Finite Group Databasebeta

← C3×#10593377 #13166721

Subgroups — C3×#10593377 #13166721

Order 1728.

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

normal subgroups only

This group has 396 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×#63873C211yesmaximal, characteristic
3C3×C4×#622C211yesmaximal, characteristic
4C3×#63740C214yesmaximal
5#10593377C311yesmaximal, characteristic, direct product factor
6C2×C32×Dic6—21no—
7C2×C3×#627C2212yes—
8C2×C3×#622C2212yes—
9C3×C4×C3⋊Dic3C2211yescharacteristic
10C32×C4⋊Dic3—21no—
11C3×#3724—21no—
12C3×#3724—21no—
13C3×#3724C2212yes—
14C3×#944—61no—
15C3×#888—61no—
16#63919C2×C311yescharacteristic
17#63873C2×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—
25C32×Dic6—42no—
26C3×#627—24no—
27C3×#622—22no—
28C3×#487—91nomaximal
29C2×C32×Q8—61no—
30C2×C3×Dic6—21no—
31C2×C3×Dic6—21no—
32C2×C3×Dic6—41no—
33C2×C3×Dic6—62no—
34C2×#627C22×C312yes—
35C2×#622C22×C312yes—
36C32×C4⋊C4—61no—
37C4×C3⋊Dic3C22×C311yescharacteristic
38C3×C4⋊Dic3—21no—
39C3×C4⋊Dic3—21no—
40C3×C4⋊Dic3—41no—
41C3×Dic3⋊C4—62no—
42C3×Dic3⋊C4—62no—
43C3×Dic3⋊C4—62no—
44C3×C4×Dic3—61no—
45C3×C4×Dic3—61no—
46#3724—21no—
47#3724—21no—
48#3724C22×C312yes—
49C22×C33C2×D411yescharacteristic
50C33×C4SD1612yes—
51C3×C3⋊Dic3Q1612yes—
52C3×C3⋊Dic3#4112yes—
53C32×Dic3—42no—
54C32×Dic3—42no—
55C3×C4⋊Q8—91no—
56C3×C4⋊Q8—91no—
57#944—61no—
58#888—61no—
59C3×#103—94no—
60C3×C4×C8—91no—
61C32×Q8—122no—
62C2×C32×C4—21no—
63C2×C32×C4—21no—
64C2×C32×C4—41no—
65C2×C32×C4—41no—
66C2×C32×C4—62no—
67C2×C32×C4—62no—
68C2×C32×C4C3×D411yescharacteristic
69C2×C3⋊Dic3C3×D411yescharacteristic
70C2×C3⋊Dic3C23×C311yescharacteristic
71C2×C3×Dic3—22no—
72C2×C3×Dic3—22no—
73C2×C3×Dic3—22no—
74C2×C3×Dic3—22no—
75C2×C3×Dic3—42no—
76C2×C3×Dic3—42no—
77C2×C3×Dic3—61no—
78C2×C3×Dic3—61no—
79C2×C3×Dic3—61no—
80C2×C3×Dic3—61no—
81C3×Dic6—42no—
82C3×Dic6—44no—
83C3×Dic6—42no—
84C3×Dic6—124no—
85#627—24no—
86#622—22no—
87#487—91noSylow
88C2×C33#12411yescharacteristic
89C2×C33C2×SD1611yescharacteristic
90C2×C33C2×Q1611yescharacteristic
91C2×C3×Q8—61no—
92C2×C3×Q8—61no—
93C2×C3×Q8—92no—
94C2×C3×Q8—121no—
95C2×Dic6—21no—
96C2×Dic6—62no—
97C2×C3×C8—92no—
98C3×C4⋊C4—61no—
99C3×C4⋊C4—61no—
100C3×C4⋊C4—92no—
101C3×C4⋊C4—121no—
102C3×C4⋊C4—181no—
103C3×C4⋊C4—181no—
104C3×C42—91no—
105C4⋊Dic3—21no—
106Dic3⋊C4—62no—
107Dic3⋊C4—62no—
108Dic3⋊C4—62no—
109C4×Dic3—61no—
110C4×Dic3—61no—
111C22×C32—21no—
112C22×C32—21no—
113C22×C32—41no—
114C22×C32—41no—
115C22×C32C2×C3×D411yescharacteristic
116C32×C4—22no—
117C32×C4—22no—
118C32×C4—42no—
119C32×C4—42no—
120C32×C4—122no—
121C32×C4—122no—
122C32×C4C3×SD1612yes—
123C3⋊Dic3C3×Q1612yes—
124C3⋊Dic3C3×#4112yes—
125C3×Dic3—42no—
126C3×Dic3—42no—
127C3×Dic3—44no—
128C3×Dic3—42no—
129C3×Dic3—42no—
130C3×Dic3—62no—
131C3×Dic3—62no—
132C3×Dic3—62no—
133C3×Dic3—62no—
134C3×Dic3—82no—
135C4⋊Q8—91no—
136C4⋊Q8—91no—
137#103—94no—
138C4×C8—91no—
139C33#48711yescharacteristic, complemented, Sylow
140C3×Q8—122no—
141C3×Q8—124no—
142C3×Q8—122no—
143C3×Q8—184no—
144C2×C3×C4—21no—
145C2×C3×C4—21no—
146C2×C3×C4—41no—
147C2×C3×C4—41no—
148C2×C3×C4—62no—
149C2×C3×C4—62no—
150C2×C3×C4—62no—
151C2×C3×C4—62no—
152C2×C3×C4—91no—
153C2×C3×C4—91no—
154C2×C3×C4—122no—
155C2×C3×C4—122no—
156C2×C3×C4GO+(4,𝔽2)11yescharacteristic
157C2×Dic3—22no—
158C2×Dic3—22no—
159C2×Dic3—61no—
160C2×Dic3—61no—
161C2×Dic3—61no—
162C2×Dic3—61no—
163Dic6—42no—
164Dic6—124no—
165C3×C8—182no—
166C2×C32—21no—
167C2×C32—21no—
168C2×C32—21no—
169C2×C32—21no—
170C2×C32—21no—
171C2×C32—21no—
172C2×C32—41no—
173C2×C32—41no—
174C2×C32—41no—
175C2×C32—41no—
176C2×C32—41no—
177C2×C32—41no—
178C2×C32C3×#12411yescharacteristic
179C2×C32C2×C3×SD1611yescharacteristic
180C2×C32C2×C3×Q1611yescharacteristic
181C2×Q8—61no—
182C2×Q8—92no—
183C2×C8—92no—
184C4⋊C4—61no—
185C4⋊C4—92no—
186C4⋊C4—181no—
187C4⋊C4—181no—
188C42—91no—
189C22×C3—21no—
190C22×C3—21no—
191C22×C3—41no—
192C22×C3—41no—
193C22×C3C2×GO+(4,𝔽2)11yescharacteristic
194C3×C4—22no—
195C3×C4—22no—
196C3×C4—42no—
197C3×C4—42no—
198C3×C4—92no—
199C3×C4—92no—
200C3×C4—122no—
201C3×C4—122no—
202C3×C4—124no—
203C3×C4—122no—
204C3×C4—122no—
205C3×C4—242no—
206C3×C4#377512yes—
207Dic3—42no—
208Dic3—42no—
209Dic3—62no—
210Dic3—62no—
211Dic3—62no—
212Dic3—62no—
213C32—21no—
214C32—21no—
215C32—41no—
216C32—41no—
217C32C3×#48711yescharacteristic, complemented
218Q8—122no—
219Q8—184no—
220C2×C4—62no—
221C2×C4—62no—
222C2×C4—91no—
223C2×C4—91no—
224C2×C4C3×GO+(4,𝔽2)11yescharacteristic
225C8—182no—
226C2×C3—21no—
227C2×C3—21no—
228C2×C3—21no—
229C2×C3—21no—
230C2×C3—21no—
231C2×C3—21no—
232C2×C3—41no—
233C2×C3—41no—
234C2×C3—41no—
235C2×C3—41no—
236C2×C3—41no—
237C2×C3—41no—
238C2×C3#6422111yescharacteristic
239C2×C3#6422811yescharacteristic
240C2×C3C2×#377511yescharacteristic
241C22C2×C3×GO+(4,𝔽2)11yescharacteristic
242C4—92no—
243C4—92no—
244C4—122no—
245C4—122no—
246C4C3×#377512yes—
247C3—21no—
248C3—21no—
249C3—41no—
250C3—41no—
251C3#1059337711yescharacteristic, direct product factor
252C2C3×#6422111yescharacteristic
253C2C3×#6422811yescharacteristic
254C2C2×C3×#377511yescharacteristic
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. #10593377C3direct (N × H)
139. C33#487semidirect
217. C32C3×#487semidirect
251. C3#10593377direct (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×#638732
C3×C4×#6222
C3×#637402
#105933773
C3×#4879