Finite Group Databasebeta

← C2×#28119 #6459394

Subgroups — C2×#28119 #6459394

Order 512.

3374 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#482C211yesmaximal, characteristic, complemented
2C22×#449C211yesmaximal, characteristic
3C2×C4×#121C211yesmaximal, characteristic, complemented
4C2×#2297C211yesmaximal, characteristic, complemented
5#28119C2116yesmaximal, direct product factor
6C2×#2066C211yesmaximal, characteristic, complemented
7C2×#2067C211yesmaximal, characteristic, complemented
8C2×#2055C211yesmaximal, characteristic, complemented
9C2×#2054C211yesmaximal, characteristic, complemented
10C2×#1928C211yesmaximal, characteristic, complemented
11C2×#1926C211yesmaximal, characteristic, complemented
12C2×#1879C211yesmaximal, characteristic, complemented
13C2×#1877C211yesmaximal, characteristic, complemented
14C2×#1825C211yesmaximal, characteristic, complemented
15C2×#1797C211yesmaximal, characteristic, complemented
16C2×#1788C211yesmaximal, characteristic, complemented
17C23×#41C2211yescharacteristic
18C23×SD16C2211yescharacteristic
19C23×D8C2211yescharacteristic
20C22×#121C2211yescharacteristic
21C22×C4×D4—21no—
22C22×C4×D4C2211yescharacteristic
23C22×#117C2211yescharacteristic
24C23×C42C2211yescharacteristic
25C2×#482—28no—
26C2×#482C2218yescomplemented
27C2×#449—28no—
28C2×#449C2218yes—
29C22×#107C2211yescharacteristic
30C22×#106C2211yescharacteristic
31C22×C4⋊C8C2211yescharacteristic
32C22×C4⋊C8C2211yescharacteristic
33C22×#103C2211yescharacteristic
34C22×#103C2211yescharacteristic
35C22×#103C2211yescharacteristic
36C22×#102C2211yescharacteristic
37C22×#102C2211yescharacteristic
38C22×#102C2211yescharacteristic
39C22×#102C2211yescharacteristic
40C22×#102C2211yescharacteristic
41C22×C22⋊C8C2211yescharacteristic
42C22×C22⋊C8C2211yescharacteristic
43C4×#121—24no—
44C4×#121C2218yescomplemented
45#2297—24no—
46#2297C2218yescomplemented
47C2×#391C2211yescharacteristic
48C2×#391C2211yescharacteristic
49C2×#390C2211yescharacteristic
50C2×#390C2211yescharacteristic
51C2×#390C2211yescharacteristic
52C2×#389C2211yescharacteristic
53C2×#388—21no—
54C2×#386—21no—
55C2×#386—21no—
56C2×#386—21no—
57C2×#380C2211yescharacteristic
58C2×C4×C4⋊C4C2211yescharacteristic
59C2×C4×C22⋊C4—21no—
60C2×C4×C22⋊C4—21no—
61C2×C4×C22⋊C4—21no—
62#2067C2218yescomplemented
63#2066C2218yescomplemented
64#2055C2218yescomplemented
65#2054C2218yescomplemented
66#1928C2218yescomplemented
67#1926C2218yescomplemented
68#1879C2218yescomplemented
69#1877C2218yescomplemented
70#1825C2218yescomplemented
71#1797C2218yescomplemented
72#1788C2218yescomplemented
73C2×#340C2211yescharacteristic
74C2×#340C2211yescharacteristic
75C2×#340C2211yescharacteristic
76C2×#340C2211yescharacteristic
77C2×#336C2211yescharacteristic
78C2×#336C2211yescharacteristic
79C22×#41—24no—
80C22×#41—24no—
81C22×#41—22no—
82C22×#41—24no—
83C22×#41—24no—
84C22×#41—42no—
85C22×#41—42no—
86C22×#41C2314yes—
87C23×Q8C2311yescharacteristic
88C23×D4—21no—
89C23×D4—21no—
90C23×D4C2311yescharacteristic
91C23×D4C2311yescharacteristic
92C24×C4—21no—
93C24×C4—21no—
94C24×C4D411yescharacteristic
95C24×C4D411yescharacteristic
96C24×C4C2311yescharacteristic
97C22×SD16—24no—
98C22×SD16—24no—
99C22×SD16—42no—
100C22×SD16C2314yes—
101C22×D8—24no—
102C22×D8—24no—
103C22×D8—42no—
104C22×D8C2314yes—
105C23×C8C2311yescharacteristic
106C23×C8C2311yescharacteristic
107C23×C8C2311yescharacteristic
108C23×C8C2311yescharacteristic
109C2×#121—22no—
110C2×#121—24no—
111C2×#121D418yes—
112C2×#121C2314yes—
113C2×C4×D4—28no—
114C2×C4×D4—22no—
115C2×C4×D4—42no—
116C2×C4×D4—42no—
117C2×C4×D4—48no—
118C2×C4×D4C2314yes—
119C2×#117—22no—
120C2×#117—24no—
121C2×#117—24no—
122C2×#117C2314yes—
123C22×C4⋊C4—21no—
124C22×C4⋊C4C2311yescharacteristic
125C22×C4⋊C4C2311yescharacteristic
126C22×C4⋊C4C2311yescharacteristic
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2311yescharacteristic
129C22×C22⋊C4—21no—
130C22×C22⋊C4—21no—
131C22×C22⋊C4—21no—
132C22×C22⋊C4—21no—
133C22×C22⋊C4—21no—
134C22×C22⋊C4—21no—
135C22×C22⋊C4—21no—
136C22×C22⋊C4—21no—
137C22×C22⋊C4—21no—
138C22×C22⋊C4—21no—
139C22×C42—21no—
140C22×C42—21no—
141C22×C42—42no—
142C22×C42—42no—
143C22×C42D411yescharacteristic
144C22×C42D411yescharacteristic
145C22×C42D414yes—
146C22×C42C2311yescharacteristic
147C22×C42C2311yescharacteristic
148C22×C42C2314yes—
149#482—232no—
150#449—232no—
151C2×#107—24no—
152C2×#107C2314yes—
153C2×#106—24no—
154C2×#106C2314yes—
155C2×C4⋊C8—42no—
156C2×C4⋊C8—42no—
157C2×C4⋊C8C2314yes—
158C2×C4⋊C8C2314yes—
159C2×#103—24no—
160C2×#103—24no—
161C2×#103—42no—
162C2×#103C2314yes—
163C2×#103C2314yes—
164C2×#103C2314yes—
165C2×#102—24no—
166C2×#102—24no—
167C2×#102—24no—
168C2×#102—24no—
169C2×#102—42no—
170C2×#102C2314yes—
171C2×#102C2314yes—
172C2×#102C2314yes—
173C2×#102C2314yes—
174C2×#102C2314yes—
175C2×C22⋊C8—24no—
176C2×C22⋊C8—24no—
177C2×C22⋊C8C2314yes—
178C2×C22⋊C8C2314yes—
179#391—22no—
180#391—22no—
181#391C2314yes—
182#391C2314yes—
183#390—22no—
184#390—22no—
185#390—22no—
186#390C2314yes—
187#390C2314yes—
188#390C2314yes—
189#389—22no—
190#389C2314yes—
191#388—28no—
192#386—28no—
193#386—28no—
194#386—28no—
195#380—22no—
196#380C2314yes—
197C4×C4⋊C4—22no—
198C4×C4⋊C4C2314yes—
199C4×C22⋊C4—28no—
200C4×C22⋊C4—28no—
201C4×C22⋊C4—28no—
202C2×#95—21no—
203C2×#95—21no—
204C2×#95—21no—
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—
216C25—21no—
217C25C2×D411yescharacteristic
218C2×#41—216no—
219C2×#41—28no—
220C2×#41—28no—
221C2×#41—28no—
222C2×#41—28no—
223C2×#41—44no—
224C2×#41—44no—
225C2×#41—416no—
226C2×#41—416no—
227C2×#41—416no—
228C2×#41—416no—
229C2×#41—48no—
230C2×#41—48no—
231C22×Q8—21no—
232C22×Q8—22no—
233C22×Q8—22no—
234C22×Q8—22no—
235C22×Q8—22no—
236C22×Q8—22no—
237C22×Q8#4114yes—
238C22×Q8C2412yes—
239C22×D4—28no—
240C22×D4—28no—
241C22×D4—24no—
242C22×D4—24no—
243C22×D4—22no—
244C22×D4—21no—
245C22×D4—21no—
246C22×D4—22no—
247C22×D4—22no—
248C22×D4—22no—
249C22×D4—22no—
250C22×D4—22no—
251C22×D4—22no—
252C22×D4—22no—
253C22×D4—22no—
254C22×D4—22no—
255C22×D4—44no—
256C22×D4—44no—
257C22×D4—44no—
258C22×D4—44no—
259C22×D4C2×D414yes—
260C22×D4#4114yes—
261C22×D4C2412yes—
262C22×D4C2412yes—
263C23×C4—22no—
264C23×C4—22no—
265C23×C4—22no—
266C23×C4—22no—
267C23×C4—28no—
268C23×C4—21no—
269C23×C4—21no—
270C23×C4—24no—
271C23×C4—24no—
272C23×C4—24no—
273C23×C4—21no—
274C23×C4—21no—
275C23×C4—21no—
276C23×C4—21no—
277C23×C4—24no—
278C23×C4—42no—
279C23×C4—42no—
280C23×C4—42no—
281C23×C4—42no—
282C23×C4—44no—
283C23×C4—44no—
284C23×C4—44no—
285C23×C4—44no—
286C23×C4—44no—
287C23×C4C2×D411yescharacteristic
288C23×C4C2×D411yescharacteristic
289C23×C4C2×D414yes—
290C23×C4C2×D412yes—
291C23×C4C2×D411yescharacteristic
292C23×C4C2×D414yes—
293C23×C4C2×D411yescharacteristic
294C23×C4C2×D411yescharacteristic
295C23×C4C2×D414yes—
296C23×C4#4114yes—
297C23×C4C2412yes—
298C23×C4C2411yescharacteristic
299C2×SD16—28no—
300C2×SD16—28no—
301C2×SD16—44no—
302C2×SD16—416no—
303C2×D8—28no—
304C2×D8—28no—
305C2×D8—44no—
306C2×D8—416no—
307C22×C8—22no—
308C22×C8—22no—
309C22×C8—22no—
310C22×C8—22no—
311C22×C8—22no—
312C22×C8—22no—
313C22×C8—22no—
314C22×C8—22no—
315C22×C8—22no—
316C22×C8—22no—
317C22×C8—22no—
318C22×C8—22no—
319C22×C8C2412yes—
320C22×C8C2412yes—
321C22×C8C2412yes—
322C22×C8C2412yes—
323#121—216no—
324#121—28no—
325#121C2×D4116yes—
326C4×D4—44no—
327C4×D4—44no—
328C4×D4—48no—
329C4×D4—432no—
330#117—28no—
331#117—28no—
332#117—48no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—22no—
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—21no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—44no—
349C2×C4⋊C4C2×D414yes—
350C2×C4⋊C4C2412yes—
351C2×C4⋊C4C2412yes—
352C2×C4⋊C4C2412yes—
353C2×C4⋊C4C2412yes—
354C2×C4⋊C4C2412yes—
355C2×C22⋊C4—28no—
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—44no—
375C2×C42—22no—
376C2×C42—22no—
377C2×C42—22no—
378C2×C42—22no—
379C2×C42—24no—
380C2×C42—24no—
381C2×C42—48no—
382C2×C42—44no—
383C2×C42—44no—
384C2×C42—42no—
385C2×C42—42no—
386C2×C42—44no—
387C2×C42—44no—
388C2×C42C2×D412yes—
389C2×C42C2×D412yes—
390C2×C42C2×D414yes—
391C2×C42C2×D414yes—
392C2×C42C2412yes—
393C2×C42C2412yes—
394#107—28no—
395#106—28no—
396C4⋊C8—44no—
397C4⋊C8—44no—
398#103—28no—
399#103—28no—
400#103—44no—
401#102—28no—
402#102—28no—
403#102—28no—
404#102—28no—
405#102—44no—
406C22⋊C8—28no—
407C22⋊C8—28no—
408#95—24no—
409#95—24no—
410#95—24no—
411#95—24no—
412#95—24no—
413#95—24no—
414#95—24no—
415C24—22no—
416C24—22no—
417C24—22no—
418C24—22no—
419C24—22no—
420C24—22no—
421C24—24no—
422C24—24no—
423C24—22no—
424C24—22no—
425C24—42no—
426C24—42no—
427C24—42no—
428C24—42no—
429C24—42no—
430C24—42no—
431C24—42no—
432C24—42no—
433C24—42no—
434C24—42no—
435C24—42no—
436C24—42no—
437C24#12114yes—
438C24C22×D412yes—
439C24C22×D411yescharacteristic
440#41—416no—
441#41—416no—
442#41—416no—
443#41—416no—
444#41—464no—
445C2×Q8—24no—
446C2×Q8—22no—
447C2×Q8—28no—
448C2×Q8—28no—
449C2×Q8—22no—
450C2×Q8—22no—
451C2×Q8—22no—
452C2×Q8—22no—
453C2×Q8—42no—
454C2×Q8—42no—
455C2×Q8—44no—
456C2×Q8—44no—
457C2×Q8C2×#4114yes—
458C2×D4—216no—
459C2×D4—216no—
460C2×D4—24no—
461C2×D4—24no—
462C2×D4—28no—
463C2×D4—28no—
464C2×D4—28no—
465C2×D4—28no—
466C2×D4—22no—
467C2×D4—22no—
468C2×D4—22no—
469C2×D4—22no—
470C2×D4—22no—
471C2×D4—22no—
472C2×D4—22no—
473C2×D4—22no—
474C2×D4—22no—
475C2×D4—22no—
476C2×D4—48no—
477C2×D4—432no—
478C2×D4—48no—
479C2×D4—48no—
480C2×D4—432no—
481C2×D4—48no—
482C2×D4—42no—
483C2×D4—42no—
484C2×D4—42no—
485C2×D4—42no—
486C2×D4—44no—
487C2×D4—44no—
488C2×D4—44no—
489C2×D4—44no—
490C2×D4C22×D414yes—
491C2×D4C2×#4114yes—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—24no—
499C22×C4—24no—
500C22×C4—28no—
501C22×C4—28no—
502C22×C4—28no—
503C22×C4—28no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—216no—
509C22×C4—24no—
510C22×C4—24no—
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—28no—
520C22×C4—28no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—44no—
526C22×C4—44no—
527C22×C4—44no—
528C22×C4—44no—
529C22×C4—416no—
530C22×C4—48no—
531C22×C4—432no—
532C22×C4—48no—
533C22×C4—48no—
534C22×C4—416no—
535C22×C4—42no—
536C22×C4—42no—
537C22×C4—42no—
538C22×C4—42no—
539C22×C4—48no—
540C22×C4—42no—
541C22×C4—42no—
542C22×C4—42no—
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—48no—
553C22×C4—816no—
554C22×C4#12114yes—
555C22×C4#12118yes—
556C22×C4#13514yes—
557C22×C4AGL(1,ℤ/8)14yes—
558C22×C4C22×D412yes—
559C22×C4C22×D412yes—
560C22×C4C22×D412yes—
561C22×C4C22×D414yes—
562C22×C4C22×D412yes—
563C22×C4C22×D412yes—
564C22×C4C22×D411yescharacteristic
565C22×C4C22×D412yes—
566C22×C4C2×#4114yes—
567C22×C4C2×#4112yes—
568C22×C4C2×#4112yes—
569C22×C4C2×#4112yes—
570C22×C4H(5,𝔽2)12yes—
571C22×C4H(5,𝔽2)12yes—
572C22×C4C2511yescharacteristic
573SD16—416no—
574D8—416no—
575C2×C8—22no—
576C2×C8—22no—
577C2×C8—22no—
578C2×C8—22no—
579C2×C8—22no—
580C2×C8—22no—
581C2×C8—22no—
582C2×C8—22no—
583C2×C8—22no—
584C2×C8—22no—
585C2×C8—22no—
586C2×C8—22no—
587C2×C8—44no—
588C2×C8—44no—
589C2×C8—44no—
590C2×C8—44no—
591C4⋊C4—24no—
592C4⋊C4—22no—
593C4⋊C4—22no—
594C4⋊C4—22no—
595C4⋊C4—22no—
596C4⋊C4—22no—
597C4⋊C4—22no—
598C4⋊C4—22no—
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—42no—
602C4⋊C4—42no—
603C4⋊C4—42no—
604C4⋊C4—42no—
605C4⋊C4—48no—
606C4⋊C4C22×D414yes—
607C22⋊C4—216no—
608C22⋊C4—48no—
609C22⋊C4—48no—
610C22⋊C4—48no—
611C22⋊C4—48no—
612C22⋊C4—48no—
613C22⋊C4—48no—
614C22⋊C4—48no—
615C22⋊C4—48no—
616C22⋊C4—48no—
617C42—24no—
618C42—24no—
619C42—22no—
620C42—22no—
621C42—22no—
622C42—22no—
623C42—44no—
624C42—44no—
625C42—48no—
626C42—48no—
627C23—22no—
628C23—22no—
629C23—28no—
630C23—28no—
631C23—28no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—24no—
637C23—24no—
638C23—44no—
639C23—44no—
640C23—44no—
641C23—44no—
642C23—48no—
643C23—48no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—48no—
649C23—48no—
650C23—48no—
651C23—48no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—84no—
661C23—84no—
662C23—84no—
663C23—84no—
664C23—84no—
665C23—84no—
666C23—84no—
667C23—84no—
668C23C2×#12114yes—
669C23C2×#12112yes—
670C23#52512yes—
671C23#53412yes—
672C23C2×#13512yes—
673C23C2×AGL(1,ℤ/8)12yes—
674C23#57512yes—
675C23#57512yes—
676C23C23×D411yescharacteristic
677Q8—24no—
678Q8—24no—
679Q8—42no—
680Q8—42no—
681Q8—48no—
682D4—24no—
683D4—24no—
684D4—24no—
685D4—24no—
686D4—432no—
687D4—432no—
688D4—42no—
689D4—42no—
690D4—42no—
691D4—42no—
692D4—48no—
693D4—48no—
694C2×C4—22no—
695C2×C4—28no—
696C2×C4—28no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—28no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—216no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—416no—
717C2×C4—432no—
718C2×C4—416no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—44no—
722C2×C4—44no—
723C2×C4—48no—
724C2×C4—48no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—816no—
740C2×C4—84no—
741C2×C4—84no—
742C2×C4—84no—
743C2×C4—84no—
744C2×C4C2×#12114yes—
745C2×C4C2×#12112yes—
746C2×C4#52512yes—
747C2×C4#53412yes—
748C2×C4#54614yes—
749C2×C4#54614yes—
750C2×C4#55114yes—
751C2×C4#55114yes—
752C2×C4C2×#13514yes—
753C2×C4C2×AGL(1,ℤ/8)14yes—
754C2×C4C23×D411yescharacteristic
755C2×C4C22×#4111yescharacteristic
756C2×C4C22×#4111yescharacteristic
757C2×C4C22×#4111yescharacteristic
758C2×C4C2×H(5,𝔽2)11yescharacteristic
759C2×C4C2×H(5,𝔽2)11yescharacteristic
760C8—42no—
761C8—42no—
762C8—42no—
763C8—42no—
764C22—24no—
765C22—24no—
766C22—24no—
767C22—42no—
768C22—42no—
769C22—42no—
770C22—42no—
771C22—416no—
772C22—44no—
773C22—44no—
774C22—44no—
775C22—44no—
776C22—44no—
777C22—44no—
778C22—82no—
779C22—82no—
780C22—82no—
781C22—82no—
782C22—82no—
783C22—82no—
784C22—816no—
785C22—816no—
786C22—82no—
787C22—82no—
788C22#253414yes—
789C22#303514yes—
790C22#303614yes—
791C22#310214yes—
792C22#311514yes—
793C22#318814yes—
794C22#319714yes—
795C22C22×#12111yescharacteristic
796C22C2×#52511yescharacteristic
797C22C2×#53411yescharacteristic
798C22C22×#13511yescharacteristic
799C22C22×AGL(1,ℤ/8)11yescharacteristic
800C22C2×#57511yescharacteristic
801C22C2×#57511yescharacteristic
802C4—24no—
803C4—24no—
804C4—24no—
805C4—44no—
806C4—42no—
807C4—42no—
808C4—44no—
809C4—82no—
810C4—82no—
811C4—82no—
812C4—82no—
813C4#253414yes—
814C4C2×#54611yescharacteristic
815C4C2×#54611yescharacteristic
816C4C2×#55111yescharacteristic
817C4C2×#55111yescharacteristic
818C2—44no—
819C2—84no—
820C2—84no—
821C2#2811918yesdirect product factor
822C2C2×#253411yescharacteristic
823C2C2×#303511yescharacteristic
824C2C2×#303611yescharacteristic
825C2C2×#310211yescharacteristic
826C2C2×#311511yescharacteristic
827C2C2×#318811yescharacteristic
828C2C2×#319711yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×#449C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C23×C42 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#482C2semidirect
3. C2×C4×#121C2semidirect
4. C2×#2297C2semidirect
5. #28119C2direct (N × H)
6. C2×#2066C2semidirect
7. C2×#2067C2semidirect
8. C2×#2055C2semidirect
9. C2×#2054C2semidirect
10. C2×#1928C2semidirect
11. C2×#1926C2semidirect
12. C2×#1879C2semidirect
13. C2×#1877C2semidirect
14. C2×#1825C2semidirect
15. C2×#1797C2semidirect
16. C2×#1788C2semidirect
26. C2×#482C22semidirect
44. C4×#121C22semidirect
46. #2297C22semidirect
62. #2067C22semidirect
63. #2066C22semidirect
64. #2055C22semidirect
65. #2054C22semidirect
66. #1928C22semidirect
67. #1926C22semidirect
68. #1879C22semidirect
69. #1877C22semidirect
70. #1825C22semidirect
71. #1797C22semidirect
72. #1788C22semidirect
821. C2#28119direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#4822
C22×#4492
C2×C4×#1212
C2×#22972
#281192
C2×#20662
C2×#20672
C2×#20552
C2×#20542
C2×#19282
C2×#19262
C2×#18792
C2×#18772
C2×#18252
C2×#17972
C2×#17882