Finite Group Databasebeta

← #11069686

Subgroups — #11069686

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×#5643C212yesmaximal, complemented
2C3×#2542C211yesmaximal, characteristic, complemented
3#83251C211yesmaximal, characteristic, complemented
4#83229C211yesmaximal, characteristic, complemented
5#82821C212yesmaximal, complemented
6#82756C212yesmaximal, complemented
7#82755C212yesmaximal, complemented
8#82378C211yesmaximal, characteristic
9#82319C211yesmaximal, characteristic, complemented
10#78073C214yesmaximal, complemented
11#78065C214yesmaximal, complemented
12#76353C212yesmaximal, complemented
13#76316C212yesmaximal, complemented
14#74369C212yesmaximal, complemented
15#74333C212yesmaximal, complemented
16#73653C211yesmaximal, characteristic, complemented
17C4×#888C211yesmaximal, characteristic, complemented
18#39387—31nomaximal, Sylow
19C2×C3×C4⋊Q8C2211yescharacteristic
20C2×C3×C22⋊Q8C2212yes—
21C2×C3×C22⋊Q8C2212yes—
22C2×C3×C4×D4C2211yescharacteristic
23C2×#947C2212yes—
24C2×#947C2212yes—
25C2×Q8×Dic3C2212yes—
26C2×#940C2212yes—
27C2×#930C2212yes—
28C2×#930C2212yes—
29C2×#926C2212yes—
30#5643—216no—
31C2×#898C2214yes—
32C2×#897C2214yes—
33C2×#893C2212yes—
34C2×#888C2211yescharacteristic
35C2×#885C2214yes—
36C2×#883C2214yes—
37C2×#874C2211yescharacteristic
38C2×C4×D12C2212yes—
39C2×C4×Dic6C2212yes—
40C3×#399C2214yes—
41C3×#390C2212yes—
42C3×#384C2212yes—
43C3×C4×C4⋊C4C2211yescharacteristic
44#5229C2212yes—
45#5221C2211yescharacteristic
46#5221C2211yescharacteristic
47C4×#217C2212yes—
48#4994C2214yes—
49#4994C2214yes—
50#4994C2214yes—
51#4992C2214yes—
52#4990C2214yes—
53#4988C2212yes—
54#4988C2212yes—
55#4988C2212yes—
56#4988C2212yes—
57#4988C2212yes—
58#4988C2212yes—
59#4987C2214yes—
60#4984C2212yes—
61#4984C2211yescharacteristic
62#4984C2211yescharacteristic
63#4984C2211yescharacteristic
64#4980C2214yes—
65#4975C2211yescharacteristic
66Dic3×C4⋊C4C2212yes—
67#4972C2211yescharacteristic
68#4961C2214yes—
69#4961C2214yes—
70#4960C2214yes—
71#4959C2214yes—
72#4959C2214yes—
73#4957C2214yes—
74#4956C2214yes—
75#4951C2212yes—
76#4951C2212yes—
77#4939C2212yes—
78C4×C4⋊Dic3C2211yescharacteristic
79C4×C4⋊Dic3C2211yescharacteristic
80C4×Dic3⋊C4C2212yes—
81C42×Dic3C2211yescharacteristic
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#2542D311yescharacteristic, complemented
92#2541—31no—
93#2538—32no—
94#2512—32no—
95#2445—32no—
96#2427—32no—
97#2426—32no—
98#2366—31no—
99#2365—31no—
100C4×C4⋊Q8—31no—
101#2293—31no—
102C22×C3×Q8C2312yes—
103C22×C3×D4C2311yescharacteristic
104C23×C3×C4C2312yes—
105C22×#67C2314yes—
106C22×#67C2314yes—
107C22×D12C2312yes—
108C22×D12C2312yes—
109C22×D12C2312yes—
110C22×C4×D3C2314yes—
111C22×Dic6C2312yes—
112C3×C4⋊Q8—24no—
113C3×C22⋊Q8—28no—
114C3×C22⋊Q8—44no—
115C3×C4×D4—24no—
116C2×C3×C4⋊C4C2311yescharacteristic
117C2×C3×C4⋊C4C2312yes—
118C2×C3×C4⋊C4C2312yes—
119C2×C3×C4⋊C4C2311yescharacteristic
120C2×C3×C4⋊C4C2314yes—
121C2×C3×C4⋊C4C2314yes—
122C2×C3×C4⋊C4C2311yescharacteristic
123C2×C3×C22⋊C4C2312yes—
124C2×C3×C22⋊C4C2314yes—
125C2×C3×C22⋊C4C2314yes—
126C2×C3×C42C2312yes—
127C2×C3×C42C2311yescharacteristic
128C2×#217C2312yes—
129C2×#217C2312yes—
130C2×#217C2312yes—
131C2×#217C2312yes—
132#947—28no—
133#947—44no—
134Q8×Dic3—28no—
135#940—44no—
136#930—28no—
137#930—44no—
138C2×(C2×D3)⋊C4C2314yes—
139C2×(C2×D3)⋊C4C2314yes—
140C2×(C2×D3)⋊C4C2314yes—
141C2×(C2×D3)⋊C4C2314yes—
142C2×(C2×D3)⋊C4C2314yes—
143C2×(C2×D3)⋊C4C2314yes—
144C2×(C2×D3)⋊C4C2314yes—
145C2×(C2×D3)⋊C4C2314yes—
146C2×(C2×D3)⋊C4C2314yes—
147#926—28no—
148C2×C4⋊Dic3C2311yescharacteristic
149C2×C4⋊Dic3C2311yescharacteristic
150C2×C4⋊Dic3C2311yescharacteristic
151C2×C4⋊Dic3C2312yes—
152C2×C4⋊Dic3C2312yes—
153C2×C4⋊Dic3C2314yes—
154C2×C4⋊Dic3C2312yes—
155C2×C4⋊Dic3C2311yescharacteristic
156C2×Dic3⋊C4C2312yes—
157C2×Dic3⋊C4C2312yes—
158C2×Dic3⋊C4C2312yes—
159C2×Dic3⋊C4C2312yes—
160C2×C4×Dic3C2311yescharacteristic
161C2×C4×Dic3C2311yescharacteristic
162C2×C4×Dic3C2311yescharacteristic
163C2×C4×Dic3C2312yes—
164C2×C4×Dic3C2312yes—
165C2×C4×Dic3C2314yes—
166C2×C4×Dic3C2311yescharacteristic
167C2×C4×Dic3C2311yescharacteristic
168C2×C4×Dic3C2311yescharacteristic
169#898—216no—
170#897—216no—
171#893—28no—
172#888D418yescomplemented
173#885—216no—
174#883—216no—
175#874—24no—
176C4×D12—44no—
177C4×Dic6—44no—
178C3×#95C2312yes—
179C3⋊#95C2312yes—
180C3⋊#95C2312yes—
181C3⋊#95C2312yes—
182C3⋊#95C2312yes—
183C3⋊#95C2312yes—
184C3⋊#95C2312yes—
185C3⋊#95C2314yes—
186C3⋊#95C2314yes—
187#542—616no—
188C2×C4⋊Q8—31no—
189C2×C4⋊Q8C2×D311yescharacteristic
190C2×#127—32no—
191C2×#127—31no—
192C2×#126—34no—
193C2×#124—32no—
194C2×#124—32no—
195C2×#124—34no—
196C2×#123—34no—
197C2×C22⋊Q8—34no—
198C2×C22⋊Q8C2×D312yes—
199C2×C22⋊Q8C2×D312yes—
200C2×#121—32no—
201C2×#121—32no—
202C2×C4×Q8—32no—
203C2×C4×Q8—32no—
204C2×C4×D4—32no—
205C2×C4×D4—32no—
206C2×C4×D4C2×D311yescharacteristic
207C2×#117—32no—
208#399C2×D314yes—
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#391—32no—
220#390—31no—
221#390—31no—
222#390—32no—
223#390—32no—
224#390—32no—
225#390—32no—
226#390—32no—
227#390—32no—
228#390—34no—
229#390—32no—
230#390C2×D312yes—
231#389—31no—
232#389—31no—
233#389—32no—
234#389—31no—
235#389—31no—
236#389—32no—
237#388—34no—
238#388—32no—
239#388—32no—
240#387—34no—
241#386—34no—
242#386—34no—
243#384—31no—
244#384C2×D312yes—
245#380—34no—
246C4×C4⋊C4—32no—
247C4×C4⋊C4—31no—
248C4×C4⋊C4—32no—
249C4×C4⋊C4—31no—
250C4×C4⋊C4C2×D311yescharacteristic
251C4×C22⋊C4—32no—
252C43—31no—
253C24×C3C2412yes—
254C23×D3C2414yes—
255C2×C3×Q8—24no—
256C2×C3×Q8—24no—
257C2×C3×Q8—24no—
258C2×C3×D4—22no—
259C2×C3×D4—22no—
260C2×C3×D4—22no—
261C22×C3×C4—24no—
262C22×C3×C4—24no—
263C22×C3×C4—24no—
264C22×C3×C4C2414yes—
265C22×C3×C4C2412yes—
266C22×C3×C4C2412yes—
267C22×C3×C4C2412yes—
268C22×C3×C4C2411yescharacteristic
269C22×C3×C4C2411yescharacteristic
270C22×C3×C4C2411yescharacteristic
271C2×#67—28no—
272C2×#67—44no—
273C2×#67—44no—
274C2×#67—44no—
275C2×#67—44no—
276C2×#67—44no—
277C22×Dic3C2411yescharacteristic
278C22×Dic3C2412yes—
279C22×Dic3C2412yes—
280C22×Dic3C2412yes—
281C22×Dic3C2411yescharacteristic
282C22×Dic3C2412yes—
283C22×Dic3C2411yescharacteristic
284C22×Dic3C2411yescharacteristic
285C2×D12—24no—
286C2×D12—24no—
287C2×D12—24no—
288C2×D12—24no—
289C2×D12—24no—
290C2×D12—24no—
291C2×D12—24no—
292C2×D12—42no—
293C2×D12—42no—
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—22no—
302C3×C4⋊C4—24no—
303C3×C4⋊C4—24no—
304C3×C4⋊C4—22no—
305C3×C4⋊C4—44no—
306C3×C4⋊C4C2×D414yes—
307C3×C22⋊C4—28no—
308C3×C22⋊C4—24no—
309C3×C22⋊C4—44no—
310C3×C42—24no—
311C3×C42#4114yes—
312#217—24no—
313#217—24no—
314#217—42no—
315#217—42no—
316(C2×D3)⋊C4—28no—
317(C2×D3)⋊C4—28no—
318(C2×D3)⋊C4—28no—
319(C2×D3)⋊C4—28no—
320(C2×D3)⋊C4—44no—
321(C2×D3)⋊C4—44no—
322(C2×D3)⋊C4—44no—
323(C2×D3)⋊C4—44no—
324(C2×D3)⋊C4—44no—
325C4⋊Dic3—22no—
326C4⋊Dic3—22no—
327C4⋊Dic3—22no—
328C4⋊Dic3—28no—
329C4⋊Dic3—24no—
330C4⋊Dic3—24no—
331C4⋊Dic3—42no—
332C4⋊Dic3C2×D414yes—
333Dic3⋊C4—42no—
334Dic3⋊C4—42no—
335Dic3⋊C4—42no—
336Dic3⋊C4C2×D418yes—
337C4×Dic3—24no—
338C4×Dic3—22no—
339C4×Dic3—24no—
340C4×Dic3—22no—
341C4×Dic3—22no—
342C4×Dic3—28no—
343C4×Dic3—41no—
344C4×Dic3—41no—
345C4×Dic3C2×D414yes—
346C22×Q8—32no—
347C22×Q8C22×D312yes—
348C22×D4—34no—
349C22×D4—34no—
350C22×D4—32no—
351C22×D4—32no—
352C22×D4—32no—
353C22×D4C22×D311yescharacteristic
354C23×C4—34no—
355C23×C4C22×D312yes—
356C4⋊Q8—24no—
357C4⋊Q8—38no—
358#127—64no—
359#127—124no—
360#126—616no—
361#124—68no—
362#124—616no—
363#124—124no—
364#123—616no—
365C22⋊Q8—28no—
366C22⋊Q8—44no—
367C22⋊Q8—616no—
368#121—68no—
369#121—124no—
370C4×Q8—68no—
371C4×Q8—124no—
372C4×D4—24no—
373C4×D4—68no—
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—31no—
384C2×C4⋊C4—32no—
385C2×C4⋊C4—32no—
386C2×C4⋊C4—32no—
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×D314yes—
394C2×C4⋊C4C22×D311yescharacteristic
395C2×C22⋊C4—32no—
396C2×C22⋊C4—32no—
397C2×C22⋊C4—34no—
398C2×C22⋊C4—34no—
399C2×C22⋊C4—34no—
400C2×C22⋊C4—34no—
401C2×C22⋊C4—32no—
402C2×C22⋊C4—32no—
403C2×C22⋊C4—34no—
404C2×C22⋊C4—34no—
405C2×C22⋊C4—34no—
406C2×C22⋊C4—34no—
407C2×C22⋊C4—34no—
408C2×C22⋊C4C22×D312yes—
409C2×C22⋊C4C22×D314yes—
410C2×C22⋊C4C22×D314yes—
411C2×C42—31no—
412C2×C42—32no—
413C2×C42—31no—
414C2×C42—34no—
415C2×C42—32no—
416C2×C42—31no—
417C2×C42—31no—
418C2×C42—31no—
419C2×C42—31no—
420C2×C42C22×D312yes—
421C2×C42C22×D311yescharacteristic
422#95—32no—
423#95—32no—
424#95—32no—
425#95—32no—
426#95—32no—
427#95—34no—
428#95—32no—
429#95—34no—
430#95C22×D312yes—
431C23×C3—22no—
432C23×C3—22no—
433C23×C3—22no—
434C23×C3—22no—
435C23×C3—22no—
436C23×C3—22no—
437C23×C3—22no—
438C23×C3C2511yescharacteristic
439C22×D3—24no—
440C22×D3—24no—
441C22×D3—24no—
442C22×D3—24no—
443C22×D3—24no—
444C22×D3—24no—
445C22×D3—24no—
446C3×Q8—48no—
447C3×D4—44no—
448C2×C3×C4—22no—
449C2×C3×C4—21no—
450C2×C3×C4—21no—
451C2×C3×C4—22no—
452C2×C3×C4—24no—
453C2×C3×C4—22no—
454C2×C3×C4—22no—
455C2×C3×C4—24no—
456C2×C3×C4—22no—
457C2×C3×C4—24no—
458C2×C3×C4—22no—
459C2×C3×C4—22no—
460C2×C3×C4—22no—
461C2×C3×C4—48no—
462C2×C3×C4C22×D414yes—
463C2×C3×C4C22×D412yes—
464C2×C3×C4C2×#4112yes—
465C2×C3×C4C2×#4112yes—
466C2×C3×C4C2×#4112yes—
467C2×C3×C4H(5,𝔽2)12yes—
468C2×C3×C4H(5,𝔽2)12yes—
469C2×C3×C42−1+412yes—
470#67—88no—
471#67—88no—
472C2×Dic3—21no—
473C2×Dic3—22no—
474C2×Dic3—21no—
475C2×Dic3—21no—
476C2×Dic3—21no—
477C2×Dic3—22no—
478C2×Dic3—22no—
479C2×Dic3—22no—
480C2×Dic3—21no—
481C2×Dic3—22no—
482C2×Dic3—21no—
483C2×Dic3—21no—
484C2×Dic3—22no—
485C2×Dic3—22no—
486C2×Dic3—21no—
487C2×Dic3—22no—
488C2×Dic3—21no—
489C2×Dic3—21no—
490C2×Dic3—22no—
491C2×Dic3—22no—
492C2×Dic3—22no—
493C2×Dic3C22×D414yes—
494C2×Dic3C22×D412yes—
495C2×Dic3C22×D412yes—
496D12—48no—
497D12—48no—
498D12—84no—
499C4×D3—88no—
500Dic6—48no—
501C24—34no—
502C24C23×D312yes—
503C2×Q8—24no—
504C2×Q8—24no—
505C2×Q8—24no—
506C2×Q8—38no—
507C2×Q8—122no—
508C2×Q8—122no—
509C2×D4—22no—
510C2×D4—22no—
511C2×D4—22no—
512C2×D4—68no—
513C2×D4—64no—
514C2×D4—64no—
515C2×D4—64no—
516C2×D4—64no—
517C2×D4—64no—
518C2×D4—64no—
519C2×D4—64no—
520C2×D4—122no—
521C2×D4—122no—
522C2×D4—124no—
523C2×D4—124no—
524C2×D4—124no—
525C2×D4—124no—
526C2×D4—124no—
527C22×C4—24no—
528C22×C4—24no—
529C22×C4—24no—
530C22×C4—32no—
531C22×C4—31no—
532C22×C4—31no—
533C22×C4—31no—
534C22×C4—32no—
535C22×C4—32no—
536C22×C4—32no—
537C22×C4—31no—
538C22×C4—68no—
539C22×C4—124no—
540C22×C4—124no—
541C22×C4C23×D314yes—
542C22×C4C23×D312yes—
543C22×C4C23×D312yes—
544C22×C4C23×D312yes—
545C22×C4C23×D311yescharacteristic
546C22×C4C23×D311yescharacteristic
547C22×C4C23×D311yescharacteristic
548C4⋊C4—28no—
549C4⋊C4—22no—
550C4⋊C4—24no—
551C4⋊C4—24no—
552C4⋊C4—22no—
553C4⋊C4—34no—
554C4⋊C4—38no—
555C4⋊C4—44no—
556C4⋊C4—64no—
557C4⋊C4—64no—
558C4⋊C4—68no—
559C4⋊C4—62no—
560C4⋊C4—62no—
561C4⋊C4—62no—
562C4⋊C4—122no—
563C4⋊C4—122no—
564C4⋊C4—122no—
565C4⋊C4—122no—
566C4⋊C4D3×D414yes—
567C22⋊C4—28no—
568C22⋊C4—24no—
569C22⋊C4—44no—
570C22⋊C4—68no—
571C22⋊C4—68no—
572C22⋊C4—68no—
573C22⋊C4—64no—
574C22⋊C4—64no—
575C22⋊C4—68no—
576C22⋊C4—124no—
577C22⋊C4—124no—
578C22⋊C4—124no—
579C22⋊C4—124no—
580C22⋊C4—124no—
581C22⋊C4—122no—
582C22⋊C4—122no—
583C42—24no—
584C42—34no—
585C42—68no—
586C42—64no—
587C42—62no—
588C42—62no—
589C42—62no—
590C42—64no—
591C42—121no—
592C42—121no—
593C42#23714yes—
594C22×C3—42no—
595C22×C3—42no—
596C22×C3—42no—
597C22×C3—42no—
598C22×C3—42no—
599C22×C3—42no—
600C22×C3—42no—
601C22×C3C23×D411yescharacteristic
602C22×C3C22×#4111yescharacteristic
603C22×C3C2×H(5,𝔽2)11yescharacteristic
604C22×C3C2×H(5,𝔽2)11yescharacteristic
605C22×C3C2×2−1+411yescharacteristic
606C22×C3#58511yescharacteristic
607C22×C3#58511yescharacteristic
608C2×D3—44no—
609C2×D3—44no—
610C2×D3—44no—
611C2×D3—44no—
612C2×D3—44no—
613C2×D3—44no—
614C2×D3—44no—
615C3×C4—24no—
616C3×C4—22no—
617C3×C4—42no—
618C3×C4—44no—
619C3×C4—42no—
620C3×C4#54214yescomplemented
621C3×C4#55014yes—
622Dic3—22no—
623Dic3—24no—
624Dic3—22no—
625Dic3—42no—
626Dic3—42no—
627Dic3—41no—
628Dic3—42no—
629Dic3—41no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—64no—
638C23—64no—
639C23—64no—
640C23—64no—
641C23—64no—
642C23—64no—
643C23—64no—
644C23C24×D311yescharacteristic
645Q8—48no—
646Q8—128no—
647D4—44no—
648D4—128no—
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—22no—
660C2×C4—24no—
661C2×C4—22no—
662C2×C4—24no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—32no—
667C2×C4—32no—
668C2×C4—34no—
669C2×C4—48no—
670C2×C4—61no—
671C2×C4—61no—
672C2×C4—62no—
673C2×C4—61no—
674C2×C4—61no—
675C2×C4—62no—
676C2×C4—62no—
677C2×C4—62no—
678C2×C4—61no—
679C2×C4—61no—
680C2×C4—62no—
681C2×C4—61no—
682C2×C4—62no—
683C2×C4—61no—
684C2×C4—62no—
685C2×C4—62no—
686C2×C4—61no—
687C2×C4—61no—
688C2×C4—62no—
689C2×C4—62no—
690C2×C4—62no—
691C2×C4—248no—
692C2×C4C2×D3×D414yes—
693C2×C4C2×D3×D412yes—
694C2×C4C2×#23712yes—
695C2×C4C2×#23712yes—
696C2×C4C2×#23712yes—
697C2×C4#100412yes—
698C2×C4#100712yes—
699C2×C4#100912yes—
700C2×C3—82no—
701C2×C3C2×#54211yescharacteristic
702C2×C3C2×#55011yescharacteristic
703C2×C3#349611yescharacteristic
704C2×C3#349711yescharacteristic
705C2×C3#351011yescharacteristic
706C2×C3#354611yescharacteristic
707C2×C3#355411yescharacteristic
708D3—84no—
709C22—42no—
710C22—42no—
711C22—42no—
712C22—42no—
713C22—42no—
714C22—42no—
715C22—42no—
716C22—124no—
717C22—124no—
718C22—124no—
719C22—124no—
720C22—124no—
721C22—124no—
722C22—124no—
723C22C22×D3×D411yescharacteristic
724C22C22×#23711yescharacteristic
725C22C2×#100411yescharacteristic
726C22C2×#100711yescharacteristic
727C22C2×#100911yescharacteristic
728C22#596811yescharacteristic
729C22#596811yescharacteristic
730C4—22no—
731C4—24no—
732C4—42no—
733C4—44no—
734C4—42no—
735C4—64no—
736C4—62no—
737C4—62no—
738C4—122no—
739C4—122no—
740C4—121no—
741C4—122no—
742C4—121no—
743C4#564314yescomplemented
744C4#571814yes—
745C3#3938711yescharacteristic, complemented, Sylow
746C2—82no—
747C2—244no—
748C2C2×#564311yescharacteristic
749C2C2×#571811yescharacteristic
750C2#8634411yescharacteristic
751C2#8670211yescharacteristic
752C2#8670711yescharacteristic
753C2#8676011yescharacteristic
754C2#8676511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2542C2
prime radical#82378C2
hypercenter#2542D3
hypocenterC3#39387
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2542

Complements

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

NH ≅ G/Ntype
1. C2×#5643C2semidirect
2. C3×#2542C2semidirect
3. #83251C2semidirect
4. #83229C2semidirect
5. #82821C2semidirect
6. #82756C2semidirect
7. #82755C2semidirect
9. #82319C2semidirect
10. #78073C2semidirect
11. #78065C2semidirect
12. #76353C2semidirect
13. #76316C2semidirect
14. #74369C2semidirect
15. #74333C2semidirect
16. #73653C2semidirect
17. C4×#888C2semidirect
91. #2542D3semidirect
172. #888D4semidirect
620. C3×C4#542semidirect
743. C4#5643semidirect
745. C3#39387semidirect

Maximal subgroups

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

subgroupindex
C2×#56432
C3×#25422
#832512
#832292
#828212
#827562
#827552
#823782
#823192
#780732
#780652
#763532
#763162
#743692
#743332
#736532
C4×#8882
#393873