Finite Group Databasebeta

← C3×#79868 #11860926

Subgroups — C3×#79868 #11860926

Order 1152.

1034 conjugacy classes of subgroups.

The subgroup lattice has 495 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#912C211yesmaximal, characteristic
2C3×#5546C212yesmaximal, complemented
3C32×#442C211yesmaximal, characteristic, complemented
4C3×#5152C211yesmaximal, characteristic, complemented
5C3×C4×#214C212yesmaximal, complemented
6C3×D3×#106C211yesmaximal, characteristic, complemented
7C3×#4853C211yesmaximal, characteristic, complemented
8C3×#4771C212yesmaximal, complemented
9C3×#4758C212yesmaximal, complemented
10C3×#4716C211yesmaximal, characteristic, complemented
11C3×#4708C211yesmaximal, characteristic, complemented
12C3×#2952—31nomaximal
13#79868C311yesmaximal, characteristic, direct product factor
14C2×C3×#237C2212yes—
15C2×C32×D8C2211yescharacteristic
16C32×C4×D4C2212yes—
17C3×D4×Dic3C2212yes—
18C2×C3×#214C2212yes—
19C3×C4×#67—22no—
20C2×C3×Dic3⋊C4—22no—
21C3×#912C418yescomplemented
22C2×C3×Dic12C2211yescharacteristic
23C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
24C2×C3×D3×C8C2211yescharacteristic
25C3×D3×C4⋊C4C2212yes—
26C3×#887C2212yes—
27C3×#67⋊C4—22no—
28C3×#877—22no—
29C3×#872C2211yescharacteristic
30C3×C4×Dic6C2212yes—
31C32×#106C2211yescharacteristic
32C32×#102C2212yes—
33C32×#97C2211yescharacteristic
34C3×#832C2212yes—
35C3×#817C2211yescharacteristic
36C3×#816C2212yes—
37C3×#815C2211yescharacteristic
38C3×C8×Dic3C2211yescharacteristic
39C3×#810C2212yes—
40C3×#808C2212yes—
41C3×C4×C3⋊C8C2211yescharacteristic
42C2×C3×#135—31no—
43C3×#520—32no—
44C2×#912C2×C311yescharacteristic
45#5546C2×C312yescomplemented
46C3×#442—21no—
47C3×#442—31no—
48C3×#442D311yescharacteristic, complemented
49C3×#442C2×C311yescharacteristic, complemented
50C3×#441—31no—
51C3×#441—31no—
52C3×C4×SD16—32no—
53C3×C4×SD16—32no—
54C2×C3×#106—31no—
55C3×#417—32no—
56C3×#405—31no—
57#5152C2×C311yescharacteristic, complemented
58C4×#214C2×C312yescomplemented
59D3×#106C2×C311yescharacteristic, complemented
60#4853C2×C311yescharacteristic, complemented
61#4771C2×C312yescomplemented
62#4758C2×C312yescomplemented
63#4716C2×C311yescharacteristic, complemented
64#4708C2×C311yescharacteristic, complemented
65C2×C32×D4C2312yes—
66C22×C32×C4—22no—
67C2×C3×#67—22no—
68C22×C3×Dic3—22no—
69C22×C3×Dic3—22no—
70C3×#237—24no—
71C3×#237C2×C418yescomplemented
72C2×C3×C4×D3—22no—
73C2×C3×C4×D3C2311yescharacteristic
74C2×C3×Dic6C2312yes—
75C32×D8C2×C414yescomplemented
76C2×C32×C8C2311yescharacteristic
77C2×C32×C8C2311yescharacteristic
78C32×C4⋊C4C2312yes—
79C32×C22⋊C4—22no—
80C32×C42C2311yescharacteristic
81C3×#217—22no—
82C3×#214C2×C418yescomplemented
83C3×(C2×D3)⋊C4D412yes—
84C3×C4⋊Dic3C2312yes—
85C3×Dic3⋊C4—22no—
86C3×Dic3⋊C4—22no—
87C3×Dic3⋊C4—22no—
88C3×Dic3⋊C4D412yes—
89C3×C4×Dic3—22no—
90C3×C4×Dic3—22no—
91C3×C4×Dic3C2311yescharacteristic
92C2×C3×C3⋊C8C2311yescharacteristic
93C2×C3×C3⋊C8C2311yescharacteristic
94C3×Dic12C2×C414yescomplemented
95C3×ΓL(1,𝔽25)—22no—
96C3×D3×C8C2×C414yescomplemented
97#2952—31noSylow
98C2×C3×#41—32no—
99C2×#237C22×C312yes—
100C3×#135—38no—
101C2×C3×Q16—31no—
102C2×C3×SD16—32no—
103C2×C3×D8—21no—
104C2×C3×D8C2×D311yescharacteristic
105C2×C3×D8C22×C311yescharacteristic
106C2×C3×M16—31no—
107C22×C3×C8—31no—
108C3×C4×Q8—32no—
109C3×C4×Q8—32no—
110C3×C4×D4—22no—
111C3×C4×D4—32no—
112C3×C4×D4—62no—
113C3×C4×D4—62no—
114C3×C4×D4C2×D312yes—
115C3×C4×D4C22×C312yes—
116C3×#117—31no—
117C3×#117—62no—
118C2×C3×C4⋊C4—32no—
119C2×C3×C4⋊C4—62no—
120D4×Dic3C22×C312yes—
121C2×#214C22×C312yes—
122C4×#67—22no—
123C2×Dic3⋊C4—22no—
124#912C3×C418yescomplemented
125C2×Dic12C22×C311yescharacteristic
126C2×ΓL(1,𝔽25)C22×C311yescharacteristic
127C2×D3×C8C22×C311yescharacteristic
128D3×C4⋊C4C22×C312yes—
129#887C22×C312yes—
130#67⋊C4—22no—
131#877—22no—
132#872C22×C311yescharacteristic
133C4×Dic6C22×C312yes—
134C3×#106—21no—
135C3×#106—31no—
136C3×#106—32no—
137C3×#106C2×D311yescharacteristic
138C3×#106C22×C311yescharacteristic
139C3×#103—32no—
140C3×#103—32no—
141C3×#102—22no—
142C3×#102—32no—
143C3×#102C2×D312yes—
144C3×#102C22×C312yes—
145C3×#97—21no—
146C3×#97—31no—
147C3×#97C2×D311yescharacteristic
148C3×#97C22×C311yescharacteristic
149C3×C4×C8—31no—
150C3×C4×C8—31no—
151#832C22×C312yes—
152#817C22×C311yescharacteristic
153#816C22×C312yes—
154#815C22×C311yescharacteristic
155C8×Dic3C22×C311yescharacteristic
156#810C22×C312yes—
157#808C22×C312yes—
158C4×C3⋊C8C22×C311yescharacteristic
159C23×C32—22no—
160C22×C3×D3C2×D411yescharacteristic
161C32×D4—22no—
162C32×D4C22×C414yes—
163C2×C32×C4—22no—
164C2×C32×C4—82no—
165C2×C32×C4C2×D412yes—
166C2×C32×C4C2411yescharacteristic
167C3×#67—28no—
168C2×C3×Dic3—22no—
169C2×C3×Dic3—28no—
170C2×C3×Dic3—22no—
171C2×C3×Dic3—82no—
172C2×C3×Dic3C2×D412yes—
173C2×C3×Dic3C2×D411yescharacteristic
174C3×C4×D3—82no—
175C3×C4×D3C22×C412yes—
176C3×C4×D3#4112yes—
177C3×Dic6—22no—
178C3×Dic6C22×C414yes—
179C32×C8—21no—
180C32×C8C22×C412yes—
181C3×C3⋊C8—21no—
182C3×C3⋊C8C22×C412yes—
183C2×#135—31no—
184#520—32no—
185#442—31no—
186#442C3×D311yescharacteristic, complemented
187#441—31no—
188#441—31no—
189C4×SD16—32no—
190C4×SD16—32no—
191C2×#106—31no—
192#417—32no—
193#405—31no—
194C3×#41—38no—
195C3×#41—64no—
196C2×C3×Q8—32no—
197C2×C3×D4—22no—
198C2×C3×D4—62no—
199C2×C3×D4C22×D312yes—
200C2×C3×D4C23×C312yes—
201C22×C3×C4—22no—
202C22×C3×C4—22no—
203C22×C3×C4—31no—
204C22×C3×C4—42no—
205C22×C3×C4—62no—
206C22×C3×C4—62no—
207C22×C3×C4—62no—
208C2×#67—22no—
209C22×Dic3—22no—
210C22×Dic3—22no—
211#237—24no—
212#237C2×C3×C418yescomplemented
213C2×C4×D3—22no—
214C2×C4×D3C23×C311yescharacteristic
215C2×Dic6C23×C312yes—
216C3×Q16—34no—
217C3×SD16—38no—
218C3×D8—24no—
219C3×D8C4×D314yescomplemented
220C3×D8C2×C3×C414yescomplemented
221C3×M16—62no—
222C2×C3×C8—21no—
223C2×C3×C8—21no—
224C2×C3×C8—31no—
225C2×C3×C8—34no—
226C2×C3×C8—31no—
227C2×C3×C8C22×D311yescharacteristic
228C2×C3×C8C22×D311yescharacteristic
229C2×C3×C8C23×C311yescharacteristic
230C2×C3×C8C23×C311yescharacteristic
231C3×C4⋊C4—22no—
232C3×C4⋊C4—32no—
233C3×C4⋊C4—32no—
234C3×C4⋊C4—62no—
235C3×C4⋊C4—62no—
236C3×C4⋊C4—62no—
237C3×C4⋊C4C22×D312yes—
238C3×C4⋊C4C23×C312yes—
239C3×C22⋊C4—22no—
240C3×C22⋊C4—22no—
241C3×C22⋊C4—32no—
242C3×C22⋊C4—42no—
243C3×C22⋊C4—62no—
244C3×C42—21no—
245C3×C42—31no—
246C3×C42—62no—
247C3×C42—62no—
248C3×C42C22×D311yescharacteristic
249C3×C42C23×C311yescharacteristic
250#217—22no—
251#214C2×C3×C418yescomplemented
252(C2×D3)⋊C4C3×D412yes—
253C4⋊Dic3C23×C312yes—
254Dic3⋊C4—22no—
255Dic3⋊C4—22no—
256Dic3⋊C4—22no—
257Dic3⋊C4C3×D412yes—
258C4×Dic3—22no—
259C4×Dic3—22no—
260C4×Dic3C23×C311yescharacteristic
261C2×C3⋊C8C23×C311yescharacteristic
262C2×C3⋊C8C23×C311yescharacteristic
263Dic12C2×C3×C414yescomplemented
264ΓL(1,𝔽25)—22no—
265D3×C8C2×C3×C414yescomplemented
266C22×C32—24no—
267C22×C32—42no—
268C22×C32—42no—
269C22×C32C22×D411yescharacteristic
270C2×C3×D3—22no—
271C2×C3×D3C4×D412yes—
272C32×C4—22no—
273C32×C4—42no—
274C32×C4C23×C411yescharacteristic
275C32×C4C2×#4111yescharacteristic
276C3×Dic3—24no—
277C3×Dic3—22no—
278C3×Dic3—42no—
279C3×Dic3C4×D412yes—
280C2×#41—32no—
281#135—38no—
282C2×Q16—31no—
283C2×SD16—32no—
284C2×D8C2×C3×D311yescharacteristic
285C2×M16—31no—
286C22×C8—31no—
287C4×Q8—32no—
288C4×Q8—32no—
289C4×D4—32no—
290C4×D4—62no—
291C4×D4—62no—
292C4×D4C2×C3×D312yes—
293#117—31no—
294#117—62no—
295C2×C4⋊C4—32no—
296C2×C4⋊C4—62no—
297#106—31no—
298#106—32no—
299#106C2×C3×D311yescharacteristic
300#103—32no—
301#103—32no—
302#102—32no—
303#102C2×C3×D312yes—
304#97—31no—
305#97C2×C3×D311yescharacteristic
306C4×C8—31no—
307C4×C8—31no—
308C23×C3—22no—
309C23×C3—22no—
310C23×C3—31no—
311C23×C3—42no—
312C22×D3C2×C3×D411yescharacteristic
313C3×Q8—34no—
314C3×Q8—62no—
315C3×D4—22no—
316C3×D4—22no—
317C3×D4—24no—
318C3×D4—42no—
319C3×D4—68no—
320C3×D4C2×C4×D314yes—
321C3×D4C22×C3×C414yes—
322C2×C3×C4—22no—
323C2×C3×C4—22no—
324C2×C3×C4—21no—
325C2×C3×C4—22no—
326C2×C3×C4—31no—
327C2×C3×C4—32no—
328C2×C3×C4—32no—
329C2×C3×C4—32no—
330C2×C3×C4—42no—
331C2×C3×C4—68no—
332C2×C3×C4—62no—
333C2×C3×C4—62no—
334C2×C3×C4—82no—
335C2×C3×C4—82no—
336C2×C3×C4—84no—
337C2×C3×C4—242no—
338C2×C3×C4—242no—
339C2×C3×C4D3×D412yes—
340C2×C3×C4C2×C3×D412yes—
341C2×C3×C4C23×D311yescharacteristic
342C2×C3×C4C24×C311yescharacteristic
343#67—28no—
344C2×Dic3—22no—
345C2×Dic3—28no—
346C2×Dic3—22no—
347C2×Dic3—82no—
348C2×Dic3C2×C3×D412yes—
349C2×Dic3C2×C3×D411yescharacteristic
350C4×D3—82no—
351C4×D3C22×C3×C412yes—
352C4×D3C3×#4112yes—
353Dic6—22no—
354Dic6C22×C3×C414yes—
355C3×C8—21no—
356C3×C8—21no—
357C3×C8—22no—
358C3×C8—32no—
359C3×C8—41no—
360C3×C8—61no—
361C3×C8C2×C4×D312yes—
362C3×C8C22×C3×C412yes—
363C3⋊C8—21no—
364C3⋊C8C22×C3×C412yes—
365C2×C32—44no—
366C2×C32C2×C4×D411yescharacteristic
367C2×C32#57712yes—
368C3×D3—22no—
369#41—38no—
370#41—64no—
371C2×Q8—32no—
372C2×D4—62no—
373C2×D4C22×C3×D312yes—
374C22×C4—22no—
375C22×C4—31no—
376C22×C4—62no—
377C22×C4—62no—
378C22×C4—62no—
379Q16—34no—
380SD16—38no—
381D8C3×C4×D314yescomplemented
382M16—62no—
383C2×C8—31no—
384C2×C8—34no—
385C2×C8—31no—
386C2×C8C22×C3×D311yescharacteristic
387C2×C8C22×C3×D311yescharacteristic
388C4⋊C4—32no—
389C4⋊C4—32no—
390C4⋊C4—62no—
391C4⋊C4—62no—
392C4⋊C4—62no—
393C4⋊C4C22×C3×D312yes—
394C22⋊C4—22no—
395C22⋊C4—32no—
396C22⋊C4—62no—
397C42—31no—
398C42—62no—
399C42—62no—
400C42C22×C3×D311yescharacteristic
401C22×C3—24no—
402C22×C3—24no—
403C22×C3—21no—
404C22×C3—32no—
405C22×C3—44no—
406C22×C3—42no—
407C22×C3—42no—
408C22×C3—42no—
409C22×C3—42no—
410C22×C3—62no—
411C22×C3—82no—
412C22×C3—82no—
413C22×C3C2×D3×D411yescharacteristic
414C22×C3C22×C3×D411yescharacteristic
415C2×D3—22no—
416C2×D3C3×C4×D412yes—
417C3×C4—22no—
418C3×C4—22no—
419C3×C4—21no—
420C3×C4—21no—
421C3×C4—32no—
422C3×C4—42no—
423C3×C4—42no—
424C3×C4—42no—
425C3×C4—62no—
426C3×C4—64no—
427C3×C4—82no—
428C3×C4—122no—
429C3×C4C22×C4×D311yescharacteristic
430C3×C4D3×#4111yescharacteristic
431C3×C4C23×C3×C411yescharacteristic
432C3×C4C2×C3×#4111yescharacteristic
433Dic3—22no—
434Dic3—24no—
435Dic3—42no—
436Dic3C3×C4×D412yes—
437C32#295211yescharacteristic, complemented, Sylow
438C23—22no—
439C23—31no—
440Q8—34no—
441Q8—62no—
442D4—22no—
443D4—68no—
444D4C2×C3×C4×D314yes—
445C2×C4—22no—
446C2×C4—31no—
447C2×C4—32no—
448C2×C4—32no—
449C2×C4—32no—
450C2×C4—68no—
451C2×C4—62no—
452C2×C4—62no—
453C2×C4—82no—
454C2×C4—242no—
455C2×C4—242no—
456C2×C4C3×D3×D412yes—
457C2×C4C23×C3×D311yescharacteristic
458C8—21no—
459C8—32no—
460C8—61no—
461C8C2×C3×C4×D312yes—
462C2×C3—22no—
463C2×C3—21no—
464C2×C3—44no—
465C2×C3—44no—
466C2×C3—62no—
467C2×C3—84no—
468C2×C3C4×D3×D411yescharacteristic
469C2×C3#577512yes—
470C2×C3C2×C3×C4×D411yescharacteristic
471C2×C3C3×#57712yes—
472D3—22no—
473C22—24no—
474C22—32no—
475C22—42no—
476C22—42no—
477C22—62no—
478C22C2×C3×D3×D411yescharacteristic
479C4—22no—
480C4—32no—
481C4—42no—
482C4—62no—
483C4—64no—
484C4—122no—
485C4C22×C3×C4×D311yescharacteristic
486C4C3×D3×#4111yescharacteristic
487C3—21no—
488C3#7986811yescharacteristic, direct product factor
489C3C3×#295211yescharacteristic, complemented
490C2—44no—
491C2—62no—
492C2C3×C4×D3×D411yescharacteristic
493C2C3×#577512yes—
subgroupG/H
centerC22×C3C2×D3×D4
commutatorC3×C4C23×C3×C4
FrattiniC2×C4C23×C3×D3
FittingC32×#442C2
socleC22×C32C22×D4
prime radicalC2×C3×#912C2
cosocleC2×C3×C4C24×C3
hypercenterC3×#442D3
hypocenterC3C3×#2952
LCSG ▷ 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
2. C3×#5546C2semidirect
3. C32×#442C2semidirect
4. C3×#5152C2semidirect
5. C3×C4×#214C2semidirect
6. C3×D3×#106C2semidirect
7. C3×#4853C2semidirect
8. C3×#4771C2semidirect
9. C3×#4758C2semidirect
10. C3×#4716C2semidirect
11. C3×#4708C2semidirect
13. #79868C3direct (N × H)
21. C3×#912C4semidirect
45. #5546C2×C3semidirect
48. C3×#442D3semidirect
49. C3×#442C2×C3semidirect
57. #5152C2×C3semidirect
58. C4×#214C2×C3semidirect
59. D3×#106C2×C3semidirect
60. #4853C2×C3semidirect
61. #4771C2×C3semidirect
62. #4758C2×C3semidirect
63. #4716C2×C3semidirect
64. #4708C2×C3semidirect
71. C3×#237C2×C4semidirect
75. C32×D8C2×C4semidirect
82. C3×#214C2×C4semidirect
94. C3×Dic12C2×C4semidirect
96. C3×D3×C8C2×C4semidirect
124. #912C3×C4semidirect
186. #442C3×D3semidirect
212. #237C2×C3×C4semidirect
219. C3×D8C4×D3semidirect
220. C3×D8C2×C3×C4semidirect
251. #214C2×C3×C4semidirect
263. Dic12C2×C3×C4semidirect
265. D3×C8C2×C3×C4semidirect
381. D8C3×C4×D3semidirect
437. C32#2952semidirect
488. C3#79868direct (N × H)
489. C3C3×#2952semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9122
C3×#55462
C32×#4422
C3×#51522
C3×C4×#2142
C3×D3×#1062
C3×#48532
C3×#47712
C3×#47582
C3×#47162
C3×#47082
C3×#29523
#798683