Finite Group Databasebeta

← #11633007

Subgroups — #11633007

Order 768.

3272 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5817C212yesmaximal, complemented
2C2×#5627C212yesmaximal, complemented
3C3×#2409C211yesmaximal, characteristic, complemented
4#82755C212yesmaximal, complemented
5C4×#937C211yesmaximal, characteristic, complemented
6#82378C211yesmaximal, characteristic, complemented
7#77176C214yesmaximal, complemented
8#76873C212yesmaximal, complemented
9#76787C212yesmaximal, complemented
10#76626C212yesmaximal, complemented
11#76491C212yesmaximal, complemented
12#74912C212yesmaximal, complemented
13#74679C212yesmaximal, complemented
14#74427C214yesmaximal, complemented
15#74019C212yesmaximal, complemented
16#59001—31nomaximal, Sylow
17C23×C3×Q8C2211yescharacteristic, complemented
18C22×#239C2212yes—
19C23×C4×D3C2211yescharacteristic
20C2×C3×C22⋊Q8C2212yes—
21C2×C3×C4×D4C2211yescharacteristic
22#5817—216no—
23C2×#947C2214yes—
24C2×#947C2212yescomplemented
25C2×#946C2212yes—
26C2×#946C2214yescomplemented
27C2×Q8×Dic3C2212yescomplemented
28C2×#940C2212yes—
29C2×#937C2211yescharacteristic
30C2×#930C2212yes—
31C2×#930C2214yes—
32C2×#930C2212yescomplemented
33C2×C4×#67C2212yes—
34C2×C4×#67C2214yescomplemented
35#5627—216no—
36C2×#895C2212yes—
37C2×#894C2214yes—
38C2×#893C2214yes—
39C2×#892C2212yes—
40C2×#882C2214yes—
41C2×#67⋊C4C2214yes—
42C2×#874C2211yescharacteristic, complemented
43C3×#395C2212yescomplemented
44C3×#393C2212yes—
45C3×#391C2212yescomplemented
46C3×#386C2212yes—
47C3×#385C2212yescomplemented
48C3×#380C2211yescharacteristic, complemented
49#5220C2211yescharacteristic
50C4×#217C2211yescharacteristic
51#4994C2214yescomplemented
52#4990C2214yescomplemented
53#4989C2212yes—
54#4988C2212yescomplemented
55#4988C2212yescomplemented
56#4972C2212yescomplemented
57#4961C2214yes—
58#4960C2214yes—
59#4960C2212yes—
60#4960C2212yescomplemented
61#4957C2214yes—
62#4957C2214yescomplemented
63#4956C2212yes—
64#4955C2211yescharacteristic
65#4946C2211yescharacteristic
66C4×(C2×D3)⋊C4C2212yes—
67C4×C4⋊Dic3C2211yescharacteristic, complemented
68#4672C2214yes—
69#4671C2214yes—
70#4671C2214yes—
71#4670C2214yes—
72#4669C2214yes—
73#4669C2214yescomplemented
74#4665C2214yescomplemented
75#4665C2214yescomplemented
76#4655C2214yescomplemented
77#4649C2214yescomplemented
78C2×#548—32no—
79C2×#525—32no—
80#2670—32no—
81#2669—32no—
82#2541—31no—
83#2463—32no—
84#2461—34no—
85#2456—34no—
86#2431—32no—
87#2426—32no—
88#2414—32no—
89#2409D311yescharacteristic, complemented
90#2366—32no—
91#2362—32no—
92C4×#120—31no—
93C24×D3C2311yescharacteristic
94C22×C3×Q8—28no—
95C22×C3×Q8—42no—
96C22×C3×Q8C2312yes—
97C22×C3×Q8C2312yes—
98C22×C3×D4C2311yescharacteristic
99C23×C3×C4C2311yescharacteristic
100C23×C3×C4C2311yescharacteristic
101C23×C3×C4C2312yes—
102C22×#67C2312yes—
103C22×#67C2314yes—
104C22×#67C2314yes—
105C23×Dic3C2311yescharacteristic
106C2×#239—28no—
107C2×#239—28no—
108C2×#239—44no—
109C22×D12C2312yes—
110C22×D12C2314yes—
111C22×D12C2312yes—
112C22×D12C2314yes—
113C22×D12C2312yes—
114C22×C4×D3—28no—
115C22×C4×D3—42no—
116C22×C4×D3C2314yes—
117C22×C4×D3C2312yes—
118C22×C4×D3C2312yes—
119C3×C22⋊Q8—28no—
120C3×C4×D4—42no—
121C2×C3×C4⋊C4C2312yes—
122C2×C3×C4⋊C4C2314yes—
123C2×C3×C4⋊C4C2311yescharacteristic
124C2×C3×C22⋊C4C2314yes—
125C2×C3×C22⋊C4C2311yescharacteristic
126C2×C3×C22⋊C4C2311yescharacteristic
127C2×C3×C22⋊C4C2312yes—
128C2×C3×C42C2311yescharacteristic
129C2×#217C2311yescharacteristic
130C2×#217C2312yes—
131C2×#217C2311yescharacteristic
132#947—28no—
133#947—216no—
134#946—216no—
135#946D4116yescomplemented
136Q8×Dic3—28no—
137#940—28no—
138#937—24no—
139#930—216no—
140#930—28no—
141#930—28no—
142C4×#67—28no—
143C4×#67—216no—
144C2×(C2×D3)⋊C4C2314yes—
145C2×(C2×D3)⋊C4C2314yes—
146C2×(C2×D3)⋊C4C2314yes—
147C2×(C2×D3)⋊C4C2314yes—
148C2×(C2×D3)⋊C4C2314yes—
149C2×(C2×D3)⋊C4C2312yes—
150C2×(C2×D3)⋊C4C2312yes—
151C2×(C2×D3)⋊C4C2314yes—
152C2×(C2×D3)⋊C4C2314yes—
153C2×(C2×D3)⋊C4C2314yes—
154C2×(C2×D3)⋊C4C2312yes—
155C2×(C2×D3)⋊C4C2314yes—
156C2×C4⋊Dic3C2314yes—
157C2×C4⋊Dic3C2312yes—
158C2×Dic3⋊C4C2312yes—
159C2×Dic3⋊C4C2314yes—
160C2×Dic3⋊C4C2314yes—
161C2×C4×Dic3C2312yes—
162C2×C4×Dic3C2314yes—
163C2×C4×Dic3C2314yes—
164C2×C4×Dic3C2312yes—
165#895—28no—
166#894—216no—
167#893—216no—
168#892—28no—
169#882—216no—
170#67⋊C4—216no—
171#874—42no—
172C3×#95C2314yes—
173C3×#95C2314yes—
174C3×#95C2312yes—
175C3⋊#95C2312yes—
176C3⋊#95C2312yes—
177C3⋊#95C2312yes—
178C3⋊#95C2314yes—
179C3⋊#95C2312yes—
180C22×#41—32no—
181C23×Q8C2×D311yescharacteristic, complemented
182C24×C4—31no—
183#548—616no—
184C2×#127—32no—
185C2×#127—31no—
186C2×#124—34no—
187C2×#124—32no—
188#525—616no—
189C2×#123—34no—
190C2×C22⋊Q8—32no—
191C2×C22⋊Q8—34no—
192C2×C22⋊Q8C2×D312yes—
193C2×#121—32no—
194C2×#121—34no—
195C2×#121—32no—
196C2×#121—32no—
197C2×#120—31no—
198C2×#120—34no—
199C2×C4×Q8—32no—
200C2×C4×D4—34no—
201C2×C4×D4—32no—
202C2×C4×D4—34no—
203C2×C4×D4—34no—
204C2×C4×D4C2×D311yescharacteristic
205C2×#117—32no—
206#396—34no—
207#395C2×D312yescomplemented
208#394—34no—
209#394—34no—
210#393C2×D312yes—
211#392—34no—
212#392—32no—
213#392—32no—
214#392—34no—
215#392—34no—
216#391C2×D312yescomplemented
217#390—32no—
218#390—32no—
219#390—34no—
220#390—34no—
221#389—32no—
222#388—34no—
223#388—34no—
224#388—34no—
225#388—34no—
226#387—34no—
227#386—31no—
228#386—32no—
229#386—34no—
230#386—34no—
231#386C2×D312yes—
232#385—32no—
233#385—31no—
234#385C2×D312yescomplemented
235#380C2×D311yescharacteristic, complemented
236#379—31no—
237C4×C4⋊C4—31no—
238C4×C4⋊C4—34no—
239C4×C22⋊C4—31no—
240C4×C22⋊C4—32no—
241C24×C3C2411yescharacteristic
242C24×C3C2411yescharacteristic
243C23×D3—22no—
244C23×D3—24no—
245C23×D3—41no—
246C23×D3—42no—
247C23×D3—41no—
248C23×D3C2414yes—
249C23×D3C2412yes—
250C2×C3×Q8—24no—
251C2×C3×Q8—28no—
252C2×C3×Q8—24no—
253C2×C3×Q8—42no—
254C2×C3×Q8—416no—
255C2×C3×Q8C2×D418yes—
256C2×C3×D4—41no—
257C2×C3×D4—41no—
258C2×C3×D4#4114yescomplemented
259C22×C3×C4—28no—
260C22×C3×C4—24no—
261C22×C3×C4—24no—
262C22×C3×C4—22no—
263C22×C3×C4—22no—
264C22×C3×C4—42no—
265C22×C3×C4C2411yescharacteristic
266C22×C3×C4C2411yescharacteristic
267C22×C3×C4C2414yes—
268C22×C3×C4C2411yescharacteristic
269C22×C3×C4C2414yes—
270C22×C3×C4C2411yescharacteristic
271C22×C3×C4C2411yescharacteristic
272C2×#67—24no—
273C2×#67—28no—
274C2×#67—28no—
275C2×#67—24no—
276C2×#67—28no—
277C2×#67—28no—
278C2×#67—44no—
279C2×#67—44no—
280C2×#67—42no—
281C22×Dic3—24no—
282C22×Dic3—41no—
283C22×Dic3C2412yes—
284C22×Dic3C2412yes—
285C22×Dic3C2414yes—
286C22×Dic3C2412yes—
287#239—432no—
288C2×D12—28no—
289C2×D12—28no—
290C2×D12—28no—
291C2×D12—24no—
292C2×D12—24no—
293C2×D12—24no—
294C2×D12—24no—
295C2×D12—44no—
296C2×D12—44no—
297C2×D12—44no—
298C2×D12—42no—
299C2×D12—42no—
300C2×D12—42no—
301C2×D12—44no—
302C2×C4×D3—24no—
303C2×C4×D3—24no—
304C2×C4×D3—24no—
305C2×C4×D3—28no—
306C2×C4×D3—24no—
307C2×C4×D3—28no—
308C2×C4×D3—416no—
309C2×C4×D3—42no—
310C2×C4×D3—44no—
311C2×C4×D3C2×D418yes—
312C3×C4⋊C4—24no—
313C3×C4⋊C4—28no—
314C3×C4⋊C4—41no—
315C3×C22⋊C4—28no—
316C3×C22⋊C4—42no—
317C3×C22⋊C4—41no—
318C3×C22⋊C4—41no—
319C3×C42—22no—
320#217—22no—
321#217—24no—
322#217—41no—
323(C2×D3)⋊C4—24no—
324(C2×D3)⋊C4—28no—
325(C2×D3)⋊C4—28no—
326(C2×D3)⋊C4—24no—
327(C2×D3)⋊C4—28no—
328(C2×D3)⋊C4—28no—
329(C2×D3)⋊C4—28no—
330(C2×D3)⋊C4—28no—
331(C2×D3)⋊C4—42no—
332(C2×D3)⋊C4—44no—
333(C2×D3)⋊C4—44no—
334(C2×D3)⋊C4C2×D4116yes—
335C4⋊Dic3—28no—
336C4⋊Dic3C2×D418yes—
337Dic3⋊C4—24no—
338Dic3⋊C4—44no—
339Dic3⋊C4C2×D4116yes—
340C4×Dic3—24no—
341C4×Dic3—24no—
342C4×Dic3—28no—
343C4×Dic3—28no—
344C25—31no—
345C2×#41—68no—
346C2×#41—68no—
347C2×#41—124no—
348C22×Q8—28no—
349C22×Q8—42no—
350C22×Q8C22×D312yes—
351C22×Q8C22×D312yes—
352C22×D4—32no—
353C22×D4—34no—
354C22×D4—34no—
355C22×D4—32no—
356C22×D4—34no—
357C22×D4—34no—
358C22×D4—32no—
359C22×D4—32no—
360C22×D4C22×D311yescharacteristic
361C23×C4—32no—
362C23×C4—31no—
363C23×C4—34no—
364C23×C4—32no—
365C23×C4—68no—
366C23×C4—122no—
367C23×C4C22×D311yescharacteristic
368C23×C4C22×D311yescharacteristic
369C23×C4C22×D312yes—
370#127—68no—
371#127—122no—
372#124—616no—
373#124—68no—
374#123—616no—
375C22⋊Q8—28no—
376C22⋊Q8—316no—
377C22⋊Q8—616no—
378#121—616no—
379#121—68no—
380#121—68no—
381#121—68no—
382#120—616no—
383#120—64no—
384C4×Q8—68no—
385C4×D4—42no—
386C4×D4—616no—
387C4×D4—616no—
388C4×D4—616no—
389C4×D4—68no—
390#117—68no—
391C2×C4⋊C4—32no—
392C2×C4⋊C4—34no—
393C2×C4⋊C4—32no—
394C2×C4⋊C4—34no—
395C2×C4⋊C4—34no—
396C2×C4⋊C4C22×D312yes—
397C2×C4⋊C4C22×D314yes—
398C2×C4⋊C4C22×D311yescharacteristic
399C2×C22⋊C4—34no—
400C2×C22⋊C4—32no—
401C2×C22⋊C4—31no—
402C2×C22⋊C4—34no—
403C2×C22⋊C4—34no—
404C2×C22⋊C4—34no—
405C2×C22⋊C4—32no—
406C2×C22⋊C4—34no—
407C2×C22⋊C4—32no—
408C2×C22⋊C4—34no—
409C2×C22⋊C4—34no—
410C2×C22⋊C4—31no—
411C2×C22⋊C4—32no—
412C2×C22⋊C4—34no—
413C2×C22⋊C4—34no—
414C2×C22⋊C4C22×D314yes—
415C2×C22⋊C4C22×D311yescharacteristic
416C2×C22⋊C4C22×D311yescharacteristic
417C2×C22⋊C4C22×D312yes—
418C2×C42—34no—
419C2×C42—32no—
420C2×C42—34no—
421C2×C42—32no—
422C2×C42C22×D311yescharacteristic
423#95—32no—
424#95—32no—
425#95—32no—
426#95—32no—
427#95—34no—
428#95C22×D314yes—
429#95C22×D312yes—
430#95C22×D314yes—
431C23×C3—22no—
432C23×C3—22no—
433C23×C3—21no—
434C23×C3—21no—
435C23×C3—21no—
436C23×C3—21no—
437C23×C3—22no—
438C23×C3—22no—
439C23×C3C2×#4112yes—
440C23×C3C2×#4112yes—
441C23×C3C2511yescharacteristic
442C22×D3—22no—
443C22×D3—22no—
444C22×D3—22no—
445C22×D3—22no—
446C22×D3—22no—
447C22×D3—22no—
448C22×D3—24no—
449C22×D3—24no—
450C22×D3—24no—
451C22×D3—24no—
452C22×D3—24no—
453C22×D3—24no—
454C22×D3—24no—
455C22×D3—44no—
456C22×D3—48no—
457C22×D3—48no—
458C22×D3—44no—
459C22×D3—44no—
460C22×D3C22×D414yes—
461C3×Q8—216no—
462C3×Q8—48no—
463C3×D4—44no—
464C2×C3×C4—24no—
465C2×C3×C4—21no—
466C2×C3×C4—24no—
467C2×C3×C4—21no—
468C2×C3×C4—24no—
469C2×C3×C4—22no—
470C2×C3×C4—22no—
471C2×C3×C4—21no—
472C2×C3×C4—21no—
473C2×C3×C4—21no—
474C2×C3×C4—24no—
475C2×C3×C4—24no—
476C2×C3×C4—22no—
477C2×C3×C4—48no—
478C2×C3×C4—44no—
479C2×C3×C4—44no—
480C2×C3×C4C22×D418yes—
481C2×C3×C4C22×D414yes—
482C2×C3×C4C2×#4112yes—
483C2×C3×C4H(5,𝔽2)12yes—
484#67—416no—
485#67—416no—
486#67—48no—
487C2×Dic3—22no—
488C2×Dic3—24no—
489C2×Dic3—22no—
490C2×Dic3—24no—
491C2×Dic3—22no—
492C2×Dic3—22no—
493C2×Dic3—22no—
494C2×Dic3—22no—
495C2×Dic3—22no—
496C2×Dic3—22no—
497C2×Dic3—44no—
498C2×Dic3C22×D418yes—
499C2×Dic3C22×D414yes—
500D12—416no—
501D12—416no—
502D12—48no—
503D12—84no—
504D12—84no—
505C4×D3—216no—
506C4×D3—416no—
507C4×D3—48no—
508C24—32no—
509C24—34no—
510C24—64no—
511C24—62no—
512C24—121no—
513C24—121no—
514C24—122no—
515C24C23×D311yescharacteristic
516C24C23×D311yescharacteristic
517#41—1232no—
518C2×Q8—24no—
519C2×Q8—28no—
520C2×Q8—24no—
521C2×Q8—42no—
522C2×Q8—416no—
523C2×Q8D3×D418yes—
524C2×D4—41no—
525C2×D4—41no—
526C2×D4—68no—
527C2×D4—68no—
528C2×D4—68no—
529C2×D4—68no—
530C2×D4—64no—
531C2×D4—64no—
532C2×D4—68no—
533C2×D4—68no—
534C2×D4—68no—
535C2×D4—64no—
536C2×D4—64no—
537C2×D4—64no—
538C2×D4—64no—
539C2×D4—124no—
540C2×D4—124no—
541C2×D4—124no—
542C2×D4—122no—
543C2×D4—122no—
544C2×D4—122no—
545C2×D4—124no—
546C2×D4—124no—
547C2×D4—124no—
548C2×D4—122no—
549C2×D4#23914yescomplemented
550C22×C4—28no—
551C22×C4—24no—
552C22×C4—24no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—34no—
556C22×C4—32no—
557C22×C4—38no—
558C22×C4—32no—
559C22×C4—32no—
560C22×C4—42no—
561C22×C4—68no—
562C22×C4—64no—
563C22×C4—64no—
564C22×C4—64no—
565C22×C4—64no—
566C22×C4—64no—
567C22×C4—68no—
568C22×C4—122no—
569C22×C4—124no—
570C22×C4—1216no—
571C22×C4—121no—
572C22×C4C23×D311yescharacteristic
573C22×C4C23×D311yescharacteristic
574C22×C4C23×D314yes—
575C22×C4C23×D311yescharacteristic
576C22×C4C23×D314yes—
577C22×C4C23×D311yescharacteristic
578C22×C4C23×D311yescharacteristic
579C4⋊C4—24no—
580C4⋊C4—28no—
581C4⋊C4—38no—
582C4⋊C4—316no—
583C4⋊C4—41no—
584C4⋊C4—64no—
585C4⋊C4—68no—
586C4⋊C4—124no—
587C22⋊C4—28no—
588C22⋊C4—316no—
589C22⋊C4—41no—
590C22⋊C4—41no—
591C22⋊C4—42no—
592C22⋊C4—68no—
593C22⋊C4—68no—
594C22⋊C4—68no—
595C22⋊C4—68no—
596C22⋊C4—64no—
597C22⋊C4—64no—
598C22⋊C4—62no—
599C22⋊C4—68no—
600C22⋊C4—68no—
601C22⋊C4—64no—
602C22⋊C4—124no—
603C22⋊C4—124no—
604C22⋊C4—122no—
605C22⋊C4—121no—
606C42—22no—
607C42—68no—
608C42—68no—
609C42—64no—
610C42—64no—
611C22×C3—24no—
612C22×C3—24no—
613C22×C3—22no—
614C22×C3—22no—
615C22×C3—41no—
616C22×C3—41no—
617C22×C3—42no—
618C22×C3—42no—
619C22×C3—41no—
620C22×C3—41no—
621C22×C3C23×D412yes—
622C22×C3C22×#4111yescharacteristic
623C22×C3C2×H(5,𝔽2)11yescharacteristic
624C22×C3#58511yescharacteristic
625C22×C3#58512yes—
626C2×D3—24no—
627C2×D3—24no—
628C2×D3—24no—
629C2×D3—416no—
630C2×D3—42no—
631C2×D3—42no—
632C2×D3—42no—
633C2×D3—42no—
634C2×D3—44no—
635C2×D3—44no—
636C2×D3—44no—
637C2×D3—44no—
638C2×D3—44no—
639C2×D3—44no—
640C2×D3—44no—
641C3×C4—28no—
642C3×C4—22no—
643C3×C4—41no—
644C3×C4—41no—
645C3×C4—44no—
646C3×C4—41no—
647C3×C4D4214yes—
648Dic3—24no—
649Dic3—28no—
650Dic3—42no—
651Dic3—42no—
652C23—22no—
653C23—22no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—22no—
659C23—22no—
660C23—34no—
661C23—62no—
662C23—62no—
663C23—62no—
664C23—62no—
665C23—62no—
666C23—62no—
667C23—64no—
668C23—64no—
669C23—64no—
670C23—64no—
671C23—64no—
672C23—64no—
673C23—64no—
674C23—128no—
675C23—124no—
676C23—124no—
677C23—128no—
678C23—124no—
679C23C2×#23912yes—
680C23C2×#23912yes—
681C23C24×D311yescharacteristic
682Q8—216no—
683Q8—48no—
684D4—44no—
685D4—1216no—
686D4—1216no—
687D4—1216no—
688D4—1216no—
689D4—128no—
690D4—128no—
691D4—244no—
692D4—244no—
693C2×C4—24no—
694C2×C4—21no—
695C2×C4—24no—
696C2×C4—21no—
697C2×C4—24no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—22no—
706C2×C4—38no—
707C2×C4—34no—
708C2×C4—48no—
709C2×C4—44no—
710C2×C4—44no—
711C2×C4—62no—
712C2×C4—62no—
713C2×C4—64no—
714C2×C4—64no—
715C2×C4—616no—
716C2×C4—62no—
717C2×C4—62no—
718C2×C4—62no—
719C2×C4—62no—
720C2×C4—62no—
721C2×C4—62no—
722C2×C4—1216no—
723C2×C4—128no—
724C2×C4—124no—
725C2×C4C2×D3×D418yes—
726C2×C4C2×D3×D414yes—
727C2×C4#100412yes—
728C2×C4C2×#23912yes—
729C2×C3—42no—
730C2×C3—42no—
731C2×C3C2×D4211yescharacteristic
732C2×C3D4×#4112yes—
733C2×C3#348712yes—
734C2×C3#350511yescharacteristic
735C2×C3#354011yescharacteristic
736D3—44no—
737D3—84no—
738C22—22no—
739C22—22no—
740C22—24no—
741C22—24no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—41no—
746C22—42no—
747C22—42no—
748C22—64no—
749C22—64no—
750C22—64no—
751C22—1216no—
752C22—122no—
753C22—122no—
754C22—122no—
755C22—122no—
756C22—124no—
757C22—124no—
758C22—124no—
759C22—124no—
760C22—124no—
761C22—124no—
762C22—124no—
763C22C22×D3×D412yes—
764C22C2×#100411yescharacteristic
765C22C22×#23911yescharacteristic
766C22#596411yescharacteristic
767C22#596812yes—
768C4—28no—
769C4—22no—
770C4—41no—
771C4—41no—
772C4—41no—
773C4—44no—
774C4—64no—
775C4—68no—
776C4—122no—
777C4—122no—
778C4#559014yes—
779C3#5900111yescharacteristic, complemented, Sylow
780C2—42no—
781C2—42no—
782C2—124no—
783C2—244no—
784C2C2×#559011yescharacteristic
785C2#8597111yescharacteristic
786C2#8634511yescharacteristic
787C2#8673612yes—
788C2D4×#23912yes—
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2409C2
hypercenter#2409D3
hypocenterC3#59001
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2409

Complements

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

NH ≅ G/Ntype
1. C2×#5817C2semidirect
2. C2×#5627C2semidirect
3. C3×#2409C2semidirect
4. #82755C2semidirect
5. C4×#937C2semidirect
6. #82378C2semidirect
7. #77176C2semidirect
8. #76873C2semidirect
9. #76787C2semidirect
10. #76626C2semidirect
11. #76491C2semidirect
12. #74912C2semidirect
13. #74679C2semidirect
14. #74427C2semidirect
15. #74019C2semidirect
17. C23×C3×Q8C22semidirect
24. C2×#947C22semidirect
26. C2×#946C22semidirect
27. C2×Q8×Dic3C22semidirect
32. C2×#930C22semidirect
34. C2×C4×#67C22semidirect
42. C2×#874C22semidirect
43. C3×#395C22semidirect
45. C3×#391C22semidirect
47. C3×#385C22semidirect
48. C3×#380C22semidirect
51. #4994C22semidirect
52. #4990C22semidirect
54. #4988C22semidirect
55. #4988C22semidirect
56. #4972C22semidirect
60. #4960C22semidirect
62. #4957C22semidirect
67. C4×C4⋊Dic3C22semidirect
73. #4669C22semidirect
74. #4665C22semidirect
75. #4665C22semidirect
76. #4655C22semidirect
77. #4649C22semidirect
89. #2409D3semidirect
135. #946D4semidirect
181. C23×Q8C2×D3semidirect
207. #395C2×D3semidirect
216. #391C2×D3semidirect
234. #385C2×D3semidirect
235. #380C2×D3semidirect
258. C2×C3×D4#41semidirect
549. C2×D4#239semidirect
779. C3#59001semidirect

Maximal subgroups

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

subgroupindex
C2×#58172
C2×#56272
C3×#24092
#827552
C4×#9372
#823782
#771762
#768732
#767872
#766262
#764912
#749122
#746792
#744272
#740192
#590013