Finite Group Databasebeta

← #68835

Subgroups — #68835

Order 384.

230 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 87 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×#817C211yesmaximal, characteristic
2#4975C211yesmaximal, characteristic
3#4972C211yesmaximal, characteristic
4C2×#808C211yesmaximal, characteristic
5C3×#340C211yesmaximal, characteristic
6#4550C211yesmaximal, characteristic
7#4529C211yesmaximal, characteristic
8#2084—31nomaximal, Sylow
9C22×C3×C8C2211yescharacteristic
10C2×C3×C4⋊C4C2211yescharacteristic
11C2×C3×C4⋊C4C2211yescharacteristic
12C2×C4⋊Dic3C2211yescharacteristic
13C2×C4⋊Dic3C2211yescharacteristic
14C2×Dic3⋊C4—21no—
15C2×Dic3⋊C4—21no—
16C2×Dic3⋊C4—21no—
17C2×C4×Dic3C2211yescharacteristic
18C22×C3⋊C8C2211yescharacteristic
19C3⋊#95—21no—
20#817—22no—
21#808—22no—
22C2×#106—31no—
23C2×#106—31no—
24#389—31no—
25#384—31no—
26#340—31no—
27#340D311yescharacteristic
28#336—31no—
29C22×C3×C4—21no—
30C22×C3×C4—21no—
31C22×C3×C4C2311yescharacteristic
32C22×Dic3—21no—
33C22×Dic3—21no—
34C22×Dic3D411yescharacteristic
35C22×Dic3D411yescharacteristic
36C2×C3×C8—21no—
37C2×C3×C8—21no—
38C2×C3×C8Q812yes—
39C3×C4⋊C4—21no—
40C3×C4⋊C4—21no—
41C3×C4⋊C4—21no—
42C3×C4⋊C4—21no—
43C4⋊Dic3—21no—
44C4⋊Dic3—21no—
45C4⋊Dic3—21no—
46C4⋊Dic3D412yes—
47Dic3⋊C4—42no—
48Dic3⋊C4—42no—
49Dic3⋊C4—42no—
50C4×Dic3—21no—
51C4×Dic3—21no—
52C2×C3⋊C8—21no—
53C2×C3⋊C8—21no—
54C2×C3⋊C8Q812yes—
55C22×C8—31no—
56C22×C8C2×D311yescharacteristic
57C2×C4⋊C4—31no—
58C2×C4⋊C4—31no—
59C2×C4⋊C4—61no—
60C2×C4⋊C4—61no—
61C2×C4⋊C4—61no—
62C2×C4⋊C4C2×D311yescharacteristic
63C2×C4⋊C4C2×D311yescharacteristic
64C2×C42—31no—
65#106—62no—
66#106—62no—
67#95—61no—
68C23×C3C2×D411yescharacteristic
69C2×C3×C4—41no—
70C2×C3×C4—41no—
71C2×C3×C4—41no—
72C2×C3×C4—41no—
73C2×C3×C4—41no—
74C2×C3×C4—41no—
75C2×C3×C4C2×D411yescharacteristic
76C2×C3×C4C2×Q811yescharacteristic
77C2×C3×C4C2×Q811yescharacteristic
78C2×C3×C4#4111yescharacteristic
79C2×C3×C4#4111yescharacteristic
80C2×C3×C4#4111yescharacteristic
81C2×Dic3—21no—
82C2×Dic3—21no—
83C2×Dic3—21no—
84C2×Dic3—21no—
85C2×Dic3—22no—
86C2×Dic3—41no—
87C2×Dic3—41no—
88C2×Dic3—41no—
89C2×Dic3—41no—
90C2×Dic3—41no—
91C2×Dic3SD1612yes—
92C2×Dic3SD1612yes—
93C3×C8—22no—
94C3⋊C8—22no—
95C22×C4—21no—
96C22×C4—21no—
97C22×C4—31no—
98C22×C4—31no—
99C22×C4—61no—
100C22×C4—61no—
101C22×C4C22×D311yescharacteristic
102C2×C8—21no—
103C2×C8—21no—
104C2×C8—32no—
105C2×C8—61no—
106C2×C8—61no—
107C2×C8Dic612yes—
108C4⋊C4—21no—
109C4⋊C4—21no—
110C4⋊C4—21no—
111C4⋊C4—21no—
112C4⋊C4—32no—
113C4⋊C4—61no—
114C4⋊C4—61no—
115C4⋊C4—61no—
116C4⋊C4—122no—
117C4⋊C4—122no—
118C4⋊C4—122no—
119C42—61no—
120C42—61no—
121C22×C3#12111yescharacteristic
122C22×C3#12311yescharacteristic
123C22×C3C4⋊Q811yescharacteristic
124C22×C3C2×SD1611yescharacteristic
125C22×C3C2×SD1611yescharacteristic
126C22×C3AGL(1,ℤ/8)11yescharacteristic
127C22×C3#13711yescharacteristic
128C3×C4—81no—
129C3×C4—81no—
130C3×C4C22⋊Q811yescharacteristic
131C3×C4C22⋊Q811yescharacteristic
132C3×C4#12511yescharacteristic
133C3×C4#12511yescharacteristic
134Dic3—22no—
135Dic3—22no—
136Dic3—42no—
137Dic3—81no—
138C23D3×D411yescharacteristic
139C2×C4—32no—
140C2×C4—32no—
141C2×C4—41no—
142C2×C4—41no—
143C2×C4—41no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—41no—
147C2×C4—61no—
148C2×C4—61no—
149C2×C4—61no—
150C2×C4—61no—
151C2×C4—62no—
152C2×C4—121no—
153C2×C4—121no—
154C2×C4—121no—
155C2×C4—121no—
156C2×C4—121no—
157C2×C4C2×Dic611yescharacteristic
158C2×C4#23511yescharacteristic
159C2×C4#23511yescharacteristic
160C2×C4D3×D411yescharacteristic
161C2×C4#23711yescharacteristic
162C2×C4D3×Q811yescharacteristic
163C8—22no—
164C8—62no—
165C2×C3#39811yescharacteristic
166C2×C3#46011yescharacteristic
167C2×C3#46111yescharacteristic
168C2×C3#48111yescharacteristic
169C2×C3#48311yescharacteristic
170C2×C3#49811yescharacteristic
171C2×C3#50111yescharacteristic
172C22#88311yescharacteristic
173C22#88411yescharacteristic
174C22#88811yescharacteristic
175C22#91111yescharacteristic
176C22D3×SD1611yescharacteristic
177C22D3×SD1611yescharacteristic
178C22#91811yescharacteristic
179C4—62no—
180C4—62no—
181C4—81no—
182C4—81no—
183C4—122no—
184C4—241no—
185C4#87011yescharacteristic
186C4#87811yescharacteristic
187C4#88911yescharacteristic
188C4#89611yescharacteristic
189C3#208411yescharacteristic, complemented, Sylow
190C2#465711yescharacteristic
191C2#476211yescharacteristic
192C2#477711yescharacteristic
193C2#480511yescharacteristic
194C2#481811yescharacteristic
195C2#485511yescharacteristic
196C2#487611yescharacteristic
subgroupG/H
centerC23D3×D4
commutator, cosocleC22×C3×C4C23
FrattiniC22×C4C22×D3
FittingC3×#340C2
socle, prime radicalC23×C3C2×D4
hypercenter#340D3
hypocenterC3#2084
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
189. C3#2084semidirect

Maximal subgroups

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

subgroupindex
C2×#8172
#49752
#49722
C2×#8082
C3×#3402
#45502
#45292
#20843