Finite Group Databasebeta

← C3×#76494 #11807112

Subgroups — C3×#76494 #11807112

Order 1152.

1085 conjugacy classes of subgroups.

The subgroup lattice has 489 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#944C211yesmaximal, characteristic
2C32×#391C211yesmaximal, characteristic
3C3×#5229C211yesmaximal, characteristic
4C3×#4976C212yesmaximal
5C3×C4×Dic3⋊C4C212yesmaximal
6C3×#4649C212yesmaximal
7C3×#4649C212yesmaximal
8C3×#4647C212yesmaximal
9C3×#4646C212yesmaximal
10C3×#2369—31nomaximal
11#76494C311yesmaximal, characteristic, direct product factor
12C22×C32×Q8C2211yescharacteristic
13C22×C3×Dic6C2211yescharacteristic
14C2×C32×C4⋊C4C2211yescharacteristic
15C2×C32×C42C2211yescharacteristic
16C3×#944C418yescomplemented
17C2×C3×C4⋊Dic3C2211yescharacteristic
18C2×C3×Dic3⋊C4C2212yes—
19C2×C3×Dic3⋊C4C2212yes—
20C2×C3×Dic3⋊C4C2212yes—
21C2×C3×Dic3⋊C4C2212yes—
22C2×C3×Dic3⋊C4C2212yes—
23C2×C3×C4×Dic3C2212yes—
24C2×C3×C4×Dic3C2212yes—
25C2×C3×C4×Dic3C2211yescharacteristic
26C2×C3×C4×Dic3C2212yes—
27C2×C3×C4×Dic3C2211yescharacteristic
28C32×#95C2212yes—
29C32×#95C2212yes—
30C3×C3⋊#95C2212yes—
31C3×C3⋊#95C2212yes—
32C3×C3⋊#95C2212yes—
33C3×C3⋊#95C2212yes—
34C2×C3×C4⋊Q8—31no—
35C2×#944C2×C311yescharacteristic
36C3×#391—21no—
37C3×#391—31no—
38C3×#391—32no—
39C3×#391D311yescharacteristic
40C3×#391C2×C311yescharacteristic
41C3×#389—32no—
42C3×#389—32no—
43C3×C4×C4⋊C4—32no—
44C3×C4×C4⋊C4—32no—
45C3×C4×C4⋊C4—32no—
46#5229C2×C311yescharacteristic
47#4976C2×C312yes—
48C4×Dic3⋊C4C2×C312yes—
49#4649C2×C312yes—
50#4649C2×C312yes—
51#4647C2×C312yes—
52#4646C2×C312yes—
53C2×C32×Q8—41no—
54C2×C32×Q8—41no—
55C2×C32×Q8C2×C414yes—
56C22×C32×C4C2312yes—
57C22×C32×C4C2311yescharacteristic
58C22×C32×C4C2311yescharacteristic
59C22×C32×C4C2311yescharacteristic
60C22×C32×C4C2312yes—
61C22×C3×Dic3C2312yes—
62C22×C3×Dic3C2312yes—
63C22×C3×Dic3C2312yes—
64C22×C3×Dic3C2312yes—
65C2×C3×Dic6—41no—
66C2×C3×Dic6—41no—
67C2×C3×Dic6C2×C414yes—
68C32×C4⋊C4—41no—
69C32×C42—41no—
70C3×C4⋊Dic3—41no—
71C3×Dic3⋊C4—24no—
72C3×Dic3⋊C4—42no—
73C3×Dic3⋊C4C2×C418yes—
74C3×Dic3⋊C4C2×C418yes—
75C3×Dic3⋊C4Q818yescomplemented
76C3×C4×Dic3—24no—
77C3×C4×Dic3—24no—
78C3×C4×Dic3—41no—
79C3×C4×Dic3—42no—
80C3×C4×Dic3C2×C414yes—
81#2369—31noSylow
82C22×C3×Q8—21no—
83C22×C3×Q8—31no—
84C22×C3×Q8C2×D311yescharacteristic
85C22×C3×Q8C22×C311yescharacteristic
86C22×Dic6C22×C311yescharacteristic
87C3×C4⋊Q8—38no—
88C2×C3×C4⋊C4—21no—
89C2×C3×C4⋊C4—32no—
90C2×C3×C4⋊C4—32no—
91C2×C3×C4⋊C4—32no—
92C2×C3×C4⋊C4—32no—
93C2×C3×C4⋊C4—32no—
94C2×C3×C4⋊C4—31no—
95C2×C3×C4⋊C4C2×D311yescharacteristic
96C2×C3×C4⋊C4C22×C311yescharacteristic
97C2×C3×C42—21no—
98C2×C3×C42—31no—
99C2×C3×C42—32no—
100C2×C3×C42—32no—
101C2×C3×C42—31no—
102C2×C3×C42—32no—
103C2×C3×C42C2×D311yescharacteristic
104C2×C3×C42C22×C311yescharacteristic
105#944C3×C418yescomplemented
106C2×C4⋊Dic3C22×C311yescharacteristic
107C2×Dic3⋊C4C22×C312yes—
108C2×Dic3⋊C4C22×C312yes—
109C2×Dic3⋊C4C22×C312yes—
110C2×Dic3⋊C4C22×C312yes—
111C2×Dic3⋊C4C22×C312yes—
112C2×C4×Dic3C22×C312yes—
113C2×C4×Dic3C22×C312yes—
114C2×C4×Dic3C22×C312yes—
115C2×C4×Dic3C22×C311yescharacteristic
116C2×C4×Dic3C22×C311yescharacteristic
117C3×#95—22no—
118C3×#95—22no—
119C3×#95—32no—
120C3×#95—32no—
121C3×#95—32no—
122C3×#95—32no—
123C3×#95C2×D312yes—
124C3×#95C2×D312yes—
125C3×#95C22×C312yes—
126C3×#95C22×C312yes—
127C3⋊#95C22×C312yes—
128C3⋊#95C22×C312yes—
129C3⋊#95C22×C312yes—
130C3⋊#95C22×C312yes—
131C23×C32C2411yescharacteristic
132C32×Q8—44no—
133C2×C32×C4—21no—
134C2×C32×C4—21no—
135C2×C32×C4—22no—
136C2×C32×C4—22no—
137C2×C32×C4—21no—
138C2×C32×C4—21no—
139C2×C32×C4—21no—
140C2×C32×C4—21no—
141C2×C32×C4—22no—
142C2×C32×C4—22no—
143C2×C32×C4—22no—
144C2×C32×C4C22×C412yes—
145C2×C32×C4C22×C412yes—
146C2×C32×C4C22×C412yes—
147C2×C32×C4C2×Q814yes—
148C2×C3×Dic3—22no—
149C2×C3×Dic3—22no—
150C2×C3×Dic3—22no—
151C2×C3×Dic3—22no—
152C2×C3×Dic3—22no—
153C2×C3×Dic3—22no—
154C2×C3×Dic3—22no—
155C2×C3×Dic3C22×C414yes—
156C2×C3×Dic3C22×C414yes—
157C2×C3×Dic3C2×Q814yes—
158C2×C3×Dic3C2×Q814yes—
159C2×C3×Dic3#4114yes—
160C3×Dic6—44no—
161C2×C4⋊Q8—31no—
162#391—31no—
163#391—32no—
164#391C3×D311yescharacteristic
165#389—32no—
166#389—32no—
167C4×C4⋊C4—32no—
168C4×C4⋊C4—32no—
169C4×C4⋊C4—32no—
170C2×C3×Q8—24no—
171C2×C3×Q8—34no—
172C2×C3×Q8—41no—
173C2×C3×Q8—41no—
174C2×C3×Q8—41no—
175C2×C3×Q8—41no—
176C2×C3×Q8—42no—
177C2×C3×Q8—42no—
178C2×C3×Q8—121no—
179C2×C3×Q8—121no—
180C2×C3×Q8C4×D314yes—
181C2×C3×Q8C2×C3×C414yes—
182C22×C3×C4—21no—
183C22×C3×C4—22no—
184C22×C3×C4—21no—
185C22×C3×C4—21no—
186C22×C3×C4—22no—
187C22×C3×C4—32no—
188C22×C3×C4—32no—
189C22×C3×C4—32no—
190C22×C3×C4—32no—
191C22×C3×C4C22×D312yes—
192C22×C3×C4C22×D311yescharacteristic
193C22×C3×C4C22×D311yescharacteristic
194C22×C3×C4C22×D311yescharacteristic
195C22×C3×C4C22×D312yes—
196C22×C3×C4C23×C312yes—
197C22×C3×C4C23×C311yescharacteristic
198C22×C3×C4C23×C311yescharacteristic
199C22×C3×C4C23×C311yescharacteristic
200C22×C3×C4C23×C312yes—
201C22×Dic3C23×C312yes—
202C22×Dic3C23×C312yes—
203C22×Dic3C23×C312yes—
204C22×Dic3C23×C312yes—
205C2×Dic6—41no—
206C2×Dic6—41no—
207C2×Dic6C2×C3×C414yes—
208C3×C4⋊C4—38no—
209C3×C4⋊C4—38no—
210C3×C4⋊C4—38no—
211C3×C4⋊C4—41no—
212C3×C4⋊C4—41no—
213C3×C4⋊C4—42no—
214C3×C4⋊C4—64no—
215C3×C4⋊C4—122no—
216C3×C4⋊C4—121no—
217C3×C42—34no—
218C3×C42—41no—
219C3×C42—41no—
220C3×C42—42no—
221C3×C42—64no—
222C3×C42—64no—
223C3×C42—122no—
224C3×C42—121no—
225C4⋊Dic3—41no—
226Dic3⋊C4—24no—
227Dic3⋊C4—42no—
228Dic3⋊C4C2×C3×C418yes—
229Dic3⋊C4C2×C3×C418yes—
230Dic3⋊C4C3×Q818yescomplemented
231C4×Dic3—24no—
232C4×Dic3—24no—
233C4×Dic3—41no—
234C4×Dic3—42no—
235C4×Dic3C2×C3×C414yes—
236C22×C32C23×C411yescharacteristic
237C22×C32C22×Q812yes—
238C22×C32C2×#4112yes—
239C22×C32H(5,𝔽2)11yescharacteristic
240C22×C32H(5,𝔽2)11yescharacteristic
241C32×C4—22no—
242C32×C4—22no—
243C32×C4—22no—
244C32×C4—24no—
245C32×C4—42no—
246C3×Dic3—24no—
247C3×Dic3—24no—
248C3×Dic3—42no—
249C3×Dic3C4×Q818yes—
250C22×Q8—31no—
251C22×Q8C2×C3×D311yescharacteristic
252C4⋊Q8—38no—
253C2×C4⋊C4—32no—
254C2×C4⋊C4—32no—
255C2×C4⋊C4—32no—
256C2×C4⋊C4—32no—
257C2×C4⋊C4—32no—
258C2×C4⋊C4—31no—
259C2×C4⋊C4C2×C3×D311yescharacteristic
260C2×C42—31no—
261C2×C42—32no—
262C2×C42—32no—
263C2×C42—31no—
264C2×C42—32no—
265C2×C42C2×C3×D311yescharacteristic
266#95—32no—
267#95—32no—
268#95—32no—
269#95—32no—
270#95C2×C3×D312yes—
271#95C2×C3×D312yes—
272C23×C3—21no—
273C23×C3C23×D311yescharacteristic
274C23×C3C24×C311yescharacteristic
275C3×Q8—44no—
276C3×Q8—44no—
277C3×Q8—48no—
278C3×Q8—124no—
279C2×C3×C4—22no—
280C2×C3×C4—22no—
281C2×C3×C4—22no—
282C2×C3×C4—21no—
283C2×C3×C4—21no—
284C2×C3×C4—21no—
285C2×C3×C4—21no—
286C2×C3×C4—21no—
287C2×C3×C4—21no—
288C2×C3×C4—22no—
289C2×C3×C4—22no—
290C2×C3×C4—22no—
291C2×C3×C4—21no—
292C2×C3×C4—21no—
293C2×C3×C4—21no—
294C2×C3×C4—21no—
295C2×C3×C4—21no—
296C2×C3×C4—21no—
297C2×C3×C4—22no—
298C2×C3×C4—22no—
299C2×C3×C4—22no—
300C2×C3×C4—22no—
301C2×C3×C4—22no—
302C2×C3×C4—22no—
303C2×C3×C4—22no—
304C2×C3×C4—22no—
305C2×C3×C4—22no—
306C2×C3×C4—24no—
307C2×C3×C4—34no—
308C2×C3×C4—34no—
309C2×C3×C4—34no—
310C2×C3×C4—34no—
311C2×C3×C4—34no—
312C2×C3×C4—42no—
313C2×C3×C4—42no—
314C2×C3×C4—41no—
315C2×C3×C4—41no—
316C2×C3×C4—41no—
317C2×C3×C4—41no—
318C2×C3×C4—42no—
319C2×C3×C4—42no—
320C2×C3×C4—42no—
321C2×C3×C4—62no—
322C2×C3×C4—62no—
323C2×C3×C4—62no—
324C2×C3×C4—62no—
325C2×C3×C4—62no—
326C2×C3×C4—62no—
327C2×C3×C4—62no—
328C2×C3×C4C2×C4×D312yes—
329C2×C3×C4C2×C4×D312yes—
330C2×C3×C4C2×C4×D312yes—
331C2×C3×C4D3×Q814yes—
332C2×C3×C4C22×C3×C412yes—
333C2×C3×C4C22×C3×C412yes—
334C2×C3×C4C22×C3×C412yes—
335C2×C3×C4C2×C3×Q814yes—
336C2×Dic3—22no—
337C2×Dic3—22no—
338C2×Dic3—22no—
339C2×Dic3—22no—
340C2×Dic3—22no—
341C2×Dic3—22no—
342C2×Dic3—22no—
343C2×Dic3C22×C3×C414yes—
344C2×Dic3C22×C3×C414yes—
345C2×Dic3C2×C3×Q814yes—
346C2×Dic3C2×C3×Q814yes—
347C2×Dic3C3×#4114yes—
348Dic6—44no—
349C2×C32C2×C4×Q812yes—
350C2×C32#51811yescharacteristic
351C2×C32#55412yes—
352C2×C32#55511yescharacteristic
353C2×C32Q8211yescharacteristic
354C2×Q8—34no—
355C2×Q8—41no—
356C2×Q8—41no—
357C2×Q8—121no—
358C2×Q8—121no—
359C2×Q8C3×C4×D314yes—
360C22×C4—32no—
361C22×C4—32no—
362C22×C4—32no—
363C22×C4—32no—
364C22×C4C22×C3×D312yes—
365C22×C4C22×C3×D311yescharacteristic
366C22×C4C22×C3×D311yescharacteristic
367C22×C4C22×C3×D311yescharacteristic
368C22×C4C22×C3×D312yes—
369C4⋊C4—38no—
370C4⋊C4—38no—
371C4⋊C4—38no—
372C4⋊C4—41no—
373C4⋊C4—64no—
374C4⋊C4—122no—
375C4⋊C4—121no—
376C42—34no—
377C42—41no—
378C42—64no—
379C42—64no—
380C42—122no—
381C42—121no—
382C22×C3—21no—
383C22×C3—21no—
384C22×C3—21no—
385C22×C3—22no—
386C22×C3—22no—
387C22×C3C22×C4×D311yescharacteristic
388C22×C3#100411yescharacteristic
389C22×C3#100411yescharacteristic
390C22×C3C2×D3×Q812yes—
391C22×C3D3×#4112yes—
392C22×C3C23×C3×C411yescharacteristic
393C22×C3C22×C3×Q812yes—
394C22×C3C2×C3×#4112yes—
395C22×C3C3×H(5,𝔽2)11yescharacteristic
396C22×C3C3×H(5,𝔽2)11yescharacteristic
397C3×C4—24no—
398C3×C4—24no—
399C3×C4—22no—
400C3×C4—22no—
401C3×C4—22no—
402C3×C4—22no—
403C3×C4—22no—
404C3×C4—22no—
405C3×C4—24no—
406C3×C4—38no—
407C3×C4—42no—
408C3×C4—42no—
409C3×C4—44no—
410C3×C4—42no—
411C3×C4—42no—
412C3×C4—64no—
413C3×C4—64no—
414C3×C4—82no—
415C3×C4—122no—
416Dic3—24no—
417Dic3—24no—
418Dic3—42no—
419Dic3C3×C4×Q818yes—
420C32#236911yescharacteristic, complemented, Sylow
421C23C23×C3×D311yescharacteristic
422Q8—44no—
423Q8—124no—
424C2×C4—22no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—22no—
432C2×C4—22no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—34no—
436C2×C4—34no—
437C2×C4—34no—
438C2×C4—34no—
439C2×C4—34no—
440C2×C4—62no—
441C2×C4—62no—
442C2×C4—62no—
443C2×C4—62no—
444C2×C4—62no—
445C2×C4—62no—
446C2×C4—62no—
447C2×C4C2×C3×C4×D312yes—
448C2×C4C2×C3×C4×D312yes—
449C2×C4C2×C3×C4×D312yes—
450C2×C4C3×D3×Q814yes—
451C2×C3—22no—
452C2×C3—22no—
453C2×C3—21no—
454C2×C3—21no—
455C2×C3—21no—
456C2×C3#548611yescharacteristic
457C2×C3C4×D3×Q812yes—
458C2×C3#563612yes—
459C2×C3#567011yescharacteristic
460C2×C3#572211yescharacteristic
461C2×C3C2×C3×C4×Q812yes—
462C2×C3C3×#51811yescharacteristic
463C2×C3C3×#55412yes—
464C2×C3C3×#55511yescharacteristic
465C2×C3C3×Q8211yescharacteristic
466C22C22×C3×C4×D311yescharacteristic
467C22C3×#100411yescharacteristic
468C22C3×#100411yescharacteristic
469C22C2×C3×D3×Q812yes—
470C22C3×D3×#4112yes—
471C4—24no—
472C4—22no—
473C4—22no—
474C4—22no—
475C4—38no—
476C4—42no—
477C4—64no—
478C4—64no—
479C4—122no—
480C3—21no—
481C3#7649411yescharacteristic, direct product factor
482C3C3×#236911yescharacteristic, complemented
483C2C3×#548611yescharacteristic
484C2C3×C4×D3×Q812yes—
485C2C3×#563612yes—
486C2C3×#567011yescharacteristic
487C2C3×#572211yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutatorC22×C3C23×C3×C4
FrattiniC23C23×C3×D3
FittingC32×#391C2
socle, prime radicalC23×C32C24
cosocleC23×C3C24×C3
hypercenterC3×#391D3
hypocenterC3C3×#2369
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C3×#391

Complements

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

NH ≅ G/Ntype
11. #76494C3direct (N × H)
16. C3×#944C4semidirect
75. C3×Dic3⋊C4Q8semidirect
105. #944C3×C4semidirect
230. Dic3⋊C4C3×Q8semidirect
420. C32#2369semidirect
481. C3#76494direct (N × H)
482. C3C3×#2369semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9442
C32×#3912
C3×#52292
C3×#49762
C3×C4×Dic3⋊C42
C3×#46492
C3×#46472
C3×#46462
C3×#23693
#764943