Finite Group Databasebeta

← C3×#79623 #11895515

Subgroups — C3×#79623 #11895515

Order 1152.

733 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5570C211yesmaximal, characteristic, complemented
2C3×#5542C211yesmaximal, characteristic
3C32×C4×SD16C211yesmaximal, characteristic
4C3×#5166C212yesmaximal
5C3×#5031C211yesmaximal, characteristic, complemented
6C3×#5007C211yesmaximal, characteristic
7C3×#4857C212yesmaximal, complemented
8C3×#4790C212yesmaximal, complemented
9C3×#4768C212yesmaximal
10C3×#4681C211yesmaximal, characteristic, complemented
11C3×C8×Dic6C211yesmaximal, characteristic, complemented
12C3×#3364—31nomaximal
13#79623C311yesmaximal, characteristic, direct product factor
14C2×C32×SD16C2211yescharacteristic
15C32×C4×Q8C2211yescharacteristic
16C32×C4×D4C2211yescharacteristic
17C3×Q8×Dic3C2212yes—
18C2×C3×#216C2212yes—
19C3×#936C2212yes—
20C3×#926—21no—
21C3×#924—21no—
22C3×#890—22no—
23C3×#890C2212yes—
24C3×#887C2212yes—
25C3×#879—22no—
26C3×#869—21no—
27C3×#869C2211yescharacteristic
28C3×#869C2211yescharacteristic
29C3×C4×Dic6—21no—
30C3×C4×Dic6C2211yescharacteristic
31C32×#106C2211yescharacteristic
32C32×#103C2211yescharacteristic
33C32×#102C2211yescharacteristic
34C32×C4×C8C2211yescharacteristic
35C3×#832C2212yes—
36C3×#816C2212yes—
37C3×#816C2212yes—
38C3×Dic3⋊C8C2212yes—
39C3×C8×Dic3C2212yes—
40C3×#810C2212yes—
41C3×#807C2212yes—
42C3×C4⋊(C3⋊C8)C2211yescharacteristic
43C3×#557—31no—
44C3×#556—31no—
45#5570C2×C311yescharacteristic, complemented
46#5542C2×C311yescharacteristic
47C3×#488—32no—
48C3×#487—31no—
49C3×#479—32no—
50C3×#474—31no—
51C3×#464—32no—
52C3×#462—31no—
53C3×C8×Q8—31no—
54C3×C4×Q16—32no—
55C3×C4×SD16—21no—
56C3×C4×SD16D311yescharacteristic
57C3×C4×SD16C2×C311yescharacteristic
58#5166C2×C312yes—
59#5031C2×C311yescharacteristic, complemented
60#5007C2×C311yescharacteristic
61#4857C2×C312yescomplemented
62#4790C2×C312yescomplemented
63#4768C2×C312yes—
64#4681C2×C311yescharacteristic, complemented
65C8×Dic6C2×C311yescharacteristic, complemented
66C2×C32×Q8C2311yescharacteristic
67C2×C32×D4C2311yescharacteristic
68C22×C32×C4—21no—
69C2×C3×Dic6—21no—
70C2×C3×Dic6D411yescharacteristic
71C2×C3×Dic6C2312yes—
72C32×SD16—22no—
73C2×C32×C8C2311yescharacteristic
74C2×C32×C8C2311yescharacteristic
75C32×C4⋊C4—21no—
76C32×C4⋊C4C2311yescharacteristic
77C32×C4⋊C4C2311yescharacteristic
78C32×C22⋊C4—21no—
79C32×C42—21no—
80C32×C42C2311yescharacteristic
81C3×#217—22no—
82C3×#217—22no—
83C3×#216—24no—
84C3×C4⋊Dic3—21no—
85C3×C4⋊Dic3—21no—
86C3×C4⋊Dic3—21no—
87C3×C4⋊Dic3—22no—
88C3×C4⋊Dic3—22no—
89C3×C4⋊Dic3D411yescharacteristic
90C3×C4⋊Dic3C2312yes—
91C3×Dic3⋊C4—22no—
92C3×Dic3⋊C4—22no—
93C3×Dic3⋊C4D412yes—
94C3×C4×Dic3—22no—
95C3×C4×Dic3—22no—
96C3×C4×Dic3C2312yes—
97C2×C3×C3⋊C8C2312yes—
98#3364—31noSylow
99C2×C3×Q16—32no—
100C2×C3×SD16—21no—
101C2×C3×SD16C2×D311yescharacteristic
102C2×C3×SD16C22×C311yescharacteristic
103C3×C4⋊Q8—31no—
104C3×C4⋊Q8—31no—
105C3×C4⋊Q8—61no—
106C3×#126—62no—
107C3×#125—32no—
108C3×#125—62no—
109C3×#124—32no—
110C3×C22⋊Q8—61no—
111C3×C4×Q8—21no—
112C3×C4×Q8—31no—
113C3×C4×Q8—32no—
114C3×C4×Q8—32no—
115C3×C4×Q8—61no—
116C3×C4×Q8C2×D311yescharacteristic
117C3×C4×Q8C22×C311yescharacteristic
118C3×C4×D4—21no—
119C3×C4×D4C2×D311yescharacteristic
120C3×C4×D4C22×C311yescharacteristic
121C3×#117—61no—
122Q8×Dic3C22×C312yes—
123C2×#216C22×C312yes—
124#936C22×C312yes—
125#926—21no—
126#924—21no—
127#890—22no—
128#890C22×C312yes—
129#887C22×C312yes—
130#879—22no—
131#869—21no—
132#869C22×C311yescharacteristic
133#869C22×C311yescharacteristic
134C4×Dic6—21no—
135C4×Dic6C22×C311yescharacteristic
136C3×#107—32no—
137C3×#106—21no—
138C3×#106C2×D311yescharacteristic
139C3×#106C22×C311yescharacteristic
140C3×C4⋊C8—32no—
141C3×C4⋊C8—31no—
142C3×#103—21no—
143C3×#103—32no—
144C3×#103—32no—
145C3×#103—32no—
146C3×#103C2×D311yescharacteristic
147C3×#103C22×C311yescharacteristic
148C3×#102—21no—
149C3×#102—32no—
150C3×#102C2×D311yescharacteristic
151C3×#102C22×C311yescharacteristic
152C3×C4×C8—21no—
153C3×C4×C8—32no—
154C3×C4×C8C2×D311yescharacteristic
155C3×C4×C8C22×C311yescharacteristic
156#832C22×C312yes—
157#816C22×C312yes—
158#816C22×C312yes—
159Dic3⋊C8C22×C312yes—
160C8×Dic3C22×C312yes—
161#810C22×C312yes—
162#807C22×C312yes—
163C4⋊(C3⋊C8)C22×C311yescharacteristic
164C23×C32—21no—
165C32×Q8—21no—
166C32×Q8#4112yes—
167C32×D4—21no—
168C32×D4—21no—
169C2×C32×C4—21no—
170C2×C32×C4—21no—
171C2×C32×C4—21no—
172C2×C32×C4—42no—
173C2×C32×C4C2×D411yescharacteristic
174C2×C32×C4C2×D411yescharacteristic
175C2×C32×C4C2411yescharacteristic
176C2×C3×Dic3—22no—
177C2×C3×Dic3—22no—
178C2×C3×Dic3C2×D412yes—
179C2×C3×Dic3C2×D412yes—
180C3×Dic6—22no—
181C3×Dic6—22no—
182C3×Dic6—22no—
183C3×Dic6—42no—
184C32×C8—21no—
185C32×C8—21no—
186C3×C3⋊C8—22no—
187#557—31no—
188#556—31no—
189#488—32no—
190#487—31no—
191#479—32no—
192#474—31no—
193#464—32no—
194#462—31no—
195C8×Q8—31no—
196C4×Q16—32no—
197C4×SD16C3×D311yescharacteristic
198C2×C3×Q8—21no—
199C2×C3×Q8—31no—
200C2×C3×Q8—32no—
201C2×C3×Q8—61no—
202C2×C3×Q8C22×D311yescharacteristic
203C2×C3×Q8C23×C311yescharacteristic
204C2×C3×D4—21no—
205C2×C3×D4C22×D311yescharacteristic
206C2×C3×D4C23×C311yescharacteristic
207C22×C3×C4—21no—
208C22×C3×C4—21no—
209C22×C3×C4—41no—
210C2×Dic6—21no—
211C2×Dic6C3×D411yescharacteristic
212C2×Dic6C23×C312yes—
213C3×Q16—64no—
214C3×SD16—24no—
215C3×SD16—22no—
216C3×SD16—22no—
217C2×C3×C8—21no—
218C2×C3×C8—21no—
219C2×C3×C8—32no—
220C2×C3×C8C22×D311yescharacteristic
221C2×C3×C8C22×D311yescharacteristic
222C2×C3×C8C23×C311yescharacteristic
223C2×C3×C8C23×C311yescharacteristic
224C3×C4⋊C4—21no—
225C3×C4⋊C4—21no—
226C3×C4⋊C4—21no—
227C3×C4⋊C4—21no—
228C3×C4⋊C4—32no—
229C3×C4⋊C4—31no—
230C3×C4⋊C4—32no—
231C3×C4⋊C4—41no—
232C3×C4⋊C4—62no—
233C3×C4⋊C4—62no—
234C3×C4⋊C4—62no—
235C3×C4⋊C4—62no—
236C3×C4⋊C4—61no—
237C3×C4⋊C4—61no—
238C3×C4⋊C4—61no—
239C3×C4⋊C4C22×D311yescharacteristic
240C3×C4⋊C4C22×D311yescharacteristic
241C3×C4⋊C4C23×C311yescharacteristic
242C3×C4⋊C4C23×C311yescharacteristic
243C3×C22⋊C4—21no—
244C3×C22⋊C4—21no—
245C3×C22⋊C4—41no—
246C3×C22⋊C4—62no—
247C3×C22⋊C4—62no—
248C3×C42—21no—
249C3×C42—21no—
250C3×C42—21no—
251C3×C42—32no—
252C3×C42—41no—
253C3×C42—62no—
254C3×C42—62no—
255C3×C42C22×D311yescharacteristic
256C3×C42C23×C311yescharacteristic
257#217—22no—
258#217—22no—
259#216—24no—
260C4⋊Dic3—21no—
261C4⋊Dic3—21no—
262C4⋊Dic3—21no—
263C4⋊Dic3—22no—
264C4⋊Dic3—22no—
265C4⋊Dic3C3×D411yescharacteristic
266C4⋊Dic3C23×C312yes—
267Dic3⋊C4—22no—
268Dic3⋊C4—22no—
269Dic3⋊C4C3×D412yes—
270C4×Dic3—22no—
271C4×Dic3—22no—
272C4×Dic3C23×C312yes—
273C2×C3⋊C8C23×C312yes—
274C22×C32—41no—
275C22×C32—41no—
276C22×C32—41no—
277C22×C32C22×D411yescharacteristic
278C32×C4—22no—
279C32×C4—21no—
280C32×C4—41no—
281C32×C4—41no—
282C32×C4#13512yes—
283C32×C4C2×#4111yescharacteristic
284C32×C42−1+411yescharacteristic
285C3×Dic3—22no—
286C3×Dic3—22no—
287C3×Dic3—42no—
288C3×Dic3—42no—
289C2×Q16—32no—
290C2×SD16C2×C3×D311yescharacteristic
291C4⋊Q8—31no—
292C4⋊Q8—31no—
293C4⋊Q8—61no—
294#126—62no—
295#125—32no—
296#125—62no—
297#124—32no—
298C22⋊Q8—61no—
299C4×Q8—31no—
300C4×Q8—32no—
301C4×Q8—32no—
302C4×Q8—61no—
303C4×Q8C2×C3×D311yescharacteristic
304C4×D4C2×C3×D311yescharacteristic
305#117—61no—
306#107—32no—
307#106C2×C3×D311yescharacteristic
308C4⋊C8—32no—
309C4⋊C8—31no—
310#103—32no—
311#103—32no—
312#103—32no—
313#103C2×C3×D311yescharacteristic
314#102—32no—
315#102C2×C3×D311yescharacteristic
316C4×C8—32no—
317C4×C8C2×C3×D311yescharacteristic
318C23×C3—21no—
319C23×C3—21no—
320C23×C3—41no—
321C3×Q8—21no—
322C3×Q8—21no—
323C3×Q8—22no—
324C3×Q8—41no—
325C3×Q8—62no—
326C3×Q8—62no—
327C3×Q8—62no—
328C3×Q8—122no—
329C3×Q8#23512yes—
330C3×Q8C3×#4112yes—
331C3×D4—22no—
332C3×D4—21no—
333C3×D4—21no—
334C3×D4—21no—
335C3×D4—21no—
336C3×D4—41no—
337C2×C3×C4—21no—
338C2×C3×C4—21no—
339C2×C3×C4—21no—
340C2×C3×C4—21no—
341C2×C3×C4—21no—
342C2×C3×C4—21no—
343C2×C3×C4—21no—
344C2×C3×C4—21no—
345C2×C3×C4—21no—
346C2×C3×C4—32no—
347C2×C3×C4—32no—
348C2×C3×C4—41no—
349C2×C3×C4—41no—
350C2×C3×C4—41no—
351C2×C3×C4—42no—
352C2×C3×C4—42no—
353C2×C3×C4—62no—
354C2×C3×C4—62no—
355C2×C3×C4—82no—
356C2×C3×C4D3×D411yescharacteristic
357C2×C3×C4D3×D411yescharacteristic
358C2×C3×C4C2×C3×D411yescharacteristic
359C2×C3×C4C2×C3×D411yescharacteristic
360C2×C3×C4C23×D311yescharacteristic
361C2×C3×C4C24×C311yescharacteristic
362C2×Dic3—22no—
363C2×Dic3—22no—
364C2×Dic3C2×C3×D412yes—
365C2×Dic3C2×C3×D412yes—
366Dic6—22no—
367Dic6—22no—
368Dic6—22no—
369Dic6—42no—
370C3×C8—22no—
371C3×C8—21no—
372C3×C8—21no—
373C3×C8—21no—
374C3×C8—21no—
375C3×C8—41no—
376C3×C8—62no—
377C3⋊C8—22no—
378C2×C32—81no—
379C2×C32#54811yescharacteristic
380C2×C32C2×#13511yescharacteristic
381C2×C32#57811yescharacteristic
382C2×Q8—31no—
383C2×Q8—32no—
384C2×Q8—61no—
385C2×Q8C22×C3×D311yescharacteristic
386C2×D4C22×C3×D311yescharacteristic
387C22×C4—21no—
388Q16—64no—
389SD16—22no—
390C2×C8—32no—
391C2×C8C22×C3×D311yescharacteristic
392C2×C8C22×C3×D311yescharacteristic
393C4⋊C4—21no—
394C4⋊C4—31no—
395C4⋊C4—32no—
396C4⋊C4—32no—
397C4⋊C4—62no—
398C4⋊C4—62no—
399C4⋊C4—62no—
400C4⋊C4—62no—
401C4⋊C4—61no—
402C4⋊C4—61no—
403C4⋊C4—61no—
404C4⋊C4C22×C3×D311yescharacteristic
405C4⋊C4C22×C3×D311yescharacteristic
406C22⋊C4—21no—
407C22⋊C4—62no—
408C22⋊C4—62no—
409C42—21no—
410C42—32no—
411C42—62no—
412C42—62no—
413C42C22×C3×D311yescharacteristic
414C22×C3—21no—
415C22×C3—42no—
416C22×C3—41no—
417C22×C3—41no—
418C22×C3—41no—
419C22×C3—41no—
420C22×C3—41no—
421C22×C3—41no—
422C22×C3—81no—
423C22×C3—81no—
424C22×C3C2×D3×D411yescharacteristic
425C22×C3C22×C3×D411yescharacteristic
426C3×C4—21no—
427C3×C4—21no—
428C3×C4—22no—
429C3×C4—22no—
430C3×C4—22no—
431C3×C4—21no—
432C3×C4—21no—
433C3×C4—41no—
434C3×C4—42no—
435C3×C4—41no—
436C3×C4—41no—
437C3×C4—41no—
438C3×C4—41no—
439C3×C4—62no—
440C3×C4—62no—
441C3×C4—81no—
442C3×C4—81no—
443C3×C4—122no—
444C3×C4—122no—
445C3×C4#91612yes—
446C3×C4C3×#13512yes—
447C3×C4C2×#23511yescharacteristic
448C3×C4#101011yescharacteristic
449C3×C4C2×C3×#4111yescharacteristic
450C3×C4C3×2−1+411yescharacteristic
451Dic3—22no—
452Dic3—22no—
453Dic3—42no—
454Dic3—42no—
455C32#336411yescharacteristic, complemented, Sylow
456C23—21no—
457Q8—21no—
458Q8—62no—
459Q8—62no—
460Q8—62no—
461Q8—122no—
462Q8C3×#23512yes—
463D4—21no—
464D4—21no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—32no—
469C2×C4—32no—
470C2×C4—42no—
471C2×C4—62no—
472C2×C4—62no—
473C2×C4C3×D3×D411yescharacteristic
474C2×C4C3×D3×D411yescharacteristic
475C2×C4C23×C3×D311yescharacteristic
476C8—21no—
477C8—21no—
478C8—62no—
479C2×C3—21no—
480C2×C3—21no—
481C2×C3—21no—
482C2×C3—82no—
483C2×C3—81no—
484C2×C3—81no—
485C2×C3#555211yescharacteristic
486C2×C3C2×#91611yescharacteristic
487C2×C3#577111yescharacteristic
488C2×C3C3×#54811yescharacteristic
489C2×C3C2×C3×#13511yescharacteristic
490C2×C3C3×#57811yescharacteristic
491C22—41no—
492C22—41no—
493C22—41no—
494C22C2×C3×D3×D411yescharacteristic
495C4—21no—
496C4—22no—
497C4—41no—
498C4—41no—
499C4—62no—
500C4—62no—
501C4—122no—
502C4—122no—
503C4C3×#91612yes—
504C4C2×C3×#23511yescharacteristic
505C4C3×#101011yescharacteristic
506C3—21no—
507C3#7962311yescharacteristic, direct product factor
508C3C3×#336411yescharacteristic, complemented
509C2—81no—
510C2C3×#555211yescharacteristic
511C2C2×C3×#91611yescharacteristic
512C2C3×#577111yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×C4×SD16C2
socleC22×C32C22×D4
prime radicalC2×C32×D4C23
hypercenterC3×C4×SD16D3
hypocenterC3C3×#3364
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×C4×SD16

Complements

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

NH ≅ G/Ntype
1. C3×#5570C2semidirect
5. C3×#5031C2semidirect
7. C3×#4857C2semidirect
8. C3×#4790C2semidirect
10. C3×#4681C2semidirect
11. C3×C8×Dic6C2semidirect
13. #79623C3direct (N × H)
45. #5570C2×C3semidirect
59. #5031C2×C3semidirect
61. #4857C2×C3semidirect
62. #4790C2×C3semidirect
64. #4681C2×C3semidirect
65. C8×Dic6C2×C3semidirect
455. C32#3364semidirect
507. C3#79623direct (N × H)
508. C3C3×#3364semidirect

Maximal subgroups

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

subgroupindex
C3×#55702
C3×#55422
C32×C4×SD162
C3×#51662
C3×#50312
C3×#50072
C3×#48572
C3×#47902
C3×#47682
C3×#46812
C3×C8×Dic62
C3×#33643
#796233