Finite Group Databasebeta

← #6441954

Subgroups — #6441954

Order 512.

1898 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#35620C211yesmaximal, characteristic
2#34266C211yesmaximal, characteristic
3#26435C212yesmaximal, complemented
4#26433C212yesmaximal, complemented
5#26430C212yesmaximal, complemented
6#26428C212yesmaximal, complemented
7#26418C212yesmaximal, complemented
8#26416C212yesmaximal, complemented
9#26415C212yesmaximal, complemented
10#26413C212yesmaximal, complemented
11#23746C211yesmaximal, characteristic, complemented
12#23666C211yesmaximal, characteristic, complemented
13#23613C211yesmaximal, characteristic, complemented
14#23457C211yesmaximal, characteristic, complemented
15#21315C211yesmaximal, characteristic, complemented
16#21035C211yesmaximal, characteristic, complemented
17#20974C211yesmaximal, characteristic
18#20913C211yesmaximal, characteristic
19#20874C211yesmaximal, characteristic, complemented
20#20849C211yesmaximal, characteristic
21#20838C211yesmaximal, characteristic
22C2×#1805C211yesmaximal, characteristic, complemented
23#20348C211yesmaximal, characteristic
24C22×#131C2211yescharacteristic
25C2×#544C2211yescharacteristic
26C2×#536C2211yescharacteristic
27C2×#520C2211yescharacteristic
28C2×#520C2211yescharacteristic
29C22×C4×Q8C2211yescharacteristic
30C2×#428C2211yescharacteristic
31C2×#427C2211yescharacteristic
32C2×#424C2211yescharacteristic
33C22×C4⋊C8C2211yescharacteristic
34C2×#419C2211yescharacteristic
35C2×#419C2211yescharacteristic
36C22×#103C2211yescharacteristic
37C22×#103C2211yescharacteristic
38C2×#408C2211yescharacteristic
39#2568—21no—
40#2566—21no—
41#2565—21no—
42#2563—21no—
43#2450—22no—
44#2450—22no—
45#2442C2212yes—
46#2442C2212yes—
47#2439C2212yes—
48#2439C2212yes—
49#2367—21no—
50#2367—21no—
51#2365—21no—
52#2365—21no—
53#2362C2212yes—
54#2362C2212yes—
55#2360C2212yes—
56#2360C2212yes—
57#2322—22no—
58#2317C2211yescharacteristic
59#2311C2211yescharacteristic
60#2310C2211yescharacteristic
61C4×#123—22no—
62#2297C2211yescharacteristic
63#2296C2211yescharacteristic
64#2296C2211yescharacteristic
65C2×#382C2211yescharacteristic
66#2274C2211yescharacteristic
67#2101C2212yes—
68#2101C2212yes—
69#2101C2212yes—
70#2101C2212yes—
71#2088C2211yescharacteristic
72#2088C2211yescharacteristic
73#2088C2211yescharacteristic
74#2088C2211yescharacteristic
75#2087C2211yescharacteristic
76#2087C2211yescharacteristic
77#2086C2211yescharacteristic
78#2086C2211yescharacteristic
79#2068C2212yes—
80#2068C2212yes—
81#2066C2212yes—
82#2066C2212yes—
83#2026C2212yes—
84#2026C2212yes—
85#2024C2212yes—
86#2024C2212yes—
87#1989C2212yes—
88#1989C2212yes—
89#1988C2212yes—
90#1987C2212yes—
91#1921C2212yes—
92#1920C2212yes—
93#1919C2212yes—
94#1918C2212yes—
95#1894C2212yes—
96#1894C2212yes—
97#1892C2212yes—
98#1892C2212yes—
99#1873C2212yes—
100#1873C2212yes—
101#1872C2212yes—
102#1872C2212yes—
103#1865C2212yes—
104#1865C2212yes—
105#1863C2212yes—
106#1863C2212yes—
107#1854C2212yes—
108#1854C2212yes—
109#1853C2212yes—
110#1852C2212yes—
111#1851C2212yes—
112#1851C2212yes—
113#1850C2212yes—
114#1850C2212yes—
115#1805C2212yes—
116#1805C2212yes—
117#1805C2212yes—
118#1805C2212yes—
119#1736C2211yescharacteristic
120#1736C2212yes—
121#1736C2211yescharacteristic
122#1736C2212yes—
123#1736C2211yescharacteristic
124#1736C2211yescharacteristic
125#1736C2211yescharacteristic
126#1735C2211yescharacteristic
127#1735C2212yes—
128#1735C2211yescharacteristic
129#1735C2211yescharacteristic
130C2×#340C2211yescharacteristic
131C2×#340C2212yes—
132C2×#340C2211yescharacteristic
133#1729C2211yescharacteristic
134#1728C2211yescharacteristic
135C22×#41C2311yescharacteristic
136C23×Q8C2311yescharacteristic
137C2×#131—24no—
138C2×#131—42no—
139C2×#131—42no—
140C22×M16C2311yescharacteristic
141C22×M16C2311yescharacteristic
142C22×M16C2312yes—
143C23×C8C2311yescharacteristic
144C23×C8C2311yescharacteristic
145C23×C8C2312yes—
146#544—24no—
147#544—42no—
148#536—24no—
149#536Q818yescomplemented
150C2×C4⋊Q8—21no—
151C2×C4⋊Q8—21no—
152C2×C4⋊Q8C2312yes—
153C2×#125—21no—
154C2×#125C2312yes—
155C2×#124—21no—
156C2×#123—22no—
157C2×C22⋊Q8—22no—
158C2×C22⋊Q8C2312yes—
159C2×C22⋊Q8C2312yes—
160#520—24no—
161#520—24no—
162#520—42no—
163#520—42no—
164C2×C4×Q8—21no—
165C2×C4×Q8—21no—
166C2×C4×Q8—21no—
167C2×C4×Q8—21no—
168C2×C4×Q8—24no—
169C2×C4×Q8—42no—
170C2×C4×Q8C2312yes—
171C2×C4×Q8C2312yes—
172C2×C4×D4—21no—
173C2×C4×D4—22no—
174C2×C4×D4—21no—
175C2×C4×D4—22no—
176C2×#117C2311yescharacteristic
177C2×#117C2311yescharacteristic
178C2×#117C2312yes—
179C2×#117C2312yes—
180C2×#117C2311yescharacteristic
181C2×#117C2311yescharacteristic
182C2×#117C2311yescharacteristic
183C22×C4⋊C4—21no—
184C22×C4⋊C4C2311yescharacteristic
185C22×C4⋊C4C2311yescharacteristic
186C22×C4⋊C4C2312yes—
187C22×C4⋊C4C2312yes—
188C22×C4⋊C4C2311yescharacteristic
189C22×C42—21no—
190C22×C42C2311yescharacteristic
191#428—24no—
192#427—42no—
193C2×#107C2312yes—
194C2×#107C2311yescharacteristic
195C2×#107C2311yescharacteristic
196C2×#106C2312yes—
197C2×#106C2311yescharacteristic
198C2×#106C2311yescharacteristic
199#424—42no—
200C2×C4⋊C8—42no—
201C2×C4⋊C8C2311yescharacteristic
202C2×C4⋊C8C2311yescharacteristic
203C2×C4⋊C8C2311yescharacteristic
204C2×C4⋊C8C2311yescharacteristic
205C2×C4⋊C8C2312yes—
206C2×C4⋊C8C2312yes—
207#419—24no—
208#419—42no—
209C2×#103—42no—
210C2×#103—42no—
211C2×#103C2312yes—
212C2×#103C2312yes—
213C2×#103C2312yes—
214C2×#103C2312yes—
215C2×#103C2312yes—
216C2×#103C2312yes—
217C2×#103C2312yes—
218C2×#103C2312yes—
219#408—24no—
220C2×C22⋊C8C2312yes—
221C2×C22⋊C8C2312yes—
222#400—22no—
223#400—22no—
224#398—22no—
225#398—22no—
226#396—22no—
227#396—22no—
228#393—22no—
229#393—22no—
230#391—21no—
231#391—21no—
232#391—21no—
233#391—22no—
234#391—22no—
235#391D411yescharacteristic
236#391D411yescharacteristic
237#391C2312yes—
238#391C2312yes—
239#390—21no—
240#390D411yescharacteristic
241#390D411yescharacteristic
242#389—22no—
243#389—22no—
244#389C2312yes—
245#389C2312yes—
246#389C2311yescharacteristic
247#389C2311yescharacteristic
248#389C2311yescharacteristic
249#389C2311yescharacteristic
250#389C2311yescharacteristic
251#389C2311yescharacteristic
252#389C2311yescharacteristic
253#389C2311yescharacteristic
254#388—22no—
255#388—22no—
256#388—22no—
257#388—22no—
258#387—22no—
259#387—22no—
260#387—22no—
261#387—22no—
262#387—22no—
263#387—22no—
264#386—22no—
265#386D412yes—
266#386D412yes—
267#385—21no—
268#385—21no—
269#385—21no—
270#385—21no—
271#385—22no—
272#385—22no—
273#385—22no—
274#385—22no—
275#385—22no—
276#384—21no—
277#382—21no—
278#382—21no—
279#382—21no—
280#382C2312yes—
281#382C2312yes—
282#381—22no—
283#380—22no—
284#380—22no—
285#380C2312yes—
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—22no—
294C4×C4⋊C4—22no—
295C4×C4⋊C4C2312yes—
296C4×C4⋊C4C2312yes—
297C4×C22⋊C4—22no—
298C4×C22⋊C4—22no—
299C4×C22⋊C4—22no—
300C4×C22⋊C4C2312yes—
301C4×C22⋊C4C2312yes—
302C2×#95—21no—
303C2×#95—21no—
304#340C2312yes—
305#340C2312yes—
306#340C2312yes—
307#340C2312yes—
308#340C2312yes—
309#340C2312yes—
310#340C2311yescharacteristic
311#340C2311yescharacteristic
312#340C2311yescharacteristic
313#340C2311yescharacteristic
314#340C2311yescharacteristic
315#340C2311yescharacteristic
316#340C2311yescharacteristic
317#340C2311yescharacteristic
318#340C2311yescharacteristic
319#340C2311yescharacteristic
320#340C2311yescharacteristic
321#340C2311yescharacteristic
322#340C2312yes—
323#340C2312yes—
324#340C2312yes—
325#340C2312yes—
326#340C2312yes—
327#340C2312yes—
328#340C2312yes—
329#340C2312yes—
330#336C2312yes—
331#336C2312yes—
332#336C2312yes—
333#336C2312yes—
334C2×#41—22no—
335C2×#41—22no—
336C2×#41—22no—
337C2×#41—22no—
338C2×#41C2×Q814yes—
339C2×#41#4114yes—
340C22×Q8—21no—
341C22×Q8—22no—
342C22×Q8—22no—
343C22×Q8—22no—
344C22×Q8—22no—
345C22×Q8—22no—
346C22×Q8—22no—
347C22×Q8C2×D411yescharacteristic
348C22×Q8C2×Q814yes—
349C22×Q8C2412yes—
350C22×D4C2×D412yes—
351C22×D4C2×D411yescharacteristic
352C23×C4—21no—
353C23×C4—21no—
354C23×C4—21no—
355C23×C4—22no—
356C23×C4—22no—
357C23×C4—21no—
358C23×C4C2×D411yescharacteristic
359C23×C4C2×D411yescharacteristic
360C23×C4C2412yes—
361C23×C4C2411yescharacteristic
362#131—416no—
363C2×M16—24no—
364C2×M16—22no—
365C2×M16—22no—
366C2×M16—22no—
367C2×M16—22no—
368C2×M16—22no—
369C2×M16—22no—
370C2×M16—42no—
371C2×M16—42no—
372C22×C8—24no—
373C22×C8—22no—
374C22×C8—22no—
375C22×C8—22no—
376C22×C8—22no—
377C22×C8—22no—
378C22×C8—22no—
379C22×C8—42no—
380C22×C8—42no—
381C22×C8C2411yescharacteristic
382C22×C8C2411yescharacteristic
383C22×C8C2412yes—
384C22×C8C2411yescharacteristic
385C22×C8C2411yescharacteristic
386C22×C8C2412yes—
387C4⋊Q8—28no—
388C4⋊Q8—24no—
389C4⋊Q8—42no—
390C4⋊Q8—44no—
391#125—24no—
392#125—42no—
393#125—44no—
394#124—28no—
395#123—216no—
396C22⋊Q8—24no—
397C22⋊Q8—24no—
398C22⋊Q8—48no—
399C22⋊Q8C2×Q818yes—
400C22⋊Q8C2×Q818yes—
401C4×Q8—24no—
402C4×Q8—24no—
403C4×Q8—42no—
404C4×Q8—42no—
405C4×Q8—44no—
406C4×Q8—44no—
407C4×Q8—44no—
408C4×Q8—44no—
409C4×D4—44no—
410C4×D4—48no—
411C4×D4—44no—
412C4×D4—48no—
413#117—22no—
414#117—22no—
415#117—22no—
416#117—22no—
417#117—22no—
418#117—22no—
419#117—22no—
420#117—22no—
421#117—24no—
422#117—24no—
423#117—42no—
424#117—42no—
425#117C2×Q814yes—
426#117#4114yes—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—22no—
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—24no—
436C2×C4⋊C4—24no—
437C2×C4⋊C4—22no—
438C2×C4⋊C4—22no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4—22no—
441C2×C4⋊C4—22no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4—22no—
444C2×C4⋊C4—22no—
445C2×C4⋊C4—22no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4—21no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4—22no—
455C2×C4⋊C4—22no—
456C2×C4⋊C4—42no—
457C2×C4⋊C4—42no—
458C2×C4⋊C4—44no—
459C2×C4⋊C4C2×D411yescharacteristic
460C2×C4⋊C4C2×D411yescharacteristic
461C2×C4⋊C4#4114yes—
462C2×C4⋊C4C2412yes—
463C2×C4⋊C4C2411yescharacteristic
464C2×C4⋊C4C2412yes—
465C2×C4⋊C4C2411yescharacteristic
466C2×C4⋊C4C2411yescharacteristic
467C2×C4⋊C4C2411yescharacteristic
468C2×C4⋊C4C2411yescharacteristic
469C2×C4⋊C4C2411yescharacteristic
470C2×C4⋊C4C2412yes—
471C2×C4⋊C4C2411yescharacteristic
472C2×C4⋊C4C2411yescharacteristic
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4—22no—
476C2×C22⋊C4—22no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4—22no—
479C2×C22⋊C4—22no—
480C2×C22⋊C4—21no—
481C2×C22⋊C4—22no—
482C2×C22⋊C4—22no—
483C2×C22⋊C4C2×D412yes—
484C2×C22⋊C4C2×D412yes—
485C2×C22⋊C4C2×D412yes—
486C2×C22⋊C4C2×D412yes—
487C2×C22⋊C4C2×D412yes—
488C2×C42—21no—
489C2×C42—21no—
490C2×C42—22no—
491C2×C42—22no—
492C2×C42—22no—
493C2×C42—21no—
494C2×C42—22no—
495C2×C42—21no—
496C2×C42—22no—
497C2×C42—22no—
498C2×C42—22no—
499C2×C42—22no—
500C2×C42—44no—
501C2×C42C2×D411yescharacteristic
502C2×C42C2×D411yescharacteristic
503C2×C42C2412yes—
504C2×C42C2411yescharacteristic
505C2×C42C2411yescharacteristic
506#107—24no—
507#107—41no—
508#107—41no—
509#106—24no—
510#106—41no—
511#106—41no—
512C4⋊C8—41no—
513C4⋊C8—41no—
514C4⋊C8—41no—
515C4⋊C8—41no—
516C4⋊C8—42no—
517C4⋊C8—42no—
518#103—24no—
519#103—24no—
520#103—42no—
521#103—42no—
522#103—42no—
523#103—42no—
524#103—42no—
525#103—42no—
526C22⋊C8—24no—
527C22⋊C8—24no—
528#95—22no—
529#95—22no—
530#95—22no—
531#95—22no—
532#95—21no—
533#95—21no—
534#95—22no—
535#95—22no—
536#95—22no—
537#95—22no—
538#95—22no—
539#95—22no—
540#95—21no—
541#95—21no—
542#95—21no—
543#95—21no—
544#95—21no—
545#95—21no—
546#95—22no—
547#95—22no—
548#95—22no—
549#95—22no—
550#95C2×D412yes—
551#95C2×D412yes—
552#95C2×D412yes—
553#95C2×D412yes—
554C24C22×D412yes—
555C24C22×D411yescharacteristic
556#41—28no—
557#41—28no—
558#41—28no—
559#41—28no—
560C2×Q8—24no—
561C2×Q8—22no—
562C2×Q8—22no—
563C2×Q8—22no—
564C2×Q8—28no—
565C2×Q8—28no—
566C2×Q8—22no—
567C2×Q8—22no—
568C2×Q8—22no—
569C2×Q8—22no—
570C2×Q8—44no—
571C2×Q8—44no—
572C2×Q8—44no—
573C2×Q8—42no—
574C2×Q8—42no—
575C2×Q8—82no—
576C2×Q8—82no—
577C2×Q8C22⋊Q814yes—
578C2×Q8C22×Q814yes—
579C2×D4—24no—
580C2×D4—24no—
581C2×D4—22no—
582C2×D4—22no—
583C2×D4C22⋊Q818yes—
584C2×D4C22⋊Q814yes—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—24no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—24no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—41no—
606C22×C4—41no—
607C22×C4—41no—
608C22×C4—41no—
609C22×C4—44no—
610C22×C4—44no—
611C22×C4—42no—
612C22×C4—42no—
613C22×C4—42no—
614C22×C4—42no—
615C22×C4—81no—
616C22×C4—81no—
617C22×C4—82no—
618C22×C4—82no—
619C22×C4—82no—
620C22×C4—82no—
621C22×C4—81no—
622C22×C4—81no—
623C22×C4—81no—
624C22×C4—81no—
625C22×C4C22×D412yes—
626C22×C4C22×D411yescharacteristic
627C22×C4C22×D411yescharacteristic
628C22×C4C22×D411yescharacteristic
629C22×C4C22×D411yescharacteristic
630C22×C4C22×D412yes—
631C22×C4C22×D412yes—
632C22×C4C22×D411yescharacteristic
633C22×C4C22×Q814yes—
634C22×C4C22×Q812yes—
635C22×C4C2×#4114yes—
636C22×C4C2×#4112yes—
637C22×C4C2×#4112yes—
638C22×C4C2×#4112yes—
639C22×C4H(5,𝔽2)12yes—
640C22×C4H(5,𝔽2)12yes—
641C22×C4C2511yescharacteristic
642M16—48no—
643M16—44no—
644M16—44no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—22no—
648C2×C8—22no—
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—22no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—21no—
662C2×C8—22no—
663C2×C8—48no—
664C2×C8—44no—
665C2×C8—44no—
666C4⋊C4—28no—
667C4⋊C4—28no—
668C4⋊C4—24no—
669C4⋊C4—22no—
670C4⋊C4—22no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—22no—
674C4⋊C4—21no—
675C4⋊C4—21no—
676C4⋊C4—21no—
677C4⋊C4—21no—
678C4⋊C4—22no—
679C4⋊C4—21no—
680C4⋊C4—22no—
681C4⋊C4—21no—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4—22no—
685C4⋊C4—22no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—44no—
689C4⋊C4—44no—
690C4⋊C4—44no—
691C4⋊C4—44no—
692C4⋊C4—44no—
693C4⋊C4—44no—
694C4⋊C4—44no—
695C4⋊C4—42no—
696C4⋊C4—42no—
697C4⋊C4—42no—
698C4⋊C4—42no—
699C4⋊C4—82no—
700C4⋊C4—81no—
701C4⋊C4—81no—
702C4⋊C4—81no—
703C4⋊C4—81no—
704C4⋊C4—82no—
705C4⋊C4—81no—
706C4⋊C4—81no—
707C4⋊C4C22×Q812yes—
708C4⋊C4C22×Q812yes—
709C4⋊C4C2×#4112yes—
710C4⋊C4C2×#4112yes—
711C4⋊C4C2×#4114yes—
712C22⋊C4—24no—
713C22⋊C4—28no—
714C22⋊C4—28no—
715C22⋊C4—24no—
716C22⋊C4—24no—
717C22⋊C4—42no—
718C22⋊C4—42no—
719C22⋊C4—42no—
720C22⋊C4—42no—
721C22⋊C4—44no—
722C22⋊C4—44no—
723C22⋊C4—42no—
724C22⋊C4—42no—
725C22⋊C4—82no—
726C22⋊C4—82no—
727C42—24no—
728C42—22no—
729C42—22no—
730C42—24no—
731C42—21no—
732C42—21no—
733C42—22no—
734C42—21no—
735C42—21no—
736C42—22no—
737C42—44no—
738C42—44no—
739C42—44no—
740C42—44no—
741C42—42no—
742C42—42no—
743C42—82no—
744C42—82no—
745C23—21no—
746C23—21no—
747C23—21no—
748C23—21no—
749C23—22no—
750C23—22no—
751C23—22no—
752C23—22no—
753C23—22no—
754C23—22no—
755C23C2×C22⋊Q814yes—
756C23C2×C22⋊Q812yes—
757C23#54612yes—
758C23#54612yes—
759C23C23×D411yescharacteristic
760Q8—28no—
761Q8—24no—
762Q8—24no—
763Q8—42no—
764Q8—42no—
765Q8—48no—
766Q8—164no—
767D4—216no—
768D4—28no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—24no—
772C2×C4—24no—
773C2×C4—24no—
774C2×C4—24no—
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—22no—
784C2×C4—22no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—24no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—24no—
799C2×C4—44no—
800C2×C4—44no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—48no—
814C2×C4—41no—
815C2×C4—42no—
816C2×C4—41no—
817C2×C4—42no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—42no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—42no—
826C2×C4—41no—
827C2×C4—42no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—42no—
832C2×C4—84no—
833C2×C4—164no—
834C2×C4—164no—
835C2×C4—162no—
836C2×C4—162no—
837C2×C4C2×C22⋊Q814yes—
838C2×C4C2×C22⋊Q812yes—
839C2×C4#52914yes—
840C2×C4#53814yes—
841C2×C4#54612yes—
842C2×C4#54612yes—
843C2×C4#55414yes—
844C2×C4#55414yes—
845C2×C4C23×Q811yescharacteristic
846C2×C4C22×#4111yescharacteristic
847C2×C4C22×#4111yescharacteristic
848C2×C4C22×#4111yescharacteristic
849C2×C4C2×H(5,𝔽2)11yescharacteristic
850C2×C4C2×H(5,𝔽2)11yescharacteristic
851C8—42no—
852C8—41no—
853C8—41no—
854C8—41no—
855C8—41no—
856C8—42no—
857C22—22no—
858C22—22no—
859C22—22no—
860C22—22no—
861C22—22no—
862C22—22no—
863C22—24no—
864C22—24no—
865C22—24no—
866C22—42no—
867C22—42no—
868C22—42no—
869C22—42no—
870C22#245014yes—
871C22C22×C22⋊Q811yescharacteristic
872C22C2×#54611yescharacteristic
873C22C2×#54611yescharacteristic
874C22#358411yescharacteristic
875C22#358411yescharacteristic
876C22#358611yescharacteristic
877C22#358611yescharacteristic
878C4—24no—
879C4—42no—
880C4—42no—
881C4—42no—
882C4—42no—
883C4—42no—
884C4—42no—
885C4—44no—
886C4—41no—
887C4—41no—
888C4—44no—
889C4—41no—
890C4—41no—
891C4—82no—
892C4—82no—
893C4—81no—
894C4—81no—
895C4—81no—
896C4—81no—
897C4#245014yes—
898C4C2×#52911yescharacteristic
899C4C2×#53811yescharacteristic
900C4C2×#55411yescharacteristic
901C4C2×#55411yescharacteristic
902C2—24no—
903C2—44no—
904C2C2×#245011yescharacteristic
905C2#6049911yescharacteristic
906C2#6049911yescharacteristic
907C2#6116911yescharacteristic
908C2#6117611yescharacteristic
909C2#6120711yescharacteristic
910C2#6120711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×#41C23
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
3. #26435C2semidirect
4. #26433C2semidirect
5. #26430C2semidirect
6. #26428C2semidirect
7. #26418C2semidirect
8. #26416C2semidirect
9. #26415C2semidirect
10. #26413C2semidirect
11. #23746C2semidirect
12. #23666C2semidirect
13. #23613C2semidirect
14. #23457C2semidirect
15. #21315C2semidirect
16. #21035C2semidirect
19. #20874C2semidirect
22. C2×#1805C2semidirect
149. #536Q8semidirect

Maximal subgroups

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

subgroupindex
#356202
#342662
#264352
#264332
#264302
#264282
#264182
#264162
#264152
#264132
#237462
#236662
#236132
#234572
#213152
#210352
#209742
#209132
#208742
#208492
#208382
C2×#18052
#203482