Finite Group Databasebeta

← #11799510

Subgroups — #11799510

Order 1152.

258 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 47 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
1C4×#3713C211yesmaximal, characteristic
2#10590312C211yesmaximal, characteristic, complemented
3C4⋊#3708C211yesmaximal, characteristic, complemented
4#10590068C212yesmaximal, complemented
5#10590061C212yesmaximal
6C3×C4×D12—21no—
7C3×#869—21no—
8C2×#3713C2211yescharacteristic
9C2×#3708C2212yes—
10C4×C3⋊(C3⋊C8)C2211yescharacteristic
11#63576—21no—
12#63576C2212yes—
13#63576C2211yescharacteristic
14#63562—21no—
15#5078—61no—
16C4×#213—61no—
17C2×C3×D12—21no—
18C2×C3×C4×D3—41no—
19C2×C3×Dic6—41no—
20C32×C42D411yescharacteristic
21C2×C3⋊(C3⋊C8)D411yescharacteristic
22C2×C3⋊(C3⋊C8)C2311yescharacteristic
23C3×(C2×D3)⋊C4—41no—
24C3×C4⋊Dic3—21no—
25C3×C4⋊Dic3—22no—
26C3×C4⋊Dic3—41no—
27#3713—21no—
28#3713Q812yescomplemented
29#3708—22no—
30#2224—91nomaximal, Sylow
31C3×C4⋊Q8—61no—
32C3×C4×D4—61no—
33C2×#213—61no—
34C4×D12—21no—
35#869—21no—
36#832—61no—
37#809—61no—
38#807—61no—
39#807—62no—
40#807—62no—
41C4×C3⋊C8—61no—
42C4×C3⋊C8—61no—
43C22×C3×D3—41no—
44C2×C32×C4D811yescharacteristic
45C2×C32×C4D811yescharacteristic
46C2×C32×C4C2×D411yescharacteristic
47C2×C3×Dic3—42no—
48C2×C3×Dic3—41no—
49C3×D12—22no—
50C3×D12—41no—
51C3×C4×D3—82no—
52C3×Dic6—82no—
53C3⋊(C3⋊C8)—21no—
54C3⋊(C3⋊C8)C2×Q811yescharacteristic
55C3⋊(C3⋊C8)#4111yescharacteristic
56#500—91no—
57C4×D8—91no—
58#366—92no—
59C4⋊C16—91no—
60#357—92no—
61C2×C3×Q8—121no—
62C2×C3×D4—61no—
63C22×C3×C4—121no—
64C2×D12—21no—
65C2×C4×D3—41no—
66C2×Dic6—41no—
67C3×C4⋊C4—62no—
68C3×C4⋊C4—61no—
69C3×C4⋊C4—121no—
70C3×C22⋊C4—121no—
71C3×C42—21no—
72C3×C42—21no—
73#213—62no—
74#213—62no—
75(C2×D3)⋊C4—41no—
76C4⋊Dic3—22no—
77C4⋊Dic3—21no—
78C4⋊Dic3—41no—
79C2×C3⋊C8—61no—
80C2×C3⋊C8—61no—
81C2×C3⋊C8—61no—
82C2×C3⋊C8—61no—
83C22×C32C2×D811yescharacteristic
84C2×C3×D3—42no—
85C2×C3×D3—81no—
86C2×C3×D3—81no—
87C32×C4—21no—
88C32×C4D1612yes—
89C32×C4C22⋊Q811yescharacteristic
90C32×C4#13711yescharacteristic
91C3×Dic3—82no—
92C3×Dic3—81no—
93C2×D8—91no—
94C4⋊Q8—61no—
95C4×D4—61no—
96C2×C16—92no—
97#107—92no—
98#107—91no—
99#107—181no—
100#102—181no—
101C4×C8—91no—
102C23×C3—121no—
103C22×D3—41no—
104C3×Q8—242no—
105C3×D4—62no—
106C3×D4—121no—
107C2×C3×C4—21no—
108C2×C3×C4—21no—
109C2×C3×C4—21no—
110C2×C3×C4—21no—
111C2×C3×C4—21no—
112C2×C3×C4—21no—
113C2×C3×C4—121no—
114C2×C3×C4—122no—
115C2×C3×C4—242no—
116C2×Dic3—42no—
117C2×Dic3—41no—
118D12—22no—
119D12—41no—
120C4×D3—82no—
121Dic6—82no—
122C3⋊C8—61no—
123C3⋊C8—61no—
124C3⋊C8—61no—
125C3⋊C8—61no—
126C3⋊C8—62no—
127C3⋊C8—121no—
128C2×C32#47411yescharacteristic
129C2×C32C2×D1611yescharacteristic
130C2×C32#51011yescharacteristic
131C3×D3—82no—
132C2×Q8—121no—
133C2×D4—61no—
134C22×C4—121no—
135D8—92no—
136D8—181no—
137C2×C8—91no—
138C2×C8—91no—
139C4⋊C4—61no—
140C4⋊C4—62no—
141C4⋊C4—121no—
142C22⋊C4—121no—
143C42GO+(4,𝔽2)11yescharacteristic
144C16—182no—
145C22×C3—21no—
146C22×C3—21no—
147C22×C3—122no—
148C22×C3—241no—
149C22×C3—241no—
150C2×D3—42no—
151C2×D3—81no—
152C2×D3—81no—
153C3×C4—22no—
154C3×C4—21no—
155C3×C4—21no—
156C3×C4—21no—
157C3×C4—21no—
158C3×C4—22no—
159C3×C4—22no—
160C3×C4—41no—
161C3×C4—241no—
162C3×C4—242no—
163Dic3—82no—
164Dic3—81no—
165C32#222411yescharacteristic, complemented, Sylow
166C23—121no—
167Q8—242no—
168D4—62no—
169D4—121no—
170C2×C4—121no—
171C2×C4—122no—
172C2×C4—242no—
173C2×C4#377411yescharacteristic
174C2×C4#377411yescharacteristic
175C2×C4C2×GO+(4,𝔽2)11yescharacteristic
176C8—91no—
177C8—91no—
178C8—181no—
179C2×C3—21no—
180C2×C3—21no—
181C2×C3—21no—
182C2×C3—21no—
183C2×C3—21no—
184C2×C3—21no—
185C2×C3—242no—
186D3—82no—
187C22—122no—
188C22—241no—
189C22—241no—
190C22C2×#377411yescharacteristic
191C4—21no—
192C4—241no—
193C4—242no—
194C4#6373412yes—
195C4D32⋊Q811yescharacteristic
196C4#6422611yescharacteristic
197C3—21no—
198C3—21no—
199C2—242no—
200C2C2×#6373411yescharacteristic
201C2#1059333611yescharacteristic
202C2#1059334711yescharacteristic
subgroupG/H
centerC22C2×#3774
commutator, cosocleC2×C3⋊(C3⋊C8)C23
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC32×C42D4
socleC22×C32C2×D8
prime radicalC2×#3713C22
hypercenterC42GO+(4,𝔽2)
hypocenterC32#2224
LCSG ▷ C2×C3⋊(C3⋊C8) ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
2. #10590312C2semidirect
3. C4⋊#3708C2semidirect
4. #10590068C2semidirect
28. #3713Q8semidirect
165. C32#2224semidirect

Maximal subgroups

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

subgroupindex
C4×#37132
#105903122
C4⋊#37082
#105900682
#105900612
#22249