Finite Group Databasebeta

← #6440565

Subgroups — #6440565

Order 512.

3759 conjugacy classes of subgroups.

The subgroup lattice has 1215 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3092C211yesmaximal, characteristic, complemented
2C22×#407C211yesmaximal, characteristic, complemented
3#36614C211yesmaximal, characteristic
4C22×#380C211yesmaximal, characteristic, complemented
5#24559C212yesmaximal, complemented
6#24558C212yesmaximal, complemented
7#24557C212yesmaximal, complemented
8#24556C212yesmaximal, complemented
9#24553C212yesmaximal, complemented
10#24552C212yesmaximal, complemented
11#24551C212yesmaximal, complemented
12#24550C212yesmaximal, complemented
13#23642C212yesmaximal, complemented
14#23482C212yesmaximal, complemented
15#20971C212yesmaximal, complemented
16#20909C211yesmaximal, characteristic, complemented
17#20844C211yesmaximal, characteristic, complemented
18#20700C211yesmaximal, characteristic, complemented
19#20661C212yesmaximal, complemented
20C25×C4C2211yescharacteristic
21C23×M16C2212yes—
22C2×#525C2211yescharacteristic
23C2×#525C2211yescharacteristic
24C2×#525C2211yescharacteristic
25C23×C4⋊C4C2211yescharacteristic
26C23×C4⋊C4C2211yescharacteristic
27C23×C22⋊C4—21no—
28#3092—28no—
29C2×#484C2212yescomplemented
30C2×#481C2212yescomplemented
31C2×#483C2212yescomplemented
32C2×#480C2212yescomplemented
33C2×#428C2212yescomplemented
34C2×#428C2212yescomplemented
35C2×#417C2212yescomplemented
36C2×#417C2212yescomplemented
37C2×#407—28no—
38C2×#407C2212yes—
39C2×#407C2211yescharacteristic
40C2×#407C2212yes—
41C2×#407C2212yes—
42C2×#407C2211yescharacteristic
43C22×C22⋊C8C2212yes—
44C22×C22⋊C8C2212yes—
45#2849—21no—
46#2849—21no—
47#2849—21no—
48#2848C2211yescharacteristic
49#2848C2211yescharacteristic
50#2848C2211yescharacteristic
51#2848C2211yescharacteristic
52#2847C2211yescharacteristic
53#2847C2211yescharacteristic
54#2847C2211yescharacteristic
55#2847C2211yescharacteristic
56#2846—21no—
57C4×#120—21no—
58C4×#120—21no—
59C4×#120—21no—
60C4×#120—21no—
61#2280C2211yescharacteristic
62#2280C2211yescharacteristic
63#2280C2211yescharacteristic
64C2×#380—21no—
65C2×#380—21no—
66C2×#380—21no—
67C2×#380—21no—
68C2×#380—21no—
69C2×#380—21no—
70C2×#380C2212yes—
71C2×#380C2212yes—
72C2×#380C2212yes—
73C2×#380C2212yes—
74C2×#380C2212yes—
75C2×#380C2212yes—
76C22×#95—21no—
77#2077C2214yescomplemented
78#2077C2214yescomplemented
79#2076C2214yescomplemented
80#2075C2214yescomplemented
81#2036C2214yescomplemented
82#2035C2214yescomplemented
83#2034C2214yescomplemented
84#2033C2214yescomplemented
85#1895C2214yescomplemented
86#1894C2214yescomplemented
87#1893C2214yescomplemented
88#1892C2214yescomplemented
89#1874C2212yescomplemented
90#1874C2212yescomplemented
91#1872C2212yescomplemented
92#1872C2212yescomplemented
93#1853C2212yescomplemented
94#1853C2212yescomplemented
95#1852C2212yescomplemented
96#1852C2212yescomplemented
97#1824C2212yescomplemented
98#1824C2212yescomplemented
99#1823C2212yescomplemented
100#1823C2212yescomplemented
101#1809C2214yescomplemented
102#1809C2214yescomplemented
103#1808C2214yescomplemented
104#1807C2214yescomplemented
105#1736C2212yescomplemented
106#1736C2212yescomplemented
107#1736C2212yescomplemented
108#1736C2212yescomplemented
109C26D411yescharacteristic
110C22×#41C2311yescharacteristic
111C24×C4—24no—
112C24×C4—24no—
113C24×C4—28no—
114C24×C4—21no—
115C24×C4—21no—
116C24×C4—44no—
117C24×C4D411yescharacteristic
118C24×C4D411yescharacteristic
119C24×C4D411yescharacteristic
120C24×C4D411yescharacteristic
121C24×C4D411yescharacteristic
122C24×C4D411yescharacteristic
123C24×C4D411yescharacteristic
124C24×C4C2311yescharacteristic
125C24×C4C2311yescharacteristic
126C24×C4C2311yescharacteristic
127C24×C4C2311yescharacteristic
128C24×C4C2311yescharacteristic
129C24×C4C2311yescharacteristic
130C24×C4C2311yescharacteristic
131C22×M16—28no—
132C22×M16—28no—
133C22×M16—44no—
134C22×M16C2312yes—
135C22×M16C2314yes—
136C22×M16C2312yes—
137C23×C8C2314yes—
138#525—24no—
139#525—24no—
140#525—28no—
141#525—44no—
142C2×#123—21no—
143C2×#123—21no—
144C2×#123—21no—
145C2×C22⋊Q8C2311yescharacteristic
146C2×C22⋊Q8C2311yescharacteristic
147C2×C22⋊Q8C2311yescharacteristic
148C2×C22⋊Q8C2311yescharacteristic
149C2×C22⋊Q8C2311yescharacteristic
150C2×C22⋊Q8C2311yescharacteristic
151C2×#121C2311yescharacteristic
152C2×#121C2311yescharacteristic
153C2×#121C2311yescharacteristic
154C2×#121C2311yescharacteristic
155C2×#121C2311yescharacteristic
156C2×#121C2311yescharacteristic
157C2×#120—21no—
158C2×#120—21no—
159C2×#120—21no—
160C2×#120—21no—
161C2×#120—21no—
162C2×#120—21no—
163C2×#120—21no—
164C2×C4×D4—21no—
165C2×C4×D4—21no—
166C2×C4×D4—21no—
167C2×C4×D4—21no—
168C2×C4×D4—21no—
169C2×C4×D4—21no—
170C2×#117C2311yescharacteristic
171C2×#117C2311yescharacteristic
172C2×#117C2311yescharacteristic
173C22×C4⋊C4—24no—
174C22×C4⋊C4—24no—
175C22×C4⋊C4—21no—
176C22×C4⋊C4—21no—
177C22×C4⋊C4—21no—
178C22×C4⋊C4—21no—
179C22×C4⋊C4—21no—
180C22×C4⋊C4—21no—
181C22×C4⋊C4—44no—
182C22×C4⋊C4C2312yes—
183C22×C4⋊C4C2312yes—
184C22×C4⋊C4C2312yes—
185C22×C4⋊C4C2312yes—
186C22×C4⋊C4C2312yes—
187C22×C4⋊C4C2312yes—
188C22×C22⋊C4—22no—
189C22×C22⋊C4—22no—
190C22×C22⋊C4—22no—
191C22×C22⋊C4—22no—
192C22×C22⋊C4—22no—
193C22×C22⋊C4—22no—
194C22×C22⋊C4—48no—
195#484—28no—
196#483—28no—
197#481—28no—
198#480—28no—
199#428—28no—
200#428—44no—
201C2×#107C2314yescomplemented
202C2×#107C2314yescomplemented
203C2×#106C2314yescomplemented
204C2×#106C2314yescomplemented
205#417—28no—
206#417—44no—
207C2×#103C2314yescomplemented
208C2×#103C2314yescomplemented
209C2×#102C2314yescomplemented
210C2×#102C2314yescomplemented
211#407—24no—
212#407—28no—
213#407—28no—
214#407—28no—
215#407D418yescomplemented
216C2×C22⋊C8—28no—
217C2×C22⋊C8—28no—
218C2×C22⋊C8C2314yes—
219C2×C22⋊C8C2314yes—
220C2×C22⋊C8C2312yes—
221C2×C22⋊C8C2312yes—
222C2×C22⋊C8C2312yes—
223C2×C22⋊C8C2312yes—
224#386—21no—
225#386—21no—
226#386—21no—
227#386—21no—
228#386—21no—
229#386—21no—
230#386—21no—
231#386—21no—
232#386—21no—
233#386—21no—
234#386—21no—
235#386—21no—
236#385—21no—
237#385—21no—
238#385—21no—
239#385—21no—
240#385—21no—
241#385—21no—
242#385—21no—
243#385—21no—
244#385—21no—
245#385—21no—
246#385—21no—
247#385—21no—
248#381—21no—
249#381—21no—
250#381—21no—
251#380—22no—
252#380—22no—
253#380—22no—
254#380—22no—
255#380—22no—
256#380—22no—
257#380—22no—
258#380—22no—
259#380—22no—
260#380—22no—
261#380—22no—
262#380—22no—
263#380C2311yescharacteristic
264#380C2314yes—
265#380C2311yescharacteristic
266#380C2311yescharacteristic
267#380C2311yescharacteristic
268#380C2314yes—
269#380C2311yescharacteristic
270#380C2314yes—
271#380C2311yescharacteristic
272#380C2314yes—
273#380C2311yescharacteristic
274#380C2311yescharacteristic
275#380C2311yescharacteristic
276#380C2311yescharacteristic
277#380C2311yescharacteristic
278#380C2311yescharacteristic
279#379—21no—
280#379—21no—
281#379—21no—
282#379—21no—
283#379—21no—
284#379—21no—
285#379—21no—
286C4×C22⋊C4—21no—
287C4×C22⋊C4—21no—
288C4×C22⋊C4—21no—
289C4×C22⋊C4—21no—
290C4×C22⋊C4—21no—
291C4×C22⋊C4—21no—
292C2×#95—22no—
293C2×#95—22no—
294C2×#95—22no—
295C2×#95—22no—
296C2×#95—22no—
297C2×#95—22no—
298#340C2314yescomplemented
299#340C2314yescomplemented
300#340C2314yescomplemented
301#340C2314yescomplemented
302#340C2314yescomplemented
303#340C2314yescomplemented
304#340C2314yescomplemented
305#340C2314yescomplemented
306C25—24no—
307C25—24no—
308C25—24no—
309C25—24no—
310C25—42no—
311C25—42no—
312C25—42no—
313C25C2×D411yescharacteristic
314C25C2×D411yescharacteristic
315C25C2×D411yescharacteristic
316C25C2×D411yescharacteristic
317C25C2×D411yescharacteristic
318C25C2×D411yescharacteristic
319C25C2×D411yescharacteristic
320C2×#41—22no—
321C2×#41—22no—
322C2×#41—24no—
323C2×#41—24no—
324C22×Q8C2411yescharacteristic
325C22×D4—21no—
326C22×D4—21no—
327C22×D4—21no—
328C22×D4—21no—
329C22×D4—21no—
330C22×D4—21no—
331C22×D4—21no—
332C22×D4C2411yescharacteristic
333C23×C4—22no—
334C23×C4—22no—
335C23×C4—24no—
336C23×C4—24no—
337C23×C4—24no—
338C23×C4—24no—
339C23×C4—24no—
340C23×C4—24no—
341C23×C4—24no—
342C23×C4—24no—
343C23×C4—24no—
344C23×C4—24no—
345C23×C4—24no—
346C23×C4—24no—
347C23×C4—24no—
348C23×C4—24no—
349C23×C4—24no—
350C23×C4—24no—
351C23×C4—24no—
352C23×C4—22no—
353C23×C4—22no—
354C23×C4—22no—
355C23×C4—22no—
356C23×C4—22no—
357C23×C4—22no—
358C23×C4—22no—
359C23×C4—22no—
360C23×C4—22no—
361C23×C4—24no—
362C23×C4—24no—
363C23×C4—24no—
364C23×C4—24no—
365C23×C4—22no—
366C23×C4—24no—
367C23×C4—24no—
368C23×C4—22no—
369C23×C4—22no—
370C23×C4—22no—
371C23×C4—22no—
372C23×C4—22no—
373C23×C4—22no—
374C23×C4—21no—
375C23×C4—42no—
376C23×C4—42no—
377C23×C4—42no—
378C23×C4—42no—
379C23×C4—42no—
380C23×C4—42no—
381C23×C4—42no—
382C23×C4—42no—
383C23×C4—42no—
384C23×C4—42no—
385C23×C4—42no—
386C23×C4—432no—
387C23×C4—432no—
388C23×C4—44no—
389C23×C4—44no—
390C23×C4—44no—
391C23×C4—44no—
392C23×C4—44no—
393C23×C4—44no—
394C23×C4C2×D411yescharacteristic
395C23×C4C2×D411yescharacteristic
396C23×C4C2×D411yescharacteristic
397C23×C4C2×D411yescharacteristic
398C23×C4C2×D411yescharacteristic
399C23×C4C2×D411yescharacteristic
400C23×C4C2×D411yescharacteristic
401C23×C4C2×D411yescharacteristic
402C23×C4C2×D411yescharacteristic
403C23×C4C2×D411yescharacteristic
404C23×C4C2×D411yescharacteristic
405C23×C4C2×D411yescharacteristic
406C23×C4C2×D411yescharacteristic
407C23×C4C2×D411yescharacteristic
408C23×C4C2×D411yescharacteristic
409C23×C4C2×D411yescharacteristic
410C23×C4C2×D411yescharacteristic
411C23×C4C2×D411yescharacteristic
412C23×C4C2×D414yes—
413C23×C4C2×D411yescharacteristic
414C23×C4C2×D411yescharacteristic
415C23×C4C2×D411yescharacteristic
416C23×C4#4114yes—
417C23×C4#4118yes—
418C23×C4C2411yescharacteristic
419C23×C4C2411yescharacteristic
420C23×C4C2411yescharacteristic
421C23×C4C2411yescharacteristic
422C23×C4C2411yescharacteristic
423C23×C4C2411yescharacteristic
424C23×C4C2411yescharacteristic
425C2×M16—24no—
426C2×M16—24no—
427C2×M16—24no—
428C2×M16—28no—
429C2×M16—24no—
430C2×M16—24no—
431C2×M16—28no—
432C2×M16—44no—
433C2×M16—432no—
434C2×M16C2×D418yes—
435C22×C8—28no—
436C22×C8—28no—
437C22×C8—44no—
438C22×C8C2414yes—
439C22×C8C2414yes—
440#123—44no—
441#123—44no—
442#123—44no—
443C22⋊Q8—22no—
444C22⋊Q8—22no—
445C22⋊Q8—22no—
446C22⋊Q8—22no—
447C22⋊Q8—24no—
448C22⋊Q8—24no—
449C22⋊Q8—42no—
450C22⋊Q8—42no—
451#121—22no—
452#121—22no—
453#121—22no—
454#121—22no—
455#121—24no—
456#121—24no—
457#121—42no—
458#121—42no—
459#120—44no—
460#120—44no—
461#120—44no—
462#120—44no—
463#120—44no—
464#120—44no—
465#120—44no—
466C4×D4—44no—
467C4×D4—44no—
468C4×D4—44no—
469C4×D4—44no—
470C4×D4—44no—
471C4×D4—44no—
472#117—22no—
473#117—22no—
474#117—24no—
475#117—24no—
476C2×C4⋊C4—24no—
477C2×C4⋊C4—24no—
478C2×C4⋊C4—24no—
479C2×C4⋊C4—24no—
480C2×C4⋊C4—24no—
481C2×C4⋊C4—24no—
482C2×C4⋊C4—24no—
483C2×C4⋊C4—24no—
484C2×C4⋊C4—22no—
485C2×C4⋊C4—22no—
486C2×C4⋊C4—22no—
487C2×C4⋊C4—22no—
488C2×C4⋊C4—22no—
489C2×C4⋊C4—22no—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—44no—
497C2×C4⋊C4—44no—
498C2×C4⋊C4—44no—
499C2×C4⋊C4—44no—
500C2×C4⋊C4—44no—
501C2×C4⋊C4—44no—
502C2×C4⋊C4—44no—
503C2×C4⋊C4—44no—
504C2×C4⋊C4C2414yes—
505C2×C4⋊C4C2414yes—
506C2×C4⋊C4C2411yescharacteristic
507C2×C4⋊C4C2411yescharacteristic
508C2×C4⋊C4C2411yescharacteristic
509C2×C4⋊C4C2411yescharacteristic
510C2×C4⋊C4C2411yescharacteristic
511C2×C4⋊C4C2411yescharacteristic
512C2×C22⋊C4—24no—
513C2×C22⋊C4—24no—
514C2×C22⋊C4—24no—
515C2×C22⋊C4—24no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4—21no—
520C2×C22⋊C4—21no—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4—21no—
540C2×C22⋊C4—21no—
541C2×C22⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C22⋊C4—48no—
544C2×C22⋊C4—48no—
545C2×C22⋊C4—48no—
546C2×C22⋊C4—48no—
547C2×C22⋊C4—48no—
548C2×C22⋊C4—48no—
549C2×C42—21no—
550C2×C42—21no—
551C2×C42—21no—
552#107—28no—
553#107—44no—
554#106—28no—
555#106—44no—
556#103—28no—
557#103—44no—
558#102—28no—
559#102—44no—
560C22⋊C8—24no—
561C22⋊C8—24no—
562C22⋊C8—28no—
563C22⋊C8—28no—
564C22⋊C8C2×D418yes—
565C22⋊C8C2×D418yes—
566#95—24no—
567#95—24no—
568#95—24no—
569#95—24no—
570#95—21no—
571#95—21no—
572#95—21no—
573#95—21no—
574#95—21no—
575#95—21no—
576#95—21no—
577#95—21no—
578#95—21no—
579#95—21no—
580#95—21no—
581#95—21no—
582C24—22no—
583C24—22no—
584C24—22no—
585C24—22no—
586C24—22no—
587C24—22no—
588C24—232no—
589C24—22no—
590C24—22no—
591C24—22no—
592C24—22no—
593C24—22no—
594C24—22no—
595C24—22no—
596C24—22no—
597C24—22no—
598C24—22no—
599C24—22no—
600C24—22no—
601C24—22no—
602C24—22no—
603C24—22no—
604C24—22no—
605C24—22no—
606C24—22no—
607C24—22no—
608C24—22no—
609C24—22no—
610C24—22no—
611C24—22no—
612C24—22no—
613C24—22no—
614C24—22no—
615C24—22no—
616C24—21no—
617C24—41no—
618C24—41no—
619C24—41no—
620C24—41no—
621C24—41no—
622C24—41no—
623C24—41no—
624C24—41no—
625C24—41no—
626C24—41no—
627C24—41no—
628C24—41no—
629C24—416no—
630C24—416no—
631C24—416no—
632C24—416no—
633C24—416no—
634C24—416no—
635C24#12114yes—
636C24#12314yes—
637C24AGL(1,ℤ/8)14yes—
638C24#13714yes—
639C24C22×D411yescharacteristic
640C24C22×D411yescharacteristic
641C24C22×D411yescharacteristic
642C24C22×D411yescharacteristic
643C24C22×D411yescharacteristic
644C24C22×D411yescharacteristic
645C24C22×D411yescharacteristic
646#41—48no—
647#41—48no—
648C2×Q8—21no—
649C2×Q8—21no—
650C2×Q8—22no—
651C2×Q8—22no—
652C2×D4—21no—
653C2×D4—22no—
654C2×D4—21no—
655C2×D4—22no—
656C2×D4—42no—
657C2×D4—42no—
658C2×D4—42no—
659C2×D4—42no—
660C2×D4—42no—
661C2×D4—42no—
662C2×D4—42no—
663C2×D4—42no—
664C2×D4—42no—
665C2×D4—42no—
666C2×D4—42no—
667C2×D4—42no—
668C2×D4—42no—
669C2×D4—42no—
670C2×D4—42no—
671C2×D4—42no—
672C2×D4—42no—
673C2×D4—42no—
674C2×D4—42no—
675C2×D4—42no—
676C2×D4—42no—
677C22×C4—22no—
678C22×C4—22no—
679C22×C4—22no—
680C22×C4—22no—
681C22×C4—22no—
682C22×C4—22no—
683C22×C4—22no—
684C22×C4—22no—
685C22×C4—22no—
686C22×C4—22no—
687C22×C4—22no—
688C22×C4—22no—
689C22×C4—216no—
690C22×C4—216no—
691C22×C4—216no—
692C22×C4—216no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—22no—
698C22×C4—22no—
699C22×C4—22no—
700C22×C4—22no—
701C22×C4—22no—
702C22×C4—22no—
703C22×C4—22no—
704C22×C4—22no—
705C22×C4—22no—
706C22×C4—22no—
707C22×C4—22no—
708C22×C4—22no—
709C22×C4—22no—
710C22×C4—22no—
711C22×C4—22no—
712C22×C4—22no—
713C22×C4—22no—
714C22×C4—22no—
715C22×C4—22no—
716C22×C4—22no—
717C22×C4—22no—
718C22×C4—22no—
719C22×C4—22no—
720C22×C4—22no—
721C22×C4—22no—
722C22×C4—22no—
723C22×C4—22no—
724C22×C4—22no—
725C22×C4—22no—
726C22×C4—22no—
727C22×C4—22no—
728C22×C4—22no—
729C22×C4—22no—
730C22×C4—22no—
731C22×C4—22no—
732C22×C4—22no—
733C22×C4—22no—
734C22×C4—22no—
735C22×C4—22no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—22no—
741C22×C4—22no—
742C22×C4—22no—
743C22×C4—22no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—24no—
751C22×C4—24no—
752C22×C4—21no—
753C22×C4—41no—
754C22×C4—41no—
755C22×C4—41no—
756C22×C4—41no—
757C22×C4—41no—
758C22×C4—41no—
759C22×C4—41no—
760C22×C4—41no—
761C22×C4—41no—
762C22×C4—41no—
763C22×C4—41no—
764C22×C4—41no—
765C22×C4—416no—
766C22×C4—416no—
767C22×C4—416no—
768C22×C4—416no—
769C22×C4—416no—
770C22×C4—48no—
771C22×C4—48no—
772C22×C4—48no—
773C22×C4—48no—
774C22×C4—48no—
775C22×C4—48no—
776C22×C4—48no—
777C22×C4—48no—
778C22×C4—416no—
779C22×C4—416no—
780C22×C4—48no—
781C22×C4—48no—
782C22×C4—44no—
783C22×C4—44no—
784C22×C4—44no—
785C22×C4—44no—
786C22×C4—44no—
787C22×C4—44no—
788C22×C4—44no—
789C22×C4—44no—
790C22×C4—44no—
791C22×C4—44no—
792C22×C4—44no—
793C22×C4—44no—
794C22×C4—44no—
795C22×C4—44no—
796C22×C4—44no—
797C22×C4—44no—
798C22×C4—44no—
799C22×C4—44no—
800C22×C4—42no—
801C22×C4—42no—
802C22×C4—42no—
803C22×C4—816no—
804C22×C4—816no—
805C22×C4#12114yes—
806C22×C4#12114yes—
807C22×C4#12114yes—
808C22×C4#12314yes—
809C22×C4#12314yes—
810C22×C4#12314yes—
811C22×C4C22×D411yescharacteristic
812C22×C4C22×D411yescharacteristic
813C22×C4C22×D411yescharacteristic
814C22×C4C22×D411yescharacteristic
815C22×C4C22×D412yes—
816C22×C4C22×D412yes—
817C22×C4C22×D411yescharacteristic
818C22×C4C22×D411yescharacteristic
819C22×C4C22×D411yescharacteristic
820C22×C4C22×D412yes—
821C22×C4C2×#4112yes—
822C22×C4C2×#4112yes—
823C22×C4C2×#4114yes—
824C22×C4C2×#4114yes—
825C22×C4C2×#4112yes—
826C22×C4C2×#4114yes—
827C22×C4H(5,𝔽2)14yes—
828C22×C4C2511yescharacteristic
829M16—216no—
830M16—416no—
831M16—48no—
832C2×C8—24no—
833C2×C8—24no—
834C2×C8—24no—
835C2×C8—24no—
836C2×C8—24no—
837C2×C8—416no—
838C2×C8C22×D418yes—
839C4⋊C4—24no—
840C4⋊C4—21no—
841C4⋊C4—21no—
842C4⋊C4—24no—
843C4⋊C4—21no—
844C4⋊C4—21no—
845C4⋊C4—22no—
846C4⋊C4—22no—
847C4⋊C4—24no—
848C4⋊C4—22no—
849C4⋊C4—24no—
850C4⋊C4—22no—
851C4⋊C4—44no—
852C4⋊C4—44no—
853C4⋊C4—42no—
854C4⋊C4—42no—
855C4⋊C4—44no—
856C4⋊C4—44no—
857C4⋊C4—44no—
858C4⋊C4—42no—
859C4⋊C4—42no—
860C4⋊C4—42no—
861C4⋊C4—42no—
862C4⋊C4—44no—
863C22⋊C4—42no—
864C22⋊C4—42no—
865C22⋊C4—48no—
866C22⋊C4—48no—
867C22⋊C4—42no—
868C22⋊C4—42no—
869C22⋊C4—42no—
870C22⋊C4—42no—
871C22⋊C4—42no—
872C22⋊C4—42no—
873C22⋊C4—42no—
874C22⋊C4—42no—
875C22⋊C4—42no—
876C22⋊C4—42no—
877C22⋊C4—42no—
878C22⋊C4—42no—
879C22⋊C4—42no—
880C22⋊C4—48no—
881C22⋊C4—48no—
882C22⋊C4—42no—
883C22⋊C4—42no—
884C22⋊C4—42no—
885C22⋊C4—42no—
886C22⋊C4—42no—
887C22⋊C4—42no—
888C22⋊C4—42no—
889C22⋊C4—42no—
890C22⋊C4—42no—
891C22⋊C4—42no—
892C22⋊C4—42no—
893C22⋊C4—42no—
894C42—42no—
895C42—42no—
896C42—42no—
897C23—28no—
898C23—28no—
899C23—28no—
900C23—28no—
901C23—21no—
902C23—21no—
903C23—21no—
904C23—28no—
905C23—21no—
906C23—21no—
907C23—21no—
908C23—28no—
909C23—28no—
910C23—21no—
911C23—21no—
912C23—21no—
913C23—21no—
914C23—21no—
915C23—21no—
916C23—21no—
917C23—21no—
918C23—21no—
919C23—21no—
920C23—28no—
921C23—28no—
922C23—28no—
923C23—28no—
924C23—28no—
925C23—28no—
926C23—21no—
927C23—21no—
928C23—21no—
929C23—21no—
930C23—21no—
931C23—28no—
932C23—21no—
933C23—21no—
934C23—21no—
935C23—28no—
936C23—28no—
937C23—21no—
938C23—21no—
939C23—21no—
940C23—21no—
941C23—21no—
942C23—21no—
943C23—21no—
944C23—21no—
945C23—21no—
946C23—21no—
947C23—44no—
948C23—44no—
949C23—44no—
950C23—44no—
951C23—44no—
952C23—44no—
953C23—44no—
954C23—44no—
955C23—44no—
956C23—44no—
957C23—44no—
958C23—44no—
959C23—44no—
960C23—44no—
961C23—44no—
962C23—44no—
963C23—44no—
964C23—44no—
965C23—44no—
966C23—44no—
967C23—44no—
968C23—44no—
969C23—44no—
970C23—44no—
971C23—44no—
972C23—44no—
973C23—44no—
974C23—4128no—
975C23—44no—
976C23—44no—
977C23—44no—
978C23—44no—
979C23—44no—
980C23—44no—
981C23—41no—
982C23—41no—
983C23—41no—
984C23—41no—
985C23—41no—
986C23—41no—
987C23—41no—
988C23C2×#12112yes—
989C23C2×#12112yes—
990C23C2×#12112yes—
991C23C2×#12312yes—
992C23C2×#12312yes—
993C23C2×#12312yes—
994C23#53412yes—
995C23C2×AGL(1,ℤ/8)12yes—
996C23C2×AGL(1,ℤ/8)12yes—
997C23C2×AGL(1,ℤ/8)12yes—
998C23C2×#13712yes—
999C23C2×#13712yes—
1000C23C2×#13712yes—
1001C23#57512yes—
1002C23#57512yes—
1003C23C23×D411yescharacteristic
1004Q8—42no—
1005Q8—42no—
1006D4—42no—
1007D4—42no—
1008D4—84no—
1009D4—84no—
1010D4—84no—
1011D4—84no—
1012D4—84no—
1013D4—84no—
1014D4—84no—
1015C2×C4—21no—
1016C2×C4—21no—
1017C2×C4—21no—
1018C2×C4—21no—
1019C2×C4—28no—
1020C2×C4—28no—
1021C2×C4—21no—
1022C2×C4—21no—
1023C2×C4—21no—
1024C2×C4—21no—
1025C2×C4—28no—
1026C2×C4—28no—
1027C2×C4—28no—
1028C2×C4—28no—
1029C2×C4—24no—
1030C2×C4—24no—
1031C2×C4—24no—
1032C2×C4—24no—
1033C2×C4—24no—
1034C2×C4—24no—
1035C2×C4—24no—
1036C2×C4—24no—
1037C2×C4—21no—
1038C2×C4—21no—
1039C2×C4—21no—
1040C2×C4—21no—
1041C2×C4—21no—
1042C2×C4—21no—
1043C2×C4—44no—
1044C2×C4—44no—
1045C2×C4—44no—
1046C2×C4—44no—
1047C2×C4—44no—
1048C2×C4—44no—
1049C2×C4—44no—
1050C2×C4—44no—
1051C2×C4—44no—
1052C2×C4—44no—
1053C2×C4—44no—
1054C2×C4—44no—
1055C2×C4—44no—
1056C2×C4—44no—
1057C2×C4—44no—
1058C2×C4—42no—
1059C2×C4—42no—
1060C2×C4—42no—
1061C2×C4—42no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—44no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—44no—
1073C2×C4—44no—
1074C2×C4—44no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4—44no—
1088C2×C4—44no—
1089C2×C4—88no—
1090C2×C4—88no—
1091C2×C4—88no—
1092C2×C4—88no—
1093C2×C4—88no—
1094C2×C4—88no—
1095C2×C4—84no—
1096C2×C4C2×#12112yes—
1097C2×C4C2×#12112yes—
1098C2×C4C2×#12112yes—
1099C2×C4C2×#12312yes—
1100C2×C4C2×#12312yes—
1101C2×C4C2×#12312yes—
1102C2×C4#53412yes—
1103C2×C4#54618yes—
1104C2×C4#55118yes—
1105C2×C4C23×D411yescharacteristic
1106C2×C4C22×#4112yes—
1107C2×C4C22×#4111yescharacteristic
1108C2×C4C2×H(5,𝔽2)12yes—
1109C8—28no—
1110C8—44no—
1111C22—232no—
1112C22—22no—
1113C22—22no—
1114C22—22no—
1115C22—22no—
1116C22—22no—
1117C22—22no—
1118C22—22no—
1119C22—22no—
1120C22—22no—
1121C22—22no—
1122C22—22no—
1123C22—22no—
1124C22—22no—
1125C22—22no—
1126C22—22no—
1127C22—22no—
1128C22—22no—
1129C22—22no—
1130C22—22no—
1131C22—22no—
1132C22—22no—
1133C22—22no—
1134C22—22no—
1135C22—22no—
1136C22—22no—
1137C22—22no—
1138C22—22no—
1139C22—22no—
1140C22—22no—
1141C22—22no—
1142C22—22no—
1143C22—22no—
1144C22—22no—
1145C22—416no—
1146C22—416no—
1147C22—416no—
1148C22—416no—
1149C22—416no—
1150C22—416no—
1151C22—41no—
1152C22—41no—
1153C22—41no—
1154C22—41no—
1155C22—41no—
1156C22—41no—
1157C22—41no—
1158C22—41no—
1159C22—41no—
1160C22—41no—
1161C22—41no—
1162C22—41no—
1163C22—81no—
1164C22—81no—
1165C22—81no—
1166C22—81no—
1167C22—81no—
1168C22—81no—
1169C22—81no—
1170C22#241214yes—
1171C22#305514yes—
1172C22#305614yes—
1173C22#309214yescomplemented
1174C22C22×#12111yescharacteristic
1175C22C22×#12311yescharacteristic
1176C22C2×#53411yescharacteristic
1177C22C22×AGL(1,ℤ/8)11yescharacteristic
1178C22C22×#13711yescharacteristic
1179C22C2×#57511yescharacteristic
1180C22C2×#57511yescharacteristic
1181C4—22no—
1182C4—22no—
1183C4—22no—
1184C4—22no—
1185C4—41no—
1186C4—41no—
1187C4—84no—
1188C4—81no—
1189C4—81no—
1190C4—84no—
1191C4—81no—
1192C4—81no—
1193C4—81no—
1194C4—81no—
1195C4—81no—
1196C4#241214yes—
1197C4C2×#54612yes—
1198C4C2×#55112yes—
1199C2—24no—
1200C2—24no—
1201C2—24no—
1202C2—24no—
1203C2—42no—
1204C2—42no—
1205C2—42no—
1206C2—161no—
1207C2C2×#241211yescharacteristic
1208C2C2×#305511yescharacteristic
1209C2C2×#305611yescharacteristic
1210C2C2×#309211yescharacteristic
1211C2#6051111yescharacteristic
1212C2#6075011yescharacteristic
1213C2#6075111yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#36614C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C25×C4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3092C2semidirect
2. C22×#407C2semidirect
4. C22×#380C2semidirect
5. #24559C2semidirect
6. #24558C2semidirect
7. #24557C2semidirect
8. #24556C2semidirect
9. #24553C2semidirect
10. #24552C2semidirect
11. #24551C2semidirect
12. #24550C2semidirect
13. #23642C2semidirect
14. #23482C2semidirect
15. #20971C2semidirect
16. #20909C2semidirect
17. #20844C2semidirect
18. #20700C2semidirect
19. #20661C2semidirect
29. C2×#484C22semidirect
30. C2×#481C22semidirect
31. C2×#483C22semidirect
32. C2×#480C22semidirect
33. C2×#428C22semidirect
34. C2×#428C22semidirect
35. C2×#417C22semidirect
36. C2×#417C22semidirect
77. #2077C22semidirect
78. #2077C22semidirect
79. #2076C22semidirect
80. #2075C22semidirect
81. #2036C22semidirect
82. #2035C22semidirect
83. #2034C22semidirect
84. #2033C22semidirect
85. #1895C22semidirect
86. #1894C22semidirect
87. #1893C22semidirect
88. #1892C22semidirect
89. #1874C22semidirect
90. #1874C22semidirect
91. #1872C22semidirect
92. #1872C22semidirect
93. #1853C22semidirect
94. #1853C22semidirect
95. #1852C22semidirect
96. #1852C22semidirect
97. #1824C22semidirect
98. #1824C22semidirect
99. #1823C22semidirect
100. #1823C22semidirect
101. #1809C22semidirect
102. #1809C22semidirect
103. #1808C22semidirect
104. #1807C22semidirect
105. #1736C22semidirect
106. #1736C22semidirect
107. #1736C22semidirect
108. #1736C22semidirect
201. C2×#107C23semidirect
202. C2×#107C23semidirect
203. C2×#106C23semidirect
204. C2×#106C23semidirect
207. C2×#103C23semidirect
208. C2×#103C23semidirect
209. C2×#102C23semidirect
210. C2×#102C23semidirect
215. #407D4semidirect
298. #340C23semidirect
299. #340C23semidirect
300. #340C23semidirect
301. #340C23semidirect
302. #340C23semidirect
303. #340C23semidirect
304. #340C23semidirect
305. #340C23semidirect
1173. C22#3092semidirect

Maximal subgroups

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

subgroupindex
C2×#30922
C22×#4072
#366142
C22×#3802
#245592
#245582
#245572
#245562
#245532
#245522
#245512
#245502
#236422
#234822
#209712
#209092
#208442
#207002
#206612