Finite Group Databasebeta

← #6494886

Subgroups — #6494886

Order 512.

1550 conjugacy classes of subgroups.

The subgroup lattice has 907 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35275C211yesmaximal, characteristic, complemented
2#34227C211yesmaximal, characteristic
3#33206C212yesmaximal, complemented
4#33205C212yesmaximal, complemented
5#29993C212yesmaximal, complemented
6#29991C212yesmaximal, complemented
7#29227C211yesmaximal, characteristic, complemented
8#29225C211yesmaximal, characteristic, complemented
9#29214C211yesmaximal, characteristic, complemented
10#29213C211yesmaximal, characteristic, complemented
11#29148C211yesmaximal, characteristic, complemented
12#29146C211yesmaximal, characteristic, complemented
13#28519C211yesmaximal, characteristic, complemented
14#28517C211yesmaximal, characteristic, complemented
15#27689C212yesmaximal, complemented
16#27687C212yesmaximal
17#24311C212yesmaximal, complemented
18#24309C212yesmaximal
19#21989C211yesmaximal, characteristic, complemented
20#21987C211yesmaximal, characteristic, complemented
21#21868C211yesmaximal, characteristic
22#21867C211yesmaximal, characteristic
23#20811C211yesmaximal, characteristic, complemented
24C2×#544C2212yes—
25C2×#529C2211yescharacteristic
26C2×#479C2212yes—
27C2×#477C2212yes—
28C2×#478C2212yes—
29C2×#476C2212yes—
30C2×#432C2211yescharacteristic
31C2×#432C2211yescharacteristic
32#2868C2211yescharacteristic
33#2868C2211yescharacteristic
34#2859C2211yescharacteristic
35#2859C2211yescharacteristic
36#2660C2212yes—
37#2660C2212yes—
38#2552—21no—
39#2552—21no—
40#2551—21no—
41#2551—21no—
42#2440—21no—
43#2440—21no—
44#2440—21no—
45#2440—21no—
46#2374—21no—
47#2374—21no—
48#2373—21no—
49#2373—21no—
50#2357—21no—
51#2353—21no—
52#2347—21no—
53#2343—21no—
54#2324C2211yescharacteristic
55#2324C2211yescharacteristic
56#2323C2211yescharacteristic
57#2323C2211yescharacteristic
58#2320C2211yescharacteristic
59#2319C2211yescharacteristic
60#2317C2212yes—
61C4×#125C2211yescharacteristic
62C4×#125C2211yescharacteristic
63C4×#124C2211yescharacteristic
64C4×#124C2211yescharacteristic
65#2285C2211yescharacteristic
66C2×#384C2211yescharacteristic
67#2283C2211yescharacteristic
68#2276C2211yescharacteristic
69#2275C2211yescharacteristic
70C4×#117C2211yescharacteristic
71#2101C2212yes—
72#2101C2212yes—
73#2100C2212yes—
74#2100C2212yes—
75#2097C2212yes—
76#2096C2212yes—
77#2093C2212yes—
78#2092C2212yes—
79#2059C2212yes—
80#2059C2212yes—
81#2058C2212yes—
82#2057C2212yes—
83#2026C2212yes—
84#2025C2212yes—
85#2024C2212yes—
86#2023C2212yes—
87#1992C2211yescharacteristic
88#1992C2211yescharacteristic
89#1992C2211yescharacteristic
90#1992C2211yescharacteristic
91#1989C2212yes—
92#1989C2212yes—
93#1988C2212yes—
94#1988C2212yes—
95#1959C2211yescharacteristic
96#1959C2211yescharacteristic
97#1959C2211yescharacteristic
98#1959C2211yescharacteristic
99#1949C2212yes—
100#1949C2212yes—
101#1949C2212yes—
102#1949C2212yes—
103#1948C2212yes—
104#1948C2212yes—
105#1947C2212yes—
106#1947C2212yes—
107#1875C2212yes—
108#1874C2212yes—
109#1873C2212yes—
110#1872C2212yes—
111#1854C2212yes—
112#1854C2212yes—
113#1853C2212yes—
114#1852C2212yes—
115#1847C2211yescharacteristic
116#1847C2211yescharacteristic
117#1847C2211yescharacteristic
118#1847C2211yescharacteristic
119#1843C2212yes—
120#1836C2211yescharacteristic
121#1836C2211yescharacteristic
122#1836C2211yescharacteristic
123#1836C2211yescharacteristic
124#1832C2212yes—
125#1805C2212yes—
126#1805C2212yes—
127#1804C2212yes—
128#1804C2212yes—
129#1803C2212yes—
130#1803C2212yes—
131#1802C2212yes—
132#1802C2212yes—
133#1798C2212yes—
134#1798C2212yes—
135#1767C2211yescharacteristic
136#1767C2211yescharacteristic
137#1767C2211yescharacteristic
138#1767C2211yescharacteristic
139#544—44no—
140#544—44no—
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#529Q818yescomplemented
150C2×#126—21no—
151C2×#125—22no—
152C2×#125C2312yes—
153C2×#125C2311yescharacteristic
154C2×#125C2312yes—
155C2×#124C2311yescharacteristic
156C2×#123—21no—
157C2×C22⋊Q8—22no—
158C2×C22⋊Q8—22no—
159C2×C22⋊Q8C2311yescharacteristic
160C2×#121C2311yescharacteristic
161C2×C4×Q8C2311yescharacteristic
162C2×C4×Q8C2311yescharacteristic
163C2×C4×Q8C2311yescharacteristic
164C2×C4×D4—21no—
165C2×C4×D4C2311yescharacteristic
166C2×C4×D4C2311yescharacteristic
167C2×C4×D4C2311yescharacteristic
168C2×#117—21no—
169C2×#117C2312yes—
170C2×#117C2311yescharacteristic
171C2×#117C2311yescharacteristic
172C22×C4⋊C4—21no—
173C22×C4⋊C4—21no—
174C22×C4⋊C4C2312yes—
175C22×C42C2311yescharacteristic
176#479—44no—
177#478—44no—
178#477—44no—
179#476—44no—
180#432—24no—
181#432—24no—
182C2×#107C2312yes—
183C2×#107C2312yes—
184C2×#107C2312yes—
185C2×#107C2312yes—
186C2×#106C2312yes—
187C2×#106C2312yes—
188C2×#106C2312yes—
189C2×#106C2312yes—
190C2×C4⋊C8C2312yes—
191C2×C4⋊C8C2312yes—
192C2×C4⋊C8C2312yes—
193C2×C4⋊C8C2312yes—
194C2×C4⋊C8C2312yes—
195C2×C4⋊C8C2312yes—
196C2×#103C2312yes—
197C2×#103C2312yes—
198C2×#103C2312yes—
199C2×#103C2312yes—
200C2×#102C2312yes—
201C2×#102C2312yes—
202C2×#102C2312yes—
203C2×#102C2312yes—
204C2×C22⋊C8C2312yes—
205C2×C22⋊C8C2312yes—
206C2×#97C2311yescharacteristic
207C2×#97C2311yescharacteristic
208C2×#97C2311yescharacteristic
209C2×#97C2311yescharacteristic
210#398—22no—
211#398—22no—
212#398—22no—
213#398—22no—
214#395—22no—
215#395—22no—
216#395—22no—
217#395—22no—
218#391C2311yescharacteristic
219#391C2311yescharacteristic
220#390—21no—
221#390—21no—
222#390C2311yescharacteristic
223#390C2311yescharacteristic
224#389—22no—
225#389—22no—
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#389C2311yescharacteristic
237#389C2311yescharacteristic
238#389C2311yescharacteristic
239#389C2311yescharacteristic
240#388—21no—
241#388—21no—
242#388—21no—
243#388—21no—
244#388—21no—
245#388—21no—
246#388—21no—
247#388—21no—
248#388—21no—
249#388—21no—
250#388—21no—
251#388—21no—
252#387—21no—
253#387—21no—
254#387—21no—
255#387—21no—
256#387—21no—
257#387—21no—
258#387—21no—
259#387—21no—
260#386—21no—
261#386—21no—
262#385—21no—
263#385—21no—
264#385—22no—
265#385—22no—
266#384—21no—
267#384—21no—
268#384—21no—
269#384—21no—
270#384—21no—
271#384—21no—
272#384C2312yes—
273#384C2312yes—
274#384C2312yes—
275#384C2311yescharacteristic
276#384C2311yescharacteristic
277#384C2311yescharacteristic
278#384C2311yescharacteristic
279#383—21no—
280#383—21no—
281#382—21no—
282#382C2311yescharacteristic
283#382C2311yescharacteristic
284#382C2312yes—
285#382C2312yes—
286#382C2312yes—
287#381—21no—
288#381—21no—
289#380—21no—
290#380—21no—
291#380—21no—
292#380C2311yescharacteristic
293#380C2311yescharacteristic
294C4×C4⋊C4—21no—
295C4×C4⋊C4—21no—
296C4×C4⋊C4—21no—
297C4×C4⋊C4—21no—
298C4×C4⋊C4—21no—
299C4×C4⋊C4—21no—
300C4×C4⋊C4—21no—
301C4×C4⋊C4—21no—
302C4×C4⋊C4—21no—
303C4×C4⋊C4D411yescharacteristic
304C4×C4⋊C4D411yescharacteristic
305C4×C4⋊C4D411yescharacteristic
306C4×C4⋊C4D411yescharacteristic
307C4×C4⋊C4C2311yescharacteristic
308C4×C4⋊C4C2311yescharacteristic
309C4×C4⋊C4C2311yescharacteristic
310C4×C4⋊C4C2311yescharacteristic
311C4×C4⋊C4C2311yescharacteristic
312C4×C4⋊C4C2311yescharacteristic
313C4×C22⋊C4—21no—
314C4×C22⋊C4—21no—
315C4×C22⋊C4—21no—
316C4×C22⋊C4—21no—
317C4×C22⋊C4—21no—
318C4×C22⋊C4—21no—
319C4×C22⋊C4—21no—
320C4×C22⋊C4—21no—
321C4×C22⋊C4D411yescharacteristic
322C4×C22⋊C4D411yescharacteristic
323C4×C22⋊C4D411yescharacteristic
324C4×C22⋊C4D411yescharacteristic
325#376—21no—
326#376—21no—
327#376C2311yescharacteristic
328#376C2311yescharacteristic
329C2×#95—21no—
330C43C2311yescharacteristic
331C43C2311yescharacteristic
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#340C2312yes—
346#340C2312yes—
347#340C2312yes—
348#336C2312yes—
349#336C2312yes—
350#336C2312yes—
351#336C2312yes—
352C22×Q8—22no—
353C22×Q8—22no—
354C22×Q8C2411yescharacteristic
355C22×D4—21no—
356C22×D4C2411yescharacteristic
357C23×C4—21no—
358C23×C4—22no—
359C23×C4—21no—
360C23×C4—21no—
361C23×C4C2×D411yescharacteristic
362C23×C4C2×D411yescharacteristic
363C23×C4C2411yescharacteristic
364C22×C8C2412yes—
365C22×C8C2412yes—
366C22×C8C2412yes—
367C22×C8C2412yes—
368C4⋊Q8—24no—
369C4⋊Q8—24no—
370C4⋊Q8—42no—
371C4⋊Q8—42no—
372C4⋊Q8—48no—
373C4⋊Q8—82no—
374C4⋊Q8—82no—
375C4⋊Q8—82no—
376C4⋊Q8—82no—
377#126—28no—
378#125—22no—
379#125—24no—
380#125—24no—
381#125—42no—
382#125—42no—
383#125—48no—
384#125C2×Q814yes—
385#124—22no—
386#124C2×Q814yes—
387#123—28no—
388C22⋊Q8—22no—
389C22⋊Q8—48no—
390C22⋊Q8—48no—
391C22⋊Q8C2×Q814yes—
392#121—22no—
393#121C2×Q814yes—
394C4×Q8—22no—
395C4×Q8—24no—
396C4×Q8—24no—
397C4×Q8C2×Q814yes—
398C4×D4—28no—
399C4×D4—22no—
400C4×D4—24no—
401C4×D4—24no—
402C4×D4C2×Q814yes—
403#117—28no—
404#117—24no—
405#117—24no—
406#117—42no—
407#117—42no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
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—22no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—22no—
430C2×C4⋊C4—22no—
431C2×C4⋊C4—22no—
432C2×C4⋊C4—22no—
433C2×C4⋊C4—22no—
434C2×C4⋊C4—22no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4—42no—
440C2×C4⋊C4—42no—
441C2×C4⋊C4—82no—
442C2×C4⋊C4—82no—
443C2×C4⋊C4C2×D411yescharacteristic
444C2×C4⋊C4C2×D411yescharacteristic
445C2×C4⋊C4C2×D411yescharacteristic
446C2×C4⋊C4C2×D411yescharacteristic
447C2×C4⋊C4C2412yes—
448C2×C4⋊C4C2412yes—
449C2×C4⋊C4C2412yes—
450C2×C4⋊C4C2412yes—
451C2×C4⋊C4C2411yescharacteristic
452C2×C4⋊C4C2411yescharacteristic
453C2×C4⋊C4C2411yescharacteristic
454C2×C4⋊C4C2411yescharacteristic
455C2×C4⋊C4C2411yescharacteristic
456C2×C4⋊C4C2411yescharacteristic
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—21no—
461C2×C22⋊C4—21no—
462C2×C22⋊C4—22no—
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⋊C4C2×D411yescharacteristic
472C2×C22⋊C4C2×D411yescharacteristic
473C2×C22⋊C4C2×D411yescharacteristic
474C2×C22⋊C4C2×D411yescharacteristic
475C2×C42—21no—
476C2×C42—22no—
477C2×C42—21no—
478C2×C42—21no—
479C2×C42—21no—
480C2×C42—21no—
481C2×C42—21no—
482C2×C42—21no—
483C2×C42—21no—
484C2×C42—21no—
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×C42C2×Q814yes—
496C2×C42#4114yes—
497C2×C42C2411yescharacteristic
498C2×C42C2411yescharacteristic
499C2×C42C2411yescharacteristic
500C2×C42C2411yescharacteristic
501C2×C42C2411yescharacteristic
502C2×C42C2411yescharacteristic
503#107—42no—
504#107—42no—
505#107—42no—
506#107—42no—
507#106—42no—
508#106—42no—
509#106—42no—
510#106—42no—
511C4⋊C8—24no—
512C4⋊C8—24no—
513C4⋊C8—24no—
514C4⋊C8—24no—
515C4⋊C8—24no—
516C4⋊C8—24no—
517#103—42no—
518#103—42no—
519#103—42no—
520#103—42no—
521#102—42no—
522#102—42no—
523#102—42no—
524#102—42no—
525C22⋊C8—24no—
526C22⋊C8—24no—
527#97—22no—
528#97—22no—
529#97—22no—
530#97—22no—
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—21no—
542#95—21no—
543#95—21no—
544#95—21no—
545#95—21no—
546#95—21no—
547#95—22no—
548#95—22no—
549#95—21no—
550#95—21no—
551#95—21no—
552#95—21no—
553#95—22no—
554#95—22no—
555#95—22no—
556#95—22no—
557#95C2×D411yescharacteristic
558#95C2×D411yescharacteristic
559#95C2×D411yescharacteristic
560#95C2×D411yescharacteristic
561#95C2×D411yescharacteristic
562#95C2×D411yescharacteristic
563#95C2×D411yescharacteristic
564#95C2×D411yescharacteristic
565C24—21no—
566C24C22×D411yescharacteristic
567C2×Q8—21no—
568C2×Q8—22no—
569C2×Q8—22no—
570C2×Q8—44no—
571C2×Q8—44no—
572C2×Q8—82no—
573C2×Q8—82no—
574C2×Q8—82no—
575C2×Q8—82no—
576C2×Q8C22×Q812yes—
577C2×D4—24no—
578C2×D4—21no—
579C2×D4—22no—
580C2×D4—22no—
581C2×D4—81no—
582C2×D4—81no—
583C2×D4C22×Q812yes—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—24no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—41no—
599C22×C4—41no—
600C22×C4—41no—
601C22×C4—41no—
602C22×C4—44no—
603C22×C4—42no—
604C22×C4—42no—
605C22×C4—81no—
606C22×C4—81no—
607C22×C4—81no—
608C22×C4—81no—
609C22×C4—81no—
610C22×C4—81no—
611C22×C4—82no—
612C22×C4—82no—
613C22×C4C22⋊Q814yes—
614C22×C4C22⋊Q814yes—
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×C4C22×D411yescharacteristic
625C22×C4C22×D411yescharacteristic
626C22×C4C22×D411yescharacteristic
627C22×C4C22×D411yescharacteristic
628C22×C4C22×Q812yes—
629C22×C4C2×#4112yes—
630C22×C4C2511yescharacteristic
631C2×C8—22no—
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—
643C4⋊C4—24no—
644C4⋊C4—24no—
645C4⋊C4—24no—
646C4⋊C4—24no—
647C4⋊C4—22no—
648C4⋊C4—22no—
649C4⋊C4—22no—
650C4⋊C4—22no—
651C4⋊C4—21no—
652C4⋊C4—21no—
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—22no—
663C4⋊C4—22no—
664C4⋊C4—22no—
665C4⋊C4—42no—
666C4⋊C4—42no—
667C4⋊C4—44no—
668C4⋊C4—42no—
669C4⋊C4—42no—
670C4⋊C4—42no—
671C4⋊C4—42no—
672C4⋊C4—44no—
673C4⋊C4—44no—
674C4⋊C4—44no—
675C4⋊C4—42no—
676C4⋊C4—42no—
677C4⋊C4—42no—
678C4⋊C4—44no—
679C4⋊C4—44no—
680C4⋊C4—44no—
681C4⋊C4—42no—
682C4⋊C4—81no—
683C4⋊C4—81no—
684C4⋊C4—81no—
685C4⋊C4—81no—
686C4⋊C4—82no—
687C4⋊C4—82no—
688C4⋊C4—82no—
689C4⋊C4—82no—
690C4⋊C4—82no—
691C4⋊C4—82no—
692C4⋊C4C22×Q812yes—
693C4⋊C4C22×Q812yes—
694C22⋊C4—24no—
695C22⋊C4—24no—
696C22⋊C4—24no—
697C22⋊C4—24no—
698C22⋊C4—24no—
699C22⋊C4—22no—
700C22⋊C4—22no—
701C22⋊C4—22no—
702C22⋊C4—22no—
703C22⋊C4—44no—
704C22⋊C4—42no—
705C22⋊C4—42no—
706C22⋊C4—81no—
707C22⋊C4—81no—
708C22⋊C4—81no—
709C22⋊C4—81no—
710C22⋊C4—81no—
711C22⋊C4—81no—
712C42—24no—
713C42—22no—
714C42—22no—
715C42—41no—
716C42—41no—
717C42—41no—
718C42—41no—
719C42—41no—
720C42—41no—
721C42—41no—
722C42—41no—
723C42—44no—
724C42—42no—
725C42—42no—
726C42—81no—
727C42—81no—
728C42—81no—
729C42—81no—
730C42—81no—
731C42—81no—
732C42C22⋊Q814yes—
733C42C22⋊Q814yes—
734C42C22×Q812yes—
735C42C22×Q812yes—
736C42C2×#4112yes—
737C42C2×#4112yes—
738C42H(5,𝔽2)14yes—
739C422−1+414yes—
740C23—21no—
741C23—21no—
742C23—21no—
743C23—21no—
744C23—21no—
745C23—21no—
746C23—22no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23C2×C22⋊Q812yes—
754C23C23×D411yescharacteristic
755Q8—24no—
756Q8—42no—
757Q8—164no—
758Q8—164no—
759D4—24no—
760D4—42no—
761D4—84no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
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—24no—
781C2×C4—24no—
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—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—44no—
798C2×C4—44no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—84no—
830C2×C4—162no—
831C2×C4—162no—
832C2×C4—164no—
833C2×C4C2×C22⋊Q812yes—
834C2×C4C2×C22⋊Q812yes—
835C2×C4C2×C22⋊Q812yes—
836C2×C4C2×C22⋊Q812yes—
837C2×C4C2×C22⋊Q812yes—
838C2×C4#53512yes—
839C2×C4#53512yes—
840C2×C4#53612yes—
841C2×C4#53612yes—
842C2×C4C23×Q811yescharacteristic
843C2×C4C22×#4111yescharacteristic
844C2×C4C2×H(5,𝔽2)12yes—
845C2×C4C2×2−1+412yes—
846C8—42no—
847C8—42no—
848C8—42no—
849C8—42no—
850C22—22no—
851C22—22no—
852C22—22no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22—41no—
857C22—42no—
858C22—42no—
859C22—42no—
860C22—81no—
861C22—81no—
862C22—81no—
863C22—81no—
864C22C22×C22⋊Q811yescharacteristic
865C22C2×#53511yescharacteristic
866C22C2×#53611yescharacteristic
867C22#358511yescharacteristic
868C22#358511yescharacteristic
869C22#358611yescharacteristic
870C22#358611yescharacteristic
871C4—22no—
872C4—22no—
873C4—22no—
874C4—22no—
875C4—22no—
876C4—22no—
877C4—22no—
878C4—22no—
879C4—22no—
880C4—42no—
881C4—42no—
882C4—41no—
883C4—41no—
884C4—42no—
885C4—41no—
886C4—41no—
887C4—82no—
888C4—81no—
889C4—81no—
890C4—82no—
891C4—82no—
892C4—82no—
893C4—81no—
894C4—81no—
895C4#350312yes—
896C4#351112yes—
897C2—42no—
898C2—82no—
899C2#3527911yescharacteristic
900C2#6049311yescharacteristic
901C2#6049311yescharacteristic
902C2#6082811yescharacteristic
903C2#6083011yescharacteristic
904C2#6088511yescharacteristic
905C2#6088711yescharacteristic
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. #33206C2semidirect
4. #33205C2semidirect
5. #29993C2semidirect
6. #29991C2semidirect
7. #29227C2semidirect
8. #29225C2semidirect
9. #29214C2semidirect
10. #29213C2semidirect
11. #29148C2semidirect
12. #29146C2semidirect
13. #28519C2semidirect
14. #28517C2semidirect
15. #27689C2semidirect
17. #24311C2semidirect
19. #21989C2semidirect
20. #21987C2semidirect
23. #20811C2semidirect
149. #529Q8semidirect

Maximal subgroups

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

subgroupindex
#352752
#342272
#332062
#332052
#299932
#299912
#292272
#292252
#292142
#292132
#291482
#291462
#285192
#285172
#276892
#276872
#243112
#243092
#219892
#219872
#218682
#218672
#208112