Finite Group Databasebeta

← C3×#73868 #11802838

Subgroups — C3×#73868 #11802838

Order 1152.

1085 conjugacy classes of subgroups.

The subgroup lattice has 617 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#926C211yesmaximal, characteristic
2C32×#380C211yesmaximal, characteristic
3C3×#5212C211yesmaximal, characteristic
4C3×#4977C211yesmaximal, characteristic, complemented
5C3×#4975C211yesmaximal, characteristic, complemented
6C3×Dic3×C4⋊C4C211yesmaximal, characteristic, complemented
7C3×Dic3×C4⋊C4C211yesmaximal, characteristic, complemented
8C3×#4945C212yesmaximal
9C3×#4944C212yesmaximal
10C3×#4654C212yesmaximal, complemented
11C3×#4653C212yesmaximal, complemented
12C3×#2314—31nomaximal
13#73868C311yesmaximal, characteristic, direct product factor
14C23×C32×C4C2211yescharacteristic
15C2×C32×C4⋊C4C2211yescharacteristic
16C2×C32×C4⋊C4C2211yescharacteristic
17C2×C32×C22⋊C4C2212yes—
18C2×C3×#217C2212yes—
19C2×C3×#217C2211yescharacteristic
20C2×C3×#217C2211yescharacteristic
21C3×#926C418yescomplemented
22C2×C3×C4⋊Dic3C2211yescharacteristic
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C2×C3×C4⋊Dic3C2211yescharacteristic
25C2×C3×C4⋊Dic3C2211yescharacteristic
26C2×C3×Dic3⋊C4C2212yes—
27C2×C3×Dic3⋊C4C2212yes—
28C2×C3×C4×Dic3C2212yes—
29C2×C3×C4×Dic3C2212yes—
30C2×C3×C4×Dic3C2211yescharacteristic
31C2×C3×C4×Dic3C2211yescharacteristic
32C32×#95C2212yes—
33C3×C3⋊#95C2212yes—
34C3×C3⋊#95C2212yes—
35C3×C3⋊#95C2212yes—
36C3×C3⋊#95C2212yes—
37C3×C3⋊#95C2212yes—
38C2×C3×#117—31no—
39C2×#926C2×C311yescharacteristic
40C3×#388—32no—
41C3×#388—32no—
42C3×#387—32no—
43C3×#387—32no—
44C3×#384—31no—
45C3×#382—31no—
46C3×#380—21no—
47C3×#380—31no—
48C3×#380D311yescharacteristic
49C3×#380C2×C311yescharacteristic
50C3×C4×C4⋊C4—31no—
51C3×C4×C4⋊C4—31no—
52#5212C2×C311yescharacteristic
53#4977C2×C311yescharacteristic, complemented
54#4975C2×C311yescharacteristic, complemented
55Dic3×C4⋊C4C2×C311yescharacteristic, complemented
56Dic3×C4⋊C4C2×C311yescharacteristic, complemented
57#4945C2×C312yes—
58#4944C2×C312yes—
59#4654C2×C312yescomplemented
60#4653C2×C312yescomplemented
61C24×C32C2311yescharacteristic
62C22×C32×C4—22no—
63C22×C32×C4—22no—
64C22×C32×C4C2×C414yes—
65C22×C32×C4C2312yes—
66C22×C32×C4C2312yes—
67C22×C32×C4C2311yescharacteristic
68C22×C32×C4C2311yescharacteristic
69C22×C3×Dic3C2312yes—
70C22×C3×Dic3C2312yes—
71C22×C3×Dic3C2311yescharacteristic
72C22×C3×Dic3C2311yescharacteristic
73C22×C3×Dic3C2311yescharacteristic
74C22×C3×Dic3C2311yescharacteristic
75C32×C4⋊C4—22no—
76C32×C4⋊C4—22no—
77C32×C22⋊C4—42no—
78C3×#217—42no—
79C3×#217C2×C414yes—
80C3×#217C2×C414yes—
81C3×C4⋊Dic3—22no—
82C3×C4⋊Dic3—22no—
83C3×C4⋊Dic3C2×C414yes—
84C3×C4⋊Dic3C2×C414yes—
85C3×Dic3⋊C4—42no—
86C3×Dic3⋊C4—42no—
87C3×C4×Dic3—42no—
88C3×C4×Dic3—42no—
89C3×C4×Dic3C2×C414yes—
90C3×C4×Dic3C2×C414yes—
91#2314—31noSylow
92C23×C3×C4—21no—
93C23×C3×C4C2×D311yescharacteristic
94C23×C3×C4C22×C311yescharacteristic
95C3×#117—38no—
96C2×C3×C4⋊C4—21no—
97C2×C3×C4⋊C4—21no—
98C2×C3×C4⋊C4—31no—
99C2×C3×C4⋊C4—31no—
100C2×C3×C4⋊C4—31no—
101C2×C3×C4⋊C4—31no—
102C2×C3×C4⋊C4—32no—
103C2×C3×C4⋊C4—32no—
104C2×C3×C4⋊C4C2×D311yescharacteristic
105C2×C3×C4⋊C4C2×D311yescharacteristic
106C2×C3×C4⋊C4C22×C311yescharacteristic
107C2×C3×C4⋊C4C22×C311yescharacteristic
108C2×C3×C22⋊C4—22no—
109C2×C3×C22⋊C4—31no—
110C2×C3×C22⋊C4—31no—
111C2×C3×C22⋊C4—32no—
112C2×C3×C22⋊C4C2×D312yes—
113C2×C3×C22⋊C4C22×C312yes—
114C2×C3×C42—31no—
115C2×C3×C42—31no—
116C2×C3×C42—32no—
117C2×C3×C42—32no—
118C2×#217C22×C312yes—
119C2×#217C22×C311yescharacteristic
120C2×#217C22×C311yescharacteristic
121#926C3×C418yescomplemented
122C2×C4⋊Dic3C22×C311yescharacteristic
123C2×C4⋊Dic3C22×C311yescharacteristic
124C2×C4⋊Dic3C22×C311yescharacteristic
125C2×C4⋊Dic3C22×C311yescharacteristic
126C2×Dic3⋊C4C22×C312yes—
127C2×Dic3⋊C4C22×C312yes—
128C2×C4×Dic3C22×C312yes—
129C2×C4×Dic3C22×C312yes—
130C2×C4×Dic3C22×C311yescharacteristic
131C2×C4×Dic3C22×C311yescharacteristic
132C3×#95—22no—
133C3×#95—32no—
134C3×#95—32no—
135C3×#95—32no—
136C3×#95—32no—
137C3×#95—32no—
138C3×#95C2×D312yes—
139C3×#95C22×C312yes—
140C3⋊#95C22×C312yes—
141C3⋊#95C22×C312yes—
142C3⋊#95C22×C312yes—
143C3⋊#95C22×C312yes—
144C3⋊#95C22×C312yes—
145C23×C32—21no—
146C23×C32—21no—
147C23×C32—21no—
148C23×C32—21no—
149C23×C32—21no—
150C23×C32—21no—
151C23×C32C22×C412yes—
152C23×C32C2411yescharacteristic
153C2×C32×C4—21no—
154C2×C32×C4—21no—
155C2×C32×C4—28no—
156C2×C32×C4—22no—
157C2×C32×C4—22no—
158C2×C32×C4—22no—
159C2×C32×C4—22no—
160C2×C32×C4—22no—
161C2×C32×C4—22no—
162C2×C32×C4C22×C412yes—
163C2×C32×C4C22×C412yes—
164C2×C32×C4#4112yes—
165C2×C32×C4#4112yes—
166C2×C3×Dic3—21no—
167C2×C3×Dic3—21no—
168C2×C3×Dic3—21no—
169C2×C3×Dic3—21no—
170C2×C3×Dic3—21no—
171C2×C3×Dic3—21no—
172C2×C3×Dic3—21no—
173C2×C3×Dic3—21no—
174C2×C3×Dic3—22no—
175C2×C3×Dic3—22no—
176C2×C3×Dic3—22no—
177C2×C3×Dic3—22no—
178C2×C3×Dic3—22no—
179C2×C3×Dic3—22no—
180C2×C3×Dic3C22×C412yes—
181C2×C3×Dic3C22×C412yes—
182C2×C3×Dic3C22×C412yes—
183C2×C3×Dic3C22×C412yes—
184C2×#117—31no—
185#388—32no—
186#388—32no—
187#387—32no—
188#387—32no—
189#384—31no—
190#382—31no—
191#380—31no—
192#380C3×D311yescharacteristic
193C4×C4⋊C4—31no—
194C4×C4⋊C4—31no—
195C24×C3—21no—
196C24×C3C22×D311yescharacteristic
197C24×C3C23×C311yescharacteristic
198C22×C3×C4—22no—
199C22×C3×C4—22no—
200C22×C3×C4—22no—
201C22×C3×C4—22no—
202C22×C3×C4—24no—
203C22×C3×C4—21no—
204C22×C3×C4—21no—
205C22×C3×C4—22no—
206C22×C3×C4—22no—
207C22×C3×C4—31no—
208C22×C3×C4—31no—
209C22×C3×C4—31no—
210C22×C3×C4—31no—
211C22×C3×C4—32no—
212C22×C3×C4—32no—
213C22×C3×C4—42no—
214C22×C3×C4—42no—
215C22×C3×C4C4×D314yes—
216C22×C3×C4C2×C3×C414yes—
217C22×C3×C4C22×D312yes—
218C22×C3×C4C22×D312yes—
219C22×C3×C4C22×D311yescharacteristic
220C22×C3×C4C22×D311yescharacteristic
221C22×C3×C4C23×C312yes—
222C22×C3×C4C23×C312yes—
223C22×C3×C4C23×C311yescharacteristic
224C22×C3×C4C23×C311yescharacteristic
225C22×Dic3C23×C312yes—
226C22×Dic3C23×C312yes—
227C22×Dic3C23×C311yescharacteristic
228C22×Dic3C23×C311yescharacteristic
229C22×Dic3C23×C311yescharacteristic
230C22×Dic3C23×C311yescharacteristic
231C3×C4⋊C4—22no—
232C3×C4⋊C4—22no—
233C3×C4⋊C4—22no—
234C3×C4⋊C4—22no—
235C3×C4⋊C4—34no—
236C3×C4⋊C4—34no—
237C3×C4⋊C4—42no—
238C3×C4⋊C4—42no—
239C3×C4⋊C4—62no—
240C3×C4⋊C4—62no—
241C3×C4⋊C4—122no—
242C3×C4⋊C4—122no—
243C3×C22⋊C4—34no—
244C3×C22⋊C4—34no—
245C3×C22⋊C4—42no—
246C3×C22⋊C4—42no—
247C3×C22⋊C4—44no—
248C3×C22⋊C4—122no—
249C3×C42—34no—
250C3×C42—34no—
251C3×C42—122no—
252C3×C42—122no—
253#217—42no—
254#217C2×C3×C414yes—
255#217C2×C3×C414yes—
256C4⋊Dic3—22no—
257C4⋊Dic3—22no—
258C4⋊Dic3C2×C3×C414yes—
259C4⋊Dic3C2×C3×C414yes—
260Dic3⋊C4—42no—
261Dic3⋊C4—42no—
262C4×Dic3—42no—
263C4×Dic3—42no—
264C4×Dic3C2×C3×C414yes—
265C4×Dic3C2×C3×C414yes—
266C22×C32—22no—
267C22×C32—22no—
268C22×C32—22no—
269C22×C32—41no—
270C22×C32—41no—
271C22×C32—41no—
272C22×C32—41no—
273C22×C32C23×C411yescharacteristic
274C22×C32C2×#4111yescharacteristic
275C22×C32C2×#4111yescharacteristic
276C22×C32H(5,𝔽2)11yescharacteristic
277C22×C32H(5,𝔽2)11yescharacteristic
278C22×C322−1+411yescharacteristic
279C22×C322−1+411yescharacteristic
280C32×C4—22no—
281C32×C4—42no—
282C32×C4—42no—
283C32×C4#11714yes—
284C3×Dic3—22no—
285C3×Dic3—22no—
286C3×Dic3—22no—
287C3×Dic3—22no—
288C3×Dic3—42no—
289C3×Dic3—42no—
290C23×C4C2×C3×D311yescharacteristic
291#117—38no—
292C2×C4⋊C4—31no—
293C2×C4⋊C4—31no—
294C2×C4⋊C4—31no—
295C2×C4⋊C4—31no—
296C2×C4⋊C4—32no—
297C2×C4⋊C4—32no—
298C2×C4⋊C4C2×C3×D311yescharacteristic
299C2×C4⋊C4C2×C3×D311yescharacteristic
300C2×C22⋊C4—31no—
301C2×C22⋊C4—31no—
302C2×C22⋊C4—32no—
303C2×C22⋊C4C2×C3×D312yes—
304C2×C42—31no—
305C2×C42—31no—
306C2×C42—32no—
307C2×C42—32no—
308#95—32no—
309#95—32no—
310#95—32no—
311#95—32no—
312#95—32no—
313#95C2×C3×D312yes—
314C23×C3—22no—
315C23×C3—22no—
316C23×C3—21no—
317C23×C3—21no—
318C23×C3—21no—
319C23×C3—21no—
320C23×C3—21no—
321C23×C3—21no—
322C23×C3—21no—
323C23×C3—21no—
324C23×C3—21no—
325C23×C3—21no—
326C23×C3—21no—
327C23×C3—21no—
328C23×C3—21no—
329C23×C3—22no—
330C23×C3—41no—
331C23×C3—41no—
332C23×C3—41no—
333C23×C3—41no—
334C23×C3C2×C4×D312yes—
335C23×C3C22×C3×C412yes—
336C23×C3C23×D311yescharacteristic
337C23×C3C24×C311yescharacteristic
338C2×C3×C4—21no—
339C2×C3×C4—21no—
340C2×C3×C4—21no—
341C2×C3×C4—21no—
342C2×C3×C4—28no—
343C2×C3×C4—28no—
344C2×C3×C4—22no—
345C2×C3×C4—22no—
346C2×C3×C4—22no—
347C2×C3×C4—22no—
348C2×C3×C4—22no—
349C2×C3×C4—22no—
350C2×C3×C4—22no—
351C2×C3×C4—22no—
352C2×C3×C4—22no—
353C2×C3×C4—22no—
354C2×C3×C4—22no—
355C2×C3×C4—22no—
356C2×C3×C4—22no—
357C2×C3×C4—22no—
358C2×C3×C4—22no—
359C2×C3×C4—22no—
360C2×C3×C4—32no—
361C2×C3×C4—32no—
362C2×C3×C4—32no—
363C2×C3×C4—32no—
364C2×C3×C4—48no—
365C2×C3×C4—41no—
366C2×C3×C4—41no—
367C2×C3×C4—42no—
368C2×C3×C4—42no—
369C2×C3×C4—42no—
370C2×C3×C4—42no—
371C2×C3×C4—42no—
372C2×C3×C4—42no—
373C2×C3×C4—61no—
374C2×C3×C4—61no—
375C2×C3×C4—61no—
376C2×C3×C4—61no—
377C2×C3×C4—61no—
378C2×C3×C4—61no—
379C2×C3×C4—61no—
380C2×C3×C4—61no—
381C2×C3×C4—62no—
382C2×C3×C4—62no—
383C2×C3×C4—62no—
384C2×C3×C4—62no—
385C2×C3×C4—62no—
386C2×C3×C4—62no—
387C2×C3×C4C2×C4×D312yes—
388C2×C3×C4C2×C4×D312yes—
389C2×C3×C4#23712yes—
390C2×C3×C4#23712yes—
391C2×C3×C4C22×C3×C412yes—
392C2×C3×C4C22×C3×C412yes—
393C2×C3×C4C3×#4112yes—
394C2×C3×C4C3×#4112yes—
395C2×Dic3—21no—
396C2×Dic3—21no—
397C2×Dic3—21no—
398C2×Dic3—21no—
399C2×Dic3—21no—
400C2×Dic3—21no—
401C2×Dic3—21no—
402C2×Dic3—21no—
403C2×Dic3—22no—
404C2×Dic3—22no—
405C2×Dic3—22no—
406C2×Dic3—22no—
407C2×Dic3—22no—
408C2×Dic3—22no—
409C2×Dic3C22×C3×C412yes—
410C2×Dic3C22×C3×C412yes—
411C2×Dic3C22×C3×C412yes—
412C2×Dic3C22×C3×C412yes—
413C2×C32—42no—
414C2×C32C2×#11711yescharacteristic
415C2×C32#52011yescharacteristic
416C2×C32#52011yescharacteristic
417C2×C32#54011yescharacteristic
418C2×C32#54111yescharacteristic
419C2×C32#54211yescharacteristic
420C2×C32#54211yescharacteristic
421C24C22×C3×D311yescharacteristic
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—31no—
425C22×C4—31no—
426C22×C4—31no—
427C22×C4—31no—
428C22×C4—32no—
429C22×C4—32no—
430C22×C4C3×C4×D314yes—
431C22×C4C22×C3×D312yes—
432C22×C4C22×C3×D312yes—
433C22×C4C22×C3×D311yescharacteristic
434C22×C4C22×C3×D311yescharacteristic
435C4⋊C4—22no—
436C4⋊C4—22no—
437C4⋊C4—34no—
438C4⋊C4—34no—
439C4⋊C4—62no—
440C4⋊C4—62no—
441C4⋊C4—122no—
442C4⋊C4—122no—
443C22⋊C4—34no—
444C22⋊C4—34no—
445C22⋊C4—42no—
446C22⋊C4—122no—
447C42—34no—
448C42—34no—
449C42—122no—
450C42—122no—
451C22×C3—24no—
452C22×C3—22no—
453C22×C3—22no—
454C22×C3—22no—
455C22×C3—22no—
456C22×C3—22no—
457C22×C3—22no—
458C22×C3—21no—
459C22×C3—21no—
460C22×C3—21no—
461C22×C3—21no—
462C22×C3—21no—
463C22×C3—21no—
464C22×C3—21no—
465C22×C3—42no—
466C22×C3—42no—
467C22×C3—42no—
468C22×C3—42no—
469C22×C3—42no—
470C22×C3—42no—
471C22×C3—41no—
472C22×C3—41no—
473C22×C3—41no—
474C22×C3—41no—
475C22×C3—41no—
476C22×C3—41no—
477C22×C3—41no—
478C22×C3—41no—
479C22×C3C22×C4×D311yescharacteristic
480C22×C3C2×#23711yescharacteristic
481C22×C3C2×#23711yescharacteristic
482C22×C3#100411yescharacteristic
483C22×C3#100711yescharacteristic
484C22×C3#100911yescharacteristic
485C22×C3#101011yescharacteristic
486C22×C3C23×C3×C411yescharacteristic
487C22×C3C2×C3×#4111yescharacteristic
488C22×C3C2×C3×#4111yescharacteristic
489C22×C3C3×H(5,𝔽2)11yescharacteristic
490C22×C3C3×H(5,𝔽2)11yescharacteristic
491C22×C3C3×2−1+411yescharacteristic
492C22×C3C3×2−1+411yescharacteristic
493C3×C4—22no—
494C3×C4—22no—
495C3×C4—24no—
496C3×C4—42no—
497C3×C4—42no—
498C3×C4—42no—
499C3×C4—42no—
500C3×C4—42no—
501C3×C4—62no—
502C3×C4—62no—
503C3×C4—62no—
504C3×C4—62no—
505C3×C4—82no—
506C3×C4—82no—
507C3×C4—122no—
508C3×C4—122no—
509C3×C4#87714yes—
510C3×C4C3×#11714yes—
511Dic3—22no—
512Dic3—22no—
513Dic3—22no—
514Dic3—22no—
515Dic3—42no—
516Dic3—42no—
517C32#231411yescharacteristic, complemented, Sylow
518C23—21no—
519C23—21no—
520C23—21no—
521C23—21no—
522C23—21no—
523C23—21no—
524C23C2×C3×C4×D312yes—
525C23C23×C3×D311yescharacteristic
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—28no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—32no—
536C2×C4—32no—
537C2×C4—32no—
538C2×C4—32no—
539C2×C4—61no—
540C2×C4—61no—
541C2×C4—61no—
542C2×C4—61no—
543C2×C4—61no—
544C2×C4—61no—
545C2×C4—61no—
546C2×C4—61no—
547C2×C4—62no—
548C2×C4—62no—
549C2×C4—62no—
550C2×C4—62no—
551C2×C4—62no—
552C2×C4—62no—
553C2×C4C2×C3×C4×D312yes—
554C2×C4C2×C3×C4×D312yes—
555C2×C4C3×#23712yes—
556C2×C4C3×#23712yes—
557C2×C3—21no—
558C2×C3—21no—
559C2×C3—21no—
560C2×C3—21no—
561C2×C3—21no—
562C2×C3—21no—
563C2×C3—21no—
564C2×C3—44no—
565C2×C3—42no—
566C2×C3—42no—
567C2×C3C2×#87711yescharacteristic
568C2×C3#550411yescharacteristic
569C2×C3#552311yescharacteristic
570C2×C3#560311yescharacteristic
571C2×C3#561911yescharacteristic
572C2×C3#562511yescharacteristic
573C2×C3#564311yescharacteristic
574C2×C3C2×C3×#11711yescharacteristic
575C2×C3C3×#52011yescharacteristic
576C2×C3C3×#52011yescharacteristic
577C2×C3C3×#54011yescharacteristic
578C2×C3C3×#54111yescharacteristic
579C2×C3C3×#54211yescharacteristic
580C2×C3C3×#54211yescharacteristic
581C22—22no—
582C22—22no—
583C22—22no—
584C22—41no—
585C22—41no—
586C22—41no—
587C22—41no—
588C22C22×C3×C4×D311yescharacteristic
589C22C2×C3×#23711yescharacteristic
590C22C2×C3×#23711yescharacteristic
591C22C3×#100411yescharacteristic
592C22C3×#100711yescharacteristic
593C22C3×#100911yescharacteristic
594C22C3×#101011yescharacteristic
595C4—22no—
596C4—42no—
597C4—42no—
598C4—62no—
599C4—62no—
600C4—62no—
601C4—62no—
602C4—122no—
603C4—122no—
604C4C3×#87714yes—
605C3—21no—
606C3#7386811yescharacteristic, direct product factor
607C3C3×#231411yescharacteristic, complemented
608C2—42no—
609C2C2×C3×#87711yescharacteristic
610C2C3×#550411yescharacteristic
611C2C3×#552311yescharacteristic
612C2C3×#560311yescharacteristic
613C2C3×#561911yescharacteristic
614C2C3×#562511yescharacteristic
615C2C3×#564311yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutatorC22×C3C23×C3×C4
FrattiniC23C23×C3×D3
FittingC32×#380C2
socleC23×C32C24
prime radicalC24×C32C23
cosocleC23×C3C24×C3
hypercenterC3×#380D3
hypocenterC3C3×#2314
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C3×#380

Complements

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

NH ≅ G/Ntype
4. C3×#4977C2semidirect
5. C3×#4975C2semidirect
6. C3×Dic3×C4⋊C4C2semidirect
7. C3×Dic3×C4⋊C4C2semidirect
10. C3×#4654C2semidirect
11. C3×#4653C2semidirect
13. #73868C3direct (N × H)
21. C3×#926C4semidirect
53. #4977C2×C3semidirect
54. #4975C2×C3semidirect
55. Dic3×C4⋊C4C2×C3semidirect
56. Dic3×C4⋊C4C2×C3semidirect
59. #4654C2×C3semidirect
60. #4653C2×C3semidirect
121. #926C3×C4semidirect
517. C32#2314semidirect
606. C3#73868direct (N × H)
607. C3C3×#2314semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9262
C32×#3802
C3×#52122
C3×#49772
C3×#49752
C3×Dic3×C4⋊C42
C3×#49452
C3×#49442
C3×#46542
C3×#46532
C3×#23143
#738683