Finite Group Databasebeta

← #11772806

Subgroups — #11772806

Order 1152.

248 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 42 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×#5058C211yesmaximal, characteristic
2#10589408C211yesmaximal, characteristic, complemented
3C3×#4541C211yesmaximal, characteristic, complemented
4#67797—31nomaximal
5#67544—31nomaximal
6C32×#124C2211yescharacteristic
7C2×C3×#215—21no—
8C2×C3×#213—21no—
9C3×#874C411yescharacteristic, complemented
10#63663—21no—
11C3×#834—21no—
12C3×#803C411yescharacteristic, complemented
13C3×#496—31no—
14#5058D311yescharacteristic
15C3×#354—31no—
16#4542—31no—
17#4542—31no—
18#4542—61no—
19#4541D311yescharacteristic, complemented
20C2×C32×Q8D411yescharacteristic
21C2×C32×D4D411yescharacteristic
22C2×C3×D12—21no—
23C2×C3×D12—41no—
24C32×C22⋊C4—41no—
25C32×C42C2×C411yescharacteristic
26#3748—41no—
27C3×#217—41no—
28C3×#215—42no—
29C3×#213—42no—
30C2×C3×C3⋊C8—21no—
31#1406—91noSylow
32C2×C3×SD16—61no—
33C2×C3×D8—61no—
34C3×#127—31no—
35C3×#124—21no—
36C3×#124C2×D311yescharacteristic
37C3×#124C2×D311yescharacteristic
38C2×#215—21no—
39C2×#213—21no—
40#874Dic311yescharacteristic, complemented
41C3×#99—61no—
42C3×#97—31no—
43#836—62no—
44#836—61no—
45#836—61no—
46#834—21no—
47#803Dic311yescharacteristic, complemented
48C23×C32—21no—
49C22×C3×D3—41no—
50C32×Q8—41no—
51C32×D4—41no—
52C2×C32×C4—21no—
53C2×C32×C4—21no—
54C2×C32×C4C22⋊C411yescharacteristic
55C2×C3×Dic3—81no—
56C3×D12—41no—
57C3×D12—41no—
58C3×D12—82no—
59C3⋊(C3⋊C8)—81no—
60C3×C3⋊C8—22no—
61#496—31no—
62#355—91no—
63#354—31no—
64C2×C3×Q8—21no—
65C2×C3×Q8D1211yescharacteristic
66C2×C3×Q8#6711yescharacteristic
67C2×C3×D4—21no—
68C2×C3×D4—61no—
69C2×C3×D4—121no—
70C2×C3×D4#6711yescharacteristic
71C2×C3×D4#6711yescharacteristic
72C2×D12—21no—
73C2×D12—41no—
74C3×SD16—122no—
75C3×D8—122no—
76C2×C3×C8—61no—
77C3×C22⋊C4—41no—
78C3×C22⋊C4—41no—
79C3×C22⋊C4—42no—
80C3×C22⋊C4—121no—
81C3×C42—21no—
82C3×C42C4×D311yescharacteristic
83C3×C42C2×Dic311yescharacteristic
84#217—41no—
85#215—42no—
86#213—42no—
87#208—122no—
88#208—121no—
89#208—121no—
90C2×C3⋊C8—21no—
91C22×C32—41no—
92C22×C32—81no—
93C22×C32#9911yescharacteristic
94C2×C3×D3—82no—
95C2×C3×D3—81no—
96C32×C4—21no—
97C32×C4—41no—
98C32×C4—41no—
99C3×Dic3—161no—
100C2×SD16—61no—
101C2×D8—61no—
102#127—31no—
103#124D3211yescharacteristic
104#101—181no—
105#99—61no—
106#97—31no—
107C23×C3—21no—
108C23×C3—21no—
109C23×C3—41no—
110C23×C3—121no—
111C22×D3—41no—
112C3×Q8—41no—
113C3×Q8—41no—
114C3×Q8—81no—
115C3×D4—41no—
116C3×D4—41no—
117C3×D4—81no—
118C3×D4—121no—
119C3×D4—121no—
120C3×D4—242no—
121C2×C3×C4—22no—
122C2×C3×C4—21no—
123C2×C3×C4—21no—
124C2×C3×C4—21no—
125C2×C3×C4—21no—
126C2×C3×C4—21no—
127C2×C3×C4—41no—
128C2×C3×C4—241no—
129C2×C3×C4(C2×D3)⋊C411yescharacteristic
130C2×C3×C4#21711yescharacteristic
131C2×Dic3—81no—
132D12—41no—
133D12—41no—
134D12—82no—
135C3×C8—62no—
136C3⋊C8—22no—
137C3⋊C8—242no—
138C3⋊C8—241no—
139C3⋊C8—241no—
140C2×C32—21no—
141C2×C32—81no—
142C2×C32#35311yescharacteristic
143C3×D3—161no—
144C2×Q8#62611yescharacteristic
145C2×D4—61no—
146C2×D4—121no—
147C2×D4#62511yescharacteristic
148SD16—122no—
149D8—122no—
150M16—361no—
151C2×C8—61no—
152C22⋊C4—41no—
153C22⋊C4—121no—
154C42D3×Dic311yescharacteristic
155C22×C3—21no—
156C22×C3—41no—
157C22×C3—41no—
158C22×C3—81no—
159C22×C3—81no—
160C22×C3—81no—
161C22×C3—82no—
162C22×C3—242no—
163C22×C3—241no—
164C22×C3#80611yescharacteristic
165C22×C3#83411yescharacteristic
166C2×D3—82no—
167C2×D3—81no—
168C3×C4—21no—
169C3×C4—21no—
170C3×C4—41no—
171C3×C4—42no—
172C3×C4—41no—
173C3×C4—41no—
174C3×C4—41no—
175C3×C4—41no—
176C3×C4—81no—
177C3×C4—481no—
178Dic3—161no—
179C32#140611yescharacteristic, complemented, Sylow
180C23—21no—
181C23—121no—
182Q8—41no—
183D4—41no—
184D4—121no—
185D4—121no—
186D4—242no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—241no—
190C2×C4(C2×D3)⋊Dic311yescharacteristic
191C8—62no—
192C8—721no—
193C2×C3—21no—
194C2×C3—21no—
195C2×C3—21no—
196C2×C3—41no—
197C2×C3—81no—
198C2×C3—81no—
199C2×C3—161no—
200C2×C3—481no—
201C2×C3#447411yescharacteristic
202C2×C3#454511yescharacteristic
203D3—161no—
204C22—41no—
205C22—81no—
206C22—242no—
207C22—241no—
208C22#6358011yescharacteristic
209C4—21no—
210C4—41no—
211C4—41no—
212C4—481no—
213C3—21no—
214C3#6754411yescharacteristic, complemented
215C3#6779711yescharacteristic, complemented
216C2—21no—
217C2—81no—
218C2—481no—
219C2#1058917811yescharacteristic
subgroupG/H
centerC2#10589178
commutatorC32×C42C2×C4
Frattini, hypercenter#124D32
Fitting, cosocleC32×#124C22
socleC2×C32#353
prime radicalC3×#5058C2
hypocenterC32#1406
LCSG ▷ C32×C42 ▷ C2×C32×C4 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #124

Complements

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

NH ≅ G/Ntype
2. #10589408C2semidirect
3. C3×#4541C2semidirect
9. C3×#874C4semidirect
12. C3×#803C4semidirect
19. #4541D3semidirect
40. #874Dic3semidirect
47. #803Dic3semidirect
179. C32#1406semidirect
214. C3#67544semidirect
215. C3#67797semidirect

Maximal subgroups

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

subgroupindex
C3×#50582
#105894082
C3×#45412
#677973
#675443