Finite Group Databasebeta

← #11867119

Subgroups — #11867119

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×#64147C211yesmaximal, characteristic, complemented
2C2×#64141C211yesmaximal, characteristic, complemented
3C2×M16×C3⋊D3C211yesmaximal, characteristic, complemented
4#10595995C211yesmaximal, characteristic, complemented
5C32×#418C211yesmaximal, characteristic, complemented
6#10592832C211yesmaximal, characteristic, complemented
7#10592694C211yesmaximal, characteristic, complemented
8#10592481C212yesmaximal, complemented
9#10592479C212yesmaximal, complemented
10#10592477C212yesmaximal, complemented
11#10592474C212yesmaximal, complemented
12#78930—34nomaximal
13C22×C32×D4C2211yescharacteristic
14C22×#638—21no—
15C2×#3828C2211yescharacteristic
16C22×C4×C3⋊D3C2211yescharacteristic
17C2×C32×M16C2211yescharacteristic
18C32×#117C2211yescharacteristic
19C2×#3757—21no—
20#64147—21no—
21#64147—21no—
22#64147C2212yes—
23#64147C2212yes—
24C2×#3754C2212yescomplemented
25#64141—24no—
26C2×#3753C2212yescomplemented
27C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
28C2×#3748C2211yescharacteristic
29M16×C3⋊D3—24no—
30C2×#3743C2212yescomplemented
31C2×C8×C3⋊D3C2212yescomplemented
32#64106C2211yescharacteristic, complemented
33#64106C2211yescharacteristic, complemented
34#64104C2211yescharacteristic, complemented
35#64104C2211yescharacteristic, complemented
36#64095—21no—
37#64091—21no—
38C4×C4⋊(C3⋊D3)—21no—
39C4×C4⋊(C3⋊D3)—21no—
40C32×#102C2212yescomplemented
41C32×#102C2212yescomplemented
42#63648C2212yescomplemented
43#63643C2212yescomplemented
44#63635C2212yescomplemented
45#63634C2212yescomplemented
46C2×#938—34no—
47C2×#932—34no—
48C2×D3×M16—34no—
49#5524—34no—
50C3×#418D314yescomplemented
51#5133—34no—
52#4995—34no—
53#4782—38no—
54#4780—38no—
55#4778—38no—
56#4775—38no—
57C24×C32—21no—
58C23×C3⋊D3D411yescharacteristic
59C2×C32×D4—22no—
60C2×C32×D4—21no—
61C2×C32×D4—22no—
62C2×C32×D4C2312yes—
63C22×C32×C4C2311yescharacteristic
64C2×#638—21no—
65C2×#638—22no—
66C2×#638—22no—
67C2×#638—44no—
68C22×C3⋊Dic3—21no—
69C22×C3⋊Dic3D411yescharacteristic
70#3828—22no—
71#3828—22no—
72C2×C4⋊(C3⋊D3)—21no—
73C2×C4⋊(C3⋊D3)—21no—
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×M16—22no—
84C2×C32×C8C2312yes—
85C32×C4⋊C4C2311yescharacteristic
86C32×C4⋊C4C2311yescharacteristic
87C32×C22⋊C4—21no—
88C32×C42—21no—
89#3757—22no—
90#3757—22no—
91#3754—24no—
92#3753—24no—
93#3752—21no—
94#3752—21no—
95#3752—21no—
96#3752—21no—
97C4⋊(C3⋊Dic3)—21no—
98C4⋊(C3⋊Dic3)—21no—
99C4⋊(C3⋊Dic3)—21no—
100C4⋊(C3⋊Dic3)C2312yes—
101#3748D414yescomplemented
102C2×C3⋊(C3⋊C8)C2312yes—
103#3743—24no—
104C8×C3⋊D3—24no—
105#3055—91noSylow
106C22×C3×D4C2×D314yes—
107C22×#67—64no—
108C2×#235—34no—
109C22×C4×D3—34no—
110C2×C3×M16C2×D314yes—
111C3×#117C2×D314yes—
112C2×#217—64no—
113#938—38no—
114#938—38no—
115#938—64no—
116#938—64no—
117C2×#214—38no—
118#932—616no—
119C2×#213—38no—
120C2×C4⋊Dic3—34no—
121C2×#208—34no—
122D3×M16—616no—
123C2×ΓL(1,𝔽25)—38no—
124C2×D3×C8—38no—
125#897—34no—
126#897—34no—
127#895—34no—
128#895—34no—
129#886—64no—
130#882—64no—
131C4×D12—64no—
132C4×D12—64no—
133C3×#102C2×D318yescomplemented
134C3×#102C2×D318yescomplemented
135#821—38no—
136#816—38no—
137#808—38no—
138#807—38no—
139C23×C32—22no—
140C23×C32—42no—
141C23×C32—42no—
142C23×C32—42no—
143C23×C32C2×D411yescharacteristic
144C22×C3⋊D3—22no—
145C22×C3⋊D3—22no—
146C22×C3⋊D3—21no—
147C22×C3⋊D3—41no—
148C22×C3⋊D3C2×D411yescharacteristic
149C22×C3⋊D3C2×D411yescharacteristic
150C32×D4—22no—
151C32×D4—22no—
152C32×D4—42no—
153C2×C32×C4—21no—
154C2×C32×C4—21no—
155C2×C32×C4C2×D411yescharacteristic
156C2×C32×C4C2×D412yes—
157C2×C32×C4#4112yes—
158C2×C32×C4C2411yescharacteristic
159#638—44no—
160#638—42no—
161#638—44no—
162C2×C3⋊Dic3—22no—
163C2×C3⋊Dic3—21no—
164C2×C3⋊Dic3—22no—
165C2×C3⋊Dic3—42no—
166C2×C3⋊Dic3C2×D411yescharacteristic
167C2×C3⋊Dic3C2×D411yescharacteristic
168C4⋊(C3⋊D3)—21no—
169C4⋊(C3⋊D3)—21no—
170C4⋊(C3⋊D3)—42no—
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×C8—22no—
182C3⋊(C3⋊C8)C2×D414yescomplemented
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#428—91no—
192#418C3⋊D311yescharacteristic, complemented
193#417—91no—
194C24×C3—24no—
195C23×D3—34no—
196C2×C3×D4—28no—
197C2×C3×D4—28no—
198C2×C3×D4—24no—
199C2×C3×D4C22×D318yes—
200C22×C3×C4C22×D314yes—
201C2×#67—68no—
202C2×#67—68no—
203C2×#67—64no—
204C2×#67—1216no—
205C22×Dic3—34no—
206C22×Dic3—64no—
207#235—68no—
208#235—68no—
209C2×D12—34no—
210C2×D12—64no—
211C2×D12—64no—
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×M16—28no—
221C2×C3×C8C22×D318yes—
222C3×C4⋊C4C22×D314yes—
223C3×C4⋊C4C22×D314yes—
224C3×C22⋊C4—24no—
225C3×C42—24no—
226#217—68no—
227#217—68no—
228#214—616no—
229#213—616no—
230(C2×D3)⋊C4—64no—
231(C2×D3)⋊C4—64no—
232(C2×D3)⋊C4—64no—
233(C2×D3)⋊C4—64no—
234C4⋊Dic3—38no—
235C4⋊Dic3—64no—
236C4⋊Dic3—64no—
237C4⋊Dic3—64no—
238#208—316no—
239C2×C3⋊C8—38no—
240ΓL(1,𝔽25)—616no—
241D3×C8—616no—
242C22×C32—21no—
243C22×C32—21no—
244C22×C32—42no—
245C22×C32—42no—
246C22×C32—42no—
247C22×C32—84no—
248C22×C32#12112yes—
249C22×C32C22×D411yescharacteristic
250C2×C3⋊D3—21no—
251C2×C3⋊D3—21no—
252C2×C3⋊D3—21no—
253C2×C3⋊D3—21no—
254C2×C3⋊D3—21no—
255C2×C3⋊D3—44no—
256C2×C3⋊D3—41no—
257C2×C3⋊D3—41no—
258C2×C3⋊D3—41no—
259C2×C3⋊D3AGL(1,ℤ/8)12yescomplemented
260C32×C4—41no—
261C32×C4—41no—
262C32×C4#12112yes—
263C32×C4C22×D411yescharacteristic
264C32×C4C2×#4111yescharacteristic
265C3⋊Dic3—21no—
266C3⋊Dic3—21no—
267C3⋊Dic3—41no—
268C3⋊Dic3—42no—
269C2×#41—91no—
270C22×D4—181no—
271C22×D4C2×C3⋊D311yescharacteristic
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⋊C4—91no—
295C2×C22⋊C4—181no—
296#107—92no—
297#106—92no—
298#103—92no—
299#102—92no—
300#102C2×C3⋊D312yescomplemented
301#102C2×C3⋊D312yescomplemented
302C23×C3—28no—
303C23×C3—48no—
304C23×C3—48no—
305C23×C3—48no—
306C23×C3D3×D414yes—
307C22×D3—34no—
308C22×D3—34no—
309C22×D3—68no—
310C22×D3—68no—
311C22×D3—64no—
312C22×D3—124no—
313C3×D4—28no—
314C3×D4—28no—
315C3×D4—48no—
316C2×C3×C4—24no—
317C2×C3×C4—24no—
318C2×C3×C4#23518yes—
319C2×C3×C4D3×D414yes—
320C2×C3×C4D3×D418yes—
321C2×C3×C4C23×D314yes—
322#67—1216no—
323#67—1216no—
324#67—128no—
325C2×Dic3—34no—
326C2×Dic3—34no—
327C2×Dic3—68no—
328C2×Dic3—68no—
329C2×Dic3—64no—
330C2×Dic3—128no—
331D12—64no—
332D12—64no—
333D12—128no—
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×C8—28no—
345C3⋊C8—316no—
346C2×C32—22no—
347C2×C32—82no—
348C2×C32C2×#12111yescharacteristic
349C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
350C2×C32#57511yescharacteristic
351C3⋊D3—22no—
352C3⋊D3—41no—
353C3⋊D3—81no—
354C24—21no—
355C24—91no—
356#41—182no—
357#41—182no—
358C2×Q8—91no—
359C2×D4—22no—
360C2×D4—22no—
361C2×D4—21no—
362C2×D4—91no—
363C2×D4—181no—
364C2×D4—181no—
365C2×D4—182no—
366C2×D4—182no—
367C2×D4—181no—
368C2×D4—364no—
369C2×D4C22×C3⋊D312yes—
370C22×C4—91no—
371C22×C4—91no—
372C22×C4—91no—
373C22×C4—91no—
374C22×C4—91no—
375C22×C4—182no—
376C22×C4—182no—
377C22×C4—181no—
378C22×C4—181no—
379C22×C4C22×C3⋊D311yescharacteristic
380SD16—184no—
381D8—184no—
382M16—22no—
383M16—94no—
384M16—184no—
385C2×C8—92no—
386C2×C8—184no—
387C2×C8C22×C3⋊D312yes—
388C4⋊C4—92no—
389C4⋊C4—181no—
390C4⋊C4—181no—
391C4⋊C4—181no—
392C4⋊C4C22×C3⋊D311yescharacteristic
393C4⋊C4C22×C3⋊D311yescharacteristic
394C22⋊C4—21no—
395C22⋊C4—181no—
396C22⋊C4—181no—
397C22⋊C4—181no—
398C22⋊C4—181no—
399C22⋊C4—182no—
400C22⋊C4—182no—
401C42—21no—
402C22×C3—24no—
403C22×C3—24no—
404C22×C3—48no—
405C22×C3—48no—
406C22×C3—48no—
407C22×C3—816no—
408C22×C3#88418yes—
409C22×C3C2×D3×D414yes—
410C2×D3—38no—
411C2×D3—64no—
412C2×D3—64no—
413C2×D3—64no—
414C2×D3—64no—
415C2×D3—64no—
416C2×D3—1216no—
417C2×D3—124no—
418C2×D3—124no—
419C2×D3—124no—
420C3×C4—44no—
421C3×C4—44no—
422C3×C4#88418yes—
423C3×C4C2×#23514yes—
424C3×C4C2×D3×D414yes—
425Dic3—64no—
426Dic3—64no—
427Dic3—124no—
428Dic3—128no—
429C32#305511yescharacteristic, complemented, Sylow
430C23—22no—
431C23—42no—
432C23—42no—
433C23—42no—
434C23—91no—
435C23—91no—
436C23—182no—
437C23—182no—
438C23—181no—
439C23—361no—
440C23D4×C3⋊D311yescharacteristic
441Q8—181no—
442Q8—181no—
443D4—22no—
444D4—22no—
445D4—42no—
446D4—181no—
447D4—181no—
448D4—362no—
449D4—362no—
450D4—364no—
451D4—364no—
452D4—362no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—91no—
456C2×C4—91no—
457C2×C4—182no—
458C2×C4—182no—
459C2×C4—182no—
460C2×C4—181no—
461C2×C4—181no—
462C2×C4—181no—
463C2×C4—181no—
464C2×C4—182no—
465C2×C4—181no—
466C2×C4—362no—
467C2×C4—362no—
468C2×C4#382812yes—
469C2×C4D4×C3⋊D311yescharacteristic
470C2×C4D4×C3⋊D312yes—
471C2×C4C23×C3⋊D311yescharacteristic
472C8—22no—
473C8—94no—
474C2×C3—28no—
475C2×C3—88no—
476C2×C3C2×#88414yes—
477C2×C3D3×AGL(1,ℤ/8)14yes—
478C2×C3#577314yes—
479D3—68no—
480D3—124no—
481D3—244no—
482C22—21no—
483C22—21no—
484C22—42no—
485C22—42no—
486C22—42no—
487C22—84no—
488C22—92no—
489C22—181no—
490C22—181no—
491C22—181no—
492C22—181no—
493C22—181no—
494C22—364no—
495C22—361no—
496C22—361no—
497C22—361no—
498C22#6409312yes—
499C22C2×D4×C3⋊D311yescharacteristic
500C4—41no—
501C4—41no—
502C4—181no—
503C4—181no—
504C4—361no—
505C4—362no—
506C4#6409312yes—
507C4C2×#382811yescharacteristic
508C4C2×D4×C3⋊D311yescharacteristic
509C3#7893014yescomplemented
510C2—22no—
511C2—82no—
512C2—182no—
513C2—361no—
514C2—721no—
515C2C2×#6409311yescharacteristic
516C2C3⋊D3×AGL(1,ℤ/8)11yescharacteristic
517C2#1059624411yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#418C2
socleC22×C32C22×D4
hypercenter#418C3⋊D3
hypocenterC32#3055
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
1. C2×#64147C2semidirect
2. C2×#64141C2semidirect
3. C2×M16×C3⋊D3C2semidirect
4. #10595995C2semidirect
5. C32×#418C2semidirect
6. #10592832C2semidirect
7. #10592694C2semidirect
8. #10592481C2semidirect
9. #10592479C2semidirect
10. #10592477C2semidirect
11. #10592474C2semidirect
24. C2×#3754C22semidirect
26. C2×#3753C22semidirect
30. C2×#3743C22semidirect
31. C2×C8×C3⋊D3C22semidirect
32. #64106C22semidirect
33. #64106C22semidirect
34. #64104C22semidirect
35. #64104C22semidirect
40. C32×#102C22semidirect
41. C32×#102C22semidirect
42. #63648C22semidirect
43. #63643C22semidirect
44. #63635C22semidirect
45. #63634C22semidirect
50. C3×#418D3semidirect
101. #3748D4semidirect
133. C3×#102C2×D3semidirect
134. C3×#102C2×D3semidirect
182. C3⋊(C3⋊C8)C2×D4semidirect
192. #418C3⋊D3semidirect
259. C2×C3⋊D3AGL(1,ℤ/8)semidirect
300. #102C2×C3⋊D3semidirect
301. #102C2×C3⋊D3semidirect
429. C32#3055semidirect
509. C3#78930semidirect

Maximal subgroups

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

subgroupindex
C2×#641472
C2×#641412
C2×M16×C3⋊D32
#105959952
C32×#4182
#105928322
#105926942
#105924812
#105924792
#105924772
#105924742
#789303