Finite Group Databasebeta

← C2×#30713 #7501602

Subgroups — C2×#30713 #7501602

Order 512.

2834 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#483C211yesmaximal, characteristic, complemented
2C22×#465C211yesmaximal, characteristic, complemented
3C2×#2540C211yesmaximal, characteristic
4C2×#2417C211yesmaximal, characteristic, complemented
5#30713C2116yesmaximal, direct product factor
6C2×#2042C211yesmaximal, characteristic, complemented
7C2×#2034C211yesmaximal, characteristic, complemented
8C2×#2015C211yesmaximal, characteristic, complemented
9C2×#2001C211yesmaximal, characteristic, complemented
10C2×#2001C211yesmaximal, characteristic, complemented
11C2×#2000C211yesmaximal, characteristic, complemented
12C2×#1927C211yesmaximal, characteristic, complemented
13C2×#1919C211yesmaximal, characteristic, complemented
14C2×#1892C211yesmaximal, characteristic, complemented
15C2×#1874C211yesmaximal, characteristic, complemented
16C2×#1869C211yesmaximal, characteristic, complemented
17C23×Q16C2211yescharacteristic
18C23×SD16C2211yescharacteristic
19C24×C8C2211yescharacteristic
20C22×#124C2211yescharacteristic
21C22×C22⋊Q8C2211yescharacteristic
22C22×C22⋊Q8C2211yescharacteristic
23C22×C22⋊Q8C2211yescharacteristic
24C22×C22⋊Q8C2211yescharacteristic
25C22×#121C2211yescharacteristic
26C22×#121C2211yescharacteristic
27C22×C4×D4C2211yescharacteristic
28C23×C4⋊C4C2211yescharacteristic
29C2×#483—28no—
30C2×#483C2218yescomplemented
31C2×#465—28no—
32C2×#465C2218yescomplemented
33C22×#106C2211yescharacteristic
34C22×#106C2211yescharacteristic
35C22×#103C2211yescharacteristic
36C22×#103C2211yescharacteristic
37C22×#103C2211yescharacteristic
38C22×#103C2211yescharacteristic
39C22×#103C2211yescharacteristic
40C22×#102C2211yescharacteristic
41C22×#102C2211yescharacteristic
42C22×#102C2211yescharacteristic
43C22×C22⋊C8C2211yescharacteristic
44C22×C22⋊C8C2211yescharacteristic
45C22×C22⋊C8C2211yescharacteristic
46#2540—24no—
47#2540C2218yes—
48#2417—24no—
49#2417C2218yescomplemented
50C2×#399—21no—
51C2×#398—21no—
52C2×#396—21no—
53C2×#392—21no—
54C2×#391C2211yescharacteristic
55C2×#390—21no—
56C2×#390—21no—
57C2×#389C2211yescharacteristic
58C2×#386—21no—
59C2×#380—21no—
60C2×#380C2211yescharacteristic
61C2×C4×C4⋊C4C2211yescharacteristic
62#2042C2218yescomplemented
63#2034C2218yescomplemented
64#2015C2218yescomplemented
65#2001C2218yescomplemented
66#2001C2218yescomplemented
67#2000C2218yescomplemented
68#1927C2218yescomplemented
69#1919C2218yescomplemented
70#1892C2218yescomplemented
71#1874C2218yescomplemented
72#1869C2218yescomplemented
73C2×#340C2211yescharacteristic
74C2×#340C2211yescharacteristic
75C2×#340C2211yescharacteristic
76C2×#340C2211yescharacteristic
77C2×#336C2211yescharacteristic
78C2×#336C2211yescharacteristic
79C23×Q8C2311yescharacteristic
80C23×Q8C2311yescharacteristic
81C23×D4—21no—
82C23×D4—21no—
83C23×D4D411yescharacteristic
84C23×D4C2311yescharacteristic
85C24×C4—21no—
86C24×C4C2311yescharacteristic
87C24×C4C2311yescharacteristic
88C22×Q16—42no—
89C22×Q16—42no—
90C22×Q16—42no—
91C22×Q16C2314yes—
92C22×SD16—24no—
93C22×SD16—42no—
94C22×SD16—42no—
95C22×SD16C2314yes—
96C23×C8—24no—
97C23×C8—42no—
98C23×C8—42no—
99C23×C8C2311yescharacteristic
100C23×C8C2311yescharacteristic
101C23×C8C2311yescharacteristic
102C23×C8C2311yescharacteristic
103C23×C8C2314yes—
104C2×#124—22no—
105C2×#124—42no—
106C2×#124—42no—
107C2×#124C2314yes—
108C2×C22⋊Q8—22no—
109C2×C22⋊Q8—22no—
110C2×C22⋊Q8—22no—
111C2×C22⋊Q8—22no—
112C2×C22⋊Q8—24no—
113C2×C22⋊Q8—24no—
114C2×C22⋊Q8—24no—
115C2×C22⋊Q8—42no—
116C2×C22⋊Q8—42no—
117C2×C22⋊Q8—42no—
118C2×C22⋊Q8—42no—
119C2×C22⋊Q8—42no—
120C2×C22⋊Q8C2314yes—
121C2×C22⋊Q8C2314yes—
122C2×C22⋊Q8C2314yes—
123C2×C22⋊Q8C2314yes—
124C2×#121—22no—
125C2×#121—22no—
126C2×#121—24no—
127C2×#121—24no—
128C2×#121—42no—
129C2×#121—42no—
130C2×#121C2314yes—
131C2×#121C2314yes—
132C2×C4×D4—42no—
133C2×C4×D4—42no—
134C2×C4×D4D414yes—
135C2×C4×D4C2314yes—
136C22×C4⋊C4—24no—
137C22×C4⋊C4—21no—
138C22×C4⋊C4—21no—
139C22×C4⋊C4—21no—
140C22×C4⋊C4—21no—
141C22×C4⋊C4—21no—
142C22×C4⋊C4—22no—
143C22×C4⋊C4—21no—
144C22×C4⋊C4—42no—
145C22×C4⋊C4D411yescharacteristic
146C22×C4⋊C4C2311yescharacteristic
147C22×C4⋊C4C2311yescharacteristic
148C22×C4⋊C4C2314yes—
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⋊C4—21no—
161C22×C22⋊C4D411yescharacteristic
162C22×C22⋊C4D411yescharacteristic
163C22×C42—21no—
164C22×C42C2311yescharacteristic
165#483—232no—
166#465—232no—
167C2×#106—24no—
168C2×#106D418yescomplemented
169C2×#106C2314yes—
170C2×#106C2314yes—
171C2×#103—24no—
172C2×#103—24no—
173C2×#103—24no—
174C2×#103—24no—
175C2×#103—42no—
176C2×#103C2314yes—
177C2×#103C2314yes—
178C2×#103C2314yes—
179C2×#103C2314yes—
180C2×#103C2314yes—
181C2×#102—24no—
182C2×#102—42no—
183C2×#102—42no—
184C2×#102C2314yes—
185C2×#102C2314yes—
186C2×#102C2314yes—
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#398—28no—
195#396—28no—
196#392—28no—
197#391—22no—
198#391C2314yes—
199#390—28no—
200#390—28no—
201#389—22no—
202#389C2314yes—
203#386—28no—
204#380—22no—
205#380—28no—
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—
220C25—21no—
221C25C2×D411yescharacteristic
222C25C2×D411yescharacteristic
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×Q8C2412yes—
238C22×Q8C2412yes—
239C22×D4—24no—
240C22×D4—24no—
241C22×D4—24no—
242C22×D4—24no—
243C22×D4—22no—
244C22×D4—21no—
245C22×D4—22no—
246C22×D4—22no—
247C22×D4—22no—
248C22×D4—22no—
249C22×D4—22no—
250C22×D4—42no—
251C22×D4—44no—
252C22×D4—44no—
253C22×D4—44no—
254C22×D4—44no—
255C22×D4—82no—
256C22×D4—82no—
257C22×D4C2×D414yes—
258C22×D4C2412yes—
259C23×C4—21no—
260C23×C4—21no—
261C23×C4—21no—
262C23×C4—22no—
263C23×C4—22no—
264C23×C4—22no—
265C23×C4—22no—
266C23×C4—22no—
267C23×C4—22no—
268C23×C4—22no—
269C23×C4—22no—
270C23×C4—22no—
271C23×C4—22no—
272C23×C4—22no—
273C23×C4—22no—
274C23×C4—21no—
275C23×C4—21no—
276C23×C4—21no—
277C23×C4—21no—
278C23×C4—24no—
279C23×C4—44no—
280C23×C4—44no—
281C23×C4—82no—
282C23×C4C2×D412yes—
283C23×C4C2×D412yes—
284C23×C4C2×D411yescharacteristic
285C23×C4C2×D411yescharacteristic
286C23×C4C2×D411yescharacteristic
287C23×C4C2×D411yescharacteristic
288C23×C4C2412yes—
289C23×C4C2412yes—
290C23×C4C2411yescharacteristic
291C2×Q16—44no—
292C2×Q16—44no—
293C2×Q16—44no—
294C2×Q16—416no—
295C2×SD16—28no—
296C2×SD16—44no—
297C2×SD16—44no—
298C2×SD16—416no—
299C22×C8—22no—
300C22×C8—22no—
301C22×C8—22no—
302C22×C8—22no—
303C22×C8—22no—
304C22×C8—22no—
305C22×C8—22no—
306C22×C8—22no—
307C22×C8—22no—
308C22×C8—22no—
309C22×C8—22no—
310C22×C8—28no—
311C22×C8—44no—
312C22×C8—44no—
313C22×C8—416no—
314C22×C8C2×D414yes—
315C22×C8C2412yes—
316C22×C8C2412yes—
317C22×C8C2412yes—
318C22×C8C2412yes—
319#124—44no—
320#124—44no—
321#124—48no—
322C22⋊Q8—28no—
323C22⋊Q8—28no—
324C22⋊Q8—28no—
325C22⋊Q8—44no—
326C22⋊Q8—44no—
327C22⋊Q8—44no—
328C22⋊Q8—44no—
329C22⋊Q8—44no—
330C22⋊Q8—48no—
331C22⋊Q8—48no—
332C22⋊Q8—48no—
333C22⋊Q8—48no—
334#121—28no—
335#121—28no—
336#121—44no—
337#121—44no—
338#121—48no—
339#121—48no—
340C4×D4—48no—
341C4×D4—44no—
342C4×D4—44no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—21no—
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—28no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—24no—
356C2×C4⋊C4—24no—
357C2×C4⋊C4—24no—
358C2×C4⋊C4—24no—
359C2×C4⋊C4—24no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—24no—
362C2×C4⋊C4—44no—
363C2×C4⋊C4—48no—
364C2×C4⋊C4—42no—
365C2×C4⋊C4—44no—
366C2×C4⋊C4—44no—
367C2×C4⋊C4—44no—
368C2×C4⋊C4—44no—
369C2×C4⋊C4—44no—
370C2×C4⋊C4—82no—
371C2×C4⋊C4C2×D414yes—
372C2×C4⋊C4C2×D414yes—
373C2×C4⋊C4C2×D414yes—
374C2×C4⋊C4#4114yes—
375C2×C4⋊C4C2412yes—
376C2×C4⋊C4C2412yes—
377C2×C4⋊C4C2412yes—
378C2×C4⋊C4C2412yes—
379C2×C4⋊C4C2412yes—
380C2×C22⋊C4—24no—
381C2×C22⋊C4—24no—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—24no—
384C2×C22⋊C4—24no—
385C2×C22⋊C4—24no—
386C2×C22⋊C4—24no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4—42no—
390C2×C22⋊C4—42no—
391C2×C22⋊C4—44no—
392C2×C22⋊C4—44no—
393C2×C22⋊C4—44no—
394C2×C22⋊C4—44no—
395C2×C22⋊C4—44no—
396C2×C22⋊C4—44no—
397C2×C22⋊C4—44no—
398C2×C22⋊C4—44no—
399C2×C22⋊C4—82no—
400C2×C22⋊C4C2×D414yes—
401C2×C22⋊C4C2×D414yes—
402C2×C42—22no—
403C2×C42—22no—
404C2×C42—24no—
405C2×C42—82no—
406C2×C42C2×D412yes—
407C2×C42C2412yes—
408#106—28no—
409#106C2×D4116yescomplemented
410#103—28no—
411#103—28no—
412#103—28no—
413#103—28no—
414#103—44no—
415#102—28no—
416#102—44no—
417#102—44no—
418C22⋊C8—28no—
419C22⋊C8—44no—
420C22⋊C8—44no—
421#95—24no—
422#95—24no—
423#95—24no—
424#95—24no—
425#95—24no—
426C24—22no—
427C24—22no—
428C24—22no—
429C24—22no—
430C24—22no—
431C24—22no—
432C24—22no—
433C24—22no—
434C24—22no—
435C24—22no—
436C24—22no—
437C24—22no—
438C24—22no—
439C24—42no—
440C24—42no—
441C24—42no—
442C24—42no—
443C24—42no—
444C24—42no—
445C24—42no—
446C24#13514yes—
447C24#13714yes—
448C24C22×D412yes—
449C24C22×D412yes—
450C24C22×D411yescharacteristic
451C2×Q8—22no—
452C2×Q8—22no—
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—42no—
464C2×Q8—42no—
465C2×Q8—42no—
466C2×Q8—42no—
467C2×Q8—42no—
468C2×Q8—42no—
469C2×Q8—44no—
470C2×Q8—44no—
471C2×Q8—44no—
472C2×Q8—44no—
473C2×Q8—44no—
474C2×Q8—44no—
475C2×Q8—44no—
476C2×Q8—44no—
477C2×D4—28no—
478C2×D4—28no—
479C2×D4—22no—
480C2×D4—22no—
481C2×D4—22no—
482C2×D4—22no—
483C2×D4—22no—
484C2×D4—22no—
485C2×D4—44no—
486C2×D4—48no—
487C2×D4—48no—
488C2×D4—416no—
489C2×D4—48no—
490C2×D4—48no—
491C2×D4—42no—
492C2×D4—44no—
493C2×D4—44no—
494C2×D4—42no—
495C2×D4—42no—
496C2×D4—44no—
497C2×D4—44no—
498C2×D4—84no—
499C2×D4—84no—
500C2×D4—816no—
501C2×D4—816no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—24no—
507C22×C4—22no—
508C22×C4—24no—
509C22×C4—22no—
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—24no—
521C22×C4—24no—
522C22×C4—24no—
523C22×C4—24no—
524C22×C4—24no—
525C22×C4—24no—
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—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—48no—
543C22×C4—42no—
544C22×C4—42no—
545C22×C4—42no—
546C22×C4—42no—
547C22×C4—42no—
548C22×C4—42no—
549C22×C4—44no—
550C22×C4—44no—
551C22×C4—44no—
552C22×C4—44no—
553C22×C4—44no—
554C22×C4—44no—
555C22×C4—44no—
556C22×C4—44no—
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—48no—
566C22×C4—42no—
567C22×C4—42no—
568C22×C4—42no—
569C22×C4—42no—
570C22×C4—84no—
571C22×C4—816no—
572C22×C4C22×D412yes—
573C22×C4C22×D412yes—
574C22×C4C22×D412yes—
575C22×C4C22×D412yes—
576C22×C4C22×D411yescharacteristic
577C22×C4C22×D412yes—
578C22×C4C2×#4112yes—
579C22×C4H(5,𝔽2)12yes—
580C22×C4H(5,𝔽2)12yes—
581C22×C4H(5,𝔽2)12yes—
582C22×C4H(5,𝔽2)12yes—
583C22×C4C2511yescharacteristic
584Q16—416no—
585SD16—416no—
586C2×C8—28no—
587C2×C8—22no—
588C2×C8—22no—
589C2×C8—22no—
590C2×C8—22no—
591C2×C8—22no—
592C2×C8—22no—
593C2×C8—22no—
594C2×C8—22no—
595C2×C8—22no—
596C2×C8—22no—
597C2×C8—22no—
598C2×C8—416no—
599C2×C8—44no—
600C2×C8—44no—
601C2×C8—44no—
602C2×C8C22×D414yes—
603C4⋊C4—24no—
604C4⋊C4—24no—
605C4⋊C4—24no—
606C4⋊C4—22no—
607C4⋊C4—22no—
608C4⋊C4—22no—
609C4⋊C4—22no—
610C4⋊C4—22no—
611C4⋊C4—22no—
612C4⋊C4—22no—
613C4⋊C4—44no—
614C4⋊C4—48no—
615C4⋊C4—48no—
616C4⋊C4—48no—
617C4⋊C4—48no—
618C4⋊C4—48no—
619C4⋊C4—42no—
620C4⋊C4—42no—
621C4⋊C4—84no—
622C4⋊C4C22×D414yes—
623C4⋊C4C22×D414yes—
624C4⋊C4C2×#4114yes—
625C22⋊C4—44no—
626C22⋊C4—44no—
627C22⋊C4—48no—
628C22⋊C4—48no—
629C22⋊C4—48no—
630C22⋊C4—48no—
631C22⋊C4—48no—
632C22⋊C4—48no—
633C22⋊C4—48no—
634C22⋊C4—48no—
635C22⋊C4—84no—
636C42—24no—
637C42—22no—
638C42—22no—
639C42—84no—
640C23—22no—
641C23—22no—
642C23—28no—
643C23—28no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—28no—
649C23—28no—
650C23—28no—
651C23—28no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—44no—
659C23—44no—
660C23—44no—
661C23—44no—
662C23—44no—
663C23—44no—
664C23—44no—
665C23—44no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—84no—
674C23—84no—
675C23—84no—
676C23—84no—
677C23—84no—
678C23—84no—
679C23—84no—
680C23#53412yes—
681C23D4212yes—
682C23#54612yes—
683C23C2×#13514yes—
684C23C2×#13512yes—
685C23C2×#13714yes—
686C23C2×#13712yes—
687C23#57712yes—
688C23#57712yes—
689C23C23×D411yescharacteristic
690Q8—42no—
691Q8—42no—
692Q8—42no—
693Q8—42no—
694Q8—42no—
695Q8—42no—
696Q8—42no—
697Q8—42no—
698Q8—84no—
699Q8—84no—
700D4—416no—
701D4—42no—
702D4—42no—
703D4—42no—
704D4—42no—
705D4—816no—
706D4—816no—
707D4—84no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—24no—
713C2×C4—22no—
714C2×C4—24no—
715C2×C4—22no—
716C2×C4—24no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—44no—
724C2×C4—44no—
725C2×C4—44no—
726C2×C4—44no—
727C2×C4—48no—
728C2×C4—48no—
729C2×C4—48no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—48no—
737C2×C4—48no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—816no—
759C2×C4—84no—
760C2×C4—84no—
761C2×C4—84no—
762C2×C4—84no—
763C2×C4#53412yes—
764C2×C4#53514yes—
765C2×C4#54014yes—
766C2×C4D4212yes—
767C2×C4#54612yes—
768C2×C4#55014yes—
769C2×C4#56014yes—
770C2×C4C23×D411yescharacteristic
771C2×C4C22×#4111yescharacteristic
772C2×C4C2×H(5,𝔽2)11yescharacteristic
773C2×C4C2×H(5,𝔽2)11yescharacteristic
774C2×C4C2×H(5,𝔽2)11yescharacteristic
775C2×C4C2×H(5,𝔽2)11yescharacteristic
776C8—24no—
777C8—42no—
778C8—42no—
779C8—42no—
780C22—24no—
781C22—24no—
782C22—24no—
783C22—24no—
784C22—24no—
785C22—24no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22—42no—
791C22—42no—
792C22—42no—
793C22—42no—
794C22—416no—
795C22—416no—
796C22—82no—
797C22—82no—
798C22—82no—
799C22—82no—
800C22—82no—
801C22—82no—
802C22—82no—
803C22—168no—
804C22#267314yes—
805C22#319014yes—
806C22#320414yes—
807C22#326614yes—
808C22#328214yes—
809C22#329614yes—
810C22#331614yes—
811C22C2×#53411yescharacteristic
812C22C2×D4211yescharacteristic
813C22C2×#54611yescharacteristic
814C22C22×#13511yescharacteristic
815C22C22×#13711yescharacteristic
816C22C2×#57711yescharacteristic
817C22C2×#57711yescharacteristic
818C4—42no—
819C4—42no—
820C4—44no—
821C4—44no—
822C4—42no—
823C4—42no—
824C4—44no—
825C4—82no—
826C4—82no—
827C4—82no—
828C4—82no—
829C4#267314yes—
830C4C2×#53511yescharacteristic
831C4C2×#54011yescharacteristic
832C4C2×#55011yescharacteristic
833C4C2×#56011yescharacteristic
834C2—44no—
835C2—44no—
836C2—162no—
837C2#3071318yesdirect product factor
838C2C2×#267311yescharacteristic
839C2C2×#319011yescharacteristic
840C2C2×#320411yescharacteristic
841C2C2×#326611yescharacteristic
842C2C2×#328211yescharacteristic
843C2C2×#329611yescharacteristic
844C2C2×#331611yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#2540C2
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×#483C2semidirect
2. C22×#465C2semidirect
4. C2×#2417C2semidirect
5. #30713C2direct (N × H)
6. C2×#2042C2semidirect
7. C2×#2034C2semidirect
8. C2×#2015C2semidirect
9. C2×#2001C2semidirect
10. C2×#2001C2semidirect
11. C2×#2000C2semidirect
12. C2×#1927C2semidirect
13. C2×#1919C2semidirect
14. C2×#1892C2semidirect
15. C2×#1874C2semidirect
16. C2×#1869C2semidirect
30. C2×#483C22semidirect
32. C2×#465C22semidirect
49. #2417C22semidirect
62. #2042C22semidirect
63. #2034C22semidirect
64. #2015C22semidirect
65. #2001C22semidirect
66. #2001C22semidirect
67. #2000C22semidirect
68. #1927C22semidirect
69. #1919C22semidirect
70. #1892C22semidirect
71. #1874C22semidirect
72. #1869C22semidirect
168. C2×#106D4semidirect
409. #106C2×D4semidirect
837. C2#30713direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#4832
C22×#4652
C2×#25402
C2×#24172
#307132
C2×#20422
C2×#20342
C2×#20152
C2×#20012
C2×#20002
C2×#19272
C2×#19192
C2×#18922
C2×#18742
C2×#18692