Subgroups — C₃×D₄×#634 #13179287

Order 1728.

2056 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×#634	C₂	1	2	yes	maximal, complemented
2	C₃³×C₄×D₄	C₂	1	1	yes	maximal, characteristic
3	C₃×D₄×C₃⋊Dic₃	C₂	1	2	yes	maximal
4	C₃×#64133	C₂	1	2	yes	maximal, complemented
5	C₃×#64097	C₂	1	2	yes	maximal, complemented
6	C₃×#64087	C₂	1	4	yes	maximal, complemented
7	C₃×#64078	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₄×#634	C₂	1	1	yes	maximal, characteristic, complemented
9	D₄×#634	C₃	1	1	yes	maximal, characteristic, direct product factor
10	C₃×D₄×Dic₆	—	3	4	no	maximal
11	C₂×C₃³×D₄	C₂²	1	1	yes	characteristic
12	C₂²×C₃³×C₄	C₂²	1	2	yes	—
13	C₂²×C₃×C₃⋊Dic₃	C₂²	1	4	yes	—
14	C₂×C₃×#634	—	2	8	no	—
15	C₂×C₃×#634	C₂²	1	2	yes	—
16	C₂×C₃×#634	C₂²	1	4	yes	—
17	C₂×C₃×#634	C₂²	1	1	yes	characteristic
18	C₃³×C₄⋊C₄	C₂²	1	1	yes	characteristic
19	C₃³×C₂²⋊C₄	C₂²	1	2	yes	—
20	C₃³×C₄²	C₂²	1	1	yes	characteristic
21	C₃×#3757	C₂²	1	4	yes	—
22	C₃×C₄⋊(C₃⋊Dic₃)	C₂²	1	1	yes	characteristic
23	C₃×C₄⋊(C₃⋊Dic₃)	C₂²	1	2	yes	—
24	C₃×C₄⋊(C₃⋊Dic₃)	C₂²	1	2	yes	—
25	C₃×#3750	C₂²	1	2	yes	—
26	C₃×#3750	C₂²	1	4	yes	—
27	C₃×C₄×C₃⋊Dic₃	C₂²	1	2	yes	—
28	C₂²×#634	C₂×C₃	1	2	yes	complemented
29	C₂²×C₃×Dic₆	—	3	8	no	—
30	C₃²×C₄×D₄	—	2	4	no	—
31	C₃²×C₄×D₄	D₃	1	4	yes	—
32	C₃²×C₄×D₄	C₂×C₃	1	1	yes	characteristic
33	D₄×C₃⋊Dic₃	C₂×C₃	1	2	yes	—
34	#64133	C₂×C₃	1	2	yes	complemented
35	#64097	C₂×C₃	1	2	yes	complemented
36	#64087	C₂×C₃	1	4	yes	complemented
37	#64078	C₂×C₃	1	1	yes	characteristic, complemented
38	C₄×#634	C₂×C₃	1	1	yes	characteristic, complemented
39	C₃×D₄×Dic₃	—	3	8	no	—
40	C₃×#924	—	3	8	no	—
41	C₃×#888	—	3	8	no	—
42	C₃×#878	—	3	16	no	—
43	C₃×#869	—	3	4	no	—
44	C₃×C₄×Dic₆	—	3	4	no	—
45	C₂³×C₃³	C₂³	1	2	yes	—
46	C₃³×D₄	Q₈	1	4	yes	complemented
47	C₂×C₃³×C₄	—	2	4	no	—
48	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
49	C₂×C₃³×C₄	C₂³	1	2	yes	—
50	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
51	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
52	C₂×C₃×C₃⋊Dic₃	—	2	8	no	—
53	C₂×C₃×C₃⋊Dic₃	C₂³	1	2	yes	—
54	C₂×C₃×C₃⋊Dic₃	C₂³	1	4	yes	—
55	C₂×C₃×C₃⋊Dic₃	C₂³	1	2	yes	—
56	C₃×#634	—	2	4	no	—
57	C₃×#634	—	2	8	no	—
58	C₃×#634	D₄	1	4	yes	direct product factor
59	C₃×D₄×Q₈	—	9	1	no	—
60	D₄×Dic₆	—	3	4	no	—
61	C₂×C₃²×D₄	—	2	4	no	—
62	C₂×C₃²×D₄	C₂×D₃	1	4	yes	—
63	C₂×C₃²×D₄	C₂²×C₃	1	1	yes	characteristic
64	C₂²×C₃²×C₄	—	2	8	no	—
65	C₂²×C₃²×C₄	C₂×D₃	1	8	yes	—
66	C₂²×C₃²×C₄	C₂²×C₃	1	2	yes	—
67	C₂²×C₃⋊Dic₃	C₂²×C₃	1	4	yes	—
68	C₂×#634	—	2	8	no	—
69	C₂×#634	C₂²×C₃	1	2	yes	—
70	C₂×#634	C₂²×C₃	1	4	yes	—
71	C₂×#634	C₂²×C₃	1	1	yes	characteristic
72	C₂²×C₃×Dic₃	—	3	16	no	—
73	C₂×C₃×Dic₆	—	3	4	no	—
74	C₂×C₃×Dic₆	—	3	16	no	—
75	C₂×C₃×Dic₆	—	3	8	no	—
76	C₂×C₃×Dic₆	—	6	32	no	—
77	C₃²×C₄⋊C₄	—	2	4	no	—
78	C₃²×C₄⋊C₄	C₂×D₃	1	4	yes	—
79	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
80	C₃²×C₂²⋊C₄	—	2	8	no	—
81	C₃²×C₂²⋊C₄	C₂×D₃	1	8	yes	—
82	C₃²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
83	C₃²×C₄²	—	2	4	no	—
84	C₃²×C₄²	C₂×D₃	1	4	yes	—
85	C₃²×C₄²	C₂²×C₃	1	1	yes	characteristic
86	#3757	C₂²×C₃	1	4	yes	—
87	C₄⋊(C₃⋊Dic₃)	C₂²×C₃	1	1	yes	characteristic
88	C₄⋊(C₃⋊Dic₃)	C₂²×C₃	1	2	yes	—
89	C₄⋊(C₃⋊Dic₃)	C₂²×C₃	1	2	yes	—
90	#3750	C₂²×C₃	1	2	yes	—
91	#3750	C₂²×C₃	1	4	yes	—
92	C₄×C₃⋊Dic₃	C₂²×C₃	1	2	yes	—
93	C₃×#217	—	3	16	no	—
94	C₃×C₄⋊Dic₃	—	3	8	no	—
95	C₃×C₄⋊Dic₃	—	3	8	no	—
96	C₃×C₄⋊Dic₃	—	3	4	no	—
97	C₃×Dic₃⋊C₄	—	3	8	no	—
98	C₃×Dic₃⋊C₄	—	3	16	no	—
99	C₃×C₄×Dic₃	—	3	8	no	—
100	C₂²×C₃³	—	2	2	no	—
101	C₂²×C₃³	—	2	2	no	—
102	C₂²×C₃³	C₂×Q₈	1	4	yes	complemented
103	C₂²×C₃³	C₂⁴	1	1	yes	characteristic
104	C₃³×C₄	—	2	2	no	—
105	C₃³×C₄	—	2	1	no	—
106	C₃³×C₄	C₂×D₄	1	2	yes	—
107	C₃³×C₄	C₂×Q₈	1	2	yes	complemented
108	C₃×C₃⋊Dic₃	—	2	4	no	—
109	C₃×C₃⋊Dic₃	—	2	2	no	—
110	C₃×C₃⋊Dic₃	C₂×D₄	1	4	yes	—
111	C₂²×C₃×Q₈	—	9	2	no	—
112	C₂²×Dic₆	—	3	8	no	—
113	C₃×C₄⋊Q₈	—	9	2	no	—
114	C₃×C₄⋊Q₈	—	9	1	no	—
115	C₃×C₂²⋊Q₈	—	9	2	no	—
116	C₃×C₂²⋊Q₈	—	9	4	no	—
117	C₃×C₄×Q₈	—	9	1	no	—
118	C₃×C₄×D₄	—	2	4	no	—
119	C₃×C₄×D₄	—	9	2	no	—
120	C₃×C₄×D₄	C₃×D₃	1	4	yes	—
121	C₃×C₄×D₄	C₃⋊D₃	1	1	yes	characteristic
122	D₄×Dic₃	—	3	8	no	—
123	#924	—	3	8	no	—
124	#888	—	3	8	no	—
125	#878	—	3	16	no	—
126	#869	—	3	4	no	—
127	C₄×Dic₆	—	3	4	no	—
128	C₂³×C₃²	—	2	8	no	—
129	C₂³×C₃²	C₂²×D₃	1	8	yes	—
130	C₂³×C₃²	C₂³×C₃	1	2	yes	—
131	C₃²×D₄	—	2	16	no	—
132	C₃²×D₄	Dic₆	1	16	yes	complemented
133	C₃²×D₄	C₃×Q₈	1	4	yes	complemented
134	C₂×C₃²×C₄	—	2	4	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	8	no	—
139	C₂×C₃²×C₄	—	2	16	no	—
140	C₂×C₃²×C₄	—	4	16	no	—
141	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
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	C₂³×C₃	1	1	yes	characteristic
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×C₃⋊Dic₃	—	2	8	no	—
150	C₂×C₃⋊Dic₃	C₂³×C₃	1	2	yes	—
151	C₂×C₃⋊Dic₃	C₂³×C₃	1	4	yes	—
152	C₂×C₃⋊Dic₃	C₂³×C₃	1	2	yes	—
153	#634	—	2	4	no	—
154	#634	—	2	8	no	—
155	#634	C₃×D₄	1	4	yes	direct product factor
156	C₂×C₃×Dic₃	—	3	8	no	—
157	C₂×C₃×Dic₃	—	3	8	no	—
158	C₂×C₃×Dic₃	—	3	16	no	—
159	C₂×C₃×Dic₃	—	6	32	no	—
160	C₃×Dic₆	—	3	16	no	—
161	C₃×Dic₆	—	6	32	no	—
162	C₃×Dic₆	—	6	16	no	—
163	D₄×Q₈	—	9	1	no	Sylow
164	C₂×C₃³	—	2	4	no	—
165	C₂×C₃³	C₂²×D₄	1	1	yes	characteristic
166	C₂×C₃³	C₂²×Q₈	1	1	yes	characteristic
167	C₂×C₃³	2₋¹⁺⁴	1	1	yes	characteristic
168	C₂×C₃×Q₈	—	9	1	no	—
169	C₂×C₃×Q₈	—	9	4	no	—
170	C₂×C₃×Q₈	—	9	2	no	—
171	C₂×C₃×Q₈	—	18	8	no	—
172	C₂×C₃×D₄	—	2	4	no	—
173	C₂×C₃×D₄	C₂×C₃×D₃	1	4	yes	—
174	C₂×C₃×D₄	C₂×C₃⋊D₃	1	1	yes	characteristic
175	C₂²×C₃×C₄	—	2	8	no	—
176	C₂²×C₃×C₄	—	9	4	no	—
177	C₂²×C₃×C₄	C₂×C₃×D₃	1	8	yes	—
178	C₂²×C₃×C₄	C₂×C₃⋊D₃	1	2	yes	—
179	C₂²×Dic₃	—	3	16	no	—
180	C₂×Dic₆	—	3	4	no	—
181	C₂×Dic₆	—	3	8	no	—
182	C₂×Dic₆	—	3	16	no	—
183	C₂×Dic₆	—	6	32	no	—
184	C₃×C₄⋊C₄	—	2	4	no	—
185	C₃×C₄⋊C₄	—	9	2	no	—
186	C₃×C₄⋊C₄	—	9	4	no	—
187	C₃×C₄⋊C₄	—	9	2	no	—
188	C₃×C₄⋊C₄	—	9	1	no	—
189	C₃×C₄⋊C₄	—	9	2	no	—
190	C₃×C₄⋊C₄	C₂×C₃×D₃	1	4	yes	—
191	C₃×C₄⋊C₄	C₂×C₃⋊D₃	1	1	yes	characteristic
192	C₃×C₂²⋊C₄	—	2	8	no	—
193	C₃×C₂²⋊C₄	—	9	4	no	—
194	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	8	yes	—
195	C₃×C₂²⋊C₄	C₂×C₃⋊D₃	1	2	yes	—
196	C₃×C₄²	—	2	4	no	—
197	C₃×C₄²	—	9	2	no	—
198	C₃×C₄²	C₂×C₃×D₃	1	4	yes	—
199	C₃×C₄²	C₂×C₃⋊D₃	1	1	yes	characteristic
200	#217	—	3	16	no	—
201	C₄⋊Dic₃	—	3	4	no	—
202	C₄⋊Dic₃	—	3	8	no	—
203	C₄⋊Dic₃	—	3	8	no	—
204	Dic₃⋊C₄	—	3	8	no	—
205	Dic₃⋊C₄	—	3	16	no	—
206	C₄×Dic₃	—	3	8	no	—
207	C₂²×C₃²	—	2	2	no	—
208	C₂²×C₃²	—	2	2	no	—
209	C₂²×C₃²	—	2	4	no	—
210	C₂²×C₃²	—	2	16	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	C₂×Dic₆	1	16	yes	complemented
216	C₂²×C₃²	C₂×C₃×Q₈	1	4	yes	complemented
217	C₂²×C₃²	C₂³×D₃	1	4	yes	—
218	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
219	C₃²×C₄	—	2	2	no	—
220	C₃²×C₄	—	2	1	no	—
221	C₃²×C₄	—	2	8	no	—
222	C₃²×C₄	—	2	8	no	—
223	C₃²×C₄	—	2	8	no	—
224	C₃²×C₄	—	2	4	no	—
225	C₃²×C₄	—	4	4	no	—
226	C₃²×C₄	—	4	8	no	—
227	C₃²×C₄	C₂×Dic₆	1	8	yes	complemented
228	C₃²×C₄	D₃×D₄	1	8	yes	—
229	C₃²×C₄	C₂×C₃×D₄	1	2	yes	—
230	C₃²×C₄	C₂×C₃×Q₈	1	2	yes	complemented
231	C₃⋊Dic₃	—	2	4	no	—
232	C₃⋊Dic₃	—	2	2	no	—
233	C₃⋊Dic₃	C₂×C₃×D₄	1	4	yes	—
234	C₃×Dic₃	—	3	16	no	—
235	C₃×Dic₃	—	6	16	no	—
236	C₃×Dic₃	—	6	8	no	—
237	C₂²×Q₈	—	9	2	no	—
238	C₄⋊Q₈	—	9	2	no	—
239	C₄⋊Q₈	—	9	1	no	—
240	C₂²⋊Q₈	—	9	2	no	—
241	C₂²⋊Q₈	—	9	4	no	—
242	C₄×Q₈	—	9	1	no	—
243	C₄×D₄	—	9	2	no	—
244	C₄×D₄	C₃×C₃⋊D₃	1	1	yes	characteristic
245	C₃³	D₄×Q₈	1	1	yes	characteristic, complemented, Sylow
246	C₂³×C₃	—	2	8	no	—
247	C₂³×C₃	C₂²×C₃×D₃	1	8	yes	—
248	C₂³×C₃	C₂²×C₃⋊D₃	1	2	yes	—
249	C₃×Q₈	—	9	4	no	—
250	C₃×Q₈	—	18	8	no	—
251	C₃×Q₈	—	18	4	no	—
252	C₃×D₄	—	2	16	no	—
253	C₃×D₄	C₃×Dic₆	1	16	yes	complemented
254	C₃×D₄	#634	1	4	yes	direct product factor
255	C₂×C₃×C₄	—	2	16	no	—
256	C₂×C₃×C₄	—	2	4	no	—
257	C₂×C₃×C₄	—	2	4	no	—
258	C₂×C₃×C₄	—	2	4	no	—
259	C₂×C₃×C₄	—	2	4	no	—
260	C₂×C₃×C₄	—	2	8	no	—
261	C₂×C₃×C₄	—	4	16	no	—
262	C₂×C₃×C₄	—	9	2	no	—
263	C₂×C₃×C₄	—	9	2	no	—
264	C₂×C₃×C₄	—	9	4	no	—
265	C₂×C₃×C₄	—	18	8	no	—
266	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
267	C₂×C₃×C₄	C₂²×C₃×D₃	1	8	yes	—
268	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
269	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
270	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
271	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	2	yes	—
272	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
273	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
274	C₂×Dic₃	—	3	8	no	—
275	C₂×Dic₃	—	3	8	no	—
276	C₂×Dic₃	—	3	16	no	—
277	C₂×Dic₃	—	6	32	no	—
278	Dic₆	—	3	16	no	—
279	Dic₆	—	6	32	no	—
280	Dic₆	—	6	16	no	—
281	C₂×C₃²	—	2	4	no	—
282	C₂×C₃²	—	2	4	no	—
283	C₂×C₃²	—	2	4	no	—
284	C₂×C₃²	—	2	4	no	—
285	C₂×C₃²	—	2	16	no	—
286	C₂×C₃²	—	4	16	no	—
287	C₂×C₃²	C₂²×Dic₆	1	4	yes	—
288	C₂×C₃²	C₂×D₃×D₄	1	4	yes	—
289	C₂×C₃²	#1010	1	4	yes	—
290	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
291	C₂×C₃²	C₂²×C₃×Q₈	1	1	yes	characteristic
292	C₂×C₃²	C₃×2₋¹⁺⁴	1	1	yes	characteristic
293	C₂×Q₈	—	9	1	no	—
294	C₂×Q₈	—	9	4	no	—
295	C₂×Q₈	—	9	2	no	—
296	C₂×Q₈	—	18	8	no	—
297	C₂×D₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
298	C₂²×C₄	—	9	4	no	—
299	C₂²×C₄	C₂×C₃×C₃⋊D₃	1	2	yes	—
300	C₄⋊C₄	—	9	2	no	—
301	C₄⋊C₄	—	9	2	no	—
302	C₄⋊C₄	—	9	1	no	—
303	C₄⋊C₄	—	9	4	no	—
304	C₄⋊C₄	—	9	2	no	—
305	C₄⋊C₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
306	C₂²⋊C₄	—	9	4	no	—
307	C₂²⋊C₄	C₂×C₃×C₃⋊D₃	1	2	yes	—
308	C₄²	—	9	2	no	—
309	C₄²	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
310	C₂²×C₃	—	2	8	no	—
311	C₂²×C₃	—	2	8	no	—
312	C₂²×C₃	—	2	2	no	—
313	C₂²×C₃	—	2	2	no	—
314	C₂²×C₃	—	2	4	no	—
315	C₂²×C₃	—	2	16	no	—
316	C₂²×C₃	—	4	8	no	—
317	C₂²×C₃	—	4	8	no	—
318	C₂²×C₃	C₂×C₃×Dic₆	1	16	yes	complemented
319	C₂²×C₃	C₂×#634	1	4	yes	complemented
320	C₂²×C₃	C₂³×C₃×D₃	1	4	yes	—
321	C₂²×C₃	C₂³×C₃⋊D₃	1	1	yes	characteristic
322	C₃×C₄	—	2	8	no	—
323	C₃×C₄	—	2	4	no	—
324	C₃×C₄	—	2	2	no	—
325	C₃×C₄	—	2	1	no	—
326	C₃×C₄	—	2	8	no	—
327	C₃×C₄	—	2	8	no	—
328	C₃×C₄	—	4	8	no	—
329	C₃×C₄	—	4	4	no	—
330	C₃×C₄	—	9	4	no	—
331	C₃×C₄	—	18	4	no	—
332	C₃×C₄	—	18	2	no	—
333	C₃×C₄	C₂×C₃×Dic₆	1	8	yes	complemented
334	C₃×C₄	C₃×D₃×D₄	1	8	yes	—
335	C₃×C₄	C₂×#634	1	2	yes	complemented
336	C₃×C₄	D₄×C₃⋊D₃	1	2	yes	—
337	Dic₃	—	3	16	no	—
338	Dic₃	—	6	16	no	—
339	Dic₃	—	6	8	no	—
340	C₃²	—	2	4	no	—
341	C₃²	D₄×Dic₆	1	4	yes	complemented
342	C₃²	C₃×D₄×Q₈	1	1	yes	characteristic, complemented
343	C₂³	C₂²×C₃×C₃⋊D₃	1	2	yes	—
344	Q₈	—	9	4	no	—
345	Q₈	—	18	8	no	—
346	Q₈	—	18	4	no	—
347	D₄	C₃×#634	1	4	yes	direct product factor
348	C₂×C₄	—	2	4	no	—
349	C₂×C₄	—	9	2	no	—
350	C₂×C₄	—	9	2	no	—
351	C₂×C₄	—	9	4	no	—
352	C₂×C₄	—	18	8	no	—
353	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
354	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	2	yes	—
355	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
356	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
357	C₂×C₃	—	2	16	no	—
358	C₂×C₃	—	2	4	no	—
359	C₂×C₃	—	2	4	no	—
360	C₂×C₃	—	2	4	no	—
361	C₂×C₃	—	2	4	no	—
362	C₂×C₃	—	4	16	no	—
363	C₂×C₃	C₂²×C₃×Dic₆	1	4	yes	—
364	C₂×C₃	C₂×C₃×D₃×D₄	1	4	yes	—
365	C₂×C₃	C₃×#1010	1	4	yes	—
366	C₂×C₃	C₂²×#634	1	1	yes	characteristic
367	C₂×C₃	C₂×D₄×C₃⋊D₃	1	1	yes	characteristic
368	C₂×C₃	#64367	1	1	yes	characteristic
369	C₂²	—	2	2	no	—
370	C₂²	—	2	2	no	—
371	C₂²	C₂×C₃×#634	1	4	yes	complemented
372	C₂²	C₂³×C₃×C₃⋊D₃	1	1	yes	characteristic
373	C₄	—	2	2	no	—
374	C₄	—	2	1	no	—
375	C₄	—	9	4	no	—
376	C₄	—	18	4	no	—
377	C₄	—	18	2	no	—
378	C₄	C₂×C₃×#634	1	2	yes	complemented
379	C₄	C₃×D₄×C₃⋊D₃	1	2	yes	—
380	C₃	—	2	4	no	—
381	C₃	C₃×D₄×Dic₆	1	4	yes	complemented
382	C₃	D₄×#634	1	1	yes	characteristic, direct product factor
383	C₂	—	2	4	no	—
384	C₂	C₂²×C₃×#634	1	1	yes	characteristic
385	C₂	C₂×C₃×D₄×C₃⋊D₃	1	1	yes	characteristic
386	C₂	C₃×#64367	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
prime radical	C₂×C₃³×D₄	C₂²
hypercenter	C₃×C₄×D₄	C₃⋊D₃
hypocenter	C₃²	C₃×D₄×Q₈
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. C₂²×C₃×#634	C₂	semidirect
4. C₃×#64133	C₂	semidirect
5. C₃×#64097	C₂	semidirect
6. C₃×#64087	C₂	semidirect
7. C₃×#64078	C₂	semidirect
8. C₃×C₄×#634	C₂	semidirect
9. D₄×#634	C₃	direct (N × H)
28. C₂²×#634	C₂×C₃	semidirect
34. #64133	C₂×C₃	semidirect
35. #64097	C₂×C₃	semidirect
36. #64087	C₂×C₃	semidirect
37. #64078	C₂×C₃	semidirect
38. C₄×#634	C₂×C₃	semidirect
46. C₃³×D₄	Q₈	semidirect
58. C₃×#634	D₄	direct (N × H)
102. C₂²×C₃³	C₂×Q₈	semidirect
107. C₃³×C₄	C₂×Q₈	semidirect
132. C₃²×D₄	Dic₆	semidirect
133. C₃²×D₄	C₃×Q₈	semidirect
155. #634	C₃×D₄	direct (N × H)
215. C₂²×C₃²	C₂×Dic₆	semidirect
216. C₂²×C₃²	C₂×C₃×Q₈	semidirect
227. C₃²×C₄	C₂×Dic₆	semidirect
230. C₃²×C₄	C₂×C₃×Q₈	semidirect
245. C₃³	D₄×Q₈	semidirect
253. C₃×D₄	C₃×Dic₆	semidirect
254. C₃×D₄	#634	direct (N × H)
318. C₂²×C₃	C₂×C₃×Dic₆	semidirect
319. C₂²×C₃	C₂×#634	semidirect
333. C₃×C₄	C₂×C₃×Dic₆	semidirect
335. C₃×C₄	C₂×#634	semidirect
341. C₃²	D₄×Dic₆	semidirect
342. C₃²	C₃×D₄×Q₈	semidirect
347. D₄	C₃×#634	direct (N × H)
371. C₂²	C₂×C₃×#634	semidirect
378. C₄	C₂×C₃×#634	semidirect
381. C₃	C₃×D₄×Dic₆	semidirect
382. C₃	D₄×#634	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃×#634	2
C₃³×C₄×D₄	2
C₃×D₄×C₃⋊Dic₃	2
C₃×#64133	2
C₃×#64097	2
C₃×#64087	2
C₃×#64078	2
C₃×C₄×#634	2
D₄×#634	3
C₃×D₄×Dic₆	3

Subgroups — C3×D4×#634 #13179287

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₄×#634 #13179287