Finite Group Databasebeta

← C2×#25389 #6444336

Subgroups — C2×#25389 #6444336

Order 512.

3172 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#467C211yesmaximal, characteristic, complemented
2C22×#465C211yesmaximal, characteristic, complemented
3C22×#464C211yesmaximal, characteristic, complemented
4C22×C8×D4C211yesmaximal, characteristic, complemented
5C2×#2536C211yesmaximal, characteristic, complemented
6C2×#2540C211yesmaximal, characteristic
7#25389C2116yesmaximal, direct product factor
8C2×#2035C211yesmaximal, characteristic, complemented
9C2×#2033C211yesmaximal, characteristic, complemented
10C2×#2001C211yesmaximal, characteristic, complemented
11C2×#2000C211yesmaximal, characteristic, complemented
12C2×#1958C211yesmaximal, characteristic, complemented
13C2×#1949C211yesmaximal, characteristic, complemented
14C2×#1893C211yesmaximal, characteristic, complemented
15C2×#1892C211yesmaximal, characteristic, complemented
16C2×C4×#103C211yesmaximal, characteristic, complemented
17C23×Q16C2211yescharacteristic
18C23×SD16C2211yescharacteristic
19C24×C8C2211yescharacteristic
20C24×C8C2211yescharacteristic
21C22×#124C2211yescharacteristic
22C22×C22⋊Q8C2211yescharacteristic
23C22×C22⋊Q8C2211yescharacteristic
24C22×C22⋊Q8C2211yescharacteristic
25C22×C22⋊Q8C2211yescharacteristic
26C22×#121C2211yescharacteristic
27C22×#121C2211yescharacteristic
28C22×C4×Q8C2211yescharacteristic
29C22×C4×D4C2211yescharacteristic
30C2×#467—28no—
31C2×#467C2218yescomplemented
32C2×#465—28no—
33C2×#465C2218yescomplemented
34C2×#464—28no—
35C2×#464C2218yescomplemented
36C2×C8×D4—28no—
37C2×C8×D4C2218yescomplemented
38C22×#107C2211yescharacteristic
39C22×#106C2211yescharacteristic
40C22×C4⋊C8C2211yescharacteristic
41C22×#103C2211yescharacteristic
42C22×#103C2211yescharacteristic
43C22×#103C2211yescharacteristic
44C22×#103C2211yescharacteristic
45C22×#103C2211yescharacteristic
46C22×#102C2211yescharacteristic
47C22×#102C2211yescharacteristic
48C22×#102C2211yescharacteristic
49C22×C22⋊C8C2211yescharacteristic
50C22×C22⋊C8C2211yescharacteristic
51C22×C4×C8C2211yescharacteristic
52#2540—24no—
53#2540C2218yes—
54#2536—24no—
55#2536C2218yescomplemented
56C2×#399—21no—
57C2×#398—21no—
58C2×#394—21no—
59C2×#392—21no—
60C2×#390—21no—
61C2×#390—21no—
62C2×#388—21no—
63C2×#388—21no—
64C2×#382C2211yescharacteristic
65C2×#380C2211yescharacteristic
66C2×#380C2211yescharacteristic
67C2×C4×C4⋊C4C2211yescharacteristic
68#2035C2218yescomplemented
69#2033C2218yescomplemented
70#2001C2218yescomplemented
71#2000C2218yescomplemented
72#1958C2218yescomplemented
73#1949C2218yescomplemented
74#1893C2218yescomplemented
75#1892C2218yescomplemented
76C4×#103C2218yescomplemented
77C2×#340C2211yescharacteristic
78C2×#340C2211yescharacteristic
79C2×#340C2211yescharacteristic
80C2×#340C2211yescharacteristic
81C23×Q8C2311yescharacteristic
82C23×Q8C2311yescharacteristic
83C23×D4—21no—
84C23×D4—21no—
85C23×D4D411yescharacteristic
86C23×D4C2311yescharacteristic
87C24×C4C2311yescharacteristic
88C24×C4C2311yescharacteristic
89C22×Q16—24no—
90C22×Q16—24no—
91C22×Q16—42no—
92C22×Q16C2314yes—
93C22×SD16—24no—
94C22×SD16—24no—
95C22×SD16—42no—
96C22×SD16C2314yes—
97C23×C8—24no—
98C23×C8—24no—
99C23×C8—24no—
100C23×C8—24no—
101C23×C8—42no—
102C23×C8—42no—
103C23×C8C2311yescharacteristic
104C23×C8C2314yes—
105C23×C8C2314yes—
106C23×C8C2311yescharacteristic
107C23×C8C2311yescharacteristic
108C23×C8C2311yescharacteristic
109C2×#124—22no—
110C2×#124—24no—
111C2×#124—24no—
112C2×#124C2314yes—
113C2×C22⋊Q8—22no—
114C2×C22⋊Q8—22no—
115C2×C22⋊Q8—22no—
116C2×C22⋊Q8—22no—
117C2×C22⋊Q8—24no—
118C2×C22⋊Q8—24no—
119C2×C22⋊Q8—24no—
120C2×C22⋊Q8—24no—
121C2×C22⋊Q8—42no—
122C2×C22⋊Q8—42no—
123C2×C22⋊Q8—42no—
124C2×C22⋊Q8—42no—
125C2×C22⋊Q8C2314yes—
126C2×C22⋊Q8C2314yes—
127C2×C22⋊Q8C2314yes—
128C2×C22⋊Q8C2314yes—
129C2×#121—22no—
130C2×#121—22no—
131C2×#121—24no—
132C2×#121—24no—
133C2×#121—42no—
134C2×#121—42no—
135C2×#121C2314yes—
136C2×#121C2314yes—
137C2×C4×Q8—22no—
138C2×C4×Q8—24no—
139C2×C4×Q8—24no—
140C2×C4×Q8C2314yes—
141C2×C4×D4—24no—
142C2×C4×D4—24no—
143C2×C4×D4D414yes—
144C2×C4×D4C2314yes—
145C22×C4⋊C4—21no—
146C22×C4⋊C4—21no—
147C22×C4⋊C4—21no—
148C22×C4⋊C4—21no—
149C22×C4⋊C4—21no—
150C22×C4⋊C4D411yescharacteristic
151C22×C4⋊C4C2311yescharacteristic
152C22×C4⋊C4C2311yescharacteristic
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⋊C4—21no—
166C22×C22⋊C4D411yescharacteristic
167C22×C22⋊C4D411yescharacteristic
168C22×C42—21no—
169C22×C42—21no—
170C22×C42C2311yescharacteristic
171#467—232no—
172#465—232no—
173#464—232no—
174C8×D4—232no—
175C2×#107—24no—
176C2×#107C2314yes—
177C2×#106—24no—
178C2×#106C2314yes—
179C2×C4⋊C8D418yescomplemented
180C2×C4⋊C8C2314yes—
181C2×#103—24no—
182C2×#103—24no—
183C2×#103—24no—
184C2×#103—42no—
185C2×#103D418yescomplemented
186C2×#103C2314yes—
187C2×#103C2314yes—
188C2×#103C2314yes—
189C2×#103C2314yes—
190C2×#103C2314yes—
191C2×#102—24no—
192C2×#102—24no—
193C2×#102—42no—
194C2×#102C2314yes—
195C2×#102C2314yes—
196C2×#102C2314yes—
197C2×C22⋊C8—24no—
198C2×C22⋊C8—24no—
199C2×C22⋊C8C2314yes—
200C2×C22⋊C8C2314yes—
201C2×C4×C8—24no—
202C2×C4×C8C2314yes—
203#399—28no—
204#398—28no—
205#394—28no—
206#392—28no—
207#390—28no—
208#390—28no—
209#388—28no—
210#388—28no—
211#382—22no—
212#382C2314yes—
213#380—22no—
214#380—22no—
215#380C2314yes—
216#380C2314yes—
217C4×C4⋊C4—22no—
218C4×C4⋊C4C2314yes—
219C2×#95—21no—
220C2×#95—21no—
221C2×#95—21no—
222C2×#95—21no—
223C2×#95—21no—
224#340C2314yes—
225#340C2314yes—
226#340C2314yes—
227#340C2314yes—
228C25—21no—
229C25C2×D411yescharacteristic
230C25C2×D411yescharacteristic
231C22×Q8—21no—
232C22×Q8—21no—
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—22no—
244C22×Q8C2×D414yes—
245C22×Q8C2412yes—
246C22×Q8C2412yes—
247C22×D4—24no—
248C22×D4—24no—
249C22×D4—24no—
250C22×D4—24no—
251C22×D4—24no—
252C22×D4—22no—
253C22×D4—22no—
254C22×D4—21no—
255C22×D4—22no—
256C22×D4—22no—
257C22×D4—22no—
258C22×D4—22no—
259C22×D4—44no—
260C22×D4—44no—
261C22×D4—44no—
262C22×D4—44no—
263C22×D4—82no—
264C22×D4—82no—
265C22×D4C2×D414yes—
266C22×D4C2412yes—
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—21no—
283C23×C4—21no—
284C23×C4—21no—
285C23×C4—21no—
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×Q16—28no—
296C2×Q16—28no—
297C2×Q16—44no—
298C2×Q16—416no—
299C2×SD16—28no—
300C2×SD16—28no—
301C2×SD16—44no—
302C2×SD16—416no—
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—22no—
312C22×C8—28no—
313C22×C8—28no—
314C22×C8—28no—
315C22×C8—28no—
316C22×C8—44no—
317C22×C8—44no—
318C22×C8—416no—
319C22×C8—416no—
320C22×C8C2×D414yes—
321C22×C8C2×D414yes—
322C22×C8C2×D414yes—
323C22×C8C2412yes—
324C22×C8C2412yes—
325C22×C8C2412yes—
326C22×C8C2412yes—
327#124—28no—
328#124—28no—
329#124—48no—
330C22⋊Q8—28no—
331C22⋊Q8—28no—
332C22⋊Q8—28no—
333C22⋊Q8—28no—
334C22⋊Q8—44no—
335C22⋊Q8—44no—
336C22⋊Q8—44no—
337C22⋊Q8—44no—
338C22⋊Q8—48no—
339C22⋊Q8—48no—
340C22⋊Q8—48no—
341C22⋊Q8—48no—
342#121—28no—
343#121—28no—
344#121—44no—
345#121—44no—
346#121—48no—
347#121—48no—
348C4×Q8—28no—
349C4×Q8—28no—
350C4×Q8—48no—
351C4×D4—216no—
352C4×D4—28no—
353C4×D4—28no—
354C2×C4⋊C4—24no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—24no—
366C2×C4⋊C4—24no—
367C2×C4⋊C4—24no—
368C2×C4⋊C4—24no—
369C2×C4⋊C4—24no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—44no—
374C2×C4⋊C4—44no—
375C2×C4⋊C4—44no—
376C2×C4⋊C4—44no—
377C2×C4⋊C4—44no—
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—24no—
396C2×C22⋊C4—24no—
397C2×C22⋊C4—24no—
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—44no—
406C2×C22⋊C4—44no—
407C2×C22⋊C4—44no—
408C2×C22⋊C4C2×D414yes—
409C2×C22⋊C4C2×D414yes—
410C2×C42—24no—
411C2×C42—24no—
412C2×C42—44no—
413C2×C42—82no—
414C2×C42C2×D412yes—
415C2×C42C2×D414yes—
416C2×C42#4114yes—
417C2×C42C2412yes—
418#107—28no—
419#106—28no—
420C4⋊C8C2×D4116yescomplemented
421#103—28no—
422#103—28no—
423#103—28no—
424#103—44no—
425#103C2×D4116yescomplemented
426#102—28no—
427#102—28no—
428#102—44no—
429C22⋊C8—28no—
430C22⋊C8—28no—
431C4×C8—28no—
432#95—24no—
433#95—24no—
434#95—24no—
435#95—24no—
436#95—24no—
437C24—22no—
438C24—22no—
439C24—22no—
440C24—22no—
441C24—22no—
442C24—22no—
443C24—22no—
444C24—22no—
445C24—22no—
446C24—22no—
447C24—22no—
448C24—22no—
449C24—22no—
450C24—42no—
451C24—42no—
452C24—42no—
453C24—42no—
454C24—42no—
455C24—42no—
456C24—42no—
457C24#13514yes—
458C24#13514yes—
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—22no—
471C2×Q8—22no—
472C2×Q8—22no—
473C2×Q8—22no—
474C2×Q8—22no—
475C2×Q8—22no—
476C2×Q8—42no—
477C2×Q8—42no—
478C2×Q8—44no—
479C2×Q8—42no—
480C2×Q8—42no—
481C2×Q8—42no—
482C2×Q8—44no—
483C2×Q8—44no—
484C2×Q8—44no—
485C2×Q8—44no—
486C2×Q8—44no—
487C2×Q8C22×D414yes—
488C2×D4—232no—
489C2×D4—28no—
490C2×D4—28no—
491C2×D4—28no—
492C2×D4—22no—
493C2×D4—22no—
494C2×D4—22no—
495C2×D4—22no—
496C2×D4—22no—
497C2×D4—22no—
498C2×D4—48no—
499C2×D4—48no—
500C2×D4—48no—
501C2×D4—48no—
502C2×D4—42no—
503C2×D4—44no—
504C2×D4—44no—
505C2×D4—44no—
506C2×D4—42no—
507C2×D4—42no—
508C2×D4—44no—
509C2×D4—84no—
510C2×D4—84no—
511C2×D4—816no—
512C2×D4—816no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—24no—
520C22×C4—22no—
521C22×C4—24no—
522C22×C4—22no—
523C22×C4—24no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—24no—
530C22×C4—24no—
531C22×C4—24no—
532C22×C4—24no—
533C22×C4—24no—
534C22×C4—24no—
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—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—42no—
552C22×C4—42no—
553C22×C4—42no—
554C22×C4—42no—
555C22×C4—42no—
556C22×C4—42no—
557C22×C4—44no—
558C22×C4—44no—
559C22×C4—44no—
560C22×C4—44no—
561C22×C4—44no—
562C22×C4—44no—
563C22×C4—44no—
564C22×C4—44no—
565C22×C4—42no—
566C22×C4—42no—
567C22×C4—42no—
568C22×C4—42no—
569C22×C4—42no—
570C22×C4—42no—
571C22×C4—42no—
572C22×C4—42no—
573C22×C4—42no—
574C22×C4—42no—
575C22×C4—42no—
576C22×C4—42no—
577C22×C4#12114yes—
578C22×C4#12114yes—
579C22×C4C22×D412yes—
580C22×C4C22×D412yes—
581C22×C4C22×D412yes—
582C22×C4C22×D412yes—
583C22×C4C22×D411yescharacteristic
584C22×C4C22×D412yes—
585C22×C4C22×D412yes—
586C22×C4C2×#4112yes—
587C22×C4C2×#4112yes—
588C22×C4H(5,𝔽2)12yes—
589C22×C4H(5,𝔽2)12yes—
590C22×C4C2511yescharacteristic
591Q16—416no—
592SD16—416no—
593C2×C8—28no—
594C2×C8—28no—
595C2×C8—28no—
596C2×C8—22no—
597C2×C8—22no—
598C2×C8—22no—
599C2×C8—22no—
600C2×C8—22no—
601C2×C8—22no—
602C2×C8—22no—
603C2×C8—22no—
604C2×C8—22no—
605C2×C8—416no—
606C2×C8—416no—
607C2×C8—44no—
608C2×C8C22×D414yes—
609C2×C8C22×D414yes—
610C2×C8C22×D414yes—
611C4⋊C4—28no—
612C4⋊C4—24no—
613C4⋊C4—24no—
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—48no—
624C4⋊C4—48no—
625C4⋊C4—48no—
626C4⋊C4—42no—
627C4⋊C4—48no—
628C4⋊C4—42no—
629C4⋊C4—42no—
630C4⋊C4C22×D414yes—
631C4⋊C4C2×#4114yes—
632C22⋊C4—28no—
633C22⋊C4—28no—
634C22⋊C4—48no—
635C22⋊C4—48no—
636C22⋊C4—48no—
637C22⋊C4—48no—
638C22⋊C4—48no—
639C22⋊C4—48no—
640C22⋊C4—48no—
641C22⋊C4—48no—
642C22⋊C4—48no—
643C22⋊C4—48no—
644C42—48no—
645C42—84no—
646C42#12118yes—
647C42C22×D414yes—
648C42C2×#4114yes—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—28no—
656C23—28no—
657C23—28no—
658C23—28no—
659C23—28no—
660C23—28no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—44no—
668C23—44no—
669C23—44no—
670C23—44no—
671C23—44no—
672C23—44no—
673C23—44no—
674C23—44no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—84no—
683C23—84no—
684C23—84no—
685C23—84no—
686C23—84no—
687C23—84no—
688C23—84no—
689C23C2×#12112yes—
690C23D4212yes—
691C23#54612yes—
692C23C2×#13514yes—
693C23C2×#13514yes—
694C23C2×#13512yes—
695C23C2×#13512yes—
696C23#57712yes—
697C23#57812yes—
698C23C23×D411yescharacteristic
699Q8—24no—
700Q8—24no—
701Q8—48no—
702Q8—42no—
703Q8—42no—
704Q8—42no—
705Q8—42no—
706Q8—42no—
707Q8—42no—
708Q8—84no—
709D4—232no—
710D4—42no—
711D4—42no—
712D4—42no—
713D4—42no—
714D4—816no—
715D4—816no—
716D4—84no—
717C2×C4—28no—
718C2×C4—28no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—24no—
726C2×C4—22no—
727C2×C4—24no—
728C2×C4—22no—
729C2×C4—24no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—42no—
733C2×C4—44no—
734C2×C4—44no—
735C2×C4—48no—
736C2×C4—42no—
737C2×C4—48no—
738C2×C4—48no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—48no—
746C2×C4—48no—
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—42no—
764C2×C4—42no—
765C2×C4—84no—
766C2×C4—84no—
767C2×C4—84no—
768C2×C4—84no—
769C2×C4C2×#12114yes—
770C2×C4C2×#12114yes—
771C2×C4C2×#12112yes—
772C2×C4#53214yes—
773C2×C4#54014yes—
774C2×C4D4212yes—
775C2×C4D4214yes—
776C2×C4#54612yes—
777C2×C4#55014yes—
778C2×C4C23×D411yescharacteristic
779C2×C4C23×D411yescharacteristic
780C2×C4C22×#4111yescharacteristic
781C2×C4C22×#4111yescharacteristic
782C2×C4C2×H(5,𝔽2)11yescharacteristic
783C2×C4C2×H(5,𝔽2)11yescharacteristic
784C8—24no—
785C8—24no—
786C8—24no—
787C8—42no—
788C22—24no—
789C22—24no—
790C22—24no—
791C22—24no—
792C22—24no—
793C22—24no—
794C22—42no—
795C22—42no—
796C22—416no—
797C22—416no—
798C22—42no—
799C22—42no—
800C22—42no—
801C22—42no—
802C22—42no—
803C22—42no—
804C22—82no—
805C22—82no—
806C22—82no—
807C22—82no—
808C22—82no—
809C22—82no—
810C22—82no—
811C22—168no—
812C22#242814yes—
813C22#305014yes—
814C22#306314yes—
815C22#328214yes—
816C22#328514yes—
817C22#329614yes—
818C22#330014yes—
819C22C22×#12111yescharacteristic
820C22C2×D4211yescharacteristic
821C22C2×#54611yescharacteristic
822C22C22×#13511yescharacteristic
823C22C22×#13511yescharacteristic
824C22C2×#57711yescharacteristic
825C22C2×#57811yescharacteristic
826C4—24no—
827C4—24no—
828C4—44no—
829C4—42no—
830C4—42no—
831C4—44no—
832C4—44no—
833C4—82no—
834C4—82no—
835C4—82no—
836C4—82no—
837C4#242814yes—
838C4C2×#53211yescharacteristic
839C4C2×#54011yescharacteristic
840C4C2×D4211yescharacteristic
841C4C2×#55011yescharacteristic
842C2—44no—
843C2—44no—
844C2—162no—
845C2#2538918yesdirect product factor
846C2C2×#242811yescharacteristic
847C2C2×#305011yescharacteristic
848C2C2×#306311yescharacteristic
849C2C2×#328211yescharacteristic
850C2C2×#328511yescharacteristic
851C2C2×#329611yescharacteristic
852C2C2×#330011yescharacteristic
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×#467C2semidirect
2. C22×#465C2semidirect
3. C22×#464C2semidirect
4. C22×C8×D4C2semidirect
5. C2×#2536C2semidirect
7. #25389C2direct (N × H)
8. C2×#2035C2semidirect
9. C2×#2033C2semidirect
10. C2×#2001C2semidirect
11. C2×#2000C2semidirect
12. C2×#1958C2semidirect
13. C2×#1949C2semidirect
14. C2×#1893C2semidirect
15. C2×#1892C2semidirect
16. C2×C4×#103C2semidirect
31. C2×#467C22semidirect
33. C2×#465C22semidirect
35. C2×#464C22semidirect
37. C2×C8×D4C22semidirect
55. #2536C22semidirect
68. #2035C22semidirect
69. #2033C22semidirect
70. #2001C22semidirect
71. #2000C22semidirect
72. #1958C22semidirect
73. #1949C22semidirect
74. #1893C22semidirect
75. #1892C22semidirect
76. C4×#103C22semidirect
179. C2×C4⋊C8D4semidirect
185. C2×#103D4semidirect
420. C4⋊C8C2×D4semidirect
425. #103C2×D4semidirect
845. C2#25389direct (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×#4652
C22×#4642
C22×C8×D42
C2×#25362
C2×#25402
#253892
C2×#20352
C2×#20332
C2×#20012
C2×#20002
C2×#19582
C2×#19492
C2×#18932
C2×#18922
C2×C4×#1032