Finite Group Databasebeta

← C2×#31025 #7503178

Subgroups — C2×#31025 #7503178

Order 512.

3122 conjugacy classes of subgroups.

The subgroup lattice has 855 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#483C211yesmaximal, characteristic, complemented
2C22×#452C211yesmaximal, characteristic, complemented
3C2×#2407C211yesmaximal, characteristic
4C2×#2417C211yesmaximal, characteristic, complemented
5#31025C2116yesmaximal, direct product factor
6C2×#2077C211yesmaximal, characteristic, complemented
7C2×#2065C211yesmaximal, characteristic, complemented
8C2×#2056C211yesmaximal, characteristic, complemented
9C2×#2035C211yesmaximal, characteristic, complemented
10C2×#2001C211yesmaximal, characteristic, complemented
11C2×#2000C211yesmaximal, characteristic, complemented
12C2×#1968C211yesmaximal, characteristic, complemented
13C2×#1954C211yesmaximal, characteristic, complemented
14C2×#1933C211yesmaximal, characteristic, complemented
15C2×#1874C211yesmaximal, characteristic, complemented
16C2×#1788C211yesmaximal, characteristic, complemented
17C23×#41C2211yescharacteristic
18C23×Q16C2211yescharacteristic
19C23×SD16C2211yescharacteristic
20C22×C22⋊Q8C2211yescharacteristic
21C22×C22⋊Q8C2211yescharacteristic
22C22×C22⋊Q8C2211yescharacteristic
23C22×#121C2211yescharacteristic
24C22×C4×D4C2211yescharacteristic
25C23×C4⋊C4C2211yescharacteristic
26C2×#483—28no—
27C2×#483C2218yescomplemented
28C2×#452—28no—
29C2×#452C2218yescomplemented
30C22×#106C2211yescharacteristic
31C22×#106C2211yescharacteristic
32C22×C4⋊C8C2211yescharacteristic
33C22×#103C2211yescharacteristic
34C22×#103C2211yescharacteristic
35C22×#103C2211yescharacteristic
36C22×#103C2211yescharacteristic
37C22×#103C2211yescharacteristic
38C22×#102C2211yescharacteristic
39C22×#102C2211yescharacteristic
40C22×#102C2211yescharacteristic
41C22×C22⋊C8C2211yescharacteristic
42C22×C22⋊C8C2211yescharacteristic
43C22×C22⋊C8C2211yescharacteristic
44C22×C22⋊C8C2211yescharacteristic
45C22×C4×C8C2211yescharacteristic
46#2417—24no—
47#2417C2218yescomplemented
48#2407—24no—
49#2407C2218yes—
50C2×#398—21no—
51C2×#396—21no—
52C2×#394—21no—
53C2×#392—21no—
54C2×#391C2211yescharacteristic
55C2×#391C2211yescharacteristic
56C2×#390C2211yescharacteristic
57C2×#389C2211yescharacteristic
58C2×#386—21no—
59C2×#386—21no—
60C2×#385—21no—
61C2×#380—21no—
62C2×#380C2211yescharacteristic
63C2×#380C2211yescharacteristic
64#2077C2218yescomplemented
65#2065C2218yescomplemented
66#2056C2218yescomplemented
67#2035C2218yescomplemented
68#2001C2218yescomplemented
69#2000C2218yescomplemented
70#1968C2218yescomplemented
71#1954C2218yescomplemented
72#1933C2218yescomplemented
73#1874C2218yescomplemented
74#1788C2218yescomplemented
75C2×#340C2211yescharacteristic
76C2×#340C2211yescharacteristic
77C2×#340C2211yescharacteristic
78C2×#340C2211yescharacteristic
79C22×#41—22no—
80C22×#41—24no—
81C22×#41—24no—
82C22×#41—42no—
83C22×#41—42no—
84C22×#41—42no—
85C22×#41—42no—
86C22×#41C2314yes—
87C23×Q8C2311yescharacteristic
88C23×Q8C2311yescharacteristic
89C23×D4—21no—
90C23×D4—21no—
91C23×D4D411yescharacteristic
92C23×D4C2311yescharacteristic
93C24×C4—21no—
94C24×C4—21no—
95C24×C4C2311yescharacteristic
96C24×C4C2311yescharacteristic
97C22×Q16—24no—
98C22×Q16—42no—
99C22×Q16—42no—
100C22×Q16C2314yes—
101C22×SD16—24no—
102C22×SD16—24no—
103C22×SD16—42no—
104C22×SD16C2314yes—
105C23×C8C2311yescharacteristic
106C23×C8C2311yescharacteristic
107C23×C8C2311yescharacteristic
108C23×C8C2311yescharacteristic
109C2×C22⋊Q8—22no—
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⋊Q8—42no—
117C2×C22⋊Q8—42no—
118C2×C22⋊Q8C2314yes—
119C2×C22⋊Q8C2314yes—
120C2×C22⋊Q8C2314yes—
121C2×#121—22no—
122C2×#121—24no—
123C2×#121—42no—
124C2×#121C2314yes—
125C2×C4×D4—42no—
126C2×C4×D4—42no—
127C2×C4×D4D414yes—
128C2×C4×D4C2314yes—
129C22×C4⋊C4—24no—
130C22×C4⋊C4—21no—
131C22×C4⋊C4—21no—
132C22×C4⋊C4—21no—
133C22×C4⋊C4—21no—
134C22×C4⋊C4—22no—
135C22×C4⋊C4—21no—
136C22×C4⋊C4—42no—
137C22×C4⋊C4D411yescharacteristic
138C22×C4⋊C4C2311yescharacteristic
139C22×C4⋊C4C2311yescharacteristic
140C22×C4⋊C4C2311yescharacteristic
141C22×C4⋊C4C2311yescharacteristic
142C22×C4⋊C4C2314yes—
143C22×C4⋊C4C2311yescharacteristic
144C22×C22⋊C4—21no—
145C22×C22⋊C4—21no—
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⋊C4D411yescharacteristic
153C22×C22⋊C4D411yescharacteristic
154C22×C42C2311yescharacteristic
155#483—232no—
156#452—232no—
157C2×#106—24no—
158C2×#106—24no—
159C2×#106C2314yes—
160C2×#106C2314yes—
161C2×C4⋊C8—42no—
162C2×C4⋊C8C2314yes—
163C2×#103—24no—
164C2×#103—42no—
165C2×#103—42no—
166C2×#103—42no—
167C2×#103D418yescomplemented
168C2×#103C2314yes—
169C2×#103C2314yes—
170C2×#103C2314yes—
171C2×#103C2314yes—
172C2×#103C2314yes—
173C2×#102—24no—
174C2×#102—42no—
175C2×#102—42no—
176C2×#102C2314yes—
177C2×#102C2314yes—
178C2×#102C2314yes—
179C2×C22⋊C8—24no—
180C2×C22⋊C8—24no—
181C2×C22⋊C8—42no—
182C2×C22⋊C8—42no—
183C2×C22⋊C8C2314yes—
184C2×C22⋊C8C2314yes—
185C2×C22⋊C8C2314yes—
186C2×C22⋊C8C2314yes—
187C2×C4×C8—42no—
188C2×C4×C8C2314yes—
189#398—28no—
190#396—28no—
191#394—28no—
192#392—28no—
193#391—22no—
194#391—22no—
195#391C2314yes—
196#391C2314yes—
197#390—22no—
198#390C2314yes—
199#389—22no—
200#389C2314yes—
201#386—28no—
202#386—28no—
203#385—28no—
204#380—22no—
205#380—22no—
206#380—28no—
207#380C2314yes—
208#380C2314yes—
209C2×#95—21no—
210C2×#95—21no—
211C2×#95—21no—
212C2×#95—21no—
213C2×#95—21no—
214C2×#95—21no—
215C2×#95—21no—
216#340C2314yes—
217#340C2314yes—
218#340C2314yes—
219#340C2314yes—
220C25—21no—
221C25C2×D411yescharacteristic
222C25C2×D411yescharacteristic
223C2×#41—28no—
224C2×#41—28no—
225C2×#41—44no—
226C2×#41—44no—
227C2×#41—44no—
228C2×#41—44no—
229C2×#41—48no—
230C2×#41—48no—
231C2×#41—48no—
232C2×#41—416no—
233C2×#41—416no—
234C2×#41—416no—
235C2×#41—416no—
236C22×Q8—21no—
237C22×Q8—21no—
238C22×Q8—22no—
239C22×Q8—22no—
240C22×Q8—22no—
241C22×Q8—22no—
242C22×Q8—22no—
243C22×Q8—22no—
244C22×Q8—22no—
245C22×Q8—22no—
246C22×Q8—22no—
247C22×Q8—22no—
248C22×Q8—22no—
249C22×Q8C2×D414yes—
250C22×Q8C2412yes—
251C22×Q8C2412yes—
252C22×D4—24no—
253C22×D4—24no—
254C22×D4—24no—
255C22×D4—24no—
256C22×D4—22no—
257C22×D4—21no—
258C22×D4—22no—
259C22×D4—22no—
260C22×D4—22no—
261C22×D4—22no—
262C22×D4—42no—
263C22×D4—44no—
264C22×D4—44no—
265C22×D4—44no—
266C22×D4—44no—
267C22×D4—44no—
268C22×D4—82no—
269C22×D4C2×D414yes—
270C22×D4#4114yes—
271C22×D4C2412yes—
272C23×C4—21no—
273C23×C4—21no—
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—22no—
283C23×C4—22no—
284C23×C4—22no—
285C23×C4—22no—
286C23×C4—21no—
287C23×C4—21no—
288C23×C4—21no—
289C23×C4—21no—
290C23×C4—21no—
291C23×C4—24no—
292C23×C4—24no—
293C23×C4—44no—
294C23×C4—44no—
295C23×C4—44no—
296C23×C4—44no—
297C23×C4—44no—
298C23×C4—82no—
299C23×C4C2×D412yes—
300C23×C4C2×D412yes—
301C23×C4C2×D411yescharacteristic
302C23×C4C2×D411yescharacteristic
303C23×C4C2×D411yescharacteristic
304C23×C4C2×D411yescharacteristic
305C23×C4C2412yes—
306C23×C4C2412yes—
307C23×C4C2411yescharacteristic
308C2×Q16—28no—
309C2×Q16—44no—
310C2×Q16—44no—
311C2×Q16—416no—
312C2×SD16—28no—
313C2×SD16—28no—
314C2×SD16—44no—
315C2×SD16—416no—
316C22×C8—22no—
317C22×C8—22no—
318C22×C8—22no—
319C22×C8—22no—
320C22×C8—22no—
321C22×C8—22no—
322C22×C8—22no—
323C22×C8—22no—
324C22×C8—22no—
325C22×C8—22no—
326C22×C8—22no—
327C22×C8C2×D414yes—
328C22×C8C2412yes—
329C22×C8C2412yes—
330C22×C8C2412yes—
331C22×C8C2412yes—
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—
341#121—28no—
342#121—44no—
343#121—48no—
344C4×D4—48no—
345C4×D4—44no—
346C4×D4—44no—
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—22no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—28no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—24no—
360C2×C4⋊C4—24no—
361C2×C4⋊C4—24no—
362C2×C4⋊C4—24no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—24no—
367C2×C4⋊C4—44no—
368C2×C4⋊C4—48no—
369C2×C4⋊C4—42no—
370C2×C4⋊C4—44no—
371C2×C4⋊C4—44no—
372C2×C4⋊C4—44no—
373C2×C4⋊C4—44no—
374C2×C4⋊C4—82no—
375C2×C4⋊C4C2×D414yes—
376C2×C4⋊C4C2×D414yes—
377C2×C4⋊C4C2412yes—
378C2×C4⋊C4C2412yes—
379C2×C4⋊C4C2412yes—
380C2×C4⋊C4C2412yes—
381C2×C4⋊C4C2412yes—
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—24no—
390C2×C22⋊C4—42no—
391C2×C22⋊C4—42no—
392C2×C22⋊C4—44no—
393C2×C22⋊C4—44no—
394C2×C22⋊C4—44no—
395C2×C22⋊C4—44no—
396C2×C22⋊C4—44no—
397C2×C22⋊C4—82no—
398C2×C22⋊C4—82no—
399C2×C22⋊C4—82no—
400C2×C22⋊C4C2×D414yes—
401C2×C22⋊C4C2×D414yes—
402C2×C42—22no—
403C2×C42—22no—
404C2×C42C2×D412yes—
405C2×C42C2412yes—
406#106—28no—
407#106—28no—
408C4⋊C8—44no—
409#103—28no—
410#103—44no—
411#103—44no—
412#103—44no—
413#103C2×D4116yescomplemented
414#102—28no—
415#102—44no—
416#102—44no—
417C22⋊C8—28no—
418C22⋊C8—28no—
419C22⋊C8—44no—
420C22⋊C8—44no—
421C4×C8—44no—
422#95—24no—
423#95—24no—
424#95—24no—
425#95—24no—
426#95—24no—
427#95—24no—
428#95—24no—
429C24—22no—
430C24—22no—
431C24—22no—
432C24—22no—
433C24—22no—
434C24—22no—
435C24—22no—
436C24—22no—
437C24—24no—
438C24—22no—
439C24—22no—
440C24—22no—
441C24—22no—
442C24—22no—
443C24—22no—
444C24—42no—
445C24—42no—
446C24—42no—
447C24—42no—
448C24—42no—
449C24—42no—
450C24#13514yes—
451C24C22×D412yes—
452C24C22×D412yes—
453C24C22×D411yescharacteristic
454#41—416no—
455#41—416no—
456#41—416no—
457#41—464no—
458#41—416no—
459C2×Q8—24no—
460C2×Q8—22no—
461C2×Q8—28no—
462C2×Q8—28no—
463C2×Q8—22no—
464C2×Q8—22no—
465C2×Q8—22no—
466C2×Q8—22no—
467C2×Q8—22no—
468C2×Q8—22no—
469C2×Q8—22no—
470C2×Q8—22no—
471C2×Q8—22no—
472C2×Q8—22no—
473C2×Q8—42no—
474C2×Q8—42no—
475C2×Q8—44no—
476C2×Q8—42no—
477C2×Q8—42no—
478C2×Q8—42no—
479C2×Q8—44no—
480C2×Q8—44no—
481C2×Q8—44no—
482C2×Q8—44no—
483C2×Q8—44no—
484C2×Q8C22×D414yes—
485C2×D4—28no—
486C2×D4—28no—
487C2×D4—28no—
488C2×D4—24no—
489C2×D4—28no—
490C2×D4—22no—
491C2×D4—22no—
492C2×D4—22no—
493C2×D4—22no—
494C2×D4—22no—
495C2×D4—44no—
496C2×D4—416no—
497C2×D4—48no—
498C2×D4—48no—
499C2×D4—48no—
500C2×D4—432no—
501C2×D4—48no—
502C2×D4—48no—
503C2×D4—42no—
504C2×D4—44no—
505C2×D4—42no—
506C2×D4—44no—
507C2×D4—84no—
508C2×D4—816no—
509C2×D4C2×#4114yes—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—24no—
516C22×C4—24no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—24no—
526C22×C4—24no—
527C22×C4—24no—
528C22×C4—24no—
529C22×C4—24no—
530C22×C4—24no—
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—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—48no—
549C22×C4—48no—
550C22×C4—48no—
551C22×C4—48no—
552C22×C4—432no—
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—48no—
573C22×C4—42no—
574C22×C4—42no—
575C22×C4—42no—
576C22×C4—42no—
577C22×C4—42no—
578C22×C4—42no—
579C22×C4—42no—
580C22×C4—42no—
581C22×C4—84no—
582C22×C4—816no—
583C22×C4#13714yes—
584C22×C4C22×D412yes—
585C22×C4C22×D412yes—
586C22×C4C22×D412yes—
587C22×C4C22×D412yes—
588C22×C4C22×D411yescharacteristic
589C22×C4C22×D412yes—
590C22×C4C2×#4112yes—
591C22×C4H(5,𝔽2)12yes—
592C22×C4H(5,𝔽2)12yes—
593C22×C4H(5,𝔽2)12yes—
594C22×C4H(5,𝔽2)12yes—
595C22×C4C2511yescharacteristic
596Q16—416no—
597SD16—416no—
598C2×C8—28no—
599C2×C8—22no—
600C2×C8—22no—
601C2×C8—22no—
602C2×C8—22no—
603C2×C8—22no—
604C2×C8—22no—
605C2×C8—22no—
606C2×C8—22no—
607C2×C8—22no—
608C2×C8—22no—
609C2×C8—22no—
610C2×C8—44no—
611C2×C8—44no—
612C2×C8—44no—
613C2×C8C22×D414yes—
614C4⋊C4—24no—
615C4⋊C4—22no—
616C4⋊C4—22no—
617C4⋊C4—22no—
618C4⋊C4—22no—
619C4⋊C4—22no—
620C4⋊C4—22no—
621C4⋊C4—22no—
622C4⋊C4—22no—
623C4⋊C4—22no—
624C4⋊C4—44no—
625C4⋊C4—48no—
626C4⋊C4—48no—
627C4⋊C4—48no—
628C4⋊C4—48no—
629C4⋊C4—42no—
630C4⋊C4—42no—
631C4⋊C4—42no—
632C4⋊C4—42no—
633C4⋊C4—84no—
634C4⋊C4C22×D414yes—
635C22⋊C4—44no—
636C22⋊C4—44no—
637C22⋊C4—48no—
638C22⋊C4—48no—
639C22⋊C4—48no—
640C22⋊C4—48no—
641C22⋊C4—48no—
642C22⋊C4—84no—
643C22⋊C4—84no—
644C22⋊C4—84no—
645C42—24no—
646C42—22no—
647C42—22no—
648C23—22no—
649C23—28no—
650C23—22no—
651C23—22no—
652C23—28no—
653C23—28no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—24no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—44no—
666C23—44no—
667C23—44no—
668C23—44no—
669C23—44no—
670C23—48no—
671C23—42no—
672C23—48no—
673C23—44no—
674C23—44no—
675C23—44no—
676C23—42no—
677C23—44no—
678C23—44no—
679C23—48no—
680C23—44no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—84no—
686C23—84no—
687C23—84no—
688C23—84no—
689C23#53412yes—
690C23D4212yes—
691C23#54612yes—
692C23C2×#13514yes—
693C23C2×#13512yes—
694C23C2×#13712yes—
695C23#57712yes—
696C23#57712yes—
697C23C23×D411yescharacteristic
698Q8—24no—
699Q8—24no—
700Q8—48no—
701Q8—42no—
702Q8—42no—
703Q8—42no—
704Q8—42no—
705Q8—42no—
706Q8—42no—
707Q8—84no—
708D4—24no—
709D4—24no—
710D4—416no—
711D4—432no—
712D4—48no—
713D4—42no—
714D4—42no—
715D4—816no—
716C2×C4—22no—
717C2×C4—28no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—432no—
731C2×C4—42no—
732C2×C4—44no—
733C2×C4—44no—
734C2×C4—48no—
735C2×C4—44no—
736C2×C4—42no—
737C2×C4—48no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—48no—
741C2×C4—48no—
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—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—816no—
766C2×C4—84no—
767C2×C4—84no—
768C2×C4—84no—
769C2×C4—84no—
770C2×C4—84no—
771C2×C4#53412yes—
772C2×C4#53514yes—
773C2×C4#53814yes—
774C2×C4D4212yes—
775C2×C4#54612yes—
776C2×C4#54614yes—
777C2×C4#56014yes—
778C2×C4C2×#13714yes—
779C2×C4C23×D411yescharacteristic
780C2×C4C22×#4111yescharacteristic
781C2×C4C2×H(5,𝔽2)11yescharacteristic
782C2×C4C2×H(5,𝔽2)11yescharacteristic
783C2×C4C2×H(5,𝔽2)11yescharacteristic
784C2×C4C2×H(5,𝔽2)11yescharacteristic
785C8—24no—
786C8—42no—
787C8—42no—
788C8—42no—
789C22—24no—
790C22—24no—
791C22—24no—
792C22—416no—
793C22—42no—
794C22—42no—
795C22—42no—
796C22—42no—
797C22—42no—
798C22—42no—
799C22—42no—
800C22—42no—
801C22—44no—
802C22—42no—
803C22—44no—
804C22—42no—
805C22—42no—
806C22—44no—
807C22—88no—
808C22—816no—
809C22—82no—
810C22—82no—
811C22—82no—
812C22—82no—
813C22#267814yes—
814C22#319014yes—
815C22#320414yes—
816C22#327814yes—
817C22#328214yes—
818C22#329614yes—
819C22#333114yes—
820C22C2×#53411yescharacteristic
821C22C2×D4211yescharacteristic
822C22C2×#54611yescharacteristic
823C22C22×#13511yescharacteristic
824C22C22×#13711yescharacteristic
825C22C2×#57711yescharacteristic
826C22C2×#57711yescharacteristic
827C4—24no—
828C4—42no—
829C4—44no—
830C4—42no—
831C4—42no—
832C4—44no—
833C4—82no—
834C4—82no—
835C4—82no—
836C4—82no—
837C4—82no—
838C4#267814yes—
839C4C2×#53511yescharacteristic
840C4C2×#53811yescharacteristic
841C4C2×#54611yescharacteristic
842C4C2×#56011yescharacteristic
843C2—44no—
844C2—82no—
845C2—84no—
846C2#3102518yesdirect product factor
847C2C2×#267811yescharacteristic
848C2C2×#319011yescharacteristic
849C2C2×#320411yescharacteristic
850C2C2×#327811yescharacteristic
851C2C2×#328211yescharacteristic
852C2C2×#329611yescharacteristic
853C2C2×#333111yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#2407C2
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×#452C2semidirect
4. C2×#2417C2semidirect
5. #31025C2direct (N × H)
6. C2×#2077C2semidirect
7. C2×#2065C2semidirect
8. C2×#2056C2semidirect
9. C2×#2035C2semidirect
10. C2×#2001C2semidirect
11. C2×#2000C2semidirect
12. C2×#1968C2semidirect
13. C2×#1954C2semidirect
14. C2×#1933C2semidirect
15. C2×#1874C2semidirect
16. C2×#1788C2semidirect
27. C2×#483C22semidirect
29. C2×#452C22semidirect
47. #2417C22semidirect
64. #2077C22semidirect
65. #2065C22semidirect
66. #2056C22semidirect
67. #2035C22semidirect
68. #2001C22semidirect
69. #2000C22semidirect
70. #1968C22semidirect
71. #1954C22semidirect
72. #1933C22semidirect
73. #1874C22semidirect
74. #1788C22semidirect
167. C2×#103D4semidirect
413. #103C2×D4semidirect
846. C2#31025direct (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×#4522
C2×#24072
C2×#24172
#310252
C2×#20772
C2×#20652
C2×#20562
C2×#20352
C2×#20012
C2×#20002
C2×#19682
C2×#19542
C2×#19332
C2×#18742
C2×#17882