Finite Group Databasebeta

← #11782958

Subgroups — #11782958

Order 1152.

306 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 49 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#10593450C211yesmaximal, characteristic, complemented
2#10593442C211yesmaximal, characteristic
3#10593395C211yesmaximal, characteristic, complemented
4#10593366C211yesmaximal, characteristic
5#10590902C211yesmaximal, characteristic, complemented
6#10590885C211yesmaximal, characteristic
7#10590169C211yesmaximal, characteristic, complemented
8C2×#3776—22no—
9C2×#3775—22no—
10#63919C2211yescharacteristic
11#63919C2211yescharacteristic
12#63919C2211yescharacteristic
13#63914C2211yescharacteristic
14C4×#622C2211yescharacteristic
15C4×#622C2211yescharacteristic
16#63743—22no—
17#63739—22no—
18C8×C3⋊Dic3C2211yescharacteristic
19C3×#821—21no—
20C3×#818—21no—
21#63576—21no—
22#63562—21no—
23#4874—61no—
24#4760—61no—
25C2×C3×D12—21no—
26C2×#627—21no—
27C2×#627—21no—
28C2×#627—21no—
29C2×#625—21no—
30C2×#625—21no—
31C2×#622D412yes—
32C2×#622D412yes—
33#3776—44no—
34#3775—44no—
35C2×C32×C8D411yescharacteristic
36C4×C3⋊Dic3C2311yescharacteristic
37C2×C3⋊(C3⋊C8)D411yescharacteristic
38C3×C4⋊Dic3—21no—
39C3×C4⋊Dic3—21no—
40C3×C4⋊Dic3—21no—
41#3724—21no—
42#3724—21no—
43#3724—21no—
44#1722—91nomaximal, Sylow
45#940—61no—
46#888—61no—
47#888—61no—
48#888—61no—
49C3×#107—61no—
50C3×#102—61no—
51#832—61no—
52#821—21no—
53#818—21no—
54C8×Dic3—61no—
55C8×Dic3—61no—
56#809—61no—
57#807—61no—
58#807—61no—
59C22×C3×D3—41no—
60C2×C32×C4C2×D411yescharacteristic
61C2×C3⋊Dic3C2×D411yescharacteristic
62C2×C3⋊Dic3C2×D411yescharacteristic
63C2×C3×Dic3—41no—
64C2×C3×Dic3—41no—
65C2×C3×Dic3—41no—
66C3×D12—41no—
67C3×D12—41no—
68#627—42no—
69#627—42no—
70#627—42no—
71#625—42no—
72#625—42no—
73#622—22no—
74#622D814yes—
75C32×C8—21no—
76C3⋊(C3⋊C8)—21no—
77#500—91no—
78#500—91no—
79#494—91no—
80#492—91no—
81#486—91no—
82#486—91no—
83#322—91no—
84C2×C3×D4—61no—
85C2×#67—121no—
86C2×#67—121no—
87C2×D12—21no—
88C2×Dic6—121no—
89C2×Dic6—121no—
90C2×Dic6—121no—
91C2×C3×C8—21no—
92C2×C3×C8—21no—
93C3×C4⋊C4—61no—
94C3×C4⋊C4—61no—
95C3×C4⋊C4—61no—
96C4⋊Dic3—21no—
97C4⋊Dic3—21no—
98C4⋊Dic3—21no—
99Dic3⋊C4—121no—
100Dic3⋊C4—121no—
101Dic3⋊C4—121no—
102C4×Dic3—61no—
103C4×Dic3—61no—
104C2×C3⋊C8—61no—
105C2×C3⋊C8—61no—
106C22×C32#12711yescharacteristic
107C2×C3×D3—81no—
108C2×C3×D3—81no—
109C2×C3×D3—81no—
110C32×C4#13711yescharacteristic
111C32×C4#13711yescharacteristic
112C3⋊Dic3C2×D812yes—
113C3⋊Dic3#13712yes—
114C3×Dic3—81no—
115C3×Dic3—81no—
116C3×Dic3—81no—
117C2×Q16—182no—
118C2×SD16—182no—
119C4⋊Q8—91no—
120C4⋊Q8—91no—
121C4⋊Q8—91no—
122#127—91no—
123#107—61no—
124#107—181no—
125#107—182no—
126#102—61no—
127#102—181no—
128#102—182no—
129C4×C8—91no—
130C4×C8—91no—
131C4×C8—91no—
132C23×C3—121no—
133C22×D3—41no—
134C3×D4—121no—
135C3×D4—121no—
136C2×C3×C4—21no—
137C2×C3×C4—21no—
138C2×C3×C4—121no—
139C2×C3×C4—121no—
140C2×C3×C4—121no—
141#67—242no—
142#67—242no—
143C2×Dic3—41no—
144C2×Dic3—41no—
145C2×Dic3—41no—
146C2×Dic3—61no—
147C2×Dic3—61no—
148C2×Dic3—61no—
149C2×Dic3—61no—
150D12—41no—
151D12—41no—
152Dic6—242no—
153Dic6—242no—
154Dic6—242no—
155C3×C8—22no—
156C3×C8—41no—
157C3⋊C8—62no—
158C3⋊C8—121no—
159C2×C32#49311yescharacteristic
160C2×C32#49711yescharacteristic
161C2×C32#49711yescharacteristic
162C3×D3—161no—
163C2×Q8—181no—
164C2×Q8—181no—
165C2×Q8—181no—
166C2×D4—61no—
167C2×D4—181no—
168C2×D4—181no—
169Q16—364no—
170SD16—364no—
171C2×C8—92no—
172C2×C8—92no—
173C2×C8—91no—
174C2×C8GO+(4,𝔽2)11yescharacteristic
175C4⋊C4—61no—
176C4⋊C4—61no—
177C4⋊C4—61no—
178C4⋊C4—181no—
179C4⋊C4—181no—
180C4⋊C4—181no—
181C42—91no—
182C22×C3—21no—
183C22×C3—21no—
184C22×C3—241no—
185C22×C3—241no—
186C22×C3—241no—
187C2×D3—81no—
188C2×D3—81no—
189C2×D3—81no—
190C3×C4—21no—
191C3×C4—21no—
192C3×C4—21no—
193C3×C4—21no—
194C3×C4—241no—
195C3×C4—241no—
196C3×C4—241no—
197Dic3—62no—
198Dic3—62no—
199Dic3—62no—
200Dic3—62no—
201Dic3—81no—
202Dic3—81no—
203Dic3—81no—
204C32#172211yescharacteristic, complemented, Sylow
205C23—121no—
206Q8—362no—
207Q8—362no—
208Q8—362no—
209D4—121no—
210D4—121no—
211D4—362no—
212D4—362no—
213C2×C4—91no—
214C2×C4—91no—
215C2×C4—121no—
216C2×C4—121no—
217C2×C4—121no—
218C2×C4C2×GO+(4,𝔽2)11yescharacteristic
219C8—21no—
220C8—94no—
221C8—182no—
222C8—181no—
223C2×C3—21no—
224C2×C3—21no—
225C2×C3—21no—
226C2×C3—21no—
227C2×C3—21no—
228C2×C3—21no—
229C2×C3—481no—
230D3—161no—
231C22—241no—
232C22—241no—
233C22—241no—
234C22#6423111yescharacteristic
235C4—92no—
236C4—92no—
237C4—241no—
238C4—241no—
239C4—241no—
240C4#6422611yescharacteristic
241C4#6423911yescharacteristic
242C3—21no—
243C3—21no—
244C2—481no—
245C2#1059329111yescharacteristic
246C2#1059329311yescharacteristic
247C2#1059344311yescharacteristic
subgroupG/H
centerC22#64231
commutator, cosocleC4×C3⋊Dic3C23
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC2×C32×C8D4
socleC22×C32#127
prime radical#63914C22
hypercenterC2×C8GO+(4,𝔽2)
hypocenterC32#1722
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
1. #10593450C2semidirect
3. #10593395C2semidirect
5. #10590902C2semidirect
7. #10590169C2semidirect
204. C32#1722semidirect

Maximal subgroups

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

subgroupindex
#105934502
#105934422
#105933952
#105933662
#105909022
#105908852
#105901692
#17229