Finite Group Databasebeta

← #6574558

Subgroups — #6574558

Order 512.

2169 conjugacy classes of subgroups.

The subgroup lattice has 870 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3081C212yesmaximal, complemented
2#39365C211yesmaximal, characteristic, complemented
3#34310C211yesmaximal, characteristic
4#33199C211yesmaximal, characteristic, complemented
5#32966C212yesmaximal, complemented
6#28516C211yesmaximal, characteristic, complemented
7#28280C211yesmaximal, characteristic, complemented
8#26475C212yesmaximal, complemented
9#26357C212yesmaximal, complemented
10#26347C212yesmaximal, complemented
11#26053C212yesmaximal, complemented
12#25968C212yesmaximal, complemented
13#25958C212yesmaximal, complemented
14#24852C212yesmaximal, complemented
15#24309C212yesmaximal, complemented
16#22662C212yesmaximal, complemented
17#22652C211yesmaximal, characteristic, complemented
18#22423C212yesmaximal
19#21613C211yesmaximal, characteristic, complemented
20C2×D42C2211yescharacteristic
21C2×#544C2212yescomplemented
22C2×#518C2212yes—
23#3081—216no—
24C2×#478C2212yes—
25C2×#478C2212yes—
26C2×#478C2212yescomplemented
27C2×#478C2212yescomplemented
28C2×#478C2212yescomplemented
29C2×#476C2212yes—
30C2×#476C2212yescomplemented
31C2×#474C2211yescharacteristic
32C2×#474C2212yescomplemented
33C2×#435C2212yes—
34C2×#428C2212yescomplemented
35C2×#427C2212yescomplemented
36C2×#424C2212yescomplemented
37C2×#418C2212yes—
38C22×#102C2212yes—
39#2859C2211yescharacteristic, complemented
40#2734—21no—
41#2732—21no—
42#2726—21no—
43#2683—21no—
44#2629C2212yescomplemented
45#2556—22no—
46#2550C2212yescomplemented
47#2441C2212yescomplemented
48#2440C2212yescomplemented
49#2429—22no—
50#2366C2211yescharacteristic
51#2363C2212yes—
52#2361—21no—
53#2358—22no—
54#2354C2211yescharacteristic
55#2352C2212yes—
56D4×C4⋊C4C2211yescharacteristic
57D4×C22⋊C4—21no—
58D4×C22⋊C4C2212yes—
59#2324C2212yes—
60#2321—22no—
61C4×C4⋊Q8C2211yescharacteristic, complemented
62C4×#127C2211yescharacteristic
63C4×#121—21no—
64#2293C2211yescharacteristic
65C2×#390—21no—
66C42×D4C2211yescharacteristic
67#2094C2212yescomplemented
68#2093C2212yescomplemented
69#2088C2212yescomplemented
70#2086C2212yescomplemented
71#2065C2212yescomplemented
72#2065C2212yescomplemented
73#2065C2212yescomplemented
74#2065C2212yescomplemented
75#2059C2212yescomplemented
76#2058C2212yescomplemented
77#2025C2212yescomplemented
78#2023C2212yescomplemented
79#1989C2212yescomplemented
80#1988C2211yescharacteristic, complemented
81#1982C2212yes—
82#1961C2212yes—
83#1949C2212yescomplemented
84#1948C2211yescharacteristic, complemented
85#1948C2212yescomplemented
86#1948C2211yescharacteristic, complemented
87#1947C2211yescharacteristic, complemented
88#1940C2212yescomplemented
89#1921C2212yescomplemented
90#1895C2212yes—
91#1893C2212yes—
92#1875C2212yes—
93#1874C2212yes—
94#1864C2212yes—
95#1864C2212yes—
96#1864C2212yescomplemented
97#1862C2212yes—
98#1862C2212yescomplemented
99#1854C2212yescomplemented
100#1854C2212yescomplemented
101#1854C2212yescomplemented
102#1853C2212yescomplemented
103#1851C2212yescomplemented
104#1850C2212yescomplemented
105#1847C2212yescomplemented
106#1842C2211yescharacteristic, complemented
107#1809C2212yescomplemented
108#1807C2212yescomplemented
109#1804C2212yes—
110#1802C2211yescharacteristic
111#1802C2211yescharacteristic
112#1802C2211yescharacteristic
113#1802C2212yescomplemented
114#1798C2212yescomplemented
115#1786C2212yes—
116#1786C2212yes—
117#1776C2212yescomplemented
118#1767C2211yescharacteristic, complemented
119#1762C2212yes—
120C23×D4—21no—
121C23×D4C2312yes—
122C22×M16C2312yes—
123C23×C8C2312yes—
124D42—24no—
125D42Q818yescomplemented
126#544—28no—
127#544—44no—
128C2×C4⋊Q8—22no—
129C2×C4⋊Q8C2312yes—
130C2×C4⋊Q8C2311yescharacteristic
131C2×#127C2311yescharacteristic
132C2×#125—22no—
133C2×#125C2312yes—
134C2×#125C2312yes—
135C2×C22⋊Q8—22no—
136C2×C22⋊Q8—22no—
137C2×C22⋊Q8—22no—
138C2×#121—21no—
139C2×#121C2312yes—
140C2×#120—22no—
141#518—28no—
142#518—44no—
143C2×C4×Q8—21no—
144C2×C4×D4—22no—
145C2×C4×D4—22no—
146C2×C4×D4—21no—
147C2×C4×D4—21no—
148C2×C4×D4—21no—
149C2×C4×D4C2312yes—
150C2×C4×D4C2312yes—
151C2×C4×D4C2312yes—
152C2×C4×D4C2311yescharacteristic
153C2×C4×D4C2311yescharacteristic
154C2×C4×D4C2311yescharacteristic
155C2×C4×D4C2311yescharacteristic
156C2×#117C2312yes—
157C2×#117C2312yes—
158C2×#117C2312yes—
159C22×C4⋊C4—21no—
160C22×C4⋊C4C2312yes—
161C22×C22⋊C4—22no—
162C22×C22⋊C4—22no—
163C22×C22⋊C4—22no—
164C22×C42—21no—
165#478—28no—
166#478—28no—
167#478—28no—
168#478—28no—
169#478—44no—
170#476—28no—
171#476—28no—
172#474—28no—
173#474D418yescomplemented
174#435—28no—
175#428—28no—
176#427—28no—
177C2×#107C2312yes—
178C2×#107C2312yes—
179C2×#107C2312yes—
180C2×#107C2312yes—
181C2×#106C2312yes—
182C2×#106C2312yes—
183C2×#106C2312yes—
184C2×#106C2312yes—
185C2×#106C2312yes—
186C2×#106C2312yes—
187#424—28no—
188C2×C4⋊C8C2312yes—
189C2×C4⋊C8C2312yes—
190C2×C4⋊C8C2311yescharacteristic
191C2×C4⋊C8C2312yes—
192C2×C4⋊C8C2312yes—
193C2×C4⋊C8C2311yescharacteristic
194C2×C4⋊C8C2311yescharacteristic
195C2×C4⋊C8C2311yescharacteristic
196#418—28no—
197C2×#102—28no—
198C2×#102C2312yes—
199C2×#102C2312yes—
200C2×#102C2312yes—
201C2×#102C2312yes—
202C2×#102C2312yes—
203C2×#102C2312yes—
204C2×#102C2312yes—
205C2×#102C2312yes—
206C2×#102C2312yes—
207C2×#102C2312yes—
208C2×#102C2312yes—
209C2×#102C2312yes—
210C2×C22⋊C8C2312yes—
211C2×C22⋊C8C2312yes—
212C2×#97C2312yes—
213#399—22no—
214#398—22no—
215#398—22no—
216#398—22no—
217#398—22no—
218#396—22no—
219#396—22no—
220#396—22no—
221#395—22no—
222#395—22no—
223#391—21no—
224#391—22no—
225#390—21no—
226#390—21no—
227#390—22no—
228#390—22no—
229#390—21no—
230#390—21no—
231#390D411yescharacteristic
232#390D411yescharacteristic
233#390C2312yes—
234#390C2312yes—
235#389—21no—
236#389—21no—
237#389—21no—
238#389—21no—
239#389—21no—
240#389—22no—
241#389—22no—
242#389D411yescharacteristic
243#389D411yescharacteristic
244#389C2312yes—
245#389C2312yes—
246#389C2312yes—
247#389C2312yes—
248#388—22no—
249#388—22no—
250#388—22no—
251#388—22no—
252#388D412yes—
253#388D412yes—
254#387—22no—
255#387—22no—
256#386—22no—
257#386—22no—
258#386—22no—
259#386—22no—
260#386—22no—
261#386—22no—
262#385—22no—
263#385—22no—
264#385—22no—
265#384C2311yescharacteristic
266#384C2311yescharacteristic
267#384C2311yescharacteristic
268#384C2311yescharacteristic
269#382C2312yes—
270#380—21no—
271#380C2312yes—
272#380C2312yes—
273#380C2312yes—
274#379—22no—
275C4×C4⋊C4—21no—
276C4×C4⋊C4—21no—
277C4×C4⋊C4C2312yes—
278C4×C4⋊C4C2311yescharacteristic
279C4×C4⋊C4C2311yescharacteristic
280C4×C4⋊C4C2311yescharacteristic
281C4×C4⋊C4C2311yescharacteristic
282C4×C22⋊C4—22no—
283C4×C22⋊C4—21no—
284C4×C22⋊C4—21no—
285C4×C22⋊C4—21no—
286C4×C22⋊C4—22no—
287C4×C22⋊C4C2312yes—
288C43C2311yescharacteristic
289#340C2312yes—
290#340C2312yes—
291#340C2312yes—
292#340C2312yes—
293#340C2312yes—
294#340C2312yes—
295#340C2312yes—
296#340C2312yes—
297#340C2312yes—
298#340C2312yes—
299#336C2312yes—
300#336C2312yes—
301#336C2312yes—
302C25—22no—
303C22×Q8—21no—
304C22×Q8—22no—
305C22×D4—24no—
306C22×D4—24no—
307C22×D4—22no—
308C22×D4—28no—
309C22×D4—22no—
310C22×D4—21no—
311C22×D4—21no—
312C22×D4—24no—
313C22×D4—42no—
314C22×D4—42no—
315C22×D4—82no—
316C22×D4—82no—
317C22×D4C2×D411yescharacteristic
318C22×D4C2×Q818yes—
319C22×D4C2412yes—
320C22×D4C2411yescharacteristic
321C23×C4—21no—
322C23×C4—21no—
323C23×C4—22no—
324C23×C4—21no—
325C23×C4—22no—
326C23×C4—22no—
327C23×C4—22no—
328C23×C4C2412yes—
329C2×M16—24no—
330C2×M16—24no—
331C2×M16—42no—
332C22×C8—24no—
333C22×C8—24no—
334C22×C8—42no—
335C22×C8C2412yes—
336C22×C8C2412yes—
337C22×C8C2412yes—
338C22×C8C2412yes—
339C4⋊Q8—24no—
340C4⋊Q8—22no—
341C4⋊Q8—42no—
342C4⋊Q8—48no—
343C4⋊Q8C2×D414yescomplemented
344#127—22no—
345#127C2×Q814yes—
346#125—24no—
347#125—24no—
348#125—24no—
349#125—42no—
350#125—48no—
351C22⋊Q8—48no—
352C22⋊Q8—48no—
353C22⋊Q8—84no—
354#121—24no—
355#121—28no—
356#121C2×Q818yes—
357#120—216no—
358C4×Q8—82no—
359C4×D4—24no—
360C4×D4—22no—
361C4×D4—24no—
362C4×D4—24no—
363C4×D4—22no—
364C4×D4—22no—
365C4×D4—24no—
366C4×D4—41no—
367C4×D4—42no—
368C4×D4—42no—
369C4×D4—48no—
370C4×D4—48no—
371C4×D4—82no—
372C4×D4—82no—
373C4×D4—82no—
374C4×D4C2×D414yes—
375C4×D4C2×Q814yes—
376C4×D4C2×Q814yes—
377C4×D4#4114yes—
378#117—24no—
379#117—24no—
380#117—24no—
381#117—24no—
382#117—42no—
383#117—42no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—24no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—42no—
405C2×C4⋊C4—82no—
406C2×C4⋊C4C2×D412yes—
407C2×C4⋊C4C2×D412yes—
408C2×C4⋊C4C2×D411yescharacteristic
409C2×C4⋊C4C2×D411yescharacteristic
410C2×C4⋊C4C2×D411yescharacteristic
411C2×C4⋊C4C2412yes—
412C2×C4⋊C4C2412yes—
413C2×C4⋊C4C2412yes—
414C2×C4⋊C4C2411yescharacteristic
415C2×C4⋊C4C2412yes—
416C2×C4⋊C4C2412yes—
417C2×C4⋊C4C2411yescharacteristic
418C2×C4⋊C4C2411yescharacteristic
419C2×C22⋊C4—21no—
420C2×C22⋊C4—21no—
421C2×C22⋊C4—22no—
422C2×C22⋊C4—22no—
423C2×C22⋊C4—22no—
424C2×C22⋊C4—22no—
425C2×C22⋊C4—22no—
426C2×C22⋊C4—22no—
427C2×C22⋊C4—22no—
428C2×C22⋊C4—21no—
429C2×C22⋊C4—22no—
430C2×C22⋊C4—22no—
431C2×C22⋊C4—22no—
432C2×C22⋊C4—22no—
433C2×C22⋊C4—22no—
434C2×C22⋊C4—22no—
435C2×C22⋊C4—48no—
436C2×C22⋊C4—48no—
437C2×C22⋊C4—84no—
438C2×C22⋊C4C2×D412yes—
439C2×C22⋊C4C2×D412yes—
440C2×C22⋊C4C2×D412yes—
441C2×C22⋊C4C2×D412yes—
442C2×C22⋊C4C2×D412yes—
443C2×C42—22no—
444C2×C42—22no—
445C2×C42—21no—
446C2×C42—22no—
447C2×C42—21no—
448C2×C42—21no—
449C2×C42—82no—
450C2×C42C2×D411yescharacteristic
451C2×C42C2×D411yescharacteristic
452C2×C42C2×D411yescharacteristic
453C2×C42C2×D411yescharacteristic
454C2×C42C2412yes—
455C2×C42C2411yescharacteristic
456C2×C42C2411yescharacteristic
457C2×C42C2411yescharacteristic
458#107—24no—
459#107—24no—
460#107—42no—
461#107C2×D418yescomplemented
462#106—24no—
463#106—24no—
464#106—24no—
465#106—24no—
466#106—42no—
467#106—42no—
468C4⋊C8—24no—
469C4⋊C8—24no—
470C4⋊C8—24no—
471C4⋊C8—24no—
472C4⋊C8—22no—
473C4⋊C8—41no—
474C4⋊C8—41no—
475C4⋊C8C2×D414yescomplemented
476#102—24no—
477#102—24no—
478#102—24no—
479#102—24no—
480#102—24no—
481#102—24no—
482#102—24no—
483#102—42no—
484#102—42no—
485#102—42no—
486#102—42no—
487#102C2×D418yes—
488C22⋊C8—24no—
489C22⋊C8—24no—
490#97—24no—
491#95—21no—
492#95—21no—
493#95—21no—
494#95—22no—
495#95—22no—
496#95—22no—
497#95—22no—
498#95—22no—
499#95—22no—
500#95—22no—
501#95—22no—
502#95—22no—
503#95—22no—
504#95C2×D412yes—
505#95C2×D412yes—
506#95C2×D412yes—
507C24—21no—
508C24—22no—
509C24—28no—
510C24—44no—
511C24—44no—
512C24—82no—
513C24—82no—
514C24—82no—
515C24—82no—
516C24C22×D412yes—
517C2×Q8—24no—
518C2×Q8—44no—
519C2×Q8—81no—
520C2×Q8—81no—
521C2×Q8—82no—
522C2×Q8—82no—
523C2×D4—216no—
524C2×D4—28no—
525C2×D4—28no—
526C2×D4—24no—
527C2×D4—24no—
528C2×D4—22no—
529C2×D4—21no—
530C2×D4—22no—
531C2×D4—21no—
532C2×D4—22no—
533C2×D4—22no—
534C2×D4—21no—
535C2×D4—22no—
536C2×D4—48no—
537C2×D4—48no—
538C2×D4—48no—
539C2×D4—41no—
540C2×D4—41no—
541C2×D4—44no—
542C2×D4—44no—
543C2×D4—42no—
544C2×D4—42no—
545C2×D4—81no—
546C2×D4—81no—
547C2×D4—816no—
548C2×D4—82no—
549C2×D4—82no—
550C2×D4C22⋊Q814yes—
551C2×D4C22×D412yes—
552C2×D4C22×Q814yes—
553C2×D4C22×Q812yes—
554C2×D42−1+412yes—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—22no—
562C22×C4—24no—
563C22×C4—24no—
564C22×C4—22no—
565C22×C4—21no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—44no—
570C22×C4—42no—
571C22×C4—42no—
572C22×C4—42no—
573C22×C4—44no—
574C22×C4—44no—
575C22×C4—42no—
576C22×C4—44no—
577C22×C4—81no—
578C22×C4—81no—
579C22×C4—81no—
580C22×C4—82no—
581C22×C4—82no—
582C22×C4—82no—
583C22×C4—82no—
584C22×C4—82no—
585C22×C4—82no—
586C22×C4—82no—
587C22×C4—82no—
588C22×C4C22×D412yes—
589C22×C4C22×D411yescharacteristic
590C22×C4C22×D412yes—
591C22×C4C22×D411yescharacteristic
592C22×C4C22×D411yescharacteristic
593C22×C4C22×D412yes—
594C22×C4C22×D411yescharacteristic
595C22×C4C22×D411yescharacteristic
596C22×C4C22×D411yescharacteristic
597C22×C4C22×Q814yes—
598C22×C4C2×#4114yes—
599C22×C4C2511yescharacteristic
600M16—48no—
601C2×C8—22no—
602C2×C8—22no—
603C2×C8—22no—
604C2×C8—22no—
605C2×C8—22no—
606C2×C8—22no—
607C2×C8—22no—
608C2×C8—22no—
609C2×C8—22no—
610C2×C8—22no—
611C2×C8—22no—
612C2×C8—48no—
613C2×C8C22×D414yes—
614C4⋊C4—24no—
615C4⋊C4—24no—
616C4⋊C4—24no—
617C4⋊C4—21no—
618C4⋊C4—22no—
619C4⋊C4—21no—
620C4⋊C4—22no—
621C4⋊C4—22no—
622C4⋊C4—22no—
623C4⋊C4—22no—
624C4⋊C4—22no—
625C4⋊C4—22no—
626C4⋊C4—22no—
627C4⋊C4—21no—
628C4⋊C4—22no—
629C4⋊C4—21no—
630C4⋊C4—41no—
631C4⋊C4—41no—
632C4⋊C4—44no—
633C4⋊C4—44no—
634C4⋊C4—44no—
635C4⋊C4—44no—
636C4⋊C4—42no—
637C4⋊C4—44no—
638C4⋊C4—42no—
639C4⋊C4—44no—
640C4⋊C4—44no—
641C4⋊C4—42no—
642C4⋊C4—81no—
643C4⋊C4—81no—
644C4⋊C4—81no—
645C4⋊C4—82no—
646C4⋊C4—82no—
647C4⋊C4—81no—
648C4⋊C4—81no—
649C4⋊C4—82no—
650C4⋊C4C22⋊Q814yes—
651C4⋊C4C22×D414yes—
652C4⋊C4C22×D412yes—
653C4⋊C4C22×Q812yes—
654C22⋊C4—24no—
655C22⋊C4—28no—
656C22⋊C4—24no—
657C22⋊C4—24no—
658C22⋊C4—24no—
659C22⋊C4—24no—
660C22⋊C4—42no—
661C22⋊C4—44no—
662C22⋊C4—44no—
663C22⋊C4—44no—
664C22⋊C4—44no—
665C22⋊C4—42no—
666C22⋊C4—44no—
667C22⋊C4—44no—
668C22⋊C4—82no—
669C22⋊C4—82no—
670C22⋊C4—82no—
671C22⋊C4—82no—
672C22⋊C4—82no—
673C22⋊C4—82no—
674C22⋊C4C22⋊Q818yes—
675C42—22no—
676C42—22no—
677C42—22no—
678C42—21no—
679C42—21no—
680C42—41no—
681C42—41no—
682C42—41no—
683C42—44no—
684C42—44no—
685C42—42no—
686C42—81no—
687C42—81no—
688C42—82no—
689C42C22×D412yes—
690C42C22×Q812yes—
691C42C2×#4112yes—
692C42H(5,𝔽2)12yes—
693C23—22no—
694C23—22no—
695C23—22no—
696C23—22no—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—24no—
703C23—416no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23—42no—
714C23—88no—
715C23—88no—
716C23—164no—
717C23—164no—
718C23—164no—
719C23—164no—
720C23C2×C22⋊Q814yes—
721C23C23×D411yescharacteristic
722Q8—84no—
723Q8—164no—
724D4—24no—
725D4—22no—
726D4—22no—
727D4—24no—
728D4—22no—
729D4—44no—
730D4—416no—
731D4—48no—
732D4—42no—
733D4—42no—
734D4—84no—
735D4—88no—
736D4D4×Q814yes—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—22no—
745C2×C4—21no—
746C2×C4—22no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—24no—
750C2×C4—24no—
751C2×C4—24no—
752C2×C4—24no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—24no—
763C2×C4—21no—
764C2×C4—22no—
765C2×C4—48no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—42no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—42no—
772C2×C4—41no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—41no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—41no—
786C2×C4—42no—
787C2×C4—84no—
788C2×C4—84no—
789C2×C4—164no—
790C2×C4—164no—
791C2×C4—164no—
792C2×C4—164no—
793C2×C4C2×C22⋊Q812yes—
794C2×C4C2×C22⋊Q812yes—
795C2×C4C2×C22⋊Q814yes—
796C2×C4D4212yes—
797C2×C4D4212yes—
798C2×C4#57712yes—
799C2×C4C23×D411yescharacteristic
800C2×C4C23×Q811yescharacteristic
801C2×C4C22×#4111yescharacteristic
802C2×C4C2×H(5,𝔽2)11yescharacteristic
803C2×C4C2×2−1+411yescharacteristic
804C2×C4#58511yescharacteristic
805C8—24no—
806C8—42no—
807C8—42no—
808C8—42no—
809C22—24no—
810C22—24no—
811C22—24no—
812C22—24no—
813C22—42no—
814C22—42no—
815C22—42no—
816C22—42no—
817C22—42no—
818C22—42no—
819C22—42no—
820C22—42no—
821C22—42no—
822C22—42no—
823C22—44no—
824C22—44no—
825C22—44no—
826C22—82no—
827C22—82no—
828C22—82no—
829C22—82no—
830C22—1616no—
831C22C22×C22⋊Q811yescharacteristic
832C22C2×D4211yescharacteristic
833C22#348911yescharacteristic
834C22C2×#57711yescharacteristic
835C22#358511yescharacteristic
836C22#358511yescharacteristic
837C22#358511yescharacteristic
838C4—22no—
839C4—22no—
840C4—22no—
841C4—22no—
842C4—22no—
843C4—24no—
844C4—41no—
845C4—42no—
846C4—42no—
847C4—42no—
848C4—44no—
849C4—42no—
850C4—82no—
851C4—82no—
852C4—82no—
853C4—82no—
854C4—81no—
855C4C2×D4×Q811yescharacteristic
856C4D4×#4111yescharacteristic
857C4#350111yescharacteristic
858C4#352011yescharacteristic
859C2—44no—
860C2—44no—
861C2—84no—
862C2D4×C22⋊Q811yescharacteristic
863C2#6049011yescharacteristic
864C2#6049511yescharacteristic
865C2#6107911yescharacteristic
866C2#6109511yescharacteristic
867C2#6216411yescharacteristic
868C2#6223511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×D42C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2293 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3081C2semidirect
2. #39365C2semidirect
4. #33199C2semidirect
5. #32966C2semidirect
6. #28516C2semidirect
7. #28280C2semidirect
8. #26475C2semidirect
9. #26357C2semidirect
10. #26347C2semidirect
11. #26053C2semidirect
12. #25968C2semidirect
13. #25958C2semidirect
14. #24852C2semidirect
15. #24309C2semidirect
16. #22662C2semidirect
17. #22652C2semidirect
19. #21613C2semidirect
21. C2×#544C22semidirect
26. C2×#478C22semidirect
27. C2×#478C22semidirect
28. C2×#478C22semidirect
30. C2×#476C22semidirect
32. C2×#474C22semidirect
34. C2×#428C22semidirect
35. C2×#427C22semidirect
36. C2×#424C22semidirect
39. #2859C22semidirect
44. #2629C22semidirect
46. #2550C22semidirect
47. #2441C22semidirect
48. #2440C22semidirect
61. C4×C4⋊Q8C22semidirect
67. #2094C22semidirect
68. #2093C22semidirect
69. #2088C22semidirect
70. #2086C22semidirect
71. #2065C22semidirect
72. #2065C22semidirect
73. #2065C22semidirect
74. #2065C22semidirect
75. #2059C22semidirect
76. #2058C22semidirect
77. #2025C22semidirect
78. #2023C22semidirect
79. #1989C22semidirect
80. #1988C22semidirect
83. #1949C22semidirect
84. #1948C22semidirect
85. #1948C22semidirect
86. #1948C22semidirect
87. #1947C22semidirect
88. #1940C22semidirect
89. #1921C22semidirect
96. #1864C22semidirect
98. #1862C22semidirect
99. #1854C22semidirect
100. #1854C22semidirect
101. #1854C22semidirect
102. #1853C22semidirect
103. #1851C22semidirect
104. #1850C22semidirect
105. #1847C22semidirect
106. #1842C22semidirect
107. #1809C22semidirect
108. #1807C22semidirect
113. #1802C22semidirect
114. #1798C22semidirect
117. #1776C22semidirect
118. #1767C22semidirect
125. D42Q8semidirect
173. #474D4semidirect
343. C4⋊Q8C2×D4semidirect
461. #107C2×D4semidirect
475. C4⋊C8C2×D4semidirect

Maximal subgroups

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

subgroupindex
C2×#30812
#393652
#343102
#331992
#329662
#285162
#282802
#264752
#263572
#263472
#260532
#259682
#259582
#248522
#243092
#226622
#226522
#224232
#216132