Finite Group Databasebeta

← #6482063

Subgroups — #6482063

Order 512.

1724 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#37634C211yesmaximal, characteristic
2#34206C211yesmaximal, characteristic
3#32989C212yesmaximal, complemented
4#32988C212yesmaximal, complemented
5#29901C212yesmaximal, complemented
6#29900C212yesmaximal, complemented
7#26302C211yesmaximal, characteristic, complemented
8#26300C211yesmaximal, characteristic, complemented
9#26299C211yesmaximal, characteristic, complemented
10#26297C211yesmaximal, characteristic, complemented
11#26236C211yesmaximal, characteristic, complemented
12#26234C211yesmaximal, characteristic, complemented
13#26233C211yesmaximal, characteristic, complemented
14#26231C211yesmaximal, characteristic, complemented
15#25021C212yesmaximal, complemented
16#25020C212yesmaximal, complemented
17#24976C212yesmaximal, complemented
18#24975C212yesmaximal, complemented
19#21985C211yesmaximal, characteristic, complemented
20#21864C211yesmaximal, characteristic, complemented
21#21787C211yesmaximal, characteristic
22#21385C211yesmaximal, characteristic, complemented
23#21361C211yesmaximal, characteristic, complemented
24C2×#533C2211yescharacteristic
25C2×#532C2211yescharacteristic
26C2×#520C2212yes—
27C2×#484C2212yes—
28C2×#485C2212yes—
29C2×#485C2212yes—
30C2×#483C2212yes—
31C2×#431C2211yescharacteristic
32C2×#431C2211yescharacteristic
33#2816—22no—
34#2660—21no—
35#2641—21no—
36#2632—22no—
37#2616C2212yes—
38#2616C2212yes—
39#2563C2211yescharacteristic
40#2563C2211yescharacteristic
41#2542C2211yescharacteristic
42#2542C2211yescharacteristic
43#2536C2212yes—
44#2536C2212yes—
45#2500—21no—
46#2500—21no—
47#2367—22no—
48#2366—21no—
49#2365—21no—
50#2354C2211yescharacteristic
51#2354C2211yescharacteristic
52#2352C2212yes—
53#2352C2212yes—
54D4×C4⋊C4C2211yescharacteristic
55D4×C4⋊C4C2211yescharacteristic
56#2325—22no—
57#2311C2212yes—
58C4×#121—21no—
59C4×#121—21no—
60#2285C2211yescharacteristic
61#2283C2211yescharacteristic
62C2×C4×C4⋊C4C2211yescharacteristic
63#2077C2212yes—
64#2077C2212yes—
65#2077C2212yes—
66#2077C2212yes—
67#2076C2212yes—
68#2076C2212yes—
69#2075C2212yes—
70#2075C2212yes—
71#2036C2212yes—
72#2036C2212yes—
73#2036C2212yes—
74#2036C2212yes—
75#2035C2212yes—
76#2035C2212yes—
77#2035C2212yes—
78#2035C2212yes—
79#1990C2211yescharacteristic
80#1990C2211yescharacteristic
81#1987C2211yescharacteristic
82#1987C2211yescharacteristic
83#1981C2211yescharacteristic
84#1981C2211yescharacteristic
85#1956C2211yescharacteristic
86#1956C2211yescharacteristic
87#1954C2211yescharacteristic
88#1954C2211yescharacteristic
89#1954C2211yescharacteristic
90#1954C2211yescharacteristic
91#1954C2212yes—
92#1954C2212yes—
93#1949C2211yescharacteristic
94#1949C2211yescharacteristic
95#1949C2211yescharacteristic
96#1949C2211yescharacteristic
97#1948C2211yescharacteristic
98#1948C2211yescharacteristic
99#1947C2211yescharacteristic
100#1947C2211yescharacteristic
101#1873C2212yes—
102#1873C2212yes—
103#1873C2212yes—
104#1873C2212yes—
105#1872C2212yes—
106#1872C2212yes—
107#1872C2212yes—
108#1872C2212yes—
109#1854C2212yes—
110#1854C2212yes—
111#1854C2212yes—
112#1854C2212yes—
113#1853C2211yescharacteristic
114#1853C2211yescharacteristic
115#1853C2212yes—
116#1852C2211yescharacteristic
117#1852C2211yescharacteristic
118#1852C2212yes—
119#1846C2212yes—
120#1835C2212yes—
121#1825C2212yes—
122#1825C2212yes—
123#1824C2212yes—
124#1823C2212yes—
125#1805C2212yes—
126#1805C2212yes—
127#1780C2212yes—
128#1780C2212yes—
129C4×#107C2211yescharacteristic
130C4×#107C2211yescharacteristic
131C4×#106C2211yescharacteristic
132C4×#106C2211yescharacteristic
133C4×#103C2212yes—
134C4×#103C2212yes—
135C22×#41C2312yes—
136#533—24no—
137#533—24no—
138#532—24no—
139#532—24no—
140C2×C4⋊Q8D411yescharacteristic
141C2×C4⋊Q8C2311yescharacteristic
142C2×C4⋊Q8C2311yescharacteristic
143C2×#127D411yescharacteristic
144C2×#125—21no—
145C2×#124D412yes—
146C2×C22⋊Q8—21no—
147C2×C22⋊Q8C2312yes—
148C2×C22⋊Q8C2312yes—
149C2×C22⋊Q8C2312yes—
150C2×C22⋊Q8C2312yes—
151C2×C22⋊Q8C2312yes—
152C2×#121D412yes—
153C2×#121D411yescharacteristic
154C2×#121D411yescharacteristic
155#520—44no—
156#520—44no—
157C2×C4×Q8—22no—
158C2×C4×Q8—21no—
159C2×C4×Q8C2312yes—
160C2×C4×D4—22no—
161C2×C4×D4—22no—
162C2×C4×D4—22no—
163C2×C4×D4—21no—
164C2×C4×D4—21no—
165C2×C4×D4C2311yescharacteristic
166C2×C4×D4C2311yescharacteristic
167C2×C4×D4C2312yes—
168C2×#117—21no—
169C2×#117C2312yes—
170C2×#117C2312yes—
171C2×#117C2312yes—
172C22×C4⋊C4C2311yescharacteristic
173C22×C4⋊C4C2312yes—
174C22×C4⋊C4C2312yes—
175C22×C4⋊C4C2311yescharacteristic
176C22×C42—21no—
177C22×C42C2311yescharacteristic
178#485—44no—
179#485—44no—
180#484—44no—
181#483—44no—
182#431—24no—
183#431—24no—
184C2×#107C2311yescharacteristic
185C2×#107C2311yescharacteristic
186C2×#107C2312yes—
187C2×#107C2312yes—
188C2×#107C2311yescharacteristic
189C2×#107C2311yescharacteristic
190C2×#106C2311yescharacteristic
191C2×#106C2311yescharacteristic
192C2×#106C2312yes—
193C2×#106C2312yes—
194C2×#106C2311yescharacteristic
195C2×#106C2311yescharacteristic
196C2×C4⋊C8C2311yescharacteristic
197C2×C4⋊C8C2311yescharacteristic
198C2×C4⋊C8C2311yescharacteristic
199C2×C4⋊C8C2311yescharacteristic
200C2×#103C2312yes—
201C2×#103C2312yes—
202C2×#103C2312yes—
203C2×#103C2312yes—
204C2×#103C2312yes—
205C2×#103C2312yes—
206C2×#103C2312yes—
207C2×#103C2312yes—
208C2×C22⋊C8C2311yescharacteristic
209C2×C22⋊C8C2311yescharacteristic
210C2×C22⋊C8C2312yes—
211C2×C22⋊C8C2312yes—
212C2×C22⋊C8C2312yes—
213C2×C22⋊C8C2312yes—
214C2×C22⋊C8C2312yes—
215C2×C22⋊C8C2312yes—
216C2×C22⋊C8C2312yes—
217C2×C22⋊C8C2312yes—
218C2×C22⋊C8C2312yes—
219C2×C4×C8C2312yes—
220C2×C4×C8C2311yescharacteristic
221C2×C4×C8C2311yescharacteristic
222#399—22no—
223#399—22no—
224#398—22no—
225#398—22no—
226#395—22no—
227#395—22no—
228#394—22no—
229#394—22no—
230#394—22no—
231#394—22no—
232#394—22no—
233#394—22no—
234#394—22no—
235#394—22no—
236#393—22no—
237#393—22no—
238#391—22no—
239#390—21no—
240#390—21no—
241#390—22no—
242#390—21no—
243#390—21no—
244#390—21no—
245#390—21no—
246#389—21no—
247#389—21no—
248#388—22no—
249#388—22no—
250#388—22no—
251#388—22no—
252#388—22no—
253#388—22no—
254#388—22no—
255#388—22no—
256#387—22no—
257#387—22no—
258#386—22no—
259#386—22no—
260#386—22no—
261#386—22no—
262#385—22no—
263#385—22no—
264#384—21no—
265#384—21no—
266#384C2311yescharacteristic
267#384C2311yescharacteristic
268#383—21no—
269#382—21no—
270#382—21no—
271#382C2312yes—
272#382C2311yescharacteristic
273#382C2311yescharacteristic
274#381—21no—
275#380—21no—
276#380—21no—
277#380C2312yes—
278#380C2312yes—
279#380C2312yes—
280#380C2312yes—
281#380C2312yes—
282#380C2312yes—
283#380C2312yes—
284#380C2312yes—
285#380C2311yescharacteristic
286#380C2311yescharacteristic
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⋊C4C2311yescharacteristic
294C4×C4⋊C4C2311yescharacteristic
295C4×C4⋊C4C2311yescharacteristic
296C4×C4⋊C4C2311yescharacteristic
297C4×C4⋊C4C2311yescharacteristic
298C4×C4⋊C4C2311yescharacteristic
299C4×C22⋊C4—21no—
300C4×C22⋊C4—22no—
301C4×C22⋊C4—22no—
302#376—21no—
303C2×#95—21no—
304#340C2312yes—
305#340C2312yes—
306#340C2312yes—
307#340C2312yes—
308#340C2311yescharacteristic
309#340C2312yes—
310#340C2312yes—
311#340C2312yes—
312#340C2311yescharacteristic
313#340C2312yes—
314#340C2311yescharacteristic
315#340C2311yescharacteristic
316#340C2312yes—
317#340C2312yes—
318#340C2311yescharacteristic
319#340C2312yes—
320#340C2311yescharacteristic
321#340C2312yes—
322#340C2311yescharacteristic
323#340C2311yescharacteristic
324C2×#41—24no—
325C2×#41—24no—
326C2×#41—42no—
327C2×#41—42no—
328C2×#41—42no—
329C2×#41—42no—
330C22×Q8—21no—
331C22×Q8C2×D412yes—
332C22×Q8C2412yes—
333C22×D4C2×D411yescharacteristic
334C22×D4C2×D411yescharacteristic
335C22×D4C2×D412yes—
336C22×D4C2×D412yes—
337C22×D4C2×D412yes—
338C22×D4C2×D412yes—
339C23×C4—21no—
340C23×C4—22no—
341C23×C4—22no—
342C23×C4—21no—
343C23×C4C2×D411yescharacteristic
344C23×C4C2×D411yescharacteristic
345C23×C4C2412yes—
346C23×C4C2412yes—
347C23×C4C2411yescharacteristic
348C22×C8C2412yes—
349C22×C8C2411yescharacteristic
350C22×C8C2411yescharacteristic
351C22×C8C2412yes—
352C22×C8C2411yescharacteristic
353C22×C8C2411yescharacteristic
354C4⋊Q8—24no—
355C4⋊Q8—22no—
356C4⋊Q8—22no—
357C4⋊Q8—22no—
358C4⋊Q8—22no—
359#127—24no—
360#125—44no—
361#124—28no—
362C22⋊Q8—24no—
363C22⋊Q8—24no—
364C22⋊Q8—44no—
365C22⋊Q8—42no—
366C22⋊Q8—42no—
367C22⋊Q8—42no—
368C22⋊Q8—42no—
369C22⋊Q8—42no—
370C22⋊Q8—42no—
371C22⋊Q8—42no—
372C22⋊Q8—42no—
373#121—24no—
374#121—24no—
375#121—28no—
376C4×Q8—24no—
377C4×Q8—24no—
378C4×Q8—48no—
379C4×Q8—44no—
380C4×D4—24no—
381C4×D4—22no—
382C4×D4—22no—
383C4×D4—24no—
384C4×D4—22no—
385C4×D4—22no—
386C4×D4—48no—
387C4×D4—48no—
388C4×D4—48no—
389C4×D4—82no—
390C4×D4—82no—
391#117—24no—
392#117—24no—
393#117—42no—
394#117—42no—
395#117—42no—
396#117—42no—
397#117—44no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—24no—
402C2×C4⋊C4—24no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—41no—
420C2×C4⋊C4—41no—
421C2×C4⋊C4—42no—
422C2×C4⋊C4—42no—
423C2×C4⋊C4C2×D411yescharacteristic
424C2×C4⋊C4C2×D411yescharacteristic
425C2×C4⋊C4C2×D412yes—
426C2×C4⋊C4C2412yes—
427C2×C4⋊C4C2411yescharacteristic
428C2×C4⋊C4C2411yescharacteristic
429C2×C4⋊C4C2412yes—
430C2×C4⋊C4C2412yes—
431C2×C4⋊C4C2411yescharacteristic
432C2×C4⋊C4C2411yescharacteristic
433C2×C4⋊C4C2411yescharacteristic
434C2×C4⋊C4C2411yescharacteristic
435C2×C4⋊C4C2411yescharacteristic
436C2×C4⋊C4C2411yescharacteristic
437C2×C22⋊C4—22no—
438C2×C22⋊C4—22no—
439C2×C22⋊C4—22no—
440C2×C22⋊C4—22no—
441C2×C22⋊C4—22no—
442C2×C22⋊C4—22no—
443C2×C22⋊C4—22no—
444C2×C22⋊C4—22no—
445C2×C22⋊C4—22no—
446C2×C22⋊C4—22no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—22no—
450C2×C22⋊C4—22no—
451C2×C22⋊C4—22no—
452C2×C22⋊C4—22no—
453C2×C22⋊C4—22no—
454C2×C22⋊C4—22no—
455C2×C22⋊C4C2×D412yes—
456C2×C22⋊C4C2×D412yes—
457C2×C22⋊C4C2×D412yes—
458C2×C22⋊C4C2×D412yes—
459C2×C42—22no—
460C2×C42—22no—
461C2×C42—22no—
462C2×C42—22no—
463C2×C42—21no—
464C2×C42—21no—
465C2×C42—21no—
466C2×C42—21no—
467C2×C42—21no—
468C2×C42—21no—
469C2×C42—82no—
470C2×C42C2×D411yescharacteristic
471C2×C42C2×D411yescharacteristic
472C2×C42#4114yes—
473C2×C42#4114yes—
474C2×C42C2411yescharacteristic
475C2×C42C2411yescharacteristic
476#107—22no—
477#107—22no—
478#107—41no—
479#107—41no—
480#107—42no—
481#107—42no—
482#106—22no—
483#106—22no—
484#106—41no—
485#106—41no—
486#106—42no—
487#106—42no—
488C4⋊C8—22no—
489C4⋊C8—22no—
490C4⋊C8—22no—
491C4⋊C8—22no—
492#103—24no—
493#103—24no—
494#103—42no—
495#103—42no—
496#103—42no—
497#103—42no—
498#103—42no—
499#103—42no—
500C22⋊C8—22no—
501C22⋊C8—22no—
502C22⋊C8—24no—
503C22⋊C8—42no—
504C22⋊C8—42no—
505C22⋊C8—42no—
506C22⋊C8—42no—
507C22⋊C8—42no—
508C22⋊C8—42no—
509C22⋊C8—42no—
510C22⋊C8—42no—
511C4×C8—24no—
512C4×C8—22no—
513C4×C8—22no—
514#95—21no—
515#95—21no—
516#95—21no—
517#95—21no—
518#95—21no—
519#95—21no—
520#95—21no—
521#95—21no—
522#95—22no—
523#95—22no—
524#95—22no—
525#95—21no—
526#95—21no—
527#95—22no—
528#95—22no—
529#95—22no—
530#95—21no—
531#95—21no—
532#95—22no—
533#95—22no—
534#95—22no—
535#95—22no—
536C24C22×D412yes—
537C24C22×D412yes—
538C24C22×D411yescharacteristic
539#41—48no—
540#41—48no—
541#41—48no—
542#41—48no—
543C2×Q8—24no—
544C2×Q8—22no—
545C2×Q8—22no—
546C2×Q8—22no—
547C2×Q8—22no—
548C2×Q8—22no—
549C2×Q8—22no—
550C2×Q8—42no—
551C2×Q8—42no—
552C2×Q8—42no—
553C2×Q8—81no—
554C2×Q8—81no—
555C2×D4—24no—
556C2×D4—24no—
557C2×D4—22no—
558C2×D4—22no—
559C2×D4—24no—
560C2×D4—24no—
561C2×D4—22no—
562C2×D4—22no—
563C2×D4—22no—
564C2×D4—22no—
565C2×D4—42no—
566C2×D4—42no—
567C2×D4—42no—
568C2×D4—42no—
569C2×D4—42no—
570C2×D4—42no—
571C2×D4—42no—
572C2×D4—42no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—24no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—41no—
605C22×C4—41no—
606C22×C4—44no—
607C22×C4—44no—
608C22×C4—42no—
609C22×C4—81no—
610C22×C4—81no—
611C22×C4—81no—
612C22×C4—81no—
613C22×C4—82no—
614C22×C4—82no—
615C22×C4—82no—
616C22×C4—82no—
617C22×C4#12314yes—
618C22×C4#12314yes—
619C22×C4C22×D412yes—
620C22×C4C22×D412yes—
621C22×C4C22×D411yescharacteristic
622C22×C4C22×D411yescharacteristic
623C22×C4C22×D411yescharacteristic
624C22×C4C22×D411yescharacteristic
625C22×C4C22×D411yescharacteristic
626C22×C4C2×#4112yes—
627C22×C4C2×#4112yes—
628C22×C4C2511yescharacteristic
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—22no—
634C2×C8—22no—
635C2×C8—22no—
636C2×C8—22no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—22no—
642C2×C8—22no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C4⋊C4—24no—
648C4⋊C4—24no—
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—21no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—44no—
672C4⋊C4—44no—
673C4⋊C4—42no—
674C4⋊C4—42no—
675C4⋊C4—42no—
676C4⋊C4—44no—
677C4⋊C4—44no—
678C4⋊C4—42no—
679C4⋊C4—42no—
680C4⋊C4—42no—
681C4⋊C4—81no—
682C4⋊C4—81no—
683C4⋊C4—82no—
684C4⋊C4—82no—
685C4⋊C4—82no—
686C4⋊C4—82no—
687C4⋊C4H(5,𝔽2)12yes—
688C4⋊C4H(5,𝔽2)12yes—
689C22⋊C4—24no—
690C22⋊C4—24no—
691C22⋊C4—24no—
692C22⋊C4—24no—
693C22⋊C4—44no—
694C22⋊C4—44no—
695C22⋊C4—44no—
696C22⋊C4—44no—
697C22⋊C4—81no—
698C22⋊C4—81no—
699C22⋊C4—82no—
700C22⋊C4—82no—
701C22⋊C4—82no—
702C22⋊C4—82no—
703C22⋊C4—82no—
704C22⋊C4—82no—
705C22⋊C4—82no—
706C22⋊C4—82no—
707C22⋊C4—82no—
708C22⋊C4—82no—
709C22⋊C4—82no—
710C22⋊C4—82no—
711C42—44no—
712C42—44no—
713C42—44no—
714C42—44no—
715C42—42no—
716C42—42no—
717C42—42no—
718C42—42no—
719C42—81no—
720C42—81no—
721C42#12314yes—
722C42#12314yes—
723C42C2×#4112yes—
724C42C2×#4112yes—
725C42C2×#4112yes—
726C42C2×#4112yes—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—22no—
734C23—22no—
735C23—22no—
736C23—22no—
737C23—22no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23C2×#12312yes—
748C23C23×D411yescharacteristic
749Q8—48no—
750Q8—42no—
751Q8—42no—
752Q8—42no—
753Q8—42no—
754Q8—84no—
755D4—48no—
756D4—48no—
757D4—48no—
758D4—44no—
759D4—44no—
760D4—84no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—28no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—44no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—42no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—42no—
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—42no—
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—42no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—42no—
825C2×C4—84no—
826C2×C4—84no—
827C2×C4—164no—
828C2×C4—164no—
829C2×C4C2×#12312yes—
830C2×C4C2×#12312yes—
831C2×C4C2×#12312yes—
832C2×C4C2×#12312yes—
833C2×C4C2×#12312yes—
834C2×C4#57712yes—
835C2×C4#57812yes—
836C2×C4C22×#4111yescharacteristic
837C2×C4C22×#4111yescharacteristic
838C2×C4C2×H(5,𝔽2)11yescharacteristic
839C2×C4C2×H(5,𝔽2)11yescharacteristic
840C2×C4#58511yescharacteristic
841C2×C4#58511yescharacteristic
842C8—41no—
843C8—41no—
844C8—41no—
845C8—41no—
846C8—42no—
847C8—42no—
848C22—22no—
849C22—22no—
850C22—22no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—42no—
856C22—42no—
857C22—42no—
858C22—42no—
859C22—42no—
860C22—42no—
861C22—42no—
862C22—42no—
863C22—42no—
864C22—42no—
865C22—42no—
866C22—42no—
867C22—42no—
868C22—42no—
869C22C22×#12311yescharacteristic
870C22#348411yescharacteristic
871C22#348511yescharacteristic
872C22C2×#57711yescharacteristic
873C22C2×#57811yescharacteristic
874C22#358411yescharacteristic
875C22#358411yescharacteristic
876C4—22no—
877C4—22no—
878C4—22no—
879C4—22no—
880C4—42no—
881C4—42no—
882C4—42no—
883C4—42no—
884C4—82no—
885C4—81no—
886C4—81no—
887C4—81no—
888C4—81no—
889C4—82no—
890C4—81no—
891C4—82no—
892C4—81no—
893C4—82no—
894C4#309714yes—
895C4#346011yescharacteristic
896C4#346011yescharacteristic
897C4#350611yescharacteristic
898C4#350611yescharacteristic
899C2—42no—
900C2—82no—
901C2—82no—
902C2#3515211yescharacteristic
903C2C2×#309711yescharacteristic
904C2#6051611yescharacteristic
905C2#6165811yescharacteristic
906C2#6166011yescharacteristic
907C2#6178511yescharacteristic
908C2#6178711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#532C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×#532 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #32989C2semidirect
4. #32988C2semidirect
5. #29901C2semidirect
6. #29900C2semidirect
7. #26302C2semidirect
8. #26300C2semidirect
9. #26299C2semidirect
10. #26297C2semidirect
11. #26236C2semidirect
12. #26234C2semidirect
13. #26233C2semidirect
14. #26231C2semidirect
15. #25021C2semidirect
16. #25020C2semidirect
17. #24976C2semidirect
18. #24975C2semidirect
19. #21985C2semidirect
20. #21864C2semidirect
22. #21385C2semidirect
23. #21361C2semidirect

Maximal subgroups

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

subgroupindex
#376342
#342062
#329892
#329882
#299012
#299002
#263022
#263002
#262992
#262972
#262362
#262342
#262332
#262312
#250212
#250202
#249762
#249752
#219852
#218642
#217872
#213852
#213612