Subgroups — C₂×C₃×#3058 #10679053

Order 768.

3062 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃×D₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×#131	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#535	C₂	1	2	yes	maximal, complemented
4	C₃×#3058	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₃×#469	C₂	1	4	yes	maximal, complemented
6	C₂×C₃×#466	C₂	1	4	yes	maximal, complemented
7	C₂×C₃×#427	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃×#418	C₂	1	2	yes	maximal, complemented
9	C₂×#3058	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
10	C₂²×C₃×#41	C₂²	1	1	yes	characteristic
11	C₂³×C₃×D₄	C₂²	1	2	yes	—
12	C₂²×C₃×D₈	—	2	8	no	—
13	C₂²×C₃×D₈	C₂²	1	2	yes	—
14	C₂²×C₃×D₈	C₂²	1	2	yes	—
15	C₂²×C₃×D₈	C₂²	1	8	yes	complemented
16	C₂×C₃×#131	—	2	8	no	—
17	C₂×C₃×#131	C₂²	1	8	yes	complemented
18	C₂²×C₃×M₁₆	C₂²	1	1	yes	characteristic
19	C₂²×C₃×M₁₆	C₂²	1	2	yes	complemented
20	C₂³×C₃×C₈	C₂²	1	1	yes	characteristic
21	C₂³×C₃×C₈	C₂²	1	2	yes	complemented
22	C₃×#535	—	2	8	no	—
23	C₃×#535	C₂²	1	16	yes	complemented
24	C₂×C₃×#127	—	2	2	no	—
25	C₂×C₃×#124	—	2	2	no	—
26	C₂×C₃×#121	C₂²	1	8	yes	complemented
27	C₂×C₃×#120	—	2	4	no	—
28	C₂×C₃×#117	C₂²	1	2	yes	—
29	C₃×#469	C₂²	1	32	yes	complemented
30	C₃×#466	C₂²	1	32	yes	complemented
31	C₃×#427	C₂²	1	8	yes	complemented
32	C₂×C₃×#107	C₂²	1	2	yes	complemented
33	C₂×C₃×#106	C₂²	1	2	yes	complemented
34	C₃×#418	C₂²	1	16	yes	complemented
35	C₂×C₃×#102	C₂²	1	8	yes	complemented
36	C₂³×D₈	C₂×C₃	1	1	yes	characteristic, complemented
37	C₂²×#131	C₂×C₃	1	1	yes	characteristic, complemented
38	C₂×#535	C₂×C₃	1	2	yes	complemented
39	#3058	C₂×C₃	1	16	yes	direct product factor
40	C₂×#469	C₂×C₃	1	4	yes	complemented
41	C₂×#466	C₂×C₃	1	4	yes	complemented
42	C₂×#427	C₂×C₃	1	1	yes	characteristic, complemented
43	C₂×#418	C₂×C₃	1	2	yes	complemented
44	C₂⁵×C₃	—	2	2	no	—
45	C₂×C₃×#41	—	2	4	no	—
46	C₂×C₃×#41	—	2	4	no	—
47	C₂×C₃×#41	D₄	1	4	yes	—
48	C₂×C₃×#41	C₂³	1	4	yes	—
49	C₂²×C₃×Q₈	D₄	1	1	yes	characteristic
50	C₂²×C₃×D₄	—	2	8	no	—
51	C₂²×C₃×D₄	—	2	8	no	—
52	C₂²×C₃×D₄	—	2	2	no	—
53	C₂²×C₃×D₄	—	2	4	no	—
54	C₂²×C₃×D₄	—	2	8	no	—
55	C₂²×C₃×D₄	D₄	1	2	yes	—
56	C₂²×C₃×D₄	D₄	1	1	yes	characteristic
57	C₂²×C₃×D₄	C₂³	1	4	yes	—
58	C₂²×C₃×D₄	C₂³	1	8	yes	—
59	C₂³×C₃×C₄	C₂³	1	2	yes	—
60	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
61	C₂×C₃×D₈	—	2	8	no	—
62	C₂×C₃×D₈	—	2	8	no	—
63	C₂×C₃×D₈	—	2	32	no	—
64	C₂×C₃×D₈	C₂³	1	8	yes	—
65	C₂×C₃×D₈	C₂³	1	8	yes	—
66	C₃×#131	—	2	32	no	—
67	C₂×C₃×M₁₆	—	2	4	no	—
68	C₂×C₃×M₁₆	—	2	8	no	—
69	C₂×C₃×M₁₆	C₂³	1	4	yes	—
70	C₂×C₃×M₁₆	C₂³	1	8	yes	complemented
71	C₂²×C₃×C₈	—	2	8	no	—
72	C₂²×C₃×C₈	D₄	1	8	yes	complemented
73	C₂²×C₃×C₈	C₂³	1	2	yes	—
74	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
75	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
76	C₂²×C₃×C₈	C₂³	1	4	yes	—
77	C₂²×C₃×C₈	C₂³	1	8	yes	complemented
78	C₃×#127	—	2	16	no	—
79	C₃×#124	—	2	16	no	—
80	C₃×#121	—	2	16	no	—
81	C₃×#121	C₂³	1	32	yes	complemented
82	C₃×#120	—	2	32	no	—
83	C₃×#117	—	2	4	no	—
84	C₃×#117	C₂³	1	8	yes	—
85	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
86	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
87	C₂×C₃×C₂²⋊C₄	—	2	8	no	—
88	C₂×C₃×C₄²	—	2	2	no	—
89	C₃×#107	C₂³	1	8	yes	complemented
90	C₃×#106	C₂³	1	8	yes	complemented
91	C₃×#102	C₂³	1	32	yes	complemented
92	C₂²×#41	C₂²×C₃	1	1	yes	characteristic
93	C₂³×D₄	C₂²×C₃	1	2	yes	—
94	C₂²×D₈	—	2	8	no	—
95	C₂²×D₈	C₂²×C₃	1	2	yes	—
96	C₂²×D₈	C₂²×C₃	1	2	yes	—
97	C₂²×D₈	C₂²×C₃	1	8	yes	complemented
98	C₂×#131	—	2	8	no	—
99	C₂×#131	C₂²×C₃	1	8	yes	complemented
100	C₂²×M₁₆	C₂²×C₃	1	1	yes	characteristic
101	C₂²×M₁₆	C₂²×C₃	1	2	yes	complemented
102	C₂³×C₈	C₂²×C₃	1	1	yes	characteristic
103	C₂³×C₈	C₂²×C₃	1	2	yes	complemented
104	#535	—	2	8	no	—
105	#535	C₂²×C₃	1	16	yes	complemented
106	C₂×#127	—	2	2	no	—
107	C₂×#124	—	2	2	no	—
108	C₂×#121	C₂²×C₃	1	8	yes	complemented
109	C₂×#120	—	2	4	no	—
110	C₂×#117	C₂²×C₃	1	2	yes	—
111	#469	C₂²×C₃	1	32	yes	complemented
112	#466	C₂²×C₃	1	32	yes	complemented
113	#427	C₂²×C₃	1	8	yes	complemented
114	C₂×#107	C₂²×C₃	1	2	yes	complemented
115	C₂×#106	C₂²×C₃	1	2	yes	complemented
116	#418	C₂²×C₃	1	16	yes	complemented
117	C₂×#102	C₂²×C₃	1	8	yes	complemented
118	C₂⁴×C₃	—	2	4	no	—
119	C₂⁴×C₃	—	2	8	no	—
120	C₂⁴×C₃	—	4	8	no	—
121	C₂⁴×C₃	—	8	8	no	—
122	C₂⁴×C₃	C₂×D₄	1	2	yes	—
123	C₂⁴×C₃	C₂×D₄	1	1	yes	characteristic
124	C₃×#41	—	2	16	no	—
125	C₃×#41	—	2	8	no	—
126	C₃×#41	—	2	8	no	—
127	C₂×C₃×Q₈	—	2	4	no	—
128	C₂×C₃×Q₈	C₂×D₄	1	4	yes	—
129	C₂×C₃×D₄	—	2	8	no	—
130	C₂×C₃×D₄	—	2	32	no	—
131	C₂×C₃×D₄	—	2	4	no	—
132	C₂×C₃×D₄	—	2	8	no	—
133	C₂×C₃×D₄	—	2	16	no	—
134	C₂×C₃×D₄	—	2	4	no	—
135	C₂×C₃×D₄	—	2	8	no	—
136	C₂×C₃×D₄	—	2	8	no	—
137	C₂×C₃×D₄	—	2	16	no	—
138	C₂×C₃×D₄	—	4	8	no	—
139	C₂×C₃×D₄	—	4	16	no	—
140	C₂×C₃×D₄	—	8	16	no	—
141	C₂×C₃×D₄	C₂×D₄	1	8	yes	—
142	C₂×C₃×D₄	C₂×D₄	1	4	yes	—
143	C₂×C₃×D₄	C₂⁴	1	8	yes	—
144	C₂²×C₃×C₄	—	2	4	no	—
145	C₂²×C₃×C₄	—	2	4	no	—
146	C₂²×C₃×C₄	—	2	4	no	—
147	C₂²×C₃×C₄	C₂×D₄	1	4	yes	—
148	C₂²×C₃×C₄	C₂×D₄	1	2	yes	—
149	C₂²×C₃×C₄	C₂×D₄	1	2	yes	—
150	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₃×C₄	C₂×D₄	1	4	yes	—
152	C₂²×C₃×C₄	#41	1	4	yes	—
153	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
154	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
155	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
156	C₃×D₈	—	2	16	no	—
157	C₃×D₈	—	2	16	no	—
158	C₃×M₁₆	—	2	8	no	—
159	C₃×M₁₆	—	2	16	no	—
160	C₂×C₃×C₈	—	2	4	no	—
161	C₂×C₃×C₈	—	2	16	no	—
162	C₂×C₃×C₈	C₂×D₄	1	4	yes	—
163	C₂×C₃×C₈	C₂×D₄	1	4	yes	—
164	C₂×C₃×C₈	C₂×D₄	1	16	yes	complemented
165	C₂×C₃×C₈	C₂⁴	1	4	yes	—
166	C₂×C₃×C₈	C₂⁴	1	2	yes	—
167	C₂×C₃×C₈	C₂⁴	1	2	yes	—
168	C₃×C₄⋊C₄	—	2	4	no	—
169	C₃×C₄⋊C₄	C₂⁴	1	8	yes	—
170	C₃×C₂²⋊C₄	—	2	8	no	—
171	C₃×C₂²⋊C₄	—	2	32	no	—
172	C₃×C₄²	—	2	8	no	—
173	C₂⁵	—	2	2	no	—
174	C₂×#41	—	2	4	no	—
175	C₂×#41	—	2	4	no	—
176	C₂×#41	C₃×D₄	1	4	yes	—
177	C₂×#41	C₂³×C₃	1	4	yes	—
178	C₂²×Q₈	C₃×D₄	1	1	yes	characteristic
179	C₂²×D₄	—	2	8	no	—
180	C₂²×D₄	—	2	8	no	—
181	C₂²×D₄	—	2	2	no	—
182	C₂²×D₄	—	2	4	no	—
183	C₂²×D₄	—	2	8	no	—
184	C₂²×D₄	C₃×D₄	1	2	yes	—
185	C₂²×D₄	C₃×D₄	1	1	yes	characteristic
186	C₂²×D₄	C₂³×C₃	1	4	yes	—
187	C₂²×D₄	C₂³×C₃	1	8	yes	—
188	C₂³×C₄	C₂³×C₃	1	2	yes	—
189	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
190	C₂×D₈	—	2	8	no	—
191	C₂×D₈	—	2	8	no	—
192	C₂×D₈	—	2	32	no	—
193	C₂×D₈	C₂³×C₃	1	8	yes	—
194	C₂×D₈	C₂³×C₃	1	8	yes	—
195	#131	—	2	32	no	—
196	C₂×M₁₆	—	2	4	no	—
197	C₂×M₁₆	—	2	8	no	—
198	C₂×M₁₆	C₂³×C₃	1	4	yes	—
199	C₂×M₁₆	C₂³×C₃	1	8	yes	complemented
200	C₂²×C₈	—	2	8	no	—
201	C₂²×C₈	C₃×D₄	1	8	yes	complemented
202	C₂²×C₈	C₂³×C₃	1	2	yes	—
203	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
204	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
205	C₂²×C₈	C₂³×C₃	1	4	yes	—
206	C₂²×C₈	C₂³×C₃	1	8	yes	complemented
207	#127	—	2	16	no	—
208	#124	—	2	16	no	—
209	#121	—	2	16	no	—
210	#121	C₂³×C₃	1	32	yes	complemented
211	#120	—	2	32	no	—
212	#117	—	2	4	no	—
213	#117	C₂³×C₃	1	8	yes	—
214	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
215	C₂×C₂²⋊C₄	—	2	2	no	—
216	C₂×C₂²⋊C₄	—	2	8	no	—
217	C₂×C₄²	—	2	2	no	—
218	#107	C₂³×C₃	1	8	yes	complemented
219	#106	C₂³×C₃	1	8	yes	complemented
220	#102	C₂³×C₃	1	32	yes	complemented
221	C₂³×C₃	—	2	4	no	—
222	C₂³×C₃	—	2	4	no	—
223	C₂³×C₃	—	2	8	no	—
224	C₂³×C₃	—	2	8	no	—
225	C₂³×C₃	—	4	16	no	—
226	C₂³×C₃	—	4	8	no	—
227	C₂³×C₃	—	4	16	no	—
228	C₂³×C₃	—	8	16	no	—
229	C₂³×C₃	—	8	32	no	—
230	C₂³×C₃	#121	1	4	yes	—
231	C₂³×C₃	C₂²×D₄	1	4	yes	—
232	C₂³×C₃	C₂²×D₄	1	2	yes	—
233	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
234	C₃×Q₈	—	2	8	no	—
235	C₃×D₄	—	2	16	no	—
236	C₃×D₄	—	2	8	no	—
237	C₃×D₄	—	2	8	no	—
238	C₃×D₄	—	2	8	no	—
239	C₃×D₄	—	4	8	no	—
240	C₃×D₄	—	4	16	no	—
241	C₃×D₄	—	8	32	no	—
242	C₂×C₃×C₄	—	2	4	no	—
243	C₂×C₃×C₄	—	2	8	no	—
244	C₂×C₃×C₄	—	2	4	no	—
245	C₂×C₃×C₄	—	2	4	no	—
246	C₂×C₃×C₄	—	2	8	no	—
247	C₂×C₃×C₄	—	4	8	no	—
248	C₂×C₃×C₄	#121	1	4	yes	—
249	C₂×C₃×C₄	#121	1	8	yes	—
250	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
251	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
252	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
253	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
254	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
255	C₂×C₃×C₄	C₂×#41	1	2	yes	—
256	C₂×C₃×C₄	C₂×#41	1	4	yes	—
257	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
258	C₃×C₈	—	2	4	no	—
259	C₃×C₈	C₂²×D₄	1	4	yes	—
260	C₃×C₈	C₂²×D₄	1	4	yes	—
261	C₂⁴	—	2	4	no	—
262	C₂⁴	—	2	8	no	—
263	C₂⁴	—	4	8	no	—
264	C₂⁴	—	8	8	no	—
265	C₂⁴	C₂×C₃×D₄	1	2	yes	—
266	C₂⁴	C₂×C₃×D₄	1	1	yes	characteristic
267	#41	—	2	16	no	—
268	#41	—	2	8	no	—
269	#41	—	2	8	no	—
270	C₂×Q₈	—	2	4	no	—
271	C₂×Q₈	C₂×C₃×D₄	1	4	yes	—
272	C₂×D₄	—	2	8	no	—
273	C₂×D₄	—	2	32	no	—
274	C₂×D₄	—	2	4	no	—
275	C₂×D₄	—	2	8	no	—
276	C₂×D₄	—	2	16	no	—
277	C₂×D₄	—	2	4	no	—
278	C₂×D₄	—	2	8	no	—
279	C₂×D₄	—	2	8	no	—
280	C₂×D₄	—	2	16	no	—
281	C₂×D₄	—	4	8	no	—
282	C₂×D₄	—	4	16	no	—
283	C₂×D₄	—	8	16	no	—
284	C₂×D₄	C₂×C₃×D₄	1	8	yes	—
285	C₂×D₄	C₂×C₃×D₄	1	4	yes	—
286	C₂×D₄	C₂⁴×C₃	1	8	yes	—
287	C₂²×C₄	—	2	4	no	—
288	C₂²×C₄	—	2	4	no	—
289	C₂²×C₄	—	2	4	no	—
290	C₂²×C₄	C₂×C₃×D₄	1	2	yes	—
291	C₂²×C₄	C₂×C₃×D₄	1	4	yes	—
292	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
293	C₂²×C₄	C₂×C₃×D₄	1	2	yes	—
294	C₂²×C₄	C₂×C₃×D₄	1	4	yes	—
295	C₂²×C₄	C₃×#41	1	4	yes	—
296	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
297	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
298	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
299	D₈	—	2	16	no	—
300	D₈	—	2	16	no	—
301	M₁₆	—	2	8	no	—
302	M₁₆	—	2	16	no	—
303	C₂×C₈	—	2	4	no	—
304	C₂×C₈	—	2	16	no	—
305	C₂×C₈	C₂×C₃×D₄	1	4	yes	—
306	C₂×C₈	C₂×C₃×D₄	1	4	yes	—
307	C₂×C₈	C₂×C₃×D₄	1	16	yes	complemented
308	C₂×C₈	C₂⁴×C₃	1	4	yes	—
309	C₂×C₈	C₂⁴×C₃	1	2	yes	—
310	C₂×C₈	C₂⁴×C₃	1	2	yes	—
311	C₄⋊C₄	—	2	4	no	—
312	C₄⋊C₄	C₂⁴×C₃	1	8	yes	—
313	C₂²⋊C₄	—	2	8	no	—
314	C₂²⋊C₄	—	2	32	no	—
315	C₄²	—	2	8	no	—
316	C₂²×C₃	—	2	8	no	—
317	C₂²×C₃	—	2	4	no	—
318	C₂²×C₃	—	2	4	no	—
319	C₂²×C₃	—	2	8	no	—
320	C₂²×C₃	—	4	8	no	—
321	C₂²×C₃	—	4	8	no	—
322	C₂²×C₃	—	4	16	no	—
323	C₂²×C₃	—	8	32	no	—
324	C₂²×C₃	—	8	16	no	—
325	C₂²×C₃	C₂×#121	1	4	yes	—
326	C₂²×C₃	C₂×#121	1	2	yes	—
327	C₂²×C₃	#576	1	4	yes	—
328	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
329	C₃×C₄	—	2	4	no	—
330	C₃×C₄	—	4	8	no	—
331	C₃×C₄	C₂×#121	1	2	yes	—
332	C₃×C₄	C₂×#121	1	4	yes	—
333	C₃×C₄	C₂³×D₄	1	1	yes	characteristic
334	C₃×C₄	C₂²×#41	1	1	yes	characteristic
335	C₂³	—	2	4	no	—
336	C₂³	—	2	8	no	—
337	C₂³	—	2	4	no	—
338	C₂³	—	2	8	no	—
339	C₂³	—	4	16	no	—
340	C₂³	—	4	16	no	—
341	C₂³	—	4	8	no	—
342	C₂³	—	8	16	no	—
343	C₂³	—	8	32	no	—
344	C₂³	C₃×#121	1	4	yes	—
345	C₂³	C₂²×C₃×D₄	1	4	yes	—
346	C₂³	C₂²×C₃×D₄	1	2	yes	—
347	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
348	Q₈	—	2	8	no	—
349	D₄	—	2	16	no	—
350	D₄	—	2	8	no	—
351	D₄	—	2	8	no	—
352	D₄	—	2	8	no	—
353	D₄	—	4	8	no	—
354	D₄	—	4	16	no	—
355	D₄	—	8	32	no	—
356	C₂×C₄	—	2	4	no	—
357	C₂×C₄	—	2	4	no	—
358	C₂×C₄	—	2	4	no	—
359	C₂×C₄	—	2	8	no	—
360	C₂×C₄	—	2	8	no	—
361	C₂×C₄	—	4	8	no	—
362	C₂×C₄	C₃×#121	1	4	yes	—
363	C₂×C₄	C₃×#121	1	8	yes	—
364	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
365	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
366	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
367	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
368	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
369	C₂×C₄	C₂×C₃×#41	1	2	yes	—
370	C₂×C₄	C₂×C₃×#41	1	4	yes	—
371	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
372	C₈	—	2	4	no	—
373	C₈	C₂²×C₃×D₄	1	4	yes	—
374	C₈	C₂²×C₃×D₄	1	4	yes	—
375	C₂×C₃	—	2	4	no	—
376	C₂×C₃	—	4	4	no	—
377	C₂×C₃	—	8	8	no	—
378	C₂×C₃	#3058	1	4	yes	direct product factor
379	C₂×C₃	C₂²×#121	1	1	yes	characteristic
380	C₂×C₃	C₂×#576	1	2	yes	—
381	C₂²	—	2	4	no	—
382	C₂²	—	2	8	no	—
383	C₂²	—	2	4	no	—
384	C₂²	—	2	8	no	—
385	C₂²	—	4	8	no	—
386	C₂²	—	4	8	no	—
387	C₂²	—	4	16	no	—
388	C₂²	—	8	32	no	—
389	C₂²	—	8	16	no	—
390	C₂²	C₂×C₃×#121	1	4	yes	—
391	C₂²	C₂×C₃×#121	1	2	yes	—
392	C₂²	C₃×#576	1	4	yes	—
393	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
394	C₄	—	2	4	no	—
395	C₄	—	4	8	no	—
396	C₄	C₂×C₃×#121	1	2	yes	—
397	C₄	C₂×C₃×#121	1	4	yes	—
398	C₄	C₂³×C₃×D₄	1	1	yes	characteristic
399	C₄	C₂²×C₃×#41	1	1	yes	characteristic
400	C₃	C₂×#3058	1	1	yes	characteristic, direct product factor, Sylow
401	C₂	—	2	4	no	—
402	C₂	—	4	4	no	—
403	C₂	—	8	8	no	—
404	C₂	C₃×#3058	1	4	yes	direct product factor
405	C₂	C₂²×C₃×#121	1	1	yes	characteristic
406	C₂	C₂×C₃×#576	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃ ◁ C₂²×C₃×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂³×C₃×D₈	C₂	semidirect
2. C₂²×C₃×#131	C₂	semidirect
3. C₂×C₃×#535	C₂	semidirect
4. C₃×#3058	C₂	direct (N × H)
5. C₂×C₃×#469	C₂	semidirect
6. C₂×C₃×#466	C₂	semidirect
7. C₂×C₃×#427	C₂	semidirect
8. C₂×C₃×#418	C₂	semidirect
9. C₂×#3058	C₃	direct (N × H)
15. C₂²×C₃×D₈	C₂²	semidirect
17. C₂×C₃×#131	C₂²	semidirect
19. C₂²×C₃×M₁₆	C₂²	semidirect
21. C₂³×C₃×C₈	C₂²	semidirect
23. C₃×#535	C₂²	semidirect
26. C₂×C₃×#121	C₂²	semidirect
29. C₃×#469	C₂²	semidirect
30. C₃×#466	C₂²	semidirect
31. C₃×#427	C₂²	semidirect
32. C₂×C₃×#107	C₂²	semidirect
33. C₂×C₃×#106	C₂²	semidirect
34. C₃×#418	C₂²	semidirect
35. C₂×C₃×#102	C₂²	semidirect
36. C₂³×D₈	C₂×C₃	semidirect
37. C₂²×#131	C₂×C₃	semidirect
38. C₂×#535	C₂×C₃	semidirect
39. #3058	C₂×C₃	direct (N × H)
40. C₂×#469	C₂×C₃	semidirect
41. C₂×#466	C₂×C₃	semidirect
42. C₂×#427	C₂×C₃	semidirect
43. C₂×#418	C₂×C₃	semidirect
70. C₂×C₃×M₁₆	C₂³	semidirect
72. C₂²×C₃×C₈	D₄	semidirect
77. C₂²×C₃×C₈	C₂³	semidirect
81. C₃×#121	C₂³	semidirect
89. C₃×#107	C₂³	semidirect
90. C₃×#106	C₂³	semidirect
91. C₃×#102	C₂³	semidirect
97. C₂²×D₈	C₂²×C₃	semidirect
99. C₂×#131	C₂²×C₃	semidirect
101. C₂²×M₁₆	C₂²×C₃	semidirect
103. C₂³×C₈	C₂²×C₃	semidirect
105. #535	C₂²×C₃	semidirect
108. C₂×#121	C₂²×C₃	semidirect
111. #469	C₂²×C₃	semidirect
112. #466	C₂²×C₃	semidirect
113. #427	C₂²×C₃	semidirect
114. C₂×#107	C₂²×C₃	semidirect
115. C₂×#106	C₂²×C₃	semidirect
116. #418	C₂²×C₃	semidirect
117. C₂×#102	C₂²×C₃	semidirect
164. C₂×C₃×C₈	C₂×D₄	semidirect
199. C₂×M₁₆	C₂³×C₃	semidirect
201. C₂²×C₈	C₃×D₄	semidirect
206. C₂²×C₈	C₂³×C₃	semidirect
210. #121	C₂³×C₃	semidirect
218. #107	C₂³×C₃	semidirect
219. #106	C₂³×C₃	semidirect
220. #102	C₂³×C₃	semidirect
307. C₂×C₈	C₂×C₃×D₄	semidirect
378. C₂×C₃	#3058	direct (N × H)
400. C₃	C₂×#3058	direct (N × H)
404. C₂	C₃×#3058	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×C₃×D₈	2
C₂²×C₃×#131	2
C₂×C₃×#535	2
C₃×#3058	2
C₂×C₃×#469	2
C₂×C₃×#466	2
C₂×C₃×#427	2
C₂×C₃×#418	2
C₂×#3058	3

Subgroups — C2×C3×#3058 #10679053

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#3058 #10679053