Finite Group Databasebeta

← #10967028

Subgroups — #10967028

Order 768.

2428 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5691C212yesmaximal, complemented
2C3×#2552C211yesmaximal, characteristic, complemented
3#83060C212yesmaximal, complemented
4#77788C214yesmaximal, complemented
5#77738C214yesmaximal, complemented
6#76238C212yesmaximal, complemented
7#76219C212yesmaximal, complemented
8#75965C212yesmaximal, complemented
9#75964C212yesmaximal, complemented
10#74368C211yesmaximal, characteristic
11#74362C212yesmaximal, complemented
12#74320C211yesmaximal, characteristic, complemented
13#74318C212yesmaximal, complemented
14#73802C211yesmaximal, characteristic, complemented
15#73800C211yesmaximal, characteristic, complemented
16C4×#893C211yesmaximal, characteristic, complemented
17C4×#893C211yesmaximal, characteristic, complemented
18#34932—31nomaximal, Sylow
19C2×C3×#125C2212yes—
20#5691—216no—
21C2×#898C2214yes—
22C2×#897C2212yes—
23C2×#897C2212yes—
24C2×#895C2212yes—
25C2×#895C2212yes—
26C2×#894C2214yes—
27C2×#893C2214yes—
28C2×#893C2211yescharacteristic
29C2×#893C2211yescharacteristic
30C2×#893C2211yescharacteristic
31C2×#893C2211yescharacteristic
32C2×#892C2214yes—
33C2×#887C2212yes—
34C2×#875C2212yes—
35C2×C4×D12C2211yescharacteristic
36C2×C4×D12C2211yescharacteristic
37C2×C42×D3C2212yes—
38C2×C42×D3C2212yes—
39C2×#869C2211yescharacteristic
40C3×#398C2214yes—
41C3×#389C2212yes—
42C3×#389C2212yes—
43C3×#384C2212yes—
44C3×#384C2211yescharacteristic
45C3×C4×C4⋊C4C2211yescharacteristic
46C3×C4×C4⋊C4C2211yescharacteristic
47#4992C2214yes—
48#4991C2214yes—
49#4991C2214yes—
50#4990C2214yes—
51#4989C2214yes—
52#4987C2212yes—
53#4987C2212yes—
54#4987C2212yes—
55#4987C2214yes—
56#4987C2212yes—
57#4986C2214yes—
58#4977C2214yes—
59Dic3×C4⋊C4C2211yescharacteristic
60Dic3×C4⋊C4C2212yes—
61Dic3×C4⋊C4C2214yes—
62Dic3×C4⋊C4C2212yes—
63Dic3×C4⋊C4C2211yescharacteristic
64Dic3×C4⋊C4C2211yescharacteristic
65Dic3×C4⋊C4C2211yescharacteristic
66#4973C2212yes—
67#4972C2212yes—
68#4972C2212yes—
69#4939C2212yes—
70C4×(C2×D3)⋊C4C2212yes—
71C4×(C2×D3)⋊C4C2212yes—
72#4935C2212yes—
73C42×Dic3C2211yescharacteristic
74#4929C2212yes—
75#4677C2214yes—
76#4674C2214yes—
77#4674C2214yes—
78#4666C2212yes—
79#4666C2212yes—
80#4666C2212yes—
81#4666C2212yes—
82#4666C2214yes—
83#4665C2214yes—
84#4654C2214yes—
85C2×#529—32no—
86#2553—34no—
87#2552D311yescharacteristic, complemented
88#2547—31no—
89#2542—31no—
90#2537—31no—
91#2496—32no—
92#2489—32no—
93#2427—32no—
94#2422—32no—
95#2395—34no—
96C4×C4⋊Q8—31no—
97C4×C22⋊Q8—32no—
98C4×#121—32no—
99#2285—32no—
100C42×D4—31no—
101C42×D4—31no—
102C22×D12C2314yes—
103C22×D12C2311yescharacteristic
104C22×D12C2311yescharacteristic
105C22×C4×D3C2312yes—
106C22×C4×D3C2312yes—
107C22×C4×D3C2312yes—
108C22×C4×D3C2312yes—
109C22×C4×D3C2312yes—
110C22×C4×D3C2312yes—
111C22×Dic6C2312yes—
112C3×#125—28no—
113C2×C3×C4⋊C4C2312yes—
114C2×C3×C4⋊C4C2312yes—
115C2×C3×C4⋊C4C2311yescharacteristic
116C2×C3×C4⋊C4C2311yescharacteristic
117C2×C3×C4⋊C4C2314yes—
118C2×C3×C4⋊C4C2314yes—
119C2×C3×C4⋊C4C2312yes—
120C2×C3×C4⋊C4C2314yes—
121C2×C3×C4⋊C4C2311yescharacteristic
122C2×C3×C4⋊C4C2311yescharacteristic
123C2×C3×C42C2312yes—
124C2×C3×C42C2312yes—
125C2×C3×C42C2311yescharacteristic
126C2×(C2×D3)⋊C4C2312yes—
127C2×(C2×D3)⋊C4C2314yes—
128C2×(C2×D3)⋊C4C2314yes—
129C2×(C2×D3)⋊C4C2312yes—
130C2×(C2×D3)⋊C4C2312yes—
131C2×(C2×D3)⋊C4C2312yes—
132C2×(C2×D3)⋊C4C2312yes—
133C2×(C2×D3)⋊C4C2314yes—
134C2×(C2×D3)⋊C4C2314yes—
135C2×(C2×D3)⋊C4C2314yes—
136C2×(C2×D3)⋊C4C2314yes—
137C2×(C2×D3)⋊C4C2312yes—
138C2×C4⋊Dic3C2314yes—
139C2×C4⋊Dic3C2311yescharacteristic
140C2×C4⋊Dic3C2312yes—
141C2×C4⋊Dic3C2314yes—
142C2×C4⋊Dic3C2311yescharacteristic
143C2×C4⋊Dic3C2312yes—
144C2×Dic3⋊C4C2314yes—
145C2×C4×Dic3C2312yes—
146C2×C4×Dic3C2311yescharacteristic
147C2×C4×Dic3C2312yes—
148C2×C4×Dic3C2312yes—
149C2×C4×Dic3C2312yes—
150C2×C4×Dic3C2314yes—
151C2×C4×Dic3C2311yescharacteristic
152C2×C4×Dic3C2311yescharacteristic
153C2×C4×Dic3C2311yescharacteristic
154C2×C4×Dic3C2311yescharacteristic
155C2×C4×Dic3C2311yescharacteristic
156#898—216no—
157#897—28no—
158#897—28no—
159#895—28no—
160#895—28no—
161#894—216no—
162#893—24no—
163#893—216no—
164#893—24no—
165#893—24no—
166#893D418yescomplemented
167#892—216no—
168#887—28no—
169#875—28no—
170C4×D12—24no—
171C4×D12—24no—
172C42×D3—28no—
173C42×D3—28no—
174#869—24no—
175C3×#95C2314yes—
176C3×#95C2312yes—
177C3×#95C2312yes—
178C3⋊#95C2312yes—
179C3⋊#95C2314yes—
180C3⋊#95C2314yes—
181C3⋊#95C2314yes—
182C3⋊#95C2312yes—
183C3⋊#95C2312yes—
184C3⋊#95C2312yes—
185C3⋊#95C2314yes—
186C3⋊#95C2314yes—
187C2×C4⋊Q8—31no—
188#529—616no—
189C2×#126—34no—
190C2×#125C2×D312yes—
191C2×#124—32no—
192C2×#123—34no—
193C2×C22⋊Q8—32no—
194C2×C22⋊Q8—32no—
195C2×#121—32no—
196C2×#121—32no—
197C2×C4×Q8—32no—
198C2×C4×D4—31no—
199C2×C4×D4—34no—
200C2×C4×D4—31no—
201C2×C4×D4—31no—
202C2×C4×D4—31no—
203C2×C4×D4—31no—
204C2×C4×D4—31no—
205C2×#117—34no—
206C22×C42—32no—
207C22×C42—32no—
208#400—34no—
209#399—34no—
210#398C2×D314yes—
211#397—34no—
212#397—34no—
213#397—34no—
214#394—34no—
215#394—34no—
216#391—32no—
217#391—32no—
218#390—32no—
219#389—32no—
220#389—32no—
221#389C2×D312yes—
222#389C2×D312yes—
223#388—34no—
224#387—34no—
225#386—34no—
226#385—34no—
227#384—32no—
228#384C2×D311yescharacteristic
229#384C2×D312yes—
230#382—34no—
231#380—32no—
232#380—34no—
233#380—32no—
234#380—32no—
235#380—32no—
236C4×C4⋊C4—32no—
237C4×C4⋊C4—32no—
238C4×C4⋊C4—34no—
239C4×C4⋊C4—31no—
240C4×C4⋊C4—31no—
241C4×C4⋊C4—31no—
242C4×C4⋊C4—31no—
243C4×C4⋊C4C2×D311yescharacteristic
244C4×C4⋊C4C2×D311yescharacteristic
245C4×C22⋊C4—32no—
246C4×C22⋊C4—32no—
247C4×C22⋊C4—32no—
248C4×C22⋊C4—32no—
249C4×C22⋊C4—34no—
250C4×C22⋊C4—32no—
251C4×C22⋊C4—32no—
252C43—31no—
253C23×D3C2412yes—
254C23×D3C2412yes—
255C22×C3×C4C2412yes—
256C22×C3×C4C2414yes—
257C22×C3×C4C2412yes—
258C22×C3×C4C2412yes—
259C22×C3×C4C2412yes—
260C22×C3×C4C2411yescharacteristic
261C22×C3×C4C2411yescharacteristic
262C22×C3×C4C2411yescharacteristic
263C22×Dic3C2411yescharacteristic
264C22×Dic3C2412yes—
265C22×Dic3C2412yes—
266C22×Dic3C2414yes—
267C22×Dic3C2411yescharacteristic
268C22×Dic3C2411yescharacteristic
269C22×Dic3C2411yescharacteristic
270C2×D12—22no—
271C2×D12—22no—
272C2×D12—22no—
273C2×D12—22no—
274C2×D12—28no—
275C2×D12—28no—
276C2×D12—44no—
277C2×D12C2×D414yes—
278C2×D12#4114yes—
279C2×C4×D3—24no—
280C2×C4×D3—24no—
281C2×C4×D3—24no—
282C2×C4×D3—24no—
283C2×C4×D3—24no—
284C2×C4×D3—24no—
285C2×C4×D3—24no—
286C2×C4×D3—24no—
287C2×C4×D3—24no—
288C2×C4×D3—24no—
289C2×C4×D3—24no—
290C2×C4×D3—24no—
291C2×C4×D3—24no—
292C2×C4×D3—24no—
293C2×C4×D3—24no—
294C2×C4×D3—42no—
295C2×C4×D3—42no—
296C2×C4×D3C2×D418yes—
297C2×Dic6—24no—
298C2×Dic6—24no—
299C2×Dic6—24no—
300C3×C4⋊C4—24no—
301C3×C4⋊C4—28no—
302C3×C4⋊C4—28no—
303C3×C4⋊C4—22no—
304C3×C4⋊C4—22no—
305C3×C4⋊C4—24no—
306C3×C4⋊C4—42no—
307C3×C4⋊C4—44no—
308C3×C4⋊C4C2×D414yes—
309C3×C4⋊C4#4114yes—
310C3×C42—24no—
311C3×C42—24no—
312C3×C42#4114yes—
313(C2×D3)⋊C4—28no—
314(C2×D3)⋊C4—28no—
315(C2×D3)⋊C4—28no—
316(C2×D3)⋊C4—24no—
317(C2×D3)⋊C4—28no—
318(C2×D3)⋊C4—28no—
319(C2×D3)⋊C4—24no—
320(C2×D3)⋊C4—24no—
321(C2×D3)⋊C4—24no—
322(C2×D3)⋊C4—28no—
323(C2×D3)⋊C4—24no—
324(C2×D3)⋊C4C2×D418yes—
325C4⋊Dic3—28no—
326C4⋊Dic3—24no—
327C4⋊Dic3—24no—
328C4⋊Dic3—22no—
329C4⋊Dic3—22no—
330C4⋊Dic3—28no—
331Dic3⋊C4—28no—
332C4×Dic3—22no—
333C4×Dic3—22no—
334C4×Dic3—24no—
335C4×Dic3—24no—
336C4×Dic3—28no—
337C4×Dic3—24no—
338C4×Dic3—24no—
339C4×Dic3—22no—
340C4×Dic3—41no—
341C4×Dic3C2×D414yes—
342C4×Dic3#4114yes—
343C22×Q8—32no—
344C22×D4—31no—
345C22×D4—31no—
346C22×D4—34no—
347C23×C4—32no—
348C23×C4—32no—
349C23×C4—32no—
350C23×C4—32no—
351C23×C4—32no—
352C23×C4—32no—
353C4⋊Q8—64no—
354#126—616no—
355#125—28no—
356#124—68no—
357#123—616no—
358C22⋊Q8—68no—
359C22⋊Q8—68no—
360#121—68no—
361#121—68no—
362C4×Q8—68no—
363C4×D4—38no—
364C4×D4—64no—
365C4×D4—616no—
366C4×D4—64no—
367C4×D4—64no—
368C4×D4—64no—
369C4×D4—64no—
370#117—616no—
371C2×C4⋊C4—34no—
372C2×C4⋊C4—31no—
373C2×C4⋊C4—31no—
374C2×C4⋊C4—34no—
375C2×C4⋊C4—34no—
376C2×C4⋊C4—32no—
377C2×C4⋊C4—32no—
378C2×C4⋊C4C22×D314yes—
379C2×C4⋊C4C22×D314yes—
380C2×C4⋊C4C22×D311yescharacteristic
381C2×C4⋊C4C22×D311yescharacteristic
382C2×C4⋊C4C22×D312yes—
383C2×C4⋊C4C22×D312yes—
384C2×C4⋊C4C22×D314yes—
385C2×C4⋊C4C22×D312yes—
386C2×C4⋊C4C22×D311yescharacteristic
387C2×C4⋊C4C22×D311yescharacteristic
388C2×C22⋊C4—32no—
389C2×C22⋊C4—34no—
390C2×C22⋊C4—34no—
391C2×C22⋊C4—34no—
392C2×C22⋊C4—34no—
393C2×C22⋊C4—32no—
394C2×C22⋊C4—32no—
395C2×C22⋊C4—32no—
396C2×C22⋊C4—32no—
397C2×C22⋊C4—32no—
398C2×C22⋊C4—34no—
399C2×C22⋊C4—34no—
400C2×C42—31no—
401C2×C42—31no—
402C2×C42—32no—
403C2×C42—34no—
404C2×C42—31no—
405C2×C42—31no—
406C2×C42—32no—
407C2×C42—31no—
408C2×C42—32no—
409C2×C42—32no—
410C2×C42—31no—
411C2×C42—68no—
412C2×C42—68no—
413C2×C42C22×D312yes—
414C2×C42C22×D312yes—
415C2×C42C22×D311yescharacteristic
416#95—32no—
417#95—32no—
418#95—32no—
419#95—32no—
420#95—34no—
421#95—34no—
422#95—34no—
423#95—34no—
424#95—34no—
425#95C22×D312yes—
426#95C22×D312yes—
427#95C22×D314yes—
428C23×C3C2511yescharacteristic
429C22×D3—22no—
430C22×D3—22no—
431C22×D3—22no—
432C22×D3—22no—
433C22×D3—22no—
434C22×D3—22no—
435C22×D3—22no—
436C22×D3—22no—
437C22×D3—22no—
438C22×D3—22no—
439C22×D3—22no—
440C22×D3—22no—
441C22×D3C22×D414yes—
442C22×D3C2×#4114yes—
443C2×C3×C4—22no—
444C2×C3×C4—22no—
445C2×C3×C4—21no—
446C2×C3×C4—22no—
447C2×C3×C4—21no—
448C2×C3×C4—22no—
449C2×C3×C4—24no—
450C2×C3×C4—22no—
451C2×C3×C4—22no—
452C2×C3×C4—22no—
453C2×C3×C4—22no—
454C2×C3×C4—24no—
455C2×C3×C4—22no—
456C2×C3×C4—22no—
457C2×C3×C4—24no—
458C2×C3×C4C22×D414yes—
459C2×C3×C4C22×D412yes—
460C2×C3×C4C2×#4112yes—
461C2×C3×C4C2×#4114yes—
462C2×C3×C4C2×#4112yes—
463C2×C3×C4C2×#4112yes—
464C2×C3×C4C2×#4112yes—
465C2×C3×C4C2×#4112yes—
466C2×C3×C4C2×#4112yes—
467C2×Dic3—21no—
468C2×Dic3—21no—
469C2×Dic3—21no—
470C2×Dic3—21no—
471C2×Dic3—22no—
472C2×Dic3—24no—
473C2×Dic3—22no—
474C2×Dic3—21no—
475C2×Dic3—21no—
476C2×Dic3—24no—
477C2×Dic3—22no—
478C2×Dic3—24no—
479C2×Dic3—22no—
480C2×Dic3—22no—
481C2×Dic3—22no—
482C2×Dic3—21no—
483C2×Dic3C22×D412yes—
484C2×Dic3C22×D412yes—
485C2×Dic3C2×#4112yes—
486C2×Dic3C2×#4112yes—
487C2×Dic32−1+412yes—
488D12—28no—
489D12—28no—
490D12—416no—
491C4×D3—216no—
492C4×D3—48no—
493C4×D3—48no—
494C4×D3—48no—
495C4×D3—48no—
496C4×D3—48no—
497Dic6—48no—
498C24—32no—
499C24—32no—
500C2×Q8—64no—
501C2×Q8—64no—
502C2×Q8—64no—
503C2×D4—34no—
504C2×D4—34no—
505C2×D4—68no—
506C2×D4—68no—
507C2×D4—62no—
508C2×D4—62no—
509C2×D4—62no—
510C2×D4—62no—
511C2×D4—124no—
512C22×C4—31no—
513C22×C4—31no—
514C22×C4—31no—
515C22×C4—38no—
516C22×C4—31no—
517C22×C4—32no—
518C22×C4—32no—
519C22×C4—34no—
520C22×C4—64no—
521C22×C4—64no—
522C22×C4—64no—
523C22×C4—64no—
524C22×C4—64no—
525C22×C4—64no—
526C22×C4—64no—
527C22×C4—64no—
528C22×C4—64no—
529C22×C4—64no—
530C22×C4—64no—
531C22×C4—64no—
532C22×C4—64no—
533C22×C4—64no—
534C22×C4—64no—
535C22×C4—122no—
536C22×C4—122no—
537C22×C4C23×D312yes—
538C22×C4C23×D312yes—
539C22×C4C23×D314yes—
540C22×C4C23×D312yes—
541C22×C4C23×D312yes—
542C22×C4C23×D311yescharacteristic
543C22×C4C23×D311yescharacteristic
544C22×C4C23×D311yescharacteristic
545C4⋊C4—28no—
546C4⋊C4—28no—
547C4⋊C4—24no—
548C4⋊C4—22no—
549C4⋊C4—22no—
550C4⋊C4—24no—
551C4⋊C4—42no—
552C4⋊C4—44no—
553C4⋊C4—68no—
554C4⋊C4—68no—
555C4⋊C4—62no—
556C4⋊C4—62no—
557C4⋊C4—68no—
558C4⋊C4—64no—
559C4⋊C4—64no—
560C4⋊C4D3×D414yes—
561C4⋊C4#23914yes—
562C22⋊C4—38no—
563C22⋊C4—64no—
564C22⋊C4—68no—
565C22⋊C4—68no—
566C22⋊C4—68no—
567C22⋊C4—64no—
568C22⋊C4—68no—
569C22⋊C4—68no—
570C22⋊C4—64no—
571C22⋊C4—64no—
572C22⋊C4—64no—
573C22⋊C4—68no—
574C42—24no—
575C42—24no—
576C42—34no—
577C42—34no—
578C42—64no—
579C42—64no—
580C42—64no—
581C42—64no—
582C42—68no—
583C42—62no—
584C42—62no—
585C42—62no—
586C42—121no—
587C42#23914yes—
588C22×C3C23×D411yescharacteristic
589C22×C3C22×#4111yescharacteristic
590C22×C3C22×#4111yescharacteristic
591C22×C3C22×#4111yescharacteristic
592C22×C3C22×#4111yescharacteristic
593C22×C3C2×2−1+411yescharacteristic
594C22×C3#58511yescharacteristic
595C2×D3—24no—
596C2×D3—24no—
597C2×D3—24no—
598C2×D3—24no—
599C2×D3—24no—
600C2×D3—24no—
601C2×D3—42no—
602C2×D3—42no—
603C2×D3—42no—
604C2×D3—42no—
605C2×D3—42no—
606C2×D3—42no—
607C2×D3—42no—
608C2×D3—42no—
609C3×C4—22no—
610C3×C4—24no—
611C3×C4—24no—
612C3×C4—42no—
613C3×C4—42no—
614C3×C4—44no—
615C3×C4#52914yescomplemented
616C3×C4#53214yes—
617Dic3—22no—
618Dic3—22no—
619Dic3—42no—
620Dic3—44no—
621Dic3—42no—
622Dic3—41no—
623Dic3#54714yes—
624C23—34no—
625C23—34no—
626C23—62no—
627C23—62no—
628C23—62no—
629C23—62no—
630C23—62no—
631C23—62no—
632C23—62no—
633C23—62no—
634C23—62no—
635C23—62no—
636C23—62no—
637C23—62no—
638C23C24×D311yescharacteristic
639Q8—128no—
640D4—68no—
641D4—68no—
642D4—1216no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—21no—
646C2×C4—22no—
647C2×C4—21no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—24no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—24no—
655C2×C4—22no—
656C2×C4—24no—
657C2×C4—22no—
658C2×C4—32no—
659C2×C4—32no—
660C2×C4—32no—
661C2×C4—32no—
662C2×C4—32no—
663C2×C4—616no—
664C2×C4—61no—
665C2×C4—61no—
666C2×C4—61no—
667C2×C4—61no—
668C2×C4—62no—
669C2×C4—64no—
670C2×C4—61no—
671C2×C4—62no—
672C2×C4—62no—
673C2×C4—64no—
674C2×C4—62no—
675C2×C4—64no—
676C2×C4—62no—
677C2×C4—61no—
678C2×C4—62no—
679C2×C4—61no—
680C2×C4—128no—
681C2×C4—128no—
682C2×C4—128no—
683C2×C4—128no—
684C2×C4—128no—
685C2×C4C2×D3×D414yes—
686C2×C4C2×D3×D412yes—
687C2×C4C2×#23912yes—
688C2×C4C2×#23914yes—
689C2×C4C2×#23912yes—
690C2×C4C2×#23912yes—
691C2×C4C2×#23912yes—
692C2×C4D3×#4112yes—
693C2×C4D3×#4112yes—
694C2×C3C2×#52911yescharacteristic
695C2×C3C2×#53211yescharacteristic
696C2×C3#346111yescharacteristic
697C2×C3C2×#54711yescharacteristic
698C2×C3D4×#4111yescharacteristic
699C2×C3#347511yescharacteristic
700C2×C3#348211yescharacteristic
701D3—44no—
702D3—44no—
703C22—64no—
704C22—64no—
705C22—64no—
706C22—64no—
707C22—64no—
708C22—64no—
709C22—122no—
710C22—122no—
711C22—122no—
712C22—122no—
713C22—122no—
714C22—122no—
715C22—122no—
716C22—122no—
717C22C22×D3×D411yescharacteristic
718C22C22×#23911yescharacteristic
719C22C22×#23911yescharacteristic
720C22C2×D3×#4111yescharacteristic
721C22C2×D3×#4111yescharacteristic
722C22#596611yescharacteristic
723C22D3×2−1+411yescharacteristic
724C4—22no—
725C4—24no—
726C4—24no—
727C4—34no—
728C4—42no—
729C4—42no—
730C4—44no—
731C4—62no—
732C4—62no—
733C4—122no—
734C4—122no—
735C4—124no—
736C4—121no—
737C4#569114yescomplemented
738C4#572514yes—
739C3#3493211yescharacteristic, complemented, Sylow
740C2—124no—
741C2—124no—
742C2C2×#569111yescharacteristic
743C2C2×#572511yescharacteristic
744C2#8658311yescharacteristic
745C2D3×#54711yescharacteristic
746C2#8676611yescharacteristic
747C2#8692211yescharacteristic
748C2#8701711yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2552C2
prime radical#74368C2
hypercenter#2552D3
hypocenterC3#34932
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2552

Complements

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

NH ≅ G/Ntype
1. C2×#5691C2semidirect
2. C3×#2552C2semidirect
3. #83060C2semidirect
4. #77788C2semidirect
5. #77738C2semidirect
6. #76238C2semidirect
7. #76219C2semidirect
8. #75965C2semidirect
9. #75964C2semidirect
11. #74362C2semidirect
12. #74320C2semidirect
13. #74318C2semidirect
14. #73802C2semidirect
15. #73800C2semidirect
16. C4×#893C2semidirect
17. C4×#893C2semidirect
87. #2552D3semidirect
166. #893D4semidirect
615. C3×C4#529semidirect
737. C4#5691semidirect
739. C3#34932semidirect

Maximal subgroups

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

subgroupindex
C2×#56912
C3×#25522
#830602
#777882
#777382
#762382
#762192
#759652
#759642
#743682
#743622
#743202
#743182
#738022
#738002
C4×#8932
#349323