Finite Group Databasebeta

← #71887

Subgroups — #71887

Order 384.

208 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 53 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×#539C211yesmaximal, characteristic
2#5044C211yesmaximal, characteristic, complemented
3#5034C211yesmaximal, characteristic
4#4986C211yesmaximal, characteristic, complemented
5#4538C211yesmaximal, characteristic, complemented
6#4537C211yesmaximal, characteristic
7#4528C211yesmaximal, characteristic, complemented
8#1615—31nomaximal, Sylow
9C3×#126—21no—
10C3×#125—21no—
11C3×#123—21no—
12C3×#123—21no—
13C3×C22⋊Q8—21no—
14C3×C22⋊Q8C2211yescharacteristic
15C3×#121C2211yescharacteristic
16C3×C4×D4—21no—
17C2×C3×C4⋊C4C2211yescharacteristic
18C2×C4⋊Dic3C2211yescharacteristic
19#835—21no—
20#832—21no—
21C3⋊#95—21no—
22C3⋊#95—21no—
23C3⋊#95C2211yescharacteristic
24#830C2211yescharacteristic
25#830C2211yescharacteristic
26#808—21no—
27#807—21no—
28#539D311yescharacteristic
29#484—31no—
30#481—31no—
31#400—31no—
32#328—31no—
33#327—31no—
34#324—31no—
35C2×C3×Q8D411yescharacteristic
36C2×C3×D4—21no—
37C2×C3×D4D411yescharacteristic
38C22×C3×C4—21no—
39C22×C3×C4D411yescharacteristic
40C22×C3×C4D411yescharacteristic
41C22×C3×C4C2311yescharacteristic
42C22×Dic3—21no—
43C22×Dic3—21no—
44C3×C4⋊C4—21no—
45C3×C4⋊C4—21no—
46C3×C4⋊C4—21no—
47C3×C4⋊C4—21no—
48C3×C4⋊C4—21no—
49C3×C4⋊C4—21no—
50C3×C4⋊C4D411yescharacteristic
51C3×C4⋊C4D411yescharacteristic
52C3×C22⋊C4—21no—
53C3×C22⋊C4—21no—
54C3×C22⋊C4—21no—
55C3×C22⋊C4—21no—
56C3×C22⋊C4—21no—
57C3×C42—21no—
58C4⋊Dic3—21no—
59C4⋊Dic3—21no—
60C2×C3⋊C8—21no—
61C2×C3⋊C8—21no—
62#126—21no—
63#125—21no—
64#123—21no—
65#123—21no—
66C22⋊Q8—21no—
67C22⋊Q8C2×D311yescharacteristic
68#121C2×D311yescharacteristic
69C4×D4—21no—
70C2×C4⋊C4—31no—
71C2×C4⋊C4C2×D311yescharacteristic
72#107—61no—
73#106—61no—
74#103—61no—
75#102—61no—
76C22⋊C8—31no—
77C22⋊C8—31no—
78#95—31no—
79#95—61no—
80#95—61no—
81C23×C3—21no—
82C23×C3C2×D411yescharacteristic
83C3×Q8—41no—
84C3×D4—41no—
85C3×D4—41no—
86C3×D4—41no—
87C2×C3×C4—21no—
88C2×C3×C4—21no—
89C2×C3×C4—21no—
90C2×C3×C4—21no—
91C2×C3×C4—21no—
92C2×C3×C4—21no—
93C2×C3×C4—21no—
94C2×C3×C4—41no—
95C2×C3×C4—41no—
96C2×C3×C4—81no—
97C2×C3×C4C2×D411yescharacteristic
98C2×C3×C4C2×D411yescharacteristic
99C2×Dic3—41no—
100C2×Dic3—41no—
101C2×Dic3—42no—
102C2×Dic3—41no—
103C2×Dic3—41no—
104C3⋊C8—41no—
105C3⋊C8—41no—
106C2×Q8#6711yescharacteristic
107C2×D4—21no—
108C2×D4#6711yescharacteristic
109C22×C4—21no—
110C22×C4—61no—
111C22×C4—61no—
112C22×C4#6711yescharacteristic
113C22×C4#6711yescharacteristic
114C22×C4C22×D311yescharacteristic
115C2×C8—61no—
116C2×C8—61no—
117C4⋊C4—21no—
118C4⋊C4—21no—
119C4⋊C4—21no—
120C4⋊C4—21no—
121C4⋊C4—21no—
122C4⋊C4—21no—
123C4⋊C4—61no—
124C4⋊C4—61no—
125C4⋊C4#6711yescharacteristic
126C4⋊C4#6711yescharacteristic
127C22⋊C4—21no—
128C22⋊C4—21no—
129C22⋊C4—21no—
130C22⋊C4—21no—
131C22⋊C4—21no—
132C42—21no—
133C22×C3—21no—
134C22×C3—21no—
135C22×C3—41no—
136C22×C3—41no—
137C22×C3—41no—
138C22×C3#12011yescharacteristic
139C22×C3#13511yescharacteristic
140C22×C3#13711yescharacteristic
141C3×C4—21no—
142C3×C4—21no—
143C3×C4—41no—
144C3×C4—41no—
145C3×C4—41no—
146C3×C4—41no—
147C3×C4—41no—
148Dic3—81no—
149Dic3—81no—
150C23—21no—
151C23C2×#6711yescharacteristic
152Q8—41no—
153D4—41no—
154D4—41no—
155D4—41no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—21no—
162C2×C4—21no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—81no—
166C2×C4—121no—
167C2×C4—121no—
168C2×C4—122no—
169C2×C4—121no—
170C2×C4—121no—
171C2×C4C2×#6711yescharacteristic
172C2×C4C2×#6711yescharacteristic
173C8—121no—
174C8—121no—
175C2×C3—21no—
176C2×C3—21no—
177C2×C3—81no—
178C2×C3#45211yescharacteristic
179C2×C3#45411yescharacteristic
180C2×C3#45811yescharacteristic
181C22—21no—
182C22—21no—
183C22—41no—
184C22—41no—
185C22—41no—
186C22#95011yescharacteristic
187C22#95111yescharacteristic
188C22#95311yescharacteristic
189C4—21no—
190C4—21no—
191C4—41no—
192C4—41no—
193C4—41no—
194C4—41no—
195C4—41no—
196C4—241no—
197C4—241no—
198C3#161511yescharacteristic, complemented, Sylow
199C2—21no—
200C2—21no—
201C2—81no—
202C2#523911yescharacteristic
203C2#524311yescharacteristic
204C2#524511yescharacteristic
subgroupG/H
centerC22#953
commutator, cosocleC22×C3×C4C23
FrattiniC22×C4C22×D3
FittingC3×#539C2
socleC22×C3#120
prime radicalC3×#121C22
hypercenter#539D3
hypocenterC3#1615
LCSG ▷ C22×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22 ◁ C22×C4 ◁ #539

Complements

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

NH ≅ G/Ntype
2. #5044C2semidirect
4. #4986C2semidirect
5. #4538C2semidirect
7. #4528C2semidirect
198. C3#1615semidirect

Maximal subgroups

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

subgroupindex
C3×#5392
#50442
#50342
#49862
#45382
#45372
#45282
#16153