Finite Group Databasebeta

← #11798892

Subgroups — #11798892

Order 1152.

403 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 403 conjugacy classes of subgroups — too many to draw. Only its 76 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
1#10592572C211yesmaximal, characteristic, complemented
2#10590886C211yesmaximal, characteristic
3C2×#63548C212yesmaximal, complemented
4C3×#4491C212yesmaximal, complemented
5#10589133C211yesmaximal, characteristic, complemented
6#69204—32nomaximal
7C2×#3746C2211yescharacteristic
8#64096—21no—
9C2×C3×D24C2212yes—
10#63914—21no—
11C2×#3713—21no—
12C32×#107C2211yescharacteristic
13C8×C3⋊Dic3C2211yescharacteristic
14#63637—21no—
15C2×C3×C3⋊C16C2212yes—
16#63548—24no—
17#5151—32no—
18C2×#827—32no—
19C2×#800—32no—
20#4873—32no—
21#4873—61no—
22C3×#357—32no—
23Dic3⋊C16—32no—
24#4491D312yescomplemented
25C2×#634—21no—
26C2×C3×D12—22no—
27C2×#625—41no—
28C2×#625—41no—
29C2×C32×C8C2311yescharacteristic
30C32×C4⋊C4—21no—
31#3750—41no—
32C4×C3⋊Dic3—41no—
33C4×C3⋊Dic3D411yescharacteristic
34C2×C3⋊(C3⋊C8)D411yescharacteristic
35#3746—21no—
36#3746D412yescomplemented
37C3×D24—22no—
38C3×D24—22no—
39#3713—42no—
40C3×C3⋊C16—22no—
41#2207—91noSylow
42C2×C3×D8—32no—
43#940—62no—
44C2×#213—62no—
45C2×Dic12—32no—
46C2×Dic12—61no—
47C2×D24C2×D312yes—
48#887—62no—
49#887—62no—
50C2×C3×C16—32no—
51C3×#107—21no—
52C3×#107C2×D312yes—
53#827—64no—
54C8×Dic3—32no—
55C8×Dic3—61no—
56C2×C3⋊C16C2×D312yes—
57#810—62no—
58#810—62no—
59#800—64no—
60C22×C3×D3—42no—
61C2×C32×C4—41no—
62C2×C32×C4C2×D411yescharacteristic
63C2×C3⋊Dic3—41no—
64C2×C3⋊Dic3D811yescharacteristic
65C2×C3⋊Dic3D811yescharacteristic
66#634—22no—
67#634—41no—
68C3×D12—42no—
69C3×D12—42no—
70#625—82no—
71#625—82no—
72C32×C8C2×D411yescharacteristic
73C32×C8#4111yescharacteristic
74C3⋊(C3⋊C8)—21no—
75C2×SD32—92no—
76#493—91no—
77C4×Q16—91no—
78C4⋊C16—91no—
79#357—32no—
80C2×C3×D4—62no—
81C2×#67—122no—
82C2×#67—122no—
83C2×D12—22no—
84C2×Dic6—62no—
85C2×Dic6—62no—
86C3×D8—62no—
87C3×D8—62no—
88C2×C3×C8—21no—
89C2×C3×C8C22×D312yes—
90C3×C4⋊C4—22no—
91C3×C4⋊C4—22no—
92#213—124no—
93Dic3⋊C4—122no—
94Dic3⋊C4—122no—
95C4×Dic3—32no—
96C4×Dic3—61no—
97C4×Dic3—122no—
98C4×Dic3—122no—
99C2×C3⋊C8—32no—
100C2×C3⋊C8—61no—
101Dic12—34no—
102Dic12—62no—
103Dic12—62no—
104Dic12—62no—
105D24—22no—
106D24—22no—
107C3×C16—62no—
108C3⋊C16—22no—
109C22×C32C2×D811yescharacteristic
110C2×C3×D3—82no—
111C2×C3×D3—82no—
112C2×C3×D3—82no—
113C32×C4—81no—
114C32×C4#12111yescharacteristic
115C32×C4AGL(1,ℤ/8)11yescharacteristic
116C3⋊Dic3—21no—
117C3⋊Dic3—42no—
118C3⋊Dic3SD3212yescomplemented
119C2×Q16—91no—
120C2×D8—32no—
121C2×D8—181no—
122#127—181no—
123C4×Q8—181no—
124SD32—184no—
125C2×C16—32no—
126#107D3211yescharacteristic
127#103—181no—
128C4×C8—91no—
129C23×C3—122no—
130C22×D3—42no—
131C3×D4—122no—
132C3×D4—122no—
133C2×C3×C4—21no—
134C2×C3×C4—42no—
135C2×C3×C4—42no—
136C2×C3×C4D3×D412yes—
137#67—244no—
138#67—244no—
139C2×Dic3—32no—
140C2×Dic3—32no—
141C2×Dic3—61no—
142C2×Dic3—61no—
143C2×Dic3—122no—
144C2×Dic3—122no—
145D12—42no—
146D12—42no—
147Dic6—64no—
148Dic6—64no—
149Dic6—122no—
150Dic6—122no—
151C3×C8—21no—
152C3×C8—21no—
153C3×C8#23512yes—
154C3×C8D3×D412yes—
155C3⋊C8—62no—
156C3⋊C8—121no—
157C2×C32#45911yescharacteristic
158C2×C32C2×SD3211yescharacteristic
159C2×C32#50911yescharacteristic
160C3×D3—162no—
161C2×Q8—181no—
162C2×D4—62no—
163C2×D4—361no—
164C2×D4—361no—
165Q16—92no—
166Q16—181no—
167D8—62no—
168D8—62no—
169D8—362no—
170C2×C8—91no—
171C2×C8C2×D3211yescharacteristic
172C4⋊C4—21no—
173C4⋊C4—361no—
174C42—91no—
175C42—361no—
176C16—62no—
177C22×C3—21no—
178C22×C3—242no—
179C22×C3—242no—
180C22×C3—242no—
181C22×C3D3×D812yes—
182C2×D3—82no—
183C2×D3—82no—
184C2×D3—82no—
185C3×C4—21no—
186C3×C4—21no—
187C3×C4—82no—
188C3×C4—82no—
189C3×C4#88412yes—
190C3×C4#91412yes—
191Dic3—34no—
192Dic3—62no—
193Dic3—62no—
194Dic3—121no—
195Dic3—124no—
196Dic3—124no—
197C32#220711yescharacteristic, complemented, Sylow
198C23—122no—
199Q8—182no—
200Q8—361no—
201D4—122no—
202D4—122no—
203D4—722no—
204D4—722no—
205C2×C4—41no—
206C2×C4—91no—
207C2×C4—91no—
208C2×C4—361no—
209C2×C4#381111yescharacteristic
210C8—181no—
211C8#379811yescharacteristic
212C8#380211yescharacteristic
213C2×C3—21no—
214C2×C3—21no—
215C2×C3—21no—
216C2×C3—482no—
217C2×C3#478612yes—
218C2×C3#491112yes—
219C2×C3D3×SD3212yes—
220D3—162no—
221C22—242no—
222C22—242no—
223C22—242no—
224C22#6392611yescharacteristic
225C4—81no—
226C4—92no—
227C4—181no—
228C4—362no—
229C4#6391211yescharacteristic
230C4#6394111yescharacteristic
231C3—21no—
232C3#6920412yescomplemented
233C2—482no—
234C2#1059055111yescharacteristic
235C2#1059102611yescharacteristic
236C2#1059103911yescharacteristic
subgroupG/H
centerC22#63926
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C2×D32
FittingC32×#107C22
socleC22×C32C2×D8
prime radical#10590886C2
hypercenter#107D32
hypocenterC32#2207
LCSG ▷ C2×C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #107

Complements

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

NH ≅ G/Ntype
1. #10592572C2semidirect
3. C2×#63548C2semidirect
4. C3×#4491C2semidirect
5. #10589133C2semidirect
24. #4491D3semidirect
36. #3746D4semidirect
118. C3⋊Dic3SD32semidirect
197. C32#2207semidirect
232. C3#69204semidirect

Maximal subgroups

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

subgroupindex
#105925722
#105908862
C2×#635482
C3×#44912
#105891332
#692043