Finite Group Databasebeta

← #11776590

Subgroups — #11776590

Order 1152.

684 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 684 conjugacy classes of subgroups — too many to draw. Only its 143 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
1C3⋊D3×C4⋊Q8C211yesmaximal, characteristic
2#10592534C211yesmaximal, characteristic
3#10592534C211yesmaximal, characteristic
4C32×#332C211yesmaximal, characteristic, complemented
5#10589413C211yesmaximal, characteristic, complemented
6#10589352C211yesmaximal, characteristic, complemented
7#10589348C211yesmaximal, characteristic, complemented
8#68428—34nomaximal
9C2×Q8×C3⋊D3—21no—
10C32×C4⋊Q8C2211yescharacteristic
11#64153—21no—
12C4⋊C4×C3⋊D3—21no—
13C4⋊C4×C3⋊D3C412yes—
14#64097—21no—
15#64097C412yes—
16C42×C3⋊D3C2211yescharacteristic
17#64078C2211yescharacteristic
18C32×C4⋊C8C2211yescharacteristic
19C32×C4⋊C8C2211yescharacteristic
20#63647—21no—
21#63647—21no—
22#63642—21no—
23#63642—21no—
24C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
25C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
26D3×C4⋊Q8—34no—
27#4835—34no—
28#4835—34no—
29C3×#332D314yescomplemented
30#4547—34no—
31#4486—34no—
32#4482—34no—
33C2×C32×Q8—21no—
34Q8×C3⋊D3—42no—
35Q8×C3⋊D3—42no—
36C2×C4×C3⋊D3—22no—
37C2×C4×C3⋊D3C2×C411yescharacteristic
38C2×C4×C3⋊D3D411yescharacteristic
39C2×C4×C3⋊D3D411yescharacteristic
40C2×#634—21no—
41C2×#634—22no—
42C2×C32×C8—21no—
43C2×C32×C8—21no—
44C32×C4⋊C4—21no—
45C32×C4⋊C4C2×C412yes—
46C32×C42C2311yescharacteristic
47C4⋊(C3⋊Dic3)—21no—
48C4⋊(C3⋊Dic3)C2×C412yes—
49#3750—22no—
50#3750—22no—
51C4×C3⋊Dic3C2×C411yescharacteristic
52C4×C3⋊Dic3D411yescharacteristic
53C4×C3⋊Dic3D411yescharacteristic
54C2×C3⋊(C3⋊C8)—21no—
55C2×C3⋊(C3⋊C8)—21no—
56#1556—91noSylow
57C2×D3×Q8—64no—
58C3×C4⋊Q8C2×D314yes—
59#944—64no—
60D3×C4⋊C4—38no—
61D3×C4⋊C4—64no—
62#888—38no—
63#888—64no—
64C42×D3—34no—
65#869—34no—
66C3×C4⋊C8C2×D314yes—
67C3×C4⋊C8C2×D314yes—
68(C2×D3)⋊C8—64no—
69(C2×D3)⋊C8—64no—
70#815—64no—
71#815—64no—
72C4⋊(C3⋊C8)—34no—
73C4⋊(C3⋊C8)—34no—
74C22×C3⋊D3C22⋊C411yescharacteristic
75C32×Q8—41no—
76C32×Q8—41no—
77C2×C32×C4—22no—
78C2×C32×C4C22×C411yescharacteristic
79C2×C32×C4C2×D411yescharacteristic
80C2×C32×C4C2×D411yescharacteristic
81C2×C3⋊Dic3—22no—
82C2×C3⋊Dic3C22⋊C411yescharacteristic
83C2×C3⋊Dic3C22⋊C411yescharacteristic
84C2×C3⋊Dic3C22⋊C411yescharacteristic
85C4×C3⋊D3—22no—
86C4×C3⋊D3—21no—
87C4×C3⋊D3—21no—
88C4×C3⋊D3—21no—
89C4×C3⋊D3—21no—
90C4×C3⋊D3—44no—
91#634—44no—
92#634—41no—
93#634—41no—
94C32×C8—41no—
95C32×C8—41no—
96C3⋊(C3⋊C8)—41no—
97C3⋊(C3⋊C8)—41no—
98C2×C4⋊Q8—91no—
99#432—91no—
100#432—91no—
101#332—91no—
102#332—91no—
103#332—91no—
104#332C3⋊D311yescharacteristic, complemented
105C2×C3×Q8—24no—
106D3×Q8—128no—
107D3×Q8—128no—
108C2×C4×D3—34no—
109C2×C4×D3—34no—
110C2×C4×D3—34no—
111C2×C4×D3—68no—
112C2×Dic6—68no—
113C2×Dic6—64no—
114C2×C3×C8—24no—
115C2×C3×C8—24no—
116C3×C4⋊C4—24no—
117C3×C4⋊C4C4×D318yes—
118C3×C42C22×D314yes—
119C4⋊Dic3—38no—
120C4⋊Dic3—64no—
121Dic3⋊C4—68no—
122Dic3⋊C4—68no—
123C4×Dic3—34no—
124C4×Dic3—34no—
125C4×Dic3—34no—
126C2×C3⋊C8—64no—
127C2×C3⋊C8—64no—
128C22×C32C2×C22⋊C411yescharacteristic
129C2×C3⋊D3—21no—
130C2×C3⋊D3—21no—
131C2×C3⋊D3#10112yes—
132C32×C4—21no—
133C32×C4—42no—
134C32×C4AGL(1,ℤ/8)11yescharacteristic
135C32×C4AGL(1,ℤ/8)11yescharacteristic
136C32×C4#13711yescharacteristic
137C32×C4#13711yescharacteristic
138C3⋊Dic3—21no—
139C3⋊Dic3—21no—
140C3⋊Dic3—21no—
141C3⋊Dic3—42no—
142C22×Q8—181no—
143C4⋊Q8—92no—
144C4⋊Q8—91no—
145C4⋊Q8—181no—
146C4⋊Q8—181no—
147C4⋊Q8C2×C3⋊D311yescharacteristic
148C2×C4⋊C4—92no—
149C2×C4⋊C4—181no—
150C2×C42—91no—
151C4⋊C8—91no—
152C4⋊C8—91no—
153C4⋊C8C2×C3⋊D311yescharacteristic
154C4⋊C8C2×C3⋊D311yescharacteristic
155C22⋊C8—181no—
156C22⋊C8—181no—
157#97—181no—
158#97—181no—
159C22×D3—34no—
160C3×Q8—44no—
161C3×Q8—44no—
162C2×C3×C4—28no—
163C2×C3×C4C2×C4×D314yes—
164C2×C3×C4D3×D414yes—
165C2×C3×C4D3×D414yes—
166C2×Dic3—34no—
167C2×Dic3—34no—
168C2×Dic3—34no—
169C2×Dic3—68no—
170C4×D3—68no—
171C4×D3—64no—
172C4×D3—64no—
173C4×D3—64no—
174C4×D3—64no—
175C4×D3—1216no—
176Dic6—1216no—
177Dic6—124no—
178Dic6—124no—
179C3×C8—44no—
180C3×C8—44no—
181C3⋊C8—124no—
182C3⋊C8—124no—
183C2×C32C2×#10111yescharacteristic
184C2×C32#41811yescharacteristic
185C2×C32#41911yescharacteristic
186C3⋊D3—22no—
187C2×Q8—21no—
188C2×Q8—182no—
189C2×Q8—181no—
190C2×Q8—362no—
191C2×Q8—362no—
192C22×C4—91no—
193C22×C4—91no—
194C22×C4—91no—
195C22×C4—182no—
196C2×C8—21no—
197C2×C8—21no—
198C2×C8—181no—
199C2×C8—181no—
200C4⋊C4—21no—
201C4⋊C4—92no—
202C4⋊C4—182no—
203C4⋊C4—182no—
204C4⋊C4—181no—
205C4⋊C4C4×C3⋊D312yes—
206C42—91no—
207C42—91no—
208C42—91no—
209C42C22×C3⋊D311yescharacteristic
210C22×C3D3×C22⋊C414yes—
211C2×D3—38no—
212C2×D3—64no—
213C2×D3—64no—
214C3×C4—24no—
215C3×C4—48no—
216C3×C4#91114yes—
217C3×C4#91414yes—
218C3×C4#91514yes—
219C3×C4#91814yes—
220Dic3—64no—
221Dic3—64no—
222Dic3—64no—
223Dic3—128no—
224C32#155611yescharacteristic, complemented, Sylow
225C23—91no—
226Q8—41no—
227Q8—41no—
228Q8—364no—
229Q8—361no—
230Q8—361no—
231C2×C4—22no—
232C2×C4—91no—
233C2×C4—91no—
234C2×C4—91no—
235C2×C4—182no—
236C2×C4—181no—
237C2×C4—181no—
238C2×C4—181no—
239C2×C4—181no—
240C2×C4—182no—
241C2×C4—364no—
242C2×C4C2×C4×C3⋊D311yescharacteristic
243C2×C4D4×C3⋊D311yescharacteristic
244C2×C4D4×C3⋊D311yescharacteristic
245C8—41no—
246C8—41no—
247C8—361no—
248C8—361no—
249C2×C3D3×#10114yes—
250C2×C3#477014yes—
251C2×C3#480214yes—
252D3—68no—
253C22—92no—
254C22—181no—
255C22—181no—
256C22C22⋊C4×C3⋊D311yescharacteristic
257C4—21no—
258C4—42no—
259C4—181no—
260C4—181no—
261C4—181no—
262C4—362no—
263C4#6412011yescharacteristic
264C4#6412311yescharacteristic
265C4#6412411yescharacteristic
266C4#6412711yescharacteristic
267C3#6842814yescomplemented
268C2—182no—
269C2C3⋊D3×#10111yescharacteristic
270C2#1059246911yescharacteristic
271C2#1059250111yescharacteristic
subgroupG/H
centerC22C22⋊C4×C3⋊D3
commutatorC2×C32×C4C22×C4
FrattiniC42C22×C3⋊D3
FittingC32×#332C2
socleC22×C32C2×C22⋊C4
prime radicalC22×C3⋊D3C22⋊C4
cosocleC32×C42C23
hypercenter#332C3⋊D3
hypocenterC32#1556
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
4. C32×#332C2semidirect
5. #10589413C2semidirect
6. #10589352C2semidirect
7. #10589348C2semidirect
29. C3×#332D3semidirect
104. #332C3⋊D3semidirect
224. C32#1556semidirect
267. C3#68428semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×C4⋊Q82
#105925342
C32×#3322
#105894132
#105893522
#105893482
#684283