Finite Group Databasebeta

← #11788158

Subgroups — #11788158

Order 1152.

1326 conjugacy classes of subgroups; only the 245 normal subgroups are shown.

normal subgroups only

This group has 1326 conjugacy classes of subgroups — too many to draw. Only its 245 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#10596262C211yesmaximal, characteristic
2C22×C4×C3⋊Dic3C211yesmaximal, characteristic, complemented
3C32×#407C211yesmaximal, characteristic, complemented
4C2×#63652C212yesmaximal, complemented
5#10589421C212yesmaximal, complemented
6#69965—34nomaximal
7C23×C32×C4C2211yescharacteristic
8C23×C3⋊Dic3—21no—
9C2×#3828C2211yescharacteristic
10C2×C32×M16C2212yes—
11#64162—21no—
12#64139C412yescomplemented
13#64138—21no—
14C4×#638—22no—
15#64135C2211yescharacteristic
16#64133C412yescomplemented
17C2×C4×C3⋊Dic3—21no—
18C2×C4×C3⋊Dic3—24no—
19C2×C4×C3⋊Dic3C2212yes—
20C32×C22⋊C8—22no—
21#63652—24no—
22#5791—34no—
23C22×C4×Dic3—34no—
24C3×#407D314yescomplemented
25C2×#825—38no—
26#4555—38no—
27C24×C32D411yescharacteristic
28C22×C32×C4—22no—
29C22×C32×C4—22no—
30C22×C32×C4C2×C412yes—
31C22×C32×C4D411yescharacteristic
32C22×C32×C4D412yes—
33C22×C32×C4C2311yescharacteristic
34C2×#638—22no—
35C2×#638—21no—
36C22×C3⋊Dic3—28no—
37C22×C3⋊Dic3—24no—
38C22×C3⋊Dic3—22no—
39#3828—22no—
40#3828—22no—
41C2×C4⋊(C3⋊D3)C2×C411yescharacteristic, complemented
42C2×C4×C3⋊D3—21no—
43C2×#634C2×C411yescharacteristic, complemented
44C32×M16—22no—
45C32×M16—22no—
46C2×C32×C8—22no—
47#3757—22no—
48#3757—21no—
49#3752—22no—
50C4⋊(C3⋊Dic3)C2×C412yescomplemented
51#3750—22no—
52C4×C3⋊Dic3—24no—
53C4×C3⋊Dic3—22no—
54C4×C3⋊Dic3—21no—
55C4×C3⋊Dic3D414yescomplemented
56#1896—91noSylow
57C23×C3×C4C2×D314yes—
58C23×Dic3—64no—
59C2×#235—34no—
60C2×C3×M16C2×D318yes—
61#953—64no—
62#930—38no—
63#929—64no—
64C4×#67—68no—
65#926—34no—
66#924—38no—
67C2×C4×Dic3—38no—
68C2×C4×Dic3—616no—
69C2×C4×Dic3—64no—
70C3×C22⋊C8—28no—
71#825—616no—
72C23×C32—24no—
73C23×C32—21no—
74C23×C32—21no—
75C23×C32C22⋊C412yes—
76C23×C32C2×D411yescharacteristic
77C22×C3⋊D3—21no—
78C2×C32×C4—21no—
79C2×C32×C4—21no—
80C2×C32×C4—24no—
81C2×C32×C4—24no—
82C2×C32×C4C22⋊C412yes—
83C2×C32×C4C22×C411yescharacteristic
84C2×C32×C4C2×D412yes—
85C2×C32×C4C2×D411yescharacteristic
86C2×C32×C4#4112yes—
87#638—44no—
88#638—41no—
89#638—41no—
90C2×C3⋊Dic3—216no—
91C2×C3⋊Dic3—28no—
92C2×C3⋊Dic3—24no—
93C2×C3⋊Dic3—22no—
94C2×C3⋊Dic3—21no—
95C4⋊(C3⋊D3)—22no—
96C4×C3⋊D3—42no—
97#634—22no—
98C32×C8—42no—
99#525—91no—
100C22×C42—91no—
101C2×#104—92no—
102#407C3⋊D311yescharacteristic, complemented
103#339—92no—
104C24×C3D1214yes—
105C22×C3×C4—28no—
106C22×C3×C4—28no—
107C22×C3×C4C4×D318yes—
108C22×C3×C4D1214yes—
109C22×C3×C4#6718yes—
110C22×C3×C4C22×D314yes—
111C2×#67—68no—
112C2×#67—64no—
113C22×Dic3—616no—
114C22×Dic3—632no—
115C22×Dic3—68no—
116#235—68no—
117#235—68no—
118C2×D12—34no—
119C2×C4×D3—64no—
120C2×Dic6—34no—
121C3×M16—28no—
122C3×M16—28no—
123C2×C3×C8—28no—
124#217—68no—
125#217—64no—
126(C2×D3)⋊C4—68no—
127C4⋊Dic3—38no—
128Dic3⋊C4—68no—
129C4×Dic3—316no—
130C4×Dic3—616no—
131C4×Dic3—68no—
132C4×Dic3—64no—
133C22×C32—24no—
134C22×C32—24no—
135C22×C32—22no—
136C22×C32—22no—
137C22×C32—22no—
138C22×C32#10414yescomplemented
139C22×C32C2×C22⋊C411yescharacteristic
140C22×C32#12011yescharacteristic
141C22×C32#12311yescharacteristic
142C2×C3⋊D3—41no—
143C2×C3⋊D3—42no—
144C32×C4—22no—
145C32×C4C4×D412yes—
146C32×C4#12112yes—
147C3⋊Dic3—28no—
148C3⋊Dic3—41no—
149C3⋊Dic3—42no—
150C2×#41—91no—
151C23×C4—181no—
152C23×C4C2×C3⋊D311yescharacteristic
153C2×M16C2×C3⋊D312yes—
154#123—181no—
155C22⋊Q8—92no—
156#121—92no—
157#120—181no—
158C4×D4—182no—
159#117—91no—
160C2×C42—92no—
161C2×C42—184no—
162C2×C42—181no—
163#104—184no—
164C22⋊C8—22no—
165C23×C3—216no—
166C23×C3—24no—
167C23×C3—24no—
168C23×C3(C2×D3)⋊C418yes—
169C23×C3C2×D1214yes—
170C22×D3—64no—
171C2×C3×C4—24no—
172C2×C3×C4—24no—
173C2×C3×C4—216no—
174C2×C3×C4—216no—
175C2×C3×C4(C2×D3)⋊C418yes—
176C2×C3×C4C2×C4×D314yes—
177C2×C3×C4D3×D418yes—
178C2×C3×C4#23718yes—
179C2×C3×C4C2×#6714yes—
180#67—1216no—
181#67—124no—
182#67—124no—
183C2×Dic3—664no—
184C2×Dic3—632no—
185C2×Dic3—616no—
186C2×Dic3—68no—
187C2×Dic3—64no—
188D12—68no—
189C4×D3—128no—
190Dic6—68no—
191C3×C8—48no—
192C2×C32—21no—
193C2×C32—24no—
194C2×C32—21no—
195C2×C32#38611yescharacteristic
196C2×C32C2×#10412yes—
197C3⋊D3—81no—
198C24C4⋊(C3⋊D3)11yescharacteristic
199#41—182no—
200#41—182no—
201C2×Q8—91no—
202C2×D4—91no—
203C2×D4—182no—
204C2×D4—181no—
205C22×C4—22no—
206C22×C4—22no—
207C22×C4—184no—
208C22×C4—188no—
209C22×C4—182no—
210C22×C4—181no—
211C22×C4C4×C3⋊D312yes—
212C22×C4C4⋊(C3⋊D3)11yescharacteristic
213C22×C4#63812yes—
214C22×C4C22×C3⋊D311yescharacteristic
215M16—22no—
216M16—22no—
217C2×C8—22no—
218C4⋊C4—92no—
219C4⋊C4—182no—
220C22⋊C4—182no—
221C22⋊C4—181no—
222C22⋊C4—182no—
223C42—94no—
224C42—184no—
225C42—182no—
226C42—181no—
227C22×C3—216no—
228C22×C3—216no—
229C22×C3—28no—
230C22×C3—28no—
231C22×C3—28no—
232C22×C3#825116yescomplemented
233C22×C3#88214yes—
234C22×C3#88614yes—
235C22×C3C2×(C2×D3)⋊C414yes—
236C2×D3—128no—
237C2×D3—124no—
238C3×C4—28no—
239C3×C4#67⋊C418yes—
240C3×C4#93918yes—
241Dic3—632no—
242Dic3—128no—
243Dic3—124no—
244C32#189611yescharacteristic, complemented, Sylow
245C23—21no—
246C23—21no—
247C23—24no—
248C23—181no—
249C23#375212yes—
250C23C2×C4⋊(C3⋊D3)11yescharacteristic
251Q8—182no—
252D4—182no—
253D4—361no—
254D4—361no—
255D4—364no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—24no—
259C2×C4—24no—
260C2×C4—1816no—
261C2×C4—188no—
262C2×C4—184no—
263C2×C4—182no—
264C2×C4—181no—
265C2×C4—362no—
266C2×C4#375212yes—
267C2×C4C2×C4×C3⋊D311yescharacteristic
268C2×C4D4×C3⋊D312yes—
269C2×C4#383012yes—
270C2×C4C2×#63811yescharacteristic
271C8—42no—
272C2×C3—24no—
273C2×C3—216no—
274C2×C3—24no—
275C2×C3#495814yes—
276C2×C3C2×#82518yes—
277D3—244no—
278C22—24no—
279C22—24no—
280C22—22no—
281C22—22no—
282C22—22no—
283C22—362no—
284C22—361no—
285C22#6365214yescomplemented
286C22#6409111yescharacteristic
287C22#6409511yescharacteristic
288C22C2×#375211yescharacteristic
289C4—22no—
290C4—188no—
291C4—362no—
292C4—361no—
293C4#6409012yes—
294C4#6414812yes—
295C3#6996514yescomplemented
296C2—21no—
297C2—21no—
298C2—24no—
299C2—721no—
300C2#1059265711yescharacteristic
301C2C2×#6365212yes—
subgroupG/H
centerC2×C4C2×#638
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC32×#407C2
socleC22×C32C2×C22⋊C4
prime radical#10596262C2
cosocleC22×C32×C4C23
hypercenter#407C3⋊D3
hypocenterC32#1896
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
2. C22×C4×C3⋊Dic3C2semidirect
3. C32×#407C2semidirect
4. C2×#63652C2semidirect
5. #10589421C2semidirect
12. #64139C4semidirect
16. #64133C4semidirect
24. C3×#407D3semidirect
41. C2×C4⋊(C3⋊D3)C2×C4semidirect
43. C2×#634C2×C4semidirect
50. C4⋊(C3⋊Dic3)C2×C4semidirect
55. C4×C3⋊Dic3D4semidirect
102. #407C3⋊D3semidirect
138. C22×C32#104semidirect
232. C22×C3#825semidirect
244. C32#1896semidirect
285. C22#63652semidirect
295. C3#69965semidirect

Maximal subgroups

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

subgroupindex
#105962622
C22×C4×C3⋊Dic32
C32×#4072
C2×#636522
#105894212
#699653