Finite Group Databasebeta

← #6468673

Subgroups — #6468673

Order 512.

1611 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35318C211yesmaximal, characteristic
2#34216C211yesmaximal, characteristic, complemented
3#29355C211yesmaximal, characteristic, complemented
4#29352C211yesmaximal, characteristic, complemented
5#29350C211yesmaximal, characteristic, complemented
6#29347C211yesmaximal, characteristic, complemented
7#29342C212yesmaximal
8#29341C212yesmaximal, complemented
9#29229C212yesmaximal, complemented
10#28758C212yesmaximal, complemented
11#27980C211yesmaximal, characteristic, complemented
12#27976C211yesmaximal, characteristic
13#25908C211yesmaximal, characteristic
14#25902C211yesmaximal, characteristic, complemented
15#23823C211yesmaximal, characteristic, complemented
16#23821C211yesmaximal, characteristic, complemented
17#23817C211yesmaximal, characteristic, complemented
18#23816C211yesmaximal, characteristic, complemented
19#21654C212yesmaximal, complemented
20#21645C212yesmaximal, complemented
21#21398C212yesmaximal, complemented
22#21397C212yesmaximal
23#20468C211yesmaximal, characteristic, complemented
24C2×#542C2211yescharacteristic
25C2×#541C2211yescharacteristic
26C22×C4⋊Q8C2211yescharacteristic
27C2×#489C2212yes—
28C2×#487C2212yes—
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#2369—21no—
47#2369—21no—
48#2365—21no—
49#2365—21no—
50#2345—21no—
51#2345—21no—
52Q8×C22⋊C4—21no—
53Q8×C22⋊C4—21no—
54#2331C2212yes—
55#2331C2212yes—
56#2327C2211yescharacteristic
57#2326C2211yescharacteristic
58#2316C2212yes—
59C4×C4⋊Q8C2211yescharacteristic
60C4×C4⋊Q8C2211yescharacteristic
61C4×C4⋊Q8C2211yescharacteristic
62C4×C4⋊Q8C2211yescharacteristic
63C4×C4⋊Q8C2211yescharacteristic
64C4×#124C2211yescharacteristic
65#2285C2211yescharacteristic
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#1993C2212yes—
93#1990C2212yes—
94#1989C2212yes—
95#1989C2212yes—
96#1988C2212yes—
97#1987C2212yes—
98#1983C2212yes—
99#1983C2212yes—
100#1981C2212yes—
101#1981C2212yes—
102#1960C2212yes—
103#1958C2212yes—
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#1835C2212yes—
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—
139C23×Q8—21no—
140#542—28no—
141#541—28no—
142C2×C4⋊Q8—28no—
143C2×C4⋊Q8—21no—
144C2×C4⋊Q8—21no—
145C2×C4⋊Q8C2311yescharacteristic
146C2×C4⋊Q8C2311yescharacteristic
147C2×C4⋊Q8C2311yescharacteristic
148C2×C4⋊Q8C2311yescharacteristic
149C2×C4⋊Q8C2311yescharacteristic
150C2×C4⋊Q8C2311yescharacteristic
151C2×C4⋊Q8C2312yes—
152C2×#126—21no—
153C2×#126—21no—
154C2×#126—21no—
155C2×#125—21no—
156C2×#125—21no—
157C2×#125C2311yescharacteristic
158C2×#124—21no—
159C2×#124C2311yescharacteristic
160C2×#124C2311yescharacteristic
161C2×#124C2311yescharacteristic
162C2×#123—21no—
163C2×C22⋊Q8—21no—
164C2×C22⋊Q8C2311yescharacteristic
165C2×C22⋊Q8C2311yescharacteristic
166C2×C22⋊Q8C2311yescharacteristic
167C2×#121C2311yescharacteristic
168C2×C4×Q8—21no—
169C2×C4×Q8—21no—
170C2×C4×Q8—21no—
171C2×C4×Q8—21no—
172C2×C4×Q8C2311yescharacteristic
173C2×C4×Q8C2311yescharacteristic
174C2×C4×Q8C2311yescharacteristic
175C2×C4×D4C2311yescharacteristic
176C2×#117C2312yes—
177C2×#117C2311yescharacteristic
178C2×#117C2311yescharacteristic
179C22×C4⋊C4—21no—
180C22×C4⋊C4C2312yes—
181C22×C42C2311yescharacteristic
182#489—28no—
183#487—28no—
184#433—28no—
185C2×C4⋊C8C2312yes—
186C2×C4⋊C8C2312yes—
187C2×#103C2312yes—
188C2×#103C2312yes—
189C2×#103C2312yes—
190C2×#103C2312yes—
191C2×#103C2312yes—
192C2×#103C2312yes—
193C2×#103C2312yes—
194C2×#103C2312yes—
195C2×#103C2312yes—
196C2×#103C2312yes—
197C2×#103C2312yes—
198C2×#103C2312yes—
199C2×#102C2312yes—
200C2×#102C2312yes—
201C2×#102C2312yes—
202C2×#102C2312yes—
203C2×C22⋊C8C2312yes—
204C2×C22⋊C8C2312yes—
205C2×#97C2312yes—
206C2×#97C2312yes—
207C2×#97C2312yes—
208C2×C4×C8C2312yes—
209C2×C4×C8C2312yes—
210C2×C4×C8C2312yes—
211#399—21no—
212#399—21no—
213#399—21no—
214#399—21no—
215#398—21no—
216#398—21no—
217#398—21no—
218#398—21no—
219#397—21no—
220#397—21no—
221#396—21no—
222#396—21no—
223#395—21no—
224#395—21no—
225#394—21no—
226#394—21no—
227#391—21no—
228#391—21no—
229#391—21no—
230#391—21no—
231#391—21no—
232#391—21no—
233#391—22no—
234#391—22no—
235#391—22no—
236#391—22no—
237#391C2311yescharacteristic
238#391C2311yescharacteristic
239#391C2311yescharacteristic
240#391C2311yescharacteristic
241#391C2311yescharacteristic
242#391C2311yescharacteristic
243#390C2311yescharacteristic
244#390C2311yescharacteristic
245#389—22no—
246#389—22no—
247#389—21no—
248#389—21no—
249#389—21no—
250#389—21no—
251#389—21no—
252#389—21no—
253#389—21no—
254#389—21no—
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—21no—
280#385—21no—
281#384C2311yescharacteristic
282#384C2311yescharacteristic
283#384C2311yescharacteristic
284#384C2311yescharacteristic
285#382—21no—
286#382—21no—
287#382C2311yescharacteristic
288#382C2312yes—
289#382C2311yescharacteristic
290#380—21no—
291#380—21no—
292#380—21no—
293#380—21no—
294#380—22no—
295#380—22no—
296C4×C4⋊C4—22no—
297C4×C4⋊C4—22no—
298C4×C4⋊C4—21no—
299C4×C4⋊C4—21no—
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—28no—
349C22×Q8—21no—
350C22×Q8—21no—
351C22×Q8—22no—
352C22×Q8—21no—
353C22×Q8—82no—
354C22×Q8—82no—
355C22×Q8C2411yescharacteristic
356C22×Q8C2411yescharacteristic
357C22×Q8C2411yescharacteristic
358C22×D4—21no—
359C22×D4C2411yescharacteristic
360C23×C4—22no—
361C23×C4—21no—
362C23×C4C2×D411yescharacteristic
363C23×C4C2×D411yescharacteristic
364C23×C4C2411yescharacteristic
365C22×C8C2412yes—
366C22×C8C2412yes—
367C22×C8C2412yes—
368C22×C8C2412yes—
369C4⋊Q8—28no—
370C4⋊Q8—28no—
371C4⋊Q8—24no—
372C4⋊Q8—24no—
373C4⋊Q8—24no—
374C4⋊Q8—24no—
375C4⋊Q8—24no—
376C4⋊Q8—24no—
377C4⋊Q8—41no—
378C4⋊Q8—41no—
379C4⋊Q8#4118yes—
380#126—44no—
381#126—44no—
382#126—44no—
383#125—24no—
384#125—44no—
385#125—44no—
386#124—24no—
387#124—24no—
388#124—41no—
389#124—41no—
390#124—44no—
391#123—44no—
392C22⋊Q8—24no—
393C22⋊Q8—24no—
394C22⋊Q8—24no—
395C22⋊Q8—44no—
396#121—24no—
397C4×Q8—24no—
398C4×Q8—24no—
399C4×Q8—24no—
400C4×Q8—82no—
401C4×Q8—82no—
402C4×Q8—82no—
403C4×Q8—82no—
404C4×D4—24no—
405#117—41no—
406#117—41no—
407#117—42no—
408#117—42no—
409#117#4118yes—
410C2×C4⋊C4—28no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—24no—
416C2×C4⋊C4—24no—
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—21no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—22no—
437C2×C4⋊C4—22no—
438C2×C4⋊C4—22no—
439C2×C4⋊C4—22no—
440C2×C4⋊C4—21no—
441C2×C4⋊C4—21no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4—21no—
444C2×C4⋊C4C2×D411yescharacteristic
445C2×C4⋊C4C2×D411yescharacteristic
446C2×C4⋊C4C2×D411yescharacteristic
447C2×C4⋊C4C2×D411yescharacteristic
448C2×C4⋊C4C2412yes—
449C2×C4⋊C4C2412yes—
450C2×C4⋊C4C2411yescharacteristic
451C2×C4⋊C4C2411yescharacteristic
452C2×C4⋊C4C2411yescharacteristic
453C2×C4⋊C4C2411yescharacteristic
454C2×C4⋊C4C2412yes—
455C2×C4⋊C4C2412yes—
456C2×C22⋊C4—22no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
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⋊C4C2×D411yescharacteristic
473C2×C22⋊C4C2×D411yescharacteristic
474C2×C22⋊C4C2×D411yescharacteristic
475C2×C22⋊C4C2×D411yescharacteristic
476C2×C42—24no—
477C2×C42—22no—
478C2×C42—21no—
479C2×C42—21no—
480C2×C42—21no—
481C2×C42—22no—
482C2×C42—22no—
483C2×C42—22no—
484C2×C42—22no—
485C2×C42C2×D411yescharacteristic
486C2×C42C2×D411yescharacteristic
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×C42C2411yescharacteristic
496C2×C42C2411yescharacteristic
497C2×C42C2411yescharacteristic
498C2×C42C2411yescharacteristic
499C2×C42C2411yescharacteristic
500C2×C42C2411yescharacteristic
501C4⋊C8—24no—
502C4⋊C8—24no—
503#103—24no—
504#103—24no—
505#103—24no—
506#103—24no—
507#103—24no—
508#103—24no—
509#103—42no—
510#103—42no—
511#103—42no—
512#103—42no—
513#103—42no—
514#103—42no—
515#102—24no—
516#102—24no—
517#102—42no—
518#102—42no—
519C22⋊C8—24no—
520C22⋊C8—24no—
521#97—24no—
522#97—24no—
523#97—42no—
524C4×C8—24no—
525C4×C8—24no—
526C4×C8—42no—
527#95—22no—
528#95—22no—
529#95—22no—
530#95—22no—
531#95—21no—
532#95—21no—
533#95—21no—
534#95—21no—
535#95—22no—
536#95—22no—
537#95—22no—
538#95—22no—
539#95—22no—
540#95—22no—
541#95—21no—
542#95—21no—
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—28no—
566C2×Q8—22no—
567C2×Q8—22no—
568C2×Q8—22no—
569C2×Q8—22no—
570C2×Q8—22no—
571C2×Q8—22no—
572C2×Q8—21no—
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—42no—
579C2×Q8—42no—
580C2×Q8—42no—
581C2×Q8—42no—
582C2×Q8—42no—
583C2×Q8—82no—
584C2×Q8—82no—
585C2×Q8—81no—
586C2×Q8—81no—
587C2×Q8—816no—
588C2×D4—22no—
589C2×D4—22no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—42no—
593C2×D4—81no—
594C2×D4—81no—
595C22×C4—22no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—28no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—41no—
615C22×C4—41no—
616C22×C4—42no—
617C22×C4—81no—
618C22×C4—81no—
619C22×C4—82no—
620C22×C4—82no—
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×C4C22×D411yescharacteristic
631C22×C4C22×D411yescharacteristic
632C22×C4C22×D411yescharacteristic
633C22×C4C22×D411yescharacteristic
634C22×C4C2×#4114yes—
635C22×C4C2511yescharacteristic
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—22no—
645C2×C8—22no—
646C2×C8—22no—
647C2×C8—22no—
648C4⋊C4—24no—
649C4⋊C4—24no—
650C4⋊C4—28no—
651C4⋊C4—28no—
652C4⋊C4—22no—
653C4⋊C4—22no—
654C4⋊C4—22no—
655C4⋊C4—22no—
656C4⋊C4—22no—
657C4⋊C4—22no—
658C4⋊C4—22no—
659C4⋊C4—22no—
660C4⋊C4—22no—
661C4⋊C4—22no—
662C4⋊C4—41no—
663C4⋊C4—41no—
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—42no—
681C4⋊C4—42no—
682C4⋊C4—42no—
683C4⋊C4—81no—
684C4⋊C4—81no—
685C4⋊C4—81no—
686C4⋊C4—81no—
687C4⋊C4—82no—
688C4⋊C4—82no—
689C4⋊C4—82no—
690C4⋊C4—82no—
691C4⋊C4#12414yes—
692C4⋊C4#12414yes—
693C4⋊C4C2×#4114yes—
694C4⋊C4C2×#4114yes—
695C22⋊C4—41no—
696C22⋊C4—41no—
697C22⋊C4—42no—
698C22⋊C4—42no—
699C22⋊C4—44no—
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—42no—
711C22⋊C4—81no—
712C22⋊C4—81no—
713C22⋊C4#12414yes—
714C22⋊C4#12414yes—
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—44no—
731C42—42no—
732C42—42no—
733C42—42no—
734C42—82no—
735C42—82no—
736C42—82no—
737C42—82no—
738C42C2×#4114yes—
739C42C2×#4114yes—
740C42C2×#4114yes—
741C23—21no—
742C23—21no—
743C23—21no—
744C23—21no—
745C23—21no—
746C23—21no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23C2×#12412yes—
755C23C23×D411yescharacteristic
756Q8—48no—
757Q8—48no—
758Q8—42no—
759Q8—42no—
760Q8—42no—
761Q8—42no—
762Q8—42no—
763Q8—42no—
764Q8—88no—
765Q8—162no—
766D4—42no—
767D4—42no—
768D4—162no—
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—21no—
786C2×C4—21no—
787C2×C4—24no—
788C2×C4—24no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—24no—
794C2×C4—24no—
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—44no—
804C2×C4—44no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—42no—
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—41no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—42no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—42no—
836C2×C4—88no—
837C2×C4—162no—
838C2×C4#52512yes—
839C2×C4#52512yes—
840C2×C4C2×#12412yes—
841C2×C4C2×#12412yes—
842C2×C4C2×#12412yes—
843C2×C4C2×#12412yes—
844C2×C4C2×#12412yes—
845C2×C4#57712yes—
846C2×C4#57812yes—
847C2×C4C22×#4112yes—
848C2×C4C22×#4112yes—
849C2×C4#58511yescharacteristic
850C2×C4#58511yescharacteristic
851C8—42no—
852C8—42no—
853C8—42no—
854C8—42no—
855C22—22no—
856C22—22no—
857C22—22no—
858C22—41no—
859C22—41no—
860C22—41no—
861C22—41no—
862C22—81no—
863C22—81no—
864C22—81no—
865C22—81no—
866C22—81no—
867C22—81no—
868C22—81no—
869C22C2×#52511yescharacteristic
870C22C22×#12411yescharacteristic
871C22#344911yescharacteristic
872C22C2×#57711yescharacteristic
873C22C2×#57811yescharacteristic
874C22#358511yescharacteristic
875C22#358611yescharacteristic
876C4—22no—
877C4—22no—
878C4—22no—
879C4—22no—
880C4—22no—
881C4—22no—
882C4—22no—
883C4—22no—
884C4—22no—
885C4—41no—
886C4—41no—
887C4—41no—
888C4—41no—
889C4—44no—
890C4—44no—
891C4—82no—
892C4—82no—
893C4—81no—
894C4—81no—
895C4—81no—
896C4—81no—
897C4—81no—
898C4—81no—
899C4—81no—
900C4#348012yes—
901C4#348012yes—
902C2—42no—
903C2—161no—
904C2#3495511yescharacteristic
905C2#6057911yescharacteristic
906C2#6058311yescharacteristic
907C2#6062311yescharacteristic
908C2#6062511yescharacteristic
909C2#6099211yescharacteristic
910C2#6099311yescharacteristic
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. #34216C2semidirect
3. #29355C2semidirect
4. #29352C2semidirect
5. #29350C2semidirect
6. #29347C2semidirect
8. #29341C2semidirect
9. #29229C2semidirect
10. #28758C2semidirect
11. #27980C2semidirect
14. #25902C2semidirect
15. #23823C2semidirect
16. #23821C2semidirect
17. #23817C2semidirect
18. #23816C2semidirect
19. #21654C2semidirect
20. #21645C2semidirect
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
#342162
#293552
#293522
#293502
#293472
#293422
#293412
#292292
#287582
#279802
#279762
#259082
#259022
#238232
#238212
#238172
#238162
#216542
#216452
#213982
#213972
#204682