Finite Group Databasebeta

← C3×#79168 #11860727

Subgroups — C3×#79168 #11860727

Order 1152.

1041 conjugacy classes of subgroups.

The subgroup lattice has 453 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#204C211yesmaximal, characteristic
2C3×#5521C211yesmaximal, characteristic
3C3×#5516C211yesmaximal, characteristic, complemented
4C32×#427C211yesmaximal, characteristic, complemented
5C3×#5101C211yesmaximal, characteristic, complemented
6C3×#5004C211yesmaximal, characteristic, complemented
7C3×#5001C211yesmaximal, characteristic
8C3×#4889C214yesmaximal, complemented
9C3×#4852C214yesmaximal, complemented
10C3×#2949—31nomaximal
11#79168C311yesmaximal, characteristic, direct product factor
12C22×C3×D12C2211yescharacteristic
13C22×C3×Dic6C2211yescharacteristic
14C22×C32×C8C2211yescharacteristic
15C32×#117C2211yescharacteristic
16C32×#117C2211yescharacteristic
17C3×#926C2211yescharacteristic
18C2×C3×#208C2211yescharacteristic
19C2×C3×#204C418yescomplemented
20C2×C3×#204C2212yes—
21C2×C3×#204C2212yes—
22C3×#893C2214yes—
23C3×#887C2214yescomplemented
24C3×D3×C22⋊C4—22no—
25C3×#877—22no—
26C3×C4×D12—22no—
27C3×C4×Dic6—22no—
28C32×#107C2212yescomplemented
29C32×#106C2212yescomplemented
30C3×#815C2212yescomplemented
31C3×C8×Dic3C2212yescomplemented
32C3×#810C2214yescomplemented
33C3×#809C2214yes—
34C22×C3×SD16—31no—
35C3×#519—31no—
36C3×#518—31no—
37C22×#204C2×C311yescharacteristic
38#5521C2×C311yescharacteristic
39#5516C2×C311yescharacteristic, complemented
40C3×#440—34no—
41C3×C4×SD16—34no—
42C3×#427—21no—
43C3×#427D311yescharacteristic, complemented
44C3×#427C2×C311yescharacteristic, complemented
45C3×#419—31no—
46C3×#418—31no—
47C3×#405—31no—
48#5101C2×C311yescharacteristic, complemented
49#5004C2×C311yescharacteristic, complemented
50#5001C2×C311yescharacteristic
51#4889C2×C314yescomplemented
52#4852C2×C314yescomplemented
53C23×C3×D3—21no—
54C22×C32×C4C2311yescharacteristic
55C22×C3×Dic3—21no—
56C2×C3×D12—21no—
57C2×C3×D12—22no—
58C2×C3×D12C2×C414yes—
59C2×C3×D12C2312yes—
60C2×C3×C4×D3—24no—
61C2×C3×Dic6—21no—
62C2×C3×Dic6—22no—
63C2×C3×Dic6C2×C414yescomplemented
64C2×C3×Dic6C2312yes—
65C2×C32×C8C2×C414yescomplemented
66C2×C32×C8C2311yescharacteristic
67C2×C32×C8C2311yescharacteristic
68C32×C4⋊C4C2312yes—
69C32×C4⋊C4C2312yes—
70C32×C22⋊C4—21no—
71C32×C22⋊C4—21no—
72C32×C42—21no—
73C32×C42—21no—
74C3×#217D412yes—
75C3×(C2×D3)⋊C4—24no—
76C3×C4⋊Dic3D412yes—
77C3×Dic3⋊C4—24no—
78C3×C4×Dic3—24no—
79C3×C4×Dic3C2312yes—
80C3×#208—22no—
81C2×C3×C3⋊C8C2312yes—
82C3×#204C2×C418yescomplemented
83C3×#204C2×C418yescomplemented
84#2949—31noSylow
85C22×C3×Q8—31no—
86C22×C3×D4—31no—
87C22×D12C22×C311yescharacteristic
88C22×Dic6C22×C311yescharacteristic
89C2×C3×SD16—38no—
90C2×C3×SD16—32no—
91C2×C3×SD16—32no—
92C2×C3×M16—31no—
93C22×C3×C8—21no—
94C22×C3×C8C2×D311yescharacteristic
95C22×C3×C8C22×C311yescharacteristic
96C3×C4×Q8—34no—
97C3×C4×Q8—62no—
98C3×C4×D4—34no—
99C3×C4×D4—62no—
100C3×#117—21no—
101C3×#117—21no—
102C3×#117—31no—
103C3×#117—62no—
104C3×#117C2×D311yescharacteristic
105C3×#117C2×D311yescharacteristic
106C3×#117C22×C311yescharacteristic
107C3×#117C22×C311yescharacteristic
108C2×C3×C22⋊C4—62no—
109#926C22×C311yescharacteristic
110C2×#208C22×C311yescharacteristic
111C2×#204C3×C418yescomplemented
112C2×#204C22×C312yes—
113C2×#204C22×C312yes—
114#893C22×C314yes—
115#887C22×C314yescomplemented
116D3×C22⋊C4—22no—
117#877—22no—
118C4×D12—22no—
119C4×Dic6—22no—
120C3×#107—22no—
121C3×#107C2×D312yescomplemented
122C3×#107C22×C312yescomplemented
123C3×#106—22no—
124C3×#106C2×D312yescomplemented
125C3×#106C22×C312yescomplemented
126C3×#103—34no—
127C3×#102—34no—
128C3×#97—32no—
129C3×C4×C8—32no—
130#815C22×C312yescomplemented
131C8×Dic3C22×C312yescomplemented
132#810C22×C314yescomplemented
133#809C22×C314yes—
134C23×C32C2×D411yescharacteristic
135C22×C3×D3—22no—
136C22×C3×D3—24no—
137C22×C3×D3—82no—
138C2×C32×C4—22no—
139C2×C32×C4—22no—
140C2×C32×C4C22×C412yes—
141C2×C32×C4C2×D411yescharacteristic
142C2×C32×C4#4112yes—
143C2×C32×C4C2411yescharacteristic
144C2×C3×Dic3—24no—
145C2×C3×Dic3—22no—
146C2×C3×Dic3C2×D414yes—
147C3×D12—24no—
148C3×D12—22no—
149C3×D12C22×C414yes—
150C3×C4×D3—84no—
151C3×Dic6—24no—
152C3×Dic6—22no—
153C3×Dic6C22×C414yes—
154C32×C8C22×C412yes—
155C32×C8C22×C412yes—
156C3×C3⋊C8—22no—
157C22×SD16—31no—
158#519—31no—
159#518—31no—
160#440—34no—
161C4×SD16—34no—
162#427C3×D311yescharacteristic, complemented
163#419—31no—
164#418—31no—
165#405—31no—
166C24×C3—61no—
167C23×D3—21no—
168C2×C3×Q8—34no—
169C2×C3×Q8—32no—
170C2×C3×Q8—61no—
171C2×C3×Q8—62no—
172C2×C3×D4—34no—
173C2×C3×D4—32no—
174C2×C3×D4—61no—
175C2×C3×D4—62no—
176C22×C3×C4—21no—
177C22×C3×C4—64no—
178C22×C3×C4—61no—
179C22×C3×C4C22×D311yescharacteristic
180C22×C3×C4C23×C311yescharacteristic
181C22×Dic3—21no—
182C2×D12—21no—
183C2×D12—22no—
184C2×D12C2×C3×C414yes—
185C2×D12C23×C312yes—
186C2×C4×D3—24no—
187C2×Dic6—21no—
188C2×Dic6—22no—
189C2×Dic6C2×C3×C414yescomplemented
190C2×Dic6C23×C312yes—
191C3×SD16—38no—
192C3×SD16—38no—
193C3×M16—62no—
194C2×C3×C8—24no—
195C2×C3×C8—21no—
196C2×C3×C8—21no—
197C2×C3×C8—32no—
198C2×C3×C8C4×D314yescomplemented
199C2×C3×C8C2×C3×C414yescomplemented
200C2×C3×C8C22×D311yescharacteristic
201C2×C3×C8C22×D311yescharacteristic
202C2×C3×C8C23×C311yescharacteristic
203C2×C3×C8C23×C311yescharacteristic
204C3×C4⋊C4—22no—
205C3×C4⋊C4—22no—
206C3×C4⋊C4—32no—
207C3×C4⋊C4—64no—
208C3×C4⋊C4C22×D312yes—
209C3×C4⋊C4C22×D312yes—
210C3×C4⋊C4C23×C312yes—
211C3×C4⋊C4C23×C312yes—
212C3×C22⋊C4—21no—
213C3×C22⋊C4—21no—
214C3×C22⋊C4—21no—
215C3×C22⋊C4—21no—
216C3×C22⋊C4—32no—
217C3×C22⋊C4—41no—
218C3×C22⋊C4—41no—
219C3×C22⋊C4—64no—
220C3×C42—21no—
221C3×C42—21no—
222C3×C42—21no—
223C3×C42—21no—
224C3×C42—32no—
225C3×C42—41no—
226C3×C42—41no—
227C3×C42—64no—
228#217C3×D412yes—
229(C2×D3)⋊C4—24no—
230C4⋊Dic3C3×D412yes—
231Dic3⋊C4—24no—
232C4×Dic3—24no—
233C4×Dic3C23×C312yes—
234#208—22no—
235C2×C3⋊C8C23×C312yes—
236#204C2×C3×C418yescomplemented
237#204C2×C3×C418yescomplemented
238C22×C32—22no—
239C22×C32C4×D412yes—
240C22×C32C22×D411yescharacteristic
241C2×C3×D3—24no—
242C2×C3×D3—44no—
243C2×C3×D3—84no—
244C32×C4—42no—
245C32×C4—42no—
246C32×C4C4×D412yes—
247C32×C4C23×C411yescharacteristic
248C32×C4C2×#4111yescharacteristic
249C3×Dic3—24no—
250C3×Dic3—24no—
251C22×Q8—31no—
252C22×D4—31no—
253C2×SD16—38no—
254C2×SD16—32no—
255C2×SD16—32no—
256C2×M16—31no—
257C22×C8C2×C3×D311yescharacteristic
258C4×Q8—34no—
259C4×Q8—62no—
260C4×D4—34no—
261C4×D4—62no—
262#117—31no—
263#117—62no—
264#117C2×C3×D311yescharacteristic
265#117C2×C3×D311yescharacteristic
266C2×C22⋊C4—62no—
267#107C2×C3×D312yescomplemented
268#106C2×C3×D312yescomplemented
269#103—34no—
270#102—34no—
271#97—32no—
272C4×C8—32no—
273C23×C3—21no—
274C23×C3—62no—
275C23×C3—64no—
276C23×C3—242no—
277C23×C3D3×D411yescharacteristic
278C23×C3C2×C3×D411yescharacteristic
279C22×D3—22no—
280C22×D3—24no—
281C22×D3—82no—
282C3×Q8—34no—
283C3×Q8—64no—
284C3×Q8—62no—
285C3×D4—34no—
286C3×D4—64no—
287C3×D4—62no—
288C2×C3×C4—22no—
289C2×C3×C4—22no—
290C2×C3×C4—22no—
291C2×C3×C4—22no—
292C2×C3×C4—21no—
293C2×C3×C4—22no—
294C2×C3×C4—21no—
295C2×C3×C4—22no—
296C2×C3×C4—34no—
297C2×C3×C4—42no—
298C2×C3×C4—42no—
299C2×C3×C4—64no—
300C2×C3×C4—62no—
301C2×C3×C4—244no—
302C2×C3×C4C2×C4×D312yes—
303C2×C3×C4D3×D411yescharacteristic
304C2×C3×C4#23912yes—
305C2×C3×C4C22×C3×C412yes—
306C2×C3×C4C2×C3×D411yescharacteristic
307C2×C3×C4C3×#4112yes—
308C2×C3×C4C23×D311yescharacteristic
309C2×C3×C4C24×C311yescharacteristic
310C2×Dic3—24no—
311C2×Dic3—22no—
312C2×Dic3C2×C3×D414yes—
313D12—24no—
314D12—22no—
315D12C22×C3×C414yes—
316C4×D3—84no—
317Dic6—24no—
318Dic6—22no—
319Dic6C22×C3×C414yes—
320C3×C8—22no—
321C3×C8—22no—
322C3×C8—62no—
323C3×C8C2×C4×D312yes—
324C3×C8C2×C4×D312yes—
325C3×C8C22×C3×C412yes—
326C3×C8C22×C3×C412yes—
327C3⋊C8—22no—
328C2×C32—22no—
329C2×C32C2×C4×D411yescharacteristic
330C2×C32#57712yes—
331C3×D3—44no—
332C24—61no—
333C2×Q8—32no—
334C2×Q8—34no—
335C2×Q8—61no—
336C2×Q8—62no—
337C2×D4—32no—
338C2×D4—34no—
339C2×D4—61no—
340C2×D4—62no—
341C22×C4—64no—
342C22×C4—61no—
343C22×C4C22×C3×D311yescharacteristic
344SD16—38no—
345SD16—38no—
346M16—62no—
347C2×C8—32no—
348C2×C8C3×C4×D314yescomplemented
349C2×C8C22×C3×D311yescharacteristic
350C2×C8C22×C3×D311yescharacteristic
351C4⋊C4—32no—
352C4⋊C4—64no—
353C4⋊C4C22×C3×D312yes—
354C4⋊C4C22×C3×D312yes—
355C22⋊C4—21no—
356C22⋊C4—21no—
357C22⋊C4—32no—
358C22⋊C4—64no—
359C42—21no—
360C42—21no—
361C42—32no—
362C42—64no—
363C22×C3—22no—
364C22×C3—22no—
365C22×C3—22no—
366C22×C3—21no—
367C22×C3—42no—
368C22×C3—64no—
369C22×C3—124no—
370C22×C3—244no—
371C22×C3#89312yes—
372C22×C3C3×C4×D412yes—
373C22×C3C2×D3×D411yescharacteristic
374C22×C3C22×C3×D411yescharacteristic
375C2×D3—24no—
376C2×D3—44no—
377C2×D3—84no—
378C3×C4—22no—
379C3×C4—21no—
380C3×C4—21no—
381C3×C4—42no—
382C3×C4—42no—
383C3×C4—42no—
384C3×C4—42no—
385C3×C4—64no—
386C3×C4—64no—
387C3×C4—82no—
388C3×C4—82no—
389C3×C4#89312yes—
390C3×C4C3×C4×D412yes—
391C3×C4C22×C4×D311yescharacteristic
392C3×C4C2×#23911yescharacteristic
393C3×C4C23×C3×C411yescharacteristic
394C3×C4C2×C3×#4111yescharacteristic
395Dic3—24no—
396Dic3—24no—
397C32#294911yescharacteristic, complemented, Sylow
398C23—62no—
399C23—64no—
400C23—242no—
401C23C3×D3×D411yescharacteristic
402Q8—34no—
403Q8—64no—
404Q8—62no—
405D4—34no—
406D4—64no—
407D4—62no—
408C2×C4—22no—
409C2×C4—22no—
410C2×C4—34no—
411C2×C4—64no—
412C2×C4—62no—
413C2×C4—244no—
414C2×C4C2×C3×C4×D312yes—
415C2×C4C3×D3×D411yescharacteristic
416C2×C4C3×#23912yes—
417C2×C4C23×C3×D311yescharacteristic
418C8—62no—
419C8C2×C3×C4×D312yes—
420C8C2×C3×C4×D312yes—
421C2×C3—22no—
422C2×C3—22no—
423C2×C3—21no—
424C2×C3—22no—
425C2×C3—42no—
426C2×C3—124no—
427C2×C3C2×#89311yescharacteristic
428C2×C3#577012yes—
429C2×C3C2×C3×C4×D411yescharacteristic
430C2×C3C3×#57712yes—
431D3—44no—
432C22—22no—
433C22—64no—
434C22—124no—
435C22—244no—
436C22C3×#89312yes—
437C22C2×C3×D3×D411yescharacteristic
438C4—42no—
439C4—42no—
440C4—64no—
441C4—64no—
442C4C3×#89312yes—
443C4C22×C3×C4×D311yescharacteristic
444C4C2×C3×#23911yescharacteristic
445C3—21no—
446C3#7916811yescharacteristic, direct product factor
447C3C3×#294911yescharacteristic, complemented
448C2—22no—
449C2—124no—
450C2C2×C3×#89311yescharacteristic
451C2C3×#577012yes—
subgroupG/H
centerC22×C3C2×D3×D4
commutatorC3×C4C23×C3×C4
FrattiniC2×C4C23×C3×D3
FittingC32×#427C2
socleC22×C32C22×D4
prime radicalC22×C3×D12C22
cosocleC2×C3×C4C24×C3
hypercenterC3×#427D3
hypocenterC3C3×#2949
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#427

Complements

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

NH ≅ G/Ntype
3. C3×#5516C2semidirect
4. C32×#427C2semidirect
5. C3×#5101C2semidirect
6. C3×#5004C2semidirect
8. C3×#4889C2semidirect
9. C3×#4852C2semidirect
11. #79168C3direct (N × H)
19. C2×C3×#204C4semidirect
23. C3×#887C22semidirect
28. C32×#107C22semidirect
29. C32×#106C22semidirect
30. C3×#815C22semidirect
31. C3×C8×Dic3C22semidirect
32. C3×#810C22semidirect
39. #5516C2×C3semidirect
43. C3×#427D3semidirect
44. C3×#427C2×C3semidirect
48. #5101C2×C3semidirect
49. #5004C2×C3semidirect
51. #4889C2×C3semidirect
52. #4852C2×C3semidirect
63. C2×C3×Dic6C2×C4semidirect
65. C2×C32×C8C2×C4semidirect
82. C3×#204C2×C4semidirect
83. C3×#204C2×C4semidirect
111. C2×#204C3×C4semidirect
115. #887C22×C3semidirect
121. C3×#107C2×D3semidirect
122. C3×#107C22×C3semidirect
124. C3×#106C2×D3semidirect
125. C3×#106C22×C3semidirect
130. #815C22×C3semidirect
131. C8×Dic3C22×C3semidirect
132. #810C22×C3semidirect
162. #427C3×D3semidirect
189. C2×Dic6C2×C3×C4semidirect
198. C2×C3×C8C4×D3semidirect
199. C2×C3×C8C2×C3×C4semidirect
236. #204C2×C3×C4semidirect
237. #204C2×C3×C4semidirect
267. #107C2×C3×D3semidirect
268. #106C2×C3×D3semidirect
348. C2×C8C3×C4×D3semidirect
397. C32#2949semidirect
446. C3#79168direct (N × H)
447. C3C3×#2949semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#2042
C3×#55212
C3×#55162
C32×#4272
C3×#51012
C3×#50042
C3×#50012
C3×#48892
C3×#48522
C3×#29493
#791683