Finite Group Databasebeta

← C3×#70101 #11785934

Subgroups — C3×#70101 #11785934

Order 1152.

545 conjugacy classes of subgroups.

The subgroup lattice has 292 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5812C211yesmaximal, characteristic
2C2×C32×#101C211yesmaximal, characteristic
3C2×C3×#836C211yesmaximal, characteristic
4C3×#4559C212yesmaximal
5C3×#4556C212yesmaximal
6C3×#1830—31nomaximal
7#70101C311yesmaximal, characteristic, direct product factor
8C22×C32×Q8C2211yescharacteristic
9C2×C32×M16C2212yes—
10C3×Q8×Dic3—22no—
11C3×Q8×Dic3—22no—
12C3×#926C414yes—
13C3×#926C2211yescharacteristic
14C3×#926C2211yescharacteristic
15C2×C3×#208C2212yes—
16C32×#101—22no—
17C3×#836—22no—
18C3×#519—31no—
19#5812C2×C311yescharacteristic
20C2×C3×#101—21no—
21C2×C3×#101—31no—
22C2×C3×#101D311yescharacteristic
23C2×C3×#101C2×C311yescharacteristic
24C2×#836C2×C311yescharacteristic
25C3×#344—32no—
26C3×#344—32no—
27#4559C2×C312yes—
28#4556C2×C312yes—
29C2×C32×Q8—22no—
30C2×C32×Q8—22no—
31C2×C32×Q8D412yes—
32C2×C32×Q8D412yes—
33C22×C32×C4C2×C412yes—
34C22×C32×C4C2311yescharacteristic
35C32×M16—22no—
36C32×M16—22no—
37C2×C32×C8—22no—
38C3×#217C2×C412yes—
39C3×#217C2×C412yes—
40C3×C4⋊Dic3—24no—
41C3×C4⋊Dic3—21no—
42C3×C4⋊Dic3—21no—
43C3×C4×Dic3—24no—
44C3×C4×Dic3—21no—
45C3×C4×Dic3—21no—
46C3×#208—22no—
47C3×#208—22no—
48C2×C3×C3⋊C8—22no—
49#1830—31noSylow
50C22×C3×Q8—21no—
51C22×C3×Q8C2×D311yescharacteristic
52C22×C3×Q8C22×C311yescharacteristic
53C2×C3×M16—22no—
54C2×C3×M16—32no—
55C2×C3×M16C2×D312yes—
56C2×C3×M16C22×C312yes—
57C3×C4×Q8—62no—
58C3×C4×Q8—62no—
59C3×#117—34no—
60C3×#117—31no—
61C3×#117—31no—
62Q8×Dic3—22no—
63Q8×Dic3—22no—
64#926C3×C414yes—
65#926C22×C311yescharacteristic
66#926C22×C311yescharacteristic
67C2×#208C22×C312yes—
68C3×#101—24no—
69C3×#101—22no—
70C3×#101—22no—
71C3×#101—62no—
72#836—22no—
73C23×C32C22×C411yescharacteristic
74C32×Q8—24no—
75C32×Q8—24no—
76C2×C32×C4—22no—
77C2×C32×C4—22no—
78C2×C32×C4C22⋊C414yes—
79C2×C32×C4C2×D411yescharacteristic
80C2×C32×C4C2×D411yescharacteristic
81C2×C32×C4#4112yes—
82C2×C32×C4#4112yes—
83C2×C3×Dic3—22no—
84C2×C3×Dic3—22no—
85C32×C8—42no—
86C3×C3⋊C8—42no—
87#519—31no—
88C2×#101—31no—
89C2×#101C3×D311yescharacteristic
90#344—32no—
91#344—32no—
92C2×C3×Q8—22no—
93C2×C3×Q8—22no—
94C2×C3×Q8—22no—
95C2×C3×Q8—22no—
96C2×C3×Q8—22no—
97C2×C3×Q8—22no—
98C2×C3×Q8—42no—
99C2×C3×Q8—42no—
100C2×C3×Q8D1212yes—
101C2×C3×Q8#6712yes—
102C2×C3×Q8C3×D412yes—
103C2×C3×Q8C3×D412yes—
104C22×C3×C4—22no—
105C22×C3×C4—21no—
106C22×C3×C4C4×D312yes—
107C22×C3×C4C2×C3×C412yes—
108C22×C3×C4C22×D311yescharacteristic
109C22×C3×C4C23×C311yescharacteristic
110C3×M16—24no—
111C3×M16—22no—
112C3×M16—22no—
113C3×M16—22no—
114C3×M16—22no—
115C3×M16—42no—
116C3×M16—62no—
117C3×M16—62no—
118C2×C3×C8—22no—
119C2×C3×C8—22no—
120C2×C3×C8—42no—
121C2×C3×C8—62no—
122C3×C4⋊C4—64no—
123C3×C4⋊C4—61no—
124C3×C4⋊C4—61no—
125C3×C22⋊C4—32no—
126C3×C22⋊C4—32no—
127C3×C42—64no—
128C3×C42—61no—
129C3×C42—61no—
130#217C2×C3×C412yes—
131#217C2×C3×C412yes—
132C4⋊Dic3—24no—
133C4⋊Dic3—21no—
134C4⋊Dic3—21no—
135C4×Dic3—24no—
136C4×Dic3—21no—
137C4×Dic3—21no—
138#208—22no—
139#208—22no—
140C2×C3⋊C8—22no—
141C22×C32—41no—
142C22×C32C2×C22⋊C411yescharacteristic
143C22×C32#11711yescharacteristic
144C22×C32#11711yescharacteristic
145C32×C4—24no—
146C32×C4#12312yes—
147C32×C4#12312yes—
148C3×Dic3—42no—
149C3×Dic3—42no—
150C22×Q8C2×C3×D311yescharacteristic
151C2×M16—32no—
152C2×M16C2×C3×D312yes—
153C4×Q8—62no—
154C4×Q8—62no—
155#117—34no—
156#117—31no—
157#117—31no—
158#101—22no—
159#101—62no—
160C23×C3—21no—
161C23×C3C2×C4×D311yescharacteristic
162C23×C3C22×C3×C411yescharacteristic
163C3×Q8—24no—
164C3×Q8—24no—
165C3×Q8—24no—
166C3×Q8—24no—
167C3×Q8—44no—
168C3×Q8—44no—
169C2×C3×C4—22no—
170C2×C3×C4—22no—
171C2×C3×C4—22no—
172C2×C3×C4—22no—
173C2×C3×C4—24no—
174C2×C3×C4—21no—
175C2×C3×C4—22no—
176C2×C3×C4—22no—
177C2×C3×C4—21no—
178C2×C3×C4—42no—
179C2×C3×C4—42no—
180C2×C3×C4—62no—
181C2×C3×C4—62no—
182C2×C3×C4(C2×D3)⋊C414yes—
183C2×C3×C4C3×C22⋊C414yes—
184C2×C3×C4C2×D1211yescharacteristic
185C2×C3×C4#23712yes—
186C2×C3×C4#23712yes—
187C2×C3×C4C2×#6711yescharacteristic
188C2×C3×C4C2×C3×D411yescharacteristic
189C2×C3×C4C2×C3×D411yescharacteristic
190C2×C3×C4C3×#4112yes—
191C2×C3×C4C3×#4112yes—
192C2×Dic3—22no—
193C2×Dic3—22no—
194C3×C8—44no—
195C3×C8—42no—
196C3×C8—42no—
197C3×C8—122no—
198C3⋊C8—42no—
199C2×C32—21no—
200C2×C32—21no—
201C2×C32—21no—
202C2×C32#38111yescharacteristic
203C2×Q8—22no—
204C2×Q8—22no—
205C2×Q8C3×D1212yes—
206C2×Q8C3×#6712yes—
207C22×C4C3×C4×D312yes—
208C22×C4C22×C3×D311yescharacteristic
209M16—22no—
210M16—22no—
211M16—62no—
212M16—62no—
213C2×C8—22no—
214C2×C8—62no—
215C4⋊C4—64no—
216C4⋊C4—61no—
217C4⋊C4—61no—
218C22⋊C4—32no—
219C22⋊C4—32no—
220C42—64no—
221C42—61no—
222C42—61no—
223C22×C3—21no—
224C22×C3—21no—
225C22×C3—21no—
226C22×C3—41no—
227C22×C3—41no—
228C22×C3—42no—
229C22×C3#87711yescharacteristic
230C22×C3#87711yescharacteristic
231C22×C3C2×(C2×D3)⋊C411yescharacteristic
232C22×C3C2×C3×C22⋊C411yescharacteristic
233C22×C3C3×#11711yescharacteristic
234C22×C3C3×#11711yescharacteristic
235C3×C4—24no—
236C3×C4—24no—
237C3×C4—22no—
238C3×C4—22no—
239C3×C4—44no—
240C3×C4—122no—
241C3×C4—122no—
242C3×C4#88612yes—
243C3×C4#93512yes—
244C3×C4C3×#12312yes—
245C3×C4C3×#12312yes—
246Dic3—42no—
247Dic3—42no—
248C32#183011yescharacteristic, complemented, Sylow
249C23C2×C3×C4×D311yescharacteristic
250Q8—24no—
251Q8—24no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—62no—
255C2×C4—62no—
256C2×C4C3×(C2×D3)⋊C414yes—
257C2×C4C2×C3×D1211yescharacteristic
258C2×C4C3×#23712yes—
259C2×C4C3×#23712yes—
260C2×C4C2×C3×#6711yescharacteristic
261C8—42no—
262C8—122no—
263C2×C3—22no—
264C2×C3—21no—
265C2×C3—21no—
266C2×C3—21no—
267C2×C3—21no—
268C2×C3—21no—
269C2×C3—21no—
270C2×C3—21no—
271C2×C3—41no—
272C2×C3—41no—
273C2×C3#494311yescharacteristic
274C2×C3C3×#38111yescharacteristic
275C22—41no—
276C22C3×#87711yescharacteristic
277C22C3×#87711yescharacteristic
278C22C2×C3×(C2×D3)⋊C411yescharacteristic
279C4—24no—
280C4—122no—
281C4—122no—
282C4C3×#88612yes—
283C4C3×#93512yes—
284C3—21no—
285C3#7010111yescharacteristic, direct product factor
286C3C3×#183011yescharacteristic, complemented
287C2—21no—
288C2—21no—
289C2—21no—
290C2C3×#494311yescharacteristic
subgroupG/H
centerC2×C3#4943
commutatorC23×C3C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC2×C32×#101C2
socleC2×C32#381
prime radicalC23×C32C22×C4
cosocleC22×C3×C4C23×C3
hypercenterC2×C3×#101D3
hypocenterC3C3×#1830
LCSG ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3 ◁ C22×C3×C4 ◁ C2×C3×#101

Complements

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

NH ≅ G/Ntype
7. #70101C3direct (N × H)
248. C32#1830semidirect
285. C3#70101direct (N × H)
286. C3C3×#1830semidirect

Maximal subgroups

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

subgroupindex
C3×#58122
C2×C32×#1012
C2×C3×#8362
C3×#45592
C3×#45562
C3×#18303
#701013