Finite Group Databasebeta

← C3×#71126 #11780229

Subgroups — C3×#71126 #11780229

Order 1152.

448 conjugacy classes of subgroups.

The subgroup lattice has 395 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5584C211yesmaximal, characteristic
2C32×#475C211yesmaximal, characteristic, complemented
3C3×#5083C211yesmaximal, characteristic
4C3×#5078C211yesmaximal, characteristic, complemented
5C3×#4535C211yesmaximal, characteristic, complemented
6C3×#4486C211yesmaximal, characteristic, complemented
7C3×#4483C211yesmaximal, characteristic
8C3×#1650—31nomaximal
9#71126C311yesmaximal, characteristic, direct product factor
10C32×C4⋊Q8C2211yescharacteristic
11C32×C4×Q8C2211yescharacteristic
12C3×#946—21no—
13C2×C3×#215—21no—
14C3×#898—22no—
15C3×#892—21no—
16C3×#875—21no—
17C3×C4×D12C2211yescharacteristic
18C3×#869C2211yescharacteristic
19C3×C4×Dic6—21no—
20C32×#106—21no—
21C32×C4⋊C8C2211yescharacteristic
22C32×#103—21no—
23C3×#835—21no—
24C3×#807—22no—
25C3×C4⋊(C3⋊C8)C2211yescharacteristic
26C3×C4×C3⋊C8C2211yescharacteristic
27C3×#556—31no—
28#5584C2×C311yescharacteristic
29C3×#500—31no—
30C3×#475—21no—
31C3×#475D311yescharacteristic, complemented
32C3×#475C2×C311yescharacteristic, complemented
33C3×#461—31no—
34#5083C2×C311yescharacteristic
35#5078C2×C311yescharacteristic, complemented
36C3×#332—31no—
37C3×Q8⋊C8—31no—
38C3×D4⋊C8—31no—
39#4535C2×C311yescharacteristic, complemented
40#4486C2×C311yescharacteristic, complemented
41#4483C2×C311yescharacteristic
42C2×C32×Q8—21no—
43C2×C32×Q8D411yescharacteristic
44C2×C3×D12D411yescharacteristic
45C2×C3×C4×D3—21no—
46C2×C3×Dic6—21no—
47C2×C32×C8—21no—
48C32×C4⋊C4—21no—
49C32×C4⋊C4—21no—
50C32×C4⋊C4—21no—
51C32×C4⋊C4D411yescharacteristic
52C32×C42—21no—
53C32×C42C2311yescharacteristic
54C3×#215—42no—
55C3×(C2×D3)⋊C4—22no—
56C3×(C2×D3)⋊C4—22no—
57C3×(C2×D3)⋊C4—21no—
58C3×C4⋊Dic3—21no—
59C3×C4⋊Dic3D412yes—
60C3×C4⋊Dic3D411yescharacteristic
61C3×Dic3⋊C4—22no—
62C3×C4×Dic3—22no—
63C2×C3×C3⋊C8—21no—
64C2×C3×C3⋊C8—21no—
65#1650—31noSylow
66C2×C3×SD16—61no—
67C3×C4⋊Q8—21no—
68C3×C4⋊Q8—31no—
69C3×C4⋊Q8C2×D311yescharacteristic
70C3×C4⋊Q8C22×C311yescharacteristic
71C3×#126—62no—
72C3×#124—61no—
73C3×C22⋊Q8—61no—
74C3×C4×Q8—21no—
75C3×C4×Q8—61no—
76C3×C4×Q8C2×D311yescharacteristic
77C3×C4×Q8C22×C311yescharacteristic
78C3×C4×D4—31no—
79C3×#117—61no—
80#946—21no—
81C2×#215—21no—
82#898—22no—
83#892—21no—
84#875—21no—
85C4×D12C22×C311yescharacteristic
86#869C22×C311yescharacteristic
87C4×Dic6—21no—
88C3×#107—62no—
89C3×#106—22no—
90C3×#106—21no—
91C3×#106—21no—
92C3×C4⋊C8—21no—
93C3×C4⋊C8—31no—
94C3×C4⋊C8C2×D311yescharacteristic
95C3×C4⋊C8C22×C311yescharacteristic
96C3×#103—22no—
97C3×#103—21no—
98C3×#103—21no—
99C3×#103—61no—
100C3×C4×C8—31no—
101#835—21no—
102#807—22no—
103C4⋊(C3⋊C8)C22×C311yescharacteristic
104C4×C3⋊C8C22×C311yescharacteristic
105C22×C3×D3—21no—
106C32×Q8—21no—
107C32×Q8—21no—
108C32×Q8—41no—
109C32×Q8—41no—
110C2×C32×C4—21no—
111C2×C32×C4—21no—
112C2×C32×C4—41no—
113C2×C32×C4C2×D411yescharacteristic
114C2×C32×C4C2×D411yescharacteristic
115C2×C32×C4C2×D411yescharacteristic
116C2×C3×Dic3—21no—
117C2×C3×Dic3—22no—
118C3×D12—21no—
119C3×D12—21no—
120C3×C4×D3—41no—
121C3×C4×D3—41no—
122C3×Dic6—41no—
123C3×Dic6—41no—
124C32×C8—41no—
125C3×C3⋊C8—22no—
126C3×C3⋊C8—41no—
127#556—31no—
128#500—31no—
129#475C3×D311yescharacteristic, complemented
130#461—31no—
131#332—31no—
132Q8⋊C8—31no—
133D4⋊C8—31no—
134C2×C3×Q8—21no—
135C2×C3×Q8—21no—
136C2×C3×Q8—21no—
137C2×C3×Q8—41no—
138C2×C3×Q8—61no—
139C2×C3×Q8#6711yescharacteristic
140C2×C3×Q8C3×D411yescharacteristic
141C2×C3×D4—31no—
142C22×C3×C4—61no—
143C2×D12C3×D411yescharacteristic
144C2×C4×D3—21no—
145C2×Dic6—21no—
146C3×SD16—122no—
147C2×C3×C8—22no—
148C2×C3×C8—21no—
149C2×C3×C8—21no—
150C2×C3×C8—61no—
151C2×C3×C8—61no—
152C3×C4⋊C4—21no—
153C3×C4⋊C4—21no—
154C3×C4⋊C4—22no—
155C3×C4⋊C4—21no—
156C3×C4⋊C4—21no—
157C3×C4⋊C4—21no—
158C3×C4⋊C4—21no—
159C3×C4⋊C4—21no—
160C3×C4⋊C4—31no—
161C3×C4⋊C4—32no—
162C3×C4⋊C4—41no—
163C3×C4⋊C4—41no—
164C3×C4⋊C4—62no—
165C3×C4⋊C4—61no—
166C3×C4⋊C4#6711yescharacteristic
167C3×C4⋊C4C3×D411yescharacteristic
168C3×C22⋊C4—62no—
169C3×C22⋊C4—62no—
170C3×C22⋊C4—61no—
171C3×C42—21no—
172C3×C42—21no—
173C3×C42—21no—
174C3×C42—41no—
175C3×C42—62no—
176C3×C42C22×D311yescharacteristic
177C3×C42C23×C311yescharacteristic
178#215—42no—
179(C2×D3)⋊C4—22no—
180(C2×D3)⋊C4—22no—
181(C2×D3)⋊C4—21no—
182C4⋊Dic3—21no—
183C4⋊Dic3C3×D412yes—
184C4⋊Dic3C3×D411yescharacteristic
185Dic3⋊C4—22no—
186C4×Dic3—22no—
187C2×C3⋊C8—21no—
188C2×C3⋊C8—21no—
189C22×C32#12011yescharacteristic
190C2×C3×D3—41no—
191C2×C3×D3—41no—
192C2×C3×D3—41no—
193C32×C4—21no—
194C32×C4—41no—
195C32×C4—41no—
196C32×C4—81no—
197C32×C4#13511yescharacteristic
198C32×C4#13511yescharacteristic
199C32×C4AGL(1,ℤ/8)11yescharacteristic
200C32×C4#13711yescharacteristic
201C3×Dic3—42no—
202C3×Dic3—41no—
203C2×SD16—61no—
204C4⋊Q8—31no—
205C4⋊Q8C2×C3×D311yescharacteristic
206#126—62no—
207#124—61no—
208C22⋊Q8—61no—
209C4×Q8—61no—
210C4×Q8C2×C3×D311yescharacteristic
211C4×D4—31no—
212#117—61no—
213#107—62no—
214#106—21no—
215C4⋊C8—31no—
216C4⋊C8C2×C3×D311yescharacteristic
217#103—21no—
218#103—61no—
219C4×C8—31no—
220C23×C3—61no—
221C22×D3—21no—
222C3×Q8—22no—
223C3×Q8—21no—
224C3×Q8—21no—
225C3×Q8—21no—
226C3×Q8—21no—
227C3×Q8—41no—
228C3×Q8—41no—
229C3×Q8—41no—
230C3×Q8—41no—
231C3×Q8—41no—
232C3×Q8—81no—
233C3×Q8—81no—
234C3×Q8—121no—
235C3×Q8—121no—
236C3×D4—61no—
237C3×D4—61no—
238C2×C3×C4—21no—
239C2×C3×C4—21no—
240C2×C3×C4—21no—
241C2×C3×C4—21no—
242C2×C3×C4—21no—
243C2×C3×C4—21no—
244C2×C3×C4—21no—
245C2×C3×C4—41no—
246C2×C3×C4—41no—
247C2×C3×C4—42no—
248C2×C3×C4—41no—
249C2×C3×C4—41no—
250C2×C3×C4—61no—
251C2×C3×C4—62no—
252C2×C3×C4—121no—
253C2×C3×C4—121no—
254C2×C3×C4D3×D411yescharacteristic
255C2×C3×C4D3×D411yescharacteristic
256C2×C3×C4C2×#6711yescharacteristic
257C2×C3×C4C2×C3×D411yescharacteristic
258C2×C3×C4C2×C3×D411yescharacteristic
259C2×C3×C4C2×C3×D411yescharacteristic
260C2×Dic3—21no—
261C2×Dic3—22no—
262D12—21no—
263D12—21no—
264C4×D3—41no—
265C4×D3—41no—
266Dic6—41no—
267Dic6—41no—
268C3×C8—42no—
269C3×C8—41no—
270C3×C8—41no—
271C3×C8—62no—
272C3×C8—121no—
273C3⋊C8—22no—
274C3⋊C8—41no—
275C2×C32#44911yescharacteristic
276C2×C32#45211yescharacteristic
277C2×C32#45611yescharacteristic
278C3×D3—81no—
279C2×Q8—21no—
280C2×Q8—61no—
281C2×Q8C3×#6711yescharacteristic
282C2×D4—31no—
283C22×C4—61no—
284SD16—122no—
285C2×C8—21no—
286C2×C8—61no—
287C2×C8—61no—
288C4⋊C4—21no—
289C4⋊C4—21no—
290C4⋊C4—21no—
291C4⋊C4—31no—
292C4⋊C4—32no—
293C4⋊C4—62no—
294C4⋊C4—61no—
295C4⋊C4C3×#6711yescharacteristic
296C22⋊C4—62no—
297C22⋊C4—62no—
298C22⋊C4—61no—
299C42—21no—
300C42—62no—
301C42C22×C3×D311yescharacteristic
302C22×C3—21no—
303C22×C3—121no—
304C22×C3—121no—
305C22×C3—121no—
306C22×C3#93711yescharacteristic
307C22×C3C3×#12011yescharacteristic
308C2×D3—41no—
309C2×D3—41no—
310C2×D3—41no—
311C3×C4—21no—
312C3×C4—21no—
313C3×C4—21no—
314C3×C4—21no—
315C3×C4—21no—
316C3×C4—21no—
317C3×C4—41no—
318C3×C4—42no—
319C3×C4—41no—
320C3×C4—41no—
321C3×C4—41no—
322C3×C4—41no—
323C3×C4—81no—
324C3×C4—82no—
325C3×C4—81no—
326C3×C4—81no—
327C3×C4—122no—
328C3×C4—121no—
329C3×C4#91411yescharacteristic
330C3×C4#91611yescharacteristic
331C3×C4#94211yescharacteristic
332C3×C4#95011yescharacteristic
333C3×C4C3×#13511yescharacteristic
334C3×C4C3×#13511yescharacteristic
335C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
336C3×C4C3×#13711yescharacteristic
337Dic3—42no—
338Dic3—41no—
339C32#165011yescharacteristic, complemented, Sylow
340C23—61no—
341Q8—21no—
342Q8—21no—
343Q8—41no—
344Q8—41no—
345Q8—121no—
346Q8—121no—
347D4—61no—
348D4—61no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—41no—
352C2×C4—61no—
353C2×C4—62no—
354C2×C4—121no—
355C2×C4—121no—
356C2×C4C3×D3×D411yescharacteristic
357C2×C4C3×D3×D411yescharacteristic
358C2×C4C2×C3×#6711yescharacteristic
359C8—41no—
360C8—62no—
361C8—121no—
362C2×C3—21no—
363C2×C3—21no—
364C2×C3—21no—
365C2×C3—241no—
366C2×C3#504711yescharacteristic
367C2×C3#517211yescharacteristic
368C2×C3#520511yescharacteristic
369C2×C3C3×#44911yescharacteristic
370C2×C3C3×#45211yescharacteristic
371C2×C3C3×#45611yescharacteristic
372D3—81no—
373C22—121no—
374C22—121no—
375C22—121no—
376C22C3×#93711yescharacteristic
377C4—21no—
378C4—41no—
379C4—41no—
380C4—81no—
381C4—122no—
382C4—121no—
383C4C3×#91411yescharacteristic
384C4C3×#91611yescharacteristic
385C4C3×#94211yescharacteristic
386C4C3×#95011yescharacteristic
387C3—21no—
388C3#7112611yescharacteristic, direct product factor
389C3C3×#165011yescharacteristic, complemented
390C2—241no—
391C2C3×#504711yescharacteristic
392C2C3×#517211yescharacteristic
393C2C3×#520511yescharacteristic
subgroupG/H
centerC22×C3#937
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
FittingC32×#475C2
socleC22×C32#120
prime radicalC2×C3×D12D4
hypercenterC3×#475D3
hypocenterC3C3×#1650
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#475

Complements

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

NH ≅ G/Ntype
2. C32×#475C2semidirect
4. C3×#5078C2semidirect
5. C3×#4535C2semidirect
6. C3×#4486C2semidirect
9. #71126C3direct (N × H)
31. C3×#475D3semidirect
32. C3×#475C2×C3semidirect
35. #5078C2×C3semidirect
39. #4535C2×C3semidirect
40. #4486C2×C3semidirect
129. #475C3×D3semidirect
339. C32#1650semidirect
388. C3#71126direct (N × H)
389. C3C3×#1650semidirect

Maximal subgroups

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

subgroupindex
C3×#55842
C32×#4752
C3×#50832
C3×#50782
C3×#45352
C3×#44862
C3×#44832
C3×#16503
#711263