Finite Group Databasebeta

← C3×#79927 #11895317

Subgroups — C3×#79927 #11895317

Order 1152.

775 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5585C211yesmaximal, characteristic, complemented
2C3×#5579C211yesmaximal, characteristic, complemented
3C32×C8×Q8C211yesmaximal, characteristic, complemented
4C3×#4850C211yesmaximal, characteristic, complemented
5C3×#4847C212yesmaximal, complemented
6C3×#4844C212yesmaximal, complemented
7C3×#4843C211yesmaximal, characteristic
8C3×#4697C212yesmaximal, complemented
9C3×#4694C211yesmaximal, characteristic, complemented
10C3×C4×D24C212yesmaximal, complemented
11C3×C4×#204C211yesmaximal, characteristic, complemented
12C3×#3361—31nomaximal
13#79927C311yesmaximal, characteristic, direct product factor
14C32×C4×Q8C2211yescharacteristic
15C3×#947—21no—
16C3×#946—21no—
17C2×C3×D24C2212yes—
18C2×C3×#204C2211yescharacteristic
19C3×#896—22no—
20C3×#894—22no—
21C3×#893—21no—
22C3×D3×C4⋊C4—21no—
23C3×#875C2212yes—
24C3×#874C2211yescharacteristic
25C3×C4×D12C2211yescharacteristic
26C3×C4×D12C2212yes—
27C3×C4×D12C2212yes—
28C3×#870C2212yes—
29C3×#869C2211yescharacteristic
30C3×C4×Dic6C2211yescharacteristic
31C32×C4⋊C8C2211yescharacteristic
32C32×C4⋊C8C2212yes—
33C32×C4×C8C2211yescharacteristic
34C32×C4×C8C2212yes—
35C3×#821C2211yescharacteristic
36C3×#821C2212yes—
37C3×#821C2212yes—
38C3×#821C2212yes—
39C3×#818C2212yes—
40C3×#817C2211yescharacteristic
41C3×#816C2211yescharacteristic
42C3×#816C2212yes—
43C3×#559—31no—
44C3×#554—31no—
45#5585C2×C311yescharacteristic, complemented
46#5579C2×C311yescharacteristic, complemented
47C3×#488—32no—
48C3×#486—31no—
49C3×#478—32no—
50C3×#477—31no—
51C3×#463—32no—
52C3×#459—31no—
53C3×C8×Q8—21no—
54C3×C8×Q8D311yescharacteristic, complemented
55C3×C8×Q8C2×C311yescharacteristic, complemented
56C3×C4×SD16—31no—
57C3×C4×D8—32no—
58#4850C2×C311yescharacteristic, complemented
59#4847C2×C312yescomplemented
60#4844C2×C312yescomplemented
61#4843C2×C311yescharacteristic
62#4697C2×C312yescomplemented
63#4694C2×C311yescharacteristic, complemented
64C4×D24C2×C312yescomplemented
65C4×#204C2×C311yescharacteristic, complemented
66C2×C32×Q8D411yescharacteristic
67C2×C3×D12—21no—
68C2×C3×D12—21no—
69C2×C3×D12C2312yes—
70C2×C3×D12C2311yescharacteristic
71C2×C3×C4×D3—21no—
72C2×C3×C4×D3—22no—
73C2×C3×C4×D3—22no—
74C2×C3×Dic6—21no—
75C2×C3×Dic6C2311yescharacteristic
76C2×C32×C8C2311yescharacteristic
77C2×C32×C8C2312yes—
78C2×C32×C8C2311yescharacteristic
79C32×C4⋊C4D411yescharacteristic
80C32×C4⋊C4D412yes—
81C32×C42C2311yescharacteristic
82C32×C42C2312yes—
83C3×(C2×D3)⋊C4—22no—
84C3×(C2×D3)⋊C4—22no—
85C3×(C2×D3)⋊C4—22no—
86C3×(C2×D3)⋊C4—21no—
87C3×(C2×D3)⋊C4—22no—
88C3×C4⋊Dic3—21no—
89C3×C4⋊Dic3C2311yescharacteristic
90C3×C4⋊Dic3C2312yes—
91C3×C4⋊Dic3C2311yescharacteristic
92C3×Dic3⋊C4—22no—
93C3×Dic3⋊C4—21no—
94C3×Dic3⋊C4—22no—
95C3×C4×Dic3—21no—
96C3×D24—24no—
97C3×#204—22no—
98#3361—31noSylow
99C2×C3×SD16—31no—
100C2×C3×D8—32no—
101C3×C4⋊Q8—31no—
102C3×#127—31no—
103C3×#125—32no—
104C3×#124—32no—
105C3×#124—61no—
106C3×#123—62no—
107C3×C22⋊Q8—61no—
108C3×C22⋊Q8—62no—
109C3×C4×Q8—21no—
110C3×C4×Q8—31no—
111C3×C4×Q8C2×D311yescharacteristic
112C3×C4×Q8C22×C311yescharacteristic
113C3×C4×D4—32no—
114C3×C4×D4—32no—
115C3×C4×D4—31no—
116C3×C4×D4—61no—
117C2×C3×C4⋊C4—61no—
118#947—21no—
119#946—21no—
120C2×D24C22×C312yes—
121C2×#204C22×C311yescharacteristic
122#896—22no—
123#894—22no—
124#893—21no—
125D3×C4⋊C4—21no—
126#875C22×C312yes—
127#874C22×C311yescharacteristic
128C4×D12C22×C311yescharacteristic
129C4×D12C22×C312yes—
130C4×D12C22×C312yes—
131#870C22×C312yes—
132#869C22×C311yescharacteristic
133C4×Dic6C22×C311yescharacteristic
134C3×#107—32no—
135C3×#106—31no—
136C3×C4⋊C8—21no—
137C3×C4⋊C8—22no—
138C3×C4⋊C8C2×D311yescharacteristic
139C3×C4⋊C8C2×D312yes—
140C3×C4⋊C8C22×C311yescharacteristic
141C3×C4⋊C8C22×C312yes—
142C3×#103—31no—
143C3×#103—32no—
144C3×#102—31no—
145C3×#102—32no—
146C3×#102—32no—
147C3×#102—32no—
148C3×C4×C8—22no—
149C3×C4×C8—21no—
150C3×C4×C8C2×D312yes—
151C3×C4×C8C2×D311yescharacteristic
152C3×C4×C8C22×C311yescharacteristic
153C3×C4×C8C22×C312yes—
154#821C22×C311yescharacteristic
155#821C22×C312yes—
156#821C22×C312yes—
157#821C22×C312yes—
158#818C22×C312yes—
159#817C22×C311yescharacteristic
160#816C22×C311yescharacteristic
161#816C22×C312yes—
162C22×C3×D3—21no—
163C22×C3×D3—22no—
164C32×Q8—22no—
165C2×C32×C4C2×D412yes—
166C2×C32×C4C2×D411yescharacteristic
167C2×C32×C4C2×D412yes—
168C2×C32×C4C2×D411yescharacteristic
169C2×C32×C4C2411yescharacteristic
170C2×C3×Dic3—21no—
171C2×C3×Dic3—21no—
172C2×C3×Dic3—21no—
173C2×C3×Dic3—22no—
174C3×D12—22no—
175C3×D12—21no—
176C3×D12—22no—
177C3×D12—42no—
178C3×D12—81no—
179C3×D12#4112yes—
180C3×C4×D3—42no—
181C3×C4×D3—82no—
182C3×C4×D3—82no—
183C3×Dic6—21no—
184C3×Dic6—21no—
185C3×Dic6—81no—
186C32×C8—21no—
187C32×C8—21no—
188C32×C8—22no—
189#559—31no—
190#554—31no—
191#488—32no—
192#486—31no—
193#478—32no—
194#477—31no—
195#463—32no—
196#459—31no—
197C8×Q8C3×D311yescharacteristic, complemented
198C4×SD16—31no—
199C4×D8—32no—
200C2×C3×Q8—21no—
201C2×C3×Q8—31no—
202C2×C3×Q8—61no—
203C2×C3×Q8D1211yescharacteristic
204C2×C3×Q8C3×D411yescharacteristic
205C2×C3×D4—31no—
206C2×C3×D4—32no—
207C2×C3×D4—61no—
208C2×C3×D4—61no—
209C22×C3×C4—61no—
210C22×C3×C4—62no—
211C22×C3×C4—62no—
212C2×D12—21no—
213C2×D12—21no—
214C2×D12C23×C312yes—
215C2×D12C23×C311yescharacteristic
216C2×C4×D3—21no—
217C2×C4×D3—22no—
218C2×C4×D3—22no—
219C2×Dic6—21no—
220C2×Dic6C23×C311yescharacteristic
221C3×SD16—62no—
222C3×D8—64no—
223C2×C3×C8—21no—
224C2×C3×C8—21no—
225C2×C3×C8—22no—
226C2×C3×C8C22×D311yescharacteristic
227C2×C3×C8C22×D311yescharacteristic
228C2×C3×C8C22×D312yes—
229C2×C3×C8C23×C312yes—
230C2×C3×C8C23×C311yescharacteristic
231C2×C3×C8C23×C311yescharacteristic
232C3×C4⋊C4—21no—
233C3×C4⋊C4—22no—
234C3×C4⋊C4—31no—
235C3×C4⋊C4—32no—
236C3×C4⋊C4—31no—
237C3×C4⋊C4—62no—
238C3×C4⋊C4—61no—
239C3×C4⋊C4—62no—
240C3×C4⋊C4—61no—
241C3×C4⋊C4D1211yescharacteristic
242C3×C4⋊C4D1212yes—
243C3×C4⋊C4C3×D411yescharacteristic
244C3×C4⋊C4C3×D412yes—
245C3×C22⋊C4—61no—
246C3×C22⋊C4—62no—
247C3×C22⋊C4—62no—
248C3×C22⋊C4—62no—
249C3×C22⋊C4—62no—
250C3×C42—22no—
251C3×C42—21no—
252C3×C42—61no—
253C3×C42C22×D312yes—
254C3×C42C22×D311yescharacteristic
255C3×C42C23×C311yescharacteristic
256C3×C42C23×C312yes—
257(C2×D3)⋊C4—22no—
258(C2×D3)⋊C4—21no—
259(C2×D3)⋊C4—22no—
260(C2×D3)⋊C4—22no—
261(C2×D3)⋊C4—22no—
262C4⋊Dic3—21no—
263C4⋊Dic3C23×C311yescharacteristic
264C4⋊Dic3C23×C312yes—
265C4⋊Dic3C23×C311yescharacteristic
266Dic3⋊C4—21no—
267Dic3⋊C4—22no—
268Dic3⋊C4—22no—
269C4×Dic3—21no—
270D24—24no—
271#204—22no—
272C22×C32C22×D411yescharacteristic
273C2×C3×D3—22no—
274C2×C3×D3—41no—
275C2×C3×D3—41no—
276C2×C3×D3—42no—
277C2×C3×D3—42no—
278C2×C3×D3—42no—
279C32×C4—22no—
280C32×C4—21no—
281C32×C4—22no—
282C32×C4#13512yes—
283C32×C4C2×#4111yescharacteristic
284C32×C42−1+411yescharacteristic
285C3×Dic3—41no—
286C3×Dic3—41no—
287C3×Dic3—42no—
288C3×Dic3—41no—
289C2×SD16—31no—
290C2×D8—32no—
291C4⋊Q8—31no—
292#127—31no—
293#125—32no—
294#124—32no—
295#124—61no—
296#123—62no—
297C22⋊Q8—61no—
298C22⋊Q8—62no—
299C4×Q8—31no—
300C4×Q8C2×C3×D311yescharacteristic
301C4×D4—32no—
302C4×D4—31no—
303C4×D4—32no—
304C4×D4—61no—
305C2×C4⋊C4—61no—
306#107—32no—
307#106—31no—
308C4⋊C8C2×C3×D311yescharacteristic
309C4⋊C8C2×C3×D312yes—
310#103—31no—
311#103—32no—
312#102—31no—
313#102—32no—
314#102—32no—
315#102—32no—
316C4×C8C2×C3×D312yes—
317C4×C8C2×C3×D311yescharacteristic
318C23×C3—61no—
319C23×C3—62no—
320C22×D3—21no—
321C22×D3—22no—
322C3×Q8—24no—
323C3×Q8—22no—
324C3×Q8—22no—
325C3×Q8—61no—
326C3×Q8—61no—
327C3×Q8—241no—
328C3×D4—32no—
329C3×D4—61no—
330C3×D4—62no—
331C3×D4—62no—
332C3×D4—122no—
333C3×D4—241no—
334C2×C3×C4—21no—
335C2×C3×C4—22no—
336C2×C3×C4—21no—
337C2×C3×C4—22no—
338C2×C3×C4—21no—
339C2×C3×C4—61no—
340C2×C3×C4—61no—
341C2×C3×C4—61no—
342C2×C3×C4—62no—
343C2×C3×C4—122no—
344C2×C3×C4—242no—
345C2×C3×C4—242no—
346C2×C3×C4C2×D1212yes—
347C2×C3×C4C2×D1212yes—
348C2×C3×C4C2×D1211yescharacteristic
349C2×C3×C4C2×D1211yescharacteristic
350C2×C3×C4C2×C3×D412yes—
351C2×C3×C4C2×C3×D411yescharacteristic
352C2×C3×C4C2×C3×D412yes—
353C2×C3×C4C2×C3×D411yescharacteristic
354C2×C3×C4C23×D311yescharacteristic
355C2×C3×C4C24×C311yescharacteristic
356C2×Dic3—21no—
357C2×Dic3—21no—
358C2×Dic3—21no—
359C2×Dic3—22no—
360D12—22no—
361D12—21no—
362D12—22no—
363D12—42no—
364D12—81no—
365D12C3×#4112yes—
366C4×D3—42no—
367C4×D3—82no—
368C4×D3—82no—
369Dic6—21no—
370Dic6—21no—
371Dic6—81no—
372C3×C8—22no—
373C3×C8—21no—
374C3×C8—22no—
375C3×C8—21no—
376C3×C8—21no—
377C3×C8—22no—
378C3×C8—21no—
379C3×C8—42no—
380C3×C8—41no—
381C2×C32#54811yescharacteristic
382C2×C32C2×#13511yescharacteristic
383C2×C32#57611yescharacteristic
384C3×D3—42no—
385C3×D3—82no—
386C2×Q8—31no—
387C2×Q8—61no—
388C2×Q8C3×D1211yescharacteristic
389C2×D4—31no—
390C2×D4—32no—
391C2×D4—61no—
392C2×D4—61no—
393C22×C4—61no—
394C22×C4—62no—
395C22×C4—62no—
396SD16—62no—
397D8—64no—
398C2×C8C22×C3×D311yescharacteristic
399C2×C8C22×C3×D311yescharacteristic
400C2×C8C22×C3×D312yes—
401C4⋊C4—31no—
402C4⋊C4—32no—
403C4⋊C4—31no—
404C4⋊C4—62no—
405C4⋊C4—61no—
406C4⋊C4—61no—
407C4⋊C4—62no—
408C4⋊C4C3×D1211yescharacteristic
409C4⋊C4C3×D1212yes—
410C22⋊C4—61no—
411C22⋊C4—62no—
412C22⋊C4—62no—
413C22⋊C4—62no—
414C22⋊C4—62no—
415C42—61no—
416C42C22×C3×D312yes—
417C42C22×C3×D311yescharacteristic
418C22×C3—21no—
419C22×C3—62no—
420C22×C3—121no—
421C22×C3—121no—
422C22×C3—122no—
423C22×C3—122no—
424C22×C3—122no—
425C22×C3C22×D1211yescharacteristic
426C22×C3C22×C3×D411yescharacteristic
427C2×D3—22no—
428C2×D3—41no—
429C2×D3—41no—
430C2×D3—42no—
431C2×D3—42no—
432C2×D3—42no—
433C3×C4—24no—
434C3×C4—22no—
435C3×C4—21no—
436C3×C4—22no—
437C3×C4—22no—
438C3×C4—22no—
439C3×C4—21no—
440C3×C4—22no—
441C3×C4—21no—
442C3×C4—21no—
443C3×C4—42no—
444C3×C4—41no—
445C3×C4—121no—
446C3×C4—121no—
447C3×C4—122no—
448C3×C4—121no—
449C3×C4#90412yes—
450C3×C4C3×#13512yes—
451C3×C4#100711yescharacteristic
452C3×C4D3×#4111yescharacteristic
453C3×C4C2×C3×#4111yescharacteristic
454C3×C4C3×2−1+411yescharacteristic
455Dic3—41no—
456Dic3—42no—
457Dic3—41no—
458Dic3—41no—
459C32#336111yescharacteristic, complemented, Sylow
460C23—61no—
461C23—62no—
462Q8—22no—
463Q8—61no—
464Q8—61no—
465Q8—241no—
466D4—32no—
467D4—61no—
468D4—62no—
469D4—62no—
470D4—122no—
471D4—241no—
472C2×C4—61no—
473C2×C4—61no—
474C2×C4—61no—
475C2×C4—62no—
476C2×C4—122no—
477C2×C4—242no—
478C2×C4—242no—
479C2×C4C2×C3×D1212yes—
480C2×C4C2×C3×D1212yes—
481C2×C4C2×C3×D1211yescharacteristic
482C2×C4C2×C3×D1211yescharacteristic
483C2×C4C23×C3×D311yescharacteristic
484C8—21no—
485C8—22no—
486C8—21no—
487C2×C3—21no—
488C2×C3—21no—
489C2×C3—21no—
490C2×C3—122no—
491C2×C3—242no—
492C2×C3#557611yescharacteristic
493C2×C3C2×#90411yescharacteristic
494C2×C3#575211yescharacteristic
495C2×C3C3×#54811yescharacteristic
496C2×C3C2×C3×#13511yescharacteristic
497C2×C3C3×#57611yescharacteristic
498D3—42no—
499D3—82no—
500C22—62no—
501C22—121no—
502C22—121no—
503C22—122no—
504C22—122no—
505C22—122no—
506C22C22×C3×D1211yescharacteristic
507C4—22no—
508C4—21no—
509C4—22no—
510C4—121no—
511C4—122no—
512C4—121no—
513C4—121no—
514C4C3×#90412yes—
515C4C3×#100711yescharacteristic
516C4C3×D3×#4111yescharacteristic
517C3—21no—
518C3#7992711yescharacteristic, direct product factor
519C3C3×#336111yescharacteristic, complemented
520C2—122no—
521C2—242no—
522C2C3×#557611yescharacteristic
523C2C2×C3×#90411yescharacteristic
524C2C3×#575211yescharacteristic
subgroupG/H
centerC22×C3C22×D12
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×C8×Q8C2
socleC22×C32C22×D4
prime radicalC3×#4843C2
hypercenterC3×C8×Q8D3
hypocenterC3C3×#3361
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C4×Q8 ◁ C3×C8×Q8

Complements

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

NH ≅ G/Ntype
1. C3×#5585C2semidirect
2. C3×#5579C2semidirect
3. C32×C8×Q8C2semidirect
4. C3×#4850C2semidirect
5. C3×#4847C2semidirect
6. C3×#4844C2semidirect
8. C3×#4697C2semidirect
9. C3×#4694C2semidirect
10. C3×C4×D24C2semidirect
11. C3×C4×#204C2semidirect
13. #79927C3direct (N × H)
45. #5585C2×C3semidirect
46. #5579C2×C3semidirect
54. C3×C8×Q8D3semidirect
55. C3×C8×Q8C2×C3semidirect
58. #4850C2×C3semidirect
59. #4847C2×C3semidirect
60. #4844C2×C3semidirect
62. #4697C2×C3semidirect
63. #4694C2×C3semidirect
64. C4×D24C2×C3semidirect
65. C4×#204C2×C3semidirect
197. C8×Q8C3×D3semidirect
459. C32#3361semidirect
518. C3#79927direct (N × H)
519. C3C3×#3361semidirect

Maximal subgroups

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

subgroupindex
C3×#55852
C3×#55792
C32×C8×Q82
C3×#48502
C3×#48472
C3×#48442
C3×#48432
C3×#46972
C3×#46942
C3×C4×D242
C3×C4×#2042
C3×#33613
#799273