Finite Group Databasebeta

← #6457465

Subgroups — #6457465

Order 512.

1781 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35592C211yesmaximal, characteristic
2#35557C211yesmaximal, characteristic, complemented
3#28092C212yesmaximal, complemented
4#28091C212yesmaximal, complemented
5#28088C212yesmaximal, complemented
6#28087C212yesmaximal, complemented
7#28069C212yesmaximal, complemented
8#28066C212yesmaximal, complemented
9#28065C212yesmaximal, complemented
10#28062C212yesmaximal, complemented
11#23734C211yesmaximal, characteristic, complemented
12#23643C211yesmaximal, characteristic, complemented
13#23552C211yesmaximal, characteristic, complemented
14#23485C211yesmaximal, characteristic
15C2×#1990C211yesmaximal, characteristic, complemented
16#21092C211yesmaximal, characteristic, complemented
17#21083C211yesmaximal, characteristic, complemented
18#21062C211yesmaximal, characteristic, complemented
19#21036C211yesmaximal, characteristic, complemented
20#20976C211yesmaximal, characteristic
21#20664C211yesmaximal, characteristic, complemented
22#20453C211yesmaximal, characteristic, complemented
23#20383C211yesmaximal, characteristic, complemented
24C22×#131C2211yescharacteristic
25C2×#537C2211yescharacteristic
26C22×C4⋊Q8C2211yescharacteristic
27C2×#428C2211yescharacteristic
28C2×#428C2211yescharacteristic
29C2×#428C2211yescharacteristic
30C2×#428C2211yescharacteristic
31C2×#417C2211yescharacteristic
32C2×#417C2211yescharacteristic
33C2×#416C2211yescharacteristic
34C2×#416C2211yescharacteristic
35C2×#408C2211yescharacteristic
36C2×#405C2211yescharacteristic
37C22×C4×C8C2211yescharacteristic
38#2591—22no—
39#2512—21no—
40#2512—21no—
41#2511—21no—
42#2511—21no—
43#2497C2212yes—
44#2497C2212yes—
45#2496C2212yes—
46#2496C2212yes—
47#2492—21no—
48#2492—21no—
49#2492C2212yes—
50#2492C2212yes—
51#2491—21no—
52#2491—21no—
53#2491C2212yes—
54#2491C2212yes—
55#2481—22no—
56#2481—22no—
57#2436—22no—
58#2316C2211yescharacteristic
59#2311C2211yescharacteristic
60#2311C2211yescharacteristic
61#2311C2211yescharacteristic
62#2311C2211yescharacteristic
63#2297C2211yescharacteristic
64#2297C2211yescharacteristic
65#2296C2211yescharacteristic
66C2×#384C2211yescharacteristic
67#2274C2211yescharacteristic
68#2274C2211yescharacteristic
69#2096C2212yes—
70#2095C2212yes—
71#2094C2212yes—
72#2093C2212yes—
73#2077C2212yes—
74#2077C2212yes—
75#2076C2212yes—
76#2075C2212yes—
77#2058C2212yes—
78#2058C2212yes—
79#2057C2212yes—
80#2057C2212yes—
81#2036C2212yes—
82#2035C2212yes—
83#2034C2212yes—
84#2033C2212yes—
85#1990C2212yes—
86#1990C2212yes—
87#1990C2212yes—
88#1990C2212yes—
89#1936C2212yes—
90#1935C2212yes—
91#1934C2211yescharacteristic
92#1934C2211yescharacteristic
93#1934C2211yescharacteristic
94#1934C2211yescharacteristic
95#1934C2212yes—
96#1933C2211yescharacteristic
97#1933C2211yescharacteristic
98#1933C2211yescharacteristic
99#1933C2211yescharacteristic
100#1933C2212yes—
101#1928C2212yes—
102#1927C2212yes—
103#1926C2212yes—
104#1925C2212yes—
105#1921C2212yes—
106#1920C2212yes—
107#1919C2212yes—
108#1918C2212yes—
109#1895C2212yes—
110#1894C2212yes—
111#1893C2212yes—
112#1892C2212yes—
113#1809C2212yes—
114#1809C2212yes—
115#1808C2212yes—
116#1807C2212yes—
117#1776C2212yes—
118#1776C2212yes—
119C4×#107C2212yes—
120C4×#106C2212yes—
121#1753C2212yes—
122#1753C2212yes—
123C8×C22⋊C4C2212yes—
124C8×C22⋊C4C2212yes—
125#1736C2211yescharacteristic
126#1736C2211yescharacteristic
127#1735C2211yescharacteristic
128#1735C2211yescharacteristic
129C2×#340C2211yescharacteristic
130C2×#340C2211yescharacteristic
131C2×#340C2211yescharacteristic
132C2×#340C2211yescharacteristic
133#1729C2211yescharacteristic
134#1728C2211yescharacteristic
135C22×#41C2311yescharacteristic
136C22×#41C2311yescharacteristic
137C23×Q8—21no—
138C2×#131—24no—
139C2×#131—24no—
140C2×#131—42no—
141C22×M16C2312yes—
142C22×M16C2311yescharacteristic
143C22×M16C2311yescharacteristic
144C23×C8C2311yescharacteristic
145C23×C8C2312yes—
146C23×C8C2311yescharacteristic
147#537—24no—
148#537—42no—
149C2×C4⋊Q8—24no—
150C2×C4⋊Q8—21no—
151C2×C4⋊Q8—21no—
152C2×C4⋊Q8—42no—
153C2×C4⋊Q8C2312yes—
154C2×C4⋊Q8C2312yes—
155C2×#126—22no—
156C2×#126—22no—
157C2×#124—22no—
158C2×#124—22no—
159C2×C22⋊Q8—21no—
160C2×C22⋊Q8C2312yes—
161C2×#121—22no—
162C2×#121—21no—
163C2×#121C2312yes—
164C2×#117C2311yescharacteristic
165C2×#117C2311yescharacteristic
166C2×#117C2311yescharacteristic
167C2×#117C2311yescharacteristic
168C22×C4⋊C4—21no—
169C22×C4⋊C4—21no—
170C22×C4⋊C4—21no—
171C22×C4⋊C4C2311yescharacteristic
172C22×C4⋊C4C2311yescharacteristic
173C22×C4⋊C4C2311yescharacteristic
174C22×C4⋊C4C2311yescharacteristic
175C22×C42C2311yescharacteristic
176#428—24no—
177#428—24no—
178#428—24no—
179#428—42no—
180C2×#107C2312yes—
181C2×#107C2312yes—
182C2×#107C2312yes—
183C2×#107C2312yes—
184C2×#106C2312yes—
185C2×#106C2312yes—
186C2×#106C2312yes—
187C2×#106C2312yes—
188#417—24no—
189#417—24no—
190#416—24no—
191#416—42no—
192C2×#103C2312yes—
193C2×#103C2312yes—
194C2×#103C2311yescharacteristic
195C2×#103C2311yescharacteristic
196C2×#103C2311yescharacteristic
197C2×#103C2311yescharacteristic
198C2×#102C2312yes—
199C2×#102C2312yes—
200C2×#102C2311yescharacteristic
201C2×#102C2311yescharacteristic
202C2×#102C2311yescharacteristic
203C2×#102C2311yescharacteristic
204#408—24no—
205C2×C22⋊C8C2312yes—
206C2×C22⋊C8C2312yes—
207#405—24no—
208C2×#97C2312yes—
209C2×C4×C8—42no—
210C2×C4×C8C2312yes—
211C2×C4×C8C2311yescharacteristic
212C2×C4×C8C2311yescharacteristic
213C2×C4×C8C2311yescharacteristic
214C2×C4×C8C2311yescharacteristic
215#400—22no—
216#400—22no—
217#400—22no—
218#400—22no—
219#400—22no—
220#400—22no—
221#397—22no—
222#397—22no—
223#396—22no—
224#396—22no—
225#394—22no—
226#394—22no—
227#393—22no—
228#393—22no—
229#393—22no—
230#393—22no—
231#391—21no—
232#391—21no—
233#391—21no—
234#391—22no—
235#391—22no—
236#391D411yescharacteristic
237#391D411yescharacteristic
238#391C2312yes—
239#391C2311yescharacteristic
240#391C2311yescharacteristic
241#390—21no—
242#390—21no—
243#390—21no—
244#390D411yescharacteristic
245#390D411yescharacteristic
246#390C2312yes—
247#390C2311yescharacteristic
248#390C2311yescharacteristic
249#389—21no—
250#389—21no—
251#389C2311yescharacteristic
252#389C2311yescharacteristic
253#389C2311yescharacteristic
254#389C2311yescharacteristic
255#389C2312yes—
256#389C2312yes—
257#388—22no—
258#388—22no—
259#388—22no—
260#388—22no—
261#388—22no—
262#388—22no—
263#387—22no—
264#387—22no—
265#387—22no—
266#387—22no—
267#386—22no—
268#386—22no—
269#386—22no—
270#386—21no—
271#386—21no—
272#386—22no—
273#386D412yes—
274#386D412yes—
275#385—21no—
276#385—21no—
277#384—21no—
278#384—21no—
279#384C2312yes—
280#384C2312yes—
281#380—21no—
282#380—21no—
283#380—22no—
284#380C2312yes—
285#380C2312yes—
286#380C2312yes—
287#380C2312yes—
288#380C2312yes—
289#380C2312yes—
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⋊C4C2312yes—
297C4×C4⋊C4C2312yes—
298C4×C4⋊C4C2312yes—
299C4×C4⋊C4C2312yes—
300C4×C22⋊C4—22no—
301C4×C22⋊C4—22no—
302C4×C22⋊C4—21no—
303C4×C22⋊C4—21no—
304C4×C22⋊C4C2312yes—
305C4×C22⋊C4C2312yes—
306#340C2312yes—
307#340C2312yes—
308#340C2312yes—
309#340C2312yes—
310#340C2311yescharacteristic
311#340C2312yes—
312#340C2311yescharacteristic
313#340C2311yescharacteristic
314#340C2311yescharacteristic
315#340C2312yes—
316#340C2311yescharacteristic
317#340C2312yes—
318#340C2311yescharacteristic
319#340C2312yes—
320#340C2311yescharacteristic
321#340C2311yescharacteristic
322#340C2312yes—
323#340C2312yes—
324#340C2312yes—
325#340C2312yes—
326#336C2312yes—
327#336C2312yes—
328#336C2312yes—
329#336C2312yes—
330C2×#41—22no—
331C2×#41—22no—
332C2×#41—22no—
333C2×#41—22no—
334C2×#41—22no—
335C2×#41—22no—
336C2×#41—22no—
337C2×#41—22no—
338C2×#41—22no—
339C2×#41—22no—
340C2×#41—22no—
341C2×#41—22no—
342C22×Q8—22no—
343C22×Q8—22no—
344C22×Q8—44no—
345C22×Q8—82no—
346C22×Q8—82no—
347C22×Q8C2×D411yescharacteristic
348C22×Q8C2411yescharacteristic
349C22×D4—21no—
350C22×D4—22no—
351C22×D4C2×D412yes—
352C22×D4C2×D411yescharacteristic
353C22×D4C2411yescharacteristic
354C23×C4—21no—
355C23×C4—21no—
356C23×C4—21no—
357C23×C4—21no—
358C23×C4—21no—
359C23×C4C2×D411yescharacteristic
360C23×C4C2×D411yescharacteristic
361C23×C4C2412yes—
362C23×C4C2411yescharacteristic
363#131—416no—
364C2×M16—22no—
365C2×M16—22no—
366C2×M16—22no—
367C2×M16—22no—
368C2×M16—24no—
369C2×M16—24no—
370C2×M16—42no—
371C2×M16#4114yes—
372C2×M16#4114yes—
373C22×C8—22no—
374C22×C8—22no—
375C22×C8—22no—
376C22×C8—22no—
377C22×C8—22no—
378C22×C8—24no—
379C22×C8—24no—
380C22×C8—42no—
381C22×C8#4114yes—
382C22×C8C2411yescharacteristic
383C22×C8C2411yescharacteristic
384C22×C8C2411yescharacteristic
385C22×C8C2412yes—
386C22×C8C2411yescharacteristic
387C22×C8C2412yes—
388C4⋊Q8—24no—
389C4⋊Q8—24no—
390C4⋊Q8—42no—
391C4⋊Q8—42no—
392C4⋊Q8—44no—
393C4⋊Q8—44no—
394#126—84no—
395#126—84no—
396#124—84no—
397#124—84no—
398C22⋊Q8—24no—
399C22⋊Q8—42no—
400C22⋊Q8—44no—
401#121—24no—
402#121—42no—
403#121—44no—
404#121—48no—
405#117—22no—
406#117—22no—
407#117—22no—
408#117—22no—
409#117—22no—
410#117—22no—
411#117—22no—
412#117—22no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—22no—
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—22no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—22no—
434C2×C4⋊C4—22no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—22no—
437C2×C4⋊C4—44no—
438C2×C4⋊C4—82no—
439C2×C4⋊C4—82no—
440C2×C4⋊C4C2×D411yescharacteristic
441C2×C4⋊C4C2×D411yescharacteristic
442C2×C4⋊C4#4114yes—
443C2×C4⋊C4C2412yes—
444C2×C4⋊C4C2412yes—
445C2×C4⋊C4C2412yes—
446C2×C4⋊C4C2411yescharacteristic
447C2×C4⋊C4C2411yescharacteristic
448C2×C4⋊C4C2411yescharacteristic
449C2×C4⋊C4C2411yescharacteristic
450C2×C4⋊C4C2411yescharacteristic
451C2×C4⋊C4C2411yescharacteristic
452C2×C4⋊C4C2412yes—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—22no—
457C2×C22⋊C4—22no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—21no—
461C2×C22⋊C4—21no—
462C2×C22⋊C4—22no—
463C2×C22⋊C4—22no—
464C2×C22⋊C4—22no—
465C2×C22⋊C4—22no—
466C2×C22⋊C4—22no—
467C2×C22⋊C4—22no—
468C2×C22⋊C4—22no—
469C2×C22⋊C4—22no—
470C2×C22⋊C4C2×D412yes—
471C2×C22⋊C4C2×D412yes—
472C2×C22⋊C4C2×D412yes—
473C2×C22⋊C4C2×D412yes—
474C2×C22⋊C4C2×D412yes—
475C2×C42—22no—
476C2×C42—22no—
477C2×C42—21no—
478C2×C42—21no—
479C2×C42—21no—
480C2×C42—22no—
481C2×C42—22no—
482C2×C42—22no—
483C2×C42—22no—
484C2×C42C2×D411yescharacteristic
485C2×C42C2×D411yescharacteristic
486C2×C42C2412yes—
487C2×C42C2411yescharacteristic
488C2×C42C2411yescharacteristic
489#107—24no—
490#107—24no—
491#107—24no—
492#107—42no—
493#106—24no—
494#106—24no—
495#106—24no—
496#106—42no—
497#103—22no—
498#103—22no—
499#103—24no—
500#103—24no—
501#103—41no—
502#103—41no—
503#102—22no—
504#102—22no—
505#102—24no—
506#102—24no—
507#102—41no—
508#102—41no—
509C22⋊C8—24no—
510C22⋊C8—24no—
511#97—24no—
512C4×C8—24no—
513C4×C8—41no—
514C4×C8—41no—
515C4×C8—41no—
516C4×C8—41no—
517#95—22no—
518#95—22no—
519#95—22no—
520#95—22no—
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—22no—
530#95—22no—
531#95—22no—
532#95—22no—
533#95—22no—
534#95—22no—
535#95—22no—
536#95—22no—
537#95—22no—
538#95—22no—
539#95C2×D412yes—
540#95C2×D412yes—
541#95C2×D412yes—
542#95C2×D412yes—
543C24—21no—
544C24C22×D412yes—
545C24C22×D411yescharacteristic
546#41—44no—
547#41—44no—
548#41—44no—
549#41—44no—
550#41—44no—
551#41—44no—
552#41—44no—
553#41—44no—
554C2×Q8—22no—
555C2×Q8—22no—
556C2×Q8—22no—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—44no—
564C2×Q8—44no—
565C2×Q8—44no—
566C2×Q8—44no—
567C2×Q8—82no—
568C2×Q8—82no—
569C2×Q8—816no—
570C2×D4—24no—
571C2×D4—24no—
572C2×D4—24no—
573C2×D4—22no—
574C2×D4—22no—
575C2×D4—22no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—44no—
583C2×D4—42no—
584C2×D4—42no—
585C2×D4—42no—
586C2×D4—82no—
587C2×D4—82no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—24no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—42no—
613C22×C4—42no—
614C22×C4—42no—
615C22×C4—42no—
616C22×C4—42no—
617C22×C4—42no—
618C22×C4—81no—
619C22×C4—81no—
620C22×C4—81no—
621C22×C4—81no—
622C22×C4—81no—
623C22×C4—81no—
624C22×C4—81no—
625C22×C4—81no—
626C22×C4C22×D412yes—
627C22×C4C22×D412yes—
628C22×C4C22×D412yes—
629C22×C4C22×D411yescharacteristic
630C22×C4C22×D411yescharacteristic
631C22×C4C22×D411yescharacteristic
632C22×C4C22×D411yescharacteristic
633C22×C4C22×D411yescharacteristic
634C22×C4C2×#4112yes—
635C22×C4C2×#4112yes—
636C22×C4C2×#4112yes—
637C22×C4C2×#4112yes—
638C22×C4H(5,𝔽2)12yes—
639C22×C42−1+412yes—
640C22×C4C2511yescharacteristic
641M16—28no—
642M16—28no—
643M16—48no—
644C2×C8—28no—
645C2×C8—22no—
646C2×C8—22no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—22no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—22no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—48no—
660C2×C8—44no—
661C2×C8C2×#4112yes—
662C2×C8C2×#4112yes—
663C2×C8C2×#4114yes—
664C2×C8C2×#4114yes—
665C4⋊C4—24no—
666C4⋊C4—22no—
667C4⋊C4—22no—
668C4⋊C4—22no—
669C4⋊C4—22no—
670C4⋊C4—22no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—21no—
675C4⋊C4—21no—
676C4⋊C4—22no—
677C4⋊C4—22no—
678C4⋊C4—21no—
679C4⋊C4—21no—
680C4⋊C4—21no—
681C4⋊C4—22no—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4—22no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—44no—
688C4⋊C4—44no—
689C4⋊C4—44no—
690C4⋊C4—42no—
691C4⋊C4—42no—
692C4⋊C4—42no—
693C4⋊C4—44no—
694C4⋊C4—42no—
695C4⋊C4—42no—
696C4⋊C4—44no—
697C4⋊C4—42no—
698C4⋊C4—42no—
699C4⋊C4—82no—
700C4⋊C4—82no—
701C4⋊C4—82no—
702C4⋊C4—82no—
703C4⋊C4C2×#4114yes—
704C22⋊C4—24no—
705C22⋊C4—24no—
706C22⋊C4—24no—
707C22⋊C4—24no—
708C22⋊C4—24no—
709C22⋊C4—44no—
710C22⋊C4—44no—
711C22⋊C4—42no—
712C22⋊C4—42no—
713C22⋊C4—42no—
714C22⋊C4—42no—
715C22⋊C4—42no—
716C22⋊C4—42no—
717C22⋊C4—42no—
718C22⋊C4—82no—
719C22⋊C4—82no—
720C22⋊C4—82no—
721C22⋊C4—82no—
722C22⋊C4—82no—
723C22⋊C4—82no—
724C22⋊C4—82no—
725C22⋊C4—82no—
726C42—22no—
727C42—22no—
728C42—22no—
729C42—21no—
730C42—21no—
731C42—21no—
732C42—21no—
733C42—22no—
734C42—42no—
735C42—42no—
736C42—42no—
737C42—82no—
738C42—82no—
739C42—82no—
740C42—82no—
741C23—21no—
742C23—21no—
743C23—21no—
744C23—21no—
745C23—22no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—22no—
751C23—22no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—41no—
758C23—41no—
759C23#53212yes—
760C23#54612yes—
761C23#54712yes—
762C23C23×D411yescharacteristic
763Q8—44no—
764Q8—41no—
765Q8—41no—
766Q8—41no—
767Q8—41no—
768Q8—88no—
769Q8—88no—
770D4—48no—
771D4—41no—
772D4—41no—
773D4—41no—
774D4—41no—
775D4—44no—
776D4—84no—
777D4—164no—
778C2×C4—28no—
779C2×C4—28no—
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—22no—
789C2×C4—24no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—42no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—42no—
819C2×C4—41no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—42no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—84no—
835C2×C4—84no—
836C2×C4—84no—
837C2×C4—162no—
838C2×C4—162no—
839C2×C4#52914yes—
840C2×C4#53212yes—
841C2×C4#54214yes—
842C2×C4#54612yes—
843C2×C4#54712yes—
844C2×C4#55114yes—
845C2×C4#55614yes—
846C2×C4#57612yes—
847C2×C4#57712yes—
848C2×C4#57712yes—
849C2×C4#57812yes—
850C2×C4C22×#4111yescharacteristic
851C2×C4C22×#4111yescharacteristic
852C2×C4C22×#4111yescharacteristic
853C2×C4C22×#4111yescharacteristic
854C2×C4C2×H(5,𝔽2)11yescharacteristic
855C2×C4C2×2−1+411yescharacteristic
856C8—24no—
857C8—22no—
858C8—22no—
859C8—24no—
860C8—41no—
861C8—41no—
862C22—22no—
863C22—22no—
864C22—22no—
865C22—22no—
866C22—22no—
867C22—22no—
868C22—42no—
869C22—42no—
870C22—42no—
871C22—42no—
872C22—42no—
873C22—42no—
874C22—42no—
875C22—81no—
876C22—81no—
877C22—81no—
878C22—81no—
879C22—81no—
880C22—81no—
881C22—81no—
882C22#252114yes—
883C22C2×#53211yescharacteristic
884C22C2×#54611yescharacteristic
885C22C2×#54711yescharacteristic
886C22C2×#57611yescharacteristic
887C22C2×#57711yescharacteristic
888C22C2×#57711yescharacteristic
889C22C2×#57811yescharacteristic
890C4—22no—
891C4—22no—
892C4—22no—
893C4—22no—
894C4—42no—
895C4—42no—
896C4—42no—
897C4—44no—
898C4—81no—
899C4—82no—
900C4—82no—
901C4—81no—
902C4—81no—
903C4—81no—
904C4—81no—
905C4—81no—
906C4—82no—
907C4—81no—
908C4#252114yes—
909C4C2×#52911yescharacteristic
910C4C2×#54211yescharacteristic
911C4C2×#55111yescharacteristic
912C4C2×#55611yescharacteristic
913C2—24no—
914C2—82no—
915C2—161no—
916C2C2×#252111yescharacteristic
917C2#6072211yescharacteristic
918C2#6072311yescharacteristic
919C2#6116711yescharacteristic
920C2#6116811yescharacteristic
921C2#6128711yescharacteristic
922C2#6128811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#537C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2297 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #35557C2semidirect
3. #28092C2semidirect
4. #28091C2semidirect
5. #28088C2semidirect
6. #28087C2semidirect
7. #28069C2semidirect
8. #28066C2semidirect
9. #28065C2semidirect
10. #28062C2semidirect
11. #23734C2semidirect
12. #23643C2semidirect
13. #23552C2semidirect
15. C2×#1990C2semidirect
16. #21092C2semidirect
17. #21083C2semidirect
18. #21062C2semidirect
19. #21036C2semidirect
21. #20664C2semidirect
22. #20453C2semidirect
23. #20383C2semidirect

Maximal subgroups

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

subgroupindex
#355922
#355572
#280922
#280912
#280882
#280872
#280692
#280662
#280652
#280622
#237342
#236432
#235522
#234852
C2×#19902
#210922
#210832
#210622
#210362
#209762
#206642
#204532
#203832