Finite Group Databasebeta

← #6468702

Subgroups — #6468702

Order 512.

2464 conjugacy classes of subgroups.

The subgroup lattice has 885 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C22⋊Q8C211yesmaximal, characteristic, complemented
2C2×C4×#121C211yesmaximal, characteristic
3#29414C214yesmaximal, complemented
4#29244C212yesmaximal, complemented
5#29234C212yesmaximal, complemented
6#28123C212yesmaximal, complemented
7#28115C212yesmaximal, complemented
8#27603C211yesmaximal, characteristic, complemented
9#24006C211yesmaximal, characteristic, complemented
10#24005C211yesmaximal, characteristic
11#23919C211yesmaximal, characteristic
12#23711C214yesmaximal, complemented
13#21581C212yesmaximal, complemented
14#21580C212yesmaximal, complemented
15#21454C212yesmaximal, complemented
16#21453C212yesmaximal, complemented
17#20715C211yesmaximal, characteristic, complemented
18C22×C22⋊Q8C2211yescharacteristic
19C22×#121C2211yescharacteristic
20C22×C4×Q8C2211yescharacteristic, complemented
21C22×C4×D4—21no—
22C22×C4×D4C2211yescharacteristic
23C23×C42C2211yescharacteristic
24C2×#484C2212yes—
25C2×#481C2212yes—
26C2×#448C2212yes—
27C2×#450C2212yes—
28C2×#440C2214yescomplemented
29C2×#432C2212yescomplemented
30C4×C22⋊Q8—21no—
31C4×C22⋊Q8—21no—
32C4×C22⋊Q8—21no—
33C4×C22⋊Q8—21no—
34C4×C22⋊Q8C2212yes—
35C4×C22⋊Q8C2212yes—
36C4×C22⋊Q8C2212yescomplemented
37C4×C22⋊Q8C2212yescomplemented
38C4×#121—21no—
39C4×#121—21no—
40C4×#121—21no—
41C4×#121—21no—
42C4×#121C2212yes—
43C4×#121C2212yes—
44C4×#121C2212yes—
45C4×#121C2212yes—
46C2×#391C2211yescharacteristic, complemented
47C2×#390C2211yescharacteristic
48C2×#389C2211yescharacteristic
49C2×#389C2211yescharacteristic, complemented
50C2×#388—21no—
51C2×#387—21no—
52C2×#386—21no—
53C2×#385—21no—
54C2×#380C2211yescharacteristic
55C2×#380C2211yescharacteristic
56C2×C4×C4⋊C4—21no—
57C2×C4×C4⋊C4C2211yescharacteristic
58C2×C4×C4⋊C4C2211yescharacteristic, complemented
59C2×C4×C22⋊C4—21no—
60C2×C4×C22⋊C4—21no—
61#2086C2214yescomplemented
62#2076C2214yescomplemented
63#2067C2214yescomplemented
64#2066C2214yescomplemented
65#2055C2214yescomplemented
66#2036C2214yescomplemented
67#2034C2214yes—
68#2000C2214yes—
69#1927C2214yescomplemented
70#1925C2214yescomplemented
71#1920C2214yescomplemented
72#1918C2214yescomplemented
73#1880C2214yescomplemented
74#1877C2214yescomplemented
75#1874C2212yes—
76#1874C2212yes—
77#1872C2212yes—
78#1872C2212yes—
79#1863C2214yescomplemented
80#1862C2214yescomplemented
81#1853C2212yes—
82#1852C2212yes—
83#1852C2212yescomplemented
84#1852C2212yescomplemented
85#1824C2212yes—
86#1824C2212yescomplemented
87#1817C2212yescomplemented
88#1797C2212yes—
89#1797C2212yescomplemented
90#1787C2212yescomplemented
91#1786C2212yes—
92#1779C2211yescharacteristic
93#1779C2211yescharacteristic
94#1776C2214yescomplemented
95#1763C2214yescomplemented
96#1762C2214yescomplemented
97#1749C2212yes—
98#1749C2212yescomplemented
99C23×Q8C2311yescharacteristic
100C23×D4—21no—
101C23×D4C2311yescharacteristic
102C24×C4—21no—
103C24×C4D411yescharacteristic
104C24×C4D411yescharacteristic
105C24×C4C2311yescharacteristic
106C22×SD16C2314yes—
107C2×C22⋊Q8—21no—
108C2×C22⋊Q8—21no—
109C2×C22⋊Q8—28no—
110C2×C22⋊Q8C2312yes—
111C2×C22⋊Q8C2312yes—
112C2×#121—21no—
113C2×#121—21no—
114C2×#121—28no—
115C2×#121C2312yes—
116C2×#121C2312yes—
117C2×C4×Q8—21no—
118C2×C4×Q8—21no—
119C2×C4×Q8—44no—
120C2×C4×Q8C2312yes—
121C2×C4×Q8C2312yes—
122C2×C4×D4—22no—
123C2×C4×D4—22no—
124C2×C4×D4—22no—
125C2×C4×D4—22no—
126C2×C4×D4—21no—
127C2×C4×D4—21no—
128C2×C4×D4—44no—
129C2×C4×D4—48no—
130C2×C4×D4C2312yes—
131C2×C4×D4C2312yes—
132C22×C4⋊C4—21no—
133C22×C4⋊C4—21no—
134C22×C4⋊C4—21no—
135C22×C4⋊C4—21no—
136C22×C4⋊C4C2311yescharacteristic
137C22×C4⋊C4C2311yescharacteristic
138C22×C4⋊C4C2311yescharacteristic
139C22×C4⋊C4C2311yescharacteristic
140C22×C4⋊C4C2311yescharacteristic
141C22×C4⋊C4C2311yescharacteristic
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×C42—21no—
150C22×C42—21no—
151C22×C42—21no—
152C22×C42—44no—
153C22×C42D411yescharacteristic
154C22×C42D411yescharacteristic
155C22×C42D411yescharacteristic
156C22×C42D411yescharacteristic
157C22×C42D411yescharacteristic
158C22×C42D411yescharacteristic
159C22×C42C2311yescharacteristic
160C22×C42C2311yescharacteristic
161C22×C42C2311yescharacteristic
162C22×C42C2311yescharacteristic
163C22×C42C2311yescharacteristic
164C22×C42C2311yescharacteristic
165#484—28no—
166#481—28no—
167#450—28no—
168#448—28no—
169#440—48no—
170#432—44no—
171C2×#107C2314yes—
172C2×#107C2314yes—
173C2×#106C2314yes—
174C2×C4⋊C8C2314yes—
175C2×#103C2314yes—
176C2×#103C2314yes—
177C2×#103C2314yes—
178C2×#102C2314yes—
179C2×#102C2314yes—
180C2×#102C2314yes—
181C2×C22⋊C8C2312yes—
182C2×C22⋊C8C2312yes—
183C2×C22⋊C8C2312yes—
184C2×C22⋊C8C2312yes—
185C2×C22⋊C8C2312yes—
186C2×C22⋊C8C2312yes—
187C2×#97C2314yes—
188#391—21no—
189#391—21no—
190#391C2312yes—
191#391C2312yes—
192#390—21no—
193#390—21no—
194#390C2312yes—
195#390C2312yes—
196#389—21no—
197#389—21no—
198#389—21no—
199#389—21no—
200#389C2312yes—
201#389C2312yes—
202#389C2312yes—
203#389C2312yes—
204#388—22no—
205#388—22no—
206#388—22no—
207#388—22no—
208#387—22no—
209#387—22no—
210#387—22no—
211#387—22no—
212#386—22no—
213#386—22no—
214#386—22no—
215#386—22no—
216#385—22no—
217#385—22no—
218#385—22no—
219#385—22no—
220#380—21no—
221#380—21no—
222#380—21no—
223#380—21no—
224#380C2312yes—
225#380C2312yes—
226#380C2312yes—
227#380C2312yes—
228C4×C4⋊C4—22no—
229C4×C4⋊C4—22no—
230C4×C4⋊C4—22no—
231C4×C4⋊C4—22no—
232C4×C4⋊C4—21no—
233C4×C4⋊C4—21no—
234C4×C4⋊C4—21no—
235C4×C4⋊C4—21no—
236C4×C4⋊C4C2312yes—
237C4×C4⋊C4C2312yes—
238C4×C4⋊C4C2312yes—
239C4×C4⋊C4C2312yes—
240C4×C22⋊C4—22no—
241C4×C22⋊C4—22no—
242C4×C22⋊C4—22no—
243C4×C22⋊C4—22no—
244C4×C22⋊C4—22no—
245C4×C22⋊C4—22no—
246C4×C22⋊C4—22no—
247C4×C22⋊C4—22no—
248C2×#95—21no—
249C2×#95—21no—
250C2×#95—21no—
251C2×#95—21no—
252C2×#95—21no—
253C2×#95—21no—
254C2×#95—21no—
255C2×#95—21no—
256#340C2314yes—
257#340C2314yes—
258#340C2314yes—
259#340C2314yes—
260#340C2314yes—
261#340C2314yes—
262#336C2314yes—
263#336C2314yes—
264C25—21no—
265C25C2×D411yescharacteristic
266C22×Q8—24no—
267C22×Q8—21no—
268C22×Q8—24no—
269C22×Q8—42no—
270C22×Q8C2412yes—
271C22×D4—28no—
272C22×D4—22no—
273C22×D4—22no—
274C22×D4—24no—
275C22×D4—21no—
276C22×D4—24no—
277C22×D4—42no—
278C22×D4—44no—
279C22×D4—44no—
280C22×D4C2412yes—
281C23×C4—24no—
282C23×C4—21no—
283C23×C4—21no—
284C23×C4—21no—
285C23×C4—24no—
286C23×C4—24no—
287C23×C4—24no—
288C23×C4—21no—
289C23×C4—21no—
290C23×C4—21no—
291C23×C4—21no—
292C23×C4—22no—
293C23×C4—22no—
294C23×C4—42no—
295C23×C4—42no—
296C23×C4—42no—
297C23×C4—42no—
298C23×C4—42no—
299C23×C4—44no—
300C23×C4—44no—
301C23×C4—44no—
302C23×C4C2×D411yescharacteristic
303C23×C4C2×D411yescharacteristic
304C23×C4C2×D411yescharacteristic
305C23×C4C2×D411yescharacteristic
306C23×C4C2×D411yescharacteristic
307C23×C4C2×D411yescharacteristic
308C23×C4C2×D411yescharacteristic
309C23×C4C2×D411yescharacteristic
310C23×C4C2×D411yescharacteristic
311C23×C4C2×D411yescharacteristic
312C23×C4C2×D411yescharacteristic
313C23×C4C2×D411yescharacteristic
314C23×C4C2×D411yescharacteristic
315C23×C4C2×D411yescharacteristic
316C23×C4C2×D411yescharacteristic
317C23×C4C2411yescharacteristic
318C23×C4C2411yescharacteristic
319C23×C4C2411yescharacteristic
320C2×SD16—28no—
321C2×SD16—28no—
322C2×SD16—44no—
323C22×C8C2414yes—
324C22×C8C2414yes—
325C22⋊Q8—28no—
326C22⋊Q8—28no—
327C22⋊Q8—24no—
328C22⋊Q8—24no—
329C22⋊Q8—24no—
330C22⋊Q8#4118yes—
331#121—28no—
332#121—28no—
333#121—24no—
334#121—24no—
335#121—24no—
336#121#4118yes—
337C4×Q8—28no—
338C4×Q8—44no—
339C4×Q8—44no—
340C4×Q8—44no—
341C4×D4—28no—
342C4×D4—44no—
343C4×D4—44no—
344C4×D4—44no—
345C4×D4—48no—
346C4×D4—48no—
347C4×D4—48no—
348C4×D4—48no—
349C2×C4⋊C4—28no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—24no—
355C2×C4⋊C4—24no—
356C2×C4⋊C4—24no—
357C2×C4⋊C4—24no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—42no—
369C2×C4⋊C4—42no—
370C2×C4⋊C4—44no—
371C2×C4⋊C4—44no—
372C2×C4⋊C4—44no—
373C2×C4⋊C4C2412yes—
374C2×C4⋊C4C2412yes—
375C2×C4⋊C4C2412yes—
376C2×C4⋊C4C2412yes—
377C2×C4⋊C4C2412yes—
378C2×C4⋊C4C2412yes—
379C2×C22⋊C4—28no—
380C2×C22⋊C4—28no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—22no—
383C2×C22⋊C4—22no—
384C2×C22⋊C4—22no—
385C2×C22⋊C4—22no—
386C2×C22⋊C4—22no—
387C2×C22⋊C4—22no—
388C2×C22⋊C4—22no—
389C2×C22⋊C4—22no—
390C2×C22⋊C4—22no—
391C2×C22⋊C4—22no—
392C2×C22⋊C4—22no—
393C2×C22⋊C4—22no—
394C2×C22⋊C4—22no—
395C2×C22⋊C4—44no—
396C2×C22⋊C4—44no—
397C2×C22⋊C4—44no—
398C2×C22⋊C4—44no—
399C2×C22⋊C4—44no—
400C2×C42—24no—
401C2×C42—24no—
402C2×C42—24no—
403C2×C42—22no—
404C2×C42—22no—
405C2×C42—22no—
406C2×C42—22no—
407C2×C42—22no—
408C2×C42—22no—
409C2×C42—42no—
410C2×C42—42no—
411C2×C42—42no—
412C2×C42—42no—
413C2×C42—42no—
414C2×C42—42no—
415C2×C42—42no—
416C2×C42—42no—
417C2×C42—42no—
418C2×C42—44no—
419C2×C42—44no—
420C2×C42—44no—
421C2×C42C2×D411yescharacteristic
422C2×C42C2×D411yescharacteristic
423C2×C42C2×D411yescharacteristic
424C2×C42C2×D411yescharacteristic
425C2×C42C2×D411yescharacteristic
426C2×C42C2×D411yescharacteristic
427C2×C42C2×D411yescharacteristic
428C2×C42C2×D411yescharacteristic
429C2×C42C2×D411yescharacteristic
430C2×C42C2×D411yescharacteristic
431C2×C42C2×D411yescharacteristic
432C2×C42C2×D411yescharacteristic
433C2×C42C2411yescharacteristic
434C2×C42C2411yescharacteristic
435C2×C42C2411yescharacteristic
436C2×C42C2411yescharacteristic
437#107—28no—
438#107—44no—
439#106—28no—
440C4⋊C8—44no—
441#103—28no—
442#103—28no—
443#103—44no—
444#102—28no—
445#102—28no—
446#102—44no—
447C22⋊C8—24no—
448C22⋊C8—24no—
449C22⋊C8—24no—
450C22⋊C8—24no—
451C22⋊C8—42no—
452C22⋊C8—42no—
453#97—28no—
454#95—22no—
455#95—22no—
456#95—22no—
457#95—22no—
458#95—22no—
459#95—22no—
460#95—22no—
461#95—22no—
462#95—22no—
463#95—22no—
464#95—22no—
465#95—22no—
466#95—22no—
467#95—22no—
468#95—22no—
469#95—22no—
470C24—22no—
471C24—22no—
472C24—22no—
473C24—22no—
474C24—24no—
475C24—22no—
476C24—41no—
477C24—41no—
478C24—42no—
479C24—42no—
480C24—42no—
481C24—42no—
482C24—42no—
483C24—42no—
484C24#13714yes—
485C24C22×D411yescharacteristic
486C24C22×D411yescharacteristic
487C24C22×D411yescharacteristic
488C2×Q8—24no—
489C2×Q8—22no—
490C2×Q8—24no—
491C2×Q8—24no—
492C2×Q8—416no—
493C2×Q8—42no—
494C2×Q8—42no—
495C2×Q8C2×#4114yes—
496C2×D4—24no—
497C2×D4—28no—
498C2×D4—28no—
499C2×D4—24no—
500C2×D4—22no—
501C2×D4—24no—
502C2×D4—416no—
503C2×D4—42no—
504C2×D4—44no—
505C2×D4—432no—
506C2×D4—44no—
507C2×D4—44no—
508C2×D4—44no—
509C2×D4—42no—
510C2×D4C2×#4114yes—
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—24no—
522C22×C4—24no—
523C22×C4—24no—
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—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—41no—
557C22×C4—41no—
558C22×C4—41no—
559C22×C4—41no—
560C22×C4—41no—
561C22×C4—41no—
562C22×C4—41no—
563C22×C4—41no—
564C22×C4—41no—
565C22×C4—41no—
566C22×C4—41no—
567C22×C4—41no—
568C22×C4—41no—
569C22×C4—41no—
570C22×C4—41no—
571C22×C4—41no—
572C22×C4—416no—
573C22×C4—416no—
574C22×C4—416no—
575C22×C4—44no—
576C22×C4—44no—
577C22×C4—44no—
578C22×C4—44no—
579C22×C4—42no—
580C22×C4—42no—
581C22×C4—42no—
582C22×C4—42no—
583C22×C4—42no—
584C22×C4—42no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4—42no—
588C22×C4—42no—
589C22×C4—42no—
590C22×C4—42no—
591C22×C4—42no—
592C22×C4—42no—
593C22×C4—42no—
594C22×C4—42no—
595C22×C4—42no—
596C22×C4—42no—
597C22×C4—44no—
598C22×C4—44no—
599C22×C4—816no—
600C22×C4AGL(1,ℤ/8)14yes—
601C22×C4C22×D411yescharacteristic
602C22×C4C22×D411yescharacteristic
603C22×C4C22×D411yescharacteristic
604C22×C4C22×D411yescharacteristic
605C22×C4C22×D411yescharacteristic
606C22×C4C22×D411yescharacteristic
607C22×C4C22×D411yescharacteristic
608C22×C4C22×D411yescharacteristic
609C22×C4C22×D411yescharacteristic
610C22×C4C22×D411yescharacteristic
611C22×C4C22×D411yescharacteristic
612C22×C4C2×#4114yes—
613C22×C4C2×#4114yes—
614C22×C4C2511yescharacteristic
615SD16—416no—
616C2×C8—24no—
617C2×C8—24no—
618C2×C8—24no—
619C2×C8—24no—
620C2×C8—24no—
621C2×C8—24no—
622C4⋊C4—24no—
623C4⋊C4—24no—
624C4⋊C4—28no—
625C4⋊C4—28no—
626C4⋊C4—22no—
627C4⋊C4—22no—
628C4⋊C4—24no—
629C4⋊C4—24no—
630C4⋊C4—24no—
631C4⋊C4—24no—
632C4⋊C4—42no—
633C4⋊C4—44no—
634C4⋊C4—42no—
635C4⋊C4—44no—
636C4⋊C4—42no—
637C4⋊C4—42no—
638C4⋊C4—44no—
639C4⋊C4—44no—
640C4⋊C4—44no—
641C4⋊C4—44no—
642C4⋊C4C2×#4114yes—
643C4⋊C4C2×#4114yes—
644C22⋊C4—28no—
645C22⋊C4—28no—
646C22⋊C4—28no—
647C22⋊C4—28no—
648C22⋊C4—44no—
649C22⋊C4—44no—
650C22⋊C4—44no—
651C22⋊C4—44no—
652C22⋊C4—44no—
653C22⋊C4—44no—
654C22⋊C4—44no—
655C22⋊C4—44no—
656C22⋊C4—44no—
657C22⋊C4—44no—
658C42—22no—
659C42—22no—
660C42—22no—
661C42—22no—
662C42—22no—
663C42—22no—
664C42—22no—
665C42—22no—
666C42—22no—
667C42—41no—
668C42—41no—
669C42—41no—
670C42—41no—
671C42—41no—
672C42—41no—
673C42—44no—
674C42—44no—
675C42—44no—
676C42—44no—
677C42—44no—
678C42—44no—
679C42H(5,𝔽2)14yes—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—28no—
689C23—28no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—24no—
697C23—44no—
698C23—44no—
699C23—44no—
700C23—44no—
701C23—44no—
702C23—48no—
703C23—48no—
704C23—48no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—84no—
712C23—84no—
713C23—84no—
714C23—84no—
715C23#52512yes—
716C23#52512yes—
717C23C2×AGL(1,ℤ/8)12yes—
718C23C2×#13712yes—
719C23C2×#13712yes—
720C23C2×#13712yes—
721C23#57512yes—
722C23C23×D411yescharacteristic
723Q8—28no—
724Q8—48no—
725Q8—44no—
726D4—28no—
727D4—48no—
728D4—416no—
729D4—416no—
730D4—44no—
731C2×C4—28no—
732C2×C4—28no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—28no—
748C2×C4—28no—
749C2×C4—21no—
750C2×C4—24no—
751C2×C4—24no—
752C2×C4—24no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—44no—
765C2×C4—44no—
766C2×C4—44no—
767C2×C4—44no—
768C2×C4—44no—
769C2×C4—44no—
770C2×C4—44no—
771C2×C4—44no—
772C2×C4—44no—
773C2×C4—44no—
774C2×C4—44no—
775C2×C4—44no—
776C2×C4—48no—
777C2×C4—44no—
778C2×C4—48no—
779C2×C4—48no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—44no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—88no—
800C2×C4—88no—
801C2×C4—84no—
802C2×C4—84no—
803C2×C4—84no—
804C2×C4—84no—
805C2×C4#52512yes—
806C2×C4#52512yes—
807C2×C4#53412yes—
808C2×C4#53412yes—
809C2×C4C2×AGL(1,ℤ/8)12yes—
810C2×C4C2×AGL(1,ℤ/8)12yes—
811C2×C4#57512yes—
812C2×C4C22×#4112yes—
813C2×C4C22×#4112yes—
814C2×C4C2×H(5,𝔽2)12yes—
815C8—44no—
816C8—44no—
817C22—22no—
818C22—22no—
819C22—22no—
820C22—22no—
821C22—22no—
822C22—22no—
823C22—22no—
824C22—22no—
825C22—22no—
826C22—22no—
827C22—22no—
828C22—22no—
829C22—22no—
830C22—22no—
831C22—22no—
832C22—416no—
833C22—41no—
834C22—41no—
835C22—41no—
836C22—41no—
837C22—44no—
838C22—44no—
839C22—44no—
840C22—816no—
841C22—82no—
842C22—82no—
843C22—82no—
844C22—82no—
845C22#311014yes—
846C22#311714yes—
847C22C2×#52511yescharacteristic
848C22C2×#52511yescharacteristic
849C22C2×#53411yescharacteristic
850C22C22×AGL(1,ℤ/8)11yescharacteristic
851C22C22×#13711yescharacteristic
852C22C2×#57511yescharacteristic
853C22C2×#57511yescharacteristic
854C4—22no—
855C4—22no—
856C4—22no—
857C4—22no—
858C4—22no—
859C4—22no—
860C4—22no—
861C4—41no—
862C4—41no—
863C4—41no—
864C4—44no—
865C4—41no—
866C4—44no—
867C4—44no—
868C4—82no—
869C4—82no—
870C4—82no—
871C4—82no—
872C4#348114yes—
873C2—24no—
874C2—24no—
875C2—42no—
876C2—84no—
877C2#3495611yescharacteristic
878C2C2×#311711yescharacteristic
879C2C2×#311011yescharacteristic
880C2#6056111yescharacteristic
881C2#6056311yescharacteristic
882C2#6075011yescharacteristic
883C2#6075111yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×#121C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C23×C42 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×C4×C22⋊Q8C2semidirect
3. #29414C2semidirect
4. #29244C2semidirect
5. #29234C2semidirect
6. #28123C2semidirect
7. #28115C2semidirect
8. #27603C2semidirect
9. #24006C2semidirect
12. #23711C2semidirect
13. #21581C2semidirect
14. #21580C2semidirect
15. #21454C2semidirect
16. #21453C2semidirect
17. #20715C2semidirect
20. C22×C4×Q8C22semidirect
28. C2×#440C22semidirect
29. C2×#432C22semidirect
36. C4×C22⋊Q8C22semidirect
37. C4×C22⋊Q8C22semidirect
46. C2×#391C22semidirect
49. C2×#389C22semidirect
58. C2×C4×C4⋊C4C22semidirect
61. #2086C22semidirect
62. #2076C22semidirect
63. #2067C22semidirect
64. #2066C22semidirect
65. #2055C22semidirect
66. #2036C22semidirect
69. #1927C22semidirect
70. #1925C22semidirect
71. #1920C22semidirect
72. #1918C22semidirect
73. #1880C22semidirect
74. #1877C22semidirect
79. #1863C22semidirect
80. #1862C22semidirect
83. #1852C22semidirect
84. #1852C22semidirect
86. #1824C22semidirect
87. #1817C22semidirect
89. #1797C22semidirect
90. #1787C22semidirect
94. #1776C22semidirect
95. #1763C22semidirect
96. #1762C22semidirect
98. #1749C22semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C22⋊Q82
C2×C4×#1212
#294142
#292442
#292342
#281232
#281152
#276032
#240062
#240052
#239192
#237112
#215812
#215802
#214542
#214532
#207152