Finite Group Databasebeta

← #11633016

Subgroups — #11633016

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×#5791C212yesmaximal, complemented
2C2×#5552C212yesmaximal, complemented
3C3×C4×#120C211yesmaximal, characteristic, complemented
4#82594C212yesmaximal, complemented
5#82378C211yesmaximal, characteristic, complemented
6#82350C212yesmaximal, complemented
7#82349C211yesmaximal, characteristic, complemented
8#74898C214yesmaximal, complemented
9#74679C212yesmaximal, complemented
10#74613C212yesmaximal, complemented
11#74431C214yesmaximal, complemented
12#73837C212yesmaximal, complemented
13#73586C212yesmaximal, complemented
14#73485C212yesmaximal, complemented
15#73468C212yesmaximal, complemented
16#59001—31nomaximal, Sylow
17C24×C3×C4C2211yescharacteristic
18C22×#235C2212yes—
19C23×Dic6C2211yescharacteristic, complemented
20C2×C3×#120C2211yescharacteristic
21C2×C3×C4×D4C2212yes—
22C2×C3×C4×D4C2211yescharacteristic
23C2×#953C2214yes—
24C2×#940C2212yes—
25C2×#939C2214yes—
26#5791—216no—
27C2×#930C2212yes—
28C2×#930C2212yes—
29C2×#930C2212yescomplemented
30C2×#929C2214yes—
31C2×C4×#67C2214yes—
32C2×C4×#67C2214yes—
33C2×#926C2212yes—
34C2×#924C2212yes—
35C2×#924C2212yes—
36#5552—216no—
37C2×#896C2214yescomplemented
38C2×#885C2214yes—
39C2×#67⋊C4C2214yescomplemented
40C2×#875C2212yescomplemented
41C2×#874C2211yescharacteristic, complemented
42C2×C4×Dic6C2212yescomplemented
43C3×#386C2212yes—
44C3×#386C2211yescharacteristic
45C3×#385C2211yescharacteristic
46C3×#385C2212yes—
47C3×#379C2211yescharacteristic
48C3×C4×C22⋊C4C2211yescharacteristic
49C3×C4×C22⋊C4C2212yes—
50#5223C2214yes—
51#5220C2212yes—
52#5212C2211yescharacteristic, complemented
53#4990C2214yescomplemented
54#4988C2212yescomplemented
55#4979C2212yescomplemented
56#4960C2214yes—
57#4960C2212yes—
58#4960C2214yes—
59#4960C2212yescomplemented
60#4959C2214yes—
61#4959C2214yes—
62#4957C2214yes—
63#4957C2214yescomplemented
64#4947C2212yes—
65#4946C2212yescomplemented
66#4945C2214yes—
67#4944C2214yes—
68#4939C2212yescomplemented
69C4×C4⋊Dic3C2211yescharacteristic, complemented
70#4929C2212yescomplemented
71#4928C2212yescomplemented
72#4676C2214yescomplemented
73#4669C2214yescomplemented
74#4665C2214yescomplemented
75#4665C2214yescomplemented
76#4652C2214yescomplemented
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#2409—31no—
90#2366—32no—
91#2362—32no—
92C4×#120D311yescharacteristic, complemented
93C25×C3C2311yescharacteristic
94C22×C3×D4C2312yes—
95C22×C3×D4C2311yescharacteristic
96C23×C3×C4—28no—
97C23×C3×C4—42no—
98C23×C3×C4C2311yescharacteristic
99C23×C3×C4C2311yescharacteristic
100C23×C3×C4C2311yescharacteristic
101C23×C3×C4C2312yes—
102C23×C3×C4C2312yes—
103C22×#67C2314yes—
104C22×#67C2314yes—
105C22×#67C2314yes—
106C22×#67C2314yes—
107C23×Dic3C2312yes—
108C2×#235—28no—
109C2×#235—28no—
110C2×#235—44no—
111C22×D12C2312yes—
112C22×D12C2312yes—
113C22×D12C2312yes—
114C22×C4×D3C2314yes—
115C22×Dic6—28no—
116C22×Dic6—42no—
117C22×Dic6C2312yes—
118C22×Dic6C2312yes—
119C3×#120—24no—
120C3×C4×D4—28no—
121C3×C4×D4—42no—
122C2×C3×C4⋊C4C2312yes—
123C2×C3×C4⋊C4C2311yescharacteristic
124C2×C3×C22⋊C4C2312yes—
125C2×C3×C22⋊C4C2312yes—
126C2×C3×C22⋊C4C2311yescharacteristic
127C2×C3×C22⋊C4C2312yes—
128C2×C3×C22⋊C4C2312yes—
129C2×C3×C22⋊C4C2311yescharacteristic
130C2×C3×C22⋊C4C2311yescharacteristic
131C2×C3×C22⋊C4C2311yescharacteristic
132C2×C3×C42C2312yes—
133C2×C3×C42C2311yescharacteristic
134#953—216no—
135C2×#217C2314yes—
136C2×#217C2314yes—
137C2×#217C2312yes—
138C2×#217C2314yes—
139#940—28no—
140#939—216no—
141#930—28no—
142#930—28no—
143#930—28no—
144#929—216no—
145C4×#67—216no—
146C4×#67—216no—
147C2×(C2×D3)⋊C4C2314yes—
148C2×(C2×D3)⋊C4C2314yes—
149C2×(C2×D3)⋊C4C2314yes—
150C2×(C2×D3)⋊C4C2314yes—
151C2×(C2×D3)⋊C4C2314yes—
152C2×(C2×D3)⋊C4C2314yes—
153C2×(C2×D3)⋊C4C2314yes—
154#926—28no—
155C2×C4⋊Dic3C2312yes—
156C2×C4⋊Dic3C2312yes—
157#924—28no—
158#924D4116yescomplemented
159C2×Dic3⋊C4C2314yes—
160C2×Dic3⋊C4C2314yes—
161C2×Dic3⋊C4C2314yes—
162C2×Dic3⋊C4C2314yes—
163C2×C4×Dic3C2312yes—
164C2×C4×Dic3C2314yes—
165C2×C4×Dic3C2314yes—
166#896—216no—
167#885—216no—
168#67⋊C4—216no—
169#875—28no—
170#874—42no—
171C4×Dic6—28no—
172C3×#95C2312yes—
173C3×#95C2312yes—
174C3×#95C2312yes—
175C3⋊#95C2314yes—
176C3⋊#95C2312yes—
177C3⋊#95C2314yes—
178C3⋊#95C2314yes—
179C3⋊#95C2312yes—
180C22×#41—32no—
181C23×Q8—31no—
182C24×C4C2×D311yescharacteristic
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—32no—
192C2×C22⋊Q8—34no—
193C2×#121—34no—
194C2×#121—32no—
195C2×#121—32no—
196C2×#121—32no—
197C2×#120—34no—
198C2×#120C2×D311yescharacteristic
199C2×C4×Q8—32no—
200C2×C4×D4—34no—
201C2×C4×D4—34no—
202C2×C4×D4—34no—
203C2×C4×D4C2×D312yes—
204C2×C4×D4C2×D311yescharacteristic
205C2×#117—32no—
206#396—34no—
207#395—32no—
208#394—34no—
209#394—34no—
210#393—32no—
211#392—34no—
212#392—34no—
213#392—34no—
214#392—32no—
215#392—32no—
216#391—32no—
217#390—32no—
218#390—34no—
219#390—34no—
220#390—32no—
221#389—32no—
222#388—34no—
223#388—34no—
224#388—34no—
225#388—34no—
226#387—34no—
227#386—32no—
228#386—34no—
229#386—34no—
230#386C2×D311yescharacteristic
231#386C2×D312yes—
232#385—32no—
233#385C2×D312yes—
234#385C2×D311yescharacteristic
235#380—31no—
236#379C2×D311yescharacteristic
237C4×C4⋊C4—31no—
238C4×C4⋊C4—34no—
239C4×C22⋊C4C2×D312yes—
240C4×C22⋊C4C2×D311yescharacteristic
241C24×C3—24no—
242C24×C3—22no—
243C24×C3—42no—
244C24×C3—41no—
245C24×C3—41no—
246C24×C3C2412yes—
247C24×C3C2411yescharacteristic
248C24×C3C2411yescharacteristic
249C23×D3C2414yes—
250C2×C3×D4—24no—
251C2×C3×D4—24no—
252C2×C3×D4—41no—
253C2×C3×D4—41no—
254C2×C3×D4—42no—
255C2×C3×D4#4114yescomplemented
256C22×C3×C4—24no—
257C22×C3×C4—24no—
258C22×C3×C4—24no—
259C22×C3×C4—24no—
260C22×C3×C4—24no—
261C22×C3×C4—24no—
262C22×C3×C4—24no—
263C22×C3×C4—22no—
264C22×C3×C4—22no—
265C22×C3×C4—41no—
266C22×C3×C4—42no—
267C22×C3×C4—416no—
268C22×C3×C4C2×D418yes—
269C22×C3×C4C2411yescharacteristic
270C22×C3×C4C2412yes—
271C22×C3×C4C2411yescharacteristic
272C22×C3×C4C2412yes—
273C22×C3×C4C2411yescharacteristic
274C22×C3×C4C2412yes—
275C22×C3×C4C2411yescharacteristic
276C22×C3×C4C2411yescharacteristic
277C2×#67—28no—
278C2×#67—28no—
279C2×#67—28no—
280C2×#67—28no—
281C2×#67—28no—
282C2×#67—28no—
283C2×#67—28no—
284C2×#67—44no—
285C2×#67—44no—
286C2×#67—44no—
287C2×#67—44no—
288C2×#67—44no—
289C22×Dic3—28no—
290C22×Dic3—42no—
291C22×Dic3C2414yes—
292C22×Dic3C2414yes—
293C22×Dic3C2414yes—
294#235—432no—
295C2×D12—24no—
296C2×D12—24no—
297C2×D12—24no—
298C2×D12—24no—
299C2×D12—42no—
300C2×D12—42no—
301C2×D12—42no—
302C2×D12—44no—
303C2×C4×D3—28no—
304C2×C4×D3—28no—
305C2×C4×D3—44no—
306C2×Dic6—24no—
307C2×Dic6—24no—
308C2×Dic6—28no—
309C2×Dic6—416no—
310C2×Dic6—42no—
311C2×Dic6C2×D418yes—
312C3×C4⋊C4—24no—
313C3×C4⋊C4—41no—
314C3×C22⋊C4—24no—
315C3×C22⋊C4—22no—
316C3×C22⋊C4—24no—
317C3×C22⋊C4—24no—
318C3×C22⋊C4—42no—
319C3×C22⋊C4—41no—
320C3×C22⋊C4—41no—
321C3×C22⋊C4—41no—
322C3×C42—24no—
323C3×C42—22no—
324#217—28no—
325#217—28no—
326#217—42no—
327#217C2×D4116yes—
328(C2×D3)⋊C4—28no—
329(C2×D3)⋊C4—28no—
330(C2×D3)⋊C4—28no—
331(C2×D3)⋊C4—28no—
332(C2×D3)⋊C4—28no—
333(C2×D3)⋊C4—44no—
334(C2×D3)⋊C4—44no—
335C4⋊Dic3—24no—
336C4⋊Dic3C2×D418yes—
337Dic3⋊C4—28no—
338Dic3⋊C4—28no—
339Dic3⋊C4—44no—
340Dic3⋊C4C2×D4116yes—
341C4×Dic3—24no—
342C4×Dic3—28no—
343C4×Dic3—28no—
344C25C22×D311yescharacteristic
345C2×#41—68no—
346C2×#41—68no—
347C2×#41—124no—
348C22×Q8—32no—
349C22×Q8—32no—
350C22×Q8—68no—
351C22×Q8—122no—
352C22×D4—34no—
353C22×D4—34no—
354C22×D4—34no—
355C22×D4—34no—
356C22×D4—32no—
357C22×D4—32no—
358C22×D4—32no—
359C22×D4C22×D312yes—
360C22×D4C22×D311yescharacteristic
361C23×C4—28no—
362C23×C4—32no—
363C23×C4—34no—
364C23×C4—42no—
365C23×C4C22×D311yescharacteristic
366C23×C4C22×D311yescharacteristic
367C23×C4C22×D311yescharacteristic
368C23×C4C22×D312yes—
369C23×C4C22×D312yes—
370#127—68no—
371#127—122no—
372#124—68no—
373#124—616no—
374#123—616no—
375C22⋊Q8—316no—
376C22⋊Q8—616no—
377C22⋊Q8—68no—
378#121—616no—
379#121—68no—
380#121—68no—
381#121—68no—
382#120—24no—
383#120—616no—
384C4×Q8—68no—
385C4×D4—28no—
386C4×D4—42no—
387C4×D4—616no—
388C4×D4—616no—
389C4×D4—616no—
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⋊C4—34no—
397C2×C4⋊C4C22×D312yes—
398C2×C4⋊C4C22×D311yescharacteristic
399C2×C22⋊C4—34no—
400C2×C22⋊C4—34no—
401C2×C22⋊C4—34no—
402C2×C22⋊C4—34no—
403C2×C22⋊C4—34no—
404C2×C22⋊C4—34no—
405C2×C22⋊C4—34no—
406C2×C22⋊C4—34no—
407C2×C22⋊C4—32no—
408C2×C22⋊C4—34no—
409C2×C22⋊C4—34no—
410C2×C22⋊C4C22×D312yes—
411C2×C22⋊C4C22×D312yes—
412C2×C22⋊C4C22×D312yes—
413C2×C22⋊C4C22×D311yescharacteristic
414C2×C22⋊C4C22×D311yescharacteristic
415C2×C22⋊C4C22×D311yescharacteristic
416C2×C22⋊C4C22×D312yes—
417C2×C22⋊C4C22×D311yescharacteristic
418C2×C42—34no—
419C2×C42—34no—
420C2×C42—32no—
421C2×C42C22×D312yes—
422C2×C42C22×D311yescharacteristic
423#95—34no—
424#95—32no—
425#95—32no—
426#95—34no—
427#95—34no—
428#95C22×D312yes—
429#95C22×D312yes—
430#95C22×D312yes—
431C23×C3—22no—
432C23×C3—22no—
433C23×C3—22no—
434C23×C3—22no—
435C23×C3—21no—
436C23×C3—21no—
437C23×C3—22no—
438C23×C3—21no—
439C23×C3—22no—
440C23×C3—21no—
441C23×C3—22no—
442C23×C3—22no—
443C23×C3—22no—
444C23×C3—22no—
445C23×C3—44no—
446C23×C3—48no—
447C23×C3—48no—
448C23×C3—44no—
449C23×C3—44no—
450C23×C3C22×D414yes—
451C23×C3C2×#4112yes—
452C23×C3C2×#4112yes—
453C23×C3C2511yescharacteristic
454C22×D3—24no—
455C22×D3—24no—
456C22×D3—24no—
457C22×D3—24no—
458C22×D3—24no—
459C22×D3—24no—
460C22×D3—24no—
461C3×D4—44no—
462C3×D4—48no—
463C2×C3×C4—22no—
464C2×C3×C4—21no—
465C2×C3×C4—22no—
466C2×C3×C4—21no—
467C2×C3×C4—216no—
468C2×C3×C4—22no—
469C2×C3×C4—22no—
470C2×C3×C4—22no—
471C2×C3×C4—22no—
472C2×C3×C4—22no—
473C2×C3×C4—21no—
474C2×C3×C4—21no—
475C2×C3×C4—21no—
476C2×C3×C4—22no—
477C2×C3×C4—22no—
478C2×C3×C4—22no—
479C2×C3×C4—22no—
480C2×C3×C4—44no—
481C2×C3×C4—48no—
482C2×C3×C4—44no—
483C2×C3×C4—44no—
484C2×C3×C4C22×D414yes—
485C2×C3×C4C22×D414yes—
486C2×C3×C4C2×#4112yes—
487C2×C3×C4H(5,𝔽2)12yes—
488#67—416no—
489#67—416no—
490#67—416no—
491#67—416no—
492C2×Dic3—24no—
493C2×Dic3—24no—
494C2×Dic3—24no—
495C2×Dic3—24no—
496C2×Dic3—24no—
497C2×Dic3—24no—
498C2×Dic3—24no—
499C2×Dic3—48no—
500C2×Dic3C22×D418yes—
501C2×Dic3C22×D418yes—
502D12—48no—
503D12—84no—
504D12—84no—
505C4×D3—416no—
506Dic6—216no—
507Dic6—48no—
508C24—22no—
509C24—24no—
510C24—34no—
511C24—41no—
512C24—42no—
513C24—41no—
514C24C23×D311yescharacteristic
515C24C23×D311yescharacteristic
516C24C23×D312yes—
517#41—1232no—
518C2×Q8—38no—
519C2×Q8—68no—
520C2×Q8—64no—
521C2×Q8—64no—
522C2×Q8—122no—
523C2×Q8—1216no—
524C2×D4—24no—
525C2×D4—24no—
526C2×D4—41no—
527C2×D4—41no—
528C2×D4—42no—
529C2×D4—68no—
530C2×D4—68no—
531C2×D4—68no—
532C2×D4—68no—
533C2×D4—68no—
534C2×D4—68no—
535C2×D4—68no—
536C2×D4—64no—
537C2×D4—64no—
538C2×D4—64no—
539C2×D4—64no—
540C2×D4—122no—
541C2×D4—122no—
542C2×D4—122no—
543C2×D4—124no—
544C2×D4—124no—
545C2×D4—124no—
546C2×D4—124no—
547C2×D4—124no—
548C2×D4—124no—
549C2×D4#23514yescomplemented
550C22×C4—24no—
551C22×C4—24no—
552C22×C4—24no—
553C22×C4—24no—
554C22×C4—24no—
555C22×C4—24no—
556C22×C4—24no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—34no—
560C22×C4—34no—
561C22×C4—34no—
562C22×C4—41no—
563C22×C4—42no—
564C22×C4—416no—
565C22×C4—68no—
566C22×C4—68no—
567C22×C4—68no—
568C22×C4—124no—
569C22×C4—122no—
570C22×C4D3×D418yes—
571C22×C4C23×D311yescharacteristic
572C22×C4C23×D312yes—
573C22×C4C23×D311yescharacteristic
574C22×C4C23×D312yes—
575C22×C4C23×D311yescharacteristic
576C22×C4C23×D311yescharacteristic
577C22×C4C23×D312yes—
578C22×C4C23×D311yescharacteristic
579C4⋊C4—24no—
580C4⋊C4—38no—
581C4⋊C4—316no—
582C4⋊C4—41no—
583C4⋊C4—68no—
584C4⋊C4—68no—
585C4⋊C4—64no—
586C4⋊C4—124no—
587C22⋊C4—22no—
588C22⋊C4—24no—
589C22⋊C4—24no—
590C22⋊C4—24no—
591C22⋊C4—316no—
592C22⋊C4—41no—
593C22⋊C4—41no—
594C22⋊C4—41no—
595C22⋊C4—42no—
596C22⋊C4—68no—
597C22⋊C4—68no—
598C22⋊C4—68no—
599C22⋊C4—68no—
600C22⋊C4—68no—
601C22⋊C4—68no—
602C22⋊C4—68no—
603C22⋊C4—124no—
604C22⋊C4—124no—
605C22⋊C4—122no—
606C42—24no—
607C42—22no—
608C42—68no—
609C42—68no—
610C42—64no—
611C22×C3—24no—
612C22×C3—24no—
613C22×C3—24no—
614C22×C3—24no—
615C22×C3—24no—
616C22×C3—22no—
617C22×C3—22no—
618C22×C3—416no—
619C22×C3—41no—
620C22×C3—41no—
621C22×C3—42no—
622C22×C3—42no—
623C22×C3—42no—
624C22×C3—42no—
625C22×C3—42no—
626C22×C3—41no—
627C22×C3—41no—
628C22×C3—42no—
629C22×C3C23×D412yes—
630C22×C3C22×#4111yescharacteristic
631C22×C3C2×H(5,𝔽2)11yescharacteristic
632C22×C3#58512yes—
633C22×C3#58511yescharacteristic
634C2×D3—44no—
635C2×D3—44no—
636C2×D3—44no—
637C2×D3—44no—
638C2×D3—44no—
639C2×D3—44no—
640C2×D3—44no—
641C3×C4—24no—
642C3×C4—22no—
643C3×C4—41no—
644C3×C4—41no—
645C3×C4—42no—
646C3×C4—42no—
647C3×C4—41no—
648C3×C4D4214yes—
649Dic3—28no—
650Dic3—28no—
651Dic3—44no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—21no—
657C23—21no—
658C23—22no—
659C23—22no—
660C23—21no—
661C23—21no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—44no—
667C23—48no—
668C23—48no—
669C23—44no—
670C23—44no—
671C23—64no—
672C23—64no—
673C23—64no—
674C23—64no—
675C23—64no—
676C23—64no—
677C23—64no—
678C23C2×#23512yes—
679C23C2×#23512yes—
680C23C2×D3×D414yes—
681C23C24×D311yescharacteristic
682Q8—616no—
683Q8—128no—
684D4—44no—
685D4—48no—
686D4—1216no—
687D4—1216no—
688D4—1216no—
689D4—1216no—
690D4—128no—
691D4—244no—
692D4—244no—
693C2×C4—22no—
694C2×C4—21no—
695C2×C4—22no—
696C2×C4—21no—
697C2×C4—216no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—38no—
711C2×C4—38no—
712C2×C4—44no—
713C2×C4—48no—
714C2×C4—44no—
715C2×C4—44no—
716C2×C4—64no—
717C2×C4—64no—
718C2×C4—64no—
719C2×C4—64no—
720C2×C4—64no—
721C2×C4—64no—
722C2×C4—64no—
723C2×C4—1216no—
724C2×C4—128no—
725C2×C4C2×#23512yes—
726C2×C4C2×D3×D414yes—
727C2×C4C2×D3×D414yes—
728C2×C4#100412yes—
729C2×C3—42no—
730C2×C3—44no—
731C2×C3—42no—
732C2×C3C2×D4211yescharacteristic
733C2×C3D4×#4112yes—
734C2×C3#348712yes—
735C2×C3#350511yescharacteristic
736C2×C3#354011yescharacteristic
737D3—84no—
738C22—24no—
739C22—24no—
740C22—24no—
741C22—24no—
742C22—22no—
743C22—22no—
744C22—24no—
745C22—416no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—41no—
752C22—42no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—124no—
757C22—124no—
758C22—124no—
759C22—124no—
760C22—124no—
761C22—124no—
762C22—124no—
763C22C22×#23511yescharacteristic
764C22C22×D3×D412yes—
765C22C2×#100411yescharacteristic
766C22#596411yescharacteristic
767C22#596412yes—
768C4—22no—
769C4—24no—
770C4—42no—
771C4—42no—
772C4—41no—
773C4—41no—
774C4—41no—
775C4—68no—
776C4—68no—
777C4—124no—
778C4#559014yes—
779C3#5900111yescharacteristic, complemented, Sylow
780C2—44no—
781C2—42no—
782C2—42no—
783C2—244no—
784C2D4×#23512yes—
785C2#8578711yescharacteristic
786C2C2×#559011yescharacteristic
787C2#8602312yes—
788C2#8605511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×C4×#120C2
hypercenterC4×#120D3
hypocenterC3#59001
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ C4×#120

Complements

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

NH ≅ G/Ntype
1. C2×#5791C2semidirect
2. C2×#5552C2semidirect
3. C3×C4×#120C2semidirect
4. #82594C2semidirect
5. #82378C2semidirect
6. #82350C2semidirect
7. #82349C2semidirect
8. #74898C2semidirect
9. #74679C2semidirect
10. #74613C2semidirect
11. #74431C2semidirect
12. #73837C2semidirect
13. #73586C2semidirect
14. #73485C2semidirect
15. #73468C2semidirect
19. C23×Dic6C22semidirect
29. C2×#930C22semidirect
37. C2×#896C22semidirect
39. C2×#67⋊C4C22semidirect
40. C2×#875C22semidirect
41. C2×#874C22semidirect
42. C2×C4×Dic6C22semidirect
52. #5212C22semidirect
53. #4990C22semidirect
54. #4988C22semidirect
55. #4979C22semidirect
59. #4960C22semidirect
63. #4957C22semidirect
65. #4946C22semidirect
68. #4939C22semidirect
69. C4×C4⋊Dic3C22semidirect
70. #4929C22semidirect
71. #4928C22semidirect
72. #4676C22semidirect
73. #4669C22semidirect
74. #4665C22semidirect
75. #4665C22semidirect
76. #4652C22semidirect
77. #4649C22semidirect
92. C4×#120D3semidirect
158. #924D4semidirect
255. C2×C3×D4#41semidirect
549. C2×D4#235semidirect
779. C3#59001semidirect

Maximal subgroups

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

subgroupindex
C2×#57912
C2×#55522
C3×C4×#1202
#825942
#823782
#823502
#823492
#748982
#746792
#746132
#744312
#738372
#735862
#734852
#734682
#590013