Subgroups — C₂×C₃²×#825 #13162574

Order 1728.

1292 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	C₂×C₃²×#235	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃³×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃²×C₄×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃²×#825	C₂	1	4	yes	maximal, direct product factor
5	C₂×C₃²×#104	—	3	1	no	maximal
6	C₂×C₃×#825	C₃	1	4	yes	maximal, direct product factor
7	C₂²×C₃³×C₄	C₂²	1	1	yes	characteristic
8	C₂×C₃²×#67	—	2	1	no	—
9	C₂²×C₃²×Dic₃	—	2	1	no	—
10	C₃²×#235	—	2	1	no	—
11	C₃²×#235	—	2	1	no	—
12	C₃²×#235	C₄	1	2	yes	complemented
13	C₃²×#235	C₂²	1	2	yes	—
14	C₂×C₃²×D₁₂	C₄	1	1	yes	characteristic, complemented
15	C₂×C₃²×C₄×D₃	—	2	1	no	—
16	C₂×C₃²×Dic₆	C₄	1	1	yes	characteristic, complemented
17	C₃³×M₁₆	—	2	1	no	—
18	C₃³×M₁₆	C₂²	1	2	yes	complemented
19	C₂×C₃³×C₈	—	2	1	no	—
20	C₃²×C₄×Dic₃	—	2	1	no	—
21	C₃²×C₄×Dic₃	C₂²	1	2	yes	complemented
22	C₂×C₃²×#41	—	3	1	no	—
23	C₂×C₃×#235	C₂×C₃	1	4	yes	—
24	C₂×C₃²×M₁₆	—	2	4	no	—
25	C₂×C₃²×M₁₆	D₃	1	1	yes	characteristic, complemented
26	C₂×C₃²×M₁₆	C₂×C₃	1	4	yes	complemented
27	C₂×C₃²×C₄²	—	3	1	no	—
28	C₂×C₃×C₄×Dic₃	C₂×C₃	1	4	yes	complemented
29	C₃²×#104	—	3	4	no	—
30	C₃×#825	C₂×C₃	1	16	yes	direct product factor
31	C₂³×C₃³	D₄	1	1	yes	characteristic
32	C₂²×C₃²×D₃	—	2	1	no	—
33	C₂×C₃³×C₄	C₂×C₄	1	1	yes	characteristic
34	C₂×C₃³×C₄	C₂×C₄	1	1	yes	characteristic
35	C₂×C₃³×C₄	D₄	1	1	yes	characteristic
36	C₂×C₃³×C₄	D₄	1	1	yes	characteristic
37	C₂×C₃³×C₄	D₄	1	1	yes	characteristic
38	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
39	C₃²×#67	—	2	2	no	—
40	C₃²×#67	—	2	2	no	—
41	C₂×C₃²×Dic₃	—	2	4	no	—
42	C₂×C₃²×Dic₃	—	2	1	no	—
43	C₂×C₃²×Dic₃	—	2	2	no	—
44	C₃²×D₁₂	—	2	1	no	—
45	C₃²×D₁₂	C₂×C₄	1	2	yes	complemented
46	C₃²×C₄×D₃	—	2	2	no	—
47	C₃²×C₄×D₃	—	2	2	no	—
48	C₃²×Dic₆	—	2	1	no	—
49	C₃²×Dic₆	C₂×C₄	1	2	yes	complemented
50	C₃³×C₈	—	2	2	no	—
51	C₂×C₃×#104	—	3	4	no	—
52	C₂×#825	C₃²	1	1	yes	characteristic, direct product factor
53	C₃²×#41	—	3	2	no	—
54	C₃²×#41	—	3	2	no	—
55	C₃²×#41	—	6	1	no	—
56	C₃²×#41	—	6	1	no	—
57	C₂×C₃²×Q₈	—	3	1	no	—
58	C₂×C₃²×D₄	—	3	1	no	—
59	C₂×C₃²×D₄	—	6	1	no	—
60	C₂²×C₃²×C₄	—	2	4	no	—
61	C₂²×C₃²×C₄	—	6	1	no	—
62	C₂²×C₃²×C₄	—	6	1	no	—
63	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic
64	C₂²×C₃²×C₄	C₂²×C₃	1	4	yes	—
65	C₂×C₃×#67	—	2	4	no	—
66	C₂²×C₃×Dic₃	—	2	4	no	—
67	C₃×#235	—	2	4	no	—
68	C₃×#235	—	2	4	no	—
69	C₃×#235	C₃×C₄	1	8	yes	complemented
70	C₃×#235	C₂²×C₃	1	8	yes	—
71	C₂×C₃×D₁₂	C₃×C₄	1	4	yes	complemented
72	C₂×C₃×C₄×D₃	—	2	4	no	—
73	C₂×C₃×Dic₆	C₃×C₄	1	4	yes	complemented
74	C₃²×M₁₆	—	2	8	no	—
75	C₃²×M₁₆	—	2	8	no	—
76	C₃²×M₁₆	—	2	1	no	—
77	C₃²×M₁₆	—	2	4	no	—
78	C₃²×M₁₆	C₂×D₃	1	2	yes	complemented
79	C₃²×M₁₆	C₂²×C₃	1	8	yes	complemented
80	C₂×C₃²×C₈	—	2	8	no	—
81	C₂×C₃²×C₈	—	2	1	no	—
82	C₂×C₃²×C₈	—	2	4	no	—
83	C₃²×C₄²	—	3	2	no	—
84	C₃²×C₄²	—	6	1	no	—
85	C₃×C₄×Dic₃	—	2	4	no	—
86	C₃×C₄×Dic₃	C₂²×C₃	1	8	yes	complemented
87	C₂²×C₃³	—	2	2	no	—
88	C₂²×C₃³	C₂²⋊C₄	1	1	yes	characteristic
89	C₂²×C₃³	C₂²⋊C₄	1	1	yes	characteristic
90	C₂²×C₃³	C₂×D₄	1	1	yes	characteristic
91	C₂×C₃²×D₃	—	2	2	no	—
92	C₂×C₃²×D₃	—	4	2	no	—
93	C₃³×C₄	C₂²⋊C₄	1	1	yes	characteristic
94	C₃³×C₄	C₂²⋊C₄	1	1	yes	characteristic
95	C₃³×C₄	C₂²×C₄	1	1	yes	characteristic
96	C₃³×C₄	C₂×D₄	1	1	yes	characteristic
97	C₃²×Dic₃	—	2	4	no	—
98	C₃²×Dic₃	—	2	2	no	—
99	C₂×C₃×#41	—	3	4	no	—
100	C₂×#235	C₂×C₃²	1	1	yes	characteristic
101	C₂×C₃×M₁₆	—	2	4	no	—
102	C₂×C₃×M₁₆	C₃×D₃	1	4	yes	complemented
103	C₂×C₃×M₁₆	C₂×C₃²	1	1	yes	characteristic, complemented
104	C₂×C₃×C₄²	—	3	4	no	—
105	C₂×C₄×Dic₃	C₂×C₃²	1	1	yes	characteristic, complemented
106	C₃×#104	—	3	16	no	—
107	#825	C₂×C₃²	1	4	yes	direct product factor
108	C₂³×C₃²	—	2	4	no	—
109	C₂³×C₃²	—	6	1	no	—
110	C₂³×C₃²	D₁₂	1	1	yes	characteristic
111	C₂³×C₃²	C₃×D₄	1	4	yes	—
112	C₂²×C₃×D₃	—	2	4	no	—
113	C₃²×Q₈	—	3	2	no	—
114	C₃²×Q₈	—	6	1	no	—
115	C₃²×D₄	—	3	2	no	—
116	C₃²×D₄	—	6	2	no	—
117	C₃²×D₄	—	6	2	no	—
118	C₃²×D₄	—	6	1	no	—
119	C₂×C₃²×C₄	—	2	4	no	—
120	C₂×C₃²×C₄	—	2	4	no	—
121	C₂×C₃²×C₄	—	2	4	no	—
122	C₂×C₃²×C₄	—	2	4	no	—
123	C₂×C₃²×C₄	—	2	4	no	—
124	C₂×C₃²×C₄	—	2	4	no	—
125	C₂×C₃²×C₄	—	6	4	no	—
126	C₂×C₃²×C₄	—	6	1	no	—
127	C₂×C₃²×C₄	—	6	2	no	—
128	C₂×C₃²×C₄	—	6	2	no	—
129	C₂×C₃²×C₄	—	6	2	no	—
130	C₂×C₃²×C₄	C₄×D₃	1	1	yes	characteristic
131	C₂×C₃²×C₄	C₄×D₃	1	1	yes	characteristic
132	C₂×C₃²×C₄	D₁₂	1	1	yes	characteristic
133	C₂×C₃²×C₄	#67	1	1	yes	characteristic
134	C₂×C₃²×C₄	#67	1	1	yes	characteristic
135	C₂×C₃²×C₄	C₂×C₃×C₄	1	4	yes	—
136	C₂×C₃²×C₄	C₂×C₃×C₄	1	4	yes	—
137	C₂×C₃²×C₄	C₃×D₄	1	4	yes	—
138	C₂×C₃²×C₄	C₃×D₄	1	4	yes	—
139	C₂×C₃²×C₄	C₃×D₄	1	4	yes	—
140	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
141	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
142	C₃×#67	—	2	8	no	—
143	C₃×#67	—	2	8	no	—
144	C₂×C₃×Dic₃	—	2	16	no	—
145	C₂×C₃×Dic₃	—	2	4	no	—
146	C₂×C₃×Dic₃	—	2	8	no	—
147	C₃×D₁₂	—	2	4	no	—
148	C₃×D₁₂	C₂×C₃×C₄	1	8	yes	complemented
149	C₃×C₄×D₃	—	2	8	no	—
150	C₃×C₄×D₃	—	2	8	no	—
151	C₃×Dic₆	—	2	4	no	—
152	C₃×Dic₆	C₂×C₃×C₄	1	8	yes	complemented
153	C₃²×C₈	—	2	16	no	—
154	C₃²×C₈	—	2	2	no	—
155	C₃²×C₈	—	2	8	no	—
156	C₂×#104	—	3	1	no	Sylow
157	C₂×C₃³	—	2	1	no	—
158	C₂×C₃³	—	2	1	no	—
159	C₂×C₃³	#104	1	2	yes	complemented
160	C₂×C₃³	C₂×C₂²⋊C₄	1	1	yes	characteristic
161	C₃²×D₃	—	4	2	no	—
162	C₃×#41	—	3	8	no	—
163	C₃×#41	—	3	8	no	—
164	C₃×#41	—	6	4	no	—
165	C₃×#41	—	6	4	no	—
166	C₂×C₃×Q₈	—	3	4	no	—
167	C₂×C₃×D₄	—	3	4	no	—
168	C₂×C₃×D₄	—	6	4	no	—
169	C₂²×C₃×C₄	—	2	4	no	—
170	C₂²×C₃×C₄	—	6	4	no	—
171	C₂²×C₃×C₄	—	6	4	no	—
172	C₂²×C₃×C₄	C₂×C₃×D₃	1	4	yes	—
173	C₂²×C₃×C₄	C₂²×C₃²	1	1	yes	characteristic
174	C₂×#67	—	2	1	no	—
175	C₂²×Dic₃	—	2	1	no	—
176	#235	—	2	1	no	—
177	#235	—	2	1	no	—
178	#235	C₃²×C₄	1	2	yes	complemented
179	#235	C₂²×C₃²	1	2	yes	—
180	C₂×D₁₂	C₃²×C₄	1	1	yes	characteristic, complemented
181	C₂×C₄×D₃	—	2	1	no	—
182	C₂×Dic₆	C₃²×C₄	1	1	yes	characteristic, complemented
183	C₃×M₁₆	—	2	8	no	—
184	C₃×M₁₆	—	2	4	no	—
185	C₃×M₁₆	—	2	1	no	—
186	C₃×M₁₆	—	2	8	no	—
187	C₃×M₁₆	C₂×C₃×D₃	1	8	yes	complemented
188	C₃×M₁₆	C₂²×C₃²	1	2	yes	complemented
189	C₂×C₃×C₈	—	2	8	no	—
190	C₂×C₃×C₈	—	2	4	no	—
191	C₂×C₃×C₈	—	2	1	no	—
192	C₃×C₄²	—	3	8	no	—
193	C₃×C₄²	—	6	4	no	—
194	C₄×Dic₃	—	2	1	no	—
195	C₄×Dic₃	C₂²×C₃²	1	2	yes	complemented
196	C₂²×C₃²	—	2	2	no	—
197	C₂²×C₃²	—	2	4	no	—
198	C₂²×C₃²	—	2	4	no	—
199	C₂²×C₃²	—	2	4	no	—
200	C₂²×C₃²	—	2	8	no	—
201	C₂²×C₃²	—	4	8	no	—
202	C₂²×C₃²	—	6	2	no	—
203	C₂²×C₃²	—	12	2	no	—
204	C₂²×C₃²	(C₂×D₃)⋊C₄	1	1	yes	characteristic
205	C₂²×C₃²	(C₂×D₃)⋊C₄	1	1	yes	characteristic
206	C₂²×C₃²	C₃×C₂²⋊C₄	1	4	yes	—
207	C₂²×C₃²	C₃×C₂²⋊C₄	1	4	yes	—
208	C₂²×C₃²	C₂×D₁₂	1	1	yes	characteristic
209	C₂²×C₃²	C₂×C₃×D₄	1	4	yes	—
210	C₂×C₃×D₃	—	2	8	no	—
211	C₂×C₃×D₃	—	4	8	no	—
212	C₃²×C₄	—	2	4	no	—
213	C₃²×C₄	—	2	4	no	—
214	C₃²×C₄	—	2	4	no	—
215	C₃²×C₄	—	2	4	no	—
216	C₃²×C₄	—	6	4	no	—
217	C₃²×C₄	—	6	2	no	—
218	C₃²×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
219	C₃²×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
220	C₃²×C₄	C₃×C₂²⋊C₄	1	4	yes	—
221	C₃²×C₄	C₃×C₂²⋊C₄	1	4	yes	—
222	C₃²×C₄	C₂×C₄×D₃	1	1	yes	characteristic
223	C₃²×C₄	C₂×#67	1	1	yes	characteristic
224	C₃²×C₄	C₂²×C₃×C₄	1	4	yes	—
225	C₃²×C₄	C₂×C₃×D₄	1	4	yes	—
226	C₃×Dic₃	—	2	16	no	—
227	C₃×Dic₃	—	2	8	no	—
228	C₂×#41	—	3	1	no	—
229	C₂×M₁₆	C₃²×D₃	1	1	yes	characteristic, complemented
230	C₂×C₄²	—	3	1	no	—
231	#104	—	3	4	no	—
232	C₃³	C₂×#104	1	1	yes	characteristic, complemented, Sylow
233	C₂³×C₃	—	2	4	no	—
234	C₂³×C₃	—	6	4	no	—
235	C₂³×C₃	C₃×D₁₂	1	4	yes	—
236	C₂³×C₃	C₃²×D₄	1	1	yes	characteristic
237	C₂²×D₃	—	2	1	no	—
238	C₃×Q₈	—	3	8	no	—
239	C₃×Q₈	—	6	4	no	—
240	C₃×D₄	—	3	8	no	—
241	C₃×D₄	—	6	8	no	—
242	C₃×D₄	—	6	8	no	—
243	C₃×D₄	—	6	4	no	—
244	C₂×C₃×C₄	—	2	4	no	—
245	C₂×C₃×C₄	—	2	4	no	—
246	C₂×C₃×C₄	—	2	4	no	—
247	C₂×C₃×C₄	—	2	4	no	—
248	C₂×C₃×C₄	—	2	4	no	—
249	C₂×C₃×C₄	—	2	4	no	—
250	C₂×C₃×C₄	—	6	16	no	—
251	C₂×C₃×C₄	—	6	4	no	—
252	C₂×C₃×C₄	—	6	8	no	—
253	C₂×C₃×C₄	—	6	8	no	—
254	C₂×C₃×C₄	—	6	8	no	—
255	C₂×C₃×C₄	C₃×C₄×D₃	1	4	yes	—
256	C₂×C₃×C₄	C₃×C₄×D₃	1	4	yes	—
257	C₂×C₃×C₄	C₃×D₁₂	1	4	yes	—
258	C₂×C₃×C₄	C₃×#67	1	4	yes	—
259	C₂×C₃×C₄	C₃×#67	1	4	yes	—
260	C₂×C₃×C₄	C₂×C₃²×C₄	1	1	yes	characteristic
261	C₂×C₃×C₄	C₂×C₃²×C₄	1	1	yes	characteristic
262	C₂×C₃×C₄	C₃²×D₄	1	1	yes	characteristic
263	C₂×C₃×C₄	C₃²×D₄	1	1	yes	characteristic
264	C₂×C₃×C₄	C₃²×D₄	1	1	yes	characteristic
265	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
266	C₂×C₃×C₄	C₂³×C₃²	1	1	yes	characteristic
267	#67	—	2	2	no	—
268	#67	—	2	2	no	—
269	C₂×Dic₃	—	2	4	no	—
270	C₂×Dic₃	—	2	1	no	—
271	C₂×Dic₃	—	2	2	no	—
272	D₁₂	—	2	1	no	—
273	D₁₂	C₂×C₃²×C₄	1	2	yes	complemented
274	C₄×D₃	—	2	2	no	—
275	C₄×D₃	—	2	2	no	—
276	Dic₆	—	2	1	no	—
277	Dic₆	C₂×C₃²×C₄	1	2	yes	complemented
278	C₃×C₈	—	2	16	no	—
279	C₃×C₈	—	2	8	no	—
280	C₃×C₈	—	2	2	no	—
281	C₂×C₃²	—	2	1	no	—
282	C₂×C₃²	—	2	1	no	—
283	C₂×C₃²	—	2	4	no	—
284	C₂×C₃²	—	2	8	no	—
285	C₂×C₃²	—	2	4	no	—
286	C₂×C₃²	—	2	4	no	—
287	C₂×C₃²	—	4	4	no	—
288	C₂×C₃²	—	4	4	no	—
289	C₂×C₃²	—	12	2	no	—
290	C₂×C₃²	#825	1	2	yes	direct product factor
291	C₂×C₃²	C₃×#104	1	8	yes	complemented
292	C₂×C₃²	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
293	C₂×C₃²	C₂×C₃×C₂²⋊C₄	1	4	yes	—
294	C₃×D₃	—	4	8	no	—
295	#41	—	3	2	no	—
296	#41	—	3	2	no	—
297	#41	—	6	1	no	—
298	#41	—	6	1	no	—
299	C₂×Q₈	—	3	1	no	—
300	C₂×D₄	—	3	1	no	—
301	C₂×D₄	—	6	1	no	—
302	C₂²×C₄	—	6	1	no	—
303	C₂²×C₄	—	6	1	no	—
304	C₂²×C₄	C₂×C₃²×D₃	1	1	yes	characteristic
305	M₁₆	—	2	1	no	—
306	M₁₆	C₂×C₃²×D₃	1	2	yes	complemented
307	C₂×C₈	—	2	1	no	—
308	C₄²	—	3	2	no	—
309	C₄²	—	6	1	no	—
310	C₂²×C₃	—	2	8	no	—
311	C₂²×C₃	—	2	2	no	—
312	C₂²×C₃	—	2	4	no	—
313	C₂²×C₃	—	2	4	no	—
314	C₂²×C₃	—	2	4	no	—
315	C₂²×C₃	—	4	8	no	—
316	C₂²×C₃	—	6	8	no	—
317	C₂²×C₃	—	12	8	no	—
318	C₂²×C₃	C₃×(C₂×D₃)⋊C₄	1	4	yes	—
319	C₂²×C₃	C₃×(C₂×D₃)⋊C₄	1	4	yes	—
320	C₂²×C₃	C₃²×C₂²⋊C₄	1	1	yes	characteristic
321	C₂²×C₃	C₃²×C₂²⋊C₄	1	1	yes	characteristic
322	C₂²×C₃	C₂×C₃×D₁₂	1	4	yes	—
323	C₂²×C₃	C₂×C₃²×D₄	1	1	yes	characteristic
324	C₂×D₃	—	2	2	no	—
325	C₂×D₃	—	4	2	no	—
326	C₃×C₄	—	2	4	no	—
327	C₃×C₄	—	2	4	no	—
328	C₃×C₄	—	2	4	no	—
329	C₃×C₄	—	2	4	no	—
330	C₃×C₄	—	6	16	no	—
331	C₃×C₄	—	6	8	no	—
332	C₃×C₄	C₃×(C₂×D₃)⋊C₄	1	4	yes	—
333	C₃×C₄	C₃×(C₂×D₃)⋊C₄	1	4	yes	—
334	C₃×C₄	C₃²×C₂²⋊C₄	1	1	yes	characteristic
335	C₃×C₄	C₃²×C₂²⋊C₄	1	1	yes	characteristic
336	C₃×C₄	C₂×C₃×C₄×D₃	1	4	yes	—
337	C₃×C₄	C₂×C₃×#67	1	4	yes	—
338	C₃×C₄	C₂²×C₃²×C₄	1	1	yes	characteristic
339	C₃×C₄	C₂×C₃²×D₄	1	1	yes	characteristic
340	Dic₃	—	2	4	no	—
341	Dic₃	—	2	2	no	—
342	C₃²	—	2	4	no	—
343	C₃²	C₂×#825	1	1	yes	characteristic, direct product factor
344	C₃²	C₂×C₃×#104	1	4	yes	complemented
345	C₂³	—	6	1	no	—
346	C₂³	C₃²×D₁₂	1	1	yes	characteristic
347	Q₈	—	3	2	no	—
348	Q₈	—	6	1	no	—
349	D₄	—	3	2	no	—
350	D₄	—	6	2	no	—
351	D₄	—	6	2	no	—
352	D₄	—	6	1	no	—
353	C₂×C₄	—	6	4	no	—
354	C₂×C₄	—	6	2	no	—
355	C₂×C₄	—	6	1	no	—
356	C₂×C₄	—	6	2	no	—
357	C₂×C₄	—	6	2	no	—
358	C₂×C₄	C₃²×C₄×D₃	1	1	yes	characteristic
359	C₂×C₄	C₃²×C₄×D₃	1	1	yes	characteristic
360	C₂×C₄	C₃²×D₁₂	1	1	yes	characteristic
361	C₂×C₄	C₃²×#67	1	1	yes	characteristic
362	C₂×C₄	C₃²×#67	1	1	yes	characteristic
363	C₂×C₄	C₂²×C₃²×D₃	1	1	yes	characteristic
364	C₈	—	2	2	no	—
365	C₂×C₃	—	2	1	no	—
366	C₂×C₃	—	2	1	no	—
367	C₂×C₃	—	2	4	no	—
368	C₂×C₃	—	2	4	no	—
369	C₂×C₃	—	2	4	no	—
370	C₂×C₃	—	2	8	no	—
371	C₂×C₃	—	4	4	no	—
372	C₂×C₃	—	4	4	no	—
373	C₂×C₃	—	12	8	no	—
374	C₂×C₃	C₃×#825	1	8	yes	direct product factor
375	C₂×C₃	C₃²×#104	1	2	yes	complemented
376	C₂×C₃	C₂×C₃×(C₂×D₃)⋊C₄	1	4	yes	—
377	C₂×C₃	C₂×C₃²×C₂²⋊C₄	1	1	yes	characteristic
378	D₃	—	4	2	no	—
379	C₂²	—	2	2	no	—
380	C₂²	—	6	2	no	—
381	C₂²	—	12	2	no	—
382	C₂²	C₃²×(C₂×D₃)⋊C₄	1	1	yes	characteristic
383	C₂²	C₃²×(C₂×D₃)⋊C₄	1	1	yes	characteristic
384	C₂²	C₂×C₃²×D₁₂	1	1	yes	characteristic
385	C₄	—	6	4	no	—
386	C₄	—	6	2	no	—
387	C₄	C₃²×(C₂×D₃)⋊C₄	1	1	yes	characteristic
388	C₄	C₃²×(C₂×D₃)⋊C₄	1	1	yes	characteristic
389	C₄	C₂×C₃²×C₄×D₃	1	1	yes	characteristic
390	C₄	C₂×C₃²×#67	1	1	yes	characteristic
391	C₃	—	2	4	no	—
392	C₃	C₂×C₃×#825	1	4	yes	direct product factor
393	C₃	C₂×C₃²×#104	1	1	yes	characteristic, complemented
394	C₂	—	2	1	no	—
395	C₂	—	2	1	no	—
396	C₂	—	12	2	no	—
397	C₂	C₃²×#825	1	2	yes	direct product factor
398	C₂	C₂×C₃²×(C₂×D₃)⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃²×C₄	#67
commutator	C₃×C₄	C₂²×C₃²×C₄
Frattini	C₂×C₄	C₂²×C₃²×D₃
Fitting	C₂×C₃³×M₁₆	C₂
socle	C₂²×C₃³	C₂²⋊C₄
prime radical	C₂×C₃²×#235	C₂
cosocle	C₂×C₃×C₄	C₂³×C₃²
hypercenter	C₂×C₃²×M₁₆	D₃
hypocenter	C₃	C₂×C₃²×#104
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃²×C₄ ◁ C₂²×C₃²×C₄ ◁ C₂×C₃²×M₁₆

Complements

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

N	H ≅ G/N	type
2. C₂×C₃³×M₁₆	C₂	semidirect
3. C₂×C₃²×C₄×Dic₃	C₂	semidirect
4. C₃²×#825	C₂	direct (N × H)
6. C₂×C₃×#825	C₃	direct (N × H)
12. C₃²×#235	C₄	semidirect
14. C₂×C₃²×D₁₂	C₄	semidirect
16. C₂×C₃²×Dic₆	C₄	semidirect
18. C₃³×M₁₆	C₂²	semidirect
21. C₃²×C₄×Dic₃	C₂²	semidirect
25. C₂×C₃²×M₁₆	D₃	semidirect
26. C₂×C₃²×M₁₆	C₂×C₃	semidirect
28. C₂×C₃×C₄×Dic₃	C₂×C₃	semidirect
30. C₃×#825	C₂×C₃	direct (N × H)
45. C₃²×D₁₂	C₂×C₄	semidirect
49. C₃²×Dic₆	C₂×C₄	semidirect
52. C₂×#825	C₃²	direct (N × H)
69. C₃×#235	C₃×C₄	semidirect
71. C₂×C₃×D₁₂	C₃×C₄	semidirect
73. C₂×C₃×Dic₆	C₃×C₄	semidirect
78. C₃²×M₁₆	C₂×D₃	semidirect
79. C₃²×M₁₆	C₂²×C₃	semidirect
86. C₃×C₄×Dic₃	C₂²×C₃	semidirect
102. C₂×C₃×M₁₆	C₃×D₃	semidirect
103. C₂×C₃×M₁₆	C₂×C₃²	semidirect
105. C₂×C₄×Dic₃	C₂×C₃²	semidirect
107. #825	C₂×C₃²	direct (N × H)
148. C₃×D₁₂	C₂×C₃×C₄	semidirect
152. C₃×Dic₆	C₂×C₃×C₄	semidirect
159. C₂×C₃³	#104	semidirect
178. #235	C₃²×C₄	semidirect
180. C₂×D₁₂	C₃²×C₄	semidirect
182. C₂×Dic₆	C₃²×C₄	semidirect
187. C₃×M₁₆	C₂×C₃×D₃	semidirect
188. C₃×M₁₆	C₂²×C₃²	semidirect
195. C₄×Dic₃	C₂²×C₃²	semidirect
229. C₂×M₁₆	C₃²×D₃	semidirect
232. C₃³	C₂×#104	semidirect
273. D₁₂	C₂×C₃²×C₄	semidirect
277. Dic₆	C₂×C₃²×C₄	semidirect
290. C₂×C₃²	#825	direct (N × H)
291. C₂×C₃²	C₃×#104	semidirect
306. M₁₆	C₂×C₃²×D₃	semidirect
343. C₃²	C₂×#825	direct (N × H)
344. C₃²	C₂×C₃×#104	semidirect
374. C₂×C₃	C₃×#825	direct (N × H)
375. C₂×C₃	C₃²×#104	semidirect
392. C₃	C₂×C₃×#825	direct (N × H)
393. C₃	C₂×C₃²×#104	semidirect
397. C₂	C₃²×#825	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃²×#235	2
C₂×C₃³×M₁₆	2
C₂×C₃²×C₄×Dic₃	2
C₃²×#825	2
C₂×C₃²×#104	3
C₂×C₃×#825	3

Subgroups — C2×C32×#825 #13162574

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃²×#825 #13162574