Finite Group Databasebeta

← C2×#30903 #7502195

Subgroups — C2×#30903 #7502195

Order 512.

2762 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#489C211yesmaximal, characteristic, complemented
2C22×#463C211yesmaximal, characteristic, complemented
3C2×#2548C211yesmaximal, characteristic, complemented
4C2×#2452C211yesmaximal, characteristic, complemented
5#30903C2116yesmaximal, direct product factor
6C2×#2065C211yesmaximal, characteristic, complemented
7C2×#2042C211yesmaximal, characteristic, complemented
8C2×#2041C211yesmaximal, characteristic, complemented
9C2×#2023C211yesmaximal, characteristic, complemented
10C2×#2012C211yesmaximal, characteristic, complemented
11C2×#2011C211yesmaximal, characteristic
12C2×#1972C211yesmaximal, characteristic, complemented
13C2×#1917C211yesmaximal, characteristic, complemented
14C2×#1880C211yesmaximal, characteristic, complemented
15C2×#1879C211yesmaximal, characteristic, complemented
16C2×#1865C211yesmaximal, characteristic, complemented
17C23×SD16C2211yescharacteristic
18C23×D8C2211yescharacteristic
19C23×D8C2211yescharacteristic
20C22×C4⋊Q8C2211yescharacteristic
21C22×#127C2211yescharacteristic
22C22×#124C2211yescharacteristic
23C22×#124C2211yescharacteristic
24C22×C22⋊Q8—21no—
25C22×C4×Q8C2211yescharacteristic
26C22×C4×D4C2211yescharacteristic
27C2×#489—28no—
28C2×#489C2218yescomplemented
29C2×#463—28no—
30C2×#463C2218yescomplemented
31C22×#106C2211yescharacteristic
32C22×C4⋊C8C2211yescharacteristic
33C22×#103C2211yescharacteristic
34C22×#103C2211yescharacteristic
35C22×#103C2211yescharacteristic
36C22×#102C2211yescharacteristic
37C22×#102C2211yescharacteristic
38C22×#102C2211yescharacteristic
39C22×#102C2211yescharacteristic
40C22×#102C2211yescharacteristic
41C22×#102C2211yescharacteristic
42C22×#102C2211yescharacteristic
43C22×#97C2211yescharacteristic
44#2548—24no—
45#2548C2218yescomplemented
46#2452—24no—
47#2452C2218yescomplemented
48C2×#396—21no—
49C2×#394—21no—
50C2×#394—21no—
51C2×#393—21no—
52C2×#390—21no—
53C2×#390—21no—
54C2×#390C2211yescharacteristic
55C2×#390C2211yescharacteristic
56C2×#390C2211yescharacteristic
57C2×#390C2211yescharacteristic
58C2×#389C2211yescharacteristic
59C2×#389C2211yescharacteristic
60C2×#385—21no—
61C2×C4×C4⋊C4C2211yescharacteristic
62#2065C2218yescomplemented
63#2042C2218yescomplemented
64#2041C2218yescomplemented
65#2023C2218yescomplemented
66#2012C2218yescomplemented
67#2011C2218yes—
68#1972C2218yescomplemented
69#1917C2218yescomplemented
70#1880C2218yescomplemented
71#1879C2218yescomplemented
72#1865C2218yescomplemented
73C2×#340C2211yescharacteristic
74C2×#340C2211yescharacteristic
75C2×#336C2211yescharacteristic
76C2×#336C2211yescharacteristic
77C2×#336C2211yescharacteristic
78C2×#336C2211yescharacteristic
79C23×Q8—21no—
80C23×Q8C2311yescharacteristic
81C23×D4—21no—
82C23×D4—21no—
83C23×D4C2311yescharacteristic
84C23×D4C2311yescharacteristic
85C23×D4C2311yescharacteristic
86C24×C4—21no—
87C22×SD16—24no—
88C22×SD16—24no—
89C22×SD16—42no—
90C22×SD16C2314yes—
91C22×D8—24no—
92C22×D8—24no—
93C22×D8—24no—
94C22×D8—42no—
95C22×D8—42no—
96C22×D8—42no—
97C22×D8C2314yes—
98C22×D8C2314yes—
99C23×C8C2311yescharacteristic
100C23×C8C2311yescharacteristic
101C23×C8C2311yescharacteristic
102C23×C8C2311yescharacteristic
103C2×C4⋊Q8—24no—
104C2×C4⋊Q8—22no—
105C2×C4⋊Q8—42no—
106C2×C4⋊Q8C2314yes—
107C2×#127—22no—
108C2×#127—42no—
109C2×#127—42no—
110C2×#127C2314yes—
111C2×#124—24no—
112C2×#124—24no—
113C2×#124—22no—
114C2×#124—22no—
115C2×#124—42no—
116C2×#124—42no—
117C2×#124C2314yes—
118C2×#124C2314yes—
119C2×C22⋊Q8—28no—
120C2×C22⋊Q8—48no—
121C2×C4×Q8—22no—
122C2×C4×Q8—42no—
123C2×C4×Q8—42no—
124C2×C4×Q8C2314yes—
125C2×C4×D4—24no—
126C2×C4×D4—22no—
127C2×C4×D4—42no—
128C2×C4×D4C2314yes—
129C22×C4⋊C4—21no—
130C22×C4⋊C4—21no—
131C22×C4⋊C4—21no—
132C22×C4⋊C4—21no—
133C22×C4⋊C4D411yescharacteristic
134C22×C4⋊C4D411yescharacteristic
135C22×C4⋊C4C2311yescharacteristic
136C22×C4⋊C4C2311yescharacteristic
137C22×C4⋊C4C2311yescharacteristic
138C22×C4⋊C4C2311yescharacteristic
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⋊C4—21no—
150C22×C22⋊C4—21no—
151C22×C22⋊C4—21no—
152C22×C42—21no—
153C22×C42C2311yescharacteristic
154C22×C42C2311yescharacteristic
155C22×C42C2311yescharacteristic
156#489—232no—
157#463—232no—
158C2×#106—42no—
159C2×#106C2314yes—
160C2×C4⋊C8—24no—
161C2×C4⋊C8C2314yes—
162C2×#103—24no—
163C2×#103—42no—
164C2×#103D418yescomplemented
165C2×#103C2314yes—
166C2×#103C2314yes—
167C2×#103C2314yes—
168C2×#102—24no—
169C2×#102—24no—
170C2×#102—24no—
171C2×#102—42no—
172C2×#102—42no—
173C2×#102—42no—
174C2×#102—42no—
175C2×#102C2314yes—
176C2×#102C2314yes—
177C2×#102C2314yes—
178C2×#102C2314yes—
179C2×#102C2314yes—
180C2×#102C2314yes—
181C2×#102C2314yes—
182C2×#97—24no—
183C2×#97C2314yes—
184#396—28no—
185#394—28no—
186#394—28no—
187#393—28no—
188#390—28no—
189#390—28no—
190#390—22no—
191#390—22no—
192#390—22no—
193#390—22no—
194#390C2314yes—
195#390C2314yes—
196#390C2314yes—
197#390C2314yes—
198#389—22no—
199#389—22no—
200#389C2314yes—
201#389C2314yes—
202#385—28no—
203C4×C4⋊C4D414yes—
204C4×C4⋊C4C2314yes—
205C2×#95—21no—
206C2×#95—21no—
207C2×#95D411yescharacteristic
208C2×#95D411yescharacteristic
209#340C2314yes—
210#340C2314yes—
211#336C2314yes—
212#336C2314yes—
213#336C2314yes—
214#336C2314yes—
215C25—21no—
216C25—21no—
217C25—21no—
218C22×Q8—21no—
219C22×Q8—24no—
220C22×Q8—22no—
221C22×Q8—22no—
222C22×Q8—22no—
223C22×Q8—22no—
224C22×Q8—22no—
225C22×Q8—44no—
226C22×Q8—44no—
227C22×Q8—82no—
228C22×Q8C2×D414yes—
229C22×Q8C2412yes—
230C22×D4—22no—
231C22×D4—21no—
232C22×D4—22no—
233C22×D4—22no—
234C22×D4—21no—
235C22×D4—21no—
236C22×D4—24no—
237C22×D4—24no—
238C22×D4—22no—
239C22×D4—22no—
240C22×D4—22no—
241C22×D4—22no—
242C22×D4—22no—
243C22×D4—22no—
244C22×D4—22no—
245C22×D4—22no—
246C22×D4—22no—
247C22×D4—22no—
248C22×D4—22no—
249C22×D4—22no—
250C22×D4—22no—
251C22×D4—22no—
252C22×D4—44no—
253C22×D4—44no—
254C22×D4—44no—
255C22×D4—44no—
256C22×D4—82no—
257C22×D4—82no—
258C22×D4#4114yes—
259C22×D4C2412yes—
260C22×D4C2412yes—
261C22×D4C2412yes—
262C23×C4—21no—
263C23×C4—21no—
264C23×C4—21no—
265C23×C4—21no—
266C23×C4—21no—
267C23×C4—24no—
268C23×C4—44no—
269C23×C4—44no—
270C23×C4—82no—
271C23×C4C2×D411yescharacteristic
272C23×C4C2×D411yescharacteristic
273C23×C4C2×D411yescharacteristic
274C23×C4C2×D411yescharacteristic
275C23×C4C2×D411yescharacteristic
276C23×C4C2×D411yescharacteristic
277C23×C4C2411yescharacteristic
278C2×SD16—28no—
279C2×SD16—28no—
280C2×SD16—44no—
281C2×SD16—416no—
282C2×D8—28no—
283C2×D8—28no—
284C2×D8—28no—
285C2×D8—44no—
286C2×D8—44no—
287C2×D8—44no—
288C2×D8—416no—
289C2×D8—416no—
290C22×C8—22no—
291C22×C8—22no—
292C22×C8—22no—
293C22×C8—22no—
294C22×C8—22no—
295C22×C8—22no—
296C22×C8—22no—
297C22×C8—22no—
298C22×C8—22no—
299C22×C8—22no—
300C22×C8—22no—
301C22×C8C2×D414yes—
302C22×C8C2412yes—
303C22×C8C2412yes—
304C22×C8C2412yes—
305C22×C8C2412yes—
306C4⋊Q8—28no—
307C4⋊Q8—44no—
308C4⋊Q8—48no—
309#127—44no—
310#127—44no—
311#127—48no—
312#124—28no—
313#124—28no—
314#124—44no—
315#124—44no—
316#124—48no—
317#124—48no—
318C22⋊Q8—432no—
319C4×Q8—44no—
320C4×Q8—44no—
321C4×Q8—48no—
322C4×D4—28no—
323C4×D4—44no—
324C4×D4—48no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—21no—
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—22no—
334C2×C4⋊C4—24no—
335C2×C4⋊C4—24no—
336C2×C4⋊C4—24no—
337C2×C4⋊C4—24no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—42no—
342C2×C4⋊C4—44no—
343C2×C4⋊C4—44no—
344C2×C4⋊C4—44no—
345C2×C4⋊C4—44no—
346C2×C4⋊C4C2×D414yes—
347C2×C4⋊C4C2×D414yes—
348C2×C4⋊C4C2×D414yes—
349C2×C4⋊C4C2412yes—
350C2×C4⋊C4C2412yes—
351C2×C4⋊C4C2412yes—
352C2×C4⋊C4C2412yes—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—44no—
367C2×C22⋊C4—44no—
368C2×C22⋊C4—44no—
369C2×C22⋊C4—44no—
370C2×C22⋊C4—44no—
371C2×C22⋊C4—44no—
372C2×C22⋊C4—44no—
373C2×C22⋊C4—44no—
374C2×C22⋊C4—82no—
375C2×C22⋊C4—82no—
376C2×C22⋊C4—82no—
377C2×C22⋊C4—82no—
378C2×C22⋊C4—82no—
379C2×C42—22no—
380C2×C42—22no—
381C2×C42—22no—
382C2×C42—22no—
383C2×C42—22no—
384C2×C42—22no—
385C2×C42—24no—
386C2×C42—44no—
387C2×C42C2×D412yes—
388C2×C42C2×D412yes—
389C2×C42C2×D412yes—
390C2×C42C2412yes—
391C2×C42C2412yes—
392C2×C42C2412yes—
393#106—44no—
394C4⋊C8—28no—
395#103—28no—
396#103—44no—
397#103C2×D4116yescomplemented
398#102—28no—
399#102—28no—
400#102—28no—
401#102—44no—
402#102—44no—
403#102—44no—
404#102—44no—
405#97—28no—
406#95—24no—
407#95—24no—
408#95C2×D414yes—
409#95C2×D414yes—
410C24—24no—
411C24—22no—
412C24—22no—
413C24—22no—
414C24—42no—
415C24—42no—
416C24—42no—
417C24—42no—
418C24—42no—
419C24—42no—
420C24—42no—
421C24—42no—
422C24—42no—
423C24—42no—
424C24—42no—
425C24—42no—
426C24—42no—
427C24—42no—
428C24—42no—
429C24—42no—
430C24—42no—
431C24—42no—
432C24—42no—
433C24—42no—
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—48no—
444C2×Q8—48no—
445C2×Q8—42no—
446C2×Q8—44no—
447C2×Q8—42no—
448C2×Q8—44no—
449C2×Q8—84no—
450C2×Q8—816no—
451C2×Q8C22×D414yes—
452C2×D4—28no—
453C2×D4—28no—
454C2×D4—24no—
455C2×D4—22no—
456C2×D4—22no—
457C2×D4—22no—
458C2×D4—22no—
459C2×D4—22no—
460C2×D4—22no—
461C2×D4—22no—
462C2×D4—22no—
463C2×D4—22no—
464C2×D4—22no—
465C2×D4—22no—
466C2×D4—22no—
467C2×D4—22no—
468C2×D4—22no—
469C2×D4—22no—
470C2×D4—22no—
471C2×D4—22no—
472C2×D4—48no—
473C2×D4—48no—
474C2×D4—48no—
475C2×D4—42no—
476C2×D4—42no—
477C2×D4—42no—
478C2×D4—44no—
479C2×D4—44no—
480C2×D4—44no—
481C2×D4—44no—
482C2×D4—44no—
483C2×D4—42no—
484C2×D4—42no—
485C2×D4—42no—
486C2×D4—44no—
487C2×D4—44no—
488C2×D4—42no—
489C2×D4—42no—
490C2×D4—44no—
491C2×D4—44no—
492C2×D4—44no—
493C2×D4—48no—
494C2×D4—84no—
495C2×D4—84no—
496C2×D4—816no—
497C2×D4—816no—
498C2×D4C2×#4114yes—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—24no—
507C22×C4—24no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—48no—
524C22×C4—48no—
525C22×C4—42no—
526C22×C4—42no—
527C22×C4—42no—
528C22×C4—42no—
529C22×C4—42no—
530C22×C4—42no—
531C22×C4—42no—
532C22×C4—42no—
533C22×C4—42no—
534C22×C4—42no—
535C22×C4—42no—
536C22×C4—42no—
537C22×C4—42no—
538C22×C4—84no—
539C22×C4—816no—
540C22×C4AGL(1,ℤ/8)14yes—
541C22×C4C22×D412yes—
542C22×C4C22×D412yes—
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—
556D8—416no—
557D8—416no—
558C2×C8—28no—
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—22no—
569C2×C8—22no—
570C2×C8—44no—
571C2×C8—44no—
572C2×C8—44no—
573C2×C8C22×D414yes—
574C4⋊C4—24no—
575C4⋊C4—28no—
576C4⋊C4—22no—
577C4⋊C4—22no—
578C4⋊C4—22no—
579C4⋊C4—22no—
580C4⋊C4—22no—
581C4⋊C4—22no—
582C4⋊C4—22no—
583C4⋊C4—44no—
584C4⋊C4—48no—
585C4⋊C4—48no—
586C4⋊C4—48no—
587C4⋊C4—42no—
588C4⋊C4—42no—
589C4⋊C4—42no—
590C4⋊C4—48no—
591C4⋊C4C22×D414yes—
592C22⋊C4—48no—
593C22⋊C4—48no—
594C22⋊C4—48no—
595C22⋊C4—48no—
596C22⋊C4—48no—
597C22⋊C4—48no—
598C22⋊C4—48no—
599C22⋊C4—48no—
600C22⋊C4—84no—
601C22⋊C4—84no—
602C22⋊C4—84no—
603C22⋊C4—84no—
604C22⋊C4—84no—
605C42—24no—
606C42—24no—
607C42—24no—
608C42—22no—
609C42—22no—
610C42—22no—
611C42—22no—
612C42—22no—
613C42—22no—
614C42—48no—
615C23—24no—
616C23—48no—
617C23—48no—
618C23—48no—
619C23—42no—
620C23—42no—
621C23—42no—
622C23—42no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—42no—
628C23—42no—
629C23—42no—
630C23—42no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23—42no—
639C23—84no—
640C23—84no—
641C23—84no—
642C23—84no—
643C23—84no—
644C23—84no—
645C23—84no—
646C23—84no—
647C23—84no—
648C23—84no—
649C23—84no—
650C23—84no—
651C23—84no—
652C23—84no—
653C23—84no—
654C23—84no—
655C23—84no—
656C23—84no—
657C23#53512yes—
658C23D4212yes—
659C23#54812yes—
660C23C2×AGL(1,ℤ/8)12yes—
661C23#57512yes—
662C23#57612yes—
663C23#57712yes—
664C23C23×D411yescharacteristic
665Q8—24no—
666Q8—24no—
667Q8—48no—
668Q8—42no—
669Q8—42no—
670Q8—816no—
671D4—24no—
672D4—24no—
673D4—48no—
674D4—42no—
675D4—42no—
676D4—42no—
677D4—42no—
678D4—42no—
679D4—42no—
680D4—42no—
681D4—42no—
682D4—42no—
683D4—42no—
684D4—816no—
685D4—816no—
686D4—84no—
687D4—84no—
688C2×C4—22no—
689C2×C4—28no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—24no—
697C2×C4—24no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—48no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—44no—
712C2×C4—44no—
713C2×C4—44no—
714C2×C4—44no—
715C2×C4—44no—
716C2×C4—48no—
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—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—816no—
729C2×C4—84no—
730C2×C4—84no—
731C2×C4—84no—
732C2×C4#53512yes—
733C2×C4#53714yes—
734C2×C4#53814yes—
735C2×C4D4212yes—
736C2×C4#54614yes—
737C2×C4#54812yes—
738C2×C4#56214yes—
739C2×C4C2×AGL(1,ℤ/8)14yes—
740C2×C4C23×D411yescharacteristic
741C2×C4C22×#4111yescharacteristic
742C2×C4C2×H(5,𝔽2)11yescharacteristic
743C2×C4C2×H(5,𝔽2)11yescharacteristic
744C2×C4C2×H(5,𝔽2)11yescharacteristic
745C2×C4C2×2−1+411yescharacteristic
746C8—24no—
747C8—42no—
748C8—42no—
749C8—42no—
750C22—44no—
751C22—44no—
752C22—44no—
753C22—82no—
754C22—82no—
755C22—82no—
756C22—82no—
757C22—816no—
758C22—82no—
759C22—82no—
760C22—82no—
761C22—82no—
762C22—82no—
763C22—82no—
764C22—82no—
765C22—82no—
766C22—82no—
767C22—82no—
768C22—82no—
769C22—82no—
770C22—82no—
771C22—82no—
772C22—168no—
773C22—168no—
774C22#267614yes—
775C22#321314yes—
776C22#322414yes—
777C22#327114yes—
778C22#327414yes—
779C22#337014yes—
780C22#337314yes—
781C22C2×#53511yescharacteristic
782C22C2×D4211yescharacteristic
783C22C2×#54811yescharacteristic
784C22C22×AGL(1,ℤ/8)11yescharacteristic
785C22C2×#57511yescharacteristic
786C22C2×#57611yescharacteristic
787C22C2×#57711yescharacteristic
788C4—24no—
789C4—42no—
790C4—42no—
791C4—42no—
792C4—42no—
793C4—44no—
794C4—42no—
795C4—44no—
796C4—82no—
797C4—82no—
798C4—82no—
799C4#267614yes—
800C4C2×#53711yescharacteristic
801C4C2×#53811yescharacteristic
802C4C2×#54611yescharacteristic
803C4C2×#56211yescharacteristic
804C2—84no—
805C2—162no—
806C2—162no—
807C2#3090318yesdirect product factor
808C2C2×#267611yescharacteristic
809C2C2×#321311yescharacteristic
810C2C2×#322411yescharacteristic
811C2C2×#327111yescharacteristic
812C2C2×#327411yescharacteristic
813C2C2×#337311yescharacteristic
814C2C2×#337011yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#2011C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#489C2semidirect
2. C22×#463C2semidirect
3. C2×#2548C2semidirect
4. C2×#2452C2semidirect
5. #30903C2direct (N × H)
6. C2×#2065C2semidirect
7. C2×#2042C2semidirect
8. C2×#2041C2semidirect
9. C2×#2023C2semidirect
10. C2×#2012C2semidirect
12. C2×#1972C2semidirect
13. C2×#1917C2semidirect
14. C2×#1880C2semidirect
15. C2×#1879C2semidirect
16. C2×#1865C2semidirect
28. C2×#489C22semidirect
30. C2×#463C22semidirect
45. #2548C22semidirect
47. #2452C22semidirect
62. #2065C22semidirect
63. #2042C22semidirect
64. #2041C22semidirect
65. #2023C22semidirect
66. #2012C22semidirect
68. #1972C22semidirect
69. #1917C22semidirect
70. #1880C22semidirect
71. #1879C22semidirect
72. #1865C22semidirect
164. C2×#103D4semidirect
397. #103C2×D4semidirect
807. C2#30903direct (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×#4632
C2×#25482
C2×#24522
#309032
C2×#20652
C2×#20422
C2×#20412
C2×#20232
C2×#20122
C2×#20112
C2×#19722
C2×#19172
C2×#18802
C2×#18792
C2×#18652