Finite Group Databasebeta

← #11861074

Subgroups — #11861074

Order 1152.

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

normal subgroups only

This group has 730 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×#63767C211yesmaximal, characteristic, complemented
4#10593331C211yesmaximal, characteristic, complemented
5#10593325C212yesmaximal, complemented
6#10593298C218yesmaximal, complemented
7#64306C2212yes—
8C2×C4×#157C2211yescharacteristic
9C2×#3787C2211yescharacteristic
10#64237C414yescomplemented
11#64228C411yescharacteristic, complemented
12#64227C412yescomplemented
13#64225C411yescharacteristic, complemented
14#64223C2214yes—
15C2×C8×C3⋊D3C2211yescharacteristic
16C3×#901—22no—
17#63818C2212yes—
18#63815—22no—
19#63805C2214yescomplemented
20#63803C2214yescomplemented
21#63791—22no—
22D32×C8—22no—
23#63767C2214yescomplemented
24#63733C2214yescomplemented
25#63731C2218yescomplemented
26D3×#131—62no—
27C22×#157—21no—
28C2×C4×C3⋊D3C2311yescharacteristic
29C3×#235—22no—
30#3811—22no—
31#3805C2×C414yes—
32#3802C2×C412yes—
33C4×D32—22no—
34#3798C2314yes—
35#3797C2×C412yes—
36#3796—22no—
37C2×#622C2×C412yes—
38C4×#157—21no—
39C4×#157C2312yes—
40#3787C2×C411yescharacteristic
41#3787C2×C411yescharacteristic
42#3787C2312yes—
43#3776C2×C414yescomplemented
44#3775C2×C418yescomplemented
45#3774C2×C414yescomplemented
46C2×C32×C8D411yescharacteristic
47C2×C3⋊(C3⋊C8)D411yescharacteristic
48C8×C3⋊D3D412yes—
49C8×C3⋊D3C2312yes—
50C3×#208—22no—
51C3×ΓL(1,𝔽25)—24no—
52C3×D3×C8—24no—
53#3712C2314yes—
54#3711—24no—
55#3710—22no—
56D3×C3⋊C8—24no—
57C2×#444—91nomaximal, Sylow
58D3×#41—62no—
59C3×#131—62no—
60#948—62no—
61#907—64no—
62#907—62no—
63D3×M16—62no—
64D3×M16—64no—
65#901—22no—
66#901—64no—
67C2×D3×C8—62no—
68C2×D3×C8—64no—
69C22×C3⋊D3#4111yescharacteristic
70C2×D32—22no—
71C2×#157—22no—
72C2×#157—42no—
73C2×C32×C4C2×D411yescharacteristic
74C2×C3⋊Dic3C22×C411yescharacteristic
75C4×C3⋊D3C22×C411yescharacteristic
76C4×C3⋊D3C2×D411yescharacteristic
77C4×C3⋊D3#4111yescharacteristic
78C4×C3⋊D3C2411yescharacteristic
79C3×#67—24no—
80C3×D12—22no—
81C3×C4×D3—24no—
82C3×Dic6—22no—
83#627C22×C414yes—
84#626—24no—
85#625C22×C414yes—
86#624—22no—
87D3×Dic3—24no—
88#622C22×C412yes—
89#622C22×C412yes—
90C32×C8C2×D412yes—
91C3⋊(C3⋊C8)C2×D412yes—
92C3×C3⋊C8—24no—
93C2×#135—91no—
94C2×#131—92no—
95#444—98no—
96C2×#108—91no—
97C2×#104—92no—
98C2×#97—91no—
99C3×#41—62no—
100#239—62no—
101D3×Q8—62no—
102#237—64no—
103#237—62no—
104D3×D4—62no—
105D3×D4—64no—
106#235—22no—
107#235—64no—
108C2×C4×D3—62no—
109C2×C4×D3—64no—
110C3×M16—64no—
111C3×M16—62no—
112C2×C3×C8—22no—
113C2×C3×C8—64no—
114#208—22no—
115#208—64no—
116C2×C3⋊C8—62no—
117C2×C3⋊C8—64no—
118ΓL(1,𝔽25)—24no—
119ΓL(1,𝔽25)—64no—
120ΓL(1,𝔽25)—64no—
121D3×C8—24no—
122D3×C8—62no—
123D3×C8—62no—
124D3×C8—62no—
125D3×C8—62no—
126D3×C8—64no—
127D3×C8—64no—
128C22×C32C4×D411yescharacteristic
129C2×C3⋊D3—22no—
130C2×C3⋊D3C4×D411yescharacteristic
131C2×C3⋊D3C2×#4111yescharacteristic
132C2×C3×D3—24no—
133D32—44no—
134#157—42no—
135C32×C4C4×D411yescharacteristic
136C32×C4C22×D411yescharacteristic
137C3⋊Dic3C4×D411yescharacteristic
138C3⋊Dic3C23×C411yescharacteristic
139C3×Dic3—24no—
140C2×#41—92no—
141#135—94no—
142#135—94no—
143C2×Q16—91no—
144C2×SD16—92no—
145C2×D8—91no—
146#131—62no—
147#131—94no—
148#131—94no—
149#131—182no—
150C2×M16—92no—
151C2×M16—182no—
152C22×C8—91no—
153C22×C8—91no—
154C22×C8—182no—
155C2×C42—91no—
156#108—94no—
157#104—98no—
158#97—94no—
159C22×D3—62no—
160C22×D3—64no—
161C3×Q8—62no—
162C3×D4—62no—
163C3×D4—64no—
164C2×C3×C4—22no—
165C2×C3×C4—64no—
166#67—24no—
167#67—64no—
168#67—64no—
169C2×Dic3—62no—
170C2×Dic3—64no—
171D12—22no—
172D12—64no—
173C4×D3—24no—
174C4×D3—62no—
175C4×D3—62no—
176C4×D3—62no—
177C4×D3—62no—
178C4×D3—64no—
179C4×D3—64no—
180Dic6—22no—
181Dic6—64no—
182C3×C8—22no—
183C3×C8—22no—
184C3×C8—64no—
185C3⋊C8—24no—
186C3⋊C8—62no—
187C3⋊C8—62no—
188C2×C32—21no—
189C2×C32C2×C4×D411yescharacteristic
190C3⋊D3—21no—
191C3⋊D3#44412yescomplemented
192C3×D3—44no—
193#41—62no—
194#41—94no—
195#41—94no—
196#41—182no—
197C2×Q8—92no—
198C2×D4—92no—
199C2×D4—182no—
200C22×C4—91no—
201C22×C4—182no—
202C22×C4—181no—
203Q16—94no—
204SD16—98no—
205D8—94no—
206M16—62no—
207M16—64no—
208M16—94no—
209M16—184no—
210C2×C8—64no—
211C2×C8—92no—
212C2×C8—91no—
213C2×C8—91no—
214C2×C8—92no—
215C2×C8—91no—
216C2×C8—92no—
217C2×C8—92no—
218C2×C8—182no—
219C2×C8—184no—
220C2×C8GO+(4,𝔽2)11yescharacteristic
221C42—92no—
222C42—181no—
223C22×C3—22no—
224C22×C3—64no—
225C2×D3—24no—
226C2×D3—62no—
227C2×D3—62no—
228C2×D3—124no—
229C2×D3—128no—
230C3×C4—22no—
231C3×C4—22no—
232C3×C4—64no—
233Dic3—24no—
234Dic3—62no—
235Dic3—62no—
236C32C2×#44411yescharacteristic, complemented, Sylow
237C23—91no—
238C23—182no—
239Q8—62no—
240Q8—94no—
241D4—64no—
242D4—62no—
243D4—94no—
244D4—184no—
245C2×C4—64no—
246C2×C4—91no—
247C2×C4—91no—
248C2×C4—91no—
249C2×C4—91no—
250C2×C4—91no—
251C2×C4—182no—
252C2×C4—184no—
253C2×C4—182no—
254C2×C4—362no—
255C2×C4C2×GO+(4,𝔽2)11yescharacteristic
256C8—64no—
257C8—92no—
258C8—92no—
259C8—92no—
260C8C2×GO+(4,𝔽2)12yes—
261C2×C3—22no—
262C2×C3—42no—
263C2×C3—124no—
264D3—44no—
265D3—64no—
266D3—122no—
267C22—64no—
268C22—91no—
269C22—91no—
270C22—182no—
271C22—364no—
272C22C4×GO+(4,𝔽2)11yescharacteristic
273C4—64no—
274C4—91no—
275C4—91no—
276C4—362no—
277C4C4×GO+(4,𝔽2)11yescharacteristic
278C4C22×GO+(4,𝔽2)11yescharacteristic
279C3—22no—
280C2—21no—
281C2—92no—
282C2—124no—
283C2—181no—
284C2C2×C4×GO+(4,𝔽2)11yescharacteristic
subgroupG/H
center, FrattiniC4C22×GO+(4,𝔽2)
commutatorC3⋊Dic3C23×C4
FittingC2×C32×C8D4
socleC2×C32C2×C4×D4
prime radical#10596500C2
cosocleC4×C3⋊D3C24
hypercenterC2×C8GO+(4,𝔽2)
hypocenterC32C2×#444
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
2. #10594669C2semidirect
3. C2×#63767C2semidirect
4. #10593331C2semidirect
5. #10593325C2semidirect
6. #10593298C2semidirect
10. #64237C4semidirect
11. #64228C4semidirect
12. #64227C4semidirect
13. #64225C4semidirect
19. #63805C22semidirect
20. #63803C22semidirect
23. #63767C22semidirect
24. #63733C22semidirect
25. #63731C22semidirect
43. #3776C2×C4semidirect
44. #3775C2×C4semidirect
45. #3774C2×C4semidirect
191. C3⋊D3#444semidirect
236. C32C2×#444semidirect

Maximal subgroups

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

subgroupindex
#105965002
#105946692
C2×#637672
#105933312
#105933252
#105932982
C2×#4449