Finite Group Databasebeta

← #11899686

Subgroups — #11899686

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#10592600C211yesmaximal, characteristic, complemented
3C3×#4904C211yesmaximal, characteristic, complemented
4C2×C3×D48C211yesmaximal, characteristic, complemented
5#10590630C212yesmaximal, complemented
6#10590244C212yesmaximal, complemented
7#10590236C214yesmaximal, complemented
8#10590234C212yesmaximal, complemented
9#82031—31nomaximal
10#82019—31nomaximal
11#64307—22no—
12#64110C2211yescharacteristic
13C3×#904C2212yescomplemented
14C2×C3×D24C2212yescomplemented
15#63823—22no—
16#63810C2214yescomplemented
17#63798—24no—
18#63797C2214yescomplemented
19C2×C32×C16C2211yescharacteristic, complemented
20#63639C2211yescharacteristic, complemented
21#63625C2212yescomplemented
22C16×C3⋊D3C2212yescomplemented
23C3×Dic24C2211yescharacteristic, complemented
24C3×#800C2212yescomplemented
25C3×D48C2211yescharacteristic, complemented
26C3×D48C2212yescomplemented
27C3×D48C2212yescomplemented
28#63547C2214yescomplemented
29#63545C2214yescomplemented
30#5769—32no—
31#5757—32no—
32C3×#508—31no—
33C2×C3×D16—31no—
34#5193—32no—
35#5147—32no—
36#4919—32no—
37#4914—34no—
38#4912—32no—
39#4911—34no—
40D3×D16—32no—
41D3×D16—32no—
42#4904D311yescharacteristic, complemented
43C2×D48D311yescharacteristic, complemented
44#4901—31no—
45#4901—31no—
46#4901—61no—
47#3828D411yescharacteristic
48C3×#235—22no—
49C2×C3×D12—22no—
50D3×#67—44no—
51#3802—24no—
52D3×D12—42no—
53#3796—24no—
54#3795—42no—
55C2×C32×C8C2311yescharacteristic
56#3748D411yescharacteristic
57#3743D412yes—
58C8×C3⋊D3C2312yes—
59C3×Dic12C2312yes—
60C3×D24—22no—
61C3×D24C2314yes—
62C3×D24C2312yes—
63C3×#204—22no—
64#3715—24no—
65#3713—24no—
66C32×C16C2311yescharacteristic
67C32×C16C2311yescharacteristic
68C3⋊(C3⋊C16)C2312yes—
69#3415—91noSylow
70#1009—62no—
71#1004—62no—
72C3×#135—32no—
73C2×C3×D8—32no—
74#949—62no—
75#932—62no—
76#919—34no—
77#914—64no—
78#912—34no—
79#911—64no—
80D3×D8—34no—
81D3×D8—34no—
82#904C2×D312yescomplemented
83C2×D24C2×D312yescomplemented
84#901—31no—
85#901—31no—
86#901—61no—
87C3×Q32—31no—
88C3×SD32—32no—
89C3×D16—32no—
90C3×D16—32no—
91C3×D16—31no—
92C2×C3×C16—21no—
93C2×C3×C16C2×D311yescharacteristic, complemented
94C2×C3×C16C2×D311yescharacteristic, complemented
95#828—34no—
96#827—34no—
97#826—34no—
98#826—34no—
99#812—31no—
100#812—31no—
101#812—61no—
102Dic24C2×D311yescharacteristic, complemented
103#800C2×D312yescomplemented
104D48C2×D312yescomplemented
105D48C2×D312yescomplemented
106D48C2×D311yescharacteristic, complemented
107#798—32no—
108#798—32no—
109#798—62no—
110D3×C16—32no—
111D3×C16—32no—
112D3×C16—62no—
113C22×C3×D3—42no—
114C2×D32—44no—
115C2×C32×C4C2×D411yescharacteristic
116#638D812yes—
117C4⋊(C3⋊D3)D811yescharacteristic
118C4×C3⋊D3C2×D412yes—
119#634D811yescharacteristic
120C3×#67—42no—
121C3×D12—22no—
122C3×D12—24no—
123C3×D12—42no—
124C3×C4×D3—42no—
125C3×Dic6—22no—
126#626—44no—
127#625—44no—
128D3×Dic3—44no—
129C32×C8C2×D411yescharacteristic
130C32×C8C2411yescharacteristic
131C3⋊(C3⋊C8)C2×D412yes—
132#576—92no—
133#509—94no—
134#509—92no—
135#508—31no—
136#508—92no—
137C2×D16—31no—
138C2×D16—92no—
139#504—91no—
140C3×#41—62no—
141C2×C3×D4—62no—
142C2×#67—124no—
143#239—64no—
144#237—64no—
145#237—122no—
146D3×D4—64no—
147D3×D4—64no—
148D3×D4—122no—
149D3×D4—124no—
150#235—22no—
151#235—31no—
152#235—31no—
153#235—61no—
154#235—122no—
155C2×D12—22no—
156C2×D12—122no—
157C3×Q16—32no—
158C3×SD16—62no—
159C3×D8—32no—
160C3×D8—34no—
161C3×D8—62no—
162C2×C3×C8—21no—
163C2×C3×C8C22×D311yescharacteristic
164C2×C3×C8C22×D311yescharacteristic
165#215—64no—
166#214—64no—
167#213—64no—
168#213—64no—
169#208—31no—
170#208—31no—
171#208—61no—
172Dic12C22×D312yes—
173D24—22no—
174D24C22×D314yes—
175D24C22×D312yes—
176#204—22no—
177ΓL(1,𝔽25)—32no—
178ΓL(1,𝔽25)—32no—
179ΓL(1,𝔽25)—62no—
180D3×C8—32no—
181D3×C8—32no—
182D3×C8—62no—
183C3×C16—21no—
184C3×C16—21no—
185C3×C16C22×D311yescharacteristic
186C3×C16C22×D311yescharacteristic
187C3×C16C22×D311yescharacteristic
188C3×C16C22×D311yescharacteristic
189C3⋊C16—32no—
190C3⋊C16—32no—
191C3⋊C16—62no—
192C22×C32C2×D811yescharacteristic
193C2×C3⋊D3C2×D812yes—
194C2×C3×D3—44no—
195C2×C3×D3—42no—
196C2×C3×D3—162no—
197D32—164no—
198C32×C4C2×D811yescharacteristic
199C32×C4C22×D411yescharacteristic
200C3⋊Dic3C2×D812yes—
201C3×Dic3—42no—
202H(5,𝔽2)—182no—
203AGL(1,ℤ/8)—184no—
204AGL(1,ℤ/8)—182no—
205#135—32no—
206#135—94no—
207C2×D8—32no—
208C2×D8—94no—
209#131—91no—
210Q32—31no—
211SD32—32no—
212SD32—94no—
213D16—32no—
214D16—32no—
215D16—31no—
216D16—94no—
217M32—91no—
218M32—92no—
219C2×C16—92no—
220C2×C16D3211yescharacteristic, complemented
221C23×C3—122no—
222C22×D3—42no—
223C22×D3—124no—
224C22×D3—124no—
225C3×Q8—62no—
226C3×D4—62no—
227C3×D4—64no—
228C3×D4—122no—
229C3×D4—122no—
230C2×C3×C4—21no—
231C2×C3×C4—122no—
232C2×C3×C4D3×D411yescharacteristic
233C2×C3×C4D3×D411yescharacteristic
234#67—32no—
235#67—32no—
236#67—42no—
237#67—62no—
238#67—124no—
239#67—124no—
240#67—124no—
241C2×Dic3—124no—
242D12—22no—
243D12—24no—
244D12—31no—
245D12—31no—
246D12—42no—
247D12—61no—
248D12—124no—
249C4×D3—32no—
250C4×D3—32no—
251C4×D3—42no—
252C4×D3—62no—
253C4×D3—124no—
254Dic6—22no—
255Dic6—31no—
256Dic6—31no—
257Dic6—61no—
258C3×C8—21no—
259C3×C8—21no—
260C3×C8D3×D411yescharacteristic
261C3×C8D3×D411yescharacteristic
262C3×C8C23×D311yescharacteristic
263C3×C8C23×D311yescharacteristic
264C3⋊C8—32no—
265C3⋊C8—32no—
266C3⋊C8—62no—
267C2×C32—21no—
268C2×C32C22×D811yescharacteristic
269C3⋊D3—22no—
270C3×D3—82no—
271C3×D3—84no—
272#41—62no—
273#41—91no—
274#41—184no—
275#41—362no—
276C2×D4—62no—
277C2×D4—184no—
278C2×D4—362no—
279C2×D4—364no—
280Q16—32no—
281SD16—62no—
282SD16—184no—
283D8—34no—
284D8—32no—
285D8—62no—
286D8—184no—
287M16—91no—
288M16—92no—
289C2×C8—92no—
290C2×C8C2×D3211yescharacteristic
291C16—92no—
292C16C2×D3211yescharacteristic
293C16C2×D3211yescharacteristic
294C22×C3—21no—
295C22×C3—124no—
296C22×C3—122no—
297C22×C3—482no—
298C22×C3D3×D811yescharacteristic
299C22×C3D3×D811yescharacteristic
300C2×D3—32no—
301C2×D3—32no—
302C2×D3—42no—
303C2×D3—44no—
304C2×D3—62no—
305C2×D3—162no—
306C2×D3—484no—
307C2×D3—484no—
308C3×C4—21no—
309C3×C4—21no—
310C3×C4—122no—
311C3×C4D3×D811yescharacteristic
312C3×C4D3×D811yescharacteristic
313C3×C4C2×D3×D411yescharacteristic
314C3×C4C2×D3×D411yescharacteristic
315Dic3—32no—
316Dic3—32no—
317Dic3—42no—
318Dic3—62no—
319C32#341511yescharacteristic, complemented, Sylow
320C23—122no—
321C23—364no—
322Q8—62no—
323Q8—91no—
324D4—64no—
325D4—62no—
326D4—92no—
327D4—91no—
328D4—122no—
329D4—122no—
330D4—364no—
331D4—364no—
332C2×C4—92no—
333C2×C4—122no—
334C2×C4—364no—
335C2×C4#380211yescharacteristic
336C8—92no—
337C8#380211yescharacteristic
338C8C22×D3211yescharacteristic
339C2×C3—21no—
340C2×C3—21no—
341C2×C3—21no—
342C2×C3—41no—
343C2×C3—242no—
344C2×C3—244no—
345C2×C3C2×D3×D811yescharacteristic
346C2×C3C2×D3×D811yescharacteristic
347D3—62no—
348D3—62no—
349D3—84no—
350D3—82no—
351D3—122no—
352C22—92no—
353C22—122no—
354C22—124no—
355C22—482no—
356C22—1444no—
357C22#6379711yescharacteristic
358C4—92no—
359C4—122no—
360C4#6379711yescharacteristic
361C4C2×#380211yescharacteristic
362C3—21no—
363C3#8201911yescharacteristic, complemented
364C3#8203111yescharacteristic, complemented
365C2—21no—
366C2—182no—
367C2—244no—
368C2—242no—
369C2C2×#6379711yescharacteristic
subgroupG/H
centerC2C2×#63797
commutator, cosocleC32×C8C24
FrattiniC8C22×D32
FittingC2×C32×C16C22
socleC2×C32C22×D8
hypercenterC2×C16D32
hypocenterC32#3415
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16

Complements

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

NH ≅ G/Ntype
1. #10594687C2semidirect
2. #10592600C2semidirect
3. C3×#4904C2semidirect
4. C2×C3×D48C2semidirect
5. #10590630C2semidirect
6. #10590244C2semidirect
7. #10590236C2semidirect
8. #10590234C2semidirect
13. C3×#904C22semidirect
14. C2×C3×D24C22semidirect
16. #63810C22semidirect
18. #63797C22semidirect
19. C2×C32×C16C22semidirect
20. #63639C22semidirect
21. #63625C22semidirect
22. C16×C3⋊D3C22semidirect
23. C3×Dic24C22semidirect
24. C3×#800C22semidirect
25. C3×D48C22semidirect
26. C3×D48C22semidirect
27. C3×D48C22semidirect
28. #63547C22semidirect
29. #63545C22semidirect
42. #4904D3semidirect
43. C2×D48D3semidirect
82. #904C2×D3semidirect
83. C2×D24C2×D3semidirect
93. C2×C3×C16C2×D3semidirect
94. C2×C3×C16C2×D3semidirect
102. Dic24C2×D3semidirect
103. #800C2×D3semidirect
104. D48C2×D3semidirect
105. D48C2×D3semidirect
106. D48C2×D3semidirect
220. C2×C16D32semidirect
319. C32#3415semidirect
363. C3#82019semidirect
364. C3#82031semidirect

Maximal subgroups

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

subgroupindex
#105946872
#105926002
C3×#49042
C2×C3×D482
#105906302
#105902442
#105902362
#105902342
#820313
#820193