Finite Group Databasebeta

← #11777660

Subgroups — #11777660

Order 1152.

456 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 137 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#10592530C211yesmaximal, characteristic
2#10592529C211yesmaximal, characteristic
3C4×#3746C211yesmaximal, characteristic
4C32×#334C211yesmaximal, characteristic
5#10589350C211yesmaximal, characteristic
6#10589350C211yesmaximal, characteristic
7#10589320C211yesmaximal, characteristic
8#68522—34nomaximal
9C2×#3746C411yescharacteristic
10C4×#634C2211yescharacteristic
11C4×#634C2211yescharacteristic
12C32×C4⋊C8C2211yescharacteristic
13C32×C4⋊C8C2211yescharacteristic
14C32×C4×C8C2211yescharacteristic
15#63645C411yescharacteristic
16#63643C411yescharacteristic
17#63643C411yescharacteristic
18#63642—21no—
19#63641—21no—
20#63641—21no—
21C8×C3⋊Dic3—21no—
22C4×C3⋊(C3⋊C8)C2211yescharacteristic
23C4×C3⋊(C3⋊C8)C2211yescharacteristic
24#4831—34no—
25#4830—34no—
26C4×Dic12—34no—
27C3×#334D314yes—
28#4484—34no—
29#4484—34no—
30#4454—34no—
31C2×#634C2×C411yescharacteristic
32C2×#634C2×C411yescharacteristic
33C2×C32×C8—21no—
34C2×C32×C8—21no—
35C2×C32×C8C2×C411yescharacteristic
36C2×C32×C8C2×C411yescharacteristic
37C32×C42C2311yescharacteristic
38C4⋊(C3⋊Dic3)C2×C411yescharacteristic
39C4⋊(C3⋊Dic3)C2×C411yescharacteristic
40#3750—21no—
41#3750—21no—
42C4×C3⋊Dic3—21no—
43C4×C3⋊Dic3—21no—
44C2×C3⋊(C3⋊C8)—21no—
45C2×C3⋊(C3⋊C8)D411yescharacteristic
46C2×C3⋊(C3⋊C8)D411yescharacteristic
47#3746—22no—
48#1587—91noSylow
49C2×Dic12—34no—
50C4×Dic6—34no—
51C4×Dic6—34no—
52C3×C4⋊C8C2×D314yes—
53C3×C4⋊C8C2×D314yes—
54C3×C4×C8C2×D314yes—
55#818—34no—
56#816—34no—
57#816—34no—
58#815—64no—
59Dic3⋊C8—64no—
60Dic3⋊C8—64no—
61C8×Dic3—64no—
62C4×C3⋊C8—34no—
63C4×C3⋊C8—34no—
64C2×C32×C4C22×C411yescharacteristic
65C2×C32×C4C2×D411yescharacteristic
66C2×C32×C4#4111yescharacteristic
67C2×C3⋊Dic3—21no—
68C2×C3⋊Dic3—21no—
69C2×C3⋊Dic3—21no—
70C2×C3⋊Dic3—21no—
71#634—21no—
72#634—21no—
73#634—21no—
74#634M1612yes—
75C32×C8—21no—
76C32×C8—21no—
77C32×C8—41no—
78C32×C8—41no—
79C3⋊(C3⋊C8)—22no—
80C3⋊(C3⋊C8)—21no—
81C3⋊(C3⋊C8)—21no—
82#446—91no—
83C8×Q8—91no—
84C4×Q16—91no—
85#334C3⋊D311yescharacteristic
86Q8⋊C8—91no—
87Q8⋊C8—91no—
88#322—91no—
89C2×Dic6—34no—
90C2×Dic6—34no—
91C2×C3×C8—24no—
92C2×C3×C8—24no—
93C2×C3×C8C4×D314yes—
94C2×C3×C8C4×D314yes—
95C3×C42C22×D314yes—
96C4⋊Dic3—34no—
97C4⋊Dic3—34no—
98Dic3⋊C4—64no—
99Dic3⋊C4—64no—
100C4×Dic3—64no—
101C4×Dic3—64no—
102C2×C3⋊C8—34no—
103C2×C3⋊C8—34no—
104C2×C3⋊C8—64no—
105Dic12—68no—
106C22×C32C4×D411yescharacteristic
107C32×C4—21no—
108C32×C4C2×M1611yescharacteristic
109C32×C4#13111yescharacteristic
110C32×C4#13711yescharacteristic
111C32×C4#13711yescharacteristic
112C3⋊Dic3—22no—
113C3⋊Dic3—41no—
114C3⋊Dic3—41no—
115C3⋊Dic3—41no—
116C2×Q16—91no—
117C4×Q8—91no—
118C4×Q8—91no—
119#107—91no—
120C4⋊C8—181no—
121C4⋊C8—181no—
122C4⋊C8C2×C3⋊D311yescharacteristic
123C4⋊C8C2×C3⋊D311yescharacteristic
124#103—91no—
125#103—91no—
126#97—181no—
127C4×C8—91no—
128C4×C8—91no—
129C4×C8—181no—
130C4×C8C2×C3⋊D311yescharacteristic
131C2×C3×C4C2×C4×D314yes—
132C2×C3×C4D3×D414yes—
133C2×C3×C4#23914yes—
134C2×Dic3—64no—
135C2×Dic3—64no—
136C2×Dic3—64no—
137C2×Dic3—64no—
138Dic6—38no—
139Dic6—64no—
140Dic6—64no—
141Dic6—64no—
142C3×C8—24no—
143C3×C8—24no—
144C3×C8—44no—
145C3×C8—44no—
146C3⋊C8—68no—
147C3⋊C8—64no—
148C3⋊C8—64no—
149C2×C32#43511yescharacteristic
150C2×C32#44111yescharacteristic
151C2×C32#44311yescharacteristic
152C2×Q8—91no—
153C2×Q8—91no—
154Q16—182no—
155C2×C8—21no—
156C2×C8—21no—
157C2×C8—91no—
158C2×C8—91no—
159C2×C8—181no—
160C2×C8C4×C3⋊D311yescharacteristic
161C2×C8C4×C3⋊D311yescharacteristic
162C4⋊C4—91no—
163C4⋊C4—91no—
164C4⋊C4—181no—
165C4⋊C4—181no—
166C42—181no—
167C42—181no—
168C42C22×C3⋊D311yescharacteristic
169C22×C3#89314yes—
170C3×C4—24no—
171C3×C4#90114yes—
172C3×C4D3×M1614yes—
173C3×C4#91514yes—
174C3×C4#91514yes—
175Dic3—68no—
176Dic3—124no—
177Dic3—124no—
178Dic3—124no—
179C32#158711yescharacteristic, complemented, Sylow
180Q8—92no—
181Q8—181no—
182Q8—181no—
183Q8—181no—
184C2×C4—181no—
185C2×C4—181no—
186C2×C4—181no—
187C2×C4—181no—
188C2×C4C2×C4×C3⋊D311yescharacteristic
189C2×C4D4×C3⋊D311yescharacteristic
190C2×C4#383211yescharacteristic
191C8—21no—
192C8—21no—
193C8—41no—
194C8—41no—
195C8—182no—
196C8—181no—
197C8—181no—
198C2×C3#483614yes—
199C2×C3#485314yes—
200C2×C3#489514yes—
201C22#6410211yescharacteristic
202C4—21no—
203C4—182no—
204C4—361no—
205C4—361no—
206C4—361no—
207C4#6411011yescharacteristic
208C4M16×C3⋊D311yescharacteristic
209C4#6412411yescharacteristic
210C4#6412411yescharacteristic
211C3#6852214yescomplemented
212C2#1059253511yescharacteristic
213C2#1059255211yescharacteristic
214C2#1059259411yescharacteristic
subgroupG/H
centerC2×C4D4×C3⋊D3
commutatorC2×C32×C4C22×C4
FrattiniC42C22×C3⋊D3
FittingC32×#334C2
socle, prime radicalC22×C32C4×D4
cosocleC32×C42C23
hypercenter#334C3⋊D3
hypocenterC32#1587
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42 ◁ #334

Complements

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

NH ≅ G/Ntype
179. C32#1587semidirect
211. C3#68522semidirect

Maximal subgroups

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

subgroupindex
#105925302
#105925292
C4×#37462
C32×#3342
#105893502
#105893202
#685223