Finite Group Databasebeta

← #71247

Subgroups — #71247

Order 384.

184 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 45 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#5672C211yesmaximal, characteristic
2C3×#489C211yesmaximal, characteristic
3#5082C211yesmaximal, characteristic, complemented
4#5081C211yesmaximal, characteristic, complemented
5#4540C211yesmaximal, characteristic
6#4465C211yesmaximal, characteristic, complemented
7#4465C211yesmaximal, characteristic, complemented
8#1664—31nomaximal, Sylow
9C3×C4⋊Q8C2211yescharacteristic
10C3×#124C2211yescharacteristic
11#944—21no—
12#935—21no—
13#879—21no—
14#879—21no—
15#878—21no—
16#878—21no—
17#870C2211yescharacteristic
18#870C2211yescharacteristic
19C3×#103—21no—
20C3×#102—21no—
21C3×#97C2211yescharacteristic
22#835—21no—
23#835—21no—
24#808—21no—
25#807—21no—
26#803C2211yescharacteristic
27#803C2211yescharacteristic
28#563—31no—
29#501—31no—
30#491—31no—
31#489D311yescharacteristic
32#330—31no—
33#330—31no—
34#329—31no—
35C2×C3×Q8—21no—
36C2×C3×Q8D411yescharacteristic
37C2×C3×D4D411yescharacteristic
38C22×Dic3—21no—
39C2×Dic6—21no—
40C2×C3×C8—21no—
41C3×C4⋊C4—21no—
42C3×C4⋊C4—21no—
43C3×C22⋊C4—21no—
44C3×C22⋊C4—21no—
45C3×C42C2311yescharacteristic
46#217—21no—
47#217—21no—
48#217—21no—
49C4⋊Dic3D411yescharacteristic
50C4⋊Dic3D411yescharacteristic
51C4⋊Dic3D411yescharacteristic
52C4⋊Dic3D411yescharacteristic
53Dic3⋊C4—21no—
54Dic3⋊C4—21no—
55Dic3⋊C4—21no—
56Dic3⋊C4—21no—
57Dic3⋊C4—21no—
58Dic3⋊C4—21no—
59C4×Dic3—21no—
60C2×C3⋊C8—21no—
61C2×C3⋊C8—21no—
62C4⋊Q8—61no—
63C4⋊Q8C2×D311yescharacteristic
64#126—61no—
65#126—61no—
66#125—31no—
67#125—31no—
68#124C2×D311yescharacteristic
69#123—61no—
70C22⋊Q8—61no—
71C22⋊Q8—61no—
72#107—61no—
73#106—61no—
74#103—21no—
75#103—61no—
76#103—61no—
77#102—21no—
78#97—31no—
79#97—31no—
80#97C2×D311yescharacteristic
81C23×C3—21no—
82C3×Q8—41no—
83C3×Q8—42no—
84C3×D4—41no—
85C2×C3×C4—21no—
86C2×C3×C4—41no—
87C2×C3×C4C2×D411yescharacteristic
88C2×C3×C4C2×D411yescharacteristic
89C2×C3×C4C2×D411yescharacteristic
90C2×Dic3—21no—
91C2×Dic3—21no—
92C2×Dic3—21no—
93C2×Dic3—21no—
94C2×Dic3—81no—
95Dic6—81no—
96C3×C8—41no—
97C3⋊C8—22no—
98C3⋊C8—41no—
99C2×Q8—21no—
100C2×Q8—61no—
101C2×Q8#6711yescharacteristic
102C2×D4#6711yescharacteristic
103C22×C4—61no—
104C2×C8—21no—
105C2×C8—61no—
106C2×C8—61no—
107C4⋊C4—21no—
108C4⋊C4—21no—
109C4⋊C4—31no—
110C4⋊C4—31no—
111C4⋊C4—31no—
112C4⋊C4—31no—
113C4⋊C4—61no—
114C4⋊C4—61no—
115C4⋊C4—61no—
116C4⋊C4—61no—
117C4⋊C4—61no—
118C4⋊C4—61no—
119C22⋊C4—21no—
120C22⋊C4—21no—
121C22⋊C4—61no—
122C22⋊C4—61no—
123C22⋊C4—61no—
124C42—61no—
125C42C22×D311yescharacteristic
126C22×C3—41no—
127C22×C3—41no—
128C22×C3—41no—
129C22×C3#12011yescharacteristic
130C3×C4—21no—
131C3×C4—21no—
132C3×C4—21no—
133C3×C4—41no—
134C3×C4—81no—
135Dic3—41no—
136Dic3—41no—
137Dic3—41no—
138Dic3—41no—
139C23—21no—
140Q8—41no—
141Q8—42no—
142Q8—241no—
143D4—41no—
144C2×C4—21no—
145C2×C4—41no—
146C2×C4—61no—
147C2×C4—61no—
148C2×C4—61no—
149C2×C4—61no—
150C2×C4—241no—
151C2×C4D3×D411yescharacteristic
152C2×C4D3×D411yescharacteristic
153C2×C4C2×#6711yescharacteristic
154C8—41no—
155C8—62no—
156C8—121no—
157C2×C3—81no—
158C2×C3#45411yescharacteristic
159C2×C3#45511yescharacteristic
160C2×C3#45611yescharacteristic
161C22—41no—
162C22—41no—
163C22—41no—
164C22#93711yescharacteristic
165C4—21no—
166C4—21no—
167C4—21no—
168C4—41no—
169C4—81no—
170C4—121no—
171C4—121no—
172C4—121no—
173C4—121no—
174C3#166411yescharacteristic, complemented, Sylow
175C2—81no—
176C2#506111yescharacteristic
177C2#520111yescharacteristic
178C2#520511yescharacteristic
subgroupG/H
centerC22#937
commutator, cosocleC3×C42C23
FrattiniC42C22×D3
FittingC3×#489C2
socleC22×C3#120
prime radicalC2×C3×D4D4
hypercenter#489D3
hypocenterC3#1664
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
3. #5082C2semidirect
4. #5081C2semidirect
6. #4465C2semidirect
7. #4465C2semidirect
174. C3#1664semidirect

Maximal subgroups

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

subgroupindex
#56722
C3×#4892
#50822
#50812
#45402
#44652
#16643