Finite Group Databasebeta

← #11861027

Subgroups — #11861027

Order 1152.

738 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 738 conjugacy classes of subgroups — too many to draw. Only its 149 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#10596500C211yesmaximal, characteristic
2#10594669C212yesmaximal, complemented
3C2×C8×#157C211yesmaximal, characteristic, complemented
4#10593331C211yesmaximal, characteristic, complemented
5#10593325C212yesmaximal, complemented
6#10593299C214yesmaximal, complemented
7#10593297C214yesmaximal, complemented
8#64306C2212yes—
9C2×C4×#157C2211yescharacteristic
10C2×#3787C2211yescharacteristic
11#64237C414yescomplemented
12#64228C411yescharacteristic, complemented
13#64227C412yescomplemented
14#64225C411yescharacteristic, complemented
15#64223C2214yes—
16C2×C8×C3⋊D3C2211yescharacteristic
17C3×#901—22no—
18#63818C2212yes—
19#63815—22no—
20#63805C2214yescomplemented
21#63803C2214yescomplemented
22#63791—22no—
23D32×C8—22no—
24C8×#157C2212yescomplemented
25C8×#157C2212yescomplemented
26#63733C2214yescomplemented
27#63731C2218yescomplemented
28D3×#131—62no—
29C22×#157—21no—
30C2×C4×C3⋊D3C2311yescharacteristic
31C3×#235—22no—
32#3811—22no—
33#3805C2×C414yes—
34#3802C2×C412yes—
35C4×D32—22no—
36#3798C2314yes—
37#3797C2×C412yes—
38#3796—22no—
39C2×#622C2×C412yes—
40C4×#157—21no—
41C4×#157C2312yes—
42#3787C2×C411yescharacteristic
43#3787C2×C411yescharacteristic
44#3787C2312yes—
45#3776C2×C414yescomplemented
46#3775C2×C418yescomplemented
47#3774C2×C414yescomplemented
48C2×C32×C8D411yescharacteristic
49C2×C3⋊(C3⋊C8)D411yescharacteristic
50C8×C3⋊D3D411yescharacteristic
51C8×C3⋊D3D411yescharacteristic
52C8×C3⋊D3C2311yescharacteristic
53C8×C3⋊D3C2311yescharacteristic
54C3×#208—22no—
55C3×ΓL(1,𝔽25)—24no—
56C3×D3×C8—24no—
57#3712C2314yes—
58#3711—24no—
59#3710—22no—
60D3×C3⋊C8—24no—
61C2×#443—91nomaximal, Sylow
62D3×#41—62no—
63C3×#131—62no—
64#948—62no—
65#907—64no—
66#907—62no—
67D3×M16—62no—
68D3×M16—64no—
69#901—22no—
70#901—64no—
71C2×D3×C8—62no—
72C2×D3×C8—64no—
73C22×C3⋊D3#4111yescharacteristic
74C2×D32—22no—
75C2×#157—24no—
76C2×#157—22no—
77C2×C32×C4C2×D411yescharacteristic
78C2×C3⋊Dic3C22×C411yescharacteristic
79C4×C3⋊D3C22×C411yescharacteristic
80C4×C3⋊D3C2×D411yescharacteristic
81C4×C3⋊D3#4111yescharacteristic
82C4×C3⋊D3C2411yescharacteristic
83C3×#67—24no—
84C3×D12—22no—
85C3×C4×D3—24no—
86C3×Dic6—22no—
87#627C22×C414yes—
88#626—24no—
89#625C22×C414yes—
90#624—22no—
91D3×Dic3—24no—
92#622C22×C412yes—
93#622C22×C412yes—
94C32×C8C2×D411yescharacteristic
95C32×C8C2×D411yescharacteristic
96C3⋊(C3⋊C8)C2×D411yescharacteristic
97C3⋊(C3⋊C8)C2×D411yescharacteristic
98C3×C3⋊C8—24no—
99C2×#135—91no—
100C2×#131—92no—
101#443—94no—
102#443—94no—
103C2×#108—91no—
104C2×#104—92no—
105C2×C4×C8—91no—
106C3×#41—62no—
107#239—62no—
108D3×Q8—62no—
109#237—64no—
110#237—62no—
111D3×D4—62no—
112D3×D4—64no—
113#235—22no—
114#235—64no—
115C2×C4×D3—62no—
116C2×C4×D3—64no—
117C3×M16—64no—
118C3×M16—62no—
119C2×C3×C8—22no—
120C2×C3×C8—64no—
121#208—22no—
122#208—64no—
123C2×C3⋊C8—62no—
124C2×C3⋊C8—64no—
125ΓL(1,𝔽25)—24no—
126ΓL(1,𝔽25)—64no—
127ΓL(1,𝔽25)—64no—
128D3×C8—24no—
129D3×C8—62no—
130D3×C8—62no—
131D3×C8—62no—
132D3×C8—62no—
133D3×C8—64no—
134D3×C8—64no—
135C22×C32C4×D411yescharacteristic
136C2×C3⋊D3—22no—
137C2×C3⋊D3C4×D411yescharacteristic
138C2×C3⋊D3C2×#4111yescharacteristic
139C2×C3×D3—24no—
140D32—44no—
141#157—24no—
142C32×C4C4×D411yescharacteristic
143C32×C4C22×D411yescharacteristic
144C3⋊Dic3C4×D411yescharacteristic
145C3⋊Dic3C23×C411yescharacteristic
146C3×Dic3—24no—
147C2×#41—92no—
148#135—94no—
149#135—94no—
150C2×Q16—91no—
151C2×SD16—92no—
152C2×D8—91no—
153#131—62no—
154#131—94no—
155#131—94no—
156#131—182no—
157C2×M16—92no—
158C2×M16—182no—
159C22×C8—91no—
160C22×C8—91no—
161C22×C8—182no—
162C2×C42—91no—
163#108—94no—
164#104—98no—
165C4×C8—92no—
166C4×C8—92no—
167C22×D3—62no—
168C22×D3—64no—
169C3×Q8—62no—
170C3×D4—62no—
171C3×D4—64no—
172C2×C3×C4—22no—
173C2×C3×C4—64no—
174#67—24no—
175#67—64no—
176#67—64no—
177C2×Dic3—62no—
178C2×Dic3—64no—
179D12—22no—
180D12—64no—
181C4×D3—24no—
182C4×D3—62no—
183C4×D3—62no—
184C4×D3—62no—
185C4×D3—62no—
186C4×D3—64no—
187C4×D3—64no—
188Dic6—22no—
189Dic6—64no—
190C3×C8—22no—
191C3×C8—22no—
192C3×C8—64no—
193C3⋊C8—24no—
194C3⋊C8—62no—
195C3⋊C8—62no—
196C2×C32—21no—
197C2×C32C2×C4×D411yescharacteristic
198C3⋊D3—21no—
199C3⋊D3#44312yescomplemented
200C3×D3—44no—
201#41—62no—
202#41—94no—
203#41—94no—
204#41—182no—
205C2×Q8—92no—
206C2×D4—92no—
207C2×D4—182no—
208C22×C4—91no—
209C22×C4—182no—
210C22×C4—181no—
211Q16—94no—
212SD16—98no—
213D8—94no—
214M16—62no—
215M16—64no—
216M16—94no—
217M16—184no—
218C2×C8—64no—
219C2×C8—92no—
220C2×C8—91no—
221C2×C8—91no—
222C2×C8—92no—
223C2×C8—91no—
224C2×C8—91no—
225C2×C8—91no—
226C2×C8—91no—
227C2×C8—91no—
228C2×C8—182no—
229C2×C8—184no—
230C2×C8GO+(4,𝔽2)11yescharacteristic
231C42—92no—
232C42—181no—
233C22×C3—22no—
234C22×C3—64no—
235C2×D3—24no—
236C2×D3—62no—
237C2×D3—62no—
238C2×D3—124no—
239C2×D3—128no—
240C3×C4—22no—
241C3×C4—22no—
242C3×C4—64no—
243Dic3—24no—
244Dic3—62no—
245Dic3—62no—
246C32C2×#44311yescharacteristic, complemented, Sylow
247C23—91no—
248C23—182no—
249Q8—62no—
250Q8—94no—
251D4—64no—
252D4—62no—
253D4—94no—
254D4—184no—
255C2×C4—64no—
256C2×C4—91no—
257C2×C4—91no—
258C2×C4—91no—
259C2×C4—91no—
260C2×C4—91no—
261C2×C4—182no—
262C2×C4—184no—
263C2×C4—182no—
264C2×C4—184no—
265C2×C4C2×GO+(4,𝔽2)11yescharacteristic
266C8—64no—
267C8—92no—
268C8—92no—
269C8—91no—
270C8—91no—
271C8C2×GO+(4,𝔽2)11yescharacteristic
272C8C2×GO+(4,𝔽2)11yescharacteristic
273C2×C3—22no—
274C2×C3—42no—
275C2×C3—124no—
276D3—44no—
277D3—64no—
278D3—122no—
279C22—64no—
280C22—91no—
281C22—91no—
282C22—182no—
283C22—364no—
284C22C4×GO+(4,𝔽2)11yescharacteristic
285C4—64no—
286C4—91no—
287C4—91no—
288C4—184no—
289C4C4×GO+(4,𝔽2)11yescharacteristic
290C4C22×GO+(4,𝔽2)11yescharacteristic
291C3—22no—
292C2—21no—
293C2—92no—
294C2—124no—
295C2—181no—
296C2C2×C4×GO+(4,𝔽2)11yescharacteristic
subgroupG/H
centerC8C2×GO+(4,𝔽2)
commutatorC3⋊Dic3C23×C4
FrattiniC4C22×GO+(4,𝔽2)
FittingC2×C32×C8D4
socleC2×C32C2×C4×D4
prime radical#10596500C2
cosocleC4×C3⋊D3C24
hypercenterC2×C8GO+(4,𝔽2)
hypocenterC32C2×#443
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C8 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
2. #10594669C2semidirect
3. C2×C8×#157C2semidirect
4. #10593331C2semidirect
5. #10593325C2semidirect
6. #10593299C2semidirect
7. #10593297C2semidirect
11. #64237C4semidirect
12. #64228C4semidirect
13. #64227C4semidirect
14. #64225C4semidirect
20. #63805C22semidirect
21. #63803C22semidirect
24. C8×#157C22semidirect
25. C8×#157C22semidirect
26. #63733C22semidirect
27. #63731C22semidirect
45. #3776C2×C4semidirect
46. #3775C2×C4semidirect
47. #3774C2×C4semidirect
199. C3⋊D3#443semidirect
246. C32C2×#443semidirect

Maximal subgroups

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

subgroupindex
#105965002
#105946692
C2×C8×#1572
#105933312
#105933252
#105932992
#105932972
C2×#4439