Finite Group Databasebeta

← #68331

Subgroups — #68331

Order 384.

202 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 51 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
1#5623C211yesmaximal, characteristic
2#5044C211yesmaximal, characteristic
3#4722C211yesmaximal, characteristic
4#4659C211yesmaximal, characteristic
5C3×#328C211yesmaximal, characteristic
6#4469C211yesmaximal, characteristic
7#4452C211yesmaximal, characteristic
8#1617—31nomaximal, Sylow
9C3×C22⋊Q8C2211yescharacteristic
10#944—21no—
11C2×C4⋊Dic3C2211yescharacteristic
12#924C2211yescharacteristic
13C2×Dic3⋊C4C2211yescharacteristic
14#889—21no—
15#889—21no—
16#888—21no—
17#878—21no—
18#877—21no—
19C3×C22⋊C8C2211yescharacteristic
20C3×#95C2211yescharacteristic
21#835—21no—
22C3⋊#95—21no—
23C3⋊#95—21no—
24#830C2211yescharacteristic
25#818—21no—
26#816—21no—
27#807—21no—
28#544—31no—
29#484—31no—
30#484—31no—
31#400—31no—
32#328—31no—
33#328D311yescharacteristic
34#324—31no—
35C2×C3×Q8D411yescharacteristic
36C22×C3×C4—21no—
37C22×C3×C4C2311yescharacteristic
38C22×Dic3—21no—
39C22×Dic3D411yescharacteristic
40C22×Dic3D411yescharacteristic
41C2×Dic6—21no—
42C2×Dic6D411yescharacteristic
43C2×C3×C8—21no—
44C3×C4⋊C4—21no—
45C3×C4⋊C4D411yescharacteristic
46C3×C22⋊C4—21no—
47#217—21no—
48C4⋊Dic3—21no—
49C4⋊Dic3—21no—
50C4⋊Dic3—21no—
51C4⋊Dic3D411yescharacteristic
52Dic3⋊C4—21no—
53Dic3⋊C4—21no—
54Dic3⋊C4—21no—
55Dic3⋊C4—21no—
56Dic3⋊C4—21no—
57Dic3⋊C4—21no—
58Dic3⋊C4—21no—
59C4×Dic3—21no—
60C4×Dic3—21no—
61C2×C3⋊C8—21no—
62C4⋊Q8—61no—
63C4⋊Q8—61no—
64#125—61no—
65#125—61no—
66C22⋊Q8—31no—
67C22⋊Q8—61no—
68C22⋊Q8C2×D311yescharacteristic
69#117—61no—
70C2×C4⋊C4—31no—
71C2×C4⋊C4—31no—
72#107—61no—
73#107—61no—
74#103—61no—
75#103—61no—
76C22⋊C8—31no—
77C22⋊C8C2×D311yescharacteristic
78#95—61no—
79#95—61no—
80#95C2×D311yescharacteristic
81C23×C3C2×D411yescharacteristic
82C3×Q8—41no—
83C2×C3×C4—21no—
84C2×C3×C4—21no—
85C2×C3×C4—41no—
86C2×C3×C4—41no—
87C2×C3×C4—41no—
88C2×C3×C4—41no—
89C2×C3×C4C2×D411yescharacteristic
90C2×C3×C4C2×D411yescharacteristic
91C2×Dic3—21no—
92C2×Dic3—21no—
93C2×Dic3—21no—
94C2×Dic3—21no—
95C2×Dic3—21no—
96C2×Dic3—41no—
97C2×Dic3—42no—
98C2×Dic3—41no—
99C2×Dic3Q1612yes—
100Dic6—41no—
101Dic6—81no—
102C3×C8—41no—
103C3⋊C8—41no—
104C2×Q8—31no—
105C2×Q8—61no—
106C2×Q8D1211yescharacteristic
107C22×C4—21no—
108C22×C4—31no—
109C22×C4—31no—
110C22×C4—61no—
111C22×C4C22×D311yescharacteristic
112C2×C8—21no—
113C2×C8—61no—
114C4⋊C4—21no—
115C4⋊C4—31no—
116C4⋊C4—61no—
117C4⋊C4—61no—
118C4⋊C4—61no—
119C4⋊C4—61no—
120C4⋊C4—61no—
121C4⋊C4—61no—
122C4⋊C4—61no—
123C4⋊C4—61no—
124C4⋊C4—61no—
125C4⋊C4—61no—
126C4⋊C4D1211yescharacteristic
127C22⋊C4—21no—
128C22⋊C4—61no—
129C42—61no—
130C42—61no—
131C22×C3—21no—
132C22×C3—21no—
133C22×C3#12011yescharacteristic
134C22×C3C2×Q1611yescharacteristic
135C22×C3#13711yescharacteristic
136C3×C4—21no—
137C3×C4—21no—
138C3×C4—41no—
139C3×C4—41no—
140C3×C4—81no—
141Dic3—22no—
142Dic3—41no—
143Dic3—41no—
144Dic3—41no—
145Dic3—81no—
146C23D3×D411yescharacteristic
147Q8—41no—
148Q8—121no—
149Q8—241no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—32no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—61no—
158C2×C4—61no—
159C2×C4—61no—
160C2×C4—61no—
161C2×C4—61no—
162C2×C4—121no—
163C2×C4—122no—
164C2×C4—121no—
165C2×C4C2×D1211yescharacteristic
166C2×C4D3×D411yescharacteristic
167C8—41no—
168C8—121no—
169C2×C3—21no—
170C2×C3—21no—
171C2×C3#45111yescharacteristic
172C2×C3#45411yescharacteristic
173C2×C3#45811yescharacteristic
174C22—21no—
175C22—21no—
176C22#88211yescharacteristic
177C22#91511yescharacteristic
178C22D3×Q1611yescharacteristic
179C4—21no—
180C4—21no—
181C4—41no—
182C4—41no—
183C4—62no—
184C4—81no—
185C4—121no—
186C4—121no—
187C4—121no—
188C4—241no—
189C3#161711yescharacteristic, complemented, Sylow
190C2—21no—
191C2—21no—
192C2#474211yescharacteristic
193C2#480911yescharacteristic
194C2#482711yescharacteristic
subgroupG/H
centerC22#882
commutator, cosocleC22×C3×C4C23
FrattiniC22×C4C22×D3
FittingC3×#328C2
socleC22×C3#120
prime radicalC23×C3C2×D4
hypercenter#328D3
hypocenterC3#1617
LCSG ▷ C22×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
189. C3#1617semidirect

Maximal subgroups

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

subgroupindex
#56232
#50442
#47222
#46592
C3×#3282
#44692
#44522
#16173