Finite Group Databasebeta

← #11867128

Subgroups — #11867128

Order 1152.

1644 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
1C2×#64117C211yesmaximal, characteristic, complemented
2C2×M16×C3⋊D3C211yesmaximal, characteristic, complemented
3#10595995C211yesmaximal, characteristic, complemented
4C2×#64104C211yesmaximal, characteristic, complemented
5C32×#428C211yesmaximal, characteristic, complemented
6#10592700C211yesmaximal, characteristic, complemented
7#10592665C211yesmaximal, characteristic, complemented
8#10592585C212yesmaximal, complemented
9#10592582C212yesmaximal, complemented
10#10592564C212yesmaximal, complemented
11#10592563C212yesmaximal, complemented
12#79211—34nomaximal
13C2×#3828C2211yescharacteristic
14C22×C4⋊(C3⋊D3)—21no—
15C22×C4⋊(C3⋊D3)C2211yescharacteristic
16C22×C4×C3⋊D3C2211yescharacteristic
17C2×C32×M16C2211yescharacteristic
18C32×#117C2211yescharacteristic
19C2×C32×C4⋊C4C2211yescharacteristic
20C2×#3752—21no—
21C2×#3748C2211yescharacteristic
22#64117—24no—
23M16×C3⋊D3—24no—
24C2×#3745C2212yescomplemented
25C2×#3744C2212yescomplemented
26C2×#3743C2212yescomplemented
27C2×C8×C3⋊D3C2212yescomplemented
28#64106C2211yescharacteristic, complemented
29#64106C2211yescharacteristic, complemented
30#64104—21no—
31#64104—21no—
32#64104C2212yes—
33#64104C2212yes—
34#64104C2211yescharacteristic, complemented
35#64104C2211yescharacteristic, complemented
36#64095—21no—
37#64091—21no—
38C4×C4⋊(C3⋊D3)—21no—
39C4×C4⋊(C3⋊D3)—21no—
40C32×#107C2212yescomplemented
41C32×#106C2212yescomplemented
42#63637C2212yescomplemented
43#63636C2212yescomplemented
44#63636C2212yescomplemented
45#63636C2212yescomplemented
46C2×#908—34no—
47C2×D3×M16—34no—
48#5524—34no—
49C2×#895—34no—
50C3×#428D314yescomplemented
51#5001—34no—
52#4966—34no—
53#4886—38no—
54#4883—38no—
55#4865—38no—
56#4864—38no—
57C23×C3⋊D3—21no—
58C23×C3⋊D3D411yescharacteristic
59C22×C32×C4—21no—
60C22×C32×C4C2311yescharacteristic
61C2×#638—21no—
62C22×C3⋊Dic3D411yescharacteristic
63#3828—22no—
64#3828—22no—
65C2×C4⋊(C3⋊D3)—22no—
66C2×C4⋊(C3⋊D3)—22no—
67C2×C4⋊(C3⋊D3)—21no—
68C2×C4⋊(C3⋊D3)—21no—
69C2×C4⋊(C3⋊D3)—22no—
70C2×C4⋊(C3⋊D3)—22no—
71C2×C4⋊(C3⋊D3)—21no—
72C2×C4⋊(C3⋊D3)—44no—
73C2×C4⋊(C3⋊D3)C2312yes—
74C2×C4⋊(C3⋊D3)C2311yescharacteristic
75C2×C4×C3⋊D3—22no—
76C2×C4×C3⋊D3—22no—
77C2×C4×C3⋊D3—21no—
78C2×C4×C3⋊D3D411yescharacteristic
79C2×C4×C3⋊D3D411yescharacteristic
80C2×C4×C3⋊D3C2311yescharacteristic
81C2×C4×C3⋊D3C2311yescharacteristic
82C2×#634C2311yescharacteristic
83C32×M16D414yescomplemented
84C2×C32×C8C2312yes—
85C32×C4⋊C4—21no—
86C32×C4⋊C4C2312yes—
87C32×C4⋊C4C2311yescharacteristic
88C32×C4⋊C4C2311yescharacteristic
89C32×C22⋊C4—21no—
90C32×C42—21no—
91#3752—21no—
92#3752—21no—
93#3752—21no—
94#3752—21no—
95#3752—22no—
96#3752—22no—
97C4⋊(C3⋊Dic3)—21no—
98C4⋊(C3⋊Dic3)—21no—
99#3748—22no—
100C2×C3⋊(C3⋊C8)C2312yes—
101#3745—24no—
102#3744—24no—
103#3743—24no—
104C8×C3⋊D3—24no—
105#3055—91noSylow
106C2×#235—34no—
107C22×D12—34no—
108C22×D12—64no—
109C22×C4×D3—34no—
110C2×C3×M16C2×D314yes—
111C3×#117C2×D314yes—
112C2×C3×C4⋊C4C2×D314yes—
113C2×(C2×D3)⋊C4—64no—
114C2×#208—34no—
115#908—616no—
116D3×M16—616no—
117C2×D24—38no—
118C2×#204—38no—
119C2×ΓL(1,𝔽25)—38no—
120C2×D3×C8—38no—
121#897—34no—
122#897—34no—
123#895—38no—
124#895—34no—
125#895—38no—
126#895—34no—
127#895—64no—
128#895—64no—
129#886—64no—
130#882—64no—
131C4×D12—64no—
132C4×D12—64no—
133C3×#107C2×D318yescomplemented
134C3×#106C2×D318yescomplemented
135#810—38no—
136#809—38no—
137#809—38no—
138#809—38no—
139C23×C32C2×D411yescharacteristic
140C22×C3⋊D3—22no—
141C22×C3⋊D3—22no—
142C22×C3⋊D3—22no—
143C22×C3⋊D3—21no—
144C22×C3⋊D3—41no—
145C22×C3⋊D3—42no—
146C22×C3⋊D3—42no—
147C22×C3⋊D3—42no—
148C22×C3⋊D3C2×D411yescharacteristic
149C22×C3⋊D3C2×D411yescharacteristic
150C2×C32×C4—21no—
151C2×C32×C4—21no—
152C2×C32×C4—22no—
153C2×C32×C4—42no—
154C2×C32×C4C2×D412yes—
155C2×C32×C4C2×D411yescharacteristic
156C2×C32×C4#4112yes—
157C2×C32×C4C2411yescharacteristic
158#638—42no—
159C2×C3⋊Dic3—22no—
160C2×C3⋊Dic3—21no—
161C2×C3⋊Dic3C2×D411yescharacteristic
162C2×C3⋊Dic3C2×D411yescharacteristic
163C4⋊(C3⋊D3)—22no—
164C4⋊(C3⋊D3)—21no—
165C4⋊(C3⋊D3)—22no—
166C4⋊(C3⋊D3)—21no—
167C4⋊(C3⋊D3)—42no—
168C4⋊(C3⋊D3)—44no—
169C4⋊(C3⋊D3)—42no—
170C4⋊(C3⋊D3)—44no—
171C4⋊(C3⋊D3)—42no—
172C4×C3⋊D3—22no—
173C4×C3⋊D3—22no—
174C4×C3⋊D3—21no—
175C4×C3⋊D3—21no—
176C4×C3⋊D3—21no—
177C4×C3⋊D3—21no—
178C4×C3⋊D3—42no—
179#634—21no—
180#634—21no—
181C32×C8C2×D414yescomplemented
182C3⋊(C3⋊C8)—22no—
183C2×AGL(1,ℤ/8)—91no—
184C22×M16—91no—
185#525—91no—
186C2×#121—91no—
187#469—92no—
188#468—92no—
189#466—92no—
190#465—92no—
191#428C3⋊D311yescharacteristic, complemented
192#418—91no—
193#417—91no—
194C23×D3—34no—
195C23×D3—64no—
196C22×C3×C4—24no—
197C22×C3×C4C22×D314yes—
198C2×#67—64no—
199C22×Dic3—34no—
200#235—68no—
201#235—68no—
202C2×D12—38no—
203C2×D12—34no—
204C2×D12—68no—
205C2×D12—68no—
206C2×D12—64no—
207C2×D12—64no—
208C2×D12—68no—
209C2×D12—68no—
210C2×D12—64no—
211C2×D12—1216no—
212C2×C4×D3—34no—
213C2×C4×D3—34no—
214C2×C4×D3—34no—
215C2×C4×D3—34no—
216C2×C4×D3—68no—
217C2×C4×D3—68no—
218C2×C4×D3—64no—
219C2×Dic6—34no—
220C3×M16D12116yescomplemented
221C2×C3×C8C22×D318yes—
222C3×C4⋊C4—24no—
223C3×C4⋊C4C22×D314yes—
224C3×C4⋊C4C22×D314yes—
225C3×C4⋊C4C22×D318yes—
226C3×C22⋊C4—24no—
227C3×C42—24no—
228(C2×D3)⋊C4—64no—
229(C2×D3)⋊C4—64no—
230(C2×D3)⋊C4—68no—
231(C2×D3)⋊C4—68no—
232(C2×D3)⋊C4—64no—
233(C2×D3)⋊C4—64no—
234C4⋊Dic3—64no—
235C4⋊Dic3—64no—
236#208—68no—
237C2×C3⋊C8—38no—
238D24—616no—
239#204—616no—
240ΓL(1,𝔽25)—616no—
241D3×C8—616no—
242C22×C32—21no—
243C22×C32—21no—
244C22×C32#12112yes—
245C22×C32C22×D411yescharacteristic
246C2×C3⋊D3—21no—
247C2×C3⋊D3—21no—
248C2×C3⋊D3—21no—
249C2×C3⋊D3—21no—
250C2×C3⋊D3—21no—
251C2×C3⋊D3—44no—
252C2×C3⋊D3—41no—
253C2×C3⋊D3—42no—
254C2×C3⋊D3—42no—
255C2×C3⋊D3—41no—
256C2×C3⋊D3—41no—
257C2×C3⋊D3—42no—
258C2×C3⋊D3—84no—
259C2×C3⋊D3AGL(1,ℤ/8)12yescomplemented
260C32×C4—42no—
261C32×C4—41no—
262C32×C4—41no—
263C32×C4#12112yes—
264C32×C4C22×D411yescharacteristic
265C32×C4C2×#4111yescharacteristic
266C3⋊Dic3—21no—
267C3⋊Dic3—21no—
268C3⋊Dic3—41no—
269C2×#41—91no—
270C22×D4—91no—
271C22×D4—181no—
272C23×C4—91no—
273AGL(1,ℤ/8)—184no—
274C2×SD16—92no—
275C2×D8—92no—
276C2×M16—91no—
277C2×M16—92no—
278C2×M16—184no—
279C2×M16C2×C3⋊D311yescharacteristic
280C22×C8—92no—
281#123—181no—
282C22⋊Q8—91no—
283C22⋊Q8—91no—
284#121—92no—
285#121—92no—
286#121—91no—
287#121—91no—
288#121—181no—
289#121—181no—
290#120—181no—
291C4×D4—181no—
292C4×D4—181no—
293#117C2×C3⋊D311yescharacteristic
294C2×C4⋊C4C2×C3⋊D311yescharacteristic
295C2×C22⋊C4—181no—
296#107C2×C3⋊D312yescomplemented
297#106C2×C3⋊D312yescomplemented
298#103—92no—
299#102—92no—
300#102—92no—
301#102—92no—
302C23×C3D3×D414yes—
303C22×D3—34no—
304C22×D3—34no—
305C22×D3—68no—
306C22×D3—68no—
307C22×D3—64no—
308C22×D3—68no—
309C22×D3—124no—
310C22×D3—128no—
311C22×D3—128no—
312C22×D3—128no—
313C2×C3×C4—24no—
314C2×C3×C4—24no—
315C2×C3×C4—28no—
316C2×C3×C4—48no—
317C2×C3×C4C2×D1218yes—
318C2×C3×C4D3×D414yes—
319C2×C3×C4#23918yes—
320C2×C3×C4C23×D314yes—
321#67—128no—
322C2×Dic3—34no—
323C2×Dic3—34no—
324C2×Dic3—68no—
325C2×Dic3—64no—
326D12—68no—
327D12—64no—
328D12—68no—
329D12—64no—
330D12—128no—
331D12—1216no—
332D12—128no—
333D12—1216no—
334D12—128no—
335C4×D3—68no—
336C4×D3—68no—
337C4×D3—64no—
338C4×D3—64no—
339C4×D3—64no—
340C4×D3—64no—
341C4×D3—128no—
342Dic6—64no—
343Dic6—64no—
344C3×C8C2×D12116yescomplemented
345C3⋊C8—68no—
346C2×C32—22no—
347C2×C32C2×#12111yescharacteristic
348C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
349C2×C32#57511yescharacteristic
350C3⋊D3—22no—
351C3⋊D3—41no—
352C3⋊D3—81no—
353C3⋊D3—82no—
354C24—91no—
355C24—181no—
356#41—182no—
357#41—182no—
358C2×Q8—91no—
359C2×D4—91no—
360C2×D4—92no—
361C2×D4—181no—
362C2×D4—181no—
363C2×D4—182no—
364C2×D4—182no—
365C2×D4—181no—
366C2×D4—182no—
367C2×D4—181no—
368C2×D4—182no—
369C2×D4—364no—
370C22×C4—21no—
371C22×C4—91no—
372C22×C4—91no—
373C22×C4—91no—
374C22×C4—91no—
375C22×C4—91no—
376C22×C4—182no—
377C22×C4—182no—
378C22×C4—181no—
379C22×C4C22×C3⋊D311yescharacteristic
380SD16—184no—
381D8—184no—
382M16—182no—
383M16—184no—
384M16C4⋊(C3⋊D3)14yescomplemented
385C2×C8—92no—
386C2×C8—184no—
387C2×C8C22×C3⋊D312yes—
388C4⋊C4—21no—
389C4⋊C4—181no—
390C4⋊C4—181no—
391C4⋊C4C22×C3⋊D311yescharacteristic
392C4⋊C4C22×C3⋊D311yescharacteristic
393C4⋊C4C22×C3⋊D312yes—
394C22⋊C4—21no—
395C22⋊C4—182no—
396C22⋊C4—182no—
397C22⋊C4—181no—
398C22⋊C4—181no—
399C22⋊C4—181no—
400C22⋊C4—181no—
401C42—21no—
402C22×C3—24no—
403C22×C3—24no—
404C22×C3#89518yes—
405C22×C3C2×D3×D414yes—
406C2×D3—38no—
407C2×D3—64no—
408C2×D3—64no—
409C2×D3—64no—
410C2×D3—64no—
411C2×D3—64no—
412C2×D3—1216no—
413C2×D3—124no—
414C2×D3—128no—
415C2×D3—128no—
416C2×D3—124no—
417C2×D3—124no—
418C2×D3—128no—
419C2×D3—2416no—
420C3×C4—48no—
421C3×C4—44no—
422C3×C4—44no—
423C3×C4#89518yes—
424C3×C4C22×D1214yes—
425C3×C4C2×#23914yes—
426Dic3—64no—
427Dic3—64no—
428Dic3—124no—
429C32#305511yescharacteristic, complemented, Sylow
430C23—91no—
431C23—91no—
432C23—182no—
433C23—182no—
434C23—181no—
435C23—182no—
436C23—361no—
437C23—362no—
438C23—362no—
439C23—362no—
440C23D4×C3⋊D311yescharacteristic
441Q8—181no—
442Q8—181no—
443D4—181no—
444D4—182no—
445D4—182no—
446D4—181no—
447D4—364no—
448D4—362no—
449D4—364no—
450D4—362no—
451D4—362no—
452D4—362no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—22no—
456C2×C4—42no—
457C2×C4—91no—
458C2×C4—91no—
459C2×C4—182no—
460C2×C4—181no—
461C2×C4—181no—
462C2×C4—182no—
463C2×C4—182no—
464C2×C4—181no—
465C2×C4—181no—
466C2×C4—181no—
467C2×C4—362no—
468C2×C4C2×C4⋊(C3⋊D3)12yes—
469C2×C4D4×C3⋊D311yescharacteristic
470C2×C4#383212yes—
471C2×C4C23×C3⋊D311yescharacteristic
472C8—182no—
473C8C2×C4⋊(C3⋊D3)14yescomplemented
474C2×C3—28no—
475C2×C3C2×#89514yes—
476C2×C3D3×AGL(1,ℤ/8)14yes—
477C2×C3#577714yes—
478D3—68no—
479D3—124no—
480D3—248no—
481D3—244no—
482C22—21no—
483C22—21no—
484C22—92no—
485C22—181no—
486C22—181no—
487C22—181no—
488C22—181no—
489C22—181no—
490C22—364no—
491C22—361no—
492C22—362no—
493C22—362no—
494C22—361no—
495C22—361no—
496C22—362no—
497C22—724no—
498C22#6410412yes—
499C22C2×D4×C3⋊D311yescharacteristic
500C4—42no—
501C4—41no—
502C4—41no—
503C4—181no—
504C4—181no—
505C4—361no—
506C4#6410412yes—
507C4C22×C4⋊(C3⋊D3)11yescharacteristic
508C4C2×#383211yescharacteristic
509C3#7921114yescomplemented
510C2—22no—
511C2—182no—
512C2—361no—
513C2—722no—
514C2—721no—
515C2C2×#6410411yescharacteristic
516C2C3⋊D3×AGL(1,ℤ/8)11yescharacteristic
517C2#1059624811yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#428C2
socleC22×C32C22×D4
hypercenter#428C3⋊D3
hypocenterC32#3055
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
1. C2×#64117C2semidirect
2. C2×M16×C3⋊D3C2semidirect
3. #10595995C2semidirect
4. C2×#64104C2semidirect
5. C32×#428C2semidirect
6. #10592700C2semidirect
7. #10592665C2semidirect
8. #10592585C2semidirect
9. #10592582C2semidirect
10. #10592564C2semidirect
11. #10592563C2semidirect
24. C2×#3745C22semidirect
25. C2×#3744C22semidirect
26. C2×#3743C22semidirect
27. C2×C8×C3⋊D3C22semidirect
28. #64106C22semidirect
29. #64106C22semidirect
34. #64104C22semidirect
35. #64104C22semidirect
40. C32×#107C22semidirect
41. C32×#106C22semidirect
42. #63637C22semidirect
43. #63636C22semidirect
44. #63636C22semidirect
45. #63636C22semidirect
50. C3×#428D3semidirect
83. C32×M16D4semidirect
133. C3×#107C2×D3semidirect
134. C3×#106C2×D3semidirect
181. C32×C8C2×D4semidirect
191. #428C3⋊D3semidirect
220. C3×M16D12semidirect
259. C2×C3⋊D3AGL(1,ℤ/8)semidirect
296. #107C2×C3⋊D3semidirect
297. #106C2×C3⋊D3semidirect
344. C3×C8C2×D12semidirect
384. M16C4⋊(C3⋊D3)semidirect
429. C32#3055semidirect
473. C8C2×C4⋊(C3⋊D3)semidirect
509. C3#79211semidirect

Maximal subgroups

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

subgroupindex
C2×#641172
C2×M16×C3⋊D32
#105959952
C2×#641042
C32×#4282
#105927002
#105926652
#105925852
#105925822
#105925642
#105925632
#792113