Finite Group Databasebeta

← #84098⋊C3 #11921372

Subgroups — #84098⋊C3 #11921372

Order 1152.

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

normal subgroups only

This group has 410 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, complemented
2C3⋊(#393⋊C3)C212yesmaximal, complemented
3#84098C311yesmaximal, characteristic, complemented
4#2615⋊C3—31nomaximal
5C3×C22⋊SL(2,𝔽3)C2211yescharacteristic
6A4×D12—41nomaximal
7C22×C3×#41C2×C311yescharacteristic, complemented
8#5948—21no—
9#5948D311yescharacteristic, complemented
10C2×#930—31no—
11#5231C2×C312yescomplemented
12#5223—32no—
13#5212—31no—
14#393⋊C3—32no—
15C2×D3×A4—42no—
16C3×#41⋊C3—82no—
17C3×C4×A4—41no—
18#2615—31noSylow
19C2×C3×#41—62no—
20C2×C3×#41—62no—
21C22×C3×Q8C22×C311yescharacteristic
22C22×C3×D4—31no—
23C23×C3×C4—31no—
24C22×#67—32no—
25C22×D12A411yescharacteristic
26C22⋊SL(2,𝔽3)—21no—
27C22⋊SL(2,𝔽3)C2×D311yescharacteristic
28D4×A4—121no—
29C2×#217—32no—
30#930—62no—
31#930—62no—
32C2×(C2×D3)⋊C4—32no—
33C2×C4⋊Dic3—31no—
34C3⋊#95—32no—
35C2×C3×A4—41no—
36D3×A4—82no—
37C3×D12—161no—
38C3×SL(2,𝔽3)—82no—
39C22×#41C3×D311yescharacteristic, complemented
40C2×#121—91no—
41#393—32no—
42#392—92no—
43#380—91no—
44C24×C3—31no—
45C23×D3C2×A412yes—
46C22×A4—122no—
47C3×#41—22no—
48C3×#41—62no—
49C3×#41—64no—
50C3×#41—62no—
51C3×#41—62no—
52C2×C3×Q8—62no—
53C2×C3×D4—62no—
54C2×C3×D4—64no—
55C22×C3×C4—32no—
56C22×C3×C4—32no—
57C22×C3×C4—31no—
58C22×C3×C4—62no—
59C22×C3×C4—62no—
60C22×C3×C4C2×A411yescharacteristic
61C2×#67—64no—
62C2×#67—124no—
63C22×Dic3—32no—
64C2×D12—61no—
65C2×D12—61no—
66#41⋊C3—82no—
67#41⋊C3—84no—
68C4×A4—41no—
69C4×A4—81no—
70#217—122no—
71(C2×D3)⋊C4—64no—
72C4⋊Dic3—61no—
73C4⋊Dic3—61no—
74C2×C3×D3—162no—
75C3×A4—41no—
76C32×C4—161no—
77C2×#41—62no—
78C2×#41—62no—
79C22×Q8C2×C3×D311yescharacteristic
80C22×D4—31no—
81C22×D4—31no—
82C22×D4—92no—
83C23×C4—31no—
84#121—182no—
85#121—182no—
86C2×C4⋊C4—91no—
87C2×C22⋊C4—92no—
88C2×C22⋊C4—92no—
89#95—92no—
90C23×C3—32no—
91C23×C3—61no—
92C23×C3—62no—
93C23×C3—62no—
94C23×C3—61no—
95C23×C3C22×A411yescharacteristic
96C22×D3—22no—
97C22×D3—62no—
98C22×D3—62no—
99C2×A4—41no—
100C2×A4—81no—
101C2×A4—242no—
102C3×Q8—22no—
103C3×Q8—62no—
104C3×D4—62no—
105C3×D4—62no—
106C3×D4—64no—
107C3×D4—481no—
108C2×C3×C4—31no—
109C2×C3×C4—31no—
110C2×C3×C4—32no—
111C2×C3×C4—62no—
112C2×C3×C4—64no—
113C2×C3×C4—62no—
114C2×C3×C4—62no—
115#67—128no—
116C2×Dic3—62no—
117C2×Dic3—64no—
118D12—41no—
119D12—121no—
120SL(2,𝔽3)—82no—
121SL(2,𝔽3)—84no—
122C2×C32—161no—
123C3×D3—322no—
124C24—31no—
125C24—32no—
126#41—22no—
127#41—62no—
128#41—64no—
129#41—62no—
130#41—62no—
131C2×Q8—62no—
132C2×D4—62no—
133C2×D4—64no—
134C2×D4—181no—
135C2×D4—181no—
136C2×D4—184no—
137C2×D4—364no—
138C22×C4—32no—
139C22×C4—32no—
140C22×C4—31no—
141C22×C4—62no—
142C22×C4—62no—
143C22×C4—92no—
144C22×C4D3×A411yescharacteristic
145C4⋊C4—181no—
146C4⋊C4—181no—
147C22⋊C4—184no—
148C22⋊C4—362no—
149C22×C3—31no—
150C22×C3—31no—
151C22×C3—62no—
152C22×C3—62no—
153C22×C3—62no—
154C22×C3—122no—
155C22×C3—122no—
156C22×C3—482no—
157C22×C32−1+4⋊C311yescharacteristic
158C2×D3—42no—
159C2×D3—122no—
160C2×D3—122no—
161A4—41no—
162A4—81no—
163C3×C4—31no—
164C3×C4—62no—
165C3×C4—161no—
166C3×C4—321no—
167C3×C4#120⋊C311yescharacteristic
168Dic3—122no—
169C32—161noSylow
170C23—32no—
171C23—61no—
172C23—62no—
173C23—62no—
174C23—61no—
175C23—62no—
176C23—182no—
177C23—182no—
178C23C2×D3×A411yescharacteristic
179Q8—22no—
180Q8—62no—
181D4—62no—
182D4—62no—
183D4—64no—
184D4—121no—
185D4—361no—
186D4—368no—
187C2×C4—31no—
188C2×C4—31no—
189C2×C4—32no—
190C2×C4—62no—
191C2×C4—64no—
192C2×C4—62no—
193C2×C4—62no—
194C2×C4—182no—
195C2×C4—184no—
196C2×C3—31no—
197C2×C3—31no—
198C2×C3—122no—
199C2×C3—161no—
200C2×C3—321no—
201C2×C3—962no—
202C2×C3C2×#120⋊C311yescharacteristic
203D3—82no—
204C22—31no—
205C22—31no—
206C22—62no—
207C22—62no—
208C22—62no—
209C22—122no—
210C22—122no—
211C22—122no—
212C22—362no—
213C22—362no—
214C22#1010⋊C311yescharacteristic
215C4—31no—
216C4—62no—
217C4—362no—
218C4C3⋊(#120⋊C3)11yescharacteristic
219C3—161no—
220C3—321no—
221C3#2615⋊C311yescharacteristic, complemented
222C2—31no—
223C2—31no—
224C2—122no—
225C2—242no—
226C2C2×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
hypercenterC4C3⋊(#120⋊C3)
LCSG ▷ C22×C3×Q8
UCSC1 ◁ C2 ◁ C4

Complements

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

NH ≅ G/Ntype
1. C3×#5948C2semidirect
2. C3⋊(#393⋊C3)C2semidirect
3. #84098C3semidirect
7. C22×C3×#41C2×C3semidirect
9. #5948D3semidirect
11. #5231C2×C3semidirect
39. C22×#41C3×D3semidirect
221. C3#2615⋊C3semidirect

Maximal subgroups

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

subgroupindex
C3×#59482
C3⋊(#393⋊C3)2
#840983
#2615⋊C33
A4×D124