Finite Group Databasebeta

← C2×#30914 #7502258

Subgroups — C2×#30914 #7502258

Order 512.

2860 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#476C211yesmaximal, characteristic, complemented
2C22×#465C211yesmaximal, characteristic, complemented
3C2×#2492C211yesmaximal, characteristic, complemented
4C2×#2428C211yesmaximal, characteristic
5#30914C2116yesmaximal, direct product factor
6C2×#2066C211yesmaximal, characteristic, complemented
7C2×#2055C211yesmaximal, characteristic, complemented
8C2×#2034C211yesmaximal, characteristic, complemented
9C2×#2023C211yesmaximal, characteristic, complemented
10C2×#2014C211yesmaximal, characteristic, complemented
11C2×#2000C211yesmaximal, characteristic, complemented
12C2×#1982C211yesmaximal, characteristic, complemented
13C2×#1919C211yesmaximal, characteristic, complemented
14C2×#1893C211yesmaximal, characteristic, complemented
15C2×#1877C211yesmaximal, characteristic, complemented
16C2×#1850C211yesmaximal, characteristic, complemented
17C23×SD16C2211yescharacteristic
18C23×SD16C2211yescharacteristic
19C24×C8C2211yescharacteristic
20C22×C4⋊Q8C2211yescharacteristic
21C22×#127C2211yescharacteristic
22C22×C22⋊Q8C2211yescharacteristic
23C22×#121—21no—
24C22×#121C2211yescharacteristic
25C22×#121C2211yescharacteristic
26C22×C4×D4C2211yescharacteristic
27C2×#476—28no—
28C2×#476C2218yescomplemented
29C2×#465—28no—
30C2×#465C2218yescomplemented
31C22×#106C2211yescharacteristic
32C22×#106C2211yescharacteristic
33C22×C4⋊C8C2211yescharacteristic
34C22×C4⋊C8C2211yescharacteristic
35C22×#103C2211yescharacteristic
36C22×#103C2211yescharacteristic
37C22×#102C2211yescharacteristic
38C22×#102C2211yescharacteristic
39C22×#102C2211yescharacteristic
40C22×#102C2211yescharacteristic
41C22×#102C2211yescharacteristic
42C22×#102C2211yescharacteristic
43C22×C22⋊C8C2211yescharacteristic
44#2492—24no—
45#2492C2218yescomplemented
46#2428—24no—
47#2428C2218yes—
48C2×#400—21no—
49C2×#394—21no—
50C2×#393—21no—
51C2×#392—21no—
52C2×#391—21no—
53C2×#391C2211yescharacteristic
54C2×#391C2211yescharacteristic
55C2×#390C2211yescharacteristic
56C2×#389C2211yescharacteristic
57C2×#388—21no—
58C2×#386—21no—
59C2×#380C2211yescharacteristic
60C2×C4×C4⋊C4C2211yescharacteristic
61C2×C4×C22⋊C4C2211yescharacteristic
62#2066C2218yescomplemented
63#2055C2218yescomplemented
64#2034C2218yescomplemented
65#2023C2218yescomplemented
66#2014C2218yescomplemented
67#2000C2218yescomplemented
68#1982C2218yescomplemented
69#1919C2218yescomplemented
70#1893C2218yescomplemented
71#1877C2218yescomplemented
72#1850C2218yescomplemented
73C2×#340C2211yescharacteristic
74C2×#340C2211yescharacteristic
75C2×#340C2211yescharacteristic
76C2×#340C2211yescharacteristic
77C2×#336C2211yescharacteristic
78C2×#336C2211yescharacteristic
79C23×Q8—21no—
80C23×Q8C2311yescharacteristic
81C23×D4—21no—
82C23×D4—21no—
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×SD16—42no—
93C22×SD16—42no—
94C22×SD16—42no—
95C22×SD16C2314yes—
96C22×SD16C2314yes—
97C23×C8—24no—
98C23×C8—42no—
99C23×C8—42no—
100C23×C8C2311yescharacteristic
101C23×C8C2311yescharacteristic
102C23×C8C2311yescharacteristic
103C23×C8C2311yescharacteristic
104C23×C8C2314yes—
105C2×C4⋊Q8—24no—
106C2×C4⋊Q8—22no—
107C2×C4⋊Q8—42no—
108C2×C4⋊Q8C2314yes—
109C2×#127—24no—
110C2×#127—22no—
111C2×#127—42no—
112C2×#127C2314yes—
113C2×C22⋊Q8—22no—
114C2×C22⋊Q8—24no—
115C2×C22⋊Q8—42no—
116C2×C22⋊Q8C2314yes—
117C2×#121—22no—
118C2×#121—22no—
119C2×#121—28no—
120C2×#121—24no—
121C2×#121—24no—
122C2×#121—42no—
123C2×#121—42no—
124C2×#121—48no—
125C2×#121C2314yes—
126C2×#121C2314yes—
127C2×C4×D4—24no—
128C2×C4×D4—22no—
129C2×C4×D4—42no—
130C2×C4×D4C2314yes—
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×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⋊C4D411yescharacteristic
147C22×C22⋊C4D411yescharacteristic
148C22×C42—21no—
149C22×C42C2311yescharacteristic
150C22×C42C2311yescharacteristic
151#476—232no—
152#465—232no—
153C2×#106—24no—
154C2×#106D418yescomplemented
155C2×#106C2314yes—
156C2×#106C2314yes—
157C2×C4⋊C8—24no—
158C2×C4⋊C8—42no—
159C2×C4⋊C8C2314yes—
160C2×C4⋊C8C2314yes—
161C2×#103—24no—
162C2×#103—42no—
163C2×#103C2314yes—
164C2×#103C2314yes—
165C2×#102—24no—
166C2×#102—24no—
167C2×#102—24no—
168C2×#102—42no—
169C2×#102—42no—
170C2×#102—42no—
171C2×#102C2314yes—
172C2×#102C2314yes—
173C2×#102C2314yes—
174C2×#102C2314yes—
175C2×#102C2314yes—
176C2×#102C2314yes—
177C2×C22⋊C8—42no—
178C2×C22⋊C8C2314yes—
179#400—28no—
180#394—28no—
181#393—28no—
182#392—28no—
183#391—22no—
184#391—22no—
185#391—28no—
186#391C2314yes—
187#391C2314yes—
188#390—22no—
189#390C2314yes—
190#389—22no—
191#389C2314yes—
192#388—28no—
193#386—28no—
194#380—22no—
195#380C2314yes—
196C4×C4⋊C4—22no—
197C4×C4⋊C4C2314yes—
198C4×C22⋊C4D414yes—
199C4×C22⋊C4C2314yes—
200C2×#95—21no—
201C2×#95—21no—
202C2×#95—21no—
203C2×#95—21no—
204C2×#95—21no—
205C2×#95—21no—
206C2×#95—21no—
207C2×#95D411yescharacteristic
208C2×#95D411yescharacteristic
209#340C2314yes—
210#340C2314yes—
211#340C2314yes—
212#340C2314yes—
213#336C2314yes—
214#336C2314yes—
215C25—21no—
216C25—21no—
217C25C2×D411yescharacteristic
218C22×Q8—21no—
219C22×Q8—24no—
220C22×Q8—22no—
221C22×Q8—22no—
222C22×Q8—22no—
223C22×Q8—22no—
224C22×Q8—22no—
225C22×Q8—22no—
226C22×Q8—44no—
227C22×Q8—44no—
228C22×Q8—82no—
229C22×Q8C2412yes—
230C22×D4—24no—
231C22×D4—24no—
232C22×D4—22no—
233C22×D4—21no—
234C22×D4—22no—
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—44no—
248C22×D4—44no—
249C22×D4—44no—
250C22×D4—44no—
251C22×D4—44no—
252C22×D4—44no—
253C22×D4—44no—
254C22×D4—44no—
255C22×D4—82no—
256C22×D4—82no—
257C22×D4—82no—
258C22×D4—82no—
259C22×D4#4114yes—
260C22×D4C2412yes—
261C22×D4C2412yes—
262C23×C4—21no—
263C23×C4—21no—
264C23×C4—22no—
265C23×C4—22no—
266C23×C4—22no—
267C23×C4—22no—
268C23×C4—22no—
269C23×C4—22no—
270C23×C4—21no—
271C23×C4—21no—
272C23×C4—21no—
273C23×C4—21no—
274C23×C4—24no—
275C23×C4—44no—
276C23×C4—44no—
277C23×C4—82no—
278C23×C4C2×D412yes—
279C23×C4C2×D411yescharacteristic
280C23×C4C2×D411yescharacteristic
281C23×C4C2×D411yescharacteristic
282C23×C4C2×D411yescharacteristic
283C23×C4C2×D411yescharacteristic
284C23×C4C2412yes—
285C23×C4C2411yescharacteristic
286C2×SD16—28no—
287C2×SD16—28no—
288C2×SD16—44no—
289C2×SD16—44no—
290C2×SD16—44no—
291C2×SD16—44no—
292C2×SD16—416no—
293C2×SD16—416no—
294C22×C8—22no—
295C22×C8—22no—
296C22×C8—22no—
297C22×C8—22no—
298C22×C8—22no—
299C22×C8—22no—
300C22×C8—22no—
301C22×C8—22no—
302C22×C8—22no—
303C22×C8—22no—
304C22×C8—22no—
305C22×C8—28no—
306C22×C8—44no—
307C22×C8—44no—
308C22×C8—416no—
309C22×C8C2×D414yes—
310C22×C8C2412yes—
311C22×C8C2412yes—
312C22×C8C2412yes—
313C22×C8C2412yes—
314C4⋊Q8—28no—
315C4⋊Q8—44no—
316C4⋊Q8—48no—
317#127—28no—
318#127—44no—
319#127—48no—
320C22⋊Q8—28no—
321C22⋊Q8—44no—
322C22⋊Q8—48no—
323#121—28no—
324#121—28no—
325#121—44no—
326#121—44no—
327#121—48no—
328#121—48no—
329#121—432no—
330C4×D4—28no—
331C4×D4—44no—
332C4×D4—48no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—24no—
344C2×C4⋊C4—24no—
345C2×C4⋊C4—24no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—44no—
350C2×C4⋊C4—44no—
351C2×C4⋊C4—44no—
352C2×C4⋊C4C2×D414yes—
353C2×C4⋊C4C2×D414yes—
354C2×C4⋊C4C2412yes—
355C2×C4⋊C4C2412yes—
356C2×C4⋊C4C2412yes—
357C2×C4⋊C4C2412yes—
358C2×C4⋊C4C2412yes—
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—42no—
367C2×C22⋊C4—44no—
368C2×C22⋊C4—44no—
369C2×C22⋊C4—44no—
370C2×C22⋊C4—44no—
371C2×C22⋊C4—44no—
372C2×C22⋊C4—82no—
373C2×C22⋊C4—82no—
374C2×C22⋊C4SD1618yescomplemented
375C2×C22⋊C4C2×D414yes—
376C2×C22⋊C4C2×D414yes—
377C2×C42—22no—
378C2×C42—22no—
379C2×C42—22no—
380C2×C42—22no—
381C2×C42—24no—
382C2×C42—82no—
383C2×C42C2×D412yes—
384C2×C42C2×D412yes—
385C2×C42C2412yes—
386C2×C42C2412yes—
387#106—28no—
388#106C2×D4116yescomplemented
389C4⋊C8—28no—
390C4⋊C8—44no—
391#103—28no—
392#103—44no—
393#102—28no—
394#102—28no—
395#102—28no—
396#102—44no—
397#102—44no—
398#102—44no—
399C22⋊C8—44no—
400#95—24no—
401#95—24no—
402#95—24no—
403#95—24no—
404#95—24no—
405#95—24no—
406#95—24no—
407#95C2×D414yes—
408#95C2×D414yes—
409C24—22no—
410C24—22no—
411C24—22no—
412C24—22no—
413C24—22no—
414C24—22no—
415C24—24no—
416C24—22no—
417C24—22no—
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—
431C24C2×SD1614yes—
432C24C22×D412yes—
433C24C22×D411yescharacteristic
434C2×Q8—22no—
435C2×Q8—22no—
436C2×Q8—22no—
437C2×Q8—22no—
438C2×Q8—22no—
439C2×Q8—22no—
440C2×Q8—48no—
441C2×Q8—48no—
442C2×Q8—42no—
443C2×Q8—42no—
444C2×Q8—42no—
445C2×Q8—44no—
446C2×Q8—44no—
447C2×Q8—44no—
448C2×Q8—44no—
449C2×Q8—84no—
450C2×Q8—816no—
451C2×D4—28no—
452C2×D4—24no—
453C2×D4—28no—
454C2×D4—22no—
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—48no—
466C2×D4—48no—
467C2×D4—48no—
468C2×D4—48no—
469C2×D4—48no—
470C2×D4—48no—
471C2×D4—48no—
472C2×D4—44no—
473C2×D4—44no—
474C2×D4—42no—
475C2×D4—42no—
476C2×D4—44no—
477C2×D4—42no—
478C2×D4—42no—
479C2×D4—42no—
480C2×D4—44no—
481C2×D4—44no—
482C2×D4—44no—
483C2×D4—48no—
484C2×D4—84no—
485C2×D4—84no—
486C2×D4—816no—
487C2×D4—84no—
488C2×D4—84no—
489C2×D4—816no—
490C2×D4—816no—
491C2×D4—816no—
492C2×D4C2×#4114yes—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—24no—
500C22×C4—22no—
501C22×C4—24no—
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—24no—
511C22×C4—24no—
512C22×C4—24no—
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—42no—
525C22×C4—42no—
526C22×C4—42no—
527C22×C4—42no—
528C22×C4—44no—
529C22×C4—44no—
530C22×C4—44no—
531C22×C4—44no—
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—42no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4—42no—
544C22×C4—48no—
545C22×C4—84no—
546C22×C4—816no—
547C22×C4C2×SD1614yes—
548C22×C4C2×SD1614yes—
549C22×C4C22×D412yes—
550C22×C4C22×D412yes—
551C22×C4C22×D412yes—
552C22×C4C22×D412yes—
553C22×C4C22×D412yes—
554C22×C4C22×D412yes—
555C22×C4C22×D411yescharacteristic
556C22×C4C2×#4112yes—
557C22×C4H(5,𝔽2)12yes—
558C22×C4H(5,𝔽2)12yes—
559C22×C4H(5,𝔽2)12yes—
560C22×C42−1+412yes—
561C22×C4C2511yescharacteristic
562SD16—416no—
563SD16—416no—
564C2×C8—28no—
565C2×C8—22no—
566C2×C8—22no—
567C2×C8—22no—
568C2×C8—22no—
569C2×C8—22no—
570C2×C8—22no—
571C2×C8—22no—
572C2×C8—22no—
573C2×C8—22no—
574C2×C8—22no—
575C2×C8—22no—
576C2×C8—416no—
577C2×C8—44no—
578C2×C8—44no—
579C2×C8—44no—
580C2×C8C22×D414yes—
581C4⋊C4—24no—
582C4⋊C4—24no—
583C4⋊C4—22no—
584C4⋊C4—22no—
585C4⋊C4—22no—
586C4⋊C4—22no—
587C4⋊C4—22no—
588C4⋊C4—22no—
589C4⋊C4—22no—
590C4⋊C4—22no—
591C4⋊C4—48no—
592C4⋊C4—48no—
593C4⋊C4—42no—
594C4⋊C4—42no—
595C4⋊C4—42no—
596C4⋊C4—48no—
597C4⋊C4C22×D414yes—
598C4⋊C4C22×D414yes—
599C22⋊C4—44no—
600C22⋊C4—48no—
601C22⋊C4—48no—
602C22⋊C4—48no—
603C22⋊C4—48no—
604C22⋊C4—48no—
605C22⋊C4—84no—
606C22⋊C4—84no—
607C22⋊C4C2×SD16116yescomplemented
608C42—24no—
609C42—24no—
610C42—22no—
611C42—22no—
612C42—22no—
613C42—22no—
614C42—84no—
615C23—22no—
616C23—22no—
617C23—22no—
618C23—28no—
619C23—28no—
620C23—28no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—24no—
625C23—44no—
626C23—44no—
627C23—44no—
628C23—44no—
629C23—48no—
630C23—42no—
631C23—42no—
632C23—48no—
633C23—48no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—84no—
646C23—84no—
647C23—84no—
648C23—84no—
649C23—84no—
650C23—84no—
651C23—84no—
652C23—84no—
653C23—84no—
654C23—84no—
655C23—84no—
656C23#53712yes—
657C23D4212yes—
658C23#54612yes—
659C23C22×SD1614yes—
660C23C22×SD1612yes—
661C23#57512yes—
662C23#57612yes—
663C23#57712yes—
664C23C23×D411yescharacteristic
665Q8—42no—
666Q8—42no—
667Q8—42no—
668Q8—42no—
669Q8—816no—
670Q8—84no—
671D4—24no—
672D4—24no—
673D4—48no—
674D4—42no—
675D4—42no—
676D4—42no—
677D4—42no—
678D4—42no—
679D4—42no—
680D4—816no—
681D4—816no—
682D4—816no—
683D4—816no—
684D4—84no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—28no—
688C2×C4—28no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—24no—
694C2×C4—22no—
695C2×C4—24no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—44no—
703C2×C4—44no—
704C2×C4—48no—
705C2×C4—48no—
706C2×C4—44no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—48no—
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—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—816no—
729C2×C4—84no—
730C2×C4—84no—
731C2×C4—84no—
732C2×C4—84no—
733C2×C4#53514yes—
734C2×C4#53712yes—
735C2×C4#53814yes—
736C2×C4D4212yes—
737C2×C4#54612yes—
738C2×C4#54814yes—
739C2×C4#56214yes—
740C2×C4C22×SD1614yes—
741C2×C4C22×SD1614yes—
742C2×C4C23×D411yescharacteristic
743C2×C4C22×#4111yescharacteristic
744C2×C4C2×H(5,𝔽2)11yescharacteristic
745C2×C4C2×H(5,𝔽2)11yescharacteristic
746C2×C4C2×H(5,𝔽2)11yescharacteristic
747C2×C4C2×2−1+411yescharacteristic
748C8—24no—
749C8—42no—
750C8—42no—
751C8—42no—
752C22—24no—
753C22—24no—
754C22—24no—
755C22—42no—
756C22—42no—
757C22—416no—
758C22—42no—
759C22—42no—
760C22—44no—
761C22—44no—
762C22—44no—
763C22—82no—
764C22—82no—
765C22—816no—
766C22—82no—
767C22—82no—
768C22—82no—
769C22—82no—
770C22—82no—
771C22—82no—
772C22—82no—
773C22—82no—
774C22—82no—
775C22—168no—
776C22#267614yes—
777C22#324614yes—
778C22#325714yes—
779C22#326814yes—
780C22D4×SD1614yes—
781C22#329514yes—
782C22#331114yes—
783C22C2×#53711yescharacteristic
784C22C2×D4211yescharacteristic
785C22C2×#54611yescharacteristic
786C22C23×SD1611yescharacteristic
787C22C2×#57511yescharacteristic
788C22C2×#57611yescharacteristic
789C22C2×#57711yescharacteristic
790C4—24no—
791C4—24no—
792C4—42no—
793C4—44no—
794C4—44no—
795C4—42no—
796C4—42no—
797C4—82no—
798C4—82no—
799C4—82no—
800C4—82no—
801C4#267614yes—
802C4C2×#53511yescharacteristic
803C4C2×#53811yescharacteristic
804C4C2×#54811yescharacteristic
805C4C2×#56211yescharacteristic
806C2—44no—
807C2—84no—
808C2—162no—
809C2#3091418yesdirect product factor
810C2C2×#267611yescharacteristic
811C2C2×#324611yescharacteristic
812C2C2×#325711yescharacteristic
813C2C2×#326811yescharacteristic
814C2C2×D4×SD1611yescharacteristic
815C2C2×#329511yescharacteristic
816C2C2×#331111yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#2428C2
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×#476C2semidirect
2. C22×#465C2semidirect
3. C2×#2492C2semidirect
5. #30914C2direct (N × H)
6. C2×#2066C2semidirect
7. C2×#2055C2semidirect
8. C2×#2034C2semidirect
9. C2×#2023C2semidirect
10. C2×#2014C2semidirect
11. C2×#2000C2semidirect
12. C2×#1982C2semidirect
13. C2×#1919C2semidirect
14. C2×#1893C2semidirect
15. C2×#1877C2semidirect
16. C2×#1850C2semidirect
28. C2×#476C22semidirect
30. C2×#465C22semidirect
45. #2492C22semidirect
62. #2066C22semidirect
63. #2055C22semidirect
64. #2034C22semidirect
65. #2023C22semidirect
66. #2014C22semidirect
67. #2000C22semidirect
68. #1982C22semidirect
69. #1919C22semidirect
70. #1893C22semidirect
71. #1877C22semidirect
72. #1850C22semidirect
154. C2×#106D4semidirect
374. C2×C22⋊C4SD16semidirect
388. #106C2×D4semidirect
607. C22⋊C4C2×SD16semidirect
809. C2#30914direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#4762
C22×#4652
C2×#24922
C2×#24282
#309142
C2×#20662
C2×#20552
C2×#20342
C2×#20232
C2×#20142
C2×#20002
C2×#19822
C2×#19192
C2×#18932
C2×#18772
C2×#18502