Finite Group Databasebeta

← #11791049

Subgroups — #11791049

Order 1152.

586 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 586 conjugacy classes of subgroups — too many to draw. Only its 77 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×#64225C211yesmaximal, characteristic
2C2×C8×#157C211yesmaximal, characteristic, complemented
3#10593407C212yesmaximal, complemented
4#10593396C211yesmaximal, characteristic, complemented
5#10590940C212yesmaximal, complemented
6C2×#3802C2212yes—
7C2×C4×#157C2211yescharacteristic
8C2×#3787C2211yescharacteristic
9C2×#3774—22no—
10C2×D32⋊C4—24no—
11#64225—22no—
12#64225C414yescomplemented
13C2×C8×C3⋊D3C2211yescharacteristic
14#63900C2212yes—
15C8×#157—22no—
16#63743—22no—
17C3×#821—22no—
18#63562—22no—
19D3×#102—62no—
20C22×D32—22no—
21C22×#157D412yes—
22C2×C4×C3⋊D3C2311yescharacteristic
23C2×C3×D12—22no—
24C2×#625—22no—
25C2×#624—22no—
26#3802—22no—
27#3802—22no—
28#3802—22no—
29#3802C2×C414yes—
30C2×#622D412yes—
31C4×#157—21no—
32C4×#157—21no—
33#3787C2×C412yes—
34#3787D412yes—
35#3774—28no—
36D32⋊C4—48no—
37C2×C32×C8D411yescharacteristic
38C2×C3⋊(C3⋊C8)D411yescharacteristic
39C8×C3⋊D3—21no—
40C8×C3⋊D3—21no—
41C3×C4⋊Dic3—22no—
42#3724—22no—
43#1970—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—22no—
58C2×#157—22no—
59C2×#157D814yescomplemented
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#622C22⋊C414yescomplemented
73C32×C8—21no—
74C3⋊(C3⋊C8)—21no—
75C22×D8—91no—
76C2×#107—91no—
77C2×#102—92no—
78C2×C4×C8—91no—
79#390—92no—
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⋊D3C4×D411yescharacteristic
99C2×C3⋊D3#12111yescharacteristic
100C2×C3⋊D3C2×D812yes—
101C2×C3⋊D3#13512yes—
102C2×C3×D3—44no—
103C2×C3×D3—82no—
104C2×C3×D3—82no—
105D32—48no—
106D32—84no—
107#157—24no—
108C32×C4C4×D411yescharacteristic
109C32×C4#12111yescharacteristic
110C3⋊Dic3C2×C22⋊C411yescharacteristic
111C3⋊Dic3#12411yescharacteristic
112C3×Dic3—82no—
113C22×D4—92no—
114C2×D8—94no—
115C2×D8—182no—
116C2×D8—182no—
117C22×C8—91no—
118C22×C8—91no—
119C2×C4⋊C4—92no—
120C2×C22⋊C4—184no—
121C2×C42—91no—
122#107—182no—
123#102—62no—
124#102—182no—
125C4×C8—182no—
126C23×C3—122no—
127C22×D3—42no—
128C22×D3—62no—
129C22×D3—124no—
130C22×D3—124no—
131C22×D3—244no—
132C22×D3—244no—
133C3×D4—64no—
134C3×D4—122no—
135C2×C3×C4—22no—
136C2×C3×C4—122no—
137#67—124no—
138#67—124no—
139C2×Dic3—42no—
140C2×Dic3—62no—
141D12—24no—
142D12—42no—
143C4×D3—62no—
144C4×D3—62no—
145C4×D3—62no—
146C4×D3—62no—
147C4×D3—244no—
148C3×C8—42no—
149C3⋊C8—122no—
150C2×C32#39011yescharacteristic
151C2×C32#49311yescharacteristic
152C2×C32#49511yescharacteristic
153C3⋊D3C4×D812yes—
154C3⋊D3#46612yes—
155C3×D3—84no—
156C24—182no—
157C2×D4—62no—
158C2×D4—94no—
159C2×D4—182no—
160C2×D4—182no—
161C2×D4—182no—
162C2×D4—182no—
163C22×C4—91no—
164C22×C4—92no—
165C22×C4—182no—
166D8—188no—
167C2×C8—92no—
168C2×C8—92no—
169C2×C8—92no—
170C2×C8—91no—
171C2×C8—181no—
172C2×C8—181no—
173C2×C8GO+(4,𝔽2)11yescharacteristic
174C4⋊C4—62no—
175C4⋊C4—182no—
176C22⋊C4—368no—
177C42—181no—
178C42—181no—
179C22×C3—22no—
180C22×C3—124no—
181C22×C3—242no—
182C22×C3—242no—
183C2×D3—44no—
184C2×D3—62no—
185C2×D3—62no—
186C2×D3—64no—
187C2×D3—64no—
188C2×D3—82no—
189C2×D3—82no—
190C2×D3—248no—
191C2×D3—248no—
192C3×C4—22no—
193C3×C4—22no—
194C3×C4—242no—
195Dic3—62no—
196Dic3—62no—
197Dic3—82no—
198C32#197011yescharacteristic, complemented, Sylow
199C23—91no—
200C23—122no—
201C23—184no—
202C23—362no—
203C23—364no—
204C23—364no—
205D4—64no—
206D4—122no—
207D4—184no—
208D4—362no—
209C2×C4—91no—
210C2×C4—91no—
211C2×C4—91no—
212C2×C4—91no—
213C2×C4—91no—
214C2×C4—94no—
215C2×C4—122no—
216C2×C4—182no—
217C2×C4—182no—
218C2×C4—364no—
219C2×C4C2×GO+(4,𝔽2)11yescharacteristic
220C8—21no—
221C8—94no—
222C8—181no—
223C2×C3—22no—
224C2×C3—22no—
225C2×C3—22no—
226C2×C3—244no—
227D3—64no—
228D3—64no—
229D3—84no—
230C22—92no—
231C22—92no—
232C22—91no—
233C22—91no—
234C22—124no—
235C22—242no—
236C22—242no—
237C22—368no—
238C22—724no—
239C22#6423111yescharacteristic
240C4—91no—
241C4—91no—
242C4—184no—
243C4—242no—
244C4C4×GO+(4,𝔽2)11yescharacteristic
245C4#6424211yescharacteristic
246C3—22no—
247C2—92no—
248C2—92no—
249C2—244no—
250C2#1059329311yescharacteristic
251C2#1059329611yescharacteristic
252C2#1059345411yescharacteristic
subgroupG/H
centerC22#64231
commutatorC4×C3⋊D3C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC2×C32×C8D4
socleC22×C32#127
prime radicalC2×#64225C2
cosocleC2×C4×C3⋊D3C23
hypercenterC2×C8GO+(4,𝔽2)
hypocenterC32#1970
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×C8×#157C2semidirect
3. #10593407C2semidirect
4. #10593396C2semidirect
5. #10590940C2semidirect
12. #64225C4semidirect
59. C2×#157D8semidirect
72. #622C22⋊C4semidirect
198. C32#1970semidirect

Maximal subgroups

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

subgroupindex
C2×#642252
C2×C8×#1572
#105934072
#105933962
#105909402
#19709