Finite Group Databasebeta

← #6476676

Subgroups — #6476676

Order 512.

2196 conjugacy classes of subgroups.

The subgroup lattice has 938 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2857C211yesmaximal, characteristic, complemented
2C4×#525C211yesmaximal, characteristic
3#33114C212yesmaximal, complemented
4#32907C212yesmaximal, complemented
5#30116C212yesmaximal, complemented
6#30113C212yesmaximal, complemented
7#29332C212yesmaximal, complemented
8#28308C212yesmaximal, complemented
9#27680C211yesmaximal, characteristic, complemented
10#27677C211yesmaximal, characteristic, complemented
11#24652C212yesmaximal, complemented
12#24651C212yesmaximal, complemented
13#24212C211yesmaximal, characteristic, complemented
14#24209C211yesmaximal, characteristic, complemented
15#24010C212yesmaximal, complemented
16#23922C212yesmaximal
17#22044C212yesmaximal, complemented
18#22041C212yesmaximal, complemented
19#20714C211yesmaximal, characteristic, complemented
20C22×C4⋊Q8C2211yescharacteristic
21C2×#525C2211yescharacteristic
22C22×C22⋊Q8C2212yes—
23C2×C4×#41C2211yescharacteristic
24C23×C42C2211yescharacteristic
25C2×#485C2214yes—
26C2×#462C2212yescomplemented
27C2×#461C2212yescomplemented
28C2×#452C2214yes—
29C2×#451C2212yes—
30C2×#448C2212yes—
31C2×#431C2212yes—
32#2857—21no—
33#2857—21no—
34#2857—21no—
35#2857—21no—
36#2857C2212yes—
37#2857C2212yes—
38#2857C2212yes—
39#2857C2212yes—
40C4×C22⋊Q8C2211yescharacteristic
41C4×C22⋊Q8C2211yescharacteristic
42C4×C22⋊Q8C2211yescharacteristic
43C4×C22⋊Q8C2211yescharacteristic
44C4×#123—21no—
45C4×#123—21no—
46C4×#121C2211yescharacteristic
47C4×#121C2211yescharacteristic
48C4×#121C2211yescharacteristic
49C4×#121C2211yescharacteristic
50C4×#120—21no—
51C4×#120—21no—
52#2297C2211yescharacteristic
53#2296C2211yescharacteristic
54C2×#391C2212yes—
55C2×#389—21no—
56C2×#389—21no—
57#2290—21no—
58#2290—21no—
59C2×#384C2211yescharacteristic
60#2280C2211yescharacteristic
61C2×#380—21no—
62C2×#380—21no—
63C42×D4—21no—
64C42×D4—21no—
65C4×#117C2211yescharacteristic
66#2099C2212yescomplemented
67#2099C2212yescomplemented
68#2096C2212yescomplemented
69#2093C2212yescomplemented
70#2043C2212yescomplemented
71#2043C2212yescomplemented
72#2036C2214yes—
73#2035C2214yes—
74#2016C2212yescomplemented
75#2013C2212yescomplemented
76#2001C2214yes—
77#2000C2214yes—
78#1981C2212yescomplemented
79#1981C2212yescomplemented
80#1969C2214yescomplemented
81#1968C2214yescomplemented
82#1948C2212yescomplemented
83#1947C2212yescomplemented
84#1933C2214yescomplemented
85#1933C2214yescomplemented
86#1928C2214yescomplemented
87#1927C2214yescomplemented
88#1878C2214yescomplemented
89#1877C2214yescomplemented
90#1874C2212yes—
91#1873C2214yes—
92#1873C2214yes—
93#1872C2212yes—
94#1853C2212yes—
95#1852C2212yes—
96#1817C2212yes—
97#1803C2212yescomplemented
98#1802C2212yescomplemented
99#1797C2211yescharacteristic
100#1797C2211yescharacteristic
101#1797C2212yes—
102#1787C2212yes—
103#1787C2212yes—
104#1779C2212yes—
105C4×C22⋊C8C2212yes—
106C4×C22⋊C8C2212yes—
107C22×#41C2311yescharacteristic
108C23×Q8C2312yes—
109C24×C4D411yescharacteristic
110C24×C4D411yescharacteristic
111C24×C4C2311yescharacteristic
112C22×Q16C2314yes—
113C22×SD16C2314yes—
114C2×C4⋊Q8—21no—
115C2×C4⋊Q8—21no—
116C2×C4⋊Q8—44no—
117C2×C4⋊Q8C2312yes—
118C2×C4⋊Q8C2312yes—
119#525—24no—
120#525—24no—
121C2×#123—21no—
122C2×C22⋊Q8—22no—
123C2×C22⋊Q8—22no—
124C2×C22⋊Q8—48no—
125C2×C22⋊Q8C2314yes—
126C2×C22⋊Q8C2311yescharacteristic
127C2×C22⋊Q8C2311yescharacteristic
128C2×C22⋊Q8C2314yes—
129C2×#121C2311yescharacteristic
130C2×#121C2311yescharacteristic
131C2×#120—21no—
132C4×#41—44no—
133C2×C4×Q8C2311yescharacteristic
134C2×C4×Q8C2311yescharacteristic
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×D4—21no—
142C2×C4×D4—21no—
143C2×C4×D4C2311yescharacteristic
144C2×C4×D4C2311yescharacteristic
145C2×#117—21no—
146C2×#117C2311yescharacteristic
147C2×#117C2311yescharacteristic
148C2×#117C2311yescharacteristic
149C22×C4⋊C4—22no—
150C22×C4⋊C4—21no—
151C22×C4⋊C4—21no—
152C22×C4⋊C4—21no—
153C22×C4⋊C4—21no—
154C22×C4⋊C4C2312yes—
155C22×C22⋊C4—22no—
156C22×C42—21no—
157C22×C42—44no—
158C22×C42D411yescharacteristic
159C22×C42D411yescharacteristic
160C22×C42D411yescharacteristic
161C22×C42D411yescharacteristic
162C22×C42D411yescharacteristic
163C22×C42D411yescharacteristic
164C22×C42C2311yescharacteristic
165C22×C42C2311yescharacteristic
166C22×C42C2311yescharacteristic
167C22×C42C2311yescharacteristic
168C22×C42C2311yescharacteristic
169C22×C42C2311yescharacteristic
170#485—48no—
171#462—44no—
172#461—44no—
173#452—48no—
174#451—28no—
175#448—28no—
176#431—44no—
177C2×#107C2314yes—
178C2×#106C2314yes—
179C2×C4⋊C8C2312yes—
180C2×C4⋊C8C2312yes—
181C2×#103C2314yes—
182C2×#103C2314yes—
183C2×#103C2314yes—
184C2×#103C2314yes—
185C2×#103C2314yes—
186C2×#103C2314yes—
187C2×#103C2314yes—
188C2×#102C2314yes—
189C2×C22⋊C8C2314yes—
190C2×C22⋊C8C2312yes—
191C2×C22⋊C8C2312yes—
192C2×C22⋊C8C2314yes—
193C2×C4×C8C2314yes—
194#391—22no—
195#391—22no—
196#391C2314yes—
197#391C2314yes—
198#391C2311yescharacteristic
199#391C2311yescharacteristic
200#390C2311yescharacteristic
201#390C2311yescharacteristic
202#389—22no—
203#389—22no—
204#389—22no—
205#389—22no—
206#389—22no—
207#389—22no—
208#389—22no—
209#389—22no—
210#389C2311yescharacteristic
211#389C2311yescharacteristic
212#389C2311yescharacteristic
213#389C2311yescharacteristic
214#388—21no—
215#388—21no—
216#388—21no—
217#388—21no—
218#387—21no—
219#387—21no—
220#387—21no—
221#387—21no—
222#386—21no—
223#386—21no—
224#386—21no—
225#386—21no—
226#386—21no—
227#386—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#381—21no—
239#380—22no—
240#380—22no—
241#380—22no—
242#380—22no—
243#380—22no—
244#380—22no—
245#380—22no—
246#380—22no—
247#380C2311yescharacteristic
248#380C2311yescharacteristic
249#380C2311yescharacteristic
250#380C2311yescharacteristic
251#379—21no—
252C4×C4⋊C4—21no—
253C4×C4⋊C4—21no—
254C4×C4⋊C4—21no—
255C4×C4⋊C4—21no—
256C4×C4⋊C4—21no—
257C4×C4⋊C4—21no—
258C4×C4⋊C4C2311yescharacteristic
259C4×C4⋊C4C2311yescharacteristic
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—
267C4×C22⋊C4—21no—
268C4×C22⋊C4—21no—
269C4×C22⋊C4—21no—
270C4×C22⋊C4—21no—
271C4×C22⋊C4—21no—
272C4×C22⋊C4—21no—
273C4×C22⋊C4—21no—
274C4×C22⋊C4—21no—
275C4×C22⋊C4—21no—
276#376—21no—
277C2×#95—22no—
278C2×#95—22no—
279C43—21no—
280#340C2314yes—
281#340C2314yes—
282#340C2314yes—
283#340C2314yes—
284#336C2312yes—
285#336C2312yes—
286#336C2314yes—
287C25C2×D411yescharacteristic
288C2×#41—22no—
289C2×#41—22no—
290C2×#41—24no—
291C2×#41—42no—
292C22×Q8—22no—
293C22×Q8—24no—
294C22×Q8—24no—
295C22×Q8—44no—
296C22×Q8—44no—
297C22×Q8C2414yes—
298C22×Q8C2411yescharacteristic
299C22×D4—21no—
300C22×D4—21no—
301C22×D4—21no—
302C22×D4C2411yescharacteristic
303C23×C4—24no—
304C23×C4—24no—
305C23×C4—24no—
306C23×C4—21no—
307C23×C4—22no—
308C23×C4—22no—
309C23×C4—24no—
310C23×C4—22no—
311C23×C4—22no—
312C23×C4—21no—
313C23×C4—21no—
314C23×C4—42no—
315C23×C4—42no—
316C23×C4—42no—
317C23×C4—42no—
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×C4C2×D411yescharacteristic
331C23×C4C2×D411yescharacteristic
332C23×C4C2×D411yescharacteristic
333C23×C4C2411yescharacteristic
334C23×C4C2411yescharacteristic
335C23×C4C2411yescharacteristic
336C2×Q16—28no—
337C2×Q16—44no—
338C2×Q16—44no—
339C2×SD16—28no—
340C2×SD16—44no—
341C2×SD16—44no—
342C22×C8C2414yes—
343C22×C8C2414yes—
344C4⋊Q8—24no—
345C4⋊Q8—24no—
346C4⋊Q8—44no—
347C4⋊Q8—44no—
348C4⋊Q8—44no—
349#123—28no—
350C22⋊Q8—22no—
351C22⋊Q8—22no—
352C22⋊Q8—22no—
353C22⋊Q8—28no—
354C22⋊Q8—28no—
355C22⋊Q8—44no—
356C22⋊Q8—44no—
357C22⋊Q8—48no—
358C22⋊Q8—48no—
359C22⋊Q8#4114yes—
360#121—22no—
361#121—22no—
362#121—22no—
363#121#4114yes—
364#120—28no—
365C4×Q8—24no—
366C4×Q8—42no—
367C4×D4—28no—
368C4×D4—28no—
369C4×D4—24no—
370C4×D4—42no—
371C4×D4—44no—
372C4×D4—44no—
373C4×D4—44no—
374C4×D4—44no—
375C4×D4—44no—
376C4×D4—44no—
377#117—22no—
378#117—22no—
379#117—24no—
380#117—44no—
381#117—42no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—24no—
385C2×C4⋊C4—24no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—44no—
402C2×C4⋊C4—44no—
403C2×C4⋊C4—48no—
404C2×C4⋊C4—44no—
405C2×C4⋊C4—44no—
406C2×C4⋊C4—44no—
407C2×C4⋊C4C2414yes—
408C2×C4⋊C4C2411yescharacteristic
409C2×C4⋊C4C2411yescharacteristic
410C2×C4⋊C4C2411yescharacteristic
411C2×C4⋊C4C2411yescharacteristic
412C2×C4⋊C4C2411yescharacteristic
413C2×C4⋊C4C2411yescharacteristic
414C2×C22⋊C4—21no—
415C2×C22⋊C4—21no—
416C2×C22⋊C4—21no—
417C2×C22⋊C4—21no—
418C2×C22⋊C4—21no—
419C2×C22⋊C4—24no—
420C2×C22⋊C4—24no—
421C2×C22⋊C4—21no—
422C2×C22⋊C4—21no—
423C2×C22⋊C4—21no—
424C2×C22⋊C4—21no—
425C2×C22⋊C4—21no—
426C2×C22⋊C4—21no—
427C2×C22⋊C4—21no—
428C2×C22⋊C4—21no—
429C2×C22⋊C4—21no—
430C2×C22⋊C4—21no—
431C2×C22⋊C4—21no—
432C2×C22⋊C4—21no—
433C2×C22⋊C4—48no—
434C2×C42—21no—
435C2×C42—24no—
436C2×C42—24no—
437C2×C42—24no—
438C2×C42—21no—
439C2×C42—21no—
440C2×C42—21no—
441C2×C42—21no—
442C2×C42—21no—
443C2×C42—21no—
444C2×C42—21no—
445C2×C42—21no—
446C2×C42—42no—
447C2×C42—42no—
448C2×C42—42no—
449C2×C42—42no—
450C2×C42—42no—
451C2×C42—42no—
452C2×C42—42no—
453C2×C42—42no—
454C2×C42—42no—
455C2×C42—44no—
456C2×C42C2×D411yescharacteristic
457C2×C42C2×D411yescharacteristic
458C2×C42C2×D411yescharacteristic
459C2×C42C2×D411yescharacteristic
460C2×C42C2×D411yescharacteristic
461C2×C42C2×D411yescharacteristic
462C2×C42C2×D411yescharacteristic
463C2×C42C2×D411yescharacteristic
464C2×C42C2×D411yescharacteristic
465C2×C42C2×D411yescharacteristic
466C2×C42C2×D411yescharacteristic
467C2×C42C2×D411yescharacteristic
468C2×C42C2411yescharacteristic
469C2×C42C2411yescharacteristic
470C2×C42C2411yescharacteristic
471C2×C42C2411yescharacteristic
472#107—44no—
473#106—44no—
474C4⋊C8—24no—
475C4⋊C8—24no—
476#103—28no—
477#103—28no—
478#103—44no—
479#103—44no—
480#103—44no—
481#103—44no—
482#103—44no—
483#102—44no—
484C22⋊C8—24no—
485C22⋊C8—24no—
486C22⋊C8—28no—
487C22⋊C8—44no—
488C4×C8—44no—
489#95—24no—
490#95—24no—
491#95—24no—
492#95—24no—
493#95—21no—
494#95—21no—
495#95—21no—
496#95—21no—
497#95—21no—
498#95—21no—
499#95—21no—
500#95—21no—
501#95—21no—
502#95—21no—
503#95—21no—
504#95—21no—
505#95—21no—
506#95—21no—
507#95—21no—
508#95—21no—
509C24—22no—
510C24—22no—
511C24—22no—
512C24—22no—
513C24—22no—
514C24—21no—
515C24—41no—
516C24—41no—
517C24C22×D411yescharacteristic
518C24C22×D411yescharacteristic
519C24C22×D411yescharacteristic
520#41—48no—
521#41—48no—
522C2×Q8—21no—
523C2×Q8—24no—
524C2×Q8—24no—
525C2×Q8—22no—
526C2×Q8—22no—
527C2×Q8—24no—
528C2×Q8—24no—
529C2×Q8—24no—
530C2×Q8—24no—
531C2×Q8—44no—
532C2×Q8—44no—
533C2×Q8—44no—
534C2×Q8—88no—
535C2×Q8—88no—
536C2×Q8C2×#4112yes—
537C2×D4—24no—
538C2×D4—24no—
539C2×D4—24no—
540C2×D4—21no—
541C2×D4—22no—
542C2×D4—22no—
543C2×D4—42no—
544C2×D4—42no—
545C2×D4—42no—
546C2×D4—42no—
547C2×D4—42no—
548C2×D4—42no—
549C2×D4C2×#4112yes—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—24no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—24no—
598C22×C4—24no—
599C22×C4—41no—
600C22×C4—41no—
601C22×C4—41no—
602C22×C4—41no—
603C22×C4—41no—
604C22×C4—41no—
605C22×C4—41no—
606C22×C4—41no—
607C22×C4—41no—
608C22×C4—41no—
609C22×C4—41no—
610C22×C4—41no—
611C22×C4—416no—
612C22×C4—48no—
613C22×C4—48no—
614C22×C4—42no—
615C22×C4—416no—
616C22×C4—42no—
617C22×C4—42no—
618C22×C4—42no—
619C22×C4—44no—
620C22×C4—44no—
621C22×C4—44no—
622C22×C4—44no—
623C22×C4—44no—
624C22×C4—44no—
625C22×C4—42no—
626C22×C4—42no—
627C22×C4—42no—
628C22×C4—42no—
629C22×C4#13514yes—
630C22×C4#13714yes—
631C22×C4#13714yes—
632C22×C4C22×D411yescharacteristic
633C22×C4C22×D411yescharacteristic
634C22×C4C22×D411yescharacteristic
635C22×C4C22×D411yescharacteristic
636C22×C4C22×D411yescharacteristic
637C22×C4C22×D411yescharacteristic
638C22×C4C22×D411yescharacteristic
639C22×C4C22×D411yescharacteristic
640C22×C4C22×D411yescharacteristic
641C22×C4C22×D411yescharacteristic
642C22×C4C22×D411yescharacteristic
643C22×C4C2×#4112yes—
644C22×C4C2×#4112yes—
645C22×C4H(5,𝔽2)14yes—
646C22×C4C2511yescharacteristic
647Q16—88no—
648SD16—88no—
649C2×C8—24no—
650C2×C8—24no—
651C2×C8—24no—
652C2×C8—24no—
653C2×C8—24no—
654C2×C8—24no—
655C4⋊C4—24no—
656C4⋊C4—24no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—24no—
660C4⋊C4—22no—
661C4⋊C4—22no—
662C4⋊C4—22no—
663C4⋊C4—22no—
664C4⋊C4—24no—
665C4⋊C4—44no—
666C4⋊C4—44no—
667C4⋊C4—48no—
668C4⋊C4—44no—
669C4⋊C4—44no—
670C4⋊C4—42no—
671C4⋊C4—44no—
672C4⋊C4—44no—
673C4⋊C4—42no—
674C4⋊C4—48no—
675C4⋊C4—44no—
676C4⋊C4—44no—
677C4⋊C4—42no—
678C4⋊C4—42no—
679C4⋊C4—42no—
680C4⋊C4—44no—
681C4⋊C4—42no—
682C4⋊C4C2×#4112yes—
683C4⋊C4C2×#4112yes—
684C22⋊C4—24no—
685C22⋊C4—24no—
686C22⋊C4—24no—
687C22⋊C4—24no—
688C22⋊C4—24no—
689C22⋊C4—42no—
690C22⋊C4—48no—
691C22⋊C4—42no—
692C22⋊C4—42no—
693C22⋊C4—48no—
694C22⋊C4—42no—
695C22⋊C4—42no—
696C22⋊C4—42no—
697C22⋊C4—42no—
698C22⋊C4—42no—
699C22⋊C4—42no—
700C22⋊C4—42no—
701C22⋊C4—42no—
702C22⋊C4—42no—
703C42—24no—
704C42—22no—
705C42—22no—
706C42—22no—
707C42—22no—
708C42—22no—
709C42—22no—
710C42—22no—
711C42—22no—
712C42—22no—
713C42—41no—
714C42—41no—
715C42—41no—
716C42—41no—
717C42—41no—
718C42—41no—
719C42—42no—
720C42—42no—
721C42—42no—
722C42—42no—
723C42—42no—
724C42—42no—
725C42—42no—
726C42—42no—
727C42H(5,𝔽2)14yes—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—28no—
733C23—21no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—21no—
739C23—21no—
740C23—21no—
741C23—21no—
742C23—21no—
743C23—21no—
744C23—21no—
745C23—22no—
746C23—44no—
747C23—44no—
748C23—44no—
749C23—44no—
750C23—44no—
751C23—44no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—41no—
758C23#52512yes—
759C23#53512yes—
760C23C2×#13512yes—
761C23C2×#13712yes—
762C23C2×#13712yes—
763C23C23×D411yescharacteristic
764Q8—24no—
765Q8—42no—
766Q8—44no—
767Q8—44no—
768Q8—44no—
769Q8—44no—
770Q8—88no—
771D4—24no—
772D4—48no—
773D4—48no—
774D4—48no—
775D4—42no—
776C2×C4—28no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—28no—
794C2×C4—28no—
795C2×C4—24no—
796C2×C4—24no—
797C2×C4—24no—
798C2×C4—24no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—21no—
802C2×C4—22no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—44no—
809C2×C4—44no—
810C2×C4—44no—
811C2×C4—44no—
812C2×C4—44no—
813C2×C4—44no—
814C2×C4—44no—
815C2×C4—44no—
816C2×C4—44no—
817C2×C4—44no—
818C2×C4—44no—
819C2×C4—48no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—44no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—44no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—44no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—44no—
836C2×C4—44no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—44no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—44no—
847C2×C4—84no—
848C2×C4—88no—
849C2×C4—88no—
850C2×C4—84no—
851C2×C4#52512yes—
852C2×C4#53412yes—
853C2×C4#53412yes—
854C2×C4#53512yes—
855C2×C4C2×#13512yes—
856C2×C4C2×#13512yes—
857C2×C4C2×#13712yes—
858C2×C4C2×#13712yes—
859C2×C4C2×#13712yes—
860C2×C4C2×#13712yes—
861C2×C4#57512yes—
862C2×C4C22×#4111yescharacteristic
863C2×C4C22×#4111yescharacteristic
864C2×C4C2×H(5,𝔽2)12yes—
865C2×C4C2×H(5,𝔽2)12yes—
866C8—44no—
867C8—44no—
868C22—22no—
869C22—22no—
870C22—22no—
871C22—22no—
872C22—22no—
873C22—22no—
874C22—22no—
875C22—22no—
876C22—22no—
877C22—22no—
878C22—22no—
879C22—22no—
880C22—416no—
881C22—41no—
882C22—41no—
883C22—41no—
884C22—41no—
885C22—41no—
886C22—41no—
887C22—41no—
888C22—41no—
889C22—42no—
890C22—42no—
891C22—42no—
892C22—81no—
893C22—81no—
894C22—81no—
895C22—81no—
896C22#310714yes—
897C22C2×#52511yescharacteristic
898C22C2×#53411yescharacteristic
899C22C2×#53511yescharacteristic
900C22C22×#13511yescharacteristic
901C22C22×#13711yescharacteristic
902C22C22×#13711yescharacteristic
903C22C2×#57511yescharacteristic
904C4—22no—
905C4—22no—
906C4—22no—
907C4—22no—
908C4—22no—
909C4—22no—
910C4—22no—
911C4—22no—
912C4—41no—
913C4—42no—
914C4—41no—
915C4—42no—
916C4—42no—
917C4—84no—
918C4—81no—
919C4—81no—
920C4—81no—
921C4—84no—
922C4—81no—
923C4#319014yes—
924C4#351912yes—
925C4#351912yes—
926C2—24no—
927C2—42no—
928C2—42no—
929C2—82no—
930C2#3507611yescharacteristic
931C2C2×#310711yescharacteristic
932C2#6056211yescharacteristic
933C2C2×#319011yescharacteristic
934C2#6075111yescharacteristic
935C2#6078211yescharacteristic
936C2#6080011yescharacteristic
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. #33114C2semidirect
4. #32907C2semidirect
5. #30116C2semidirect
6. #30113C2semidirect
7. #29332C2semidirect
8. #28308C2semidirect
9. #27680C2semidirect
10. #27677C2semidirect
11. #24652C2semidirect
12. #24651C2semidirect
13. #24212C2semidirect
14. #24209C2semidirect
15. #24010C2semidirect
17. #22044C2semidirect
18. #22041C2semidirect
19. #20714C2semidirect
26. C2×#462C22semidirect
27. C2×#461C22semidirect
66. #2099C22semidirect
67. #2099C22semidirect
68. #2096C22semidirect
69. #2093C22semidirect
70. #2043C22semidirect
71. #2043C22semidirect
74. #2016C22semidirect
75. #2013C22semidirect
78. #1981C22semidirect
79. #1981C22semidirect
80. #1969C22semidirect
81. #1968C22semidirect
82. #1948C22semidirect
83. #1947C22semidirect
84. #1933C22semidirect
85. #1933C22semidirect
86. #1928C22semidirect
87. #1927C22semidirect
88. #1878C22semidirect
89. #1877C22semidirect
97. #1803C22semidirect
98. #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
#331142
#329072
#301162
#301132
#293322
#283082
#276802
#276772
#246522
#246512
#242122
#242092
#240102
#239222
#220442
#220412
#207142