Finite Group Databasebeta

← C2×#25510 #6452065

Subgroups — C2×#25510 #6452065

Order 512.

3658 conjugacy classes of subgroups.

The subgroup lattice has 841 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#542C211yesmaximal, characteristic, complemented
2C22×#468C211yesmaximal, characteristic, complemented
3C22×#466C211yesmaximal, characteristic
4C2×#2624C211yesmaximal, characteristic, complemented
5#25510C2116yesmaximal, direct product factor
6C2×#2057C211yesmaximal, characteristic, complemented
7C2×#2042C211yesmaximal, characteristic, complemented
8C2×#2023C211yesmaximal, characteristic, complemented
9C2×#2012C211yesmaximal, characteristic, complemented
10C2×#1895C211yesmaximal, characteristic, complemented
11C2×#1892C211yesmaximal, characteristic, complemented
12C2×#1880C211yesmaximal, characteristic, complemented
13C2×#1879C211yesmaximal, characteristic, complemented
14C2×#1863C211yesmaximal, characteristic, complemented
15C2×#1862C211yesmaximal, characteristic, complemented
16C2×#1729C211yesmaximal, characteristic, complemented
17C23×SD16C2211yescharacteristic
18C23×D8C2211yescharacteristic
19C23×M16C2211yescharacteristic
20C24×C8C2211yescharacteristic
21C2×#542—28no—
22C2×#542—28no—
23C2×#542—24no—
24C2×#542C2218yescomplemented
25C22×C4⋊Q8C2211yescharacteristic
26C22×#126—21no—
27C22×#124—21no—
28C22×#124C2211yescharacteristic
29C22×#123—21no—
30C22×C22⋊Q8—21no—
31C22×C22⋊Q8C2211yescharacteristic
32C22×#121C2211yescharacteristic
33C22×#121C2211yescharacteristic
34C22×C4×Q8C2211yescharacteristic
35C22×C4×D4C2211yescharacteristic
36C22×#117C2211yescharacteristic
37C2×#468—28no—
38C2×#468C2218yescomplemented
39C2×#466—28no—
40C2×#466C2218yes—
41C22×#107C2211yescharacteristic
42C22×#107C2211yescharacteristic
43C22×#103C2211yescharacteristic
44C22×#103C2211yescharacteristic
45C22×#103C2211yescharacteristic
46C22×#102C2211yescharacteristic
47C22×#102C2211yescharacteristic
48C22×#102C2211yescharacteristic
49C22×#102C2211yescharacteristic
50C22×#102C2211yescharacteristic
51#2624—24no—
52#2624C2218yescomplemented
53C2×#399—21no—
54C2×#397—21no—
55C2×#394—21no—
56C2×#394—21no—
57C2×#390C2211yescharacteristic
58C2×#390C2211yescharacteristic
59C2×#389C2211yescharacteristic
60C2×#389C2211yescharacteristic
61C2×#380C2211yescharacteristic
62#2057C2218yescomplemented
63#2042C2218yescomplemented
64#2023C2218yescomplemented
65#2012C2218yescomplemented
66#1895C2218yescomplemented
67#1892C2218yescomplemented
68#1880C2218yescomplemented
69#1879C2218yescomplemented
70#1863C2218yescomplemented
71#1862C2218yescomplemented
72C2×#340C2211yescharacteristic
73C2×#340C2211yescharacteristic
74C2×#340C2211yescharacteristic
75C2×#340C2211yescharacteristic
76#1729C2218yescomplemented
77C2×#336C2211yescharacteristic
78C2×#336C2211yescharacteristic
79C2×#336C2211yescharacteristic
80C2×#336C2211yescharacteristic
81C23×Q8—21no—
82C23×Q8C2311yescharacteristic
83C23×D4—21no—
84C23×D4—21no—
85C23×D4C2311yescharacteristic
86C23×D4C2311yescharacteristic
87C24×C4—21no—
88C24×C4C2311yescharacteristic
89C22×SD16—24no—
90C22×SD16—24no—
91C22×SD16—42no—
92C22×SD16C2314yes—
93C22×D8—24no—
94C22×D8—24no—
95C22×D8—42no—
96C22×D8C2314yes—
97C22×M16—24no—
98C22×M16—24no—
99C22×M16—42no—
100C22×M16C2314yes—
101C23×C8—24no—
102C23×C8—24no—
103C23×C8—42no—
104C23×C8C2311yescharacteristic
105C23×C8C2311yescharacteristic
106C23×C8C2314yes—
107C23×C8C2311yescharacteristic
108C23×C8C2311yescharacteristic
109#542—264no—
110#542—232no—
111#542—232no—
112C2×C4⋊Q8—24no—
113C2×C4⋊Q8—24no—
114C2×C4⋊Q8—22no—
115C2×C4⋊Q8C2314yes—
116C2×#126—216no—
117C2×#126—28no—
118C2×#124—216no—
119C2×#124—24no—
120C2×#124—24no—
121C2×#124—28no—
122C2×#124—22no—
123C2×#124C2314yes—
124C2×#123—216no—
125C2×#123—28no—
126C2×C22⋊Q8—216no—
127C2×C22⋊Q8—24no—
128C2×C22⋊Q8—22no—
129C2×C22⋊Q8—28no—
130C2×C22⋊Q8D418yes—
131C2×C22⋊Q8C2314yes—
132C2×#121—24no—
133C2×#121—22no—
134C2×#121—22no—
135C2×#121—24no—
136C2×#121—24no—
137C2×#121D418yes—
138C2×#121C2314yes—
139C2×#121C2314yes—
140C2×C4×Q8—24no—
141C2×C4×Q8—24no—
142C2×C4×Q8—22no—
143C2×C4×Q8C2314yes—
144C2×C4×D4—24no—
145C2×C4×D4—24no—
146C2×C4×D4—22no—
147C2×C4×D4C2314yes—
148C2×#117—24no—
149C2×#117—24no—
150C2×#117D414yes—
151C2×#117C2314yes—
152C22×C4⋊C4—21no—
153C22×C4⋊C4—21no—
154C22×C4⋊C4—21no—
155C22×C4⋊C4—21no—
156C22×C4⋊C4—21no—
157C22×C4⋊C4D411yescharacteristic
158C22×C4⋊C4D411yescharacteristic
159C22×C4⋊C4C2311yescharacteristic
160C22×C4⋊C4C2311yescharacteristic
161C22×C4⋊C4C2311yescharacteristic
162C22×C4⋊C4C2311yescharacteristic
163C22×C4⋊C4C2311yescharacteristic
164C22×C22⋊C4—21no—
165C22×C22⋊C4—21no—
166C22×C22⋊C4—21no—
167C22×C22⋊C4—21no—
168C22×C22⋊C4—21no—
169C22×C22⋊C4—21no—
170C22×C22⋊C4—21no—
171C22×C22⋊C4—21no—
172C22×C22⋊C4—21no—
173C22×C22⋊C4—21no—
174C22×C22⋊C4—21no—
175C22×C22⋊C4D411yescharacteristic
176C22×C22⋊C4D411yescharacteristic
177C22×C42—21no—
178C22×C42C2311yescharacteristic
179C22×C42C2311yescharacteristic
180#468—232no—
181#466—232no—
182C2×#107—24no—
183C2×#107—24no—
184C2×#107C2314yes—
185C2×#107C2314yes—
186C2×#103—24no—
187C2×#103—24no—
188C2×#103—42no—
189C2×#103C2314yes—
190C2×#103C2314yes—
191C2×#103C2314yes—
192C2×#102—24no—
193C2×#102—24no—
194C2×#102—24no—
195C2×#102—24no—
196C2×#102—42no—
197C2×#102C2314yes—
198C2×#102C2314yes—
199C2×#102C2314yes—
200C2×#102C2314yes—
201C2×#102C2314yes—
202#399—28no—
203#397—28no—
204#394—28no—
205#394—28no—
206#390—22no—
207#390—22no—
208#390C2314yes—
209#390C2314yes—
210#389—22no—
211#389—22no—
212#389C2314yes—
213#389C2314yes—
214#380—22no—
215#380C2314yes—
216C2×#95—21no—
217C2×#95—21no—
218C2×#95—21no—
219#340C2314yes—
220#340C2314yes—
221#340C2314yes—
222#340C2314yes—
223#336C2314yes—
224#336C2314yes—
225#336C2314yes—
226#336C2314yes—
227C25—21no—
228C25—21no—
229C25C2×D411yescharacteristic
230C22×Q8—28no—
231C22×Q8—22no—
232C22×Q8—21no—
233C22×Q8—24no—
234C22×Q8—22no—
235C22×Q8—22no—
236C22×Q8—22no—
237C22×Q8—22no—
238C22×Q8—82no—
239C22×Q8—82no—
240C22×Q8C2×D414yes—
241C22×Q8C2412yes—
242C22×D4—28no—
243C22×D4—24no—
244C22×D4—24no—
245C22×D4—21no—
246C22×D4—22no—
247C22×D4—22no—
248C22×D4—22no—
249C22×D4—21no—
250C22×D4—22no—
251C22×D4—22no—
252C22×D4—22no—
253C22×D4—22no—
254C22×D4—22no—
255C22×D4—22no—
256C22×D4—22no—
257C22×D4—22no—
258C22×D4—44no—
259C22×D4—82no—
260C22×D4—82no—
261C22×D4—82no—
262C22×D4—82no—
263C22×D4C2×D414yes—
264C22×D4C2412yes—
265C22×D4C2412yes—
266C23×C4—22no—
267C23×C4—22no—
268C23×C4—22no—
269C23×C4—22no—
270C23×C4—21no—
271C23×C4—21no—
272C23×C4—21no—
273C23×C4—28no—
274C23×C4—24no—
275C23×C4—21no—
276C23×C4—21no—
277C23×C4—21no—
278C23×C4—82no—
279C23×C4—82no—
280C23×C4C2×D411yescharacteristic
281C23×C4C2×D411yescharacteristic
282C23×C4C2×D411yescharacteristic
283C23×C4C2×D411yescharacteristic
284C23×C4C2×D412yes—
285C23×C4C2×D411yescharacteristic
286C23×C4C2×D414yes—
287C23×C4C2×D414yes—
288C23×C4C2412yes—
289C23×C4C2411yescharacteristic
290C2×SD16—28no—
291C2×SD16—28no—
292C2×SD16—44no—
293C2×SD16—416no—
294C2×D8—28no—
295C2×D8—28no—
296C2×D8—44no—
297C2×D8—416no—
298C2×M16—28no—
299C2×M16—28no—
300C2×M16—44no—
301C2×M16—416no—
302C22×C8—22no—
303C22×C8—22no—
304C22×C8—22no—
305C22×C8—22no—
306C22×C8—22no—
307C22×C8—28no—
308C22×C8—22no—
309C22×C8—22no—
310C22×C8—22no—
311C22×C8—22no—
312C22×C8—22no—
313C22×C8—28no—
314C22×C8—44no—
315C22×C8—416no—
316C22×C8#4114yes—
317C22×C8#4114yes—
318C22×C8C2412yes—
319C22×C8C2412yes—
320C22×C8C2412yes—
321C22×C8C2412yes—
322C4⋊Q8—216no—
323C4⋊Q8—28no—
324C4⋊Q8—28no—
325#126—264no—
326#124—264no—
327#124—216no—
328#124—28no—
329#124—28no—
330#123—264no—
331C22⋊Q8—264no—
332C22⋊Q8—216no—
333C22⋊Q8—28no—
334C22⋊Q8C2×D4116yes—
335#121—216no—
336#121—28no—
337#121—28no—
338#121—28no—
339#121—48no—
340#121C2×D4116yes—
341C4×Q8—216no—
342C4×Q8—28no—
343C4×Q8—28no—
344C4×D4—216no—
345C4×D4—28no—
346C4×D4—28no—
347#117—216no—
348#117—28no—
349#117—28no—
350C2×C4⋊C4—28no—
351C2×C4⋊C4—28no—
352C2×C4⋊C4—28no—
353C2×C4⋊C4—24no—
354C2×C4⋊C4—24no—
355C2×C4⋊C4—24no—
356C2×C4⋊C4—24no—
357C2×C4⋊C4—24no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—24no—
372C2×C4⋊C4—24no—
373C2×C4⋊C4—82no—
374C2×C4⋊C4—82no—
375C2×C4⋊C4C2×D414yes—
376C2×C4⋊C4C2×D414yes—
377C2×C4⋊C4C2×D414yes—
378C2×C4⋊C4C2×D414yes—
379C2×C4⋊C4C2412yes—
380C2×C4⋊C4C2412yes—
381C2×C4⋊C4C2412yes—
382C2×C4⋊C4C2412yes—
383C2×C4⋊C4C2412yes—
384C2×C22⋊C4—28no—
385C2×C22⋊C4—28no—
386C2×C22⋊C4—28no—
387C2×C22⋊C4—28no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—24no—
391C2×C22⋊C4—28no—
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—24no—
399C2×C22⋊C4—24no—
400C2×C22⋊C4—24no—
401C2×C22⋊C4—24no—
402C2×C22⋊C4—44no—
403C2×C22⋊C4—82no—
404C2×C22⋊C4—82no—
405C2×C22⋊C4—82no—
406C2×C22⋊C4—82no—
407C2×C22⋊C4—82no—
408C2×C22⋊C4C2×D414yes—
409C2×C22⋊C4C2×D414yes—
410C2×C42—28no—
411C2×C42—22no—
412C2×C42—22no—
413C2×C42—22no—
414C2×C42—22no—
415C2×C42—24no—
416C2×C42C2×D412yes—
417C2×C42C2×D412yes—
418C2×C42C2412yes—
419C2×C42C2412yes—
420#107—28no—
421#107—28no—
422#103—28no—
423#103—28no—
424#103—44no—
425#102—28no—
426#102—28no—
427#102—28no—
428#102—28no—
429#102—44no—
430#95—24no—
431#95—24no—
432#95—24no—
433C24—22no—
434C24—22no—
435C24—22no—
436C24—22no—
437C24—22no—
438C24—22no—
439C24—24no—
440C24—22no—
441C24—22no—
442C24—42no—
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#12014yes—
456C24C22×D412yes—
457C24C22×D411yescharacteristic
458C2×Q8—216no—
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—42no—
468C2×Q8—42no—
469C2×Q8—44no—
470C2×Q8—44no—
471C2×Q8—84no—
472C2×Q8—84no—
473C2×Q8—816no—
474C2×Q8C22×D414yes—
475C2×D4—216no—
476C2×D4—24no—
477C2×D4—28no—
478C2×D4—28no—
479C2×D4—22no—
480C2×D4—22no—
481C2×D4—22no—
482C2×D4—22no—
483C2×D4—22no—
484C2×D4—22no—
485C2×D4—22no—
486C2×D4—22no—
487C2×D4—22no—
488C2×D4—22no—
489C2×D4—22no—
490C2×D4—48no—
491C2×D4—42no—
492C2×D4—42no—
493C2×D4—42no—
494C2×D4—42no—
495C2×D4—42no—
496C2×D4—44no—
497C2×D4—44no—
498C2×D4—44no—
499C2×D4—44no—
500C2×D4—44no—
501C2×D4—44no—
502C2×D4—816no—
503C2×D4—84no—
504C2×D4—84no—
505C2×D4—84no—
506C2×D4—84no—
507C2×D4—816no—
508C2×D4C22×D414yes—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—24no—
512C22×C4—24no—
513C22×C4—28no—
514C22×C4—28no—
515C22×C4—28no—
516C22×C4—28no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—24no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—24no—
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—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—216no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—42no—
544C22×C4—42no—
545C22×C4—42no—
546C22×C4—42no—
547C22×C4—42no—
548C22×C4—42no—
549C22×C4—42no—
550C22×C4—42no—
551C22×C4—42no—
552C22×C4—42no—
553C22×C4—42no—
554C22×C4—42no—
555C22×C4—42no—
556C22×C4—42no—
557C22×C4—42no—
558C22×C4—84no—
559C22×C4—84no—
560C22×C4—816no—
561C22×C4#12014yes—
562C22×C4#12018yes—
563C22×C4C22×D412yes—
564C22×C4C22×D412yes—
565C22×C4C22×D412yes—
566C22×C4C22×D412yes—
567C22×C4C22×D412yes—
568C22×C4C22×D414yes—
569C22×C4C22×D414yes—
570C22×C4C22×D411yescharacteristic
571C22×C4C22×D412yes—
572C22×C4C22×D412yes—
573C22×C4C2×#4112yes—
574C22×C4C2×#4112yes—
575C22×C4H(5,𝔽2)12yes—
576C22×C42−1+412yes—
577C22×C4C2511yescharacteristic
578SD16—416no—
579D8—416no—
580M16—416no—
581C2×C8—28no—
582C2×C8—28no—
583C2×C8—22no—
584C2×C8—22no—
585C2×C8—22no—
586C2×C8—22no—
587C2×C8—22no—
588C2×C8—22no—
589C2×C8—22no—
590C2×C8—22no—
591C2×C8—22no—
592C2×C8—22no—
593C2×C8—416no—
594C2×C8—44no—
595C2×C8—44no—
596C2×C8C2×#4114yes—
597C2×C8C2×#4114yes—
598C4⋊C4—216no—
599C4⋊C4—216no—
600C4⋊C4—216no—
601C4⋊C4—28no—
602C4⋊C4—28no—
603C4⋊C4—24no—
604C4⋊C4—24no—
605C4⋊C4—22no—
606C4⋊C4—22no—
607C4⋊C4—22no—
608C4⋊C4—22no—
609C4⋊C4—22no—
610C4⋊C4—22no—
611C4⋊C4—22no—
612C4⋊C4—22no—
613C4⋊C4—42no—
614C4⋊C4—42no—
615C4⋊C4—42no—
616C4⋊C4—84no—
617C4⋊C4—84no—
618C4⋊C4C22×D414yes—
619C4⋊C4C22×D414yes—
620C22⋊C4—216no—
621C22⋊C4—216no—
622C22⋊C4—216no—
623C22⋊C4—216no—
624C22⋊C4—28no—
625C22⋊C4—28no—
626C22⋊C4—216no—
627C22⋊C4—48no—
628C22⋊C4—84no—
629C22⋊C4—84no—
630C22⋊C4—84no—
631C22⋊C4—84no—
632C22⋊C4—84no—
633C42—216no—
634C42—24no—
635C42—24no—
636C42—22no—
637C42—22no—
638C42—22no—
639C42—22no—
640C23—22no—
641C23—22no—
642C23—28no—
643C23—28no—
644C23—28no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—24no—
650C23—44no—
651C23—44no—
652C23—44no—
653C23—44no—
654C23—42no—
655C23—42no—
656C23—48no—
657C23—48no—
658C23—48no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—84no—
671C23—84no—
672C23—84no—
673C23—84no—
674C23—84no—
675C23—84no—
676C23—84no—
677C23—84no—
678C23—84no—
679C23—84no—
680C23—84no—
681C23C2×#12014yes—
682C23C2×#12012yes—
683C23#53212yes—
684C23#53712yes—
685C23#57612yes—
686C23#57612yes—
687C23#57712yes—
688C23#57812yes—
689C23C23×D411yescharacteristic
690Q8—24no—
691Q8—24no—
692Q8—48no—
693Q8—42no—
694Q8—42no—
695Q8—816no—
696D4—24no—
697D4—24no—
698D4—48no—
699D4—42no—
700D4—42no—
701D4—42no—
702D4—42no—
703D4—42no—
704D4—42no—
705D4—816no—
706D4—816no—
707D4—84no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—28no—
711C2×C4—216no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—24no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—24no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—48no—
734C2×C4—44no—
735C2×C4—44no—
736C2×C4—48no—
737C2×C4—48no—
738C2×C4—44no—
739C2×C4—44no—
740C2×C4—42no—
741C2×C4—42no—
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—816no—
754C2×C4—84no—
755C2×C4—84no—
756C2×C4—84no—
757C2×C4C2×#12014yes—
758C2×C4C2×#12012yes—
759C2×C4#53212yes—
760C2×C4#53712yes—
761C2×C4#54614yes—
762C2×C4#54614yes—
763C2×C4#54714yes—
764C2×C4#54714yes—
765C2×C4C23×D411yescharacteristic
766C2×C4C23×D411yescharacteristic
767C2×C4C22×#4111yescharacteristic
768C2×C4C22×#4111yescharacteristic
769C2×C4C2×H(5,𝔽2)11yescharacteristic
770C2×C4C2×2−1+411yescharacteristic
771C8—24no—
772C8—24no—
773C8—42no—
774C8—42no—
775C22—24no—
776C22—24no—
777C22—24no—
778C22—42no—
779C22—42no—
780C22—416no—
781C22—42no—
782C22—42no—
783C22—44no—
784C22—44no—
785C22—44no—
786C22—82no—
787C22—82no—
788C22—816no—
789C22—82no—
790C22—82no—
791C22—82no—
792C22—82no—
793C22—82no—
794C22—82no—
795C22—82no—
796C22—82no—
797C22—82no—
798C22—168no—
799C22#243014yes—
800C22#300814yes—
801C22#301314yes—
802C22#317514yes—
803C22#317914yes—
804C22#325714yes—
805C22#326214yes—
806C22C22×#12011yescharacteristic
807C22C2×#53211yescharacteristic
808C22C2×#53711yescharacteristic
809C22C2×#57611yescharacteristic
810C22C2×#57611yescharacteristic
811C22C2×#57711yescharacteristic
812C22C2×#57811yescharacteristic
813C4—24no—
814C4—44no—
815C4—42no—
816C4—42no—
817C4—44no—
818C4—44no—
819C4—42no—
820C4—42no—
821C4—82no—
822C4—82no—
823C4—82no—
824C4#243014yes—
825C4C2×#54611yescharacteristic
826C4C2×#54611yescharacteristic
827C4C2×#54711yescharacteristic
828C4C2×#54711yescharacteristic
829C2—44no—
830C2—84no—
831C2—162no—
832C2#2551018yesdirect product factor
833C2C2×#243011yescharacteristic
834C2C2×#300811yescharacteristic
835C2C2×#301311yescharacteristic
836C2C2×#317511yescharacteristic
837C2C2×#317911yescharacteristic
838C2C2×#325711yescharacteristic
839C2C2×#326211yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×#466C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C22×#117 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#542C2semidirect
2. C22×#468C2semidirect
4. C2×#2624C2semidirect
5. #25510C2direct (N × H)
6. C2×#2057C2semidirect
7. C2×#2042C2semidirect
8. C2×#2023C2semidirect
9. C2×#2012C2semidirect
10. C2×#1895C2semidirect
11. C2×#1892C2semidirect
12. C2×#1880C2semidirect
13. C2×#1879C2semidirect
14. C2×#1863C2semidirect
15. C2×#1862C2semidirect
16. C2×#1729C2semidirect
24. C2×#542C22semidirect
38. C2×#468C22semidirect
52. #2624C22semidirect
62. #2057C22semidirect
63. #2042C22semidirect
64. #2023C22semidirect
65. #2012C22semidirect
66. #1895C22semidirect
67. #1892C22semidirect
68. #1880C22semidirect
69. #1879C22semidirect
70. #1863C22semidirect
71. #1862C22semidirect
76. #1729C22semidirect
832. C2#25510direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#5422
C22×#4682
C22×#4662
C2×#26242
#255102
C2×#20572
C2×#20422
C2×#20232
C2×#20122
C2×#18952
C2×#18922
C2×#18802
C2×#18792
C2×#18632
C2×#18622
C2×#17292