Subgroups — C₂×D₃×#12705 #72254083

Order 3072.

At least 9750 conjugacy classes of subgroups; only the 2279 normal subgroups are shown.

The subgroup lattice has 638 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10710714	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#12705	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#10710711	C₂	1	4	yes	maximal, complemented
4	C₂×#10710713	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#10710712	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₃×#2121	C₂	1	4	yes	maximal, complemented
7	C₂×D₃×#1783	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×D₃×#1781	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×D₃×#3484	C₂	1	1	yes	maximal, characteristic
10	D₃×#12705	C₂	1	16	yes	maximal, direct product factor
11	C₂²×D₃×H(5,𝔽₂)	C₄	1	1	yes	characteristic, complemented
12	C₂⁴×D₃×D₄	C₂²	1	1	yes	characteristic
13	C₂×#85867	C₄	1	1	yes	characteristic, complemented
14	C₂×#87239	C₂²	1	1	yes	characteristic
15	C₂×#86308	C₂²	1	2	yes	—
16	C₂×#87284	C₄	1	1	yes	characteristic, complemented
17	C₂×#85919	C₄	1	2	yes	complemented
18	D₃×#3484	C₄	1	8	yes	complemented
19	D₃×#3484	C₂²	1	8	yes	—
20	C₂×D₃×#534	C₂²	1	2	yes	—
21	C₂²×D₃×#120	C₄	1	2	yes	complemented
22	C₂×D₃×#518	C₄	1	1	yes	characteristic, complemented
23	C₂²×D₃×#100	C₂²	1	2	yes	complemented
24	C₂²×D₃×#99	C₂²	1	2	yes	complemented
25	C₂×#70094	C₂²	1	4	yes	complemented
26	C₂×#71847	C₂²	1	4	yes	complemented
27	C₂×#70015	C₂²	1	4	yes	complemented
28	D₃×#2121	C₂²	1	32	yes	complemented
29	C₂×#72129	C₂²	1	1	yes	characteristic, complemented
30	C₂×#70079	C₂²	1	2	yes	complemented
31	D₃×#1783	C₂²	1	8	yes	complemented
32	C₂×#72130	C₂²	1	1	yes	characteristic, complemented
33	C₂×#70035	C₂²	1	2	yes	complemented
34	D₃×#1781	C₂²	1	8	yes	complemented
35	#10710714	C₂²	1	8	yes	complemented
36	#10710713	C₂²	1	8	yes	complemented
37	#10710712	C₂²	1	8	yes	complemented
38	#10710711	C₂²	1	32	yes	complemented
39	C₂×C₃×#3484	C₂²	1	1	yes	characteristic
40	C₂×C₃×#2121	C₂²	1	4	yes	complemented
41	C₂×C₃×#1783	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₃×#1781	C₂²	1	1	yes	characteristic, complemented
43	C₃×#12705	C₂²	1	8	yes	complemented
44	C₂×#12705	D₃	1	1	yes	characteristic, direct product factor
45	C₂⁶×D₃	C₂×C₄	1	1	yes	characteristic
46	C₂⁶×D₃	D₄	1	1	yes	characteristic
47	C₂²×C₃×H(5,𝔽₂)	C₂×C₄	1	1	yes	characteristic, complemented
48	C₂⁴×C₃×D₄	C₂³	1	1	yes	characteristic
49	C₂⁴×#67	C₂×C₄	1	1	yes	characteristic
50	C₂⁴×#67	D₄	1	1	yes	characteristic
51	C₂×D₃×H(5,𝔽₂)	C₂×C₄	1	8	yes	complemented
52	C₂²×#1004	C₂×C₄	1	2	yes	complemented
53	C₂²×#1004	C₂×C₄	1	1	yes	characteristic, complemented
54	C₂³×D₃×D₄	C₂×C₄	1	1	yes	characteristic
55	C₂³×D₃×D₄	C₂×C₄	1	4	yes	—
56	C₂³×D₃×D₄	C₂×C₄	1	1	yes	characteristic
57	C₂³×D₃×D₄	C₂×C₄	1	2	yes	—
58	C₂³×D₃×D₄	D₄	1	1	yes	characteristic
59	C₂³×D₃×D₄	D₄	1	4	yes	—
60	C₂³×D₃×D₄	D₄	1	1	yes	characteristic
61	C₂³×D₃×D₄	D₄	1	1	yes	characteristic
62	C₂³×D₃×D₄	D₄	1	4	yes	—
63	C₂³×D₃×D₄	D₄	1	1	yes	characteristic
64	C₂³×D₃×D₄	C₂³	1	4	yes	—
65	C₂³×D₃×D₄	C₂³	1	1	yes	characteristic
66	C₂³×D₃×D₄	C₂³	1	1	yes	characteristic
67	C₂⁴×D₁₂	D₄	1	1	yes	characteristic
68	C₂⁴×C₄×D₃	D₄	1	1	yes	characteristic
69	C₃×#3484	C₂×C₄	1	4	yes	complemented
70	C₃×#3484	C₂³	1	4	yes	—
71	C₂×C₃×#534	C₂³	1	2	yes	—
72	C₂²×C₃×#120	C₂×C₄	1	2	yes	complemented
73	C₂×C₃×#518	C₂×C₄	1	1	yes	characteristic, complemented
74	C₂²×#953	C₂×C₄	1	2	yes	complemented
75	#87284	C₂×C₄	1	8	yes	complemented
76	#87239	C₂×C₄	1	4	yes	complemented
77	#87239	C₂³	1	4	yes	—
78	C₂×#5804	C₂×C₄	1	2	yes	—
79	C₂×#5804	C₂³	1	2	yes	—
80	C₂²×#937	C₂×C₄	1	2	yes	complemented
81	C₂×#5798	C₂×C₄	1	1	yes	characteristic, complemented
82	#86308	C₂×C₄	1	8	yes	complemented
83	#86308	C₂³	1	8	yes	—
84	D₃×#534	C₂×C₄	1	8	yes	—
85	D₃×#534	D₄	1	16	yes	—
86	D₃×#534	C₂³	1	8	yes	—
87	C₂×#5653	D₄	1	4	yes	—
88	C₂×D₃×#123	D₄	1	4	yes	—
89	#85919	C₂×C₄	1	16	yes	complemented
90	C₂×#5589	D₄	1	4	yes	—
91	C₂×D₃×#120	C₂×C₄	1	16	yes	complemented
92	C₂×D₃×#120	D₄	1	4	yes	—
93	#85867	C₂×C₄	1	8	yes	complemented
94	D₃×#518	C₂×C₄	1	8	yes	complemented
95	C₂×#5493	C₂×C₄	1	2	yes	—
96	C₂²×#882	C₂×C₄	1	2	yes	complemented
97	C₂×#5486	C₂×C₄	1	2	yes	complemented
98	C₂²×D₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
99	C₂²×C₃×#100	C₂³	1	2	yes	complemented
100	C₂²×C₃×#99	C₂³	1	2	yes	complemented
101	C₂²×#834	C₂³	1	2	yes	complemented
102	C₂²×#833	C₂³	1	2	yes	complemented
103	C₂×D₃×#100	C₂³	1	8	yes	complemented
104	C₂×D₃×#99	C₂³	1	8	yes	complemented
105	C₃×#2121	C₂³	1	16	yes	complemented
106	C₃×#1783	C₂³	1	4	yes	complemented
107	C₃×#1781	C₂³	1	4	yes	complemented
108	#72130	C₂³	1	4	yes	complemented
109	#72129	C₂³	1	4	yes	complemented
110	#71847	C₂³	1	16	yes	complemented
111	#70094	C₂³	1	16	yes	complemented
112	#70079	C₂³	1	8	yes	complemented
113	#70035	C₂³	1	8	yes	complemented
114	#70015	C₂³	1	16	yes	complemented
115	C₂×#3484	C₂×D₃	1	1	yes	characteristic
116	C₂×#2121	C₂×D₃	1	4	yes	complemented
117	C₂×#1783	C₂×D₃	1	1	yes	characteristic, complemented
118	C₂×#1781	C₂×D₃	1	1	yes	characteristic, complemented
119	#12705	C₂×D₃	1	8	yes	direct product factor
120	C₂⁶×C₃	C₂²×C₄	1	1	yes	characteristic
121	C₂⁶×C₃	C₂×D₄	1	1	yes	characteristic
122	C₂⁵×D₃	C₂²⋊C₄	1	1	yes	characteristic
123	C₂⁵×D₃	C₂²⋊C₄	1	1	yes	characteristic
124	C₂⁵×D₃	C₂²⋊C₄	1	1	yes	characteristic
125	C₂⁵×D₃	C₂²⋊C₄	1	4	yes	—
126	C₂⁵×D₃	C₂²⋊C₄	1	1	yes	characteristic
127	C₂⁵×D₃	C₂²⋊C₄	1	1	yes	characteristic
128	C₂⁵×D₃	C₂²⋊C₄	1	1	yes	characteristic
129	C₂⁵×D₃	C₂²⋊C₄	1	1	yes	characteristic
130	C₂⁵×D₃	C₂²⋊C₄	1	4	yes	—
131	C₂⁵×D₃	C₂²⋊C₄	1	2	yes	complemented
132	C₂⁵×D₃	C₂²×C₄	1	1	yes	characteristic
133	C₂⁵×D₃	C₂²×C₄	1	4	yes	—
134	C₂⁵×D₃	C₂²×C₄	1	1	yes	characteristic
135	C₂⁵×D₃	C₂×D₄	1	4	yes	—
136	C₂⁵×D₃	C₂×D₄	1	1	yes	characteristic
137	C₂⁵×D₃	C₂×D₄	1	1	yes	characteristic
138	C₂×C₃×H(5,𝔽₂)	C₂²×C₄	1	4	yes	complemented
139	C₂³×C₃×D₄	C₂²×C₄	1	1	yes	characteristic
140	C₂³×C₃×D₄	C₂²×C₄	1	2	yes	—
141	C₂³×C₃×D₄	C₂²×C₄	1	2	yes	—
142	C₂³×C₃×D₄	C₂×D₄	1	1	yes	characteristic
143	C₂³×C₃×D₄	C₂×D₄	1	2	yes	—
144	C₂³×C₃×D₄	C₂×D₄	1	1	yes	characteristic
145	C₂³×C₃×D₄	C₂×D₄	1	2	yes	—
146	C₂³×C₃×D₄	C₂⁴	1	2	yes	—
147	C₂³×C₃×D₄	C₂⁴	1	1	yes	characteristic
148	C₂⁴×C₃×C₄	C₂×D₄	1	1	yes	characteristic
149	C₂³×#67	C₂²⋊C₄	1	1	yes	characteristic
150	C₂³×#67	C₂²⋊C₄	1	1	yes	characteristic
151	C₂³×#67	C₂²⋊C₄	1	1	yes	characteristic
152	C₂³×#67	C₂²⋊C₄	1	1	yes	characteristic
153	C₂³×#67	C₂²⋊C₄	1	4	yes	—
154	C₂³×#67	C₂²⋊C₄	1	4	yes	—
155	C₂³×#67	C₂²⋊C₄	1	2	yes	complemented
156	C₂³×#67	C₂²×C₄	1	1	yes	characteristic
157	C₂³×#67	C₂²×C₄	1	4	yes	—
158	C₂³×#67	C₂²×C₄	1	1	yes	characteristic
159	C₂³×#67	C₂²×C₄	1	2	yes	—
160	C₂³×#67	C₂×D₄	1	1	yes	characteristic
161	C₂³×#67	C₂×D₄	1	4	yes	—
162	C₂³×#67	C₂×D₄	1	1	yes	characteristic
163	C₂⁴×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
164	C₂×#1004	C₂²×C₄	1	8	yes	complemented
165	C₂×#1004	C₂²×C₄	1	4	yes	complemented
166	C₂²×D₃×D₄	C₂²⋊C₄	1	4	yes	—
167	C₂²×D₃×D₄	C₂²⋊C₄	1	4	yes	—
168	C₂²×D₃×D₄	C₂²⋊C₄	1	4	yes	—
169	C₂²×D₃×D₄	C₂²⋊C₄	1	4	yes	—
170	C₂²×D₃×D₄	C₂²⋊C₄	1	4	yes	—
171	C₂²×D₃×D₄	C₂²⋊C₄	1	4	yes	—
172	C₂²×D₃×D₄	C₂²⋊C₄	1	8	yes	complemented
173	C₂²×D₃×D₄	C₂²×C₄	1	4	yes	—
174	C₂²×D₃×D₄	C₂²×C₄	1	2	yes	—
175	C₂²×D₃×D₄	C₂²×C₄	1	4	yes	—
176	C₂²×D₃×D₄	C₂²×C₄	1	2	yes	—
177	C₂²×D₃×D₄	C₂²×C₄	1	8	yes	—
178	C₂²×D₃×D₄	C₂×D₄	1	4	yes	—
179	C₂²×D₃×D₄	C₂×D₄	1	2	yes	—
180	C₂²×D₃×D₄	C₂×D₄	1	4	yes	—
181	C₂²×D₃×D₄	C₂×D₄	1	2	yes	—
182	C₂²×D₃×D₄	C₂×D₄	1	8	yes	—
183	C₂²×D₃×D₄	C₂×D₄	1	4	yes	—
184	C₂²×D₃×D₄	C₂×D₄	1	4	yes	—
185	C₂²×D₃×D₄	C₂×D₄	1	4	yes	—
186	C₂²×D₃×D₄	C₂×D₄	1	2	yes	—
187	C₂²×D₃×D₄	C₂×D₄	1	4	yes	—
188	C₂²×D₃×D₄	C₂×D₄	1	2	yes	—
189	C₂²×D₃×D₄	C₂⁴	1	2	yes	—
190	C₂²×D₃×D₄	C₂⁴	1	2	yes	—
191	C₂³×D₁₂	C₂²⋊C₄	1	1	yes	characteristic
192	C₂³×D₁₂	C₂²⋊C₄	1	1	yes	characteristic
193	C₂³×D₁₂	C₂²⋊C₄	1	4	yes	—
194	C₂³×D₁₂	C₂²⋊C₄	1	2	yes	complemented
195	C₂³×D₁₂	C₂×D₄	1	1	yes	characteristic
196	C₂³×D₁₂	C₂×D₄	1	4	yes	—
197	C₂³×D₁₂	C₂×D₄	1	1	yes	characteristic
198	C₂³×C₄×D₃	C₂²⋊C₄	1	4	yes	—
199	C₂³×C₄×D₃	C₂²⋊C₄	1	1	yes	characteristic
200	C₂³×C₄×D₃	C₂²⋊C₄	1	1	yes	characteristic
201	C₂³×C₄×D₃	C₂²⋊C₄	1	2	yes	complemented
202	C₂³×C₄×D₃	C₂×D₄	1	4	yes	—
203	C₂³×C₄×D₃	C₂×D₄	1	1	yes	characteristic
204	C₂³×C₄×D₃	C₂×D₄	1	1	yes	characteristic
205	C₃×#534	C₂²×C₄	1	4	yes	—
206	C₃×#534	C₂×D₄	1	8	yes	—
207	C₃×#534	C₂⁴	1	4	yes	—
208	C₂×C₃×#123	C₂×D₄	1	4	yes	—
209	C₂×C₃×#120	C₂²×C₄	1	8	yes	complemented
210	C₂×C₃×#120	C₂×D₄	1	4	yes	—
211	C₃×#518	C₂²×C₄	1	4	yes	complemented
212	C₂²×C₃×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
213	C₂×#953	C₂²⋊C₄	1	4	yes	complemented
214	C₂×#953	C₂²×C₄	1	8	yes	complemented
215	C₂²×#217	C₂²×C₄	1	2	yes	—
216	#5804	C₂²⋊C₄	1	8	yes	complemented
217	#5804	C₂²×C₄	1	4	yes	—
218	#5804	C₂²×C₄	1	8	yes	—
219	#5804	C₂×D₄	1	8	yes	—
220	#5804	C₂⁴	1	4	yes	—
221	C₂×#937	C₂²×C₄	1	8	yes	complemented
222	C₂×#937	C₂×D₄	1	4	yes	—
223	#5798	C₂²×C₄	1	4	yes	complemented
224	C₂×#935	C₂×D₄	1	4	yes	—
225	C₂×#929	C₂²⋊C₄	1	4	yes	complemented
226	#5653	C₂²⋊C₄	1	16	yes	complemented
227	#5653	C₂×D₄	1	16	yes	—
228	D₃×#123	C₂²⋊C₄	1	16	yes	complemented
229	D₃×#123	C₂×D₄	1	16	yes	—
230	#5589	C₂²⋊C₄	1	16	yes	complemented
231	#5589	C₂×D₄	1	16	yes	—
232	D₃×#120	C₂²⋊C₄	1	16	yes	complemented
233	D₃×#120	C₂×D₄	1	16	yes	—
234	#5493	C₂²⋊C₄	1	8	yes	complemented
235	#5493	C₂²×C₄	1	8	yes	—
236	C₂×#886	C₂²⋊C₄	1	4	yes	complemented
237	C₂×#882	C₂²⋊C₄	1	4	yes	complemented
238	C₂×#882	C₂²×C₄	1	8	yes	complemented
239	#5486	C₂²×C₄	1	8	yes	complemented
240	C₂×D₃×C₂²⋊C₄	C₂²⋊C₄	1	4	yes	complemented
241	C₂×D₃×C₂²⋊C₄	C₂²⋊C₄	1	4	yes	complemented
242	C₂×D₃×C₂²⋊C₄	C₂²⋊C₄	1	8	yes	complemented
243	C₂×D₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
244	C₂×C₃×#100	C₂⁴	1	4	yes	complemented
245	C₂×C₃×#99	C₂⁴	1	4	yes	complemented
246	C₂×#834	C₂⁴	1	4	yes	complemented
247	C₂×#833	C₂⁴	1	4	yes	complemented
248	C₂²×H(5,𝔽₂)	C₄×D₃	1	1	yes	characteristic, complemented
249	C₂⁴×D₄	C₂²×D₃	1	1	yes	characteristic
250	#3484	C₄×D₃	1	4	yes	complemented
251	#3484	C₂²×D₃	1	4	yes	—
252	C₂×#534	C₂²×D₃	1	2	yes	—
253	C₂²×#120	C₄×D₃	1	2	yes	complemented
254	C₂×#518	C₄×D₃	1	1	yes	characteristic, complemented
255	C₂²×#100	C₂²×D₃	1	2	yes	complemented
256	C₂²×#99	C₂²×D₃	1	2	yes	complemented
257	#2121	C₂²×D₃	1	16	yes	complemented
258	#1783	C₂²×D₃	1	4	yes	complemented
259	#1781	C₂²×D₃	1	4	yes	complemented
260	C₂⁵×C₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
261	C₂⁵×C₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
262	C₂⁵×C₃	C₂×C₂²⋊C₄	1	2	yes	—
263	C₂⁵×C₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
264	C₂⁵×C₃	C₂×C₂²⋊C₄	1	2	yes	—
265	C₂⁵×C₃	C₂×C₂²⋊C₄	1	2	yes	complemented
266	C₂⁵×C₃	C₂³×C₄	1	1	yes	characteristic
267	C₂⁵×C₃	C₂³×C₄	1	2	yes	—
268	C₂⁵×C₃	C₂²×D₄	1	2	yes	—
269	C₂⁵×C₃	C₂²×D₄	1	1	yes	characteristic
270	C₂⁴×D₃	#99	1	2	yes	—
271	C₂⁴×D₃	#99	1	4	yes	—
272	C₂⁴×D₃	#99	1	2	yes	—
273	C₂⁴×D₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
274	C₂⁴×D₃	C₂×C₂²⋊C₄	1	4	yes	—
275	C₂⁴×D₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
276	C₂⁴×D₃	C₂×C₂²⋊C₄	1	4	yes	—
277	C₂⁴×D₃	C₂×C₂²⋊C₄	1	2	yes	—
278	C₂⁴×D₃	C₂×C₂²⋊C₄	1	4	yes	—
279	C₂⁴×D₃	C₂×C₂²⋊C₄	1	4	yes	—
280	C₂⁴×D₃	C₂×C₂²⋊C₄	1	2	yes	—
281	C₂⁴×D₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
282	C₂⁴×D₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
283	C₂⁴×D₃	C₂×C₂²⋊C₄	1	2	yes	—
284	C₂⁴×D₃	C₂×C₂²⋊C₄	1	2	yes	—
285	C₂⁴×D₃	C₂×C₂²⋊C₄	1	4	yes	—
286	C₂⁴×D₃	C₂×C₂²⋊C₄	1	2	yes	—
287	C₂⁴×D₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
288	C₂⁴×D₃	C₂×C₂²⋊C₄	1	4	yes	—
289	C₂⁴×D₃	C₂×C₂²⋊C₄	1	4	yes	—
290	C₂⁴×D₃	C₂×C₂²⋊C₄	1	2	yes	—
291	C₂⁴×D₃	C₂×C₂²⋊C₄	1	4	yes	—
292	C₂⁴×D₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
293	C₂⁴×D₃	C₂×C₂²⋊C₄	1	8	yes	complemented
294	C₂⁴×D₃	C₂×C₂²⋊C₄	1	2	yes	complemented
295	C₂⁴×D₃	#120	1	2	yes	—
296	C₂⁴×D₃	#120	1	2	yes	—
297	C₂⁴×D₃	#120	1	4	yes	—
298	C₂⁴×D₃	C₂³×C₄	1	2	yes	—
299	C₂⁴×D₃	C₂³×C₄	1	2	yes	—
300	C₂⁴×D₃	C₂²×D₄	1	2	yes	—
301	C₂⁴×D₃	C₂²×D₄	1	2	yes	—
302	C₂²×C₃×D₄	C₂×C₂²⋊C₄	1	2	yes	—
303	C₂²×C₃×D₄	C₂×C₂²⋊C₄	1	2	yes	—
304	C₂²×C₃×D₄	C₂×C₂²⋊C₄	1	2	yes	—
305	C₂²×C₃×D₄	C₂×C₂²⋊C₄	1	4	yes	complemented
306	C₂²×C₃×D₄	C₂³×C₄	1	2	yes	—
307	C₂²×C₃×D₄	C₂³×C₄	1	1	yes	characteristic
308	C₂²×C₃×D₄	C₂³×C₄	1	4	yes	—
309	C₂²×C₃×D₄	C₂²×D₄	1	2	yes	—
310	C₂²×C₃×D₄	C₂²×D₄	1	1	yes	characteristic
311	C₂²×C₃×D₄	C₂²×D₄	1	4	yes	—
312	C₂²×C₃×D₄	C₂²×D₄	1	4	yes	—
313	C₂²×C₃×D₄	C₂²×D₄	1	2	yes	—
314	C₂²×C₃×D₄	C₂²×D₄	1	1	yes	characteristic
315	C₂²×C₃×D₄	C₂⁵	1	1	yes	characteristic
316	C₂³×C₃×C₄	C₂×C₂²⋊C₄	1	2	yes	—
317	C₂³×C₃×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
318	C₂³×C₃×C₄	C₂×C₂²⋊C₄	1	2	yes	complemented
319	C₂³×C₃×C₄	C₂²×D₄	1	2	yes	—
320	C₂³×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
321	C₂²×#67	C₂×C₂²⋊C₄	1	4	yes	—
322	C₂²×#67	C₂×C₂²⋊C₄	1	2	yes	—
323	C₂²×#67	C₂×C₂²⋊C₄	1	4	yes	—
324	C₂²×#67	C₂×C₂²⋊C₄	1	2	yes	—
325	C₂²×#67	C₂×C₂²⋊C₄	1	4	yes	—
326	C₂²×#67	C₂×C₂²⋊C₄	1	4	yes	—
327	C₂²×#67	C₂×C₂²⋊C₄	1	2	yes	—
328	C₂²×#67	C₂×C₂²⋊C₄	1	2	yes	—
329	C₂²×#67	C₂×C₂²⋊C₄	1	4	yes	—
330	C₂²×#67	C₂×C₂²⋊C₄	1	4	yes	—
331	C₂²×#67	C₂×C₂²⋊C₄	1	8	yes	complemented
332	C₂²×#67	C₂×C₂²⋊C₄	1	4	yes	complemented
333	C₂²×#67	#120	1	4	yes	—
334	C₂²×#67	#120	1	4	yes	—
335	C₂²×#67	C₂³×C₄	1	2	yes	—
336	C₂²×#67	C₂³×C₄	1	2	yes	—
337	C₂²×#67	C₂³×C₄	1	4	yes	—
338	C₂²×#67	C₂²×D₄	1	2	yes	—
339	C₂²×#67	C₂²×D₄	1	2	yes	—
340	C₂³×Dic₃	C₂×C₂²⋊C₄	1	4	yes	—
341	C₂³×Dic₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
342	C₂³×Dic₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
343	C₂³×Dic₃	C₂×C₂²⋊C₄	1	2	yes	complemented
344	C₂×D₃×D₄	C₂×C₂²⋊C₄	1	8	yes	—
345	C₂×D₃×D₄	C₂×C₂²⋊C₄	1	8	yes	—
346	C₂×D₃×D₄	#120	1	8	yes	—
347	C₂×D₃×D₄	#120	1	8	yes	—
348	C₂×D₃×D₄	#120	1	8	yes	—
349	C₂×D₃×D₄	#120	1	8	yes	—
350	C₂×D₃×D₄	C₂²×D₄	1	8	yes	—
351	C₂×D₃×D₄	C₂²×D₄	1	8	yes	—
352	C₂²×D₁₂	C₂×C₂²⋊C₄	1	4	yes	—
353	C₂²×D₁₂	C₂×C₂²⋊C₄	1	2	yes	—
354	C₂²×D₁₂	C₂×C₂²⋊C₄	1	4	yes	—
355	C₂²×D₁₂	C₂×C₂²⋊C₄	1	2	yes	—
356	C₂²×D₁₂	C₂×C₂²⋊C₄	1	8	yes	complemented
357	C₂²×D₁₂	#120	1	4	yes	—
358	C₂²×D₁₂	#120	1	4	yes	—
359	C₂²×D₁₂	C₂²×D₄	1	2	yes	—
360	C₂²×D₁₂	C₂²×D₄	1	2	yes	—
361	C₂²×C₄×D₃	#99	1	2	yes	—
362	C₂²×C₄×D₃	#99	1	2	yes	—
363	C₂²×C₄×D₃	#99	1	4	yes	—
364	C₂²×C₄×D₃	C₂×C₂²⋊C₄	1	2	yes	—
365	C₂²×C₄×D₃	C₂×C₂²⋊C₄	1	4	yes	—
366	C₂²×C₄×D₃	C₂×C₂²⋊C₄	1	2	yes	—
367	C₂²×C₄×D₃	C₂×C₂²⋊C₄	1	4	yes	—
368	C₂²×C₄×D₃	C₂×C₂²⋊C₄	1	8	yes	complemented
369	C₂²×C₄×D₃	#120	1	4	yes	—
370	C₂²×C₄×D₃	#120	1	2	yes	—
371	C₂²×C₄×D₃	#120	1	2	yes	—
372	C₂²×C₄×D₃	C₂²×D₄	1	2	yes	—
373	C₂²×C₄×D₃	C₂²×D₄	1	2	yes	—
374	C₃×#123	C₂×C₂²⋊C₄	1	8	yes	complemented
375	C₃×#123	C₂²×D₄	1	8	yes	—
376	C₃×#120	C₂×C₂²⋊C₄	1	8	yes	complemented
377	C₃×#120	C₂²×D₄	1	8	yes	—
378	C₂×C₃×C₂²⋊C₄	C₂×C₂²⋊C₄	1	4	yes	complemented
379	C₂×C₃×C₂²⋊C₄	C₂×C₂²⋊C₄	1	4	yes	complemented
380	C₂×C₃×C₂²⋊C₄	C₂³×C₄	1	4	yes	—
381	#953	C₂×C₂²⋊C₄	1	16	yes	complemented
382	C₂×#217	C₂×C₂²⋊C₄	1	4	yes	complemented
383	C₂×#217	C₂×C₂²⋊C₄	1	4	yes	complemented
384	C₂×#217	C₂³×C₄	1	4	yes	—
385	#937	C₂×C₂²⋊C₄	1	8	yes	complemented
386	#937	C₂²×D₄	1	8	yes	—
387	#935	C₂×C₂²⋊C₄	1	8	yes	complemented
388	#935	C₂²×D₄	1	8	yes	—
389	#929	C₂×C₂²⋊C₄	1	16	yes	complemented
390	#886	C₂×C₂²⋊C₄	1	16	yes	complemented
391	#882	C₂×C₂²⋊C₄	1	16	yes	complemented
392	D₃×C₂²⋊C₄	C₂×C₂²⋊C₄	1	16	yes	complemented
393	D₃×C₂²⋊C₄	C₂×C₂²⋊C₄	1	16	yes	complemented
394	C₂⁶	C₂×C₄×D₃	1	1	yes	characteristic
395	C₂⁶	D₃×D₄	1	1	yes	characteristic
396	C₂×H(5,𝔽₂)	C₂×C₄×D₃	1	4	yes	complemented
397	C₂³×D₄	C₂×C₄×D₃	1	1	yes	characteristic
398	C₂³×D₄	C₂×C₄×D₃	1	2	yes	—
399	C₂³×D₄	C₂×C₄×D₃	1	2	yes	—
400	C₂³×D₄	D₃×D₄	1	1	yes	characteristic
401	C₂³×D₄	D₃×D₄	1	2	yes	—
402	C₂³×D₄	D₃×D₄	1	1	yes	characteristic
403	C₂³×D₄	D₃×D₄	1	2	yes	—
404	C₂³×D₄	C₂³×D₃	1	2	yes	—
405	C₂³×D₄	C₂³×D₃	1	1	yes	characteristic
406	C₂⁴×C₄	D₃×D₄	1	1	yes	characteristic
407	#534	C₂×C₄×D₃	1	4	yes	—
408	#534	D₃×D₄	1	8	yes	—
409	#534	C₂³×D₃	1	4	yes	—
410	C₂×#123	D₃×D₄	1	4	yes	—
411	C₂×#120	C₂×C₄×D₃	1	8	yes	complemented
412	C₂×#120	D₃×D₄	1	4	yes	—
413	#518	C₂×C₄×D₃	1	4	yes	complemented
414	C₂²×C₂²⋊C₄	C₂×C₄×D₃	1	2	yes	—
415	C₂×#100	C₂³×D₃	1	4	yes	complemented
416	C₂×#99	C₂³×D₃	1	4	yes	complemented
417	C₂⁴×C₃	C₂×#99	1	2	yes	—
418	C₂⁴×C₃	C₂×#99	1	2	yes	—
419	C₂⁴×C₃	C₂²×C₂²⋊C₄	1	2	yes	—
420	C₂⁴×C₃	C₂²×C₂²⋊C₄	1	2	yes	—
421	C₂⁴×C₃	C₂²×C₂²⋊C₄	1	2	yes	—
422	C₂⁴×C₃	C₂²×C₂²⋊C₄	1	2	yes	—
423	C₂⁴×C₃	C₂²×C₂²⋊C₄	1	2	yes	—
424	C₂⁴×C₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
425	C₂⁴×C₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
426	C₂⁴×C₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
427	C₂⁴×C₃	C₂²×C₂²⋊C₄	1	4	yes	complemented
428	C₂⁴×C₃	C₂×#120	1	2	yes	—
429	C₂⁴×C₃	C₂×#120	1	2	yes	—
430	C₂⁴×C₃	C₂⁴×C₄	1	1	yes	characteristic
431	C₂⁴×C₃	C₂³×D₄	1	1	yes	characteristic
432	C₂³×D₃	#379	1	1	yes	characteristic
433	C₂³×D₃	#379	1	4	yes	—
434	C₂³×D₃	#379	1	4	yes	—
435	C₂³×D₃	#379	1	2	yes	—
436	C₂³×D₃	#379	1	2	yes	—
437	C₂³×D₃	#379	1	2	yes	—
438	C₂³×D₃	#379	1	4	yes	—
439	C₂³×D₃	#379	1	2	yes	—
440	C₂³×D₃	#379	1	4	yes	—
441	C₂³×D₃	#379	1	2	yes	—
442	C₂³×D₃	#379	1	1	yes	characteristic
443	C₂³×D₃	C₂×#99	1	1	yes	characteristic
444	C₂³×D₃	C₂×#99	1	1	yes	characteristic
445	C₂³×D₃	C₂×#99	1	2	yes	—
446	C₂³×D₃	C₂×#99	1	8	yes	—
447	C₂³×D₃	C₂×#99	1	2	yes	—
448	C₂³×D₃	C₂×#99	1	8	yes	—
449	C₂³×D₃	C₂×#99	1	2	yes	—
450	C₂³×D₃	C₂×#99	1	1	yes	characteristic
451	C₂³×D₃	C₂×#99	1	2	yes	—
452	C₂³×D₃	C₂×#99	1	1	yes	characteristic
453	C₂³×D₃	C₂²×C₂²⋊C₄	1	2	yes	—
454	C₂³×D₃	C₂²×C₂²⋊C₄	1	2	yes	—
455	C₂³×D₃	C₂²×C₂²⋊C₄	1	4	yes	—
456	C₂³×D₃	C₂²×C₂²⋊C₄	1	2	yes	—
457	C₂³×D₃	C₂²×C₂²⋊C₄	1	2	yes	—
458	C₂³×D₃	C₂²×C₂²⋊C₄	1	4	yes	—
459	C₂³×D₃	C₂²×C₂²⋊C₄	1	2	yes	—
460	C₂³×D₃	C₂²×C₂²⋊C₄	1	2	yes	—
461	C₂³×D₃	C₂²×C₂²⋊C₄	1	4	yes	complemented
462	C₂³×D₃	C₂×#120	1	4	yes	—
463	C₂³×D₃	C₂×#120	1	4	yes	—
464	C₂×C₃×D₄	C₂²×C₂²⋊C₄	1	4	yes	—
465	C₂×C₃×D₄	C₂×#120	1	4	yes	—
466	C₂×C₃×D₄	C₂×#120	1	4	yes	—
467	C₂×C₃×D₄	C₂³×D₄	1	4	yes	—
468	C₂²×C₃×C₄	C₂×#99	1	2	yes	—
469	C₂²×C₃×C₄	C₂×#99	1	2	yes	—
470	C₂²×C₃×C₄	C₂²×C₂²⋊C₄	1	2	yes	—
471	C₂²×C₃×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
472	C₂²×C₃×C₄	C₂²×C₂²⋊C₄	1	4	yes	complemented
473	C₂²×C₃×C₄	C₂×#120	1	2	yes	—
474	C₂²×C₃×C₄	C₂×#120	1	2	yes	—
475	C₂²×C₃×C₄	C₂³×D₄	1	1	yes	characteristic
476	C₂×#67	#379	1	8	yes	—
477	C₂×#67	#379	1	8	yes	—
478	C₂×#67	C₂²×C₂²⋊C₄	1	8	yes	—
479	C₂×#67	C₂×#120	1	8	yes	—
480	C₂²×Dic₃	#379	1	2	yes	—
481	C₂²×Dic₃	#379	1	2	yes	—
482	C₂²×Dic₃	C₂×#99	1	2	yes	—
483	C₂²×Dic₃	C₂×#99	1	2	yes	—
484	C₂²×Dic₃	C₂²×C₂²⋊C₄	1	2	yes	—
485	C₂²×Dic₃	C₂²×C₂²⋊C₄	1	2	yes	—
486	C₂²×Dic₃	C₂²×C₂²⋊C₄	1	4	yes	complemented
487	C₂×D₁₂	#379	1	8	yes	—
488	C₂×D₁₂	C₂×#120	1	8	yes	—
489	C₂×C₄×D₃	#379	1	4	yes	—
490	C₂×C₄×D₃	#379	1	4	yes	—
491	C₂×C₄×D₃	C₂×#99	1	8	yes	—
492	C₂×C₄×D₃	C₂×#99	1	8	yes	—
493	C₂×C₄×D₃	C₂×#120	1	4	yes	—
494	C₂×C₄×D₃	C₂×#120	1	4	yes	—
495	C₃×C₂²⋊C₄	C₂²×C₂²⋊C₄	1	8	yes	complemented
496	#217	C₂²×C₂²⋊C₄	1	8	yes	complemented
497	C₂⁵	D₃×C₂²⋊C₄	1	1	yes	characteristic
498	C₂⁵	D₃×C₂²⋊C₄	1	1	yes	characteristic
499	C₂⁵	D₃×C₂²⋊C₄	1	2	yes	—
500	C₂⁵	D₃×C₂²⋊C₄	1	1	yes	characteristic
501	C₂⁵	D₃×C₂²⋊C₄	1	2	yes	—
502	C₂⁵	D₃×C₂²⋊C₄	1	2	yes	complemented
503	C₂⁵	C₂²×C₄×D₃	1	1	yes	characteristic
504	C₂⁵	C₂²×C₄×D₃	1	2	yes	—
505	C₂⁵	C₂×D₃×D₄	1	2	yes	—
506	C₂⁵	C₂×D₃×D₄	1	1	yes	characteristic
507	C₂²×D₄	D₃×C₂²⋊C₄	1	2	yes	—
508	C₂²×D₄	D₃×C₂²⋊C₄	1	2	yes	—
509	C₂²×D₄	D₃×C₂²⋊C₄	1	2	yes	—
510	C₂²×D₄	D₃×C₂²⋊C₄	1	4	yes	complemented
511	C₂²×D₄	C₂²×C₄×D₃	1	2	yes	—
512	C₂²×D₄	C₂²×C₄×D₃	1	1	yes	characteristic
513	C₂²×D₄	C₂²×C₄×D₃	1	4	yes	—
514	C₂²×D₄	C₂×D₃×D₄	1	2	yes	—
515	C₂²×D₄	C₂×D₃×D₄	1	1	yes	characteristic
516	C₂²×D₄	C₂×D₃×D₄	1	2	yes	—
517	C₂²×D₄	C₂×D₃×D₄	1	1	yes	characteristic
518	C₂²×D₄	C₂×D₃×D₄	1	4	yes	—
519	C₂²×D₄	C₂×D₃×D₄	1	4	yes	—
520	C₂²×D₄	C₂⁴×D₃	1	1	yes	characteristic
521	C₂³×C₄	D₃×C₂²⋊C₄	1	2	yes	—
522	C₂³×C₄	D₃×C₂²⋊C₄	1	1	yes	characteristic
523	C₂³×C₄	D₃×C₂²⋊C₄	1	2	yes	complemented
524	C₂³×C₄	C₂×D₃×D₄	1	2	yes	—
525	C₂³×C₄	C₂×D₃×D₄	1	1	yes	characteristic
526	#123	D₃×C₂²⋊C₄	1	8	yes	complemented
527	#123	C₂×D₃×D₄	1	8	yes	—
528	#120	D₃×C₂²⋊C₄	1	8	yes	complemented
529	#120	C₂×D₃×D₄	1	8	yes	—
530	C₂×C₂²⋊C₄	D₃×C₂²⋊C₄	1	4	yes	complemented
531	C₂×C₂²⋊C₄	D₃×C₂²⋊C₄	1	4	yes	complemented
532	C₂×C₂²⋊C₄	C₂²×C₄×D₃	1	4	yes	—
533	C₂³×C₃	C₂×#379	1	1	yes	characteristic
534	C₂³×C₃	C₂×#379	1	2	yes	—
535	C₂³×C₃	C₂×#379	1	2	yes	—
536	C₂³×C₃	C₂×#379	1	1	yes	characteristic
537	C₂³×C₃	C₂²×#99	1	1	yes	characteristic
538	C₂³×C₃	C₂²×#99	1	1	yes	characteristic
539	C₂³×C₃	C₂²×#99	1	4	yes	—
540	C₂³×C₃	C₂²×#99	1	1	yes	characteristic
541	C₂³×C₃	C₂²×#99	1	1	yes	characteristic
542	C₂³×C₃	C₂³×C₂²⋊C₄	1	2	yes	—
543	C₂³×C₃	C₂³×C₂²⋊C₄	1	1	yes	characteristic
544	C₂³×C₃	C₂²×#120	1	2	yes	—
545	C₂²×D₃	#1781	1	2	yes	—
546	C₂²×D₃	#1781	1	1	yes	characteristic
547	C₂²×D₃	#1781	1	1	yes	characteristic
548	C₂²×D₃	#1781	1	1	yes	characteristic
549	C₂²×D₃	#1781	1	2	yes	—
550	C₂²×D₃	#1781	1	2	yes	—
551	C₂²×D₃	#1781	1	2	yes	—
552	C₂²×D₃	#1781	1	2	yes	—
553	C₂²×D₃	#1781	1	2	yes	—
554	C₂²×D₃	#1781	1	1	yes	characteristic
555	C₂²×D₃	C₂×#379	1	2	yes	—
556	C₂²×D₃	C₂×#379	1	4	yes	—
557	C₂²×D₃	C₂×#379	1	4	yes	—
558	C₂²×D₃	C₂×#379	1	2	yes	—
559	C₂²×D₃	C₂²×#99	1	2	yes	—
560	C₂²×D₃	C₂²×#99	1	2	yes	—
561	C₂²×D₃	C₂²×#99	1	4	yes	—
562	C₂²×D₃	C₂²×#99	1	2	yes	—
563	C₂²×D₃	C₂²×#99	1	2	yes	—
564	C₂×C₃×C₄	C₂×#379	1	2	yes	—
565	C₂×C₃×C₄	C₂²×#99	1	4	yes	—
566	C₂×C₃×C₄	C₂²×#120	1	2	yes	—
567	C₂×Dic₃	C₂×#379	1	4	yes	—
568	C₂×Dic₃	C₂²×#99	1	4	yes	—
569	C₂⁴	D₃×#99	1	2	yes	—
570	C₂⁴	D₃×#99	1	2	yes	—
571	C₂⁴	C₂×D₃×C₂²⋊C₄	1	2	yes	—
572	C₂⁴	C₂×D₃×C₂²⋊C₄	1	2	yes	—
573	C₂⁴	C₂×D₃×C₂²⋊C₄	1	2	yes	—
574	C₂⁴	C₂×D₃×C₂²⋊C₄	1	2	yes	—
575	C₂⁴	C₂×D₃×C₂²⋊C₄	1	1	yes	characteristic
576	C₂⁴	C₂×D₃×C₂²⋊C₄	1	2	yes	—
577	C₂⁴	C₂×D₃×C₂²⋊C₄	1	1	yes	characteristic
578	C₂⁴	C₂×D₃×C₂²⋊C₄	1	1	yes	characteristic
579	C₂⁴	C₂×D₃×C₂²⋊C₄	1	4	yes	complemented
580	C₂⁴	D₃×#120	1	2	yes	—
581	C₂⁴	D₃×#120	1	2	yes	—
582	C₂⁴	C₂³×C₄×D₃	1	1	yes	characteristic
583	C₂⁴	C₂²×D₃×D₄	1	1	yes	characteristic
584	C₂×D₄	C₂×D₃×C₂²⋊C₄	1	4	yes	—
585	C₂×D₄	D₃×#120	1	4	yes	—
586	C₂×D₄	D₃×#120	1	4	yes	—
587	C₂×D₄	C₂²×D₃×D₄	1	4	yes	—
588	C₂²×C₄	D₃×#99	1	2	yes	—
589	C₂²×C₄	D₃×#99	1	2	yes	—
590	C₂²×C₄	C₂×D₃×C₂²⋊C₄	1	2	yes	—
591	C₂²×C₄	C₂×D₃×C₂²⋊C₄	1	1	yes	characteristic
592	C₂²×C₄	C₂×D₃×C₂²⋊C₄	1	4	yes	complemented
593	C₂²×C₄	D₃×#120	1	2	yes	—
594	C₂²×C₄	D₃×#120	1	2	yes	—
595	C₂²×C₄	C₂²×D₃×D₄	1	1	yes	characteristic
596	C₂²⋊C₄	C₂×D₃×C₂²⋊C₄	1	8	yes	complemented
597	C₂²×C₃	C₂×#1781	1	1	yes	characteristic
598	C₂²×C₃	C₂×#1781	1	1	yes	characteristic
599	C₂²×C₃	C₂×#1781	1	1	yes	characteristic
600	C₂²×C₃	C₂×#1781	1	1	yes	characteristic
601	C₂²×C₃	C₂²×#379	1	1	yes	characteristic
602	C₂²×C₃	C₂³×#99	1	1	yes	characteristic
603	C₂²×C₃	C₂³×#99	1	1	yes	characteristic
604	C₂×D₃	#12705	1	4	yes	direct product factor
605	C₂×D₃	C₂×#1781	1	2	yes	—
606	C₂×D₃	C₂×#1781	1	2	yes	—
607	C₂×D₃	C₂×#1781	1	2	yes	—
608	C₂×D₃	C₂×#1781	1	2	yes	—
609	C₂³	D₃×#379	1	1	yes	characteristic
610	C₂³	D₃×#379	1	2	yes	—
611	C₂³	D₃×#379	1	2	yes	—
612	C₂³	D₃×#379	1	1	yes	characteristic
613	C₂³	C₂×D₃×#99	1	1	yes	characteristic
614	C₂³	C₂×D₃×#99	1	1	yes	characteristic
615	C₂³	C₂×D₃×#99	1	4	yes	—
616	C₂³	C₂×D₃×#99	1	1	yes	characteristic
617	C₂³	C₂×D₃×#99	1	1	yes	characteristic
618	C₂³	C₂²×D₃×C₂²⋊C₄	1	2	yes	—
619	C₂³	C₂²×D₃×C₂²⋊C₄	1	1	yes	characteristic
620	C₂³	C₂×D₃×#120	1	2	yes	—
621	C₂×C₄	D₃×#379	1	2	yes	—
622	C₂×C₄	C₂×D₃×#99	1	4	yes	—
623	C₂×C₄	C₂×D₃×#120	1	2	yes	—
624	C₂×C₃	C₂×#12705	1	2	yes	complemented
625	C₂×C₃	C₂²×#1781	1	1	yes	characteristic
626	D₃	C₂×#12705	1	4	yes	direct product factor
627	C₂²	D₃×#1781	1	1	yes	characteristic
628	C₂²	D₃×#1781	1	1	yes	characteristic
629	C₂²	D₃×#1781	1	1	yes	characteristic
630	C₂²	D₃×#1781	1	1	yes	characteristic
631	C₂²	C₂×D₃×#379	1	1	yes	characteristic
632	C₂²	C₂²×D₃×#99	1	1	yes	characteristic
633	C₂²	C₂²×D₃×#99	1	1	yes	characteristic
634	C₃	C₂²×#12705	1	1	yes	characteristic, complemented, Sylow
635	C₂	D₃×#12705	1	2	yes	direct product factor
636	C₂	C₂×D₃×#1781	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₃×#1781
commutator	C₂⁴×C₃	C₂⁴×C₄
Frattini	C₂²×D₄	C₂⁴×D₃
Fitting	C₂×C₃×#12705	C₂
socle	C₂²×C₃	C₂×#1781
prime radical	C₂×D₃×#3484	C₂
cosocle	C₂²×C₃×D₄	C₂⁵
hypercenter	C₂×#12705	D₃
hypocenter	C₃	C₂²×#12705
LCS	G ▷ C₂⁴×C₃ ▷ C₂²×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₂⁴ ◁ C₂⁴×D₄ ◁ C₂×#12705

Complements

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

N	H ≅ G/N	type
1. C₂×#10710714	C₂	semidirect
2. C₂×C₃×#12705	C₂	semidirect
3. C₂×#10710711	C₂	semidirect
4. C₂×#10710713	C₂	semidirect
5. C₂×#10710712	C₂	semidirect
6. C₂×D₃×#2121	C₂	semidirect
7. C₂×D₃×#1783	C₂	semidirect
8. C₂×D₃×#1781	C₂	semidirect
10. D₃×#12705	C₂	direct (N × H)
11. C₂²×D₃×H(5,𝔽₂)	C₄	semidirect
13. C₂×#85867	C₄	semidirect
16. C₂×#87284	C₄	semidirect
17. C₂×#85919	C₄	semidirect
18. D₃×#3484	C₄	semidirect
21. C₂²×D₃×#120	C₄	semidirect
22. C₂×D₃×#518	C₄	semidirect
23. C₂²×D₃×#100	C₂²	semidirect
24. C₂²×D₃×#99	C₂²	semidirect
25. C₂×#70094	C₂²	semidirect
26. C₂×#71847	C₂²	semidirect
27. C₂×#70015	C₂²	semidirect
28. D₃×#2121	C₂²	semidirect
29. C₂×#72129	C₂²	semidirect
30. C₂×#70079	C₂²	semidirect
31. D₃×#1783	C₂²	semidirect
32. C₂×#72130	C₂²	semidirect
33. C₂×#70035	C₂²	semidirect
34. D₃×#1781	C₂²	semidirect
35. #10710714	C₂²	semidirect
36. #10710713	C₂²	semidirect
37. #10710712	C₂²	semidirect
38. #10710711	C₂²	semidirect
40. C₂×C₃×#2121	C₂²	semidirect
41. C₂×C₃×#1783	C₂²	semidirect
42. C₂×C₃×#1781	C₂²	semidirect
43. C₃×#12705	C₂²	semidirect
44. C₂×#12705	D₃	direct (N × H)
47. C₂²×C₃×H(5,𝔽₂)	C₂×C₄	semidirect
51. C₂×D₃×H(5,𝔽₂)	C₂×C₄	semidirect
52. C₂²×#1004	C₂×C₄	semidirect
53. C₂²×#1004	C₂×C₄	semidirect
69. C₃×#3484	C₂×C₄	semidirect
72. C₂²×C₃×#120	C₂×C₄	semidirect
73. C₂×C₃×#518	C₂×C₄	semidirect
74. C₂²×#953	C₂×C₄	semidirect
75. #87284	C₂×C₄	semidirect
76. #87239	C₂×C₄	semidirect
80. C₂²×#937	C₂×C₄	semidirect
81. C₂×#5798	C₂×C₄	semidirect
82. #86308	C₂×C₄	semidirect
89. #85919	C₂×C₄	semidirect
91. C₂×D₃×#120	C₂×C₄	semidirect
93. #85867	C₂×C₄	semidirect
94. D₃×#518	C₂×C₄	semidirect
96. C₂²×#882	C₂×C₄	semidirect
97. C₂×#5486	C₂×C₄	semidirect
99. C₂²×C₃×#100	C₂³	semidirect
100. C₂²×C₃×#99	C₂³	semidirect
101. C₂²×#834	C₂³	semidirect
102. C₂²×#833	C₂³	semidirect
103. C₂×D₃×#100	C₂³	semidirect
104. C₂×D₃×#99	C₂³	semidirect
105. C₃×#2121	C₂³	semidirect
106. C₃×#1783	C₂³	semidirect
107. C₃×#1781	C₂³	semidirect
108. #72130	C₂³	semidirect
109. #72129	C₂³	semidirect
110. #71847	C₂³	semidirect
111. #70094	C₂³	semidirect
112. #70079	C₂³	semidirect
113. #70035	C₂³	semidirect
114. #70015	C₂³	semidirect
116. C₂×#2121	C₂×D₃	semidirect
117. C₂×#1783	C₂×D₃	semidirect
118. C₂×#1781	C₂×D₃	semidirect
119. #12705	C₂×D₃	direct (N × H)
131. C₂⁵×D₃	C₂²⋊C₄	semidirect
138. C₂×C₃×H(5,𝔽₂)	C₂²×C₄	semidirect
155. C₂³×#67	C₂²⋊C₄	semidirect
164. C₂×#1004	C₂²×C₄	semidirect
165. C₂×#1004	C₂²×C₄	semidirect
172. C₂²×D₃×D₄	C₂²⋊C₄	semidirect
194. C₂³×D₁₂	C₂²⋊C₄	semidirect
201. C₂³×C₄×D₃	C₂²⋊C₄	semidirect
209. C₂×C₃×#120	C₂²×C₄	semidirect
211. C₃×#518	C₂²×C₄	semidirect
213. C₂×#953	C₂²⋊C₄	semidirect
214. C₂×#953	C₂²×C₄	semidirect
216. #5804	C₂²⋊C₄	semidirect
221. C₂×#937	C₂²×C₄	semidirect
223. #5798	C₂²×C₄	semidirect
225. C₂×#929	C₂²⋊C₄	semidirect
226. #5653	C₂²⋊C₄	semidirect
228. D₃×#123	C₂²⋊C₄	semidirect
230. #5589	C₂²⋊C₄	semidirect
232. D₃×#120	C₂²⋊C₄	semidirect
234. #5493	C₂²⋊C₄	semidirect
236. C₂×#886	C₂²⋊C₄	semidirect
237. C₂×#882	C₂²⋊C₄	semidirect
238. C₂×#882	C₂²×C₄	semidirect
239. #5486	C₂²×C₄	semidirect
240. C₂×D₃×C₂²⋊C₄	C₂²⋊C₄	semidirect
241. C₂×D₃×C₂²⋊C₄	C₂²⋊C₄	semidirect
242. C₂×D₃×C₂²⋊C₄	C₂²⋊C₄	semidirect
244. C₂×C₃×#100	C₂⁴	semidirect
245. C₂×C₃×#99	C₂⁴	semidirect
246. C₂×#834	C₂⁴	semidirect
247. C₂×#833	C₂⁴	semidirect
248. C₂²×H(5,𝔽₂)	C₄×D₃	semidirect
250. #3484	C₄×D₃	semidirect
253. C₂²×#120	C₄×D₃	semidirect
254. C₂×#518	C₄×D₃	semidirect
255. C₂²×#100	C₂²×D₃	semidirect
256. C₂²×#99	C₂²×D₃	semidirect
257. #2121	C₂²×D₃	semidirect
258. #1783	C₂²×D₃	semidirect
259. #1781	C₂²×D₃	semidirect
265. C₂⁵×C₃	C₂×C₂²⋊C₄	semidirect
293. C₂⁴×D₃	C₂×C₂²⋊C₄	semidirect
294. C₂⁴×D₃	C₂×C₂²⋊C₄	semidirect
305. C₂²×C₃×D₄	C₂×C₂²⋊C₄	semidirect
318. C₂³×C₃×C₄	C₂×C₂²⋊C₄	semidirect
331. C₂²×#67	C₂×C₂²⋊C₄	semidirect
332. C₂²×#67	C₂×C₂²⋊C₄	semidirect
343. C₂³×Dic₃	C₂×C₂²⋊C₄	semidirect
356. C₂²×D₁₂	C₂×C₂²⋊C₄	semidirect
368. C₂²×C₄×D₃	C₂×C₂²⋊C₄	semidirect
374. C₃×#123	C₂×C₂²⋊C₄	semidirect
376. C₃×#120	C₂×C₂²⋊C₄	semidirect
378. C₂×C₃×C₂²⋊C₄	C₂×C₂²⋊C₄	semidirect
379. C₂×C₃×C₂²⋊C₄	C₂×C₂²⋊C₄	semidirect
381. #953	C₂×C₂²⋊C₄	semidirect
382. C₂×#217	C₂×C₂²⋊C₄	semidirect
383. C₂×#217	C₂×C₂²⋊C₄	semidirect
385. #937	C₂×C₂²⋊C₄	semidirect
387. #935	C₂×C₂²⋊C₄	semidirect
389. #929	C₂×C₂²⋊C₄	semidirect
390. #886	C₂×C₂²⋊C₄	semidirect
391. #882	C₂×C₂²⋊C₄	semidirect
392. D₃×C₂²⋊C₄	C₂×C₂²⋊C₄	semidirect
393. D₃×C₂²⋊C₄	C₂×C₂²⋊C₄	semidirect
396. C₂×H(5,𝔽₂)	C₂×C₄×D₃	semidirect
411. C₂×#120	C₂×C₄×D₃	semidirect
413. #518	C₂×C₄×D₃	semidirect
415. C₂×#100	C₂³×D₃	semidirect
416. C₂×#99	C₂³×D₃	semidirect
427. C₂⁴×C₃	C₂²×C₂²⋊C₄	semidirect
461. C₂³×D₃	C₂²×C₂²⋊C₄	semidirect
472. C₂²×C₃×C₄	C₂²×C₂²⋊C₄	semidirect
486. C₂²×Dic₃	C₂²×C₂²⋊C₄	semidirect
495. C₃×C₂²⋊C₄	C₂²×C₂²⋊C₄	semidirect
496. #217	C₂²×C₂²⋊C₄	semidirect
502. C₂⁵	D₃×C₂²⋊C₄	semidirect
510. C₂²×D₄	D₃×C₂²⋊C₄	semidirect
523. C₂³×C₄	D₃×C₂²⋊C₄	semidirect
526. #123	D₃×C₂²⋊C₄	semidirect
528. #120	D₃×C₂²⋊C₄	semidirect
530. C₂×C₂²⋊C₄	D₃×C₂²⋊C₄	semidirect
531. C₂×C₂²⋊C₄	D₃×C₂²⋊C₄	semidirect
579. C₂⁴	C₂×D₃×C₂²⋊C₄	semidirect
592. C₂²×C₄	C₂×D₃×C₂²⋊C₄	semidirect
596. C₂²⋊C₄	C₂×D₃×C₂²⋊C₄	semidirect
604. C₂×D₃	#12705	direct (N × H)
624. C₂×C₃	C₂×#12705	semidirect
626. D₃	C₂×#12705	direct (N × H)
634. C₃	C₂²×#12705	semidirect
635. C₂	D₃×#12705	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×#10710714	2
C₂×C₃×#12705	2
C₂×#10710711	2
C₂×#10710713	2
C₂×#10710712	2
C₂×D₃×#2121	2
C₂×D₃×#1783	2
C₂×D₃×#1781	2
C₂×D₃×#3484	2
C₂²×#12705	3
D₃×#12705	2

Subgroups — C2×D3×#12705 #72254083

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₃×#12705 #72254083