Finite Group Databasebeta

← #11785501

Subgroups — #11785501

Order 1152.

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

normal subgroups only

This group has 418 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
1C2×#64287C211yesmaximal, characteristic
2#10593511C212yesmaximal, complemented
3#10591529C212yesmaximal
4#10590073C212yesmaximal, complemented
5C2×#3830C2211yescharacteristic
6C2×#3792C411yescharacteristic, complemented
7C2×#3792C2211yescharacteristic
8C22×#622C411yescharacteristic, complemented
9C22×#622C2211yescharacteristic
10#64287—22no—
11#64287—22no—
12C2×#3788C411yescharacteristic, complemented
13C2×#3787C411yescharacteristic, complemented
14#63957C2214yes—
15#63743—22no—
16#63742—22no—
17C3×#834—22no—
18#63581—22no—
19#4740—62no—
20C2×C32×D4D411yescharacteristic
21C2×#638D411yescharacteristic
22C2×#638Q811yescharacteristic
23C22×C3⋊Dic3C2×C411yescharacteristic
24C22×C3⋊Dic3C2311yescharacteristic
25#3830—22no—
26#3830—22no—
27C2×C4×C3⋊D3C2×C411yescharacteristic
28C2×#634Q811yescharacteristic
29#3792—22no—
30#3792—22no—
31C2×#622—21no—
32C2×#622—21no—
33C2×#622C2×C411yescharacteristic
34C2×#622C2×C411yescharacteristic
35C2×#622C2×C411yescharacteristic
36C2×#622C2×C411yescharacteristic
37C2×#622D412yes—
38C2×#622D412yes—
39#3788—22no—
40#3787—21no—
41#3787—21no—
42C3×#217—24no—
43#3724—24no—
44Dic32—24no—
45#1812—91nomaximal, Sylow
46C2×#237—62no—
47#877—64no—
48C3×#99—62no—
49#834—22no—
50#806—64no—
51C23×C32C4⋊C411yescharacteristic
52C23×C32C2×D411yescharacteristic
53C22×C3⋊D3C4⋊C411yescharacteristic
54C32×D4—22no—
55C2×C32×C4C4⋊C411yescharacteristic
56#638—22no—
57#638—22no—
58C2×C3⋊Dic3—21no—
59C2×C3⋊Dic3—21no—
60C2×C3⋊Dic3C4⋊C411yescharacteristic
61C2×C3⋊Dic3C22×C411yescharacteristic
62C2×C3⋊Dic3C2×D412yes—
63C2×C3⋊Dic3C2×Q811yescharacteristic
64C2×C3⋊Dic3#4112yes—
65C4×C3⋊D3—21no—
66C4×C3⋊D3—21no—
67#634—22no—
68C2×C3×Dic3—44no—
69#622—21no—
70#622—21no—
71#622C22⋊C411yescharacteristic
72#622C22⋊C411yescharacteristic
73#622C22⋊C412yes—
74C2×#131—91no—
75#427—92no—
76#410—92no—
77H(3,ℤ/4)—92no—
78C2×C3×D4—22no—
79C2×#67—62no—
80C2×#67—62no—
81C22×Dic3—62no—
82C22×Dic3—62no—
83#237—124no—
84#237—124no—
85C2×C4×D3—62no—
86C2×Dic6—62no—
87C3×C22⋊C4—64no—
88#217—24no—
89Dic3⋊C4—124no—
90C4×Dic3—124no—
91C22×C32—21no—
92C22×C32—41no—
93C22×C32—41no—
94C22×C32C2×C4⋊C411yescharacteristic
95C22×C32#12112yes—
96C2×C3⋊D3—21no—
97C2×C3⋊D3—41no—
98C32×C4—21no—
99C3⋊Dic3—21no—
100C3⋊Dic3C2×C22⋊C411yescharacteristic
101C3⋊Dic3#11711yescharacteristic
102C3⋊Dic3C22⋊Q812yes—
103C3×Dic3—84no—
104C2×#41—91no—
105#131—182no—
106#131—182no—
107C2×M16—91no—
108C2×M16—91no—
109C2×M16—91no—
110C22×C8—91no—
111C22×C8—91no—
112C22×C8—91no—
113#117—94no—
114#107—182no—
115#106—182no—
116#99—62no—
117#99—182no—
118C23×C3—22no—
119C23×C3—22no—
120C22×D3—62no—
121C3×D4—44no—
122C2×C3×C4—22no—
123C2×C3×C4—124no—
124#67—124no—
125#67—124no—
126C2×Dic3—44no—
127C2×Dic3—62no—
128C2×Dic3—64no—
129C2×Dic3—62no—
130C2×Dic3—64no—
131C2×Dic3—62no—
132C2×Dic3—122no—
133C2×Dic3—122no—
134C4×D3—122no—
135C4×D3—122no—
136Dic6—124no—
137C2×C32—22no—
138C2×C32—21no—
139C2×C32—41no—
140C2×C32#38011yescharacteristic
141C3⋊D3—41no—
142#41—182no—
143#41—182no—
144C2×Q8—91no—
145C2×D4—91no—
146C2×D4—91no—
147C2×D4GO+(4,𝔽2)11yescharacteristic
148C22×C4—91no—
149C22×C4—91no—
150C22×C4—91no—
151M16—182no—
152M16—182no—
153M16—182no—
154C2×C8—92no—
155C2×C8—92no—
156C2×C8—91no—
157C2×C8—91no—
158C2×C8—91no—
159C2×C8—91no—
160C2×C8—181no—
161C2×C8—181no—
162C2×C8—181no—
163C2×C8—181no—
164C4⋊C4—184no—
165C22⋊C4—64no—
166C42—184no—
167C22×C3—22no—
168C22×C3—24no—
169C22×C3—42no—
170C22×C3—82no—
171C22×C3—82no—
172C2×D3—122no—
173C2×D3—242no—
174C3×C4—42no—
175C3×C4—244no—
176Dic3—64no—
177Dic3—62no—
178Dic3—62no—
179Dic3—84no—
180Dic3—122no—
181C32#181211yescharacteristic, complemented, Sylow
182C23—91no—
183C23#377311yescharacteristic
184C23C2×GO+(4,𝔽2)11yescharacteristic
185Q8—182no—
186D4—22no—
187D4—182no—
188D4—182no—
189C2×C4—91no—
190C2×C4—91no—
191C2×C4—92no—
192C2×C4—92no—
193C2×C4—91no—
194C2×C4—124no—
195C2×C4—181no—
196C2×C4—181no—
197C2×C4—181no—
198C2×C4—181no—
199C2×C4#377311yescharacteristic
200C8—91no—
201C8—91no—
202C8—92no—
203C8—181no—
204C8—181no—
205C2×C3—22no—
206C2×C3—44no—
207C2×C3—42no—
208C2×C3—82no—
209D3—242no—
210C22—21no—
211C22—41no—
212C22—41no—
213C22—181no—
214C22—361no—
215C22C2×#377311yescharacteristic
216C22#6424212yes—
217C4—21no—
218C4—91no—
219C4—91no—
220C4—92no—
221C4—181no—
222C4—244no—
223C3—22no—
224C2—22no—
225C2—21no—
226C2—41no—
227C2—361no—
228C2#1059351611yescharacteristic
subgroupG/H
centerC2#10593516
commutatorC2×C3⋊Dic3C22×C4
FrattiniC23C2×GO+(4,𝔽2)
FittingC2×C32×D4D4
socleC2×C32#380
prime radicalC2×#3830C22
cosocleC22×C3⋊Dic3C23
hypercenterC2×D4GO+(4,𝔽2)
hypocenterC32#1812
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C23 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
2. #10593511C2semidirect
4. #10590073C2semidirect
6. C2×#3792C4semidirect
8. C22×#622C4semidirect
12. C2×#3788C4semidirect
13. C2×#3787C4semidirect
181. C32#1812semidirect

Maximal subgroups

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

subgroupindex
C2×#642872
#105935112
#105915292
#105900732
#18129