Finite Group Databasebeta

← C3×#67457 #11771974

Subgroups — C3×#67457 #11771974

Order 1152.

319 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 319 conjugacy classes of subgroups — too many to draw. Only its 70 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
1C3×#4979C211yesmaximal, characteristic
2C32×#324C211yesmaximal, characteristic
3C3×#4530C211yesmaximal, characteristic
4C3×#1354—31nomaximal
5#67457C311yesmaximal, characteristic, direct product factor
6C22×C3×Dic6C411yescharacteristic
7C2×C32×C4⋊C4C2211yescharacteristic
8C2×C3×Dic3⋊C4—21no—
9C2×C3×#208—21no—
10C32×C22⋊C8—21no—
11C3×C3⋊#95—21no—
12C3×C3⋊#95C411yescharacteristic
13C3×#395—31no—
14#4979C2×C311yescharacteristic
15C3×#343—31no—
16C3×#324—21no—
17C3×#324D311yescharacteristic
18C3×#324C2×C311yescharacteristic
19#4530C2×C311yescharacteristic
20C22×C32×C4C2×C411yescharacteristic
21C22×C32×C4D411yescharacteristic
22C22×C32×C4D411yescharacteristic
23C22×C3×Dic3—21no—
24C22×C3×Dic3—21no—
25C2×C3×Dic6—41no—
26C2×C3×Dic6—42no—
27C2×C32×C8—41no—
28C32×C4⋊C4—41no—
29C3×Dic3⋊C4—42no—
30C3×#208—22no—
31C3×#208—41no—
32C2×C3×C3⋊C8—41no—
33#1354—31noSylow
34C22×C3×Q8—31no—
35C22×Dic6C3×C411yescharacteristic
36C2×C3×M16—61no—
37C2×C3×C4⋊C4—21no—
38C2×C3×C4⋊C4—61no—
39C2×C3×C4⋊C4C2×D311yescharacteristic
40C2×C3×C4⋊C4C22×C311yescharacteristic
41C2×Dic3⋊C4—21no—
42C2×#208—21no—
43C3×C22⋊C8—22no—
44C3×C22⋊C8—21no—
45C3×C22⋊C8—21no—
46C3×#95—31no—
47C3×#95—61no—
48C3⋊#95—21no—
49C3⋊#95C3×C411yescharacteristic
50C23×C32C22⋊C411yescharacteristic
51C2×C32×C4—21no—
52C2×C32×C4—21no—
53C2×C32×C4—21no—
54C2×C32×C4—21no—
55C2×C32×C4—41no—
56C2×C32×C4—41no—
57C2×C32×C4SD1611yescharacteristic
58C2×C32×C4Q1611yescharacteristic
59C2×C3×Dic3—22no—
60C2×C3×Dic3—22no—
61C2×C3×Dic3—41no—
62C2×C3×Dic3—41no—
63C2×C3×Dic3—41no—
64C2×C3×Dic3—41no—
65C3×Dic6—42no—
66C3×Dic6—42no—
67C32×C8—81no—
68C3×C3⋊C8—42no—
69#395—31no—
70#343—31no—
71#324C3×D311yescharacteristic
72C2×C3×Q8—121no—
73C2×C3×Q8—122no—
74C22×C3×C4—21no—
75C22×C3×C4—21no—
76C22×C3×C4—21no—
77C22×C3×C4—61no—
78C22×C3×C4—61no—
79C22×C3×C4C4×D311yescharacteristic
80C22×C3×C4D1211yescharacteristic
81C22×C3×C4#6711yescharacteristic
82C22×C3×C4C2×C3×C411yescharacteristic
83C22×C3×C4C3×D411yescharacteristic
84C22×C3×C4C3×D411yescharacteristic
85C22×Dic3—21no—
86C22×Dic3—21no—
87C2×Dic6—41no—
88C2×Dic6—42no—
89C3×M16—62no—
90C3×M16—121no—
91C2×C3×C8—42no—
92C2×C3×C8—41no—
93C2×C3×C8—41no—
94C2×C3×C8—121no—
95C3×C4⋊C4—41no—
96C3×C4⋊C4—41no—
97C3×C4⋊C4—42no—
98C3×C4⋊C4—122no—
99Dic3⋊C4—42no—
100#208—22no—
101#208—41no—
102C2×C3⋊C8—41no—
103C22×C32—21no—
104C22×C32—21no—
105C22×C32#9911yescharacteristic
106C22×C32#10311yescharacteristic
107C22×C32#10411yescharacteristic
108C32×C4—21no—
109C32×C4—21no—
110C32×C4—41no—
111C32×C4—41no—
112C3×Dic3—42no—
113C3×Dic3—42no—
114C22×Q8—31no—
115C2×M16—61no—
116C2×C4⋊C4—61no—
117C2×C4⋊C4C2×C3×D311yescharacteristic
118C22⋊C8—21no—
119#95—31no—
120#95—61no—
121C23×C3—21no—
122C23×C3(C2×D3)⋊C411yescharacteristic
123C23×C3C3×C22⋊C411yescharacteristic
124C3×Q8—122no—
125C3×Q8—122no—
126C2×C3×C4—21no—
127C2×C3×C4—21no—
128C2×C3×C4—21no—
129C2×C3×C4—21no—
130C2×C3×C4—22no—
131C2×C3×C4—21no—
132C2×C3×C4—21no—
133C2×C3×C4—21no—
134C2×C3×C4—21no—
135C2×C3×C4—21no—
136C2×C3×C4—21no—
137C2×C3×C4—41no—
138C2×C3×C4—41no—
139C2×C3×C4—41no—
140C2×C3×C4—41no—
141C2×C3×C4—41no—
142C2×C3×C4—41no—
143C2×C3×C4—41no—
144C2×C3×C4—62no—
145C2×C3×C4—62no—
146C2×C3×C4—81no—
147C2×C3×C4—81no—
148C2×C3×C4—121no—
149C2×C3×C4—121no—
150C2×C3×C4—121no—
151C2×C3×C4—121no—
152C2×C3×C4#20411yescharacteristic
153C2×C3×C4Dic1211yescharacteristic
154C2×C3×C4C3×SD1611yescharacteristic
155C2×C3×C4C3×Q1611yescharacteristic
156C2×Dic3—22no—
157C2×Dic3—22no—
158C2×Dic3—41no—
159C2×Dic3—41no—
160C2×Dic3—41no—
161C2×Dic3—41no—
162Dic6—42no—
163Dic6—42no—
164C3×C8—82no—
165C3×C8—81no—
166C3×C8—81no—
167C3×C8—122no—
168C3⋊C8—42no—
169C2×C32—21no—
170C2×C32—21no—
171C2×C32#32811yescharacteristic
172C2×C32AΣL(1,𝔽16)11yescharacteristic
173C2×C32#35611yescharacteristic
174C2×Q8—121no—
175C2×Q8—122no—
176C22×C4—61no—
177C22×C4—61no—
178C22×C4C3×C4×D311yescharacteristic
179C22×C4C3×D1211yescharacteristic
180C22×C4C3×#6711yescharacteristic
181M16—62no—
182M16—121no—
183C2×C8—41no—
184C2×C8—121no—
185C4⋊C4—41no—
186C4⋊C4—122no—
187C22×C3—21no—
188C22×C3—21no—
189C22×C3—21no—
190C22×C3—21no—
191C22×C3—21no—
192C22×C3—21no—
193C22×C3—21no—
194C22×C3—41no—
195C22×C3—41no—
196C22×C3#80611yescharacteristic
197C22×C3#81611yescharacteristic
198C22×C3#82511yescharacteristic
199C22×C3C3×#9911yescharacteristic
200C22×C3C3×#10311yescharacteristic
201C22×C3C3×#10411yescharacteristic
202C3×C4—21no—
203C3×C4—21no—
204C3×C4—21no—
205C3×C4—21no—
206C3×C4—41no—
207C3×C4—41no—
208C3×C4—42no—
209C3×C4—41no—
210C3×C4—41no—
211C3×C4—41no—
212C3×C4—41no—
213C3×C4—81no—
214C3×C4—122no—
215C3×C4—122no—
216Dic3—42no—
217Dic3—42no—
218C32#135411yescharacteristic, complemented, Sylow
219C23C3×(C2×D3)⋊C411yescharacteristic
220Q8—122no—
221Q8—122no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—62no—
229C2×C4—62no—
230C2×C4—121no—
231C2×C4—121no—
232C2×C4—121no—
233C2×C4—121no—
234C2×C4C3×#20411yescharacteristic
235C2×C4C3×Dic1211yescharacteristic
236C8—81no—
237C8—122no—
238C2×C3—21no—
239C2×C3—21no—
240C2×C3—21no—
241C2×C3—21no—
242C2×C3—21no—
243C2×C3—21no—
244C2×C3—21no—
245C2×C3—41no—
246C2×C3—41no—
247C2×C3#446711yescharacteristic
248C2×C3#447111yescharacteristic
249C2×C3#447811yescharacteristic
250C2×C3C3×#32811yescharacteristic
251C2×C3C3×AΣL(1,𝔽16)11yescharacteristic
252C2×C3C3×#35611yescharacteristic
253C22—21no—
254C22—21no—
255C22C3×#80611yescharacteristic
256C22C3×#81611yescharacteristic
257C22C3×#82511yescharacteristic
258C4—21no—
259C4—21no—
260C4—41no—
261C4—41no—
262C4—122no—
263C4—122no—
264C3—21no—
265C3#6745711yescharacteristic, direct product factor
266C3C3×#135411yescharacteristic, complemented
267C2—21no—
268C2—21no—
269C2C3×#446711yescharacteristic
270C2C3×#447111yescharacteristic
271C2C3×#447811yescharacteristic
subgroupG/H
centerC22×C3#806
commutatorC22×C3×C4C2×C3×C4
FrattiniC2×C4⋊C4C2×C3×D3
FittingC32×#324C2
socleC22×C32#99
prime radicalC23×C32C22⋊C4
cosocleC2×C3×C4⋊C4C22×C3
hypercenterC3×#324D3
hypocenterC3C3×#1354
LCSG ▷ C22×C3×C4 ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C23×C3 ◁ C2×C3×C4⋊C4 ◁ C3×#324

Complements

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

NH ≅ G/Ntype
5. #67457C3direct (N × H)
218. C32#1354semidirect
265. C3#67457direct (N × H)
266. C3C3×#1354semidirect

Maximal subgroups

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

subgroupindex
C3×#49792
C32×#3242
C3×#45302
C3×#13543
#674573