Finite Group Databasebeta

← #11781469

Subgroups — #11781469

Order 1152.

498 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 498 conjugacy classes of subgroups — too many to draw. Only its 119 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#10592774C211yesmaximal, characteristic
2#10592769C211yesmaximal, characteristic
3#10592548C211yesmaximal, characteristic, complemented
4#10592529C211yesmaximal, characteristic, complemented
5C32×#331C211yesmaximal, characteristic
6#10589352C211yesmaximal, characteristic, complemented
7#10589345C211yesmaximal, characteristic, complemented
8#68411—34nomaximal
9C32×#127C2211yescharacteristic
10C2×#3754—21no—
11C2×#3746—21no—
12#64078C2211yescharacteristic
13C4×#634C2211yescharacteristic
14C32×C4⋊C8C2211yescharacteristic
15C32×C4⋊C8C2211yescharacteristic
16#63659—21no—
17#63659—21no—
18#63659—21no—
19#63643—21no—
20#63641—21no—
21C8×C3⋊Dic3—21no—
22C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
23C4×C3⋊(C3⋊C8)C2211yescharacteristic
24#5075—34no—
25#5070—34no—
26#4849—34no—
27#4830—34no—
28C3×#331D314yes—
29#4486—34no—
30#4479—34no—
31C2×C32×D4—21no—
32C2×C32×D4—21no—
33C2×C32×D4—21no—
34C2×#634—21no—
35C2×#634D411yescharacteristic
36C2×C32×C8—21no—
37C2×C32×C8—21no—
38C32×C42C2311yescharacteristic
39#3754—42no—
40C4⋊(C3⋊Dic3)—21no—
41C4⋊(C3⋊Dic3)—21no—
42C4⋊(C3⋊Dic3)D411yescharacteristic
43#3750—21no—
44C4×C3⋊Dic3—21no—
45C2×C3⋊(C3⋊C8)—21no—
46C2×C3⋊(C3⋊C8)D411yescharacteristic
47C2×C3⋊(C3⋊C8)D411yescharacteristic
48#3746—42no—
49#1682—91noSylow
50C3×#127C2×D314yes—
51C2×#214—64no—
52C2×Dic12—64no—
53#869—34no—
54C4×Dic6—34no—
55C3×C4⋊C8C2×D314yes—
56C3×C4⋊C8C2×D314yes—
57#832—64no—
58#832—64no—
59#832—64no—
60#816—64no—
61Dic3⋊C8—64no—
62C8×Dic3—64no—
63C4⋊(C3⋊C8)—34no—
64C4×C3⋊C8—34no—
65C23×C32—41no—
66C32×D4—41no—
67C32×D4—41no—
68C32×D4—41no—
69C32×D4—41no—
70C32×D4—81no—
71C2×C32×C4C2×D411yescharacteristic
72C2×C32×C4C2×D411yescharacteristic
73C2×C32×C4#4111yescharacteristic
74C2×C3⋊Dic3—21no—
75C2×C3⋊Dic3—21no—
76C2×C3⋊Dic3—41no—
77#634—21no—
78#634—41no—
79#634—41no—
80#634D812yes—
81C32×C8—41no—
82C32×C8—41no—
83C3⋊(C3⋊C8)—21no—
84C3⋊(C3⋊C8)—21no—
85C3⋊(C3⋊C8)—41no—
86#486—91no—
87#462—91no—
88#460—91no—
89C8×Q8—91no—
90#335—91no—
91#332—91no—
92#331C3⋊D311yescharacteristic
93C2×C3×D4—24no—
94C2×C3×D4—24no—
95C2×C3×D4—24no—
96C2×Dic6—34no—
97C2×Dic6—64no—
98C2×C3×C8—24no—
99C2×C3×C8—24no—
100C3×C42C22×D314yes—
101#214—128no—
102C4⋊Dic3—34no—
103C4⋊Dic3—64no—
104C4⋊Dic3—64no—
105Dic3⋊C4—64no—
106C4×Dic3—64no—
107C2×C3⋊C8—34no—
108C2×C3⋊C8—34no—
109C2×C3⋊C8—64no—
110Dic12—128no—
111C22×C32—81no—
112C22×C32—81no—
113C22×C32—81no—
114C22×C32#12111yescharacteristic
115C32×C4—21no—
116C32×C4C2×D811yescharacteristic
117C32×C4#13511yescharacteristic
118C32×C4#13511yescharacteristic
119C32×C4#13711yescharacteristic
120C3⋊Dic3—22no—
121C3⋊Dic3—41no—
122C3⋊Dic3—81no—
123C2×Q16—181no—
124C2×SD16—181no—
125C4⋊Q8—91no—
126#127C2×C3⋊D311yescharacteristic
127C4×Q8—91no—
128C4⋊C8—91no—
129C4⋊C8—181no—
130C4⋊C8C2×C3⋊D311yescharacteristic
131C4⋊C8C2×C3⋊D311yescharacteristic
132#103—181no—
133#102—181no—
134#102—181no—
135#102—181no—
136C4×C8—91no—
137C4×C8—181no—
138C23×C3—44no—
139C3×D4—44no—
140C3×D4—44no—
141C3×D4—44no—
142C3×D4—44no—
143C3×D4—84no—
144C2×C3×C4#23514yes—
145C2×C3×C4D3×D414yes—
146C2×C3×C4D3×D414yes—
147C2×Dic3—64no—
148C2×Dic3—64no—
149C2×Dic3—124no—
150Dic6—38no—
151Dic6—64no—
152Dic6—124no—
153Dic6—124no—
154C3×C8—44no—
155C3×C8—44no—
156C3⋊C8—64no—
157C3⋊C8—64no—
158C3⋊C8—124no—
159C2×C32—161no—
160C2×C32#46411yescharacteristic
161C2×C32#46611yescharacteristic
162C2×C32#47111yescharacteristic
163C2×Q8—91no—
164C2×Q8—181no—
165C2×D4—21no—
166C2×D4—21no—
167C2×D4—21no—
168Q16—362no—
169SD16—362no—
170C2×C8—21no—
171C2×C8—21no—
172C2×C8—91no—
173C2×C8—91no—
174C2×C8—181no—
175C4⋊C4—91no—
176C4⋊C4—181no—
177C4⋊C4—181no—
178C4⋊C4—181no—
179C42—181no—
180C42C22×C3⋊D311yescharacteristic
181C22×C3—84no—
182C22×C3—84no—
183C22×C3—84no—
184C22×C3#88414yes—
185C3×C4—24no—
186C3×C4D3×D814yes—
187C3×C4#91214yes—
188C3×C4#91514yes—
189C3×C4#91614yes—
190Dic3—68no—
191Dic3—124no—
192Dic3—244no—
193C32#168211yescharacteristic, complemented, Sylow
194C23—41no—
195Q8—92no—
196Q8—181no—
197Q8—361no—
198Q8—361no—
199D4—41no—
200D4—41no—
201D4—41no—
202D4—41no—
203D4—81no—
204C2×C4—181no—
205C2×C4—181no—
206C2×C4—361no—
207C2×C4#382811yescharacteristic
208C2×C4D4×C3⋊D311yescharacteristic
209C2×C4D4×C3⋊D311yescharacteristic
210C8—41no—
211C8—41no—
212C8—181no—
213C8—181no—
214C8—361no—
215C2×C3—164no—
216C2×C3#474814yes—
217C2×C3#476714yes—
218C2×C3#477514yes—
219C22—81no—
220C22—81no—
221C22—81no—
222C22#6409311yescharacteristic
223C4—21no—
224C4—182no—
225C4—361no—
226C4—721no—
227C4D8×C3⋊D311yescharacteristic
228C4#6412111yescharacteristic
229C4#6412411yescharacteristic
230C4#6412511yescharacteristic
231C3#6841114yescomplemented
232C2—161no—
233C2#1059244711yescharacteristic
234C2#1059246611yescharacteristic
235C2#1059247411yescharacteristic
subgroupG/H
centerC22#64093
commutator, cosocleC32×C42C23
FrattiniC42C22×C3⋊D3
FittingC32×#331C2
socleC22×C32#121
prime radicalC32×#127C22
hypercenter#331C3⋊D3
hypocenterC32#1682
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
3. #10592548C2semidirect
4. #10592529C2semidirect
6. #10589352C2semidirect
7. #10589345C2semidirect
193. C32#1682semidirect
231. C3#68411semidirect

Maximal subgroups

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

subgroupindex
#105927742
#105927692
#105925482
#105925292
C32×#3312
#105893522
#105893452
#684113