Finite Group Databasebeta

← C3×#67648 #11771971

Subgroups — C3×#67648 #11771971

Order 1152.

371 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 371 conjugacy classes of subgroups — too many to draw. Only its 74 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#395C211yesmaximal, characteristic
2C3×#4530C211yesmaximal, characteristic
3C3×#4528C211yesmaximal, characteristic
4C3×#1354—31nomaximal
5#67648C311yesmaximal, characteristic, direct product factor
6C22×C32×Q8C411yescharacteristic
7C2×C32×C4⋊C4—21no—
8C2×C32×C4⋊C4C2211yescharacteristic
9C2×C3×#208—21no—
10C32×#95—21no—
11C32×#95C411yescharacteristic
12C3×#830—21no—
13C3×#395—21no—
14C3×#395D311yescharacteristic
15C3×#395C2×C311yescharacteristic
16C3×#343—31no—
17C3×#324—31no—
18#4530C2×C311yescharacteristic
19#4528C2×C311yescharacteristic
20C2×C32×Q8—42no—
21C2×C32×Q8—41no—
22C22×C32×C4—21no—
23C22×C32×C4—21no—
24C22×C32×C4C2×C411yescharacteristic
25C22×C32×C4D411yescharacteristic
26C22×C32×C4D411yescharacteristic
27C32×C4⋊C4—41no—
28C32×C4⋊C4—42no—
29C3×#208—22no—
30C3×#208—41no—
31C2×C3×C3⋊C8—41no—
32C2×C3×C3⋊C8—41no—
33#1354—31noSylow
34C22×C3×Q8—21no—
35C22×C3×Q8Dic311yescharacteristic
36C22×C3×Q8C3×C411yescharacteristic
37C2×C3×M16—61no—
38C2×C3×C4⋊C4—22no—
39C2×C3×C4⋊C4—21no—
40C2×C3×C4⋊C4—21no—
41C2×C3×C4⋊C4—21no—
42C2×C3×C4⋊C4C2×D311yescharacteristic
43C2×C3×C4⋊C4C22×C311yescharacteristic
44C2×#208—21no—
45C3×C22⋊C8—61no—
46C3×#95—22no—
47C3×#95—21no—
48C3×#95—21no—
49C3×#95—21no—
50C3×#95Dic311yescharacteristic
51C3×#95C3×C411yescharacteristic
52#830—21no—
53C23×C32C22⋊C411yescharacteristic
54C32×Q8—42no—
55C32×Q8—42no—
56C2×C32×C4—22no—
57C2×C32×C4—22no—
58C2×C32×C4—21no—
59C2×C32×C4—21no—
60C2×C32×C4—21no—
61C2×C32×C4—21no—
62C2×C32×C4—41no—
63C2×C32×C4—41no—
64C2×C32×C4—41no—
65C2×C32×C4—41no—
66C2×C32×C4—41no—
67C2×C32×C4—41no—
68C2×C32×C4SD1611yescharacteristic
69C2×C32×C4Q1611yescharacteristic
70C3×C3⋊C8—42no—
71C3×C3⋊C8—81no—
72#395C3×D311yescharacteristic
73#343—31no—
74#324—31no—
75C2×C3×Q8—42no—
76C2×C3×Q8—42no—
77C2×C3×Q8—44no—
78C2×C3×Q8—42no—
79C2×C3×Q8—41no—
80C2×C3×Q8—41no—
81C22×C3×C4—22no—
82C22×C3×C4—22no—
83C22×C3×C4—21no—
84C22×C3×C4—21no—
85C22×C3×C4—21no—
86C22×C3×C4—21no—
87C22×C3×C4—21no—
88C22×C3×C4—21no—
89C22×C3×C4—21no—
90C22×C3×C4C2×Dic311yescharacteristic
91C22×C3×C4#6711yescharacteristic
92C22×C3×C4#6711yescharacteristic
93C22×C3×C4C2×C3×C411yescharacteristic
94C22×C3×C4C3×D411yescharacteristic
95C22×C3×C4C3×D411yescharacteristic
96C3×M16—62no—
97C3×M16—121no—
98C2×C3×C8—121no—
99C2×C3×C8—121no—
100C3×C4⋊C4—41no—
101C3×C4⋊C4—41no—
102C3×C4⋊C4—42no—
103C3×C4⋊C4—42no—
104C3×C4⋊C4—42no—
105C3×C4⋊C4—44no—
106#208—22no—
107#208—41no—
108C2×C3⋊C8—41no—
109C2×C3⋊C8—41no—
110C22×C32—21no—
111C22×C32—21no—
112C22×C32#9911yescharacteristic
113C22×C32#10311yescharacteristic
114C22×C32#10411yescharacteristic
115C32×C4—21no—
116C32×C4—21no—
117C32×C4—42no—
118C32×C4—42no—
119C32×C4—41no—
120C32×C4—41no—
121C22×Q8C3×Dic311yescharacteristic
122C2×M16—61no—
123C2×C4⋊C4—21no—
124C2×C4⋊C4C2×C3×D311yescharacteristic
125C22⋊C8—61no—
126#95—21no—
127#95C3×Dic311yescharacteristic
128C23×C3—21no—
129C23×C3#21711yescharacteristic
130C23×C3C3×C22⋊C411yescharacteristic
131C3×Q8—42no—
132C3×Q8—42no—
133C3×Q8—44no—
134C3×Q8—44no—
135C3×Q8—42no—
136C3×Q8—42no—
137C2×C3×C4—21no—
138C2×C3×C4—21no—
139C2×C3×C4—21no—
140C2×C3×C4—21no—
141C2×C3×C4—24no—
142C2×C3×C4—22no—
143C2×C3×C4—22no—
144C2×C3×C4—22no—
145C2×C3×C4—24no—
146C2×C3×C4—22no—
147C2×C3×C4—22no—
148C2×C3×C4—21no—
149C2×C3×C4—21no—
150C2×C3×C4—21no—
151C2×C3×C4—21no—
152C2×C3×C4—21no—
153C2×C3×C4—21no—
154C2×C3×C4—41no—
155C2×C3×C4—41no—
156C2×C3×C4—41no—
157C2×C3×C4—42no—
158C2×C3×C4—41no—
159C2×C3×C4—41no—
160C2×C3×C4—42no—
161C2×C3×C4—42no—
162C2×C3×C4—41no—
163C2×C3×C4—41no—
164C2×C3×C4—42no—
165C2×C3×C4—42no—
166C2×C3×C4—41no—
167C2×C3×C4—41no—
168C2×C3×C4—41no—
169C2×C3×C4—41no—
170C2×C3×C4—41no—
171C2×C3×C4—41no—
172C2×C3×C4—41no—
173C2×C3×C4—41no—
174C2×C3×C4—42no—
175C2×C3×C4#21511yescharacteristic
176C2×C3×C4#21611yescharacteristic
177C2×C3×C4C3×SD1611yescharacteristic
178C2×C3×C4C3×Q1611yescharacteristic
179C3×C8—122no—
180C3×C8—241no—
181C3⋊C8—42no—
182C3⋊C8—81no—
183C2×C32—21no—
184C2×C32—21no—
185C2×C32#32811yescharacteristic
186C2×C32AΣL(1,𝔽16)11yescharacteristic
187C2×C32#35611yescharacteristic
188C2×Q8—42no—
189C2×Q8—41no—
190C22×C4—21no—
191C22×C4—21no—
192C22×C4C2×C3×Dic311yescharacteristic
193C22×C4C3×#6711yescharacteristic
194C22×C4C3×#6711yescharacteristic
195M16—62no—
196M16—121no—
197C2×C8—121no—
198C2×C8—121no—
199C4⋊C4—41no—
200C4⋊C4—42no—
201C22×C3—22no—
202C22×C3—22no—
203C22×C3—21no—
204C22×C3—21no—
205C22×C3—21no—
206C22×C3—21no—
207C22×C3—21no—
208C22×C3—21no—
209C22×C3—21no—
210C22×C3#83411yescharacteristic
211C22×C3#83511yescharacteristic
212C22×C3#83711yescharacteristic
213C22×C3C3×#9911yescharacteristic
214C22×C3C3×#10311yescharacteristic
215C22×C3C3×#10411yescharacteristic
216C3×C4—21no—
217C3×C4—21no—
218C3×C4—21no—
219C3×C4—21no—
220C3×C4—41no—
221C3×C4—41no—
222C3×C4—44no—
223C3×C4—42no—
224C3×C4—44no—
225C3×C4—42no—
226C3×C4—42no—
227C3×C4—41no—
228C3×C4—42no—
229C3×C4—41no—
230C3×C4—41no—
231C3×C4—42no—
232C3×C4—41no—
233C3×C4—81no—
234C32#135411yescharacteristic, complemented, Sylow
235C23C3×#21711yescharacteristic
236Q8—42no—
237Q8—42no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4C3×#21511yescharacteristic
251C2×C4C3×#21611yescharacteristic
252C8—122no—
253C8—241no—
254C2×C3—22no—
255C2×C3—22no—
256C2×C3—21no—
257C2×C3—21no—
258C2×C3—21no—
259C2×C3—21no—
260C2×C3—21no—
261C2×C3—21no—
262C2×C3—21no—
263C2×C3#453611yescharacteristic
264C2×C3#453811yescharacteristic
265C2×C3#454811yescharacteristic
266C2×C3C3×#32811yescharacteristic
267C2×C3C3×AΣL(1,𝔽16)11yescharacteristic
268C2×C3C3×#35611yescharacteristic
269C22—21no—
270C22—21no—
271C22C3×#83411yescharacteristic
272C22C3×#83511yescharacteristic
273C22C3×#83711yescharacteristic
274C4—21no—
275C4—21no—
276C4—42no—
277C4—41no—
278C4—42no—
279C4—41no—
280C3—21no—
281C3#6764811yescharacteristic, direct product factor
282C3C3×#135411yescharacteristic, complemented
283C2—21no—
284C2—21no—
285C2C3×#453611yescharacteristic
286C2C3×#453811yescharacteristic
287C2C3×#454811yescharacteristic
subgroupG/H
centerC22×C3#834
commutatorC22×C3×C4C2×C3×C4
FrattiniC2×C4⋊C4C2×C3×D3
FittingC32×#395C2
socleC22×C32#99
prime radicalC23×C32C22⋊C4
cosocleC2×C3×C4⋊C4C22×C3
hypercenterC3×#395D3
hypocenterC3C3×#1354
LCSG ▷ C22×C3×C4 ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C23×C3 ◁ C2×C3×C4⋊C4 ◁ C3×#395

Complements

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

NH ≅ G/Ntype
5. #67648C3direct (N × H)
234. C32#1354semidirect
281. C3#67648direct (N × H)
282. C3C3×#1354semidirect

Maximal subgroups

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

subgroupindex
C32×#3952
C3×#45302
C3×#45282
C3×#13543
#676483