Finite Group Databasebeta

← C3×#71532 #11788165

Subgroups — C3×#71532 #11788165

Order 1152.

1133 conjugacy classes of subgroups.

The subgroup lattice has 459 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C32×C42C211yesmaximal, characteristic, complemented
2C3×#5791C211yesmaximal, characteristic
3C3×#5207C211yesmaximal, characteristic, complemented
4C2×C3×#805C212yesmaximal, complemented
5C3×#4523C212yesmaximal, complemented
6C3×#1896—31nomaximal
7#71532C311yesmaximal, characteristic, direct product factor
8C23×C32×C4—21no—
9C23×C32×C4C2211yescharacteristic
10C2×C3×#235C2211yescharacteristic
11C2×C32×C42—21no—
12C2×C32×C42—24no—
13C2×C32×C42C2212yes—
14C3×#953—21no—
15C3×#930C412yescomplemented
16C3×#929—21no—
17C3×C4×#67—22no—
18C3×#926C2211yescharacteristic
19C3×#924C412yescomplemented
20C2×C3×#208C2212yes—
21C3×#830—22no—
22C3×#805—24no—
23C3×#525—31no—
24C22×C3×C42—21no—
25C22×C3×C42D311yescharacteristic, complemented
26C22×C3×C42C2×C311yescharacteristic, complemented
27#5791C2×C311yescharacteristic
28C2×C3×#104—32no—
29C3×#407—31no—
30#5207C2×C311yescharacteristic, complemented
31C2×#805C2×C312yescomplemented
32C3×#339—32no—
33#4523C2×C312yescomplemented
34C24×C32D411yescharacteristic
35C22×C32×C4—28no—
36C22×C32×C4—24no—
37C22×C32×C4—22no—
38C22×C32×C4—22no—
39C22×C32×C4—22no—
40C22×C32×C4C2×C412yes—
41C22×C32×C4D411yescharacteristic
42C22×C32×C4D412yes—
43C22×C32×C4C2311yescharacteristic
44C2×C3×#67—22no—
45C2×C3×#67—21no—
46C3×#235—22no—
47C3×#235—22no—
48C2×C3×D12C2×C411yescharacteristic, complemented
49C2×C3×C4×D3—21no—
50C2×C3×Dic6C2×C411yescharacteristic, complemented
51C32×C42—24no—
52C32×C42—22no—
53C32×C42D414yescomplemented
54C3×#217—22no—
55C3×#217—21no—
56C3×(C2×D3)⋊C4—22no—
57C3×C4⋊Dic3C2×C412yescomplemented
58C3×Dic3⋊C4—22no—
59C3×C4×Dic3—21no—
60C3×#208—22no—
61C3×#208—22no—
62C2×C3×C3⋊C8—22no—
63#1896—31noSylow
64C2×C3×#41—31no—
65C23×C3×C4—22no—
66C23×C3×C4—21no—
67C23×C3×C4—21no—
68C23×C3×C4—21no—
69C23×C3×C4C2×D311yescharacteristic
70C23×C3×C4C22×C311yescharacteristic
71C2×#235C22×C311yescharacteristic
72C2×C3×M16—32no—
73C3×#123—61no—
74C3×C22⋊Q8—32no—
75C3×#121—32no—
76C3×#120—61no—
77C3×C4×D4—62no—
78C3×#117—31no—
79C2×C3×C42—22no—
80C2×C3×C42—28no—
81C2×C3×C42—21no—
82C2×C3×C42—21no—
83C2×C3×C42—24no—
84C2×C3×C42—24no—
85C2×C3×C42—22no—
86C2×C3×C42C2×D312yes—
87C2×C3×C42C22×C312yes—
88#953—21no—
89#930C3×C412yescomplemented
90#929—21no—
91C4×#67—22no—
92#926C22×C311yescharacteristic
93#924C3×C412yescomplemented
94C2×#208C22×C312yes—
95C3×#104—64no—
96C3×C22⋊C8—62no—
97#830—22no—
98#805—24no—
99C23×C32—24no—
100C23×C32—21no—
101C23×C32—21no—
102C23×C32C22⋊C412yes—
103C23×C32C2×D411yescharacteristic
104C22×C3×D3—21no—
105C2×C32×C4—216no—
106C2×C32×C4—28no—
107C2×C32×C4—21no—
108C2×C32×C4—24no—
109C2×C32×C4—21no—
110C2×C32×C4—24no—
111C2×C32×C4—24no—
112C2×C32×C4C22⋊C412yes—
113C2×C32×C4C22×C411yescharacteristic
114C2×C32×C4C2×D411yescharacteristic
115C2×C32×C4C2×D412yes—
116C2×C32×C4#4112yes—
117C3×#67—44no—
118C3×#67—41no—
119C3×#67—41no—
120C2×C3×Dic3—22no—
121C2×C3×Dic3—21no—
122C3×D12—22no—
123C3×C4×D3—42no—
124C3×Dic6—22no—
125C3×C3⋊C8—42no—
126#525—31no—
127C22×C42C3×D311yescharacteristic, complemented
128C2×#104—32no—
129#407—31no—
130#339—32no—
131C24×C3—21no—
132C24×C3#6711yescharacteristic
133C24×C3C3×D411yescharacteristic
134C3×#41—62no—
135C3×#41—62no—
136C2×C3×Q8—31no—
137C2×C3×D4—31no—
138C2×C3×D4—62no—
139C2×C3×D4—61no—
140C22×C3×C4—28no—
141C22×C3×C4—24no—
142C22×C3×C4—24no—
143C22×C3×C4—24no—
144C22×C3×C4—24no—
145C22×C3×C4—216no—
146C22×C3×C4—28no—
147C22×C3×C4—28no—
148C22×C3×C4—24no—
149C22×C3×C4—22no—
150C22×C3×C4—22no—
151C22×C3×C4—22no—
152C22×C3×C4—22no—
153C22×C3×C4—22no—
154C22×C3×C4—22no—
155C22×C3×C4—22no—
156C22×C3×C4—22no—
157C22×C3×C4—21no—
158C22×C3×C4—21no—
159C22×C3×C4—61no—
160C22×C3×C4C4×D312yes—
161C22×C3×C4D1212yes—
162C22×C3×C4#6711yescharacteristic
163C22×C3×C4C2×C3×C412yes—
164C22×C3×C4C3×D412yes—
165C22×C3×C4C3×D411yescharacteristic
166C22×C3×C4C22×D311yescharacteristic
167C22×C3×C4C23×C311yescharacteristic
168C2×#67—22no—
169C2×#67—21no—
170#235—22no—
171#235—22no—
172C2×D12C2×C3×C411yescharacteristic, complemented
173C2×C4×D3—21no—
174C2×Dic6C2×C3×C411yescharacteristic, complemented
175C3×M16—62no—
176C3×M16—62no—
177C2×C3×C8—62no—
178C3×C4⋊C4—32no—
179C3×C4⋊C4—62no—
180C3×C22⋊C4—62no—
181C3×C22⋊C4—61no—
182C3×C22⋊C4—62no—
183C3×C42—28no—
184C3×C42—24no—
185C3×C42—24no—
186C3×C42—24no—
187C3×C42—22no—
188C3×C42—22no—
189C3×C42—24no—
190C3×C42—61no—
191C3×C42#6714yescomplemented
192C3×C42C3×D414yescomplemented
193#217—22no—
194#217—21no—
195(C2×D3)⋊C4—22no—
196C4⋊Dic3C2×C3×C412yescomplemented
197Dic3⋊C4—22no—
198C4×Dic3—21no—
199#208—22no—
200#208—22no—
201C2×C3⋊C8—22no—
202C22×C32—24no—
203C22×C32—24no—
204C22×C32—22no—
205C22×C32—22no—
206C22×C32—22no—
207C22×C32#10414yescomplemented
208C22×C32C2×C22⋊C411yescharacteristic
209C22×C32#12011yescharacteristic
210C22×C32#12311yescharacteristic
211C2×C3×D3—41no—
212C2×C3×D3—42no—
213C32×C4—28no—
214C32×C4—22no—
215C32×C4C4×D412yes—
216C32×C4#12112yes—
217C3×Dic3—41no—
218C3×Dic3—42no—
219C2×#41—31no—
220C23×C4—21no—
221C23×C4C2×C3×D311yescharacteristic
222C2×M16—32no—
223#123—61no—
224C22⋊Q8—32no—
225#121—32no—
226#120—61no—
227C4×D4—62no—
228#117—31no—
229C2×C42—21no—
230C2×C42—24no—
231C2×C42C2×C3×D312yes—
232#104—64no—
233C22⋊C8—62no—
234C23×C3—22no—
235C23×C3—22no—
236C23×C3—28no—
237C23×C3—24no—
238C23×C3—24no—
239C23×C3—21no—
240C23×C3—21no—
241C23×C3—21no—
242C23×C3—21no—
243C23×C3—22no—
244C23×C3—21no—
245C23×C3—61no—
246C23×C3(C2×D3)⋊C412yes—
247C23×C3C3×C22⋊C412yes—
248C23×C3C2×#6711yescharacteristic
249C23×C3C2×C3×D411yescharacteristic
250C22×D3—21no—
251C3×Q8—62no—
252C3×D4—62no—
253C3×D4—124no—
254C3×D4—121no—
255C3×D4—121no—
256C2×C3×C4—22no—
257C2×C3×C4—28no—
258C2×C3×C4—232no—
259C2×C3×C4—216no—
260C2×C3×C4—216no—
261C2×C3×C4—216no—
262C2×C3×C4—28no—
263C2×C3×C4—28no—
264C2×C3×C4—22no—
265C2×C3×C4—28no—
266C2×C3×C4—28no—
267C2×C3×C4—21no—
268C2×C3×C4—21no—
269C2×C3×C4—24no—
270C2×C3×C4—21no—
271C2×C3×C4—24no—
272C2×C3×C4—21no—
273C2×C3×C4—24no—
274C2×C3×C4—24no—
275C2×C3×C4—24no—
276C2×C3×C4—24no—
277C2×C3×C4—22no—
278C2×C3×C4—21no—
279C2×C3×C4—21no—
280C2×C3×C4—22no—
281C2×C3×C4—22no—
282C2×C3×C4—62no—
283C2×C3×C4—61no—
284C2×C3×C4—122no—
285C2×C3×C4(C2×D3)⋊C412yes—
286C2×C3×C4C3×C22⋊C412yes—
287C2×C3×C4C2×C4×D311yescharacteristic
288C2×C3×C4C2×D1211yescharacteristic
289C2×C3×C4#23512yes—
290C2×C3×C4C2×#6712yes—
291C2×C3×C4C22×C3×C411yescharacteristic
292C2×C3×C4C2×C3×D411yescharacteristic
293C2×C3×C4C2×C3×D412yes—
294C2×C3×C4C3×#4112yes—
295#67—44no—
296#67—41no—
297#67—41no—
298C2×Dic3—22no—
299C2×Dic3—21no—
300D12—22no—
301C4×D3—42no—
302Dic6—22no—
303C3×C8—122no—
304C3⋊C8—42no—
305C2×C32—21no—
306C2×C32—24no—
307C2×C32—21no—
308C2×C32#38611yescharacteristic
309C2×C32C2×#10412yes—
310C3×D3—81no—
311C24C3×#6711yescharacteristic
312#41—62no—
313#41—62no—
314C2×Q8—31no—
315C2×D4—31no—
316C2×D4—62no—
317C2×D4—61no—
318C22×C4—24no—
319C22×C4—28no—
320C22×C4—22no—
321C22×C4—22no—
322C22×C4—22no—
323C22×C4—61no—
324C22×C4C3×C4×D312yes—
325C22×C4C3×D1212yes—
326C22×C4C3×#6711yescharacteristic
327C22×C4C22×C3×D311yescharacteristic
328M16—62no—
329M16—62no—
330C2×C8—62no—
331C4⋊C4—32no—
332C4⋊C4—62no—
333C22⋊C4—62no—
334C22⋊C4—61no—
335C22⋊C4—62no—
336C42—24no—
337C42—22no—
338C42—61no—
339C42C3×#6714yescomplemented
340C22×C3—28no—
341C22×C3—24no—
342C22×C3—24no—
343C22×C3—24no—
344C22×C3—24no—
345C22×C3—28no—
346C22×C3—24no—
347C22×C3—24no—
348C22×C3—24no—
349C22×C3—22no—
350C22×C3—22no—
351C22×C3—22no—
352C22×C3—22no—
353C22×C3—22no—
354C22×C3—22no—
355C22×C3—21no—
356C22×C3—21no—
357C22×C3—21no—
358C22×C3—24no—
359C22×C3—122no—
360C22×C3—121no—
361C22×C3#80514yescomplemented
362C22×C3C3×#10414yescomplemented
363C22×C3C2×(C2×D3)⋊C411yescharacteristic
364C22×C3#92911yescharacteristic
365C22×C3#95311yescharacteristic
366C22×C3C2×C3×C22⋊C411yescharacteristic
367C22×C3C3×#12011yescharacteristic
368C22×C3C3×#12311yescharacteristic
369C2×D3—41no—
370C2×D3—42no—
371C3×C4—216no—
372C3×C4—28no—
373C3×C4—28no—
374C3×C4—24no—
375C3×C4—22no—
376C3×C4—22no—
377C3×C4—22no—
378C3×C4—22no—
379C3×C4—122no—
380C3×C4—121no—
381C3×C4C4×#6712yes—
382C3×C4#93012yes—
383C3×C4C3×C4×D412yes—
384C3×C4C3×#12112yes—
385Dic3—41no—
386Dic3—42no—
387C32#189611yescharacteristic, complemented, Sylow
388C23—21no—
389C23—21no—
390C23—24no—
391C23—61no—
392C23C3×(C2×D3)⋊C412yes—
393C23C2×C3×#6711yescharacteristic
394Q8—62no—
395D4—62no—
396D4—121no—
397D4—121no—
398D4—124no—
399C2×C4—216no—
400C2×C4—28no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—24no—
404C2×C4—24no—
405C2×C4—24no—
406C2×C4—62no—
407C2×C4—61no—
408C2×C4—122no—
409C2×C4C3×(C2×D3)⋊C412yes—
410C2×C4C2×C3×C4×D311yescharacteristic
411C2×C4C2×C3×D1211yescharacteristic
412C2×C4C3×#23512yes—
413C2×C4C2×C3×#6712yes—
414C8—122no—
415C2×C3—22no—
416C2×C3—22no—
417C2×C3—28no—
418C2×C3—21no—
419C2×C3—24no—
420C2×C3—21no—
421C2×C3—21no—
422C2×C3—24no—
423C2×C3—21no—
424C2×C3—22no—
425C2×C3—21no—
426C2×C3—241no—
427C2×C3C2×#80512yes—
428C2×C3#521311yescharacteristic
429C2×C3C3×#38611yescharacteristic
430C2×C3C2×C3×#10412yes—
431D3—81no—
432C22—24no—
433C22—24no—
434C22—22no—
435C22—22no—
436C22—22no—
437C22—122no—
438C22—121no—
439C22C3×#80514yescomplemented
440C22C2×C3×(C2×D3)⋊C411yescharacteristic
441C22C3×#92911yescharacteristic
442C22C3×#95311yescharacteristic
443C4—28no—
444C4—22no—
445C4—122no—
446C4—121no—
447C4C3×C4×#6712yes—
448C4C3×#93012yes—
449C3—21no—
450C3#7153211yescharacteristic, direct product factor
451C3C3×#189611yescharacteristic, complemented
452C2—21no—
453C2—21no—
454C2—24no—
455C2—241no—
456C2C2×C3×#80512yes—
457C2C3×#521311yescharacteristic
subgroupG/H
centerC2×C3×C4C2×D12
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC22×C32×C42C2
socleC22×C32C2×C22⋊C4
prime radicalC3×#5791C2
cosocleC22×C3×C4C23×C3
hypercenterC22×C3×C42D3
hypocenterC3C3×#1896
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3×C4 ◁ C23×C3×C4 ◁ C22×C3×C42

Complements

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

NH ≅ G/Ntype
1. C22×C32×C42C2semidirect
3. C3×#5207C2semidirect
4. C2×C3×#805C2semidirect
5. C3×#4523C2semidirect
7. #71532C3direct (N × H)
15. C3×#930C4semidirect
19. C3×#924C4semidirect
25. C22×C3×C42D3semidirect
26. C22×C3×C42C2×C3semidirect
30. #5207C2×C3semidirect
31. C2×#805C2×C3semidirect
33. #4523C2×C3semidirect
48. C2×C3×D12C2×C4semidirect
50. C2×C3×Dic6C2×C4semidirect
53. C32×C42D4semidirect
57. C3×C4⋊Dic3C2×C4semidirect
89. #930C3×C4semidirect
93. #924C3×C4semidirect
127. C22×C42C3×D3semidirect
172. C2×D12C2×C3×C4semidirect
174. C2×Dic6C2×C3×C4semidirect
191. C3×C42#67semidirect
192. C3×C42C3×D4semidirect
196. C4⋊Dic3C2×C3×C4semidirect
207. C22×C32#104semidirect
339. C42C3×#67semidirect
361. C22×C3#805semidirect
362. C22×C3C3×#104semidirect
387. C32#1896semidirect
439. C22C3×#805semidirect
450. C3#71532direct (N × H)
451. C3C3×#1896semidirect

Maximal subgroups

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

subgroupindex
C22×C32×C422
C3×#57912
C3×#52072
C2×C3×#8052
C3×#45232
C3×#18963
#715323