Finite Group Databasebeta

← C3×#68121 #11773913

Subgroups — C3×#68121 #11773913

Order 1152.

681 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#67⋊C4C211yesmaximal, characteristic
2C3×#4726C212yesmaximal, complemented
3C32×#323C211yesmaximal, characteristic, complemented
4C3×#4525C211yesmaximal, characteristic, complemented
5C3×#4469C212yesmaximal, complemented
6C3×#1465—31nomaximal
7#68121C311yesmaximal, characteristic, direct product factor
8C22×C3×#67C411yescharacteristic
9C23×C3×Dic3C411yescharacteristic
10C22×C3×C4×D3C2211yescharacteristic
11C2×C32×C22⋊C4C2211yescharacteristic
12C2×C3×(C2×D3)⋊C4C411yescharacteristic
13C2×C3×Dic3⋊C4C2211yescharacteristic
14C2×C3×C4×Dic3C411yescharacteristic
15C2×C3×ΓL(1,𝔽25)—22no—
16C3×#67⋊C4—22no—
17C3×#67⋊C4—22no—
18C32×C22⋊C8C2212yes—
19C3×#830C2212yes—
20C3×(C2×D3)⋊C8—22no—
21C2×C3×C4×D4—31no—
22C2×#67⋊C4C2×C311yescharacteristic
23C3×#407—32no—
24#4726C2×C312yescomplemented
25C3×#324—32no—
26C3×#323—21no—
27C3×#323—31no—
28C3×#323D311yescharacteristic, complemented
29C3×#323C2×C311yescharacteristic, complemented
30#4525C2×C311yescharacteristic, complemented
31#4469C2×C312yescomplemented
32C24×C32C2×C411yescharacteristic
33C23×C3×D3C2×C411yescharacteristic
34C22×C32×C4C2×C411yescharacteristic
35C22×C32×C4C2311yescharacteristic
36C2×C3×#67—22no—
37C2×C3×#67—22no—
38C2×C3×#67—22no—
39C22×C3×Dic3—21no—
40C22×C3×Dic3—21no—
41C22×C3×Dic3—42no—
42C22×C3×Dic3C2×C411yescharacteristic
43C22×C3×Dic3C2×C411yescharacteristic
44C22×C3×Dic3C2×C411yescharacteristic
45C2×C3×C4×D3—42no—
46C2×C3×C4×D3D412yes—
47C2×C3×C4×D3D412yes—
48C2×C32×C8—22no—
49C32×C22⋊C4—22no—
50C3×(C2×D3)⋊C4—22no—
51C3×Dic3⋊C4—22no—
52C3×C4×Dic3—21no—
53C3×C4×Dic3—21no—
54C2×C3×C3⋊C8—22no—
55C3×ΓL(1,𝔽25)—44no—
56#1465—31noSylow
57C22×C3×D4—31no—
58C23×C3×C4—31no—
59C23×C3×C4—31no—
60C22×#67C3×C411yescharacteristic
61C23×Dic3C3×C411yescharacteristic
62C22×C4×D3C22×C311yescharacteristic
63C2×C3×M16—62no—
64C3×C4×D4—62no—
65C3×C4×D4—62no—
66C2×C3×C4⋊C4—31no—
67C2×C3×C22⋊C4—21no—
68C2×C3×C22⋊C4—31no—
69C2×C3×C22⋊C4C2×D311yescharacteristic
70C2×C3×C22⋊C4C22×C311yescharacteristic
71C2×C3×C42—31no—
72C2×(C2×D3)⋊C4C3×C411yescharacteristic
73C2×Dic3⋊C4C22×C311yescharacteristic
74C2×C4×Dic3C3×C411yescharacteristic
75C2×ΓL(1,𝔽25)—22no—
76#67⋊C4—22no—
77#67⋊C4—22no—
78C3×C22⋊C8—22no—
79C3×C22⋊C8—32no—
80C3×C22⋊C8—62no—
81C3×C22⋊C8C2×D312yes—
82C3×C22⋊C8C22×C312yes—
83#830C22×C312yes—
84(C2×D3)⋊C8—22no—
85C23×C32—21no—
86C23×C32—21no—
87C23×C32—41no—
88C23×C32—41no—
89C23×C32M1612yescomplemented
90C23×C32C22×C411yescharacteristic
91C22×C3×D3—21no—
92C22×C3×D3—21no—
93C22×C3×D3—41no—
94C22×C3×D3—41no—
95C22×C3×D3C22⋊C412yes—
96C2×C32×C4—21no—
97C2×C32×C4—41no—
98C2×C32×C4—41no—
99C2×C32×C4C2×D412yes—
100C3×#67—28no—
101C2×C3×Dic3—21no—
102C2×C3×Dic3—21no—
103C2×C3×Dic3—22no—
104C2×C3×Dic3—21no—
105C2×C3×Dic3—42no—
106C2×C3×Dic3—42no—
107C2×C3×Dic3—41no—
108C2×C3×Dic3C22⋊C411yescharacteristic
109C2×C3×Dic3C22⋊C411yescharacteristic
110C2×C3×Dic3M1612yescomplemented
111C3×C4×D3—24no—
112C3×C4×D3—42no—
113C32×C8—42no—
114C3×C3⋊C8—42no—
115C2×C4×D4—31no—
116#407—32no—
117#324—32no—
118#323—31no—
119#323C3×D311yescharacteristic, complemented
120C24×C3—21no—
121C24×C3—31no—
122C24×C3C4×D311yescharacteristic
123C24×C3C2×C3×C411yescharacteristic
124C23×D3C2×C3×C411yescharacteristic
125C2×C3×D4—62no—
126C2×C3×D4—62no—
127C2×C3×D4—62no—
128C22×C3×C4—21no—
129C22×C3×C4—21no—
130C22×C3×C4—31no—
131C22×C3×C4—31no—
132C22×C3×C4—32no—
133C22×C3×C4—32no—
134C22×C3×C4—31no—
135C22×C3×C4—61no—
136C22×C3×C4—61no—
137C22×C3×C4—122no—
138C22×C3×C4—122no—
139C22×C3×C4C4×D311yescharacteristic
140C22×C3×C4C2×C3×C411yescharacteristic
141C22×C3×C4C22×D311yescharacteristic
142C22×C3×C4C23×C311yescharacteristic
143C2×#67—22no—
144C2×#67—22no—
145C2×#67—22no—
146C22×Dic3—21no—
147C22×Dic3—21no—
148C22×Dic3—42no—
149C22×Dic3C2×C3×C411yescharacteristic
150C22×Dic3C2×C3×C411yescharacteristic
151C22×Dic3C2×C3×C411yescharacteristic
152C2×C4×D3—42no—
153C2×C4×D3C3×D412yes—
154C2×C4×D3C3×D412yes—
155C3×M16—124no—
156C2×C3×C8—22no—
157C2×C3×C8—22no—
158C2×C3×C8—42no—
159C2×C3×C8—62no—
160C3×C4⋊C4—62no—
161C3×C22⋊C4—22no—
162C3×C22⋊C4—22no—
163C3×C22⋊C4—42no—
164C3×C22⋊C4—62no—
165C3×C42—61no—
166C3×C42—61no—
167(C2×D3)⋊C4—22no—
168Dic3⋊C4—22no—
169C4×Dic3—21no—
170C4×Dic3—21no—
171C2×C3⋊C8—22no—
172ΓL(1,𝔽25)—44no—
173C22×C32—21no—
174C22×C32—21no—
175C22×C32—22no—
176C22×C32—42no—
177C22×C32—42no—
178C22×C32—41no—
179C22×C32—41no—
180C22×C32C2×C22⋊C411yescharacteristic
181C22×C32C2×M1611yescharacteristic
182C22×C32C2×M1611yescharacteristic
183C2×C3×D3—22no—
184C2×C3×D3—22no—
185C2×C3×D3—22no—
186C2×C3×D3—42no—
187C2×C3×D3—42no—
188C32×C4—22no—
189C32×C4—41no—
190C3×Dic3—22no—
191C3×Dic3—21no—
192C3×Dic3—41no—
193C3×Dic3#9912yes—
194C22×D4—31no—
195C23×C4—31no—
196C23×C4—31no—
197C2×M16—62no—
198C4×D4—62no—
199C4×D4—62no—
200C2×C4⋊C4—31no—
201C2×C22⋊C4—31no—
202C2×C22⋊C4C2×C3×D311yescharacteristic
203C2×C42—31no—
204C22⋊C8—32no—
205C22⋊C8—62no—
206C22⋊C8C2×C3×D312yes—
207C23×C3—21no—
208C23×C3—21no—
209C23×C3—21no—
210C23×C3—21no—
211C23×C3—22no—
212C23×C3—21no—
213C23×C3—32no—
214C23×C3—41no—
215C23×C3—41no—
216C23×C3—41no—
217C23×C3—41no—
218C23×C3—41no—
219C23×C3—41no—
220C23×C3—61no—
221C23×C3—61no—
222C23×C3—81no—
223C23×C3—81no—
224C23×C3—121no—
225C23×C3—121no—
226C23×C3ΓL(1,𝔽25)12yescomplemented
227C23×C3C3×M1612yescomplemented
228C23×C3C2×C4×D311yescharacteristic
229C23×C3C22×C3×C411yescharacteristic
230C22×D3—21no—
231C22×D3—21no—
232C22×D3—41no—
233C22×D3—41no—
234C22×D3C3×C22⋊C412yes—
235C3×D4—68no—
236C2×C3×C4—21no—
237C2×C3×C4—21no—
238C2×C3×C4—22no—
239C2×C3×C4—31no—
240C2×C3×C4—31no—
241C2×C3×C4—32no—
242C2×C3×C4—41no—
243C2×C3×C4—41no—
244C2×C3×C4—41no—
245C2×C3×C4—41no—
246C2×C3×C4—41no—
247C2×C3×C4—64no—
248C2×C3×C4—62no—
249C2×C3×C4—61no—
250C2×C3×C4—61no—
251C2×C3×C4—61no—
252C2×C3×C4—81no—
253C2×C3×C4—81no—
254C2×C3×C4—122no—
255C2×C3×C4—122no—
256C2×C3×C4—122no—
257C2×C3×C4—121no—
258C2×C3×C4D3×D412yes—
259C2×C3×C4C2×C3×D412yes—
260#67—28no—
261C2×Dic3—21no—
262C2×Dic3—21no—
263C2×Dic3—22no—
264C2×Dic3—21no—
265C2×Dic3—42no—
266C2×Dic3—42no—
267C2×Dic3—41no—
268C2×Dic3C3×C22⋊C411yescharacteristic
269C2×Dic3C3×C22⋊C411yescharacteristic
270C2×Dic3C3×M1612yescomplemented
271C4×D3—24no—
272C4×D3—42no—
273C3×C8—42no—
274C3×C8—42no—
275C3×C8—82no—
276C3×C8—122no—
277C3⋊C8—42no—
278C2×C32—21no—
279C2×C32—21no—
280C2×C32—42no—
281C2×C32#40711yescharacteristic
282C2×C32C2×#9911yescharacteristic
283C2×C32#41311yescharacteristic
284C3×D3—42no—
285C24—31no—
286C24C3×C4×D311yescharacteristic
287C2×D4—62no—
288C2×D4—62no—
289C2×D4—62no—
290C22×C4—31no—
291C22×C4—31no—
292C22×C4—32no—
293C22×C4—32no—
294C22×C4—31no—
295C22×C4—61no—
296C22×C4—61no—
297C22×C4—122no—
298C22×C4—122no—
299C22×C4C3×C4×D311yescharacteristic
300C22×C4C22×C3×D311yescharacteristic
301M16—124no—
302C2×C8—22no—
303C2×C8—62no—
304C4⋊C4—62no—
305C22⋊C4—22no—
306C22⋊C4—62no—
307C42—61no—
308C42—61no—
309C22×C3—21no—
310C22×C3—21no—
311C22×C3—21no—
312C22×C3—21no—
313C22×C3—22no—
314C22×C3—22no—
315C22×C3—21no—
316C22×C3—21no—
317C22×C3—21no—
318C22×C3—41no—
319C22×C3—41no—
320C22×C3—42no—
321C22×C3—42no—
322C22×C3—42no—
323C22×C3—42no—
324C22×C3—42no—
325C22×C3—41no—
326C22×C3—41no—
327C22×C3—41no—
328C22×C3—41no—
329C22×C3—62no—
330C22×C3—62no—
331C22×C3—62no—
332C22×C3—81no—
333C22×C3—81no—
334C22×C3—82no—
335C22×C3—82no—
336C22×C3—122no—
337C22×C3—122no—
338C22×C3D3×C22⋊C411yescharacteristic
339C22×C3C2×ΓL(1,𝔽25)11yescharacteristic
340C22×C3D3×M1611yescharacteristic
341C22×C3C2×C3×C22⋊C411yescharacteristic
342C22×C3C2×C3×M1611yescharacteristic
343C22×C3C2×C3×M1611yescharacteristic
344C2×D3—22no—
345C2×D3—22no—
346C2×D3—22no—
347C2×D3—42no—
348C2×D3—42no—
349C3×C4—22no—
350C3×C4—22no—
351C3×C4—32no—
352C3×C4—42no—
353C3×C4—41no—
354C3×C4—41no—
355C3×C4—62no—
356C3×C4—61no—
357C3×C4—81no—
358C3×C4—121no—
359Dic3—22no—
360Dic3—21no—
361Dic3—41no—
362Dic3C3×#9912yes—
363C32#146511yescharacteristic, complemented, Sylow
364C23—21no—
365C23—21no—
366C23—32no—
367C23—41no—
368C23—41no—
369C23—61no—
370C23—61no—
371C23—121no—
372C23—121no—
373C23C3×ΓL(1,𝔽25)12yescomplemented
374C23C2×C3×C4×D311yescharacteristic
375D4—68no—
376C2×C4—21no—
377C2×C4—31no—
378C2×C4—31no—
379C2×C4—32no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—64no—
383C2×C4—62no—
384C2×C4—61no—
385C2×C4—61no—
386C2×C4—61no—
387C2×C4—122no—
388C2×C4—122no—
389C2×C4—122no—
390C2×C4—121no—
391C2×C4C3×D3×D412yes—
392C8—42no—
393C8—122no—
394C2×C3—21no—
395C2×C3—21no—
396C2×C3—21no—
397C2×C3—21no—
398C2×C3—21no—
399C2×C3—21no—
400C2×C3—21no—
401C2×C3—41no—
402C2×C3—41no—
403C2×C3—42no—
404C2×C3—42no—
405C2×C3—82no—
406C2×C3—122no—
407C2×C3#472611yescharacteristic
408C2×C3D3×#9911yescharacteristic
409C2×C3#474511yescharacteristic
410C2×C3C3×#40711yescharacteristic
411C2×C3C2×C3×#9911yescharacteristic
412C2×C3C3×#41311yescharacteristic
413D3—42no—
414C22—21no—
415C22—21no—
416C22—22no—
417C22—42no—
418C22—42no—
419C22—41no—
420C22—41no—
421C22—62no—
422C22—62no—
423C22—62no—
424C22—122no—
425C22—122no—
426C22C3×D3×C22⋊C411yescharacteristic
427C22C2×C3×ΓL(1,𝔽25)11yescharacteristic
428C22C3×D3×M1611yescharacteristic
429C4—22no—
430C4—32no—
431C4—41no—
432C4—62no—
433C4—61no—
434C4—121no—
435C3—21no—
436C3#6812111yescharacteristic, direct product factor
437C3C3×#146511yescharacteristic, complemented
438C2—21no—
439C2—21no—
440C2—42no—
441C2—122no—
442C2C3×#472611yescharacteristic
443C2C3×D3×#9911yescharacteristic
444C2C3×#474511yescharacteristic
subgroupG/H
centerC22×C3D3×C22⋊C4
commutatorC23×C3C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC32×#323C2
socleC22×C32C2×C22⋊C4
prime radicalC22×C3×#67C4
cosocleC22×C3×C4C23×C3
hypercenterC3×#323D3
hypocenterC3C3×#1465
LCSG ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#323

Complements

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

NH ≅ G/Ntype
2. C3×#4726C2semidirect
3. C32×#323C2semidirect
4. C3×#4525C2semidirect
5. C3×#4469C2semidirect
7. #68121C3direct (N × H)
24. #4726C2×C3semidirect
28. C3×#323D3semidirect
29. C3×#323C2×C3semidirect
30. #4525C2×C3semidirect
31. #4469C2×C3semidirect
89. C23×C32M16semidirect
110. C2×C3×Dic3M16semidirect
119. #323C3×D3semidirect
226. C23×C3ΓL(1,𝔽25)semidirect
227. C23×C3C3×M16semidirect
270. C2×Dic3C3×M16semidirect
363. C32#1465semidirect
373. C23C3×ΓL(1,𝔽25)semidirect
436. C3#68121direct (N × H)
437. C3C3×#1465semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#67⋊C42
C3×#47262
C32×#3232
C3×#45252
C3×#44692
C3×#14653
#681213