Subgroups — C₂×#72234146 #72338116

Order 2048.

At least 6688 conjugacy classes of subgroups; only the 5168 normal subgroups are shown.

The subgroup lattice has 586 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×#494596	C₂	1	2	yes	maximal, complemented
2	C₂×#499844	C₂	1	4	yes	maximal, complemented
3	C₂×#493430	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#494682	C₂	1	2	yes	maximal, complemented
5	C₂²×#60388	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#499831	C₂	1	4	yes	maximal, complemented
7	C₂×#6628896	C₂	1	2	yes	maximal, complemented
8	C₂×#498927	C₂	1	4	yes	maximal, complemented
9	C₂×#499832	C₂	1	4	yes	maximal, complemented
10	#72234146	C₂	1	32	yes	maximal, direct product factor
11	C₂×#499843	C₂	1	4	yes	maximal, complemented
12	C₂³×#2196	C₂	1	2	yes	maximal, complemented
13	C₂×#7737411	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²×H(7,𝔽₂)	C₂²	1	1	yes	characteristic, complemented
15	C₂²×#3498	C₂²	1	1	yes	characteristic
16	C₂³×D₄²	C₂²	1	1	yes	characteristic, complemented
17	C₂³×B(4,𝔽₂)	C₂²	1	4	yes	complemented
18	C₂×#60388	C₂²	1	16	yes	complemented
19	C₂²×#3018	C₂²	1	2	yes	complemented
20	C₂²×#3021	C₂²	1	2	yes	complemented
21	C₂²×#3019	C₂²	1	2	yes	complemented
22	C₂²×#3019	C₂²	1	2	yes	complemented
23	C₂³×#453	C₂²	1	2	yes	—
24	C₂³×#453	C₂²	1	2	yes	complemented
25	C₂²×#2888	C₂²	1	1	yes	characteristic, complemented
26	#7737411	C₂²	1	16	yes	complemented
27	C₂×#52004	C₂²	1	2	yes	complemented
28	C₂×#52004	C₂²	1	2	yes	complemented
29	C₂×#59041	C₂²	1	2	yes	complemented
30	C₂×#59126	C₂²	1	2	yes	complemented
31	C₂×#36702	C₂²	1	2	yes	complemented
32	C₂×#35346	C₂²	1	2	yes	—
33	C₂×#34364	C₂²	1	1	yes	characteristic, complemented
34	C₂²×#2196	C₂²	1	8	yes	complemented
35	C₂²×#2196	C₂²	1	8	yes	complemented
36	C₂²×#2196	C₂²	1	32	yes	complemented
37	C₂²×#2127	C₂²	1	2	yes	complemented
38	C₂³×#353	C₂²	1	2	yes	complemented
39	C₂³×AΣL(1,𝔽₁₆)	C₂²	1	4	yes	complemented
40	#6628896	C₂²	1	32	yes	complemented
41	C₂×#32899	C₂²	1	8	yes	complemented
42	C₂×#32898	C₂²	1	8	yes	complemented
43	C₂×#20609	C₂²	1	4	yes	complemented
44	C₂×#20585	C₂²	1	2	yes	complemented
45	#499844	C₂²	1	64	yes	complemented
46	#499843	C₂²	1	64	yes	complemented
47	#499832	C₂²	1	64	yes	complemented
48	#499831	C₂²	1	64	yes	complemented
49	#498927	C₂²	1	64	yes	complemented
50	C₂×#13348	C₂²	1	16	yes	complemented
51	C₂×#13346	C₂²	1	16	yes	complemented
52	#494682	C₂²	1	32	yes	complemented
53	C₂×#13083	C₂²	1	8	yes	complemented
54	C₂×#13082	C₂²	1	8	yes	complemented
55	#494596	C₂²	1	32	yes	complemented
56	C₂×#13049	C₂²	1	8	yes	complemented
57	C₂×#13047	C₂²	1	8	yes	complemented
58	#493430	C₂²	1	16	yes	complemented
59	C₂×#12697	C₂²	1	2	yes	complemented
60	C₂×#12696	C₂²	1	2	yes	complemented
61	C₂×#12695	C₂²	1	2	yes	complemented
62	C₂×#12693	C₂²	1	2	yes	complemented
63	C₂×#12574	C₂²	1	4	yes	complemented
64	C₂×H(7,𝔽₂)	C₂³	1	8	yes	complemented
65	C₂²×#585	C₂³	1	2	yes	complemented
66	C₂³×H(5,𝔽₂)	D₄	1	1	yes	characteristic, complemented
67	C₂³×H(5,𝔽₂)	C₂³	1	2	yes	—
68	C₂³×H(5,𝔽₂)	C₂³	1	1	yes	characteristic
69	C₂³×H(5,𝔽₂)	C₂³	1	2	yes	complemented
70	C₂×#3498	D₄	1	8	yes	complemented
71	C₂×#3498	C₂³	1	8	yes	—
72	C₂²×D₄²	C₂³	1	2	yes	complemented
73	C₂²×D₄²	C₂³	1	8	yes	complemented
74	C₂²×D₄²	C₂³	1	2	yes	complemented
75	C₂²×#535	D₄	1	1	yes	characteristic, complemented
76	C₂²×#535	D₄	1	1	yes	characteristic, complemented
77	C₂²×#535	D₄	1	1	yes	characteristic, complemented
78	C₂²×#535	C₂³	1	1	yes	characteristic
79	C₂²×#535	C₂³	1	1	yes	characteristic
80	C₂²×#535	C₂³	1	1	yes	characteristic
81	C₂²×#532	D₄	1	1	yes	characteristic, complemented
82	C₂²×#532	D₄	1	1	yes	characteristic, complemented
83	C₂²×#532	C₂³	1	1	yes	characteristic
84	C₂³×#127	D₄	1	1	yes	characteristic, complemented
85	C₂³×#127	C₂³	1	1	yes	characteristic
86	C₂³×#127	C₂³	1	1	yes	characteristic
87	C₂³×#120	D₄	1	2	yes	complemented
88	C₂³×#120	D₄	1	2	yes	complemented
89	C₂³×#120	C₂³	1	2	yes	—
90	C₂²×C₄×#41	D₄	1	1	yes	characteristic, complemented
91	C₂²×B(4,𝔽₂)	C₂³	1	16	yes	—
92	C₂²×B(4,𝔽₂)	C₂³	1	32	yes	complemented
93	C₂×#3021	C₂³	1	16	yes	complemented
94	C₂×#3019	C₂³	1	16	yes	complemented
95	C₂×#3019	C₂³	1	16	yes	complemented
96	C₂×#3018	C₂³	1	16	yes	complemented
97	C₂²×#455	C₂³	1	4	yes	complemented
98	C₂²×#453	D₄	1	32	yes	complemented
99	C₂²×#453	C₂³	1	4	yes	—
100	C₂²×#453	C₂³	1	16	yes	—
101	C₂²×#453	C₂³	1	4	yes	—
102	C₂²×#453	C₂³	1	4	yes	complemented
103	C₂²×#453	C₂³	1	16	yes	complemented
104	C₂×#2888	C₂³	1	8	yes	complemented
105	C₂²×#413	C₂³	1	2	yes	complemented
106	C₂³×#100	C₂³	1	2	yes	—
107	C₂³×#100	C₂³	1	2	yes	complemented
108	C₂³×#99	C₂³	1	4	yes	—
109	#59126	C₂³	1	16	yes	complemented
110	#59041	C₂³	1	16	yes	complemented
111	C₂×#2684	C₂³	1	4	yes	complemented
112	C₂×#2669	C₂³	1	4	yes	complemented
113	#52004	C₂³	1	16	yes	complemented
114	#52004	C₂³	1	16	yes	complemented
115	#36702	C₂³	1	16	yes	complemented
116	#35346	D₄	1	16	yes	complemented
117	#35346	C₂³	1	16	yes	—
118	C₂×#2404	D₄	1	4	yes	complemented
119	C₂×#2404	C₂³	1	4	yes	—
120	C₂×#2403	D₄	1	4	yes	complemented
121	C₂×#2403	C₂³	1	4	yes	—
122	#34364	C₂³	1	8	yes	complemented
123	C₂×#2380	C₂³	1	2	yes	complemented
124	C₂×#2366	C₂³	1	2	yes	complemented
125	C₂×#2308	D₄	1	2	yes	complemented
126	C₂×#2308	D₄	1	2	yes	complemented
127	C₂×#2308	C₂³	1	2	yes	—
128	C₂×#2196	C₂³	1	64	yes	complemented
129	C₂×#2196	C₂³	1	64	yes	complemented
130	C₂×#2127	C₂³	1	16	yes	complemented
131	C₂²×#354	C₂³	1	4	yes	complemented
132	C₂²×#353	C₂³	1	4	yes	complemented
133	C₂²×#353	C₂³	1	16	yes	complemented
134	C₂²×#353	C₂³	1	4	yes	complemented
135	C₂²×#353	C₂³	1	4	yes	complemented
136	C₂²×AΣL(1,𝔽₁₆)	C₂³	1	16	yes	complemented
137	C₂²×AΣL(1,𝔽₁₆)	C₂³	1	32	yes	complemented
138	#32899	C₂³	1	64	yes	complemented
139	#32898	C₂³	1	64	yes	complemented
140	#20609	C₂³	1	32	yes	complemented
141	C₂×#1790	C₂³	1	16	yes	complemented
142	#20585	C₂³	1	16	yes	complemented
143	C₂×#1782	C₂³	1	4	yes	complemented
144	C₂×#1781	C₂³	1	4	yes	complemented
145	#13348	C₂³	1	128	yes	complemented
146	#13346	C₂³	1	128	yes	complemented
147	#13083	C₂³	1	64	yes	complemented
148	#13082	C₂³	1	64	yes	complemented
149	#13049	C₂³	1	64	yes	complemented
150	#13047	C₂³	1	64	yes	complemented
151	#12697	C₂³	1	16	yes	complemented
152	#12696	C₂³	1	16	yes	complemented
153	#12695	C₂³	1	16	yes	complemented
154	#12693	C₂³	1	16	yes	complemented
155	#12574	C₂³	1	32	yes	complemented
156	C₂×#1390	C₂³	1	16	yes	complemented
157	C₂⁷	C₂×D₄	1	2	yes	—
158	C₂×#585	C₂⁴	1	8	yes	complemented
159	C₂²×H(5,𝔽₂)	C₂×D₄	1	4	yes	—
160	C₂²×H(5,𝔽₂)	C₂×D₄	1	8	yes	—
161	C₂²×H(5,𝔽₂)	C₂×D₄	1	8	yes	complemented
162	C₂²×H(5,𝔽₂)	C₂×D₄	1	16	yes	complemented
163	C₂²×H(5,𝔽₂)	C₂⁴	1	4	yes	—
164	C₂²×H(5,𝔽₂)	C₂⁴	1	8	yes	—
165	C₂²×H(5,𝔽₂)	C₂⁴	1	4	yes	—
166	C₂²×H(5,𝔽₂)	C₂⁴	1	8	yes	complemented
167	C₂³×#41	C₂×D₄	1	1	yes	characteristic
168	C₂³×#41	C₂×D₄	1	1	yes	characteristic
169	C₂³×#41	C₂×D₄	1	1	yes	characteristic
170	C₂³×#41	C₂×D₄	1	2	yes	—
171	C₂³×#41	C₂×D₄	1	1	yes	characteristic
172	C₂³×#41	C₂×D₄	1	1	yes	characteristic, complemented
173	C₂³×#41	C₂×D₄	1	1	yes	characteristic, complemented
174	C₂³×#41	C₂⁴	1	1	yes	characteristic
175	C₂⁴×D₄	C₂×D₄	1	2	yes	—
176	C₂⁴×D₄	C₂×D₄	1	2	yes	—
177	C₂⁴×D₄	C₂×D₄	1	2	yes	—
178	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
179	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
180	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic, complemented
181	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic, complemented
182	C₂⁴×D₄	C₂×D₄	1	4	yes	complemented
183	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
184	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
185	C₂×D₄²	C₂⁴	1	8	yes	complemented
186	C₂×D₄²	C₂⁴	1	8	yes	complemented
187	C₂×#535	C₂×D₄	1	4	yes	—
188	C₂×#535	C₂×D₄	1	8	yes	complemented
189	C₂×#535	C₂×D₄	1	4	yes	complemented
190	C₂×#535	C₂×D₄	1	8	yes	complemented
191	C₂×#535	C₂×D₄	1	4	yes	complemented
192	C₂×#535	C₂×D₄	1	8	yes	complemented
193	C₂×#535	C₂⁴	1	4	yes	—
194	C₂×#535	C₂⁴	1	4	yes	—
195	C₂×#535	C₂⁴	1	4	yes	—
196	C₂×#532	C₂×D₄	1	4	yes	complemented
197	C₂×#532	C₂×D₄	1	8	yes	complemented
198	C₂×#532	C₂×D₄	1	8	yes	complemented
199	C₂×#532	C₂⁴	1	4	yes	—
200	C₂²×C₄⋊Q₈	C₂×D₄	1	1	yes	characteristic, complemented
201	C₂²×#127	C₂×D₄	1	1	yes	characteristic
202	C₂²×#127	C₂×D₄	1	1	yes	characteristic
203	C₂²×#127	C₂×D₄	1	4	yes	—
204	C₂²×#127	C₂×D₄	1	1	yes	characteristic
205	C₂²×#127	C₂×D₄	1	16	yes	—
206	C₂²×#127	C₂×D₄	1	4	yes	complemented
207	C₂²×#127	C₂×D₄	1	8	yes	complemented
208	C₂²×#127	C₂×D₄	1	1	yes	characteristic, complemented
209	C₂²×#127	C₂×D₄	1	1	yes	characteristic, complemented
210	C₂²×#127	C₂×D₄	1	1	yes	characteristic, complemented
211	C₂²×#127	C₂⁴	1	1	yes	characteristic
212	C₂²×#127	C₂⁴	1	4	yes	—
213	C₂²×#127	C₂⁴	1	1	yes	characteristic
214	C₂²×#127	C₂⁴	1	4	yes	—
215	C₂²×#127	C₂⁴	1	1	yes	characteristic
216	C₂²×#124	C₂×D₄	1	1	yes	characteristic
217	C₂²×#124	C₂×D₄	1	1	yes	characteristic, complemented
218	C₂²×#124	C₂×D₄	1	1	yes	characteristic, complemented
219	C₂²×#124	C₂×D₄	1	1	yes	characteristic, complemented
220	C₂²×#124	C₂×D₄	1	1	yes	characteristic, complemented
221	C₂²×#124	C₂⁴	1	1	yes	characteristic
222	C₂²×#120	C₂×D₄	1	8	yes	—
223	C₂²×#120	C₂×D₄	1	4	yes	—
224	C₂²×#120	C₂×D₄	1	16	yes	complemented
225	C₂²×#120	C₂×D₄	1	4	yes	complemented
226	C₂²×#120	C₂×D₄	1	4	yes	complemented
227	C₂²×#120	C₂×D₄	1	16	yes	complemented
228	C₂²×#120	C₂⁴	1	8	yes	—
229	C₂²×#120	C₂⁴	1	4	yes	—
230	C₂×C₄×#41	C₂×D₄	1	8	yes	complemented
231	C₂²×#117	C₂×D₄	1	1	yes	characteristic
232	C₂²×#117	C₂×D₄	1	1	yes	characteristic, complemented
233	C₂²×#117	C₂×D₄	1	1	yes	characteristic, complemented
234	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
235	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
236	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
237	C₂³×C₂²⋊C₄	C₂×D₄	1	4	yes	complemented
238	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic
239	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic, complemented
240	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic, complemented
241	C₂×B(4,𝔽₂)	C₂⁴	1	64	yes	—
242	C₂×#455	C₂⁴	1	16	yes	complemented
243	C₂×#453	C₂×D₄	1	32	yes	complemented
244	C₂×#453	C₂×D₄	1	32	yes	complemented
245	C₂×#453	C₂×D₄	1	128	yes	complemented
246	C₂×#453	C₂⁴	1	16	yes	—
247	C₂×#453	C₂⁴	1	16	yes	—
248	C₂×#453	C₂⁴	1	16	yes	complemented
249	C₂×#413	C₂⁴	1	8	yes	complemented
250	C₂²×#100	C₂×D₄	1	16	yes	complemented
251	C₂²×#100	C₂⁴	1	4	yes	—
252	C₂²×#100	C₂⁴	1	8	yes	—
253	C₂²×#100	C₂⁴	1	8	yes	complemented
254	C₂²×#99	C₂⁴	1	8	yes	—
255	C₂²×#99	C₂⁴	1	16	yes	—
256	#2684	C₂⁴	1	16	yes	complemented
257	#2669	C₂⁴	1	16	yes	complemented
258	#2404	C₂×D₄	1	16	yes	complemented
259	#2404	C₂×D₄	1	32	yes	complemented
260	#2404	C₂⁴	1	16	yes	—
261	#2403	C₂×D₄	1	16	yes	complemented
262	#2403	C₂×D₄	1	32	yes	complemented
263	#2403	C₂⁴	1	16	yes	—
264	#2380	C₂⁴	1	8	yes	complemented
265	#2366	C₂⁴	1	8	yes	complemented
266	#2308	C₂×D₄	1	8	yes	—
267	#2308	C₂×D₄	1	16	yes	complemented
268	#2308	C₂×D₄	1	16	yes	complemented
269	#2308	C₂⁴	1	8	yes	—
270	C₂×#386	C₂×D₄	1	4	yes	—
271	C₂×#386	C₂×D₄	1	4	yes	complemented
272	C₂×#386	C₂×D₄	1	4	yes	complemented
273	C₂×#386	C₂⁴	1	4	yes	—
274	C₂×#381	C₂×D₄	1	4	yes	complemented
275	C₂×#379	C₂×D₄	1	4	yes	complemented
276	C₂×#354	C₂⁴	1	16	yes	complemented
277	C₂×#353	C₂⁴	1	16	yes	complemented
278	C₂×#353	C₂⁴	1	16	yes	complemented
279	C₂×#353	C₂⁴	1	16	yes	complemented
280	C₂×AΣL(1,𝔽₁₆)	C₂⁴	1	64	yes	complemented
281	#1790	C₂⁴	1	64	yes	complemented
282	#1782	C₂⁴	1	16	yes	complemented
283	#1781	C₂⁴	1	16	yes	complemented
284	#1390	C₂⁴	1	64	yes	complemented
285	C₂⁶	#120	1	2	yes	—
286	C₂⁶	C₂²×D₄	1	2	yes	—
287	C₂⁶	C₂²×D₄	1	2	yes	—
288	C₂⁶	C₂²×D₄	1	4	yes	—
289	C₂⁶	C₂²×D₄	1	8	yes	—
290	C₂×H(5,𝔽₂)	C₂²×D₄	1	16	yes	—
291	C₂×H(5,𝔽₂)	C₂²×D₄	1	32	yes	complemented
292	C₂×H(5,𝔽₂)	C₂⁵	1	8	yes	—
293	C₂²×#41	#120	1	4	yes	—
294	C₂²×#41	#120	1	4	yes	—
295	C₂²×#41	#120	1	4	yes	—
296	C₂²×#41	#120	1	8	yes	—
297	C₂²×#41	C₂²×D₄	1	4	yes	—
298	C₂²×#41	C₂²×D₄	1	4	yes	—
299	C₂²×#41	C₂²×D₄	1	4	yes	—
300	C₂²×#41	C₂²×D₄	1	2	yes	—
301	C₂²×#41	C₂²×D₄	1	8	yes	—
302	C₂²×#41	C₂²×D₄	1	4	yes	—
303	C₂²×#41	C₂²×D₄	1	4	yes	—
304	C₂²×#41	C₂²×D₄	1	4	yes	complemented
305	C₂²×#41	C₂²×D₄	1	4	yes	complemented
306	C₂²×#41	C₂⁵	1	2	yes	—
307	C₂³×Q₈	#120	1	1	yes	characteristic
308	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
309	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
310	C₂³×D₄	#120	1	1	yes	characteristic
311	C₂³×D₄	#120	1	2	yes	—
312	C₂³×D₄	#120	1	8	yes	—
313	C₂³×D₄	#120	1	8	yes	—
314	C₂³×D₄	#120	1	2	yes	—
315	C₂³×D₄	#120	1	2	yes	—
316	C₂³×D₄	#120	1	1	yes	characteristic
317	C₂³×D₄	#120	1	4	yes	—
318	C₂³×D₄	#120	1	8	yes	—
319	C₂³×D₄	#120	1	1	yes	characteristic
320	C₂³×D₄	#120	1	8	yes	complemented
321	C₂³×D₄	C₂²×D₄	1	8	yes	—
322	C₂³×D₄	C₂²×D₄	1	2	yes	—
323	C₂³×D₄	C₂²×D₄	1	2	yes	—
324	C₂³×D₄	C₂²×D₄	1	8	yes	—
325	C₂³×D₄	C₂²×D₄	1	4	yes	—
326	C₂³×D₄	C₂²×D₄	1	8	yes	—
327	C₂³×D₄	C₂²×D₄	1	4	yes	—
328	C₂³×D₄	C₂²×D₄	1	2	yes	—
329	C₂³×D₄	C₂²×D₄	1	8	yes	—
330	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
331	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
332	C₂³×D₄	C₂²×D₄	1	4	yes	—
333	C₂³×D₄	C₂²×D₄	1	2	yes	—
334	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
335	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
336	C₂³×D₄	C₂²×D₄	1	4	yes	—
337	C₂³×D₄	C₂²×D₄	1	2	yes	—
338	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
339	C₂³×D₄	C₂²×D₄	1	4	yes	complemented
340	C₂³×D₄	C₂²×D₄	1	4	yes	complemented
341	C₂³×D₄	C₂²×D₄	1	16	yes	complemented
342	C₂³×D₄	H(5,𝔽₂)	1	8	yes	—
343	C₂³×D₄	C₂⁵	1	2	yes	—
344	C₂³×D₄	C₂⁵	1	2	yes	—
345	C₂³×D₄	C₂⁵	1	1	yes	characteristic
346	C₂⁴×C₄	#120	1	2	yes	—
347	C₂⁴×C₄	#120	1	2	yes	—
348	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
349	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
350	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
351	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
352	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
353	C₂×C₄⋊Q₈	C₂²×D₄	1	4	yes	complemented
354	C₂×#127	#120	1	8	yes	complemented
355	C₂×#127	#120	1	8	yes	complemented
356	C₂×#127	#120	1	32	yes	complemented
357	C₂×#127	C₂²×D₄	1	8	yes	—
358	C₂×#127	C₂²×D₄	1	8	yes	—
359	C₂×#127	C₂²×D₄	1	32	yes	—
360	C₂×#127	C₂²×D₄	1	4	yes	—
361	C₂×#127	C₂²×D₄	1	2	yes	—
362	C₂×#127	C₂²×D₄	1	2	yes	—
363	C₂×#127	C₂²×D₄	1	2	yes	—
364	C₂×#127	C₂²×D₄	1	4	yes	—
365	C₂×#127	C₂²×D₄	1	4	yes	—
366	C₂×#127	C₂²×D₄	1	4	yes	complemented
367	C₂×#127	C₂²×D₄	1	4	yes	complemented
368	C₂×#127	C₂²×D₄	1	4	yes	complemented
369	C₂×#127	C₂⁵	1	2	yes	—
370	C₂×#127	C₂⁵	1	2	yes	—
371	C₂×#127	C₂⁵	1	2	yes	—
372	C₂×#124	C₂²×D₄	1	4	yes	—
373	C₂×#124	C₂²×D₄	1	2	yes	—
374	C₂×#124	C₂²×D₄	1	4	yes	complemented
375	C₂×#124	C₂²×D₄	1	4	yes	complemented
376	C₂×#124	C₂²×D₄	1	4	yes	complemented
377	C₂×#124	C₂²×D₄	1	4	yes	complemented
378	C₂×#124	C₂⁵	1	2	yes	—
379	C₂×#120	C₂²×D₄	1	16	yes	—
380	C₂×#120	C₂²×D₄	1	8	yes	—
381	C₂×#120	C₂²×D₄	1	16	yes	complemented
382	C₂×#120	C₂²×D₄	1	16	yes	complemented
383	C₂×#120	C₂⁵	1	8	yes	—
384	C₂×#117	C₂²×D₄	1	4	yes	—
385	C₂×#117	C₂²×D₄	1	4	yes	complemented
386	C₂×#117	C₂²×D₄	1	4	yes	complemented
387	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
388	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
389	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
390	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
391	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
392	C₂²×C₂²⋊C₄	C₂²×D₄	1	16	yes	complemented
393	C₂²×C₄²	#120	1	8	yes	complemented
394	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
395	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
396	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
397	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
398	C₂²×C₄²	C₂²×D₄	1	4	yes	—
399	C₂²×C₄²	C₂²×D₄	1	4	yes	complemented
400	C₂²×C₄²	C₂²×D₄	1	4	yes	complemented
401	#453	C₂²×D₄	1	64	yes	complemented
402	#453	C₂²×D₄	1	64	yes	complemented
403	C₂×#100	C₂²×D₄	1	16	yes	—
404	C₂×#100	C₂²×D₄	1	32	yes	complemented
405	C₂×#100	C₂⁵	1	8	yes	—
406	C₂×#99	C₂⁵	1	16	yes	—
407	#386	C₂²×D₄	1	8	yes	—
408	#386	C₂²×D₄	1	16	yes	—
409	#386	C₂²×D₄	1	16	yes	complemented
410	#386	C₂²×D₄	1	16	yes	complemented
411	#386	C₂⁵	1	8	yes	—
412	#381	C₂²×D₄	1	16	yes	complemented
413	#379	C₂²×D₄	1	16	yes	complemented
414	C₂⁵	C₂×#120	1	2	yes	—
415	C₂⁵	C₂×#120	1	2	yes	—
416	C₂⁵	C₂×#120	1	1	yes	characteristic
417	C₂⁵	C₂×#120	1	1	yes	characteristic
418	C₂⁵	C₂×#120	1	4	yes	—
419	C₂⁵	C₂×#120	1	8	yes	—
420	C₂⁵	C₂×#120	1	4	yes	—
421	C₂⁵	C₂×#120	1	1	yes	characteristic
422	C₂⁵	D₄²	1	16	yes	—
423	C₂⁵	C₂³×D₄	1	2	yes	—
424	C₂⁵	C₂³×D₄	1	4	yes	—
425	C₂⁵	C₂³×D₄	1	4	yes	—
426	C₂⁵	C₂³×D₄	1	8	yes	—
427	H(5,𝔽₂)	C₂³×D₄	1	16	yes	—
428	C₂²×Q₈	C₂×#120	1	4	yes	—
429	C₂²×Q₈	C₂×#120	1	2	yes	—
430	C₂²×Q₈	C₂³×D₄	1	2	yes	—
431	C₂²×Q₈	C₂³×D₄	1	2	yes	—
432	C₂²×D₄	B(4,𝔽₂)	1	4	yes	—
433	C₂²×D₄	B(4,𝔽₂)	1	8	yes	—
434	C₂²×D₄	B(4,𝔽₂)	1	4	yes	—
435	C₂²×D₄	C₂×#120	1	4	yes	—
436	C₂²×D₄	C₂×#120	1	8	yes	—
437	C₂²×D₄	C₂×#120	1	4	yes	—
438	C₂²×D₄	C₂×#120	1	8	yes	—
439	C₂²×D₄	C₂×#120	1	8	yes	—
440	C₂²×D₄	C₂×#120	1	4	yes	—
441	C₂²×D₄	C₂×#120	1	4	yes	—
442	C₂²×D₄	C₂×#120	1	4	yes	—
443	C₂²×D₄	C₂×#120	1	2	yes	—
444	C₂²×D₄	C₂×#120	1	4	yes	—
445	C₂²×D₄	C₂×#120	1	4	yes	—
446	C₂²×D₄	C₂×#120	1	4	yes	—
447	C₂²×D₄	C₂×#120	1	2	yes	—
448	C₂²×D₄	C₂×#120	1	4	yes	—
449	C₂²×D₄	C₂×#120	1	8	yes	—
450	C₂²×D₄	C₂×#120	1	16	yes	complemented
451	C₂²×D₄	#534	1	4	yes	—
452	C₂²×D₄	#534	1	8	yes	—
453	C₂²×D₄	D₄²	1	16	yes	—
454	C₂²×D₄	D₄²	1	32	yes	—
455	C₂²×D₄	C₂³×D₄	1	2	yes	—
456	C₂²×D₄	C₂³×D₄	1	2	yes	—
457	C₂²×D₄	C₂³×D₄	1	2	yes	—
458	C₂²×D₄	C₂³×D₄	1	2	yes	—
459	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
460	C₂²×D₄	C₂³×D₄	1	2	yes	—
461	C₂²×D₄	C₂³×D₄	1	4	yes	—
462	C₂²×D₄	C₂³×D₄	1	4	yes	—
463	C₂²×D₄	C₂³×D₄	1	4	yes	—
464	C₂²×D₄	C₂³×D₄	1	8	yes	—
465	C₂²×D₄	C₂³×D₄	1	4	yes	—
466	C₂²×D₄	C₂³×D₄	1	2	yes	—
467	C₂²×D₄	C₂×H(5,𝔽₂)	1	4	yes	—
468	C₂²×D₄	C₂×H(5,𝔽₂)	1	8	yes	—
469	C₂²×D₄	C₂⁶	1	1	yes	characteristic
470	C₂³×C₄	C₂×#120	1	2	yes	—
471	C₂³×C₄	C₂×#120	1	2	yes	—
472	C₂³×C₄	C₂×#120	1	2	yes	—
473	C₂³×C₄	C₂×#120	1	8	yes	—
474	C₂³×C₄	C₂×#120	1	4	yes	—
475	C₂³×C₄	C₂×#120	1	1	yes	characteristic
476	C₂³×C₄	C₂×#120	1	2	yes	—
477	C₂³×C₄	C₂×#120	1	4	yes	—
478	C₂³×C₄	C₂×#120	1	1	yes	characteristic
479	C₂³×C₄	C₂×#120	1	1	yes	characteristic
480	C₂³×C₄	C₂×#120	1	8	yes	—
481	C₂³×C₄	#534	1	4	yes	—
482	C₂³×C₄	C₂³×D₄	1	2	yes	—
483	C₂³×C₄	C₂³×D₄	1	2	yes	—
484	C₂³×C₄	C₂³×D₄	1	4	yes	—
485	C₂³×C₄	C₂³×D₄	1	2	yes	—
486	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
487	C₂³×C₄	C₂³×D₄	1	8	yes	—
488	#127	C₂×#120	1	8	yes	—
489	#127	C₂×#120	1	8	yes	—
490	#127	C₂×#120	1	16	yes	complemented
491	#127	C₂×#120	1	16	yes	complemented
492	#127	C₂³×D₄	1	8	yes	—
493	#127	C₂³×D₄	1	8	yes	—
494	C₂×C₂²⋊C₄	C₂³×D₄	1	8	yes	—
495	C₂×C₂²⋊C₄	C₂³×D₄	1	8	yes	—
496	C₂×C₄²	C₂×#120	1	4	yes	—
497	C₂×C₄²	C₂×#120	1	4	yes	—
498	C₂×C₄²	C₂×#120	1	16	yes	complemented
499	C₂×C₄²	C₂³×D₄	1	2	yes	—
500	C₂×C₄²	C₂³×D₄	1	2	yes	—
501	C₂×C₄²	C₂³×D₄	1	2	yes	—
502	C₂×C₄²	C₂³×D₄	1	2	yes	—
503	#100	C₂³×D₄	1	16	yes	—
504	C₂⁴	#2403	1	8	yes	—
505	C₂⁴	#2403	1	16	yes	—
506	C₂⁴	#2403	1	4	yes	—
507	C₂⁴	C₂×B(4,𝔽₂)	1	2	yes	—
508	C₂⁴	C₂×B(4,𝔽₂)	1	2	yes	—
509	C₂⁴	C₂×B(4,𝔽₂)	1	4	yes	—
510	C₂⁴	C₂×B(4,𝔽₂)	1	2	yes	—
511	C₂⁴	C₂×B(4,𝔽₂)	1	4	yes	—
512	C₂⁴	C₂×B(4,𝔽₂)	1	2	yes	—
513	C₂⁴	C₂²×#120	1	1	yes	characteristic
514	C₂⁴	C₂²×#120	1	4	yes	—
515	C₂⁴	C₂²×#120	1	4	yes	—
516	C₂⁴	C₂²×#120	1	2	yes	—
517	C₂⁴	C₂²×#120	1	2	yes	—
518	C₂⁴	C₂²×#120	1	2	yes	—
519	C₂⁴	C₂²×#120	1	2	yes	—
520	C₂⁴	C₂×D₄²	1	8	yes	—
521	C₂⁴	C₂×D₄²	1	16	yes	—
522	C₂⁴	C₂⁴×D₄	1	2	yes	—
523	C₂×D₄	#2403	1	16	yes	—
524	C₂×D₄	#2403	1	8	yes	—
525	C₂×D₄	C₂×B(4,𝔽₂)	1	16	yes	—
526	C₂×D₄	C₂×B(4,𝔽₂)	1	16	yes	—
527	C₂×D₄	C₂²×#120	1	4	yes	—
528	C₂×D₄	C₂²×#120	1	4	yes	—
529	C₂×D₄	C₂²×#120	1	2	yes	—
530	C₂×D₄	C₂²×#120	1	4	yes	—
531	C₂×D₄	C₂×#534	1	4	yes	—
532	C₂×D₄	C₂×#534	1	2	yes	—
533	C₂×D₄	C₂×D₄²	1	16	yes	—
534	C₂×D₄	C₂×D₄²	1	8	yes	—
535	C₂×D₄	C₂⁴×D₄	1	2	yes	—
536	C₂×D₄	C₂²×H(5,𝔽₂)	1	2	yes	—
537	C₂²×C₄	#2403	1	4	yes	—
538	C₂²×C₄	#2403	1	8	yes	—
539	C₂²×C₄	C₂×B(4,𝔽₂)	1	4	yes	—
540	C₂²×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
541	C₂²×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
542	C₂²×C₄	C₂²×#120	1	4	yes	—
543	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
544	C₂²×C₄	C₂²×#120	1	2	yes	—
545	C₂²×C₄	C₂²×#120	1	2	yes	—
546	C₂²×C₄	C₂²×#120	1	4	yes	—
547	C₂²×C₄	C₂²×#120	1	2	yes	—
548	C₂²×C₄	C₂²×#120	1	2	yes	—
549	C₂²×C₄	C₂×#534	1	2	yes	—
550	C₂²×C₄	C₂×#534	1	4	yes	—
551	C₂²×C₄	C₂⁴×D₄	1	1	yes	characteristic
552	C₄²	C₂²×#120	1	4	yes	—
553	C₄²	C₂²×#120	1	4	yes	—
554	C₂³	#23900	1	8	yes	—
555	C₂³	#23900	1	8	yes	—
556	C₂³	C₂×#2403	1	2	yes	—
557	C₂³	C₂×#2403	1	4	yes	—
558	C₂³	C₂×#2403	1	8	yes	—
559	C₂³	C₂×#2403	1	4	yes	—
560	C₂³	C₂²×B(4,𝔽₂)	1	4	yes	—
561	C₂³	C₂²×B(4,𝔽₂)	1	4	yes	—
562	C₂³	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
563	C₂³	C₂²×B(4,𝔽₂)	1	2	yes	—
564	C₂³	C₂²×B(4,𝔽₂)	1	4	yes	—
565	C₂³	C₂²×B(4,𝔽₂)	1	4	yes	—
566	C₂³	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
567	C₂³	C₂³×#120	1	1	yes	characteristic
568	C₂³	C₂²×D₄²	1	4	yes	—
569	C₂×C₄	C₂×#2403	1	2	yes	—
570	C₂×C₄	C₂×#2403	1	4	yes	—
571	C₂×C₄	C₂²×B(4,𝔽₂)	1	4	yes	—
572	C₂×C₄	C₂²×B(4,𝔽₂)	1	4	yes	—
573	C₂×C₄	C₂³×#120	1	1	yes	characteristic
574	C₂×C₄	C₂²×#534	1	1	yes	characteristic
575	C₂²	C₂×#23900	1	2	yes	—
576	C₂²	C₂×#23900	1	8	yes	—
577	C₂²	C₂×#23900	1	2	yes	—
578	C₂²	#7622880	1	4	yes	—
579	C₂²	C₂²×#2403	1	1	yes	characteristic
580	C₂²	C₂³×B(4,𝔽₂)	1	1	yes	characteristic
581	C₂²	C₂³×B(4,𝔽₂)	1	1	yes	characteristic
582	C₂	C₂²×#23900	1	1	yes	characteristic
583	C₂	C₂×#7622880	1	2	yes	—
584	C₂	#72234146	1	4	yes	direct product factor

	subgroup	G/H
center, socle	C₂³	C₂²×B(4,𝔽₂)
commutator, Frattini, cosocle	C₂²×D₄	C₂⁶
LCS	G ▷ C₂²×D₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ C₂³×D₄ ◁ C₂³×H(5,𝔽₂) ◁ G
LECS	G ▷ C₂²×D₄ ▷ C₂² ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. C₂×#494596	C₂	semidirect
2. C₂×#499844	C₂	semidirect
3. C₂×#493430	C₂	semidirect
4. C₂×#494682	C₂	semidirect
5. C₂²×#60388	C₂	semidirect
6. C₂×#499831	C₂	semidirect
7. C₂×#6628896	C₂	semidirect
8. C₂×#498927	C₂	semidirect
9. C₂×#499832	C₂	semidirect
10. #72234146	C₂	direct (N × H)
11. C₂×#499843	C₂	semidirect
12. C₂³×#2196	C₂	semidirect
13. C₂×#7737411	C₂	semidirect
14. C₂²×H(7,𝔽₂)	C₂²	semidirect
16. C₂³×D₄²	C₂²	semidirect
17. C₂³×B(4,𝔽₂)	C₂²	semidirect
18. C₂×#60388	C₂²	semidirect
19. C₂²×#3018	C₂²	semidirect
20. C₂²×#3021	C₂²	semidirect
21. C₂²×#3019	C₂²	semidirect
22. C₂²×#3019	C₂²	semidirect
24. C₂³×#453	C₂²	semidirect
25. C₂²×#2888	C₂²	semidirect
26. #7737411	C₂²	semidirect
27. C₂×#52004	C₂²	semidirect
28. C₂×#52004	C₂²	semidirect
29. C₂×#59041	C₂²	semidirect
30. C₂×#59126	C₂²	semidirect
31. C₂×#36702	C₂²	semidirect
33. C₂×#34364	C₂²	semidirect
34. C₂²×#2196	C₂²	semidirect
35. C₂²×#2196	C₂²	semidirect
36. C₂²×#2196	C₂²	semidirect
37. C₂²×#2127	C₂²	semidirect
38. C₂³×#353	C₂²	semidirect
39. C₂³×AΣL(1,𝔽₁₆)	C₂²	semidirect
40. #6628896	C₂²	semidirect
41. C₂×#32899	C₂²	semidirect
42. C₂×#32898	C₂²	semidirect
43. C₂×#20609	C₂²	semidirect
44. C₂×#20585	C₂²	semidirect
45. #499844	C₂²	semidirect
46. #499843	C₂²	semidirect
47. #499832	C₂²	semidirect
48. #499831	C₂²	semidirect
49. #498927	C₂²	semidirect
50. C₂×#13348	C₂²	semidirect
51. C₂×#13346	C₂²	semidirect
52. #494682	C₂²	semidirect
53. C₂×#13083	C₂²	semidirect
54. C₂×#13082	C₂²	semidirect
55. #494596	C₂²	semidirect
56. C₂×#13049	C₂²	semidirect
57. C₂×#13047	C₂²	semidirect
58. #493430	C₂²	semidirect
59. C₂×#12697	C₂²	semidirect
60. C₂×#12696	C₂²	semidirect
61. C₂×#12695	C₂²	semidirect
62. C₂×#12693	C₂²	semidirect
63. C₂×#12574	C₂²	semidirect
64. C₂×H(7,𝔽₂)	C₂³	semidirect
65. C₂²×#585	C₂³	semidirect
66. C₂³×H(5,𝔽₂)	D₄	semidirect
69. C₂³×H(5,𝔽₂)	C₂³	semidirect
70. C₂×#3498	D₄	semidirect
72. C₂²×D₄²	C₂³	semidirect
73. C₂²×D₄²	C₂³	semidirect
74. C₂²×D₄²	C₂³	semidirect
75. C₂²×#535	D₄	semidirect
76. C₂²×#535	D₄	semidirect
77. C₂²×#535	D₄	semidirect
81. C₂²×#532	D₄	semidirect
82. C₂²×#532	D₄	semidirect
84. C₂³×#127	D₄	semidirect
87. C₂³×#120	D₄	semidirect
88. C₂³×#120	D₄	semidirect
90. C₂²×C₄×#41	D₄	semidirect
92. C₂²×B(4,𝔽₂)	C₂³	semidirect
93. C₂×#3021	C₂³	semidirect
94. C₂×#3019	C₂³	semidirect
95. C₂×#3019	C₂³	semidirect
96. C₂×#3018	C₂³	semidirect
97. C₂²×#455	C₂³	semidirect
98. C₂²×#453	D₄	semidirect
102. C₂²×#453	C₂³	semidirect
103. C₂²×#453	C₂³	semidirect
104. C₂×#2888	C₂³	semidirect
105. C₂²×#413	C₂³	semidirect
107. C₂³×#100	C₂³	semidirect
109. #59126	C₂³	semidirect
110. #59041	C₂³	semidirect
111. C₂×#2684	C₂³	semidirect
112. C₂×#2669	C₂³	semidirect
113. #52004	C₂³	semidirect
114. #52004	C₂³	semidirect
115. #36702	C₂³	semidirect
116. #35346	D₄	semidirect
118. C₂×#2404	D₄	semidirect
120. C₂×#2403	D₄	semidirect
122. #34364	C₂³	semidirect
123. C₂×#2380	C₂³	semidirect
124. C₂×#2366	C₂³	semidirect
125. C₂×#2308	D₄	semidirect
126. C₂×#2308	D₄	semidirect
128. C₂×#2196	C₂³	semidirect
129. C₂×#2196	C₂³	semidirect
130. C₂×#2127	C₂³	semidirect
131. C₂²×#354	C₂³	semidirect
132. C₂²×#353	C₂³	semidirect
133. C₂²×#353	C₂³	semidirect
134. C₂²×#353	C₂³	semidirect
135. C₂²×#353	C₂³	semidirect
136. C₂²×AΣL(1,𝔽₁₆)	C₂³	semidirect
137. C₂²×AΣL(1,𝔽₁₆)	C₂³	semidirect
138. #32899	C₂³	semidirect
139. #32898	C₂³	semidirect
140. #20609	C₂³	semidirect
141. C₂×#1790	C₂³	semidirect
142. #20585	C₂³	semidirect
143. C₂×#1782	C₂³	semidirect
144. C₂×#1781	C₂³	semidirect
145. #13348	C₂³	semidirect
146. #13346	C₂³	semidirect
147. #13083	C₂³	semidirect
148. #13082	C₂³	semidirect
149. #13049	C₂³	semidirect
150. #13047	C₂³	semidirect
151. #12697	C₂³	semidirect
152. #12696	C₂³	semidirect
153. #12695	C₂³	semidirect
154. #12693	C₂³	semidirect
155. #12574	C₂³	semidirect
156. C₂×#1390	C₂³	semidirect
158. C₂×#585	C₂⁴	semidirect
161. C₂²×H(5,𝔽₂)	C₂×D₄	semidirect
162. C₂²×H(5,𝔽₂)	C₂×D₄	semidirect
166. C₂²×H(5,𝔽₂)	C₂⁴	semidirect
172. C₂³×#41	C₂×D₄	semidirect
173. C₂³×#41	C₂×D₄	semidirect
180. C₂⁴×D₄	C₂×D₄	semidirect
181. C₂⁴×D₄	C₂×D₄	semidirect
182. C₂⁴×D₄	C₂×D₄	semidirect
185. C₂×D₄²	C₂⁴	semidirect
186. C₂×D₄²	C₂⁴	semidirect
188. C₂×#535	C₂×D₄	semidirect
189. C₂×#535	C₂×D₄	semidirect
190. C₂×#535	C₂×D₄	semidirect
191. C₂×#535	C₂×D₄	semidirect
192. C₂×#535	C₂×D₄	semidirect
196. C₂×#532	C₂×D₄	semidirect
197. C₂×#532	C₂×D₄	semidirect
198. C₂×#532	C₂×D₄	semidirect
200. C₂²×C₄⋊Q₈	C₂×D₄	semidirect
206. C₂²×#127	C₂×D₄	semidirect
207. C₂²×#127	C₂×D₄	semidirect
208. C₂²×#127	C₂×D₄	semidirect
209. C₂²×#127	C₂×D₄	semidirect
210. C₂²×#127	C₂×D₄	semidirect
217. C₂²×#124	C₂×D₄	semidirect
218. C₂²×#124	C₂×D₄	semidirect
219. C₂²×#124	C₂×D₄	semidirect
220. C₂²×#124	C₂×D₄	semidirect
224. C₂²×#120	C₂×D₄	semidirect
225. C₂²×#120	C₂×D₄	semidirect
226. C₂²×#120	C₂×D₄	semidirect
227. C₂²×#120	C₂×D₄	semidirect
230. C₂×C₄×#41	C₂×D₄	semidirect
232. C₂²×#117	C₂×D₄	semidirect
233. C₂²×#117	C₂×D₄	semidirect
237. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
239. C₂³×C₄²	C₂×D₄	semidirect
240. C₂³×C₄²	C₂×D₄	semidirect
242. C₂×#455	C₂⁴	semidirect
243. C₂×#453	C₂×D₄	semidirect
244. C₂×#453	C₂×D₄	semidirect
245. C₂×#453	C₂×D₄	semidirect
248. C₂×#453	C₂⁴	semidirect
249. C₂×#413	C₂⁴	semidirect
250. C₂²×#100	C₂×D₄	semidirect
253. C₂²×#100	C₂⁴	semidirect
256. #2684	C₂⁴	semidirect
257. #2669	C₂⁴	semidirect
258. #2404	C₂×D₄	semidirect
259. #2404	C₂×D₄	semidirect
261. #2403	C₂×D₄	semidirect
262. #2403	C₂×D₄	semidirect
264. #2380	C₂⁴	semidirect
265. #2366	C₂⁴	semidirect
267. #2308	C₂×D₄	semidirect
268. #2308	C₂×D₄	semidirect
271. C₂×#386	C₂×D₄	semidirect
272. C₂×#386	C₂×D₄	semidirect
274. C₂×#381	C₂×D₄	semidirect
275. C₂×#379	C₂×D₄	semidirect
276. C₂×#354	C₂⁴	semidirect
277. C₂×#353	C₂⁴	semidirect
278. C₂×#353	C₂⁴	semidirect
279. C₂×#353	C₂⁴	semidirect
280. C₂×AΣL(1,𝔽₁₆)	C₂⁴	semidirect
281. #1790	C₂⁴	semidirect
282. #1782	C₂⁴	semidirect
283. #1781	C₂⁴	semidirect
284. #1390	C₂⁴	semidirect
291. C₂×H(5,𝔽₂)	C₂²×D₄	semidirect
304. C₂²×#41	C₂²×D₄	semidirect
305. C₂²×#41	C₂²×D₄	semidirect
320. C₂³×D₄	#120	semidirect
339. C₂³×D₄	C₂²×D₄	semidirect
340. C₂³×D₄	C₂²×D₄	semidirect
341. C₂³×D₄	C₂²×D₄	semidirect
353. C₂×C₄⋊Q₈	C₂²×D₄	semidirect
354. C₂×#127	#120	semidirect
355. C₂×#127	#120	semidirect
356. C₂×#127	#120	semidirect
366. C₂×#127	C₂²×D₄	semidirect
367. C₂×#127	C₂²×D₄	semidirect
368. C₂×#127	C₂²×D₄	semidirect
374. C₂×#124	C₂²×D₄	semidirect
375. C₂×#124	C₂²×D₄	semidirect
376. C₂×#124	C₂²×D₄	semidirect
377. C₂×#124	C₂²×D₄	semidirect
381. C₂×#120	C₂²×D₄	semidirect
382. C₂×#120	C₂²×D₄	semidirect
385. C₂×#117	C₂²×D₄	semidirect
386. C₂×#117	C₂²×D₄	semidirect
392. C₂²×C₂²⋊C₄	C₂²×D₄	semidirect
393. C₂²×C₄²	#120	semidirect
399. C₂²×C₄²	C₂²×D₄	semidirect
400. C₂²×C₄²	C₂²×D₄	semidirect
401. #453	C₂²×D₄	semidirect
402. #453	C₂²×D₄	semidirect
404. C₂×#100	C₂²×D₄	semidirect
409. #386	C₂²×D₄	semidirect
410. #386	C₂²×D₄	semidirect
412. #381	C₂²×D₄	semidirect
413. #379	C₂²×D₄	semidirect
450. C₂²×D₄	C₂×#120	semidirect
490. #127	C₂×#120	semidirect
491. #127	C₂×#120	semidirect
498. C₂×C₄²	C₂×#120	semidirect
584. C₂	#72234146	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×#494596	2
C₂×#499844	2
C₂×#493430	2
C₂×#494682	2
C₂²×#60388	2
C₂×#499831	2
C₂×#6628896	2
C₂×#498927	2
C₂×#499832	2
#72234146	2
C₂×#499843	2
C₂³×#2196	2
C₂×#7737411	2

Subgroups — C2×#72234146 #72338116

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#72234146 #72338116