Finite Group Databasebeta

← #11780598

Subgroups — #11780598

Order 1152.

588 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 588 conjugacy classes of subgroups — too many to draw. Only its 105 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#10596143C211yesmaximal, characteristic
2#10592759C211yesmaximal, characteristic
3#10592401C212yesmaximal, complemented
4C32×#329C211yesmaximal, characteristic
5#10589331C212yesmaximal, complemented
6#68355—34nomaximal
7C32×#124C2211yescharacteristic
8#64153—21no—
9C2×#3756—21no—
10#64144—21no—
11C2×#3754—21no—
12#64088—22no—
13#64087—22no—
14#64079C2212yes—
15#64078C2211yescharacteristic
16C32×#97C2212yes—
17#63645—22no—
18#63644—22no—
19#63630C2211yescharacteristic
20#5672—34no—
21#5060—34no—
22#4702—38no—
23C3×#329D314yes—
24#4465—38no—
25C2×C32×Q8D411yescharacteristic
26C2×C32×D4D411yescharacteristic
27C22×C3⋊Dic3—21no—
28C2×#634—21no—
29C2×#634—21no—
30C2×C32×C8—22no—
31C32×C22⋊C4—22no—
32C32×C42C2311yescharacteristic
33#3757—22no—
34#3757—21no—
35#3756—42no—
36#3754—42no—
37C4⋊(C3⋊Dic3)—22no—
38C4⋊(C3⋊Dic3)D412yes—
39C4⋊(C3⋊Dic3)D412yes—
40#3750—22no—
41#3750—22no—
42#3750—22no—
43C4×C3⋊Dic3—21no—
44C2×C3⋊(C3⋊C8)—21no—
45#1660—91noSylow
46C3×#124C2×D314yes—
47#944—64no—
48C2×#216—64no—
49#935—64no—
50C2×#214—64no—
51#879—68no—
52#878—68no—
53#870—38no—
54#869—34no—
55C3×#97C2×D318yes—
56#818—68no—
57#817—68no—
58#803—34no—
59C23×C32—21no—
60C32×Q8—41no—
61C32×D4—41no—
62C2×C32×C4—21no—
63C2×C32×C4C2×D411yescharacteristic
64C2×C32×C4C2×D412yes—
65C2×C3⋊Dic3—22no—
66C2×C3⋊Dic3—22no—
67C2×C3⋊Dic3—41no—
68C2×C3⋊Dic3—81no—
69#634—41no—
70#634—41no—
71#634—81no—
72C32×C8—24no—
73C3⋊(C3⋊C8)—22no—
74#563—91no—
75#501—92no—
76#497—91no—
77#330—92no—
78#329C3⋊D311yescharacteristic
79C2×C3×Q8D1214yes—
80C2×C3×D4D1214yes—
81C22×Dic3—64no—
82C2×Dic6—64no—
83C2×Dic6—64no—
84C2×C3×C8—28no—
85C3×C22⋊C4—28no—
86C3×C42C22×D314yes—
87#217—68no—
88#217—64no—
89#216—128no—
90#214—128no—
91C4⋊Dic3—38no—
92C4⋊Dic3—38no—
93C4⋊Dic3—68no—
94Dic3⋊C4—68no—
95Dic3⋊C4—68no—
96Dic3⋊C4—68no—
97C4×Dic3—64no—
98C2×C3⋊C8—64no—
99C22×C32—41no—
100C22×C32—42no—
101C22×C32#12011yescharacteristic
102C32×C4—21no—
103C32×C4—22no—
104C32×C4—41no—
105C3⋊Dic3—42no—
106C3⋊Dic3—42no—
107C3⋊Dic3—81no—
108C2×Q16—181no—
109C2×SD16—181no—
110C4⋊Q8—91no—
111C4⋊Q8—181no—
112#126—182no—
113#125—92no—
114#124C2×C3⋊D311yescharacteristic
115#123—181no—
116C22⋊Q8—182no—
117#107—182no—
118#106—182no—
119#97—91no—
120#97C2×C3⋊D312yes—
121C23×C3—24no—
122C3×Q8—44no—
123C3×D4—44no—
124C2×C3×C4—24no—
125C2×C3×C4C2×D1214yes—
126C2×C3×C4D3×D418yes—
127C2×Dic3—68no—
128C2×Dic3—68no—
129C2×Dic3—124no—
130C2×Dic3—244no—
131Dic6—124no—
132Dic6—124no—
133Dic6—244no—
134C3×C8—216no—
135C3⋊C8—68no—
136C2×C32—81no—
137C2×C32#45311yescharacteristic
138C2×C32#45612yes—
139C2×Q8—181no—
140C2×Q8—181no—
141C2×Q8C4⋊(C3⋊D3)11yescharacteristic
142C2×D4C4⋊(C3⋊D3)11yescharacteristic
143C22×C4—181no—
144Q16—362no—
145SD16—362no—
146C2×C8—22no—
147C2×C8—181no—
148C4⋊C4—92no—
149C4⋊C4—92no—
150C4⋊C4—182no—
151C4⋊C4—182no—
152C4⋊C4—182no—
153C4⋊C4—182no—
154C22⋊C4—22no—
155C22⋊C4—182no—
156C22⋊C4—181no—
157C42—181no—
158C42C22×C3⋊D311yescharacteristic
159C22×C3—44no—
160C22×C3—48no—
161C22×C3#88214yes—
162C3×C4—24no—
163C3×C4—28no—
164C3×C4—44no—
165Dic3—128no—
166Dic3—128no—
167Dic3—244no—
168C32#166011yescharacteristic, complemented, Sylow
169C23—21no—
170Q8—41no—
171Q8—361no—
172Q8—361no—
173Q8—721no—
174D4—41no—
175C2×C4—21no—
176C2×C4—182no—
177C2×C4—182no—
178C2×C4—361no—
179C2×C4—721no—
180C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
181C2×C4D4×C3⋊D312yes—
182C8—24no—
183C8—182no—
184C2×C3—84no—
185C2×C3#474714yes—
186C2×C3#482618yes—
187C22—42no—
188C22—41no—
189C22#6409111yescharacteristic
190C4—22no—
191C4—21no—
192C4—41no—
193C4—362no—
194C4—362no—
195C4—721no—
196C3#6835514yescomplemented
197C2—81no—
198C2#1059244611yescharacteristic
199C2#1059252512yes—
subgroupG/H
centerC22#64091
commutator, cosocleC32×C42C23
FrattiniC42C22×C3⋊D3
FittingC32×#329C2
socleC22×C32#120
prime radicalC2×C32×D4D4
hypercenter#329C3⋊D3
hypocenterC32#1660
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
3. #10592401C2semidirect
5. #10589331C2semidirect
168. C32#1660semidirect
196. C3#68355semidirect

Maximal subgroups

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

subgroupindex
#105961432
#105927592
#105924012
C32×#3292
#105893312
#683553