Finite Group Databasebeta

← C3×#80994 #11895518

Subgroups — C3×#80994 #11895518

Order 1152.

726 conjugacy classes of subgroups.

The subgroup lattice has 505 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5721C211yesmaximal, characteristic, complemented
2C3×#5542C211yesmaximal, characteristic
3C32×#474C211yesmaximal, characteristic
4C3×#5093C211yesmaximal, characteristic, complemented
5C3×C4×#214C211yesmaximal, characteristic
6C3×#4877C212yesmaximal, complemented
7C3×#4873C212yesmaximal, complemented
8C3×#4849C211yesmaximal, characteristic, complemented
9C3×#4830C211yesmaximal, characteristic, complemented
10C3×#4768C212yesmaximal
11C3×#4767C212yesmaximal
12C3×#3364—31nomaximal
13#80994C311yesmaximal, characteristic, direct product factor
14C32×C4⋊Q8C2211yescharacteristic
15C32×C4×D4C2211yescharacteristic
16C3×Q8×Dic3—21no—
17C3×#944—21no—
18C3×#936C2212yes—
19C2×C3×#214C2211yescharacteristic
20C3×#926—21no—
21C3×#924—21no—
22C2×C3×Dic12C2212yes—
23C3×#890C2212yes—
24C3×#889—22no—
25C3×#887C2212yes—
26C3×#887C2212yes—
27C3×#879—22no—
28C3×#869C2211yescharacteristic
29C3×C4×Dic6C2211yescharacteristic
30C3×C4×Dic6C2211yescharacteristic
31C32×#107C2212yes—
32C32×C4⋊C8C2211yescharacteristic
33C32×#102C2212yes—
34C3×#832C2211yescharacteristic
35C3×#816C2212yes—
36C3×Dic3⋊C8C2212yes—
37C3×C8×Dic3C2212yes—
38C3×#810C2211yescharacteristic
39C3×#810C2212yes—
40C3×#810C2212yes—
41C3×#808C2211yescharacteristic
42C3×C4×C3⋊C8C2211yescharacteristic
43C3×#557—31no—
44C3×#556—31no—
45#5721C2×C311yescharacteristic, complemented
46#5542C2×C311yescharacteristic
47C3×#488—32no—
48C3×#487—31no—
49C3×#479—32no—
50C3×#474—21no—
51C3×#474D311yescharacteristic
52C3×#474C2×C311yescharacteristic
53C3×#464—32no—
54C3×#462—31no—
55C3×C8×Q8—31no—
56C3×C4×Q16—32no—
57C3×C4×SD16—31no—
58#5093C2×C311yescharacteristic, complemented
59C4×#214C2×C311yescharacteristic
60#4877C2×C312yescomplemented
61#4873C2×C312yescomplemented
62#4849C2×C311yescharacteristic, complemented
63#4830C2×C311yescharacteristic, complemented
64#4768C2×C312yes—
65#4767C2×C312yes—
66C2×C32×Q8—21no—
67C2×C32×D4C2311yescharacteristic
68C22×C32×C4—21no—
69C2×C3×Dic6D411yescharacteristic
70C2×C3×Dic6C2312yes—
71C2×C3×Dic6C2311yescharacteristic
72C2×C32×C8C2312yes—
73C32×C4⋊C4—21no—
74C32×C4⋊C4C2311yescharacteristic
75C32×C4⋊C4C2312yes—
76C32×C22⋊C4—21no—
77C32×C42C2311yescharacteristic
78C3×#217—22no—
79C3×#217—22no—
80C3×#214—22no—
81C3×C4⋊Dic3—21no—
82C3×C4⋊Dic3—21no—
83C3×C4⋊Dic3—22no—
84C3×C4⋊Dic3D411yescharacteristic
85C3×C4⋊Dic3C2311yescharacteristic
86C3×Dic3⋊C4—21no—
87C3×Dic3⋊C4—22no—
88C3×Dic3⋊C4—22no—
89C3×Dic3⋊C4—22no—
90C3×Dic3⋊C4D412yes—
91C3×C4×Dic3—21no—
92C3×C4×Dic3—22no—
93C3×C4×Dic3—22no—
94C3×C4×Dic3C2312yes—
95C2×C3×C3⋊C8C2311yescharacteristic
96C2×C3×C3⋊C8C2311yescharacteristic
97C3×Dic12—24no—
98#3364—31noSylow
99C2×C3×Q16—32no—
100C2×C3×SD16—31no—
101C3×C4⋊Q8—21no—
102C3×C4⋊Q8—31no—
103C3×C4⋊Q8—61no—
104C3×C4⋊Q8C2×D311yescharacteristic
105C3×C4⋊Q8C22×C311yescharacteristic
106C3×#126—62no—
107C3×#125—32no—
108C3×#125—62no—
109C3×#124—32no—
110C3×C22⋊Q8—61no—
111C3×C4×Q8—31no—
112C3×C4×Q8—32no—
113C3×C4×Q8—32no—
114C3×C4×Q8—31no—
115C3×C4×Q8—61no—
116C3×C4×D4—21no—
117C3×C4×D4C2×D311yescharacteristic
118C3×C4×D4C22×C311yescharacteristic
119C3×#117—61no—
120Q8×Dic3—21no—
121#944—21no—
122#936C22×C312yes—
123C2×#214C22×C311yescharacteristic
124#926—21no—
125#924—21no—
126C2×Dic12C22×C312yes—
127#890C22×C312yes—
128#889—22no—
129#887C22×C312yes—
130#887C22×C312yes—
131#879—22no—
132#869C22×C311yescharacteristic
133C4×Dic6C22×C311yescharacteristic
134C4×Dic6C22×C311yescharacteristic
135C3×#107—22no—
136C3×#107C2×D312yes—
137C3×#107C22×C312yes—
138C3×#106—31no—
139C3×C4⋊C8—21no—
140C3×C4⋊C8—32no—
141C3×C4⋊C8C2×D311yescharacteristic
142C3×C4⋊C8C22×C311yescharacteristic
143C3×#103—32no—
144C3×#103—31no—
145C3×#103—32no—
146C3×#103—32no—
147C3×#102—22no—
148C3×#102—31no—
149C3×#102C2×D312yes—
150C3×#102C22×C312yes—
151C3×C4×C8—32no—
152C3×C4×C8—31no—
153#832C22×C311yescharacteristic
154#816C22×C312yes—
155Dic3⋊C8C22×C312yes—
156C8×Dic3C22×C312yes—
157#810C22×C311yescharacteristic
158#810C22×C312yes—
159#810C22×C312yes—
160#808C22×C311yescharacteristic
161C4×C3⋊C8C22×C311yescharacteristic
162C23×C32—21no—
163C32×Q8—42no—
164C32×D4—21no—
165C32×D4—21no—
166C2×C32×C4—21no—
167C2×C32×C4—22no—
168C2×C32×C4—42no—
169C2×C32×C4C2×D411yescharacteristic
170C2×C32×C4C2×D411yescharacteristic
171C2×C32×C4C2411yescharacteristic
172C2×C3×Dic3—21no—
173C2×C3×Dic3—21no—
174C2×C3×Dic3—22no—
175C2×C3×Dic3C2×D412yes—
176C2×C3×Dic3C2×D412yes—
177C3×Dic6—22no—
178C3×Dic6—21no—
179C3×Dic6—22no—
180C3×Dic6—22no—
181C3×Dic6#4112yes—
182C32×C8—22no—
183C3×C3⋊C8—21no—
184C3×C3⋊C8—21no—
185#557—31no—
186#556—31no—
187#488—32no—
188#487—31no—
189#479—32no—
190#474C3×D311yescharacteristic
191#464—32no—
192#462—31no—
193C8×Q8—31no—
194C4×Q16—32no—
195C4×SD16—31no—
196C2×C3×Q8—21no—
197C2×C3×Q8—21no—
198C2×C3×Q8—31no—
199C2×C3×Q8—31no—
200C2×C3×Q8—32no—
201C2×C3×Q8—41no—
202C2×C3×D4—21no—
203C2×C3×D4C22×D311yescharacteristic
204C2×C3×D4C23×C311yescharacteristic
205C22×C3×C4—21no—
206C22×C3×C4—21no—
207C22×C3×C4—41no—
208C2×Dic6C3×D411yescharacteristic
209C2×Dic6C23×C312yes—
210C2×Dic6C23×C311yescharacteristic
211C3×Q16—64no—
212C3×SD16—62no—
213C2×C3×C8—22no—
214C2×C3×C8—31no—
215C2×C3×C8—31no—
216C2×C3×C8C22×D312yes—
217C2×C3×C8C23×C312yes—
218C3×C4⋊C4—21no—
219C3×C4⋊C4—21no—
220C3×C4⋊C4—22no—
221C3×C4⋊C4—21no—
222C3×C4⋊C4—32no—
223C3×C4⋊C4—31no—
224C3×C4⋊C4—31no—
225C3×C4⋊C4—41no—
226C3×C4⋊C4—62no—
227C3×C4⋊C4—62no—
228C3×C4⋊C4—62no—
229C3×C4⋊C4—62no—
230C3×C4⋊C4—61no—
231C3×C4⋊C4—61no—
232C3×C4⋊C4—61no—
233C3×C4⋊C4C22×D312yes—
234C3×C4⋊C4C22×D311yescharacteristic
235C3×C4⋊C4C23×C311yescharacteristic
236C3×C4⋊C4C23×C312yes—
237C3×C22⋊C4—21no—
238C3×C22⋊C4—21no—
239C3×C22⋊C4—41no—
240C3×C22⋊C4—62no—
241C3×C22⋊C4—62no—
242C3×C42—21no—
243C3×C42—32no—
244C3×C42—62no—
245C3×C42—62no—
246C3×C42—61no—
247C3×C42C22×D311yescharacteristic
248C3×C42C23×C311yescharacteristic
249#217—22no—
250#217—22no—
251#214—22no—
252C4⋊Dic3—21no—
253C4⋊Dic3—21no—
254C4⋊Dic3—22no—
255C4⋊Dic3C3×D411yescharacteristic
256C4⋊Dic3C23×C311yescharacteristic
257Dic3⋊C4—21no—
258Dic3⋊C4—22no—
259Dic3⋊C4—22no—
260Dic3⋊C4—22no—
261Dic3⋊C4C3×D412yes—
262C4×Dic3—21no—
263C4×Dic3—22no—
264C4×Dic3—22no—
265C4×Dic3C23×C312yes—
266C2×C3⋊C8C23×C311yescharacteristic
267C2×C3⋊C8C23×C311yescharacteristic
268Dic12—24no—
269C22×C32—41no—
270C22×C32—41no—
271C22×C32—41no—
272C22×C32C22×D411yescharacteristic
273C32×C4—21no—
274C32×C4—41no—
275C32×C4—42no—
276C32×C4#13512yes—
277C32×C4C2×#4111yescharacteristic
278C32×C42−1+411yescharacteristic
279C3×Dic3—22no—
280C3×Dic3—22no—
281C3×Dic3—22no—
282C3×Dic3—42no—
283C3×Dic3—41no—
284C2×Q16—32no—
285C2×SD16—31no—
286C4⋊Q8—31no—
287C4⋊Q8—61no—
288C4⋊Q8C2×C3×D311yescharacteristic
289#126—62no—
290#125—32no—
291#125—62no—
292#124—32no—
293C22⋊Q8—61no—
294C4×Q8—31no—
295C4×Q8—32no—
296C4×Q8—32no—
297C4×Q8—31no—
298C4×Q8—61no—
299C4×D4C2×C3×D311yescharacteristic
300#117—61no—
301#107C2×C3×D312yes—
302#106—31no—
303C4⋊C8—32no—
304C4⋊C8C2×C3×D311yescharacteristic
305#103—32no—
306#103—31no—
307#103—32no—
308#103—32no—
309#102—31no—
310#102C2×C3×D312yes—
311C4×C8—32no—
312C4×C8—31no—
313C23×C3—21no—
314C23×C3—21no—
315C23×C3—41no—
316C3×Q8—32no—
317C3×Q8—42no—
318C3×Q8—42no—
319C3×Q8—62no—
320C3×Q8—61no—
321C3×Q8—62no—
322C3×Q8—62no—
323C3×Q8—82no—
324C3×D4—22no—
325C3×D4—21no—
326C3×D4—21no—
327C3×D4—21no—
328C3×D4—21no—
329C3×D4—41no—
330C2×C3×C4—21no—
331C2×C3×C4—22no—
332C2×C3×C4—21no—
333C2×C3×C4—22no—
334C2×C3×C4—21no—
335C2×C3×C4—21no—
336C2×C3×C4—21no—
337C2×C3×C4—32no—
338C2×C3×C4—32no—
339C2×C3×C4—41no—
340C2×C3×C4—42no—
341C2×C3×C4—42no—
342C2×C3×C4—42no—
343C2×C3×C4—61no—
344C2×C3×C4—62no—
345C2×C3×C4—61no—
346C2×C3×C4—82no—
347C2×C3×C4D3×D411yescharacteristic
348C2×C3×C4D3×D411yescharacteristic
349C2×C3×C4C2×C3×D411yescharacteristic
350C2×C3×C4C2×C3×D411yescharacteristic
351C2×C3×C4C23×D311yescharacteristic
352C2×C3×C4C24×C311yescharacteristic
353C2×Dic3—21no—
354C2×Dic3—21no—
355C2×Dic3—22no—
356C2×Dic3C2×C3×D412yes—
357C2×Dic3C2×C3×D412yes—
358Dic6—22no—
359Dic6—21no—
360Dic6—22no—
361Dic6—22no—
362Dic6C3×#4112yes—
363C3×C8—22no—
364C3×C8—22no—
365C3×C8—42no—
366C3×C8—61no—
367C3×C8—61no—
368C3⋊C8—21no—
369C3⋊C8—21no—
370C2×C32—81no—
371C2×C32#54811yescharacteristic
372C2×C32C2×#13511yescharacteristic
373C2×C32#57811yescharacteristic
374C2×Q8—21no—
375C2×Q8—31no—
376C2×Q8—31no—
377C2×Q8—32no—
378C2×D4C22×C3×D311yescharacteristic
379C22×C4—21no—
380Q16—64no—
381SD16—62no—
382C2×C8—31no—
383C2×C8—31no—
384C2×C8C22×C3×D312yes—
385C4⋊C4—21no—
386C4⋊C4—31no—
387C4⋊C4—32no—
388C4⋊C4—31no—
389C4⋊C4—62no—
390C4⋊C4—62no—
391C4⋊C4—62no—
392C4⋊C4—62no—
393C4⋊C4—61no—
394C4⋊C4—61no—
395C4⋊C4—61no—
396C4⋊C4C22×C3×D312yes—
397C4⋊C4C22×C3×D311yescharacteristic
398C22⋊C4—21no—
399C22⋊C4—62no—
400C22⋊C4—62no—
401C42—32no—
402C42—62no—
403C42—62no—
404C42—61no—
405C42C22×C3×D311yescharacteristic
406C22×C3—21no—
407C22×C3—42no—
408C22×C3—41no—
409C22×C3—41no—
410C22×C3—41no—
411C22×C3—41no—
412C22×C3—41no—
413C22×C3—41no—
414C22×C3—81no—
415C22×C3—81no—
416C22×C3C2×D3×D411yescharacteristic
417C22×C3C22×C3×D411yescharacteristic
418C3×C4—21no—
419C3×C4—21no—
420C3×C4—22no—
421C3×C4—21no—
422C3×C4—21no—
423C3×C4—41no—
424C3×C4—41no—
425C3×C4—42no—
426C3×C4—41no—
427C3×C4—42no—
428C3×C4—62no—
429C3×C4—62no—
430C3×C4—62no—
431C3×C4—81no—
432C3×C4—82no—
433C3×C4—122no—
434C3×C4—121no—
435C3×C4#91212yes—
436C3×C4C3×#13512yes—
437C3×C4#100711yescharacteristic
438C3×C4D3×#4111yescharacteristic
439C3×C4C2×C3×#4111yescharacteristic
440C3×C4C3×2−1+411yescharacteristic
441Dic3—22no—
442Dic3—22no—
443Dic3—22no—
444Dic3—41no—
445Dic3—42no—
446C32#336411yescharacteristic, complemented, Sylow
447C23—21no—
448Q8—32no—
449Q8—42no—
450Q8—62no—
451Q8—61no—
452Q8—62no—
453Q8—62no—
454D4—21no—
455D4—21no—
456C2×C4—21no—
457C2×C4—22no—
458C2×C4—32no—
459C2×C4—32no—
460C2×C4—42no—
461C2×C4—61no—
462C2×C4—62no—
463C2×C4—61no—
464C2×C4C3×D3×D411yescharacteristic
465C2×C4C3×D3×D411yescharacteristic
466C2×C4C23×C3×D311yescharacteristic
467C8—22no—
468C8—61no—
469C8—61no—
470C2×C3—21no—
471C2×C3—21no—
472C2×C3—21no—
473C2×C3—82no—
474C2×C3—81no—
475C2×C3—81no—
476C2×C3#563311yescharacteristic
477C2×C3C2×#91211yescharacteristic
478C2×C3#577911yescharacteristic
479C2×C3C3×#54811yescharacteristic
480C2×C3C2×C3×#13511yescharacteristic
481C2×C3C3×#57811yescharacteristic
482C22—41no—
483C22—41no—
484C22—41no—
485C22C2×C3×D3×D411yescharacteristic
486C4—21no—
487C4—41no—
488C4—42no—
489C4—62no—
490C4—62no—
491C4—62no—
492C4—121no—
493C4—122no—
494C4C3×#91212yes—
495C4C3×#100711yescharacteristic
496C4C3×D3×#4111yescharacteristic
497C3—21no—
498C3#8099411yescharacteristic, direct product factor
499C3C3×#336411yescharacteristic, complemented
500C2—81no—
501C2C3×#563311yescharacteristic
502C2C2×C3×#91211yescharacteristic
503C2C3×#577911yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#474C2
socleC22×C32C22×D4
prime radicalC2×C32×D4C23
hypercenterC3×#474D3
hypocenterC3C3×#3364
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#474

Complements

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

NH ≅ G/Ntype
1. C3×#5721C2semidirect
4. C3×#5093C2semidirect
6. C3×#4877C2semidirect
7. C3×#4873C2semidirect
8. C3×#4849C2semidirect
9. C3×#4830C2semidirect
13. #80994C3direct (N × H)
45. #5721C2×C3semidirect
58. #5093C2×C3semidirect
60. #4877C2×C3semidirect
61. #4873C2×C3semidirect
62. #4849C2×C3semidirect
63. #4830C2×C3semidirect
446. C32#3364semidirect
498. C3#80994direct (N × H)
499. C3C3×#3364semidirect

Maximal subgroups

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

subgroupindex
C3×#57212
C3×#55422
C32×#4742
C3×#50932
C3×C4×#2142
C3×#48772
C3×#48732
C3×#48492
C3×#48302
C3×#47682
C3×#47672
C3×#33643
#809943