Finite Group Databasebeta

← C3×#70462 #11795181

Subgroups — C3×#70462 #11795181

Order 1152.

517 conjugacy classes of subgroups.

The subgroup lattice has 310 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C4⋊C8C211yesmaximal, characteristic
2C2×C3×#818C211yesmaximal, characteristic
3C3×#4928C212yesmaximal
4C3×#4551C212yesmaximal
5C3×#4551C211yesmaximal, characteristic
6C3×#2086—31nomaximal
7#70462C311yesmaximal, characteristic, direct product factor
8C22×C32×C8C2211yescharacteristic
9C22×C32×C8C2211yescharacteristic
10C2×C32×C42C2211yescharacteristic
11C2×C3×C4⋊Dic3C2212yes—
12C2×C3×C4⋊Dic3C2212yes—
13C2×C3×Dic3⋊C4—22no—
14C32×C4⋊C8—22no—
15C3×C3⋊#95—22no—
16C3×#818—22no—
17C2×C3×#107—31no—
18C2×C3×C4⋊C8—21no—
19C2×C3×C4⋊C8D311yescharacteristic
20C2×C3×C4⋊C8C2×C311yescharacteristic
21C3×#389—32no—
22C2×#818C2×C311yescharacteristic
23#4928C2×C312yes—
24C3×#340—31no—
25C3×#340—32no—
26#4551C2×C312yes—
27#4551C2×C311yescharacteristic
28C22×C32×C4D411yescharacteristic
29C22×C32×C4D411yescharacteristic
30C22×C32×C4C2311yescharacteristic
31C22×C3×Dic3—22no—
32C22×C3×Dic3—22no—
33C2×C32×C8—22no—
34C2×C32×C8—21no—
35C2×C32×C8—22no—
36C2×C32×C8D412yes—
37C32×C42—21no—
38C32×C42—21no—
39C3×C4⋊Dic3—22no—
40C3×C4⋊Dic3—22no—
41C3×C4⋊Dic3—22no—
42C3×C4⋊Dic3Q814yes—
43C3×Dic3⋊C4—44no—
44#2086—31noSylow
45C22×C3×C8—21no—
46C22×C3×C8—21no—
47C22×C3×C8C2×D311yescharacteristic
48C22×C3×C8C2×D311yescharacteristic
49C22×C3×C8C22×C311yescharacteristic
50C22×C3×C8C22×C311yescharacteristic
51C2×C3×C4⋊C4—32no—
52C2×C3×C4⋊C4—32no—
53C2×C3×C4⋊C4—62no—
54C2×C3×C42—21no—
55C2×C3×C42C2×D311yescharacteristic
56C2×C3×C42C22×C311yescharacteristic
57C2×C4⋊Dic3C22×C312yes—
58C2×C4⋊Dic3C22×C312yes—
59C2×Dic3⋊C4—22no—
60C3×#107—62no—
61C3×C4⋊C8—24no—
62C3×C4⋊C8—22no—
63C3×C4⋊C8—22no—
64C3×#95—62no—
65C3⋊#95—22no—
66#818—22no—
67C23×C32C2×D411yescharacteristic
68C2×C32×C4—21no—
69C2×C32×C4—21no—
70C2×C32×C4—21no—
71C2×C32×C4—22no—
72C2×C32×C4D812yes—
73C2×C32×C4C2×D411yescharacteristic
74C2×C32×C4C2×Q812yes—
75C2×C32×C4#4111yescharacteristic
76C2×C32×C4#4112yes—
77C2×C3×Dic3—24no—
78C2×C3×Dic3—42no—
79C2×C3×Dic3—42no—
80C2×C3×Dic3—42no—
81C2×C3×Dic3—42no—
82C2×C3×Dic3—42no—
83C32×C8—22no—
84C32×C8—41no—
85C2×#107—31no—
86C2×C4⋊C8C3×D311yescharacteristic
87#389—32no—
88#340—31no—
89#340—32no—
90C22×C3×C4—21no—
91C22×C3×C4—21no—
92C22×C3×C4—21no—
93C22×C3×C4—62no—
94C22×C3×C4—62no—
95C22×C3×C4D1211yescharacteristic
96C22×C3×C4D1211yescharacteristic
97C22×C3×C4C3×D411yescharacteristic
98C22×C3×C4C3×D411yescharacteristic
99C22×C3×C4C22×D311yescharacteristic
100C22×C3×C4C23×C311yescharacteristic
101C22×Dic3—22no—
102C22×Dic3—22no—
103C2×C3×C8—22no—
104C2×C3×C8—22no—
105C2×C3×C8—22no—
106C2×C3×C8—22no—
107C2×C3×C8—21no—
108C2×C3×C8—21no—
109C2×C3×C8—22no—
110C2×C3×C8—22no—
111C2×C3×C8—42no—
112C2×C3×C8—42no—
113C2×C3×C8#6712yes—
114C2×C3×C8C3×D412yes—
115C3×C4⋊C4—34no—
116C3×C4⋊C4—62no—
117C3×C4⋊C4—62no—
118C3×C4⋊C4—62no—
119C3×C4⋊C4—124no—
120C3×C42—22no—
121C3×C42—22no—
122C3×C42—21no—
123C3×C42—21no—
124C3×C42—21no—
125C3×C42—21no—
126C4⋊Dic3—22no—
127C4⋊Dic3—22no—
128C4⋊Dic3—22no—
129C4⋊Dic3C3×Q814yes—
130Dic3⋊C4—44no—
131C22×C32#12111yescharacteristic
132C22×C32C22⋊Q812yes—
133C22×C32C2×D811yescharacteristic
134C22×C32#13511yescharacteristic
135C22×C32#13712yes—
136C32×C4—22no—
137C32×C4—41no—
138C32×C4#12311yescharacteristic
139C32×C4#12512yes—
140C32×C4C4⋊Q811yescharacteristic
141C3×Dic3—44no—
142C3×Dic3—82no—
143C22×C8C2×C3×D311yescharacteristic
144C22×C8C2×C3×D311yescharacteristic
145C2×C4⋊C4—32no—
146C2×C4⋊C4—32no—
147C2×C4⋊C4—62no—
148C2×C42C2×C3×D311yescharacteristic
149#107—62no—
150C4⋊C8—22no—
151#95—62no—
152C23×C3—21no—
153C23×C3C2×D1211yescharacteristic
154C23×C3C2×C3×D411yescharacteristic
155C2×C3×C4—22no—
156C2×C3×C4—22no—
157C2×C3×C4—21no—
158C2×C3×C4—21no—
159C2×C3×C4—21no—
160C2×C3×C4—21no—
161C2×C3×C4—22no—
162C2×C3×C4—22no—
163C2×C3×C4—21no—
164C2×C3×C4—21no—
165C2×C3×C4—22no—
166C2×C3×C4—22no—
167C2×C3×C4—21no—
168C2×C3×C4—22no—
169C2×C3×C4—22no—
170C2×C3×C4—21no—
171C2×C3×C4—42no—
172C2×C3×C4—64no—
173C2×C3×C4—122no—
174C2×C3×C4—122no—
175C2×C3×C4—122no—
176C2×C3×C4—122no—
177C2×C3×C4—122no—
178C2×C3×C4D2412yes—
179C2×C3×C4C3×D812yes—
180C2×C3×C4#23511yescharacteristic
181C2×C3×C4#23712yes—
182C2×C3×C4D3×Q812yes—
183C2×C3×C4C2×#6711yescharacteristic
184C2×C3×C4C2×C3×D411yescharacteristic
185C2×C3×C4C2×C3×Q812yes—
186C2×C3×C4C3×#4111yescharacteristic
187C2×C3×C4C3×#4112yes—
188C2×Dic3—24no—
189C2×Dic3—42no—
190C2×Dic3—42no—
191C2×Dic3—42no—
192C2×Dic3—42no—
193C2×Dic3—42no—
194C3×C8—22no—
195C3×C8—22no—
196C3×C8—42no—
197C3×C8—42no—
198C3×C8—41no—
199C3×C8—41no—
200C2×C32#39811yescharacteristic
201C2×C32#46611yescharacteristic
202C2×C32#47011yescharacteristic
203C2×C32#47412yes—
204C2×C32#47912yes—
205C22×C4—62no—
206C22×C4—62no—
207C22×C4C3×D1211yescharacteristic
208C22×C4C3×D1211yescharacteristic
209C22×C4C22×C3×D311yescharacteristic
210C2×C8—22no—
211C2×C8—22no—
212C2×C8—21no—
213C2×C8C3×#6712yes—
214C4⋊C4—34no—
215C4⋊C4—62no—
216C4⋊C4—62no—
217C4⋊C4—62no—
218C4⋊C4—124no—
219C42—21no—
220C42—21no—
221C22×C3—22no—
222C22×C3—21no—
223C22×C3—21no—
224C22×C3—22no—
225C22×C3—21no—
226C22×C3#89712yes—
227C22×C3C2×D2411yescharacteristic
228C22×C3#90411yescharacteristic
229C22×C3#90912yes—
230C22×C3#93011yescharacteristic
231C22×C3C3×#12111yescharacteristic
232C22×C3C3×C22⋊Q812yes—
233C22×C3C2×C3×D811yescharacteristic
234C22×C3C3×#13511yescharacteristic
235C22×C3C3×#13712yes—
236C3×C4—24no—
237C3×C4—22no—
238C3×C4—22no—
239C3×C4—22no—
240C3×C4—21no—
241C3×C4—21no—
242C3×C4—42no—
243C3×C4—41no—
244C3×C4—41no—
245C3×C4—124no—
246C3×C4—242no—
247C3×C4#88912yes—
248C3×C4#93511yescharacteristic
249C3×C4#94411yescharacteristic
250C3×C4C3×#12311yescharacteristic
251C3×C4C3×#12512yes—
252C3×C4C3×C4⋊Q811yescharacteristic
253Dic3—44no—
254Dic3—82no—
255C32#208611yescharacteristic, complemented, Sylow
256C23C2×C3×D1211yescharacteristic
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—22no—
260C2×C4—21no—
261C2×C4—64no—
262C2×C4—122no—
263C2×C4—122no—
264C2×C4—122no—
265C2×C4—122no—
266C2×C4—122no—
267C2×C4C3×D2412yes—
268C2×C4C3×#23511yescharacteristic
269C2×C4C3×#23712yes—
270C2×C4C3×D3×Q812yes—
271C2×C4C2×C3×#6711yescharacteristic
272C8—22no—
273C8—41no—
274C2×C3—21no—
275C2×C3—22no—
276C2×C3—22no—
277C2×C3—21no—
278C2×C3—21no—
279C2×C3#482912yes—
280C2×C3#484612yes—
281C2×C3#498111yescharacteristic
282C2×C3#511511yescharacteristic
283C2×C3#513711yescharacteristic
284C2×C3C3×#39811yescharacteristic
285C2×C3C3×#46611yescharacteristic
286C2×C3C3×#47011yescharacteristic
287C2×C3C3×#47412yes—
288C2×C3C3×#47912yes—
289C22C3×#89712yes—
290C22C2×C3×D2411yescharacteristic
291C22C3×#90411yescharacteristic
292C22C3×#90912yes—
293C22C3×#93011yescharacteristic
294C4—22no—
295C4—41no—
296C4—124no—
297C4—242no—
298C4C3×#88912yes—
299C4C3×#93511yescharacteristic
300C4C3×#94411yescharacteristic
301C3—21no—
302C3#7046211yescharacteristic, direct product factor
303C3C3×#208611yescharacteristic, complemented
304C2C3×#482912yes—
305C2C3×#484612yes—
306C2C3×#498111yescharacteristic
307C2C3×#511511yescharacteristic
308C2C3×#513711yescharacteristic
subgroupG/H
centerC23×C3C2×D12
commutator, cosocleC22×C3×C4C23×C3
FrattiniC22×C4C22×C3×D3
FittingC2×C32×C4⋊C8C2
socle, prime radicalC23×C32C2×D4
hypercenterC2×C3×C4⋊C8D3
hypocenterC3C3×#2086
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×C42 ◁ C2×C3×C4⋊C8

Complements

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

NH ≅ G/Ntype
7. #70462C3direct (N × H)
255. C32#2086semidirect
302. C3#70462direct (N × H)
303. C3C3×#2086semidirect

Maximal subgroups

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

subgroupindex
C2×C32×C4⋊C82
C2×C3×#8182
C3×#49282
C3×#45512
C3×#20863
#704623