Finite Group Databasebeta

← #11778813

Subgroups — #11778813

Order 1152.

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

normal subgroups only

This group has 606 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#10592685C211yesmaximal, characteristic
3#10592421C212yesmaximal
4C32×#324C211yesmaximal, characteristic
5#10589333C212yesmaximal
6#68141—34nomaximal
7C2×C32×C4⋊C4C2211yescharacteristic
8#64135—21no—
9C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
10#64133—21no—
11#64133C2212yes—
12#64099—22no—
13#64097—22no—
14C32×C22⋊C8C2212yes—
15#63658—21no—
16#63658—21no—
17#63658C2211yescharacteristic
18#63645—22no—
19#63643—22no—
20#5500—34no—
21#4986—34no—
22#4722—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—
42C4×C3⋊Dic3—22no—
43#1617—91noSylow
44C2×C3×C4⋊C4C2×D314yes—
45#926—64no—
46C2×C4⋊Dic3—34no—
47#924—38no—
48#924—64no—
49#890—68no—
50#888—68no—
51C3×C22⋊C8C2×D318yes—
52C3⋊#95—34no—
53C3⋊#95—64no—
54C3⋊#95—64no—
55#818—68no—
56#816—68no—
57C23×C32C2×D411yescharacteristic
58C2×C32×C4—21no—
59C2×C32×C4—21no—
60C2×C32×C4—21no—
61C2×C32×C4—41no—
62C2×C32×C4—41no—
63C2×C32×C4Q1612yes—
64C2×C32×C4C2×D412yes—
65C2×C3⋊Dic3—22no—
66C2×C3⋊Dic3—22no—
67C2×C3⋊Dic3—41no—
68C2×C3⋊Dic3—41no—
69C2×C3⋊Dic3—42no—
70C2×C3⋊Dic3—41no—
71C2×C3⋊Dic3—41no—
72#634—42no—
73#634—81no—
74C32×C8—42no—
75#544—91no—
76#484—92no—
77#400—91no—
78#328—92no—
79#324C3⋊D311yescharacteristic
80C22×C3×C4D1214yes—
81C22×C3×C4D1214yes—
82C22×C3×C4C22×D314yes—
83C22×Dic3—64no—
84C22×Dic3—64no—
85C2×Dic6—38no—
86C2×Dic6—64no—
87C2×C3×C8—28no—
88C3×C4⋊C4—28no—
89#217—68no—
90C4⋊Dic3—38no—
91C4⋊Dic3—64no—
92C4⋊Dic3—64no—
93C4⋊Dic3—64no—
94C4⋊Dic3—68no—
95Dic3⋊C4—68no—
96Dic3⋊C4—68no—
97C4×Dic3—68no—
98C22×C32—21no—
99C22×C32—21no—
100C22×C32#12011yescharacteristic
101C22×C32C2×Q1611yescharacteristic
102C22×C32#13711yescharacteristic
103C32×C4—22no—
104C32×C4—22no—
105C32×C4—41no—
106C3⋊Dic3—42no—
107C3⋊Dic3—42no—
108C3⋊Dic3—81no—
109C3⋊Dic3—81no—
110C4⋊Q8—182no—
111#125—182no—
112C22⋊Q8—92no—
113C22⋊Q8—181no—
114#117—181no—
115C2×C4⋊C4—91no—
116C2×C4⋊C4C2×C3⋊D311yescharacteristic
117#107—182no—
118#103—182no—
119C22⋊C8C2×C3⋊D312yes—
120#95—91no—
121#95—181no—
122#95—181no—
123C23×C3C2×D1214yes—
124C2×C3×C4—24no—
125C2×C3×C4—24no—
126C2×C3×C4—24no—
127C2×C3×C4—44no—
128C2×C3×C4—44no—
129C2×C3×C4Dic1218yes—
130C2×C3×C4D3×D418yes—
131C2×Dic3—68no—
132C2×Dic3—68no—
133C2×Dic3—124no—
134C2×Dic3—124no—
135C2×Dic3—128no—
136C2×Dic3—124no—
137C2×Dic3—124no—
138Dic6—128no—
139Dic6—244no—
140C3×C8—48no—
141C2×C32—21no—
142C2×C32—21no—
143C2×C32#45111yescharacteristic
144C2×C32#45411yescharacteristic
145C2×C32#45811yescharacteristic
146C2×Q8—92no—
147C2×Q8—181no—
148C22×C4—181no—
149C22×C4—181no—
150C22×C4C4⋊(C3⋊D3)11yescharacteristic
151C22×C4C4⋊(C3⋊D3)11yescharacteristic
152C22×C4C22×C3⋊D311yescharacteristic
153C2×C8—22no—
154C4⋊C4—22no—
155C4⋊C4—92no—
156C4⋊C4—181no—
157C4⋊C4—181no—
158C4⋊C4—181no—
159C4⋊C4—182no—
160C4⋊C4—182no—
161C4⋊C4—182no—
162C22⋊C4—182no—
163C42—182no—
164C22×C3—24no—
165C22×C3—24no—
166C22×C3#88214yes—
167C22×C3C2×Dic1214yes—
168C22×C3#90914yes—
169C3×C4—28no—
170C3×C4—28no—
171C3×C4—44no—
172Dic3—128no—
173Dic3—128no—
174Dic3—244no—
175Dic3—244no—
176C32#161711yescharacteristic, complemented, Sylow
177C23C2×C4⋊(C3⋊D3)11yescharacteristic
178Q8—362no—
179Q8—721no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—182no—
186C2×C4—182no—
187C2×C4—361no—
188C2×C4—361no—
189C2×C4—362no—
190C2×C4—361no—
191C2×C4—361no—
192C2×C4#374612yes—
193C2×C4D4×C3⋊D312yes—
194C8—42no—
195C2×C3—24no—
196C2×C3—24no—
197C2×C3#473914yes—
198C2×C3#474214yes—
199C2×C3#475314yes—
200C22—21no—
201C22—21no—
202C22#6409111yescharacteristic
203C22C2×#374611yescharacteristic
204C22#6411811yescharacteristic
205C4—22no—
206C4—22no—
207C4—41no—
208C4—362no—
209C4—362no—
210C4—721no—
211C4—721no—
212C3#6814114yescomplemented
213C2—21no—
214C2—21no—
215C2#1059243811yescharacteristic
216C2#1059244111yescharacteristic
217C2#1059245211yescharacteristic
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#1617
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
176. C32#1617semidirect
212. C3#68141semidirect

Maximal subgroups

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

subgroupindex
#105959712
#105926852
#105924212
C32×#3242
#105893332
#681413