Finite Group Databasebeta

← C3×#79838 #11877020

Subgroups — C3×#79838 #11877020

Order 1152.

770 conjugacy classes of subgroups.

The subgroup lattice has 455 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5578C212yesmaximal
2C32×#441C211yesmaximal, characteristic, complemented
3C3×#5189C211yesmaximal, characteristic
4C3×#5183C211yesmaximal, characteristic, complemented
5C3×#5030C212yesmaximal, complemented
6C3×#4867C211yesmaximal, characteristic
7C3×#4855C211yesmaximal, characteristic, complemented
8C3×#4816C212yesmaximal
9C3×#4792C212yesmaximal, complemented
10C3×#4716C211yesmaximal, characteristic, complemented
11C3×#4707C211yesmaximal, characteristic
12C3×#3185—31nomaximal
13#79838C311yesmaximal, characteristic, direct product factor
14C2×C32×Q16C2211yescharacteristic
15C32×C4×Q8C2212yes—
16C3×#946C2212yes—
17C3×#944C2212yes—
18C2×C3×#216C2212yes—
19C2×C3×Dic12C2211yescharacteristic
20C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
21C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
22C3×#897C2212yes—
23C3×#896—22no—
24C3×#889—22no—
25C3×#888C2212yes—
26C3×#872—22no—
27C3×C42×D3C2211yescharacteristic
28C3×C4×Dic6—22no—
29C3×C4×Dic6C2212yes—
30C32×#106C2211yescharacteristic
31C32×#103C2212yes—
32C32×#97C2211yescharacteristic
33C3×#835C2212yes—
34C3×#817C2211yescharacteristic
35C3×#816C2212yes—
36C3×C8×Dic3C2211yescharacteristic
37C3×C8×Dic3C2211yescharacteristic
38C3×#810C2212yes—
39C3×#808C2212yes—
40C3×#803C2211yescharacteristic
41C3×#533—32no—
42#5578C2×C312yes—
43C3×#498—31no—
44C3×#494—31no—
45C3×#487—32no—
46C3×#470—31no—
47C3×#470—31no—
48C3×#470—32no—
49C3×#441—21no—
50C3×#441—32no—
51C3×#441—31no—
52C3×#441D311yescharacteristic, complemented
53C3×#441C2×C311yescharacteristic, complemented
54C3×C4×M16—31no—
55#5189C2×C311yescharacteristic
56#5183C2×C311yescharacteristic, complemented
57#5030C2×C312yescomplemented
58#4867C2×C311yescharacteristic
59#4855C2×C311yescharacteristic, complemented
60#4816C2×C312yes—
61#4792C2×C312yescomplemented
62#4716C2×C311yescharacteristic, complemented
63#4707C2×C311yescharacteristic
64C2×C32×Q8C2312yes—
65C2×C3×C4×D3D412yes—
66C2×C3×C4×D3C2311yescharacteristic
67C2×C3×Dic6—22no—
68C2×C3×Dic6C2312yes—
69C32×Q16—22no—
70C2×C32×C8C2311yescharacteristic
71C2×C32×C8C2311yescharacteristic
72C32×C4⋊C4—22no—
73C32×C4⋊C4C2312yes—
74C32×C42—22no—
75C32×C42C2311yescharacteristic
76C3×#216—24no—
77C3×(C2×D3)⋊C4—22no—
78C3×(C2×D3)⋊C4—22no—
79C3×C4⋊Dic3—22no—
80C3×C4⋊Dic3C2312yes—
81C3×Dic3⋊C4—22no—
82C3×Dic3⋊C4—22no—
83C3×Dic3⋊C4—22no—
84C3×Dic3⋊C4—22no—
85C3×Dic3⋊C4—22no—
86C3×C4×Dic3—22no—
87C3×C4×Dic3D412yes—
88C3×C4×Dic3C2311yescharacteristic
89C2×C3×C3⋊C8C2311yescharacteristic
90C2×C3×C3⋊C8C2311yescharacteristic
91C3×Dic12—22no—
92C3×ΓL(1,𝔽25)—22no—
93C3×ΓL(1,𝔽25)—22no—
94#3185—31noSylow
95C2×C3×Q16—21no—
96C2×C3×Q16—32no—
97C2×C3×Q16—31no—
98C2×C3×Q16C2×D311yescharacteristic
99C2×C3×Q16C22×C311yescharacteristic
100C2×C3×M16—31no—
101C2×C3×M16—31no—
102C3×C4⋊Q8—32no—
103C3×C4⋊Q8—32no—
104C3×#125—62no—
105C3×C22⋊Q8—32no—
106C3×C22⋊Q8—32no—
107C3×C22⋊Q8—62no—
108C3×C4×Q8—22no—
109C3×C4×Q8—32no—
110C3×C4×Q8—62no—
111C3×C4×Q8C2×D312yes—
112C3×C4×Q8C22×C312yes—
113C3×#117—62no—
114C2×C3×C42—31no—
115#946C22×C312yes—
116#944C22×C312yes—
117C2×#216C22×C312yes—
118C2×Dic12C22×C311yescharacteristic
119C2×ΓL(1,𝔽25)C22×C311yescharacteristic
120C2×ΓL(1,𝔽25)C22×C311yescharacteristic
121#897C22×C312yes—
122#896—22no—
123#889—22no—
124#888C22×C312yes—
125#872—22no—
126C42×D3C22×C311yescharacteristic
127C4×Dic6—22no—
128C4×Dic6C22×C312yes—
129C3×#106—21no—
130C3×#106—31no—
131C3×#106—32no—
132C3×#106C2×D311yescharacteristic
133C3×#106C22×C311yescharacteristic
134C3×#103—22no—
135C3×#103—32no—
136C3×#103—32no—
137C3×#103—32no—
138C3×#103C2×D312yes—
139C3×#103C22×C312yes—
140C3×#97—21no—
141C3×#97—31no—
142C3×#97C2×D311yescharacteristic
143C3×#97C22×C311yescharacteristic
144C3×C4×C8—31no—
145C3×C4×C8—31no—
146#835C22×C312yes—
147#817C22×C311yescharacteristic
148#816C22×C312yes—
149C8×Dic3C22×C311yescharacteristic
150C8×Dic3C22×C311yescharacteristic
151#810C22×C312yes—
152#808C22×C312yes—
153#803C22×C311yescharacteristic
154C22×C3×D3C2×D411yescharacteristic
155C32×Q8—22no—
156C32×Q8—22no—
157C2×C32×C4—22no—
158C2×C32×C4—22no—
159C2×C32×C4C2×D412yes—
160C2×C32×C4C2411yescharacteristic
161C2×C3×Dic3—22no—
162C2×C3×Dic3—22no—
163C2×C3×Dic3C2×D411yescharacteristic
164C2×C3×Dic3C2×D412yes—
165C3×C4×D3—21no—
166C3×C4×D3—21no—
167C3×C4×D3—24no—
168C3×Dic6—22no—
169C3×Dic6—22no—
170C3×Dic6—44no—
171C32×C8—21no—
172C32×C8#4112yes—
173C3×C3⋊C8—21no—
174C3×C3⋊C8#4112yes—
175#533—32no—
176#498—31no—
177#494—31no—
178#487—32no—
179#470—31no—
180#470—31no—
181#470—32no—
182#441—32no—
183#441—31no—
184#441C3×D311yescharacteristic, complemented
185C4×M16—31no—
186C2×C3×Q8—22no—
187C2×C3×Q8—32no—
188C2×C3×Q8—62no—
189C2×C3×Q8C22×D312yes—
190C2×C3×Q8C23×C312yes—
191C22×C3×C4—32no—
192C22×C3×C4—31no—
193C2×C4×D3C3×D412yes—
194C2×C4×D3C23×C311yescharacteristic
195C2×Dic6—22no—
196C2×Dic6C23×C312yes—
197C3×Q16—24no—
198C3×Q16—22no—
199C3×Q16—22no—
200C3×Q16—64no—
201C3×Q16—62no—
202C3×M16—62no—
203C3×M16—62no—
204C2×C3×C8—21no—
205C2×C3×C8—21no—
206C2×C3×C8—31no—
207C2×C3×C8—31no—
208C2×C3×C8C22×D311yescharacteristic
209C2×C3×C8C22×D311yescharacteristic
210C2×C3×C8C23×C311yescharacteristic
211C2×C3×C8C23×C311yescharacteristic
212C3×C4⋊C4—22no—
213C3×C4⋊C4—22no—
214C3×C4⋊C4—22no—
215C3×C4⋊C4—32no—
216C3×C4⋊C4—42no—
217C3×C4⋊C4—62no—
218C3×C4⋊C4—62no—
219C3×C4⋊C4—62no—
220C3×C4⋊C4—62no—
221C3×C4⋊C4—62no—
222C3×C4⋊C4—62no—
223C3×C4⋊C4C22×D312yes—
224C3×C4⋊C4C23×C312yes—
225C3×C22⋊C4—62no—
226C3×C22⋊C4—62no—
227C3×C42—22no—
228C3×C42—22no—
229C3×C42—21no—
230C3×C42—32no—
231C3×C42—31no—
232C3×C42—42no—
233C3×C42—62no—
234C3×C42C22×D311yescharacteristic
235C3×C42C23×C311yescharacteristic
236#216—24no—
237(C2×D3)⋊C4—22no—
238(C2×D3)⋊C4—22no—
239C4⋊Dic3—22no—
240C4⋊Dic3C23×C312yes—
241Dic3⋊C4—22no—
242Dic3⋊C4—22no—
243Dic3⋊C4—22no—
244Dic3⋊C4—22no—
245Dic3⋊C4—22no—
246C4×Dic3—22no—
247C4×Dic3C3×D412yes—
248C4×Dic3C23×C311yescharacteristic
249C2×C3⋊C8C23×C311yescharacteristic
250C2×C3⋊C8C23×C311yescharacteristic
251Dic12—22no—
252ΓL(1,𝔽25)—22no—
253ΓL(1,𝔽25)—22no—
254C22×C32C22×D411yescharacteristic
255C2×C3×D3—21no—
256C2×C3×D3—22no—
257C32×C4—22no—
258C32×C4—42no—
259C32×C4—42no—
260C32×C4C2×#4111yescharacteristic
261C32×C4C2×#4111yescharacteristic
262C3×Dic3—21no—
263C3×Dic3—42no—
264C3×Dic3—42no—
265C3×Dic3#13714yes—
266C2×Q16—32no—
267C2×Q16—31no—
268C2×Q16C2×C3×D311yescharacteristic
269C2×M16—31no—
270C2×M16—31no—
271C4⋊Q8—32no—
272C4⋊Q8—32no—
273#125—62no—
274C22⋊Q8—32no—
275C22⋊Q8—32no—
276C22⋊Q8—62no—
277C4×Q8—32no—
278C4×Q8—62no—
279C4×Q8C2×C3×D312yes—
280#117—62no—
281C2×C42—31no—
282#106—31no—
283#106—32no—
284#106C2×C3×D311yescharacteristic
285#103—32no—
286#103—32no—
287#103—32no—
288#103C2×C3×D312yes—
289#97—31no—
290#97C2×C3×D311yescharacteristic
291C4×C8—31no—
292C4×C8—31no—
293C23×C3—31no—
294C22×D3C2×C3×D411yescharacteristic
295C3×Q8—24no—
296C3×Q8—22no—
297C3×Q8—22no—
298C3×Q8—22no—
299C3×Q8—22no—
300C3×Q8—42no—
301C3×Q8—62no—
302C3×Q8—62no—
303C3×Q8—124no—
304C2×C3×C4—22no—
305C2×C3×C4—22no—
306C2×C3×C4—22no—
307C2×C3×C4—22no—
308C2×C3×C4—21no—
309C2×C3×C4—22no—
310C2×C3×C4—32no—
311C2×C3×C4—31no—
312C2×C3×C4—42no—
313C2×C3×C4—42no—
314C2×C3×C4—64no—
315C2×C3×C4—61no—
316C2×C3×C4—61no—
317C2×C3×C4—62no—
318C2×C3×C4—62no—
319C2×C3×C4D3×D412yes—
320C2×C3×C4C2×C3×D412yes—
321C2×C3×C4C23×D311yescharacteristic
322C2×C3×C4C24×C311yescharacteristic
323C2×Dic3—22no—
324C2×Dic3—22no—
325C2×Dic3C2×C3×D411yescharacteristic
326C2×Dic3C2×C3×D412yes—
327C4×D3—21no—
328C4×D3—21no—
329C4×D3—24no—
330Dic6—22no—
331Dic6—22no—
332Dic6—44no—
333C3×C8—21no—
334C3×C8—21no—
335C3×C8—22no—
336C3×C8—32no—
337C3×C8—41no—
338C3×C8—61no—
339C3×C8#23512yes—
340C3×C8C3×#4112yes—
341C3⋊C8—21no—
342C3⋊C8C3×#4112yes—
343C2×C32#53211yescharacteristic
344C2×C32C2×#13712yes—
345C3×D3—41no—
346C2×Q8—32no—
347C2×Q8—62no—
348C2×Q8C22×C3×D312yes—
349C22×C4—31no—
350C22×C4—32no—
351Q16—22no—
352Q16—64no—
353Q16—62no—
354M16—62no—
355M16—62no—
356C2×C8—31no—
357C2×C8—31no—
358C2×C8C22×C3×D311yescharacteristic
359C2×C8C22×C3×D311yescharacteristic
360C4⋊C4—22no—
361C4⋊C4—32no—
362C4⋊C4—62no—
363C4⋊C4—62no—
364C4⋊C4—62no—
365C4⋊C4—62no—
366C4⋊C4—62no—
367C4⋊C4—62no—
368C4⋊C4C22×C3×D312yes—
369C22⋊C4—62no—
370C22⋊C4—62no—
371C42—22no—
372C42—31no—
373C42—32no—
374C42—62no—
375C42C22×C3×D311yescharacteristic
376C22×C3—21no—
377C22×C3—62no—
378C22×C3—61no—
379C22×C3C2×D3×D411yescharacteristic
380C22×C3C22×C3×D411yescharacteristic
381C2×D3—22no—
382C2×D3—21no—
383C3×C4—22no—
384C3×C4—22no—
385C3×C4—21no—
386C3×C4—21no—
387C3×C4—34no—
388C3×C4—42no—
389C3×C4—44no—
390C3×C4—42no—
391C3×C4—42no—
392C3×C4—42no—
393C3×C4—42no—
394C3×C4—61no—
395C3×C4—82no—
396C3×C4—122no—
397C3×C4—122no—
398C3×C4C2×#23511yescharacteristic
399C3×C4D3×#4111yescharacteristic
400C3×C4C2×C3×#4111yescharacteristic
401C3×C4C2×C3×#4111yescharacteristic
402Dic3—21no—
403Dic3—42no—
404Dic3—42no—
405Dic3C3×#13714yes—
406C32#318511yescharacteristic, complemented, Sylow
407C23—31no—
408Q8—22no—
409Q8—22no—
410Q8—62no—
411Q8—62no—
412Q8—124no—
413C2×C4—22no—
414C2×C4—22no—
415C2×C4—32no—
416C2×C4—31no—
417C2×C4—64no—
418C2×C4—61no—
419C2×C4—61no—
420C2×C4—62no—
421C2×C4—62no—
422C2×C4C3×D3×D412yes—
423C2×C4C23×C3×D311yescharacteristic
424C8—21no—
425C8—32no—
426C8—61no—
427C8C3×#23512yes—
428C2×C3—22no—
429C2×C3—21no—
430C2×C3—121no—
431C2×C3#554811yescharacteristic
432C2×C3D3×#13712yes—
433C2×C3C3×#53211yescharacteristic
434C2×C3C2×C3×#13712yes—
435D3—41no—
436C22—62no—
437C22—61no—
438C22C2×C3×D3×D411yescharacteristic
439C4—22no—
440C4—34no—
441C4—42no—
442C4—42no—
443C4—61no—
444C4—122no—
445C4—122no—
446C4C2×C3×#23511yescharacteristic
447C4C3×D3×#4111yescharacteristic
448C3—21no—
449C3#7983811yescharacteristic, direct product factor
450C3C3×#318511yescharacteristic, complemented
451C2—121no—
452C2C3×#554811yescharacteristic
453C2C3×D3×#13712yes—
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#441C2
socleC22×C32C22×D4
prime radicalC22×C3×D3C2×D4
hypercenterC3×#441D3
hypocenterC3C3×#3185
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#441

Complements

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

NH ≅ G/Ntype
2. C32×#441C2semidirect
4. C3×#5183C2semidirect
5. C3×#5030C2semidirect
7. C3×#4855C2semidirect
9. C3×#4792C2semidirect
10. C3×#4716C2semidirect
13. #79838C3direct (N × H)
52. C3×#441D3semidirect
53. C3×#441C2×C3semidirect
56. #5183C2×C3semidirect
57. #5030C2×C3semidirect
59. #4855C2×C3semidirect
61. #4792C2×C3semidirect
62. #4716C2×C3semidirect
184. #441C3×D3semidirect
406. C32#3185semidirect
449. C3#79838direct (N × H)
450. C3C3×#3185semidirect

Maximal subgroups

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

subgroupindex
C3×#55782
C32×#4412
C3×#51892
C3×#51832
C3×#50302
C3×#48672
C3×#48552
C3×#48162
C3×#47922
C3×#47162
C3×#47072
C3×#31853
#798383