Finite Group Databasebeta

← #11798862

Subgroups — #11798862

Order 1152.

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

normal subgroups only

This group has 334 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×#63734C212yesmaximal, complemented
2#10590352C211yesmaximal, characteristic, complemented
3C4×#3713C211yesmaximal, characteristic, complemented
4C4⋊#3708C211yesmaximal, characteristic, complemented
5#10590061C212yesmaximal, complemented
6C3×#874—21no—
7C3×C4×D12—21no—
8C2×#3713—21no—
9C2×#3713C2212yes—
10C2×#3713C2211yescharacteristic
11C2×#3708C2212yes—
12#63734—24no—
13C4×C3⋊(C3⋊C8)C2211yescharacteristic
14#63576C2211yescharacteristic
15#63562—21no—
16#5073—61no—
17C4×#213—61no—
18C2×C3×D12—21no—
19C2×C3×D12—22no—
20C2×C3×D12—41no—
21C2×C3×D12—41no—
22C2×C3×C4×D3—41no—
23C32×C42D411yescharacteristic
24C2×C3⋊(C3⋊C8)D411yescharacteristic
25C2×C3⋊(C3⋊C8)C2311yescharacteristic
26C3×(C2×D3)⋊C4—41no—
27C3×C4⋊Dic3—21no—
28#3713—22no—
29#3713—21no—
30#3713—22no—
31#3713—42no—
32#3713D412yescomplemented
33#3708—22no—
34#2206—91nomaximal, Sylow
35C3×#127—61no—
36C3×C4×D4—61no—
37C2×#213—61no—
38C2×#213—62no—
39C2×#213—62no—
40#874—21no—
41C4×D12—21no—
42#832—61no—
43#809—61no—
44#807—61no—
45C4×C3⋊C8—61no—
46C4×C3⋊C8—61no—
47C22×C3×D3—41no—
48C22×C3×D3—42no—
49C2×C32×C4D811yescharacteristic
50C2×C32×C4D811yescharacteristic
51C2×C32×C4C2×D411yescharacteristic
52C2×C3×Dic3—41no—
53C3×D12—22no—
54C3×D12—42no—
55C3×D12—41no—
56C3×D12—42no—
57C3×D12—82no—
58C3×D12—82no—
59C3×C4×D3—82no—
60C3⋊(C3⋊C8)—21no—
61C3⋊(C3⋊C8)C2×D411yescharacteristic
62C3⋊(C3⋊C8)#4111yescharacteristic
63C2×D16—92no—
64#493—91no—
65C4×D8—91no—
66C4⋊C16—91no—
67#357—92no—
68C2×C3×D4—61no—
69C2×C3×D4—62no—
70C2×C3×D4—121no—
71C2×C3×D4—121no—
72C22×C3×C4—121no—
73C2×D12—21no—
74C2×D12—22no—
75C2×D12—41no—
76C2×D12—41no—
77C2×C4×D3—41no—
78C3×C4⋊C4—61no—
79C3×C22⋊C4—121no—
80C3×C42—21no—
81C3×C42—21no—
82#213—62no—
83#213—62no—
84#213—122no—
85#213—122no—
86#213—124no—
87(C2×D3)⋊C4—41no—
88C4⋊Dic3—21no—
89C2×C3⋊C8—61no—
90C2×C3⋊C8—61no—
91C2×C3⋊C8—61no—
92C2×C3⋊C8—61no—
93C22×C32C2×D811yescharacteristic
94C2×C3×D3—42no—
95C2×C3×D3—81no—
96C2×C3×D3—81no—
97C2×C3×D3—82no—
98C2×C3×D3—82no—
99C2×C3×D3—82no—
100C32×C4—21no—
101C32×C4D1612yescomplemented
102C32×C4#12111yescharacteristic
103C32×C4AGL(1,ℤ/8)11yescharacteristic
104C3×Dic3—81no—
105C2×D8—91no—
106C2×D8—92no—
107C2×D8—181no—
108#127—61no—
109C4×D4—61no—
110D16—184no—
111C2×C16—92no—
112#107—91no—
113#102—181no—
114C4×C8—91no—
115C23×C3—121no—
116C23×C3—122no—
117C22×D3—41no—
118C22×D3—42no—
119C3×D4—62no—
120C3×D4—121no—
121C3×D4—122no—
122C3×D4—122no—
123C3×D4—242no—
124C3×D4—242no—
125C2×C3×C4—21no—
126C2×C3×C4—21no—
127C2×C3×C4—21no—
128C2×C3×C4—21no—
129C2×C3×C4—21no—
130C2×C3×C4—21no—
131C2×C3×C4—121no—
132C2×C3×C4—242no—
133C2×Dic3—41no—
134D12—22no—
135D12—41no—
136D12—42no—
137D12—42no—
138D12—82no—
139D12—82no—
140C4×D3—82no—
141C3⋊C8—61no—
142C3⋊C8—61no—
143C3⋊C8—61no—
144C3⋊C8—61no—
145C3⋊C8—62no—
146C3⋊C8—121no—
147C2×C32#45911yescharacteristic
148C2×C32C2×D1611yescharacteristic
149C2×C32#50911yescharacteristic
150C3×D3—82no—
151C3×D3—162no—
152C2×D4—61no—
153C2×D4—62no—
154C2×D4—121no—
155C2×D4—121no—
156C22×C4—121no—
157D8—92no—
158D8—181no—
159D8—182no—
160D8—182no—
161D8—362no—
162C2×C8—91no—
163C2×C8—91no—
164C4⋊C4—61no—
165C22⋊C4—121no—
166C42GO+(4,𝔽2)11yescharacteristic
167C16—182no—
168C22×C3—21no—
169C22×C3—21no—
170C22×C3—122no—
171C22×C3—241no—
172C22×C3—241no—
173C22×C3—242no—
174C22×C3—242no—
175C22×C3—242no—
176C2×D3—42no—
177C2×D3—81no—
178C2×D3—81no—
179C2×D3—82no—
180C2×D3—82no—
181C2×D3—82no—
182C3×C4—22no—
183C3×C4—21no—
184C3×C4—21no—
185C3×C4—21no—
186C3×C4—21no—
187C3×C4—22no—
188C3×C4—22no—
189C3×C4—41no—
190C3×C4—241no—
191Dic3—81no—
192C32#220611yescharacteristic, complemented, Sylow
193C23—121no—
194C23—122no—
195D4—62no—
196D4—121no—
197D4—122no—
198D4—122no—
199D4—242no—
200D4—242no—
201C2×C4—121no—
202C2×C4—242no—
203C2×C4#377411yescharacteristic
204C2×C4#377411yescharacteristic
205C2×C4C2×GO+(4,𝔽2)11yescharacteristic
206C8—91no—
207C8—91no—
208C8—181no—
209C2×C3—21no—
210C2×C3—21no—
211C2×C3—21no—
212C2×C3—21no—
213C2×C3—21no—
214C2×C3—21no—
215C2×C3—242no—
216C2×C3—482no—
217D3—82no—
218D3—162no—
219C22—122no—
220C22—241no—
221C22—241no—
222C22—242no—
223C22—242no—
224C22—242no—
225C22C2×#377411yescharacteristic
226C4—21no—
227C4—241no—
228C4#6373412yescomplemented
229C4#6422411yescharacteristic
230C4#6423011yescharacteristic
231C3—21no—
232C3—21no—
233C2—242no—
234C2—482no—
235C2C2×#6373411yescharacteristic
236C2#1059333411yescharacteristic
237C2#1059341711yescharacteristic
subgroupG/H
centerC22C2×#3774
commutator, cosocleC2×C3⋊(C3⋊C8)C23
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC32×C42D4
socleC22×C32C2×D8
hypercenterC42GO+(4,𝔽2)
hypocenterC32#2206
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
1. C2×#63734C2semidirect
2. #10590352C2semidirect
3. C4×#3713C2semidirect
4. C4⋊#3708C2semidirect
5. #10590061C2semidirect
32. #3713D4semidirect
101. C32×C4D16semidirect
192. C32#2206semidirect
228. C4#63734semidirect

Maximal subgroups

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

subgroupindex
C2×#637342
#105903522
C4×#37132
C4⋊#37082
#105900612
#22069