Finite Group Databasebeta

← C2×C4×#468 #6372846

Subgroups — C2×C4×#468 #6372846

Order 512.

3294 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#468C211yesmaximal, characteristic
2C22×C4×SD16C211yesmaximal, characteristic, complemented
3C22×C4×M16C211yesmaximal, characteristic, complemented
4C2×C4×C22⋊Q8C211yesmaximal, characteristic, complemented
5C2×C4×#121C211yesmaximal, characteristic
6C4×#468C2116yesmaximal, direct product factor
7C2×#1973C211yesmaximal, characteristic, complemented
8C2×#1943C211yesmaximal, characteristic, complemented
9C2×#1936C211yesmaximal, characteristic, complemented
10C2×#1935C211yesmaximal, characteristic, complemented
11C2×#1895C211yesmaximal, characteristic
12C2×#1894C211yesmaximal, characteristic, complemented
13C2×#1809C211yesmaximal, characteristic, complemented
14C2×C4×#107C211yesmaximal, characteristic, complemented
15C2×C4×#103C211yesmaximal, characteristic, complemented
16C2×C4×#102C211yesmaximal, characteristic, complemented
17C23×SD16C2211yescharacteristic
18C23×M16C2211yescharacteristic
19C23×M16C2211yescharacteristic
20C22×C22⋊Q8C2211yescharacteristic
21C22×#121C2211yescharacteristic
22C22×C4×Q8C2211yescharacteristic
23C22×C4×D4—21no—
24C22×C4×D4C2211yescharacteristic
25C23×C42C2211yescharacteristic
26C2×#468C4116yesdirect product factor
27C2×#468C2218yes—
28C2×C4×SD16—28no—
29C2×C4×SD16C2218yescomplemented
30C22×#107C2211yescharacteristic
31C22×#107C2211yescharacteristic
32C22×#106C2211yescharacteristic
33C22×#103C2211yescharacteristic
34C22×#103C2211yescharacteristic
35C22×#103C2211yescharacteristic
36C22×#102C2211yescharacteristic
37C22×#102C2211yescharacteristic
38C22×#102C2211yescharacteristic
39C2×C4×M16—28no—
40C2×C4×M16C2218yescomplemented
41C22×#97C2211yescharacteristic
42C22×#97C2211yescharacteristic
43C22×C4×C8C2211yescharacteristic
44C22×C4×C8C2211yescharacteristic
45C4×C22⋊Q8—24no—
46C4×C22⋊Q8C2218yescomplemented
47C4×#121—24no—
48C4×#121C2218yes—
49C2×#391C2211yescharacteristic
50C2×#390C2211yescharacteristic
51C2×#389C2211yescharacteristic
52C2×#389C2211yescharacteristic
53C2×#388—21no—
54C2×#387—21no—
55C2×#386—21no—
56C2×#385—21no—
57C2×#380C2211yescharacteristic
58C2×#380C2211yescharacteristic
59C2×C4×C4⋊C4—21no—
60C2×C4×C4⋊C4C2211yescharacteristic
61C2×C4×C4⋊C4C2211yescharacteristic
62C2×C4×C22⋊C4—21no—
63C2×C4×C22⋊C4—21no—
64#1973C2218yescomplemented
65#1943C2218yescomplemented
66#1936C2218yescomplemented
67#1935C2218yescomplemented
68#1895C2218yes—
69#1894C2218yescomplemented
70#1809C2218yescomplemented
71C4×#107C2218yescomplemented
72C4×#103C2218yescomplemented
73C4×#102C2218yescomplemented
74C2×#340C2211yescharacteristic
75C2×#340C2211yescharacteristic
76C2×#340C2211yescharacteristic
77C2×#340C2211yescharacteristic
78C2×#340C2211yescharacteristic
79C2×#340C2211yescharacteristic
80C23×Q8C2311yescharacteristic
81C23×D4—21no—
82C23×D4C2311yescharacteristic
83C24×C4—21no—
84C24×C4D411yescharacteristic
85C24×C4D411yescharacteristic
86C24×C4C2311yescharacteristic
87C22×SD16—24no—
88C22×SD16—24no—
89C22×SD16C2×C418yescomplemented
90C22×SD16C2314yes—
91C22×M16—24no—
92C22×M16—24no—
93C22×M16—24no—
94C22×M16—24no—
95C22×M16—24no—
96C22×M16C2×C418yescomplemented
97C22×M16C2314yes—
98C22×M16C2314yes—
99C23×C8C2311yescharacteristic
100C23×C8C2311yescharacteristic
101C23×C8C2311yescharacteristic
102C23×C8C2311yescharacteristic
103C2×C22⋊Q8—22no—
104C2×C22⋊Q8—24no—
105C2×C22⋊Q8C2×C418yescomplemented
106C2×C22⋊Q8C2314yes—
107C2×#121—22no—
108C2×#121—24no—
109C2×#121C2×C418yes—
110C2×#121C2314yes—
111C2×C4×Q8—22no—
112C2×C4×Q8—24no—
113C2×C4×Q8—24no—
114C2×C4×Q8C2314yes—
115C2×C4×D4—28no—
116C2×C4×D4—22no—
117C2×C4×D4—24no—
118C2×C4×D4—24no—
119C2×C4×D4—48no—
120C2×C4×D4C2314yes—
121C22×C4⋊C4—21no—
122C22×C4⋊C4—21no—
123C22×C4⋊C4—21no—
124C22×C4⋊C4—21no—
125C22×C4⋊C4C2311yescharacteristic
126C22×C4⋊C4C2311yescharacteristic
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2311yescharacteristic
129C22×C4⋊C4C2311yescharacteristic
130C22×C4⋊C4C2311yescharacteristic
131C22×C22⋊C4—21no—
132C22×C22⋊C4—21no—
133C22×C22⋊C4—21no—
134C22×C22⋊C4—21no—
135C22×C22⋊C4—21no—
136C22×C22⋊C4—21no—
137C22×C22⋊C4—21no—
138C22×C42—24no—
139C22×C42—24no—
140C22×C42—21no—
141C22×C42—21no—
142C22×C42—21no—
143C22×C42D411yescharacteristic
144C22×C42D414yes—
145C22×C42D411yescharacteristic
146C22×C42C2311yescharacteristic
147C22×C42C2314yes—
148C22×C42C2311yescharacteristic
149#468C2×C4164yesdirect product factor
150C4×SD16—232no—
151C2×#107—24no—
152C2×#107C2×C418yescomplemented
153C2×#107C2314yes—
154C2×#107C2314yes—
155C2×#106—24no—
156C2×#106C2314yes—
157C2×#103—24no—
158C2×#103—24no—
159C2×#103C2×C418yescomplemented
160C2×#103C2314yes—
161C2×#103C2314yes—
162C2×#103C2314yes—
163C2×#102—24no—
164C2×#102—24no—
165C2×#102C2×C418yescomplemented
166C2×#102C2314yes—
167C2×#102C2314yes—
168C2×#102C2314yes—
169C4×M16—232no—
170C2×#97—24no—
171C2×#97—24no—
172C2×#97C2314yes—
173C2×#97C2314yes—
174C2×C4×C8—24no—
175C2×C4×C8D418yescomplemented
176C2×C4×C8C2314yes—
177C2×C4×C8C2314yes—
178#391—22no—
179#391C2314yes—
180#390—22no—
181#390C2314yes—
182#389—22no—
183#389—22no—
184#389C2314yes—
185#389C2314yes—
186#388—28no—
187#387—28no—
188#386—28no—
189#385—28no—
190#380—22no—
191#380—22no—
192#380C2314yes—
193#380C2314yes—
194C4×C4⋊C4—28no—
195C4×C4⋊C4—22no—
196C4×C4⋊C4—22no—
197C4×C4⋊C4C2314yes—
198C4×C4⋊C4C2314yes—
199C4×C22⋊C4—28no—
200C4×C22⋊C4—28no—
201C2×#95—21no—
202C2×#95—21no—
203C2×#95—21no—
204C2×#95—21no—
205C2×#95—21no—
206C2×#95—21no—
207C2×#95—21no—
208C2×#95—21no—
209#340C2314yes—
210#340C2314yes—
211#340C2314yes—
212#340C2314yes—
213#340C2314yes—
214#340C2314yes—
215C25—21no—
216C25C2×D411yescharacteristic
217C22×Q8—21no—
218C22×Q8—22no—
219C22×Q8—22no—
220C22×Q8—22no—
221C22×Q8—22no—
222C22×Q8—22no—
223C22×Q8C22×C414yes—
224C22×Q8C2412yes—
225C22×D4—28no—
226C22×D4—24no—
227C22×D4—22no—
228C22×D4—21no—
229C22×D4—22no—
230C22×D4—22no—
231C22×D4—22no—
232C22×D4—22no—
233C22×D4—44no—
234C22×D4—44no—
235C22×D4C22×C414yes—
236C22×D4C2412yes—
237C23×C4—22no—
238C23×C4—22no—
239C23×C4—22no—
240C23×C4—22no—
241C23×C4—21no—
242C23×C4—21no—
243C23×C4—21no—
244C23×C4—24no—
245C23×C4—24no—
246C23×C4—24no—
247C23×C4—24no—
248C23×C4—21no—
249C23×C4—21no—
250C23×C4—21no—
251C23×C4—21no—
252C23×C4—24no—
253C23×C4—42no—
254C23×C4—42no—
255C23×C4—44no—
256C23×C4—44no—
257C23×C4—44no—
258C23×C4C22×C414yes—
259C23×C4C2×D411yescharacteristic
260C23×C4C2×D411yescharacteristic
261C23×C4C2×D414yes—
262C23×C4C2×D411yescharacteristic
263C23×C4C2×D412yes—
264C23×C4C2×D411yescharacteristic
265C23×C4C2×D414yes—
266C23×C4C2×D411yescharacteristic
267C23×C4#4114yes—
268C23×C4C2412yes—
269C23×C4C2411yescharacteristic
270C2×SD16—232no—
271C2×SD16—28no—
272C2×SD16—28no—
273C2×SD16C22×C4116yescomplemented
274C2×M16—232no—
275C2×M16—28no—
276C2×M16—232no—
277C2×M16—28no—
278C2×M16—28no—
279C2×M16—28no—
280C2×M16—28no—
281C2×M16C22×C4116yescomplemented
282C22×C8—22no—
283C22×C8—22no—
284C22×C8—22no—
285C22×C8—22no—
286C22×C8—22no—
287C22×C8—22no—
288C22×C8C22×C414yes—
289C22×C8C22×C414yes—
290C22×C8C2×D414yes—
291C22×C8C2×D414yes—
292C22×C8#4114yes—
293C22×C8#4114yes—
294C22×C8C2412yes—
295C22×C8C2412yes—
296C22×C8C2412yes—
297C22×C8C2412yes—
298C22⋊Q8—216no—
299C22⋊Q8—28no—
300C22⋊Q8C22×C4116yescomplemented
301#121—216no—
302#121—28no—
303#121C22×C4116yes—
304C4×Q8—28no—
305C4×Q8—28no—
306C4×Q8—48no—
307C4×D4—28no—
308C4×D4—28no—
309C4×D4—432no—
310C4×D4—48no—
311C2×C4⋊C4—28no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—44no—
333C2×C4⋊C4—44no—
334C2×C4⋊C4—44no—
335C2×C4⋊C4C22×C414yes—
336C2×C4⋊C4C22×C414yes—
337C2×C4⋊C4C2412yes—
338C2×C4⋊C4C2412yes—
339C2×C4⋊C4C2412yes—
340C2×C4⋊C4C2412yes—
341C2×C4⋊C4C2412yes—
342C2×C4⋊C4C2412yes—
343C2×C22⋊C4—28no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—28no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—24no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—44no—
353C2×C22⋊C4—44no—
354C2×C22⋊C4—44no—
355C2×C22⋊C4—44no—
356C2×C22⋊C4—44no—
357C2×C42—24no—
358C2×C42—24no—
359C2×C42—22no—
360C2×C42—22no—
361C2×C42—216no—
362C2×C42—28no—
363C2×C42—28no—
364C2×C42—24no—
365C2×C42—24no—
366C2×C42—24no—
367C2×C42—44no—
368C2×C42—44no—
369C2×C42—44no—
370C2×C42C2×D414yes—
371C2×C42C2×D414yes—
372C2×C42C2×D412yes—
373C2×C42C2×D412yes—
374C2×C42C2×D414yes—
375C2×C42#4114yes—
376C2×C42C2412yes—
377C2×C42C2412yes—
378#107—28no—
379#107C22×C4116yescomplemented
380#106—28no—
381#103—28no—
382#103—28no—
383#103C22×C4116yescomplemented
384#102—28no—
385#102—28no—
386#102C22×C4116yescomplemented
387#97—28no—
388#97—28no—
389C4×C8—28no—
390C4×C8C2×D4116yescomplemented
391#95—24no—
392#95—24no—
393#95—24no—
394#95—24no—
395#95—24no—
396#95—24no—
397#95—24no—
398#95—24no—
399C24—22no—
400C24—22no—
401C24—22no—
402C24—22no—
403C24—22no—
404C24—22no—
405C24—24no—
406C24—22no—
407C24—42no—
408C24—42no—
409C24—42no—
410C24—42no—
411C24—42no—
412C24—42no—
413C24C4×D414yes—
414C24C22×D412yes—
415C24C22×D411yescharacteristic
416C2×Q8—24no—
417C2×Q8—22no—
418C2×Q8—28no—
419C2×Q8—28no—
420C2×Q8—22no—
421C2×Q8—22no—
422C2×Q8—22no—
423C2×Q8—22no—
424C2×Q8—42no—
425C2×Q8—44no—
426C2×Q8—44no—
427C2×Q8—42no—
428C2×Q8C23×C414yes—
429C2×D4—216no—
430C2×D4—28no—
431C2×D4—24no—
432C2×D4—28no—
433C2×D4—22no—
434C2×D4—22no—
435C2×D4—22no—
436C2×D4—22no—
437C2×D4—22no—
438C2×D4—48no—
439C2×D4—432no—
440C2×D4—48no—
441C2×D4—42no—
442C2×D4—44no—
443C2×D4—44no—
444C2×D4—42no—
445C2×D4C23×C414yes—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—28no—
451C22×C4—28no—
452C22×C4—24no—
453C22×C4—28no—
454C22×C4—28no—
455C22×C4—24no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—24no—
461C22×C4—24no—
462C22×C4—24no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—28no—
473C22×C4—28no—
474C22×C4—28no—
475C22×C4—28no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—44no—
481C22×C4—44no—
482C22×C4—416no—
483C22×C4—42no—
484C22×C4—42no—
485C22×C4—42no—
486C22×C4—42no—
487C22×C4—42no—
488C22×C4—42no—
489C22×C4—416no—
490C22×C4—42no—
491C22×C4—42no—
492C22×C4—42no—
493C22×C4—42no—
494C22×C4—42no—
495C22×C4—42no—
496C22×C4—42no—
497C22×C4—42no—
498C22×C4—42no—
499C22×C4—42no—
500C22×C4—42no—
501C22×C4—42no—
502C22×C4—48no—
503C22×C4—48no—
504C22×C4—48no—
505C22×C4—816no—
506C22×C4C4×D414yes—
507C22×C4C4×D418yes—
508C22×C4#12114yes—
509C22×C4#12114yes—
510C22×C4AGL(1,ℤ/8)14yes—
511C22×C4#13714yes—
512C22×C4C23×C414yes—
513C22×C4C23×C412yes—
514C22×C4C22×D412yes—
515C22×C4C22×D412yes—
516C22×C4C22×D412yes—
517C22×C4C22×D412yes—
518C22×C4C22×D411yescharacteristic
519C22×C4C22×D412yes—
520C22×C4C22×D412yes—
521C22×C4C2×#4114yes—
522C22×C4C2×#4112yes—
523C22×C4C2×#4112yes—
524C22×C4C2×#4112yes—
525C22×C4C2×#4112yes—
526C22×C4C2511yescharacteristic
527SD16—232no—
528M16—232no—
529M16—232no—
530C2×C8—28no—
531C2×C8—28no—
532C2×C8—28no—
533C2×C8—22no—
534C2×C8—22no—
535C2×C8—22no—
536C2×C8—22no—
537C2×C8—22no—
538C2×C8—22no—
539C2×C8C4×D4116yescomplemented
540C2×C8C23×C414yes—
541C2×C8C23×C414yes—
542C2×C8C22×D414yes—
543C2×C8C22×D414yes—
544C2×C8C2×#4114yes—
545C2×C8C2×#4114yes—
546C4⋊C4—216no—
547C4⋊C4—24no—
548C4⋊C4—24no—
549C4⋊C4—22no—
550C4⋊C4—22no—
551C4⋊C4—22no—
552C4⋊C4—22no—
553C4⋊C4—22no—
554C4⋊C4—22no—
555C4⋊C4—22no—
556C4⋊C4—22no—
557C4⋊C4—22no—
558C4⋊C4—22no—
559C4⋊C4—48no—
560C4⋊C4—48no—
561C4⋊C4—42no—
562C4⋊C4—42no—
563C4⋊C4—48no—
564C4⋊C4—42no—
565C4⋊C4—42no—
566C4⋊C4C23×C414yes—
567C4⋊C4C23×C414yes—
568C22⋊C4—216no—
569C22⋊C4—216no—
570C22⋊C4—48no—
571C22⋊C4—48no—
572C22⋊C4—48no—
573C22⋊C4—48no—
574C22⋊C4—48no—
575C42—28no—
576C42—28no—
577C42—24no—
578C42—22no—
579C42—22no—
580C42—48no—
581C42—48no—
582C42—48no—
583C42#12118yes—
584C42C22×D414yes—
585C42C2×#4114yes—
586C23—22no—
587C23—22no—
588C23—28no—
589C23—28no—
590C23—22no—
591C23—22no—
592C23—28no—
593C23—22no—
594C23—22no—
595C23—24no—
596C23—44no—
597C23—44no—
598C23—44no—
599C23—44no—
600C23—42no—
601C23—42no—
602C23—48no—
603C23—48no—
604C23—42no—
605C23—42no—
606C23—48no—
607C23—42no—
608C23—42no—
609C23—84no—
610C23—84no—
611C23—84no—
612C23—84no—
613C23C2×C4×D414yes—
614C23C2×C4×D412yes—
615C23C2×#12112yes—
616C23#53212yes—
617C23C2×AGL(1,ℤ/8)12yes—
618C23C2×#13712yes—
619C23#57512yes—
620C23#57512yes—
621C23C23×D411yescharacteristic
622Q8—24no—
623Q8—24no—
624Q8—42no—
625Q8—42no—
626Q8—48no—
627D4—24no—
628D4—24no—
629D4—432no—
630D4—42no—
631D4—42no—
632D4—48no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—28no—
636C2×C4—28no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—24no—
640C2×C4—24no—
641C2×C4—24no—
642C2×C4—24no—
643C2×C4—216no—
644C2×C4—24no—
645C2×C4—24no—
646C2×C4—24no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—416no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—48no—
657C2×C4—48no—
658C2×C4—44no—
659C2×C4—44no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—48no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—416no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—84no—
679C2×C4—84no—
680C2×C4—84no—
681C2×C4—84no—
682C2×C4—816no—
683C2×C4#468116yesdirect product factor
684C2×C4C2×C4×D414yes—
685C2×C4C2×C4×D414yes—
686C2×C4C2×C4×D412yes—
687C2×C4C4×#4114yes—
688C2×C4C2×#12114yes—
689C2×C4C2×#12114yes—
690C2×C4C2×#12112yes—
691C2×C4#52514yes—
692C2×C4#52914yes—
693C2×C4#53212yes—
694C2×C4C2×AGL(1,ℤ/8)14yes—
695C2×C4C2×#13714yes—
696C2×C4C24×C411yescharacteristic
697C2×C4C23×D411yescharacteristic
698C2×C4C22×#4111yescharacteristic
699C2×C4C22×#4111yescharacteristic
700C2×C4C22×#4111yescharacteristic
701C2×C4C22×#4111yescharacteristic
702C8—24no—
703C8—24no—
704C8—24no—
705C8C2×C4×D418yescomplemented
706C22—24no—
707C22—24no—
708C22—24no—
709C22—42no—
710C22—42no—
711C22—42no—
712C22—42no—
713C22—416no—
714C22—44no—
715C22—44no—
716C22—44no—
717C22—82no—
718C22—82no—
719C22—82no—
720C22—82no—
721C22—816no—
722C22C4×#12114yes—
723C22C4×AGL(1,ℤ/8)14yes—
724C22C4×#13714yes—
725C22C2×#46814yes—
726C22#305414yes—
727C22#317114yes—
728C22#317214yes—
729C22C22×C4×D411yescharacteristic
730C22C22×#12111yescharacteristic
731C22C2×#53211yescharacteristic
732C22C22×AGL(1,ℤ/8)11yescharacteristic
733C22C22×#13711yescharacteristic
734C22C2×#57511yescharacteristic
735C22C2×#57511yescharacteristic
736C4—24no—
737C4—24no—
738C4—42no—
739C4—42no—
740C4—44no—
741C4—44no—
742C4—44no—
743C4—82no—
744C4—82no—
745C4—82no—
746C4—82no—
747C4C4×#12114yes—
748C4C2×#46818yesdirect product factor
749C4C22×C4×D411yescharacteristic
750C4C2×C4×#4111yescharacteristic
751C4C2×#52511yescharacteristic
752C4C2×#52911yescharacteristic
753C2—44no—
754C2—84no—
755C2C4×#46818yesdirect product factor
756C2C2×C4×#12111yescharacteristic
757C2C2×C4×AGL(1,ℤ/8)11yescharacteristic
758C2C2×C4×#13711yescharacteristic
759C2C22×#46811yescharacteristic
760C2C2×#305411yescharacteristic
761C2C2×#317111yescharacteristic
762C2C2×#317211yescharacteristic
subgroupG/H
centerC23×C4C2×D4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
socleC24C22×D4
prime radicalC22×#121C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C4 ◁ C23×C42 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C22×C4×SD16C2semidirect
3. C22×C4×M16C2semidirect
4. C2×C4×C22⋊Q8C2semidirect
6. C4×#468C2direct (N × H)
7. C2×#1973C2semidirect
8. C2×#1943C2semidirect
9. C2×#1936C2semidirect
10. C2×#1935C2semidirect
12. C2×#1894C2semidirect
13. C2×#1809C2semidirect
14. C2×C4×#107C2semidirect
15. C2×C4×#103C2semidirect
16. C2×C4×#102C2semidirect
26. C2×#468C4direct (N × H)
29. C2×C4×SD16C22semidirect
40. C2×C4×M16C22semidirect
46. C4×C22⋊Q8C22semidirect
64. #1973C22semidirect
65. #1943C22semidirect
66. #1936C22semidirect
67. #1935C22semidirect
69. #1894C22semidirect
70. #1809C22semidirect
71. C4×#107C22semidirect
72. C4×#103C22semidirect
73. C4×#102C22semidirect
89. C22×SD16C2×C4semidirect
96. C22×M16C2×C4semidirect
105. C2×C22⋊Q8C2×C4semidirect
149. #468C2×C4direct (N × H)
152. C2×#107C2×C4semidirect
159. C2×#103C2×C4semidirect
165. C2×#102C2×C4semidirect
175. C2×C4×C8D4semidirect
273. C2×SD16C22×C4semidirect
281. C2×M16C22×C4semidirect
300. C22⋊Q8C22×C4semidirect
379. #107C22×C4semidirect
383. #103C22×C4semidirect
386. #102C22×C4semidirect
390. C4×C8C2×D4semidirect
539. C2×C8C4×D4semidirect
683. C2×C4#468direct (N × H)
705. C8C2×C4×D4semidirect
748. C4C2×#468direct (N × H)
755. C2C4×#468direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#4682
C22×C4×SD162
C22×C4×M162
C2×C4×C22⋊Q82
C2×C4×#1212
C4×#4682
C2×#19732
C2×#19432
C2×#19362
C2×#19352
C2×#18952
C2×#18942
C2×#18092
C2×C4×#1072
C2×C4×#1032
C2×C4×#1022