Finite Group Databasebeta

← #11781877

Subgroups — #11781877

Order 1152.

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

normal subgroups only

This group has 438 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#10592789C211yesmaximal, characteristic
2#10592779C211yesmaximal, characteristic
3#10592549C211yesmaximal, characteristic
4#10592530C211yesmaximal, characteristic
5C32×#332C211yesmaximal, characteristic
6#10589347C211yesmaximal, characteristic
7#10589345C211yesmaximal, characteristic
8#68474—34nomaximal
9C32×C4⋊Q8C2211yescharacteristic
10C2×#3756—21no—
11#64078C2211yescharacteristic
12C4×#634C2211yescharacteristic
13C32×C4⋊C8C2211yescharacteristic
14C32×C4⋊C8C2211yescharacteristic
15#63662—21no—
16#63645—21no—
17#63643—21no—
18#63642—21no—
19#63641—21no—
20#63635—21no—
21#63635—21no—
22C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
23C4×C3⋊(C3⋊C8)C2211yescharacteristic
24#5090—34no—
25#5080—34no—
26#4850—34no—
27#4831—34no—
28C3×#332D314yes—
29#4481—34no—
30#4479—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
39#3756—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#1692—91noSylow
49C3×C4⋊Q8C2×D314yes—
50C2×#216—64no—
51#869—34no—
52C4×Dic6—34no—
53C3×C4⋊C8C2×D314yes—
54C3×C4⋊C8C2×D314yes—
55#835—64no—
56#818—64no—
57#816—64no—
58#815—64no—
59Dic3⋊C8—64no—
60#808—64no—
61#808—64no—
62C4⋊(C3⋊C8)—34no—
63C4×C3⋊C8—34no—
64C32×Q8—41no—
65C32×Q8—41no—
66C2×C32×C4—41no—
67C2×C32×C4C2×D411yescharacteristic
68C2×C32×C4C2×D411yescharacteristic
69C2×C32×C4#4111yescharacteristic
70C2×C3⋊Dic3—21no—
71C2×C3⋊Dic3—21no—
72C2×C3⋊Dic3—41no—
73#634—21no—
74#634—21no—
75#634—81no—
76C32×C8—41no—
77C32×C8—41no—
78C3⋊(C3⋊C8)—21no—
79C3⋊(C3⋊C8)—41no—
80C3⋊(C3⋊C8)Q1612yescomplemented
81#498—91no—
82#477—91no—
83#462—91no—
84#446—91no—
85#335—91no—
86#333—91no—
87#332C3⋊D311yescharacteristic
88C2×C3×Q8—24no—
89C2×Dic6—34no—
90C2×Dic6—64no—
91C2×C3×C8—24no—
92C2×C3×C8—24no—
93C3×C4⋊C4—24no—
94C3×C4⋊C4—24no—
95C3×C42C22×D314yes—
96#216—128no—
97C4⋊Dic3—34no—
98C4⋊Dic3—64no—
99C4⋊Dic3—64no—
100Dic3⋊C4—64no—
101C4×Dic3—64no—
102C2×C3⋊C8—34no—
103C2×C3⋊C8—34no—
104C2×C3⋊C8—64no—
105C22×C32#12111yescharacteristic
106C32×C4—21no—
107C32×C4—81no—
108C32×C4C2×Q1611yescharacteristic
109C32×C4AGL(1,ℤ/8)11yescharacteristic
110C32×C4#13711yescharacteristic
111C32×C4#13711yescharacteristic
112C3⋊Dic3—41no—
113C3⋊Dic3—41no—
114C3⋊Dic3—81no—
115C2×Q16—181no—
116C4⋊Q8—91no—
117C4⋊Q8C2×C3⋊D311yescharacteristic
118C4×Q8—91no—
119#107—181no—
120#106—181no—
121#106—181no—
122C4⋊C8—91no—
123C4⋊C8—181no—
124C4⋊C8C2×C3⋊D311yescharacteristic
125C4⋊C8C2×C3⋊D311yescharacteristic
126#103—181no—
127#103—181no—
128#97—181no—
129C4×C8—91no—
130C3×Q8—44no—
131C3×Q8—44no—
132C2×C3×C4—44no—
133C2×C3×C4#23514yes—
134C2×C3×C4D3×D414yes—
135C2×C3×C4D3×D414yes—
136C2×Dic3—64no—
137C2×Dic3—64no—
138C2×Dic3—124no—
139Dic6—64no—
140Dic6—64no—
141Dic6—244no—
142C3×C8—44no—
143C3×C8—44no—
144C3⋊C8—38no—
145C3⋊C8—64no—
146C3⋊C8—124no—
147C2×C32#46211yescharacteristic
148C2×C32#46811yescharacteristic
149C2×C32#47111yescharacteristic
150C2×Q8—21no—
151C2×Q8—91no—
152C2×Q8—181no—
153Q16—362no—
154C2×C8—21no—
155C2×C8—21no—
156C2×C8—91no—
157C2×C8—91no—
158C2×C8—181no—
159C4⋊C4—21no—
160C4⋊C4—21no—
161C4⋊C4—91no—
162C4⋊C4—181no—
163C4⋊C4—181no—
164C4⋊C4—181no—
165C42—181no—
166C42C22×C3⋊D311yescharacteristic
167C22×C3#88414yes—
168C3×C4—24no—
169C3×C4—84no—
170C3×C4#91114yes—
171C3×C4#91514yes—
172C3×C4#91514yes—
173C3×C4D3×Q1614yes—
174Dic3—124no—
175Dic3—124no—
176Dic3—244no—
177C32#169211yescharacteristic, complemented, Sylow
178Q8—41no—
179Q8—41no—
180Q8—181no—
181Q8—181no—
182Q8—721no—
183C2×C4—41no—
184C2×C4—181no—
185C2×C4—181no—
186C2×C4—361no—
187C2×C4#382811yescharacteristic
188C2×C4D4×C3⋊D311yescharacteristic
189C2×C4D4×C3⋊D311yescharacteristic
190C8—41no—
191C8—41no—
192C8—92no—
193C8—181no—
194C8—361no—
195C2×C3#475414yes—
196C2×C3#478014yes—
197C2×C3#479514yes—
198C22#6409311yescharacteristic
199C4—21no—
200C4—81no—
201C4—361no—
202C4—361no—
203C4—721no—
204C4#6412011yescharacteristic
205C4#6412411yescharacteristic
206C4#6412411yescharacteristic
207C4Q16×C3⋊D311yescharacteristic
208C3#6847414yescomplemented
209C2#1059245311yescharacteristic
210C2#1059247911yescharacteristic
211C2#1059249411yescharacteristic
subgroupG/H
centerC22#64093
commutator, cosocleC32×C42C23
FrattiniC42C22×C3⋊D3
FittingC32×#332C2
socle, prime radicalC22×C32#121
hypercenter#332C3⋊D3
hypocenterC32#1692
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
80. C3⋊(C3⋊C8)Q16semidirect
177. C32#1692semidirect
208. C3#68474semidirect

Maximal subgroups

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

subgroupindex
#105927892
#105927792
#105925492
#105925302
C32×#3322
#105893472
#105893452
#684743