Finite Group Databasebeta

← C3×#68533 #11777028

Subgroups — C3×#68533 #11777028

Order 1152.

327 conjugacy classes of subgroups.

The subgroup lattice has 326 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#4835C211yesmaximal, characteristic
2C3×#4833C211yesmaximal, characteristic
3C3×#4685C211yesmaximal, characteristic
4C32×#334C211yesmaximal, characteristic, complemented
5C3×#4479C211yesmaximal, characteristic, complemented
6C3×#4479C211yesmaximal, characteristic, complemented
7C3×#4457C211yesmaximal, characteristic, complemented
8C3×#1572—31nomaximal
9#68533C311yesmaximal, characteristic, direct product factor
10C3×C42×D3C2211yescharacteristic
11C32×C4⋊C8C2211yescharacteristic
12C32×C4⋊C8C2211yescharacteristic
13C32×C4×C8C2211yescharacteristic
14C3×(C2×D3)⋊C8—21no—
15C3×(C2×D3)⋊C8—21no—
16C3×(C2×D3)⋊C8C411yescharacteristic
17C3×(C2×D3)⋊C8C411yescharacteristic
18C3×#815—21no—
19C3×Dic3⋊C8C411yescharacteristic
20C3×Dic3⋊C8C411yescharacteristic
21C3×C8×Dic3—21no—
22C3×C4⋊(C3⋊C8)C2211yescharacteristic
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×C4×C3⋊C8C2211yescharacteristic
25C3×#432—31no—
26C3×#431—31no—
27C3×#431—31no—
28#4835C2×C311yescharacteristic
29#4833C2×C311yescharacteristic
30#4685C2×C311yescharacteristic
31C3×#335—31no—
32C3×#335—31no—
33C3×#334—21no—
34C3×#334—31no—
35C3×#334D311yescharacteristic, complemented
36C3×#334C2×C311yescharacteristic, complemented
37#4479C2×C311yescharacteristic, complemented
38#4479C2×C311yescharacteristic, complemented
39#4457C2×C311yescharacteristic, complemented
40C2×C3×C4×D3C2×C411yescharacteristic
41C2×C3×C4×D3D411yescharacteristic
42C2×C3×C4×D3Q811yescharacteristic
43C2×C32×C8—21no—
44C2×C32×C8—21no—
45C2×C32×C8C2×C411yescharacteristic
46C2×C32×C8C2×C411yescharacteristic
47C32×C42C2311yescharacteristic
48C3×C4×Dic3C2×C411yescharacteristic
49C3×C4×Dic3D411yescharacteristic
50C3×C4×Dic3Q811yescharacteristic
51C2×C3×C3⋊C8—21no—
52C2×C3×C3⋊C8—21no—
53C2×C3×C3⋊C8C2×C411yescharacteristic
54C2×C3×C3⋊C8C2×C411yescharacteristic
55#1572—31noSylow
56C2×C3×C42—31no—
57C42×D3C22×C311yescharacteristic
58C3×C4⋊C8—21no—
59C3×C4⋊C8—21no—
60C3×C4⋊C8—31no—
61C3×C4⋊C8—31no—
62C3×C4⋊C8—31no—
63C3×C4⋊C8—31no—
64C3×C4⋊C8C2×D311yescharacteristic
65C3×C4⋊C8C2×D311yescharacteristic
66C3×C4⋊C8C22×C311yescharacteristic
67C3×C4⋊C8C22×C311yescharacteristic
68C3×C22⋊C8—31no—
69C3×C22⋊C8—31no—
70C3×C22⋊C8—61no—
71C3×C22⋊C8—61no—
72C3×#97—61no—
73C3×C4×C8—21no—
74C3×C4×C8—31no—
75C3×C4×C8—61no—
76C3×C4×C8C2×D311yescharacteristic
77C3×C4×C8C22×C311yescharacteristic
78(C2×D3)⋊C8—21no—
79(C2×D3)⋊C8—21no—
80(C2×D3)⋊C8C3×C411yescharacteristic
81(C2×D3)⋊C8C3×C411yescharacteristic
82#815—21no—
83Dic3⋊C8C3×C411yescharacteristic
84Dic3⋊C8C3×C411yescharacteristic
85C8×Dic3—21no—
86C4⋊(C3⋊C8)C22×C311yescharacteristic
87C4⋊(C3⋊C8)C22×C311yescharacteristic
88C4×C3⋊C8C22×C311yescharacteristic
89C22×C3×D3C4⋊C411yescharacteristic
90C2×C32×C4C22×C411yescharacteristic
91C2×C32×C4C2×D411yescharacteristic
92C2×C32×C4C2×Q811yescharacteristic
93C2×C3×Dic3C4⋊C411yescharacteristic
94C2×C3×Dic3C4⋊C411yescharacteristic
95C2×C3×Dic3C4⋊C411yescharacteristic
96C3×C4×D3—21no—
97C3×C4×D3—21no—
98C3×C4×D3—21no—
99C3×C4×D3—21no—
100C3×C4×D3—41no—
101C32×C8—21no—
102C32×C8—21no—
103C32×C8—41no—
104C32×C8—41no—
105C3×C3⋊C8—21no—
106C3×C3⋊C8—21no—
107C3×C3⋊C8—41no—
108C3×C3⋊C8—41no—
109#432—31no—
110#431—31no—
111#431—31no—
112#335—31no—
113#335—31no—
114#334—31no—
115#334C3×D311yescharacteristic, complemented
116C22×C3×C4—31no—
117C22×C3×C4—31no—
118C22×C3×C4—31no—
119C2×C4×D3C2×C3×C411yescharacteristic
120C2×C4×D3C3×D411yescharacteristic
121C2×C4×D3C3×Q811yescharacteristic
122C2×C3×C8—21no—
123C2×C3×C8—21no—
124C2×C3×C8—21no—
125C2×C3×C8—21no—
126C2×C3×C8—21no—
127C2×C3×C8—21no—
128C2×C3×C8—31no—
129C2×C3×C8—31no—
130C2×C3×C8—41no—
131C2×C3×C8—41no—
132C2×C3×C8—61no—
133C2×C3×C8—61no—
134C2×C3×C8C4×D311yescharacteristic
135C2×C3×C8C4×D311yescharacteristic
136C2×C3×C8C2×C3×C411yescharacteristic
137C2×C3×C8C2×C3×C411yescharacteristic
138C3×C42—21no—
139C3×C42—31no—
140C3×C42—31no—
141C3×C42—31no—
142C3×C42C22×D311yescharacteristic
143C3×C42C23×C311yescharacteristic
144C4×Dic3C2×C3×C411yescharacteristic
145C4×Dic3C3×D411yescharacteristic
146C4×Dic3C3×Q811yescharacteristic
147C2×C3⋊C8—21no—
148C2×C3⋊C8—21no—
149C2×C3⋊C8C2×C3×C411yescharacteristic
150C2×C3⋊C8C2×C3×C411yescharacteristic
151C22×C32C2×C4⋊C411yescharacteristic
152C2×C3×D3—21no—
153C2×C3×D3—21no—
154C2×C3×D3—21no—
155C32×C4—21no—
156C32×C4#13111yescharacteristic
157C32×C4#13111yescharacteristic
158C32×C4#13511yescharacteristic
159C32×C4#13511yescharacteristic
160C3×Dic3—21no—
161C3×Dic3—21no—
162C3×Dic3—21no—
163C2×C42—31no—
164C4⋊C8—31no—
165C4⋊C8—31no—
166C4⋊C8—31no—
167C4⋊C8—31no—
168C4⋊C8C2×C3×D311yescharacteristic
169C4⋊C8C2×C3×D311yescharacteristic
170C22⋊C8—31no—
171C22⋊C8—31no—
172C22⋊C8—61no—
173C22⋊C8—61no—
174#97—61no—
175C4×C8—31no—
176C4×C8—61no—
177C4×C8C2×C3×D311yescharacteristic
178C23×C3—31no—
179C22×D3C3×C4⋊C411yescharacteristic
180C2×C3×C4—21no—
181C2×C3×C4—21no—
182C2×C3×C4—21no—
183C2×C3×C4—31no—
184C2×C3×C4—31no—
185C2×C3×C4—31no—
186C2×C3×C4—61no—
187C2×C3×C4—61no—
188C2×C3×C4—61no—
189C2×C3×C4—61no—
190C2×C3×C4—121no—
191C2×C3×C4C2×C4×D311yescharacteristic
192C2×C3×C4D3×D411yescharacteristic
193C2×C3×C4D3×Q811yescharacteristic
194C2×C3×C4C22×C3×C411yescharacteristic
195C2×C3×C4C2×C3×D411yescharacteristic
196C2×C3×C4C2×C3×Q811yescharacteristic
197C2×Dic3C3×C4⋊C411yescharacteristic
198C2×Dic3C3×C4⋊C411yescharacteristic
199C2×Dic3C3×C4⋊C411yescharacteristic
200C4×D3—21no—
201C4×D3—21no—
202C4×D3—21no—
203C4×D3—21no—
204C4×D3—41no—
205C3×C8—22no—
206C3×C8—21no—
207C3×C8—21no—
208C3×C8—21no—
209C3×C8—21no—
210C3×C8—41no—
211C3×C8—41no—
212C3×C8—41no—
213C3×C8—41no—
214C3×C8—41no—
215C3×C8—61no—
216C3×C8—61no—
217C3×C8—81no—
218C3×C8—81no—
219C3×C8—121no—
220C3×C8—121no—
221C3⋊C8—21no—
222C3⋊C8—21no—
223C3⋊C8—41no—
224C3⋊C8—41no—
225C2×C32#42411yescharacteristic
226C2×C32#42711yescharacteristic
227C2×C32#43011yescharacteristic
228C3×D3—41no—
229C22×C4—31no—
230C22×C4—31no—
231C22×C4—31no—
232C2×C8—21no—
233C2×C8—21no—
234C2×C8—31no—
235C2×C8—31no—
236C2×C8—61no—
237C2×C8—61no—
238C2×C8C3×C4×D311yescharacteristic
239C2×C8C3×C4×D311yescharacteristic
240C42—31no—
241C42—31no—
242C42—31no—
243C42C22×C3×D311yescharacteristic
244C22×C3—21no—
245C22×C3—61no—
246C22×C3—61no—
247C22×C3—61no—
248C22×C3D3×C4⋊C411yescharacteristic
249C22×C3C2×C3×C4⋊C411yescharacteristic
250C2×D3—21no—
251C2×D3—21no—
252C2×D3—21no—
253C3×C4—21no—
254C3×C4—21no—
255C3×C4—21no—
256C3×C4—21no—
257C3×C4—21no—
258C3×C4—21no—
259C3×C4—41no—
260C3×C4—61no—
261C3×C4—61no—
262C3×C4—61no—
263C3×C4#90111yescharacteristic
264C3×C4#90711yescharacteristic
265C3×C4#91611yescharacteristic
266C3×C4#91611yescharacteristic
267C3×C4C3×#13111yescharacteristic
268C3×C4C3×#13111yescharacteristic
269C3×C4C3×#13511yescharacteristic
270C3×C4C3×#13511yescharacteristic
271Dic3—21no—
272Dic3—21no—
273Dic3—21no—
274C32#157211yescharacteristic, complemented, Sylow
275C23—31no—
276C2×C4—31no—
277C2×C4—31no—
278C2×C4—31no—
279C2×C4—61no—
280C2×C4—61no—
281C2×C4—61no—
282C2×C4—61no—
283C2×C4—121no—
284C2×C4C2×C3×C4×D311yescharacteristic
285C2×C4C3×D3×D411yescharacteristic
286C2×C4C3×D3×Q811yescharacteristic
287C8—21no—
288C8—21no—
289C8—41no—
290C8—41no—
291C8—61no—
292C8—61no—
293C8—121no—
294C8—121no—
295C2×C3—21no—
296C2×C3—21no—
297C2×C3—21no—
298C2×C3—121no—
299C2×C3#483911yescharacteristic
300C2×C3#486011yescharacteristic
301C2×C3#489311yescharacteristic
302C2×C3C3×#42411yescharacteristic
303C2×C3C3×#42711yescharacteristic
304C2×C3C3×#43011yescharacteristic
305D3—41no—
306C22—61no—
307C22—61no—
308C22—61no—
309C22C3×D3×C4⋊C411yescharacteristic
310C4—21no—
311C4—61no—
312C4—61no—
313C4—61no—
314C4C3×#90111yescharacteristic
315C4C3×#90711yescharacteristic
316C4C3×#91611yescharacteristic
317C4C3×#91611yescharacteristic
318C3—21no—
319C3#6853311yescharacteristic, direct product factor
320C3C3×#157211yescharacteristic, complemented
321C2—121no—
322C2C3×#483911yescharacteristic
323C2C3×#486011yescharacteristic
324C2C3×#489311yescharacteristic
subgroupG/H
centerC2×C3×C4D3×D4
commutatorC2×C3×C4C22×C3×C4
FrattiniC42C22×C3×D3
FittingC32×#334C2
socleC22×C32C2×C4⋊C4
prime radicalC22×C3×D3C4⋊C4
cosocleC3×C42C23×C3
hypercenterC3×#334D3
hypocenterC3C3×#1572
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3×C4 ◁ C3×C42 ◁ C3×#334

Complements

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

NH ≅ G/Ntype
4. C32×#334C2semidirect
5. C3×#4479C2semidirect
6. C3×#4479C2semidirect
7. C3×#4457C2semidirect
9. #68533C3direct (N × H)
35. C3×#334D3semidirect
36. C3×#334C2×C3semidirect
37. #4479C2×C3semidirect
38. #4479C2×C3semidirect
39. #4457C2×C3semidirect
115. #334C3×D3semidirect
274. C32#1572semidirect
319. C3#68533direct (N × H)
320. C3C3×#1572semidirect

Maximal subgroups

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

subgroupindex
C3×#48352
C3×#48332
C3×#46852
C32×#3342
C3×#44792
C3×#44572
C3×#15723
#685333