Subgroups — C₃×#10596034 #13179314

Order 1728.

1792 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×C₄×D₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#64147	C₂	1	2	yes	maximal, complemented
3	C₃×#64139	C₂	1	2	yes	maximal, complemented
4	C₃×#64135	C₂	1	2	yes	maximal, complemented
5	C₃×#64101	C₂	1	2	yes	maximal, complemented
6	C₃×#64094	C₂	1	4	yes	maximal, complemented
7	C₃×C₄×C₄⋊(C₃⋊D₃)	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#64078	C₂	1	1	yes	maximal, characteristic, complemented
9	#10596034	C₃	1	1	yes	maximal, characteristic, direct product factor
10	C₃×#5563	—	3	4	no	maximal
11	C₂×C₃³×D₄	C₂²	1	1	yes	characteristic
12	C₂²×C₃³×C₄	C₂²	1	2	yes	—
13	C₂×C₃×#638	C₂²	1	4	yes	—
14	C₂×C₃×C₄⋊(C₃⋊D₃)	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₄×C₃⋊D₃	C₂²	1	2	yes	—
16	C₂×C₃×#634	C₂²	1	2	yes	—
17	C₃³×C₄⋊C₄	C₂²	1	1	yes	characteristic
18	C₃³×C₂²⋊C₄	C₂²	1	2	yes	—
19	C₃³×C₄²	C₂²	1	1	yes	characteristic
20	C₃×#3757	C₂²	1	4	yes	—
21	C₃×#3752	C₂²	1	2	yes	—
22	C₃×#3752	C₂²	1	4	yes	—
23	C₃×C₄⋊(C₃⋊Dic₃)	C₂²	1	2	yes	—
24	C₃×C₄⋊(C₃⋊Dic₃)	C₂²	1	2	yes	—
25	C₃×C₄⋊(C₃⋊Dic₃)	C₂²	1	1	yes	characteristic
26	C₃×C₄×C₃⋊Dic₃	C₂²	1	4	yes	—
27	C₃²×C₄×D₄	—	2	4	no	—
28	C₃²×C₄×D₄	D₃	1	4	yes	complemented
29	C₃²×C₄×D₄	C₂×C₃	1	1	yes	characteristic, complemented
30	#64147	C₂×C₃	1	2	yes	complemented
31	#64139	C₂×C₃	1	2	yes	complemented
32	#64135	C₂×C₃	1	2	yes	complemented
33	#64101	C₂×C₃	1	2	yes	complemented
34	#64094	C₂×C₃	1	4	yes	complemented
35	C₄×C₄⋊(C₃⋊D₃)	C₂×C₃	1	1	yes	characteristic, complemented
36	#64078	C₂×C₃	1	1	yes	characteristic, complemented
37	C₃×#938	—	3	8	no	—
38	C₃×#930	—	3	8	no	—
39	C₃×#926	—	3	8	no	—
40	C₃×#892	—	3	8	no	—
41	C₃×#885	—	3	16	no	—
42	C₃×C₄×D₁₂	—	3	4	no	—
43	C₃×#869	—	3	4	no	—
44	C₂³×C₃³	C₂³	1	2	yes	—
45	C₂²×C₃×C₃⋊D₃	C₂³	1	2	yes	—
46	C₃³×D₄	—	2	2	no	—
47	C₂×C₃³×C₄	—	2	4	no	—
48	C₂×C₃³×C₄	C₂³	1	2	yes	—
49	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
50	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
51	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
52	C₃×#638	—	4	4	no	—
53	C₂×C₃×C₃⋊Dic₃	C₂³	1	2	yes	—
54	C₂×C₃×C₃⋊Dic₃	C₂³	1	4	yes	—
55	C₃×C₄⋊(C₃⋊D₃)	—	2	2	no	—
56	C₃×C₄×C₃⋊D₃	—	2	4	no	—
57	C₃×#634	—	4	2	no	—
58	C₃×#555	—	9	1	no	—
59	#5563	—	3	4	no	—
60	C₂×C₃²×D₄	—	2	4	no	—
61	C₂×C₃²×D₄	C₂×D₃	1	4	yes	—
62	C₂×C₃²×D₄	C₂²×C₃	1	1	yes	characteristic
63	C₂²×C₃²×C₄	—	2	8	no	—
64	C₂²×C₃²×C₄	C₂×D₃	1	8	yes	—
65	C₂²×C₃²×C₄	C₂²×C₃	1	2	yes	—
66	C₂×#638	C₂²×C₃	1	4	yes	—
67	C₂×C₄⋊(C₃⋊D₃)	C₂²×C₃	1	1	yes	characteristic
68	C₂×C₄×C₃⋊D₃	C₂²×C₃	1	2	yes	—
69	C₂×#634	C₂²×C₃	1	2	yes	—
70	C₂×C₃×#67	—	3	16	no	—
71	C₂×C₃×D₁₂	—	3	4	no	—
72	C₂×C₃×C₄×D₃	—	3	8	no	—
73	C₂×C₃×Dic₆	—	3	8	no	—
74	C₃²×C₄⋊C₄	—	2	4	no	—
75	C₃²×C₄⋊C₄	C₂×D₃	1	4	yes	—
76	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
77	C₃²×C₂²⋊C₄	—	2	8	no	—
78	C₃²×C₂²⋊C₄	C₂×D₃	1	8	yes	—
79	C₃²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
80	C₃²×C₄²	—	2	4	no	—
81	C₃²×C₄²	C₂×D₃	1	4	yes	—
82	C₃²×C₄²	C₂²×C₃	1	1	yes	characteristic
83	#3757	C₂²×C₃	1	4	yes	—
84	#3752	C₂²×C₃	1	2	yes	—
85	#3752	C₂²×C₃	1	4	yes	—
86	C₄⋊(C₃⋊Dic₃)	C₂²×C₃	1	2	yes	—
87	C₄⋊(C₃⋊Dic₃)	C₂²×C₃	1	2	yes	—
88	C₄⋊(C₃⋊Dic₃)	C₂²×C₃	1	1	yes	characteristic
89	C₄×C₃⋊Dic₃	C₂²×C₃	1	4	yes	—
90	C₃×#217	—	3	16	no	—
91	C₃×(C₂×D₃)⋊C₄	—	3	8	no	—
92	C₃×(C₂×D₃)⋊C₄	—	3	16	no	—
93	C₃×C₄⋊Dic₃	—	3	8	no	—
94	C₃×C₄⋊Dic₃	—	3	4	no	—
95	C₃×C₄⋊Dic₃	—	3	8	no	—
96	C₃×C₄×Dic₃	—	3	16	no	—
97	C₂²×C₃³	—	2	2	no	—
98	C₂²×C₃³	—	2	2	no	—
99	C₂²×C₃³	—	2	2	no	—
100	C₂²×C₃³	C₂⁴	1	1	yes	characteristic
101	C₂×C₃×C₃⋊D₃	—	2	2	no	—
102	C₂×C₃×C₃⋊D₃	—	2	2	no	—
103	C₂×C₃×C₃⋊D₃	—	2	2	no	—
104	C₃³×C₄	—	2	2	no	—
105	C₃³×C₄	—	2	1	no	—
106	C₃³×C₄	#41	1	2	yes	—
107	C₃³×C₄	#41	1	2	yes	—
108	C₃×C₃⋊Dic₃	—	2	2	no	—
109	C₃×C₃⋊Dic₃	—	2	4	no	—
110	C₃×C₄⋊Q₈	—	9	1	no	—
111	C₃×#124	—	9	4	no	—
112	C₃×#121	—	9	2	no	—
113	C₃×#121	—	9	2	no	—
114	C₃×C₄×D₄	—	2	4	no	—
115	C₃×C₄×D₄	—	9	1	no	—
116	C₃×C₄×D₄	C₃×D₃	1	4	yes	complemented
117	C₃×C₄×D₄	C₃⋊D₃	1	1	yes	characteristic, complemented
118	C₃×#117	—	9	2	no	—
119	C₃×#117	—	9	2	no	—
120	#938	—	3	8	no	—
121	#930	—	3	8	no	—
122	#926	—	3	8	no	—
123	#892	—	3	8	no	—
124	#885	—	3	16	no	—
125	C₄×D₁₂	—	3	4	no	—
126	#869	—	3	4	no	—
127	C₂³×C₃²	—	2	8	no	—
128	C₂³×C₃²	C₂²×D₃	1	8	yes	—
129	C₂³×C₃²	C₂³×C₃	1	2	yes	—
130	C₂²×C₃⋊D₃	C₂³×C₃	1	2	yes	—
131	C₂²×C₃×D₃	—	3	8	no	—
132	C₃²×D₄	—	2	16	no	—
133	C₃²×D₄	—	2	8	no	—
134	C₃²×D₄	—	2	2	no	—
135	C₂×C₃²×C₄	—	2	4	no	—
136	C₂×C₃²×C₄	—	2	4	no	—
137	C₂×C₃²×C₄	—	2	4	no	—
138	C₂×C₃²×C₄	—	2	4	no	—
139	C₂×C₃²×C₄	—	2	8	no	—
140	C₂×C₃²×C₄	—	2	16	no	—
141	C₂×C₃²×C₄	—	4	16	no	—
142	C₂×C₃²×C₄	C₂²×D₃	1	8	yes	—
143	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
144	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
145	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
146	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
147	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
148	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
149	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
150	#638	—	4	4	no	—
151	C₂×C₃⋊Dic₃	C₂³×C₃	1	2	yes	—
152	C₂×C₃⋊Dic₃	C₂³×C₃	1	4	yes	—
153	C₄⋊(C₃⋊D₃)	—	2	2	no	—
154	C₄×C₃⋊D₃	—	2	4	no	—
155	#634	—	4	2	no	—
156	C₃×#67	—	12	16	no	—
157	C₂×C₃×Dic₃	—	3	8	no	—
158	C₂×C₃×Dic₃	—	3	16	no	—
159	C₃×D₁₂	—	6	8	no	—
160	C₃×C₄×D₃	—	6	16	no	—
161	C₃×Dic₆	—	12	8	no	—
162	#555	—	9	1	no	Sylow
163	C₂×C₃³	—	4	2	no	—
164	C₂×C₃³	C₂×#41	1	1	yes	characteristic
165	C₂×C₃³	C₂×#41	1	1	yes	characteristic
166	C₂×C₃³	H(5,𝔽₂)	1	1	yes	characteristic
167	C₃×C₃⋊D₃	—	4	2	no	—
168	C₂×C₃×Q₈	—	9	2	no	—
169	C₂×C₃×D₄	—	2	4	no	—
170	C₂×C₃×D₄	—	9	4	no	—
171	C₂×C₃×D₄	—	9	1	no	—
172	C₂×C₃×D₄	C₂×C₃×D₃	1	4	yes	—
173	C₂×C₃×D₄	C₂×C₃⋊D₃	1	1	yes	characteristic
174	C₂²×C₃×C₄	—	2	8	no	—
175	C₂²×C₃×C₄	—	9	2	no	—
176	C₂²×C₃×C₄	C₂×C₃×D₃	1	8	yes	—
177	C₂²×C₃×C₄	C₂×C₃⋊D₃	1	2	yes	—
178	C₂×#67	—	3	16	no	—
179	C₂×D₁₂	—	3	4	no	—
180	C₂×C₄×D₃	—	3	8	no	—
181	C₂×Dic₆	—	3	8	no	—
182	C₃×C₄⋊C₄	—	2	4	no	—
183	C₃×C₄⋊C₄	—	9	1	no	—
184	C₃×C₄⋊C₄	—	9	2	no	—
185	C₃×C₄⋊C₄	—	9	2	no	—
186	C₃×C₄⋊C₄	C₂×C₃×D₃	1	4	yes	—
187	C₃×C₄⋊C₄	C₂×C₃⋊D₃	1	1	yes	characteristic
188	C₃×C₂²⋊C₄	—	2	8	no	—
189	C₃×C₂²⋊C₄	—	9	4	no	—
190	C₃×C₂²⋊C₄	—	9	4	no	—
191	C₃×C₂²⋊C₄	—	9	2	no	—
192	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	8	yes	—
193	C₃×C₂²⋊C₄	C₂×C₃⋊D₃	1	2	yes	—
194	C₃×C₄²	—	2	4	no	—
195	C₃×C₄²	—	9	4	no	—
196	C₃×C₄²	C₂×C₃×D₃	1	4	yes	—
197	C₃×C₄²	C₂×C₃⋊D₃	1	1	yes	characteristic
198	#217	—	3	16	no	—
199	(C₂×D₃)⋊C₄	—	3	8	no	—
200	(C₂×D₃)⋊C₄	—	3	16	no	—
201	C₄⋊Dic₃	—	3	8	no	—
202	C₄⋊Dic₃	—	3	8	no	—
203	C₄⋊Dic₃	—	3	4	no	—
204	C₄×Dic₃	—	3	16	no	—
205	C₂²×C₃²	—	2	16	no	—
206	C₂²×C₃²	—	2	8	no	—
207	C₂²×C₃²	—	2	2	no	—
208	C₂²×C₃²	—	2	2	no	—
209	C₂²×C₃²	—	2	2	no	—
210	C₂²×C₃²	—	2	4	no	—
211	C₂²×C₃²	—	2	8	no	—
212	C₂²×C₃²	—	2	8	no	—
213	C₂²×C₃²	—	4	8	no	—
214	C₂²×C₃²	—	4	8	no	—
215	C₂²×C₃²	C₂³×D₃	1	4	yes	—
216	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
217	C₂×C₃⋊D₃	—	2	2	no	—
218	C₂×C₃⋊D₃	—	2	2	no	—
219	C₂×C₃⋊D₃	—	2	2	no	—
220	C₂×C₃×D₃	—	6	8	no	—
221	C₂×C₃×D₃	—	6	8	no	—
222	C₂×C₃×D₃	—	6	8	no	—
223	C₃²×C₄	—	2	2	no	—
224	C₃²×C₄	—	2	1	no	—
225	C₃²×C₄	—	2	8	no	—
226	C₃²×C₄	—	2	8	no	—
227	C₃²×C₄	—	2	8	no	—
228	C₃²×C₄	—	2	4	no	—
229	C₃²×C₄	—	4	4	no	—
230	C₃²×C₄	—	4	8	no	—
231	C₃²×C₄	#235	1	8	yes	—
232	C₃²×C₄	#237	1	8	yes	—
233	C₃²×C₄	C₃×#41	1	2	yes	—
234	C₃²×C₄	C₃×#41	1	2	yes	—
235	C₃⋊Dic₃	—	2	2	no	—
236	C₃⋊Dic₃	—	2	4	no	—
237	C₃×Dic₃	—	6	8	no	—
238	C₃×Dic₃	—	6	16	no	—
239	C₄⋊Q₈	—	9	1	no	—
240	#124	—	9	4	no	—
241	#121	—	9	2	no	—
242	#121	—	9	2	no	—
243	C₄×D₄	—	9	1	no	—
244	C₄×D₄	C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
245	#117	—	9	2	no	—
246	#117	—	9	2	no	—
247	C₃³	#555	1	1	yes	characteristic, complemented, Sylow
248	C₂³×C₃	—	2	8	no	—
249	C₂³×C₃	—	9	2	no	—
250	C₂³×C₃	C₂²×C₃×D₃	1	8	yes	—
251	C₂³×C₃	C₂²×C₃⋊D₃	1	2	yes	—
252	C₂²×D₃	—	3	8	no	—
253	C₃×Q₈	—	36	2	no	—
254	C₃×D₄	—	2	16	no	—
255	C₃×D₄	—	2	8	no	—
256	C₃×D₄	—	2	2	no	—
257	C₃×D₄	—	18	2	no	—
258	C₃×D₄	—	36	4	no	—
259	C₂×C₃×C₄	—	2	16	no	—
260	C₂×C₃×C₄	—	2	4	no	—
261	C₂×C₃×C₄	—	2	4	no	—
262	C₂×C₃×C₄	—	2	4	no	—
263	C₂×C₃×C₄	—	2	4	no	—
264	C₂×C₃×C₄	—	2	8	no	—
265	C₂×C₃×C₄	—	4	16	no	—
266	C₂×C₃×C₄	—	9	2	no	—
267	C₂×C₃×C₄	—	9	4	no	—
268	C₂×C₃×C₄	—	18	4	no	—
269	C₂×C₃×C₄	C₂²×C₃×D₃	1	8	yes	—
270	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
271	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
272	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
273	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	2	yes	—
274	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
275	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
276	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
277	#67	—	12	16	no	—
278	C₂×Dic₃	—	3	8	no	—
279	C₂×Dic₃	—	3	16	no	—
280	D₁₂	—	6	8	no	—
281	C₄×D₃	—	6	16	no	—
282	Dic₆	—	12	8	no	—
283	C₂×C₃²	—	2	4	no	—
284	C₂×C₃²	—	2	4	no	—
285	C₂×C₃²	—	2	4	no	—
286	C₂×C₃²	—	4	16	no	—
287	C₂×C₃²	—	4	8	no	—
288	C₂×C₃²	—	4	2	no	—
289	C₂×C₃²	C₂×#235	1	4	yes	—
290	C₂×C₃²	C₂×#237	1	4	yes	—
291	C₂×C₃²	#1009	1	4	yes	—
292	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
293	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
294	C₂×C₃²	C₃×H(5,𝔽₂)	1	1	yes	characteristic
295	C₃⋊D₃	—	4	2	no	—
296	C₃×D₃	—	12	8	no	—
297	C₂×Q₈	—	9	2	no	—
298	C₂×D₄	—	9	4	no	—
299	C₂×D₄	—	9	1	no	—
300	C₂×D₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
301	C₂²×C₄	—	9	2	no	—
302	C₂²×C₄	C₂×C₃×C₃⋊D₃	1	2	yes	—
303	C₄⋊C₄	—	9	1	no	—
304	C₄⋊C₄	—	9	2	no	—
305	C₄⋊C₄	—	9	2	no	—
306	C₄⋊C₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
307	C₂²⋊C₄	—	9	4	no	—
308	C₂²⋊C₄	—	9	4	no	—
309	C₂²⋊C₄	—	9	2	no	—
310	C₂²⋊C₄	C₂×C₃×C₃⋊D₃	1	2	yes	—
311	C₄²	—	9	4	no	—
312	C₄²	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
313	C₂²×C₃	—	2	16	no	—
314	C₂²×C₃	—	2	8	no	—
315	C₂²×C₃	—	2	8	no	—
316	C₂²×C₃	—	2	8	no	—
317	C₂²×C₃	—	2	2	no	—
318	C₂²×C₃	—	2	2	no	—
319	C₂²×C₃	—	2	2	no	—
320	C₂²×C₃	—	2	4	no	—
321	C₂²×C₃	—	4	8	no	—
322	C₂²×C₃	—	4	8	no	—
323	C₂²×C₃	—	18	2	no	—
324	C₂²×C₃	—	18	2	no	—
325	C₂²×C₃	—	18	2	no	—
326	C₂²×C₃	C₂³×C₃×D₃	1	4	yes	—
327	C₂²×C₃	C₂³×C₃⋊D₃	1	1	yes	characteristic
328	C₂×D₃	—	6	8	no	—
329	C₂×D₃	—	6	8	no	—
330	C₂×D₃	—	6	8	no	—
331	C₃×C₄	—	2	8	no	—
332	C₃×C₄	—	2	4	no	—
333	C₃×C₄	—	2	2	no	—
334	C₃×C₄	—	2	1	no	—
335	C₃×C₄	—	2	8	no	—
336	C₃×C₄	—	2	8	no	—
337	C₃×C₄	—	4	8	no	—
338	C₃×C₄	—	4	4	no	—
339	C₃×C₄	—	18	2	no	—
340	C₃×C₄	—	18	4	no	—
341	C₃×C₄	C₃×#235	1	8	yes	—
342	C₃×C₄	C₃×#237	1	8	yes	—
343	C₃×C₄	#3828	1	2	yes	—
344	C₃×C₄	#3830	1	2	yes	—
345	Dic₃	—	6	8	no	—
346	Dic₃	—	6	16	no	—
347	C₃²	—	2	4	no	—
348	C₃²	#5563	1	4	yes	complemented
349	C₃²	C₃×#555	1	1	yes	characteristic, complemented
350	C₂³	—	9	2	no	—
351	C₂³	C₂²×C₃×C₃⋊D₃	1	2	yes	—
352	Q₈	—	36	2	no	—
353	D₄	—	2	2	no	—
354	D₄	—	18	2	no	—
355	D₄	—	36	4	no	—
356	C₂×C₄	—	2	4	no	—
357	C₂×C₄	—	9	2	no	—
358	C₂×C₄	—	9	4	no	—
359	C₂×C₄	—	18	4	no	—
360	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	2	yes	—
361	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
362	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
363	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
364	C₂×C₃	—	2	4	no	—
365	C₂×C₃	—	2	4	no	—
366	C₂×C₃	—	2	4	no	—
367	C₂×C₃	—	4	16	no	—
368	C₂×C₃	—	4	8	no	—
369	C₂×C₃	—	4	2	no	—
370	C₂×C₃	—	36	2	no	—
371	C₂×C₃	C₂×C₃×#235	1	4	yes	—
372	C₂×C₃	C₂×C₃×#237	1	4	yes	—
373	C₂×C₃	C₃×#1009	1	4	yes	—
374	C₂×C₃	C₂×#3828	1	1	yes	characteristic
375	C₂×C₃	C₂×#3830	1	1	yes	characteristic
376	C₂×C₃	#64366	1	1	yes	characteristic
377	D₃	—	12	8	no	—
378	C₂²	—	2	2	no	—
379	C₂²	—	2	2	no	—
380	C₂²	—	2	2	no	—
381	C₂²	—	18	2	no	—
382	C₂²	—	18	2	no	—
383	C₂²	—	18	2	no	—
384	C₂²	C₂³×C₃×C₃⋊D₃	1	1	yes	characteristic
385	C₄	—	2	2	no	—
386	C₄	—	2	1	no	—
387	C₄	—	18	2	no	—
388	C₄	—	18	4	no	—
389	C₄	C₃×#3828	1	2	yes	—
390	C₄	C₃×#3830	1	2	yes	—
391	C₃	—	2	4	no	—
392	C₃	C₃×#5563	1	4	yes	complemented
393	C₃	#10596034	1	1	yes	characteristic, direct product factor
394	C₂	—	4	2	no	—
395	C₂	—	36	2	no	—
396	C₂	C₂×C₃×#3828	1	1	yes	characteristic
397	C₂	C₂×C₃×#3830	1	1	yes	characteristic
398	C₂	C₃×#64366	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂³×C₃⋊D₃
commutator, cosocle	C₂²×C₃²	C₂⁴×C₃
Frattini	C₂²	C₂³×C₃×C₃⋊D₃
Fitting	C₃³×C₄×D₄	C₂
socle	C₂²×C₃³	C₂⁴
hypercenter	C₃×C₄×D₄	C₃⋊D₃
hypocenter	C₃²	C₃×#555
LCS	G ▷ C₂²×C₃² ▷ C₃²
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄×D₄

Complements

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

N	H ≅ G/N	type
1. C₃³×C₄×D₄	C₂	semidirect
2. C₃×#64147	C₂	semidirect
3. C₃×#64139	C₂	semidirect
4. C₃×#64135	C₂	semidirect
5. C₃×#64101	C₂	semidirect
6. C₃×#64094	C₂	semidirect
7. C₃×C₄×C₄⋊(C₃⋊D₃)	C₂	semidirect
8. C₃×#64078	C₂	semidirect
9. #10596034	C₃	direct (N × H)
28. C₃²×C₄×D₄	D₃	semidirect
29. C₃²×C₄×D₄	C₂×C₃	semidirect
30. #64147	C₂×C₃	semidirect
31. #64139	C₂×C₃	semidirect
32. #64135	C₂×C₃	semidirect
33. #64101	C₂×C₃	semidirect
34. #64094	C₂×C₃	semidirect
35. C₄×C₄⋊(C₃⋊D₃)	C₂×C₃	semidirect
36. #64078	C₂×C₃	semidirect
116. C₃×C₄×D₄	C₃×D₃	semidirect
117. C₃×C₄×D₄	C₃⋊D₃	semidirect
244. C₄×D₄	C₃×C₃⋊D₃	semidirect
247. C₃³	#555	semidirect
348. C₃²	#5563	semidirect
349. C₃²	C₃×#555	semidirect
392. C₃	C₃×#5563	semidirect
393. C₃	#10596034	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃³×C₄×D₄	2
C₃×#64147	2
C₃×#64139	2
C₃×#64135	2
C₃×#64101	2
C₃×#64094	2
C₃×C₄×C₄⋊(C₃⋊D₃)	2
C₃×#64078	2
#10596034	3
C₃×#5563	3

Subgroups — C3×#10596034 #13179314

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10596034 #13179314