Finite Group Databasebeta

← #11798757

Subgroups — #11798757

Order 1152.

648 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 648 conjugacy classes of subgroups — too many to draw. Only its 93 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, complemented
2C32×#454C211yesmaximal, characteristic
3#10592945C212yesmaximal, complemented
4#10589408C211yesmaximal, characteristic, complemented
5#10589344C212yesmaximal, complemented
6#70989—34nomaximal
7C32×2−1+4C2211yescharacteristic
8C32×AGL(1,ℤ/8)—21no—
9C32×#124C2211yescharacteristic
10#64160—22no—
11#64153C2212yes—
12#64144—21no—
13#64088—22no—
14#64087—22no—
15#64079—21no—
16C32×#104—21no—
17C32×#101C2211yescharacteristic
18#63664—22no—
19#63663C2212yes—
20#5672—34no—
21C3×#454D314yes—
22#5246—38no—
23#4542—34no—
24#4478—38no—
25C32×#41—22no—
26C32×#41—21no—
27C32×#41—41no—
28C2×C32×Q8—41no—
29C2×C32×Q8C2311yescharacteristic
30C2×C32×D4D411yescharacteristic
31C22×C3⋊Dic3—21no—
32C2×#634D412yes—
33C32×SD16—41no—
34C32×D8—41no—
35C32×M16—21no—
36C32×C22⋊C4—22no—
37C32×C42D411yescharacteristic
38#3757—22no—
39#3757—21no—
40#3756—42no—
41#3754—42no—
42C4⋊(C3⋊Dic3)—21no—
43C4⋊(C3⋊Dic3)—21no—
44#3750—22no—
45#3750—22no—
46#3750—22no—
47C4×C3⋊Dic3D412yes—
48#3748—22no—
49#2203—91noSylow
50C3×2−1+4C2×D314yes—
51C3×AGL(1,ℤ/8)—24no—
52C3×#124C2×D314yes—
53#951—68no—
54#944—38no—
55#935—64no—
56#879—68no—
57#878—68no—
58#870—64no—
59C3×#104—24no—
60C3×#101C2×D314yes—
61#837—68no—
62#836—38no—
63C23×C32—21no—
64C32×Q8—22no—
65C32×Q8—21no—
66C32×Q8—41no—
67C32×D4—22no—
68C32×D4—21no—
69C32×D4—41no—
70C32×D4—41no—
71C2×C32×C4—21no—
72C2×C32×C4—42no—
73C2×C32×C4—41no—
74C2×C32×C4C2×D412yes—
75C2×C32×C4C2×D411yescharacteristic
76C2×C3⋊Dic3—22no—
77C2×C3⋊Dic3—22no—
78C2×C3⋊Dic3—81no—
79#634—42no—
80C32×C8—41no—
81C3⋊(C3⋊C8)—42no—
82#563—91no—
83#456—92no—
84#454C3⋊D311yescharacteristic
85#356—92no—
86#355—91no—
87C3×#41—28no—
88C3×#41—24no—
89C3×#41—44no—
90C2×C3×Q8—44no—
91C2×C3×Q8C22×D314yes—
92C2×C3×D4#6714yes—
93C22×Dic3—64no—
94C2×Dic6—38no—
95C3×SD16—44no—
96C3×D8—44no—
97C3×M16—24no—
98C3×C22⋊C4—28no—
99C3×C42#6714yes—
100#217—68no—
101#217—64no—
102#216—128no—
103#214—128no—
104C4⋊Dic3—64no—
105C4⋊Dic3—64no—
106Dic3⋊C4—68no—
107Dic3⋊C4—68no—
108Dic3⋊C4—68no—
109C4×Dic3—38no—
110#208—68no—
111C22×C32—42no—
112C22×C32—41no—
113C22×C32—41no—
114C22×C32#12011yescharacteristic
115C32×C4—22no—
116C32×C4—21no—
117C32×C4—41no—
118C32×C4—41no—
119C3⋊Dic3—42no—
120C3⋊Dic3—42no—
1212−1+4C2×C3⋊D311yescharacteristic
122#137—182no—
123AGL(1,ℤ/8)—21no—
124C4⋊Q8—92no—
125#126—182no—
126#125—181no—
127#124C2×C3⋊D311yescharacteristic
128#123—181no—
129C22⋊Q8—182no—
130#104—21no—
131#104—182no—
132#101—92no—
133#101C2×C3⋊D311yescharacteristic
134C23×C3—24no—
135C3×Q8—28no—
136C3×Q8—24no—
137C3×Q8—44no—
138C3×D4—28no—
139C3×D4—24no—
140C3×D4—44no—
141C3×D4—44no—
142C2×C3×C4—24no—
143C2×C3×C4—48no—
144C2×C3×C4—44no—
145C2×C3×C4D3×D418yes—
146C2×C3×C4C2×#6714yes—
147C2×Dic3—68no—
148C2×Dic3—68no—
149C2×Dic3—244no—
150Dic6—128no—
151C3×C8—44no—
152C3⋊C8—128no—
153C2×C32—21no—
154C2×C32—81no—
155C2×C32—81no—
156C2×C32B(4,𝔽2)11yescharacteristic
157#41—22no—
158#41—21no—
159#41—41no—
160C2×Q8—41no—
161C2×Q8—92no—
162C2×Q8C22×C3⋊D311yescharacteristic
163C2×D4#63811yescharacteristic
164C22×C4—181no—
165Q16—362no—
166SD16—41no—
167SD16—362no—
168D8—41no—
169M16—21no—
170M16—182no—
171C4⋊C4—181no—
172C4⋊C4—182no—
173C4⋊C4—181no—
174C4⋊C4—182no—
175C4⋊C4—182no—
176C22⋊C4—22no—
177C22⋊C4—182no—
178C22⋊C4—181no—
179C42—92no—
180C42#63811yescharacteristic
181C22×C3—48no—
182C22×C3—44no—
183C22×C3—44no—
184C22×C3#93714yes—
185C3×C4—28no—
186C3×C4—24no—
187C3×C4—44no—
188C3×C4—44no—
189Dic3—128no—
190Dic3—128no—
191C32#220311yescharacteristic, complemented, Sylow
192C23—21no—
193Q8—21no—
194Q8—22no—
195Q8—41no—
196Q8—362no—
197D4—21no—
198D4—22no—
199D4—41no—
200D4—41no—
201C2×C4—21no—
202C2×C4—41no—
203C2×C4—42no—
204C2×C4—182no—
205C2×C4—182no—
206C2×C4—721no—
207C2×C4D4×C3⋊D312yes—
208C2×C4C2×#63811yescharacteristic
209C8—41no—
210C8—362no—
211C2×C3—24no—
212C2×C3—84no—
213C2×C3—84no—
214C2×C3#503214yes—
215C22—42no—
216C22—41no—
217C22—41no—
218C22#6414611yescharacteristic
219C4—21no—
220C4—22no—
221C4—41no—
222C4—41no—
223C4—362no—
224C4—362no—
225C3#7098914yescomplemented
226C2—21no—
227C2—81no—
228C2—81no—
229C2#1059273111yescharacteristic
subgroupG/H
centerC2#10592731
commutator, cosocleC2×C32×Q8C23
FrattiniC2×Q8C22×C3⋊D3
Fitting, prime radicalC32×#454C2
socleC2×C32B(4,𝔽2)
hypercenter#454C3⋊D3
hypocenterC32#2203
LCSG ▷ C2×C32×Q8 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #454

Complements

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

NH ≅ G/Ntype
1. #10596143C2semidirect
3. #10592945C2semidirect
4. #10589408C2semidirect
5. #10589344C2semidirect
191. C32#2203semidirect
225. C3#70989semidirect

Maximal subgroups

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

subgroupindex
#105961432
C32×#4542
#105929452
#105894082
#105893442
#709893