Finite Group Databasebeta

← C3×#63959 #11723284

Subgroups — C3×#63959 #11723284

Order 864.

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

normal subgroups only

This group has 458 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×#67C211yesmaximal, characteristic
2C2×C3×#627C211yesmaximal, characteristic, complemented
3C3×#3757C211yesmaximal, characteristic, complemented
4C32×#217C211yesmaximal, characteristic, complemented
5C3×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
6C3×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
7C3×Dic32C211yesmaximal, characteristic, complemented
8C3×#936—31nomaximal
9C3×#885—31nomaximal
10#63959C311yesmaximal, characteristic, direct product factor
11C23×C33C2211yescharacteristic
12C22×C32×D3C2211yescharacteristic
13C2×C3×C3⋊Dic3C2211yescharacteristic
14C2×C3×C3⋊Dic3C2211yescharacteristic
15C32×#67—22no—
16C2×C32×Dic3C2211yescharacteristic
17C2×C32×Dic3C2211yescharacteristic
18C2×C32×Dic3C2211yescharacteristic
19C3×#627—22no—
20C2×C32×D4—31no—
21C2×C3×#67—21no—
22C2×C3×#67D311yescharacteristic
23C2×C3×#67C2×C311yescharacteristic
24C2×C3×Dic6—31no—
25C2×C3×Dic6—31no—
26C2×#627C2×C311yescharacteristic, complemented
27C32×C22⋊C4—31no—
28#3757C2×C311yescharacteristic, complemented
29C3×#217—21no—
30C3×#217—31no—
31C3×#217—31no—
32C3×#217—31no—
33C3×#217—31no—
34C3×#217—61no—
35C3×#217D311yescharacteristic, complemented
36C3×#217C2×C311yescharacteristic, complemented
37C3×(C2×D3)⋊C4—31no—
38C3×(C2×D3)⋊C4—31no—
39C3×C4×Dic3—31no—
40C3×C4×Dic3—31no—
41(C2×D3)⋊Dic3C2×C311yescharacteristic, complemented
42(C2×D3)⋊Dic3C2×C311yescharacteristic, complemented
43Dic32C2×C311yescharacteristic, complemented
44C22×C33—21no—
45C22×C33—21no—
46C22×C33—21no—
47C22×C33C2311yescharacteristic
48C2×C32×D3—21no—
49C2×C32×D3—21no—
50C2×C32×D3—21no—
51C3×C3⋊Dic3—21no—
52C3×C3⋊Dic3—21no—
53C32×Dic3—21no—
54C32×Dic3—21no—
55C32×Dic3D412yes—
56C3×#124—91no—
57#936—31no—
58#885—31no—
59C23×C32—21no—
60C23×C32—21no—
61C23×C32—21no—
62C23×C32—31no—
63C23×C32—41no—
64C23×C32C2×D311yescharacteristic
65C23×C32C2×D311yescharacteristic
66C23×C32C22×C311yescharacteristic
67C22×C3×D3—21no—
68C22×C3×D3C2×D311yescharacteristic
69C22×C3×D3C22×C311yescharacteristic
70C32×D4—62no—
71C2×C32×C4—31no—
72C2×C32×C4—31no—
73C2×C32×C4—31no—
74C2×C3⋊Dic3C22×C311yescharacteristic
75C2×C3⋊Dic3C22×C311yescharacteristic
76C3×#67—24no—
77C3×#67—22no—
78C3×#67—22no—
79C2×C3×Dic3—21no—
80C2×C3×Dic3—21no—
81C2×C3×Dic3—21no—
82C2×C3×Dic3—31no—
83C2×C3×Dic3—31no—
84C2×C3×Dic3—31no—
85C2×C3×Dic3—31no—
86C2×C3×Dic3—61no—
87C2×C3×Dic3—61no—
88C2×C3×Dic3C2×D311yescharacteristic
89C2×C3×Dic3C2×D311yescharacteristic
90C2×C3×Dic3C2×D311yescharacteristic
91C2×C3×Dic3C22×C311yescharacteristic
92C2×C3×Dic3C22×C311yescharacteristic
93C2×C3×Dic3C22×C311yescharacteristic
94C3×Dic6—62no—
95C3×Dic6—62no—
96#627—22no—
97C2×C33—41no—
98C2×C33C2×D411yescharacteristic
99C2×C33#4111yescharacteristic
100C2×C33#4111yescharacteristic
101C32×D3—41no—
102C2×C3×Q8—91no—
103C2×C3×D4—31no—
104C2×C3×D4—31no—
105C2×C3×D4—61no—
106C2×#67C3×D311yescharacteristic
107C2×Dic6—31no—
108C2×Dic6—31no—
109C3×C22⋊C4—31no—
110C3×C22⋊C4—31no—
111C3×C22⋊C4—61no—
112C3×C22⋊C4—91no—
113C3×C22⋊C4—91no—
114C3×C22⋊C4—91no—
115C3×C42—91no—
116#217—31no—
117#217—31no—
118#217—31no—
119#217—31no—
120#217—61no—
121#217C3×D311yescharacteristic, complemented
122(C2×D3)⋊C4—31no—
123(C2×D3)⋊C4—31no—
124C4×Dic3—31no—
125C4×Dic3—31no—
126C22×C32—21no—
127C22×C32—21no—
128C22×C32—21no—
129C22×C32—22no—
130C22×C32—22no—
131C22×C32—22no—
132C22×C32—21no—
133C22×C32—21no—
134C22×C32—21no—
135C22×C32—21no—
136C22×C32—21no—
137C22×C32—21no—
138C22×C32—21no—
139C22×C32—21no—
140C22×C32—21no—
141C22×C32—41no—
142C22×C32—41no—
143C22×C32—41no—
144C22×C32—41no—
145C22×C32—41no—
146C22×C32—41no—
147C22×C32—41no—
148C22×C32—42no—
149C22×C32—42no—
150C22×C32—42no—
151C22×C32—61no—
152C22×C32—61no—
153C22×C32—61no—
154C22×C32C22×D311yescharacteristic
155C22×C32C22×D311yescharacteristic
156C22×C32C23×C311yescharacteristic
157C2×C3×D3—22no—
158C2×C3×D3—21no—
159C2×C3×D3—21no—
160C2×C3×D3—21no—
161C2×C3×D3—21no—
162C2×C3×D3—21no—
163C2×C3×D3—21no—
164C2×C3×D3—41no—
165C2×C3×D3—41no—
166C32×C4—32no—
167C32×C4—61no—
168C32×C4—61no—
169C3⋊Dic3—21no—
170C3⋊Dic3—21no—
171C3×Dic3—21no—
172C3×Dic3—21no—
173C3×Dic3—21no—
174C3×Dic3—21no—
175C3×Dic3—22no—
176C3×Dic3—41no—
177C3×Dic3—41no—
178C3×Dic3—61no—
179C3×Dic3—61no—
180C3×Dic3—61no—
181C3×Dic3—61no—
182C3×Dic3—121no—
183C3×Dic3—121no—
184C3×Dic3#6712yes—
185C3×Dic3C3×D412yes—
186#124—91noSylow
187C33#12411yescharacteristic, complemented, Sylow
188C23×C3—21no—
189C23×C3—21no—
190C23×C3—21no—
191C23×C3—31no—
192C23×C3—31no—
193C23×C3—41no—
194C23×C3—61no—
195C23×C3D3211yescharacteristic
196C23×C3C2×C3×D311yescharacteristic
197C23×C3C2×C3×D311yescharacteristic
198C22×D3C2×C3×D311yescharacteristic
199C3×Q8—182no—
200C3×D4—62no—
201C3×D4—62no—
202C3×D4—64no—
203C2×C3×C4—31no—
204C2×C3×C4—31no—
205C2×C3×C4—31no—
206C2×C3×C4—31no—
207C2×C3×C4—31no—
208C2×C3×C4—31no—
209C2×C3×C4—61no—
210C2×C3×C4—61no—
211C2×C3×C4—61no—
212C2×C3×C4—91no—
213C2×C3×C4—91no—
214#67—22no—
215C2×Dic3—31no—
216C2×Dic3—31no—
217C2×Dic3—31no—
218C2×Dic3—31no—
219C2×Dic3—61no—
220C2×Dic3—61no—
221C2×Dic3C2×C3×D311yescharacteristic
222C2×Dic3C2×C3×D311yescharacteristic
223C2×Dic3C2×C3×D311yescharacteristic
224Dic6—62no—
225Dic6—62no—
226C2×C32—21no—
227C2×C32—21no—
228C2×C32—21no—
229C2×C32—21no—
230C2×C32—21no—
231C2×C32—21no—
232C2×C32—21no—
233C2×C32—21no—
234C2×C32—21no—
235C2×C32—41no—
236C2×C32—41no—
237C2×C32—41no—
238C2×C32—42no—
239C2×C32—42no—
240C2×C32—42no—
241C2×C32—44no—
242C2×C32—41no—
243C2×C32—41no—
244C2×C32—41no—
245C2×C32—121no—
246C2×C32#23511yescharacteristic
247C2×C32D3×D411yescharacteristic
248C2×C32#23711yescharacteristic
249C2×C32#23711yescharacteristic
250C2×C32#23711yescharacteristic
251C2×C32C2×#6711yescharacteristic
252C2×C32C2×C3×D411yescharacteristic
253C2×C32C3×#4111yescharacteristic
254C2×C32C3×#4111yescharacteristic
255C3×D3—42no—
256C3×D3—41no—
257C3×D3—41no—
258C2×Q8—91no—
259C2×D4—31no—
260C22⋊C4—31no—
261C22⋊C4—91no—
262C22⋊C4—91no—
263C22⋊C4—91no—
264C42—91no—
265C22×C3—22no—
266C22×C3—22no—
267C22×C3—22no—
268C22×C3—21no—
269C22×C3—21no—
270C22×C3—21no—
271C22×C3—21no—
272C22×C3—21no—
273C22×C3—21no—
274C22×C3—21no—
275C22×C3—21no—
276C22×C3—21no—
277C22×C3—21no—
278C22×C3—21no—
279C22×C3—21no—
280C22×C3—41no—
281C22×C3—41no—
282C22×C3—41no—
283C22×C3—41no—
284C22×C3—41no—
285C22×C3—41no—
286C22×C3—42no—
287C22×C3—42no—
288C22×C3—42no—
289C22×C3—41no—
290C22×C3—62no—
291C22×C3—61no—
292C22×C3—61no—
293C22×C3—61no—
294C22×C3—61no—
295C22×C3—61no—
296C22×C3—61no—
297C22×C3—121no—
298C22×C3—121no—
299C22×C3C2×D3211yescharacteristic
300C22×C3C22×C3×D311yescharacteristic
301C22×C3C22×C3×D311yescharacteristic
302C2×D3—21no—
303C2×D3—21no—
304C2×D3—21no—
305C3×C4—32no—
306C3×C4—32no—
307C3×C4—62no—
308C3×C4—61no—
309C3×C4—61no—
310C3×C4—61no—
311C3×C4—61no—
312C3×C4—121no—
313C3×C4—121no—
314C3×C4—181no—
315C3×C4—181no—
316Dic3—21no—
317Dic3—21no—
318Dic3—61no—
319Dic3—61no—
320Dic3—61no—
321Dic3—61no—
322Dic3—121no—
323Dic3—121no—
324Dic3C3×#6712yes—
325C32—21no—
326C32—21no—
327C32—21no—
328C32—41no—
329C32#88511yescharacteristic, complemented
330C32#93611yescharacteristic, complemented
331C32C3×#12411yescharacteristic, complemented
332C23—31no—
333C23C3×D3211yescharacteristic
334Q8—182no—
335D4—62no—
336C2×C4—31no—
337C2×C4—31no—
338C2×C4—31no—
339C2×C4—91no—
340C2×C4—91no—
341C2×C3—21no—
342C2×C3—21no—
343C2×C3—21no—
344C2×C3—21no—
345C2×C3—21no—
346C2×C3—21no—
347C2×C3—21no—
348C2×C3—21no—
349C2×C3—21no—
350C2×C3—42no—
351C2×C3—42no—
352C2×C3—42no—
353C2×C3—44no—
354C2×C3—41no—
355C2×C3—41no—
356C2×C3—41no—
357C2×C3—41no—
358C2×C3—41no—
359C2×C3—41no—
360C2×C3—122no—
361C2×C3—121no—
362C2×C3—121no—
363C2×C3#380411yescharacteristic
364C2×C3#380511yescharacteristic
365C2×C3D3×#6711yescharacteristic
366C2×C3C3×#23511yescharacteristic
367C2×C3C3×D3×D411yescharacteristic
368C2×C3C3×#23711yescharacteristic
369C2×C3C3×#23711yescharacteristic
370C2×C3C3×#23711yescharacteristic
371C2×C3C2×C3×#6711yescharacteristic
372D3—41no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—61no—
377C22—61no—
378C22—61no—
379C22C2×C3×D3211yescharacteristic
380C4—32no—
381C4—61no—
382C4—61no—
383C4—181no—
384C4—181no—
385C3—21no—
386C3—21no—
387C3—21no—
388C3—41no—
389C3#6395911yescharacteristic, direct product factor
390C3C3×#88511yescharacteristic, complemented
391C3C3×#93611yescharacteristic, complemented
392C2—41no—
393C2—121no—
394C2C3×#380411yescharacteristic
395C2C3×#380511yescharacteristic
396C2C3×D3×#6711yescharacteristic
subgroupG/H
centerC22×C3C2×D32
commutator, cosocleC22×C32C23×C3
FrattiniC22C2×C3×D32
FittingC23×C33C22
socleC22×C33C23
prime radicalC2×C32×#67C2
hypercenterC23×C3D32
hypocenterC32C3×#124
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C23×C3

Complements

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

NH ≅ G/Ntype
2. C2×C3×#627C2semidirect
3. C3×#3757C2semidirect
4. C32×#217C2semidirect
5. C3×(C2×D3)⋊Dic3C2semidirect
6. C3×(C2×D3)⋊Dic3C2semidirect
7. C3×Dic32C2semidirect
10. #63959C3direct (N × H)
26. C2×#627C2×C3semidirect
28. #3757C2×C3semidirect
35. C3×#217D3semidirect
36. C3×#217C2×C3semidirect
41. (C2×D3)⋊Dic3C2×C3semidirect
42. (C2×D3)⋊Dic3C2×C3semidirect
43. Dic32C2×C3semidirect
121. #217C3×D3semidirect
187. C33#124semidirect
329. C32#885semidirect
330. C32#936semidirect
331. C32C3×#124semidirect
389. C3#63959direct (N × H)
390. C3C3×#885semidirect
391. C3C3×#936semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#672
C2×C3×#6272
C3×#37572
C32×#2172
C3×(C2×D3)⋊Dic32
C3×Dic322
C3×#9363
C3×#8853
#639593