Finite Group Databasebeta

← C3×#82348 #11808769

Subgroups — C3×#82348 #11808769

Order 1152.

1349 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C4×D4C211yesmaximal, characteristic
2C2×C3×C4×Dic6C211yesmaximal, characteristic, complemented
3C3×#5222C212yesmaximal
4C3×C4×#217C214yesmaximal, complemented
5C3×#4985C212yesmaximal, complemented
6C3×#4953C212yesmaximal, complemented
7C3×#4947C212yesmaximal, complemented
8C3×#4932C211yesmaximal, characteristic, complemented
9C3×#2398—31nomaximal
10#82348C311yesmaximal, characteristic, direct product factor
11C22×C32×D4C2211yescharacteristic
12C23×C32×C4C2212yes—
13C22×C3×Dic6C2211yescharacteristic
14C32×C4×D4—24no—
15C2×C32×C4⋊C4C2211yescharacteristic
16C2×C32×C22⋊C4C2212yes—
17C2×C32×C42C2211yescharacteristic
18C2×C3×#217C2214yes—
19C2×C3×#217C2214yes—
20C2×C3×C4⋊Dic3C2211yescharacteristic
21C2×C3×Dic3⋊C4C2212yes—
22C2×C3×C4×Dic3C2212yes—
23C2×C3×C4×Dic3C2212yes—
24C3×C4×Dic6—24no—
25C3×C3⋊#95C2212yes—
26C3×C3⋊#95C2212yes—
27C3×C3⋊#95C2214yes—
28C3×C3⋊#95C2214yes—
29C2×C3×C4×Q8—31no—
30C2×C3×C4×D4—21no—
31C2×C3×C4×D4D311yescharacteristic
32C2×C3×C4×D4C2×C311yescharacteristic
33C2×C4×Dic6C2×C311yescharacteristic, complemented
34C3×#400—32no—
35C3×#397—32no—
36C3×#394—32no—
37C3×#393—32no—
38C3×C4×C22⋊C4—34no—
39C3×#376—31no—
40#5222C2×C312yes—
41C4×#217C2×C314yescomplemented
42#4985C2×C312yescomplemented
43#4953C2×C312yescomplemented
44#4947C2×C312yescomplemented
45#4932C2×C311yescharacteristic, complemented
46C24×C32C2312yes—
47C2×C32×D4—24no—
48C2×C32×D4—22no—
49C22×C32×C4—24no—
50C22×C32×C4—28no—
51C22×C32×C4C2312yes—
52C22×C32×C4C2311yescharacteristic
53C22×C32×C4C2311yescharacteristic
54C22×C32×C4C2311yescharacteristic
55C22×C3×Dic3C2312yes—
56C22×C3×Dic3C2314yes—
57C22×C3×Dic3C2312yes—
58C2×C3×Dic6—22no—
59C2×C3×Dic6—24no—
60C32×C4⋊C4—22no—
61C32×C22⋊C4—24no—
62C32×C42D414yes—
63C3×#217—28no—
64C3×#217—28no—
65C3×C4⋊Dic3—22no—
66C3×Dic3⋊C4—24no—
67C3×C4×Dic3—24no—
68C3×C4×Dic3—24no—
69#2398—31noSylow
70C22×C3×Q8—31no—
71C22×C3×D4—21no—
72C22×C3×D4C2×D311yescharacteristic
73C22×C3×D4C22×C311yescharacteristic
74C23×C3×C4—22no—
75C23×C3×C4C2×D312yes—
76C23×C3×C4C22×C312yes—
77C22×Dic6C22×C311yescharacteristic
78C3×C4×Q8—64no—
79C3×C4×D4—28no—
80C3×C4×D4—24no—
81C3×C4×D4—24no—
82C2×C3×C4⋊C4—21no—
83C2×C3×C4⋊C4—32no—
84C2×C3×C4⋊C4—31no—
85C2×C3×C4⋊C4C2×D311yescharacteristic
86C2×C3×C4⋊C4C22×C311yescharacteristic
87C2×C3×C22⋊C4—22no—
88C2×C3×C22⋊C4—34no—
89C2×C3×C22⋊C4—34no—
90C2×C3×C22⋊C4C2×D312yes—
91C2×C3×C22⋊C4C22×C312yes—
92C2×C3×C42—21no—
93C2×C3×C42—32no—
94C2×C3×C42—32no—
95C2×C3×C42C2×D311yescharacteristic
96C2×C3×C42C22×C311yescharacteristic
97C2×#217C22×C314yes—
98C2×#217C22×C314yes—
99C2×C4⋊Dic3C22×C311yescharacteristic
100C2×Dic3⋊C4C22×C312yes—
101C2×C4×Dic3C22×C312yes—
102C2×C4×Dic3C22×C312yes—
103C4×Dic6—24no—
104C3×#95—32no—
105C3×#95—32no—
106C3×#95—34no—
107C3×#95—34no—
108C3⋊#95C22×C312yes—
109C3⋊#95C22×C312yes—
110C3⋊#95C22×C314yes—
111C3⋊#95C22×C314yes—
112C23×C32—22no—
113C23×C32—22no—
114C23×C32—24no—
115C23×C32—24no—
116C23×C32#4114yes—
117C23×C32C2411yescharacteristic
118C32×D4—28no—
119C2×C32×C4—22no—
120C2×C32×C4—22no—
121C2×C32×C4—22no—
122C2×C32×C4—24no—
123C2×C32×C4—48no—
124C2×C32×C4C2×D412yes—
125C2×C32×C4C2×D412yes—
126C2×C32×C4C2×D412yes—
127C2×C32×C4#4114yes—
128C2×C3×Dic3—22no—
129C2×C3×Dic3—22no—
130C2×C3×Dic3—22no—
131C2×C3×Dic3—24no—
132C2×C3×Dic3—24no—
133C2×C3×Dic3—24no—
134C2×C3×Dic3—24no—
135C2×C3×Dic3#4114yes—
136C3×Dic6—28no—
137C2×C4×Q8—31no—
138C2×C4×D4C3×D311yescharacteristic
139#400—32no—
140#397—32no—
141#394—32no—
142#393—32no—
143C4×C22⋊C4—34no—
144#376—31no—
145C24×C3—22no—
146C24×C3C22×D312yes—
147C24×C3C23×C312yes—
148C2×C3×Q8—64no—
149C2×C3×Q8—62no—
150C2×C3×D4—24no—
151C2×C3×D4—28no—
152C2×C3×D4—24no—
153C2×C3×D4—24no—
154C2×C3×D4—22no—
155C2×C3×D4—22no—
156C22×C3×C4—28no—
157C22×C3×C4—28no—
158C22×C3×C4—24no—
159C22×C3×C4—24no—
160C22×C3×C4—28no—
161C22×C3×C4—21no—
162C22×C3×C4—21no—
163C22×C3×C4—21no—
164C22×C3×C4—22no—
165C22×C3×C4—32no—
166C22×C3×C4—34no—
167C22×C3×C4—32no—
168C22×C3×C4—48no—
169C22×C3×C4C22×D312yes—
170C22×C3×C4C22×D311yescharacteristic
171C22×C3×C4C22×D311yescharacteristic
172C22×C3×C4C22×D311yescharacteristic
173C22×C3×C4C23×C312yes—
174C22×C3×C4C23×C311yescharacteristic
175C22×C3×C4C23×C311yescharacteristic
176C22×C3×C4C23×C311yescharacteristic
177C22×Dic3C23×C314yes—
178C22×Dic3C23×C312yes—
179C22×Dic3C23×C312yes—
180C2×Dic6—22no—
181C2×Dic6—24no—
182C3×C4⋊C4—24no—
183C3×C4⋊C4—22no—
184C3×C4⋊C4—22no—
185C3×C4⋊C4—64no—
186C3×C4⋊C4—62no—
187C3×C22⋊C4—28no—
188C3×C22⋊C4—24no—
189C3×C22⋊C4—24no—
190C3×C22⋊C4—68no—
191C3×C22⋊C4—68no—
192C3×C42—24no—
193C3×C42—64no—
194C3×C42—64no—
195C3×C42#6714yes—
196C3×C42C3×D414yes—
197#217—28no—
198#217—28no—
199C4⋊Dic3—22no—
200Dic3⋊C4—24no—
201C4×Dic3—24no—
202C4×Dic3—24no—
203C22×C32—24no—
204C22×C32—28no—
205C22×C32—42no—
206C22×C32—42no—
207C22×C32—44no—
208C22×C32C22×D411yescharacteristic
209C22×C32C2×#4112yes—
210C22×C32C2×#4112yes—
211C22×C32C2×#4112yes—
212C32×C4—22no—
213C32×C4—22no—
214C32×C4—42no—
215C32×C4#12414yes—
216C3×Dic3—24no—
217C3×Dic3—42no—
218C3×Dic3—44no—
219C22×Q8—31no—
220C22×D4C2×C3×D311yescharacteristic
221C23×C4C2×C3×D312yes—
222C4×Q8—64no—
223C4×D4—24no—
224C2×C4⋊C4—32no—
225C2×C4⋊C4—31no—
226C2×C4⋊C4C2×C3×D311yescharacteristic
227C2×C22⋊C4—34no—
228C2×C22⋊C4—34no—
229C2×C22⋊C4C2×C3×D312yes—
230C2×C42—32no—
231C2×C42—32no—
232C2×C42C2×C3×D311yescharacteristic
233#95—32no—
234#95—32no—
235#95—34no—
236#95—34no—
237C23×C3—24no—
238C23×C3—24no—
239C23×C3—22no—
240C23×C3—24no—
241C23×C3—24no—
242C23×C3—22no—
243C23×C3—22no—
244C23×C3—24no—
245C23×C3—24no—
246C23×C3—22no—
247C23×C3—21no—
248C23×C3—24no—
249C23×C3—44no—
250C23×C3—44no—
251C23×C3#23514yes—
252C23×C3C3×#4114yes—
253C23×C3C23×D311yescharacteristic
254C23×C3C24×C311yescharacteristic
255C3×Q8—68no—
256C3×D4—216no—
257C3×D4—28no—
258C3×D4—28no—
259C2×C3×C4—24no—
260C2×C3×C4—22no—
261C2×C3×C4—22no—
262C2×C3×C4—22no—
263C2×C3×C4—22no—
264C2×C3×C4—24no—
265C2×C3×C4—24no—
266C2×C3×C4—22no—
267C2×C3×C4—22no—
268C2×C3×C4—24no—
269C2×C3×C4—24no—
270C2×C3×C4—22no—
271C2×C3×C4—22no—
272C2×C3×C4—22no—
273C2×C3×C4—34no—
274C2×C3×C4—42no—
275C2×C3×C4—44no—
276C2×C3×C4—416no—
277C2×C3×C4—48no—
278C2×C3×C4—48no—
279C2×C3×C4—62no—
280C2×C3×C4—62no—
281C2×C3×C4—64no—
282C2×C3×C4—64no—
283C2×C3×C4—64no—
284C2×C3×C4—64no—
285C2×C3×C4—62no—
286C2×C3×C4#23714yes—
287C2×C3×C4C2×#6712yes—
288C2×C3×C4C2×#6712yes—
289C2×C3×C4C2×#6712yes—
290C2×C3×C4C2×C3×D412yes—
291C2×C3×C4C2×C3×D412yes—
292C2×C3×C4C2×C3×D412yes—
293C2×C3×C4C3×#4114yes—
294C2×Dic3—22no—
295C2×Dic3—22no—
296C2×Dic3—22no—
297C2×Dic3—24no—
298C2×Dic3—24no—
299C2×Dic3—24no—
300C2×Dic3—24no—
301C2×Dic3C3×#4114yes—
302Dic6—28no—
303C2×C32—44no—
304C2×C32#52511yescharacteristic
305C2×C32#52511yescharacteristic
306C2×C32C2×#12411yescharacteristic
307C2×C32#52914yes—
308C24C22×C3×D312yes—
309C2×Q8—64no—
310C2×Q8—62no—
311C2×D4—24no—
312C2×D4—22no—
313C22×C4—28no—
314C22×C4—24no—
315C22×C4—32no—
316C22×C4—34no—
317C22×C4—32no—
318C22×C4C22×C3×D312yes—
319C22×C4C22×C3×D311yescharacteristic
320C22×C4C22×C3×D311yescharacteristic
321C22×C4C22×C3×D311yescharacteristic
322C4⋊C4—22no—
323C4⋊C4—64no—
324C4⋊C4—62no—
325C22⋊C4—24no—
326C22⋊C4—68no—
327C22⋊C4—68no—
328C42—64no—
329C42—64no—
330C42C3×#6714yes—
331C22×C3—28no—
332C22×C3—24no—
333C22×C3—28no—
334C22×C3—24no—
335C22×C3—28no—
336C22×C3—22no—
337C22×C3—22no—
338C22×C3—22no—
339C22×C3—21no—
340C22×C3—48no—
341C22×C3—44no—
342C22×C3—48no—
343C22×C3—44no—
344C22×C3—44no—
345C22×C3—42no—
346C22×C3—42no—
347C22×C3—42no—
348C22×C3—42no—
349C22×C3—44no—
350C22×C3C2×#23512yes—
351C22×C3C2×#23712yes—
352C22×C3D3×#4112yes—
353C22×C3C22×#6711yescharacteristic
354C22×C3C22×C3×D411yescharacteristic
355C22×C3C2×C3×#4112yes—
356C22×C3C2×C3×#4112yes—
357C22×C3C2×C3×#4112yes—
358C3×C4—24no—
359C3×C4—22no—
360C3×C4—22no—
361C3×C4—22no—
362C3×C4—22no—
363C3×C4—24no—
364C3×C4—42no—
365C3×C4—44no—
366C3×C4—42no—
367C3×C4—42no—
368C3×C4—64no—
369C3×C4—122no—
370C3×C4—124no—
371C3×C4#93614yes—
372C3×C4C3×#12414yes—
373Dic3—24no—
374Dic3—42no—
375Dic3—44no—
376C32#239811yescharacteristic, complemented, Sylow
377C23—22no—
378C23—24no—
379C23—24no—
380C23—22no—
381C23C3×#23514yes—
382C23C23×C3×D311yescharacteristic
383Q8—68no—
384D4—28no—
385C2×C4—22no—
386C2×C4—22no—
387C2×C4—24no—
388C2×C4—22no—
389C2×C4—34no—
390C2×C4—48no—
391C2×C4—62no—
392C2×C4—62no—
393C2×C4—64no—
394C2×C4—64no—
395C2×C4—64no—
396C2×C4—64no—
397C2×C4—62no—
398C2×C4C3×#23714yes—
399C2×C4C2×C3×#6712yes—
400C2×C4C2×C3×#6712yes—
401C2×C4C2×C3×#6712yes—
402C2×C3—21no—
403C2×C3—24no—
404C2×C3—21no—
405C2×C3—21no—
406C2×C3—48no—
407C2×C3—44no—
408C2×C3—44no—
409C2×C3#553814yes—
410C2×C3#579111yescharacteristic
411C2×C3C2×#93611yescharacteristic
412C2×C3#582811yescharacteristic
413C2×C3C3×#52511yescharacteristic
414C2×C3C3×#52511yescharacteristic
415C2×C3C2×C3×#12411yescharacteristic
416C2×C3C3×#52914yes—
417C22—24no—
418C22—28no—
419C22—44no—
420C22—42no—
421C22—42no—
422C22C2×C3×#23512yes—
423C22C2×C3×#23712yes—
424C22C3×D3×#4112yes—
425C22C22×C3×#6711yescharacteristic
426C4—22no—
427C4—22no—
428C4—42no—
429C4—64no—
430C4—122no—
431C4—124no—
432C4C3×#93614yes—
433C3—21no—
434C3#8234811yescharacteristic, direct product factor
435C3C3×#239811yescharacteristic, complemented
436C2—44no—
437C2C3×#553814yes—
438C2C3×#579111yescharacteristic
439C2C2×C3×#93611yescharacteristic
440C2C3×#582811yescharacteristic
subgroupG/H
centerC22×C3×C4C22×D3
commutator, cosocleC23×C3C24×C3
FrattiniC23C23×C3×D3
FittingC2×C32×C4×D4C2
socleC23×C32C24
prime radicalC22×C32×D4C22
hypercenterC2×C3×C4×D4D3
hypocenterC3C3×#2398
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C22×C3×C4 ◁ C2×C3×C4×D4

Complements

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

NH ≅ G/Ntype
2. C2×C3×C4×Dic6C2semidirect
4. C3×C4×#217C2semidirect
5. C3×#4985C2semidirect
6. C3×#4953C2semidirect
7. C3×#4947C2semidirect
8. C3×#4932C2semidirect
10. #82348C3direct (N × H)
33. C2×C4×Dic6C2×C3semidirect
41. C4×#217C2×C3semidirect
42. #4985C2×C3semidirect
43. #4953C2×C3semidirect
44. #4947C2×C3semidirect
45. #4932C2×C3semidirect
376. C32#2398semidirect
434. C3#82348direct (N × H)
435. C3C3×#2398semidirect

Maximal subgroups

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

subgroupindex
C2×C32×C4×D42
C2×C3×C4×Dic62
C3×#52222
C3×C4×#2172
C3×#49852
C3×#49532
C3×#49472
C3×#49322
C3×#23983
#823483