Finite Group Databasebeta

← C2×#30909 #7502269

Subgroups — C2×#30909 #7502269

Order 512.

2612 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#475C211yesmaximal, characteristic, complemented
2C22×#465C211yesmaximal, characteristic
3C2×#2491C211yesmaximal, characteristic
4C2×#2429C211yesmaximal, characteristic, complemented
5#30909C2116yesmaximal, direct product factor
6C2×#2065C211yesmaximal, characteristic, complemented
7C2×#2055C211yesmaximal, characteristic, complemented
8C2×#2035C211yesmaximal, characteristic, complemented
9C2×#2024C211yesmaximal, characteristic, complemented
10C2×#2013C211yesmaximal, characteristic, complemented
11C2×#2000C211yesmaximal, characteristic
12C2×#1981C211yesmaximal, characteristic, complemented
13C2×#1920C211yesmaximal, characteristic, complemented
14C2×#1892C211yesmaximal, characteristic, complemented
15C2×#1880C211yesmaximal, characteristic, complemented
16C2×#1850C211yesmaximal, characteristic, complemented
17C23×SD16C2211yescharacteristic
18C23×SD16C2211yescharacteristic
19C24×C8C2211yescharacteristic
20C22×C4⋊Q8C2211yescharacteristic
21C22×C4⋊Q8C2211yescharacteristic
22C22×#124—21no—
23C22×C22⋊Q8C2211yescharacteristic
24C22×C22⋊Q8C2211yescharacteristic
25C22×#121C2211yescharacteristic
26C22×C4×Q8C2211yescharacteristic
27C2×#475—28no—
28C2×#475C2218yescomplemented
29C2×#465—28no—
30C2×#465C2218yes—
31C22×#106C2211yescharacteristic
32C22×#106C2211yescharacteristic
33C22×C4⋊C8C2211yescharacteristic
34C22×C4⋊C8C2211yescharacteristic
35C22×#103C2211yescharacteristic
36C22×#103C2211yescharacteristic
37C22×#103C2211yescharacteristic
38C22×#103C2211yescharacteristic
39C22×#103C2211yescharacteristic
40C22×#103C2211yescharacteristic
41C22×#102C2211yescharacteristic
42C22×#102C2211yescharacteristic
43C22×C22⋊C8C2211yescharacteristic
44#2491—24no—
45#2491C2218yes—
46#2429—24no—
47#2429C2218yescomplemented
48C2×#398—21no—
49C2×#396—21no—
50C2×#394—21no—
51C2×#393—21no—
52C2×#391C2211yescharacteristic
53C2×#390C2211yescharacteristic
54C2×#390C2211yescharacteristic
55C2×#389—21no—
56C2×#389C2211yescharacteristic
57C2×#388—21no—
58C2×#388—21no—
59C2×#380C2211yescharacteristic
60C2×C4×C4⋊C4C2211yescharacteristic
61C2×C4×C22⋊C4C2211yescharacteristic
62#2065C2218yescomplemented
63#2055C2218yescomplemented
64#2035C2218yescomplemented
65#2024C2218yescomplemented
66#2013C2218yescomplemented
67#2000C2218yes—
68#1981C2218yescomplemented
69#1920C2218yescomplemented
70#1892C2218yescomplemented
71#1880C2218yescomplemented
72#1850C2218yescomplemented
73C2×#340C2211yescharacteristic
74C2×#340C2211yescharacteristic
75C2×#340C2211yescharacteristic
76C2×#340C2211yescharacteristic
77C2×#336C2211yescharacteristic
78C2×#336C2211yescharacteristic
79C23×Q8—21no—
80C23×Q8C2311yescharacteristic
81C23×Q8C2311yescharacteristic
82C23×D4—21no—
83C23×D4C2311yescharacteristic
84C24×C4C2311yescharacteristic
85C22×SD16—24no—
86C22×SD16—24no—
87C22×SD16—42no—
88C22×SD16—42no—
89C22×SD16—42no—
90C22×SD16—42no—
91C22×SD16C2314yes—
92C22×SD16C2314yes—
93C23×C8—24no—
94C23×C8—42no—
95C23×C8—42no—
96C23×C8C2311yescharacteristic
97C23×C8C2311yescharacteristic
98C23×C8C2311yescharacteristic
99C23×C8C2311yescharacteristic
100C23×C8C2314yes—
101C2×C4⋊Q8—24no—
102C2×C4⋊Q8—24no—
103C2×C4⋊Q8—22no—
104C2×C4⋊Q8—22no—
105C2×C4⋊Q8—42no—
106C2×C4⋊Q8—42no—
107C2×C4⋊Q8C2314yes—
108C2×C4⋊Q8C2314yes—
109C2×#124—28no—
110C2×#124—48no—
111C2×C22⋊Q8—22no—
112C2×C22⋊Q8—22no—
113C2×C22⋊Q8—24no—
114C2×C22⋊Q8—24no—
115C2×C22⋊Q8—42no—
116C2×C22⋊Q8—42no—
117C2×C22⋊Q8C2314yes—
118C2×C22⋊Q8C2314yes—
119C2×#121—22no—
120C2×#121—24no—
121C2×#121—42no—
122C2×#121C2314yes—
123C2×C4×Q8—22no—
124C2×C4×Q8—24no—
125C2×C4×Q8—42no—
126C2×C4×Q8C2314yes—
127C22×C4⋊C4—21no—
128C22×C4⋊C4—21no—
129C22×C4⋊C4—21no—
130C22×C4⋊C4—21no—
131C22×C4⋊C4—21no—
132C22×C4⋊C4—21no—
133C22×C4⋊C4—21no—
134C22×C4⋊C4C2311yescharacteristic
135C22×C4⋊C4C2311yescharacteristic
136C22×C4⋊C4C2311yescharacteristic
137C22×C4⋊C4C2311yescharacteristic
138C22×C4⋊C4C2311yescharacteristic
139C22×C22⋊C4—21no—
140C22×C22⋊C4—21no—
141C22×C22⋊C4—21no—
142C22×C22⋊C4—21no—
143C22×C22⋊C4—21no—
144C22×C22⋊C4—21no—
145C22×C22⋊C4—21no—
146C22×C22⋊C4—21no—
147C22×C22⋊C4D411yescharacteristic
148C22×C22⋊C4D411yescharacteristic
149C22×C42—21no—
150C22×C42—21no—
151C22×C42C2311yescharacteristic
152C22×C42C2311yescharacteristic
153#475—232no—
154#465—232no—
155C2×#106—24no—
156C2×#106D418yes—
157C2×#106C2314yes—
158C2×#106C2314yes—
159C2×C4⋊C8—24no—
160C2×C4⋊C8—42no—
161C2×C4⋊C8C2314yes—
162C2×C4⋊C8C2314yes—
163C2×#103—24no—
164C2×#103—24no—
165C2×#103—24no—
166C2×#103—42no—
167C2×#103—42no—
168C2×#103—42no—
169C2×#103C2314yes—
170C2×#103C2314yes—
171C2×#103C2314yes—
172C2×#103C2314yes—
173C2×#103C2314yes—
174C2×#103C2314yes—
175C2×#102—24no—
176C2×#102—42no—
177C2×#102C2314yes—
178C2×#102C2314yes—
179C2×C22⋊C8—42no—
180C2×C22⋊C8C2314yes—
181#398—28no—
182#396—28no—
183#394—28no—
184#393—28no—
185#391—22no—
186#391C2314yes—
187#390—22no—
188#390—22no—
189#390C2314yes—
190#390C2314yes—
191#389—22no—
192#389—28no—
193#389C2314yes—
194#388—28no—
195#388—28no—
196#380—22no—
197#380C2314yes—
198C4×C4⋊C4—22no—
199C4×C4⋊C4C2314yes—
200C4×C22⋊C4D414yes—
201C4×C22⋊C4C2314yes—
202C2×#95—21no—
203C2×#95—21no—
204C2×#95—21no—
205C2×#95—21no—
206C2×#95—21no—
207C2×#95D411yescharacteristic
208C2×#95D411yescharacteristic
209#340C2314yes—
210#340C2314yes—
211#340C2314yes—
212#340C2314yes—
213#336C2314yes—
214#336C2314yes—
215C25—21no—
216C25C2×D411yescharacteristic
217C22×Q8—21no—
218C22×Q8—21no—
219C22×Q8—24no—
220C22×Q8—22no—
221C22×Q8—22no—
222C22×Q8—22no—
223C22×Q8—22no—
224C22×Q8—22no—
225C22×Q8—22no—
226C22×Q8—22no—
227C22×Q8—22no—
228C22×Q8—22no—
229C22×Q8—22no—
230C22×Q8—22no—
231C22×Q8—44no—
232C22×Q8—44no—
233C22×Q8—82no—
234C22×Q8#4114yes—
235C22×Q8C2412yes—
236C22×Q8C2412yes—
237C22×D4—24no—
238C22×D4—22no—
239C22×D4—21no—
240C22×D4—22no—
241C22×D4—22no—
242C22×D4—22no—
243C22×D4—22no—
244C22×D4—22no—
245C22×D4—44no—
246C22×D4—44no—
247C22×D4—82no—
248C22×D4C2412yes—
249C23×C4—21no—
250C23×C4—21no—
251C23×C4—21no—
252C23×C4—22no—
253C23×C4—22no—
254C23×C4—22no—
255C23×C4—22no—
256C23×C4—22no—
257C23×C4—22no—
258C23×C4—21no—
259C23×C4—21no—
260C23×C4—21no—
261C23×C4—21no—
262C23×C4C2×D412yes—
263C23×C4C2×D411yescharacteristic
264C23×C4C2×D411yescharacteristic
265C23×C4C2×D411yescharacteristic
266C23×C4C2×D411yescharacteristic
267C23×C4C2×D411yescharacteristic
268C23×C4C2412yes—
269C23×C4C2411yescharacteristic
270C2×SD16—28no—
271C2×SD16—28no—
272C2×SD16—44no—
273C2×SD16—44no—
274C2×SD16—44no—
275C2×SD16—44no—
276C2×SD16—416no—
277C2×SD16—416no—
278C22×C8—22no—
279C22×C8—22no—
280C22×C8—22no—
281C22×C8—22no—
282C22×C8—22no—
283C22×C8—22no—
284C22×C8—22no—
285C22×C8—22no—
286C22×C8—22no—
287C22×C8—22no—
288C22×C8—22no—
289C22×C8—28no—
290C22×C8—44no—
291C22×C8—44no—
292C22×C8—416no—
293C22×C8C2×D414yes—
294C22×C8C2412yes—
295C22×C8C2412yes—
296C22×C8C2412yes—
297C22×C8C2412yes—
298C4⋊Q8—28no—
299C4⋊Q8—28no—
300C4⋊Q8—44no—
301C4⋊Q8—48no—
302C4⋊Q8—44no—
303C4⋊Q8—48no—
304#124—432no—
305C22⋊Q8—28no—
306C22⋊Q8—28no—
307C22⋊Q8—44no—
308C22⋊Q8—44no—
309C22⋊Q8—48no—
310C22⋊Q8—48no—
311#121—28no—
312#121—44no—
313#121—48no—
314C4×Q8—28no—
315C4×Q8—44no—
316C4×Q8—48no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—21no—
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—22no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—24no—
330C2×C4⋊C4—24no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—24no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—44no—
338C2×C4⋊C4—44no—
339C2×C4⋊C4—44no—
340C2×C4⋊C4—44no—
341C2×C4⋊C4—44no—
342C2×C4⋊C4—44no—
343C2×C4⋊C4—44no—
344C2×C4⋊C4C2×D414yes—
345C2×C4⋊C4C2×D414yes—
346C2×C4⋊C4C2412yes—
347C2×C4⋊C4C2412yes—
348C2×C4⋊C4C2412yes—
349C2×C4⋊C4C2412yes—
350C2×C4⋊C4C2412yes—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—42no—
360C2×C22⋊C4—44no—
361C2×C22⋊C4—44no—
362C2×C22⋊C4—44no—
363C2×C22⋊C4—44no—
364C2×C22⋊C4—44no—
365C2×C22⋊C4—44no—
366C2×C22⋊C4—44no—
367C2×C22⋊C4—82no—
368C2×C22⋊C4SD1618yescomplemented
369C2×C22⋊C4C2×D414yes—
370C2×C22⋊C4C2×D414yes—
371C2×C42—22no—
372C2×C42—22no—
373C2×C42—22no—
374C2×C42—22no—
375C2×C42—24no—
376C2×C42—24no—
377C2×C42—44no—
378C2×C42—44no—
379C2×C42C2×D412yes—
380C2×C42C2×D412yes—
381C2×C42C2412yes—
382C2×C42C2412yes—
383#106—28no—
384#106C2×D4116yes—
385C4⋊C8—28no—
386C4⋊C8—44no—
387#103—28no—
388#103—28no—
389#103—28no—
390#103—44no—
391#103—44no—
392#103—44no—
393#102—28no—
394#102—44no—
395C22⋊C8—44no—
396#95—24no—
397#95—24no—
398#95—24no—
399#95—24no—
400#95—24no—
401#95C2×D414yes—
402#95C2×D414yes—
403C24—22no—
404C24—22no—
405C24—22no—
406C24—22no—
407C24—22no—
408C24—22no—
409C24—22no—
410C24—42no—
411C24—42no—
412C24—42no—
413C24—42no—
414C24—42no—
415C24—42no—
416C24—42no—
417C24C2×SD1614yes—
418C24C22×D412yes—
419C24C22×D411yescharacteristic
420C2×Q8—24no—
421C2×Q8—22no—
422C2×Q8—28no—
423C2×Q8—28no—
424C2×Q8—22no—
425C2×Q8—22no—
426C2×Q8—22no—
427C2×Q8—22no—
428C2×Q8—22no—
429C2×Q8—22no—
430C2×Q8—22no—
431C2×Q8—22no—
432C2×Q8—22no—
433C2×Q8—22no—
434C2×Q8—48no—
435C2×Q8—44no—
436C2×Q8—42no—
437C2×Q8—42no—
438C2×Q8—42no—
439C2×Q8—42no—
440C2×Q8—42no—
441C2×Q8—44no—
442C2×Q8—48no—
443C2×Q8—44no—
444C2×Q8—44no—
445C2×Q8—44no—
446C2×Q8—44no—
447C2×Q8—84no—
448C2×Q8—816no—
449C2×Q8C2×#4114yes—
450C2×D4—22no—
451C2×D4—22no—
452C2×D4—22no—
453C2×D4—22no—
454C2×D4—22no—
455C2×D4—22no—
456C2×D4—48no—
457C2×D4—48no—
458C2×D4—44no—
459C2×D4—42no—
460C2×D4—44no—
461C2×D4—42no—
462C2×D4—42no—
463C2×D4—44no—
464C2×D4—44no—
465C2×D4—84no—
466C2×D4—816no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—24no—
474C22×C4—22no—
475C22×C4—24no—
476C22×C4—22no—
477C22×C4—24no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—24no—
487C22×C4—24no—
488C22×C4—24no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—42no—
500C22×C4—42no—
501C22×C4—42no—
502C22×C4—42no—
503C22×C4—42no—
504C22×C4—42no—
505C22×C4—44no—
506C22×C4—44no—
507C22×C4—44no—
508C22×C4—44no—
509C22×C4—42no—
510C22×C4—42no—
511C22×C4—42no—
512C22×C4—42no—
513C22×C4—42no—
514C22×C4—42no—
515C22×C4—42no—
516C22×C4—42no—
517C22×C4—42no—
518C22×C4—42no—
519C22×C4—42no—
520C22×C4—42no—
521C22×C4C2×SD1614yes—
522C22×C4C2×SD1614yes—
523C22×C4C22×D412yes—
524C22×C4C22×D412yes—
525C22×C4C22×D412yes—
526C22×C4C22×D412yes—
527C22×C4C22×D412yes—
528C22×C4C22×D412yes—
529C22×C4C22×D411yescharacteristic
530C22×C4C2×#4112yes—
531C22×C4H(5,𝔽2)12yes—
532C22×C4H(5,𝔽2)12yes—
533C22×C4H(5,𝔽2)12yes—
534C22×C42−1+412yes—
535C22×C4C2511yescharacteristic
536SD16—416no—
537SD16—416no—
538C2×C8—28no—
539C2×C8—22no—
540C2×C8—22no—
541C2×C8—22no—
542C2×C8—22no—
543C2×C8—22no—
544C2×C8—22no—
545C2×C8—22no—
546C2×C8—22no—
547C2×C8—22no—
548C2×C8—22no—
549C2×C8—22no—
550C2×C8—416no—
551C2×C8—44no—
552C2×C8—44no—
553C2×C8—44no—
554C2×C8C22×D414yes—
555C4⋊C4—24no—
556C4⋊C4—24no—
557C4⋊C4—22no—
558C4⋊C4—22no—
559C4⋊C4—22no—
560C4⋊C4—22no—
561C4⋊C4—22no—
562C4⋊C4—22no—
563C4⋊C4—22no—
564C4⋊C4—22no—
565C4⋊C4—48no—
566C4⋊C4—48no—
567C4⋊C4—48no—
568C4⋊C4—48no—
569C4⋊C4—48no—
570C4⋊C4—48no—
571C4⋊C4—48no—
572C4⋊C4—42no—
573C4⋊C4—42no—
574C4⋊C4—42no—
575C4⋊C4C22×D414yes—
576C4⋊C4C22×D414yes—
577C22⋊C4—44no—
578C22⋊C4—48no—
579C22⋊C4—48no—
580C22⋊C4—48no—
581C22⋊C4—48no—
582C22⋊C4—48no—
583C22⋊C4—48no—
584C22⋊C4—48no—
585C22⋊C4—84no—
586C22⋊C4C2×SD16116yescomplemented
587C42—24no—
588C42—24no—
589C42—22no—
590C42—22no—
591C42—22no—
592C42—22no—
593C42—48no—
594C42—48no—
595C23—22no—
596C23—22no—
597C23—22no—
598C23—28no—
599C23—28no—
600C23—28no—
601C23—22no—
602C23—22no—
603C23—22no—
604C23—44no—
605C23—44no—
606C23—44no—
607C23—44no—
608C23—42no—
609C23—42no—
610C23—42no—
611C23—42no—
612C23—42no—
613C23—42no—
614C23—42no—
615C23—84no—
616C23—84no—
617C23—84no—
618C23—84no—
619C23—84no—
620C23—84no—
621C23—84no—
622C23#53712yes—
623C23D4212yes—
624C23#54612yes—
625C23C22×SD1614yes—
626C23C22×SD1612yes—
627C23#57512yes—
628C23#57712yes—
629C23#57812yes—
630C23C23×D411yescharacteristic
631Q8—24no—
632Q8—24no—
633Q8—48no—
634Q8—42no—
635Q8—42no—
636Q8—42no—
637Q8—42no—
638Q8—42no—
639Q8—42no—
640Q8—816no—
641Q8—84no—
642D4—42no—
643D4—42no—
644D4—42no—
645D4—42no—
646D4—816no—
647D4—84no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—28no—
651C2×C4—28no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—24no—
657C2×C4—22no—
658C2×C4—24no—
659C2×C4—22no—
660C2×C4—24no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—44no—
667C2×C4—48no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—44no—
671C2×C4—48no—
672C2×C4—48no—
673C2×C4—42no—
674C2×C4—44no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—48no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—84no—
696C2×C4—84no—
697C2×C4—84no—
698C2×C4—84no—
699C2×C4#53514yes—
700C2×C4#53712yes—
701C2×C4#53814yes—
702C2×C4D4212yes—
703C2×C4#54612yes—
704C2×C4#54814yes—
705C2×C4#56214yes—
706C2×C4C22×SD1614yes—
707C2×C4C22×SD1614yes—
708C2×C4C23×D411yescharacteristic
709C2×C4C22×#4111yescharacteristic
710C2×C4C2×H(5,𝔽2)11yescharacteristic
711C2×C4C2×H(5,𝔽2)11yescharacteristic
712C2×C4C2×H(5,𝔽2)11yescharacteristic
713C2×C4C2×2−1+411yescharacteristic
714C8—24no—
715C8—42no—
716C8—42no—
717C8—42no—
718C22—24no—
719C22—24no—
720C22—24no—
721C22—42no—
722C22—42no—
723C22—416no—
724C22—42no—
725C22—42no—
726C22—82no—
727C22—82no—
728C22—82no—
729C22—82no—
730C22—82no—
731C22—82no—
732C22—82no—
733C22—168no—
734C22#267614yes—
735C22#324614yes—
736C22#325814yes—
737C22#326914yes—
738C22D4×SD1614yes—
739C22#329814yes—
740C22#332114yes—
741C22C2×#53711yescharacteristic
742C22C2×D4211yescharacteristic
743C22C2×#54611yescharacteristic
744C22C23×SD1611yescharacteristic
745C22C2×#57511yescharacteristic
746C22C2×#57711yescharacteristic
747C22C2×#57811yescharacteristic
748C4—24no—
749C4—24no—
750C4—42no—
751C4—44no—
752C4—44no—
753C4—42no—
754C4—44no—
755C4—42no—
756C4—82no—
757C4—82no—
758C4—82no—
759C4—82no—
760C4#267614yes—
761C4C2×#53511yescharacteristic
762C4C2×#53811yescharacteristic
763C4C2×#54811yescharacteristic
764C4C2×#56211yescharacteristic
765C2—44no—
766C2—162no—
767C2#3090918yesdirect product factor
768C2C2×#267611yescharacteristic
769C2C2×#324611yescharacteristic
770C2C2×#325811yescharacteristic
771C2C2×#326911yescharacteristic
772C2C2×D4×SD1611yescharacteristic
773C2C2×#329811yescharacteristic
774C2C2×#332111yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×#121C22
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×#475C2semidirect
4. C2×#2429C2semidirect
5. #30909C2direct (N × H)
6. C2×#2065C2semidirect
7. C2×#2055C2semidirect
8. C2×#2035C2semidirect
9. C2×#2024C2semidirect
10. C2×#2013C2semidirect
12. C2×#1981C2semidirect
13. C2×#1920C2semidirect
14. C2×#1892C2semidirect
15. C2×#1880C2semidirect
16. C2×#1850C2semidirect
28. C2×#475C22semidirect
47. #2429C22semidirect
62. #2065C22semidirect
63. #2055C22semidirect
64. #2035C22semidirect
65. #2024C22semidirect
66. #2013C22semidirect
68. #1981C22semidirect
69. #1920C22semidirect
70. #1892C22semidirect
71. #1880C22semidirect
72. #1850C22semidirect
368. C2×C22⋊C4SD16semidirect
586. C22⋊C4C2×SD16semidirect
767. C2#30909direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#4752
C22×#4652
C2×#24912
C2×#24292
#309092
C2×#20652
C2×#20552
C2×#20352
C2×#20242
C2×#20132
C2×#20002
C2×#19812
C2×#19202
C2×#18922
C2×#18802
C2×#18502