Finite Group Databasebeta

← #11781412

Subgroups — #11781412

Order 1152.

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

normal subgroups only

This group has 250 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#10593376C211yesmaximal, characteristic
3#10590901C211yesmaximal, characteristic
4#10590645C211yesmaximal, characteristic
5#10590170C211yesmaximal, characteristic
6#10590039C211yesmaximal, characteristic
7#10590038C211yesmaximal, characteristic
8C2×#3776—21no—
9#63919C2211yescharacteristic
10C4×#627C2211yescharacteristic
11#63873C2211yescharacteristic
12C4⋊#622C2211yescharacteristic
13C4⋊#622C2211yescharacteristic
14#63742—21no—
15#63740—21no—
16#63740—21no—
17C8×C3⋊Dic3C2211yescharacteristic
18C3×#816—21no—
19C3×Dic3⋊C8—21no—
20#63572C2211yescharacteristic
21#63565—21no—
22Dic3×C3⋊C8—21no—
23#4830—61no—
24#4792—61no—
25C2×C3×Dic6—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—
36C2×C3×C3⋊C8—21no—
37#3724—21no—
38#3724—21no—
39#3724—21no—
40#3724D411yescharacteristic
41Dic3⋊Dic3—21no—
42#1680—91nomaximal, Sylow
43#944—61no—
44#888—61no—
45C4×Dic6—61no—
46C3×C4⋊C8—61no—
47C3×#103—61no—
48#835—61no—
49#816—21no—
50Dic3⋊C8—21no—
51Dic3⋊C8—61no—
52C8×Dic3—61no—
53C8×Dic3—61no—
54C8×Dic3—61no—
55#810—61no—
56C4×C3⋊C8—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—
64C3×Dic6—41no—
65C3×Dic6—41no—
66#627—21no—
67#627—41no—
68#627—41no—
69#627SD1612yes—
70#622—41no—
71#622—41no—
72C32×C8—21no—
73C3⋊(C3⋊C8)—21no—
74C3×C3⋊C8—41no—
75#487—91no—
76#475—91no—
77#462—91no—
78C8×Q8—91no—
79#334—91no—
80#332—91no—
81#332—91no—
82C2×C3×Q8—61no—
83C2×Dic6—21no—
84C2×Dic6—61no—
85C2×Dic6—121no—
86C2×C3×C8—21no—
87C2×C3×C8—21no—
88C2×C3×C8—61no—
89C3×C4⋊C4—61no—
90C3×C42—61no—
91C4⋊Dic3—21no—
92C4⋊Dic3—61no—
93Dic3⋊C4—61no—
94Dic3⋊C4—61no—
95Dic3⋊C4—121no—
96Dic3⋊C4—121no—
97Dic3⋊C4—121no—
98C4×Dic3—21no—
99C4×Dic3—61no—
100C4×Dic3—61no—
101C2×C3⋊C8—21no—
102C2×C3⋊C8—61no—
103C2×C3⋊C8—61no—
104C22×C32#12111yescharacteristic
105C32×C4#13511yescharacteristic
106C32×C4#13711yescharacteristic
107C3⋊Dic3—21no—
108C3⋊Dic3C2×SD1611yescharacteristic
109C3⋊Dic3#13511yescharacteristic
110C3×Dic3—22no—
111C3×Dic3—41no—
112C3×Dic3—81no—
113C3×Dic3—81no—
114C2×Q16—181no—
115C4⋊Q8—91no—
116C4⋊Q8—91no—
117C4×Q8—91no—
118#106—181no—
119C4⋊C8—61no—
120C4⋊C8—91no—
121C4⋊C8—91no—
122C4⋊C8—91no—
123#103—61no—
124#103—181no—
125#103—181no—
126#103—181no—
127C4×C8—91no—
128C4×C8—181no—
129C3×Q8—121no—
130C3×Q8—121no—
131C2×C3×C4—21no—
132C2×C3×C4—21no—
133C2×C3×C4—61no—
134C2×C3×C4—61no—
135C2×C3×C4—121no—
136C2×C3×C4—121no—
137C2×Dic3—21no—
138C2×Dic3—21no—
139C2×Dic3—41no—
140C2×Dic3—41no—
141C2×Dic3—61no—
142C2×Dic3—61no—
143C2×Dic3—61no—
144C2×Dic3—61no—
145Dic6—41no—
146Dic6—41no—
147Dic6—62no—
148Dic6—62no—
149Dic6—241no—
150Dic6—241no—
151C3×C8—41no—
152C3×C8—41no—
153C3×C8—121no—
154C3⋊C8—41no—
155C3⋊C8—62no—
156C3⋊C8—121no—
157C2×C32#46411yescharacteristic
158C2×C32#46511yescharacteristic
159C2×C32#47311yescharacteristic
160C2×Q8—61no—
161C2×Q8—91no—
162C2×Q8—181no—
163Q16—362no—
164C2×C8—61no—
165C2×C8—91no—
166C2×C8—181no—
167C2×C8—181no—
168C2×C8GO+(4,𝔽2)11yescharacteristic
169C4⋊C4—61no—
170C4⋊C4—91no—
171C4⋊C4—181no—
172C4⋊C4—181no—
173C4⋊C4—181no—
174C4⋊C4—181no—
175C42—61no—
176C42—91no—
177C22×C3—21no—
178C22×C3—21no—
179C3×C4—21no—
180C3×C4—21no—
181C3×C4—21no—
182C3×C4—21no—
183C3×C4—62no—
184C3×C4—121no—
185C3×C4—241no—
186C3×C4—241no—
187Dic3—22no—
188Dic3—41no—
189Dic3—61no—
190Dic3—61no—
191Dic3—61no—
192Dic3—61no—
193Dic3—62no—
194Dic3—81no—
195Dic3—81no—
196Dic3—121no—
197C32#168011yescharacteristic, complemented, Sylow
198Q8—92no—
199Q8—121no—
200Q8—121no—
201Q8—181no—
202Q8—361no—
203Q8—361no—
204C2×C4—61no—
205C2×C4—61no—
206C2×C4—91no—
207C2×C4—91no—
208C2×C4—121no—
209C2×C4—121no—
210C2×C4C2×GO+(4,𝔽2)11yescharacteristic
211C8—21no—
212C8—121no—
213C8—181no—
214C8—361no—
215C8—361no—
216C2×C3—21no—
217C2×C3—21no—
218C2×C3—21no—
219C2×C3—21no—
220C2×C3—21no—
221C2×C3—21no—
222C22#6423011yescharacteristic
223C4—62no—
224C4—91no—
225C4—91no—
226C4—121no—
227C4—181no—
228C4—241no—
229C4—241no—
230C4#6422611yescharacteristic
231C4#6423711yescharacteristic
232C3—21no—
233C3—21no—
234C2#1059328411yescharacteristic
235C2#1059330511yescharacteristic
236C2#1059344011yescharacteristic
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#1680
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
197. C32#1680semidirect

Maximal subgroups

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

subgroupindex
#105934472
#105933762
#105909012
#105906452
#105901702
#105900392
#105900382
#16809