Finite Group Databasebeta

← #11899692

Subgroups — #11899692

Order 1152.

782 conjugacy classes of subgroups; only the 148 normal subgroups are shown.

normal subgroups only

This group has 782 conjugacy classes of subgroups — too many to draw. Only its 148 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#10594687C212yesmaximal, complemented
2#10592606C211yesmaximal, characteristic, complemented
3C3×#4908C212yesmaximal, complemented
4#10590629C211yesmaximal, characteristic, complemented
5C2×#63545C211yesmaximal, characteristic, complemented
6#10590245C212yesmaximal, complemented
7#10590236C214yesmaximal, complemented
8#10590234C212yesmaximal, complemented
9#82036—32nomaximal
10#64307—22no—
11#64110C2211yescharacteristic
12C3×#904C2212yescomplemented
13C2×C3×D24C2212yescomplemented
14#63823—22no—
15#63810C2214yescomplemented
16#63798—24no—
17#63797C2214yescomplemented
18C32×M32C2211yescharacteristic, complemented
19C2×C3⋊(C3⋊C16)C2211yescharacteristic, complemented
20#63625C2212yescomplemented
21C16×C3⋊D3C2212yescomplemented
22C3×#800C2214yescomplemented
23C3×D48C2214yescomplemented
24#63550C2211yescharacteristic, complemented
25#63547C2212yescomplemented
26#63545C2211yescharacteristic, complemented
27#63545C2212yescomplemented
28#63545C2212yescomplemented
29#5769—32no—
30#5757—32no—
31C3×#509—32no—
32#5194—32no—
33C2×#826—32no—
34#4916—34no—
35#4914—34no—
36#4911—34no—
37D3×D16—34no—
38#4908D312yescomplemented
39#4907—32no—
40#4907—61no—
41#3828D411yescharacteristic
42C3×#235—22no—
43C2×C3×D12—22no—
44D3×#67—44no—
45#3802—24no—
46D3×D12—42no—
47#3796—24no—
48#3795—42no—
49C2×C32×C8C2311yescharacteristic
50#3748D411yescharacteristic
51#3743D412yes—
52C8×C3⋊D3C2312yes—
53C3×Dic12C2312yes—
54C3×D24—22no—
55C3×D24C2314yes—
56C3×D24C2312yes—
57C3×#204—22no—
58#3715—24no—
59#3713—24no—
60C32×C16C2312yes—
61C3⋊(C3⋊C16)C2311yescharacteristic
62C3⋊(C3⋊C16)C2311yescharacteristic
63#3415—91noSylow
64#1009—62no—
65#1004—62no—
66C3×#135—32no—
67C2×C3×D8—32no—
68#949—62no—
69#932—62no—
70#919—34no—
71#914—64no—
72#912—34no—
73#911—64no—
74D3×D8—34no—
75D3×D8—34no—
76#904C2×D312yescomplemented
77C2×D24C2×D312yescomplemented
78#901—32no—
79#901—61no—
80C3×SD32—34no—
81C3×D16—34no—
82C3×M32—21no—
83C3×M32C2×D312yescomplemented
84#829—32no—
85#828—32no—
86#827—32no—
87#826—34no—
88#826—34no—
89#826—32no—
90C2×C3⋊C16—32no—
91C2×C3⋊C16—61no—
92#800C2×D314yescomplemented
93D48C2×D314yescomplemented
94#798—34no—
95#798—62no—
96D3×C16—34no—
97D3×C16—62no—
98C22×C3×D3—42no—
99C2×D32—44no—
100C2×C32×C4C2×D411yescharacteristic
101#638D812yes—
102C4⋊(C3⋊D3)D811yescharacteristic
103C4×C3⋊D3C2×D412yes—
104#634D811yescharacteristic
105C3×#67—42no—
106C3×D12—22no—
107C3×D12—24no—
108C3×D12—42no—
109C3×C4×D3—42no—
110C3×Dic6—22no—
111#626—44no—
112#625—44no—
113D3×Dic3—44no—
114C32×C8C2×D411yescharacteristic
115C32×C8C2411yescharacteristic
116C3⋊(C3⋊C8)C2×D412yes—
117#576—92no—
118#509—32no—
119#509—94no—
120#508—92no—
121#508—91no—
122C2×D16—92no—
123C2×D16—91no—
124#504—91no—
125C3×#41—62no—
126C2×C3×D4—62no—
127C2×#67—124no—
128#239—64no—
129#237—64no—
130#237—122no—
131D3×D4—64no—
132D3×D4—64no—
133D3×D4—122no—
134D3×D4—124no—
135#235—22no—
136#235—32no—
137#235—61no—
138#235—122no—
139C2×D12—22no—
140C2×D12—122no—
141C3×Q16—32no—
142C3×SD16—62no—
143C3×D8—34no—
144C3×D8—32no—
145C3×D8—62no—
146C2×C3×C8—21no—
147C2×C3×C8C22×D312yes—
148#215—64no—
149#214—64no—
150#213—64no—
151#213—64no—
152#208—32no—
153#208—61no—
154Dic12C22×D312yes—
155D24—22no—
156D24C22×D312yes—
157D24C22×D314yes—
158#204—22no—
159ΓL(1,𝔽25)—34no—
160ΓL(1,𝔽25)—62no—
161D3×C8—34no—
162D3×C8—62no—
163C3×C16—22no—
164C3×C16C22×D314yes—
165C3⋊C16—32no—
166C3⋊C16—32no—
167C3⋊C16—61no—
168C3⋊C16—61no—
169C22×C32C2×D811yescharacteristic
170C2×C3⋊D3C2×D812yes—
171C2×C3×D3—44no—
172C2×C3×D3—42no—
173C2×C3×D3—162no—
174D32—164no—
175C32×C4C2×D811yescharacteristic
176C32×C4C22×D411yescharacteristic
177C3⋊Dic3C2×D812yes—
178C3×Dic3—42no—
179H(5,𝔽2)—182no—
180AGL(1,ℤ/8)—184no—
181AGL(1,ℤ/8)—182no—
182#135—32no—
183#135—94no—
184C2×D8—32no—
185C2×D8—94no—
186#131—91no—
187Q32—91no—
188SD32—34no—
189SD32—92no—
190D16—34no—
191D16—91no—
192D16—92no—
193D16—92no—
194M32—92no—
195M32D3211yescharacteristic, complemented
196C2×C16—91no—
197C2×C16—92no—
198C23×C3—122no—
199C22×D3—42no—
200C22×D3—124no—
201C22×D3—124no—
202C3×Q8—62no—
203C3×D4—62no—
204C3×D4—64no—
205C3×D4—122no—
206C3×D4—122no—
207C2×C3×C4—21no—
208C2×C3×C4—122no—
209C2×C3×C4D3×D412yes—
210#67—34no—
211#67—42no—
212#67—62no—
213#67—124no—
214#67—124no—
215#67—124no—
216C2×Dic3—124no—
217D12—22no—
218D12—24no—
219D12—32no—
220D12—42no—
221D12—61no—
222D12—124no—
223C4×D3—34no—
224C4×D3—42no—
225C4×D3—62no—
226C4×D3—124no—
227Dic6—22no—
228Dic6—32no—
229Dic6—61no—
230C3×C8—21no—
231C3×C8—21no—
232C3×C8D3×D412yes—
233C3×C8C23×D312yes—
234C3⋊C8—34no—
235C3⋊C8—62no—
236C2×C32—21no—
237C2×C32C22×D811yescharacteristic
238C3⋊D3—22no—
239C3×D3—82no—
240C3×D3—84no—
241#41—62no—
242#41—91no—
243#41—184no—
244#41—362no—
245C2×D4—62no—
246C2×D4—184no—
247C2×D4—362no—
248C2×D4—364no—
249Q16—32no—
250SD16—62no—
251SD16—184no—
252D8—32no—
253D8—34no—
254D8—62no—
255D8—184no—
256M16—91no—
257M16—92no—
258C2×C8—92no—
259C2×C8C2×D3211yescharacteristic
260C16—91no—
261C16—91no—
262C16C2×D3212yes—
263C22×C3—21no—
264C22×C3—124no—
265C22×C3—122no—
266C22×C3—482no—
267C22×C3D3×D812yes—
268C2×D3—34no—
269C2×D3—42no—
270C2×D3—44no—
271C2×D3—62no—
272C2×D3—162no—
273C2×D3—484no—
274C2×D3—484no—
275C3×C4—21no—
276C3×C4—21no—
277C3×C4—122no—
278C3×C4D3×D812yes—
279C3×C4C2×D3×D412yes—
280Dic3—34no—
281Dic3—42no—
282Dic3—62no—
283C32#341511yescharacteristic, complemented, Sylow
284C23—122no—
285C23—364no—
286Q8—62no—
287Q8—91no—
288D4—64no—
289D4—62no—
290D4—92no—
291D4—91no—
292D4—122no—
293D4—122no—
294D4—364no—
295D4—364no—
296C2×C4—92no—
297C2×C4—122no—
298C2×C4—364no—
299C2×C4#380211yescharacteristic
300C8—92no—
301C8#380211yescharacteristic
302C8C22×D3211yescharacteristic
303C2×C3—22no—
304C2×C3—21no—
305C2×C3—41no—
306C2×C3—242no—
307C2×C3—244no—
308C2×C3C2×D3×D812yes—
309D3—64no—
310D3—84no—
311D3—82no—
312D3—122no—
313C22—92no—
314C22—122no—
315C22—124no—
316C22—482no—
317C22—1444no—
318C22#6379711yescharacteristic
319C4—92no—
320C4—122no—
321C4#6379711yescharacteristic
322C4C2×#380211yescharacteristic
323C3—21no—
324C3#8203612yescomplemented
325C2—21no—
326C2—182no—
327C2—244no—
328C2—242no—
329C2C2×#6379711yescharacteristic
subgroupG/H
centerC2C2×#63797
commutator, cosocleC32×C8C24
FrattiniC8C22×D32
FittingC32×M32C22
socleC2×C32C22×D8
hypercenterM32D32
hypocenterC32#3415
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ M32

Complements

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

NH ≅ G/Ntype
1. #10594687C2semidirect
2. #10592606C2semidirect
3. C3×#4908C2semidirect
4. #10590629C2semidirect
5. C2×#63545C2semidirect
6. #10590245C2semidirect
7. #10590236C2semidirect
8. #10590234C2semidirect
12. C3×#904C22semidirect
13. C2×C3×D24C22semidirect
15. #63810C22semidirect
17. #63797C22semidirect
18. C32×M32C22semidirect
19. C2×C3⋊(C3⋊C16)C22semidirect
20. #63625C22semidirect
21. C16×C3⋊D3C22semidirect
22. C3×#800C22semidirect
23. C3×D48C22semidirect
24. #63550C22semidirect
25. #63547C22semidirect
26. #63545C22semidirect
27. #63545C22semidirect
28. #63545C22semidirect
38. #4908D3semidirect
76. #904C2×D3semidirect
77. C2×D24C2×D3semidirect
83. C3×M32C2×D3semidirect
92. #800C2×D3semidirect
93. D48C2×D3semidirect
195. M32D32semidirect
283. C32#3415semidirect
324. C3#82036semidirect

Maximal subgroups

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

subgroupindex
#105946872
#105926062
C3×#49082
#105906292
C2×#635452
#105902452
#105902362
#105902342
#820363