Finite Group Databasebeta

← C3×#83904 #11874418

Subgroups — C3×#83904 #11874418

Order 1152.

1261 conjugacy classes of subgroups.

The subgroup lattice has 517 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#135C211yesmaximal, characteristic, complemented
2C3×#5832C212yesmaximal, complemented
3C2×C3×#950C212yesmaximal, complemented
4C2×C3×#904C211yesmaximal, characteristic, complemented
5C3×#5190C212yesmaximal, complemented
6C3×#5176C212yesmaximal, complemented
7C3×#5167C212yesmaximal, complemented
8C3×#5154C212yesmaximal, complemented
9C2×C3×#815C211yesmaximal, characteristic, complemented
10C3×#3150—31nomaximal
11#83904C311yesmaximal, characteristic, direct product factor
12C2×C32×#41C2212yes—
13C2×C3×#235C2212yes—
14C32×#135—24no—
15C2×C32×Q16C2211yescharacteristic
16C2×C32×SD16C2212yes—
17C2×C32×D8C2211yescharacteristic
18C22×C32×C8C2211yescharacteristic
19C3×#950—28no—
20C3×#947C2212yes—
21C3×#944C2212yes—
22C2×C3×#216C2212yes—
23C2×C3×#215C2212yes—
24C3×#940C2212yes—
25C3×#939—24no—
26C3×#936C2212yes—
27C2×C3×#214C2212yes—
28C2×C3×#213C2212yes—
29C3×C4×#67—24no—
30C2×C3×C4×Dic3C2211yescharacteristic
31C22×C3×C3⋊C8C2211yescharacteristic
32C2×C3×Dic12C2211yescharacteristic
33C3×#904—24no—
34C2×C3×D24C2211yescharacteristic
35C2×C3×#204C2212yes—
36C3×#815C2212yes—
37C3×#815C2212yes—
38C2×C3×#135—21no—
39C2×C3×#135—32no—
40C2×C3×#135—31no—
41C2×C3×#135D311yescharacteristic, complemented
42C2×C3×#135C2×C311yescharacteristic, complemented
43C3×#532—32no—
44#5832C2×C312yescomplemented
45C2×#950C2×C312yescomplemented
46C2×#904C2×C311yescharacteristic, complemented
47C3×#497—32no—
48C3×#497—32no—
49C3×#496—32no—
50C3×#496—32no—
51C2×C3×#97—31no—
52#5190C2×C312yescomplemented
53#5176C2×C312yescomplemented
54#5167C2×C312yescomplemented
55#5154C2×C312yescomplemented
56C2×#815C2×C311yescharacteristic, complemented
57C32×#41—24no—
58C32×#41—24no—
59C2×C32×Q8C2312yes—
60C2×C32×D4—22no—
61C2×C32×D4C2312yes—
62C22×C32×C4—22no—
63C22×C32×C4C2311yescharacteristic
64C2×C3×#67—22no—
65C2×C3×#67—24no—
66C22×C3×Dic3D412yes—
67C3×#235—24no—
68C3×#235—24no—
69C2×C3×D12C2312yes—
70C2×C3×C4×D3—22no—
71C2×C3×Dic6C2312yes—
72C32×Q16—22no—
73C32×SD16—24no—
74C32×D8—22no—
75C2×C32×C8D414yescomplemented
76C2×C32×C8C2311yescharacteristic
77C2×C32×C8C2311yescharacteristic
78C3×#217—24no—
79C3×#216—24no—
80C3×#215—24no—
81C3×#214—24no—
82C3×#213—24no—
83C3×(C2×D3)⋊C4—24no—
84C3×Dic3⋊C4—24no—
85C3×C4×Dic3D412yes—
86C3×C4×Dic3C2312yes—
87C2×C3×C3⋊C8D414yescomplemented
88C2×C3×C3⋊C8C2312yes—
89C3×Dic12—22no—
90C3×D24—22no—
91C3×#204—24no—
92#3150—31noSylow
93C2×C3×#41—22no—
94C2×C3×#41—32no—
95C2×C3×#41C2×D312yes—
96C2×C3×#41C22×C312yes—
97C2×#235C22×C312yes—
98C3×#135—28no—
99C3×#135—24no—
100C3×#135—24no—
101C3×#135—68no—
102C3×#135—64no—
103C2×C3×Q16—21no—
104C2×C3×Q16—32no—
105C2×C3×Q16—31no—
106C2×C3×Q16C2×D311yescharacteristic
107C2×C3×Q16C22×C311yescharacteristic
108C2×C3×SD16—22no—
109C2×C3×SD16—32no—
110C2×C3×SD16—32no—
111C2×C3×SD16—32no—
112C2×C3×SD16C2×D312yes—
113C2×C3×SD16C22×C312yes—
114C2×C3×D8—21no—
115C2×C3×D8—32no—
116C2×C3×D8—31no—
117C2×C3×D8C2×D311yescharacteristic
118C2×C3×D8C22×C311yescharacteristic
119C22×C3×C8—21no—
120C22×C3×C8—31no—
121C22×C3×C8C2×D311yescharacteristic
122C22×C3×C8C22×C311yescharacteristic
123C3×C4⋊Q8—32no—
124C3×#127—32no—
125C3×#124—32no—
126C3×#124—32no—
127C3×#121—64no—
128C3×C4×D4—64no—
129C2×C3×C42—31no—
130#950—28no—
131#947C22×C312yes—
132#944C22×C312yes—
133C2×#216C22×C312yes—
134C2×#215C22×C312yes—
135#940C22×C312yes—
136#939—24no—
137#936C22×C312yes—
138C2×#214C22×C312yes—
139C2×#213C22×C312yes—
140C4×#67—24no—
141C2×C4×Dic3C22×C311yescharacteristic
142C22×C3⋊C8C22×C311yescharacteristic
143C2×Dic12C22×C311yescharacteristic
144#904—24no—
145C2×D24C22×C311yescharacteristic
146C2×#204C22×C312yes—
147C3×#97—32no—
148C3×#97—32no—
149#815C22×C312yes—
150#815C22×C312yes—
151C23×C32—22no—
152C23×C32C2×D411yescharacteristic
153C22×C3×D3—22no—
154C32×Q8—22no—
155C32×Q8—22no—
156C32×D4—22no—
157C32×D4—22no—
158C32×D4—44no—
159C2×C32×C4—22no—
160C2×C32×C4—44no—
161C2×C32×C4C2×D412yes—
162C2×C32×C4C2×D411yescharacteristic
163C2×C32×C4C2×D412yes—
164C2×C32×C4C2411yescharacteristic
165C3×#67—48no—
166C3×#67—44no—
167C2×C3×Dic3—22no—
168C2×C3×Dic3—42no—
169C2×C3×Dic3C2×D414yes—
170C3×D12—22no—
171C3×D12—22no—
172C3×C4×D3—44no—
173C3×Dic6—22no—
174C3×Dic6—22no—
175C32×C8C2×D412yes—
176C32×C8C2×D412yes—
177C3×C3⋊C8C2×D414yes—
178C2×#135—32no—
179C2×#135—31no—
180C2×#135C3×D311yescharacteristic, complemented
181#532—32no—
182#497—32no—
183#497—32no—
184#496—32no—
185#496—32no—
186C2×#97—31no—
187C3×#41—28no—
188C3×#41—24no—
189C3×#41—24no—
190C3×#41—24no—
191C3×#41—24no—
192C3×#41—44no—
193C3×#41—64no—
194C3×#41—64no—
195C2×C3×Q8—22no—
196C2×C3×Q8—32no—
197C2×C3×Q8C22×D312yes—
198C2×C3×Q8C23×C312yes—
199C2×C3×D4—22no—
200C2×C3×D4—22no—
201C2×C3×D4—22no—
202C2×C3×D4—32no—
203C2×C3×D4—42no—
204C2×C3×D4—64no—
205C2×C3×D4—62no—
206C2×C3×D4C22×D312yes—
207C2×C3×D4C23×C312yes—
208C22×C3×C4—22no—
209C22×C3×C4—22no—
210C22×C3×C4—21no—
211C22×C3×C4—32no—
212C22×C3×C4—42no—
213C22×C3×C4—62no—
214C22×C3×C4C22×D311yescharacteristic
215C22×C3×C4C23×C311yescharacteristic
216C2×#67—22no—
217C2×#67—24no—
218C22×Dic3C3×D412yes—
219#235—24no—
220#235—24no—
221C2×D12C23×C312yes—
222C2×C4×D3—22no—
223C2×Dic6C23×C312yes—
224C3×Q16—24no—
225C3×Q16—22no—
226C3×Q16—22no—
227C3×Q16—64no—
228C3×Q16—62no—
229C3×SD16—28no—
230C3×SD16—24no—
231C3×SD16—24no—
232C3×SD16—64no—
233C3×SD16—64no—
234C3×SD16—64no—
235C3×D8—24no—
236C3×D8—22no—
237C3×D8—22no—
238C3×D8—64no—
239C3×D8—62no—
240C2×C3×C8—24no—
241C2×C3×C8—21no—
242C2×C3×C8—21no—
243C2×C3×C8—34no—
244C2×C3×C8—32no—
245C2×C3×C8#6714yescomplemented
246C2×C3×C8C3×D414yescomplemented
247C2×C3×C8C22×D311yescharacteristic
248C2×C3×C8C22×D311yescharacteristic
249C2×C3×C8C23×C311yescharacteristic
250C2×C3×C8C23×C311yescharacteristic
251C3×C4⋊C4—64no—
252C3×C22⋊C4—64no—
253C3×C22⋊C4—64no—
254C3×C42—32no—
255C3×C42—32no—
256#217—24no—
257#216—24no—
258#215—24no—
259#214—24no—
260#213—24no—
261(C2×D3)⋊C4—24no—
262Dic3⋊C4—24no—
263C4×Dic3C3×D412yes—
264C4×Dic3C23×C312yes—
265C2×C3⋊C8C3×D414yescomplemented
266C2×C3⋊C8C23×C312yes—
267Dic12—22no—
268D24—22no—
269#204—24no—
270C22×C32—22no—
271C22×C32—42no—
272C22×C32—44no—
273C22×C32#12712yes—
274C22×C32C22×D411yescharacteristic
275C2×C3×D3—42no—
276C2×C3×D3—44no—
277C32×C4—42no—
278C32×C4#12712yes—
279C32×C4C22×D411yescharacteristic
280C32×C4C22×D411yescharacteristic
281C3×Dic3—24no—
282C3×Dic3—42no—
283C2×#41—32no—
284C2×#41C2×C3×D312yes—
285#135—24no—
286#135—68no—
287#135—64no—
288C2×Q16—32no—
289C2×Q16—31no—
290C2×Q16C2×C3×D311yescharacteristic
291C2×SD16—32no—
292C2×SD16—32no—
293C2×SD16—32no—
294C2×SD16C2×C3×D312yes—
295C2×D8—32no—
296C2×D8—31no—
297C2×D8C2×C3×D311yescharacteristic
298C22×C8—31no—
299C22×C8C2×C3×D311yescharacteristic
300C4⋊Q8—32no—
301#127—32no—
302#124—32no—
303#124—32no—
304#121—64no—
305C4×D4—64no—
306C2×C42—31no—
307#97—32no—
308#97—32no—
309C23×C3—22no—
310C23×C3—22no—
311C23×C3—21no—
312C23×C3—42no—
313C23×C3—62no—
314C23×C3D3×D411yescharacteristic
315C23×C3C2×C3×D411yescharacteristic
316C22×D3—22no—
317C3×Q8—24no—
318C3×Q8—22no—
319C3×Q8—22no—
320C3×Q8—22no—
321C3×Q8—22no—
322C3×Q8—42no—
323C3×Q8—62no—
324C3×Q8—62no—
325C3×D4—24no—
326C3×D4—22no—
327C3×D4—22no—
328C3×D4—22no—
329C3×D4—22no—
330C3×D4—42no—
331C3×D4—48no—
332C3×D4—44no—
333C3×D4—44no—
334C3×D4—62no—
335C3×D4—62no—
336C3×D4—128no—
337C3×D4—124no—
338C2×C3×C4—22no—
339C2×C3×C4—22no—
340C2×C3×C4—21no—
341C2×C3×C4—21no—
342C2×C3×C4—22no—
343C2×C3×C4—22no—
344C2×C3×C4—34no—
345C2×C3×C4—42no—
346C2×C3×C4—48no—
347C2×C3×C4—44no—
348C2×C3×C4—44no—
349C2×C3×C4—62no—
350C2×C3×C4—122no—
351C2×C3×C4—124no—
352C2×C3×C4D3×D412yes—
353C2×C3×C4D3×D411yescharacteristic
354C2×C3×C4C2×#6712yes—
355C2×C3×C4C2×C3×D411yescharacteristic
356C2×C3×C4C2×C3×D412yes—
357C2×C3×C4C2×C3×D412yes—
358C2×C3×C4C23×D311yescharacteristic
359C2×C3×C4C24×C311yescharacteristic
360#67—48no—
361#67—44no—
362C2×Dic3—22no—
363C2×Dic3—42no—
364C2×Dic3C2×C3×D414yes—
365D12—22no—
366D12—22no—
367C4×D3—44no—
368Dic6—22no—
369Dic6—22no—
370C3×C8—22no—
371C3×C8—22no—
372C3×C8—34no—
373C3×C8C2×#6712yes—
374C3×C8C2×#6712yes—
375C3×C8C2×C3×D412yes—
376C3×C8C2×C3×D412yes—
377C3⋊C8C2×C3×D414yes—
378C2×C32—22no—
379C2×C32—82no—
380C2×C32C2×#12711yescharacteristic
381C2×C32#57512yes—
382C3×D3—82no—
383#41—24no—
384#41—24no—
385#41—64no—
386#41—64no—
387C2×Q8—32no—
388C2×Q8C22×C3×D312yes—
389C2×D4—22no—
390C2×D4—32no—
391C2×D4—64no—
392C2×D4—62no—
393C2×D4C22×C3×D312yes—
394C22×C4—22no—
395C22×C4—32no—
396C22×C4—62no—
397C22×C4C22×C3×D311yescharacteristic
398Q16—22no—
399Q16—64no—
400Q16—62no—
401SD16—24no—
402SD16—64no—
403SD16—64no—
404SD16—64no—
405D8—22no—
406D8—64no—
407D8—62no—
408C2×C8—32no—
409C2×C8—34no—
410C2×C8C3×#6714yescomplemented
411C2×C8C22×C3×D311yescharacteristic
412C2×C8C22×C3×D311yescharacteristic
413C4⋊C4—64no—
414C22⋊C4—64no—
415C22⋊C4—64no—
416C42—32no—
417C42—32no—
418C22×C3—22no—
419C22×C3—22no—
420C22×C3—22no—
421C22×C3—21no—
422C22×C3—42no—
423C22×C3—44no—
424C22×C3—44no—
425C22×C3—44no—
426C22×C3—42no—
427C22×C3—42no—
428C22×C3—84no—
429C22×C3—124no—
430C22×C3—122no—
431C22×C3#94012yes—
432C22×C3C3×#12712yes—
433C22×C3C2×D3×D411yescharacteristic
434C22×C3C22×C3×D411yescharacteristic
435C2×D3—44no—
436C2×D3—42no—
437C3×C4—22no—
438C3×C4—21no—
439C3×C4—21no—
440C3×C4—44no—
441C3×C4—42no—
442C3×C4—42no—
443C3×C4—64no—
444C3×C4—122no—
445C3×C4#94012yes—
446C3×C4C3×#12712yes—
447C3×C4C2×D3×D411yescharacteristic
448C3×C4C22×#6711yescharacteristic
449C3×C4C22×C3×D411yescharacteristic
450C3×C4C22×C3×D411yescharacteristic
451Dic3—24no—
452Dic3—42no—
453C32#315011yescharacteristic, complemented, Sylow
454C23—22no—
455C23—62no—
456C23C3×D3×D411yescharacteristic
457Q8—22no—
458Q8—22no—
459Q8—62no—
460Q8—62no—
461D4—22no—
462D4—22no—
463D4—44no—
464D4—62no—
465D4—62no—
466D4—128no—
467D4—124no—
468C2×C4—22no—
469C2×C4—34no—
470C2×C4—44no—
471C2×C4—62no—
472C2×C4—122no—
473C2×C4—124no—
474C2×C4C3×D3×D411yescharacteristic
475C2×C4C3×D3×D412yes—
476C2×C4C2×C3×#6712yes—
477C2×C4C23×C3×D311yescharacteristic
478C8—34no—
479C8C2×C3×#6712yes—
480C8C2×C3×#6712yes—
481C2×C3—22no—
482C2×C3—22no—
483C2×C3—22no—
484C2×C3—21no—
485C2×C3—42no—
486C2×C3—84no—
487C2×C3—82no—
488C2×C3—82no—
489C2×C3—242no—
490C2×C3#576812yes—
491C2×C3C2×#94011yescharacteristic
492C2×C3C2×C3×#12711yescharacteristic
493C2×C3C3×#57512yes—
494D3—82no—
495C22—22no—
496C22—44no—
497C22—42no—
498C22—124no—
499C22—122no—
500C22C3×#94012yes—
501C22C2×C3×D3×D411yescharacteristic
502C4—42no—
503C4—64no—
504C4—122no—
505C4C3×#94012yes—
506C4C2×C3×D3×D411yescharacteristic
507C4C22×C3×#6711yescharacteristic
508C3—21no—
509C3#8390411yescharacteristic, direct product factor
510C3C3×#315011yescharacteristic, complemented
511C2—22no—
512C2—82no—
513C2—242no—
514C2C3×#576812yes—
515C2C2×C3×#94011yescharacteristic
subgroupG/H
centerC2×C3×C4D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC2×C32×#135C2
socleC22×C32C22×D4
hypercenterC2×C3×#135D3
hypocenterC3C3×#3150
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3×C4 ◁ C22×C3×C4 ◁ C2×C3×#135

Complements

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

NH ≅ G/Ntype
1. C2×C32×#135C2semidirect
2. C3×#5832C2semidirect
3. C2×C3×#950C2semidirect
4. C2×C3×#904C2semidirect
5. C3×#5190C2semidirect
6. C3×#5176C2semidirect
7. C3×#5167C2semidirect
8. C3×#5154C2semidirect
9. C2×C3×#815C2semidirect
11. #83904C3direct (N × H)
41. C2×C3×#135D3semidirect
42. C2×C3×#135C2×C3semidirect
44. #5832C2×C3semidirect
45. C2×#950C2×C3semidirect
46. C2×#904C2×C3semidirect
52. #5190C2×C3semidirect
53. #5176C2×C3semidirect
54. #5167C2×C3semidirect
55. #5154C2×C3semidirect
56. C2×#815C2×C3semidirect
75. C2×C32×C8D4semidirect
87. C2×C3×C3⋊C8D4semidirect
180. C2×#135C3×D3semidirect
245. C2×C3×C8#67semidirect
246. C2×C3×C8C3×D4semidirect
265. C2×C3⋊C8C3×D4semidirect
410. C2×C8C3×#67semidirect
453. C32#3150semidirect
509. C3#83904direct (N × H)
510. C3C3×#3150semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#1352
C3×#58322
C2×C3×#9502
C2×C3×#9042
C3×#51902
C3×#51762
C3×#51672
C3×#51542
C2×C3×#8152
C3×#31503
#839043