Finite Group Databasebeta

← #11772822

Subgroups — #11772822

Order 1152.

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

normal subgroups only

This group has 228 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×#5060C211yesmaximal, characteristic
2#10589408C211yesmaximal, characteristic
3C3×#4541C211yesmaximal, characteristic
4#67798—31nomaximal
5#67545—31nomaximal
6C32×#124C2211yescharacteristic
7C2×C3×#216—21no—
8C2×C3×#214—21no—
9C3×#869C411yescharacteristic, complemented
10#63663—21no—
11C3×#834—21no—
12C3×#803C411yescharacteristic, complemented
13C3×#497—31no—
14#5060D311yescharacteristic
15C3×#354—31no—
16#4542—31no—
17#4542—31no—
18#4542—61no—
19#4541D311yescharacteristic
20C2×C32×Q8D411yescharacteristic
21C2×C32×D4D411yescharacteristic
22C2×C3×Dic6—21no—
23C32×C22⋊C4—41no—
24C32×C42C2×C411yescharacteristic
25#3748—41no—
26C3×#217—41no—
27C3×#216—42no—
28C3×#214—42no—
29C3×C4⋊Dic3—41no—
30C2×C3×C3⋊C8—21no—
31#1407—91noSylow
32C2×C3×Q16—61no—
33C2×C3×SD16—61no—
34C3×C4⋊Q8—31no—
35C3×#124—21no—
36C3×#124C2×D311yescharacteristic
37C3×#124C2×D311yescharacteristic
38C2×#216—21no—
39C2×#214—21no—
40#869Dic311yescharacteristic, 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—
49C32×Q8—41no—
50C32×D4—41no—
51C2×C32×C4—21no—
52C2×C32×C4—21no—
53C2×C32×C4C22⋊C411yescharacteristic
54C2×C3×Dic3—41no—
55C2×C3×Dic3—81no—
56C3×Dic6—41no—
57C3×Dic6—41no—
58C3⋊(C3⋊C8)—81no—
59C3×C3⋊C8—22no—
60#497—31no—
61#355—91no—
62#354—31no—
63C2×C3×Q8—21no—
64C2×C3×Q8—61no—
65C2×C3×Q8D1211yescharacteristic
66C2×C3×Q8#6711yescharacteristic
67C2×C3×D4—21no—
68C2×C3×D4#6711yescharacteristic
69C2×C3×D4#6711yescharacteristic
70C2×Dic6—21no—
71C3×Q16—122no—
72C3×SD16—122no—
73C2×C3×C8—61no—
74C3×C4⋊C4—121no—
75C3×C22⋊C4—41no—
76C3×C22⋊C4—41no—
77C3×C22⋊C4—42no—
78C3×C22⋊C4—121no—
79C3×C42—21no—
80C3×C42C4×D311yescharacteristic
81C3×C42C2×Dic311yescharacteristic
82#217—41no—
83#216—42no—
84#214—42no—
85C4⋊Dic3—41no—
86#208—122no—
87#208—121no—
88#208—121no—
89C2×C3⋊C8—21no—
90C22×C32—41no—
91C22×C32—81no—
92C22×C32#9911yescharacteristic
93C32×C4—21no—
94C32×C4—41no—
95C32×C4—41no—
96C3×Dic3—81no—
97C3×Dic3—161no—
98C2×Q16—61no—
99C2×SD16—61no—
100C4⋊Q8—31no—
101#124D3211yescharacteristic
102#101—181no—
103#99—61no—
104#97—31no—
105C23×C3—21no—
106C23×C3—21no—
107C23×C3—41no—
108C3×Q8—41no—
109C3×Q8—41no—
110C3×Q8—81no—
111C3×Q8—121no—
112C3×Q8—121no—
113C3×D4—41no—
114C3×D4—41no—
115C3×D4—81no—
116C2×C3×C4—22no—
117C2×C3×C4—21no—
118C2×C3×C4—21no—
119C2×C3×C4—21no—
120C2×C3×C4—21no—
121C2×C3×C4—21no—
122C2×C3×C4—41no—
123C2×C3×C4—121no—
124C2×C3×C4—241no—
125C2×C3×C4(C2×D3)⋊C411yescharacteristic
126C2×C3×C4#21711yescharacteristic
127C2×Dic3—41no—
128C2×Dic3—81no—
129Dic6—41no—
130Dic6—41no—
131C3×C8—62no—
132C3⋊C8—22no—
133C3⋊C8—242no—
134C3⋊C8—241no—
135C3⋊C8—241no—
136C2×C32—21no—
137C2×C32—81no—
138C2×C32#35311yescharacteristic
139C2×Q8—61no—
140C2×Q8#62611yescharacteristic
141C2×D4#62511yescharacteristic
142Q16—122no—
143SD16—122no—
144M16—361no—
145C2×C8—61no—
146C4⋊C4—121no—
147C22⋊C4—41no—
148C22⋊C4—121no—
149C42D3×Dic311yescharacteristic
150C22×C3—21no—
151C22×C3—41no—
152C22×C3—41no—
153C22×C3—81no—
154C22×C3—81no—
155C22×C3—81no—
156C22×C3—82no—
157C22×C3#80611yescharacteristic
158C22×C3#83411yescharacteristic
159C3×C4—21no—
160C3×C4—21no—
161C3×C4—41no—
162C3×C4—42no—
163C3×C4—41no—
164C3×C4—41no—
165C3×C4—41no—
166C3×C4—41no—
167C3×C4—81no—
168C3×C4—241no—
169C3×C4—481no—
170Dic3—81no—
171Dic3—161no—
172C32#140711yescharacteristic, complemented, Sylow
173C23—21no—
174Q8—41no—
175Q8—121no—
176Q8—121no—
177D4—41no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—121no—
181C2×C4—241no—
182C2×C4(C2×D3)⋊Dic311yescharacteristic
183C8—62no—
184C8—721no—
185C2×C3—21no—
186C2×C3—21no—
187C2×C3—21no—
188C2×C3—41no—
189C2×C3—81no—
190C2×C3—81no—
191C2×C3—161no—
192C2×C3#447411yescharacteristic
193C2×C3#454511yescharacteristic
194C22—41no—
195C22—81no—
196C22#6358011yescharacteristic
197C4—21no—
198C4—41no—
199C4—41no—
200C4—241no—
201C4—481no—
202C3—21no—
203C3#6754511yescharacteristic, complemented
204C3#6779811yescharacteristic, complemented
205C2—21no—
206C2—81no—
207C2#1058917811yescharacteristic
subgroupG/H
centerC2#10589178
commutatorC32×C42C2×C4
Frattini, hypercenter#124D32
Fitting, cosocleC32×#124C22
socleC2×C32#353
prime radicalC2×C32×D4D4
hypocenterC32#1407
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
9. C3×#869C4semidirect
12. C3×#803C4semidirect
40. #869Dic3semidirect
47. #803Dic3semidirect
172. C32#1407semidirect
203. C3#67545semidirect
204. C3#67798semidirect

Maximal subgroups

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

subgroupindex
C3×#50602
#105894082
C3×#45412
#677983
#675453