Finite Group Databasebeta

← C3×#71879 #11792234

Subgroups — C3×#71879 #11792234

Order 1152.

959 conjugacy classes of subgroups.

The subgroup lattice has 465 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#537C211yesmaximal, characteristic, complemented
2C2×C3×#949C212yesmaximal, complemented
3C2×C3×#837C212yesmaximal, complemented
4C3×#4988C211yesmaximal, characteristic, complemented
5C3×#4530C211yesmaximal, characteristic, complemented
6C3×#2006—31nomaximal
7#71879C311yesmaximal, characteristic, direct product factor
8C2×C32×#41C2212yes—
9C22×C3×D12C2211yescharacteristic
10C32×C22⋊Q8—22no—
11C32×#121—22no—
12C32×#121—22no—
13C2×C32×C4⋊C4C2211yescharacteristic
14C3×#949—24no—
15C3×#949—24no—
16C2×C3×#215—22no—
17C2×C3×#213—22no—
18C2×C3×(C2×D3)⋊C4—22no—
19C2×C3×C4×Dic3C2211yescharacteristic
20C2×C3×#208C2212yes—
21C3×#837—24no—
22C2×C3×AGL(1,ℤ/8)—32no—
23C3×#537—21no—
24C3×#537D311yescharacteristic, complemented
25C3×#537C2×C311yescharacteristic, complemented
26C2×#949C2×C312yescomplemented
27C2×C3×#104—32no—
28C3×#390—31no—
29C2×#837C2×C312yescomplemented
30#4988C2×C311yescharacteristic, complemented
31C3×#343—31no—
32#4530C2×C311yescharacteristic, complemented
33C23×C3×D3—21no—
34C32×#41—22no—
35C32×#41—22no—
36C32×#41—22no—
37C32×#41—22no—
38C2×C32×Q8D412yes—
39C2×C32×D4—22no—
40C2×C32×D4—22no—
41C2×C32×D4D412yes—
42C22×C32×C4—22no—
43C22×C32×C4D412yes—
44C22×C32×C4C2311yescharacteristic
45C22×C3×Dic3—21no—
46C2×C3×D12—22no—
47C2×C3×D12—22no—
48C2×C3×D12—21no—
49C2×C3×D12D412yescomplemented
50C32×C4⋊C4—22no—
51C32×C4⋊C4—22no—
52C32×C22⋊C4—24no—
53C3×#215—28no—
54C3×#213—28no—
55C3×(C2×D3)⋊C4—44no—
56C3×C4×Dic3—22no—
57C3×#208—22no—
58C3×#208D414yescomplemented
59C2×C3×C3⋊C8—22no—
60#2006—31noSylow
61C2×C3×#41—22no—
62C2×C3×#41C2×D312yes—
63C2×C3×#41C22×C312yes—
64C22×C3×D4—31no—
65C22×D12C22×C311yescharacteristic
66C3×AGL(1,ℤ/8)—64no—
67C3×AGL(1,ℤ/8)—64no—
68C2×C3×SD16—62no—
69C2×C3×D8—62no—
70C2×C3×M16—32no—
71C3×C22⋊Q8—24no—
72C3×C22⋊Q8—22no—
73C3×C22⋊Q8—22no—
74C3×#121—24no—
75C3×#121—24no—
76C3×#121—22no—
77C3×#121—22no—
78C3×#121—22no—
79C3×#121—22no—
80C2×C3×C4⋊C4—21no—
81C2×C3×C4⋊C4C2×D311yescharacteristic
82C2×C3×C4⋊C4C22×C311yescharacteristic
83C2×C3×C22⋊C4—62no—
84C2×C3×C42—31no—
85#949—24no—
86#949—24no—
87C2×#215—22no—
88C2×#213—22no—
89C2×(C2×D3)⋊C4—22no—
90C2×C4×Dic3C22×C311yescharacteristic
91C2×#208C22×C312yes—
92C3×#104—64no—
93#837—24no—
94C23×C32—22no—
95C23×C32C2×D411yescharacteristic
96C22×C3×D3—22no—
97C22×C3×D3—42no—
98C22×C3×D3—42no—
99C22×C3×D3—41no—
100C22×C3×D3—41no—
101C32×Q8—22no—
102C32×Q8—22no—
103C32×D4—22no—
104C32×D4—22no—
105C32×D4—42no—
106C32×D4—42no—
107C32×D4—82no—
108C2×C32×C4—22no—
109C2×C32×C4—22no—
110C2×C32×C4—42no—
111C2×C32×C4—42no—
112C2×C32×C4—42no—
113C2×C32×C4C2×D411yescharacteristic
114C2×C32×C4C2×D412yes—
115C2×C32×C4C2×D412yes—
116C2×C32×C4#4111yescharacteristic
117C2×C3×Dic3—22no—
118C2×C3×Dic3—41no—
119C2×C3×Dic3—41no—
120C3×D12—24no—
121C3×D12—42no—
122C3×C3⋊C8—24no—
123C2×AGL(1,ℤ/8)—32no—
124#537C3×D311yescharacteristic, complemented
125C2×#104—32no—
126#390—31no—
127#343—31no—
128C24×C3—61no—
129C23×D3—21no—
130C3×#41—22no—
131C3×#41—22no—
132C3×#41—22no—
133C3×#41—22no—
134C3×#41—22no—
135C3×#41—22no—
136C3×#41—22no—
137C3×#41—22no—
138C3×#41—42no—
139C3×#41—42no—
140C3×#41—42no—
141C3×#41—42no—
142C2×C3×Q8—22no—
143C2×C3×Q8#6712yes—
144C2×C3×Q8C3×D412yes—
145C2×C3×D4—24no—
146C2×C3×D4—22no—
147C2×C3×D4—22no—
148C2×C3×D4—24no—
149C2×C3×D4—22no—
150C2×C3×D4—22no—
151C2×C3×D4—22no—
152C2×C3×D4—32no—
153C2×C3×D4—62no—
154C2×C3×D4—61no—
155C2×C3×D4—62no—
156C2×C3×D4#6712yes—
157C2×C3×D4C3×D412yes—
158C22×C3×C4—24no—
159C22×C3×C4—22no—
160C22×C3×C4—22no—
161C22×C3×C4—22no—
162C22×C3×C4—21no—
163C22×C3×C4—61no—
164C22×C3×C4#6712yes—
165C22×C3×C4C3×D412yes—
166C22×C3×C4C22×D311yescharacteristic
167C22×C3×C4C23×C311yescharacteristic
168C22×Dic3—21no—
169C2×D12—22no—
170C2×D12—22no—
171C2×D12—21no—
172C2×D12C3×D412yescomplemented
173C3×SD16—68no—
174C3×D8—68no—
175C3×M16—34no—
176C3×M16—62no—
177C2×C3×C8—62no—
178C3×C4⋊C4—24no—
179C3×C4⋊C4—24no—
180C3×C4⋊C4—22no—
181C3×C4⋊C4—22no—
182C3×C4⋊C4—22no—
183C3×C4⋊C4—22no—
184C3×C22⋊C4—28no—
185C3×C22⋊C4—24no—
186C3×C22⋊C4—24no—
187C3×C22⋊C4—124no—
188C3×C42—62no—
189#215—28no—
190#213—28no—
191(C2×D3)⋊C4—44no—
192C4×Dic3—22no—
193#208—22no—
194#208C3×D414yescomplemented
195C2×C3⋊C8—22no—
196C22×C32—21no—
197C22×C32—21no—
198C22×C32—42no—
199C22×C32—42no—
200C22×C32—42no—
201C22×C32#12011yescharacteristic
202C22×C32#12111yescharacteristic
203C22×C32#12711yescharacteristic
204C2×C3×D3—44no—
205C2×C3×D3—42no—
206C2×C3×D3—82no—
207C2×C3×D3—81no—
208C2×C3×D3—81no—
209C32×C4—42no—
210C32×C4—42no—
211C32×C4#12012yes—
212C32×C4#12112yes—
213C3×Dic3—42no—
214C2×#41C2×C3×D312yes—
215C22×D4—31no—
216AGL(1,ℤ/8)—64no—
217AGL(1,ℤ/8)—64no—
218C2×SD16—62no—
219C2×D8—62no—
220C2×M16—32no—
221C22⋊Q8—22no—
222#121—22no—
223#121—22no—
224C2×C4⋊C4C2×C3×D311yescharacteristic
225C2×C22⋊C4—62no—
226C2×C42—31no—
227#104—64no—
228C23×C3—24no—
229C23×C3—22no—
230C23×C3—22no—
231C23×C3—21no—
232C23×C3—62no—
233C23×C3—122no—
234C23×C3—122no—
235C23×C3—121no—
236C23×C3—121no—
237C23×C3C2×#6711yescharacteristic
238C23×C3C2×C3×D411yescharacteristic
239C22×D3—22no—
240C22×D3—42no—
241C22×D3—42no—
242C22×D3—41no—
243C22×D3—41no—
244C3×Q8—22no—
245C3×Q8—22no—
246C3×Q8—22no—
247C3×Q8—22no—
248C3×Q8—42no—
249C3×Q8—42no—
250C3×D4—22no—
251C3×D4—22no—
252C3×D4—22no—
253C3×D4—22no—
254C3×D4—42no—
255C3×D4—42no—
256C3×D4—44no—
257C3×D4—44no—
258C3×D4—42no—
259C3×D4—42no—
260C3×D4—42no—
261C3×D4—42no—
262C3×D4—64no—
263C3×D4—84no—
264C3×D4—82no—
265C3×D4—82no—
266C3×D4—122no—
267C2×C3×C4—24no—
268C2×C3×C4—24no—
269C2×C3×C4—22no—
270C2×C3×C4—22no—
271C2×C3×C4—22no—
272C2×C3×C4—22no—
273C2×C3×C4—21no—
274C2×C3×C4—22no—
275C2×C3×C4—21no—
276C2×C3×C4—22no—
277C2×C3×C4—44no—
278C2×C3×C4—44no—
279C2×C3×C4—42no—
280C2×C3×C4—42no—
281C2×C3×C4—42no—
282C2×C3×C4—42no—
283C2×C3×C4—42no—
284C2×C3×C4—42no—
285C2×C3×C4—62no—
286C2×C3×C4—82no—
287C2×C3×C4—121no—
288C2×C3×C4—121no—
289C2×C3×C4D3×D411yescharacteristic
290C2×C3×C4D3×D412yes—
291C2×C3×C4#23711yescharacteristic
292C2×C3×C4C2×#6712yes—
293C2×C3×C4C2×C3×D411yescharacteristic
294C2×C3×C4C2×C3×D412yes—
295C2×C3×C4C2×C3×D412yes—
296C2×C3×C4C3×#4111yescharacteristic
297C2×Dic3—22no—
298C2×Dic3—41no—
299C2×Dic3—41no—
300D12—24no—
301D12—42no—
302C3×C8—64no—
303C3⋊C8—24no—
304C2×C32—21no—
305C2×C32—21no—
306C2×C32—82no—
307C2×C32#39211yescharacteristic
308C2×C32#45311yescharacteristic
309C2×C32#45411yescharacteristic
310C3×D3—82no—
311C24—61no—
312#41—22no—
313#41—22no—
314#41—22no—
315#41—22no—
316C2×Q8C3×#6712yes—
317C2×D4—22no—
318C2×D4—22no—
319C2×D4—32no—
320C2×D4—62no—
321C2×D4—61no—
322C2×D4—62no—
323C2×D4C3×#6712yes—
324C22×C4—22no—
325C22×C4—61no—
326C22×C4C3×#6712yes—
327C22×C4C22×C3×D311yescharacteristic
328SD16—68no—
329D8—68no—
330M16—34no—
331M16—62no—
332C2×C8—62no—
333C4⋊C4—22no—
334C4⋊C4—22no—
335C22⋊C4—24no—
336C22⋊C4—124no—
337C42—62no—
338C22×C3—21no—
339C22×C3—21no—
340C22×C3—21no—
341C22×C3—21no—
342C22×C3—21no—
343C22×C3—21no—
344C22×C3—21no—
345C22×C3—41no—
346C22×C3—41no—
347C22×C3—44no—
348C22×C3—44no—
349C22×C3—44no—
350C22×C3—42no—
351C22×C3—42no—
352C22×C3—42no—
353C22×C3—42no—
354C22×C3—42no—
355C22×C3—42no—
356C22×C3—124no—
357C22×C3—122no—
358C22×C3—242no—
359C22×C3—241no—
360C22×C3—241no—
361C22×C3#93811yescharacteristic
362C22×C3#94011yescharacteristic
363C22×C3#95311yescharacteristic
364C22×C3C3×#12011yescharacteristic
365C22×C3C3×#12111yescharacteristic
366C22×C3C3×#12711yescharacteristic
367C2×D3—44no—
368C2×D3—42no—
369C2×D3—82no—
370C2×D3—81no—
371C2×D3—81no—
372C3×C4—22no—
373C3×C4—22no—
374C3×C4—44no—
375C3×C4—44no—
376C3×C4—42no—
377C3×C4—42no—
378C3×C4—42no—
379C3×C4—42no—
380C3×C4—122no—
381C3×C4#93712yes—
382C3×C4#93912yes—
383C3×C4C3×#12012yes—
384C3×C4C3×#12112yes—
385Dic3—42no—
386C32#200611yescharacteristic, complemented, Sylow
387C23—22no—
388C23—62no—
389C23—122no—
390C23—122no—
391C23—121no—
392C23—121no—
393C23C2×C3×#6711yescharacteristic
394Q8—22no—
395Q8—22no—
396D4—22no—
397D4—22no—
398D4—42no—
399D4—42no—
400D4—64no—
401D4—82no—
402D4—122no—
403C2×C4—22no—
404C2×C4—22no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4—42no—
408C2×C4—62no—
409C2×C4—121no—
410C2×C4—121no—
411C2×C4C3×D3×D411yescharacteristic
412C2×C4C3×D3×D412yes—
413C2×C4C3×#23711yescharacteristic
414C2×C4C2×C3×#6712yes—
415C8—64no—
416C2×C3—21no—
417C2×C3—21no—
418C2×C3—21no—
419C2×C3—21no—
420C2×C3—21no—
421C2×C3—21no—
422C2×C3—21no—
423C2×C3—41no—
424C2×C3—41no—
425C2×C3—84no—
426C2×C3—82no—
427C2×C3—82no—
428C2×C3—242no—
429C2×C3#522311yescharacteristic
430C2×C3#524111yescharacteristic
431C2×C3#524511yescharacteristic
432C2×C3C3×#39211yescharacteristic
433C2×C3C3×#45311yescharacteristic
434C2×C3C3×#45411yescharacteristic
435D3—82no—
436C22—21no—
437C22—21no—
438C22—42no—
439C22—42no—
440C22—42no—
441C22—124no—
442C22—122no—
443C22—242no—
444C22—241no—
445C22—241no—
446C22C3×#93811yescharacteristic
447C22C3×#94011yescharacteristic
448C22C3×#95311yescharacteristic
449C4—42no—
450C4—42no—
451C4—122no—
452C4C3×#93712yes—
453C4C3×#93912yes—
454C3—21no—
455C3#7187911yescharacteristic, direct product factor
456C3C3×#200611yescharacteristic, complemented
457C2—21no—
458C2—21no—
459C2—82no—
460C2—242no—
461C2C3×#522311yescharacteristic
462C2C3×#524111yescharacteristic
463C2C3×#524511yescharacteristic
subgroupG/H
centerC22×C3#953
commutator, cosocleC22×C3×C4C23×C3
FrattiniC22×C4C22×C3×D3
FittingC32×#537C2
socleC22×C32#120
hypercenterC3×#537D3
hypocenterC3C3×#2006
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
1. C32×#537C2semidirect
2. C2×C3×#949C2semidirect
3. C2×C3×#837C2semidirect
4. C3×#4988C2semidirect
5. C3×#4530C2semidirect
7. #71879C3direct (N × H)
24. C3×#537D3semidirect
25. C3×#537C2×C3semidirect
26. C2×#949C2×C3semidirect
29. C2×#837C2×C3semidirect
30. #4988C2×C3semidirect
32. #4530C2×C3semidirect
49. C2×C3×D12D4semidirect
58. C3×#208D4semidirect
124. #537C3×D3semidirect
172. C2×D12C3×D4semidirect
194. #208C3×D4semidirect
386. C32#2006semidirect
455. C3#71879direct (N × H)
456. C3C3×#2006semidirect

Maximal subgroups

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

subgroupindex
C32×#5372
C2×C3×#9492
C2×C3×#8372
C3×#49882
C3×#45302
C3×#20063
#718793