Finite Group Databasebeta

← #11787852

Subgroups — #11787852

Order 1152.

793 conjugacy classes of subgroups; only the 132 normal subgroups are shown.

normal subgroups only

This group has 793 conjugacy classes of subgroups — too many to draw. Only its 132 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
1C2×#64078C211yesmaximal, characteristic
2#10594828C211yesmaximal, characteristic
3#10591107C212yesmaximal
4C2×#63561C211yesmaximal, characteristic
5C3×#4523C212yesmaximal
6#68765—32nomaximal
7C22×#634C2211yescharacteristic
8C22×#634C2211yescharacteristic
9C2×C32×C42C2211yescharacteristic
10C2×C4⋊(C3⋊Dic3)—22no—
11#64078—22no—
12#64078C414yescomplemented
13C3×#926C2212yes—
14C2×C3×#208C2212yes—
15#63957—22no—
16#63844—24no—
17#63567—24no—
18#63561—22no—
19#5516—32no—
20C2×#869—32no—
21C2×#869—61no—
22C2×#824—32no—
23#5120—32no—
24#5004—32no—
25C3×#339—32no—
26#4523D312yes—
27C22×C32×C4—21no—
28C22×C32×C4C2311yescharacteristic
29C22×C3⋊Dic3—21no—
30C22×C3⋊Dic3D412yes—
31C2×#634—22no—
32C2×#634—22no—
33C2×#634—22no—
34C2×#634—22no—
35C2×#634—21no—
36C2×#634C2×C412yes—
37C2×#634C2×C412yes—
38C2×#634D412yes—
39C32×C42—21no—
40C32×C42C2×C412yes—
41C4⋊(C3⋊Dic3)—28no—
42C3×#217—22no—
43C3×C4⋊Dic3D414yes—
44C3×C4×Dic3—22no—
45C3×#208—22no—
46C3×#208—22no—
47C2×C3×C3⋊C8—22no—
48#3724—24no—
49Dic32—24no—
50#1886—91noSylow
51C22×Dic6—32no—
52C22×Dic6—32no—
53C22×Dic6—61no—
54C22×Dic6—61no—
55C2×C3×M16—32no—
56C3×#117—32no—
57C2×C3×C42—21no—
58C2×C3×C42C2×D312yes—
59#926C2×D312yes—
60C2×C4⋊Dic3—64no—
61C2×C4⋊Dic3—64no—
62C2×#208C2×D312yes—
63#887—64no—
64#877—64no—
65#869—38no—
66#869—64no—
67#869—64no—
68#869—64no—
69C4×Dic6—64no—
70#824—64no—
71#816—64no—
72#810—64no—
73C23×C32C2×D411yescharacteristic
74C2×C32×C4—24no—
75C2×C32×C4—22no—
76C2×C32×C4C22×C411yescharacteristic
77C2×C32×C4C2×D412yes—
78C2×C32×C4C2×D411yescharacteristic
79C2×C32×C4#4112yes—
80C2×C3⋊Dic3—22no—
81C2×C3⋊Dic3—22no—
82C2×C3⋊Dic3—22no—
83C2×C3⋊Dic3—41no—
84C2×C3⋊Dic3—41no—
85C2×C3⋊Dic3C22⋊C414yes—
86#634—24no—
87#634—24no—
88#634—24no—
89#634—42no—
90C2×C3×Dic3—24no—
91C3×C3⋊C8—42no—
92C2×C4⋊Q8—91no—
93#519—91no—
94#419—92no—
95C2×#101—91no—
96#339—32no—
97C22×C3×C4—22no—
98C22×C3×C4—22no—
99C22×C3×C4—21no—
100C22×C3×C4C22×D312yes—
101C22×Dic3—34no—
102C22×Dic3—62no—
103C22×Dic3—62no—
104C22×Dic3—62no—
105C2×Dic6—34no—
106C2×Dic6—34no—
107C2×Dic6—34no—
108C2×Dic6—62no—
109C2×Dic6—62no—
110C2×Dic6—62no—
111C2×Dic6—62no—
112C2×Dic6—62no—
113C2×Dic6—62no—
114C2×Dic6—62no—
115C2×Dic6—62no—
116C2×Dic6—62no—
117C2×Dic6—62no—
118C2×Dic6—62no—
119C2×Dic6—62no—
120C2×Dic6—62no—
121C2×Dic6—122no—
122C2×Dic6—122no—
123C2×Dic6—122no—
124C2×Dic6—122no—
125C3×M16—62no—
126C3×M16—62no—
127C2×C3×C8—62no—
128C3×C4⋊C4—34no—
129C3×C22⋊C4—62no—
130C3×C42—22no—
131C3×C42—22no—
132C3×C42—22no—
133C3×C42—62no—
134C3×C42C4×D314yes—
135#217—22no—
136C4⋊Dic3—616no—
137C4⋊Dic3—616no—
138C4⋊Dic3D1214yes—
139Dic3⋊C4—68no—
140C4×Dic3—22no—
141C4×Dic3—68no—
142#208—22no—
143#208—22no—
144C2×C3⋊C8—22no—
145C22×C32—22no—
146C22×C32C2×C22⋊C411yescharacteristic
147C22×C32#12011yescharacteristic
148C22×C32#12311yescharacteristic
149C32×C4—24no—
150C32×C4C4×D412yes—
151C32×C4#12112yes—
152C3⋊Dic3—24no—
153C3⋊Dic3—42no—
154C3×Dic3—44no—
155C22×Q8—91no—
156C22×Q8—91no—
157C2×M16—32no—
158C4⋊Q8—94no—
159C4⋊Q8—182no—
160C4×Q8—184no—
161#117—32no—
162#117—182no—
163C2×C4⋊C4—182no—
164C2×C42D3211yescharacteristic
165#103—184no—
166#101—182no—
167C23×C3—21no—
168C23×C3D3×D412yes—
169C2×C3×C4—24no—
170C2×C3×C4—28no—
171C2×C3×C4—28no—
172C2×C3×C4—24no—
173C2×C3×C4—22no—
174C2×C3×C4—22no—
175C2×C3×C4—21no—
176C2×C3×C4—21no—
177C2×C3×C4—64no—
178C2×C3×C4C2×C4×D312yes—
179C2×C3×C4C2×D1212yes—
180C2×C3×C4#23512yes—
181C2×C3×C4D3×D412yes—
182C2×C3×C4D3×D412yes—
183C2×C3×C4#23912yes—
184C2×Dic3—24no—
185C2×Dic3—38no—
186C2×Dic3—64no—
187C2×Dic3—64no—
188C2×Dic3—64no—
189C2×Dic3—64no—
190C2×Dic3—64no—
191C2×Dic3—122no—
192C2×Dic3—122no—
193C2×Dic3—122no—
194C2×Dic3—122no—
195C2×Dic3—122no—
196C2×Dic3—122no—
197Dic6—64no—
198Dic6—64no—
199Dic6—64no—
200Dic6—64no—
201Dic6—64no—
202Dic6—64no—
203Dic6—124no—
204Dic6—124no—
205Dic6—124no—
206Dic6—124no—
207Dic6—122no—
208Dic6—122no—
209C3×C8—122no—
210C3⋊C8—42no—
211C2×C32—21no—
212C2×C32—21no—
213C2×C32#38611yescharacteristic
214C2×C32#45612yes—
215C2×Q8—92no—
216C2×Q8—92no—
217C2×Q8—92no—
218C2×Q8—182no—
219C2×Q8—182no—
220C2×Q8—181no—
221C2×Q8—182no—
222C2×Q8—182no—
223C22×C4—21no—
224C22×C4—92no—
225C22×C4—181no—
226C22×C4C2×D3211yescharacteristic
227M16—62no—
228M16—62no—
229C2×C8—62no—
230C4⋊C4—34no—
231C4⋊C4—188no—
232C4⋊C4—184no—
233C22⋊C4—62no—
234C42—21no—
235C42—62no—
236C42—184no—
237C42#62412yes—
238C22×C3—24no—
239C22×C3—24no—
240C22×C3—21no—
241C22×C3—21no—
242C22×C3—21no—
243C22×C3D3×C22⋊C412yes—
244C22×C3#88212yes—
245C22×C3#89412yes—
246C3×C4—28no—
247C3×C4—28no—
248C3×C4—22no—
249C3×C4—22no—
250C3×C4—124no—
251C3×C4C4×D1212yes—
252C3×C4#88412yes—
253C3×C4#89312yes—
254C3×C4#89512yes—
255Dic3—44no—
256Dic3—68no—
257Dic3—124no—
258Dic3—124no—
259Dic3—124no—
260C32#188611yescharacteristic, complemented, Sylow
261C23#381111yescharacteristic
262Q8—184no—
263Q8—184no—
264Q8—184no—
265Q8—362no—
266C2×C4—24no—
267C2×C4—22no—
268C2×C4—64no—
269C2×C4—94no—
270C2×C4—182no—
271C2×C4—182no—
272C2×C4—182no—
273C2×C4—361no—
274C2×C4—361no—
275C2×C4#379912yes—
276C2×C4D3×D1212yes—
277C2×C4C2×#62411yescharacteristic
278C2×C4#381111yescharacteristic
279C8—122no—
280C2×C3—22no—
281C2×C3—22no—
282C2×C3—22no—
283C2×C3—22no—
284C2×C3—21no—
285C2×C3—22no—
286C2×C3#466512yes—
287C2×C3#482614yes—
288C22—22no—
289C22#6389711yescharacteristic
290C22#6392311yescharacteristic
291C22#6397411yescharacteristic
292C4—24no—
293C4—124no—
294C4—184no—
295C4—362no—
296C4#6389412yes—
297C4#6391012yes—
298C3—21no—
299C3#6876512yescomplemented
300C2—21no—
301C2—21no—
302C2#1059040112yes—
303C2#1059138011yescharacteristic
subgroupG/H
centerC22#63923
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C42C22
socleC22×C32#120
prime radicalC23×C32C2×D4
cosocleC22×C32×C4C23
hypercenterC2×C42D32
hypocenterC32#1886
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
12. #64078C4semidirect
260. C32#1886semidirect
299. C3#68765semidirect

Maximal subgroups

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

subgroupindex
C2×#640782
#105948282
#105911072
C2×#635612
C3×#45232
#687653