Finite Group Databasebeta

← C3×#79634 #11897615

Subgroups — C3×#79634 #11897615

Order 1152.

741 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×Q8×Dic6C211yesmaximal, characteristic, complemented
2C3×#5543C211yesmaximal, characteristic
3C32×C4×SD16C211yesmaximal, characteristic
4C3×#5164C212yesmaximal
5C3×#5021C211yesmaximal, characteristic, complemented
6C3×#5008C211yesmaximal, characteristic
7C3×#4856C212yesmaximal, complemented
8C3×#4796C212yesmaximal, complemented
9C3×#4759C212yesmaximal
10C3×#4682C211yesmaximal, characteristic, complemented
11C3×#4679C211yesmaximal, characteristic, complemented
12C3×#3385—31nomaximal
13#79634C311yesmaximal, characteristic, direct product factor
14C2×C32×SD16C2211yescharacteristic
15C32×C4×Q8C2211yescharacteristic
16C32×C4×D4C2211yescharacteristic
17C3×Q8×Dic3C2212yes—
18C3×D4×Dic3C2212yes—
19C2×C3×C4⋊Dic3—21no—
20C3×#924—21no—
21C3×#890C2212yes—
22C3×#888—22no—
23C3×#888C2212yes—
24C3×#878—22no—
25C3×#869—21no—
26C3×#869C2211yescharacteristic
27C3×#869C2211yescharacteristic
28C3×C4×Dic6—21no—
29C3×C4×Dic6C2211yescharacteristic
30C32×#106C2211yescharacteristic
31C32×#103C2211yescharacteristic
32C32×#102C2211yescharacteristic
33C32×C4×C8C2211yescharacteristic
34C3×#835C2212yes—
35C3×#832C2212yes—
36C3×#818C2212yes—
37C3×#818C2212yes—
38C3×#815C2212yes—
39C3×Dic3⋊C8C2212yes—
40C3×#808C2212yes—
41C3×#807C2212yes—
42C3×C4⋊(C3⋊C8)C2211yescharacteristic
43C3×Q82—31no—
44C3×#554—31no—
45Q8×Dic6C2×C311yescharacteristic, complemented
46#5543C2×C311yescharacteristic
47C3×#501—32no—
48C3×#500—31no—
49C3×#479—32no—
50C3×#477—31no—
51C3×#476—31no—
52C3×#474—32no—
53C3×#446—31no—
54C3×#440—32no—
55C3×C4×SD16—21no—
56C3×C4×SD16D311yescharacteristic
57C3×C4×SD16C2×C311yescharacteristic
58#5164C2×C312yes—
59#5021C2×C311yescharacteristic, complemented
60#5008C2×C311yescharacteristic
61#4856C2×C312yescomplemented
62#4796C2×C312yescomplemented
63#4759C2×C312yes—
64#4682C2×C311yescharacteristic, complemented
65#4679C2×C311yescharacteristic, complemented
66C2×C32×Q8C2311yescharacteristic
67C2×C32×D4C2311yescharacteristic
68C22×C32×C4—21no—
69C22×C3×Dic3—22no—
70C2×C3×Dic6—21no—
71C2×C3×Dic6—21no—
72C2×C3×Dic6—22no—
73C2×C3×Dic6D411yescharacteristic
74C32×SD16Q814yescomplemented
75C2×C32×C8C2311yescharacteristic
76C2×C32×C8C2311yescharacteristic
77C32×C4⋊C4—21no—
78C32×C4⋊C4C2311yescharacteristic
79C32×C4⋊C4C2311yescharacteristic
80C32×C22⋊C4—21no—
81C32×C42—21no—
82C32×C42C2311yescharacteristic
83C3×#217—22no—
84C3×C4⋊Dic3—21no—
85C3×C4⋊Dic3—21no—
86C3×C4⋊Dic3—22no—
87C3×C4⋊Dic3—22no—
88C3×C4⋊Dic3D411yescharacteristic
89C3×C4⋊Dic3C2312yes—
90C3×C4⋊Dic3C2312yes—
91C3×Dic3⋊C4—22no—
92C3×Dic3⋊C4—22no—
93C3×Dic3⋊C4D412yes—
94C3×C4×Dic3—22no—
95C3×C4×Dic3C2312yes—
96C2×C3×C3⋊C8C2312yes—
97#3385—31noSylow
98C2×C3×SD16—21no—
99C2×C3×SD16C2×D311yescharacteristic
100C2×C3×SD16C22×C311yescharacteristic
101C3×C4⋊Q8—32no—
102C3×C4⋊Q8—31no—
103C3×C4⋊Q8—31no—
104C3×C4⋊Q8—61no—
105C3×C4⋊Q8—62no—
106C3×#125—32no—
107C3×C22⋊Q8—62no—
108C3×C22⋊Q8—61no—
109C3×C4×Q8—21no—
110C3×C4×Q8—31no—
111C3×C4×Q8—32no—
112C3×C4×Q8—61no—
113C3×C4×Q8C2×D311yescharacteristic
114C3×C4×Q8C22×C311yescharacteristic
115C3×C4×D4—21no—
116C3×C4×D4—32no—
117C3×C4×D4C2×D311yescharacteristic
118C3×C4×D4C22×C311yescharacteristic
119C2×C3×C4⋊C4—61no—
120Q8×Dic3C22×C312yes—
121D4×Dic3C22×C312yes—
122C2×C4⋊Dic3—21no—
123#924—21no—
124#890C22×C312yes—
125#888—22no—
126#888C22×C312yes—
127#878—22no—
128#869—21no—
129#869C22×C311yescharacteristic
130#869C22×C311yescharacteristic
131C4×Dic6—21no—
132C4×Dic6C22×C311yescharacteristic
133C3×#107—32no—
134C3×#107—32no—
135C3×#107—32no—
136C3×#106—21no—
137C3×#106—32no—
138C3×#106C2×D311yescharacteristic
139C3×#106C22×C311yescharacteristic
140C3×C4⋊C8—32no—
141C3×C4⋊C8—31no—
142C3×#103—21no—
143C3×#103—32no—
144C3×#103C2×D311yescharacteristic
145C3×#103C22×C311yescharacteristic
146C3×#102—21no—
147C3×#102—32no—
148C3×#102C2×D311yescharacteristic
149C3×#102C22×C311yescharacteristic
150C3×#97—32no—
151C3×C4×C8—21no—
152C3×C4×C8C2×D311yescharacteristic
153C3×C4×C8C22×C311yescharacteristic
154#835C22×C312yes—
155#832C22×C312yes—
156#818C22×C312yes—
157#818C22×C312yes—
158#815C22×C312yes—
159Dic3⋊C8C22×C312yes—
160#808C22×C312yes—
161#807C22×C312yes—
162C4⋊(C3⋊C8)C22×C311yescharacteristic
163C23×C32—21no—
164C32×Q8—21no—
165C32×Q8C2×Q812yes—
166C32×D4—21no—
167C32×D4C2×Q812yes—
168C2×C32×C4—21no—
169C2×C32×C4—21no—
170C2×C32×C4—21no—
171C2×C32×C4—42no—
172C2×C32×C4C2×D411yescharacteristic
173C2×C32×C4C2×D411yescharacteristic
174C2×C32×C4C2411yescharacteristic
175C2×C3×Dic3—22no—
176C2×C3×Dic3—22no—
177C2×C3×Dic3—82no—
178C2×C3×Dic3C2×D412yes—
179C2×C3×Dic3C2×D412yes—
180C3×Dic6—22no—
181C3×Dic6—82no—
182C3×Dic6—81no—
183C3×Dic6—81no—
184C32×C8—21no—
185C32×C8C2×Q812yes—
186C3×C3⋊C8—22no—
187Q82—31no—
188#554—31no—
189#501—32no—
190#500—31no—
191#479—32no—
192#477—31no—
193#476—31no—
194#474—32no—
195#446—31no—
196#440—32no—
197C4×SD16C3×D311yescharacteristic
198C2×C3×Q8—21no—
199C2×C3×Q8—31no—
200C2×C3×Q8—62no—
201C2×C3×Q8—61no—
202C2×C3×Q8—61no—
203C2×C3×Q8C22×D311yescharacteristic
204C2×C3×Q8C23×C311yescharacteristic
205C2×C3×D4—21no—
206C2×C3×D4C22×D311yescharacteristic
207C2×C3×D4C23×C311yescharacteristic
208C22×C3×C4—21no—
209C22×C3×C4—21no—
210C22×C3×C4—41no—
211C22×C3×C4—62no—
212C22×Dic3—22no—
213C2×Dic6—21no—
214C2×Dic6—21no—
215C2×Dic6—22no—
216C2×Dic6C3×D411yescharacteristic
217C3×SD16—24no—
218C3×SD16Dic614yescomplemented
219C3×SD16C3×Q814yescomplemented
220C2×C3×C8—21no—
221C2×C3×C8—21no—
222C2×C3×C8—32no—
223C2×C3×C8C22×D311yescharacteristic
224C2×C3×C8C22×D311yescharacteristic
225C2×C3×C8C23×C311yescharacteristic
226C2×C3×C8C23×C311yescharacteristic
227C3×C4⋊C4—21no—
228C3×C4⋊C4—21no—
229C3×C4⋊C4—21no—
230C3×C4⋊C4—21no—
231C3×C4⋊C4—32no—
232C3×C4⋊C4—31no—
233C3×C4⋊C4—32no—
234C3×C4⋊C4—32no—
235C3×C4⋊C4—41no—
236C3×C4⋊C4—62no—
237C3×C4⋊C4—62no—
238C3×C4⋊C4—62no—
239C3×C4⋊C4—62no—
240C3×C4⋊C4—61no—
241C3×C4⋊C4—61no—
242C3×C4⋊C4C22×D311yescharacteristic
243C3×C4⋊C4C22×D311yescharacteristic
244C3×C4⋊C4C23×C311yescharacteristic
245C3×C4⋊C4C23×C311yescharacteristic
246C3×C22⋊C4—21no—
247C3×C22⋊C4—21no—
248C3×C22⋊C4—41no—
249C3×C22⋊C4—62no—
250C3×C42—21no—
251C3×C42—21no—
252C3×C42—21no—
253C3×C42—32no—
254C3×C42—41no—
255C3×C42—62no—
256C3×C42C22×D311yescharacteristic
257C3×C42C23×C311yescharacteristic
258#217—22no—
259C4⋊Dic3—21no—
260C4⋊Dic3—21no—
261C4⋊Dic3—22no—
262C4⋊Dic3—22no—
263C4⋊Dic3C3×D411yescharacteristic
264C4⋊Dic3C23×C312yes—
265C4⋊Dic3C23×C312yes—
266Dic3⋊C4—22no—
267Dic3⋊C4—22no—
268Dic3⋊C4C3×D412yes—
269C4×Dic3—22no—
270C4×Dic3C23×C312yes—
271C2×C3⋊C8C23×C312yes—
272C22×C32—22no—
273C22×C32—41no—
274C22×C32—41no—
275C22×C32C22×D411yescharacteristic
276C32×C4—22no—
277C32×C4—21no—
278C32×C4—41no—
279C32×C4—41no—
280C32×C4#13712yes—
281C32×C4C22×Q811yescharacteristic
282C32×C42−1+411yescharacteristic
283C3×Dic3—22no—
284C3×Dic3—22no—
285C3×Dic3—42no—
286C3×Dic3—42no—
287C2×SD16C2×C3×D311yescharacteristic
288C4⋊Q8—32no—
289C4⋊Q8—31no—
290C4⋊Q8—31no—
291C4⋊Q8—61no—
292C4⋊Q8—62no—
293#125—32no—
294C22⋊Q8—62no—
295C22⋊Q8—61no—
296C4×Q8—31no—
297C4×Q8—32no—
298C4×Q8—61no—
299C4×Q8C2×C3×D311yescharacteristic
300C4×D4—32no—
301C4×D4C2×C3×D311yescharacteristic
302C2×C4⋊C4—61no—
303#107—32no—
304#107—32no—
305#107—32no—
306#106—32no—
307#106C2×C3×D311yescharacteristic
308C4⋊C8—32no—
309C4⋊C8—31no—
310#103—32no—
311#103C2×C3×D311yescharacteristic
312#102—32no—
313#102C2×C3×D311yescharacteristic
314#97—32no—
315C4×C8C2×C3×D311yescharacteristic
316C23×C3—21no—
317C23×C3—21no—
318C23×C3—41no—
319C3×Q8—21no—
320C3×Q8—21no—
321C3×Q8—22no—
322C3×Q8—41no—
323C3×Q8—62no—
324C3×Q8—241no—
325C3×Q8—241no—
326C3×Q8—242no—
327C3×Q8C2×Dic612yes—
328C3×Q8C2×C3×Q812yes—
329C3×D4—21no—
330C3×D4—21no—
331C3×D4—22no—
332C3×D4—41no—
333C3×D4C2×Dic612yes—
334C3×D4C2×C3×Q812yes—
335C2×C3×C4—21no—
336C2×C3×C4—21no—
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—32no—
345C2×C3×C4—32no—
346C2×C3×C4—41no—
347C2×C3×C4—41no—
348C2×C3×C4—41no—
349C2×C3×C4—42no—
350C2×C3×C4—42no—
351C2×C3×C4—62no—
352C2×C3×C4—62no—
353C2×C3×C4—82no—
354C2×C3×C4—242no—
355C2×C3×C4D3×D411yescharacteristic
356C2×C3×C4D3×D411yescharacteristic
357C2×C3×C4C2×C3×D411yescharacteristic
358C2×C3×C4C2×C3×D411yescharacteristic
359C2×C3×C4C23×D311yescharacteristic
360C2×C3×C4C24×C311yescharacteristic
361C2×Dic3—22no—
362C2×Dic3—22no—
363C2×Dic3—82no—
364C2×Dic3C2×C3×D412yes—
365C2×Dic3C2×C3×D412yes—
366Dic6—22no—
367Dic6—82no—
368Dic6—81no—
369Dic6—81no—
370C3×C8—21no—
371C3×C8—21no—
372C3×C8—22no—
373C3×C8—41no—
374C3×C8—62no—
375C3×C8C2×Dic612yes—
376C3×C8C2×C3×Q812yes—
377C3⋊C8—22no—
378C2×C32—42no—
379C2×C32D4×Q811yescharacteristic
380C2×C32C2×#13711yescharacteristic
381C2×C32#57611yescharacteristic
382C2×Q8—31no—
383C2×Q8—62no—
384C2×Q8—61no—
385C2×Q8—61no—
386C2×Q8C22×C3×D311yescharacteristic
387C2×D4C22×C3×D311yescharacteristic
388C22×C4—21no—
389C22×C4—62no—
390SD16C3×Dic614yescomplemented
391C2×C8—32no—
392C2×C8C22×C3×D311yescharacteristic
393C2×C8C22×C3×D311yescharacteristic
394C4⋊C4—21no—
395C4⋊C4—31no—
396C4⋊C4—32no—
397C4⋊C4—32no—
398C4⋊C4—32no—
399C4⋊C4—62no—
400C4⋊C4—62no—
401C4⋊C4—62no—
402C4⋊C4—62no—
403C4⋊C4—61no—
404C4⋊C4—61no—
405C4⋊C4C22×C3×D311yescharacteristic
406C4⋊C4C22×C3×D311yescharacteristic
407C22⋊C4—21no—
408C22⋊C4—62no—
409C42—21no—
410C42—32no—
411C42—62no—
412C42C22×C3×D311yescharacteristic
413C22×C3—22no—
414C22×C3—22no—
415C22×C3—21no—
416C22×C3—42no—
417C22×C3—41no—
418C22×C3—41no—
419C22×C3—41no—
420C22×C3—41no—
421C22×C3—81no—
422C22×C3—81no—
423C22×C3C2×D3×D411yescharacteristic
424C22×C3C22×C3×D411yescharacteristic
425C3×C4—21no—
426C3×C4—21no—
427C3×C4—22no—
428C3×C4—22no—
429C3×C4—22no—
430C3×C4—21no—
431C3×C4—21no—
432C3×C4—41no—
433C3×C4—42no—
434C3×C4—41no—
435C3×C4—41no—
436C3×C4—41no—
437C3×C4—41no—
438C3×C4—62no—
439C3×C4—62no—
440C3×C4—81no—
441C3×C4—81no—
442C3×C4—122no—
443C3×C4—122no—
444C3×C4#91512yes—
445C3×C4C3×#13712yes—
446C3×C4C22×Dic611yescharacteristic
447C3×C4#101011yescharacteristic
448C3×C4C22×C3×Q811yescharacteristic
449C3×C4C3×2−1+411yescharacteristic
450Dic3—22no—
451Dic3—22no—
452Dic3—42no—
453Dic3—42no—
454C32#338511yescharacteristic, complemented, Sylow
455C23—21no—
456Q8—21no—
457Q8—62no—
458Q8—241no—
459Q8—241no—
460Q8—242no—
461Q8C2×C3×Dic612yes—
462D4—21no—
463D4C2×C3×Dic612yes—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—32no—
468C2×C4—32no—
469C2×C4—42no—
470C2×C4—62no—
471C2×C4—62no—
472C2×C4—242no—
473C2×C4C3×D3×D411yescharacteristic
474C2×C4C3×D3×D411yescharacteristic
475C2×C4C23×C3×D311yescharacteristic
476C8—21no—
477C8—62no—
478C8C2×C3×Dic612yes—
479C2×C3—21no—
480C2×C3—21no—
481C2×C3—21no—
482C2×C3—42no—
483C2×C3—42no—
484C2×C3—82no—
485C2×C3D4×Dic611yescharacteristic
486C2×C3C2×#91511yescharacteristic
487C2×C3#576911yescharacteristic
488C2×C3C3×D4×Q811yescharacteristic
489C2×C3C2×C3×#13711yescharacteristic
490C2×C3C3×#57611yescharacteristic
491C22—22no—
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×#91512yes—
504C4C22×C3×Dic611yescharacteristic
505C4C3×#101011yescharacteristic
506C3—21no—
507C3#7963411yescharacteristic, direct product factor
508C3C3×#338511yescharacteristic, complemented
509C2—42no—
510C2C3×D4×Dic611yescharacteristic
511C2C2×C3×#91511yescharacteristic
512C2C3×#576911yescharacteristic
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×#3385
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×Q8×Dic6C2semidirect
5. C3×#5021C2semidirect
7. C3×#4856C2semidirect
8. C3×#4796C2semidirect
10. C3×#4682C2semidirect
11. C3×#4679C2semidirect
13. #79634C3direct (N × H)
45. Q8×Dic6C2×C3semidirect
59. #5021C2×C3semidirect
61. #4856C2×C3semidirect
62. #4796C2×C3semidirect
64. #4682C2×C3semidirect
65. #4679C2×C3semidirect
74. C32×SD16Q8semidirect
218. C3×SD16Dic6semidirect
219. C3×SD16C3×Q8semidirect
390. SD16C3×Dic6semidirect
454. C32#3385semidirect
507. C3#79634direct (N × H)
508. C3C3×#3385semidirect

Maximal subgroups

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

subgroupindex
C3×Q8×Dic62
C3×#55432
C32×C4×SD162
C3×#51642
C3×#50212
C3×#50082
C3×#48562
C3×#47962
C3×#47592
C3×#46822
C3×#46792
C3×#33853
#796343