Finite Group Databasebeta

← #11876982

Subgroups — #11876982

Order 1152.

957 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595139C212yesmaximal, complemented
2#10592858C211yesmaximal, characteristic, complemented
3C3×#5152C211yesmaximal, characteristic, complemented
4C3×#5151C211yesmaximal, characteristic, complemented
5#10591487C212yesmaximal, complemented
6#10591454C212yesmaximal, complemented
7#10591430C212yesmaximal, complemented
8#10590889C211yesmaximal, characteristic, complemented
9#10590846C211yesmaximal, characteristic, complemented
10#10590771C211yesmaximal, characteristic, complemented
11#10590664C211yesmaximal, characteristic, complemented
12#81777—31nomaximal
13#79877—31nomaximal
14C2×#3804—22no—
15C2×C32×D8C2211yescharacteristic
16#64147C2212yes—
17C2×#3743C2211yescharacteristic
18C3×#940C2212yes—
19C3×D4×Dic3C2212yes—
20C2×C3×#213C2212yes—
21C2×C3×D24C2211yescharacteristic
22Dic3×#67—22no—
23#63959—22no—
24#63958—22no—
25#63918C2212yes—
26#63916C2212yes—
27Dic3×D12C2212yes—
28C4×#624C2211yescharacteristic
29C2×#3712C2211yescharacteristic
30#63659C2212yes—
31#63644C2211yescharacteristic
32C3×#832C2212yes—
33C3×#817C2211yescharacteristic
34C3×#815C2211yescharacteristic
35C3×C8×Dic3C2211yescharacteristic
36#63573C2212yes—
37#63563C2212yes—
38#63562C2212yes—
39#63554C2211yescharacteristic
40Dic3×C3⋊C8C2211yescharacteristic
41#5716—32no—
42#5548—32no—
43C3×#493—31no—
44C3×#442—31no—
45#5159—31no—
46#5159—31no—
47#5159—32no—
48#5159—31no—
49#5159—61no—
50#5152—32no—
51#5152—31no—
52#5152D311yescharacteristic, complemented
53#5151D311yescharacteristic, complemented
54#5070—32no—
55#5014—32no—
56#4865—31no—
57#4855—31no—
58#4782—32no—
59#4760—32no—
60#4711—31no—
61#4707—31no—
62C4×ΓL(1,𝔽25)—31no—
63#4680—31no—
64C2×C32×D4C2312yes—
65C2×#638—22no—
66C2×C4×C3⋊D3C2311yescharacteristic
67C2×C3×#67—22no—
68C2×C3×#67—22no—
69C22×C3×Dic3—22no—
70C2×C3×D12C2312yes—
71C2×#627—22no—
72C2×#626—22no—
73C2×#624D412yes—
74#3804—48no—
75C2×D3×Dic3—22no—
76C32×D8—22no—
77C2×C32×C8C2311yescharacteristic
78#3757—22no—
79C4⋊(C3⋊Dic3)C2312yes—
80C2×C3⋊(C3⋊C8)C2311yescharacteristic
81#3743—22no—
82C3×#217—22no—
83C3×#213—24no—
84C3×C4⋊Dic3C2312yes—
85C3×C4×Dic3C2311yescharacteristic
86C3×C4×Dic3C2311yescharacteristic
87C2×C3×C3⋊C8C2311yescharacteristic
88C2×C3×C3⋊C8C2311yescharacteristic
89C3×D24—22no—
90Dic3⋊Dic3—22no—
91(C2×D3)⋊Dic3—22no—
92(C2×D3)⋊Dic3—22no—
93Dic32D412yes—
94#3712—22no—
95#3184—91noSylow
96C2×#237—62no—
97C2×#235—62no—
98C2×C3×D8—21no—
99C2×C3×D8—32no—
100C2×C3×D8—31no—
101C2×C3×D8C2×D311yescharacteristic
102C2×C3×D8C2×D311yescharacteristic
103C3×#127—32no—
104C3×C4×D4—32no—
105#940C2×D312yes—
106#938—32no—
107#938—32no—
108#938—32no—
109#938—62no—
110#938—62no—
111#936—62no—
112D4×Dic3—32no—
113D4×Dic3—62no—
114D4×Dic3C2×D312yes—
115C2×#213C2×D312yes—
116C4×#67—62no—
117C2×D24C2×D311yescharacteristic
118C2×ΓL(1,𝔽25)—31no—
119C2×ΓL(1,𝔽25)—31no—
120C2×ΓL(1,𝔽25)—31no—
121C2×ΓL(1,𝔽25)—31no—
122C2×ΓL(1,𝔽25)—61no—
123#895—32no—
124#888—32no—
125#885—62no—
126#884—62no—
127C4×D12—32no—
128C42×D3—31no—
129C42×D3—31no—
130#869—32no—
131C3×#106—31no—
132C3×#102—32no—
133C3×#97—31no—
134C3×C4×C8—31no—
135#832—32no—
136#832—32no—
137#832—32no—
138#832—32no—
139#832—62no—
140#832C2×D312yes—
141#821—32no—
142#817—31no—
143#817—31no—
144#817—32no—
145#817—61no—
146#817C2×D311yescharacteristic
147#815—31no—
148#815C2×D311yescharacteristic
149C8×Dic3—31no—
150C8×Dic3C2×D311yescharacteristic
151#809—32no—
152#808—32no—
153#803—31no—
154C4×C3⋊C8—31no—
155C23×C32—22no—
156C22×C3⋊D3C2×D411yescharacteristic
157C22×C3×D3—22no—
158C32×D4—22no—
159C32×D4—22no—
160C2×C32×C4C2411yescharacteristic
161#638—44no—
162C2×C3⋊Dic3—22no—
163C2×C3⋊Dic3C2×D411yescharacteristic
164C4×C3⋊D3—21no—
165C4×C3⋊D3—21no—
166C3×#67—44no—
167C3×#67—44no—
168C2×C3×Dic3—22no—
169C2×C3×Dic3—44no—
170C2×C3×Dic3C2×D412yes—
171C2×C3×Dic3C2×D412yes—
172C3×D12—22no—
173C3×D12—22no—
174#627—44no—
175#626—44no—
176#624—24no—
177D3×Dic3—44no—
178C32×C8#4112yescomplemented
179C3⋊(C3⋊C8)—21no—
180C3×C3⋊C8—21no—
181C3×C3⋊C8#4112yescomplemented
182#532—92no—
183#498—91no—
184#493—31no—
185#486—92no—
186#469—92no—
187#469—91no—
188#469—91no—
189#442—31no—
190#442—91no—
191#442—92no—
192C4×M16—91no—
193C2×C3×D4—22no—
194C2×C3×D4—32no—
195C2×C3×D4—62no—
196C2×C3×D4—62no—
197C2×C3×D4C22×D312yes—
198C2×C3×D4C22×D312yes—
199C22×C3×C4—62no—
200C2×#67—22no—
201C2×#67—22no—
202C2×#67—62no—
203C2×#67—62no—
204C2×#67—62no—
205C2×#67—122no—
206C22×Dic3—22no—
207C22×Dic3—62no—
208#237—128no—
209#235—128no—
210C2×D12—62no—
211C2×D12C22×D312yes—
212C2×C4×D3—31no—
213C2×C4×D3—31no—
214C2×C4×D3—32no—
215C2×C4×D3—32no—
216C2×C4×D3—61no—
217C2×C4×D3—62no—
218C2×Dic6—62no—
219C2×Dic6—62no—
220C3×D8—22no—
221C3×D8—22no—
222C3×D8—42no—
223C3×D8—64no—
224C3×D8—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×C22⋊C4—62no—
232C3×C42—31no—
233C3×C42—31no—
234#217—22no—
235#217—62no—
236#217—62no—
237#217—62no—
238#217—62no—
239#217—122no—
240#213—24no—
241(C2×D3)⋊C4—62no—
242(C2×D3)⋊C4—62no—
243C4⋊Dic3—32no—
244C4⋊Dic3—32no—
245C4⋊Dic3—62no—
246C4⋊Dic3—62no—
247C4⋊Dic3C22×D312yes—
248Dic3⋊C4—62no—
249C4×Dic3—32no—
250C4×Dic3—32no—
251C4×Dic3C22×D311yescharacteristic
252C4×Dic3C22×D311yescharacteristic
253C2×C3⋊C8—31no—
254C2×C3⋊C8—31no—
255C2×C3⋊C8—61no—
256C2×C3⋊C8C22×D311yescharacteristic
257C2×C3⋊C8C22×D311yescharacteristic
258D24—22no—
259ΓL(1,𝔽25)—62no—
260ΓL(1,𝔽25)—62no—
261ΓL(1,𝔽25)—62no—
262ΓL(1,𝔽25)—62no—
263ΓL(1,𝔽25)—122no—
264C22×C32—42no—
265C22×C32—42no—
266C22×C32—42no—
267C22×C32C22×D411yescharacteristic
268C2×C3⋊D3—21no—
269C2×C3⋊D3—22no—
270C2×C3×D3—42no—
271C2×C3×D3—42no—
272C2×C3×D3—42no—
273C32×C4C2×#4111yescharacteristic
274C32×C4C2×#4111yescharacteristic
275C3⋊Dic3—21no—
276C3⋊Dic3—42no—
277C3×Dic3—22no—
278C3×Dic3—42no—
279C3×Dic3AGL(1,ℤ/8)14yes—
280C2×#41—182no—
281C2×D8—32no—
282C2×D8—31no—
283C2×D8D3211yescharacteristic
284C2×M16—91no—
285C2×M16—91no—
286C4⋊Q8—92no—
287#127—32no—
288#124—182no—
289#121—92no—
290#121—92no—
291#121—182no—
292C4×D4—32no—
293C4×D4—92no—
294C4×D4—182no—
295C2×C42—91no—
296#106—31no—
297#106—92no—
298#106—91no—
299#102—32no—
300#102—92no—
301#102—92no—
302#102—92no—
303#97—31no—
304#97—91no—
305C4×C8—31no—
306C4×C8—91no—
307C23×C3—22no—
308C23×C3—22no—
309C23×C3—42no—
310C23×C3—62no—
311C22×D3—22no—
312C22×D3—31no—
313C22×D3—31no—
314C22×D3—61no—
315C3×D4—22no—
316C3×D4—22no—
317C3×D4—22no—
318C3×D4—22no—
319C3×D4—42no—
320C3×D4—42no—
321C3×D4—62no—
322C3×D4—62no—
323C3×D4—124no—
324C3×D4—124no—
325C2×C3×C4—21no—
326C2×C3×C4—32no—
327C2×C3×C4—32no—
328C2×C3×C4—62no—
329C2×C3×C4—124no—
330C2×C3×C4C23×D311yescharacteristic
331C2×C3×C4C23×D311yescharacteristic
332#67—44no—
333#67—44no—
334#67—124no—
335#67—124no—
336#67—124no—
337#67—244no—
338C2×Dic3—22no—
339C2×Dic3—31no—
340C2×Dic3—31no—
341C2×Dic3—44no—
342C2×Dic3—61no—
343C2×Dic3—62no—
344C2×Dic3—62no—
345C2×Dic3—122no—
346C2×Dic3—124no—
347C2×Dic3D3×D412yes—
348C2×Dic3D3×D412yes—
349D12—22no—
350D12—22no—
351D12—124no—
352C4×D3—64no—
353C4×D3—61no—
354C4×D3—61no—
355C4×D3—61no—
356C4×D3—61no—
357C4×D3—64no—
358C4×D3—121no—
359C4×D3—121no—
360C4×D3—124no—
361Dic6—124no—
362Dic6—124no—
363C3×C8—22no—
364C3×C8—32no—
365C3×C8—61no—
366C3×C8#23512yescomplemented
367C3×C8#23712yescomplemented
368C3⋊C8—21no—
369C3⋊C8—61no—
370C3⋊C8—61no—
371C3⋊C8—121no—
372C3⋊C8#23712yescomplemented
373C2×C32—82no—
374C2×C32#53211yescharacteristic
375C2×C32C2×AGL(1,ℤ/8)12yes—
376C3⋊D3—41no—
377C3×D3—82no—
378#41—368no—
379C2×Q8—182no—
380C2×D4—32no—
381C2×D4—62no—
382C2×D4—62no—
383C2×D4—182no—
384C2×D4—182no—
385C2×D4C2×D3212yes—
386C22×C4—62no—
387C22×C4—92no—
388C22×C4—91no—
389C22×C4—182no—
390D8—22no—
391D8—64no—
392D8—62no—
393M16—182no—
394M16—182no—
395C2×C8—31no—
396C2×C8—31no—
397C2×C8—91no—
398C2×C8C2×D3211yescharacteristic
399C4⋊C4—32no—
400C4⋊C4—92no—
401C4⋊C4—182no—
402C22⋊C4—62no—
403C22⋊C4—182no—
404C22⋊C4—182no—
405C22⋊C4—182no—
406C42—31no—
407C42—31no—
408C42—92no—
409C22×C3—21no—
410C22×C3—42no—
411C22×C3—42no—
412C22×C3—42no—
413C22×C3—42no—
414C22×C3—42no—
415C22×C3—42no—
416C22×C3—82no—
417C22×C3—82no—
418C22×C3—82no—
419C22×C3—122no—
420C22×C3—122no—
421C22×C3—122no—
422C22×C3C2×D3×D411yescharacteristic
423C22×C3C2×D3×D411yescharacteristic
424C2×D3—42no—
425C2×D3—42no—
426C2×D3—42no—
427C2×D3—61no—
428C2×D3—62no—
429C2×D3—62no—
430C2×D3—61no—
431C2×D3—121no—
432C2×D3—122no—
433C3×C4—21no—
434C3×C4—21no—
435C3×C4—34no—
436C3×C4—62no—
437C3×C4—122no—
438C3×C4C2×#23511yescharacteristic
439C3×C4C2×#23711yescharacteristic
440C3×C4C2×#23711yescharacteristic
441C3×C4D3×#4111yescharacteristic
442Dic3—22no—
443Dic3—42no—
444Dic3—61no—
445Dic3—61no—
446Dic3—121no—
447Dic3—122no—
448Dic3—122no—
449Dic3—242no—
450Dic3#91114yes—
451C32#318411yescharacteristic, complemented, Sylow
452C23—22no—
453C23—62no—
454C23—91no—
455Q8—364no—
456D4—22no—
457D4—22no—
458D4—62no—
459D4—62no—
460D4—124no—
461D4—124no—
462D4—364no—
463D4—364no—
464C2×C4—32no—
465C2×C4—32no—
466C2×C4—62no—
467C2×C4—91no—
468C2×C4—124no—
469C2×C4—184no—
470C2×C4—181no—
471C2×C4—181no—
472C2×C4—182no—
473C2×C4—364no—
474C2×C4C22×D3211yescharacteristic
475C8—32no—
476C8—61no—
477C8—181no—
478C8#380412yescomplemented
479C2×C3—21no—
480C2×C3—22no—
481C2×C3—82no—
482C2×C3—82no—
483C2×C3—162no—
484C2×C3—242no—
485C2×C3#554811yescharacteristic
486C2×C3#571611yescharacteristic
487C2×C3C2×#91112yes—
488C2×C3D3×AGL(1,ℤ/8)12yes—
489D3—82no—
490D3—121no—
491D3—121no—
492D3—241no—
493C22—42no—
494C22—42no—
495C22—42no—
496C22—122no—
497C22—122no—
498C22—122no—
499C22—181no—
500C22—182no—
501C22D32×D411yescharacteristic
502C4—34no—
503C4—62no—
504C4—122no—
505C4—181no—
506C4—362no—
507C4D3×#23711yescharacteristic
508C4C2×#380411yescharacteristic
509C3—21no—
510C3#7987711yescharacteristic, complemented
511C3#8177711yescharacteristic, complemented
512C2—82no—
513C2—242no—
514C2—361no—
515C2D3×#91112yes—
516C2#1059513911yescharacteristic
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. #10595139C2semidirect
2. #10592858C2semidirect
3. C3×#5152C2semidirect
4. C3×#5151C2semidirect
5. #10591487C2semidirect
6. #10591454C2semidirect
7. #10591430C2semidirect
8. #10590889C2semidirect
9. #10590846C2semidirect
10. #10590771C2semidirect
11. #10590664C2semidirect
52. #5152D3semidirect
53. #5151D3semidirect
178. C32×C8#41semidirect
181. C3×C3⋊C8#41semidirect
366. C3×C8#235semidirect
367. C3×C8#237semidirect
372. C3⋊C8#237semidirect
451. C32#3184semidirect
478. C8#3804semidirect
510. C3#79877semidirect
511. C3#81777semidirect

Maximal subgroups

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

subgroupindex
#105951392
#105928582
C3×#51522
C3×#51512
#105914872
#105914542
#105914302
#105908892
#105908462
#105907712
#105906642
#817773
#798773