Finite Group Databasebeta

← #11876984

Subgroups — #11876984

Order 1152.

973 conjugacy classes of subgroups.

The subgroup lattice has 519 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595131C212yesmaximal, complemented
2#10592850C211yesmaximal, characteristic, complemented
3C3×#5159C211yesmaximal, characteristic, complemented
4C3×#5152C211yesmaximal, characteristic, complemented
5#10591453C212yesmaximal, complemented
6#10591404C212yesmaximal, complemented
7#10591402C212yesmaximal, complemented
8#10590900C211yesmaximal, characteristic, complemented
9#10590835C211yesmaximal, characteristic, complemented
10#10590768C211yesmaximal, characteristic, complemented
11#10590667C211yesmaximal, characteristic, complemented
12#80853—31nomaximal
13#79877—31nomaximal
14C2×#3804—22no—
15C2×C32×D8C2211yescharacteristic
16#64149C2212yes—
17C2×#3753C2212yes—
18C2×#3745C2211yescharacteristic
19C3×#938C2212yes—
20C3×D4×Dic3C2212yes—
21C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
22#63971—22no—
23#63953—22no—
24#63952—22no—
25#63919C2212yes—
26#63909C2212yes—
27#63894C2212yes—
28C4×D3×Dic3C2211yescharacteristic
29C2×#3711C2211yescharacteristic
30C8×C3⋊Dic3C2211yescharacteristic
31C3×#832C2212yes—
32C3×#832C2212yes—
33C3×#817C2211yescharacteristic
34C3×#817C2211yescharacteristic
35C3×#815C2211yescharacteristic
36#63574C2212yes—
37#63564C2212yes—
38#63564C2212yes—
39#63554C2211yescharacteristic
40#63553C2211yescharacteristic
41#5596—32no—
42#5548—32no—
43C3×#469—31no—
44C3×#442—31no—
45#5159D311yescharacteristic, complemented
46#5152D311yescharacteristic, complemented
47#5151—31no—
48#5151—31no—
49#5151—61no—
50#5135—31no—
51Dic3×M16—31no—
52#5039—32no—
53#5014—32no—
54#4869—31no—
55#4865—31no—
56#4855—31no—
57#4855—31no—
58#4785—32no—
59#4782—32no—
60#4760—32no—
61#4760—32no—
62#4711—31no—
63#4707—31no—
64C2×C32×D4C2312yes—
65C2×#638—22no—
66C2×#638—22no—
67C2×C4⋊(C3⋊D3)C2312yes—
68C2×C3×#67—22no—
69C22×C3×Dic3—22no—
70C2×C3×C4×D3C2311yescharacteristic
71C2×#627—22no—
72C2×#626—22no—
73C2×#624—22no—
74#3804—48no—
75C2×D3×Dic3D412yes—
76C32×D8—22no—
77C2×C32×C8C2311yescharacteristic
78#3753—24no—
79C4×C3⋊Dic3C2311yescharacteristic
80C2×C3⋊(C3⋊C8)C2311yescharacteristic
81#3745—22no—
82C3×#217—22no—
83C3×#217—22no—
84C3×C4⋊Dic3C2312yes—
85C3×C4⋊Dic3C2312yes—
86C3×C4×Dic3C2311yescharacteristic
87C2×C3×C3⋊C8C2311yescharacteristic
88C2×C3×C3⋊C8C2311yescharacteristic
89C3×ΓL(1,𝔽25)—22no—
90#3724—22no—
91#3722—22no—
92#3722—22no—
93Dic32D412yes—
94#3711—22no—
95#3184—91noSylow
96C2×#237—62no—
97C2×#235—62no—
98C2×C3×D8—21no—
99C2×C3×D8C2×D311yescharacteristic
100C2×C3×D8C2×D311yescharacteristic
101C2×C3×M16—31no—
102C3×#121—32no—
103C3×C4×D4—32no—
104#940—32no—
105#940—32no—
106#940—62no—
107#939—62no—
108#938C2×D312yes—
109D4×Dic3C2×D312yes—
110C2×#213—32no—
111C2×#213—32no—
112C2×#213—62no—
113#930—32no—
114C4×#67—62no—
115C2×C4×Dic3—31no—
116C2×#208—31no—
117C2×D24—31no—
118C2×D24—31no—
119C2×D24—61no—
120C2×ΓL(1,𝔽25)—31no—
121C2×ΓL(1,𝔽25)C2×D311yescharacteristic
122#895—32no—
123#893—32no—
124#888—32no—
125#888—32no—
126#885—62no—
127#885—62no—
128#884—62no—
129#67⋊C4—62no—
130C4×D12—32no—
131C42×D3—31no—
132C3×#106—31no—
133C3×#106—31no—
134C3×#102—32no—
135C3×#102—32no—
136C3×#97—31no—
137#832C2×D312yes—
138#832C2×D312yes—
139#821—32no—
140#821—32no—
141#817C2×D311yescharacteristic
142#817C2×D311yescharacteristic
143#815—31no—
144#815C2×D311yescharacteristic
145C8×Dic3—31no—
146C8×Dic3—31no—
147C8×Dic3—31no—
148C8×Dic3—31no—
149C8×Dic3—61no—
150#809—32no—
151#809—32no—
152#808—32no—
153#808—32no—
154#803—31no—
155C23×C32—22no—
156C22×C3⋊D3—22no—
157C22×C3×D3C2×D411yescharacteristic
158C32×D4—22no—
159C32×D4—22no—
160C2×C32×C4C2411yescharacteristic
161#638—44no—
162#638—44no—
163C2×C3⋊Dic3C2×D412yes—
164C4⋊(C3⋊D3)—22no—
165C4⋊(C3⋊D3)—22no—
166C3×#67—44no—
167C2×C3×Dic3—22no—
168C2×C3×Dic3—22no—
169C2×C3×Dic3—44no—
170C2×C3×Dic3C2×D411yescharacteristic
171C2×C3×Dic3C2×D412yes—
172C3×C4×D3—21no—
173C3×C4×D3—21no—
174#627—44no—
175#626—44no—
176#624—44no—
177D3×Dic3—24no—
178C32×C8#4112yescomplemented
179C3⋊(C3⋊C8)#4112yescomplemented
180C3×C3⋊C8—21no—
181C3×C3⋊C8—21no—
182#532—92no—
183#498—91no—
184#493—91no—
185#486—92no—
186#469—31no—
187#469—92no—
188#469—91no—
189#442—31no—
190#442—91no—
191#442—92no—
192C4×M16—91no—
193C2×C3×D4—22no—
194C2×C3×D4—62no—
195C2×C3×D4C22×D312yes—
196C2×C3×D4C22×D312yes—
197C22×C3×C4—31no—
198C22×C3×C4—62no—
199C2×#67—22no—
200C2×#67—62no—
201C2×#67—62no—
202C2×#67—62no—
203C2×#67—62no—
204C2×#67—62no—
205C2×#67—122no—
206C2×#67—122no—
207C22×Dic3—22no—
208C22×Dic3—32no—
209#237—128no—
210#235—128no—
211C2×D12—32no—
212C2×D12—32no—
213C2×D12—62no—
214C2×D12—62no—
215C2×C4×D3—32no—
216C2×C4×D3—62no—
217C2×C4×D3—62no—
218C2×C4×D3C22×D311yescharacteristic
219C2×Dic6—62no—
220C2×Dic6—62no—
221C3×D8—22no—
222C3×D8—22no—
223C3×D8—42no—
224C3×M16—62no—
225C2×C3×C8—21no—
226C2×C3×C8—31no—
227C2×C3×C8—31no—
228C2×C3×C8C22×D311yescharacteristic
229C2×C3×C8C22×D311yescharacteristic
230C3×C4⋊C4—32no—
231C3×C4⋊C4—32no—
232C3×C22⋊C4—62no—
233C3×C22⋊C4—62no—
234C3×C42—31no—
235#217—22no—
236#217—22no—
237#213—64no—
238#213—64no—
239#213—124no—
240(C2×D3)⋊C4—62no—
241(C2×D3)⋊C4—62no—
242(C2×D3)⋊C4—62no—
243(C2×D3)⋊C4—62no—
244C4⋊Dic3C22×D312yes—
245C4⋊Dic3C22×D312yes—
246Dic3⋊C4—62no—
247Dic3⋊C4—62no—
248C4×Dic3—31no—
249C4×Dic3—31no—
250C4×Dic3—32no—
251C4×Dic3—32no—
252C4×Dic3—61no—
253C4×Dic3C22×D311yescharacteristic
254#208—62no—
255C2×C3⋊C8—31no—
256C2×C3⋊C8—31no—
257C2×C3⋊C8—61no—
258C2×C3⋊C8C22×D311yescharacteristic
259C2×C3⋊C8C22×D311yescharacteristic
260D24—62no—
261D24—62no—
262D24—122no—
263ΓL(1,𝔽25)—22no—
264ΓL(1,𝔽25)—62no—
265C22×C32—42no—
266C22×C32—42no—
267C22×C32—42no—
268C22×C32C22×D411yescharacteristic
269C2×C3⋊D3—42no—
270C2×C3⋊D3—42no—
271C2×C3⋊D3—42no—
272C2×C3×D3—21no—
273C2×C3×D3—22no—
274C32×C4C2×#4111yescharacteristic
275C32×C4C2×#4111yescharacteristic
276C3⋊Dic3AGL(1,ℤ/8)14yes—
277C3×Dic3—21no—
278C3×Dic3—22no—
279C3×Dic3—42no—
280C3×Dic3—42no—
281C2×#41—182no—
282C2×D8—92no—
283C2×D8—91no—
284C2×D8D3211yescharacteristic
285C2×M16—31no—
286C2×M16—91no—
287C4⋊Q8—92no—
288#127—92no—
289#124—182no—
290#121—32no—
291#121—92no—
292#121—182no—
293C4×D4—32no—
294C4×D4—92no—
295C4×D4—182no—
296C2×C42—91no—
297#106—31no—
298#106—31no—
299#106—92no—
300#102—32no—
301#102—32no—
302#102—92no—
303#102—92no—
304#97—31no—
305#97—91no—
306C4×C8—91no—
307C4×C8—91no—
308C23×C3—22no—
309C23×C3—22no—
310C23×C3—31no—
311C23×C3—42no—
312C22×D3—62no—
313C22×D3—62no—
314C22×D3—122no—
315C22×D3D3×D411yescharacteristic
316C3×D4—22no—
317C3×D4—22no—
318C3×D4—22no—
319C3×D4—22no—
320C3×D4—42no—
321C3×D4—42no—
322C3×D4—124no—
323C2×C3×C4—21no—
324C2×C3×C4—31no—
325C2×C3×C4—32no—
326C2×C3×C4—61no—
327C2×C3×C4—61no—
328C2×C3×C4—62no—
329C2×C3×C4—62no—
330C2×C3×C4—124no—
331C2×C3×C4C23×D311yescharacteristic
332C2×C3×C4C23×D311yescharacteristic
333#67—44no—
334#67—124no—
335#67—124no—
336#67—124no—
337#67—124no—
338#67—124no—
339#67—244no—
340#67—244no—
341C2×Dic3—22no—
342C2×Dic3—22no—
343C2×Dic3—32no—
344C2×Dic3—32no—
345C2×Dic3—44no—
346C2×Dic3—62no—
347C2×Dic3—64no—
348C2×Dic3D3×D411yescharacteristic
349C2×Dic3D3×D412yes—
350D12—62no—
351D12—62no—
352D12—62no—
353D12—62no—
354D12—122no—
355D12—122no—
356D12—124no—
357C4×D3—21no—
358C4×D3—21no—
359C4×D3—64no—
360C4×D3—124no—
361C4×D3—124no—
362Dic6—124no—
363Dic6—124no—
364C3×C8—22no—
365C3×C8—61no—
366C3×C8—61no—
367C3×C8#23512yescomplemented
368C3×C8#23712yescomplemented
369C3⋊C8—21no—
370C3⋊C8—21no—
371C3⋊C8—32no—
372C3⋊C8—32no—
373C3⋊C8—62no—
374C2×C32—82no—
375C2×C32#53211yescharacteristic
376C2×C32C2×AGL(1,ℤ/8)12yes—
377C3⋊D3—82no—
378C3×D3—41no—
379#41—368no—
380C2×Q8—182no—
381C2×D4—62no—
382C2×D4—92no—
383C2×D4—182no—
384C2×D4—182no—
385C2×D4—182no—
386C2×D4C2×D3212yes—
387C22×C4—31no—
388C22×C4—62no—
389C22×C4—92no—
390C22×C4—182no—
391D8—22no—
392D8—184no—
393D8—182no—
394M16—62no—
395M16—182no—
396C2×C8—31no—
397C2×C8—31no—
398C2×C8—91no—
399C2×C8C2×D3211yescharacteristic
400C4⋊C4—32no—
401C4⋊C4—32no—
402C4⋊C4—182no—
403C22⋊C4—62no—
404C22⋊C4—62no—
405C22⋊C4—182no—
406C22⋊C4—182no—
407C42—31no—
408C42—92no—
409C42—91no—
410C22×C3—21no—
411C22×C3—42no—
412C22×C3—42no—
413C22×C3—42no—
414C22×C3—42no—
415C22×C3—42no—
416C22×C3—42no—
417C22×C3—62no—
418C22×C3—61no—
419C22×C3—82no—
420C22×C3—82no—
421C22×C3—82no—
422C22×C3C2×D3×D411yescharacteristic
423C22×C3C2×D3×D411yescharacteristic
424C2×D3—22no—
425C2×D3—21no—
426C2×D3—122no—
427C2×D3—122no—
428C2×D3—122no—
429C2×D3—122no—
430C2×D3—122no—
431C2×D3—122no—
432C2×D3—242no—
433C2×D3—242no—
434C2×D3—242no—
435C3×C4—21no—
436C3×C4—21no—
437C3×C4—62no—
438C3×C4—61no—
439C3×C4—122no—
440C3×C4—122no—
441C3×C4C2×#23511yescharacteristic
442C3×C4C2×#23711yescharacteristic
443C3×C4D3×#4111yescharacteristic
444C3×C4D3×#4111yescharacteristic
445Dic3—22no—
446Dic3—21no—
447Dic3—34no—
448Dic3—34no—
449Dic3—42no—
450Dic3—42no—
451Dic3—64no—
452C32#318411yescharacteristic, complemented, Sylow
453C23—22no—
454C23—31no—
455C23—182no—
456Q8—364no—
457D4—22no—
458D4—22no—
459D4—124no—
460D4—182no—
461D4—182no—
462D4—364no—
463D4—364no—
464D4—364no—
465C2×C4—32no—
466C2×C4—31no—
467C2×C4—61no—
468C2×C4—61no—
469C2×C4—62no—
470C2×C4—62no—
471C2×C4—92no—
472C2×C4—124no—
473C2×C4—184no—
474C2×C4—364no—
475C2×C4C22×D3211yescharacteristic
476C8—61no—
477C8—61no—
478C8—92no—
479C8#380412yescomplemented
480C2×C3—21no—
481C2×C3—22no—
482C2×C3—82no—
483C2×C3—82no—
484C2×C3—121no—
485C2×C3—162no—
486C2×C3#554811yescharacteristic
487C2×C3#559611yescharacteristic
488C2×C3D3×AGL(1,ℤ/8)12yes—
489C2×C3D3×AGL(1,ℤ/8)12yes—
490D3—41no—
491D3—242no—
492D3—242no—
493D3—482no—
494C22—42no—
495C22—42no—
496C22—42no—
497C22—61no—
498C22—62no—
499C22—362no—
500C22—362no—
501C22—362no—
502C22D32×D411yescharacteristic
503C4—61no—
504C4—62no—
505C4—94no—
506C4—122no—
507C4—122no—
508C4#6431211yescharacteristic
509C4C2×#380411yescharacteristic
510C3—21no—
511C3#7987711yescharacteristic, complemented
512C3#8085311yescharacteristic, complemented
513C2—82no—
514C2—121no—
515C2—722no—
516C2#1059472612yes—
517C2#1059513111yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×D8C22
socleC22×C32C22×D4
hypercenterC2×D8D32
hypocenterC32#3184
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. #10595131C2semidirect
2. #10592850C2semidirect
3. C3×#5159C2semidirect
4. C3×#5152C2semidirect
5. #10591453C2semidirect
6. #10591404C2semidirect
7. #10591402C2semidirect
8. #10590900C2semidirect
9. #10590835C2semidirect
10. #10590768C2semidirect
11. #10590667C2semidirect
45. #5159D3semidirect
46. #5152D3semidirect
178. C32×C8#41semidirect
179. C3⋊(C3⋊C8)#41semidirect
367. C3×C8#235semidirect
368. C3×C8#237semidirect
452. C32#3184semidirect
479. C8#3804semidirect
511. C3#79877semidirect
512. C3#80853semidirect

Maximal subgroups

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

subgroupindex
#105951312
#105928502
C3×#51592
C3×#51522
#105914532
#105914042
#105914022
#105909002
#105908352
#105907682
#105906672
#808533
#798773