—
509#95—22no—
510#95—22no—
511#95C2×D412yes—
512#95C2×D412yes—
513#95C2×D412yes—
514#95C2×D412yes—
515#95C2×D412yes—
516C24—22no—
517C24—21no—
518C24—22no—
519C24—44no—
520C24—44no—
521C24—44no—
522C24—44no—
523C24—82no—
524C24—82no—
525C24—82no—
526C24C22×D411yescharacteristic
527C24C22×D411yescharacteristic
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—22no—
531C2×Q8—22no—
532C2×Q8—42no—
533C2×Q8—82no—
534C2×D4—22no—
535C2×D4—28no—
536C2×D4—21no—
537C2×D4—22no—
538C2×D4—22no—
539C2×D4—22no—
540C2×D4—22no—
541C2×D4—22no—
542C2×D4—22no—
543C2×D4—21no—
544C2×D4—22no—
545C2×D4—22no—
546C2×D4—22no—
547C2×D4—22no—
548C2×D4—22no—
549C2×D4—22no—
550C2×D4—22no—
551C2×D4—48no—
552C2×D4—48no—
553C2×D4—42no—
554C2×D4—44no—
555C2×D4—44no—
556C2×D4—44no—
557C2×D4—44no—
558C2×D4—44no—
559C2×D4—42no—
560C2×D4—44no—
561C2×D4—42no—
562C2×D4—44no—
563C2×D4—44no—
564C2×D4—84no—
565C2×D4—84no—
566C2×D4—82no—
567C2×D4—82no—
568C2×D4—82no—
569C2×D4—82no—
570C2×D4—82no—
571C2×D4—82no—
572C2×D4—82no—
573C2×D4—82no—
574C2×D4—832no—
575C2×D4—82no—
576C2×D4—82no—
577C2×D4—82no—
578C2×D4—82no—
579C2×D4—82no—
580C2×D4—82no—
581C2×D4C2×#4114yes—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—22no—
585C22×C4—24no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—22no—
597C22×C4—21no—
598C22×C4—22no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4—44no—
602C22×C4—42no—
603C22×C4—42no—
604C22×C4—82no—
605C22×C4—82no—
606C22×C4—82no—
607C22×C4—82no—
608C22×C4—82no—
609C22×C4—82no—
610C22×C4—82no—
611C22×C4C22×D412yes—
612C22×C4C22×D412yes—
613C22×C4C22×D412yes—
614C22×C4C22×D411yescharacteristic
615C22×C4C22×D411yescharacteristic
616C22×C4C22×D411yescharacteristic
617C22×C4C22×D411yescharacteristic
618C22×C4C22×D412yes—
619C22×C4H(5,𝔽2)14yes—
620C22×C4C2511yescharacteristic
621SD16—84no—
622SD16—84no—
623D8—84no—
624D8—84no—
625M16—48no—
626C2×C8—22no—
627C2×C8—22no—
628C2×C8—22no—
629C2×C8—22no—
630C2×C8—22no—
631C2×C8—22no—
632C2×C8—22no—
633C2×C8—22no—
634C2×C8—22no—
635C2×C8—22no—
636C2×C8—22no—
637C2×C8—22no—
638C4⋊C4—22no—
639C4⋊C4—24no—
640C4⋊C4—22no—
641C4⋊C4—22no—
642C4⋊C4—22no—
643C4⋊C4—22no—
644C4⋊C4—22no—
645C4⋊C4—22no—
646C4⋊C4—22no—
647C4⋊C4—22no—
648C4⋊C4—22no—
649C4⋊C4—22no—
650C4⋊C4—42no—
651C4⋊C4—42no—
652C4⋊C4—42no—
653C4⋊C4—42no—
654C4⋊C4—42no—
655C4⋊C4—42no—
656C4⋊C4—44no—
657C4⋊C4—42no—
658C4⋊C4—42no—
659C4⋊C4—44no—
660C4⋊C4—82no—
661C4⋊C4—82no—
662C4⋊C4—82no—
663C4⋊C4—82no—
664C22⋊C4—22no—
665C22⋊C4—22no—
666C22⋊C4—24no—
667C22⋊C4—42no—
668C22⋊C4—42no—
669C22⋊C4—44no—
670C22⋊C4—44no—
671C22⋊C4—42no—
672C22⋊C4—42no—
673C22⋊C4—44no—
674C22⋊C4—42no—
675C22⋊C4—42no—
676C22⋊C4—42no—
677C22⋊C4—42no—
678C22⋊C4—42no—
679C22⋊C4—42no—
680C22⋊C4—44no—
681C22⋊C4—82no—
682C22⋊C4—82no—
683C22⋊C4—82no—
684C22⋊C4—82no—
685C22⋊C4—82no—
686C22⋊C4—82no—
687C22⋊C4—82no—
688C22⋊C4—82no—
689C22⋊C4—82no—
690C22⋊C4—82no—
691C22⋊C4—82no—
692C22⋊C4—82no—
693C22⋊C4—82no—
694C42—24no—
695C42—21no—
696C42—21no—
697C42—21no—
698C42—21no—
699C42—22no—
700C42—22no—
701C42—42no—
702C42—42no—
703C42—42no—
704C42—42no—
705C42C2×#4112yes—
706C42H(5,𝔽2)12yes—
707C23—22no—
708C23—22no—
709C23—21no—
710C23—21no—
711C23—22no—
712C23—22no—
713C23—21no—
714C23—21no—
715C23—24no—
716C23—21no—
717C23—42no—
718C23—42no—
719C23—42no—
720C23—42no—
721C23—42no—
722C23—42no—
723C23—42no—
724C23—42no—
725C23—42no—
726C23—42no—
727C23—42no—
728C23—42no—
729C23—41no—
730C23—42no—
731C23—41no—
732C23—42no—
733C23—42no—
734C23—41no—
735C23—88no—
736C23—88no—
737C23—88no—
738C23—88no—
739C23—164no—
740C23—164no—
741C23—164no—
742C23#53512yes—
743C23C23×D411yescharacteristic
744Q8—42no—
745Q8—42no—
746Q8—84no—
747D4—24no—
748D4—24no—
749D4—42no—
750D4—42no—
751D4—42no—
752D4—42no—
753D4—42no—
754D4—42no—
755D4—42no—
756D4—42no—
757D4—88no—
758D4—88no—
759D4—88no—
760D4—82no—
761D4—88no—
762D4—88no—
763D4—84no—
764D4—162no—
765D4—164no—
766D4—164no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—24no—
772C2×C4—24no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—21no—
787C2×C4—22no—
788C2×C4—21no—
789C2×C4—48no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—42no—
810C2×C4—41no—
811C2×C4—42no—
812C2×C4—41no—
813C2×C4—164no—
814C2×C4—162no—
815C2×C4—164no—
816C2×C4—162no—
817C2×C4#53512yes—
818C2×C4#54614yes—
819C2×C4C22×#4111yescharacteristic
820C2×C4C2×H(5,𝔽2)12yes—
821C2×C4C2×H(5,𝔽2)11yescharacteristic
822C2×C4#58512yes—
823C8—42no—
824C8—42no—
825C8—42no—
826C8—42no—
827C22—22no—
828C22—22no—
829C22—22no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—41no—
834C22—41no—
835C22—41no—
836C22—44no—
837C22—44no—
838C22—44no—
839C22—42no—
840C22—82no—
841C22—82no—
842C22—82no—
843C22—82no—
844C22—82no—
845C22—82no—
846C22—82no—
847C22—81no—
848C22—82no—
849C22—81no—
850C22—82no—
851C22—82no—
852C22—81no—
853C22—82no—
854C22—82no—
855C22—82no—
856C22—1616no—
857C22C2×#53511yescharacteristic
858C22C2×#54611yescharacteristic
859C22#350011yescharacteristic
860C22#358512yes—
861C22#358512yes—
862C4—22no—
863C4—24no—
864C4—42no—
865C4—41no—
866C4—41no—
867C4—41no—
868C4—42no—
869C4—42no—
870C4—82no—
871C4—81no—
872C4—81no—
873C4—81no—
874C4—81no—
875C4—81no—
876C4—81no—
877C4—81no—
878C4—82no—
879C4#351312yes—
880C4#354212yes—
881C2—42no—
882C2—81no—
883C2—84no—
884C2—161no—
885C2—162no—
886C2#3808211yescharacteristic
887C2#6080811yescharacteristic
888C2#6082511yescharacteristic
889C2#6117512yes—
890C2#6256412yes—
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2290 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #37870C2semidirect
2. #37694C2semidirect
3. #33050C2semidirect
4. #31855C2semidirect
5. #31850C2semidirect
6. #31665C2semidirect
7. #31662C2semidirect
8. #30209C2semidirect
9. #29816C2semidirect
10. #29152C2semidirect
11. #28630C2semidirect
12. #27986C2semidirect
13. #27967C2semidirect
14. #25725C2semidirect
15. #25611C2semidirect
16. #24539C2semidirect
17. #24538C2semidirect
18. #23979C2semidirect
19. #23973C2semidirect
20. #22279C2semidirect
21. #21872C2semidirect
22. #21203C2semidirect
23. #21104C2semidirect
30. C2×#488C22semidirect
33. C2×#433C22semidirect
43. #2660C22semidirect
45. #2620C22semidirect
47. #2565C22semidirect
48. #2563C22semidirect
49. #2503C22semidirect
51. #2500C22semidirect
62. #2326C22semidirect
63. #2317C22semidirect
66. #2101C22semidirect
67. #2101C22semidirect
68. #2073C22semidirect
69. #2073C22semidirect
70. #2071C22semidirect
71. #2071C22semidirect
72. #2055C22semidirect
73. #2055C22semidirect
74. #2054C22semidirect
75. #2054C22semidirect
76. #2025C22semidirect
77. #2025C22semidirect
78. #2023C22semidirect
79. #2023C22semidirect
82. #2000C22semidirect
83. #2000C22semidirect
84. #1999C22semidirect
85. #1999C22semidirect
86. #1992C22semidirect
87. #1992C22semidirect
88. #1991C22semidirect
93. #1958C22semidirect
98. #1936C22semidirect
99. #1935C22semidirect
100. #1924C22semidirect
101. #1917C22semidirect
104. #1880C22semidirect
105. #1880C22semidirect
106. #1879C22semidirect
107. #1879C22semidirect
108. #1879C22semidirect
109. #1879C22semidirect
110. #1877C22semidirect
111. #1877C22semidirect
112. #1875C22semidirect
113. #1875C22semidirect
114. #1874C22semidirect
115. #1874C22semidirect
118. #1836C22semidirect
119. #1836C22semidirect
120. #1835C22semidirect
123. #1804C22semidirect
124. #1804C22semidirect
125. #1802C22semidirect
126. #1802C22semidirect
127. #1768C22semidirect
128. #1750C22semidirect
130. #1746C22semidirect

Maximal subgroups

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

subgroupindex
#378702
#376942
#330502
#318552
#318502
#316652
#316622
#302092
#298162
#291522
#286302
#279862
#279672
#257252
#256112
#245392
#245382
#239792
#239732
#222792
#218722
#212032
#211042