Finite Group Databasebeta

← #6468805

Subgroups — #6468805

Order 512.

1959 conjugacy classes of subgroups.

The subgroup lattice has 893 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34627C211yesmaximal, characteristic, complemented
2C4×#535C211yesmaximal, characteristic
3#29488C212yesmaximal, complemented
4#29472C212yesmaximal, complemented
5#29344C211yesmaximal, characteristic, complemented
6#29311C211yesmaximal, characteristic, complemented
7#29174C212yesmaximal, complemented
8#29116C211yesmaximal, characteristic, complemented
9#28583C212yesmaximal, complemented
10#28320C211yesmaximal, characteristic, complemented
11#24569C212yesmaximal, complemented
12#24394C212yesmaximal
13#23758C212yesmaximal, complemented
14#23568C212yesmaximal, complemented
15C4×#485C212yesmaximal, complemented
16C4×#468C212yesmaximal, complemented
17C4×#465C212yesmaximal, complemented
18C4×#450C212yesmaximal, complemented
19C4×#408C211yesmaximal, characteristic, complemented
20C2×#535C2211yescharacteristic
21C2×#533C2211yescharacteristic, complemented
22C2×C4×#41C2211yescharacteristic
23C22×C4×D4C2211yescharacteristic
24C2×#485C2212yes—
25C2×#468C2212yes—
26C2×#465C2212yes—
27C2×#450C2212yes—
28C2×C4×SD16C2212yes—
29C2×C4×SD16C2212yes—
30C2×#408C2212yes—
31C2×C4×M16C2211yescharacteristic, complemented
32C22×C4×C8C2211yescharacteristic, complemented
33#2638—21no—
34#2638—21no—
35#2634—21no—
36#2633—21no—
37#2628C2211yescharacteristic
38#2628C2211yescharacteristic, complemented
39#2625C2212yescomplemented
40#2621C2211yescharacteristic
41#2621C2211yescharacteristic, complemented
42#2616C2212yes—
43#2399—21no—
44#2398—21no—
45#2395—21no—
46#2395—21no—
47#2328—21no—
48#2326—21no—
49#2324C2212yes—
50#2324C2212yes—
51#2321—21no—
52#2321—21no—
53#2317C2211yescharacteristic
54#2311C2211yescharacteristic
55#2309C2211yescharacteristic
56C4×#127—21no—
57C4×#124—21no—
58C4×C22⋊Q8C2212yes—
59C4×C22⋊Q8C2212yescomplemented
60C4×#121C2212yes—
61C4×#121C2212yes—
62C4×#120—21no—
63C4×#120—21no—
64#2283C2211yescharacteristic, complemented
65C4×#117C2211yescharacteristic
66#2101C2212yescomplemented
67#2092C2212yes—
68#2085C2212yescomplemented
69#2077C2212yescomplemented
70#2076C2212yescomplemented
71#2073C2212yes—
72#2058C2212yescomplemented
73#2043C2212yescomplemented
74#2035C2212yescomplemented
75#2035C2212yescomplemented
76#2034C2212yes—
77#2033C2212yes—
78#2023C2212yes—
79#2013C2212yes—
80#2000C2212yes—
81#2000C2212yes—
82#1973C2212yes—
83#1968C2212yes—
84#1943C2212yescomplemented
85#1941C2212yescomplemented
86#1936C2212yes—
87#1935C2212yescomplemented
88#1934C2212yes—
89#1933C2212yescomplemented
90#1928C2212yescomplemented
91#1927C2212yescomplemented
92#1919C2212yescomplemented
93#1918C2212yescomplemented
94#1895C2212yes—
95#1894C2212yescomplemented
96#1893C2212yes—
97#1892C2212yescomplemented
98#1877C2212yes—
99#1877C2212yes—
100#1873C2212yes—
101#1872C2212yes—
102#1864C2212yes—
103#1864C2212yes—
104#1854C2212yes—
105#1853C2212yes—
106#1825C2212yes—
107#1809C2212yescomplemented
108#1807C2212yescomplemented
109#1786C2212yes—
110C4×#107C2212yescomplemented
111C4×#106C2212yescomplemented
112C4×#103C2212yescomplemented
113C4×#103C2212yescomplemented
114C4×#102C2212yes—
115C4×#102C2212yes—
116#1750C2211yescharacteristic
117#1750C2211yescharacteristic
118#1750C2211yescharacteristic, complemented
119#1750C2211yescharacteristic, complemented
120C4×C22⋊C8C2212yes—
121C4×C22⋊C8C2212yescomplemented
122#1729C2212yescomplemented
123C22×#41C2311yescharacteristic
124C23×D4C2311yescharacteristic
125C24×C4—21no—
126C22×SD16C2312yes—
127C22×SD16C2312yes—
128C22×M16C2312yes—
129C23×C8C2312yes—
130#535—28no—
131#533—42no—
132#533—42no—
133C2×C4⋊Q8C2311yescharacteristic
134C2×C4⋊Q8C2311yescharacteristic
135C2×#127—21no—
136C2×#125—21no—
137C2×#124—21no—
138C2×C22⋊Q8—21no—
139C2×C22⋊Q8C2312yes—
140C2×C22⋊Q8C2312yes—
141C2×C22⋊Q8C2312yes—
142C2×#121C2312yes—
143C2×#121C2312yes—
144C2×#120—21no—
145C2×#120—21no—
146C4×#41—42no—
147C4×#41—42no—
148C2×C4×Q8—21no—
149C2×C4×Q8D411yescharacteristic
150C2×C4×Q8D411yescharacteristic
151C2×C4×Q8C2312yes—
152C2×C4×D4—22no—
153C2×C4×D4—22no—
154C2×C4×D4—21no—
155C2×C4×D4—21no—
156C2×C4×D4—42no—
157C2×C4×D4—42no—
158C2×C4×D4D411yescharacteristic
159C2×C4×D4D411yescharacteristic
160C2×C4×D4D411yescharacteristic
161C2×C4×D4D411yescharacteristic
162C2×C4×D4D411yescharacteristic
163C2×C4×D4D411yescharacteristic
164C2×C4×D4C2312yes—
165C2×C4×D4C2312yes—
166C2×#117—21no—
167C2×#117C2311yescharacteristic
168C2×#117C2311yescharacteristic
169C2×#117C2311yescharacteristic
170C2×#117C2311yescharacteristic
171C2×#117C2311yescharacteristic
172C22×C4⋊C4C2311yescharacteristic
173C22×C22⋊C4—21no—
174C22×C42C2311yescharacteristic
175C22×C42C2311yescharacteristic
176C22×C42C2311yescharacteristic
177#485—28no—
178#468—28no—
179#465—28no—
180#450—28no—
181C4×SD16—44no—
182C4×SD16—44no—
183C2×#107C2312yes—
184C2×#107C2312yes—
185C2×#106C2312yes—
186C2×#106C2312yes—
187C2×#106C2312yes—
188C2×#106C2312yes—
189C2×#103C2312yes—
190C2×#103C2312yes—
191C2×#103C2312yes—
192C2×#103C2312yes—
193C2×#103C2312yes—
194C2×#103C2312yes—
195C2×#102C2312yes—
196C2×#102C2312yes—
197C2×#102C2312yes—
198C2×#102C2312yes—
199C2×#102C2312yes—
200C2×#102C2312yes—
201#408—28no—
202C2×C22⋊C8C2312yes—
203C2×C22⋊C8C2312yes—
204C2×C22⋊C8C2312yes—
205C2×C22⋊C8C2312yes—
206C4×M16—42no—
207C2×#97C2311yescharacteristic
208C2×#97C2311yescharacteristic
209C2×C4×C8—42no—
210C2×C4×C8C2312yes—
211C2×C4×C8C2312yes—
212C2×C4×C8C2311yescharacteristic
213C2×C4×C8C2311yescharacteristic
214#400—22no—
215#400—21no—
216#400—21no—
217#399—21no—
218#399—21no—
219#398—21no—
220#398—21no—
221#398—21no—
222#398—21no—
223#398—22no—
224#397—21no—
225#397—21no—
226#397—21no—
227#397—21no—
228#397—22no—
229#397—22no—
230#395—22no—
231#395—21no—
232#395—21no—
233#394—22no—
234#394—22no—
235#394—22no—
236#393—21no—
237#393—21no—
238#391—21no—
239#391C2312yes—
240#391C2312yes—
241#390—21no—
242#390—21no—
243#390—21no—
244#390—22no—
245#390—22no—
246#390C2312yes—
247#390C2312yes—
248#389C2312yes—
249#389C2312yes—
250#389C2312yes—
251#389C2312yes—
252#388—22no—
253#388—22no—
254#388—22no—
255#388—22no—
256#387—22no—
257#387—22no—
258#386—21no—
259#386—21no—
260#386—22no—
261#386—22no—
262#386—22no—
263#386—22no—
264#385—22no—
265#385—22no—
266#385—22no—
267#385—22no—
268#385—21no—
269#385—21no—
270#384—21no—
271#383—21no—
272#382—21no—
273#382C2311yescharacteristic
274#382C2311yescharacteristic
275#381—21no—
276#380C2312yes—
277#380C2312yes—
278#380C2312yes—
279#380C2312yes—
280#380C2312yes—
281#379—21no—
282#379—21no—
283C4×C4⋊C4—22no—
284C4×C4⋊C4—22no—
285C4×C4⋊C4C2312yes—
286C4×C4⋊C4C2312yes—
287C4×C4⋊C4C2312yes—
288C4×C22⋊C4—21no—
289C4×C22⋊C4—21no—
290C4×C22⋊C4—22no—
291C4×C22⋊C4—22no—
292C4×C22⋊C4—21no—
293C4×C22⋊C4—22no—
294C4×C22⋊C4—22no—
295#376—21no—
296#376—21no—
297C43—21no—
298#340C2312yes—
299#340C2312yes—
300#340C2312yes—
301#340C2312yes—
302#340C2312yes—
303#340C2312yes—
304#340C2312yes—
305#340C2312yes—
306#340C2312yes—
307#340C2312yes—
308#340C2312yes—
309#340C2312yes—
310#336C2312yes—
311#336C2312yes—
312#336C2312yes—
313#336C2312yes—
314C25—21no—
315C2×#41—24no—
316C2×#41—24no—
317C2×#41—41no—
318C2×#41—41no—
319C22×Q8—21no—
320C22×Q8C2×D411yescharacteristic
321C22×Q8C2412yes—
322C22×D4—22no—
323C22×D4—22no—
324C22×D4—24no—
325C22×D4—21no—
326C22×D4—24no—
327C22×D4—41no—
328C22×D4—41no—
329C22×D4C2×D411yescharacteristic
330C22×D4C2×D411yescharacteristic
331C22×D4C2×D411yescharacteristic
332C22×D4C2412yes—
333C23×C4—21no—
334C23×C4—22no—
335C23×C4—22no—
336C23×C4—44no—
337C23×C4—84no—
338C23×C4C2×D411yescharacteristic
339C23×C4C2×D411yescharacteristic
340C23×C4C2×D411yescharacteristic
341C23×C4C2×D411yescharacteristic
342C23×C4C2×D411yescharacteristic
343C23×C4C2×D411yescharacteristic
344C23×C4C2411yescharacteristic
345C23×C4C2411yescharacteristic
346C23×C4C2411yescharacteristic
347C2×SD16—24no—
348C2×SD16—24no—
349C2×SD16—24no—
350C2×SD16—24no—
351C2×SD16—42no—
352C2×SD16—42no—
353C2×M16—24no—
354C2×M16—24no—
355C2×M16—42no—
356C22×C8—24no—
357C22×C8—24no—
358C22×C8—42no—
359C22×C8C2412yes—
360C22×C8C2412yes—
361C22×C8C2412yes—
362C22×C8C2412yes—
363C4⋊Q8—41no—
364C4⋊Q8—41no—
365C4⋊Q8—41no—
366C4⋊Q8—41no—
367#127—28no—
368#125—44no—
369#124—28no—
370C22⋊Q8—24no—
371C22⋊Q8—24no—
372C22⋊Q8—24no—
373C22⋊Q8—24no—
374C22⋊Q8—42no—
375C22⋊Q8—42no—
376C22⋊Q8—44no—
377#121—24no—
378#121—24no—
379#121—24no—
380#121#4118yes—
381#120—28no—
382#120—28no—
383C4×Q8—24no—
384C4×Q8—24no—
385C4×Q8—42no—
386C4×Q8—42no—
387C4×Q8—44no—
388C4×D4—24no—
389C4×D4—24no—
390C4×D4—42no—
391C4×D4—42no—
392C4×D4—42no—
393C4×D4—42no—
394C4×D4—42no—
395C4×D4—42no—
396C4×D4—42no—
397C4×D4—42no—
398C4×D4—44no—
399C4×D4—44no—
400C4×D4—84no—
401C4×D4—84no—
402#117—24no—
403#117—24no—
404#117—41no—
405#117—41no—
406#117—41no—
407#117—41no—
408#117—41no—
409#117—41no—
410#117—44no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—41no—
424C2×C4⋊C4—41no—
425C2×C4⋊C4C2×D411yescharacteristic
426C2×C4⋊C4C2×D411yescharacteristic
427C2×C4⋊C4C2×D411yescharacteristic
428C2×C4⋊C4C2×D411yescharacteristic
429C2×C4⋊C4C2×D411yescharacteristic
430C2×C4⋊C4C2×D411yescharacteristic
431C2×C4⋊C4C2412yes—
432C2×C4⋊C4C2412yes—
433C2×C4⋊C4C2412yes—
434C2×C4⋊C4C2412yes—
435C2×C4⋊C4C2412yes—
436C2×C4⋊C4C2412yes—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—22no—
439C2×C22⋊C4—22no—
440C2×C22⋊C4—22no—
441C2×C22⋊C4—21no—
442C2×C22⋊C4—22no—
443C2×C22⋊C4—22no—
444C2×C22⋊C4—22no—
445C2×C22⋊C4—22no—
446C2×C22⋊C4—22no—
447C2×C22⋊C4—22no—
448C2×C22⋊C4—22no—
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⋊C4—44no—
456C2×C22⋊C4C2×D411yescharacteristic
457C2×C22⋊C4C2×D411yescharacteristic
458C2×C22⋊C4C2×D411yescharacteristic
459C2×C22⋊C4C2×D411yescharacteristic
460C2×C22⋊C4C2×D411yescharacteristic
461C2×C22⋊C4C2×D411yescharacteristic
462C2×C42—21no—
463C2×C42—22no—
464C2×C42—22no—
465C2×C42—22no—
466C2×C42—22no—
467C2×C42—22no—
468C2×C42—22no—
469C2×C42—21no—
470C2×C42—22no—
471C2×C42—22no—
472C2×C42—22no—
473C2×C42—22no—
474C2×C42C2×D411yescharacteristic
475C2×C42C2×D411yescharacteristic
476C2×C42C2×D411yescharacteristic
477C2×C42C2×D411yescharacteristic
478C2×C42C2×D411yescharacteristic
479C2×C42C2×D411yescharacteristic
480C2×C42C2411yescharacteristic
481C2×C42C2411yescharacteristic
482C2×C42C2411yescharacteristic
483C2×C42C2411yescharacteristic
484#107—24no—
485#107—24no—
486#106—24no—
487#106—24no—
488#106—42no—
489#106—42no—
490#103—24no—
491#103—24no—
492#103—24no—
493#103—24no—
494#103—42no—
495#103—42no—
496#102—24no—
497#102—24no—
498#102—24no—
499#102—24no—
500#102—42no—
501#102—42no—
502C22⋊C8—24no—
503C22⋊C8—24no—
504C22⋊C8—24no—
505C22⋊C8#4118yes—
506#97—41no—
507#97—41no—
508C4×C8—24no—
509C4×C8—24no—
510C4×C8—41no—
511C4×C8—41no—
512#95—22no—
513#95—22no—
514#95—22no—
515#95—21no—
516#95—21no—
517#95—22no—
518#95—22no—
519#95—22no—
520#95—22no—
521#95—21no—
522#95—21no—
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—
532C24—24no—
533C24—22no—
534C24—42no—
535C24—42no—
536C24—82no—
537C24—82no—
538C24C22×D411yescharacteristic
539C24C22×D411yescharacteristic
540C24C22×D411yescharacteristic
541#41—48no—
542#41—48no—
543C2×Q8—22no—
544C2×Q8—22no—
545C2×Q8—22no—
546C2×Q8—22no—
547C2×Q8—22no—
548C2×Q8—22no—
549C2×Q8—22no—
550C2×Q8—22no—
551C2×Q8—41no—
552C2×Q8—42no—
553C2×Q8—82no—
554C2×D4—24no—
555C2×D4—22no—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—22no—
559C2×D4—28no—
560C2×D4—28no—
561C2×D4—22no—
562C2×D4—22no—
563C2×D4—22no—
564C2×D4—22no—
565C2×D4—22no—
566C2×D4—22no—
567C2×D4—22no—
568C2×D4—48no—
569C2×D4—48no—
570C2×D4—41no—
571C2×D4—41no—
572C2×D4—41no—
573C2×D4—42no—
574C2×D4—42no—
575C2×D4—82no—
576C2×D4—82no—
577C2×D4—82no—
578C2×D4—82no—
579C2×D4C2×#4114yes—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—24no—
592C22×C4—24no—
593C22×C4—24no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—42no—
607C22×C4—42no—
608C22×C4—42no—
609C22×C4—44no—
610C22×C4—42no—
611C22×C4—44no—
612C22×C4—44no—
613C22×C4—44no—
614C22×C4—82no—
615C22×C4—82no—
616C22×C4—82no—
617C22×C4—816no—
618C22×C4C22×D411yescharacteristic
619C22×C4C22×D411yescharacteristic
620C22×C4C22×D411yescharacteristic
621C22×C4C22×D411yescharacteristic
622C22×C4C22×D411yescharacteristic
623C22×C4C22×D411yescharacteristic
624C22×C4C22×D411yescharacteristic
625C22×C4C22×D411yescharacteristic
626C22×C4C22×D411yescharacteristic
627C22×C4C22×D411yescharacteristic
628C22×C4C22×D411yescharacteristic
629C22×C4C2×#4114yes—
630C22×C4C2×#4114yes—
631C22×C4C2511yescharacteristic
632SD16—48no—
633SD16—48no—
634M16—48no—
635C2×C8—22no—
636C2×C8—22no—
637C2×C8—22no—
638C2×C8—22no—
639C2×C8—22no—
640C2×C8—22no—
641C2×C8—22no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—22no—
645C2×C8—48no—
646C2×C8C2×#4114yes—
647C2×C8C2×#4114yes—
648C4⋊C4—22no—
649C4⋊C4—22no—
650C4⋊C4—22no—
651C4⋊C4—22no—
652C4⋊C4—22no—
653C4⋊C4—22no—
654C4⋊C4—22no—
655C4⋊C4—22no—
656C4⋊C4—22no—
657C4⋊C4—22no—
658C4⋊C4—22no—
659C4⋊C4—41no—
660C4⋊C4—41no—
661C4⋊C4—41no—
662C4⋊C4—41no—
663C4⋊C4—41no—
664C4⋊C4—41no—
665C4⋊C4—42no—
666C4⋊C4—42no—
667C4⋊C4—42no—
668C4⋊C4—44no—
669C4⋊C4—42no—
670C4⋊C4—44no—
671C4⋊C4—44no—
672C4⋊C4—44no—
673C4⋊C4—82no—
674C4⋊C4—82no—
675C4⋊C4—82no—
676C4⋊C4—82no—
677C4⋊C4C2×#4114yes—
678C22⋊C4—24no—
679C22⋊C4—28no—
680C22⋊C4—28no—
681C22⋊C4—41no—
682C22⋊C4—41no—
683C22⋊C4—41no—
684C22⋊C4—41no—
685C22⋊C4—41no—
686C22⋊C4—41no—
687C22⋊C4—44no—
688C22⋊C4—44no—
689C22⋊C4—44no—
690C22⋊C4—42no—
691C22⋊C4—44no—
692C22⋊C4—44no—
693C22⋊C4—82no—
694C22⋊C4—82no—
695C22⋊C4—82no—
696C22⋊C4—82no—
697C22⋊C4—82no—
698C22⋊C4—82no—
699C22⋊C4—82no—
700C22⋊C4—82no—
701C22⋊C4—82no—
702C42—24no—
703C42—22no—
704C42—22no—
705C42—22no—
706C42—22no—
707C42—22no—
708C42—22no—
709C42—21no—
710C42—21no—
711C42—21no—
712C42—21no—
713C42—21no—
714C42—21no—
715C42—42no—
716C42—44no—
717C42—44no—
718C42—44no—
719C42—82no—
720C42H(5,𝔽2)12yes—
721C42H(5,𝔽2)12yes—
722C23—22no—
723C23—22no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—22no—
729C23—22no—
730C23—22no—
731C23—24no—
732C23—21no—
733C23—21no—
734C23—21no—
735C23—22no—
736C23—48no—
737C23—42no—
738C23—42no—
739C23—42no—
740C23—42no—
741C23—42no—
742C23—42no—
743C23—88no—
744C23—88no—
745C23—84no—
746C23—84no—
747C23#52512yes—
748C23#53212yes—
749C23C23×D411yescharacteristic
750Q8—44no—
751Q8—42no—
752Q8—42no—
753Q8—42no—
754Q8—42no—
755Q8—84no—
756D4—24no—
757D4—24no—
758D4—44no—
759D4—44no—
760D4—48no—
761D4—44no—
762D4—42no—
763D4—42no—
764D4—88no—
765D4—88no—
766C2×C4—22no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—24no—
772C2×C4—24no—
773C2×C4—24no—
774C2×C4—24no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—24no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—44no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—44no—
795C2×C4—44no—
796C2×C4—44no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—82no—
818C2×C4—82no—
819C2×C4—88no—
820C2×C4—84no—
821C2×C4—88no—
822C2×C4#52512yes—
823C2×C4#53212yes—
824C2×C4#53412yes—
825C2×C4#53412yes—
826C2×C4#57714yes—
827C2×C4C22×#4112yes—
828C2×C4C22×#4112yes—
829C2×C4C2×H(5,𝔽2)11yescharacteristic
830C2×C4C2×H(5,𝔽2)11yescharacteristic
831C8—24no—
832C8—24no—
833C8—42no—
834C8—42no—
835C22—24no—
836C22—22no—
837C22—22no—
838C22—24no—
839C22—42no—
840C22—41no—
841C22—41no—
842C22—41no—
843C22—41no—
844C22—42no—
845C22—42no—
846C22—41no—
847C22—41no—
848C22—41no—
849C22—44no—
850C22—42no—
851C22—44no—
852C22—44no—
853C22—816no—
854C22—82no—
855C22—82no—
856C22—82no—
857C22—82no—
858C22C2×#52511yescharacteristic
859C22C2×#53211yescharacteristic
860C22C2×#53411yescharacteristic
861C22C2×#57712yes—
862C22#358412yes—
863C4—22no—
864C4—22no—
865C4—22no—
866C4—41no—
867C4—41no—
868C4—41no—
869C4—41no—
870C4—41no—
871C4—41no—
872C4—41no—
873C4—44no—
874C4—82no—
875C4—82no—
876C4—82no—
877C4—82no—
878C4—82no—
879C4—82no—
880C4#320014yes—
881C4#348112yes—
882C4#348112yes—
883C2—42no—
884C2—42no—
885C2—81no—
886C2—84no—
887C2#3495711yescharacteristic
888C2#6057112yes—
889C2#6069412yes—
890C2C2×#320011yescharacteristic
891C2#6074911yescharacteristic
subgroupG/H
centerC22×C4C22×D4
commutator, Frattini, cosocleC22×C4C25
socleC23C23×D4
prime radicalC2×#535C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4 ◁ C2×C4×#41 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #34627C2semidirect
3. #29488C2semidirect
4. #29472C2semidirect
5. #29344C2semidirect
6. #29311C2semidirect
7. #29174C2semidirect
8. #29116C2semidirect
9. #28583C2semidirect
10. #28320C2semidirect
11. #24569C2semidirect
13. #23758C2semidirect
14. #23568C2semidirect
15. C4×#485C2semidirect
16. C4×#468C2semidirect
17. C4×#465C2semidirect
18. C4×#450C2semidirect
19. C4×#408C2semidirect
21. C2×#533C22semidirect
31. C2×C4×M16C22semidirect
32. C22×C4×C8C22semidirect
38. #2628C22semidirect
39. #2625C22semidirect
41. #2621C22semidirect
59. C4×C22⋊Q8C22semidirect
64. #2283C22semidirect
66. #2101C22semidirect
68. #2085C22semidirect
69. #2077C22semidirect
70. #2076C22semidirect
72. #2058C22semidirect
73. #2043C22semidirect
74. #2035C22semidirect
75. #2035C22semidirect
84. #1943C22semidirect
85. #1941C22semidirect
87. #1935C22semidirect
89. #1933C22semidirect
90. #1928C22semidirect
91. #1927C22semidirect
92. #1919C22semidirect
93. #1918C22semidirect
95. #1894C22semidirect
97. #1892C22semidirect
107. #1809C22semidirect
108. #1807C22semidirect
110. C4×#107C22semidirect
111. C4×#106C22semidirect
112. C4×#103C22semidirect
113. C4×#103C22semidirect
118. #1750C22semidirect
119. #1750C22semidirect
121. C4×C22⋊C8C22semidirect
122. #1729C22semidirect

Maximal subgroups

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

subgroupindex
#346272
C4×#5352
#294882
#294722
#293442
#293112
#291742
#291162
#285832
#283202
#245692
#243942
#237582
#235682
C4×#4852
C4×#4682
C4×#4652
C4×#4502
C4×#4082