Finite Group Databasebeta

← #11782021

Subgroups — #11782021

Order 1152.

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

normal subgroups only

This group has 420 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#10592790C211yesmaximal, characteristic
2#10592777C211yesmaximal, characteristic
3#10592549C211yesmaximal, characteristic
4#10592530C211yesmaximal, characteristic
5C32×#333C211yesmaximal, characteristic
6#10589347C211yesmaximal, characteristic
7#10589346C211yesmaximal, characteristic
8#68513—34nomaximal
9C32×C4⋊Q8C2211yescharacteristic
10#64078C2211yescharacteristic
11C4×#634C2211yescharacteristic
12C32×C4⋊C8C2211yescharacteristic
13C32×C4⋊C8C2211yescharacteristic
14#63645—21no—
15#63643—21no—
16#63642—21no—
17#63641—21no—
18#63637—21no—
19#63634—21no—
20#63634—21no—
21#63634—21no—
22C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
23C4×C3⋊(C3⋊C8)C2211yescharacteristic
24#5091—34no—
25#5078—34no—
26#4850—34no—
27#4831—34no—
28C3×#333D314yes—
29#4481—34no—
30#4480—34no—
31C2×C32×Q8—21no—
32C2×#634—21no—
33C2×#634D411yescharacteristic
34C2×C32×C8—21no—
35C2×C32×C8—21no—
36C32×C4⋊C4—21no—
37C32×C4⋊C4—21no—
38C32×C42C2311yescharacteristic
39C4⋊(C3⋊Dic3)—21no—
40C4⋊(C3⋊Dic3)—21no—
41C4⋊(C3⋊Dic3)D411yescharacteristic
42#3750—21no—
43C4×C3⋊Dic3—21no—
44C2×C3⋊(C3⋊C8)—21no—
45C2×C3⋊(C3⋊C8)D411yescharacteristic
46C2×C3⋊(C3⋊C8)D411yescharacteristic
47#1696—91noSylow
48C3×C4⋊Q8C2×D314yes—
49#869—34no—
50C4×Dic6—34no—
51C3×C4⋊C8C2×D314yes—
52C3×C4⋊C8C2×D314yes—
53#818—64no—
54#816—64no—
55#815—64no—
56Dic3⋊C8—64no—
57#810—64no—
58#807—64no—
59#807—64no—
60#807—64no—
61C4⋊(C3⋊C8)—34no—
62C4×C3⋊C8—34no—
63C32×Q8—81no—
64C2×C32×C4—41no—
65C2×C32×C4C2×D411yescharacteristic
66C2×C32×C4C2×D411yescharacteristic
67C2×C32×C4#4111yescharacteristic
68C2×C3⋊Dic3—21no—
69C2×C3⋊Dic3—21no—
70C2×C3⋊Dic3—41no—
71#634—21no—
72#634—21no—
73#634—81no—
74C32×C8—41no—
75C32×C8—41no—
76C3⋊(C3⋊C8)—21no—
77C3⋊(C3⋊C8)—41no—
78C3⋊(C3⋊C8)Q1612yes—
79#500—91no—
80#477—91no—
81#477—91no—
82#446—91no—
83#334—91no—
84#333—91no—
85#333C3⋊D311yescharacteristic
86C2×C3×Q8—24no—
87C2×Dic6—34no—
88C2×Dic6—64no—
89C2×C3×C8—24no—
90C2×C3×C8—24no—
91C3×C4⋊C4—24no—
92C3×C4⋊C4—24no—
93C3×C42C22×D314yes—
94C4⋊Dic3—34no—
95C4⋊Dic3—64no—
96C4⋊Dic3—64no—
97Dic3⋊C4—64no—
98C4×Dic3—64no—
99C2×C3⋊C8—34no—
100C2×C3⋊C8—34no—
101C2×C3⋊C8—64no—
102C22×C32#12111yescharacteristic
103C32×C4—21no—
104C32×C4—81no—
105C32×C4C2×Q1611yescharacteristic
106C32×C4#13711yescharacteristic
107C32×C4#13711yescharacteristic
108C32×C4#13711yescharacteristic
109C3⋊Dic3—41no—
110C3⋊Dic3—41no—
111C3⋊Dic3—81no—
112C4⋊Q8—91no—
113C4⋊Q8C2×C3⋊D311yescharacteristic
114C4×Q8—91no—
115#107—181no—
116#107—181no—
117#107—181no—
118#107—181no—
119C4⋊C8—91no—
120C4⋊C8—181no—
121C4⋊C8C2×C3⋊D311yescharacteristic
122C4⋊C8C2×C3⋊D311yescharacteristic
123#103—181no—
124#103—181no—
125#97—181no—
126C4×C8—91no—
127C3×Q8—84no—
128C2×C3×C4—44no—
129C2×C3×C4#23514yes—
130C2×C3×C4D3×D414yes—
131C2×C3×C4D3×D414yes—
132C2×Dic3—64no—
133C2×Dic3—64no—
134C2×Dic3—124no—
135Dic6—64no—
136Dic6—64no—
137Dic6—244no—
138C3×C8—44no—
139C3×C8—44no—
140C3⋊C8—38no—
141C3⋊C8—64no—
142C3⋊C8—124no—
143C2×C32#46211yescharacteristic
144C2×C32#47011yescharacteristic
145C2×C32#47211yescharacteristic
146C2×Q8—21no—
147C2×Q8—91no—
148C2×Q8—181no—
149C2×C8—21no—
150C2×C8—21no—
151C2×C8—91no—
152C2×C8—91no—
153C2×C8—181no—
154C4⋊C4—21no—
155C4⋊C4—21no—
156C4⋊C4—91no—
157C4⋊C4—181no—
158C4⋊C4—181no—
159C4⋊C4—181no—
160C42—181no—
161C42C22×C3⋊D311yescharacteristic
162C22×C3#88414yes—
163C3×C4—24no—
164C3×C4—84no—
165C3×C4#91514yes—
166C3×C4#91514yes—
167C3×C4D3×Q1614yes—
168C3×C4#91814yes—
169Dic3—124no—
170Dic3—124no—
171Dic3—244no—
172C32#169611yescharacteristic, complemented, Sylow
173Q8—81no—
174Q8—181no—
175Q8—181no—
176Q8—721no—
177C2×C4—41no—
178C2×C4—181no—
179C2×C4—181no—
180C2×C4—361no—
181C2×C4#382811yescharacteristic
182C2×C4D4×C3⋊D311yescharacteristic
183C2×C4D4×C3⋊D311yescharacteristic
184C8—41no—
185C8—41no—
186C8—92no—
187C8—181no—
188C8—361no—
189C2×C3#474914yes—
190C2×C3#479514yes—
191C2×C3#481614yes—
192C22#6409311yescharacteristic
193C4—21no—
194C4—81no—
195C4—361no—
196C4—361no—
197C4—721no—
198C4#6412411yescharacteristic
199C4#6412411yescharacteristic
200C4Q16×C3⋊D311yescharacteristic
201C4#6412711yescharacteristic
202C3#6851314yescomplemented
203C2#1059244811yescharacteristic
204C2#1059249411yescharacteristic
205C2#1059251511yescharacteristic
subgroupG/H
centerC22#64093
commutator, cosocleC32×C42C23
FrattiniC42C22×C3⋊D3
FittingC32×#333C2
socle, prime radicalC22×C32#121
hypercenter#333C3⋊D3
hypocenterC32#1696
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
172. C32#1696semidirect
202. C3#68513semidirect

Maximal subgroups

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

subgroupindex
#105927902
#105927772
#105925492
#105925302
C32×#3332
#105893472
#105893462
#685133