Finite Group Databasebeta

← C2×#27250 #6440650

Subgroups — C2×#27250 #6440650

Order 512.

3140 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#475C211yesmaximal, characteristic, complemented
2C22×#449C211yesmaximal, characteristic
3C2×#2491C211yesmaximal, characteristic, complemented
4C2×#2341C211yesmaximal, characteristic, complemented
5#27250C2116yesmaximal, direct product factor
6C2×#2077C211yesmaximal, characteristic, complemented
7C2×#2054C211yesmaximal, characteristic, complemented
8C2×#2034C211yesmaximal, characteristic, complemented
9C2×#2023C211yesmaximal, characteristic, complemented
10C2×#1972C211yesmaximal, characteristic, complemented
11C2×#1926C211yesmaximal, characteristic, complemented
12C2×#1924C211yesmaximal, characteristic, complemented
13C2×#1880C211yesmaximal, characteristic, complemented
14C2×#1880C211yesmaximal, characteristic, complemented
15C2×#1788C211yesmaximal, characteristic, complemented
16C2×#1763C211yesmaximal, characteristic, complemented
17C23×#41C2211yescharacteristic
18C23×SD16C2211yescharacteristic
19C23×D8C2211yescharacteristic
20C22×C4⋊Q8C2211yescharacteristic
21C22×#124—21no—
22C22×#121C2211yescharacteristic
23C22×C4×Q8C2211yescharacteristic
24C22×C4×Q8C2211yescharacteristic
25C2×#475—28no—
26C2×#475C2218yescomplemented
27C2×#449—28no—
28C2×#449C2218yes—
29C22×#106C2211yescharacteristic
30C22×#106C2211yescharacteristic
31C22×C4⋊C8C2211yescharacteristic
32C22×#103C2211yescharacteristic
33C22×#103C2211yescharacteristic
34C22×#103C2211yescharacteristic
35C22×#102C2211yescharacteristic
36C22×#102C2211yescharacteristic
37C22×#102C2211yescharacteristic
38C22×#102C2211yescharacteristic
39C22×#102C2211yescharacteristic
40C22×C22⋊C8C2211yescharacteristic
41C22×C22⋊C8C2211yescharacteristic
42C22×#97C2211yescharacteristic
43#2491—24no—
44#2491C2218yescomplemented
45C2×#394—21no—
46C2×#393—21no—
47#2341—24no—
48#2341C2218yescomplemented
49C2×#390—21no—
50C2×#390—21no—
51C2×#390C2211yescharacteristic
52C2×#390C2211yescharacteristic
53C2×#390C2211yescharacteristic
54C2×#390C2211yescharacteristic
55C2×#388—21no—
56C2×#380—21no—
57C2×#380C2211yescharacteristic
58C2×#380C2211yescharacteristic
59C2×C4×C4⋊C4C2211yescharacteristic
60C2×C4×C22⋊C4—21no—
61C2×C4×C22⋊C4C2211yescharacteristic
62#2077C2218yescomplemented
63#2054C2218yescomplemented
64#2034C2218yescomplemented
65#2023C2218yescomplemented
66#1972C2218yescomplemented
67#1926C2218yescomplemented
68#1924C2218yescomplemented
69#1880C2218yescomplemented
70#1880C2218yescomplemented
71#1788C2218yescomplemented
72#1763C2218yescomplemented
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×Q8—21no—
88C23×Q8C2311yescharacteristic
89C23×D4—21no—
90C23×D4—21no—
91C23×D4C2311yescharacteristic
92C23×D4C2311yescharacteristic
93C24×C4—21no—
94C24×C4C2311yescharacteristic
95C22×SD16—24no—
96C22×SD16—24no—
97C22×SD16—24no—
98C22×SD16C2314yes—
99C22×D8—24no—
100C22×D8—24no—
101C22×D8—42no—
102C22×D8C2314yes—
103C23×C8C2311yescharacteristic
104C23×C8C2311yescharacteristic
105C23×C8C2311yescharacteristic
106C23×C8C2311yescharacteristic
107C2×C4⋊Q8—24no—
108C2×C4⋊Q8—22no—
109C2×C4⋊Q8—42no—
110C2×C4⋊Q8C2314yes—
111C2×#124—28no—
112C2×#124—48no—
113C2×#121—22no—
114C2×#121—24no—
115C2×#121—42no—
116C2×#121C2314yes—
117C2×C4×Q8—22no—
118C2×C4×Q8—22no—
119C2×C4×Q8—24no—
120C2×C4×Q8—24no—
121C2×C4×Q8—42no—
122C2×C4×Q8—42no—
123C2×C4×Q8C2314yes—
124C2×C4×Q8C2314yes—
125C22×C4⋊C4—21no—
126C22×C4⋊C4—21no—
127C22×C4⋊C4—21no—
128C22×C4⋊C4C2311yescharacteristic
129C22×C4⋊C4C2311yescharacteristic
130C22×C4⋊C4C2311yescharacteristic
131C22×C4⋊C4C2311yescharacteristic
132C22×C4⋊C4C2311yescharacteristic
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×C22⋊C4—21no—
140C22×C22⋊C4—21no—
141C22×C22⋊C4—21no—
142C22×C22⋊C4—21no—
143C22×C22⋊C4—21no—
144C22×C22⋊C4D411yescharacteristic
145C22×C22⋊C4D411yescharacteristic
146C22×C42—21no—
147C22×C42—21no—
148C22×C42—21no—
149C22×C42C2311yescharacteristic
150C22×C42C2311yescharacteristic
151#475—232no—
152#449—232no—
153C2×#106—24no—
154C2×#106—24no—
155C2×#106C2314yes—
156C2×#106C2314yes—
157C2×C4⋊C8—24no—
158C2×C4⋊C8C2314yes—
159C2×#103—24no—
160C2×#103—24no—
161C2×#103D418yes—
162C2×#103C2314yes—
163C2×#103C2314yes—
164C2×#103C2314yes—
165C2×#102—24no—
166C2×#102—24no—
167C2×#102—42no—
168C2×#102—42no—
169C2×#102—42no—
170C2×#102C2314yes—
171C2×#102C2314yes—
172C2×#102C2314yes—
173C2×#102C2314yes—
174C2×#102C2314yes—
175C2×C22⋊C8—24no—
176C2×C22⋊C8—42no—
177C2×C22⋊C8C2314yes—
178C2×C22⋊C8C2314yes—
179C2×#97—42no—
180C2×#97C2314yes—
181#394—28no—
182#393—28no—
183#390—28no—
184#390—28no—
185#390—22no—
186#390—22no—
187#390—22no—
188#390—22no—
189#390C2314yes—
190#390C2314yes—
191#390C2314yes—
192#390C2314yes—
193#388—28no—
194#380—22no—
195#380—22no—
196#380—28no—
197#380C2314yes—
198#380C2314yes—
199C4×C4⋊C4—22no—
200C4×C4⋊C4C2314yes—
201C4×C22⋊C4—28no—
202C4×C22⋊C4D414yes—
203C4×C22⋊C4C2314yes—
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
218C2×#41—216no—
219C2×#41—28no—
220C2×#41—28no—
221C2×#41—28no—
222C2×#41—28no—
223C2×#41—44no—
224C2×#41—44no—
225C2×#41—48no—
226C2×#41—48no—
227C2×#41—416no—
228C2×#41—416no—
229C2×#41—416no—
230C2×#41—416no—
231C22×Q8—21no—
232C22×Q8—24no—
233C22×Q8—22no—
234C22×Q8—22no—
235C22×Q8—22no—
236C22×Q8—44no—
237C22×Q8—44no—
238C22×Q8—82no—
239C22×Q8C2×D414yes—
240C22×Q8#4114yes—
241C22×Q8#4114yes—
242C22×Q8C2412yes—
243C22×D4—28no—
244C22×D4—24no—
245C22×D4—24no—
246C22×D4—22no—
247C22×D4—21no—
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—22no—
259C22×D4—44no—
260C22×D4—44no—
261C22×D4—44no—
262C22×D4—44no—
263C22×D4—82no—
264C22×D4#4114yes—
265C22×D4C2412yes—
266C22×D4C2412yes—
267C23×C4—21no—
268C23×C4—28no—
269C23×C4—21no—
270C23×C4—22no—
271C23×C4—24no—
272C23×C4—22no—
273C23×C4—22no—
274C23×C4—22no—
275C23×C4—22no—
276C23×C4—22no—
277C23×C4—21no—
278C23×C4—21no—
279C23×C4—21no—
280C23×C4—21no—
281C23×C4—44no—
282C23×C4—44no—
283C23×C4C2×D412yes—
284C23×C4C2×D411yescharacteristic
285C23×C4C2×D411yescharacteristic
286C23×C4C2×D411yescharacteristic
287C23×C4C2×D411yescharacteristic
288C23×C4C2×D411yescharacteristic
289C23×C4C2412yes—
290C23×C4C2411yescharacteristic
291C2×SD16—28no—
292C2×SD16—28no—
293C2×SD16—28no—
294C2×SD16—416no—
295C2×D8—28no—
296C2×D8—28no—
297C2×D8—44no—
298C2×D8—416no—
299C22×C8—22no—
300C22×C8—22no—
301C22×C8—22no—
302C22×C8—22no—
303C22×C8—22no—
304C22×C8—22no—
305C22×C8—22no—
306C22×C8—22no—
307C22×C8—22no—
308C22×C8—22no—
309C22×C8—22no—
310C22×C8C2×D414yes—
311C22×C8C2412yes—
312C22×C8C2412yes—
313C22×C8C2412yes—
314C22×C8C2412yes—
315C4⋊Q8—28no—
316C4⋊Q8—44no—
317C4⋊Q8—48no—
318#124—432no—
319#121—28no—
320#121—44no—
321#121—48no—
322C4×Q8—28no—
323C4×Q8—28no—
324C4×Q8—44no—
325C4×Q8—44no—
326C4×Q8—48no—
327C4×Q8—48no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—22no—
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—44no—
346C2×C4⋊C4—44no—
347C2×C4⋊C4—44no—
348C2×C4⋊C4C2×D414yes—
349C2×C4⋊C4C2412yes—
350C2×C4⋊C4C2412yes—
351C2×C4⋊C4C2412yes—
352C2×C4⋊C4C2412yes—
353C2×C4⋊C4C2412yes—
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—42no—
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⋊C4C2×D414yes—
379C2×C22⋊C4C2×D414yes—
380C2×C42—22no—
381C2×C42—22no—
382C2×C42—22no—
383C2×C42—22no—
384C2×C42—24no—
385C2×C42—24no—
386C2×C42—24no—
387C2×C42—44no—
388C2×C42—44no—
389C2×C42—44no—
390C2×C42C2×D412yes—
391C2×C42C2×D412yes—
392C2×C42C2412yes—
393C2×C42C2412yes—
394#106—28no—
395#106—28no—
396C4⋊C8—28no—
397#103—28no—
398#103—28no—
399#103C2×D4116yes—
400#102—28no—
401#102—28no—
402#102—44no—
403#102—44no—
404#102—44no—
405C22⋊C8—28no—
406C22⋊C8—44no—
407#97—44no—
408#95—24no—
409#95—24no—
410#95—24no—
411#95C2×D414yes—
412#95C2×D414yes—
413C24—22no—
414C24—24no—
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—
430C24—42no—
431C24—42no—
432C24—42no—
433C24—42no—
434C24—42no—
435C24—42no—
436C24C22×D412yes—
437C24C22×D411yescharacteristic
438#41—416no—
439#41—416no—
440#41—416no—
441#41—464no—
442#41—416no—
443C2×Q8—24no—
444C2×Q8—28no—
445C2×Q8—24no—
446C2×Q8—24no—
447C2×Q8—28no—
448C2×Q8—28no—
449C2×Q8—22no—
450C2×Q8—22no—
451C2×Q8—22no—
452C2×Q8—48no—
453C2×Q8—48no—
454C2×Q8—84no—
455C2×Q8—816no—
456C2×Q8#124116yescomplemented
457C2×Q8C22×D414yes—
458C2×Q8C2×#4114yes—
459C2×Q8C2×#4114yes—
460C2×D4—216no—
461C2×D4—24no—
462C2×D4—28no—
463C2×D4—28no—
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—22no—
473C2×D4—22no—
474C2×D4—22no—
475C2×D4—48no—
476C2×D4—48no—
477C2×D4—432no—
478C2×D4—48no—
479C2×D4—48no—
480C2×D4—42no—
481C2×D4—44no—
482C2×D4—44no—
483C2×D4—44no—
484C2×D4—44no—
485C2×D4—42no—
486C2×D4—42no—
487C2×D4—42no—
488C2×D4—44no—
489C2×D4—42no—
490C2×D4—44no—
491C2×D4—84no—
492C2×D4—816no—
493C2×D4C2×#4114yes—
494C22×C4—24no—
495C22×C4—22no—
496C22×C4—24no—
497C22×C4—24no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—216no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—24no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—24no—
516C22×C4—24no—
517C22×C4—24no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—48no—
529C22×C4—48no—
530C22×C4—432no—
531C22×C4—42no—
532C22×C4—42no—
533C22×C4—44no—
534C22×C4—44no—
535C22×C4—44no—
536C22×C4—44no—
537C22×C4—42no—
538C22×C4—42no—
539C22×C4—42no—
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×C4AGL(1,ℤ/8)14yes—
550C22×C4C22×D412yes—
551C22×C4C22×D412yes—
552C22×C4C22×D412yes—
553C22×C4C22×D412yes—
554C22×C4C22×D412yes—
555C22×C4C22×D411yescharacteristic
556C22×C4C22×D412yes—
557C22×C4C2×#4112yes—
558C22×C4C2×#4112yes—
559C22×C4C2×#4112yes—
560C22×C4H(5,𝔽2)12yes—
561C22×C4H(5,𝔽2)12yes—
562C22×C4C2511yescharacteristic
563SD16—416no—
564D8—416no—
565C2×C8—28no—
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—22no—
577C2×C8—44no—
578C2×C8—44no—
579C2×C8—44no—
580C2×C8C22×D414yes—
581C4⋊C4—24no—
582C4⋊C4—22no—
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—48no—
594C4⋊C4—42no—
595C4⋊C4—42no—
596C4⋊C4—42no—
597C4⋊C4—42no—
598C4⋊C4C22×D414yes—
599C22⋊C4—28no—
600C22⋊C4—44no—
601C22⋊C4—48no—
602C22⋊C4—48no—
603C22⋊C4—48no—
604C22⋊C4—48no—
605C22⋊C4—48no—
606C22⋊C4—48no—
607C22⋊C4—48no—
608C22⋊C4—84no—
609C22⋊C4—84no—
610C22⋊C4—84no—
611C22⋊C4—84no—
612C42—24no—
613C42—24no—
614C42—22no—
615C42—22no—
616C42—22no—
617C42—22no—
618C42—48no—
619C42—48no—
620C42—48no—
621C23—22no—
622C23—24no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—44no—
630C23—44no—
631C23—48no—
632C23—44no—
633C23—48no—
634C23—42no—
635C23—42no—
636C23—48no—
637C23—44no—
638C23—44no—
639C23—44no—
640C23—44no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—84no—
653C23—84no—
654C23—84no—
655C23—84no—
656C23—84no—
657C23—84no—
658C23—84no—
659C23—84no—
660C23—84no—
661C23—84no—
662C23—84no—
663C23#52512yes—
664C23D4212yes—
665C23#54612yes—
666C23C2×AGL(1,ℤ/8)12yes—
667C23#57512yes—
668C23#57712yes—
669C23#57712yes—
670C23C23×D411yescharacteristic
671Q8—24no—
672Q8—24no—
673Q8—24no—
674Q8—216no—
675Q8—816no—
676Q8C2×#12418yescomplemented
677D4—24no—
678D4—24no—
679D4—432no—
680D4—42no—
681D4—42no—
682D4—42no—
683D4—42no—
684D4—42no—
685D4—42no—
686D4—48no—
687D4—816no—
688D4—84no—
689C2×C4—24no—
690C2×C4—22no—
691C2×C4—24no—
692C2×C4—24no—
693C2×C4—216no—
694C2×C4—28no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—24no—
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—22no—
709C2×C4—432no—
710C2×C4—44no—
711C2×C4—44no—
712C2×C4—48no—
713C2×C4—44no—
714C2×C4—44no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—48no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
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—84no—
735C2×C4—84no—
736C2×C4—84no—
737C2×C4—84no—
738C2×C4#52512yes—
739C2×C4C2×#12414yes—
740C2×C4#53814yes—
741C2×C4D4212yes—
742C2×C4#54614yes—
743C2×C4#54612yes—
744C2×C4#55114yes—
745C2×C4C2×AGL(1,ℤ/8)14yes—
746C2×C4C23×D411yescharacteristic
747C2×C4C22×#4111yescharacteristic
748C2×C4C22×#4111yescharacteristic
749C2×C4C22×#4111yescharacteristic
750C2×C4C2×H(5,𝔽2)11yescharacteristic
751C2×C4C2×H(5,𝔽2)11yescharacteristic
752C8—24no—
753C8—42no—
754C8—42no—
755C8—42no—
756C22—42no—
757C22—44no—
758C22—42no—
759C22—42no—
760C22—42no—
761C22—44no—
762C22—42no—
763C22—44no—
764C22—42no—
765C22—42no—
766C22—82no—
767C22—82no—
768C22—88no—
769C22—816no—
770C22—82no—
771C22—82no—
772C22—82no—
773C22—82no—
774C22—82no—
775C22—82no—
776C22—82no—
777C22—82no—
778C22—82no—
779C22—168no—
780C22#247214yes—
781C22#311514yes—
782C22#312514yes—
783C22#326514yes—
784C22#327114yes—
785C22#332114yes—
786C22#333214yes—
787C22C2×#52511yescharacteristic
788C22C2×D4211yescharacteristic
789C22C2×#54611yescharacteristic
790C22C22×AGL(1,ℤ/8)11yescharacteristic
791C22C2×#57511yescharacteristic
792C22C2×#57711yescharacteristic
793C22C2×#57711yescharacteristic
794C4—24no—
795C4—28no—
796C4—44no—
797C4—42no—
798C4—42no—
799C4—42no—
800C4—42no—
801C4—82no—
802C4—82no—
803C4—82no—
804C4—82no—
805C4#247214yes—
806C4C22×#12411yescharacteristic
807C4C2×#53811yescharacteristic
808C4C2×#54611yescharacteristic
809C4C2×#55111yescharacteristic
810C2—82no—
811C2—84no—
812C2—162no—
813C2#2725018yesdirect product factor
814C2C2×#247211yescharacteristic
815C2C2×#311511yescharacteristic
816C2C2×#312511yescharacteristic
817C2C2×#326511yescharacteristic
818C2C2×#327111yescharacteristic
819C2C2×#332111yescharacteristic
820C2C2×#333211yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×#449C2
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×#475C2semidirect
3. C2×#2491C2semidirect
4. C2×#2341C2semidirect
5. #27250C2direct (N × H)
6. C2×#2077C2semidirect
7. C2×#2054C2semidirect
8. C2×#2034C2semidirect
9. C2×#2023C2semidirect
10. C2×#1972C2semidirect
11. C2×#1926C2semidirect
12. C2×#1924C2semidirect
13. C2×#1880C2semidirect
14. C2×#1880C2semidirect
15. C2×#1788C2semidirect
16. C2×#1763C2semidirect
26. C2×#475C22semidirect
44. #2491C22semidirect
48. #2341C22semidirect
62. #2077C22semidirect
63. #2054C22semidirect
64. #2034C22semidirect
65. #2023C22semidirect
66. #1972C22semidirect
67. #1926C22semidirect
68. #1924C22semidirect
69. #1880C22semidirect
70. #1880C22semidirect
71. #1788C22semidirect
72. #1763C22semidirect
456. C2×Q8#124semidirect
676. Q8C2×#124semidirect
813. C2#27250direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#4752
C22×#4492
C2×#24912
C2×#23412
#272502
C2×#20772
C2×#20542
C2×#20342
C2×#20232
C2×#19722
C2×#19262
C2×#19242
C2×#18802
C2×#17882
C2×#17632