Finite Group Databasebeta

← #11797936

Subgroups — #11797936

Order 1152.

336 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 76 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#10592593C211yesmaximal, characteristic
2#10590819C211yesmaximal, characteristic, complemented
3#10590642C211yesmaximal, characteristic
4C3×#4496C211yesmaximal, characteristic, complemented
5C3×#4494C211yesmaximal, characteristic, complemented
6#10589125C211yesmaximal, characteristic
7#10589106C211yesmaximal, characteristic, complemented
8#69309—31nomaximal
9#69264—31nomaximal
10#64116—21no—
11#64113C2211yescharacteristic
12C2×C3×Dic12C2211yescharacteristic
13#63843—21no—
14C32×#108C2211yescharacteristic
15#63652—21no—
16#63642C2211yescharacteristic
17C3×#817C2211yescharacteristic
18C3×#812C2211yescharacteristic
19C3×#812C2211yescharacteristic
20#63565—21no—
21#63551C412yescomplemented
22#63549C412yescomplemented
23#5184—31no—
24#5179—31no—
25#4909—31no—
26#4894—31no—
27#4894—31no—
28#4894—61no—
29#4853—31no—
30C3×#365—31no—
31C3×#362—31no—
32#4518—31no—
33#4512—31no—
34#4512—31no—
35#4496D311yescharacteristic, complemented
36#4494D311yescharacteristic, complemented
37#4488—31no—
38#3828—21no—
39C2×C3×Dic6—21no—
40C32×M16—21no—
41C2×C32×C8C2311yescharacteristic
42C4×C3⋊Dic3D411yescharacteristic
43C2×C3⋊(C3⋊C8)D411yescharacteristic
44#3746C2×C411yescharacteristic
45#3745C2×C411yescharacteristic
46#3744—21no—
47#3743—41no—
48C8×C3⋊D3—41no—
49C3×C4⋊Dic3—21no—
50C3×Dic12—21no—
51C3×Dic12C2×C412yes—
52Dic3⋊Dic3—41no—
53Dic32—41no—
54C3×C3⋊C16—21no—
55C3×C3⋊C16C2×C412yes—
56#2180—91noSylow
57C2×C3×Q16—31no—
58Q8×Dic3—61no—
59#907—61no—
60#907—61no—
61#907—62no—
62C2×Dic12C2×D311yescharacteristic
63#904—31no—
64#904—31no—
65#904—61no—
66#887—61no—
67C3×M32—31no—
68C3×M32—31no—
69C3×#108—21no—
70C3×#108C2×D311yescharacteristic
71C3×#108C2×D311yescharacteristic
72C3×#106—31no—
73#835—61no—
74#829—32no—
75#828—32no—
76#825—61no—
77#825—61no—
78#825—62no—
79#817C2×D311yescharacteristic
80#815—31no—
81#815—31no—
82#815—61no—
83#812C2×D311yescharacteristic
84#812C2×D311yescharacteristic
85#810—61no—
86Dic24—32no—
87#800—32no—
88C2×C32×C4C2×D411yescharacteristic
89#638—41no—
90C2×C3⋊Dic3—21no—
91C4⋊(C3⋊D3)—21no—
92C4×C3⋊D3—41no—
93#634—21no—
94C2×C3×Dic3—41no—
95C2×C3×Dic3—41no—
96C3×Dic6—22no—
97C3×Dic6—41no—
98C32×C8—41no—
99C32×C8C22×C411yescharacteristic
100C32×C8#4111yescharacteristic
101C3⋊(C3⋊C8)—21no—
102#510—91no—
103#444—91no—
104#441—91no—
105#365—31no—
106#362—31no—
107#360—91no—
108#347—91no—
109C2×C3×Q8—61no—
110#235—62no—
111#235—61no—
112#235—61no—
113C2×Dic6—21no—
114C3×Q16—32no—
115C3×Q16—61no—
116C3×M16—22no—
117C3×M16—21no—
118C3×M16—21no—
119C2×C3×C8—21no—
120C2×C3×C8C22×D311yescharacteristic
121C2×C3×C8C22×D311yescharacteristic
122C3×C4⋊C4—61no—
123C4⋊Dic3—21no—
124C4⋊Dic3—121no—
125Dic3⋊C4—121no—
126C4×Dic3—31no—
127C4×Dic3—31no—
128C4×Dic3—61no—
129C4×Dic3—121no—
130C4×Dic3—121no—
131C2×C3⋊C8—31no—
132C2×C3⋊C8—31no—
133C2×C3⋊C8—61no—
134Dic12—21no—
135Dic12—31no—
136Dic12—31no—
137Dic12—61no—
138Dic12C4×D312yes—
139D24—31no—
140D24—31no—
141D24—61no—
142#204—62no—
143#204—61no—
144#204—61no—
145ΓL(1,𝔽25)—122no—
146ΓL(1,𝔽25)—121no—
147ΓL(1,𝔽25)—121no—
148D3×C8—122no—
149D3×C8—121no—
150D3×C8—121no—
151C3×C16—32no—
152C3×C16—61no—
153C3⋊C16—21no—
154C3⋊C16C4×D312yes—
155C22×C32AGL(1,ℤ/8)11yescharacteristic
156C2×C3⋊D3—41no—
157C32×C4C4×D411yescharacteristic
158C32×C4AGL(1,ℤ/8)11yescharacteristic
159C3⋊Dic3—41no—
160C3⋊Dic3—41no—
161C3×Dic3—42no—
162C3×Dic3—81no—
163#135—91no—
164C2×Q16—31no—
165#131—181no—
166C4×Q8—181no—
167Q32—92no—
168SD32—92no—
169M32—31no—
170M32—31no—
171#108D3211yescharacteristic
172#106—31no—
173#104—181no—
174#103—181no—
175#97—91no—
176C3×Q8—62no—
177C3×Q8—121no—
178C2×C3×C4—21no—
179C2×C3×C4—121no—
180C2×C3×C4—121no—
181C2×C3×C4D3×D411yescharacteristic
182C2×C3×C4D3×D411yescharacteristic
183#67—122no—
184#67—121no—
185#67—121no—
186C2×Dic3—41no—
187C2×Dic3—41no—
188C2×Dic3—61no—
189C2×Dic3—61no—
190C2×Dic3—121no—
191D12—62no—
192D12—61no—
193D12—61no—
194C4×D3—122no—
195C4×D3—121no—
196C4×D3—121no—
197Dic6—22no—
198Dic6—41no—
199Dic6—62no—
200Dic6—61no—
201Dic6—61no—
202C3×C8—21no—
203C3×C8—21no—
204C3×C8—42no—
205C3×C8—41no—
206C3×C8—41no—
207C3×C8C2×C4×D311yescharacteristic
208C3×C8C2×C4×D311yescharacteristic
209C3×C8#23711yescharacteristic
210C3×C8#23911yescharacteristic
211C3⋊C8—62no—
212C3⋊C8—61no—
213C3⋊C8—61no—
214C2×C32—21no—
215C2×C32#44211yescharacteristic
216C3⋊D3—81no—
217#41—181no—
218C2×Q8—61no—
219Q16—32no—
220Q16—61no—
221Q16—91no—
222SD16—181no—
223D8—91no—
224M16—21no—
225M16—361no—
226C2×C8—91no—
227C2×C8—361no—
228C2×C8C2×D3211yescharacteristic
229C4⋊C4—61no—
230C4⋊C4—361no—
231C42—91no—
232C42—361no—
233C16—32no—
234C16—61no—
235C22×C3—21no—
236C22×C3#91411yescharacteristic
237C22×C3#91411yescharacteristic
238C2×D3—122no—
239C2×D3—121no—
240C2×D3—121no—
241C3×C4—21no—
242C3×C4—21no—
243C3×C4—122no—
244C3×C4—241no—
245C3×C4#67⋊C411yescharacteristic
246C3×C4#89311yescharacteristic
247C3×C4#91111yescharacteristic
248C3×C4#91411yescharacteristic
249Dic3—42no—
250Dic3—81no—
251Dic3—122no—
252Dic3—121no—
253Dic3—121no—
254Dic3—121no—
255Dic3—121no—
256Dic3—241no—
257C32#218011yescharacteristic, complemented, Sylow
258Q8—62no—
259Q8—121no—
260Q8—181no—
261D4—181no—
262D4—361no—
263C2×C4—121no—
264C2×C4—121no—
265C2×C4—181no—
266C2×C4—361no—
267C2×C4#381111yescharacteristic
268C8—41no—
269C8—181no—
270C8#379611yescharacteristic
271C8C4×D3211yescharacteristic
272C2×C3—21no—
273C2×C3—21no—
274C2×C3—21no—
275C2×C3—41no—
276C2×C3#478511yescharacteristic
277C2×C3#486911yescharacteristic
278D3—242no—
279D3—241no—
280D3—241no—
281C22—361no—
282C22#6394111yescharacteristic
283C4—122no—
284C4—241no—
285C4—361no—
286C4—361no—
287C4#6388111yescharacteristic
288C4#6393711yescharacteristic
289C3—21no—
290C3#6926411yescharacteristic, complemented
291C3#6930911yescharacteristic, complemented
292C2—21no—
293C2—721no—
294C2#1059046211yescharacteristic
subgroupG/H
centerC2#10590462
commutatorC32×C8C22×C4
FrattiniC2×C8C2×D32
FittingC32×#108C22
socleC2×C32#442
prime radical#64113C22
cosocleC2×C32×C8C23
hypercenter#108D32
hypocenterC32#2180
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #108

Complements

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

NH ≅ G/Ntype
2. #10590819C2semidirect
4. C3×#4496C2semidirect
5. C3×#4494C2semidirect
7. #10589106C2semidirect
21. #63551C4semidirect
22. #63549C4semidirect
35. #4496D3semidirect
36. #4494D3semidirect
257. C32#2180semidirect
290. C3#69264semidirect
291. C3#69309semidirect

Maximal subgroups

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

subgroupindex
#105925932
#105908192
#105906422
C3×#44962
C3×#44942
#105891252
#105891062
#693093
#692643