Finite Group Databasebeta

← #6498401

Subgroups — #6498401

Order 512.

2178 conjugacy classes of subgroups.

The subgroup lattice has 855 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3228C211yesmaximal, characteristic, complemented
2C2×#3207C211yesmaximal, characteristic
3#36639C211yesmaximal, characteristic, complemented
4C4×#532C211yesmaximal, characteristic, complemented
5#33028C214yesmaximal, complemented
6#29832C214yesmaximal, complemented
7#28656C211yesmaximal, characteristic, complemented
8#28655C211yesmaximal, characteristic, complemented
9#28654C211yesmaximal, characteristic, complemented
10#28653C211yesmaximal, characteristic, complemented
11#28615C211yesmaximal, characteristic, complemented
12#28615C211yesmaximal, characteristic, complemented
13#28613C211yesmaximal, characteristic, complemented
14#28613C211yesmaximal, characteristic, complemented
15#28119C214yesmaximal, complemented
16#28116C214yesmaximal, complemented
17#21835C211yesmaximal, characteristic, complemented
18#21805C211yesmaximal, characteristic, complemented
19#20808C211yesmaximal, characteristic, complemented
20C2×#533C2211yescharacteristic
21C2×#532C2211yescharacteristic
22C2×#532C2211yescharacteristic
23C2×C4×#41—21no—
24#3228—28no—
25#3207—28no—
26C2×#500C2211yescharacteristic
27C2×#498C2211yescharacteristic
28C2×#493C2211yescharacteristic
29C2×#492C2211yescharacteristic
30C2×#487C2211yescharacteristic
31C2×#486C2211yescharacteristic
32C2×#486C2211yescharacteristic
33C2×#486C2211yescharacteristic
34C2×#482C2214yes—
35C2×#478C2214yes—
36C2×#463C2214yes—
37C2×#449C2214yes—
38C2×#431C2211yescharacteristic
39C2×#431C2211yescharacteristic
40#2862C2211yescharacteristic
41#2862C2211yescharacteristic
42#2861C2212yes—
43#2861C2212yes—
44#2858C2211yescharacteristic
45#2858C2211yescharacteristic
46#2850—21no—
47#2850—21no—
48#2850—21no—
49#2850—21no—
50C4×C4⋊Q8C2211yescharacteristic
51C4×C4⋊Q8C2211yescharacteristic
52C4×#127C2211yescharacteristic
53C4×#127C2211yescharacteristic
54C4×#124—21no—
55C4×#124—21no—
56C4×#124—21no—
57C4×#124—21no—
58C4×#124—21no—
59C4×#124—21no—
60C4×#121—21no—
61C4×#121—21no—
62C4×#121C2212yes—
63C4×#121C2212yes—
64#2297—21no—
65#2297C2212yes—
66#2297C2212yes—
67#2293—21no—
68#2293C2212yes—
69#2285C2211yescharacteristic
70C42×D4—21no—
71C42×D4C2212yes—
72C2×C43C2211yescharacteristic
73#2068C2214yes—
74#2067C2214yes—
75#2066C2214yes—
76#2065C2214yes—
77#2055C2214yes—
78#2055C2214yes—
79#2054C2214yes—
80#2054C2214yes—
81#1990C2211yescharacteristic
82#1990C2211yescharacteristic
83#1990C2211yescharacteristic
84#1990C2211yescharacteristic
85#1989C2214yes—
86#1983C2214yes—
87#1957C2211yescharacteristic
88#1957C2211yescharacteristic
89#1956C2211yescharacteristic
90#1956C2211yescharacteristic
91#1928C2214yes—
92#1927C2214yes—
93#1926C2214yes—
94#1925C2214yes—
95#1879C2214yes—
96#1879C2214yes—
97#1877C2214yes—
98#1877C2214yes—
99#1842C2212yes—
100#1831C2212yes—
101#1825C2214yes—
102#1797C2212yes—
103#1797C2212yes—
104#1788C2214yes—
105C4×C4⋊C8C2211yescharacteristic
106C4×C4⋊C8C2211yescharacteristic
107C4×C4⋊C8C2211yescharacteristic
108C4×C4⋊C8C2211yescharacteristic
109C22×#41—21no—
110C22×#41C2312yes—
111C22×SD16C2314yes—
112C22×D8C2314yes—
113#533—24no—
114#533—24no—
115#532—24no—
116#532—24no—
117#532—24no—
118#532D418yes—
119C2×C4⋊Q8C2311yescharacteristic
120C2×C4⋊Q8C2311yescharacteristic
121C2×C4⋊Q8C2311yescharacteristic
122C2×C4⋊Q8C2311yescharacteristic
123C2×#127C2311yescharacteristic
124C2×#127C2311yescharacteristic
125C2×#125C2312yes—
126C2×#124—21no—
127C2×#124—21no—
128C2×#124—21no—
129C2×#124—21no—
130C2×#124—21no—
131C2×#124C2312yes—
132C2×C22⋊Q8—21no—
133C2×C22⋊Q8—21no—
134C2×#121—21no—
135C2×#121—21no—
136C2×#121—21no—
137C2×#121C2312yes—
138C4×#41—48no—
139C2×C4×Q8—21no—
140C2×C4×Q8—21no—
141C2×C4×Q8—21no—
142C2×C4×Q8—21no—
143C2×C4×D4—22no—
144C2×C4×D4—22no—
145C2×C4×D4—21no—
146C2×C4×D4—21no—
147C2×C4×D4—21no—
148C2×C4×D4—21no—
149C2×C4×D4—21no—
150C2×C4×D4—21no—
151C2×C4×D4—21no—
152C2×C4×D4C2312yes—
153C2×C4×D4C2312yes—
154C2×C4×D4C2312yes—
155C2×#117—21no—
156C2×#117—22no—
157C2×#117C2312yes—
158C22×C42—22no—
159C22×C42D411yescharacteristic
160C22×C42D411yescharacteristic
161C22×C42D411yescharacteristic
162C22×C42D411yescharacteristic
163C22×C42C2311yescharacteristic
164C22×C42C2311yescharacteristic
165C22×C42C2311yescharacteristic
166#500—24no—
167#498—24no—
168#493—24no—
169#492—24no—
170#487—24no—
171#486—24no—
172#486—24no—
173#486—24no—
174#482—216no—
175#478—216no—
176#463—216no—
177#449—216no—
178#431—24no—
179#431—24no—
180C2×#107C2314yes—
181C2×#106C2314yes—
182C2×C4⋊C8C2312yes—
183C2×C4⋊C8C2312yes—
184C2×C4⋊C8C2312yes—
185C2×C4⋊C8C2312yes—
186C2×C4⋊C8C2312yes—
187C2×C4⋊C8C2312yes—
188C2×#103C2314yes—
189C2×#103C2314yes—
190C2×#103C2314yes—
191C2×#102C2314yes—
192C2×#102C2314yes—
193C2×#102C2314yes—
194C2×#102C2314yes—
195C2×#102C2314yes—
196C2×C22⋊C8C2312yes—
197C2×C22⋊C8C2312yes—
198C2×C4×C8C2311yescharacteristic
199C2×C4×C8C2311yescharacteristic
200C2×C4×C8C2311yescharacteristic
201C2×C4×C8C2311yescharacteristic
202#391—21no—
203#391—21no—
204#391—21no—
205#391—21no—
206#391—21no—
207#391—21no—
208#391C2312yes—
209#391C2312yes—
210#391C2312yes—
211#391C2312yes—
212#390—21no—
213#390—21no—
214#390—21no—
215#390—21no—
216#390—21no—
217#390—21no—
218#390—21no—
219#390—21no—
220#390C2312yes—
221#390C2312yes—
222#390C2312yes—
223#390C2312yes—
224#390C2312yes—
225#390C2312yes—
226#389—21no—
227#389—21no—
228#389C2312yes—
229#389C2312yes—
230#388—22no—
231#388—22no—
232#388—22no—
233#388—22no—
234#388—22no—
235#388—22no—
236#388—22no—
237#388—22no—
238#388—22no—
239#388—22no—
240#388—22no—
241#388—22no—
242#386—22no—
243#386—22no—
244#386—22no—
245#386—22no—
246#386—22no—
247#386—22no—
248#384C2311yescharacteristic
249#384C2311yescharacteristic
250#382—21no—
251#382—21no—
252#382—21no—
253#382—21no—
254#382—21no—
255#380—21no—
256#380C2312yes—
257C4×C4⋊C4—21no—
258C4×C4⋊C4—21no—
259C4×C4⋊C4—21no—
260C4×C4⋊C4C2312yes—
261C4×C4⋊C4C2312yes—
262C4×C4⋊C4C2312yes—
263C4×C22⋊C4—22no—
264C4×C22⋊C4—22no—
265C4×C22⋊C4—22no—
266C4×C22⋊C4—22no—
267C4×C22⋊C4—22no—
268C4×C22⋊C4—22no—
269C4×C22⋊C4—22no—
270C4×C22⋊C4—22no—
271C4×C22⋊C4—22no—
272C4×C22⋊C4—22no—
273C43D411yescharacteristic
274C43D411yescharacteristic
275C43D411yescharacteristic
276C43D411yescharacteristic
277C43C2311yescharacteristic
278C43C2311yescharacteristic
279C43C2311yescharacteristic
280C43C2311yescharacteristic
281#340C2314yes—
282#340C2314yes—
283#340C2314yes—
284#340C2314yes—
285#336C2312yes—
286#336C2312yes—
287#336C2312yes—
288#336C2312yes—
289C2×#41—28no—
290C2×#41—24no—
291C2×#41—24no—
292C2×#41—44no—
293C2×#41—44no—
294C2×#41—44no—
295C2×#41—44no—
296C22×Q8—21no—
297C22×Q8—21no—
298C22×Q8—21no—
299C22×Q8C2412yes—
300C22×D4—22no—
301C22×D4—22no—
302C22×D4—21no—
303C22×D4—21no—
304C22×D4—21no—
305C22×D4—21no—
306C22×D4C2412yes—
307C22×D4C2412yes—
308C23×C4—22no—
309C23×C4—22no—
310C23×C4—22no—
311C23×C4—22no—
312C23×C4C2×D411yescharacteristic
313C23×C4C2×D411yescharacteristic
314C23×C4C2×D411yescharacteristic
315C23×C4C2×D411yescharacteristic
316C23×C4C2×D411yescharacteristic
317C23×C4C2×D411yescharacteristic
318C23×C4C2411yescharacteristic
319C2×SD16—28no—
320C2×SD16—44no—
321C2×SD16—44no—
322C2×D8—28no—
323C2×D8—44no—
324C2×D8—44no—
325C22×C8C2412yes—
326C22×C8C2412yes—
327C22×C8C2412yes—
328C22×C8C2412yes—
329C4⋊Q8—22no—
330C4⋊Q8—22no—
331C4⋊Q8—22no—
332C4⋊Q8—22no—
333C4⋊Q8—22no—
334C4⋊Q8—22no—
335C4⋊Q8—22no—
336C4⋊Q8C2×D414yes—
337#127—22no—
338#127—22no—
339#127—22no—
340#127C2×D414yes—
341#125—24no—
342#125—24no—
343#124—28no—
344#124—24no—
345#124—24no—
346#124—44no—
347#124—44no—
348#124—44no—
349#124—44no—
350C22⋊Q8—44no—
351C22⋊Q8—44no—
352#121—28no—
353#121—24no—
354#121—44no—
355#121—44no—
356#121C2×D418yes—
357C4×Q8—44no—
358C4×Q8—44no—
359C4×Q8—44no—
360C4×Q8—44no—
361C4×D4—28no—
362C4×D4—24no—
363C4×D4—44no—
364C4×D4—44no—
365C4×D4—44no—
366C4×D4—44no—
367C4×D4—48no—
368C4×D4—48no—
369C4×D4—44no—
370C4×D4—44no—
371C4×D4—44no—
372C4×D4—44no—
373C4×D4C2×D418yes—
374#117—24no—
375#117—24no—
376#117—48no—
377#117—44no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—22no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4C2412yes—
392C2×C4⋊C4C2412yes—
393C2×C4⋊C4C2412yes—
394C2×C4⋊C4C2412yes—
395C2×C4⋊C4C2412yes—
396C2×C22⋊C4—22no—
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⋊C4—22no—
415C2×C22⋊C4—22no—
416C2×C42—24no—
417C2×C42—24no—
418C2×C42—22no—
419C2×C42—22no—
420C2×C42—22no—
421C2×C42—22no—
422C2×C42—42no—
423C2×C42—42no—
424C2×C42—42no—
425C2×C42—42no—
426C2×C42—48no—
427C2×C42C2×D411yescharacteristic
428C2×C42C2×D411yescharacteristic
429C2×C42C2×D411yescharacteristic
430C2×C42C2×D411yescharacteristic
431C2×C42C2×D411yescharacteristic
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×C42C2×D411yescharacteristic
445C2×C42C2×D411yescharacteristic
446C2×C42C2×D411yescharacteristic
447C2×C42C2×D414yes—
448C2×C42C2×D411yescharacteristic
449C2×C42C2×D411yescharacteristic
450C2×C42#4114yes—
451C2×C42C2411yescharacteristic
452C2×C42C2411yescharacteristic
453C2×C42C2411yescharacteristic
454C2×C42C2411yescharacteristic
455C2×C42C2411yescharacteristic
456C2×C42C2411yescharacteristic
457#107—28no—
458#106—28no—
459C4⋊C8—24no—
460C4⋊C8—24no—
461C4⋊C8—42no—
462C4⋊C8—42no—
463C4⋊C8—42no—
464C4⋊C8—42no—
465#103—28no—
466#103—44no—
467#103—44no—
468#102—28no—
469#102—28no—
470#102—28no—
471#102—44no—
472#102—44no—
473C22⋊C8—24no—
474C22⋊C8—24no—
475C4×C8—22no—
476C4×C8—22no—
477C4×C8—22no—
478C4×C8—22no—
479#95—22no—
480#95—22no—
481#95—22no—
482#95—22no—
483#95—22no—
484#95—22no—
485#95—22no—
486#95—22no—
487#95—22no—
488#95—22no—
489#95—22no—
490#95—22no—
491#95—22no—
492#95—22no—
493C24—22no—
494C24—22no—
495C24C22×D411yescharacteristic
496#41—432no—
497#41—88no—
498#41—88no—
499C2×Q8—24no—
500C2×Q8—22no—
501C2×Q8—22no—
502C2×Q8—24no—
503C2×Q8—24no—
504C2×Q8—42no—
505C2×Q8—42no—
506C2×Q8—42no—
507C2×Q8—42no—
508C2×Q8—42no—
509C2×Q8—42no—
510C2×Q8—42no—
511C2×Q8—42no—
512C2×D4—28no—
513C2×D4—24no—
514C2×D4—24no—
515C2×D4—22no—
516C2×D4—22no—
517C2×D4—22no—
518C2×D4—24no—
519C2×D4—24no—
520C2×D4—24no—
521C2×D4—24no—
522C2×D4—44no—
523C2×D4—44no—
524C2×D4—44no—
525C2×D4—44no—
526C2×D4—44no—
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—42no—
537C2×D4C22×D414yes—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—28no—
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—41no—
556C22×C4—41no—
557C22×C4—41no—
558C22×C4—41no—
559C22×C4—41no—
560C22×C4—41no—
561C22×C4—41no—
562C22×C4—41no—
563C22×C4—44no—
564C22×C4—44no—
565C22×C4—44no—
566C22×C4—44no—
567C22×C4—44no—
568C22×C4—44no—
569C22×C4—44no—
570C22×C4—44no—
571C22×C4—44no—
572C22×C4—44no—
573C22×C4—44no—
574C22×C4#12114yes—
575C22×C4#12114yes—
576C22×C4C22×D411yescharacteristic
577C22×C4C22×D411yescharacteristic
578C22×C4C22×D411yescharacteristic
579C22×C4C22×D411yescharacteristic
580C22×C4C22×D411yescharacteristic
581C22×C4C22×D411yescharacteristic
582C22×C4C22×D411yescharacteristic
583C22×C4C22×D412yes—
584C22×C4C22×D411yescharacteristic
585C22×C4C22×D411yescharacteristic
586C22×C4C22×D411yescharacteristic
587C22×C4C22×D411yescharacteristic
588C22×C4C22×D411yescharacteristic
589C22×C4C22×D411yescharacteristic
590C22×C4C2×#4112yes—
591C22×C4C2511yescharacteristic
592SD16—88no—
593D8—88no—
594C2×C8—22no—
595C2×C8—22no—
596C2×C8—22no—
597C2×C8—22no—
598C2×C8—22no—
599C2×C8—22no—
600C2×C8—22no—
601C2×C8—22no—
602C2×C8—22no—
603C2×C8—22no—
604C2×C8—22no—
605C2×C8—22no—
606C4⋊C4—24no—
607C4⋊C4—22no—
608C4⋊C4—22no—
609C4⋊C4—22no—
610C4⋊C4—22no—
611C4⋊C4—22no—
612C4⋊C4—24no—
613C4⋊C4—24no—
614C4⋊C4—44no—
615C4⋊C4—42no—
616C4⋊C4—42no—
617C4⋊C4—44no—
618C4⋊C4—44no—
619C4⋊C4—42no—
620C4⋊C4—42no—
621C4⋊C4—42no—
622C4⋊C4—44no—
623C4⋊C4—42no—
624C4⋊C4—42no—
625C4⋊C4—42no—
626C4⋊C4C22×D414yes—
627C22⋊C4—28no—
628C22⋊C4—28no—
629C22⋊C4—44no—
630C22⋊C4—44no—
631C22⋊C4—44no—
632C22⋊C4—44no—
633C22⋊C4—44no—
634C22⋊C4—44no—
635C22⋊C4—44no—
636C22⋊C4—44no—
637C22⋊C4—44no—
638C22⋊C4—44no—
639C22⋊C4—44no—
640C22⋊C4—44no—
641C22⋊C4—44no—
642C22⋊C4—44no—
643C22⋊C4—44no—
644C22⋊C4—44no—
645C22⋊C4—44no—
646C22⋊C4—44no—
647C42—22no—
648C42—22no—
649C42—22no—
650C42—22no—
651C42—22no—
652C42—22no—
653C42—22no—
654C42—22no—
655C42—22no—
656C42—22no—
657C42—22no—
658C42—22no—
659C42—22no—
660C42—22no—
661C42—41no—
662C42—41no—
663C42—41no—
664C42—41no—
665C42—41no—
666C42—41no—
667C42—41no—
668C42—41no—
669C42—44no—
670C42—44no—
671C42—44no—
672C42—44no—
673C42#12114yes—
674C42#12114yes—
675C42#13514yes—
676C42AGL(1,ℤ/8)14yes—
677C42C22×D412yes—
678C42C22×D412yes—
679C42C2×#4112yes—
680C42C2×#4112yes—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—24no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—42no—
699C23—42no—
700C23—42no—
701C23C2×#12112yes—
702C23C23×D411yescharacteristic
703Q8—48no—
704Q8—44no—
705Q8—44no—
706Q8—84no—
707Q8—84no—
708D4—28no—
709D4—416no—
710D4—44no—
711D4—44no—
712D4—44no—
713D4—48no—
714D4—48no—
715D4—88no—
716D4—84no—
717D4—84no—
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—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—28no—
735C2×C4—28no—
736C2×C4—24no—
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—44no—
750C2×C4—44no—
751C2×C4—44no—
752C2×C4—416no—
753C2×C4—44no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—88no—
772C2×C4—88no—
773C2×C4—88no—
774C2×C4C2×#12112yes—
775C2×C4C2×#12112yes—
776C2×C4C2×#12112yes—
777C2×C4C2×#12112yes—
778C2×C4C2×#12112yes—
779C2×C4C2×#13512yes—
780C2×C4C2×#13512yes—
781C2×C4C2×#13512yes—
782C2×C4C2×AGL(1,ℤ/8)12yes—
783C2×C4C2×AGL(1,ℤ/8)12yes—
784C2×C4C2×AGL(1,ℤ/8)12yes—
785C2×C4#57512yes—
786C2×C4#57512yes—
787C2×C4C23×D411yescharacteristic
788C2×C4C22×#4111yescharacteristic
789C2×C4#58512yes—
790C2×C4#58512yes—
791C8—42no—
792C8—42no—
793C8—42no—
794C8—42no—
795C22—22no—
796C22—22no—
797C22—22no—
798C22—41no—
799C22—41no—
800C22—41no—
801C22—41no—
802C22—44no—
803C22—44no—
804C22—44no—
805C22—82no—
806C22—82no—
807C22—82no—
808C22—82no—
809C22—82no—
810C22—82no—
811C22—82no—
812C22—82no—
813C22—82no—
814C22—82no—
815C22—82no—
816C22C22×#12111yescharacteristic
817C22#344911yescharacteristic
818C22#344911yescharacteristic
819C22C22×#13511yescharacteristic
820C22C22×AGL(1,ℤ/8)11yescharacteristic
821C22C2×#57511yescharacteristic
822C22C2×#57511yescharacteristic
823C4—22no—
824C4—22no—
825C4—22no—
826C4—22no—
827C4—22no—
828C4—22no—
829C4—22no—
830C4—41no—
831C4—41no—
832C4—41no—
833C4—41no—
834C4—44no—
835C4—82no—
836C4—82no—
837C4—82no—
838C4—82no—
839C4—82no—
840C4#303514yes—
841C4#303614yes—
842C4#350012yes—
843C4#351012yes—
844C2—42no—
845C2—84no—
846C2—162no—
847C2#3532711yescharacteristic
848C2C2×#303511yescharacteristic
849C2C2×#303611yescharacteristic
850C2#6094411yescharacteristic
851C2#6094611yescharacteristic
852C2#6096511yescharacteristic
853C2#6097211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#3207C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C43 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3228C2semidirect
3. #36639C2semidirect
4. C4×#532C2semidirect
5. #33028C2semidirect
6. #29832C2semidirect
7. #28656C2semidirect
8. #28655C2semidirect
9. #28654C2semidirect
10. #28653C2semidirect
11. #28615C2semidirect
12. #28615C2semidirect
13. #28613C2semidirect
14. #28613C2semidirect
15. #28119C2semidirect
16. #28116C2semidirect
17. #21835C2semidirect
18. #21805C2semidirect
19. #20808C2semidirect

Maximal subgroups

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

subgroupindex
C2×#32282
C2×#32072
#366392
C4×#5322
#330282
#298322
#286562
#286552
#286542
#286532
#286152
#286132
#281192
#281162
#218352
#218052
#208082