Finite Group Databasebeta

← C2×#31676 #7505937

Subgroups — C2×#31676 #7505937

Order 512.

3290 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2485C211yesmaximal, characteristic, complemented
2C2×#2408C211yesmaximal, characteristic
3#31676C2116yesmaximal, direct product factor
4C2×#2077C211yesmaximal, characteristic, complemented
5C2×#2075C211yesmaximal, characteristic, complemented
6C2×#2067C211yesmaximal, characteristic, complemented
7C2×#2065C211yesmaximal, characteristic, complemented
8C2×#2034C211yesmaximal, characteristic, complemented
9C2×#2033C211yesmaximal, characteristic, complemented
10C2×#1955C211yesmaximal, characteristic, complemented
11C2×#1936C211yesmaximal, characteristic, complemented
12C2×#1936C211yesmaximal, characteristic, complemented
13C2×#1875C211yesmaximal, characteristic, complemented
14C2×#1875C211yesmaximal, characteristic, complemented
15C2×#1786C211yesmaximal, characteristic, complemented
16C2×#1786C211yesmaximal, characteristic, complemented
17C24×D4C2211yescharacteristic
18C22×#121C2211yescharacteristic
19C22×#121C2211yescharacteristic
20C22×#120—21no—
21C22×C4×D4C2211yescharacteristic
22C22×#117C2211yescharacteristic, complemented
23C22×#107C2211yescharacteristic, complemented
24C22×#106C2211yescharacteristic, complemented
25C22×C4⋊C8C2211yescharacteristic, complemented
26C22×#102C2211yescharacteristic
27C22×#102C2211yescharacteristic
28C22×#102C2211yescharacteristic
29C22×#102C2211yescharacteristic
30C22×#102C2211yescharacteristic
31C22×#102C2211yescharacteristic
32C22×#102C2211yescharacteristic
33C22×#102C2211yescharacteristic
34C22×C22⋊C8C2211yescharacteristic
35C22×C22⋊C8C2211yescharacteristic
36C22×C22⋊C8C2211yescharacteristic, complemented
37C22×C22⋊C8C2211yescharacteristic, complemented
38C22×#97C2211yescharacteristic, complemented
39#2485—24no—
40#2485C2218yescomplemented
41#2408—24no—
42#2408C2218yes—
43C2×#397—21no—
44C2×#394—21no—
45C2×#394—21no—
46C2×#392—21no—
47C2×#390C2211yescharacteristic
48C2×#390C2211yescharacteristic
49C2×#389C2211yescharacteristic, complemented
50C2×#389C2211yescharacteristic, complemented
51C2×#388—21no—
52C2×#387—21no—
53C2×#380C2211yescharacteristic
54C2×#380C2211yescharacteristic
55C2×#380C2211yescharacteristic
56C2×#380C2211yescharacteristic, complemented
57C2×#379—21no—
58#2077C2218yescomplemented
59#2075C2218yescomplemented
60#2067C2218yescomplemented
61#2065C2218yescomplemented
62#2034C2218yescomplemented
63#2033C2218yescomplemented
64#1955C2218yescomplemented
65#1936C2218yescomplemented
66#1936C2218yescomplemented
67#1875C2218yescomplemented
68#1875C2218yescomplemented
69#1786C2218yescomplemented
70#1786C2218yescomplemented
71C2×#340C2211yescharacteristic, complemented
72C2×#340C2211yescharacteristic, complemented
73C2×#340C2211yescharacteristic, complemented
74C2×#340C2211yescharacteristic, complemented
75C2×#340C2211yescharacteristic, complemented
76C2×#340C2211yescharacteristic, complemented
77C26—21no—
78C23×D4—24no—
79C23×D4—24no—
80C23×D4—21no—
81C23×D4—21no—
82C23×D4—21no—
83C23×D4—22no—
84C23×D4—42no—
85C23×D4—42no—
86C23×D4—42no—
87C23×D4—42no—
88C23×D4D411yescharacteristic
89C23×D4C2311yescharacteristic
90C23×D4C2311yescharacteristic
91C23×D4C2314yes—
92C24×C4C2311yescharacteristic
93C24×C4C2311yescharacteristic
94C23×C8C2311yescharacteristic
95C23×C8C2311yescharacteristic
96C23×C8C2311yescharacteristic
97C23×C8C2311yescharacteristic
98C2×#121—22no—
99C2×#121—22no—
100C2×#121—24no—
101C2×#121—24no—
102C2×#121—42no—
103C2×#121—42no—
104C2×#121C2314yes—
105C2×#121C2314yes—
106C2×#120—28no—
107C2×#120—48no—
108C2×C4×D4—42no—
109C2×C4×D4—42no—
110C2×C4×D4D414yes—
111C2×C4×D4C2314yes—
112C2×#117—22no—
113C2×#117—42no—
114C2×#117—42no—
115C2×#117C2314yescomplemented
116C22×C4⋊C4—21no—
117C22×C4⋊C4—21no—
118C22×C4⋊C4D411yescharacteristic
119C22×C4⋊C4C2311yescharacteristic
120C22×C4⋊C4C2311yescharacteristic
121C22×C4⋊C4C2311yescharacteristic
122C22×C4⋊C4C2311yescharacteristic
123C22×C4⋊C4C2311yescharacteristic
124C22×C4⋊C4C2311yescharacteristic
125C22×C22⋊C4—21no—
126C22×C22⋊C4—21no—
127C22×C22⋊C4—21no—
128C22×C22⋊C4—21no—
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⋊C4D411yescharacteristic
137C22×C22⋊C4D411yescharacteristic
138C22×C42—21no—
139C22×C42C2311yescharacteristic
140C2×#107—42no—
141C2×#107C2314yescomplemented
142C2×#106—42no—
143C2×#106C2314yescomplemented
144C2×C4⋊C8—42no—
145C2×C4⋊C8C2314yescomplemented
146C2×#102—24no—
147C2×#102—24no—
148C2×#102—42no—
149C2×#102—42no—
150C2×#102—42no—
151C2×#102—42no—
152C2×#102—42no—
153C2×#102—42no—
154C2×#102C2314yes—
155C2×#102C2314yes—
156C2×#102C2314yes—
157C2×#102C2314yes—
158C2×#102C2314yes—
159C2×#102C2314yes—
160C2×#102C2314yes—
161C2×#102C2314yes—
162C2×C22⋊C8—42no—
163C2×C22⋊C8—42no—
164C2×C22⋊C8—42no—
165C2×C22⋊C8—42no—
166C2×C22⋊C8C2314yes—
167C2×C22⋊C8C2314yes—
168C2×C22⋊C8C2314yescomplemented
169C2×C22⋊C8C2314yescomplemented
170C2×#97—42no—
171C2×#97C2314yescomplemented
172#397—28no—
173#394—28no—
174#394—28no—
175#392—28no—
176#390—22no—
177#390—22no—
178#390C2314yes—
179#390C2314yes—
180#389—22no—
181#389—22no—
182#389C2314yescomplemented
183#389C2314yescomplemented
184#388—28no—
185#387—28no—
186#380—22no—
187#380—22no—
188#380—22no—
189#380—22no—
190#380C2314yes—
191#380C2314yes—
192#380C2314yes—
193#380C2314yescomplemented
194#379—28no—
195C2×#95—21no—
196C2×#95—21no—
197C2×#95—21no—
198C2×#95—21no—
199C2×#95—21no—
200C2×#95—21no—
201#340C2314yescomplemented
202#340C2314yescomplemented
203#340C2314yescomplemented
204#340C2314yescomplemented
205#340C2314yescomplemented
206#340C2314yescomplemented
207C25—21no—
208C25—21no—
209C25—24no—
210C25—44no—
211C25—44no—
212C25—44no—
213C25—44no—
214C25—44no—
215C25—82no—
216C25—82no—
217C25C2×D411yescharacteristic
218C25C2×D411yescharacteristic
219C22×D4—24no—
220C22×D4—28no—
221C22×D4—28no—
222C22×D4—24no—
223C22×D4—24no—
224C22×D4—21no—
225C22×D4—21no—
226C22×D4—24no—
227C22×D4—22no—
228C22×D4—22no—
229C22×D4—22no—
230C22×D4—22no—
231C22×D4—22no—
232C22×D4—22no—
233C22×D4—22no—
234C22×D4—22no—
235C22×D4—22no—
236C22×D4—22no—
237C22×D4—44no—
238C22×D4—44no—
239C22×D4—44no—
240C22×D4—44no—
241C22×D4—48no—
242C22×D4—48no—
243C22×D4—42no—
244C22×D4—42no—
245C22×D4—44no—
246C22×D4—44no—
247C22×D4—44no—
248C22×D4—48no—
249C22×D4—416no—
250C22×D4—416no—
251C22×D4—416no—
252C22×D4—416no—
253C22×D4—44no—
254C22×D4—44no—
255C22×D4—44no—
256C22×D4—44no—
257C22×D4—82no—
258C22×D4—82no—
259C22×D4C2×D414yes—
260C22×D4#4114yes—
261C22×D4#4114yes—
262C22×D4C2412yes—
263C22×D4C2412yes—
264C23×C4—22no—
265C23×C4—22no—
266C23×C4—22no—
267C23×C4—22no—
268C23×C4—22no—
269C23×C4—22no—
270C23×C4—22no—
271C23×C4—22no—
272C23×C4—22no—
273C23×C4—22no—
274C23×C4—22no—
275C23×C4—22no—
276C23×C4—21no—
277C23×C4—21no—
278C23×C4—21no—
279C23×C4—21no—
280C23×C4—21no—
281C23×C4—21no—
282C23×C4C2×D412yes—
283C23×C4C2×D412yes—
284C23×C4C2×D411yescharacteristic
285C23×C4C2×D411yescharacteristic
286C23×C4C2×D411yescharacteristic
287C23×C4C2×D411yescharacteristic
288C23×C4C2412yes—
289C23×C4C2412yes—
290C23×C4C2411yescharacteristic
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×C8—22no—
302C22×C8—22no—
303C22×C8C2412yes—
304C22×C8C2412yes—
305C22×C8C2412yes—
306C22×C8C2412yes—
307#121—28no—
308#121—28no—
309#121—44no—
310#121—44no—
311#121—48no—
312#121—48no—
313#120—432no—
314C4×D4—48no—
315C4×D4—44no—
316C4×D4—44no—
317#117—44no—
318#117—44no—
319#117—48no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—22no—
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—24no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—24no—
340C2×C4⋊C4—42no—
341C2×C4⋊C4—44no—
342C2×C4⋊C4—82no—
343C2×C4⋊C4C2×D414yes—
344C2×C4⋊C4C2412yes—
345C2×C4⋊C4C2412yes—
346C2×C4⋊C4C2412yes—
347C2×C4⋊C4C2412yes—
348C2×C4⋊C4C2412yes—
349C2×C4⋊C4C2412yes—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—24no—
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—42no—
362C2×C22⋊C4—42no—
363C2×C22⋊C4—44no—
364C2×C22⋊C4—44no—
365C2×C22⋊C4—44no—
366C2×C22⋊C4—44no—
367C2×C22⋊C4—44no—
368C2×C22⋊C4—44no—
369C2×C22⋊C4—44no—
370C2×C22⋊C4—82no—
371C2×C22⋊C4—82no—
372C2×C22⋊C4—82no—
373C2×C22⋊C4—82no—
374C2×C22⋊C4C2×D414yes—
375C2×C22⋊C4C2×D414yes—
376C2×C42—22no—
377C2×C42—22no—
378C2×C42—24no—
379C2×C42—44no—
380C2×C42C2×D412yes—
381C2×C42C2412yes—
382#107—44no—
383#106—44no—
384C4⋊C8—44no—
385#102—28no—
386#102—28no—
387#102—44no—
388#102—44no—
389#102—44no—
390#102—44no—
391#102—44no—
392#102—44no—
393C22⋊C8—44no—
394C22⋊C8—44no—
395C22⋊C8—44no—
396C22⋊C8—44no—
397#97—44no—
398#95—24no—
399#95—24no—
400#95—24no—
401#95—24no—
402#95—24no—
403#95—24no—
404C24—22no—
405C24—22no—
406C24—22no—
407C24—22no—
408C24—22no—
409C24—22no—
410C24—22no—
411C24—24no—
412C24—24no—
413C24—22no—
414C24—22no—
415C24—22no—
416C24—22no—
417C24—22no—
418C24—22no—
419C24—22no—
420C24—22no—
421C24—48no—
422C24—48no—
423C24—48no—
424C24—48no—
425C24—432no—
426C24—42no—
427C24—42no—
428C24—42no—
429C24—42no—
430C24—42no—
431C24—42no—
432C24—42no—
433C24—42no—
434C24—42no—
435C24—42no—
436C24—42no—
437C24—42no—
438C24—48no—
439C24—84no—
440C24—84no—
441C24—816no—
442C24—816no—
443C24—816no—
444C24—816no—
445C24—816no—
446C24—816no—
447C24AGL(1,ℤ/8)14yes—
448C24C22×D412yes—
449C24C22×D412yes—
450C24C22×D411yescharacteristic
451C2×D4—28no—
452C2×D4—28no—
453C2×D4—28no—
454C2×D4—24no—
455C2×D4—24no—
456C2×D4—28no—
457C2×D4—28no—
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—44no—
469C2×D4—44no—
470C2×D4—48no—
471C2×D4—48no—
472C2×D4—48no—
473C2×D4—416no—
474C2×D4—416no—
475C2×D4—416no—
476C2×D4—416no—
477C2×D4—432no—
478C2×D4—464no—
479C2×D4—416no—
480C2×D4—48no—
481C2×D4—48no—
482C2×D4—48no—
483C2×D4—48no—
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—84no—
493C2×D4—84no—
494C2×D4—816no—
495C2×D4—816no—
496C2×D4C2×#4114yes—
497C2×D4C2×#4114yes—
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—24no—
511C22×C4—24no—
512C22×C4—24no—
513C22×C4—24no—
514C22×C4—24no—
515C22×C4—24no—
516C22×C4—22no—
517C22×C4—22no—
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—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—44no—
535C22×C4—44no—
536C22×C4—44no—
537C22×C4—44no—
538C22×C4—44no—
539C22×C4—44no—
540C22×C4—44no—
541C22×C4—44no—
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—42no—
553C22×C4—42no—
554C22×C4—42no—
555C22×C4—42no—
556C22×C4—42no—
557C22×C4—42no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4C22×D412yes—
561C22×C4C22×D412yes—
562C22×C4C22×D412yes—
563C22×C4C22×D412yes—
564C22×C4C22×D411yescharacteristic
565C22×C4C2×#4112yes—
566C22×C4C2×#4112yes—
567C22×C4H(5,𝔽2)12yes—
568C22×C4H(5,𝔽2)12yes—
569C22×C4H(5,𝔽2)12yes—
570C22×C4H(5,𝔽2)12yes—
571C22×C4C2511yescharacteristic
572C2×C8—22no—
573C2×C8—22no—
574C2×C8—22no—
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—44no—
585C2×C8—44no—
586C2×C8—44no—
587C2×C8—44no—
588C4⋊C4—22no—
589C4⋊C4—22no—
590C4⋊C4—22no—
591C4⋊C4—22no—
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—44no—
601C4⋊C4—48no—
602C4⋊C4—42no—
603C4⋊C4—42no—
604C4⋊C4—42no—
605C4⋊C4—42no—
606C4⋊C4—42no—
607C4⋊C4—42no—
608C4⋊C4—84no—
609C22⋊C4—44no—
610C22⋊C4—44no—
611C22⋊C4—48no—
612C22⋊C4—48no—
613C22⋊C4—48no—
614C22⋊C4—48no—
615C22⋊C4—48no—
616C22⋊C4—48no—
617C22⋊C4—48no—
618C22⋊C4—84no—
619C22⋊C4—84no—
620C22⋊C4—84no—
621C22⋊C4—84no—
622C42—24no—
623C42—22no—
624C42—22no—
625C42—48no—
626C23—22no—
627C23—28no—
628C23—22no—
629C23—22no—
630C23—28no—
631C23—28no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—24no—
637C23—24no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—44no—
645C23—44no—
646C23—44no—
647C23—44no—
648C23—432no—
649C23—42no—
650C23—42no—
651C23—44no—
652C23—44no—
653C23—42no—
654C23—42no—
655C23—44no—
656C23—48no—
657C23—48no—
658C23—44no—
659C23—48no—
660C23—44no—
661C23—48no—
662C23—44no—
663C23—48no—
664C23—44no—
665C23—48no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—816no—
675C23—816no—
676C23—816no—
677C23—816no—
678C23—816no—
679C23—816no—
680C23—8128no—
681C23—84no—
682C23—84no—
683C23—84no—
684C23—84no—
685C23—84no—
686C23—84no—
687C23—84no—
688C23—84no—
689C23#53412yes—
690C23#54612yes—
691C23#54612yes—
692C23C2×AGL(1,ℤ/8)14yes—
693C23C2×AGL(1,ℤ/8)12yes—
694C23#57512yes—
695C23#57612yes—
696C23#57712yes—
697C23C23×D411yescharacteristic
698D4—24no—
699D4—24no—
700D4—24no—
701D4—24no—
702D4—416no—
703D4—432no—
704D4—42no—
705D4—42no—
706D4—48no—
707D4—48no—
708D4—42no—
709D4—42no—
710D4—816no—
711D4—816no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—44no—
725C2×C4—44no—
726C2×C4—44no—
727C2×C4—44no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—48no—
733C2×C4—48no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—84no—
757C2×C4—84no—
758C2×C4—84no—
759C2×C4—84no—
760C2×C4—84no—
761C2×C4—84no—
762C2×C4#53412yes—
763C2×C4#53814yes—
764C2×C4#53814yes—
765C2×C4#54612yes—
766C2×C4#54612yes—
767C2×C4#55114yes—
768C2×C4#56014yes—
769C2×C4C22×#4111yescharacteristic
770C2×C4C22×#4111yescharacteristic
771C2×C4C2×H(5,𝔽2)11yescharacteristic
772C2×C4C2×H(5,𝔽2)11yescharacteristic
773C2×C4C2×H(5,𝔽2)11yescharacteristic
774C2×C4C2×H(5,𝔽2)11yescharacteristic
775C8—42no—
776C8—42no—
777C8—42no—
778C8—42no—
779C22—24no—
780C22—24no—
781C22—24no—
782C22—42no—
783C22—42no—
784C22—416no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22—44no—
791C22—44no—
792C22—42no—
793C22—44no—
794C22—42no—
795C22—44no—
796C22—42no—
797C22—44no—
798C22—42no—
799C22—44no—
800C22—864no—
801C22—82no—
802C22—82no—
803C22—82no—
804C22—82no—
805C22—88no—
806C22—816no—
807C22—816no—
808C22—82no—
809C22—82no—
810C22—82no—
811C22—82no—
812C22#269714yes—
813C22#319414yes—
814C22#319814yes—
815C22#331014yes—
816C22#331114yes—
817C22#331814yes—
818C22#331914yes—
819C22C2×#53411yescharacteristic
820C22C2×#54611yescharacteristic
821C22C2×#54611yescharacteristic
822C22C22×AGL(1,ℤ/8)11yescharacteristic
823C22C2×#57511yescharacteristic
824C22C2×#57611yescharacteristic
825C22C2×#57711yescharacteristic
826C4—42no—
827C4—42no—
828C4—42no—
829C4—42no—
830C4—82no—
831C4—82no—
832C4—82no—
833C4—82no—
834C4—82no—
835C4—82no—
836C4#269714yes—
837C4C2×#53811yescharacteristic
838C4C2×#53811yescharacteristic
839C4C2×#55111yescharacteristic
840C4C2×#56011yescharacteristic
841C2—44no—
842C2—82no—
843C2—84no—
844C2—84no—
845C2#3167618yesdirect product factor
846C2C2×#269711yescharacteristic
847C2C2×#319411yescharacteristic
848C2C2×#319811yescharacteristic
849C2C2×#331011yescharacteristic
850C2C2×#331811yescharacteristic
851C2C2×#331111yescharacteristic
852C2C2×#331911yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#2408C2
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. C2×#2485C2semidirect
3. #31676C2direct (N × H)
4. C2×#2077C2semidirect
5. C2×#2075C2semidirect
6. C2×#2067C2semidirect
7. C2×#2065C2semidirect
8. C2×#2034C2semidirect
9. C2×#2033C2semidirect
10. C2×#1955C2semidirect
11. C2×#1936C2semidirect
12. C2×#1936C2semidirect
13. C2×#1875C2semidirect
14. C2×#1875C2semidirect
15. C2×#1786C2semidirect
16. C2×#1786C2semidirect
22. C22×#117C22semidirect
23. C22×#107C22semidirect
24. C22×#106C22semidirect
25. C22×C4⋊C8C22semidirect
36. C22×C22⋊C8C22semidirect
37. C22×C22⋊C8C22semidirect
38. C22×#97C22semidirect
40. #2485C22semidirect
49. C2×#389C22semidirect
50. C2×#389C22semidirect
56. C2×#380C22semidirect
58. #2077C22semidirect
59. #2075C22semidirect
60. #2067C22semidirect
61. #2065C22semidirect
62. #2034C22semidirect
63. #2033C22semidirect
64. #1955C22semidirect
65. #1936C22semidirect
66. #1936C22semidirect
67. #1875C22semidirect
68. #1875C22semidirect
69. #1786C22semidirect
70. #1786C22semidirect
71. C2×#340C22semidirect
72. C2×#340C22semidirect
73. C2×#340C22semidirect
74. C2×#340C22semidirect
75. C2×#340C22semidirect
76. C2×#340C22semidirect
115. C2×#117C23semidirect
141. C2×#107C23semidirect
143. C2×#106C23semidirect
145. C2×C4⋊C8C23semidirect
168. C2×C22⋊C8C23semidirect
169. C2×C22⋊C8C23semidirect
171. C2×#97C23semidirect
182. #389C23semidirect
183. #389C23semidirect
193. #380C23semidirect
201. #340C23semidirect
202. #340C23semidirect
203. #340C23semidirect
204. #340C23semidirect
205. #340C23semidirect
206. #340C23semidirect
845. C2#31676direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#24852
C2×#24082
#316762
C2×#20772
C2×#20752
C2×#20672
C2×#20652
C2×#20342
C2×#20332
C2×#19552
C2×#19362
C2×#18752
C2×#17862