Finite Group Databasebeta

← C3×#71881 #11792267

Subgroups — C3×#71881 #11792267

Order 1152.

887 conjugacy classes of subgroups.

The subgroup lattice has 433 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#537C211yesmaximal, characteristic
2C2×C3×#951C212yesmaximal, complemented
3C2×C3×#837C212yesmaximal, complemented
4C3×#4973C211yesmaximal, characteristic, complemented
5C3×#4530C211yesmaximal, characteristic, complemented
6C3×#2007—31nomaximal
7#71881C311yesmaximal, characteristic, direct product factor
8C2×C32×#41C2212yes—
9C22×C3×Dic6C2211yescharacteristic
10C32×C22⋊Q8—22no—
11C32×#121—22no—
12C32×#121—22no—
13C2×C32×C4⋊C4C2211yescharacteristic
14C3×#951—24no—
15C3×#951—24no—
16C2×C3×#216—22no—
17C2×C3×#214—22no—
18C2×C3×C4×Dic3C2211yescharacteristic
19C2×C3×#208C2212yes—
20C3×#837—24no—
21C3×C3⋊#95—22no—
22C2×C3×#137—32no—
23C3×#537—21no—
24C3×#537D311yescharacteristic
25C3×#537C2×C311yescharacteristic
26C2×#951C2×C312yescomplemented
27C2×C3×#104—32no—
28C3×#391—31no—
29C2×#837C2×C312yescomplemented
30#4973C2×C311yescharacteristic, complemented
31C3×#343—31no—
32#4530C2×C311yescharacteristic, complemented
33C32×#41—22no—
34C32×#41—22no—
35C32×#41—22no—
36C32×#41—22no—
37C2×C32×Q8D412yes—
38C2×C32×D4—22no—
39C2×C32×D4—22no—
40C2×C32×D4D412yes—
41C22×C32×C4—22no—
42C22×C32×C4D412yes—
43C22×C32×C4C2311yescharacteristic
44C22×C3×Dic3—21no—
45C22×C3×Dic3—21no—
46C2×C3×Dic6—22no—
47C2×C3×Dic6—22no—
48C2×C3×Dic6—21no—
49C2×C3×Dic6D412yescomplemented
50C32×C4⋊C4—22no—
51C32×C4⋊C4—22no—
52C32×C22⋊C4—24no—
53C3×#216—28no—
54C3×#214—28no—
55C3×C4×Dic3—22no—
56C3×#208—22no—
57C3×#208D414yescomplemented
58C2×C3×C3⋊C8—22no—
59#2007—31noSylow
60C2×C3×#41—22no—
61C2×C3×#41C2×D312yes—
62C2×C3×#41C22×C312yes—
63C22×C3×Q8—31no—
64C22×Dic6C22×C311yescharacteristic
65C3×#137—64no—
66C3×#137—64no—
67C2×C3×Q16—62no—
68C2×C3×SD16—62no—
69C2×C3×M16—32no—
70C3×C22⋊Q8—24no—
71C3×C22⋊Q8—22no—
72C3×C22⋊Q8—22no—
73C3×#121—24no—
74C3×#121—24no—
75C3×#121—22no—
76C3×#121—22no—
77C3×#121—22no—
78C3×#121—22no—
79C2×C3×C4⋊C4—21no—
80C2×C3×C4⋊C4C2×D311yescharacteristic
81C2×C3×C4⋊C4C22×C311yescharacteristic
82C2×C3×C42—31no—
83#951—24no—
84#951—24no—
85C2×#216—22no—
86C2×#214—22no—
87C2×C4×Dic3C22×C311yescharacteristic
88C2×#208C22×C312yes—
89C3×#104—64no—
90C3×#95—62no—
91#837—24no—
92C3⋊#95—22no—
93C23×C32—22no—
94C23×C32C2×D411yescharacteristic
95C32×Q8—22no—
96C32×Q8—22no—
97C32×D4—22no—
98C32×D4—22no—
99C32×D4—42no—
100C32×D4—42no—
101C32×D4—82no—
102C2×C32×C4—22no—
103C2×C32×C4—22no—
104C2×C32×C4—42no—
105C2×C32×C4—42no—
106C2×C32×C4—42no—
107C2×C32×C4C2×D411yescharacteristic
108C2×C32×C4C2×D412yes—
109C2×C32×C4C2×D412yes—
110C2×C32×C4#4111yescharacteristic
111C2×C3×Dic3—22no—
112C2×C3×Dic3—22no—
113C2×C3×Dic3—41no—
114C2×C3×Dic3—41no—
115C2×C3×Dic3—41no—
116C2×C3×Dic3—41no—
117C3×Dic6—24no—
118C3×Dic6—42no—
119C3×C3⋊C8—24no—
120C2×#137—32no—
121#537C3×D311yescharacteristic
122C2×#104—32no—
123#391—31no—
124#343—31no—
125C3×#41—22no—
126C3×#41—22no—
127C3×#41—22no—
128C3×#41—22no—
129C3×#41—22no—
130C3×#41—22no—
131C3×#41—22no—
132C3×#41—22no—
133C3×#41—42no—
134C3×#41—42no—
135C3×#41—42no—
136C3×#41—42no—
137C2×C3×Q8—22no—
138C2×C3×Q8—32no—
139C2×C3×Q8—61no—
140C2×C3×Q8—62no—
141C2×C3×Q8—62no—
142C2×C3×Q8#6712yes—
143C2×C3×Q8C3×D412yes—
144C2×C3×D4—24no—
145C2×C3×D4—22no—
146C2×C3×D4—22no—
147C2×C3×D4—24no—
148C2×C3×D4—22no—
149C2×C3×D4—22no—
150C2×C3×D4—22no—
151C2×C3×D4#6712yes—
152C2×C3×D4C3×D412yes—
153C22×C3×C4—24no—
154C22×C3×C4—22no—
155C22×C3×C4—22no—
156C22×C3×C4—22no—
157C22×C3×C4—21no—
158C22×C3×C4—61no—
159C22×C3×C4—61no—
160C22×C3×C4#6712yes—
161C22×C3×C4C3×D412yes—
162C22×C3×C4C22×D311yescharacteristic
163C22×C3×C4C23×C311yescharacteristic
164C22×Dic3—21no—
165C22×Dic3—21no—
166C2×Dic6—22no—
167C2×Dic6—22no—
168C2×Dic6—21no—
169C2×Dic6C3×D412yescomplemented
170C3×Q16—68no—
171C3×SD16—68no—
172C3×M16—34no—
173C3×M16—62no—
174C2×C3×C8—62no—
175C3×C4⋊C4—24no—
176C3×C4⋊C4—24no—
177C3×C4⋊C4—22no—
178C3×C4⋊C4—22no—
179C3×C4⋊C4—22no—
180C3×C4⋊C4—22no—
181C3×C22⋊C4—28no—
182C3×C22⋊C4—24no—
183C3×C22⋊C4—24no—
184C3×C42—62no—
185#216—28no—
186#214—28no—
187C4×Dic3—22no—
188#208—22no—
189#208C3×D414yescomplemented
190C2×C3⋊C8—22no—
191C22×C32—21no—
192C22×C32—21no—
193C22×C32—42no—
194C22×C32—42no—
195C22×C32—42no—
196C22×C32#12011yescharacteristic
197C22×C32#12111yescharacteristic
198C22×C32#12711yescharacteristic
199C32×C4—42no—
200C32×C4—42no—
201C32×C4#12012yes—
202C32×C4#12112yes—
203C3×Dic3—42no—
204C3×Dic3—42no—
205C2×#41C2×C3×D312yes—
206C22×Q8—31no—
207#137—64no—
208#137—64no—
209C2×Q16—62no—
210C2×SD16—62no—
211C2×M16—32no—
212C22⋊Q8—22no—
213#121—22no—
214#121—22no—
215C2×C4⋊C4C2×C3×D311yescharacteristic
216C2×C42—31no—
217#104—64no—
218#95—62no—
219C23×C3—24no—
220C23×C3—22no—
221C23×C3—22no—
222C23×C3—21no—
223C23×C3C2×#6711yescharacteristic
224C23×C3C2×C3×D411yescharacteristic
225C3×Q8—22no—
226C3×Q8—22no—
227C3×Q8—22no—
228C3×Q8—22no—
229C3×Q8—42no—
230C3×Q8—42no—
231C3×Q8—64no—
232C3×Q8—122no—
233C3×D4—22no—
234C3×D4—22no—
235C3×D4—22no—
236C3×D4—22no—
237C3×D4—42no—
238C3×D4—42no—
239C3×D4—44no—
240C3×D4—44no—
241C3×D4—42no—
242C3×D4—42no—
243C3×D4—42no—
244C3×D4—42no—
245C3×D4—84no—
246C3×D4—82no—
247C3×D4—82no—
248C2×C3×C4—24no—
249C2×C3×C4—24no—
250C2×C3×C4—22no—
251C2×C3×C4—22no—
252C2×C3×C4—22no—
253C2×C3×C4—22no—
254C2×C3×C4—21no—
255C2×C3×C4—22no—
256C2×C3×C4—21no—
257C2×C3×C4—22no—
258C2×C3×C4—44no—
259C2×C3×C4—44no—
260C2×C3×C4—42no—
261C2×C3×C4—42no—
262C2×C3×C4—42no—
263C2×C3×C4—42no—
264C2×C3×C4—42no—
265C2×C3×C4—42no—
266C2×C3×C4—62no—
267C2×C3×C4—62no—
268C2×C3×C4—82no—
269C2×C3×C4—121no—
270C2×C3×C4—121no—
271C2×C3×C4—121no—
272C2×C3×C4—121no—
273C2×C3×C4D3×D411yescharacteristic
274C2×C3×C4D3×D412yes—
275C2×C3×C4#23711yescharacteristic
276C2×C3×C4C2×#6712yes—
277C2×C3×C4C2×C3×D411yescharacteristic
278C2×C3×C4C2×C3×D412yes—
279C2×C3×C4C2×C3×D412yes—
280C2×C3×C4C3×#4111yescharacteristic
281C2×Dic3—22no—
282C2×Dic3—22no—
283C2×Dic3—41no—
284C2×Dic3—41no—
285C2×Dic3—41no—
286C2×Dic3—41no—
287Dic6—24no—
288Dic6—42no—
289C3×C8—64no—
290C3⋊C8—24no—
291C2×C32—21no—
292C2×C32—21no—
293C2×C32—82no—
294C2×C32#39211yescharacteristic
295C2×C32#45511yescharacteristic
296C2×C32#45611yescharacteristic
297#41—22no—
298#41—22no—
299#41—22no—
300#41—22no—
301C2×Q8—32no—
302C2×Q8—61no—
303C2×Q8—62no—
304C2×Q8—62no—
305C2×Q8C3×#6712yes—
306C2×D4—22no—
307C2×D4—22no—
308C2×D4C3×#6712yes—
309C22×C4—22no—
310C22×C4—61no—
311C22×C4—61no—
312C22×C4C3×#6712yes—
313C22×C4C22×C3×D311yescharacteristic
314Q16—68no—
315SD16—68no—
316M16—34no—
317M16—62no—
318C2×C8—62no—
319C4⋊C4—22no—
320C4⋊C4—22no—
321C22⋊C4—24no—
322C42—62no—
323C22×C3—21no—
324C22×C3—21no—
325C22×C3—21no—
326C22×C3—21no—
327C22×C3—21no—
328C22×C3—21no—
329C22×C3—21no—
330C22×C3—41no—
331C22×C3—41no—
332C22×C3—44no—
333C22×C3—44no—
334C22×C3—44no—
335C22×C3—42no—
336C22×C3—42no—
337C22×C3—42no—
338C22×C3—42no—
339C22×C3—42no—
340C22×C3—42no—
341C22×C3#93811yescharacteristic
342C22×C3#94011yescharacteristic
343C22×C3#95311yescharacteristic
344C22×C3C3×#12011yescharacteristic
345C22×C3C3×#12111yescharacteristic
346C22×C3C3×#12711yescharacteristic
347C3×C4—22no—
348C3×C4—22no—
349C3×C4—44no—
350C3×C4—44no—
351C3×C4—42no—
352C3×C4—42no—
353C3×C4—42no—
354C3×C4—42no—
355C3×C4—122no—
356C3×C4—122no—
357C3×C4#93712yes—
358C3×C4#93912yes—
359C3×C4C3×#12012yes—
360C3×C4C3×#12112yes—
361Dic3—42no—
362Dic3—42no—
363C32#200711yescharacteristic, complemented, Sylow
364C23—22no—
365C23C2×C3×#6711yescharacteristic
366Q8—22no—
367Q8—22no—
368Q8—64no—
369Q8—122no—
370D4—22no—
371D4—22no—
372D4—42no—
373D4—42no—
374D4—82no—
375C2×C4—22no—
376C2×C4—22no—
377C2×C4—42no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—62no—
381C2×C4—62no—
382C2×C4—121no—
383C2×C4—121no—
384C2×C4—121no—
385C2×C4—121no—
386C2×C4C3×D3×D411yescharacteristic
387C2×C4C3×D3×D412yes—
388C2×C4C3×#23711yescharacteristic
389C2×C4C2×C3×#6712yes—
390C8—64no—
391C2×C3—21no—
392C2×C3—21no—
393C2×C3—21no—
394C2×C3—21no—
395C2×C3—21no—
396C2×C3—21no—
397C2×C3—21no—
398C2×C3—41no—
399C2×C3—41no—
400C2×C3—84no—
401C2×C3—82no—
402C2×C3—82no—
403C2×C3#522311yescharacteristic
404C2×C3#524211yescharacteristic
405C2×C3#524611yescharacteristic
406C2×C3C3×#39211yescharacteristic
407C2×C3C3×#45511yescharacteristic
408C2×C3C3×#45611yescharacteristic
409C22—21no—
410C22—21no—
411C22—42no—
412C22—42no—
413C22—42no—
414C22C3×#93811yescharacteristic
415C22C3×#94011yescharacteristic
416C22C3×#95311yescharacteristic
417C4—42no—
418C4—42no—
419C4—122no—
420C4—122no—
421C4C3×#93712yes—
422C4C3×#93912yes—
423C3—21no—
424C3#7188111yescharacteristic, direct product factor
425C3C3×#200711yescharacteristic, complemented
426C2—21no—
427C2—21no—
428C2—82no—
429C2C3×#522311yescharacteristic
430C2C3×#524211yescharacteristic
431C2C3×#524611yescharacteristic
subgroupG/H
centerC22×C3#953
commutator, cosocleC22×C3×C4C23×C3
FrattiniC22×C4C22×C3×D3
Fitting, prime radicalC32×#537C2
socleC22×C32#120
hypercenterC3×#537D3
hypocenterC3C3×#2007
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#537

Complements

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

NH ≅ G/Ntype
2. C2×C3×#951C2semidirect
3. C2×C3×#837C2semidirect
4. C3×#4973C2semidirect
5. C3×#4530C2semidirect
7. #71881C3direct (N × H)
26. C2×#951C2×C3semidirect
29. C2×#837C2×C3semidirect
30. #4973C2×C3semidirect
32. #4530C2×C3semidirect
49. C2×C3×Dic6D4semidirect
57. C3×#208D4semidirect
169. C2×Dic6C3×D4semidirect
189. #208C3×D4semidirect
363. C32#2007semidirect
424. C3#71881direct (N × H)
425. C3C3×#2007semidirect

Maximal subgroups

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

subgroupindex
C32×#5372
C2×C3×#9512
C2×C3×#8372
C3×#49732
C3×#45302
C3×#20073
#718813