Finite Group Databasebeta

← #6377516

Subgroups — #6377516

Order 512.

2662 conjugacy classes of subgroups.

The subgroup lattice has 913 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3187C211yesmaximal, characteristic
2C2×C4×C22⋊Q8C211yesmaximal, characteristic, complemented
3C2×C4×#121C211yesmaximal, characteristic
4#22185C214yesmaximal, complemented
5#22084C212yesmaximal, complemented
6#22082C212yesmaximal, complemented
7#22049C212yesmaximal, complemented
8#22047C212yesmaximal, complemented
9#21940C211yesmaximal, characteristic, complemented
10#21759C211yesmaximal, characteristic, complemented
11#21758C211yesmaximal, characteristic
12#21580C212yesmaximal, complemented
13#21579C212yesmaximal, complemented
14#21528C214yesmaximal, complemented
15#21454C212yesmaximal, complemented
16#21453C212yesmaximal, complemented
17C2×#1749C211yesmaximal, characteristic, complemented
18C22×C22⋊Q8C2211yescharacteristic
19C22×#121C2211yescharacteristic
20C22×C4×Q8C2211yescharacteristic, complemented
21C22×C4×D4—21no—
22C22×C4×D4C2211yescharacteristic
23C23×C42C2211yescharacteristic
24#3187C4116yescomplemented
25C2×#481C2212yes—
26C2×#483C2212yes—
27C2×#465C2214yes—
28C2×#448C2212yes—
29C2×#450C2212yes—
30C2×#440C2214yescomplemented
31C22×C22⋊C8C2211yescharacteristic
32C22×C22⋊C8C2211yescharacteristic
33C22×#97C2212yescomplemented
34C4×C22⋊Q8—21no—
35C4×C22⋊Q8—21no—
36C4×C22⋊Q8—21no—
37C4×C22⋊Q8—21no—
38C4×C22⋊Q8C2212yes—
39C4×C22⋊Q8C2212yes—
40C4×C22⋊Q8C2212yescomplemented
41C4×C22⋊Q8C2212yescomplemented
42C4×#121—21no—
43C4×#121—21no—
44C4×#121—21no—
45C4×#121—21no—
46C4×#121C2212yes—
47C4×#121C2212yes—
48C4×#121C2212yes—
49C4×#121C2212yes—
50C2×#391C2211yescharacteristic, complemented
51C2×#390C2211yescharacteristic
52C2×#389C2211yescharacteristic
53C2×#389C2211yescharacteristic, complemented
54C2×#388—21no—
55C2×#387—21no—
56C2×#386—21no—
57C2×#385—21no—
58C2×#380C2211yescharacteristic
59C2×#380C2211yescharacteristic
60C2×C4×C4⋊C4—21no—
61C2×C4×C4⋊C4C2211yescharacteristic
62C2×C4×C4⋊C4C2211yescharacteristic, complemented
63C2×C4×C22⋊C4—21no—
64C2×C4×C22⋊C4—21no—
65#1973C2214yescomplemented
66#1944C2214yescomplemented
67#1936C2214yescomplemented
68#1935C2214yescomplemented
69#1928C2214yescomplemented
70#1925C2214yescomplemented
71#1920C2214yescomplemented
72#1919C2214yescomplemented
73#1893C2214yes—
74#1892C2214yescomplemented
75#1880C2214yescomplemented
76#1877C2214yescomplemented
77#1874C2212yes—
78#1874C2212yes—
79#1872C2212yes—
80#1872C2212yes—
81#1863C2214yescomplemented
82#1862C2214yescomplemented
83#1852C2212yes—
84#1852C2212yes—
85#1852C2212yescomplemented
86#1852C2212yescomplemented
87#1824C2212yescomplemented
88#1823C2212yes—
89#1808C2214yescomplemented
90#1787C2212yescomplemented
91#1786C2212yes—
92#1776C2214yescomplemented
93#1763C2214yescomplemented
94#1762C2214yescomplemented
95#1749C2212yes—
96#1749C2212yes—
97#1749C2212yescomplemented
98#1749C2212yescomplemented
99C2×#336C2212yescomplemented
100C23×Q8C2311yescharacteristic
101C23×D4—21no—
102C23×D4C2311yescharacteristic
103C24×C4—21no—
104C24×C4D411yescharacteristic
105C24×C4D411yescharacteristic
106C24×C4C2311yescharacteristic
107C22×SD16C2314yes—
108C23×C8C2312yes—
109C23×C8C2312yes—
110C2×C22⋊Q8—21no—
111C2×C22⋊Q8—21no—
112C2×C22⋊Q8—24no—
113C2×C22⋊Q8C2×C418yescomplemented
114C2×C22⋊Q8C2312yes—
115C2×C22⋊Q8C2312yes—
116C2×#121—21no—
117C2×#121—21no—
118C2×#121—24no—
119C2×#121C2×C418yes—
120C2×#121C2312yes—
121C2×#121C2312yes—
122C2×C4×Q8—21no—
123C2×C4×Q8—21no—
124C2×C4×Q8—44no—
125C2×C4×Q8C2312yes—
126C2×C4×Q8C2312yes—
127C2×C4×D4—22no—
128C2×C4×D4—22no—
129C2×C4×D4—22no—
130C2×C4×D4—22no—
131C2×C4×D4—21no—
132C2×C4×D4—21no—
133C2×C4×D4—44no—
134C2×C4×D4—48no—
135C2×C4×D4C2312yes—
136C2×C4×D4C2312yes—
137C22×C4⋊C4—21no—
138C22×C4⋊C4—21no—
139C22×C4⋊C4—21no—
140C22×C4⋊C4—21no—
141C22×C4⋊C4C2311yescharacteristic
142C22×C4⋊C4C2311yescharacteristic
143C22×C4⋊C4C2311yescharacteristic
144C22×C4⋊C4C2311yescharacteristic
145C22×C4⋊C4C2311yescharacteristic
146C22×C4⋊C4C2311yescharacteristic
147C22×C22⋊C4—21no—
148C22×C22⋊C4—21no—
149C22×C22⋊C4—21no—
150C22×C22⋊C4—21no—
151C22×C22⋊C4—21no—
152C22×C22⋊C4—21no—
153C22×C22⋊C4—21no—
154C22×C42—21no—
155C22×C42—21no—
156C22×C42—21no—
157C22×C42—44no—
158C22×C42D411yescharacteristic
159C22×C42D411yescharacteristic
160C22×C42D411yescharacteristic
161C22×C42D411yescharacteristic
162C22×C42D411yescharacteristic
163C22×C42D411yescharacteristic
164C22×C42C2311yescharacteristic
165C22×C42C2311yescharacteristic
166C22×C42C2311yescharacteristic
167C22×C42C2311yescharacteristic
168C22×C42C2311yescharacteristic
169C22×C42C2311yescharacteristic
170#483C2×C4116yescomplemented
171#481C2×C4116yescomplemented
172#465C2×C4132yescomplemented
173#450C2×C4116yescomplemented
174#448C2×C4116yescomplemented
175#440—48no—
176C2×#107C2314yes—
177C2×#107C2314yes—
178C2×#106C2314yes—
179C2×#103C2314yes—
180C2×#103C2314yes—
181C2×#103C2314yes—
182C2×#102C2314yes—
183C2×#102C2314yes—
184C2×#102C2314yes—
185C2×C22⋊C8—24no—
186C2×C22⋊C8C2×C418yescomplemented
187C2×C22⋊C8C2312yes—
188C2×C22⋊C8C2312yes—
189C2×C22⋊C8C2312yes—
190C2×C22⋊C8C2312yes—
191C2×#97—44no—
192C2×#97C2314yes—
193C2×#97C2314yes—
194#391—21no—
195#391—21no—
196#391C2312yes—
197#391C2312yes—
198#390—21no—
199#390—21no—
200#390C2312yes—
201#390C2312yes—
202#389—21no—
203#389—21no—
204#389—21no—
205#389—21no—
206#389C2312yes—
207#389C2312yes—
208#389C2312yes—
209#389C2312yes—
210#388—22no—
211#388—22no—
212#388—22no—
213#388—22no—
214#387—22no—
215#387—22no—
216#387—22no—
217#387—22no—
218#386—22no—
219#386—22no—
220#386—22no—
221#386—22no—
222#385—22no—
223#385—22no—
224#385—22no—
225#385—22no—
226#380—21no—
227#380—21no—
228#380—21no—
229#380—21no—
230#380C2312yes—
231#380C2312yes—
232#380C2312yes—
233#380C2312yes—
234C4×C4⋊C4—22no—
235C4×C4⋊C4—22no—
236C4×C4⋊C4—22no—
237C4×C4⋊C4—22no—
238C4×C4⋊C4—21no—
239C4×C4⋊C4—21no—
240C4×C4⋊C4—21no—
241C4×C4⋊C4—21no—
242C4×C4⋊C4C2312yes—
243C4×C4⋊C4C2312yes—
244C4×C4⋊C4C2312yes—
245C4×C4⋊C4C2312yes—
246C4×C22⋊C4—22no—
247C4×C22⋊C4—22no—
248C4×C22⋊C4—22no—
249C4×C22⋊C4—22no—
250C4×C22⋊C4—22no—
251C4×C22⋊C4—22no—
252C4×C22⋊C4—22no—
253C4×C22⋊C4—22no—
254C2×#95—21no—
255C2×#95—21no—
256C2×#95—21no—
257C2×#95—21no—
258C2×#95—21no—
259C2×#95—21no—
260C2×#95—21no—
261C2×#95—21no—
262#340C2314yes—
263#340C2314yes—
264#340C2314yes—
265#340C2314yes—
266#340C2314yes—
267#340C2314yes—
268#336C2314yes—
269#336C2314yes—
270C25—21no—
271C25C2×D411yescharacteristic
272C22×Q8—21no—
273C22×Q8—22no—
274C22×Q8—42no—
275C22×Q8—42no—
276C22×Q8C22×C414yescomplemented
277C22×Q8C2412yes—
278C22×D4—28no—
279C22×D4—22no—
280C22×D4—22no—
281C22×D4—21no—
282C22×D4—22no—
283C22×D4—42no—
284C22×D4—42no—
285C22×D4—44no—
286C22×D4—44no—
287C22×D4C22×C414yes—
288C22×D4C2412yes—
289C23×C4—24no—
290C23×C4—24no—
291C23×C4—21no—
292C23×C4—21no—
293C23×C4—21no—
294C23×C4—21no—
295C23×C4—21no—
296C23×C4—21no—
297C23×C4—21no—
298C23×C4—22no—
299C23×C4—22no—
300C23×C4—42no—
301C23×C4—42no—
302C23×C4—42no—
303C23×C4—42no—
304C23×C4—42no—
305C23×C4—42no—
306C23×C4—44no—
307C23×C4—44no—
308C23×C4—44no—
309C23×C4C22×C414yes—
310C23×C4C2×D411yescharacteristic
311C23×C4C2×D411yescharacteristic
312C23×C4C2×D411yescharacteristic
313C23×C4C2×D411yescharacteristic
314C23×C4C2×D411yescharacteristic
315C23×C4C2×D411yescharacteristic
316C23×C4C2×D411yescharacteristic
317C23×C4C2×D411yescharacteristic
318C23×C4C2×D411yescharacteristic
319C23×C4C2×D411yescharacteristic
320C23×C4C2×D411yescharacteristic
321C23×C4C2×D411yescharacteristic
322C23×C4C2×D411yescharacteristic
323C23×C4C2×D411yescharacteristic
324C23×C4C2×D411yescharacteristic
325C23×C4#4114yes—
326C23×C4C2411yescharacteristic
327C23×C4C2411yescharacteristic
328C23×C4C2411yescharacteristic
329C2×SD16—44no—
330C2×SD16—44no—
331C2×SD16C22×C4116yescomplemented
332C22×C8—24no—
333C22×C8—42no—
334C22×C8—42no—
335C22×C8—42no—
336C22×C8—42no—
337C22×C8C22×C418yescomplemented
338C22×C8C2414yes—
339C22×C8C2414yes—
340C22⋊Q8—28no—
341C22⋊Q8—28no—
342C22⋊Q8—24no—
343C22⋊Q8—24no—
344C22⋊Q8C22×C418yes—
345C22⋊Q8C22×C418yescomplemented
346#121—28no—
347#121—28no—
348#121—24no—
349#121—24no—
350#121C22×C418yes—
351#121C22×C418yes—
352C4×Q8—28no—
353C4×Q8—44no—
354C4×Q8—44no—
355C4×Q8—44no—
356C4×D4—28no—
357C4×D4—44no—
358C4×D4—44no—
359C4×D4—44no—
360C4×D4—48no—
361C4×D4—48no—
362C4×D4—48no—
363C4×D4—48no—
364C2×C4⋊C4—28no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—42no—
382C2×C4⋊C4—42no—
383C2×C4⋊C4—42no—
384C2×C4⋊C4—42no—
385C2×C4⋊C4—44no—
386C2×C4⋊C4—44no—
387C2×C4⋊C4—44no—
388C2×C4⋊C4C22×C414yes—
389C2×C4⋊C4C22×C414yescomplemented
390C2×C4⋊C4C2412yes—
391C2×C4⋊C4C2412yes—
392C2×C4⋊C4C2412yes—
393C2×C4⋊C4C2412yes—
394C2×C4⋊C4C2412yes—
395C2×C4⋊C4C2412yes—
396C2×C22⋊C4—28no—
397C2×C22⋊C4—22no—
398C2×C22⋊C4—22no—
399C2×C22⋊C4—28no—
400C2×C22⋊C4—22no—
401C2×C22⋊C4—22no—
402C2×C22⋊C4—22no—
403C2×C22⋊C4—22no—
404C2×C22⋊C4—22no—
405C2×C22⋊C4—22no—
406C2×C22⋊C4—22no—
407C2×C22⋊C4—22no—
408C2×C22⋊C4—22no—
409C2×C22⋊C4—22no—
410C2×C22⋊C4—22no—
411C2×C22⋊C4—22no—
412C2×C22⋊C4—44no—
413C2×C22⋊C4—44no—
414C2×C22⋊C4—44no—
415C2×C22⋊C4—44no—
416C2×C22⋊C4—44no—
417C2×C42—24no—
418C2×C42—24no—
419C2×C42—24no—
420C2×C42—22no—
421C2×C42—22no—
422C2×C42—22no—
423C2×C42—22no—
424C2×C42—22no—
425C2×C42—22no—
426C2×C42—42no—
427C2×C42—42no—
428C2×C42—42no—
429C2×C42—42no—
430C2×C42—42no—
431C2×C42—42no—
432C2×C42—42no—
433C2×C42—42no—
434C2×C42—42no—
435C2×C42—44no—
436C2×C42—44no—
437C2×C42—44no—
438C2×C42C2×D411yescharacteristic
439C2×C42C2×D411yescharacteristic
440C2×C42C2×D411yescharacteristic
441C2×C42C2×D411yescharacteristic
442C2×C42C2×D411yescharacteristic
443C2×C42C2×D411yescharacteristic
444C2×C42C2×D411yescharacteristic
445C2×C42C2×D411yescharacteristic
446C2×C42C2×D411yescharacteristic
447C2×C42C2×D411yescharacteristic
448C2×C42C2×D411yescharacteristic
449C2×C42C2×D411yescharacteristic
450C2×C42C2411yescharacteristic
451C2×C42C2411yescharacteristic
452C2×C42C2411yescharacteristic
453C2×C42C2411yescharacteristic
454#107—44no—
455#107—44no—
456#106C22×C4116yescomplemented
457#103—44no—
458#103—44no—
459#103C22×C4116yescomplemented
460#102—44no—
461#102—44no—
462#102C22×C4116yescomplemented
463C22⋊C8—24no—
464C22⋊C8—24no—
465C22⋊C8C22×C418yes—
466C22⋊C8C22×C418yescomplemented
467#97—28no—
468#97—44no—
469#95—22no—
470#95—22no—
471#95—22no—
472#95—22no—
473#95—22no—
474#95—22no—
475#95—22no—
476#95—22no—
477#95—22no—
478#95—22no—
479#95—22no—
480#95—22no—
481#95—22no—
482#95—22no—
483#95—22no—
484#95—22no—
485C24—24no—
486C24—22no—
487C24—41no—
488C24—41no—
489C24—41no—
490C24—41no—
491C24—42no—
492C24—42no—
493C24—42no—
494C24—42no—
495C24—42no—
496C24—42no—
497C24C4×D414yes—
498C24AGL(1,ℤ/8)14yes—
499C24#13714yes—
500C24C22×D411yescharacteristic
501C24C22×D411yescharacteristic
502C24C22×D411yescharacteristic
503C2×Q8—24no—
504C2×Q8—22no—
505C2×Q8—24no—
506C2×Q8—24no—
507C2×Q8—48no—
508C2×Q8—42no—
509C2×Q8—42no—
510C2×Q8—48no—
511C2×Q8C23×C414yes—
512C2×D4—28no—
513C2×D4—28no—
514C2×D4—24no—
515C2×D4—22no—
516C2×D4—24no—
517C2×D4—24no—
518C2×D4—48no—
519C2×D4—42no—
520C2×D4—42no—
521C2×D4—48no—
522C2×D4—44no—
523C2×D4—44no—
524C2×D4—44no—
525C2×D4—44no—
526C2×D4—432no—
527C2×D4C23×C414yes—
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—24no—
541C22×C4—24no—
542C22×C4—24no—
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—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—48no—
569C22×C4—48no—
570C22×C4—41no—
571C22×C4—41no—
572C22×C4—41no—
573C22×C4—41no—
574C22×C4—41no—
575C22×C4—41no—
576C22×C4—41no—
577C22×C4—41no—
578C22×C4—41no—
579C22×C4—41no—
580C22×C4—41no—
581C22×C4—41no—
582C22×C4—41no—
583C22×C4—41no—
584C22×C4—41no—
585C22×C4—41no—
586C22×C4—41no—
587C22×C4—41no—
588C22×C4—416no—
589C22×C4—416no—
590C22×C4—44no—
591C22×C4—44no—
592C22×C4—44no—
593C22×C4—44no—
594C22×C4—42no—
595C22×C4—42no—
596C22×C4—42no—
597C22×C4—42no—
598C22×C4—42no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4—42no—
603C22×C4—42no—
604C22×C4—42no—
605C22×C4—42no—
606C22×C4—42no—
607C22×C4—42no—
608C22×C4—42no—
609C22×C4—42no—
610C22×C4—42no—
611C22×C4—42no—
612C22×C4—44no—
613C22×C4—44no—
614C22×C4—816no—
615C22×C4C4×D414yes—
616C22×C4C4×D414yes—
617C22×C4C4×D414yes—
618C22×C4C23×C412yes—
619C22×C4C23×C412yes—
620C22×C4C23×C412yes—
621C22×C4C22×D411yescharacteristic
622C22×C4C22×D411yescharacteristic
623C22×C4C22×D411yescharacteristic
624C22×C4C22×D411yescharacteristic
625C22×C4C22×D411yescharacteristic
626C22×C4C22×D411yescharacteristic
627C22×C4C22×D411yescharacteristic
628C22×C4C22×D411yescharacteristic
629C22×C4C22×D411yescharacteristic
630C22×C4C22×D411yescharacteristic
631C22×C4C22×D411yescharacteristic
632C22×C4C2×#4112yes—
633C22×C4C2×#4112yes—
634C22×C4C2×#4112yes—
635C22×C4C2511yescharacteristic
636SD16—416no—
637C2×C8—24no—
638C2×C8—24no—
639C2×C8—24no—
640C2×C8—24no—
641C2×C8—24no—
642C2×C8—48no—
643C2×C8—48no—
644C2×C8C23×C418yes—
645C4⋊C4—28no—
646C4⋊C4—28no—
647C4⋊C4—24no—
648C4⋊C4—24no—
649C4⋊C4—22no—
650C4⋊C4—22no—
651C4⋊C4—24no—
652C4⋊C4—24no—
653C4⋊C4—24no—
654C4⋊C4—24no—
655C4⋊C4—42no—
656C4⋊C4—42no—
657C4⋊C4—44no—
658C4⋊C4—42no—
659C4⋊C4—44no—
660C4⋊C4—44no—
661C4⋊C4—42no—
662C4⋊C4—44no—
663C4⋊C4—44no—
664C4⋊C4—44no—
665C4⋊C4C23×C414yes—
666C4⋊C4C23×C414yes—
667C22⋊C4—28no—
668C22⋊C4—28no—
669C22⋊C4—28no—
670C22⋊C4—28no—
671C22⋊C4—44no—
672C22⋊C4—44no—
673C22⋊C4—44no—
674C22⋊C4—44no—
675C22⋊C4—44no—
676C22⋊C4—44no—
677C22⋊C4—44no—
678C22⋊C4—44no—
679C22⋊C4—44no—
680C22⋊C4—44no—
681C42—22no—
682C42—22no—
683C42—22no—
684C42—22no—
685C42—22no—
686C42—22no—
687C42—22no—
688C42—22no—
689C42—22no—
690C42—41no—
691C42—41no—
692C42—41no—
693C42—41no—
694C42—41no—
695C42—41no—
696C42—44no—
697C42—44no—
698C42—44no—
699C42—44no—
700C42—44no—
701C42—44no—
702C42H(5,𝔽2)14yes—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—24no—
716C23—44no—
717C23—44no—
718C23—44no—
719C23—44no—
720C23—44no—
721C23—44no—
722C23—48no—
723C23—48no—
724C23—42no—
725C23—42no—
726C23—48no—
727C23—42no—
728C23—42no—
729C23—42no—
730C23—42no—
731C23—84no—
732C23—84no—
733C23—84no—
734C23—84no—
735C23#440116yescomplemented
736C23C2×C4×D412yes—
737C23C2×C4×D412yes—
738C23C2×C4×D412yes—
739C23C2×AGL(1,ℤ/8)12yes—
740C23C2×AGL(1,ℤ/8)12yes—
741C23C2×AGL(1,ℤ/8)12yes—
742C23C2×#13712yes—
743C23C2×#13712yes—
744C23C2×#13712yes—
745C23C23×D411yescharacteristic
746Q8—28no—
747Q8—48no—
748Q8—44no—
749D4—28no—
750D4—48no—
751D4—416no—
752D4—416no—
753D4—44no—
754C2×C4—28no—
755C2×C4—28no—
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—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—24no—
771C2×C4—24no—
772C2×C4—24no—
773C2×C4—24no—
774C2×C4—24no—
775C2×C4—24no—
776C2×C4—24no—
777C2×C4—24no—
778C2×C4—24no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—44no—
792C2×C4—44no—
793C2×C4—44no—
794C2×C4—44no—
795C2×C4—44no—
796C2×C4—44no—
797C2×C4—44no—
798C2×C4—44no—
799C2×C4—44no—
800C2×C4—44no—
801C2×C4—44no—
802C2×C4—48no—
803C2×C4—44no—
804C2×C4—44no—
805C2×C4—48no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—48no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—88no—
826C2×C4—88no—
827C2×C4—84no—
828C2×C4—84no—
829C2×C4—84no—
830C2×C4—84no—
831C2×C4C2×C4×D412yes—
832C2×C4C2×C4×D412yes—
833C2×C4C2×C4×D412yes—
834C2×C4#53412yes—
835C2×C4#53412yes—
836C2×C4#57512yes—
837C2×C4#57512yes—
838C2×C4C24×C411yescharacteristic
839C2×C4C22×#4111yescharacteristic
840C2×C4C2×H(5,𝔽2)12yes—
841C2×C4#58512yes—
842C8—28no—
843C8—44no—
844C22—22no—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—22no—
850C22—22no—
851C22—22no—
852C22—22no—
853C22—22no—
854C22—22no—
855C22—22no—
856C22—22no—
857C22—22no—
858C22—22no—
859C22—22no—
860C22—22no—
861C22—22no—
862C22—416no—
863C22—44no—
864C22—44no—
865C22—44no—
866C22—816no—
867C22—82no—
868C22—82no—
869C22—82no—
870C22—82no—
871C22C2×#44014yes—
872C22C2×#44014yes—
873C22C2×#44014yes—
874C22C22×C4×D411yescharacteristic
875C22C2×#53411yescharacteristic
876C22#344911yescharacteristic
877C22C22×AGL(1,ℤ/8)11yescharacteristic
878C22C22×#13711yescharacteristic
879C22C2×#57511yescharacteristic
880C22C2×#57511yescharacteristic
881C4—22no—
882C4—22no—
883C4—22no—
884C4—22no—
885C4—22no—
886C4—22no—
887C4—22no—
888C4—44no—
889C4—41no—
890C4—41no—
891C4—41no—
892C4—41no—
893C4—44no—
894C4—44no—
895C4—82no—
896C4—82no—
897C4—82no—
898C4—82no—
899C4C4×H(5,𝔽2)12yes—
900C4#345912yes—
901C2—24no—
902C2—24no—
903C2—24no—
904C2—84no—
905C2C4×#53411yescharacteristic
906C2C22×#44011yescharacteristic
907C2C4×#57511yescharacteristic
908C2#6075011yescharacteristic
909C2#6075111yescharacteristic
910C2#6095811yescharacteristic
911C2#6096011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
prime radicalC22×#121C22
LCSG ▷ C2×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
2. C2×C4×C22⋊Q8C2semidirect
4. #22185C2semidirect
5. #22084C2semidirect
6. #22082C2semidirect
7. #22049C2semidirect
8. #22047C2semidirect
9. #21940C2semidirect
10. #21759C2semidirect
12. #21580C2semidirect
13. #21579C2semidirect
14. #21528C2semidirect
15. #21454C2semidirect
16. #21453C2semidirect
17. C2×#1749C2semidirect
20. C22×C4×Q8C22semidirect
24. #3187C4semidirect
30. C2×#440C22semidirect
33. C22×#97C22semidirect
40. C4×C22⋊Q8C22semidirect
41. C4×C22⋊Q8C22semidirect
50. C2×#391C22semidirect
53. C2×#389C22semidirect
62. C2×C4×C4⋊C4C22semidirect
65. #1973C22semidirect
66. #1944C22semidirect
67. #1936C22semidirect
68. #1935C22semidirect
69. #1928C22semidirect
70. #1925C22semidirect
71. #1920C22semidirect
72. #1919C22semidirect
74. #1892C22semidirect
75. #1880C22semidirect
76. #1877C22semidirect
81. #1863C22semidirect
82. #1862C22semidirect
85. #1852C22semidirect
86. #1852C22semidirect
87. #1824C22semidirect
89. #1808C22semidirect
90. #1787C22semidirect
92. #1776C22semidirect
93. #1763C22semidirect
94. #1762C22semidirect
97. #1749C22semidirect
98. #1749C22semidirect
99. C2×#336C22semidirect
113. C2×C22⋊Q8C2×C4semidirect
170. #483C2×C4semidirect
171. #481C2×C4semidirect
172. #465C2×C4semidirect
173. #450C2×C4semidirect
174. #448C2×C4semidirect
186. C2×C22⋊C8C2×C4semidirect
276. C22×Q8C22×C4semidirect
331. C2×SD16C22×C4semidirect
337. C22×C8C22×C4semidirect
345. C22⋊Q8C22×C4semidirect
389. C2×C4⋊C4C22×C4semidirect
456. #106C22×C4semidirect
459. #103C22×C4semidirect
462. #102C22×C4semidirect
466. C22⋊C8C22×C4semidirect
735. C23#440semidirect

Maximal subgroups

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

subgroupindex
C2×#31872
C2×C4×C22⋊Q82
C2×C4×#1212
#221852
#220842
#220822
#220492
#220472
#219402
#217592
#217582
#215802
#215792
#215282
#214542
#214532
C2×#17492