Finite Group Databasebeta

← C2×#24137 #6448581

Subgroups — C2×#24137 #6448581

Order 512.

3808 conjugacy classes of subgroups.

The subgroup lattice has 847 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#552C211yesmaximal, characteristic, complemented
2C22×#478C211yesmaximal, characteristic, complemented
3C22×#440C211yesmaximal, characteristic, complemented
4C2×#2537C211yesmaximal, characteristic
5#24137C2116yesmaximal, direct product factor
6C2×#2036C211yesmaximal, characteristic, complemented
7C2×#2035C211yesmaximal, characteristic, complemented
8C2×#2000C211yesmaximal, characteristic, complemented
9C2×#2000C211yesmaximal, characteristic, complemented
10C2×#1992C211yesmaximal, characteristic, complemented
11C2×#1955C211yesmaximal, characteristic, complemented
12C2×#1875C211yesmaximal, characteristic, complemented
13C2×#1874C211yesmaximal, characteristic, complemented
14C2×#1854C211yesmaximal, characteristic, complemented
15C2×#1852C211yesmaximal, characteristic, complemented
16C2×#1803C211yesmaximal, characteristic, complemented
17C23×SD16C2211yescharacteristic
18C2×#552—28no—
19C2×#552—28no—
20C2×#552—24no—
21C2×#552C2218yescomplemented
22C22×#126—21no—
23C22×#125—21no—
24C22×#125C2211yescharacteristic
25C22×#123—21no—
26C22×C22⋊Q8C2211yescharacteristic
27C22×C22⋊Q8C2211yescharacteristic
28C22×#121—21no—
29C22×#121C2211yescharacteristic
30C22×#121C2211yescharacteristic
31C22×C4×Q8C2211yescharacteristic
32C22×C4×D4C2211yescharacteristic
33C22×C4×D4C2211yescharacteristic
34C22×#117—21no—
35C22×#117C2211yescharacteristic
36C23×C4⋊C4C2211yescharacteristic
37C2×#478—28no—
38C2×#478C2218yescomplemented
39C2×#440—28no—
40C2×#440C2218yescomplemented
41C22×#107C2211yescharacteristic
42C22×#107C2211yescharacteristic
43C22×#106C2211yescharacteristic
44C22×C4⋊C8C2211yescharacteristic
45C22×#103C2211yescharacteristic
46C22×#103C2211yescharacteristic
47C22×#103C2211yescharacteristic
48C22×#102C2211yescharacteristic
49C22×#102C2211yescharacteristic
50C22×#102C2211yescharacteristic
51C22×C22⋊C8C2211yescharacteristic
52C22×C22⋊C8C2211yescharacteristic
53C22×C22⋊C8C2211yescharacteristic
54C22×C22⋊C8C2211yescharacteristic
55C22×#97C2211yescharacteristic
56#2537—24no—
57#2537C2218yes—
58C2×#394—21no—
59C2×#394—21no—
60C2×#384C2211yescharacteristic
61C2×#380—21no—
62C2×#380C2211yescharacteristic
63C2×#380C2211yescharacteristic
64#2036C2218yescomplemented
65#2035C2218yescomplemented
66#2000C2218yescomplemented
67#2000C2218yescomplemented
68#1992C2218yescomplemented
69#1955C2218yescomplemented
70#1875C2218yescomplemented
71#1874C2218yescomplemented
72#1854C2218yescomplemented
73#1852C2218yescomplemented
74#1803C2218yescomplemented
75C2×#340C2211yescharacteristic
76C2×#340C2211yescharacteristic
77C2×#340C2211yescharacteristic
78C2×#340C2211yescharacteristic
79C2×#340C2211yescharacteristic
80C2×#340C2211yescharacteristic
81C23×Q8C2311yescharacteristic
82C23×D4—21no—
83C23×D4—21no—
84C23×D4D411yescharacteristic
85C23×D4C2311yescharacteristic
86C24×C4—21no—
87C24×C4—21no—
88C24×C4C2311yescharacteristic
89C24×C4C2311yescharacteristic
90C22×SD16—24no—
91C22×SD16—24no—
92C22×SD16—24no—
93C22×SD16C2314yes—
94C23×C8C2311yescharacteristic
95C23×C8C2311yescharacteristic
96C23×C8C2311yescharacteristic
97C23×C8C2311yescharacteristic
98#552—264no—
99#552—232no—
100#552—232no—
101C2×#126—216no—
102C2×#126—28no—
103C2×#125—216no—
104C2×#125—28no—
105C2×#125—22no—
106C2×#125—24no—
107C2×#125D418yescomplemented
108C2×#125C2314yes—
109C2×#123—216no—
110C2×#123—28no—
111C2×C22⋊Q8—24no—
112C2×C22⋊Q8—24no—
113C2×C22⋊Q8—22no—
114C2×C22⋊Q8—22no—
115C2×C22⋊Q8—24no—
116C2×C22⋊Q8—24no—
117C2×C22⋊Q8C2314yes—
118C2×C22⋊Q8C2314yes—
119C2×#121—28no—
120C2×#121—22no—
121C2×#121—22no—
122C2×#121—24no—
123C2×#121—24no—
124C2×#121—42no—
125C2×#121—42no—
126C2×#121—48no—
127C2×#121C2314yes—
128C2×#121C2314yes—
129C2×C4×Q8—24no—
130C2×C4×Q8—22no—
131C2×C4×Q8D418yescomplemented
132C2×C4×Q8C2314yes—
133C2×C4×D4—24no—
134C2×C4×D4—24no—
135C2×C4×D4—22no—
136C2×C4×D4—24no—
137C2×C4×D4—24no—
138C2×C4×D4D414yes—
139C2×C4×D4C2314yes—
140C2×C4×D4C2314yes—
141C2×#117—216no—
142C2×#117—22no—
143C2×#117—24no—
144C2×#117—24no—
145C2×#117—28no—
146C2×#117C2314yes—
147C22×C4⋊C4—21no—
148C22×C4⋊C4—22no—
149C22×C4⋊C4—21no—
150C22×C4⋊C4—21no—
151C22×C4⋊C4—21no—
152C22×C4⋊C4—21no—
153C22×C4⋊C4—21no—
154C22×C4⋊C4—24no—
155C22×C4⋊C4—24no—
156C22×C4⋊C4—21no—
157C22×C4⋊C4—21no—
158C22×C4⋊C4D411yescharacteristic
159C22×C4⋊C4C2314yes—
160C22×C4⋊C4C2311yescharacteristic
161C22×C4⋊C4C2311yescharacteristic
162C22×C4⋊C4C2311yescharacteristic
163C22×C4⋊C4C2311yescharacteristic
164C22×C4⋊C4C2311yescharacteristic
165C22×C4⋊C4C2311yescharacteristic
166C22×C22⋊C4—21no—
167C22×C22⋊C4—21no—
168C22×C22⋊C4—21no—
169C22×C22⋊C4—21no—
170C22×C22⋊C4—21no—
171C22×C22⋊C4—21no—
172C22×C22⋊C4—21no—
173C22×C22⋊C4—21no—
174C22×C22⋊C4D411yescharacteristic
175C22×C22⋊C4D411yescharacteristic
176C22×C42—21no—
177C22×C42—21no—
178C22×C42C2311yescharacteristic
179#478—232no—
180#440—232no—
181C2×#107—24no—
182C2×#107—24no—
183C2×#107C2314yes—
184C2×#107C2314yes—
185C2×#106—24no—
186C2×#106C2314yes—
187C2×C4⋊C8—24no—
188C2×C4⋊C8C2314yes—
189C2×#103—24no—
190C2×#103—42no—
191C2×#103—42no—
192C2×#103C2314yes—
193C2×#103C2314yes—
194C2×#103C2314yes—
195C2×#102—24no—
196C2×#102—24no—
197C2×#102—24no—
198C2×#102C2314yes—
199C2×#102C2314yes—
200C2×#102C2314yes—
201C2×C22⋊C8—24no—
202C2×C22⋊C8—24no—
203C2×C22⋊C8—42no—
204C2×C22⋊C8—42no—
205C2×C22⋊C8C2314yes—
206C2×C22⋊C8C2314yes—
207C2×C22⋊C8C2314yes—
208C2×C22⋊C8C2314yes—
209C2×#97—24no—
210C2×#97C2314yes—
211#394—28no—
212#394—28no—
213#384—22no—
214#384C2314yes—
215#380—22no—
216#380—22no—
217#380—28no—
218#380C2314yes—
219#380C2314yes—
220C2×#95—21no—
221C2×#95—21no—
222#340C2314yes—
223#340C2314yes—
224#340C2314yes—
225#340C2314yes—
226#340C2314yes—
227#340C2314yes—
228C25—21no—
229C25C2×D411yescharacteristic
230C25C2×D411yescharacteristic
231C22×Q8—22no—
232C22×Q8—21no—
233C22×Q8—22no—
234C22×Q8—22no—
235C22×Q8—22no—
236C22×Q8—22no—
237C22×Q8C2×D414yes—
238C22×Q8C2412yes—
239C22×D4—24no—
240C22×D4—24no—
241C22×D4—24no—
242C22×D4—24no—
243C22×D4—22no—
244C22×D4—22no—
245C22×D4—21no—
246C22×D4—22no—
247C22×D4—22no—
248C22×D4—22no—
249C22×D4—42no—
250C22×D4—44no—
251C22×D4—44no—
252C22×D4—44no—
253C22×D4—44no—
254C22×D4—82no—
255C22×D4—82no—
256C22×D4C2×D414yes—
257C22×D4#4114yes—
258C22×D4C2412yes—
259C23×C4—28no—
260C23×C4—24no—
261C23×C4—21no—
262C23×C4—21no—
263C23×C4—21no—
264C23×C4—21no—
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—22no—
276C23×C4—22no—
277C23×C4—21no—
278C23×C4—21no—
279C23×C4—21no—
280C23×C4—24no—
281C23×C4—44no—
282C23×C4—44no—
283C23×C4—44no—
284C23×C4—44no—
285C23×C4—44no—
286C23×C4C2×D412yes—
287C23×C4C2×D412yes—
288C23×C4C2×D411yescharacteristic
289C23×C4C2×D411yescharacteristic
290C23×C4C2×D411yescharacteristic
291C23×C4C2×D411yescharacteristic
292C23×C4C2412yes—
293C23×C4C2412yes—
294C23×C4C2411yescharacteristic
295C2×SD16—232no—
296C2×SD16—28no—
297C2×SD16—28no—
298C2×SD16—28no—
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#4114yes—
311C22×C8C2412yes—
312C22×C8C2412yes—
313C22×C8C2412yes—
314C22×C8C2412yes—
315#126—264no—
316#125—264no—
317#125—216no—
318#125—28no—
319#125C2×D4116yescomplemented
320#123—264no—
321C22⋊Q8—216no—
322C22⋊Q8—216no—
323C22⋊Q8—28no—
324C22⋊Q8—28no—
325C22⋊Q8—28no—
326C22⋊Q8—28no—
327#121—28no—
328#121—28no—
329#121—44no—
330#121—44no—
331#121—48no—
332#121—48no—
333#121—432no—
334C4×Q8—216no—
335C4×Q8—28no—
336C4×Q8C2×D4116yescomplemented
337C4×D4—216no—
338C4×D4—28no—
339C4×D4—28no—
340C4×D4—28no—
341C4×D4—28no—
342C4×D4—48no—
343#117—216no—
344#117—264no—
345#117—28no—
346#117—28no—
347C2×C4⋊C4—28no—
348C2×C4⋊C4—216no—
349C2×C4⋊C4—28no—
350C2×C4⋊C4—28no—
351C2×C4⋊C4—28no—
352C2×C4⋊C4—28no—
353C2×C4⋊C4—28no—
354C2×C4⋊C4—24no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—22no—
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—22no—
367C2×C4⋊C4—28no—
368C2×C4⋊C4—28no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—24no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—24no—
380C2×C4⋊C4—44no—
381C2×C4⋊C4—82no—
382C2×C4⋊C4C2×D414yes—
383C2×C4⋊C4C2×D414yes—
384C2×C4⋊C4C2×D414yes—
385C2×C4⋊C4C2×D414yes—
386C2×C4⋊C4C2412yes—
387C2×C4⋊C4C2412yes—
388C2×C4⋊C4C2412yes—
389C2×C4⋊C4C2412yes—
390C2×C4⋊C4C2412yes—
391C2×C4⋊C4C2412yes—
392C2×C22⋊C4—28no—
393C2×C22⋊C4—28no—
394C2×C22⋊C4—28no—
395C2×C22⋊C4—24no—
396C2×C22⋊C4—24no—
397C2×C22⋊C4—24no—
398C2×C22⋊C4—24no—
399C2×C22⋊C4—24no—
400C2×C22⋊C4—24no—
401C2×C22⋊C4—24no—
402C2×C22⋊C4—24no—
403C2×C22⋊C4—24no—
404C2×C22⋊C4—24no—
405C2×C22⋊C4—44no—
406C2×C22⋊C4—44no—
407C2×C22⋊C4—44no—
408C2×C22⋊C4—44no—
409C2×C22⋊C4—44no—
410C2×C22⋊C4C2×D414yes—
411C2×C22⋊C4C2×D414yes—
412C2×C42—28no—
413C2×C42—28no—
414C2×C42—24no—
415C2×C42—24no—
416C2×C42C2×D412yes—
417C2×C42C2×D414yes—
418C2×C42C2×D414yes—
419C2×C42C2412yes—
420#107—28no—
421#107—28no—
422#106—28no—
423C4⋊C8—28no—
424#103—28no—
425#103—44no—
426#103—44no—
427#102—28no—
428#102—28no—
429#102—28no—
430C22⋊C8—28no—
431C22⋊C8—28no—
432C22⋊C8—44no—
433C22⋊C8—44no—
434#97—28no—
435#95—24no—
436#95—24no—
437C24—22no—
438C24—22no—
439C24—22no—
440C24—22no—
441C24—22no—
442C24—22no—
443C24—22no—
444C24—24no—
445C24—22no—
446C24—22no—
447C24—22no—
448C24—22no—
449C24—22no—
450C24—22no—
451C24—22no—
452C24—42no—
453C24—42no—
454C24—42no—
455C24—42no—
456C24—42no—
457C24—42no—
458C24AGL(1,ℤ/8)14yes—
459C24C22×D412yes—
460C24C22×D412yes—
461C24C22×D411yescharacteristic
462C2×Q8—24no—
463C2×Q8—22no—
464C2×Q8—28no—
465C2×Q8—28no—
466C2×Q8—22no—
467C2×Q8—22no—
468C2×Q8—22no—
469C2×Q8—22no—
470C2×Q8—42no—
471C2×Q8—42no—
472C2×Q8—44no—
473C2×Q8—44no—
474C2×Q8C22×D414yes—
475C2×D4—28no—
476C2×D4—28no—
477C2×D4—28no—
478C2×D4—24no—
479C2×D4—28no—
480C2×D4—22no—
481C2×D4—22no—
482C2×D4—22no—
483C2×D4—22no—
484C2×D4—22no—
485C2×D4—44no—
486C2×D4—416no—
487C2×D4—48no—
488C2×D4—48no—
489C2×D4—48no—
490C2×D4—48no—
491C2×D4—42no—
492C2×D4—44no—
493C2×D4—42no—
494C2×D4—44no—
495C2×D4—84no—
496C2×D4—84no—
497C2×D4—816no—
498C2×D4—816no—
499C2×D4C2×#4114yes—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—216no—
505C22×C4—22no—
506C22×C4—24no—
507C22×C4—24no—
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—24no—
520C22×C4—24no—
521C22×C4—24no—
522C22×C4—24no—
523C22×C4—24no—
524C22×C4—24no—
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—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—48no—
541C22×C4—48no—
542C22×C4—432no—
543C22×C4—48no—
544C22×C4—42no—
545C22×C4—42no—
546C22×C4—48no—
547C22×C4—42no—
548C22×C4—42no—
549C22×C4—42no—
550C22×C4—42no—
551C22×C4—42no—
552C22×C4—42no—
553C22×C4—44no—
554C22×C4—44no—
555C22×C4—44no—
556C22×C4—44no—
557C22×C4—44no—
558C22×C4—44no—
559C22×C4—44no—
560C22×C4—44no—
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—816no—
572C22×C4#12014yes—
573C22×C4#12014yes—
574C22×C4C22×D412yes—
575C22×C4C22×D412yes—
576C22×C4C22×D412yes—
577C22×C4C22×D412yes—
578C22×C4C22×D411yescharacteristic
579C22×C4C22×D412yes—
580C22×C4C22×D412yes—
581C22×C4C2×#4112yes—
582C22×C4C2×#4112yes—
583C22×C4H(5,𝔽2)12yes—
584C22×C42−1+412yes—
585C22×C4C2511yescharacteristic
586SD16—232no—
587C2×C8—28no—
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—22no—
599C2×C8—44no—
600C2×C8—44no—
601C2×C8—44no—
602C2×C8C2×#4114yes—
603C4⋊C4—216no—
604C4⋊C4—216no—
605C4⋊C4—216no—
606C4⋊C4—24no—
607C4⋊C4—24no—
608C4⋊C4—216no—
609C4⋊C4—216no—
610C4⋊C4—216no—
611C4⋊C4—24no—
612C4⋊C4—28no—
613C4⋊C4—22no—
614C4⋊C4—22no—
615C4⋊C4—22no—
616C4⋊C4—22no—
617C4⋊C4—22no—
618C4⋊C4—22no—
619C4⋊C4—22no—
620C4⋊C4—22no—
621C4⋊C4—22no—
622C4⋊C4—48no—
623C4⋊C4—42no—
624C4⋊C4—42no—
625C4⋊C4—42no—
626C4⋊C4—84no—
627C4⋊C4C22×D414yes—
628C4⋊C4C22×D414yes—
629C4⋊C4C22×D414yes—
630C22⋊C4—216no—
631C22⋊C4—216no—
632C22⋊C4—216no—
633C22⋊C4—28no—
634C22⋊C4—28no—
635C22⋊C4—48no—
636C22⋊C4—48no—
637C22⋊C4—48no—
638C22⋊C4—48no—
639C22⋊C4—48no—
640C42—216no—
641C42—216no—
642C42#12018yes—
643C42C22×D414yes—
644C42C22×D414yes—
645C23—28no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—28no—
650C23—28no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—24no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—44no—
663C23—44no—
664C23—44no—
665C23—44no—
666C23—44no—
667C23—44no—
668C23—44no—
669C23—48no—
670C23—42no—
671C23—42no—
672C23—44no—
673C23—44no—
674C23—44no—
675C23—48no—
676C23—44no—
677C23—48no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—84no—
683C23—84no—
684C23—84no—
685C23—84no—
686C23C2×#12012yes—
687C23#54612yes—
688C23#54712yes—
689C23C2×AGL(1,ℤ/8)14yes—
690C23C2×AGL(1,ℤ/8)12yes—
691C23#57512yes—
692C23#57712yes—
693C23#57812yes—
694C23C23×D411yescharacteristic
695Q8—24no—
696Q8—24no—
697Q8—48no—
698Q8—42no—
699Q8—42no—
700D4—24no—
701D4—24no—
702D4—416no—
703D4—48no—
704D4—42no—
705D4—42no—
706D4—816no—
707D4—816no—
708C2×C4—28no—
709C2×C4—28no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—24no—
716C2×C4—24no—
717C2×C4—24no—
718C2×C4—22no—
719C2×C4—24no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—432no—
725C2×C4—44no—
726C2×C4—44no—
727C2×C4—48no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—48no—
731C2×C4—48no—
732C2×C4—48no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—48no—
740C2×C4—48no—
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×C4C2×#12014yes—
763C2×C4C2×#12014yes—
764C2×C4C2×#12012yes—
765C2×C4#52514yes—
766C2×C4#53714yes—
767C2×C4#54612yes—
768C2×C4#54712yes—
769C2×C4#54814yes—
770C2×C4#55014yes—
771C2×C4C23×D411yescharacteristic
772C2×C4C23×D411yescharacteristic
773C2×C4C22×#4111yescharacteristic
774C2×C4C22×#4111yescharacteristic
775C2×C4C2×H(5,𝔽2)11yescharacteristic
776C2×C4C2×2−1+411yescharacteristic
777C8—24no—
778C8—42no—
779C8—42no—
780C8—42no—
781C22—24no—
782C22—24no—
783C22—24no—
784C22—42no—
785C22—416no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22—42no—
791C22—42no—
792C22—44no—
793C22—42no—
794C22—42no—
795C22—44no—
796C22—42no—
797C22—42no—
798C22—44no—
799C22—82no—
800C22—82no—
801C22—88no—
802C22—816no—
803C22—82no—
804C22—82no—
805C22#240714yes—
806C22#300614yes—
807C22#301314yes—
808C22#331014yes—
809C22#331514yes—
810C22#334314yes—
811C22#334814yes—
812C22C22×#12011yescharacteristic
813C22C2×#54611yescharacteristic
814C22C2×#54711yescharacteristic
815C22C22×AGL(1,ℤ/8)11yescharacteristic
816C22C2×#57511yescharacteristic
817C22C2×#57711yescharacteristic
818C22C2×#57811yescharacteristic
819C4—24no—
820C4—24no—
821C4—42no—
822C4—42no—
823C4—44no—
824C4—44no—
825C4—44no—
826C4—44no—
827C4—82no—
828C4—82no—
829C4—82no—
830C4#240714yes—
831C4C2×#52511yescharacteristic
832C4C2×#53711yescharacteristic
833C4C2×#54811yescharacteristic
834C4C2×#55011yescharacteristic
835C2—44no—
836C2—82no—
837C2—84no—
838C2#2413718yesdirect product factor
839C2C2×#240711yescharacteristic
840C2C2×#300611yescharacteristic
841C2C2×#301311yescharacteristic
842C2C2×#331011yescharacteristic
843C2C2×#331511yescharacteristic
844C2C2×#334311yescharacteristic
845C2C2×#334811yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#2537C2
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×#552C2semidirect
2. C22×#478C2semidirect
3. C22×#440C2semidirect
5. #24137C2direct (N × H)
6. C2×#2036C2semidirect
7. C2×#2035C2semidirect
8. C2×#2000C2semidirect
9. C2×#2000C2semidirect
10. C2×#1992C2semidirect
11. C2×#1955C2semidirect
12. C2×#1875C2semidirect
13. C2×#1874C2semidirect
14. C2×#1854C2semidirect
15. C2×#1852C2semidirect
16. C2×#1803C2semidirect
21. C2×#552C22semidirect
38. C2×#478C22semidirect
40. C2×#440C22semidirect
64. #2036C22semidirect
65. #2035C22semidirect
66. #2000C22semidirect
67. #2000C22semidirect
68. #1992C22semidirect
69. #1955C22semidirect
70. #1875C22semidirect
71. #1874C22semidirect
72. #1854C22semidirect
73. #1852C22semidirect
74. #1803C22semidirect
107. C2×#125D4semidirect
131. C2×C4×Q8D4semidirect
319. #125C2×D4semidirect
336. C4×Q8C2×D4semidirect
838. C2#24137direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#5522
C22×#4782
C22×#4402
C2×#25372
#241372
C2×#20362
C2×#20352
C2×#20002
C2×#19922
C2×#19552
C2×#18752
C2×#18742
C2×#18542
C2×#18522
C2×#18032