Finite Group Databasebeta

← #76186

Subgroups — #76186

Order 384.

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

normal subgroups only

This group has 368 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×#389C211yesmaximal, characteristic
2#4983C212yesmaximal
3#4981C212yesmaximal
4#4980C212yesmaximal
5#4978C212yesmaximal
6#4929C211yesmaximal, characteristic
7#4928C211yesmaximal, characteristic
8#4660C212yesmaximal
9#4646C212yesmaximal
10#2809—31nomaximal, Sylow
11C22×Dic6C2211yescharacteristic
12C2×C3×C4⋊C4C2212yes—
13C2×C3×C4⋊C4C2211yescharacteristic
14C2×C3×C4⋊C4C2211yescharacteristic
15C2×C3×C42C2211yescharacteristic
16C2×C4⋊Dic3C2211yescharacteristic
17C2×C4⋊Dic3C2211yescharacteristic
18C2×C4⋊Dic3C2211yescharacteristic
19C2×Dic3⋊C4C2212yes—
20C2×Dic3⋊C4C2212yes—
21C2×Dic3⋊C4C2212yes—
22C2×C4×Dic3C2212yes—
23C3×#95C2212yes—
24C3⋊#95C2212yes—
25C3⋊#95C2212yes—
26C3⋊#95C2212yes—
27C3⋊#95C2212yes—
28C3⋊#95C2212yes—
29C3⋊#95C2212yes—
30C3⋊#95C2212yes—
31C3⋊#95C2212yes—
32#400—32no—
33#398—32no—
34#398—32no—
35#391—31no—
36#391—32no—
37#389—31no—
38#389D311yescharacteristic
39#387—32no—
40#387—32no—
41C22×C3×C4C2312yes—
42C22×C3×C4C2312yes—
43C22×C3×C4C2311yescharacteristic
44C22×C3×C4C2311yescharacteristic
45C22×C3×C4C2311yescharacteristic
46C22×Dic3C2312yes—
47C22×Dic3C2312yes—
48C22×Dic3C2312yes—
49C22×Dic3C2312yes—
50C2×Dic6—41no—
51C2×Dic6—41no—
52C2×Dic6Q814yes—
53C3×C4⋊C4—22no—
54C3×C4⋊C4—24no—
55C3×C4⋊C4—41no—
56C3×C42—41no—
57C4⋊Dic3—22no—
58C4⋊Dic3—41no—
59C4⋊Dic3—41no—
60Dic3⋊C4—24no—
61Dic3⋊C4—42no—
62Dic3⋊C4—42no—
63C4×Dic3—42no—
64C22×Q8—31no—
65C2×C4⋊C4—32no—
66C2×C4⋊C4—31no—
67C2×C4⋊C4—31no—
68C2×C4⋊C4—32no—
69C2×C4⋊C4—31no—
70C2×C4⋊C4—32no—
71C2×C4⋊C4C2×D312yes—
72C2×C4⋊C4C2×D311yescharacteristic
73C2×C4⋊C4C2×D311yescharacteristic
74C2×C42—32no—
75C2×C42C2×D311yescharacteristic
76#95—32no—
77#95—32no—
78#95—32no—
79#95—32no—
80#95—32no—
81#95—32no—
82#95—32no—
83#95—32no—
84#95C2×D312yes—
85C23×C3C2411yescharacteristic
86C2×C3×C4—21no—
87C2×C3×C4—21no—
88C2×C3×C4—21no—
89C2×C3×C4—21no—
90C2×C3×C4—21no—
91C2×C3×C4—21no—
92C2×C3×C4—22no—
93C2×C3×C4—22no—
94C2×C3×C4—22no—
95C2×C3×C4—22no—
96C2×C3×C4—22no—
97C2×C3×C4—22no—
98C2×C3×C4C2×Q812yes—
99C2×C3×C4#4112yes—
100C2×C3×C4#4112yes—
101C2×Dic3—22no—
102C2×Dic3—22no—
103C2×Dic3—22no—
104C2×Dic3—22no—
105C2×Dic3—22no—
106C2×Dic3—22no—
107C2×Dic3—22no—
108C2×Dic3—22no—
109C2×Dic3—22no—
110C2×Dic3—22no—
111C2×Dic3—22no—
112C2×Dic3C2×Q814yes—
113Dic6—44no—
114C2×Q8—34no—
115C2×Q8—121no—
116C2×Q8—121no—
117C22×C4—32no—
118C22×C4—32no—
119C22×C4—32no—
120C22×C4—32no—
121C22×C4C22×D312yes—
122C22×C4C22×D312yes—
123C22×C4C22×D311yescharacteristic
124C22×C4C22×D311yescharacteristic
125C22×C4C22×D311yescharacteristic
126C4⋊C4—22no—
127C4⋊C4—24no—
128C4⋊C4—41no—
129C4⋊C4—64no—
130C4⋊C4—62no—
131C4⋊C4—122no—
132C4⋊C4—122no—
133C4⋊C4—121no—
134C4⋊C4—121no—
135C42—41no—
136C42—122no—
137C22×C3C22×Q811yescharacteristic
138C22×C3C2×#4111yescharacteristic
139C22×C3C2×#4111yescharacteristic
140C22×C3H(5,𝔽2)11yescharacteristic
141C22×C3H(5,𝔽2)11yescharacteristic
142C22×C32−1+411yescharacteristic
143C22×C32−1+411yescharacteristic
144C3×C4—22no—
145C3×C4—22no—
146C3×C4—22no—
147C3×C4—42no—
148C3×C4—42no—
149Dic3—24no—
150Dic3—42no—
151Dic3—42no—
152Dic3—42no—
153C23C23×D311yescharacteristic
154Q8—124no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—22no—
164C2×C4—22no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—34no—
168C2×C4—62no—
169C2×C4—62no—
170C2×C4—62no—
171C2×C4—62no—
172C2×C4—62no—
173C2×C4—62no—
174C2×C4—62no—
175C2×C4—62no—
176C2×C4—62no—
177C2×C4—62no—
178C2×C4—62no—
179C2×C4#23512yes—
180C2×C4#23712yes—
181C2×C4D3×Q812yes—
182C2×C3#53911yescharacteristic
183C2×C3#53911yescharacteristic
184C2×C3#54311yescharacteristic
185C2×C3#55511yescharacteristic
186C2×C3#55711yescharacteristic
187C2×C3#55711yescharacteristic
188C2×C3#56311yescharacteristic
189C22C2×#23511yescharacteristic
190C22C2×#23711yescharacteristic
191C22#100411yescharacteristic
192C22C2×D3×Q811yescharacteristic
193C22#100711yescharacteristic
194C22#100911yescharacteristic
195C22#101011yescharacteristic
196C4—22no—
197C4—22no—
198C4—22no—
199C4—42no—
200C4—42no—
201C4—64no—
202C4—122no—
203C4—122no—
204C4—122no—
205C3#280911yescharacteristic, complemented, Sylow
206C2#551511yescharacteristic
207C2#556311yescharacteristic
208C2#556711yescharacteristic
209C2#560211yescharacteristic
210C2#563411yescharacteristic
211C2#569911yescharacteristic
212C2#572111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D3
commutator, socle, prime radical, cosocleC23×C3C24
FittingC3×#389C2
hypercenter#389D3
hypocenterC3#2809
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
205. C3#2809semidirect

Maximal subgroups

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

subgroupindex
C3×#3892
#49832
#49812
#49802
#49782
#49292
#49282
#46602
#46462
#28093