Finite Group Databasebeta

← #6477084

Subgroups — #6477084

Order 512.

2108 conjugacy classes of subgroups.

The subgroup lattice has 918 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2857C211yesmaximal, characteristic, complemented
2C4×#525C211yesmaximal, characteristic
3#33153C212yesmaximal, complemented
4#32958C212yesmaximal, complemented
5#30175C212yesmaximal, complemented
6#30172C212yesmaximal, complemented
7#29299C212yesmaximal, complemented
8#29107C212yesmaximal, complemented
9#27647C211yesmaximal, characteristic, complemented
10#27644C211yesmaximal, characteristic, complemented
11#27602C212yesmaximal, complemented
12#24702C212yesmaximal, complemented
13#24701C212yesmaximal, complemented
14#24302C211yesmaximal, characteristic, complemented
15#24299C211yesmaximal, characteristic, complemented
16#24004C212yesmaximal
17#22078C212yesmaximal, complemented
18#22075C212yesmaximal, complemented
19#20714C211yesmaximal, characteristic, complemented
20C22×C4⋊Q8C2211yescharacteristic
21C2×#525C2211yescharacteristic
22C22×C22⋊Q8—21no—
23C2×C4×#41C2211yescharacteristic
24C23×C42C2211yescharacteristic
25C2×#483C2212yes—
26C2×#480C2212yes—
27C2×#477C2212yescomplemented
28C2×#476C2212yescomplemented
29C2×#431C2212yes—
30#2857—21no—
31#2857—21no—
32#2857—21no—
33#2857—21no—
34#2857C2212yes—
35#2857C2212yes—
36#2857C2212yes—
37#2857C2212yes—
38C4×C22⋊Q8C2211yescharacteristic
39C4×C22⋊Q8C2211yescharacteristic
40C4×C22⋊Q8C2211yescharacteristic
41C4×C22⋊Q8C2211yescharacteristic
42C4×#123—21no—
43C4×#123—21no—
44C4×#121C2211yescharacteristic
45C4×#121C2211yescharacteristic
46C4×#121C2211yescharacteristic
47C4×#121C2211yescharacteristic
48C4×#120—21no—
49C4×#120—21no—
50#2297C2211yescharacteristic
51#2296C2211yescharacteristic
52C2×#391—21no—
53C2×#389—21no—
54C2×#389C2212yes—
55#2290—21no—
56#2290—21no—
57C2×#384C2211yescharacteristic
58#2280C2211yescharacteristic
59C2×#380—21no—
60C2×#380C2212yes—
61C42×D4—21no—
62C42×D4—21no—
63C4×#117C2211yescharacteristic
64#2084C2212yescomplemented
65#2083C2212yescomplemented
66#2077C2214yes—
67#2076C2214yes—
68#2072C2212yescomplemented
69#2071C2212yescomplemented
70#2058C2212yescomplemented
71#2057C2212yescomplemented
72#2036C2214yes—
73#2034C2214yes—
74#2024C2212yescomplemented
75#2023C2212yescomplemented
76#1987C2212yescomplemented
77#1987C2212yescomplemented
78#1948C2212yescomplemented
79#1947C2212yescomplemented
80#1942C2214yescomplemented
81#1941C2214yescomplemented
82#1934C2214yescomplemented
83#1933C2214yescomplemented
84#1919C2214yescomplemented
85#1918C2214yescomplemented
86#1874C2212yes—
87#1872C2212yes—
88#1865C2214yescomplemented
89#1862C2214yescomplemented
90#1854C2214yes—
91#1854C2214yes—
92#1853C2212yes—
93#1852C2212yes—
94#1825C2214yes—
95#1823C2212yes—
96#1823C2212yes—
97#1817C2212yes—
98#1803C2212yescomplemented
99#1802C2212yescomplemented
100#1797C2212yes—
101#1797C2211yescharacteristic
102#1797C2211yescharacteristic
103#1788C2214yes—
104#1779C2212yes—
105C4×C22⋊C8C2212yes—
106C4×C22⋊C8C2212yes—
107C22×#41C2311yescharacteristic
108C23×Q8—21no—
109C24×C4D411yescharacteristic
110C24×C4D411yescharacteristic
111C24×C4C2311yescharacteristic
112C2×C4⋊Q8—21no—
113C2×C4⋊Q8—21no—
114C2×C4⋊Q8—44no—
115C2×C4⋊Q8C2312yes—
116C2×C4⋊Q8C2312yes—
117#525—24no—
118#525—24no—
119C2×#123—21no—
120C2×C22⋊Q8—22no—
121C2×C22⋊Q8—22no—
122C2×C22⋊Q8—22no—
123C2×C22⋊Q8—22no—
124C2×C22⋊Q8—48no—
125C2×C22⋊Q8C2311yescharacteristic
126C2×C22⋊Q8C2311yescharacteristic
127C2×#121C2311yescharacteristic
128C2×#121C2311yescharacteristic
129C2×#120—21no—
130C4×#41—44no—
131C2×C4×Q8C2311yescharacteristic
132C2×C4×Q8C2311yescharacteristic
133C2×C4×D4—21no—
134C2×C4×D4—21no—
135C2×C4×D4—21no—
136C2×C4×D4—21no—
137C2×C4×D4—21no—
138C2×C4×D4—21no—
139C2×C4×D4—21no—
140C2×C4×D4—21no—
141C2×C4×D4C2311yescharacteristic
142C2×C4×D4C2311yescharacteristic
143C2×#117—21no—
144C2×#117C2311yescharacteristic
145C2×#117C2311yescharacteristic
146C2×#117C2311yescharacteristic
147C22×C4⋊C4—21no—
148C22×C4⋊C4—22no—
149C22×C4⋊C4—21no—
150C22×C4⋊C4—21no—
151C22×C4⋊C4C2312yes—
152C22×C4⋊C4C2312yes—
153C22×C22⋊C4—22no—
154C22×C42—21no—
155C22×C42—44no—
156C22×C42D411yescharacteristic
157C22×C42D411yescharacteristic
158C22×C42D411yescharacteristic
159C22×C42D411yescharacteristic
160C22×C42D411yescharacteristic
161C22×C42D411yescharacteristic
162C22×C42C2311yescharacteristic
163C22×C42C2311yescharacteristic
164C22×C42C2311yescharacteristic
165C22×C42C2311yescharacteristic
166C22×C42C2311yescharacteristic
167C22×C42C2311yescharacteristic
168#483—28no—
169#480—28no—
170#477—44no—
171#476—44no—
172#431—44no—
173C2×#107C2314yes—
174C2×#107C2314yes—
175C2×#106C2314yes—
176C2×#106C2314yes—
177C2×C4⋊C8C2312yes—
178C2×C4⋊C8C2312yes—
179C2×#103C2314yes—
180C2×#103C2314yes—
181C2×#102C2314yes—
182C2×#102C2314yes—
183C2×C22⋊C8C2312yes—
184C2×C22⋊C8C2312yes—
185C2×C22⋊C8C2314yes—
186C2×C22⋊C8C2314yes—
187C2×C4×C8C2314yes—
188#391—22no—
189#391—22no—
190#391—22no—
191#391—22no—
192#391C2311yescharacteristic
193#391C2311yescharacteristic
194#390C2311yescharacteristic
195#390C2311yescharacteristic
196#389—22no—
197#389—22no—
198#389—22no—
199#389—22no—
200#389—22no—
201#389—22no—
202#389C2311yescharacteristic
203#389C2311yescharacteristic
204#389C2314yes—
205#389C2314yes—
206#389C2311yescharacteristic
207#389C2311yescharacteristic
208#388—21no—
209#388—21no—
210#388—21no—
211#388—21no—
212#387—21no—
213#387—21no—
214#387—21no—
215#387—21no—
216#386—21no—
217#386—21no—
218#386—21no—
219#386—21no—
220#386—21no—
221#386—21no—
222#385—21no—
223#385—21no—
224#385—21no—
225#385—21no—
226#385—21no—
227#385—21no—
228#384—21no—
229#384—21no—
230#384C2312yes—
231#384C2312yes—
232#381—21no—
233#380—22no—
234#380—22no—
235#380—22no—
236#380—22no—
237#380—22no—
238#380—22no—
239#380C2311yescharacteristic
240#380C2314yes—
241#380C2311yescharacteristic
242#380C2311yescharacteristic
243#380C2311yescharacteristic
244#380C2314yes—
245#379—21no—
246C4×C4⋊C4—21no—
247C4×C4⋊C4—21no—
248C4×C4⋊C4—21no—
249C4×C4⋊C4—21no—
250C4×C4⋊C4—21no—
251C4×C4⋊C4—21no—
252C4×C4⋊C4C2311yescharacteristic
253C4×C4⋊C4C2311yescharacteristic
254C4×C4⋊C4C2311yescharacteristic
255C4×C4⋊C4C2311yescharacteristic
256C4×C22⋊C4—21no—
257C4×C22⋊C4—21no—
258C4×C22⋊C4—21no—
259C4×C22⋊C4—21no—
260C4×C22⋊C4—21no—
261C4×C22⋊C4—21no—
262C4×C22⋊C4—21no—
263C4×C22⋊C4—21no—
264C4×C22⋊C4—21no—
265C4×C22⋊C4—21no—
266C4×C22⋊C4—21no—
267C4×C22⋊C4—21no—
268C4×C22⋊C4—21no—
269C4×C22⋊C4—21no—
270#376—21no—
271C2×#95—22no—
272C2×#95—22no—
273C43—21no—
274#340C2314yes—
275#340C2314yes—
276#340C2314yes—
277#340C2314yes—
278#340C2314yes—
279#340C2314yes—
280#340C2314yes—
281#340C2314yes—
282#336C2312yes—
283#336C2312yes—
284#336C2314yes—
285C25C2×D411yescharacteristic
286C2×#41—22no—
287C2×#41—22no—
288C2×#41—24no—
289C2×#41—42no—
290C22×Q8—22no—
291C22×Q8—22no—
292C22×Q8—44no—
293C22×Q8—44no—
294C22×Q8—44no—
295C22×Q8C2411yescharacteristic
296C22×D4—21no—
297C22×D4—21no—
298C22×D4—21no—
299C22×D4C2411yescharacteristic
300C23×C4—24no—
301C23×C4—24no—
302C23×C4—24no—
303C23×C4—21no—
304C23×C4—22no—
305C23×C4—22no—
306C23×C4—24no—
307C23×C4—22no—
308C23×C4—22no—
309C23×C4—21no—
310C23×C4—21no—
311C23×C4—42no—
312C23×C4—42no—
313C23×C4—42no—
314C23×C4—42no—
315C23×C4C2×D411yescharacteristic
316C23×C4C2×D411yescharacteristic
317C23×C4C2×D411yescharacteristic
318C23×C4C2×D411yescharacteristic
319C23×C4C2×D411yescharacteristic
320C23×C4C2×D411yescharacteristic
321C23×C4C2×D411yescharacteristic
322C23×C4C2×D411yescharacteristic
323C23×C4C2×D411yescharacteristic
324C23×C4C2×D411yescharacteristic
325C23×C4C2×D411yescharacteristic
326C23×C4C2×D411yescharacteristic
327C23×C4C2×D411yescharacteristic
328C23×C4C2×D411yescharacteristic
329C23×C4C2×D411yescharacteristic
330C23×C4C2411yescharacteristic
331C23×C4C2411yescharacteristic
332C23×C4C2411yescharacteristic
333C22×C8C2414yes—
334C22×C8C2414yes—
335C4⋊Q8—24no—
336C4⋊Q8—24no—
337C4⋊Q8—44no—
338C4⋊Q8—44no—
339C4⋊Q8—44no—
340#123—28no—
341C22⋊Q8—22no—
342C22⋊Q8—22no—
343C22⋊Q8—22no—
344C22⋊Q8—48no—
345C22⋊Q8—48no—
346C22⋊Q8—48no—
347C22⋊Q8—48no—
348C22⋊Q8#4114yes—
349#121—22no—
350#121—22no—
351#121—22no—
352#121#4114yes—
353#120—28no—
354C4×Q8—24no—
355C4×Q8—42no—
356C4×D4—28no—
357C4×D4—28no—
358C4×D4—24no—
359C4×D4—42no—
360C4×D4—44no—
361C4×D4—44no—
362C4×D4—44no—
363C4×D4—44no—
364C4×D4—44no—
365C4×D4—44no—
366#117—22no—
367#117—22no—
368#117—24no—
369#117—44no—
370#117—42no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—24no—
374C2×C4⋊C4—24no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—24no—
378C2×C4⋊C4—24no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—22no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—22no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—44no—
392C2×C4⋊C4—44no—
393C2×C4⋊C4—44no—
394C2×C4⋊C4—44no—
395C2×C4⋊C4—48no—
396C2×C4⋊C4C2414yes—
397C2×C4⋊C4C2414yes—
398C2×C4⋊C4C2411yescharacteristic
399C2×C4⋊C4C2411yescharacteristic
400C2×C4⋊C4C2411yescharacteristic
401C2×C4⋊C4C2411yescharacteristic
402C2×C4⋊C4C2411yescharacteristic
403C2×C4⋊C4C2411yescharacteristic
404C2×C22⋊C4—21no—
405C2×C22⋊C4—21no—
406C2×C22⋊C4—21no—
407C2×C22⋊C4—21no—
408C2×C22⋊C4—21no—
409C2×C22⋊C4—24no—
410C2×C22⋊C4—24no—
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—21no—
420C2×C22⋊C4—21no—
421C2×C22⋊C4—21no—
422C2×C22⋊C4—21no—
423C2×C22⋊C4—48no—
424C2×C42—21no—
425C2×C42—24no—
426C2×C42—24no—
427C2×C42—24no—
428C2×C42—21no—
429C2×C42—21no—
430C2×C42—21no—
431C2×C42—21no—
432C2×C42—21no—
433C2×C42—21no—
434C2×C42—21no—
435C2×C42—21no—
436C2×C42—42no—
437C2×C42—42no—
438C2×C42—42no—
439C2×C42—42no—
440C2×C42—42no—
441C2×C42—42no—
442C2×C42—42no—
443C2×C42—42no—
444C2×C42—42no—
445C2×C42—44no—
446C2×C42C2×D411yescharacteristic
447C2×C42C2×D411yescharacteristic
448C2×C42C2×D411yescharacteristic
449C2×C42C2×D411yescharacteristic
450C2×C42C2×D411yescharacteristic
451C2×C42C2×D411yescharacteristic
452C2×C42C2×D411yescharacteristic
453C2×C42C2×D411yescharacteristic
454C2×C42C2×D411yescharacteristic
455C2×C42C2×D411yescharacteristic
456C2×C42C2×D411yescharacteristic
457C2×C42C2×D411yescharacteristic
458C2×C42C2411yescharacteristic
459C2×C42C2411yescharacteristic
460C2×C42C2411yescharacteristic
461C2×C42C2411yescharacteristic
462#107—28no—
463#107—44no—
464#106—28no—
465#106—44no—
466C4⋊C8—24no—
467C4⋊C8—24no—
468#103—28no—
469#103—44no—
470#102—28no—
471#102—44no—
472C22⋊C8—24no—
473C22⋊C8—24no—
474C22⋊C8—28no—
475C22⋊C8—44no—
476C4×C8—44no—
477#95—24no—
478#95—24no—
479#95—24no—
480#95—24no—
481#95—21no—
482#95—21no—
483#95—21no—
484#95—21no—
485#95—21no—
486#95—21no—
487#95—21no—
488#95—21no—
489#95—21no—
490#95—21no—
491#95—21no—
492#95—21no—
493#95—21no—
494#95—21no—
495#95—21no—
496#95—21no—
497C24—22no—
498C24—22no—
499C24—22no—
500C24—22no—
501C24—22no—
502C24—21no—
503C24—41no—
504C24—41no—
505C24C22×D411yescharacteristic
506C24C22×D411yescharacteristic
507C24C22×D411yescharacteristic
508#41—48no—
509#41—48no—
510C2×Q8—21no—
511C2×Q8—22no—
512C2×Q8—22no—
513C2×Q8—44no—
514C2×Q8—44no—
515C2×Q8—44no—
516C2×Q8—44no—
517C2×Q8—44no—
518C2×Q8—44no—
519C2×Q8—816no—
520C2×Q8C2×#4112yes—
521C2×D4—24no—
522C2×D4—24no—
523C2×D4—24no—
524C2×D4—21no—
525C2×D4—22no—
526C2×D4—22no—
527C2×D4—42no—
528C2×D4—42no—
529C2×D4—42no—
530C2×D4—42no—
531C2×D4—42no—
532C2×D4—42no—
533C2×D4C2×#4112yes—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—24no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—24no—
582C22×C4—24no—
583C22×C4—41no—
584C22×C4—41no—
585C22×C4—41no—
586C22×C4—41no—
587C22×C4—41no—
588C22×C4—41no—
589C22×C4—41no—
590C22×C4—41no—
591C22×C4—41no—
592C22×C4—41no—
593C22×C4—41no—
594C22×C4—41no—
595C22×C4—416no—
596C22×C4—48no—
597C22×C4—48no—
598C22×C4—42no—
599C22×C4—416no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4—42no—
603C22×C4—44no—
604C22×C4—44no—
605C22×C4—44no—
606C22×C4—44no—
607C22×C4—44no—
608C22×C4—44no—
609C22×C4—42no—
610C22×C4—42no—
611C22×C4—42no—
612C22×C4—42no—
613C22×C4#13514yes—
614C22×C4AGL(1,ℤ/8)14yes—
615C22×C4#13714yes—
616C22×C4C22×D411yescharacteristic
617C22×C4C22×D411yescharacteristic
618C22×C4C22×D411yescharacteristic
619C22×C4C22×D411yescharacteristic
620C22×C4C22×D411yescharacteristic
621C22×C4C22×D411yescharacteristic
622C22×C4C22×D411yescharacteristic
623C22×C4C22×D411yescharacteristic
624C22×C4C22×D411yescharacteristic
625C22×C4C22×D411yescharacteristic
626C22×C4C22×D411yescharacteristic
627C22×C4C2×#4112yes—
628C22×C4C2×#4112yes—
629C22×C42−1+414yes—
630C22×C4C2511yescharacteristic
631C2×C8—24no—
632C2×C8—24no—
633C2×C8—24no—
634C2×C8—24no—
635C2×C8—24no—
636C2×C8—24no—
637C4⋊C4—24no—
638C4⋊C4—24no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—24no—
642C4⋊C4—24no—
643C4⋊C4—24no—
644C4⋊C4—24no—
645C4⋊C4—22no—
646C4⋊C4—22no—
647C4⋊C4—22no—
648C4⋊C4—22no—
649C4⋊C4—44no—
650C4⋊C4—44no—
651C4⋊C4—44no—
652C4⋊C4—44no—
653C4⋊C4—42no—
654C4⋊C4—44no—
655C4⋊C4—44no—
656C4⋊C4—42no—
657C4⋊C4—44no—
658C4⋊C4—44no—
659C4⋊C4—42no—
660C4⋊C4—48no—
661C4⋊C4—48no—
662C4⋊C4—42no—
663C4⋊C4—42no—
664C4⋊C4—42no—
665C4⋊C4C2×#4112yes—
666C4⋊C4C2×#4112yes—
667C22⋊C4—24no—
668C22⋊C4—24no—
669C22⋊C4—24no—
670C22⋊C4—24no—
671C22⋊C4—24no—
672C22⋊C4—42no—
673C22⋊C4—48no—
674C22⋊C4—48no—
675C22⋊C4—42no—
676C22⋊C4—42no—
677C22⋊C4—42no—
678C22⋊C4—42no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—42no—
683C22⋊C4—42no—
684C22⋊C4—42no—
685C22⋊C4—42no—
686C42—24no—
687C42—22no—
688C42—22no—
689C42—22no—
690C42—22no—
691C42—22no—
692C42—22no—
693C42—22no—
694C42—22no—
695C42—22no—
696C42—41no—
697C42—41no—
698C42—41no—
699C42—41no—
700C42—41no—
701C42—41no—
702C42—42no—
703C42—42no—
704C42—42no—
705C42—42no—
706C42—42no—
707C42—42no—
708C42—42no—
709C42—42no—
710C42H(5,𝔽2)14yes—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—28no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—22no—
729C23—44no—
730C23—44no—
731C23—44no—
732C23—44no—
733C23—44no—
734C23—44no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23#52512yes—
742C23#53612yes—
743C23C2×#13512yes—
744C23C2×AGL(1,ℤ/8)12yes—
745C23C2×#13712yes—
746C23C23×D411yescharacteristic
747Q8—24no—
748Q8—42no—
749Q8—88no—
750Q8—88no—
751D4—24no—
752D4—48no—
753D4—48no—
754D4—48no—
755D4—42no—
756C2×C4—28no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—28no—
774C2×C4—28no—
775C2×C4—24no—
776C2×C4—24no—
777C2×C4—24no—
778C2×C4—24no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—21no—
782C2×C4—22no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—44no—
789C2×C4—44no—
790C2×C4—44no—
791C2×C4—44no—
792C2×C4—44no—
793C2×C4—44no—
794C2×C4—44no—
795C2×C4—44no—
796C2×C4—44no—
797C2×C4—44no—
798C2×C4—44no—
799C2×C4—48no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—44no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—44no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—44no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—44no—
818C2×C4—41no—
819C2×C4—44no—
820C2×C4—44no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—44no—
827C2×C4—84no—
828C2×C4—88no—
829C2×C4—88no—
830C2×C4—84no—
831C2×C4#52512yes—
832C2×C4#53412yes—
833C2×C4#53412yes—
834C2×C4#53612yes—
835C2×C4C2×#13512yes—
836C2×C4C2×#13512yes—
837C2×C4C2×AGL(1,ℤ/8)12yes—
838C2×C4C2×AGL(1,ℤ/8)12yes—
839C2×C4C2×#13712yes—
840C2×C4C2×#13712yes—
841C2×C4#57512yes—
842C2×C4C22×#4111yescharacteristic
843C2×C4C22×#4111yescharacteristic
844C2×C4C2×H(5,𝔽2)12yes—
845C2×C4C2×2−1+412yes—
846C8—44no—
847C8—44no—
848C22—22no—
849C22—22no—
850C22—22no—
851C22—22no—
852C22—22no—
853C22—22no—
854C22—22no—
855C22—22no—
856C22—22no—
857C22—22no—
858C22—22no—
859C22—22no—
860C22—416no—
861C22—41no—
862C22—41no—
863C22—41no—
864C22—41no—
865C22—41no—
866C22—41no—
867C22—41no—
868C22—41no—
869C22—42no—
870C22—42no—
871C22—42no—
872C22—81no—
873C22—81no—
874C22—81no—
875C22—81no—
876C22#310614yes—
877C22C2×#52511yescharacteristic
878C22C2×#53411yescharacteristic
879C22C2×#53611yescharacteristic
880C22C22×#13511yescharacteristic
881C22C22×AGL(1,ℤ/8)11yescharacteristic
882C22C22×#13711yescharacteristic
883C22C2×#57511yescharacteristic
884C4—22no—
885C4—22no—
886C4—22no—
887C4—22no—
888C4—22no—
889C4—22no—
890C4—22no—
891C4—22no—
892C4—41no—
893C4—42no—
894C4—41no—
895C4—42no—
896C4—42no—
897C4—81no—
898C4—81no—
899C4—84no—
900C4—84no—
901C4—81no—
902C4—81no—
903C4#319014yes—
904C4#352012yes—
905C4#352012yes—
906C2—24no—
907C2—42no—
908C2—42no—
909C2—82no—
910C2#3508411yescharacteristic
911C2C2×#310611yescharacteristic
912C2#6056211yescharacteristic
913C2C2×#319011yescharacteristic
914C2#6075011yescharacteristic
915C2#6084611yescharacteristic
916C2#6086011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#525C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C23×C42 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#2857C2semidirect
3. #33153C2semidirect
4. #32958C2semidirect
5. #30175C2semidirect
6. #30172C2semidirect
7. #29299C2semidirect
8. #29107C2semidirect
9. #27647C2semidirect
10. #27644C2semidirect
11. #27602C2semidirect
12. #24702C2semidirect
13. #24701C2semidirect
14. #24302C2semidirect
15. #24299C2semidirect
17. #22078C2semidirect
18. #22075C2semidirect
19. #20714C2semidirect
27. C2×#477C22semidirect
28. C2×#476C22semidirect
64. #2084C22semidirect
65. #2083C22semidirect
68. #2072C22semidirect
69. #2071C22semidirect
70. #2058C22semidirect
71. #2057C22semidirect
74. #2024C22semidirect
75. #2023C22semidirect
76. #1987C22semidirect
77. #1987C22semidirect
78. #1948C22semidirect
79. #1947C22semidirect
80. #1942C22semidirect
81. #1941C22semidirect
82. #1934C22semidirect
83. #1933C22semidirect
84. #1919C22semidirect
85. #1918C22semidirect
88. #1865C22semidirect
89. #1862C22semidirect
98. #1803C22semidirect
99. #1802C22semidirect

Maximal subgroups

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

subgroupindex
C2×#28572
C4×#5252
#331532
#329582
#301752
#301722
#292992
#291072
#276472
#276442
#276022
#247022
#247012
#243022
#242992
#240042
#220782
#220752
#207142