Finite Group Databasebeta

← C3×#71450 #11796852

Subgroups — C3×#71450 #11796852

Order 1152.

493 conjugacy classes of subgroups.

The subgroup lattice has 377 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#904C211yesmaximal, characteristic
2C2×C32×M32C211yesmaximal, characteristic, complemented
3C3×#5106C211yesmaximal, characteristic, complemented
4C3×#4518C214yesmaximal, complemented
5C3×#2145—31nomaximal
6#71450C311yesmaximal, characteristic, direct product factor
7C2×C3×#235—21no—
8C22×C32×C8C2211yescharacteristic
9C3×#926—21no—
10C2×C3×Dic12C411yescharacteristic, complemented
11C3×#904—21no—
12C3×#904—21no—
13C3×#904C412yescomplemented
14C3×#904C2212yes—
15C2×C3×D24C411yescharacteristic, complemented
16C2×C3×#204—21no—
17C32×M32—21no—
18C32×M32C2212yescomplemented
19C2×C32×C16—21no—
20C3×#818—21no—
21C3×#817C2212yescomplemented
22C2×C3×#135—31no—
23C2×#904C2×C311yescharacteristic
24C2×C3×M32—21no—
25C2×C3×M32D311yescharacteristic, complemented
26C2×C3×M32C2×C311yescharacteristic, complemented
27C3×#427—31no—
28#5106C2×C311yescharacteristic, complemented
29C3×#360—34no—
30#4518C2×C314yescomplemented
31C22×C32×C4D411yescharacteristic
32C2×C3×#67—41no—
33C3×#235—22no—
34C3×#235—22no—
35C3×#235—41no—
36C3×#235—41no—
37C2×C3×D12—21no—
38C2×C3×C4×D3—41no—
39C2×C3×Dic6—21no—
40C2×C32×C8C2×C411yescharacteristic
41C2×C32×C8C2×C411yescharacteristic
42C2×C32×C8D411yescharacteristic
43C2×C32×C8D411yescharacteristic
44C2×C32×C8D411yescharacteristic
45C2×C32×C8C2311yescharacteristic
46C3×#217—41no—
47C3×C4⋊Dic3—22no—
48C3×C4×Dic3—41no—
49C3×Dic12—21no—
50C3×Dic12C2×C412yes—
51C3×D24—21no—
52C3×D24C2×C412yes—
53C3×#204—22no—
54C3×#204—22no—
55C32×C16—22no—
56#2145—31noSylow
57C2×C3×#41—61no—
58C2×#235—21no—
59C3×#135—32no—
60C3×#135—32no—
61C3×#135—61no—
62C3×#135—61no—
63C2×C3×Q16—31no—
64C2×C3×SD16—61no—
65C2×C3×D8—31no—
66C22×C3×C8—21no—
67C22×C3×C8C2×D311yescharacteristic
68C22×C3×C8C22×C311yescharacteristic
69C3×#117—61no—
70#926—21no—
71C2×Dic12C3×C411yescharacteristic, complemented
72#904—21no—
73#904—21no—
74#904C3×C412yescomplemented
75#904C22×C312yes—
76C2×D24C3×C411yescharacteristic, complemented
77C2×#204—21no—
78C3×M32—22no—
79C3×M32—21no—
80C3×M32—21no—
81C3×M32—22no—
82C3×M32C2×D312yescomplemented
83C3×M32C22×C312yescomplemented
84C2×C3×C16—22no—
85C2×C3×C16—21no—
86C2×C3×C16—21no—
87C3×#107—61no—
88C3×#106—32no—
89#818—21no—
90#817C22×C312yescomplemented
91C23×C32D811yescharacteristic
92C22×C3×D3—41no—
93C2×C32×C4C22⋊C411yescharacteristic
94C2×C32×C4C22⋊C411yescharacteristic
95C2×C32×C4D811yescharacteristic
96C2×C32×C4SD1611yescharacteristic
97C2×C32×C4SD1611yescharacteristic
98C2×C32×C4C2×D411yescharacteristic
99C3×#67—42no—
100C3×#67—42no—
101C2×C3×Dic3—41no—
102C2×C3×Dic3—42no—
103C3×D12—22no—
104C3×D12—41no—
105C3×C4×D3—42no—
106C3×C4×D3—42no—
107C3×Dic6—22no—
108C3×Dic6—41no—
109C32×C8C22⋊C411yescharacteristic
110C32×C8C22⋊C411yescharacteristic
111C32×C8C22×C411yescharacteristic
112C32×C8C2×D411yescharacteristic
113C2×#135—31no—
114C2×M32C3×D311yescharacteristic, complemented
115#427—31no—
116#360—34no—
117C3×#41—62no—
118C3×#41—62no—
119C3×#41—121no—
120C3×#41—121no—
121C2×C3×Q8—61no—
122C2×C3×D4—61no—
123C2×C3×D4—121no—
124C22×C3×C4—21no—
125C22×C3×C4—121no—
126C22×C3×C4D1211yescharacteristic
127C22×C3×C4C3×D411yescharacteristic
128C2×#67—41no—
129#235—22no—
130#235—22no—
131#235—41no—
132#235—41no—
133C2×D12—21no—
134C2×C4×D3—41no—
135C2×Dic6—21no—
136C3×Q16—32no—
137C3×Q16—61no—
138C3×SD16—62no—
139C3×SD16—62no—
140C3×D8—32no—
141C3×D8—61no—
142C2×C3×C8—21no—
143C2×C3×C8—21no—
144C2×C3×C8—21no—
145C2×C3×C8—21no—
146C2×C3×C8—21no—
147C2×C3×C8—21no—
148C2×C3×C8C4×D311yescharacteristic
149C2×C3×C8C4×D311yescharacteristic
150C2×C3×C8D1211yescharacteristic
151C2×C3×C8#6711yescharacteristic
152C2×C3×C8#6711yescharacteristic
153C2×C3×C8C2×C3×C411yescharacteristic
154C2×C3×C8C2×C3×C411yescharacteristic
155C2×C3×C8C3×D411yescharacteristic
156C2×C3×C8C3×D411yescharacteristic
157C2×C3×C8C3×D411yescharacteristic
158C2×C3×C8C22×D311yescharacteristic
159C2×C3×C8C23×C311yescharacteristic
160C3×C4⋊C4—62no—
161C3×C22⋊C4—121no—
162C3×C42—121no—
163#217—41no—
164C4⋊Dic3—22no—
165C4×Dic3—41no—
166Dic12—21no—
167Dic12C2×C3×C412yes—
168D24—21no—
169D24C2×C3×C412yes—
170#204—22no—
171#204—22no—
172C3×C16—24no—
173C3×C16—22no—
174C3×C16—22no—
175C22×C32—41no—
176C22×C32#10211yescharacteristic
177C22×C32#10211yescharacteristic
178C22×C32C2×D811yescharacteristic
179C2×C3×D3—42no—
180C2×C3×D3—82no—
181C32×C4#10211yescharacteristic
182C32×C4#10211yescharacteristic
183C32×C4C2×C22⋊C411yescharacteristic
184C32×C4C2×SD1611yescharacteristic
185C3×Dic3—42no—
186C3×Dic3—82no—
187C2×#41—61no—
188#135—32no—
189#135—32no—
190#135—61no—
191#135—61no—
192C2×Q16—31no—
193C2×SD16—61no—
194C2×D8—31no—
195C22×C8C2×C3×D311yescharacteristic
196#117—61no—
197M32—21no—
198M32C2×C3×D312yescomplemented
199C2×C16—21no—
200#107—61no—
201#106—32no—
202C23×C3—21no—
203C23×C3—121no—
204C23×C3D2411yescharacteristic
205C23×C3C3×D811yescharacteristic
206C22×D3—41no—
207C3×Q8—62no—
208C3×Q8—121no—
209C3×D4—62no—
210C3×D4—122no—
211C3×D4—122no—
212C3×D4—121no—
213C2×C3×C4—21no—
214C2×C3×C4—21no—
215C2×C3×C4—21no—
216C2×C3×C4—21no—
217C2×C3×C4—21no—
218C2×C3×C4—21no—
219C2×C3×C4—121no—
220C2×C3×C4—122no—
221C2×C3×C4—122no—
222C2×C3×C4—122no—
223C2×C3×C4#20411yescharacteristic
224C2×C3×C4#20411yescharacteristic
225C2×C3×C4D2411yescharacteristic
226C2×C3×C4(C2×D3)⋊C411yescharacteristic
227C2×C3×C4(C2×D3)⋊C411yescharacteristic
228C2×C3×C4C3×C22⋊C411yescharacteristic
229C2×C3×C4C3×C22⋊C411yescharacteristic
230C2×C3×C4C3×D811yescharacteristic
231C2×C3×C4C3×SD1611yescharacteristic
232C2×C3×C4C3×SD1611yescharacteristic
233C2×C3×C4C2×D1211yescharacteristic
234C2×C3×C4C2×C3×D411yescharacteristic
235#67—42no—
236#67—42no—
237C2×Dic3—41no—
238C2×Dic3—42no—
239D12—22no—
240D12—41no—
241C4×D3—42no—
242C4×D3—42no—
243Dic6—22no—
244Dic6—41no—
245C3×C8—21no—
246C3×C8—21no—
247C3×C8—21no—
248C3×C8—21no—
249C3×C8(C2×D3)⋊C411yescharacteristic
250C3×C8(C2×D3)⋊C411yescharacteristic
251C3×C8C3×C22⋊C411yescharacteristic
252C3×C8C3×C22⋊C411yescharacteristic
253C3×C8C2×C4×D311yescharacteristic
254C3×C8C2×#6711yescharacteristic
255C3×C8C22×C3×C411yescharacteristic
256C3×C8C2×C3×D411yescharacteristic
257C2×C32—21no—
258C2×C32—21no—
259C2×C32—21no—
260C2×C32C2×#10211yescharacteristic
261C3×D3—82no—
262#41—62no—
263#41—62no—
264#41—121no—
265#41—121no—
266C2×Q8—61no—
267C2×D4—61no—
268C2×D4—121no—
269C22×C4—121no—
270C22×C4C3×D1211yescharacteristic
271Q16—32no—
272Q16—61no—
273SD16—62no—
274SD16—62no—
275D8—32no—
276D8—61no—
277C2×C8C3×C4×D311yescharacteristic
278C2×C8C3×C4×D311yescharacteristic
279C2×C8C3×D1211yescharacteristic
280C2×C8C3×#6711yescharacteristic
281C2×C8C3×#6711yescharacteristic
282C2×C8C22×C3×D311yescharacteristic
283C4⋊C4—62no—
284C22⋊C4—121no—
285C42—121no—
286C16—22no—
287C22×C3—21no—
288C22×C3—21no—
289C22×C3—21no—
290C22×C3—41no—
291C22×C3—41no—
292C22×C3—42no—
293C22×C3—122no—
294C22×C3—242no—
295C22×C3#82111yescharacteristic
296C22×C3#82111yescharacteristic
297C22×C3C3×#10211yescharacteristic
298C22×C3C3×#10211yescharacteristic
299C22×C3C2×D2411yescharacteristic
300C22×C3C2×C3×D811yescharacteristic
301C2×D3—42no—
302C2×D3—82no—
303C3×C4—21no—
304C3×C4—21no—
305C3×C4—21no—
306C3×C4—21no—
307C3×C4—122no—
308C3×C4—242no—
309C3×C4#82111yescharacteristic
310C3×C4#82111yescharacteristic
311C3×C4C3×#10211yescharacteristic
312C3×C4C3×#10211yescharacteristic
313C3×C4C2×#20411yescharacteristic
314C3×C4C2×(C2×D3)⋊C411yescharacteristic
315C3×C4C2×C3×C22⋊C411yescharacteristic
316C3×C4C2×C3×SD1611yescharacteristic
317Dic3—42no—
318Dic3—82no—
319C32#214511yescharacteristic, complemented, Sylow
320C23—121no—
321C23C3×D2411yescharacteristic
322Q8—62no—
323Q8—121no—
324D4—62no—
325D4—122no—
326D4—122no—
327D4—121no—
328C2×C4—121no—
329C2×C4—122no—
330C2×C4—122no—
331C2×C4—122no—
332C2×C4C3×#20411yescharacteristic
333C2×C4C3×#20411yescharacteristic
334C2×C4C3×D2411yescharacteristic
335C2×C4C3×(C2×D3)⋊C411yescharacteristic
336C2×C4C3×(C2×D3)⋊C411yescharacteristic
337C2×C4C2×C3×D1211yescharacteristic
338C8C3×(C2×D3)⋊C411yescharacteristic
339C8C3×(C2×D3)⋊C411yescharacteristic
340C8C2×C3×C4×D311yescharacteristic
341C8C2×C3×#6711yescharacteristic
342C2×C3—22no—
343C2×C3—21no—
344C2×C3—21no—
345C2×C3—21no—
346C2×C3—21no—
347C2×C3—21no—
348C2×C3—21no—
349C2×C3—21no—
350C2×C3—41no—
351C2×C3—41no—
352C2×C3—242no—
353C2×C3C2×#82111yescharacteristic
354C2×C3C2×C3×#10211yescharacteristic
355D3—82no—
356C22—41no—
357C22—122no—
358C22—242no—
359C22C3×#82111yescharacteristic
360C22C3×#82111yescharacteristic
361C22C2×C3×D2411yescharacteristic
362C4—122no—
363C4—242no—
364C4C3×#82111yescharacteristic
365C4C3×#82111yescharacteristic
366C4C2×C3×#20411yescharacteristic
367C4C2×C3×(C2×D3)⋊C411yescharacteristic
368C3—21no—
369C3#7145011yescharacteristic, direct product factor
370C3C3×#214511yescharacteristic, complemented
371C2—21no—
372C2—21no—
373C2—21no—
374C2—242no—
375C2C2×C3×#82111yescharacteristic
subgroupG/H
centerC3×C4#821
commutatorC3×C8C22×C3×C4
FrattiniC2×C8C22×C3×D3
FittingC2×C32×M32C2
socleC2×C32C2×#102
prime radicalC2×C3×#904C2
cosocleC2×C3×C8C23×C3
hypercenterC2×C3×M32D3
hypocenterC3C3×#2145
LCSG ▷ C3×C8 ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C3×C4 ◁ C22×C3×C4 ◁ C22×C3×C8 ◁ C2×C3×M32

Complements

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

NH ≅ G/Ntype
2. C2×C32×M32C2semidirect
3. C3×#5106C2semidirect
4. C3×#4518C2semidirect
6. #71450C3direct (N × H)
10. C2×C3×Dic12C4semidirect
13. C3×#904C4semidirect
15. C2×C3×D24C4semidirect
18. C32×M32C22semidirect
21. C3×#817C22semidirect
25. C2×C3×M32D3semidirect
26. C2×C3×M32C2×C3semidirect
28. #5106C2×C3semidirect
30. #4518C2×C3semidirect
71. C2×Dic12C3×C4semidirect
74. #904C3×C4semidirect
76. C2×D24C3×C4semidirect
82. C3×M32C2×D3semidirect
83. C3×M32C22×C3semidirect
90. #817C22×C3semidirect
114. C2×M32C3×D3semidirect
198. M32C2×C3×D3semidirect
319. C32#2145semidirect
369. C3#71450direct (N × H)
370. C3C3×#2145semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9042
C2×C32×M322
C3×#51062
C3×#45182
C3×#21453
#714503