Finite Group Databasebeta

← #6375628

Subgroups — #6375628

Order 512.

2636 conjugacy classes of subgroups.

The subgroup lattice has 905 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3094C211yesmaximal, characteristic
2C2×C4×#121C211yesmaximal, characteristic
3C2×#2296C211yesmaximal, characteristic, complemented
4#22086C214yesmaximal, complemented
5#22082C212yesmaximal, complemented
6#22081C212yesmaximal, complemented
7#22080C214yesmaximal, complemented
8#22076C212yesmaximal, complemented
9#22075C212yesmaximal, complemented
10#21159C212yesmaximal, complemented
11#21095C212yesmaximal, complemented
12#21033C212yesmaximal, complemented
13#20912C211yesmaximal, characteristic
14#20873C212yesmaximal, complemented
15#20846C211yesmaximal, characteristic, complemented
16#20702C211yesmaximal, characteristic, complemented
17C4×#407C211yesmaximal, characteristic, complemented
18C22×#121C2211yescharacteristic
19C22×C4×D4—21no—
20C22×C4×D4C2211yescharacteristic
21C22×#117C2211yescharacteristic
22C22×#117C2211yescharacteristic
23C23×C42C2211yescharacteristic
24#3094C4116yescomplemented
25C2×#481C2212yes—
26C2×#482C2214yes—
27C2×#480C2212yes—
28C2×#428C2212yes—
29C2×#428C2212yes—
30C2×#418C2212yes—
31C2×#418C2212yes—
32C2×#407C2211yescharacteristic
33C2×#407C2211yescharacteristic
34C2×C4×M16C2212yes—
35C4×#121—21no—
36C4×#121—21no—
37C4×#121—21no—
38C4×#121—21no—
39C4×#121C2212yes—
40C4×#121C2212yes—
41C4×#121C2212yes—
42C4×#121C2212yes—
43#2296—21no—
44#2296—21no—
45#2296—21no—
46#2296—21no—
47#2296C2212yes—
48#2296C2212yes—
49#2296C2212yescomplemented
50#2296C2212yescomplemented
51C2×#390C2211yescharacteristic
52C2×#389C2211yescharacteristic
53C2×#389C2211yescharacteristic, complemented
54C2×#389C2211yescharacteristic, complemented
55C2×#389C2211yescharacteristic, complemented
56C2×#389C2211yescharacteristic, complemented
57C2×#388—21no—
58C2×#386—21no—
59C2×#385—21no—
60C2×#385—21no—
61C2×#380C2211yescharacteristic
62C2×C4×C4⋊C4—21no—
63C2×C4×C4⋊C4—21no—
64C2×C4×C4⋊C4C2211yescharacteristic
65C2×C4×C22⋊C4—21no—
66#1944C2214yescomplemented
67#1943C2214yescomplemented
68#1942C2214yescomplemented
69#1941C2214yescomplemented
70#1936C2214yescomplemented
71#1936C2214yescomplemented
72#1934C2214yescomplemented
73#1934C2214yescomplemented
74#1921C2214yescomplemented
75#1920C2214yescomplemented
76#1919C2214yescomplemented
77#1918C2214yescomplemented
78#1875C2214yes—
79#1874C2212yes—
80#1874C2212yes—
81#1864C2214yescomplemented
82#1864C2214yescomplemented
83#1862C2214yescomplemented
84#1862C2214yescomplemented
85#1854C2214yescomplemented
86#1853C2212yescomplemented
87#1852C2212yescomplemented
88#1825C2214yescomplemented
89#1824C2212yescomplemented
90#1823C2212yescomplemented
91#1749C2212yescomplemented
92#1749C2212yescomplemented
93C4×C22⋊C8C2212yescomplemented
94C4×C22⋊C8C2212yescomplemented
95#1736C2212yes—
96#1736C2212yes—
97#1736C2212yes—
98#1736C2212yes—
99#1728C2212yes—
100C23×D4—21no—
101C23×D4C2311yescharacteristic
102C24×C4—21no—
103C24×C4D411yescharacteristic
104C24×C4D411yescharacteristic
105C24×C4C2311yescharacteristic
106C22×M16C2312yes—
107C22×M16C2312yes—
108C2×#121—21no—
109C2×#121—21no—
110C2×#121—24no—
111C2×#121C2×C418yes—
112C2×#121C2312yes—
113C2×#121C2312yes—
114C2×C4×D4—22no—
115C2×C4×D4—22no—
116C2×C4×D4—22no—
117C2×C4×D4—22no—
118C2×C4×D4—21no—
119C2×C4×D4—21no—
120C2×C4×D4—44no—
121C2×C4×D4—48no—
122C2×C4×D4C2312yes—
123C2×C4×D4C2312yes—
124C2×#117—21no—
125C2×#117—21no—
126C2×#117—24no—
127C2×#117—21no—
128C2×#117—21no—
129C2×#117—44no—
130C2×#117C2×C418yescomplemented
131C2×#117C2312yes—
132C2×#117C2312yes—
133C2×#117C2312yes—
134C2×#117C2312yes—
135C22×C4⋊C4—21no—
136C22×C4⋊C4—21no—
137C22×C4⋊C4—21no—
138C22×C4⋊C4—21no—
139C22×C4⋊C4—21no—
140C22×C4⋊C4C2311yescharacteristic
141C22×C4⋊C4C2311yescharacteristic
142C22×C4⋊C4C2311yescharacteristic
143C22×C4⋊C4C2311yescharacteristic
144C22×C4⋊C4C2311yescharacteristic
145C22×C4⋊C4C2311yescharacteristic
146C22×C4⋊C4C2311yescharacteristic
147C22×C22⋊C4—21no—
148C22×C22⋊C4—21no—
149C22×C22⋊C4—21no—
150C22×C22⋊C4—21no—
151C22×C22⋊C4—21no—
152C22×C22⋊C4—21no—
153C22×C22⋊C4—21no—
154C22×C42—21no—
155C22×C42—21no—
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#482C2×C4132yescomplemented
171#481C2×C4116yescomplemented
172#480C2×C4116yescomplemented
173#428—44no—
174#428C2×C4116yescomplemented
175C2×#107C2314yes—
176C2×#107C2314yes—
177C2×#106C2314yes—
178C2×#106C2314yes—
179#418—44no—
180#418C2×C4116yescomplemented
181C2×#102C2314yes—
182C2×#102C2314yes—
183C2×#102C2314yes—
184C2×#102C2314yes—
185#407—24no—
186#407C2×C418yescomplemented
187C2×C22⋊C8C2312yes—
188C2×C22⋊C8C2312yes—
189C2×C22⋊C8C2312yes—
190C2×C22⋊C8C2312yes—
191C4×M16—44no—
192C2×#97C2314yes—
193C2×C4×C8C2314yes—
194#390—21no—
195#390—21no—
196#390C2312yes—
197#390C2312yes—
198#389—21no—
199#389—21no—
200#389—21no—
201#389—21no—
202#389—21no—
203#389—21no—
204#389—21no—
205#389—21no—
206#389—21no—
207#389—21no—
208#389C2312yes—
209#389C2312yes—
210#389C2312yes—
211#389C2312yes—
212#389C2312yes—
213#389C2312yes—
214#389C2312yes—
215#389C2312yes—
216#389C2312yes—
217#389C2312yes—
218#388—22no—
219#388—22no—
220#388—22no—
221#388—22no—
222#386—22no—
223#386—22no—
224#386—22no—
225#386—22no—
226#385—22no—
227#385—22no—
228#385—22no—
229#385—22no—
230#385—22no—
231#385—22no—
232#385—22no—
233#385—22no—
234#380—21no—
235#380—21no—
236#380C2312yes—
237#380C2312yes—
238C4×C4⋊C4—22no—
239C4×C4⋊C4—22no—
240C4×C4⋊C4—22no—
241C4×C4⋊C4—22no—
242C4×C4⋊C4—22no—
243C4×C4⋊C4—22no—
244C4×C4⋊C4—22no—
245C4×C4⋊C4—22no—
246C4×C4⋊C4—21no—
247C4×C4⋊C4—21no—
248C4×C4⋊C4C2312yes—
249C4×C4⋊C4C2312yes—
250C4×C22⋊C4—22no—
251C4×C22⋊C4—22no—
252C4×C22⋊C4—22no—
253C4×C22⋊C4—22no—
254C2×#95—21no—
255C2×#95—21no—
256C2×#95—21no—
257C2×#95—21no—
258C2×#95—21no—
259C2×#95—21no—
260C2×#95—21no—
261#340C2314yes—
262#340C2314yes—
263#340C2314yes—
264#340C2314yes—
265#340C2314yes—
266#340C2314yes—
267#340C2314yes—
268#340C2314yes—
269#336C2314yes—
270#336C2314yes—
271C25—21no—
272C25C2×D411yescharacteristic
273C22×D4—28no—
274C22×D4—22no—
275C22×D4—22no—
276C22×D4—21no—
277C22×D4—22no—
278C22×D4—24no—
279C22×D4—24no—
280C22×D4—44no—
281C22×D4—44no—
282C22×D4C22×C414yes—
283C22×D4C2412yes—
284C23×C4—24no—
285C23×C4—24no—
286C23×C4—21no—
287C23×C4—21no—
288C23×C4—21no—
289C23×C4—24no—
290C23×C4—21no—
291C23×C4—21no—
292C23×C4—21no—
293C23×C4—21no—
294C23×C4—22no—
295C23×C4—22no—
296C23×C4—42no—
297C23×C4—42no—
298C23×C4—42no—
299C23×C4—42no—
300C23×C4—42no—
301C23×C4—44no—
302C23×C4—44no—
303C23×C4—44no—
304C23×C4C22×C414yes—
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×C4#4114yes—
321C23×C4C2411yescharacteristic
322C23×C4C2411yescharacteristic
323C23×C4C2411yescharacteristic
324C2×M16—24no—
325C2×M16—24no—
326C2×M16—24no—
327C2×M16—24no—
328C2×M16—24no—
329C2×M16C22×C418yes—
330C22×C8C2414yes—
331C22×C8C2414yes—
332#121—28no—
333#121—28no—
334#121—24no—
335#121—24no—
336#121C22×C418yes—
337#121C22×C418yes—
338C4×D4—44no—
339C4×D4—44no—
340C4×D4—44no—
341C4×D4—44no—
342C4×D4—48no—
343C4×D4—48no—
344C4×D4—48no—
345C4×D4—48no—
346#117—28no—
347#117—28no—
348#117—24no—
349#117—24no—
350#117—24no—
351#117—24no—
352#117—42no—
353#117—42no—
354#117—44no—
355#117—44no—
356#117C22×C418yes—
357#117C22×C418yescomplemented
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—22no—
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—22no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—42no—
381C2×C4⋊C4—42no—
382C2×C4⋊C4—44no—
383C2×C4⋊C4—44no—
384C2×C4⋊C4—44no—
385C2×C4⋊C4—44no—
386C2×C4⋊C4—44no—
387C2×C4⋊C4C22×C414yes—
388C2×C4⋊C4C22×C414yescomplemented
389C2×C4⋊C4C22×C414yescomplemented
390C2×C4⋊C4C2412yes—
391C2×C4⋊C4C2412yes—
392C2×C4⋊C4C2412yes—
393C2×C4⋊C4C2412yes—
394C2×C4⋊C4C2412yes—
395C2×C4⋊C4C2412yes—
396C2×C4⋊C4C2412yes—
397C2×C22⋊C4—28no—
398C2×C22⋊C4—22no—
399C2×C22⋊C4—22no—
400C2×C22⋊C4—28no—
401C2×C22⋊C4—22no—
402C2×C22⋊C4—22no—
403C2×C22⋊C4—22no—
404C2×C22⋊C4—22no—
405C2×C22⋊C4—22no—
406C2×C22⋊C4—22no—
407C2×C22⋊C4—22no—
408C2×C22⋊C4—22no—
409C2×C22⋊C4—22no—
410C2×C22⋊C4—22no—
411C2×C22⋊C4—22no—
412C2×C22⋊C4—22no—
413C2×C22⋊C4—44no—
414C2×C22⋊C4—44no—
415C2×C22⋊C4—44no—
416C2×C22⋊C4—44no—
417C2×C22⋊C4—44no—
418C2×C42—28no—
419C2×C42—22no—
420C2×C42—22no—
421C2×C42—24no—
422C2×C42—24no—
423C2×C42—22no—
424C2×C42—22no—
425C2×C42—22no—
426C2×C42—22no—
427C2×C42—42no—
428C2×C42—42no—
429C2×C42—42no—
430C2×C42—42no—
431C2×C42—42no—
432C2×C42—42no—
433C2×C42—42no—
434C2×C42—42no—
435C2×C42—42no—
436C2×C42—42no—
437C2×C42—44no—
438C2×C42—44no—
439C2×C42C2×D411yescharacteristic
440C2×C42C2×D411yescharacteristic
441C2×C42C2×D411yescharacteristic
442C2×C42C2×D411yescharacteristic
443C2×C42C2×D411yescharacteristic
444C2×C42C2×D411yescharacteristic
445C2×C42C2×D411yescharacteristic
446C2×C42C2×D411yescharacteristic
447C2×C42C2×D411yescharacteristic
448C2×C42C2×D411yescharacteristic
449C2×C42C2×D411yescharacteristic
450C2×C42C2×D411yescharacteristic
451C2×C42C2411yescharacteristic
452C2×C42C2411yescharacteristic
453C2×C42C2411yescharacteristic
454C2×C42C2411yescharacteristic
455#107—44no—
456#107C22×C4116yescomplemented
457#106—44no—
458#106C22×C4116yescomplemented
459#102—44no—
460#102—44no—
461#102C22×C4116yescomplemented
462#102C22×C4116yescomplemented
463C22⋊C8—24no—
464C22⋊C8—24no—
465C22⋊C8C22×C418yescomplemented
466C22⋊C8C22×C418yescomplemented
467#97—44no—
468C4×C8—44no—
469#95—22no—
470#95—22no—
471#95—22no—
472#95—22no—
473#95—22no—
474#95—22no—
475#95—22no—
476#95—22no—
477#95—22no—
478#95—22no—
479#95—22no—
480#95—22no—
481#95—22no—
482#95—22no—
483C24—22no—
484C24—22no—
485C24—22no—
486C24—22no—
487C24—24no—
488C24—22no—
489C24—41no—
490C24—41no—
491C24—42no—
492C24—42no—
493C24—42no—
494C24—42no—
495C24—42no—
496C24—42no—
497C24C4×D414yes—
498C24C22×D411yescharacteristic
499C24C22×D411yescharacteristic
500C24C22×D411yescharacteristic
501C2×D4—28no—
502C2×D4—28no—
503C2×D4—24no—
504C2×D4—216no—
505C2×D4—22no—
506C2×D4—24no—
507C2×D4—24no—
508C2×D4—44no—
509C2×D4—432no—
510C2×D4—44no—
511C2×D4—44no—
512C2×D4—44no—
513C2×D4—42no—
514C2×D4—42no—
515C2×D4—48no—
516C2×D4C23×C414yes—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—216no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—216no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—24no—
533C22×C4—24no—
534C22×C4—24no—
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—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—41no—
557C22×C4—41no—
558C22×C4—41no—
559C22×C4—41no—
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—416no—
575C22×C4—44no—
576C22×C4—44no—
577C22×C4—44no—
578C22×C4—44no—
579C22×C4—42no—
580C22×C4—42no—
581C22×C4—42no—
582C22×C4—42no—
583C22×C4—416no—
584C22×C4—42no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4—42no—
588C22×C4—42no—
589C22×C4—42no—
590C22×C4—42no—
591C22×C4—42no—
592C22×C4—42no—
593C22×C4—42no—
594C22×C4—42no—
595C22×C4—42no—
596C22×C4—42no—
597C22×C4—42no—
598C22×C4—44no—
599C22×C4—44no—
600C22×C4—816no—
601C22×C4C4×D414yes—
602C22×C4C4×D414yes—
603C22×C4C4×D414yes—
604C22×C4AGL(1,ℤ/8)14yes—
605C22×C4C23×C412yes—
606C22×C4C23×C412yes—
607C22×C4C23×C412yes—
608C22×C4C22×D411yescharacteristic
609C22×C4C22×D411yescharacteristic
610C22×C4C22×D411yescharacteristic
611C22×C4C22×D411yescharacteristic
612C22×C4C22×D411yescharacteristic
613C22×C4C22×D411yescharacteristic
614C22×C4C22×D411yescharacteristic
615C22×C4C22×D411yescharacteristic
616C22×C4C22×D411yescharacteristic
617C22×C4C22×D411yescharacteristic
618C22×C4C22×D411yescharacteristic
619C22×C4C2×#4112yes—
620C22×C4C2×#4112yes—
621C22×C4C2×#4112yes—
622C22×C4H(5,𝔽2)14yes—
623C22×C42−1+414yes—
624C22×C4C2511yescharacteristic
625M16—216no—
626M16—48no—
627C2×C8—24no—
628C2×C8—24no—
629C2×C8—24no—
630C2×C8—24no—
631C2×C8—24no—
632C2×C8C23×C418yes—
633C4⋊C4—24no—
634C4⋊C4—24no—
635C4⋊C4—24no—
636C4⋊C4—22no—
637C4⋊C4—22no—
638C4⋊C4—22no—
639C4⋊C4—22no—
640C4⋊C4—22no—
641C4⋊C4—22no—
642C4⋊C4—24no—
643C4⋊C4—22no—
644C4⋊C4—24no—
645C4⋊C4—44no—
646C4⋊C4—44no—
647C4⋊C4—44no—
648C4⋊C4—44no—
649C4⋊C4—42no—
650C4⋊C4—42no—
651C4⋊C4—44no—
652C4⋊C4—42no—
653C4⋊C4—42no—
654C4⋊C4—44no—
655C4⋊C4—44no—
656C4⋊C4—44no—
657C4⋊C4—44no—
658C4⋊C4—44no—
659C4⋊C4C23×C414yes—
660C4⋊C4C23×C414yes—
661C4⋊C4C23×C414yes—
662C22⋊C4—28no—
663C22⋊C4—28no—
664C22⋊C4—28no—
665C22⋊C4—28no—
666C22⋊C4—44no—
667C22⋊C4—44no—
668C22⋊C4—44no—
669C22⋊C4—44no—
670C22⋊C4—44no—
671C22⋊C4—44no—
672C22⋊C4—44no—
673C22⋊C4—44no—
674C22⋊C4—44no—
675C22⋊C4—44no—
676C42—28no—
677C42—28no—
678C42—22no—
679C42—22no—
680C42—22no—
681C42—22no—
682C42—22no—
683C42—22no—
684C42—22no—
685C42—22no—
686C42—41no—
687C42—41no—
688C42—41no—
689C42—41no—
690C42—41no—
691C42—41no—
692C42—41no—
693C42—41no—
694C42—44no—
695C42—44no—
696C42—44no—
697C42—44no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—28no—
707C23—21no—
708C23—21no—
709C23—28no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—24no—
715C23—44no—
716C23—44no—
717C23—44no—
718C23—44no—
719C23—44no—
720C23—48no—
721C23—48no—
722C23—48no—
723C23—42no—
724C23—42no—
725C23—42no—
726C23—42no—
727C23—42no—
728C23—42no—
729C23—84no—
730C23—84no—
731C23—84no—
732C23—84no—
733C23C2×C4×D412yes—
734C23C2×C4×D412yes—
735C23C2×C4×D412yes—
736C23#53412yes—
737C23#53612yes—
738C23C2×AGL(1,ℤ/8)12yes—
739C23#57512yes—
740C23C23×D411yescharacteristic
741D4—28no—
742D4—416no—
743D4—416no—
744D4—48no—
745D4—44no—
746C2×C4—28no—
747C2×C4—28no—
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—21no—
760C2×C4—28no—
761C2×C4—28no—
762C2×C4—24no—
763C2×C4—24no—
764C2×C4—24no—
765C2×C4—24no—
766C2×C4—24no—
767C2×C4—24no—
768C2×C4—24no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—44no—
782C2×C4—44no—
783C2×C4—44no—
784C2×C4—44no—
785C2×C4—44no—
786C2×C4—44no—
787C2×C4—44no—
788C2×C4—44no—
789C2×C4—48no—
790C2×C4—44no—
791C2×C4—44no—
792C2×C4—48no—
793C2×C4—44no—
794C2×C4—48no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—88no—
814C2×C4—88no—
815C2×C4—84no—
816C2×C4—84no—
817C2×C4—84no—
818C2×C4—84no—
819C2×C4C2×C4×D412yes—
820C2×C4C2×C4×D412yes—
821C2×C4C2×C4×D412yes—
822C2×C4#52018yes—
823C2×C4#53412yes—
824C2×C4#53612yes—
825C2×C4#53918yes—
826C2×C4C2×AGL(1,ℤ/8)12yes—
827C2×C4C2×AGL(1,ℤ/8)12yes—
828C2×C4#57512yes—
829C2×C4#57512yes—
830C2×C4C24×C411yescharacteristic
831C2×C4C22×#4111yescharacteristic
832C2×C4C2×H(5,𝔽2)12yes—
833C2×C4C2×2−1+412yes—
834C8—28no—
835C8—44no—
836C22—22no—
837C22—22no—
838C22—22no—
839C22—22no—
840C22—22no—
841C22—22no—
842C22—22no—
843C22—22no—
844C22—22no—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—22no—
850C22—22no—
851C22—416no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22—44no—
857C22—44no—
858C22—44no—
859C22—816no—
860C22—82no—
861C22—82no—
862C22—82no—
863C22—82no—
864C22#232214yes—
865C22C4×AGL(1,ℤ/8)14yes—
866C22C22×C4×D411yescharacteristic
867C22C2×#53411yescharacteristic
868C22C2×#53611yescharacteristic
869C22C22×AGL(1,ℤ/8)11yescharacteristic
870C22C2×#57511yescharacteristic
871C22C2×#57511yescharacteristic
872C22C2×#57511yescharacteristic
873C4—22no—
874C4—22no—
875C4—22no—
876C4—22no—
877C4—22no—
878C4—22no—
879C4—41no—
880C4—41no—
881C4—41no—
882C4—41no—
883C4—44no—
884C4—44no—
885C4—44no—
886C4—82no—
887C4—82no—
888C4—82no—
889C4—82no—
890C4#232214yes—
891C4C2×#52012yes—
892C4C2×#53912yes—
893C2—24no—
894C2—24no—
895C2—42no—
896C2—84no—
897C2C2×#232211yescharacteristic
898C2C2×C4×AGL(1,ℤ/8)11yescharacteristic
899C2C4×#57511yescharacteristic
900C2#6075011yescharacteristic
901C2#6075211yescharacteristic
902C2#6086411yescharacteristic
903C2#6086611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
prime radicalC22×#121C22
LCSG ▷ C2×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
3. C2×#2296C2semidirect
4. #22086C2semidirect
5. #22082C2semidirect
6. #22081C2semidirect
7. #22080C2semidirect
8. #22076C2semidirect
9. #22075C2semidirect
10. #21159C2semidirect
11. #21095C2semidirect
12. #21033C2semidirect
14. #20873C2semidirect
15. #20846C2semidirect
16. #20702C2semidirect
17. C4×#407C2semidirect
24. #3094C4semidirect
49. #2296C22semidirect
50. #2296C22semidirect
53. C2×#389C22semidirect
54. C2×#389C22semidirect
55. C2×#389C22semidirect
56. C2×#389C22semidirect
66. #1944C22semidirect
67. #1943C22semidirect
68. #1942C22semidirect
69. #1941C22semidirect
70. #1936C22semidirect
71. #1936C22semidirect
72. #1934C22semidirect
73. #1934C22semidirect
74. #1921C22semidirect
75. #1920C22semidirect
76. #1919C22semidirect
77. #1918C22semidirect
81. #1864C22semidirect
82. #1864C22semidirect
83. #1862C22semidirect
84. #1862C22semidirect
85. #1854C22semidirect
86. #1853C22semidirect
87. #1852C22semidirect
88. #1825C22semidirect
89. #1824C22semidirect
90. #1823C22semidirect
91. #1749C22semidirect
92. #1749C22semidirect
93. C4×C22⋊C8C22semidirect
94. C4×C22⋊C8C22semidirect
130. C2×#117C2×C4semidirect
170. #482C2×C4semidirect
171. #481C2×C4semidirect
172. #480C2×C4semidirect
174. #428C2×C4semidirect
180. #418C2×C4semidirect
186. #407C2×C4semidirect
357. #117C22×C4semidirect
388. C2×C4⋊C4C22×C4semidirect
389. C2×C4⋊C4C22×C4semidirect
456. #107C22×C4semidirect
458. #106C22×C4semidirect
461. #102C22×C4semidirect
462. #102C22×C4semidirect
465. C22⋊C8C22×C4semidirect
466. C22⋊C8C22×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#30942
C2×C4×#1212
C2×#22962
#220862
#220822
#220812
#220802
#220762
#220752
#211592
#210952
#210332
#209122
#208732
#208462
#207022
C4×#4072