Finite Group Databasebeta

← C2×#24739 #6442815

Subgroups — C2×#24739 #6442815

Order 512.

2960 conjugacy classes of subgroups.

The subgroup lattice has 795 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#464C211yesmaximal, characteristic, complemented
2C22×#464C211yesmaximal, characteristic, complemented
3C22×#460C211yesmaximal, characteristic
4C22×#440C211yesmaximal, characteristic, complemented
5C2×#2544C211yesmaximal, characteristic
6C2×Q8×C4⋊C4C211yesmaximal, characteristic, complemented
7#24739C2116yesmaximal, direct product factor
8C2×#2068C211yesmaximal, characteristic, complemented
9C2×#2067C211yesmaximal, characteristic, complemented
10C2×#2042C211yesmaximal, characteristic, complemented
11C2×#2041C211yesmaximal, characteristic
12C2×#1959C211yesmaximal, characteristic, complemented
13C2×#1940C211yesmaximal, characteristic, complemented
14C2×#1880C211yesmaximal, characteristic, complemented
15C2×#1878C211yesmaximal, characteristic, complemented
16C2×#1802C211yesmaximal, characteristic, complemented
17C23×Q16C2211yescharacteristic
18C23×SD16C2211yescharacteristic
19C23×SD16C2211yescharacteristic
20C22×#127C2211yescharacteristic
21C22×#124C2211yescharacteristic
22C22×#124C2211yescharacteristic
23C22×C4×Q8C2211yescharacteristic
24C22×C4×Q8C2211yescharacteristic
25C22×C4×Q8C2211yescharacteristic
26C22×C4×D4C2211yescharacteristic
27C2×#464—28no—
28C2×#464—28no—
29C2×#464C2218yescomplemented
30C2×#464C2218yescomplemented
31C2×#460—28no—
32C2×#460C2218yes—
33C2×#440—28no—
34C2×#440C2218yescomplemented
35C22×#107C2211yescharacteristic
36C22×C4⋊C8C2211yescharacteristic
37C22×C4⋊C8C2211yescharacteristic
38C22×C4⋊C8C2211yescharacteristic
39C22×#103C2211yescharacteristic
40C22×#103C2211yescharacteristic
41C22×#103C2211yescharacteristic
42C22×#103C2211yescharacteristic
43C22×#102C2211yescharacteristic
44C22×#102C2211yescharacteristic
45C22×#102C2211yescharacteristic
46C22×#102C2211yescharacteristic
47C22×#102C2211yescharacteristic
48C22×#102C2211yescharacteristic
49C22×#97C2211yescharacteristic
50#2544—24no—
51#2544C2218yes—
52C2×#394—21no—
53C2×#394—21no—
54Q8×C4⋊C4—24no—
55Q8×C4⋊C4C2218yescomplemented
56C2×#391C2211yescharacteristic
57C2×#390C2211yescharacteristic
58C2×#389—21no—
59C2×#389—21no—
60C2×#389C2211yescharacteristic
61C2×#389C2211yescharacteristic
62C2×#386—21no—
63C2×#386—21no—
64C2×#384—21no—
65C2×#384C2211yescharacteristic
66C2×C4×C4⋊C4—21no—
67C2×C4×C4⋊C4C2211yescharacteristic
68#2068C2218yescomplemented
69#2067C2218yescomplemented
70#2042C2218yescomplemented
71#2041C2218yes—
72#1959C2218yescomplemented
73#1940C2218yescomplemented
74#1880C2218yescomplemented
75#1878C2218yescomplemented
76#1802C2218yescomplemented
77C2×#340C2211yescharacteristic
78C2×#340C2211yescharacteristic
79C2×#336C2211yescharacteristic
80C2×#336C2211yescharacteristic
81C23×Q8C2311yescharacteristic
82C23×Q8C2311yescharacteristic
83C23×D4—21no—
84C23×D4—21no—
85C23×D4C2311yescharacteristic
86C23×D4C2311yescharacteristic
87C24×C4—21no—
88C22×Q16—24no—
89C22×Q16—24no—
90C22×Q16—24no—
91C22×Q16C2314yes—
92C22×SD16—24no—
93C22×SD16—24no—
94C22×SD16—24no—
95C22×SD16—24no—
96C22×SD16—24no—
97C22×SD16D418yes—
98C22×SD16C2314yes—
99C22×SD16C2314yes—
100C23×C8C2311yescharacteristic
101C23×C8C2311yescharacteristic
102C23×C8C2311yescharacteristic
103C23×C8C2311yescharacteristic
104C2×#127—24no—
105C2×#127—22no—
106C2×#127—42no—
107C2×#127C2314yes—
108C2×#124—24no—
109C2×#124—22no—
110C2×#124—22no—
111C2×#124—24no—
112C2×#124—24no—
113C2×#124—42no—
114C2×#124C2314yes—
115C2×#124C2314yes—
116C2×C4×Q8—22no—
117C2×C4×Q8—22no—
118C2×C4×Q8—22no—
119C2×C4×Q8—24no—
120C2×C4×Q8—24no—
121C2×C4×Q8—24no—
122C2×C4×Q8—42no—
123C2×C4×Q8—42no—
124C2×C4×Q8D418yescomplemented
125C2×C4×Q8C2314yes—
126C2×C4×Q8C2314yes—
127C2×C4×Q8C2314yes—
128C2×C4×D4—22no—
129C2×C4×D4—24no—
130C2×C4×D4—24no—
131C2×C4×D4C2314yes—
132C22×C4⋊C4—21no—
133C22×C4⋊C4—21no—
134C22×C4⋊C4—21no—
135C22×C4⋊C4—21no—
136C22×C4⋊C4—21no—
137C22×C4⋊C4—21no—
138C22×C4⋊C4—21no—
139C22×C4⋊C4D411yescharacteristic
140C22×C4⋊C4D411yescharacteristic
141C22×C4⋊C4C2311yescharacteristic
142C22×C4⋊C4C2311yescharacteristic
143C22×C4⋊C4C2311yescharacteristic
144C22×C4⋊C4C2311yescharacteristic
145C22×C22⋊C4—21no—
146C22×C22⋊C4—21no—
147C22×C22⋊C4—21no—
148C22×C22⋊C4—21no—
149C22×C22⋊C4—21no—
150C22×C22⋊C4—21no—
151C22×C22⋊C4—21no—
152C22×C42—21no—
153C22×C42—21no—
154C22×C42—21no—
155C22×C42C2311yescharacteristic
156C22×C42C2311yescharacteristic
157C22×C42C2311yescharacteristic
158#464—232no—
159#464—232no—
160#460—232no—
161#440—232no—
162C2×#107—24no—
163C2×#107C2314yes—
164C2×C4⋊C8—24no—
165C2×C4⋊C8—24no—
166C2×C4⋊C8—24no—
167C2×C4⋊C8C2314yes—
168C2×C4⋊C8C2314yes—
169C2×C4⋊C8C2314yes—
170C2×#103—24no—
171C2×#103—24no—
172C2×#103—24no—
173C2×#103—42no—
174C2×#103C2314yes—
175C2×#103C2314yes—
176C2×#103C2314yes—
177C2×#103C2314yes—
178C2×#102—24no—
179C2×#102—24no—
180C2×#102—24no—
181C2×#102—24no—
182C2×#102—24no—
183C2×#102—42no—
184C2×#102C2314yes—
185C2×#102C2314yes—
186C2×#102C2314yes—
187C2×#102C2314yes—
188C2×#102C2314yes—
189C2×#102C2314yes—
190C2×#97—24no—
191C2×#97C2314yes—
192#394—28no—
193#394—28no—
194#391—22no—
195#391C2314yes—
196#390—22no—
197#390C2314yes—
198#389—22no—
199#389—22no—
200#389—28no—
201#389—28no—
202#389C2314yes—
203#389C2314yes—
204#386—28no—
205#386—28no—
206#384—28no—
207#384—22no—
208#384C2314yes—
209C4×C4⋊C4—28no—
210C4×C4⋊C4D414yes—
211C4×C4⋊C4C2314yes—
212C2×#95—21no—
213C2×#95—21no—
214C2×#95—21no—
215C2×#95—21no—
216C2×#95D411yescharacteristic
217C2×#95D411yescharacteristic
218#340C2314yes—
219#340C2314yes—
220#336C2314yes—
221#336C2314yes—
222C25—21no—
223C25—21no—
224C22×Q8—21no—
225C22×Q8—21no—
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×Q8C2×D414yes—
236C22×Q8C2×D414yes—
237C22×Q8#4114yes—
238C22×Q8C2412yes—
239C22×Q8C2412yes—
240C22×D4—22no—
241C22×D4—21no—
242C22×D4—22no—
243C22×D4—22no—
244C22×D4—21no—
245C22×D4—24no—
246C22×D4—24no—
247C22×D4—22no—
248C22×D4—22no—
249C22×D4—22no—
250C22×D4—22no—
251C22×D4—22no—
252C22×D4—22no—
253C22×D4—22no—
254C22×D4—22no—
255C22×D4—44no—
256C22×D4—44no—
257C22×D4—44no—
258C22×D4—44no—
259C22×D4—82no—
260C22×D4—82no—
261C22×D4C2×D414yes—
262C22×D4C2412yes—
263C22×D4C2412yes—
264C23×C4—21no—
265C23×C4—21no—
266C23×C4—21no—
267C23×C4—21no—
268C23×C4—21no—
269C23×C4—21no—
270C23×C4—24no—
271C23×C4—44no—
272C23×C4—82no—
273C23×C4—82no—
274C23×C4C2×D411yescharacteristic
275C23×C4C2×D411yescharacteristic
276C23×C4C2×D411yescharacteristic
277C23×C4C2×D411yescharacteristic
278C23×C4C2×D411yescharacteristic
279C23×C4C2×D411yescharacteristic
280C23×C4C2411yescharacteristic
281C2×Q16—28no—
282C2×Q16—28no—
283C2×Q16—28no—
284C2×Q16—416no—
285C2×SD16—232no—
286C2×SD16—28no—
287C2×SD16—28no—
288C2×SD16—28no—
289C2×SD16—28no—
290C2×SD16—28no—
291C2×SD16—416no—
292C2×SD16C2×D4116yes—
293C22×C8—22no—
294C22×C8—22no—
295C22×C8—22no—
296C22×C8—22no—
297C22×C8—22no—
298C22×C8—22no—
299C22×C8—22no—
300C22×C8—22no—
301C22×C8—22no—
302C22×C8—22no—
303C22×C8—22no—
304C22×C8C2×D414yes—
305C22×C8C2412yes—
306C22×C8C2412yes—
307C22×C8C2412yes—
308C22×C8C2412yes—
309#127—28no—
310#127—44no—
311#127—48no—
312#124—28no—
313#124—28no—
314#124—28no—
315#124—44no—
316#124—48no—
317#124—48no—
318C4×Q8—216no—
319C4×Q8—28no—
320C4×Q8—28no—
321C4×Q8—28no—
322C4×Q8—44no—
323C4×Q8—44no—
324C4×Q8—48no—
325C4×Q8—48no—
326C4×Q8C2×D4116yescomplemented
327C4×D4—28no—
328C4×D4—28no—
329C4×D4—48no—
330C2×C4⋊C4—28no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—24no—
342C2×C4⋊C4—24no—
343C2×C4⋊C4—24no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—24no—
348C2×C4⋊C4—24no—
349C2×C4⋊C4—24no—
350C2×C4⋊C4—42no—
351C2×C4⋊C4—44no—
352C2×C4⋊C4—44no—
353C2×C4⋊C4—44no—
354C2×C4⋊C4—82no—
355C2×C4⋊C4—82no—
356C2×C4⋊C4—82no—
357C2×C4⋊C4C2×D414yes—
358C2×C4⋊C4C2×D414yes—
359C2×C4⋊C4C2×D414yes—
360C2×C4⋊C4C2412yes—
361C2×C4⋊C4C2412yes—
362C2×C4⋊C4C2412yes—
363C2×C4⋊C4C2412yes—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—24no—
367C2×C22⋊C4—24no—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—44no—
372C2×C22⋊C4—44no—
373C2×C22⋊C4—44no—
374C2×C22⋊C4—44no—
375C2×C22⋊C4—44no—
376C2×C22⋊C4—82no—
377C2×C22⋊C4—82no—
378C2×C42—28no—
379C2×C42—22no—
380C2×C42—22no—
381C2×C42—24no—
382C2×C42—22no—
383C2×C42—22no—
384C2×C42—24no—
385C2×C42—24no—
386C2×C42—44no—
387C2×C42—44no—
388C2×C42C2×D412yes—
389C2×C42C2×D412yes—
390C2×C42C2×D412yes—
391C2×C42C2×D414yes—
392C2×C42#4114yes—
393C2×C42C2412yes—
394C2×C42C2412yes—
395C2×C42C2412yes—
396#107—28no—
397C4⋊C8—28no—
398C4⋊C8—28no—
399C4⋊C8—28no—
400#103—28no—
401#103—28no—
402#103—28no—
403#103—44no—
404#102—28no—
405#102—28no—
406#102—28no—
407#102—28no—
408#102—28no—
409#102—44no—
410#97—28no—
411#95—24no—
412#95—24no—
413#95—24no—
414#95—24no—
415#95C2×D414yes—
416#95C2×D414yes—
417C24—24no—
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—
433C24C22×D411yescharacteristic
434C2×Q8—24no—
435C2×Q8—28no—
436C2×Q8—24no—
437C2×Q8—28no—
438C2×Q8—24no—
439C2×Q8—28no—
440C2×Q8—22no—
441C2×Q8—22no—
442C2×Q8—22no—
443C2×Q8—22no—
444C2×Q8—22no—
445C2×Q8—22no—
446C2×Q8—22no—
447C2×Q8—22no—
448C2×Q8—22no—
449C2×Q8—42no—
450C2×Q8—42no—
451C2×Q8—42no—
452C2×Q8—44no—
453C2×Q8—44no—
454C2×Q8—44no—
455C2×Q8—44no—
456C2×Q8#121116yes—
457C2×Q8C22×D414yes—
458C2×Q8C22×D414yes—
459C2×Q8C2×#4114yes—
460C2×D4—28no—
461C2×D4—24no—
462C2×D4—28no—
463C2×D4—22no—
464C2×D4—22no—
465C2×D4—22no—
466C2×D4—22no—
467C2×D4—22no—
468C2×D4—22no—
469C2×D4—22no—
470C2×D4—22no—
471C2×D4—22no—
472C2×D4—22no—
473C2×D4—22no—
474C2×D4—48no—
475C2×D4—48no—
476C2×D4—48no—
477C2×D4—42no—
478C2×D4—44no—
479C2×D4—42no—
480C2×D4—44no—
481C2×D4—44no—
482C2×D4—42no—
483C2×D4—44no—
484C2×D4—42no—
485C2×D4—42no—
486C2×D4—44no—
487C2×D4—44no—
488C2×D4—48no—
489C2×D4—84no—
490C2×D4—84no—
491C2×D4—816no—
492C2×D4—816no—
493C2×D4C22×D414yes—
494C22×C4—24no—
495C22×C4—22no—
496C22×C4—24no—
497C22×C4—24no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—24no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—42no—
520C22×C4—42no—
521C22×C4—42no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4—42no—
525C22×C4—42no—
526C22×C4—42no—
527C22×C4—42no—
528C22×C4—42no—
529C22×C4—42no—
530C22×C4—42no—
531C22×C4—42no—
532C22×C4—42no—
533C22×C4—48no—
534C22×C4—84no—
535C22×C4—84no—
536C22×C4—816no—
537C22×C4#12114yes—
538C22×C4#12114yes—
539C22×C4#13714yes—
540C22×C4C22×D412yes—
541C22×C4C22×D412yes—
542C22×C4C22×D412yes—
543C22×C4C22×D412yes—
544C22×C4C22×D412yes—
545C22×C4C22×D412yes—
546C22×C4C22×D412yes—
547C22×C4C22×D411yescharacteristic
548C22×C4C22×D412yes—
549C22×C4C2×#4112yes—
550C22×C4C2×#4112yes—
551C22×C4H(5,𝔽2)12yes—
552C22×C42−1+412yes—
553C22×C4C2511yescharacteristic
554Q16—416no—
555SD16—232no—
556SD16—416no—
557C2×C8—28no—
558C2×C8—22no—
559C2×C8—22no—
560C2×C8—22no—
561C2×C8—22no—
562C2×C8—22no—
563C2×C8—22no—
564C2×C8—22no—
565C2×C8—22no—
566C2×C8—22no—
567C2×C8—22no—
568C2×C8—22no—
569C2×C8—44no—
570C2×C8—44no—
571C2×C8—44no—
572C2×C8C22×D414yes—
573C4⋊C4—216no—
574C4⋊C4—24no—
575C4⋊C4—28no—
576C4⋊C4—22no—
577C4⋊C4—22no—
578C4⋊C4—22no—
579C4⋊C4—22no—
580C4⋊C4—22no—
581C4⋊C4—22no—
582C4⋊C4—22no—
583C4⋊C4—44no—
584C4⋊C4—48no—
585C4⋊C4—48no—
586C4⋊C4—48no—
587C4⋊C4—42no—
588C4⋊C4—42no—
589C4⋊C4—42no—
590C4⋊C4—84no—
591C4⋊C4—84no—
592C4⋊C4—84no—
593C4⋊C4C22×D414yes—
594C22⋊C4—48no—
595C22⋊C4—48no—
596C22⋊C4—48no—
597C22⋊C4—48no—
598C22⋊C4—48no—
599C22⋊C4—84no—
600C22⋊C4—84no—
601C42—216no—
602C42—24no—
603C42—24no—
604C42—22no—
605C42—22no—
606C42—22no—
607C42—22no—
608C42—48no—
609C42—48no—
610C42#12118yes—
611C42C22×D414yes—
612C42C2×#4114yes—
613C23—24no—
614C23—42no—
615C23—48no—
616C23—42no—
617C23—48no—
618C23—48no—
619C23—42no—
620C23—42no—
621C23—42no—
622C23—42no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—42no—
628C23—42no—
629C23—42no—
630C23—84no—
631C23—84no—
632C23—84no—
633C23—84no—
634C23—84no—
635C23—84no—
636C23—84no—
637C23—84no—
638C23—84no—
639C23—84no—
640C23—84no—
641C23C2×#12112yes—
642C23D4212yes—
643C23#54812yes—
644C23C2×#13712yes—
645C23#57512yes—
646C23#57612yes—
647C23#57712yes—
648C23C23×D411yescharacteristic
649Q8—216no—
650Q8—24no—
651Q8—24no—
652Q8—24no—
653Q8—42no—
654Q8—42no—
655Q8—42no—
656Q8—42no—
657Q8—84no—
658Q8C2×#12118yes—
659D4—24no—
660D4—24no—
661D4—42no—
662D4—48no—
663D4—42no—
664D4—42no—
665D4—42no—
666D4—42no—
667D4—42no—
668D4—816no—
669D4—816no—
670D4—84no—
671C2×C4—24no—
672C2×C4—216no—
673C2×C4—22no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—28no—
677C2×C4—28no—
678C2×C4—28no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—24no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—44no—
695C2×C4—44no—
696C2×C4—44no—
697C2×C4—48no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—816no—
713C2×C4—84no—
714C2×C4—84no—
715C2×C4—84no—
716C2×C4—84no—
717C2×C4C2×#12114yes—
718C2×C4C2×#12114yes—
719C2×C4C2×#12114yes—
720C2×C4C2×#12112yes—
721C2×C4#53714yes—
722C2×C4D4212yes—
723C2×C4#54714yes—
724C2×C4#54812yes—
725C2×C4#55314yes—
726C2×C4C2×#13714yes—
727C2×C4C23×D411yescharacteristic
728C2×C4C23×D411yescharacteristic
729C2×C4C22×#4111yescharacteristic
730C2×C4C22×#4111yescharacteristic
731C2×C4C2×H(5,𝔽2)11yescharacteristic
732C2×C4C2×2−1+411yescharacteristic
733C8—24no—
734C8—42no—
735C8—42no—
736C8—42no—
737C22—44no—
738C22—44no—
739C22—44no—
740C22—82no—
741C22—82no—
742C22—82no—
743C22—816no—
744C22—82no—
745C22—82no—
746C22—82no—
747C22—82no—
748C22—82no—
749C22—82no—
750C22—82no—
751C22—82no—
752C22—168no—
753C22#241614yes—
754C22#303714yes—
755C22#304514yes—
756C22#326614yes—
757C22#326814yes—
758C22#337114yes—
759C22#337514yes—
760C22C22×#12111yescharacteristic
761C22C2×D4211yescharacteristic
762C22C2×#54811yescharacteristic
763C22C22×#13711yescharacteristic
764C22C2×#57511yescharacteristic
765C22C2×#57611yescharacteristic
766C22C2×#57711yescharacteristic
767C4—24no—
768C4—24no—
769C4—28no—
770C4—24no—
771C4—44no—
772C4—42no—
773C4—42no—
774C4—42no—
775C4—82no—
776C4—82no—
777C4—82no—
778C4—82no—
779C4#241614yes—
780C4C22×#12111yescharacteristic
781C4C2×#53711yescharacteristic
782C4C2×#54711yescharacteristic
783C4C2×#55311yescharacteristic
784C2—84no—
785C2—162no—
786C2#2473918yesdirect product factor
787C2C2×#241611yescharacteristic
788C2C2×#303711yescharacteristic
789C2C2×#304511yescharacteristic
790C2C2×#326611yescharacteristic
791C2C2×#326811yescharacteristic
792C2C2×#337511yescharacteristic
793C2C2×#337111yescharacteristic
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×#464C2semidirect
2. C22×#464C2semidirect
4. C22×#440C2semidirect
6. C2×Q8×C4⋊C4C2semidirect
7. #24739C2direct (N × H)
8. C2×#2068C2semidirect
9. C2×#2067C2semidirect
10. C2×#2042C2semidirect
12. C2×#1959C2semidirect
13. C2×#1940C2semidirect
14. C2×#1880C2semidirect
15. C2×#1878C2semidirect
16. C2×#1802C2semidirect
29. C2×#464C22semidirect
30. C2×#464C22semidirect
34. C2×#440C22semidirect
55. Q8×C4⋊C4C22semidirect
68. #2068C22semidirect
69. #2067C22semidirect
70. #2042C22semidirect
72. #1959C22semidirect
73. #1940C22semidirect
74. #1880C22semidirect
75. #1878C22semidirect
76. #1802C22semidirect
124. C2×C4×Q8D4semidirect
326. C4×Q8C2×D4semidirect
786. C2#24739direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#4642
C22×#4602
C22×#4402
C2×#25442
C2×Q8×C4⋊C42
#247392
C2×#20682
C2×#20672
C2×#20422
C2×#20412
C2×#19592
C2×#19402
C2×#18802
C2×#18782
C2×#18022