Finite Group Databasebeta

← #6441649

Subgroups — #6441649

Order 512.

2303 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#483C211yesmaximal, characteristic, complemented
2C2×#3056C211yesmaximal, characteristic
3#35227C211yesmaximal, characteristic
4#34203C211yesmaximal, characteristic, complemented
5#25231C214yesmaximal, complemented
6#25219C214yesmaximal, complemented
7#25208C214yesmaximal, complemented
8#25204C214yesmaximal, complemented
9#23661C211yesmaximal, characteristic, complemented
10#23633C211yesmaximal, characteristic, complemented
11#23610C211yesmaximal, characteristic, complemented
12#23545C211yesmaximal, characteristic, complemented
13#21174C211yesmaximal, characteristic, complemented
14#21068C211yesmaximal, characteristic, complemented
15#20930C211yesmaximal, characteristic, complemented
16#20908C211yesmaximal, characteristic
17#20836C211yesmaximal, characteristic, complemented
18#20651C211yesmaximal, characteristic, complemented
19C2×#1736C211yesmaximal, characteristic, complemented
20C22×#137C2211yescharacteristic
21C23×M16C2211yescharacteristic
22C2×#525C2211yescharacteristic
23C22×C22⋊Q8C2211yescharacteristic
24C2×#519C2211yescharacteristic
25C22×#117C2211yescharacteristic
26C23×C4⋊C4C2211yescharacteristic
27C2×#483—28no—
28C2×#483C2214yes—
29C2×#483C2214yes—
30#3056—28no—
31C2×#470C2212yes—
32C2×#468C2212yes—
33C2×#467C2212yes—
34C2×#465C2212yes—
35C2×#428C2211yescharacteristic
36C22×#106C2211yescharacteristic
37C22×#106C2211yescharacteristic
38C2×#424C2211yescharacteristic
39C2×#424C2211yescharacteristic
40C2×#417C2211yescharacteristic
41C2×#419C2211yescharacteristic
42C2×#416C2211yescharacteristic
43C2×#416C2211yescharacteristic
44C22×#103C2211yescharacteristic
45C22×#103C2211yescharacteristic
46C22×C22⋊C8C2211yescharacteristic
47#2849—22no—
48#2623—22no—
49#2504C2212yes—
50#2503C2212yes—
51#2502C2212yes—
52#2501C2212yes—
53#2487—22no—
54#2486—22no—
55#2362C2214yes—
56#2360C2214yes—
57#2344—22no—
58#2342—22no—
59#2323—22no—
60#2317C2211yescharacteristic
61#2317C2211yescharacteristic
62#2316C2211yescharacteristic
63#2311C2211yescharacteristic
64#2311C2211yescharacteristic
65#2310C2211yescharacteristic
66C4×C22⋊Q8—22no—
67#2280C2211yescharacteristic
68#2274C2211yescharacteristic
69#2085C2214yescomplemented
70#2084C2214yescomplemented
71#2074C2214yescomplemented
72#2072C2214yescomplemented
73#2066C2214yescomplemented
74#2065C2214yescomplemented
75#2056C2214yescomplemented
76#2055C2214yescomplemented
77#1949C2214yescomplemented
78#1948C2214yescomplemented
79#1927C2214yescomplemented
80#1926C2214yescomplemented
81#1880C2214yescomplemented
82#1878C2214yescomplemented
83#1875C2212yes—
84#1874C2212yes—
85#1873C2212yes—
86#1872C2212yes—
87#1851C2214yes—
88#1850C2214yes—
89#1805C2214yescomplemented
90#1803C2214yescomplemented
91#1736C2211yescharacteristic
92#1736C2211yescharacteristic
93#1736C2211yescharacteristic
94#1736C2214yes—
95#1736C2211yescharacteristic
96#1735C2211yescharacteristic
97#1735C2211yescharacteristic
98C2×#340C2214yes—
99#1729C2211yescharacteristic
100#1729C2211yescharacteristic
101C22×#41C2311yescharacteristic
102C23×Q8C2311yescharacteristic
103C24×C4—21no—
104C24×C4C2311yescharacteristic
105C2×#137—24no—
106C2×#137—24no—
107C2×#137—42no—
108C22×Q16C2312yes—
109C22×SD16C2312yes—
110C22×M16—24no—
111C22×M16—24no—
112C22×M16—42no—
113C22×M16C2311yescharacteristic
114C22×M16C2312yes—
115C22×M16C2311yescharacteristic
116C23×C8C2311yescharacteristic
117C23×C8C2311yescharacteristic
118C23×C8C2312yes—
119#525—24no—
120#525—24no—
121C2×#123—21no—
122C2×#123—24no—
123C2×C22⋊Q8—21no—
124C2×C22⋊Q8—21no—
125C2×C22⋊Q8—24no—
126C2×C22⋊Q8D418yes—
127C2×C22⋊Q8C2311yescharacteristic
128C2×C22⋊Q8C2311yescharacteristic
129C2×C22⋊Q8C2312yes—
130C2×C22⋊Q8C2312yes—
131C2×#121C2311yescharacteristic
132C2×#121C2311yescharacteristic
133C2×#120—21no—
134#519—24no—
135#519—42no—
136C2×C4×Q8—22no—
137C2×C4×Q8C2314yes—
138C2×C4×D4—21no—
139C2×C4×D4—21no—
140C2×#117—21no—
141C2×#117—21no—
142C2×#117—22no—
143C2×#117—24no—
144C2×#117—42no—
145C2×#117C2311yescharacteristic
146C2×#117C2311yescharacteristic
147C2×#117C2312yes—
148C2×#117C2311yescharacteristic
149C2×#117C2311yescharacteristic
150C2×#117C2311yescharacteristic
151C22×C4⋊C4—21no—
152C22×C4⋊C4—24no—
153C22×C4⋊C4—24no—
154C22×C4⋊C4—21no—
155C22×C4⋊C4—21no—
156C22×C4⋊C4—21no—
157C22×C4⋊C4C2311yescharacteristic
158C22×C4⋊C4C2311yescharacteristic
159C22×C4⋊C4C2312yes—
160C22×C4⋊C4C2312yes—
161C22×C4⋊C4C2312yes—
162C22×C4⋊C4C2311yescharacteristic
163C22×C22⋊C4—21no—
164C22×C22⋊C4—21no—
165C22×C42—21no—
166#483—216no—
167#483—216no—
168#470—28no—
169#468—28no—
170#467—28no—
171#465—28no—
172#428—24no—
173C2×#107C2312yes—
174C2×#106—24no—
175C2×#106—24no—
176C2×#106C2314yes—
177C2×#106C2314yes—
178C2×#106C2312yes—
179#424—24no—
180#424—42no—
181C2×C4⋊C8C2314yes—
182C2×C4⋊C8C2314yes—
183#419—24no—
184#417—24no—
185#416—24no—
186#416—42no—
187C2×#103—24no—
188C2×#103—24no—
189C2×#103C2314yes—
190C2×#103C2312yes—
191C2×#103C2312yes—
192C2×#103C2314yes—
193C2×#103C2312yes—
194C2×#103C2312yes—
195C2×#103C2312yes—
196C2×#102C2312yes—
197C2×#102C2312yes—
198C2×#102C2312yes—
199C2×C22⋊C8—24no—
200C2×C22⋊C8C2312yes—
201C2×C22⋊C8C2312yes—
202#400—24no—
203#399—24no—
204#398—24no—
205#397—24no—
206#391—22no—
207#391C2314yes—
208#391C2312yes—
209#391C2312yes—
210#390C2312yes—
211#390C2312yes—
212#389—22no—
213#389—22no—
214#389—22no—
215#389—24no—
216#389C2314yes—
217#388—24no—
218#388—24no—
219#387—24no—
220#387—24no—
221#386—22no—
222#386—22no—
223#386—24no—
224#385—22no—
225#385—22no—
226#385—24no—
227#385—24no—
228#384C2312yes—
229#384C2312yes—
230#382C2312yes—
231#382C2312yes—
232#381—22no—
233#381—24no—
234#381D412yes—
235#380—22no—
236#380—22no—
237#380—22no—
238#380D412yes—
239#380D412yes—
240#379D412yes—
241C4×C4⋊C4—22no—
242C4×C4⋊C4—24no—
243C4×C4⋊C4C2314yes—
244C4×C22⋊C4—22no—
245C4×C22⋊C4—24no—
246C4×C22⋊C4C2312yes—
247C4×C22⋊C4C2312yes—
248#340C2314yes—
249#340C2312yes—
250#340C2314yes—
251#340C2312yes—
252#340C2314yes—
253#340C2312yes—
254#340C2312yes—
255#340C2314yes—
256#336C2314yes—
257#336C2314yes—
258C25C2×D411yescharacteristic
259C2×#41—22no—
260C2×#41—22no—
261C2×#41—22no—
262C2×#41—22no—
263C2×#41—22no—
264C2×#41—22no—
265C22×Q8—21no—
266C22×Q8—22no—
267C22×Q8—22no—
268C22×Q8—22no—
269C22×Q8—22no—
270C22×Q8—22no—
271C22×Q8C2×D414yes—
272C22×Q8C2411yescharacteristic
273C22×Q8C2412yes—
274C22×D4—21no—
275C22×D4—21no—
276C22×D4—21no—
277C22×D4C2411yescharacteristic
278C23×C4—22no—
279C23×C4—22no—
280C23×C4—22no—
281C23×C4—22no—
282C23×C4—21no—
283C23×C4—21no—
284C23×C4—22no—
285C23×C4—22no—
286C23×C4—22no—
287C23×C4—21no—
288C23×C4—21no—
289C23×C4—21no—
290C23×C4—44no—
291C23×C4—84no—
292C23×C4C2×D411yescharacteristic
293C23×C4C2×D411yescharacteristic
294C23×C4C2×D411yescharacteristic
295C23×C4C2×D414yes—
296C23×C4#4114yes—
297C23×C4C2411yescharacteristic
298C23×C4C2411yescharacteristic
299C23×C4C2411yescharacteristic
300#137—416no—
301C2×Q16—24no—
302C2×Q16—24no—
303C2×Q16—42no—
304C2×SD16—24no—
305C2×SD16—24no—
306C2×SD16—42no—
307C2×M16—22no—
308C2×M16—22no—
309C2×M16—22no—
310C2×M16—24no—
311C2×M16—22no—
312C2×M16—22no—
313C2×M16—24no—
314C2×M16—42no—
315C2×M16—416no—
316C2×M16#4114yes—
317C22×C8—24no—
318C22×C8—22no—
319C22×C8—22no—
320C22×C8—22no—
321C22×C8—22no—
322C22×C8—22no—
323C22×C8—22no—
324C22×C8—24no—
325C22×C8—42no—
326C22×C8C2412yes—
327C22×C8C2412yes—
328C22×C8C2412yes—
329C22×C8C2412yes—
330#123—44no—
331#123—88no—
332C22⋊Q8—28no—
333C22⋊Q8—28no—
334C22⋊Q8—24no—
335C22⋊Q8—24no—
336C22⋊Q8—22no—
337C22⋊Q8—22no—
338C22⋊Q8—22no—
339C22⋊Q8—22no—
340C22⋊Q8C2×D418yes—
341C22⋊Q8C2×D418yes—
342#121—22no—
343#121—22no—
344#121—22no—
345#121—22no—
346#120—44no—
347C4×Q8—28no—
348C4×Q8—44no—
349C4×Q8—48no—
350C4×D4—44no—
351C4×D4—44no—
352#117—22no—
353#117—22no—
354#117—22no—
355#117—22no—
356#117—22no—
357#117—22no—
358#117—22no—
359#117—22no—
360#117—22no—
361#117—24no—
362#117—44no—
363#117—48no—
364#117—44no—
365#117—42no—
366#117#4114yes—
367C2×C4⋊C4—28no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—24no—
375C2×C4⋊C4—24no—
376C2×C4⋊C4—24no—
377C2×C4⋊C4—24no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—24no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—24no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—24no—
390C2×C4⋊C4—24no—
391C2×C4⋊C4—24no—
392C2×C4⋊C4—42no—
393C2×C4⋊C4—44no—
394C2×C4⋊C4—44no—
395C2×C4⋊C4—44no—
396C2×C4⋊C4C2×D412yes—
397C2×C4⋊C4C2×D412yes—
398C2×C4⋊C4C2×D414yes—
399C2×C4⋊C4C2412yes—
400C2×C4⋊C4C2412yes—
401C2×C4⋊C4C2412yes—
402C2×C4⋊C4C2411yescharacteristic
403C2×C4⋊C4C2411yescharacteristic
404C2×C4⋊C4C2412yes—
405C2×C4⋊C4C2412yes—
406C2×C22⋊C4—28no—
407C2×C22⋊C4—21no—
408C2×C22⋊C4—22no—
409C2×C22⋊C4—22no—
410C2×C22⋊C4—21no—
411C2×C22⋊C4—22no—
412C2×C22⋊C4—21no—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—21no—
415C2×C22⋊C4—21no—
416C2×C22⋊C4—21no—
417C2×C22⋊C4—24no—
418C2×C22⋊C4—24no—
419C2×C22⋊C4—44no—
420C2×C22⋊C4C2×D412yes—
421C2×C22⋊C4C2×D412yes—
422C2×C22⋊C4C2×D414yes—
423C2×C22⋊C4C2×D414yes—
424C2×C42—21no—
425C2×C42—22no—
426C2×C42—21no—
427C2×C42—24no—
428C2×C42—21no—
429C2×C42—24no—
430C2×C42—44no—
431C2×C42C2412yes—
432C2×C42C2412yes—
433#107—24no—
434#106—28no—
435#106—28no—
436#106—24no—
437C4⋊C8—28no—
438C4⋊C8—44no—
439#103—28no—
440#103—28no—
441#103—24no—
442#103—24no—
443#103—24no—
444#103—24no—
445#103—42no—
446#102—24no—
447#102—24no—
448#102—42no—
449C22⋊C8—24no—
450C22⋊C8—24no—
451#95—24no—
452#95—24no—
453#95—24no—
454#95—24no—
455#95—24no—
456#95—24no—
457#95—24no—
458#95—24no—
459#95C2×D414yes—
460#95C2×D414yes—
461C24—22no—
462C24—22no—
463C24—24no—
464C24—21no—
465C24—42no—
466C24#12114yes—
467C24C22×D411yescharacteristic
468C24C22×D411yescharacteristic
469C24C22×D411yescharacteristic
470#41—44no—
471#41—44no—
472#41—44no—
473#41—44no—
474C2×Q8—24no—
475C2×Q8—22no—
476C2×Q8—28no—
477C2×Q8—28no—
478C2×Q8—21no—
479C2×Q8—22no—
480C2×Q8—22no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—22no—
485C2×Q8—21no—
486C2×Q8—22no—
487C2×Q8—21no—
488C2×Q8—44no—
489C2×Q8—44no—
490C2×Q8—42no—
491C2×Q8—42no—
492C2×Q8C22×D414yes—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—44no—
500C2×D4—42no—
501C2×D4—42no—
502C2×D4—42no—
503C2×D4—42no—
504C2×D4—42no—
505C2×D4—44no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—28no—
509C22×C4—28no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—28no—
513C22×C4—28no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—24no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—24no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—21no—
535C22×C4—44no—
536C22×C4—42no—
537C22×C4—42no—
538C22×C4—44no—
539C22×C4—42no—
540C22×C4—42no—
541C22×C4—44no—
542C22×C4—48no—
543C22×C4—44no—
544C22×C4—42no—
545C22×C4—42no—
546C22×C4—42no—
547C22×C4—82no—
548C22×C4—82no—
549C22×C4—82no—
550C22×C4—82no—
551C22×C4—84no—
552C22×C4—816no—
553C22×C4#12114yes—
554C22×C4#12114yes—
555C22×C4#12114yes—
556C22×C4C22×D414yes—
557C22×C4C22×D414yes—
558C22×C4C22×D411yescharacteristic
559C22×C4C22×D411yescharacteristic
560C22×C4C22×D412yes—
561C22×C4C22×D412yes—
562C22×C4C22×D411yescharacteristic
563C22×C4C22×D412yes—
564C22×C4C2×#4112yes—
565C22×C4C2×#4112yes—
566C22×C4C2×#4112yes—
567C22×C4C2×#4112yes—
568C22×C4C2×#4112yes—
569C22×C4H(5,𝔽2)12yes—
570C22×C42−1+412yes—
571C22×C4C2511yescharacteristic
572Q16—48no—
573SD16—48no—
574M16—28no—
575M16—48no—
576M16—44no—
577C2×C8—22no—
578C2×C8—22no—
579C2×C8—22no—
580C2×C8—22no—
581C2×C8—22no—
582C2×C8—22no—
583C2×C8—22no—
584C2×C8—22no—
585C2×C8—22no—
586C2×C8—22no—
587C2×C8—22no—
588C2×C8—48no—
589C2×C8—44no—
590C2×C8—44no—
591C2×C8C2×#4114yes—
592C4⋊C4—28no—
593C4⋊C4—28no—
594C4⋊C4—24no—
595C4⋊C4—24no—
596C4⋊C4—24no—
597C4⋊C4—22no—
598C4⋊C4—22no—
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—22no—
604C4⋊C4—22no—
605C4⋊C4—22no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—22no—
609C4⋊C4—44no—
610C4⋊C4—48no—
611C4⋊C4—44no—
612C4⋊C4—44no—
613C4⋊C4—42no—
614C4⋊C4—42no—
615C4⋊C4—42no—
616C4⋊C4—42no—
617C4⋊C4—84no—
618C4⋊C4—84no—
619C4⋊C4—84no—
620C4⋊C4C22×D414yes—
621C4⋊C4C2×#4114yes—
622C22⋊C4—28no—
623C22⋊C4—28no—
624C22⋊C4—24no—
625C22⋊C4—24no—
626C22⋊C4—24no—
627C22⋊C4—28no—
628C22⋊C4—44no—
629C22⋊C4—44no—
630C22⋊C4—42no—
631C22⋊C4—42no—
632C22⋊C4—42no—
633C22⋊C4—42no—
634C22⋊C4—42no—
635C22⋊C4—42no—
636C22⋊C4—84no—
637C22⋊C4—84no—
638C42—24no—
639C42—22no—
640C42—22no—
641C42—22no—
642C42—22no—
643C42—44no—
644C42—48no—
645C42—42no—
646C42—42no—
647C42—84no—
648C23—22no—
649C23—22no—
650C23—21no—
651C23—21no—
652C23—22no—
653C23—22no—
654C23—28no—
655C23—21no—
656C23—21no—
657C23—28no—
658C23—22no—
659C23—44no—
660C23—48no—
661C23—48no—
662C23—42no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—42no—
667C23C2×#12112yes—
668C23C2×#12112yes—
669C23C2×#12112yes—
670C23#54612yes—
671C23#54712yes—
672C23#57714yes—
673C23C23×D411yescharacteristic
674Q8—24no—
675Q8—24no—
676Q8—42no—
677Q8—48no—
678Q8—42no—
679Q8—41no—
680Q8—41no—
681Q8—41no—
682Q8—41no—
683D4—41no—
684D4—41no—
685D4—41no—
686D4—41no—
687D4—84no—
688D4—84no—
689D4—84no—
690C2×C4—28no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—28no—
698C2×C4—28no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—42no—
715C2×C4—44no—
716C2×C4—48no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—44no—
731C2×C4—44no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—84no—
735C2×C4—88no—
736C2×C4—84no—
737C2×C4—84no—
738C2×C4—88no—
739C2×C4—88no—
740C2×C4—84no—
741C2×C4C2×#12112yes—
742C2×C4C2×#12112yes—
743C2×C4C2×#12112yes—
744C2×C4#52914yes—
745C2×C4#53914yes—
746C2×C4#54612yes—
747C2×C4#54614yes—
748C2×C4#54712yes—
749C2×C4#54714yes—
750C2×C4C23×D411yescharacteristic
751C2×C4C22×#4111yescharacteristic
752C2×C4C22×#4111yescharacteristic
753C2×C4C22×#4111yescharacteristic
754C2×C4C2×H(5,𝔽2)11yescharacteristic
755C2×C4C2×2−1+411yescharacteristic
756C8—24no—
757C8—42no—
758C8—42no—
759C8—42no—
760C22—22no—
761C22—24no—
762C22—24no—
763C22—22no—
764C22—22no—
765C22—24no—
766C22—24no—
767C22—22no—
768C22—22no—
769C22—22no—
770C22—22no—
771C22—416no—
772C22—42no—
773C22—42no—
774C22—81no—
775C22—82no—
776C22—81no—
777C22—82no—
778C22—81no—
779C22#242514yes—
780C22#304314yes—
781C22C22×#12111yescharacteristic
782C22C2×#54611yescharacteristic
783C22C2×#54711yescharacteristic
784C22C2×#57712yes—
785C22#358612yes—
786C4—22no—
787C4—22no—
788C4—44no—
789C4—44no—
790C4—44no—
791C4—44no—
792C4—44no—
793C4—82no—
794C4—82no—
795C4—81no—
796C4—82no—
797C4—81no—
798C4—81no—
799C4#242514yes—
800C4C2×#52911yescharacteristic
801C4C2×#53911yescharacteristic
802C4C2×#54611yescharacteristic
803C4C2×#54711yescharacteristic
804C2—24no—
805C2—24no—
806C2—42no—
807C2—161no—
808C2C2×#242511yescharacteristic
809C2C2×#304311yescharacteristic
810C2#6042711yescharacteristic
811C2#6119312yes—
812C2#6127112yes—
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#525C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2280 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#483C2semidirect
4. #34203C2semidirect
5. #25231C2semidirect
6. #25219C2semidirect
7. #25208C2semidirect
8. #25204C2semidirect
9. #23661C2semidirect
10. #23633C2semidirect
11. #23610C2semidirect
12. #23545C2semidirect
13. #21174C2semidirect
14. #21068C2semidirect
15. #20930C2semidirect
17. #20836C2semidirect
18. #20651C2semidirect
19. C2×#1736C2semidirect
69. #2085C22semidirect
70. #2084C22semidirect
71. #2074C22semidirect
72. #2072C22semidirect
73. #2066C22semidirect
74. #2065C22semidirect
75. #2056C22semidirect
76. #2055C22semidirect
77. #1949C22semidirect
78. #1948C22semidirect
79. #1927C22semidirect
80. #1926C22semidirect
81. #1880C22semidirect
82. #1878C22semidirect
89. #1805C22semidirect
90. #1803C22semidirect

Maximal subgroups

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

subgroupindex
C22×#4832
C2×#30562
#352272
#342032
#252312
#252192
#252082
#252042
#236612
#236332
#236102
#235452
#211742
#210682
#209302
#209082
#208362
#206512
C2×#17362