Finite Group Databasebeta

← #6438348

Subgroups — #6438348

Order 512.

2948 conjugacy classes of subgroups.

The subgroup lattice has 889 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#482C211yesmaximal, characteristic, complemented
2C2×#2897C211yesmaximal, characteristic, complemented
3#35512C211yesmaximal, characteristic
4#34201C211yesmaximal, characteristic, complemented
5#24889C214yesmaximal, complemented
6#24886C214yesmaximal, complemented
7#24873C214yesmaximal, complemented
8#24870C214yesmaximal, complemented
9#23738C211yesmaximal, characteristic, complemented
10#23632C211yesmaximal, characteristic, complemented
11#23480C211yesmaximal, characteristic, complemented
12#23479C211yesmaximal, characteristic, complemented
13#21067C211yesmaximal, characteristic, complemented
14#21065C211yesmaximal, characteristic, complemented
15#20910C211yesmaximal, characteristic, complemented
16#20899C211yesmaximal, characteristic, complemented
17#20847C211yesmaximal, characteristic, complemented
18#20662C211yesmaximal, characteristic, complemented
19#20602C211yesmaximal, characteristic, complemented
20C22×H(5,𝔽2)C2211yescharacteristic
21C22×#131C2211yescharacteristic
22C2×#525C2211yescharacteristic
23C2×#525C2211yescharacteristic
24C22×#121C2211yescharacteristic
25C2×#520C2211yescharacteristic
26C22×#117C2211yescharacteristic, complemented
27C2×#482—28no—
28C2×#482C2214yescomplemented
29C2×#482C2214yescomplemented
30C2×#428C2211yescharacteristic, complemented
31C2×#427C2211yescharacteristic, complemented
32C22×#107C2211yescharacteristic, complemented
33C22×#106C2211yescharacteristic, complemented
34#2897—28no—
35C2×#417C2211yescharacteristic
36C2×#417C2211yescharacteristic
37C2×#417C2212yescomplemented
38C2×#418C2211yescharacteristic
39C2×#418C2211yescharacteristic
40C2×#418C2212yescomplemented
41C2×#416C2211yescharacteristic
42C2×#416C2211yescharacteristic
43C2×#416C2212yescomplemented
44C22×#102C2211yescharacteristic
45C22×#102C2211yescharacteristic
46C22×#102C2212yescomplemented
47C2×#408C2211yescharacteristic
48C2×#407C2211yescharacteristic, complemented
49C22×C22⋊C8C2211yescharacteristic, complemented
50#2408—22no—
51#2408C2214yes—
52#2407—22no—
53#2407C2214yes—
54#2405—22no—
55#2403—22no—
56#2363—22no—
57#2362—22no—
58#2354C2214yescomplemented
59#2352C2214yescomplemented
60#2321—22no—
61#2317C2211yescharacteristic, complemented
62#2311C2211yescharacteristic
63#2311C2211yescharacteristic
64#2311C2211yescharacteristic
65#2309C2211yescharacteristic
66C4×#123—22no—
67#2280C2211yescharacteristic, complemented
68#2274C2211yescharacteristic, complemented
69#2097C2212yescomplemented
70#2096C2212yescomplemented
71#2094C2212yescomplemented
72#2092C2212yescomplemented
73#2073C2214yescomplemented
74#2071C2214yescomplemented
75#2036C2212yescomplemented
76#2035C2212yescomplemented
77#2034C2214yescomplemented
78#2034C2212yescomplemented
79#2033C2214yescomplemented
80#2033C2212yescomplemented
81#1928C2214yescomplemented
82#1926C2214yescomplemented
83#1925C2214yescomplemented
84#1925C2214yescomplemented
85#1875C2214yescomplemented
86#1873C2214yescomplemented
87#1870C2214yescomplemented
88#1869C2214yescomplemented
89#1854C2214yescomplemented
90#1852C2214yescomplemented
91#1809C2214yescomplemented
92#1807C2214yescomplemented
93#1788C2214yescomplemented
94#1786C2214yescomplemented
95#1736C2211yescharacteristic, complemented
96#1736C2211yescharacteristic, complemented
97#1736C2211yescharacteristic, complemented
98#1735C2211yescharacteristic, complemented
99#1729C2211yescharacteristic, complemented
100#1729C2211yescharacteristic, complemented
101C2×H(5,𝔽2)—24no—
102C2×H(5,𝔽2)—24no—
103C2×H(5,𝔽2)—24no—
104C2×H(5,𝔽2)—24no—
105C2×H(5,𝔽2)—42no—
106C2×H(5,𝔽2)—42no—
107C22×#41—21no—
108C22×#41C2311yescharacteristic
109C22×#41C2312yes—
110C22×#41C2311yescharacteristic
111C23×D4—21no—
112C23×D4—22no—
113C23×D4—21no—
114C23×D4C2311yescharacteristic
115C23×D4C2312yes—
116C24×C4C2311yescharacteristic
117C2×#131—24no—
118C2×#131—24no—
119C2×#131—42no—
120C22×M16C2311yescharacteristic
121C22×M16C2311yescharacteristic
122C22×M16C2312yes—
123C23×C8C2311yescharacteristic
124C23×C8C2312yes—
125C23×C8C2311yescharacteristic
126#525—24no—
127#525—24no—
128#525—24no—
129#525—42no—
130C2×#123—21no—
131C2×#123D412yes—
132C2×C22⋊Q8D412yes—
133C2×C22⋊Q8C2312yes—
134C2×#121—22no—
135C2×#121—24no—
136C2×#121—42no—
137C2×#121D412yes—
138C2×#121C2314yes—
139C2×#121C2312yes—
140C2×#120—21no—
141C2×#120—24no—
142C2×#120D412yes—
143#520—24no—
144#520—42no—
145C2×C4×Q8—21no—
146C2×C4×D4—22no—
147C2×C4×D4—21no—
148C2×C4×D4—22no—
149C2×C4×D4C2314yes—
150C2×#117—22no—
151C2×#117—24no—
152C2×#117—42no—
153C2×#117C2311yescharacteristic
154C2×#117C2311yescharacteristic
155C2×#117C2311yescharacteristic
156C2×#117C2314yes—
157C2×#117C2312yes—
158C2×#117C2311yescharacteristic
159C22×C4⋊C4C2311yescharacteristic
160C22×C4⋊C4C2311yescharacteristic
161C22×C4⋊C4C2312yes—
162C22×C4⋊C4C2311yescharacteristic
163C22×C22⋊C4—21no—
164C22×C22⋊C4—21no—
165C22×C42—21no—
166#482—216no—
167#482—216no—
168#428—42no—
169#427—42no—
170C2×#107—24no—
171C2×#107C2314yes—
172C2×#107C2312yes—
173C2×#107C2312yes—
174C2×#106—24no—
175C2×#106C2312yes—
176C2×#106C2312yes—
177C2×#106C2312yes—
178C2×#106C2312yes—
179#418—24no—
180#418—28no—
181#418—42no—
182#417—24no—
183#417—28no—
184#417—42no—
185#416—24no—
186#416—24no—
187#416—28no—
188C2×#103C2311yescharacteristic
189C2×#103C2311yescharacteristic
190C2×#103C2312yes—
191C2×#103C2312yes—
192C2×#103C2312yes—
193C2×#102—24no—
194C2×#102—28no—
195C2×#102D418yescomplemented
196C2×#102C2314yes—
197C2×#102C2312yes—
198C2×#102C2312yes—
199C2×#102C2311yescharacteristic
200C2×#102C2311yescharacteristic
201C2×#102C2312yes—
202C2×#102C2312yes—
203C2×#102C2312yes—
204C2×#102C2314yes—
205C2×#102C2312yes—
206C2×#102C2312yes—
207#408—24no—
208#407—42no—
209C2×C22⋊C8—24no—
210C2×C22⋊C8C2312yes—
211C2×C22⋊C8C2312yes—
212C2×C22⋊C8C2314yes—
213C2×C22⋊C8C2314yes—
214#394—24no—
215#394—24no—
216#392—24no—
217#392—24no—
218#391—21no—
219#391—21no—
220#391C2312yes—
221#390—21no—
222#390—21no—
223#390—24no—
224#390—22no—
225#390C2314yes—
226#390C2312yes—
227#389—22no—
228#388—24no—
229#388—24no—
230#388—24no—
231#387—24no—
232#386—22no—
233#386—22no—
234#386—24no—
235#386—22no—
236#386—24no—
237#385—24no—
238#385—22no—
239#384C2312yes—
240#382C2312yes—
241#381—21no—
242#380—22no—
243#380C2314yes—
244#380C2314yes—
245#380C2312yes—
246#380C2312yes—
247#379—21no—
248#379—22no—
249#379—24no—
250C4×C4⋊C4—24no—
251C4×C4⋊C4—22no—
252C4×C4⋊C4C2314yes—
253C4×C22⋊C4—22no—
254C4×C22⋊C4—22no—
255C4×C22⋊C4—24no—
256#340C2314yes—
257#340C2314yes—
258#340C2312yes—
259#340C2312yes—
260#340C2314yes—
261#336C2314yes—
262#336C2312yes—
263#336C2312yes—
264C25—21no—
265C25—22no—
266C25C2×D411yescharacteristic
267H(5,𝔽2)—232no—
268H(5,𝔽2)—416no—
269H(5,𝔽2)—416no—
270H(5,𝔽2)—416no—
271C2×#41—22no—
272C2×#41—22no—
273C2×#41—22no—
274C2×#41—22no—
275C2×#41—22no—
276C2×#41—24no—
277C2×#41—24no—
278C2×#41—22no—
279C2×#41—24no—
280C2×#41—22no—
281C2×#41—22no—
282C2×#41—24no—
283C2×#41—22no—
284C2×#41—42no—
285C2×#41—42no—
286C2×#41—44no—
287C2×#41—44no—
288C2×#41—44no—
289C2×#41#4114yes—
290C2×#41#4114yes—
291C2×#41#4114yes—
292C22×Q8C2×D411yescharacteristic
293C22×Q8C2411yescharacteristic
294C22×D4—24no—
295C22×D4—24no—
296C22×D4—21no—
297C22×D4—22no—
298C22×D4—22no—
299C22×D4—24no—
300C22×D4—21no—
301C22×D4—22no—
302C22×D4—24no—
303C22×D4—22no—
304C22×D4—22no—
305C22×D4—22no—
306C22×D4—24no—
307C22×D4—22no—
308C22×D4—22no—
309C22×D4—42no—
310C22×D4—42no—
311C22×D4—44no—
312C22×D4—48no—
313C22×D4—44no—
314C22×D4—48no—
315C22×D4—48no—
316C22×D4—44no—
317C22×D4—44no—
318C22×D4—84no—
319C22×D4C2×D414yes—
320C22×D4C2×D412yes—
321C22×D4C2×D411yescharacteristic
322C22×D4C2×D414yes—
323C22×D4C2412yes—
324C22×D4C2411yescharacteristic
325C23×C4—21no—
326C23×C4—22no—
327C23×C4—21no—
328C23×C4—22no—
329C23×C4—22no—
330C23×C4—22no—
331C23×C4—22no—
332C23×C4—22no—
333C23×C4—21no—
334C23×C4—21no—
335C23×C4—22no—
336C23×C4—22no—
337C23×C4C2×D411yescharacteristic
338C23×C4C2×D412yes—
339C23×C4C2412yes—
340C23×C4C2412yes—
341C23×C4C2411yescharacteristic
342#131—416no—
343C2×M16—22no—
344C2×M16—24no—
345C2×M16—22no—
346C2×M16—22no—
347C2×M16—22no—
348C2×M16—22no—
349C2×M16—22no—
350C2×M16—24no—
351C2×M16—42no—
352C22×C8—22no—
353C22×C8—22no—
354C22×C8—22no—
355C22×C8—24no—
356C22×C8—22no—
357C22×C8—22no—
358C22×C8—24no—
359C22×C8—42no—
360C22×C8C2×D414yes—
361C22×C8C2412yes—
362C22×C8C2412yes—
363C22×C8C2412yes—
364C22×C8C2411yescharacteristic
365C22×C8C2411yescharacteristic
366#123—28no—
367#123—44no—
368C22⋊Q8—28no—
369C22⋊Q8—24no—
370C22⋊Q8—42no—
371#121—28no—
372#121—28no—
373#121—24no—
374#121—44no—
375#121—42no—
376#121—48no—
377#120—28no—
378#120—44no—
379#120—88no—
380C4×Q8—44no—
381C4×D4—28no—
382C4×D4—28no—
383C4×D4—44no—
384C4×D4—48no—
385C4×D4—48no—
386#117—22no—
387#117—22no—
388#117—22no—
389#117—22no—
390#117—22no—
391#117—22no—
392#117—22no—
393#117—22no—
394#117—28no—
395#117—24no—
396#117—44no—
397#117—42no—
398#117—48no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—24no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—24no—
411C2×C4⋊C4—42no—
412C2×C4⋊C4C2×D412yes—
413C2×C4⋊C4C2×D414yes—
414C2×C4⋊C4C2×D414yes—
415C2×C4⋊C4C2411yescharacteristic
416C2×C4⋊C4C2412yes—
417C2×C4⋊C4C2412yes—
418C2×C4⋊C4C2411yescharacteristic
419C2×C4⋊C4C2412yes—
420C2×C4⋊C4C2412yes—
421C2×C4⋊C4C2412yes—
422C2×C22⋊C4—24no—
423C2×C22⋊C4—21no—
424C2×C22⋊C4—22no—
425C2×C22⋊C4—21no—
426C2×C22⋊C4—21no—
427C2×C22⋊C4—22no—
428C2×C22⋊C4—24no—
429C2×C22⋊C4—22no—
430C2×C22⋊C4—24no—
431C2×C22⋊C4—22no—
432C2×C22⋊C4—22no—
433C2×C22⋊C4—24no—
434C2×C22⋊C4—24no—
435C2×C22⋊C4—24no—
436C2×C22⋊C4—24no—
437C2×C22⋊C4—44no—
438C2×C22⋊C4—44no—
439C2×C22⋊C4C2×D412yes—
440C2×C22⋊C4C2×D414yes—
441C2×C22⋊C4C2×D414yes—
442C2×C42—24no—
443C2×C42—21no—
444C2×C42—21no—
445C2×C42—22no—
446C2×C42—21no—
447C2×C42—24no—
448C2×C42—44no—
449C2×C42C2412yes—
450#107—28no—
451#107—42no—
452#107—42no—
453#106—24no—
454#106—24no—
455#106—42no—
456#106—42no—
457#103—24no—
458#103—22no—
459#103—22no—
460#103—24no—
461#103—42no—
462#102—24no—
463#102—28no—
464#102—24no—
465#102—24no—
466#102—22no—
467#102—22no—
468#102—24no—
469#102—42no—
470#102—44no—
471#102C2×D418yes—
472#102C2×D418yes—
473C22⋊C8—28no—
474C22⋊C8—24no—
475C22⋊C8—24no—
476C22⋊C8—44no—
477#95—22no—
478#95—22no—
479#95—24no—
480#95—24no—
481#95—24no—
482#95—24no—
483#95—24no—
484C24—22no—
485C24—22no—
486C24—21no—
487C24—22no—
488C24—24no—
489C24—22no—
490C24—42no—
491C24—42no—
492C24—44no—
493C24—44no—
494C24—44no—
495C24—42no—
496C24—42no—
497C24—82no—
498C24—82no—
499C24—84no—
500C24—84no—
501C24C22×D412yes—
502C24C22×D412yes—
503C24C22×D411yescharacteristic
504#41—28no—
505#41—28no—
506#41—28no—
507#41—28no—
508#41—216no—
509#41—28no—
510#41—28no—
511#41—48no—
512#41—48no—
513#41—48no—
514#41—432no—
515#41—44no—
516#41—44no—
517C2×Q8—22no—
518C2×Q8—22no—
519C2×Q8—21no—
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8#12314yes—
525C2×Q8C2×#4112yes—
526C2×D4—24no—
527C2×D4—24no—
528C2×D4—216no—
529C2×D4—24no—
530C2×D4—28no—
531C2×D4—28no—
532C2×D4—22no—
533C2×D4—24no—
534C2×D4—22no—
535C2×D4—28no—
536C2×D4—21no—
537C2×D4—22no—
538C2×D4—21no—
539C2×D4—22no—
540C2×D4—22no—
541C2×D4—21no—
542C2×D4—22no—
543C2×D4—21no—
544C2×D4—22no—
545C2×D4—21no—
546C2×D4—48no—
547C2×D4—48no—
548C2×D4—44no—
549C2×D4—44no—
550C2×D4—44no—
551C2×D4—48no—
552C2×D4—44no—
553C2×D4—44no—
554C2×D4—464no—
555C2×D4—432no—
556C2×D4—44no—
557C2×D4—44no—
558C2×D4—42no—
559C2×D4—42no—
560C2×D4—44no—
561C2×D4—48no—
562C2×D4—44no—
563C2×D4—48no—
564C2×D4—44no—
565C2×D4—42no—
566C2×D4—44no—
567C2×D4—42no—
568C2×D4—44no—
569C2×D4—82no—
570C2×D4—84no—
571C2×D4—816no—
572C2×D4#12318yes—
573C2×D4#12314yes—
574C2×D4C22×D414yes—
575C2×D4C2×#4112yes—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—21no—
584C22×C4—22no—
585C22×C4—24no—
586C22×C4—24no—
587C22×C4—24no—
588C22×C4—24no—
589C22×C4—24no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—21no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—21no—
601C22×C4—22no—
602C22×C4—44no—
603C22×C4—44no—
604C22×C4—44no—
605C22×C4—44no—
606C22×C4—42no—
607C22×C4—44no—
608C22×C4—44no—
609C22×C4—42no—
610C22×C4—44no—
611C22×C4—44no—
612C22×C4—42no—
613C22×C4—42no—
614C22×C4—82no—
615C22×C4—82no—
616C22×C4—82no—
617C22×C4—84no—
618C22×C4C22×D414yes—
619C22×C4C22×D412yes—
620C22×C4C22×D412yes—
621C22×C4C22×D411yescharacteristic
622C22×C4C22×D412yes—
623C22×C4C2×#4114yes—
624C22×C4C2×#4114yes—
625C22×C4C2×#4112yes—
626C22×C4C2×#4112yes—
627C22×C4C2×#4112yes—
628C22×C4H(5,𝔽2)12yes—
629C22×C4H(5,𝔽2)12yes—
630C22×C4C2511yescharacteristic
631M16—48no—
632M16—44no—
633M16—44no—
634C2×C8—28no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—22no—
640C2×C8—22no—
641C2×C8—22no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—22no—
645C2×C8—22no—
646C2×C8—22no—
647C2×C8—22no—
648C2×C8—48no—
649C2×C8—44no—
650C2×C8C22×D412yes—
651C2×C8C22×D412yes—
652C4⋊C4—24no—
653C4⋊C4—28no—
654C4⋊C4—24no—
655C4⋊C4—22no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—22no—
659C4⋊C4—22no—
660C4⋊C4—22no—
661C4⋊C4—22no—
662C4⋊C4—22no—
663C4⋊C4—22no—
664C4⋊C4—21no—
665C4⋊C4—22no—
666C4⋊C4—22no—
667C4⋊C4—21no—
668C4⋊C4—44no—
669C4⋊C4—44no—
670C4⋊C4—42no—
671C4⋊C4—42no—
672C4⋊C4—84no—
673C4⋊C4C22×D414yes—
674C22⋊C4—24no—
675C22⋊C4—28no—
676C22⋊C4—28no—
677C22⋊C4—48no—
678C22⋊C4—48no—
679C22⋊C4—44no—
680C22⋊C4—44no—
681C22⋊C4—44no—
682C22⋊C4—42no—
683C22⋊C4—42no—
684C22⋊C4—42no—
685C22⋊C4—84no—
686C22⋊C4—84no—
687C22⋊C4—84no—
688C22⋊C4—82no—
689C22⋊C4—84no—
690C22⋊C4—82no—
691C22⋊C4—84no—
692C42—22no—
693C42—22no—
694C42—48no—
695C42—44no—
696C42—42no—
697C42—42no—
698C42—42no—
699C42—84no—
700C23—22no—
701C23—22no—
702C23—24no—
703C23—24no—
704C23—22no—
705C23—22no—
706C23—22no—
707C23—22no—
708C23—22no—
709C23—22no—
710C23—22no—
711C23—22no—
712C23—24no—
713C23—22no—
714C23—22no—
715C23—44no—
716C23—44no—
717C23—416no—
718C23—44no—
719C23—42no—
720C23—42no—
721C23—44no—
722C23—42no—
723C23—41no—
724C23—44no—
725C23—41no—
726C23—42no—
727C23—48no—
728C23—84no—
729C23—84no—
730C23—84no—
731C23—84no—
732C23—164no—
733C23—164no—
734C23—168no—
735C23—168no—
736C23—164no—
737C23—164no—
738C23C2×#12314yes—
739C23C2×#12312yes—
740C23D4212yes—
741C23#54612yes—
742C23C23×D411yescharacteristic
743Q8—28no—
744Q8—22no—
745Q8—22no—
746Q8—41no—
747Q8—41no—
748D4—216no—
749D4—24no—
750D4—22no—
751D4—28no—
752D4—24no—
753D4—22no—
754D4—416no—
755D4—416no—
756D4—48no—
757D4—48no—
758D4—42no—
759D4—41no—
760D4—41no—
761D4—42no—
762D4—88no—
763D4—88no—
764D4—816no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—24no—
768C2×C4—24no—
769C2×C4—24no—
770C2×C4—24no—
771C2×C4—24no—
772C2×C4—24no—
773C2×C4—24no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—24no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—416no—
780C2×C4—44no—
781C2×C4—41no—
782C2×C4—44no—
783C2×C4—41no—
784C2×C4—42no—
785C2×C4—48no—
786C2×C4—48no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—44no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—44no—
797C2×C4—42no—
798C2×C4—41no—
799C2×C4—42no—
800C2×C4—41no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—84no—
805C2×C4—84no—
806C2×C4—84no—
807C2×C4—164no—
808C2×C4C2×#12314yes—
809C2×C4C2×#12312yes—
810C2×C4#52514yes—
811C2×C4#53814yes—
812C2×C4D4212yes—
813C2×C4#54612yes—
814C2×C4#54614yes—
815C2×C4#55114yes—
816C2×C4C23×D411yescharacteristic
817C2×C4C22×#4111yescharacteristic
818C2×C4C22×#4111yescharacteristic
819C2×C4C22×#4111yescharacteristic
820C2×C4C2×H(5,𝔽2)11yescharacteristic
821C2×C4C2×H(5,𝔽2)11yescharacteristic
822C8—22no—
823C8—22no—
824C8—42no—
825C8—42no—
826C8—42no—
827C22—24no—
828C22—24no—
829C22—22no—
830C22—22no—
831C22—24no—
832C22—28no—
833C22—44no—
834C22—42no—
835C22—42no—
836C22—42no—
837C22—44no—
838C22—42no—
839C22—42no—
840C22—44no—
841C22—42no—
842C22—42no—
843C22—42no—
844C22—42no—
845C22—44no—
846C22—42no—
847C22—44no—
848C22—88no—
849C22—84no—
850C22—84no—
851C22—82no—
852C22—81no—
853C22—81no—
854C22—168no—
855C22—1616no—
856C22#241814yes—
857C22C22×#12311yescharacteristic
858C22C2×D4211yescharacteristic
859C22C2×#54611yescharacteristic
860C22#358412yes—
861C22#358512yes—
862C4—24no—
863C4—42no—
864C4—42no—
865C4—44no—
866C4—44no—
867C4—82no—
868C4—82no—
869C4—81no—
870C4—82no—
871C4—82no—
872C4—81no—
873C4#241814yes—
874C4C2×#52511yescharacteristic
875C4C2×#53811yescharacteristic
876C4C2×#54611yescharacteristic
877C4C2×#55111yescharacteristic
878C2—24no—
879C2—44no—
880C2—82no—
881C2—82no—
882C2—84no—
883C2C2×#241811yescharacteristic
884C2#6052312yes—
885C2#6105211yescharacteristic
886C2#6105811yescharacteristic
887C2#6119512yes—
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#35512C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×#525 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#482C2semidirect
2. C2×#2897C2semidirect
4. #34201C2semidirect
5. #24889C2semidirect
6. #24886C2semidirect
7. #24873C2semidirect
8. #24870C2semidirect
9. #23738C2semidirect
10. #23632C2semidirect
11. #23480C2semidirect
12. #23479C2semidirect
13. #21067C2semidirect
14. #21065C2semidirect
15. #20910C2semidirect
16. #20899C2semidirect
17. #20847C2semidirect
18. #20662C2semidirect
19. #20602C2semidirect
26. C22×#117C22semidirect
28. C2×#482C22semidirect
29. C2×#482C22semidirect
30. C2×#428C22semidirect
31. C2×#427C22semidirect
32. C22×#107C22semidirect
33. C22×#106C22semidirect
37. C2×#417C22semidirect
40. C2×#418C22semidirect
43. C2×#416C22semidirect
46. C22×#102C22semidirect
48. C2×#407C22semidirect
49. C22×C22⋊C8C22semidirect
58. #2354C22semidirect
59. #2352C22semidirect
61. #2317C22semidirect
67. #2280C22semidirect
68. #2274C22semidirect
69. #2097C22semidirect
70. #2096C22semidirect
71. #2094C22semidirect
72. #2092C22semidirect
73. #2073C22semidirect
74. #2071C22semidirect
75. #2036C22semidirect
76. #2035C22semidirect
77. #2034C22semidirect
78. #2034C22semidirect
79. #2033C22semidirect
80. #2033C22semidirect
81. #1928C22semidirect
82. #1926C22semidirect
83. #1925C22semidirect
84. #1925C22semidirect
85. #1875C22semidirect
86. #1873C22semidirect
87. #1870C22semidirect
88. #1869C22semidirect
89. #1854C22semidirect
90. #1852C22semidirect
91. #1809C22semidirect
92. #1807C22semidirect
93. #1788C22semidirect
94. #1786C22semidirect
95. #1736C22semidirect
96. #1736C22semidirect
97. #1736C22semidirect
98. #1735C22semidirect
99. #1729C22semidirect
100. #1729C22semidirect
195. C2×#102D4semidirect

Maximal subgroups

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

subgroupindex
C22×#4822
C2×#28972
#355122
#342012
#248892
#248862
#248732
#248702
#237382
#236322
#234802
#234792
#210672
#210652
#209102
#208992
#208472
#206622
#206022