Finite Group Databasebeta

← C3×#10590892 #13157857

Subgroups — C3×#10590892 #13157857

Order 1728.

494 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#63918C211yesmaximal, characteristic
2C3×#63869C211yesmaximal, characteristic
3C3×#63645C211yesmaximal, characteristic
4C32×#817C211yesmaximal, characteristic
5C32×#815C211yesmaximal, characteristic
6C3×#63575C211yesmaximal, characteristic
7C3×#63573C211yesmaximal, characteristic
8C3×#4856—31nomaximal
9C3×#4702—31nomaximal
10#10590892C311yesmaximal, characteristic, direct product factor
11C2×C3×#627—21no—
12C2×C33×C8C2211yescharacteristic
13C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
15C32×C4⋊Dic3C2211yescharacteristic
16C32×C4⋊Dic3C2211yescharacteristic
17C32×C4×Dic3C2211yescharacteristic
18C2×C32×C3⋊C8C2211yescharacteristic
19C3×#3724—21no—
20C3×Dic3⋊Dic3—21no—
21C3×Dic3⋊Dic3—21no—
22C3×#890—31no—
23C3×#888—31no—
24C3×#870—31no—
25C3×#869—31no—
26#63918C2×C311yescharacteristic
27#63869C2×C311yescharacteristic
28C32×#106—31no—
29C32×#97—31no—
30#63645C2×C311yescharacteristic
31C3×#818—31no—
32C3×#818—31no—
33C3×#818—31no—
34C3×#818—61no—
35C3×#817—21no—
36C3×#817—31no—
37C3×#817D311yescharacteristic
38C3×#817C2×C311yescharacteristic
39C3×#815—21no—
40C3×#815D311yescharacteristic
41C3×#815C2×C311yescharacteristic
42C3×#808—31no—
43C3×#807—31no—
44#63575C2×C311yescharacteristic
45#63573C2×C311yescharacteristic
46C2×C33×C4C2311yescharacteristic
47C2×C3×C3⋊Dic3—21no—
48C2×C3×C3⋊Dic3—21no—
49C2×C32×Dic3—21no—
50C2×C32×Dic3—21no—
51C2×C32×Dic3D411yescharacteristic
52C2×C32×Dic3D411yescharacteristic
53C3×#627—42no—
54C33×C8Q812yescomplemented
55C32×C3⋊C8Q812yescomplemented
56C3×#501—91no—
57#4856—31no—
58#4702—31no—
59C2×C3×Dic6—61no—
60C2×C3×Dic6—61no—
61C2×#627—21no—
62C2×C32×C8—21no—
63C2×C32×C8—21no—
64C2×C32×C8—21no—
65C2×C32×C8—31no—
66C2×C32×C8—41no—
67C2×C32×C8C2×D311yescharacteristic
68C2×C32×C8C2×D311yescharacteristic
69C2×C32×C8C22×C311yescharacteristic
70C32×C4⋊C4—31no—
71C32×C4⋊C4—31no—
72C32×C42—31no—
73C4⋊(C3⋊Dic3)C22×C311yescharacteristic
74C4⋊(C3⋊Dic3)C22×C311yescharacteristic
75C3×C4⋊Dic3—21no—
76C3×C4⋊Dic3—21no—
77C3×C4⋊Dic3—31no—
78C3×C4⋊Dic3—31no—
79C3×C4⋊Dic3—31no—
80C3×C4⋊Dic3—31no—
81C3×C4⋊Dic3—61no—
82C3×C4⋊Dic3—61no—
83C3×C4⋊Dic3—61no—
84C3×C4⋊Dic3—61no—
85C3×C4⋊Dic3C2×D311yescharacteristic
86C3×C4⋊Dic3C2×D311yescharacteristic
87C3×C4⋊Dic3C22×C311yescharacteristic
88C3×C4⋊Dic3C22×C311yescharacteristic
89C3×Dic3⋊C4—61no—
90C3×Dic3⋊C4—61no—
91C3×Dic3⋊C4—61no—
92C3×Dic3⋊C4—61no—
93C3×C4×Dic3—21no—
94C3×C4×Dic3C2×D311yescharacteristic
95C3×C4×Dic3C22×C311yescharacteristic
96C2×C3×C3⋊C8—21no—
97C2×C3×C3⋊C8C2×D311yescharacteristic
98C2×C3×C3⋊C8C22×C311yescharacteristic
99#3724—21no—
100Dic3⋊Dic3—21no—
101Dic3⋊Dic3—21no—
102C22×C33C2×D411yescharacteristic
103C33×C4C2×Q811yescharacteristic
104C33×C4C2×Q811yescharacteristic
105C3×C3⋊Dic3—41no—
106C3×C3⋊Dic3—41no—
107C32×Dic3—21no—
108C32×Dic3—21no—
109C32×Dic3—41no—
110C32×Dic3—41no—
111C3×C4⋊Q8—91no—
112C3×#125—91no—
113#890—31no—
114#888—31no—
115#870—31no—
116#869—31no—
117C3×#107—91no—
118C3×#107—91no—
119C3×#106—31no—
120C3×#106—31no—
121C3×#106—61no—
122C3×#106—91no—
123C3×#97—31no—
124C3×#97—31no—
125C3×#97—61no—
126#818—31no—
127#818—31no—
128#818—31no—
129#818—61no—
130#817—31no—
131#817C3×D311yescharacteristic
132#815C3×D311yescharacteristic
133#808—31no—
134#807—31no—
135C2×C32×C4—21no—
136C2×C32×C4—21no—
137C2×C32×C4—21no—
138C2×C32×C4—31no—
139C2×C32×C4—31no—
140C2×C32×C4—41no—
141C2×C32×C4—61no—
142C2×C32×C4—61no—
143C2×C32×C4C22×D311yescharacteristic
144C2×C32×C4C22×D311yescharacteristic
145C2×C32×C4C23×C311yescharacteristic
146C2×C3⋊Dic3—21no—
147C2×C3⋊Dic3—21no—
148C2×C3×Dic3—21no—
149C2×C3×Dic3—21no—
150C2×C3×Dic3—21no—
151C2×C3×Dic3—21no—
152C2×C3×Dic3—21no—
153C2×C3×Dic3—21no—
154C2×C3×Dic3—41no—
155C2×C3×Dic3—41no—
156C2×C3×Dic3—61no—
157C2×C3×Dic3—61no—
158C2×C3×Dic3—61no—
159C2×C3×Dic3—61no—
160C2×C3×Dic3—121no—
161C2×C3×Dic3—121no—
162C2×C3×Dic3D1211yescharacteristic
163C2×C3×Dic3D1211yescharacteristic
164C2×C3×Dic3C3×D411yescharacteristic
165C2×C3×Dic3C3×D411yescharacteristic
166C3×Dic6—122no—
167C3×Dic6—122no—
168#627—42no—
169C32×C8—22no—
170C32×C8—22no—
171C32×C8—22no—
172C32×C8—32no—
173C32×C8—42no—
174C32×C8Dic612yescomplemented
175C32×C8Dic612yescomplemented
176C32×C8C3×Q812yescomplemented
177C3×C3⋊C8—22no—
178C3×C3⋊C8Dic612yescomplemented
179C3×C3⋊C8C3×Q812yescomplemented
180#501—91noSylow
181C2×C33C4⋊Q811yescharacteristic
182C2×C33AGL(1,ℤ/8)11yescharacteristic
183C2×C33#13711yescharacteristic
184C2×C3×Q8—181no—
185C2×Dic6—61no—
186C2×Dic6—61no—
187C2×C3×C8—21no—
188C2×C3×C8—21no—
189C2×C3×C8—21no—
190C2×C3×C8—31no—
191C2×C3×C8—31no—
192C2×C3×C8—41no—
193C2×C3×C8—61no—
194C2×C3×C8D3211yescharacteristic
195C2×C3×C8C2×C3×D311yescharacteristic
196C2×C3×C8C2×C3×D311yescharacteristic
197C3×C4⋊C4—31no—
198C3×C4⋊C4—31no—
199C3×C4⋊C4—31no—
200C3×C4⋊C4—31no—
201C3×C4⋊C4—61no—
202C3×C4⋊C4—61no—
203C3×C4⋊C4—91no—
204C3×C4⋊C4—91no—
205C3×C4⋊C4—181no—
206C3×C4⋊C4—181no—
207C3×C4⋊C4—181no—
208C3×C42—31no—
209C3×C42—31no—
210C3×C42—61no—
211C4⋊Dic3—31no—
212C4⋊Dic3—31no—
213C4⋊Dic3—31no—
214C4⋊Dic3—31no—
215C4⋊Dic3—61no—
216C4⋊Dic3—61no—
217C4⋊Dic3—61no—
218C4⋊Dic3—61no—
219C4⋊Dic3C2×C3×D311yescharacteristic
220C4⋊Dic3C2×C3×D311yescharacteristic
221Dic3⋊C4—61no—
222Dic3⋊C4—61no—
223Dic3⋊C4—61no—
224Dic3⋊C4—61no—
225C4×Dic3C2×C3×D311yescharacteristic
226C2×C3⋊C8C2×C3×D311yescharacteristic
227C22×C32—21no—
228C22×C32—21no—
229C22×C32—21no—
230C22×C32—41no—
231C22×C32C2×D1211yescharacteristic
232C22×C32D3×D411yescharacteristic
233C22×C32C2×C3×D411yescharacteristic
234C32×C4—21no—
235C32×C4—21no—
236C32×C4—21no—
237C32×C4—21no—
238C32×C4—21no—
239C32×C4—21no—
240C32×C4—41no—
241C32×C4—41no—
242C32×C4—61no—
243C32×C4—61no—
244C32×C4—121no—
245C32×C4—121no—
246C32×C4C2×Dic611yescharacteristic
247C32×C4C2×Dic611yescharacteristic
248C32×C4C2×Dic611yescharacteristic
249C32×C4D3×Q811yescharacteristic
250C32×C4C2×C3×Q811yescharacteristic
251C32×C4C2×C3×Q811yescharacteristic
252C3⋊Dic3—41no—
253C3⋊Dic3—41no—
254C3×Dic3—21no—
255C3×Dic3—21no—
256C3×Dic3—21no—
257C3×Dic3—21no—
258C3×Dic3—41no—
259C3×Dic3—41no—
260C3×Dic3—41no—
261C3×Dic3—41no—
262C3×Dic3—41no—
263C3×Dic3—41no—
264C3×Dic3—81no—
265C3×Dic3—81no—
266C3×Dic3—121no—
267C3×Dic3—121no—
268C3×Dic3—121no—
269C3×Dic3—121no—
270C3×Dic3—241no—
271C3×Dic3—241no—
272C4⋊Q8—91no—
273#125—91no—
274#107—91no—
275#107—91no—
276#106—31no—
277#106—91no—
278#97—31no—
279C33#50111yescharacteristic, complemented, Sylow
280C3×Q8—362no—
281C2×C3×C4—21no—
282C2×C3×C4—21no—
283C2×C3×C4—21no—
284C2×C3×C4—31no—
285C2×C3×C4—31no—
286C2×C3×C4—31no—
287C2×C3×C4—31no—
288C2×C3×C4—41no—
289C2×C3×C4—61no—
290C2×C3×C4—61no—
291C2×C3×C4—61no—
292C2×C3×C4—61no—
293C2×C3×C4—61no—
294C2×C3×C4—61no—
295C2×C3×C4—121no—
296C2×C3×C4—121no—
297C2×C3×C4—181no—
298C2×C3×C4—181no—
299C2×C3×C4C2×D3211yescharacteristic
300C2×C3×C4C22×C3×D311yescharacteristic
301C2×C3×C4C22×C3×D311yescharacteristic
302C2×Dic3—21no—
303C2×Dic3—21no—
304C2×Dic3—61no—
305C2×Dic3—61no—
306C2×Dic3—61no—
307C2×Dic3—61no—
308C2×Dic3—121no—
309C2×Dic3—121no—
310C2×Dic3C3×D1211yescharacteristic
311C2×Dic3C3×D1211yescharacteristic
312Dic6—122no—
313Dic6—122no—
314C3×C8—22no—
315C3×C8—22no—
316C3×C8—22no—
317C3×C8—32no—
318C3×C8—32no—
319C3×C8—42no—
320C3×C8—62no—
321C3×C8#62712yescomplemented
322C3×C8C3×Dic612yescomplemented
323C3×C8C3×Dic612yescomplemented
324C3⋊C8C3×Dic612yescomplemented
325C2×C32—21no—
326C2×C32—21no—
327C2×C32—21no—
328C2×C32—21no—
329C2×C32—21no—
330C2×C32—21no—
331C2×C32—21no—
332C2×C32—21no—
333C2×C32—21no—
334C2×C32—41no—
335C2×C32—41no—
336C2×C32—41no—
337C2×C32#86911yescharacteristic
338C2×C32#88811yescharacteristic
339C2×C32#90811yescharacteristic
340C2×C32#90911yescharacteristic
341C2×C32#91411yescharacteristic
342C2×C32#91511yescharacteristic
343C2×C32C3×C4⋊Q811yescharacteristic
344C2×C32C3×AGL(1,ℤ/8)11yescharacteristic
345C2×C32C3×#13711yescharacteristic
346C2×Q8—181no—
347C2×C8—31no—
348C2×C8C3×D3211yescharacteristic
349C4⋊C4—31no—
350C4⋊C4—31no—
351C4⋊C4—91no—
352C4⋊C4—91no—
353C4⋊C4—181no—
354C4⋊C4—181no—
355C4⋊C4—181no—
356C42—31no—
357C22×C3—21no—
358C22×C3—21no—
359C22×C3—21no—
360C22×C3—41no—
361C22×C3D3×D1211yescharacteristic
362C22×C3C2×C3×D1211yescharacteristic
363C22×C3C3×D3×D411yescharacteristic
364C3×C4—21no—
365C3×C4—21no—
366C3×C4—21no—
367C3×C4—21no—
368C3×C4—21no—
369C3×C4—21no—
370C3×C4—41no—
371C3×C4—41no—
372C3×C4—61no—
373C3×C4—61no—
374C3×C4—61no—
375C3×C4—61no—
376C3×C4—121no—
377C3×C4—121no—
378C3×C4—121no—
379C3×C4—121no—
380C3×C4—121no—
381C3×C4—121no—
382C3×C4—241no—
383C3×C4—241no—
384C3×C4—361no—
385C3×C4—361no—
386C3×C4D3×Dic611yescharacteristic
387C3×C4C2×#62711yescharacteristic
388C3×C4C2×C3×Dic611yescharacteristic
389C3×C4C2×C3×Dic611yescharacteristic
390C3×C4C2×C3×Dic611yescharacteristic
391C3×C4C3×D3×Q811yescharacteristic
392Dic3—21no—
393Dic3—21no—
394Dic3—41no—
395Dic3—41no—
396Dic3—121no—
397Dic3—121no—
398Dic3—121no—
399Dic3—121no—
400Dic3—241no—
401Dic3—241no—
402C32—21no—
403C32—21no—
404C32—21no—
405C32—41no—
406C32#470211yescharacteristic, complemented
407C32#485611yescharacteristic, complemented
408C32C3×#50111yescharacteristic, complemented
409Q8—362no—
410C2×C4—31no—
411C2×C4—31no—
412C2×C4—61no—
413C2×C4—61no—
414C2×C4—181no—
415C2×C4—181no—
416C2×C4C2×C3×D3211yescharacteristic
417C8—32no—
418C8C3×#62712yescomplemented
419C2×C3—21no—
420C2×C3—21no—
421C2×C3—21no—
422C2×C3—21no—
423C2×C3—21no—
424C2×C3—21no—
425C2×C3—21no—
426C2×C3—21no—
427C2×C3—21no—
428C2×C3—41no—
429C2×C3—41no—
430C2×C3—41no—
431C2×C3#6379411yescharacteristic
432C2×C3#6380011yescharacteristic
433C2×C3#6391811yescharacteristic
434C2×C3C3×#86911yescharacteristic
435C2×C3C3×#88811yescharacteristic
436C2×C3C3×#90811yescharacteristic
437C2×C3C3×#90911yescharacteristic
438C2×C3C3×#91411yescharacteristic
439C2×C3C3×#91511yescharacteristic
440C22C3×D3×D1211yescharacteristic
441C4—61no—
442C4—61no—
443C4—121no—
444C4—121no—
445C4—361no—
446C4—361no—
447C4C3×D3×Dic611yescharacteristic
448C4C2×C3×#62711yescharacteristic
449C3—21no—
450C3—21no—
451C3—21no—
452C3—41no—
453C3#1059089211yescharacteristic, direct product factor
454C3C3×#470211yescharacteristic, complemented
455C3C3×#485611yescharacteristic, complemented
456C2C3×#6379411yescharacteristic
457C2C3×#6380011yescharacteristic
458C2C3×#6391811yescharacteristic
subgroupG/H
centerC22×C3D3×D12
commutator, cosocleC2×C32×C4C23×C3
FrattiniC2×C4C2×C3×D32
FittingC2×C33×C8C22
socle, prime radicalC22×C33C2×D4
hypercenterC2×C3×C8D32
hypocenterC32C3×#501
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C2×C3×C4 ◁ C2×C3×C8

Complements

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

NH ≅ G/Ntype
10. #10590892C3direct (N × H)
54. C33×C8Q8semidirect
55. C32×C3⋊C8Q8semidirect
174. C32×C8Dic6semidirect
175. C32×C8Dic6semidirect
176. C32×C8C3×Q8semidirect
178. C3×C3⋊C8Dic6semidirect
179. C3×C3⋊C8C3×Q8semidirect
279. C33#501semidirect
321. C3×C8#627semidirect
322. C3×C8C3×Dic6semidirect
323. C3×C8C3×Dic6semidirect
324. C3⋊C8C3×Dic6semidirect
406. C32#4702semidirect
407. C32#4856semidirect
408. C32C3×#501semidirect
418. C8C3×#627semidirect
453. C3#10590892direct (N × H)
454. C3C3×#4702semidirect
455. C3C3×#4856semidirect

Maximal subgroups

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

subgroupindex
C3×#639182
C3×#638692
C3×#636452
C32×#8172
C32×#8152
C3×#635752
C3×#635732
C3×#48563
C3×#47023
#105908923