Finite Group Databasebeta

← #68769

Subgroups — #68769

Order 384.

246 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 67 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#5519C211yesmaximal, characteristic
2#5120C211yesmaximal, characteristic
3#5004C211yesmaximal, characteristic
4#4929C211yesmaximal, characteristic
5C3×#339C211yesmaximal, characteristic
6#4554C211yesmaximal, characteristic
7#4523C211yesmaximal, characteristic
8#2028—31nomaximal, Sylow
9C22×Dic6C2211yescharacteristic
10C2×C3×M16C2211yescharacteristic
11C3×#117C2211yescharacteristic
12C2×C3×C42C2211yescharacteristic
13#926C2211yescharacteristic
14C2×C4⋊Dic3C2211yescharacteristic
15C2×#208C2211yescharacteristic
16#890—21no—
17#888—21no—
18#878—22no—
19#870—21no—
20#869—21no—
21C3⋊#95—22no—
22#816—21no—
23#816—21no—
24#810—21no—
25#810—21no—
26#544—31no—
27#419—31no—
28#419—31no—
29#391—31no—
30#343—31no—
31#339—31no—
32#339D311yescharacteristic
33C22×C3×C4—21no—
34C22×C3×C4C2311yescharacteristic
35C22×Dic3—21no—
36C22×Dic3D412yes—
37C2×Dic6—21no—
38C2×Dic6—21no—
39C2×Dic6—21no—
40C2×Dic6—21no—
41C2×Dic6—21no—
42C2×Dic6—22no—
43C2×Dic6Q812yescomplemented
44C3×M16—21no—
45C3×M16—21no—
46C2×C3×C8—21no—
47C3×C4⋊C4D411yescharacteristic
48C3×C4⋊C4D411yescharacteristic
49C3×C22⋊C4—21no—
50C3×C42—21no—
51C3×C42—21no—
52C3×C42—21no—
53#217—21no—
54C4⋊Dic3—22no—
55C4⋊Dic3—21no—
56C4⋊Dic3—21no—
57C4⋊Dic3D411yescharacteristic
58C4⋊Dic3D411yescharacteristic
59Dic3⋊C4—22no—
60Dic3⋊C4—22no—
61C4×Dic3—21no—
62#208—21no—
63#208—21no—
64C2×C3⋊C8—21no—
65C22×Q8—31no—
66C2×M16—31no—
67C2×M16C2×D311yescharacteristic
68C4⋊Q8—61no—
69C4⋊Q8—61no—
70#125—61no—
71#125—61no—
72C22⋊Q8—62no—
73#117—31no—
74#117C2×D311yescharacteristic
75C2×C4⋊C4—31no—
76C2×C42C2×D311yescharacteristic
77#103—61no—
78#103—61no—
79#103—61no—
80#103—61no—
81#95—62no—
82C23×C3C2×D411yescharacteristic
83C2×C3×C4—22no—
84C2×C3×C4—21no—
85C2×C3×C4—21no—
86C2×C3×C4—41no—
87C2×C3×C4—41no—
88C2×C3×C4C2×D411yescharacteristic
89C2×C3×C4C2×D411yescharacteristic
90C2×C3×C4C2×Q811yescharacteristic
91C2×C3×C4#4111yescharacteristic
92C2×C3×C4#4111yescharacteristic
93C2×C3×C4#4111yescharacteristic
94C2×Dic3—21no—
95C2×Dic3—21no—
96C2×Dic3—22no—
97C2×Dic3—22no—
98C2×Dic3—41no—
99C2×Dic3—41no—
100C2×Dic3—42no—
101Dic6—22no—
102Dic6—22no—
103Dic6—41no—
104Dic6—41no—
105Dic6—82no—
106C3×C8—41no—
107C3⋊C8—41no—
108C2×Q8—32no—
109C2×Q8—62no—
110C2×Q8—61no—
111C2×Q8—61no—
112C2×Q8—61no—
113C2×Q8—61no—
114C2×Q8—61no—
115C22×C4—21no—
116C22×C4—32no—
117C22×C4—61no—
118C22×C4C22×D311yescharacteristic
119M16—21no—
120M16—21no—
121M16—61no—
122M16—61no—
123C2×C8—21no—
124C2×C8—61no—
125C4⋊C4—31no—
126C4⋊C4—31no—
127C4⋊C4—62no—
128C4⋊C4—62no—
129C4⋊C4—62no—
130C4⋊C4—61no—
131C4⋊C4—61no—
132C4⋊C4D1211yescharacteristic
133C4⋊C4D1211yescharacteristic
134C22⋊C4—21no—
135C22⋊C4—61no—
136C42—21no—
137C42—21no—
138C42—21no—
139C42—61no—
140C22×C3—21no—
141C22×C3—21no—
142C22×C3#12011yescharacteristic
143C22×C3C22⋊Q811yescharacteristic
144C22×C3#12411yescharacteristic
145C3×C4—42no—
146C3×C4—41no—
147C3×C4—41no—
148C3×C4C22⋊Q811yescharacteristic
149C3×C4C22⋊Q811yescharacteristic
150C3×C4#12411yescharacteristic
151C3×C4#12411yescharacteristic
152Dic3—42no—
153Dic3—41no—
154Dic3—42no—
155Dic3—41no—
156C23D3×D411yescharacteristic
157Q8—62no—
158Q8—62no—
159Q8—121no—
160Q8—121no—
161Q8—242no—
162C2×C4—22no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—41no—
166C2×C4—41no—
167C2×C4—61no—
168C2×C4—61no—
169C2×C4—62no—
170C2×C4—62no—
171C2×C4—121no—
172C2×C4—121no—
173C2×C4—122no—
174C2×C4C2×D1211yescharacteristic
175C2×C4#23511yescharacteristic
176C2×C4#23511yescharacteristic
177C2×C4D3×D411yescharacteristic
178C2×C4#23711yescharacteristic
179C2×C4D3×Q811yescharacteristic
180C8—41no—
181C8—121no—
182C2×C3—21no—
183C2×C3—21no—
184C2×C3#39311yescharacteristic
185C2×C3#45511yescharacteristic
186C2×C3#45611yescharacteristic
187C22—21no—
188C22—21no—
189C22#88211yescharacteristic
190C22#88511yescharacteristic
191C22#89611yescharacteristic
192C4—42no—
193C4—41no—
194C4—41no—
195C4—122no—
196C4—122no—
197C4—121no—
198C4—121no—
199C4#87511yescharacteristic
200C4#88511yescharacteristic
201C4#89611yescharacteristic
202C4#89711yescharacteristic
203C3#202811yescharacteristic, complemented, Sylow
204C2—21no—
205C2—21no—
206C2#467311yescharacteristic
207C2#482511yescharacteristic
208C2#482611yescharacteristic
subgroupG/H
centerC22#882
commutator, cosocleC22×C3×C4C23
FrattiniC22×C4C22×D3
FittingC3×#339C2
socleC22×C3#120
prime radicalC23×C3C2×D4
hypercenter#339D3
hypocenterC3#2028
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
43. C2×Dic6Q8semidirect
203. C3#2028semidirect

Maximal subgroups

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

subgroupindex
#55192
#51202
#50042
#49292
C3×#3392
#45542
#45232
#20283