Finite Group Databasebeta

← #6661064

Subgroups — #6661064

Order 512.

1929 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2857C211yesmaximal, characteristic, complemented
2#36621C211yesmaximal, characteristic
3#32744C212yesmaximal, complemented
4#32742C212yesmaximal, complemented
5#30295C212yesmaximal, complemented
6#30200C212yesmaximal, complemented
7#29972C212yesmaximal, complemented
8#29941C212yesmaximal, complemented
9#29760C212yesmaximal, complemented
10#29689C212yesmaximal, complemented
11#27647C211yesmaximal, characteristic, complemented
12#27644C211yesmaximal, characteristic, complemented
13#24845C212yesmaximal, complemented
14#24844C212yesmaximal, complemented
15#24559C212yesmaximal, complemented
16#24558C212yesmaximal
17#24301C211yesmaximal, characteristic, complemented
18#24298C211yesmaximal, characteristic, complemented
19#20626C211yesmaximal, characteristic, complemented
20C22×C4⋊Q8C2211yescharacteristic
21C2×#529C2211yescharacteristic
22C22×C22⋊Q8—21no—
23C23×C42C2211yescharacteristic
24C2×#483C2212yes—
25C2×#480C2212yes—
26C2×#475C2212yescomplemented
27C2×#474C2212yescomplemented
28C2×#423C2212yes—
29C2×#407C2212yes—
30#2857—21no—
31#2857—21no—
32#2857—21no—
33#2857—21no—
34#2857C2212yes—
35#2857C2212yes—
36#2857C2212yes—
37#2857C2212yes—
38#2855C2211yescharacteristic
39#2854C2211yescharacteristic
40#2853—21no—
41#2852—21no—
42#2852—21no—
43#2851C2211yescharacteristic
44#2851C2211yescharacteristic
45#2850C2211yescharacteristic
46#2850C2211yescharacteristic
47#2849—21no—
48#2848C2211yescharacteristic
49#2847C2211yescharacteristic
50C4×C22⋊Q8C2211yescharacteristic
51C4×C22⋊Q8C2211yescharacteristic
52C4×#123—21no—
53C4×#121C2211yescharacteristic
54C4×#121C2211yescharacteristic
55C4×#120—21no—
56C2×#391—21no—
57C2×#389—21no—
58C2×#389C2212yes—
59#2290—21no—
60#2290—21no—
61C2×#384C2211yescharacteristic
62#2283C2211yescharacteristic
63C2×#380—21no—
64C2×#380C2212yes—
65#2101C2214yescomplemented
66#2088C2214yescomplemented
67#2087C2214yescomplemented
68#2085C2214yescomplemented
69#2084C2212yescomplemented
70#2083C2212yescomplemented
71#2077C2214yes—
72#2076C2214yes—
73#2072C2212yescomplemented
74#2071C2212yescomplemented
75#2068C2214yescomplemented
76#2065C2214yescomplemented
77#2059C2214yescomplemented
78#2058C2212yescomplemented
79#2057C2212yescomplemented
80#2042C2214yescomplemented
81#2036C2214yes—
82#2034C2214yes—
83#2024C2212yescomplemented
84#2023C2212yescomplemented
85#1988C2212yescomplemented
86#1988C2212yescomplemented
87#1948C2212yescomplemented
88#1947C2212yescomplemented
89#1895C2214yes—
90#1894C2214yes—
91#1874C2212yes—
92#1872C2212yes—
93#1853C2212yes—
94#1852C2212yes—
95#1823C2212yes—
96#1823C2212yes—
97#1809C2214yes—
98#1809C2214yes—
99#1803C2212yescomplemented
100#1802C2212yescomplemented
101#1797C2212yes—
102#1797C2212yes—
103#1797C2211yescharacteristic
104#1797C2211yescharacteristic
105#1797C2212yes—
106#1728C2212yes—
107C23×Q8—21no—
108C24×C4D411yescharacteristic
109C24×C4D411yescharacteristic
110C24×C4C2311yescharacteristic
111C22×M16C2314yes—
112C2×C4⋊Q8—21no—
113C2×C4⋊Q8—21no—
114C2×C4⋊Q8—44no—
115C2×C4⋊Q8C2312yes—
116C2×C4⋊Q8C2312yes—
117#529—44no—
118C2×#126—21no—
119C2×#125C2311yescharacteristic
120C2×#124C2311yescharacteristic
121C2×#123—21no—
122C2×#123—21no—
123C2×C22⋊Q8—22no—
124C2×C22⋊Q8—22no—
125C2×C22⋊Q8—22no—
126C2×C22⋊Q8—22no—
127C2×C22⋊Q8—48no—
128C2×C22⋊Q8C2311yescharacteristic
129C2×C22⋊Q8C2311yescharacteristic
130C2×C22⋊Q8C2311yescharacteristic
131C2×#121C2311yescharacteristic
132C2×#121C2311yescharacteristic
133C2×#121C2311yescharacteristic
134C2×#120—21no—
135C2×C4×Q8C2311yescharacteristic
136C2×C4×D4—21no—
137C2×C4×D4—21no—
138C2×C4×D4—21no—
139C2×C4×D4C2311yescharacteristic
140C2×#117—21no—
141C22×C4⋊C4—21no—
142C22×C4⋊C4—22no—
143C22×C4⋊C4—21no—
144C22×C4⋊C4—21no—
145C22×C4⋊C4C2312yes—
146C22×C4⋊C4C2312yes—
147C22×C22⋊C4—22no—
148C22×C42—44no—
149C22×C42D411yescharacteristic
150C22×C42D411yescharacteristic
151C22×C42D411yescharacteristic
152C22×C42D411yescharacteristic
153C22×C42D411yescharacteristic
154C22×C42D411yescharacteristic
155C22×C42C2311yescharacteristic
156C22×C42C2311yescharacteristic
157C22×C42C2311yescharacteristic
158C22×C42C2311yescharacteristic
159C22×C42C2311yescharacteristic
160C22×C42C2311yescharacteristic
161#483—44no—
162#480—44no—
163#475—44no—
164#474—44no—
165C2×#107C2314yes—
166C2×#107C2314yes—
167C2×#106C2314yes—
168C2×#106C2314yes—
169#423—44no—
170C2×C4⋊C8C2312yes—
171C2×C4⋊C8C2312yes—
172C2×C4⋊C8C2314yes—
173C2×#103C2314yes—
174C2×#103C2314yes—
175C2×#102C2314yes—
176C2×#102C2314yes—
177#407—44no—
178C2×C22⋊C8C2312yes—
179C2×C22⋊C8C2312yes—
180C2×C22⋊C8C2314yes—
181#391—22no—
182#391—22no—
183#391—22no—
184#391—22no—
185#391C2311yescharacteristic
186#391C2311yescharacteristic
187#390C2311yescharacteristic
188#390C2311yescharacteristic
189#389—22no—
190#389—22no—
191#389—22no—
192#389—22no—
193#389—22no—
194#389—22no—
195#389C2311yescharacteristic
196#389C2311yescharacteristic
197#389C2314yes—
198#389C2314yes—
199#389C2311yescharacteristic
200#389C2311yescharacteristic
201#388—21no—
202#388—21no—
203#388—21no—
204#388—21no—
205#388—21no—
206#388—21no—
207#388—21no—
208#388—21no—
209#387—21no—
210#387—21no—
211#387—21no—
212#387—21no—
213#387—21no—
214#387—21no—
215#387—21no—
216#387—21no—
217#386—21no—
218#386—21no—
219#386—21no—
220#386—21no—
221#386—21no—
222#386—21no—
223#386—21no—
224#386—21no—
225#386—21no—
226#386—21no—
227#385—21no—
228#385—21no—
229#385—21no—
230#385—21no—
231#385—21no—
232#385—21no—
233#385—21no—
234#385—21no—
235#385—21no—
236#385—21no—
237#384—21no—
238#384—21no—
239#384C2312yes—
240#384C2312yes—
241#383—21no—
242#382C2311yescharacteristic
243#382C2311yescharacteristic
244#381—21no—
245#381—21no—
246#380—22no—
247#380—22no—
248#380—22no—
249#380—22no—
250#380—22no—
251#380—22no—
252#380C2311yescharacteristic
253#380C2311yescharacteristic
254#380C2314yes—
255#380C2311yescharacteristic
256#380C2314yes—
257#380C2311yescharacteristic
258#380C2311yescharacteristic
259#380C2311yescharacteristic
260#379—21no—
261C4×C4⋊C4—21no—
262C4×C4⋊C4—21no—
263C4×C4⋊C4C2311yescharacteristic
264C4×C4⋊C4C2311yescharacteristic
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—
273#340C2314yes—
274#340C2314yes—
275#340C2314yes—
276#340C2314yes—
277#340C2314yes—
278#340C2314yes—
279#340C2314yes—
280#340C2314yes—
281#336C2312yes—
282#336C2312yes—
283#336C2314yes—
284C25C2×D411yescharacteristic
285C22×Q8—22no—
286C22×Q8—22no—
287C22×Q8—44no—
288C22×Q8—44no—
289C22×Q8—44no—
290C22×Q8C2411yescharacteristic
291C22×D4—21no—
292C22×D4—21no—
293C22×D4—21no—
294C22×D4C2411yescharacteristic
295C23×C4—24no—
296C23×C4—24no—
297C23×C4—22no—
298C23×C4—24no—
299C23×C4—22no—
300C23×C4—22no—
301C23×C4—22no—
302C23×C4—21no—
303C23×C4—42no—
304C23×C4—42no—
305C23×C4—42no—
306C23×C4—42no—
307C23×C4—42no—
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×C4C2×D411yescharacteristic
321C23×C4C2×D411yescharacteristic
322C23×C4C2×D411yescharacteristic
323C23×C4C2411yescharacteristic
324C23×C4C2411yescharacteristic
325C23×C4C2411yescharacteristic
326C2×M16—28no—
327C2×M16—44no—
328C2×M16—44no—
329C22×C8C2414yes—
330C22×C8C2414yes—
331C4⋊Q8—24no—
332C4⋊Q8—24no—
333C4⋊Q8—44no—
334C4⋊Q8—44no—
335C4⋊Q8—44no—
336#126—44no—
337#125—42no—
338#124—42no—
339#123—44no—
340#123—44no—
341C22⋊Q8—22no—
342C22⋊Q8—24no—
343C22⋊Q8—22no—
344C22⋊Q8—42no—
345C22⋊Q8—48no—
346C22⋊Q8—48no—
347C22⋊Q8—48no—
348C22⋊Q8—48no—
349#121—22no—
350#121—24no—
351#121—22no—
352#121—42no—
353#120—44no—
354C4×Q8—24no—
355C4×D4—24no—
356C4×D4—44no—
357C4×D4—44no—
358C4×D4—44no—
359#117—44no—
360C2×C4⋊C4—24no—
361C2×C4⋊C4—24no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—24no—
365C2×C4⋊C4—24no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—44no—
383C2×C4⋊C4—44no—
384C2×C4⋊C4—48no—
385C2×C4⋊C4—44no—
386C2×C4⋊C4—44no—
387C2×C4⋊C4C2414yes—
388C2×C4⋊C4C2414yes—
389C2×C4⋊C4C2411yescharacteristic
390C2×C4⋊C4C2411yescharacteristic
391C2×C4⋊C4C2411yescharacteristic
392C2×C4⋊C4C2411yescharacteristic
393C2×C4⋊C4C2411yescharacteristic
394C2×C4⋊C4C2411yescharacteristic
395C2×C22⋊C4—24no—
396C2×C22⋊C4—24no—
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—21no—
410C2×C22⋊C4—21no—
411C2×C22⋊C4—21no—
412C2×C22⋊C4—21no—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—21no—
415C2×C22⋊C4—21no—
416C2×C22⋊C4—48no—
417C2×C42—24no—
418C2×C42—24no—
419C2×C42—24no—
420C2×C42—21no—
421C2×C42—21no—
422C2×C42—21no—
423C2×C42—42no—
424C2×C42—42no—
425C2×C42—42no—
426C2×C42—42no—
427C2×C42—42no—
428C2×C42—42no—
429C2×C42—42no—
430C2×C42—42no—
431C2×C42—42no—
432C2×C42C2×D411yescharacteristic
433C2×C42C2×D411yescharacteristic
434C2×C42C2×D411yescharacteristic
435C2×C42C2×D411yescharacteristic
436C2×C42C2×D411yescharacteristic
437C2×C42C2×D411yescharacteristic
438C2×C42C2×D411yescharacteristic
439C2×C42C2×D411yescharacteristic
440C2×C42C2×D411yescharacteristic
441C2×C42C2×D411yescharacteristic
442C2×C42C2×D411yescharacteristic
443C2×C42C2×D411yescharacteristic
444C2×C42C2411yescharacteristic
445C2×C42C2411yescharacteristic
446C2×C42C2411yescharacteristic
447C2×C42C2411yescharacteristic
448#107—44no—
449#107—44no—
450#106—44no—
451#106—44no—
452C4⋊C8—24no—
453C4⋊C8—24no—
454C4⋊C8—44no—
455#103—44no—
456#103—44no—
457#102—44no—
458#102—44no—
459C22⋊C8—24no—
460C22⋊C8—24no—
461C22⋊C8—44no—
462#95—24no—
463#95—24no—
464#95—24no—
465#95—24no—
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—
480#95—21no—
481#95—21no—
482#95—21no—
483#95—21no—
484#95—21no—
485#95—21no—
486C24—22no—
487C24—22no—
488C24—22no—
489C24—22no—
490C24—22no—
491C24—21no—
492C24—41no—
493C24—41no—
494C24C22×D411yescharacteristic
495C24C22×D411yescharacteristic
496C24C22×D411yescharacteristic
497C2×Q8—21no—
498C2×Q8—22no—
499C2×Q8—22no—
500C2×Q8—21no—
501C2×Q8—44no—
502C2×Q8—44no—
503C2×Q8—44no—
504C2×Q8—44no—
505C2×Q8—44no—
506C2×Q8—44no—
507C2×Q8—816no—
508C2×D4—21no—
509C2×D4—22no—
510C2×D4—22no—
511C2×D4—21no—
512C2×D4—42no—
513C2×D4—42no—
514C2×D4—42no—
515C2×D4—42no—
516C2×D4—42no—
517C2×D4—42no—
518C2×D4—42no—
519C2×D4—42no—
520C2×D4—42no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—21no—
529C22×C4—22no—
530C22×C4—21no—
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—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—21no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—24no—
565C22×C4—24no—
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—41no—
579C22×C4—41no—
580C22×C4—41no—
581C22×C4—41no—
582C22×C4—48no—
583C22×C4—48no—
584C22×C4—416no—
585C22×C4—416no—
586C22×C4—44no—
587C22×C4—44no—
588C22×C4—44no—
589C22×C4—44no—
590C22×C4—44no—
591C22×C4—44no—
592C22×C4—42no—
593C22×C4—42no—
594C22×C4—42no—
595C22×C4AGL(1,ℤ/8)14yes—
596C22×C4#13714yes—
597C22×C4C22×D411yescharacteristic
598C22×C4C22×D411yescharacteristic
599C22×C4C22×D411yescharacteristic
600C22×C4C22×D411yescharacteristic
601C22×C4C22×D411yescharacteristic
602C22×C4C22×D411yescharacteristic
603C22×C4C22×D411yescharacteristic
604C22×C4C22×D411yescharacteristic
605C22×C4C22×D411yescharacteristic
606C22×C4C22×D411yescharacteristic
607C22×C4C22×D411yescharacteristic
608C22×C4H(5,𝔽2)12yes—
609C22×C42−1+414yes—
610C22×C42−1+412yes—
611C22×C4C2511yescharacteristic
612M16—88no—
613C2×C8—24no—
614C2×C8—24no—
615C2×C8—24no—
616C2×C8—24no—
617C2×C8—24no—
618C2×C8—24no—
619C4⋊C4—24no—
620C4⋊C4—24no—
621C4⋊C4—24no—
622C4⋊C4—21no—
623C4⋊C4—22no—
624C4⋊C4—21no—
625C4⋊C4—22no—
626C4⋊C4—24no—
627C4⋊C4—22no—
628C4⋊C4—21no—
629C4⋊C4—22no—
630C4⋊C4—21no—
631C4⋊C4—44no—
632C4⋊C4—44no—
633C4⋊C4—48no—
634C4⋊C4—48no—
635C4⋊C4—44no—
636C4⋊C4—44no—
637C4⋊C4—42no—
638C4⋊C4—42no—
639C4⋊C4—42no—
640C4⋊C4—42no—
641C4⋊C4—44no—
642C4⋊C4—42no—
643C4⋊C4—42no—
644C4⋊C4—44no—
645C4⋊C4—42no—
646C4⋊C4—44no—
647C4⋊C4—44no—
648C4⋊C4—42no—
649C4⋊C4—42no—
650C4⋊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—
665C22⋊C4—42no—
666C22⋊C4—42no—
667C22⋊C4—42no—
668C22⋊C4—42no—
669C22⋊C4—42no—
670C22⋊C4—42no—
671C22⋊C4—42no—
672C42—22no—
673C42—22no—
674C42—22no—
675C42—22no—
676C42—22no—
677C42—22no—
678C42—22no—
679C42—22no—
680C42—22no—
681C42—41no—
682C42—41no—
683C42—41no—
684C42—41no—
685C42—41no—
686C42—41no—
687C42—42no—
688C42—42no—
689C42—42no—
690C42H(5,𝔽2)14yes—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—28no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—44no—
709C23—44no—
710C23—44no—
711C23—44no—
712C23—44no—
713C23—44no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23#53612yes—
722C23#53712yes—
723C23C2×AGL(1,ℤ/8)12yes—
724C23C2×#13712yes—
725C23#57512yes—
726C23C23×D411yescharacteristic
727Q8—42no—
728Q8—42no—
729Q8—88no—
730Q8—88no—
731D4—42no—
732D4—42no—
733D4—84no—
734D4—84no—
735D4—84no—
736C2×C4—28no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
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—28no—
750C2×C4—24no—
751C2×C4—24no—
752C2×C4—24no—
753C2×C4—24no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
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—44no—
767C2×C4—44no—
768C2×C4—44no—
769C2×C4—44no—
770C2×C4—44no—
771C2×C4—44no—
772C2×C4—44no—
773C2×C4—44no—
774C2×C4—44no—
775C2×C4—44no—
776C2×C4—44no—
777C2×C4—44no—
778C2×C4—44no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—44no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—44no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—44no—
795C2×C4—44no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—44no—
807C2×C4—44no—
808C2×C4—88no—
809C2×C4—88no—
810C2×C4—84no—
811C2×C4#53412yes—
812C2×C4#53412yes—
813C2×C4#53612yes—
814C2×C4#53712yes—
815C2×C4C2×AGL(1,ℤ/8)12yes—
816C2×C4C2×AGL(1,ℤ/8)12yes—
817C2×C4C2×#13712yes—
818C2×C4C2×#13712yes—
819C2×C4#57512yes—
820C2×C4C2×H(5,𝔽2)11yescharacteristic
821C2×C4C2×H(5,𝔽2)12yes—
822C2×C4C2×2−1+412yes—
823C2×C4C2×2−1+411yescharacteristic
824C8—44no—
825C8—44no—
826C22—22no—
827C22—22no—
828C22—22no—
829C22—22no—
830C22—22no—
831C22—22no—
832C22—22no—
833C22—22no—
834C22—22no—
835C22—22no—
836C22—22no—
837C22—22no—
838C22—416no—
839C22—41no—
840C22—41no—
841C22—41no—
842C22—41no—
843C22—41no—
844C22—41no—
845C22—41no—
846C22—41no—
847C22—81no—
848C22—81no—
849C22—81no—
850C22—81no—
851C22—81no—
852C22—81no—
853C22—81no—
854C22#325114yes—
855C22C2×#53411yescharacteristic
856C22C2×#53611yescharacteristic
857C22C2×#53711yescharacteristic
858C22C22×AGL(1,ℤ/8)11yescharacteristic
859C22C22×#13711yescharacteristic
860C22C2×#57511yescharacteristic
861C22C2×#57511yescharacteristic
862C4—22no—
863C4—22no—
864C4—22no—
865C4—22no—
866C4—22no—
867C4—22no—
868C4—41no—
869C4—41no—
870C4—41no—
871C4—41no—
872C4—81no—
873C4—84no—
874C4—81no—
875C4—81no—
876C4—81no—
877C4—81no—
878C4—84no—
879C4—81no—
880C4—81no—
881C4#319414yes—
882C4#353612yes—
883C4#353812yes—
884C2—24no—
885C2—42no—
886C2—42no—
887C2—161no—
888C2#3744211yescharacteristic
889C2C2×#319411yescharacteristic
890C2#6075111yescharacteristic
891C2#6086011yescharacteristic
892C2#6086611yescharacteristic
893C2C2×#325111yescharacteristic
894C2#6091811yescharacteristic
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. #32744C2semidirect
4. #32742C2semidirect
5. #30295C2semidirect
6. #30200C2semidirect
7. #29972C2semidirect
8. #29941C2semidirect
9. #29760C2semidirect
10. #29689C2semidirect
11. #27647C2semidirect
12. #27644C2semidirect
13. #24845C2semidirect
14. #24844C2semidirect
15. #24559C2semidirect
17. #24301C2semidirect
18. #24298C2semidirect
19. #20626C2semidirect
26. C2×#475C22semidirect
27. C2×#474C22semidirect
65. #2101C22semidirect
66. #2088C22semidirect
67. #2087C22semidirect
68. #2085C22semidirect
69. #2084C22semidirect
70. #2083C22semidirect
73. #2072C22semidirect
74. #2071C22semidirect
75. #2068C22semidirect
76. #2065C22semidirect
77. #2059C22semidirect
78. #2058C22semidirect
79. #2057C22semidirect
80. #2042C22semidirect
83. #2024C22semidirect
84. #2023C22semidirect
85. #1988C22semidirect
86. #1988C22semidirect
87. #1948C22semidirect
88. #1947C22semidirect
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
#327442
#327422
#302952
#302002
#299722
#299412
#297602
#296892
#276472
#276442
#248452
#248442
#245592
#245582
#243012
#242982
#206262