Finite Group Databasebeta

← C2×#30543 #7501035

Subgroups — C2×#30543 #7501035

Order 512.

3458 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#489C211yesmaximal, characteristic, complemented
2C22×#450C211yesmaximal, characteristic
3C2×#2492C211yesmaximal, characteristic, complemented
4C2×#2435C211yesmaximal, characteristic
5#30543C2116yesmaximal, direct product factor
6C2×#2055C211yesmaximal, characteristic, complemented
7C2×#2036C211yesmaximal, characteristic, complemented
8C2×#2023C211yesmaximal, characteristic, complemented
9C2×#2015C211yesmaximal, characteristic, complemented
10C2×#2015C211yesmaximal, characteristic, complemented
11C2×#2001C211yesmaximal, characteristic, complemented
12C2×#1983C211yesmaximal, characteristic, complemented
13C2×#1973C211yesmaximal, characteristic, complemented
14C2×#1925C211yesmaximal, characteristic, complemented
15C2×#1924C211yesmaximal, characteristic, complemented
16C2×#1786C211yesmaximal, characteristic
17C24×D4C2211yescharacteristic
18C23×Q16C2211yescharacteristic, complemented
19C23×SD16C2211yescharacteristic
20C23×SD16C2211yescharacteristic
21C22×C4⋊Q8C2211yescharacteristic, complemented
22C22×#124C2211yescharacteristic
23C22×#124C2211yescharacteristic
24C22×C22⋊Q8C2211yescharacteristic
25C22×C22⋊Q8C2211yescharacteristic
26C2×#489—28no—
27C2×#489C2218yescomplemented
28C2×#450—28no—
29C2×#450C2218yes—
30C22×#107C2211yescharacteristic, complemented
31C22×C4⋊C8C2211yescharacteristic, complemented
32C22×#103C2211yescharacteristic, complemented
33C22×#103C2211yescharacteristic, complemented
34C22×#103C2211yescharacteristic, complemented
35C22×#103C2211yescharacteristic, complemented
36C22×#102C2211yescharacteristic
37C22×#102C2211yescharacteristic
38C22×#102C2211yescharacteristic
39C22×#102C2211yescharacteristic
40C22×#102C2211yescharacteristic
41C22×#102C2211yescharacteristic
42C22×C22⋊C8C2211yescharacteristic
43C22×C22⋊C8C2211yescharacteristic
44C22×#97C2211yescharacteristic, complemented
45#2492—24no—
46#2492C2218yescomplemented
47#2435—24no—
48#2435C2218yes—
49C2×#400—21no—
50C2×#394—21no—
51C2×#394—21no—
52C2×#393—21no—
53C2×#391—21no—
54C2×#391C2211yescharacteristic, complemented
55C2×#391C2211yescharacteristic, complemented
56C2×#390C2211yescharacteristic
57C2×#390C2211yescharacteristic
58C2×#388—21no—
59C2×#380C2211yescharacteristic
60C2×#379—21no—
61C2×#379—21no—
62C2×C4×C4⋊C4C2211yescharacteristic, complemented
63C2×C4×C22⋊C4C2211yescharacteristic
64#2055C2218yescomplemented
65#2036C2218yescomplemented
66#2023C2218yescomplemented
67#2015C2218yescomplemented
68#2015C2218yescomplemented
69#2001C2218yescomplemented
70#1983C2218yescomplemented
71#1973C2218yescomplemented
72#1925C2218yescomplemented
73#1924C2218yescomplemented
74#1786C2218yes—
75C2×#340C2211yescharacteristic, complemented
76C2×#340C2211yescharacteristic, complemented
77C2×#336C2211yescharacteristic, complemented
78C2×#336C2211yescharacteristic, complemented
79C26—21no—
80C23×Q8—21no—
81C23×Q8C2311yescharacteristic
82C23×Q8C2311yescharacteristic
83C23×D4—24no—
84C23×D4—24no—
85C23×D4—21no—
86C23×D4—22no—
87C23×D4—42no—
88C23×D4—42no—
89C23×D4—42no—
90C23×D4—42no—
91C23×D4C2311yescharacteristic
92C23×D4C2311yescharacteristic
93C23×D4C2314yes—
94C24×C4C2311yescharacteristic
95C22×Q16—42no—
96C22×Q16—42no—
97C22×Q16—42no—
98C22×Q16C2314yescomplemented
99C22×SD16—24no—
100C22×SD16—24no—
101C22×SD16—24no—
102C22×SD16—42no—
103C22×SD16—42no—
104C22×SD16—42no—
105C22×SD16C2314yes—
106C22×SD16C2314yes—
107C23×C8C2311yescharacteristic
108C23×C8C2311yescharacteristic
109C23×C8C2311yescharacteristic
110C23×C8C2311yescharacteristic
111C2×C4⋊Q8—24no—
112C2×C4⋊Q8—22no—
113C2×C4⋊Q8—42no—
114C2×C4⋊Q8C2314yescomplemented
115C2×#124—24no—
116C2×#124—24no—
117C2×#124—22no—
118C2×#124—22no—
119C2×#124—42no—
120C2×#124—42no—
121C2×#124C2314yes—
122C2×#124C2314yes—
123C2×C22⋊Q8—22no—
124C2×C22⋊Q8—22no—
125C2×C22⋊Q8—24no—
126C2×C22⋊Q8—42no—
127C2×C22⋊Q8—42no—
128C2×C22⋊Q8—42no—
129C2×C22⋊Q8C2314yes—
130C2×C22⋊Q8C2314yes—
131C22×C4⋊C4—21no—
132C22×C4⋊C4—21no—
133C22×C4⋊C4—21no—
134C22×C4⋊C4C2311yescharacteristic
135C22×C4⋊C4C2311yescharacteristic
136C22×C4⋊C4C2311yescharacteristic
137C22×C4⋊C4C2311yescharacteristic
138C22×C22⋊C4—21no—
139C22×C22⋊C4—21no—
140C22×C22⋊C4—21no—
141C22×C22⋊C4—21no—
142C22×C22⋊C4—21no—
143C22×C22⋊C4—21no—
144C22×C22⋊C4—21no—
145C22×C22⋊C4—21no—
146C22×C22⋊C4—21no—
147C22×C22⋊C4—21no—
148C22×C22⋊C4—21no—
149C22×C22⋊C4D411yescharacteristic
150C22×C22⋊C4D411yescharacteristic
151C22×C42—21no—
152C22×C42C2311yescharacteristic
153C22×C42C2311yescharacteristic
154#489—232no—
155#450—232no—
156C2×#107—42no—
157C2×#107C2314yescomplemented
158C2×C4⋊C8—42no—
159C2×C4⋊C8C2314yescomplemented
160C2×#103—24no—
161C2×#103—24no—
162C2×#103—42no—
163C2×#103—42no—
164C2×#103C2314yescomplemented
165C2×#103C2314yescomplemented
166C2×#103C2314yescomplemented
167C2×#103C2314yescomplemented
168C2×#102—24no—
169C2×#102—24no—
170C2×#102—42no—
171C2×#102—42no—
172C2×#102—42no—
173C2×#102D418yes—
174C2×#102C2314yes—
175C2×#102C2314yes—
176C2×#102C2314yes—
177C2×#102C2314yes—
178C2×#102C2314yes—
179C2×#102C2314yes—
180C2×C22⋊C8—24no—
181C2×C22⋊C8—42no—
182C2×C22⋊C8C2314yes—
183C2×C22⋊C8C2314yes—
184C2×#97—24no—
185C2×#97C2314yescomplemented
186#400—28no—
187#394—28no—
188#394—28no—
189#393—28no—
190#391—22no—
191#391—22no—
192#391—28no—
193#391C2314yescomplemented
194#391C2314yescomplemented
195#390—22no—
196#390—22no—
197#390C2314yes—
198#390C2314yes—
199#388—28no—
200#380—22no—
201#380C2314yes—
202#379—28no—
203#379—28no—
204C4×C4⋊C4—22no—
205C4×C4⋊C4C2314yescomplemented
206C4×C22⋊C4D414yes—
207C4×C22⋊C4C2314yes—
208C2×#95—21no—
209C2×#95—21no—
210C2×#95—21no—
211C2×#95—21no—
212C2×#95—21no—
213C2×#95—21no—
214C2×#95D411yescharacteristic
215C2×#95D411yescharacteristic
216#340C2314yescomplemented
217#340C2314yescomplemented
218#336C2314yescomplemented
219#336C2314yescomplemented
220C25—21no—
221C25—21no—
222C25—24no—
223C25—44no—
224C25—44no—
225C25—44no—
226C25—44no—
227C25—44no—
228C25—82no—
229C25—82no—
230C25C2×D411yescharacteristic
231C22×Q8—21no—
232C22×Q8—21no—
233C22×Q8—24no—
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×Q8—22no—
245C22×Q8—22no—
246C22×Q8—44no—
247C22×Q8—44no—
248C22×Q8—82no—
249C22×Q8C2412yes—
250C22×Q8C2412yes—
251C22×D4—28no—
252C22×D4—28no—
253C22×D4—22no—
254C22×D4—21no—
255C22×D4—21no—
256C22×D4—24no—
257C22×D4—22no—
258C22×D4—22no—
259C22×D4—22no—
260C22×D4—22no—
261C22×D4—22no—
262C22×D4—22no—
263C22×D4—22no—
264C22×D4—22no—
265C22×D4—22no—
266C22×D4—44no—
267C22×D4—44no—
268C22×D4—44no—
269C22×D4—44no—
270C22×D4—48no—
271C22×D4—48no—
272C22×D4—44no—
273C22×D4—44no—
274C22×D4—44no—
275C22×D4—48no—
276C22×D4—416no—
277C22×D4—416no—
278C22×D4—416no—
279C22×D4—416no—
280C22×D4C2×D414yes—
281C22×D4#4114yes—
282C22×D4C2412yes—
283C22×D4C2412yes—
284C23×C4—21no—
285C23×C4—22no—
286C23×C4—22no—
287C23×C4—22no—
288C23×C4—22no—
289C23×C4—22no—
290C23×C4—22no—
291C23×C4—21no—
292C23×C4—21no—
293C23×C4—21no—
294C23×C4—21no—
295C23×C4—21no—
296C23×C4C2×D412yes—
297C23×C4C2×D411yescharacteristic
298C23×C4C2×D411yescharacteristic
299C23×C4C2×D411yescharacteristic
300C23×C4C2×D411yescharacteristic
301C23×C4C2×D411yescharacteristic
302C23×C4C2412yes—
303C23×C4C2411yescharacteristic
304C2×Q16—44no—
305C2×Q16—44no—
306C2×Q16—44no—
307C2×Q16—416no—
308C2×SD16—28no—
309C2×SD16—28no—
310C2×SD16—28no—
311C2×SD16—44no—
312C2×SD16—44no—
313C2×SD16—44no—
314C2×SD16—416no—
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—
332C4⋊Q8—28no—
333C4⋊Q8—44no—
334C4⋊Q8—48no—
335#124—28no—
336#124—28no—
337#124—44no—
338#124—44no—
339#124—48no—
340#124—48no—
341C22⋊Q8—28no—
342C22⋊Q8—44no—
343C22⋊Q8—44no—
344C22⋊Q8—44no—
345C22⋊Q8—48no—
346C22⋊Q8—48no—
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—24no—
356C2×C4⋊C4—24no—
357C2×C4⋊C4—24no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—44no—
362C2×C4⋊C4—44no—
363C2×C4⋊C4—44no—
364C2×C4⋊C4C2×D414yes—
365C2×C4⋊C4C2412yes—
366C2×C4⋊C4C2412yes—
367C2×C4⋊C4C2412yes—
368C2×C4⋊C4C2412yes—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—24no—
373C2×C22⋊C4—24no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—24no—
379C2×C22⋊C4—24no—
380C2×C22⋊C4—24no—
381C2×C22⋊C4—42no—
382C2×C22⋊C4—44no—
383C2×C22⋊C4—44no—
384C2×C22⋊C4—44no—
385C2×C22⋊C4—44no—
386C2×C22⋊C4—44no—
387C2×C22⋊C4—44no—
388C2×C22⋊C4—82no—
389C2×C22⋊C4—82no—
390C2×C22⋊C4—82no—
391C2×C22⋊C4—82no—
392C2×C22⋊C4—82no—
393C2×C22⋊C4C2×D414yes—
394C2×C22⋊C4C2×D414yes—
395C2×C42—22no—
396C2×C42—22no—
397C2×C42—22no—
398C2×C42—22no—
399C2×C42—24no—
400C2×C42—82no—
401C2×C42C2×D412yes—
402C2×C42C2×D412yes—
403C2×C42C2412yes—
404C2×C42C2412yes—
405#107—44no—
406C4⋊C8—44no—
407#103—28no—
408#103—28no—
409#103—44no—
410#103—44no—
411#102—28no—
412#102—28no—
413#102—44no—
414#102—44no—
415#102—44no—
416#102C2×D4116yes—
417C22⋊C8—28no—
418C22⋊C8—44no—
419#97—28no—
420#95—24no—
421#95—24no—
422#95—24no—
423#95—24no—
424#95—24no—
425#95—24no—
426#95C2×D414yes—
427#95C2×D414yes—
428C24—22no—
429C24—22no—
430C24—22no—
431C24—22no—
432C24—22no—
433C24—22no—
434C24—24no—
435C24—24no—
436C24—22no—
437C24—22no—
438C24—48no—
439C24—48no—
440C24—48no—
441C24—48no—
442C24—432no—
443C24—42no—
444C24—42no—
445C24—42no—
446C24—42no—
447C24—42no—
448C24—42no—
449C24—42no—
450C24—42no—
451C24—42no—
452C24—42no—
453C24—42no—
454C24—42no—
455C24—48no—
456C24—84no—
457C24—84no—
458C24—816no—
459C24—816no—
460C24—816no—
461C24—816no—
462C24—816no—
463C24—816no—
464C24#13714yes—
465C24C22×D412yes—
466C24C22×D411yescharacteristic
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—22no—
477C2×Q8—22no—
478C2×Q8—22no—
479C2×Q8—48no—
480C2×Q8—48no—
481C2×Q8—42no—
482C2×Q8—42no—
483C2×Q8—42no—
484C2×Q8—42no—
485C2×Q8—42no—
486C2×Q8—42no—
487C2×Q8—44no—
488C2×Q8—44no—
489C2×Q8—44no—
490C2×Q8—44no—
491C2×Q8—44no—
492C2×Q8—44no—
493C2×Q8—44no—
494C2×Q8—44no—
495C2×Q8—84no—
496C2×Q8—816no—
497C2×D4—28no—
498C2×D4—28no—
499C2×D4—24no—
500C2×D4—28no—
501C2×D4—28no—
502C2×D4—24no—
503C2×D4—22no—
504C2×D4—22no—
505C2×D4—22no—
506C2×D4—22no—
507C2×D4—22no—
508C2×D4—22no—
509C2×D4—22no—
510C2×D4—22no—
511C2×D4—22no—
512C2×D4—22no—
513C2×D4—48no—
514C2×D4—48no—
515C2×D4—48no—
516C2×D4—416no—
517C2×D4—416no—
518C2×D4—416no—
519C2×D4—432no—
520C2×D4—464no—
521C2×D4—416no—
522C2×D4—42no—
523C2×D4—42no—
524C2×D4—44no—
525C2×D4—44no—
526C2×D4—42no—
527C2×D4—42no—
528C2×D4—44no—
529C2×D4—44no—
530C2×D4C22×D414yes—
531C2×D4C2×#4114yes—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—24no—
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—24no—
550C22×C4—24no—
551C22×C4—24no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—42no—
564C22×C4—42no—
565C22×C4—44no—
566C22×C4—44no—
567C22×C4—44no—
568C22×C4—44no—
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—42no—
578C22×C4—42no—
579C22×C4—42no—
580C22×C4—42no—
581C22×C4—42no—
582C22×C4—42no—
583C22×C4—42no—
584C22×C4C22×D412yes—
585C22×C4C22×D412yes—
586C22×C4C22×D412yes—
587C22×C4C22×D412yes—
588C22×C4C22×D412yes—
589C22×C4C22×D411yescharacteristic
590C22×C4C22×D412yes—
591C22×C4C2×#4112yes—
592C22×C4H(5,𝔽2)12yes—
593C22×C4H(5,𝔽2)12yes—
594C22×C4H(5,𝔽2)12yes—
595C22×C4H(5,𝔽2)12yes—
596C22×C4C2511yescharacteristic
597Q16—416no—
598SD16—416no—
599SD16—416no—
600C2×C8—28no—
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—22no—
611C2×C8—22no—
612C2×C8—44no—
613C2×C8—44no—
614C2×C8—44no—
615C2×C8C22×D414yes—
616C4⋊C4—24no—
617C4⋊C4—22no—
618C4⋊C4—22no—
619C4⋊C4—22no—
620C4⋊C4—22no—
621C4⋊C4—22no—
622C4⋊C4—22no—
623C4⋊C4—22no—
624C4⋊C4—48no—
625C4⋊C4—48no—
626C4⋊C4—48no—
627C4⋊C4—42no—
628C4⋊C4—42no—
629C4⋊C4—42no—
630C4⋊C4C22×D414yes—
631C22⋊C4—28no—
632C22⋊C4—44no—
633C22⋊C4—48no—
634C22⋊C4—48no—
635C22⋊C4—48no—
636C22⋊C4—48no—
637C22⋊C4—48no—
638C22⋊C4—48no—
639C22⋊C4—84no—
640C22⋊C4—84no—
641C22⋊C4—84no—
642C22⋊C4—84no—
643C22⋊C4—84no—
644C42—24no—
645C42—24no—
646C42—22no—
647C42—22no—
648C42—22no—
649C42—22no—
650C42—84no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—28no—
655C23—28no—
656C23—28no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—24no—
661C23—24no—
662C23—44no—
663C23—44no—
664C23—44no—
665C23—44no—
666C23—432no—
667C23—48no—
668C23—48no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—48no—
674C23—48no—
675C23—48no—
676C23—48no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—816no—
686C23—816no—
687C23—816no—
688C23—816no—
689C23—816no—
690C23—8128no—
691C23—816no—
692C23—84no—
693C23—84no—
694C23—84no—
695C23—84no—
696C23—84no—
697C23—84no—
698C23—84no—
699C23—84no—
700C23#53512yes—
701C23D4212yes—
702C23#54612yes—
703C23C2×#13714yes—
704C23C2×#13712yes—
705C23#57512yes—
706C23#57612yes—
707C23#57712yes—
708C23C23×D411yescharacteristic
709Q8—42no—
710Q8—42no—
711Q8—42no—
712Q8—42no—
713Q8—42no—
714Q8—42no—
715Q8—42no—
716Q8—42no—
717Q8—816no—
718Q8—84no—
719Q8—84no—
720D4—24no—
721D4—24no—
722D4—24no—
723D4—24no—
724D4—432no—
725D4—48no—
726D4—48no—
727D4—42no—
728D4—42no—
729D4—42no—
730D4—42no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—24no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—44no—
748C2×C4—44no—
749C2×C4—44no—
750C2×C4—48no—
751C2×C4—44no—
752C2×C4—44no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—48no—
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—42no—
775C2×C4—84no—
776C2×C4—84no—
777C2×C4—84no—
778C2×C4—84no—
779C2×C4—84no—
780C2×C4#53512yes—
781C2×C4#53514yes—
782C2×C4#53814yes—
783C2×C4D4212yes—
784C2×C4#54612yes—
785C2×C4#54614yes—
786C2×C4H(3,𝔽4)14yes—
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—416no—
801C22—42no—
802C22—42no—
803C22—42no—
804C22—42no—
805C22—44no—
806C22—44no—
807C22—44no—
808C22—44no—
809C22—44no—
810C22—44no—
811C22—864no—
812C22—816no—
813C22—816no—
814C22—82no—
815C22—82no—
816C22—82no—
817C22—82no—
818C22—82no—
819C22—82no—
820C22—82no—
821C22—82no—
822C22#267014yes—
823C22#321514yes—
824C22#322414yes—
825C22#326614yes—
826C22#327314yes—
827C22#331114yes—
828C22#331414yes—
829C22C2×#53511yescharacteristic
830C22C2×D4211yescharacteristic
831C22C2×#54611yescharacteristic
832C22C22×#13711yescharacteristic
833C22C2×#57511yescharacteristic
834C22C2×#57611yescharacteristic
835C22C2×#57711yescharacteristic
836C4—42no—
837C4—42no—
838C4—44no—
839C4—42no—
840C4—42no—
841C4—42no—
842C4—82no—
843C4—82no—
844C4—82no—
845C4—82no—
846C4—82no—
847C4#267014yes—
848C4C2×#53511yescharacteristic
849C4C2×#53811yescharacteristic
850C4C2×#54611yescharacteristic
851C4C2×H(3,𝔽4)11yescharacteristic
852C2—44no—
853C2—84no—
854C2—84no—
855C2#3054318yesdirect product factor
856C2C2×#267011yescharacteristic
857C2C2×#321511yescharacteristic
858C2C2×#322411yescharacteristic
859C2C2×#326611yescharacteristic
860C2C2×#327311yescharacteristic
861C2C2×#331411yescharacteristic
862C2C2×#331111yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC24×D4C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C22×#489C2semidirect
3. C2×#2492C2semidirect
5. #30543C2direct (N × H)
6. C2×#2055C2semidirect
7. C2×#2036C2semidirect
8. C2×#2023C2semidirect
9. C2×#2015C2semidirect
10. C2×#2015C2semidirect
11. C2×#2001C2semidirect
12. C2×#1983C2semidirect
13. C2×#1973C2semidirect
14. C2×#1925C2semidirect
15. C2×#1924C2semidirect
18. C23×Q16C22semidirect
21. C22×C4⋊Q8C22semidirect
27. C2×#489C22semidirect
30. C22×#107C22semidirect
31. C22×C4⋊C8C22semidirect
32. C22×#103C22semidirect
33. C22×#103C22semidirect
34. C22×#103C22semidirect
35. C22×#103C22semidirect
44. C22×#97C22semidirect
46. #2492C22semidirect
54. C2×#391C22semidirect
55. C2×#391C22semidirect
62. C2×C4×C4⋊C4C22semidirect
64. #2055C22semidirect
65. #2036C22semidirect
66. #2023C22semidirect
67. #2015C22semidirect
68. #2015C22semidirect
69. #2001C22semidirect
70. #1983C22semidirect
71. #1973C22semidirect
72. #1925C22semidirect
73. #1924C22semidirect
75. C2×#340C22semidirect
76. C2×#340C22semidirect
77. C2×#336C22semidirect
78. C2×#336C22semidirect
98. C22×Q16C23semidirect
114. C2×C4⋊Q8C23semidirect
157. C2×#107C23semidirect
159. C2×C4⋊C8C23semidirect
164. C2×#103C23semidirect
165. C2×#103C23semidirect
166. C2×#103C23semidirect
167. C2×#103C23semidirect
185. C2×#97C23semidirect
193. #391C23semidirect
194. #391C23semidirect
205. C4×C4⋊C4C23semidirect
216. #340C23semidirect
217. #340C23semidirect
218. #336C23semidirect
219. #336C23semidirect
855. C2#30543direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#4892
C22×#4502
C2×#24922
C2×#24352
#305432
C2×#20552
C2×#20362
C2×#20232
C2×#20152
C2×#20012
C2×#19832
C2×#19732
C2×#19252
C2×#19242
C2×#17862