Finite Group Databasebeta

← C3×#81764 #11878686

Subgroups — C3×#81764 #11878686

Order 1152.

927 conjugacy classes of subgroups.

The subgroup lattice has 501 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D3×C4⋊Q8C211yesmaximal, characteristic, complemented
2C3×#5716C211yesmaximal, characteristic
3C32×#492C211yesmaximal, characteristic, complemented
4C3×#5170C214yesmaximal, complemented
5C3×#5162C214yesmaximal, complemented
6C3×#5079C211yesmaximal, characteristic, complemented
7C3×#5076C211yesmaximal, characteristic, complemented
8C3×#4685C211yesmaximal, characteristic, complemented
9C3×#4681C211yesmaximal, characteristic, complemented
10C3×#3206—31nomaximal
11#81764C311yesmaximal, characteristic, direct product factor
12C2×C3×D3×Q8C2212yes—
13C2×C3×#237—21no—
14C2×C32×SD16C2214yes—
15C32×C4⋊Q8C2211yescharacteristic
16C32×#127C2211yescharacteristic
17C3×#944C2212yes—
18C3×#938—21no—
19C3×#938C2212yes—
20C3×#936—21no—
21C3×D4×Dic3—21no—
22C3×D4×Dic3C2212yes—
23C2×C3×#214C2214yes—
24C3×D3×C4⋊C4—21no—
25C3×D3×C4⋊C4—21no—
26C3×#888—21no—
27C3×#888—21no—
28C3×C42×D3C2211yescharacteristic
29C3×#869C2211yescharacteristic
30C3×#869C2211yescharacteristic
31C32×C4×C8C2211yescharacteristic
32C3×#835C2214yes—
33C3×(C2×D3)⋊C8C2212yes—
34C3×#816C2214yes—
35C3×Dic3⋊C8C2212yes—
36C3×C4×C3⋊C8C2211yescharacteristic
37C3×#532—31no—
38C2×C3×C4⋊Q8—31no—
39D3×C4⋊Q8C2×C311yescharacteristic, complemented
40#5716C2×C311yescharacteristic
41C3×#492—21no—
42C3×#492—31no—
43C3×#492D311yescharacteristic, complemented
44C3×#492C2×C311yescharacteristic, complemented
45C3×#487—31no—
46C3×#487—31no—
47C3×#461—34no—
48C3×#448—34no—
49C3×#431—31no—
50#5170C2×C314yescomplemented
51#5162C2×C314yescomplemented
52#5079C2×C311yescharacteristic, complemented
53#5076C2×C311yescharacteristic, complemented
54#4685C2×C311yescharacteristic, complemented
55#4681C2×C311yescharacteristic, complemented
56C2×C32×Q8C2312yes—
57C2×C32×D4—21no—
58C2×C32×D4—21no—
59C2×C32×D4C2312yes—
60C2×C3×#67—22no—
61C22×C3×Dic3—22no—
62C3×D3×Q8—44no—
63C3×#237—44no—
64C2×C3×C4×D3—22no—
65C2×C3×C4×D3D411yescharacteristic
66C2×C3×C4×D3D411yescharacteristic
67C2×C3×C4×D3C2311yescharacteristic
68C2×C3×Dic6—21no—
69C2×C3×Dic6—22no—
70C2×C3×Dic6C2312yes—
71C32×SD16—44no—
72C2×C32×C8C2312yes—
73C32×C4⋊C4—21no—
74C32×C4⋊C4—21no—
75C32×C42C2311yescharacteristic
76C3×#217—22no—
77C3×#217—22no—
78C3×#214—44no—
79C3×C4⋊Dic3—21no—
80C3×C4⋊Dic3—21no—
81C3×C4⋊Dic3—21no—
82C3×C4⋊Dic3C2312yes—
83C3×Dic3⋊C4—22no—
84C3×Dic3⋊C4—22no—
85C3×C4×Dic3D411yescharacteristic
86C3×C4×Dic3D411yescharacteristic
87C3×C4×Dic3C2311yescharacteristic
88C2×C3×C3⋊C8C2312yes—
89#3206—31noSylow
90C2×C3×#41—61no—
91C22×C3×Q8—32no—
92C2×D3×Q8C22×C312yes—
93C2×#237—21no—
94C2×C3×SD16—24no—
95C2×C3×SD16—34no—
96C2×C3×SD16C2×D314yes—
97C2×C3×SD16C22×C314yes—
98C3×C4⋊Q8—21no—
99C3×C4⋊Q8—32no—
100C3×C4⋊Q8—31no—
101C3×C4⋊Q8—31no—
102C3×C4⋊Q8—61no—
103C3×C4⋊Q8—61no—
104C3×C4⋊Q8C2×D311yescharacteristic
105C3×C4⋊Q8C22×C311yescharacteristic
106C3×#127—21no—
107C3×#127C2×D311yescharacteristic
108C3×#127C22×C311yescharacteristic
109C3×#124—61no—
110C3×#121—32no—
111C3×#121—61no—
112C3×C4×D4—32no—
113C3×C4×D4—61no—
114C2×C3×C4⋊C4—61no—
115C2×C3×C4⋊C4—61no—
116C2×C3×C42—31no—
117#944C22×C312yes—
118#938—21no—
119#938C22×C312yes—
120#936—21no—
121D4×Dic3—21no—
122D4×Dic3C22×C312yes—
123C2×#214C22×C314yes—
124D3×C4⋊C4—21no—
125D3×C4⋊C4—21no—
126#888—21no—
127#888—21no—
128C42×D3C22×C311yescharacteristic
129#869C22×C311yescharacteristic
130#869C22×C311yescharacteristic
131C3×C4⋊C8—32no—
132C3×#103—34no—
133C3×#103—34no—
134C3×C22⋊C8—32no—
135C3×C4×C8—21no—
136C3×C4×C8—31no—
137C3×C4×C8C2×D311yescharacteristic
138C3×C4×C8C22×C311yescharacteristic
139#835C22×C314yes—
140(C2×D3)⋊C8C22×C312yes—
141#816C22×C314yes—
142Dic3⋊C8C22×C312yes—
143C4×C3⋊C8C22×C311yescharacteristic
144C23×C32—22no—
145C22×C3×D3C2×D411yescharacteristic
146C32×Q8—24no—
147C32×D4—24no—
148C32×D4—42no—
149C32×D4—42no—
150C2×C32×C4—22no—
151C2×C32×C4C2×D411yescharacteristic
152C2×C32×C4C2×D411yescharacteristic
153C2×C32×C4C2411yescharacteristic
154C3×#67—44no—
155C2×C3×Dic3—22no—
156C2×C3×Dic3—22no—
157C2×C3×Dic3—44no—
158C2×C3×Dic3C2×D411yescharacteristic
159C2×C3×Dic3C2×D411yescharacteristic
160C2×C3×Dic3C2×D411yescharacteristic
161C3×C4×D3—22no—
162C3×C4×D3—22no—
163C3×C4×D3—44no—
164C3×C4×D3SD1614yescomplemented
165C3×Dic6—24no—
166C3×Dic6—44no—
167C3×Dic6—42no—
168C32×C8—22no—
169C3×C3⋊C8—22no—
170#532—31no—
171C2×C4⋊Q8—31no—
172#492—31no—
173#492C3×D311yescharacteristic, complemented
174#487—31no—
175#487—31no—
176#461—34no—
177#448—34no—
178#431—31no—
179C3×#41—124no—
180C2×C3×Q8—22no—
181C2×C3×Q8—32no—
182C2×C3×Q8—62no—
183C2×C3×Q8—61no—
184C2×C3×Q8—124no—
185C2×C3×Q8C22×D312yes—
186C2×C3×Q8C23×C312yes—
187C2×C3×D4—21no—
188C2×C3×D4—21no—
189C2×C3×D4—21no—
190C2×C3×D4—21no—
191C2×C3×D4—22no—
192C2×C3×D4—41no—
193C2×C3×D4—41no—
194C2×C3×D4—62no—
195C2×C3×D4C22×D312yes—
196C2×C3×D4C23×C312yes—
197C22×C3×C4—31no—
198C22×C3×C4—31no—
199C22×C3×C4—31no—
200C22×C3×C4—62no—
201C22×C3×C4—62no—
202C2×#67—22no—
203C22×Dic3—22no—
204D3×Q8—44no—
205#237—44no—
206C2×C4×D3—22no—
207C2×C4×D3C3×D411yescharacteristic
208C2×C4×D3C3×D411yescharacteristic
209C2×C4×D3C23×C311yescharacteristic
210C2×Dic6—21no—
211C2×Dic6—22no—
212C2×Dic6C23×C312yes—
213C3×SD16—44no—
214C3×SD16—44no—
215C3×SD16—48no—
216C3×SD16—124no—
217C2×C3×C8—22no—
218C2×C3×C8—32no—
219C2×C3×C8C22×D312yes—
220C2×C3×C8C23×C312yes—
221C3×C4⋊C4—21no—
222C3×C4⋊C4—21no—
223C3×C4⋊C4—21no—
224C3×C4⋊C4—21no—
225C3×C4⋊C4—32no—
226C3×C4⋊C4—41no—
227C3×C4⋊C4—41no—
228C3×C4⋊C4—62no—
229C3×C4⋊C4—62no—
230C3×C4⋊C4—61no—
231C3×C4⋊C4—61no—
232C3×C4⋊C4—61no—
233C3×C22⋊C4—62no—
234C3×C22⋊C4—62no—
235C3×C42—21no—
236C3×C42—31no—
237C3×C42—31no—
238C3×C42—31no—
239C3×C42C22×D311yescharacteristic
240C3×C42C23×C311yescharacteristic
241#217—22no—
242#217—22no—
243#214—44no—
244C4⋊Dic3—21no—
245C4⋊Dic3—21no—
246C4⋊Dic3—21no—
247C4⋊Dic3C23×C312yes—
248Dic3⋊C4—22no—
249Dic3⋊C4—22no—
250C4×Dic3C3×D411yescharacteristic
251C4×Dic3C3×D411yescharacteristic
252C4×Dic3C23×C311yescharacteristic
253C2×C3⋊C8C23×C312yes—
254C22×C32—42no—
255C22×C32—42no—
256C22×C32—42no—
257C22×C32C22×D411yescharacteristic
258C2×C3×D3—21no—
259C2×C3×D3—21no—
260C2×C3×D3C2×SD1612yes—
261C32×C4—42no—
262C32×C4C2×SD1612yes—
263C32×C4#13712yes—
264C32×C4H(5,𝔽2)12yes—
265C3×Dic3—21no—
266C3×Dic3—21no—
267C3×Dic3—42no—
268C3×Dic3—42no—
269C3×Dic3C2×SD1612yes—
270C2×#41—61no—
271C22×Q8—32no—
272C2×SD16—34no—
273C2×SD16C2×C3×D314yes—
274C4⋊Q8—32no—
275C4⋊Q8—31no—
276C4⋊Q8—31no—
277C4⋊Q8—61no—
278C4⋊Q8—61no—
279C4⋊Q8C2×C3×D311yescharacteristic
280#127C2×C3×D311yescharacteristic
281#124—61no—
282#121—32no—
283#121—61no—
284C4×D4—32no—
285C4×D4—61no—
286C2×C4⋊C4—61no—
287C2×C4⋊C4—61no—
288C2×C42—31no—
289C4⋊C8—32no—
290#103—34no—
291#103—34no—
292C22⋊C8—32no—
293C4×C8—31no—
294C4×C8C2×C3×D311yescharacteristic
295C23×C3—22no—
296C23×C3—22no—
297C23×C3—31no—
298C23×C3—42no—
299C22×D3C2×C3×D411yescharacteristic
300C3×Q8—24no—
301C3×Q8—24no—
302C3×Q8—44no—
303C3×Q8—64no—
304C3×Q8—124no—
305C3×Q8—122no—
306C3×D4—24no—
307C3×D4—24no—
308C3×D4—44no—
309C3×D4—42no—
310C3×D4—42no—
311C3×D4—42no—
312C3×D4—42no—
313C3×D4—82no—
314C3×D4—82no—
315C3×D4—124no—
316C2×C3×C4—22no—
317C2×C3×C4—22no—
318C2×C3×C4—21no—
319C2×C3×C4—21no—
320C2×C3×C4—21no—
321C2×C3×C4—31no—
322C2×C3×C4—34no—
323C2×C3×C4—31no—
324C2×C3×C4—31no—
325C2×C3×C4—42no—
326C2×C3×C4—62no—
327C2×C3×C4—62no—
328C2×C3×C4—62no—
329C2×C3×C4—62no—
330C2×C3×C4—124no—
331C2×C3×C4—124no—
332C2×C3×C4D3×D411yescharacteristic
333C2×C3×C4D3×D411yescharacteristic
334C2×C3×C4C2×C3×D411yescharacteristic
335C2×C3×C4C2×C3×D411yescharacteristic
336C2×C3×C4C23×D311yescharacteristic
337C2×C3×C4C24×C311yescharacteristic
338#67—44no—
339C2×Dic3—22no—
340C2×Dic3—22no—
341C2×Dic3—44no—
342C2×Dic3C2×C3×D411yescharacteristic
343C2×Dic3C2×C3×D411yescharacteristic
344C2×Dic3C2×C3×D411yescharacteristic
345C4×D3—22no—
346C4×D3—22no—
347C4×D3—44no—
348C4×D3C3×SD1614yescomplemented
349Dic6—24no—
350Dic6—44no—
351Dic6—42no—
352C3×C8—24no—
353C3×C8—22no—
354C3×C8—22no—
355C3×C8—62no—
356C3⋊C8—22no—
357C2×C32—82no—
358C2×C32#53511yescharacteristic
359C2×C32C22×SD1611yescharacteristic
360C2×C32C2×#13711yescharacteristic
361C3×D3—22no—
362#41—124no—
363C2×Q8—32no—
364C2×Q8—62no—
365C2×Q8—61no—
366C2×Q8—124no—
367C2×Q8C22×C3×D312yes—
368C2×D4—21no—
369C2×D4—21no—
370C2×D4—62no—
371C2×D4C22×C3×D312yes—
372C22×C4—31no—
373C22×C4—31no—
374C22×C4—31no—
375C22×C4—62no—
376C22×C4—62no—
377SD16—44no—
378SD16—124no—
379C2×C8—32no—
380C2×C8C22×C3×D312yes—
381C4⋊C4—21no—
382C4⋊C4—21no—
383C4⋊C4—32no—
384C4⋊C4—62no—
385C4⋊C4—62no—
386C4⋊C4—61no—
387C4⋊C4—61no—
388C4⋊C4—61no—
389C22⋊C4—62no—
390C22⋊C4—62no—
391C42—31no—
392C42—31no—
393C42—31no—
394C42C22×C3×D311yescharacteristic
395C22×C3—21no—
396C22×C3—32no—
397C22×C3—42no—
398C22×C3—42no—
399C22×C3—42no—
400C22×C3—42no—
401C22×C3—42no—
402C22×C3—42no—
403C22×C3—61no—
404C22×C3—61no—
405C22×C3—82no—
406C22×C3—82no—
407C22×C3—82no—
408C22×C3C2×D3×D411yescharacteristic
409C22×C3C22×C3×D411yescharacteristic
410C2×D3—21no—
411C2×D3—21no—
412C2×D3C2×C3×SD1612yes—
413C3×C4—22no—
414C3×C4—22no—
415C3×C4—22no—
416C3×C4—32no—
417C3×C4—42no—
418C3×C4—42no—
419C3×C4—61no—
420C3×C4—61no—
421C3×C4—82no—
422C3×C4—122no—
423C3×C4—122no—
424C3×C4D3×SD1612yes—
425C3×C4#91512yes—
426C3×C4C2×C3×SD1612yes—
427C3×C4C3×#13712yes—
428C3×C4#100412yes—
429C3×C4C3×H(5,𝔽2)12yes—
430Dic3—21no—
431Dic3—21no—
432Dic3—42no—
433Dic3—42no—
434Dic3C2×C3×SD1612yes—
435C32#320611yescharacteristic, complemented, Sylow
436C23—22no—
437C23—31no—
438Q8—24no—
439Q8—64no—
440Q8—124no—
441Q8—122no—
442D4—24no—
443D4—42no—
444D4—42no—
445D4—124no—
446C2×C4—22no—
447C2×C4—31no—
448C2×C4—34no—
449C2×C4—31no—
450C2×C4—31no—
451C2×C4—62no—
452C2×C4—62no—
453C2×C4—62no—
454C2×C4—62no—
455C2×C4—124no—
456C2×C4—124no—
457C2×C4C3×D3×D411yescharacteristic
458C2×C4C3×D3×D411yescharacteristic
459C2×C4C23×C3×D311yescharacteristic
460C8—22no—
461C8—62no—
462C2×C3—21no—
463C2×C3—21no—
464C2×C3—21no—
465C2×C3—62no—
466C2×C3—82no—
467C2×C3—82no—
468C2×C3—162no—
469C2×C3#571511yescharacteristic
470C2×C3C2×D3×SD1611yescharacteristic
471C2×C3C2×#91511yescharacteristic
472C2×C3C3×#53511yescharacteristic
473C2×C3C22×C3×SD1611yescharacteristic
474C2×C3C2×C3×#13711yescharacteristic
475D3—22no—
476C22—32no—
477C22—42no—
478C22—42no—
479C22—42no—
480C22—61no—
481C22—61no—
482C22C2×C3×D3×D411yescharacteristic
483C4—32no—
484C4—42no—
485C4—61no—
486C4—61no—
487C4—122no—
488C4—122no—
489C4C3×D3×SD1612yes—
490C4C3×#91512yes—
491C4C3×#100412yes—
492C3—21no—
493C3#8176411yescharacteristic, direct product factor
494C3C3×#320611yescharacteristic, complemented
495C2—62no—
496C2—82no—
497C2C3×#571511yescharacteristic
498C2C2×C3×D3×SD1611yescharacteristic
499C2C2×C3×#91511yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#492C2
socleC22×C32C22×D4
prime radicalC3×#5716C2
hypercenterC3×#492D3
hypocenterC3C3×#3206
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#492

Complements

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

NH ≅ G/Ntype
1. C3×D3×C4⋊Q8C2semidirect
3. C32×#492C2semidirect
4. C3×#5170C2semidirect
5. C3×#5162C2semidirect
6. C3×#5079C2semidirect
7. C3×#5076C2semidirect
8. C3×#4685C2semidirect
9. C3×#4681C2semidirect
11. #81764C3direct (N × H)
39. D3×C4⋊Q8C2×C3semidirect
43. C3×#492D3semidirect
44. C3×#492C2×C3semidirect
50. #5170C2×C3semidirect
51. #5162C2×C3semidirect
52. #5079C2×C3semidirect
53. #5076C2×C3semidirect
54. #4685C2×C3semidirect
55. #4681C2×C3semidirect
164. C3×C4×D3SD16semidirect
173. #492C3×D3semidirect
348. C4×D3C3×SD16semidirect
435. C32#3206semidirect
493. C3#81764direct (N × H)
494. C3C3×#3206semidirect

Maximal subgroups

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

subgroupindex
C3×D3×C4⋊Q82
C3×#57162
C32×#4922
C3×#51702
C3×#51622
C3×#50792
C3×#50762
C3×#46852
C3×#46812
C3×#32063
#817643