Finite Group Databasebeta

← #11876985

Subgroups — #11876985

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#10594910C212yesmaximal, complemented
2#10592834C211yesmaximal, characteristic, complemented
3C3×#5135C211yesmaximal, characteristic, complemented
4C3×Dic3×M16C211yesmaximal, characteristic, complemented
5#10591165C212yesmaximal, complemented
6#10590889C211yesmaximal, characteristic, complemented
7#10590880C211yesmaximal, characteristic, complemented
8#10590878C212yesmaximal, complemented
9#10590771C211yesmaximal, characteristic, complemented
10#10590768C211yesmaximal, characteristic, complemented
11#10590746C212yesmaximal, complemented
12#80853—31nomaximal
13#78535—31nomaximal
14C2×#3804—22no—
15C2×C32×M16C2211yescharacteristic
16#64139C2212yes—
17C2×#3745C2211yescharacteristic
18C3×#930C2212yes—
19C2×C3×C4×Dic3C2211yescharacteristic
20C2×C3×#208C2211yescharacteristic
21C2×C3×D24C2211yescharacteristic
22#63978—22no—
23#63918C2212yes—
24#63911C2212yes—
25#63894C2212yes—
26Dic3×D12C2212yes—
27#63880—22no—
28#63852—22no—
29C2×#3714C2212yes—
30#63648C2212yes—
31#63644C2211yescharacteristic
32C3×#821C2212yes—
33C3×#817C2211yescharacteristic
34C3×#815C2211yescharacteristic
35C3×#815C2211yescharacteristic
36C3×C8×Dic3C2211yescharacteristic
37C3×C8×Dic3C2211yescharacteristic
38#63573C2212yes—
39#63564C2212yes—
40#63563C2212yes—
41#5596—32no—
42#5477—32no—
43C3×#469—31no—
44C3×C4×M16—31no—
45#5152—31no—
46#5151—31no—
47#5135—31no—
48#5135—31no—
49#5135—32no—
50#5135—61no—
51#5135D311yescharacteristic, complemented
52Dic3×M16D311yescharacteristic, complemented
53#5039—32no—
54#4869—31no—
55#4855—31no—
56#4785—32no—
57#4760—32no—
58#4711—31no—
59#4711—32no—
60#4711—31no—
61#4695—31no—
62#4694—32no—
63#4680—31no—
64C22×C32×C4C2311yescharacteristic
65C2×#638—22no—
66C2×C4⋊(C3⋊D3)C2312yes—
67C2×C3×#67—22no—
68C22×C3×Dic3D412yes—
69C2×C3×D12C2312yes—
70C2×#627—22no—
71C2×#626—22no—
72C2×#626—22no—
73C2×#624—22no—
74#3804—48no—
75C2×D3×Dic3—22no—
76C32×M16—22no—
77C2×C32×C8C2311yescharacteristic
78C2×C32×C8C2311yescharacteristic
79#3752—22no—
80C4⋊(C3⋊Dic3)C2312yes—
81#3745—22no—
82C3×(C2×D3)⋊C4—22no—
83C3×C4⋊Dic3C2312yes—
84C3×C4×Dic3D412yes—
85C3×C4×Dic3C2311yescharacteristic
86C3×C4×Dic3C2311yescharacteristic
87C3×#208—22no—
88C2×C3×C3⋊C8C2311yescharacteristic
89C2×C3×C3⋊C8C2311yescharacteristic
90C3×D24—22no—
91Dic3⋊Dic3—22no—
92#3722—22no—
93(C2×D3)⋊Dic3—22no—
94#3714—24no—
95#3184—91noSylow
96C2×#237—62no—
97C2×#235—62no—
98C2×C3×D8—31no—
99C2×C3×M16—21no—
100C2×C3×M16—31no—
101C2×C3×M16C2×D311yescharacteristic
102C2×C3×M16C2×D311yescharacteristic
103C3×#121—32no—
104C2×C3×C42—31no—
105#940—32no—
106#939—62no—
107D4×Dic3—32no—
108C2×#213—32no—
109#930—32no—
110#930—32no—
111#930—62no—
112#930—62no—
113#930C2×D312yes—
114C2×C4×Dic3C2×D311yescharacteristic
115C2×#208C2×D311yescharacteristic
116C2×D24—32no—
117C2×D24—31no—
118C2×D24—31no—
119C2×D24—61no—
120C2×D24C2×D311yescharacteristic
121#893—32no—
122#888—32no—
123#885—62no—
124#67⋊C4—62no—
125#875—62no—
126#874—32no—
127C4×D12—32no—
128C4×D12—32no—
129C4×D12—62no—
130#869—32no—
131C3×#106—31no—
132C3×#102—32no—
133C3×#97—31no—
134C3×#97—31no—
135C3×C4×C8—31no—
136C3×C4×C8—31no—
137#832—32no—
138#821—32no—
139#821—32no—
140#821—32no—
141#821—32no—
142#821—62no—
143#821C2×D312yes—
144#817—31no—
145#817—31no—
146#817—32no—
147#817—61no—
148#817C2×D311yescharacteristic
149#815C2×D311yescharacteristic
150#815C2×D311yescharacteristic
151C8×Dic3C2×D311yescharacteristic
152C8×Dic3C2×D311yescharacteristic
153#809—32no—
154#808—32no—
155C23×C32C2×D411yescharacteristic
156C22×C3⋊D3—22no—
157C22×C3×D3—22no—
158C2×C32×C4—21no—
159C2×C32×C4—21no—
160C2×C32×C4C2×D411yescharacteristic
161C2×C32×C4C2411yescharacteristic
162#638—44no—
163C2×C3⋊Dic3—22no—
164C4⋊(C3⋊D3)—22no—
165C4⋊(C3⋊D3)—22no—
166C3×#67—44no—
167C2×C3×Dic3—24no—
168C2×C3×Dic3—22no—
169C2×C3×Dic3C2×D412yes—
170C2×C3×Dic3C2×D412yes—
171C3×D12—22no—
172C3×D12—22no—
173#627—44no—
174#626—44no—
175#626—44no—
176#624—44no—
177D3×Dic3—44no—
178C32×C8—21no—
179C32×C8#4112yescomplemented
180C3×C3⋊C8—21no—
181C3×C3⋊C8#4112yescomplemented
182#532—92no—
183#498—91no—
184#493—91no—
185#486—92no—
186#469—31no—
187#469—92no—
188#469—91no—
189#442—92no—
190#442—91no—
191#442—91no—
192C4×M16—31no—
193C2×C3×D4—32no—
194C2×C3×D4—62no—
195C22×C3×C4—21no—
196C22×C3×C4—32no—
197C22×C3×C4C22×D311yescharacteristic
198C22×C3×C4C22×D311yescharacteristic
199C2×#67—22no—
200C2×#67—62no—
201C2×#67—62no—
202C2×#67—62no—
203C2×#67—62no—
204C2×#67—122no—
205C22×Dic3—62no—
206C22×Dic3D1212yes—
207#237—128no—
208#235—128no—
209C2×D12—32no—
210C2×D12—32no—
211C2×D12—62no—
212C2×D12—62no—
213C2×D12—62no—
214C2×D12C22×D312yes—
215C2×C4×D3—62no—
216C2×C4×D3—62no—
217C2×C4×D3—62no—
218C2×Dic6—62no—
219C2×Dic6—62no—
220C3×D8—62no—
221C3×M16—22no—
222C3×M16—22no—
223C3×M16—42no—
224C3×M16—62no—
225C2×C3×C8—21no—
226C2×C3×C8—21no—
227C2×C3×C8—31no—
228C2×C3×C8—31no—
229C2×C3×C8C22×D311yescharacteristic
230C2×C3×C8C22×D311yescharacteristic
231C2×C3×C8C22×D311yescharacteristic
232C2×C3×C8C22×D311yescharacteristic
233C3×C4⋊C4—32no—
234C3×C22⋊C4—62no—
235C3×C42—32no—
236C3×C42—31no—
237C3×C42—31no—
238#217—62no—
239#213—64no—
240(C2×D3)⋊C4—22no—
241(C2×D3)⋊C4—62no—
242(C2×D3)⋊C4—62no—
243(C2×D3)⋊C4—62no—
244(C2×D3)⋊C4—62no—
245(C2×D3)⋊C4—62no—
246(C2×D3)⋊C4—122no—
247C4⋊Dic3—32no—
248C4⋊Dic3—32no—
249C4⋊Dic3—62no—
250C4⋊Dic3—62no—
251C4⋊Dic3C22×D312yes—
252Dic3⋊C4—62no—
253C4×Dic3D1212yes—
254C4×Dic3C22×D311yescharacteristic
255C4×Dic3C22×D311yescharacteristic
256#208—22no—
257C2×C3⋊C8C22×D311yescharacteristic
258C2×C3⋊C8C22×D311yescharacteristic
259D24—22no—
260D24—64no—
261D24—62no—
262D24—62no—
263D24—122no—
264C22×C32—21no—
265C22×C32—22no—
266C22×C32C22×D411yescharacteristic
267C2×C3⋊D3—42no—
268C2×C3⋊D3—42no—
269C2×C3⋊D3—42no—
270C2×C3×D3—42no—
271C2×C3×D3—42no—
272C2×C3×D3—42no—
273C32×C4—21no—
274C32×C4C2×#4111yescharacteristic
275C32×C4C2×#4111yescharacteristic
276C3⋊Dic3—42no—
277C3×Dic3—22no—
278C3×Dic3—42no—
279C3×Dic3AGL(1,ℤ/8)14yes—
280C2×#41—182no—
281C2×D8—31no—
282C2×D8—92no—
283C2×D8—91no—
284C2×M16—31no—
285C2×M16D3211yescharacteristic
286C4⋊Q8—92no—
287#127—92no—
288#124—182no—
289#121—32no—
290#121—92no—
291#121—182no—
292C4×D4—92no—
293C4×D4—92no—
294C4×D4—182no—
295C2×C42—31no—
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—31no—
305C4×C8—31no—
306C4×C8—31no—
307C23×C3—21no—
308C23×C3—62no—
309C23×C3C2×D1211yescharacteristic
310C23×C3D3×D411yescharacteristic
311C22×D3—22no—
312C22×D3—62no—
313C22×D3—62no—
314C22×D3—122no—
315C3×D4—62no—
316C3×D4—62no—
317C3×D4—124no—
318C2×C3×C4—21no—
319C2×C3×C4—21no—
320C2×C3×C4—21no—
321C2×C3×C4—21no—
322C2×C3×C4—21no—
323C2×C3×C4—21no—
324C2×C3×C4—32no—
325C2×C3×C4—32no—
326C2×C3×C4—41no—
327C2×C3×C4—41no—
328C2×C3×C4—64no—
329C2×C3×C4—62no—
330C2×C3×C4C2×D1211yescharacteristic
331C2×C3×C4D3×D411yescharacteristic
332C2×C3×C4C23×D311yescharacteristic
333C2×C3×C4C23×D311yescharacteristic
334#67—44no—
335#67—124no—
336#67—124no—
337#67—124no—
338#67—124no—
339#67—244no—
340C2×Dic3—24no—
341C2×Dic3—22no—
342C2×Dic3—62no—
343C2×Dic3—62no—
344C2×Dic3—122no—
345C2×Dic3—124no—
346C2×Dic3C2×D1212yes—
347C2×Dic3C2×D1212yes—
348D12—22no—
349D12—22no—
350D12—62no—
351D12—62no—
352D12—62no—
353D12—62no—
354D12—122no—
355D12—122no—
356D12—124no—
357D12—124no—
358C4×D3—124no—
359C4×D3—124no—
360C4×D3—124no—
361Dic6—124no—
362Dic6—124no—
363C3×C8—21no—
364C3×C8—21no—
365C3×C8—22no—
366C3×C8—32no—
367C3×C8—41no—
368C3×C8—61no—
369C3×C8#23512yescomplemented
370C3×C8#23712yescomplemented
371C3⋊C8—21no—
372C3⋊C8#23512yescomplemented
373C2×C32—41no—
374C2×C32#53211yescharacteristic
375C2×C32C2×AGL(1,ℤ/8)12yes—
376C3⋊D3—82no—
377C3×D3—82no—
378#41—368no—
379C2×Q8—182no—
380C2×D4—32no—
381C2×D4—62no—
382C2×D4—92no—
383C2×D4—182no—
384C2×D4—182no—
385C2×D4—182no—
386C22×C4—32no—
387C22×C4—182no—
388C22×C4—182no—
389C22×C4C2×D3211yescharacteristic
390D8—62no—
391D8—184no—
392D8—182no—
393M16—22no—
394M16—62no—
395C2×C8—31no—
396C2×C8—31no—
397C2×C8C2×D3211yescharacteristic
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—32no—
409C22×C3—21no—
410C22×C3—22no—
411C22×C3—22no—
412C22×C3—21no—
413C22×C3—21no—
414C22×C3—42no—
415C22×C3—41no—
416C22×C3—122no—
417C22×C3—122no—
418C22×C3—122no—
419C22×C3C22×D1211yescharacteristic
420C22×C3C2×D3×D411yescharacteristic
421C2×D3—42no—
422C2×D3—42no—
423C2×D3—42no—
424C2×D3—122no—
425C2×D3—122no—
426C2×D3—122no—
427C2×D3—122no—
428C2×D3—122no—
429C2×D3—122no—
430C2×D3—242no—
431C2×D3—242no—
432C2×D3—242no—
433C3×C4—21no—
434C3×C4—21no—
435C3×C4—21no—
436C3×C4—21no—
437C3×C4—34no—
438C3×C4—41no—
439C3×C4—62no—
440C3×C4—122no—
441C3×C4C2×#23511yescharacteristic
442C3×C4C2×#23511yescharacteristic
443C3×C4C2×#23711yescharacteristic
444C3×C4D3×#4111yescharacteristic
445Dic3—22no—
446Dic3—42no—
447Dic3—122no—
448Dic3—122no—
449Dic3—242no—
450Dic3#90814yes—
451C32#318411yescharacteristic, complemented, Sylow
452C23—62no—
453C23—182no—
454C23D3×D1211yescharacteristic
455Q8—364no—
456D4—62no—
457D4—62no—
458D4—124no—
459D4—182no—
460D4—182no—
461D4—364no—
462D4—364no—
463D4—364no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—32no—
467C2×C4—32no—
468C2×C4—64no—
469C2×C4—62no—
470C2×C4—182no—
471C2×C4—364no—
472C2×C4—364no—
473C2×C4D3×D1211yescharacteristic
474C2×C4C22×D3211yescharacteristic
475C8—21no—
476C8—32no—
477C8—61no—
478C8#380412yescomplemented
479C2×C3—21no—
480C2×C3—22no—
481C2×C3—41no—
482C2×C3—41no—
483C2×C3—81no—
484C2×C3—242no—
485C2×C3#547711yescharacteristic
486C2×C3#559611yescharacteristic
487C2×C3C2×#90812yes—
488C2×C3D3×AGL(1,ℤ/8)12yes—
489D3—82no—
490D3—242no—
491D3—242no—
492D3—482no—
493C22—21no—
494C22—22no—
495C22—122no—
496C22—122no—
497C22—122no—
498C22—362no—
499C22—362no—
500C22—362no—
501C22C2×D3×D1211yescharacteristic
502C4—21no—
503C4—34no—
504C4—62no—
505C4—122no—
506C4—362no—
507C4D3×#23511yescharacteristic
508C4C2×#380411yescharacteristic
509C3—21no—
510C3#7853511yescharacteristic, complemented
511C3#8085311yescharacteristic, complemented
512C2—41no—
513C2—242no—
514C2—722no—
515C2D3×#90812yes—
516C2#1059491011yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×M16C22
socleC22×C32C22×D4
hypercenterC2×M16D32
hypocenterC32#3184
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. #10594910C2semidirect
2. #10592834C2semidirect
3. C3×#5135C2semidirect
4. C3×Dic3×M16C2semidirect
5. #10591165C2semidirect
6. #10590889C2semidirect
7. #10590880C2semidirect
8. #10590878C2semidirect
9. #10590771C2semidirect
10. #10590768C2semidirect
11. #10590746C2semidirect
51. #5135D3semidirect
52. Dic3×M16D3semidirect
179. C32×C8#41semidirect
181. C3×C3⋊C8#41semidirect
369. C3×C8#235semidirect
370. C3×C8#237semidirect
372. C3⋊C8#235semidirect
451. C32#3184semidirect
478. C8#3804semidirect
510. C3#78535semidirect
511. C3#80853semidirect

Maximal subgroups

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

subgroupindex
#105949102
#105928342
C3×#51352
C3×Dic3×M162
#105911652
#105908892
#105908802
#105908782
#105907712
#105907682
#105907462
#808533
#785353