Finite Group Databasebeta

← C3×#73378 #11824538

Subgroups — C3×#73378 #11824538

Order 1152.

1613 conjugacy classes of subgroups.

The subgroup lattice has 703 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#930C212yesmaximal, complemented
2C2×C3×#930C211yesmaximal, characteristic, complemented
3C2×C3×C4×#67C211yesmaximal, characteristic, complemented
4C2×C32×#95C211yesmaximal, characteristic, complemented
5C3×#5213C212yesmaximal, complemented
6C3×#4674C211yesmaximal, characteristic, complemented
7C3×#4672C211yesmaximal, characteristic, complemented
8C3×#4671C211yesmaximal, characteristic, complemented
9C3×#4670C212yesmaximal, complemented
10C3×#4665C212yesmaximal, complemented
11C3×#4661C211yesmaximal, characteristic, complemented
12C3×#2543—31nomaximal
13#73378C311yesmaximal, characteristic, direct product factor
14C23×C32×C4C2212yes—
15C23×C32×C4C2211yescharacteristic
16C22×C3×#67C2212yes—
17C22×C3×#67C2211yescharacteristic
18C22×C3×D12C2212yes—
19C22×C3×D12C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic
21C2×C3×#217C2211yescharacteristic
22C3×#930—24no—
23C3×#930—28no—
24C3×C4×#67—24no—
25C2×C3×(C2×D3)⋊C4C2212yes—
26C2×C3×(C2×D3)⋊C4C2212yes—
27C2×C3×(C2×D3)⋊C4C2212yes—
28C2×C3×(C2×D3)⋊C4C2212yes—
29C2×C3×(C2×D3)⋊C4C2211yescharacteristic
30C2×C3×(C2×D3)⋊C4C2212yes—
31C2×C3×C4⋊Dic3C2212yes—
32C2×C3×C4⋊Dic3C2211yescharacteristic
33C2×C3×Dic3⋊C4C2211yescharacteristic
34C2×C3×C4×Dic3C2211yescharacteristic
35C32×#95C2211yescharacteristic
36C32×#95C2212yes—
37C32×#95C2211yescharacteristic
38C3×C3⋊#95C2212yes—
39C3×C3⋊#95C2212yes—
40C2×C3×#121—31no—
41C2×C3×#121—32no—
42C2×C3×C4×D4—31no—
43C2×#930C2×C312yescomplemented
44C2×#930C2×C311yescharacteristic, complemented
45C2×C4×#67C2×C311yescharacteristic, complemented
46C3×#398—31no—
47C3×#397—31no—
48C3×#394—31no—
49C3×#392—31no—
50C3×#388—32no—
51C3×#386—32no—
52C3×#386—32no—
53C2×C3×#95—21no—
54C2×C3×#95D311yescharacteristic, complemented
55C2×C3×#95C2×C311yescharacteristic, complemented
56#5213C2×C312yescomplemented
57#4674C2×C311yescharacteristic, complemented
58#4672C2×C311yescharacteristic, complemented
59#4671C2×C311yescharacteristic, complemented
60#4670C2×C312yescomplemented
61#4665C2×C312yescomplemented
62#4661C2×C311yescharacteristic, complemented
63C24×C32C2311yescharacteristic
64C23×C3×D3C2312yes—
65C23×C3×D3C2311yescharacteristic
66C22×C32×C4—24no—
67C22×C32×C4—24no—
68C22×C32×C4—42no—
69C22×C32×C4—42no—
70C22×C32×C4D414yescomplemented
71C22×C32×C4C2312yes—
72C22×C32×C4C2311yescharacteristic
73C22×C32×C4C2311yescharacteristic
74C22×C32×C4C2312yes—
75C2×C3×#67—22no—
76C2×C3×#67—22no—
77C2×C3×#67—24no—
78C2×C3×#67—24no—
79C2×C3×#67—24no—
80C2×C3×#67D414yescomplemented
81C22×C3×Dic3C2311yescharacteristic
82C22×C3×Dic3C2311yescharacteristic
83C22×C3×Dic3C2312yes—
84C22×C3×Dic3C2311yescharacteristic
85C2×C3×D12—24no—
86C2×C3×D12—22no—
87C2×C3×D12—24no—
88C2×C3×D12—42no—
89C2×C3×D12—42no—
90C2×C3×C4×D3—22no—
91C2×C3×C4×D3—42no—
92C3×#217—22no—
93C3×(C2×D3)⋊C4—24no—
94C3×(C2×D3)⋊C4—22no—
95C3×(C2×D3)⋊C4—24no—
96C3×(C2×D3)⋊C4—24no—
97C3×(C2×D3)⋊C4—24no—
98C3×(C2×D3)⋊C4—42no—
99C3×C4⋊Dic3—22no—
100C3×C4⋊Dic3—24no—
101C3×Dic3⋊C4—22no—
102C3×C4×Dic3—22no—
103#2543—31noSylow
104C22×C3×D4—31no—
105C22×C3×D4—32no—
106C22×C3×D4—32no—
107C22×C3×D4—31no—
108C23×C3×C4—22no—
109C23×C3×C4—21no—
110C23×C3×C4—31no—
111C23×C3×C4C2×D312yes—
112C23×C3×C4C2×D311yescharacteristic
113C23×C3×C4C22×C312yes—
114C23×C3×C4C22×C311yescharacteristic
115C22×#67C22×C312yes—
116C22×#67C22×C311yescharacteristic
117C22×D12C22×C312yes—
118C22×D12C22×C311yescharacteristic
119C22×C4×D3C22×C311yescharacteristic
120C3×#121—68no—
121C3×#121—64no—
122C3×C4×D4—64no—
123C2×C3×C4⋊C4—31no—
124C2×C3×C4⋊C4—32no—
125C2×C3×C4⋊C4—31no—
126C2×C3×C22⋊C4—31no—
127C2×C3×C22⋊C4—32no—
128C2×C3×C22⋊C4—32no—
129C2×C3×C22⋊C4—32no—
130C2×C3×C22⋊C4—32no—
131C2×C3×C22⋊C4—31no—
132C2×C3×C22⋊C4—32no—
133C2×C3×C42—31no—
134C2×#217C22×C311yescharacteristic
135#930—24no—
136#930—28no—
137C4×#67—24no—
138C2×(C2×D3)⋊C4C22×C312yes—
139C2×(C2×D3)⋊C4C22×C312yes—
140C2×(C2×D3)⋊C4C22×C312yes—
141C2×(C2×D3)⋊C4C22×C312yes—
142C2×(C2×D3)⋊C4C22×C311yescharacteristic
143C2×(C2×D3)⋊C4C22×C312yes—
144C2×C4⋊Dic3C22×C312yes—
145C2×C4⋊Dic3C22×C311yescharacteristic
146C2×Dic3⋊C4C22×C311yescharacteristic
147C2×C4×Dic3C22×C311yescharacteristic
148C3×#95—22no—
149C3×#95—21no—
150C3×#95—21no—
151C3×#95—32no—
152C3×#95—32no—
153C3×#95C2×D312yes—
154C3×#95C2×D311yescharacteristic
155C3×#95C2×D311yescharacteristic
156C3×#95C22×C311yescharacteristic
157C3×#95C22×C312yes—
158C3×#95C22×C311yescharacteristic
159C3⋊#95C22×C312yes—
160C3⋊#95C22×C312yes—
161C23×C32—22no—
162C23×C32—22no—
163C23×C32C2×D412yes—
164C23×C32C2×D412yes—
165C23×C32#4112yes—
166C23×C32C2411yescharacteristic
167C22×C3×D3—21no—
168C22×C3×D3—22no—
169C22×C3×D3—21no—
170C22×C3×D3—22no—
171C22×C3×D3—22no—
172C22×C3×D3—22no—
173C22×C3×D3—22no—
174C22×C3×D3—22no—
175C22×C3×D3—22no—
176C22×C3×D3—22no—
177C22×C3×D3—22no—
178C22×C3×D3C2×D412yes—
179C2×C32×C4—22no—
180C2×C32×C4—22no—
181C2×C32×C4—22no—
182C2×C32×C4—22no—
183C2×C32×C4—22no—
184C2×C32×C4—22no—
185C2×C32×C4—22no—
186C2×C32×C4—44no—
187C2×C32×C4—48no—
188C2×C32×C4C2×D412yes—
189C2×C32×C4C2×D412yes—
190C2×C32×C4#4114yes—
191C3×#67—28no—
192C3×#67—48no—
193C2×C3×Dic3—21no—
194C2×C3×Dic3—21no—
195C2×C3×Dic3—21no—
196C2×C3×Dic3—21no—
197C2×C3×Dic3—22no—
198C2×C3×Dic3—22no—
199C2×C3×Dic3—22no—
200C2×C3×Dic3—22no—
201C2×C3×Dic3—22no—
202C2×C3×Dic3C2×D412yes—
203C3×D12—48no—
204C3×D12—44no—
205C3×C4×D3—44no—
206C2×#121—31no—
207C2×#121—32no—
208C2×C4×D4—31no—
209#398—31no—
210#397—31no—
211#394—31no—
212#392—31no—
213#388—32no—
214#386—32no—
215#386—32no—
216C2×#95C3×D311yescharacteristic, complemented
217C24×C3—21no—
218C24×C3—31no—
219C24×C3—32no—
220C24×C3C22×D311yescharacteristic
221C24×C3C23×C311yescharacteristic
222C23×D3C23×C312yes—
223C23×D3C23×C311yescharacteristic
224C2×C3×D4—34no—
225C2×C3×D4—64no—
226C2×C3×D4—62no—
227C2×C3×D4—62no—
228C2×C3×D4—64no—
229C2×C3×D4—64no—
230C2×C3×D4—64no—
231C2×C3×D4—62no—
232C2×C3×D4—64no—
233C2×C3×D4—122no—
234C2×C3×D4—122no—
235C22×C3×C4—28no—
236C22×C3×C4—24no—
237C22×C3×C4—24no—
238C22×C3×C4—24no—
239C22×C3×C4—24no—
240C22×C3×C4—24no—
241C22×C3×C4—22no—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4—22no—
245C22×C3×C4—31no—
246C22×C3×C4—31no—
247C22×C3×C4—31no—
248C22×C3×C4—32no—
249C22×C3×C4—44no—
250C22×C3×C4—42no—
251C22×C3×C4—42no—
252C22×C3×C4—42no—
253C22×C3×C4—42no—
254C22×C3×C4—44no—
255C22×C3×C4—44no—
256C22×C3×C4—62no—
257C22×C3×C4—122no—
258C22×C3×C4D1214yescomplemented
259C22×C3×C4C3×D414yescomplemented
260C22×C3×C4C22×D312yes—
261C22×C3×C4C22×D311yescharacteristic
262C22×C3×C4C22×D311yescharacteristic
263C22×C3×C4C22×D312yes—
264C22×C3×C4C23×C312yes—
265C22×C3×C4C23×C311yescharacteristic
266C22×C3×C4C23×C311yescharacteristic
267C22×C3×C4C23×C312yes—
268C2×#67—22no—
269C2×#67—22no—
270C2×#67—24no—
271C2×#67—24no—
272C2×#67—24no—
273C2×#67C3×D414yescomplemented
274C22×Dic3C23×C311yescharacteristic
275C22×Dic3C23×C311yescharacteristic
276C22×Dic3C23×C312yes—
277C22×Dic3C23×C311yescharacteristic
278C2×D12—24no—
279C2×D12—22no—
280C2×D12—24no—
281C2×D12—42no—
282C2×D12—42no—
283C2×C4×D3—22no—
284C2×C4×D3—42no—
285C3×C4⋊C4—64no—
286C3×C4⋊C4—62no—
287C3×C4⋊C4—62no—
288C3×C22⋊C4—64no—
289C3×C22⋊C4—64no—
290C3×C22⋊C4—62no—
291C3×C22⋊C4—62no—
292C3×C22⋊C4—64no—
293C3×C22⋊C4—64no—
294C3×C22⋊C4—122no—
295C3×C42—62no—
296#217—22no—
297(C2×D3)⋊C4—24no—
298(C2×D3)⋊C4—22no—
299(C2×D3)⋊C4—24no—
300(C2×D3)⋊C4—24no—
301(C2×D3)⋊C4—24no—
302(C2×D3)⋊C4—42no—
303C4⋊Dic3—22no—
304C4⋊Dic3—24no—
305Dic3⋊C4—22no—
306C4×Dic3—22no—
307C22×C32—22no—
308C22×C32—22no—
309C22×C32—24no—
310C22×C32—24no—
311C22×C32#12114yes—
312C22×C32C22×D411yescharacteristic
313C22×C32C22×D411yescharacteristic
314C22×C32C2×#4112yes—
315C22×C32C2×#4111yescharacteristic
316C22×C32H(5,𝔽2)12yes—
317C2×C3×D3—22no—
318C2×C3×D3—24no—
319C2×C3×D3—41no—
320C2×C3×D3—41no—
321C2×C3×D3—42no—
322C2×C3×D3—42no—
323C2×C3×D3—42no—
324C2×C3×D3—42no—
325C2×C3×D3—42no—
326C2×C3×D3—42no—
327C2×C3×D3—42no—
328C2×C3×D3—42no—
329C32×C4—22no—
330C32×C4—22no—
331C32×C4—24no—
332C32×C4—42no—
333C3×Dic3—22no—
334C3×Dic3—42no—
335C3×Dic3—41no—
336C3×Dic3—41no—
337C22×D4—31no—
338C22×D4—32no—
339C22×D4—32no—
340C22×D4—31no—
341C23×C4—31no—
342C23×C4C2×C3×D312yes—
343C23×C4C2×C3×D311yescharacteristic
344#121—68no—
345#121—64no—
346C4×D4—64no—
347C2×C4⋊C4—31no—
348C2×C4⋊C4—32no—
349C2×C4⋊C4—31no—
350C2×C22⋊C4—31no—
351C2×C22⋊C4—31no—
352C2×C22⋊C4—32no—
353C2×C22⋊C4—32no—
354C2×C22⋊C4—32no—
355C2×C22⋊C4—32no—
356C2×C22⋊C4—32no—
357C2×C42—31no—
358#95—32no—
359#95—32no—
360#95C2×C3×D312yes—
361#95C2×C3×D311yescharacteristic
362#95C2×C3×D311yescharacteristic
363C23×C3—24no—
364C23×C3—24no—
365C23×C3—22no—
366C23×C3—22no—
367C23×C3—22no—
368C23×C3—22no—
369C23×C3—21no—
370C23×C3—22no—
371C23×C3—22no—
372C23×C3—22no—
373C23×C3—32no—
374C23×C3—61no—
375C23×C3—62no—
376C23×C3—62no—
377C23×C3—61no—
378C23×C3—62no—
379C23×C3—62no—
380C23×C3—62no—
381C23×C3—62no—
382C23×C3—62no—
383C23×C3—62no—
384C23×C3—62no—
385C23×C3C2×D1212yes—
386C23×C3D3×D412yes—
387C23×C3#23912yes—
388C23×C3C2×C3×D412yes—
389C23×C3C2×C3×D412yes—
390C23×C3C3×#4112yes—
391C23×C3C23×D311yescharacteristic
392C23×C3C24×C311yescharacteristic
393C22×D3—21no—
394C22×D3—22no—
395C22×D3—21no—
396C22×D3—22no—
397C22×D3—22no—
398C22×D3—22no—
399C22×D3—22no—
400C22×D3—22no—
401C22×D3—22no—
402C22×D3—22no—
403C22×D3—22no—
404C22×D3C2×C3×D412yes—
405C3×D4—68no—
406C3×D4—128no—
407C3×D4—124no—
408C3×D4—128no—
409C2×C3×C4—22no—
410C2×C3×C4—22no—
411C2×C3×C4—22no—
412C2×C3×C4—22no—
413C2×C3×C4—22no—
414C2×C3×C4—22no—
415C2×C3×C4—22no—
416C2×C3×C4—22no—
417C2×C3×C4—24no—
418C2×C3×C4—22no—
419C2×C3×C4—22no—
420C2×C3×C4—22no—
421C2×C3×C4—22no—
422C2×C3×C4—22no—
423C2×C3×C4—22no—
424C2×C3×C4—22no—
425C2×C3×C4—22no—
426C2×C3×C4—24no—
427C2×C3×C4—32no—
428C2×C3×C4—42no—
429C2×C3×C4—42no—
430C2×C3×C4—42no—
431C2×C3×C4—42no—
432C2×C3×C4—42no—
433C2×C3×C4—42no—
434C2×C3×C4—44no—
435C2×C3×C4—44no—
436C2×C3×C4—48no—
437C2×C3×C4—48no—
438C2×C3×C4—48no—
439C2×C3×C4—416no—
440C2×C3×C4—61no—
441C2×C3×C4—61no—
442C2×C3×C4—61no—
443C2×C3×C4—61no—
444C2×C3×C4—62no—
445C2×C3×C4—62no—
446C2×C3×C4—62no—
447C2×C3×C4—62no—
448C2×C3×C4—62no—
449C2×C3×C4—124no—
450C2×C3×C4C2×D1212yes—
451C2×C3×C4C2×D1212yes—
452C2×C3×C4#23514yes—
453C2×C3×C4C2×C3×D412yes—
454C2×C3×C4C2×C3×D412yes—
455C2×C3×C4C3×#4114yes—
456#67—28no—
457#67—48no—
458C2×Dic3—21no—
459C2×Dic3—21no—
460C2×Dic3—21no—
461C2×Dic3—21no—
462C2×Dic3—22no—
463C2×Dic3—22no—
464C2×Dic3—22no—
465C2×Dic3—22no—
466C2×Dic3—22no—
467C2×Dic3C2×C3×D412yes—
468D12—48no—
469D12—44no—
470C4×D3—44no—
471C2×C32—24no—
472C2×C32C2×#12111yescharacteristic
473C2×C32#53211yescharacteristic
474C2×C32#53411yescharacteristic
475C2×C32#54612yes—
476C2×C32#55312yes—
477C3×D3—42no—
478C3×D3—82no—
479C24—31no—
480C24—32no—
481C24C22×C3×D311yescharacteristic
482C2×D4—34no—
483C2×D4—64no—
484C2×D4—62no—
485C2×D4—62no—
486C2×D4—64no—
487C2×D4—64no—
488C2×D4—64no—
489C2×D4—62no—
490C2×D4—64no—
491C2×D4—122no—
492C2×D4—122no—
493C22×C4—24no—
494C22×C4—24no—
495C22×C4—31no—
496C22×C4—31no—
497C22×C4—31no—
498C22×C4—32no—
499C22×C4—42no—
500C22×C4—42no—
501C22×C4—62no—
502C22×C4—122no—
503C22×C4C3×D1214yescomplemented
504C22×C4C22×C3×D312yes—
505C22×C4C22×C3×D311yescharacteristic
506C22×C4C22×C3×D311yescharacteristic
507C22×C4C22×C3×D312yes—
508C4⋊C4—64no—
509C4⋊C4—62no—
510C4⋊C4—62no—
511C22⋊C4—64no—
512C22⋊C4—64no—
513C22⋊C4—62no—
514C22⋊C4—62no—
515C22⋊C4—64no—
516C22⋊C4—64no—
517C22⋊C4—122no—
518C42—62no—
519C22×C3—28no—
520C22×C3—24no—
521C22×C3—28no—
522C22×C3—24no—
523C22×C3—22no—
524C22×C3—24no—
525C22×C3—22no—
526C22×C3—24no—
527C22×C3—22no—
528C22×C3—22no—
529C22×C3—24no—
530C22×C3—24no—
531C22×C3—24no—
532C22×C3—21no—
533C22×C3—22no—
534C22×C3—21no—
535C22×C3—22no—
536C22×C3—21no—
537C22×C3—64no—
538C22×C3—62no—
539C22×C3—121no—
540C22×C3—121no—
541C22×C3—122no—
542C22×C3—122no—
543C22×C3—122no—
544C22×C3—122no—
545C22×C3—122no—
546C22×C3—122no—
547C22×C3—122no—
548C22×C3—122no—
549C22×C3#89514yes—
550C22×C3C3×#12114yes—
551C22×C3C22×D1211yescharacteristic
552C22×C3C2×#23512yes—
553C22×C3C2×D3×D411yescharacteristic
554C22×C3#100412yes—
555C22×C3C2×#23911yescharacteristic
556C22×C3C22×C3×D411yescharacteristic
557C22×C3C22×C3×D411yescharacteristic
558C22×C3C2×C3×#4112yes—
559C22×C3C2×C3×#4111yescharacteristic
560C22×C3C3×H(5,𝔽2)12yes—
561C2×D3—22no—
562C2×D3—24no—
563C2×D3—41no—
564C2×D3—41no—
565C2×D3—42no—
566C2×D3—42no—
567C2×D3—42no—
568C2×D3—42no—
569C2×D3—42no—
570C2×D3—42no—
571C2×D3—42no—
572C2×D3—42no—
573C3×C4—24no—
574C3×C4—22no—
575C3×C4—22no—
576C3×C4—22no—
577C3×C4—22no—
578C3×C4—24no—
579C3×C4—44no—
580C3×C4—42no—
581C3×C4—42no—
582C3×C4—44no—
583C3×C4—42no—
584C3×C4—42no—
585C3×C4—62no—
586C3×C4—121no—
587C3×C4—121no—
588C3×C4—122no—
589Dic3—22no—
590Dic3—42no—
591Dic3—41no—
592Dic3—41no—
593C32#254311yescharacteristic, complemented, Sylow
594C23—22no—
595C23—22no—
596C23—32no—
597C23—61no—
598C23—62no—
599C23—62no—
600C23—61no—
601C23—62no—
602C23—62no—
603C23—62no—
604C23—62no—
605C23—62no—
606C23—62no—
607C23—62no—
608C23C2×C3×D1212yes—
609C23C3×D3×D412yes—
610C23C3×#23912yes—
611C23C23×C3×D311yescharacteristic
612D4—68no—
613D4—128no—
614D4—124no—
615D4—128no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—32no—
624C2×C4—44no—
625C2×C4—48no—
626C2×C4—61no—
627C2×C4—61no—
628C2×C4—61no—
629C2×C4—61no—
630C2×C4—62no—
631C2×C4—62no—
632C2×C4—62no—
633C2×C4—62no—
634C2×C4—62no—
635C2×C4—124no—
636C2×C4C2×C3×D1212yes—
637C2×C4C2×C3×D1212yes—
638C2×C4C3×#23514yes—
639C2×C3—28no—
640C2×C3—24no—
641C2×C3—24no—
642C2×C3—22no—
643C2×C3—21no—
644C2×C3—21no—
645C2×C3—22no—
646C2×C3—21no—
647C2×C3—122no—
648C2×C3—242no—
649C2×C3#547711yescharacteristic
650C2×C3#549012yes—
651C2×C3#549311yescharacteristic
652C2×C3C2×#89511yescharacteristic
653C2×C3#551412yes—
654C2×C3C2×C3×#12111yescharacteristic
655C2×C3C3×#53211yescharacteristic
656C2×C3C3×#53411yescharacteristic
657C2×C3C3×#54612yes—
658C2×C3C3×#55312yes—
659D3—42no—
660D3—82no—
661C22—24no—
662C22—22no—
663C22—24no—
664C22—22no—
665C22—64no—
666C22—62no—
667C22—121no—
668C22—122no—
669C22—121no—
670C22—122no—
671C22—122no—
672C22—122no—
673C22—122no—
674C22—122no—
675C22—122no—
676C22—122no—
677C22C3×#89514yes—
678C22C22×C3×D1211yescharacteristic
679C22C2×C3×#23512yes—
680C22C2×C3×D3×D411yescharacteristic
681C22C3×#100412yes—
682C22C2×C3×#23911yescharacteristic
683C4—24no—
684C4—22no—
685C4—22no—
686C4—42no—
687C4—62no—
688C4—121no—
689C4—122no—
690C4—121no—
691C3—21no—
692C3#7337811yescharacteristic, direct product factor
693C3C3×#254311yescharacteristic, complemented
694C2—24no—
695C2—122no—
696C2—242no—
697C2C3×#547711yescharacteristic
698C2C3×#549012yes—
699C2C3×#549311yescharacteristic
700C2C2×C3×#89511yescharacteristic
701C2C3×#551412yes—
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC23×C3C24×C3
FrattiniC23C23×C3×D3
FittingC2×C32×#95C2
socleC23×C32C24
hypercenterC2×C3×#95D3
hypocenterC3C3×#2543
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×#95

Complements

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

NH ≅ G/Ntype
1. C2×C3×#930C2semidirect
2. C2×C3×#930C2semidirect
3. C2×C3×C4×#67C2semidirect
4. C2×C32×#95C2semidirect
5. C3×#5213C2semidirect
6. C3×#4674C2semidirect
7. C3×#4672C2semidirect
8. C3×#4671C2semidirect
9. C3×#4670C2semidirect
10. C3×#4665C2semidirect
11. C3×#4661C2semidirect
13. #73378C3direct (N × H)
43. C2×#930C2×C3semidirect
44. C2×#930C2×C3semidirect
45. C2×C4×#67C2×C3semidirect
54. C2×C3×#95D3semidirect
55. C2×C3×#95C2×C3semidirect
56. #5213C2×C3semidirect
57. #4674C2×C3semidirect
58. #4672C2×C3semidirect
59. #4671C2×C3semidirect
60. #4670C2×C3semidirect
61. #4665C2×C3semidirect
62. #4661C2×C3semidirect
70. C22×C32×C4D4semidirect
80. C2×C3×#67D4semidirect
216. C2×#95C3×D3semidirect
258. C22×C3×C4D12semidirect
259. C22×C3×C4C3×D4semidirect
273. C2×#67C3×D4semidirect
503. C22×C4C3×D12semidirect
593. C32#2543semidirect
692. C3#73378direct (N × H)
693. C3C3×#2543semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9302
C2×C3×C4×#672
C2×C32×#952
C3×#52132
C3×#46742
C3×#46722
C3×#46712
C3×#46702
C3×#46652
C3×#46612
C3×#25433
#733783