Finite Group Databasebeta

← #6444912

Subgroups — #6444912

Order 512.

2031 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
1C2×#3177C211yesmaximal, characteristic, complemented
2C22×C4×Q16C211yesmaximal, characteristic, complemented
3#35244C212yesmaximal
4#27268C212yesmaximal, complemented
5#26972C212yesmaximal, complemented
6#26831C212yesmaximal, complemented
7#26483C211yesmaximal, characteristic, complemented
8#26255C211yesmaximal, characteristic, complemented
9#26067C211yesmaximal, characteristic, complemented
10#25780C211yesmaximal, characteristic, complemented
11#25415C211yesmaximal, characteristic, complemented
12#25126C212yesmaximal
13#25033C211yesmaximal, characteristic, complemented
14#24781C211yesmaximal, characteristic
15#24268C211yesmaximal, characteristic
16#23691C212yesmaximal, complemented
17#23586C212yesmaximal, complemented
18#21698C211yesmaximal, characteristic, complemented
19#21525C211yesmaximal, characteristic, complemented
20C4×#467C211yesmaximal, characteristic, complemented
21#21455C212yesmaximal, complemented
22#21281C211yesmaximal, characteristic, complemented
23#20484C211yesmaximal, characteristic
24C23×Q16C2211yescharacteristic
25C2×#541C2212yes—
26C22×C4×Q8C2212yes—
27#3177—28no—
28C2×#499C2211yescharacteristic
29C2×#494C2211yescharacteristic
30C2×#494C2211yescharacteristic
31C2×#491C2212yes—
32C2×#470C2212yes—
33C2×#467C2211yescharacteristic
34C2×#467C2211yescharacteristic
35C2×#467C2211yescharacteristic
36C2×#467C2211yescharacteristic
37C2×#451C2212yes—
38C2×#441C2212yes—
39C2×#441C2212yes—
40C2×C4×Q16—28no—
41C2×C4×Q16C2211yescharacteristic
42C2×C4×Q16C2211yescharacteristic
43C2×C4×Q16C2212yes—
44C2×C4×Q16C2211yescharacteristic
45C2×C4×Q16C2212yes—
46C2×C4×Q16C2211yescharacteristic
47C2×C4×Q16C2211yescharacteristic
48C2×#435C2211yescharacteristic
49C2×C8×D4C2211yescharacteristic
50C22×#107C2211yescharacteristic
51C22×#103C2212yes—
52C2×#405C2211yescharacteristic
53C22×C4×C8C2211yescharacteristic
54#2852—22no—
55#2851—22no—
56#2637—22no—
57#2634—22no—
58#2481—22no—
59#2473—22no—
60#2469—22no—
61#2462—22no—
62#2453C2212yes—
63#2446C2212yes—
64#2442C2212yes—
65#2434C2212yes—
66#2429C2212yes—
67#2421C2212yes—
68#2417C2212yes—
69#2409C2212yes—
70#2327C2212yes—
71#2323C2212yes—
72#2320C2212yes—
73C4×C22⋊Q8C2212yes—
74#2290C2211yescharacteristic
75#2085C2212yes—
76#2074C2212yes—
77#2068C2212yes—
78#2066C2212yes—
79#2059C2212yes—
80#2056C2212yes—
81#2056C2212yes—
82#2043C2212yes—
83#2043C2212yes—
84#2036C2212yes—
85#2035C2212yes—
86#2026C2212yes—
87#2016C2212yes—
88#2016C2212yes—
89#2001C2212yes—
90#2001C2212yes—
91#1971C2212yes—
92#1969C2211yescharacteristic
93#1969C2211yescharacteristic
94#1969C2211yescharacteristic
95#1969C2211yescharacteristic
96#1969C2211yescharacteristic
97#1969C2211yescharacteristic
98#1960C2212yes—
99#1942C2211yescharacteristic
100#1942C2211yescharacteristic
101#1942C2211yescharacteristic
102#1942C2211yescharacteristic
103#1935C2212yes—
104#1935C2212yes—
105#1935C2212yes—
106#1933C2212yes—
107#1894C2212yes—
108#1892C2212yes—
109#1878C2212yes—
110#1878C2212yes—
111#1872C2212yes—
112#1865C2212yes—
113#1865C2212yes—
114#1853C2212yes—
115#1846C2211yescharacteristic
116#1808C2211yescharacteristic
117#1808C2211yescharacteristic
118#1787C2212yes—
119C4×#107C2211yescharacteristic
120#1771C2211yescharacteristic
121C8×C4⋊C4C2211yescharacteristic
122#1768C2211yescharacteristic
123#1763C2212yes—
124#1763C2212yes—
125C4×#103C2212yes—
126#1753C2211yescharacteristic
127#1752C2211yescharacteristic
128C8×C22⋊C4C2211yescharacteristic
129C8×C22⋊C4C2211yescharacteristic
130#1750C2211yescharacteristic
131#1749C2211yescharacteristic
132#1726C2211yescharacteristic
133C23×Q8C2312yes—
134C22×Q16—24no—
135C22×Q16—24no—
136C22×Q16—24no—
137C22×Q16C2312yes—
138C22×Q16C2311yescharacteristic
139C22×Q16C2312yes—
140C22×Q16C2312yes—
141C22×Q16C2311yescharacteristic
142C22×Q16C2311yescharacteristic
143C22×M16C2311yescharacteristic
144C23×C8C2311yescharacteristic
145C23×C8C2311yescharacteristic
146C23×C8C2311yescharacteristic
147#541—28no—
148#541—44no—
149C2×C4⋊Q8C2312yes—
150C2×C4⋊Q8C2312yes—
151C2×#126—22no—
152C2×#126—22no—
153C2×#125—22no—
154C2×#125—22no—
155C2×#125C2312yes—
156C2×C22⋊Q8C2312yes—
157C2×C22⋊Q8C2312yes—
158C2×C22⋊Q8C2312yes—
159C2×C22⋊Q8C2312yes—
160C2×C4×Q8—22no—
161C2×C4×Q8—22no—
162C2×C4×Q8—28no—
163C2×C4×Q8—44no—
164C2×C4×Q8C2312yes—
165C2×C4×Q8C2312yes—
166C2×C4×Q8C2312yes—
167C2×C4×Q8C2312yes—
168C2×C4×Q8C2312yes—
169C2×C4×D4C2311yescharacteristic
170C2×#117C2311yescharacteristic
171C22×C4⋊C4—22no—
172C22×C4⋊C4C2312yes—
173C22×C42—22no—
174C22×C42C2311yescharacteristic
175#499—24no—
176#494—24no—
177#494—24no—
178#491—28no—
179#470—28no—
180#467—24no—
181#467—24no—
182#467—24no—
183#467—24no—
184#451—28no—
185#441—28no—
186#441—44no—
187C4×Q16—24no—
188C4×Q16—28no—
189C4×Q16—24no—
190C4×Q16—28no—
191C4×Q16—24no—
192C4×Q16—24no—
193C4×Q16D418yescomplemented
194#435—24no—
195C8×D4—24no—
196C2×#107—24no—
197C2×#107C2312yes—
198C2×#107C2311yescharacteristic
199C2×#107C2311yescharacteristic
200C2×#107C2311yescharacteristic
201C2×#107C2311yescharacteristic
202C2×#107C2311yescharacteristic
203C2×#106C2312yes—
204C2×#106C2312yes—
205C2×C4⋊C8C2311yescharacteristic
206C2×C4⋊C8C2311yescharacteristic
207C2×#103—28no—
208C2×#103C2312yes—
209C2×#103C2312yes—
210C2×#103C2312yes—
211C2×#103C2312yes—
212C2×#103C2312yes—
213C2×#103C2312yes—
214C2×#103C2312yes—
215C2×#103C2312yes—
216C2×#103C2312yes—
217C2×#103C2312yes—
218C2×#103C2312yes—
219C2×#103C2312yes—
220C2×#103C2312yes—
221C2×#103C2312yes—
222C2×#103C2312yes—
223C2×C22⋊C8C2311yescharacteristic
224C2×C22⋊C8C2311yescharacteristic
225C2×C22⋊C8C2311yescharacteristic
226C2×C22⋊C8C2311yescharacteristic
227#405—24no—
228C2×#97C2311yescharacteristic
229C2×#97C2311yescharacteristic
230C2×#97C2311yescharacteristic
231C2×#97C2311yescharacteristic
232C2×#97C2311yescharacteristic
233C2×C4×C8—24no—
234C2×C4×C8C2311yescharacteristic
235C2×C4×C8C2311yescharacteristic
236C2×C4×C8C2311yescharacteristic
237C2×C4×C8C2311yescharacteristic
238C2×C4×C8C2311yescharacteristic
239C2×C4×C8C2311yescharacteristic
240C2×C4×C8C2311yescharacteristic
241#400—22no—
242#400—22no—
243#400—22no—
244#400—22no—
245#398—22no—
246#398—22no—
247#398—22no—
248#398—22no—
249#398—22no—
250#397—22no—
251#396—22no—
252#396—22no—
253#395—22no—
254#395—22no—
255#395—22no—
256#393—22no—
257#391C2312yes—
258#391C2312yes—
259#391C2312yes—
260#391C2312yes—
261#391C2312yes—
262#391C2312yes—
263#389—22no—
264#389—22no—
265#389—22no—
266#389C2312yes—
267#389C2312yes—
268#389C2312yes—
269#389C2312yes—
270#388—22no—
271#388—22no—
272#388—22no—
273#388—22no—
274#388D411yescharacteristic
275#388D411yescharacteristic
276#387—22no—
277#387—22no—
278#387—22no—
279#387—22no—
280#387—22no—
281#387—22no—
282#387—22no—
283#387—22no—
284#387—22no—
285#387—22no—
286#387—22no—
287#387—22no—
288#387D411yescharacteristic
289#387D411yescharacteristic
290#386—22no—
291#386—22no—
292#386D411yescharacteristic
293#386D411yescharacteristic
294#385—22no—
295#385—22no—
296#385—22no—
297#385—22no—
298#385—22no—
299#385D411yescharacteristic
300#385D411yescharacteristic
301#383—22no—
302#382—22no—
303#382C2312yes—
304#380—22no—
305#380—22no—
306#380C2312yes—
307#380C2312yes—
308C4×C4⋊C4—22no—
309C4×C4⋊C4C2312yes—
310C4×C4⋊C4C2311yescharacteristic
311C4×C22⋊C4—22no—
312C4×C22⋊C4C2311yescharacteristic
313C4×C22⋊C4C2311yescharacteristic
314#376C2311yescharacteristic
315#340C2312yes—
316#340C2312yes—
317#340C2312yes—
318#340C2312yes—
319#340C2312yes—
320#340C2312yes—
321#340C2312yes—
322#336C2311yescharacteristic
323#336C2311yescharacteristic
324#336C2311yescharacteristic
325#336C2311yescharacteristic
326#336C2311yescharacteristic
327#336C2311yescharacteristic
328C22×Q8—22no—
329C22×Q8—24no—
330C22×Q8—24no—
331C22×Q8—24no—
332C22×Q8—24no—
333C22×Q8—42no—
334C22×Q8—42no—
335C22×Q8C2412yes—
336C22×Q8C2412yes—
337C22×Q8C2412yes—
338C22×D4C2×D411yescharacteristic
339C23×C4—22no—
340C23×C4—22no—
341C23×C4C2×D411yescharacteristic
342C23×C4C2×D411yescharacteristic
343C23×C4C2411yescharacteristic
344C23×C4C2411yescharacteristic
345C2×Q16—232no—
346C2×Q16—24no—
347C2×Q16—24no—
348C2×Q16—24no—
349C2×Q16—24no—
350C2×Q16—22no—
351C2×Q16—22no—
352C2×Q16—24no—
353C2×Q16—22no—
354C2×Q16—22no—
355C2×Q16—22no—
356C2×Q16—24no—
357C2×Q16—24no—
358C2×Q16—22no—
359C2×Q16—22no—
360C2×Q16—42no—
361C2×Q16—42no—
362C2×Q16C2×D414yes—
363C2×Q16#4114yes—
364C2×M16—22no—
365C2×M16—22no—
366C2×M16—41no—
367C22×C8—22no—
368C22×C8—22no—
369C22×C8—22no—
370C22×C8—22no—
371C22×C8—22no—
372C22×C8—22no—
373C22×C8—22no—
374C22×C8—41no—
375C22×C8#4114yes—
376C22×C8C2411yescharacteristic
377C22×C8C2411yescharacteristic
378C22×C8C2411yescharacteristic
379C22×C8C2411yescharacteristic
380C22×C8C2411yescharacteristic
381C22×C8C2411yescharacteristic
382C22×C8C2411yescharacteristic
383C22×C8C2411yescharacteristic
384C4⋊Q8—24no—
385C4⋊Q8—24no—
386C4⋊Q8—42no—
387C4⋊Q8—42no—
388#126—48no—
389#126—48no—
390#125—24no—
391#125—42no—
392#125—48no—
393#125—48no—
394C22⋊Q8—24no—
395C22⋊Q8—24no—
396C22⋊Q8—24no—
397C22⋊Q8—24no—
398C22⋊Q8—24no—
399C22⋊Q8—42no—
400C22⋊Q8—42no—
401C22⋊Q8—42no—
402C4×Q8—24no—
403C4×Q8—24no—
404C4×Q8—24no—
405C4×Q8—24no—
406C4×Q8—24no—
407C4×Q8—24no—
408C4×Q8—24no—
409C4×Q8—48no—
410C4×Q8—42no—
411C4×Q8—42no—
412C4×Q8—48no—
413C4×Q8C2×D418yes—
414C4×D4—22no—
415C4×D4—22no—
416#117—22no—
417#117—22no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—24no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—22no—
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—22no—
436C2×C4⋊C4—22no—
437C2×C4⋊C4—22no—
438C2×C4⋊C4—22no—
439C2×C4⋊C4—42no—
440C2×C4⋊C4—48no—
441C2×C4⋊C4C2×D411yescharacteristic
442C2×C4⋊C4C2×D411yescharacteristic
443C2×C4⋊C4C2×D411yescharacteristic
444C2×C4⋊C4C2×D411yescharacteristic
445C2×C4⋊C4C2×D411yescharacteristic
446C2×C4⋊C4C2412yes—
447C2×C4⋊C4C2412yes—
448C2×C4⋊C4C2412yes—
449C2×C4⋊C4C2412yes—
450C2×C4⋊C4C2412yes—
451C2×C22⋊C4—22no—
452C2×C22⋊C4—22no—
453C2×C22⋊C4—22no—
454C2×C22⋊C4—22no—
455C2×C22⋊C4—22no—
456C2×C22⋊C4—22no—
457C2×C22⋊C4C2×D411yescharacteristic
458C2×C22⋊C4C2×D411yescharacteristic
459C2×C22⋊C4C2×D411yescharacteristic
460C2×C22⋊C4C2×D411yescharacteristic
461C2×C22⋊C4C2×D411yescharacteristic
462C2×C22⋊C4C2×D411yescharacteristic
463C2×C22⋊C4C2×D411yescharacteristic
464C2×C22⋊C4C2×D411yescharacteristic
465C2×C42—22no—
466C2×C42—22no—
467C2×C42—22no—
468C2×C42—22no—
469C2×C42—22no—
470C2×C42—22no—
471C2×C42—22no—
472C2×C42—22no—
473C2×C42—48no—
474C2×C42C2×D411yescharacteristic
475C2×C42C2×D411yescharacteristic
476C2×C42C2411yescharacteristic
477C2×C42C2411yescharacteristic
478C2×C42C2411yescharacteristic
479C2×C42C2411yescharacteristic
480C2×C42C2411yescharacteristic
481#107—22no—
482#107—22no—
483#107—22no—
484#107—22no—
485#107—24no—
486#107C2×D414yes—
487#106—24no—
488#106—42no—
489C4⋊C8—22no—
490C4⋊C8—22no—
491#103—24no—
492#103—24no—
493#103—24no—
494#103—24no—
495#103—24no—
496#103—24no—
497#103—24no—
498#103—24no—
499#103—24no—
500#103—24no—
501#103—42no—
502#103—42no—
503#103—42no—
504#103—42no—
505#103C2×D418yes—
506C22⋊C8—22no—
507C22⋊C8—22no—
508C22⋊C8—22no—
509C22⋊C8#4114yes—
510#97—22no—
511#97—22no—
512#97—22no—
513#97—22no—
514#97—41no—
515C4×C8—22no—
516C4×C8—22no—
517C4×C8—22no—
518C4×C8—22no—
519C4×C8—22no—
520C4×C8—22no—
521C4×C8C2×D414yes—
522#95—22no—
523#95—22no—
524#95—22no—
525#95—22no—
526#95—22no—
527#95—22no—
528#95—22no—
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#95—22no—
540#95—22no—
541#95—22no—
542#95—22no—
543#95C2×D411yescharacteristic
544#95C2×D411yescharacteristic
545#95C2×D411yescharacteristic
546#95C2×D411yescharacteristic
547#95C2×D411yescharacteristic
548#95C2×D411yescharacteristic
549#95C2×D411yescharacteristic
550#95C2×D411yescharacteristic
551#95C2×D411yescharacteristic
552#95C2×D411yescharacteristic
553C24C22×D411yescharacteristic
554C24C22×D411yescharacteristic
555C2×Q8—22no—
556C2×Q8—22no—
557C2×Q8—216no—
558C2×Q8—22no—
559C2×Q8—22no—
560C2×Q8—22no—
561C2×Q8—22no—
562C2×Q8—22no—
563C2×Q8—22no—
564C2×Q8—22no—
565C2×Q8—22no—
566C2×Q8—22no—
567C2×Q8—22no—
568C2×Q8—22no—
569C2×Q8—22no—
570C2×Q8—22no—
571C2×Q8—22no—
572C2×Q8—44no—
573C2×Q8—44no—
574C2×Q8—48no—
575C2×Q8—48no—
576C2×Q8—48no—
577C2×Q8—44no—
578C2×Q8C22×D414yes—
579C2×Q8C2×#4114yes—
580C2×D4—22no—
581C2×D4—22no—
582C2×D4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—41no—
607C22×C4—44no—
608C22×C4—44no—
609C22×C4—44no—
610C22×C4—44no—
611C22×C4—44no—
612C22×C4—82no—
613C22×C4C22×D411yescharacteristic
614C22×C4C22×D411yescharacteristic
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×C4C2×#4112yes—
626C22×C4C2×#4112yes—
627C22×C4C2511yescharacteristic
628Q16—216no—
629Q16—28no—
630Q16—28no—
631Q16—48no—
632Q16—48no—
633Q16—44no—
634M16—44no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—28no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—44no—
654C2×C8—44no—
655C2×C8C22×D412yes—
656C2×C8C22×D412yes—
657C2×C8C2×#4112yes—
658C2×C8C2×#4112yes—
659C2×C8C2×#4112yes—
660C2×C8C2×#4112yes—
661C2×C8C2×#4112yes—
662C4⋊C4—22no—
663C4⋊C4—28no—
664C4⋊C4—22no—
665C4⋊C4—22no—
666C4⋊C4—22no—
667C4⋊C4—22no—
668C4⋊C4—22no—
669C4⋊C4—22no—
670C4⋊C4—22no—
671C4⋊C4—22no—
672C4⋊C4—22no—
673C4⋊C4—22no—
674C4⋊C4—22no—
675C4⋊C4—22no—
676C4⋊C4—41no—
677C4⋊C4—44no—
678C4⋊C4—44no—
679C4⋊C4—44no—
680C4⋊C4—44no—
681C4⋊C4—44no—
682C4⋊C4—44no—
683C4⋊C4—44no—
684C4⋊C4—44no—
685C4⋊C4—44no—
686C4⋊C4—44no—
687C4⋊C4—44no—
688C4⋊C4—44no—
689C4⋊C4—44no—
690C4⋊C4—44no—
691C4⋊C4—44no—
692C4⋊C4—44no—
693C4⋊C4—82no—
694C4⋊C4—82no—
695C4⋊C4—82no—
696C4⋊C4C22×D414yes—
697C22⋊C4—22no—
698C22⋊C4—22no—
699C22⋊C4—22no—
700C22⋊C4—22no—
701C22⋊C4—22no—
702C22⋊C4—22no—
703C22⋊C4—22no—
704C22⋊C4—41no—
705C22⋊C4—44no—
706C22⋊C4—44no—
707C22⋊C4—44no—
708C22⋊C4—44no—
709C22⋊C4—44no—
710C22⋊C4—82no—
711C42—22no—
712C42—22no—
713C42—28no—
714C42—21no—
715C42—21no—
716C42—21no—
717C42—21no—
718C42—21no—
719C42—21no—
720C42—21no—
721C42—21no—
722C42—44no—
723C42—44no—
724C42—44no—
725C42—44no—
726C42—82no—
727C42C22×D412yes—
728C42H(5,𝔽2)12yes—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—21no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—21no—
739C23—21no—
740C23#53212yes—
741C23#57812yes—
742C23#57812yes—
743C23C23×D411yescharacteristic
744Q8—24no—
745Q8—24no—
746Q8—24no—
747Q8—24no—
748Q8—416no—
749Q8—42no—
750Q8—42no—
751Q8—42no—
752Q8—42no—
753Q8—42no—
754Q8—42no—
755Q8—42no—
756Q8—42no—
757D4—44no—
758C2×C4—28no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
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—24no—
780C2×C4—24no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—24no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—44no—
799C2×C4—416no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—88no—
826C2×C4#53212yes—
827C2×C4D4212yes—
828C2×C4D4212yes—
829C2×C4#57812yes—
830C2×C4C23×D411yescharacteristic
831C2×C4C22×#4111yescharacteristic
832C2×C4C22×#4111yescharacteristic
833C2×C4C22×#4111yescharacteristic
834C2×C4C2×H(5,𝔽2)11yescharacteristic
835C2×C4#58511yescharacteristic
836C8—22no—
837C8—22no—
838C8—22no—
839C8—22no—
840C8—41no—
841C8—41no—
842C8—41no—
843C8#52514yes—
844C22—22no—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—22no—
850C22—41no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22—41no—
857C22#317714yescomplemented
858C22C2×#53211yescharacteristic
859C22C2×D4211yescharacteristic
860C22D4×#4111yescharacteristic
861C22C2×#57811yescharacteristic
862C22C2×#57811yescharacteristic
863C22C2×#57811yescharacteristic
864C22#358411yescharacteristic
865C4—22no—
866C4—22no—
867C4—22no—
868C4—22no—
869C4—41no—
870C4—41no—
871C4—41no—
872C4—41no—
873C4—41no—
874C4—44no—
875C4—44no—
876C4—41no—
877C4—41no—
878C4—41no—
879C4—44no—
880C4—82no—
881C4—82no—
882C4—82no—
883C4—82no—
884C4—82no—
885C4C2×#52511yescharacteristic
886C4#346011yescharacteristic
887C4D4×#4111yescharacteristic
888C4#348111yescharacteristic
889C2—24no—
890C2—81no—
891C2#3468111yescharacteristic
892C2C2×#317711yescharacteristic
893C2#6069611yescharacteristic
894C2#6105311yescharacteristic
895C2#6105711yescharacteristic
896C2#6147311yescharacteristic
897C2#6148411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×D4C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2290 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3177C2semidirect
2. C22×C4×Q16C2semidirect
4. #27268C2semidirect
5. #26972C2semidirect
6. #26831C2semidirect
7. #26483C2semidirect
8. #26255C2semidirect
9. #26067C2semidirect
10. #25780C2semidirect
11. #25415C2semidirect
13. #25033C2semidirect
16. #23691C2semidirect
17. #23586C2semidirect
18. #21698C2semidirect
19. #21525C2semidirect
20. C4×#467C2semidirect
21. #21455C2semidirect
22. #21281C2semidirect
193. C4×Q16D4semidirect
857. C22#3177semidirect

Maximal subgroups

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

subgroupindex
C2×#31772
C22×C4×Q162
#352442
#272682
#269722
#268312
#264832
#262552
#260672
#257802
#254152
#251262
#250332
#247812
#242682
#236912
#235862
#216982
#215252
C4×#4672
#214552
#212812
#204842