Finite Group Databasebeta

← #78214

Subgroups — #78214

Order 384.

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

normal subgroups only

This group has 416 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
1C2×#889C211yesmaximal, characteristic
2C2×#888C211yesmaximal, characteristic
3C3×#400C211yesmaximal, characteristic
4#4986C211yesmaximal, characteristic
5#4985C211yesmaximal, characteristic
6#4660C212yesmaximal
7#4659C211yesmaximal, characteristic
8#4658C212yesmaximal
9#4648C211yesmaximal, characteristic
10#4646C212yesmaximal
11#4646C212yesmaximal
12#2642—31nomaximal, Sylow
13C22×Dic6C2212yes—
14C2×C3×C4⋊C4C2211yescharacteristic
15C2×C3×C4⋊C4C2211yescharacteristic
16C2×C4⋊Dic3C2211yescharacteristic
17C2×C4⋊Dic3C2211yescharacteristic
18C2×Dic3⋊C4C2211yescharacteristic
19C2×Dic3⋊C4C2211yescharacteristic
20C2×Dic3⋊C4C2211yescharacteristic
21C2×Dic3⋊C4C2212yes—
22C2×Dic3⋊C4C2211yescharacteristic
23C2×C4×Dic3C2212yes—
24C2×C4×Dic3C2211yescharacteristic
25#889—24no—
26#888—24no—
27C3×#95C2212yes—
28C3×#95C2212yes—
29C3×#95C2211yescharacteristic
30C3⋊#95C2212yes—
31C3⋊#95C2212yes—
32C3⋊#95C2212yes—
33C3⋊#95C2212yes—
34C3⋊#95C2212yes—
35C3⋊#95C2212yes—
36C3⋊#95C2212yes—
37C3⋊#95C2211yescharacteristic
38C2×C4⋊Q8—31no—
39C2×#125—31no—
40#400—31no—
41#400—31no—
42#400—32no—
43#400—31no—
44#400—32no—
45#400D311yescharacteristic
46#391—32no—
47#391—32no—
48#376—31no—
49C22×C3×C4C2312yes—
50C22×C3×C4C2311yescharacteristic
51C22×C3×C4C2311yescharacteristic
52C22×C3×C4C2312yes—
53C22×C3×C4C2311yescharacteristic
54C22×Dic3C2312yes—
55C22×Dic3C2311yescharacteristic
56C22×Dic3C2311yescharacteristic
57C22×Dic3C2312yes—
58C22×Dic3C2311yescharacteristic
59C22×Dic3C2311yescharacteristic
60C2×Dic6—24no—
61C2×Dic6—28no—
62C3×C4⋊C4—22no—
63C3×C4⋊C4—22no—
64C4⋊Dic3—22no—
65C4⋊Dic3—22no—
66Dic3⋊C4—22no—
67Dic3⋊C4—24no—
68Dic3⋊C4—22no—
69Dic3⋊C4—22no—
70Dic3⋊C4—22no—
71C4×Dic3—24no—
72C4×Dic3D414yes—
73C22×Q8—32no—
74C4⋊Q8—64no—
75#125—64no—
76C2×C4⋊C4—31no—
77C2×C4⋊C4—31no—
78C2×C4⋊C4—31no—
79C2×C4⋊C4—31no—
80C2×C4⋊C4—31no—
81C2×C4⋊C4—32no—
82C2×C4⋊C4—31no—
83C2×C4⋊C4C2×D311yescharacteristic
84C2×C4⋊C4C2×D311yescharacteristic
85C2×C42—31no—
86C2×C42—32no—
87#95—32no—
88#95—31no—
89#95—32no—
90#95—32no—
91#95—32no—
92#95—32no—
93#95—32no—
94#95—32no—
95#95C2×D311yescharacteristic
96#95C2×D312yes—
97#95C2×D312yes—
98C23×C3C2411yescharacteristic
99C2×C3×C4—22no—
100C2×C3×C4—21no—
101C2×C3×C4—21no—
102C2×C3×C4—22no—
103C2×C3×C4—22no—
104C2×C3×C4—24no—
105C2×C3×C4—21no—
106C2×C3×C4—21no—
107C2×C3×C4—22no—
108C2×C3×C4—22no—
109C2×C3×C4—22no—
110C2×C3×C4C2×D412yes—
111C2×Dic3—21no—
112C2×Dic3—21no—
113C2×Dic3—21no—
114C2×Dic3—21no—
115C2×Dic3—22no—
116C2×Dic3—22no—
117C2×Dic3—24no—
118C2×Dic3—21no—
119C2×Dic3—22no—
120C2×Dic3—22no—
121C2×Dic3—21no—
122C2×Dic3—22no—
123C2×Dic3C2×D412yes—
124C2×Dic3C2×D412yes—
125C2×Dic3#4114yes—
126Dic6—48no—
127C2×Q8—64no—
128C2×Q8—68no—
129C22×C4—31no—
130C22×C4—31no—
131C22×C4—32no—
132C22×C4—31no—
133C22×C4—31no—
134C22×C4—32no—
135C22×C4C22×D312yes—
136C22×C4C22×D311yescharacteristic
137C22×C4C22×D311yescharacteristic
138C22×C4C22×D312yes—
139C22×C4C22×D311yescharacteristic
140C4⋊C4—22no—
141C4⋊C4—22no—
142C4⋊C4—62no—
143C4⋊C4—62no—
144C4⋊C4—62no—
145C4⋊C4—62no—
146C4⋊C4—64no—
147C4⋊C4—62no—
148C4⋊C4—62no—
149C42—34no—
150C42—64no—
151C22×C3C22×D411yescharacteristic
152C22×C3C2×#4112yes—
153C22×C32−1+411yescharacteristic
154C22×C32−1+412yes—
155C22×C32−1+411yescharacteristic
156C3×C4—22no—
157C3×C4—42no—
158C3×C4—41no—
159C3×C4—41no—
160C3×C4—42no—
161Dic3—22no—
162Dic3—42no—
163Dic3—41no—
164Dic3—41no—
165Dic3—42no—
166Dic3#12414yes—
167C23C23×D311yescharacteristic
168Q8—128no—
169C2×C4—22no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—22no—
173C2×C4—21no—
174C2×C4—22no—
175C2×C4—24no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—21no—
180C2×C4—32no—
181C2×C4—34no—
182C2×C4—32no—
183C2×C4—61no—
184C2×C4—61no—
185C2×C4—61no—
186C2×C4—61no—
187C2×C4—62no—
188C2×C4—62no—
189C2×C4—61no—
190C2×C4—62no—
191C2×C4—64no—
192C2×C4—62no—
193C2×C4—62no—
194C2×C4—61no—
195C2×C4D3×D412yes—
196C2×C3C2×#12411yescharacteristic
197C2×C3#53611yescharacteristic
198C2×C3#53611yescharacteristic
199C2×C3#54112yes—
200C2×C3#54112yes—
201C22C2×D3×D411yescharacteristic
202C22#100711yescharacteristic
203C22D3×#4112yes—
204C22#101012yes—
205C22#101011yescharacteristic
206C4—22no—
207C4—34no—
208C4—41no—
209C4—42no—
210C4—42no—
211C4—41no—
212C4—62no—
213C4—121no—
214C4—122no—
215C4—122no—
216C4—121no—
217C3#264211yescharacteristic, complemented, Sylow
218C2#562811yescharacteristic
219C2#564811yescharacteristic
220C2D3×#12411yescharacteristic
221C2#569612yes—
222C2#570112yes—
subgroupG/H
center, FrattiniC23C23×D3
commutator, socle, prime radical, cosocleC23×C3C24
FittingC3×#400C2
hypercenter#400D3
hypocenterC3#2642
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
217. C3#2642semidirect

Maximal subgroups

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

subgroupindex
C2×#8892
C2×#8882
C3×#4002
#49862
#49852
#46602
#46592
#46582
#46482
#46462
#26423