Finite Group Databasebeta

← C3×#68952 #11783743

Subgroups — C3×#68952 #11783743

Order 1152.

895 conjugacy classes of subgroups.

The subgroup lattice has 523 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#67⋊C4C211yesmaximal, characteristic
2C2×C3×#806C212yesmaximal
3C3×Dic3×C22⋊C4C212yesmaximal, complemented
4C32×#342C211yesmaximal, characteristic, complemented
5C3×#4526C211yesmaximal, characteristic, complemented
6C3×C4×#99—31nomaximal
7#68952C311yesmaximal, characteristic, direct product factor
8C22×C3×#67C2211yescharacteristic
9C23×C3×Dic3C2211yescharacteristic
10C22×C3×C4×D3C411yescharacteristic, complemented
11C2×C32×C22⋊C4C2211yescharacteristic
12C2×C32×C22⋊C4C2212yes—
13C2×C3×#217C2212yes—
14C2×C3×(C2×D3)⋊C4C411yescharacteristic, complemented
15C2×C3×Dic3⋊C4C411yescharacteristic, complemented
16C2×C3×C4×Dic3—22no—
17C2×C3×C4×Dic3C411yescharacteristic, complemented
18C3×#67⋊C4—22no—
19C3×#67⋊C4—22no—
20C3×C3⋊#95—22no—
21C3×#806C418yescomplemented
22C2×C3×C4×D4—31no—
23C2×#67⋊C4C2×C311yescharacteristic
24C2×C3×#99—32no—
25C3×C4×C22⋊C4—32no—
26C2×#806C2×C312yes—
27Dic3×C22⋊C4C2×C312yescomplemented
28C3×#342—21no—
29C3×#342—31no—
30C3×#342D311yescharacteristic, complemented
31C3×#342C2×C311yescharacteristic, complemented
32#4526C2×C311yescharacteristic, complemented
33C24×C32C2311yescharacteristic
34C23×C3×D3C2×C411yescharacteristic
35C22×C32×C4—22no—
36C22×C32×C4C2×C411yescharacteristic
37C22×C32×C4C2×C411yescharacteristic
38C2×C3×#67—22no—
39C2×C3×#67—21no—
40C2×C3×#67—21no—
41C2×C3×#67C2×C414yes—
42C22×C3×Dic3—22no—
43C22×C3×Dic3—42no—
44C22×C3×Dic3C2×C411yescharacteristic
45C22×C3×Dic3C2×C411yescharacteristic
46C22×C3×Dic3C2×C411yescharacteristic
47C22×C3×Dic3D412yes—
48C22×C3×Dic3D412yes—
49C2×C3×C4×D3—21no—
50C2×C3×C4×D3—21no—
51C2×C3×C4×D3—42no—
52C32×C22⋊C4—22no—
53C32×C22⋊C4—22no—
54C32×C22⋊C4C2×C414yescomplemented
55C3×#217—22no—
56C3×#217C2×C414yescomplemented
57C3×(C2×D3)⋊C4—22no—
58C3×Dic3⋊C4—22no—
59C3×C4×Dic3—21no—
60C3×C4×Dic3—21no—
61C3×C4×Dic3—44no—
62C4×#99—31noSylow
63C22×C3×D4—31no—
64C23×C3×C4—31no—
65C23×C3×C4—31no—
66C22×#67C22×C311yescharacteristic
67C23×Dic3C22×C311yescharacteristic
68C22×C4×D3C3×C411yescharacteristic, complemented
69C3×C4×D4—62no—
70C3×C4×D4—62no—
71C2×C3×C4⋊C4—31no—
72C2×C3×C22⋊C4—22no—
73C2×C3×C22⋊C4—21no—
74C2×C3×C22⋊C4—32no—
75C2×C3×C22⋊C4—31no—
76C2×C3×C22⋊C4C2×D311yescharacteristic
77C2×C3×C22⋊C4C2×D312yes—
78C2×C3×C22⋊C4C22×C311yescharacteristic
79C2×C3×C22⋊C4C22×C312yes—
80C2×C3×C42—31no—
81C2×C3×C42—62no—
82C2×#217C22×C312yes—
83C2×(C2×D3)⋊C4C3×C411yescharacteristic, complemented
84C2×Dic3⋊C4C3×C411yescharacteristic, complemented
85C2×C4×Dic3—22no—
86C2×C4×Dic3C3×C411yescharacteristic, complemented
87#67⋊C4—22no—
88#67⋊C4—22no—
89C3×#99—38no—
90C3×#95—62no—
91C3⋊#95—22no—
92#806C3×C418yescomplemented
93C23×C32—41no—
94C23×C32—41no—
95C23×C32C22×C411yescharacteristic
96C23×C32C22×C412yes—
97C23×C32C2×D412yes—
98C23×C32#4111yescharacteristic
99C23×C32#4111yescharacteristic
100C22×C3×D3—21no—
101C22×C3×D3—21no—
102C22×C3×D3—41no—
103C22×C3×D3—41no—
104C22×C3×D3C4212yescomplemented
105C2×C32×C4—21no—
106C2×C32×C4—21no—
107C2×C32×C4—24no—
108C2×C32×C4—42no—
109C2×C32×C4—42no—
110C2×C32×C4—41no—
111C2×C32×C4—41no—
112C3×#67—24no—
113C3×#67—24no—
114C2×C3×Dic3—21no—
115C2×C3×Dic3—21no—
116C2×C3×Dic3—24no—
117C2×C3×Dic3—22no—
118C2×C3×Dic3—24no—
119C2×C3×Dic3—41no—
120C2×C3×Dic3—42no—
121C2×C3×Dic3—42no—
122C2×C3×Dic3—42no—
123C2×C3×Dic3C4212yescomplemented
124C2×C3×Dic3C22⋊C411yescharacteristic
125C2×C3×Dic3C22⋊C412yes—
126C2×C3×Dic3C22⋊C411yescharacteristic
127C3×C4×D3—42no—
128C3×C4×D3—42no—
129C2×C4×D4—31no—
130C2×#99—32no—
131C4×C22⋊C4—32no—
132#342—31no—
133#342C3×D311yescharacteristic, complemented
134C24×C3—21no—
135C24×C3—31no—
136C24×C3C22×D311yescharacteristic
137C24×C3C23×C311yescharacteristic
138C23×D3C2×C3×C411yescharacteristic
139C2×C3×D4—34no—
140C2×C3×D4—62no—
141C2×C3×D4—61no—
142C2×C3×D4—61no—
143C22×C3×C4—22no—
144C22×C3×C4—22no—
145C22×C3×C4—21no—
146C22×C3×C4—21no—
147C22×C3×C4—31no—
148C22×C3×C4—31no—
149C22×C3×C4—32no—
150C22×C3×C4—31no—
151C22×C3×C4—32no—
152C22×C3×C4—42no—
153C22×C3×C4—61no—
154C22×C3×C4—61no—
155C22×C3×C4—62no—
156C22×C3×C4—122no—
157C22×C3×C4—122no—
158C22×C3×C4C4×D311yescharacteristic
159C22×C3×C4C4×D311yescharacteristic
160C22×C3×C4C2×C3×C411yescharacteristic
161C22×C3×C4C2×C3×C411yescharacteristic
162C2×#67—22no—
163C2×#67—21no—
164C2×#67—21no—
165C2×#67C2×C3×C414yes—
166C22×Dic3—22no—
167C22×Dic3—42no—
168C22×Dic3C2×C3×C411yescharacteristic
169C22×Dic3C2×C3×C411yescharacteristic
170C22×Dic3C2×C3×C411yescharacteristic
171C22×Dic3C3×D412yes—
172C22×Dic3C3×D412yes—
173C2×C4×D3—21no—
174C2×C4×D3—21no—
175C2×C4×D3—42no—
176C3×C4⋊C4—62no—
177C3×C22⋊C4—22no—
178C3×C22⋊C4—22no—
179C3×C22⋊C4—22no—
180C3×C22⋊C4—22no—
181C3×C22⋊C4—24no—
182C3×C22⋊C4—34no—
183C3×C22⋊C4—42no—
184C3×C22⋊C4—42no—
185C3×C22⋊C4—62no—
186C3×C22⋊C4—62no—
187C3×C22⋊C4C4×D314yescomplemented
188C3×C22⋊C4C2×C3×C414yescomplemented
189C3×C42—61no—
190C3×C42—61no—
191C3×C42—124no—
192#217—22no—
193#217C2×C3×C414yescomplemented
194(C2×D3)⋊C4—22no—
195Dic3⋊C4—22no—
196C4×Dic3—21no—
197C4×Dic3—21no—
198C4×Dic3—44no—
199C22×C32—22no—
200C22×C32—21no—
201C22×C32—22no—
202C22×C32—21no—
203C22×C32—42no—
204C22×C32—41no—
205C22×C32—41no—
206C22×C32C2×C4211yescharacteristic
207C22×C32C2×C22⋊C411yescharacteristic
208C22×C32#11711yescharacteristic
209C22×C32C4×D412yes—
210C22×C32C4×D412yes—
211C2×C3×D3—22no—
212C2×C3×D3—42no—
213C2×C3×D3—41no—
214C2×C3×D3—41no—
215C2×C3×D3—42no—
216C32×C4—44no—
217C32×C4—41no—
218C32×C4—41no—
219C3×Dic3—22no—
220C3×Dic3—21no—
221C3×Dic3—22no—
222C3×Dic3—44no—
223C3×Dic3#9912yescomplemented
224C22×D4—31no—
225C23×C4—31no—
226C23×C4—31no—
227C4×D4—62no—
228C4×D4—62no—
229C2×C4⋊C4—31no—
230C2×C22⋊C4—32no—
231C2×C22⋊C4—31no—
232C2×C22⋊C4C2×C3×D311yescharacteristic
233C2×C22⋊C4C2×C3×D312yes—
234C2×C42—31no—
235C2×C42—62no—
236#99—38no—
237#95—62no—
238C23×C3—21no—
239C23×C3—22no—
240C23×C3—22no—
241C23×C3—21no—
242C23×C3—21no—
243C23×C3—32no—
244C23×C3—41no—
245C23×C3—41no—
246C23×C3—41no—
247C23×C3—41no—
248C23×C3—61no—
249C23×C3—61no—
250C23×C3—81no—
251C23×C3—81no—
252C23×C3—121no—
253C23×C3—121no—
254C23×C3C2×C4×D311yescharacteristic
255C23×C3C2×C4×D312yes—
256C23×C3D3×D412yes—
257C23×C3#23711yescharacteristic
258C23×C3#23911yescharacteristic
259C23×C3C22×C3×C411yescharacteristic
260C23×C3C22×C3×C412yes—
261C23×C3C2×C3×D412yes—
262C23×C3C3×#4111yescharacteristic
263C23×C3C3×#4111yescharacteristic
264C22×D3—21no—
265C22×D3—21no—
266C22×D3—41no—
267C22×D3—41no—
268C22×D3C3×C4212yescomplemented
269C3×D4—64no—
270C3×D4—64no—
271C2×C3×C4—21no—
272C2×C3×C4—21no—
273C2×C3×C4—24no—
274C2×C3×C4—21no—
275C2×C3×C4—21no—
276C2×C3×C4—24no—
277C2×C3×C4—31no—
278C2×C3×C4—32no—
279C2×C3×C4—31no—
280C2×C3×C4—32no—
281C2×C3×C4—44no—
282C2×C3×C4—41no—
283C2×C3×C4—41no—
284C2×C3×C4—42no—
285C2×C3×C4—42no—
286C2×C3×C4—42no—
287C2×C3×C4—42no—
288C2×C3×C4—41no—
289C2×C3×C4—41no—
290C2×C3×C4—41no—
291C2×C3×C4—41no—
292C2×C3×C4—64no—
293C2×C3×C4—62no—
294C2×C3×C4—61no—
295C2×C3×C4—61no—
296C2×C3×C4—64no—
297C2×C3×C4—82no—
298C2×C3×C4—82no—
299C2×C3×C4—81no—
300C2×C3×C4—81no—
301C2×C3×C4—122no—
302C2×C3×C4—122no—
303C2×C3×C4—122no—
304C2×C3×C4—121no—
305C2×C3×C4—122no—
306C2×C3×C4—122no—
307#67—24no—
308#67—24no—
309C2×Dic3—21no—
310C2×Dic3—21no—
311C2×Dic3—24no—
312C2×Dic3—22no—
313C2×Dic3—24no—
314C2×Dic3—41no—
315C2×Dic3—42no—
316C2×Dic3—42no—
317C2×Dic3—42no—
318C2×Dic3C3×C4212yescomplemented
319C2×Dic3C3×C22⋊C411yescharacteristic
320C2×Dic3C3×C22⋊C412yes—
321C2×Dic3C3×C22⋊C411yescharacteristic
322C4×D3—42no—
323C4×D3—42no—
324C2×C32—22no—
325C2×C32—22no—
326C2×C32—21no—
327C2×C32—21no—
328C2×C32C4×C22⋊C411yescharacteristic
329C2×C32C2×#9911yescharacteristic
330C2×C32#41011yescharacteristic
331C3×D3—42no—
332C24—31no—
333C24C22×C3×D311yescharacteristic
334C2×D4—34no—
335C2×D4—62no—
336C2×D4—61no—
337C2×D4—61no—
338C22×C4—22no—
339C22×C4—31no—
340C22×C4—31no—
341C22×C4—32no—
342C22×C4—31no—
343C22×C4—32no—
344C22×C4—61no—
345C22×C4—61no—
346C22×C4—62no—
347C22×C4—122no—
348C22×C4—122no—
349C22×C4C3×C4×D311yescharacteristic
350C22×C4C3×C4×D311yescharacteristic
351C4⋊C4—62no—
352C22⋊C4—22no—
353C22⋊C4—22no—
354C22⋊C4—34no—
355C22⋊C4—62no—
356C22⋊C4—62no—
357C22⋊C4C3×C4×D314yescomplemented
358C42—61no—
359C42—61no—
360C42—124no—
361C22×C3—22no—
362C22×C3—21no—
363C22×C3—22no—
364C22×C3—21no—
365C22×C3—22no—
366C22×C3—21no—
367C22×C3—22no—
368C22×C3—21no—
369C22×C3—21no—
370C22×C3—22no—
371C22×C3—21no—
372C22×C3—22no—
373C22×C3—21no—
374C22×C3—42no—
375C22×C3—41no—
376C22×C3—42no—
377C22×C3—41no—
378C22×C3—42no—
379C22×C3—41no—
380C22×C3—41no—
381C22×C3—42no—
382C22×C3—41no—
383C22×C3—41no—
384C22×C3—62no—
385C22×C3—82no—
386C22×C3—81no—
387C22×C3—81no—
388C22×C3—122no—
389C22×C3—122no—
390C22×C3—121no—
391C22×C3—121no—
392C22×C3C42×D311yescharacteristic
393C22×C3D3×C22⋊C411yescharacteristic
394C22×C3#67⋊C412yes—
395C22×C3#89211yescharacteristic
396C22×C3#89312yes—
397C22×C3C2×C3×C4211yescharacteristic
398C22×C3C2×C3×C22⋊C411yescharacteristic
399C22×C3C3×#11711yescharacteristic
400C22×C3C3×C4×D412yes—
401C22×C3C3×C4×D412yes—
402C2×D3—22no—
403C2×D3—42no—
404C2×D3—41no—
405C2×D3—41no—
406C2×D3—42no—
407C3×C4—32no—
408C3×C4—44no—
409C3×C4—44no—
410C3×C4—41no—
411C3×C4—41no—
412C3×C4—41no—
413C3×C4—41no—
414C3×C4—62no—
415C3×C4—61no—
416C3×C4—62no—
417C3×C4—81no—
418C3×C4—81no—
419C3×C4—84no—
420C3×C4—124no—
421Dic3—22no—
422Dic3—21no—
423Dic3—22no—
424Dic3—44no—
425Dic3C3×#9912yescomplemented
426C32C4×#9911yescharacteristic, complemented, Sylow
427C23—32no—
428C23—41no—
429C23—41no—
430C23—61no—
431C23—61no—
432C23—121no—
433C23—121no—
434C23C2×C3×C4×D311yescharacteristic
435C23C2×C3×C4×D312yes—
436C23C3×D3×D412yes—
437C23C3×#23711yescharacteristic
438C23C3×#23911yescharacteristic
439D4—64no—
440D4—64no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—24no—
444C2×C4—31no—
445C2×C4—31no—
446C2×C4—32no—
447C2×C4—32no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—64no—
453C2×C4—62no—
454C2×C4—61no—
455C2×C4—61no—
456C2×C4—64no—
457C2×C4—122no—
458C2×C4—122no—
459C2×C4—122no—
460C2×C4—121no—
461C2×C4—122no—
462C2×C4—122no—
463C2×C3—22no—
464C2×C3—22no—
465C2×C3—21no—
466C2×C3—21no—
467C2×C3—22no—
468C2×C3—22no—
469C2×C3—21no—
470C2×C3—21no—
471C2×C3—21no—
472C2×C3—21no—
473C2×C3—21no—
474C2×C3—42no—
475C2×C3—42no—
476C2×C3—41no—
477C2×C3—41no—
478C2×C3—122no—
479C2×C3#466611yescharacteristic
480C2×C3#474011yescharacteristic
481C2×C3D3×#9911yescharacteristic
482C2×C3C3×C4×C22⋊C411yescharacteristic
483C2×C3C2×C3×#9911yescharacteristic
484C2×C3C3×#41011yescharacteristic
485D3—42no—
486C22—22no—
487C22—21no—
488C22—22no—
489C22—21no—
490C22—42no—
491C22—41no—
492C22—41no—
493C22—62no—
494C22—122no—
495C22—122no—
496C22—121no—
497C22—121no—
498C22C3×C42×D311yescharacteristic
499C22C3×D3×C22⋊C411yescharacteristic
500C22C3×#67⋊C412yes—
501C22C3×#89211yescharacteristic
502C22C3×#89312yes—
503C4—32no—
504C4—44no—
505C4—41no—
506C4—41no—
507C4—62no—
508C4—61no—
509C4—62no—
510C4—124no—
511C3—21no—
512C3#6895211yescharacteristic, direct product factor
513C3C3×C4×#9911yescharacteristic, complemented
514C2—22no—
515C2—22no—
516C2—21no—
517C2—21no—
518C2—122no—
519C2C3×#466611yescharacteristic
520C2C3×#474011yescharacteristic
521C2C3×D3×#9911yescharacteristic
subgroupG/H
centerC22×C3D3×C22⋊C4
commutatorC22×C3C2×C3×C42
FrattiniC24C22×C3×D3
FittingC32×#342C2
socleC22×C32C2×C22⋊C4
prime radicalC22×C3×#67C22
cosocleC24×C3C23×C3
hypercenterC3×#342D3
hypocenterC3C3×C4×#99
LCSG ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C24×C3 ◁ C3×#342

Complements

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

NH ≅ G/Ntype
3. C3×Dic3×C22⋊C4C2semidirect
4. C32×#342C2semidirect
5. C3×#4526C2semidirect
7. #68952C3direct (N × H)
10. C22×C3×C4×D3C4semidirect
14. C2×C3×(C2×D3)⋊C4C4semidirect
15. C2×C3×Dic3⋊C4C4semidirect
17. C2×C3×C4×Dic3C4semidirect
21. C3×#806C4semidirect
27. Dic3×C22⋊C4C2×C3semidirect
30. C3×#342D3semidirect
31. C3×#342C2×C3semidirect
32. #4526C2×C3semidirect
54. C32×C22⋊C4C2×C4semidirect
56. C3×#217C2×C4semidirect
68. C22×C4×D3C3×C4semidirect
83. C2×(C2×D3)⋊C4C3×C4semidirect
84. C2×Dic3⋊C4C3×C4semidirect
86. C2×C4×Dic3C3×C4semidirect
92. #806C3×C4semidirect
104. C22×C3×D3C42semidirect
123. C2×C3×Dic3C42semidirect
133. #342C3×D3semidirect
187. C3×C22⋊C4C4×D3semidirect
188. C3×C22⋊C4C2×C3×C4semidirect
193. #217C2×C3×C4semidirect
223. C3×Dic3#99semidirect
268. C22×D3C3×C42semidirect
318. C2×Dic3C3×C42semidirect
357. C22⋊C4C3×C4×D3semidirect
425. Dic3C3×#99semidirect
426. C32C4×#99semidirect
512. C3#68952direct (N × H)
513. C3C3×C4×#99semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#67⋊C42
C2×C3×#8062
C3×Dic3×C22⋊C42
C32×#3422
C3×#45262
C3×C4×#993
#689523