Finite Group Databasebeta

← C3×#79877 #11876967

Subgroups — C3×#79877 #11876967

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
1C3×#5548C212yesmaximal, complemented
2C32×#442C211yesmaximal, characteristic, complemented
3C3×#5159C211yesmaximal, characteristic, complemented
4C3×#5151C211yesmaximal, characteristic, complemented
5C3×#5014C212yesmaximal, complemented
6C3×#4865C211yesmaximal, characteristic, complemented
7C3×#4855C211yesmaximal, characteristic, complemented
8C3×#4782C212yesmaximal, complemented
9C3×#4760C212yesmaximal, complemented
10C3×#4711C211yesmaximal, characteristic, complemented
11C3×#4707C211yesmaximal, characteristic, complemented
12C3×#3184—31nomaximal
13#79877C311yesmaximal, characteristic, direct product factor
14C2×C3×#235—22no—
15C2×C32×D8C2211yescharacteristic
16C32×C4×D4C2212yes—
17C3×#940C2212yes—
18C3×#938C2212yes—
19C2×C3×#213C2212yes—
20C3×C4×#67—22no—
21C2×C3×D24C2211yescharacteristic
22C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
23C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
24C3×#895C2212yes—
25C3×#888C2212yes—
26C3×#885—22no—
27C3×#884—22no—
28C3×C4×D12C2212yes—
29C3×C42×D3C2211yescharacteristic
30C32×#106C2211yescharacteristic
31C32×#102C2212yes—
32C32×#97C2211yescharacteristic
33C3×#832C2212yes—
34C3×#821C2212yes—
35C3×#817C2211yescharacteristic
36C3×C8×Dic3C2211yescharacteristic
37C3×C8×Dic3C2211yescharacteristic
38C3×#809C2212yes—
39C3×#808C2212yes—
40C3×#803C2211yescharacteristic
41C3×#532—32no—
42#5548C2×C312yescomplemented
43C3×#498—31no—
44C3×#493—31no—
45C3×#486—32no—
46C3×#469—31no—
47C3×#469—31no—
48C3×#469—32no—
49C3×#442—21no—
50C3×#442—32no—
51C3×#442—31no—
52C3×#442D311yescharacteristic, complemented
53C3×#442C2×C311yescharacteristic, complemented
54C3×C4×M16—31no—
55#5159C2×C311yescharacteristic, complemented
56#5151C2×C311yescharacteristic, complemented
57#5014C2×C312yescomplemented
58#4865C2×C311yescharacteristic, complemented
59#4855C2×C311yescharacteristic, complemented
60#4782C2×C312yescomplemented
61#4760C2×C312yescomplemented
62#4711C2×C311yescharacteristic, complemented
63#4707C2×C311yescharacteristic, complemented
64C2×C32×D4C2312yes—
65C22×C32×C4—22no—
66C2×C3×#67—22no—
67C2×C3×#67—22no—
68C2×C3×#67—22no—
69C3×#235—48no—
70C2×C3×D12—22no—
71C2×C3×D12C2312yes—
72C2×C3×C4×D3—22no—
73C2×C3×C4×D3D412yes—
74C2×C3×C4×D3C2311yescharacteristic
75C2×C3×Dic6—22no—
76C32×D8—22no—
77C2×C32×C8C2311yescharacteristic
78C2×C32×C8C2311yescharacteristic
79C32×C4⋊C4C2312yes—
80C32×C22⋊C4—22no—
81C32×C42C2311yescharacteristic
82C3×#217—22no—
83C3×#213—24no—
84C3×(C2×D3)⋊C4—22no—
85C3×(C2×D3)⋊C4—22no—
86C3×C4⋊Dic3C2312yes—
87C3×Dic3⋊C4—22no—
88C3×C4×Dic3D412yes—
89C3×C4×Dic3C2311yescharacteristic
90C2×C3×C3⋊C8C2311yescharacteristic
91C2×C3×C3⋊C8C2311yescharacteristic
92C3×D24—22no—
93C3×ΓL(1,𝔽25)—22no—
94C3×ΓL(1,𝔽25)—22no—
95#3184—31noSylow
96C2×C3×#41—62no—
97C2×#235—22no—
98C2×C3×D8—21no—
99C2×C3×D8—32no—
100C2×C3×D8—31no—
101C2×C3×D8C2×D311yescharacteristic
102C2×C3×D8C22×C311yescharacteristic
103C2×C3×M16—31no—
104C2×C3×M16—31no—
105C3×C4⋊Q8—32no—
106C3×#127—32no—
107C3×#124—62no—
108C3×#121—32no—
109C3×#121—32no—
110C3×#121—62no—
111C3×C4×D4—22no—
112C3×C4×D4—32no—
113C3×C4×D4—62no—
114C3×C4×D4C2×D312yes—
115C3×C4×D4C22×C312yes—
116C2×C3×C42—31no—
117#940C22×C312yes—
118#938C22×C312yes—
119C2×#213C22×C312yes—
120C4×#67—22no—
121C2×D24C22×C311yescharacteristic
122C2×ΓL(1,𝔽25)C22×C311yescharacteristic
123C2×ΓL(1,𝔽25)C22×C311yescharacteristic
124#895C22×C312yes—
125#888C22×C312yes—
126#885—22no—
127#884—22no—
128C4×D12C22×C312yes—
129C42×D3C22×C311yescharacteristic
130C3×#106—21no—
131C3×#106—31no—
132C3×#106—32no—
133C3×#106C2×D311yescharacteristic
134C3×#106C22×C311yescharacteristic
135C3×#102—22no—
136C3×#102—32no—
137C3×#102—32no—
138C3×#102—32no—
139C3×#102C2×D312yes—
140C3×#102C22×C312yes—
141C3×#97—21no—
142C3×#97—31no—
143C3×#97C2×D311yescharacteristic
144C3×#97C22×C311yescharacteristic
145C3×C4×C8—31no—
146C3×C4×C8—31no—
147#832C22×C312yes—
148#821C22×C312yes—
149#817C22×C311yescharacteristic
150C8×Dic3C22×C311yescharacteristic
151C8×Dic3C22×C311yescharacteristic
152#809C22×C312yes—
153#808C22×C312yes—
154#803C22×C311yescharacteristic
155C23×C32—22no—
156C22×C3×D3—22no—
157C22×C3×D3C2×D411yescharacteristic
158C32×D4—22no—
159C32×D4—22no—
160C2×C32×C4—22no—
161C2×C32×C4—44no—
162C2×C32×C4C2×D412yes—
163C2×C32×C4C2411yescharacteristic
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×D12—44no—
173C3×C4×D3—21no—
174C3×C4×D3—21no—
175C3×C4×D3—24no—
176C3×C4×D3—44no—
177C3×Dic6—44no—
178C32×C8—21no—
179C32×C8#4112yescomplemented
180C3×C3⋊C8—21no—
181C3×C3⋊C8#4112yescomplemented
182#532—32no—
183#498—31no—
184#493—31no—
185#486—32no—
186#469—31no—
187#469—31no—
188#469—32no—
189#442—32no—
190#442—31no—
191#442C3×D311yescharacteristic, complemented
192C4×M16—31no—
193C3×#41—128no—
194C2×C3×Q8—62no—
195C2×C3×D4—22no—
196C2×C3×D4—32no—
197C2×C3×D4—62no—
198C2×C3×D4—62no—
199C2×C3×D4—62no—
200C2×C3×D4—62no—
201C2×C3×D4C22×D312yes—
202C2×C3×D4C23×C312yes—
203C22×C3×C4—22no—
204C22×C3×C4—22no—
205C22×C3×C4—32no—
206C22×C3×C4—31no—
207C22×C3×C4—42no—
208C22×C3×C4—62no—
209C2×#67—22no—
210C2×#67—22no—
211C2×#67—22no—
212#235—48no—
213C2×D12—22no—
214C2×D12C23×C312yes—
215C2×C4×D3—22no—
216C2×C4×D3C3×D412yes—
217C2×C4×D3C23×C311yescharacteristic
218C2×Dic6—22no—
219C3×D8—24no—
220C3×D8—22no—
221C3×D8—22no—
222C3×D8—64no—
223C3×D8—62no—
224C3×M16—62no—
225C3×M16—62no—
226C2×C3×C8—21no—
227C2×C3×C8—21no—
228C2×C3×C8—31no—
229C2×C3×C8—31no—
230C2×C3×C8C22×D311yescharacteristic
231C2×C3×C8C22×D311yescharacteristic
232C2×C3×C8C23×C311yescharacteristic
233C2×C3×C8C23×C311yescharacteristic
234C3×C4⋊C4—22no—
235C3×C4⋊C4—32no—
236C3×C4⋊C4—62no—
237C3×C4⋊C4C22×D312yes—
238C3×C4⋊C4C23×C312yes—
239C3×C22⋊C4—22no—
240C3×C22⋊C4—22no—
241C3×C22⋊C4—42no—
242C3×C22⋊C4—62no—
243C3×C22⋊C4—62no—
244C3×C22⋊C4—62no—
245C3×C42—21no—
246C3×C42—32no—
247C3×C42—31no—
248C3×C42C22×D311yescharacteristic
249C3×C42C23×C311yescharacteristic
250#217—22no—
251#213—24no—
252(C2×D3)⋊C4—22no—
253(C2×D3)⋊C4—22no—
254C4⋊Dic3C23×C312yes—
255Dic3⋊C4—22no—
256C4×Dic3C3×D412yes—
257C4×Dic3C23×C311yescharacteristic
258C2×C3⋊C8C23×C311yescharacteristic
259C2×C3⋊C8C23×C311yescharacteristic
260D24—22no—
261ΓL(1,𝔽25)—22no—
262ΓL(1,𝔽25)—22no—
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×C4—22no—
273C32×C4—42no—
274C32×C4C2×#4111yescharacteristic
275C32×C4C2×#4111yescharacteristic
276C3×Dic3—21no—
277C3×Dic3—42no—
278C3×Dic3AGL(1,ℤ/8)14yes—
279C2×#41—62no—
280C2×D8—32no—
281C2×D8—31no—
282C2×D8C2×C3×D311yescharacteristic
283C2×M16—31no—
284C2×M16—31no—
285C4⋊Q8—32no—
286#127—32no—
287#124—62no—
288#121—32no—
289#121—32no—
290#121—62no—
291C4×D4—32no—
292C4×D4—62no—
293C4×D4C2×C3×D312yes—
294C2×C42—31no—
295#106—31no—
296#106—32no—
297#106C2×C3×D311yescharacteristic
298#102—32no—
299#102—32no—
300#102—32no—
301#102C2×C3×D312yes—
302#97—31no—
303#97C2×C3×D311yescharacteristic
304C4×C8—31no—
305C4×C8—31no—
306C23×C3—22no—
307C23×C3—22no—
308C23×C3—31no—
309C23×C3—42no—
310C23×C3—62no—
311C22×D3—22no—
312C22×D3C2×C3×D411yescharacteristic
313C3×Q8—124no—
314C3×D4—24no—
315C3×D4—22no—
316C3×D4—22no—
317C3×D4—22no—
318C3×D4—22no—
319C3×D4—42no—
320C3×D4—62no—
321C3×D4—62no—
322C3×D4—124no—
323C3×D4—124no—
324C3×D4—124no—
325C3×D4—124no—
326C2×C3×C4—22no—
327C2×C3×C4—22no—
328C2×C3×C4—21no—
329C2×C3×C4—22no—
330C2×C3×C4—32no—
331C2×C3×C4—31no—
332C2×C3×C4—42no—
333C2×C3×C4—44no—
334C2×C3×C4—44no—
335C2×C3×C4—64no—
336C2×C3×C4—61no—
337C2×C3×C4—61no—
338C2×C3×C4—62no—
339C2×C3×C4—84no—
340C2×C3×C4—124no—
341C2×C3×C4D3×D412yes—
342C2×C3×C4C2×C3×D412yes—
343C2×C3×C4C23×D311yescharacteristic
344C2×C3×C4C24×C311yescharacteristic
345#67—44no—
346#67—44no—
347#67—44no—
348C2×Dic3—22no—
349C2×Dic3C2×C3×D411yescharacteristic
350C2×Dic3C2×C3×D412yes—
351D12—22no—
352D12—22no—
353D12—44no—
354C4×D3—21no—
355C4×D3—21no—
356C4×D3—24no—
357C4×D3—44no—
358Dic6—44no—
359C3×C8—21no—
360C3×C8—21no—
361C3×C8—22no—
362C3×C8—32no—
363C3×C8—41no—
364C3×C8—61no—
365C3×C8#23512yescomplemented
366C3×C8C3×#4112yescomplemented
367C3⋊C8—21no—
368C3⋊C8C3×#4112yescomplemented
369C2×C32—82no—
370C2×C32#53211yescharacteristic
371C2×C32C2×AGL(1,ℤ/8)12yes—
372C3×D3—41no—
373C3×D3—82no—
374#41—128no—
375C2×Q8—62no—
376C2×D4—32no—
377C2×D4—62no—
378C2×D4—62no—
379C2×D4—62no—
380C2×D4—62no—
381C2×D4C22×C3×D312yes—
382C22×C4—22no—
383C22×C4—31no—
384C22×C4—32no—
385C22×C4—62no—
386D8—22no—
387D8—64no—
388D8—62no—
389M16—62no—
390M16—62no—
391C2×C8—31no—
392C2×C8—31no—
393C2×C8C22×C3×D311yescharacteristic
394C2×C8C22×C3×D311yescharacteristic
395C4⋊C4—32no—
396C4⋊C4—62no—
397C4⋊C4C22×C3×D312yes—
398C22⋊C4—22no—
399C22⋊C4—62no—
400C22⋊C4—62no—
401C22⋊C4—62no—
402C42—31no—
403C42—32no—
404C42C22×C3×D311yescharacteristic
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—62no—
414C22×C3—61no—
415C22×C3—82no—
416C22×C3—82no—
417C22×C3—122no—
418C22×C3—122no—
419C22×C3—122no—
420C22×C3C2×D3×D411yescharacteristic
421C22×C3C22×C3×D411yescharacteristic
422C2×D3—22no—
423C2×D3—21no—
424C2×D3—42no—
425C2×D3—42no—
426C2×D3—42no—
427C3×C4—22no—
428C3×C4—22no—
429C3×C4—21no—
430C3×C4—21no—
431C3×C4—34no—
432C3×C4—42no—
433C3×C4—42no—
434C3×C4—42no—
435C3×C4—61no—
436C3×C4—82no—
437C3×C4—122no—
438C3×C4C2×#23511yescharacteristic
439C3×C4D3×#4111yescharacteristic
440C3×C4C2×C3×#4111yescharacteristic
441C3×C4C2×C3×#4111yescharacteristic
442Dic3—21no—
443Dic3—42no—
444Dic3C3×AGL(1,ℤ/8)14yes—
445C32#318411yescharacteristic, complemented, Sylow
446C23—22no—
447C23—31no—
448C23—62no—
449Q8—124no—
450D4—22no—
451D4—22no—
452D4—62no—
453D4—62no—
454D4—124no—
455D4—124no—
456D4—124no—
457D4—124no—
458C2×C4—22no—
459C2×C4—32no—
460C2×C4—31no—
461C2×C4—44no—
462C2×C4—64no—
463C2×C4—61no—
464C2×C4—61no—
465C2×C4—62no—
466C2×C4—124no—
467C2×C4C3×D3×D412yes—
468C2×C4C23×C3×D311yescharacteristic
469C8—21no—
470C8—32no—
471C8—61no—
472C8C3×#23512yescomplemented
473C2×C3—22no—
474C2×C3—21no—
475C2×C3—84no—
476C2×C3—82no—
477C2×C3—82no—
478C2×C3—121no—
479C2×C3—242no—
480C2×C3#554811yescharacteristic
481C2×C3D3×AGL(1,ℤ/8)12yes—
482C2×C3C3×#53211yescharacteristic
483C2×C3C2×C3×AGL(1,ℤ/8)12yes—
484D3—41no—
485D3—82no—
486C22—42no—
487C22—42no—
488C22—42no—
489C22—62no—
490C22—61no—
491C22—122no—
492C22—122no—
493C22—122no—
494C22C2×C3×D3×D411yescharacteristic
495C4—22no—
496C4—34no—
497C4—42no—
498C4—61no—
499C4—122no—
500C4C2×C3×#23511yescharacteristic
501C4C3×D3×#4111yescharacteristic
502C3—21no—
503C3#7987711yescharacteristic, direct product factor
504C3C3×#318411yescharacteristic, complemented
505C2—82no—
506C2—121no—
507C2—242no—
508C2C3×#554811yescharacteristic
509C2C3×D3×AGL(1,ℤ/8)12yes—
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#442C2
socleC22×C32C22×D4
hypercenterC3×#442D3
hypocenterC3C3×#3184
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#442

Complements

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

NH ≅ G/Ntype
1. C3×#5548C2semidirect
2. C32×#442C2semidirect
3. C3×#5159C2semidirect
4. C3×#5151C2semidirect
5. C3×#5014C2semidirect
6. C3×#4865C2semidirect
7. C3×#4855C2semidirect
8. C3×#4782C2semidirect
9. C3×#4760C2semidirect
10. C3×#4711C2semidirect
11. C3×#4707C2semidirect
13. #79877C3direct (N × H)
42. #5548C2×C3semidirect
52. C3×#442D3semidirect
53. C3×#442C2×C3semidirect
55. #5159C2×C3semidirect
56. #5151C2×C3semidirect
57. #5014C2×C3semidirect
58. #4865C2×C3semidirect
59. #4855C2×C3semidirect
60. #4782C2×C3semidirect
61. #4760C2×C3semidirect
62. #4711C2×C3semidirect
63. #4707C2×C3semidirect
179. C32×C8#41semidirect
181. C3×C3⋊C8#41semidirect
191. #442C3×D3semidirect
365. C3×C8#235semidirect
366. C3×C8C3×#41semidirect
368. C3⋊C8C3×#41semidirect
445. C32#3184semidirect
472. C8C3×#235semidirect
503. C3#79877direct (N × H)
504. C3C3×#3184semidirect

Maximal subgroups

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

subgroupindex
C3×#55482
C32×#4422
C3×#51592
C3×#51512
C3×#50142
C3×#48652
C3×#48552
C3×#47822
C3×#47602
C3×#47112
C3×#47072
C3×#31843
#798773