Finite Group Databasebeta

← C3×#71539 #11773852

Subgroups — C3×#71539 #11773852

Order 1152.

1217 conjugacy classes of subgroups.

The subgroup lattice has 451 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C32×C22⋊C4C211yesmaximal, characteristic
2C3×#5207C212yesmaximal, complemented
3C3×#4525C214yesmaximal, complemented
4C3×#1462—31nomaximal
5#71539C311yesmaximal, characteristic, direct product factor
6C25×C32C411yescharacteristic
7C23×C32×C4C411yescharacteristic
8C23×C32×C4C2211yescharacteristic
9C2×C32×C22⋊C4—22no—
10C2×C32×C22⋊C4—22no—
11C2×C32×C22⋊C4C412yes—
12C2×C32×C22⋊C4C2212yes—
13C2×C3×#208—22no—
14C3×#830—22no—
15C3×#830C2214yescomplemented
16C22×C3×C22⋊C4—21no—
17C22×C3×C22⋊C4D311yescharacteristic
18C22×C3×C22⋊C4C2×C311yescharacteristic
19C3×#407—32no—
20#5207C2×C312yescomplemented
21C3×#323—34no—
22#4525C2×C314yescomplemented
23C24×C32—21no—
24C24×C32—21no—
25C24×C32—24no—
26C24×C32—42no—
27C24×C32—42no—
28C24×C32C2×C411yescharacteristic
29C24×C32C2×C412yes—
30C22×C32×C4—21no—
31C22×C32×C4—21no—
32C22×C32×C4—42no—
33C22×C32×C4—42no—
34C22×C32×C4C2×C412yes—
35C22×C32×C4C2×C411yescharacteristic
36C22×C32×C4D412yes—
37C22×C32×C4D412yes—
38C22×C32×C4C2311yescharacteristic
39C32×C22⋊C4—24no—
40C32×C22⋊C4—24no—
41C3×#208—44no—
42C2×C3×C3⋊C8—24no—
43#1462—31noSylow
44C25×C3—21no—
45C25×C3Dic311yescharacteristic
46C25×C3C3×C411yescharacteristic
47C23×C3×C4—21no—
48C23×C3×C4—21no—
49C23×C3×C4Dic311yescharacteristic
50C23×C3×C4C3×C411yescharacteristic
51C23×C3×C4C2×D311yescharacteristic
52C23×C3×C4C22×C311yescharacteristic
53C2×C3×M16—62no—
54C2×C3×C22⋊C4—24no—
55C2×C3×C22⋊C4—24no—
56C2×C3×C22⋊C4—22no—
57C2×C3×C22⋊C4—22no—
58C2×C3×C22⋊C4—22no—
59C2×C3×C22⋊C4—22no—
60C2×C3×C22⋊C4—22no—
61C2×C3×C22⋊C4—22no—
62C2×C3×C22⋊C4Dic312yes—
63C2×C3×C22⋊C4C3×C412yes—
64C2×C3×C22⋊C4C2×D312yes—
65C2×C3×C22⋊C4C22×C312yes—
66C2×#208—22no—
67C3×C22⋊C8—34no—
68C3×C22⋊C8—62no—
69#830—22no—
70#830C22×C314yescomplemented
71C23×C32—22no—
72C23×C32—22no—
73C23×C32—22no—
74C23×C32—24no—
75C23×C32—24no—
76C23×C32—22no—
77C23×C32—22no—
78C23×C32—42no—
79C23×C32—42no—
80C23×C32—416no—
81C23×C32—42no—
82C23×C32—42no—
83C23×C32—42no—
84C23×C32—42no—
85C23×C32C22⋊C411yescharacteristic
86C23×C32C22⋊C411yescharacteristic
87C23×C32M1614yescomplemented
88C23×C32C22×C411yescharacteristic
89C2×C32×C4—22no—
90C2×C32×C4—24no—
91C2×C32×C4—41no—
92C2×C32×C4—42no—
93C2×C32×C4—41no—
94C2×C32×C4—42no—
95C2×C32×C4—42no—
96C2×C32×C4—42no—
97C2×C32×C4C22⋊C412yes—
98C2×C32×C4C2×D412yes—
99C3×C3⋊C8—44no—
100C22×C22⋊C4C3×D311yescharacteristic
101#407—32no—
102#323—34no—
103C24×C3—28no—
104C24×C3—22no—
105C24×C3—22no—
106C24×C3—24no—
107C24×C3—21no—
108C24×C3—21no—
109C24×C3—21no—
110C24×C3—21no—
111C24×C3—24no—
112C24×C3—21no—
113C24×C3—22no—
114C24×C3—42no—
115C24×C3—42no—
116C24×C3—42no—
117C24×C3—42no—
118C24×C3—44no—
119C24×C3—44no—
120C24×C3C2×Dic311yescharacteristic
121C24×C3C2×Dic312yes—
122C24×C3C2×C3×C411yescharacteristic
123C24×C3C2×C3×C412yes—
124C22×C3×C4—22no—
125C22×C3×C4—22no—
126C22×C3×C4—21no—
127C22×C3×C4—21no—
128C22×C3×C4—21no—
129C22×C3×C4—21no—
130C22×C3×C4—22no—
131C22×C3×C4—21no—
132C22×C3×C4—22no—
133C22×C3×C4—22no—
134C22×C3×C4—21no—
135C22×C3×C4—42no—
136C22×C3×C4—42no—
137C22×C3×C4—44no—
138C22×C3×C4—44no—
139C22×C3×C4—42no—
140C22×C3×C4—42no—
141C22×C3×C4C2×Dic312yes—
142C22×C3×C4C2×Dic311yescharacteristic
143C22×C3×C4#6712yes—
144C22×C3×C4#6712yes—
145C22×C3×C4C2×C3×C412yes—
146C22×C3×C4C2×C3×C411yescharacteristic
147C22×C3×C4C3×D412yes—
148C22×C3×C4C3×D412yes—
149C22×C3×C4C22×D311yescharacteristic
150C22×C3×C4C23×C311yescharacteristic
151C3×M16—124no—
152C2×C3×C8—64no—
153C3×C22⋊C4—28no—
154C3×C22⋊C4—28no—
155C3×C22⋊C4—24no—
156C3×C22⋊C4—24no—
157C3×C22⋊C4—24no—
158C3×C22⋊C4—24no—
159#208—44no—
160C2×C3⋊C8—24no—
161C22×C32—28no—
162C22×C32—21no—
163C22×C32—21no—
164C22×C32—21no—
165C22×C32—21no—
166C22×C32—21no—
167C22×C32—21no—
168C22×C32—24no—
169C22×C32—44no—
170C22×C32—48no—
171C22×C32—48no—
172C22×C32—44no—
173C22×C32—42no—
174C22×C32—42no—
175C22×C32#9912yes—
176C22×C32#10012yes—
177C22×C32C2×C22⋊C411yescharacteristic
178C22×C32C2×M1612yes—
179C32×C4—22no—
180C32×C4—22no—
181C32×C4—42no—
182C25C3×Dic311yescharacteristic
183C23×C4C3×Dic311yescharacteristic
184C23×C4C2×C3×D311yescharacteristic
185C2×M16—62no—
186C2×C22⋊C4—22no—
187C2×C22⋊C4—22no—
188C2×C22⋊C4C3×Dic312yes—
189C2×C22⋊C4C2×C3×D312yes—
190C22⋊C8—34no—
191C22⋊C8—62no—
192C23×C3—24no—
193C23×C3—24no—
194C23×C3—24no—
195C23×C3—22no—
196C23×C3—22no—
197C23×C3—22no—
198C23×C3—22no—
199C23×C3—22no—
200C23×C3—22no—
201C23×C3—24no—
202C23×C3—28no—
203C23×C3—28no—
204C23×C3—24no—
205C23×C3—24no—
206C23×C3—24no—
207C23×C3—24no—
208C23×C3—24no—
209C23×C3—22no—
210C23×C3—22no—
211C23×C3—22no—
212C23×C3—22no—
213C23×C3—24no—
214C23×C3—21no—
215C23×C3—21no—
216C23×C3—21no—
217C23×C3—42no—
218C23×C3—42no—
219C23×C3—42no—
220C23×C3—42no—
221C23×C3—44no—
222C23×C3—44no—
223C23×C3—44no—
224C23×C3—44no—
225C23×C3—416no—
226C23×C3—416no—
227C23×C3—432no—
228C23×C3—42no—
229C23×C3—42no—
230C23×C3—42no—
231C23×C3—42no—
232C23×C3—44no—
233C23×C3—44no—
234C23×C3—42no—
235C23×C3—42no—
236C23×C3—42no—
237C23×C3—42no—
238C23×C3#20814yescomplemented
239C23×C3#21711yescharacteristic
240C23×C3#21711yescharacteristic
241C23×C3C3×C22⋊C411yescharacteristic
242C23×C3C3×C22⋊C411yescharacteristic
243C23×C3C3×M1614yescomplemented
244C23×C3C22×Dic311yescharacteristic
245C23×C3C22×C3×C411yescharacteristic
246C2×C3×C4—24no—
247C2×C3×C4—24no—
248C2×C3×C4—24no—
249C2×C3×C4—22no—
250C2×C3×C4—22no—
251C2×C3×C4—22no—
252C2×C3×C4—22no—
253C2×C3×C4—44no—
254C2×C3×C4—41no—
255C2×C3×C4—42no—
256C2×C3×C4—41no—
257C2×C3×C4—42no—
258C2×C3×C4—41no—
259C2×C3×C4—41no—
260C2×C3×C4—42no—
261C2×C3×C4—44no—
262C2×C3×C4—42no—
263C2×C3×C4—44no—
264C2×C3×C4—42no—
265C2×C3×C4—42no—
266C2×C3×C4—44no—
267C2×C3×C4—44no—
268C2×C3×C4—42no—
269C2×C3×C4—42no—
270C2×C3×C4—42no—
271C2×C3×C4—42no—
272C2×C3×C4#21712yes—
273C2×C3×C4C3×C22⋊C412yes—
274C2×C3×C4C2×#6712yes—
275C2×C3×C4C2×C3×D412yes—
276C3×C8—124no—
277C3⋊C8—44no—
278C2×C32—22no—
279C2×C32—22no—
280C2×C32—22no—
281C2×C32—44no—
282C2×C32#40711yescharacteristic
283C2×C32C2×#9911yescharacteristic
284C2×C32C2×#10011yescharacteristic
285C24—24no—
286C24—21no—
287C24—21no—
288C24—42no—
289C24—42no—
290C24C2×C3×Dic311yescharacteristic
291C24C2×C3×Dic312yes—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—42no—
295C22×C4—42no—
296C22×C4C2×C3×Dic312yes—
297C22×C4C2×C3×Dic311yescharacteristic
298C22×C4C3×#6712yes—
299C22×C4C3×#6712yes—
300C22×C4C22×C3×D311yescharacteristic
301M16—124no—
302C2×C8—64no—
303C22⋊C4—24no—
304C22⋊C4—24no—
305C22×C3—22no—
306C22×C3—22no—
307C22×C3—22no—
308C22×C3—22no—
309C22×C3—22no—
310C22×C3—22no—
311C22×C3—216no—
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—28no—
327C22×C3—24no—
328C22×C3—24no—
329C22×C3—22no—
330C22×C3—21no—
331C22×C3—22no—
332C22×C3—22no—
333C22×C3—44no—
334C22×C3—44no—
335C22×C3—48no—
336C22×C3—48no—
337C22×C3—416no—
338C22×C3—416no—
339C22×C3—48no—
340C22×C3—48no—
341C22×C3—44no—
342C22×C3—48no—
343C22×C3—48no—
344C22×C3—44no—
345C22×C3—44no—
346C22×C3—44no—
347C22×C3—42no—
348C22×C3—42no—
349C22×C3—42no—
350C22×C3—42no—
351C22×C3#83312yes—
352C22×C3#83412yes—
353C22×C3C3×#9912yes—
354C22×C3C3×#10012yes—
355C22×C3C2×#20812yes—
356C22×C3C2×#21711yescharacteristic
357C22×C3C2×C3×C22⋊C411yescharacteristic
358C22×C3C2×C3×M1612yes—
359C3×C4—22no—
360C3×C4—22no—
361C3×C4—22no—
362C3×C4—22no—
363C3×C4—42no—
364C3×C4—42no—
365C3×C4—44no—
366C3×C4—42no—
367C3×C4—42no—
368C32#146211yescharacteristic, complemented, Sylow
369C23—22no—
370C23—22no—
371C23—22no—
372C23—24no—
373C23—24no—
374C23—22no—
375C23—22no—
376C23—42no—
377C23—42no—
378C23—416no—
379C23—42no—
380C23—42no—
381C23—42no—
382C23—42no—
383C23C3×#20814yescomplemented
384C23C3×#21711yescharacteristic
385C23C3×#21711yescharacteristic
386C23C22×C3×Dic311yescharacteristic
387C2×C4—24no—
388C2×C4—22no—
389C2×C4—41no—
390C2×C4—42no—
391C2×C4—41no—
392C2×C4—42no—
393C2×C4—42no—
394C2×C4—42no—
395C2×C4C3×#21712yes—
396C2×C4C2×C3×#6712yes—
397C8—124no—
398C2×C3—24no—
399C2×C3—24no—
400C2×C3—24no—
401C2×C3—22no—
402C2×C3—22no—
403C2×C3—22no—
404C2×C3—22no—
405C2×C3—22no—
406C2×C3—22no—
407C2×C3—21no—
408C2×C3—21no—
409C2×C3—21no—
410C2×C3—48no—
411C2×C3—44no—
412C2×C3—44no—
413C2×C3#520711yescharacteristic
414C2×C3C2×#83311yescharacteristic
415C2×C3C2×#83411yescharacteristic
416C2×C3C3×#40711yescharacteristic
417C2×C3C2×C3×#9911yescharacteristic
418C2×C3C2×C3×#10011yescharacteristic
419C22—28no—
420C22—21no—
421C22—21no—
422C22—21no—
423C22—21no—
424C22—21no—
425C22—21no—
426C22—24no—
427C22—44no—
428C22—44no—
429C22—48no—
430C22—48no—
431C22—42no—
432C22—42no—
433C22C3×#83312yes—
434C22C3×#83412yes—
435C22C2×C3×#20812yes—
436C22C2×C3×#21711yescharacteristic
437C4—22no—
438C4—22no—
439C4—42no—
440C3—21no—
441C3#7153911yescharacteristic, direct product factor
442C3C3×#146211yescharacteristic, complemented
443C2—22no—
444C2—22no—
445C2—22no—
446C2—44no—
447C2C3×#520711yescharacteristic
448C2C2×C3×#83311yescharacteristic
449C2C2×C3×#83411yescharacteristic
subgroupG/H
centerC22×C3C2×#217
commutatorC23×C3C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC22×C32×C22⋊C4C2
socleC22×C32C2×C22⋊C4
prime radicalC25×C32C4
cosocleC22×C3×C4C23×C3
hypercenterC22×C3×C22⋊C4D3
hypocenterC3C3×#1462
LCSG ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C23×C3×C4 ◁ C22×C3×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C3×#5207C2semidirect
3. C3×#4525C2semidirect
5. #71539C3direct (N × H)
15. C3×#830C22semidirect
20. #5207C2×C3semidirect
22. #4525C2×C3semidirect
70. #830C22×C3semidirect
87. C23×C32M16semidirect
238. C23×C3#208semidirect
243. C23×C3C3×M16semidirect
368. C32#1462semidirect
383. C23C3×#208semidirect
441. C3#71539direct (N × H)
442. C3C3×#1462semidirect

Maximal subgroups

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

subgroupindex
C22×C32×C22⋊C42
C3×#52072
C3×#45252
C3×#14623
#715393