Finite Group Databasebeta

← #6577887

Subgroups — #6577887

Order 512.

2153 conjugacy classes of subgroups.

The subgroup lattice has 875 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3123C212yesmaximal, complemented
2#39373C211yesmaximal, characteristic, complemented
3#34310C211yesmaximal, characteristic
4#33199C211yesmaximal, characteristic, complemented
5#32966C212yesmaximal, complemented
6#28516C211yesmaximal, characteristic, complemented
7#28252C211yesmaximal, characteristic, complemented
8#26572C212yesmaximal, complemented
9#26557C212yesmaximal, complemented
10#25025C212yesmaximal, complemented
11#24921C212yesmaximal, complemented
12#24901C212yesmaximal, complemented
13#24713C212yesmaximal, complemented
14#24252C212yesmaximal
15#24163C212yesmaximal, complemented
16#23010C212yesmaximal, complemented
17#22798C211yesmaximal, characteristic, complemented
18#22677C212yesmaximal, complemented
19#21504C211yesmaximal, characteristic, complemented
20C2×D42C2211yescharacteristic
21C2×#541C2212yescomplemented
22C2×#518C2212yes—
23#3123—216no—
24C2×#485C2212yescomplemented
25C2×#485C2212yescomplemented
26C2×#478C2212yes—
27C2×#478C2212yescomplemented
28C2×#478C2212yescomplemented
29C2×#460C2212yes—
30C2×#461C2211yescharacteristic
31C2×#461C2212yescomplemented
32C2×#450C2212yes—
33C2×#450C2212yes—
34C2×#440C2212yes—
35C2×#440C2212yes—
36C2×#440C2212yescomplemented
37C2×C4×SD16C2212yes—
38C2×C4×SD16C2212yescomplemented
39C2×#433C2212yescomplemented
40#2859C2211yescharacteristic, complemented
41#2727—21no—
42#2727—21no—
43#2726—21no—
44#2726—21no—
45#2629C2212yescomplemented
46#2536C2212yes—
47#2519—22no—
48#2519—22no—
49#2423C2212yescomplemented
50#2423C2212yescomplemented
51#2366C2211yescharacteristic
52#2363C2212yes—
53#2361—21no—
54#2358—22no—
55#2354C2211yescharacteristic
56#2351C2212yescomplemented
57D4×C4⋊C4C2211yescharacteristic
58D4×C22⋊C4—21no—
59D4×C22⋊C4C2212yes—
60#2324C2212yes—
61#2321—22no—
62C4×C4⋊Q8C2211yescharacteristic, complemented
63C4×#127C2211yescharacteristic
64C4×#121—21no—
65#2293C2211yescharacteristic
66C2×#390—21no—
67C42×D4C2211yescharacteristic
68#2094C2212yescomplemented
69#2093C2212yescomplemented
70#2077C2212yescomplemented
71#2076C2212yescomplemented
72#2055C2212yescomplemented
73#2055C2212yescomplemented
74#2036C2212yescomplemented
75#2035C2212yescomplemented
76#2033C2212yes—
77#2033C2212yes—
78#2000C2212yes—
79#2000C2212yes—
80#1989C2212yescomplemented
81#1981C2211yescharacteristic, complemented
82#1961C2212yes—
83#1955C2212yes—
84#1949C2212yescomplemented
85#1948C2211yescharacteristic, complemented
86#1947C2211yescharacteristic, complemented
87#1947C2211yescharacteristic, complemented
88#1943C2212yescomplemented
89#1942C2212yescomplemented
90#1936C2212yescomplemented
91#1934C2212yescomplemented
92#1928C2212yescomplemented
93#1924C2212yescomplemented
94#1923C2212yescomplemented
95#1880C2212yescomplemented
96#1880C2212yescomplemented
97#1877C2212yes—
98#1865C2212yescomplemented
99#1864C2212yes—
100#1864C2212yescomplemented
101#1863C2212yescomplemented
102#1862C2212yes—
103#1862C2212yescomplemented
104#1854C2212yescomplemented
105#1854C2212yescomplemented
106#1847C2212yescomplemented
107#1842C2211yescharacteristic, complemented
108#1804C2212yes—
109#1803C2212yescomplemented
110#1802C2211yescharacteristic
111#1802C2211yescharacteristic
112#1802C2211yescharacteristic
113#1802C2212yescomplemented
114#1798C2212yescomplemented
115#1786C2212yes—
116#1786C2212yes—
117#1771C2212yescomplemented
118#1767C2211yescharacteristic, complemented
119#1763C2212yescomplemented
120C23×D4—21no—
121C23×D4C2312yes—
122C22×SD16C2312yes—
123C22×SD16C2312yes—
124C22×SD16C2312yes—
125D42—24no—
126D42—24no—
127#541—28no—
128#541—44no—
129C2×C4⋊Q8C2311yescharacteristic
130C2×#127C2311yescharacteristic
131C2×#126—22no—
132C2×#126—22no—
133C2×#125—22no—
134C2×#125—22no—
135C2×#125C2312yes—
136C2×C22⋊Q8C2312yes—
137C2×C22⋊Q8C2312yes—
138C2×#121—21no—
139C2×#121C2312yes—
140C2×#120—22no—
141#518—28no—
142#518—44no—
143C2×C4×Q8C2312yes—
144C2×C4×Q8C2312yes—
145C2×C4×Q8C2312yes—
146C2×C4×D4—22no—
147C2×C4×D4—22no—
148C2×C4×D4—21no—
149C2×C4×D4—21no—
150C2×C4×D4—21no—
151C2×C4×D4C2312yes—
152C2×C4×D4C2311yescharacteristic
153C2×C4×D4C2312yes—
154C2×C4×D4C2312yes—
155C2×C4×D4C2311yescharacteristic
156C2×C4×D4C2311yescharacteristic
157C2×C4×D4C2311yescharacteristic
158C2×#117C2312yes—
159C2×#117C2312yes—
160C22×C4⋊C4—21no—
161C22×C22⋊C4—22no—
162C22×C22⋊C4—22no—
163C22×C22⋊C4—22no—
164C22×C42—21no—
165#485—28no—
166#485—28no—
167#478—28no—
168#478—28no—
169#478—44no—
170#461—28no—
171#461D418yescomplemented
172#460—28no—
173#450—28no—
174#450—28no—
175#440—28no—
176#440—28no—
177#440—28no—
178C4×SD16—28no—
179C4×SD16—28no—
180#433—28no—
181C2×#107C2312yes—
182C2×#107C2312yes—
183C2×#107C2312yes—
184C2×#107C2312yes—
185C2×#106C2312yes—
186C2×#106C2312yes—
187C2×#106C2312yes—
188C2×C4⋊C8C2312yes—
189C2×C4⋊C8C2311yescharacteristic
190C2×C4⋊C8C2312yes—
191C2×C4⋊C8C2311yescharacteristic
192C2×C4⋊C8C2311yescharacteristic
193C2×C4⋊C8C2311yescharacteristic
194C2×#103C2312yes—
195C2×#103C2312yes—
196C2×#103C2312yes—
197C2×#103C2312yes—
198C2×#103C2312yes—
199C2×#102C2312yes—
200C2×#102C2312yes—
201C2×#102C2312yes—
202C2×#102C2312yes—
203C2×#102C2312yes—
204C2×#102C2312yes—
205C2×#102C2312yes—
206C2×#102C2312yes—
207C2×#102C2312yes—
208C2×C22⋊C8C2312yes—
209C2×C22⋊C8C2312yes—
210C2×C22⋊C8C2312yes—
211C2×C22⋊C8C2312yes—
212C2×#97C2312yes—
213C2×#97C2312yes—
214C2×C4×C8C2312yes—
215#399—22no—
216#399—22no—
217#398—22no—
218#398—22no—
219#398—22no—
220#398—22no—
221#398—22no—
222#396—22no—
223#396—22no—
224#394—22no—
225#391C2312yes—
226#390—21no—
227#390—21no—
228#390—22no—
229#390—22no—
230#390—21no—
231#390—21no—
232#390D411yescharacteristic
233#390D411yescharacteristic
234#390C2312yes—
235#390C2312yes—
236#389—22no—
237#389—22no—
238#389—21no—
239#389—21no—
240#389—21no—
241#389—21no—
242#389—21no—
243#389—21no—
244#389D411yescharacteristic
245#389D411yescharacteristic
246#389C2312yes—
247#389C2312yes—
248#389C2312yes—
249#388—22no—
250#388—22no—
251#388—22no—
252#388—22no—
253#388—22no—
254#388—22no—
255#388—22no—
256#388D412yes—
257#388D412yes—
258#387—22no—
259#387—22no—
260#386—22no—
261#386—22no—
262#386—22no—
263#386—22no—
264#386—22no—
265#385—22no—
266#385—22no—
267#384C2311yescharacteristic
268#384C2311yescharacteristic
269#384C2311yescharacteristic
270#384C2311yescharacteristic
271#382—22no—
272#382C2312yes—
273#380—21no—
274#380C2312yes—
275#380C2312yes—
276#380C2312yes—
277#379—22no—
278C4×C4⋊C4—21no—
279C4×C4⋊C4—21no—
280C4×C4⋊C4—21no—
281C4×C4⋊C4—22no—
282C4×C4⋊C4C2311yescharacteristic
283C4×C4⋊C4C2311yescharacteristic
284C4×C4⋊C4C2311yescharacteristic
285C4×C4⋊C4C2311yescharacteristic
286C4×C22⋊C4—21no—
287C4×C22⋊C4—21no—
288C4×C22⋊C4—21no—
289C4×C22⋊C4—22no—
290C4×C22⋊C4C2312yes—
291C43C2311yescharacteristic
292#340C2312yes—
293#340C2312yes—
294#340C2312yes—
295#340C2312yes—
296#340C2312yes—
297#340C2312yes—
298#340C2312yes—
299#340C2312yes—
300#336C2312yes—
301#336C2312yes—
302#336C2312yes—
303C25—22no—
304C22×Q8C2412yes—
305C22×D4—28no—
306C22×D4—22no—
307C22×D4—24no—
308C22×D4—24no—
309C22×D4—24no—
310C22×D4—24no—
311C22×D4—22no—
312C22×D4—21no—
313C22×D4—21no—
314C22×D4—42no—
315C22×D4—42no—
316C22×D4—82no—
317C22×D4—82no—
318C22×D4C2×D411yescharacteristic
319C22×D4C2412yes—
320C22×D4C2411yescharacteristic
321C23×C4—21no—
322C23×C4—21no—
323C23×C4—21no—
324C23×C4—22no—
325C23×C4—22no—
326C23×C4—22no—
327C23×C4C2412yes—
328C2×SD16—24no—
329C2×SD16—24no—
330C2×SD16—24no—
331C2×SD16—24no—
332C2×SD16—24no—
333C2×SD16—24no—
334C2×SD16—42no—
335C2×SD16—42no—
336C2×SD16C2×D418yes—
337C22×C8C2412yes—
338C22×C8C2412yes—
339C22×C8C2412yes—
340C22×C8C2412yes—
341C4⋊Q8—22no—
342C4⋊Q8C2×D414yescomplemented
343#127—22no—
344#127#4114yes—
345#126—48no—
346#126—48no—
347#125—24no—
348#125—24no—
349#125—48no—
350#125—48no—
351C22⋊Q8—24no—
352C22⋊Q8—24no—
353C22⋊Q8—42no—
354C22⋊Q8—42no—
355#121—28no—
356#121—24no—
357#121—24no—
358#120—216no—
359C4×Q8—24no—
360C4×Q8—24no—
361C4×Q8—24no—
362C4×Q8—24no—
363C4×Q8—42no—
364C4×Q8—42no—
365C4×D4—24no—
366C4×D4—22no—
367C4×D4—24no—
368C4×D4—24no—
369C4×D4—22no—
370C4×D4—22no—
371C4×D4—22no—
372C4×D4—22no—
373C4×D4—24no—
374C4×D4—41no—
375C4×D4—42no—
376C4×D4—42no—
377C4×D4—48no—
378C4×D4—48no—
379C4×D4—82no—
380C4×D4—82no—
381C4×D4—82no—
382C4×D4C2×D414yes—
383C4×D4#4114yes—
384#117—24no—
385#117—24no—
386#117—24no—
387#117—42no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—22no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—82no—
409C2×C4⋊C4C2×D412yes—
410C2×C4⋊C4C2×D412yes—
411C2×C4⋊C4C2×D411yescharacteristic
412C2×C4⋊C4C2×D411yescharacteristic
413C2×C4⋊C4C2×D411yescharacteristic
414C2×C4⋊C4C2412yes—
415C2×C4⋊C4C2411yescharacteristic
416C2×C4⋊C4C2412yes—
417C2×C4⋊C4C2412yes—
418C2×C4⋊C4C2412yes—
419C2×C4⋊C4C2411yescharacteristic
420C2×C4⋊C4C2411yescharacteristic
421C2×C22⋊C4—21no—
422C2×C22⋊C4—21no—
423C2×C22⋊C4—22no—
424C2×C22⋊C4—22no—
425C2×C22⋊C4—22no—
426C2×C22⋊C4—22no—
427C2×C22⋊C4—22no—
428C2×C22⋊C4—22no—
429C2×C22⋊C4—22no—
430C2×C22⋊C4—22no—
431C2×C22⋊C4—21no—
432C2×C22⋊C4—22no—
433C2×C22⋊C4—22no—
434C2×C22⋊C4—22no—
435C2×C22⋊C4—22no—
436C2×C22⋊C4—22no—
437C2×C22⋊C4—22no—
438C2×C22⋊C4—48no—
439C2×C22⋊C4—48no—
440C2×C22⋊C4—84no—
441C2×C22⋊C4C2×D412yes—
442C2×C22⋊C4C2×D412yes—
443C2×C22⋊C4C2×D412yes—
444C2×C22⋊C4C2×D412yes—
445C2×C22⋊C4C2×D412yes—
446C2×C42—22no—
447C2×C42—21no—
448C2×C42—22no—
449C2×C42—22no—
450C2×C42—22no—
451C2×C42—21no—
452C2×C42—21no—
453C2×C42—82no—
454C2×C42C2×D411yescharacteristic
455C2×C42C2×D411yescharacteristic
456C2×C42C2×D411yescharacteristic
457C2×C42C2×D411yescharacteristic
458C2×C42C2412yes—
459C2×C42C2411yescharacteristic
460C2×C42C2411yescharacteristic
461C2×C42C2411yescharacteristic
462#107—24no—
463#107—24no—
464#107—24no—
465#107—42no—
466#106—24no—
467#106—24no—
468#106—42no—
469C4⋊C8—24no—
470C4⋊C8—24no—
471C4⋊C8—22no—
472C4⋊C8—41no—
473C4⋊C8—41no—
474C4⋊C8C2×D414yescomplemented
475#103—24no—
476#103—24no—
477#103—24no—
478#103—42no—
479#103C2×D418yescomplemented
480#102—24no—
481#102—24no—
482#102—24no—
483#102—24no—
484#102—24no—
485#102—24no—
486#102—24no—
487#102—42no—
488#102—42no—
489C22⋊C8—24no—
490C22⋊C8—24no—
491C22⋊C8—42no—
492C22⋊C8—42no—
493#97—24no—
494#97—24no—
495C4×C8—24no—
496#95—21no—
497#95—21no—
498#95—21no—
499#95—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#95C2×D412yes—
510#95C2×D412yes—
511#95C2×D412yes—
512C24—21no—
513C24—28no—
514C24—22no—
515C24—44no—
516C24—44no—
517C24—82no—
518C24—82no—
519C24—82no—
520C24—82no—
521C24C22×D412yes—
522C2×Q8—22no—
523C2×Q8—22no—
524C2×Q8—22no—
525C2×Q8—22no—
526C2×Q8—22no—
527C2×Q8C22×D414yes—
528C2×D4—28no—
529C2×D4—28no—
530C2×D4—22no—
531C2×D4—24no—
532C2×D4—24no—
533C2×D4—22no—
534C2×D4—21no—
535C2×D4—22no—
536C2×D4—21no—
537C2×D4—22no—
538C2×D4—22no—
539C2×D4—21no—
540C2×D4—22no—
541C2×D4—41no—
542C2×D4—41no—
543C2×D4—44no—
544C2×D4—44no—
545C2×D4—42no—
546C2×D4—42no—
547C2×D4—48no—
548C2×D4—48no—
549C2×D4—48no—
550C2×D4—48no—
551C2×D4—81no—
552C2×D4—81no—
553C2×D4—816no—
554C2×D4—82no—
555C2×D4—82no—
556C2×D4C22×D412yes—
557C2×D4C2×#4114yes—
558C2×D4C2×#4112yes—
559C2×D42−1+412yes—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—22no—
563C22×C4—24no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—24no—
571C22×C4—22no—
572C22×C4—21no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—44no—
577C22×C4—42no—
578C22×C4—42no—
579C22×C4—42no—
580C22×C4—44no—
581C22×C4—42no—
582C22×C4—44no—
583C22×C4—81no—
584C22×C4—81no—
585C22×C4—81no—
586C22×C4—82no—
587C22×C4—82no—
588C22×C4—82no—
589C22×C4—82no—
590C22×C4—82no—
591C22×C4—82no—
592C22×C4C22×D412yes—
593C22×C4C22×D411yescharacteristic
594C22×C4C22×D412yes—
595C22×C4C22×D412yes—
596C22×C4C22×D411yescharacteristic
597C22×C4C22×D411yescharacteristic
598C22×C4C22×D411yescharacteristic
599C22×C4C22×D411yescharacteristic
600C22×C4C22×D411yescharacteristic
601C22×C4C2511yescharacteristic
602SD16—216no—
603SD16—48no—
604SD16—48no—
605C2×C8—22no—
606C2×C8—22no—
607C2×C8—22no—
608C2×C8—22no—
609C2×C8—22no—
610C2×C8—22no—
611C2×C8—22no—
612C2×C8—22no—
613C2×C8—22no—
614C2×C8—22no—
615C2×C8—22no—
616C2×C8C22×D414yes—
617C4⋊C4—22no—
618C4⋊C4—24no—
619C4⋊C4—24no—
620C4⋊C4—24no—
621C4⋊C4—24no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—22no—
625C4⋊C4—22no—
626C4⋊C4—22no—
627C4⋊C4—22no—
628C4⋊C4—22no—
629C4⋊C4—22no—
630C4⋊C4—22no—
631C4⋊C4—22no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—41no—
635C4⋊C4—41no—
636C4⋊C4—44no—
637C4⋊C4—44no—
638C4⋊C4—44no—
639C4⋊C4—44no—
640C4⋊C4—42no—
641C4⋊C4—42no—
642C4⋊C4—44no—
643C4⋊C4—44no—
644C4⋊C4—44no—
645C4⋊C4—42no—
646C4⋊C4—81no—
647C4⋊C4—81no—
648C4⋊C4—81no—
649C4⋊C4—81no—
650C4⋊C4—82no—
651C4⋊C4—82no—
652C4⋊C4—82no—
653C4⋊C4—81no—
654C4⋊C4C22×D412yes—
655C4⋊C4C2×#4112yes—
656C22⋊C4—28no—
657C22⋊C4—24no—
658C22⋊C4—24no—
659C22⋊C4—24no—
660C22⋊C4—24no—
661C22⋊C4—24no—
662C22⋊C4—24no—
663C22⋊C4—42no—
664C22⋊C4—44no—
665C22⋊C4—44no—
666C22⋊C4—44no—
667C22⋊C4—42no—
668C22⋊C4—44no—
669C22⋊C4—44no—
670C22⋊C4—44no—
671C22⋊C4—44no—
672C22⋊C4—82no—
673C22⋊C4—82no—
674C22⋊C4—82no—
675C22⋊C4—82no—
676C22⋊C4—82no—
677C22⋊C4—82no—
678C42—22no—
679C42—22no—
680C42—22no—
681C42—21no—
682C42—21no—
683C42—41no—
684C42—41no—
685C42—41no—
686C42—44no—
687C42—44no—
688C42—44no—
689C42—42no—
690C42—44no—
691C42—81no—
692C42—81no—
693C42C22×D412yes—
694C42C2×#4112yes—
695C42C2×#4112yes—
696C42H(5,𝔽2)12yes—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—24no—
705C23—22no—
706C23—22no—
707C23—22no—
708C23—416no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—42no—
714C23—42no—
715C23—42no—
716C23—42no—
717C23—42no—
718C23—42no—
719C23—88no—
720C23—88no—
721C23—164no—
722C23—164no—
723C23—164no—
724C23—164no—
725C23C23×D411yescharacteristic
726Q8—24no—
727Q8—24no—
728Q8—42no—
729Q8—42no—
730D4—22no—
731D4—24no—
732D4—22no—
733D4—22no—
734D4—24no—
735D4—48no—
736D4—44no—
737D4—416no—
738D4—42no—
739D4—42no—
740D4—84no—
741D4—88no—
742D4#54714yes—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—21no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—24no—
764C2×C4—22no—
765C2×C4—21no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—48no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—41no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—41no—
791C2×C4—42no—
792C2×C4—41no—
793C2×C4—42no—
794C2×C4—84no—
795C2×C4—84no—
796C2×C4—164no—
797C2×C4—164no—
798C2×C4—164no—
799C2×C4#52512yes—
800C2×C4#52512yes—
801C2×C4D4212yes—
802C2×C4D4212yes—
803C2×C4#57712yes—
804C2×C4C23×D411yescharacteristic
805C2×C4C22×#4111yescharacteristic
806C2×C4C22×#4111yescharacteristic
807C2×C4C2×H(5,𝔽2)11yescharacteristic
808C2×C4C2×2−1+411yescharacteristic
809C2×C4#58511yescharacteristic
810C8—24no—
811C8—42no—
812C8—42no—
813C8—42no—
814C22—24no—
815C22—42no—
816C22—42no—
817C22—42no—
818C22—42no—
819C22—42no—
820C22—42no—
821C22—42no—
822C22—44no—
823C22—42no—
824C22—42no—
825C22—44no—
826C22—42no—
827C22—42no—
828C22—44no—
829C22—42no—
830C22—42no—
831C22—82no—
832C22—82no—
833C22—82no—
834C22—82no—
835C22—1616no—
836C22C2×#52511yescharacteristic
837C22C2×D4211yescharacteristic
838C22#348911yescharacteristic
839C22C2×#57711yescharacteristic
840C22#358511yescharacteristic
841C22#358511yescharacteristic
842C22#358611yescharacteristic
843C4—22no—
844C4—22no—
845C4—22no—
846C4—22no—
847C4—22no—
848C4—42no—
849C4—44no—
850C4—41no—
851C4—42no—
852C4—42no—
853C4—42no—
854C4—42no—
855C4—82no—
856C4—82no—
857C4—82no—
858C4—82no—
859C4—81no—
860C4C2×#54711yescharacteristic
861C4D4×#4111yescharacteristic
862C4#350611yescharacteristic
863C4#352011yescharacteristic
864C2—44no—
865C2—82no—
866C2—84no—
867C2#3610011yescharacteristic
868C2#6056411yescharacteristic
869C2#6059111yescharacteristic
870C2#6108011yescharacteristic
871C2#6109511yescharacteristic
872C2#6216411yescharacteristic
873C2#6223611yescharacteristic
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×#3123C2semidirect
2. #39373C2semidirect
4. #33199C2semidirect
5. #32966C2semidirect
6. #28516C2semidirect
7. #28252C2semidirect
8. #26572C2semidirect
9. #26557C2semidirect
10. #25025C2semidirect
11. #24921C2semidirect
12. #24901C2semidirect
13. #24713C2semidirect
15. #24163C2semidirect
16. #23010C2semidirect
17. #22798C2semidirect
18. #22677C2semidirect
19. #21504C2semidirect
21. C2×#541C22semidirect
24. C2×#485C22semidirect
25. C2×#485C22semidirect
27. C2×#478C22semidirect
28. C2×#478C22semidirect
31. C2×#461C22semidirect
36. C2×#440C22semidirect
38. C2×C4×SD16C22semidirect
39. C2×#433C22semidirect
40. #2859C22semidirect
45. #2629C22semidirect
49. #2423C22semidirect
50. #2423C22semidirect
56. #2351C22semidirect
62. C4×C4⋊Q8C22semidirect
68. #2094C22semidirect
69. #2093C22semidirect
70. #2077C22semidirect
71. #2076C22semidirect
72. #2055C22semidirect
73. #2055C22semidirect
74. #2036C22semidirect
75. #2035C22semidirect
80. #1989C22semidirect
81. #1981C22semidirect
84. #1949C22semidirect
85. #1948C22semidirect
86. #1947C22semidirect
87. #1947C22semidirect
88. #1943C22semidirect
89. #1942C22semidirect
90. #1936C22semidirect
91. #1934C22semidirect
92. #1928C22semidirect
93. #1924C22semidirect
94. #1923C22semidirect
95. #1880C22semidirect
96. #1880C22semidirect
98. #1865C22semidirect
100. #1864C22semidirect
101. #1863C22semidirect
103. #1862C22semidirect
104. #1854C22semidirect
105. #1854C22semidirect
106. #1847C22semidirect
107. #1842C22semidirect
109. #1803C22semidirect
113. #1802C22semidirect
114. #1798C22semidirect
117. #1771C22semidirect
118. #1767C22semidirect
119. #1763C22semidirect
171. #461D4semidirect
342. C4⋊Q8C2×D4semidirect
474. C4⋊C8C2×D4semidirect
479. #103C2×D4semidirect

Maximal subgroups

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

subgroupindex
C2×#31232
#393732
#343102
#331992
#329662
#285162
#282522
#265722
#265572
#250252
#249212
#249012
#247132
#242522
#241632
#230102
#227982
#226772
#215042