Finite Group Databasebeta

← C3×#68309 #11775073

Subgroups — C3×#68309 #11775073

Order 1152.

520 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5622C211yesmaximal, characteristic
2C3×#4718C211yesmaximal, characteristic
3C3×#4649C211yesmaximal, characteristic
4C32×#328C211yesmaximal, characteristic
5C3×#4538C211yesmaximal, characteristic
6C3×#4467C211yesmaximal, characteristic
7C3×#4452C211yesmaximal, characteristic
8C3×#1503—31nomaximal
9#68309C311yesmaximal, characteristic, direct product factor
10C32×C22⋊Q8C2211yescharacteristic
11C3×Q8×Dic3C411yescharacteristic, complemented
12C3×#944C411yescharacteristic, complemented
13C3×#924C2211yescharacteristic
14C2×C3×Dic3⋊C4—21no—
15C2×C3×C4×Dic3—21no—
16C2×C3×C4×Dic3C2211yescharacteristic
17C3×#889—21no—
18C3×#888C411yescharacteristic, complemented
19C3×#887—21no—
20C3×#887C411yescharacteristic, complemented
21C3×#878—21no—
22C3×#877—21no—
23C32×C22⋊C8C2211yescharacteristic
24C32×#95C2211yescharacteristic
25C3×C3⋊#95C2211yescharacteristic
26C3×#830C2211yescharacteristic
27C3×Dic3⋊C8—21no—
28C3×C8×Dic3—21no—
29C3×#533—31no—
30#5622C2×C311yescharacteristic
31C3×#431—31no—
32C3×C4×C4⋊C4—31no—
33#4718C2×C311yescharacteristic
34#4649C2×C311yescharacteristic
35C3×#328—21no—
36C3×#328—31no—
37C3×#328—31no—
38C3×#328—31no—
39C3×#328D311yescharacteristic
40C3×#328C2×C311yescharacteristic
41#4538C2×C311yescharacteristic
42#4467C2×C311yescharacteristic
43#4452C2×C311yescharacteristic
44C2×C32×Q8C2×C411yescharacteristic
45C22×C32×C4—21no—
46C22×C32×C4C2311yescharacteristic
47C22×C3×Dic3—21no—
48C22×C3×Dic3D411yescharacteristic
49C22×C3×Dic3D411yescharacteristic
50C2×C3×Dic6—21no—
51C2×C3×Dic6C2×C411yescharacteristic
52C2×C32×C8—21no—
53C32×C4⋊C4—21no—
54C32×C4⋊C4C2×C411yescharacteristic
55C32×C22⋊C4—21no—
56C3×#217—21no—
57C3×C4⋊Dic3—21no—
58C3×C4⋊Dic3C2×C411yescharacteristic
59C3×Dic3⋊C4—24no—
60C3×Dic3⋊C4—21no—
61C3×Dic3⋊C4—21no—
62C3×Dic3⋊C4—21no—
63C3×Dic3⋊C4—21no—
64C3×Dic3⋊C4—21no—
65C3×C4×Dic3—21no—
66C3×C4×Dic3—21no—
67C3×C4×Dic3—42no—
68C3×C4×Dic3C2×C411yescharacteristic
69C3×C4×Dic3C2×C411yescharacteristic
70C3×C4×Dic3D411yescharacteristic
71C3×C4×Dic3D411yescharacteristic
72C2×C3×C3⋊C8—21no—
73#1503—31noSylow
74C3×C4⋊Q8—31no—
75C3×C4⋊Q8—31no—
76C3×#125—61no—
77C3×C22⋊Q8—21no—
78C3×C22⋊Q8—31no—
79C3×C22⋊Q8—61no—
80C3×C22⋊Q8C2×D311yescharacteristic
81C3×C22⋊Q8C22×C311yescharacteristic
82C3×C4×Q8—31no—
83C3×C4×Q8—31no—
84C3×C4×Q8—61no—
85C3×#117—61no—
86C2×C3×C4⋊C4—61no—
87C2×C3×C42—31no—
88C2×C3×C42—61no—
89Q8×Dic3C3×C411yescharacteristic, complemented
90#944C3×C411yescharacteristic, complemented
91#924C22×C311yescharacteristic
92C2×Dic3⋊C4—21no—
93C2×C4×Dic3—21no—
94C2×C4×Dic3C22×C311yescharacteristic
95#889—21no—
96#888C3×C411yescharacteristic, complemented
97#887—21no—
98#887C3×C411yescharacteristic, complemented
99#878—21no—
100#877—21no—
101C3×C4⋊C8—61no—
102C3×C22⋊C8—21no—
103C3×C22⋊C8—31no—
104C3×C22⋊C8C2×D311yescharacteristic
105C3×C22⋊C8C22×C311yescharacteristic
106C3×C4×C8—61no—
107C3×#95—21no—
108C3×#95—31no—
109C3×#95C2×D311yescharacteristic
110C3×#95C22×C311yescharacteristic
111C3⋊#95C22×C311yescharacteristic
112#830C22×C311yescharacteristic
113Dic3⋊C8—21no—
114C8×Dic3—21no—
115C23×C32C2×D411yescharacteristic
116C32×Q8—41no—
117C2×C32×C4—22no—
118C2×C32×C4—21no—
119C2×C32×C4—21no—
120C2×C32×C4—41no—
121C2×C32×C4—41no—
122C2×C32×C4—41no—
123C2×C32×C4C22×C411yescharacteristic
124C2×C32×C4C2×D411yescharacteristic
125C2×C3×Dic3—22no—
126C2×C3×Dic3—22no—
127C2×C3×Dic3—21no—
128C2×C3×Dic3—21no—
129C2×C3×Dic3—41no—
130C2×C3×Dic3—41no—
131C2×C3×Dic3C22⋊C411yescharacteristic
132C2×C3×Dic3C22⋊C411yescharacteristic
133C2×C3×Dic3C22⋊C411yescharacteristic
134C2×C3×Dic3C22⋊C411yescharacteristic
135C2×C3×Dic3SD1612yes—
136C2×C3×Dic3Q1612yes—
137C3×Dic6—42no—
138C3×Dic6—41no—
139C32×C8—41no—
140C3×C3⋊C8—41no—
141#533—31no—
142#431—31no—
143C4×C4⋊C4—31no—
144#328—31no—
145#328—31no—
146#328—31no—
147#328C3×D311yescharacteristic
148C2×C3×Q8—21no—
149C2×C3×Q8—31no—
150C2×C3×Q8—61no—
151C2×C3×Q8C4×D311yescharacteristic
152C2×C3×Q8C2×C3×C411yescharacteristic
153C22×C3×C4—21no—
154C22×C3×C4—21no—
155C22×C3×C4—21no—
156C22×C3×C4—31no—
157C22×C3×C4—31no—
158C22×C3×C4—41no—
159C22×C3×C4—61no—
160C22×C3×C4C22×D311yescharacteristic
161C22×C3×C4C23×C311yescharacteristic
162C22×Dic3—21no—
163C22×Dic3C3×D411yescharacteristic
164C22×Dic3C3×D411yescharacteristic
165C2×Dic6—21no—
166C2×Dic6C2×C3×C411yescharacteristic
167C2×C3×C8—21no—
168C2×C3×C8—21no—
169C2×C3×C8—41no—
170C2×C3×C8—61no—
171C3×C4⋊C4—21no—
172C3×C4⋊C4—21no—
173C3×C4⋊C4—21no—
174C3×C4⋊C4—31no—
175C3×C4⋊C4—41no—
176C3×C4⋊C4—61no—
177C3×C4⋊C4—61no—
178C3×C4⋊C4—61no—
179C3×C4⋊C4—61no—
180C3×C4⋊C4—61no—
181C3×C4⋊C4—64no—
182C3×C4⋊C4—61no—
183C3×C4⋊C4C4×D311yescharacteristic
184C3×C4⋊C4C2×C3×C411yescharacteristic
185C3×C22⋊C4—21no—
186C3×C22⋊C4—21no—
187C3×C22⋊C4—41no—
188C3×C22⋊C4—61no—
189C3×C42—31no—
190C3×C42—31no—
191C3×C42—31no—
192C3×C42—31no—
193C3×C42—61no—
194C3×C42—61no—
195C3×C42—122no—
196#217—21no—
197C4⋊Dic3—21no—
198C4⋊Dic3C2×C3×C411yescharacteristic
199Dic3⋊C4—24no—
200Dic3⋊C4—21no—
201Dic3⋊C4—21no—
202Dic3⋊C4—21no—
203Dic3⋊C4—21no—
204Dic3⋊C4—21no—
205C4×Dic3—21no—
206C4×Dic3—21no—
207C4×Dic3—42no—
208C4×Dic3C2×C3×C411yescharacteristic
209C4×Dic3C2×C3×C411yescharacteristic
210C4×Dic3C3×D411yescharacteristic
211C4×Dic3C3×D411yescharacteristic
212C2×C3⋊C8—21no—
213C22×C32—21no—
214C22×C32—21no—
215C22×C32C2×C22⋊C411yescharacteristic
216C22×C32C2×SD1611yescharacteristic
217C22×C32C2×Q1611yescharacteristic
218C32×C4—21no—
219C32×C4—21no—
220C32×C4—42no—
221C32×C4—41no—
222C32×C4—41no—
223C3×Dic3—21no—
224C3×Dic3—42no—
225C3×Dic3—41no—
226C3×Dic3—41no—
227C3×Dic3#10312yes—
228C3×Dic3#10312yes—
229C3×Dic3#10412yes—
230C4⋊Q8—31no—
231C4⋊Q8—31no—
232#125—61no—
233C22⋊Q8—31no—
234C22⋊Q8—61no—
235C22⋊Q8C2×C3×D311yescharacteristic
236C4×Q8—31no—
237C4×Q8—31no—
238C4×Q8—61no—
239#117—61no—
240C2×C4⋊C4—61no—
241C2×C42—31no—
242C2×C42—61no—
243C4⋊C8—61no—
244C22⋊C8—31no—
245C22⋊C8C2×C3×D311yescharacteristic
246C4×C8—61no—
247#95—31no—
248#95C2×C3×D311yescharacteristic
249C23×C3—21no—
250C23×C3D3×D411yescharacteristic
251C23×C3C2×C3×D411yescharacteristic
252C3×Q8—41no—
253C3×Q8—41no—
254C3×Q8—81no—
255C3×Q8—121no—
256C3×Q8—122no—
257C2×C3×C4—22no—
258C2×C3×C4—22no—
259C2×C3×C4—21no—
260C2×C3×C4—21no—
261C2×C3×C4—21no—
262C2×C3×C4—21no—
263C2×C3×C4—21no—
264C2×C3×C4—21no—
265C2×C3×C4—31no—
266C2×C3×C4—31no—
267C2×C3×C4—31no—
268C2×C3×C4—32no—
269C2×C3×C4—32no—
270C2×C3×C4—31no—
271C2×C3×C4—41no—
272C2×C3×C4—41no—
273C2×C3×C4—42no—
274C2×C3×C4—41no—
275C2×C3×C4—41no—
276C2×C3×C4—41no—
277C2×C3×C4—41no—
278C2×C3×C4—41no—
279C2×C3×C4—41no—
280C2×C3×C4—62no—
281C2×C3×C4—62no—
282C2×C3×C4—61no—
283C2×C3×C4—61no—
284C2×C3×C4—81no—
285C2×C3×C4—81no—
286C2×C3×C4—81no—
287C2×C3×C4—121no—
288C2×C3×C4—121no—
289C2×C3×C4C2×C4×D311yescharacteristic
290C2×C3×C4D3×D411yescharacteristic
291C2×C3×C4C22×C3×C411yescharacteristic
292C2×C3×C4C2×C3×D411yescharacteristic
293C2×Dic3—22no—
294C2×Dic3—22no—
295C2×Dic3—21no—
296C2×Dic3—21no—
297C2×Dic3—41no—
298C2×Dic3—41no—
299C2×Dic3C3×C22⋊C411yescharacteristic
300C2×Dic3C3×C22⋊C411yescharacteristic
301C2×Dic3C3×C22⋊C411yescharacteristic
302C2×Dic3C3×C22⋊C411yescharacteristic
303C2×Dic3C3×SD1612yes—
304C2×Dic3C3×Q1612yes—
305Dic6—42no—
306Dic6—41no—
307C3×C8—41no—
308C3×C8—41no—
309C3×C8—81no—
310C3×C8—121no—
311C3⋊C8—41no—
312C2×C32—21no—
313C2×C32—21no—
314C2×C32#41011yescharacteristic
315C2×C32C2×#10311yescharacteristic
316C2×C32C2×#10411yescharacteristic
317C2×Q8—31no—
318C2×Q8—61no—
319C2×Q8C3×C4×D311yescharacteristic
320C22×C4—21no—
321C22×C4—31no—
322C22×C4—31no—
323C22×C4—61no—
324C22×C4C22×C3×D311yescharacteristic
325C2×C8—21no—
326C2×C8—61no—
327C4⋊C4—21no—
328C4⋊C4—31no—
329C4⋊C4—61no—
330C4⋊C4—61no—
331C4⋊C4—61no—
332C4⋊C4—61no—
333C4⋊C4—61no—
334C4⋊C4—64no—
335C4⋊C4—61no—
336C4⋊C4C3×C4×D311yescharacteristic
337C22⋊C4—21no—
338C22⋊C4—61no—
339C42—31no—
340C42—31no—
341C42—31no—
342C42—31no—
343C42—61no—
344C42—61no—
345C42—122no—
346C22×C3—21no—
347C22×C3—21no—
348C22×C3—21no—
349C22×C3—21no—
350C22×C3—21no—
351C22×C3—21no—
352C22×C3—21no—
353C22×C3—41no—
354C22×C3—41no—
355C22×C3D3×C22⋊C411yescharacteristic
356C22×C3D3×SD1611yescharacteristic
357C22×C3D3×Q1611yescharacteristic
358C22×C3C2×C3×C22⋊C411yescharacteristic
359C22×C3C2×C3×SD1611yescharacteristic
360C22×C3C2×C3×Q1611yescharacteristic
361C3×C4—21no—
362C3×C4—21no—
363C3×C4—21no—
364C3×C4—21no—
365C3×C4—32no—
366C3×C4—32no—
367C3×C4—32no—
368C3×C4—41no—
369C3×C4—41no—
370C3×C4—42no—
371C3×C4—42no—
372C3×C4—41no—
373C3×C4—41no—
374C3×C4—41no—
375C3×C4—41no—
376C3×C4—61no—
377C3×C4—81no—
378C3×C4—81no—
379C3×C4—82no—
380C3×C4—122no—
381C3×C4—121no—
382C3×C4—121no—
383Dic3—21no—
384Dic3—42no—
385Dic3—41no—
386Dic3—41no—
387Dic3C3×#10312yes—
388Dic3C3×#10312yes—
389Dic3C3×#10412yes—
390C32#150311yescharacteristic, complemented, Sylow
391C23C3×D3×D411yescharacteristic
392Q8—41no—
393Q8—121no—
394Q8—122no—
395C2×C4—22no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—31no—
399C2×C4—31no—
400C2×C4—31no—
401C2×C4—32no—
402C2×C4—32no—
403C2×C4—31no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—62no—
408C2×C4—62no—
409C2×C4—61no—
410C2×C4—61no—
411C2×C4—121no—
412C2×C4—121no—
413C2×C4C2×C3×C4×D311yescharacteristic
414C2×C4C3×D3×D411yescharacteristic
415C8—41no—
416C8—121no—
417C2×C3—21no—
418C2×C3—21no—
419C2×C3—21no—
420C2×C3—21no—
421C2×C3—21no—
422C2×C3—21no—
423C2×C3—21no—
424C2×C3—41no—
425C2×C3—41no—
426C2×C3#474011yescharacteristic
427C2×C3D3×#10311yescharacteristic
428C2×C3D3×#10411yescharacteristic
429C2×C3C3×#41011yescharacteristic
430C2×C3C2×C3×#10311yescharacteristic
431C2×C3C2×C3×#10411yescharacteristic
432C22—21no—
433C22—21no—
434C22C3×D3×C22⋊C411yescharacteristic
435C22C3×D3×SD1611yescharacteristic
436C22C3×D3×Q1611yescharacteristic
437C4—21no—
438C4—21no—
439C4—32no—
440C4—32no—
441C4—32no—
442C4—42no—
443C4—41no—
444C4—41no—
445C4—61no—
446C4—122no—
447C4—121no—
448C4—121no—
449C3—21no—
450C3#6830911yescharacteristic, direct product factor
451C3C3×#150311yescharacteristic, complemented
452C2—21no—
453C2—21no—
454C2C3×#474011yescharacteristic
455C2C3×D3×#10311yescharacteristic
456C2C3×D3×#10411yescharacteristic
subgroupG/H
centerC22×C3D3×C22⋊C4
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC32×#328C2
socleC22×C32C2×C22⋊C4
prime radicalC23×C32C2×D4
cosocleC22×C3×C4C23×C3
hypercenterC3×#328D3
hypocenterC3C3×#1503
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#328

Complements

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

NH ≅ G/Ntype
9. #68309C3direct (N × H)
11. C3×Q8×Dic3C4semidirect
12. C3×#944C4semidirect
18. C3×#888C4semidirect
20. C3×#887C4semidirect
89. Q8×Dic3C3×C4semidirect
90. #944C3×C4semidirect
96. #888C3×C4semidirect
98. #887C3×C4semidirect
390. C32#1503semidirect
450. C3#68309direct (N × H)
451. C3C3×#1503semidirect

Maximal subgroups

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

subgroupindex
C3×#56222
C3×#47182
C3×#46492
C32×#3282
C3×#45382
C3×#44672
C3×#44522
C3×#15033
#683093