Finite Group Databasebeta

← C3×#83697 #11895622

Subgroups — C3×#83697 #11895622

Order 1152.

796 conjugacy classes of subgroups.

The subgroup lattice has 523 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#557C211yesmaximal, characteristic, complemented
2C3×#5585C211yesmaximal, characteristic
3C3×#5094C211yesmaximal, characteristic, complemented
4C3×#5088C211yesmaximal, characteristic
5C3×#5068C212yesmaximal, complemented
6C3×#5066C212yesmaximal, complemented
7C3×C4×#216C211yesmaximal, characteristic, complemented
8C3×#5028C212yesmaximal, complemented
9C3×#5027C211yesmaximal, characteristic
10C3×C4×#215C212yesmaximal, complemented
11C3×Q8×C3⋊C8C211yesmaximal, characteristic, complemented
12C3×#3365—31nomaximal
13#83697C311yesmaximal, characteristic, direct product factor
14C32×C4⋊Q8—21no—
15C32×C4⋊Q8C2211yescharacteristic
16C32×#125—22no—
17C32×#125C2212yes—
18C32×C4×Q8—21no—
19C32×C4×Q8C2212yes—
20C32×C4×Q8C2211yescharacteristic
21C32×C4×Q8C2211yescharacteristic
22C3×#947—21no—
23C2×C3×#216C2211yescharacteristic
24C2×C3×#215C2212yes—
25C3×#894—22no—
26C3×#893—21no—
27C3×#875C2212yes—
28C3×#874C2211yescharacteristic
29C3×C4×D12C2212yes—
30C3×C4×Dic6C2211yescharacteristic
31C3×#835C2211yescharacteristic
32C3×#810C2212yes—
33C3×#810C2211yescharacteristic
34C3×#809C2212yes—
35C3×#809C2212yes—
36C3×#809C2212yes—
37C3×#808C2212yes—
38C3×#807C2211yescharacteristic
39C3×C4⋊(C3⋊C8)C2211yescharacteristic
40C3×C4⋊(C3⋊C8)C2212yes—
41C3×C4×C3⋊C8C2212yes—
42C3×C4×C3⋊C8C2211yescharacteristic
43C3×#559—31no—
44C3×#557—21no—
45C3×#557D311yescharacteristic, complemented
46C3×#557C2×C311yescharacteristic, complemented
47#5585C2×C311yescharacteristic
48C3×#488—32no—
49C3×#486—31no—
50C3×#478—32no—
51C3×#475—31no—
52C3×#464—32no—
53C3×#460—31no—
54C3×C8×Q8—31no—
55C3×C4×Q16—31no—
56C3×C4×SD16—32no—
57#5094C2×C311yescharacteristic, complemented
58#5088C2×C311yescharacteristic
59#5068C2×C312yescomplemented
60#5066C2×C312yescomplemented
61C4×#216C2×C311yescharacteristic, complemented
62#5028C2×C312yescomplemented
63#5027C2×C311yescharacteristic
64C4×#215C2×C312yescomplemented
65Q8×C3⋊C8C2×C311yescharacteristic, complemented
66C2×C32×Q8—21no—
67C2×C32×Q8D411yescharacteristic
68C2×C32×Q8C2311yescharacteristic
69C2×C3×D12—21no—
70C2×C3×D12—21no—
71C2×C3×D12C2312yes—
72C2×C3×C4×D3—22no—
73C2×C3×Dic6C2311yescharacteristic
74C32×C4⋊C4—22no—
75C32×C4⋊C4—21no—
76C32×C4⋊C4—22no—
77C32×C4⋊C4—21no—
78C32×C4⋊C4—22no—
79C32×C4⋊C4D411yescharacteristic
80C32×C4⋊C4D412yes—
81C32×C4⋊C4C2311yescharacteristic
82C32×C4⋊C4C2312yes—
83C32×C42—22no—
84C32×C42—21no—
85C32×C42C2312yes—
86C32×C42C2311yescharacteristic
87C3×#216—22no—
88C3×#215—24no—
89C3×(C2×D3)⋊C4—22no—
90C3×(C2×D3)⋊C4—22no—
91C3×(C2×D3)⋊C4—22no—
92C3×C4⋊Dic3C2311yescharacteristic
93C3×Dic3⋊C4—21no—
94C3×C4×Dic3—21no—
95C2×C3×C3⋊C8C2312yes—
96C2×C3×C3⋊C8C2311yescharacteristic
97C2×C3×C3⋊C8C2311yescharacteristic
98#3365—31noSylow
99C2×C3×Q16—31no—
100C2×C3×SD16—32no—
101C3×C4⋊Q8—22no—
102C3×C4⋊Q8—21no—
103C3×C4⋊Q8—21no—
104C3×C4⋊Q8—21no—
105C3×C4⋊Q8C2×D311yescharacteristic
106C3×C4⋊Q8C22×C311yescharacteristic
107C3×#127—31no—
108C3×#125—24no—
109C3×#125—22no—
110C3×#125—22no—
111C3×#125—22no—
112C3×#125C2×D312yes—
113C3×#125C22×C312yes—
114C3×#124—32no—
115C3×#124—61no—
116C3×#123—62no—
117C3×C4×Q8—22no—
118C3×C4×Q8—21no—
119C3×C4×Q8—21no—
120C3×C4×Q8—22no—
121C3×C4×Q8—21no—
122C3×C4×Q8—21no—
123C3×C4×Q8—31no—
124C3×C4×Q8C2×D312yes—
125C3×C4×Q8C2×D311yescharacteristic
126C3×C4×Q8C2×D311yescharacteristic
127C3×C4×Q8C22×C312yes—
128C3×C4×Q8C22×C311yescharacteristic
129C3×C4×Q8C22×C311yescharacteristic
130C3×C4×D4—32no—
131C3×C4×D4—61no—
132#947—21no—
133C2×#216C22×C311yescharacteristic
134C2×#215C22×C312yes—
135#894—22no—
136#893—21no—
137#875C22×C312yes—
138#874C22×C311yescharacteristic
139C4×D12C22×C312yes—
140C4×Dic6C22×C311yescharacteristic
141C3×#107—31no—
142C3×#106—32no—
143C3×C4⋊C8—31no—
144C3×C4⋊C8—32no—
145C3×#103—31no—
146C3×#103—31no—
147C3×#103—32no—
148C3×#102—32no—
149C3×#102—32no—
150C3×#102—32no—
151C3×C4×C8—32no—
152C3×C4×C8—31no—
153#835C22×C311yescharacteristic
154#810C22×C312yes—
155#810C22×C311yescharacteristic
156#809C22×C312yes—
157#809C22×C312yes—
158#809C22×C312yes—
159#808C22×C312yes—
160#807C22×C311yescharacteristic
161C4⋊(C3⋊C8)C22×C311yescharacteristic
162C4⋊(C3⋊C8)C22×C312yes—
163C4×C3⋊C8C22×C312yes—
164C4×C3⋊C8C22×C311yescharacteristic
165C22×C3×D3—22no—
166C32×Q8—21no—
167C32×Q8—22no—
168C32×Q8—42no—
169C32×Q8#4112yes—
170C2×C32×C4—21no—
171C2×C32×C4—21no—
172C2×C32×C4—22no—
173C2×C32×C4C2×D411yescharacteristic
174C2×C32×C4C2×D412yes—
175C2×C32×C4C2×D412yes—
176C2×C32×C4C2×D411yescharacteristic
177C2×C32×C4C2411yescharacteristic
178C2×C3×Dic3—21no—
179C2×C3×Dic3—21no—
180C3×D12—22no—
181C3×D12—22no—
182C3×D12—42no—
183C3×D12—81no—
184C3×C4×D3—82no—
185C3×Dic6—21no—
186C3×Dic6—21no—
187C3×C3⋊C8—22no—
188C3×C3⋊C8—21no—
189C3×C3⋊C8—21no—
190#559—31no—
191#557C3×D311yescharacteristic, complemented
192#488—32no—
193#486—31no—
194#478—32no—
195#475—31no—
196#464—32no—
197#460—31no—
198C8×Q8—31no—
199C4×Q16—31no—
200C4×SD16—32no—
201C2×C3×Q8—22no—
202C2×C3×Q8—21no—
203C2×C3×Q8—21no—
204C2×C3×Q8—21no—
205C2×C3×Q8—21no—
206C2×C3×Q8—31no—
207C2×C3×Q8#6711yescharacteristic
208C2×C3×Q8C3×D411yescharacteristic
209C2×C3×Q8C22×D311yescharacteristic
210C2×C3×Q8C23×C311yescharacteristic
211C2×C3×D4—32no—
212C2×C3×D4—61no—
213C2×C3×D4—61no—
214C22×C3×C4—62no—
215C2×D12—21no—
216C2×D12—21no—
217C2×D12C23×C312yes—
218C2×C4×D3—22no—
219C2×Dic6C23×C311yescharacteristic
220C3×Q16—62no—
221C3×SD16—64no—
222C2×C3×C8—31no—
223C2×C3×C8—31no—
224C2×C3×C8—32no—
225C3×C4⋊C4—24no—
226C3×C4⋊C4—22no—
227C3×C4⋊C4—24no—
228C3×C4⋊C4—22no—
229C3×C4⋊C4—24no—
230C3×C4⋊C4—22no—
231C3×C4⋊C4—21no—
232C3×C4⋊C4—22no—
233C3×C4⋊C4—21no—
234C3×C4⋊C4—22no—
235C3×C4⋊C4—22no—
236C3×C4⋊C4—21no—
237C3×C4⋊C4—22no—
238C3×C4⋊C4—21no—
239C3×C4⋊C4—22no—
240C3×C4⋊C4—21no—
241C3×C4⋊C4—22no—
242C3×C4⋊C4—21no—
243C3×C4⋊C4—22no—
244C3×C4⋊C4—31no—
245C3×C4⋊C4—61no—
246C3×C4⋊C4#6711yescharacteristic
247C3×C4⋊C4#6712yes—
248C3×C4⋊C4C3×D411yescharacteristic
249C3×C4⋊C4C3×D412yes—
250C3×C4⋊C4C22×D312yes—
251C3×C4⋊C4C22×D311yescharacteristic
252C3×C4⋊C4C23×C311yescharacteristic
253C3×C4⋊C4C23×C312yes—
254C3×C22⋊C4—62no—
255C3×C22⋊C4—62no—
256C3×C22⋊C4—62no—
257C3×C42—24no—
258C3×C42—22no—
259C3×C42—22no—
260C3×C42—21no—
261C3×C42—22no—
262C3×C42—21no—
263C3×C42—22no—
264C3×C42—21no—
265C3×C42—61no—
266C3×C42C22×D312yes—
267C3×C42C22×D311yescharacteristic
268C3×C42C23×C311yescharacteristic
269C3×C42C23×C312yes—
270#216—22no—
271#215—24no—
272(C2×D3)⋊C4—22no—
273(C2×D3)⋊C4—22no—
274(C2×D3)⋊C4—22no—
275C4⋊Dic3C23×C311yescharacteristic
276Dic3⋊C4—21no—
277C4×Dic3—21no—
278C2×C3⋊C8C23×C311yescharacteristic
279C2×C3⋊C8C23×C311yescharacteristic
280C2×C3⋊C8C23×C312yes—
281C22×C32C22×D411yescharacteristic
282C2×C3×D3—42no—
283C2×C3×D3—42no—
284C2×C3×D3—42no—
285C32×C4—22no—
286C32×C4—22no—
287C32×C4—22no—
288C32×C4—21no—
289C32×C4—42no—
290C32×C4—41no—
291C32×C4#13512yes—
292C32×C4C2×#4111yescharacteristic
293C32×C42−1+411yescharacteristic
294C3×Dic3—41no—
295C3×Dic3—41no—
296C2×Q16—31no—
297C2×SD16—32no—
298C4⋊Q8—21no—
299C4⋊Q8C2×C3×D311yescharacteristic
300#127—31no—
301#125—22no—
302#125C2×C3×D312yes—
303#124—32no—
304#124—61no—
305#123—62no—
306C4×Q8—21no—
307C4×Q8—31no—
308C4×Q8C2×C3×D312yes—
309C4×Q8C2×C3×D311yescharacteristic
310C4×Q8C2×C3×D311yescharacteristic
311C4×D4—32no—
312C4×D4—61no—
313#107—31no—
314#106—32no—
315C4⋊C8—31no—
316C4⋊C8—32no—
317#103—31no—
318#103—31no—
319#103—32no—
320#102—32no—
321#102—32no—
322#102—32no—
323C4×C8—32no—
324C4×C8—31no—
325C23×C3—62no—
326C22×D3—22no—
327C3×Q8—22no—
328C3×Q8—22no—
329C3×Q8—22no—
330C3×Q8—21no—
331C3×Q8—21no—
332C3×Q8—22no—
333C3×Q8—42no—
334C3×Q8—44no—
335C3×Q8—42no—
336C3×Q8—42no—
337C3×Q8—61no—
338C3×Q8—61no—
339C3×Q8#23912yes—
340C3×Q8C3×#4112yes—
341C3×D4—62no—
342C3×D4—62no—
343C3×D4—122no—
344C3×D4—241no—
345C2×C3×C4—22no—
346C2×C3×C4—21no—
347C2×C3×C4—21no—
348C2×C3×C4—22no—
349C2×C3×C4—24no—
350C2×C3×C4—21no—
351C2×C3×C4—22no—
352C2×C3×C4—21no—
353C2×C3×C4—22no—
354C2×C3×C4—21no—
355C2×C3×C4—21no—
356C2×C3×C4—22no—
357C2×C3×C4—21no—
358C2×C3×C4—22no—
359C2×C3×C4—61no—
360C2×C3×C4—61no—
361C2×C3×C4—242no—
362C2×C3×C4C2×#6712yes—
363C2×C3×C4C2×#6712yes—
364C2×C3×C4C2×#6711yescharacteristic
365C2×C3×C4C2×#6711yescharacteristic
366C2×C3×C4C2×C3×D411yescharacteristic
367C2×C3×C4C2×C3×D412yes—
368C2×C3×C4C2×C3×D412yes—
369C2×C3×C4C2×C3×D411yescharacteristic
370C2×C3×C4C23×D311yescharacteristic
371C2×C3×C4C24×C311yescharacteristic
372C2×Dic3—21no—
373C2×Dic3—21no—
374D12—22no—
375D12—22no—
376D12—42no—
377D12—81no—
378C4×D3—82no—
379Dic6—21no—
380Dic6—21no—
381C3×C8—62no—
382C3×C8—61no—
383C3×C8—61no—
384C3⋊C8—22no—
385C3⋊C8—21no—
386C3⋊C8—21no—
387C2×C32#54811yescharacteristic
388C2×C32C2×#13511yescharacteristic
389C2×C32#57711yescharacteristic
390C3×D3—82no—
391C2×Q8—21no—
392C2×Q8—31no—
393C2×Q8C3×#6711yescharacteristic
394C2×Q8C22×C3×D311yescharacteristic
395C2×D4—32no—
396C2×D4—61no—
397C2×D4—61no—
398C22×C4—62no—
399Q16—62no—
400SD16—64no—
401C2×C8—31no—
402C2×C8—31no—
403C2×C8—32no—
404C4⋊C4—22no—
405C4⋊C4—21no—
406C4⋊C4—22no—
407C4⋊C4—21no—
408C4⋊C4—22no—
409C4⋊C4—31no—
410C4⋊C4—61no—
411C4⋊C4C3×#6711yescharacteristic
412C4⋊C4C3×#6712yes—
413C4⋊C4C22×C3×D312yes—
414C4⋊C4C22×C3×D311yescharacteristic
415C22⋊C4—62no—
416C22⋊C4—62no—
417C22⋊C4—62no—
418C42—22no—
419C42—21no—
420C42—61no—
421C42C22×C3×D312yes—
422C42C22×C3×D311yescharacteristic
423C22×C3—21no—
424C22×C3—122no—
425C22×C3—122no—
426C22×C3—122no—
427C22×C3C22×#6711yescharacteristic
428C22×C3C22×C3×D411yescharacteristic
429C2×D3—42no—
430C2×D3—42no—
431C2×D3—42no—
432C3×C4—24no—
433C3×C4—22no—
434C3×C4—22no—
435C3×C4—21no—
436C3×C4—22no—
437C3×C4—22no—
438C3×C4—22no—
439C3×C4—21no—
440C3×C4—22no—
441C3×C4—22no—
442C3×C4—21no—
443C3×C4—21no—
444C3×C4—42no—
445C3×C4—42no—
446C3×C4—41no—
447C3×C4—44no—
448C3×C4—42no—
449C3×C4—42no—
450C3×C4—41no—
451C3×C4—42no—
452C3×C4—41no—
453C3×C4—121no—
454C3×C4—121no—
455C3×C4#95012yes—
456C3×C4C3×#13512yes—
457C3×C4C2×#23911yescharacteristic
458C3×C4#100711yescharacteristic
459C3×C4C2×C3×#4111yescharacteristic
460C3×C4C3×2−1+411yescharacteristic
461Dic3—41no—
462Dic3—41no—
463C32#336511yescharacteristic, complemented, Sylow
464C23—62no—
465Q8—22no—
466Q8—21no—
467Q8—42no—
468Q8—61no—
469Q8—61no—
470Q8C3×#23912yes—
471D4—62no—
472D4—62no—
473D4—122no—
474D4—241no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—22no—
478C2×C4—61no—
479C2×C4—61no—
480C2×C4—242no—
481C2×C4C2×C3×#6712yes—
482C2×C4C2×C3×#6712yes—
483C2×C4C2×C3×#6711yescharacteristic
484C2×C4C2×C3×#6711yescharacteristic
485C2×C4C23×C3×D311yescharacteristic
486C8—62no—
487C8—61no—
488C8—61no—
489C2×C3—21no—
490C2×C3—21no—
491C2×C3—21no—
492C2×C3—242no—
493C2×C3#581711yescharacteristic
494C2×C3C2×#95011yescharacteristic
495C2×C3#583711yescharacteristic
496C2×C3C3×#54811yescharacteristic
497C2×C3C2×C3×#13511yescharacteristic
498C2×C3C3×#57711yescharacteristic
499D3—82no—
500C22—122no—
501C22—122no—
502C22—122no—
503C22C22×C3×#6711yescharacteristic
504C4—22no—
505C4—22no—
506C4—22no—
507C4—21no—
508C4—42no—
509C4—41no—
510C4—121no—
511C4—121no—
512C4C3×#95012yes—
513C4C2×C3×#23911yescharacteristic
514C4C3×#100711yescharacteristic
515C3—21no—
516C3#8369711yescharacteristic, direct product factor
517C3C3×#336511yescharacteristic, complemented
518C2—242no—
519C2C3×#581711yescharacteristic
520C2C2×C3×#95011yescharacteristic
521C2C3×#583711yescharacteristic
subgroupG/H
centerC22×C3C22×#67
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#557C2
socleC22×C32C22×D4
prime radicalC3×#874C22
hypercenterC3×#557D3
hypocenterC3C3×#3365
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C4×Q8 ◁ C3×#557

Complements

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

NH ≅ G/Ntype
1. C32×#557C2semidirect
3. C3×#5094C2semidirect
5. C3×#5068C2semidirect
6. C3×#5066C2semidirect
7. C3×C4×#216C2semidirect
8. C3×#5028C2semidirect
10. C3×C4×#215C2semidirect
11. C3×Q8×C3⋊C8C2semidirect
13. #83697C3direct (N × H)
45. C3×#557D3semidirect
46. C3×#557C2×C3semidirect
57. #5094C2×C3semidirect
59. #5068C2×C3semidirect
60. #5066C2×C3semidirect
61. C4×#216C2×C3semidirect
62. #5028C2×C3semidirect
64. C4×#215C2×C3semidirect
65. Q8×C3⋊C8C2×C3semidirect
191. #557C3×D3semidirect
463. C32#3365semidirect
516. C3#83697direct (N × H)
517. C3C3×#3365semidirect

Maximal subgroups

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

subgroupindex
C32×#5572
C3×#55852
C3×#50942
C3×#50882
C3×#50682
C3×#50662
C3×C4×#2162
C3×#50282
C3×#50272
C3×C4×#2152
C3×Q8×C3⋊C82
C3×#33653
#836973