Finite Group Databasebeta

← C3×#10591495 #13158507

Subgroups — C3×#10591495 #13158507

Order 1728.

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

normal subgroups only

This group has 680 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
2C3×#63919C211yesmaximal, characteristic, complemented
3C32×#832C212yesmaximal
4C3×#63573C212yesmaximal, complemented
5C3×#63572C211yesmaximal, characteristic, complemented
6C3×#4761—32nomaximal
7#10591495C311yesmaximal, characteristic, direct product factor
8C2×C33×D4C2211yescharacteristic
9C22×C3×C3⋊Dic3—21no—
10C2×C3×#627—21no—
11C3×#3757—21no—
12C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
13C3×C4×C3⋊Dic3C2211yescharacteristic
14C32×C4⋊Dic3C2212yes—
15C2×C32×C3⋊C8C2212yes—
16C3×#3724—21no—
17D4×C3⋊Dic3C2×C311yescharacteristic
18C3×D4×Dic3—32no—
19C3×D4×Dic3—61no—
20C3×#888—32no—
21#63919C2×C311yescharacteristic, complemented
22C32×#102—32no—
23C3×#832—22no—
24C3×#832D312yes—
25C3×#832C2×C312yes—
26C3×#817—32no—
27C3×Dic3⋊C8—32no—
28C3×#808—32no—
29#63573C2×C312yescomplemented
30#63572C2×C311yescharacteristic, complemented
31C23×C33—21no—
32C33×D4—21no—
33C33×D4Q812yescomplemented
34C2×C33×C4C2311yescharacteristic
35C2×C3×C3⋊Dic3—21no—
36C2×C3×C3⋊Dic3—42no—
37C2×C3×C3⋊Dic3D411yescharacteristic
38C2×C3×C3⋊Dic3D411yescharacteristic
39C2×C32×Dic3—22no—
40C3×#627—42no—
41C32×C3⋊C8—22no—
42C3×#476—91no—
43#4761—32no—
44C2×C32×D4—21no—
45C2×C32×D4—22no—
46C2×C32×D4—41no—
47C2×C32×D4C2×D312yes—
48C2×C32×D4C22×C311yescharacteristic
49C22×C3⋊Dic3—21no—
50C22×C3×Dic3—62no—
51C22×C3×Dic3—62no—
52C2×C3×Dic6—62no—
53C2×#627—21no—
54C2×C32×C8—32no—
55C32×C4⋊C4—32no—
56#3757—21no—
57C4⋊(C3⋊Dic3)C22×C311yescharacteristic
58C4×C3⋊Dic3C22×C311yescharacteristic
59C3×#217—62no—
60C3×#217—62no—
61C3×C4⋊Dic3—22no—
62C3×C4⋊Dic3—32no—
63C3×C4⋊Dic3—61no—
64C3×C4⋊Dic3C2×D312yes—
65C3×C4⋊Dic3C22×C312yes—
66C3×Dic3⋊C4—62no—
67C3×C4×Dic3—32no—
68C3×C4×Dic3—61no—
69C2×C3×C3⋊C8—22no—
70C2×C3×C3⋊C8C2×D312yes—
71C2×C3×C3⋊C8C22×C312yes—
72#3724—21no—
73C22×C33—22no—
74C22×C33—41no—
75C22×C33—41no—
76C22×C33C2×D411yescharacteristic
77C33×C4C2×Q811yescharacteristic
78C33×C4#4111yescharacteristic
79C3×C3⋊Dic3—21no—
80C3×C3⋊Dic3—41no—
81C3×C3⋊Dic3SD1612yes—
82C32×Dic3—42no—
83C3×C4⋊Q8—91no—
84C3×C4×D4—91no—
85D4×Dic3—32no—
86D4×Dic3—61no—
87#888—32no—
88C3×#106—92no—
89C3×C4⋊C8—91no—
90C3×#102—32no—
91C3×#102—32no—
92C3×#102—62no—
93#832C3×D312yes—
94#817—32no—
95Dic3⋊C8—32no—
96#808—32no—
97C23×C32—21no—
98C23×C32—22no—
99C23×C32—22no—
100C23×C32—42no—
101C23×C32—42no—
102C32×D4—21no—
103C32×D4—22no—
104C32×D4—22no—
105C32×D4—22no—
106C32×D4—24no—
107C32×D4—42no—
108C32×D4—42no—
109C32×D4—42no—
110C32×D4Dic614yescomplemented
111C32×D4C3×Q812yescomplemented
112C2×C32×C4—21no—
113C2×C32×C4—22no—
114C2×C32×C4—41no—
115C2×C32×C4—62no—
116C2×C32×C4C22×D312yes—
117C2×C32×C4C23×C311yescharacteristic
118C2×C3⋊Dic3—21no—
119C2×C3⋊Dic3—42no—
120C2×C3⋊Dic3C3×D411yescharacteristic
121C2×C3⋊Dic3C3×D411yescharacteristic
122C2×C3×Dic3—22no—
123C2×C3×Dic3—22no—
124C2×C3×Dic3—32no—
125C2×C3×Dic3—32no—
126C2×C3×Dic3—42no—
127C2×C3×Dic3—61no—
128C2×C3×Dic3—61no—
129C2×C3×Dic3—62no—
130C2×C3×Dic3—62no—
131C2×C3×Dic3—124no—
132C2×C3×Dic3—124no—
133C3×Dic6—124no—
134#627—42no—
135C32×C8—62no—
136C3×C3⋊C8—22no—
137C3×C3⋊C8—22no—
138C3×C3⋊C8—42no—
139#476—91noSylow
140C2×C33—42no—
141C2×C33C22⋊Q811yescharacteristic
142C2×C33C2×SD1611yescharacteristic
143C2×C33AGL(1,ℤ/8)11yescharacteristic
144C2×C3×Q8—181no—
145C2×C3×D4—21no—
146C2×C3×D4—22no—
147C2×C3×D4—41no—
148C2×C3×D4D3211yescharacteristic
149C2×C3×D4C2×C3×D312yes—
150C22×C3×C4—181no—
151C22×Dic3—62no—
152C22×Dic3—62no—
153C2×Dic6—62no—
154C2×C3×C8—32no—
155C2×C3×C8—32no—
156C2×C3×C8—62no—
157C3×C4⋊C4—32no—
158C3×C4⋊C4—32no—
159C3×C4⋊C4—62no—
160C3×C4⋊C4—91no—
161C3×C4⋊C4—181no—
162C3×C22⋊C4—181no—
163C3×C42—91no—
164#217—62no—
165#217—62no—
166C4⋊Dic3—32no—
167C4⋊Dic3—61no—
168C4⋊Dic3C2×C3×D312yes—
169Dic3⋊C4—62no—
170C4×Dic3—32no—
171C4×Dic3—61no—
172C2×C3⋊C8C2×C3×D312yes—
173C22×C32—22no—
174C22×C32—24no—
175C22×C32—24no—
176C22×C32—21no—
177C22×C32—22no—
178C22×C32—41no—
179C22×C32—44no—
180C22×C32—44no—
181C22×C32—41no—
182C22×C32—41no—
183C22×C32—42no—
184C22×C32—42no—
185C22×C32—42no—
186C22×C32—42no—
187C22×C32—82no—
188C22×C32—82no—
189C22×C32—82no—
190C22×C32—82no—
191C22×C32D3×D412yes—
192C22×C32C2×C3×D411yescharacteristic
193C32×C4—21no—
194C32×C4—21no—
195C32×C4—22no—
196C32×C4—22no—
197C32×C4—41no—
198C32×C4—41no—
199C32×C4—122no—
200C32×C4C2×Dic612yes—
201C32×C4#23712yes—
202C32×C4C2×C3×Q811yescharacteristic
203C32×C4C3×#4111yescharacteristic
204C3⋊Dic3—21no—
205C3⋊Dic3—41no—
206C3⋊Dic3C3×SD1612yes—
207C3×Dic3—34no—
208C3×Dic3—42no—
209C3×Dic3—42no—
210C3×Dic3—62no—
211C3×Dic3—62no—
212C3×Dic3—82no—
213C3×Dic3—121no—
214C3×Dic3—122no—
215C3×Dic3—122no—
216C4⋊Q8—91no—
217C4×D4—91no—
218#106—92no—
219C4⋊C8—91no—
220#102—32no—
221C33#47611yescharacteristic, complemented, Sylow
222C23×C3—22no—
223C23×C3—21no—
224C23×C3—22no—
225C23×C3—42no—
226C23×C3—42no—
227C3×Q8—362no—
228C3×D4—22no—
229C3×D4—21no—
230C3×D4—22no—
231C3×D4—22no—
232C3×D4—24no—
233C3×D4—42no—
234C3×D4—42no—
235C3×D4—42no—
236C3×D4#62712yescomplemented
237C3×D4C3×Dic614yescomplemented
238C2×C3×C4—22no—
239C2×C3×C4—21no—
240C2×C3×C4—41no—
241C2×C3×C4—62no—
242C2×C3×C4—62no—
243C2×C3×C4—91no—
244C2×C3×C4—91no—
245C2×C3×C4—122no—
246C2×C3×C4—181no—
247C2×C3×C4—362no—
248C2×C3×C4C2×D3211yescharacteristic
249C2×C3×C4C22×C3×D312yes—
250C2×Dic3—22no—
251C2×Dic3—32no—
252C2×Dic3—32no—
253C2×Dic3—61no—
254C2×Dic3—61no—
255C2×Dic3—62no—
256C2×Dic3—62no—
257C2×Dic3—124no—
258C2×Dic3—124no—
259Dic6—124no—
260C3×C8—62no—
261C3×C8—62no—
262C3×C8—122no—
263C3⋊C8—22no—
264C2×C32—22no—
265C2×C32—22no—
266C2×C32—22no—
267C2×C32—21no—
268C2×C32—21no—
269C2×C32—21no—
270C2×C32—41no—
271C2×C32—41no—
272C2×C32—41no—
273C2×C32—42no—
274C2×C32—44no—
275C2×C32—44no—
276C2×C32—84no—
277C2×C32—84no—
278C2×C32#87812yes—
279C2×C32#91112yes—
280C2×C32D3×SD1612yes—
281C2×C32C3×C22⋊Q811yescharacteristic
282C2×C32C2×C3×SD1611yescharacteristic
283C2×C32C3×AGL(1,ℤ/8)11yescharacteristic
284C2×Q8—181no—
285C2×D4C3×D3211yescharacteristic
286C22×C4—181no—
287C2×C8—32no—
288C4⋊C4—32no—
289C4⋊C4—91no—
290C4⋊C4—181no—
291C22⋊C4—181no—
292C42—91no—
293C22×C3—24no—
294C22×C3—24no—
295C22×C3—22no—
296C22×C3—21no—
297C22×C3—22no—
298C22×C3—44no—
299C22×C3—44no—
300C22×C3—42no—
301C22×C3—42no—
302C22×C3—42no—
303C22×C3—42no—
304C22×C3—41no—
305C22×C3—41no—
306C22×C3—41no—
307C22×C3—82no—
308C22×C3—82no—
309C22×C3—82no—
310C22×C3—82no—
311C22×C3#381111yescharacteristic
312C22×C3C3×D3×D412yes—
313C3×C4—22no—
314C3×C4—21no—
315C3×C4—22no—
316C3×C4—21no—
317C3×C4—41no—
318C3×C4—41no—
319C3×C4—92no—
320C3×C4—122no—
321C3×C4—122no—
322C3×C4—181no—
323C3×C4—242no—
324C3×C4—361no—
325C3×C4#380511yescharacteristic
326C3×C4C2×#62711yescharacteristic
327C3×C4C2×C3×Dic612yes—
328C3×C4C3×#23712yes—
329Dic3—34no—
330Dic3—42no—
331Dic3—62no—
332Dic3—62no—
333Dic3—121no—
334Dic3—122no—
335Dic3—122no—
336C32—21no—
337C32—22no—
338C32—41no—
339C32#476112yescomplemented
340C32C3×#47611yescharacteristic, complemented
341C23—21no—
342Q8—362no—
343D4—21no—
344D4C3×#62712yescomplemented
345C2×C4—62no—
346C2×C4—91no—
347C2×C4—91no—
348C2×C4—181no—
349C2×C4—362no—
350C2×C4C2×C3×D3211yescharacteristic
351C8—62no—
352C2×C3—21no—
353C2×C3—22no—
354C2×C3—21no—
355C2×C3—22no—
356C2×C3—21no—
357C2×C3—22no—
358C2×C3—44no—
359C2×C3—42no—
360C2×C3—44no—
361C2×C3—41no—
362C2×C3—41no—
363C2×C3—41no—
364C2×C3—84no—
365C2×C3—84no—
366C2×C3#6392711yescharacteristic
367C2×C3#6393011yescharacteristic
368C2×C3#6398211yescharacteristic
369C2×C3C3×#87812yes—
370C2×C3C3×#91112yes—
371C2×C3C3×D3×SD1612yes—
372C22—22no—
373C22—41no—
374C22—41no—
375C22C3×#381111yescharacteristic
376C4—92no—
377C4—122no—
378C4—181no—
379C4—361no—
380C4C3×#380511yescharacteristic
381C4C2×C3×#62711yescharacteristic
382C3—21no—
383C3—22no—
384C3—41no—
385C3#1059149511yescharacteristic, direct product factor
386C3C3×#476112yescomplemented
387C2—42no—
388C2C3×#6392711yescharacteristic
389C2C3×#6393011yescharacteristic
390C2C3×#6398211yescharacteristic
subgroupG/H
centerC22×C3#3811
commutator, cosocleC2×C32×C4C23×C3
FrattiniC2×C4C2×C3×D32
Fitting, prime radicalC2×C33×D4C22
socleC22×C33C2×D4
hypercenterC2×C3×D4D32
hypocenterC32C3×#476
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
2. C3×#63919C2semidirect
4. C3×#63573C2semidirect
5. C3×#63572C2semidirect
7. #10591495C3direct (N × H)
21. #63919C2×C3semidirect
29. #63573C2×C3semidirect
30. #63572C2×C3semidirect
33. C33×D4Q8semidirect
110. C32×D4Dic6semidirect
111. C32×D4C3×Q8semidirect
221. C33#476semidirect
236. C3×D4#627semidirect
237. C3×D4C3×Dic6semidirect
339. C32#4761semidirect
340. C32C3×#476semidirect
344. D4C3×#627semidirect
385. C3#10591495direct (N × H)
386. C3C3×#4761semidirect

Maximal subgroups

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

subgroupindex
C3×D4×C3⋊Dic32
C3×#639192
C32×#8322
C3×#635732
C3×#635722
C3×#47613
#105914953