Finite Group Databasebeta

← #11861242

Subgroups — #11861242

Order 1152.

710 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 710 conjugacy classes of subgroups — too many to draw. Only its 147 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#10594708C212yesmaximal, complemented
3#10593775C211yesmaximal, characteristic, complemented
4C2×#63733C211yesmaximal, characteristic, complemented
5#10593324C212yesmaximal, complemented
6#10593299C212yesmaximal, complemented
7#10593298C214yesmaximal, complemented
8#10593297C212yesmaximal, complemented
9#64306C2212yes—
10#64286C2211yescharacteristic
11C2×#3787C2211yescharacteristic
12#64237C412yescomplemented
13#64237C412yescomplemented
14#64228C411yescharacteristic, complemented
15#64227C412yescomplemented
16#64225C411yescharacteristic, complemented
17#64223C2212yes—
18#64223C2212yes—
19M16×C3⋊D3C2211yescharacteristic
20C3×#907—22no—
21C2×#3712C2212yes—
22#63814—22no—
23#63805C2214yescomplemented
24#63803C2214yescomplemented
25D3×ΓL(1,𝔽25)—24no—
26#63767C2212yescomplemented
27C8×#157C2212yescomplemented
28#63733C2211yescharacteristic, complemented
29#63733C2212yescomplemented
30#63733C2211yescharacteristic, complemented
31#63731C2214yescomplemented
32#63731C2214yescomplemented
33#5750—62no—
34C2×C4×C3⋊D3C2311yescharacteristic
35C3×#235—22no—
36#3811—22no—
37#3805C2×C414yes—
38#3802C2×C412yes—
39C4×D32—22no—
40#3798C2314yes—
41#3797C2×C412yes—
42#3796—22no—
43C22⋊#157—21no—
44C2×#622C2×C411yescharacteristic
45C2×#622C2×C411yescharacteristic
46C4⋊#157—21no—
47C4×#157C2312yes—
48#3787C2×C411yescharacteristic
49#3787C2×C411yescharacteristic
50#3787C2311yescharacteristic
51#3787C2311yescharacteristic
52#3776C2×C412yes—
53#3776C2×C412yes—
54#3775C2×C414yes—
55#3775C2×C414yes—
56#3774C2×C412yes—
57#3774C2×C412yes—
58C32×M16D411yescharacteristic
59#3748D411yescharacteristic
60#3743D412yes—
61C8×C3⋊D3C2312yes—
62C2×C3×C3⋊C8—22no—
63C3×ΓL(1,𝔽25)—24no—
64C3×D3×C8—24no—
65#3712—22no—
66#3712C2312yes—
67#3712C2312yes—
68#3711—24no—
69D3×C3⋊C8—24no—
70#2957—91nomaximal, Sylow
71D3×#41—62no—
72C3×#131—62no—
73#948—62no—
74#907—22no—
75#907—64no—
76D3×M16—62no—
77D3×M16—64no—
78#901—64no—
79#901—62no—
80C2×ΓL(1,𝔽25)—62no—
81C2×ΓL(1,𝔽25)—64no—
82C22×C3⋊D3#4111yescharacteristic
83C2×D32—22no—
84C2×#157—22no—
85C2×C32×C4C2×D411yescharacteristic
86C2×C3⋊Dic3C22×C411yescharacteristic
87C4×C3⋊D3C22×C411yescharacteristic
88C4×C3⋊D3C2×D411yescharacteristic
89C4×C3⋊D3#4111yescharacteristic
90C4×C3⋊D3C2411yescharacteristic
91C3×#67—24no—
92C3×D12—22no—
93C3×C4×D3—24no—
94C3×Dic6—22no—
95#627C22×C414yes—
96#626—24no—
97#625C22×C414yes—
98#624—22no—
99D3×Dic3—24no—
100#622C22×C411yescharacteristic
101#622C22×C411yescharacteristic
102#622C22×C411yescharacteristic
103#622C22×C411yescharacteristic
104C32×C8C2×D412yes—
105C3⋊(C3⋊C8)C2×D412yes—
106C3×C3⋊C8—22no—
107C3×C3⋊C8—22no—
108C2×#135—91no—
109#568—92no—
110#444—94no—
111#443—92no—
112#443—92no—
113C2×#108—91no—
114#421—92no—
115#405—91no—
116C3×#41—62no—
117#239—62no—
118D3×Q8—62no—
119#237—64no—
120#237—62no—
121D3×D4—62no—
122D3×D4—64no—
123#235—22no—
124#235—64no—
125C2×C4×D3—62no—
126C2×C4×D3—64no—
127C3×M16—22no—
128C3×M16—64no—
129C2×C3×C8—64no—
130C2×C3×C8—62no—
131#208—62no—
132#208—64no—
133C2×C3⋊C8—22no—
134C2×C3⋊C8—64no—
135ΓL(1,𝔽25)—24no—
136ΓL(1,𝔽25)—62no—
137ΓL(1,𝔽25)—62no—
138ΓL(1,𝔽25)—64no—
139ΓL(1,𝔽25)—62no—
140ΓL(1,𝔽25)—62no—
141ΓL(1,𝔽25)—64no—
142D3×C8—24no—
143D3×C8—64no—
144D3×C8—64no—
145C22×C32C4×D411yescharacteristic
146C2×C3⋊D3—41no—
147C2×C3⋊D3C4×D411yescharacteristic
148C2×C3⋊D3C2×#4111yescharacteristic
149C2×C3×D3—24no—
150D32—82no—
151#157—42no—
152C32×C4C4×D411yescharacteristic
153C32×C4C22×D411yescharacteristic
154C3⋊Dic3C4×D411yescharacteristic
155C3⋊Dic3C23×C411yescharacteristic
156C3×Dic3—24no—
157C2×#41—92no—
158#135—92no—
159#135—92no—
160#135—92no—
161#135—92no—
162C2×Q16—91no—
163C2×SD16—92no—
164C2×D8—91no—
165#131—62no—
166#131—94no—
167#131—94no—
168#131—182no—
169C2×M16—92no—
170C2×M16—91no—
171C2×M16—184no—
172C22×C8—91no—
173#117—91no—
174#108—91no—
175#108—91no—
176#108—92no—
177#104—94no—
178#104—94no—
179#97—92no—
180C4×C8—92no—
181C22×D3—62no—
182C22×D3—64no—
183C3×Q8—62no—
184C3×D4—62no—
185C3×D4—64no—
186C2×C3×C4—22no—
187C2×C3×C4—64no—
188#67—24no—
189#67—64no—
190#67—64no—
191C2×Dic3—62no—
192C2×Dic3—64no—
193D12—22no—
194D12—64no—
195C4×D3—24no—
196C4×D3—62no—
197C4×D3—62no—
198C4×D3—62no—
199C4×D3—62no—
200C4×D3—64no—
201C4×D3—64no—
202Dic6—22no—
203Dic6—64no—
204C3×C8—24no—
205C3×C8—62no—
206C3×C8—62no—
207C3⋊C8—22no—
208C3⋊C8—22no—
209C3⋊C8—64no—
210C2×C32—21no—
211C2×C32C2×C4×D411yescharacteristic
212C3⋊D3—21no—
213C3⋊D3—21no—
214C3×D3—44no—
215#41—62no—
216#41—94no—
217#41—94no—
218#41—182no—
219C2×Q8—92no—
220C2×D4—92no—
221C2×D4—182no—
222C22×C4—91no—
223C22×C4—182no—
224Q16—92no—
225Q16—92no—
226SD16—94no—
227SD16—94no—
228D8—92no—
229D8—92no—
230M16—64no—
231M16—92no—
232M16—92no—
233M16—91no—
234M16—92no—
235M16—182no—
236M16—184no—
237M16GO+(4,𝔽2)11yescharacteristic
238C2×C8—62no—
239C2×C8—64no—
240C2×C8—91no—
241C2×C8—91no—
242C2×C8—91no—
243C2×C8—91no—
244C2×C8—91no—
245C2×C8—91no—
246C2×C8—92no—
247C2×C8—184no—
248C4⋊C4—181no—
249C22⋊C4—181no—
250C42—92no—
251C22×C3—22no—
252C22×C3—64no—
253C2×D3—24no—
254C2×D3—62no—
255C2×D3—62no—
256C2×D3—242no—
257C2×D3—244no—
258C3×C4—22no—
259C3×C4—22no—
260C3×C4—64no—
261Dic3—24no—
262Dic3—62no—
263Dic3—62no—
264C32#295711yescharacteristic, complemented, Sylow
265C23—91no—
266C23—182no—
267Q8—62no—
268Q8—94no—
269D4—64no—
270D4—62no—
271D4—94no—
272D4—184no—
273C2×C4—64no—
274C2×C4—91no—
275C2×C4—91no—
276C2×C4—91no—
277C2×C4—91no—
278C2×C4—91no—
279C2×C4—182no—
280C2×C4—184no—
281C2×C4—182no—
282C2×C4C2×GO+(4,𝔽2)11yescharacteristic
283C8—62no—
284C8—62no—
285C8—91no—
286C8—91no—
287C8—91no—
288C8—91no—
289C8—92no—
290C8C2×GO+(4,𝔽2)12yes—
291C2×C3—22no—
292C2×C3—42no—
293C2×C3—124no—
294D3—44no—
295D3—122no—
296D3—122no—
297C22—64no—
298C22—91no—
299C22—91no—
300C22—361no—
301C22—722no—
302C22C4×GO+(4,𝔽2)11yescharacteristic
303C4—64no—
304C4—91no—
305C4—91no—
306C4—362no—
307C4C4×GO+(4,𝔽2)11yescharacteristic
308C4C22×GO+(4,𝔽2)11yescharacteristic
309C3—22no—
310C2—21no—
311C2—124no—
312C2—181no—
313C2—181no—
314C2C2×C4×GO+(4,𝔽2)11yescharacteristic
subgroupG/H
center, FrattiniC4C22×GO+(4,𝔽2)
commutatorC3⋊Dic3C23×C4
FittingC32×M16D4
socleC2×C32C2×C4×D4
prime radical#10596500C2
cosocleC4×C3⋊D3C24
hypercenterM16GO+(4,𝔽2)
hypocenterC32#2957
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ M16

Complements

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

NH ≅ G/Ntype
2. #10594708C2semidirect
3. #10593775C2semidirect
4. C2×#63733C2semidirect
5. #10593324C2semidirect
6. #10593299C2semidirect
7. #10593298C2semidirect
8. #10593297C2semidirect
12. #64237C4semidirect
13. #64237C4semidirect
14. #64228C4semidirect
15. #64227C4semidirect
16. #64225C4semidirect
23. #63805C22semidirect
24. #63803C22semidirect
26. #63767C22semidirect
27. C8×#157C22semidirect
28. #63733C22semidirect
29. #63733C22semidirect
30. #63733C22semidirect
31. #63731C22semidirect
32. #63731C22semidirect
264. C32#2957semidirect

Maximal subgroups

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

subgroupindex
#105965002
#105947082
#105937752
C2×#637332
#105933242
#105932992
#105932982
#105932972
#29579