Finite Group Databasebeta

← #11792405

Subgroups — #11792405

Order 1152.

1182 conjugacy classes of subgroups; only the 179 normal subgroups are shown.

normal subgroups only

This group has 1182 conjugacy classes of subgroups — too many to draw. Only its 179 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#10596219C211yesmaximal, characteristic, complemented
2#10595995C212yesmaximal, complemented
3#10592825C211yesmaximal, characteristic, complemented
4#10592704C212yesmaximal, complemented
5C32×H(3,ℤ/4)C211yesmaximal, characteristic, complemented
6#68703—34nomaximal
7C2×#3828C2212yes—
8C22×C4×C3⋊D3C2211yescharacteristic
9C2×C32×M16C2211yescharacteristic
10C32×#117C2212yes—
11C2×#3748C2211yescharacteristic
12#64118—22no—
13#64117—22no—
14#64113—22no—
15#64106—22no—
16#64104—22no—
17#64095—22no—
18#64091—22no—
19C4×C4⋊(C3⋊D3)—24no—
20#63647—22no—
21#63632—24no—
22#5748—34no—
23#5524—38no—
24#5126—34no—
25#5005—38no—
26C3×H(3,ℤ/4)D314yescomplemented
27C23×C3⋊D3D411yescharacteristic
28C22×C32×C4C2311yescharacteristic
29C2×#638—22no—
30C22×C3⋊Dic3D411yescharacteristic
31#3828—22no—
32#3828—22no—
33#3828—22no—
34#3828—22no—
35C2×C4⋊(C3⋊D3)—24no—
36C2×C4⋊(C3⋊D3)D412yescomplemented
37C2×C4×C3⋊D3—22no—
38C2×C4×C3⋊D3—22no—
39C2×C4×C3⋊D3—22no—
40C2×C4×C3⋊D3—21no—
41C2×C4×C3⋊D3—21no—
42C2×#634D412yescomplemented
43C32×M16—22no—
44C2×C32×C8D412yescomplemented
45C32×C4⋊C4—22no—
46C32×C22⋊C4—22no—
47C32×C42D414yescomplemented
48#3752—24no—
49#3752—24no—
50C4⋊(C3⋊Dic3)—24no—
51#3748—22no—
52C2×C3⋊(C3⋊C8)—21no—
53#3746—22no—
54#3745—22no—
55#3744—24no—
56#2010—91noSylow
57C2×#235—38no—
58C22×C4×D3—34no—
59C2×C3×M16C2×D314yes—
60C3×#117C2×D318yes—
61C2×#208—34no—
62#909—68no—
63#908—68no—
64#904—68no—
65#897—68no—
66#895—68no—
67#886—68no—
68#882—68no—
69C4×D12—616no—
70(C2×D3)⋊C8—68no—
71#805—616no—
72C23×C32C2×D411yescharacteristic
73C22×C3⋊D3—22no—
74C22×C3⋊D3—21no—
75C22×C3⋊D3—22no—
76C22×C3⋊D3—42no—
77C2×C32×C4—24no—
78C2×C32×C4C2×D411yescharacteristic
79C2×C32×C4C2×D412yes—
80C2×C32×C4C2×D412yes—
81C2×C32×C4#4111yescharacteristic
82#638—42no—
83#638—42no—
84C2×C3⋊Dic3—22no—
85C2×C3⋊Dic3—22no—
86C2×C3⋊Dic3—21no—
87C4⋊(C3⋊D3)—22no—
88C4⋊(C3⋊D3)—22no—
89C4⋊(C3⋊D3)—48no—
90C4×C3⋊D3—41no—
91C4×C3⋊D3—42no—
92C4×C3⋊D3—42no—
93C4×C3⋊D3—41no—
94C4×C3⋊D3—42no—
95#634—22no—
96#634—22no—
97C32×C8—22no—
98C3⋊(C3⋊C8)—41no—
99#575—91no—
100#525—92no—
101#421—92no—
102#407—91no—
103H(3,ℤ/4)C3⋊D311yescharacteristic, complemented
104C23×D3—34no—
105C22×C3×C4C22×D314yes—
106C2×#67—68no—
107C22×Dic3—34no—
108#235—68no—
109#235—68no—
110#235—68no—
111#235—68no—
112C2×D12—38no—
113C2×D12—616no—
114C2×C4×D3—64no—
115C2×C4×D3—68no—
116C2×C4×D3—68no—
117C2×C4×D3—68no—
118C2×C4×D3—64no—
119C2×Dic6—38no—
120C3×M16—28no—
121C2×C3×C8D1218yescomplemented
122C3×C4⋊C4—28no—
123C3×C22⋊C4—28no—
124C3×C42D12116yescomplemented
125(C2×D3)⋊C4—616no—
126(C2×D3)⋊C4—616no—
127C4⋊Dic3—616no—
128#208—68no—
129C2×C3⋊C8—64no—
130Dic12—68no—
131D24—68no—
132#204—616no—
133C22×C32—41no—
134C22×C32#12012yes—
135C22×C32#12111yescharacteristic
136C2×C3⋊D3—24no—
137C2×C3⋊D3—22no—
138C2×C3⋊D3—42no—
139C2×C3⋊D3—41no—
140C2×C3⋊D3—41no—
141C2×C3⋊D3—44no—
142C2×C3⋊D3—42no—
143C32×C4—44no—
144C32×C4#12011yescharacteristic
145C32×C4#12112yes—
146C32×C4#12711yescharacteristic
147C3⋊Dic3—42no—
148C3⋊Dic3—41no—
149C2×#41—92no—
150C23×C4—91no—
151#137—182no—
152AGL(1,ℤ/8)—182no—
153#135—182no—
154C2×M16—91no—
155C2×M16C2×C3⋊D311yescharacteristic
156#123—182no—
157C22⋊Q8—182no—
158#121—182no—
159#120—182no—
160C4×D4—184no—
161#117C2×C3⋊D312yes—
162#104—184no—
163C22⋊C8—182no—
164C23×C3D3×D414yes—
165C22×D3—68no—
166C22×D3—64no—
167C22×D3—68no—
168C22×D3—128no—
169C2×C3×C4—216no—
170C2×C3×C4C2×D1214yes—
171C2×C3×C4C2×D1218yes—
172C2×C3×C4D3×D418yes—
173C2×C3×C4#23914yes—
174#67—128no—
175#67—128no—
176C2×Dic3—68no—
177C2×Dic3—68no—
178C2×Dic3—64no—
179D12—68no—
180D12—68no—
181D12—1232no—
182C4×D3—124no—
183C4×D3—128no—
184C4×D3—124no—
185C4×D3—128no—
186C4×D3—128no—
187Dic6—68no—
188Dic6—68no—
189C3×C8—28no—
190C3⋊C8—124no—
191C2×C32—22no—
192C2×C32—21no—
193C2×C32#39211yescharacteristic
194C3⋊D3—42no—
195C3⋊D3—82no—
196C24—91no—
197#41—182no—
198#41—182no—
199#41—182no—
200#41—182no—
201C2×Q8—92no—
202C2×D4—92no—
203C2×D4—184no—
204C2×D4—182no—
205C22×C4—91no—
206C22×C4—181no—
207C22×C4—182no—
208C22×C4—182no—
209C22×C4—182no—
210C22×C4—181no—
211C22×C4C22×C3⋊D311yescharacteristic
212Q16—182no—
213SD16—184no—
214D8—182no—
215M16—22no—
216M16—182no—
217C2×C8—181no—
218C2×C8C4⋊(C3⋊D3)12yescomplemented
219C4⋊C4—22no—
220C4⋊C4—184no—
221C22⋊C4—22no—
222C22⋊C4—184no—
223C22⋊C4—184no—
224C42C4⋊(C3⋊D3)14yescomplemented
225C22×C3—44no—
226C22×C3#88218yes—
227C22×C3#89514yes—
228C2×D3—616no—
229C2×D3—68no—
230C2×D3—128no—
231C2×D3—124no—
232C2×D3—124no—
233C2×D3—1216no—
234C2×D3—128no—
235C3×C4—416no—
236C3×C4#87414yes—
237C3×C4#88214yes—
238C3×C4#89518yes—
239Dic3—128no—
240Dic3—124no—
241C32#201011yescharacteristic, complemented, Sylow
242C23—182no—
243C23—181no—
244C23—182no—
245C23—362no—
246C23D4×C3⋊D311yescharacteristic
247Q8—182no—
248Q8—182no—
249D4—182no—
250D4—182no—
251D4—368no—
252D4—362no—
253D4—362no—
254C2×C4—24no—
255C2×C4—182no—
256C2×C4—182no—
257C2×C4—181no—
258C2×C4—361no—
259C2×C4—362no—
260C2×C4—361no—
261C2×C4—362no—
262C2×C4—362no—
263C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
264C2×C4C2×C4⋊(C3⋊D3)12yes—
265C2×C4D4×C3⋊D312yes—
266C2×C4#383211yescharacteristic
267C8—22no—
268C8—361no—
269C2×C3—28no—
270C2×C3—24no—
271C2×C3#467114yes—
272D3—128no—
273D3—248no—
274C22—41no—
275C22—184no—
276C22—182no—
277C22—362no—
278C22—361no—
279C22—364no—
280C22—361no—
281C22—362no—
282C22#6409112yes—
283C22#6410411yescharacteristic
284C4—44no—
285C4—361no—
286C4—362no—
287C4#6408311yescharacteristic
288C4#6409111yescharacteristic
289C4#6410412yes—
290C3#6870314yescomplemented
291C2—22no—
292C2—21no—
293C2—362no—
294C2—722no—
295C2#1059237011yescharacteristic
subgroupG/H
centerC4#64083
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C22×C3⋊D3
FittingC32×H(3,ℤ/4)C2
socleC2×C32#392
hypercenterH(3,ℤ/4)C3⋊D3
hypocenterC32#2010
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ H(3,ℤ/4)

Complements

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

NH ≅ G/Ntype
1. #10596219C2semidirect
2. #10595995C2semidirect
3. #10592825C2semidirect
4. #10592704C2semidirect
5. C32×H(3,ℤ/4)C2semidirect
26. C3×H(3,ℤ/4)D3semidirect
36. C2×C4⋊(C3⋊D3)D4semidirect
42. C2×#634D4semidirect
44. C2×C32×C8D4semidirect
47. C32×C42D4semidirect
103. H(3,ℤ/4)C3⋊D3semidirect
121. C2×C3×C8D12semidirect
124. C3×C42D12semidirect
218. C2×C8C4⋊(C3⋊D3)semidirect
224. C42C4⋊(C3⋊D3)semidirect
241. C32#2010semidirect
290. C3#68703semidirect

Maximal subgroups

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

subgroupindex
#105962192
#105959952
#105928252
#105927042
C32×H(3,ℤ/4)2
#687033