Finite Group Databasebeta

← C3×#69971 #11773869

Subgroups — C3×#69971 #11773869

Order 1152.

719 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×Dic3⋊C4C211yesmaximal, characteristic
2C32×#407C211yesmaximal, characteristic
3C3×#5207C211yesmaximal, characteristic
4C3×#4469C214yesmaximal, complemented
5C3×#1463—31nomaximal
6#69971C311yesmaximal, characteristic, direct product factor
7C23×C32×C4C2211yescharacteristic
8C23×C3×Dic3C411yescharacteristic
9C23×C3×Dic3C411yescharacteristic
10C2×C32×M16—21no—
11C2×C3×Dic3⋊C4—21no—
12C2×C3×Dic3⋊C4—21no—
13C2×C3×Dic3⋊C4—21no—
14C2×C3×Dic3⋊C4—21no—
15C2×C3×Dic3⋊C4C412yes—
16C2×C3×Dic3⋊C4C2212yes—
17C2×C3×#208—21no—
18C32×C22⋊C8—21no—
19C32×C22⋊C8C2212yes—
20C3×#830—21no—
21C3×#830C2212yes—
22C22×C3×C4⋊C4—31no—
23C22×Dic3⋊C4C2×C311yescharacteristic
24C3×#407—21no—
25C3×#407—31no—
26C3×#407D311yescharacteristic
27C3×#407C2×C311yescharacteristic
28#5207C2×C311yescharacteristic
29C3×#324—34no—
30#4469C2×C314yescomplemented
31C24×C32C2×C411yescharacteristic
32C22×C32×C4—42no—
33C22×C32×C4C2×C411yescharacteristic
34C22×C32×C4D411yescharacteristic
35C22×C32×C4D411yescharacteristic
36C22×C32×C4D411yescharacteristic
37C22×C32×C4D411yescharacteristic
38C22×C32×C4C2311yescharacteristic
39C22×C3×Dic3—21no—
40C22×C3×Dic3—21no—
41C22×C3×Dic3—24no—
42C22×C3×Dic3—21no—
43C22×C3×Dic3—21no—
44C22×C3×Dic3—42no—
45C22×C3×Dic3C2×C412yes—
46C22×C3×Dic3C2×C412yes—
47C32×M16—42no—
48C2×C32×C8—22no—
49C3×Dic3⋊C4—22no—
50C3×Dic3⋊C4—22no—
51C3×Dic3⋊C4—22no—
52C3×Dic3⋊C4—22no—
53C3×#208—42no—
54C2×C3×C3⋊C8—22no—
55#1463—31noSylow
56C23×C3×C4—21no—
57C23×C3×C4—31no—
58C23×C3×C4—31no—
59C23×C3×C4C2×D311yescharacteristic
60C23×C3×C4C22×C311yescharacteristic
61C23×Dic3C3×C411yescharacteristic
62C23×Dic3C3×C411yescharacteristic
63C2×C3×M16—22no—
64C2×C3×M16—21no—
65C2×C3×M16—21no—
66C2×C3×M16—61no—
67C2×C3×C4⋊C4—32no—
68C2×C3×C4⋊C4—32no—
69C2×C3×C4⋊C4—61no—
70C2×C3×C4⋊C4—61no—
71C2×C3×C4⋊C4—61no—
72C2×C3×C4⋊C4—61no—
73C2×Dic3⋊C4—21no—
74C2×Dic3⋊C4—21no—
75C2×Dic3⋊C4—21no—
76C2×Dic3⋊C4—21no—
77C2×Dic3⋊C4C3×C412yes—
78C2×Dic3⋊C4C22×C312yes—
79C2×#208—21no—
80C3×C22⋊C8—22no—
81C3×C22⋊C8—21no—
82C3×C22⋊C8—21no—
83C3×C22⋊C8—22no—
84C3×C22⋊C8—32no—
85C3×C22⋊C8—61no—
86C3×C22⋊C8C2×D312yes—
87C3×C22⋊C8C22×C312yes—
88#830—21no—
89#830C22×C312yes—
90C23×C32—22no—
91C23×C32—22no—
92C23×C32—22no—
93C23×C32C22⋊C411yescharacteristic
94C23×C32C22⋊C411yescharacteristic
95C23×C32C22×C411yescharacteristic
96C2×C32×C4—22no—
97C2×C32×C4—22no—
98C2×C32×C4—41no—
99C2×C32×C4—41no—
100C2×C32×C4—41no—
101C2×C32×C4—41no—
102C2×C32×C4C22⋊C411yescharacteristic
103C2×C32×C4C22⋊C411yescharacteristic
104C2×C32×C4C2×D411yescharacteristic
105C2×C32×C4C2×D411yescharacteristic
106C2×C3×Dic3—24no—
107C2×C3×Dic3—24no—
108C2×C3×Dic3—22no—
109C2×C3×Dic3—22no—
110C2×C3×Dic3—22no—
111C2×C3×Dic3—42no—
112C2×C3×Dic3—42no—
113C2×C3×Dic3—42no—
114C2×C3×Dic3M1614yescomplemented
115C32×C8—42no—
116C3×C3⋊C8—42no—
117C22×C4⋊C4—31no—
118#407—31no—
119#407C3×D311yescharacteristic
120#324—34no—
121C24×C3—21no—
122C24×C3C4×D311yescharacteristic
123C24×C3C2×C3×C411yescharacteristic
124C22×C3×C4—21no—
125C22×C3×C4—21no—
126C22×C3×C4—21no—
127C22×C3×C4—21no—
128C22×C3×C4—21no—
129C22×C3×C4—21no—
130C22×C3×C4—32no—
131C22×C3×C4—32no—
132C22×C3×C4—42no—
133C22×C3×C4—42no—
134C22×C3×C4—44no—
135C22×C3×C4—64no—
136C22×C3×C4—61no—
137C22×C3×C4—61no—
138C22×C3×C4—61no—
139C22×C3×C4—61no—
140C22×C3×C4—122no—
141C22×C3×C4C4×D311yescharacteristic
142C22×C3×C4D1211yescharacteristic
143C22×C3×C4D1211yescharacteristic
144C22×C3×C4#6711yescharacteristic
145C22×C3×C4#6711yescharacteristic
146C22×C3×C4C2×C3×C411yescharacteristic
147C22×C3×C4C3×D411yescharacteristic
148C22×C3×C4C3×D411yescharacteristic
149C22×C3×C4C3×D411yescharacteristic
150C22×C3×C4C3×D411yescharacteristic
151C22×C3×C4C22×D311yescharacteristic
152C22×C3×C4C23×C311yescharacteristic
153C22×Dic3—21no—
154C22×Dic3—21no—
155C22×Dic3—24no—
156C22×Dic3—21no—
157C22×Dic3—21no—
158C22×Dic3—42no—
159C22×Dic3C2×C3×C412yes—
160C22×Dic3C2×C3×C412yes—
161C3×M16—44no—
162C3×M16—42no—
163C3×M16—42no—
164C3×M16—122no—
165C2×C3×C8—24no—
166C2×C3×C8—22no—
167C2×C3×C8—22no—
168C2×C3×C8—62no—
169C3×C4⋊C4—62no—
170C3×C4⋊C4—62no—
171C3×C4⋊C4—62no—
172C3×C4⋊C4—62no—
173Dic3⋊C4—22no—
174Dic3⋊C4—22no—
175Dic3⋊C4—22no—
176Dic3⋊C4—22no—
177#208—42no—
178C2×C3⋊C8—22no—
179C22×C32—28no—
180C22×C32—21no—
181C22×C32—21no—
182C22×C32—21no—
183C22×C32—21no—
184C22×C32—21no—
185C22×C32—21no—
186C22×C32#9912yes—
187C22×C32#10112yes—
188C22×C32C2×C22⋊C411yescharacteristic
189C22×C32C2×M1612yes—
190C32×C4—21no—
191C32×C4—21no—
192C32×C4—21no—
193C32×C4—21no—
194C3×Dic3—24no—
195C3×Dic3—42no—
196C23×C4—31no—
197C23×C4—31no—
198C23×C4C2×C3×D311yescharacteristic
199C2×M16—21no—
200C2×M16—61no—
201C2×C4⋊C4—32no—
202C2×C4⋊C4—32no—
203C2×C4⋊C4—61no—
204C2×C4⋊C4—61no—
205C2×C4⋊C4—61no—
206C2×C4⋊C4—61no—
207C22⋊C8—21no—
208C22⋊C8—32no—
209C22⋊C8—61no—
210C22⋊C8C2×C3×D312yes—
211C23×C3—22no—
212C23×C3—22no—
213C23×C3—22no—
214C23×C3—22no—
215C23×C3—22no—
216C23×C3—22no—
217C23×C3—21no—
218C23×C3—21no—
219C23×C3—21no—
220C23×C3—42no—
221C23×C3—42no—
222C23×C3—42no—
223C23×C3(C2×D3)⋊C411yescharacteristic
224C23×C3(C2×D3)⋊C411yescharacteristic
225C23×C3C3×C22⋊C411yescharacteristic
226C23×C3C3×C22⋊C411yescharacteristic
227C23×C3C2×C4×D311yescharacteristic
228C23×C3C22×C3×C411yescharacteristic
229C2×C3×C4—24no—
230C2×C3×C4—22no—
231C2×C3×C4—22no—
232C2×C3×C4—22no—
233C2×C3×C4—22no—
234C2×C3×C4—21no—
235C2×C3×C4—21no—
236C2×C3×C4—21no—
237C2×C3×C4—21no—
238C2×C3×C4—34no—
239C2×C3×C4—42no—
240C2×C3×C4—41no—
241C2×C3×C4—41no—
242C2×C3×C4—41no—
243C2×C3×C4—41no—
244C2×C3×C4—41no—
245C2×C3×C4—41no—
246C2×C3×C4—41no—
247C2×C3×C4—41no—
248C2×C3×C4—42no—
249C2×C3×C4—42no—
250C2×C3×C4—42no—
251C2×C3×C4—42no—
252C2×C3×C4—64no—
253C2×C3×C4—64no—
254C2×C3×C4—62no—
255C2×C3×C4—62no—
256C2×C3×C4—62no—
257C2×C3×C4—122no—
258C2×C3×C4—122no—
259C2×C3×C4—122no—
260C2×C3×C4(C2×D3)⋊C411yescharacteristic
261C2×C3×C4(C2×D3)⋊C411yescharacteristic
262C2×C3×C4C3×C22⋊C411yescharacteristic
263C2×C3×C4C3×C22⋊C411yescharacteristic
264C2×C3×C4C2×D1211yescharacteristic
265C2×C3×C4C2×#6711yescharacteristic
266C2×C3×C4C2×C3×D411yescharacteristic
267C2×C3×C4C2×C3×D411yescharacteristic
268C2×Dic3—24no—
269C2×Dic3—24no—
270C2×Dic3—22no—
271C2×Dic3—22no—
272C2×Dic3—22no—
273C2×Dic3—42no—
274C2×Dic3—42no—
275C2×Dic3—42no—
276C2×Dic3C3×M1614yescomplemented
277C3×C8—44no—
278C3×C8—42no—
279C3×C8—42no—
280C3×C8—122no—
281C3⋊C8—42no—
282C2×C32—22no—
283C2×C32—22no—
284C2×C32—22no—
285C2×C32#40711yescharacteristic
286C2×C32C2×#9911yescharacteristic
287C2×C32C2×#10111yescharacteristic
288C24C3×C4×D311yescharacteristic
289C22×C4—32no—
290C22×C4—32no—
291C22×C4—42no—
292C22×C4—64no—
293C22×C4—61no—
294C22×C4—61no—
295C22×C4—61no—
296C22×C4—61no—
297C22×C4—122no—
298C22×C4C3×C4×D311yescharacteristic
299C22×C4C3×D1211yescharacteristic
300C22×C4C3×D1211yescharacteristic
301C22×C4C3×#6711yescharacteristic
302C22×C4C3×#6711yescharacteristic
303C22×C4C22×C3×D311yescharacteristic
304M16—42no—
305M16—122no—
306C2×C8—22no—
307C2×C8—62no—
308C4⋊C4—62no—
309C4⋊C4—62no—
310C4⋊C4—62no—
311C4⋊C4—62no—
312C22×C3—28no—
313C22×C3—28no—
314C22×C3—21no—
315C22×C3—21no—
316C22×C3—21no—
317C22×C3—21no—
318C22×C3—21no—
319C22×C3—21no—
320C22×C3—21no—
321C22×C3—21no—
322C22×C3—21no—
323C22×C3—21no—
324C22×C3—21no—
325C22×C3—21no—
326C22×C3—22no—
327C22×C3—21no—
328C22×C3—22no—
329C22×C3—22no—
330C22×C3—41no—
331C22×C3—41no—
332C22×C3—41no—
333C22×C3—41no—
334C22×C3—41no—
335C22×C3—41no—
336C22×C3—48no—
337C22×C3#80612yes—
338C22×C3#82412yes—
339C22×C3C3×#9912yes—
340C22×C3C3×#10112yes—
341C22×C3D3×M1612yes—
342C22×C3C2×(C2×D3)⋊C411yescharacteristic
343C22×C3C2×C3×C22⋊C411yescharacteristic
344C22×C3C2×C3×M1612yes—
345C3×C4—22no—
346C3×C4—22no—
347C3×C4—21no—
348C3×C4—21no—
349C3×C4—21no—
350C3×C4—21no—
351C3×C4—21no—
352C3×C4—21no—
353C3×C4—21no—
354C3×C4—21no—
355C3×C4—41no—
356C3×C4—41no—
357C3×C4—64no—
358C3×C4—122no—
359Dic3—24no—
360Dic3—42no—
361C32#146311yescharacteristic, complemented, Sylow
362C23—22no—
363C23—22no—
364C23—22no—
365C23C3×(C2×D3)⋊C411yescharacteristic
366C23C3×(C2×D3)⋊C411yescharacteristic
367C23C2×C3×C4×D311yescharacteristic
368C2×C4—22no—
369C2×C4—22no—
370C2×C4—34no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—64no—
376C2×C4—64no—
377C2×C4—62no—
378C2×C4—62no—
379C2×C4—62no—
380C2×C4—122no—
381C2×C4—122no—
382C2×C4—122no—
383C2×C4C3×(C2×D3)⋊C411yescharacteristic
384C2×C4C3×(C2×D3)⋊C411yescharacteristic
385C2×C4C2×C3×D1211yescharacteristic
386C2×C4C2×C3×#6711yescharacteristic
387C8—42no—
388C8—122no—
389C2×C3—22no—
390C2×C3—22no—
391C2×C3—22no—
392C2×C3—22no—
393C2×C3—22no—
394C2×C3—22no—
395C2×C3—21no—
396C2×C3—21no—
397C2×C3—21no—
398C2×C3—42no—
399C2×C3—42no—
400C2×C3—42no—
401C2×C3C2×#80611yescharacteristic
402C2×C3#512611yescharacteristic
403C2×C3C2×#82411yescharacteristic
404C2×C3C3×#40711yescharacteristic
405C2×C3C2×C3×#9911yescharacteristic
406C2×C3C2×C3×#10111yescharacteristic
407C22—28no—
408C22—21no—
409C22—21no—
410C22—21no—
411C22—21no—
412C22—21no—
413C22—21no—
414C22C3×#80612yes—
415C22C3×#82412yes—
416C22C3×D3×M1612yes—
417C22C2×C3×(C2×D3)⋊C411yescharacteristic
418C4—21no—
419C4—21no—
420C4—21no—
421C4—21no—
422C4—64no—
423C4—122no—
424C3—21no—
425C3#6997111yescharacteristic, direct product factor
426C3C3×#146311yescharacteristic, complemented
427C2—22no—
428C2—22no—
429C2—22no—
430C2C2×C3×#80611yescharacteristic
431C2C3×#512611yescharacteristic
432C2C2×C3×#82411yescharacteristic
subgroupG/H
centerC22×C3C2×(C2×D3)⋊C4
commutatorC23×C3C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC32×#407C2
socleC22×C32C2×C22⋊C4
prime radicalC24×C32C2×C4
cosocleC22×C3×C4C23×C3
hypercenterC3×#407D3
hypocenterC3C3×#1463
LCSG ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C23×C3×C4 ◁ C3×#407

Complements

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

NH ≅ G/Ntype
4. C3×#4469C2semidirect
6. #69971C3direct (N × H)
30. #4469C2×C3semidirect
114. C2×C3×Dic3M16semidirect
276. C2×Dic3C3×M16semidirect
361. C32#1463semidirect
425. C3#69971direct (N × H)
426. C3C3×#1463semidirect

Maximal subgroups

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

subgroupindex
C22×C3×Dic3⋊C42
C32×#4072
C3×#52072
C3×#44692
C3×#14633
#699713