Finite Group Databasebeta

← C3×#10590039 #13154889

Subgroups — C3×#10590039 #13154889

Order 1728.

282 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 282 conjugacy classes of subgroups — too many to draw. Only its 54 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×#63919C211yesmaximal, characteristic
2C3×C4⋊#622C211yesmaximal, characteristic
3C3×#63572C211yesmaximal, characteristic
4#10590039C311yesmaximal, characteristic, direct product factor
5C2×C3×#627—21no—
6C2×C3×#622—21no—
7C3×C4×C3⋊Dic3C2211yescharacteristic
8C32×C4⋊Dic3—21no—
9C2×C32×C3⋊C8—21no—
10C3×#3724C412yes—
11C3×#888—61no—
12#63919C2×C311yescharacteristic
13C4⋊#622C2×C311yescharacteristic
14C3×Dic3⋊C8—61no—
15#63572C2×C311yescharacteristic
16C2×C33×C4D411yescharacteristic
17C2×C3×C3⋊Dic3C2×C411yescharacteristic
18C2×C3×C3⋊Dic3D411yescharacteristic
19C2×C32×Dic3—22no—
20C3×#627—41no—
21C3×#627—41no—
22C3×#622—41no—
23C32×C3⋊C8—41no—
24C3×#332—91nomaximal
25C2×C3×Dic6—62no—
26C2×#627—21no—
27C2×#622—21no—
28C2×C32×C8—61no—
29C32×C4⋊C4—61no—
30C4×C3⋊Dic3C22×C311yescharacteristic
31C3×C4⋊Dic3—21no—
32C3×C4⋊Dic3—21no—
33C3×C4⋊Dic3—41no—
34C3×Dic3⋊C4—62no—
35C3×C4×Dic3—61no—
36C3×C4×Dic3—61no—
37C2×C3×C3⋊C8—21no—
38C2×C3×C3⋊C8—21no—
39C2×C3×C3⋊C8—41no—
40#3724C3×C412yes—
41C22×C33C22⋊C411yescharacteristic
42C33×C4SD1611yescharacteristic
43C33×C4Q1611yescharacteristic
44C3×C3⋊Dic3—21no—
45C3×C3⋊Dic3D811yescharacteristic
46C3×C3⋊Dic3SD1611yescharacteristic
47C32×Dic3—42no—
48C3×C4⋊Q8—91no—
49#888—61no—
50C3×C4⋊C8—91no—
51C3×C4⋊C8—91no—
52Dic3⋊C8—61no—
53C2×C32×C4—21no—
54C2×C32×C4—21no—
55C2×C32×C4—41no—
56C2×C32×C4—41no—
57C2×C32×C4—62no—
58C2×C32×C4C3×D411yescharacteristic
59C2×C3⋊Dic3C2×C3×C411yescharacteristic
60C2×C3⋊Dic3C3×D411yescharacteristic
61C2×C3×Dic3—22no—
62C2×C3×Dic3—22no—
63C2×C3×Dic3—42no—
64C2×C3×Dic3—61no—
65C2×C3×Dic3—61no—
66C2×C3×Dic3—61no—
67C2×C3×Dic3—61no—
68C3×Dic6—122no—
69C3×Dic6—122no—
70#627—41no—
71#627—41no—
72#622—41no—
73C32×C8—121no—
74C3×C3⋊C8—41no—
75C3×C3⋊C8—42no—
76C3×C3⋊C8—41no—
77#332—91noSylow
78C2×C33#10111yescharacteristic
79C2×C33#10211yescharacteristic
80C2×C33#10311yescharacteristic
81C2×C3×Q8—181no—
82C2×Dic6—62no—
83C2×C3×C8—61no—
84C2×C3×C8—61no—
85C2×C3×C8—121no—
86C2×C3×C8—181no—
87C3×C4⋊C4—61no—
88C3×C4⋊C4—61no—
89C3×C4⋊C4—92no—
90C3×C4⋊C4—121no—
91C3×C42—91no—
92C4⋊Dic3—21no—
93Dic3⋊C4—62no—
94C4×Dic3—61no—
95C4×Dic3—61no—
96C2×C3⋊C8—21no—
97C22×C32—21no—
98C22×C32—21no—
99C22×C32—41no—
100C22×C32—41no—
101C22×C32C3×C22⋊C411yescharacteristic
102C32×C4—21no—
103C32×C4—21no—
104C32×C4—21no—
105C32×C4—21no—
106C32×C4—41no—
107C32×C4—41no—
108C32×C4—41no—
109C32×C4—41no—
110C32×C4—122no—
111C32×C4C3×SD1611yescharacteristic
112C32×C4C3×Q1611yescharacteristic
113C3⋊Dic3—21no—
114C3⋊Dic3C3×D811yescharacteristic
115C3⋊Dic3C3×SD1611yescharacteristic
116C3×Dic3—42no—
117C3×Dic3—42no—
118C3×Dic3—61no—
119C3×Dic3—61no—
120C3×Dic3—61no—
121C3×Dic3—61no—
122C3×Dic3—62no—
123C3×Dic3—82no—
124C3×Dic3—121no—
125C4⋊Q8—91no—
126C4⋊C8—91no—
127C4⋊C8—91no—
128C33#33211yescharacteristic, complemented, Sylow
129C3×Q8—361no—
130C3×Q8—361no—
131C2×C3×C4—21no—
132C2×C3×C4—21no—
133C2×C3×C4—41no—
134C2×C3×C4—41no—
135C2×C3×C4—62no—
136C2×C3×C4—62no—
137C2×C3×C4—91no—
138C2×C3×C4—91no—
139C2×C3×C4—122no—
140C2×C3×C4GO+(4,𝔽2)11yescharacteristic
141C2×Dic3—22no—
142C2×Dic3—61no—
143C2×Dic3—61no—
144C2×Dic3—61no—
145C2×Dic3—61no—
146Dic6—122no—
147Dic6—122no—
148C3×C8—121no—
149C3×C8—122no—
150C3×C8—121no—
151C3×C8—361no—
152C3⋊C8—41no—
153C2×C32—21no—
154C2×C32—21no—
155C2×C32—21no—
156C2×C32—21no—
157C2×C32—21no—
158C2×C32—21no—
159C2×C32—41no—
160C2×C32—41no—
161C2×C32—41no—
162C2×C32—41no—
163C2×C32—41no—
164C2×C32—41no—
165C2×C32C3×#10111yescharacteristic
166C2×C32C3×#10211yescharacteristic
167C2×C32C3×#10311yescharacteristic
168C2×Q8—181no—
169C2×C8—61no—
170C2×C8—181no—
171C4⋊C4—61no—
172C4⋊C4—92no—
173C42—91no—
174C22×C3—21no—
175C22×C3—21no—
176C22×C3—41no—
177C22×C3—41no—
178C22×C3D32⋊C411yescharacteristic
179C3×C4—21no—
180C3×C4—21no—
181C3×C4—21no—
182C3×C4—21no—
183C3×C4—41no—
184C3×C4—41no—
185C3×C4—41no—
186C3×C4—41no—
187C3×C4—91no—
188C3×C4—91no—
189C3×C4—122no—
190C3×C4—122no—
191C3×C4—181no—
192C3×C4—242no—
193C3×C4#377511yescharacteristic
194C3×C4#377611yescharacteristic
195Dic3—42no—
196Dic3—61no—
197Dic3—61no—
198Dic3—61no—
199Dic3—61no—
200Dic3—62no—
201Dic3—121no—
202C32—21no—
203C32—21no—
204C32—41no—
205C32—41no—
206C32C3×#33211yescharacteristic, complemented
207Q8—361no—
208Q8—361no—
209C2×C4—62no—
210C2×C4—91no—
211C2×C4—91no—
212C2×C4C3×GO+(4,𝔽2)11yescharacteristic
213C8—121no—
214C8—361no—
215C2×C3—21no—
216C2×C3—21no—
217C2×C3—21no—
218C2×C3—21no—
219C2×C3—21no—
220C2×C3—21no—
221C2×C3—41no—
222C2×C3—41no—
223C2×C3—41no—
224C2×C3—41no—
225C2×C3—41no—
226C2×C3—41no—
227C2×C3#6372811yescharacteristic
228C2×C3#6372911yescharacteristic
229C2×C3#6374011yescharacteristic
230C22C3×D32⋊C411yescharacteristic
231C4—91no—
232C4—91no—
233C4—122no—
234C4—181no—
235C4C3×#377511yescharacteristic
236C4C3×#377611yescharacteristic
237C3—21no—
238C3—21no—
239C3—41no—
240C3—41no—
241C3#1059003911yescharacteristic, direct product factor
242C2C3×#6372811yescharacteristic
243C2C3×#6372911yescharacteristic
244C2C3×#6374011yescharacteristic
subgroupG/H
centerC22×C3D32⋊C4
commutatorC2×C3⋊Dic3C2×C3×C4
FrattiniC2×C4C3×GO+(4,𝔽2)
FittingC2×C33×C4D4
socle, prime radicalC22×C33C22⋊C4
cosocleC4×C3⋊Dic3C22×C3
hypercenterC2×C3×C4GO+(4,𝔽2)
hypocenterC32C3×#332
LCSG ▷ C2×C3⋊Dic3 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C2×C3×C4

Complements

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

NH ≅ G/Ntype
4. #10590039C3direct (N × H)
128. C33#332semidirect
206. C32C3×#332semidirect
241. C3#10590039direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#639192
C3×C4⋊#6222
C3×#635722
#105900393
C3×#3329