Finite Group Databasebeta

← #6660380

Subgroups — #6660380

Order 512.

3056 conjugacy classes of subgroups.

The subgroup lattice has 1071 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2848C211yesmaximal, characteristic
2C2×#2848C211yesmaximal, characteristic
3#32711C214yesmaximal, complemented
4#29894C212yesmaximal, complemented
5#29893C212yesmaximal, complemented
6#29743C214yesmaximal, complemented
7#29599C212yesmaximal, complemented
8#29597C212yesmaximal, complemented
9#27601C211yesmaximal, characteristic, complemented
10#24559C212yesmaximal, complemented
11#24556C212yesmaximal, complemented
12#24386C212yesmaximal, complemented
13#24386C212yesmaximal, complemented
14#24006C211yesmaximal, characteristic, complemented
15#24003C211yesmaximal, characteristic, complemented
16#23921C211yesmaximal, characteristic, complemented
17#20579C211yesmaximal, characteristic
18C25×C4C2211yescharacteristic
19C22×C22⋊Q8C2211yescharacteristic
20C22×C22⋊Q8C2211yescharacteristic
21C22×C22⋊Q8C2211yescharacteristic
22C22×C22⋊Q8C2211yescharacteristic
23C22×C22⋊Q8C2211yescharacteristic
24C22×C22⋊Q8C2211yescharacteristic
25C2×#484C2212yescomplemented
26C2×#483C2212yescomplemented
27C2×#470C2214yescomplemented
28C2×#451C2212yescomplemented
29C2×#451C2212yescomplemented
30C2×#407C2212yes—
31C2×#407C2212yes—
32C2×#407C2212yes—
33#2848—21no—
34#2848—21no—
35#2848—21no—
36#2848—21no—
37#2848—21no—
38#2848—21no—
39#2848—21no—
40#2848—21no—
41#2848C2212yes—
42#2848C2212yes—
43#2848C2212yes—
44#2848C2212yes—
45#2848C2212yes—
46#2848C2212yes—
47#2848C2212yes—
48#2848C2212yes—
49C2×#385—21no—
50C2×#385—21no—
51C2×#385—21no—
52C2×#385—21no—
53C2×#385—21no—
54C2×#385—21no—
55C2×#380C2211yescharacteristic
56C2×#380C2211yescharacteristic
57C2×#380C2211yescharacteristic
58C2×#380C2211yescharacteristic
59C2×#380C2211yescharacteristic
60C2×#380C2211yescharacteristic
61C2×#379—21no—
62C2×#379—21no—
63#2077C2214yescomplemented
64#2077C2214yescomplemented
65#2077C2214yescomplemented
66#2075C2214yescomplemented
67#2036C2214yescomplemented
68#2036C2214yescomplemented
69#2036C2214yescomplemented
70#2035C2214yescomplemented
71#2035C2214yescomplemented
72#2035C2214yescomplemented
73#2035C2214yescomplemented
74#2035C2214yescomplemented
75#2001C2214yescomplemented
76#2001C2214yescomplemented
77#2001C2214yescomplemented
78#2001C2214yescomplemented
79#1894C2214yescomplemented
80#1894C2214yescomplemented
81#1872C2212yescomplemented
82#1872C2212yescomplemented
83#1872C2212yescomplemented
84#1872C2212yescomplemented
85#1853C2212yescomplemented
86#1853C2212yescomplemented
87#1853C2212yescomplemented
88#1852C2212yescomplemented
89#1824C2212yescomplemented
90#1823C2212yescomplemented
91#1809C2214yescomplemented
92#1787C2212yescomplemented
93#1787C2212yescomplemented
94#1779C2211yescharacteristic
95#1779C2212yes—
96#1779C2212yes—
97#1779C2211yescharacteristic
98#1779C2212yes—
99C26D411yescharacteristic
100C23×Q8C2311yescharacteristic
101C23×Q8C2311yescharacteristic
102C24×C4—44no—
103C24×C4—44no—
104C24×C4—44no—
105C24×C4D411yescharacteristic
106C24×C4D411yescharacteristic
107C24×C4D411yescharacteristic
108C24×C4D411yescharacteristic
109C24×C4D411yescharacteristic
110C24×C4D411yescharacteristic
111C24×C4D411yescharacteristic
112C24×C4C2311yescharacteristic
113C24×C4C2311yescharacteristic
114C24×C4C2311yescharacteristic
115C24×C4C2311yescharacteristic
116C24×C4C2311yescharacteristic
117C24×C4C2311yescharacteristic
118C24×C4C2311yescharacteristic
119C22×Q16C2314yescomplemented
120C22×M16C2314yes—
121C2×C22⋊Q8—21no—
122C2×C22⋊Q8—21no—
123C2×C22⋊Q8—21no—
124C2×C22⋊Q8—21no—
125C2×C22⋊Q8—21no—
126C2×C22⋊Q8—21no—
127C2×C22⋊Q8—21no—
128C2×C22⋊Q8—21no—
129C2×C22⋊Q8—21no—
130C2×C22⋊Q8—21no—
131C2×C22⋊Q8—21no—
132C2×C22⋊Q8—21no—
133C2×C22⋊Q8—44no—
134C2×C22⋊Q8—44no—
135C2×C22⋊Q8—44no—
136C2×C22⋊Q8—44no—
137C2×C22⋊Q8—44no—
138C2×C22⋊Q8—44no—
139C2×C22⋊Q8C2312yes—
140C2×C22⋊Q8C2312yes—
141C2×C22⋊Q8C2312yes—
142C2×C22⋊Q8C2312yes—
143C2×C22⋊Q8C2312yes—
144C2×C22⋊Q8C2312yes—
145C2×C22⋊Q8C2312yes—
146C2×C22⋊Q8C2312yes—
147C2×C22⋊Q8C2312yes—
148C2×C22⋊Q8C2312yes—
149C2×C22⋊Q8C2312yes—
150C2×C22⋊Q8C2312yes—
151C22×C4⋊C4—21no—
152C22×C4⋊C4—21no—
153C22×C4⋊C4—21no—
154C22×C4⋊C4—21no—
155C22×C4⋊C4—21no—
156C22×C4⋊C4—21no—
157C22×C4⋊C4C2311yescharacteristic
158C22×C4⋊C4C2311yescharacteristic
159C22×C4⋊C4C2311yescharacteristic
160C22×C4⋊C4C2311yescharacteristic
161C22×C4⋊C4C2311yescharacteristic
162C22×C4⋊C4C2311yescharacteristic
163C22×C22⋊C4—21no—
164C22×C22⋊C4—21no—
165C22×C22⋊C4—21no—
166C22×C22⋊C4—21no—
167C22×C22⋊C4—21no—
168C22×C22⋊C4—21no—
169C22×C22⋊C4—21no—
170C22×C22⋊C4—21no—
171C22×C22⋊C4—21no—
172C22×C22⋊C4—21no—
173C22×C22⋊C4—21no—
174C22×C22⋊C4—21no—
175#484—44no—
176#483—44no—
177#470—48no—
178#451—44no—
179#451—44no—
180C2×#107C2314yescomplemented
181C2×#106C2314yescomplemented
182C2×#106C2314yescomplemented
183C2×#103C2314yescomplemented
184C2×#103C2314yescomplemented
185C2×#103C2314yescomplemented
186C2×#103C2314yescomplemented
187C2×#103C2314yescomplemented
188C2×#103C2314yescomplemented
189#407—44no—
190#407—44no—
191#407—44no—
192C2×C22⋊C8C2312yes—
193C2×C22⋊C8C2312yes—
194C2×C22⋊C8C2312yes—
195C2×C22⋊C8C2312yes—
196C2×C22⋊C8C2314yes—
197C2×C22⋊C8C2312yes—
198C2×C22⋊C8C2314yes—
199C2×C22⋊C8C2314yes—
200C2×C22⋊C8C2312yes—
201#385—22no—
202#385—22no—
203#385—22no—
204#385—22no—
205#385—22no—
206#385—22no—
207#385—22no—
208#385—22no—
209#385—22no—
210#385—22no—
211#385—22no—
212#385—22no—
213#385—22no—
214#385—22no—
215#385—22no—
216#385—22no—
217#385—22no—
218#385—22no—
219#385—22no—
220#385—22no—
221#385—22no—
222#385—22no—
223#385—22no—
224#385—22no—
225#380—21no—
226#380—21no—
227#380—21no—
228#380—21no—
229#380—21no—
230#380—21no—
231#380—21no—
232#380—21no—
233#380—21no—
234#380—21no—
235#380—21no—
236#380—21no—
237#380C2312yes—
238#380C2312yes—
239#380C2312yes—
240#380C2312yes—
241#380C2312yes—
242#380C2312yes—
243#380C2312yes—
244#380C2312yes—
245#380C2312yes—
246#380C2312yes—
247#380C2312yes—
248#380C2312yes—
249#379—22no—
250#379—22no—
251#379—22no—
252#379—22no—
253#379—22no—
254#379—22no—
255#379—22no—
256#379—22no—
257C2×#95—21no—
258C2×#95—21no—
259C2×#95—21no—
260C2×#95—21no—
261C2×#95—21no—
262C2×#95—21no—
263#340C2314yescomplemented
264#340C2314yescomplemented
265#340C2314yescomplemented
266#340C2314yescomplemented
267#340C2314yescomplemented
268#340C2314yescomplemented
269C25—24no—
270C25—24no—
271C25—42no—
272C25—42no—
273C25—42no—
274C25—42no—
275C25—42no—
276C25C2×D411yescharacteristic
277C25C2×D411yescharacteristic
278C25C2×D411yescharacteristic
279C25C2×D411yescharacteristic
280C25C2×D411yescharacteristic
281C25C2×D411yescharacteristic
282C25C2×D411yescharacteristic
283C22×Q8—21no—
284C22×Q8—21no—
285C22×Q8—24no—
286C22×Q8—24no—
287C22×Q8—42no—
288C22×Q8—42no—
289C22×Q8—42no—
290C22×Q8—42no—
291C22×Q8C2412yes—
292C22×Q8C2412yes—
293C23×C4—24no—
294C23×C4—24no—
295C23×C4—24no—
296C23×C4—24no—
297C23×C4—24no—
298C23×C4—24no—
299C23×C4—24no—
300C23×C4—24no—
301C23×C4—24no—
302C23×C4—21no—
303C23×C4—21no—
304C23×C4—21no—
305C23×C4—21no—
306C23×C4—21no—
307C23×C4—21no—
308C23×C4—21no—
309C23×C4—21no—
310C23×C4—42no—
311C23×C4—42no—
312C23×C4—42no—
313C23×C4—42no—
314C23×C4—42no—
315C23×C4—42no—
316C23×C4—42no—
317C23×C4—42no—
318C23×C4—42no—
319C23×C4—42no—
320C23×C4—42no—
321C23×C4—42no—
322C23×C4—42no—
323C23×C4—42no—
324C23×C4—42no—
325C23×C4—42no—
326C23×C4—42no—
327C23×C4—42no—
328C23×C4—42no—
329C23×C4—42no—
330C23×C4—42no—
331C23×C4—42no—
332C23×C4—42no—
333C23×C4—42no—
334C23×C4—42no—
335C23×C4—42no—
336C23×C4—42no—
337C23×C4—42no—
338C23×C4—42no—
339C23×C4—42no—
340C23×C4—42no—
341C23×C4—42no—
342C23×C4—42no—
343C23×C4—464no—
344C23×C4C2×D411yescharacteristic
345C23×C4C2×D411yescharacteristic
346C23×C4C2×D411yescharacteristic
347C23×C4C2×D411yescharacteristic
348C23×C4C2×D411yescharacteristic
349C23×C4C2×D411yescharacteristic
350C23×C4C2×D411yescharacteristic
351C23×C4C2×D411yescharacteristic
352C23×C4C2×D411yescharacteristic
353C23×C4C2×D411yescharacteristic
354C23×C4C2×D411yescharacteristic
355C23×C4C2×D411yescharacteristic
356C23×C4C2×D411yescharacteristic
357C23×C4C2×D411yescharacteristic
358C23×C4C2×D411yescharacteristic
359C23×C4C2×D411yescharacteristic
360C23×C4C2×D411yescharacteristic
361C23×C4C2×D411yescharacteristic
362C23×C4C2×D411yescharacteristic
363C23×C4C2×D411yescharacteristic
364C23×C4C2×D411yescharacteristic
365C23×C4C2411yescharacteristic
366C23×C4C2411yescharacteristic
367C23×C4C2411yescharacteristic
368C23×C4C2411yescharacteristic
369C23×C4C2411yescharacteristic
370C23×C4C2411yescharacteristic
371C23×C4C2411yescharacteristic
372C2×Q16—44no—
373C2×Q16—44no—
374C2×Q16—44no—
375C2×M16—28no—
376C2×M16—44no—
377C2×M16—44no—
378C22×C8C2414yes—
379C22×C8C2414yes—
380C22⋊Q8—24no—
381C22⋊Q8—24no—
382C22⋊Q8—28no—
383C22⋊Q8—28no—
384C22⋊Q8—24no—
385C22⋊Q8—24no—
386C22⋊Q8—42no—
387C22⋊Q8—42no—
388C22⋊Q8—44no—
389C22⋊Q8—44no—
390C22⋊Q8—44no—
391C22⋊Q8—44no—
392C22⋊Q8—44no—
393C22⋊Q8—44no—
394C22⋊Q8—42no—
395C22⋊Q8—42no—
396C22⋊Q8—44no—
397C22⋊Q8—44no—
398C22⋊Q8—44no—
399C22⋊Q8—44no—
400C22⋊Q8—44no—
401C22⋊Q8—44no—
402C22⋊Q8—44no—
403C22⋊Q8—44no—
404C22⋊Q8—44no—
405C22⋊Q8—44no—
406C22⋊Q8—44no—
407C22⋊Q8—44no—
408C2×C4⋊C4—24no—
409C2×C4⋊C4—24no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—22no—
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—22no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—42no—
429C2×C4⋊C4—42no—
430C2×C4⋊C4—42no—
431C2×C4⋊C4—42no—
432C2×C4⋊C4—44no—
433C2×C4⋊C4—44no—
434C2×C4⋊C4—44no—
435C2×C4⋊C4—44no—
436C2×C4⋊C4—44no—
437C2×C4⋊C4—44no—
438C2×C4⋊C4C2412yes—
439C2×C4⋊C4C2412yes—
440C2×C4⋊C4C2412yes—
441C2×C4⋊C4C2412yes—
442C2×C4⋊C4C2412yes—
443C2×C4⋊C4C2412yes—
444C2×C22⋊C4—22no—
445C2×C22⋊C4—22no—
446C2×C22⋊C4—22no—
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—22no—
454C2×C22⋊C4—22no—
455C2×C22⋊C4—22no—
456C2×C22⋊C4—22no—
457C2×C22⋊C4—22no—
458C2×C22⋊C4—22no—
459C2×C22⋊C4—22no—
460C2×C22⋊C4—22no—
461C2×C22⋊C4—22no—
462C2×C22⋊C4—22no—
463C2×C22⋊C4—22no—
464C2×C22⋊C4—22no—
465C2×C22⋊C4—22no—
466C2×C22⋊C4—22no—
467C2×C22⋊C4—22no—
468C2×C22⋊C4—44no—
469C2×C22⋊C4—44no—
470C2×C22⋊C4—44no—
471C2×C22⋊C4—44no—
472C2×C22⋊C4—44no—
473C2×C22⋊C4—44no—
474C2×C22⋊C4—44no—
475C2×C22⋊C4—44no—
476C2×C22⋊C4—44no—
477C2×C22⋊C4—44no—
478C2×C22⋊C4—44no—
479C2×C22⋊C4—44no—
480#107—44no—
481#106—44no—
482#106—44no—
483#103—44no—
484#103—44no—
485#103—44no—
486#103—44no—
487#103—44no—
488#103—44no—
489C22⋊C8—24no—
490C22⋊C8—24no—
491C22⋊C8—24no—
492C22⋊C8—24no—
493C22⋊C8—44no—
494C22⋊C8—44no—
495C22⋊C8—42no—
496C22⋊C8—44no—
497C22⋊C8—42no—
498#95—22no—
499#95—22no—
500#95—22no—
501#95—22no—
502#95—22no—
503#95—22no—
504#95—22no—
505#95—22no—
506#95—22no—
507#95—22no—
508#95—22no—
509#95—22no—
510C24—22no—
511C24—22no—
512C24—22no—
513C24—22no—
514C24—22no—
515C24—22no—
516C24—22no—
517C24—22no—
518C24—22no—
519C24—22no—
520C24—22no—
521C24—22no—
522C24—22no—
523C24—22no—
524C24—22no—
525C24—22no—
526C24—22no—
527C24—22no—
528C24—22no—
529C24—22no—
530C24—22no—
531C24—22no—
532C24—22no—
533C24—22no—
534C24—22no—
535C24—22no—
536C24—22no—
537C24—41no—
538C24—41no—
539C24—41no—
540C24—41no—
541C24—41no—
542C24—41no—
543C24—41no—
544C24—41no—
545C24—41no—
546C24—41no—
547C24—41no—
548C24—41no—
549C24—41no—
550C24—41no—
551C24—41no—
552C24—41no—
553C24—41no—
554C24—41no—
555C24—41no—
556C24—41no—
557C24—416no—
558C24—416no—
559C24—416no—
560C24—416no—
561C24—416no—
562C24—416no—
563C24—416no—
564C24#13714yes—
565C24#13714yes—
566C24C22×D411yescharacteristic
567C24C22×D411yescharacteristic
568C24C22×D411yescharacteristic
569C24C22×D411yescharacteristic
570C24C22×D411yescharacteristic
571C24C22×D411yescharacteristic
572C24C22×D411yescharacteristic
573C2×Q8—22no—
574C2×Q8—22no—
575C2×Q8—24no—
576C2×Q8—24no—
577C2×Q8—24no—
578C2×Q8—24no—
579C2×Q8—22no—
580C2×Q8—22no—
581C2×Q8—42no—
582C2×Q8—42no—
583C2×Q8—42no—
584C2×Q8—42no—
585C2×Q8—42no—
586C2×Q8—42no—
587C2×Q8—88no—
588C2×Q8—88no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—41no—
643C22×C4—41no—
644C22×C4—41no—
645C22×C4—41no—
646C22×C4—41no—
647C22×C4—41no—
648C22×C4—41no—
649C22×C4—41no—
650C22×C4—41no—
651C22×C4—41no—
652C22×C4—41no—
653C22×C4—41no—
654C22×C4—41no—
655C22×C4—41no—
656C22×C4—41no—
657C22×C4—41no—
658C22×C4—41no—
659C22×C4—41no—
660C22×C4—41no—
661C22×C4—41no—
662C22×C4—41no—
663C22×C4—41no—
664C22×C4—41no—
665C22×C4—41no—
666C22×C4—41no—
667C22×C4—41no—
668C22×C4—41no—
669C22×C4—41no—
670C22×C4—41no—
671C22×C4—41no—
672C22×C4—41no—
673C22×C4—41no—
674C22×C4—41no—
675C22×C4—41no—
676C22×C4—41no—
677C22×C4—41no—
678C22×C4—416no—
679C22×C4—416no—
680C22×C4—416no—
681C22×C4—416no—
682C22×C4—416no—
683C22×C4—416no—
684C22×C4—416no—
685C22×C4—416no—
686C22×C4—416no—
687C22×C4—416no—
688C22×C4—416no—
689C22×C4—416no—
690C22×C4—416no—
691C22×C4—416no—
692C22×C4—42no—
693C22×C4—42no—
694C22×C4—42no—
695C22×C4—42no—
696C22×C4—42no—
697C22×C4—42no—
698C22×C4—42no—
699C22×C4—42no—
700C22×C4—42no—
701C22×C4—42no—
702C22×C4—42no—
703C22×C4—42no—
704C22×C4—42no—
705C22×C4—42no—
706C22×C4—42no—
707C22×C4—42no—
708C22×C4—42no—
709C22×C4—42no—
710C22×C4—42no—
711C22×C4—42no—
712C22×C4—42no—
713C22×C4—42no—
714C22×C4—42no—
715C22×C4—42no—
716C22×C4C22×D411yescharacteristic
717C22×C4C22×D411yescharacteristic
718C22×C4C22×D411yescharacteristic
719C22×C4C22×D411yescharacteristic
720C22×C4C22×D411yescharacteristic
721C22×C4C22×D411yescharacteristic
722C22×C4C22×D411yescharacteristic
723C22×C4H(5,𝔽2)14yes—
724C22×C4H(5,𝔽2)14yes—
725C22×C4H(5,𝔽2)14yes—
726C22×C4C2511yescharacteristic
727Q16—88no—
728M16—88no—
729C2×C8—24no—
730C2×C8—24no—
731C2×C8—24no—
732C2×C8—24no—
733C2×C8—24no—
734C2×C8—24no—
735C4⋊C4—22no—
736C4⋊C4—22no—
737C4⋊C4—24no—
738C4⋊C4—24no—
739C4⋊C4—24no—
740C4⋊C4—24no—
741C4⋊C4—22no—
742C4⋊C4—22no—
743C4⋊C4—42no—
744C4⋊C4—42no—
745C4⋊C4—42no—
746C4⋊C4—42no—
747C4⋊C4—44no—
748C4⋊C4—44no—
749C4⋊C4—44no—
750C4⋊C4—44no—
751C4⋊C4—44no—
752C4⋊C4—44no—
753C4⋊C4—44no—
754C4⋊C4—44no—
755C4⋊C4—42no—
756C4⋊C4—42no—
757C4⋊C4—44no—
758C4⋊C4—44no—
759C4⋊C4—44no—
760C4⋊C4—44no—
761C22⋊C4—44no—
762C22⋊C4—44no—
763C22⋊C4—44no—
764C22⋊C4—44no—
765C22⋊C4—44no—
766C22⋊C4—44no—
767C22⋊C4—44no—
768C22⋊C4—44no—
769C22⋊C4—44no—
770C22⋊C4—44no—
771C22⋊C4—44no—
772C22⋊C4—44no—
773C22⋊C4—44no—
774C22⋊C4—44no—
775C22⋊C4—44no—
776C22⋊C4—44no—
777C22⋊C4—44no—
778C22⋊C4—44no—
779C22⋊C4—44no—
780C22⋊C4—44no—
781C22⋊C4—44no—
782C22⋊C4—44no—
783C22⋊C4—44no—
784C22⋊C4—44no—
785C23—21no—
786C23—21no—
787C23—21no—
788C23—21no—
789C23—21no—
790C23—21no—
791C23—21no—
792C23—21no—
793C23—28no—
794C23—28no—
795C23—28no—
796C23—21no—
797C23—21no—
798C23—21no—
799C23—21no—
800C23—21no—
801C23—21no—
802C23—21no—
803C23—21no—
804C23—21no—
805C23—21no—
806C23—21no—
807C23—21no—
808C23—21no—
809C23—21no—
810C23—28no—
811C23—28no—
812C23—28no—
813C23—21no—
814C23—21no—
815C23—21no—
816C23—21no—
817C23—21no—
818C23—21no—
819C23—21no—
820C23—21no—
821C23—21no—
822C23—21no—
823C23—21no—
824C23—21no—
825C23—21no—
826C23—21no—
827C23—21no—
828C23—21no—
829C23—44no—
830C23—44no—
831C23—44no—
832C23—44no—
833C23—44no—
834C23—44no—
835C23—44no—
836C23—44no—
837C23—44no—
838C23—44no—
839C23—44no—
840C23—44no—
841C23—44no—
842C23—44no—
843C23—44no—
844C23—44no—
845C23—44no—
846C23—44no—
847C23—44no—
848C23—44no—
849C23—44no—
850C23—44no—
851C23—44no—
852C23—44no—
853C23—44no—
854C23—44no—
855C23—44no—
856C23—44no—
857C23—44no—
858C23—44no—
859C23—44no—
860C23—44no—
861C23—44no—
862C23—44no—
863C23—44no—
864C23—44no—
865C23—44no—
866C23—44no—
867C23—44no—
868C23—4128no—
869C23—44no—
870C23—44no—
871C23—44no—
872C23—44no—
873C23#53412yes—
874C23#53412yes—
875C23#53412yes—
876C23C2×#13712yes—
877C23C2×#13712yes—
878C23C2×#13712yes—
879C23C2×#13712yes—
880C23C2×#13712yes—
881C23C2×#13712yes—
882C23#57512yes—
883C23#57512yes—
884C23C23×D411yescharacteristic
885Q8—44no—
886Q8—44no—
887Q8—44no—
888Q8—44no—
889Q8—84no—
890Q8—84no—
891C2×C4—21no—
892C2×C4—21no—
893C2×C4—21no—
894C2×C4—21no—
895C2×C4—21no—
896C2×C4—21no—
897C2×C4—28no—
898C2×C4—28no—
899C2×C4—28no—
900C2×C4—21no—
901C2×C4—21no—
902C2×C4—21no—
903C2×C4—21no—
904C2×C4—21no—
905C2×C4—21no—
906C2×C4—21no—
907C2×C4—21no—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—44no—
913C2×C4—44no—
914C2×C4—44no—
915C2×C4—44no—
916C2×C4—44no—
917C2×C4—44no—
918C2×C4—44no—
919C2×C4—44no—
920C2×C4—44no—
921C2×C4—44no—
922C2×C4—44no—
923C2×C4—44no—
924C2×C4—44no—
925C2×C4—44no—
926C2×C4—44no—
927C2×C4—44no—
928C2×C4—44no—
929C2×C4—44no—
930C2×C4—44no—
931C2×C4—44no—
932C2×C4—44no—
933C2×C4—44no—
934C2×C4—44no—
935C2×C4—44no—
936C2×C4—44no—
937C2×C4—42no—
938C2×C4—42no—
939C2×C4—42no—
940C2×C4—42no—
941C2×C4—42no—
942C2×C4—42no—
943C2×C4—42no—
944C2×C4—42no—
945C2×C4—42no—
946C2×C4—42no—
947C2×C4—42no—
948C2×C4—42no—
949C2×C4—42no—
950C2×C4—42no—
951C2×C4—42no—
952C2×C4—42no—
953C2×C4—42no—
954C2×C4—42no—
955C2×C4—42no—
956C2×C4—42no—
957C2×C4—42no—
958C2×C4—42no—
959C2×C4—42no—
960C2×C4—42no—
961C2×C4—84no—
962C2×C4—84no—
963C2×C4—84no—
964C2×C4—84no—
965C2×C4—84no—
966C2×C4—84no—
967C2×C4—84no—
968C2×C4—84no—
969C2×C4#53412yes—
970C2×C4#53412yes—
971C2×C4#53412yes—
972C2×C4C2×H(5,𝔽2)12yes—
973C2×C4C2×H(5,𝔽2)12yes—
974C2×C4C2×H(5,𝔽2)12yes—
975C8—44no—
976C8—44no—
977C22—22no—
978C22—22no—
979C22—22no—
980C22—22no—
981C22—22no—
982C22—22no—
983C22—22no—
984C22—22no—
985C22—22no—
986C22—22no—
987C22—22no—
988C22—22no—
989C22—22no—
990C22—22no—
991C22—22no—
992C22—22no—
993C22—22no—
994C22—22no—
995C22—22no—
996C22—22no—
997C22—22no—
998C22—22no—
999C22—22no—
1000C22—22no—
1001C22—22no—
1002C22—22no—
1003C22—22no—
1004C22—416no—
1005C22—416no—
1006C22—416no—
1007C22—416no—
1008C22—416no—
1009C22—416no—
1010C22—416no—
1011C22—41no—
1012C22—41no—
1013C22—41no—
1014C22—41no—
1015C22—41no—
1016C22—41no—
1017C22—41no—
1018C22—41no—
1019C22—41no—
1020C22—41no—
1021C22—41no—
1022C22—41no—
1023C22—41no—
1024C22—41no—
1025C22—41no—
1026C22—41no—
1027C22—41no—
1028C22—41no—
1029C22—41no—
1030C22—41no—
1031C22#319514yes—
1032C22#319614yes—
1033C22C2×#53411yescharacteristic
1034C22C2×#53411yescharacteristic
1035C22C2×#53411yescharacteristic
1036C22C22×#13711yescharacteristic
1037C22C22×#13711yescharacteristic
1038C22C2×#57511yescharacteristic
1039C22C2×#57511yescharacteristic
1040C4—22no—
1041C4—22no—
1042C4—22no—
1043C4—41no—
1044C4—41no—
1045C4—41no—
1046C4—41no—
1047C4—82no—
1048C4—82no—
1049C4—82no—
1050C4—82no—
1051C4—82no—
1052C4—82no—
1053C4—82no—
1054C4—82no—
1055C4#353214yes—
1056C2—24no—
1057C2—24no—
1058C2—42no—
1059C2—42no—
1060C2—42no—
1061C2—42no—
1062C2—42no—
1063C2#3743611yescharacteristic
1064C2C2×#319511yescharacteristic
1065C2C2×#319611yescharacteristic
1066C2#6075111yescharacteristic
1067C2#6075111yescharacteristic
1068C2#6075111yescharacteristic
1069C2#6075211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC26D4
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
3. #32711C2semidirect
4. #29894C2semidirect
5. #29893C2semidirect
6. #29743C2semidirect
7. #29599C2semidirect
8. #29597C2semidirect
9. #27601C2semidirect
10. #24559C2semidirect
11. #24556C2semidirect
12. #24386C2semidirect
13. #24386C2semidirect
14. #24006C2semidirect
15. #24003C2semidirect
16. #23921C2semidirect
25. C2×#484C22semidirect
26. C2×#483C22semidirect
27. C2×#470C22semidirect
28. C2×#451C22semidirect
29. C2×#451C22semidirect
63. #2077C22semidirect
64. #2077C22semidirect
65. #2077C22semidirect
66. #2075C22semidirect
67. #2036C22semidirect
68. #2036C22semidirect
69. #2036C22semidirect
70. #2035C22semidirect
71. #2035C22semidirect
72. #2035C22semidirect
73. #2035C22semidirect
74. #2035C22semidirect
75. #2001C22semidirect
76. #2001C22semidirect
77. #2001C22semidirect
78. #2001C22semidirect
79. #1894C22semidirect
80. #1894C22semidirect
81. #1872C22semidirect
82. #1872C22semidirect
83. #1872C22semidirect
84. #1872C22semidirect
85. #1853C22semidirect
86. #1853C22semidirect
87. #1853C22semidirect
88. #1852C22semidirect
89. #1824C22semidirect
90. #1823C22semidirect
91. #1809C22semidirect
92. #1787C22semidirect
93. #1787C22semidirect
119. C22×Q16C23semidirect
180. C2×#107C23semidirect
181. C2×#106C23semidirect
182. C2×#106C23semidirect
183. C2×#103C23semidirect
184. C2×#103C23semidirect
185. C2×#103C23semidirect
186. C2×#103C23semidirect
187. C2×#103C23semidirect
188. C2×#103C23semidirect
263. #340C23semidirect
264. #340C23semidirect
265. #340C23semidirect
266. #340C23semidirect
267. #340C23semidirect
268. #340C23semidirect

Maximal subgroups

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

subgroupindex
C2×#28482
#327112
#298942
#298932
#297432
#295992
#295972
#276012
#245592
#245562
#243862
#240062
#240032
#239212
#205792