Finite Group Databasebeta

← #7540381

Subgroups — #7540381

Order 512.

1766 conjugacy classes of subgroups.

The subgroup lattice has 899 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59125C211yesmaximal, characteristic
2#36551C211yesmaximal, characteristic, complemented
3#32196C212yesmaximal, complemented
4#31690C212yesmaximal, complemented
5#28706C211yesmaximal, characteristic, complemented
6#27727C211yesmaximal, characteristic, complemented
7#27330C212yesmaximal, complemented
8#26510C211yesmaximal, characteristic, complemented
9#26298C211yesmaximal, characteristic, complemented
10#26202C212yesmaximal, complemented
11#25992C212yesmaximal, complemented
12#25811C211yesmaximal, characteristic, complemented
13#25699C211yesmaximal, characteristic, complemented
14#25451C211yesmaximal, characteristic, complemented
15#25238C212yesmaximal, complemented
16#24935C212yesmaximal, complemented
17#24836C211yesmaximal, characteristic, complemented
18#23156C211yesmaximal, characteristic, complemented
19#22985C211yesmaximal, characteristic, complemented
20#22703C212yesmaximal, complemented
21#22485C211yesmaximal, characteristic, complemented
22C4×#481C211yesmaximal, characteristic, complemented
23C2×#1988C211yesmaximal, characteristic, complemented
24C2×#548—21no—
25C2×#547C2211yescharacteristic
26C22×C4⋊Q8C2211yescharacteristic
27C2×#498C2211yescharacteristic
28C2×#498C2211yescharacteristic
29C2×#481C2211yescharacteristic
30C2×#476C2211yescharacteristic
31C2×C8×D4C2212yes—
32C2×C8×D4C2211yescharacteristic
33C22×C4⋊C8C2211yescharacteristic
34#2857C2211yescharacteristic
35#2851—21no—
36#2674—22no—
37#2589—22no—
38#2563C2211yescharacteristic
39#2552C2211yescharacteristic
40#2547C2211yescharacteristic
41#2542C2211yescharacteristic
42#2509—21no—
43#2497C2212yes—
44#2491C2212yes—
45#2487C2212yes—
46#2454—21no—
47#2450—22no—
48#2443—22no—
49#2440C2212yes—
50#2432—21no—
51#2429—21no—
52#2416C2212yes—
53#2409—21no—
54#2369C2211yescharacteristic
55#2365C2211yescharacteristic
56D4×C4⋊C4C2212yes—
57D4×C4⋊C4C2212yes—
58D4×C4⋊C4C2211yescharacteristic
59#2345C2212yes—
60C4×#121—21no—
61C4×#121C2211yescharacteristic
62C4×#121C2211yescharacteristic
63C2×C4×C4⋊C4C2211yescharacteristic
64#2100C2212yes—
65#2099C2212yes—
66#2088C2212yes—
67#2088C2212yes—
68#2084C2212yes—
69#2077C2212yes—
70#2077C2212yes—
71#2077C2212yes—
72#2077C2212yes—
73#2071C2212yes—
74#2065C2212yes—
75#2065C2212yes—
76#2058C2212yes—
77#2058C2212yes—
78#2034C2212yes—
79#2034C2212yes—
80#1990C2211yescharacteristic
81#1990C2211yescharacteristic
82#1988C2211yescharacteristic
83#1988C2211yescharacteristic
84#1988C2211yescharacteristic
85#1988C2211yescharacteristic
86#1988C2212yes—
87#1988C2212yes—
88#1987C2211yescharacteristic
89#1954C2211yescharacteristic
90#1948C2211yescharacteristic
91#1948C2212yes—
92#1948C2212yes—
93#1941C2212yes—
94#1939C2211yescharacteristic
95#1934C2212yes—
96#1926C2211yescharacteristic
97#1926C2211yescharacteristic
98#1926C2212yes—
99#1923C2212yes—
100#1920C2212yes—
101#1920C2212yes—
102#1919C2211yescharacteristic
103#1919C2211yescharacteristic
104#1919C2212yes—
105#1893C2212yes—
106#1893C2212yes—
107#1874C2211yescharacteristic
108#1874C2212yes—
109#1869C2212yes—
110#1853C2211yescharacteristic
111#1853C2212yes—
112#1853C2212yes—
113#1853C2212yes—
114#1853C2212yes—
115#1853C2212yes—
116#1850C2212yes—
117#1834C2212yes—
118#1824C2211yescharacteristic
119#1824C2212yes—
120#1823C2212yes—
121#1807C2212yes—
122#1807C2212yes—
123#1807C2212yes—
124#1802C2211yescharacteristic
125C4×#106C2211yescharacteristic
126C4×#106C2211yescharacteristic
127C4×#106C2212yes—
128C8×C4⋊C4C2211yescharacteristic
129C4×#102C2211yescharacteristic
130C4×#102C2211yescharacteristic
131C4×C22⋊C8C2211yescharacteristic
132C2×#340C2212yes—
133C2×#340C2212yes—
134C2×#340C2212yes—
135C22×#41—21no—
136C23×Q8—21no—
137C23×C8C2312yes—
138C23×C8C2312yes—
139#548—48no—
140#547—24no—
141#547—42no—
142C2×C4⋊Q8—24no—
143C2×C4⋊Q8—21no—
144C2×C4⋊Q8—21no—
145C2×C4⋊Q8—42no—
146C2×C4⋊Q8C2311yescharacteristic
147C2×C4⋊Q8C2311yescharacteristic
148C2×C4⋊Q8C2312yes—
149C2×C4⋊Q8C2311yescharacteristic
150C2×#125—21no—
151C2×#124—21no—
152C2×#124—22no—
153C2×#123—22no—
154C2×C22⋊Q8—21no—
155C2×C22⋊Q8—21no—
156C2×C22⋊Q8—21no—
157C2×C22⋊Q8—21no—
158C2×C22⋊Q8—22no—
159C2×#121—22no—
160C2×#121D411yescharacteristic
161C2×#121C2311yescharacteristic
162C2×#121C2312yes—
163C2×C4×Q8—21no—
164C2×C4×D4—22no—
165C2×C4×D4—21no—
166C2×C4×D4—22no—
167C2×C4×D4—21no—
168C2×C4×D4C2311yescharacteristic
169C2×C4×D4C2311yescharacteristic
170C2×C4×D4C2312yes—
171C22×C4⋊C4—21no—
172C22×C4⋊C4C2311yescharacteristic
173C22×C4⋊C4C2312yes—
174C22×C4⋊C4C2312yes—
175C22×C4⋊C4C2311yescharacteristic
176C22×C4⋊C4C2312yes—
177C22×C42—21no—
178C22×C42C2311yescharacteristic
179#498—24no—
180#498—42no—
181#481—24no—
182#476—42no—
183C8×D4—28no—
184C8×D4—42no—
185C2×#106C2312yes—
186C2×#106C2312yes—
187C2×#106C2311yescharacteristic
188C2×#106C2311yescharacteristic
189C2×#106C2311yescharacteristic
190C2×#106C2312yes—
191C2×#106C2312yes—
192C2×#106C2311yescharacteristic
193C2×#106C2312yes—
194C2×#106C2312yes—
195C2×C4⋊C8—42no—
196C2×C4⋊C8C2311yescharacteristic
197C2×C4⋊C8C2312yes—
198C2×C4⋊C8C2311yescharacteristic
199C2×C4⋊C8C2312yes—
200C2×#102C2311yescharacteristic
201C2×#102C2311yescharacteristic
202C2×#102C2311yescharacteristic
203C2×#102C2312yes—
204C2×#102C2312yes—
205C2×#102C2311yescharacteristic
206C2×C22⋊C8C2312yes—
207C2×C22⋊C8C2311yescharacteristic
208C2×C22⋊C8C2312yes—
209C2×C22⋊C8C2312yes—
210C2×C22⋊C8C2311yescharacteristic
211C2×C4×C8C2312yes—
212C2×C4×C8C2311yescharacteristic
213C2×C4×C8C2311yescharacteristic
214#400—22no—
215#400—22no—
216#399—22no—
217#399—22no—
218#398—22no—
219#398—22no—
220#397—22no—
221#396—22no—
222#396—22no—
223#395—22no—
224#394—22no—
225#394—22no—
226#393—22no—
227#393—22no—
228#391—21no—
229#391—21no—
230#391—21no—
231#391—22no—
232#390—21no—
233#390D411yescharacteristic
234#390C2311yescharacteristic
235#390C2312yes—
236#389—22no—
237#389—21no—
238#389—21no—
239#389—22no—
240#389—21no—
241#389—21no—
242#389D411yescharacteristic
243#389C2312yes—
244#389C2312yes—
245#389C2311yescharacteristic
246#389C2312yes—
247#389C2312yes—
248#388—22no—
249#388—21no—
250#388—22no—
251#388D412yes—
252#387—22no—
253#387—22no—
254#387—22no—
255#387—22no—
256#386—22no—
257#386—21no—
258#386—22no—
259#386D412yes—
260#385—22no—
261#385—22no—
262#385—22no—
263#385—22no—
264#385—22no—
265#385—22no—
266#385—22no—
267#384C2311yescharacteristic
268#384C2312yes—
269#384C2312yes—
270#382—21no—
271#380—21no—
272#380—22no—
273#380D411yescharacteristic
274#380C2312yes—
275#380C2312yes—
276#380C2311yescharacteristic
277#380C2312yes—
278#380C2312yes—
279#380C2312yes—
280#380C2312yes—
281C4×C4⋊C4—21no—
282C4×C4⋊C4—21no—
283C4×C4⋊C4—21no—
284C4×C4⋊C4C2311yescharacteristic
285C4×C4⋊C4C2311yescharacteristic
286C4×C4⋊C4C2312yes—
287C4×C4⋊C4C2312yes—
288C4×C4⋊C4C2311yescharacteristic
289C4×C4⋊C4C2311yescharacteristic
290C4×C4⋊C4C2311yescharacteristic
291C4×C4⋊C4C2311yescharacteristic
292C4×C22⋊C4—22no—
293C4×C22⋊C4—21no—
294C4×C22⋊C4C2312yes—
295C2×#95—21no—
296#340C2312yes—
297#340C2312yes—
298#340C2312yes—
299#340C2312yes—
300#340C2312yes—
301#340C2312yes—
302#340C2312yes—
303#340C2312yes—
304#340C2312yes—
305#340C2312yes—
306#340C2311yescharacteristic
307#340C2311yescharacteristic
308#340C2311yescharacteristic
309#340C2312yes—
310#340C2311yescharacteristic
311#340C2312yes—
312#340C2311yescharacteristic
313#340C2311yescharacteristic
314#340C2312yes—
315#340C2312yes—
316#340C2311yescharacteristic
317#340C2312yes—
318#340C2311yescharacteristic
319#340C2312yes—
320#336C2311yescharacteristic
321#336C2311yescharacteristic
322#336C2312yes—
323#336C2312yes—
324C2×#41—44no—
325C2×#41—44no—
326C2×#41—82no—
327C22×Q8—21no—
328C22×Q8—21no—
329C22×Q8—22no—
330C22×Q8—21no—
331C22×Q8—44no—
332C22×Q8—44no—
333C22×Q8—82no—
334C22×D4—21no—
335C22×D4—22no—
336C22×D4C2×D412yes—
337C22×D4C2×D411yescharacteristic
338C22×D4C2411yescharacteristic
339C23×C4—22no—
340C23×C4—21no—
341C23×C4—22no—
342C23×C4—22no—
343C23×C4—21no—
344C23×C4—21no—
345C23×C4C2×D411yescharacteristic
346C23×C4C2×D411yescharacteristic
347C23×C4C2412yes—
348C23×C4C2411yescharacteristic
349C22×C8—24no—
350C22×C8—24no—
351C22×C8—42no—
352C22×C8—42no—
353C22×C8—42no—
354C22×C8—42no—
355C22×C8C2412yes—
356C22×C8C2412yes—
357C22×C8C2411yescharacteristic
358C22×C8C2411yescharacteristic
359C22×C8C2411yescharacteristic
360C22×C8C2411yescharacteristic
361C4⋊Q8—24no—
362C4⋊Q8—22no—
363C4⋊Q8—22no—
364C4⋊Q8—22no—
365C4⋊Q8—22no—
366C4⋊Q8—22no—
367C4⋊Q8—42no—
368C4⋊Q8—44no—
369C4⋊Q8—44no—
370C4⋊Q8#4114yes—
371#125—82no—
372#124—44no—
373#124—48no—
374#123—48no—
375C22⋊Q8—44no—
376C22⋊Q8—44no—
377C22⋊Q8—48no—
378C22⋊Q8—82no—
379C22⋊Q8—82no—
380#121—22no—
381#121—22no—
382#121—24no—
383#121—42no—
384#121—48no—
385#121SD1618yes—
386C4×Q8—44no—
387C4×D4—24no—
388C4×D4—24no—
389C4×D4—22no—
390C4×D4—22no—
391C4×D4—22no—
392C4×D4—22no—
393C4×D4—48no—
394C4×D4—44no—
395C4×D4—82no—
396C4×D4—84no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—24no—
401C2×C4⋊C4—24no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—24no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—41no—
424C2×C4⋊C4—42no—
425C2×C4⋊C4—42no—
426C2×C4⋊C4—42no—
427C2×C4⋊C4—44no—
428C2×C4⋊C4C2×D411yescharacteristic
429C2×C4⋊C4C2×D412yes—
430C2×C4⋊C4C2×D411yescharacteristic
431C2×C4⋊C4C2×D411yescharacteristic
432C2×C4⋊C4C2411yescharacteristic
433C2×C4⋊C4C2412yes—
434C2×C4⋊C4C2411yescharacteristic
435C2×C4⋊C4C2411yescharacteristic
436C2×C4⋊C4C2411yescharacteristic
437C2×C4⋊C4C2412yes—
438C2×C4⋊C4C2411yescharacteristic
439C2×C4⋊C4C2412yes—
440C2×C4⋊C4C2411yescharacteristic
441C2×C4⋊C4C2412yes—
442C2×C4⋊C4C2411yescharacteristic
443C2×C22⋊C4—21no—
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—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—22no—
454C2×C22⋊C4—22no—
455C2×C22⋊C4—22no—
456C2×C22⋊C4—22no—
457C2×C22⋊C4C2×D412yes—
458C2×C22⋊C4C2×D412yes—
459C2×C22⋊C4C2×D412yes—
460C2×C22⋊C4C2×D412yes—
461C2×C22⋊C4C2×D412yes—
462C2×C42—22no—
463C2×C42—22no—
464C2×C42—21no—
465C2×C42—22no—
466C2×C42—21no—
467C2×C42—21no—
468C2×C42—22no—
469C2×C42—21no—
470C2×C42—21no—
471C2×C42—82no—
472C2×C42C2×D411yescharacteristic
473C2×C42C2×D411yescharacteristic
474C2×C42C2412yes—
475C2×C42C2411yescharacteristic
476C2×C42C2411yescharacteristic
477#106—22no—
478#106—22no—
479#106—24no—
480#106—24no—
481#106—22no—
482#106—41no—
483#106—42no—
484#106—42no—
485#106—42no—
486#106—42no—
487C4⋊C8—24no—
488C4⋊C8—22no—
489C4⋊C8—22no—
490C4⋊C8—42no—
491#102—22no—
492#102—22no—
493#102—22no—
494#102—41no—
495#102—42no—
496#102—42no—
497C22⋊C8—22no—
498C22⋊C8—24no—
499C22⋊C8—42no—
500C22⋊C8—42no—
501C22⋊C8#4114yescomplemented
502C4×C8—24no—
503C4×C8—22no—
504C4×C8—22no—
505#95—21no—
506#95—21no—
507#95—21no—
508#95—21no—
509#95—22no—
510#95—21no—
511#95—21no—
512#95—22no—
513#95—22no—
514#95—22no—
515#95—22no—
516#95—21no—
517#95—22no—
518#95—22no—
519#95—22no—
520#95—22no—
521#95—22no—
522#95—22no—
523#95—22no—
524#95C2×D412yes—
525#95C2×D412yes—
526#95C2×D412yes—
527C24—21no—
528C24C22×D412yes—
529C24C22×D411yescharacteristic
530#41—816no—
531C2×Q8—24no—
532C2×Q8—44no—
533C2×Q8—42no—
534C2×Q8—42no—
535C2×Q8—42no—
536C2×Q8—44no—
537C2×Q8—42no—
538C2×Q8—42no—
539C2×Q8—42no—
540C2×Q8—82no—
541C2×Q8—81no—
542C2×Q8—81no—
543C2×Q8—816no—
544C2×D4—24no—
545C2×D4—24no—
546C2×D4—22no—
547C2×D4—22no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—44no—
555C2×D4—42no—
556C2×D4—42no—
557C2×D4—44no—
558C2×D4—42no—
559C2×D4—82no—
560C2×D4C2×SD1618yes—
561C2×D4C2×SD1614yes—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—22no—
569C22×C4—21no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—22no—
583C22×C4—21no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—21no—
587C22×C4—41no—
588C22×C4—44no—
589C22×C4—44no—
590C22×C4—42no—
591C22×C4—44no—
592C22×C4—42no—
593C22×C4—44no—
594C22×C4—44no—
595C22×C4—42no—
596C22×C4—42no—
597C22×C4—42no—
598C22×C4—42no—
599C22×C4—81no—
600C22×C4—81no—
601C22×C4—81no—
602C22×C4—82no—
603C22×C4—82no—
604C22×C4—82no—
605C22×C4—82no—
606C22×C4C2×SD1614yes—
607C22×C4C22×D412yes—
608C22×C4C22×D411yescharacteristic
609C22×C4C22×D412yes—
610C22×C4C22×D411yescharacteristic
611C22×C4C22×D411yescharacteristic
612C22×C4C22×D411yescharacteristic
613C22×C4C22×D412yes—
614C22×C4C22×D411yescharacteristic
615C22×C4C2×#4112yes—
616C22×C42−1+412yes—
617C22×C4C2511yescharacteristic
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—22no—
624C2×C8—22no—
625C2×C8—21no—
626C2×C8—22no—
627C2×C8—22no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—22no—
633C2×C8—22no—
634C2×C8—84no—
635C2×C8—84no—
636C2×C8C2×#4112yes—
637C2×C8C2×#4112yes—
638C4⋊C4—24no—
639C4⋊C4—22no—
640C4⋊C4—24no—
641C4⋊C4—22no—
642C4⋊C4—22no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—22no—
648C4⋊C4—21no—
649C4⋊C4—22no—
650C4⋊C4—22no—
651C4⋊C4—21no—
652C4⋊C4—22no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—22no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—22no—
661C4⋊C4—21no—
662C4⋊C4—42no—
663C4⋊C4—44no—
664C4⋊C4—44no—
665C4⋊C4—44no—
666C4⋊C4—44no—
667C4⋊C4—42no—
668C4⋊C4—42no—
669C4⋊C4—42no—
670C4⋊C4—42no—
671C4⋊C4—44no—
672C4⋊C4—44no—
673C4⋊C4—42no—
674C4⋊C4—82no—
675C4⋊C4—82no—
676C4⋊C4—81no—
677C4⋊C4—82no—
678C4⋊C4—82no—
679C4⋊C4—82no—
680C4⋊C4—82no—
681C4⋊C4C2×SD1614yes—
682C4⋊C4C2×#4114yes—
683C4⋊C42−1+412yes—
684C22⋊C4—24no—
685C22⋊C4—24no—
686C22⋊C4—24no—
687C22⋊C4—42no—
688C22⋊C4—44no—
689C22⋊C4—42no—
690C22⋊C4—42no—
691C22⋊C4—44no—
692C22⋊C4—44no—
693C22⋊C4—44no—
694C22⋊C4—42no—
695C22⋊C4—42no—
696C22⋊C4—42no—
697C22⋊C4—44no—
698C22⋊C4—82no—
699C22⋊C4—82no—
700C22⋊C4—82no—
701C22⋊C4—82no—
702C22⋊C4C2×SD1618yes—
703C42—22no—
704C42—22no—
705C42—22no—
706C42—21no—
707C42—21no—
708C42—22no—
709C42—44no—
710C42—42no—
711C42—42no—
712C42—42no—
713C42—81no—
714C42—81no—
715C42—82no—
716C42C2×#4112yes—
717C42H(5,𝔽2)12yes—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23#54712yes—
736C23C22×SD1614yes—
737C23C22×SD1612yes—
738C23#57712yes—
739C23C23×D411yescharacteristic
740Q8—48no—
741Q8—88no—
742Q8—84no—
743Q8—162no—
744D4—216no—
745D4—28no—
746D4—41no—
747D4—41no—
748D4—41no—
749D4—41no—
750D4—88no—
751D4—84no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—22no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—22no—
759C2×C4—21no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—28no—
764C2×C4—22no—
765C2×C4—21no—
766C2×C4—22no—
767C2×C4—21no—
768C2×C4—22no—
769C2×C4—24no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—21no—
776C2×C4—44no—
777C2×C4—42no—
778C2×C4—41no—
779C2×C4—42no—
780C2×C4—41no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—42no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—42no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—42no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—41no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—84no—
813C2×C4—88no—
814C2×C4—88no—
815C2×C4—84no—
816C2×C4—84no—
817C2×C4—164no—
818C2×C4#54612yes—
819C2×C4#54612yes—
820C2×C4#54712yes—
821C2×C4C22×SD1614yes—
822C2×C4C22×SD1612yes—
823C2×C4C22×SD1612yes—
824C2×C4#57612yes—
825C2×C4C22×#4111yescharacteristic
826C2×C4C22×#4111yescharacteristic
827C2×C4C2×H(5,𝔽2)11yescharacteristic
828C2×C4C2×2−1+411yescharacteristic
829C2×C4C2×2−1+411yescharacteristic
830C2×C4#58511yescharacteristic
831C8—22no—
832C8—22no—
833C8—42no—
834C8—42no—
835C8—41no—
836C8—41no—
837C22—22no—
838C22—22no—
839C22—22no—
840C22—22no—
841C22—22no—
842C22—22no—
843C22—24no—
844C22—24no—
845C22—24no—
846C22—42no—
847C22—42no—
848C22—42no—
849C22—42no—
850C22—81no—
851C22—81no—
852C22—81no—
853C22—81no—
854C22—81no—
855C22—81no—
856C22—81no—
857C22#333514yes—
858C22C2×#54611yescharacteristic
859C22C2×#54711yescharacteristic
860C22#348911yescharacteristic
861C22C23×SD1611yescharacteristic
862C22C2×#57611yescharacteristic
863C22C2×#57711yescharacteristic
864C22#358611yescharacteristic
865C4—22no—
866C4—24no—
867C4—22no—
868C4—22no—
869C4—41no—
870C4—42no—
871C4—42no—
872C4—44no—
873C4—42no—
874C4—82no—
875C4—81no—
876C4—81no—
877C4—81no—
878C4—81no—
879C4—81no—
880C4—82no—
881C4—81no—
882C4—82no—
883C4#329514yes—
884C4#348211yescharacteristic
885C4#351411yescharacteristic
886C4#351611yescharacteristic
887C4#355211yescharacteristic
888C2—24no—
889C2—44no—
890C2—161no—
891C2#5906111yescharacteristic
892C2C2×#329511yescharacteristic
893C2#6118511yescharacteristic
894C2C2×#333511yescharacteristic
895C2#6127811yescharacteristic
896C2#6209911yescharacteristic
897C2#6219911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#59125C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#121 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #36551C2semidirect
3. #32196C2semidirect
4. #31690C2semidirect
5. #28706C2semidirect
6. #27727C2semidirect
7. #27330C2semidirect
8. #26510C2semidirect
9. #26298C2semidirect
10. #26202C2semidirect
11. #25992C2semidirect
12. #25811C2semidirect
13. #25699C2semidirect
14. #25451C2semidirect
15. #25238C2semidirect
16. #24935C2semidirect
17. #24836C2semidirect
18. #23156C2semidirect
19. #22985C2semidirect
20. #22703C2semidirect
21. #22485C2semidirect
22. C4×#481C2semidirect
23. C2×#1988C2semidirect
501. C22⋊C8#41semidirect

Maximal subgroups

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

subgroupindex
#591252
#365512
#321962
#316902
#287062
#277272
#273302
#265102
#262982
#262022
#259922
#258112
#256992
#254512
#252382
#249352
#248362
#231562
#229852
#227032
#224852
C4×#4812
C2×#19882