Finite Group Databasebeta

← #11886927

Subgroups — #11886927

Order 1152.

1005 conjugacy classes of subgroups.

The subgroup lattice has 453 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594687C212yesmaximal, complemented
2#10594678C212yesmaximal, complemented
3#10592399C211yesmaximal, characteristic, complemented
4C3×#4700C211yesmaximal, characteristic, complemented
5C3×#4695C211yesmaximal, characteristic, complemented
6#10590929C212yesmaximal, complemented
7#10590926C212yesmaximal, complemented
8#10590395C214yesmaximal, complemented
9#81791—31nomaximal
10#79894—31nomaximal
11#64307C2214yescomplemented
12#64113C2211yescharacteristic
13#64110C2212yescomplemented
14C3×#904C2211yescharacteristic
15C2×C3×D24C2212yescomplemented
16C2×C3×D24C2212yescomplemented
17C3×#901C2212yescomplemented
18C3×#874C2212yescomplemented
19#63830C2214yescomplemented
20#63823C2214yescomplemented
21#63810—22no—
22#63807—22no—
23#63798—24no—
24#63797—22no—
25#63795—24no—
26D3×D24—22no—
27C32×C4×C8C2211yescharacteristic, complemented
28#63646C2211yescharacteristic, complemented
29#63632C2212yescomplemented
30C3×#819C2211yescharacteristic, complemented
31C3×#805C2212yescomplemented
32#63558C2214yescomplemented
33#5769—32no—
34#5757—32no—
35#5757—32no—
36#5752—32no—
37C3×#493—31no—
38C3×#443—31no—
39#5160—32no—
40#5160—32no—
41#5142—32no—
42#5077—34no—
43#4897—32no—
44#4822—34no—
45#4700—31no—
46#4700—31no—
47#4700—61no—
48#4700D311yescharacteristic, complemented
49#4695D311yescharacteristic, complemented
50#3828C2312yes—
51C3×#235C2312yes—
52C2×C3×D12—42no—
53C2×C3×D12C2314yes—
54D3×#67—44no—
55#3802—24no—
56D3×D12—24no—
57#3796—24no—
58#3795—24no—
59C2×C32×C8C2311yescharacteristic
60C2×C32×C8C2311yescharacteristic
61C32×C42C2311yescharacteristic
62#3748C2312yes—
63#3746D411yescharacteristic, complemented
64#3745D411yescharacteristic, complemented
65#3744D412yescomplemented
66#3743—22no—
67C8×C3⋊D3—22no—
68C3×#208C2312yes—
69C3×Dic12D411yescharacteristic, complemented
70C3×D24—22no—
71C3×D24—22no—
72C3×D24—22no—
73C3×D24—22no—
74C3×D24D411yescharacteristic, complemented
75C3×#204D412yescomplemented
76C3×ΓL(1,𝔽25)—22no—
77C3×D3×C8—22no—
78#3716—24no—
79#3715—24no—
80#3714—24no—
81#3713—24no—
82#3292—91noSylow
83#1009—34no—
84#1004—34no—
85C3×#135—31no—
86C2×C3×D8—32no—
87C2×C3×D8—32no—
88C3×#131—32no—
89C3×#127—32no—
90#949—34no—
91#932—34no—
92#932—34no—
93#919—62no—
94#914—64no—
95#912—62no—
96#912—62no—
97#911—64no—
98#911—64no—
99D3×D8—62no—
100D3×D8—62no—
101D3×D8—62no—
102#908—34no—
103#908—64no—
104#904—31no—
105#904—31no—
106#904—61no—
107#904—62no—
108#904C2×D311yescharacteristic
109C2×D24—62no—
110C2×D24C2×D312yescomplemented
111C2×D24C2×D312yescomplemented
112#901—32no—
113#901—32no—
114#901—62no—
115#901C2×D312yescomplemented
116#874C2×D312yescomplemented
117C3×#108—31no—
118C3×#104—32no—
119C3×C4×C8—21no—
120C3×C4×C8C2×D311yescharacteristic, complemented
121C3×C4×C8C2×D311yescharacteristic, complemented
122#833—34no—
123#823—34no—
124#819—31no—
125#819—31no—
126#819—61no—
127#819C2×D311yescharacteristic, complemented
128#805—32no—
129#805—32no—
130#805—62no—
131#805C2×D312yescomplemented
132C22×C3×D3—24no—
133C2×D32—44no—
134C2×C32×C4—21no—
135C2×C32×C4C2411yescharacteristic
136#638—22no—
137C4⋊(C3⋊D3)C2×D412yes—
138C4×C3⋊D3—22no—
139#634C2×D412yes—
140C3×#67—22no—
141C3×D12—24no—
142C3×D12—24no—
143C3×D12—84no—
144C3×D12C2×D412yes—
145C3×C4×D3—22no—
146C3×Dic6C2×D412yes—
147#626—44no—
148#625—44no—
149D3×Dic3—44no—
150C32×C8C2×D411yescharacteristic
151C32×C8C2×D411yescharacteristic
152C32×C8C2×D411yescharacteristic
153C32×C8C2×D411yescharacteristic
154C3⋊(C3⋊C8)—22no—
155C3×C3⋊C8—22no—
156#576—92no—
157#576—92no—
158#493—31no—
159#472—92no—
160#472—92no—
161#453—94no—
162#443—31no—
163#443—91no—
164C3×#41—32no—
165C2×C3×D4—34no—
166C2×C3×D4—122no—
167C2×#67—124no—
168#239—64no—
169#237—64no—
170#237—64no—
171D3×D4—64no—
172D3×D4—64no—
173D3×D4—64no—
174D3×D4—124no—
175#235—32no—
176#235—32no—
177#235—62no—
178#235—64no—
179#235C22×D312yes—
180C2×D12—42no—
181C2×D12—64no—
182C2×D12C22×D314yes—
183C3×Q16—31no—
184C3×SD16—32no—
185C3×D8—31no—
186C3×D8—62no—
187C3×D8—62no—
188C3×D8—62no—
189C3×D8—62no—
190C3×M16—32no—
191C3×M16—62no—
192C2×C3×C8—21no—
193C2×C3×C8—21no—
194C2×C3×C8—62no—
195C2×C3×C8C22×D311yescharacteristic
196C2×C3×C8C22×D311yescharacteristic
197C2×C3×C8C22×D311yescharacteristic
198C2×C3×C8C22×D311yescharacteristic
199C3×C42—21no—
200C3×C42C22×D311yescharacteristic
201C3×C42C22×D311yescharacteristic
202#215—64no—
203#214—64no—
204#214—64no—
205#213—64no—
206#213—64no—
207#213—64no—
208#208—32no—
209#208—32no—
210#208—62no—
211#208C22×D312yes—
212Dic12—31no—
213Dic12—31no—
214Dic12—61no—
215Dic12D1211yescharacteristic, complemented
216D24—22no—
217D24—22no—
218D24—22no—
219D24—22no—
220D24—31no—
221D24—31no—
222D24—61no—
223D24—64no—
224D24D1211yescharacteristic, complemented
225#204—32no—
226#204—32no—
227#204—62no—
228#204—64no—
229#204D1212yescomplemented
230ΓL(1,𝔽25)—22no—
231ΓL(1,𝔽25)—62no—
232ΓL(1,𝔽25)—62no—
233ΓL(1,𝔽25)—122no—
234D3×C8—22no—
235D3×C8—62no—
236D3×C8—62no—
237D3×C8—122no—
238C22×C32H(5,𝔽2)11yescharacteristic
239C2×C3⋊D3—22no—
240C2×C3×D3—22no—
241C2×C3×D3—44no—
242C2×C3×D3—84no—
243D32—164no—
244C32×C4—22no—
245C32×C4C22×D411yescharacteristic
246C32×C4C22×D411yescharacteristic
247C3⋊Dic3—22no—
248C3×Dic3—22no—
249H(5,𝔽2)—94no—
250AGL(1,ℤ/8)—94no—
251AGL(1,ℤ/8)—94no—
252AGL(1,ℤ/8)—184no—
253AGL(1,ℤ/8)—184no—
254#135—31no—
255#135—91no—
256#135—182no—
257#135—182no—
258C2×D8—32no—
259C2×D8—32no—
260C2×D8—182no—
261C2×D8—182no—
262#131—32no—
263#131—92no—
264#127—32no—
265#108—31no—
266#108—91no—
267#104—32no—
268#104—92no—
269#100—94no—
270C4×C8D3211yescharacteristic, complemented
271C23×C3—64no—
272C22×D3—24no—
273C22×D3—124no—
274C22×D3—124no—
275C3×Q8—32no—
276C3×D4—32no—
277C3×D4—62no—
278C3×D4—64no—
279C3×D4—64no—
280C3×D4—244no—
281C2×C3×C4—21no—
282C2×C3×C4—21no—
283C2×C3×C4—21no—
284C2×C3×C4—41no—
285C2×C3×C4—62no—
286C2×C3×C4C23×D311yescharacteristic
287C2×C3×C4C23×D311yescharacteristic
288#67—22no—
289#67—62no—
290#67—62no—
291#67—122no—
292#67—124no—
293#67—124no—
294#67—124no—
295C2×Dic3—124no—
296D12—24no—
297D12—24no—
298D12—32no—
299D12—32no—
300D12—62no—
301D12—84no—
302D12—124no—
303D12C2×D1212yes—
304C4×D3—22no—
305C4×D3—62no—
306C4×D3—62no—
307C4×D3—122no—
308C4×D3—124no—
309Dic6—32no—
310Dic6—32no—
311Dic6—62no—
312Dic6C2×D1212yes—
313C3×C8—21no—
314C3×C8—21no—
315C3×C8—21no—
316C3×C8—21no—
317C3×C8—62no—
318C3×C8C2×D1211yescharacteristic
319C3×C8C2×D1211yescharacteristic
320C3×C8D3×D411yescharacteristic
321C3×C8D3×D411yescharacteristic
322C3×C8D3×D411yescharacteristic
323C3×C8D3×D411yescharacteristic
324C3×C8D3×D411yescharacteristic
325C3×C8D3×D411yescharacteristic
326C3⋊C8—22no—
327C3⋊C8—62no—
328C3⋊C8—62no—
329C3⋊C8—122no—
330C2×C32—21no—
331C2×C32D4211yescharacteristic
332C3⋊D3—42no—
333C3×D3—42no—
334C3×D3—84no—
335#41—32no—
336#41—92no—
337#41—184no—
338#41—184no—
339C2×D4—34no—
340C2×D4—122no—
341C2×D4—184no—
342C2×D4—184no—
343C2×D4—364no—
344Q16—31no—
345Q16—91no—
346SD16—32no—
347SD16—92no—
348SD16—184no—
349SD16—184no—
350D8—31no—
351D8—62no—
352D8—62no—
353D8—62no—
354D8—62no—
355D8—91no—
356D8—184no—
357D8—184no—
358M16—32no—
359M16—62no—
360M16—92no—
361M16—182no—
362C2×C8—62no—
363C2×C8—182no—
364C2×C8C2×D3211yescharacteristic
365C2×C8C2×D3211yescharacteristic
366C42C2×D3211yescharacteristic
367C22×C3—21no—
368C22×C3—62no—
369C22×C3—124no—
370C22×C3—244no—
371C22×C3#100411yescharacteristic
372C22×C3#100911yescharacteristic
373C2×D3—22no—
374C2×D3—44no—
375C2×D3—62no—
376C2×D3—62no—
377C2×D3—84no—
378C2×D3—122no—
379C2×D3—484no—
380C2×D3—484no—
381C3×C4—22no—
382C3×C4—22no—
383C3×C4—21no—
384C3×C4—21no—
385C3×C4—42no—
386C3×C4—62no—
387C3×C4C22×D1211yescharacteristic
388C3×C4C2×D3×D411yescharacteristic
389C3×C4C2×D3×D411yescharacteristic
390C3×C4C2×D3×D411yescharacteristic
391Dic3—22no—
392Dic3—62no—
393Dic3—62no—
394Dic3—122no—
395C32#329211yescharacteristic, complemented, Sylow
396C23—64no—
397C23—364no—
398Q8—32no—
399Q8—92no—
400D4—32no—
401D4—62no—
402D4—64no—
403D4—64no—
404D4—92no—
405D4—182no—
406D4—244no—
407D4—364no—
408D4—364no—
409C2×C4—21no—
410C2×C4—62no—
411C2×C4—182no—
412C2×C4—364no—
413C2×C4C22×D3211yescharacteristic
414C8—62no—
415C8—182no—
416C8D3×D1211yescharacteristic
417C8D3×D1211yescharacteristic
418C8#380211yescharacteristic
419C8#380211yescharacteristic
420C2×C3—21no—
421C2×C3—21no—
422C2×C3—21no—
423C2×C3—41no—
424C2×C3—122no—
425C2×C3—244no—
426C2×C3D4×D1211yescharacteristic
427C2×C3#571711yescharacteristic
428D3—42no—
429D3—84no—
430D3—122no—
431D3—122no—
432D3—242no—
433C22—62no—
434C22—124no—
435C22—182no—
436C22—244no—
437C22—1444no—
438C22#6430711yescharacteristic
439C4—22no—
440C4—62no—
441C4—182no—
442C4C2×D3×D1211yescharacteristic
443C4C2×#380211yescharacteristic
444C3—21no—
445C3#7989411yescharacteristic, complemented
446C3#8179111yescharacteristic, complemented
447C2—21no—
448C2—122no—
449C2—244no—
450C2—362no—
451C2#1059400411yescharacteristic
subgroupG/H
centerC2#10594004
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC2×C32D42
hypercenterC4×C8D32
hypocenterC32#3292
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
1. #10594687C2semidirect
2. #10594678C2semidirect
3. #10592399C2semidirect
4. C3×#4700C2semidirect
5. C3×#4695C2semidirect
6. #10590929C2semidirect
7. #10590926C2semidirect
8. #10590395C2semidirect
11. #64307C22semidirect
13. #64110C22semidirect
15. C2×C3×D24C22semidirect
16. C2×C3×D24C22semidirect
17. C3×#901C22semidirect
18. C3×#874C22semidirect
19. #63830C22semidirect
20. #63823C22semidirect
27. C32×C4×C8C22semidirect
28. #63646C22semidirect
29. #63632C22semidirect
30. C3×#819C22semidirect
31. C3×#805C22semidirect
32. #63558C22semidirect
48. #4700D3semidirect
49. #4695D3semidirect
63. #3746D4semidirect
64. #3745D4semidirect
65. #3744D4semidirect
69. C3×Dic12D4semidirect
74. C3×D24D4semidirect
75. C3×#204D4semidirect
110. C2×D24C2×D3semidirect
111. C2×D24C2×D3semidirect
115. #901C2×D3semidirect
116. #874C2×D3semidirect
120. C3×C4×C8C2×D3semidirect
121. C3×C4×C8C2×D3semidirect
127. #819C2×D3semidirect
131. #805C2×D3semidirect
215. Dic12D12semidirect
224. D24D12semidirect
229. #204D12semidirect
270. C4×C8D32semidirect
395. C32#3292semidirect
445. C3#79894semidirect
446. C3#81791semidirect

Maximal subgroups

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

subgroupindex
#105946872
#105946782
#105923992
C3×#47002
C3×#46952
#105909292
#105909262
#105903952
#817913
#798943