Finite Group Databasebeta

← C3×#79701 #11895616

Subgroups — C3×#79701 #11895616

Order 1152.

751 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5585C211yesmaximal, characteristic
2C3×#5570C211yesmaximal, characteristic, complemented
3C32×C4×Q16C211yesmaximal, characteristic, complemented
4C3×#5185C212yesmaximal, complemented
5C3×#5027C211yesmaximal, characteristic
6C3×#5020C211yesmaximal, characteristic, complemented
7C3×#4891C212yesmaximal, complemented
8C3×#4800C212yesmaximal, complemented
9C3×#4788C212yesmaximal, complemented
10C3×#4694C211yesmaximal, characteristic
11C3×C8×Dic6C211yesmaximal, characteristic, complemented
12C3×#3365—31nomaximal
13#79701C311yesmaximal, characteristic, direct product factor
14C2×C32×Q16C2211yescharacteristic
15C32×C4×Q8C2211yescharacteristic
16C32×C4×Q8C2211yescharacteristic
17C3×#947C2212yes—
18C3×Q8×Dic3C2212yes—
19C2×C3×#215C2212yes—
20C3×#894—22no—
21C3×#893C2212yes—
22C3×#890—22no—
23C3×#890C2212yes—
24C3×#875—21no—
25C3×#874C2211yescharacteristic
26C3×C4×D12—21no—
27C3×#869—21no—
28C3×#869C2211yescharacteristic
29C3×C4×Dic6—21no—
30C3×C4×Dic6C2211yescharacteristic
31C32×#107C2211yescharacteristic
32C32×#103C2211yescharacteristic
33C32×#103C2211yescharacteristic
34C32×C4×C8C2211yescharacteristic
35C3×#835C2212yes—
36C3×#821C2212yes—
37C3×#821C2212yes—
38C3×Dic3⋊C8C2212yes—
39C3×C8×Dic3C2212yes—
40C3×#809C2212yes—
41C3×#808C2212yes—
42C3×C4⋊(C3⋊C8)C2211yescharacteristic
43C3×#559—31no—
44C3×#557—31no—
45#5585C2×C311yescharacteristic
46#5570C2×C311yescharacteristic, complemented
47C3×#488—32no—
48C3×#486—31no—
49C3×#478—32no—
50C3×#475—31no—
51C3×#464—32no—
52C3×#460—31no—
53C3×C8×Q8—31no—
54C3×C4×Q16—21no—
55C3×C4×Q16D311yescharacteristic, complemented
56C3×C4×Q16C2×C311yescharacteristic, complemented
57C3×C4×SD16—32no—
58#5185C2×C312yescomplemented
59#5027C2×C311yescharacteristic
60#5020C2×C311yescharacteristic, complemented
61#4891C2×C312yescomplemented
62#4800C2×C312yescomplemented
63#4788C2×C312yescomplemented
64#4694C2×C311yescharacteristic
65C8×Dic6C2×C311yescharacteristic, complemented
66C2×C32×Q8C2311yescharacteristic
67C2×C32×Q8C2311yescharacteristic
68C2×C3×D12—21no—
69C2×C3×D12—21no—
70C2×C3×D12C2312yes—
71C2×C3×C4×D3—22no—
72C2×C3×Dic6—21no—
73C2×C3×Dic6D411yescharacteristic
74C32×Q16—22no—
75C2×C32×C8C2311yescharacteristic
76C2×C32×C8C2311yescharacteristic
77C32×C4⋊C4—21no—
78C32×C4⋊C4—21no—
79C32×C4⋊C4C2311yescharacteristic
80C32×C4⋊C4C2311yescharacteristic
81C32×C42—21no—
82C32×C42—21no—
83C32×C42C2311yescharacteristic
84C3×#215—24no—
85C3×(C2×D3)⋊C4—22no—
86C3×(C2×D3)⋊C4—22no—
87C3×(C2×D3)⋊C4—22no—
88C3×C4⋊Dic3—21no—
89C3×C4⋊Dic3—22no—
90C3×C4⋊Dic3—22no—
91C3×C4⋊Dic3D411yescharacteristic
92C3×C4⋊Dic3C2312yes—
93C3×Dic3⋊C4—22no—
94C3×Dic3⋊C4D412yes—
95C3×C4×Dic3—22no—
96C3×C4×Dic3C2312yes—
97C2×C3×C3⋊C8C2312yes—
98#3365—31noSylow
99C2×C3×Q16—21no—
100C2×C3×Q16C2×D311yescharacteristic
101C2×C3×Q16C22×C311yescharacteristic
102C2×C3×SD16—32no—
103C3×C4⋊Q8—31no—
104C3×C4⋊Q8—61no—
105C3×#127—31no—
106C3×#125—32no—
107C3×#125—62no—
108C3×#124—32no—
109C3×#124—61no—
110C3×#123—62no—
111C3×C4×Q8—21no—
112C3×C4×Q8—21no—
113C3×C4×Q8—31no—
114C3×C4×Q8—32no—
115C3×C4×Q8—61no—
116C3×C4×Q8C2×D311yescharacteristic
117C3×C4×Q8C2×D311yescharacteristic
118C3×C4×Q8C22×C311yescharacteristic
119C3×C4×Q8C22×C311yescharacteristic
120C3×C4×D4—32no—
121C3×C4×D4—61no—
122#947C22×C312yes—
123Q8×Dic3C22×C312yes—
124C2×#215C22×C312yes—
125#894—22no—
126#893C22×C312yes—
127#890—22no—
128#890C22×C312yes—
129#875—21no—
130#874C22×C311yescharacteristic
131C4×D12—21no—
132#869—21no—
133#869C22×C311yescharacteristic
134C4×Dic6—21no—
135C4×Dic6C22×C311yescharacteristic
136C3×#107—21no—
137C3×#107C2×D311yescharacteristic
138C3×#107C22×C311yescharacteristic
139C3×#106—32no—
140C3×C4⋊C8—32no—
141C3×C4⋊C8—31no—
142C3×#103—21no—
143C3×#103—21no—
144C3×#103—32no—
145C3×#103C2×D311yescharacteristic
146C3×#103C2×D311yescharacteristic
147C3×#103C22×C311yescharacteristic
148C3×#103C22×C311yescharacteristic
149C3×#102—32no—
150C3×#102—32no—
151C3×#102—32no—
152C3×C4×C8—21no—
153C3×C4×C8—32no—
154C3×C4×C8C2×D311yescharacteristic
155C3×C4×C8C22×C311yescharacteristic
156#835C22×C312yes—
157#821C22×C312yes—
158#821C22×C312yes—
159Dic3⋊C8C22×C312yes—
160C8×Dic3C22×C312yes—
161#809C22×C312yes—
162#808C22×C312yes—
163C4⋊(C3⋊C8)C22×C311yescharacteristic
164C22×C3×D3—22no—
165C32×Q8—21no—
166C32×Q8—21no—
167C32×Q8—21no—
168C32×Q8#4112yes—
169C2×C32×C4—21no—
170C2×C32×C4—21no—
171C2×C32×C4—21no—
172C2×C32×C4—21no—
173C2×C32×C4C2×D411yescharacteristic
174C2×C32×C4C2×D411yescharacteristic
175C2×C32×C4C2411yescharacteristic
176C2×C3×Dic3—22no—
177C2×C3×Dic3C2×D412yes—
178C2×C3×Dic3C2×D412yes—
179C3×D12—22no—
180C3×D12—22no—
181C3×D12—42no—
182C3×D12—81no—
183C3×C4×D3—82no—
184C3×Dic6—22no—
185C3×Dic6—42no—
186C32×C8—21no—
187C32×C8—21no—
188C3×C3⋊C8—22no—
189#559—31no—
190#557—31no—
191#488—32no—
192#486—31no—
193#478—32no—
194#475—31no—
195#464—32no—
196#460—31no—
197C8×Q8—31no—
198C4×Q16C3×D311yescharacteristic, complemented
199C4×SD16—32no—
200C2×C3×Q8—21no—
201C2×C3×Q8—21no—
202C2×C3×Q8—31no—
203C2×C3×Q8—61no—
204C2×C3×Q8C22×D311yescharacteristic
205C2×C3×Q8C22×D311yescharacteristic
206C2×C3×Q8C23×C311yescharacteristic
207C2×C3×Q8C23×C311yescharacteristic
208C2×C3×D4—32no—
209C2×C3×D4—61no—
210C2×C3×D4—61no—
211C22×C3×C4—62no—
212C2×D12—21no—
213C2×D12—21no—
214C2×D12C23×C312yes—
215C2×C4×D3—22no—
216C2×Dic6—21no—
217C2×Dic6C3×D411yescharacteristic
218C3×Q16—24no—
219C3×Q16—22no—
220C3×Q16—22no—
221C3×SD16—64no—
222C2×C3×C8—21no—
223C2×C3×C8—21no—
224C2×C3×C8—32no—
225C2×C3×C8C22×D311yescharacteristic
226C2×C3×C8C22×D311yescharacteristic
227C2×C3×C8C23×C311yescharacteristic
228C2×C3×C8C23×C311yescharacteristic
229C3×C4⋊C4—21no—
230C3×C4⋊C4—21no—
231C3×C4⋊C4—21no—
232C3×C4⋊C4—21no—
233C3×C4⋊C4—21no—
234C3×C4⋊C4—21no—
235C3×C4⋊C4—32no—
236C3×C4⋊C4—31no—
237C3×C4⋊C4—32no—
238C3×C4⋊C4—41no—
239C3×C4⋊C4—41no—
240C3×C4⋊C4—62no—
241C3×C4⋊C4—62no—
242C3×C4⋊C4—62no—
243C3×C4⋊C4—61no—
244C3×C4⋊C4C22×D311yescharacteristic
245C3×C4⋊C4C22×D311yescharacteristic
246C3×C4⋊C4C23×C311yescharacteristic
247C3×C4⋊C4C23×C311yescharacteristic
248C3×C22⋊C4—62no—
249C3×C22⋊C4—62no—
250C3×C22⋊C4—62no—
251C3×C42—21no—
252C3×C42—21no—
253C3×C42—21no—
254C3×C42—21no—
255C3×C42—21no—
256C3×C42—32no—
257C3×C42—41no—
258C3×C42—41no—
259C3×C42—62no—
260C3×C42C22×D311yescharacteristic
261C3×C42C23×C311yescharacteristic
262#215—24no—
263(C2×D3)⋊C4—22no—
264(C2×D3)⋊C4—22no—
265(C2×D3)⋊C4—22no—
266C4⋊Dic3—21no—
267C4⋊Dic3—22no—
268C4⋊Dic3—22no—
269C4⋊Dic3C3×D411yescharacteristic
270C4⋊Dic3C23×C312yes—
271Dic3⋊C4—22no—
272Dic3⋊C4C3×D412yes—
273C4×Dic3—22no—
274C4×Dic3C23×C312yes—
275C2×C3⋊C8C23×C312yes—
276C22×C32C22×D411yescharacteristic
277C2×C3×D3—42no—
278C2×C3×D3—42no—
279C2×C3×D3—42no—
280C32×C4—22no—
281C32×C4—21no—
282C32×C4—41no—
283C32×C4—41no—
284C32×C4—41no—
285C32×C4#13512yes—
286C32×C4C2×#4111yescharacteristic
287C32×C42−1+411yescharacteristic
288C3×Dic3—22no—
289C3×Dic3—22no—
290C3×Dic3—42no—
291C2×Q16C2×C3×D311yescharacteristic
292C2×SD16—32no—
293C4⋊Q8—31no—
294C4⋊Q8—61no—
295#127—31no—
296#125—32no—
297#125—62no—
298#124—32no—
299#124—61no—
300#123—62no—
301C4×Q8—31no—
302C4×Q8—32no—
303C4×Q8—61no—
304C4×Q8C2×C3×D311yescharacteristic
305C4×Q8C2×C3×D311yescharacteristic
306C4×D4—32no—
307C4×D4—61no—
308#107C2×C3×D311yescharacteristic
309#106—32no—
310C4⋊C8—32no—
311C4⋊C8—31no—
312#103—32no—
313#103C2×C3×D311yescharacteristic
314#103C2×C3×D311yescharacteristic
315#102—32no—
316#102—32no—
317#102—32no—
318C4×C8—32no—
319C4×C8C2×C3×D311yescharacteristic
320C23×C3—62no—
321C22×D3—22no—
322C3×Q8—21no—
323C3×Q8—21no—
324C3×Q8—22no—
325C3×Q8—21no—
326C3×Q8—21no—
327C3×Q8—21no—
328C3×Q8—21no—
329C3×Q8—22no—
330C3×Q8—41no—
331C3×Q8—41no—
332C3×Q8—62no—
333C3×Q8—122no—
334C3×Q8#23512yes—
335C3×Q8C3×#4112yes—
336C3×D4—62no—
337C3×D4—62no—
338C3×D4—122no—
339C3×D4—241no—
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—21no—
347C2×C3×C4—21no—
348C2×C3×C4—21no—
349C2×C3×C4—21no—
350C2×C3×C4—21no—
351C2×C3×C4—32no—
352C2×C3×C4—32no—
353C2×C3×C4—41no—
354C2×C3×C4—41no—
355C2×C3×C4—41no—
356C2×C3×C4—41no—
357C2×C3×C4—62no—
358C2×C3×C4—242no—
359C2×C3×C4D3×D411yescharacteristic
360C2×C3×C4D3×D411yescharacteristic
361C2×C3×C4C2×C3×D411yescharacteristic
362C2×C3×C4C2×C3×D411yescharacteristic
363C2×C3×C4C23×D311yescharacteristic
364C2×C3×C4C24×C311yescharacteristic
365C2×Dic3—22no—
366C2×Dic3C2×C3×D412yes—
367C2×Dic3C2×C3×D412yes—
368D12—22no—
369D12—22no—
370D12—42no—
371D12—81no—
372C4×D3—82no—
373Dic6—22no—
374Dic6—42no—
375C3×C8—22no—
376C3×C8—21no—
377C3×C8—21no—
378C3×C8—21no—
379C3×C8—21no—
380C3×C8—41no—
381C3×C8—62no—
382C3⋊C8—22no—
383C2×C32#54811yescharacteristic
384C2×C32C2×#13511yescharacteristic
385C2×C32#57711yescharacteristic
386C3×D3—82no—
387C2×Q8—31no—
388C2×Q8—61no—
389C2×Q8C22×C3×D311yescharacteristic
390C2×Q8C22×C3×D311yescharacteristic
391C2×D4—32no—
392C2×D4—61no—
393C2×D4—61no—
394C22×C4—62no—
395Q16—22no—
396SD16—64no—
397C2×C8—32no—
398C2×C8C22×C3×D311yescharacteristic
399C2×C8C22×C3×D311yescharacteristic
400C4⋊C4—21no—
401C4⋊C4—21no—
402C4⋊C4—31no—
403C4⋊C4—32no—
404C4⋊C4—32no—
405C4⋊C4—62no—
406C4⋊C4—62no—
407C4⋊C4—62no—
408C4⋊C4—61no—
409C4⋊C4C22×C3×D311yescharacteristic
410C4⋊C4C22×C3×D311yescharacteristic
411C22⋊C4—62no—
412C22⋊C4—62no—
413C22⋊C4—62no—
414C42—21no—
415C42—21no—
416C42—32no—
417C42—62no—
418C42C22×C3×D311yescharacteristic
419C22×C3—21no—
420C22×C3—122no—
421C22×C3—122no—
422C22×C3—122no—
423C22×C3C2×D3×D411yescharacteristic
424C22×C3C22×C3×D411yescharacteristic
425C2×D3—42no—
426C2×D3—42no—
427C2×D3—42no—
428C3×C4—21no—
429C3×C4—21no—
430C3×C4—22no—
431C3×C4—22no—
432C3×C4—22no—
433C3×C4—21no—
434C3×C4—21no—
435C3×C4—41no—
436C3×C4—42no—
437C3×C4—42no—
438C3×C4—41no—
439C3×C4—41no—
440C3×C4—41no—
441C3×C4—41no—
442C3×C4—41no—
443C3×C4—41no—
444C3×C4—62no—
445C3×C4—62no—
446C3×C4—81no—
447C3×C4—81no—
448C3×C4—122no—
449C3×C4#91912yes—
450C3×C4C3×#13512yes—
451C3×C4C2×#23511yescharacteristic
452C3×C4#101011yescharacteristic
453C3×C4C2×C3×#4111yescharacteristic
454C3×C4C3×2−1+411yescharacteristic
455Dic3—22no—
456Dic3—22no—
457Dic3—42no—
458C32#336511yescharacteristic, complemented, Sylow
459C23—62no—
460Q8—21no—
461Q8—21no—
462Q8—21no—
463Q8—62no—
464Q8—122no—
465Q8C3×#23512yes—
466D4—62no—
467D4—62no—
468D4—122no—
469D4—241no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—21no—
473C2×C4—21no—
474C2×C4—32no—
475C2×C4—32no—
476C2×C4—62no—
477C2×C4—242no—
478C2×C4C3×D3×D411yescharacteristic
479C2×C4C3×D3×D411yescharacteristic
480C2×C4C23×C3×D311yescharacteristic
481C8—21no—
482C8—21no—
483C8—62no—
484C2×C3—21no—
485C2×C3—21no—
486C2×C3—21no—
487C2×C3—242no—
488C2×C3#555211yescharacteristic
489C2×C3C2×#91911yescharacteristic
490C2×C3#577011yescharacteristic
491C2×C3C3×#54811yescharacteristic
492C2×C3C2×C3×#13511yescharacteristic
493C2×C3C3×#57711yescharacteristic
494D3—82no—
495C22—122no—
496C22—122no—
497C22—122no—
498C22C2×C3×D3×D411yescharacteristic
499C4—21no—
500C4—22no—
501C4—41no—
502C4—41no—
503C4—41no—
504C4—62no—
505C4—62no—
506C4—122no—
507C4C3×#91912yes—
508C4C2×C3×#23511yescharacteristic
509C4C3×#101011yescharacteristic
510C3—21no—
511C3#7970111yescharacteristic, direct product factor
512C3C3×#336511yescharacteristic, complemented
513C2—242no—
514C2C3×#555211yescharacteristic
515C2C2×C3×#91911yescharacteristic
516C2C3×#577011yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×C4×Q16C2
socleC22×C32C22×D4
prime radicalC3×#874C22
hypercenterC3×C4×Q16D3
hypocenterC3C3×#3365
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×C4×Q16

Complements

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

NH ≅ G/Ntype
2. C3×#5570C2semidirect
3. C32×C4×Q16C2semidirect
4. C3×#5185C2semidirect
6. C3×#5020C2semidirect
7. C3×#4891C2semidirect
8. C3×#4800C2semidirect
9. C3×#4788C2semidirect
11. C3×C8×Dic6C2semidirect
13. #79701C3direct (N × H)
46. #5570C2×C3semidirect
55. C3×C4×Q16D3semidirect
56. C3×C4×Q16C2×C3semidirect
58. #5185C2×C3semidirect
60. #5020C2×C3semidirect
61. #4891C2×C3semidirect
62. #4800C2×C3semidirect
63. #4788C2×C3semidirect
65. C8×Dic6C2×C3semidirect
198. C4×Q16C3×D3semidirect
458. C32#3365semidirect
511. C3#79701direct (N × H)
512. C3C3×#3365semidirect

Maximal subgroups

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

subgroupindex
C3×#55852
C3×#55702
C32×C4×Q162
C3×#51852
C3×#50272
C3×#50202
C3×#48912
C3×#48002
C3×#47882
C3×#46942
C3×C8×Dic62
C3×#33653
#797013