Finite Group Databasebeta

← C3×#10591486 #13158497

Subgroups — C3×#10591486 #13158497

Order 1728.

860 conjugacy classes of subgroups; only the 136 normal subgroups are shown.

normal subgroups only

This group has 860 conjugacy classes of subgroups — too many to draw. Only its 136 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D4×C3⋊Dic3C211yesmaximal, characteristic, complemented
2C2×C32×#213C212yesmaximal, complemented
3C3×#63914C211yesmaximal, characteristic, complemented
4C3×#63572C211yesmaximal, characteristic, complemented
5C3×#63563C212yesmaximal, complemented
6C3×#5150—32nomaximal
7#10591486C311yesmaximal, characteristic, direct product factor
8C2×C33×D4C2211yescharacteristic
9C22×C3×C3⋊Dic3—21no—
10C2×C32×D12C2212yes—
11C2×C3×#625—21no—
12C2×C3×#625—21no—
13C3×#3757—21no—
14C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
15C3×C4×C3⋊Dic3C2211yescharacteristic
16C32×#213—24no—
17C2×C32×C3⋊C8C2212yes—
18C2×C32×D8—32no—
19D4×C3⋊Dic3C2×C311yescharacteristic, complemented
20C3×#940—32no—
21C3×D4×Dic3—32no—
22C3×D4×Dic3—61no—
23C2×C3×#213—22no—
24C2×C3×#213D312yescomplemented
25C2×C3×#213C2×C312yescomplemented
26#63914C2×C311yescharacteristic, complemented
27C3×#832—32no—
28C3×#821—32no—
29C3×Dic3⋊C8—32no—
30#63572C2×C311yescharacteristic, complemented
31#63563C2×C312yescomplemented
32C23×C33—21no—
33C22×C32×D3—22no—
34C33×D4—21no—
35C33×D4D412yescomplemented
36C2×C33×C4C2311yescharacteristic
37C2×C3×C3⋊Dic3—21no—
38C2×C3×C3⋊Dic3—42no—
39C2×C3×C3⋊Dic3D411yescharacteristic
40C2×C3×C3⋊Dic3D411yescharacteristic
41C32×D12—22no—
42C32×D12—22no—
43C3×#625—42no—
44C3×#625—42no—
45C32×C3⋊C8—22no—
46C3×#459—91no—
47#5150—32no—
48C2×C32×D4—21no—
49C2×C32×D4—22no—
50C2×C32×D4—32no—
51C2×C32×D4—41no—
52C2×C32×D4C2×D312yes—
53C2×C32×D4C22×C311yescharacteristic
54C22×C3⋊Dic3—21no—
55C2×C3×#67—62no—
56C2×C3×#67—62no—
57C22×C3×Dic3—62no—
58C22×C3×Dic3—62no—
59C2×C3×D12—22no—
60C2×C3×D12C2×D312yes—
61C2×C3×D12C22×C312yes—
62C2×#625—21no—
63C2×#625—21no—
64C32×D8—64no—
65C2×C32×C8—32no—
66#3757—21no—
67C4⋊(C3⋊Dic3)C22×C311yescharacteristic
68C4×C3⋊Dic3C22×C311yescharacteristic
69C3×#217—62no—
70C3×#217—62no—
71C3×#213—28no—
72C3×#213—24no—
73C3×#213—24no—
74C3×C4⋊Dic3—32no—
75C3×C4⋊Dic3—61no—
76C3×C4×Dic3—32no—
77C3×C4×Dic3—61no—
78C2×C3×C3⋊C8—22no—
79C2×C3×C3⋊C8C2×D312yes—
80C2×C3×C3⋊C8C22×C312yes—
81C22×C33—22no—
82C22×C33—41no—
83C22×C33—41no—
84C22×C33C2×D411yescharacteristic
85C2×C32×D3—42no—
86C2×C32×D3—42no—
87C2×C32×D3—42no—
88C33×C4C2×D411yescharacteristic
89C33×C4#4111yescharacteristic
90C3×C3⋊Dic3—21no—
91C3×C3⋊Dic3—41no—
92C3×C3⋊Dic3D812yescomplemented
93C2×C3×D8—32no—
94C2×C3×D8—32no—
95C2×C3×D8—62no—
96C3×#127—91no—
97C3×C4×D4—91no—
98#940—32no—
99D4×Dic3—32no—
100D4×Dic3—61no—
101C2×#213C3×D312yescomplemented
102C3×C4⋊C8—91no—
103C3×#102—92no—
104#832—32no—
105#821—32no—
106Dic3⋊C8—32no—
107C23×C32—21no—
108C23×C32—22no—
109C23×C32—22no—
110C23×C32—42no—
111C23×C32—42no—
112C23×C32—62no—
113C22×C3×D3—22no—
114C22×C3×D3—22no—
115C22×C3×D3—42no—
116C32×D4—21no—
117C32×D4—22no—
118C32×D4—22no—
119C32×D4—22no—
120C32×D4—24no—
121C32×D4—42no—
122C32×D4—42no—
123C32×D4—42no—
124C32×D4—62no—
125C32×D4—62no—
126C32×D4#6714yescomplemented
127C32×D4C3×D412yescomplemented
128C2×C32×C4—21no—
129C2×C32×C4—22no—
130C2×C32×C4—41no—
131C2×C32×C4C22×D312yes—
132C2×C32×C4C23×C311yescharacteristic
133C2×C3⋊Dic3—21no—
134C2×C3⋊Dic3—42no—
135C2×C3⋊Dic3C3×D411yescharacteristic
136C2×C3⋊Dic3C3×D411yescharacteristic
137C3×#67—124no—
138C3×#67—124no—
139C2×C3×Dic3—32no—
140C2×C3×Dic3—32no—
141C2×C3×Dic3—61no—
142C2×C3×Dic3—61no—
143C2×C3×Dic3—62no—
144C2×C3×Dic3—62no—
145C2×C3×Dic3—124no—
146C2×C3×Dic3—124no—
147C3×D12—24no—
148C3×D12—22no—
149C3×D12—22no—
150C3×D12—22no—
151C3×D12—22no—
152C3×D12—42no—
153#625—42no—
154#625—42no—
155C32×C8—62no—
156C3×C3⋊C8—24no—
157C3×C3⋊C8—22no—
158C3×C3⋊C8—22no—
159#459—91noSylow
160C2×C33—42no—
161C2×C33#12111yescharacteristic
162C2×C33C2×D811yescharacteristic
163C2×C33AGL(1,ℤ/8)11yescharacteristic
164C32×D3—82no—
165C2×C3×D4—21no—
166C2×C3×D4—22no—
167C2×C3×D4—32no—
168C2×C3×D4—32no—
169C2×C3×D4—41no—
170C2×C3×D4—62no—
171C2×C3×D4—181no—
172C2×C3×D4—181no—
173C2×C3×D4D3211yescharacteristic
174C2×C3×D4C2×C3×D312yes—
175C22×C3×C4—181no—
176C2×#67—62no—
177C2×#67—62no—
178C22×Dic3—62no—
179C22×Dic3—62no—
180C2×D12C2×C3×D312yes—
181C3×D8—68no—
182C3×D8—64no—
183C3×D8—64no—
184C2×C3×C8—32no—
185C2×C3×C8—32no—
186C2×C3×C8—62no—
187C3×C4⋊C4—91no—
188C3×C22⋊C4—181no—
189C3×C42—91no—
190#217—62no—
191#217—62no—
192#213—24no—
193C4⋊Dic3—32no—
194C4⋊Dic3—61no—
195C4×Dic3—32no—
196C4×Dic3—61no—
197C2×C3⋊C8C2×C3×D312yes—
198C22×C32—22no—
199C22×C32—24no—
200C22×C32—24no—
201C22×C32—21no—
202C22×C32—22no—
203C22×C32—41no—
204C22×C32—44no—
205C22×C32—44no—
206C22×C32—41no—
207C22×C32—41no—
208C22×C32—42no—
209C22×C32—42no—
210C22×C32—42no—
211C22×C32—42no—
212C22×C32—82no—
213C22×C32—82no—
214C22×C32—82no—
215C22×C32—82no—
216C22×C32—122no—
217C22×C32—122no—
218C22×C32—122no—
219C22×C32D3×D412yes—
220C22×C32C2×C3×D411yescharacteristic
221C2×C3×D3—44no—
222C2×C3×D3—42no—
223C2×C3×D3—42no—
224C2×C3×D3—42no—
225C2×C3×D3—42no—
226C2×C3×D3—42no—
227C2×C3×D3—42no—
228C2×C3×D3—82no—
229C2×C3×D3—82no—
230C32×C4—21no—
231C32×C4—21no—
232C32×C4—22no—
233C32×C4—22no—
234C32×C4—41no—
235C32×C4—41no—
236C32×C4#23712yes—
237C32×C4C2×#6712yes—
238C32×C4C2×C3×D411yescharacteristic
239C32×C4C3×#4111yescharacteristic
240C3⋊Dic3—21no—
241C3⋊Dic3—41no—
242C3⋊Dic3C3×D812yescomplemented
243C3×Dic3—34no—
244C3×Dic3—62no—
245C3×Dic3—62no—
246C3×Dic3—121no—
247C3×Dic3—122no—
248C3×Dic3—122no—
249C2×D8—32no—
250#127—91no—
251C4×D4—91no—
252C4⋊C8—91no—
253#102—92no—
254C33#45911yescharacteristic, complemented, Sylow
255C23×C3—22no—
256C23×C3—21no—
257C23×C3—22no—
258C23×C3—42no—
259C23×C3—42no—
260C23×C3—62no—
261C23×C3—62no—
262C23×C3—122no—
263C22×D3—22no—
264C3×D4—22no—
265C3×D4—21no—
266C3×D4—22no—
267C3×D4—22no—
268C3×D4—24no—
269C3×D4—42no—
270C3×D4—42no—
271C3×D4—42no—
272C3×D4—64no—
273C3×D4—62no—
274C3×D4—62no—
275C3×D4—62no—
276C3×D4—62no—
277C3×D4—122no—
278C3×D4—362no—
279C3×D4—362no—
280C3×D4#62512yescomplemented
281C3×D4C3×#6714yescomplemented
282C2×C3×C4—22no—
283C2×C3×C4—21no—
284C2×C3×C4—41no—
285C2×C3×C4—91no—
286C2×C3×C4—91no—
287C2×C3×C4—181no—
288C2×C3×C4—362no—
289C2×C3×C4C2×D3211yescharacteristic
290C2×C3×C4C22×C3×D312yes—
291#67—124no—
292#67—124no—
293C2×Dic3—32no—
294C2×Dic3—32no—
295C2×Dic3—61no—
296C2×Dic3—61no—
297C2×Dic3—62no—
298C2×Dic3—62no—
299C2×Dic3—124no—
300C2×Dic3—124no—
301D12—22no—
302D12—22no—
303C3×C8—64no—
304C3×C8—62no—
305C3×C8—62no—
306C3⋊C8—22no—
307C2×C32—22no—
308C2×C32—22no—
309C2×C32—22no—
310C2×C32—21no—
311C2×C32—21no—
312C2×C32—21no—
313C2×C32—41no—
314C2×C32—41no—
315C2×C32—41no—
316C2×C32—42no—
317C2×C32—44no—
318C2×C32—44no—
319C2×C32—84no—
320C2×C32—84no—
321C2×C32—242no—
322C2×C32D3×D812yes—
323C2×C32#91112yes—
324C2×C32#93912yes—
325C2×C32C3×#12111yescharacteristic
326C2×C32C2×C3×D811yescharacteristic
327C2×C32C3×AGL(1,ℤ/8)11yescharacteristic
328C3×D3—84no—
329C3×D3—82no—
330C3×D3—82no—
331C2×D4—32no—
332C2×D4—181no—
333C2×D4—181no—
334C2×D4C3×D3211yescharacteristic
335C22×C4—181no—
336D8—64no—
337C2×C8—32no—
338C4⋊C4—91no—
339C22⋊C4—181no—
340C42—91no—
341C22×C3—24no—
342C22×C3—24no—
343C22×C3—22no—
344C22×C3—21no—
345C22×C3—22no—
346C22×C3—44no—
347C22×C3—44no—
348C22×C3—42no—
349C22×C3—42no—
350C22×C3—42no—
351C22×C3—42no—
352C22×C3—41no—
353C22×C3—41no—
354C22×C3—41no—
355C22×C3—82no—
356C22×C3—82no—
357C22×C3—82no—
358C22×C3—82no—
359C22×C3—124no—
360C22×C3—122no—
361C22×C3—122no—
362C22×C3—122no—
363C22×C3—122no—
364C22×C3—122no—
365C22×C3—122no—
366C22×C3—242no—
367C22×C3—242no—
368C22×C3#381111yescharacteristic
369C22×C3C3×D3×D412yes—
370C2×D3—42no—
371C2×D3—42no—
372C2×D3—42no—
373C3×C4—21no—
374C3×C4—22no—
375C3×C4—22no—
376C3×C4—21no—
377C3×C4—41no—
378C3×C4—41no—
379C3×C4—92no—
380C3×C4—181no—
381C3×C4—361no—
382C3×C4#380511yescharacteristic
383C3×C4C2×#62511yescharacteristic
384C3×C4C3×#23712yes—
385C3×C4C2×C3×#6712yes—
386Dic3—34no—
387Dic3—62no—
388Dic3—62no—
389Dic3—121no—
390Dic3—122no—
391Dic3—122no—
392C32—22no—
393C32—21no—
394C32—41no—
395C32#515012yescomplemented
396C32C3×#45911yescharacteristic, complemented
397C23—21no—
398C23—62no—
399D4—21no—
400D4—62no—
401D4—62no—
402D4—362no—
403D4—362no—
404D4C3×#62512yescomplemented
405C2×C4—91no—
406C2×C4—91no—
407C2×C4—181no—
408C2×C4—362no—
409C2×C4C2×C3×D3211yescharacteristic
410C8—62no—
411C2×C3—21no—
412C2×C3—22no—
413C2×C3—21no—
414C2×C3—22no—
415C2×C3—21no—
416C2×C3—22no—
417C2×C3—44no—
418C2×C3—44no—
419C2×C3—42no—
420C2×C3—41no—
421C2×C3—41no—
422C2×C3—41no—
423C2×C3—84no—
424C2×C3—84no—
425C2×C3—244no—
426C2×C3—242no—
427C2×C3—242no—
428C2×C3#6392611yescharacteristic
429C2×C3#6392711yescharacteristic
430C2×C3#6398011yescharacteristic
431C2×C3C3×D3×D812yes—
432C2×C3C3×#91112yes—
433C2×C3C3×#93912yes—
434D3—82no—
435C22—22no—
436C22—41no—
437C22—41no—
438C22—122no—
439C22—122no—
440C22—122no—
441C22C3×#381111yescharacteristic
442C4—92no—
443C4—181no—
444C4—361no—
445C4C3×#380511yescharacteristic
446C4C2×C3×#62511yescharacteristic
447C3—21no—
448C3—22no—
449C3—41no—
450C3#1059148611yescharacteristic, direct product factor
451C3C3×#515012yescomplemented
452C2—42no—
453C2—242no—
454C2C3×#6392611yescharacteristic
455C2C3×#6392711yescharacteristic
456C2C3×#6398011yescharacteristic
subgroupG/H
centerC22×C3#3811
commutator, cosocleC2×C32×C4C23×C3
FrattiniC2×C4C2×C3×D32
FittingC2×C33×D4C22
socleC22×C33C2×D4
hypercenterC2×C3×D4D32
hypocenterC32C3×#459
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C2×C3×C4 ◁ C2×C3×D4

Complements

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

NH ≅ G/Ntype
1. C3×D4×C3⋊Dic3C2semidirect
2. C2×C32×#213C2semidirect
3. C3×#63914C2semidirect
4. C3×#63572C2semidirect
5. C3×#63563C2semidirect
7. #10591486C3direct (N × H)
19. D4×C3⋊Dic3C2×C3semidirect
24. C2×C3×#213D3semidirect
25. C2×C3×#213C2×C3semidirect
26. #63914C2×C3semidirect
30. #63572C2×C3semidirect
31. #63563C2×C3semidirect
35. C33×D4D4semidirect
92. C3×C3⋊Dic3D8semidirect
101. C2×#213C3×D3semidirect
126. C32×D4#67semidirect
127. C32×D4C3×D4semidirect
242. C3⋊Dic3C3×D8semidirect
254. C33#459semidirect
280. C3×D4#625semidirect
281. C3×D4C3×#67semidirect
395. C32#5150semidirect
396. C32C3×#459semidirect
404. D4C3×#625semidirect
450. C3#10591486direct (N × H)
451. C3C3×#5150semidirect

Maximal subgroups

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

subgroupindex
C3×D4×C3⋊Dic32
C2×C32×#2132
C3×#639142
C3×#635722
C3×#635632
C3×#51503
#105914863