Finite Group Databasebeta

← #11798924

Subgroups — #11798924

Order 1152.

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

normal subgroups only

This group has 294 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
1C2×#63735C212yesmaximal
2#10590387C211yesmaximal, characteristic, complemented
3C4×#3713C211yesmaximal, characteristic
4C4⋊#3708C211yesmaximal, characteristic, complemented
5#10590062C212yesmaximal, complemented
6C3×C4×D12—21no—
7C3×#869—21no—
8C2×#3718—21no—
9C2×#3718C2212yes—
10C2×#3713C2211yescharacteristic
11C2×#3708C2212yes—
12#63735—24no—
13C4×C3⋊(C3⋊C8)C2211yescharacteristic
14#63576C2211yescharacteristic
15#63562—21no—
16#5092—61no—
17C4×#213—61no—
18C2×C3×D12—21no—
19C2×C3×C4×D3—41no—
20C2×C3×Dic6—22no—
21C32×C42D411yescharacteristic
22C2×C3⋊(C3⋊C8)D411yescharacteristic
23C2×C3⋊(C3⋊C8)C2311yescharacteristic
24C3×(C2×D3)⋊C4—41no—
25C3×C4⋊Dic3—21no—
26C3×C4⋊Dic3—41no—
27C3×C4⋊Dic3—41no—
28#3718—22no—
29#3718—22no—
30#3718—42no—
31#3713—21no—
32#3713D412yes—
33#3708—22no—
34#2208—91nomaximal, Sylow
35C3×C4⋊Q8—61no—
36C3×C4×D4—61no—
37C2×#216—62no—
38C2×#216—62no—
39C2×#213—61no—
40C4×D12—21no—
41#869—21no—
42#832—61no—
43#809—61no—
44#807—61no—
45C4×C3⋊C8—61no—
46C4×C3⋊C8—61no—
47C22×C3×D3—41no—
48C2×C32×C4D811yescharacteristic
49C2×C32×C4D811yescharacteristic
50C2×C32×C4C2×D411yescharacteristic
51C2×C3×Dic3—41no—
52C2×C3×Dic3—42no—
53C3×D12—22no—
54C3×D12—41no—
55C3×C4×D3—82no—
56C3×Dic6—42no—
57C3×Dic6—42no—
58C3⋊(C3⋊C8)—21no—
59C3⋊(C3⋊C8)C2×D411yescharacteristic
60C3⋊(C3⋊C8)#4111yescharacteristic
61C2×SD32—92no—
62#494—91no—
63C4×D8—91no—
64C4⋊C16—91no—
65#358—92no—
66C2×C3×Q8—62no—
67C2×C3×D4—61no—
68C22×C3×C4—121no—
69C2×D12—21no—
70C2×C4×D3—41no—
71C2×Dic6—22no—
72C3×C4⋊C4—61no—
73C3×C4⋊C4—121no—
74C3×C4⋊C4—121no—
75C3×C22⋊C4—121no—
76C3×C42—21no—
77C3×C42—21no—
78#216—122no—
79#216—122no—
80#216—124no—
81#213—62no—
82#213—62no—
83(C2×D3)⋊C4—41no—
84C4⋊Dic3—21no—
85C4⋊Dic3—41no—
86C4⋊Dic3—41no—
87C2×C3⋊C8—61no—
88C2×C3⋊C8—61no—
89C2×C3⋊C8—61no—
90C2×C3⋊C8—61no—
91C22×C32C2×D811yescharacteristic
92C2×C3×D3—42no—
93C2×C3×D3—81no—
94C2×C3×D3—81no—
95C32×C4—21no—
96C32×C4SD3212yescomplemented
97C32×C4#12111yescharacteristic
98C32×C4AGL(1,ℤ/8)11yescharacteristic
99C3×Dic3—82no—
100C3×Dic3—81no—
101C2×Q16—92no—
102C2×Q16—181no—
103C2×D8—91no—
104C4⋊Q8—61no—
105C4×D4—61no—
106SD32—184no—
107C2×C16—92no—
108#107—91no—
109#102—181no—
110C4×C8—91no—
111C23×C3—121no—
112C22×D3—41no—
113C3×Q8—122no—
114C3×Q8—122no—
115C3×D4—62no—
116C3×D4—121no—
117C2×C3×C4—21no—
118C2×C3×C4—21no—
119C2×C3×C4—21no—
120C2×C3×C4—21no—
121C2×C3×C4—21no—
122C2×C3×C4—21no—
123C2×C3×C4—121no—
124C2×C3×C4—122no—
125C2×C3×C4—242no—
126C2×Dic3—41no—
127C2×Dic3—42no—
128D12—22no—
129D12—41no—
130C4×D3—82no—
131Dic6—42no—
132Dic6—42no—
133C3⋊C8—61no—
134C3⋊C8—61no—
135C3⋊C8—61no—
136C3⋊C8—61no—
137C3⋊C8—62no—
138C3⋊C8—121no—
139C2×C32#45911yescharacteristic
140C2×C32C2×SD3211yescharacteristic
141C2×C32#51011yescharacteristic
142C3×D3—82no—
143C2×Q8—62no—
144C2×D4—61no—
145C22×C4—121no—
146Q16—182no—
147Q16—182no—
148Q16—362no—
149D8—92no—
150D8—181no—
151C2×C8—91no—
152C2×C8—91no—
153C4⋊C4—61no—
154C4⋊C4—121no—
155C4⋊C4—121no—
156C22⋊C4—121no—
157C42GO+(4,𝔽2)11yescharacteristic
158C16—182no—
159C22×C3—21no—
160C22×C3—21no—
161C22×C3—122no—
162C22×C3—241no—
163C22×C3—241no—
164C2×D3—42no—
165C2×D3—81no—
166C2×D3—81no—
167C3×C4—22no—
168C3×C4—21no—
169C3×C4—21no—
170C3×C4—21no—
171C3×C4—21no—
172C3×C4—22no—
173C3×C4—22no—
174C3×C4—41no—
175C3×C4—241no—
176C3×C4—242no—
177Dic3—82no—
178Dic3—81no—
179C32#220811yescharacteristic, complemented, Sylow
180C23—121no—
181Q8—122no—
182Q8—122no—
183D4—62no—
184D4—121no—
185C2×C4—121no—
186C2×C4—122no—
187C2×C4—242no—
188C2×C4#377411yescharacteristic
189C2×C4#377411yescharacteristic
190C2×C4C2×GO+(4,𝔽2)11yescharacteristic
191C8—91no—
192C8—91no—
193C8—181no—
194C2×C3—21no—
195C2×C3—21no—
196C2×C3—21no—
197C2×C3—21no—
198C2×C3—21no—
199C2×C3—21no—
200C2×C3—242no—
201D3—82no—
202C22—122no—
203C22—241no—
204C22—241no—
205C22C2×#377411yescharacteristic
206C4—21no—
207C4—241no—
208C4—242no—
209C4#6373512yescomplemented
210C4#6422411yescharacteristic
211C4#6423011yescharacteristic
212C3—21no—
213C3—21no—
214C2—242no—
215C2C2×#6373511yescharacteristic
216C2#1059333611yescharacteristic
217C2#1059341711yescharacteristic
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#2208
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. #10590387C2semidirect
4. C4⋊#3708C2semidirect
5. #10590062C2semidirect
96. C32×C4SD32semidirect
179. C32#2208semidirect
209. C4#63735semidirect

Maximal subgroups

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

subgroupindex
C2×#637352
#105903872
C4×#37132
C4⋊#37082
#105900622
#22089