Finite Group Databasebeta

← #10847439

Subgroups — #10847439

Order 768.

1226 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5580C211yesmaximal, characteristic, complemented
2C2×#5171C211yesmaximal, characteristic, complemented
3C2×#4775C211yesmaximal, characteristic
4#76475C211yesmaximal, characteristic, complemented
5C3×#1880C211yesmaximal, characteristic, complemented
6#72055C211yesmaximal, characteristic, complemented
7#71628C211yesmaximal, characteristic, complemented
8#70270C211yesmaximal, characteristic, complemented
9#70245C211yesmaximal, characteristic, complemented
10#70164C211yesmaximal, characteristic, complemented
11#69657C211yesmaximal, characteristic, complemented
12#68883C211yesmaximal, characteristic, complemented
13#68828C211yesmaximal, characteristic, complemented
14#68671C211yesmaximal, characteristic, complemented
15D3×#336C211yesmaximal, characteristic, complemented
16#25500—31nomaximal, Sylow
17C22×C3×SD16C2211yescharacteristic
18C2×C3×C4×Q8C2211yescharacteristic
19C2×#947C2211yescharacteristic
20C2×#946C2211yescharacteristic
21C2×#938C2211yescharacteristic
22C22×#213C2211yescharacteristic
23C22×D3×C8C2211yescharacteristic
24C22×D3×C8C2211yescharacteristic
25#5580—24no—
26#5580—24no—
27C2×#898—21no—
28C2×#895C2211yescharacteristic
29C2×#894—21no—
30C2×#890C2211yescharacteristic
31C2×#883—21no—
32C2×C4×D12—21no—
33C2×C4×D12C2211yescharacteristic
34C2×#872—21no—
35C2×C42×D3C2211yescharacteristic
36C2×C3×#103C2211yescharacteristic
37C2×C3×#102C2211yescharacteristic
38C3×#390C2211yescharacteristic
39C2×#835C2211yescharacteristic
40C2×#835C2211yescharacteristic
41#5221C2211yescharacteristic
42C2×#832C2211yescharacteristic
43#5171—24no—
44C2×#821C2211yescharacteristic
45C2×#821C2211yescharacteristic
46C2×#817C2211yescharacteristic
47#4987C2211yescharacteristic
48#4984C2211yescharacteristic
49C2×#809C2211yescharacteristic
50C2×#807C2211yescharacteristic
51#4956—21no—
52#4951—21no—
53#4945—21no—
54#4928C2211yescharacteristic
55#4775—24no—
56C3×#340C2211yescharacteristic
57C3×#336C2211yescharacteristic
58#4551C2211yescharacteristic
59#4550C2211yescharacteristic
60#4550C2211yescharacteristic
61#4529C2211yescharacteristic
62#4529C2211yescharacteristic
63#4524C2211yescharacteristic
64C2×#529—31no—
65C2×#466—31no—
66C2×#465—31no—
67#2854—31no—
68#2059—31no—
69#2042—31no—
70#2025—31no—
71#2012—31no—
72#1893—31no—
73#1892—31no—
74#1880D311yescharacteristic, complemented
75#1879—31no—
76#1864—31no—
77#1863—31no—
78C2×#336—31no—
79C22×C3×Q8C2311yescharacteristic
80C22×C3×D4C2311yescharacteristic
81C22×#67—21no—
82C22×D12—21no—
83C22×D12C2311yescharacteristic
84C22×C4×D3—21no—
85C22×C4×D3D411yescharacteristic
86C22×C4×D3D411yescharacteristic
87C22×C4×D3C2311yescharacteristic
88C2×C3×SD16—22no—
89C2×C3×SD16—22no—
90C2×C3×SD16—41no—
91C22×C3×C8C2311yescharacteristic
92C22×C3×C8C2311yescharacteristic
93C3×C4×Q8—22no—
94C3×C4×Q8—22no—
95C2×C3×C4⋊C4—21no—
96C2×C3×C4⋊C4C2311yescharacteristic
97C2×C3×C4⋊C4C2311yescharacteristic
98C2×C3×C22⋊C4—21no—
99C2×C3×C22⋊C4—21no—
100C2×C3×C42—21no—
101C2×C3×C42C2311yescharacteristic
102C2×#217—21no—
103C2×#217—21no—
104C2×#217—21no—
105#947—22no—
106#947—22no—
107#946—22no—
108#946D414yes—
109#938—22no—
110#938—22no—
111C2×#213—22no—
112C2×#213—22no—
113C2×#213—41no—
114C2×(C2×D3)⋊C4—21no—
115C2×(C2×D3)⋊C4—21no—
116C2×(C2×D3)⋊C4—21no—
117C2×(C2×D3)⋊C4—21no—
118C2×(C2×D3)⋊C4—21no—
119C2×(C2×D3)⋊C4—21no—
120C2×C4⋊Dic3—21no—
121C2×C4⋊Dic3—21no—
122C2×C4⋊Dic3C2311yescharacteristic
123C2×C4⋊Dic3C2311yescharacteristic
124C2×C4⋊Dic3C2311yescharacteristic
125C2×Dic3⋊C4—21no—
126C2×Dic3⋊C4—21no—
127C2×Dic3⋊C4—21no—
128C2×C4×Dic3D411yescharacteristic
129C2×C4×Dic3D411yescharacteristic
130C2×C4×Dic3C2311yescharacteristic
131C22×C3⋊C8C2311yescharacteristic
132C22×C3⋊C8C2311yescharacteristic
133C2×D3×C8—22no—
134C2×D3×C8—22no—
135C2×D3×C8—22no—
136C2×D3×C8—22no—
137C2×D3×C8—41no—
138C2×D3×C8—41no—
139#898—28no—
140#895—22no—
141#895D414yes—
142#894—28no—
143#890—22no—
144#890—22no—
145#883—44no—
146C4×D12—28no—
147C4×D12—22no—
148C4×D12—22no—
149#872—28no—
150C42×D3—22no—
151C42×D3—22no—
152C3×#103—41no—
153C3×#102—22no—
154#835—22no—
155#835—22no—
156#832—22no—
157C3⋊#95—21no—
158C3⋊#95—21no—
159C3⋊#95—21no—
160#821—22no—
161#821—22no—
162#817—22no—
163#809—41no—
164#807—22no—
165C22×SD16C2×D311yescharacteristic
166C22×D8—31no—
167C23×C8—31no—
168C23×C8—31no—
169#529—64no—
170#529—64no—
171C2×#126—61no—
172C2×#125—31no—
173C2×#124—31no—
174C2×#123—61no—
175C2×#123—61no—
176C2×C22⋊Q8—31no—
177C2×#121—31no—
178C2×#121—31no—
179C2×C4×Q8C2×D311yescharacteristic
180C2×C4×D4—31no—
181C2×C4×D4—61no—
182C2×#117—61no—
183C22×C42—31no—
184#466—64no—
185#465—64no—
186C2×#107—31no—
187C2×#106—31no—
188C2×#103—31no—
189C2×#103—31no—
190C2×#103C2×D311yescharacteristic
191C2×#102—31no—
192C2×#102—31no—
193C2×#102—31no—
194C2×#102—31no—
195C2×#102C2×D311yescharacteristic
196#390—31no—
197#390C2×D311yescharacteristic
198#389—31no—
199#389—31no—
200#388—61no—
201#388—61no—
202#386—61no—
203#380—31no—
204#340—31no—
205#340—31no—
206#340—31no—
207#340C2×D311yescharacteristic
208#336—31no—
209#336—31no—
210#336—31no—
211#336C2×D311yescharacteristic
212C24×C3—21no—
213C23×D3—21no—
214C23×D3C2×D411yescharacteristic
215C2×C3×Q8—21no—
216C2×C3×Q8—21no—
217C2×C3×Q8—21no—
218C2×C3×Q8—21no—
219C2×C3×Q8—21no—
220C2×C3×Q8C2×D412yes—
221C2×C3×D4—21no—
222C2×C3×D4—21no—
223C2×C3×D4—21no—
224C2×C3×D4—21no—
225C2×C3×D4—21no—
226C2×C3×D4—21no—
227C22×C3×C4—21no—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4C2×D411yescharacteristic
231C22×C3×C4C2×D411yescharacteristic
232C22×C3×C4C2411yescharacteristic
233C2×#67—42no—
234C2×#67—42no—
235C2×#67—42no—
236C22×Dic3—21no—
237C22×Dic3—21no—
238C22×Dic3—21no—
239C22×Dic3C2×D411yescharacteristic
240C22×Dic3C2×D411yescharacteristic
241C22×Dic3C2×D411yescharacteristic
242C2×D12—21no—
243C2×D12—21no—
244C2×D12—21no—
245C2×D12—21no—
246C2×D12—24no—
247C2×D12—21no—
248C2×D12—42no—
249C2×D12—42no—
250C2×D12C2×D412yes—
251C2×C4×D3—21no—
252C2×C4×D3—21no—
253C2×C4×D3—21no—
254C2×C4×D3—21no—
255C2×C4×D3—24no—
256C2×C4×D3—22no—
257C2×C4×D3—22no—
258C2×C4×D3—22no—
259C2×C4×D3—22no—
260C2×C4×D3—22no—
261C2×C4×D3—41no—
262C2×C4×D3—42no—
263C2×C4×D3—42no—
264C2×C4×D3C2×D412yes—
265C2×C4×D3C2×D412yes—
266C3×SD16—44no—
267C2×C3×C8—21no—
268C2×C3×C8—21no—
269C2×C3×C8—21no—
270C2×C3×C8—21no—
271C2×C3×C8—21no—
272C2×C3×C8#4112yes—
273C3×C4⋊C4—24no—
274C3×C4⋊C4—21no—
275C3×C4⋊C4—21no—
276C3×C4⋊C4—21no—
277C3×C4⋊C4C2×D412yes—
278C3×C22⋊C4—42no—
279C3×C22⋊C4—42no—
280C3×C42—24no—
281C3×C42—21no—
282C3×C42—21no—
283#217—42no—
284#217—42no—
285#217—42no—
286#213—44no—
287(C2×D3)⋊C4—24no—
288(C2×D3)⋊C4—24no—
289(C2×D3)⋊C4—24no—
290(C2×D3)⋊C4—24no—
291(C2×D3)⋊C4—24no—
292(C2×D3)⋊C4—42no—
293C4⋊Dic3—24no—
294C4⋊Dic3—21no—
295C4⋊Dic3—21no—
296C4⋊Dic3—21no—
297C4⋊Dic3—21no—
298C4⋊Dic3—21no—
299C4⋊Dic3—42no—
300C4⋊Dic3C2×D412yes—
301Dic3⋊C4—24no—
302Dic3⋊C4—24no—
303Dic3⋊C4—42no—
304C4×Dic3—21no—
305C4×Dic3—21no—
306C4×Dic3—22no—
307C4×Dic3—22no—
308C2×C3⋊C8—21no—
309C2×C3⋊C8—21no—
310C2×C3⋊C8—21no—
311C2×C3⋊C8—21no—
312C2×C3⋊C8—21no—
313C2×C3⋊C8#4112yes—
314D3×C8—44no—
315D3×C8—44no—
316C22×Q8C22×D311yescharacteristic
317C22×D4—31no—
318C22×D4—61no—
319C22×D4—61no—
320C22×D4C22×D311yescharacteristic
321C23×C4—31no—
322C23×C4—31no—
323C23×C4—31no—
324C23×C4—61no—
325C2×SD16—22no—
326C2×SD16—22no—
327C2×SD16—41no—
328C2×D8—62no—
329C2×D8—62no—
330C2×D8—121no—
331C22×C8—31no—
332C22×C8—31no—
333C22×C8—62no—
334C22×C8—62no—
335C22×C8—62no—
336C22×C8—62no—
337C22×C8—121no—
338C22×C8—121no—
339C22×C8C22×D311yescharacteristic
340C22×C8C22×D311yescharacteristic
341#126—68no—
342#125—62no—
343#125—62no—
344#124—62no—
345#124—62no—
346#123—68no—
347#123—124no—
348C22⋊Q8—34no—
349C22⋊Q8—62no—
350#121—34no—
351#121—62no—
352#121—62no—
353#121—62no—
354C4×Q8—22no—
355C4×Q8—22no—
356C4×D4—62no—
357C4×D4—62no—
358C4×D4—68no—
359#117—68no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—31no—
362C2×C4⋊C4—31no—
363C2×C4⋊C4—31no—
364C2×C4⋊C4—61no—
365C2×C4⋊C4—61no—
366C2×C4⋊C4—61no—
367C2×C4⋊C4—61no—
368C2×C4⋊C4—61no—
369C2×C4⋊C4C22×D311yescharacteristic
370C2×C4⋊C4C22×D311yescharacteristic
371C2×C22⋊C4—21no—
372C2×C22⋊C4—21no—
373C2×C22⋊C4—61no—
374C2×C22⋊C4—61no—
375C2×C22⋊C4—61no—
376C2×C22⋊C4—61no—
377C2×C22⋊C4—61no—
378C2×C22⋊C4—61no—
379C2×C22⋊C4—61no—
380C2×C22⋊C4—61no—
381C2×C22⋊C4—61no—
382C2×C42—21no—
383C2×C42—31no—
384C2×C42—31no—
385C2×C42—31no—
386C2×C42—62no—
387C2×C42—62no—
388C2×C42C22×D311yescharacteristic
389#107—62no—
390#106—62no—
391#103—41no—
392#103—62no—
393#103—62no—
394#102—22no—
395#102—62no—
396#102—62no—
397#102—62no—
398#102—121no—
399#95—61no—
400#95—61no—
401#95—61no—
402C23×C3—41no—
403C23×C3—41no—
404C23×C3—41no—
405C23×C3—41no—
406C23×C3—41no—
407C23×C3—41no—
408C23×C3—41no—
409C23×C3C22×D411yescharacteristic
410C22×D3—21no—
411C22×D3—21no—
412C22×D3—21no—
413C22×D3—21no—
414C22×D3—22no—
415C22×D3—41no—
416C22×D3—41no—
417C22×D3—41no—
418C22×D3—41no—
419C22×D3—41no—
420C22×D3—41no—
421C22×D3#12012yes—
422C22×D3#13512yes—
423C22×D3AGL(1,ℤ/8)12yes—
424C3×Q8—22no—
425C3×Q8—22no—
426C3×Q8—41no—
427C3×Q8—41no—
428C3×D4—41no—
429C3×D4—41no—
430C3×D4—41no—
431C3×D4—41no—
432C2×C3×C4—21no—
433C2×C3×C4—21no—
434C2×C3×C4—21no—
435C2×C3×C4—22no—
436C2×C3×C4—22no—
437C2×C3×C4—21no—
438C2×C3×C4—21no—
439C2×C3×C4—41no—
440C2×C3×C4—41no—
441C2×C3×C4—41no—
442C2×C3×C4—41no—
443C2×C3×C4—41no—
444C2×C3×C4—41no—
445C2×C3×C4—41no—
446C2×C3×C4#13512yes—
447C2×C3×C4C22×D411yescharacteristic
448C2×C3×C4C22×D411yescharacteristic
449C2×C3×C4C2×#4111yescharacteristic
450C2×C3×C4C2×#4111yescharacteristic
451C2×C3×C4H(5,𝔽2)11yescharacteristic
452C2×C3×C42−1+411yescharacteristic
453#67—84no—
454C2×Dic3—21no—
455C2×Dic3—21no—
456C2×Dic3—21no—
457C2×Dic3—21no—
458C2×Dic3—22no—
459C2×Dic3—21no—
460C2×Dic3—21no—
461C2×Dic3—21no—
462C2×Dic3—21no—
463C2×Dic3—41no—
464C2×Dic3—41no—
465C2×Dic3—41no—
466C2×Dic3—41no—
467C2×Dic3—41no—
468C2×Dic3—41no—
469C2×Dic3—41no—
470C2×Dic3—41no—
471C2×Dic3#12012yes—
472D12—22no—
473D12—22no—
474D12—48no—
475D12—41no—
476D12—41no—
477C4×D3—22no—
478C4×D3—22no—
479C4×D3—22no—
480C4×D3—22no—
481C4×D3—44no—
482C4×D3—48no—
483C4×D3—44no—
484C3×C8—22no—
485C3×C8—41no—
486C3⋊C8—22no—
487C3⋊C8—41no—
488C24—21no—
489C24—31no—
490C24—61no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8D3×D412yes—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—32no—
504C2×D4—64no—
505C2×D4—61no—
506C2×D4—61no—
507C2×D4—61no—
508C2×D4—61no—
509C2×D4—61no—
510C2×D4—122no—
511C2×D4—122no—
512C2×D4—122no—
513C2×D4—122no—
514C2×D4—122no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—31no—
519C22×C4—32no—
520C22×C4—32no—
521C22×C4—31no—
522C22×C4—31no—
523C22×C4—62no—
524C22×C4—62no—
525C22×C4—62no—
526C22×C4—62no—
527C22×C4—64no—
528C22×C4—61no—
529C22×C4—61no—
530C22×C4—61no—
531C22×C4—61no—
532C22×C4—61no—
533C22×C4—62no—
534C22×C4—61no—
535C22×C4—61no—
536C22×C4—121no—
537C22×C4—122no—
538C22×C4—122no—
539C22×C4D3×D411yescharacteristic
540C22×C4D3×D411yescharacteristic
541C22×C4C23×D311yescharacteristic
542SD16—44no—
543D8—124no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—32no—
550C2×C8—61no—
551C2×C8—61no—
552C2×C8—61no—
553C2×C8—61no—
554C2×C8—61no—
555C2×C8—124no—
556C2×C8—124no—
557C2×C8#23512yes—
558C4⋊C4—24no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—32no—
563C4⋊C4—64no—
564C4⋊C4—64no—
565C4⋊C4—64no—
566C4⋊C4—61no—
567C4⋊C4—61no—
568C4⋊C4—61no—
569C4⋊C4—61no—
570C4⋊C4—61no—
571C4⋊C4—122no—
572C4⋊C4—122no—
573C4⋊C4D3×D412yes—
574C22⋊C4—42no—
575C22⋊C4—42no—
576C22⋊C4—64no—
577C22⋊C4—64no—
578C22⋊C4—64no—
579C22⋊C4—64no—
580C22⋊C4—64no—
581C22⋊C4—122no—
582C22⋊C4—122no—
583C22⋊C4—122no—
584C22⋊C4—122no—
585C42—24no—
586C42—21no—
587C42—21no—
588C42—62no—
589C42—62no—
590C42—61no—
591C42—61no—
592C22×C3—81no—
593C22×C3—81no—
594C22×C3—81no—
595C22×C3—81no—
596C22×C3—81no—
597C22×C3—81no—
598C22×C3—81no—
599C22×C3C2×#12011yescharacteristic
600C22×C3#53211yescharacteristic
601C22×C3#53711yescharacteristic
602C22×C3C2×#13511yescharacteristic
603C22×C3C2×#13511yescharacteristic
604C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
605C22×C3#57511yescharacteristic
606C2×D3—22no—
607C2×D3—22no—
608C2×D3—22no—
609C2×D3—22no—
610C2×D3—22no—
611C2×D3—22no—
612C2×D3—42no—
613C2×D3—42no—
614C2×D3—42no—
615C2×D3—81no—
616C2×D3—81no—
617C2×D3—81no—
618C2×D3—81no—
619C2×D3#44914yes—
620C3×C4—22no—
621C3×C4—42no—
622C3×C4—41no—
623C3×C4—42no—
624C3×C4—81no—
625C3×C4#54611yescharacteristic
626C3×C4#54611yescharacteristic
627C3×C4#54711yescharacteristic
628C3×C4#54711yescharacteristic
629Dic3—22no—
630Dic3—41no—
631Dic3—41no—
632Dic3—42no—
633Dic3—81no—
634Dic3—81no—
635C23—32no—
636C23—32no—
637C23—32no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—61no—
646C23—61no—
647C23—61no—
648C23—61no—
649C23—62no—
650C23—121no—
651C23—121no—
652C23—121no—
653C23—121no—
654C23—121no—
655C23—121no—
656C23C2×D3×D411yescharacteristic
657Q8—22no—
658Q8—22no—
659Q8—41no—
660Q8—41no—
661D4—41no—
662D4—41no—
663D4—41no—
664D4—41no—
665D4—62no—
666D4—62no—
667D4—128no—
668D4—121no—
669D4—121no—
670D4—244no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—32no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—61no—
687C2×C4—61no—
688C2×C4—62no—
689C2×C4—62no—
690C2×C4—62no—
691C2×C4—62no—
692C2×C4—61no—
693C2×C4—61no—
694C2×C4—61no—
695C2×C4—61no—
696C2×C4—61no—
697C2×C4—61no—
698C2×C4—62no—
699C2×C4—124no—
700C2×C4—128no—
701C2×C4—124no—
702C2×C4—121no—
703C2×C4—121no—
704C2×C4—121no—
705C2×C4—121no—
706C2×C4—121no—
707C2×C4—121no—
708C2×C4—121no—
709C2×C4—121no—
710C2×C4#91612yes—
711C2×C4C2×#23511yescharacteristic
712C2×C4C2×D3×D411yescharacteristic
713C2×C4C2×D3×D411yescharacteristic
714C2×C4#100411yescharacteristic
715C2×C4D3×#4111yescharacteristic
716C2×C4#101011yescharacteristic
717C8—22no—
718C8—41no—
719C8—62no—
720C8—121no—
721C2×C3—161no—
722C2×C3#243011yescharacteristic
723C2×C3C2×#44911yescharacteristic
724C2×C3#300211yescharacteristic
725C2×C3#316811yescharacteristic
726C2×C3#318011yescharacteristic
727C2×C3#324711yescharacteristic
728C2×C3#325011yescharacteristic
729D3—24no—
730D3—82no—
731C22—34no—
732C22—62no—
733C22—62no—
734C22—62no—
735C22—62no—
736C22—62no—
737C22—62no—
738C22—81no—
739C22—81no—
740C22—81no—
741C22—81no—
742C22—81no—
743C22—81no—
744C22—81no—
745C22—122no—
746C22—122no—
747C22—122no—
748C22—241no—
749C22—241no—
750C22—241no—
751C22—241no—
752C22#554811yescharacteristic
753C22D3×#12011yescharacteristic
754C22#560811yescharacteristic
755C22C2×#91611yescharacteristic
756C22D3×#13511yescharacteristic
757C22D3×AGL(1,ℤ/8)11yescharacteristic
758C22#577711yescharacteristic
759C4—22no—
760C4—42no—
761C4—41no—
762C4—42no—
763C4—62no—
764C4—81no—
765C4—121no—
766C4—122no—
767C4—121no—
768C4—241no—
769C4—241no—
770C4#549011yescharacteristic
771C4#555111yescharacteristic
772C4#561211yescharacteristic
773C4#565511yescharacteristic
774C3#2550011yescharacteristic, complemented, Sylow
775C2—64no—
776C2—161no—
777C2—242no—
778C2#7489611yescharacteristic
779C2#7966311yescharacteristic
780C2#7979011yescharacteristic
781C2#8003811yescharacteristic
782C2D3×#44911yescharacteristic
783C2#8040111yescharacteristic
784C2#8062311yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1880C2
socleC23×C3C22×D4
prime radicalC2×#4775C2
hypercenter#1880D3
hypocenterC3#25500
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1880

Complements

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

NH ≅ G/Ntype
1. C2×#5580C2semidirect
2. C2×#5171C2semidirect
4. #76475C2semidirect
5. C3×#1880C2semidirect
6. #72055C2semidirect
7. #71628C2semidirect
8. #70270C2semidirect
9. #70245C2semidirect
10. #70164C2semidirect
11. #69657C2semidirect
12. #68883C2semidirect
13. #68828C2semidirect
14. #68671C2semidirect
15. D3×#336C2semidirect
74. #1880D3semidirect
774. C3#25500semidirect

Maximal subgroups

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

subgroupindex
C2×#55802
C2×#51712
C2×#47752
#764752
C3×#18802
#720552
#716282
#702702
#702452
#701642
#696572
#688832
#688282
#686712
D3×#3362
#255003