Finite Group Databasebeta

← C3×#81596 #11877026

Subgroups — C3×#81596 #11877026

Order 1152.

765 conjugacy classes of subgroups.

The subgroup lattice has 451 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5728C211yesmaximal, characteristic
2C3×#5728C211yesmaximal, characteristic
3C32×#487C211yesmaximal, characteristic, complemented
4C3×#5092C211yesmaximal, characteristic, complemented
5C3×#5080C211yesmaximal, characteristic, complemented
6C3×#4816C214yesmaximal
7C3×#4789C214yesmaximal, complemented
8C3×C4×ΓL(1,𝔽25)C211yesmaximal, characteristic
9C3×#4681C211yesmaximal, characteristic, complemented
10C3×#3185—31nomaximal
11#81596C311yesmaximal, characteristic, direct product factor
12C32×C4⋊Q8C2211yescharacteristic
13C32×C4⋊Q8C2211yescharacteristic
14C3×#946—21no—
15C3×#946C2212yes—
16C3×Q8×Dic3—21no—
17C3×Q8×Dic3C2212yes—
18C2×C3×#216C2214yes—
19C2×C3×ΓL(1,𝔽25)C2212yes—
20C3×#897—21no—
21C3×#897C2212yes—
22C3×#892—21no—
23C3×#892—21no—
24C3×#890—21no—
25C3×#890—21no—
26C3×#887—21no—
27C3×#887C2212yes—
28C3×C42×D3C2211yescharacteristic
29C3×#869C2211yescharacteristic
30C3×#869C2211yescharacteristic
31C32×#103C2214yes—
32C32×C4×C8C2211yescharacteristic
33C3×#816C2214yes—
34C3×#815C2212yes—
35C3×#808C2214yes—
36C3×C4×C3⋊C8C2211yescharacteristic
37C3×#533—31no—
38C3×#533—31no—
39#5728C2×C311yescharacteristic
40#5728C2×C311yescharacteristic
41C3×#498—31no—
42C3×#494—31no—
43C3×#487—21no—
44C3×#487—31no—
45C3×#487D311yescharacteristic, complemented
46C3×#487C2×C311yescharacteristic, complemented
47C3×#470—34no—
48C3×#441—34no—
49C3×C4×M16—31no—
50#5092C2×C311yescharacteristic, complemented
51#5080C2×C311yescharacteristic, complemented
52#4816C2×C314yes—
53#4789C2×C314yescomplemented
54C4×ΓL(1,𝔽25)C2×C311yescharacteristic
55#4681C2×C311yescharacteristic, complemented
56C2×C32×Q8—21no—
57C2×C32×Q8C2312yes—
58C2×C3×C4×D3D411yescharacteristic
59C2×C3×C4×D3D411yescharacteristic
60C2×C3×C4×D3C2311yescharacteristic
61C2×C3×Dic6—21no—
62C2×C3×Dic6C2312yes—
63C2×C32×C8C2312yes—
64C32×C4⋊C4—21no—
65C32×C4⋊C4—21no—
66C32×C4⋊C4—21no—
67C32×C4⋊C4C2312yes—
68C32×C42C2311yescharacteristic
69C3×#216—28no—
70C3×(C2×D3)⋊C4—22no—
71C3×(C2×D3)⋊C4—22no—
72C3×C4⋊Dic3—21no—
73C3×C4⋊Dic3—21no—
74C3×C4⋊Dic3—21no—
75C3×C4⋊Dic3—22no—
76C3×C4⋊Dic3—22no—
77C3×C4⋊Dic3C2312yes—
78C3×Dic3⋊C4—22no—
79C3×Dic3⋊C4—22no—
80C3×C4×Dic3—22no—
81C3×C4×Dic3—22no—
82C3×C4×Dic3D411yescharacteristic
83C3×C4×Dic3D411yescharacteristic
84C3×C4×Dic3C2311yescharacteristic
85C2×C3×C3⋊C8C2312yes—
86C3×ΓL(1,𝔽25)—24no—
87#3185—31noSylow
88C2×C3×Q16—34no—
89C2×C3×M16—32no—
90C3×C4⋊Q8—21no—
91C3×C4⋊Q8—21no—
92C3×C4⋊Q8—31no—
93C3×C4⋊Q8—31no—
94C3×C4⋊Q8C2×D311yescharacteristic
95C3×C4⋊Q8C2×D311yescharacteristic
96C3×C4⋊Q8C22×C311yescharacteristic
97C3×C4⋊Q8C22×C311yescharacteristic
98C3×#125—61no—
99C3×#125—61no—
100C3×C22⋊Q8—32no—
101C3×C22⋊Q8—32no—
102C3×C22⋊Q8—61no—
103C3×C22⋊Q8—61no—
104C3×C4×Q8—32no—
105C3×C4×Q8—32no—
106C3×C4×Q8—61no—
107C3×C4×Q8—61no—
108C3×#117—61no—
109C3×#117—61no—
110C2×C3×C42—31no—
111#946—21no—
112#946C22×C312yes—
113Q8×Dic3—21no—
114Q8×Dic3C22×C312yes—
115C2×#216C22×C314yes—
116C2×ΓL(1,𝔽25)C22×C312yes—
117#897—21no—
118#897C22×C312yes—
119#892—21no—
120#892—21no—
121#890—21no—
122#890—21no—
123#887—21no—
124#887C22×C312yes—
125C42×D3C22×C311yescharacteristic
126#869C22×C311yescharacteristic
127#869C22×C311yescharacteristic
128C3×#106—34no—
129C3×#103—24no—
130C3×#103—34no—
131C3×#103C2×D314yes—
132C3×#103C22×C314yes—
133C3×#97—32no—
134C3×C4×C8—21no—
135C3×C4×C8—31no—
136C3×C4×C8C2×D311yescharacteristic
137C3×C4×C8C22×C311yescharacteristic
138#816C22×C314yes—
139#815C22×C312yes—
140#808C22×C314yes—
141C4×C3⋊C8C22×C311yescharacteristic
142C22×C3×D3C2×D411yescharacteristic
143C32×Q8—24no—
144C32×Q8—42no—
145C2×C32×C4—22no—
146C2×C32×C4—22no—
147C2×C32×C4C2×D411yescharacteristic
148C2×C32×C4C2×D411yescharacteristic
149C2×C32×C4C2411yescharacteristic
150C2×C3×Dic3—22no—
151C2×C3×Dic3—22no—
152C2×C3×Dic3C2×D411yescharacteristic
153C2×C3×Dic3C2×D411yescharacteristic
154C2×C3×Dic3C2×D411yescharacteristic
155C3×C4×D3—22no—
156C3×C4×D3—22no—
157C3×C4×D3—22no—
158C3×Dic6—24no—
159C3×Dic6—42no—
160C32×C8—22no—
161C3×C3⋊C8#4114yes—
162#533—31no—
163#533—31no—
164#498—31no—
165#494—31no—
166#487—31no—
167#487C3×D311yescharacteristic, complemented
168#470—34no—
169#441—34no—
170C4×M16—31no—
171C2×C3×Q8—21no—
172C2×C3×Q8—21no—
173C2×C3×Q8—22no—
174C2×C3×Q8—32no—
175C2×C3×Q8—41no—
176C2×C3×Q8—61no—
177C2×C3×Q8C22×D312yes—
178C2×C3×Q8C23×C312yes—
179C22×C3×C4—31no—
180C22×C3×C4—31no—
181C22×C3×C4—31no—
182C2×C4×D3C3×D411yescharacteristic
183C2×C4×D3C3×D411yescharacteristic
184C2×C4×D3C23×C311yescharacteristic
185C2×Dic6—21no—
186C2×Dic6C23×C312yes—
187C3×Q16—68no—
188C3×M16—64no—
189C2×C3×C8—22no—
190C2×C3×C8—32no—
191C2×C3×C8C22×D312yes—
192C2×C3×C8C23×C312yes—
193C3×C4⋊C4—21no—
194C3×C4⋊C4—21no—
195C3×C4⋊C4—21no—
196C3×C4⋊C4—21no—
197C3×C4⋊C4—21no—
198C3×C4⋊C4—21no—
199C3×C4⋊C4—22no—
200C3×C4⋊C4—32no—
201C3×C4⋊C4—41no—
202C3×C4⋊C4—41no—
203C3×C4⋊C4—41no—
204C3×C4⋊C4—62no—
205C3×C4⋊C4—62no—
206C3×C4⋊C4—62no—
207C3×C4⋊C4—62no—
208C3×C4⋊C4—61no—
209C3×C4⋊C4—61no—
210C3×C4⋊C4—61no—
211C3×C4⋊C4C22×D312yes—
212C3×C4⋊C4C23×C312yes—
213C3×C22⋊C4—62no—
214C3×C22⋊C4—62no—
215C3×C42—21no—
216C3×C42—31no—
217C3×C42—31no—
218C3×C42—31no—
219C3×C42—62no—
220C3×C42—62no—
221C3×C42C22×D311yescharacteristic
222C3×C42C23×C311yescharacteristic
223#216—28no—
224(C2×D3)⋊C4—22no—
225(C2×D3)⋊C4—22no—
226C4⋊Dic3—21no—
227C4⋊Dic3—21no—
228C4⋊Dic3—21no—
229C4⋊Dic3—22no—
230C4⋊Dic3—22no—
231C4⋊Dic3C23×C312yes—
232Dic3⋊C4—22no—
233Dic3⋊C4—22no—
234C4×Dic3—22no—
235C4×Dic3—22no—
236C4×Dic3C3×D411yescharacteristic
237C4×Dic3C3×D411yescharacteristic
238C4×Dic3C23×C311yescharacteristic
239C2×C3⋊C8C23×C312yes—
240ΓL(1,𝔽25)—24no—
241C22×C32C22×D411yescharacteristic
242C2×C3×D3—21no—
243C2×C3×D3—21no—
244C2×C3×D3—21no—
245C32×C4—42no—
246C32×C4—42no—
247C32×C4#13712yes—
248C32×C4#13712yes—
249C32×C4C2×#4112yes—
250C3×Dic3—21no—
251C3×Dic3—21no—
252C3×Dic3—21no—
253C3×Dic3—42no—
254C3×Dic3—42no—
255C2×Q16—34no—
256C2×M16—32no—
257C4⋊Q8—31no—
258C4⋊Q8—31no—
259C4⋊Q8C2×C3×D311yescharacteristic
260C4⋊Q8C2×C3×D311yescharacteristic
261#125—61no—
262#125—61no—
263C22⋊Q8—32no—
264C22⋊Q8—32no—
265C22⋊Q8—61no—
266C22⋊Q8—61no—
267C4×Q8—32no—
268C4×Q8—32no—
269C4×Q8—61no—
270C4×Q8—61no—
271#117—61no—
272#117—61no—
273C2×C42—31no—
274#106—34no—
275#103—34no—
276#103C2×C3×D314yes—
277#97—32no—
278C4×C8—31no—
279C4×C8C2×C3×D311yescharacteristic
280C23×C3—31no—
281C22×D3C2×C3×D411yescharacteristic
282C3×Q8—24no—
283C3×Q8—24no—
284C3×Q8—44no—
285C3×Q8—42no—
286C3×Q8—42no—
287C3×Q8—64no—
288C3×Q8—82no—
289C3×Q8—122no—
290C2×C3×C4—22no—
291C2×C3×C4—22no—
292C2×C3×C4—22no—
293C2×C3×C4—22no—
294C2×C3×C4—21no—
295C2×C3×C4—21no—
296C2×C3×C4—21no—
297C2×C3×C4—31no—
298C2×C3×C4—31no—
299C2×C3×C4—31no—
300C2×C3×C4—42no—
301C2×C3×C4—42no—
302C2×C3×C4—62no—
303C2×C3×C4—62no—
304C2×C3×C4—62no—
305C2×C3×C4—62no—
306C2×C3×C4—62no—
307C2×C3×C4D3×D411yescharacteristic
308C2×C3×C4D3×D411yescharacteristic
309C2×C3×C4C2×C3×D411yescharacteristic
310C2×C3×C4C2×C3×D411yescharacteristic
311C2×C3×C4C23×D311yescharacteristic
312C2×C3×C4C24×C311yescharacteristic
313C2×Dic3—22no—
314C2×Dic3—22no—
315C2×Dic3C2×C3×D411yescharacteristic
316C2×Dic3C2×C3×D411yescharacteristic
317C2×Dic3C2×C3×D411yescharacteristic
318C4×D3—22no—
319C4×D3—22no—
320C4×D3—22no—
321Dic6—24no—
322Dic6—42no—
323C3×C8—22no—
324C3×C8—22no—
325C3×C8—34no—
326C3×C8—42no—
327C3⋊C8C3×#4114yes—
328C2×C32#53211yescharacteristic
329C2×C32C2×#13711yescharacteristic
330C2×C32C2×#13711yescharacteristic
331C3×D3—41no—
332C2×Q8—21no—
333C2×Q8—32no—
334C2×Q8—61no—
335C2×Q8C22×C3×D312yes—
336C22×C4—31no—
337C22×C4—31no—
338C22×C4—31no—
339Q16—68no—
340M16—64no—
341C2×C8—32no—
342C2×C8C22×C3×D312yes—
343C4⋊C4—21no—
344C4⋊C4—21no—
345C4⋊C4—21no—
346C4⋊C4—32no—
347C4⋊C4—62no—
348C4⋊C4—62no—
349C4⋊C4—62no—
350C4⋊C4—62no—
351C4⋊C4—61no—
352C4⋊C4—61no—
353C4⋊C4—61no—
354C4⋊C4C22×C3×D312yes—
355C22⋊C4—62no—
356C22⋊C4—62no—
357C42—31no—
358C42—31no—
359C42—31no—
360C42—62no—
361C42—62no—
362C42C22×C3×D311yescharacteristic
363C22×C3—21no—
364C22×C3—61no—
365C22×C3—61no—
366C22×C3—61no—
367C22×C3C2×D3×D411yescharacteristic
368C22×C3C22×C3×D411yescharacteristic
369C2×D3—21no—
370C2×D3—21no—
371C2×D3—21no—
372C3×C4—22no—
373C3×C4—22no—
374C3×C4—22no—
375C3×C4—42no—
376C3×C4—42no—
377C3×C4—42no—
378C3×C4—42no—
379C3×C4—61no—
380C3×C4—61no—
381C3×C4—61no—
382C3×C4—82no—
383C3×C4—82no—
384C3×C4—122no—
385C3×C4—122no—
386C3×C4#91512yes—
387C3×C4#91812yes—
388C3×C4C3×#13712yes—
389C3×C4C3×#13712yes—
390C3×C4D3×#4112yes—
391C3×C4C2×C3×#4112yes—
392Dic3—21no—
393Dic3—21no—
394Dic3—21no—
395Dic3—42no—
396Dic3—42no—
397C32#318511yescharacteristic, complemented, Sylow
398C23—31no—
399Q8—24no—
400Q8—42no—
401Q8—64no—
402Q8—122no—
403C2×C4—22no—
404C2×C4—22no—
405C2×C4—31no—
406C2×C4—31no—
407C2×C4—31no—
408C2×C4—62no—
409C2×C4—62no—
410C2×C4—62no—
411C2×C4—62no—
412C2×C4—62no—
413C2×C4C3×D3×D411yescharacteristic
414C2×C4C3×D3×D411yescharacteristic
415C2×C4C23×C3×D311yescharacteristic
416C8—22no—
417C8—34no—
418C2×C3—21no—
419C2×C3—21no—
420C2×C3—21no—
421C2×C3—121no—
422C2×C3#566811yescharacteristic
423C2×C3C2×#91511yescharacteristic
424C2×C3C2×#91811yescharacteristic
425C2×C3C3×#53211yescharacteristic
426C2×C3C2×C3×#13711yescharacteristic
427C2×C3C2×C3×#13711yescharacteristic
428D3—41no—
429C22—61no—
430C22—61no—
431C22—61no—
432C22C2×C3×D3×D411yescharacteristic
433C4—42no—
434C4—42no—
435C4—61no—
436C4—61no—
437C4—61no—
438C4—122no—
439C4—122no—
440C4C3×#91512yes—
441C4C3×#91812yes—
442C4C3×D3×#4112yes—
443C3—21no—
444C3#8159611yescharacteristic, direct product factor
445C3C3×#318511yescharacteristic, complemented
446C2—121no—
447C2C3×#566811yescharacteristic
448C2C2×C3×#91511yescharacteristic
449C2C2×C3×#91811yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#487C2
socleC22×C32C22×D4
prime radicalC22×C3×D3C2×D4
hypercenterC3×#487D3
hypocenterC3C3×#3185
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#487

Complements

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

NH ≅ G/Ntype
3. C32×#487C2semidirect
4. C3×#5092C2semidirect
5. C3×#5080C2semidirect
7. C3×#4789C2semidirect
9. C3×#4681C2semidirect
11. #81596C3direct (N × H)
45. C3×#487D3semidirect
46. C3×#487C2×C3semidirect
50. #5092C2×C3semidirect
51. #5080C2×C3semidirect
53. #4789C2×C3semidirect
55. #4681C2×C3semidirect
167. #487C3×D3semidirect
397. C32#3185semidirect
444. C3#81596direct (N × H)
445. C3C3×#3185semidirect

Maximal subgroups

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

subgroupindex
C3×#57282
C32×#4872
C3×#50922
C3×#50802
C3×#48162
C3×#47892
C3×C4×ΓL(1,𝔽25)2
C3×#46812
C3×#31853
#815963