Finite Group Databasebeta

← #6497399

Subgroups — #6497399

Order 512.

1543 conjugacy classes of subgroups.

The subgroup lattice has 918 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35275C211yesmaximal, characteristic, complemented
2#35139C211yesmaximal, characteristic
3#33297C211yesmaximal, characteristic, complemented
4#33294C211yesmaximal, characteristic, complemented
5#33282C211yesmaximal, characteristic, complemented
6#33282C211yesmaximal, characteristic, complemented
7#30235C211yesmaximal, characteristic, complemented
8#30235C211yesmaximal, characteristic, complemented
9#30216C211yesmaximal, characteristic, complemented
10#30216C211yesmaximal, characteristic, complemented
11#27827C212yesmaximal, complemented
12#27825C212yesmaximal, complemented
13#27741C212yesmaximal, complemented
14#27739C212yesmaximal, complemented
15#27713C212yesmaximal, complemented
16#27711C212yesmaximal
17#27697C212yesmaximal, complemented
18#27695C212yesmaximal
19#21867C211yesmaximal, characteristic
20#21838C211yesmaximal, characteristic, complemented
21#21406C211yesmaximal, characteristic
22C2×#1992C211yesmaximal, characteristic, complemented
23#20479C211yesmaximal, characteristic, complemented
24C2×#544—21no—
25C2×#529C2211yescharacteristic
26C22×#125C2211yescharacteristic
27C2×#432C2211yescharacteristic
28C22×#97C2211yescharacteristic
29#2868C2211yescharacteristic
30#2868C2211yescharacteristic
31#2861C2211yescharacteristic
32#2861C2211yescharacteristic
33#2859C2211yescharacteristic
34#2859C2211yescharacteristic
35#2859C2211yescharacteristic
36#2859C2211yescharacteristic
37#2664—21no—
38#2664—21no—
39#2660—21no—
40#2660—21no—
41#2611—21no—
42#2611—21no—
43#2566C2211yescharacteristic
44#2566C2211yescharacteristic
45#2565C2211yescharacteristic
46#2565C2211yescharacteristic
47#2552—21no—
48#2552C2212yes—
49#2551—21no—
50#2551C2212yes—
51#2504C2211yescharacteristic
52#2503C2211yescharacteristic
53#2502C2211yescharacteristic
54#2501C2211yescharacteristic
55#2440—21no—
56#2440—21no—
57#2440C2212yes—
58#2440C2212yes—
59#2413—21no—
60#2413—21no—
61#2322—21no—
62#2322—21no—
63#2317—21no—
64#2285C2211yescharacteristic
65C2×#384C2211yescharacteristic
66C4×#117C2211yescharacteristic
67#2101C2212yes—
68#2101C2212yes—
69#2101C2212yes—
70#2101C2212yes—
71#2100C2212yes—
72#2100C2212yes—
73#2099C2212yes—
74#2099C2212yes—
75#2072C2212yes—
76#2072C2212yes—
77#2071C2212yes—
78#2071C2212yes—
79#2024C2212yes—
80#2024C2212yes—
81#2023C2212yes—
82#2023C2212yes—
83#1993C2212yes—
84#1993C2212yes—
85#1992C2211yescharacteristic
86#1992C2211yescharacteristic
87#1992C2211yescharacteristic
88#1992C2211yescharacteristic
89#1992C2211yescharacteristic
90#1992C2211yescharacteristic
91#1992C2211yescharacteristic
92#1992C2211yescharacteristic
93#1992C2211yescharacteristic
94#1992C2211yescharacteristic
95#1992C2211yescharacteristic
96#1992C2211yescharacteristic
97#1992C2212yes—
98#1992C2212yes—
99#1990C2212yes—
100#1990C2212yes—
101#1989C2212yes—
102#1989C2212yes—
103#1959C2211yescharacteristic
104#1959C2211yescharacteristic
105#1959C2211yescharacteristic
106#1959C2211yescharacteristic
107#1936C2212yes—
108#1936C2212yes—
109#1935C2212yes—
110#1935C2212yes—
111#1934C2212yes—
112#1934C2212yes—
113#1933C2212yes—
114#1933C2212yes—
115#1893C2212yes—
116#1892C2212yes—
117#1874C2212yes—
118#1872C2212yes—
119#1836C2212yes—
120#1836C2212yes—
121#1834C2212yes—
122#1834C2212yes—
123#1824C2212yes—
124#1823C2212yes—
125#1803C2212yes—
126#1802C2212yes—
127#1771C2212yes—
128#1771C2212yes—
129#1763C2212yes—
130#1762C2212yes—
131#1752C2212yes—
132C8×C22⋊C4C2212yes—
133#1745C2211yescharacteristic
134#1745C2211yescharacteristic
135C2×#340C2212yes—
136C2×#340C2212yes—
137C4×#97C2211yescharacteristic
138C4×#97C2211yescharacteristic
139C23×C8C2312yes—
140#544—48no—
141C2×C4⋊Q8—22no—
142C2×C4⋊Q8—21no—
143C2×C4⋊Q8—21no—
144C2×C4⋊Q8—21no—
145C2×C4⋊Q8—21no—
146C2×C4⋊Q8C2312yes—
147C2×C4⋊Q8C2312yes—
148#529—24no—
149#529—24no—
150C2×#126—21no—
151C2×#125—22no—
152C2×#125—21no—
153C2×#125—21no—
154C2×#125—21no—
155C2×#125—21no—
156C2×#125—24no—
157C2×#125—24no—
158C2×#125C2311yescharacteristic
159C2×#125C2311yescharacteristic
160C2×#125C2311yescharacteristic
161C2×#125C2311yescharacteristic
162C2×#125C2311yescharacteristic
163C2×#124C2311yescharacteristic
164C2×#123—21no—
165C2×#123—21no—
166C2×#123—21no—
167C2×C22⋊Q8—22no—
168C2×C22⋊Q8—22no—
169C2×C22⋊Q8C2311yescharacteristic
170C2×#121C2311yescharacteristic
171C2×C4×Q8C2311yescharacteristic
172C2×C4×D4—21no—
173C2×C4×D4C2311yescharacteristic
174C2×#117—21no—
175C2×#117—21no—
176C2×#117D411yescharacteristic
177C2×#117D411yescharacteristic
178C22×C4⋊C4—21no—
179C22×C4⋊C4—21no—
180C22×C4⋊C4—21no—
181C22×C4⋊C4—21no—
182C22×C4⋊C4C2311yescharacteristic
183C22×C4⋊C4C2311yescharacteristic
184C22×C4⋊C4C2312yes—
185C22×C42C2311yescharacteristic
186#432—24no—
187C2×C4⋊C8C2312yes—
188C2×#103C2312yes—
189C2×#103C2312yes—
190C2×#103C2312yes—
191C2×#103C2312yes—
192C2×#102C2312yes—
193C2×#102C2312yes—
194C2×#102C2312yes—
195C2×#102C2312yes—
196C2×C22⋊C8C2312yes—
197C2×#97—24no—
198C2×#97C2312yes—
199C2×#97C2311yescharacteristic
200C2×#97C2311yescharacteristic
201C2×#97C2312yes—
202C2×#97C2311yescharacteristic
203C2×#97C2311yescharacteristic
204C2×#97C2312yes—
205C2×C4×C8C2312yes—
206C2×C4×C8C2312yes—
207#400—21no—
208#400—21no—
209#399—21no—
210#399—21no—
211#398—21no—
212#398—21no—
213#398—21no—
214#398—21no—
215#398—21no—
216#398—21no—
217#398—22no—
218#398—22no—
219#398—22no—
220#398—22no—
221#397—21no—
222#397—21no—
223#396—21no—
224#396—21no—
225#396—21no—
226#396—21no—
227#395—22no—
228#395—22no—
229#395—22no—
230#395—22no—
231#391C2311yescharacteristic
232#391C2311yescharacteristic
233#391C2311yescharacteristic
234#391C2311yescharacteristic
235#390C2311yescharacteristic
236#390C2311yescharacteristic
237#390C2311yescharacteristic
238#390C2311yescharacteristic
239#389—22no—
240#389—22no—
241#389—21no—
242#389—21no—
243#389—21no—
244#389—21no—
245#389—21no—
246#389—21no—
247#389—21no—
248#389—21no—
249#389—21no—
250#389—21no—
251#389—21no—
252#389—21no—
253#389C2312yes—
254#389C2312yes—
255#389C2312yes—
256#389C2312yes—
257#388—21no—
258#388—21no—
259#388—21no—
260#388—21no—
261#388—21no—
262#388—21no—
263#388—21no—
264#388—21no—
265#387—21no—
266#387—21no—
267#387—21no—
268#387—21no—
269#386—21no—
270#386—21no—
271#385—22no—
272#385—22no—
273#385—21no—
274#385—21no—
275#385—21no—
276#385—21no—
277#385—21no—
278#385—21no—
279#384—21no—
280#384—21no—
281#384—21no—
282#384—21no—
283#384—21no—
284#384—21no—
285#384C2311yescharacteristic
286#384C2311yescharacteristic
287#384C2311yescharacteristic
288#384C2311yescharacteristic
289#384C2312yes—
290#384C2312yes—
291#384C2312yes—
292#384C2311yescharacteristic
293#384C2311yescharacteristic
294#384C2311yescharacteristic
295#384C2311yescharacteristic
296#382—21no—
297#382—21no—
298#382—21no—
299#382C2311yescharacteristic
300#382C2311yescharacteristic
301#382C2311yescharacteristic
302#382C2311yescharacteristic
303#381—21no—
304#381—21no—
305#380—21no—
306#380C2312yes—
307C4×C4⋊C4—21no—
308C4×C4⋊C4D411yescharacteristic
309C4×C4⋊C4D411yescharacteristic
310C4×C4⋊C4C2312yes—
311C4×C4⋊C4C2311yescharacteristic
312C4×C4⋊C4C2311yescharacteristic
313C4×C22⋊C4D411yescharacteristic
314C4×C22⋊C4D411yescharacteristic
315C4×C22⋊C4C2311yescharacteristic
316C4×C22⋊C4C2311yescharacteristic
317#376D411yescharacteristic
318#376D411yescharacteristic
319C43C2311yescharacteristic
320C43C2311yescharacteristic
321#340C2312yes—
322#340C2312yes—
323#340C2312yes—
324#340C2312yes—
325#340C2312yes—
326#340C2312yes—
327#340C2312yes—
328#340C2312yes—
329#340C2312yes—
330#340C2312yes—
331#340C2312yes—
332#340C2312yes—
333#340C2312yes—
334#340C2312yes—
335#340C2312yes—
336#340C2312yes—
337#340C2312yes—
338#340C2312yes—
339#340C2312yes—
340#340C2312yes—
341#340C2312yes—
342#340C2312yes—
343#340C2312yes—
344#340C2312yes—
345#336C2312yes—
346#336C2312yes—
347#336C2312yes—
348#336C2312yes—
349C22×Q8—22no—
350C22×Q8—22no—
351C22×Q8C2411yescharacteristic
352C22×D4—21no—
353C22×D4C2411yescharacteristic
354C23×C4—21no—
355C23×C4—22no—
356C23×C4—21no—
357C23×C4—21no—
358C23×C4C2×D411yescharacteristic
359C23×C4C2×D411yescharacteristic
360C23×C4C2411yescharacteristic
361C22×C8—24no—
362C22×C8—24no—
363C22×C8—42no—
364C22×C8C2412yes—
365C22×C8C2412yes—
366C22×C8C2412yes—
367C22×C8C2412yes—
368C4⋊Q8—42no—
369C4⋊Q8—42no—
370C4⋊Q8—42no—
371C4⋊Q8—42no—
372C4⋊Q8—44no—
373C4⋊Q8—44no—
374C4⋊Q8—48no—
375C4⋊Q8—82no—
376C4⋊Q8—82no—
377#126—44no—
378#125—22no—
379#125—22no—
380#125—22no—
381#125—22no—
382#125—22no—
383#125—22no—
384#125—22no—
385#125—22no—
386#125—22no—
387#125—22no—
388#125—44no—
389#125—44no—
390#125—48no—
391#125—44no—
392#125—44no—
393#124—22no—
394#124—22no—
395#123—44no—
396#123—44no—
397#123—44no—
398C22⋊Q8—22no—
399C22⋊Q8—22no—
400C22⋊Q8—48no—
401C22⋊Q8—48no—
402#121—22no—
403#121—22no—
404C4×Q8—22no—
405C4×Q8—22no—
406C4×D4—22no—
407C4×D4—22no—
408C4×D4—44no—
409#117—24no—
410#117—24no—
411#117—44no—
412#117—44no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—22no—
439C2×C4⋊C4—22no—
440C2×C4⋊C4—22no—
441C2×C4⋊C4—22no—
442C2×C4⋊C4—22no—
443C2×C4⋊C4—22no—
444C2×C4⋊C4—21no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4—21no—
450C2×C4⋊C4—22no—
451C2×C4⋊C4—22no—
452C2×C4⋊C4—22no—
453C2×C4⋊C4—22no—
454C2×C4⋊C4—22no—
455C2×C4⋊C4—22no—
456C2×C4⋊C4—21no—
457C2×C4⋊C4—21no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4—42no—
461C2×C4⋊C4—42no—
462C2×C4⋊C4—44no—
463C2×C4⋊C4—44no—
464C2×C4⋊C4—44no—
465C2×C4⋊C4—82no—
466C2×C4⋊C4C2×D411yescharacteristic
467C2×C4⋊C4C2×D411yescharacteristic
468C2×C4⋊C4C2×D411yescharacteristic
469C2×C4⋊C4C2×D411yescharacteristic
470C2×C4⋊C4C2411yescharacteristic
471C2×C4⋊C4C2411yescharacteristic
472C2×C4⋊C4C2411yescharacteristic
473C2×C4⋊C4C2411yescharacteristic
474C2×C4⋊C4C2412yes—
475C2×C4⋊C4C2412yes—
476C2×C4⋊C4C2411yescharacteristic
477C2×C4⋊C4C2411yescharacteristic
478C2×C4⋊C4C2412yes—
479C2×C4⋊C4C2412yes—
480C2×C22⋊C4—22no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
486C2×C22⋊C4—21no—
487C2×C22⋊C4—21no—
488C2×C22⋊C4—21no—
489C2×C22⋊C4—21no—
490C2×C22⋊C4—21no—
491C2×C22⋊C4—21no—
492C2×C22⋊C4—21no—
493C2×C22⋊C4—21no—
494C2×C22⋊C4C2×D411yescharacteristic
495C2×C22⋊C4C2×D411yescharacteristic
496C2×C22⋊C4C2×D411yescharacteristic
497C2×C22⋊C4C2×D411yescharacteristic
498C2×C42—21no—
499C2×C42—22no—
500C2×C42C2×D411yescharacteristic
501C2×C42C2×D411yescharacteristic
502C2×C42C2×D411yescharacteristic
503C2×C42C2×D411yescharacteristic
504C2×C42C2×D411yescharacteristic
505C2×C42C2×D411yescharacteristic
506C2×C42C2×D411yescharacteristic
507C2×C42C2×D411yescharacteristic
508C2×C42C2×D411yescharacteristic
509C2×C42C2×D411yescharacteristic
510C2×C42#4114yes—
511C2×C42#4114yes—
512C2×C42C2411yescharacteristic
513C2×C42C2411yescharacteristic
514C2×C42C2411yescharacteristic
515C2×C42C2411yescharacteristic
516C2×C42C2411yescharacteristic
517C2×C42C2411yescharacteristic
518C4⋊C8—24no—
519#103—24no—
520#103—42no—
521#103—42no—
522#103—42no—
523#102—24no—
524#102—42no—
525#102—42no—
526#102—42no—
527C22⋊C8—24no—
528#97—24no—
529#97—24no—
530#97—22no—
531#97—22no—
532#97—22no—
533#97—22no—
534#97—42no—
535C4×C8—24no—
536C4×C8—42no—
537#95—22no—
538#95—22no—
539#95—21no—
540#95—21no—
541#95—21no—
542#95—21no—
543#95—21no—
544#95—21no—
545#95—21no—
546#95—21no—
547#95—22no—
548#95—22no—
549#95—22no—
550#95—22no—
551#95—21no—
552#95—21no—
553#95—21no—
554#95—21no—
555#95—21no—
556#95—21no—
557#95—21no—
558#95—21no—
559#95C2×D411yescharacteristic
560#95C2×D411yescharacteristic
561#95C2×D411yescharacteristic
562#95C2×D411yescharacteristic
563#95C2×D411yescharacteristic
564#95C2×D411yescharacteristic
565#95C2×D411yescharacteristic
566#95C2×D411yescharacteristic
567C24—21no—
568C24C22×D411yescharacteristic
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—22no—
572C2×Q8—22no—
573C2×Q8—44no—
574C2×Q8—44no—
575C2×Q8—82no—
576C2×Q8—82no—
577C2×Q8—82no—
578C2×Q8—82no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—22no—
582C2×D4—22no—
583C2×D4—42no—
584C2×D4—42no—
585C2×D4—42no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—21no—
591C22×C4—22no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—41no—
602C22×C4—41no—
603C22×C4—42no—
604C22×C4—42no—
605C22×C4—42no—
606C22×C4—42no—
607C22×C4—44no—
608C22×C4—42no—
609C22×C4—81no—
610C22×C4—81no—
611C22×C4—81no—
612C22×C4—81no—
613C22×C4—82no—
614C22×C4—82no—
615C22×C4#12414yes—
616C22×C4#12414yes—
617C22×C4C22×D411yescharacteristic
618C22×C4C22×D411yescharacteristic
619C22×C4C22×D411yescharacteristic
620C22×C4C22×D411yescharacteristic
621C22×C4C22×D411yescharacteristic
622C22×C4C22×D411yescharacteristic
623C22×C4C22×D411yescharacteristic
624C22×C4C22×D411yescharacteristic
625C22×C4C22×D411yescharacteristic
626C22×C4C22×D411yescharacteristic
627C22×C4C22×D411yescharacteristic
628C22×C4C22×D411yescharacteristic
629C22×C4C22×D411yescharacteristic
630C22×C4C2×#4112yes—
631C22×C4C2×#4112yes—
632C22×C4C2511yescharacteristic
633C2×C8—22no—
634C2×C8—22no—
635C2×C8—22no—
636C2×C8—22no—
637C2×C8—22no—
638C2×C8—22no—
639C2×C8—22no—
640C2×C8—22no—
641C2×C8—22no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—48no—
645C2×C82−1+414yes—
646C4⋊C4—22no—
647C4⋊C4—22no—
648C4⋊C4—22no—
649C4⋊C4—22no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—22no—
663C4⋊C4—22no—
664C4⋊C4—22no—
665C4⋊C4—22no—
666C4⋊C4—22no—
667C4⋊C4—22no—
668C4⋊C4—22no—
669C4⋊C4—22no—
670C4⋊C4—42no—
671C4⋊C4—42no—
672C4⋊C4—42no—
673C4⋊C4—44no—
674C4⋊C4—42no—
675C4⋊C4—42no—
676C4⋊C4—42no—
677C4⋊C4—42no—
678C4⋊C4—44no—
679C4⋊C4—44no—
680C4⋊C4—44no—
681C4⋊C4—42no—
682C4⋊C4—42no—
683C4⋊C4—42no—
684C4⋊C4—42no—
685C4⋊C4—42no—
686C4⋊C4—42no—
687C4⋊C4—42no—
688C4⋊C4—42no—
689C4⋊C4—42no—
690C4⋊C4—42no—
691C4⋊C4—42no—
692C4⋊C4—42no—
693C4⋊C4—42no—
694C4⋊C4—42no—
695C4⋊C4—42no—
696C4⋊C4—44no—
697C4⋊C4—44no—
698C4⋊C4—44no—
699C4⋊C4—42no—
700C4⋊C4—42no—
701C4⋊C4—42no—
702C4⋊C4—42no—
703C4⋊C4—81no—
704C4⋊C4—81no—
705C4⋊C4—81no—
706C4⋊C4—81no—
707C4⋊C4—82no—
708C4⋊C4—82no—
709C4⋊C4—82no—
710C4⋊C4—82no—
711C4⋊C4—82no—
712C4⋊C4—82no—
713C22⋊C4—22no—
714C22⋊C4—22no—
715C22⋊C4—42no—
716C22⋊C4—44no—
717C22⋊C4—42no—
718C22⋊C4—42no—
719C22⋊C4—42no—
720C22⋊C4—42no—
721C22⋊C4—42no—
722C22⋊C4—42no—
723C22⋊C4—42no—
724C22⋊C4—42no—
725C22⋊C4—81no—
726C22⋊C4—81no—
727C22⋊C4—81no—
728C22⋊C4—81no—
729C22⋊C4AGL(1,ℤ/8)14yes—
730C22⋊C4#13714yes—
731C42—22no—
732C42—22no—
733C42—22no—
734C42—22no—
735C42—22no—
736C42—22no—
737C42—22no—
738C42—22no—
739C42—41no—
740C42—41no—
741C42—41no—
742C42—41no—
743C42—44no—
744C42—42no—
745C42#12414yes—
746C42#12414yes—
747C42C2×#4112yes—
748C42C2×#4112yes—
749C42C2×#4112yes—
750C42C2×#4112yes—
751C23—21no—
752C23—21no—
753C23—21no—
754C23—21no—
755C23—41no—
756C23—41no—
757C23—41no—
758C23—41no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23C2×#12412yes—
763C23C2×AGL(1,ℤ/8)12yes—
764C23C2×#13712yes—
765C23C23×D411yescharacteristic
766Q8—42no—
767Q8—42no—
768Q8—164no—
769Q8—164no—
770D4—42no—
771D4—42no—
772D4—84no—
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—28no—
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—24no—
793C2×C4—24no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—44no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—42no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—42no—
825C2×C4—41no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—41no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—84no—
841C2×C4—84no—
842C2×C4—84no—
843C2×C4—164no—
844C2×C4C2×#12412yes—
845C2×C4C2×#12412yes—
846C2×C4C2×#12412yes—
847C2×C4C2×#12412yes—
848C2×C4C2×#12412yes—
849C2×C4C2×AGL(1,ℤ/8)12yes—
850C2×C4C2×AGL(1,ℤ/8)12yes—
851C2×C4C2×#13712yes—
852C2×C4C2×#13712yes—
853C2×C4C22×#4111yescharacteristic
854C2×C4C22×#4111yescharacteristic
855C2×C4C2×2−1+412yes—
856C2×C4#58512yes—
857C8—24no—
858C8—42no—
859C8—42no—
860C8—42no—
861C22—22no—
862C22—22no—
863C22—22no—
864C22—22no—
865C22—22no—
866C22—22no—
867C22—81no—
868C22—81no—
869C22—81no—
870C22—81no—
871C22—81no—
872C22—81no—
873C22—81no—
874C22#314114yes—
875C22C22×#12411yescharacteristic
876C22#349911yescharacteristic
877C22#350011yescharacteristic
878C22C22×AGL(1,ℤ/8)11yescharacteristic
879C22C22×#13711yescharacteristic
880C22#358511yescharacteristic
881C22#358611yescharacteristic
882C4—22no—
883C4—22no—
884C4—22no—
885C4—22no—
886C4—22no—
887C4—22no—
888C4—22no—
889C4—22no—
890C4—22no—
891C4—41no—
892C4—41no—
893C4—41no—
894C4—41no—
895C4—82no—
896C4—82no—
897C4—82no—
898C4—82no—
899C4—81no—
900C4—81no—
901C4—81no—
902C4—81no—
903C4—81no—
904C4—81no—
905C4—81no—
906C4#346112yes—
907C4#349512yes—
908C2—24no—
909C2—161no—
910C2#3531211yescharacteristic
911C2C2×#314111yescharacteristic
912C2#6062111yescharacteristic
913C2#6250311yescharacteristic
914C2#6250411yescharacteristic
915C2#6257611yescharacteristic
916C2#6257711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#121C23
LCSG ▷ C22×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
1. #35275C2semidirect
3. #33297C2semidirect
4. #33294C2semidirect
5. #33282C2semidirect
6. #33282C2semidirect
7. #30235C2semidirect
8. #30235C2semidirect
9. #30216C2semidirect
10. #30216C2semidirect
11. #27827C2semidirect
12. #27825C2semidirect
13. #27741C2semidirect
14. #27739C2semidirect
15. #27713C2semidirect
17. #27697C2semidirect
20. #21838C2semidirect
22. C2×#1992C2semidirect
23. #20479C2semidirect

Maximal subgroups

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

subgroupindex
#352752
#351392
#332972
#332942
#332822
#302352
#302162
#278272
#278252
#277412
#277392
#277132
#277112
#276972
#276952
#218672
#218382
#214062
C2×#19922
#204792