Finite Group Databasebeta

← C3×#73671 #11808948

Subgroups — C3×#73671 #11808948

Order 1152.

897 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C4×C4⋊C4C211yesmaximal, characteristic
2C3×#4986C212yesmaximal
3C3×#4982C212yesmaximal
4C3×C4×C4⋊Dic3C211yesmaximal, characteristic
5C3×C4×C4⋊Dic3C212yesmaximal
6C3×#4932C211yesmaximal, characteristic
7C3×C4×Dic3⋊C4C212yesmaximal
8C3×#4661C212yesmaximal
9C3×#4660C212yesmaximal
10C3×#2402—31nomaximal
11#73671C311yesmaximal, characteristic, direct product factor
12C2×C32×C4⋊C4C2212yes—
13C2×C32×C42C2212yes—
14C2×C32×C42C2211yescharacteristic
15C2×C3×C4⋊Dic3C2212yes—
16C2×C3×C4⋊Dic3C2212yes—
17C2×C3×C4⋊Dic3C2212yes—
18C2×C3×Dic3⋊C4C2212yes—
19C2×C3×Dic3⋊C4C2212yes—
20C2×C3×C4×Dic3C2211yescharacteristic
21C2×C3×C4×Dic3C2212yes—
22C2×C3×C4×Dic3C2211yescharacteristic
23C32×#95C2211yescharacteristic
24C32×#95C2211yescharacteristic
25C3×C3⋊#95C2212yes—
26C3×C3⋊#95C2212yes—
27C3×C3⋊#95C2212yes—
28C3×C3⋊#95C2212yes—
29C3×C3⋊#95C2212yes—
30C3×C3⋊#95C2212yes—
31C3×C3⋊#95C2211yescharacteristic
32C3×C3⋊#95C2211yescharacteristic
33C3×#400—32no—
34C3×#400—32no—
35C3×#398—32no—
36C3×#398—32no—
37C3×C4×C4⋊C4—21no—
38C3×C4×C4⋊C4—32no—
39C3×C4×C4⋊C4—31no—
40C3×C4×C4⋊C4—32no—
41C3×C4×C4⋊C4D311yescharacteristic
42C3×C4×C4⋊C4C2×C311yescharacteristic
43C3×#376—31no—
44#4986C2×C312yes—
45#4982C2×C312yes—
46C4×C4⋊Dic3C2×C312yes—
47C4×C4⋊Dic3C2×C311yescharacteristic
48#4932C2×C311yescharacteristic
49C4×Dic3⋊C4C2×C312yes—
50#4661C2×C312yes—
51#4660C2×C312yes—
52C22×C32×C4C2312yes—
53C22×C32×C4C2311yescharacteristic
54C22×C32×C4C2311yescharacteristic
55C22×C32×C4C2312yes—
56C22×C32×C4C2311yescharacteristic
57C22×C3×Dic3C2312yes—
58C22×C3×Dic3C2312yes—
59C22×C3×Dic3C2312yes—
60C22×C3×Dic3C2312yes—
61C32×C4⋊C4—24no—
62C32×C42—24no—
63C32×C42Q814yes—
64C3×C4⋊Dic3—24no—
65C3×C4⋊Dic3—24no—
66C3×C4⋊Dic3—24no—
67C3×Dic3⋊C4—24no—
68C3×Dic3⋊C4—24no—
69C3×C4×Dic3—24no—
70C3×C4×Dic3—22no—
71C3×C4×Dic3—22no—
72#2402—31noSylow
73C2×C3×C4⋊C4—22no—
74C2×C3×C4⋊C4—32no—
75C2×C3×C4⋊C4—32no—
76C2×C3×C4⋊C4—32no—
77C2×C3×C4⋊C4—32no—
78C2×C3×C4⋊C4—32no—
79C2×C3×C4⋊C4C2×D312yes—
80C2×C3×C4⋊C4C22×C312yes—
81C2×C3×C42—21no—
82C2×C3×C42—22no—
83C2×C3×C42—31no—
84C2×C3×C42—31no—
85C2×C3×C42—32no—
86C2×C3×C42C2×D312yes—
87C2×C3×C42C2×D311yescharacteristic
88C2×C3×C42C22×C312yes—
89C2×C3×C42C22×C311yescharacteristic
90C2×C4⋊Dic3C22×C312yes—
91C2×C4⋊Dic3C22×C312yes—
92C2×C4⋊Dic3C22×C312yes—
93C2×Dic3⋊C4C22×C312yes—
94C2×Dic3⋊C4C22×C312yes—
95C2×C4×Dic3C22×C311yescharacteristic
96C2×C4×Dic3C22×C312yes—
97C2×C4×Dic3C22×C311yescharacteristic
98C3×#95—21no—
99C3×#95—21no—
100C3×#95—32no—
101C3×#95—32no—
102C3×#95—31no—
103C3×#95—32no—
104C3×#95—32no—
105C3×#95—32no—
106C3×#95—32no—
107C3×#95—31no—
108C3×#95C2×D311yescharacteristic
109C3×#95C2×D311yescharacteristic
110C3×#95C22×C311yescharacteristic
111C3×#95C22×C311yescharacteristic
112C3⋊#95C22×C312yes—
113C3⋊#95C22×C312yes—
114C3⋊#95C22×C312yes—
115C3⋊#95C22×C312yes—
116C3⋊#95C22×C312yes—
117C3⋊#95C22×C312yes—
118C3⋊#95C22×C311yescharacteristic
119C3⋊#95C22×C311yescharacteristic
120C23×C32C2411yescharacteristic
121C2×C32×C4—22no—
122C2×C32×C4—22no—
123C2×C32×C4—22no—
124C2×C32×C4—22no—
125C2×C32×C4—22no—
126C2×C32×C4—22no—
127C2×C32×C4—22no—
128C2×C32×C4C2×Q812yes—
129C2×C32×C4C2×Q812yes—
130C2×C32×C4C2×Q812yes—
131C2×C32×C4#4114yes—
132C2×C32×C4#4112yes—
133C2×C32×C4#4112yes—
134C2×C3×Dic3—22no—
135C2×C3×Dic3—22no—
136C2×C3×Dic3—22no—
137C2×C3×Dic3—22no—
138C2×C3×Dic3—22no—
139C2×C3×Dic3—22no—
140C2×C3×Dic3—22no—
141C2×C3×Dic3—22no—
142C2×C3×Dic3—22no—
143C2×C3×Dic3—22no—
144C2×C3×Dic3—22no—
145C2×C3×Dic3#4114yes—
146#400—32no—
147#400—32no—
148#398—32no—
149#398—32no—
150C4×C4⋊C4—32no—
151C4×C4⋊C4—31no—
152C4×C4⋊C4—32no—
153C4×C4⋊C4C3×D311yescharacteristic
154#376—31no—
155C22×C3×C4—21no—
156C22×C3×C4—21no—
157C22×C3×C4—21no—
158C22×C3×C4—22no—
159C22×C3×C4—22no—
160C22×C3×C4—32no—
161C22×C3×C4—32no—
162C22×C3×C4—32no—
163C22×C3×C4—32no—
164C22×C3×C4C22×D312yes—
165C22×C3×C4C22×D311yescharacteristic
166C22×C3×C4C22×D311yescharacteristic
167C22×C3×C4C22×D312yes—
168C22×C3×C4C22×D311yescharacteristic
169C22×C3×C4C23×C312yes—
170C22×C3×C4C23×C311yescharacteristic
171C22×C3×C4C23×C311yescharacteristic
172C22×C3×C4C23×C312yes—
173C22×C3×C4C23×C311yescharacteristic
174C22×Dic3C23×C312yes—
175C22×Dic3C23×C312yes—
176C22×Dic3C23×C312yes—
177C22×Dic3C23×C312yes—
178C3×C4⋊C4—28no—
179C3×C4⋊C4—24no—
180C3×C4⋊C4—24no—
181C3×C4⋊C4—64no—
182C3×C4⋊C4—64no—
183C3×C4⋊C4—64no—
184C3×C4⋊C4—64no—
185C3×C4⋊C4—64no—
186C3×C42—24no—
187C3×C42—24no—
188C3×C42—24no—
189C3×C42—44no—
190C3×C42—62no—
191C3×C42—64no—
192C3×C42—62no—
193C3×C42Dic614yes—
194C3×C42C3×Q814yes—
195C4⋊Dic3—24no—
196C4⋊Dic3—24no—
197C4⋊Dic3—24no—
198Dic3⋊C4—24no—
199Dic3⋊C4—24no—
200C4×Dic3—22no—
201C4×Dic3—24no—
202C4×Dic3—22no—
203C22×C32C22×Q811yescharacteristic
204C22×C32C2×#4112yes—
205C22×C32C2×#4111yescharacteristic
206C22×C32C2×#4111yescharacteristic
207C22×C32C2×#4112yes—
208C32×C4—22no—
209C32×C4—24no—
210C32×C4—22no—
211C32×C4—42no—
212C32×C4#12514yes—
213C3×Dic3—24no—
214C3×Dic3—42no—
215C3×Dic3—42no—
216C3×Dic3—42no—
217C2×C4⋊C4—32no—
218C2×C4⋊C4—32no—
219C2×C4⋊C4—32no—
220C2×C4⋊C4—32no—
221C2×C4⋊C4—32no—
222C2×C4⋊C4C2×C3×D312yes—
223C2×C42—31no—
224C2×C42—31no—
225C2×C42—32no—
226C2×C42C2×C3×D312yes—
227C2×C42C2×C3×D311yescharacteristic
228#95—32no—
229#95—32no—
230#95—31no—
231#95—32no—
232#95—32no—
233#95—32no—
234#95—32no—
235#95—31no—
236#95C2×C3×D311yescharacteristic
237#95C2×C3×D311yescharacteristic
238C23×C3—21no—
239C23×C3C23×D311yescharacteristic
240C23×C3C24×C311yescharacteristic
241C2×C3×C4—24no—
242C2×C3×C4—22no—
243C2×C3×C4—22no—
244C2×C3×C4—22no—
245C2×C3×C4—22no—
246C2×C3×C4—22no—
247C2×C3×C4—22no—
248C2×C3×C4—22no—
249C2×C3×C4—22no—
250C2×C3×C4—24no—
251C2×C3×C4—22no—
252C2×C3×C4—22no—
253C2×C3×C4—22no—
254C2×C3×C4—22no—
255C2×C3×C4—22no—
256C2×C3×C4—22no—
257C2×C3×C4—22no—
258C2×C3×C4—22no—
259C2×C3×C4—22no—
260C2×C3×C4—24no—
261C2×C3×C4—22no—
262C2×C3×C4—22no—
263C2×C3×C4—34no—
264C2×C3×C4—42no—
265C2×C3×C4—42no—
266C2×C3×C4—42no—
267C2×C3×C4—42no—
268C2×C3×C4—42no—
269C2×C3×C4—62no—
270C2×C3×C4—62no—
271C2×C3×C4—62no—
272C2×C3×C4—62no—
273C2×C3×C4—62no—
274C2×C3×C4—62no—
275C2×C3×C4—62no—
276C2×C3×C4—62no—
277C2×C3×C4—62no—
278C2×C3×C4—62no—
279C2×C3×C4—62no—
280C2×C3×C4C2×Dic612yes—
281C2×C3×C4C2×Dic612yes—
282C2×C3×C4C2×Dic612yes—
283C2×C3×C4#23514yes—
284C2×C3×C4#23712yes—
285C2×C3×C4#23912yes—
286C2×C3×C4C2×C3×Q812yes—
287C2×C3×C4C2×C3×Q812yes—
288C2×C3×C4C2×C3×Q812yes—
289C2×C3×C4C3×#4114yes—
290C2×C3×C4C3×#4112yes—
291C2×C3×C4C3×#4112yes—
292C2×Dic3—22no—
293C2×Dic3—22no—
294C2×Dic3—22no—
295C2×Dic3—22no—
296C2×Dic3—22no—
297C2×Dic3—22no—
298C2×Dic3—22no—
299C2×Dic3—22no—
300C2×Dic3—22no—
301C2×Dic3—22no—
302C2×Dic3—22no—
303C2×Dic3C3×#4114yes—
304C2×C32C2×#12511yescharacteristic
305C2×C32#52912yes—
306C2×C32#52912yes—
307C2×C32#53311yescharacteristic
308C2×C32#53311yescharacteristic
309C22×C4—32no—
310C22×C4—32no—
311C22×C4—32no—
312C22×C4—32no—
313C22×C4C22×C3×D312yes—
314C22×C4C22×C3×D311yescharacteristic
315C22×C4C22×C3×D311yescharacteristic
316C22×C4C22×C3×D312yes—
317C22×C4C22×C3×D311yescharacteristic
318C4⋊C4—24no—
319C4⋊C4—64no—
320C4⋊C4—64no—
321C4⋊C4—64no—
322C4⋊C4—64no—
323C4⋊C4—64no—
324C42—24no—
325C42—62no—
326C42—64no—
327C42—62no—
328C42C3×Dic614yes—
329C22×C3—21no—
330C22×C3—22no—
331C22×C3—21no—
332C22×C3—21no—
333C22×C3—22no—
334C22×C3C22×Dic611yescharacteristic
335C22×C3C2×#23512yes—
336C22×C3C2×#23711yescharacteristic
337C22×C3C2×#23911yescharacteristic
338C22×C3D3×#4112yes—
339C22×C3C22×C3×Q811yescharacteristic
340C22×C3C2×C3×#4112yes—
341C22×C3C2×C3×#4111yescharacteristic
342C22×C3C2×C3×#4111yescharacteristic
343C22×C3C2×C3×#4112yes—
344C3×C4—24no—
345C3×C4—22no—
346C3×C4—22no—
347C3×C4—24no—
348C3×C4—24no—
349C3×C4—22no—
350C3×C4—22no—
351C3×C4—24no—
352C3×C4—42no—
353C3×C4—44no—
354C3×C4—44no—
355C3×C4—42no—
356C3×C4—42no—
357C3×C4—64no—
358C3×C4—122no—
359C3×C4—122no—
360C3×C4—122no—
361C3×C4#89014yes—
362C3×C4C3×#12514yes—
363Dic3—24no—
364Dic3—42no—
365Dic3—42no—
366Dic3—42no—
367C32#240211yescharacteristic, complemented, Sylow
368C23C23×C3×D311yescharacteristic
369C2×C4—22no—
370C2×C4—22no—
371C2×C4—22no—
372C2×C4—22no—
373C2×C4—22no—
374C2×C4—22no—
375C2×C4—22no—
376C2×C4—34no—
377C2×C4—62no—
378C2×C4—62no—
379C2×C4—62no—
380C2×C4—62no—
381C2×C4—62no—
382C2×C4—62no—
383C2×C4—62no—
384C2×C4—62no—
385C2×C4—62no—
386C2×C4—62no—
387C2×C4—62no—
388C2×C4C2×C3×Dic612yes—
389C2×C4C2×C3×Dic612yes—
390C2×C4C2×C3×Dic612yes—
391C2×C4C3×#23514yes—
392C2×C4C3×#23712yes—
393C2×C4C3×#23912yes—
394C2×C3—21no—
395C2×C3—21no—
396C2×C3—22no—
397C2×C3—22no—
398C2×C3—21no—
399C2×C3#547011yescharacteristic
400C2×C3C2×#89011yescharacteristic
401C2×C3#551711yescharacteristic
402C2×C3#553812yes—
403C2×C3#558012yes—
404C2×C3C2×C3×#12511yescharacteristic
405C2×C3C3×#52912yes—
406C2×C3C3×#52912yes—
407C2×C3C3×#53311yescharacteristic
408C2×C3C3×#53311yescharacteristic
409C22C22×C3×Dic611yescharacteristic
410C22C2×C3×#23512yes—
411C22C2×C3×#23711yescharacteristic
412C22C2×C3×#23911yescharacteristic
413C22C3×D3×#4112yes—
414C4—22no—
415C4—24no—
416C4—22no—
417C4—42no—
418C4—64no—
419C4—122no—
420C4—122no—
421C4—122no—
422C4C3×#89014yes—
423C3—21no—
424C3#7367111yescharacteristic, direct product factor
425C3C3×#240211yescharacteristic, complemented
426C2C3×#547011yescharacteristic
427C2C2×C3×#89011yescharacteristic
428C2C3×#551711yescharacteristic
429C2C3×#553812yes—
430C2C3×#558012yes—
subgroupG/H
centerC22×C3×C4C22×D3
commutator, cosocleC23×C3C24×C3
FrattiniC23C23×C3×D3
FittingC32×C4×C4⋊C4C2
socle, prime radicalC23×C32C24
hypercenterC3×C4×C4⋊C4D3
hypocenterC3C3×#2402
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C22×C3×C4 ◁ C3×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
11. #73671C3direct (N × H)
367. C32#2402semidirect
424. C3#73671direct (N × H)
425. C3C3×#2402semidirect

Maximal subgroups

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

subgroupindex
C32×C4×C4⋊C42
C3×#49862
C3×#49822
C3×C4×C4⋊Dic32
C3×#49322
C3×C4×Dic3⋊C42
C3×#46612
C3×#46602
C3×#24023
#736713