Finite Group Databasebeta

← #11069150

Subgroups — #11069150

Order 768.

2276 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×#5733C212yesmaximal, complemented
2C3×#2551C211yesmaximal, characteristic, complemented
3#83259C212yesmaximal, complemented
4#83257C212yesmaximal, complemented
5#83236C212yesmaximal, complemented
6#77259C214yesmaximal, complemented
7#77222C214yesmaximal, complemented
8#76249C212yesmaximal, complemented
9#76215C212yesmaximal, complemented
10#76047C212yesmaximal, complemented
11#76007C212yesmaximal, complemented
12#74375C211yesmaximal, characteristic
13#74323C211yesmaximal, characteristic, complemented
14C4×#897C211yesmaximal, characteristic, complemented
15#73753C211yesmaximal, characteristic, complemented
16#73712C211yesmaximal, characteristic, complemented
17#73653C211yesmaximal, characteristic, complemented
18#39351—31nomaximal, Sylow
19C2×C3×C4⋊Q8C2212yes—
20C2×C3×C4⋊Q8C2212yes—
21C2×#947C2214yes—
22C2×#946C2214yes—
23C2×#946C2214yes—
24#5733—216no—
25C2×#898C2214yes—
26C2×#897C2211yescharacteristic
27C2×#895C2212yes—
28C2×#895C2212yes—
29C2×#895C2212yes—
30C2×#894C2214yes—
31C2×#893C2212yes—
32C2×#887C2212yes—
33C2×#875C2212yes—
34C2×#874C2211yescharacteristic
35C2×C4×D12C2212yes—
36C2×#872C2212yes—
37C2×C42×D3C2211yescharacteristic
38C2×C4×Dic6C2211yescharacteristic
39C3×#395C2214yes—
40C3×#389C2212yes—
41C3×#389C2212yes—
42C3×#384C2211yescharacteristic
43C3×C4×C4⋊C4C2211yescharacteristic
44C3×C4×C4⋊C4C2211yescharacteristic
45#5231C2214yes—
46#4994C2214yes—
47#4993C2214yes—
48#4993C2214yes—
49#4991C2214yes—
50#4990C2214yes—
51#4989C2214yes—
52#4988C2212yes—
53#4988C2212yes—
54#4988C2212yes—
55#4988C2212yes—
56#4988C2212yes—
57#4988C2212yes—
58#4987C2211yescharacteristic
59#4987C2211yescharacteristic
60#4987C2211yescharacteristic
61#4984C2211yescharacteristic
62#4976C2214yes—
63#4975C2211yescharacteristic
64#4975C2211yescharacteristic
65#4975C2212yes—
66Dic3×C4⋊C4C2212yes—
67#4973C2211yescharacteristic
68#4972C2212yes—
69#4939C2212yes—
70#4939C2212yes—
71C4×(C2×D3)⋊C4C2212yes—
72C4×C4⋊Dic3C2212yes—
73C4×C4⋊Dic3C2211yescharacteristic
74C4×Dic3⋊C4C2212yes—
75#4675C2214yes—
76#4675C2214yes—
77#4672C2214yes—
78#4672C2214yes—
79#4669C2214yes—
80#4668C2212yes—
81#4667C2212yes—
82#4665C2214yes—
83#4653C2212yes—
84#4650C2212yes—
85C2×#542—32no—
86#2856—31no—
87#2723—34no—
88#2672—34no—
89#2624—32no—
90#2551D311yescharacteristic, complemented
91#2548—31no—
92#2542—32no—
93#2512—32no—
94#2491—32no—
95#2452—32no—
96#2448—32no—
97#2422—32no—
98#2366—31no—
99Q8×C4⋊C4—31no—
100C4×C22⋊Q8—31no—
101#2285—31no—
102C22×C3×Q8C2314yes—
103C22×D12C2312yes—
104C22×D12C2312yes—
105C22×D12C2312yes—
106C22×D12C2314yes—
107C22×C4×D3C2311yescharacteristic
108C22×C4×D3C2311yescharacteristic
109C22×C4×D3C2311yescharacteristic
110C22×C4×D3C2314yes—
111C22×Dic6C2311yescharacteristic
112C3×C4⋊Q8—28no—
113C3×C4⋊Q8—44no—
114C2×C3×C4⋊C4C2312yes—
115C2×C3×C4⋊C4C2311yescharacteristic
116C2×C3×C4⋊C4C2312yes—
117C2×C3×C4⋊C4C2311yescharacteristic
118C2×C3×C4⋊C4C2311yescharacteristic
119C2×C3×C4⋊C4C2314yes—
120C2×C3×C4⋊C4C2312yes—
121C2×C3×C4⋊C4C2314yes—
122C2×C3×C4⋊C4C2311yescharacteristic
123C2×C3×C42C2312yes—
124C2×C3×C42C2312yes—
125C2×C3×C42C2311yescharacteristic
126#947—216no—
127#946—216no—
128#946—48no—
129C2×(C2×D3)⋊C4C2314yes—
130C2×(C2×D3)⋊C4C2312yes—
131C2×(C2×D3)⋊C4C2312yes—
132C2×(C2×D3)⋊C4C2314yes—
133C2×(C2×D3)⋊C4C2314yes—
134C2×(C2×D3)⋊C4C2314yes—
135C2×(C2×D3)⋊C4C2314yes—
136C2×(C2×D3)⋊C4C2314yes—
137C2×(C2×D3)⋊C4C2314yes—
138C2×(C2×D3)⋊C4C2312yes—
139C2×(C2×D3)⋊C4C2314yes—
140C2×(C2×D3)⋊C4C2314yes—
141C2×(C2×D3)⋊C4C2314yes—
142C2×(C2×D3)⋊C4C2312yes—
143C2×C4⋊Dic3C2312yes—
144C2×C4⋊Dic3C2311yescharacteristic
145C2×C4⋊Dic3C2311yescharacteristic
146C2×C4⋊Dic3C2311yescharacteristic
147C2×C4⋊Dic3C2312yes—
148C2×Dic3⋊C4C2312yes—
149C2×Dic3⋊C4C2312yes—
150C2×Dic3⋊C4C2312yes—
151C2×Dic3⋊C4C2312yes—
152C2×Dic3⋊C4C2314yes—
153C2×Dic3⋊C4C2312yes—
154C2×Dic3⋊C4C2314yes—
155C2×C4×Dic3C2311yescharacteristic
156C2×C4×Dic3C2314yes—
157C2×C4×Dic3C2311yescharacteristic
158C2×C4×Dic3C2312yes—
159C2×C4×Dic3C2311yescharacteristic
160C2×C4×Dic3C2312yes—
161#898—216no—
162#897D418yescomplemented
163#895—28no—
164#895—44no—
165#895—44no—
166#894—216no—
167#893—28no—
168#887—28no—
169#875—28no—
170#874—24no—
171C4×D12—44no—
172#872—28no—
173C42×D3—24no—
174C4×Dic6—24no—
175C3×#95C2312yes—
176C3×#95C2312yes—
177C3×#95C2314yes—
178C3⋊#95C2312yes—
179C3⋊#95C2312yes—
180C3⋊#95C2312yes—
181C3⋊#95C2312yes—
182C3⋊#95C2312yes—
183C3⋊#95C2312yes—
184C3⋊#95C2312yes—
185C3⋊#95C2314yes—
186#542—616no—
187C2×C4⋊Q8C2×D312yes—
188C2×C4⋊Q8C2×D312yes—
189C2×#127—31no—
190C2×#126—34no—
191C2×#124—34no—
192C2×#124—32no—
193C2×#123—34no—
194C2×C22⋊Q8—34no—
195C2×C22⋊Q8—34no—
196C2×C22⋊Q8—31no—
197C2×#121—32no—
198C2×#121—32no—
199C2×#121—32no—
200C2×C4×Q8—32no—
201C2×C4×Q8—31no—
202C2×C4×D4—32no—
203C2×C4×D4—32no—
204C2×#117—32no—
205C22×C42—31no—
206#399—34no—
207#399—34no—
208#397—34no—
209#397—34no—
210#396—34no—
211#395C2×D314yes—
212#394—34no—
213#394—34no—
214#394—34no—
215#393—34no—
216#391—31no—
217#390—32no—
218#390—32no—
219#390—32no—
220#390—32no—
221#390—32no—
222#390—32no—
223#390—32no—
224#390—32no—
225#389—32no—
226#389—34no—
227#389—31no—
228#389C2×D312yes—
229#389C2×D312yes—
230#388—34no—
231#388—34no—
232#387—32no—
233#386—34no—
234#385—34no—
235#385—32no—
236#384—32no—
237#384—31no—
238#384—31no—
239#384C2×D311yescharacteristic
240#382—32no—
241#380—31no—
242#380—31no—
243#380—31no—
244#380—32no—
245C4×C4⋊C4—32no—
246C4×C4⋊C4—31no—
247C4×C4⋊C4—32no—
248C4×C4⋊C4—32no—
249C4×C4⋊C4C2×D311yescharacteristic
250C4×C4⋊C4C2×D311yescharacteristic
251C4×C22⋊C4—32no—
252C23×D3C2414yes—
253C23×D3C2411yescharacteristic
254C2×C3×Q8—28no—
255C2×C3×Q8—44no—
256C2×C3×Q8—44no—
257C22×C3×C4C2412yes—
258C22×C3×C4C2412yes—
259C22×C3×C4C2414yes—
260C22×C3×C4C2412yes—
261C22×C3×C4C2412yes—
262C22×C3×C4C2411yescharacteristic
263C22×C3×C4C2411yescharacteristic
264C22×C3×C4C2411yescharacteristic
265C22×Dic3C2411yescharacteristic
266C22×Dic3C2412yes—
267C22×Dic3C2412yes—
268C22×Dic3C2412yes—
269C22×Dic3C2412yes—
270C22×Dic3C2411yescharacteristic
271C22×Dic3C2411yescharacteristic
272C2×D12—24no—
273C2×D12—24no—
274C2×D12—24no—
275C2×D12—24no—
276C2×D12—24no—
277C2×D12—24no—
278C2×D12—28no—
279C2×D12—24no—
280C2×D12—42no—
281C2×D12—44no—
282C2×D12—44no—
283C2×D12—42no—
284C2×C4×D3—22no—
285C2×C4×D3—22no—
286C2×C4×D3—22no—
287C2×C4×D3—22no—
288C2×C4×D3—22no—
289C2×C4×D3—22no—
290C2×C4×D3—22no—
291C2×C4×D3—28no—
292C2×C4×D3—41no—
293C2×C4×D3—44no—
294C2×C4×D3—44no—
295C2×C4×D3C2×D414yes—
296C2×Dic6—22no—
297C2×Dic6—22no—
298C2×Dic6C2×D414yes—
299C3×C4⋊C4—24no—
300C3×C4⋊C4—28no—
301C3×C4⋊C4—24no—
302C3×C4⋊C4—22no—
303C3×C4⋊C4—22no—
304C3×C4⋊C4—22no—
305C3×C4⋊C4—42no—
306C3×C4⋊C4—44no—
307C3×C4⋊C4C2×D414yes—
308C3×C42—24no—
309C3×C42—24no—
310C3×C42#4114yes—
311(C2×D3)⋊C4—24no—
312(C2×D3)⋊C4—24no—
313(C2×D3)⋊C4—28no—
314(C2×D3)⋊C4—28no—
315(C2×D3)⋊C4—28no—
316(C2×D3)⋊C4—28no—
317(C2×D3)⋊C4—28no—
318(C2×D3)⋊C4—44no—
319(C2×D3)⋊C4—44no—
320(C2×D3)⋊C4—44no—
321(C2×D3)⋊C4—44no—
322(C2×D3)⋊C4—42no—
323(C2×D3)⋊C4—44no—
324(C2×D3)⋊C4C2×D418yes—
325C4⋊Dic3—22no—
326C4⋊Dic3—22no—
327C4⋊Dic3—22no—
328C4⋊Dic3—24no—
329C4⋊Dic3C2×D418yes—
330Dic3⋊C4—24no—
331Dic3⋊C4—24no—
332Dic3⋊C4—24no—
333Dic3⋊C4—28no—
334Dic3⋊C4—24no—
335Dic3⋊C4—42no—
336Dic3⋊C4—44no—
337C4×Dic3—24no—
338C4×Dic3—24no—
339C4×Dic3—22no—
340C4×Dic3—22no—
341C4×Dic3—22no—
342C4×Dic3—28no—
343C22×Q8—31no—
344C22×Q8C22×D314yes—
345C22×D4—32no—
346C22×D4—32no—
347C22×D4—34no—
348C22×D4—32no—
349C23×C4—31no—
350C23×C4—31no—
351C23×C4—31no—
352C23×C4—34no—
353C4⋊Q8—28no—
354C4⋊Q8—44no—
355#127—64no—
356#126—616no—
357#124—68no—
358#124—616no—
359#123—616no—
360C22⋊Q8—38no—
361C22⋊Q8—616no—
362C22⋊Q8—128no—
363#121—68no—
364#121—124no—
365#121—124no—
366C4×Q8—68no—
367C4×Q8—64no—
368C4×D4—68no—
369C4×D4—124no—
370#117—68no—
371C2×C4⋊C4—32no—
372C2×C4⋊C4—32no—
373C2×C4⋊C4—32no—
374C2×C4⋊C4—31no—
375C2×C4⋊C4—34no—
376C2×C4⋊C4—31no—
377C2×C4⋊C4—32no—
378C2×C4⋊C4—32no—
379C2×C4⋊C4—32no—
380C2×C4⋊C4—31no—
381C2×C4⋊C4—34no—
382C2×C4⋊C4—32no—
383C2×C4⋊C4C22×D312yes—
384C2×C4⋊C4C22×D312yes—
385C2×C4⋊C4C22×D314yes—
386C2×C4⋊C4C22×D311yescharacteristic
387C2×C4⋊C4C22×D311yescharacteristic
388C2×C4⋊C4C22×D311yescharacteristic
389C2×C4⋊C4C22×D312yes—
390C2×C4⋊C4C22×D314yes—
391C2×C4⋊C4C22×D311yescharacteristic
392C2×C22⋊C4—32no—
393C2×C22⋊C4—32no—
394C2×C22⋊C4—32no—
395C2×C22⋊C4—34no—
396C2×C22⋊C4—34no—
397C2×C22⋊C4—34no—
398C2×C22⋊C4—34no—
399C2×C22⋊C4—34no—
400C2×C22⋊C4—34no—
401C2×C22⋊C4—34no—
402C2×C22⋊C4—34no—
403C2×C22⋊C4—32no—
404C2×C22⋊C4—34no—
405C2×C22⋊C4—34no—
406C2×C42—32no—
407C2×C42—34no—
408C2×C42—32no—
409C2×C42—31no—
410C2×C42—31no—
411C2×C42—31no—
412C2×C42—64no—
413C2×C42C22×D312yes—
414C2×C42C22×D312yes—
415C2×C42C22×D311yescharacteristic
416#95—32no—
417#95—32no—
418#95—32no—
419#95—32no—
420#95—32no—
421#95—32no—
422#95—32no—
423#95—34no—
424#95C22×D312yes—
425#95C22×D312yes—
426#95C22×D314yes—
427C23×C3C2511yescharacteristic
428C22×D3—21no—
429C22×D3—21no—
430C22×D3—21no—
431C22×D3—21no—
432C22×D3—21no—
433C22×D3—21no—
434C22×D3—24no—
435C22×D3—24no—
436C22×D3—24no—
437C22×D3—24no—
438C22×D3—24no—
439C22×D3—24no—
440C22×D3—24no—
441C22×D3C22×D412yes—
442C3×Q8—88no—
443C2×C3×C4—22no—
444C2×C3×C4—22no—
445C2×C3×C4—21no—
446C2×C3×C4—21no—
447C2×C3×C4—24no—
448C2×C3×C4—22no—
449C2×C3×C4—22no—
450C2×C3×C4—22no—
451C2×C3×C4—24no—
452C2×C3×C4—22no—
453C2×C3×C4—24no—
454C2×C3×C4—22no—
455C2×C3×C4—22no—
456C2×C3×C4—22no—
457C2×C3×C4—22no—
458C2×C3×C4—22no—
459C2×C3×C4C22×D414yes—
460C2×C3×C4C22×D412yes—
461C2×C3×C4C2×#4112yes—
462C2×C3×C4C2×#4112yes—
463C2×C3×C4C2×#4112yes—
464C2×C3×C4H(5,𝔽2)12yes—
465C2×C3×C42−1+412yes—
466C2×C3×C42−1+412yes—
467C2×Dic3—21no—
468C2×Dic3—21no—
469C2×Dic3—22no—
470C2×Dic3—22no—
471C2×Dic3—21no—
472C2×Dic3—21no—
473C2×Dic3—22no—
474C2×Dic3—22no—
475C2×Dic3—21no—
476C2×Dic3—22no—
477C2×Dic3—22no—
478C2×Dic3—22no—
479C2×Dic3—22no—
480C2×Dic3—21no—
481C2×Dic3—22no—
482C2×Dic3—21no—
483C2×Dic3—22no—
484C2×Dic3—22no—
485C2×Dic3C22×D414yes—
486C2×Dic3C22×D412yes—
487C2×Dic3H(5,𝔽2)12yes—
488D12—48no—
489D12—48no—
490D12—84no—
491D12—88no—
492C4×D3—28no—
493C4×D3—44no—
494C4×D3—44no—
495C4×D3—88no—
496Dic6—28no—
497C24—31no—
498C24—34no—
499C2×Q8—28no—
500C2×Q8—34no—
501C2×Q8—44no—
502C2×Q8—44no—
503C2×Q8—62no—
504C2×Q8—62no—
505C2×D4—68no—
506C2×D4—64no—
507C2×D4—64no—
508C2×D4—64no—
509C2×D4—64no—
510C2×D4—64no—
511C2×D4—64no—
512C2×D4—64no—
513C2×D4—122no—
514C2×D4—124no—
515C2×D4—124no—
516C2×D4—122no—
517C22×C4—32no—
518C22×C4—31no—
519C22×C4—31no—
520C22×C4—34no—
521C22×C4—31no—
522C22×C4—32no—
523C22×C4—32no—
524C22×C4—32no—
525C22×C4—62no—
526C22×C4—62no—
527C22×C4—62no—
528C22×C4—62no—
529C22×C4—62no—
530C22×C4—62no—
531C22×C4—62no—
532C22×C4—68no—
533C22×C4—121no—
534C22×C4—124no—
535C22×C4—124no—
536C22×C4C23×D312yes—
537C22×C4C23×D312yes—
538C22×C4C23×D314yes—
539C22×C4C23×D312yes—
540C22×C4C23×D312yes—
541C22×C4C23×D311yescharacteristic
542C22×C4C23×D311yescharacteristic
543C22×C4C23×D311yescharacteristic
544C4⋊C4—24no—
545C4⋊C4—28no—
546C4⋊C4—24no—
547C4⋊C4—22no—
548C4⋊C4—22no—
549C4⋊C4—22no—
550C4⋊C4—38no—
551C4⋊C4—42no—
552C4⋊C4—44no—
553C4⋊C4—64no—
554C4⋊C4—64no—
555C4⋊C4—68no—
556C4⋊C4—64no—
557C4⋊C4—64no—
558C4⋊C4—62no—
559C4⋊C4—64no—
560C4⋊C4—62no—
561C4⋊C4—62no—
562C4⋊C4—124no—
563C4⋊C4—122no—
564C4⋊C4D3×D414yes—
565C22⋊C4—38no—
566C22⋊C4—68no—
567C22⋊C4—68no—
568C22⋊C4—68no—
569C22⋊C4—68no—
570C22⋊C4—64no—
571C22⋊C4—64no—
572C22⋊C4—68no—
573C22⋊C4—124no—
574C22⋊C4—124no—
575C22⋊C4—124no—
576C22⋊C4—122no—
577C22⋊C4—124no—
578C22⋊C4—124no—
579C42—24no—
580C42—24no—
581C42—68no—
582C42—64no—
583C42—62no—
584C42—62no—
585C42—62no—
586C42—64no—
587C42#23914yes—
588C22×C3C23×D411yescharacteristic
589C22×C3C22×#4111yescharacteristic
590C22×C3C2×H(5,𝔽2)11yescharacteristic
591C22×C3C2×H(5,𝔽2)11yescharacteristic
592C22×C3C2×2−1+411yescharacteristic
593C22×C3C2×2−1+411yescharacteristic
594C22×C3#58511yescharacteristic
595C2×D3—22no—
596C2×D3—22no—
597C2×D3—22no—
598C2×D3—41no—
599C2×D3—41no—
600C2×D3—41no—
601C2×D3—41no—
602C2×D3—44no—
603C2×D3—44no—
604C2×D3—44no—
605C2×D3—44no—
606C2×D3—44no—
607C2×D3—44no—
608C2×D3—44no—
609C3×C4—22no—
610C3×C4—24no—
611C3×C4—42no—
612C3×C4—44no—
613C3×C4—42no—
614C3×C4—42no—
615C3×C4#54214yescomplemented
616C3×C4#54714yes—
617Dic3—24no—
618Dic3—22no—
619Dic3—22no—
620Dic3—41no—
621Dic3—42no—
622Dic3—42no—
623Dic3—42no—
624C23—32no—
625C23—61no—
626C23—61no—
627C23—61no—
628C23—61no—
629C23—61no—
630C23—61no—
631C23—64no—
632C23—64no—
633C23—64no—
634C23—64no—
635C23—64no—
636C23—64no—
637C23—64no—
638C23C24×D311yescharacteristic
639Q8—68no—
640Q8—88no—
641D4—128no—
642D4—128no—
643D4—244no—
644D4—248no—
645C2×C4—22no—
646C2×C4—21no—
647C2×C4—22no—
648C2×C4—21no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—24no—
652C2×C4—22no—
653C2×C4—24no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—24no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—34no—
662C2×C4—32no—
663C2×C4—32no—
664C2×C4—61no—
665C2×C4—61no—
666C2×C4—62no—
667C2×C4—61no—
668C2×C4—62no—
669C2×C4—61no—
670C2×C4—68no—
671C2×C4—62no—
672C2×C4—62no—
673C2×C4—61no—
674C2×C4—62no—
675C2×C4—61no—
676C2×C4—62no—
677C2×C4—62no—
678C2×C4—61no—
679C2×C4—62no—
680C2×C4—62no—
681C2×C4—62no—
682C2×C4—62no—
683C2×C4—124no—
684C2×C4—124no—
685C2×C4—248no—
686C2×C4C2×D3×D414yes—
687C2×C4C2×D3×D412yes—
688C2×C4#100412yes—
689C2×C4C2×#23912yes—
690C2×C4C2×#23912yes—
691C2×C4C2×#23912yes—
692C2×C4#100712yes—
693C2×C4#100712yes—
694C2×C3C2×#54211yescharacteristic
695C2×C3C2×#54711yescharacteristic
696C2×C3#349411yescharacteristic
697C2×C3#349711yescharacteristic
698C2×C3#349811yescharacteristic
699C2×C3#355011yescharacteristic
700C2×C3#355411yescharacteristic
701D3—42no—
702D3—84no—
703C22—62no—
704C22—62no—
705C22—62no—
706C22—121no—
707C22—121no—
708C22—121no—
709C22—121no—
710C22—124no—
711C22—124no—
712C22—124no—
713C22—124no—
714C22—124no—
715C22—124no—
716C22—124no—
717C22C22×D3×D411yescharacteristic
718C22C2×#100411yescharacteristic
719C22C22×#23911yescharacteristic
720C22C2×#100711yescharacteristic
721C22C2×#100711yescharacteristic
722C22D3×H(5,𝔽2)11yescharacteristic
723C22#596811yescharacteristic
724C4—22no—
725C4—24no—
726C4—44no—
727C4—42no—
728C4—42no—
729C4—42no—
730C4—62no—
731C4—62no—
732C4—64no—
733C4—122no—
734C4—122no—
735C4—121no—
736C4—122no—
737C4#572614yes—
738C4#573314yescomplemented
739C3#3935111yescharacteristic, complemented, Sylow
740C2—122no—
741C2—244no—
742C2C2×#573311yescharacteristic
743C2C2×#572611yescharacteristic
744C2#8659711yescharacteristic
745C2#8660811yescharacteristic
746C2#8676011yescharacteristic
747C2#8676511yescharacteristic
748C2#8704411yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2551C2
prime radical#74375C2
hypercenter#2551D3
hypocenterC3#39351
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2551

Complements

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

NH ≅ G/Ntype
1. C2×#5733C2semidirect
2. C3×#2551C2semidirect
3. #83259C2semidirect
4. #83257C2semidirect
5. #83236C2semidirect
6. #77259C2semidirect
7. #77222C2semidirect
8. #76249C2semidirect
9. #76215C2semidirect
10. #76047C2semidirect
11. #76007C2semidirect
13. #74323C2semidirect
14. C4×#897C2semidirect
15. #73753C2semidirect
16. #73712C2semidirect
17. #73653C2semidirect
90. #2551D3semidirect
162. #897D4semidirect
615. C3×C4#542semidirect
738. C4#5733semidirect
739. C3#39351semidirect

Maximal subgroups

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

subgroupindex
C2×#57332
C3×#25512
#832592
#832572
#832362
#772592
#772222
#762492
#762152
#760472
#760072
#743752
#743232
C4×#8972
#737532
#737122
#736532
#393513