Finite Group Databasebeta

← #6383013

Subgroups — #6383013

Order 512.

1986 conjugacy classes of subgroups.

The subgroup lattice has 883 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3182C211yesmaximal, characteristic
2#34236C211yesmaximal, characteristic
3#34231C211yesmaximal, characteristic, complemented
4#23223C211yesmaximal, characteristic, complemented
5#23221C211yesmaximal, characteristic, complemented
6#23217C211yesmaximal, characteristic, complemented
7#23215C211yesmaximal, characteristic, complemented
8#23190C211yesmaximal, characteristic, complemented
9#23182C211yesmaximal, characteristic, complemented
10#23162C211yesmaximal, characteristic, complemented
11#23158C211yesmaximal, characteristic, complemented
12#23141C212yesmaximal, complemented
13#23138C212yesmaximal, complemented
14#23040C212yesmaximal, complemented
15#23034C212yesmaximal, complemented
16#21390C211yesmaximal, characteristic
17#21385C211yesmaximal, characteristic, complemented
18#21291C212yesmaximal, complemented
19#21128C212yesmaximal, complemented
20#21125C212yesmaximal, complemented
21#20504C212yesmaximal, complemented
22#20482C211yesmaximal, characteristic, complemented
23C4×#428C211yesmaximal, characteristic, complemented
24C2×#533C2211yescharacteristic
25C2×#532C2211yescharacteristic
26#3182C4116yescomplemented
27C2×#500C2211yescharacteristic
28C2×#492C2211yescharacteristic
29C2×#487C2211yescharacteristic
30C2×#486C2211yescharacteristic
31C2×#468C2212yes—
32C2×#468C2212yes—
33C2×#440C2212yes—
34C2×#440C2212yes—
35C2×#440C2212yes—
36C2×C4×SD16C2212yes—
37C2×#431C2211yescharacteristic
38C2×#428C2211yescharacteristic
39C2×#428C2211yescharacteristic
40C2×C4×M16C2211yescharacteristic
41#2369C2211yescharacteristic
42#2369C2211yescharacteristic
43#2369C2211yescharacteristic
44#2369C2211yescharacteristic
45#2366C2211yescharacteristic
46#2366C2211yescharacteristic
47#2365C2211yescharacteristic
48#2365C2211yescharacteristic
49#2362C2212yes—
50#2362C2212yes—
51#2361C2212yes—
52#2361C2212yes—
53#2357—21no—
54#2356—22no—
55#2349—21no—
56#2347—21no—
57#2346—21no—
58#2339—22no—
59#2337—22no—
60#2332—22no—
61#2320C2212yes—
62#2319C2212yes—
63C4×#125—21no—
64C4×#125—21no—
65C4×#121—21no—
66C4×#121—21no—
67#2283C2211yescharacteristic
68#2276C2212yes—
69#2275C2212yes—
70C4×#117C2211yescharacteristic
71C2×C4×C4⋊C4C2211yescharacteristic
72#1987C2211yescharacteristic
73#1987C2211yescharacteristic
74#1987C2211yescharacteristic
75#1987C2211yescharacteristic
76#1982C2211yescharacteristic
77#1982C2211yescharacteristic
78#1981C2211yescharacteristic
79#1981C2211yescharacteristic
80#1973C2212yes—
81#1968C2212yes—
82#1943C2212yes—
83#1942C2212yes—
84#1936C2212yes—
85#1935C2212yes—
86#1934C2212yes—
87#1933C2212yes—
88#1928C2212yes—
89#1927C2212yes—
90#1926C2212yes—
91#1925C2212yes—
92#1921C2212yes—
93#1921C2212yes—
94#1918C2212yes—
95#1918C2212yes—
96#1880C2212yes—
97#1880C2212yes—
98#1877C2212yes—
99#1877C2212yes—
100#1875C2212yes—
101#1875C2212yes—
102#1872C2212yes—
103#1872C2212yes—
104#1865C2212yes—
105#1864C2212yes—
106#1863C2212yes—
107#1862C2212yes—
108#1776C2211yescharacteristic
109#1776C2212yes—
110#1776C2211yescharacteristic
111#1776C2211yescharacteristic
112#1776C2211yescharacteristic
113C4×#107C2212yes—
114C4×#107C2211yescharacteristic
115C4×#107C2211yescharacteristic
116C4×#106C2211yescharacteristic
117C4×#106C2211yescharacteristic
118#1770C2211yescharacteristic
119#1770C2211yescharacteristic
120C8×C4⋊C4C2211yescharacteristic
121C8×C4⋊C4C2211yescharacteristic
122#1763C2212yes—
123#1762C2212yes—
124C4×#103C2212yes—
125C4×#103C2212yes—
126C4×#103C2212yes—
127C4×#102C2212yes—
128C4×#102C2212yes—
129C4×#102C2212yes—
130#1753C2212yes—
131#1753C2212yes—
132#1746C2212yes—
133#1736C2211yescharacteristic
134#1736C2211yescharacteristic
135#1726C2212yes—
136C22×#41—21no—
137C22×SD16C2312yes—
138C22×SD16C2312yes—
139C22×M16C2311yescharacteristic
140C22×M16C2311yescharacteristic
141#533—24no—
142#533C2×C418yescomplemented
143#532—24no—
144#532C2×C418yes—
145C2×C4⋊Q8C2311yescharacteristic
146C2×C4⋊Q8C2311yescharacteristic
147C2×C4⋊Q8C2311yescharacteristic
148C2×#127C2311yescharacteristic
149C2×#125—21no—
150C2×#124—21no—
151C2×C22⋊Q8—21no—
152C2×C22⋊Q8C2312yes—
153C2×#121—21no—
154C2×#121C2312yes—
155C2×C4×Q8—21no—
156C2×C4×Q8C2312yes—
157C2×C4×Q8C2312yes—
158C2×C4×Q8C2312yes—
159C2×C4×D4—21no—
160C2×C4×D4—21no—
161C2×C4×D4—22no—
162C2×C4×D4—22no—
163C2×C4×D4—21no—
164C2×C4×D4C2312yes—
165C2×C4×D4C2312yes—
166C2×C4×D4C2312yes—
167C2×#117—21no—
168C2×#117C2311yescharacteristic
169C2×#117C2311yescharacteristic
170C22×C4⋊C4C2311yescharacteristic
171C22×C4⋊C4C2311yescharacteristic
172C22×C42—21no—
173C22×C42C2311yescharacteristic
174#500C2×C418yescomplemented
175#492C2×C418yescomplemented
176#487C2×C418yescomplemented
177#486C2×C418yescomplemented
178#468C2×C4116yescomplemented
179#468C2×C4116yescomplemented
180#440—28no—
181#440C2×C4116yescomplemented
182#440C2×C4116yescomplemented
183C4×SD16—28no—
184#431—24no—
185#428—24no—
186#428—24no—
187C2×#107C2311yescharacteristic
188C2×#107C2311yescharacteristic
189C2×#107C2311yescharacteristic
190C2×#107C2312yes—
191C2×#107C2312yes—
192C2×#107C2311yescharacteristic
193C2×#106C2311yescharacteristic
194C2×#106C2311yescharacteristic
195C2×#106C2311yescharacteristic
196C2×#106C2311yescharacteristic
197C2×C4⋊C8C2311yescharacteristic
198C2×C4⋊C8C2311yescharacteristic
199C2×#103C2312yes—
200C2×#103C2312yes—
201C2×#103C2312yes—
202C2×#103C2312yes—
203C2×#103C2312yes—
204C2×#103C2312yes—
205C2×#102C2312yes—
206C2×#102C2312yes—
207C2×#102C2312yes—
208C2×#102C2312yes—
209C2×#102C2312yes—
210C2×#102C2312yes—
211C2×C22⋊C8C2312yes—
212C4×M16C2×C418yescomplemented
213C2×#97C2312yes—
214C2×#97C2312yes—
215C2×#97C2311yescharacteristic
216C2×#97C2311yescharacteristic
217C2×C4×C8C2312yes—
218C2×C4×C8C2312yes—
219C2×C4×C8C2312yes—
220C2×C4×C8C2311yescharacteristic
221C2×C4×C8C2311yescharacteristic
222#391—22no—
223#391—22no—
224#391—22no—
225#391—22no—
226#391C2312yes—
227#391C2312yes—
228#390—21no—
229#390—21no—
230#390C2312yes—
231#390C2312yes—
232#389—21no—
233#389—21no—
234#389—21no—
235#389—21no—
236#389—21no—
237#389—21no—
238#389C2312yes—
239#389C2312yes—
240#389C2312yes—
241#389C2312yes—
242#388—22no—
243#388—22no—
244#388—22no—
245#388—22no—
246#388—22no—
247#388—22no—
248#388—22no—
249#388—22no—
250#387—22no—
251#387—22no—
252#387—22no—
253#387—22no—
254#387—22no—
255#387—22no—
256#386—22no—
257#386—22no—
258#386—22no—
259#386—22no—
260#385—22no—
261#385—22no—
262#383—22no—
263#383D412yes—
264#382—22no—
265#382D411yescharacteristic
266#382D411yescharacteristic
267#381—22no—
268#381D412yes—
269#380—22no—
270#380D411yescharacteristic
271#380D411yescharacteristic
272C4×C4⋊C4—21no—
273C4×C4⋊C4—21no—
274C4×C4⋊C4—21no—
275C4×C4⋊C4—21no—
276C4×C4⋊C4—21no—
277C4×C4⋊C4—21no—
278C4×C4⋊C4—21no—
279C4×C4⋊C4—21no—
280C4×C4⋊C4—22no—
281C4×C4⋊C4—22no—
282C4×C4⋊C4—22no—
283C4×C4⋊C4—22no—
284C4×C4⋊C4—22no—
285C4×C4⋊C4C2311yescharacteristic
286C4×C4⋊C4C2311yescharacteristic
287C4×C4⋊C4C2312yes—
288C4×C4⋊C4C2312yes—
289C4×C4⋊C4C2312yes—
290C4×C4⋊C4C2312yes—
291C4×C4⋊C4C2311yescharacteristic
292C4×C4⋊C4C2311yescharacteristic
293C4×C4⋊C4C2311yescharacteristic
294C4×C4⋊C4C2311yescharacteristic
295C4×C4⋊C4C2311yescharacteristic
296C4×C4⋊C4C2311yescharacteristic
297C4×C4⋊C4C2311yescharacteristic
298C4×C4⋊C4C2311yescharacteristic
299C4×C22⋊C4—21no—
300C4×C22⋊C4—21no—
301C4×C22⋊C4—22no—
302C4×C22⋊C4—22no—
303C4×C22⋊C4—22no—
304C4×C22⋊C4C2312yes—
305#376—21no—
306#376—22no—
307#376C2312yes—
308C2×#95—21no—
309C2×#95—22no—
310C43—21no—
311#340C2312yes—
312#340C2312yes—
313#340C2312yes—
314#340C2312yes—
315#340C2312yes—
316#340C2312yes—
317#340C2312yes—
318#340C2312yes—
319#340C2311yescharacteristic
320#340C2311yescharacteristic
321#340C2311yescharacteristic
322#340C2311yescharacteristic
323#340C2311yescharacteristic
324#340C2311yescharacteristic
325#340C2311yescharacteristic
326#340C2311yescharacteristic
327#336C2312yes—
328#336C2312yes—
329#336C2312yes—
330#336C2312yes—
331C2×#41—28no—
332C2×#41—82no—
333C2×#41—82no—
334C22×Q8—21no—
335C22×Q8—21no—
336C22×Q8C2412yes—
337C22×D4—22no—
338C22×D4—21no—
339C22×D4—21no—
340C22×D4C2412yes—
341C23×C4—22no—
342C23×C4—21no—
343C23×C4—21no—
344C23×C4—22no—
345C23×C4—22no—
346C23×C4C2×D411yescharacteristic
347C23×C4C2×D411yescharacteristic
348C23×C4C2411yescharacteristic
349C2×SD16—24no—
350C2×SD16—24no—
351C2×SD16—42no—
352C2×SD16—42no—
353C2×SD16C22×C418yes—
354C2×SD16C22×C418yes—
355C2×M16—22no—
356C2×M16—22no—
357C2×M16—41no—
358C2×M16—41no—
359C2×M16C22×C414yes—
360C2×M16C22×C414yes—
361C22×C8C2412yes—
362C22×C8C2412yes—
363C22×C8C2411yescharacteristic
364C22×C8C2411yescharacteristic
365C22×C8C2411yescharacteristic
366C22×C8C2411yescharacteristic
367C4⋊Q8—22no—
368C4⋊Q8—22no—
369C4⋊Q8—22no—
370C4⋊Q8C22×C414yes—
371C4⋊Q8C22×C414yes—
372C4⋊Q8C22×C414yes—
373#127—22no—
374#127C22×C414yes—
375#125—28no—
376#124—28no—
377C22⋊Q8—28no—
378C22⋊Q8—24no—
379C22⋊Q8C22×C418yes—
380#121—28no—
381#121—24no—
382#121C22×C418yes—
383C4×Q8—28no—
384C4×Q8—24no—
385C4×Q8—24no—
386C4×Q8—24no—
387C4×Q8—42no—
388C4×Q8—42no—
389C4×Q8C22×C418yes—
390C4×D4—24no—
391C4×D4—24no—
392C4×D4—28no—
393C4×D4—24no—
394C4×D4—42no—
395C4×D4—42no—
396C4×D4—82no—
397C4×D4—82no—
398C4×D4—84no—
399C4×D4—84no—
400C4×D4C22×C418yes—
401#117—28no—
402#117—22no—
403#117—22no—
404#117—41no—
405#117—41no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
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—41no—
423C2×C4⋊C4—41no—
424C2×C4⋊C4C2×D411yescharacteristic
425C2×C4⋊C4C2×D411yescharacteristic
426C2×C4⋊C4C2×D411yescharacteristic
427C2×C4⋊C4C2×D411yescharacteristic
428C2×C4⋊C4C2411yescharacteristic
429C2×C4⋊C4C2411yescharacteristic
430C2×C4⋊C4C2411yescharacteristic
431C2×C4⋊C4C2411yescharacteristic
432C2×C4⋊C4C2412yes—
433C2×C4⋊C4C2412yes—
434C2×C4⋊C4C2411yescharacteristic
435C2×C4⋊C4C2411yescharacteristic
436C2×C4⋊C4C2411yescharacteristic
437C2×C4⋊C4C2411yescharacteristic
438C2×C22⋊C4—22no—
439C2×C22⋊C4—22no—
440C2×C22⋊C4—22no—
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⋊C4C2×D412yes—
450C2×C22⋊C4C2×D412yes—
451C2×C42—22no—
452C2×C42—21no—
453C2×C42—21no—
454C2×C42—21no—
455C2×C42—21no—
456C2×C42—22no—
457C2×C42—22no—
458C2×C42—21no—
459C2×C42—21no—
460C2×C42—22no—
461C2×C42—22no—
462C2×C42—21no—
463C2×C42—21no—
464C2×C42—21no—
465C2×C42—22no—
466C2×C42—22no—
467C2×C42—21no—
468C2×C42—82no—
469C2×C42C22×C414yes—
470C2×C42C2×D411yescharacteristic
471C2×C42C2×D411yescharacteristic
472C2×C42#4114yes—
473C2×C42C2412yes—
474C2×C42C2412yes—
475C2×C42C2411yescharacteristic
476C2×C42C2411yescharacteristic
477#107—22no—
478#107—22no—
479#107—22no—
480#107C22×C418yes—
481#107C22×C418yes—
482#107#4114yescomplemented
483#106—22no—
484#106—22no—
485#106—22no—
486#106#4114yescomplemented
487C4⋊C8—22no—
488C4⋊C8—22no—
489#103—24no—
490#103—24no—
491#103—42no—
492#103—42no—
493#103C22×C418yes—
494#103C22×C418yes—
495#102—24no—
496#102—24no—
497#102—42no—
498#102—42no—
499#102C22×C418yes—
500#102C22×C418yes—
501C22⋊C8—24no—
502#97—24no—
503#97—42no—
504#97C22×C414yes—
505#97C22×C414yes—
506C4×C8—24no—
507C4×C8—24no—
508C4×C8—42no—
509C4×C8C22×C414yes—
510C4×C8C22×C414yes—
511#95—21no—
512#95—22no—
513#95—22no—
514#95—21no—
515#95—21no—
516#95—21no—
517#95—21no—
518#95—21no—
519#95—21no—
520#95—21no—
521#95—22no—
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#95C2×D412yes—
532#95C2×D412yes—
533#95C2×D412yes—
534#95C2×D412yes—
535#95C2×D412yes—
536#95C2×D412yes—
537#95C2×D412yes—
538#95C2×D412yes—
539C24—22no—
540C24C22×D411yescharacteristic
541#41—816no—
542C2×Q8—24no—
543C2×Q8—24no—
544C2×Q8—22no—
545C2×Q8—22no—
546C2×Q8—22no—
547C2×Q8—22no—
548C2×Q8—22no—
549C2×Q8—81no—
550C2×Q8—81no—
551C2×Q8—81no—
552C2×Q8—81no—
553C2×Q8C23×C414yes—
554C2×D4—28no—
555C2×D4—24no—
556C2×D4—24no—
557C2×D4—22no—
558C2×D4—22no—
559C2×D4—22no—
560C2×D4—22no—
561C2×D4—22no—
562C2×D4—44no—
563C2×D4—44no—
564C2×D4—42no—
565C2×D4—42no—
566C2×D4—81no—
567C2×D4—81no—
568C2×D4C23×C414yes—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—28no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—41no—
588C22×C4—41no—
589C22×C4—44no—
590C22×C4—44no—
591C22×C4—42no—
592C22×C4—42no—
593C22×C4—42no—
594C22×C4—42no—
595C22×C4—82no—
596C22×C4—82no—
597C22×C4—82no—
598C22×C4—82no—
599C22×C4—82no—
600C22×C4—82no—
601C22×C4—81no—
602C22×C4—81no—
603C22×C4C4×D414yes—
604C22×C4C4×D414yes—
605C22×C4C23×C412yes—
606C22×C4C22×D412yes—
607C22×C4C22×D412yes—
608C22×C4C22×D412yes—
609C22×C4C22×D412yes—
610C22×C4C22×D411yescharacteristic
611C22×C4C22×D411yescharacteristic
612C22×C4C22×D411yescharacteristic
613C22×C4C22×D411yescharacteristic
614C22×C4C22×D411yescharacteristic
615C22×C4C2×#4112yes—
616C22×C4C2511yescharacteristic
617SD16—216no—
618SD16—48no—
619M16—28no—
620M16—44no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—22no—
628C2×C8—22no—
629C2×C8—22no—
630C2×C8—22no—
631C2×C8—22no—
632C2×C8—22no—
633C2×C8C23×C412yes—
634C2×C8C23×C412yes—
635C2×C8C23×C412yes—
636C2×C8C23×C412yes—
637C2×C8C2×#4112yes—
638C2×C8C2×#4112yes—
639C4⋊C4—24no—
640C4⋊C4—24no—
641C4⋊C4—24no—
642C4⋊C4—24no—
643C4⋊C4—28no—
644C4⋊C4—28no—
645C4⋊C4—22no—
646C4⋊C4—22no—
647C4⋊C4—22no—
648C4⋊C4—22no—
649C4⋊C4—22no—
650C4⋊C4—22no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—42no—
664C4⋊C4—42no—
665C4⋊C4—44no—
666C4⋊C4—44no—
667C4⋊C4—82no—
668C4⋊C4—82no—
669C4⋊C4—82no—
670C4⋊C4—82no—
671C4⋊C4C23×C414yes—
672C4⋊C4C23×C414yes—
673C4⋊C4C2×#4112yes—
674C4⋊C4C2×#4112yes—
675C4⋊C4C2×#4112yes—
676C4⋊C4C2×#4112yes—
677C22⋊C4—28no—
678C22⋊C4—28no—
679C22⋊C4—28no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—44no—
683C22⋊C4—44no—
684C22⋊C4—42no—
685C22⋊C4—42no—
686C22⋊C4—82no—
687C22⋊C4—82no—
688C22⋊C4—82no—
689C22⋊C4—82no—
690C42—28no—
691C42—22no—
692C42—22no—
693C42—22no—
694C42—22no—
695C42—42no—
696C42—42no—
697C42—44no—
698C42—44no—
699C42—42no—
700C42—42no—
701C42—42no—
702C42—42no—
703C42—81no—
704C42—81no—
705C42—82no—
706C42—82no—
707C42—81no—
708C42—81no—
709C42—82no—
710C42—82no—
711C42C4×D414yes—
712C42C4×D414yes—
713C42C23×C412yes—
714C42C23×C412yes—
715C42C2×#4112yes—
716C42C2×#4112yes—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—24no—
724C23—42no—
725C23—42no—
726C23—42no—
727C23—42no—
728C23—42no—
729C23—42no—
730C23C2×C4×D412yes—
731C23C23×D411yescharacteristic
732Q8—24no—
733Q8—24no—
734Q8—42no—
735Q8—42no—
736Q8—84no—
737Q8—84no—
738D4—24no—
739D4—24no—
740D4—416no—
741D4—48no—
742D4—42no—
743D4—42no—
744D4—84no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—28no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—24no—
763C2×C4—24no—
764C2×C4—24no—
765C2×C4—22no—
766C2×C4—22no—
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—44no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—88no—
805C2×C4—84no—
806C2×C4—84no—
807C2×C4—164no—
808C2×C4—164no—
809C2×C4C2×C4×D412yes—
810C2×C4C2×C4×D412yes—
811C2×C4C2×C4×D412yes—
812C2×C4C2×C4×D412yes—
813C2×C4C2×C4×D412yes—
814C2×C4#57712yes—
815C2×C4#57812yes—
816C2×C4C24×C411yescharacteristic
817C2×C4C22×#4111yescharacteristic
818C2×C4C22×#4111yescharacteristic
819C2×C4C22×#4111yescharacteristic
820C2×C4#58511yescharacteristic
821C2×C4#58511yescharacteristic
822C8—22no—
823C8—22no—
824C8—22no—
825C8—42no—
826C8—42no—
827C8C4×#4114yes—
828C22—22no—
829C22—22no—
830C22—22no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—44no—
836C22—44no—
837C22—44no—
838C22—82no—
839C22—82no—
840C22—82no—
841C22—82no—
842C22C22×C4×D411yescharacteristic
843C22D4×#4111yescharacteristic
844C22D4×#4111yescharacteristic
845C22C2×#57711yescharacteristic
846C22C2×#57811yescharacteristic
847C22#358511yescharacteristic
848C22#358511yescharacteristic
849C4—22no—
850C4—22no—
851C4—22no—
852C4—22no—
853C4—44no—
854C4—44no—
855C4—44no—
856C4—42no—
857C4—42no—
858C4—42no—
859C4—42no—
860C4—42no—
861C4—42no—
862C4—42no—
863C4—42no—
864C4—81no—
865C4—81no—
866C4—81no—
867C4—81no—
868C4#294714yes—
869C4C2×C4×#4111yescharacteristic
870C4#342811yescharacteristic
871C4#348011yescharacteristic
872C4#348011yescharacteristic
873C2—42no—
874C2—84no—
875C2#3414111yescharacteristic
876C2C2×#294711yescharacteristic
877C2#6016811yescharacteristic
878C2#6154211yescharacteristic
879C2#6154311yescharacteristic
880C2#6155111yescharacteristic
881C2#6155811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
prime radicalC2×#532C22
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
3. #34231C2semidirect
4. #23223C2semidirect
5. #23221C2semidirect
6. #23217C2semidirect
7. #23215C2semidirect
8. #23190C2semidirect
9. #23182C2semidirect
10. #23162C2semidirect
11. #23158C2semidirect
12. #23141C2semidirect
13. #23138C2semidirect
14. #23040C2semidirect
15. #23034C2semidirect
17. #21385C2semidirect
18. #21291C2semidirect
19. #21128C2semidirect
20. #21125C2semidirect
21. #20504C2semidirect
22. #20482C2semidirect
23. C4×#428C2semidirect
26. #3182C4semidirect
142. #533C2×C4semidirect
174. #500C2×C4semidirect
175. #492C2×C4semidirect
176. #487C2×C4semidirect
177. #486C2×C4semidirect
178. #468C2×C4semidirect
179. #468C2×C4semidirect
181. #440C2×C4semidirect
182. #440C2×C4semidirect
212. C4×M16C2×C4semidirect
482. #107#41semidirect
486. #106#41semidirect

Maximal subgroups

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

subgroupindex
C2×#31822
#342362
#342312
#232232
#232212
#232172
#232152
#231902
#231822
#231622
#231582
#231412
#231382
#230402
#230342
#213902
#213852
#212912
#211282
#211252
#205042
#204822
C4×#4282