Finite Group Databasebeta

← C2×#30561 #7501151

Subgroups — C2×#30561 #7501151

Order 512.

2780 conjugacy classes of subgroups.

The subgroup lattice has 815 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#483C211yesmaximal, characteristic, complemented
2C22×#465C211yesmaximal, characteristic, complemented
3C2×#2538C211yesmaximal, characteristic, complemented
4C2×#2416C211yesmaximal, characteristic
5#30561C2116yesmaximal, direct product factor
6C2×#2094C211yesmaximal, characteristic, complemented
7C2×#2084C211yesmaximal, characteristic, complemented
8C2×#2034C211yesmaximal, characteristic, complemented
9C2×#2034C211yesmaximal, characteristic, complemented
10C2×#2035C211yesmaximal, characteristic, complemented
11C2×#2000C211yesmaximal, characteristic, complemented
12C2×#1880C211yesmaximal, characteristic, complemented
13C2×#1869C211yesmaximal, characteristic, complemented
14C2×#1865C211yesmaximal, characteristic, complemented
15C2×#1853C211yesmaximal, characteristic, complemented
16C2×#1807C211yesmaximal, characteristic, complemented
17C23×SD16C2211yescharacteristic
18C24×C8C2211yescharacteristic
19C22×C22⋊Q8C2211yescharacteristic
20C22×C22⋊Q8C2211yescharacteristic
21C22×#121—21no—
22C22×#121C2211yescharacteristic
23C22×#121C2211yescharacteristic
24C22×C4×Q8C2211yescharacteristic
25C22×C4×D4C2211yescharacteristic
26C23×C4⋊C4C2211yescharacteristic
27C2×#483—28no—
28C2×#483C2218yescomplemented
29C2×#465—28no—
30C2×#465C2218yescomplemented
31C22×#106C2211yescharacteristic
32C22×#106C2211yescharacteristic
33C22×#106C2211yescharacteristic
34C22×#106C2211yescharacteristic
35C22×#106C2211yescharacteristic
36C22×#103C2211yescharacteristic
37C22×#103C2211yescharacteristic
38C22×#103C2211yescharacteristic
39C22×#102C2211yescharacteristic
40C22×#102C2211yescharacteristic
41C22×#102C2211yescharacteristic
42C22×C22⋊C8C2211yescharacteristic
43C22×C22⋊C8C2211yescharacteristic
44C22×C22⋊C8C2211yescharacteristic
45#2538—24no—
46#2538C2218yescomplemented
47#2416—24no—
48#2416C2218yes—
49C2×#396—21no—
50C2×#396—21no—
51C2×#396—21no—
52C2×#394—21no—
53C2×#390—21no—
54C2×#390C2211yescharacteristic
55C2×#389—21no—
56C2×#389C2211yescharacteristic
57C2×#386—21no—
58C2×#384C2211yescharacteristic
59C2×#380C2211yescharacteristic
60C2×#380C2211yescharacteristic
61C2×#380C2211yescharacteristic
62#2094C2218yescomplemented
63#2084C2218yescomplemented
64#2035C2218yescomplemented
65#2034C2218yescomplemented
66#2034C2218yescomplemented
67#2000C2218yescomplemented
68#1880C2218yescomplemented
69#1869C2218yescomplemented
70#1865C2218yescomplemented
71#1853C2218yescomplemented
72#1807C2218yescomplemented
73C2×#340C2211yescharacteristic
74C2×#340C2211yescharacteristic
75C2×#340C2211yescharacteristic
76C2×#340C2211yescharacteristic
77C2×#336C2211yescharacteristic
78C2×#336C2211yescharacteristic
79C23×Q8C2311yescharacteristic
80C23×D4—21no—
81C23×D4—21no—
82C23×D4D411yescharacteristic
83C23×D4C2311yescharacteristic
84C24×C4—21no—
85C24×C4C2311yescharacteristic
86C24×C4C2311yescharacteristic
87C22×SD16—24no—
88C22×SD16—24no—
89C22×SD16—42no—
90C22×SD16C2314yes—
91C23×C8—24no—
92C23×C8—24no—
93C23×C8—42no—
94C23×C8C2311yescharacteristic
95C23×C8C2311yescharacteristic
96C23×C8C2314yes—
97C23×C8C2311yescharacteristic
98C23×C8C2311yescharacteristic
99C2×C22⋊Q8—22no—
100C2×C22⋊Q8—22no—
101C2×C22⋊Q8—24no—
102C2×C22⋊Q8—24no—
103C2×C22⋊Q8—42no—
104C2×C22⋊Q8—42no—
105C2×C22⋊Q8C2314yes—
106C2×C22⋊Q8C2314yes—
107C2×#121—28no—
108C2×#121—22no—
109C2×#121—22no—
110C2×#121—24no—
111C2×#121—42no—
112C2×#121—42no—
113C2×#121—42no—
114C2×#121—48no—
115C2×#121C2314yes—
116C2×#121C2314yes—
117C2×C4×Q8—22no—
118C2×C4×Q8—42no—
119C2×C4×Q8—42no—
120C2×C4×Q8C2314yes—
121C2×C4×D4—42no—
122C2×C4×D4—42no—
123C2×C4×D4D414yes—
124C2×C4×D4C2314yes—
125C22×C4⋊C4—24no—
126C22×C4⋊C4—21no—
127C22×C4⋊C4—21no—
128C22×C4⋊C4—21no—
129C22×C4⋊C4—21no—
130C22×C4⋊C4—21no—
131C22×C4⋊C4—22no—
132C22×C4⋊C4—21no—
133C22×C4⋊C4—21no—
134C22×C4⋊C4—42no—
135C22×C4⋊C4D411yescharacteristic
136C22×C4⋊C4C2311yescharacteristic
137C22×C4⋊C4C2311yescharacteristic
138C22×C4⋊C4C2311yescharacteristic
139C22×C4⋊C4C2311yescharacteristic
140C22×C4⋊C4C2311yescharacteristic
141C22×C4⋊C4C2314yes—
142C22×C4⋊C4C2311yescharacteristic
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⋊C4—21no—
152C22×C22⋊C4D411yescharacteristic
153C22×C22⋊C4D411yescharacteristic
154C22×C42—21no—
155C22×C42C2311yescharacteristic
156#483—232no—
157#465—232no—
158C2×#106—24no—
159C2×#106—24no—
160C2×#106—24no—
161C2×#106—42no—
162C2×#106—42no—
163C2×#106C2314yes—
164C2×#106C2314yes—
165C2×#106C2314yes—
166C2×#106C2314yes—
167C2×#106C2314yes—
168C2×#103—24no—
169C2×#103—42no—
170C2×#103D418yescomplemented
171C2×#103C2314yes—
172C2×#103C2314yes—
173C2×#103C2314yes—
174C2×#102—24no—
175C2×#102—42no—
176C2×#102—42no—
177C2×#102C2314yes—
178C2×#102C2314yes—
179C2×#102C2314yes—
180C2×C22⋊C8—24no—
181C2×C22⋊C8—24no—
182C2×C22⋊C8—42no—
183C2×C22⋊C8C2314yes—
184C2×C22⋊C8C2314yes—
185C2×C22⋊C8C2314yes—
186#396—28no—
187#396—28no—
188#396—28no—
189#394—28no—
190#390—28no—
191#390—22no—
192#390C2314yes—
193#389—28no—
194#389—22no—
195#389C2314yes—
196#386—28no—
197#384—22no—
198#384C2314yes—
199#380—22no—
200#380—22no—
201#380—22no—
202#380C2314yes—
203#380C2314yes—
204#380C2314yes—
205C2×#95—21no—
206C2×#95—21no—
207C2×#95—21no—
208C2×#95—21no—
209#340C2314yes—
210#340C2314yes—
211#340C2314yes—
212#340C2314yes—
213#336C2314yes—
214#336C2314yes—
215C25—21no—
216C25C2×D411yescharacteristic
217C25C2×D411yescharacteristic
218C22×Q8—21no—
219C22×Q8—22no—
220C22×Q8—22no—
221C22×Q8—22no—
222C22×Q8—22no—
223C22×Q8—22no—
224C22×Q8C2×D414yes—
225C22×Q8C2412yes—
226C22×D4—24no—
227C22×D4—24no—
228C22×D4—22no—
229C22×D4—21no—
230C22×D4—22no—
231C22×D4—22no—
232C22×D4—22no—
233C22×D4—22no—
234C22×D4—22no—
235C22×D4—42no—
236C22×D4—42no—
237C22×D4—44no—
238C22×D4—44no—
239C22×D4—44no—
240C22×D4—44no—
241C22×D4—44no—
242C22×D4—82no—
243C22×D4SD1618yescomplemented
244C22×D4C2×D414yes—
245C22×D4C2412yes—
246C23×C4—21no—
247C23×C4—21no—
248C23×C4—22no—
249C23×C4—22no—
250C23×C4—22no—
251C23×C4—22no—
252C23×C4—22no—
253C23×C4—22no—
254C23×C4—22no—
255C23×C4—22no—
256C23×C4—22no—
257C23×C4—22no—
258C23×C4—22no—
259C23×C4—22no—
260C23×C4—21no—
261C23×C4—21no—
262C23×C4—21no—
263C23×C4—21no—
264C23×C4—21no—
265C23×C4—24no—
266C23×C4—44no—
267C23×C4—44no—
268C23×C4—82no—
269C23×C4C2×D412yes—
270C23×C4C2×D412yes—
271C23×C4C2×D411yescharacteristic
272C23×C4C2×D411yescharacteristic
273C23×C4C2×D411yescharacteristic
274C23×C4C2×D411yescharacteristic
275C23×C4C2412yes—
276C23×C4C2412yes—
277C23×C4C2411yescharacteristic
278C2×SD16—28no—
279C2×SD16—28no—
280C2×SD16—44no—
281C2×SD16—416no—
282C22×C8—22no—
283C22×C8—22no—
284C22×C8—22no—
285C22×C8—22no—
286C22×C8—22no—
287C22×C8—22no—
288C22×C8—22no—
289C22×C8—22no—
290C22×C8—22no—
291C22×C8—22no—
292C22×C8—28no—
293C22×C8—28no—
294C22×C8—44no—
295C22×C8—416no—
296C22×C8C2×D414yes—
297C22×C8#4114yes—
298C22×C8C2412yes—
299C22×C8C2412yes—
300C22×C8C2412yes—
301C22×C8C2412yes—
302C22⋊Q8—28no—
303C22⋊Q8—28no—
304C22⋊Q8—44no—
305C22⋊Q8—44no—
306C22⋊Q8—48no—
307C22⋊Q8—48no—
308#121—28no—
309#121—44no—
310#121—44no—
311#121—44no—
312#121—48no—
313#121—48no—
314#121—432no—
315C4×Q8—44no—
316C4×Q8—44no—
317C4×Q8—48no—
318C4×D4—48no—
319C4×D4—44no—
320C4×D4—44no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—28no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—24no—
336C2×C4⋊C4—24no—
337C2×C4⋊C4—24no—
338C2×C4⋊C4—24no—
339C2×C4⋊C4—24no—
340C2×C4⋊C4—24no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—24no—
346C2×C4⋊C4—44no—
347C2×C4⋊C4—48no—
348C2×C4⋊C4—42no—
349C2×C4⋊C4—44no—
350C2×C4⋊C4—44no—
351C2×C4⋊C4—44no—
352C2×C4⋊C4—44no—
353C2×C4⋊C4—44no—
354C2×C4⋊C4—44no—
355C2×C4⋊C4—82no—
356C2×C4⋊C4C2×D414yes—
357C2×C4⋊C4C2×D414yes—
358C2×C4⋊C4C2412yes—
359C2×C4⋊C4C2412yes—
360C2×C4⋊C4C2412yes—
361C2×C4⋊C4C2412yes—
362C2×C4⋊C4C2412yes—
363C2×C4⋊C4C2412yes—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—24no—
367C2×C22⋊C4—24no—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—24no—
373C2×C22⋊C4—42no—
374C2×C22⋊C4—42no—
375C2×C22⋊C4—44no—
376C2×C22⋊C4—44no—
377C2×C22⋊C4—44no—
378C2×C22⋊C4—44no—
379C2×C22⋊C4—44no—
380C2×C22⋊C4—44no—
381C2×C22⋊C4—82no—
382C2×C22⋊C4—82no—
383C2×C22⋊C4—82no—
384C2×C22⋊C4C2×D414yes—
385C2×C22⋊C4C2×D414yes—
386C2×C42—22no—
387C2×C42—22no—
388C2×C42—24no—
389C2×C42—44no—
390C2×C42C2×D412yes—
391C2×C42C2412yes—
392#106—28no—
393#106—28no—
394#106—28no—
395#106—44no—
396#106—44no—
397#103—28no—
398#103—44no—
399#103C2×D4116yescomplemented
400#102—28no—
401#102—44no—
402#102—44no—
403C22⋊C8—28no—
404C22⋊C8—28no—
405C22⋊C8—44no—
406#95—24no—
407#95—24no—
408#95—24no—
409#95—24no—
410C24—22no—
411C24—22no—
412C24—22no—
413C24—22no—
414C24—22no—
415C24—22no—
416C24—22no—
417C24—22no—
418C24—22no—
419C24—22no—
420C24—22no—
421C24—22no—
422C24—22no—
423C24—42no—
424C24—42no—
425C24—42no—
426C24—42no—
427C24—42no—
428C24—42no—
429C24—42no—
430C24C2×SD1614yes—
431C24C2×SD1614yes—
432C24C22×D412yes—
433C24C22×D412yes—
434C24C22×D411yescharacteristic
435C2×Q8—24no—
436C2×Q8—22no—
437C2×Q8—28no—
438C2×Q8—28no—
439C2×Q8—22no—
440C2×Q8—22no—
441C2×Q8—22no—
442C2×Q8—22no—
443C2×Q8—42no—
444C2×Q8—44no—
445C2×Q8—42no—
446C2×Q8—44no—
447C2×Q8C22×D414yes—
448C2×D4—22no—
449C2×D4—22no—
450C2×D4—22no—
451C2×D4—22no—
452C2×D4—22no—
453C2×D4—22no—
454C2×D4—44no—
455C2×D4—416no—
456C2×D4—44no—
457C2×D4—48no—
458C2×D4—48no—
459C2×D4—48no—
460C2×D4—48no—
461C2×D4—48no—
462C2×D4—42no—
463C2×D4—44no—
464C2×D4—44no—
465C2×D4—42no—
466C2×D4—44no—
467C2×D4—42no—
468C2×D4—44no—
469C2×D4—84no—
470C2×D4—816no—
471C2×D4—816no—
472C2×D4C2×SD16116yescomplemented
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—24no—
480C22×C4—24no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—24no—
489C22×C4—24no—
490C22×C4—24no—
491C22×C4—24no—
492C22×C4—24no—
493C22×C4—24no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—48no—
512C22×C4—42no—
513C22×C4—42no—
514C22×C4—42no—
515C22×C4—42no—
516C22×C4—44no—
517C22×C4—44no—
518C22×C4—44no—
519C22×C4—44no—
520C22×C4—44no—
521C22×C4—44no—
522C22×C4—44no—
523C22×C4—44no—
524C22×C4—42no—
525C22×C4—42no—
526C22×C4—42no—
527C22×C4—42no—
528C22×C4—42no—
529C22×C4—42no—
530C22×C4—42no—
531C22×C4—48no—
532C22×C4—42no—
533C22×C4—42no—
534C22×C4—42no—
535C22×C4—42no—
536C22×C4—42no—
537C22×C4—42no—
538C22×C4—42no—
539C22×C4—42no—
540C22×C4—84no—
541C22×C4—816no—
542C22×C4C2×SD1614yes—
543C22×C4C22×D412yes—
544C22×C4C22×D412yes—
545C22×C4C22×D412yes—
546C22×C4C22×D412yes—
547C22×C4C22×D411yescharacteristic
548C22×C4C22×D412yes—
549C22×C4C2×#4112yes—
550C22×C4H(5,𝔽2)12yes—
551C22×C4H(5,𝔽2)12yes—
552C22×C4H(5,𝔽2)12yes—
553C22×C42−1+412yes—
554C22×C4C2511yescharacteristic
555SD16—416no—
556C2×C8—28no—
557C2×C8—28no—
558C2×C8—22no—
559C2×C8—22no—
560C2×C8—22no—
561C2×C8—22no—
562C2×C8—22no—
563C2×C8—22no—
564C2×C8—22no—
565C2×C8—22no—
566C2×C8—22no—
567C2×C8—22no—
568C2×C8—416no—
569C2×C8—44no—
570C2×C8—44no—
571C2×C8C22×D414yes—
572C2×C8C2×#4114yes—
573C4⋊C4—24no—
574C4⋊C4—22no—
575C4⋊C4—22no—
576C4⋊C4—22no—
577C4⋊C4—22no—
578C4⋊C4—22no—
579C4⋊C4—22no—
580C4⋊C4—22no—
581C4⋊C4—22no—
582C4⋊C4—22no—
583C4⋊C4—22no—
584C4⋊C4—22no—
585C4⋊C4—44no—
586C4⋊C4—48no—
587C4⋊C4—48no—
588C4⋊C4—48no—
589C4⋊C4—48no—
590C4⋊C4—48no—
591C4⋊C4—42no—
592C4⋊C4—42no—
593C4⋊C4—42no—
594C4⋊C4—42no—
595C4⋊C4—42no—
596C4⋊C4—48no—
597C4⋊C4—84no—
598C4⋊C4C22×D414yes—
599C22⋊C4—44no—
600C22⋊C4—44no—
601C22⋊C4—48no—
602C22⋊C4—48no—
603C22⋊C4—48no—
604C22⋊C4—48no—
605C22⋊C4—48no—
606C22⋊C4—48no—
607C22⋊C4—84no—
608C22⋊C4—84no—
609C22⋊C4—84no—
610C42—24no—
611C42—22no—
612C42—22no—
613C42—48no—
614C23—28no—
615C23—28no—
616C23—28no—
617C23—28no—
618C23—22no—
619C23—22no—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—28no—
625C23—28no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—44no—
633C23—44no—
634C23—44no—
635C23—44no—
636C23—44no—
637C23—44no—
638C23—44no—
639C23—44no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—84no—
648C23—84no—
649C23—84no—
650C23—84no—
651C23—84no—
652C23—84no—
653C23—84no—
654C23#53412yes—
655C23D4212yes—
656C23#54712yes—
657C23C22×SD1614yes—
658C23C22×SD1614yes—
659C23C22×SD1612yes—
660C23#57512yes—
661C23#57712yes—
662C23#57712yes—
663C23C23×D411yescharacteristic
664Q8—24no—
665Q8—24no—
666Q8—48no—
667Q8—42no—
668Q8—42no—
669D4—416no—
670D4—42no—
671D4—42no—
672D4—42no—
673D4—42no—
674D4—816no—
675D4—816no—
676D4—84no—
677C2×C4—28no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—24no—
685C2×C4—24no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—44no—
692C2×C4—44no—
693C2×C4—48no—
694C2×C4—42no—
695C2×C4—44no—
696C2×C4—42no—
697C2×C4—48no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—48no—
701C2×C4—48no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—816no—
726C2×C4—84no—
727C2×C4—84no—
728C2×C4—84no—
729C2×C4—84no—
730C2×C4—84no—
731C2×C4#53412yes—
732C2×C4#53714yes—
733C2×C4#54014yes—
734C2×C4D4212yes—
735C2×C4#54614yes—
736C2×C4#54712yes—
737C2×C4#56214yes—
738C2×C4C22×SD1614yes—
739C2×C4C23×D411yescharacteristic
740C2×C4C22×#4111yescharacteristic
741C2×C4C2×H(5,𝔽2)11yescharacteristic
742C2×C4C2×H(5,𝔽2)11yescharacteristic
743C2×C4C2×H(5,𝔽2)11yescharacteristic
744C2×C4C2×2−1+411yescharacteristic
745C8—24no—
746C8—24no—
747C8—42no—
748C8—42no—
749C22—24no—
750C22—24no—
751C22—24no—
752C22—24no—
753C22—24no—
754C22—24no—
755C22—42no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—416no—
760C22—416no—
761C22—42no—
762C22—42no—
763C22—42no—
764C22—42no—
765C22—82no—
766C22—82no—
767C22—82no—
768C22—82no—
769C22—82no—
770C22—82no—
771C22—82no—
772C22—168no—
773C22#267114yes—
774C22#318714yes—
775C22#320414yes—
776C22#327114yes—
777C22D4×SD1614yes—
778C22#333514yes—
779C22#335014yes—
780C22C2×#53411yescharacteristic
781C22C2×D4211yescharacteristic
782C22C2×#54711yescharacteristic
783C22C23×SD1611yescharacteristic
784C22C2×#57511yescharacteristic
785C22C2×#57711yescharacteristic
786C22C2×#57711yescharacteristic
787C4—24no—
788C4—42no—
789C4—44no—
790C4—42no—
791C4—42no—
792C4—44no—
793C4—82no—
794C4—82no—
795C4—82no—
796C4—82no—
797C4—82no—
798C4#267114yes—
799C4C2×#53711yescharacteristic
800C4C2×#54011yescharacteristic
801C4C2×#54611yescharacteristic
802C4C2×#56211yescharacteristic
803C2—44no—
804C2—44no—
805C2—162no—
806C2#3056118yesdirect product factor
807C2C2×#267111yescharacteristic
808C2C2×#318711yescharacteristic
809C2C2×#320411yescharacteristic
810C2C2×#327111yescharacteristic
811C2C2×D4×SD1611yescharacteristic
812C2C2×#333511yescharacteristic
813C2C2×#335011yescharacteristic
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×#465C2semidirect
3. C2×#2538C2semidirect
5. #30561C2direct (N × H)
6. C2×#2094C2semidirect
7. C2×#2084C2semidirect
8. C2×#2034C2semidirect
9. C2×#2034C2semidirect
10. C2×#2035C2semidirect
11. C2×#2000C2semidirect
12. C2×#1880C2semidirect
13. C2×#1869C2semidirect
14. C2×#1865C2semidirect
15. C2×#1853C2semidirect
16. C2×#1807C2semidirect
28. C2×#483C22semidirect
30. C2×#465C22semidirect
46. #2538C22semidirect
62. #2094C22semidirect
63. #2084C22semidirect
64. #2035C22semidirect
65. #2034C22semidirect
66. #2034C22semidirect
67. #2000C22semidirect
68. #1880C22semidirect
69. #1869C22semidirect
70. #1865C22semidirect
71. #1853C22semidirect
72. #1807C22semidirect
170. C2×#103D4semidirect
243. C22×D4SD16semidirect
399. #103C2×D4semidirect
472. C2×D4C2×SD16semidirect
806. C2#30561direct (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×#4652
C2×#25382
C2×#24162
#305612
C2×#20942
C2×#20842
C2×#20342
C2×#20352
C2×#20002
C2×#18802
C2×#18692
C2×#18652
C2×#18532
C2×#18072