Finite Group Databasebeta

← C3×#83213 #11878698

Subgroups — C3×#83213 #11878698

Order 1152.

1001 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C4⋊Q8C211yesmaximal, characteristic, complemented
2C3×#5477C211yesmaximal, characteristic
3C3×#5227C214yesmaximal, complemented
4C3×#5085C212yesmaximal, complemented
5C3×#5083C214yesmaximal, complemented
6C3×#5079C212yesmaximal, complemented
7C3×#4925C211yesmaximal, characteristic, complemented
8C3×#3206—31nomaximal
9#83213C311yesmaximal, characteristic, direct product factor
10C22×C32×Q8C2212yes—
11C2×C3×#235—21no—
12C32×C4⋊Q8—21no—
13C32×C4⋊Q8—21no—
14C32×C4⋊Q8C2212yes—
15C32×C4⋊Q8C2212yes—
16C2×C32×C4⋊C4—21no—
17C2×C32×C4⋊C4—21no—
18C2×C32×C42C2211yescharacteristic
19C2×C3×#215C2218yes—
20C3×#930—21no—
21C3×#930C2212yes—
22C3×#875—21no—
23C3×#874C2211yescharacteristic
24C3×C4×D12—21no—
25C3×C4×D12C2212yes—
26C3×#869C2211yescharacteristic
27C3×#835C2218yes—
28C3×#830C2212yes—
29C3×C4⋊(C3⋊C8)C2212yes—
30C3×C4×C3⋊C8C2212yes—
31C3×#532—31no—
32C2×C3×C4⋊Q8—21no—
33C2×C3×C4⋊Q8D311yescharacteristic, complemented
34C2×C3×C4⋊Q8C2×C311yescharacteristic, complemented
35#5477C2×C311yescharacteristic
36C3×#492—32no—
37C3×#487—32no—
38C3×#461—34no—
39C3×#448—34no—
40C3×#431—31no—
41#5227C2×C314yescomplemented
42#5085C2×C312yescomplemented
43#5083C2×C314yescomplemented
44#5079C2×C312yescomplemented
45#4925C2×C311yescharacteristic, complemented
46C2×C32×Q8—22no—
47C2×C32×Q8—44no—
48C2×C32×Q8C2314yes—
49C22×C32×C4—22no—
50C22×C32×C4D411yescharacteristic
51C22×C32×C4D411yescharacteristic
52C22×C32×C4C2311yescharacteristic
53C2×C3×#67—22no—
54C3×#235—44no—
55C2×C3×D12—21no—
56C2×C3×D12—21no—
57C2×C3×D12C2312yes—
58C2×C3×C4×D3—22no—
59C2×C3×Dic6—21no—
60C32×C4⋊C4—22no—
61C32×C4⋊C4—22no—
62C32×C4⋊C4—22no—
63C32×C4⋊C4—22no—
64C32×C42D411yescharacteristic
65C32×C42D411yescharacteristic
66C32×C42C2311yescharacteristic
67C32×C42C2311yescharacteristic
68C3×#215—48no—
69C3×(C2×D3)⋊C4—22no—
70C3×(C2×D3)⋊C4—22no—
71C3×C4⋊Dic3—21no—
72C3×C4⋊Dic3C2312yes—
73C2×C3×C3⋊C8C2314yes—
74#3206—31noSylow
75C2×C3×#41—61no—
76C22×C3×Q8—22no—
77C22×C3×Q8C2×D312yes—
78C22×C3×Q8C22×C312yes—
79C2×#235—21no—
80C2×C3×SD16—38no—
81C3×C4⋊Q8—22no—
82C3×C4⋊Q8—22no—
83C3×C4⋊Q8—21no—
84C3×C4⋊Q8—21no—
85C3×C4⋊Q8—21no—
86C3×C4⋊Q8—21no—
87C3×C4⋊Q8—22no—
88C3×C4⋊Q8—22no—
89C3×C4⋊Q8—31no—
90C3×C4⋊Q8C2×D312yes—
91C3×C4⋊Q8C2×D312yes—
92C3×C4⋊Q8C22×C312yes—
93C3×C4⋊Q8C22×C312yes—
94C3×#127—31no—
95C3×#124—61no—
96C3×#121—32no—
97C3×#121—61no—
98C3×C4×D4—32no—
99C3×C4×D4—61no—
100C2×C3×C4⋊C4—22no—
101C2×C3×C4⋊C4—22no—
102C2×C3×C4⋊C4—21no—
103C2×C3×C4⋊C4—21no—
104C2×C3×C4⋊C4—21no—
105C2×C3×C4⋊C4—21no—
106C2×C3×C42—21no—
107C2×C3×C42C2×D311yescharacteristic
108C2×C3×C42C22×C311yescharacteristic
109C2×#215C22×C318yes—
110#930—21no—
111#930C22×C312yes—
112#875—21no—
113#874C22×C311yescharacteristic
114C4×D12—21no—
115C4×D12C22×C312yes—
116#869C22×C311yescharacteristic
117C3×C4⋊C8—32no—
118C3×#103—38no—
119C3×C22⋊C8—32no—
120C3×C4×C8—32no—
121#835C22×C318yes—
122#830C22×C312yes—
123C4⋊(C3⋊C8)C22×C312yes—
124C4×C3⋊C8C22×C312yes—
125C23×C32C2×D411yescharacteristic
126C22×C3×D3—22no—
127C32×Q8—28no—
128C32×Q8—44no—
129C2×C32×C4—22no—
130C2×C32×C4—22no—
131C2×C32×C4—24no—
132C2×C32×C4—44no—
133C2×C32×C4SD1614yescomplemented
134C2×C32×C4C2×D411yescharacteristic
135C2×C32×C4C2×D411yescharacteristic
136C2×C32×C4C2×D411yescharacteristic
137C2×C32×C4C2×D411yescharacteristic
138C2×C32×C4C2×D411yescharacteristic
139C2×C32×C4C2411yescharacteristic
140C3×#67—44no—
141C2×C3×Dic3—22no—
142C3×D12—24no—
143C3×D12—42no—
144C3×D12—42no—
145C3×C4×D3—44no—
146C3×Dic6—42no—
147C3×C3⋊C8—24no—
148#532—31no—
149C2×C4⋊Q8C3×D311yescharacteristic, complemented
150#492—32no—
151#487—32no—
152#461—34no—
153#448—34no—
154#431—31no—
155C3×#41—124no—
156C2×C3×Q8—24no—
157C2×C3×Q8—22no—
158C2×C3×Q8—22no—
159C2×C3×Q8—24no—
160C2×C3×Q8—44no—
161C2×C3×Q8—44no—
162C2×C3×Q8—48no—
163C2×C3×Q8—61no—
164C2×C3×Q8C22×D314yes—
165C2×C3×Q8C23×C314yes—
166C2×C3×D4—32no—
167C2×C3×D4—62no—
168C2×C3×D4—61no—
169C2×C3×D4—61no—
170C22×C3×C4—24no—
171C22×C3×C4—22no—
172C22×C3×C4—22no—
173C22×C3×C4—21no—
174C22×C3×C4—21no—
175C22×C3×C4—21no—
176C22×C3×C4—62no—
177C22×C3×C4#6711yescharacteristic
178C22×C3×C4#6711yescharacteristic
179C22×C3×C4C3×D411yescharacteristic
180C22×C3×C4C3×D411yescharacteristic
181C22×C3×C4C22×D311yescharacteristic
182C22×C3×C4C23×C311yescharacteristic
183C2×#67—22no—
184#235—44no—
185C2×D12—21no—
186C2×D12—21no—
187C2×D12C23×C312yes—
188C2×C4×D3—22no—
189C2×Dic6—21no—
190C3×SD16—128no—
191C2×C3×C8—34no—
192C3×C4⋊C4—24no—
193C3×C4⋊C4—24no—
194C3×C4⋊C4—24no—
195C3×C4⋊C4—24no—
196C3×C4⋊C4—22no—
197C3×C4⋊C4—22no—
198C3×C4⋊C4—22no—
199C3×C4⋊C4—22no—
200C3×C4⋊C4—22no—
201C3×C4⋊C4—22no—
202C3×C4⋊C4—22no—
203C3×C4⋊C4—22no—
204C3×C4⋊C4—32no—
205C3×C4⋊C4—61no—
206C3×C22⋊C4—62no—
207C3×C22⋊C4—62no—
208C3×C42—21no—
209C3×C42—21no—
210C3×C42—21no—
211C3×C42—21no—
212C3×C42#6711yescharacteristic
213C3×C42#6711yescharacteristic
214C3×C42C3×D411yescharacteristic
215C3×C42C3×D411yescharacteristic
216C3×C42C22×D311yescharacteristic
217C3×C42C22×D311yescharacteristic
218C3×C42C23×C311yescharacteristic
219C3×C42C23×C311yescharacteristic
220#215—48no—
221(C2×D3)⋊C4—22no—
222(C2×D3)⋊C4—22no—
223C4⋊Dic3—21no—
224C4⋊Dic3C23×C312yes—
225C2×C3⋊C8C23×C314yes—
226C22×C32—21no—
227C22×C32—21no—
228C22×C32C2×SD1612yes—
229C22×C32C22×D411yescharacteristic
230C2×C3×D3—42no—
231C2×C3×D3—42no—
232C2×C3×D3—42no—
233C32×C4—21no—
234C32×C4—21no—
235C32×C4—44no—
236C32×C4C2×SD1612yes—
237C32×C4C2×SD1612yes—
238C32×C4#13712yes—
239C32×C4H(5,𝔽2)12yes—
240C3×Dic3—42no—
241C2×#41—61no—
242C22×Q8C2×C3×D312yes—
243C2×SD16—38no—
244C4⋊Q8—21no—
245C4⋊Q8—21no—
246C4⋊Q8—31no—
247C4⋊Q8C2×C3×D312yes—
248C4⋊Q8C2×C3×D312yes—
249#127—31no—
250#124—61no—
251#121—32no—
252#121—61no—
253C4×D4—32no—
254C4×D4—61no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—21no—
257C2×C42C2×C3×D311yescharacteristic
258C4⋊C8—32no—
259#103—38no—
260C22⋊C8—32no—
261C4×C8—32no—
262C23×C3—21no—
263C23×C3—62no—
264C23×C3C2×#6711yescharacteristic
265C23×C3C2×C3×D411yescharacteristic
266C22×D3—22no—
267C3×Q8—28no—
268C3×Q8—28no—
269C3×Q8—48no—
270C3×Q8—48no—
271C3×Q8—44no—
272C3×Q8—44no—
273C3×Q8—122no—
274C3×D4—64no—
275C3×D4—124no—
276C3×D4—122no—
277C3×D4—122no—
278C2×C3×C4—24no—
279C2×C3×C4—24no—
280C2×C3×C4—22no—
281C2×C3×C4—22no—
282C2×C3×C4—22no—
283C2×C3×C4—22no—
284C2×C3×C4—28no—
285C2×C3×C4—24no—
286C2×C3×C4—24no—
287C2×C3×C4—21no—
288C2×C3×C4—24no—
289C2×C3×C4—21no—
290C2×C3×C4—21no—
291C2×C3×C4—21no—
292C2×C3×C4—21no—
293C2×C3×C4—21no—
294C2×C3×C4—48no—
295C2×C3×C4—44no—
296C2×C3×C4—44no—
297C2×C3×C4—62no—
298C2×C3×C4—124no—
299C2×C3×C4#21514yescomplemented
300C2×C3×C4C3×SD1614yescomplemented
301C2×C3×C4C2×#6711yescharacteristic
302C2×C3×C4C2×#6711yescharacteristic
303C2×C3×C4C2×#6711yescharacteristic
304C2×C3×C4C2×#6711yescharacteristic
305C2×C3×C4C2×#6711yescharacteristic
306C2×C3×C4C2×C3×D411yescharacteristic
307C2×C3×C4C2×C3×D411yescharacteristic
308C2×C3×C4C2×C3×D411yescharacteristic
309C2×C3×C4C2×C3×D411yescharacteristic
310C2×C3×C4C2×C3×D411yescharacteristic
311C2×C3×C4C23×D311yescharacteristic
312C2×C3×C4C24×C311yescharacteristic
313#67—44no—
314C2×Dic3—22no—
315D12—24no—
316D12—42no—
317D12—42no—
318C4×D3—44no—
319Dic6—42no—
320C3×C8—64no—
321C3⋊C8—24no—
322C2×C32—22no—
323C2×C32#53511yescharacteristic
324C2×C32C22×SD1611yescharacteristic
325C2×C32C2×#13711yescharacteristic
326C3×D3—82no—
327#41—124no—
328C2×Q8—22no—
329C2×Q8—44no—
330C2×Q8—61no—
331C2×Q8C22×C3×D314yes—
332C2×D4—32no—
333C2×D4—62no—
334C2×D4—61no—
335C2×D4—61no—
336C22×C4—22no—
337C22×C4—62no—
338C22×C4C3×#6711yescharacteristic
339C22×C4C3×#6711yescharacteristic
340C22×C4C22×C3×D311yescharacteristic
341SD16—128no—
342C2×C8—34no—
343C4⋊C4—22no—
344C4⋊C4—22no—
345C4⋊C4—22no—
346C4⋊C4—22no—
347C4⋊C4—32no—
348C4⋊C4—61no—
349C22⋊C4—62no—
350C22⋊C4—62no—
351C42C3×#6711yescharacteristic
352C42C3×#6711yescharacteristic
353C42C22×C3×D311yescharacteristic
354C42C22×C3×D311yescharacteristic
355C22×C3—22no—
356C22×C3—22no—
357C22×C3—21no—
358C22×C3—21no—
359C22×C3—21no—
360C22×C3—21no—
361C22×C3—22no—
362C22×C3—21no—
363C22×C3—122no—
364C22×C3—122no—
365C22×C3—122no—
366C22×C3C2×#21512yes—
367C22×C3C2×C3×SD1612yes—
368C22×C3C22×#6711yescharacteristic
369C22×C3C22×C3×D411yescharacteristic
370C2×D3—42no—
371C2×D3—42no—
372C2×D3—42no—
373C3×C4—22no—
374C3×C4—22no—
375C3×C4—21no—
376C3×C4—21no—
377C3×C4—21no—
378C3×C4—21no—
379C3×C4—22no—
380C3×C4—22no—
381C3×C4—22no—
382C3×C4—22no—
383C3×C4—48no—
384C3×C4—44no—
385C3×C4—44no—
386C3×C4—122no—
387C3×C4C2×#21512yes—
388C3×C4C2×#21512yes—
389C3×C4#94212yes—
390C3×C4C2×C3×SD1612yes—
391C3×C4C2×C3×SD1612yes—
392C3×C4C3×#13712yes—
393C3×C4#100412yes—
394C3×C4C3×H(5,𝔽2)12yes—
395Dic3—42no—
396C32#320611yescharacteristic, complemented, Sylow
397C23—62no—
398C23C2×C3×#6711yescharacteristic
399Q8—28no—
400Q8—44no—
401Q8—122no—
402D4—64no—
403D4—124no—
404D4—122no—
405D4—122no—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—24no—
409C2×C4—44no—
410C2×C4—62no—
411C2×C4—124no—
412C2×C4C3×#21514yescomplemented
413C2×C4C2×C3×#6711yescharacteristic
414C2×C4C2×C3×#6711yescharacteristic
415C2×C4C2×C3×#6711yescharacteristic
416C2×C4C2×C3×#6711yescharacteristic
417C2×C4C2×C3×#6711yescharacteristic
418C2×C4C23×C3×D311yescharacteristic
419C8—64no—
420C2×C3—24no—
421C2×C3—22no—
422C2×C3—22no—
423C2×C3—21no—
424C2×C3—21no—
425C2×C3—21no—
426C2×C3—242no—
427C2×C3#580511yescharacteristic
428C2×C3C22×#21511yescharacteristic
429C2×C3C2×#94211yescharacteristic
430C2×C3C3×#53511yescharacteristic
431C2×C3C22×C3×SD1611yescharacteristic
432C2×C3C2×C3×#13711yescharacteristic
433D3—82no—
434C22—21no—
435C22—21no—
436C22—122no—
437C22—122no—
438C22—122no—
439C22C2×C3×#21512yes—
440C22C22×C3×#6711yescharacteristic
441C4—21no—
442C4—21no—
443C4—44no—
444C4—122no—
445C4C2×C3×#21512yes—
446C4C2×C3×#21512yes—
447C4C3×#94212yes—
448C4C3×#100412yes—
449C3—21no—
450C3#8321311yescharacteristic, direct product factor
451C3C3×#320611yescharacteristic, complemented
452C2—22no—
453C2—242no—
454C2C3×#580511yescharacteristic
455C2C22×C3×#21511yescharacteristic
456C2C2×C3×#94211yescharacteristic
subgroupG/H
centerC22×C3C22×#67
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC2×C32×C4⋊Q8C2
socleC22×C32C22×D4
prime radicalC3×#5477C2
hypercenterC2×C3×C4⋊Q8D3
hypocenterC3C3×#3206
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C2×C3×C42 ◁ C2×C3×C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×C32×C4⋊Q8C2semidirect
3. C3×#5227C2semidirect
4. C3×#5085C2semidirect
5. C3×#5083C2semidirect
6. C3×#5079C2semidirect
7. C3×#4925C2semidirect
9. #83213C3direct (N × H)
33. C2×C3×C4⋊Q8D3semidirect
34. C2×C3×C4⋊Q8C2×C3semidirect
41. #5227C2×C3semidirect
42. #5085C2×C3semidirect
43. #5083C2×C3semidirect
44. #5079C2×C3semidirect
45. #4925C2×C3semidirect
133. C2×C32×C4SD16semidirect
149. C2×C4⋊Q8C3×D3semidirect
299. C2×C3×C4#215semidirect
300. C2×C3×C4C3×SD16semidirect
396. C32#3206semidirect
412. C2×C4C3×#215semidirect
450. C3#83213direct (N × H)
451. C3C3×#3206semidirect

Maximal subgroups

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

subgroupindex
C2×C32×C4⋊Q82
C3×#54772
C3×#52272
C3×#50852
C3×#50832
C3×#50792
C3×#49252
C3×#32063
#832133