Finite Group Databasebeta

← #11790768

Subgroups — #11790768

Order 1152.

614 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 614 conjugacy classes of subgroups — too many to draw. Only its 73 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
1C2×#64231C211yesmaximal, characteristic
2C2×#63767C211yesmaximal, characteristic, complemented
3#10593365C212yesmaximal, complemented
4#10593344C211yesmaximal, characteristic, complemented
5#10590940C212yesmaximal, complemented
6C22×GO+(4,𝔽2)—22no—
7C2×#3802C2212yes—
8C2×C4×#157C2211yescharacteristic
9C2×#3787C2211yescharacteristic
10#64231—22no—
11#64231C414yescomplemented
12C2×C8×C3⋊D3C2211yescharacteristic
13#63900C2212yes—
14#63767—22no—
15#63739—24no—
16#63737—22no—
17C3×#821—22no—
18#63562—22no—
19D3×#102—62no—
20C22×D32—22no—
21C22×#157D412yes—
22C2×GO+(4,𝔽2)—28no—
23C2×GO+(4,𝔽2)—48no—
24C2×C4×C3⋊D3C2311yescharacteristic
25C2×C3×D12—22no—
26C2×#625—22no—
27C2×#624—22no—
28#3802—22no—
29#3802—22no—
30#3802—22no—
31#3802C2×C414yes—
32C2×#622D412yescomplemented
33C4×#157C2×C412yes—
34C4×#157D412yes—
35#3787—21no—
36#3787—21no—
37C2×C32×C8D411yescharacteristic, complemented
38C2×C3⋊(C3⋊C8)D411yescharacteristic, complemented
39C8×C3⋊D3—21no—
40C8×C3⋊D3—21no—
41C3×C4⋊Dic3—22no—
42#3724—22no—
43#1961—91nomaximal, Sylow
44C2×D3×D4—62no—
45C2×D3×C8—62no—
46D3×C4⋊C4—62no—
47C3×#102—62no—
48#832—62no—
49#821—22no—
50#809—62no—
51C22×C3⋊D3C2×D411yescharacteristic
52C22×C3×D3—42no—
53C2×D32—24no—
54C2×D32—42no—
55C2×D32—44no—
56C2×D32—44no—
57C2×#157—24no—
58C2×#157C22⋊C414yes—
59GO+(4,𝔽2)—416no—
60C2×C32×C4C2×D411yescharacteristic
61C2×C3⋊Dic3C2×D411yescharacteristic
62C4×C3⋊D3C22×C411yescharacteristic
63C4×C3⋊D3C2×D411yescharacteristic
64C4×C3⋊D3#4111yescharacteristic
65C4×C3⋊D3#4111yescharacteristic
66C2×C3×Dic3—42no—
67C3×D12—24no—
68C3×D12—42no—
69#625—24no—
70#625—42no—
71#624—44no—
72#622—22no—
73C32×C8—21no—
74C3⋊(C3⋊C8)—21no—
75C2×#127—91no—
76C2×#102—92no—
77C2×#102—92no—
78C2×#97—91no—
79#382—91no—
80C23×D3—122no—
81C2×C3×D4—62no—
82C2×#67—122no—
83D3×D4—64no—
84D3×D4—64no—
85D3×D4—122no—
86D3×D4—122no—
87C2×D12—22no—
88C2×C4×D3—62no—
89C2×C4×D3—122no—
90C2×C3×C8—22no—
91C3×C4⋊C4—62no—
92C4⋊Dic3—22no—
93Dic3⋊C4—122no—
94C2×C3⋊C8—62no—
95D3×C8—122no—
96D3×C8—122no—
97C22×C32#12711yescharacteristic
98C2×C3⋊D3C2×C22⋊C411yescharacteristic
99C2×C3⋊D3#12411yescharacteristic
100C2×C3⋊D3AGL(1,ℤ/8)14yes—
101C2×C3×D3—44no—
102C2×C3×D3—82no—
103C2×C3×D3—82no—
104D32—48no—
105D32—84no—
106#157—24no—
107C32×C4C4×D411yescharacteristic
108C32×C4#12111yescharacteristic
109C3⋊Dic3C4×D411yescharacteristic
110C3⋊Dic3#12111yescharacteristic
111C3×Dic3—82no—
112C22×D4—92no—
113C22×D4—182no—
114C22×C8—91no—
115C22×C8—91no—
116#127—94no—
117#127—182no—
118C2×C4⋊C4—92no—
119C2×C42—91no—
120#102—62no—
121#102—182no—
122#102—184no—
123#97—182no—
124#95—182no—
125C23×C3—122no—
126C22×D3—42no—
127C22×D3—62no—
128C22×D3—124no—
129C22×D3—124no—
130C22×D3—244no—
131C22×D3—244no—
132C3×D4—64no—
133C3×D4—122no—
134C2×C3×C4—22no—
135C2×C3×C4—122no—
136#67—124no—
137#67—124no—
138C2×Dic3—42no—
139C2×Dic3—62no—
140D12—24no—
141D12—42no—
142C4×D3—62no—
143C4×D3—62no—
144C4×D3—62no—
145C4×D3—62no—
146C4×D3—244no—
147C3×C8—42no—
148C3⋊C8—122no—
149C2×C32#39011yescharacteristic
150C2×C32#49612yes—
151C3⋊D3#41812yes—
152C3⋊D3#49012yes—
153C3×D3—84no—
154C24—182no—
155C2×D4—62no—
156C2×D4—94no—
157C2×D4—182no—
158C2×D4—182no—
159C2×D4—182no—
160C2×D4—182no—
161C2×D4—188no—
162C2×D4—368no—
163C22×C4—91no—
164C22×C4—92no—
165C22×C4—182no—
166C2×C8—92no—
167C2×C8—91no—
168C2×C8—181no—
169C2×C8—181no—
170C2×C8—181no—
171C2×C8—181no—
172C2×C8GO+(4,𝔽2)11yescharacteristic, complemented
173C4⋊C4—62no—
174C4⋊C4—182no—
175C42—92no—
176C42—92no—
177C22×C3—22no—
178C22×C3—124no—
179C22×C3—242no—
180C22×C3—242no—
181C2×D3—44no—
182C2×D3—62no—
183C2×D3—62no—
184C2×D3—64no—
185C2×D3—64no—
186C2×D3—82no—
187C2×D3—82no—
188C2×D3—248no—
189C2×D3—248no—
190C3×C4—22no—
191C3×C4—22no—
192C3×C4—242no—
193Dic3—62no—
194Dic3—62no—
195Dic3—82no—
196C32#196111yescharacteristic, complemented, Sylow
197C23—91no—
198C23—122no—
199C23—184no—
200C23—362no—
201C23—364no—
202C23—364no—
203D4—64no—
204D4—122no—
205D4—184no—
206D4—362no—
207D4—3616no—
208C2×C4—91no—
209C2×C4—91no—
210C2×C4—91no—
211C2×C4—91no—
212C2×C4—91no—
213C2×C4—94no—
214C2×C4—122no—
215C2×C4—184no—
216C2×C4—364no—
217C2×C4C2×GO+(4,𝔽2)11yescharacteristic
218C8—21no—
219C8—182no—
220C8—181no—
221C2×C3—22no—
222C2×C3—22no—
223C2×C3—22no—
224C2×C3—244no—
225D3—64no—
226D3—64no—
227D3—84no—
228C22—94no—
229C22—91no—
230C22—91no—
231C22—124no—
232C22—242no—
233C22—242no—
234C22—368no—
235C22—724no—
236C22#6423111yescharacteristic
237C4—91no—
238C4—91no—
239C4—184no—
240C4—242no—
241C4C4×GO+(4,𝔽2)11yescharacteristic
242C4#6424211yescharacteristic
243C3—22no—
244C2—92no—
245C2—92no—
246C2—244no—
247C2#1059329412yes—
248C2#1059345411yescharacteristic
subgroupG/H
centerC22#64231
commutatorC4×C3⋊D3C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC2×C32×C8D4
socleC22×C32#127
prime radicalC2×#64231C2
cosocleC2×C4×C3⋊D3C23
hypercenterC2×C8GO+(4,𝔽2)
hypocenterC32#1961
LCSG ▷ C4×C3⋊D3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
2. C2×#63767C2semidirect
3. #10593365C2semidirect
4. #10593344C2semidirect
5. #10590940C2semidirect
11. #64231C4semidirect
32. C2×#622D4semidirect
37. C2×C32×C8D4semidirect
38. C2×C3⋊(C3⋊C8)D4semidirect
172. C2×C8GO+(4,𝔽2)semidirect
196. C32#1961semidirect

Maximal subgroups

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

subgroupindex
C2×#642312
C2×#637672
#105933652
#105933442
#105909402
#19619