Finite Group Databasebeta

← C2×#31012 #7503099

Subgroups — C2×#31012 #7503099

Order 512.

3442 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#464C211yesmaximal, characteristic, complemented
2C22×#450C211yesmaximal, characteristic
3C2×#2435C211yesmaximal, characteristic
4C2×#2423C211yesmaximal, characteristic, complemented
5#31012C2116yesmaximal, direct product factor
6C2×#2071C211yesmaximal, characteristic, complemented
7C2×#2067C211yesmaximal, characteristic, complemented
8C2×#2042C211yesmaximal, characteristic, complemented
9C2×#2036C211yesmaximal, characteristic, complemented
10C2×#2015C211yesmaximal, characteristic, complemented
11C2×#2001C211yesmaximal, characteristic, complemented
12C2×#1973C211yesmaximal, characteristic, complemented
13C2×#1959C211yesmaximal, characteristic, complemented
14C2×#1924C211yesmaximal, characteristic, complemented
15C2×#1880C211yesmaximal, characteristic, complemented
16C2×#1786C211yesmaximal, characteristic
17C24×D4C2211yescharacteristic
18C23×Q16C2211yescharacteristic, complemented
19C23×SD16C2211yescharacteristic
20C23×SD16C2211yescharacteristic
21C22×#124C2211yescharacteristic
22C22×#124C2211yescharacteristic
23C22×C22⋊Q8C2211yescharacteristic
24C22×C22⋊Q8C2211yescharacteristic
25C22×C4×Q8C2211yescharacteristic, complemented
26C2×#464—28no—
27C2×#464C2218yescomplemented
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#2435—24no—
46#2435C2218yes—
47#2423—24no—
48#2423C2218yescomplemented
49C2×#399—21no—
50C2×#398—21no—
51C2×#394—21no—
52C2×#394—21no—
53C2×#391C2211yescharacteristic, complemented
54C2×#390C2211yescharacteristic
55C2×#390C2211yescharacteristic
56C2×#389C2211yescharacteristic, complemented
57C2×#388—21no—
58C2×#387—21no—
59C2×#384C2211yescharacteristic, complemented
60C2×#380C2211yescharacteristic
61C2×#379—21no—
62C2×#379—21no—
63C2×C4×C22⋊C4C2211yescharacteristic
64#2071C2218yescomplemented
65#2067C2218yescomplemented
66#2042C2218yescomplemented
67#2036C2218yescomplemented
68#2015C2218yescomplemented
69#2001C2218yescomplemented
70#1973C2218yescomplemented
71#1959C2218yescomplemented
72#1924C2218yescomplemented
73#1880C2218yescomplemented
74#1786C2218yes—
75C2×#340C2211yescharacteristic, complemented
76C2×#340C2211yescharacteristic, complemented
77C2×#336C2211yescharacteristic, complemented
78C2×#336C2211yescharacteristic, complemented
79C26—21no—
80C23×Q8C2311yescharacteristic
81C23×Q8C2311yescharacteristic
82C23×D4—24no—
83C23×D4—24no—
84C23×D4—21no—
85C23×D4—22no—
86C23×D4—42no—
87C23×D4—42no—
88C23×D4—42no—
89C23×D4—42no—
90C23×D4C2311yescharacteristic
91C23×D4C2311yescharacteristic
92C23×D4C2314yes—
93C24×C4C2311yescharacteristic
94C22×Q16—24no—
95C22×Q16—42no—
96C22×Q16—42no—
97C22×Q16C2314yescomplemented
98C22×SD16—24no—
99C22×SD16—24no—
100C22×SD16—42no—
101C22×SD16—42no—
102C22×SD16—42no—
103C22×SD16D418yes—
104C22×SD16C2314yes—
105C22×SD16C2314yes—
106C23×C8C2311yescharacteristic
107C23×C8C2311yescharacteristic
108C23×C8C2311yescharacteristic
109C23×C8C2311yescharacteristic
110C2×#124—24no—
111C2×#124—24no—
112C2×#124—22no—
113C2×#124—22no—
114C2×#124—42no—
115C2×#124—42no—
116C2×#124C2314yes—
117C2×#124C2314yes—
118C2×C22⋊Q8—22no—
119C2×C22⋊Q8—22no—
120C2×C22⋊Q8—24no—
121C2×C22⋊Q8—42no—
122C2×C22⋊Q8—42no—
123C2×C22⋊Q8—42no—
124C2×C22⋊Q8C2314yes—
125C2×C22⋊Q8C2314yes—
126C2×C4×Q8—22no—
127C2×C4×Q8—24no—
128C2×C4×Q8—42no—
129C2×C4×Q8C2314yescomplemented
130C22×C4⋊C4—21no—
131C22×C4⋊C4—21no—
132C22×C4⋊C4—21no—
133C22×C4⋊C4—21no—
134C22×C4⋊C4—21no—
135C22×C4⋊C4—21no—
136C22×C4⋊C4C2311yescharacteristic
137C22×C4⋊C4C2311yescharacteristic
138C22×C4⋊C4C2311yescharacteristic
139C22×C4⋊C4C2311yescharacteristic
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⋊C4—21no—
150C22×C22⋊C4—21no—
151C22×C22⋊C4D411yescharacteristic
152C22×C22⋊C4D411yescharacteristic
153C22×C42—21no—
154C22×C42C2311yescharacteristic
155C22×C42C2311yescharacteristic
156#464—232no—
157#450—232no—
158C2×#107—42no—
159C2×#107C2314yescomplemented
160C2×C4⋊C8—24no—
161C2×C4⋊C8C2314yescomplemented
162C2×#103—24no—
163C2×#103—42no—
164C2×#103—42no—
165C2×#103—42no—
166C2×#103C2314yescomplemented
167C2×#103C2314yescomplemented
168C2×#103C2314yescomplemented
169C2×#103C2314yescomplemented
170C2×#102—24no—
171C2×#102—24no—
172C2×#102—24no—
173C2×#102—42no—
174C2×#102—42no—
175C2×#102—42no—
176C2×#102C2314yes—
177C2×#102C2314yes—
178C2×#102C2314yes—
179C2×#102C2314yes—
180C2×#102C2314yes—
181C2×#102C2314yes—
182C2×C22⋊C8—24no—
183C2×C22⋊C8—42no—
184C2×C22⋊C8C2314yes—
185C2×C22⋊C8C2314yes—
186C2×#97—42no—
187C2×#97C2314yescomplemented
188#399—28no—
189#398—28no—
190#394—28no—
191#394—28no—
192#391—22no—
193#391C2314yescomplemented
194#390—22no—
195#390—22no—
196#390C2314yes—
197#390C2314yes—
198#389—22no—
199#389C2314yescomplemented
200#388—28no—
201#387—28no—
202#384—22no—
203#384C2314yescomplemented
204#380—22no—
205#380C2314yes—
206#379—28no—
207#379—28no—
208C4×C22⋊C4D414yes—
209C4×C22⋊C4C2314yes—
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—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—28no—
248C22×D4—28no—
249C22×D4—22no—
250C22×D4—21no—
251C22×D4—21no—
252C22×D4—24no—
253C22×D4—22no—
254C22×D4—22no—
255C22×D4—22no—
256C22×D4—22no—
257C22×D4—22no—
258C22×D4—22no—
259C22×D4—22no—
260C22×D4—22no—
261C22×D4—22no—
262C22×D4—44no—
263C22×D4—44no—
264C22×D4—44no—
265C22×D4—44no—
266C22×D4—48no—
267C22×D4—48no—
268C22×D4—44no—
269C22×D4—44no—
270C22×D4—44no—
271C22×D4—48no—
272C22×D4—416no—
273C22×D4—416no—
274C22×D4—416no—
275C22×D4—416no—
276C22×D4C2×D414yes—
277C22×D4#4114yes—
278C22×D4C2412yes—
279C22×D4C2412yes—
280C23×C4—21no—
281C23×C4—22no—
282C23×C4—22no—
283C23×C4—22no—
284C23×C4—22no—
285C23×C4—22no—
286C23×C4—22no—
287C23×C4—21no—
288C23×C4—21no—
289C23×C4—21no—
290C23×C4—21no—
291C23×C4—21no—
292C23×C4C2×D412yes—
293C23×C4C2×D411yescharacteristic
294C23×C4C2×D411yescharacteristic
295C23×C4C2×D411yescharacteristic
296C23×C4C2×D411yescharacteristic
297C23×C4C2×D411yescharacteristic
298C23×C4C2412yes—
299C23×C4C2411yescharacteristic
300C2×Q16—28no—
301C2×Q16—44no—
302C2×Q16—44no—
303C2×Q16—416no—
304C2×SD16—28no—
305C2×SD16—28no—
306C2×SD16—416no—
307C2×SD16—44no—
308C2×SD16—44no—
309C2×SD16—44no—
310C2×SD16—416no—
311C2×SD16C2×D4116yes—
312C22×C8—22no—
313C22×C8—22no—
314C22×C8—22no—
315C22×C8—22no—
316C22×C8—22no—
317C22×C8—22no—
318C22×C8—22no—
319C22×C8—22no—
320C22×C8—22no—
321C22×C8—22no—
322C22×C8—22no—
323C22×C8C2×D414yes—
324C22×C8C2412yes—
325C22×C8C2412yes—
326C22×C8C2412yes—
327C22×C8C2412yes—
328#124—28no—
329#124—28no—
330#124—44no—
331#124—44no—
332#124—48no—
333#124—48no—
334C22⋊Q8—28no—
335C22⋊Q8—44no—
336C22⋊Q8—44no—
337C22⋊Q8—44no—
338C22⋊Q8—48no—
339C22⋊Q8—48no—
340C4×Q8—28no—
341C4×Q8—44no—
342C4×Q8—48no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—24no—
352C2×C4⋊C4—24no—
353C2×C4⋊C4—24no—
354C2×C4⋊C4—24no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—24no—
360C2×C4⋊C4—24no—
361C2×C4⋊C4—44no—
362C2×C4⋊C4—44no—
363C2×C4⋊C4—44no—
364C2×C4⋊C4—44no—
365C2×C4⋊C4—82no—
366C2×C4⋊C4—82no—
367C2×C4⋊C4C2412yes—
368C2×C4⋊C4C2412yes—
369C2×C4⋊C4C2412yes—
370C2×C4⋊C4C2412yes—
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—24no—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—42no—
384C2×C22⋊C4—44no—
385C2×C22⋊C4—44no—
386C2×C22⋊C4—44no—
387C2×C22⋊C4—44no—
388C2×C22⋊C4—44no—
389C2×C22⋊C4—44no—
390C2×C22⋊C4—82no—
391C2×C22⋊C4—82no—
392C2×C22⋊C4—82no—
393C2×C22⋊C4—82no—
394C2×C22⋊C4—82no—
395C2×C22⋊C4C2×D414yes—
396C2×C22⋊C4C2×D414yes—
397C2×C42—22no—
398C2×C42—22no—
399C2×C42—22no—
400C2×C42—22no—
401C2×C42—24no—
402C2×C42—44no—
403C2×C42C2×D412yes—
404C2×C42C2×D412yes—
405C2×C42C2412yes—
406C2×C42C2412yes—
407#107—44no—
408C4⋊C8—28no—
409#103—28no—
410#103—44no—
411#103—44no—
412#103—44no—
413#102—28no—
414#102—28no—
415#102—28no—
416#102—44no—
417#102—44no—
418#102—44no—
419C22⋊C8—28no—
420C22⋊C8—44no—
421#97—44no—
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—24no—
468C2×Q8—22no—
469C2×Q8—28no—
470C2×Q8—28no—
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—22no—
480C2×Q8—22no—
481C2×Q8—42no—
482C2×Q8—42no—
483C2×Q8—44no—
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×Q8C22×D414yes—
493C2×D4—28no—
494C2×D4—28no—
495C2×D4—24no—
496C2×D4—28no—
497C2×D4—28no—
498C2×D4—24no—
499C2×D4—22no—
500C2×D4—22no—
501C2×D4—22no—
502C2×D4—22no—
503C2×D4—22no—
504C2×D4—22no—
505C2×D4—22no—
506C2×D4—22no—
507C2×D4—22no—
508C2×D4—22no—
509C2×D4—48no—
510C2×D4—48no—
511C2×D4—48no—
512C2×D4—416no—
513C2×D4—416no—
514C2×D4—416no—
515C2×D4—432no—
516C2×D4—464no—
517C2×D4—416no—
518C2×D4—44no—
519C2×D4—42no—
520C2×D4—42no—
521C2×D4—44no—
522C2×D4—42no—
523C2×D4—42no—
524C2×D4—44no—
525C2×D4—44no—
526C2×D4C22×D414yes—
527C2×D4C2×#4114yes—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—24no—
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—24no—
546C22×C4—24no—
547C22×C4—24no—
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—22no—
558C22×C4—22no—
559C22×C4—42no—
560C22×C4—42no—
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—42no—
578C22×C4—42no—
579C22×C4—42no—
580C22×C4C22×D412yes—
581C22×C4C22×D412yes—
582C22×C4C22×D412yes—
583C22×C4C22×D412yes—
584C22×C4C22×D412yes—
585C22×C4C22×D412yes—
586C22×C4C22×D411yescharacteristic
587C22×C4C2×#4112yes—
588C22×C4H(5,𝔽2)12yes—
589C22×C4H(5,𝔽2)12yes—
590C22×C4H(5,𝔽2)12yes—
591C22×C4H(5,𝔽2)12yes—
592C22×C4C2511yescharacteristic
593Q16—416no—
594SD16—416no—
595SD16—416no—
596C2×C8—28no—
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—22no—
606C2×C8—22no—
607C2×C8—22no—
608C2×C8—44no—
609C2×C8—44no—
610C2×C8—44no—
611C2×C8C22×D414yes—
612C4⋊C4—22no—
613C4⋊C4—22no—
614C4⋊C4—22no—
615C4⋊C4—22no—
616C4⋊C4—22no—
617C4⋊C4—22no—
618C4⋊C4—22no—
619C4⋊C4—22no—
620C4⋊C4—48no—
621C4⋊C4—48no—
622C4⋊C4—48no—
623C4⋊C4—48no—
624C4⋊C4—42no—
625C4⋊C4—42no—
626C4⋊C4—42no—
627C4⋊C4—42no—
628C4⋊C4—84no—
629C4⋊C4—84no—
630C22⋊C4—28no—
631C22⋊C4—44no—
632C22⋊C4—48no—
633C22⋊C4—48no—
634C22⋊C4—48no—
635C22⋊C4—48no—
636C22⋊C4—48no—
637C22⋊C4—48no—
638C22⋊C4—84no—
639C22⋊C4—84no—
640C22⋊C4—84no—
641C22⋊C4—84no—
642C22⋊C4—84no—
643C42—24no—
644C42—24no—
645C42—22no—
646C42—22no—
647C42—22no—
648C42—22no—
649C42—48no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—28no—
654C23—28no—
655C23—28no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—24no—
660C23—24no—
661C23—44no—
662C23—44no—
663C23—44no—
664C23—44no—
665C23—432no—
666C23—48no—
667C23—48no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—48no—
673C23—48no—
674C23—48no—
675C23—48no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—816no—
685C23—816no—
686C23—816no—
687C23—816no—
688C23—816no—
689C23—8128no—
690C23—816no—
691C23—84no—
692C23—84no—
693C23—84no—
694C23—84no—
695C23—84no—
696C23—84no—
697C23—84no—
698C23—84no—
699C23#53512yes—
700C23D4212yes—
701C23#54612yes—
702C23C2×#13714yes—
703C23C2×#13712yes—
704C23#57512yes—
705C23#57612yes—
706C23#57712yes—
707C23C23×D411yescharacteristic
708Q8—24no—
709Q8—24no—
710Q8—48no—
711Q8—42no—
712Q8—42no—
713Q8—42no—
714Q8—42no—
715Q8—42no—
716Q8—42no—
717Q8—84no—
718D4—24no—
719D4—24no—
720D4—24no—
721D4—24no—
722D4—432no—
723D4—42no—
724D4—48no—
725D4—48no—
726D4—42no—
727D4—42no—
728D4—42no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—24no—
733C2×C4—22no—
734C2×C4—22no—
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—44no—
746C2×C4—48no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—44no—
750C2×C4—44no—
751C2×C4—44no—
752C2×C4—44no—
753C2×C4—42no—
754C2×C4—48no—
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—84no—
774C2×C4—84no—
775C2×C4—84no—
776C2×C4—84no—
777C2×C4—84no—
778C2×C4#53414yes—
779C2×C4#53512yes—
780C2×C4#53814yes—
781C2×C4D4212yes—
782C2×C4#54612yes—
783C2×C4#54614yes—
784C2×C4#56014yes—
785C2×C4C23×D411yescharacteristic
786C2×C4C22×#4111yescharacteristic
787C2×C4C2×H(5,𝔽2)11yescharacteristic
788C2×C4C2×H(5,𝔽2)11yescharacteristic
789C2×C4C2×H(5,𝔽2)11yescharacteristic
790C2×C4C2×H(5,𝔽2)11yescharacteristic
791C8—24no—
792C8—42no—
793C8—42no—
794C8—42no—
795C22—24no—
796C22—24no—
797C22—24no—
798C22—416no—
799C22—42no—
800C22—42no—
801C22—42no—
802C22—42no—
803C22—44no—
804C22—44no—
805C22—44no—
806C22—44no—
807C22—44no—
808C22—44no—
809C22—864no—
810C22—816no—
811C22—816no—
812C22—82no—
813C22—82no—
814C22—82no—
815C22—82no—
816C22—82no—
817C22—82no—
818C22—82no—
819C22—82no—
820C22#267814yes—
821C22#321514yes—
822C22#322414yes—
823C22#326614yes—
824C22#326814yes—
825C22#331414yes—
826C22#332314yes—
827C22C2×#53511yescharacteristic
828C22C2×D4211yescharacteristic
829C22C2×#54611yescharacteristic
830C22C22×#13711yescharacteristic
831C22C2×#57511yescharacteristic
832C22C2×#57611yescharacteristic
833C22C2×#57711yescharacteristic
834C4—42no—
835C4—42no—
836C4—42no—
837C4—44no—
838C4—42no—
839C4—42no—
840C4—82no—
841C4—82no—
842C4—82no—
843C4—82no—
844C4—82no—
845C4#267814yes—
846C4C2×#53411yescharacteristic
847C4C2×#53811yescharacteristic
848C4C2×#54611yescharacteristic
849C4C2×#56011yescharacteristic
850C2—44no—
851C2—84no—
852C2—84no—
853C2#3101218yesdirect product factor
854C2C2×#267811yescharacteristic
855C2C2×#321511yescharacteristic
856C2C2×#322411yescharacteristic
857C2C2×#326611yescharacteristic
858C2C2×#326811yescharacteristic
859C2C2×#331411yescharacteristic
860C2C2×#332311yescharacteristic
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×#464C2semidirect
4. C2×#2423C2semidirect
5. #31012C2direct (N × H)
6. C2×#2071C2semidirect
7. C2×#2067C2semidirect
8. C2×#2042C2semidirect
9. C2×#2036C2semidirect
10. C2×#2015C2semidirect
11. C2×#2001C2semidirect
12. C2×#1973C2semidirect
13. C2×#1959C2semidirect
14. C2×#1924C2semidirect
15. C2×#1880C2semidirect
18. C23×Q16C22semidirect
25. C22×C4×Q8C22semidirect
27. C2×#464C22semidirect
30. C22×#107C22semidirect
31. C22×C4⋊C8C22semidirect
32. C22×#103C22semidirect
33. C22×#103C22semidirect
34. C22×#103C22semidirect
35. C22×#103C22semidirect
44. C22×#97C22semidirect
48. #2423C22semidirect
53. C2×#391C22semidirect
56. C2×#389C22semidirect
59. C2×#384C22semidirect
64. #2071C22semidirect
65. #2067C22semidirect
66. #2042C22semidirect
67. #2036C22semidirect
68. #2015C22semidirect
69. #2001C22semidirect
70. #1973C22semidirect
71. #1959C22semidirect
72. #1924C22semidirect
73. #1880C22semidirect
75. C2×#340C22semidirect
76. C2×#340C22semidirect
77. C2×#336C22semidirect
78. C2×#336C22semidirect
97. C22×Q16C23semidirect
129. C2×C4×Q8C23semidirect
159. C2×#107C23semidirect
161. C2×C4⋊C8C23semidirect
166. C2×#103C23semidirect
167. C2×#103C23semidirect
168. C2×#103C23semidirect
169. C2×#103C23semidirect
187. C2×#97C23semidirect
193. #391C23semidirect
199. #389C23semidirect
203. #384C23semidirect
216. #340C23semidirect
217. #340C23semidirect
218. #336C23semidirect
219. #336C23semidirect
853. C2#31012direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#4642
C22×#4502
C2×#24352
C2×#24232
#310122
C2×#20712
C2×#20672
C2×#20422
C2×#20362
C2×#20152
C2×#20012
C2×#19732
C2×#19592
C2×#19242
C2×#18802
C2×#17862