Finite Group Databasebeta

← #11920962

Subgroups — #11920962

Order 1152.

270 conjugacy classes of subgroups; only the 25 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 25 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
1C3×#399⋊C3C211yesmaximal, characteristic, complemented
2C3⋊#4622C211yesmaximal, characteristic, complemented
3C3⋊#4621C211yesmaximal, characteristic, complemented
4#73006—33nomaximal
5#69715—31nomaximal
6#64269—41nomaximal
7C3×#95⋊C3C2211yescharacteristic
8#5494—31no—
9C3×#399D311yescharacteristic, complemented
10#4970—31no—
11#4968—31no—
12#399⋊C3D313yescomplemented
13#4622—33no—
14#4621—33no—
15#4525—31no—
16#4452—31no—
17#4451—31no—
18C22×C3×A4—41no—
19C2×C3⋊S4—41no—
20C3⋊SL(2,ℤ/4)—41no—
21#1618—91noSylow
22GL(2,ℤ/4)—123no—
23C2×C3×C4⋊C4—31no—
24C2×C3×C22⋊C4—31no—
25#953—61no—
26#930—31no—
27C4×#67—61no—
28#924—31no—
29#885—61no—
30#884—61no—
31#883—61no—
32#879—61no—
33C3×#95C2×D311yescharacteristic
34#830—31no—
35#830—31no—
36#810—61no—
37#809—61no—
38#808—61no—
39#807—61no—
40#95⋊C3C2×D313yes—
41C2×C3×A4—41no—
42C2×C3×A4—81no—
43C3⋊S4—81no—
44#638—161no—
45#538—91no—
46#484—91no—
47#481—91no—
48#399C3⋊D311yescharacteristic, complemented
49#328—91no—
50#327—91no—
51#323—91no—
52C24×C3S411yescharacteristic
53C22×A4—43no—
54C2×S4—123no—
55C22×C3×C4—31no—
56C22×C3×C4—31no—
57C2×#67—61no—
58C2×#67—61no—
59C2×#67—61no—
60C2×D12—31no—
61C2×C4×D3—61no—
62C2×Dic6—31no—
63SL(2,ℤ/4)—123no—
64C3×C4⋊C4—61no—
65C3×C4⋊C4—61no—
66C3×C22⋊C4—61no—
67C3×C22⋊C4—61no—
68#217—61no—
69#217—61no—
70#217—61no—
71(C2×D3)⋊C4—61no—
72(C2×D3)⋊C4—61no—
73C4⋊Dic3—31no—
74C4⋊Dic3—31no—
75Dic3⋊C4—61no—
76Dic3⋊C4—61no—
77C4×Dic3—61no—
78C2×C3⋊C8—61no—
79C2×C3⋊C8—61no—
80C22×C32—161no—
81C2×C3⋊D3—161no—
82C3×A4—41no—
83C3⋊Dic3—161no—
84#126—181no—
85#124—181no—
86#123—181no—
87C22⋊Q8—91no—
88#121—91no—
89#121—181no—
90#120—181no—
91C4×D4—181no—
92C2×C4⋊C4—31no—
93C2×C22⋊C4—31no—
94#107—181no—
95#106—181no—
96#103—181no—
97#102—181no—
98C22⋊C8—91no—
99C22⋊C8—91no—
100#95C2×C3⋊D311yescharacteristic
101C23×C3—21no—
102C23×C3—61no—
103C23×C3—61no—
104C23×C3C2×S411yescharacteristic
105C22×D3—61no—
106C2×A4—43no—
107C2×A4—83no—
108S4—243no—
109C2×C3×C4—31no—
110C2×C3×C4—31no—
111C2×C3×C4—61no—
112C2×C3×C4—121no—
113C2×C3×C4—121no—
114#67—121no—
115#67—121no—
116#67—241no—
117#67—241no—
118#67—483no—
119C2×Dic3—61no—
120C2×Dic3—61no—
121C2×Dic3—61no—
122D12—121no—
123C4×D3—241no—
124Dic6—121no—
125C3⋊C8—121no—
126C3⋊C8—121no—
127C2×C32—161no—
128C2×C32—321no—
129C3⋊D3—321no—
130C24C3⋊S411yescharacteristic
131C2×Q8—91no—
132C2×D4—91no—
133C2×D4—181no—
134C2×D4—181no—
135C2×D4—181no—
136C22×C4—31no—
137C22×C4—31no—
138C22×C4—181no—
139C2×C8—181no—
140C2×C8—181no—
141C4⋊C4—61no—
142C4⋊C4—61no—
143C4⋊C4—91no—
144C4⋊C4—91no—
145C4⋊C4—181no—
146C4⋊C4—181no—
147C22⋊C4—61no—
148C22⋊C4—61no—
149C22⋊C4—181no—
150C22⋊C4—181no—
151C22⋊C4—181no—
152C22⋊C4—181no—
153C22⋊C4—181no—
154C42—181no—
155C22×C3—31no—
156C22×C3—31no—
157C22×C3—41no—
158C22×C3—121no—
159C22×C3—121no—
160C22×C3—163no—
161C22×C3#98311yescharacteristic
162C2×D3—121no—
163C2×D3—121no—
164C2×D3—121no—
165C2×D3—483no—
166A4—43no—
167C3×C4—61no—
168C3×C4—61no—
169C3×C4—121no—
170Dic3—121no—
171Dic3—121no—
172Dic3—121no—
173Dic3—483no—
174C32—161noSylow
175C23—21no—
176C23—61no—
177C23—61no—
178C23—181no—
179C23C2×C3⋊S411yescharacteristic
180Q8—361no—
181D4—361no—
182D4—361no—
183D4—361no—
184D4—721no—
185D4—721no—
186C2×C4—31no—
187C2×C4—31no—
188C2×C4—61no—
189C2×C4—121no—
190C2×C4—121no—
191C2×C4—181no—
192C2×C4—181no—
193C2×C4—181no—
194C2×C4—721no—
195C8—361no—
196C8—361no—
197C2×C3—31no—
198C2×C3—31no—
199C2×C3—81no—
200C2×C3—163no—
201C2×C3—323no—
202C2×C3#857⋊C211yescharacteristic
203D3—241no—
204D3—963no—
205C22—31no—
206C22—31no—
207C22—41no—
208C22—121no—
209C22—121no—
210C22—361no—
211C22—361no—
212C22—361no—
213C22#6426411yescharacteristic
214C4—61no—
215C4—61no—
216C4—121no—
217C4—361no—
218C4—361no—
219C4—361no—
220C3—163no—
221C3#7300611yescharacteristic, complemented
222C2—31no—
223C2—31no—
224C2—81no—
225C2—721no—
226C2#1059363111yescharacteristic
subgroupG/H
center, hypercenterC2#10593631
commutator, cosocle, hypocenterC3×#95⋊C3C22
FrattiniC23C2×C3⋊S4
FittingC3×#399D3
socleC23×C3C2×S4
LCSG ▷ C3×#95⋊C3
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C3×#399⋊C3C2semidirect
2. C3⋊#4622C2semidirect
3. C3⋊#4621C2semidirect
9. C3×#399D3semidirect
12. #399⋊C3D3semidirect
48. #399C3⋊D3semidirect
221. C3#73006semidirect

Maximal subgroups

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

subgroupindex
C3×#399⋊C32
C3⋊#46222
C3⋊#46212
#730063
#697153
#642694