Finite Group Databasebeta

← C3×#79136 #11860857

Subgroups — C3×#79136 #11860857

Order 1152.

1033 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#904C211yesmaximal, characteristic
2C3×#5504C212yesmaximal, complemented
3C2×C32×#107C211yesmaximal, characteristic, complemented
4C3×#5101C211yesmaximal, characteristic, complemented
5C3×#4966C212yesmaximal, complemented
6C3×#4889C214yesmaximal, complemented
7C3×#4873C212yesmaximal, complemented
8C3×#4872C212yesmaximal, complemented
9C3×#2951—31nomaximal
10#79136C311yesmaximal, characteristic, direct product factor
11C2×C3×#235C2212yes—
12C22×C32×C8C2211yescharacteristic
13C2×C32×C4⋊C4C2212yes—
14C3×C4×#67—24no—
15C3×#926C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C2×C3×Dic12C2211yescharacteristic
18C3×#904C418yescomplemented
19C2×C3×D24C2211yescharacteristic
20C2×C3×#204C2212yes—
21C3×#893C2214yes—
22C3×#892—22no—
23C3×D3×C4⋊C4—22no—
24C3×#887C2214yes—
25C32×#107C2212yes—
26C32×#107C2212yes—
27C3×#815C2212yes—
28C3×C8×Dic3C2212yes—
29C3×#810C2214yes—
30C3×#809C2214yes—
31C2×C3×#135—31no—
32C3×#520—32no—
33C2×#904C2×C311yescharacteristic
34#5504C2×C312yescomplemented
35C3×#440—34no—
36C3×C4×Q16—32no—
37C3×C4×D8—32no—
38C2×C3×#107—21no—
39C2×C3×#107D311yescharacteristic, complemented
40C2×C3×#107C2×C311yescharacteristic, complemented
41C3×#417—32no—
42C3×#405—31no—
43#5101C2×C311yescharacteristic, complemented
44#4966C2×C312yescomplemented
45#4889C2×C314yescomplemented
46#4873C2×C312yescomplemented
47#4872C2×C312yescomplemented
48C22×C32×C4—22no—
49C22×C32×C4C2311yescharacteristic
50C2×C3×#67—22no—
51C3×#235—24no—
52C3×#235C2×C418yescomplemented
53C2×C3×D12C2312yes—
54C2×C3×C4×D3—22no—
55C2×C3×C4×D3—24no—
56C2×C3×Dic6C2312yes—
57C2×C32×C8C2×C414yescomplemented
58C2×C32×C8C2311yescharacteristic
59C2×C32×C8C2311yescharacteristic
60C32×C4⋊C4—22no—
61C32×C4⋊C4C2314yes—
62C3×#217D412yes—
63C3×(C2×D3)⋊C4—24no—
64C3×C4⋊Dic3D411yescharacteristic
65C3×C4⋊Dic3D411yescharacteristic
66C3×Dic3⋊C4—24no—
67C3×C4×Dic3—24no—
68C3×C4×Dic3C2312yes—
69C3×#208—22no—
70C2×C3×C3⋊C8C2312yes—
71C3×Dic12C2×C414yescomplemented
72C3×D24C2×C414yescomplemented
73C3×#204C2×C418yescomplemented
74#2951—31noSylow
75C2×C3×#41—32no—
76C2×#235C22×C312yes—
77C3×#135—38no—
78C2×C3×Q16—31no—
79C2×C3×SD16—32no—
80C2×C3×D8—31no—
81C2×C3×M16—31no—
82C22×C3×C8—21no—
83C22×C3×C8C2×D311yescharacteristic
84C22×C3×C8C22×C311yescharacteristic
85C3×C4×Q8—34no—
86C3×C4×D4—34no—
87C3×C4×D4—64no—
88C3×#117—31no—
89C3×#117—62no—
90C2×C3×C4⋊C4—22no—
91C2×C3×C4⋊C4—62no—
92C2×C3×C4⋊C4C2×D312yes—
93C2×C3×C4⋊C4C22×C312yes—
94C4×#67—24no—
95#926C22×C311yescharacteristic
96C2×#208C22×C311yescharacteristic
97C2×Dic12C22×C311yescharacteristic
98#904C3×C418yescomplemented
99C2×D24C22×C311yescharacteristic
100C2×#204C22×C312yes—
101#893C22×C314yes—
102#892—22no—
103D3×C4⋊C4—22no—
104#887C22×C314yes—
105C3×#107—22no—
106C3×#107—22no—
107C3×#107C2×D312yes—
108C3×#107C2×D312yes—
109C3×#107C22×C312yes—
110C3×#107C22×C312yes—
111C3×#103—34no—
112C3×#102—34no—
113C3×#97—32no—
114C3×C4×C8—32no—
115#815C22×C312yes—
116C8×Dic3C22×C312yes—
117#810C22×C314yes—
118#809C22×C314yes—
119C23×C32C2×D411yescharacteristic
120C22×C3×D3—22no—
121C2×C32×C4—24no—
122C2×C32×C4—82no—
123C2×C32×C4C22×C412yes—
124C2×C32×C4C2×D411yescharacteristic
125C2×C32×C4#4112yes—
126C2×C32×C4C2411yescharacteristic
127C3×#67—28no—
128C2×C3×Dic3—22no—
129C2×C3×Dic3C2×D412yes—
130C2×C3×Dic3C2×D412yes—
131C3×D12—22no—
132C3×D12C22×C414yes—
133C3×C4×D3—28no—
134C3×C4×D3—84no—
135C3×Dic6—22no—
136C3×Dic6C22×C414yes—
137C32×C8C22×C412yes—
138C32×C8C22×C412yes—
139C3×C3⋊C8—22no—
140C2×#135—31no—
141#520—32no—
142#440—34no—
143C4×Q16—32no—
144C4×D8—32no—
145C2×#107C3×D311yescharacteristic, complemented
146#417—32no—
147#405—31no—
148C3×#41—38no—
149C3×#41—64no—
150C2×C3×Q8—32no—
151C2×C3×D4—32no—
152C2×C3×D4—62no—
153C22×C3×C4—22no—
154C22×C3×C4—22no—
155C22×C3×C4—21no—
156C22×C3×C4—42no—
157C22×C3×C4—64no—
158C22×C3×C4—62no—
159C22×C3×C4C22×D311yescharacteristic
160C22×C3×C4C23×C311yescharacteristic
161C2×#67—22no—
162#235—24no—
163#235C2×C3×C418yescomplemented
164C2×D12C23×C312yes—
165C2×C4×D3—22no—
166C2×C4×D3—24no—
167C2×Dic6C23×C312yes—
168C3×Q16—34no—
169C3×SD16—38no—
170C3×D8—34no—
171C3×M16—62no—
172C2×C3×C8—24no—
173C2×C3×C8—21no—
174C2×C3×C8—21no—
175C2×C3×C8—32no—
176C2×C3×C8C4×D314yescomplemented
177C2×C3×C8C2×C3×C414yescomplemented
178C2×C3×C8C22×D311yescharacteristic
179C2×C3×C8C22×D311yescharacteristic
180C2×C3×C8C23×C311yescharacteristic
181C2×C3×C8C23×C311yescharacteristic
182C3×C4⋊C4—22no—
183C3×C4⋊C4—22no—
184C3×C4⋊C4—24no—
185C3×C4⋊C4—31no—
186C3×C4⋊C4—31no—
187C3×C4⋊C4—42no—
188C3×C4⋊C4—64no—
189C3×C4⋊C4C22×D314yes—
190C3×C4⋊C4C23×C314yes—
191C3×C22⋊C4—32no—
192C3×C22⋊C4—64no—
193C3×C42—32no—
194C3×C42—64no—
195#217C3×D412yes—
196(C2×D3)⋊C4—24no—
197C4⋊Dic3C3×D411yescharacteristic
198C4⋊Dic3C3×D411yescharacteristic
199Dic3⋊C4—24no—
200C4×Dic3—24no—
201C4×Dic3C23×C312yes—
202#208—22no—
203C2×C3⋊C8C23×C312yes—
204Dic12C2×C3×C414yescomplemented
205D24C2×C3×C414yescomplemented
206#204C2×C3×C418yescomplemented
207C22×C32—21no—
208C22×C32—21no—
209C22×C32C4×D412yes—
210C22×C32C22×D411yescharacteristic
211C2×C3×D3—24no—
212C2×C3×D3—42no—
213C2×C3×D3—42no—
214C32×C4—44no—
215C32×C4C4×D412yes—
216C32×C4C23×C411yescharacteristic
217C32×C4C2×#4111yescharacteristic
218C3×Dic3—24no—
219C3×Dic3—22no—
220C3×Dic3—22no—
221C2×#41—32no—
222#135—38no—
223C2×Q16—31no—
224C2×SD16—32no—
225C2×D8—31no—
226C2×M16—31no—
227C22×C8C2×C3×D311yescharacteristic
228C4×Q8—34no—
229C4×D4—34no—
230C4×D4—64no—
231#117—31no—
232#117—62no—
233C2×C4⋊C4—62no—
234C2×C4⋊C4C2×C3×D312yes—
235#107C2×C3×D312yes—
236#107C2×C3×D312yes—
237#103—34no—
238#102—34no—
239#97—32no—
240C4×C8—32no—
241C23×C3—21no—
242C23×C3—62no—
243C23×C3D3×D411yescharacteristic
244C23×C3C2×C3×D411yescharacteristic
245C22×D3—22no—
246C3×Q8—34no—
247C3×Q8—62no—
248C3×D4—34no—
249C3×D4—68no—
250C3×D4—62no—
251C2×C3×C4—24no—
252C2×C3×C4—24no—
253C2×C3×C4—21no—
254C2×C3×C4—22no—
255C2×C3×C4—21no—
256C2×C3×C4—22no—
257C2×C3×C4—32no—
258C2×C3×C4—32no—
259C2×C3×C4—44no—
260C2×C3×C4—62no—
261C2×C3×C4—68no—
262C2×C3×C4—82no—
263C2×C3×C4—82no—
264C2×C3×C4—84no—
265C2×C3×C4—244no—
266C2×C3×C4C2×C4×D312yes—
267C2×C3×C4D3×D411yescharacteristic
268C2×C3×C4#23912yes—
269C2×C3×C4C22×C3×C412yes—
270C2×C3×C4C2×C3×D411yescharacteristic
271C2×C3×C4C3×#4112yes—
272C2×C3×C4C23×D311yescharacteristic
273C2×C3×C4C24×C311yescharacteristic
274#67—28no—
275C2×Dic3—22no—
276C2×Dic3C2×C3×D412yes—
277C2×Dic3C2×C3×D412yes—
278D12—22no—
279D12C22×C3×C414yes—
280C4×D3—28no—
281C4×D3—84no—
282Dic6—22no—
283Dic6C22×C3×C414yes—
284C3×C8—22no—
285C3×C8—22no—
286C3×C8—62no—
287C3×C8C2×C4×D312yes—
288C3×C8C2×C4×D312yes—
289C3×C8C22×C3×C412yes—
290C3×C8C22×C3×C412yes—
291C3⋊C8—22no—
292C2×C32—22no—
293C2×C32C2×C4×D411yescharacteristic
294C2×C32#57611yescharacteristic
295C2×C32#57811yescharacteristic
296C3×D3—44no—
297#41—38no—
298#41—64no—
299C2×Q8—32no—
300C2×D4—32no—
301C2×D4—62no—
302C22×C4—22no—
303C22×C4—64no—
304C22×C4—62no—
305C22×C4C22×C3×D311yescharacteristic
306Q16—34no—
307SD16—38no—
308D8—34no—
309M16—62no—
310C2×C8—32no—
311C2×C8C3×C4×D314yescomplemented
312C2×C8C22×C3×D311yescharacteristic
313C2×C8C22×C3×D311yescharacteristic
314C4⋊C4—22no—
315C4⋊C4—31no—
316C4⋊C4—31no—
317C4⋊C4—64no—
318C4⋊C4C22×C3×D314yes—
319C22⋊C4—32no—
320C22⋊C4—64no—
321C42—32no—
322C42—64no—
323C22×C3—22no—
324C22×C3—22no—
325C22×C3—21no—
326C22×C3—21no—
327C22×C3—21no—
328C22×C3—21no—
329C22×C3—22no—
330C22×C3—21no—
331C22×C3—64no—
332C22×C3—122no—
333C22×C3—122no—
334C22×C3#89312yes—
335C22×C3C3×C4×D412yes—
336C22×C3C2×D3×D411yescharacteristic
337C22×C3C22×C3×D411yescharacteristic
338C2×D3—24no—
339C2×D3—42no—
340C2×D3—42no—
341C3×C4—22no—
342C3×C4—21no—
343C3×C4—21no—
344C3×C4—44no—
345C3×C4—44no—
346C3×C4—62no—
347C3×C4—64no—
348C3×C4—62no—
349C3×C4—84no—
350C3×C4#89312yes—
351C3×C4C3×C4×D412yes—
352C3×C4C22×C4×D311yescharacteristic
353C3×C4C2×#23911yescharacteristic
354C3×C4C23×C3×C411yescharacteristic
355C3×C4C2×C3×#4111yescharacteristic
356Dic3—22no—
357Dic3—22no—
358Dic3—24no—
359C32#295111yescharacteristic, complemented, Sylow
360C23—62no—
361C23C3×D3×D411yescharacteristic
362Q8—34no—
363Q8—62no—
364D4—34no—
365D4—68no—
366D4—62no—
367C2×C4—24no—
368C2×C4—32no—
369C2×C4—32no—
370C2×C4—62no—
371C2×C4—68no—
372C2×C4—82no—
373C2×C4—244no—
374C2×C4C2×C3×C4×D312yes—
375C2×C4C3×D3×D411yescharacteristic
376C2×C4C3×#23912yes—
377C2×C4C23×C3×D311yescharacteristic
378C8—62no—
379C8C2×C3×C4×D312yes—
380C8C2×C3×C4×D312yes—
381C2×C3—24no—
382C2×C3—22no—
383C2×C3—22no—
384C2×C3—21no—
385C2×C3—21no—
386C2×C3—21no—
387C2×C3—124no—
388C2×C3C2×#89311yescharacteristic
389C2×C3#575711yescharacteristic
390C2×C3#576611yescharacteristic
391C2×C3C2×C3×C4×D411yescharacteristic
392C2×C3C3×#57611yescharacteristic
393C2×C3C3×#57811yescharacteristic
394D3—44no—
395C22—21no—
396C22—21no—
397C22—64no—
398C22—122no—
399C22—122no—
400C22C3×#89312yes—
401C22C2×C3×D3×D411yescharacteristic
402C4—44no—
403C4—62no—
404C4—64no—
405C4—62no—
406C4C3×#89312yes—
407C4C22×C3×C4×D311yescharacteristic
408C4C2×C3×#23911yescharacteristic
409C3—21no—
410C3#7913611yescharacteristic, direct product factor
411C3C3×#295111yescharacteristic, complemented
412C2—22no—
413C2—124no—
414C2C2×C3×#89311yescharacteristic
415C2C3×#575711yescharacteristic
416C2C3×#576611yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutatorC3×C4C23×C3×C4
FrattiniC2×C4C23×C3×D3
FittingC2×C32×#107C2
socleC22×C32C22×D4
prime radicalC2×C3×#904C2
cosocleC2×C3×C4C24×C3
hypercenterC2×C3×#107D3
hypocenterC3C3×#2951
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C2×C3×#107

Complements

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

NH ≅ G/Ntype
2. C3×#5504C2semidirect
3. C2×C32×#107C2semidirect
4. C3×#5101C2semidirect
5. C3×#4966C2semidirect
6. C3×#4889C2semidirect
7. C3×#4873C2semidirect
8. C3×#4872C2semidirect
10. #79136C3direct (N × H)
18. C3×#904C4semidirect
34. #5504C2×C3semidirect
39. C2×C3×#107D3semidirect
40. C2×C3×#107C2×C3semidirect
43. #5101C2×C3semidirect
44. #4966C2×C3semidirect
45. #4889C2×C3semidirect
46. #4873C2×C3semidirect
47. #4872C2×C3semidirect
52. C3×#235C2×C4semidirect
57. C2×C32×C8C2×C4semidirect
71. C3×Dic12C2×C4semidirect
72. C3×D24C2×C4semidirect
73. C3×#204C2×C4semidirect
98. #904C3×C4semidirect
145. C2×#107C3×D3semidirect
163. #235C2×C3×C4semidirect
176. C2×C3×C8C4×D3semidirect
177. C2×C3×C8C2×C3×C4semidirect
204. Dic12C2×C3×C4semidirect
205. D24C2×C3×C4semidirect
206. #204C2×C3×C4semidirect
311. C2×C8C3×C4×D3semidirect
359. C32#2951semidirect
410. C3#79136direct (N × H)
411. C3C3×#2951semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9042
C3×#55042
C2×C32×#1072
C3×#51012
C3×#49662
C3×#48892
C3×#48732
C3×#48722
C3×#29513
#791363