Finite Group Databasebeta

← #6396458

Subgroups — #6396458

Order 512.

2274 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3207C211yesmaximal, characteristic
2#34226C211yesmaximal, characteristic, complemented
3#34207C211yesmaximal, characteristic, complemented
4#23105C214yesmaximal, complemented
5#23011C214yesmaximal, complemented
6#22878C214yesmaximal, complemented
7#22863C214yesmaximal, complemented
8#22269C211yesmaximal, characteristic, complemented
9#22268C211yesmaximal, characteristic, complemented
10#22221C211yesmaximal, characteristic, complemented
11#22220C211yesmaximal, characteristic, complemented
12#21982C211yesmaximal, characteristic, complemented
13#21692C211yesmaximal, characteristic, complemented
14C4×#493C211yesmaximal, characteristic, complemented
15#21646C211yesmaximal, characteristic, complemented
16C4×#487C211yesmaximal, characteristic, complemented
17#21410C211yesmaximal, characteristic, complemented
18#21200C211yesmaximal, characteristic, complemented
19#20472C211yesmaximal, characteristic, complemented
20C2×#532C2211yescharacteristic
21C2×#532C2211yescharacteristic
22C2×#520—21no—
23#3207C4116yescomplemented
24C2×#493C2211yescharacteristic
25C2×#492C2211yescharacteristic
26C2×#487C2211yescharacteristic
27C2×#486C2211yescharacteristic
28C2×#463C2214yes—
29C2×#449C2214yes—
30C2×#440C2214yes—
31C2×C4×D8C2214yes—
32C2×#431C2211yescharacteristic
33C2×#417C2214yes—
34C2×C4×M16C2211yescharacteristic
35#2367C2212yes—
36#2367C2212yes—
37#2363—21no—
38#2363—21no—
39#2361—21no—
40#2361—21no—
41#2361C2212yes—
42#2361C2212yes—
43#2357—21no—
44#2354—21no—
45#2354C2212yes—
46#2349—21no—
47D4×C4⋊C4—21no—
48D4×C4⋊C4C2212yes—
49#2341C2212yes—
50#2339C2212yes—
51#2326—21no—
52#2326—21no—
53#2324—21no—
54#2324—21no—
55#2319—21no—
56#2311—21no—
57C4×C4⋊Q8C2211yescharacteristic
58C4×C4⋊Q8C2211yescharacteristic
59C4×C4⋊Q8C2211yescharacteristic
60C4×C4⋊Q8C2211yescharacteristic
61C4×#127C2211yescharacteristic
62C4×#127C2211yescharacteristic
63C4×#127C2211yescharacteristic
64C4×#127C2211yescharacteristic
65#2285C2211yescharacteristic
66C2×#384C2211yescharacteristic
67#2275—21no—
68C4×#117C2211yescharacteristic
69#1990C2211yescharacteristic
70#1990C2211yescharacteristic
71#1973C2214yes—
72#1970C2214yes—
73#1959C2214yes—
74#1957C2211yescharacteristic
75#1957C2211yescharacteristic
76#1957C2211yescharacteristic
77#1957C2211yescharacteristic
78#1956C2211yescharacteristic
79#1956C2211yescharacteristic
80#1947C2214yes—
81#1936C2214yes—
82#1933C2214yes—
83#1928C2214yes—
84#1925C2214yes—
85#1895C2214yes—
86#1880C2214yes—
87#1879C2214yes—
88#1879C2214yes—
89#1877C2214yes—
90#1863C2214yes—
91#1862C2214yes—
92#1852C2214yes—
93#1845C2211yescharacteristic
94#1845C2211yescharacteristic
95#1834C2211yescharacteristic
96#1834C2211yescharacteristic
97#1771C2212yes—
98#1771C2212yes—
99#1762C2214yes—
100#1762C2214yes—
101C4×#103C2214yes—
102#1753C2212yes—
103#1753C2212yes—
104#1744C2211yescharacteristic
105#1744C2211yescharacteristic
106C4×#97C2211yescharacteristic
107C42×C8C2211yescharacteristic
108C22×#41—21no—
109C22×#41C2312yes—
110C22×SD16C2314yes—
111C22×D8C2314yes—
112C22×M16C2312yes—
113#532—24no—
114#532—24no—
115#532C2×C418yescomplemented
116#532C2×C418yescomplemented
117C2×C4⋊Q8C2311yescharacteristic
118C2×C4⋊Q8C2311yescharacteristic
119C2×#127C2311yescharacteristic
120C2×#127C2311yescharacteristic
121C2×#124—21no—
122C2×#124C2312yes—
123C2×#121—21no—
124C2×#121—21no—
125C2×#121—21no—
126C2×#121C2312yes—
127#520—48no—
128C2×C4×Q8—21no—
129C2×C4×Q8—21no—
130C2×C4×Q8C2312yes—
131C2×C4×Q8C2312yes—
132C2×C4×D4—22no—
133C2×C4×D4—22no—
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×D4—21no—
142C2×C4×D4—21no—
143C2×C4×D4—21no—
144C2×C4×D4—21no—
145C2×C4×D4C2312yes—
146C2×C4×D4C2312yes—
147C2×C4×D4C2312yes—
148C2×C4×D4C2312yes—
149C2×C4×D4C2312yes—
150C2×#117—21no—
151C2×#117—22no—
152C2×#117D411yescharacteristic
153C2×#117D411yescharacteristic
154C22×C4⋊C4—21no—
155C22×C4⋊C4—21no—
156C22×C4⋊C4—22no—
157C22×C4⋊C4C2312yes—
158C22×C42C2311yescharacteristic
159#493C2×C418yescomplemented
160#492C2×C418yescomplemented
161#487C2×C418yescomplemented
162#486C2×C418yescomplemented
163#463C2×C4132yescomplemented
164#449C2×C4132yescomplemented
165#440—48no—
166C4×D8—48no—
167#431C2×C418yescomplemented
168C2×#107C2314yes—
169C2×#107C2314yes—
170C2×C4⋊C8C2312yes—
171#417—48no—
172C2×#103C2314yes—
173C2×#103C2314yes—
174C2×#103C2314yes—
175C2×#102C2314yes—
176C2×#102C2314yes—
177C2×#102C2314yes—
178C2×#102C2314yes—
179C2×#102C2314yes—
180C2×C22⋊C8C2312yes—
181C4×M16—24no—
182C2×#97C2312yes—
183C2×#97C2312yes—
184C2×#97C2312yes—
185C2×C4×C8C2311yescharacteristic
186C2×C4×C8C2311yescharacteristic
187C2×C4×C8C2312yes—
188C2×C4×C8C2312yes—
189C2×C4×C8C2311yescharacteristic
190C2×C4×C8C2311yescharacteristic
191#391—21no—
192#391—21no—
193#391C2312yes—
194#391C2312yes—
195#390—22no—
196#390—22no—
197#390—21no—
198#390—21no—
199#390—21no—
200#390—21no—
201#390—21no—
202#390—21no—
203#390—21no—
204#390—21no—
205#390C2312yes—
206#390C2312yes—
207#390C2312yes—
208#390C2312yes—
209#389—21no—
210#389—21no—
211#389—21no—
212#389—21no—
213#389—21no—
214#389—21no—
215#389C2312yes—
216#389C2312yes—
217#388—22no—
218#388—22no—
219#388—22no—
220#388—22no—
221#388—22no—
222#388—22no—
223#388—22no—
224#388—22no—
225#386—22no—
226#386—22no—
227#386—22no—
228#386—22no—
229#385—22no—
230#385—22no—
231#385—22no—
232#385—22no—
233#385—22no—
234#385—22no—
235#384—21no—
236#384—21no—
237#384C2311yescharacteristic
238#384C2311yescharacteristic
239#384C2311yescharacteristic
240#384C2311yescharacteristic
241#384C2312yes—
242#382—21no—
243#381—22no—
244#380—21no—
245#380—22no—
246#380—22no—
247#380—22no—
248#380C2312yes—
249C4×C4⋊C4—21no—
250C4×C4⋊C4—21no—
251C4×C4⋊C4—21no—
252C4×C4⋊C4—21no—
253C4×C4⋊C4—21no—
254C4×C4⋊C4—21no—
255C4×C4⋊C4—21no—
256C4×C4⋊C4D411yescharacteristic
257C4×C4⋊C4D411yescharacteristic
258C4×C4⋊C4C2312yes—
259C4×C4⋊C4C2312yes—
260C4×C4⋊C4C2312yes—
261C4×C4⋊C4C2311yescharacteristic
262C4×C4⋊C4C2311yescharacteristic
263C4×C22⋊C4—22no—
264C4×C22⋊C4—22no—
265C4×C22⋊C4—22no—
266C4×C22⋊C4D411yescharacteristic
267C4×C22⋊C4D411yescharacteristic
268C4×C22⋊C4C2311yescharacteristic
269C4×C22⋊C4C2311yescharacteristic
270#376D411yescharacteristic
271#376D411yescharacteristic
272C2×#95—22no—
273C43C2311yescharacteristic
274C43C2311yescharacteristic
275#340C2314yes—
276#340C2314yes—
277#340C2314yes—
278#340C2314yes—
279#336C2312yes—
280#336C2312yes—
281#336C2312yes—
282#336C2312yes—
283C2×#41—28no—
284C2×#41—24no—
285C2×#41—44no—
286C2×#41—44no—
287C2×#41—44no—
288C2×#41—44no—
289C2×#41C22×C418yes—
290C22×Q8—21no—
291C22×Q8C2412yes—
292C22×D4—22no—
293C22×D4—22no—
294C22×D4—21no—
295C22×D4—21no—
296C22×D4—21no—
297C22×D4—21no—
298C22×D4C2412yes—
299C22×D4C2412yes—
300C23×C4—22no—
301C23×C4—22no—
302C23×C4—22no—
303C23×C4—22no—
304C23×C4—22no—
305C23×C4—22no—
306C23×C4—22no—
307C23×C4C2×D411yescharacteristic
308C23×C4C2×D411yescharacteristic
309C23×C4C2411yescharacteristic
310C2×SD16—44no—
311C2×SD16—44no—
312C2×SD16C22×C4116yes—
313C2×D8—44no—
314C2×D8—44no—
315C2×D8C22×C4116yes—
316C2×M16—24no—
317C2×M16—24no—
318C2×M16—42no—
319C22×C8C2412yes—
320C22×C8C2412yes—
321C22×C8C2412yes—
322C22×C8C2412yes—
323C4⋊Q8—22no—
324C4⋊Q8—22no—
325C4⋊Q8C22×C414yes—
326C4⋊Q8C22×C414yes—
327#127—22no—
328#127—22no—
329#127C22×C414yes—
330#127C22×C414yes—
331#124—28no—
332#124—24no—
333#124C22×C418yes—
334#121—28no—
335#121—28no—
336#121—28no—
337#121—24no—
338#121C22×C418yes—
339C4×Q8—44no—
340C4×Q8—44no—
341C4×Q8—44no—
342C4×Q8—44no—
343C4×D4—28no—
344C4×D4—28no—
345C4×D4—28no—
346C4×D4—24no—
347C4×D4—44no—
348C4×D4—44no—
349C4×D4—44no—
350C4×D4—44no—
351C4×D4—44no—
352C4×D4—44no—
353C4×D4—48no—
354C4×D4—48no—
355C4×D4—44no—
356C4×D4—44no—
357C4×D4—82no—
358C4×D4—82no—
359C4×D4—82no—
360C4×D4—82no—
361C4×D4C22×C418yes—
362#117—24no—
363#117—42no—
364#117—48no—
365#117—82no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—22no—
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—22no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—22no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—44no—
385C2×C4⋊C4—48no—
386C2×C4⋊C4—44no—
387C2×C4⋊C4—82no—
388C2×C4⋊C4C2×D411yescharacteristic
389C2×C4⋊C4C2×D411yescharacteristic
390C2×C4⋊C4C2×D411yescharacteristic
391C2×C4⋊C4C2×D411yescharacteristic
392C2×C4⋊C4C2412yes—
393C2×C4⋊C4C2412yes—
394C2×C4⋊C4C2412yes—
395C2×C4⋊C4C2412yes—
396C2×C4⋊C4C2412yes—
397C2×C22⋊C4—22no—
398C2×C22⋊C4—22no—
399C2×C22⋊C4—22no—
400C2×C22⋊C4—22no—
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—22no—
414C2×C22⋊C4C2×D411yescharacteristic
415C2×C22⋊C4C2×D411yescharacteristic
416C2×C22⋊C4C2×D411yescharacteristic
417C2×C22⋊C4C2×D411yescharacteristic
418C2×C42—22no—
419C2×C42—22no—
420C2×C42—22no—
421C2×C42—22no—
422C2×C42—22no—
423C2×C42C22×C414yes—
424C2×C42C2×D411yescharacteristic
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×C42#4114yes—
435C2×C42C2411yescharacteristic
436C2×C42C2411yescharacteristic
437C2×C42C2411yescharacteristic
438C2×C42C2411yescharacteristic
439C2×C42C2411yescharacteristic
440C2×C42C2411yescharacteristic
441#107—44no—
442#107—44no—
443C4⋊C8C22×C418yes—
444#103—28no—
445#103—44no—
446#103C22×C4116yes—
447#102—28no—
448#102—28no—
449#102—44no—
450#102—44no—
451#102C22×C4116yes—
452C22⋊C8C22×C418yes—
453#97—24no—
454#97—24no—
455#97—42no—
456C4×C8—24no—
457C4×C8—22no—
458C4×C8—22no—
459C4×C8—42no—
460C4×C8C22×C414yes—
461C4×C8C22×C414yes—
462#95—22no—
463#95—22no—
464#95—22no—
465#95—22no—
466#95—22no—
467#95—22no—
468#95—22no—
469#95—22no—
470#95—22no—
471#95—22no—
472#95C2×D411yescharacteristic
473#95C2×D411yescharacteristic
474#95C2×D411yescharacteristic
475#95C2×D411yescharacteristic
476#95C2×D411yescharacteristic
477#95C2×D411yescharacteristic
478#95C2×D411yescharacteristic
479#95C2×D411yescharacteristic
480C24—22no—
481C24—22no—
482C24C22×D411yescharacteristic
483#41—432no—
484#41—416no—
485#41—88no—
486C2×Q8—24no—
487C2×Q8—22no—
488C2×Q8—24no—
489C2×Q8—24no—
490C2×Q8—42no—
491C2×Q8—42no—
492C2×Q8C23×C414yes—
493C2×D4—28no—
494C2×D4—28no—
495C2×D4—24no—
496C2×D4—24no—
497C2×D4—24no—
498C2×D4—24no—
499C2×D4—22no—
500C2×D4—22no—
501C2×D4—24no—
502C2×D4—24no—
503C2×D4—24no—
504C2×D4—24no—
505C2×D4—44no—
506C2×D4—44no—
507C2×D4—42no—
508C2×D4—42no—
509C2×D4—42no—
510C2×D4—42no—
511C2×D4—42no—
512C2×D4—42no—
513C2×D4—42no—
514C2×D4—42no—
515C2×D4—82no—
516C2×D4—82no—
517C2×D4C23×C414yes—
518C2×D4C23×C414yes—
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—28no—
528C22×C4—28no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—44no—
534C22×C4—44no—
535C22×C4—44no—
536C22×C4—44no—
537C22×C4—44no—
538C22×C4—44no—
539C22×C4—44no—
540C22×C4—82no—
541C22×C4—82no—
542C22×C4—82no—
543C22×C4—82no—
544C22×C4—82no—
545C22×C4—82no—
546C22×C4—82no—
547C22×C4—82no—
548C22×C4—82no—
549C22×C4—82no—
550C22×C4—82no—
551C22×C4—82no—
552C22×C4C4×D414yes—
553C22×C4C4×D414yes—
554C22×C4C23×C412yes—
555C22×C4C22×D411yescharacteristic
556C22×C4C22×D411yescharacteristic
557C22×C4C22×D411yescharacteristic
558C22×C4C22×D411yescharacteristic
559C22×C4C22×D411yescharacteristic
560C22×C4C22×D411yescharacteristic
561C22×C4C22×D411yescharacteristic
562C22×C4C22×D411yescharacteristic
563C22×C4C22×D411yescharacteristic
564C22×C4C22×D411yescharacteristic
565C22×C4C22×D411yescharacteristic
566C22×C4C22×D411yescharacteristic
567C22×C4C22×D411yescharacteristic
568C22×C4C2×#4112yes—
569C22×C4C2511yescharacteristic
570SD16—416no—
571D8—416no—
572M16—48no—
573C2×C8—22no—
574C2×C8—22no—
575C2×C8—22no—
576C2×C8—22no—
577C2×C8—22no—
578C2×C8—22no—
579C2×C8—22no—
580C2×C8—22no—
581C2×C8—22no—
582C2×C8C23×C414yes—
583C2×C8C23×C414yes—
584C2×C8H(5,𝔽2)14yes—
585C4⋊C4—24no—
586C4⋊C4—24no—
587C4⋊C4—24no—
588C4⋊C4—22no—
589C4⋊C4—22no—
590C4⋊C4—22no—
591C4⋊C4—24no—
592C4⋊C4—24no—
593C4⋊C4—24no—
594C4⋊C4—24no—
595C4⋊C4—41no—
596C4⋊C4—41no—
597C4⋊C4—44no—
598C4⋊C4—44no—
599C4⋊C4—44no—
600C4⋊C4—42no—
601C4⋊C4—42no—
602C4⋊C4—42no—
603C4⋊C4—42no—
604C4⋊C4—42no—
605C4⋊C4—42no—
606C4⋊C4—42no—
607C4⋊C4—42no—
608C4⋊C4—82no—
609C4⋊C4—82no—
610C4⋊C4—82no—
611C4⋊C4—82no—
612C4⋊C4C23×C414yes—
613C22⋊C4—28no—
614C22⋊C4—28no—
615C22⋊C4—28no—
616C22⋊C4—28no—
617C22⋊C4—22no—
618C22⋊C4—22no—
619C22⋊C4—41no—
620C22⋊C4—41no—
621C22⋊C4—44no—
622C22⋊C4—44no—
623C22⋊C4—44no—
624C22⋊C4—44no—
625C22⋊C4—82no—
626C22⋊C4—82no—
627C22⋊C4—82no—
628C22⋊C4—82no—
629C22⋊C4—82no—
630C22⋊C4—82no—
631C22⋊C4—82no—
632C22⋊C4—82no—
633C22⋊C4—82no—
634C42—22no—
635C42—22no—
636C42—22no—
637C42—22no—
638C42—22no—
639C42—22no—
640C42—22no—
641C42—22no—
642C42—22no—
643C42—22no—
644C42—22no—
645C42—44no—
646C42—44no—
647C42—82no—
648C42—82no—
649C42—82no—
650C42C4×D414yes—
651C42C4×D414yes—
652C42AGL(1,ℤ/8)14yes—
653C42C23×C412yes—
654C42C23×C412yes—
655C42C2×#4112yes—
656C42C2×#4112yes—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—24no—
664C23—24no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23C2×C4×D412yes—
678C23C23×D411yescharacteristic
679Q8—28no—
680Q8—48no—
681Q8—44no—
682D4—28no—
683D4—28no—
684D4—416no—
685D4—48no—
686D4—48no—
687D4—48no—
688D4—48no—
689D4—44no—
690D4—44no—
691D4—88no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—24no—
703C2×C4—28no—
704C2×C4—28no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—416no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—88no—
744C2×C4—164no—
745C2×C4—164no—
746C2×C4—164no—
747C2×C4—164no—
748C2×C4—164no—
749C2×C4C2×C4×D412yes—
750C2×C4C2×C4×D412yes—
751C2×C4C2×C4×D412yes—
752C2×C4C2×C4×D412yes—
753C2×C4C2×C4×D412yes—
754C2×C4C2×AGL(1,ℤ/8)12yes—
755C2×C4C2×AGL(1,ℤ/8)12yes—
756C2×C4C2×AGL(1,ℤ/8)12yes—
757C2×C4#57512yes—
758C2×C4#57612yes—
759C2×C4#57812yes—
760C2×C4C24×C411yescharacteristic
761C2×C4C22×#4111yescharacteristic
762C2×C4C2×H(5,𝔽2)12yes—
763C2×C4#58512yes—
764C8—24no—
765C8—24no—
766C8—24no—
767C8—42no—
768C22—22no—
769C22—22no—
770C22—22no—
771C22—41no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—44no—
776C22—44no—
777C22—44no—
778C22—44no—
779C22—44no—
780C22—44no—
781C22—82no—
782C22—82no—
783C22—82no—
784C22—82no—
785C22—82no—
786C22—82no—
787C22—82no—
788C22—82no—
789C22C22×C4×D411yescharacteristic
790C22#349811yescharacteristic
791C22#350011yescharacteristic
792C22C22×AGL(1,ℤ/8)11yescharacteristic
793C22C2×#57511yescharacteristic
794C22C2×#57611yescharacteristic
795C22C2×#57811yescharacteristic
796C4—22no—
797C4—22no—
798C4—22no—
799C4—22no—
800C4—22no—
801C4—41no—
802C4—41no—
803C4—41no—
804C4—41no—
805C4—41no—
806C4—41no—
807C4—44no—
808C4—44no—
809C4—82no—
810C4—82no—
811C4—82no—
812C4—82no—
813C4C4×AGL(1,ℤ/8)14yes—
814C4#295114yes—
815C4C4×H(5,𝔽2)12yes—
816C4#349412yes—
817C2—42no—
818C2—84no—
819C2—84no—
820C2#3427511yescharacteristic
821C2C2×C4×AGL(1,ℤ/8)11yescharacteristic
822C2C2×#295111yescharacteristic
823C2#6242311yescharacteristic
824C2#6242511yescharacteristic
825C2#6253811yescharacteristic
826C2#6254611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
prime radicalC2×#3207C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#117 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #34226C2semidirect
3. #34207C2semidirect
4. #23105C2semidirect
5. #23011C2semidirect
6. #22878C2semidirect
7. #22863C2semidirect
8. #22269C2semidirect
9. #22268C2semidirect
10. #22221C2semidirect
11. #22220C2semidirect
12. #21982C2semidirect
13. #21692C2semidirect
14. C4×#493C2semidirect
15. #21646C2semidirect
16. C4×#487C2semidirect
17. #21410C2semidirect
18. #21200C2semidirect
19. #20472C2semidirect
23. #3207C4semidirect
115. #532C2×C4semidirect
116. #532C2×C4semidirect
159. #493C2×C4semidirect
160. #492C2×C4semidirect
161. #487C2×C4semidirect
162. #486C2×C4semidirect
163. #463C2×C4semidirect
164. #449C2×C4semidirect
167. #431C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#32072
#342262
#342072
#231052
#230112
#228782
#228632
#222692
#222682
#222212
#222202
#219822
#216922
C4×#4932
#216462
C4×#4872
#214102
#212002
#204722