Finite Group Databasebeta

← #81043

Subgroups — #81043

Order 384.

326 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 125 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#5721C211yesmaximal, characteristic
2Q8×Dic6C211yesmaximal, characteristic
3C3×#475C211yesmaximal, characteristic
4#5080C211yesmaximal, characteristic
5C4×#216C211yesmaximal, characteristic
6#4856C212yesmaximal
7#4854C212yesmaximal
8#4850C211yesmaximal, characteristic
9#4831C211yesmaximal, characteristic
10#4796C212yesmaximal
11#4789C212yesmaximal
12#3387—31nomaximal, Sylow
13C3×C4⋊Q8C2211yescharacteristic
14C3×C4×Q8C2211yescharacteristic
15Q8×Dic3—21no—
16Q8×Dic3C2212yes—
17#944—21no—
18C2×#216C2211yescharacteristic
19#890C2212yes—
20#889—22no—
21#888—22no—
22#888C2212yes—
23#887C2212yes—
24#869—21no—
25#869C2211yescharacteristic
26C4×Dic6—21no—
27C4×Dic6C2211yescharacteristic
28C4×Dic6C2211yescharacteristic
29C3×#106C2212yes—
30C3×C4⋊C8C2211yescharacteristic
31C3×#103C2212yes—
32#835C2211yescharacteristic
33#818C2212yes—
34#816C2212yes—
35#815C2212yes—
36Dic3⋊C8C2212yes—
37#810C2211yescharacteristic
38#808C2212yes—
39#808C2212yes—
40#807C2211yescharacteristic
41C4×C3⋊C8C2211yescharacteristic
42Q82—31no—
43#557—31no—
44#501—32no—
45#498—31no—
46#479—32no—
47#477—31no—
48#475—32no—
49#475D311yescharacteristic
50#446—31no—
51#441—32no—
52C4×Q16—31no—
53C2×C3×Q8—21no—
54C2×C3×Q8C2311yescharacteristic
55C2×Dic6—21no—
56C2×Dic6—22no—
57C2×Dic6D411yescharacteristic
58C2×Dic6C2311yescharacteristic
59C2×C3×C8C2312yes—
60C3×C4⋊C4—21no—
61C3×C4⋊C4—21no—
62C3×C4⋊C4C2311yescharacteristic
63C3×C4⋊C4C2312yes—
64C3×C42—21no—
65C3×C42C2311yescharacteristic
66#216Q814yescomplemented
67C4⋊Dic3—21no—
68C4⋊Dic3—22no—
69C4⋊Dic3—22no—
70C4⋊Dic3D411yescharacteristic
71C4⋊Dic3C2311yescharacteristic
72C4⋊Dic3C2312yes—
73Dic3⋊C4—21no—
74Dic3⋊C4—22no—
75Dic3⋊C4—22no—
76Dic3⋊C4—22no—
77Dic3⋊C4D412yes—
78C4×Dic3—21no—
79C4×Dic3—22no—
80C4×Dic3—22no—
81C4×Dic3C2312yes—
82C2×C3⋊C8C2311yescharacteristic
83C2×C3⋊C8C2311yescharacteristic
84C2×Q16—31no—
85C4⋊Q8—32no—
86C4⋊Q8—31no—
87C4⋊Q8—61no—
88C4⋊Q8—62no—
89C4⋊Q8—61no—
90C4⋊Q8C2×D311yescharacteristic
91#125—32no—
92#125—62no—
93C4×Q8—31no—
94C4×Q8—32no—
95C4×Q8—32no—
96C4×Q8—31no—
97C4×Q8—61no—
98C4×Q8—61no—
99C4×Q8C2×D311yescharacteristic
100#107—32no—
101#107—31no—
102#106—32no—
103#106—32no—
104#106C2×D312yes—
105C4⋊C8—32no—
106C4⋊C8C2×D311yescharacteristic
107#103—31no—
108#103—32no—
109#103—31no—
110#103C2×D312yes—
111#97—32no—
112C4×C8—31no—
113C3×Q8—21no—
114C3×Q8—42no—
115C3×Q8C2×Q812yes—
116C2×C3×C4—21no—
117C2×C3×C4—22no—
118C2×C3×C4—21no—
119C2×C3×C4C2×D411yescharacteristic
120C2×C3×C4C2×D411yescharacteristic
121C2×C3×C4C2411yescharacteristic
122C2×Dic3—21no—
123C2×Dic3—21no—
124C2×Dic3—22no—
125C2×Dic3C2×D412yes—
126C2×Dic3C2×D412yes—
127Dic6—22no—
128Dic6—21no—
129Dic6—82no—
130Dic6—81no—
131Dic6C2×Q812yes—
132C3×C8—22no—
133C3⋊C8—21no—
134C3⋊C8C2×Q812yes—
135C2×Q8—21no—
136C2×Q8—31no—
137C2×Q8—31no—
138C2×Q8—62no—
139C2×Q8—61no—
140C2×Q8C22×D311yescharacteristic
141Q16—34no—
142C2×C8—31no—
143C2×C8—31no—
144C2×C8C22×D312yes—
145C4⋊C4—21no—
146C4⋊C4—21no—
147C4⋊C4—31no—
148C4⋊C4—32no—
149C4⋊C4—32no—
150C4⋊C4—31no—
151C4⋊C4—62no—
152C4⋊C4—62no—
153C4⋊C4—62no—
154C4⋊C4—62no—
155C4⋊C4—62no—
156C4⋊C4—61no—
157C4⋊C4—61no—
158C4⋊C4C22×D311yescharacteristic
159C4⋊C4C22×D312yes—
160C42—21no—
161C42—32no—
162C42—62no—
163C42—62no—
164C42—61no—
165C42C22×D311yescharacteristic
166C22×C3C22×D411yescharacteristic
167C3×C4—22no—
168C3×C4—21no—
169C3×C4—42no—
170C3×C4—41no—
171C3×C4#13712yes—
172C3×C4C22×Q811yescharacteristic
173C3×C42−1+411yescharacteristic
174Dic3—22no—
175Dic3—22no—
176Dic3—22no—
177Dic3—42no—
178Dic3—41no—
179Q8—21no—
180Q8—32no—
181Q8—42no—
182Q8—62no—
183Q8—61no—
184Q8—241no—
185Q8—242no—
186Q8D3×Q812yes—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—22no—
190C2×C4—32no—
191C2×C4—32no—
192C2×C4—61no—
193C2×C4—61no—
194C2×C4—62no—
195C2×C4D3×D411yescharacteristic
196C2×C4D3×D411yescharacteristic
197C2×C4C23×D311yescharacteristic
198C8—22no—
199C8—32no—
200C8—61no—
201C2×C3D4×Q811yescharacteristic
202C2×C3C2×#13711yescharacteristic
203C2×C3#57711yescharacteristic
204C22C2×D3×D411yescharacteristic
205C4—22no—
206C4—21no—
207C4—42no—
208C4—41no—
209C4—62no—
210C4—62no—
211C4—62no—
212C4—122no—
213C4—121no—
214C4#91512yes—
215C4C2×D3×Q811yescharacteristic
216C4#101011yescharacteristic
217C3#338711yescharacteristic, complemented, Sylow
218C2#563211yescharacteristic
219C2C2×#91511yescharacteristic
220C2#577811yescharacteristic
subgroupG/H
centerC22C2×D3×D4
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#475C2
socle, prime radicalC22×C3C22×D4
hypercenter#475D3
hypocenterC3#3387
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
66. #216Q8semidirect
217. C3#3387semidirect

Maximal subgroups

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

subgroupindex
#57212
Q8×Dic62
C3×#4752
#50802
C4×#2162
#48562
#48542
#48502
#48312
#47962
#47892
#33873