Finite Group Databasebeta

← C3×#10592938 #13163274

Subgroups — C3×#10592938 #13163274

Order 1728.

1568 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C33×#41C211yesmaximal, characteristic
2C2×C3×#3756C211yesmaximal, characteristic, complemented
3C2×C3×#3754C211yesmaximal, characteristic, complemented
4C3×#64133C211yesmaximal, characteristic, complemented
5C3×#63662C211yesmaximal, characteristic, complemented
6C3×#63659C211yesmaximal, characteristic, complemented
7C3×#63657C211yesmaximal, characteristic, complemented
8#10592938C311yesmaximal, characteristic, direct product factor
9C3×#5239—34nomaximal
10C33×#41—22no—
11C33×#41—22no—
12C2×C33×Q8C2211yescharacteristic
13C2×C33×D4—21no—
14C2×C33×D4C2211yescharacteristic
15C22×C33×C4—21no—
16C22×C33×C4C2211yescharacteristic
17C2×C3×#634C2211yescharacteristic
18C3×#3757—21no—
19C3×#3756—22no—
20C3×#3754—22no—
21C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
22C3×#3750—21no—
23C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic
24C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic
25C2×C32×#41—24no—
26C2×C32×#41D314yes—
27C2×C32×#41C2×C311yescharacteristic
28C2×#3756C2×C311yescharacteristic, complemented
29C2×#3754C2×C311yescharacteristic, complemented
30#64133C2×C311yescharacteristic, complemented
31C2×C3×#216—34no—
32C2×C3×#214—34no—
33C3×#924—34no—
34#63662C2×C311yescharacteristic, complemented
35#63659C2×C311yescharacteristic, complemented
36#63657C2×C311yescharacteristic, complemented
37C3×#835—34no—
38C3×#832—34no—
39C3×#830—34no—
40C23×C33—21no—
41C23×C33D411yescharacteristic
42C33×Q8—21no—
43C33×Q8D412yes—
44C33×D4—24no—
45C33×D4—21no—
46C33×D4D412yes—
47C2×C33×C4—24no—
48C2×C33×C4—21no—
49C2×C33×C4—21no—
50C2×C33×C4—21no—
51C2×C33×C4D411yescharacteristic
52C2×C33×C4C2311yescharacteristic
53C2×C3×C3⋊Dic3—21no—
54C2×C3×C3⋊Dic3—21no—
55C3×#634—21no—
56C3×#634—21no—
57C3×C3⋊(C3⋊C8)—21no—
58C3×C3⋊(C3⋊C8)—21no—
59C3×#452—91no—
60#5239—34no—
61C32×#41—216no—
62C32×#41—216no—
63C32×#41—28no—
64C32×#41—22no—
65C32×#41—28no—
66C32×#41—22no—
67C2×C32×Q8—24no—
68C2×C32×Q8C2×D314yes—
69C2×C32×Q8C22×C311yescharacteristic
70C2×C32×D4—28no—
71C2×C32×D4—24no—
72C2×C32×D4—24no—
73C2×C32×D4—21no—
74C2×C32×D4C2×D314yes—
75C2×C32×D4C22×C311yescharacteristic
76C22×C32×C4—28no—
77C22×C32×C4—24no—
78C22×C32×C4—24no—
79C22×C32×C4—21no—
80C22×C32×C4C2×D314yes—
81C22×C32×C4C22×C311yescharacteristic
82C2×#634C22×C311yescharacteristic
83C2×C3×Dic6—34no—
84#3757—21no—
85#3756—22no—
86#3754—22no—
87C4⋊(C3⋊Dic3)C22×C311yescharacteristic
88#3750—21no—
89C2×C3⋊(C3⋊C8)C22×C311yescharacteristic
90C2×C3⋊(C3⋊C8)C22×C311yescharacteristic
91C3×#217—64no—
92C3×#216—68no—
93C3×#214—68no—
94C3×C4⋊Dic3—34no—
95C3×Dic3⋊C4—64no—
96C2×C3×C3⋊C8—34no—
97C2×C3×C3⋊C8—34no—
98C22×C33—21no—
99C22×C33—22no—
100C22×C33—21no—
101C22×C33—21no—
102C22×C33—41no—
103C22×C33—41no—
104C22×C33C2×D411yescharacteristic
105C33×C4—21no—
106C33×C4—22no—
107C33×C4C2×D411yescharacteristic
108C33×C4C2×D411yescharacteristic
109C3×C3⋊Dic3—41no—
110C3×C3⋊Dic3—41no—
111C2×C3×#41—24no—
112C2×C3×#41C3×D314yes—
113C2×C3×#41C3⋊D311yescharacteristic
114C2×C3×Q16—91no—
115C2×C3×SD16—91no—
116C3×C22⋊Q8—91no—
117C2×#216—34no—
118C2×#214—34no—
119#924—34no—
120C3×#103—91no—
121C3×#102—91no—
122C3×C22⋊C8—91no—
123#835—34no—
124#832—34no—
125#830—34no—
126C23×C32—28no—
127C23×C32—24no—
128C23×C32—21no—
129C23×C32—24no—
130C23×C32#6714yes—
131C23×C32C3×D411yescharacteristic
132C32×Q8—28no—
133C32×Q8—24no—
134C32×Q8—21no—
135C32×Q8—28no—
136C32×Q8#6718yes—
137C32×Q8C3×D412yes—
138C32×D4—232no—
139C32×D4—216no—
140C32×D4—24no—
141C32×D4—28no—
142C32×D4—24no—
143C32×D4—21no—
144C32×D4—28no—
145C32×D4#6718yes—
146C32×D4C3×D412yes—
147C2×C32×C4—28no—
148C2×C32×C4—232no—
149C2×C32×C4—216no—
150C2×C32×C4—24no—
151C2×C32×C4—28no—
152C2×C32×C4—28no—
153C2×C32×C4—24no—
154C2×C32×C4—21no—
155C2×C32×C4—24no—
156C2×C32×C4—24no—
157C2×C32×C4—21no—
158C2×C32×C4—21no—
159C2×C32×C4—24no—
160C2×C32×C4—24no—
161C2×C32×C4#6714yes—
162C2×C32×C4C3×D411yescharacteristic
163C2×C32×C4C22×D314yes—
164C2×C32×C4C23×C311yescharacteristic
165C2×C3⋊Dic3—21no—
166C2×C3⋊Dic3—21no—
167#634—21no—
168#634—21no—
169C2×C3×Dic3—64no—
170C2×C3×Dic3—64no—
171C3×Dic6—64no—
172C3×Dic6—64no—
173C3⋊(C3⋊C8)—21no—
174C3⋊(C3⋊C8)—21no—
175C3×C3⋊C8—64no—
176C3×C3⋊C8—64no—
177#452—91noSylow
178C2×C33—41no—
179C2×C33—42no—
180C2×C33#12011yescharacteristic
181C2×C33#13511yescharacteristic
182C2×C33#13711yescharacteristic
183C3×#41—216no—
184C3×#41—216no—
185C3×#41—28no—
186C3×#41—22no—
187C3×#41—28no—
188C3×#41—22no—
189C2×C3×Q8—24no—
190C2×C3×Q8—91no—
191C2×C3×Q8C2×C3×D314yes—
192C2×C3×Q8C2×C3⋊D311yescharacteristic
193C2×C3×D4—28no—
194C2×C3×D4—24no—
195C2×C3×D4—21no—
196C2×C3×D4—24no—
197C2×C3×D4C2×C3×D314yes—
198C2×C3×D4C2×C3⋊D311yescharacteristic
199C22×C3×C4—28no—
200C22×C3×C4—24no—
201C22×C3×C4—21no—
202C22×C3×C4—24no—
203C22×C3×C4C2×C3×D314yes—
204C22×C3×C4C2×C3⋊D311yescharacteristic
205C2×Dic6—34no—
206C3×Q16—182no—
207C3×SD16—182no—
208C2×C3×C8—91no—
209C2×C3×C8—91no—
210C3×C4⋊C4—91no—
211C3×C4⋊C4—181no—
212C3×C22⋊C4—181no—
213#217—64no—
214#216—68no—
215#214—68no—
216C4⋊Dic3—34no—
217Dic3⋊C4—64no—
218C2×C3⋊C8—34no—
219C2×C3⋊C8—34no—
220C22×C32—28no—
221C22×C32—216no—
222C22×C32—24no—
223C22×C32—28no—
224C22×C32—21no—
225C22×C32—22no—
226C22×C32—21no—
227C22×C32—21no—
228C22×C32—24no—
229C22×C32—24no—
230C22×C32—24no—
231C22×C32—44no—
232C22×C32—44no—
233C22×C32—48no—
234C22×C32—48no—
235C22×C32—44no—
236C22×C32—44no—
237C22×C32—41no—
238C22×C32—41no—
239C22×C32C2×#6714yes—
240C22×C32C2×C3×D411yescharacteristic
241C32×C4—28no—
242C32×C4—216no—
243C32×C4—24no—
244C32×C4—28no—
245C32×C4—21no—
246C32×C4—22no—
247C32×C4—24no—
248C32×C4—24no—
249C32×C4C2×#6714yes—
250C32×C4C2×#6714yes—
251C32×C4C2×C3×D411yescharacteristic
252C32×C4C2×C3×D411yescharacteristic
253C3⋊Dic3—41no—
254C3⋊Dic3—41no—
255C3×Dic3—124no—
256C3×Dic3—124no—
257C2×#41C3×C3⋊D311yescharacteristic
258C2×Q16—91no—
259C2×SD16—91no—
260C22⋊Q8—91no—
261#103—91no—
262#102—91no—
263C22⋊C8—91no—
264C33#45211yescharacteristic, complemented, Sylow
265C23×C3—28no—
266C23×C3—24no—
267C23×C3—21no—
268C23×C3—24no—
269C23×C3C3×#6714yes—
270C23×C3#63811yescharacteristic
271C3×Q8—28no—
272C3×Q8—24no—
273C3×Q8—21no—
274C3×Q8—28no—
275C3×Q8—181no—
276C3×Q8—181no—
277C3×Q8C3×#6718yes—
278C3×Q8#63812yes—
279C3×D4—232no—
280C3×D4—216no—
281C3×D4—24no—
282C3×D4—28no—
283C3×D4—24no—
284C3×D4—21no—
285C3×D4—28no—
286C3×D4C3×#6718yes—
287C3×D4#63812yes—
288C2×C3×C4—28no—
289C2×C3×C4—232no—
290C2×C3×C4—216no—
291C2×C3×C4—24no—
292C2×C3×C4—28no—
293C2×C3×C4—28no—
294C2×C3×C4—24no—
295C2×C3×C4—21no—
296C2×C3×C4—24no—
297C2×C3×C4—24no—
298C2×C3×C4—21no—
299C2×C3×C4—21no—
300C2×C3×C4—24no—
301C2×C3×C4—24no—
302C2×C3×C4—181no—
303C2×C3×C4—181no—
304C2×C3×C4C3×#6714yes—
305C2×C3×C4#63811yescharacteristic
306C2×C3×C4C22×C3×D314yes—
307C2×C3×C4C22×C3⋊D311yescharacteristic
308C2×Dic3—64no—
309C2×Dic3—64no—
310Dic6—64no—
311Dic6—64no—
312C3×C8—181no—
313C3×C8—181no—
314C3⋊C8—64no—
315C3⋊C8—64no—
316C2×C32—24no—
317C2×C32—24no—
318C2×C32—24no—
319C2×C32—48no—
320C2×C32—416no—
321C2×C32—44no—
322C2×C32—48no—
323C2×C32—41no—
324C2×C32—42no—
325C2×C32#95014yes—
326C2×C32#95114yes—
327C2×C32#95314yes—
328C2×C32C3×#12011yescharacteristic
329C2×C32C3×#13511yescharacteristic
330C2×C32C3×#13711yescharacteristic
331#41—22no—
332#41—22no—
333C2×Q8—91no—
334C2×Q8C2×C3×C3⋊D311yescharacteristic
335C2×D4—21no—
336C2×D4C2×C3×C3⋊D311yescharacteristic
337C22×C4—21no—
338C22×C4C2×C3×C3⋊D311yescharacteristic
339Q16—182no—
340SD16—182no—
341C2×C8—91no—
342C2×C8—91no—
343C4⋊C4—91no—
344C4⋊C4—181no—
345C22⋊C4—181no—
346C22×C3—28no—
347C22×C3—216no—
348C22×C3—24no—
349C22×C3—24no—
350C22×C3—24no—
351C22×C3—28no—
352C22×C3—21no—
353C22×C3—21no—
354C22×C3—21no—
355C22×C3—22no—
356C22×C3—24no—
357C22×C3—44no—
358C22×C3—44no—
359C22×C3—48no—
360C22×C3—48no—
361C22×C3—44no—
362C22×C3—44no—
363C22×C3—41no—
364C22×C3—41no—
365C22×C3C2×C3×#6714yes—
366C22×C3C2×#63811yescharacteristic
367C3×C4—28no—
368C3×C4—216no—
369C3×C4—24no—
370C3×C4—28no—
371C3×C4—21no—
372C3×C4—22no—
373C3×C4—24no—
374C3×C4—24no—
375C3×C4—361no—
376C3×C4—361no—
377C3×C4C2×C3×#6714yes—
378C3×C4C2×C3×#6714yes—
379C3×C4C2×#63811yescharacteristic
380C3×C4C2×#63811yescharacteristic
381Dic3—124no—
382Dic3—124no—
383C32—24no—
384C32#523914yescomplemented
385C32C3×#45211yescharacteristic, complemented
386C23—21no—
387C23C3×#63811yescharacteristic
388Q8—21no—
389Q8—181no—
390Q8—181no—
391Q8C3×#63812yes—
392D4—24no—
393D4—21no—
394D4C3×#63812yes—
395C2×C4—24no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—181no—
400C2×C4—181no—
401C2×C4C3×#63811yescharacteristic
402C2×C4C22×C3×C3⋊D311yescharacteristic
403C8—181no—
404C8—181no—
405C2×C3—24no—
406C2×C3—24no—
407C2×C3—24no—
408C2×C3—48no—
409C2×C3—416no—
410C2×C3—44no—
411C2×C3—48no—
412C2×C3—41no—
413C2×C3—42no—
414C2×C3C3×#95014yes—
415C2×C3C3×#95114yes—
416C2×C3C3×#95314yes—
417C2×C3#6415911yescharacteristic
418C2×C3#6416011yescharacteristic
419C2×C3#6416211yescharacteristic
420C22—21no—
421C22—21no—
422C22—21no—
423C22—22no—
424C22—41no—
425C22—41no—
426C22C2×C3×#63811yescharacteristic
427C4—21no—
428C4—22no—
429C4—361no—
430C4—361no—
431C4C2×C3×#63811yescharacteristic
432C4C2×C3×#63811yescharacteristic
433C3—24no—
434C3C3×#523914yescomplemented
435C3#1059293811yescharacteristic, direct product factor
436C2—41no—
437C2—42no—
438C2C3×#6415911yescharacteristic
439C2C3×#6416011yescharacteristic
440C2C3×#6416211yescharacteristic
subgroupG/H
centerC22×C3C2×#638
commutator, cosocleC2×C32×C4C23×C3
FrattiniC2×C4C22×C3×C3⋊D3
Fitting, prime radicalC2×C33×#41C2
socleC22×C33C2×D4
hypercenterC2×C3×#41C3⋊D3
hypocenterC32C3×#452
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C2×C3×#41

Complements

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

NH ≅ G/Ntype
2. C2×C3×#3756C2semidirect
3. C2×C3×#3754C2semidirect
4. C3×#64133C2semidirect
5. C3×#63662C2semidirect
6. C3×#63659C2semidirect
7. C3×#63657C2semidirect
8. #10592938C3direct (N × H)
28. C2×#3756C2×C3semidirect
29. C2×#3754C2×C3semidirect
30. #64133C2×C3semidirect
34. #63662C2×C3semidirect
35. #63659C2×C3semidirect
36. #63657C2×C3semidirect
264. C33#452semidirect
384. C32#5239semidirect
385. C32C3×#452semidirect
434. C3C3×#5239semidirect
435. C3#10592938direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C33×#412
C2×C3×#37562
C2×C3×#37542
C3×#641332
C3×#636622
C3×#636592
C3×#636572
#105929383
C3×#52393