Finite Group Databasebeta

← #78953

Subgroups — #78953

Order 384.

380 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 129 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×#944C211yesmaximal, characteristic
2#5517C211yesmaximal, characteristic
3C3×#419C211yesmaximal, characteristic
4#5225C211yesmaximal, characteristic
5#5120C211yesmaximal, characteristic
6Dic3×M16C211yesmaximal, characteristic
7#5004C211yesmaximal, characteristic
8#4797C214yesmaximal, complemented
9#4792C214yesmaximal, complemented
10#3139—31nomaximal, Sylow
11C22×C3×Q8C2211yescharacteristic
12C22×Dic6C2211yescharacteristic
13C2×C3×M16C2211yescharacteristic
14C3×#117C2211yescharacteristic
15#944—22no—
16#944C2212yes—
17#944C2212yes—
18#926C2211yescharacteristic
19C2×Dic3⋊C4—22no—
20C2×C4×Dic3C2211yescharacteristic
21C2×#208C2211yescharacteristic
22#890C2212yes—
23#888C2212yes—
24#878—22no—
25C4×Dic6—22no—
26C3×#103C2214yes—
27#835C2214yes—
28#816C2214yes—
29#815C2212yes—
30C8×Dic3C2212yes—
31#810C2214yes—
32#533—31no—
33C2×C4⋊Q8—31no—
34#491—34no—
35#487—34no—
36#419—31no—
37#419—31no—
38#419—31no—
39#419D311yescharacteristic
40C4×M16—31no—
41C2×C3×Q8—21no—
42C2×C3×Q8—22no—
43C2×C3×Q8—22no—
44C2×C3×Q8C2312yes—
45C22×C3×C4—21no—
46C22×C3×C4C2311yescharacteristic
47C22×Dic3—21no—
48C22×Dic3D412yes—
49C2×Dic6—22no—
50C2×Dic6—22no—
51C2×Dic6—21no—
52C2×Dic6—22no—
53C2×Dic6C2312yes—
54C3×M16—22no—
55C2×C3×C8C2312yes—
56C3×C4⋊C4C2312yes—
57C3×C22⋊C4—21no—
58C3×C42—21no—
59#217—21no—
60C4⋊Dic3—22no—
61C4⋊Dic3C2312yes—
62Dic3⋊C4—22no—
63Dic3⋊C4—22no—
64Dic3⋊C4—24no—
65Dic3⋊C4—24no—
66C4×Dic3—21no—
67C4×Dic3D412yes—
68C4×Dic3C2311yescharacteristic
69C4×Dic3C2311yescharacteristic
70#208—22no—
71C2×C3⋊C8C2312yes—
72C22×Q8—31no—
73C22×Q8C2×D311yescharacteristic
74C2×M16—31no—
75C2×M16C2×D311yescharacteristic
76C4⋊Q8—32no—
77C4⋊Q8—32no—
78C4⋊Q8—32no—
79C4⋊Q8—62no—
80#125—32no—
81C22⋊Q8—62no—
82C4×Q8—62no—
83#117—31no—
84#117C2×D311yescharacteristic
85C2×C4⋊C4—62no—
86C2×C42—31no—
87#103—34no—
88#103—34no—
89#103—34no—
90#103C2×D314yes—
91#97—32no—
92C4×C8—32no—
93C23×C3C2×D411yescharacteristic
94C3×Q8—22no—
95C3×Q8—22no—
96C3×Q8—42no—
97C2×C3×C4—22no—
98C2×C3×C4—22no—
99C2×C3×C4—42no—
100C2×C3×C4C2×D411yescharacteristic
101C2×C3×C4#4112yes—
102C2×C3×C4#4112yes—
103C2×C3×C4C2411yescharacteristic
104C2×Dic3—24no—
105C2×Dic3—22no—
106C2×Dic3—22no—
107C2×Dic3—42no—
108C2×Dic3C2×D412yes—
109C2×Dic3C2×D412yes—
110Dic6—22no—
111Dic6—22no—
112Dic6—42no—
113Dic6—44no—
114C3×C8—22no—
115C3⋊C8—22no—
116C2×Q8—21no—
117C2×Q8—22no—
118C2×Q8—22no—
119C2×Q8—32no—
120C2×Q8—62no—
121C2×Q8—61no—
122C2×Q8—62no—
123C2×Q8—62no—
124C2×Q8C22×D312yes—
125C22×C4—21no—
126C22×C4—32no—
127C22×C4—61no—
128C22×C4C22×D311yescharacteristic
129M16—22no—
130M16—62no—
131C2×C8—32no—
132C2×C8C22×D312yes—
133C4⋊C4—32no—
134C4⋊C4—64no—
135C4⋊C4—64no—
136C4⋊C4—62no—
137C4⋊C4—62no—
138C4⋊C4—62no—
139C4⋊C4C22×D312yes—
140C22⋊C4—21no—
141C22⋊C4—61no—
142C42—21no—
143C42—32no—
144C42—31no—
145C42—31no—
146C42—61no—
147C22×C3—22no—
148C22×C3#12412yes—
149C22×C3C22×D411yescharacteristic
150C3×C4—42no—
151C3×C4—42no—
152C3×C4#12412yes—
153C3×C4C2×#4111yescharacteristic
154C3×C4C2×#4111yescharacteristic
155Dic3—22no—
156Dic3—42no—
157Dic3—42no—
158Dic3#13714yes—
159C23D3×D411yescharacteristic
160Q8—22no—
161Q8—22no—
162Q8—42no—
163Q8—62no—
164Q8—62no—
165Q8—124no—
166Q8—122no—
167C2×C4—22no—
168C2×C4—22no—
169C2×C4—32no—
170C2×C4—32no—
171C2×C4—42no—
172C2×C4—64no—
173C2×C4—62no—
174C2×C4—62no—
175C2×C4—122no—
176C2×C4#23512yes—
177C2×C4D3×D411yescharacteristic
178C2×C4#23712yes—
179C2×C4C23×D311yescharacteristic
180C8—22no—
181C8—62no—
182C2×C3—22no—
183C2×C3C2×#12411yescharacteristic
184C2×C3C2×#13712yes—
185C22—22no—
186C22#88512yes—
187C22C2×D3×D411yescharacteristic
188C4—34no—
189C4—42no—
190C4—42no—
191C4—62no—
192C4—122no—
193C4—122no—
194C4#88512yes—
195C4C2×#23511yescharacteristic
196C4C2×#23711yescharacteristic
197C3#313911yescharacteristic, complemented, Sylow
198C2—22no—
199C2C2×#88511yescharacteristic
200C2D3×#13712yes—
subgroupG/H
centerC22C2×D3×D4
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#419C2
socleC22×C3C22×D4
prime radicalC23×C3C2×D4
hypercenter#419D3
hypocenterC3#3139
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
8. #4797C2semidirect
9. #4792C2semidirect
197. C3#3139semidirect

Maximal subgroups

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

subgroupindex
C2×#9442
#55172
C3×#4192
#52252
#51202
Dic3×M162
#50042
#47972
#47922
#31393