Finite Group Databasebeta

← #6382469

Subgroups — #6382469

Order 512.

2022 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3106C211yesmaximal, characteristic
2#34232C211yesmaximal, characteristic, complemented
3#34195C211yesmaximal, characteristic, complemented
4#23106C212yesmaximal, complemented
5#23073C212yesmaximal, complemented
6#23008C212yesmaximal, complemented
7#22975C212yesmaximal, complemented
8#22933C212yesmaximal, complemented
9#22923C212yesmaximal, complemented
10#22872C212yesmaximal, complemented
11#22860C212yesmaximal, complemented
12#21408C211yesmaximal, characteristic, complemented
13#21360C211yesmaximal, characteristic, complemented
14#21285C211yesmaximal, characteristic, complemented
15#21280C211yesmaximal, characteristic, complemented
16#21134C211yesmaximal, characteristic, complemented
17#21133C211yesmaximal, characteristic, complemented
18#21130C211yesmaximal, characteristic, complemented
19#21129C211yesmaximal, characteristic, complemented
20#20508C211yesmaximal, characteristic, complemented
21#20503C211yesmaximal, characteristic, complemented
22#20481C211yesmaximal, characteristic, complemented
23#20411C211yesmaximal, characteristic, complemented
24C2×#532C2211yescharacteristic
25C2×C4×#41C2211yescharacteristic
26#3106C4116yescomplemented
27C2×#482C2211yescharacteristic
28C2×#482C2211yescharacteristic
29C2×#477C2211yescharacteristic
30C2×#476C2211yescharacteristic
31C2×#460C2211yescharacteristic
32C2×#459C2211yescharacteristic
33C2×#449C2211yescharacteristic
34C2×#449C2211yescharacteristic
35C2×#442C2212yes—
36C2×C4×SD16C2211yescharacteristic
37C2×C4×SD16C2211yescharacteristic
38C2×C4×D8C2212yes—
39C2×C4×D8C2211yescharacteristic
40C2×C4×D8C2211yescharacteristic
41C2×#431C2211yescharacteristic
42C2×#416C2212yes—
43C22×#97C2211yescharacteristic
44#2366C2212yes—
45#2365C2212yes—
46#2363C2212yes—
47#2363C2212yes—
48#2356C2212yes—
49#2353—21no—
50#2353—21no—
51#2353—22no—
52#2349C2212yes—
53#2347C2212yes—
54#2343—22no—
55#2341—21no—
56#2339—21no—
57#2339C2212yes—
58#2333—22no—
59#2320C2211yescharacteristic
60#2320C2211yescharacteristic
61#2319C2211yescharacteristic
62#2319C2211yescharacteristic
63#2318—21no—
64#2318—21no—
65C4×#124—22no—
66#2283—21no—
67#2283C2211yescharacteristic
68#2283C2211yescharacteristic
69C2×#383—21no—
70#2275C2211yescharacteristic
71#2275C2211yescharacteristic
72#2275C2211yescharacteristic
73#2275C2211yescharacteristic
74C4×#117C2211yescharacteristic
75#1993C2212yes—
76#1973C2212yes—
77#1968C2212yes—
78#1961C2212yes—
79#1949C2212yes—
80#1949C2212yes—
81#1944C2212yes—
82#1941C2212yes—
83#1936C2212yes—
84#1935C2212yes—
85#1934C2212yes—
86#1933C2212yes—
87#1928C2212yes—
88#1927C2212yes—
89#1926C2212yes—
90#1925C2212yes—
91#1921C2212yes—
92#1920C2212yes—
93#1919C2212yes—
94#1918C2212yes—
95#1893C2212yes—
96#1893C2212yes—
97#1879C2212yes—
98#1879C2212yes—
99#1877C2212yes—
100#1877C2212yes—
101#1864C2212yes—
102#1864C2212yes—
103#1862C2212yes—
104#1862C2212yes—
105#1854C2212yes—
106#1854C2212yes—
107#1776C2212yes—
108C4×#107C2212yes—
109C4×#107C2211yescharacteristic
110C4×#107C2211yescharacteristic
111C4×#106C2211yescharacteristic
112C4×#106C2211yescharacteristic
113#1771C2212yes—
114#1771C2212yes—
115#1763C2211yescharacteristic
116#1763C2212yes—
117#1763C2211yescharacteristic
118#1762C2211yescharacteristic
119#1762C2211yescharacteristic
120#1762C2211yescharacteristic
121#1762C2212yes—
122#1762C2212yes—
123#1762C2211yescharacteristic
124#1762C2211yescharacteristic
125#1762C2211yescharacteristic
126#1762C2212yes—
127C4×#102C2212yes—
128C4×#102C2212yes—
129#1752C2212yes—
130C8×C22⋊C4C2212yes—
131#1746C2211yescharacteristic
132#1746C2211yescharacteristic
133#1735C2212yes—
134#1726C2211yescharacteristic
135#1726C2211yescharacteristic
136C22×#41—21no—
137C22×#41C2311yescharacteristic
138C22×SD16C2311yescharacteristic
139C22×SD16C2311yescharacteristic
140C22×D8C2311yescharacteristic
141C22×D8C2311yescharacteristic
142C23×C8C2312yes—
143#532—24no—
144#532C2×C418yescomplemented
145C2×C4⋊Q8C2311yescharacteristic
146C2×#127C2311yescharacteristic
147C2×#124—21no—
148C2×#121—21no—
149C2×#121C2311yescharacteristic
150C2×#121C2311yescharacteristic
151C4×#41—24no—
152C4×#41C2×C418yescomplemented
153C2×C4×Q8—22no—
154C2×C4×Q8C2311yescharacteristic
155C2×C4×Q8C2311yescharacteristic
156C2×C4×D4—21no—
157C2×C4×D4—21no—
158C2×C4×D4—22no—
159C2×C4×D4—21no—
160C2×C4×D4C2312yes—
161C2×C4×D4C2312yes—
162C2×C4×D4C2312yes—
163C2×C4×D4C2312yes—
164C2×C4×D4C2311yescharacteristic
165C2×C4×D4C2311yescharacteristic
166C2×C4×D4C2311yescharacteristic
167C2×C4×D4C2311yescharacteristic
168C2×#117—21no—
169C2×#117C2312yes—
170C2×#117C2311yescharacteristic
171C22×C42—21no—
172C22×C42C2311yescharacteristic
173#482C2×C418yescomplemented
174#482C2×C418yescomplemented
175#477C2×C418yescomplemented
176#476C2×C418yescomplemented
177#460C2×C418yescomplemented
178#459C2×C418yes—
179#449C2×C418yescomplemented
180#449C2×C418yescomplemented
181#442—28no—
182C4×SD16C2×C418yescomplemented
183C4×SD16C2×C418yescomplemented
184C4×D8—28no—
185C4×D8C2×C418yescomplemented
186C4×D8C2×C418yescomplemented
187#431C2×C418yescomplemented
188C2×#107C2312yes—
189C2×#107C2312yes—
190C2×#107C2311yescharacteristic
191C2×#107C2311yescharacteristic
192C2×#106C2312yes—
193C2×#106C2312yes—
194C2×#106C2311yescharacteristic
195C2×#106C2311yescharacteristic
196C2×C4⋊C8C2311yescharacteristic
197C2×C4⋊C8C2311yescharacteristic
198#416—28no—
199C2×#103C2312yes—
200C2×#103C2312yes—
201C2×#103C2311yescharacteristic
202C2×#103C2311yescharacteristic
203C2×#102C2312yes—
204C2×#102C2312yes—
205C2×#102C2312yes—
206C2×#102C2312yes—
207C2×#102C2312yes—
208C2×#102C2311yescharacteristic
209C2×#102C2311yescharacteristic
210C2×#102C2311yescharacteristic
211C2×#102C2311yescharacteristic
212C2×#102C2311yescharacteristic
213C2×#102C2311yescharacteristic
214C2×#102C2312yes—
215C2×C22⋊C8C2311yescharacteristic
216C2×C22⋊C8C2311yescharacteristic
217C2×#97—24no—
218C2×#97C2312yes—
219C2×#97C2311yescharacteristic
220C2×#97C2311yescharacteristic
221C2×#97C2312yes—
222C2×#97C2312yes—
223C2×C4×C8C2312yes—
224C2×C4×C8C2312yes—
225C2×C4×C8C2311yescharacteristic
226C2×C4×C8C2311yescharacteristic
227#391—22no—
228#391C2312yes—
229#391C2312yes—
230#390—22no—
231#390—22no—
232#390—22no—
233#390C2312yes—
234#390C2312yes—
235#389C2312yes—
236#389C2312yes—
237#389C2312yes—
238#389C2312yes—
239#388—22no—
240#388—22no—
241#388—22no—
242#388—22no—
243#388—22no—
244#388—22no—
245#387—22no—
246#387—22no—
247#387—22no—
248#387—22no—
249#387—22no—
250#387—22no—
251#386—22no—
252#386—22no—
253#386—22no—
254#386—22no—
255#386—22no—
256#386—22no—
257#385—22no—
258#385—22no—
259#383—21no—
260#383—21no—
261#383—21no—
262#383—22no—
263#383—22no—
264#383D411yescharacteristic
265#383D411yescharacteristic
266#382—21no—
267#382—21no—
268#382D412yes—
269#382C2312yes—
270#381—21no—
271#381—21no—
272#381—21no—
273#381—22no—
274#381D412yes—
275#380—21no—
276#380—21no—
277#380—22no—
278#380D411yescharacteristic
279#380D411yescharacteristic
280#380C2312yes—
281C4×C4⋊C4—22no—
282C4×C4⋊C4C2311yescharacteristic
283C4×C4⋊C4C2311yescharacteristic
284C4×C4⋊C4C2311yescharacteristic
285C4×C4⋊C4C2312yes—
286C4×C4⋊C4C2312yes—
287C4×C4⋊C4C2312yes—
288C4×C4⋊C4C2312yes—
289C4×C4⋊C4C2312yes—
290C4×C4⋊C4C2311yescharacteristic
291C4×C4⋊C4C2312yes—
292C4×C22⋊C4—21no—
293C4×C22⋊C4—21no—
294C4×C22⋊C4—21no—
295C4×C22⋊C4—21no—
296C4×C22⋊C4—21no—
297C4×C22⋊C4—22no—
298C4×C22⋊C4—22no—
299C4×C22⋊C4—21no—
300C4×C22⋊C4—21no—
301C4×C22⋊C4—22no—
302C4×C22⋊C4—22no—
303C4×C22⋊C4—22no—
304C4×C22⋊C4—22no—
305C4×C22⋊C4C2312yes—
306#376—21no—
307#376—21no—
308#376—22no—
309#376C2311yescharacteristic
310#376C2311yescharacteristic
311C2×#95—21no—
312C2×#95—21no—
313C2×#95—21no—
314C2×#95—21no—
315C2×#95—22no—
316C2×#95—22no—
317C43—21no—
318#340C2312yes—
319#340C2312yes—
320#340C2312yes—
321#340C2312yes—
322#340C2312yes—
323#340C2312yes—
324#340C2312yes—
325#340C2312yes—
326#340C2312yes—
327#340C2312yes—
328#340C2312yes—
329#340C2312yes—
330#336C2312yes—
331#336C2312yes—
332#336C2312yes—
333#336C2312yes—
334C2×#41—28no—
335C2×#41—22no—
336C2×#41—24no—
337C2×#41—42no—
338C2×#41—84no—
339C2×#41C22×C414yes—
340C22×Q8—21no—
341C22×Q8C2411yescharacteristic
342C22×D4—21no—
343C22×D4—21no—
344C22×D4—21no—
345C22×D4—21no—
346C22×D4—21no—
347C22×D4C2411yescharacteristic
348C22×D4C2411yescharacteristic
349C22×D4C2411yescharacteristic
350C23×C4—21no—
351C23×C4—21no—
352C23×C4—21no—
353C23×C4—21no—
354C23×C4—21no—
355C23×C4—22no—
356C23×C4—22no—
357C23×C4—22no—
358C23×C4—22no—
359C23×C4C2×D411yescharacteristic
360C23×C4C2×D411yescharacteristic
361C23×C4C2411yescharacteristic
362C2×SD16—42no—
363C2×SD16—42no—
364C2×SD16C22×C414yes—
365C2×SD16C22×C414yes—
366C2×D8—24no—
367C2×D8—24no—
368C2×D8C22×C414yes—
369C2×D8C22×C414yes—
370C22×C8—24no—
371C22×C8—24no—
372C22×C8—42no—
373C22×C8C2412yes—
374C22×C8C2411yescharacteristic
375C22×C8C2411yescharacteristic
376C22×C8C2411yescharacteristic
377C22×C8C2411yescharacteristic
378C22×C8C2412yes—
379C4⋊Q8—22no—
380C4⋊Q8C22×C414yes—
381#127—22no—
382#127C22×C414yes—
383#124—28no—
384#121—28no—
385#121—22no—
386#121—22no—
387#121C22×C414yes—
388#121C22×C414yes—
389C4×Q8—22no—
390C4×Q8—22no—
391C4×Q8—84no—
392C4×Q8C22×C414yes—
393C4×Q8C22×C414yes—
394C4×D4—28no—
395C4×D4—28no—
396C4×D4—24no—
397C4×D4—24no—
398C4×D4—24no—
399C4×D4—24no—
400C4×D4—28no—
401C4×D4—22no—
402C4×D4—22no—
403C4×D4—22no—
404C4×D4—22no—
405C4×D4—42no—
406C4×D4—42no—
407C4×D4—42no—
408C4×D4—42no—
409C4×D4—84no—
410C4×D4C22×C414yes—
411C4×D4C22×C414yes—
412C4×D4C22×C414yes—
413C4×D4C22×C414yes—
414#117—22no—
415#117—28no—
416#117—24no—
417#117—42no—
418#117C22×C414yes—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4C2×D412yes—
427C2×C4⋊C4C2×D412yes—
428C2×C4⋊C4C2412yes—
429C2×C4⋊C4C2412yes—
430C2×C4⋊C4C2412yes—
431C2×C4⋊C4C2411yescharacteristic
432C2×C4⋊C4C2411yescharacteristic
433C2×C4⋊C4C2411yescharacteristic
434C2×C4⋊C4C2411yescharacteristic
435C2×C4⋊C4C2412yes—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4—21no—
440C2×C22⋊C4—21no—
441C2×C22⋊C4—21no—
442C2×C22⋊C4—21no—
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⋊C4C2×D412yes—
454C2×C22⋊C4C2×D412yes—
455C2×C42—21no—
456C2×C42—21no—
457C2×C42—21no—
458C2×C42—28no—
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—22no—
468C2×C42—22no—
469C2×C42C22×C414yes—
470C2×C42C2×D411yescharacteristic
471C2×C42C2×D411yescharacteristic
472C2×C42#4114yes—
473C2×C42C2412yes—
474C2×C42C2412yes—
475C2×C42C2411yescharacteristic
476C2×C42C2411yescharacteristic
477#107—24no—
478#107—42no—
479#107C22×C414yes—
480#107C22×C414yes—
481#106—24no—
482#106—42no—
483#106C22×C414yes—
484#106C22×C414yes—
485C4⋊C8C22×C414yes—
486C4⋊C8C22×C414yes—
487#103—24no—
488#103—24no—
489#103C22×C414yes—
490#103C22×C414yes—
491#102—24no—
492#102—24no—
493#102—24no—
494#102—42no—
495#102—42no—
496#102C22×C414yes—
497#102C22×C414yes—
498#102C22×C414yes—
499#102C22×C414yes—
500#102C22×C414yes—
501#102C22×C414yes—
502#102#4118yescomplemented
503C22⋊C8C22×C414yes—
504C22⋊C8C22×C414yes—
505#97—24no—
506#97—22no—
507#97—22no—
508#97—24no—
509#97—42no—
510C4×C8—24no—
511C4×C8—42no—
512C4×C8C22×C414yes—
513C4×C8C22×C414yes—
514#95—21no—
515#95—22no—
516#95—22no—
517#95—21no—
518#95—21no—
519#95—22no—
520#95—22no—
521#95—22no—
522#95—22no—
523#95—22no—
524#95—22no—
525#95—22no—
526#95—22no—
527#95—21no—
528#95—22no—
529#95—22no—
530#95—22no—
531#95—22no—
532#95—22no—
533#95—22no—
534#95C2×D411yescharacteristic
535#95C2×D411yescharacteristic
536#95C2×D411yescharacteristic
537#95C2×D412yes—
538#95C2×D412yes—
539#95C2×D412yes—
540#95C2×D411yescharacteristic
541#95C2×D412yes—
542#95C2×D412yes—
543#95C2×D412yes—
544C24—21no—
545C24—21no—
546C24—21no—
547C24C22×D411yescharacteristic
548#41—28no—
549#41—44no—
550#41—48no—
551#41—816no—
552C2×Q8—24no—
553C2×Q8—21no—
554C2×Q8—22no—
555C2×Q8—22no—
556C2×Q8—44no—
557C2×Q8C23×C412yes—
558C2×D4—24no—
559C2×D4—24no—
560C2×D4—24no—
561C2×D4—24no—
562C2×D4—24no—
563C2×D4—21no—
564C2×D4—22no—
565C2×D4—22no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—22no—
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—44no—
572C2×D4—44no—
573C2×D4—81no—
574C2×D4—81no—
575C2×D4—82no—
576C2×D4—82no—
577C2×D4C23×C412yes—
578C2×D4C23×C412yes—
579C2×D4C23×C412yes—
580C2×D4C2×#4114yes—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—22no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—24no—
590C22×C4—24no—
591C22×C4—24no—
592C22×C4—24no—
593C22×C4—24no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—41no—
598C22×C4—41no—
599C22×C4—42no—
600C22×C4—44no—
601C22×C4—44no—
602C22×C4—44no—
603C22×C4—44no—
604C22×C4—44no—
605C22×C4—81no—
606C22×C4—81no—
607C22×C4—82no—
608C22×C4—82no—
609C22×C4—82no—
610C22×C4—82no—
611C22×C4—82no—
612C22×C4—82no—
613C22×C4—82no—
614C22×C4—82no—
615C22×C4—82no—
616C22×C4—82no—
617C22×C4—82no—
618C22×C4C4×D414yes—
619C22×C4C4×D414yes—
620C22×C4C23×C412yes—
621C22×C4C22×D412yes—
622C22×C4C22×D412yes—
623C22×C4C22×D412yes—
624C22×C4C22×D412yes—
625C22×C4C22×D411yescharacteristic
626C22×C4C22×D411yescharacteristic
627C22×C4C22×D411yescharacteristic
628C22×C4C22×D411yescharacteristic
629C22×C4C22×D411yescharacteristic
630C22×C4C2×#4112yes—
631C22×C4C2511yescharacteristic
632SD16—44no—
633SD16—44no—
634D8—28no—
635D8—28no—
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×C8C23×C412yes—
647C2×C8C23×C412yes—
648C2×C8C23×C412yes—
649C2×C8C23×C412yes—
650C2×C8C2×#4114yes—
651C4⋊C4—24no—
652C4⋊C4—24no—
653C4⋊C4—24no—
654C4⋊C4—21no—
655C4⋊C4—21no—
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—22no—
665C4⋊C4—42no—
666C4⋊C4—42no—
667C4⋊C4—82no—
668C4⋊C4—82no—
669C4⋊C4—82no—
670C4⋊C4—82no—
671C4⋊C4C23×C412yes—
672C4⋊C4C23×C412yes—
673C4⋊C4C23×C412yes—
674C4⋊C4C23×C412yes—
675C4⋊C4C2×#4114yes—
676C22⋊C4—24no—
677C22⋊C4—24no—
678C22⋊C4—24no—
679C22⋊C4—24no—
680C22⋊C4—24no—
681C22⋊C4—24no—
682C22⋊C4—24no—
683C22⋊C4—42no—
684C22⋊C4—42no—
685C22⋊C4—44no—
686C22⋊C4—44no—
687C22⋊C4—44no—
688C22⋊C4—44no—
689C22⋊C4—44no—
690C22⋊C4—82no—
691C22⋊C4—82no—
692C22⋊C4—82no—
693C22⋊C4—82no—
694C22⋊C4—82no—
695C42—24no—
696C42—24no—
697C42—24no—
698C42—22no—
699C42—22no—
700C42—22no—
701C42—22no—
702C42—44no—
703C42—44no—
704C42—81no—
705C42—81no—
706C42—81no—
707C42—81no—
708C42—82no—
709C42—82no—
710C42—82no—
711C42—82no—
712C42C4×D414yes—
713C42C4×D414yes—
714C42C23×C412yes—
715C42C23×C412yes—
716C42C2×#4112yes—
717C42C2×#4112yes—
718C23—21no—
719C23—21no—
720C23—22no—
721C23—22no—
722C23—22no—
723C23—24no—
724C23—22no—
725C23—22no—
726C23—41no—
727C23—41no—
728C23—42no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—42no—
734C23—42no—
735C23—42no—
736C23—42no—
737C23C2×C4×D412yes—
738C23C23×D411yescharacteristic
739Q8—22no—
740Q8—22no—
741Q8—48no—
742Q8—42no—
743D4—22no—
744D4—22no—
745D4—22no—
746D4—22no—
747D4—22no—
748D4—24no—
749D4—48no—
750D4—48no—
751D4—42no—
752D4—42no—
753D4—84no—
754D4—84no—
755D4—84no—
756D4C4×#4114yes—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—24no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
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—22no—
783C2×C4—22no—
784C2×C4—24no—
785C2×C4—44no—
786C2×C4—44no—
787C2×C4—48no—
788C2×C4—42no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
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—84no—
806C2×C4—84no—
807C2×C4—84no—
808C2×C4—84no—
809C2×C4—164no—
810C2×C4—164no—
811C2×C4—164no—
812C2×C4—164no—
813C2×C4C2×C4×D412yes—
814C2×C4C2×C4×D412yes—
815C2×C4C2×C4×D412yes—
816C2×C4C2×C4×D412yes—
817C2×C4C2×C4×D412yes—
818C2×C4C24×C411yescharacteristic
819C2×C4C22×#4112yes—
820C2×C4C22×#4111yescharacteristic
821C2×C4#58512yes—
822C8—22no—
823C8—22no—
824C8—22no—
825C8—22no—
826C8—24no—
827C8—42no—
828C22—22no—
829C22—22no—
830C22—22no—
831C22—24no—
832C22—42no—
833C22—42no—
834C22—44no—
835C22—42no—
836C22—44no—
837C22—42no—
838C22—42no—
839C22—42no—
840C22—42no—
841C22—42no—
842C22—42no—
843C22—42no—
844C22—82no—
845C22—82no—
846C22—82no—
847C22—82no—
848C22C22×C4×D411yescharacteristic
849C22D4×#4112yes—
850C22#358411yescharacteristic
851C22#358411yescharacteristic
852C22#358512yes—
853C4—22no—
854C4—22no—
855C4—22no—
856C4—22no—
857C4—22no—
858C4—42no—
859C4—42no—
860C4—42no—
861C4—42no—
862C4—42no—
863C4—42no—
864C4—42no—
865C4—44no—
866C4—42no—
867C4—42no—
868C4—82no—
869C4—82no—
870C4—82no—
871C4C2×C4×#4111yescharacteristic
872C4#342811yescharacteristic
873C4#347512yes—
874C2—42no—
875C2—44no—
876C2—82no—
877C2—82no—
878C2#3413611yescharacteristic
879C2#6016711yescharacteristic
880C2#6016811yescharacteristic
881C2#6152912yes—
882C2#6153112yes—
subgroupG/H
center, socleC23C23×D4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
prime radicalC2×#3106C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2283 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #34232C2semidirect
3. #34195C2semidirect
4. #23106C2semidirect
5. #23073C2semidirect
6. #23008C2semidirect
7. #22975C2semidirect
8. #22933C2semidirect
9. #22923C2semidirect
10. #22872C2semidirect
11. #22860C2semidirect
12. #21408C2semidirect
13. #21360C2semidirect
14. #21285C2semidirect
15. #21280C2semidirect
16. #21134C2semidirect
17. #21133C2semidirect
18. #21130C2semidirect
19. #21129C2semidirect
20. #20508C2semidirect
21. #20503C2semidirect
22. #20481C2semidirect
23. #20411C2semidirect
26. #3106C4semidirect
144. #532C2×C4semidirect
152. C4×#41C2×C4semidirect
173. #482C2×C4semidirect
174. #482C2×C4semidirect
175. #477C2×C4semidirect
176. #476C2×C4semidirect
177. #460C2×C4semidirect
179. #449C2×C4semidirect
180. #449C2×C4semidirect
182. C4×SD16C2×C4semidirect
183. C4×SD16C2×C4semidirect
185. C4×D8C2×C4semidirect
186. C4×D8C2×C4semidirect
187. #431C2×C4semidirect
502. #102#41semidirect

Maximal subgroups

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

subgroupindex
C2×#31062
#342322
#341952
#231062
#230732
#230082
#229752
#229332
#229232
#228722
#228602
#214082
#213602
#212852
#212802
#211342
#211332
#211302
#211292
#205082
#205032
#204812
#204112