Finite Group Databasebeta

← C3×#69450 #11786393

Subgroups — C3×#69450 #11786393

Order 1152.

777 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#208C211yesmaximal, characteristic
2C32×C4×C22⋊C4C211yesmaximal, characteristic
3C2×C3×#830C211yesmaximal, characteristic
4C2×C3×C4⋊(C3⋊C8)C212yesmaximal, complemented
5C3×#4524C212yesmaximal, complemented
6C3×#1851—31nomaximal
7#69450C311yesmaximal, characteristic, direct product factor
8C23×C32×C4C2211yescharacteristic
9C2×C32×C22⋊C4C412yes—
10C2×C32×C42C2212yes—
11C2×C3×#208—22no—
12C2×C3×#208—24no—
13C22×C3×C3⋊C8C2211yescharacteristic
14C22×C3×C3⋊C8C2211yescharacteristic
15C22×C3×C3⋊C8C2212yes—
16C32×#95C411yescharacteristic
17C32×#95C411yescharacteristic
18C3×#830—22no—
19C3×C4⋊(C3⋊C8)—24no—
20C22×C3×M16—31no—
21C22×#208C2×C311yescharacteristic
22C2×C3×C4⋊C8—32no—
23C2×C3×C22⋊C8—31no—
24C3×C4×C22⋊C4—21no—
25C3×C4×C22⋊C4D311yescharacteristic
26C3×C4×C22⋊C4C2×C311yescharacteristic
27C2×#830C2×C311yescharacteristic
28C2×C4⋊(C3⋊C8)C2×C312yescomplemented
29C3×#336—32no—
30#4524C2×C312yescomplemented
31C24×C32C2×C411yescharacteristic
32C22×C32×C4—22no—
33C22×C32×C4—22no—
34C22×C32×C4C2×C412yes—
35C22×C32×C4C2×C411yescharacteristic
36C22×C32×C4C2×C412yes—
37C22×C32×C4D412yes—
38C22×C32×C4Q812yes—
39C22×C32×C4C2311yescharacteristic
40C32×C22⋊C4—24no—
41C32×C42—22no—
42C32×C42—22no—
43C3×#208—28no—
44C2×C3×C3⋊C8—22no—
45C2×C3×C3⋊C8—22no—
46C2×C3×C3⋊C8—22no—
47C2×C3×C3⋊C8—21no—
48C2×C3×C3⋊C8—21no—
49C2×C3×C3⋊C8—22no—
50C2×C3×C3⋊C8D414yes—
51#1851—31noSylow
52C23×C3×C4—21no—
53C23×C3×C4C2×D311yescharacteristic
54C23×C3×C4C22×C311yescharacteristic
55C2×C3×M16—64no—
56C2×C3×M16—62no—
57C22×C3×C8—32no—
58C22×C3×C8—31no—
59C22×C3×C8—31no—
60C2×C3×C22⋊C4—22no—
61C2×C3×C22⋊C4Dic312yes—
62C2×C3×C22⋊C4C3×C412yes—
63C2×C3×C42—22no—
64C2×C3×C42C2×D312yes—
65C2×C3×C42C22×C312yes—
66C2×#208—22no—
67C2×#208—24no—
68C22×C3⋊C8C22×C311yescharacteristic
69C22×C3⋊C8C22×C311yescharacteristic
70C22×C3⋊C8C22×C312yes—
71C3×C4⋊C8—64no—
72C3×C22⋊C8—62no—
73C3×#95—21no—
74C3×#95—21no—
75C3×#95Dic311yescharacteristic
76C3×#95Dic311yescharacteristic
77C3×#95C3×C411yescharacteristic
78C3×#95C3×C411yescharacteristic
79#830—22no—
80C4⋊(C3⋊C8)—24no—
81C23×C32—22no—
82C23×C32—22no—
83C23×C32—21no—
84C23×C32—21no—
85C23×C32C4⋊C412yes—
86C23×C32C22×C411yescharacteristic
87C2×C32×C4—22no—
88C2×C32×C4—22no—
89C2×C32×C4—22no—
90C2×C32×C4—22no—
91C2×C32×C4—22no—
92C2×C32×C4—24no—
93C2×C32×C4—22no—
94C2×C32×C4—22no—
95C2×C32×C4—22no—
96C2×C32×C4C4⋊C412yes—
97C2×C32×C4M1614yescomplemented
98C2×C32×C4C2×D411yescharacteristic
99C2×C32×C4C2×D412yes—
100C2×C32×C4C2×Q811yescharacteristic
101C2×C32×C4#4112yes—
102C3×C3⋊C8—24no—
103C3×C3⋊C8—41no—
104C3×C3⋊C8—41no—
105C22×M16—31no—
106C2×C4⋊C8—32no—
107C2×C22⋊C8—31no—
108C4×C22⋊C4C3×D311yescharacteristic
109#336—32no—
110C24×C3—21no—
111C24×C3C2×Dic311yescharacteristic
112C24×C3C2×C3×C411yescharacteristic
113C22×C3×C4—22no—
114C22×C3×C4—22no—
115C22×C3×C4—22no—
116C22×C3×C4—22no—
117C22×C3×C4—22no—
118C22×C3×C4—22no—
119C22×C3×C4—21no—
120C22×C3×C4—22no—
121C22×C3×C4—22no—
122C22×C3×C4—21no—
123C22×C3×C4—42no—
124C22×C3×C4—42no—
125C22×C3×C4Dic612yes—
126C22×C3×C4D1212yes—
127C22×C3×C4C2×Dic312yes—
128C22×C3×C4C2×Dic312yes—
129C22×C3×C4C2×Dic311yescharacteristic
130C22×C3×C4C2×C3×C412yes—
131C22×C3×C4C2×C3×C411yescharacteristic
132C22×C3×C4C2×C3×C412yes—
133C22×C3×C4C3×D412yes—
134C22×C3×C4C3×Q812yes—
135C22×C3×C4C22×D311yescharacteristic
136C22×C3×C4C23×C311yescharacteristic
137C3×M16—68no—
138C2×C3×C8—34no—
139C2×C3×C8—62no—
140C2×C3×C8—62no—
141C2×C3×C8—61no—
142C2×C3×C8—61no—
143C2×C3×C8—62no—
144C2×C3×C8—62no—
145C3×C22⋊C4—28no—
146C3×C22⋊C4—24no—
147C3×C22⋊C4—24no—
148C3×C42—22no—
149C3×C42—22no—
150C3×C42—22no—
151C3×C42—22no—
152C3×C42—42no—
153C3×C42—42no—
154#208—28no—
155C2×C3⋊C8—22no—
156C2×C3⋊C8—22no—
157C2×C3⋊C8—22no—
158C2×C3⋊C8—21no—
159C2×C3⋊C8—21no—
160C2×C3⋊C8—22no—
161C2×C3⋊C8C3×D414yes—
162C22×C32—22no—
163C22×C32—22no—
164C22×C32—22no—
165C22×C32—42no—
166C22×C32—42no—
167C22×C32C2×C4⋊C411yescharacteristic
168C22×C32C4×D412yes—
169C22×C32C2×M1612yes—
170C22×C32#13111yescharacteristic
171C22×C32#13111yescharacteristic
172C32×C4—22no—
173C32×C4—24no—
174C32×C4—42no—
175C32×C4#12011yescharacteristic
176C32×C4C22⋊Q812yes—
177C32×C4#12311yescharacteristic
178C23×C4C2×C3×D311yescharacteristic
179C2×M16—64no—
180C2×M16—62no—
181C22×C8—32no—
182C22×C8—31no—
183C22×C8—31no—
184C2×C22⋊C4C3×Dic312yes—
185C2×C42C2×C3×D312yes—
186C4⋊C8—64no—
187C22⋊C8—62no—
188#95C3×Dic311yescharacteristic
189#95C3×Dic311yescharacteristic
190C23×C3—24no—
191C23×C3—22no—
192C23×C3—22no—
193C23×C3—21no—
194C23×C3—21no—
195C23×C3—22no—
196C23×C3—22no—
197C23×C3—21no—
198C23×C3—21no—
199C23×C3—22no—
200C23×C3—21no—
201C23×C3—42no—
202C23×C3—41no—
203C23×C3—41no—
204C23×C3C4⋊Dic312yes—
205C23×C3C3×C4⋊C412yes—
206C23×C3C22×Dic311yescharacteristic
207C23×C3C22×C3×C411yescharacteristic
208C2×C3×C4—22no—
209C2×C3×C4—22no—
210C2×C3×C4—22no—
211C2×C3×C4—22no—
212C2×C3×C4—22no—
213C2×C3×C4—22no—
214C2×C3×C4—24no—
215C2×C3×C4—22no—
216C2×C3×C4—22no—
217C2×C3×C4—22no—
218C2×C3×C4—24no—
219C2×C3×C4—22no—
220C2×C3×C4—24no—
221C2×C3×C4—22no—
222C2×C3×C4—22no—
223C2×C3×C4—22no—
224C2×C3×C4—22no—
225C2×C3×C4—22no—
226C2×C3×C4—22no—
227C2×C3×C4—24no—
228C2×C3×C4—22no—
229C2×C3×C4—21no—
230C2×C3×C4—21no—
231C2×C3×C4—22no—
232C2×C3×C4—22no—
233C2×C3×C4—44no—
234C2×C3×C4—42no—
235C2×C3×C4—42no—
236C2×C3×C4—42no—
237C2×C3×C4—42no—
238C2×C3×C4—42no—
239C2×C3×C4—42no—
240C2×C3×C4—42no—
241C2×C3×C4#20814yescomplemented
242C2×C3×C4C4⋊Dic312yes—
243C2×C3×C4C3×C4⋊C412yes—
244C2×C3×C4C3×M1614yescomplemented
245C2×C3×C4C2×Dic611yescharacteristic
246C2×C3×C4C2×D1211yescharacteristic
247C2×C3×C4D3×D412yes—
248C2×C3×C4#23712yes—
249C2×C3×C4C2×C3×D411yescharacteristic
250C2×C3×C4C2×C3×D412yes—
251C2×C3×C4C2×C3×Q811yescharacteristic
252C2×C3×C4C3×#4112yes—
253C3×C8—64no—
254C3×C8—121no—
255C3×C8—121no—
256C3⋊C8—24no—
257C3⋊C8—41no—
258C3⋊C8—41no—
259C2×C32—42no—
260C2×C32#38511yescharacteristic
261C2×C32#42311yescharacteristic
262C2×C32#42411yescharacteristic
263C2×C32#43512yes—
264C2×C32#43612yes—
265C24C2×C3×Dic311yescharacteristic
266C22×C4—22no—
267C22×C4—22no—
268C22×C4C3×Dic612yes—
269C22×C4C3×D1212yes—
270C22×C4C2×C3×Dic312yes—
271C22×C4C2×C3×Dic312yes—
272C22×C4C2×C3×Dic311yescharacteristic
273C22×C4C22×C3×D311yescharacteristic
274M16—68no—
275C2×C8—34no—
276C2×C8—62no—
277C2×C8—62no—
278C2×C8—61no—
279C2×C8—61no—
280C2×C8—62no—
281C2×C8—62no—
282C22⋊C4—24no—
283C42—22no—
284C42—22no—
285C22×C3—24no—
286C22×C3—22no—
287C22×C3—22no—
288C22×C3—22no—
289C22×C3—22no—
290C22×C3—22no—
291C22×C3—22no—
292C22×C3—22no—
293C22×C3—21no—
294C22×C3—22no—
295C22×C3—21no—
296C22×C3—21no—
297C22×C3—42no—
298C22×C3—42no—
299C22×C3—44no—
300C22×C3—44no—
301C22×C3—42no—
302C22×C3—42no—
303C22×C3—42no—
304C22×C3—42no—
305C22×C3C2×#20812yes—
306C22×C3C2×C4⋊Dic311yescharacteristic
307C22×C3D4×Dic312yes—
308C22×C3#94811yescharacteristic
309C22×C3#94811yescharacteristic
310C22×C3C2×C3×C4⋊C411yescharacteristic
311C22×C3C3×C4×D412yes—
312C22×C3C2×C3×M1612yes—
313C22×C3C3×#13111yescharacteristic
314C22×C3C3×#13111yescharacteristic
315C3×C4—22no—
316C3×C4—22no—
317C3×C4—24no—
318C3×C4—24no—
319C3×C4—22no—
320C3×C4—21no—
321C3×C4—21no—
322C3×C4—42no—
323C3×C4—44no—
324C3×C4—44no—
325C3×C4—42no—
326C3×C4—42no—
327C3×C4#87812yes—
328C3×C4#88211yescharacteristic
329C3×C4#88611yescharacteristic
330C3×C4C3×#12011yescharacteristic
331C3×C4C3×C22⋊Q812yes—
332C3×C4C3×#12311yescharacteristic
333C32#185111yescharacteristic, complemented, Sylow
334C23—22no—
335C23—22no—
336C23—21no—
337C23—21no—
338C23C3×C4⋊Dic312yes—
339C23C22×C3×Dic311yescharacteristic
340C2×C4—22no—
341C2×C4—22no—
342C2×C4—22no—
343C2×C4—24no—
344C2×C4—22no—
345C2×C4—22no—
346C2×C4—22no—
347C2×C4—22no—
348C2×C4—22no—
349C2×C4C3×#20814yescomplemented
350C2×C4C3×C4⋊Dic312yes—
351C2×C4C2×C3×Dic611yescharacteristic
352C2×C4C2×C3×D1211yescharacteristic
353C2×C4C3×D3×D412yes—
354C2×C4C3×#23712yes—
355C8—64no—
356C8—121no—
357C8—121no—
358C2×C3—21no—
359C2×C3—21no—
360C2×C3—21no—
361C2×C3—22no—
362C2×C3—22no—
363C2×C3—44no—
364C2×C3—42no—
365C2×C3—42no—
366C2×C3#492411yescharacteristic
367C2×C3#495011yescharacteristic
368C2×C3#499911yescharacteristic
369C2×C3#501112yes—
370C2×C3#501212yes—
371C2×C3C3×#38511yescharacteristic
372C2×C3C3×#42311yescharacteristic
373C2×C3C3×#42411yescharacteristic
374C2×C3C3×#43512yes—
375C2×C3C3×#43612yes—
376C22—22no—
377C22—22no—
378C22—22no—
379C22—42no—
380C22—42no—
381C22C2×C3×#20812yes—
382C22C2×C3×C4⋊Dic311yescharacteristic
383C22C3×D4×Dic312yes—
384C22C3×#94811yescharacteristic
385C22C3×#94811yescharacteristic
386C4—22no—
387C4—24no—
388C4—42no—
389C4C3×#87812yes—
390C4C3×#88211yescharacteristic
391C4C3×#88611yescharacteristic
392C3—21no—
393C3#6945011yescharacteristic, direct product factor
394C3C3×#185111yescharacteristic, complemented
395C2—42no—
396C2C3×#492411yescharacteristic
397C2C3×#495011yescharacteristic
398C2C3×#499911yescharacteristic
399C2C3×#501112yes—
400C2C3×#501212yes—
subgroupG/H
centerC22×C3×C4C22×D3
commutatorC23×C3C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC32×C4×C22⋊C4C2
socleC23×C32C22×C4
prime radicalC24×C32C2×C4
cosocleC22×C3×C4C23×C3
hypercenterC3×C4×C22⋊C4D3
hypocenterC3C3×#1851
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C22×C3×C4 ◁ C3×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
4. C2×C3×C4⋊(C3⋊C8)C2semidirect
5. C3×#4524C2semidirect
7. #69450C3direct (N × H)
28. C2×C4⋊(C3⋊C8)C2×C3semidirect
30. #4524C2×C3semidirect
97. C2×C32×C4M16semidirect
241. C2×C3×C4#208semidirect
244. C2×C3×C4C3×M16semidirect
333. C32#1851semidirect
349. C2×C4C3×#208semidirect
393. C3#69450direct (N × H)
394. C3C3×#1851semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#2082
C32×C4×C22⋊C42
C2×C3×#8302
C2×C3×C4⋊(C3⋊C8)2
C3×#45242
C3×#18513
#694503