Finite Group Databasebeta

← #11792393

Subgroups — #11792393

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
1C32×#575C211yesmaximal, characteristic, complemented
2#10596299C212yesmaximal, complemented
3#10592935C212yesmaximal, complemented
4#10592825C211yesmaximal, characteristic, complemented
5#10589423C211yesmaximal, characteristic, complemented
6#72118—34nomaximal
7C2×C32×#41C2212yes—
8C22×C4×C3⋊D3C2211yescharacteristic
9C32×#137—22no—
10C32×AGL(1,ℤ/8)—22no—
11C32×#135—22no—
12C2×C32×M16C2211yescharacteristic
13#64155—22no—
14#64147—22no—
15#64146—22no—
16#64144—22no—
17C4×#638—24no—
18#64135C2212yes—
19C2×#3748C2211yescharacteristic
20#63664—24no—
21#63647—22no—
22C3×#575D314yescomplemented
23#5828—38no—
24#5236—38no—
25#5126—34no—
26#4557—34no—
27C23×C3⋊D3D411yescharacteristic
28C32×#41—22no—
29C32×#41—22no—
30C32×#41—22no—
31C32×#41—22no—
32C2×C32×Q8D412yescomplemented
33C2×C32×D4—22no—
34C2×C32×D4D412yescomplemented
35C22×C32×C4—22no—
36C22×C32×C4C2311yescharacteristic
37C2×#638—24no—
38C22×C3⋊Dic3D411yescharacteristic
39C2×C4×C3⋊D3—22no—
40C2×C4×C3⋊D3—22no—
41C2×C4×C3⋊D3—21no—
42C2×C4×C3⋊D3—21no—
43C32×Q16—22no—
44C32×SD16—24no—
45C32×D8—22no—
46C32×M16—22no—
47C2×C32×C8D412yescomplemented
48#3757—24no—
49#3757—22no—
50#3752—24no—
51C4⋊(C3⋊Dic3)—22no—
52#3750—24no—
53C4×C3⋊Dic3D414yescomplemented
54#3748—22no—
55C2×C3⋊(C3⋊C8)—21no—
56#2010—91noSylow
57C2×C3×#41C2×D318yes—
58C22×C4×D3—34no—
59C3×#137—28no—
60C3×AGL(1,ℤ/8)—28no—
61C3×#135—28no—
62C2×C3×M16C2×D314yes—
63#946—68no—
64#938—68no—
65#937—68no—
66#935—68no—
67C4×#67—616no—
68#926—38no—
69C2×#208—34no—
70#837—616no—
71(C2×D3)⋊C8—68no—
72C23×C32—22no—
73C23×C32C2×D411yescharacteristic
74C22×C3⋊D3—22no—
75C22×C3⋊D3—21no—
76C22×C3⋊D3—42no—
77C32×Q8—22no—
78C32×Q8—22no—
79C32×D4—22no—
80C32×D4—22no—
81C32×D4—42no—
82C32×D4—42no—
83C2×C32×C4—22no—
84C2×C32×C4—42no—
85C2×C32×C4—42no—
86C2×C32×C4C2×D412yes—
87C2×C32×C4C2×D412yes—
88C2×C32×C4C2×D411yescharacteristic
89C2×C32×C4#4111yescharacteristic
90#638—48no—
91C2×C3⋊Dic3—24no—
92C2×C3⋊Dic3—22no—
93C2×C3⋊Dic3—21no—
94C4×C3⋊D3—41no—
95C4×C3⋊D3—42no—
96C4×C3⋊D3—41no—
97C32×C8—22no—
98C3⋊(C3⋊C8)—41no—
99#575C3⋊D311yescharacteristic, complemented
100#525—92no—
101#421—92no—
102#407—91no—
103H(3,ℤ/4)—91no—
104C23×D3—34no—
105C3×#41—28no—
106C3×#41—28no—
107C3×#41—28no—
108C3×#41—28no—
109C2×C3×Q8#6718yescomplemented
110C2×C3×D4—28no—
111C2×C3×D4#6718yescomplemented
112C22×C3×C4—28no—
113C22×C3×C4C22×D314yes—
114C2×#67—616no—
115C22×Dic3—34no—
116C2×C4×D3—68no—
117C2×C4×D3—64no—
118C2×C4×D3—64no—
119C2×C4×D3—68no—
120C3×Q16—28no—
121C3×SD16—216no—
122C3×D8—28no—
123C3×M16—28no—
124C2×C3×C8#6718yescomplemented
125#217—616no—
126#217—68no—
127(C2×D3)⋊C4—616no—
128C4⋊Dic3—68no—
129Dic3⋊C4—616no—
130C4×Dic3—316no—
131#208—68no—
132C2×C3⋊C8—64no—
133C22×C32—41no—
134C22×C32—44no—
135C22×C32—42no—
136C22×C32#12012yes—
137C22×C32#12111yescharacteristic
138C2×C3⋊D3—24no—
139C2×C3⋊D3—22no—
140C2×C3⋊D3—42no—
141C2×C3⋊D3—41no—
142C2×C3⋊D3—41no—
143C32×C4—42no—
144C32×C4#12011yescharacteristic
145C32×C4#12112yes—
146C32×C4#12711yescharacteristic
147C3⋊Dic3—44no—
148C3⋊Dic3—41no—
149C2×#41C2×C3⋊D312yes—
150C23×C4—91no—
151#137—22no—
152AGL(1,ℤ/8)—22no—
153#135—22no—
154C2×M16—91no—
155C2×M16C2×C3⋊D311yescharacteristic
156#123—182no—
157C22⋊Q8—182no—
158#121—182no—
159#120—182no—
160C4×D4—184no—
161#117—92no—
162#104—184no—
163C22⋊C8—182no—
164C23×C3—28no—
165C23×C3D3×D414yes—
166C22×D3—68no—
167C22×D3—64no—
168C22×D3—128no—
169C3×Q8—28no—
170C3×Q8—28no—
171C3×D4—28no—
172C3×D4—28no—
173C3×D4—48no—
174C3×D4—48no—
175C2×C3×C4—28no—
176C2×C3×C4—48no—
177C2×C3×C4—48no—
178C2×C3×C4D3×D418yes—
179C2×C3×C4#23714yes—
180C2×C3×C4C2×#6718yes—
181C2×C3×C4C2×#6714yes—
182#67—1232no—
183C2×Dic3—616no—
184C2×Dic3—68no—
185C2×Dic3—64no—
186C4×D3—128no—
187C4×D3—124no—
188C4×D3—124no—
189C3×C8—28no—
190C3⋊C8—124no—
191C2×C32—22no—
192C2×C32—21no—
193C2×C32—82no—
194C2×C32#39211yescharacteristic
195C3⋊D3—42no—
196C24—91no—
197#41—22no—
198#41—22no—
199#41—22no—
200#41—22no—
201C2×Q8#63812yescomplemented
202C2×D4—22no—
203C2×D4—184no—
204C2×D4#63812yescomplemented
205C22×C4—22no—
206C22×C4—91no—
207C22×C4—182no—
208C22×C4—181no—
209C22×C4—181no—
210C22×C4—182no—
211C22×C4C22×C3⋊D311yescharacteristic
212Q16—22no—
213SD16—24no—
214D8—22no—
215M16—22no—
216M16—182no—
217C2×C8—181no—
218C2×C8#63812yescomplemented
219C4⋊C4—184no—
220C4⋊C4—182no—
221C22⋊C4—184no—
222C22⋊C4—184no—
223C22⋊C4—182no—
224C42—94no—
225C22×C3—44no—
226C22×C3—416no—
227C22×C3—48no—
228C22×C3#93718yes—
229C22×C3#93814yes—
230C2×D3—616no—
231C2×D3—68no—
232C2×D3—128no—
233C2×D3—124no—
234C2×D3—124no—
235C3×C4—48no—
236C3×C4#93918yes—
237C3×C4#94014yes—
238C3×C4#95314yes—
239Dic3—1216no—
240Dic3—124no—
241C32#201011yescharacteristic, complemented, Sylow
242C23—22no—
243C23—182no—
244C23—181no—
245C23—362no—
246C23D4×C3⋊D311yescharacteristic
247Q8—22no—
248Q8—22no—
249D4—22no—
250D4—22no—
251D4—42no—
252D4—42no—
253D4—368no—
254C2×C4—22no—
255C2×C4—42no—
256C2×C4—42no—
257C2×C4—184no—
258C2×C4—182no—
259C2×C4—181no—
260C2×C4—362no—
261C2×C4—361no—
262C2×C4—361no—
263C2×C4D4×C3⋊D312yes—
264C2×C4#383011yescharacteristic
265C2×C4C2×#63812yes—
266C2×C4C2×#63811yescharacteristic
267C8—22no—
268C8—361no—
269C2×C3—28no—
270C2×C3—24no—
271C2×C3—88no—
272C2×C3#522314yes—
273D3—128no—
274C22—41no—
275C22—44no—
276C22—42no—
277C22—184no—
278C22—182no—
279C22—362no—
280C22—361no—
281C22—361no—
282C22#6414612yes—
283C22#6414711yescharacteristic
284C4—42no—
285C4—364no—
286C4—361no—
287C4#6414812yes—
288C4#6414911yescharacteristic
289C4#6416211yescharacteristic
290C3#7211814yescomplemented
291C2—22no—
292C2—21no—
293C2—82no—
294C2—362no—
295C2#1059292211yescharacteristic
subgroupG/H
centerC4#64149
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C22×C3⋊D3
FittingC32×#575C2
socleC2×C32#392
hypercenter#575C3⋊D3
hypocenterC32#2010
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ #575

Complements

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

NH ≅ G/Ntype
1. C32×#575C2semidirect
2. #10596299C2semidirect
3. #10592935C2semidirect
4. #10592825C2semidirect
5. #10589423C2semidirect
22. C3×#575D3semidirect
32. C2×C32×Q8D4semidirect
34. C2×C32×D4D4semidirect
47. C2×C32×C8D4semidirect
53. C4×C3⋊Dic3D4semidirect
99. #575C3⋊D3semidirect
109. C2×C3×Q8#67semidirect
111. C2×C3×D4#67semidirect
124. C2×C3×C8#67semidirect
201. C2×Q8#638semidirect
204. C2×D4#638semidirect
218. C2×C8#638semidirect
241. C32#2010semidirect
290. C3#72118semidirect

Maximal subgroups

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

subgroupindex
C32×#5752
#105962992
#105929352
#105928252
#105894232
#721183