Finite Group Databasebeta

← C2×#31006 #7503102

Subgroups — C2×#31006 #7503102

Order 512.

2840 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#462C211yesmaximal, characteristic, complemented
2C22×#451C211yesmaximal, characteristic
3C2×#2421C211yesmaximal, characteristic
4C2×#2434C211yesmaximal, characteristic
5#31006C2116yesmaximal, direct product factor
6C2×#2074C211yesmaximal, characteristic, complemented
7C2×#2066C211yesmaximal, characteristic, complemented
8C2×#2043C211yesmaximal, characteristic, complemented
9C2×#2035C211yesmaximal, characteristic
10C2×#2016C211yesmaximal, characteristic, complemented
11C2×#2001C211yesmaximal, characteristic
12C2×#1971C211yesmaximal, characteristic, complemented
13C2×#1960C211yesmaximal, characteristic, complemented
14C2×#1924C211yesmaximal, characteristic
15C2×#1878C211yesmaximal, characteristic, complemented
16C2×#1787C211yesmaximal, characteristic
17C24×Q8C2211yescharacteristic
18C23×Q16C2211yescharacteristic
19C23×Q16C2211yescharacteristic
20C23×Q16C2211yescharacteristic
21C22×C4⋊Q8C2211yescharacteristic
22C22×C4⋊Q8C2211yescharacteristic
23C22×C22⋊Q8C2211yescharacteristic
24C22×C22⋊Q8C2211yescharacteristic
25C22×C4×Q8C2211yescharacteristic
26C2×#462—28no—
27C2×#462C2218yescomplemented
28C2×#451—28no—
29C2×#451C2218yes—
30C22×#106C2211yescharacteristic
31C22×C4⋊C8C2211yescharacteristic
32C22×#103C2211yescharacteristic
33C22×#103C2211yescharacteristic
34C22×#103C2211yescharacteristic
35C22×#103C2211yescharacteristic
36C22×#103C2211yescharacteristic
37C22×#103C2211yescharacteristic
38C22×#103C2211yescharacteristic
39C22×#103C2211yescharacteristic
40C22×#103C2211yescharacteristic
41C22×#103C2211yescharacteristic
42C22×C22⋊C8C2211yescharacteristic
43C22×C22⋊C8C2211yescharacteristic
44C22×#97C2211yescharacteristic
45#2434—24no—
46#2434C2218yes—
47#2421—24no—
48#2421C2218yes—
49C2×#400—21no—
50C2×#397—21no—
51C2×#395—21no—
52C2×#395—21no—
53C2×#391C2211yescharacteristic
54C2×#391C2211yescharacteristic
55C2×#391C2211yescharacteristic
56C2×#389C2211yescharacteristic
57C2×#388—21no—
58C2×#387—21no—
59C2×#385—21no—
60C2×#385—21no—
61C2×#382C2211yescharacteristic
62C2×#380C2211yescharacteristic
63C2×C4×C22⋊C4C2211yescharacteristic
64#2074C2218yescomplemented
65#2066C2218yescomplemented
66#2043C2218yescomplemented
67#2035C2218yes—
68#2016C2218yescomplemented
69#2001C2218yes—
70#1971C2218yescomplemented
71#1960C2218yescomplemented
72#1924C2218yes—
73#1878C2218yescomplemented
74#1787C2218yes—
75C2×#340C2211yescharacteristic
76C2×#340C2211yescharacteristic
77C2×#336C2211yescharacteristic
78C2×#336C2211yescharacteristic
79C23×Q8—21no—
80C23×Q8—22no—
81C23×Q8—24no—
82C23×Q8—24no—
83C23×Q8—42no—
84C23×Q8—42no—
85C23×Q8—42no—
86C23×Q8—42no—
87C23×Q8C2311yescharacteristic
88C23×Q8C2311yescharacteristic
89C23×Q8C2311yescharacteristic
90C23×Q8C2311yescharacteristic
91C23×Q8C2314yes—
92C24×C4—21no—
93C24×C4C2311yescharacteristic
94C22×Q16—24no—
95C22×Q16—24no—
96C22×Q16—24no—
97C22×Q16—42no—
98C22×Q16—42no—
99C22×Q16—42no—
100C22×Q16—42no—
101C22×Q16—42no—
102C22×Q16D418yes—
103C22×Q16C2314yes—
104C22×Q16C2314yes—
105C22×Q16C2314yes—
106C23×C8C2311yescharacteristic
107C23×C8C2311yescharacteristic
108C23×C8C2311yescharacteristic
109C23×C8C2311yescharacteristic
110C2×C4⋊Q8—24no—
111C2×C4⋊Q8—24no—
112C2×C4⋊Q8—22no—
113C2×C4⋊Q8—22no—
114C2×C4⋊Q8—42no—
115C2×C4⋊Q8—42no—
116C2×C4⋊Q8C2314yes—
117C2×C4⋊Q8C2314yes—
118C2×C22⋊Q8—22no—
119C2×C22⋊Q8—22no—
120C2×C22⋊Q8—24no—
121C2×C22⋊Q8—42no—
122C2×C22⋊Q8—42no—
123C2×C22⋊Q8—42no—
124C2×C22⋊Q8C2314yes—
125C2×C22⋊Q8C2314yes—
126C2×C4×Q8—22no—
127C2×C4×Q8—24no—
128C2×C4×Q8—42no—
129C2×C4×Q8C2314yes—
130C22×C4⋊C4—21no—
131C22×C4⋊C4—21no—
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⋊C4C2311yescharacteristic
139C22×C4⋊C4C2311yescharacteristic
140C22×C4⋊C4C2311yescharacteristic
141C22×C4⋊C4C2311yescharacteristic
142C22×C22⋊C4—21no—
143C22×C22⋊C4—21no—
144C22×C22⋊C4—21no—
145C22×C22⋊C4D411yescharacteristic
146C22×C22⋊C4D411yescharacteristic
147C22×C42—21no—
148C22×C42C2311yescharacteristic
149C22×C42C2311yescharacteristic
150#462—232no—
151#451—232no—
152C2×#106—42no—
153C2×#106C2314yes—
154C2×C4⋊C8—24no—
155C2×C4⋊C8C2314yes—
156C2×#103—24no—
157C2×#103—24no—
158C2×#103—24no—
159C2×#103—24no—
160C2×#103—42no—
161C2×#103—42no—
162C2×#103—42no—
163C2×#103—42no—
164C2×#103—42no—
165C2×#103—42no—
166C2×#103C2314yes—
167C2×#103C2314yes—
168C2×#103C2314yes—
169C2×#103C2314yes—
170C2×#103C2314yes—
171C2×#103C2314yes—
172C2×#103C2314yes—
173C2×#103C2314yes—
174C2×#103C2314yes—
175C2×#103C2314yes—
176C2×C22⋊C8—24no—
177C2×C22⋊C8—42no—
178C2×C22⋊C8C2314yes—
179C2×C22⋊C8C2314yes—
180C2×#97—42no—
181C2×#97C2314yes—
182#400—28no—
183#397—28no—
184#395—28no—
185#395—28no—
186#391—22no—
187#391—22no—
188#391—22no—
189#391C2314yes—
190#391C2314yes—
191#391C2314yes—
192#389—22no—
193#389C2314yes—
194#388—28no—
195#387—28no—
196#385—28no—
197#385—28no—
198#382—22no—
199#382C2314yes—
200#380—22no—
201#380C2314yes—
202C4×C22⋊C4D414yes—
203C4×C22⋊C4C2314yes—
204C2×#95—21no—
205C2×#95—21no—
206C2×#95—21no—
207C2×#95—21no—
208C2×#95—21no—
209C2×#95—21no—
210C2×#95—21no—
211C2×#95—21no—
212C2×#95—21no—
213C2×#95—21no—
214C2×#95D411yescharacteristic
215C2×#95D411yescharacteristic
216#340C2314yes—
217#340C2314yes—
218#336C2314yes—
219#336C2314yes—
220C25C2×D411yescharacteristic
221C22×Q8—21no—
222C22×Q8—21no—
223C22×Q8—21no—
224C22×Q8—21no—
225C22×Q8—24no—
226C22×Q8—22no—
227C22×Q8—22no—
228C22×Q8—22no—
229C22×Q8—28no—
230C22×Q8—28no—
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×Q8—22no—
242C22×Q8—22no—
243C22×Q8—22no—
244C22×Q8—22no—
245C22×Q8—22no—
246C22×Q8—22no—
247C22×Q8—22no—
248C22×Q8—22no—
249C22×Q8—44no—
250C22×Q8—44no—
251C22×Q8—44no—
252C22×Q8—44no—
253C22×Q8—44no—
254C22×Q8—44no—
255C22×Q8—48no—
256C22×Q8—48no—
257C22×Q8—44no—
258C22×Q8—48no—
259C22×Q8—416no—
260C22×Q8—416no—
261C22×Q8—416no—
262C22×Q8—416no—
263C22×Q8C2×D414yes—
264C22×Q8C2×D414yes—
265C22×Q8#4114yes—
266C22×Q8C2412yes—
267C22×Q8C2412yes—
268C22×Q8C2412yes—
269C22×Q8C2412yes—
270C23×C4—21no—
271C23×C4—21no—
272C23×C4—21no—
273C23×C4—22no—
274C23×C4—22no—
275C23×C4—22no—
276C23×C4—22no—
277C23×C4—22no—
278C23×C4—22no—
279C23×C4—24no—
280C23×C4—21no—
281C23×C4—21no—
282C23×C4—21no—
283C23×C4—21no—
284C23×C4—21no—
285C23×C4—44no—
286C23×C4—44no—
287C23×C4—44no—
288C23×C4C2×D412yes—
289C23×C4C2×D411yescharacteristic
290C23×C4C2×D411yescharacteristic
291C23×C4C2×D411yescharacteristic
292C23×C4C2×D411yescharacteristic
293C23×C4C2×D411yescharacteristic
294C23×C4C2412yes—
295C23×C4C2411yescharacteristic
296C2×Q16—28no—
297C2×Q16—28no—
298C2×Q16—28no—
299C2×Q16—416no—
300C2×Q16—44no—
301C2×Q16—44no—
302C2×Q16—44no—
303C2×Q16—44no—
304C2×Q16—44no—
305C2×Q16—416no—
306C2×Q16—416no—
307C2×Q16C2×D4116yes—
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×C8—22no—
318C22×C8—22no—
319C22×C8C2×D414yes—
320C22×C8C2412yes—
321C22×C8C2412yes—
322C22×C8C2412yes—
323C22×C8C2412yes—
324C4⋊Q8—28no—
325C4⋊Q8—28no—
326C4⋊Q8—44no—
327C4⋊Q8—44no—
328C4⋊Q8—48no—
329C4⋊Q8—48no—
330C22⋊Q8—28no—
331C22⋊Q8—44no—
332C22⋊Q8—44no—
333C22⋊Q8—44no—
334C22⋊Q8—48no—
335C22⋊Q8—48no—
336C4×Q8—28no—
337C4×Q8—44no—
338C4×Q8—48no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—24no—
348C2×C4⋊C4—24no—
349C2×C4⋊C4—24no—
350C2×C4⋊C4—24no—
351C2×C4⋊C4—24no—
352C2×C4⋊C4—24no—
353C2×C4⋊C4—24no—
354C2×C4⋊C4—24no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—44no—
360C2×C4⋊C4—44no—
361C2×C4⋊C4—44no—
362C2×C4⋊C4—44no—
363C2×C4⋊C4—44no—
364C2×C4⋊C4—44no—
365C2×C4⋊C4—44no—
366C2×C4⋊C4—44no—
367C2×C4⋊C4C2412yes—
368C2×C4⋊C4C2412yes—
369C2×C4⋊C4C2412yes—
370C2×C4⋊C4C2412yes—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—24no—
373C2×C22⋊C4—24no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—44no—
377C2×C22⋊C4—44no—
378C2×C22⋊C4—44no—
379C2×C22⋊C4C2×D414yes—
380C2×C22⋊C4C2×D414yes—
381C2×C42—22no—
382C2×C42—22no—
383C2×C42—22no—
384C2×C42—22no—
385C2×C42—24no—
386C2×C42—44no—
387C2×C42C2×D412yes—
388C2×C42C2×D412yes—
389C2×C42C2412yes—
390C2×C42C2412yes—
391#106—44no—
392C4⋊C8—28no—
393#103—28no—
394#103—28no—
395#103—28no—
396#103—28no—
397#103—44no—
398#103—44no—
399#103—44no—
400#103—44no—
401#103—44no—
402#103—44no—
403C22⋊C8—28no—
404C22⋊C8—44no—
405#97—44no—
406#95—24no—
407#95—24no—
408#95—24no—
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—22no—
421C24—22no—
422C24—22no—
423C24—22no—
424C24#13714yes—
425C24C22×D412yes—
426C24C22×D411yescharacteristic
427C2×Q8—24no—
428C2×Q8—24no—
429C2×Q8—24no—
430C2×Q8—22no—
431C2×Q8—22no—
432C2×Q8—22no—
433C2×Q8—28no—
434C2×Q8—28no—
435C2×Q8—28no—
436C2×Q8—28no—
437C2×Q8—28no—
438C2×Q8—28no—
439C2×Q8—22no—
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—22no—
450C2×Q8—22no—
451C2×Q8—22no—
452C2×Q8—22no—
453C2×Q8—22no—
454C2×Q8—22no—
455C2×Q8—22no—
456C2×Q8—22no—
457C2×Q8—48no—
458C2×Q8—48no—
459C2×Q8—48no—
460C2×Q8—416no—
461C2×Q8—416no—
462C2×Q8—416no—
463C2×Q8—464no—
464C2×Q8—416no—
465C2×Q8—432no—
466C2×Q8—44no—
467C2×Q8—42no—
468C2×Q8—42no—
469C2×Q8—42no—
470C2×Q8—42no—
471C2×Q8—44no—
472C2×Q8—44no—
473C2×Q8—42no—
474C2×Q8—42no—
475C2×Q8—42no—
476C2×Q8—42no—
477C2×Q8—42no—
478C2×Q8—44no—
479C2×Q8—44no—
480C2×Q8—44no—
481C2×Q8—44no—
482C2×Q8—44no—
483C2×Q8—44no—
484C2×Q8—44no—
485C2×Q8C22×D414yes—
486C2×Q8C22×D414yes—
487C2×Q8C2×#4114yes—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—24no—
493C22×C4—22no—
494C22×C4—24no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—24no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—24no—
509C22×C4—24no—
510C22×C4—24no—
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—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—48no—
523C22×C4—48no—
524C22×C4—48no—
525C22×C4—432no—
526C22×C4—42no—
527C22×C4—42no—
528C22×C4—42no—
529C22×C4—42no—
530C22×C4—42no—
531C22×C4—42no—
532C22×C4—44no—
533C22×C4—44no—
534C22×C4—44no—
535C22×C4—44no—
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—42no—
550C22×C4—42no—
551C22×C4#13714yes—
552C22×C4C22×D412yes—
553C22×C4C22×D412yes—
554C22×C4C22×D412yes—
555C22×C4C22×D412yes—
556C22×C4C22×D412yes—
557C22×C4C22×D412yes—
558C22×C4C22×D411yescharacteristic
559C22×C4C2×#4112yes—
560C22×C4H(5,𝔽2)12yes—
561C22×C4H(5,𝔽2)12yes—
562C22×C4H(5,𝔽2)12yes—
563C22×C4H(5,𝔽2)12yes—
564C22×C4C2511yescharacteristic
565Q16—416no—
566Q16—416no—
567Q16—416no—
568C2×C8—28no—
569C2×C8—22no—
570C2×C8—22no—
571C2×C8—22no—
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—44no—
581C2×C8—44no—
582C2×C8—44no—
583C2×C8C22×D414yes—
584C4⋊C4—22no—
585C4⋊C4—22no—
586C4⋊C4—22no—
587C4⋊C4—22no—
588C4⋊C4—22no—
589C4⋊C4—22no—
590C4⋊C4—22no—
591C4⋊C4—22no—
592C4⋊C4—48no—
593C4⋊C4—48no—
594C4⋊C4—48no—
595C4⋊C4—48no—
596C4⋊C4—48no—
597C4⋊C4—48no—
598C4⋊C4—48no—
599C4⋊C4—42no—
600C4⋊C4—42no—
601C4⋊C4—42no—
602C4⋊C4—42no—
603C4⋊C4—48no—
604C22⋊C4—28no—
605C22⋊C4—28no—
606C22⋊C4—48no—
607C22⋊C4—48no—
608C22⋊C4—48no—
609C42—24no—
610C42—24no—
611C42—22no—
612C42—22no—
613C42—22no—
614C42—22no—
615C42—48no—
616C23—22no—
617C23—22no—
618C23—22no—
619C23—28no—
620C23—28no—
621C23—28no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—44no—
626C23—44no—
627C23—44no—
628C23—44no—
629C23#53512yes—
630C23D4212yes—
631C23#54612yes—
632C23C2×#13714yes—
633C23C2×#13712yes—
634C23C2×#13712yes—
635C23#57812yes—
636C23#57812yes—
637C23C23×D411yescharacteristic
638Q8—24no—
639Q8—24no—
640Q8—24no—
641Q8—24no—
642Q8—24no—
643Q8—24no—
644Q8—432no—
645Q8—42no—
646Q8—48no—
647Q8—48no—
648Q8—48no—
649Q8—42no—
650Q8—42no—
651Q8—42no—
652Q8—42no—
653Q8—42no—
654Q8—42no—
655Q8—42no—
656Q8—42no—
657Q8—42no—
658Q8—84no—
659C2×C4—22no—
660C2×C4—28no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—24no—
665C2×C4—22no—
666C2×C4—24no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—24no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—432no—
678C2×C4—44no—
679C2×C4—44no—
680C2×C4—48no—
681C2×C4—48no—
682C2×C4—48no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—44no—
690C2×C4—44no—
691C2×C4—42no—
692C2×C4—48no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
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—84no—
712C2×C4—84no—
713C2×C4—84no—
714C2×C4—84no—
715C2×C4—84no—
716C2×C4#53414yes—
717C2×C4#53512yes—
718C2×C4#53814yes—
719C2×C4D4212yes—
720C2×C4#54612yes—
721C2×C4#54614yes—
722C2×C4#56014yes—
723C2×C4C2×#13714yes—
724C2×C4C23×D411yescharacteristic
725C2×C4C22×#4111yescharacteristic
726C2×C4C2×H(5,𝔽2)11yescharacteristic
727C2×C4C2×H(5,𝔽2)11yescharacteristic
728C2×C4C2×H(5,𝔽2)11yescharacteristic
729C2×C4C2×H(5,𝔽2)11yescharacteristic
730C8—24no—
731C8—42no—
732C8—42no—
733C8—42no—
734C22—24no—
735C22—24no—
736C22—24no—
737C22—416no—
738C22—42no—
739C22—42no—
740C22—42no—
741C22—42no—
742C22#267814yes—
743C22#321814yes—
744C22#322314yes—
745C22#327014yes—
746C22#327014yes—
747C22#331214yes—
748C22#332814yes—
749C22C2×#53511yescharacteristic
750C22C2×D4211yescharacteristic
751C22C2×#54611yescharacteristic
752C22C22×#13711yescharacteristic
753C22C22×#13711yescharacteristic
754C22C2×#57811yescharacteristic
755C22C2×#57811yescharacteristic
756C4—24no—
757C4—42no—
758C4—42no—
759C4—44no—
760C4—44no—
761C4—44no—
762C4—42no—
763C4—42no—
764C4—82no—
765C4—82no—
766C4—82no—
767C4—82no—
768C4—82no—
769C4#267814yes—
770C4C2×#53411yescharacteristic
771C4C2×#53811yescharacteristic
772C4C2×#54611yescharacteristic
773C4C2×#56011yescharacteristic
774C2—44no—
775C2#3100618yesdirect product factor
776C2C2×#267811yescharacteristic
777C2C2×#321811yescharacteristic
778C2C2×#322311yescharacteristic
779C2C2×#327011yescharacteristic
780C2C2×#327011yescharacteristic
781C2C2×#331211yescharacteristic
782C2C2×#332811yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC25C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#462C2semidirect
5. #31006C2direct (N × H)
6. C2×#2074C2semidirect
7. C2×#2066C2semidirect
8. C2×#2043C2semidirect
10. C2×#2016C2semidirect
12. C2×#1971C2semidirect
13. C2×#1960C2semidirect
15. C2×#1878C2semidirect
27. C2×#462C22semidirect
64. #2074C22semidirect
65. #2066C22semidirect
66. #2043C22semidirect
68. #2016C22semidirect
70. #1971C22semidirect
71. #1960C22semidirect
73. #1878C22semidirect
775. C2#31006direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#4622
C22×#4512
C2×#24212
C2×#24342
#310062
C2×#20742
C2×#20662
C2×#20432
C2×#20352
C2×#20162
C2×#20012
C2×#19712
C2×#19602
C2×#19242
C2×#18782
C2×#17872