Finite Group Databasebeta

← #6475543

Subgroups — #6475543

Order 512.

2148 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36624C211yesmaximal, characteristic
2C2×C4×C22⋊Q8C211yesmaximal, characteristic, complemented
3#33147C211yesmaximal, characteristic, complemented
4#33107C211yesmaximal, characteristic, complemented
5#32954C211yesmaximal, characteristic, complemented
6#32903C211yesmaximal, characteristic, complemented
7#29892C212yesmaximal, complemented
8#29593C212yesmaximal, complemented
9#29466C214yesmaximal, complemented
10#29410C214yesmaximal, complemented
11#27628C212yesmaximal, complemented
12#24703C212yesmaximal, complemented
13#24653C212yesmaximal, complemented
14#24154C212yesmaximal, complemented
15#22076C212yesmaximal, complemented
16#22041C212yesmaximal, complemented
17#20714C211yesmaximal, characteristic, complemented
18C2×#532C2211yescharacteristic
19C2×#525—21no—
20C22×C22⋊Q8C2211yescharacteristic
21C22×C4×Q8C2211yescharacteristic
22C23×C42C2211yescharacteristic
23C2×#481C2212yes—
24C2×#475C2212yescomplemented
25C2×#460C2212yescomplemented
26C2×#448C2212yes—
27C2×#431C2212yes—
28#2857C2211yescharacteristic
29#2857C2211yescharacteristic
30#2856C2211yescharacteristic
31#2856C2211yescharacteristic
32#2854—21no—
33#2854C2212yes—
34#2850—21no—
35#2850—21no—
36#2847—21no—
37#2847C2212yes—
38C4×C22⋊Q8—21no—
39C4×C22⋊Q8—21no—
40C4×C22⋊Q8—21no—
41C4×C22⋊Q8—21no—
42C4×C22⋊Q8C2212yes—
43C4×C22⋊Q8C2212yes—
44C4×C22⋊Q8C2212yes—
45C4×C22⋊Q8C2212yes—
46C4×#121—21no—
47C4×#121—21no—
48C4×#121C2212yes—
49C4×#121C2212yes—
50#2297—21no—
51C2×#391C2211yescharacteristic
52C2×#389C2211yescharacteristic
53C2×#387—21no—
54C2×#385—21no—
55#2285C2211yescharacteristic
56C2×#380C2211yescharacteristic
57C2×C4×C4⋊C4—21no—
58C2×C4×C4⋊C4C2211yescharacteristic
59C2×C4×C22⋊C4—21no—
60#2077C2214yes—
61#2077C2214yes—
62#2035C2214yes—
63#2035C2214yes—
64#2034C2214yes—
65#2034C2214yes—
66#2000C2214yes—
67#2000C2214yes—
68#1988C2212yescomplemented
69#1982C2212yescomplemented
70#1968C2214yescomplemented
71#1948C2212yescomplemented
72#1948C2212yescomplemented
73#1941C2214yescomplemented
74#1934C2214yescomplemented
75#1933C2214yescomplemented
76#1927C2214yescomplemented
77#1926C2214yescomplemented
78#1920C2214yescomplemented
79#1919C2214yescomplemented
80#1880C2214yescomplemented
81#1877C2214yescomplemented
82#1874C2212yes—
83#1874C2212yes—
84#1865C2214yescomplemented
85#1864C2214yescomplemented
86#1853C2212yes—
87#1853C2212yes—
88#1824C2212yes—
89#1817C2212yes—
90#1803C2212yescomplemented
91#1803C2212yescomplemented
92#1797C2211yescharacteristic
93#1797C2212yes—
94#1797C2211yescharacteristic
95#1787C2212yes—
96#1779C2212yes—
97C4×C22⋊C8C2212yes—
98C4×C22⋊C8C2212yes—
99C22×#41—21no—
100C23×Q8C2311yescharacteristic
101C24×C4D411yescharacteristic
102C24×C4D411yescharacteristic
103C24×C4C2311yescharacteristic
104C22×SD16C2314yes—
105#532—44no—
106C2×C4⋊Q8C2311yescharacteristic
107C2×#127C2311yescharacteristic
108C2×#124—21no—
109#525—48no—
110C2×#123—22no—
111C2×C22⋊Q8—24no—
112C2×C22⋊Q8—21no—
113C2×C22⋊Q8—21no—
114C2×C22⋊Q8—21no—
115C2×C22⋊Q8—21no—
116C2×C22⋊Q8—24no—
117C2×C22⋊Q8C2312yes—
118C2×C22⋊Q8C2312yes—
119C2×#121—21no—
120C2×#121—21no—
121C2×#121—21no—
122C2×#121—21no—
123C2×#121—21no—
124C2×#121C2312yes—
125C2×#121C2312yes—
126C2×#121C2312yes—
127C2×#120—22no—
128C2×C4×Q8—21no—
129C2×C4×Q8—21no—
130C2×C4×Q8—44no—
131C2×C4×Q8C2312yes—
132C2×C4×Q8C2312yes—
133C2×C4×D4—22no—
134C2×C4×D4—22no—
135C2×C4×D4—21no—
136C2×C4×D4C2312yes—
137C2×#117—21no—
138C22×C4⋊C4—21no—
139C22×C4⋊C4—21no—
140C22×C4⋊C4—21no—
141C22×C4⋊C4C2311yescharacteristic
142C22×C4⋊C4C2311yescharacteristic
143C22×C4⋊C4C2311yescharacteristic
144C22×C22⋊C4—21no—
145C22×C22⋊C4—21no—
146C22×C42—21no—
147C22×C42—21no—
148C22×C42—44no—
149C22×C42D411yescharacteristic
150C22×C42D411yescharacteristic
151C22×C42D411yescharacteristic
152C22×C42D411yescharacteristic
153C22×C42D411yescharacteristic
154C22×C42D411yescharacteristic
155C22×C42C2311yescharacteristic
156C22×C42C2311yescharacteristic
157C22×C42C2311yescharacteristic
158C22×C42C2311yescharacteristic
159C22×C42C2311yescharacteristic
160C22×C42C2311yescharacteristic
161#481—28no—
162#475—44no—
163#460—44no—
164#448—28no—
165#431—44no—
166C2×#106C2314yes—
167C2×#106C2314yes—
168C2×#106C2314yes—
169C2×C4⋊C8C2312yes—
170C2×C4⋊C8C2312yes—
171C2×#103C2314yes—
172C2×#103C2314yes—
173C2×#103C2314yes—
174C2×#102C2314yes—
175C2×#102C2314yes—
176C2×#102C2314yes—
177C2×C22⋊C8C2312yes—
178C2×C22⋊C8C2312yes—
179C2×C22⋊C8C2314yes—
180C2×C22⋊C8C2314yes—
181C2×C4×C8C2314yes—
182#391—21no—
183#391—21no—
184#391—21no—
185#391—21no—
186#391C2312yes—
187#391C2312yes—
188#390—21no—
189#390—21no—
190#390—21no—
191#390—21no—
192#390C2312yes—
193#390C2312yes—
194#389—21no—
195#389—21no—
196#389—21no—
197#389—21no—
198#389C2312yes—
199#389C2312yes—
200#389C2312yes—
201#389C2312yes—
202#388—22no—
203#388—22no—
204#388—22no—
205#388—22no—
206#387—22no—
207#387—22no—
208#387—22no—
209#387—22no—
210#386—22no—
211#386—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#384C2311yescharacteristic
221#384C2311yescharacteristic
222#382—21no—
223#380—21no—
224#380—21no—
225#380—21no—
226#380—21no—
227#380—21no—
228#380C2312yes—
229#380C2312yes—
230#380C2312yes—
231#380C2312yes—
232#380C2312yes—
233C4×C4⋊C4—22no—
234C4×C4⋊C4—22no—
235C4×C4⋊C4—22no—
236C4×C4⋊C4—22no—
237C4×C4⋊C4—21no—
238C4×C4⋊C4—21no—
239C4×C4⋊C4—21no—
240C4×C4⋊C4C2312yes—
241C4×C4⋊C4C2312yes—
242C4×C4⋊C4C2312yes—
243C4×C22⋊C4—22no—
244C4×C22⋊C4—22no—
245C4×C22⋊C4—22no—
246C4×C22⋊C4—22no—
247C4×C22⋊C4—22no—
248C4×C22⋊C4—22no—
249C2×#95—21no—
250C2×#95—21no—
251C2×#95—21no—
252C2×#95—21no—
253C2×#95—21no—
254#340C2314yes—
255#340C2314yes—
256#340C2314yes—
257#340C2314yes—
258#340C2314yes—
259#340C2314yes—
260#336C2314yes—
261#336C2312yes—
262#336C2312yes—
263C25C2×D411yescharacteristic
264C2×#41—44no—
265C2×#41—44no—
266C2×#41—44no—
267C22×Q8—21no—
268C22×Q8—21no—
269C22×Q8—22no—
270C22×Q8—42no—
271C22×Q8—42no—
272C22×Q8#4114yescomplemented
273C22×Q8C2412yes—
274C22×D4—22no—
275C22×D4—22no—
276C22×D4—22no—
277C22×D4—21no—
278C22×D4—21no—
279C22×D4C2412yes—
280C23×C4—21no—
281C23×C4—21no—
282C23×C4—22no—
283C23×C4—22no—
284C23×C4—21no—
285C23×C4—21no—
286C23×C4—22no—
287C23×C4—42no—
288C23×C4—42no—
289C23×C4—42no—
290C23×C4—42no—
291C23×C4—42no—
292C23×C4—42no—
293C23×C4—42no—
294C23×C4SD1618yescomplemented
295C23×C4C2×D411yescharacteristic
296C23×C4C2×D411yescharacteristic
297C23×C4C2×D411yescharacteristic
298C23×C4C2×D411yescharacteristic
299C23×C4C2×D411yescharacteristic
300C23×C4C2×D411yescharacteristic
301C23×C4C2×D411yescharacteristic
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×C4C2411yescharacteristic
311C23×C4C2411yescharacteristic
312C23×C4C2411yescharacteristic
313C2×SD16—28no—
314C2×SD16—44no—
315C2×SD16—44no—
316C22×C8C2414yes—
317C22×C8C2414yes—
318C4⋊Q8—24no—
319#127—24no—
320#124—44no—
321#123—48no—
322C22⋊Q8—28no—
323C22⋊Q8—28no—
324C22⋊Q8—24no—
325C22⋊Q8—24no—
326C22⋊Q8—24no—
327C22⋊Q8—24no—
328C22⋊Q8—44no—
329C22⋊Q8—44no—
330#121—24no—
331#121—24no—
332#121—44no—
333#121—44no—
334#121—44no—
335#121—44no—
336#121—44no—
337#121—44no—
338#121—44no—
339#120—48no—
340C4×Q8—24no—
341C4×Q8—24no—
342C4×Q8—42no—
343C4×Q8—42no—
344C4×Q8—44no—
345C4×Q8—44no—
346C4×D4—44no—
347C4×D4—44no—
348C4×D4—48no—
349C4×D4—48no—
350#117—44no—
351C2×C4⋊C4—28no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—42no—
370C2×C4⋊C4—42no—
371C2×C4⋊C4—44no—
372C2×C4⋊C4—44no—
373C2×C4⋊C4#4114yescomplemented
374C2×C4⋊C4C2412yes—
375C2×C4⋊C4C2412yes—
376C2×C4⋊C4C2412yes—
377C2×C4⋊C4C2412yes—
378C2×C4⋊C4C2412yes—
379C2×C4⋊C4C2412yes—
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—22no—
396C2×C22⋊C4—44no—
397C2×C42—24no—
398C2×C42—24no—
399C2×C42—24no—
400C2×C42—22no—
401C2×C42—22no—
402C2×C42—22no—
403C2×C42—22no—
404C2×C42—22no—
405C2×C42—42no—
406C2×C42—42no—
407C2×C42—42no—
408C2×C42—42no—
409C2×C42—42no—
410C2×C42—42no—
411C2×C42—42no—
412C2×C42—42no—
413C2×C42—42no—
414C2×C42—44no—
415C2×C42—44no—
416C2×C42C2×D411yescharacteristic
417C2×C42C2×D411yescharacteristic
418C2×C42C2×D411yescharacteristic
419C2×C42C2×D411yescharacteristic
420C2×C42C2×D411yescharacteristic
421C2×C42C2×D411yescharacteristic
422C2×C42C2×D411yescharacteristic
423C2×C42C2×D411yescharacteristic
424C2×C42C2×D411yescharacteristic
425C2×C42C2×D411yescharacteristic
426C2×C42C2×D411yescharacteristic
427C2×C42C2×D411yescharacteristic
428C2×C42C2411yescharacteristic
429C2×C42C2411yescharacteristic
430C2×C42C2411yescharacteristic
431C2×C42C2411yescharacteristic
432#106—28no—
433#106—44no—
434#106—44no—
435C4⋊C8—24no—
436C4⋊C8—24no—
437#103—28no—
438#103—44no—
439#103—44no—
440#102—28no—
441#102—44no—
442#102—44no—
443C22⋊C8—24no—
444C22⋊C8—24no—
445C22⋊C8—44no—
446C22⋊C8—44no—
447C4×C8—44no—
448#95—22no—
449#95—22no—
450#95—22no—
451#95—22no—
452#95—22no—
453#95—22no—
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—
464C24—22no—
465C24—22no—
466C24—22no—
467C24—41no—
468C24—41no—
469C24—41no—
470C24—41no—
471C24C2×SD1614yes—
472C24C22×D411yescharacteristic
473C24C22×D411yescharacteristic
474C24C22×D411yescharacteristic
475#41—816no—
476C2×Q8—24no—
477C2×Q8—22no—
478C2×Q8—22no—
479C2×Q8—22no—
480C2×Q8—22no—
481C2×Q8—22no—
482C2×Q8—48no—
483C2×Q8—42no—
484C2×Q8—42no—
485C2×Q8—48no—
486C2×Q8—42no—
487C2×Q8—42no—
488C2×Q8—42no—
489C2×Q8C2×#4114yes—
490C2×D4—22no—
491C2×D4—22no—
492C2×D4—24no—
493C2×D4—24no—
494C2×D4—42no—
495C2×D4—42no—
496C2×D4—44no—
497C2×D4—44no—
498C2×D4—44no—
499C2×D4—44no—
500C2×D4—44no—
501C2×D4—44no—
502C2×D4—44no—
503C2×D4—44no—
504C2×D4—44no—
505C2×D4—42no—
506C2×D4—42no—
507C2×D4—42no—
508C2×D4—42no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—24no—
518C22×C4—24no—
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—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
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—416no—
546C22×C4—41no—
547C22×C4—41no—
548C22×C4—41no—
549C22×C4—41no—
550C22×C4—41no—
551C22×C4—41no—
552C22×C4—41no—
553C22×C4—41no—
554C22×C4—41no—
555C22×C4—41no—
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—48no—
569C22×C4—48no—
570C22×C4—44no—
571C22×C4—44no—
572C22×C4—42no—
573C22×C4—42no—
574C22×C4—42no—
575C22×C4—42no—
576C22×C4—416no—
577C22×C4—42no—
578C22×C4—42no—
579C22×C4—42no—
580C22×C4—42no—
581C22×C4—42no—
582C22×C4—42no—
583C22×C4—44no—
584C22×C4C2×SD1614yes—
585C22×C4C2×SD1614yes—
586C22×C4C2×SD1614yes—
587C22×C4C2×SD1614yes—
588C22×C4C2×SD1614yes—
589C22×C4C2×SD1614yes—
590C22×C4C22×D411yescharacteristic
591C22×C4C22×D411yescharacteristic
592C22×C4C22×D411yescharacteristic
593C22×C4C22×D411yescharacteristic
594C22×C4C22×D411yescharacteristic
595C22×C4C22×D411yescharacteristic
596C22×C4C22×D411yescharacteristic
597C22×C4C22×D411yescharacteristic
598C22×C4C22×D411yescharacteristic
599C22×C4C22×D411yescharacteristic
600C22×C4C22×D411yescharacteristic
601C22×C4C2×#4112yes—
602C22×C4C2×#4112yes—
603C22×C4C2511yescharacteristic
604SD16—88no—
605C2×C8—24no—
606C2×C8—24no—
607C2×C8—24no—
608C2×C8—24no—
609C2×C8—24no—
610C2×C8—24no—
611C4⋊C4—28no—
612C4⋊C4—28no—
613C4⋊C4—24no—
614C4⋊C4—22no—
615C4⋊C4—22no—
616C4⋊C4—22no—
617C4⋊C4—22no—
618C4⋊C4—24no—
619C4⋊C4—22no—
620C4⋊C4—22no—
621C4⋊C4—24no—
622C4⋊C4—22no—
623C4⋊C4—42no—
624C4⋊C4—44no—
625C4⋊C4—42no—
626C4⋊C4—44no—
627C4⋊C4—42no—
628C4⋊C4—42no—
629C4⋊C4—44no—
630C4⋊C4—42no—
631C4⋊C4—42no—
632C4⋊C4—42no—
633C4⋊C4—44no—
634C4⋊C4—44no—
635C4⋊C4—44no—
636C4⋊C4C2×#4114yes—
637C22⋊C4—28no—
638C22⋊C4—28no—
639C22⋊C4—44no—
640C22⋊C4—44no—
641C22⋊C4—44no—
642C22⋊C4—44no—
643C22⋊C4—44no—
644C22⋊C4—44no—
645C22⋊C4—44no—
646C22⋊C4—44no—
647C22⋊C4—44no—
648C22⋊C4—44no—
649C22⋊C4—44no—
650C22⋊C4—44no—
651C22⋊C4—44no—
652C42—22no—
653C42—22no—
654C42—22no—
655C42—22no—
656C42—22no—
657C42—22no—
658C42—22no—
659C42—22no—
660C42—22no—
661C42—41no—
662C42—41no—
663C42—41no—
664C42—41no—
665C42—41no—
666C42—41no—
667C42—44no—
668C42—44no—
669C42—44no—
670C42—44no—
671C42—44no—
672C42H(5,𝔽2)14yes—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—28no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—44no—
691C23—44no—
692C23—44no—
693C23—44no—
694C23—44no—
695C23—44no—
696C23—42no—
697C23—42no—
698C23—42no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23#52512yes—
704C23C22×SD1612yes—
705C23C22×SD1612yes—
706C23C22×SD1612yes—
707C23#57512yes—
708C23C23×D411yescharacteristic
709Q8—24no—
710Q8—24no—
711Q8—48no—
712Q8—42no—
713Q8—42no—
714Q8—84no—
715D4—44no—
716D4—44no—
717D4—84no—
718D4—88no—
719D4—88no—
720D4—88no—
721D4—84no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—28no—
735C2×C4—28no—
736C2×C4—28no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—44no—
754C2×C4—44no—
755C2×C4—44no—
756C2×C4—44no—
757C2×C4—44no—
758C2×C4—44no—
759C2×C4—44no—
760C2×C4—44no—
761C2×C4—44no—
762C2×C4—44no—
763C2×C4—48no—
764C2×C4—44no—
765C2×C4—48no—
766C2×C4—44no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—88no—
791C2×C4—84no—
792C2×C4—84no—
793C2×C4#52512yes—
794C2×C4#53412yes—
795C2×C4#53412yes—
796C2×C4C22×SD1612yes—
797C2×C4C22×SD1612yes—
798C2×C4C22×SD1612yes—
799C2×C4C22×SD1612yes—
800C2×C4#57512yes—
801C2×C4#57512yes—
802C2×C4C22×#4111yescharacteristic
803C2×C4C22×#4111yescharacteristic
804C2×C4C2×H(5,𝔽2)12yes—
805C2×C4#58512yes—
806C8—44no—
807C8—44no—
808C22—22no—
809C22—22no—
810C22—22no—
811C22—22no—
812C22—22no—
813C22—22no—
814C22—22no—
815C22—22no—
816C22—22no—
817C22—22no—
818C22—22no—
819C22—22no—
820C22—416no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—82no—
830C22—82no—
831C22—82no—
832C22—82no—
833C22—82no—
834C22—82no—
835C22—82no—
836C22#310314yes—
837C22C2×#52511yescharacteristic
838C22C2×#53411yescharacteristic
839C22#344911yescharacteristic
840C22C23×SD1611yescharacteristic
841C22C2×#57511yescharacteristic
842C22C2×#57511yescharacteristic
843C22C2×#57511yescharacteristic
844C4—22no—
845C4—22no—
846C4—22no—
847C4—22no—
848C4—22no—
849C4—22no—
850C4—41no—
851C4—41no—
852C4—44no—
853C4—41no—
854C4—41no—
855C4—44no—
856C4—82no—
857C4—82no—
858C4—82no—
859C4—82no—
860C4—82no—
861C4#318714yes—
862C4#350512yes—
863C4#350612yes—
864C2—24no—
865C2—42no—
866C2—42no—
867C2—162no—
868C2#3503111yescharacteristic
869C2C2×#310311yescharacteristic
870C2#6055911yescharacteristic
871C2C2×#318711yescharacteristic
872C2#6075211yescharacteristic
873C2#6094111yescharacteristic
874C2#6097011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#36624C2
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
2. C2×C4×C22⋊Q8C2semidirect
3. #33147C2semidirect
4. #33107C2semidirect
5. #32954C2semidirect
6. #32903C2semidirect
7. #29892C2semidirect
8. #29593C2semidirect
9. #29466C2semidirect
10. #29410C2semidirect
11. #27628C2semidirect
12. #24703C2semidirect
13. #24653C2semidirect
14. #24154C2semidirect
15. #22076C2semidirect
16. #22041C2semidirect
17. #20714C2semidirect
24. C2×#475C22semidirect
25. C2×#460C22semidirect
68. #1988C22semidirect
69. #1982C22semidirect
70. #1968C22semidirect
71. #1948C22semidirect
72. #1948C22semidirect
73. #1941C22semidirect
74. #1934C22semidirect
75. #1933C22semidirect
76. #1927C22semidirect
77. #1926C22semidirect
78. #1920C22semidirect
79. #1919C22semidirect
80. #1880C22semidirect
81. #1877C22semidirect
84. #1865C22semidirect
85. #1864C22semidirect
90. #1803C22semidirect
91. #1803C22semidirect
272. C22×Q8#41semidirect
294. C23×C4SD16semidirect
373. C2×C4⋊C4#41semidirect

Maximal subgroups

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

subgroupindex
#366242
C2×C4×C22⋊Q82
#331472
#331072
#329542
#329032
#298922
#295932
#294662
#294102
#276282
#247032
#246532
#241542
#220762
#220412
#207142