Finite Group Databasebeta

← C3×#63905 #11723230

Subgroups — C3×#63905 #11723230

Order 864.

442 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 96 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
1C2×C32×C4×D3C211yesmaximal, characteristic, complemented
2C2×C3×#625C211yesmaximal, characteristic
3C3×#3750C211yesmaximal, characteristic, complemented
4C32×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
5C3×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
6C3×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
7C3×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
8C3×#929—31nomaximal
9C3×#883—31nomaximal
10#63905C311yesmaximal, characteristic, direct product factor
11C22×C32×D3C2211yescharacteristic
12C22×C32×D3C2211yescharacteristic
13C2×C33×C4C2211yescharacteristic
14C2×C3×C3⋊Dic3C2211yescharacteristic
15C2×C3×C3⋊Dic3C2211yescharacteristic
16C2×C32×Dic3C2211yescharacteristic
17C2×C32×Dic3C2211yescharacteristic
18C32×C4×D3—22no—
19C3×#625—22no—
20C22×C32×C4—31no—
21C2×C3×#67—31no—
22C2×C3×#67—31no—
23C2×C3×C4×D3—21no—
24C2×C3×C4×D3D311yescharacteristic, complemented
25C2×C3×C4×D3C2×C311yescharacteristic, complemented
26C2×#625C2×C311yescharacteristic
27C32×C22⋊C4—31no—
28#3750C2×C311yescharacteristic, complemented
29C3×#217—31no—
30C3×#217—31no—
31C3×(C2×D3)⋊C4—21no—
32C3×(C2×D3)⋊C4—31no—
33C3×(C2×D3)⋊C4—31no—
34C3×(C2×D3)⋊C4D311yescharacteristic, complemented
35C3×(C2×D3)⋊C4C2×C311yescharacteristic, complemented
36C3×C4⋊Dic3—31no—
37C3×Dic3⋊C4—31no—
38C3×Dic3⋊C4—31no—
39C3×Dic3⋊C4—31no—
40C3×Dic3⋊C4—61no—
41Dic3⋊Dic3C2×C311yescharacteristic, complemented
42(C2×D3)⋊Dic3C2×C311yescharacteristic, complemented
43(C2×D3)⋊Dic3C2×C311yescharacteristic, complemented
44C22×C33C2311yescharacteristic
45C2×C32×D3—21no—
46C2×C32×D3—21no—
47C2×C32×D3—21no—
48C2×C32×D3—21no—
49C2×C32×D3—21no—
50C2×C32×D3D412yes—
51C33×C4—21no—
52C3×C3⋊Dic3—21no—
53C3×C3⋊Dic3—21no—
54C32×Dic3—21no—
55C32×Dic3—21no—
56C3×#123—91no—
57#929—31no—
58#883—31no—
59C23×C32—31no—
60C23×C32—31no—
61C22×C3×D3—21no—
62C22×C3×D3—21no—
63C22×C3×D3C2×D311yescharacteristic
64C22×C3×D3C2×D311yescharacteristic
65C22×C3×D3C22×C311yescharacteristic
66C22×C3×D3C22×C311yescharacteristic
67C2×C32×C4—21no—
68C2×C32×C4—21no—
69C2×C32×C4—21no—
70C2×C32×C4—31no—
71C2×C32×C4—31no—
72C2×C32×C4—41no—
73C2×C32×C4—62no—
74C2×C32×C4C2×D311yescharacteristic
75C2×C32×C4C2×D311yescharacteristic
76C2×C32×C4C22×C311yescharacteristic
77C2×C3⋊Dic3C22×C311yescharacteristic
78C2×C3⋊Dic3C22×C311yescharacteristic
79C3×#67—62no—
80C3×#67—62no—
81C2×C3×Dic3—21no—
82C2×C3×Dic3—21no—
83C2×C3×Dic3—31no—
84C2×C3×Dic3—31no—
85C2×C3×Dic3—31no—
86C2×C3×Dic3—31no—
87C2×C3×Dic3—61no—
88C2×C3×Dic3—61no—
89C2×C3×Dic3C2×D311yescharacteristic
90C2×C3×Dic3C2×D311yescharacteristic
91C2×C3×Dic3C22×C311yescharacteristic
92C2×C3×Dic3C22×C311yescharacteristic
93C3×C4×D3—24no—
94C3×C4×D3—22no—
95C3×C4×D3—22no—
96#625—22no—
97C2×C33C2×D411yescharacteristic
98C2×C33#4111yescharacteristic
99C2×C33#4111yescharacteristic
100C32×D3—22no—
101C32×D3—41no—
102C2×C3×D4—91no—
103C22×C3×C4—31no—
104C22×C3×C4—31no—
105C22×C3×C4—61no—
106C2×#67—31no—
107C2×#67—31no—
108C2×C4×D3C3×D311yescharacteristic, complemented
109C3×C4⋊C4—91no—
110C3×C4⋊C4—91no—
111C3×C22⋊C4—31no—
112C3×C22⋊C4—31no—
113C3×C22⋊C4—61no—
114C3×C22⋊C4—91no—
115C3×C22⋊C4—91no—
116#217—31no—
117#217—31no—
118(C2×D3)⋊C4—31no—
119(C2×D3)⋊C4—31no—
120(C2×D3)⋊C4C3×D311yescharacteristic, complemented
121C4⋊Dic3—31no—
122Dic3⋊C4—31no—
123Dic3⋊C4—31no—
124Dic3⋊C4—31no—
125Dic3⋊C4—61no—
126C22×C32—21no—
127C22×C32—21no—
128C22×C32—21no—
129C22×C32—32no—
130C22×C32—41no—
131C22×C32—61no—
132C22×C32—61no—
133C22×C32—61no—
134C22×C32—61no—
135C22×C32—61no—
136C22×C32C22×D311yescharacteristic
137C22×C32C22×D311yescharacteristic
138C22×C32C23×C311yescharacteristic
139C2×C3×D3—22no—
140C2×C3×D3—22no—
141C2×C3×D3—21no—
142C2×C3×D3—21no—
143C2×C3×D3—21no—
144C2×C3×D3—21no—
145C2×C3×D3—22no—
146C2×C3×D3—21no—
147C2×C3×D3—21no—
148C2×C3×D3—21no—
149C2×C3×D3—21no—
150C2×C3×D3—21no—
151C2×C3×D3—21no—
152C2×C3×D3—22no—
153C2×C3×D3—41no—
154C2×C3×D3—41no—
155C2×C3×D3#6712yes—
156C2×C3×D3C3×D412yes—
157C32×C4—21no—
158C32×C4—22no—
159C32×C4—21no—
160C32×C4—21no—
161C32×C4—41no—
162C32×C4—41no—
163C32×C4—42no—
164C32×C4—61no—
165C32×C4—61no—
166C3⋊Dic3—21no—
167C3⋊Dic3—21no—
168C3×Dic3—22no—
169C3×Dic3—21no—
170C3×Dic3—21no—
171C3×Dic3—21no—
172C3×Dic3—21no—
173C3×Dic3—41no—
174C3×Dic3—62no—
175C3×Dic3—61no—
176C3×Dic3—61no—
177C3×Dic3—61no—
178C3×Dic3—61no—
179C3×Dic3—121no—
180#123—91noSylow
181C33#12311yescharacteristic, complemented, Sylow
182C23×C3—31no—
183C23×C3—31no—
184C23×C3—31no—
185C23×C3—31no—
186C23×C3—61no—
187C23×C3—61no—
188C22×D3C2×C3×D311yescharacteristic
189C22×D3C2×C3×D311yescharacteristic
190C3×D4—182no—
191C2×C3×C4—21no—
192C2×C3×C4—21no—
193C2×C3×C4—21no—
194C2×C3×C4—31no—
195C2×C3×C4—31no—
196C2×C3×C4—31no—
197C2×C3×C4—31no—
198C2×C3×C4—41no—
199C2×C3×C4—61no—
200C2×C3×C4—61no—
201C2×C3×C4—62no—
202C2×C3×C4—62no—
203C2×C3×C4—64no—
204C2×C3×C4—91no—
205C2×C3×C4—91no—
206C2×C3×C4D3211yescharacteristic
207C2×C3×C4C2×C3×D311yescharacteristic
208C2×C3×C4C2×C3×D311yescharacteristic
209#67—62no—
210#67—62no—
211C2×Dic3—31no—
212C2×Dic3—31no—
213C2×Dic3—31no—
214C2×Dic3—31no—
215C2×Dic3—61no—
216C2×Dic3—61no—
217C2×Dic3C2×C3×D311yescharacteristic
218C2×Dic3C2×C3×D311yescharacteristic
219C4×D3—22no—
220C2×C32—21no—
221C2×C32—21no—
222C2×C32—21no—
223C2×C32—21no—
224C2×C32—21no—
225C2×C32—21no—
226C2×C32—21no—
227C2×C32—21no—
228C2×C32—21no—
229C2×C32—41no—
230C2×C32—41no—
231C2×C32—41no—
232C2×C32—62no—
233C2×C32—121no—
234C2×C32#23511yescharacteristic
235C2×C32#23511yescharacteristic
236C2×C32#23511yescharacteristic
237C2×C32D3×D411yescharacteristic
238C2×C32#23711yescharacteristic
239C2×C32C2×#6711yescharacteristic
240C2×C32C2×C3×D411yescharacteristic
241C2×C32C3×#4111yescharacteristic
242C2×C32C3×#4111yescharacteristic
243C3×D3—24no—
244C3×D3—22no—
245C3×D3—22no—
246C3×D3—42no—
247C3×D3—41no—
248C3×D3—41no—
249C2×D4—91no—
250C22×C4—31no—
251C4⋊C4—91no—
252C4⋊C4—91no—
253C22⋊C4—31no—
254C22⋊C4—91no—
255C22⋊C4—91no—
256C22×C3—21no—
257C22×C3—21no—
258C22×C3—21no—
259C22×C3—32no—
260C22×C3—32no—
261C22×C3—41no—
262C22×C3—62no—
263C22×C3—62no—
264C22×C3—62no—
265C22×C3—62no—
266C22×C3—61no—
267C22×C3—61no—
268C22×C3—61no—
269C22×C3—61no—
270C22×C3—61no—
271C22×C3—61no—
272C22×C3—61no—
273C22×C3—61no—
274C22×C3—61no—
275C22×C3—61no—
276C22×C3—121no—
277C22×C3—121no—
278C22×C3C2×D3211yescharacteristic
279C22×C3C22×C3×D311yescharacteristic
280C22×C3C22×C3×D311yescharacteristic
281C2×D3—21no—
282C2×D3—21no—
283C2×D3—21no—
284C2×D3—21no—
285C2×D3—21no—
286C2×D3C3×#6712yes—
287C3×C4—22no—
288C3×C4—21no—
289C3×C4—21no—
290C3×C4—21no—
291C3×C4—41no—
292C3×C4—41no—
293C3×C4—42no—
294C3×C4—62no—
295C3×C4—61no—
296C3×C4—61no—
297C3×C4—61no—
298C3×C4—61no—
299C3×C4—121no—
300C3×C4—181no—
301C3×C4—181no—
302Dic3—21no—
303Dic3—21no—
304Dic3—62no—
305Dic3—61no—
306Dic3—61no—
307Dic3—61no—
308Dic3—61no—
309Dic3—121no—
310C32—21no—
311C32—21no—
312C32—21no—
313C32—41no—
314C32#88311yescharacteristic, complemented
315C32#92911yescharacteristic, complemented
316C32C3×#12311yescharacteristic, complemented
317C23—31no—
318C23—31no—
319D4—182no—
320C2×C4—31no—
321C2×C4—31no—
322C2×C4—62no—
323C2×C4—91no—
324C2×C4—91no—
325C2×C4C3×D3211yescharacteristic
326C2×C3—21no—
327C2×C3—21no—
328C2×C3—21no—
329C2×C3—21no—
330C2×C3—21no—
331C2×C3—21no—
332C2×C3—21no—
333C2×C3—21no—
334C2×C3—21no—
335C2×C3—41no—
336C2×C3—41no—
337C2×C3—41no—
338C2×C3—64no—
339C2×C3—62no—
340C2×C3—62no—
341C2×C3—122no—
342C2×C3—121no—
343C2×C3—121no—
344C2×C3#379511yescharacteristic
345C2×C3#379811yescharacteristic
346C2×C3D3×#6711yescharacteristic
347C2×C3C3×#23511yescharacteristic
348C2×C3C3×#23511yescharacteristic
349C2×C3C3×#23511yescharacteristic
350C2×C3C3×D3×D411yescharacteristic
351C2×C3C3×#23711yescharacteristic
352C2×C3C2×C3×#6711yescharacteristic
353D3—22no—
354D3—41no—
355C22—32no—
356C22—61no—
357C22—61no—
358C22—61no—
359C22—61no—
360C22—61no—
361C22C2×C3×D3211yescharacteristic
362C4—21no—
363C4—61no—
364C4—61no—
365C4—181no—
366C4—181no—
367C3—21no—
368C3—21no—
369C3—21no—
370C3—41no—
371C3#6390511yescharacteristic, direct product factor
372C3C3×#88311yescharacteristic, complemented
373C3C3×#92911yescharacteristic, complemented
374C2—62no—
375C2—121no—
376C2C3×#379511yescharacteristic
377C2C3×#379811yescharacteristic
378C2C3×D3×#6711yescharacteristic
subgroupG/H
centerC22×C3C2×D32
commutator, cosocleC22×C32C23×C3
FrattiniC22C2×C3×D32
FittingC2×C33×C4C22
socleC22×C33C23
prime radicalC2×C3×#625C2
hypercenterC2×C3×C4D32
hypocenterC32C3×#123
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C2×C3×C4

Complements

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

NH ≅ G/Ntype
1. C2×C32×C4×D3C2semidirect
3. C3×#3750C2semidirect
4. C32×(C2×D3)⋊C4C2semidirect
5. C3×Dic3⋊Dic3C2semidirect
6. C3×(C2×D3)⋊Dic3C2semidirect
7. C3×(C2×D3)⋊Dic3C2semidirect
10. #63905C3direct (N × H)
24. C2×C3×C4×D3D3semidirect
25. C2×C3×C4×D3C2×C3semidirect
28. #3750C2×C3semidirect
34. C3×(C2×D3)⋊C4D3semidirect
35. C3×(C2×D3)⋊C4C2×C3semidirect
41. Dic3⋊Dic3C2×C3semidirect
42. (C2×D3)⋊Dic3C2×C3semidirect
43. (C2×D3)⋊Dic3C2×C3semidirect
108. C2×C4×D3C3×D3semidirect
120. (C2×D3)⋊C4C3×D3semidirect
181. C33#123semidirect
314. C32#883semidirect
315. C32#929semidirect
316. C32C3×#123semidirect
371. C3#63905direct (N × H)
372. C3C3×#883semidirect
373. C3C3×#929semidirect

Maximal subgroups

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

subgroupindex
C2×C32×C4×D32
C2×C3×#6252
C3×#37502
C32×(C2×D3)⋊C42
C3×Dic3⋊Dic32
C3×(C2×D3)⋊Dic32
C3×#9293
C3×#8833
#639053