Finite Group Databasebeta

← #76560

Subgroups — #76560

Order 384.

352 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 352 conjugacy classes of subgroups — too many to draw. Only its 133 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×#391C211yesmaximal, characteristic
2#5229C211yesmaximal, characteristic
3#5229C211yesmaximal, characteristic
4#4984C211yesmaximal, characteristic
5#4972C211yesmaximal, characteristic
6#4932C211yesmaximal, characteristic
7#4928C211yesmaximal, characteristic
8C3⋊#401C212yesmaximal
9#4660C212yesmaximal
10#4659C212yesmaximal
11#4658C212yesmaximal
12#2645—31nomaximal, Sylow
13C22×C3×Q8C2211yescharacteristic
14C2×C3×C4⋊C4C2211yescharacteristic
15C2×C3×C42C2211yescharacteristic
16C2×C4⋊Dic3C2211yescharacteristic
17C2×C4⋊Dic3C2211yescharacteristic
18C2×C4⋊Dic3C2212yes—
19C2×Dic3⋊C4C2212yes—
20C2×Dic3⋊C4C2212yes—
21C2×C4×Dic3C2211yescharacteristic
22C2×C4×Dic3C2211yescharacteristic
23C3×#95C2212yes—
24C3×#95C2212yes—
25C3⋊#95C2211yescharacteristic
26C3⋊#95C2212yes—
27C3⋊#95C2212yes—
28C3⋊#95C2212yes—
29C3⋊#95C2211yescharacteristic
30C3⋊#95C2212yes—
31C3⋊#95C2212yes—
32C3⋊#95C2211yescharacteristic
33C3⋊#95C2212yes—
34C3⋊#95C2212yes—
35C3⋊#95C2211yescharacteristic
36#401—32no—
37#400—32no—
38#400—32no—
39#400—32no—
40#391—31no—
41#391—31no—
42#391D311yescharacteristic
43#389—31no—
44#389—31no—
45#389—31no—
46#376—31no—
47C2×C3×Q8—22no—
48C2×C3×Q8—22no—
49C2×C3×Q8—22no—
50C22×C3×C4C2311yescharacteristic
51C22×C3×C4C2312yes—
52C22×C3×C4C2311yescharacteristic
53C22×C3×C4C2312yes—
54C22×C3×C4C2311yescharacteristic
55C22×Dic3C2311yescharacteristic
56C22×Dic3C2311yescharacteristic
57C22×Dic3C2311yescharacteristic
58C22×Dic3C2311yescharacteristic
59C22×Dic3C2312yes—
60C22×Dic3C2312yes—
61C3×C4⋊C4—22no—
62C3×C42—22no—
63C4⋊Dic3—22no—
64C4⋊Dic3—22no—
65C4⋊Dic3—42no—
66Dic3⋊C4—42no—
67Dic3⋊C4—42no—
68C4×Dic3—22no—
69C4×Dic3—22no—
70C22×Q8C2×D311yescharacteristic
71C2×C4⋊C4—31no—
72C2×C4⋊C4—31no—
73C2×C4⋊C4—32no—
74C2×C4⋊C4—32no—
75C2×C4⋊C4—32no—
76C2×C4⋊C4C2×D311yescharacteristic
77C2×C42—31no—
78C2×C42—31no—
79C2×C42C2×D311yescharacteristic
80#95—31no—
81#95—31no—
82#95—31no—
83#95—31no—
84#95—32no—
85#95—32no—
86#95—32no—
87#95—32no—
88#95—32no—
89#95—32no—
90#95—32no—
91#95C2×D312yes—
92#95C2×D312yes—
93C23×C3C2411yescharacteristic
94C3×Q8—44no—
95C2×C3×C4—21no—
96C2×C3×C4—21no—
97C2×C3×C4—22no—
98C2×C3×C4—22no—
99C2×C3×C4—22no—
100C2×C3×C4—22no—
101C2×C3×C4—21no—
102C2×C3×C4—22no—
103C2×C3×C4—21no—
104C2×C3×C4—21no—
105C2×C3×C4—21no—
106C2×C3×C4—22no—
107C2×C3×C4#4112yes—
108C2×C3×C4#4112yes—
109C2×C3×C4#4112yes—
110C2×Dic3—21no—
111C2×Dic3—21no—
112C2×Dic3—21no—
113C2×Dic3—21no—
114C2×Dic3—22no—
115C2×Dic3—22no—
116C2×Dic3—21no—
117C2×Dic3—22no—
118C2×Dic3—22no—
119C2×Dic3—21no—
120C2×Dic3—21no—
121C2×Dic3—21no—
122C2×Dic3—21no—
123C2×Dic3—21no—
124C2×Dic3—22no—
125C2×Dic3—22no—
126C2×Dic3—21no—
127C2×Dic3—21no—
128C2×Q8—22no—
129C2×Q8—22no—
130C2×Q8—22no—
131C22×C4—31no—
132C22×C4—31no—
133C22×C4—31no—
134C22×C4—31no—
135C22×C4—32no—
136C22×C4—32no—
137C22×C4C22×D311yescharacteristic
138C22×C4C22×D312yes—
139C22×C4C22×D311yescharacteristic
140C22×C4C22×D312yes—
141C22×C4C22×D311yescharacteristic
142C4⋊C4—22no—
143C4⋊C4—62no—
144C4⋊C4—62no—
145C4⋊C4—122no—
146C4⋊C4—122no—
147C4⋊C4—122no—
148C42—22no—
149C42—62no—
150C42—62no—
151C22×C3C2×#4111yescharacteristic
152C22×C3C2×#4111yescharacteristic
153C22×C3C2×#4111yescharacteristic
154C22×C3H(5,𝔽2)11yescharacteristic
155C22×C32−1+411yescharacteristic
156C22×C32−1+411yescharacteristic
157C22×C32−1+411yescharacteristic
158C3×C4—42no—
159C3×C4—41no—
160C3×C4—41no—
161C3×C4—42no—
162C3×C4#12614yes—
163Dic3—41no—
164Dic3—41no—
165Dic3—42no—
166Dic3—41no—
167Dic3—41no—
168Dic3—42no—
169C23C23×D311yescharacteristic
170Q8—44no—
171C2×C4—22no—
172C2×C4—21no—
173C2×C4—21no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—21no—
183C2×C4—61no—
184C2×C4—61no—
185C2×C4—62no—
186C2×C4—61no—
187C2×C4—61no—
188C2×C4—62no—
189C2×C4—62no—
190C2×C4—61no—
191C2×C4—61no—
192C2×C4—61no—
193C2×C4—62no—
194C2×C4—61no—
195C2×C4—62no—
196C2×C4—61no—
197C2×C4—62no—
198C2×C4—61no—
199C2×C4—61no—
200C2×C4—61no—
201C2×C4#23512yes—
202C2×C4#23712yes—
203C2×C4#23712yes—
204C2×C3C2×#12611yescharacteristic
205C2×C3#54111yescharacteristic
206C2×C3#54111yescharacteristic
207C2×C3#54111yescharacteristic
208C2×C3#54211yescharacteristic
209C2×C3#54211yescharacteristic
210C2×C3#54211yescharacteristic
211C22C2×#23511yescharacteristic
212C22C2×#23711yescharacteristic
213C22C2×#23711yescharacteristic
214C22#100711yescharacteristic
215C22#100711yescharacteristic
216C22#100911yescharacteristic
217C22#101011yescharacteristic
218C4—41no—
219C4—42no—
220C4—42no—
221C4—41no—
222C4—122no—
223C4—121no—
224C4—121no—
225C4—121no—
226C4—122no—
227C4—121no—
228C4#87914yes—
229C3#264511yescharacteristic, complemented, Sylow
230C2C2×#87911yescharacteristic
231C2#558211yescharacteristic
232C2#558311yescharacteristic
233C2#562511yescharacteristic
234C2#564311yescharacteristic
235C2#568211yescharacteristic
236C2#573111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D3
commutator, socle, prime radical, cosocleC23×C3C24
FittingC3×#391C2
hypercenter#391D3
hypocenterC3#2645
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
229. C3#2645semidirect

Maximal subgroups

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

subgroupindex
C3×#3912
#52292
#49842
#49722
#49322
#49282
C3⋊#4012
#46602
#46592
#46582
#26453