Finite Group Databasebeta

← #11876983

Subgroups — #11876983

Order 1152.

958 conjugacy classes of subgroups.

The subgroup lattice has 511 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595133C212yesmaximal, complemented
2#10592851C211yesmaximal, characteristic, complemented
3C3×#5159C211yesmaximal, characteristic, complemented
4C3×#5151C211yesmaximal, characteristic, complemented
5#10591487C212yesmaximal, complemented
6#10591451C212yesmaximal, complemented
7#10591436C212yesmaximal, complemented
8#10590889C211yesmaximal, characteristic, complemented
9#10590836C211yesmaximal, characteristic, complemented
10#10590781C211yesmaximal, characteristic, complemented
11Dic3×ΓL(1,𝔽25)C211yesmaximal, characteristic, complemented
12#81777—31nomaximal
13#80853—31nomaximal
14C2×#3805—22no—
15C2×C32×D8C2211yescharacteristic
16D4×C3⋊Dic3C2212yes—
17C3×#940C2212yes—
18C3×#938C2212yes—
19C2×C3×#213C2212yes—
20C2×C3×D24C2211yescharacteristic
21C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
22#67⋊Dic3—22no—
23#63970—22no—
24#63959—22no—
25#63918C2212yes—
26#63908C2212yes—
27#63898C2212yes—
28C4×D3×Dic3C2211yescharacteristic
29C2×#3711C2211yescharacteristic
30#63659C2212yes—
31#63644C2211yescharacteristic
32#63642C2211yescharacteristic
33C3×#832C2212yes—
34C3×#817C2211yescharacteristic
35C3×C8×Dic3C2211yescharacteristic
36#63573C2212yes—
37#63563C2212yes—
38#63562C2212yes—
39#63555C2211yescharacteristic
40Dic3×C3⋊C8C2211yescharacteristic
41#5716—32no—
42#5596—32no—
43C3×#493—31no—
44C3×#469—31no—
45#5159—32no—
46#5159—31no—
47#5159D311yescharacteristic, complemented
48#5152—31no—
49#5152—31no—
50#5152—32no—
51#5152—31no—
52#5152—61no—
53#5151D311yescharacteristic, complemented
54#5135—31no—
55Dic3×M16—31no—
56#5070—32no—
57#5039—32no—
58#4869—31no—
59#4855—31no—
60#4785—32no—
61#4760—32no—
62C4×ΓL(1,𝔽25)—31no—
63#4680—31no—
64C2×C32×D4C2312yes—
65C22×C3⋊Dic3—22no—
66C2×C3×#67—22no—
67C2×C3×#67—22no—
68C2×C3×#67—22no—
69C2×C3×D12C2312yes—
70C2×C3×C4×D3C2311yescharacteristic
71C2×#627—22no—
72C2×#625—22no—
73#3805—48no—
74C2×D3×Dic3—22no—
75C2×D3×Dic3D412yes—
76C32×D8—22no—
77C2×C32×C8C2311yescharacteristic
78#3757—22no—
79C4⋊(C3⋊Dic3)C2312yes—
80C4×C3⋊Dic3C2311yescharacteristic
81C2×C3⋊(C3⋊C8)C2311yescharacteristic
82C3×#217—22no—
83C3×#213—24no—
84C3×C4⋊Dic3C2312yes—
85C3×C4×Dic3C2311yescharacteristic
86C2×C3×C3⋊C8C2311yescharacteristic
87C2×C3×C3⋊C8C2311yescharacteristic
88C3×D24—22no—
89C3×ΓL(1,𝔽25)—22no—
90Dic3⋊Dic3—22no—
91(C2×D3)⋊Dic3—22no—
92(C2×D3)⋊Dic3—22no—
93Dic32D412yes—
94#3711—22no—
95#3184—91noSylow
96C2×#237—62no—
97C2×#237—62no—
98C2×C3×D8—21no—
99C2×C3×D8—32no—
100C2×C3×D8—31no—
101C2×C3×D8C2×D311yescharacteristic
102C2×C3×D8C2×D311yescharacteristic
103C2×C3×M16—31no—
104C3×#127—32no—
105C3×#121—32no—
106#940C2×D312yes—
107#939—62no—
108#938—32no—
109#938—62no—
110#938C2×D312yes—
111#936—62no—
112D4×Dic3—32no—
113D4×Dic3—32no—
114D4×Dic3—32no—
115D4×Dic3—62no—
116D4×Dic3—62no—
117C2×#213C2×D312yes—
118#930—32no—
119C2×C4×Dic3—31no—
120C2×#208—31no—
121C2×D24C2×D311yescharacteristic
122C2×ΓL(1,𝔽25)—31no—
123C2×ΓL(1,𝔽25)C2×D311yescharacteristic
124#893—32no—
125#888—32no—
126#885—62no—
127#67⋊C4—62no—
128C42×D3—31no—
129#869—32no—
130C3×#106—31no—
131C3×#102—32no—
132C3×C4×C8—31no—
133#832—32no—
134#832—32no—
135#832—32no—
136#832—32no—
137#832—62no—
138#832C2×D312yes—
139#821—32no—
140#817—31no—
141#817—31no—
142#817—32no—
143#817—61no—
144#817C2×D311yescharacteristic
145#815—31no—
146#815—31no—
147#815—31no—
148#815—31no—
149#815—61no—
150C8×Dic3—31no—
151C8×Dic3C2×D311yescharacteristic
152#809—32no—
153#808—32no—
154C4×C3⋊C8—31no—
155C23×C32—22no—
156C22×C3×D3—22no—
157C22×C3×D3C2×D411yescharacteristic
158C32×D4—22no—
159C32×D4—22no—
160C2×C32×C4C2411yescharacteristic
161C2×C3⋊Dic3—22no—
162C2×C3⋊Dic3—44no—
163C2×C3⋊Dic3C2×D412yes—
164C3×#67—44no—
165C3×#67—44no—
166C3×#67—44no—
167C2×C3×Dic3—22no—
168C2×C3×Dic3C2×D411yescharacteristic
169C2×C3×Dic3C2×D412yes—
170C3×D12—22no—
171C3×D12—22no—
172C3×C4×D3—21no—
173C3×C4×D3—21no—
174#627—44no—
175#625—44no—
176D3×Dic3—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—31no—
187#469—92no—
188#469—91no—
189#442—92no—
190#442—91no—
191#442—91no—
192C4×M16—91no—
193C2×C3×D4—22no—
194C2×C3×D4—32no—
195C2×C3×D4—62no—
196C2×C3×D4—62no—
197C2×C3×D4—62no—
198C2×C3×D4C22×D312yes—
199C2×C3×D4C22×D312yes—
200C22×C3×C4—31no—
201C2×#67—22no—
202C2×#67—22no—
203C2×#67—22no—
204C2×#67—62no—
205C2×#67—62no—
206C22×Dic3—32no—
207C22×Dic3—62no—
208C22×Dic3—62no—
209C22×Dic3—62no—
210C22×Dic3—122no—
211#237—128no—
212#237—128no—
213C2×D12C22×D312yes—
214C2×C4×D3—32no—
215C2×C4×D3—62no—
216C2×C4×D3C22×D311yescharacteristic
217C2×Dic6—62no—
218C2×Dic6—62no—
219C3×D8—24no—
220C3×D8—22no—
221C3×D8—22no—
222C3×D8—64no—
223C3×D8—62no—
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×C22⋊C4—62no—
232C3×C42—31no—
233#217—22no—
234#217—62no—
235#217—62no—
236#217—62no—
237#217—62no—
238#217—122no—
239#213—24no—
240(C2×D3)⋊C4—62no—
241(C2×D3)⋊C4—62no—
242C4⋊Dic3—32no—
243C4⋊Dic3—32no—
244C4⋊Dic3—62no—
245C4⋊Dic3—62no—
246C4⋊Dic3C22×D312yes—
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—22no—
261ΓL(1,𝔽25)—22no—
262ΓL(1,𝔽25)—62no—
263C22×C32—42no—
264C22×C32—42no—
265C22×C32—42no—
266C22×C32C22×D411yescharacteristic
267C2×C3×D3—21no—
268C2×C3×D3—22no—
269C2×C3×D3—42no—
270C2×C3×D3—42no—
271C2×C3×D3—42no—
272C32×C4C2×#4111yescharacteristic
273C32×C4C2×#4111yescharacteristic
274C3⋊Dic3—22no—
275C3⋊Dic3—42no—
276C3×Dic3—21no—
277C3×Dic3—42no—
278C3×Dic3AGL(1,ℤ/8)14yes—
279C2×#41—182no—
280C2×D8—32no—
281C2×D8—31no—
282C2×D8D3211yescharacteristic
283C2×M16—31no—
284C2×M16—91no—
285C4⋊Q8—92no—
286#127—32no—
287#124—182no—
288#121—32no—
289#121—92no—
290#121—182no—
291C4×D4—92no—
292C4×D4—92no—
293C4×D4—182no—
294C2×C42—91no—
295#106—31no—
296#106—92no—
297#106—91no—
298#102—32no—
299#102—92no—
300#102—92no—
301#102—92no—
302#97—91no—
303#97—91no—
304C4×C8—31no—
305C4×C8—91no—
306C23×C3—22no—
307C23×C3—22no—
308C23×C3—31no—
309C23×C3—42no—
310C23×C3—62no—
311C22×D3—22no—
312C22×D3D3×D411yescharacteristic
313C3×D4—24no—
314C3×D4—22no—
315C3×D4—22no—
316C3×D4—22no—
317C3×D4—22no—
318C3×D4—42no—
319C3×D4—62no—
320C3×D4—62no—
321C3×D4—124no—
322C3×D4—124no—
323C3×D4—124no—
324C2×C3×C4—21no—
325C2×C3×C4—32no—
326C2×C3×C4—31no—
327C2×C3×C4—61no—
328C2×C3×C4—61no—
329C2×C3×C4—62no—
330C2×C3×C4C23×D311yescharacteristic
331C2×C3×C4C23×D311yescharacteristic
332#67—44no—
333#67—44no—
334#67—44no—
335#67—124no—
336#67—124no—
337C2×Dic3—22no—
338C2×Dic3—32no—
339C2×Dic3—32no—
340C2×Dic3—62no—
341C2×Dic3—64no—
342C2×Dic3—62no—
343C2×Dic3—62no—
344C2×Dic3—122no—
345C2×Dic3—124no—
346C2×Dic3—124no—
347C2×Dic3—124no—
348C2×Dic3—244no—
349C2×Dic3D3×D411yescharacteristic
350C2×Dic3D3×D412yes—
351D12—22no—
352D12—22no—
353C4×D3—21no—
354C4×D3—21no—
355C4×D3—64no—
356C4×D3—124no—
357Dic6—124no—
358Dic6—124no—
359C3×C8—22no—
360C3×C8—32no—
361C3×C8—61no—
362C3×C8#23712yescomplemented
363C3×C8#23712yescomplemented
364C3⋊C8—21no—
365C3⋊C8—61no—
366C3⋊C8—61no—
367C3⋊C8—121no—
368C3⋊C8#23712yescomplemented
369C2×C32—82no—
370C2×C32#53211yescharacteristic
371C2×C32C2×AGL(1,ℤ/8)12yes—
372C3×D3—41no—
373C3×D3—82no—
374#41—368no—
375C2×Q8—182no—
376C2×D4—32no—
377C2×D4—62no—
378C2×D4—62no—
379C2×D4—62no—
380C2×D4—182no—
381C2×D4C2×D3212yes—
382C22×C4—31no—
383C22×C4—92no—
384C22×C4—182no—
385C22×C4—182no—
386D8—22no—
387D8—64no—
388D8—62no—
389M16—62no—
390M16—182no—
391C2×C8—31no—
392C2×C8—31no—
393C2×C8—91no—
394C2×C8C2×D3211yescharacteristic
395C4⋊C4—32no—
396C4⋊C4—92no—
397C4⋊C4—182no—
398C22⋊C4—62no—
399C22⋊C4—182no—
400C22⋊C4—182no—
401C22⋊C4—182no—
402C42—31no—
403C42—92no—
404C42—91no—
405C22×C3—21no—
406C22×C3—44no—
407C22×C3—42no—
408C22×C3—42no—
409C22×C3—42no—
410C22×C3—42no—
411C22×C3—42no—
412C22×C3—42no—
413C22×C3—61no—
414C22×C3—62no—
415C22×C3—82no—
416C22×C3—82no—
417C22×C3—122no—
418C22×C3—122no—
419C22×C3—122no—
420C22×C3C2×D3×D411yescharacteristic
421C22×C3C2×D3×D411yescharacteristic
422C2×D3—22no—
423C2×D3—21no—
424C2×D3—42no—
425C2×D3—42no—
426C2×D3—42no—
427C3×C4—21no—
428C3×C4—21no—
429C3×C4—34no—
430C3×C4—61no—
431C3×C4—122no—
432C3×C4C2×#23711yescharacteristic
433C3×C4C2×#23711yescharacteristic
434C3×C4C2×#23711yescharacteristic
435C3×C4D3×#4111yescharacteristic
436Dic3—21no—
437Dic3—42no—
438Dic3—62no—
439Dic3—62no—
440Dic3—122no—
441Dic3—122no—
442Dic3—122no—
443Dic3—242no—
444Dic3#91114yes—
445C32#318411yescharacteristic, complemented, Sylow
446C23—22no—
447C23—31no—
448C23—62no—
449Q8—364no—
450D4—22no—
451D4—22no—
452D4—62no—
453D4—62no—
454D4—124no—
455D4—124no—
456D4—124no—
457D4—364no—
458C2×C4—32no—
459C2×C4—31no—
460C2×C4—61no—
461C2×C4—61no—
462C2×C4—62no—
463C2×C4—92no—
464C2×C4—184no—
465C2×C4—182no—
466C2×C4—364no—
467C2×C4—364no—
468C2×C4C22×D3211yescharacteristic
469C8—32no—
470C8—61no—
471C8—181no—
472C8#380512yescomplemented
473C2×C3—21no—
474C2×C3—22no—
475C2×C3—84no—
476C2×C3—82no—
477C2×C3—82no—
478C2×C3—121no—
479C2×C3—242no—
480C2×C3#559611yescharacteristic
481C2×C3#571611yescharacteristic
482C2×C3C2×#91112yes—
483C2×C3D3×AGL(1,ℤ/8)12yes—
484D3—41no—
485D3—82no—
486C22—42no—
487C22—42no—
488C22—42no—
489C22—61no—
490C22—62no—
491C22—122no—
492C22—122no—
493C22—122no—
494C22D32×D411yescharacteristic
495C4—34no—
496C4—61no—
497C4—122no—
498C4—182no—
499C4—362no—
500C4D3×#23711yescharacteristic
501C4C2×#380511yescharacteristic
502C3—21no—
503C3#8085311yescharacteristic, complemented
504C3#8177711yescharacteristic, complemented
505C2—82no—
506C2—121no—
507C2—242no—
508C2D3×#91112yes—
509C2#1059513311yescharacteristic
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. #10595133C2semidirect
2. #10592851C2semidirect
3. C3×#5159C2semidirect
4. C3×#5151C2semidirect
5. #10591487C2semidirect
6. #10591451C2semidirect
7. #10591436C2semidirect
8. #10590889C2semidirect
9. #10590836C2semidirect
10. #10590781C2semidirect
11. Dic3×ΓL(1,𝔽25)C2semidirect
47. #5159D3semidirect
53. #5151D3semidirect
178. C32×C8#41semidirect
181. C3×C3⋊C8#41semidirect
362. C3×C8#237semidirect
363. C3×C8#237semidirect
368. C3⋊C8#237semidirect
445. C32#3184semidirect
472. C8#3805semidirect
503. C3#80853semidirect
504. C3#81777semidirect

Maximal subgroups

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

subgroupindex
#105951332
#105928512
C3×#51592
C3×#51512
#105914872
#105914512
#105914362
#105908892
#105908362
#105907812
Dic3×ΓL(1,𝔽25)2
#817773
#808533