Finite Group Databasebeta

← #6388296

Subgroups — #6388296

Order 512.

1858 conjugacy classes of subgroups.

The subgroup lattice has 882 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3102C211yesmaximal, characteristic
2#34224C211yesmaximal, characteristic, complemented
3#34121C211yesmaximal, characteristic, complemented
4#23107C212yesmaximal, complemented
5#23105C212yesmaximal, complemented
6#23074C212yesmaximal, complemented
7#23072C212yesmaximal, complemented
8#22815C211yesmaximal, characteristic, complemented
9#22812C211yesmaximal, characteristic, complemented
10#22810C211yesmaximal, characteristic, complemented
11#22806C211yesmaximal, characteristic, complemented
12#22773C211yesmaximal, characteristic, complemented
13#22769C211yesmaximal, characteristic, complemented
14#22764C211yesmaximal, characteristic, complemented
15#22760C211yesmaximal, characteristic, complemented
16#22048C212yesmaximal, complemented
17#22045C212yesmaximal
18#21985C211yesmaximal, characteristic, complemented
19#21868C211yesmaximal, characteristic, complemented
20#21582C212yesmaximal, complemented
21C4×#485C212yesmaximal, complemented
22#20742C211yesmaximal, characteristic, complemented
23#20535C211yesmaximal, characteristic, complemented
24C2×#529C2211yescharacteristic
25C2×C4×#41C2211yescharacteristic
26#3102C4116yescomplemented
27C2×#485C2211yescharacteristic
28C2×#482C2211yescharacteristic
29C2×#479C2211yescharacteristic
30C2×#478C2211yescharacteristic
31C2×#464C2211yescharacteristic
32C2×#463C2211yescharacteristic
33C2×#452C2211yescharacteristic
34C2×#449C2211yescharacteristic
35C2×C4×Q16C2211yescharacteristic
36C2×C4×SD16C2211yescharacteristic
37C2×C4×SD16C2211yescharacteristic
38C2×C4×D8C2211yescharacteristic
39C2×#432C2211yescharacteristic
40C2×#431C2211yescharacteristic
41#2373—22no—
42#2370C2212yes—
43#2367C2212yes—
44#2357C2211yescharacteristic
45#2357C2211yescharacteristic
46#2357C2211yescharacteristic
47#2356C2211yescharacteristic
48#2356C2211yescharacteristic
49#2356C2211yescharacteristic
50#2355C2212yes—
51#2354C2212yes—
52#2353—21no—
53#2353—21no—
54#2352—22no—
55#2351C2211yescharacteristic
56#2349C2211yescharacteristic
57#2347—21no—
58#2343—21no—
59#2322—22no—
60#2318—21no—
61C4×C22⋊Q8C2212yes—
62C4×#121C2212yes—
63#2298—22no—
64#2297C2212yes—
65#2285C2211yescharacteristic
66#2283—21no—
67#2283C2211yescharacteristic
68#2275—21no—
69C4×#117—21no—
70C4×#117C2212yes—
71C2×C4×C4⋊C4C2211yescharacteristic
72#1992C2212yes—
73#1973C2212yes—
74#1971C2212yes—
75#1970C2212yes—
76#1968C2212yes—
77#1959C2212yes—
78#1948C2212yes—
79#1947C2212yes—
80#1936C2212yes—
81#1935C2212yes—
82#1934C2212yes—
83#1933C2212yes—
84#1928C2212yes—
85#1928C2212yes—
86#1928C2212yes—
87#1927C2212yes—
88#1926C2212yes—
89#1926C2212yes—
90#1926C2212yes—
91#1925C2212yes—
92#1919C2212yes—
93#1919C2212yes—
94#1918C2212yes—
95#1918C2212yes—
96#1880C2212yes—
97#1879C2212yes—
98#1878C2212yes—
99#1877C2212yes—
100#1875C2212yes—
101#1873C2212yes—
102#1854C2212yes—
103#1854C2212yes—
104#1846C2211yescharacteristic
105#1846C2211yescharacteristic
106#1835C2211yescharacteristic
107#1835C2211yescharacteristic
108#1825C2212yes—
109#1805C2211yescharacteristic
110#1805C2211yescharacteristic
111#1805C2211yescharacteristic
112#1805C2211yescharacteristic
113#1804C2211yescharacteristic
114#1804C2211yescharacteristic
115#1804C2211yescharacteristic
116#1804C2211yescharacteristic
117#1788C2212yes—
118#1776C2212yes—
119#1776C2212yes—
120C4×#107C2212yes—
121C4×#106C2212yes—
122#1771C2212yes—
123#1771C2212yes—
124#1770C2211yescharacteristic
125#1770C2211yescharacteristic
126C8×C4⋊C4C2211yescharacteristic
127C8×C4⋊C4C2211yescharacteristic
128#1763C2212yes—
129#1762C2212yes—
130#1762C2212yes—
131#1762C2212yes—
132C4×#103C2212yes—
133C4×#103C2212yes—
134#1749C2212yes—
135C4×C22⋊C8C2212yes—
136C22×#41C2311yescharacteristic
137C22×Q16C2311yescharacteristic
138C22×SD16C2311yescharacteristic
139C22×SD16C2311yescharacteristic
140C22×D8C2311yescharacteristic
141#529—24no—
142#529C2×C418yes—
143C2×#126—21no—
144C2×#125C2311yescharacteristic
145C2×#124C2311yescharacteristic
146C2×#123—21no—
147C2×C22⋊Q8C2311yescharacteristic
148C2×#121C2311yescharacteristic
149C4×#41—24no—
150C4×#41C2×C418yescomplemented
151C2×C4×Q8C2311yescharacteristic
152C2×C4×Q8C2311yescharacteristic
153C2×C4×Q8C2311yescharacteristic
154C2×C4×Q8C2312yes—
155C2×C4×D4—21no—
156C2×C4×D4—21no—
157C2×C4×D4—21no—
158C2×C4×D4—22no—
159C2×C4×D4C2311yescharacteristic
160C2×C4×D4C2311yescharacteristic
161C2×C4×D4C2311yescharacteristic
162C2×C4×D4C2312yes—
163C2×#117—22no—
164C2×#117—21no—
165C2×#117—21no—
166C2×#117C2311yescharacteristic
167C2×#117C2312yes—
168C22×C4⋊C4D412yes—
169C22×C42—21no—
170C22×C42C2312yes—
171C22×C42C2311yescharacteristic
172#485C2×C418yescomplemented
173#482C2×C418yes—
174#479C2×C418yescomplemented
175#478C2×C418yescomplemented
176#464C2×C418yescomplemented
177#463C2×C418yescomplemented
178#452C2×C418yescomplemented
179#449C2×C418yes—
180C4×Q16C2×C418yescomplemented
181C4×SD16C2×C418yescomplemented
182C4×SD16C2×C418yescomplemented
183C4×D8C2×C418yescomplemented
184#432—24no—
185#431C2×C418yescomplemented
186C2×#107C2312yes—
187C2×#107C2312yes—
188C2×#107C2311yescharacteristic
189C2×#107C2311yescharacteristic
190C2×#106C2312yes—
191C2×#106C2312yes—
192C2×#106C2311yescharacteristic
193C2×#106C2311yescharacteristic
194C2×C4⋊C8C2311yescharacteristic
195C2×C4⋊C8C2311yescharacteristic
196C2×C4⋊C8C2311yescharacteristic
197C2×C4⋊C8C2311yescharacteristic
198C2×#103C2312yes—
199C2×#103C2312yes—
200C2×#103C2312yes—
201C2×#103C2312yes—
202C2×#103C2311yescharacteristic
203C2×#103C2311yescharacteristic
204C2×#103C2311yescharacteristic
205C2×#103C2311yescharacteristic
206C2×#102C2312yes—
207C2×#102C2312yes—
208C2×#102C2312yes—
209C2×#102C2312yes—
210C2×#102C2311yescharacteristic
211C2×#102C2311yescharacteristic
212C2×#102C2311yescharacteristic
213C2×#102C2311yescharacteristic
214C2×C22⋊C8C2312yes—
215C2×C22⋊C8C2311yescharacteristic
216C2×C22⋊C8C2311yescharacteristic
217C2×#97C2312yes—
218C2×#97C2312yes—
219C2×#97C2312yes—
220C2×C4×C8C2312yes—
221C2×C4×C8C2312yes—
222C2×C4×C8C2311yescharacteristic
223C2×C4×C8C2311yescharacteristic
224#391C2312yes—
225#391C2312yes—
226#391C2312yes—
227#390C2312yes—
228#390C2312yes—
229#390C2312yes—
230#389—22no—
231#389—22no—
232#389C2312yes—
233#389C2312yes—
234#388—22no—
235#388—22no—
236#388—22no—
237#388—22no—
238#388—22no—
239#388—22no—
240#388—22no—
241#388—22no—
242#387—22no—
243#387—22no—
244#387—22no—
245#387—22no—
246#387—22no—
247#387—22no—
248#387—22no—
249#387—22no—
250#386—22no—
251#386—22no—
252#386—22no—
253#385—22no—
254#385—22no—
255#385—22no—
256#384C2312yes—
257#383—21no—
258#383—21no—
259#383—21no—
260#383—21no—
261#382—22no—
262#382—21no—
263#382C2311yescharacteristic
264#382C2311yescharacteristic
265#382C2311yescharacteristic
266#382C2311yescharacteristic
267#381—21no—
268#381—21no—
269#381—21no—
270#381—21no—
271#380—21no—
272#380—21no—
273#380—22no—
274#380—21no—
275#380C2312yes—
276C4×C4⋊C4—22no—
277C4×C4⋊C4—22no—
278C4×C4⋊C4—21no—
279C4×C4⋊C4—21no—
280C4×C4⋊C4—21no—
281C4×C4⋊C4—22no—
282C4×C4⋊C4D411yescharacteristic
283C4×C4⋊C4D411yescharacteristic
284C4×C4⋊C4D412yes—
285C4×C4⋊C4C2312yes—
286C4×C4⋊C4C2312yes—
287C4×C4⋊C4C2312yes—
288C4×C4⋊C4C2312yes—
289C4×C4⋊C4C2312yes—
290C4×C4⋊C4C2312yes—
291C4×C4⋊C4C2312yes—
292C4×C4⋊C4C2311yescharacteristic
293C4×C4⋊C4C2311yescharacteristic
294C4×C4⋊C4C2312yes—
295C4×C22⋊C4—21no—
296C4×C22⋊C4—22no—
297C4×C22⋊C4—22no—
298C4×C22⋊C4—22no—
299C4×C22⋊C4—22no—
300C4×C22⋊C4—22no—
301C4×C22⋊C4—22no—
302C4×C22⋊C4—21no—
303C4×C22⋊C4—21no—
304C4×C22⋊C4—21no—
305C4×C22⋊C4—22no—
306#376—21no—
307#376—22no—
308#376—21no—
309#376—21no—
310#376—21no—
311C2×#95—21no—
312C2×#95D411yescharacteristic
313C2×#95D411yescharacteristic
314C43—22no—
315#340C2312yes—
316#340C2312yes—
317#340C2312yes—
318#340C2312yes—
319#340C2312yes—
320#340C2312yes—
321#340C2312yes—
322#340C2312yes—
323#340C2312yes—
324#340C2312yes—
325#340C2312yes—
326#340C2312yes—
327#336C2312yes—
328#336C2312yes—
329#336C2312yes—
330#336C2312yes—
331C2×#41—22no—
332C2×#41—41no—
333C2×#41—41no—
334C2×#41—41no—
335C2×#41—41no—
336C2×#41C22×C414yes—
337C22×Q8C2411yescharacteristic
338C22×Q8C2411yescharacteristic
339C22×D4—21no—
340C22×D4—21no—
341C22×D4C2411yescharacteristic
342C22×D4C2411yescharacteristic
343C23×C4—21no—
344C23×C4—21no—
345C23×C4—21no—
346C23×C4—21no—
347C23×C4—22no—
348C23×C4C2×D412yes—
349C23×C4C2×D412yes—
350C23×C4C2×D411yescharacteristic
351C23×C4C2×D411yescharacteristic
352C23×C4C2411yescharacteristic
353C2×Q16—41no—
354C2×Q16—41no—
355C2×Q16C22×C414yes—
356C2×SD16—41no—
357C2×SD16—41no—
358C2×SD16—41no—
359C2×SD16—41no—
360C2×SD16C22×C414yes—
361C2×SD16C22×C414yes—
362C2×D8—41no—
363C2×D8—41no—
364C2×D8C22×C414yes—
365C22×C8C2412yes—
366C22×C8C2412yes—
367C22×C8C2411yescharacteristic
368C22×C8C2411yescharacteristic
369C22×C8C2411yescharacteristic
370C22×C8C2411yescharacteristic
371#126—28no—
372#125—22no—
373#125C22×C414yes—
374#124—22no—
375#124C22×C414yes—
376#123—28no—
377C22⋊Q8—22no—
378C22⋊Q8C22×C414yes—
379#121—22no—
380#121C22×C414yes—
381C4×Q8—22no—
382C4×Q8—22no—
383C4×Q8—22no—
384C4×Q8—42no—
385C4×Q8—42no—
386C4×Q8C22×C414yes—
387C4×Q8C22×C414yes—
388C4×Q8C22×C414yes—
389C4×D4—28no—
390C4×D4—28no—
391C4×D4—28no—
392C4×D4—22no—
393C4×D4—22no—
394C4×D4—22no—
395C4×D4—42no—
396C4×D4—42no—
397C4×D4—48no—
398C4×D4C22×C414yes—
399C4×D4C22×C414yes—
400C4×D4C22×C414yes—
401#117—22no—
402#117—28no—
403#117—28no—
404#117—42no—
405#117—42no—
406#117—48no—
407#117C22×C414yes—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—44no—
420C2×C4⋊C4C2×D412yes—
421C2×C4⋊C4C2×D412yes—
422C2×C4⋊C4C2×D412yes—
423C2×C4⋊C4C2×D412yes—
424C2×C4⋊C4C2412yes—
425C2×C4⋊C4C2412yes—
426C2×C4⋊C4C2412yes—
427C2×C4⋊C4C2412yes—
428C2×C4⋊C4C2411yescharacteristic
429C2×C4⋊C4C2411yescharacteristic
430C2×C4⋊C4C2411yescharacteristic
431C2×C4⋊C4C2411yescharacteristic
432C2×C22⋊C4—21no—
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4—21no—
440C2×C22⋊C4—22no—
441C2×C22⋊C4—22no—
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×C42—21no—
450C2×C42—21no—
451C2×C42—21no—
452C2×C42—21no—
453C2×C42—28no—
454C2×C42—22no—
455C2×C42—22no—
456C2×C42—22no—
457C2×C42—22no—
458C2×C42—22no—
459C2×C42—22no—
460C2×C42—22no—
461C2×C42—22no—
462C2×C42—22no—
463C2×C42—42no—
464C2×C42—42no—
465C2×C42C22×C414yes—
466C2×C42C2×D412yes—
467C2×C42C2×D412yes—
468C2×C42C2×D411yescharacteristic
469C2×C42C2×D411yescharacteristic
470C2×C42#4114yes—
471C2×C42C2412yes—
472C2×C42C2412yes—
473C2×C42C2411yescharacteristic
474C2×C42C2411yescharacteristic
475#107—42no—
476#107—42no—
477#107C22×C414yes—
478#107C22×C414yes—
479#106—42no—
480#106—42no—
481#106C22×C414yes—
482#106C22×C414yes—
483C4⋊C8—22no—
484C4⋊C8—22no—
485C4⋊C8C22×C414yes—
486C4⋊C8C22×C414yes—
487#103—42no—
488#103—42no—
489#103—42no—
490#103—42no—
491#103C22×C414yes—
492#103C22×C414yes—
493#103C22×C414yes—
494#103C22×C414yes—
495#102—42no—
496#102—42no—
497#102—42no—
498#102—42no—
499#102C22×C414yes—
500#102C22×C414yes—
501#102C22×C414yes—
502#102C22×C414yes—
503C22⋊C8—24no—
504C22⋊C8C22×C414yes—
505C22⋊C8C22×C414yes—
506#97—24no—
507#97—42no—
508#97—42no—
509C4×C8—42no—
510C4×C8—42no—
511C4×C8C22×C414yes—
512C4×C8C22×C414yes—
513#95—21no—
514#95—22no—
515#95—21no—
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—21no—
527#95—21no—
528#95—22no—
529#95—22no—
530#95—22no—
531#95—21no—
532#95—21no—
533#95—22no—
534#95—22no—
535#95—22no—
536#95—22no—
537#95C2×D411yescharacteristic
538#95C2×D411yescharacteristic
539#95C2×D411yescharacteristic
540#95C2×D412yes—
541#95C2×D411yescharacteristic
542#95C2×D412yes—
543C24—21no—
544C24—21no—
545C24C22×D411yescharacteristic
546#41—44no—
547#41—44no—
548#41—44no—
549#41—44no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8—21no—
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8C23×C412yes—
561C2×Q8C23×C412yes—
562C2×D4—24no—
563C2×D4—24no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—44no—
575C2×D4—42no—
576C2×D4—42no—
577C2×D4C23×C412yes—
578C2×D4C23×C412yes—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
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—22no—
598C22×C4—42no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4—42no—
603C22×C4—42no—
604C22×C4—42no—
605C22×C4—44no—
606C22×C4—42no—
607C22×C4—42no—
608C22×C4—44no—
609C22×C4—82no—
610C22×C4—82no—
611C22×C4—82no—
612C22×C4—82no—
613C22×C4C4×D414yes—
614C22×C4C4×D414yes—
615C22×C4C23×C412yes—
616C22×C4C22×D412yes—
617C22×C4C22×D412yes—
618C22×C4C22×D412yes—
619C22×C4C22×D411yescharacteristic
620C22×C4C22×D411yescharacteristic
621C22×C4C22×D411yescharacteristic
622C22×C4C22×D411yescharacteristic
623C22×C4C22×D411yescharacteristic
624C22×C4C22×D412yes—
625C22×C4C2×#4112yes—
626C22×C4C2511yescharacteristic
627Q16—44no—
628SD16—44no—
629SD16—44no—
630D8—44no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
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×C8C23×C412yes—
646C2×C8C23×C412yes—
647C2×C8C23×C412yes—
648C2×C8C23×C412yes—
649C4⋊C4—24no—
650C4⋊C4—24no—
651C4⋊C4—24no—
652C4⋊C4—24no—
653C4⋊C4—24no—
654C4⋊C4—24no—
655C4⋊C4—24no—
656C4⋊C4—24no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—22no—
662C4⋊C4—22no—
663C4⋊C4—22no—
664C4⋊C4—22no—
665C4⋊C4—22no—
666C4⋊C4—22no—
667C4⋊C4—22no—
668C4⋊C4—22no—
669C4⋊C4—42no—
670C4⋊C4—42no—
671C4⋊C4—44no—
672C4⋊C4—44no—
673C4⋊C4—82no—
674C4⋊C4—82no—
675C4⋊C4—82no—
676C4⋊C4C23×C412yes—
677C4⋊C4C23×C412yes—
678C4⋊C4C23×C412yes—
679C4⋊C4C23×C412yes—
680C22⋊C4—24no—
681C22⋊C4—24no—
682C22⋊C4—24no—
683C22⋊C4—24no—
684C22⋊C4—24no—
685C22⋊C4—24no—
686C22⋊C4—24no—
687C22⋊C4—24no—
688C22⋊C4—44no—
689C22⋊C4—44no—
690C22⋊C4—44no—
691C22⋊C4—44no—
692C22⋊C4—44no—
693C22⋊C4—82no—
694C22⋊C4—82no—
695C22⋊C4—82no—
696C22⋊C4—82no—
697C42—24no—
698C42—24no—
699C42—24no—
700C42—24no—
701C42—22no—
702C42—22no—
703C42—22no—
704C42—22no—
705C42—42no—
706C42—42no—
707C42—44no—
708C42—44no—
709C42—44no—
710C42—44no—
711C42—82no—
712C42—82no—
713C42—82no—
714C42—82no—
715C42—82no—
716C42C4×D414yes—
717C42C4×D414yes—
718C42C23×C412yes—
719C42C23×C412yes—
720C42C2×#4112yes—
721C42C2×#4112yes—
722C23—22no—
723C23—21no—
724C23—21no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—42no—
729C23—42no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—42no—
735C23—42no—
736C23C2×C4×D412yes—
737C23C23×D411yescharacteristic
738Q8—22no—
739Q8—22no—
740Q8—22no—
741Q8—22no—
742Q8—41no—
743Q8—41no—
744Q8—41no—
745Q8—41no—
746D4—22no—
747D4—22no—
748D4—22no—
749D4—22no—
750D4—48no—
751D4—48no—
752D4—41no—
753D4—41no—
754D4—41no—
755D4—41no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
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—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—44no—
784C2×C4—44no—
785C2×C4—48no—
786C2×C4—48no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
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—42no—
806C2×C4—42no—
807C2×C4—84no—
808C2×C4—84no—
809C2×C4—84no—
810C2×C4—84no—
811C2×C4—164no—
812C2×C4C2×C4×D412yes—
813C2×C4C2×C4×D412yes—
814C2×C4C2×C4×D412yes—
815C2×C4C2×C4×D412yes—
816C2×C4C2×C4×D412yes—
817C2×C4#57514yes—
818C2×C4C24×C411yescharacteristic
819C2×C4C22×#4111yescharacteristic
820C2×C4#58511yescharacteristic
821C2×C4#58511yescharacteristic
822C2×C4#58511yescharacteristic
823C2×C4#58511yescharacteristic
824C8—22no—
825C8—22no—
826C8—22no—
827C8—22no—
828C8—42no—
829C8—42no—
830C22—22no—
831C22—22no—
832C22—22no—
833C22—42no—
834C22—42no—
835C22—42no—
836C22—42no—
837C22—42no—
838C22—42no—
839C22—42no—
840C22—42no—
841C22—82no—
842C22—82no—
843C22—82no—
844C22—82no—
845C22C22×C4×D411yescharacteristic
846C22#348511yescharacteristic
847C22#348711yescharacteristic
848C22C2×#57512yes—
849C22#358412yes—
850C4—22no—
851C4—22no—
852C4—24no—
853C4—22no—
854C4—22no—
855C4—22no—
856C4—42no—
857C4—42no—
858C4—42no—
859C4—42no—
860C4—42no—
861C4—42no—
862C4—42no—
863C4—42no—
864C4—42no—
865C4—82no—
866C4—82no—
867C4—82no—
868C4—82no—
869C4#342811yescharacteristic
870C4#342811yescharacteristic
871C4#349311yescharacteristic
872C4#349311yescharacteristic
873C2—42no—
874C2—82no—
875C2—82no—
876C2#3420111yescharacteristic
877C2C4×#57511yescharacteristic
878C2#6016711yescharacteristic
879C2#6174112yes—
880C2#6190812yes—
subgroupG/H
center, socleC23C23×D4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
prime radicalC2×#449C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C4×C4⋊C4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #34224C2semidirect
3. #34121C2semidirect
4. #23107C2semidirect
5. #23105C2semidirect
6. #23074C2semidirect
7. #23072C2semidirect
8. #22815C2semidirect
9. #22812C2semidirect
10. #22810C2semidirect
11. #22806C2semidirect
12. #22773C2semidirect
13. #22769C2semidirect
14. #22764C2semidirect
15. #22760C2semidirect
16. #22048C2semidirect
18. #21985C2semidirect
19. #21868C2semidirect
20. #21582C2semidirect
21. C4×#485C2semidirect
22. #20742C2semidirect
23. #20535C2semidirect
26. #3102C4semidirect
150. C4×#41C2×C4semidirect
172. #485C2×C4semidirect
174. #479C2×C4semidirect
175. #478C2×C4semidirect
176. #464C2×C4semidirect
177. #463C2×C4semidirect
178. #452C2×C4semidirect
180. C4×Q16C2×C4semidirect
181. C4×SD16C2×C4semidirect
182. C4×SD16C2×C4semidirect
183. C4×D8C2×C4semidirect
185. #431C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#31022
#342242
#341212
#231072
#231052
#230742
#230722
#228152
#228122
#228102
#228062
#227732
#227692
#227642
#227602
#220482
#220452
#219852
#218682
#215822
C4×#4852
#207422
#205352