Finite Group Databasebeta

← C3×#68143 #11773782

Subgroups — C3×#68143 #11773782

Order 1152.

703 conjugacy classes of subgroups.

The subgroup lattice has 439 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#893C211yesmaximal, characteristic
2C3×D3×C22⋊C8C212yesmaximal, complemented
3C32×#324C211yesmaximal, characteristic, complemented
4C3×#4528C211yesmaximal, characteristic, complemented
5C3×#4468C212yesmaximal, complemented
6C3×#1459—31nomaximal
7#68143C311yesmaximal, characteristic, direct product factor
8C22×C3×D12C411yescharacteristic
9C22×C3×C4×D3C411yescharacteristic
10C22×C3×C4×D3C2211yescharacteristic
11C2×C32×C4⋊C4C2211yescharacteristic
12C2×C3×(C2×D3)⋊C4C411yescharacteristic
13C2×C3×(C2×D3)⋊C4C2211yescharacteristic
14C2×C3×C4×Dic3C411yescharacteristic
15C2×C3×D3×C8—22no—
16C3×#893—22no—
17C3×#893—22no—
18C32×C22⋊C8C2212yes—
19C3×#830C2212yes—
20C3×(C2×D3)⋊C8—22no—
21C2×C3×C4×D4—31no—
22C2×#893C2×C311yescharacteristic
23C2×C3×C22⋊C8—32no—
24D3×C22⋊C8C2×C312yescomplemented
25C3×#324—21no—
26C3×#324—31no—
27C3×#324D311yescharacteristic, complemented
28C3×#324C2×C311yescharacteristic, complemented
29C3×#323—32no—
30#4528C2×C311yescharacteristic, complemented
31#4468C2×C312yescomplemented
32C23×C3×D3C2×C411yescharacteristic
33C23×C3×D3C2×C411yescharacteristic
34C22×C32×C4C2×C411yescharacteristic
35C22×C32×C4C2×C411yescharacteristic
36C22×C32×C4C2311yescharacteristic
37C22×C3×Dic3C2×C411yescharacteristic
38C22×C3×Dic3C2×C411yescharacteristic
39C2×C3×D12—22no—
40C2×C3×D12—22no—
41C2×C3×D12C814yescomplemented
42C2×C3×C4×D3—21no—
43C2×C3×C4×D3—21no—
44C2×C3×C4×D3—42no—
45C2×C3×C4×D3—42no—
46C2×C3×C4×D3D412yes—
47C2×C3×C4×D3D412yes—
48C2×C32×C8—22no—
49C32×C4⋊C4—22no—
50C3×(C2×D3)⋊C4—22no—
51C3×(C2×D3)⋊C4—22no—
52C3×C4×Dic3—21no—
53C3×C4×Dic3—21no—
54C2×C3×C3⋊C8—22no—
55C3×D3×C8—44no—
56#1459—31noSylow
57C22×C3×D4—31no—
58C23×C3×C4—31no—
59C23×C3×C4—31no—
60C22×D12C3×C411yescharacteristic
61C22×C4×D3C3×C411yescharacteristic
62C22×C4×D3C22×C311yescharacteristic
63C22×C3×C8—62no—
64C3×C4×D4—62no—
65C3×C4×D4—62no—
66C2×C3×C4⋊C4—21no—
67C2×C3×C4⋊C4C2×D311yescharacteristic
68C2×C3×C4⋊C4C22×C311yescharacteristic
69C2×C3×C22⋊C4—31no—
70C2×C3×C22⋊C4—31no—
71C2×C3×C42—31no—
72C2×(C2×D3)⋊C4C3×C411yescharacteristic
73C2×(C2×D3)⋊C4C22×C311yescharacteristic
74C2×C4×Dic3C3×C411yescharacteristic
75C2×D3×C8—22no—
76#893—22no—
77#893—22no—
78C3×C22⋊C8—22no—
79C3×C22⋊C8—32no—
80C3×C22⋊C8—62no—
81C3×C22⋊C8C2×D312yes—
82C3×C22⋊C8C22×C312yes—
83#830C22×C312yes—
84(C2×D3)⋊C8—22no—
85C23×C32C22×C411yescharacteristic
86C22×C3×D3—21no—
87C22×C3×D3—21no—
88C22×C3×D3—41no—
89C22×C3×D3—41no—
90C22×C3×D3—41no—
91C22×C3×D3—41no—
92C22×C3×D3C22⋊C412yes—
93C22×C3×D3C2×C812yes—
94C22×C3×D3C2×C812yescomplemented
95C22×C3×D3M1612yes—
96C2×C32×C4—21no—
97C2×C32×C4—21no—
98C2×C32×C4—21no—
99C2×C32×C4—41no—
100C2×C32×C4—41no—
101C2×C32×C4C2×C812yescomplemented
102C2×C32×C4C2×D412yes—
103C2×C3×Dic3—22no—
104C2×C3×Dic3—21no—
105C2×C3×Dic3—41no—
106C2×C3×Dic3C22⋊C411yescharacteristic
107C2×C3×Dic3C22⋊C411yescharacteristic
108C3×D12—28no—
109C3×C4×D3—24no—
110C3×C4×D3—42no—
111C3×C4×D3—42no—
112C3×C4×D3—42no—
113C32×C8—42no—
114C3×C3⋊C8—42no—
115C2×C4×D4—31no—
116C2×C22⋊C8—32no—
117#324—31no—
118#324C3×D311yescharacteristic, complemented
119#323—32no—
120C24×C3—31no—
121C24×C3—31no—
122C23×D3C2×C3×C411yescharacteristic
123C23×D3C2×C3×C411yescharacteristic
124C2×C3×D4—34no—
125C2×C3×D4—62no—
126C2×C3×D4—62no—
127C22×C3×C4—21no—
128C22×C3×C4—21no—
129C22×C3×C4—21no—
130C22×C3×C4—31no—
131C22×C3×C4—32no—
132C22×C3×C4—32no—
133C22×C3×C4—31no—
134C22×C3×C4—61no—
135C22×C3×C4—61no—
136C22×C3×C4—122no—
137C22×C3×C4—122no—
138C22×C3×C4C4×D311yescharacteristic
139C22×C3×C4C4×D311yescharacteristic
140C22×C3×C4C2×C3×C411yescharacteristic
141C22×C3×C4C2×C3×C411yescharacteristic
142C22×C3×C4C22×D311yescharacteristic
143C22×C3×C4C23×C311yescharacteristic
144C22×Dic3C2×C3×C411yescharacteristic
145C22×Dic3C2×C3×C411yescharacteristic
146C2×D12—22no—
147C2×D12—22no—
148C2×D12C3×C814yescomplemented
149C2×C4×D3—21no—
150C2×C4×D3—21no—
151C2×C4×D3—42no—
152C2×C4×D3—42no—
153C2×C4×D3C3×D412yes—
154C2×C4×D3C3×D412yes—
155C2×C3×C8—22no—
156C2×C3×C8—22no—
157C2×C3×C8—42no—
158C2×C3×C8—62no—
159C2×C3×C8—124no—
160C3×C4⋊C4—22no—
161C3×C4⋊C4—22no—
162C3×C4⋊C4—42no—
163C3×C22⋊C4—62no—
164C3×C22⋊C4—62no—
165C3×C42—61no—
166C3×C42—61no—
167(C2×D3)⋊C4—22no—
168(C2×D3)⋊C4—22no—
169C4×Dic3—21no—
170C4×Dic3—21no—
171C2×C3⋊C8—22no—
172D3×C8—44no—
173C22×C32—21no—
174C22×C32—21no—
175C22×C32C2×C22⋊C411yescharacteristic
176C22×C32C22×C811yescharacteristic
177C22×C32C2×M1611yescharacteristic
178C2×C3×D3—22no—
179C2×C3×D3—22no—
180C2×C3×D3—22no—
181C2×C3×D3—42no—
182C2×C3×D3—42no—
183C2×C3×D3—42no—
184C2×C3×D3—41no—
185C2×C3×D3—41no—
186C2×C3×D3—42no—
187C2×C3×D3C22⋊C814yes—
188C32×C4—22no—
189C32×C4—22no—
190C32×C4—41no—
191C3×Dic3—21no—
192C3×Dic3—41no—
193C3×Dic3#9912yes—
194C22×D4—31no—
195C23×C4—31no—
196C23×C4—31no—
197C22×C8—62no—
198C4×D4—62no—
199C4×D4—62no—
200C2×C4⋊C4C2×C3×D311yescharacteristic
201C2×C22⋊C4—31no—
202C2×C22⋊C4—31no—
203C2×C42—31no—
204C22⋊C8—32no—
205C22⋊C8—62no—
206C22⋊C8C2×C3×D312yes—
207C23×C3—21no—
208C23×C3—32no—
209C23×C3—32no—
210C23×C3—32no—
211C23×C3—32no—
212C23×C3—61no—
213C23×C3—61no—
214C23×C3—121no—
215C23×C3—121no—
216C23×C3—121no—
217C23×C3—121no—
218C23×C3C2×C4×D311yescharacteristic
219C23×C3C22×C3×C411yescharacteristic
220C22×D3—21no—
221C22×D3—21no—
222C22×D3—41no—
223C22×D3—41no—
224C22×D3—41no—
225C22×D3—41no—
226C22×D3C3×C22⋊C412yes—
227C22×D3C2×C3×C812yes—
228C22×D3C2×C3×C812yescomplemented
229C22×D3C3×M1612yes—
230C3×D4—68no—
231C2×C3×C4—21no—
232C2×C3×C4—21no—
233C2×C3×C4—21no—
234C2×C3×C4—21no—
235C2×C3×C4—21no—
236C2×C3×C4—21no—
237C2×C3×C4—22no—
238C2×C3×C4—22no—
239C2×C3×C4—31no—
240C2×C3×C4—31no—
241C2×C3×C4—41no—
242C2×C3×C4—41no—
243C2×C3×C4—41no—
244C2×C3×C4—41no—
245C2×C3×C4—41no—
246C2×C3×C4—41no—
247C2×C3×C4—41no—
248C2×C3×C4—64no—
249C2×C3×C4—62no—
250C2×C3×C4—61no—
251C2×C3×C4—81no—
252C2×C3×C4—81no—
253C2×C3×C4—122no—
254C2×C3×C4—122no—
255C2×C3×C4—122no—
256C2×C3×C4—121no—
257C2×C3×C4D3×C812yescomplemented
258C2×C3×C4C2×C3×C812yescomplemented
259C2×C3×C4D3×D412yes—
260C2×C3×C4C2×C3×D412yes—
261C2×Dic3—22no—
262C2×Dic3—21no—
263C2×Dic3—41no—
264C2×Dic3C3×C22⋊C411yescharacteristic
265C2×Dic3C3×C22⋊C411yescharacteristic
266D12—28no—
267C4×D3—24no—
268C4×D3—42no—
269C4×D3—42no—
270C4×D3—42no—
271C3×C8—42no—
272C3×C8—42no—
273C3×C8—82no—
274C3×C8—122no—
275C3⋊C8—42no—
276C2×C32—21no—
277C2×C32—21no—
278C2×C32C2×C22⋊C811yescharacteristic
279C2×C32C2×#9911yescharacteristic
280C2×C32#41311yescharacteristic
281C3×D3—24no—
282C3×D3—42no—
283C24—31no—
284C24—31no—
285C2×D4—34no—
286C2×D4—62no—
287C2×D4—62no—
288C22×C4—31no—
289C22×C4—32no—
290C22×C4—32no—
291C22×C4—31no—
292C22×C4—61no—
293C22×C4—61no—
294C22×C4—122no—
295C22×C4—122no—
296C22×C4C3×C4×D311yescharacteristic
297C22×C4C3×C4×D311yescharacteristic
298C22×C4C22×C3×D311yescharacteristic
299C2×C8—22no—
300C2×C8—62no—
301C2×C8—124no—
302C4⋊C4—22no—
303C22⋊C4—62no—
304C22⋊C4—62no—
305C42—61no—
306C42—61no—
307C22×C3—21no—
308C22×C3—21no—
309C22×C3—21no—
310C22×C3—21no—
311C22×C3—21no—
312C22×C3—21no—
313C22×C3—21no—
314C22×C3—34no—
315C22×C3—41no—
316C22×C3—41no—
317C22×C3—62no—
318C22×C3—62no—
319C22×C3—62no—
320C22×C3—122no—
321C22×C3—122no—
322C22×C3—122no—
323C22×C3—122no—
324C22×C3—121no—
325C22×C3—121no—
326C22×C3D3×C22⋊C411yescharacteristic
327C22×C3C2×D3×C811yescharacteristic
328C22×C3D3×M1611yescharacteristic
329C22×C3C2×C3×C22⋊C411yescharacteristic
330C22×C3C22×C3×C811yescharacteristic
331C22×C3C2×C3×M1611yescharacteristic
332C2×D3—22no—
333C2×D3—22no—
334C2×D3—22no—
335C2×D3—42no—
336C2×D3—42no—
337C2×D3—42no—
338C2×D3—41no—
339C2×D3—41no—
340C2×D3—42no—
341C2×D3C3×C22⋊C814yes—
342C3×C4—22no—
343C3×C4—22no—
344C3×C4—22no—
345C3×C4—22no—
346C3×C4—32no—
347C3×C4—42no—
348C3×C4—42no—
349C3×C4—41no—
350C3×C4—41no—
351C3×C4—61no—
352C3×C4—81no—
353C3×C4—121no—
354Dic3—21no—
355Dic3—41no—
356Dic3C3×#9912yes—
357C32#145911yescharacteristic, complemented, Sylow
358C23—32no—
359C23—32no—
360C23—32no—
361C23—32no—
362C23—61no—
363C23—61no—
364C23—121no—
365C23—121no—
366C23—121no—
367C23—121no—
368C23C2×C3×C4×D311yescharacteristic
369D4—68no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—31no—
374C2×C4—31no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—64no—
378C2×C4—62no—
379C2×C4—61no—
380C2×C4—122no—
381C2×C4—122no—
382C2×C4—122no—
383C2×C4—121no—
384C2×C4C3×D3×C812yescomplemented
385C2×C4C3×D3×D412yes—
386C8—42no—
387C8—122no—
388C2×C3—21no—
389C2×C3—21no—
390C2×C3—21no—
391C2×C3—21no—
392C2×C3—21no—
393C2×C3—21no—
394C2×C3—21no—
395C2×C3—41no—
396C2×C3—41no—
397C2×C3—64no—
398C2×C3—122no—
399C2×C3D3×C22⋊C811yescharacteristic
400C2×C3D3×#9911yescharacteristic
401C2×C3#475111yescharacteristic
402C2×C3C2×C3×C22⋊C811yescharacteristic
403C2×C3C2×C3×#9911yescharacteristic
404C2×C3C3×#41311yescharacteristic
405D3—24no—
406D3—42no—
407C22—21no—
408C22—21no—
409C22—34no—
410C22—62no—
411C22—62no—
412C22—62no—
413C22—122no—
414C22—122no—
415C22—122no—
416C22—122no—
417C22—121no—
418C22—121no—
419C22C3×D3×C22⋊C411yescharacteristic
420C22C2×C3×D3×C811yescharacteristic
421C22C3×D3×M1611yescharacteristic
422C4—22no—
423C4—22no—
424C4—32no—
425C4—41no—
426C4—61no—
427C4—121no—
428C3—21no—
429C3#6814311yescharacteristic, direct product factor
430C3C3×#145911yescharacteristic, complemented
431C2—21no—
432C2—21no—
433C2—64no—
434C2—122no—
435C2C3×D3×C22⋊C811yescharacteristic
436C2C3×D3×#9911yescharacteristic
437C2C3×#475111yescharacteristic
subgroupG/H
centerC22×C3D3×C22⋊C4
commutatorC22×C3C22×C3×C8
FrattiniC22×C4C22×C3×D3
FittingC32×#324C2
socleC22×C32C2×C22⋊C4
prime radicalC22×C3×D12C4
cosocleC22×C3×C4C23×C3
hypercenterC3×#324D3
hypocenterC3C3×#1459
LCSG ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#324

Complements

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

NH ≅ G/Ntype
2. C3×D3×C22⋊C8C2semidirect
3. C32×#324C2semidirect
4. C3×#4528C2semidirect
5. C3×#4468C2semidirect
7. #68143C3direct (N × H)
24. D3×C22⋊C8C2×C3semidirect
27. C3×#324D3semidirect
28. C3×#324C2×C3semidirect
30. #4528C2×C3semidirect
31. #4468C2×C3semidirect
41. C2×C3×D12C8semidirect
94. C22×C3×D3C2×C8semidirect
101. C2×C32×C4C2×C8semidirect
118. #324C3×D3semidirect
148. C2×D12C3×C8semidirect
228. C22×D3C2×C3×C8semidirect
257. C2×C3×C4D3×C8semidirect
258. C2×C3×C4C2×C3×C8semidirect
357. C32#1459semidirect
384. C2×C4C3×D3×C8semidirect
429. C3#68143direct (N × H)
430. C3C3×#1459semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8932
C3×D3×C22⋊C82
C32×#3242
C3×#45282
C3×#44682
C3×#14593
#681433