Finite Group Databasebeta

← C3×#73419 #11808775

Subgroups — C3×#73419 #11808775

Order 1152.

1225 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×D12C211yesmaximal, characteristic
2C2×C3×C4×Dic6C211yesmaximal, characteristic, complemented
3C32×#376C211yesmaximal, characteristic, complemented
4C3×C4×(C2×D3)⋊C4C214yesmaximal, complemented
5C3×#4674C212yesmaximal, complemented
6C3×#4673C212yesmaximal, complemented
7C3×#4672C212yesmaximal
8C3×#4659C212yesmaximal, complemented
9C3×#2398—31nomaximal
10#73419C311yesmaximal, characteristic, direct product factor
11C22×C3×D12C2211yescharacteristic
12C22×C3×C4×D3C2212yes—
13C22×C3×Dic6C2211yescharacteristic
14C2×C32×C42C2212yes—
15C2×C32×C42C2211yescharacteristic
16C2×C3×(C2×D3)⋊C4C2214yes—
17C2×C3×(C2×D3)⋊C4C2214yes—
18C2×C3×(C2×D3)⋊C4C2212yes—
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C2×C3×C4⋊Dic3C2211yescharacteristic
21C2×C3×Dic3⋊C4C2212yes—
22C2×C3×C4×Dic3C2212yes—
23C3×C4×D12—24no—
24C3×C4×Dic6—24no—
25C32×#95C2212yes—
26C32×#95C2212yes—
27C3×C3⋊#95C2214yes—
28C3×C3⋊#95C2214yes—
29C2×C3×C4×Q8—31no—
30C2×C3×C4×D4—31no—
31C2×C4×D12C2×C311yescharacteristic
32C2×C4×Dic6C2×C311yescharacteristic, complemented
33C3×#400—32no—
34C3×#397—32no—
35C3×#394—32no—
36C3×#393—32no—
37C3×C4×C22⋊C4—34no—
38C3×#376—21no—
39C3×#376D311yescharacteristic, complemented
40C3×#376C2×C311yescharacteristic, complemented
41C4×(C2×D3)⋊C4C2×C314yescomplemented
42#4674C2×C312yescomplemented
43#4673C2×C312yescomplemented
44#4672C2×C312yes—
45#4659C2×C312yescomplemented
46C23×C3×D3C2312yes—
47C22×C32×C4C2314yes—
48C22×C32×C4C2311yescharacteristic
49C22×C32×C4C2311yescharacteristic
50C22×C32×C4C2311yescharacteristic
51C22×C3×Dic3C2312yes—
52C22×C3×Dic3C2312yes—
53C22×C3×Dic3C2312yes—
54C2×C3×D12—24no—
55C2×C3×D12—22no—
56C2×C3×C4×D3—24no—
57C2×C3×C4×D3—28no—
58C2×C3×Dic6—22no—
59C2×C3×Dic6—24no—
60C32×C42—24no—
61C32×C42D414yes—
62C3×(C2×D3)⋊C4—28no—
63C3×(C2×D3)⋊C4—24no—
64C3×(C2×D3)⋊C4—28no—
65C3×C4⋊Dic3—22no—
66C3×C4⋊Dic3—22no—
67C3×Dic3⋊C4—24no—
68C3×C4×Dic3—24no—
69#2398—31noSylow
70C22×C3×Q8—31no—
71C22×C3×D4—31no—
72C23×C3×C4—32no—
73C22×D12C22×C311yescharacteristic
74C22×C4×D3C22×C312yes—
75C22×Dic6C22×C311yescharacteristic
76C3×C4×Q8—64no—
77C3×C4×D4—64no—
78C2×C3×C4⋊C4—32no—
79C2×C3×C4⋊C4—31no—
80C2×C3×C4⋊C4—31no—
81C2×C3×C22⋊C4—34no—
82C2×C3×C22⋊C4—34no—
83C2×C3×C22⋊C4—32no—
84C2×C3×C42—22no—
85C2×C3×C42—21no—
86C2×C3×C42—32no—
87C2×C3×C42C2×D312yes—
88C2×C3×C42C2×D311yescharacteristic
89C2×C3×C42C22×C312yes—
90C2×C3×C42C22×C311yescharacteristic
91C2×(C2×D3)⋊C4C22×C314yes—
92C2×(C2×D3)⋊C4C22×C314yes—
93C2×(C2×D3)⋊C4C22×C312yes—
94C2×C4⋊Dic3C22×C311yescharacteristic
95C2×C4⋊Dic3C22×C311yescharacteristic
96C2×Dic3⋊C4C22×C312yes—
97C2×C4×Dic3C22×C312yes—
98C4×D12—24no—
99C4×Dic6—24no—
100C3×#95—22no—
101C3×#95—22no—
102C3×#95—34no—
103C3×#95—34no—
104C3×#95C2×D312yes—
105C3×#95C2×D312yes—
106C3×#95C22×C312yes—
107C3×#95C22×C312yes—
108C3⋊#95C22×C314yes—
109C3⋊#95C22×C314yes—
110C23×C32C2411yescharacteristic
111C22×C3×D3—22no—
112C22×C3×D3—24no—
113C22×C3×D3—24no—
114C22×C3×D3—22no—
115C22×C3×D3#4114yes—
116C2×C32×C4—24no—
117C2×C32×C4—22no—
118C2×C32×C4—22no—
119C2×C32×C4—24no—
120C2×C32×C4—24no—
121C2×C32×C4C2×D412yes—
122C2×C32×C4C2×D412yes—
123C2×C32×C4C2×D412yes—
124C2×C32×C4#4114yes—
125C2×C3×Dic3—22no—
126C2×C3×Dic3—22no—
127C2×C3×Dic3—22no—
128C2×C3×Dic3—22no—
129C2×C3×Dic3—24no—
130C2×C3×Dic3—24no—
131C2×C3×Dic3#4114yes—
132C3×D12—28no—
133C3×C4×D3—48no—
134C3×Dic6—28no—
135C2×C4×Q8—31no—
136C2×C4×D4—31no—
137#400—32no—
138#397—32no—
139#394—32no—
140#393—32no—
141C4×C22⋊C4—34no—
142#376C3×D311yescharacteristic, complemented
143C24×C3—32no—
144C23×D3C23×C312yes—
145C2×C3×Q8—64no—
146C2×C3×Q8—62no—
147C2×C3×D4—64no—
148C2×C3×D4—62no—
149C22×C3×C4—21no—
150C22×C3×C4—24no—
151C22×C3×C4—21no—
152C22×C3×C4—21no—
153C22×C3×C4—32no—
154C22×C3×C4—32no—
155C22×C3×C4—32no—
156C22×C3×C4—64no—
157C22×C3×C4—68no—
158C22×C3×C4C22×D314yes—
159C22×C3×C4C22×D311yescharacteristic
160C22×C3×C4C22×D311yescharacteristic
161C22×C3×C4C22×D311yescharacteristic
162C22×C3×C4C23×C314yes—
163C22×C3×C4C23×C311yescharacteristic
164C22×C3×C4C23×C311yescharacteristic
165C22×C3×C4C23×C311yescharacteristic
166C22×Dic3C23×C312yes—
167C22×Dic3C23×C312yes—
168C22×Dic3C23×C312yes—
169C2×D12—24no—
170C2×D12—22no—
171C2×C4×D3—24no—
172C2×C4×D3—28no—
173C2×Dic6—22no—
174C2×Dic6—24no—
175C3×C4⋊C4—64no—
176C3×C4⋊C4—62no—
177C3×C4⋊C4—62no—
178C3×C22⋊C4—68no—
179C3×C22⋊C4—68no—
180C3×C22⋊C4—64no—
181C3×C42—28no—
182C3×C42—24no—
183C3×C42—24no—
184C3×C42—24no—
185C3×C42—64no—
186C3×C42D1214yes—
187C3×C42C3×D414yes—
188(C2×D3)⋊C4—28no—
189(C2×D3)⋊C4—24no—
190(C2×D3)⋊C4—28no—
191C4⋊Dic3—22no—
192C4⋊Dic3—22no—
193Dic3⋊C4—24no—
194C4×Dic3—24no—
195C22×C32C22×D411yescharacteristic
196C22×C32C2×#4112yes—
197C22×C32C2×#4112yes—
198C22×C32C2×#4112yes—
199C2×C3×D3—24no—
200C2×C3×D3—28no—
201C2×C3×D3—42no—
202C2×C3×D3—42no—
203C2×C3×D3—44no—
204C32×C4—22no—
205C32×C4—22no—
206C32×C4—44no—
207C32×C4#12414yes—
208C3×Dic3—24no—
209C3×Dic3—42no—
210C3×Dic3—42no—
211C22×Q8—31no—
212C22×D4—31no—
213C23×C4—32no—
214C4×Q8—64no—
215C4×D4—64no—
216C2×C4⋊C4—31no—
217C2×C4⋊C4—32no—
218C2×C4⋊C4—31no—
219C2×C22⋊C4—32no—
220C2×C22⋊C4—34no—
221C2×C22⋊C4—34no—
222C2×C42—32no—
223C2×C42C2×C3×D312yes—
224C2×C42C2×C3×D311yescharacteristic
225#95—34no—
226#95—34no—
227#95C2×C3×D312yes—
228#95C2×C3×D312yes—
229C23×C3—21no—
230C23×C3—34no—
231C23×C3—62no—
232C23×C3—64no—
233C23×C3—64no—
234C23×C3—62no—
235C23×C3C23×D311yescharacteristic
236C23×C3C24×C311yescharacteristic
237C22×D3—22no—
238C22×D3—24no—
239C22×D3—24no—
240C22×D3—22no—
241C22×D3C3×#4114yes—
242C3×Q8—68no—
243C3×D4—68no—
244C2×C3×C4—22no—
245C2×C3×C4—22no—
246C2×C3×C4—22no—
247C2×C3×C4—22no—
248C2×C3×C4—28no—
249C2×C3×C4—24no—
250C2×C3×C4—24no—
251C2×C3×C4—24no—
252C2×C3×C4—24no—
253C2×C3×C4—24no—
254C2×C3×C4—24no—
255C2×C3×C4—22no—
256C2×C3×C4—22no—
257C2×C3×C4—22no—
258C2×C3×C4—24no—
259C2×C3×C4—34no—
260C2×C3×C4—42no—
261C2×C3×C4—42no—
262C2×C3×C4—44no—
263C2×C3×C4—44no—
264C2×C3×C4—62no—
265C2×C3×C4—62no—
266C2×C3×C4—62no—
267C2×C3×C4—62no—
268C2×C3×C4—64no—
269C2×C3×C4—64no—
270C2×C3×C4—128no—
271C2×C3×C4C2×D1212yes—
272C2×C3×C4C2×D1212yes—
273C2×C3×C4C2×D1212yes—
274C2×C3×C4#23514yes—
275C2×C3×C4C2×C3×D412yes—
276C2×C3×C4C2×C3×D412yes—
277C2×C3×C4C2×C3×D412yes—
278C2×C3×C4C3×#4114yes—
279C2×Dic3—22no—
280C2×Dic3—22no—
281C2×Dic3—22no—
282C2×Dic3—22no—
283C2×Dic3—24no—
284C2×Dic3—24no—
285C2×Dic3C3×#4114yes—
286D12—28no—
287C4×D3—48no—
288Dic6—28no—
289C2×C32#52511yescharacteristic
290C2×C32#52511yescharacteristic
291C2×C32C2×#12411yescharacteristic
292C2×C32#52914yes—
293C3×D3—44no—
294C24—32no—
295C2×Q8—64no—
296C2×Q8—62no—
297C2×D4—64no—
298C2×D4—62no—
299C22×C4—32no—
300C22×C4—32no—
301C22×C4—32no—
302C22×C4—64no—
303C22×C4—68no—
304C22×C4C22×C3×D314yes—
305C22×C4C22×C3×D311yescharacteristic
306C22×C4C22×C3×D311yescharacteristic
307C22×C4C22×C3×D311yescharacteristic
308C4⋊C4—62no—
309C4⋊C4—64no—
310C4⋊C4—62no—
311C22⋊C4—68no—
312C22⋊C4—68no—
313C22⋊C4—64no—
314C42—24no—
315C42—64no—
316C42C3×D1214yes—
317C22×C3—21no—
318C22×C3—22no—
319C22×C3—22no—
320C22×C3—22no—
321C22×C3—64no—
322C22×C3—68no—
323C22×C3—122no—
324C22×C3—122no—
325C22×C3—124no—
326C22×C3C22×D1211yescharacteristic
327C22×C3C2×#23512yes—
328C22×C3D3×#4112yes—
329C22×C3D3×#4112yes—
330C22×C3C22×C3×D411yescharacteristic
331C22×C3C2×C3×#4112yes—
332C22×C3C2×C3×#4112yes—
333C22×C3C2×C3×#4112yes—
334C2×D3—24no—
335C2×D3—28no—
336C2×D3—42no—
337C2×D3—42no—
338C2×D3—44no—
339C3×C4—22no—
340C3×C4—22no—
341C3×C4—22no—
342C3×C4—22no—
343C3×C4—24no—
344C3×C4—42no—
345C3×C4—42no—
346C3×C4—48no—
347C3×C4—44no—
348C3×C4—44no—
349C3×C4—64no—
350C3×C4—122no—
351C3×C4—122no—
352C3×C4#87514yes—
353C3×C4C3×#12414yes—
354Dic3—24no—
355Dic3—42no—
356Dic3—42no—
357C32#239811yescharacteristic, complemented, Sylow
358C23—34no—
359C23—62no—
360C23—64no—
361C23—64no—
362C23—62no—
363C23C23×C3×D311yescharacteristic
364Q8—68no—
365D4—68no—
366C2×C4—22no—
367C2×C4—22no—
368C2×C4—24no—
369C2×C4—24no—
370C2×C4—24no—
371C2×C4—34no—
372C2×C4—62no—
373C2×C4—62no—
374C2×C4—62no—
375C2×C4—62no—
376C2×C4—64no—
377C2×C4—64no—
378C2×C4—128no—
379C2×C4C2×C3×D1212yes—
380C2×C4C2×C3×D1212yes—
381C2×C4C2×C3×D1212yes—
382C2×C4C3×#23514yes—
383C2×C3—21no—
384C2×C3—21no—
385C2×C3—24no—
386C2×C3—21no—
387C2×C3—124no—
388C2×C3C2×#87511yescharacteristic
389C2×C3#552411yescharacteristic
390C2×C3#552411yescharacteristic
391C2×C3#552814yes—
392C2×C3C3×#52511yescharacteristic
393C2×C3C3×#52511yescharacteristic
394C2×C3C2×C3×#12411yescharacteristic
395C2×C3C3×#52914yes—
396D3—44no—
397C22—64no—
398C22—68no—
399C22—122no—
400C22—124no—
401C22—122no—
402C22C22×C3×D1211yescharacteristic
403C22C2×C3×#23512yes—
404C22C3×D3×#4112yes—
405C22C3×D3×#4112yes—
406C4—22no—
407C4—22no—
408C4—44no—
409C4—64no—
410C4—122no—
411C4—122no—
412C4C3×#87514yes—
413C3—21no—
414C3#7341911yescharacteristic, direct product factor
415C3C3×#239811yescharacteristic, complemented
416C2—124no—
417C2C2×C3×#87511yescharacteristic
418C2C3×#552411yescharacteristic
419C2C3×#552411yescharacteristic
420C2C3×#552814yes—
subgroupG/H
centerC22×C3×C4C22×D3
commutator, cosocleC23×C3C24×C3
FrattiniC23C23×C3×D3
FittingC32×#376C2
socleC23×C32C24
prime radicalC22×C3×D12C22
hypercenterC3×#376D3
hypocenterC3C3×#2398
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C22×C3×C4 ◁ C3×#376

Complements

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

NH ≅ G/Ntype
2. C2×C3×C4×Dic6C2semidirect
3. C32×#376C2semidirect
4. C3×C4×(C2×D3)⋊C4C2semidirect
5. C3×#4674C2semidirect
6. C3×#4673C2semidirect
8. C3×#4659C2semidirect
10. #73419C3direct (N × H)
32. C2×C4×Dic6C2×C3semidirect
39. C3×#376D3semidirect
40. C3×#376C2×C3semidirect
41. C4×(C2×D3)⋊C4C2×C3semidirect
42. #4674C2×C3semidirect
43. #4673C2×C3semidirect
45. #4659C2×C3semidirect
142. #376C3×D3semidirect
357. C32#2398semidirect
414. C3#73419direct (N × H)
415. C3C3×#2398semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4×D122
C2×C3×C4×Dic62
C32×#3762
C3×C4×(C2×D3)⋊C42
C3×#46742
C3×#46732
C3×#46722
C3×#46592
C3×#23983
#734193