Finite Group Databasebeta

← C2×#30712 #7501612

Subgroups — C2×#30712 #7501612

Order 512.

2618 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#485C211yesmaximal, characteristic, complemented
2C22×#467C211yesmaximal, characteristic, complemented
3C2×#2542C211yesmaximal, characteristic
4C2×#2415C211yesmaximal, characteristic
5#30712C2116yesmaximal, direct product factor
6C2×#2043C211yesmaximal, characteristic, complemented
7C2×#2035C211yesmaximal, characteristic, complemented
8C2×#2016C211yesmaximal, characteristic, complemented
9C2×#2001C211yesmaximal, characteristic, complemented
10C2×#2001C211yesmaximal, characteristic, complemented
11C2×#2001C211yesmaximal, characteristic, complemented
12C2×#1927C211yesmaximal, characteristic, complemented
13C2×#1918C211yesmaximal, characteristic, complemented
14C2×#1892C211yesmaximal, characteristic, complemented
15C2×#1873C211yesmaximal, characteristic, complemented
16C2×#1869C211yesmaximal, characteristic
17C23×Q16C2211yescharacteristic
18C23×Q16C2211yescharacteristic
19C24×C8C2211yescharacteristic
20C22×C4⋊Q8C2211yescharacteristic
21C22×C22⋊Q8C2211yescharacteristic
22C22×C22⋊Q8C2211yescharacteristic
23C22×C22⋊Q8C2211yescharacteristic
24C22×C22⋊Q8C2211yescharacteristic
25C22×C22⋊Q8C2211yescharacteristic
26C22×C22⋊Q8C2211yescharacteristic
27C22×C4×D4C2211yescharacteristic
28C22×#117C2211yescharacteristic
29C2×#485—28no—
30C2×#485C2218yescomplemented
31C2×#467—28no—
32C2×#467C2218yescomplemented
33C22×#107C2211yescharacteristic
34C22×#106C2211yescharacteristic
35C22×#103C2211yescharacteristic
36C22×#103C2211yescharacteristic
37C22×#103C2211yescharacteristic
38C22×#103C2211yescharacteristic
39C22×#103C2211yescharacteristic
40C22×#103C2211yescharacteristic
41C22×#103C2211yescharacteristic
42C22×#103C2211yescharacteristic
43C22×C22⋊C8C2211yescharacteristic
44C22×C22⋊C8C2211yescharacteristic
45C22×C22⋊C8C2211yescharacteristic
46#2542—24no—
47#2542C2218yes—
48#2415—24no—
49#2415C2218yes—
50C2×#399—21no—
51C2×#399—21no—
52C2×#397—21no—
53C2×#394—21no—
54C2×#391C2211yescharacteristic
55C2×#390—21no—
56C2×#389—21no—
57C2×#389C2211yescharacteristic
58C2×#388—21no—
59C2×#384—21no—
60C2×#380C2211yescharacteristic
61C2×C4×C4⋊C4C2211yescharacteristic
62#2043C2218yescomplemented
63#2035C2218yescomplemented
64#2016C2218yescomplemented
65#2001C2218yescomplemented
66#2001C2218yescomplemented
67#2001C2218yescomplemented
68#1927C2218yescomplemented
69#1918C2218yescomplemented
70#1892C2218yescomplemented
71#1873C2218yescomplemented
72#1869C2218yes—
73C2×#340C2211yescharacteristic
74C2×#340C2211yescharacteristic
75C2×#340C2211yescharacteristic
76C2×#340C2211yescharacteristic
77C2×#336C2211yescharacteristic
78C2×#336C2211yescharacteristic
79C23×Q8C2311yescharacteristic
80C23×Q8C2311yescharacteristic
81C23×Q8C2311yescharacteristic
82C23×D4D411yescharacteristic
83C24×C4C2311yescharacteristic
84C24×C4C2311yescharacteristic
85C22×Q16—24no—
86C22×Q16—42no—
87C22×Q16—42no—
88C22×Q16—42no—
89C22×Q16—42no—
90C22×Q16—42no—
91C22×Q16C2314yes—
92C22×Q16C2314yes—
93C23×C8—24no—
94C23×C8—42no—
95C23×C8—42no—
96C23×C8C2311yescharacteristic
97C23×C8C2311yescharacteristic
98C23×C8C2311yescharacteristic
99C23×C8C2311yescharacteristic
100C23×C8C2314yes—
101C2×C4⋊Q8—22no—
102C2×C4⋊Q8—42no—
103C2×C4⋊Q8—42no—
104C2×C4⋊Q8C2314yes—
105C2×C22⋊Q8—22no—
106C2×C22⋊Q8—22no—
107C2×C22⋊Q8—22no—
108C2×C22⋊Q8—22no—
109C2×C22⋊Q8—22no—
110C2×C22⋊Q8—22no—
111C2×C22⋊Q8—24no—
112C2×C22⋊Q8—24no—
113C2×C22⋊Q8—24no—
114C2×C22⋊Q8—24no—
115C2×C22⋊Q8—24no—
116C2×C22⋊Q8—42no—
117C2×C22⋊Q8—42no—
118C2×C22⋊Q8—42no—
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×C22⋊Q8C2314yes—
128C2×C22⋊Q8C2314yes—
129C2×C4×D4—42no—
130C2×C4×D4—42no—
131C2×C4×D4D414yes—
132C2×C4×D4C2314yes—
133C2×#117—22no—
134C2×#117—24no—
135C2×#117—42no—
136C2×#117C2314yes—
137C22×C4⋊C4—21no—
138C22×C4⋊C4—21no—
139C22×C4⋊C4—21no—
140C22×C4⋊C4—21no—
141C22×C4⋊C4—21no—
142C22×C4⋊C4—21no—
143C22×C4⋊C4—21no—
144C22×C4⋊C4—21no—
145C22×C4⋊C4—21no—
146C22×C4⋊C4D411yescharacteristic
147C22×C4⋊C4C2311yescharacteristic
148C22×C4⋊C4C2311yescharacteristic
149C22×C4⋊C4C2311yescharacteristic
150C22×C4⋊C4C2311yescharacteristic
151C22×C4⋊C4C2311yescharacteristic
152C22×C22⋊C4—21no—
153C22×C22⋊C4—21no—
154C22×C22⋊C4—21no—
155C22×C22⋊C4—21no—
156C22×C22⋊C4—21no—
157C22×C22⋊C4—21no—
158C22×C22⋊C4—21no—
159C22×C22⋊C4—21no—
160C22×C22⋊C4D411yescharacteristic
161C22×C22⋊C4D411yescharacteristic
162C22×C42—21no—
163C22×C42—21no—
164C22×C42C2311yescharacteristic
165#485—232no—
166#467—232no—
167C2×#107D418yescomplemented
168C2×#107C2314yes—
169C2×#106—24no—
170C2×#106C2314yes—
171C2×#103—24no—
172C2×#103—24no—
173C2×#103—24no—
174C2×#103—24no—
175C2×#103—24no—
176C2×#103—42no—
177C2×#103—42no—
178C2×#103—42no—
179C2×#103C2314yes—
180C2×#103C2314yes—
181C2×#103C2314yes—
182C2×#103C2314yes—
183C2×#103C2314yes—
184C2×#103C2314yes—
185C2×#103C2314yes—
186C2×#103C2314yes—
187C2×C22⋊C8—24no—
188C2×C22⋊C8—42no—
189C2×C22⋊C8—42no—
190C2×C22⋊C8C2314yes—
191C2×C22⋊C8C2314yes—
192C2×C22⋊C8C2314yes—
193#399—28no—
194#399—28no—
195#397—28no—
196#394—28no—
197#391—22no—
198#391C2314yes—
199#390—28no—
200#389—28no—
201#389—22no—
202#389C2314yes—
203#388—28no—
204#384—28no—
205#380—22no—
206#380C2314yes—
207C4×C4⋊C4—22no—
208C4×C4⋊C4C2314yes—
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—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×Q8—22no—
242C22×Q8—22no—
243C22×Q8C2412yes—
244C22×Q8C2412yes—
245C22×Q8C2412yes—
246C22×D4—24no—
247C22×D4—24no—
248C22×D4—42no—
249C22×D4C2×D414yes—
250C23×C4—21no—
251C23×C4—21no—
252C23×C4—21no—
253C23×C4—22no—
254C23×C4—22no—
255C23×C4—22no—
256C23×C4—22no—
257C23×C4—22no—
258C23×C4—22no—
259C23×C4—22no—
260C23×C4—22no—
261C23×C4—22no—
262C23×C4—22no—
263C23×C4—22no—
264C23×C4—22no—
265C23×C4—21no—
266C23×C4—21no—
267C23×C4—21no—
268C23×C4—21no—
269C23×C4—21no—
270C23×C4C2×D412yes—
271C23×C4C2×D412yes—
272C23×C4C2×D411yescharacteristic
273C23×C4C2×D411yescharacteristic
274C23×C4C2×D411yescharacteristic
275C23×C4C2×D411yescharacteristic
276C23×C4C2412yes—
277C23×C4C2412yes—
278C23×C4C2411yescharacteristic
279C2×Q16—28no—
280C2×Q16—44no—
281C2×Q16—44no—
282C2×Q16—44no—
283C2×Q16—44no—
284C2×Q16—44no—
285C2×Q16—416no—
286C2×Q16—416no—
287C22×C8—22no—
288C22×C8—22no—
289C22×C8—22no—
290C22×C8—22no—
291C22×C8—22no—
292C22×C8—22no—
293C22×C8—22no—
294C22×C8—22no—
295C22×C8—22no—
296C22×C8—22no—
297C22×C8—22no—
298C22×C8—28no—
299C22×C8—44no—
300C22×C8—44no—
301C22×C8—416no—
302C22×C8C2×D414yes—
303C22×C8C2412yes—
304C22×C8C2412yes—
305C22×C8C2412yes—
306C22×C8C2412yes—
307C4⋊Q8—44no—
308C4⋊Q8—44no—
309C4⋊Q8—48no—
310C22⋊Q8—28no—
311C22⋊Q8—28no—
312C22⋊Q8—28no—
313C22⋊Q8—28no—
314C22⋊Q8—28no—
315C22⋊Q8—44no—
316C22⋊Q8—44no—
317C22⋊Q8—44no—
318C22⋊Q8—44no—
319C22⋊Q8—44no—
320C22⋊Q8—44no—
321C22⋊Q8—44no—
322C22⋊Q8—48no—
323C22⋊Q8—48no—
324C22⋊Q8—48no—
325C22⋊Q8—48no—
326C22⋊Q8—48no—
327C22⋊Q8—48no—
328C4×D4—48no—
329C4×D4—44no—
330C4×D4—44no—
331#117—28no—
332#117—44no—
333#117—48no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—24no—
345C2×C4⋊C4—24no—
346C2×C4⋊C4—24no—
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—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—42no—
356C2×C4⋊C4—44no—
357C2×C4⋊C4—44no—
358C2×C4⋊C4—44no—
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⋊C4C2×D414yes—
366C2×C4⋊C4C2×D414yes—
367C2×C4⋊C4C2×D414yes—
368C2×C4⋊C4#4114yes—
369C2×C4⋊C4C2412yes—
370C2×C4⋊C4C2412yes—
371C2×C4⋊C4C2412yes—
372C2×C4⋊C4C2412yes—
373C2×C4⋊C4C2412yes—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—24no—
379C2×C22⋊C4—24no—
380C2×C22⋊C4—24no—
381C2×C22⋊C4—24no—
382C2×C22⋊C4—42no—
383C2×C22⋊C4—42no—
384C2×C22⋊C4—44no—
385C2×C22⋊C4—44no—
386C2×C22⋊C4—44no—
387C2×C22⋊C4—44no—
388C2×C22⋊C4—44no—
389C2×C22⋊C4—44no—
390C2×C22⋊C4—44no—
391C2×C22⋊C4—44no—
392C2×C22⋊C4C2×D414yes—
393C2×C22⋊C4C2×D414yes—
394C2×C42—22no—
395C2×C42—22no—
396C2×C42—24no—
397C2×C42—24no—
398C2×C42—44no—
399C2×C42—44no—
400C2×C42C2×D412yes—
401C2×C42C2412yes—
402#107C2×D4116yescomplemented
403#106—28no—
404#103—28no—
405#103—28no—
406#103—28no—
407#103—28no—
408#103—28no—
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—
420C24—22no—
421C24—22no—
422C24—22no—
423C24—22no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24—22no—
429C24—22no—
430C24—22no—
431C24—22no—
432C24—22no—
433C24#13714yes—
434C24C22×D412yes—
435C24C22×D412yes—
436C24C22×D411yescharacteristic
437C2×Q8—22no—
438C2×Q8—22no—
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—42no—
456C2×Q8—42no—
457C2×Q8—42no—
458C2×Q8—42no—
459C2×Q8—42no—
460C2×Q8—42no—
461C2×Q8—42no—
462C2×Q8—42no—
463C2×Q8—42no—
464C2×Q8—44no—
465C2×Q8—44no—
466C2×Q8—44no—
467C2×Q8—44no—
468C2×Q8—44no—
469C2×Q8—44no—
470C2×Q8—44no—
471C2×Q8—44no—
472C2×Q8—44no—
473C2×Q8—44no—
474C2×Q8—44no—
475C2×Q8—44no—
476C2×D4—28no—
477C2×D4—28no—
478C2×D4—44no—
479C2×D4—416no—
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—22no—
489C22×C4—24no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—24no—
498C22×C4—24no—
499C22×C4—24no—
500C22×C4—24no—
501C22×C4—24no—
502C22×C4—24no—
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—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—42no—
521C22×C4—42no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4—42no—
525C22×C4—42no—
526C22×C4—44no—
527C22×C4—44no—
528C22×C4—44no—
529C22×C4—44no—
530C22×C4—44no—
531C22×C4—44no—
532C22×C4—44no—
533C22×C4—44no—
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#13514yes—
550C22×C4C22×D412yes—
551C22×C4C22×D412yes—
552C22×C4C22×D412yes—
553C22×C4C22×D412yes—
554C22×C4C22×D411yescharacteristic
555C22×C4C22×D412yes—
556C22×C4C2×#4112yes—
557C22×C4H(5,𝔽2)12yes—
558C22×C4H(5,𝔽2)12yes—
559C22×C4H(5,𝔽2)12yes—
560C22×C4H(5,𝔽2)12yes—
561C22×C4C2511yescharacteristic
562Q16—416no—
563Q16—416no—
564C2×C8—28no—
565C2×C8—22no—
566C2×C8—22no—
567C2×C8—22no—
568C2×C8—22no—
569C2×C8—22no—
570C2×C8—22no—
571C2×C8—22no—
572C2×C8—22no—
573C2×C8—22no—
574C2×C8—22no—
575C2×C8—22no—
576C2×C8—416no—
577C2×C8—44no—
578C2×C8—44no—
579C2×C8—44no—
580C2×C8C22×D414yes—
581C4⋊C4—24no—
582C4⋊C4—24no—
583C4⋊C4—24no—
584C4⋊C4—22no—
585C4⋊C4—22no—
586C4⋊C4—22no—
587C4⋊C4—22no—
588C4⋊C4—22no—
589C4⋊C4—22no—
590C4⋊C4—22no—
591C4⋊C4—44no—
592C4⋊C4—48no—
593C4⋊C4—48no—
594C4⋊C4—48no—
595C4⋊C4—48no—
596C4⋊C4—48no—
597C4⋊C4—48no—
598C4⋊C4—48no—
599C4⋊C4—48no—
600C4⋊C4—42no—
601C4⋊C4—42no—
602C4⋊C4—48no—
603C4⋊C4C22×D414yes—
604C4⋊C4C22×D414yes—
605C4⋊C4C2×#4114yes—
606C22⋊C4—44no—
607C22⋊C4—44no—
608C22⋊C4—48no—
609C22⋊C4—48no—
610C22⋊C4—48no—
611C22⋊C4—48no—
612C22⋊C4—48no—
613C22⋊C4—48no—
614C22⋊C4—48no—
615C22⋊C4—48no—
616C42—24no—
617C42—22no—
618C42—22no—
619C42—48no—
620C42—48no—
621C23—22no—
622C23—28no—
623C23—22no—
624C23—22no—
625C23—28no—
626C23—28no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—44no—
638C23—44no—
639C23—44no—
640C23—44no—
641C23—44no—
642C23—44no—
643C23—44no—
644C23—44no—
645C23—44no—
646C23—44no—
647C23—44no—
648C23#53412yes—
649C23D4212yes—
650C23#54612yes—
651C23C2×#13512yes—
652C23C2×#13714yes—
653C23C2×#13712yes—
654C23#57812yes—
655C23#57812yes—
656C23C23×D411yescharacteristic
657Q8—42no—
658Q8—42no—
659Q8—42no—
660Q8—42no—
661Q8—42no—
662Q8—42no—
663Q8—42no—
664Q8—42no—
665Q8—42no—
666Q8—42no—
667Q8—42no—
668Q8—42no—
669Q8—84no—
670Q8—84no—
671Q8—84no—
672D4—416no—
673C2×C4—22no—
674C2×C4—28no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—24no—
681C2×C4—24no—
682C2×C4—22no—
683C2×C4—24no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—44no—
689C2×C4—44no—
690C2×C4—44no—
691C2×C4—48no—
692C2×C4—48no—
693C2×C4—48no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—48no—
701C2×C4—48no—
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—42no—
713C2×C4—42no—
714C2×C4—42no—
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—84no—
726C2×C4—84no—
727C2×C4—84no—
728C2×C4—84no—
729C2×C4—84no—
730C2×C4#53412yes—
731C2×C4#53514yes—
732C2×C4#54014yes—
733C2×C4D4212yes—
734C2×C4#54612yes—
735C2×C4#55014yes—
736C2×C4#56014yes—
737C2×C4C2×#13514yes—
738C2×C4C23×D411yescharacteristic
739C2×C4C22×#4111yescharacteristic
740C2×C4C2×H(5,𝔽2)11yescharacteristic
741C2×C4C2×H(5,𝔽2)11yescharacteristic
742C2×C4C2×H(5,𝔽2)11yescharacteristic
743C2×C4C2×H(5,𝔽2)11yescharacteristic
744C8—24no—
745C8—42no—
746C8—42no—
747C8—42no—
748C22—24no—
749C22—24no—
750C22—24no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—416no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22—42no—
761C22—42no—
762C22—42no—
763C22—88no—
764C22#267314yes—
765C22#319014yes—
766C22#320214yes—
767C22#327014yes—
768C22#328314yes—
769C22#330214yes—
770C22#331214yes—
771C22C2×#53411yescharacteristic
772C22C2×D4211yescharacteristic
773C22C2×#54611yescharacteristic
774C22C22×#13511yescharacteristic
775C22C22×#13711yescharacteristic
776C22C2×#57811yescharacteristic
777C22C2×#57811yescharacteristic
778C4—24no—
779C4—42no—
780C4—44no—
781C4—44no—
782C4—42no—
783C4—42no—
784C4—44no—
785C4—82no—
786C4—82no—
787C4—82no—
788C4—82no—
789C4—82no—
790C4#267314yes—
791C4C2×#53511yescharacteristic
792C4C2×#54011yescharacteristic
793C4C2×#55011yescharacteristic
794C4C2×#56011yescharacteristic
795C2—44no—
796C2—82no—
797C2#3071218yesdirect product factor
798C2C2×#267311yescharacteristic
799C2C2×#319011yescharacteristic
800C2C2×#320211yescharacteristic
801C2C2×#327011yescharacteristic
802C2C2×#328311yescharacteristic
803C2C2×#330211yescharacteristic
804C2C2×#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×#485C2semidirect
2. C22×#467C2semidirect
5. #30712C2direct (N × H)
6. C2×#2043C2semidirect
7. C2×#2035C2semidirect
8. C2×#2016C2semidirect
9. C2×#2001C2semidirect
10. C2×#2001C2semidirect
11. C2×#2001C2semidirect
12. C2×#1927C2semidirect
13. C2×#1918C2semidirect
14. C2×#1892C2semidirect
15. C2×#1873C2semidirect
30. C2×#485C22semidirect
32. C2×#467C22semidirect
62. #2043C22semidirect
63. #2035C22semidirect
64. #2016C22semidirect
65. #2001C22semidirect
66. #2001C22semidirect
67. #2001C22semidirect
68. #1927C22semidirect
69. #1918C22semidirect
70. #1892C22semidirect
71. #1873C22semidirect
167. C2×#107D4semidirect
402. #107C2×D4semidirect
797. C2#30712direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#4852
C22×#4672
C2×#25422
C2×#24152
#307122
C2×#20432
C2×#20352
C2×#20162
C2×#20012
C2×#19272
C2×#19182
C2×#18922
C2×#18732
C2×#18692