Finite Group Databasebeta

← #84094⋊C3 #11921369

Subgroups — #84094⋊C3 #11921369

Order 1152.

358 conjugacy classes of subgroups; only the 29 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 29 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×#5948C211yesmaximal, characteristic
2C3⋊(#395⋊C3)C212yesmaximal, complemented
3#84094C311yesmaximal, characteristic, complemented
4#2616⋊C3—31nomaximal
5C3×C22⋊SL(2,𝔽3)C2211yescharacteristic
6A4×Dic6—41nomaximal
7C22×C3×#41C2×C311yescharacteristic
8#5948—21no—
9#5948D311yescharacteristic
10C2×#924—31no—
11#5230C2×C312yes—
12#5222—32no—
13#5212—31no—
14#395⋊C3—32no—
15C3×#41⋊C3—82no—
16C3×C4×A4—41no—
17Dic3×A4—42no—
18#2616—31noSylow
19C2×C3×#41—62no—
20C2×C3×#41—62no—
21C22×C3×Q8C22×C311yescharacteristic
22C22×C3×D4—31no—
23C23×C3×C4—31no—
24C22×Dic6A411yescharacteristic
25C22⋊SL(2,𝔽3)—21no—
26C22⋊SL(2,𝔽3)C2×D311yescharacteristic
27Q8×A4—121no—
28C2×#217—32no—
29C2×#217—32no—
30C2×C4⋊Dic3—31no—
31#924—62no—
32#924—62no—
33C2×Dic3⋊C4—32no—
34C3⋊#95—32no—
35C2×C3×A4—41no—
36C3×Dic6—161no—
37C3×SL(2,𝔽3)—82no—
38C22×#41C3×D311yescharacteristic
39C2×C22⋊Q8—91no—
40#395—32no—
41#394—92no—
42#380—91no—
43C24×C3—31no—
44C3×#41—22no—
45C3×#41—62no—
46C3×#41—64no—
47C3×#41—62no—
48C3×#41—62no—
49C2×C3×Q8—62no—
50C2×C3×D4—62no—
51C2×C3×D4—64no—
52C22×C3×C4—32no—
53C22×C3×C4—32no—
54C22×C3×C4—31no—
55C22×C3×C4—62no—
56C22×C3×C4—62no—
57C22×C3×C4C2×A411yescharacteristic
58C22×Dic3—32no—
59C22×Dic3C2×A412yes—
60C2×Dic6—61no—
61C2×Dic6—61no—
62#41⋊C3—82no—
63#41⋊C3—84no—
64C4×A4—41no—
65C4×A4—81no—
66C4×A4—122no—
67#217—64no—
68#217—122no—
69C4⋊Dic3—61no—
70C4⋊Dic3—61no—
71Dic3⋊C4—64no—
72C3×A4—41no—
73C32×C4—161no—
74C3×Dic3—162no—
75C2×#41—62no—
76C2×#41—62no—
77C22×Q8—31no—
78C22×Q8C2×C3×D311yescharacteristic
79C22×D4—31no—
80C23×C4—31no—
81C22⋊Q8—182no—
82C22⋊Q8—182no—
83C2×C4⋊C4—92no—
84C2×C4⋊C4—91no—
85C2×C22⋊C4—92no—
86C2×C22⋊C4—92no—
87#95—92no—
88C23×C3—32no—
89C23×C3—62no—
90C23×C3—61no—
91C23×C3—62no—
92C23×C3—61no—
93C23×C3C22×A411yescharacteristic
94C2×A4—41no—
95C2×A4—81no—
96C3×Q8—22no—
97C3×Q8—62no—
98C3×Q8—481no—
99C3×D4—62no—
100C3×D4—62no—
101C3×D4—64no—
102C2×C3×C4—31no—
103C2×C3×C4—31no—
104C2×C3×C4—32no—
105C2×C3×C4—62no—
106C2×C3×C4—64no—
107C2×C3×C4—62no—
108C2×C3×C4—62no—
109C2×Dic3—62no—
110C2×Dic3—62no—
111C2×Dic3—62no—
112C2×Dic3—62no—
113Dic6—41no—
114Dic6—121no—
115SL(2,𝔽3)—82no—
116SL(2,𝔽3)—84no—
117C2×C32—161no—
118C24—31no—
119#41—22no—
120#41—62no—
121#41—64no—
122#41—62no—
123#41—62no—
124C2×Q8—62no—
125C2×Q8—181no—
126C2×Q8—181no—
127C2×D4—62no—
128C2×D4—64no—
129C22×C4—32no—
130C22×C4—32no—
131C22×C4—31no—
132C22×C4—32no—
133C22×C4—62no—
134C22×C4—62no—
135C22×C4—92no—
136C22×C4D3×A411yescharacteristic
137C4⋊C4—184no—
138C4⋊C4—181no—
139C4⋊C4—181no—
140C22⋊C4—184no—
141C22⋊C4—362no—
142C22×C3—31no—
143C22×C3—31no—
144C22×C3—62no—
145C22×C3—62no—
146C22×C3—62no—
147C22×C3—122no—
148C22×C3—122no—
149C22×C3#99411yescharacteristic
150A4—41no—
151A4—81no—
152C3×C4—31no—
153C3×C4—62no—
154C3×C4—161no—
155C3×C4—321no—
156C3×C4—482no—
157C3×C4#120⋊C311yescharacteristic
158Dic3—42no—
159Dic3—122no—
160C32—161noSylow
161C23—32no—
162C23—62no—
163C23—61no—
164C23—62no—
165C23—61no—
166C23C2×D3×A411yescharacteristic
167Q8—22no—
168Q8—62no—
169Q8—121no—
170Q8—361no—
171D4—62no—
172D4—62no—
173D4—64no—
174C2×C4—31no—
175C2×C4—31no—
176C2×C4—32no—
177C2×C4—62no—
178C2×C4—64no—
179C2×C4—62no—
180C2×C4—62no—
181C2×C4—182no—
182C2×C4—182no—
183C2×C4—182no—
184C2×C4—182no—
185C2×C3—31no—
186C2×C3—31no—
187C2×C3—122no—
188C2×C3—161no—
189C2×C3—321no—
190C2×C3C2×#120⋊C311yescharacteristic
191C22—31no—
192C22—31no—
193C22—62no—
194C22—62no—
195C22—62no—
196C22—122no—
197C22—122no—
198C22C3⋊#99411yescharacteristic
199C4—31no—
200C4—62no—
201C4—122no—
202C4—362no—
203C4C3⋊(#120⋊C3)11yescharacteristic
204C3—161no—
205C3—321no—
206C3#2616⋊C311yescharacteristic, complemented
207C2—31no—
208C2—31no—
209C2—122no—
210C2C2×C3⋊(#120⋊C3)11yescharacteristic
subgroupG/H
centerC2C2×C3⋊(#120⋊C3)
commutator, cosocle, hypocenterC22×C3×Q8C22×C3
FrattiniC23C2×D3×A4
FittingC22×C3×#41C2×C3
socleC23×C3C22×A4
prime radicalC3×#5948C2
hypercenterC4C3⋊(#120⋊C3)
LCSG ▷ C22×C3×Q8
UCSC1 ◁ C2 ◁ C4

Complements

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

NH ≅ G/Ntype
2. C3⋊(#395⋊C3)C2semidirect
3. #84094C3semidirect
206. C3#2616⋊C3semidirect

Maximal subgroups

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

subgroupindex
C3×#59482
C3⋊(#395⋊C3)2
#840943
#2616⋊C33
A4×Dic64