Finite Group Databasebeta

← #6660605

Subgroups — #6660605

Order 512.

1873 conjugacy classes of subgroups.

The subgroup lattice has 889 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2857C211yesmaximal, characteristic, complemented
2#36621C211yesmaximal, characteristic
3#32787C212yesmaximal, complemented
4#32772C212yesmaximal, complemented
5#30367C212yesmaximal, complemented
6#30364C212yesmaximal, complemented
7#29942C212yesmaximal, complemented
8#29893C212yesmaximal, complemented
9#29890C212yesmaximal
10#29692C212yesmaximal, complemented
11#29336C212yesmaximal, complemented
12#29303C212yesmaximal, complemented
13#27681C211yesmaximal, characteristic, complemented
14#27678C211yesmaximal, characteristic, complemented
15#24711C212yesmaximal, complemented
16#24708C212yesmaximal, complemented
17#24302C211yesmaximal, characteristic, complemented
18#24299C211yesmaximal, characteristic, complemented
19#20715C211yesmaximal, characteristic, complemented
20C22×C4⋊Q8C2211yescharacteristic
21C2×#529C2211yescharacteristic
22C22×C22⋊Q8—21no—
23C23×C42C2211yescharacteristic
24C2×#477C2212yescomplemented
25C2×#476C2212yescomplemented
26C2×#432C2212yes—
27#2857—21no—
28#2857—21no—
29#2857—21no—
30#2857—21no—
31#2857C2212yes—
32#2857C2212yes—
33#2857C2212yes—
34#2857C2212yes—
35#2855C2211yescharacteristic
36#2854C2211yescharacteristic
37#2853—21no—
38#2852—21no—
39#2852—21no—
40#2851C2211yescharacteristic
41#2851C2211yescharacteristic
42#2850C2211yescharacteristic
43#2850C2211yescharacteristic
44#2849—21no—
45#2848C2211yescharacteristic
46#2847C2211yescharacteristic
47C4×C22⋊Q8C2211yescharacteristic
48C4×C22⋊Q8C2211yescharacteristic
49C4×#123—21no—
50C4×#121C2211yescharacteristic
51C4×#121C2211yescharacteristic
52C4×#120—21no—
53C2×#391—21no—
54C2×#389—21no—
55C2×#389C2212yes—
56#2290—21no—
57#2290—21no—
58C2×#384C2211yescharacteristic
59#2283C2211yescharacteristic
60C2×#380—21no—
61C2×#380C2212yes—
62#2101C2214yescomplemented
63#2100C2212yescomplemented
64#2100C2212yescomplemented
65#2095C2212yescomplemented
66#2094C2212yescomplemented
67#2085C2214yescomplemented
68#2077C2214yes—
69#2077C2214yes—
70#2075C2214yes—
71#2075C2214yes—
72#2059C2214yescomplemented
73#2058C2212yescomplemented
74#2057C2212yescomplemented
75#2042C2214yescomplemented
76#2035C2214yes—
77#2035C2214yes—
78#2033C2214yes—
79#2033C2214yes—
80#2024C2212yescomplemented
81#2023C2212yescomplemented
82#1987C2212yescomplemented
83#1987C2212yescomplemented
84#1948C2212yescomplemented
85#1947C2212yescomplemented
86#1944C2214yescomplemented
87#1943C2214yescomplemented
88#1936C2214yescomplemented
89#1935C2214yescomplemented
90#1874C2212yes—
91#1874C2212yes—
92#1872C2212yes—
93#1872C2212yes—
94#1853C2212yes—
95#1853C2212yes—
96#1852C2212yes—
97#1852C2212yes—
98#1817C2212yes—
99#1803C2212yescomplemented
100#1802C2212yescomplemented
101#1797C2211yescharacteristic
102#1797C2211yescharacteristic
103#1797C2212yes—
104#1779C2212yes—
105#1749C2212yes—
106#1749C2212yes—
107C23×Q8—21no—
108C24×C4D411yescharacteristic
109C24×C4D411yescharacteristic
110C24×C4C2311yescharacteristic
111C2×C4⋊Q8—21no—
112C2×C4⋊Q8—21no—
113C2×C4⋊Q8—44no—
114C2×C4⋊Q8C2312yes—
115C2×C4⋊Q8C2312yes—
116#529—44no—
117C2×#126—21no—
118C2×#125C2311yescharacteristic
119C2×#124C2311yescharacteristic
120C2×#123—21no—
121C2×#123—21no—
122C2×C22⋊Q8—22no—
123C2×C22⋊Q8—22no—
124C2×C22⋊Q8—22no—
125C2×C22⋊Q8—22no—
126C2×C22⋊Q8—48no—
127C2×C22⋊Q8C2311yescharacteristic
128C2×C22⋊Q8C2311yescharacteristic
129C2×C22⋊Q8C2311yescharacteristic
130C2×#121C2311yescharacteristic
131C2×#121C2311yescharacteristic
132C2×#121C2311yescharacteristic
133C2×#120—21no—
134C2×C4×Q8C2311yescharacteristic
135C2×C4×D4—21no—
136C2×C4×D4—21no—
137C2×C4×D4—21no—
138C2×C4×D4C2311yescharacteristic
139C2×#117—21no—
140C22×C4⋊C4—21no—
141C22×C4⋊C4—22no—
142C22×C4⋊C4—21no—
143C22×C4⋊C4—21no—
144C22×C4⋊C4C2312yes—
145C22×C4⋊C4C2312yes—
146C22×C22⋊C4—22no—
147C22×C42—44no—
148C22×C42D411yescharacteristic
149C22×C42D411yescharacteristic
150C22×C42D411yescharacteristic
151C22×C42D411yescharacteristic
152C22×C42D411yescharacteristic
153C22×C42D411yescharacteristic
154C22×C42C2311yescharacteristic
155C22×C42C2311yescharacteristic
156C22×C42C2311yescharacteristic
157C22×C42C2311yescharacteristic
158C22×C42C2311yescharacteristic
159C22×C42C2311yescharacteristic
160#477—44no—
161#476—44no—
162#432—44no—
163C2×#107C2314yes—
164C2×#107C2314yes—
165C2×#106C2314yes—
166C2×#106C2314yes—
167C2×C4⋊C8C2312yes—
168C2×C4⋊C8C2312yes—
169C2×#103C2314yes—
170C2×#103C2314yes—
171C2×#102C2314yes—
172C2×#102C2314yes—
173C2×C22⋊C8C2312yes—
174C2×C22⋊C8C2312yes—
175C2×C22⋊C8C2314yes—
176C2×C22⋊C8C2314yes—
177C2×#97C2314yes—
178#391—22no—
179#391—22no—
180#391—22no—
181#391—22no—
182#391C2311yescharacteristic
183#391C2311yescharacteristic
184#390C2311yescharacteristic
185#390C2311yescharacteristic
186#389—22no—
187#389—22no—
188#389—22no—
189#389—22no—
190#389—22no—
191#389—22no—
192#389C2311yescharacteristic
193#389C2311yescharacteristic
194#389C2314yes—
195#389C2311yescharacteristic
196#389C2311yescharacteristic
197#389C2314yes—
198#388—21no—
199#388—21no—
200#388—21no—
201#388—21no—
202#388—21no—
203#388—21no—
204#388—21no—
205#388—21no—
206#387—21no—
207#387—21no—
208#387—21no—
209#387—21no—
210#387—21no—
211#387—21no—
212#387—21no—
213#387—21no—
214#386—21no—
215#386—21no—
216#386—21no—
217#386—21no—
218#386—21no—
219#386—21no—
220#386—21no—
221#386—21no—
222#386—21no—
223#386—21no—
224#385—21no—
225#385—21no—
226#385—21no—
227#385—21no—
228#385—21no—
229#385—21no—
230#385—21no—
231#385—21no—
232#385—21no—
233#385—21no—
234#384—21no—
235#384—21no—
236#384C2312yes—
237#384C2312yes—
238#383—21no—
239#382C2311yescharacteristic
240#382C2311yescharacteristic
241#381—21no—
242#381—21no—
243#380—22no—
244#380—22no—
245#380—22no—
246#380—22no—
247#380—22no—
248#380—22no—
249#380C2311yescharacteristic
250#380C2311yescharacteristic
251#380C2314yes—
252#380C2314yes—
253#380C2311yescharacteristic
254#380C2311yescharacteristic
255#380C2311yescharacteristic
256#380C2311yescharacteristic
257#379—21no—
258C4×C4⋊C4—21no—
259C4×C4⋊C4—21no—
260C4×C4⋊C4C2311yescharacteristic
261C4×C4⋊C4C2311yescharacteristic
262C4×C22⋊C4—21no—
263C4×C22⋊C4—21no—
264C4×C22⋊C4—21no—
265C4×C22⋊C4—21no—
266C4×C22⋊C4—21no—
267#376—21no—
268C2×#95—22no—
269C2×#95—22no—
270#340C2314yes—
271#340C2314yes—
272#340C2314yes—
273#340C2314yes—
274#340C2314yes—
275#340C2314yes—
276#340C2314yes—
277#340C2314yes—
278#336C2312yes—
279#336C2312yes—
280#336C2314yes—
281C25C2×D411yescharacteristic
282C22×Q8—22no—
283C22×Q8—22no—
284C22×Q8—44no—
285C22×Q8—44no—
286C22×Q8—44no—
287C22×Q8C2411yescharacteristic
288C22×D4—21no—
289C22×D4—21no—
290C22×D4—21no—
291C22×D4C2411yescharacteristic
292C23×C4—24no—
293C23×C4—24no—
294C23×C4—22no—
295C23×C4—22no—
296C23×C4—22no—
297C23×C4—22no—
298C23×C4—21no—
299C23×C4—42no—
300C23×C4—42no—
301C23×C4—42no—
302C23×C4—42no—
303C23×C4—42no—
304C23×C4—42no—
305C23×C4C2×D411yescharacteristic
306C23×C4C2×D411yescharacteristic
307C23×C4C2×D411yescharacteristic
308C23×C4C2×D411yescharacteristic
309C23×C4C2×D411yescharacteristic
310C23×C4C2×D411yescharacteristic
311C23×C4C2×D411yescharacteristic
312C23×C4C2×D411yescharacteristic
313C23×C4C2×D411yescharacteristic
314C23×C4C2×D411yescharacteristic
315C23×C4C2×D411yescharacteristic
316C23×C4C2×D411yescharacteristic
317C23×C4C2×D411yescharacteristic
318C23×C4C2×D411yescharacteristic
319C23×C4C2×D411yescharacteristic
320C23×C4C2411yescharacteristic
321C23×C4C2411yescharacteristic
322C23×C4C2411yescharacteristic
323C22×C8C2414yes—
324C22×C8C2414yes—
325C4⋊Q8—24no—
326C4⋊Q8—24no—
327C4⋊Q8—44no—
328C4⋊Q8—44no—
329C4⋊Q8—44no—
330#126—44no—
331#125—42no—
332#124—42no—
333#123—44no—
334#123—44no—
335C22⋊Q8—22no—
336C22⋊Q8—22no—
337C22⋊Q8—42no—
338C22⋊Q8—42no—
339C22⋊Q8—48no—
340C22⋊Q8—48no—
341C22⋊Q8—48no—
342C22⋊Q8—48no—
343#121—22no—
344#121—22no—
345#121—42no—
346#121—42no—
347#120—44no—
348C4×Q8—24no—
349C4×D4—24no—
350C4×D4—44no—
351C4×D4—44no—
352C4×D4—44no—
353#117—44no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—24no—
357C2×C4⋊C4—24no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—44no—
375C2×C4⋊C4—44no—
376C2×C4⋊C4—44no—
377C2×C4⋊C4—44no—
378C2×C4⋊C4—48no—
379C2×C4⋊C4—44no—
380C2×C4⋊C4C2414yes—
381C2×C4⋊C4C2414yes—
382C2×C4⋊C4C2411yescharacteristic
383C2×C4⋊C4C2411yescharacteristic
384C2×C4⋊C4C2411yescharacteristic
385C2×C4⋊C4C2411yescharacteristic
386C2×C4⋊C4C2411yescharacteristic
387C2×C4⋊C4C2411yescharacteristic
388C2×C22⋊C4—24no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—21no—
391C2×C22⋊C4—21no—
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4—21no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—21no—
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—21no—
401C2×C22⋊C4—21no—
402C2×C22⋊C4—21no—
403C2×C22⋊C4—21no—
404C2×C22⋊C4—21no—
405C2×C22⋊C4—21no—
406C2×C22⋊C4—21no—
407C2×C22⋊C4—21no—
408C2×C22⋊C4—21no—
409C2×C22⋊C4—48no—
410C2×C42—24no—
411C2×C42—24no—
412C2×C42—24no—
413C2×C42—21no—
414C2×C42—21no—
415C2×C42—21no—
416C2×C42—42no—
417C2×C42—42no—
418C2×C42—42no—
419C2×C42—42no—
420C2×C42—42no—
421C2×C42—42no—
422C2×C42—42no—
423C2×C42—42no—
424C2×C42—42no—
425C2×C42C2×D411yescharacteristic
426C2×C42C2×D411yescharacteristic
427C2×C42C2×D411yescharacteristic
428C2×C42C2×D411yescharacteristic
429C2×C42C2×D411yescharacteristic
430C2×C42C2×D411yescharacteristic
431C2×C42C2×D411yescharacteristic
432C2×C42C2×D411yescharacteristic
433C2×C42C2×D411yescharacteristic
434C2×C42C2×D411yescharacteristic
435C2×C42C2×D411yescharacteristic
436C2×C42C2×D411yescharacteristic
437C2×C42C2411yescharacteristic
438C2×C42C2411yescharacteristic
439C2×C42C2411yescharacteristic
440C2×C42C2411yescharacteristic
441#107—44no—
442#107—44no—
443#106—44no—
444#106—44no—
445C4⋊C8—24no—
446C4⋊C8—24no—
447#103—44no—
448#103—44no—
449#102—44no—
450#102—44no—
451C22⋊C8—24no—
452C22⋊C8—24no—
453C22⋊C8—44no—
454C22⋊C8—44no—
455#97—44no—
456#95—24no—
457#95—24no—
458#95—24no—
459#95—24no—
460#95—21no—
461#95—21no—
462#95—21no—
463#95—21no—
464#95—21no—
465#95—21no—
466#95—21no—
467#95—21no—
468#95—21no—
469#95—21no—
470#95—21no—
471#95—21no—
472#95—21no—
473#95—21no—
474#95—21no—
475#95—21no—
476#95—21no—
477#95—21no—
478#95—21no—
479#95—21no—
480C24—22no—
481C24—22no—
482C24—21no—
483C24—41no—
484C24—41no—
485C24—41no—
486C24—41no—
487C24AGL(1,ℤ/8)14yes—
488C24C22×D411yescharacteristic
489C24C22×D411yescharacteristic
490C24C22×D411yescharacteristic
491C2×Q8—22no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8—22no—
495C2×Q8—44no—
496C2×Q8—44no—
497C2×Q8—44no—
498C2×Q8—44no—
499C2×Q8—44no—
500C2×Q8—44no—
501C2×Q8—816no—
502C2×D4—22no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—22no—
506C2×D4—42no—
507C2×D4—42no—
508C2×D4—42no—
509C2×D4—42no—
510C2×D4—42no—
511C2×D4—42no—
512C2×D4—42no—
513C2×D4—42no—
514C2×D4—42no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—24no—
559C22×C4—24no—
560C22×C4—41no—
561C22×C4—41no—
562C22×C4—41no—
563C22×C4—41no—
564C22×C4—41no—
565C22×C4—41no—
566C22×C4—41no—
567C22×C4—41no—
568C22×C4—41no—
569C22×C4—41no—
570C22×C4—41no—
571C22×C4—41no—
572C22×C4—41no—
573C22×C4—41no—
574C22×C4—41no—
575C22×C4—41no—
576C22×C4—41no—
577C22×C4—41no—
578C22×C4—416no—
579C22×C4—416no—
580C22×C4—48no—
581C22×C4—48no—
582C22×C4—44no—
583C22×C4—44no—
584C22×C4—44no—
585C22×C4—44no—
586C22×C4—44no—
587C22×C4—44no—
588C22×C4—42no—
589C22×C4—42no—
590C22×C4—42no—
591C22×C4#13714yes—
592C22×C4C22×D411yescharacteristic
593C22×C4C22×D411yescharacteristic
594C22×C4C22×D411yescharacteristic
595C22×C4C22×D411yescharacteristic
596C22×C4C22×D411yescharacteristic
597C22×C4C22×D411yescharacteristic
598C22×C4C22×D411yescharacteristic
599C22×C4C22×D411yescharacteristic
600C22×C4C22×D411yescharacteristic
601C22×C4C22×D411yescharacteristic
602C22×C4C22×D411yescharacteristic
603C22×C42−1+412yes—
604C22×C42−1+412yes—
605C22×C4C2511yescharacteristic
606C2×C8—24no—
607C2×C8—24no—
608C2×C8—24no—
609C2×C8—24no—
610C2×C8—24no—
611C2×C8—24no—
612C4⋊C4—24no—
613C4⋊C4—24no—
614C4⋊C4—22no—
615C4⋊C4—22no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—24no—
621C4⋊C4—22no—
622C4⋊C4—24no—
623C4⋊C4—22no—
624C4⋊C4—44no—
625C4⋊C4—44no—
626C4⋊C4—44no—
627C4⋊C4—44no—
628C4⋊C4—48no—
629C4⋊C4—48no—
630C4⋊C4—44no—
631C4⋊C4—44no—
632C4⋊C4—42no—
633C4⋊C4—42no—
634C4⋊C4—42no—
635C4⋊C4—42no—
636C4⋊C4—42no—
637C4⋊C4—42no—
638C4⋊C4—44no—
639C4⋊C4—42no—
640C4⋊C4—42no—
641C4⋊C4—42no—
642C4⋊C4—44no—
643C4⋊C4—42no—
644C22⋊C4—42no—
645C22⋊C4—42no—
646C22⋊C4—42no—
647C22⋊C4—42no—
648C22⋊C4—42no—
649C22⋊C4—42no—
650C22⋊C4—42no—
651C22⋊C4—42no—
652C22⋊C4—42no—
653C22⋊C4—42no—
654C22⋊C4—42no—
655C22⋊C4—48no—
656C22⋊C4—48no—
657C22⋊C4—42no—
658C22⋊C4—42no—
659C22⋊C4—42no—
660C22⋊C4—42no—
661C22⋊C4—42no—
662C22⋊C4—42no—
663C22⋊C4—42no—
664C22⋊C4—42no—
665C42—22no—
666C42—22no—
667C42—22no—
668C42—22no—
669C42—22no—
670C42—22no—
671C42—22no—
672C42—22no—
673C42—22no—
674C42—41no—
675C42—41no—
676C42—41no—
677C42—41no—
678C42—41no—
679C42—41no—
680C42—42no—
681C42—42no—
682C42—42no—
683C42H(5,𝔽2)14yes—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—28no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—44no—
702C23—44no—
703C23—44no—
704C23—44no—
705C23—44no—
706C23—44no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23#53612yes—
715C23C2×AGL(1,ℤ/8)12yes—
716C23C2×AGL(1,ℤ/8)12yes—
717C23C2×AGL(1,ℤ/8)12yes—
718C23C2×#13712yes—
719C23C23×D411yescharacteristic
720Q8—42no—
721Q8—42no—
722Q8—88no—
723Q8—88no—
724D4—42no—
725D4—42no—
726D4—84no—
727D4—84no—
728D4—84no—
729C2×C4—28no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—28no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—21no—
742C2×C4—21no—
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—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—44no—
760C2×C4—44no—
761C2×C4—44no—
762C2×C4—44no—
763C2×C4—44no—
764C2×C4—44no—
765C2×C4—44no—
766C2×C4—44no—
767C2×C4—44no—
768C2×C4—44no—
769C2×C4—44no—
770C2×C4—44no—
771C2×C4—44no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—44no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—44no—
787C2×C4—44no—
788C2×C4—44no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—44no—
801C2×C4—41no—
802C2×C4—44no—
803C2×C4—88no—
804C2×C4—88no—
805C2×C4—84no—
806C2×C4#53412yes—
807C2×C4#53412yes—
808C2×C4#53612yes—
809C2×C4C2×#13712yes—
810C2×C4C2×#13712yes—
811C2×C4#57512yes—
812C2×C4#57512yes—
813C2×C4C2×H(5,𝔽2)12yes—
814C2×C4C2×2−1+411yescharacteristic
815C2×C4C2×2−1+411yescharacteristic
816C2×C4#58512yes—
817C8—44no—
818C8—44no—
819C22—22no—
820C22—22no—
821C22—22no—
822C22—22no—
823C22—22no—
824C22—22no—
825C22—22no—
826C22—22no—
827C22—22no—
828C22—22no—
829C22—22no—
830C22—22no—
831C22—416no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—41no—
836C22—41no—
837C22—41no—
838C22—41no—
839C22—41no—
840C22—81no—
841C22—81no—
842C22—81no—
843C22—81no—
844C22—81no—
845C22—81no—
846C22—81no—
847C22#323814yes—
848C22C2×#53411yescharacteristic
849C22C2×#53611yescharacteristic
850C22#344911yescharacteristic
851C22C22×AGL(1,ℤ/8)11yescharacteristic
852C22C22×#13711yescharacteristic
853C22C2×#57511yescharacteristic
854C22C2×#57511yescharacteristic
855C4—22no—
856C4—22no—
857C4—22no—
858C4—22no—
859C4—41no—
860C4—41no—
861C4—41no—
862C4—41no—
863C4—41no—
864C4—41no—
865C4—84no—
866C4—81no—
867C4—81no—
868C4—81no—
869C4—81no—
870C4—84no—
871C4—81no—
872C4—81no—
873C4—81no—
874C4#319614yes—
875C4#354112yes—
876C4#354112yes—
877C2—24no—
878C2—42no—
879C2—42no—
880C2—161no—
881C2#3743811yescharacteristic
882C2C2×#319611yescharacteristic
883C2#6075011yescharacteristic
884C2C2×#323811yescharacteristic
885C2#6086311yescharacteristic
886C2#6095811yescharacteristic
887C2#6096611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2847C22
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. #32787C2semidirect
4. #32772C2semidirect
5. #30367C2semidirect
6. #30364C2semidirect
7. #29942C2semidirect
8. #29893C2semidirect
10. #29692C2semidirect
11. #29336C2semidirect
12. #29303C2semidirect
13. #27681C2semidirect
14. #27678C2semidirect
15. #24711C2semidirect
16. #24708C2semidirect
17. #24302C2semidirect
18. #24299C2semidirect
19. #20715C2semidirect
24. C2×#477C22semidirect
25. C2×#476C22semidirect
62. #2101C22semidirect
63. #2100C22semidirect
64. #2100C22semidirect
65. #2095C22semidirect
66. #2094C22semidirect
67. #2085C22semidirect
72. #2059C22semidirect
73. #2058C22semidirect
74. #2057C22semidirect
75. #2042C22semidirect
80. #2024C22semidirect
81. #2023C22semidirect
82. #1987C22semidirect
83. #1987C22semidirect
84. #1948C22semidirect
85. #1947C22semidirect
86. #1944C22semidirect
87. #1943C22semidirect
88. #1936C22semidirect
89. #1935C22semidirect
99. #1803C22semidirect
100. #1802C22semidirect

Maximal subgroups

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

subgroupindex
C2×#28572
#366212
#327872
#327722
#303672
#303642
#299422
#298932
#298902
#296922
#293362
#293032
#276812
#276782
#247112
#247082
#243022
#242992
#207152