Finite Group Databasebeta

← C3×#81885 #11886661

Subgroups — C3×#81885 #11886661

Order 1152.

958 conjugacy classes of subgroups.

The subgroup lattice has 559 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5766C212yesmaximal, complemented
2C3×#5762C212yesmaximal, complemented
3C32×#497C211yesmaximal, characteristic, complemented
4C3×#5192C212yesmaximal, complemented
5C3×#5177C212yesmaximal, complemented
6C3×#5095C212yesmaximal, complemented
7C3×#5062C211yesmaximal, characteristic, complemented
8C3×#5061C211yesmaximal, characteristic, complemented
9C3×#4717C212yesmaximal, complemented
10C3×#3289—31nomaximal
11#81885C311yesmaximal, characteristic, direct product factor
12C3×#1007C2212yes—
13C3×#1007C2211yescharacteristic, complemented
14C3×#1004C2211yescharacteristic
15C2×C32×Q16C2212yescomplemented
16C2×C32×SD16C2212yes—
17C32×C4⋊Q8C2211yescharacteristic, complemented
18C32×#124C2211yescharacteristic
19C3×#942C2212yes—
20C3×#942C2212yes—
21C3×#942C2212yescomplemented
22C3×#932C2212yes—
23C3×#919—22no—
24C3×#918—22no—
25C3×#918—22no—
26C3×D3×Q16—22no—
27C3×#916—22no—
28C3×#915—22no—
29C3×#914—22no—
30C3×D3×SD16—22no—
31C3×#904C2212yes—
32C3×#901C2212yes—
33C3×#901C2212yescomplemented
34C32×#97C2211yescharacteristic, complemented
35C3×#836C2212yescomplemented
36C3×#836C2211yescharacteristic, complemented
37C3×#833C2211yescharacteristic
38C3×#819C2212yescomplemented
39C3×#805C2212yes—
40C3×#805C2212yescomplemented
41C3×#578—32no—
42C3×#577—32no—
43#5766C2×C312yescomplemented
44#5762C2×C312yescomplemented
45C3×#497—21no—
46C3×#497D311yescharacteristic, complemented
47C3×#497C2×C311yescharacteristic, complemented
48C3×#473—32no—
49C3×#471—32no—
50C3×#456—32no—
51C3×#455—31no—
52C3×#454—31no—
53C3×#444—32no—
54#5192C2×C312yescomplemented
55#5177C2×C312yescomplemented
56#5095C2×C312yescomplemented
57#5062C2×C311yescharacteristic, complemented
58#5061C2×C311yescharacteristic, complemented
59#4717C2×C312yescomplemented
60C2×C32×Q8C2311yescharacteristic
61C2×C32×Q8C2312yes—
62C2×C32×D4C2311yescharacteristic
63C2×C3×#67—41no—
64C3×#239—22no—
65C3×#239—22no—
66C3×#239—22no—
67C3×D3×Q8—22no—
68C3×D3×Q8—22no—
69C3×D3×Q8—22no—
70C3×#237—22no—
71C3×D3×D4—22no—
72C3×#235—42no—
73C3×#235—41no—
74C3×#235C2312yes—
75C3×#235C2312yes—
76C32×Q16—22no—
77C32×Q16—22no—
78C32×SD16—22no—
79C32×SD16—22no—
80C2×C32×C8C2312yes—
81C32×C4⋊C4—41no—
82C32×C22⋊C4—41no—
83C32×C42C2311yescharacteristic
84C3×#216—22no—
85C3×#216—22no—
86C3×#216—22no—
87C3×#215—22no—
88C3×#215—22no—
89C3×#215—22no—
90C3×#214—22no—
91C3×#213—22no—
92C3×#208C2312yes—
93C3×#208C2312yes—
94C3×Dic12D412yes—
95C3×D24D412yes—
96C3×#204D412yes—
97C3×#204D412yes—
98C3×ΓL(1,𝔽25)—22no—
99C3×ΓL(1,𝔽25)—22no—
100C3×D3×C8—22no—
101C3×D3×C8—22no—
102#3289—31noSylow
103C3×2−1+4—32no—
104C3×2−1+4—31no—
105C3×H(5,𝔽2)—31no—
106#1007C22×C312yes—
107#1007C22×C311yescharacteristic, complemented
108#1004C22×C311yescharacteristic
109C3×#137—32no—
110C3×#137—32no—
111C3×#137—32no—
112C3×#137—62no—
113C3×#137—62no—
114C3×#137—62no—
115C3×AGL(1,ℤ/8)—32no—
116C3×AGL(1,ℤ/8)—62no—
117C3×#135—32no—
118C3×#135—62no—
119C3×#135—62no—
120C2×C3×Q16—22no—
121C2×C3×Q16—62no—
122C2×C3×Q16C2×D312yescomplemented
123C2×C3×Q16C22×C312yescomplemented
124C2×C3×SD16—22no—
125C2×C3×SD16—62no—
126C2×C3×SD16C2×D312yes—
127C2×C3×SD16C22×C312yes—
128C3×#131—32no—
129C3×#131—32no—
130C3×C4⋊Q8—21no—
131C3×C4⋊Q8C2×D311yescharacteristic, complemented
132C3×C4⋊Q8C22×C311yescharacteristic, complemented
133C3×#124—21no—
134C3×#124C2×D311yescharacteristic
135C3×#124C22×C311yescharacteristic
136#942C22×C312yes—
137#942C22×C312yes—
138#942C22×C312yescomplemented
139#932C22×C312yes—
140#919—22no—
141#918—22no—
142#918—22no—
143D3×Q16—22no—
144#916—22no—
145#915—22no—
146#914—22no—
147D3×SD16—22no—
148#904C22×C312yes—
149#901C22×C312yes—
150#901C22×C312yescomplemented
151C3×#108—32no—
152C3×#104—32no—
153C3×#104—32no—
154C3×#101—31no—
155C3×#101—32no—
156C3×#100—31no—
157C3×#97—21no—
158C3×#97C2×D311yescharacteristic, complemented
159C3×#97C22×C311yescharacteristic, complemented
160#836C22×C312yescomplemented
161#836C22×C311yescharacteristic, complemented
162#833C22×C311yescharacteristic
163#819C22×C312yescomplemented
164#805C22×C312yes—
165#805C22×C312yescomplemented
166C23×C32—21no—
167C22×C3×D3—41no—
168C32×Q8—22no—
169C32×Q8—22no—
170C32×Q8—22no—
171C32×D4—22no—
172C2×C32×C4—21no—
173C2×C32×C4—21no—
174C2×C32×C4—22no—
175C2×C32×C4C2411yescharacteristic
176C3×#67—22no—
177C3×#67—22no—
178C3×#67—42no—
179C2×C3×Dic3—41no—
180C3×D12—41no—
181C3×D12—42no—
182C3×D12C2×D412yes—
183C3×D12C2×D412yes—
184C3×C4×D3—22no—
185C3×C4×D3—22no—
186C3×C4×D3—42no—
187C3×C4×D3—42no—
188C3×C4×D3—42no—
189C3×Dic6—41no—
190C3×Dic6—42no—
191C3×Dic6C2×D412yes—
192C3×Dic6C2×D412yes—
193C32×C8C2×D412yes—
194C32×C8C2×D412yes—
195C3×C3⋊C8—22no—
196C3×C3⋊C8—22no—
197#578—32no—
198#577—32no—
199#497C3×D311yescharacteristic, complemented
200#473—32no—
201#471—32no—
202#456—32no—
203#455—31no—
204#454—31no—
205#444—32no—
206C3×#41—32no—
207C3×#41—32no—
208C3×#41—62no—
209C3×#41—62no—
210C3×#41—62no—
211C3×#41—62no—
212C3×#41—121no—
213C3×#41—122no—
214C2×C3×Q8—21no—
215C2×C3×Q8—22no—
216C2×C3×Q8—62no—
217C2×C3×Q8—62no—
218C2×C3×Q8—62no—
219C2×C3×Q8C22×D311yescharacteristic
220C2×C3×Q8C22×D312yes—
221C2×C3×Q8C23×C311yescharacteristic
222C2×C3×Q8C23×C312yes—
223C2×C3×D4—21no—
224C2×C3×D4—62no—
225C2×C3×D4—121no—
226C2×C3×D4C22×D311yescharacteristic
227C2×C3×D4C23×C311yescharacteristic
228C2×#67—41no—
229#239—22no—
230#239—22no—
231#239—22no—
232D3×Q8—22no—
233D3×Q8—22no—
234D3×Q8—22no—
235#237—22no—
236D3×D4—22no—
237#235—42no—
238#235—41no—
239#235C23×C312yes—
240#235C23×C312yes—
241C3×Q16—22no—
242C3×Q16—22no—
243C3×Q16—22no—
244C3×Q16—22no—
245C3×Q16—32no—
246C3×Q16—42no—
247C3×Q16—42no—
248C3×Q16—62no—
249C3×Q16—62no—
250C3×Q16—62no—
251C3×SD16—22no—
252C3×SD16—22no—
253C3×SD16—22no—
254C3×SD16—22no—
255C3×SD16—32no—
256C3×SD16—32no—
257C3×SD16—42no—
258C3×SD16—42no—
259C3×SD16—62no—
260C3×SD16—62no—
261C3×SD16—62no—
262C3×SD16—62no—
263C3×D8—32no—
264C3×D8—62no—
265C3×M16—32no—
266C3×M16—32no—
267C3×M16—62no—
268C3×M16—62no—
269C2×C3×C8—22no—
270C2×C3×C8—62no—
271C2×C3×C8—62no—
272C2×C3×C8C22×D312yes—
273C2×C3×C8C23×C312yes—
274C3×C4⋊C4—41no—
275C3×C4⋊C4—41no—
276C3×C4⋊C4—42no—
277C3×C22⋊C4—41no—
278C3×C22⋊C4—41no—
279C3×C22⋊C4—42no—
280C3×C42—21no—
281C3×C42C22×D311yescharacteristic
282C3×C42C23×C311yescharacteristic
283#216—22no—
284#216—22no—
285#216—22no—
286#215—22no—
287#215—22no—
288#215—22no—
289#214—22no—
290#213—22no—
291#208C23×C312yes—
292#208C23×C312yes—
293Dic12C3×D412yes—
294D24C3×D412yes—
295#204C3×D412yes—
296#204C3×D412yes—
297ΓL(1,𝔽25)—22no—
298ΓL(1,𝔽25)—22no—
299D3×C8—22no—
300D3×C8—22no—
301C22×C32—41no—
302C22×C32—81no—
303C22×C32H(5,𝔽2)11yescharacteristic
304C2×C3×D3—22no—
305C2×C3×D3—22no—
306C2×C3×D3—161no—
307C32×C4—41no—
308C32×C4—41no—
309C32×C4—42no—
310C32×C4C22×D412yes—
311C3×Dic3—22no—
312C3×Dic3—22no—
3132−1+4—32no—
3142−1+4—31no—
315H(5,𝔽2)—31no—
316#137—32no—
317#137—32no—
318#137—32no—
319#137—62no—
320#137—62no—
321#137—62no—
322AGL(1,ℤ/8)—32no—
323AGL(1,ℤ/8)—62no—
324#135—32no—
325#135—62no—
326#135—62no—
327C2×Q16—62no—
328C2×Q16C2×C3×D312yescomplemented
329C2×SD16—62no—
330C2×SD16C2×C3×D312yes—
331#131—32no—
332#131—32no—
333C4⋊Q8C2×C3×D311yescharacteristic, complemented
334#124C2×C3×D311yescharacteristic
335#108—32no—
336#104—32no—
337#104—32no—
338#101—31no—
339#101—32no—
340#100—31no—
341#97C2×C3×D311yescharacteristic, complemented
342C23×C3—21no—
343C23×C3—21no—
344C23×C3—41no—
345C23×C3—121no—
346C22×D3—41no—
347C3×Q8—22no—
348C3×Q8—22no—
349C3×Q8—22no—
350C3×Q8—22no—
351C3×Q8—22no—
352C3×Q8—22no—
353C3×Q8—32no—
354C3×Q8—32no—
355C3×Q8—42no—
356C3×Q8—42no—
357C3×Q8—42no—
358C3×Q8—122no—
359C3×Q8—121no—
360C3×D4—22no—
361C3×D4—22no—
362C3×D4—32no—
363C3×D4—32no—
364C3×D4—42no—
365C3×D4—62no—
366C3×D4—62no—
367C3×D4—121no—
368C3×D4—122no—
369C3×D4—122no—
370C2×C3×C4—22no—
371C2×C3×C4—21no—
372C2×C3×C4—21no—
373C2×C3×C4—22no—
374C2×C3×C4—21no—
375C2×C3×C4—21no—
376C2×C3×C4—22no—
377C2×C3×C4—21no—
378C2×C3×C4—41no—
379C2×C3×C4—42no—
380C2×C3×C4—62no—
381C2×C3×C4—62no—
382C2×C3×C4—122no—
383C2×C3×C4—122no—
384C2×C3×C4—122no—
385C2×C3×C4—121no—
386C2×C3×C4C23×D311yescharacteristic
387C2×C3×C4C24×C311yescharacteristic
388#67—22no—
389#67—22no—
390#67—42no—
391C2×Dic3—41no—
392D12—41no—
393D12—42no—
394D12C2×C3×D412yes—
395D12C2×C3×D412yes—
396C4×D3—22no—
397C4×D3—22no—
398C4×D3—42no—
399C4×D3—42no—
400C4×D3—42no—
401Dic6—41no—
402Dic6—42no—
403Dic6C2×C3×D412yes—
404Dic6C2×C3×D412yes—
405C3×C8—22no—
406C3×C8—22no—
407C3×C8—62no—
408C3×C8—62no—
409C3×C8D3×D412yes—
410C3×C8D3×D412yes—
411C3×C8C2×C3×D412yes—
412C3×C8C2×C3×D412yes—
413C3⋊C8—22no—
414C3⋊C8—22no—
415C2×C32—21no—
416C2×C32—81no—
417C2×C32D4211yescharacteristic
418C3×D3—42no—
419C3×D3—42no—
420#41—32no—
421#41—32no—
422#41—62no—
423#41—62no—
424#41—62no—
425#41—62no—
426#41—121no—
427#41—122no—
428C2×Q8—62no—
429C2×Q8—62no—
430C2×Q8—62no—
431C2×Q8C22×C3×D311yescharacteristic
432C2×Q8C22×C3×D312yes—
433C2×D4—62no—
434C2×D4—121no—
435C2×D4C22×C3×D311yescharacteristic
436Q16—22no—
437Q16—22no—
438Q16—32no—
439Q16—62no—
440Q16—62no—
441Q16—62no—
442SD16—22no—
443SD16—22no—
444SD16—32no—
445SD16—32no—
446SD16—62no—
447SD16—62no—
448SD16—62no—
449SD16—62no—
450D8—32no—
451D8—62no—
452M16—32no—
453M16—32no—
454M16—62no—
455M16—62no—
456C2×C8—62no—
457C2×C8—62no—
458C2×C8C22×C3×D312yes—
459C4⋊C4—41no—
460C22⋊C4—41no—
461C42C22×C3×D311yescharacteristic
462C22×C3—21no—
463C22×C3—41no—
464C22×C3—41no—
465C22×C3—62no—
466C22×C3—62no—
467C22×C3—81no—
468C22×C3—81no—
469C22×C3—81no—
470C22×C3—82no—
471C22×C3—481no—
472C22×C3#100411yescharacteristic
473C22×C3C3×H(5,𝔽2)11yescharacteristic
474C2×D3—22no—
475C2×D3—22no—
476C2×D3—161no—
477C3×C4—22no—
478C3×C4—42no—
479C3×C4—41no—
480C3×C4—41no—
481C3×C4—41no—
482C3×C4—42no—
483C3×C4—41no—
484C3×C4—42no—
485C3×C4—62no—
486C3×C4—62no—
487C3×C4—81no—
488C3×C4—82no—
489C3×C4C2×D3×D412yes—
490C3×C4C22×C3×D412yes—
491Dic3—22no—
492Dic3—22no—
493C32#328911yescharacteristic, complemented, Sylow
494C23—21no—
495C23—121no—
496Q8—22no—
497Q8—22no—
498Q8—22no—
499Q8—32no—
500Q8—32no—
501Q8—122no—
502Q8—121no—
503D4—22no—
504D4—32no—
505D4—32no—
506D4—62no—
507D4—62no—
508D4—121no—
509D4—122no—
510D4—122no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—22no—
514C2×C4—62no—
515C2×C4—62no—
516C2×C4—122no—
517C2×C4—122no—
518C2×C4—122no—
519C2×C4—121no—
520C2×C4C23×C3×D311yescharacteristic
521C8—62no—
522C8—62no—
523C8C3×D3×D412yes—
524C8C3×D3×D412yes—
525C2×C3—22no—
526C2×C3—21no—
527C2×C3—21no—
528C2×C3—21no—
529C2×C3—81no—
530C2×C3—81no—
531C2×C3—122no—
532C2×C3—122no—
533C2×C3—161no—
534C2×C3#571711yescharacteristic
535C2×C3C3×D4211yescharacteristic
536D3—42no—
537D3—42no—
538C22—41no—
539C22—62no—
540C22—62no—
541C22—81no—
542C22—481no—
543C22C3×#100411yescharacteristic
544C4—41no—
545C4—41no—
546C4—42no—
547C4—62no—
548C4—62no—
549C4C2×C3×D3×D412yes—
550C3—21no—
551C3#8188511yescharacteristic, direct product factor
552C3C3×#328911yescharacteristic, complemented
553C2—21no—
554C2—81no—
555C2—122no—
556C2—122no—
557C2C3×#571711yescharacteristic
subgroupG/H
centerC2×C3#5717
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#497C2
socleC2×C32D42
hypercenterC3×#497D3
hypocenterC3C3×#3289
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3 ◁ C2×C3×C4 ◁ C3×#497

Complements

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

NH ≅ G/Ntype
1. C3×#5766C2semidirect
2. C3×#5762C2semidirect
3. C32×#497C2semidirect
4. C3×#5192C2semidirect
5. C3×#5177C2semidirect
6. C3×#5095C2semidirect
7. C3×#5062C2semidirect
8. C3×#5061C2semidirect
9. C3×#4717C2semidirect
11. #81885C3direct (N × H)
13. C3×#1007C22semidirect
15. C2×C32×Q16C22semidirect
17. C32×C4⋊Q8C22semidirect
21. C3×#942C22semidirect
33. C3×#901C22semidirect
34. C32×#97C22semidirect
35. C3×#836C22semidirect
36. C3×#836C22semidirect
38. C3×#819C22semidirect
40. C3×#805C22semidirect
43. #5766C2×C3semidirect
44. #5762C2×C3semidirect
46. C3×#497D3semidirect
47. C3×#497C2×C3semidirect
54. #5192C2×C3semidirect
55. #5177C2×C3semidirect
56. #5095C2×C3semidirect
57. #5062C2×C3semidirect
58. #5061C2×C3semidirect
59. #4717C2×C3semidirect
107. #1007C22×C3semidirect
122. C2×C3×Q16C2×D3semidirect
123. C2×C3×Q16C22×C3semidirect
131. C3×C4⋊Q8C2×D3semidirect
132. C3×C4⋊Q8C22×C3semidirect
138. #942C22×C3semidirect
150. #901C22×C3semidirect
158. C3×#97C2×D3semidirect
159. C3×#97C22×C3semidirect
160. #836C22×C3semidirect
161. #836C22×C3semidirect
163. #819C22×C3semidirect
165. #805C22×C3semidirect
199. #497C3×D3semidirect
328. C2×Q16C2×C3×D3semidirect
333. C4⋊Q8C2×C3×D3semidirect
341. #97C2×C3×D3semidirect
493. C32#3289semidirect
551. C3#81885direct (N × H)
552. C3C3×#3289semidirect

Maximal subgroups

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

subgroupindex
C3×#57662
C3×#57622
C32×#4972
C3×#51922
C3×#51772
C3×#50952
C3×#50622
C3×#50612
C3×#47172
C3×#32893
#818853