Finite Group Databasebeta

← #6380931

Subgroups — #6380931

Order 512.

2042 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
1C2×C4×#137C211yesmaximal, characteristic
2#34128C211yesmaximal, characteristic, complemented
3#34125C211yesmaximal, characteristic
4#22812C211yesmaximal, characteristic, complemented
5#22806C211yesmaximal, characteristic, complemented
6#22773C211yesmaximal, characteristic, complemented
7#22769C211yesmaximal, characteristic, complemented
8#22765C211yesmaximal, characteristic, complemented
9#22761C211yesmaximal, characteristic, complemented
10#22685C211yesmaximal, characteristic, complemented
11#22675C211yesmaximal, characteristic, complemented
12#22622C212yesmaximal, complemented
13#22583C212yesmaximal
14#22581C212yesmaximal, complemented
15#22445C212yesmaximal
16#21288C212yesmaximal, complemented
17#21124C212yesmaximal, complemented
18#21123C212yesmaximal, complemented
19#20825C211yesmaximal, characteristic, complemented
20#20742C211yesmaximal, characteristic
21#20741C211yesmaximal, characteristic, complemented
22C4×#441C212yesmaximal, complemented
23#20480C211yesmaximal, characteristic, complemented
24C22×#137C2211yescharacteristic
25C2×C4×#41C2211yescharacteristic
26C22×C4×Q8C2211yescharacteristic
27C4×#137C4116yescomplemented
28C2×#441C2212yes—
29C2×#441C2211yescharacteristic
30C2×#441C2211yescharacteristic
31C2×#440C2211yescharacteristic
32C2×#440C2211yescharacteristic
33C2×C4×Q16C2212yes—
34C2×C4×Q16C2211yescharacteristic
35C2×C4×Q16C2211yescharacteristic
36C2×C4×SD16C2211yescharacteristic
37C2×C4×SD16C2211yescharacteristic
38C2×#432C2211yescharacteristic
39C2×#428C2211yescharacteristic
40C2×#417C2211yescharacteristic
41C2×#419C2211yescharacteristic
42C2×C4×M16C2211yescharacteristic
43#2357—21no—
44#2357—21no—
45#2357C2211yescharacteristic
46#2357C2211yescharacteristic
47#2356—21no—
48#2356—21no—
49#2356C2211yescharacteristic
50#2356C2211yescharacteristic
51#2351C2211yescharacteristic
52#2351C2211yescharacteristic
53#2351C2211yescharacteristic
54#2351C2211yescharacteristic
55#2347—22no—
56#2347C2212yes—
57#2344—22no—
58#2344C2212yes—
59#2341C2212yes—
60Q8×C22⋊C4C2212yes—
61#2295—22no—
62#2295C2212yes—
63#2293—22no—
64#2293C2212yes—
65#2283—21no—
66#2283—21no—
67#2283C2211yescharacteristic
68#2283C2211yescharacteristic
69C42×Q8C2212yes—
70C42×Q8C2212yes—
71C4×#117—21no—
72C4×#117—21no—
73C4×#117C2211yescharacteristic
74#1973C2212yes—
75#1968C2212yes—
76#1943C2212yes—
77#1942C2212yes—
78#1936C2212yes—
79#1935C2212yes—
80#1934C2212yes—
81#1933C2212yes—
82#1928C2212yes—
83#1927C2212yes—
84#1926C2212yes—
85#1925C2212yes—
86#1921C2212yes—
87#1920C2212yes—
88#1919C2212yes—
89#1918C2212yes—
90#1880C2212yes—
91#1880C2212yes—
92#1878C2212yes—
93#1878C2212yes—
94#1865C2212yes—
95#1865C2212yes—
96#1863C2212yes—
97#1863C2212yes—
98#1846C2211yescharacteristic
99#1846C2211yescharacteristic
100#1835C2211yescharacteristic
101#1835C2211yescharacteristic
102#1825C2212yes—
103#1824C2212yes—
104#1809C2212yes—
105#1809C2212yes—
106#1805C2211yescharacteristic
107#1805C2211yescharacteristic
108#1805C2211yescharacteristic
109#1805C2211yescharacteristic
110#1805C2211yescharacteristic
111#1805C2211yescharacteristic
112#1804C2211yescharacteristic
113#1804C2211yescharacteristic
114#1788C2212yes—
115#1787C2212yes—
116#1776C2212yes—
117#1776C2212yes—
118#1776C2212yes—
119C4×#106C2212yes—
120#1770C2211yescharacteristic
121#1770C2211yescharacteristic
122C8×C4⋊C4C2211yescharacteristic
123C8×C4⋊C4C2211yescharacteristic
124#1763C2212yes—
125#1763C2212yes—
126#1763C2212yes—
127#1763C2212yes—
128#1763C2212yes—
129#1762C2212yes—
130C4×#103C2212yes—
131C4×#103C2212yes—
132#1753C2212yes—
133#1753C2212yes—
134#1745C2212yes—
135C4×#97C2212yes—
136C22×#41C2311yescharacteristic
137C23×Q8C2311yescharacteristic
138C2×#137—24no—
139C2×#137—24no—
140C2×#137C2×C418yes—
141C22×Q16C2311yescharacteristic
142C22×Q16C2311yescharacteristic
143C22×SD16C2311yescharacteristic
144C22×SD16C2311yescharacteristic
145C22×M16C2311yescharacteristic
146C22×M16C2311yescharacteristic
147C4×#41—24no—
148C4×#41C2×C418yes—
149C2×C4×Q8—21no—
150C2×C4×Q8—21no—
151C2×C4×Q8—24no—
152C2×C4×Q8C2×C418yes—
153C2×C4×Q8C2312yes—
154C2×C4×Q8C2312yes—
155C2×C4×Q8C2312yes—
156C2×C4×Q8C2312yes—
157C2×C4×Q8C2311yescharacteristic
158C2×C4×Q8C2311yescharacteristic
159C2×C4×Q8C2311yescharacteristic
160C2×C4×Q8C2311yescharacteristic
161C2×C4×Q8C2311yescharacteristic
162C2×C4×Q8C2311yescharacteristic
163C2×C4×D4—21no—
164C2×C4×D4—21no—
165C2×C4×D4C2311yescharacteristic
166C2×C4×D4C2311yescharacteristic
167C2×#117—22no—
168C2×#117—21no—
169C2×#117—22no—
170C2×#117D412yes—
171C2×#117C2311yescharacteristic
172C22×C4⋊C4—21no—
173C22×C4⋊C4C2311yescharacteristic
174C22×C42—21no—
175C22×C42—21no—
176C22×C42C2311yescharacteristic
177#441—28no—
178#441C2×C418yes—
179#441C2×C418yes—
180#440C2×C418yes—
181#440C2×C418yes—
182C4×Q16—28no—
183C4×Q16C2×C418yes—
184C4×Q16C2×C418yes—
185C4×SD16C2×C418yes—
186C4×SD16C2×C418yes—
187#432—24no—
188#428C2×C418yes—
189C2×#107C2312yes—
190C2×#107C2312yes—
191C2×#107C2311yescharacteristic
192C2×#107C2311yescharacteristic
193C2×#106C2312yes—
194C2×#106C2312yes—
195C2×#106C2311yescharacteristic
196C2×#106C2311yescharacteristic
197C2×C4⋊C8C2311yescharacteristic
198C2×C4⋊C8C2311yescharacteristic
199#419C2×C418yes—
200#417C2×C418yes—
201C2×#103C2312yes—
202C2×#103C2312yes—
203C2×#103C2312yes—
204C2×#103C2312yes—
205C2×#103C2312yes—
206C2×#103C2312yes—
207C2×#103C2311yescharacteristic
208C2×#103C2311yescharacteristic
209C2×#103C2311yescharacteristic
210C2×#103C2311yescharacteristic
211C2×#103C2311yescharacteristic
212C2×#103C2311yescharacteristic
213C2×#102C2312yes—
214C2×#102C2312yes—
215C2×#102C2311yescharacteristic
216C2×#102C2311yescharacteristic
217C2×C22⋊C8C2312yes—
218C4×M16C2×C418yes—
219C2×#97C2312yes—
220C2×#97C2312yes—
221C2×#97C2312yes—
222C2×#97C2311yescharacteristic
223C2×#97C2311yescharacteristic
224C2×C4×C8C2312yes—
225C2×C4×C8C2312yes—
226C2×C4×C8C2311yescharacteristic
227C2×C4×C8C2311yescharacteristic
228#391—22no—
229#391—22no—
230#391C2312yes—
231#391C2312yes—
232#390—22no—
233#390—22no—
234#390C2312yes—
235#390C2312yes—
236#389—22no—
237#389—22no—
238#389—22no—
239#389—22no—
240#389C2312yes—
241#389C2312yes—
242#389C2312yes—
243#389C2312yes—
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#383—21no—
257#383—21no—
258#383—22no—
259#383—21no—
260#383—21no—
261#382—21no—
262#382—21no—
263#382—21no—
264#382—21no—
265#382C2311yescharacteristic
266#382C2311yescharacteristic
267#382C2311yescharacteristic
268#382C2311yescharacteristic
269#381—21no—
270#381—21no—
271#381—22no—
272#381—21no—
273#381—21no—
274#380—22no—
275#380—22no—
276#380C2312yes—
277#380C2312yes—
278C4×C4⋊C4—22no—
279C4×C4⋊C4—22no—
280C4×C4⋊C4—22no—
281C4×C4⋊C4—22no—
282C4×C4⋊C4—22no—
283C4×C4⋊C4—22no—
284C4×C4⋊C4—22no—
285C4×C4⋊C4—22no—
286C4×C4⋊C4—21no—
287C4×C4⋊C4—21no—
288C4×C4⋊C4—21no—
289C4×C4⋊C4—21no—
290C4×C4⋊C4D412yes—
291C4×C4⋊C4C2312yes—
292C4×C4⋊C4C2312yes—
293C4×C4⋊C4C2312yes—
294C4×C4⋊C4C2312yes—
295C4×C4⋊C4C2312yes—
296C4×C4⋊C4C2312yes—
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⋊C4—21no—
305C4×C22⋊C4—21no—
306C4×C22⋊C4D411yescharacteristic
307C4×C22⋊C4D411yescharacteristic
308C4×C22⋊C4C2312yes—
309#376—21no—
310#376—22no—
311#376—21no—
312#376—21no—
313#376—21no—
314#376D411yescharacteristic
315#376D411yescharacteristic
316C43—22no—
317C43—22no—
318C43C2312yes—
319#340C2312yes—
320#340C2312yes—
321#340C2312yes—
322#340C2312yes—
323#340C2312yes—
324#340C2312yes—
325#340C2312yes—
326#340C2312yes—
327#340C2312yes—
328#340C2312yes—
329#340C2312yes—
330#340C2312yes—
331#336C2312yes—
332#336C2312yes—
333#336C2312yes—
334#336C2312yes—
335C2×#41—22no—
336C2×#41—22no—
337C2×#41—22no—
338C2×#41—41no—
339C2×#41—41no—
340C2×#41C22×C414yes—
341C22×Q8—21no—
342C22×Q8—22no—
343C22×Q8—22no—
344C22×Q8—22no—
345C22×Q8—41no—
346C22×Q8—41no—
347C22×Q8C22×C414yes—
348C22×Q8C2411yescharacteristic
349C22×Q8C2411yescharacteristic
350C22×Q8C2411yescharacteristic
351C22×D4—21no—
352C22×D4C2411yescharacteristic
353C23×C4—21no—
354C23×C4—21no—
355C23×C4—21no—
356C23×C4—21no—
357C23×C4—21no—
358C23×C4C2×D411yescharacteristic
359C23×C4C2×D411yescharacteristic
360C23×C4C2411yescharacteristic
361#137—232no—
362C2×Q16—22no—
363C2×Q16—22no—
364C2×Q16C22×C414yes—
365C2×Q16C22×C414yes—
366C2×Q16#4114yes—
367C2×Q16#4114yes—
368C2×SD16—22no—
369C2×SD16—22no—
370C2×SD16—22no—
371C2×SD16—22no—
372C2×SD16C22×C414yes—
373C2×SD16C22×C414yes—
374C2×M16—22no—
375C2×M16—22no—
376C2×M16—41no—
377C2×M16—41no—
378C2×M16C22×C414yes—
379C2×M16C22×C414yes—
380C22×C8C2412yes—
381C22×C8C2412yes—
382C22×C8C2411yescharacteristic
383C22×C8C2411yescharacteristic
384C22×C8C2411yescharacteristic
385C22×C8C2411yescharacteristic
386C4×Q8—28no—
387C4×Q8—28no—
388C4×Q8—22no—
389C4×Q8—22no—
390C4×Q8—22no—
391C4×Q8—22no—
392C4×Q8—22no—
393C4×Q8—22no—
394C4×Q8—24no—
395C4×Q8—24no—
396C4×Q8—24no—
397C4×Q8—24no—
398C4×Q8—42no—
399C4×Q8—42no—
400C4×Q8—42no—
401C4×Q8—42no—
402C4×Q8C22×C414yes—
403C4×Q8C22×C414yes—
404C4×Q8C22×C414yes—
405C4×Q8C22×C414yes—
406C4×Q8C22×C414yes—
407C4×Q8C22×C414yes—
408C4×D4—28no—
409C4×D4—28no—
410C4×D4—22no—
411C4×D4—22no—
412C4×D4C22×C414yes—
413C4×D4C22×C414yes—
414#117—22no—
415#117—28no—
416#117—44no—
417#117—48no—
418#117—48no—
419#117C22×C414yes—
420C2×C4⋊C4—28no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4—22no—
430C2×C4⋊C4—22no—
431C2×C4⋊C4—22no—
432C2×C4⋊C4—22no—
433C2×C4⋊C4—22no—
434C2×C4⋊C4—22no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—22no—
437C2×C4⋊C4C22×C414yes—
438C2×C4⋊C4C2×D412yes—
439C2×C4⋊C4C2×D412yes—
440C2×C4⋊C4C2412yes—
441C2×C4⋊C4C2412yes—
442C2×C4⋊C4C2412yes—
443C2×C4⋊C4C2412yes—
444C2×C4⋊C4C2411yescharacteristic
445C2×C4⋊C4C2411yescharacteristic
446C2×C4⋊C4C2411yescharacteristic
447C2×C4⋊C4C2411yescharacteristic
448C2×C22⋊C4—21no—
449C2×C22⋊C4—21no—
450C2×C22⋊C4—21no—
451C2×C22⋊C4—22no—
452C2×C22⋊C4—22no—
453C2×C22⋊C4—22no—
454C2×C22⋊C4—22no—
455C2×C22⋊C4—22no—
456C2×C22⋊C4—22no—
457C2×C22⋊C4C2×D412yes—
458C2×C22⋊C4C2×D412yes—
459C2×C42—28no—
460C2×C42—21no—
461C2×C42—21no—
462C2×C42—21no—
463C2×C42—21no—
464C2×C42—21no—
465C2×C42—21no—
466C2×C42—21no—
467C2×C42—28no—
468C2×C42—22no—
469C2×C42—22no—
470C2×C42—22no—
471C2×C42—22no—
472C2×C42—22no—
473C2×C42—22no—
474C2×C42—22no—
475C2×C42—22no—
476C2×C42—22no—
477C2×C42—22no—
478C2×C42C22×C414yes—
479C2×C42C2×D412yes—
480C2×C42C2×D412yes—
481C2×C42C2×D412yes—
482C2×C42C2×D412yes—
483C2×C42C2×D411yescharacteristic
484C2×C42C2×D411yescharacteristic
485C2×C42#4114yes—
486C2×C42C2412yes—
487C2×C42C2412yes—
488C2×C42C2411yescharacteristic
489C2×C42C2411yescharacteristic
490#107—24no—
491#107—42no—
492#107C22×C414yes—
493#107C22×C414yes—
494#106—24no—
495#106—42no—
496#106C22×C414yes—
497#106C22×C414yes—
498C4⋊C8—22no—
499C4⋊C8—22no—
500#103—24no—
501#103—24no—
502#103—24no—
503#103—24no—
504#103—42no—
505#103—42no—
506#103C22×C414yes—
507#103C22×C414yes—
508#103C22×C414yes—
509#103C22×C414yes—
510#103C22×C414yes—
511#103C22×C414yes—
512#102—42no—
513#102—42no—
514#102C22×C414yes—
515#102C22×C414yes—
516C22⋊C8—24no—
517#97—24no—
518#97—24no—
519#97—42no—
520#97C22×C414yes—
521#97C22×C414yes—
522C4×C8—24no—
523C4×C8—42no—
524C4×C8C22×C414yes—
525C4×C8C22×C414yes—
526#95—22no—
527#95—21no—
528#95—21no—
529#95—21no—
530#95—21no—
531#95—22no—
532#95—22no—
533#95—22no—
534#95—22no—
535#95—22no—
536#95—22no—
537#95—22no—
538#95—21no—
539#95—21no—
540#95—22no—
541#95—22no—
542#95—21no—
543#95—21no—
544#95—22no—
545#95—22no—
546#95—22no—
547#95—22no—
548#95—22no—
549#95—22no—
550#95C2×D411yescharacteristic
551#95C2×D411yescharacteristic
552#95C2×D411yescharacteristic
553#95C2×D412yes—
554#95C2×D411yescharacteristic
555#95C2×D412yes—
556C24—21no—
557C24C22×D411yescharacteristic
558#41—28no—
559#41—44no—
560#41—44no—
561#41—44no—
562C2×Q8—24no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8—21no—
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—28no—
571C2×Q8—21no—
572C2×Q8—21no—
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—42no—
576C2×Q8—42no—
577C2×Q8—44no—
578C2×Q8—44no—
579C2×Q8—44no—
580C2×Q8C23×C412yes—
581C2×Q8C23×C412yes—
582C2×Q8C23×C412yes—
583C2×Q8C2×#4112yes—
584C2×Q8C2×#4112yes—
585C2×Q8C2×#4112yes—
586C2×Q8C2×#4112yes—
587C2×D4—24no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—42no—
594C2×D4—42no—
595C2×D4C23×C412yes—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—24no—
603C22×C4—24no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—24no—
610C22×C4—24no—
611C22×C4—24no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—42no—
617C22×C4—42no—
618C22×C4—42no—
619C22×C4—42no—
620C22×C4—42no—
621C22×C4—42no—
622C22×C4—44no—
623C22×C4—44no—
624C22×C4—82no—
625C22×C4C4×D414yes—
626C22×C4C4×D414yes—
627C22×C4C23×C412yes—
628C22×C4C22×D412yes—
629C22×C4C22×D412yes—
630C22×C4C22×D412yes—
631C22×C4C22×D411yescharacteristic
632C22×C4C22×D411yescharacteristic
633C22×C4C22×D411yescharacteristic
634C22×C4C22×D411yescharacteristic
635C22×C4C22×D411yescharacteristic
636C22×C4C22×D412yes—
637C22×C4C2×#4112yes—
638C22×C4C2511yescharacteristic
639Q16—28no—
640Q16#117116yescomplemented
641SD16—28no—
642SD16—28no—
643M16—28no—
644M16—44no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—22no—
652C2×C8—22no—
653C2×C8—22no—
654C2×C8—22no—
655C2×C8—22no—
656C2×C8—22no—
657C2×C8C23×C412yes—
658C2×C8C23×C412yes—
659C2×C8C23×C412yes—
660C2×C8C23×C412yes—
661C2×C8C2×#4112yes—
662C2×C8C2×#4112yes—
663C4⋊C4—24no—
664C4⋊C4—24no—
665C4⋊C4—24no—
666C4⋊C4—24no—
667C4⋊C4—24no—
668C4⋊C4—24no—
669C4⋊C4—24no—
670C4⋊C4—24no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—21no—
675C4⋊C4—22no—
676C4⋊C4—22no—
677C4⋊C4—22no—
678C4⋊C4—22no—
679C4⋊C4—22no—
680C4⋊C4—22no—
681C4⋊C4—22no—
682C4⋊C4—22no—
683C4⋊C4—42no—
684C4⋊C4—44no—
685C4⋊C4—44no—
686C4⋊C4—44no—
687C4⋊C4—44no—
688C4⋊C4—44no—
689C4⋊C4—44no—
690C4⋊C4—44no—
691C4⋊C4—44no—
692C4⋊C4C23×C412yes—
693C4⋊C4C23×C412yes—
694C4⋊C4C23×C412yes—
695C4⋊C4C23×C412yes—
696C22⋊C4—24no—
697C22⋊C4—24no—
698C22⋊C4—24no—
699C22⋊C4—24no—
700C22⋊C4—42no—
701C22⋊C4—44no—
702C22⋊C4—44no—
703C22⋊C4—44no—
704C22⋊C4—82no—
705C22⋊C4—82no—
706C22⋊C4—82no—
707C42—24no—
708C42—24no—
709C42—24no—
710C42—24no—
711C42—24no—
712C42—24no—
713C42—24no—
714C42—24no—
715C42—22no—
716C42—22no—
717C42—22no—
718C42—22no—
719C42—42no—
720C42—42no—
721C42—42no—
722C42—44no—
723C42—44no—
724C42—44no—
725C42—44no—
726C42—44no—
727C42—44no—
728C42—44no—
729C42—44no—
730C42—82no—
731C42—82no—
732C42C4×D414yes—
733C42C4×D414yes—
734C42C23×C412yes—
735C42C23×C412yes—
736C42C2×#4112yes—
737C42C2×#4112yes—
738C23—22no—
739C23—21no—
740C23—21no—
741C23—22no—
742C23—22no—
743C23—42no—
744C23—41no—
745C23—41no—
746C23—42no—
747C23C2×C4×D412yes—
748C23C23×D411yescharacteristic
749Q8—22no—
750Q8—22no—
751Q8—22no—
752Q8—22no—
753Q8—22no—
754Q8—22no—
755Q8—22no—
756Q8—22no—
757Q8—48no—
758Q8—41no—
759Q8—41no—
760Q8C2×#11714yes—
761Q8C2×#11714yes—
762D4—22no—
763D4—22no—
764D4—48no—
765D4—41no—
766D4—41no—
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—21no—
778C2×C4—21no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—44no—
800C2×C4—44no—
801C2×C4—48no—
802C2×C4—48no—
803C2×C4—48no—
804C2×C4—48no—
805C2×C4—42no—
806C2×C4—41no—
807C2×C4—41no—
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—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—84no—
824C2×C4C2×C4×D412yes—
825C2×C4C2×C4×D412yes—
826C2×C4C2×C4×D412yes—
827C2×C4C2×C4×D412yes—
828C2×C4C2×C4×D412yes—
829C2×C4#57514yes—
830C2×C4C24×C411yescharacteristic
831C2×C4C22×#4111yescharacteristic
832C2×C4C22×#4111yescharacteristic
833C2×C4C22×#4111yescharacteristic
834C2×C4#58511yescharacteristic
835C2×C4#58511yescharacteristic
836C8—22no—
837C8—22no—
838C8—22no—
839C8—42no—
840C8—42no—
841C8C2×#11714yes—
842C22—22no—
843C22—22no—
844C22—22no—
845C22—42no—
846C22—42no—
847C22—42no—
848C22—42no—
849C22—42no—
850C22—82no—
851C22—82no—
852C22C22×C4×D411yescharacteristic
853C22D4×#4111yescharacteristic
854C22D4×#4111yescharacteristic
855C22C2×#57512yes—
856C22#358612yes—
857C4—22no—
858C4—22no—
859C4—24no—
860C4—22no—
861C4—24no—
862C4—24no—
863C4—22no—
864C4—22no—
865C4—42no—
866C4—42no—
867C4—42no—
868C4—42no—
869C4—42no—
870C4—42no—
871C4—42no—
872C4—42no—
873C4—82no—
874C4—82no—
875C4—82no—
876C4—82no—
877C4C22×#11711yescharacteristic
878C4#342811yescharacteristic
879C4#347511yescharacteristic
880C4#347511yescharacteristic
881C2—42no—
882C2—82no—
883C2D4×#11711yescharacteristic
884C2C4×#57511yescharacteristic
885C2#6016911yescharacteristic
886C2#6145812yes—
887C2#6146712yes—
subgroupG/H
center, socleC23C23×D4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
prime radicalC22×#41C23
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#117 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #34128C2semidirect
4. #22812C2semidirect
5. #22806C2semidirect
6. #22773C2semidirect
7. #22769C2semidirect
8. #22765C2semidirect
9. #22761C2semidirect
10. #22685C2semidirect
11. #22675C2semidirect
12. #22622C2semidirect
14. #22581C2semidirect
16. #21288C2semidirect
17. #21124C2semidirect
18. #21123C2semidirect
19. #20825C2semidirect
21. #20741C2semidirect
22. C4×#441C2semidirect
23. #20480C2semidirect
27. C4×#137C4semidirect
640. Q16#117semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#1372
#341282
#341252
#228122
#228062
#227732
#227692
#227652
#227612
#226852
#226752
#226222
#225832
#225812
#224452
#212882
#211242
#211232
#208252
#207422
#207412
C4×#4412
#204802