Finite Group Databasebeta

← #11781913

Subgroups — #11781913

Order 1152.

242 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 242 conjugacy classes of subgroups — too many to draw. Only its 43 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#10593447C211yesmaximal, characteristic
2#10593393C211yesmaximal, characteristic
3#10590900C211yesmaximal, characteristic
4#10590788C211yesmaximal, characteristic
5#10590173C211yesmaximal, characteristic
6#10590040C211yesmaximal, characteristic
7#10590039C211yesmaximal, characteristic
8C2×#3776—21no—
9#63919C2211yescharacteristic
10#63919C2211yescharacteristic
11C4×#627C2211yescharacteristic
12C4⋊#622C2211yescharacteristic
13C4⋊#622C2211yescharacteristic
14#63743—21no—
15#63740—21no—
16#63740—21no—
17C8×C3⋊Dic3C2211yescharacteristic
18C3×#817—21no—
19C3×Dic3⋊C8—21no—
20#63574—21no—
21#63572C2211yescharacteristic
22#63554—21no—
23#4855—61no—
24#4828—61no—
25C2×#627—21no—
26C2×#627—21no—
27C2×#627D411yescharacteristic
28C2×#622—21no—
29C2×#622—21no—
30#3776—42no—
31C2×C32×C8D411yescharacteristic
32C4×C3⋊Dic3C2311yescharacteristic
33C2×C3⋊(C3⋊C8)D411yescharacteristic
34C3×C4⋊Dic3—21no—
35C3×C4⋊Dic3—21no—
36C3×C4×Dic3—21no—
37C2×C3×C3⋊C8—21no—
38#3724—21no—
39#3724—21no—
40#3724D411yescharacteristic
41Dic3⋊Dic3—21no—
42#1692—91nomaximal, Sylow
43#888—61no—
44#888—61no—
45C4×Dic6—61no—
46C3×#106—61no—
47C3×C4⋊C8—61no—
48#817—21no—
49#815—61no—
50Dic3⋊C8—21no—
51Dic3⋊C8—61no—
52C8×Dic3—61no—
53C8×Dic3—61no—
54#808—61no—
55#808—61no—
56#803—61no—
57C2×C32×C4C2×D411yescharacteristic
58C2×C3⋊Dic3C2×D411yescharacteristic
59C2×C3⋊Dic3#4111yescharacteristic
60C2×C3×Dic3—21no—
61C2×C3×Dic3—21no—
62C2×C3×Dic3—41no—
63C2×C3×Dic3—41no—
64#627—21no—
65#627—21no—
66#627—41no—
67#627—41no—
68#627—81no—
69#622—41no—
70#622—41no—
71C32×C8—21no—
72C3⋊(C3⋊C8)Q1612yescomplemented
73C3×C3⋊C8—41no—
74#498—91no—
75#477—91no—
76#462—91no—
77#446—91no—
78#335—91no—
79#333—91no—
80#332—91no—
81C2×Dic6—61no—
82C2×Dic6—121no—
83C2×Dic6—121no—
84C2×C3×C8—21no—
85C2×C3×C8—21no—
86C2×C3×C8—61no—
87C3×C4⋊C4—61no—
88C3×C4⋊C4—61no—
89C3×C42—61no—
90C4⋊Dic3—21no—
91C4⋊Dic3—21no—
92C4⋊Dic3—61no—
93Dic3⋊C4—61no—
94Dic3⋊C4—61no—
95Dic3⋊C4—121no—
96Dic3⋊C4—121no—
97C4×Dic3—21no—
98C4×Dic3—61no—
99C4×Dic3—61no—
100C2×C3⋊C8—21no—
101C2×C3⋊C8—61no—
102C2×C3⋊C8—61no—
103C22×C32#12111yescharacteristic
104C32×C4C2×Q1611yescharacteristic
105C32×C4#13711yescharacteristic
106C3⋊Dic3—21no—
107C3⋊Dic3AGL(1,ℤ/8)11yescharacteristic
108C3⋊Dic3#13711yescharacteristic
109C3×Dic3—41no—
110C3×Dic3—41no—
111C3×Dic3—81no—
112C3×Dic3—81no—
113C2×Q16—181no—
114C4⋊Q8—91no—
115C4⋊Q8—91no—
116C4×Q8—91no—
117#107—181no—
118#106—61no—
119#106—181no—
120C4⋊C8—61no—
121C4⋊C8—91no—
122C4⋊C8—91no—
123C4⋊C8—91no—
124#103—181no—
125#103—181no—
126#97—181no—
127C4×C8—91no—
128C2×C3×C4—21no—
129C2×C3×C4—21no—
130C2×C3×C4—61no—
131C2×C3×C4—61no—
132C2×C3×C4—121no—
133C2×C3×C4—121no—
134C2×Dic3—21no—
135C2×Dic3—21no—
136C2×Dic3—41no—
137C2×Dic3—41no—
138C2×Dic3—61no—
139C2×Dic3—61no—
140C2×Dic3—61no—
141C2×Dic3—61no—
142Dic6—121no—
143Dic6—121no—
144Dic6—241no—
145Dic6—241no—
146Dic6—242no—
147C3×C8—22no—
148C3×C8—41no—
149C3×C8—121no—
150C3⋊C8—41no—
151C3⋊C8—62no—
152C3⋊C8—62no—
153C2×C32#46211yescharacteristic
154C2×C32#46811yescharacteristic
155C2×C32#47111yescharacteristic
156C2×Q8—91no—
157C2×Q8—181no—
158C2×Q8—181no—
159Q16—362no—
160C2×C8—61no—
161C2×C8—91no—
162C2×C8—181no—
163C2×C8—181no—
164C2×C8GO+(4,𝔽2)11yescharacteristic
165C4⋊C4—61no—
166C4⋊C4—61no—
167C4⋊C4—91no—
168C4⋊C4—181no—
169C4⋊C4—181no—
170C4⋊C4—181no—
171C42—61no—
172C42—91no—
173C22×C3—21no—
174C22×C3—21no—
175C3×C4—21no—
176C3×C4—21no—
177C3×C4—21no—
178C3×C4—21no—
179C3×C4—121no—
180C3×C4—121no—
181C3×C4—241no—
182C3×C4—241no—
183Dic3—41no—
184Dic3—41no—
185Dic3—61no—
186Dic3—61no—
187Dic3—61no—
188Dic3—61no—
189Dic3—62no—
190Dic3—81no—
191Dic3—81no—
192Dic3—121no—
193C32#169211yescharacteristic, complemented, Sylow
194Q8—181no—
195Q8—181no—
196Q8—361no—
197Q8—361no—
198Q8—721no—
199C2×C4—61no—
200C2×C4—61no—
201C2×C4—91no—
202C2×C4—91no—
203C2×C4—121no—
204C2×C4—121no—
205C2×C4C2×GO+(4,𝔽2)11yescharacteristic
206C8—21no—
207C8—92no—
208C8—121no—
209C8—361no—
210C8—361no—
211C2×C3—21no—
212C2×C3—21no—
213C2×C3—21no—
214C2×C3—21no—
215C2×C3—21no—
216C2×C3—21no—
217C22#6423011yescharacteristic
218C4—91no—
219C4—91no—
220C4—121no—
221C4—121no—
222C4—181no—
223C4—241no—
224C4—241no—
225C4#6422811yescharacteristic
226C4#6423911yescharacteristic
227C3—21no—
228C3—21no—
229C2#1059328611yescharacteristic
230C2#1059330011yescharacteristic
231C2#1059344811yescharacteristic
subgroupG/H
centerC22#64230
commutator, cosocleC4×C3⋊Dic3C23
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC2×C32×C8D4
socle, prime radicalC22×C32#121
hypercenterC2×C8GO+(4,𝔽2)
hypocenterC32#1692
LCSG ▷ C4×C3⋊Dic3 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
72. C3⋊(C3⋊C8)Q16semidirect
193. C32#1692semidirect

Maximal subgroups

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

subgroupindex
#105934472
#105933932
#105909002
#105907882
#105901732
#105900402
#105900392
#16929