Finite Group Databasebeta

← #11779761

Subgroups — #11779761

Order 1152.

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

normal subgroups only

This group has 636 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#10596184C211yesmaximal, characteristic
2#10592769C211yesmaximal, characteristic
3#10592550C211yesmaximal, characteristic, complemented
4#10592548C211yesmaximal, characteristic, complemented
5C32×#331C211yesmaximal, characteristic
6#10589350C211yesmaximal, characteristic, complemented
7#10589350C211yesmaximal, characteristic, complemented
8#68406—34nomaximal
9C32×#127C2211yescharacteristic
10#64145—21no—
11#64145—21no—
12#64144—22no—
13D4×C3⋊Dic3—21no—
14D4×C3⋊Dic3—21no—
15C2×#3746—21no—
16#64078C2211yescharacteristic
17C4×#634C2211yescharacteristic
18C4×#634C2211yescharacteristic
19C32×C4⋊C8C2211yescharacteristic
20C32×C4⋊C8C2211yescharacteristic
21#63659—22no—
22#63644—21no—
23#63643—21no—
24#63643—21no—
25C4×C3⋊(C3⋊C8)C2211yescharacteristic
26#5713—34no—
27#5070—34no—
28#4851—34no—
29#4849—34no—
30C3×#331D314yes—
31#4484—34no—
32#4484—34no—
33C2×C32×D4—21no—
34C2×C32×D4—21no—
35C2×C32×D4D412yes—
36C22×C3⋊Dic3—22no—
37C2×#634—21no—
38C2×#634D411yescharacteristic
39C2×#634D411yescharacteristic
40C2×C32×C8—21no—
41C2×C32×C8—21no—
42C32×C42C2311yescharacteristic
43#3757—22no—
44#3757—22no—
45#3757—22no—
46C4⋊(C3⋊Dic3)—21no—
47C4⋊(C3⋊Dic3)—21no—
48C4⋊(C3⋊Dic3)D411yescharacteristic
49C4⋊(C3⋊Dic3)D411yescharacteristic
50#3750—21no—
51#3750—21no—
52C4×C3⋊Dic3—21no—
53C4×C3⋊Dic3—21no—
54C2×C3⋊(C3⋊C8)—21no—
55#3746—42no—
56#1640—91noSylow
57C3×#127C2×D314yes—
58#936—64no—
59#936—64no—
60#935—68no—
61D4×Dic3—64no—
62D4×Dic3—64no—
63C2×Dic12—64no—
64#869—34no—
65C4×Dic6—34no—
66C4×Dic6—34no—
67C3×C4⋊C8C2×D314yes—
68C3×C4⋊C8C2×D314yes—
69#832—68no—
70#817—64no—
71#816—64no—
72#816—64no—
73C4×C3⋊C8—34no—
74C23×C32—22no—
75C32×D4—42no—
76C32×D4—41no—
77C32×D4—41no—
78C32×D4—41no—
79C32×D4—41no—
80C2×C32×C4C2×D411yescharacteristic
81C2×C32×C4C2×D411yescharacteristic
82C2×C32×C4C2×D411yescharacteristic
83C2×C3⋊Dic3—21no—
84C2×C3⋊Dic3—21no—
85C2×C3⋊Dic3—21no—
86C2×C3⋊Dic3—21no—
87C2×C3⋊Dic3—41no—
88C2×C3⋊Dic3—82no—
89#634—21no—
90#634—21no—
91#634—21no—
92#634—21no—
93#634—41no—
94#634—41no—
95C32×C8—41no—
96C32×C8—41no—
97C3⋊(C3⋊C8)—41no—
98#559—91no—
99#486—91no—
100#475—91no—
101#462—91no—
102#331C3⋊D311yescharacteristic
103Q8⋊C8—91no—
104Q8⋊C8—91no—
105C2×C3×D4—24no—
106C2×C3×D4—24no—
107C2×C3×D4D1218yes—
108C22×Dic3—68no—
109C2×Dic6—34no—
110C2×Dic6—34no—
111C2×Dic6—64no—
112C2×C3×C8—24no—
113C2×C3×C8—24no—
114C3×C42C22×D314yes—
115#217—68no—
116#217—68no—
117#217—68no—
118C4⋊Dic3—34no—
119C4⋊Dic3—34no—
120C4⋊Dic3—64no—
121C4⋊Dic3—64no—
122Dic3⋊C4—64no—
123Dic3⋊C4—64no—
124C4×Dic3—64no—
125C4×Dic3—64no—
126C2×C3⋊C8—64no—
127Dic12—128no—
128C22×C32—42no—
129C22×C32—42no—
130C22×C32—42no—
131C22×C32#12011yescharacteristic
132C32×C4—21no—
133C32×C4#13511yescharacteristic
134C32×C4#13511yescharacteristic
135C32×C4AGL(1,ℤ/8)11yescharacteristic
136C32×C4#13711yescharacteristic
137C3⋊Dic3—41no—
138C3⋊Dic3—41no—
139C3⋊Dic3—41no—
140C3⋊Dic3—41no—
141C3⋊Dic3—81no—
142C2×Q16—181no—
143C4⋊Q8—91no—
144#127C2×C3⋊D311yescharacteristic
145#124—181no—
146#124—181no—
147#123—182no—
148C4×Q8—91no—
149C4×Q8—91no—
150C4×D4—181no—
151C4×D4—181no—
152#106—181no—
153C4⋊C8C2×C3⋊D311yescharacteristic
154C4⋊C8C2×C3⋊D311yescharacteristic
155#103—181no—
156#103—181no—
157#102—182no—
158C4×C8—91no—
159C23×C3—28no—
160C3×D4—48no—
161C3×D4—44no—
162C3×D4—44no—
163C3×D4—44no—
164C3×D4—44no—
165C2×C3×C4C2×D1214yes—
166C2×C3×C4D3×D414yes—
167C2×C3×C4D3×D414yes—
168C2×Dic3—64no—
169C2×Dic3—64no—
170C2×Dic3—64no—
171C2×Dic3—64no—
172C2×Dic3—124no—
173C2×Dic3—248no—
174Dic6—64no—
175Dic6—64no—
176Dic6—64no—
177Dic6—64no—
178Dic6—124no—
179Dic6—124no—
180C3×C8—44no—
181C3×C8—44no—
182C3⋊C8—124no—
183C2×C32—82no—
184C2×C32#44911yescharacteristic
185C2×C32#45211yescharacteristic
186C2×C32#45511yescharacteristic
187C2×Q8—91no—
188C2×Q8—91no—
189C2×Q8—181no—
190C2×D4—21no—
191C2×D4—21no—
192C2×D4C4⋊(C3⋊D3)12yes—
193C22×C4—182no—
194Q16—362no—
195C2×C8—21no—
196C2×C8—21no—
197C2×C8—181no—
198C4⋊C4—91no—
199C4⋊C4—91no—
200C4⋊C4—181no—
201C4⋊C4—181no—
202C4⋊C4—181no—
203C4⋊C4—181no—
204C22⋊C4—182no—
205C22⋊C4—182no—
206C22⋊C4—182no—
207C42—181no—
208C42—181no—
209C42C22×C3⋊D311yescharacteristic
210C22×C3—48no—
211C22×C3—48no—
212C22×C3—48no—
213C22×C3#88214yes—
214C3×C4—24no—
215C3×C4#91114yes—
216C3×C4#91214yes—
217C3×C4#91514yes—
218C3×C4#91614yes—
219Dic3—124no—
220Dic3—124no—
221Dic3—124no—
222Dic3—124no—
223Dic3—244no—
224C32#164011yescharacteristic, complemented, Sylow
225C23—22no—
226Q8—181no—
227Q8—181no—
228Q8—181no—
229Q8—181no—
230Q8—361no—
231Q8—361no—
232D4—42no—
233D4—41no—
234D4—41no—
235D4—41no—
236D4—41no—
237C2×C4—181no—
238C2×C4—181no—
239C2×C4—181no—
240C2×C4—181no—
241C2×C4—361no—
242C2×C4—722no—
243C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
244C2×C4D4×C3⋊D311yescharacteristic
245C2×C4D4×C3⋊D311yescharacteristic
246C8—41no—
247C8—41no—
248C8—361no—
249C2×C3—88no—
250C2×C3#474614yes—
251C2×C3#478114yes—
252C2×C3#478314yes—
253C22—42no—
254C22—42no—
255C22—42no—
256C22#6409111yescharacteristic
257C4—21no—
258C4—361no—
259C4—361no—
260C4—361no—
261C4—361no—
262C4—721no—
263C4#6412011yescharacteristic
264C4#6412111yescharacteristic
265C4#6412411yescharacteristic
266C4#6412511yescharacteristic
267C3#6840614yescomplemented
268C2—82no—
269C2#1059244511yescharacteristic
270C2#1059248011yescharacteristic
271C2#1059248211yescharacteristic
subgroupG/H
centerC22#64091
commutator, cosocleC32×C42C23
FrattiniC42C22×C3⋊D3
FittingC32×#331C2
socleC22×C32#120
prime radicalC32×#127C22
hypercenter#331C3⋊D3
hypocenterC32#1640
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
3. #10592550C2semidirect
4. #10592548C2semidirect
6. #10589350C2semidirect
7. #10589350C2semidirect
224. C32#1640semidirect
267. C3#68406semidirect

Maximal subgroups

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

subgroupindex
#105961842
#105927692
#105925502
#105925482
C32×#3312
#105893502
#684063