Finite Group Databasebeta

← C3×#76759 #11824523

Subgroups — C3×#76759 #11824523

Order 1152.

1609 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#938C212yesmaximal, complemented
2C2×C3×#938C211yesmaximal, characteristic, complemented
3C2×C3×#67⋊C4C211yesmaximal, characteristic, complemented
4C32×#392C211yesmaximal, characteristic, complemented
5C3×#5222C211yesmaximal, characteristic, complemented
6C3×#5220C212yesmaximal, complemented
7C3×#4956C212yesmaximal, complemented
8C3×#4953C211yesmaximal, characteristic, complemented
9C3×#4951C212yesmaximal, complemented
10C3×D3×#95C211yesmaximal, characteristic, complemented
11C3×#4661C211yesmaximal, characteristic, complemented
12C3×#2543—31nomaximal
13#76759C311yesmaximal, characteristic, direct product factor
14C22×C32×D4C2212yes—
15C22×C32×D4C2211yescharacteristic
16C22×C3×#67C2212yes—
17C22×C3×#67C2211yescharacteristic
18C23×C3×Dic3C2211yescharacteristic
19C22×C3×C4×D3C2212yes—
20C22×C3×C4×D3C2211yescharacteristic
21C2×C32×C22⋊C4C2212yes—
22C2×C32×C22⋊C4C2211yescharacteristic
23C2×C3×#217C2212yes—
24C2×C3×#217C2212yes—
25C2×C3×#217C2212yes—
26C2×C3×#217C2212yes—
27C3×#938—28no—
28C3×#938—24no—
29C2×C3×(C2×D3)⋊C4C2211yescharacteristic
30C2×C3×C4⋊Dic3C2212yes—
31C2×C3×C4⋊Dic3C2211yescharacteristic
32C2×C3×Dic3⋊C4C2211yescharacteristic
33C2×C3×C4×Dic3C2211yescharacteristic
34C3×#67⋊C4—24no—
35C32×#95C2211yescharacteristic
36C3×C3⋊#95C2212yes—
37C3×C3⋊#95C2212yes—
38C3×C3⋊#95C2211yescharacteristic
39C3×C3⋊#95C2212yes—
40C2×C3×#121—31no—
41C2×C3×#121—32no—
42C2×C3×C4×D4—31no—
43C2×#938C2×C312yescomplemented
44C2×#938C2×C311yescharacteristic, complemented
45C2×#67⋊C4C2×C311yescharacteristic, complemented
46C3×#398—31no—
47C3×#397—31no—
48C3×#394—31no—
49C3×#392—21no—
50C3×#392D311yescharacteristic, complemented
51C3×#392C2×C311yescharacteristic, complemented
52C3×#388—32no—
53C3×#386—32no—
54C3×#386—32no—
55C2×C3×#95—31no—
56#5222C2×C311yescharacteristic, complemented
57#5220C2×C312yescomplemented
58#4956C2×C312yescomplemented
59#4953C2×C311yescharacteristic, complemented
60#4951C2×C312yescomplemented
61D3×#95C2×C311yescharacteristic, complemented
62#4661C2×C311yescharacteristic, complemented
63C24×C32C2312yes—
64C24×C32C2311yescharacteristic
65C23×C3×D3C2311yescharacteristic
66C2×C32×D4—24no—
67C2×C32×D4—22no—
68C2×C32×D4—24no—
69C2×C32×D4—42no—
70C2×C32×D4—42no—
71C22×C32×C4C2311yescharacteristic
72C22×C32×C4C2311yescharacteristic
73C22×C32×C4C2312yes—
74C2×C3×#67—22no—
75C2×C3×#67—22no—
76C2×C3×#67—24no—
77C2×C3×#67—24no—
78C2×C3×#67—24no—
79C2×C3×#67D414yescomplemented
80C22×C3×Dic3—22no—
81C22×C3×Dic3—42no—
82C22×C3×Dic3C2311yescharacteristic
83C22×C3×Dic3C2312yes—
84C22×C3×Dic3C2312yes—
85C22×C3×Dic3C2311yescharacteristic
86C22×C3×Dic3C2311yescharacteristic
87C2×C3×C4×D3—24no—
88C2×C3×C4×D3—24no—
89C2×C3×C4×D3—42no—
90C2×C3×C4×D3—42no—
91C2×C3×C4×D3D414yescomplemented
92C32×C22⋊C4—22no—
93C32×C22⋊C4—24no—
94C3×#217—24no—
95C3×#217—24no—
96C3×#217—24no—
97C3×#217—42no—
98C3×(C2×D3)⋊C4—22no—
99C3×C4⋊Dic3—22no—
100C3×C4⋊Dic3—24no—
101C3×Dic3⋊C4—22no—
102C3×C4×Dic3—22no—
103#2543—31noSylow
104C22×C3×D4—22no—
105C22×C3×D4—21no—
106C22×C3×D4—31no—
107C22×C3×D4—32no—
108C22×C3×D4C2×D312yes—
109C22×C3×D4C2×D311yescharacteristic
110C22×C3×D4C22×C312yes—
111C22×C3×D4C22×C311yescharacteristic
112C23×C3×C4—31no—
113C23×C3×C4—31no—
114C23×C3×C4—32no—
115C22×#67C22×C312yes—
116C22×#67C22×C311yescharacteristic
117C23×Dic3C22×C311yescharacteristic
118C22×C4×D3C22×C312yes—
119C22×C4×D3C22×C311yescharacteristic
120C3×#121—64no—
121C3×#121—68no—
122C3×C4×D4—64no—
123C2×C3×C4⋊C4—31no—
124C2×C3×C4⋊C4—32no—
125C2×C3×C4⋊C4—31no—
126C2×C3×C22⋊C4—21no—
127C2×C3×C22⋊C4—22no—
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×C22⋊C4C2×D312yes—
134C2×C3×C22⋊C4C2×D311yescharacteristic
135C2×C3×C22⋊C4C22×C312yes—
136C2×C3×C22⋊C4C22×C311yescharacteristic
137C2×C3×C42—31no—
138C2×#217C22×C312yes—
139C2×#217C22×C312yes—
140C2×#217C22×C312yes—
141C2×#217C22×C312yes—
142#938—28no—
143#938—24no—
144C2×(C2×D3)⋊C4C22×C311yescharacteristic
145C2×C4⋊Dic3C22×C312yes—
146C2×C4⋊Dic3C22×C311yescharacteristic
147C2×Dic3⋊C4C22×C311yescharacteristic
148C2×C4×Dic3C22×C311yescharacteristic
149#67⋊C4—24no—
150C3×#95—21no—
151C3×#95—32no—
152C3×#95—31no—
153C3×#95—32no—
154C3×#95—32no—
155C3×#95C2×D311yescharacteristic
156C3×#95C22×C311yescharacteristic
157C3⋊#95C22×C312yes—
158C3⋊#95C22×C312yes—
159C3⋊#95C22×C311yescharacteristic
160C3⋊#95C22×C312yes—
161C23×C32—22no—
162C23×C32—21no—
163C23×C32—21no—
164C23×C32—22no—
165C23×C32—22no—
166C23×C32—22no—
167C23×C32—22no—
168C23×C32—22no—
169C23×C32—22no—
170C23×C32—22no—
171C23×C32—22no—
172C23×C32C2×D412yes—
173C23×C32C2411yescharacteristic
174C22×C3×D3—22no—
175C22×C3×D3—22no—
176C22×C3×D3C2×D412yes—
177C22×C3×D3C2×D412yes—
178C22×C3×D3#4112yes—
179C32×D4—48no—
180C32×D4—44no—
181C2×C32×C4—22no—
182C2×C32×C4—22no—
183C2×C32×C4—22no—
184C2×C32×C4—21no—
185C2×C32×C4—22no—
186C2×C32×C4C2×D412yes—
187C2×C32×C4#4114yes—
188C3×#67—28no—
189C3×#67—48no—
190C2×C3×Dic3—21no—
191C2×C3×Dic3—21no—
192C2×C3×Dic3—22no—
193C2×C3×Dic3—21no—
194C2×C3×Dic3—22no—
195C2×C3×Dic3—22no—
196C2×C3×Dic3—22no—
197C2×C3×Dic3—22no—
198C2×C3×Dic3—22no—
199C2×C3×Dic3—22no—
200C2×C3×Dic3—22no—
201C2×C3×Dic3—44no—
202C2×C3×Dic3C2×D412yes—
203C2×C3×Dic3C2×D412yes—
204C3×C4×D3—44no—
205C3×C4×D3—48no—
206C2×#121—31no—
207C2×#121—32no—
208C2×C4×D4—31no—
209#398—31no—
210#397—31no—
211#394—31no—
212#392C3×D311yescharacteristic, complemented
213#388—32no—
214#386—32no—
215#386—32no—
216C2×#95—31no—
217C24×C3—22no—
218C24×C3—21no—
219C24×C3—31no—
220C24×C3C22×D312yes—
221C24×C3C22×D311yescharacteristic
222C24×C3C23×C312yes—
223C24×C3C23×C311yescharacteristic
224C23×D3C23×C311yescharacteristic
225C2×C3×D4—24no—
226C2×C3×D4—24no—
227C2×C3×D4—22no—
228C2×C3×D4—24no—
229C2×C3×D4—22no—
230C2×C3×D4—24no—
231C2×C3×D4—34no—
232C2×C3×D4—42no—
233C2×C3×D4—44no—
234C2×C3×D4—44no—
235C2×C3×D4—42no—
236C2×C3×D4—42no—
237C2×C3×D4—42no—
238C2×C3×D4—42no—
239C2×C3×D4—44no—
240C2×C3×D4—44no—
241C2×C3×D4—62no—
242C2×C3×D4—62no—
243C2×C3×D4—64no—
244C2×C3×D4—64no—
245C2×C3×D4—64no—
246C22×C3×C4—21no—
247C22×C3×C4—22no—
248C22×C3×C4—21no—
249C22×C3×C4—31no—
250C22×C3×C4—31no—
251C22×C3×C4—34no—
252C22×C3×C4—32no—
253C22×C3×C4—31no—
254C22×C3×C4—32no—
255C22×C3×C4—64no—
256C22×C3×C4—62no—
257C22×C3×C4—64no—
258C22×C3×C4—122no—
259C22×C3×C4—122no—
260C22×C3×C4—122no—
261C22×C3×C4C22×D311yescharacteristic
262C22×C3×C4C22×D311yescharacteristic
263C22×C3×C4C22×D312yes—
264C22×C3×C4C23×C311yescharacteristic
265C22×C3×C4C23×C311yescharacteristic
266C22×C3×C4C23×C312yes—
267C2×#67—22no—
268C2×#67—22no—
269C2×#67—24no—
270C2×#67—24no—
271C2×#67—24no—
272C2×#67C3×D414yescomplemented
273C22×Dic3—22no—
274C22×Dic3—42no—
275C22×Dic3C23×C312yes—
276C22×Dic3C23×C311yescharacteristic
277C22×Dic3C23×C312yes—
278C22×Dic3C23×C311yescharacteristic
279C22×Dic3C23×C311yescharacteristic
280C2×C4×D3—24no—
281C2×C4×D3—24no—
282C2×C4×D3—42no—
283C2×C4×D3—42no—
284C2×C4×D3C3×D414yescomplemented
285C3×C4⋊C4—64no—
286C3×C4⋊C4—62no—
287C3×C4⋊C4—62no—
288C3×C22⋊C4—22no—
289C3×C22⋊C4—24no—
290C3×C22⋊C4—22no—
291C3×C22⋊C4—24no—
292C3×C22⋊C4—42no—
293C3×C22⋊C4—44no—
294C3×C22⋊C4—62no—
295C3×C22⋊C4—64no—
296C3×C22⋊C4—64no—
297C3×C22⋊C4—64no—
298C3×C22⋊C4—122no—
299C3×C42—62no—
300#217—24no—
301#217—24no—
302#217—24no—
303#217—42no—
304(C2×D3)⋊C4—22no—
305C4⋊Dic3—22no—
306C4⋊Dic3—24no—
307Dic3⋊C4—22no—
308C4×Dic3—22no—
309C22×C32—22no—
310C22×C32—24no—
311C22×C32—42no—
312C22×C32—42no—
313C22×C32—42no—
314C22×C32—41no—
315C22×C32—41no—
316C22×C32—42no—
317C22×C32—42no—
318C22×C32—42no—
319C22×C32—42no—
320C22×C32—42no—
321C22×C32C22×D411yescharacteristic
322C22×C32C22×D411yescharacteristic
323C22×C32C2×#4112yes—
324C22×C32C2×#4111yescharacteristic
325C22×C32H(5,𝔽2)12yes—
326C2×C3×D3—22no—
327C2×C3×D3—22no—
328C2×C3×D3—24no—
329C2×C3×D3—24no—
330C2×C3×D3#12114yes—
331C32×C4—22no—
332C32×C4—24no—
333C32×C4—41no—
334C3×Dic3—22no—
335C3×Dic3—22no—
336C3×Dic3—42no—
337C3×Dic3—41no—
338C3×Dic3—42no—
339C22×D4—31no—
340C22×D4—32no—
341C22×D4C2×C3×D312yes—
342C22×D4C2×C3×D311yescharacteristic
343C23×C4—31no—
344C23×C4—31no—
345C23×C4—32no—
346#121—64no—
347#121—68no—
348C4×D4—64no—
349C2×C4⋊C4—31no—
350C2×C4⋊C4—32no—
351C2×C4⋊C4—31no—
352C2×C22⋊C4—32no—
353C2×C22⋊C4—32no—
354C2×C22⋊C4—32no—
355C2×C22⋊C4—31no—
356C2×C22⋊C4—32no—
357C2×C22⋊C4C2×C3×D311yescharacteristic
358C2×C22⋊C4C2×C3×D312yes—
359C2×C42—31no—
360#95—32no—
361#95—31no—
362#95—32no—
363#95—32no—
364#95C2×C3×D311yescharacteristic
365C23×C3—21no—
366C23×C3—22no—
367C23×C3—22no—
368C23×C3—21no—
369C23×C3—21no—
370C23×C3—21no—
371C23×C3—22no—
372C23×C3—22no—
373C23×C3—24no—
374C23×C3—22no—
375C23×C3—22no—
376C23×C3—22no—
377C23×C3—22no—
378C23×C3—22no—
379C23×C3—22no—
380C23×C3—22no—
381C23×C3—22no—
382C23×C3—22no—
383C23×C3—22no—
384C23×C3—22no—
385C23×C3—22no—
386C23×C3—22no—
387C23×C3—22no—
388C23×C3—21no—
389C23×C3—22no—
390C23×C3—32no—
391C23×C3—32no—
392C23×C3—32no—
393C23×C3—41no—
394C23×C3—42no—
395C23×C3—42no—
396C23×C3—42no—
397C23×C3—42no—
398C23×C3—42no—
399C23×C3—42no—
400C23×C3—42no—
401C23×C3—41no—
402C23×C3—42no—
403C23×C3—62no—
404C23×C3—62no—
405C23×C3D3×D412yes—
406C23×C3C2×C3×D412yes—
407C23×C3C23×D311yescharacteristic
408C23×C3C24×C311yescharacteristic
409C22×D3—22no—
410C22×D3—22no—
411C22×D3C2×C3×D412yes—
412C22×D3C2×C3×D412yes—
413C22×D3C3×#4112yes—
414C3×D4—48no—
415C3×D4—48no—
416C3×D4—44no—
417C3×D4—44no—
418C3×D4—416no—
419C3×D4—48no—
420C3×D4—68no—
421C3×D4—128no—
422C2×C3×C4—22no—
423C2×C3×C4—22no—
424C2×C3×C4—22no—
425C2×C3×C4—22no—
426C2×C3×C4—22no—
427C2×C3×C4—22no—
428C2×C3×C4—21no—
429C2×C3×C4—22no—
430C2×C3×C4—21no—
431C2×C3×C4—22no—
432C2×C3×C4—22no—
433C2×C3×C4—24no—
434C2×C3×C4—32no—
435C2×C3×C4—32no—
436C2×C3×C4—42no—
437C2×C3×C4—42no—
438C2×C3×C4—42no—
439C2×C3×C4—41no—
440C2×C3×C4—42no—
441C2×C3×C4—61no—
442C2×C3×C4—62no—
443C2×C3×C4—61no—
444C2×C3×C4—62no—
445C2×C3×C4—61no—
446C2×C3×C4—62no—
447C2×C3×C4—62no—
448C2×C3×C4—62no—
449C2×C3×C4—62no—
450C2×C3×C4—62no—
451C2×C3×C4—62no—
452C2×C3×C4—124no—
453C2×C3×C4—128no—
454C2×C3×C4—124no—
455C2×C3×C4D3×D412yes—
456C2×C3×C4#23714yes—
457C2×C3×C4C2×C3×D412yes—
458C2×C3×C4C3×#4114yes—
459#67—28no—
460#67—48no—
461C2×Dic3—21no—
462C2×Dic3—21no—
463C2×Dic3—22no—
464C2×Dic3—21no—
465C2×Dic3—22no—
466C2×Dic3—22no—
467C2×Dic3—22no—
468C2×Dic3—22no—
469C2×Dic3—22no—
470C2×Dic3—22no—
471C2×Dic3—22no—
472C2×Dic3—44no—
473C2×Dic3C2×C3×D412yes—
474C2×Dic3C2×C3×D412yes—
475C4×D3—44no—
476C4×D3—48no—
477C2×C32—42no—
478C2×C32—82no—
479C2×C32C2×#12111yescharacteristic
480C2×C32#53211yescharacteristic
481C2×C32#53411yescharacteristic
482C2×C32#54612yes—
483C2×C32#55312yes—
484C3×D3—24no—
485C24—31no—
486C24C22×C3×D312yes—
487C24C22×C3×D311yescharacteristic
488C2×D4—24no—
489C2×D4—22no—
490C2×D4—24no—
491C2×D4—34no—
492C2×D4—42no—
493C2×D4—42no—
494C2×D4—62no—
495C2×D4—62no—
496C2×D4—64no—
497C2×D4—64no—
498C2×D4—64no—
499C22×C4—31no—
500C22×C4—31no—
501C22×C4—34no—
502C22×C4—32no—
503C22×C4—31no—
504C22×C4—32no—
505C22×C4—64no—
506C22×C4—62no—
507C22×C4—64no—
508C22×C4—122no—
509C22×C4—122no—
510C22×C4—122no—
511C22×C4C22×C3×D311yescharacteristic
512C22×C4C22×C3×D311yescharacteristic
513C22×C4C22×C3×D312yes—
514C4⋊C4—64no—
515C4⋊C4—62no—
516C4⋊C4—62no—
517C22⋊C4—22no—
518C22⋊C4—24no—
519C22⋊C4—62no—
520C22⋊C4—64no—
521C22⋊C4—64no—
522C22⋊C4—64no—
523C22⋊C4—122no—
524C42—62no—
525C22×C3—24no—
526C22×C3—22no—
527C22×C3—22no—
528C22×C3—24no—
529C22×C3—21no—
530C22×C3—21no—
531C22×C3—22no—
532C22×C3—22no—
533C22×C3—21no—
534C22×C3—34no—
535C22×C3—44no—
536C22×C3—42no—
537C22×C3—44no—
538C22×C3—44no—
539C22×C3—44no—
540C22×C3—41no—
541C22×C3—41no—
542C22×C3—41no—
543C22×C3—41no—
544C22×C3—42no—
545C22×C3—42no—
546C22×C3—42no—
547C22×C3—42no—
548C22×C3—42no—
549C22×C3—42no—
550C22×C3—42no—
551C22×C3—42no—
552C22×C3—42no—
553C22×C3—42no—
554C22×C3—42no—
555C22×C3—42no—
556C22×C3—42no—
557C22×C3—42no—
558C22×C3—42no—
559C22×C3—42no—
560C22×C3—62no—
561C22×C3—62no—
562C22×C3—64no—
563C22×C3—64no—
564C22×C3—81no—
565C22×C3—82no—
566C22×C3—81no—
567C22×C3—82no—
568C22×C3—82no—
569C22×C3—82no—
570C22×C3—82no—
571C22×C3C2×D3×D411yescharacteristic
572C22×C3C2×D3×D411yescharacteristic
573C22×C3C2×#23712yes—
574C22×C3#100412yes—
575C22×C3D3×#4111yescharacteristic
576C22×C3C22×C3×D411yescharacteristic
577C22×C3C22×C3×D411yescharacteristic
578C22×C3C2×C3×#4112yes—
579C22×C3C2×C3×#4111yescharacteristic
580C22×C3C3×H(5,𝔽2)12yes—
581C2×D3—22no—
582C2×D3—22no—
583C2×D3—24no—
584C2×D3—24no—
585C2×D3C3×#12114yes—
586C3×C4—22no—
587C3×C4—24no—
588C3×C4—22no—
589C3×C4—24no—
590C3×C4—42no—
591C3×C4—44no—
592C3×C4—41no—
593C3×C4—41no—
594C3×C4—62no—
595C3×C4—62no—
596C3×C4—81no—
597C3×C4—121no—
598C3×C4—122no—
599C3×C4—122no—
600Dic3—22no—
601Dic3—22no—
602Dic3—42no—
603Dic3—41no—
604Dic3—42no—
605C32#254311yescharacteristic, complemented, Sylow
606C23—21no—
607C23—22no—
608C23—22no—
609C23—21no—
610C23—22no—
611C23—22no—
612C23—22no—
613C23—22no—
614C23—22no—
615C23—22no—
616C23—22no—
617C23—32no—
618C23—32no—
619C23—32no—
620C23—62no—
621C23—62no—
622C23C3×D3×D412yes—
623C23C23×C3×D311yescharacteristic
624D4—48no—
625D4—44no—
626D4—68no—
627D4—128no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—21no—
632C2×C4—22no—
633C2×C4—32no—
634C2×C4—32no—
635C2×C4—61no—
636C2×C4—62no—
637C2×C4—61no—
638C2×C4—62no—
639C2×C4—61no—
640C2×C4—62no—
641C2×C4—62no—
642C2×C4—62no—
643C2×C4—62no—
644C2×C4—62no—
645C2×C4—62no—
646C2×C4—124no—
647C2×C4—128no—
648C2×C4—124no—
649C2×C4C3×D3×D412yes—
650C2×C4C3×#23714yes—
651C2×C3—21no—
652C2×C3—22no—
653C2×C3—21no—
654C2×C3—22no—
655C2×C3—21no—
656C2×C3—42no—
657C2×C3—42no—
658C2×C3—64no—
659C2×C3—82no—
660C2×C3—84no—
661C2×C3—82no—
662C2×C3—82no—
663C2×C3#558911yescharacteristic
664C2×C3#559112yes—
665C2×C3D3×#12111yescharacteristic
666C2×C3#561412yes—
667C2×C3#571611yescharacteristic
668C2×C3C2×C3×#12111yescharacteristic
669C2×C3C3×#53211yescharacteristic
670C2×C3C3×#53411yescharacteristic
671C2×C3C3×#54612yes—
672C2×C3C3×#55312yes—
673D3—24no—
674C22—24no—
675C22—22no—
676C22—34no—
677C22—41no—
678C22—42no—
679C22—41no—
680C22—42no—
681C22—42no—
682C22—42no—
683C22—42no—
684C22—42no—
685C22—42no—
686C22—42no—
687C22—62no—
688C22—64no—
689C22—64no—
690C22—62no—
691C22C2×C3×D3×D411yescharacteristic
692C22C2×C3×D3×D411yescharacteristic
693C22C2×C3×#23712yes—
694C22C3×#100412yes—
695C22C3×D3×#4111yescharacteristic
696C4—22no—
697C4—24no—
698C4—41no—
699C4—62no—
700C4—62no—
701C4—121no—
702C4—122no—
703C4—122no—
704C3—21no—
705C3#7675911yescharacteristic, direct product factor
706C3C3×#254311yescharacteristic, complemented
707C2—42no—
708C2—64no—
709C2—82no—
710C2C3×#558911yescharacteristic
711C2C3×#559112yes—
712C2C3×D3×#12111yescharacteristic
713C2C3×#561412yes—
714C2C3×#571611yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC23×C3C24×C3
FrattiniC23C23×C3×D3
FittingC32×#392C2
socleC23×C32C24
hypercenterC3×#392D3
hypocenterC3C3×#2543
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C3×#392

Complements

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

NH ≅ G/Ntype
1. C2×C3×#938C2semidirect
2. C2×C3×#938C2semidirect
3. C2×C3×#67⋊C4C2semidirect
4. C32×#392C2semidirect
5. C3×#5222C2semidirect
6. C3×#5220C2semidirect
7. C3×#4956C2semidirect
8. C3×#4953C2semidirect
9. C3×#4951C2semidirect
10. C3×D3×#95C2semidirect
11. C3×#4661C2semidirect
13. #76759C3direct (N × H)
43. C2×#938C2×C3semidirect
44. C2×#938C2×C3semidirect
45. C2×#67⋊C4C2×C3semidirect
50. C3×#392D3semidirect
51. C3×#392C2×C3semidirect
56. #5222C2×C3semidirect
57. #5220C2×C3semidirect
58. #4956C2×C3semidirect
59. #4953C2×C3semidirect
60. #4951C2×C3semidirect
61. D3×#95C2×C3semidirect
62. #4661C2×C3semidirect
79. C2×C3×#67D4semidirect
91. C2×C3×C4×D3D4semidirect
212. #392C3×D3semidirect
272. C2×#67C3×D4semidirect
284. C2×C4×D3C3×D4semidirect
605. C32#2543semidirect
705. C3#76759direct (N × H)
706. C3C3×#2543semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9382
C2×C3×#67⋊C42
C32×#3922
C3×#52222
C3×#52202
C3×#49562
C3×#49532
C3×#49512
C3×D3×#952
C3×#46612
C3×#25433
#767593