Finite Group Databasebeta

← #6395731

Subgroups — #6395731

Order 512.

2268 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3213C211yesmaximal, characteristic
2#34240C211yesmaximal, characteristic, complemented
3#34141C211yesmaximal, characteristic, complemented
4#23228C212yesmaximal, complemented
5#23226C212yesmaximal, complemented
6#23195C212yesmaximal, complemented
7#23193C212yesmaximal, complemented
8#22875C212yesmaximal, complemented
9#22870C212yesmaximal, complemented
10#22858C212yesmaximal, complemented
11#22855C212yesmaximal, complemented
12#22155C212yesmaximal, complemented
13#22149C212yesmaximal, complemented
14#21888C211yesmaximal, characteristic, complemented
15#21507C212yesmaximal, complemented
16C4×#463C212yesmaximal, complemented
17#21363C211yesmaximal, characteristic, complemented
18C2×#1983C211yesmaximal, characteristic, complemented
19#20546C211yesmaximal, characteristic, complemented
20C2×#532C2211yescharacteristic
21C22×#124C2211yescharacteristic
22C2×C4×#41—21no—
23#3213C4116yescomplemented
24C2×#496C2211yescharacteristic
25C2×#496C2211yescharacteristic
26C2×#489C2211yescharacteristic
27C2×#489C2211yescharacteristic
28C2×#463C2212yes—
29C2×#463C2212yes—
30C2×#448C2212yes—
31C2×#447C2212yes—
32C2×#442C2212yes—
33C2×#440C2212yescomplemented
34C2×C4×SD16C2212yescomplemented
35C2×C4×D8C2212yes—
36C2×#432C2211yescharacteristic
37C22×C4⋊C8C2211yescharacteristic
38C22×#103C2212yes—
39C22×#102C2212yes—
40#2372—22no—
41#2367—22no—
42#2367C2212yes—
43#2367C2212yes—
44#2366C2212yescomplemented
45#2365C2212yescomplemented
46#2364—21no—
47#2364—21no—
48#2361C2212yes—
49#2361C2212yes—
50#2342—21no—
51#2342—21no—
52Q8×C22⋊C4C2211yescharacteristic
53Q8×C22⋊C4C2211yescharacteristic
54D4×C22⋊C4C2211yescharacteristic
55D4×C22⋊C4C2211yescharacteristic
56#2337—22no—
57#2312—21no—
58C4×#124C2212yes—
59C4×#124C2212yes—
60#2297—21no—
61#2293C2212yescomplemented
62#2290—22no—
63#2283C2211yescharacteristic
64#2273—21no—
65C42×D4C2212yescomplemented
66C4×#117C2211yescharacteristic
67C2×C4×C4⋊C4C2211yescharacteristic
68#1987C2212yescomplemented
69#1983C2211yescharacteristic
70#1983C2211yescharacteristic
71#1983C2211yescharacteristic
72#1983C2212yes—
73#1983C2212yes—
74#1983C2211yescharacteristic
75#1982C2212yescomplemented
76#1973C2212yescomplemented
77#1972C2212yes—
78#1970C2212yes—
79#1968C2212yescomplemented
80#1949C2212yescomplemented
81#1949C2212yescomplemented
82#1936C2212yes—
83#1935C2212yescomplemented
84#1934C2212yes—
85#1933C2212yescomplemented
86#1928C2212yescomplemented
87#1927C2212yescomplemented
88#1926C2212yes—
89#1925C2212yes—
90#1893C2212yes—
91#1893C2212yes—
92#1880C2212yescomplemented
93#1880C2212yescomplemented
94#1879C2212yes—
95#1879C2212yes—
96#1879C2212yes—
97#1879C2212yes—
98#1877C2212yescomplemented
99#1877C2212yescomplemented
100#1865C2212yescomplemented
101#1864C2212yes—
102#1863C2212yescomplemented
103#1862C2212yes—
104#1853C2212yes—
105#1852C2212yes—
106#1804C2212yescomplemented
107#1804C2212yescomplemented
108#1776C2212yescomplemented
109#1776C2212yescomplemented
110#1771C2212yescomplemented
111#1771C2212yescomplemented
112#1767C2212yescomplemented
113C4×C4⋊C8C2212yescomplemented
114#1763C2212yescomplemented
115#1762C2212yes—
116C4×#103C2212yescomplemented
117C4×#102C2212yes—
118#1752C2212yes—
119C8×C22⋊C4C2212yes—
120C22×#41—21no—
121C23×Q8C2311yescharacteristic
122C23×D4C2311yescharacteristic
123C22×SD16C2312yes—
124C22×SD16C2312yes—
125C22×D8C2312yes—
126C22×D8C2312yes—
127C23×C8C2312yes—
128#532—24no—
129#532C2×C418yescomplemented
130C2×C4⋊Q8C2311yescharacteristic
131C2×#127C2311yescharacteristic
132C2×#124—21no—
133C2×#124—21no—
134C2×#124—21no—
135C2×#124—24no—
136C2×#124C2×C418yescomplemented
137C2×#124C2311yescharacteristic
138C2×#124C2311yescharacteristic
139C2×#124C2311yescharacteristic
140C2×#124C2311yescharacteristic
141C2×#121—21no—
142C2×#121C2312yes—
143C4×#41—48no—
144C2×C4×Q8—22no—
145C2×C4×Q8C2312yes—
146C2×C4×Q8C2312yes—
147C2×C4×D4—22no—
148C2×C4×D4—22no—
149C2×C4×D4—22no—
150C2×C4×D4—21no—
151C2×C4×D4C2312yes—
152C2×C4×D4C2312yes—
153C2×C4×D4C2312yes—
154C2×C4×D4C2312yes—
155C2×C4×D4C2312yes—
156C2×#117—22no—
157C2×#117D411yescharacteristic
158C2×#117D411yescharacteristic
159C22×C4⋊C4C2312yes—
160C22×C22⋊C4—21no—
161C22×C22⋊C4—21no—
162C22×C22⋊C4—21no—
163C22×C22⋊C4—21no—
164C22×C42—21no—
165C22×C42—22no—
166C22×C42C2311yescharacteristic
167#496C2×C418yescomplemented
168#496C2×C418yescomplemented
169#489C2×C418yescomplemented
170#489C2×C418yescomplemented
171#463C2×C4116yescomplemented
172#463C2×C4116yescomplemented
173#448C2×C4116yescomplemented
174#447C2×C4116yescomplemented
175#442—44no—
176#440—44no—
177C4×SD16—44no—
178C4×D8—44no—
179#432C2×C418yescomplemented
180C2×#107C2312yes—
181C2×#107C2312yes—
182C2×#106C2312yes—
183C2×#106C2312yes—
184C2×C4⋊C8—24no—
185C2×C4⋊C8C2311yescharacteristic
186C2×C4⋊C8C2311yescharacteristic
187C2×C4⋊C8C2312yes—
188C2×C4⋊C8C2312yes—
189C2×#103—44no—
190C2×#103C2312yes—
191C2×#103C2312yes—
192C2×#103C2312yes—
193C2×#103C2312yes—
194C2×#103C2312yes—
195C2×#103C2312yes—
196C2×#102—44no—
197C2×#102C2312yes—
198C2×#102C2312yes—
199C2×#102C2312yes—
200C2×#102C2312yes—
201C2×#102C2312yes—
202C2×#102C2312yes—
203C2×#102C2312yes—
204C2×#102C2312yes—
205C2×#102C2312yes—
206C2×#102C2312yes—
207C2×C22⋊C8C2312yes—
208C2×#97C2312yes—
209C2×#97C2312yes—
210C2×#97C2311yescharacteristic
211C2×#97C2311yescharacteristic
212C2×C4×C8C2312yes—
213C2×C4×C8C2312yes—
214#391—22no—
215#391—22no—
216#391—22no—
217#391C2312yes—
218#391C2312yes—
219#390—22no—
220#390C2312yes—
221#390C2312yes—
222#390C2312yes—
223#390C2312yes—
224#389C2312yes—
225#389C2312yes—
226#388—22no—
227#388—22no—
228#388—22no—
229#388—22no—
230#388—22no—
231#388—22no—
232#388—22no—
233#388—22no—
234#388—22no—
235#388—22no—
236#388—22no—
237#388—22no—
238#387—22no—
239#387—22no—
240#386—22no—
241#386—22no—
242#386—22no—
243#386—22no—
244#386—22no—
245#386—22no—
246#385—22no—
247#385—22no—
248#385—22no—
249#385—22no—
250#383—21no—
251#382C2312yes—
252#381—21no—
253#380—21no—
254#380—21no—
255#380C2311yescharacteristic
256#380C2311yescharacteristic
257#379—21no—
258#379—21no—
259C4×C4⋊C4—21no—
260C4×C4⋊C4—21no—
261C4×C4⋊C4D412yes—
262C4×C4⋊C4C2312yes—
263C4×C4⋊C4C2312yes—
264C4×C4⋊C4C2312yes—
265C4×C4⋊C4C2312yes—
266C4×C4⋊C4C2311yescharacteristic
267C4×C4⋊C4C2311yescharacteristic
268C4×C4⋊C4C2312yes—
269C4×C22⋊C4—21no—
270C4×C22⋊C4—21no—
271C4×C22⋊C4—21no—
272C4×C22⋊C4—22no—
273C4×C22⋊C4—22no—
274C4×C22⋊C4—22no—
275C4×C22⋊C4—22no—
276C4×C22⋊C4—22no—
277C4×C22⋊C4—22no—
278C4×C22⋊C4—22no—
279C4×C22⋊C4—22no—
280C4×C22⋊C4—22no—
281C4×C22⋊C4—22no—
282C4×C22⋊C4D411yescharacteristic
283C4×C22⋊C4D411yescharacteristic
284C4×C22⋊C4C2311yescharacteristic
285C4×C22⋊C4C2311yescharacteristic
286#376—21no—
287#376D412yes—
288C2×#95—21no—
289C43C2312yes—
290#340C2312yes—
291#340C2312yes—
292#340C2312yes—
293#340C2312yes—
294#340C2312yes—
295#340C2312yes—
296#340C2312yes—
297#340C2312yes—
298#336C2312yes—
299#336C2312yes—
300#336C2312yes—
301#336C2312yes—
302C25—21no—
303C2×#41—28no—
304C2×#41—44no—
305C2×#41—44no—
306C22×Q8—21no—
307C22×Q8—21no—
308C22×Q8—22no—
309C22×Q8—42no—
310C22×Q8—42no—
311C22×Q8C22×C414yes—
312C22×Q8C2411yescharacteristic
313C22×Q8C2411yescharacteristic
314C22×D4—22no—
315C22×D4—21no—
316C22×D4—21no—
317C22×D4—21no—
318C22×D4—22no—
319C22×D4—42no—
320C22×D4—42no—
321C22×D4C22×C414yes—
322C22×D4C2412yes—
323C22×D4C2411yescharacteristic
324C22×D4C2411yescharacteristic
325C23×C4—21no—
326C23×C4—22no—
327C23×C4—22no—
328C23×C4—22no—
329C23×C4—22no—
330C23×C4—22no—
331C23×C4—22no—
332C23×C4C2×D411yescharacteristic
333C23×C4C2×D411yescharacteristic
334C23×C4C2411yescharacteristic
335C2×SD16—42no—
336C2×SD16—42no—
337C2×SD16—42no—
338C2×SD16—42no—
339C2×SD16C22×C418yes—
340C2×SD16C22×C418yes—
341C2×D8—42no—
342C2×D8—42no—
343C2×D8—42no—
344C2×D8—42no—
345C2×D8C22×C418yes—
346C2×D8C22×C418yes—
347C22×C8—24no—
348C22×C8—42no—
349C22×C8—42no—
350C22×C8C2412yes—
351C22×C8C2412yes—
352C22×C8C2412yes—
353C22×C8C2412yes—
354C4⋊Q8—22no—
355C4⋊Q8C22×C414yes—
356#127—22no—
357#127C22×C414yes—
358#124—28no—
359#124—28no—
360#124—28no—
361#124—22no—
362#124—22no—
363#124—22no—
364#124—22no—
365#124C22×C414yes—
366#124C22×C414yes—
367#124C22×C414yes—
368#124C22×C414yes—
369#121—28no—
370#121—24no—
371#121C22×C418yes—
372C4×Q8—42no—
373C4×Q8—42no—
374C4×Q8—42no—
375C4×Q8—42no—
376C4×Q8—48no—
377C4×D4—24no—
378C4×D4—24no—
379C4×D4—28no—
380C4×D4—24no—
381C4×D4—42no—
382C4×D4—42no—
383C4×D4—42no—
384C4×D4—42no—
385C4×D4—42no—
386C4×D4—42no—
387C4×D4—48no—
388C4×D4—48no—
389C4×D4—48no—
390C4×D4C22×C418yes—
391#117—24no—
392#117—48no—
393#117—42no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—24no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—42no—
402C2×C4⋊C4C2×D412yes—
403C2×C4⋊C4C2×D412yes—
404C2×C4⋊C4C2412yes—
405C2×C4⋊C4C2412yes—
406C2×C4⋊C4C2412yes—
407C2×C4⋊C4C2412yes—
408C2×C4⋊C4C2412yes—
409C2×C22⋊C4—28no—
410C2×C22⋊C4—28no—
411C2×C22⋊C4—21no—
412C2×C22⋊C4—21no—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—21no—
415C2×C22⋊C4—21no—
416C2×C22⋊C4—21no—
417C2×C22⋊C4—21no—
418C2×C22⋊C4—21no—
419C2×C22⋊C4—22no—
420C2×C22⋊C4—22no—
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—22no—
432C2×C22⋊C4—22no—
433C2×C22⋊C4—22no—
434C2×C22⋊C4—22no—
435C2×C22⋊C4—44no—
436C2×C22⋊C4—44no—
437C2×C22⋊C4C2×D411yescharacteristic
438C2×C22⋊C4C2×D411yescharacteristic
439C2×C22⋊C4C2×D411yescharacteristic
440C2×C22⋊C4C2×D411yescharacteristic
441C2×C42—21no—
442C2×C42—22no—
443C2×C42—22no—
444C2×C42—22no—
445C2×C42—21no—
446C2×C42—22no—
447C2×C42—22no—
448C2×C42—22no—
449C2×C42—48no—
450C2×C42—44no—
451C2×C42C22×C414yes—
452C2×C42C2×D412yes—
453C2×C42C2×D412yes—
454C2×C42C2×D412yes—
455C2×C42C2×D412yes—
456C2×C42C2×D411yescharacteristic
457C2×C42C2×D411yescharacteristic
458C2×C42#4114yes—
459C2×C42C2412yes—
460C2×C42C2412yes—
461C2×C42C2411yescharacteristic
462C2×C42C2411yescharacteristic
463#107—24no—
464#107—42no—
465#106—24no—
466#106—42no—
467C4⋊C8—22no—
468C4⋊C8—22no—
469C4⋊C8—24no—
470C4⋊C8C22×C418yes—
471#103—24no—
472#103—24no—
473#103—42no—
474#103—42no—
475#103C22×C418yes—
476#103C22×C418yes—
477#102—24no—
478#102—24no—
479#102—42no—
480#102—42no—
481#102—42no—
482#102—42no—
483#102—42no—
484#102—42no—
485#102C22×C418yes—
486#102C22×C418yes—
487C22⋊C8C22×C418yes—
488#97—42no—
489#97—42no—
490#97C22×C414yes—
491#97C22×C414yes—
492C4×C8—42no—
493C4×C8—42no—
494#95—21no—
495#95—22no—
496#95—21no—
497#95—22no—
498#95—21no—
499#95—21no—
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#95C2×D412yes—
511#95C2×D412yes—
512#95C2×D412yes—
513#95C2×D412yes—
514C24—21no—
515C24—21no—
516C24—22no—
517C24—24no—
518C24—42no—
519C24—42no—
520C24—82no—
521C24—82no—
522C24C22×D411yescharacteristic
523#41—432no—
524C2×Q8—24no—
525C2×Q8—24no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—22no—
529C2×Q8—22no—
530C2×Q8—22no—
531C2×Q8—22no—
532C2×Q8—42no—
533C2×Q8—42no—
534C2×Q8—48no—
535C2×Q8—82no—
536C2×Q8—82no—
537C2×Q8—82no—
538C2×Q8C23×C412yes—
539C2×Q8C23×C412yes—
540C2×D4—28no—
541C2×D4—24no—
542C2×D4—24no—
543C2×D4—24no—
544C2×D4—22no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—22no—
548C2×D4—22no—
549C2×D4—22no—
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—22no—
555C2×D4—48no—
556C2×D4—42no—
557C2×D4—42no—
558C2×D4—44no—
559C2×D4—44no—
560C2×D4—82no—
561C2×D4—82no—
562C2×D4—82no—
563C2×D4—82no—
564C2×D4C23×C412yes—
565C2×D4C23×C412yes—
566C2×D4C23×C414yes—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—22no—
575C22×C4—24no—
576C22×C4—28no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—42no—
581C22×C4—44no—
582C22×C4—44no—
583C22×C4—44no—
584C22×C4—44no—
585C22×C4—44no—
586C22×C4—44no—
587C22×C4—44no—
588C22×C4—44no—
589C22×C4—44no—
590C22×C4—44no—
591C22×C4—82no—
592C22×C4—82no—
593C22×C4—82no—
594C22×C4—82no—
595C22×C4—82no—
596C22×C4—82no—
597C22×C4—82no—
598C22×C4—82no—
599C22×C4C4×D414yes—
600C22×C4C4×D414yes—
601C22×C4C23×C412yes—
602C22×C4C22×D412yes—
603C22×C4C22×D412yes—
604C22×C4C22×D412yes—
605C22×C4C22×D411yescharacteristic
606C22×C4C22×D411yescharacteristic
607C22×C4C22×D411yescharacteristic
608C22×C4C22×D411yescharacteristic
609C22×C4C22×D411yescharacteristic
610C22×C4C22×D412yes—
611C22×C4C2×#4112yes—
612C22×C4C2511yescharacteristic
613SD16—48no—
614SD16—48no—
615D8—48no—
616D8—48no—
617C2×C8—22no—
618C2×C8—22no—
619C2×C8—22no—
620C2×C8—22no—
621C2×C8—22no—
622C2×C8—22no—
623C2×C8—22no—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—22no—
627C2×C8—84no—
628C2×C8C23×C414yes—
629C2×C8C23×C414yes—
630C4⋊C4—24no—
631C4⋊C4—24no—
632C4⋊C4—22no—
633C4⋊C4—22no—
634C4⋊C4—22no—
635C4⋊C4—22no—
636C4⋊C4—22no—
637C4⋊C4—22no—
638C4⋊C4—22no—
639C4⋊C4—22no—
640C4⋊C4—42no—
641C4⋊C4—44no—
642C4⋊C4—44no—
643C4⋊C4—44no—
644C4⋊C4—82no—
645C4⋊C4—82no—
646C4⋊C4C23×C414yes—
647C4⋊C4H(5,𝔽2)14yes—
648C22⋊C4—22no—
649C22⋊C4—22no—
650C22⋊C4—22no—
651C22⋊C4—24no—
652C22⋊C4—24no—
653C22⋊C4—24no—
654C22⋊C4—24no—
655C22⋊C4—24no—
656C22⋊C4—24no—
657C22⋊C4—24no—
658C22⋊C4—24no—
659C22⋊C4—28no—
660C22⋊C4—28no—
661C22⋊C4—44no—
662C22⋊C4—44no—
663C22⋊C4—44no—
664C22⋊C4—44no—
665C22⋊C4—42no—
666C22⋊C4—42no—
667C22⋊C4—44no—
668C22⋊C4—44no—
669C22⋊C4—82no—
670C22⋊C4—82no—
671C22⋊C4—82no—
672C22⋊C4—82no—
673C22⋊C4—82no—
674C22⋊C4—82no—
675C22⋊C4AGL(1,ℤ/8)14yes—
676C42—24no—
677C42—22no—
678C42—22no—
679C42—22no—
680C42—22no—
681C42—42no—
682C42—42no—
683C42—42no—
684C42—42no—
685C42—42no—
686C42—44no—
687C42—44no—
688C42—44no—
689C42—82no—
690C42—82no—
691C42—82no—
692C42C4×D414yes—
693C42C4×D414yes—
694C42C23×C412yes—
695C42C23×C412yes—
696C42C2×#4112yes—
697C42C2×#4112yes—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—24no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—42no—
717C23—48no—
718C23—84no—
719C23—84no—
720C23—164no—
721C23—164no—
722C23C2×C4×D412yes—
723C23C2×AGL(1,ℤ/8)12yes—
724C23#57512yes—
725C23C23×D411yescharacteristic
726Q8—24no—
727Q8—24no—
728Q8—48no—
729Q8—41no—
730Q8—41no—
731Q8—41no—
732Q8—41no—
733Q8—84no—
734D4—24no—
735D4—24no—
736D4—24no—
737D4—24no—
738D4—48no—
739D4—416no—
740D4—42no—
741D4—41no—
742D4—41no—
743D4—42no—
744D4—41no—
745D4—41no—
746D4—84no—
747D4—84no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—28no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—24no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—24no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—24no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—44no—
775C2×C4—416no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
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—42no—
791C2×C4—88no—
792C2×C4—84no—
793C2×C4—88no—
794C2×C4—88no—
795C2×C4—164no—
796C2×C4—164no—
797C2×C4C2×C4×D412yes—
798C2×C4C2×C4×D412yes—
799C2×C4C2×C4×D412yes—
800C2×C4C2×C4×D412yes—
801C2×C4C2×C4×D412yes—
802C2×C4C2×AGL(1,ℤ/8)14yes—
803C2×C4C24×C411yescharacteristic
804C2×C4C22×#4111yescharacteristic
805C2×C4C2×H(5,𝔽2)12yes—
806C2×C4#58512yes—
807C8—24no—
808C8—24no—
809C8—42no—
810C8—42no—
811C22—22no—
812C22—24no—
813C22—24no—
814C22—22no—
815C22—44no—
816C22—42no—
817C22—42no—
818C22—42no—
819C22—42no—
820C22—44no—
821C22—44no—
822C22—42no—
823C22—42no—
824C22—82no—
825C22—82no—
826C22—82no—
827C22—82no—
828C22—82no—
829C22—82no—
830C22—82no—
831C22—82no—
832C22—168no—
833C22C4×AGL(1,ℤ/8)14yes—
834C22C22×C4×D411yescharacteristic
835C22#348812yes—
836C22C22×AGL(1,ℤ/8)11yescharacteristic
837C22C2×#57511yescharacteristic
838C22#358412yes—
839C4—22no—
840C4—22no—
841C4—24no—
842C4—22no—
843C4—22no—
844C4—22no—
845C4—42no—
846C4—44no—
847C4—42no—
848C4—42no—
849C4—42no—
850C4—42no—
851C4—44no—
852C4—82no—
853C4—82no—
854C4—82no—
855C4C4×H(5,𝔽2)12yes—
856C4#350811yescharacteristic
857C4#351011yescharacteristic
858C2—24no—
859C2—84no—
860C2—82no—
861C2—82no—
862C2#3426911yescharacteristic
863C2C2×C4×AGL(1,ℤ/8)11yescharacteristic
864C2#6016111yescharacteristic
865C2#6198912yes—
866C2#6199212yes—
subgroupG/H
center, socleC23C23×D4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
prime radicalC2×#3213C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#117 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #34240C2semidirect
3. #34141C2semidirect
4. #23228C2semidirect
5. #23226C2semidirect
6. #23195C2semidirect
7. #23193C2semidirect
8. #22875C2semidirect
9. #22870C2semidirect
10. #22858C2semidirect
11. #22855C2semidirect
12. #22155C2semidirect
13. #22149C2semidirect
14. #21888C2semidirect
15. #21507C2semidirect
16. C4×#463C2semidirect
17. #21363C2semidirect
18. C2×#1983C2semidirect
19. #20546C2semidirect
23. #3213C4semidirect
33. C2×#440C22semidirect
34. C2×C4×SD16C22semidirect
44. #2366C22semidirect
45. #2365C22semidirect
61. #2293C22semidirect
65. C42×D4C22semidirect
68. #1987C22semidirect
75. #1982C22semidirect
76. #1973C22semidirect
79. #1968C22semidirect
80. #1949C22semidirect
81. #1949C22semidirect
83. #1935C22semidirect
85. #1933C22semidirect
86. #1928C22semidirect
87. #1927C22semidirect
92. #1880C22semidirect
93. #1880C22semidirect
98. #1877C22semidirect
99. #1877C22semidirect
100. #1865C22semidirect
102. #1863C22semidirect
106. #1804C22semidirect
107. #1804C22semidirect
108. #1776C22semidirect
109. #1776C22semidirect
110. #1771C22semidirect
111. #1771C22semidirect
112. #1767C22semidirect
113. C4×C4⋊C8C22semidirect
114. #1763C22semidirect
116. C4×#103C22semidirect
129. #532C2×C4semidirect
136. C2×#124C2×C4semidirect
167. #496C2×C4semidirect
168. #496C2×C4semidirect
169. #489C2×C4semidirect
170. #489C2×C4semidirect
171. #463C2×C4semidirect
172. #463C2×C4semidirect
173. #448C2×C4semidirect
174. #447C2×C4semidirect
179. #432C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#32132
#342402
#341412
#232282
#232262
#231952
#231932
#228752
#228702
#228582
#228552
#221552
#221492
#218882
#215072
C4×#4632
#213632
C2×#19832
#205462