Finite Group Databasebeta

← #11779492

Subgroups — #11779492

Order 1152.

654 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 654 conjugacy classes of subgroups — too many to draw. Only its 129 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#10596034C211yesmaximal, characteristic
2#10592707C211yesmaximal, characteristic, complemented
3#10592541C211yesmaximal, characteristic, complemented
4#10592398C211yesmaximal, characteristic, complemented
5C32×D4⋊C8C211yesmaximal, characteristic, complemented
6#10589347C211yesmaximal, characteristic, complemented
7#10589325C211yesmaximal, characteristic, complemented
8#68203—34nomaximal
9C32×C4×D4C2211yescharacteristic
10#64147—21no—
11#64139—21no—
12#64135—21no—
13C2×#3746—22no—
14#64101—21no—
15#64094—22no—
16C4×C4⋊(C3⋊D3)C2211yescharacteristic
17#64078C2211yescharacteristic
18#64078C2211yescharacteristic
19C32×C4⋊C8C2211yescharacteristic
20C32×C4×C8C2211yescharacteristic
21#63659—21no—
22#63648—21no—
23#63644—21no—
24#63635—21no—
25C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
26#5563—34no—
27#5008—34no—
28#4842—34no—
29#4699—34no—
30C3×D4⋊C8D314yescomplemented
31#4481—34no—
32#4459—34no—
33C2×C32×D4D411yescharacteristic
34C22×C32×C4—21no—
35C2×#638—22no—
36C2×C4⋊(C3⋊D3)D411yescharacteristic
37C2×C4×C3⋊D3—21no—
38C2×#634—21no—
39C2×#634D412yes—
40C2×C32×C8—21no—
41C2×C32×C8—21no—
42C32×C4⋊C4D411yescharacteristic
43C32×C22⋊C4—21no—
44C32×C42C2311yescharacteristic
45#3757—22no—
46#3752—22no—
47#3752—21no—
48C4⋊(C3⋊Dic3)—21no—
49C4⋊(C3⋊Dic3)—21no—
50C4⋊(C3⋊Dic3)—21no—
51C4⋊(C3⋊Dic3)—21no—
52C4⋊(C3⋊Dic3)D411yescharacteristic
53C4×C3⋊Dic3—22no—
54C2×C3⋊(C3⋊C8)—21no—
55#3746—44no—
56#1634—91noSylow
57C3×C4×D4C2×D314yes—
58#938—64no—
59#930—64no—
60#926—64no—
61C2×Dic12—68no—
62#892—64no—
63#885—68no—
64C4×D12—34no—
65#869—34no—
66#869—34no—
67C3×C4⋊C8C2×D314yes—
68C3×C4×C8C2×D314yes—
69#832—64no—
70#821—64no—
71#817—64no—
72#808—64no—
73C4⋊(C3⋊C8)—34no—
74C23×C32—21no—
75C22×C3⋊D3—21no—
76C32×D4—21no—
77C32×D4—21no—
78C2×C32×C4—21no—
79C2×C32×C4—41no—
80C2×C32×C4—41no—
81C2×C32×C4C2×D411yescharacteristic
82C2×C32×C4C2×D411yescharacteristic
83C2×C32×C4C2×D411yescharacteristic
84#638—82no—
85C2×C3⋊Dic3—21no—
86C2×C3⋊Dic3—22no—
87C2×C3⋊Dic3—41no—
88C4⋊(C3⋊D3)—21no—
89C4⋊(C3⋊D3)—21no—
90C4×C3⋊D3—41no—
91C4×C3⋊D3—41no—
92#634—42no—
93#634—42no—
94C32×C8—22no—
95C32×C8—41no—
96C3⋊(C3⋊C8)—41no—
97#555—91no—
98#494—91no—
99#476—91no—
100#476—91no—
101#333—91no—
102D4⋊C8—91no—
103D4⋊C8C3⋊D311yescharacteristic, complemented
104C2×C3×D4D1214yes—
105C22×C3×C4—24no—
106C2×#67—68no—
107C2×D12—34no—
108C2×C4×D3—64no—
109C2×Dic6—38no—
110C2×Dic6—64no—
111C2×C3×C8—24no—
112C2×C3×C8—24no—
113C3×C4⋊C4D1214yes—
114C3×C22⋊C4—24no—
115C3×C42C22×D314yes—
116#217—68no—
117(C2×D3)⋊C4—68no—
118(C2×D3)⋊C4—64no—
119C4⋊Dic3—34no—
120C4⋊Dic3—64no—
121C4⋊Dic3—64no—
122C4⋊Dic3—64no—
123C4⋊Dic3—64no—
124C4×Dic3—68no—
125C2×C3⋊C8—64no—
126Dic12—1216no—
127C22×C32—41no—
128C22×C32—41no—
129C22×C32—41no—
130C22×C32#12011yescharacteristic
131C2×C3⋊D3—41no—
132C2×C3⋊D3—41no—
133C2×C3⋊D3—41no—
134C32×C4—21no—
135C32×C4—41no—
136C32×C4#13511yescharacteristic
137C32×C4#13511yescharacteristic
138C32×C4#13711yescharacteristic
139C32×C4#13711yescharacteristic
140C3⋊Dic3—41no—
141C3⋊Dic3—42no—
142C3⋊Dic3—81no—
143C2×Q16—182no—
144C4⋊Q8—91no—
145C4⋊Q8—91no—
146#124—182no—
147#121—181no—
148#121—181no—
149C4×D4—91no—
150C4×D4C2×C3⋊D311yescharacteristic
151#117—181no—
152#117—181no—
153#106—181no—
154#106—181no—
155C4⋊C8—91no—
156C4⋊C8C2×C3⋊D311yescharacteristic
157#102—181no—
158#102—181no—
159C4×C8C2×C3⋊D311yescharacteristic
160C23×C3—24no—
161C22×D3—64no—
162C3×D4—24no—
163C3×D4—24no—
164C2×C3×C4—24no—
165C2×C3×C4—44no—
166C2×C3×C4—44no—
167C2×C3×C4C2×D1214yes—
168C2×C3×C4D3×D414yes—
169C2×C3×C4D3×D414yes—
170#67—248no—
171C2×Dic3—64no—
172C2×Dic3—68no—
173C2×Dic3—124no—
174D12—64no—
175D12—64no—
176C4×D3—124no—
177C4×D3—124no—
178Dic6—128no—
179Dic6—128no—
180C3×C8—28no—
181C3×C8—44no—
182C3⋊C8—124no—
183C2×C32—81no—
184C2×C32#45211yescharacteristic
185C2×C32#45211yescharacteristic
186C2×C32#45311yescharacteristic
187C3⋊D3—81no—
188C2×Q8—92no—
189C2×Q8—181no—
190C2×D4—91no—
191C2×D4—182no—
192C2×D4C4⋊(C3⋊D3)11yescharacteristic
193C22×C4—21no—
194C22×C4—181no—
195Q16—364no—
196C2×C8—21no—
197C2×C8—21no—
198C2×C8—181no—
199C4⋊C4—91no—
200C4⋊C4—181no—
201C4⋊C4—181no—
202C4⋊C4—181no—
203C4⋊C4—181no—
204C4⋊C4C4⋊(C3⋊D3)11yescharacteristic
205C22⋊C4—21no—
206C22⋊C4—182no—
207C22⋊C4—182no—
208C22⋊C4—181no—
209C42—182no—
210C42C22×C3⋊D311yescharacteristic
211C22×C3—44no—
212C22×C3—44no—
213C22×C3—44no—
214C22×C3#88214yes—
215C2×D3—124no—
216C2×D3—124no—
217C2×D3—124no—
218C3×C4—24no—
219C3×C4—44no—
220C3×C4#90414yes—
221C3×C4#90914yes—
222C3×C4#91214yes—
223C3×C4#91514yes—
224Dic3—124no—
225Dic3—128no—
226Dic3—244no—
227C32#163411yescharacteristic, complemented, Sylow
228C23—21no—
229C23—181no—
230Q8—362no—
231Q8—362no—
232D4—21no—
233D4—21no—
234D4—181no—
235D4—181no—
236D4—722no—
237C2×C4—21no—
238C2×C4—41no—
239C2×C4—41no—
240C2×C4—181no—
241C2×C4—182no—
242C2×C4—361no—
243C2×C4—361no—
244C2×C4—361no—
245C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
246C2×C4D4×C3⋊D311yescharacteristic
247C2×C4D4×C3⋊D311yescharacteristic
248C8—22no—
249C8—41no—
250C8—361no—
251C2×C3—84no—
252C2×C3#473314yes—
253C2×C3#478314yes—
254C2×C3#482214yes—
255D3—244no—
256C22—41no—
257C22—41no—
258C22—41no—
259C22—361no—
260C22—361no—
261C22—361no—
262C22#6409111yescharacteristic
263C4—21no—
264C4—41no—
265C4—362no—
266C4—361no—
267C4—721no—
268C4#6411311yescharacteristic
269C4#6411811yescharacteristic
270C4#6412111yescharacteristic
271C4#6412411yescharacteristic
272C3#6820314yescomplemented
273C2—81no—
274C2—721no—
275C2#1059243211yescharacteristic
276C2#1059248211yescharacteristic
277C2#1059252111yescharacteristic
subgroupG/H
centerC22#64091
commutator, cosocleC32×C42C23
FrattiniC42C22×C3⋊D3
FittingC32×D4⋊C8C2
socleC22×C32#120
prime radical#10596034C2
hypercenterD4⋊C8C3⋊D3
hypocenterC32#1634
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #10592707C2semidirect
3. #10592541C2semidirect
4. #10592398C2semidirect
5. C32×D4⋊C8C2semidirect
6. #10589347C2semidirect
7. #10589325C2semidirect
30. C3×D4⋊C8D3semidirect
103. D4⋊C8C3⋊D3semidirect
227. C32#1634semidirect
272. C3#68203semidirect

Maximal subgroups

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

subgroupindex
#105960342
#105927072
#105925412
#105923982
C32×D4⋊C82
#105893472
#105893252
#682033