Finite Group Databasebeta

← C2×#31027 #7503182

Subgroups — C2×#31027 #7503182

Order 512.

3252 conjugacy classes of subgroups.

The subgroup lattice has 863 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#483C211yesmaximal, characteristic, complemented
2C22×#448C211yesmaximal, characteristic, complemented
3C2×#2409C211yesmaximal, characteristic, complemented
4C2×#2416C211yesmaximal, characteristic
5#31027C2116yesmaximal, direct product factor
6C2×#2077C211yesmaximal, characteristic, complemented
7C2×#2066C211yesmaximal, characteristic, complemented
8C2×#2055C211yesmaximal, characteristic, complemented
9C2×#2034C211yesmaximal, characteristic, complemented
10C2×#2000C211yesmaximal, characteristic, complemented
11C2×#2000C211yesmaximal, characteristic, complemented
12C2×#1968C211yesmaximal, characteristic, complemented
13C2×#1954C211yesmaximal, characteristic, complemented
14C2×#1933C211yesmaximal, characteristic, complemented
15C2×#1872C211yesmaximal, characteristic, complemented
16C2×#1787C211yesmaximal, characteristic, complemented
17C24×Q8C2211yescharacteristic
18C23×SD16C2211yescharacteristic
19C23×SD16C2211yescharacteristic
20C22×C22⋊Q8C2211yescharacteristic
21C22×C22⋊Q8C2211yescharacteristic
22C22×#121—21no—
23C22×#121C2211yescharacteristic
24C22×#121C2211yescharacteristic
25C22×C4×D4C2211yescharacteristic
26C23×C4⋊C4C2211yescharacteristic
27C2×#483—28no—
28C2×#483C2218yescomplemented
29C2×#448—28no—
30C2×#448C2218yescomplemented
31C22×#106C2211yescharacteristic
32C22×#106C2211yescharacteristic
33C22×C4⋊C8C2211yescharacteristic
34C22×#103C2211yescharacteristic
35C22×#103C2211yescharacteristic
36C22×#103C2211yescharacteristic
37C22×#103C2211yescharacteristic
38C22×#103C2211yescharacteristic
39C22×#103C2211yescharacteristic
40C22×#102C2211yescharacteristic
41C22×#102C2211yescharacteristic
42C22×C22⋊C8C2211yescharacteristic
43C22×C22⋊C8C2211yescharacteristic
44C22×C22⋊C8C2211yescharacteristic
45C22×C22⋊C8C2211yescharacteristic
46C22×C4×C8C2211yescharacteristic
47#2416—24no—
48#2416C2218yes—
49#2409—24no—
50#2409C2218yescomplemented
51C2×#396—21no—
52C2×#395—21no—
53C2×#394—21no—
54C2×#393—21no—
55C2×#391C2211yescharacteristic
56C2×#391C2211yescharacteristic
57C2×#390C2211yescharacteristic
58C2×#389C2211yescharacteristic
59C2×#386—21no—
60C2×#386—21no—
61C2×#385—21no—
62C2×#380C2211yescharacteristic
63C2×#380C2211yescharacteristic
64#2077C2218yescomplemented
65#2066C2218yescomplemented
66#2055C2218yescomplemented
67#2034C2218yescomplemented
68#2000C2218yescomplemented
69#2000C2218yescomplemented
70#1968C2218yescomplemented
71#1954C2218yescomplemented
72#1933C2218yescomplemented
73#1872C2218yescomplemented
74#1787C2218yescomplemented
75C2×#340C2211yescharacteristic
76C2×#340C2211yescharacteristic
77C2×#340C2211yescharacteristic
78C2×#340C2211yescharacteristic
79C23×Q8—21no—
80C23×Q8—22no—
81C23×Q8—24no—
82C23×Q8—24no—
83C23×Q8—42no—
84C23×Q8—42no—
85C23×Q8—42no—
86C23×Q8—42no—
87C23×Q8C2311yescharacteristic
88C23×Q8C2311yescharacteristic
89C23×Q8C2314yes—
90C23×D4—21no—
91C23×D4—21no—
92C23×D4D411yescharacteristic
93C23×D4C2311yescharacteristic
94C24×C4—21no—
95C24×C4—21no—
96C24×C4C2311yescharacteristic
97C24×C4C2311yescharacteristic
98C22×SD16—24no—
99C22×SD16—24no—
100C22×SD16—24no—
101C22×SD16—42no—
102C22×SD16—42no—
103C22×SD16—42no—
104C22×SD16C2314yes—
105C22×SD16C2314yes—
106C23×C8C2311yescharacteristic
107C23×C8C2311yescharacteristic
108C23×C8C2311yescharacteristic
109C23×C8C2311yescharacteristic
110C2×C22⋊Q8—22no—
111C2×C22⋊Q8—22no—
112C2×C22⋊Q8—24no—
113C2×C22⋊Q8—24no—
114C2×C22⋊Q8—42no—
115C2×C22⋊Q8—42no—
116C2×C22⋊Q8C2314yes—
117C2×C22⋊Q8C2314yes—
118C2×#121—28no—
119C2×#121—22no—
120C2×#121—22no—
121C2×#121—24no—
122C2×#121—42no—
123C2×#121—42no—
124C2×#121—42no—
125C2×#121—48no—
126C2×#121C2314yes—
127C2×#121C2314yes—
128C2×C4×D4—42no—
129C2×C4×D4—42no—
130C2×C4×D4D414yes—
131C2×C4×D4C2314yes—
132C22×C4⋊C4—24no—
133C22×C4⋊C4—21no—
134C22×C4⋊C4—21no—
135C22×C4⋊C4—21no—
136C22×C4⋊C4—21no—
137C22×C4⋊C4—22no—
138C22×C4⋊C4—42no—
139C22×C4⋊C4D411yescharacteristic
140C22×C4⋊C4C2311yescharacteristic
141C22×C4⋊C4C2311yescharacteristic
142C22×C4⋊C4C2311yescharacteristic
143C22×C4⋊C4C2311yescharacteristic
144C22×C4⋊C4C2314yes—
145C22×C4⋊C4C2311yescharacteristic
146C22×C22⋊C4—21no—
147C22×C22⋊C4—21no—
148C22×C22⋊C4—21no—
149C22×C22⋊C4—21no—
150C22×C22⋊C4—21no—
151C22×C22⋊C4—21no—
152C22×C22⋊C4—21no—
153C22×C22⋊C4—21no—
154C22×C22⋊C4D411yescharacteristic
155C22×C22⋊C4D411yescharacteristic
156C22×C42C2311yescharacteristic
157#483—232no—
158#448—232no—
159C2×#106—24no—
160C2×#106—24no—
161C2×#106C2314yes—
162C2×#106C2314yes—
163C2×C4⋊C8—42no—
164C2×C4⋊C8C2314yes—
165C2×#103—24no—
166C2×#103—24no—
167C2×#103—42no—
168C2×#103—42no—
169C2×#103—42no—
170C2×#103D418yescomplemented
171C2×#103C2314yes—
172C2×#103C2314yes—
173C2×#103C2314yes—
174C2×#103C2314yes—
175C2×#103C2314yes—
176C2×#103C2314yes—
177C2×#102—42no—
178C2×#102—42no—
179C2×#102C2314yes—
180C2×#102C2314yes—
181C2×C22⋊C8—24no—
182C2×C22⋊C8—24no—
183C2×C22⋊C8—42no—
184C2×C22⋊C8—42no—
185C2×C22⋊C8C2314yes—
186C2×C22⋊C8C2314yes—
187C2×C22⋊C8C2314yes—
188C2×C22⋊C8C2314yes—
189C2×C4×C8—42no—
190C2×C4×C8C2314yes—
191#396—28no—
192#395—28no—
193#394—28no—
194#393—28no—
195#391—22no—
196#391—22no—
197#391C2314yes—
198#391C2314yes—
199#390—22no—
200#390C2314yes—
201#389—22no—
202#389C2314yes—
203#386—28no—
204#386—28no—
205#385—28no—
206#380—22no—
207#380—22no—
208#380C2314yes—
209#380C2314yes—
210C2×#95—21no—
211C2×#95—21no—
212C2×#95—21no—
213C2×#95—21no—
214C2×#95—21no—
215C2×#95—21no—
216C2×#95—21no—
217#340C2314yes—
218#340C2314yes—
219#340C2314yes—
220#340C2314yes—
221C25—21no—
222C25C2×D411yescharacteristic
223C25C2×D411yescharacteristic
224C22×Q8—21no—
225C22×Q8—21no—
226C22×Q8—24no—
227C22×Q8—22no—
228C22×Q8—22no—
229C22×Q8—28no—
230C22×Q8—28no—
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—44no—
240C22×Q8—44no—
241C22×Q8—44no—
242C22×Q8—44no—
243C22×Q8—44no—
244C22×Q8—44no—
245C22×Q8—48no—
246C22×Q8—48no—
247C22×Q8—44no—
248C22×Q8—48no—
249C22×Q8—416no—
250C22×Q8—416no—
251C22×Q8—416no—
252C22×Q8—416no—
253C22×Q8C2×D414yes—
254C22×Q8#4114yes—
255C22×Q8C2412yes—
256C22×Q8C2412yes—
257C22×D4—24no—
258C22×D4—24no—
259C22×D4—22no—
260C22×D4—21no—
261C22×D4—22no—
262C22×D4—22no—
263C22×D4—22no—
264C22×D4—22no—
265C22×D4—22no—
266C22×D4—42no—
267C22×D4—42no—
268C22×D4—44no—
269C22×D4—44no—
270C22×D4—44no—
271C22×D4—44no—
272C22×D4—44no—
273C22×D4—82no—
274C22×D4SD1618yescomplemented
275C22×D4C2×D414yes—
276C22×D4C2412yes—
277C23×C4—21no—
278C23×C4—21no—
279C23×C4—21no—
280C23×C4—22no—
281C23×C4—22no—
282C23×C4—22no—
283C23×C4—22no—
284C23×C4—22no—
285C23×C4—22no—
286C23×C4—22no—
287C23×C4—22no—
288C23×C4—22no—
289C23×C4—22no—
290C23×C4—22no—
291C23×C4—22no—
292C23×C4—24no—
293C23×C4—21no—
294C23×C4—21no—
295C23×C4—21no—
296C23×C4—21no—
297C23×C4—24no—
298C23×C4—44no—
299C23×C4—44no—
300C23×C4—44no—
301C23×C4—44no—
302C23×C4—44no—
303C23×C4—82no—
304C23×C4C2×D412yes—
305C23×C4C2×D412yes—
306C23×C4C2×D411yescharacteristic
307C23×C4C2×D411yescharacteristic
308C23×C4C2×D411yescharacteristic
309C23×C4C2×D411yescharacteristic
310C23×C4C2412yes—
311C23×C4C2412yes—
312C23×C4C2411yescharacteristic
313C2×SD16—28no—
314C2×SD16—28no—
315C2×SD16—28no—
316C2×SD16—44no—
317C2×SD16—44no—
318C2×SD16—44no—
319C2×SD16—416no—
320C2×SD16—416no—
321C22×C8—22no—
322C22×C8—22no—
323C22×C8—22no—
324C22×C8—22no—
325C22×C8—22no—
326C22×C8—22no—
327C22×C8—22no—
328C22×C8—22no—
329C22×C8—22no—
330C22×C8—22no—
331C22×C8—22no—
332C22×C8C2×D414yes—
333C22×C8C2412yes—
334C22×C8C2412yes—
335C22×C8C2412yes—
336C22×C8C2412yes—
337C22⋊Q8—28no—
338C22⋊Q8—28no—
339C22⋊Q8—44no—
340C22⋊Q8—44no—
341C22⋊Q8—48no—
342C22⋊Q8—48no—
343#121—28no—
344#121—44no—
345#121—44no—
346#121—44no—
347#121—48no—
348#121—48no—
349#121—432no—
350C4×D4—48no—
351C4×D4—44no—
352C4×D4—44no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—22no—
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—28no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—24no—
366C2×C4⋊C4—24no—
367C2×C4⋊C4—24no—
368C2×C4⋊C4—24no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—44no—
373C2×C4⋊C4—48no—
374C2×C4⋊C4—42no—
375C2×C4⋊C4—44no—
376C2×C4⋊C4—44no—
377C2×C4⋊C4—44no—
378C2×C4⋊C4—44no—
379C2×C4⋊C4C2×D414yes—
380C2×C4⋊C4C2×D414yes—
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—42no—
395C2×C22⋊C4—42no—
396C2×C22⋊C4—44no—
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—82no—
404C2×C22⋊C4C2×D414yes—
405C2×C22⋊C4C2×D414yes—
406C2×C42—22no—
407C2×C42—22no—
408C2×C42C2×D412yes—
409C2×C42C2412yes—
410#106—28no—
411#106—28no—
412C4⋊C8—44no—
413#103—28no—
414#103—28no—
415#103—44no—
416#103—44no—
417#103—44no—
418#103C2×D4116yescomplemented
419#102—44no—
420#102—44no—
421C22⋊C8—28no—
422C22⋊C8—28no—
423C22⋊C8—44no—
424C22⋊C8—44no—
425C4×C8—44no—
426#95—24no—
427#95—24no—
428#95—24no—
429#95—24no—
430#95—24no—
431#95—24no—
432#95—24no—
433C24—22no—
434C24—22no—
435C24—22no—
436C24—22no—
437C24—22no—
438C24—22no—
439C24—22no—
440C24—22no—
441C24—22no—
442C24—22no—
443C24—22no—
444C24—22no—
445C24—22no—
446C24—42no—
447C24—42no—
448C24—42no—
449C24—42no—
450C24—42no—
451C24—42no—
452C24—42no—
453C24C2×SD1614yes—
454C24C2×SD1614yes—
455C24C22×D412yes—
456C24C22×D412yes—
457C24C22×D411yescharacteristic
458C2×Q8—24no—
459C2×Q8—24no—
460C2×Q8—22no—
461C2×Q8—22no—
462C2×Q8—28no—
463C2×Q8—28no—
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—48no—
475C2×Q8—48no—
476C2×Q8—48no—
477C2×Q8—416no—
478C2×Q8—416no—
479C2×Q8—416no—
480C2×Q8—464no—
481C2×Q8—416no—
482C2×Q8—432no—
483C2×Q8—42no—
484C2×Q8—42no—
485C2×Q8—44no—
486C2×Q8—44no—
487C2×Q8—42no—
488C2×Q8—42no—
489C2×Q8—44no—
490C2×Q8—44no—
491C2×Q8C22×D414yes—
492C2×Q8C2×#4114yes—
493C2×D4—22no—
494C2×D4—22no—
495C2×D4—22no—
496C2×D4—22no—
497C2×D4—22no—
498C2×D4—22no—
499C2×D4—44no—
500C2×D4—416no—
501C2×D4—44no—
502C2×D4—48no—
503C2×D4—48no—
504C2×D4—48no—
505C2×D4—48no—
506C2×D4—48no—
507C2×D4—42no—
508C2×D4—44no—
509C2×D4—44no—
510C2×D4—42no—
511C2×D4—44no—
512C2×D4—42no—
513C2×D4—44no—
514C2×D4—84no—
515C2×D4—816no—
516C2×D4—816no—
517C2×D4C2×SD16116yescomplemented
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—24no—
525C22×C4—24no—
526C22×C4—22no—
527C22×C4—24no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—24no—
536C22×C4—24no—
537C22×C4—24no—
538C22×C4—24no—
539C22×C4—24no—
540C22×C4—24no—
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—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—48no—
558C22×C4—48no—
559C22×C4—48no—
560C22×C4—48no—
561C22×C4—432no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—42no—
565C22×C4—42no—
566C22×C4—42no—
567C22×C4—42no—
568C22×C4—44no—
569C22×C4—44no—
570C22×C4—44no—
571C22×C4—44no—
572C22×C4—44no—
573C22×C4—44no—
574C22×C4—44no—
575C22×C4—44no—
576C22×C4—42no—
577C22×C4—42no—
578C22×C4—42no—
579C22×C4—42no—
580C22×C4—42no—
581C22×C4—42no—
582C22×C4—48no—
583C22×C4—42no—
584C22×C4—42no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4—42no—
588C22×C4—42no—
589C22×C4—84no—
590C22×C4—816no—
591C22×C4C2×SD1614yes—
592C22×C4C22×D412yes—
593C22×C4C22×D412yes—
594C22×C4C22×D412yes—
595C22×C4C22×D412yes—
596C22×C4C22×D411yescharacteristic
597C22×C4C22×D412yes—
598C22×C4C2×#4112yes—
599C22×C4H(5,𝔽2)12yes—
600C22×C4H(5,𝔽2)12yes—
601C22×C4H(5,𝔽2)12yes—
602C22×C4H(5,𝔽2)12yes—
603C22×C4C2511yescharacteristic
604SD16—416no—
605SD16—416no—
606C2×C8—28no—
607C2×C8—22no—
608C2×C8—22no—
609C2×C8—22no—
610C2×C8—22no—
611C2×C8—22no—
612C2×C8—22no—
613C2×C8—22no—
614C2×C8—22no—
615C2×C8—22no—
616C2×C8—22no—
617C2×C8—22no—
618C2×C8—44no—
619C2×C8—44no—
620C2×C8—44no—
621C2×C8C22×D414yes—
622C4⋊C4—24no—
623C4⋊C4—22no—
624C4⋊C4—22no—
625C4⋊C4—22no—
626C4⋊C4—22no—
627C4⋊C4—22no—
628C4⋊C4—22no—
629C4⋊C4—22no—
630C4⋊C4—22no—
631C4⋊C4—22no—
632C4⋊C4—44no—
633C4⋊C4—48no—
634C4⋊C4—48no—
635C4⋊C4—48no—
636C4⋊C4—42no—
637C4⋊C4—42no—
638C4⋊C4—42no—
639C4⋊C4—42no—
640C4⋊C4—48no—
641C4⋊C4C22×D414yes—
642C22⋊C4—44no—
643C22⋊C4—44no—
644C22⋊C4—48no—
645C22⋊C4—48no—
646C22⋊C4—48no—
647C22⋊C4—48no—
648C22⋊C4—48no—
649C22⋊C4—48no—
650C22⋊C4—48no—
651C22⋊C4—84no—
652C42—24no—
653C42—22no—
654C42—22no—
655C23—28no—
656C23—28no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—28no—
664C23—28no—
665C23—28no—
666C23—28no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—22no—
671C23—22no—
672C23—22no—
673C23—44no—
674C23—44no—
675C23—44no—
676C23—44no—
677C23—44no—
678C23—44no—
679C23—44no—
680C23—44no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—84no—
689C23—84no—
690C23—84no—
691C23—84no—
692C23—84no—
693C23—84no—
694C23—84no—
695C23#53412yes—
696C23D4212yes—
697C23#54612yes—
698C23C22×SD1614yes—
699C23C22×SD1614yes—
700C23C22×SD1612yes—
701C23#57512yes—
702C23#57712yes—
703C23#57812yes—
704C23C23×D411yescharacteristic
705Q8—24no—
706Q8—24no—
707Q8—24no—
708Q8—24no—
709Q8—432no—
710Q8—48no—
711Q8—48no—
712Q8—42no—
713Q8—42no—
714Q8—42no—
715Q8—42no—
716D4—416no—
717D4—42no—
718D4—42no—
719D4—42no—
720D4—42no—
721D4—816no—
722D4—816no—
723D4—84no—
724C2×C4—28no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—24no—
732C2×C4—24no—
733C2×C4—22no—
734C2×C4—24no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—432no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—44no—
743C2×C4—44no—
744C2×C4—48no—
745C2×C4—48no—
746C2×C4—44no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—48no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—48no—
753C2×C4—48no—
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—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—816no—
775C2×C4—84no—
776C2×C4—84no—
777C2×C4—84no—
778C2×C4—84no—
779C2×C4#53412yes—
780C2×C4#53514yes—
781C2×C4#53814yes—
782C2×C4D4212yes—
783C2×C4#54612yes—
784C2×C4#54614yes—
785C2×C4#56014yes—
786C2×C4C22×SD1614yes—
787C2×C4C23×D411yescharacteristic
788C2×C4C22×#4111yescharacteristic
789C2×C4C2×H(5,𝔽2)11yescharacteristic
790C2×C4C2×H(5,𝔽2)11yescharacteristic
791C2×C4C2×H(5,𝔽2)11yescharacteristic
792C2×C4C2×H(5,𝔽2)11yescharacteristic
793C8—24no—
794C8—42no—
795C8—42no—
796C8—42no—
797C22—24no—
798C22—24no—
799C22—24no—
800C22—24no—
801C22—24no—
802C22—24no—
803C22—416no—
804C22—416no—
805C22—42no—
806C22—42no—
807C22—42no—
808C22—42no—
809C22—42no—
810C22—42no—
811C22—42no—
812C22—42no—
813C22—82no—
814C22—82no—
815C22—82no—
816C22—82no—
817C22—82no—
818C22—82no—
819C22—82no—
820C22—168no—
821C22#267814yes—
822C22#318714yes—
823C22#320114yes—
824C22#327714yes—
825C22D4×SD1614yes—
826C22#329814yes—
827C22#332614yes—
828C22C2×#53411yescharacteristic
829C22C2×D4211yescharacteristic
830C22C2×#54611yescharacteristic
831C22C23×SD1611yescharacteristic
832C22C2×#57511yescharacteristic
833C22C2×#57711yescharacteristic
834C22C2×#57811yescharacteristic
835C4—24no—
836C4—42no—
837C4—44no—
838C4—42no—
839C4—42no—
840C4—44no—
841C4—44no—
842C4—82no—
843C4—82no—
844C4—82no—
845C4—82no—
846C4#267814yes—
847C4C2×#53511yescharacteristic
848C4C2×#53811yescharacteristic
849C4C2×#54611yescharacteristic
850C4C2×#56011yescharacteristic
851C2—44no—
852C2—44no—
853C2—162no—
854C2#3102718yesdirect product factor
855C2C2×#267811yescharacteristic
856C2C2×#318711yescharacteristic
857C2C2×#320111yescharacteristic
858C2C2×#327711yescharacteristic
859C2C2×D4×SD1611yescharacteristic
860C2C2×#329811yescharacteristic
861C2C2×#332611yescharacteristic
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×#448C2semidirect
3. C2×#2409C2semidirect
5. #31027C2direct (N × H)
6. C2×#2077C2semidirect
7. C2×#2066C2semidirect
8. C2×#2055C2semidirect
9. C2×#2034C2semidirect
10. C2×#2000C2semidirect
11. C2×#2000C2semidirect
12. C2×#1968C2semidirect
13. C2×#1954C2semidirect
14. C2×#1933C2semidirect
15. C2×#1872C2semidirect
16. C2×#1787C2semidirect
28. C2×#483C22semidirect
30. C2×#448C22semidirect
50. #2409C22semidirect
64. #2077C22semidirect
65. #2066C22semidirect
66. #2055C22semidirect
67. #2034C22semidirect
68. #2000C22semidirect
69. #2000C22semidirect
70. #1968C22semidirect
71. #1954C22semidirect
72. #1933C22semidirect
73. #1872C22semidirect
74. #1787C22semidirect
170. C2×#103D4semidirect
274. C22×D4SD16semidirect
418. #103C2×D4semidirect
517. C2×D4C2×SD16semidirect
854. C2#31027direct (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×#4482
C2×#24092
C2×#24162
#310272
C2×#20772
C2×#20662
C2×#20552
C2×#20342
C2×#20002
C2×#19682
C2×#19542
C2×#19332
C2×#18722
C2×#17872