Finite Group Databasebeta

← C3×#10593379 #13166723

Subgroups — C3×#10593379 #13166723

Order 1728.

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

normal subgroups only

This group has 384 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
1C3×#63919C211yesmaximal, characteristic
2C3×#63919C211yesmaximal, characteristic
3C3×C4×#622C211yesmaximal, characteristic
4C3×#63740C214yesmaximal
5#10593379C311yesmaximal, characteristic, direct product factor
6C2×C3×#627—21no—
7C2×C3×#627C2212yes—
8C2×C3×#622C2212yes—
9C3×C4×C3⋊Dic3C2211yescharacteristic
10C32×C4⋊Dic3—21no—
11C32×C4⋊Dic3—21no—
12C3×#3724—21no—
13C3×#3724C2212yes—
14C3×#888—61no—
15C3×#888—61no—
16#63919C2×C311yescharacteristic
17#63919C2×C311yescharacteristic
18C4×#622C2×C311yescharacteristic
19#63740C2×C314yes—
20C2×C33×C4D411yescharacteristic
21C2×C3×C3⋊Dic3D411yescharacteristic
22C2×C3×C3⋊Dic3C2311yescharacteristic
23C2×C32×Dic3—22no—
24C2×C32×Dic3—22no—
25C3×#627—24no—
26C3×#627—42no—
27C3×#622—22no—
28C3×#487—91nomaximal
29C2×C3×Dic6—62no—
30C2×C3×Dic6—62no—
31C2×#627—21no—
32C2×#627C22×C312yes—
33C2×#622C22×C312yes—
34C32×C4⋊C4—61no—
35C32×C4⋊C4—61no—
36C4×C3⋊Dic3C22×C311yescharacteristic
37C3×C4⋊Dic3—21no—
38C3×C4⋊Dic3—21no—
39C3×C4⋊Dic3—21no—
40C3×C4⋊Dic3—21no—
41C3×C4⋊Dic3—41no—
42C3×C4⋊Dic3—41no—
43C3×Dic3⋊C4—62no—
44C3×Dic3⋊C4—62no—
45C3×C4×Dic3—61no—
46C3×C4×Dic3—61no—
47#3724—21no—
48#3724C22×C312yes—
49C22×C33C2×D411yescharacteristic
50C33×C4Q1612yes—
51C3×C3⋊Dic3SD1612yes—
52C3×C3⋊Dic3#4112yes—
53C32×Dic3—42no—
54C32×Dic3—42no—
55C3×C4⋊Q8—91no—
56C3×C4⋊Q8—91no—
57#888—61no—
58#888—61no—
59C3×#103—94no—
60C3×C4×C8—91no—
61C2×C32×C4—21no—
62C2×C32×C4—21no—
63C2×C32×C4—41no—
64C2×C32×C4—41no—
65C2×C32×C4—62no—
66C2×C32×C4—62no—
67C2×C32×C4C3×D411yescharacteristic
68C2×C3⋊Dic3C3×D411yescharacteristic
69C2×C3⋊Dic3C23×C311yescharacteristic
70C2×C3×Dic3—22no—
71C2×C3×Dic3—22no—
72C2×C3×Dic3—22no—
73C2×C3×Dic3—22no—
74C2×C3×Dic3—42no—
75C2×C3×Dic3—42no—
76C2×C3×Dic3—61no—
77C2×C3×Dic3—61no—
78C2×C3×Dic3—61no—
79C2×C3×Dic3—61no—
80C3×Dic6—124no—
81C3×Dic6—124no—
82#627—24no—
83#627—42no—
84#622—22no—
85#487—91noSylow
86C2×C33#12411yescharacteristic
87C2×C33C2×SD1611yescharacteristic
88C2×C33C2×Q1611yescharacteristic
89C2×C3×Q8—92no—
90C2×C3×Q8—181no—
91C2×Dic6—62no—
92C2×Dic6—62no—
93C2×C3×C8—92no—
94C3×C4⋊C4—61no—
95C3×C4⋊C4—61no—
96C3×C4⋊C4—61no—
97C3×C4⋊C4—61no—
98C3×C4⋊C4—92no—
99C3×C4⋊C4—121no—
100C3×C4⋊C4—121no—
101C3×C4⋊C4—181no—
102C3×C42—91no—
103C4⋊Dic3—21no—
104C4⋊Dic3—21no—
105Dic3⋊C4—62no—
106Dic3⋊C4—62no—
107C4×Dic3—61no—
108C4×Dic3—61no—
109C22×C32—21no—
110C22×C32—21no—
111C22×C32—41no—
112C22×C32—41no—
113C22×C32C2×C3×D411yescharacteristic
114C32×C4—22no—
115C32×C4—22no—
116C32×C4—42no—
117C32×C4—42no—
118C32×C4—122no—
119C32×C4—122no—
120C32×C4C3×Q1612yes—
121C3⋊Dic3C3×SD1612yes—
122C3⋊Dic3C3×#4112yes—
123C3×Dic3—42no—
124C3×Dic3—42no—
125C3×Dic3—42no—
126C3×Dic3—42no—
127C3×Dic3—62no—
128C3×Dic3—62no—
129C3×Dic3—62no—
130C3×Dic3—62no—
131C3×Dic3—82no—
132C3×Dic3—82no—
133C4⋊Q8—91no—
134C4⋊Q8—91no—
135#103—94no—
136C4×C8—91no—
137C33#48711yescharacteristic, complemented, Sylow
138C3×Q8—184no—
139C3×Q8—362no—
140C2×C3×C4—21no—
141C2×C3×C4—21no—
142C2×C3×C4—41no—
143C2×C3×C4—41no—
144C2×C3×C4—62no—
145C2×C3×C4—62no—
146C2×C3×C4—62no—
147C2×C3×C4—62no—
148C2×C3×C4—91no—
149C2×C3×C4—91no—
150C2×C3×C4—122no—
151C2×C3×C4—122no—
152C2×C3×C4GO+(4,𝔽2)11yescharacteristic
153C2×Dic3—22no—
154C2×Dic3—22no—
155C2×Dic3—61no—
156C2×Dic3—61no—
157C2×Dic3—61no—
158C2×Dic3—61no—
159Dic6—124no—
160Dic6—124no—
161C3×C8—182no—
162C2×C32—21no—
163C2×C32—21no—
164C2×C32—21no—
165C2×C32—21no—
166C2×C32—21no—
167C2×C32—21no—
168C2×C32—41no—
169C2×C32—41no—
170C2×C32—41no—
171C2×C32—41no—
172C2×C32—41no—
173C2×C32—41no—
174C2×C32C3×#12411yescharacteristic
175C2×C32C2×C3×SD1611yescharacteristic
176C2×C32C2×C3×Q1611yescharacteristic
177C2×Q8—92no—
178C2×Q8—181no—
179C2×C8—92no—
180C4⋊C4—61no—
181C4⋊C4—61no—
182C4⋊C4—92no—
183C4⋊C4—181no—
184C42—91no—
185C22×C3—21no—
186C22×C3—21no—
187C22×C3—41no—
188C22×C3—41no—
189C22×C3C2×GO+(4,𝔽2)11yescharacteristic
190C3×C4—22no—
191C3×C4—22no—
192C3×C4—42no—
193C3×C4—42no—
194C3×C4—92no—
195C3×C4—92no—
196C3×C4—122no—
197C3×C4—122no—
198C3×C4—122no—
199C3×C4—122no—
200C3×C4—242no—
201C3×C4—242no—
202C3×C4#377612yes—
203Dic3—42no—
204Dic3—42no—
205Dic3—62no—
206Dic3—62no—
207Dic3—62no—
208Dic3—62no—
209C32—21no—
210C32—21no—
211C32—41no—
212C32—41no—
213C32C3×#48711yescharacteristic, complemented
214Q8—184no—
215Q8—362no—
216C2×C4—62no—
217C2×C4—62no—
218C2×C4—91no—
219C2×C4—91no—
220C2×C4C3×GO+(4,𝔽2)11yescharacteristic
221C8—182no—
222C2×C3—21no—
223C2×C3—21no—
224C2×C3—21no—
225C2×C3—21no—
226C2×C3—21no—
227C2×C3—21no—
228C2×C3—41no—
229C2×C3—41no—
230C2×C3—41no—
231C2×C3—41no—
232C2×C3—41no—
233C2×C3—41no—
234C2×C3#6422111yescharacteristic
235C2×C3#6422711yescharacteristic
236C2×C3C2×#377611yescharacteristic
237C22C2×C3×GO+(4,𝔽2)11yescharacteristic
238C4—92no—
239C4—92no—
240C4—122no—
241C4—122no—
242C4C3×#377612yes—
243C3—21no—
244C3—21no—
245C3—41no—
246C3—41no—
247C3#1059337911yescharacteristic, direct product factor
248C2C3×#6422111yescharacteristic
249C2C3×#6422711yescharacteristic
250C2C2×C3×#377611yescharacteristic
subgroupG/H
centerC22×C3C2×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊Dic3C23×C3
FrattiniC22C2×C3×GO+(4,𝔽2)
FittingC2×C33×C4D4
socle, prime radicalC22×C33C2×D4
hypercenterC2×C3×C4GO+(4,𝔽2)
hypocenterC32C3×#487
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C2×C3×C4

Complements

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

NH ≅ G/Ntype
5. #10593379C3direct (N × H)
137. C33#487semidirect
213. C32C3×#487semidirect
247. C3#10593379direct (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×#637402
#105933793
C3×#4879