Finite Group Databasebeta

← #11785447

Subgroups — #11785447

Order 1152.

482 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 482 conjugacy classes of subgroups — too many to draw. Only its 77 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
1C22×#3787C211yesmaximal, characteristic
2C2×#63733C212yesmaximal, complemented
3#10591159C212yesmaximal
4#10590051C212yesmaximal, complemented
5C22×C4×C3⋊D3C2211yescharacteristic
6C22×#622C412yes—
7C2×#3787—24no—
8C2×#3787C412yes—
9C2×#3787C2211yescharacteristic
10C2×#3787C2211yescharacteristic
11C2×#3712C2214yes—
12#63733—24no—
13C3×#830—22no—
14#63557—22no—
15#4726—62no—
16C23×C3⋊D3Q811yescharacteristic
17C22×C32×C4D411yescharacteristic
18C22×C3⋊Dic3C2×C411yescharacteristic
19C2×C4×C3⋊D3—22no—
20C2×C4×C3⋊D3—22no—
21C2×C4×C3⋊D3C2×C411yescharacteristic
22C2×C4×C3⋊D3D411yescharacteristic
23C2×C4×C3⋊D3Q811yescharacteristic
24C2×C4×C3⋊D3C2311yescharacteristic
25C2×#622—24no—
26C2×#622C2×C412yes—
27C2×#622C2×C412yes—
28#3787—22no—
29#3787—24no—
30#3787D414yes—
31C2×C3×C3⋊C8—24no—
32#3712—24no—
33#3712—24no—
34#1810—91nomaximal, Sylow
35C22×C4×D3—62no—
36C2×ΓL(1,𝔽25)—64no—
37C3×C22⋊C8—62no—
38#830—22no—
39(C2×D3)⋊C8—64no—
40C23×C32C4⋊C411yescharacteristic
41C22×C3⋊D3—22no—
42C22×C3⋊D3—22no—
43C22×C3⋊D3—22no—
44C22×C3⋊D3C4⋊C411yescharacteristic
45C22×C3⋊D3C2×Q811yescharacteristic
46C2×C32×C4—22no—
47C2×C32×C4C4⋊C411yescharacteristic
48C2×C32×C4C2×D411yescharacteristic
49C2×C3⋊Dic3—21no—
50C2×C3⋊Dic3—21no—
51C2×C3⋊Dic3C4⋊C411yescharacteristic
52C2×C3⋊Dic3C22×C411yescharacteristic
53C4×C3⋊D3—22no—
54C4×C3⋊D3—22no—
55C4×C3⋊D3—21no—
56C4×C3⋊D3—21no—
57C4×C3⋊D3C2×D412yes—
58C4×C3⋊D3#4112yes—
59#622—22no—
60#622C22⋊C414yes—
61C3×C3⋊C8—44no—
62C23×C8—91no—
63C2×#108—92no—
64#407—92no—
65#341—92no—
66C23×D3—62no—
67C22×C3×C4—22no—
68C22×Dic3—62no—
69C2×C4×D3—62no—
70C2×C4×D3—62no—
71C2×C4×D3—62no—
72C2×C4×D3—62no—
73C2×C4×D3—124no—
74C2×C4×D3—124no—
75C2×C3×C8—64no—
76C2×C3⋊C8—24no—
77ΓL(1,𝔽25)—124no—
78ΓL(1,𝔽25)—124no—
79C22×C32—21no—
80C22×C32—21no—
81C22×C32#10812yescomplemented
82C22×C32C2×C4⋊C411yescharacteristic
83C2×C3⋊D3—28no—
84C2×C3⋊D3—21no—
85C2×C3⋊D3—21no—
86C2×C3⋊D3—21no—
87C2×C3⋊D3—21no—
88C2×C3⋊D3#10812yescomplemented
89C2×C3⋊D3C22⋊Q812yes—
90C32×C4—21no—
91C32×C4#12112yes—
92C3⋊Dic3—21no—
93C3⋊Dic3C2×C22⋊C411yescharacteristic
94C3⋊Dic3#11711yescharacteristic
95C23×C4—91no—
96C2×M16—94no—
97C22×C8—91no—
98C22×C8—92no—
99C22×C8—91no—
100C22×C8—92no—
101C22×C8—184no—
102#108—184no—
103C22⋊C8—62no—
104C22⋊C8—182no—
105C23×C3—22no—
106C22×D3—62no—
107C22×D3—62no—
108C22×D3—124no—
109C22×D3—124no—
110C22×D3—124no—
111C2×C3×C4—22no—
112C2×C3×C4—22no—
113C2×C3×C4—44no—
114C2×Dic3—62no—
115C2×Dic3—62no—
116C2×Dic3—122no—
117C2×Dic3—122no—
118C4×D3—64no—
119C4×D3—64no—
120C4×D3—122no—
121C4×D3—122no—
122C4×D3—124no—
123C4×D3—124no—
124C3×C8—124no—
125C3⋊C8—44no—
126C2×C32—22no—
127C2×C32#38011yescharacteristic
128C2×C32C2×#10811yescharacteristic
129C2×C32C2×#10811yescharacteristic
130C3⋊D3—22no—
131C3⋊D3—22no—
132C24—91no—
133C22×C4—91no—
134C22×C4—91no—
135C22×C4—91no—
136C22×C4—91no—
137C22×C4—91no—
138C22×C4—182no—
139C22×C4—182no—
140C22×C4GO+(4,𝔽2)11yescharacteristic
141M16—184no—
142M16—184no—
143C2×C8—64no—
144C2×C8—94no—
145C2×C8—92no—
146C2×C8—92no—
147C2×C8—184no—
148C2×C8—184no—
149C2×C8—182no—
150C22×C3—22no—
151C22×C3—24no—
152C22×C3—42no—
153C22×C3—42no—
154C2×D3—64no—
155C2×D3—64no—
156C2×D3—122no—
157C2×D3—122no—
158C2×D3—122no—
159C2×D3—122no—
160C2×D3—1216no—
161C3×C4—24no—
162C3×C4—42no—
163Dic3—62no—
164Dic3—62no—
165Dic3—122no—
166C32#181011yescharacteristic, complemented, Sylow
167C23—91no—
168C23—91no—
169C23—182no—
170C23—182no—
171C23—182no—
172C23#377311yescharacteristic
173C2×C4—22no—
174C2×C4—91no—
175C2×C4—92no—
176C2×C4—92no—
177C2×C4—91no—
178C2×C4—181no—
179C2×C4—181no—
180C2×C4—182no—
181C2×C4—181no—
182C2×C4—181no—
183C2×C4—182no—
184C2×C4#377311yescharacteristic
185C2×C4C2×GO+(4,𝔽2)11yescharacteristic
186C8—94no—
187C8—124no—
188C8—182no—
189C2×C3—22no—
190C2×C3—22no—
191C2×C3—22no—
192C2×C3—44no—
193D3—124no—
194D3—124no—
195C22—21no—
196C22—21no—
197C22—92no—
198C22—92no—
199C22—188no—
200C22—181no—
201C22—181no—
202C22—181no—
203C22—181no—
204C22#6373312yescomplemented
205C22C2×#377311yescharacteristic
206C4—21no—
207C4—91no—
208C4—91no—
209C4—181no—
210C4#6424212yes—
211C3—22no—
212C2—22no—
213C2—182no—
214C2—182no—
215C2C2×#6373311yescharacteristic
216C2#1059333111yescharacteristic
217C2#1059351611yescharacteristic
subgroupG/H
center, FrattiniC2×C4C2×GO+(4,𝔽2)
commutatorC2×C3⋊Dic3C22×C4
FittingC22×C32×C4D4
socleC22×C32C2×C4⋊C4
prime radicalC23×C3⋊D3Q8
cosocleC2×C4×C3⋊D3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1810
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C2×#63733C2semidirect
4. #10590051C2semidirect
81. C22×C32#108semidirect
88. C2×C3⋊D3#108semidirect
166. C32#1810semidirect
204. C22#63733semidirect

Maximal subgroups

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

subgroupindex
C22×#37872
C2×#637332
#105911592
#105900512
#18109