Finite Group Databasebeta

← C2×#30411 #7500642

Subgroups — C2×#30411 #7500642

Order 512.

3008 conjugacy classes of subgroups.

The subgroup lattice has 819 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#467C211yesmaximal, characteristic, complemented
2C22×#451C211yesmaximal, characteristic, complemented
3C2×#2536C211yesmaximal, characteristic
4C2×#2409C211yesmaximal, characteristic
5#30411C2116yesmaximal, direct product factor
6C2×#2097C211yesmaximal, characteristic, complemented
7C2×#2075C211yesmaximal, characteristic, complemented
8C2×#2074C211yesmaximal, characteristic, complemented
9C2×#2035C211yesmaximal, characteristic, complemented
10C2×#2035C211yesmaximal, characteristic, complemented
11C2×#2001C211yesmaximal, characteristic, complemented
12C2×#1892C211yesmaximal, characteristic, complemented
13C2×#1878C211yesmaximal, characteristic, complemented
14C2×#1878C211yesmaximal, characteristic, complemented
15C2×#1869C211yesmaximal, characteristic
16C2×#1787C211yesmaximal, characteristic, complemented
17C24×Q8C2211yescharacteristic
18C23×Q16C2211yescharacteristic
19C23×Q16C2211yescharacteristic
20C24×C8C2211yescharacteristic
21C22×C22⋊Q8C2211yescharacteristic
22C22×C22⋊Q8C2211yescharacteristic
23C22×C22⋊Q8C2211yescharacteristic
24C22×C22⋊Q8C2211yescharacteristic
25C22×C4×Q8C2211yescharacteristic
26C22×C4×D4C2211yescharacteristic
27C2×#467—28no—
28C2×#467C2218yescomplemented
29C2×#451—28no—
30C2×#451C2218yescomplemented
31C22×#107C2211yescharacteristic
32C22×#106C2211yescharacteristic
33C22×#103C2211yescharacteristic
34C22×#103C2211yescharacteristic
35C22×#103C2211yescharacteristic
36C22×#103C2211yescharacteristic
37C22×#103C2211yescharacteristic
38C22×#103C2211yescharacteristic
39C22×#103C2211yescharacteristic
40C22×#103C2211yescharacteristic
41C22×C22⋊C8C2211yescharacteristic
42C22×C22⋊C8C2211yescharacteristic
43C22×C22⋊C8C2211yescharacteristic
44#2536—24no—
45#2536C2218yes—
46#2409—24no—
47#2409C2218yes—
48C2×#398—21no—
49C2×#395—21no—
50C2×#394—21no—
51C2×#393—21no—
52C2×#391C2211yescharacteristic
53C2×#391C2211yescharacteristic
54C2×#388—21no—
55C2×#388—21no—
56C2×#386—21no—
57C2×#385—21no—
58C2×#382C2211yescharacteristic
59C2×#380C2211yescharacteristic
60C2×#380C2211yescharacteristic
61C2×#380C2211yescharacteristic
62#2097C2218yescomplemented
63#2075C2218yescomplemented
64#2074C2218yescomplemented
65#2035C2218yescomplemented
66#2035C2218yescomplemented
67#2001C2218yescomplemented
68#1892C2218yescomplemented
69#1878C2218yescomplemented
70#1878C2218yescomplemented
71#1869C2218yes—
72#1787C2218yescomplemented
73C2×#340C2211yescharacteristic
74C2×#340C2211yescharacteristic
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×Q8C2314yes—
91C23×D4D411yescharacteristic
92C24×C4—21no—
93C24×C4C2311yescharacteristic
94C24×C4C2311yescharacteristic
95C22×Q16—24no—
96C22×Q16—24no—
97C22×Q16—42no—
98C22×Q16—42no—
99C22×Q16—42no—
100C22×Q16D418yescomplemented
101C22×Q16C2314yes—
102C22×Q16C2314yes—
103C23×C8—24no—
104C23×C8—42no—
105C23×C8—42no—
106C23×C8C2311yescharacteristic
107C23×C8C2311yescharacteristic
108C23×C8C2311yescharacteristic
109C23×C8C2311yescharacteristic
110C23×C8C2314yes—
111C2×C22⋊Q8—22no—
112C2×C22⋊Q8—22no—
113C2×C22⋊Q8—22no—
114C2×C22⋊Q8—22no—
115C2×C22⋊Q8—24no—
116C2×C22⋊Q8—24no—
117C2×C22⋊Q8—24no—
118C2×C22⋊Q8—24no—
119C2×C22⋊Q8—42no—
120C2×C22⋊Q8—42no—
121C2×C22⋊Q8—42no—
122C2×C22⋊Q8—42no—
123C2×C22⋊Q8C2314yes—
124C2×C22⋊Q8C2314yes—
125C2×C22⋊Q8C2314yes—
126C2×C22⋊Q8C2314yes—
127C2×C4×Q8—22no—
128C2×C4×Q8—42no—
129C2×C4×Q8—42no—
130C2×C4×Q8C2314yes—
131C2×C4×D4—42no—
132C2×C4×D4—42no—
133C2×C4×D4D414yes—
134C2×C4×D4C2314yes—
135C22×C4⋊C4—21no—
136C22×C4⋊C4—21no—
137C22×C4⋊C4—21no—
138C22×C4⋊C4—21no—
139C22×C4⋊C4—21no—
140C22×C4⋊C4D411yescharacteristic
141C22×C4⋊C4C2311yescharacteristic
142C22×C4⋊C4C2311yescharacteristic
143C22×C4⋊C4C2311yescharacteristic
144C22×C4⋊C4C2311yescharacteristic
145C22×C4⋊C4C2311yescharacteristic
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×C22⋊C4—21no—
153C22×C22⋊C4D411yescharacteristic
154C22×C22⋊C4D411yescharacteristic
155C22×C42—21no—
156C22×C42C2311yescharacteristic
157#467—232no—
158#451—232no—
159C2×#107—24no—
160C2×#107C2314yes—
161C2×#106—42no—
162C2×#106C2314yes—
163C2×#103—24no—
164C2×#103—24no—
165C2×#103—24no—
166C2×#103—24no—
167C2×#103—42no—
168C2×#103—42no—
169C2×#103—42no—
170C2×#103—42no—
171C2×#103C2314yes—
172C2×#103C2314yes—
173C2×#103C2314yes—
174C2×#103C2314yes—
175C2×#103C2314yes—
176C2×#103C2314yes—
177C2×#103C2314yes—
178C2×#103C2314yes—
179C2×C22⋊C8—24no—
180C2×C22⋊C8—42no—
181C2×C22⋊C8—42no—
182C2×C22⋊C8C2314yes—
183C2×C22⋊C8C2314yes—
184C2×C22⋊C8C2314yes—
185#398—28no—
186#395—28no—
187#394—28no—
188#393—28no—
189#391—22no—
190#391—22no—
191#391C2314yes—
192#391C2314yes—
193#388—28no—
194#388—28no—
195#386—28no—
196#385—28no—
197#382—22no—
198#382C2314yes—
199#380—22no—
200#380—22no—
201#380—22no—
202#380C2314yes—
203#380C2314yes—
204#380C2314yes—
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—
214#340C2314yes—
215#340C2314yes—
216#340C2314yes—
217#340C2314yes—
218#336C2314yes—
219#336C2314yes—
220C25C2×D411yescharacteristic
221C25C2×D411yescharacteristic
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—44no—
244C22×Q8—44no—
245C22×Q8—44no—
246C22×Q8—44no—
247C22×Q8—44no—
248C22×Q8—44no—
249C22×Q8—48no—
250C22×Q8—48no—
251C22×Q8—44no—
252C22×Q8—48no—
253C22×Q8—416no—
254C22×Q8—416no—
255C22×Q8—416no—
256C22×Q8—416no—
257C22×Q8C2×D414yes—
258C22×Q8C2×D414yes—
259C22×Q8#4114yes—
260C22×Q8C2412yes—
261C22×Q8C2412yes—
262C22×Q8C2412yes—
263C22×D4—24no—
264C22×D4—24no—
265C22×D4—42no—
266C22×D4C2×D414yes—
267C23×C4—21no—
268C23×C4—21no—
269C23×C4—21no—
270C23×C4—22no—
271C23×C4—22no—
272C23×C4—22no—
273C23×C4—22no—
274C23×C4—22no—
275C23×C4—22no—
276C23×C4—22no—
277C23×C4—22no—
278C23×C4—22no—
279C23×C4—22no—
280C23×C4—22no—
281C23×C4—22no—
282C23×C4—24no—
283C23×C4—21no—
284C23×C4—21no—
285C23×C4—21no—
286C23×C4—21no—
287C23×C4—21no—
288C23×C4—44no—
289C23×C4—44no—
290C23×C4—44no—
291C23×C4C2×D412yes—
292C23×C4C2×D412yes—
293C23×C4C2×D411yescharacteristic
294C23×C4C2×D411yescharacteristic
295C23×C4C2×D411yescharacteristic
296C23×C4C2×D411yescharacteristic
297C23×C4C2412yes—
298C23×C4C2412yes—
299C23×C4C2411yescharacteristic
300C2×Q16—28no—
301C2×Q16—28no—
302C2×Q16—416no—
303C2×Q16—44no—
304C2×Q16—44no—
305C2×Q16—44no—
306C2×Q16—416no—
307C2×Q16C2×D4116yescomplemented
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×C8—28no—
320C22×C8—44no—
321C22×C8—44no—
322C22×C8—416no—
323C22×C8C2×D414yes—
324C22×C8C2412yes—
325C22×C8C2412yes—
326C22×C8C2412yes—
327C22×C8C2412yes—
328C22⋊Q8—28no—
329C22⋊Q8—28no—
330C22⋊Q8—28no—
331C22⋊Q8—28no—
332C22⋊Q8—44no—
333C22⋊Q8—44no—
334C22⋊Q8—44no—
335C22⋊Q8—44no—
336C22⋊Q8—48no—
337C22⋊Q8—48no—
338C22⋊Q8—48no—
339C22⋊Q8—48no—
340C4×Q8—44no—
341C4×Q8—44no—
342C4×Q8—48no—
343C4×D4—48no—
344C4×D4—44no—
345C4×D4—44no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—24no—
357C2×C4⋊C4—24no—
358C2×C4⋊C4—24no—
359C2×C4⋊C4—24no—
360C2×C4⋊C4—24no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—42no—
367C2×C4⋊C4—44no—
368C2×C4⋊C4—44no—
369C2×C4⋊C4—44no—
370C2×C4⋊C4—44no—
371C2×C4⋊C4—44no—
372C2×C4⋊C4C2×D414yes—
373C2×C4⋊C4C2412yes—
374C2×C4⋊C4C2412yes—
375C2×C4⋊C4C2412yes—
376C2×C4⋊C4C2412yes—
377C2×C4⋊C4C2412yes—
378C2×C22⋊C4—24no—
379C2×C22⋊C4—24no—
380C2×C22⋊C4—24no—
381C2×C22⋊C4—24no—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—24no—
384C2×C22⋊C4—24no—
385C2×C22⋊C4—42no—
386C2×C22⋊C4—42no—
387C2×C22⋊C4—44no—
388C2×C22⋊C4—44no—
389C2×C22⋊C4—44no—
390C2×C22⋊C4—44no—
391C2×C22⋊C4—44no—
392C2×C22⋊C4—44no—
393C2×C22⋊C4—44no—
394C2×C22⋊C4C2×D414yes—
395C2×C22⋊C4C2×D414yes—
396C2×C42—22no—
397C2×C42—22no—
398C2×C42—24no—
399C2×C42—44no—
400C2×C42C2×D412yes—
401C2×C42C2412yes—
402#107—28no—
403#106—44no—
404#103—28no—
405#103—28no—
406#103—28no—
407#103—28no—
408#103—44no—
409#103—44no—
410#103—44no—
411#103—44no—
412C22⋊C8—28no—
413C22⋊C8—44no—
414C22⋊C8—44no—
415#95—24no—
416#95—24no—
417#95—24no—
418#95—24no—
419#95—24no—
420#95—24no—
421#95—24no—
422#95—24no—
423#95—24no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24—22no—
429C24—22no—
430C24—22no—
431C24—22no—
432C24—22no—
433C24—22no—
434C24—22no—
435C24—22no—
436C24#13514yes—
437C24#13714yes—
438C24C22×D412yes—
439C24C22×D412yes—
440C24C22×D411yescharacteristic
441C2×Q8—24no—
442C2×Q8—24no—
443C2×Q8—24no—
444C2×Q8—22no—
445C2×Q8—22no—
446C2×Q8—22no—
447C2×Q8—28no—
448C2×Q8—28no—
449C2×Q8—28no—
450C2×Q8—28no—
451C2×Q8—28no—
452C2×Q8—28no—
453C2×Q8—22no—
454C2×Q8—22no—
455C2×Q8—22no—
456C2×Q8—22no—
457C2×Q8—22no—
458C2×Q8—22no—
459C2×Q8—22no—
460C2×Q8—22no—
461C2×Q8—22no—
462C2×Q8—22no—
463C2×Q8—22no—
464C2×Q8—22no—
465C2×Q8—48no—
466C2×Q8—48no—
467C2×Q8—48no—
468C2×Q8—416no—
469C2×Q8—416no—
470C2×Q8—416no—
471C2×Q8—464no—
472C2×Q8—416no—
473C2×Q8—432no—
474C2×Q8—42no—
475C2×Q8—44no—
476C2×Q8—42no—
477C2×Q8—42no—
478C2×Q8—44no—
479C2×Q8—44no—
480C2×Q8—42no—
481C2×Q8—42no—
482C2×Q8—42no—
483C2×Q8—44no—
484C2×Q8—44no—
485C2×Q8—44no—
486C2×Q8C22×D414yes—
487C2×Q8C22×D414yes—
488C2×Q8C2×#4114yes—
489C2×D4—28no—
490C2×D4—28no—
491C2×D4—44no—
492C2×D4—416no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—24no—
498C22×C4—24no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—24no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—24no—
512C22×C4—24no—
513C22×C4—24no—
514C22×C4—24no—
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—22no—
534C22×C4—48no—
535C22×C4—48no—
536C22×C4—48no—
537C22×C4—432no—
538C22×C4—42no—
539C22×C4—42no—
540C22×C4—42no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4—42no—
544C22×C4—44no—
545C22×C4—44no—
546C22×C4—44no—
547C22×C4—44no—
548C22×C4—44no—
549C22×C4—44no—
550C22×C4—44no—
551C22×C4—44no—
552C22×C4—42no—
553C22×C4—42no—
554C22×C4—42no—
555C22×C4—42no—
556C22×C4—42no—
557C22×C4—42no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—42no—
565C22×C4—42no—
566C22×C4—42no—
567C22×C4C22×D412yes—
568C22×C4C22×D412yes—
569C22×C4C22×D412yes—
570C22×C4C22×D412yes—
571C22×C4C22×D411yescharacteristic
572C22×C4C22×D412yes—
573C22×C4C2×#4112yes—
574C22×C4H(5,𝔽2)12yes—
575C22×C4H(5,𝔽2)12yes—
576C22×C4H(5,𝔽2)12yes—
577C22×C4H(5,𝔽2)12yes—
578C22×C4C2511yescharacteristic
579Q16—416no—
580Q16—416no—
581C2×C8—28no—
582C2×C8—22no—
583C2×C8—22no—
584C2×C8—22no—
585C2×C8—22no—
586C2×C8—22no—
587C2×C8—22no—
588C2×C8—22no—
589C2×C8—22no—
590C2×C8—22no—
591C2×C8—22no—
592C2×C8—22no—
593C2×C8—416no—
594C2×C8—44no—
595C2×C8—44no—
596C2×C8—44no—
597C2×C8C22×D414yes—
598C4⋊C4—22no—
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—22no—
602C4⋊C4—22no—
603C4⋊C4—22no—
604C4⋊C4—22no—
605C4⋊C4—22no—
606C4⋊C4—22no—
607C4⋊C4—22no—
608C4⋊C4—44no—
609C4⋊C4—48no—
610C4⋊C4—48no—
611C4⋊C4—48no—
612C4⋊C4—48no—
613C4⋊C4—48no—
614C4⋊C4—42no—
615C4⋊C4—42no—
616C4⋊C4—42no—
617C4⋊C4—42no—
618C4⋊C4—42no—
619C22⋊C4—44no—
620C22⋊C4—44no—
621C22⋊C4—48no—
622C22⋊C4—48no—
623C22⋊C4—48no—
624C22⋊C4—48no—
625C22⋊C4—48no—
626C22⋊C4—48no—
627C22⋊C4—48no—
628C42—24no—
629C42—22no—
630C42—22no—
631C42—48no—
632C23—22no—
633C23—22no—
634C23—28no—
635C23—28no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—28no—
641C23—28no—
642C23—28no—
643C23—28no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—44no—
651C23—44no—
652C23—44no—
653C23—44no—
654C23—44no—
655C23—44no—
656C23—44no—
657C23—44no—
658C23#53412yes—
659C23D4212yes—
660C23#54612yes—
661C23C2×#13514yes—
662C23C2×#13512yes—
663C23C2×#13714yes—
664C23C2×#13712yes—
665C23#57812yes—
666C23#57812yes—
667C23C23×D411yescharacteristic
668Q8—24no—
669Q8—24no—
670Q8—24no—
671Q8—24no—
672Q8—24no—
673Q8—24no—
674Q8—432no—
675Q8—48no—
676Q8—48no—
677Q8—48no—
678Q8—42no—
679Q8—42no—
680Q8—42no—
681Q8—42no—
682Q8—42no—
683Q8—42no—
684D4—416no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—24no—
690C2×C4—24no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—24no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—432no—
701C2×C4—44no—
702C2×C4—44no—
703C2×C4—48no—
704C2×C4—48no—
705C2×C4—48no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—44no—
710C2×C4—44no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—48no—
715C2×C4—48no—
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—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—84no—
740C2×C4—84no—
741C2×C4—84no—
742C2×C4—84no—
743C2×C4—84no—
744C2×C4#53412yes—
745C2×C4#53414yes—
746C2×C4#53814yes—
747C2×C4D4212yes—
748C2×C4#54612yes—
749C2×C4#54614yes—
750C2×C4#56014yes—
751C2×C4C23×D411yescharacteristic
752C2×C4C22×#4111yescharacteristic
753C2×C4C2×H(5,𝔽2)11yescharacteristic
754C2×C4C2×H(5,𝔽2)11yescharacteristic
755C2×C4C2×H(5,𝔽2)11yescharacteristic
756C2×C4C2×H(5,𝔽2)11yescharacteristic
757C8—24no—
758C8—42no—
759C8—42no—
760C8—42no—
761C22—24no—
762C22—24no—
763C22—24no—
764C22—24no—
765C22—24no—
766C22—24no—
767C22—42no—
768C22—42no—
769C22—42no—
770C22—42no—
771C22—42no—
772C22—42no—
773C22—42no—
774C22—416no—
775C22—416no—
776C22—42no—
777C22#266814yes—
778C22#319014yes—
779C22#320214yes—
780C22#327014yes—
781C22#328514yes—
782C22#330014yes—
783C22#331214yes—
784C22C2×#53411yescharacteristic
785C22C2×D4211yescharacteristic
786C22C2×#54611yescharacteristic
787C22C22×#13511yescharacteristic
788C22C22×#13711yescharacteristic
789C22C2×#57811yescharacteristic
790C22C2×#57811yescharacteristic
791C4—42no—
792C4—42no—
793C4—42no—
794C4—42no—
795C4—44no—
796C4—44no—
797C4—44no—
798C4—82no—
799C4—82no—
800C4—82no—
801C4—82no—
802C4—82no—
803C4#266814yes—
804C4C2×#53411yescharacteristic
805C4C2×#53811yescharacteristic
806C4C2×#54611yescharacteristic
807C4C2×#56011yescharacteristic
808C2—44no—
809C2—44no—
810C2#3041118yesdirect product factor
811C2C2×#266811yescharacteristic
812C2C2×#319011yescharacteristic
813C2C2×#320211yescharacteristic
814C2C2×#327011yescharacteristic
815C2C2×#328511yescharacteristic
816C2C2×#330011yescharacteristic
817C2C2×#331211yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC23×D4D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C22×C4×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#467C2semidirect
2. C22×#451C2semidirect
5. #30411C2direct (N × H)
6. C2×#2097C2semidirect
7. C2×#2075C2semidirect
8. C2×#2074C2semidirect
9. C2×#2035C2semidirect
10. C2×#2035C2semidirect
11. C2×#2001C2semidirect
12. C2×#1892C2semidirect
13. C2×#1878C2semidirect
14. C2×#1878C2semidirect
16. C2×#1787C2semidirect
28. C2×#467C22semidirect
30. C2×#451C22semidirect
62. #2097C22semidirect
63. #2075C22semidirect
64. #2074C22semidirect
65. #2035C22semidirect
66. #2035C22semidirect
67. #2001C22semidirect
68. #1892C22semidirect
69. #1878C22semidirect
70. #1878C22semidirect
72. #1787C22semidirect
100. C22×Q16D4semidirect
307. C2×Q16C2×D4semidirect
810. C2#30411direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#4672
C22×#4512
C2×#25362
C2×#24092
#304112
C2×#20972
C2×#20752
C2×#20742
C2×#20352
C2×#20012
C2×#18922
C2×#18782
C2×#18692
C2×#17872