Finite Group Databasebeta

← #11778586

Subgroups — #11778586

Order 1152.

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

normal subgroups only

This group has 630 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
1#10595971C211yesmaximal, characteristic
2#10592680C211yesmaximal, characteristic
3#10592420C212yesmaximal
4C32×#324C211yesmaximal, characteristic
5#10589333C212yesmaximal
6#68140—34nomaximal
7C2×C32×C4⋊C4C2211yescharacteristic
8#64135—21no—
9C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
10#64133—21no—
11#64133C2212yes—
12C2×#3750—21no—
13#64099—22no—
14#64097—22no—
15C32×C22⋊C8C2212yes—
16#63658—21no—
17#63658C2211yescharacteristic
18#63644—22no—
19#63643—22no—
20#5500—34no—
21#4981—34no—
22#4721—38no—
23C3×#324D314yes—
24#4467—38no—
25C22×C32×C4D411yescharacteristic
26C22×C32×C4D411yescharacteristic
27C22×C32×C4C2311yescharacteristic
28C22×C3⋊Dic3—21no—
29C22×C3⋊Dic3—21no—
30C2×#634—21no—
31C2×#634D412yes—
32C2×C32×C8—22no—
33C32×C4⋊C4—22no—
34#3757—22no—
35C4⋊(C3⋊Dic3)—21no—
36C4⋊(C3⋊Dic3)—21no—
37C4⋊(C3⋊Dic3)—21no—
38C4⋊(C3⋊Dic3)—22no—
39C4⋊(C3⋊Dic3)D412yes—
40#3750—22no—
41#3750—22no—
42#3750—42no—
43C4×C3⋊Dic3—22no—
44#1611—91noSylow
45C2×C3×C4⋊C4C2×D314yes—
46#926—64no—
47C2×C4⋊Dic3—34no—
48#924—38no—
49#924—64no—
50C2×Dic3⋊C4—64no—
51#890—68no—
52#888—68no—
53C3×C22⋊C8C2×D318yes—
54C3⋊#95—34no—
55C3⋊#95—64no—
56#817—68no—
57#816—68no—
58C23×C32C2×D411yescharacteristic
59C2×C32×C4—21no—
60C2×C32×C4—21no—
61C2×C32×C4—21no—
62C2×C32×C4—41no—
63C2×C32×C4—41no—
64C2×C32×C4SD1612yes—
65C2×C32×C4C2×D412yes—
66C2×C3⋊Dic3—22no—
67C2×C3⋊Dic3—22no—
68C2×C3⋊Dic3—22no—
69C2×C3⋊Dic3—41no—
70C2×C3⋊Dic3—41no—
71C2×C3⋊Dic3—41no—
72C2×C3⋊Dic3—41no—
73C2×C3⋊Dic3—41no—
74#634—42no—
75#634—81no—
76C32×C8—42no—
77#544—91no—
78#483—92no—
79#398—91no—
80#328—92no—
81#324C3⋊D311yescharacteristic
82C22×C3×C4D1214yes—
83C22×C3×C4D1214yes—
84C22×C3×C4C22×D314yes—
85C22×Dic3—64no—
86C22×Dic3—64no—
87C2×Dic6—38no—
88C2×Dic6—64no—
89C2×C3×C8—28no—
90C3×C4⋊C4—28no—
91#217—68no—
92C4⋊Dic3—38no—
93C4⋊Dic3—64no—
94C4⋊Dic3—64no—
95C4⋊Dic3—64no—
96C4⋊Dic3—68no—
97Dic3⋊C4—68no—
98Dic3⋊C4—68no—
99Dic3⋊C4—128no—
100C4×Dic3—68no—
101C22×C32—21no—
102C22×C32—21no—
103C22×C32#12011yescharacteristic
104C22×C32C2×SD1611yescharacteristic
105C22×C32#13711yescharacteristic
106C32×C4—22no—
107C32×C4—22no—
108C32×C4—41no—
109C3⋊Dic3—42no—
110C3⋊Dic3—42no—
111C3⋊Dic3—42no—
112C3⋊Dic3—81no—
113C4⋊Q8—182no—
114#125—182no—
115C22⋊Q8—92no—
116C22⋊Q8—181no—
117#117—181no—
118C2×C4⋊C4—91no—
119C2×C4⋊C4—181no—
120C2×C4⋊C4C2×C3⋊D311yescharacteristic
121#106—182no—
122#103—182no—
123C22⋊C8C2×C3⋊D312yes—
124#95—91no—
125#95—181no—
126C23×C3C2×D1214yes—
127C2×C3×C4—24no—
128C2×C3×C4—24no—
129C2×C3×C4—24no—
130C2×C3×C4—44no—
131C2×C3×C4—44no—
132C2×C3×C4#20418yes—
133C2×C3×C4D3×D418yes—
134C2×Dic3—68no—
135C2×Dic3—68no—
136C2×Dic3—68no—
137C2×Dic3—124no—
138C2×Dic3—124no—
139C2×Dic3—124no—
140C2×Dic3—124no—
141C2×Dic3—124no—
142Dic6—128no—
143Dic6—244no—
144C3×C8—48no—
145C2×C32—21no—
146C2×C32—21no—
147C2×C32#44811yescharacteristic
148C2×C32#45611yescharacteristic
149C2×C32#45811yescharacteristic
150C2×Q8—92no—
151C2×Q8—181no—
152C22×C4—181no—
153C22×C4—181no—
154C22×C4C4⋊(C3⋊D3)11yescharacteristic
155C22×C4C4⋊(C3⋊D3)11yescharacteristic
156C22×C4C22×C3⋊D311yescharacteristic
157C2×C8—22no—
158C4⋊C4—22no—
159C4⋊C4—92no—
160C4⋊C4—181no—
161C4⋊C4—181no—
162C4⋊C4—181no—
163C4⋊C4—182no—
164C4⋊C4—182no—
165C4⋊C4—182no—
166C4⋊C4—362no—
167C22⋊C4—182no—
168C42—182no—
169C22×C3—24no—
170C22×C3—24no—
171C22×C3#88214yes—
172C22×C3C2×#20414yes—
173C22×C3#90914yes—
174C3×C4—28no—
175C3×C4—28no—
176C3×C4—44no—
177Dic3—128no—
178Dic3—128no—
179Dic3—128no—
180Dic3—244no—
181C32#161111yescharacteristic, complemented, Sylow
182C23C2×C4⋊(C3⋊D3)11yescharacteristic
183Q8—362no—
184Q8—721no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—182no—
191C2×C4—182no—
192C2×C4—182no—
193C2×C4—361no—
194C2×C4—361no—
195C2×C4—361no—
196C2×C4—361no—
197C2×C4—361no—
198C2×C4#374412yes—
199C2×C4D4×C3⋊D312yes—
200C8—42no—
201C2×C3—24no—
202C2×C3—24no—
203C2×C3#473814yes—
204C2×C3#474214yes—
205C2×C3#475214yes—
206C22—21no—
207C22—21no—
208C22#6409111yescharacteristic
209C22C2×#374411yescharacteristic
210C22#6411811yescharacteristic
211C4—22no—
212C4—22no—
213C4—41no—
214C4—362no—
215C4—362no—
216C4—362no—
217C4—721no—
218C3#6814014yescomplemented
219C2—21no—
220C2—21no—
221C2#1059243711yescharacteristic
222C2#1059244111yescharacteristic
223C2#1059245111yescharacteristic
subgroupG/H
centerC22#64091
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C22×C3⋊D3
FittingC32×#324C2
socleC22×C32#120
prime radicalC23×C32C2×D4
hypercenter#324C3⋊D3
hypocenterC32#1611
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
181. C32#1611semidirect
218. C3#68140semidirect

Maximal subgroups

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

subgroupindex
#105959712
#105926802
#105924202
C32×#3242
#105893332
#681403