Subgroups — C₂×C₃²×#924 #13179161

Order 1728.

2876 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃³×C₄	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃²×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃²×#217	C₂	1	2	yes	maximal
4	C₂×C₃²×C₄⋊Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃²×#924	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₃²×Dic₃⋊C₄	C₂	1	2	yes	maximal, complemented
7	C₂×C₃²×C₂²⋊Q₈	—	3	1	no	maximal
8	C₂×C₃×#924	C₃	1	4	yes	maximal, direct product factor
9	C₂⁴×C₃³	C₂²	1	1	yes	characteristic
10	C₂²×C₃³×C₄	—	2	4	no	—
11	C₂²×C₃³×C₄	C₂²	1	1	yes	characteristic
12	C₂²×C₃³×C₄	C₂²	1	4	yes	—
13	C₂²×C₃³×C₄	C₂²	1	1	yes	characteristic
14	C₂²×C₃²×Dic₃	C₂²	1	2	yes	—
15	C₂²×C₃²×Dic₃	C₂²	1	2	yes	—
16	C₂×C₃²×Dic₆	—	2	4	no	—
17	C₂×C₃²×Dic₆	C₂²	1	4	yes	complemented
18	C₃²×#217	C₂²	1	8	yes	—
19	C₃²×C₄⋊Dic₃	C₂²	1	4	yes	complemented
20	C₃²×Dic₃⋊C₄	C₂²	1	8	yes	complemented
21	C₂²×C₃²×Q₈	—	3	1	no	—
22	C₂³×C₃²×C₄	—	2	4	no	—
23	C₂³×C₃²×C₄	D₃	1	1	yes	characteristic
24	C₂³×C₃²×C₄	C₂×C₃	1	4	yes	—
25	C₂²×C₃×Dic₆	C₂×C₃	1	4	yes	complemented
26	C₃²×C₂²⋊Q₈	—	3	8	no	—
27	C₂×C₃²×C₄⋊C₄	—	3	2	no	—
28	C₂×C₃²×C₄⋊C₄	—	3	1	no	—
29	C₂×C₃²×C₂²⋊C₄	—	3	2	no	—
30	C₂×C₃×#217	C₂×C₃	1	8	yes	—
31	C₂×C₃×C₄⋊Dic₃	C₂×C₃	1	4	yes	complemented
32	C₃×#924	C₂×C₃	1	32	yes	direct product factor
33	C₂×C₃×Dic₃⋊C₄	C₂×C₃	1	8	yes	complemented
34	C₂³×C₃³	—	2	2	no	—
35	C₂³×C₃³	—	2	2	no	—
36	C₂³×C₃³	Q₈	1	4	yes	complemented
37	C₂³×C₃³	C₂³	1	2	yes	—
38	C₂³×C₃³	C₂³	1	1	yes	characteristic
39	C₂×C₃³×C₄	—	2	2	no	—
40	C₂×C₃³×C₄	—	2	8	no	—
41	C₂×C₃³×C₄	D₄	1	4	yes	—
42	C₂×C₃³×C₄	C₂³	1	2	yes	—
43	C₂×C₃³×C₄	C₂³	1	2	yes	—
44	C₂×C₃²×Dic₃	—	2	4	no	—
45	C₂×C₃²×Dic₃	—	2	4	no	—
46	C₂×C₃²×Dic₃	C₂³	1	4	yes	—
47	C₂×C₃²×Dic₃	C₂³	1	4	yes	—
48	C₃²×Dic₆	—	2	8	no	—
49	C₂×C₃×C₂²⋊Q₈	—	3	4	no	—
50	C₂×#924	C₃²	1	1	yes	characteristic, direct product factor
51	C₂⁴×C₃²	—	2	4	no	—
52	C₂⁴×C₃²	C₂×D₃	1	1	yes	characteristic
53	C₂⁴×C₃²	C₂²×C₃	1	4	yes	—
54	C₂×C₃²×Q₈	—	3	4	no	—
55	C₂×C₃²×Q₈	—	6	4	no	—
56	C₂²×C₃²×C₄	—	2	32	no	—
57	C₂²×C₃²×C₄	—	2	4	no	—
58	C₂²×C₃²×C₄	—	2	16	no	—
59	C₂²×C₃²×C₄	—	2	4	no	—
60	C₂²×C₃²×C₄	—	2	4	no	—
61	C₂²×C₃²×C₄	—	2	16	no	—
62	C₂²×C₃²×C₄	—	3	2	no	—
63	C₂²×C₃²×C₄	—	3	2	no	—
64	C₂²×C₃²×C₄	C₂×D₃	1	4	yes	—
65	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic
66	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic
67	C₂²×C₃²×C₄	C₂²×C₃	1	4	yes	—
68	C₂²×C₃²×C₄	C₂²×C₃	1	16	yes	—
69	C₂²×C₃²×C₄	C₂²×C₃	1	4	yes	—
70	C₂²×C₃×Dic₃	C₂²×C₃	1	8	yes	—
71	C₂²×C₃×Dic₃	C₂²×C₃	1	8	yes	—
72	C₂×C₃×Dic₆	—	2	16	no	—
73	C₂×C₃×Dic₆	C₂²×C₃	1	16	yes	complemented
74	C₃²×C₄⋊C₄	—	3	8	no	—
75	C₃²×C₄⋊C₄	—	3	4	no	—
76	C₃²×C₂²⋊C₄	—	3	8	no	—
77	C₃×#217	C₂²×C₃	1	32	yes	—
78	C₃×C₄⋊Dic₃	C₂²×C₃	1	16	yes	complemented
79	C₃×Dic₃⋊C₄	C₂²×C₃	1	32	yes	complemented
80	C₂²×C₃³	—	2	8	no	—
81	C₂²×C₃³	—	2	2	no	—
82	C₂²×C₃³	—	2	2	no	—
83	C₂²×C₃³	C₂×D₄	1	2	yes	—
84	C₂²×C₃³	C₂×Q₈	1	2	yes	—
85	C₂²×C₃³	C₂×Q₈	1	4	yes	complemented
86	C₂²×C₃³	#41	1	2	yes	—
87	C₂²×C₃³	C₂⁴	1	1	yes	characteristic
88	C₃³×C₄	—	2	2	no	—
89	C₃³×C₄	C₂×D₄	1	4	yes	—
90	C₃²×Dic₃	—	2	4	no	—
91	C₃²×Dic₃	—	2	4	no	—
92	C₂²×C₃×Q₈	—	3	4	no	—
93	C₂³×C₃×C₄	—	2	4	no	—
94	C₂³×C₃×C₄	C₃×D₃	1	4	yes	—
95	C₂³×C₃×C₄	C₂×C₃²	1	1	yes	characteristic
96	C₂²×Dic₆	C₂×C₃²	1	1	yes	characteristic, complemented
97	C₃×C₂²⋊Q₈	—	3	32	no	—
98	C₂×C₃×C₄⋊C₄	—	3	8	no	—
99	C₂×C₃×C₄⋊C₄	—	3	4	no	—
100	C₂×C₃×C₂²⋊C₄	—	3	8	no	—
101	C₂×#217	C₂×C₃²	1	2	yes	—
102	C₂×C₄⋊Dic₃	C₂×C₃²	1	1	yes	characteristic, complemented
103	#924	C₂×C₃²	1	8	yes	direct product factor
104	C₂×Dic₃⋊C₄	C₂×C₃²	1	2	yes	complemented
105	C₂³×C₃²	—	2	16	no	—
106	C₂³×C₃²	—	2	16	no	—
107	C₂³×C₃²	—	2	2	no	—
108	C₂³×C₃²	—	2	2	no	—
109	C₂³×C₃²	—	2	8	no	—
110	C₂³×C₃²	—	2	8	no	—
111	C₂³×C₃²	—	2	16	no	—
112	C₂³×C₃²	—	2	8	no	—
113	C₂³×C₃²	—	2	4	no	—
114	C₂³×C₃²	Dic₆	1	4	yes	complemented
115	C₂³×C₃²	C₃×Q₈	1	16	yes	complemented
116	C₂³×C₃²	C₂²×D₃	1	2	yes	—
117	C₂³×C₃²	C₂²×D₃	1	1	yes	characteristic
118	C₂³×C₃²	C₂³×C₃	1	8	yes	—
119	C₂³×C₃²	C₂³×C₃	1	4	yes	—
120	C₃²×Q₈	—	6	8	no	—
121	C₂×C₃²×C₄	—	2	16	no	—
122	C₂×C₃²×C₄	—	2	64	no	—
123	C₂×C₃²×C₄	—	2	2	no	—
124	C₂×C₃²×C₄	—	2	8	no	—
125	C₂×C₃²×C₄	—	2	8	no	—
126	C₂×C₃²×C₄	—	2	32	no	—
127	C₂×C₃²×C₄	—	2	16	no	—
128	C₂×C₃²×C₄	—	2	8	no	—
129	C₂×C₃²×C₄	—	2	8	no	—
130	C₂×C₃²×C₄	—	3	4	no	—
131	C₂×C₃²×C₄	—	3	4	no	—
132	C₂×C₃²×C₄	—	6	4	no	—
133	C₂×C₃²×C₄	—	6	4	no	—
134	C₂×C₃²×C₄	#67	1	4	yes	—
135	C₂×C₃²×C₄	C₃×D₄	1	16	yes	—
136	C₂×C₃²×C₄	C₂²×D₃	1	2	yes	—
137	C₂×C₃²×C₄	C₂²×D₃	1	2	yes	—
138	C₂×C₃²×C₄	C₂³×C₃	1	8	yes	—
139	C₂×C₃²×C₄	C₂³×C₃	1	8	yes	—
140	C₂×C₃×Dic₃	—	2	16	no	—
141	C₂×C₃×Dic₃	—	2	16	no	—
142	C₂×C₃×Dic₃	C₂³×C₃	1	16	yes	—
143	C₂×C₃×Dic₃	C₂³×C₃	1	16	yes	—
144	C₃×Dic₆	—	2	32	no	—
145	C₂×C₂²⋊Q₈	—	3	1	no	Sylow
146	C₂×C₃³	—	2	4	no	—
147	C₂×C₃³	C₂²⋊Q₈	1	4	yes	complemented
148	C₂×C₃³	C₂²×D₄	1	1	yes	characteristic
149	C₂×C₃³	C₂²×Q₈	1	1	yes	characteristic
150	C₂×C₃³	C₂×#41	1	1	yes	characteristic
151	C₂⁴×C₃	—	2	4	no	—
152	C₂⁴×C₃	C₂×C₃×D₃	1	4	yes	—
153	C₂⁴×C₃	C₂²×C₃²	1	1	yes	characteristic
154	C₂×C₃×Q₈	—	3	16	no	—
155	C₂×C₃×Q₈	—	6	16	no	—
156	C₂²×C₃×C₄	—	2	32	no	—
157	C₂²×C₃×C₄	—	2	16	no	—
158	C₂²×C₃×C₄	—	2	4	no	—
159	C₂²×C₃×C₄	—	2	4	no	—
160	C₂²×C₃×C₄	—	2	16	no	—
161	C₂²×C₃×C₄	—	2	4	no	—
162	C₂²×C₃×C₄	—	3	8	no	—
163	C₂²×C₃×C₄	—	3	8	no	—
164	C₂²×C₃×C₄	C₂×C₃×D₃	1	4	yes	—
165	C₂²×C₃×C₄	C₂×C₃×D₃	1	16	yes	—
166	C₂²×C₃×C₄	C₂×C₃×D₃	1	4	yes	—
167	C₂²×C₃×C₄	C₂²×C₃²	1	1	yes	characteristic
168	C₂²×C₃×C₄	C₂²×C₃²	1	4	yes	—
169	C₂²×C₃×C₄	C₂²×C₃²	1	1	yes	characteristic
170	C₂²×Dic₃	C₂²×C₃²	1	2	yes	—
171	C₂²×Dic₃	C₂²×C₃²	1	2	yes	—
172	C₂×Dic₆	—	2	4	no	—
173	C₂×Dic₆	C₂²×C₃²	1	4	yes	complemented
174	C₃×C₄⋊C₄	—	3	32	no	—
175	C₃×C₄⋊C₄	—	3	16	no	—
176	C₃×C₂²⋊C₄	—	3	32	no	—
177	#217	C₂²×C₃²	1	8	yes	—
178	C₄⋊Dic₃	C₂²×C₃²	1	4	yes	complemented
179	Dic₃⋊C₄	C₂²×C₃²	1	8	yes	complemented
180	C₂²×C₃²	—	2	16	no	—
181	C₂²×C₃²	—	2	64	no	—
182	C₂²×C₃²	—	2	16	no	—
183	C₂²×C₃²	—	2	8	no	—
184	C₂²×C₃²	—	2	32	no	—
185	C₂²×C₃²	—	2	2	no	—
186	C₂²×C₃²	—	2	2	no	—
187	C₂²×C₃²	—	2	8	no	—
188	C₂²×C₃²	—	2	8	no	—
189	C₂²×C₃²	—	2	4	no	—
190	C₂²×C₃²	—	2	8	no	—
191	C₂²×C₃²	—	2	16	no	—
192	C₂²×C₃²	—	2	8	no	—
193	C₂²×C₃²	—	2	8	no	—
194	C₂²×C₃²	C₂×Dic₆	1	2	yes	—
195	C₂²×C₃²	C₂×Dic₆	1	4	yes	complemented
196	C₂²×C₃²	#235	1	2	yes	—
197	C₂²×C₃²	C₂×#67	1	2	yes	—
198	C₂²×C₃²	C₂×C₃×D₄	1	8	yes	—
199	C₂²×C₃²	C₂×C₃×Q₈	1	8	yes	—
200	C₂²×C₃²	C₂×C₃×Q₈	1	16	yes	complemented
201	C₂²×C₃²	C₃×#41	1	8	yes	—
202	C₂²×C₃²	C₂³×D₃	1	1	yes	characteristic
203	C₂²×C₃²	C₂⁴×C₃	1	4	yes	—
204	C₃²×C₄	—	2	16	no	—
205	C₃²×C₄	—	2	2	no	—
206	C₃²×C₄	—	2	8	no	—
207	C₃²×C₄	—	2	16	no	—
208	C₃²×C₄	—	6	4	no	—
209	C₃²×C₄	—	6	4	no	—
210	C₃²×C₄	C₂×#67	1	4	yes	—
211	C₃²×C₄	C₂×C₃×D₄	1	16	yes	—
212	C₃×Dic₃	—	2	16	no	—
213	C₃×Dic₃	—	2	16	no	—
214	C₂²×Q₈	—	3	1	no	—
215	C₂³×C₄	C₃²×D₃	1	1	yes	characteristic
216	C₂²⋊Q₈	—	3	8	no	—
217	C₂×C₄⋊C₄	—	3	2	no	—
218	C₂×C₄⋊C₄	—	3	1	no	—
219	C₂×C₂²⋊C₄	—	3	2	no	—
220	C₃³	C₂×C₂²⋊Q₈	1	1	yes	characteristic, complemented, Sylow
221	C₂³×C₃	—	2	16	no	—
222	C₂³×C₃	—	2	16	no	—
223	C₂³×C₃	—	2	8	no	—
224	C₂³×C₃	—	2	8	no	—
225	C₂³×C₃	—	2	2	no	—
226	C₂³×C₃	—	2	2	no	—
227	C₂³×C₃	—	2	16	no	—
228	C₂³×C₃	—	2	8	no	—
229	C₂³×C₃	—	2	4	no	—
230	C₂³×C₃	C₃×Dic₆	1	16	yes	complemented
231	C₂³×C₃	C₃²×Q₈	1	4	yes	complemented
232	C₂³×C₃	C₂²×C₃×D₃	1	8	yes	—
233	C₂³×C₃	C₂²×C₃×D₃	1	4	yes	—
234	C₂³×C₃	C₂³×C₃²	1	2	yes	—
235	C₂³×C₃	C₂³×C₃²	1	1	yes	characteristic
236	C₃×Q₈	—	6	32	no	—
237	C₂×C₃×C₄	—	2	16	no	—
238	C₂×C₃×C₄	—	2	64	no	—
239	C₂×C₃×C₄	—	2	8	no	—
240	C₂×C₃×C₄	—	2	2	no	—
241	C₂×C₃×C₄	—	2	32	no	—
242	C₂×C₃×C₄	—	2	8	no	—
243	C₂×C₃×C₄	—	2	16	no	—
244	C₂×C₃×C₄	—	2	8	no	—
245	C₂×C₃×C₄	—	2	8	no	—
246	C₂×C₃×C₄	—	3	16	no	—
247	C₂×C₃×C₄	—	3	16	no	—
248	C₂×C₃×C₄	—	6	16	no	—
249	C₂×C₃×C₄	—	6	16	no	—
250	C₂×C₃×C₄	C₃×#67	1	16	yes	—
251	C₂×C₃×C₄	C₃²×D₄	1	4	yes	—
252	C₂×C₃×C₄	C₂²×C₃×D₃	1	8	yes	—
253	C₂×C₃×C₄	C₂²×C₃×D₃	1	8	yes	—
254	C₂×C₃×C₄	C₂³×C₃²	1	2	yes	—
255	C₂×C₃×C₄	C₂³×C₃²	1	2	yes	—
256	C₂×Dic₃	—	2	4	no	—
257	C₂×Dic₃	—	2	4	no	—
258	C₂×Dic₃	C₂³×C₃²	1	4	yes	—
259	C₂×Dic₃	C₂³×C₃²	1	4	yes	—
260	Dic₆	—	2	8	no	—
261	C₂×C₃²	—	2	32	no	—
262	C₂×C₃²	—	2	4	no	—
263	C₂×C₃²	—	2	16	no	—
264	C₂×C₃²	—	2	16	no	—
265	C₂×C₃²	—	2	4	no	—
266	C₂×C₃²	—	2	4	no	—
267	C₂×C₃²	—	2	4	no	—
268	C₂×C₃²	#924	1	4	yes	direct product factor
269	C₂×C₃²	C₃×C₂²⋊Q₈	1	16	yes	complemented
270	C₂×C₃²	C₂²×Dic₆	1	1	yes	characteristic
271	C₂×C₃²	C₂×#235	1	1	yes	characteristic
272	C₂×C₃²	C₂²×#67	1	1	yes	characteristic
273	C₂×C₃²	C₂²×C₃×D₄	1	4	yes	—
274	C₂×C₃²	C₂²×C₃×Q₈	1	4	yes	—
275	C₂×C₃²	C₂×C₃×#41	1	4	yes	—
276	C₂⁴	C₂×C₃²×D₃	1	1	yes	characteristic
277	C₂×Q₈	—	3	4	no	—
278	C₂×Q₈	—	6	4	no	—
279	C₂²×C₄	—	2	4	no	—
280	C₂²×C₄	—	3	2	no	—
281	C₂²×C₄	—	3	2	no	—
282	C₂²×C₄	C₂×C₃²×D₃	1	1	yes	characteristic
283	C₂²×C₄	C₂×C₃²×D₃	1	4	yes	—
284	C₂²×C₄	C₂×C₃²×D₃	1	1	yes	characteristic
285	C₄⋊C₄	—	3	8	no	—
286	C₄⋊C₄	—	3	4	no	—
287	C₂²⋊C₄	—	3	8	no	—
288	C₂²×C₃	—	2	16	no	—
289	C₂²×C₃	—	2	64	no	—
290	C₂²×C₃	—	2	16	no	—
291	C₂²×C₃	—	2	32	no	—
292	C₂²×C₃	—	2	8	no	—
293	C₂²×C₃	—	2	8	no	—
294	C₂²×C₃	—	2	2	no	—
295	C₂²×C₃	—	2	2	no	—
296	C₂²×C₃	—	2	8	no	—
297	C₂²×C₃	—	2	4	no	—
298	C₂²×C₃	—	2	8	no	—
299	C₂²×C₃	—	2	16	no	—
300	C₂²×C₃	—	2	8	no	—
301	C₂²×C₃	—	2	8	no	—
302	C₂²×C₃	C₂×C₃×Dic₆	1	8	yes	—
303	C₂²×C₃	C₂×C₃×Dic₆	1	16	yes	complemented
304	C₂²×C₃	C₃×#235	1	8	yes	—
305	C₂²×C₃	C₂×C₃×#67	1	8	yes	—
306	C₂²×C₃	C₂×C₃²×D₄	1	2	yes	—
307	C₂²×C₃	C₂×C₃²×Q₈	1	2	yes	—
308	C₂²×C₃	C₂×C₃²×Q₈	1	4	yes	complemented
309	C₂²×C₃	C₃²×#41	1	2	yes	—
310	C₂²×C₃	C₂³×C₃×D₃	1	4	yes	—
311	C₂²×C₃	C₂⁴×C₃²	1	1	yes	characteristic
312	C₃×C₄	—	2	16	no	—
313	C₃×C₄	—	2	8	no	—
314	C₃×C₄	—	2	2	no	—
315	C₃×C₄	—	2	16	no	—
316	C₃×C₄	—	6	16	no	—
317	C₃×C₄	—	6	16	no	—
318	C₃×C₄	C₂×C₃×#67	1	16	yes	—
319	C₃×C₄	C₂×C₃²×D₄	1	4	yes	—
320	Dic₃	—	2	4	no	—
321	Dic₃	—	2	4	no	—
322	C₃²	—	2	4	no	—
323	C₃²	C₂×#924	1	1	yes	characteristic, direct product factor
324	C₃²	C₂×C₃×C₂²⋊Q₈	1	4	yes	complemented
325	C₂³	—	2	2	no	—
326	C₂³	—	2	2	no	—
327	C₂³	C₃²×Dic₆	1	4	yes	complemented
328	C₂³	C₂²×C₃²×D₃	1	2	yes	—
329	C₂³	C₂²×C₃²×D₃	1	1	yes	characteristic
330	Q₈	—	6	8	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	8	no	—
333	C₂×C₄	—	3	4	no	—
334	C₂×C₄	—	3	4	no	—
335	C₂×C₄	—	6	4	no	—
336	C₂×C₄	—	6	4	no	—
337	C₂×C₄	C₃²×#67	1	4	yes	—
338	C₂×C₄	C₂²×C₃²×D₃	1	2	yes	—
339	C₂×C₄	C₂²×C₃²×D₃	1	2	yes	—
340	C₂×C₃	—	2	32	no	—
341	C₂×C₃	—	2	16	no	—
342	C₂×C₃	—	2	4	no	—
343	C₂×C₃	—	2	16	no	—
344	C₂×C₃	—	2	4	no	—
345	C₂×C₃	—	2	4	no	—
346	C₂×C₃	—	2	4	no	—
347	C₂×C₃	C₃×#924	1	16	yes	direct product factor
348	C₂×C₃	C₃²×C₂²⋊Q₈	1	4	yes	complemented
349	C₂×C₃	C₂²×C₃×Dic₆	1	4	yes	—
350	C₂×C₃	C₂×C₃×#235	1	4	yes	—
351	C₂×C₃	C₂²×C₃×#67	1	4	yes	—
352	C₂×C₃	C₂²×C₃²×D₄	1	1	yes	characteristic
353	C₂×C₃	C₂²×C₃²×Q₈	1	1	yes	characteristic
354	C₂×C₃	C₂×C₃²×#41	1	1	yes	characteristic
355	C₂²	—	2	8	no	—
356	C₂²	—	2	2	no	—
357	C₂²	—	2	2	no	—
358	C₂²	C₂×C₃²×Dic₆	1	2	yes	—
359	C₂²	C₂×C₃²×Dic₆	1	4	yes	complemented
360	C₂²	C₃²×#235	1	2	yes	—
361	C₂²	C₂×C₃²×#67	1	2	yes	—
362	C₂²	C₂³×C₃²×D₃	1	1	yes	characteristic
363	C₄	—	2	2	no	—
364	C₄	—	6	4	no	—
365	C₄	—	6	4	no	—
366	C₄	C₂×C₃²×#67	1	4	yes	—
367	C₃	—	2	4	no	—
368	C₃	C₂×C₃×#924	1	4	yes	direct product factor
369	C₃	C₂×C₃²×C₂²⋊Q₈	1	1	yes	characteristic, complemented
370	C₂	—	2	4	no	—
371	C₂	C₃²×#924	1	4	yes	direct product factor
372	C₂	C₂²×C₃²×Dic₆	1	1	yes	characteristic
373	C₂	C₂×C₃²×#235	1	1	yes	characteristic
374	C₂	C₂²×C₃²×#67	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₂²×C₃²×Dic₆	C₂	semidirect
4. C₂×C₃²×C₄⋊Dic₃	C₂	semidirect
5. C₃²×#924	C₂	direct (N × H)
6. C₂×C₃²×Dic₃⋊C₄	C₂	semidirect
8. C₂×C₃×#924	C₃	direct (N × H)
17. C₂×C₃²×Dic₆	C₂²	semidirect
19. C₃²×C₄⋊Dic₃	C₂²	semidirect
20. C₃²×Dic₃⋊C₄	C₂²	semidirect
25. C₂²×C₃×Dic₆	C₂×C₃	semidirect
31. C₂×C₃×C₄⋊Dic₃	C₂×C₃	semidirect
32. C₃×#924	C₂×C₃	direct (N × H)
33. C₂×C₃×Dic₃⋊C₄	C₂×C₃	semidirect
36. C₂³×C₃³	Q₈	semidirect
50. C₂×#924	C₃²	direct (N × H)
73. C₂×C₃×Dic₆	C₂²×C₃	semidirect
78. C₃×C₄⋊Dic₃	C₂²×C₃	semidirect
79. C₃×Dic₃⋊C₄	C₂²×C₃	semidirect
85. C₂²×C₃³	C₂×Q₈	semidirect
96. C₂²×Dic₆	C₂×C₃²	semidirect
102. C₂×C₄⋊Dic₃	C₂×C₃²	semidirect
103. #924	C₂×C₃²	direct (N × H)
104. C₂×Dic₃⋊C₄	C₂×C₃²	semidirect
114. C₂³×C₃²	Dic₆	semidirect
115. C₂³×C₃²	C₃×Q₈	semidirect
147. C₂×C₃³	C₂²⋊Q₈	semidirect
173. C₂×Dic₆	C₂²×C₃²	semidirect
178. C₄⋊Dic₃	C₂²×C₃²	semidirect
179. Dic₃⋊C₄	C₂²×C₃²	semidirect
195. C₂²×C₃²	C₂×Dic₆	semidirect
200. C₂²×C₃²	C₂×C₃×Q₈	semidirect
220. C₃³	C₂×C₂²⋊Q₈	semidirect
230. C₂³×C₃	C₃×Dic₆	semidirect
231. C₂³×C₃	C₃²×Q₈	semidirect
268. C₂×C₃²	#924	direct (N × H)
269. C₂×C₃²	C₃×C₂²⋊Q₈	semidirect
303. C₂²×C₃	C₂×C₃×Dic₆	semidirect
308. C₂²×C₃	C₂×C₃²×Q₈	semidirect
323. C₃²	C₂×#924	direct (N × H)
324. C₃²	C₂×C₃×C₂²⋊Q₈	semidirect
327. C₂³	C₃²×Dic₆	semidirect
347. C₂×C₃	C₃×#924	direct (N × H)
348. C₂×C₃	C₃²×C₂²⋊Q₈	semidirect
359. C₂²	C₂×C₃²×Dic₆	semidirect
368. C₃	C₂×C₃×#924	direct (N × H)
369. C₃	C₂×C₃²×C₂²⋊Q₈	semidirect
371. C₂	C₃²×#924	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₃³×C₄	2
C₂²×C₃²×Dic₆	2
C₂×C₃²×#217	2
C₂×C₃²×C₄⋊Dic₃	2
C₃²×#924	2
C₂×C₃²×Dic₃⋊C₄	2
C₂×C₃²×C₂²⋊Q₈	3
C₂×C₃×#924	3

Subgroups — C2×C32×#924 #13179161

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃²×#924 #13179161