Finite Group Databasebeta

← #6468677

Subgroups — #6468677

Order 512.

1583 conjugacy classes of subgroups.

The subgroup lattice has 910 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35318C211yesmaximal, characteristic
2#34214C211yesmaximal, characteristic, complemented
3#29355C211yesmaximal, characteristic, complemented
4#29352C211yesmaximal, characteristic, complemented
5#29350C211yesmaximal, characteristic, complemented
6#29347C211yesmaximal, characteristic, complemented
7#29345C212yesmaximal
8#29344C212yesmaximal, complemented
9#29228C212yesmaximal, complemented
10#28760C212yesmaximal, complemented
11#27978C211yesmaximal, characteristic
12#27972C211yesmaximal, characteristic, complemented
13#25910C211yesmaximal, characteristic, complemented
14#25906C211yesmaximal, characteristic
15#23823C211yesmaximal, characteristic, complemented
16#23821C211yesmaximal, characteristic, complemented
17#23817C211yesmaximal, characteristic, complemented
18#23816C211yesmaximal, characteristic, complemented
19#21653C212yesmaximal, complemented
20#21643C212yesmaximal, complemented
21#21398C212yesmaximal, complemented
22#21397C212yesmaximal
23#20468C211yesmaximal, characteristic, complemented
24C2×#542C2211yescharacteristic
25C2×#541C2211yescharacteristic
26C2×#533C2211yescharacteristic
27C2×#491C2212yes—
28C2×#488C2212yes—
29C2×#433C2212yes—
30#2862C2211yescharacteristic
31#2861C2211yescharacteristic
32#2857C2211yescharacteristic
33#2850C2211yescharacteristic
34#2660C2211yescharacteristic
35#2658C2211yescharacteristic
36#2621C2211yescharacteristic
37#2620C2211yescharacteristic
38#2556—21no—
39#2556—21no—
40#2553—21no—
41#2553—21no—
42#2521—21no—
43#2521—21no—
44#2519—21no—
45#2519—21no—
46#2360—21no—
47#2360—21no—
48#2360—21no—
49#2360—21no—
50#2355—21no—
51#2355—21no—
52Q8×C4⋊C4—21no—
53Q8×C4⋊C4—21no—
54#2330C2212yes—
55#2330C2212yes—
56#2327C2211yescharacteristic
57#2326C2211yescharacteristic
58#2317C2212yes—
59C4×C4⋊Q8C2211yescharacteristic
60C4×C4⋊Q8C2211yescharacteristic
61C4×C4⋊Q8C2211yescharacteristic
62C4×C4⋊Q8C2211yescharacteristic
63C4×C4⋊Q8C2211yescharacteristic
64C4×#124C2211yescharacteristic
65C2×#384C2211yescharacteristic
66#2274C2212yes—
67C4×#117C2211yescharacteristic
68#2101C2212yes—
69#2101C2212yes—
70#2100C2212yes—
71#2099C2212yes—
72#2072C2211yescharacteristic
73#2072C2211yescharacteristic
74#2072C2211yescharacteristic
75#2072C2211yescharacteristic
76#2072C2211yescharacteristic
77#2072C2211yescharacteristic
78#2071C2211yescharacteristic
79#2071C2211yescharacteristic
80#2043C2212yes—
81#2043C2212yes—
82#2042C2212yes—
83#2042C2212yes—
84#2024C2211yescharacteristic
85#2024C2211yescharacteristic
86#2024C2211yescharacteristic
87#2024C2211yescharacteristic
88#2024C2211yescharacteristic
89#2024C2211yescharacteristic
90#2023C2211yescharacteristic
91#2023C2211yescharacteristic
92#1992C2212yes—
93#1991C2212yes—
94#1989C2212yes—
95#1989C2212yes—
96#1988C2212yes—
97#1987C2212yes—
98#1983C2212yes—
99#1983C2212yes—
100#1981C2212yes—
101#1981C2212yes—
102#1959C2212yes—
103#1956C2212yes—
104#1936C2212yes—
105#1935C2212yes—
106#1935C2212yes—
107#1935C2212yes—
108#1934C2212yes—
109#1933C2212yes—
110#1933C2212yes—
111#1933C2212yes—
112#1875C2212yes—
113#1874C2212yes—
114#1873C2212yes—
115#1873C2212yes—
116#1873C2212yes—
117#1872C2212yes—
118#1872C2212yes—
119#1872C2212yes—
120#1836C2212yes—
121#1834C2212yes—
122#1768C2212yes—
123#1767C2211yescharacteristic
124C4×C4⋊C8C2211yescharacteristic
125#1763C2212yes—
126#1763C2212yes—
127#1763C2212yes—
128#1762C2212yes—
129C4×#103C2212yes—
130C4×#103C2212yes—
131C4×#103C2212yes—
132C4×#102C2212yes—
133#1750C2212yes—
134#1749C2211yescharacteristic
135C4×C22⋊C8C2211yescharacteristic
136#1745C2211yescharacteristic
137#1744C2211yescharacteristic
138#1726C2212yes—
139#542—28no—
140#541—28no—
141#533—28no—
142C2×C4⋊Q8C2311yescharacteristic
143C2×C4⋊Q8C2311yescharacteristic
144C2×C4⋊Q8C2311yescharacteristic
145C2×C4⋊Q8C2311yescharacteristic
146C2×C4⋊Q8C2311yescharacteristic
147C2×C4⋊Q8C2311yescharacteristic
148C2×#126—21no—
149C2×#126—21no—
150C2×#126—21no—
151C2×#125—21no—
152C2×#125—21no—
153C2×#125C2311yescharacteristic
154C2×#125C2312yes—
155C2×#124—21no—
156C2×#124C2311yescharacteristic
157C2×#124C2311yescharacteristic
158C2×#124C2311yescharacteristic
159C2×#123—21no—
160C2×C22⋊Q8—21no—
161C2×C22⋊Q8—21no—
162C2×C22⋊Q8—21no—
163C2×C22⋊Q8C2311yescharacteristic
164C2×C22⋊Q8C2311yescharacteristic
165C2×C22⋊Q8C2311yescharacteristic
166C2×#121C2311yescharacteristic
167C2×C4×Q8—21no—
168C2×C4×Q8—21no—
169C2×C4×Q8—21no—
170C2×C4×Q8—21no—
171C2×C4×Q8—21no—
172C2×C4×Q8—21no—
173C2×C4×Q8C2311yescharacteristic
174C2×C4×Q8C2311yescharacteristic
175C2×C4×Q8C2311yescharacteristic
176C2×C4×D4C2311yescharacteristic
177C2×#117C2312yes—
178C2×#117C2311yescharacteristic
179C2×#117C2311yescharacteristic
180C22×C4⋊C4—21no—
181C22×C4⋊C4—21no—
182C22×C4⋊C4C2312yes—
183C22×C42C2311yescharacteristic
184#491—28no—
185#488—28no—
186#433—28no—
187C2×C4⋊C8C2312yes—
188C2×C4⋊C8C2312yes—
189C2×#103C2312yes—
190C2×#103C2312yes—
191C2×#103C2312yes—
192C2×#103C2312yes—
193C2×#103C2312yes—
194C2×#103C2312yes—
195C2×#103C2312yes—
196C2×#103C2312yes—
197C2×#103C2312yes—
198C2×#103C2312yes—
199C2×#103C2312yes—
200C2×#103C2312yes—
201C2×#102C2312yes—
202C2×#102C2312yes—
203C2×#102C2312yes—
204C2×#102C2312yes—
205C2×C22⋊C8C2312yes—
206C2×C22⋊C8C2312yes—
207C2×#97C2312yes—
208C2×#97C2312yes—
209C2×#97C2312yes—
210C2×C4×C8C2312yes—
211C2×C4×C8C2312yes—
212C2×C4×C8C2312yes—
213#399—21no—
214#399—21no—
215#399—21no—
216#399—21no—
217#398—21no—
218#398—21no—
219#398—21no—
220#398—21no—
221#397—21no—
222#397—21no—
223#396—21no—
224#396—21no—
225#395—21no—
226#395—21no—
227#394—21no—
228#394—21no—
229#391—21no—
230#391—21no—
231#391—21no—
232#391—21no—
233#391—21no—
234#391—21no—
235#391C2311yescharacteristic
236#391C2311yescharacteristic
237#391C2311yescharacteristic
238#391C2311yescharacteristic
239#391C2311yescharacteristic
240#391C2311yescharacteristic
241#390C2311yescharacteristic
242#390C2311yescharacteristic
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—22no—
252#389—22no—
253#389—22no—
254#389—22no—
255#389C2312yes—
256#389C2312yes—
257#389C2312yes—
258#389C2312yes—
259#388—21no—
260#388—21no—
261#388—21no—
262#388—21no—
263#388—21no—
264#388—21no—
265#388—21no—
266#388—21no—
267#388—21no—
268#388—21no—
269#387—21no—
270#387—21no—
271#387—21no—
272#387—21no—
273#387—22no—
274#387—22no—
275#387—22no—
276#387—22no—
277#386—21no—
278#386—21no—
279#385—22no—
280#385—22no—
281#385—21no—
282#385—21no—
283#384—22no—
284#384—21no—
285#384—21no—
286#384C2311yescharacteristic
287#384C2311yescharacteristic
288#384C2311yescharacteristic
289#384C2311yescharacteristic
290#384C2312yes—
291#382—22no—
292#382—21no—
293#382—21no—
294#382C2311yescharacteristic
295#382C2311yescharacteristic
296#380—21no—
297#380—21no—
298C4×C4⋊C4—22no—
299C4×C4⋊C4—22no—
300C4×C4⋊C4—21no—
301C4×C4⋊C4—21no—
302C4×C4⋊C4—21no—
303C4×C4⋊C4—21no—
304C4×C4⋊C4—21no—
305C4×C4⋊C4—21no—
306C4×C4⋊C4D411yescharacteristic
307C4×C4⋊C4D411yescharacteristic
308C4×C4⋊C4D411yescharacteristic
309C4×C4⋊C4D411yescharacteristic
310C4×C4⋊C4C2312yes—
311C4×C4⋊C4C2312yes—
312C4×C4⋊C4C2312yes—
313C4×C4⋊C4C2312yes—
314C4×C22⋊C4—22no—
315C4×C22⋊C4—22no—
316C4×C22⋊C4—21no—
317C4×C22⋊C4—21no—
318C4×C22⋊C4D411yescharacteristic
319C4×C22⋊C4D411yescharacteristic
320C4×C22⋊C4D411yescharacteristic
321C4×C22⋊C4D411yescharacteristic
322#376C2311yescharacteristic
323#376C2311yescharacteristic
324C43C2311yescharacteristic
325C43C2311yescharacteristic
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#336C2311yescharacteristic
343#336C2311yescharacteristic
344#336C2311yescharacteristic
345#336C2311yescharacteristic
346#336C2312yes—
347#336C2312yes—
348C22×Q8—21no—
349C22×Q8—21no—
350C22×Q8—21no—
351C22×Q8C2411yescharacteristic
352C22×Q8C2411yescharacteristic
353C22×Q8C2411yescharacteristic
354C22×D4—21no—
355C22×D4C2411yescharacteristic
356C23×C4—22no—
357C23×C4—21no—
358C23×C4C2×D411yescharacteristic
359C23×C4C2×D411yescharacteristic
360C23×C4C2411yescharacteristic
361C22×C8C2412yes—
362C22×C8C2412yes—
363C22×C8C2412yes—
364C22×C8C2412yes—
365C4⋊Q8—24no—
366C4⋊Q8—24no—
367C4⋊Q8—24no—
368C4⋊Q8—24no—
369C4⋊Q8—24no—
370C4⋊Q8—41no—
371C4⋊Q8—41no—
372#126—44no—
373#126—44no—
374#126—44no—
375#125—24no—
376#125—24no—
377#125—44no—
378#125—44no—
379#125#4118yes—
380#124—24no—
381#124—24no—
382#124—41no—
383#124—41no—
384#124—44no—
385#123—44no—
386C22⋊Q8—28no—
387C22⋊Q8—28no—
388C22⋊Q8—24no—
389C22⋊Q8—24no—
390C22⋊Q8—24no—
391C22⋊Q8—44no—
392#121—24no—
393C4×Q8—28no—
394C4×Q8—28no—
395C4×Q8—24no—
396C4×Q8—24no—
397C4×Q8—24no—
398C4×Q8—82no—
399C4×Q8—82no—
400C4×Q8—82no—
401C4×Q8—82no—
402C4×D4—24no—
403#117—24no—
404#117—24no—
405#117—41no—
406#117—41no—
407#117#4118yes—
408C2×C4⋊C4—22no—
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—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—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—22no—
433C2×C4⋊C4—22no—
434C2×C4⋊C4—22no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—22no—
437C2×C4⋊C4—22no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4—21no—
441C2×C4⋊C4—21no—
442C2×C4⋊C4—42no—
443C2×C4⋊C4—42no—
444C2×C4⋊C4—82no—
445C2×C4⋊C4—82no—
446C2×C4⋊C4C2×D411yescharacteristic
447C2×C4⋊C4C2×D411yescharacteristic
448C2×C4⋊C4C2×D411yescharacteristic
449C2×C4⋊C4C2×D411yescharacteristic
450C2×C4⋊C4C2412yes—
451C2×C4⋊C4C2412yes—
452C2×C4⋊C4C2411yescharacteristic
453C2×C4⋊C4C2411yescharacteristic
454C2×C4⋊C4C2411yescharacteristic
455C2×C4⋊C4C2411yescharacteristic
456C2×C4⋊C4C2412yes—
457C2×C4⋊C4C2412yes—
458C2×C22⋊C4—22no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—21no—
461C2×C22⋊C4—21no—
462C2×C22⋊C4—21no—
463C2×C22⋊C4—21no—
464C2×C22⋊C4—21no—
465C2×C22⋊C4—21no—
466C2×C22⋊C4—21no—
467C2×C22⋊C4—21no—
468C2×C22⋊C4—21no—
469C2×C22⋊C4—21no—
470C2×C22⋊C4—21no—
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4C2×D411yescharacteristic
475C2×C22⋊C4C2×D411yescharacteristic
476C2×C22⋊C4C2×D411yescharacteristic
477C2×C22⋊C4C2×D411yescharacteristic
478C2×C42—22no—
479C2×C42—24no—
480C2×C42—21no—
481C2×C42—21no—
482C2×C42—21no—
483C2×C42—22no—
484C2×C42—22no—
485C2×C42—22no—
486C2×C42—22no—
487C2×C42C2×D411yescharacteristic
488C2×C42C2×D411yescharacteristic
489C2×C42C2×D411yescharacteristic
490C2×C42C2×D411yescharacteristic
491C2×C42C2×D411yescharacteristic
492C2×C42C2×D411yescharacteristic
493C2×C42C2×D411yescharacteristic
494C2×C42C2×D411yescharacteristic
495C2×C42C2×D411yescharacteristic
496C2×C42C2×D411yescharacteristic
497C2×C42C2411yescharacteristic
498C2×C42C2411yescharacteristic
499C2×C42C2411yescharacteristic
500C2×C42C2411yescharacteristic
501C2×C42C2411yescharacteristic
502C2×C42C2411yescharacteristic
503C4⋊C8—24no—
504C4⋊C8—24no—
505#103—24no—
506#103—24no—
507#103—24no—
508#103—24no—
509#103—24no—
510#103—24no—
511#103—42no—
512#103—42no—
513#103—42no—
514#103—42no—
515#103—42no—
516#103—42no—
517#102—24no—
518#102—24no—
519#102—42no—
520#102—42no—
521C22⋊C8—24no—
522C22⋊C8—24no—
523#97—24no—
524#97—24no—
525#97—42no—
526C4×C8—24no—
527C4×C8—24no—
528C4×C8—42no—
529#95—22no—
530#95—22no—
531#95—22no—
532#95—22no—
533#95—21no—
534#95—21no—
535#95—21no—
536#95—21no—
537#95—21no—
538#95—21no—
539#95—22no—
540#95—22no—
541#95—22no—
542#95—22no—
543#95—21no—
544#95—21no—
545#95—21no—
546#95—21no—
547#95—21no—
548#95—21no—
549#95—21no—
550#95—21no—
551#95—21no—
552#95—21no—
553#95C2×D411yescharacteristic
554#95C2×D411yescharacteristic
555#95C2×D411yescharacteristic
556#95C2×D411yescharacteristic
557#95C2×D411yescharacteristic
558#95C2×D411yescharacteristic
559#95C2×D411yescharacteristic
560#95C2×D411yescharacteristic
561C24—21no—
562C24C22×D411yescharacteristic
563C2×Q8—24no—
564C2×Q8—24no—
565C2×Q8—22no—
566C2×Q8—22no—
567C2×Q8—22no—
568C2×Q8—22no—
569C2×Q8—22no—
570C2×Q8—22no—
571C2×Q8—21no—
572C2×Q8—21no—
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—42no—
578C2×Q8—42no—
579C2×Q8—42no—
580C2×Q8—42no—
581C2×Q8—42no—
582C2×Q8—81no—
583C2×Q8—81no—
584C2×D4—22no—
585C2×D4—22no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—42no—
589C2×D4—81no—
590C2×D4—81no—
591C22×C4—22no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—41no—
610C22×C4—41no—
611C22×C4—44no—
612C22×C4—42no—
613C22×C4—81no—
614C22×C4—81no—
615C22×C4—82no—
616C22×C4—82no—
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×#4114yes—
631C22×C4C2511yescharacteristic
632C2×C8—22no—
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—
644C4⋊C4—24no—
645C4⋊C4—24no—
646C4⋊C4—28no—
647C4⋊C4—28no—
648C4⋊C4—22no—
649C4⋊C4—22no—
650C4⋊C4—22no—
651C4⋊C4—22no—
652C4⋊C4—22no—
653C4⋊C4—22no—
654C4⋊C4—22no—
655C4⋊C4—22no—
656C4⋊C4—22no—
657C4⋊C4—22no—
658C4⋊C4—41no—
659C4⋊C4—41no—
660C4⋊C4—44no—
661C4⋊C4—42no—
662C4⋊C4—42no—
663C4⋊C4—42no—
664C4⋊C4—42no—
665C4⋊C4—42no—
666C4⋊C4—42no—
667C4⋊C4—42no—
668C4⋊C4—42no—
669C4⋊C4—42no—
670C4⋊C4—42no—
671C4⋊C4—42no—
672C4⋊C4—42no—
673C4⋊C4—42no—
674C4⋊C4—42no—
675C4⋊C4—42no—
676C4⋊C4—42no—
677C4⋊C4—42no—
678C4⋊C4—42no—
679C4⋊C4—42no—
680C4⋊C4—81no—
681C4⋊C4—81no—
682C4⋊C4—81no—
683C4⋊C4—81no—
684C4⋊C4—82no—
685C4⋊C4—82no—
686C4⋊C4—82no—
687C4⋊C4—82no—
688C4⋊C4—82no—
689C4⋊C4—82no—
690C4⋊C4#12414yes—
691C4⋊C4#12414yes—
692C4⋊C4C2×#4114yes—
693C4⋊C4C2×#4114yes—
694C22⋊C4—28no—
695C22⋊C4—41no—
696C22⋊C4—41no—
697C22⋊C4—42no—
698C22⋊C4—42no—
699C22⋊C4—42no—
700C22⋊C4—42no—
701C22⋊C4—42no—
702C22⋊C4—42no—
703C22⋊C4—42no—
704C22⋊C4—42no—
705C22⋊C4—42no—
706C22⋊C4—42no—
707C22⋊C4—42no—
708C22⋊C4—42no—
709C22⋊C4—42no—
710C22⋊C4—81no—
711C22⋊C4—81no—
712C22⋊C4#12414yes—
713C22⋊C4#12414yes—
714C42—28no—
715C42—22no—
716C42—22no—
717C42—22no—
718C42—22no—
719C42—22no—
720C42—22no—
721C42—22no—
722C42—21no—
723C42—21no—
724C42—21no—
725C42—21no—
726C42—41no—
727C42—41no—
728C42—41no—
729C42—41no—
730C42—42no—
731C42—42no—
732C42—42no—
733C42—82no—
734C42—82no—
735C42—82no—
736C42—82no—
737C42C2×#4114yes—
738C42C2×#4114yes—
739C42C2×#4114yes—
740C23—21no—
741C23—21no—
742C23—21no—
743C23—21no—
744C23—21no—
745C23—21no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23C2×#12412yes—
754C23C23×D411yescharacteristic
755Q8—48no—
756Q8—48no—
757Q8—42no—
758Q8—42no—
759Q8—42no—
760Q8—42no—
761Q8—42no—
762Q8—42no—
763Q8—162no—
764D4—42no—
765D4—42no—
766D4—162no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
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—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—24no—
786C2×C4—24no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—24no—
792C2×C4—24no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—44no—
802C2×C4—44no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—41no—
810C2×C4—41no—
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—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—162no—
835C2×C4—164no—
836C2×C4#52512yes—
837C2×C4#52512yes—
838C2×C4C2×#12412yes—
839C2×C4C2×#12412yes—
840C2×C4C2×#12412yes—
841C2×C4C2×#12412yes—
842C2×C4C2×#12412yes—
843C2×C4#57712yes—
844C2×C4#57812yes—
845C2×C4C22×#4112yes—
846C2×C4C22×#4112yes—
847C2×C4#58511yescharacteristic
848C2×C4#58511yescharacteristic
849C8—42no—
850C8—42no—
851C8—42no—
852C8—42no—
853C22—22no—
854C22—22no—
855C22—22no—
856C22—41no—
857C22—41no—
858C22—41no—
859C22—41no—
860C22—81no—
861C22—81no—
862C22—81no—
863C22—81no—
864C22—81no—
865C22—81no—
866C22—81no—
867C22C2×#52511yescharacteristic
868C22C22×#12411yescharacteristic
869C22#344911yescharacteristic
870C22C2×#57711yescharacteristic
871C22C2×#57811yescharacteristic
872C22#358511yescharacteristic
873C22#358611yescharacteristic
874C4—22no—
875C4—22no—
876C4—22no—
877C4—22no—
878C4—22no—
879C4—22no—
880C4—22no—
881C4—22no—
882C4—22no—
883C4—41no—
884C4—41no—
885C4—41no—
886C4—41no—
887C4—44no—
888C4—44no—
889C4—82no—
890C4—82no—
891C4—81no—
892C4—81no—
893C4—81no—
894C4—81no—
895C4—81no—
896C4—81no—
897C4—81no—
898C4#348012yes—
899C4#348012yes—
900C2—42no—
901C2—161no—
902C2#3495511yescharacteristic
903C2#6058511yescharacteristic
904C2#6058911yescharacteristic
905C2#6062311yescharacteristic
906C2#6062511yescharacteristic
907C2#6099411yescharacteristic
908C2#6099511yescharacteristic
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
2. #34214C2semidirect
3. #29355C2semidirect
4. #29352C2semidirect
5. #29350C2semidirect
6. #29347C2semidirect
8. #29344C2semidirect
9. #29228C2semidirect
10. #28760C2semidirect
12. #27972C2semidirect
13. #25910C2semidirect
15. #23823C2semidirect
16. #23821C2semidirect
17. #23817C2semidirect
18. #23816C2semidirect
19. #21653C2semidirect
20. #21643C2semidirect
21. #21398C2semidirect
23. #20468C2semidirect

Maximal subgroups

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

subgroupindex
#353182
#342142
#293552
#293522
#293502
#293472
#293452
#293442
#292282
#287602
#279782
#279722
#259102
#259062
#238232
#238212
#238172
#238162
#216532
#216432
#213982
#213972
#204682