Subgroups — C₃×#10596206 #13179486

Order 1728.

1448 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#64156	C₂	1	1	yes	maximal, characteristic
3	C₃×#64155	C₂	1	2	yes	maximal, complemented
4	C₃×#64153	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#64107	C₂	1	2	yes	maximal, complemented
6	C₃×#64105	C₂	1	2	yes	maximal, complemented
7	C₃×#64103	C₂	1	2	yes	maximal
8	C₃×#64098	C₂	1	2	yes	maximal, complemented
9	C₃×#64085	C₂	1	2	yes	maximal, complemented
10	#10596206	C₃	1	1	yes	maximal, characteristic, direct product factor
11	C₃×#5735	—	3	4	no	maximal
12	C₂×C₃³×Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₃³×Q₈	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
17	C₃³×C₄⋊C₄	C₂²	1	2	yes	—
18	C₃³×C₄⋊C₄	C₂²	1	2	yes	—
19	C₃³×C₄²	C₂²	1	1	yes	characteristic
20	C₃×#3752	C₂²	1	2	yes	—
21	C₃×#3752	C₂²	1	2	yes	—
22	C₃×#3752	C₂²	1	2	yes	—
23	C₃×#3752	C₂²	1	2	yes	—
24	C₃×#3752	C₂²	1	2	yes	—
25	C₃×C₄⋊(C₃⋊Dic₃)	C₂²	1	2	yes	—
26	C₃×#3750	C₂²	1	2	yes	—
27	C₃×#3750	C₂²	1	2	yes	—
28	C₃×#3750	C₂²	1	2	yes	—
29	C₃×#3750	C₂²	1	2	yes	—
30	C₃×#3750	C₂²	1	2	yes	—
31	C₃×C₄×C₃⋊Dic₃	C₂²	1	1	yes	characteristic
32	C₃×C₄×C₃⋊Dic₃	C₂²	1	1	yes	characteristic
33	C₃²×C₄⋊Q₈	—	2	4	no	—
34	C₃²×C₄⋊Q₈	D₃	1	4	yes	complemented
35	C₃²×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
36	#64156	C₂×C₃	1	1	yes	characteristic
37	#64155	C₂×C₃	1	2	yes	complemented
38	#64153	C₂×C₃	1	1	yes	characteristic, complemented
39	#64107	C₂×C₃	1	2	yes	complemented
40	#64105	C₂×C₃	1	2	yes	complemented
41	#64103	C₂×C₃	1	2	yes	—
42	#64098	C₂×C₃	1	2	yes	complemented
43	#64085	C₂×C₃	1	2	yes	complemented
44	C₃×#947	—	3	4	no	—
45	C₃×#946	—	3	8	no	—
46	C₃×#944	—	3	4	no	—
47	C₃×#898	—	3	8	no	—
48	C₃×#896	—	3	8	no	—
49	C₃×#894	—	3	8	no	—
50	C₃×#889	—	3	8	no	—
51	C₃×#876	—	3	8	no	—
52	C₂²×C₃×C₃⋊D₃	C₂³	1	2	yes	—
53	C₃³×Q₈	—	4	1	no	—
54	C₃³×Q₈	—	4	1	no	—
55	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
56	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
57	C₂×C₃³×C₄	C₂³	1	2	yes	—
58	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
59	C₂×C₃³×C₄	C₂³	1	2	yes	—
60	C₂×C₃×C₃⋊Dic₃	C₂³	1	2	yes	—
61	C₂×C₃×C₃⋊Dic₃	C₂³	1	2	yes	—
62	C₂×C₃×C₃⋊Dic₃	C₂³	1	2	yes	—
63	C₃×C₄⋊(C₃⋊D₃)	—	4	1	no	—
64	C₃×C₄×C₃⋊D₃	—	4	2	no	—
65	C₃×#634	—	4	1	no	—
66	C₃×#563	—	9	1	no	—
67	#5735	—	3	4	no	—
68	C₂×C₃²×Q₈	—	2	4	no	—
69	C₂×C₃²×Q₈	—	2	4	no	—
70	C₂×C₃²×Q₈	C₂×D₃	1	4	yes	—
71	C₂×C₃²×Q₈	C₂×D₃	1	4	yes	—
72	C₂×C₃²×Q₈	C₂²×C₃	1	1	yes	characteristic
73	C₂×C₃²×Q₈	C₂²×C₃	1	1	yes	characteristic
74	C₂×C₄⋊(C₃⋊D₃)	C₂²×C₃	1	1	yes	characteristic
75	C₂×C₄×C₃⋊D₃	C₂²×C₃	1	2	yes	—
76	C₂×#634	C₂²×C₃	1	1	yes	characteristic
77	C₂×C₃×D₁₂	—	3	4	no	—
78	C₂×C₃×C₄×D₃	—	3	8	no	—
79	C₂×C₃×Dic₆	—	3	4	no	—
80	C₃²×C₄⋊C₄	—	2	8	no	—
81	C₃²×C₄⋊C₄	—	2	8	no	—
82	C₃²×C₄⋊C₄	C₂×D₃	1	8	yes	—
83	C₃²×C₄⋊C₄	C₂×D₃	1	8	yes	—
84	C₃²×C₄⋊C₄	C₂²×C₃	1	2	yes	—
85	C₃²×C₄⋊C₄	C₂²×C₃	1	2	yes	—
86	C₃²×C₄²	—	2	4	no	—
87	C₃²×C₄²	C₂×D₃	1	4	yes	—
88	C₃²×C₄²	C₂²×C₃	1	1	yes	characteristic
89	#3752	C₂²×C₃	1	2	yes	—
90	#3752	C₂²×C₃	1	2	yes	—
91	#3752	C₂²×C₃	1	2	yes	—
92	#3752	C₂²×C₃	1	2	yes	—
93	#3752	C₂²×C₃	1	2	yes	—
94	C₄⋊(C₃⋊Dic₃)	C₂²×C₃	1	2	yes	—
95	#3750	C₂²×C₃	1	2	yes	—
96	#3750	C₂²×C₃	1	2	yes	—
97	#3750	C₂²×C₃	1	2	yes	—
98	#3750	C₂²×C₃	1	2	yes	—
99	#3750	C₂²×C₃	1	2	yes	—
100	C₄×C₃⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
101	C₄×C₃⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
102	C₃×(C₂×D₃)⋊C₄	—	3	8	no	—
103	C₃×(C₂×D₃)⋊C₄	—	3	8	no	—
104	C₃×(C₂×D₃)⋊C₄	—	3	8	no	—
105	C₃×(C₂×D₃)⋊C₄	—	3	8	no	—
106	C₃×(C₂×D₃)⋊C₄	—	3	8	no	—
107	C₃×C₄⋊Dic₃	—	3	8	no	—
108	C₃×Dic₃⋊C₄	—	3	8	no	—
109	C₃×Dic₃⋊C₄	—	3	8	no	—
110	C₃×Dic₃⋊C₄	—	3	8	no	—
111	C₃×Dic₃⋊C₄	—	3	8	no	—
112	C₃×Dic₃⋊C₄	—	3	8	no	—
113	C₃×C₄×Dic₃	—	3	4	no	—
114	C₃×C₄×Dic₃	—	3	4	no	—
115	C₂²×C₃³	C₂⁴	1	1	yes	characteristic
116	C₂×C₃×C₃⋊D₃	—	2	2	no	—
117	C₂×C₃×C₃⋊D₃	—	2	4	no	—
118	C₃³×C₄	—	2	1	no	—
119	C₃³×C₄	—	2	1	no	—
120	C₃³×C₄	—	2	2	no	—
121	C₃³×C₄	—	2	1	no	—
122	C₃³×C₄	—	2	2	no	—
123	C₃×C₃⋊Dic₃	—	2	2	no	—
124	C₃×C₃⋊Dic₃	—	2	2	no	—
125	C₃×C₃⋊Dic₃	—	2	2	no	—
126	C₃×C₄⋊Q₈	—	2	4	no	—
127	C₃×C₄⋊Q₈	—	9	1	no	—
128	C₃×C₄⋊Q₈	C₃×D₃	1	4	yes	complemented
129	C₃×C₄⋊Q₈	C₃⋊D₃	1	1	yes	characteristic, complemented
130	C₃×#126	—	9	2	no	—
131	C₃×#126	—	9	2	no	—
132	C₃×#125	—	9	2	no	—
133	C₃×#124	—	9	1	no	—
134	C₃×#123	—	9	2	no	—
135	C₃×C₂²⋊Q₈	—	9	2	no	—
136	C₃×C₂²⋊Q₈	—	9	2	no	—
137	#947	—	3	4	no	—
138	#946	—	3	8	no	—
139	#944	—	3	4	no	—
140	#898	—	3	8	no	—
141	#896	—	3	8	no	—
142	#894	—	3	8	no	—
143	#889	—	3	8	no	—
144	#876	—	3	8	no	—
145	C₂²×C₃⋊D₃	C₂³×C₃	1	2	yes	—
146	C₂²×C₃×D₃	—	3	8	no	—
147	C₃²×Q₈	—	4	4	no	—
148	C₃²×Q₈	—	4	4	no	—
149	C₃²×Q₈	—	4	1	no	—
150	C₃²×Q₈	—	4	1	no	—
151	C₃²×Q₈	—	4	8	no	—
152	C₃²×Q₈	—	4	8	no	—
153	C₂×C₃²×C₄	—	2	8	no	—
154	C₂×C₃²×C₄	—	2	4	no	—
155	C₂×C₃²×C₄	—	2	4	no	—
156	C₂×C₃²×C₄	—	2	4	no	—
157	C₂×C₃²×C₄	—	2	8	no	—
158	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
159	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
160	C₂×C₃²×C₄	C₂²×D₃	1	8	yes	—
161	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
162	C₂×C₃²×C₄	C₂²×D₃	1	8	yes	—
163	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
164	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
165	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
166	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
167	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
168	C₂×C₃⋊Dic₃	C₂³×C₃	1	2	yes	—
169	C₂×C₃⋊Dic₃	C₂³×C₃	1	2	yes	—
170	C₂×C₃⋊Dic₃	C₂³×C₃	1	2	yes	—
171	C₄⋊(C₃⋊D₃)	—	4	1	no	—
172	C₄×C₃⋊D₃	—	4	2	no	—
173	#634	—	4	1	no	—
174	C₂×C₃×Dic₃	—	3	8	no	—
175	C₂×C₃×Dic₃	—	3	8	no	—
176	C₂×C₃×Dic₃	—	3	8	no	—
177	C₃×D₁₂	—	12	4	no	—
178	C₃×C₄×D₃	—	12	8	no	—
179	C₃×Dic₆	—	12	4	no	—
180	#563	—	9	1	no	Sylow
181	C₂×C₃³	H(5,𝔽₂)	1	1	yes	characteristic
182	C₂×C₃³	2₋¹⁺⁴	1	2	yes	—
183	C₃×C₃⋊D₃	—	4	2	no	—
184	C₂×C₃×Q₈	—	2	4	no	—
185	C₂×C₃×Q₈	—	2	4	no	—
186	C₂×C₃×Q₈	—	9	1	no	—
187	C₂×C₃×Q₈	C₂×C₃×D₃	1	4	yes	—
188	C₂×C₃×Q₈	C₂×C₃×D₃	1	4	yes	—
189	C₂×C₃×Q₈	C₂×C₃⋊D₃	1	1	yes	characteristic
190	C₂×C₃×Q₈	C₂×C₃⋊D₃	1	1	yes	characteristic
191	C₂×C₃×D₄	—	9	1	no	—
192	C₂²×C₃×C₄	—	9	2	no	—
193	C₂×D₁₂	—	3	4	no	—
194	C₂×C₄×D₃	—	3	8	no	—
195	C₂×Dic₆	—	3	4	no	—
196	C₃×C₄⋊C₄	—	2	8	no	—
197	C₃×C₄⋊C₄	—	2	8	no	—
198	C₃×C₄⋊C₄	—	9	2	no	—
199	C₃×C₄⋊C₄	—	9	2	no	—
200	C₃×C₄⋊C₄	—	9	2	no	—
201	C₃×C₄⋊C₄	—	9	2	no	—
202	C₃×C₄⋊C₄	—	9	2	no	—
203	C₃×C₄⋊C₄	—	9	2	no	—
204	C₃×C₄⋊C₄	C₂×C₃×D₃	1	8	yes	—
205	C₃×C₄⋊C₄	C₂×C₃×D₃	1	8	yes	—
206	C₃×C₄⋊C₄	C₂×C₃⋊D₃	1	2	yes	—
207	C₃×C₄⋊C₄	C₂×C₃⋊D₃	1	2	yes	—
208	C₃×C₂²⋊C₄	—	9	2	no	—
209	C₃×C₂²⋊C₄	—	9	2	no	—
210	C₃×C₂²⋊C₄	—	9	2	no	—
211	C₃×C₂²⋊C₄	—	9	2	no	—
212	C₃×C₂²⋊C₄	—	9	2	no	—
213	C₃×C₄²	—	2	4	no	—
214	C₃×C₄²	—	9	1	no	—
215	C₃×C₄²	—	9	1	no	—
216	C₃×C₄²	C₂×C₃×D₃	1	4	yes	—
217	C₃×C₄²	C₂×C₃⋊D₃	1	1	yes	characteristic
218	(C₂×D₃)⋊C₄	—	3	8	no	—
219	(C₂×D₃)⋊C₄	—	3	8	no	—
220	(C₂×D₃)⋊C₄	—	3	8	no	—
221	(C₂×D₃)⋊C₄	—	3	8	no	—
222	(C₂×D₃)⋊C₄	—	3	8	no	—
223	C₄⋊Dic₃	—	3	8	no	—
224	Dic₃⋊C₄	—	3	8	no	—
225	Dic₃⋊C₄	—	3	8	no	—
226	Dic₃⋊C₄	—	3	8	no	—
227	Dic₃⋊C₄	—	3	8	no	—
228	Dic₃⋊C₄	—	3	8	no	—
229	C₄×Dic₃	—	3	4	no	—
230	C₄×Dic₃	—	3	4	no	—
231	C₂²×C₃²	—	2	4	no	—
232	C₂²×C₃²	C₂³×D₃	1	4	yes	—
233	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
234	C₂×C₃⋊D₃	—	2	2	no	—
235	C₂×C₃⋊D₃	—	2	4	no	—
236	C₂×C₃×D₃	—	6	8	no	—
237	C₂×C₃×D₃	—	6	16	no	—
238	C₃²×C₄	—	2	16	no	—
239	C₃²×C₄	—	2	8	no	—
240	C₃²×C₄	—	2	4	no	—
241	C₃²×C₄	—	2	8	no	—
242	C₃²×C₄	—	2	1	no	—
243	C₃²×C₄	—	2	2	no	—
244	C₃²×C₄	—	2	1	no	—
245	C₃²×C₄	—	2	1	no	—
246	C₃²×C₄	—	2	2	no	—
247	C₃²×C₄	—	2	4	no	—
248	C₃²×C₄	—	2	8	no	—
249	C₃²×C₄	—	2	4	no	—
250	C₃²×C₄	—	4	4	no	—
251	C₃²×C₄	—	4	8	no	—
252	C₃²×C₄	—	4	4	no	—
253	C₃⋊Dic₃	—	2	2	no	—
254	C₃⋊Dic₃	—	2	2	no	—
255	C₃⋊Dic₃	—	2	2	no	—
256	C₃×Dic₃	—	6	8	no	—
257	C₃×Dic₃	—	6	8	no	—
258	C₃×Dic₃	—	6	8	no	—
259	C₄⋊Q₈	—	9	1	no	—
260	C₄⋊Q₈	C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
261	#126	—	9	2	no	—
262	#126	—	9	2	no	—
263	#125	—	9	2	no	—
264	#124	—	9	1	no	—
265	#123	—	9	2	no	—
266	C₂²⋊Q₈	—	9	2	no	—
267	C₂²⋊Q₈	—	9	2	no	—
268	C₃³	#563	1	1	yes	characteristic, complemented, Sylow
269	C₂³×C₃	—	9	2	no	—
270	C₂²×D₃	—	3	8	no	—
271	C₃×Q₈	—	4	4	no	—
272	C₃×Q₈	—	4	4	no	—
273	C₃×Q₈	—	4	1	no	—
274	C₃×Q₈	—	4	1	no	—
275	C₃×Q₈	—	4	8	no	—
276	C₃×Q₈	—	4	8	no	—
277	C₃×Q₈	—	36	1	no	—
278	C₃×D₄	—	36	1	no	—
279	C₂×C₃×C₄	—	2	8	no	—
280	C₂×C₃×C₄	—	2	4	no	—
281	C₂×C₃×C₄	—	2	4	no	—
282	C₂×C₃×C₄	—	2	4	no	—
283	C₂×C₃×C₄	—	2	8	no	—
284	C₂×C₃×C₄	—	9	2	no	—
285	C₂×C₃×C₄	—	9	2	no	—
286	C₂×C₃×C₄	—	9	2	no	—
287	C₂×C₃×C₄	—	36	2	no	—
288	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
289	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
290	C₂×C₃×C₄	C₂²×C₃×D₃	1	8	yes	—
291	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
292	C₂×C₃×C₄	C₂²×C₃×D₃	1	8	yes	—
293	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
294	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
295	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	2	yes	—
296	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
297	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	2	yes	—
298	C₂×Dic₃	—	3	8	no	—
299	C₂×Dic₃	—	3	8	no	—
300	C₂×Dic₃	—	3	8	no	—
301	D₁₂	—	12	4	no	—
302	C₄×D₃	—	12	8	no	—
303	Dic₆	—	12	4	no	—
304	C₂×C₃²	—	2	4	no	—
305	C₂×C₃²	—	2	8	no	—
306	C₂×C₃²	#1004	1	4	yes	—
307	C₂×C₃²	#1007	1	8	yes	—
308	C₂×C₃²	C₃×H(5,𝔽₂)	1	1	yes	characteristic
309	C₂×C₃²	C₃×2₋¹⁺⁴	1	2	yes	—
310	C₃⋊D₃	—	4	2	no	—
311	C₃×D₃	—	12	8	no	—
312	C₂×Q₈	—	9	1	no	—
313	C₂×Q₈	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
314	C₂×Q₈	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
315	C₂×D₄	—	9	1	no	—
316	C₂²×C₄	—	9	2	no	—
317	C₄⋊C₄	—	9	2	no	—
318	C₄⋊C₄	—	9	2	no	—
319	C₄⋊C₄	—	9	2	no	—
320	C₄⋊C₄	—	9	2	no	—
321	C₄⋊C₄	—	9	2	no	—
322	C₄⋊C₄	—	9	2	no	—
323	C₄⋊C₄	C₂×C₃×C₃⋊D₃	1	2	yes	—
324	C₄⋊C₄	C₂×C₃×C₃⋊D₃	1	2	yes	—
325	C₂²⋊C₄	—	9	2	no	—
326	C₂²⋊C₄	—	9	2	no	—
327	C₂²⋊C₄	—	9	2	no	—
328	C₂²⋊C₄	—	9	2	no	—
329	C₂²⋊C₄	—	9	2	no	—
330	C₄²	—	9	1	no	—
331	C₄²	—	9	1	no	—
332	C₄²	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
333	C₂²×C₃	—	2	4	no	—
334	C₂²×C₃	—	18	2	no	—
335	C₂²×C₃	—	18	4	no	—
336	C₂²×C₃	C₂³×C₃×D₃	1	4	yes	—
337	C₂²×C₃	C₂³×C₃⋊D₃	1	1	yes	characteristic
338	C₂×D₃	—	6	8	no	—
339	C₂×D₃	—	6	16	no	—
340	C₃×C₄	—	2	8	no	—
341	C₃×C₄	—	2	16	no	—
342	C₃×C₄	—	2	4	no	—
343	C₃×C₄	—	2	8	no	—
344	C₃×C₄	—	2	4	no	—
345	C₃×C₄	—	2	4	no	—
346	C₃×C₄	—	2	8	no	—
347	C₃×C₄	—	2	2	no	—
348	C₃×C₄	—	2	1	no	—
349	C₃×C₄	—	2	1	no	—
350	C₃×C₄	—	2	1	no	—
351	C₃×C₄	—	2	2	no	—
352	C₃×C₄	—	4	8	no	—
353	C₃×C₄	—	4	4	no	—
354	C₃×C₄	—	4	4	no	—
355	C₃×C₄	—	18	2	no	—
356	C₃×C₄	—	18	2	no	—
357	C₃×C₄	—	18	2	no	—
358	Dic₃	—	6	8	no	—
359	Dic₃	—	6	8	no	—
360	Dic₃	—	6	8	no	—
361	C₃²	—	2	4	no	—
362	C₃²	#5735	1	4	yes	complemented
363	C₃²	C₃×#563	1	1	yes	characteristic, complemented
364	C₂³	—	9	2	no	—
365	Q₈	—	4	1	no	—
366	Q₈	—	4	1	no	—
367	Q₈	—	36	1	no	—
368	D₄	—	36	1	no	—
369	C₂×C₄	—	9	2	no	—
370	C₂×C₄	—	9	2	no	—
371	C₂×C₄	—	9	2	no	—
372	C₂×C₄	—	36	2	no	—
373	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
374	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
375	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	2	yes	—
376	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
377	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	2	yes	—
378	C₂×C₃	—	2	4	no	—
379	C₂×C₃	—	2	8	no	—
380	C₂×C₃	—	36	2	no	—
381	C₂×C₃	C₃×#1004	1	4	yes	—
382	C₂×C₃	C₃×#1007	1	8	yes	—
383	C₂×C₃	#64361	1	1	yes	characteristic
384	C₂×C₃	#64364	1	2	yes	—
385	D₃	—	12	8	no	—
386	C₂²	—	18	2	no	—
387	C₂²	—	18	4	no	—
388	C₂²	C₂³×C₃×C₃⋊D₃	1	1	yes	characteristic
389	C₄	—	2	2	no	—
390	C₄	—	2	1	no	—
391	C₄	—	2	1	no	—
392	C₄	—	2	1	no	—
393	C₄	—	2	2	no	—
394	C₄	—	18	2	no	—
395	C₄	—	18	2	no	—
396	C₄	—	18	2	no	—
397	C₃	—	2	4	no	—
398	C₃	C₃×#5735	1	4	yes	complemented
399	C₃	#10596206	1	1	yes	characteristic, direct product factor
400	C₂	—	36	2	no	—
401	C₂	C₃×#64361	1	1	yes	characteristic
402	C₂	C₃×#64364	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃	C₂³×C₃⋊D₃
commutator, cosocle	C₂²×C₃²	C₂⁴×C₃
Frattini	C₂²	C₂³×C₃×C₃⋊D₃
Fitting	C₃³×C₄⋊Q₈	C₂
socle	C₂²×C₃³	C₂⁴
prime radical	C₂×C₃×C₄⋊(C₃⋊D₃)	C₂²
hypercenter	C₃×C₄⋊Q₈	C₃⋊D₃
hypocenter	C₃²	C₃×#563
LCS	G ▷ C₂²×C₃² ▷ C₃²
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
1. C₃³×C₄⋊Q₈	C₂	semidirect
3. C₃×#64155	C₂	semidirect
4. C₃×#64153	C₂	semidirect
5. C₃×#64107	C₂	semidirect
6. C₃×#64105	C₂	semidirect
8. C₃×#64098	C₂	semidirect
9. C₃×#64085	C₂	semidirect
10. #10596206	C₃	direct (N × H)
34. C₃²×C₄⋊Q₈	D₃	semidirect
35. C₃²×C₄⋊Q₈	C₂×C₃	semidirect
37. #64155	C₂×C₃	semidirect
38. #64153	C₂×C₃	semidirect
39. #64107	C₂×C₃	semidirect
40. #64105	C₂×C₃	semidirect
42. #64098	C₂×C₃	semidirect
43. #64085	C₂×C₃	semidirect
128. C₃×C₄⋊Q₈	C₃×D₃	semidirect
129. C₃×C₄⋊Q₈	C₃⋊D₃	semidirect
260. C₄⋊Q₈	C₃×C₃⋊D₃	semidirect
268. C₃³	#563	semidirect
362. C₃²	#5735	semidirect
363. C₃²	C₃×#563	semidirect
398. C₃	C₃×#5735	semidirect
399. C₃	#10596206	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⋊Q₈	2
C₃×#64156	2
C₃×#64155	2
C₃×#64153	2
C₃×#64107	2
C₃×#64105	2
C₃×#64103	2
C₃×#64098	2
C₃×#64085	2
#10596206	3
C₃×#5735	3

Subgroups — C3×#10596206 #13179486

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10596206 #13179486