Finite Group Databasebeta

← #6396465

Subgroups — #6396465

Order 512.

2462 conjugacy classes of subgroups.

The subgroup lattice has 875 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3205C211yesmaximal, characteristic
2#34226C211yesmaximal, characteristic, complemented
3#34210C211yesmaximal, characteristic, complemented
4#23108C214yesmaximal, complemented
5#23008C214yesmaximal, complemented
6#22880C214yesmaximal, complemented
7#22868C214yesmaximal, complemented
8#22269C211yesmaximal, characteristic, complemented
9#22269C211yesmaximal, characteristic, complemented
10#22220C211yesmaximal, characteristic, complemented
11#22219C211yesmaximal, characteristic, complemented
12#21984C211yesmaximal, characteristic, complemented
13#21690C211yesmaximal, characteristic, complemented
14C4×#493C211yesmaximal, characteristic, complemented
15#21646C211yesmaximal, characteristic, complemented
16C4×#486C211yesmaximal, characteristic, complemented
17#21410C211yesmaximal, characteristic, complemented
18#21203C211yesmaximal, characteristic, complemented
19#20472C211yesmaximal, characteristic, complemented
20C2×#532C2211yescharacteristic
21C22×#127C2211yescharacteristic
22C2×#518—21no—
23#3205C4116yescomplemented
24C2×#493C2211yescharacteristic
25C2×#493C2211yescharacteristic
26C2×#486C2211yescharacteristic
27C2×#486C2211yescharacteristic
28C2×#459C2214yes—
29C2×#447C2214yes—
30C2×#442C2214yescomplemented
31C2×C4×D8C2214yescomplemented
32C2×#431C2211yescharacteristic
33C2×#418C2214yes—
34C2×C4×M16C2211yescharacteristic
35#2367—21no—
36#2367—21no—
37#2366—21no—
38#2366—21no—
39#2366C2212yes—
40#2366C2212yes—
41#2363C2212yes—
42#2363C2212yes—
43#2357C2212yescomplemented
44#2349C2212yescomplemented
45#2341—21no—
46#2339—21no—
47D4×C22⋊C4—21no—
48D4×C22⋊C4—21no—
49D4×C22⋊C4C2212yes—
50D4×C22⋊C4C2212yes—
51#2328—21no—
52#2328—21no—
53#2324—21no—
54#2324—21no—
55#2319—21no—
56#2309—21no—
57C4×C4⋊Q8C2211yescharacteristic, complemented
58C4×C4⋊Q8C2211yescharacteristic, complemented
59C4×#127C2211yescharacteristic
60C4×#127C2211yescharacteristic
61C4×#127C2211yescharacteristic
62C4×#127C2211yescharacteristic
63C4×#127C2211yescharacteristic, complemented
64C4×#127C2211yescharacteristic, complemented
65#2285C2211yescharacteristic
66#2285C2211yescharacteristic
67#2275—21no—
68C4×#117C2211yescharacteristic
69#1990C2211yescharacteristic, complemented
70#1990C2211yescharacteristic, complemented
71#1972C2214yescomplemented
72#1970C2214yescomplemented
73#1961C2214yes—
74#1957C2211yescharacteristic
75#1957C2211yescharacteristic
76#1957C2211yescharacteristic
77#1957C2211yescharacteristic
78#1957C2211yescharacteristic, complemented
79#1957C2211yescharacteristic, complemented
80#1949C2214yescomplemented
81#1936C2214yescomplemented
82#1934C2214yescomplemented
83#1926C2214yescomplemented
84#1925C2214yescomplemented
85#1895C2214yes—
86#1879C2214yescomplemented
87#1879C2214yescomplemented
88#1879C2214yescomplemented
89#1879C2214yescomplemented
90#1864C2214yescomplemented
91#1862C2214yescomplemented
92#1854C2214yes—
93#1845C2211yescharacteristic, complemented
94#1844C2211yescharacteristic, complemented
95#1834C2211yescharacteristic, complemented
96#1834C2211yescharacteristic, complemented
97#1771C2212yescomplemented
98#1771C2212yescomplemented
99#1762C2214yescomplemented
100#1762C2214yescomplemented
101C4×#102C2214yescomplemented
102#1753C2212yes—
103#1753C2212yes—
104#1744C2211yescharacteristic, complemented
105#1744C2211yescharacteristic, complemented
106C4×#97C2211yescharacteristic, complemented
107C42×C8C2211yescharacteristic, complemented
108C22×#41—21no—
109C23×D4—21no—
110C23×D4—21no—
111C23×D4C2312yes—
112C22×D8C2314yes—
113C22×D8C2314yes—
114C22×M16C2312yes—
115#532—24no—
116#532C2×C418yescomplemented
117C2×C4⋊Q8C2311yescharacteristic
118C2×#127—21no—
119C2×#127—21no—
120C2×#127—24no—
121C2×#127C2×C418yescomplemented
122C2×#127C2311yescharacteristic
123C2×#127C2311yescharacteristic
124C2×#127C2311yescharacteristic
125C2×#127C2312yes—
126C2×#124—21no—
127C2×#121—21no—
128C2×#121C2312yes—
129#518—48no—
130C2×C4×Q8—21no—
131C2×C4×Q8—21no—
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×D4—21no—
146C2×C4×D4—21no—
147C2×C4×D4C2312yes—
148C2×C4×D4C2312yes—
149C2×C4×D4C2312yes—
150C2×C4×D4C2312yes—
151C2×C4×D4C2312yes—
152C2×C4×D4C2312yes—
153C2×C4×D4C2312yes—
154C2×#117—21no—
155C2×#117D411yescharacteristic
156C2×#117D411yescharacteristic
157C2×#117C2312yes—
158C22×C22⋊C4—22no—
159C22×C22⋊C4—22no—
160C22×C42C2311yescharacteristic
161#493C2×C418yescomplemented
162#493C2×C418yescomplemented
163#486C2×C418yescomplemented
164#486C2×C418yescomplemented
165#459C2×C4132yescomplemented
166#447C2×C4132yescomplemented
167#442—48no—
168C4×D8—48no—
169#431C2×C418yescomplemented
170C2×#107C2314yes—
171C2×#106C2314yes—
172C2×C4⋊C8C2312yes—
173#418—48no—
174C2×#102C2314yes—
175C2×#102C2314yes—
176C2×#102C2314yes—
177C2×#102C2314yes—
178C2×#102C2314yes—
179C2×#102C2314yes—
180C2×#102C2314yes—
181C2×#102C2314yes—
182C2×C22⋊C8C2312yes—
183C4×M16—24no—
184C2×#97C2312yes—
185C2×#97C2312yes—
186C2×#97C2312yes—
187C2×C4×C8C2311yescharacteristic
188C2×C4×C8C2311yescharacteristic
189C2×C4×C8C2312yes—
190C2×C4×C8C2312yes—
191C2×C4×C8C2311yescharacteristic
192C2×C4×C8C2311yescharacteristic
193#391—21no—
194#391—21no—
195#390—22no—
196#390—22no—
197#390—22no—
198#390—22no—
199#390—21no—
200#390—21no—
201#390—21no—
202#390—21no—
203#390—21no—
204#390—21no—
205#390—21no—
206#390—21no—
207#390—21no—
208#390—21no—
209#390—21no—
210#390—21no—
211#390C2312yes—
212#390C2312yes—
213#390C2312yes—
214#390C2312yes—
215#390C2312yes—
216#390C2312yes—
217#389—21no—
218#389—21no—
219#389C2312yes—
220#389C2312yes—
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#386—22no—
230#386—22no—
231#386—22no—
232#386—22no—
233#386—22no—
234#386—22no—
235#385—22no—
236#385—22no—
237#384C2311yescharacteristic
238#384C2311yescharacteristic
239#384C2311yescharacteristic
240#384C2311yescharacteristic
241#382—21no—
242#382C2312yes—
243#381—22no—
244#380—21no—
245#380—21no—
246#380—21no—
247#380—22no—
248#380C2312yes—
249#379—22no—
250#379—22no—
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—
283C25—22no—
284C2×#41—28no—
285C2×#41—82no—
286C2×#41—82no—
287C22×Q8—21no—
288C22×D4—22no—
289C22×D4—28no—
290C22×D4—28no—
291C22×D4—21no—
292C22×D4—21no—
293C22×D4—22no—
294C22×D4—21no—
295C22×D4—21no—
296C22×D4—21no—
297C22×D4—21no—
298C22×D4—22no—
299C22×D4—22no—
300C22×D4—24no—
301C22×D4—44no—
302C22×D4—44no—
303C22×D4—44no—
304C22×D4—44no—
305C22×D4—82no—
306C22×D4—82no—
307C22×D4C22×C418yes—
308C22×D4C2412yes—
309C22×D4C2412yes—
310C22×D4C2412yes—
311C23×C4—22no—
312C23×C4—22no—
313C23×C4—22no—
314C23×C4—22no—
315C23×C4—22no—
316C23×C4—22no—
317C23×C4—22no—
318C23×C4C2×D411yescharacteristic
319C23×C4C2×D411yescharacteristic
320C23×C4C2411yescharacteristic
321C2×D8—44no—
322C2×D8—44no—
323C2×D8—44no—
324C2×D8—44no—
325C2×D8C22×C4116yes—
326C2×D8C22×C4116yes—
327C2×M16—24no—
328C2×M16—24no—
329C2×M16—42no—
330C22×C8C2412yes—
331C22×C8C2412yes—
332C22×C8C2412yes—
333C22×C8C2412yes—
334C4⋊Q8—22no—
335C4⋊Q8C22×C414yes—
336#127—28no—
337#127—28no—
338#127—22no—
339#127—22no—
340#127—24no—
341#127—22no—
342#127C22×C418yes—
343#127C22×C414yes—
344#127C22×C414yes—
345#127C22×C414yes—
346#124—28no—
347#121—28no—
348#121—24no—
349#121C22×C418yes—
350C4×Q8—82no—
351C4×Q8—82no—
352C4×D4—28no—
353C4×D4—24no—
354C4×D4—44no—
355C4×D4—44no—
356C4×D4—44no—
357C4×D4—44no—
358C4×D4—44no—
359C4×D4—44no—
360C4×D4—44no—
361C4×D4—44no—
362C4×D4—44no—
363C4×D4—48no—
364C4×D4—48no—
365C4×D4—44no—
366C4×D4—44no—
367C4×D4—44no—
368C4×D4—82no—
369C4×D4—82no—
370C4×D4—82no—
371C4×D4—82no—
372C4×D4—82no—
373C4×D4—82no—
374C4×D4C22×C418yes—
375#117—24no—
376#117—42no—
377#117—44no—
378#117—44no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4C2×D411yescharacteristic
391C2×C4⋊C4C2×D411yescharacteristic
392C2×C4⋊C4C2×D411yescharacteristic
393C2×C4⋊C4C2×D411yescharacteristic
394C2×C4⋊C4C2412yes—
395C2×C4⋊C4C2412yes—
396C2×C4⋊C4C2412yes—
397C2×C4⋊C4C2412yes—
398C2×C4⋊C4C2412yes—
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⋊C4—22no—
415C2×C22⋊C4—22no—
416C2×C22⋊C4—22no—
417C2×C22⋊C4—22no—
418C2×C22⋊C4—22no—
419C2×C22⋊C4—22no—
420C2×C22⋊C4—22no—
421C2×C22⋊C4—48no—
422C2×C22⋊C4—48no—
423C2×C22⋊C4C2×D411yescharacteristic
424C2×C22⋊C4C2×D411yescharacteristic
425C2×C22⋊C4C2×D411yescharacteristic
426C2×C22⋊C4C2×D411yescharacteristic
427C2×C42—22no—
428C2×C42—22no—
429C2×C42—22no—
430C2×C42—22no—
431C2×C42C22×C414yes—
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×C42#4114yes—
443C2×C42C2411yescharacteristic
444C2×C42C2411yescharacteristic
445C2×C42C2411yescharacteristic
446C2×C42C2411yescharacteristic
447C2×C42C2411yescharacteristic
448C2×C42C2411yescharacteristic
449#107—44no—
450#106—44no—
451C4⋊C8C22×C418yes—
452#102—28no—
453#102—28no—
454#102—28no—
455#102—44no—
456#102—44no—
457#102—44no—
458#102C22×C4116yes—
459#102C22×C4116yes—
460C22⋊C8C22×C418yes—
461#97—24no—
462#97—24no—
463#97—42no—
464C4×C8—24no—
465C4×C8—22no—
466C4×C8—22no—
467C4×C8—42no—
468C4×C8C22×C414yes—
469C4×C8C22×C414yes—
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#95C2×D411yescharacteristic
479#95C2×D411yescharacteristic
480#95C2×D411yescharacteristic
481#95C2×D411yescharacteristic
482#95C2×D411yescharacteristic
483#95C2×D411yescharacteristic
484#95C2×D411yescharacteristic
485#95C2×D411yescharacteristic
486C24—22no—
487C24—22no—
488C24—22no—
489C24—28no—
490C24—44no—
491C24—44no—
492C24—82no—
493C24—82no—
494C24—82no—
495C24—82no—
496C24C22×D411yescharacteristic
497#41—816no—
498C2×Q8—24no—
499C2×Q8—42no—
500C2×Q8—42no—
501C2×D4—28no—
502C2×D4—24no—
503C2×D4—24no—
504C2×D4—28no—
505C2×D4—24no—
506C2×D4—24no—
507C2×D4—24no—
508C2×D4—24no—
509C2×D4—28no—
510C2×D4—28no—
511C2×D4—22no—
512C2×D4—22no—
513C2×D4—22no—
514C2×D4—24no—
515C2×D4—24no—
516C2×D4—24no—
517C2×D4—24no—
518C2×D4—24no—
519C2×D4—24no—
520C2×D4—416no—
521C2×D4—44no—
522C2×D4—44no—
523C2×D4—432no—
524C2×D4—42no—
525C2×D4—42no—
526C2×D4—42no—
527C2×D4—42no—
528C2×D4—42no—
529C2×D4—42no—
530C2×D4—42no—
531C2×D4—42no—
532C2×D4—42no—
533C2×D4—42no—
534C2×D4—42no—
535C2×D4—42no—
536C2×D4—88no—
537C2×D4—816no—
538C2×D4—82no—
539C2×D4—82no—
540C2×D4—82no—
541C2×D4—82no—
542C2×D4—82no—
543C2×D4—82no—
544C2×D4C23×C414yes—
545C2×D4C23×C414yes—
546C2×D4C23×C414yes—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—28no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—44no—
560C22×C4—44no—
561C22×C4—44no—
562C22×C4—44no—
563C22×C4—44no—
564C22×C4—44no—
565C22×C4—82no—
566C22×C4—82no—
567C22×C4—82no—
568C22×C4—82no—
569C22×C4—82no—
570C22×C4—82no—
571C22×C4—82no—
572C22×C4—82no—
573C22×C4—82no—
574C22×C4—82no—
575C22×C4—82no—
576C22×C4—82no—
577C22×C4—82no—
578C22×C4—82no—
579C22×C4C4×D414yes—
580C22×C4C4×D414yes—
581C22×C4C23×C412yes—
582C22×C4C22×D411yescharacteristic
583C22×C4C22×D411yescharacteristic
584C22×C4C22×D411yescharacteristic
585C22×C4C22×D411yescharacteristic
586C22×C4C22×D411yescharacteristic
587C22×C4C22×D411yescharacteristic
588C22×C4C22×D411yescharacteristic
589C22×C4C22×D411yescharacteristic
590C22×C4C22×D411yescharacteristic
591C22×C4C22×D411yescharacteristic
592C22×C4C22×D411yescharacteristic
593C22×C4C22×D411yescharacteristic
594C22×C4C22×D411yescharacteristic
595C22×C4C2×#4112yes—
596C22×C4C2511yescharacteristic
597D8—416no—
598D8—416no—
599M16—48no—
600C2×C8—22no—
601C2×C8—22no—
602C2×C8—22no—
603C2×C8—22no—
604C2×C8—22no—
605C2×C8—22no—
606C2×C8—22no—
607C2×C8—22no—
608C2×C8—22no—
609C2×C8C23×C414yes—
610C2×C8C23×C414yes—
611C2×C8H(5,𝔽2)14yes—
612C4⋊C4—24no—
613C4⋊C4—22no—
614C4⋊C4—22no—
615C4⋊C4—22no—
616C4⋊C4—24no—
617C4⋊C4—24no—
618C4⋊C4—24no—
619C4⋊C4—24no—
620C4⋊C4—41no—
621C4⋊C4—41no—
622C4⋊C4—42no—
623C4⋊C4—42no—
624C4⋊C4—42no—
625C4⋊C4—42no—
626C4⋊C4—42no—
627C4⋊C4—42no—
628C4⋊C4—42no—
629C4⋊C4—42no—
630C4⋊C4—82no—
631C4⋊C4—82no—
632C4⋊C4C23×C414yes—
633C22⋊C4—28no—
634C22⋊C4—28no—
635C22⋊C4—22no—
636C22⋊C4—22no—
637C22⋊C4—41no—
638C22⋊C4—41no—
639C22⋊C4—44no—
640C22⋊C4—44no—
641C22⋊C4—44no—
642C22⋊C4—44no—
643C22⋊C4—44no—
644C22⋊C4—44no—
645C22⋊C4—44no—
646C22⋊C4—82no—
647C22⋊C4—82no—
648C22⋊C4—82no—
649C22⋊C4—82no—
650C22⋊C4—82no—
651C22⋊C4—82no—
652C22⋊C4—82no—
653C22⋊C4—82no—
654C22⋊C4—82no—
655C22⋊C4—82no—
656C22⋊C4—82no—
657C22⋊C4—82no—
658C22⋊C4—82no—
659C42—22no—
660C42—22no—
661C42—22no—
662C42—22no—
663C42—22no—
664C42—22no—
665C42—22no—
666C42—22no—
667C42—22no—
668C42—22no—
669C42—22no—
670C42—44no—
671C42—82no—
672C42—82no—
673C42—82no—
674C42C4×D414yes—
675C42C4×D414yes—
676C42AGL(1,ℤ/8)14yes—
677C42C23×C412yes—
678C42C23×C412yes—
679C42C2×#4112yes—
680C42C2×#4112yes—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—24no—
688C23—24no—
689C23—24no—
690C23—416no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—42no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—88no—
710C23—88no—
711C23—164no—
712C23—164no—
713C23—164no—
714C23—164no—
715C23C2×C4×D412yes—
716C23C23×D411yescharacteristic
717Q8—48no—
718D4—28no—
719D4—28no—
720D4—28no—
721D4—416no—
722D4—48no—
723D4—48no—
724D4—48no—
725D4—48no—
726D4—48no—
727D4—48no—
728D4—44no—
729D4—44no—
730D4—44no—
731D4—88no—
732D4—88no—
733D4—88no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—24no—
745C2×C4—28no—
746C2×C4—28no—
747C2×C4—24no—
748C2×C4—24no—
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—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—88no—
782C2×C4—164no—
783C2×C4—164no—
784C2×C4—164no—
785C2×C4—164no—
786C2×C4—164no—
787C2×C4—164no—
788C2×C4C2×C4×D412yes—
789C2×C4C2×C4×D412yes—
790C2×C4C2×C4×D412yes—
791C2×C4C2×C4×D412yes—
792C2×C4C2×C4×D412yes—
793C2×C4C2×AGL(1,ℤ/8)12yes—
794C2×C4C2×AGL(1,ℤ/8)12yes—
795C2×C4C2×AGL(1,ℤ/8)12yes—
796C2×C4#57512yes—
797C2×C4#57612yes—
798C2×C4#57612yes—
799C2×C4C24×C411yescharacteristic
800C2×C4C22×#4111yescharacteristic
801C2×C4C2×H(5,𝔽2)12yes—
802C2×C4#58512yes—
803C8—24no—
804C8—24no—
805C8—24no—
806C8—42no—
807C22—22no—
808C22—22no—
809C22—22no—
810C22—41no—
811C22—41no—
812C22—41no—
813C22—41no—
814C22—44no—
815C22—44no—
816C22—44no—
817C22—44no—
818C22—44no—
819C22—44no—
820C22—44no—
821C22—44no—
822C22—44no—
823C22—82no—
824C22—82no—
825C22—82no—
826C22—82no—
827C22—82no—
828C22—82no—
829C22—82no—
830C22—82no—
831C22—82no—
832C22—82no—
833C22—82no—
834C22—82no—
835C22—1616no—
836C22C22×C4×D411yescharacteristic
837C22#349811yescharacteristic
838C22#350011yescharacteristic
839C22C22×AGL(1,ℤ/8)11yescharacteristic
840C22C2×#57511yescharacteristic
841C22C2×#57611yescharacteristic
842C22C2×#57611yescharacteristic
843C4—22no—
844C4—22no—
845C4—22no—
846C4—22no—
847C4—22no—
848C4—44no—
849C4—41no—
850C4—41no—
851C4—41no—
852C4—41no—
853C4—41no—
854C4—41no—
855C4—82no—
856C4—82no—
857C4—82no—
858C4—82no—
859C4C4×AGL(1,ℤ/8)14yes—
860C4#294814yes—
861C4C4×H(5,𝔽2)12yes—
862C4#349412yes—
863C2—42no—
864C2—84no—
865C2—84no—
866C2—84no—
867C2#3427511yescharacteristic
868C2C2×C4×AGL(1,ℤ/8)11yescharacteristic
869C2C2×#294811yescharacteristic
870C2#6242311yescharacteristic
871C2#6242611yescharacteristic
872C2#6253511yescharacteristic
873C2#6254611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
prime radicalC2×#3205C2
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. #34210C2semidirect
4. #23108C2semidirect
5. #23008C2semidirect
6. #22880C2semidirect
7. #22868C2semidirect
8. #22269C2semidirect
9. #22269C2semidirect
10. #22220C2semidirect
11. #22219C2semidirect
12. #21984C2semidirect
13. #21690C2semidirect
14. C4×#493C2semidirect
15. #21646C2semidirect
16. C4×#486C2semidirect
17. #21410C2semidirect
18. #21203C2semidirect
19. #20472C2semidirect
23. #3205C4semidirect
30. C2×#442C22semidirect
31. C2×C4×D8C22semidirect
43. #2357C22semidirect
44. #2349C22semidirect
57. C4×C4⋊Q8C22semidirect
58. C4×C4⋊Q8C22semidirect
63. C4×#127C22semidirect
64. C4×#127C22semidirect
69. #1990C22semidirect
70. #1990C22semidirect
71. #1972C22semidirect
72. #1970C22semidirect
78. #1957C22semidirect
79. #1957C22semidirect
80. #1949C22semidirect
81. #1936C22semidirect
82. #1934C22semidirect
83. #1926C22semidirect
84. #1925C22semidirect
86. #1879C22semidirect
87. #1879C22semidirect
88. #1879C22semidirect
89. #1879C22semidirect
90. #1864C22semidirect
91. #1862C22semidirect
93. #1845C22semidirect
94. #1844C22semidirect
95. #1834C22semidirect
96. #1834C22semidirect
97. #1771C22semidirect
98. #1771C22semidirect
99. #1762C22semidirect
100. #1762C22semidirect
101. C4×#102C22semidirect
104. #1744C22semidirect
105. #1744C22semidirect
106. C4×#97C22semidirect
107. C42×C8C22semidirect
116. #532C2×C4semidirect
121. C2×#127C2×C4semidirect
161. #493C2×C4semidirect
162. #493C2×C4semidirect
163. #486C2×C4semidirect
164. #486C2×C4semidirect
165. #459C2×C4semidirect
166. #447C2×C4semidirect
169. #431C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#32052
#342262
#342102
#231082
#230082
#228802
#228682
#222692
#222202
#222192
#219842
#216902
C4×#4932
#216462
C4×#4862
#214102
#212032
#204722