Finite Group Databasebeta

← #11069673

Subgroups — #11069673

Order 768.

2306 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5582C212yesmaximal, complemented
2C3×#2365C211yesmaximal, characteristic, complemented
3#83259C211yesmaximal, characteristic, complemented
4#83251C211yesmaximal, characteristic, complemented
5#82495C212yesmaximal, complemented
6#76640C212yesmaximal, complemented
7#76624C212yesmaximal, complemented
8#76059C212yesmaximal, complemented
9#76004C212yesmaximal, complemented
10#75399C214yesmaximal, complemented
11#75153C214yesmaximal, complemented
12#73799C211yesmaximal, characteristic
13#73712C212yesmaximal, complemented
14#73693C212yesmaximal, complemented
15#73653C211yesmaximal, characteristic, complemented
16C4×#888C211yesmaximal, characteristic, complemented
17#73617C211yesmaximal, characteristic, complemented
18#39387—31nomaximal, Sylow
19C2×C3×C4⋊Q8C2211yescharacteristic
20C2×C3×C4×Q8C2212yes—
21C2×#947C2212yes—
22C2×#947C2212yes—
23C2×#946C2212yes—
24C2×#946C2212yes—
25#5582—216no—
26C2×#896C2214yes—
27C2×#895C2212yes—
28C2×#895C2212yes—
29C2×#894C2214yes—
30C2×#893C2212yes—
31C2×#888C2211yescharacteristic
32C2×#876C2214yes—
33C2×#875C2214yes—
34C2×#874C2211yescharacteristic
35C2×#874C2212yes—
36C2×C4×D12C2212yes—
37C2×C4×D12C2211yescharacteristic
38C2×#872C2212yes—
39C2×C4×Dic6C2212yes—
40C3×#391C2212yes—
41C3×#389C2212yes—
42C3×#387C2214yes—
43C3×C4×C4⋊C4C2211yescharacteristic
44C3×C4×C4⋊C4C2211yescharacteristic
45C3×C4×C4⋊C4C2212yes—
46#4994C2214yes—
47#4993C2214yes—
48#4991C2214yes—
49#4988C2212yes—
50#4988C2212yes—
51#4988C2212yes—
52#4988C2212yes—
53#4988C2212yes—
54#4988C2211yescharacteristic
55#4988C2211yescharacteristic
56#4988C2212yes—
57#4984C2211yescharacteristic
58#4975C2212yes—
59#4975C2211yescharacteristic
60#4972C2211yescharacteristic
61#4972C2211yescharacteristic
62#4972C2211yescharacteristic
63#4940C2214yes—
64#4939C2212yes—
65#4939C2212yes—
66#4939C2214yes—
67C4×(C2×D3)⋊C4C2212yes—
68C4×C4⋊Dic3C2211yescharacteristic
69C4×Dic3⋊C4C2212yes—
70C42×Dic3C2211yescharacteristic
71#4676C2214yes—
72#4676C2214yes—
73#4675C2214yes—
74#4672C2214yes—
75#4672C2214yes—
76#4672C2214yes—
77#4671C2214yes—
78#4669C2212yes—
79#4669C2212yes—
80#4667C2214yes—
81#4665C2214yes—
82#4665C2214yes—
83#4647C2212yes—
84#4646C2212yes—
85C2×#542—32no—
86#2858—31no—
87#2730—34no—
88#2705—34no—
89#2620—32no—
90#2548—32no—
91#2542—31no—
92#2541—31no—
93#2538—32no—
94#2512—32no—
95#2445—32no—
96#2427—32no—
97#2426—32no—
98#2366—31no—
99#2365D311yescharacteristic, complemented
100C4×C4⋊Q8—31no—
101#2293—31no—
102C22×C3×Q8C2312yes—
103C22×D12C2312yes—
104C22×D12C2312yes—
105C22×D12C2311yescharacteristic
106C22×D12C2312yes—
107C22×D12C2314yes—
108C22×D12C2314yes—
109C22×C4×D3C2312yes—
110C22×C4×D3C2314yes—
111C22×Dic6C2312yes—
112C3×C4⋊Q8—24no—
113C3×C4×Q8—28no—
114C2×C3×C4⋊C4C2311yescharacteristic
115C2×C3×C4⋊C4C2311yescharacteristic
116C2×C3×C4⋊C4C2311yescharacteristic
117C2×C3×C4⋊C4C2312yes—
118C2×C3×C4⋊C4C2312yes—
119C2×C3×C4⋊C4C2314yes—
120C2×C3×C4⋊C4C2311yescharacteristic
121C2×C3×C42C2312yes—
122C2×C3×C42C2312yes—
123C2×C3×C42C2314yes—
124C2×C3×C42C2311yescharacteristic
125#947—28no—
126#947—44no—
127#946—28no—
128#946—44no—
129C2×(C2×D3)⋊C4C2314yes—
130C2×(C2×D3)⋊C4C2314yes—
131C2×(C2×D3)⋊C4C2312yes—
132C2×(C2×D3)⋊C4C2312yes—
133C2×(C2×D3)⋊C4C2312yes—
134C2×(C2×D3)⋊C4C2314yes—
135C2×(C2×D3)⋊C4C2314yes—
136C2×(C2×D3)⋊C4C2314yes—
137C2×(C2×D3)⋊C4C2312yes—
138C2×(C2×D3)⋊C4C2314yes—
139C2×(C2×D3)⋊C4C2314yes—
140C2×(C2×D3)⋊C4C2314yes—
141C2×(C2×D3)⋊C4C2314yes—
142C2×(C2×D3)⋊C4C2314yes—
143C2×(C2×D3)⋊C4C2312yes—
144C2×(C2×D3)⋊C4C2314yes—
145C2×C4⋊Dic3C2311yescharacteristic
146C2×C4⋊Dic3C2311yescharacteristic
147C2×C4⋊Dic3C2312yes—
148C2×C4⋊Dic3C2311yescharacteristic
149C2×Dic3⋊C4C2314yes—
150C2×Dic3⋊C4C2312yes—
151C2×Dic3⋊C4C2312yes—
152C2×Dic3⋊C4C2312yes—
153C2×Dic3⋊C4C2312yes—
154C2×Dic3⋊C4C2312yes—
155C2×Dic3⋊C4C2314yes—
156C2×Dic3⋊C4C2312yes—
157C2×C4×Dic3C2311yescharacteristic
158C2×C4×Dic3C2311yescharacteristic
159C2×C4×Dic3C2311yescharacteristic
160C2×C4×Dic3C2312yes—
161C2×C4×Dic3C2311yescharacteristic
162C2×C4×Dic3C2311yescharacteristic
163C2×C4×Dic3C2311yescharacteristic
164#896—216no—
165#895—28no—
166#895—44no—
167#894—216no—
168#893—44no—
169#888D418yescomplemented
170#876—216no—
171#875—216no—
172#874—24no—
173#874—44no—
174C4×D12—24no—
175C4×D12—28no—
176#872—28no—
177C4×Dic6—44no—
178C3×#95C2312yes—
179C3×#95C2312yes—
180C3×#95C2314yes—
181C3×#95C2314yes—
182C3⋊#95C2312yes—
183C3⋊#95C2312yes—
184C3⋊#95C2312yes—
185C3⋊#95C2312yes—
186C3⋊#95C2312yes—
187#542—616no—
188C2×C4⋊Q8—31no—
189C2×C4⋊Q8C2×D311yescharacteristic
190C2×#127—31no—
191C2×#127—32no—
192C2×#126—34no—
193C2×#124—32no—
194C2×#124—32no—
195C2×#124—34no—
196C2×#123—34no—
197C2×C22⋊Q8—32no—
198C2×C22⋊Q8—32no—
199C2×C22⋊Q8—34no—
200C2×#121—32no—
201C2×#121—32no—
202C2×C4×Q8—32no—
203C2×C4×Q8C2×D312yes—
204C2×C4×D4—32no—
205C2×C4×D4—32no—
206C2×C4×D4—31no—
207C2×#117—32no—
208#399—34no—
209#397—34no—
210#396—34no—
211#396—34no—
212#396—34no—
213#394—34no—
214#394—34no—
215#394—34no—
216#394—34no—
217#392—34no—
218#391—32no—
219#391C2×D312yes—
220#390—32no—
221#390—32no—
222#390—32no—
223#390—32no—
224#390—32no—
225#390—31no—
226#390—32no—
227#390—31no—
228#390—32no—
229#390—34no—
230#390—32no—
231#389—31no—
232#389—31no—
233#389—31no—
234#389—31no—
235#389—32no—
236#389C2×D312yes—
237#388—34no—
238#388—32no—
239#388—32no—
240#387C2×D314yes—
241#386—34no—
242#386—34no—
243#384—31no—
244#384—32no—
245#380—34no—
246C4×C4⋊C4—31no—
247C4×C4⋊C4—32no—
248C4×C4⋊C4C2×D311yescharacteristic
249C4×C4⋊C4C2×D311yescharacteristic
250C4×C4⋊C4C2×D312yes—
251C4×C22⋊C4—32no—
252C43—31no—
253C23×D3C2412yes—
254C23×D3C2414yes—
255C2×C3×Q8—24no—
256C2×C3×Q8—24no—
257C2×C3×Q8—24no—
258C22×C3×C4C2412yes—
259C22×C3×C4C2412yes—
260C22×C3×C4C2412yes—
261C22×C3×C4C2414yes—
262C22×C3×C4C2412yes—
263C22×C3×C4C2411yescharacteristic
264C22×C3×C4C2411yescharacteristic
265C22×C3×C4C2411yescharacteristic
266C22×Dic3C2411yescharacteristic
267C22×Dic3C2411yescharacteristic
268C22×Dic3C2412yes—
269C22×Dic3C2412yes—
270C22×Dic3C2412yes—
271C22×Dic3C2411yescharacteristic
272C22×Dic3C2411yescharacteristic
273C2×D12—24no—
274C2×D12—22no—
275C2×D12—24no—
276C2×D12—24no—
277C2×D12—22no—
278C2×D12—24no—
279C2×D12—24no—
280C2×D12—24no—
281C2×D12—22no—
282C2×D12—28no—
283C2×D12—24no—
284C2×D12—44no—
285C2×D12—44no—
286C2×D12—44no—
287C2×D12—42no—
288C2×D12—42no—
289C2×D12—44no—
290C2×D12—44no—
291C2×C4×D3—24no—
292C2×C4×D3—24no—
293C2×C4×D3—24no—
294C2×C4×D3—28no—
295C2×C4×D3—44no—
296C2×C4×D3—44no—
297C2×Dic6—42no—
298C2×Dic6—42no—
299C2×Dic6C2×D418yes—
300C3×C4⋊C4—28no—
301C3×C4⋊C4—24no—
302C3×C4⋊C4—24no—
303C3×C4⋊C4—22no—
304C3×C4⋊C4—22no—
305C3×C4⋊C4—22no—
306C3×C4⋊C4C2×D414yes—
307C3×C42—24no—
308C3×C42—28no—
309C3×C42—24no—
310C3×C42#4114yes—
311(C2×D3)⋊C4—28no—
312(C2×D3)⋊C4—24no—
313(C2×D3)⋊C4—24no—
314(C2×D3)⋊C4—24no—
315(C2×D3)⋊C4—28no—
316(C2×D3)⋊C4—28no—
317(C2×D3)⋊C4—28no—
318(C2×D3)⋊C4—28no—
319(C2×D3)⋊C4—44no—
320(C2×D3)⋊C4—44no—
321(C2×D3)⋊C4—42no—
322(C2×D3)⋊C4—42no—
323(C2×D3)⋊C4—44no—
324(C2×D3)⋊C4—44no—
325(C2×D3)⋊C4—44no—
326(C2×D3)⋊C4—44no—
327C4⋊Dic3—22no—
328C4⋊Dic3—22no—
329C4⋊Dic3—42no—
330C4⋊Dic3C2×D414yes—
331Dic3⋊C4—24no—
332Dic3⋊C4—24no—
333Dic3⋊C4—28no—
334Dic3⋊C4—42no—
335Dic3⋊C4—42no—
336Dic3⋊C4—42no—
337Dic3⋊C4—44no—
338Dic3⋊C4C2×D418yes—
339C4×Dic3—22no—
340C4×Dic3—24no—
341C4×Dic3—22no—
342C4×Dic3—22no—
343C4×Dic3—41no—
344C4×Dic3—41no—
345C4×Dic3C2×D414yes—
346C22×Q8—32no—
347C22×Q8C22×D312yes—
348C22×D4—32no—
349C22×D4—31no—
350C22×D4—32no—
351C22×D4—34no—
352C22×D4—32no—
353C22×D4—34no—
354C23×C4—32no—
355C23×C4—34no—
356C4⋊Q8—24no—
357C4⋊Q8—38no—
358#127—64no—
359#127—124no—
360#126—616no—
361#124—616no—
362#124—68no—
363#124—124no—
364#123—616no—
365C22⋊Q8—616no—
366C22⋊Q8—68no—
367C22⋊Q8—124no—
368#121—68no—
369#121—124no—
370C4×Q8—28no—
371C4×Q8—124no—
372C4×D4—68no—
373C4×D4—64no—
374C4×D4—124no—
375#117—68no—
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—31no—
383C2×C4⋊C4—32no—
384C2×C4⋊C4—32no—
385C2×C4⋊C4—32no—
386C2×C4⋊C4—34no—
387C2×C4⋊C4—32no—
388C2×C4⋊C4C22×D311yescharacteristic
389C2×C4⋊C4C22×D314yes—
390C2×C4⋊C4C22×D311yescharacteristic
391C2×C4⋊C4C22×D312yes—
392C2×C4⋊C4C22×D312yes—
393C2×C4⋊C4C22×D311yescharacteristic
394C2×C4⋊C4C22×D311yescharacteristic
395C2×C22⋊C4—32no—
396C2×C22⋊C4—32no—
397C2×C22⋊C4—34no—
398C2×C22⋊C4—32no—
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—34no—
408C2×C22⋊C4—32no—
409C2×C22⋊C4—32no—
410C2×C22⋊C4—34no—
411C2×C42—31no—
412C2×C42—32no—
413C2×C42—31no—
414C2×C42—31no—
415C2×C42—31no—
416C2×C42—31no—
417C2×C42—31no—
418C2×C42C22×D312yes—
419C2×C42C22×D312yes—
420C2×C42C22×D314yes—
421C2×C42C22×D311yescharacteristic
422#95—32no—
423#95—32no—
424#95—32no—
425#95—32no—
426#95—32no—
427#95C22×D312yes—
428#95C22×D312yes—
429#95C22×D314yes—
430#95C22×D314yes—
431C23×C3C2511yescharacteristic
432C22×D3—22no—
433C22×D3—24no—
434C22×D3—22no—
435C22×D3—24no—
436C22×D3—24no—
437C22×D3—22no—
438C22×D3—24no—
439C22×D3—22no—
440C22×D3—22no—
441C22×D3—24no—
442C22×D3—22no—
443C22×D3—24no—
444C22×D3—22no—
445C22×D3—24no—
446C3×Q8—48no—
447C2×C3×C4—22no—
448C2×C3×C4—21no—
449C2×C3×C4—21no—
450C2×C3×C4—22no—
451C2×C3×C4—22no—
452C2×C3×C4—24no—
453C2×C3×C4—22no—
454C2×C3×C4—24no—
455C2×C3×C4—22no—
456C2×C3×C4—24no—
457C2×C3×C4—22no—
458C2×C3×C4—22no—
459C2×C3×C4—22no—
460C2×C3×C4—22no—
461C2×C3×C4—22no—
462C2×C3×C4—22no—
463C2×C3×C4C22×D414yes—
464C2×C3×C4C22×D412yes—
465C2×C3×C4C2×#4112yes—
466C2×C3×C4C2×#4112yes—
467C2×C3×C4C2×#4112yes—
468C2×C3×C4H(5,𝔽2)12yes—
469C2×C3×C4H(5,𝔽2)12yes—
470C2×C3×C42−1+412yes—
471C2×Dic3—21no—
472C2×Dic3—22no—
473C2×Dic3—21no—
474C2×Dic3—21no—
475C2×Dic3—21no—
476C2×Dic3—22no—
477C2×Dic3—22no—
478C2×Dic3—22no—
479C2×Dic3—21no—
480C2×Dic3—22no—
481C2×Dic3—21no—
482C2×Dic3—21no—
483C2×Dic3—22no—
484C2×Dic3—22no—
485C2×Dic3—21no—
486C2×Dic3—21no—
487C2×Dic3—21no—
488C2×Dic3—22no—
489C2×Dic3C22×D412yes—
490C2×Dic3C22×D412yes—
491C2×Dic3C22×D414yes—
492D12—44no—
493D12—48no—
494D12—48no—
495D12—88no—
496D12—84no—
497D12—88no—
498C4×D3—48no—
499C4×D3—88no—
500Dic6—48no—
501C24—32no—
502C24—34no—
503C2×Q8—24no—
504C2×Q8—24no—
505C2×Q8—24no—
506C2×Q8—38no—
507C2×Q8—122no—
508C2×Q8—122no—
509C2×D4—62no—
510C2×D4—64no—
511C2×D4—64no—
512C2×D4—64no—
513C2×D4—64no—
514C2×D4—68no—
515C2×D4—62no—
516C2×D4—64no—
517C2×D4—64no—
518C2×D4—64no—
519C2×D4—62no—
520C2×D4—124no—
521C2×D4—124no—
522C2×D4—124no—
523C2×D4—122no—
524C2×D4—122no—
525C2×D4—124no—
526C2×D4—124no—
527C22×C4—32no—
528C22×C4—31no—
529C22×C4—31no—
530C22×C4—31no—
531C22×C4—31no—
532C22×C4—32no—
533C22×C4—32no—
534C22×C4—68no—
535C22×C4—64no—
536C22×C4—64no—
537C22×C4—64no—
538C22×C4—124no—
539C22×C4—124no—
540C22×C4C23×D312yes—
541C22×C4C23×D312yes—
542C22×C4C23×D312yes—
543C22×C4C23×D314yes—
544C22×C4C23×D311yescharacteristic
545C22×C4C23×D312yes—
546C22×C4C23×D311yescharacteristic
547C22×C4C23×D311yescharacteristic
548C4⋊C4—24no—
549C4⋊C4—24no—
550C4⋊C4—28no—
551C4⋊C4—22no—
552C4⋊C4—22no—
553C4⋊C4—22no—
554C4⋊C4—34no—
555C4⋊C4—38no—
556C4⋊C4—64no—
557C4⋊C4—64no—
558C4⋊C4—68no—
559C4⋊C4—62no—
560C4⋊C4—62no—
561C4⋊C4—122no—
562C4⋊C4—122no—
563C4⋊C4—122no—
564C4⋊C4—124no—
565C4⋊C4—122no—
566C4⋊C4D3×D414yes—
567C22⋊C4—64no—
568C22⋊C4—64no—
569C22⋊C4—68no—
570C22⋊C4—68no—
571C22⋊C4—68no—
572C22⋊C4—68no—
573C22⋊C4—64no—
574C22⋊C4—68no—
575C22⋊C4—124no—
576C22⋊C4—124no—
577C22⋊C4—124no—
578C22⋊C4—124no—
579C22⋊C4—124no—
580C22⋊C4—122no—
581C22⋊C4—124no—
582C22⋊C4—122no—
583C42—24no—
584C42—28no—
585C42—24no—
586C42—34no—
587C42—62no—
588C42—64no—
589C42—62no—
590C42—62no—
591C42—121no—
592C42—121no—
593C42#23514yes—
594C22×C3C23×D411yescharacteristic
595C22×C3C22×#4111yescharacteristic
596C22×C3C2×H(5,𝔽2)11yescharacteristic
597C22×C3C2×H(5,𝔽2)11yescharacteristic
598C22×C3C2×2−1+411yescharacteristic
599C22×C3#58511yescharacteristic
600C22×C3#58511yescharacteristic
601C2×D3—42no—
602C2×D3—44no—
603C2×D3—42no—
604C2×D3—44no—
605C2×D3—44no—
606C2×D3—42no—
607C2×D3—42no—
608C2×D3—44no—
609C2×D3—44no—
610C2×D3—42no—
611C2×D3—42no—
612C2×D3—44no—
613C2×D3—44no—
614C2×D3—42no—
615C3×C4—24no—
616C3×C4—22no—
617C3×C4—44no—
618C3×C4—42no—
619C3×C4—42no—
620C3×C4—42no—
621C3×C4#54214yescomplemented
622C3×C4#55014yes—
623Dic3—22no—
624Dic3—24no—
625Dic3—22no—
626Dic3—42no—
627Dic3—41no—
628Dic3—42no—
629Dic3—41no—
630C23—62no—
631C23—64no—
632C23—64no—
633C23—62no—
634C23—62no—
635C23—64no—
636C23—64no—
637C23—62no—
638C23—64no—
639C23—62no—
640C23—64no—
641C23—62no—
642C23—62no—
643C23—64no—
644C23C24×D311yescharacteristic
645Q8—48no—
646Q8—128no—
647D4—128no—
648D4—124no—
649D4—128no—
650D4—244no—
651D4—248no—
652D4—248no—
653C2×C4—22no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—22no—
657C2×C4—24no—
658C2×C4—22no—
659C2×C4—24no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—24no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—32no—
670C2×C4—32no—
671C2×C4—34no—
672C2×C4—61no—
673C2×C4—61no—
674C2×C4—62no—
675C2×C4—61no—
676C2×C4—61no—
677C2×C4—62no—
678C2×C4—62no—
679C2×C4—62no—
680C2×C4—61no—
681C2×C4—61no—
682C2×C4—61no—
683C2×C4—62no—
684C2×C4—61no—
685C2×C4—62no—
686C2×C4—62no—
687C2×C4—61no—
688C2×C4—61no—
689C2×C4—62no—
690C2×C4—128no—
691C2×C4—248no—
692C2×C4C2×#23512yes—
693C2×C4C2×#23512yes—
694C2×C4C2×#23512yes—
695C2×C4C2×D3×D414yes—
696C2×C4C2×D3×D412yes—
697C2×C4#100712yes—
698C2×C4#100912yes—
699C2×C4#100912yes—
700C2×C3C2×#54211yescharacteristic
701C2×C3C2×#55011yescharacteristic
702C2×C3#349611yescharacteristic
703C2×C3#349711yescharacteristic
704C2×C3#351011yescharacteristic
705C2×C3#354611yescharacteristic
706C2×C3#355411yescharacteristic
707D3—82no—
708D3—84no—
709C22—122no—
710C22—124no—
711C22—124no—
712C22—122no—
713C22—124no—
714C22—122no—
715C22—122no—
716C22—124no—
717C22—124no—
718C22—122no—
719C22—124no—
720C22—122no—
721C22—122no—
722C22—124no—
723C22C22×#23511yescharacteristic
724C22C22×D3×D411yescharacteristic
725C22C2×#100711yescharacteristic
726C22C2×#100911yescharacteristic
727C22C2×#100911yescharacteristic
728C22#596811yescharacteristic
729C22#596811yescharacteristic
730C4—22no—
731C4—24no—
732C4—42no—
733C4—42no—
734C4—42no—
735C4—44no—
736C4—64no—
737C4—62no—
738C4—62no—
739C4—121no—
740C4—122no—
741C4—121no—
742C4—122no—
743C4#555314yes—
744C4#558214yescomplemented
745C3#3938711yescharacteristic, complemented, Sylow
746C2—244no—
747C2—242no—
748C2C2×#555311yescharacteristic
749C2C2×#558211yescharacteristic
750C2#8587711yescharacteristic
751C2#8670211yescharacteristic
752C2#8676011yescharacteristic
753C2#8700911yescharacteristic
754C2#8703511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2365C2
prime radical#73799C2
hypercenter#2365D3
hypocenterC3#39387
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2365

Complements

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

NH ≅ G/Ntype
1. C2×#5582C2semidirect
2. C3×#2365C2semidirect
3. #83259C2semidirect
4. #83251C2semidirect
5. #82495C2semidirect
6. #76640C2semidirect
7. #76624C2semidirect
8. #76059C2semidirect
9. #76004C2semidirect
10. #75399C2semidirect
11. #75153C2semidirect
13. #73712C2semidirect
14. #73693C2semidirect
15. #73653C2semidirect
16. C4×#888C2semidirect
17. #73617C2semidirect
99. #2365D3semidirect
169. #888D4semidirect
621. C3×C4#542semidirect
744. C4#5582semidirect
745. C3#39387semidirect

Maximal subgroups

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

subgroupindex
C2×#55822
C3×#23652
#832592
#832512
#824952
#766402
#766242
#760592
#760042
#753992
#751532
#737992
#737122
#736932
#736532
C4×#8882
#736172
#393873