Finite Group Databasebeta

← C2×#30705 #7501601

Subgroups — C2×#30705 #7501601

Order 512.

2932 conjugacy classes of subgroups.

The subgroup lattice has 852 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×#2542C211yesmaximal, characteristic, complemented
4C2×#2416C211yesmaximal, characteristic
5#30705C2116yesmaximal, direct product factor
6C2×#2043C211yesmaximal, characteristic, complemented
7C2×#2035C211yesmaximal, characteristic, complemented
8C2×#2013C211yesmaximal, characteristic, complemented
9C2×#2000C211yesmaximal, characteristic, complemented
10C2×#2000C211yesmaximal, characteristic, complemented
11C2×#2000C211yesmaximal, characteristic, complemented
12C2×#1926C211yesmaximal, characteristic, complemented
13C2×#1919C211yesmaximal, characteristic, complemented
14C2×#1892C211yesmaximal, characteristic, complemented
15C2×#1872C211yesmaximal, characteristic, complemented
16C2×#1869C211yesmaximal, characteristic, complemented
17C23×SD16C2211yescharacteristic
18C23×SD16C2211yescharacteristic
19C24×C8C2211yescharacteristic
20C22×C4⋊Q8C2211yescharacteristic
21C22×C22⋊Q8C2211yescharacteristic
22C22×C22⋊Q8C2211yescharacteristic
23C22×C22⋊Q8C2211yescharacteristic
24C22×C22⋊Q8C2211yescharacteristic
25C22×#121—21no—
26C22×#121C2211yescharacteristic
27C22×#121C2211yescharacteristic
28C22×C4×D4C2211yescharacteristic
29C23×C4⋊C4C2211yescharacteristic
30C2×#483—28no—
31C2×#483C2218yescomplemented
32C2×#465—28no—
33C2×#465C2218yescomplemented
34C22×#106C2211yescharacteristic
35C22×#106C2211yescharacteristic
36C22×#103C2211yescharacteristic
37C22×#103C2211yescharacteristic
38C22×#103C2211yescharacteristic
39C22×#103C2211yescharacteristic
40C22×#103C2211yescharacteristic
41C22×#103C2211yescharacteristic
42C22×#102C2211yescharacteristic
43C22×#102C2211yescharacteristic
44C22×C22⋊C8C2211yescharacteristic
45C22×C22⋊C8C2211yescharacteristic
46C22×C22⋊C8C2211yescharacteristic
47#2542—24no—
48#2542C2218yescomplemented
49#2416—24no—
50#2416C2218yes—
51C2×#399—21no—
52C2×#399—21no—
53C2×#396—21no—
54C2×#394—21no—
55C2×#390—21no—
56C2×#390C2211yescharacteristic
57C2×#389C2211yescharacteristic
58C2×#386—21no—
59C2×#384—21no—
60C2×#380C2211yescharacteristic
61C2×C4×C4⋊C4C2211yescharacteristic
62#2043C2218yescomplemented
63#2035C2218yescomplemented
64#2013C2218yescomplemented
65#2000C2218yescomplemented
66#2000C2218yescomplemented
67#2000C2218yescomplemented
68#1926C2218yescomplemented
69#1919C2218yescomplemented
70#1892C2218yescomplemented
71#1872C2218yescomplemented
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×SD16—24no—
89C22×SD16—42no—
90C22×SD16—42no—
91C22×SD16—42no—
92C22×SD16—42no—
93C22×SD16—42no—
94C22×SD16C2314yes—
95C22×SD16C2314yes—
96C23×C8—24no—
97C23×C8—42no—
98C23×C8—42no—
99C23×C8C2311yescharacteristic
100C23×C8C2311yescharacteristic
101C23×C8C2311yescharacteristic
102C23×C8C2311yescharacteristic
103C23×C8C2314yes—
104C2×C4⋊Q8—22no—
105C2×C4⋊Q8—42no—
106C2×C4⋊Q8—42no—
107C2×C4⋊Q8C2314yes—
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—24no—
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—28no—
125C2×#121—22no—
126C2×#121—22no—
127C2×#121—24no—
128C2×#121—42no—
129C2×#121—42no—
130C2×#121—42no—
131C2×#121—48no—
132C2×#121C2314yes—
133C2×#121C2314yes—
134C2×C4×D4—42no—
135C2×C4×D4—42no—
136C2×C4×D4D414yes—
137C2×C4×D4C2314yes—
138C22×C4⋊C4—24no—
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⋊C4—22no—
147C22×C4⋊C4—21no—
148C22×C4⋊C4—42no—
149C22×C4⋊C4D411yescharacteristic
150C22×C4⋊C4C2311yescharacteristic
151C22×C4⋊C4C2311yescharacteristic
152C22×C4⋊C4C2314yes—
153C22×C4⋊C4C2311yescharacteristic
154C22×C4⋊C4C2311yescharacteristic
155C22×C4⋊C4C2311yescharacteristic
156C22×C22⋊C4—21no—
157C22×C22⋊C4—21no—
158C22×C22⋊C4—21no—
159C22×C22⋊C4—21no—
160C22×C22⋊C4—21no—
161C22×C22⋊C4—21no—
162C22×C22⋊C4—21no—
163C22×C22⋊C4—21no—
164C22×C22⋊C4—21no—
165C22×C22⋊C4D411yescharacteristic
166C22×C22⋊C4D411yescharacteristic
167C22×C42—21no—
168C22×C42C2311yescharacteristic
169#483—232no—
170#465—232no—
171C2×#106—24no—
172C2×#106D418yescomplemented
173C2×#106C2314yes—
174C2×#106C2314yes—
175C2×#103—24no—
176C2×#103—24no—
177C2×#103—24no—
178C2×#103—42no—
179C2×#103—42no—
180C2×#103—42no—
181C2×#103C2314yes—
182C2×#103C2314yes—
183C2×#103C2314yes—
184C2×#103C2314yes—
185C2×#103C2314yes—
186C2×#103C2314yes—
187C2×#102—24no—
188C2×#102—24no—
189C2×#102C2314yes—
190C2×#102C2314yes—
191C2×C22⋊C8—24no—
192C2×C22⋊C8—42no—
193C2×C22⋊C8—42no—
194C2×C22⋊C8C2314yes—
195C2×C22⋊C8C2314yes—
196C2×C22⋊C8C2314yes—
197#399—28no—
198#399—28no—
199#396—28no—
200#394—28no—
201#390—28no—
202#390—22no—
203#390C2314yes—
204#389—22no—
205#389C2314yes—
206#386—28no—
207#384—28no—
208#380—22no—
209#380C2314yes—
210C4×C4⋊C4—22no—
211C4×C4⋊C4C2314yes—
212C2×#95—21no—
213C2×#95—21no—
214C2×#95—21no—
215#340C2314yes—
216#340C2314yes—
217#340C2314yes—
218#340C2314yes—
219#336C2314yes—
220#336C2314yes—
221C25—21no—
222C25C2×D411yescharacteristic
223C25C2×D411yescharacteristic
224C22×Q8—21no—
225C22×Q8—21no—
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×Q8C2412yes—
239C22×Q8C2412yes—
240C22×D4—24no—
241C22×D4—24no—
242C22×D4—22no—
243C22×D4—21no—
244C22×D4—22no—
245C22×D4—22no—
246C22×D4—22no—
247C22×D4—22no—
248C22×D4—22no—
249C22×D4—42no—
250C22×D4—42no—
251C22×D4—44no—
252C22×D4—44no—
253C22×D4—44no—
254C22×D4—44no—
255C22×D4—44no—
256C22×D4—82no—
257C22×D4SD1618yescomplemented
258C22×D4C2×D414yes—
259C22×D4C2412yes—
260C23×C4—21no—
261C23×C4—21no—
262C23×C4—21no—
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—22no—
275C23×C4—21no—
276C23×C4—21no—
277C23×C4—21no—
278C23×C4—21no—
279C23×C4—24no—
280C23×C4—44no—
281C23×C4—44no—
282C23×C4—82no—
283C23×C4C2×D412yes—
284C23×C4C2×D412yes—
285C23×C4C2×D411yescharacteristic
286C23×C4C2×D411yescharacteristic
287C23×C4C2×D411yescharacteristic
288C23×C4C2×D411yescharacteristic
289C23×C4C2412yes—
290C23×C4C2412yes—
291C23×C4C2411yescharacteristic
292C2×SD16—28no—
293C2×SD16—44no—
294C2×SD16—44no—
295C2×SD16—44no—
296C2×SD16—44no—
297C2×SD16—44no—
298C2×SD16—416no—
299C2×SD16—416no—
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—22no—
311C22×C8—28no—
312C22×C8—44no—
313C22×C8—44no—
314C22×C8—416no—
315C22×C8C2×D414yes—
316C22×C8C2412yes—
317C22×C8C2412yes—
318C22×C8C2412yes—
319C22×C8C2412yes—
320C4⋊Q8—44no—
321C4⋊Q8—44no—
322C4⋊Q8—48no—
323C22⋊Q8—28no—
324C22⋊Q8—28no—
325C22⋊Q8—28no—
326C22⋊Q8—28no—
327C22⋊Q8—44no—
328C22⋊Q8—44no—
329C22⋊Q8—44no—
330C22⋊Q8—44no—
331C22⋊Q8—48no—
332C22⋊Q8—48no—
333C22⋊Q8—48no—
334C22⋊Q8—48no—
335#121—28no—
336#121—44no—
337#121—44no—
338#121—44no—
339#121—48no—
340#121—48no—
341#121—432no—
342C4×D4—48no—
343C4×D4—44no—
344C4×D4—44no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
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—28no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—24no—
358C2×C4⋊C4—24no—
359C2×C4⋊C4—24no—
360C2×C4⋊C4—24no—
361C2×C4⋊C4—24no—
362C2×C4⋊C4—24no—
363C2×C4⋊C4—24no—
364C2×C4⋊C4—24no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—44no—
367C2×C4⋊C4—48no—
368C2×C4⋊C4—42no—
369C2×C4⋊C4—44no—
370C2×C4⋊C4—44no—
371C2×C4⋊C4—44no—
372C2×C4⋊C4—44no—
373C2×C4⋊C4—44no—
374C2×C4⋊C4—44no—
375C2×C4⋊C4—44no—
376C2×C4⋊C4—44no—
377C2×C4⋊C4C2×D414yes—
378C2×C4⋊C4C2×D414yes—
379C2×C4⋊C4C2×D414yes—
380C2×C4⋊C4#4114yes—
381C2×C4⋊C4C2412yes—
382C2×C4⋊C4C2412yes—
383C2×C4⋊C4C2412yes—
384C2×C4⋊C4C2412yes—
385C2×C4⋊C4C2412yes—
386C2×C22⋊C4—24no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—24no—
391C2×C22⋊C4—24no—
392C2×C22⋊C4—24no—
393C2×C22⋊C4—24no—
394C2×C22⋊C4—24no—
395C2×C22⋊C4—42no—
396C2×C22⋊C4—42no—
397C2×C22⋊C4—44no—
398C2×C22⋊C4—44no—
399C2×C22⋊C4—44no—
400C2×C22⋊C4—44no—
401C2×C22⋊C4—44no—
402C2×C22⋊C4—44no—
403C2×C22⋊C4—44no—
404C2×C22⋊C4—44no—
405C2×C22⋊C4—82no—
406C2×C22⋊C4C2×D414yes—
407C2×C22⋊C4C2×D414yes—
408C2×C42—22no—
409C2×C42—22no—
410C2×C42—24no—
411C2×C42—44no—
412C2×C42C2×D412yes—
413C2×C42C2412yes—
414#106—28no—
415#106C2×D4116yescomplemented
416#103—28no—
417#103—28no—
418#103—28no—
419#103—44no—
420#103—44no—
421#103—44no—
422#102—28no—
423#102—28no—
424C22⋊C8—28no—
425C22⋊C8—44no—
426C22⋊C8—44no—
427#95—24no—
428#95—24no—
429#95—24no—
430C24—22no—
431C24—22no—
432C24—22no—
433C24—22no—
434C24—22no—
435C24—22no—
436C24—22no—
437C24—22no—
438C24—22no—
439C24—22no—
440C24—22no—
441C24—22no—
442C24—22no—
443C24—42no—
444C24—42no—
445C24—42no—
446C24—42no—
447C24—42no—
448C24—42no—
449C24—42no—
450C24C2×SD1614yes—
451C24C2×SD1614yes—
452C24C22×D412yes—
453C24C22×D412yes—
454C24C22×D411yescharacteristic
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—22no—
466C2×Q8—22no—
467C2×Q8—42no—
468C2×Q8—42no—
469C2×Q8—42no—
470C2×Q8—42no—
471C2×Q8—42no—
472C2×Q8—42no—
473C2×Q8—44no—
474C2×Q8—44no—
475C2×Q8—44no—
476C2×Q8—44no—
477C2×Q8—44no—
478C2×Q8—44no—
479C2×Q8—44no—
480C2×Q8—44no—
481C2×D4—22no—
482C2×D4—22no—
483C2×D4—22no—
484C2×D4—22no—
485C2×D4—22no—
486C2×D4—22no—
487C2×D4—44no—
488C2×D4—416no—
489C2×D4—44no—
490C2×D4—48no—
491C2×D4—48no—
492C2×D4—48no—
493C2×D4—48no—
494C2×D4—48no—
495C2×D4—42no—
496C2×D4—44no—
497C2×D4—44no—
498C2×D4—42no—
499C2×D4—42no—
500C2×D4—44no—
501C2×D4—44no—
502C2×D4—84no—
503C2×D4—816no—
504C2×D4—816no—
505C2×D4C2×SD16116yescomplemented
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—24no—
512C22×C4—22no—
513C22×C4—24no—
514C22×C4—22no—
515C22×C4—24no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—24no—
524C22×C4—24no—
525C22×C4—24no—
526C22×C4—24no—
527C22×C4—24no—
528C22×C4—24no—
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—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—48no—
546C22×C4—42no—
547C22×C4—42no—
548C22×C4—42no—
549C22×C4—42no—
550C22×C4—42no—
551C22×C4—42no—
552C22×C4—44no—
553C22×C4—44no—
554C22×C4—44no—
555C22×C4—44no—
556C22×C4—44no—
557C22×C4—44no—
558C22×C4—44no—
559C22×C4—44no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—42no—
565C22×C4—42no—
566C22×C4—42no—
567C22×C4—42no—
568C22×C4—42no—
569C22×C4—42no—
570C22×C4—48no—
571C22×C4—42no—
572C22×C4—42no—
573C22×C4—84no—
574C22×C4—816no—
575C22×C4C2×SD1614yes—
576C22×C4C22×D412yes—
577C22×C4C22×D412yes—
578C22×C4C22×D412yes—
579C22×C4C22×D412yes—
580C22×C4C22×D411yescharacteristic
581C22×C4C22×D412yes—
582C22×C4C2×#4112yes—
583C22×C4H(5,𝔽2)12yes—
584C22×C4H(5,𝔽2)12yes—
585C22×C4H(5,𝔽2)12yes—
586C22×C4H(5,𝔽2)12yes—
587C22×C4C2511yescharacteristic
588SD16—416no—
589SD16—416no—
590C2×C8—28no—
591C2×C8—22no—
592C2×C8—22no—
593C2×C8—22no—
594C2×C8—22no—
595C2×C8—22no—
596C2×C8—22no—
597C2×C8—22no—
598C2×C8—22no—
599C2×C8—22no—
600C2×C8—22no—
601C2×C8—22no—
602C2×C8—416no—
603C2×C8—44no—
604C2×C8—44no—
605C2×C8—44no—
606C2×C8C22×D414yes—
607C4⋊C4—24no—
608C4⋊C4—24no—
609C4⋊C4—24no—
610C4⋊C4—22no—
611C4⋊C4—22no—
612C4⋊C4—22no—
613C4⋊C4—22no—
614C4⋊C4—22no—
615C4⋊C4—22no—
616C4⋊C4—22no—
617C4⋊C4—44no—
618C4⋊C4—48no—
619C4⋊C4—48no—
620C4⋊C4—48no—
621C4⋊C4—48no—
622C4⋊C4—48no—
623C4⋊C4—48no—
624C4⋊C4—48no—
625C4⋊C4—42no—
626C4⋊C4—42no—
627C4⋊C4—48no—
628C4⋊C4C22×D414yes—
629C4⋊C4C22×D414yes—
630C4⋊C4C2×#4114yes—
631C22⋊C4—44no—
632C22⋊C4—44no—
633C22⋊C4—48no—
634C22⋊C4—48no—
635C22⋊C4—48no—
636C22⋊C4—48no—
637C22⋊C4—48no—
638C22⋊C4—48no—
639C22⋊C4—48no—
640C22⋊C4—48no—
641C22⋊C4—84no—
642C42—24no—
643C42—22no—
644C42—22no—
645C42—48no—
646C23—28no—
647C23—28no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—28no—
655C23—28no—
656C23—28no—
657C23—28no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—44no—
665C23—44no—
666C23—44no—
667C23—44no—
668C23—44no—
669C23—44no—
670C23—44no—
671C23—44no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—84no—
680C23—84no—
681C23—84no—
682C23—84no—
683C23—84no—
684C23—84no—
685C23—84no—
686C23#53412yes—
687C23D4212yes—
688C23#54612yes—
689C23C22×SD1614yes—
690C23C22×SD1614yes—
691C23C22×SD1612yes—
692C23#57512yes—
693C23#57712yes—
694C23#57812yes—
695C23C23×D411yescharacteristic
696Q8—42no—
697Q8—42no—
698Q8—42no—
699Q8—42no—
700Q8—42no—
701Q8—42no—
702Q8—42no—
703Q8—42no—
704Q8—84no—
705Q8—84no—
706D4—416no—
707D4—42no—
708D4—42no—
709D4—42no—
710D4—42no—
711D4—816no—
712D4—816no—
713D4—84no—
714C2×C4—28no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—24no—
721C2×C4—22no—
722C2×C4—24no—
723C2×C4—22no—
724C2×C4—24no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—44no—
730C2×C4—44no—
731C2×C4—44no—
732C2×C4—48no—
733C2×C4—48no—
734C2×C4—48no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—48no—
742C2×C4—48no—
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—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—816no—
764C2×C4—84no—
765C2×C4—84no—
766C2×C4—84no—
767C2×C4—84no—
768C2×C4#53412yes—
769C2×C4#53514yes—
770C2×C4#54014yes—
771C2×C4D4212yes—
772C2×C4#54612yes—
773C2×C4#55014yes—
774C2×C4#56014yes—
775C2×C4C22×SD1614yes—
776C2×C4C23×D411yescharacteristic
777C2×C4C22×#4111yescharacteristic
778C2×C4C2×H(5,𝔽2)11yescharacteristic
779C2×C4C2×H(5,𝔽2)11yescharacteristic
780C2×C4C2×H(5,𝔽2)11yescharacteristic
781C2×C4C2×H(5,𝔽2)11yescharacteristic
782C8—24no—
783C8—42no—
784C8—42no—
785C8—42no—
786C22—24no—
787C22—24no—
788C22—24no—
789C22—24no—
790C22—24no—
791C22—24no—
792C22—42no—
793C22—42no—
794C22—42no—
795C22—42no—
796C22—42no—
797C22—42no—
798C22—42no—
799C22—42no—
800C22—416no—
801C22—416no—
802C22—82no—
803C22—82no—
804C22—82no—
805C22—82no—
806C22—82no—
807C22—82no—
808C22—82no—
809C22—168no—
810C22#267314yes—
811C22#318714yes—
812C22#320114yes—
813C22#326914yes—
814C22D4×SD1614yes—
815C22#329814yes—
816C22#330714yes—
817C22C2×#53411yescharacteristic
818C22C2×D4211yescharacteristic
819C22C2×#54611yescharacteristic
820C22C23×SD1611yescharacteristic
821C22C2×#57511yescharacteristic
822C22C2×#57711yescharacteristic
823C22C2×#57811yescharacteristic
824C4—24no—
825C4—42no—
826C4—44no—
827C4—44no—
828C4—42no—
829C4—42no—
830C4—44no—
831C4—82no—
832C4—82no—
833C4—82no—
834C4—82no—
835C4#267314yes—
836C4C2×#53511yescharacteristic
837C4C2×#54011yescharacteristic
838C4C2×#55011yescharacteristic
839C4C2×#56011yescharacteristic
840C2—44no—
841C2—44no—
842C2—162no—
843C2#3070518yesdirect product factor
844C2C2×#267311yescharacteristic
845C2C2×#318711yescharacteristic
846C2C2×#320111yescharacteristic
847C2C2×#326911yescharacteristic
848C2C2×D4×SD1611yescharacteristic
849C2C2×#329811yescharacteristic
850C2C2×#330711yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#2416C2
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
3. C2×#2542C2semidirect
5. #30705C2direct (N × H)
6. C2×#2043C2semidirect
7. C2×#2035C2semidirect
8. C2×#2013C2semidirect
9. C2×#2000C2semidirect
10. C2×#2000C2semidirect
11. C2×#2000C2semidirect
12. C2×#1926C2semidirect
13. C2×#1919C2semidirect
14. C2×#1892C2semidirect
15. C2×#1872C2semidirect
16. C2×#1869C2semidirect
31. C2×#483C22semidirect
33. C2×#465C22semidirect
48. #2542C22semidirect
62. #2043C22semidirect
63. #2035C22semidirect
64. #2013C22semidirect
65. #2000C22semidirect
66. #2000C22semidirect
67. #2000C22semidirect
68. #1926C22semidirect
69. #1919C22semidirect
70. #1892C22semidirect
71. #1872C22semidirect
72. #1869C22semidirect
172. C2×#106D4semidirect
257. C22×D4SD16semidirect
415. #106C2×D4semidirect
505. C2×D4C2×SD16semidirect
843. C2#30705direct (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×#25422
C2×#24162
#307052
C2×#20432
C2×#20352
C2×#20132
C2×#20002
C2×#19262
C2×#19192
C2×#18922
C2×#18722
C2×#18692