Finite Group Databasebeta

← #11779151

Subgroups — #11779151

Order 1152.

630 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 630 conjugacy classes of subgroups — too many to draw. Only its 131 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#10596038C211yesmaximal, characteristic, complemented
2C32×#460C211yesmaximal, characteristic
3#10592774C211yesmaximal, characteristic
4#10592769C211yesmaximal, characteristic
5#10589401C211yesmaximal, characteristic, complemented
6#10589350C211yesmaximal, characteristic, complemented
7#10589348C211yesmaximal, characteristic, complemented
8#71034—34nomaximal
9C2×C32×SD16—21no—
10C32×#127C2211yescharacteristic
11C32×C4×Q8C2211yescharacteristic
12#64153—21no—
13C2×#3754—21no—
14#64098—22no—
15#64096—21no—
16#64079—21no—
17#64078C2211yescharacteristic
18C4×#634—21no—
19C4×#634C2211yescharacteristic
20C32×C4⋊C8C2211yescharacteristic
21C32×#102—21no—
22#63659—22no—
23#63659—21no—
24C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
25C4×C3⋊(C3⋊C8)C2211yescharacteristic
26#5567—34no—
27C3×#460D314yes—
28#5075—34no—
29#5070—34no—
30#4535—34no—
31#4484—34no—
32#4482—34no—
33C2×C32×Q8D411yescharacteristic
34C2×C32×D4—21no—
35C2×C32×D4—21no—
36C2×C32×D4—21no—
37C2×#634—21no—
38C2×#634D411yescharacteristic
39C32×SD16—42no—
40C2×C32×C8—21no—
41C32×C4⋊C4—21no—
42C32×C4⋊C4D411yescharacteristic
43C32×C42—21no—
44C32×C42C2311yescharacteristic
45#3754—42no—
46C4⋊(C3⋊Dic3)—21no—
47C4⋊(C3⋊Dic3)D411yescharacteristic
48C4⋊(C3⋊Dic3)D412yes—
49#3750—22no—
50#3750—22no—
51#3750—22no—
52#3750—21no—
53C4×C3⋊Dic3—22no—
54C4×C3⋊Dic3—21no—
55C2×C3⋊(C3⋊C8)—21no—
56C2×C3⋊(C3⋊C8)—21no—
57#1626—91noSylow
58C2×C3×SD16—24no—
59C3×#127C2×D314yes—
60C3×C4×Q8C2×D314yes—
61#944—64no—
62C2×#214—64no—
63#889—68no—
64#887—64no—
65#870—64no—
66#869—34no—
67C4×Dic6—34no—
68C4×Dic6—64no—
69C3×C4⋊C8C2×D314yes—
70C3×#102—24no—
71#832—68no—
72#832—64no—
73C4⋊(C3⋊C8)—34no—
74C4×C3⋊C8—34no—
75C23×C32—41no—
76C32×Q8—21no—
77C32×Q8—21no—
78C32×D4—42no—
79C32×D4—41no—
80C32×D4—41no—
81C32×D4—41no—
82C32×D4—41no—
83C2×C32×C4—21no—
84C2×C32×C4—21no—
85C2×C32×C4C2×D411yescharacteristic
86C2×C32×C4C2×D411yescharacteristic
87C2×C32×C4C2×D411yescharacteristic
88C2×C3⋊Dic3—21no—
89C2×C3⋊Dic3—21no—
90C2×C3⋊Dic3—22no—
91#634—21no—
92#634—41no—
93#634—41no—
94#634SD1612yescomplemented
95C32×C8—41no—
96C3⋊(C3⋊C8)—41no—
97C3⋊(C3⋊C8)—41no—
98#557—91no—
99#486—91no—
100#460—91no—
101#460C3⋊D311yescharacteristic
102#332—91no—
103Q8⋊C8—91no—
104Q8⋊C8—91no—
105C2×C3×Q8#6714yes—
106C2×C3×D4—24no—
107C2×C3×D4—24no—
108C2×C3×D4—24no—
109C2×Dic6—34no—
110C2×Dic6—64no—
111C3×SD16—48no—
112C2×C3×C8—24no—
113C3×C4⋊C4—24no—
114C3×C4⋊C4#6714yes—
115C3×C42—24no—
116C3×C42C22×D314yes—
117#214—128no—
118C4⋊Dic3—34no—
119C4⋊Dic3—38no—
120C4⋊Dic3—64no—
121Dic3⋊C4—68no—
122Dic3⋊C4—68no—
123Dic3⋊C4—68no—
124Dic3⋊C4—64no—
125C4×Dic3—68no—
126C4×Dic3—64no—
127C2×C3⋊C8—64no—
128C2×C3⋊C8—64no—
129C22×C32—81no—
130C22×C32—81no—
131C22×C32—81no—
132C22×C32#12011yescharacteristic
133C32×C4—21no—
134C32×C4—41no—
135C32×C4—41no—
136C32×C4C2×SD1611yescharacteristic
137C32×C4#13511yescharacteristic
138C32×C4AGL(1,ℤ/8)11yescharacteristic
139C32×C4#13711yescharacteristic
140C3⋊Dic3—22no—
141C3⋊Dic3—42no—
142C3⋊Dic3—41no—
143C2×SD16—21no—
144C2×SD16—181no—
145C4⋊Q8—91no—
146C4⋊Q8—181no—
147#127C2×C3⋊D311yescharacteristic
148#125—181no—
149#125—182no—
150C4×Q8—91no—
151C4×Q8—181no—
152C4×Q8—181no—
153C4×Q8C2×C3⋊D311yescharacteristic
154C4⋊C8—91no—
155C4⋊C8C2×C3⋊D311yescharacteristic
156#102—21no—
157#102—181no—
158#102—182no—
159C4×C8—91no—
160C23×C3—44no—
161C3×Q8—24no—
162C3×Q8—24no—
163C3×D4—48no—
164C3×D4—44no—
165C3×D4—44no—
166C3×D4—44no—
167C3×D4—44no—
168C2×C3×C4—24no—
169C2×C3×C4—24no—
170C2×C3×C4D3×D414yes—
171C2×C3×C4D3×D414yes—
172C2×C3×C4C2×#6714yes—
173C2×Dic3—64no—
174C2×Dic3—64no—
175C2×Dic3—68no—
176Dic6—38no—
177Dic6—64no—
178Dic6—124no—
179Dic6—124no—
180C3×C8—44no—
181C3⋊C8—124no—
182C3⋊C8—124no—
183C2×C32—161no—
184C2×C32#44811yescharacteristic
185C2×C32#44911yescharacteristic
186C2×C32#45411yescharacteristic
187C2×Q8—91no—
188C2×Q8—181no—
189C2×Q8#63811yescharacteristic
190C2×D4—21no—
191C2×D4—21no—
192C2×D4—21no—
193SD16—42no—
194SD16—362no—
195C2×C8—21no—
196C2×C8—181no—
197C2×C8—181no—
198C4⋊C4—21no—
199C4⋊C4—91no—
200C4⋊C4—92no—
201C4⋊C4—182no—
202C4⋊C4—182no—
203C4⋊C4—182no—
204C4⋊C4—181no—
205C4⋊C4—181no—
206C4⋊C4#63811yescharacteristic
207C42—21no—
208C42—182no—
209C42—181no—
210C42C22×C3⋊D311yescharacteristic
211C22×C3—84no—
212C22×C3—84no—
213C22×C3—84no—
214C22×C3#93714yes—
215C3×C4—24no—
216C3×C4—44no—
217C3×C4—44no—
218C3×C4D3×SD1614yes—
219C3×C4#91514yes—
220C3×C4#93214yes—
221C3×C4#95014yes—
222Dic3—68no—
223Dic3—124no—
224Dic3—128no—
225C32#162611yescharacteristic, complemented, Sylow
226C23—41no—
227Q8—21no—
228Q8—21no—
229Q8—92no—
230Q8—181no—
231Q8—361no—
232Q8—361no—
233D4—42no—
234D4—41no—
235D4—41no—
236D4—41no—
237D4—41no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—181no—
241C2×C4—181no—
242C2×C4—182no—
243C2×C4D4×C3⋊D311yescharacteristic
244C2×C4D4×C3⋊D311yescharacteristic
245C2×C4C2×#63811yescharacteristic
246C8—41no—
247C8—361no—
248C8—361no—
249C2×C3—164no—
250C2×C3#503714yes—
251C2×C3#517014yes—
252C2×C3#520114yes—
253C22—81no—
254C22—81no—
255C22—81no—
256C22#6414611yescharacteristic
257C4—21no—
258C4—41no—
259C4—41no—
260C4—182no—
261C4—361no—
262C4—362no—
263C4SD16×C3⋊D311yescharacteristic
264C4#6412411yescharacteristic
265C4#6414111yescharacteristic
266C4#6415911yescharacteristic
267C3#7103414yescomplemented
268C2—161no—
269C2#1059273611yescharacteristic
270C2#1059286911yescharacteristic
271C2#1059290011yescharacteristic
subgroupG/H
centerC22#64146
commutator, cosocleC32×C42C23
FrattiniC42C22×C3⋊D3
FittingC32×#460C2
socleC22×C32#120
prime radicalC32×#127C22
hypercenter#460C3⋊D3
hypocenterC32#1626
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
1. #10596038C2semidirect
5. #10589401C2semidirect
6. #10589350C2semidirect
7. #10589348C2semidirect
94. #634SD16semidirect
225. C32#1626semidirect
267. C3#71034semidirect

Maximal subgroups

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

subgroupindex
#105960382
C32×#4602
#105927742
#105927692
#105894012
#105893502
#105893482
#710343