Finite Group Databasebeta

← C3×#82467 #11808832

Subgroups — C3×#82467 #11808832

Order 1152.

1157 conjugacy classes of subgroups.

The subgroup lattice has 397 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C4×Q8C211yesmaximal, characteristic
2C2×C3×C4×Dic6C211yesmaximal, characteristic
3C3×#5230C212yesmaximal
4C3×#4983C212yesmaximal
5C3×#4981C212yesmaximal
6C3×#4979C212yesmaximal
7C3×#4932C211yesmaximal, characteristic
8C3×C4×Dic3⋊C4C214yesmaximal
9C3×#2399—31nomaximal
10#82467C311yesmaximal, characteristic, direct product factor
11C22×C32×Q8C2211yescharacteristic
12C22×C3×Dic6C2211yescharacteristic
13C32×C4×Q8—24no—
14C2×C32×C4⋊C4C2212yes—
15C2×C32×C4⋊C4C2211yescharacteristic
16C2×C32×C42C2212yes—
17C2×C32×C42C2211yescharacteristic
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C2×C3×Dic3⋊C4C2214yes—
20C2×C3×Dic3⋊C4C2214yes—
21C2×C3×Dic3⋊C4C2212yes—
22C2×C3×C4×Dic3C2212yes—
23C2×C3×C4×Dic3C2212yes—
24C3×C4×Dic6—24no—
25C3×C3⋊#95C2214yes—
26C3×C3⋊#95C2214yes—
27C3×C3⋊#95C2212yes—
28C3×C3⋊#95C2212yes—
29C2×C3×C4×Q8—21no—
30C2×C3×C4×Q8—31no—
31C2×C3×C4×Q8D311yescharacteristic
32C2×C3×C4×Q8C2×C311yescharacteristic
33C2×C4×Dic6C2×C311yescharacteristic
34C3×#398—32no—
35C3×#398—32no—
36C3×#395—32no—
37C3×#395—32no—
38C3×C4×C4⋊C4—34no—
39C3×#376—31no—
40#5230C2×C312yes—
41#4983C2×C312yes—
42#4981C2×C312yes—
43#4979C2×C312yes—
44#4932C2×C311yescharacteristic
45C4×Dic3⋊C4C2×C314yes—
46C2×C32×Q8—22no—
47C2×C32×Q8—24no—
48C22×C32×C4C2312yes—
49C22×C32×C4C2311yescharacteristic
50C22×C32×C4C2311yescharacteristic
51C22×C32×C4C2312yes—
52C22×C32×C4C2311yescharacteristic
53C22×C3×Dic3C2312yes—
54C22×C3×Dic3C2314yes—
55C22×C3×Dic3C2312yes—
56C2×C3×Dic6—22no—
57C2×C3×Dic6—24no—
58C32×C4⋊C4—24no—
59C32×C4⋊C4—22no—
60C32×C42—24no—
61C32×C42D414yes—
62C3×C4⋊Dic3—22no—
63C3×Dic3⋊C4—24no—
64C3×Dic3⋊C4—28no—
65C3×Dic3⋊C4—28no—
66C3×C4×Dic3—24no—
67C3×C4×Dic3Q818yescomplemented
68#2399—31noSylow
69C22×C3×Q8—21no—
70C22×C3×Q8—31no—
71C22×C3×Q8C2×D311yescharacteristic
72C22×C3×Q8C22×C311yescharacteristic
73C22×Dic6C22×C311yescharacteristic
74C3×C4×Q8—28no—
75C3×C4×Q8—24no—
76C3×C4×Q8—24no—
77C3×C4×Q8—64no—
78C2×C3×C4⋊C4—22no—
79C2×C3×C4⋊C4—21no—
80C2×C3×C4⋊C4—34no—
81C2×C3×C4⋊C4—34no—
82C2×C3×C4⋊C4—32no—
83C2×C3×C4⋊C4—31no—
84C2×C3×C4⋊C4C2×D312yes—
85C2×C3×C4⋊C4C2×D311yescharacteristic
86C2×C3×C4⋊C4C22×C312yes—
87C2×C3×C4⋊C4C22×C311yescharacteristic
88C2×C3×C42—22no—
89C2×C3×C42—21no—
90C2×C3×C42—32no—
91C2×C3×C42—32no—
92C2×C3×C42C2×D312yes—
93C2×C3×C42C2×D311yescharacteristic
94C2×C3×C42C22×C312yes—
95C2×C3×C42C22×C311yescharacteristic
96C2×C4⋊Dic3C22×C311yescharacteristic
97C2×Dic3⋊C4C22×C314yes—
98C2×Dic3⋊C4C22×C314yes—
99C2×Dic3⋊C4C22×C312yes—
100C2×C4×Dic3C22×C312yes—
101C2×C4×Dic3C22×C312yes—
102C4×Dic6—24no—
103C3×#95—32no—
104C3×#95—32no—
105C3×#95—34no—
106C3×#95—34no—
107C3⋊#95C22×C314yes—
108C3⋊#95C22×C314yes—
109C3⋊#95C22×C312yes—
110C3⋊#95C22×C312yes—
111C23×C32C2411yescharacteristic
112C32×Q8—28no—
113C2×C32×C4—22no—
114C2×C32×C4—22no—
115C2×C32×C4—22no—
116C2×C32×C4—22no—
117C2×C32×C4—22no—
118C2×C32×C4—24no—
119C2×C32×C4C2×D412yes—
120C2×C32×C4C2×D412yes—
121C2×C32×C4C2×D412yes—
122C2×C32×C4C2×Q814yes—
123C2×C32×C4#4114yes—
124C2×C3×Dic3—22no—
125C2×C3×Dic3—24no—
126C2×C3×Dic3—24no—
127C2×C3×Dic3—22no—
128C2×C3×Dic3—22no—
129C2×C3×Dic3—24no—
130C2×C3×Dic3C2×Q818yes—
131C2×C3×Dic3#4114yes—
132C3×Dic6—28no—
133C2×C4×Q8—31no—
134C2×C4×Q8C3×D311yescharacteristic
135#398—32no—
136#398—32no—
137#395—32no—
138#395—32no—
139C4×C4⋊C4—34no—
140#376—31no—
141C2×C3×Q8—24no—
142C2×C3×Q8—28no—
143C2×C3×Q8—24no—
144C2×C3×Q8—22no—
145C2×C3×Q8—22no—
146C2×C3×Q8—24no—
147C2×C3×Q8—64no—
148C2×C3×Q8—62no—
149C22×C3×C4—21no—
150C22×C3×C4—22no—
151C22×C3×C4—21no—
152C22×C3×C4—22no—
153C22×C3×C4—21no—
154C22×C3×C4—34no—
155C22×C3×C4—32no—
156C22×C3×C4—32no—
157C22×C3×C4C22×D312yes—
158C22×C3×C4C22×D312yes—
159C22×C3×C4C22×D311yescharacteristic
160C22×C3×C4C22×D311yescharacteristic
161C22×C3×C4C22×D311yescharacteristic
162C22×C3×C4C23×C312yes—
163C22×C3×C4C23×C311yescharacteristic
164C22×C3×C4C23×C311yescharacteristic
165C22×C3×C4C23×C312yes—
166C22×C3×C4C23×C311yescharacteristic
167C22×Dic3C23×C312yes—
168C22×Dic3C23×C314yes—
169C22×Dic3C23×C312yes—
170C2×Dic6—22no—
171C2×Dic6—24no—
172C3×C4⋊C4—28no—
173C3×C4⋊C4—24no—
174C3×C4⋊C4—24no—
175C3×C4⋊C4—22no—
176C3×C4⋊C4—24no—
177C3×C4⋊C4—22no—
178C3×C4⋊C4—68no—
179C3×C4⋊C4—68no—
180C3×C4⋊C4—64no—
181C3×C4⋊C4—62no—
182C3×C42—28no—
183C3×C42—24no—
184C3×C42—24no—
185C3×C42—24no—
186C3×C42—38no—
187C3×C42—64no—
188C3×C42#6714yes—
189C3×C42C3×D414yes—
190C4⋊Dic3—22no—
191Dic3⋊C4—24no—
192Dic3⋊C4—28no—
193Dic3⋊C4—28no—
194C4×Dic3—24no—
195C4×Dic3C3×Q818yescomplemented
196C22×C32C22×D411yescharacteristic
197C22×C32C22×Q812yes—
198C22×C32C2×#4112yes—
199C22×C32C2×#4112yes—
200C32×C4—22no—
201C32×C4—24no—
202C32×C4—22no—
203C32×C4—42no—
204C32×C4C4⋊Q814yes—
205C3×Dic3—24no—
206C3×Dic3—28no—
207C3×Dic3—42no—
208C22×Q8—31no—
209C22×Q8C2×C3×D311yescharacteristic
210C4×Q8—24no—
211C4×Q8—64no—
212C2×C4⋊C4—32no—
213C2×C4⋊C4—31no—
214C2×C4⋊C4—34no—
215C2×C4⋊C4—34no—
216C2×C4⋊C4C2×C3×D312yes—
217C2×C4⋊C4C2×C3×D311yescharacteristic
218C2×C42—32no—
219C2×C42—32no—
220C2×C42C2×C3×D312yes—
221C2×C42C2×C3×D311yescharacteristic
222#95—32no—
223#95—32no—
224#95—34no—
225#95—34no—
226C23×C3—21no—
227C23×C3C23×D311yescharacteristic
228C23×C3C24×C311yescharacteristic
229C3×Q8—216no—
230C3×Q8—28no—
231C3×Q8—28no—
232C3×Q8—68no—
233C2×C3×C4—24no—
234C2×C3×C4—24no—
235C2×C3×C4—24no—
236C2×C3×C4—22no—
237C2×C3×C4—22no—
238C2×C3×C4—22no—
239C2×C3×C4—22no—
240C2×C3×C4—22no—
241C2×C3×C4—22no—
242C2×C3×C4—22no—
243C2×C3×C4—22no—
244C2×C3×C4—24no—
245C2×C3×C4—24no—
246C2×C3×C4—22no—
247C2×C3×C4—22no—
248C2×C3×C4—24no—
249C2×C3×C4—24no—
250C2×C3×C4—24no—
251C2×C3×C4—22no—
252C2×C3×C4—22no—
253C2×C3×C4—22no—
254C2×C3×C4—38no—
255C2×C3×C4—34no—
256C2×C3×C4—42no—
257C2×C3×C4—44no—
258C2×C3×C4—64no—
259C2×C3×C4—64no—
260C2×C3×C4—62no—
261C2×C3×C4—62no—
262C2×C3×C4—64no—
263C2×C3×C4—62no—
264C2×C3×C4#23514yes—
265C2×C3×C4D3×Q814yes—
266C2×C3×C4C2×#6712yes—
267C2×C3×C4C2×#6712yes—
268C2×C3×C4C2×#6712yes—
269C2×C3×C4C2×C3×D412yes—
270C2×C3×C4C2×C3×D412yes—
271C2×C3×C4C2×C3×D412yes—
272C2×C3×C4C2×C3×Q814yes—
273C2×C3×C4C3×#4114yes—
274C2×Dic3—22no—
275C2×Dic3—24no—
276C2×Dic3—24no—
277C2×Dic3—22no—
278C2×Dic3—22no—
279C2×Dic3—24no—
280C2×Dic3C2×C3×Q818yes—
281C2×Dic3C3×#4114yes—
282Dic6—28no—
283C2×C32#52511yescharacteristic
284C2×C32#52511yescharacteristic
285C2×C32C2×C4⋊Q811yescharacteristic
286C2×C32#53314yes—
287C2×Q8—24no—
288C2×Q8—22no—
289C2×Q8—64no—
290C2×Q8—62no—
291C22×C4—34no—
292C22×C4—32no—
293C22×C4—32no—
294C22×C4C22×C3×D312yes—
295C22×C4C22×C3×D312yes—
296C22×C4C22×C3×D311yescharacteristic
297C22×C4C22×C3×D311yescharacteristic
298C22×C4C22×C3×D311yescharacteristic
299C4⋊C4—24no—
300C4⋊C4—22no—
301C4⋊C4—68no—
302C4⋊C4—68no—
303C4⋊C4—64no—
304C4⋊C4—62no—
305C42—24no—
306C42—38no—
307C42—64no—
308C42C3×#6714yes—
309C22×C3—22no—
310C22×C3—22no—
311C22×C3—22no—
312C22×C3—21no—
313C22×C3C2×#23512yes—
314C22×C3C2×D3×Q812yes—
315C22×C3D3×#4112yes—
316C22×C3C22×#6711yescharacteristic
317C22×C3C22×C3×D411yescharacteristic
318C22×C3C22×C3×Q812yes—
319C22×C3C2×C3×#4112yes—
320C22×C3C2×C3×#4112yes—
321C3×C4—28no—
322C3×C4—24no—
323C3×C4—24no—
324C3×C4—22no—
325C3×C4—22no—
326C3×C4—22no—
327C3×C4—22no—
328C3×C4—24no—
329C3×C4—24no—
330C3×C4—42no—
331C3×C4—44no—
332C3×C4—42no—
333C3×C4—42no—
334C3×C4—64no—
335C3×C4—68no—
336C3×C4—122no—
337C3×C4#94414yes—
338C3×C4C3×C4⋊Q814yes—
339Dic3—24no—
340Dic3—28no—
341Dic3—42no—
342C32#239911yescharacteristic, complemented, Sylow
343C23C23×C3×D311yescharacteristic
344Q8—28no—
345Q8—68no—
346C2×C4—22no—
347C2×C4—22no—
348C2×C4—22no—
349C2×C4—22no—
350C2×C4—24no—
351C2×C4—22no—
352C2×C4—38no—
353C2×C4—34no—
354C2×C4—64no—
355C2×C4—64no—
356C2×C4—62no—
357C2×C4—62no—
358C2×C4—64no—
359C2×C4—62no—
360C2×C4C3×#23514yes—
361C2×C4C3×D3×Q814yes—
362C2×C4C2×C3×#6712yes—
363C2×C4C2×C3×#6712yes—
364C2×C4C2×C3×#6712yes—
365C2×C3—21no—
366C2×C3—21no—
367C2×C3—21no—
368C2×C3—24no—
369C2×C3#557814yes—
370C2×C3#579111yescharacteristic
371C2×C3C2×#94411yescharacteristic
372C2×C3#582811yescharacteristic
373C2×C3C3×#52511yescharacteristic
374C2×C3C3×#52511yescharacteristic
375C2×C3C2×C3×C4⋊Q811yescharacteristic
376C2×C3C3×#53314yes—
377C22C2×C3×#23512yes—
378C22C2×C3×D3×Q812yes—
379C22C3×D3×#4112yes—
380C22C22×C3×#6711yescharacteristic
381C4—24no—
382C4—22no—
383C4—22no—
384C4—42no—
385C4—64no—
386C4—68no—
387C4—122no—
388C4C3×#94414yes—
389C3—21no—
390C3#8246711yescharacteristic, direct product factor
391C3C3×#239911yescharacteristic, complemented
392C2C3×#557814yes—
393C2C3×#579111yescharacteristic
394C2C2×C3×#94411yescharacteristic
395C2C3×#582811yescharacteristic
subgroupG/H
centerC22×C3×C4C22×D3
commutator, cosocleC23×C3C24×C3
FrattiniC23C23×C3×D3
FittingC2×C32×C4×Q8C2
socle, prime radicalC23×C32C24
hypercenterC2×C3×C4×Q8D3
hypocenterC3C3×#2399
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C22×C3×C4 ◁ C2×C3×C4×Q8

Complements

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

NH ≅ G/Ntype
10. #82467C3direct (N × H)
67. C3×C4×Dic3Q8semidirect
195. C4×Dic3C3×Q8semidirect
342. C32#2399semidirect
390. C3#82467direct (N × H)
391. C3C3×#2399semidirect

Maximal subgroups

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

subgroupindex
C2×C32×C4×Q82
C2×C3×C4×Dic62
C3×#52302
C3×#49832
C3×#49812
C3×#49792
C3×#49322
C3×C4×Dic3⋊C42
C3×#23993
#824673