Finite Group Databasebeta

← #6500047

Subgroups — #6500047

Order 512.

3428 conjugacy classes of subgroups.

The subgroup lattice has 859 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3501C211yesmaximal, characteristic, complemented
2C2×#3193C211yesmaximal, characteristic, complemented
3C22×#468C211yesmaximal, characteristic, complemented
4#35076C211yesmaximal, characteristic
5#25559C214yesmaximal, complemented
6#25503C214yesmaximal, complemented
7#24445C214yesmaximal, complemented
8#24387C214yesmaximal, complemented
9#24098C212yesmaximal, complemented
10#24042C212yesmaximal, complemented
11#23969C212yesmaximal, complemented
12#23855C212yesmaximal, complemented
13#21768C211yesmaximal, characteristic, complemented
14#20972C211yesmaximal, characteristic, complemented
15#20898C211yesmaximal, characteristic, complemented
16C23×SD16C2211yescharacteristic, complemented
17C23×M16C2211yescharacteristic
18#3501—28no—
19#3501—28no—
20C2×#554—22no—
21C2×#554—22no—
22C2×#554C2212yes—
23C2×#554C2212yescomplemented
24C2×D4×Q8C2212yes—
25C2×D4×Q8C2212yescomplemented
26C2×#544—21no—
27C2×#543—21no—
28C2×#543—21no—
29C2×#533C2212yescomplemented
30C22×C22⋊Q8C2211yescharacteristic
31C22×C22⋊Q8C2211yescharacteristic
32C22×C22⋊Q8C2212yescomplemented
33C22×#121C2211yescharacteristic
34C2×#518—21no—
35C22×C4×D4C2211yescharacteristic
36#3193—28no—
37C2×#484C2212yescomplemented
38C2×#480C2212yescomplemented
39C2×#468—28no—
40C2×#468C2214yes—
41C2×#468C2214yes—
42C2×#468C2214yescomplemented
43C2×#448C2212yescomplemented
44C2×#448C2214yescomplemented
45C2×#450C2212yescomplemented
46C22×#107C2211yescharacteristic, complemented
47C2×#419C2212yescomplemented
48C22×#103C2211yescharacteristic, complemented
49C22×#102C2211yescharacteristic, complemented
50C2×#407C2211yescharacteristic
51C2×#407C2212yescomplemented
52#2854C2212yes—
53#2847C2212yes—
54#2635—22no—
55#2591—21no—
56#2539—21no—
57#2487C2212yes—
58#2414C2214yes—
59#2408C2212yes—
60#2405—21no—
61#2403—21no—
62#2321—22no—
63#2280C2211yescharacteristic
64#2057C2214yescomplemented
65#2043C2214yescomplemented
66#2036C2214yescomplemented
67#2036C2214yescomplemented
68#2023C2214yescomplemented
69#2013C2214yescomplemented
70#2000C2214yescomplemented
71#2000C2214yescomplemented
72#1894C2214yescomplemented
73#1894C2214yescomplemented
74#1892C2212yescomplemented
75#1892C2212yescomplemented
76#1880C2214yescomplemented
77#1880C2214yescomplemented
78#1874C2214yescomplemented
79#1873C2214yescomplemented
80#1870C2214yescomplemented
81#1869C2212yes—
82#1869C2212yes—
83#1863C2214yescomplemented
84#1863C2214yescomplemented
85#1852C2214yescomplemented
86#1824C2212yescomplemented
87#1787C2212yescomplemented
88#1787C2214yescomplemented
89#1736C2212yescomplemented
90#1728C2212yescomplemented
91C23×Q8C2312yes—
92C23×Q8C2311yescharacteristic
93C23×Q8C2311yescharacteristic
94C23×D4—21no—
95C23×D4D411yescharacteristic
96C23×D4C2311yescharacteristic
97C24×C4C2311yescharacteristic
98C24×C4C2311yescharacteristic
99C22×SD16—24no—
100C22×SD16—44no—
101C22×SD16C2314yes—
102C22×SD16C2314yes—
103C22×M16—24no—
104C22×M16—44no—
105C22×M16C2312yes—
106C22×M16C2312yes—
107C22×M16C2312yes—
108C23×C8C2311yescharacteristic
109C23×C8C2311yescharacteristic
110#554—232no—
111#554—232no—
112#554—28no—
113#554—28no—
114#554—28no—
115#554—28no—
116D4×Q8—28no—
117D4×Q8—28no—
118D4×Q8—28no—
119D4×Q8—28no—
120#544—216no—
121#543—216no—
122#543—216no—
123#533—28no—
124#533—28no—
125C2×C4⋊Q8—22no—
126C2×C4⋊Q8—22no—
127C2×C4⋊Q8C2312yes—
128C2×C4⋊Q8C2312yes—
129C2×#125—22no—
130C2×#125—22no—
131C2×#125—22no—
132C2×#123—22no—
133C2×C22⋊Q8—21no—
134C2×C22⋊Q8—21no—
135C2×C22⋊Q8—21no—
136C2×C22⋊Q8—21no—
137C2×C22⋊Q8—24no—
138C2×C22⋊Q8—24no—
139C2×C22⋊Q8—22no—
140C2×C22⋊Q8—22no—
141C2×C22⋊Q8—22no—
142C2×C22⋊Q8—28no—
143C2×C22⋊Q8—28no—
144C2×C22⋊Q8—22no—
145C2×C22⋊Q8—22no—
146C2×C22⋊Q8—22no—
147C2×C22⋊Q8—22no—
148C2×C22⋊Q8—22no—
149C2×C22⋊Q8—22no—
150C2×C22⋊Q8—22no—
151C2×C22⋊Q8—22no—
152C2×C22⋊Q8D418yescomplemented
153C2×C22⋊Q8D418yescomplemented
154C2×C22⋊Q8C2312yes—
155C2×C22⋊Q8C2312yes—
156C2×C22⋊Q8C2312yes—
157C2×C22⋊Q8C2312yes—
158C2×C22⋊Q8C2312yes—
159C2×C22⋊Q8C2312yes—
160C2×#121—21no—
161C2×#121—21no—
162C2×#121—24no—
163C2×#121—24no—
164C2×#121C2312yes—
165C2×#121C2312yes—
166C2×#121C2314yes—
167C2×#120—22no—
168C2×#120—22no—
169#518—216no—
170C2×C4×Q8—22no—
171C2×C4×Q8C2312yes—
172C2×C4×Q8C2312yes—
173C2×C4×D4—22no—
174C2×C4×D4—22no—
175C2×C4×D4—22no—
176C2×C4×D4—22no—
177C2×C4×D4—24no—
178C2×C4×D4—24no—
179C2×C4×D4D412yes—
180C2×C4×D4D412yes—
181C2×C4×D4C2312yes—
182C2×C4×D4C2312yes—
183C2×#117—22no—
184C2×#117C2312yes—
185C22×C4⋊C4—21no—
186C22×C4⋊C4—21no—
187C22×C4⋊C4—22no—
188C22×C4⋊C4D411yescharacteristic
189C22×C4⋊C4C2311yescharacteristic
190C22×C4⋊C4C2312yes—
191C22×C4⋊C4C2311yescharacteristic
192C22×C4⋊C4C2311yescharacteristic
193C22×C22⋊C4—21no—
194C22×C22⋊C4—21no—
195C22×C22⋊C4—22no—
196C22×C22⋊C4—21no—
197C22×C22⋊C4D411yescharacteristic
198C22×C22⋊C4D411yescharacteristic
199C22×C42C2311yescharacteristic
200#484—28no—
201#480—28no—
202#468—216no—
203#468—216no—
204#468—216no—
205#450—28no—
206#448—28no—
207#448—48no—
208C2×#107—24no—
209C2×#107C2314yes—
210C2×#107C2314yes—
211#419—44no—
212C2×#103—24no—
213C2×#103C2314yes—
214C2×#103C2314yes—
215C2×#103C2314yes—
216C2×#103C2314yes—
217C2×#103C2314yes—
218C2×#103C2314yes—
219C2×#102—24no—
220C2×#102C2314yes—
221C2×#102C2314yes—
222#407—24no—
223#407—44no—
224C2×C22⋊C8C2312yes—
225C2×C22⋊C8C2312yes—
226C2×C22⋊C8C2314yes—
227C2×C22⋊C8C2314yes—
228#400—22no—
229#399—22no—
230#394—22no—
231#394—24no—
232#392—24no—
233#392—22no—
234#390—24no—
235#390C2314yes—
236#389C2314yes—
237#388—24no—
238#388—24no—
239#386—22no—
240#386—24no—
241#386—22no—
242#386—22no—
243#385—22no—
244#381—21no—
245#380C2312yes—
246#380C2314yes—
247#380C2312yes—
248#379—21no—
249#379—22no—
250C4×C22⋊C4—21no—
251C4×C22⋊C4—21no—
252#340C2314yes—
253#340C2314yes—
254#340C2314yes—
255#340C2314yes—
256#336C2314yes—
257#336C2314yes—
258C25—21no—
259C25C2×D411yescharacteristic
260C25C2×D411yescharacteristic
261C22×Q8—24no—
262C22×Q8—24no—
263C22×Q8—22no—
264C22×Q8—22no—
265C22×Q8—21no—
266C22×Q8—21no—
267C22×Q8—22no—
268C22×Q8—22no—
269C22×Q8—42no—
270C22×Q8—42no—
271C22×Q8—42no—
272C22×Q8—42no—
273C22×Q8—44no—
274C22×Q8—44no—
275C22×Q8C2×D414yes—
276C22×Q8C2×D414yes—
277C22×Q8C2412yes—
278C22×Q8C2412yes—
279C22×D4—24no—
280C22×D4—28no—
281C22×D4—22no—
282C22×D4—24no—
283C22×D4—22no—
284C22×D4—22no—
285C22×D4—22no—
286C22×D4—21no—
287C22×D4—42no—
288C22×D4—42no—
289C22×D4—44no—
290C22×D4—84no—
291C22×D4C2×D412yes—
292C22×D4C2×D412yes—
293C22×D4C2412yes—
294C23×C4—22no—
295C23×C4—21no—
296C23×C4—21no—
297C23×C4—22no—
298C23×C4—21no—
299C23×C4—21no—
300C23×C4—22no—
301C23×C4—22no—
302C23×C4—21no—
303C23×C4—42no—
304C23×C4—42no—
305C23×C4—42no—
306C23×C4—42no—
307C23×C4C2×D411yescharacteristic
308C23×C4C2×D411yescharacteristic
309C23×C4C2×D411yescharacteristic
310C23×C4C2×D412yes—
311C23×C4C2×D411yescharacteristic
312C23×C4C2×D411yescharacteristic
313C23×C4C2×D411yescharacteristic
314C23×C4C2×D414yes—
315C23×C4C2×D414yes—
316C23×C4C2412yes—
317C23×C4C2411yescharacteristic
318C23×C4C2411yescharacteristic
319C23×C4C2411yescharacteristic
320C2×SD16—28no—
321C2×SD16—28no—
322C2×SD16—28no—
323C2×SD16—44no—
324C2×SD16—416no—
325C2×SD16—44no—
326C2×SD16—44no—
327C2×M16—24no—
328C2×M16—24no—
329C2×M16—24no—
330C2×M16—24no—
331C2×M16—24no—
332C2×M16—42no—
333C2×M16—42no—
334C2×M16—42no—
335C2×M16—42no—
336C2×M16—416no—
337C22×C8—22no—
338C22×C8—24no—
339C22×C8—22no—
340C22×C8—42no—
341C22×C8C2412yes—
342C22×C8C2414yes—
343C22×C8C2412yes—
344C4⋊Q8—216no—
345C4⋊Q8—216no—
346C4⋊Q8—24no—
347C4⋊Q8—24no—
348C4⋊Q8—24no—
349C4⋊Q8—24no—
350#125—216no—
351#125—216no—
352#125—216no—
353#123—84no—
354C22⋊Q8—216no—
355C22⋊Q8—216no—
356C22⋊Q8—216no—
357C22⋊Q8—216no—
358C22⋊Q8—216no—
359C22⋊Q8—216no—
360C22⋊Q8—216no—
361C22⋊Q8—216no—
362C22⋊Q8—216no—
363C22⋊Q8—216no—
364C22⋊Q8—216no—
365C22⋊Q8—24no—
366C22⋊Q8—24no—
367C22⋊Q8—28no—
368C22⋊Q8—28no—
369C22⋊Q8—28no—
370C22⋊Q8—28no—
371C22⋊Q8—24no—
372C22⋊Q8—24no—
373C22⋊Q8—24no—
374C22⋊Q8—24no—
375C22⋊Q8—24no—
376C22⋊Q8—24no—
377C22⋊Q8C2×D418yes—
378C22⋊Q8C2×D418yes—
379C22⋊Q8C2×D418yes—
380C22⋊Q8C2×D418yes—
381#121—24no—
382#121—24no—
383#121—24no—
384#121—24no—
385#121—44no—
386#121—44no—
387#121—44no—
388#121—44no—
389#120—48no—
390#120—84no—
391C4×Q8—216no—
392C4×Q8—24no—
393C4×Q8—24no—
394C4×Q8—24no—
395C4×Q8—24no—
396C4×D4—216no—
397C4×D4—216no—
398C4×D4—216no—
399C4×D4—216no—
400C4×D4—28no—
401C4×D4—28no—
402C4×D4—24no—
403C4×D4—24no—
404C4×D4—24no—
405C4×D4—24no—
406#117—216no—
407#117—42no—
408#117—42no—
409C2×C4⋊C4—216no—
410C2×C4⋊C4—28no—
411C2×C4⋊C4—28no—
412C2×C4⋊C4—24no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4—24no—
430C2×C4⋊C4—24no—
431C2×C4⋊C4—22no—
432C2×C4⋊C4—22no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—24no—
435C2×C4⋊C4C2×D412yes—
436C2×C4⋊C4C2×D412yes—
437C2×C4⋊C4C2×D414yes—
438C2×C4⋊C4C2×D414yes—
439C2×C4⋊C4C2412yes—
440C2×C4⋊C4C2414yes—
441C2×C4⋊C4C2412yes—
442C2×C4⋊C4C2412yes—
443C2×C22⋊C4—216no—
444C2×C22⋊C4—28no—
445C2×C22⋊C4—28no—
446C2×C22⋊C4—24no—
447C2×C22⋊C4—22no—
448C2×C22⋊C4—22no—
449C2×C22⋊C4—22no—
450C2×C22⋊C4—22no—
451C2×C22⋊C4—22no—
452C2×C22⋊C4—22no—
453C2×C22⋊C4—24no—
454C2×C22⋊C4—22no—
455C2×C22⋊C4—22no—
456C2×C22⋊C4—22no—
457C2×C22⋊C4—22no—
458C2×C22⋊C4—24no—
459C2×C22⋊C4—22no—
460C2×C22⋊C4—24no—
461C2×C22⋊C4—24no—
462C2×C22⋊C4—24no—
463C2×C22⋊C4—44no—
464C2×C22⋊C4C2×D412yes—
465C2×C22⋊C4C2×D412yes—
466C2×C22⋊C4C2×D412yes—
467C2×C22⋊C4C2×D412yes—
468C2×C42—22no—
469C2×C42—22no—
470C2×C42—22no—
471C2×C42—22no—
472C2×C42—22no—
473C2×C42C2×D412yes—
474C2×C42C2412yes—
475#107—28no—
476#107—28no—
477#103—28no—
478#103—28no—
479#103—28no—
480#103—44no—
481#103—44no—
482#103—44no—
483#102—28no—
484#102—28no—
485C22⋊C8—24no—
486C22⋊C8—24no—
487C22⋊C8—28no—
488C22⋊C8—44no—
489#95—22no—
490#95—22no—
491#95—24no—
492#95—24no—
493C24—22no—
494C24—24no—
495C24—24no—
496C24—22no—
497C24—42no—
498C24—42no—
499C24—42no—
500C24—42no—
501C24—42no—
502C24—44no—
503C24—82no—
504C24—82no—
505C24#12014yes—
506C24C22×D411yescharacteristic
507C24C22×D411yescharacteristic
508C24C22×D412yes—
509C24C22×D411yescharacteristic
510C2×Q8—28no—
511C2×Q8—28no—
512C2×Q8—24no—
513C2×Q8—24no—
514C2×Q8—22no—
515C2×Q8—22no—
516C2×Q8—24no—
517C2×Q8—24no—
518C2×Q8—24no—
519C2×Q8—24no—
520C2×Q8—44no—
521C2×Q8—44no—
522C2×Q8—48no—
523C2×Q8—84no—
524C2×Q8—82no—
525C2×Q8—82no—
526C2×Q8—84no—
527C2×Q8—82no—
528C2×Q8—82no—
529C2×Q8—84no—
530C2×Q8—84no—
531C2×Q8—84no—
532C2×Q8—88no—
533C2×Q8C22×D414yes—
534C2×Q8C22×D414yes—
535C2×D4—232no—
536C2×D4—24no—
537C2×D4—24no—
538C2×D4—24no—
539C2×D4—24no—
540C2×D4—24no—
541C2×D4—22no—
542C2×D4—22no—
543C2×D4—24no—
544C2×D4—24no—
545C2×D4—44no—
546C2×D4—44no—
547C2×D4—44no—
548C2×D4—44no—
549C2×D4—44no—
550C2×D4—44no—
551C2×D4—48no—
552C2×D4—42no—
553C2×D4—84no—
554C2×D4—82no—
555C2×D4—82no—
556C2×D4—82no—
557C2×D4—84no—
558C2×D4—84no—
559C2×D4—816no—
560C2×D4#13718yes—
561C22×C4—22no—
562C22×C4—24no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—28no—
574C22×C4—28no—
575C22×C4—22no—
576C22×C4—24no—
577C22×C4—24no—
578C22×C4—24no—
579C22×C4—24no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—24no—
584C22×C4—24no—
585C22×C4—24no—
586C22×C4—24no—
587C22×C4—22no—
588C22×C4—44no—
589C22×C4—44no—
590C22×C4—48no—
591C22×C4—42no—
592C22×C4—42no—
593C22×C4—42no—
594C22×C4—42no—
595C22×C4—44no—
596C22×C4—42no—
597C22×C4—42no—
598C22×C4—82no—
599C22×C4—82no—
600C22×C4—84no—
601C22×C4—82no—
602C22×C4—82no—
603C22×C4—84no—
604C22×C4—82no—
605C22×C4—82no—
606C22×C4—82no—
607C22×C4—84no—
608C22×C4#12014yes—
609C22×C4#12014yes—
610C22×C4#12014yes—
611C22×C4C22×D412yes—
612C22×C4C22×D412yes—
613C22×C4C22×D411yescharacteristic
614C22×C4C22×D411yescharacteristic
615C22×C4C22×D411yescharacteristic
616C22×C4C22×D412yes—
617C22×C4C22×D412yes—
618C22×C4C22×D412yes—
619C22×C4C22×D412yes—
620C22×C4C22×D412yes—
621C22×C4C22×D412yes—
622C22×C4C22×D412yes—
623C22×C4C2511yescharacteristic
624SD16—416no—
625SD16—88no—
626M16—48no—
627M16—48no—
628M16—84no—
629C2×C8—28no—
630C2×C8—22no—
631C2×C8—22no—
632C2×C8—24no—
633C2×C8—22no—
634C2×C8—24no—
635C2×C8—22no—
636C2×C8—22no—
637C2×C8—24no—
638C2×C8—44no—
639C2×C8H(5,𝔽2)14yes—
640C4⋊C4—28no—
641C4⋊C4—28no—
642C4⋊C4—28no—
643C4⋊C4—28no—
644C4⋊C4—28no—
645C4⋊C4—28no—
646C4⋊C4—28no—
647C4⋊C4—28no—
648C4⋊C4—28no—
649C4⋊C4—28no—
650C4⋊C4—28no—
651C4⋊C4—28no—
652C4⋊C4—24no—
653C4⋊C4—24no—
654C4⋊C4—24no—
655C4⋊C4—24no—
656C4⋊C4—22no—
657C4⋊C4—22no—
658C4⋊C4—22no—
659C4⋊C4—22no—
660C4⋊C4—24no—
661C4⋊C4—24no—
662C4⋊C4—42no—
663C4⋊C4—84no—
664C4⋊C4C22×D414yes—
665C4⋊C4C22×D414yes—
666C22⋊C4—28no—
667C22⋊C4—28no—
668C22⋊C4—28no—
669C22⋊C4—28no—
670C22⋊C4—28no—
671C22⋊C4—28no—
672C22⋊C4—24no—
673C22⋊C4—24no—
674C22⋊C4—24no—
675C22⋊C4—24no—
676C22⋊C4—44no—
677C22⋊C4—44no—
678C22⋊C4—44no—
679C22⋊C4—44no—
680C22⋊C4—48no—
681C22⋊C4—84no—
682C22⋊C4—84no—
683C22⋊C4—82no—
684C22⋊C4—84no—
685C42—28no—
686C42—28no—
687C42—24no—
688C42—22no—
689C42—22no—
690C42—82no—
691C23—22no—
692C23—22no—
693C23—28no—
694C23—22no—
695C23—24no—
696C23—22no—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—24no—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—28no—
705C23—44no—
706C23—44no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23—44no—
711C23—44no—
712C23—82no—
713C23—88no—
714C23—88no—
715C23—82no—
716C23—84no—
717C23—84no—
718C23—84no—
719C23—168no—
720C23C2×#12012yes—
721C23C2×#12012yes—
722C23C2×#12012yes—
723C23C2×#13714yes—
724C23C2×#13714yes—
725C23C23×D411yescharacteristic
726Q8—24no—
727Q8—24no—
728Q8—28no—
729Q8—42no—
730Q8—42no—
731Q8—44no—
732Q8—84no—
733Q8—84no—
734Q8—88no—
735Q8—88no—
736D4—216no—
737D4—216no—
738D4—42no—
739D4—42no—
740D4—44no—
741D4—84no—
742D4—88no—
743D4—88no—
744D4—168no—
745C2×C4—28no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—24no—
758C2×C4—24no—
759C2×C4—24no—
760C2×C4—24no—
761C2×C4—22no—
762C2×C4—24no—
763C2×C4—24no—
764C2×C4—24no—
765C2×C4—24no—
766C2×C4—22no—
767C2×C4—24no—
768C2×C4—44no—
769C2×C4—44no—
770C2×C4—44no—
771C2×C4—44no—
772C2×C4—44no—
773C2×C4—44no—
774C2×C4—44no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—44no—
778C2×C4—44no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—44no—
783C2×C4—44no—
784C2×C4—84no—
785C2×C4—82no—
786C2×C4—82no—
787C2×C4—84no—
788C2×C4—84no—
789C2×C4—84no—
790C2×C4—84no—
791C2×C4—88no—
792C2×C4—88no—
793C2×C4—84no—
794C2×C4C2×#12012yes—
795C2×C4C2×#12012yes—
796C2×C4C2×#12012yes—
797C2×C4C2×#13714yes—
798C2×C4C23×D411yescharacteristic
799C2×C4C23×D411yescharacteristic
800C2×C4C2×H(5,𝔽2)12yes—
801C2×C4#58512yes—
802C8—24no—
803C8—42no—
804C8—44no—
805C22—22no—
806C22—28no—
807C22—22no—
808C22—22no—
809C22—22no—
810C22—28no—
811C22—22no—
812C22—22no—
813C22—24no—
814C22—22no—
815C22—22no—
816C22—42no—
817C22—44no—
818C22—44no—
819C22—44no—
820C22—42no—
821C22—88no—
822C22—88no—
823C22—82no—
824C22—84no—
825C22—84no—
826C22—82no—
827C22—82no—
828C22—168no—
829C22#300414yes—
830C22C22×#12011yescharacteristic
831C22#349612yes—
832C22C22×#13712yes—
833C22#358512yes—
834C4—22no—
835C4—22no—
836C4—22no—
837C4—24no—
838C4—42no—
839C4—44no—
840C4—44no—
841C4—42no—
842C4—44no—
843C4—44no—
844C4—84no—
845C4—82no—
846C4#348411yescharacteristic
847C4#348511yescharacteristic
848C4#349612yes—
849C2—24no—
850C2—42no—
851C2—44no—
852C2—42no—
853C2—162no—
854C2#3534711yescharacteristic
855C2C2×#300411yescharacteristic
856C2#6036911yescharacteristic
857C2#6229614yes—
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#35076C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ 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×#3501C2semidirect
2. C2×#3193C2semidirect
3. C22×#468C2semidirect
5. #25559C2semidirect
6. #25503C2semidirect
7. #24445C2semidirect
8. #24387C2semidirect
9. #24098C2semidirect
10. #24042C2semidirect
11. #23969C2semidirect
12. #23855C2semidirect
13. #21768C2semidirect
14. #20972C2semidirect
15. #20898C2semidirect
16. C23×SD16C22semidirect
23. C2×#554C22semidirect
25. C2×D4×Q8C22semidirect
29. C2×#533C22semidirect
32. C22×C22⋊Q8C22semidirect
37. C2×#484C22semidirect
38. C2×#480C22semidirect
42. C2×#468C22semidirect
43. C2×#448C22semidirect
44. C2×#448C22semidirect
45. C2×#450C22semidirect
46. C22×#107C22semidirect
47. C2×#419C22semidirect
48. C22×#103C22semidirect
49. C22×#102C22semidirect
51. C2×#407C22semidirect
64. #2057C22semidirect
65. #2043C22semidirect
66. #2036C22semidirect
67. #2036C22semidirect
68. #2023C22semidirect
69. #2013C22semidirect
70. #2000C22semidirect
71. #2000C22semidirect
72. #1894C22semidirect
73. #1894C22semidirect
74. #1892C22semidirect
75. #1892C22semidirect
76. #1880C22semidirect
77. #1880C22semidirect
78. #1874C22semidirect
79. #1873C22semidirect
80. #1870C22semidirect
83. #1863C22semidirect
84. #1863C22semidirect
85. #1852C22semidirect
86. #1824C22semidirect
87. #1787C22semidirect
88. #1787C22semidirect
89. #1736C22semidirect
90. #1728C22semidirect
152. C2×C22⋊Q8D4semidirect
153. C2×C22⋊Q8D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35012
C2×#31932
C22×#4682
#350762
#255592
#255032
#244452
#243872
#240982
#240422
#239692
#238552
#217682
#209722
#208982