Finite Group Databasebeta

← C2×C3×#5033 #11869325

Subgroups — C2×C3×#5033 #11869325

Order 1152.

1237 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#121C211yesmaximal, characteristic
2C22×C3×C4⋊Dic3C211yesmaximal, characteristic, complemented
3C2×C3×#832C212yesmaximal, complemented
4C2×C3×#830C211yesmaximal, characteristic, complemented
5C3×#5033C218yesmaximal, direct product factor
6C2×C3×#807C212yesmaximal, complemented
7C2×C3×#480—31nomaximal
8C2×#5033C311yesmaximal, characteristic, direct product factor
9C22×C32×D4—21no—
10C22×C32×D4C2211yescharacteristic
11C23×C32×C4C2211yescharacteristic
12C23×C3×Dic3—21no—
13C32×#121—22no—
14C32×#121C2214yes—
15C2×C32×C4⋊C4C2211yescharacteristic
16C2×C32×C22⋊C4—21no—
17C2×C3×C4⋊Dic3—22no—
18C2×C3×C4⋊Dic3—21no—
19C2×C3×C4⋊Dic3C2212yes—
20C2×C3×C4⋊Dic3C2214yescomplemented
21C22×C3×C3⋊C8C2212yes—
22C3×#832C2218yescomplemented
23C3×#830C2214yescomplemented
24C3×#807C2218yescomplemented
25C2×C3×#121—21no—
26C2×C3×#121D311yescharacteristic
27C2×C3×#121C2×C311yescharacteristic
28C22×C3×C4⋊C4—31no—
29C22×C4⋊Dic3C2×C311yescharacteristic, complemented
30C3×#480—38no—
31C2×C3×#107—32no—
32C2×C3×#102—32no—
33C2×C3×C22⋊C8—31no—
34C2×#832C2×C312yescomplemented
35C2×#830C2×C311yescharacteristic, complemented
36#5033C2×C318yesdirect product factor
37C2×#807C2×C312yescomplemented
38C24×C32—21no—
39C24×C32D411yescharacteristic
40C2×C32×D4—24no—
41C2×C32×D4—21no—
42C2×C32×D4—24no—
43C2×C32×D4—44no—
44C2×C32×D4C2312yes—
45C22×C32×C4—24no—
46C22×C32×C4—21no—
47C22×C32×C4D411yescharacteristic
48C22×C32×C4D412yes—
49C22×C32×C4C2312yes—
50C22×C32×C4C2311yescharacteristic
51C22×C3×Dic3—22no—
52C22×C3×Dic3—24no—
53C22×C3×Dic3—44no—
54C32×C4⋊C4—21no—
55C32×C4⋊C4C2312yes—
56C32×C22⋊C4—24no—
57C3×C4⋊Dic3—22no—
58C3×C4⋊Dic3—24no—
59C3×C4⋊Dic3C2314yes—
60C2×C3×C3⋊C8—24no—
61C2×C3×C3⋊C8C2314yes—
62C2×#480—31noSylow
63C22×C3×D4—22no—
64C22×C3×D4—21no—
65C22×C3×D4—21no—
66C22×C3×D4—21no—
67C22×C3×D4C2×D311yescharacteristic
68C22×C3×D4C22×C311yescharacteristic
69C23×C3×C4—21no—
70C23×C3×C4—61no—
71C23×C3×C4C2×D311yescharacteristic
72C23×C3×C4C22×C311yescharacteristic
73C23×Dic3—21no—
74C22×C3×C8—32no—
75C3×#121—24no—
76C3×#121—22no—
77C3×#121—22no—
78C3×#121—24no—
79C3×#121C2×D314yes—
80C3×#121C22×C314yes—
81C2×C3×C4⋊C4—21no—
82C2×C3×C4⋊C4—32no—
83C2×C3×C4⋊C4—34no—
84C2×C3×C4⋊C4—62no—
85C2×C3×C4⋊C4—61no—
86C2×C3×C4⋊C4C2×D311yescharacteristic
87C2×C3×C4⋊C4C22×C311yescharacteristic
88C2×C3×C22⋊C4—22no—
89C2×C3×C22⋊C4—21no—
90C2×C3×C22⋊C4—21no—
91C2×C4⋊Dic3—22no—
92C2×C4⋊Dic3—21no—
93C2×C4⋊Dic3C22×C312yes—
94C2×C4⋊Dic3C22×C314yescomplemented
95C22×C3⋊C8C22×C312yes—
96C3×#107—38no—
97C3×#102—38no—
98C3×C22⋊C8—34no—
99#832C22×C318yescomplemented
100#830C22×C314yescomplemented
101#807C22×C318yescomplemented
102C23×C32—22no—
103C23×C32—22no—
104C23×C32—22no—
105C23×C32—42no—
106C23×C32—42no—
107C23×C32—42no—
108C23×C32D814yes—
109C23×C32C2×D412yes—
110C23×C32C2×D411yescharacteristic
111C32×D4—24no—
112C32×D4—48no—
113C32×D4—42no—
114C2×C32×C4—22no—
115C2×C32×C4—22no—
116C2×C32×C4—24no—
117C2×C32×C4—24no—
118C2×C32×C4—42no—
119C2×C32×C4C2×D412yes—
120C2×C32×C4C2×D411yescharacteristic
121C2×C32×C4#4114yes—
122C2×C32×C4C2411yescharacteristic
123C2×C3×Dic3—24no—
124C2×C3×Dic3—48no—
125C2×C3×Dic3—44no—
126C3×C3⋊C8—24no—
127C2×#121C3×D311yescharacteristic
128C22×C4⋊C4—31no—
129#480—38no—
130C2×#107—32no—
131C2×#102—32no—
132C2×C22⋊C8—31no—
133C24×C3—22no—
134C24×C3—21no—
135C24×C3—21no—
136C24×C3—21no—
137C24×C3#6711yescharacteristic
138C24×C3C3×D411yescharacteristic
139C2×C3×D4—28no—
140C2×C3×D4—22no—
141C2×C3×D4—24no—
142C2×C3×D4—24no—
143C2×C3×D4—24no—
144C2×C3×D4—21no—
145C2×C3×D4—21no—
146C2×C3×D4—24no—
147C2×C3×D4—22no—
148C2×C3×D4—44no—
149C2×C3×D4—48no—
150C2×C3×D4—44no—
151C2×C3×D4—44no—
152C2×C3×D4C22×D312yes—
153C2×C3×D4C23×C312yes—
154C22×C3×C4—24no—
155C22×C3×C4—24no—
156C22×C3×C4—22no—
157C22×C3×C4—21no—
158C22×C3×C4—21no—
159C22×C3×C4—21no—
160C22×C3×C4—22no—
161C22×C3×C4—21no—
162C22×C3×C4—22no—
163C22×C3×C4—44no—
164C22×C3×C4—64no—
165C22×C3×C4—62no—
166C22×C3×C4—124no—
167C22×C3×C4#6712yes—
168C22×C3×C4#6711yescharacteristic
169C22×C3×C4C3×D411yescharacteristic
170C22×C3×C4C3×D412yes—
171C22×C3×C4C22×D312yes—
172C22×C3×C4C22×D311yescharacteristic
173C22×C3×C4C23×C312yes—
174C22×C3×C4C23×C311yescharacteristic
175C22×Dic3—22no—
176C22×Dic3—24no—
177C22×Dic3—44no—
178C2×C3×C8—34no—
179C2×C3×C8—64no—
180C3×C4⋊C4—22no—
181C3×C4⋊C4—21no—
182C3×C4⋊C4—21no—
183C3×C4⋊C4—22no—
184C3×C4⋊C4—34no—
185C3×C4⋊C4—64no—
186C3×C4⋊C4—62no—
187C3×C4⋊C4C22×D312yes—
188C3×C4⋊C4C23×C312yes—
189C3×C22⋊C4—28no—
190C3×C22⋊C4—24no—
191C3×C22⋊C4—24no—
192C4⋊Dic3—22no—
193C4⋊Dic3—24no—
194C4⋊Dic3C23×C314yes—
195C2×C3⋊C8—24no—
196C2×C3⋊C8C23×C314yes—
197C22×C32—22no—
198C22×C32—22no—
199C22×C32—28no—
200C22×C32—42no—
201C22×C32—42no—
202C22×C32—42no—
203C22×C32—84no—
204C22×C32#12312yes—
205C22×C32C2×D814yes—
206C22×C32C2×D812yes—
207C22×C32#13712yes—
208C22×C32C22×D411yescharacteristic
209C32×C4—22no—
210C32×C4—42no—
211C32×C4#12312yes—
212C32×C4C2×#4112yes—
213C3×Dic3—44no—
214C22×D4—21no—
215C22×D4C2×C3×D311yescharacteristic
216C23×C4—61no—
217C23×C4C2×C3×D311yescharacteristic
218C22×C8—32no—
219#121—22no—
220#121C2×C3×D314yes—
221C2×C4⋊C4—32no—
222C2×C4⋊C4—34no—
223C2×C4⋊C4—61no—
224C2×C4⋊C4—62no—
225C2×C4⋊C4C2×C3×D311yescharacteristic
226C2×C22⋊C4—21no—
227#107—38no—
228#102—38no—
229C22⋊C8—34no—
230C23×C3—22no—
231C23×C3—22no—
232C23×C3—22no—
233C23×C3—22no—
234C23×C3—24no—
235C23×C3—22no—
236C23×C3—22no—
237C23×C3—24no—
238C23×C3—21no—
239C23×C3—22no—
240C23×C3—42no—
241C23×C3—42no—
242C23×C3—44no—
243C23×C3—44no—
244C23×C3—44no—
245C23×C3—42no—
246C23×C3—42no—
247C23×C3—42no—
248C23×C3—42no—
249C23×C3—42no—
250C23×C3—42no—
251C23×C3#21314yes—
252C23×C3C3×D814yes—
253C23×C3C2×#6712yes—
254C23×C3C2×#6711yescharacteristic
255C23×C3C2×C3×D412yes—
256C23×C3C2×C3×D411yescharacteristic
257C3×D4—24no—
258C3×D4—24no—
259C3×D4—44no—
260C3×D4—44no—
261C3×D4—416no—
262C3×D4—48no—
263C3×D4—48no—
264C3×D4—42no—
265C3×D4—42no—
266C2×C3×C4—22no—
267C2×C3×C4—22no—
268C2×C3×C4—24no—
269C2×C3×C4—24no—
270C2×C3×C4—24no—
271C2×C3×C4—24no—
272C2×C3×C4—24no—
273C2×C3×C4—22no—
274C2×C3×C4—22no—
275C2×C3×C4—21no—
276C2×C3×C4—24no—
277C2×C3×C4—21no—
278C2×C3×C4—22no—
279C2×C3×C4—44no—
280C2×C3×C4—44no—
281C2×C3×C4—42no—
282C2×C3×C4—44no—
283C2×C3×C4—42no—
284C2×C3×C4—42no—
285C2×C3×C4—64no—
286C2×C3×C4—128no—
287C2×C3×C4—124no—
288C2×C3×C4#23714yes—
289C2×C3×C4C2×#6712yes—
290C2×C3×C4C2×#6711yescharacteristic
291C2×C3×C4C2×C3×D412yes—
292C2×C3×C4C2×C3×D411yescharacteristic
293C2×C3×C4C3×#4114yes—
294C2×C3×C4C23×D311yescharacteristic
295C2×C3×C4C24×C311yescharacteristic
296C2×Dic3—24no—
297C2×Dic3—48no—
298C2×Dic3—44no—
299C3×C8—64no—
300C3⋊C8—24no—
301C2×C32—24no—
302C2×C32—82no—
303C2×C32#48014yescomplemented
304C2×C32C2×#12311yescharacteristic
305C2×C32C22×D811yescharacteristic
306C2×C32C2×#13711yescharacteristic
307C24—21no—
308C24C3×#6711yescharacteristic
309C2×D4—24no—
310C2×D4—24no—
311C2×D4—21no—
312C2×D4—44no—
313C2×D4C22×C3×D312yes—
314C22×C4—24no—
315C22×C4—21no—
316C22×C4—64no—
317C22×C4—62no—
318C22×C4—124no—
319C22×C4C3×#6711yescharacteristic
320C22×C4C3×#6712yes—
321C22×C4C22×C3×D312yes—
322C22×C4C22×C3×D311yescharacteristic
323C2×C8—34no—
324C2×C8—64no—
325C4⋊C4—21no—
326C4⋊C4—34no—
327C4⋊C4—64no—
328C4⋊C4—62no—
329C4⋊C4C22×C3×D312yes—
330C22⋊C4—24no—
331C22×C3—22no—
332C22×C3—22no—
333C22×C3—28no—
334C22×C3—22no—
335C22×C3—22no—
336C22×C3—28no—
337C22×C3—22no—
338C22×C3—24no—
339C22×C3—22no—
340C22×C3—22no—
341C22×C3—21no—
342C22×C3—42no—
343C22×C3—42no—
344C22×C3—48no—
345C22×C3—44no—
346C22×C3—44no—
347C22×C3—44no—
348C22×C3—42no—
349C22×C3—42no—
350C22×C3—42no—
351C22×C3—42no—
352C22×C3—42no—
353C22×C3—42no—
354C22×C3—88no—
355C22×C3—84no—
356C22×C3—84no—
357C22×C3C2×#21314yes—
358C22×C3C2×#21312yes—
359C22×C3#93512yes—
360C22×C3#95112yes—
361C22×C3C3×#12312yes—
362C22×C3C2×C3×D814yes—
363C22×C3C2×C3×D812yes—
364C22×C3C3×#13712yes—
365C22×C3C22×#6711yescharacteristic
366C22×C3C22×C3×D411yescharacteristic
367C3×C4—22no—
368C3×C4—22no—
369C3×C4—22no—
370C3×C4—22no—
371C3×C4—42no—
372C3×C4—44no—
373C3×C4—42no—
374C3×C4—42no—
375C3×C4—124no—
376C3×C4#93512yes—
377C3×C4C3×#12312yes—
378C3×C4C2×#23712yes—
379C3×C4C2×C3×#4112yes—
380Dic3—44no—
381C32C2×#48011yescharacteristic, complemented, Sylow
382C23—22no—
383C23—22no—
384C23—22no—
385C23—42no—
386C23—42no—
387C23—42no—
388C23C3×#21314yes—
389C23C2×C3×#6712yes—
390C23C2×C3×#6711yescharacteristic
391D4—24no—
392D4—48no—
393D4—42no—
394C2×C4—22no—
395C2×C4—24no—
396C2×C4—24no—
397C2×C4—22no—
398C2×C4—42no—
399C2×C4—64no—
400C2×C4—128no—
401C2×C4—124no—
402C2×C4C3×#23714yes—
403C2×C4C2×C3×#6712yes—
404C2×C4C2×C3×#6711yescharacteristic
405C2×C4C23×C3×D311yescharacteristic
406C8—64no—
407C2×C3—24no—
408C2×C3—24no—
409C2×C3—21no—
410C2×C3—21no—
411C2×C3—21no—
412C2×C3—24no—
413C2×C3—44no—
414C2×C3—84no—
415C2×C3—82no—
416C2×C3—82no—
417C2×C3#503314yesdirect product factor
418C2×C3C3×#48014yescomplemented
419C2×C3C22×#21311yescharacteristic
420C2×C3C2×#93511yescharacteristic
421C2×C3C2×#95111yescharacteristic
422C2×C3C2×C3×#12311yescharacteristic
423C2×C3C22×C3×D811yescharacteristic
424C2×C3C2×C3×#13711yescharacteristic
425C22—22no—
426C22—22no—
427C22—28no—
428C22—42no—
429C22—42no—
430C22—42no—
431C22—84no—
432C22C2×C3×#21314yes—
433C22C2×C3×#21312yes—
434C22C3×#93512yes—
435C22C3×#95112yes—
436C22C22×C3×#6711yescharacteristic
437C4—22no—
438C4—42no—
439C4—124no—
440C4C3×#93512yes—
441C4C2×C3×#23712yes—
442C3—21no—
443C3C2×#503311yescharacteristic, direct product factor
444C3C2×C3×#48011yescharacteristic, complemented
445C2—24no—
446C2—82no—
447C2C3×#503314yesdirect product factor
448C2C22×C3×#21311yescharacteristic
449C2C2×C3×#93511yescharacteristic
450C2C2×C3×#95111yescharacteristic
subgroupG/H
centerC23×C3C2×#67
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
Fitting, prime radicalC2×C32×#121C2
socleC23×C32C2×D4
hypercenterC2×C3×#121D3
hypocenterC3C2×C3×#480
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C23×C3×C4 ◁ C2×C3×#121

Complements

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

NH ≅ G/Ntype
2. C22×C3×C4⋊Dic3C2semidirect
3. C2×C3×#832C2semidirect
4. C2×C3×#830C2semidirect
5. C3×#5033C2direct (N × H)
6. C2×C3×#807C2semidirect
8. C2×#5033C3direct (N × H)
20. C2×C3×C4⋊Dic3C22semidirect
22. C3×#832C22semidirect
23. C3×#830C22semidirect
24. C3×#807C22semidirect
29. C22×C4⋊Dic3C2×C3semidirect
34. C2×#832C2×C3semidirect
35. C2×#830C2×C3semidirect
36. #5033C2×C3direct (N × H)
37. C2×#807C2×C3semidirect
94. C2×C4⋊Dic3C22×C3semidirect
99. #832C22×C3semidirect
100. #830C22×C3semidirect
101. #807C22×C3semidirect
303. C2×C32#480semidirect
381. C32C2×#480semidirect
417. C2×C3#5033direct (N × H)
418. C2×C3C3×#480semidirect
443. C3C2×#5033direct (N × H)
444. C3C2×C3×#480semidirect
447. C2C3×#5033direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C32×#1212
C22×C3×C4⋊Dic32
C2×C3×#8322
C2×C3×#8302
C3×#50332
C2×C3×#8072
C2×C3×#4803
C2×#50333