Finite Group Databasebeta

← #6479924

Subgroups — #6479924

Order 512.

1454 conjugacy classes of subgroups.

The subgroup lattice has 919 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35288C211yesmaximal, characteristic
2C4×#544C211yesmaximal, characteristic, complemented
3#33153C211yesmaximal, characteristic, complemented
4#33149C211yesmaximal, characteristic, complemented
5#33113C211yesmaximal, characteristic
6#33106C211yesmaximal, characteristic
7#29917C212yesmaximal, complemented
8#29646C212yesmaximal, complemented
9#29530C212yesmaximal, complemented
10#29527C212yesmaximal, complemented
11#29404C212yesmaximal, complemented
12#29401C212yesmaximal, complemented
13#29354C211yesmaximal, characteristic, complemented
14#29348C211yesmaximal, characteristic, complemented
15#29321C211yesmaximal, characteristic, complemented
16#29312C211yesmaximal, characteristic, complemented
17#29277C211yesmaximal, characteristic, complemented
18#29275C211yesmaximal, characteristic, complemented
19#29256C211yesmaximal, characteristic, complemented
20#29254C211yesmaximal, characteristic, complemented
21#22093C212yesmaximal, complemented
22#22088C212yesmaximal, complemented
23#20786C211yesmaximal, characteristic, complemented
24C2×#544C2211yescharacteristic
25C2×#482C2212yes—
26C2×#480C2212yes—
27#2859C2211yescharacteristic
28#2858C2211yescharacteristic
29#2857C2211yescharacteristic
30#2856C2211yescharacteristic
31#2644C2212yes—
32#2624C2212yes—
33#2513—21no—
34#2490—21no—
35#2454—21no—
36#2448—21no—
37#2447—21no—
38#2427—21no—
39#2426—21no—
40#2420—21no—
41#2331—21no—
42#2331C2211yescharacteristic
43#2331C2211yescharacteristic
44#2330—21no—
45#2330C2211yescharacteristic
46#2330C2211yescharacteristic
47#2329—21no—
48#2329—21no—
49#2324C2212yes—
50#2319C2212yes—
51#2317C2211yescharacteristic
52#2317C2211yescharacteristic
53#2316C2211yescharacteristic
54C4×C4⋊Q8—21no—
55C4×C4⋊Q8C2211yescharacteristic
56C4×C4⋊Q8C2211yescharacteristic
57C4×C4⋊Q8C2211yescharacteristic
58C4×#127C2211yescharacteristic
59C4×#125—21no—
60C4×#125C2211yescharacteristic
61C4×#125C2211yescharacteristic
62C4×C22⋊Q8—21no—
63C4×C22⋊Q8—21no—
64C4×#117C2211yescharacteristic
65C4×#117C2211yescharacteristic
66C2×C4×C4⋊C4C2211yescharacteristic
67#2101C2212yes—
68#2100C2212yes—
69#2093C2212yes—
70#2092C2212yes—
71#2085C2212yes—
72#2083C2212yes—
73#2073C2212yes—
74#2071C2212yes—
75#2059C2212yes—
76#2059C2212yes—
77#2057C2212yes—
78#2057C2212yes—
79#2025C2212yes—
80#2025C2212yes—
81#2023C2212yes—
82#2023C2212yes—
83#1987C2211yescharacteristic
84#1987C2211yescharacteristic
85#1987C2211yescharacteristic
86#1987C2211yescharacteristic
87#1982C2211yescharacteristic
88#1982C2211yescharacteristic
89#1982C2211yescharacteristic
90#1982C2211yescharacteristic
91#1948C2211yescharacteristic
92#1948C2211yescharacteristic
93#1947C2211yescharacteristic
94#1947C2211yescharacteristic
95#1947C2211yescharacteristic
96#1947C2211yescharacteristic
97#1947C2211yescharacteristic
98#1947C2211yescharacteristic
99#1944C2212yes—
100#1943C2212yes—
101#1942C2212yes—
102#1942C2212yes—
103#1936C2212yes—
104#1936C2212yes—
105#1934C2212yes—
106#1934C2212yes—
107#1926C2212yes—
108#1925C2212yes—
109#1925C2212yes—
110#1925C2212yes—
111#1921C2212yes—
112#1921C2212yes—
113#1921C2212yes—
114#1921C2212yes—
115#1920C2212yes—
116#1919C2212yes—
117#1918C2212yes—
118#1918C2212yes—
119#1875C2212yes—
120#1874C2212yes—
121#1864C2212yes—
122#1862C2212yes—
123#1862C2212yes—
124#1862C2212yes—
125#1854C2212yes—
126#1852C2212yes—
127#1840C2212yes—
128#1831C2211yescharacteristic
129#1831C2211yescharacteristic
130#1825C2212yes—
131#1824C2212yes—
132#1818C2212yes—
133#1797C2211yescharacteristic
134#1797C2211yescharacteristic
135#1767C2211yescharacteristic
136C4×C4⋊C8C2211yescharacteristic
137#1750C2212yes—
138#1746C2212yes—
139#544—24no—
140#544—24no—
141C2×C4⋊Q8—21no—
142C2×C4⋊Q8C2311yescharacteristic
143C2×C4⋊Q8C2311yescharacteristic
144C2×C4⋊Q8C2311yescharacteristic
145C2×#127C2311yescharacteristic
146C2×#125—21no—
147C2×#125—21no—
148C2×#125C2311yescharacteristic
149C2×#125C2311yescharacteristic
150C2×#124—21no—
151C2×#124—21no—
152C2×C22⋊Q8—21no—
153C2×C22⋊Q8—21no—
154C2×C22⋊Q8—21no—
155C2×#121—21no—
156C2×#121—21no—
157C2×#121C2312yes—
158C2×C4×Q8—21no—
159C2×C4×Q8—21no—
160C2×C4×Q8—21no—
161C2×C4×D4—21no—
162C2×C4×D4—21no—
163C2×C4×D4C2312yes—
164C2×#117C2311yescharacteristic
165C2×#117C2311yescharacteristic
166C2×#117C2311yescharacteristic
167C2×#117C2311yescharacteristic
168C22×C4⋊C4C2311yescharacteristic
169C22×C4⋊C4C2311yescharacteristic
170C22×C42—21no—
171C22×C42C2311yescharacteristic
172#482—28no—
173#480—28no—
174C2×#107C2312yes—
175C2×#107C2312yes—
176C2×#107C2312yes—
177C2×#107C2312yes—
178C2×#107C2312yes—
179C2×#107C2312yes—
180C2×#106C2312yes—
181C2×#106C2312yes—
182C2×C4⋊C8C2311yescharacteristic
183C2×C4⋊C8C2311yescharacteristic
184C2×C4⋊C8C2311yescharacteristic
185C2×C4⋊C8C2311yescharacteristic
186C2×#102C2312yes—
187C2×#102C2312yes—
188C2×#102C2312yes—
189C2×#102C2312yes—
190C2×#102C2312yes—
191C2×#102C2312yes—
192C2×#102C2312yes—
193C2×#102C2312yes—
194C2×C22⋊C8C2312yes—
195C2×C22⋊C8C2312yes—
196C2×#97C2312yes—
197C2×C4×C8C2312yes—
198#399—22no—
199#397—22no—
200#397—22no—
201#397—22no—
202#397—22no—
203#396—22no—
204#394—22no—
205#394—22no—
206#391—21no—
207#391—21no—
208#391—21no—
209#391—21no—
210#391—21no—
211#391—21no—
212#391—21no—
213#391—21no—
214#390—22no—
215#390—21no—
216#390—21no—
217#390—21no—
218#390—21no—
219#390—21no—
220#390—21no—
221#390C2312yes—
222#390C2312yes—
223#390C2312yes—
224#390C2312yes—
225#389—21no—
226#389—21no—
227#389—21no—
228#389—21no—
229#389—21no—
230#389—21no—
231#389—21no—
232#389—21no—
233#389—21no—
234#389—21no—
235#389—21no—
236#389—21no—
237#389—21no—
238#389—21no—
239#389C2311yescharacteristic
240#389C2311yescharacteristic
241#389C2311yescharacteristic
242#389C2311yescharacteristic
243#389C2312yes—
244#389C2311yescharacteristic
245#389C2311yescharacteristic
246#389C2311yescharacteristic
247#389C2311yescharacteristic
248#389C2312yes—
249#389C2312yes—
250#389C2312yes—
251#388—22no—
252#388—22no—
253#388—22no—
254#387—21no—
255#387—21no—
256#387—21no—
257#387—21no—
258#387—21no—
259#387—21no—
260#387—21no—
261#387—21no—
262#387—21no—
263#387—21no—
264#387—21no—
265#387—21no—
266#386—22no—
267#385—22no—
268#385—21no—
269#385—21no—
270#385—21no—
271#385—21no—
272#384—21no—
273#384C2311yescharacteristic
274#384C2311yescharacteristic
275#384C2311yescharacteristic
276#384C2311yescharacteristic
277#382—21no—
278#382—21no—
279#382C2311yescharacteristic
280#382C2311yescharacteristic
281#381—22no—
282#380—21no—
283#380—21no—
284#380—21no—
285#380—22no—
286#380C2312yes—
287C4×C4⋊C4—21no—
288C4×C4⋊C4—21no—
289C4×C4⋊C4—21no—
290C4×C4⋊C4—21no—
291C4×C4⋊C4—21no—
292C4×C4⋊C4—21no—
293C4×C4⋊C4—21no—
294C4×C4⋊C4—21no—
295C4×C4⋊C4—21no—
296C4×C4⋊C4D411yescharacteristic
297C4×C4⋊C4D411yescharacteristic
298C4×C4⋊C4D411yescharacteristic
299C4×C4⋊C4D411yescharacteristic
300C4×C4⋊C4C2311yescharacteristic
301C4×C4⋊C4C2311yescharacteristic
302C4×C4⋊C4C2311yescharacteristic
303C4×C4⋊C4C2311yescharacteristic
304C4×C4⋊C4C2312yes—
305C4×C4⋊C4C2311yescharacteristic
306C4×C4⋊C4C2311yescharacteristic
307C4×C4⋊C4C2311yescharacteristic
308C4×C4⋊C4C2311yescharacteristic
309C4×C22⋊C4—21no—
310C4×C22⋊C4—21no—
311C4×C22⋊C4D411yescharacteristic
312C4×C22⋊C4D411yescharacteristic
313C4×C22⋊C4D411yescharacteristic
314C4×C22⋊C4D411yescharacteristic
315#376—21no—
316#376C2311yescharacteristic
317#376C2311yescharacteristic
318C2×#95—21no—
319C43—21no—
320C43C2311yescharacteristic
321C43C2311yescharacteristic
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#336C2312yes—
339#336C2312yes—
340#336C2312yes—
341#336C2312yes—
342#336C2312yes—
343#336C2312yes—
344#336C2312yes—
345#336C2312yes—
346C22×Q8—21no—
347C22×Q8—21no—
348C22×Q8—21no—
349C22×D4—22no—
350C22×D4—21no—
351C22×D4—21no—
352C22×D4C2412yes—
353C23×C4—21no—
354C23×C4—21no—
355C23×C4—22no—
356C23×C4C2×D411yescharacteristic
357C23×C4C2×D411yescharacteristic
358C23×C4C2411yescharacteristic
359C22×C8C2412yes—
360C22×C8C2412yes—
361C22×C8C2412yes—
362C22×C8C2412yes—
363C4⋊Q8—28no—
364C4⋊Q8—22no—
365C4⋊Q8—22no—
366C4⋊Q8—22no—
367C4⋊Q8—22no—
368C4⋊Q8—22no—
369C4⋊Q8—22no—
370#127—22no—
371#127—22no—
372#125—28no—
373#125—22no—
374#125—22no—
375#125—22no—
376#125—22no—
377#125—82no—
378#124—82no—
379#124—82no—
380C22⋊Q8—28no—
381C22⋊Q8—28no—
382C22⋊Q8—82no—
383#121—24no—
384#121—24no—
385#121—82no—
386#121—82no—
387C4×Q8—82no—
388C4×Q8—82no—
389C4×Q8—82no—
390C4×D4—42no—
391C4×D4—42no—
392C4×D4—82no—
393C4×D4—82no—
394#117—22no—
395#117—22no—
396#117—22no—
397#117—41no—
398#117—41no—
399#117—41no—
400#117—41no—
401#117#4114yes—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—41no—
433C2×C4⋊C4—41no—
434C2×C4⋊C4C2×D411yescharacteristic
435C2×C4⋊C4C2×D411yescharacteristic
436C2×C4⋊C4C2×D411yescharacteristic
437C2×C4⋊C4C2×D411yescharacteristic
438C2×C4⋊C4#4114yes—
439C2×C4⋊C4C2411yescharacteristic
440C2×C4⋊C4C2411yescharacteristic
441C2×C4⋊C4C2411yescharacteristic
442C2×C4⋊C4C2411yescharacteristic
443C2×C4⋊C4C2412yes—
444C2×C4⋊C4C2412yes—
445C2×C4⋊C4C2412yes—
446C2×C4⋊C4C2411yescharacteristic
447C2×C4⋊C4C2411yescharacteristic
448C2×C4⋊C4C2411yescharacteristic
449C2×C4⋊C4C2411yescharacteristic
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—22no—
453C2×C22⋊C4—22no—
454C2×C22⋊C4—22no—
455C2×C22⋊C4—22no—
456C2×C22⋊C4—22no—
457C2×C22⋊C4—22no—
458C2×C22⋊C4—22no—
459C2×C22⋊C4—22no—
460C2×C22⋊C4—22no—
461C2×C22⋊C4—22no—
462C2×C22⋊C4—22no—
463C2×C22⋊C4C2×D411yescharacteristic
464C2×C22⋊C4C2×D411yescharacteristic
465C2×C22⋊C4C2×D411yescharacteristic
466C2×C22⋊C4C2×D411yescharacteristic
467C2×C42—21no—
468C2×C42—22no—
469C2×C42—22no—
470C2×C42—21no—
471C2×C42—21no—
472C2×C42—21no—
473C2×C42—21no—
474C2×C42—21no—
475C2×C42—22no—
476C2×C42—21no—
477C2×C42—21no—
478C2×C42—21no—
479C2×C42—21no—
480C2×C42—82no—
481C2×C42C2×D411yescharacteristic
482C2×C42C2×D411yescharacteristic
483C2×C42C2×D411yescharacteristic
484C2×C42C2×D411yescharacteristic
485C2×C42C2×D411yescharacteristic
486C2×C42C2×D411yescharacteristic
487C2×C42C2×D411yescharacteristic
488C2×C42C2×D411yescharacteristic
489C2×C42C2×D411yescharacteristic
490C2×C42C2×D411yescharacteristic
491C2×C42C2411yescharacteristic
492C2×C42C2411yescharacteristic
493C2×C42C2411yescharacteristic
494C2×C42C2411yescharacteristic
495C2×C42C2411yescharacteristic
496C2×C42C2411yescharacteristic
497#107—24no—
498#107—24no—
499#107—24no—
500#107—42no—
501#107—42no—
502#107—42no—
503#106—24no—
504#106—42no—
505C4⋊C8—22no—
506C4⋊C8—22no—
507C4⋊C8—22no—
508C4⋊C8—22no—
509#102—24no—
510#102—24no—
511#102—24no—
512#102—24no—
513#102—42no—
514#102—42no—
515#102—42no—
516#102—42no—
517C22⋊C8—24no—
518C22⋊C8—24no—
519#97—42no—
520C4×C8—42no—
521#95—21no—
522#95—21no—
523#95—21no—
524#95—21no—
525#95—21no—
526#95—21no—
527#95—21no—
528#95—21no—
529#95—21no—
530#95—21no—
531#95—21no—
532#95—21no—
533#95—21no—
534#95—21no—
535#95—21no—
536#95—21no—
537#95—21no—
538#95—21no—
539#95—21no—
540#95—21no—
541#95—22no—
542#95—22no—
543#95—22no—
544#95—22no—
545#95—22no—
546#95—22no—
547#95C2×D411yescharacteristic
548#95C2×D411yescharacteristic
549#95C2×D411yescharacteristic
550#95C2×D411yescharacteristic
551#95C2×D411yescharacteristic
552#95C2×D411yescharacteristic
553#95C2×D411yescharacteristic
554#95C2×D411yescharacteristic
555C24—22no—
556C24C22×D411yescharacteristic
557C2×Q8—24no—
558C2×Q8—24no—
559C2×Q8—42no—
560C2×Q8—42no—
561C2×Q8—42no—
562C2×Q8—81no—
563C2×Q8—81no—
564C2×Q8—81no—
565C2×Q8—81no—
566C2×D4—22no—
567C2×D4—22no—
568C2×D4—22no—
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—22no—
572C2×D4—42no—
573C2×D4—42no—
574C2×D4—44no—
575C2×D4—42no—
576C2×D4—42no—
577C2×D4—42no—
578C2×D4—42no—
579C2×D4—82no—
580C2×D4—82no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—24no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
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—44no—
604C22×C4—42no—
605C22×C4—82no—
606C22×C4—82no—
607C22×C4—81no—
608C22×C4—81no—
609C22×C4—81no—
610C22×C4—81no—
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×C4C22×D411yescharacteristic
620C22×C4C22×D411yescharacteristic
621C22×C4C22×D411yescharacteristic
622C22×C4C22×D411yescharacteristic
623C22×C4C22×D411yescharacteristic
624C22×C4C2×#4112yes—
625C22×C4C2×#4112yes—
626C22×C4C2511yescharacteristic
627C2×C8—22no—
628C2×C8—22no—
629C2×C8—22no—
630C2×C8—22no—
631C2×C8—22no—
632C2×C8—22no—
633C2×C8—22no—
634C2×C8—22no—
635C2×C8—22no—
636C2×C8—22no—
637C2×C8—22no—
638C2×C8—22no—
639C4⋊C4—24no—
640C4⋊C4—24no—
641C4⋊C4—24no—
642C4⋊C4—24no—
643C4⋊C4—24no—
644C4⋊C4—24no—
645C4⋊C4—24no—
646C4⋊C4—22no—
647C4⋊C4—22no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—22no—
653C4⋊C4—22no—
654C4⋊C4—22no—
655C4⋊C4—22no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—22no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—22no—
666C4⋊C4—41no—
667C4⋊C4—41no—
668C4⋊C4—42no—
669C4⋊C4—42no—
670C4⋊C4—42no—
671C4⋊C4—42no—
672C4⋊C4—42no—
673C4⋊C4—42no—
674C4⋊C4—81no—
675C4⋊C4—81no—
676C4⋊C4—81no—
677C4⋊C4—81no—
678C4⋊C4—81no—
679C4⋊C4—81no—
680C4⋊C4—82no—
681C4⋊C4—81no—
682C4⋊C4—81no—
683C4⋊C4—81no—
684C4⋊C4—81no—
685C4⋊C4—81no—
686C4⋊C4—81no—
687C4⋊C4—82no—
688C4⋊C4—82no—
689C4⋊C4—82no—
690C4⋊C4C2×#4112yes—
691C4⋊C4C2×#4112yes—
692C4⋊C4C2×#4112yes—
693C4⋊C4C2×#4112yes—
694C22⋊C4—24no—
695C22⋊C4—22no—
696C22⋊C4—22no—
697C22⋊C4—41no—
698C22⋊C4—41no—
699C22⋊C4—44no—
700C22⋊C4—42no—
701C22⋊C4—44no—
702C22⋊C4—82no—
703C22⋊C4—82no—
704C22⋊C4—82no—
705C22⋊C4—82no—
706C22⋊C4—82no—
707C22⋊C4—82no—
708C22⋊C4—82no—
709C22⋊C4—82no—
710C22⋊C4—82no—
711C42—24no—
712C42—22no—
713C42—22no—
714C42—22no—
715C42—22no—
716C42—22no—
717C42—22no—
718C42—21no—
719C42—21no—
720C42—21no—
721C42—21no—
722C42—21no—
723C42—21no—
724C42—21no—
725C42—21no—
726C42—21no—
727C42—21no—
728C42—41no—
729C42—41no—
730C42—41no—
731C42—41no—
732C42—42no—
733C42—42no—
734C42—42no—
735C42—42no—
736C42—42no—
737C42—81no—
738C42—81no—
739C42—81no—
740C42—81no—
741C42—82no—
742C422−1+412yes—
743C422−1+412yes—
744C23—21no—
745C23—21no—
746C23—21no—
747C23—21no—
748C23—21no—
749C23—21no—
750C23—42no—
751C23—42no—
752C23—42no—
753C23—42no—
754C23—42no—
755C23—42no—
756C23—42no—
757C23#52512yes—
758C23C23×D411yescharacteristic
759Q8—84no—
760Q8—84no—
761Q8—84no—
762D4—42no—
763D4—42no—
764D4—42no—
765D4—42no—
766D4—84no—
767D4—84no—
768D4—164no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—22no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
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—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—44no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—42no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—42no—
839C2×C4—42no—
840C2×C4—41no—
841C2×C4—82no—
842C2×C4—84no—
843C2×C4—84no—
844C2×C4—164no—
845C2×C4#52512yes—
846C2×C4#53612yes—
847C2×C4#53612yes—
848C2×C4#57612yes—
849C2×C4#57812yes—
850C2×C4C22×#4111yescharacteristic
851C2×C4C22×#4111yescharacteristic
852C2×C4C2×2−1+411yescharacteristic
853C2×C4C2×2−1+411yescharacteristic
854C2×C4#58511yescharacteristic
855C2×C4#58511yescharacteristic
856C8—42no—
857C8—42no—
858C8—42no—
859C8—42no—
860C22—22no—
861C22—22no—
862C22—22no—
863C22—41no—
864C22—41no—
865C22—41no—
866C22—41no—
867C22—82no—
868C22—82no—
869C22—82no—
870C22—82no—
871C22—82no—
872C22—82no—
873C22—82no—
874C22C2×#52511yescharacteristic
875C22C2×#53611yescharacteristic
876C22#344911yescharacteristic
877C22C2×#57611yescharacteristic
878C22C2×#57811yescharacteristic
879C22#358511yescharacteristic
880C22#358511yescharacteristic
881C4—22no—
882C4—22no—
883C4—41no—
884C4—41no—
885C4—41no—
886C4—41no—
887C4—41no—
888C4—41no—
889C4—42no—
890C4—42no—
891C4—42no—
892C4—41no—
893C4—41no—
894C4—42no—
895C4—41no—
896C4—41no—
897C4—81no—
898C4—81no—
899C4—81no—
900C4—82no—
901C4—81no—
902C4—82no—
903C4—82no—
904C4#324314yes—
905C4#350711yescharacteristic
906C4#350711yescharacteristic
907C4#350711yescharacteristic
908C4#350711yescharacteristic
909C2—42no—
910C2—162no—
911C2#3511111yescharacteristic
912C2#6059011yescharacteristic
913C2#6060011yescharacteristic
914C2C2×#324311yescharacteristic
915C2#6086811yescharacteristic
916C2#6099011yescharacteristic
917C2#6099311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2856C22
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
2. C4×#544C2semidirect
3. #33153C2semidirect
4. #33149C2semidirect
7. #29917C2semidirect
8. #29646C2semidirect
9. #29530C2semidirect
10. #29527C2semidirect
11. #29404C2semidirect
12. #29401C2semidirect
13. #29354C2semidirect
14. #29348C2semidirect
15. #29321C2semidirect
16. #29312C2semidirect
17. #29277C2semidirect
18. #29275C2semidirect
19. #29256C2semidirect
20. #29254C2semidirect
21. #22093C2semidirect
22. #22088C2semidirect
23. #20786C2semidirect

Maximal subgroups

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

subgroupindex
#352882
C4×#5442
#331532
#331492
#331132
#331062
#299172
#296462
#295302
#295272
#294042
#294012
#293542
#293482
#293212
#293122
#292772
#292752
#292562
#292542
#220932
#220882
#207862