Finite Group Databasebeta

← C2×#30762 #7501713

Subgroups — C2×#30762 #7501713

Order 512.

2658 conjugacy classes of subgroups.

The subgroup lattice has 807 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#497C211yesmaximal, characteristic, complemented
2C22×#464C211yesmaximal, characteristic, complemented
3C2×#2548C211yesmaximal, characteristic
4C2×#2446C211yesmaximal, characteristic, complemented
5#30762C2116yesmaximal, direct product factor
6C2×#2055C211yesmaximal, characteristic, complemented
7C2×#2042C211yesmaximal, characteristic, complemented
8C2×#2013C211yesmaximal, characteristic, complemented
9C2×#2015C211yesmaximal, characteristic, complemented
10C2×#2014C211yesmaximal, characteristic
11C2×#2014C211yesmaximal, characteristic
12C2×#1936C211yesmaximal, characteristic, complemented
13C2×#1917C211yesmaximal, characteristic, complemented
14C2×#1880C211yesmaximal, characteristic, complemented
15C2×#1878C211yesmaximal, characteristic, complemented
16C2×#1878C211yesmaximal, characteristic, complemented
17C23×Q16C2211yescharacteristic
18C23×Q16C2211yescharacteristic
19C23×SD16C2211yescharacteristic
20C23×SD16C2211yescharacteristic
21C23×SD16C2211yescharacteristic
22C23×SD16C2211yescharacteristic
23C22×C4⋊Q8C2211yescharacteristic
24C22×#127C2211yescharacteristic
25C22×#124C2211yescharacteristic
26C22×#124C2211yescharacteristic
27C22×C4×Q8C2211yescharacteristic
28C22×C4×Q8C2211yescharacteristic
29C2×#497—28no—
30C2×#497C2218yescomplemented
31C2×#464—28no—
32C2×#464C2218yescomplemented
33C22×C4⋊C8C2211yescharacteristic
34C22×#103C2211yescharacteristic
35C22×#103C2211yescharacteristic
36C22×#103C2211yescharacteristic
37C22×#103C2211yescharacteristic
38C22×#102C2211yescharacteristic
39C22×#102C2211yescharacteristic
40C22×#102C2211yescharacteristic
41C22×#102C2211yescharacteristic
42C22×#97C2211yescharacteristic
43#2548—24no—
44#2548C2218yes—
45#2446—24no—
46#2446C2218yescomplemented
47C2×#400—21no—
48C2×#398—21no—
49C2×#394—21no—
50C2×#394—21no—
51C2×#391C2211yescharacteristic
52C2×#391C2211yescharacteristic
53C2×#391C2211yescharacteristic
54C2×#390—21no—
55C2×#390—21no—
56C2×#390C2211yescharacteristic
57C2×#390C2211yescharacteristic
58C2×#389C2211yescharacteristic
59C2×#387—21no—
60C2×#387—21no—
61C2×C4×C4⋊C4C2211yescharacteristic
62#2055C2218yescomplemented
63#2042C2218yescomplemented
64#2015C2218yescomplemented
65#2014C2218yes—
66#2014C2218yes—
67#2013C2218yescomplemented
68#1936C2218yescomplemented
69#1917C2218yescomplemented
70#1880C2218yescomplemented
71#1878C2218yescomplemented
72#1878C2218yescomplemented
73C2×#340C2211yescharacteristic
74C2×#340C2211yescharacteristic
75C2×#336C2211yescharacteristic
76C2×#336C2211yescharacteristic
77C2×#336C2211yescharacteristic
78C2×#336C2211yescharacteristic
79C23×Q8C2311yescharacteristic
80C23×Q8C2311yescharacteristic
81C23×Q8C2311yescharacteristic
82C23×D4—21no—
83C23×D4—21no—
84C23×D4C2311yescharacteristic
85C23×D4C2311yescharacteristic
86C22×Q16—24no—
87C22×Q16—24no—
88C22×Q16—42no—
89C22×Q16—42no—
90C22×Q16—42no—
91C22×Q16D418yescomplemented
92C22×Q16C2314yes—
93C22×Q16C2314yes—
94C22×SD16—24no—
95C22×SD16—24no—
96C22×SD16—24no—
97C22×SD16—24no—
98C22×SD16—42no—
99C22×SD16—42no—
100C22×SD16—42no—
101C22×SD16—42no—
102C22×SD16—42no—
103C22×SD16—42no—
104C22×SD16—42no—
105C22×SD16—42no—
106C22×SD16C2314yes—
107C22×SD16C2314yes—
108C22×SD16C2314yes—
109C22×SD16C2314yes—
110C23×C8C2311yescharacteristic
111C23×C8C2311yescharacteristic
112C23×C8C2311yescharacteristic
113C23×C8C2311yescharacteristic
114C2×C4⋊Q8—24no—
115C2×C4⋊Q8—22no—
116C2×C4⋊Q8—42no—
117C2×C4⋊Q8C2314yes—
118C2×#127—22no—
119C2×#127—42no—
120C2×#127—42no—
121C2×#127C2314yes—
122C2×#124—24no—
123C2×#124—24no—
124C2×#124—22no—
125C2×#124—22no—
126C2×#124—42no—
127C2×#124—42no—
128C2×#124C2314yes—
129C2×#124C2314yes—
130C2×C4×Q8—22no—
131C2×C4×Q8—22no—
132C2×C4×Q8—24no—
133C2×C4×Q8—42no—
134C2×C4×Q8—42no—
135C2×C4×Q8—42no—
136C2×C4×Q8C2314yes—
137C2×C4×Q8C2314yes—
138C22×C4⋊C4—21no—
139C22×C4⋊C4—21no—
140C22×C4⋊C4—21no—
141C22×C4⋊C4—21no—
142C22×C4⋊C4—21no—
143C22×C4⋊C4D411yescharacteristic
144C22×C4⋊C4D411yescharacteristic
145C22×C4⋊C4C2311yescharacteristic
146C22×C4⋊C4C2311yescharacteristic
147C22×C4⋊C4C2311yescharacteristic
148C22×C22⋊C4—21no—
149C22×C22⋊C4—21no—
150C22×C22⋊C4—21no—
151C22×C22⋊C4—21no—
152C22×C22⋊C4—21no—
153C22×C22⋊C4—21no—
154C22×C22⋊C4—21no—
155C22×C22⋊C4—21no—
156C22×C42—21no—
157C22×C42—21no—
158C22×C42C2311yescharacteristic
159C22×C42C2311yescharacteristic
160C22×C42C2311yescharacteristic
161#497—232no—
162#464—232no—
163C2×C4⋊C8—24no—
164C2×C4⋊C8C2314yes—
165C2×#103—24no—
166C2×#103—42no—
167C2×#103—42no—
168C2×#103—42no—
169C2×#103C2314yes—
170C2×#103C2314yes—
171C2×#103C2314yes—
172C2×#103C2314yes—
173C2×#102—24no—
174C2×#102—24no—
175C2×#102—42no—
176C2×#102—42no—
177C2×#102C2314yes—
178C2×#102C2314yes—
179C2×#102C2314yes—
180C2×#102C2314yes—
181C2×#97—24no—
182C2×#97C2314yes—
183#400—28no—
184#398—28no—
185#394—28no—
186#394—28no—
187#391—22no—
188#391—22no—
189#391—22no—
190#391C2314yes—
191#391C2314yes—
192#391C2314yes—
193#390—28no—
194#390—28no—
195#390—22no—
196#390—22no—
197#390C2314yes—
198#390C2314yes—
199#389—22no—
200#389C2314yes—
201#387—28no—
202#387—28no—
203C4×C4⋊C4D414yes—
204C4×C4⋊C4C2314yes—
205C2×#95—21no—
206C2×#95—21no—
207C2×#95—21no—
208C2×#95—21no—
209C2×#95—21no—
210C2×#95—21no—
211C2×#95—21no—
212C2×#95D411yescharacteristic
213C2×#95D411yescharacteristic
214#340C2314yes—
215#340C2314yes—
216#336C2314yes—
217#336C2314yes—
218#336C2314yes—
219#336C2314yes—
220C25—21no—
221C25—21no—
222C22×Q8—21no—
223C22×Q8—21no—
224C22×Q8—21no—
225C22×Q8—22no—
226C22×Q8—22no—
227C22×Q8—22no—
228C22×Q8—22no—
229C22×Q8—22no—
230C22×Q8—22no—
231C22×Q8—22no—
232C22×Q8—22no—
233C22×Q8—22no—
234C22×Q8—22no—
235C22×Q8—22no—
236C22×Q8—22no—
237C22×Q8—22no—
238C22×Q8—22no—
239C22×Q8—22no—
240C22×Q8—22no—
241C22×Q8C2×D414yes—
242C22×Q8C2×D414yes—
243C22×Q8C2412yes—
244C22×Q8C2412yes—
245C22×Q8C2412yes—
246C22×D4—22no—
247C22×D4—22no—
248C22×D4—21no—
249C22×D4—21no—
250C22×D4—24no—
251C22×D4—24no—
252C22×D4—22no—
253C22×D4—22no—
254C22×D4—22no—
255C22×D4—22no—
256C22×D4—22no—
257C22×D4—22no—
258C22×D4—22no—
259C22×D4—22no—
260C22×D4—22no—
261C22×D4—22no—
262C22×D4—44no—
263C22×D4—44no—
264C22×D4—44no—
265C22×D4—44no—
266C22×D4—82no—
267C22×D4—82no—
268C22×D4C2412yes—
269C22×D4C2412yes—
270C23×C4—21no—
271C23×C4—21no—
272C23×C4—21no—
273C23×C4—21no—
274C23×C4—21no—
275C23×C4—21no—
276C23×C4C2×D411yescharacteristic
277C23×C4C2×D411yescharacteristic
278C23×C4C2×D411yescharacteristic
279C23×C4C2×D411yescharacteristic
280C23×C4C2×D411yescharacteristic
281C23×C4C2×D411yescharacteristic
282C23×C4C2411yescharacteristic
283C2×Q16—28no—
284C2×Q16—28no—
285C2×Q16—416no—
286C2×Q16—44no—
287C2×Q16—44no—
288C2×Q16—44no—
289C2×Q16—416no—
290C2×Q16C2×D4116yescomplemented
291C2×SD16—28no—
292C2×SD16—28no—
293C2×SD16—28no—
294C2×SD16—28no—
295C2×SD16—44no—
296C2×SD16—44no—
297C2×SD16—44no—
298C2×SD16—44no—
299C2×SD16—44no—
300C2×SD16—44no—
301C2×SD16—44no—
302C2×SD16—44no—
303C2×SD16—416no—
304C2×SD16—416no—
305C2×SD16—416no—
306C2×SD16—416no—
307C22×C8—22no—
308C22×C8—22no—
309C22×C8—22no—
310C22×C8—22no—
311C22×C8—22no—
312C22×C8—22no—
313C22×C8—22no—
314C22×C8—22no—
315C22×C8—22no—
316C22×C8—22no—
317C22×C8C2×D414yes—
318C22×C8#4114yes—
319C22×C8C2412yes—
320C22×C8C2412yes—
321C22×C8C2412yes—
322C22×C8C2412yes—
323C4⋊Q8—28no—
324C4⋊Q8—44no—
325C4⋊Q8—48no—
326#127—44no—
327#127—44no—
328#127—48no—
329#124—28no—
330#124—28no—
331#124—44no—
332#124—44no—
333#124—48no—
334#124—48no—
335C4×Q8—28no—
336C4×Q8—44no—
337C4×Q8—44no—
338C4×Q8—44no—
339C4×Q8—48no—
340C4×Q8—48no—
341C2×C4⋊C4—24no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—24no—
349C2×C4⋊C4—24no—
350C2×C4⋊C4—24no—
351C2×C4⋊C4—24no—
352C2×C4⋊C4—24no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—42no—
357C2×C4⋊C4—44no—
358C2×C4⋊C4—44no—
359C2×C4⋊C4—44no—
360C2×C4⋊C4—44no—
361C2×C4⋊C4—44no—
362C2×C4⋊C4C2×D414yes—
363C2×C4⋊C4C2×D414yes—
364C2×C4⋊C4C2412yes—
365C2×C4⋊C4C2412yes—
366C2×C4⋊C4C2412yes—
367C2×C22⋊C4—24no—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—24no—
373C2×C22⋊C4—24no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—44no—
376C2×C22⋊C4—44no—
377C2×C22⋊C4—44no—
378C2×C22⋊C4—44no—
379C2×C22⋊C4—82no—
380C2×C22⋊C4—82no—
381C2×C22⋊C4—82no—
382C2×C22⋊C4—82no—
383C2×C42—22no—
384C2×C42—22no—
385C2×C42—22no—
386C2×C42—22no—
387C2×C42—22no—
388C2×C42—22no—
389C2×C42—24no—
390C2×C42—24no—
391C2×C42—44no—
392C2×C42—44no—
393C2×C42C2×D412yes—
394C2×C42C2×D412yes—
395C2×C42C2×D412yes—
396C2×C42C2412yes—
397C2×C42C2412yes—
398C2×C42C2412yes—
399C4⋊C8—28no—
400#103—28no—
401#103—44no—
402#103—44no—
403#103—44no—
404#102—28no—
405#102—28no—
406#102—44no—
407#102—44no—
408#97—28no—
409#95—24no—
410#95—24no—
411#95—24no—
412#95—24no—
413#95—24no—
414#95—24no—
415#95—24no—
416#95C2×D414yes—
417#95C2×D414yes—
418C24—22no—
419C24—22no—
420C24—42no—
421C24—42no—
422C24—42no—
423C24—42no—
424C24—42no—
425C24—42no—
426C24—42no—
427C24—42no—
428C24—42no—
429C24—42no—
430C24—42no—
431C24—42no—
432C24—42no—
433C24—42no—
434C24C22×D411yescharacteristic
435C2×Q8—24no—
436C2×Q8—24no—
437C2×Q8—22no—
438C2×Q8—22no—
439C2×Q8—28no—
440C2×Q8—28no—
441C2×Q8—28no—
442C2×Q8—28no—
443C2×Q8—22no—
444C2×Q8—22no—
445C2×Q8—22no—
446C2×Q8—22no—
447C2×Q8—22no—
448C2×Q8—22no—
449C2×Q8—22no—
450C2×Q8—22no—
451C2×Q8—22no—
452C2×Q8—22no—
453C2×Q8—22no—
454C2×Q8—22no—
455C2×Q8—22no—
456C2×Q8—22no—
457C2×Q8—42no—
458C2×Q8—42no—
459C2×Q8—42no—
460C2×Q8—44no—
461C2×Q8—44no—
462C2×Q8—42no—
463C2×Q8—42no—
464C2×Q8—42no—
465C2×Q8—42no—
466C2×Q8—44no—
467C2×Q8—44no—
468C2×Q8—44no—
469C2×Q8—44no—
470C2×Q8—44no—
471C2×Q8—44no—
472C2×Q8C22×D414yes—
473C2×Q8C22×D414yes—
474C2×D4—22no—
475C2×D4—22no—
476C2×D4—22no—
477C2×D4—22no—
478C2×D4—22no—
479C2×D4—22no—
480C2×D4—22no—
481C2×D4—22no—
482C2×D4—22no—
483C2×D4—22no—
484C2×D4—22no—
485C2×D4—22no—
486C2×D4—48no—
487C2×D4—48no—
488C2×D4—48no—
489C2×D4—44no—
490C2×D4—44no—
491C2×D4—42no—
492C2×D4—42no—
493C2×D4—44no—
494C2×D4—44no—
495C2×D4—42no—
496C2×D4—42no—
497C2×D4—44no—
498C2×D4—44no—
499C2×D4—42no—
500C2×D4—42no—
501C2×D4—44no—
502C2×D4—44no—
503C2×D4—48no—
504C2×D4—84no—
505C2×D4—84no—
506C2×D4—816no—
507C2×D4—816no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—24no—
516C22×C4—24no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—42no—
534C22×C4—42no—
535C22×C4—42no—
536C22×C4—42no—
537C22×C4—42no—
538C22×C4—42no—
539C22×C4—42no—
540C22×C4—42no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4—42no—
544C22×C4—42no—
545C22×C4—42no—
546C22×C4—42no—
547C22×C4—42no—
548C22×C4—42no—
549C22×C4#13714yes—
550C22×C4C22×D412yes—
551C22×C4C22×D412yes—
552C22×C4C22×D412yes—
553C22×C4C22×D412yes—
554C22×C4C22×D412yes—
555C22×C4C22×D412yes—
556C22×C4C22×D412yes—
557C22×C4C22×D411yescharacteristic
558C22×C4C2×#4112yes—
559C22×C4H(5,𝔽2)12yes—
560C22×C4H(5,𝔽2)12yes—
561C22×C4H(5,𝔽2)12yes—
562C22×C4H(5,𝔽2)12yes—
563C22×C4C2511yescharacteristic
564Q16—416no—
565Q16—416no—
566SD16—416no—
567SD16—416no—
568SD16—416no—
569SD16—416no—
570C2×C8—28no—
571C2×C8—28no—
572C2×C8—22no—
573C2×C8—22no—
574C2×C8—22no—
575C2×C8—22no—
576C2×C8—22no—
577C2×C8—22no—
578C2×C8—22no—
579C2×C8—22no—
580C2×C8—22no—
581C2×C8—22no—
582C2×C8—44no—
583C2×C8—44no—
584C2×C8C22×D414yes—
585C2×C8C2×#4114yes—
586C4⋊C4—28no—
587C4⋊C4—22no—
588C4⋊C4—22no—
589C4⋊C4—22no—
590C4⋊C4—22no—
591C4⋊C4—22no—
592C4⋊C4—22no—
593C4⋊C4—44no—
594C4⋊C4—48no—
595C4⋊C4—48no—
596C4⋊C4—48no—
597C4⋊C4—48no—
598C4⋊C4—48no—
599C4⋊C4—42no—
600C4⋊C4—42no—
601C4⋊C4—42no—
602C22⋊C4—48no—
603C22⋊C4—48no—
604C22⋊C4—48no—
605C22⋊C4—48no—
606C22⋊C4—84no—
607C22⋊C4—84no—
608C22⋊C4—84no—
609C22⋊C4—84no—
610C42—24no—
611C42—24no—
612C42—24no—
613C42—22no—
614C42—22no—
615C42—22no—
616C42—22no—
617C42—22no—
618C42—22no—
619C42—48no—
620C42—48no—
621C23—42no—
622C23—42no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—42no—
628C23—42no—
629C23—42no—
630C23—42no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—84no—
636C23—84no—
637C23—84no—
638C23—84no—
639C23—84no—
640C23—84no—
641C23—84no—
642C23—84no—
643C23—84no—
644C23—84no—
645C23—84no—
646C23—84no—
647C23—84no—
648C23—84no—
649C23#53512yes—
650C23D4212yes—
651C23#55012yes—
652C23C2×#13712yes—
653C23#57512yes—
654C23#57712yes—
655C23#57712yes—
656C23C23×D411yescharacteristic
657Q8—24no—
658Q8—24no—
659Q8—24no—
660Q8—24no—
661Q8—48no—
662Q8—48no—
663Q8—42no—
664Q8—42no—
665Q8—42no—
666Q8—42no—
667Q8—42no—
668Q8—42no—
669Q8—42no—
670Q8—42no—
671Q8—84no—
672D4—42no—
673D4—42no—
674D4—42no—
675D4—42no—
676D4—42no—
677D4—42no—
678D4—42no—
679D4—42no—
680D4—816no—
681D4—816no—
682D4—84no—
683D4—84no—
684C2×C4—22no—
685C2×C4—28no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—24no—
693C2×C4—24no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—48no—
705C2×C4—48no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—44no—
711C2×C4—44no—
712C2×C4—44no—
713C2×C4—44no—
714C2×C4—44no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—84no—
728C2×C4—84no—
729C2×C4—84no—
730C2×C4—84no—
731C2×C4#53414yes—
732C2×C4#53512yes—
733C2×C4#54014yes—
734C2×C4D4212yes—
735C2×C4#54614yes—
736C2×C4#55012yes—
737C2×C4#56014yes—
738C2×C4C2×#13714yes—
739C2×C4C23×D411yescharacteristic
740C2×C4C22×#4111yescharacteristic
741C2×C4C2×H(5,𝔽2)11yescharacteristic
742C2×C4C2×H(5,𝔽2)11yescharacteristic
743C2×C4C2×H(5,𝔽2)11yescharacteristic
744C2×C4C2×H(5,𝔽2)11yescharacteristic
745C8—24no—
746C8—24no—
747C8—42no—
748C8—42no—
749C22—82no—
750C22—82no—
751C22—82no—
752C22—82no—
753C22—82no—
754C22—82no—
755C22—82no—
756C22—82no—
757C22—82no—
758C22—82no—
759C22—82no—
760C22—82no—
761C22—82no—
762C22—82no—
763C22—168no—
764C22—168no—
765C22#267314yes—
766C22#321514yes—
767C22#322214yes—
768C22#327114yes—
769C22#327814yes—
770C22#340014yes—
771C22#340114yes—
772C22C2×#53511yescharacteristic
773C22C2×D4211yescharacteristic
774C22C2×#55011yescharacteristic
775C22C22×#13711yescharacteristic
776C22C2×#57511yescharacteristic
777C22C2×#57711yescharacteristic
778C22C2×#57711yescharacteristic
779C4—24no—
780C4—42no—
781C4—42no—
782C4—42no—
783C4—42no—
784C4—42no—
785C4—44no—
786C4—44no—
787C4—82no—
788C4—82no—
789C4—82no—
790C4—82no—
791C4#267314yes—
792C4C2×#53411yescharacteristic
793C4C2×#54011yescharacteristic
794C4C2×#54611yescharacteristic
795C4C2×#56011yescharacteristic
796C2—162no—
797C2—162no—
798C2#3076218yesdirect product factor
799C2C2×#267311yescharacteristic
800C2C2×#321511yescharacteristic
801C2C2×#322211yescharacteristic
802C2C2×#327111yescharacteristic
803C2C2×#327811yescharacteristic
804C2C2×#340011yescharacteristic
805C2C2×#340111yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×#127C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#497C2semidirect
2. C22×#464C2semidirect
4. C2×#2446C2semidirect
5. #30762C2direct (N × H)
6. C2×#2055C2semidirect
7. C2×#2042C2semidirect
8. C2×#2013C2semidirect
9. C2×#2015C2semidirect
12. C2×#1936C2semidirect
13. C2×#1917C2semidirect
14. C2×#1880C2semidirect
15. C2×#1878C2semidirect
16. C2×#1878C2semidirect
30. C2×#497C22semidirect
32. C2×#464C22semidirect
46. #2446C22semidirect
62. #2055C22semidirect
63. #2042C22semidirect
64. #2015C22semidirect
67. #2013C22semidirect
68. #1936C22semidirect
69. #1917C22semidirect
70. #1880C22semidirect
71. #1878C22semidirect
72. #1878C22semidirect
91. C22×Q16D4semidirect
290. C2×Q16C2×D4semidirect
798. C2#30762direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#4972
C22×#4642
C2×#25482
C2×#24462
#307622
C2×#20552
C2×#20422
C2×#20132
C2×#20152
C2×#20142
C2×#19362
C2×#19172
C2×#18802
C2×#18782