Subgroups — #72262758

Order 2048.

At least 7492 conjugacy classes of subgroups; only the 2816 normal subgroups are shown.

The subgroup lattice has 691 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72262716	C₂	1	1	yes	maximal, characteristic, complemented
2	#72256427	C₂	1	1	yes	maximal, characteristic, complemented
3	#72255991	C₂	1	4	yes	maximal, complemented
4	#72255959	C₂	1	4	yes	maximal, complemented
5	#72255720	C₂	1	1	yes	maximal, characteristic, complemented
6	#72255679	C₂	1	1	yes	maximal, characteristic, complemented
7	#72255631	C₂	1	1	yes	maximal, characteristic, complemented
8	#72255601	C₂	1	1	yes	maximal, characteristic, complemented
9	#72252150	C₂	1	1	yes	maximal, characteristic, complemented
10	#72252132	C₂	1	1	yes	maximal, characteristic, complemented
11	#72252112	C₂	1	1	yes	maximal, characteristic, complemented
12	#72237236	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#359476	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#383145	C₂	1	4	yes	maximal, complemented
15	#72236779	C₂	1	4	yes	maximal, complemented
16	C₂×#392113	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#359507	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂³×#3003	C₂	1	1	yes	maximal, characteristic
19	#72231771	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂⁶×D₄	C₂²	1	1	yes	characteristic
21	C₂⁴×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
22	C₂⁴×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
23	C₂³×#525	C₂²	1	1	yes	characteristic
24	C₂²×#3003	C₄	1	16	yes	complemented
25	C₂²×#3003	C₂²	1	2	yes	—
26	C₂²×#3003	C₂²	1	2	yes	—
27	C₂²×#3003	C₂²	1	2	yes	—
28	C₂²×#3003	C₂²	1	2	yes	—
29	C₂×#60064	C₂²	1	1	yes	characteristic, complemented
30	C₂³×#407	C₂²	1	1	yes	characteristic
31	C₂³×#418	C₂²	1	1	yes	characteristic
32	C₂³×#418	C₂²	1	1	yes	characteristic
33	C₂×#21249	C₂²	1	2	yes	complemented
34	C₂×#21249	C₂²	1	2	yes	complemented
35	C₂×#21005	C₂²	1	4	yes	complemented
36	C₂²×#1903	C₂²	1	2	yes	complemented
37	C₂²×#1903	C₂²	1	2	yes	complemented
38	C₂²×#1891	C₂²	1	4	yes	complemented
39	C₂×#20667	C₂²	1	1	yes	characteristic, complemented
40	C₂×#20605	C₂²	1	1	yes	characteristic, complemented
41	#6370715	C₂²	1	1	yes	characteristic, complemented
42	C₂×#20598	C₂²	1	1	yes	characteristic
43	C₂×#20598	C₂²	1	1	yes	characteristic
44	C₂×#20598	C₂²	1	1	yes	characteristic
45	C₂×#20598	C₂²	1	1	yes	characteristic
46	C₂×#20598	C₂²	1	4	yes	complemented
47	C₂×#20598	C₂²	1	4	yes	complemented
48	C₂×#20591	C₂²	1	1	yes	characteristic, complemented
49	C₂²×#1783	C₂²	1	1	yes	characteristic
50	C₂²×#1783	C₂²	1	1	yes	characteristic
51	C₂²×#1783	C₂²	1	1	yes	characteristic
52	C₂²×#1783	C₂²	1	1	yes	characteristic
53	C₂²×#1783	C₂²	1	4	yes	complemented
54	C₂²×#1783	C₂²	1	4	yes	complemented
55	C₂×#20579	C₂²	1	1	yes	characteristic
56	C₂×#20579	C₂²	1	1	yes	characteristic
57	C₂×#20579	C₂²	1	1	yes	characteristic
58	#6369812	C₂²	1	1	yes	characteristic, complemented
59	#607558	C₂²	1	1	yes	characteristic
60	C₂×#11187	C₂²	1	4	yes	complemented
61	C₂×#11181	C₂²	1	4	yes	complemented
62	C₂×#11133	C₂²	1	4	yes	complemented
63	C₂×#11101	C₂²	1	4	yes	complemented
64	C₂×#11034	C₂²	1	4	yes	complemented
65	C₂×#11034	C₂²	1	4	yes	complemented
66	#357581	C₂²	1	4	yes	complemented
67	C₂×#11014	C₂²	1	2	yes	complemented
68	C₂×#11014	C₂²	1	2	yes	complemented
69	C₂×#10994	C₂²	1	4	yes	complemented
70	C₂×#10994	C₂²	1	4	yes	complemented
71	#357541	C₂²	1	2	yes	complemented
72	#357541	C₂²	1	2	yes	complemented
73	C₂×#10993	C₂²	1	4	yes	complemented
74	C₂×#10953	C₂²	1	4	yes	complemented
75	C₂×#10937	C₂²	1	4	yes	complemented
76	#353416	C₂²	1	1	yes	characteristic, complemented
77	C₂×#10738	C₂²	1	1	yes	characteristic, complemented
78	C₂×#10738	C₂²	1	1	yes	characteristic, complemented
79	C₂×#10737	C₂²	1	1	yes	characteristic, complemented
80	#353403	C₂²	1	1	yes	characteristic, complemented
81	#353403	C₂²	1	1	yes	characteristic, complemented
82	#353386	C₂²	1	1	yes	characteristic, complemented
83	C₂×#10729	C₂²	1	1	yes	characteristic, complemented
84	C₂×C₂²⋊#338	C₂²	1	1	yes	characteristic, complemented
85	C₂×#10716	C₂²	1	1	yes	characteristic, complemented
86	#123644	C₂²	1	4	yes	complemented
87	#123628	C₂²	1	4	yes	complemented
88	#123619	C₂²	1	4	yes	complemented
89	#123619	C₂²	1	4	yes	complemented
90	#123535	C₂²	1	4	yes	complemented
91	#123532	C₂²	1	4	yes	complemented
92	C₂⁴×#41	C₂³	1	1	yes	characteristic
93	C₂⁵×D₄	C₂×C₄	1	8	yes	—
94	C₂⁵×D₄	C₂³	1	2	yes	—
95	C₂⁵×D₄	C₂³	1	2	yes	—
96	C₂⁵×D₄	C₂³	1	1	yes	characteristic
97	C₂⁵×D₄	C₂³	1	1	yes	characteristic
98	C₂⁶×C₄	C₂³	1	1	yes	characteristic
99	C₂³×AGL(1,ℤ/8)	C₂×C₄	1	8	yes	—
100	C₂³×AGL(1,ℤ/8)	C₂×C₄	1	8	yes	—
101	C₂³×AGL(1,ℤ/8)	D₄	1	8	yes	—
102	C₂³×AGL(1,ℤ/8)	D₄	1	2	yes	—
103	C₂³×AGL(1,ℤ/8)	D₄	1	2	yes	—
104	C₂³×AGL(1,ℤ/8)	C₂³	1	2	yes	—
105	C₂³×AGL(1,ℤ/8)	C₂³	1	2	yes	—
106	C₂³×AGL(1,ℤ/8)	C₂³	1	1	yes	characteristic
107	C₂³×AGL(1,ℤ/8)	C₂³	1	1	yes	characteristic
108	C₂³×AGL(1,ℤ/8)	C₂³	1	1	yes	characteristic
109	C₂³×AGL(1,ℤ/8)	C₂³	1	1	yes	characteristic
110	C₂⁴×SD₁₆	D₄	1	2	yes	—
111	C₂⁴×D₈	D₄	1	2	yes	—
112	C₂²×#568	C₂³	1	2	yes	complemented
113	C₂⁴×M₁₆	C₂³	1	1	yes	characteristic
114	C₂⁴×M₁₆	C₂³	1	1	yes	characteristic
115	C₂²×#525	C₂×C₄	1	8	yes	—
116	C₂²×#525	C₂³	1	2	yes	—
117	C₂²×#525	C₂³	1	2	yes	—
118	C₂³×#117	C₂³	1	1	yes	characteristic
119	C₂×#3003	C₂×C₄	1	16	yes	—
120	C₂×#3003	C₂×C₄	1	16	yes	—
121	C₂×#3003	C₂×C₄	1	16	yes	—
122	C₂×#3003	C₂×C₄	1	16	yes	—
123	C₂×#3003	D₄	1	32	yes	—
124	C₂²×#430	C₂³	1	2	yes	complemented
125	C₂²×#421	C₂³	1	2	yes	complemented
126	C₂²×#421	C₂³	1	2	yes	complemented
127	C₂×#2896	C₂³	1	2	yes	complemented
128	C₂×#2896	C₂³	1	2	yes	complemented
129	C₂²×#418	C₂×C₄	1	8	yes	—
130	C₂²×#418	C₂×C₄	1	8	yes	—
131	C₂²×#418	C₂³	1	2	yes	—
132	C₂²×#418	C₂³	1	2	yes	—
133	C₂²×#418	C₂³	1	2	yes	—
134	C₂²×#418	C₂³	1	2	yes	—
135	C₂²×#418	C₂³	1	2	yes	—
136	C₂²×#418	C₂³	1	2	yes	—
137	C₂²×#418	C₂³	1	2	yes	—
138	C₂²×#418	C₂³	1	2	yes	—
139	C₂²×#418	C₂³	1	4	yes	—
140	C₂²×#418	C₂³	1	4	yes	—
141	C₂²×#413	C₂³	1	2	yes	complemented
142	C₂²×#413	C₂³	1	2	yes	complemented
143	C₂³×#100	C₂³	1	2	yes	—
144	C₂³×#100	C₂³	1	2	yes	—
145	C₂³×#100	C₂³	1	4	yes	—
146	C₂³×#100	C₂³	1	2	yes	—
147	C₂³×#100	C₂³	1	2	yes	—
148	C₂³×#100	C₂³	1	4	yes	—
149	C₂×#2879	C₂³	1	2	yes	complemented
150	C₂²×#407	C₂×C₄	1	8	yes	—
151	C₂²×#407	C₂³	1	2	yes	—
152	C₂²×#407	C₂³	1	4	yes	—
153	C₂²×#407	C₂³	1	2	yes	—
154	C₂²×#407	C₂³	1	4	yes	—
155	C₂²×#407	C₂³	1	4	yes	—
156	C₂²×#407	C₂³	1	1	yes	characteristic
157	C₂²×#407	C₂³	1	1	yes	characteristic
158	C₂²×#407	C₂³	1	1	yes	characteristic
159	C₂²×#407	C₂³	1	1	yes	characteristic
160	C₂²×#407	C₂³	1	1	yes	characteristic
161	C₂²×#407	C₂³	1	1	yes	characteristic
162	C₂×#2873	C₂³	1	2	yes	complemented
163	C₂×#2280	C₂³	1	4	yes	—
164	C₂×#2280	C₂³	1	1	yes	characteristic
165	C₂×#2280	C₂³	1	1	yes	characteristic
166	C₂×#1786	D₄	1	8	yes	complemented
167	#20579	D₄	1	8	yes	—
168	C₂²×#344	C₂³	1	2	yes	complemented
169	C₂²×#344	C₂³	1	4	yes	complemented
170	C₂²×#344	C₂³	1	4	yes	complemented
171	C₂²×#344	C₂³	1	2	yes	complemented
172	C₂²×#344	C₂³	1	4	yes	complemented
173	C₂×#1742	C₂³	1	4	yes	complemented
174	C₂×#1738	C₂³	1	4	yes	complemented
175	C₂×#1738	C₂³	1	2	yes	complemented
176	C₂×#1738	C₂³	1	4	yes	complemented
177	C₂×#1733	C₂³	1	4	yes	complemented
178	C₂²×#338	C₂³	1	2	yes	complemented
179	C₂²×#338	C₂³	1	2	yes	complemented
180	C₂²×H(3,ℤ/4)	C₂³	1	4	yes	complemented
181	#20335	C₂³	1	2	yes	complemented
182	C₂⁷	#41	1	1	yes	characteristic
183	C₂³×#41	C₂²×C₄	1	4	yes	—
184	C₂³×#41	C₂×D₄	1	4	yes	—
185	C₂³×#41	C₂×D₄	1	1	yes	characteristic
186	C₂³×#41	C₂×D₄	1	1	yes	characteristic
187	C₂³×#41	C₂⁴	1	1	yes	characteristic
188	C₂³×#41	C₂⁴	1	1	yes	characteristic
189	C₂⁴×Q₈	C₂×D₄	1	1	yes	characteristic
190	C₂⁴×D₄	C₂²×C₄	1	4	yes	—
191	C₂⁴×D₄	C₂²×C₄	1	4	yes	—
192	C₂⁴×D₄	C₂²×C₄	1	8	yes	—
193	C₂⁴×D₄	C₂²×C₄	1	8	yes	—
194	C₂⁴×D₄	C₂×D₄	1	2	yes	—
195	C₂⁴×D₄	C₂×D₄	1	4	yes	—
196	C₂⁴×D₄	C₂×D₄	1	2	yes	—
197	C₂⁴×D₄	C₂×D₄	1	4	yes	—
198	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
199	C₂⁴×D₄	C₂×D₄	1	16	yes	—
200	C₂⁴×D₄	#41	1	4	yes	—
201	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
202	C₂⁴×D₄	C₂⁴	1	2	yes	—
203	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
204	C₂⁵×C₄	C₂²×C₄	1	4	yes	—
205	C₂⁵×C₄	C₂×D₄	1	4	yes	—
206	C₂⁵×C₄	#41	1	1	yes	characteristic
207	C₂⁵×C₄	#41	1	2	yes	—
208	C₂⁵×C₄	C₂⁴	1	2	yes	—
209	C₂⁵×C₄	C₂⁴	1	1	yes	characteristic
210	C₂²×AGL(1,ℤ/8)	C₂²⋊C₄	1	16	yes	complemented
211	C₂²×AGL(1,ℤ/8)	C₂²⋊C₄	1	16	yes	complemented
212	C₂²×AGL(1,ℤ/8)	C₂²×C₄	1	8	yes	—
213	C₂²×AGL(1,ℤ/8)	C₂²×C₄	1	8	yes	—
214	C₂²×AGL(1,ℤ/8)	C₂²×C₄	1	4	yes	—
215	C₂²×AGL(1,ℤ/8)	C₂²×C₄	1	4	yes	—
216	C₂²×AGL(1,ℤ/8)	C₂²×C₄	1	4	yes	—
217	C₂²×AGL(1,ℤ/8)	C₂²×C₄	1	4	yes	—
218	C₂²×AGL(1,ℤ/8)	C₂×D₄	1	16	yes	—
219	C₂²×AGL(1,ℤ/8)	C₂×D₄	1	4	yes	—
220	C₂²×AGL(1,ℤ/8)	C₂×D₄	1	4	yes	—
221	C₂²×AGL(1,ℤ/8)	C₂×D₄	1	4	yes	—
222	C₂²×AGL(1,ℤ/8)	C₂×D₄	1	4	yes	—
223	C₂²×AGL(1,ℤ/8)	C₂×D₄	1	16	yes	—
224	C₂³×SD₁₆	C₂²⋊C₄	1	16	yes	complemented
225	C₂³×SD₁₆	C₂×D₄	1	2	yes	—
226	C₂³×SD₁₆	C₂×D₄	1	2	yes	—
227	C₂³×SD₁₆	C₂×D₄	1	2	yes	—
228	C₂³×SD₁₆	C₂×D₄	1	2	yes	—
229	C₂³×D₈	C₂²⋊C₄	1	16	yes	complemented
230	C₂³×D₈	C₂×D₄	1	2	yes	—
231	C₂³×D₈	C₂×D₄	1	2	yes	—
232	C₂³×D₈	C₂×D₄	1	2	yes	—
233	C₂³×D₈	C₂×D₄	1	2	yes	—
234	C₂³×M₁₆	C₂²×C₄	1	4	yes	—
235	C₂³×M₁₆	C₂²×C₄	1	4	yes	—
236	C₂³×M₁₆	C₂×D₄	1	4	yes	—
237	C₂³×M₁₆	C₂×D₄	1	2	yes	—
238	C₂³×M₁₆	C₂⁴	1	2	yes	—
239	C₂³×M₁₆	C₂⁴	1	2	yes	—
240	C₂³×M₁₆	C₂⁴	1	2	yes	—
241	C₂³×M₁₆	C₂⁴	1	2	yes	—
242	C₂³×M₁₆	C₂⁴	1	2	yes	—
243	C₂³×M₁₆	C₂⁴	1	2	yes	—
244	C₂³×M₁₆	C₂⁴	1	2	yes	—
245	C₂³×M₁₆	C₂⁴	1	1	yes	characteristic
246	C₂³×M₁₆	C₂⁴	1	1	yes	characteristic
247	C₂⁴×C₈	C₂×D₄	1	2	yes	—
248	C₂×#525	C₂²×C₄	1	8	yes	—
249	C₂×#525	C₂²×C₄	1	8	yes	—
250	C₂×#525	C₂×D₄	1	16	yes	—
251	C₂²×#117	C₂²×C₄	1	4	yes	—
252	C₂²×#117	C₂⁴	1	2	yes	—
253	C₂²×#117	C₂⁴	1	2	yes	—
254	C₂²×#117	C₂⁴	1	2	yes	—
255	#3003	C₂²⋊C₄	1	128	yes	complemented
256	C₂×#418	C₂²×C₄	1	8	yes	—
257	C₂×#418	C₂²×C₄	1	8	yes	—
258	C₂×#418	C₂²×C₄	1	8	yes	—
259	C₂×#418	C₂²×C₄	1	8	yes	—
260	C₂×#418	C₂×D₄	1	16	yes	—
261	C₂×#418	C₂×D₄	1	16	yes	—
262	C₂²×#102	C₂×D₄	1	16	yes	complemented
263	C₂×#407	C₂²×C₄	1	8	yes	—
264	C₂×#407	C₂²×C₄	1	8	yes	—
265	C₂×#407	C₂×D₄	1	4	yes	—
266	C₂×#407	C₂×D₄	1	4	yes	—
267	C₂×#407	C₂×D₄	1	16	yes	—
268	C₂×#407	C₂×D₄	1	16	yes	—
269	C₂²×C₂²⋊C₈	C₂×D₄	1	4	yes	—
270	C₂×#380	C₂×D₄	1	4	yes	—
271	C₂⁶	C₄×D₄	1	4	yes	—
272	C₂⁶	C₂×#41	1	2	yes	—
273	C₂⁶	C₂×#41	1	1	yes	characteristic
274	C₂²×#41	C₂×C₂²⋊C₄	1	4	yes	—
275	C₂²×#41	C₂×C₂²⋊C₄	1	4	yes	—
276	C₂²×#41	C₂³×C₄	1	2	yes	—
277	C₂²×#41	C₂³×C₄	1	2	yes	—
278	C₂²×#41	C₂²×D₄	1	2	yes	—
279	C₂²×#41	C₂²×D₄	1	2	yes	—
280	C₂²×#41	C₂²×D₄	1	8	yes	—
281	C₂³×Q₈	C₂×C₂²⋊C₄	1	4	yes	—
282	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
283	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
284	C₂³×D₄	C₂×C₂²⋊C₄	1	8	yes	—
285	C₂³×D₄	C₂×C₂²⋊C₄	1	8	yes	—
286	C₂³×D₄	C₂×C₂²⋊C₄	1	4	yes	—
287	C₂³×D₄	C₂×C₂²⋊C₄	1	32	yes	—
288	C₂³×D₄	C₄×D₄	1	16	yes	—
289	C₂³×D₄	C₂³×C₄	1	2	yes	—
290	C₂³×D₄	C₂³×C₄	1	4	yes	—
291	C₂³×D₄	C₂³×C₄	1	2	yes	—
292	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
293	C₂³×D₄	C₂²×D₄	1	2	yes	—
294	C₂³×D₄	C₂²×D₄	1	2	yes	—
295	C₂³×D₄	C₂²×D₄	1	8	yes	—
296	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
297	C₂³×D₄	C₂²×D₄	1	2	yes	—
298	C₂³×D₄	C₂²×D₄	1	2	yes	—
299	C₂³×D₄	C₂²×D₄	1	8	yes	—
300	C₂³×D₄	C₂²×D₄	1	4	yes	—
301	C₂³×D₄	C₂×#41	1	4	yes	—
302	C₂³×D₄	H(5,𝔽₂)	1	8	yes	—
303	C₂³×D₄	H(5,𝔽₂)	1	8	yes	—
304	C₂⁴×C₄	C₄×D₄	1	4	yes	—
305	C₂⁴×C₄	C₄×D₄	1	8	yes	—
306	C₂⁴×C₄	C₂³×C₄	1	4	yes	—
307	C₂⁴×C₄	C₂³×C₄	1	2	yes	—
308	C₂⁴×C₄	C₂²×D₄	1	8	yes	—
309	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
310	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
311	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
312	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
313	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
314	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
315	C₂⁴×C₄	C₂×#41	1	2	yes	—
316	C₂⁴×C₄	C₂×#41	1	1	yes	characteristic
317	C₂⁴×C₄	C₂×#41	1	2	yes	—
318	C₂⁴×C₄	H(5,𝔽₂)	1	8	yes	—
319	C₂⁴×C₄	H(5,𝔽₂)	1	2	yes	—
320	C₂⁴×C₄	H(5,𝔽₂)	1	2	yes	—
321	C₂⁴×C₄	H(5,𝔽₂)	1	2	yes	—
322	C₂⁴×C₄	H(5,𝔽₂)	1	2	yes	—
323	C₂⁴×C₄	H(5,𝔽₂)	1	1	yes	characteristic
324	C₂⁴×C₄	H(5,𝔽₂)	1	1	yes	characteristic
325	C₂⁴×C₄	H(5,𝔽₂)	1	2	yes	—
326	C₂⁴×C₄	H(5,𝔽₂)	1	2	yes	—
327	C₂⁴×C₄	H(5,𝔽₂)	1	2	yes	—
328	C₂⁴×C₄	C₂⁵	1	1	yes	characteristic
329	C₂×AGL(1,ℤ/8)	C₂×C₂²⋊C₄	1	32	yes	—
330	C₂×AGL(1,ℤ/8)	C₂×C₂²⋊C₄	1	32	yes	—
331	C₂×AGL(1,ℤ/8)	#120	1	32	yes	—
332	C₂²×SD₁₆	C₂×C₂²⋊C₄	1	8	yes	—
333	C₂²×SD₁₆	C₂×C₂²⋊C₄	1	8	yes	—
334	C₂²×SD₁₆	C₂×C₂²⋊C₄	1	8	yes	—
335	C₂²×SD₁₆	C₂×C₂²⋊C₄	1	8	yes	—
336	C₂²×SD₁₆	#120	1	16	yes	—
337	C₂²×D₈	C₂×C₂²⋊C₄	1	8	yes	—
338	C₂²×D₈	C₂×C₂²⋊C₄	1	8	yes	—
339	C₂²×D₈	C₂×C₂²⋊C₄	1	8	yes	—
340	C₂²×D₈	C₂×C₂²⋊C₄	1	8	yes	—
341	C₂²×D₈	#120	1	16	yes	—
342	C₂²×M₁₆	C₂×C₂²⋊C₄	1	8	yes	—
343	C₂²×M₁₆	C₂³×C₄	1	4	yes	—
344	C₂²×M₁₆	C₂³×C₄	1	2	yes	—
345	C₂²×M₁₆	C₂³×C₄	1	2	yes	—
346	C₂²×M₁₆	C₂²×D₄	1	4	yes	—
347	C₂²×M₁₆	C₂²×D₄	1	4	yes	—
348	C₂²×M₁₆	C₂²×D₄	1	8	yes	—
349	C₂²×M₁₆	C₂²×D₄	1	2	yes	—
350	C₂²×M₁₆	C₂²×D₄	1	2	yes	—
351	C₂²×M₁₆	C₂²×D₄	1	8	yes	—
352	C₂³×C₈	C₂×C₂²⋊C₄	1	8	yes	—
353	C₂³×C₈	C₂²×D₄	1	4	yes	—
354	C₂³×C₈	C₂²×D₄	1	2	yes	—
355	C₂³×C₈	C₂²×D₄	1	2	yes	—
356	#525	C₂×C₂²⋊C₄	1	32	yes	—
357	C₂×#117	C₂³×C₄	1	4	yes	—
358	C₂×#117	C₂²×D₄	1	8	yes	—
359	C₂²×C₄⋊C₄	C₂²×D₄	1	4	yes	—
360	#418	C₂×C₂²⋊C₄	1	32	yes	—
361	#418	C₂×C₂²⋊C₄	1	32	yes	—
362	#407	C₂×C₂²⋊C₄	1	32	yes	—
363	C₂⁵	C₂×C₄×D₄	1	4	yes	—
364	C₂⁵	C₂×C₄×D₄	1	2	yes	—
365	C₂⁵	#538	1	2	yes	—
366	C₂⁵	#538	1	2	yes	—
367	C₂⁵	#546	1	1	yes	characteristic
368	C₂⁵	#546	1	2	yes	—
369	C₂⁵	#546	1	8	yes	—
370	C₂⁵	#546	1	1	yes	characteristic
371	C₂⁵	#546	1	2	yes	—
372	C₂⁵	#551	1	2	yes	—
373	C₂⁵	C₂²×#41	1	1	yes	characteristic
374	C₂×#41	C₂²×C₂²⋊C₄	1	8	yes	—
375	C₂×#41	C₂×#120	1	8	yes	—
376	C₂²×Q₈	C₂²×C₂²⋊C₄	1	2	yes	—
377	C₂²×Q₈	C₂²×C₂²⋊C₄	1	2	yes	—
378	C₂²×Q₈	C₂×#120	1	4	yes	—
379	C₂²×D₄	C₂²×C₂²⋊C₄	1	2	yes	—
380	C₂²×D₄	C₂²×C₂²⋊C₄	1	4	yes	—
381	C₂²×D₄	C₂²×C₂²⋊C₄	1	8	yes	—
382	C₂²×D₄	C₂²×C₂²⋊C₄	1	2	yes	—
383	C₂²×D₄	C₂²×C₂²⋊C₄	1	4	yes	—
384	C₂²×D₄	C₂²×C₂²⋊C₄	1	8	yes	—
385	C₂²×D₄	C₂×C₄×D₄	1	8	yes	—
386	C₂²×D₄	#518	1	8	yes	—
387	C₂²×D₄	#518	1	8	yes	—
388	C₂²×D₄	C₂×#120	1	4	yes	—
389	C₂²×D₄	C₂×#120	1	8	yes	—
390	C₂²×D₄	C₂×#120	1	8	yes	—
391	C₂²×D₄	#534	1	8	yes	—
392	C₂²×D₄	#534	1	8	yes	—
393	C₂²×D₄	D₄²	1	16	yes	—
394	C₂²×D₄	#546	1	16	yes	—
395	C₂³×C₄	C₂²×C₂²⋊C₄	1	8	yes	—
396	C₂³×C₄	C₂²×C₂²⋊C₄	1	2	yes	—
397	C₂³×C₄	C₂²×C₂²⋊C₄	1	2	yes	—
398	C₂³×C₄	C₂×C₄×D₄	1	4	yes	—
399	C₂³×C₄	C₂×C₄×D₄	1	2	yes	—
400	C₂³×C₄	C₂×C₄×D₄	1	4	yes	—
401	C₂³×C₄	#518	1	8	yes	—
402	C₂³×C₄	#518	1	4	yes	—
403	C₂³×C₄	#518	1	4	yes	—
404	C₂³×C₄	#518	1	2	yes	—
405	C₂³×C₄	#518	1	2	yes	—
406	C₂³×C₄	#518	1	4	yes	—
407	C₂³×C₄	#534	1	2	yes	—
408	C₂³×C₄	#534	1	2	yes	—
409	C₂³×C₄	#534	1	2	yes	—
410	C₂³×C₄	#534	1	2	yes	—
411	C₂³×C₄	#534	1	4	yes	—
412	C₂³×C₄	#534	1	4	yes	—
413	C₂³×C₄	#534	1	2	yes	—
414	C₂³×C₄	#534	1	2	yes	—
415	C₂³×C₄	#534	1	4	yes	—
416	C₂³×C₄	#535	1	4	yes	—
417	C₂³×C₄	#535	1	4	yes	—
418	C₂³×C₄	#538	1	4	yes	—
419	C₂³×C₄	#538	1	2	yes	—
420	C₂³×C₄	#538	1	2	yes	—
421	C₂³×C₄	#538	1	2	yes	—
422	C₂³×C₄	#538	1	2	yes	—
423	C₂³×C₄	D₄²	1	16	yes	—
424	C₂³×C₄	D₄²	1	2	yes	—
425	C₂³×C₄	D₄²	1	2	yes	—
426	C₂³×C₄	D₄²	1	4	yes	—
427	C₂³×C₄	D₄²	1	2	yes	—
428	C₂³×C₄	D₄²	1	2	yes	—
429	C₂³×C₄	D₄²	1	2	yes	—
430	C₂³×C₄	D₄²	1	2	yes	—
431	C₂³×C₄	D₄²	1	4	yes	—
432	C₂³×C₄	#546	1	8	yes	—
433	C₂³×C₄	#546	1	1	yes	characteristic
434	C₂³×C₄	#546	1	1	yes	characteristic
435	C₂³×C₄	#546	1	2	yes	—
436	C₂³×C₄	#546	1	2	yes	—
437	C₂³×C₄	#546	1	4	yes	—
438	C₂³×C₄	#546	1	2	yes	—
439	C₂³×C₄	#546	1	2	yes	—
440	C₂³×C₄	#546	1	4	yes	—
441	C₂³×C₄	#551	1	2	yes	—
442	C₂³×C₄	#560	1	4	yes	—
443	C₂³×C₄	#560	1	2	yes	—
444	C₂³×C₄	#560	1	2	yes	—
445	C₂³×C₄	#560	1	4	yes	—
446	C₂³×C₄	H(3,𝔽₄)	1	2	yes	—
447	C₂³×C₄	H(3,𝔽₄)	1	2	yes	—
448	C₂³×C₄	C₂⁴×C₄	1	1	yes	characteristic
449	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
450	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
451	C₂³×C₄	C₂³×D₄	1	4	yes	—
452	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
453	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
454	C₂³×C₄	C₂²×#41	1	1	yes	characteristic
455	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
456	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
457	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
458	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
459	C₂³×C₄	C₂×H(5,𝔽₂)	1	4	yes	—
460	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
461	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
462	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
463	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
464	C₂³×C₄	C₂×H(5,𝔽₂)	1	4	yes	—
465	C₂³×C₄	C₂×H(5,𝔽₂)	1	4	yes	—
466	C₂×SD₁₆	#379	1	32	yes	complemented
467	C₂×D₈	#379	1	32	yes	complemented
468	C₂×M₁₆	C₂²×C₂²⋊C₄	1	8	yes	—
469	C₂×M₁₆	C₂²×C₂²⋊C₄	1	8	yes	—
470	C₂×M₁₆	C₂×#120	1	8	yes	—
471	C₂²×C₈	C₂²×C₂²⋊C₄	1	4	yes	—
472	C₂²×C₈	C₂²×C₂²⋊C₄	1	4	yes	—
473	C₂²×C₈	C₂×#120	1	8	yes	—
474	#117	C₂²×C₂²⋊C₄	1	8	yes	—
475	C₂⁴	#2321	1	4	yes	—
476	C₂⁴	D₄×C₂²⋊C₄	1	2	yes	—
477	C₂⁴	D₄×C₂²⋊C₄	1	8	yes	—
478	C₂⁴	D₄×C₂²⋊C₄	1	2	yes	—
479	C₂⁴	#2358	1	4	yes	—
480	C₂⁴	#2668	1	2	yes	—
481	C₂⁴	#2668	1	2	yes	—
482	C₂⁴	#2678	1	4	yes	—
483	C₂⁴	#2684	1	2	yes	—
484	C₂⁴	#2684	1	2	yes	—
485	C₂⁴	#2697	1	4	yes	—
486	C₂⁴	C₂²×C₄×D₄	1	1	yes	characteristic
487	C₂⁴	C₂×#538	1	1	yes	characteristic
488	C₂⁴	C₂×#538	1	1	yes	characteristic
489	C₂⁴	C₂×#546	1	1	yes	characteristic
490	C₂⁴	C₂×#546	1	1	yes	characteristic
491	C₂⁴	C₂×#546	1	4	yes	—
492	C₂⁴	C₂×#546	1	1	yes	characteristic
493	C₂⁴	C₂×#551	1	1	yes	characteristic
494	C₂⁴	#3490	1	4	yes	—
495	C₂×Q₈	C₂×#379	1	4	yes	—
496	C₂×D₄	C₂×#379	1	8	yes	—
497	C₂×D₄	C₂×#379	1	4	yes	—
498	C₂×D₄	#2308	1	8	yes	—
499	C₂×D₄	D₄×C₂²⋊C₄	1	16	yes	—
500	C₂²×C₄	#2308	1	4	yes	—
501	C₂²×C₄	#2308	1	4	yes	—
502	C₂²×C₄	#2321	1	4	yes	—
503	C₂²×C₄	#2321	1	4	yes	—
504	C₂²×C₄	#2321	1	4	yes	—
505	C₂²×C₄	D₄×C₂²⋊C₄	1	8	yes	—
506	C₂²×C₄	D₄×C₂²⋊C₄	1	2	yes	—
507	C₂²×C₄	D₄×C₂²⋊C₄	1	2	yes	—
508	C₂²×C₄	D₄×C₂²⋊C₄	1	4	yes	—
509	C₂²×C₄	D₄×C₂²⋊C₄	1	4	yes	—
510	C₂²×C₄	#2358	1	4	yes	—
511	C₂²×C₄	#2375	1	4	yes	—
512	C₂²×C₄	#2375	1	4	yes	—
513	C₂²×C₄	#2668	1	2	yes	—
514	C₂²×C₄	#2668	1	2	yes	—
515	C₂²×C₄	#2668	1	4	yes	—
516	C₂²×C₄	#2668	1	4	yes	—
517	C₂²×C₄	#2669	1	4	yes	—
518	C₂²×C₄	#2669	1	4	yes	—
519	C₂²×C₄	#2678	1	4	yes	—
520	C₂²×C₄	#2678	1	4	yes	—
521	C₂²×C₄	#2678	1	4	yes	—
522	C₂²×C₄	#2679	1	4	yes	—
523	C₂²×C₄	#2679	1	4	yes	—
524	C₂²×C₄	#2684	1	2	yes	—
525	C₂²×C₄	#2684	1	2	yes	—
526	C₂²×C₄	#2697	1	4	yes	—
527	C₂²×C₄	C₂³×C₂²⋊C₄	1	2	yes	—
528	C₂²×C₄	C₂³×C₂²⋊C₄	1	1	yes	characteristic
529	C₂²×C₄	C₂²×C₄×D₄	1	1	yes	characteristic
530	C₂²×C₄	C₂×#518	1	1	yes	characteristic
531	C₂²×C₄	C₂×#518	1	1	yes	characteristic
532	C₂²×C₄	C₂×#518	1	1	yes	characteristic
533	C₂²×C₄	C₂×#518	1	1	yes	characteristic
534	C₂²×C₄	C₂×#518	1	2	yes	—
535	C₂²×C₄	C₂×#518	1	2	yes	—
536	C₂²×C₄	C₂×#518	1	2	yes	—
537	C₂²×C₄	C₂²×#120	1	2	yes	—
538	C₂²×C₄	C₂²×#120	1	2	yes	—
539	C₂²×C₄	C₂×#534	1	1	yes	characteristic
540	C₂²×C₄	C₂×#534	1	1	yes	characteristic
541	C₂²×C₄	C₂×#534	1	2	yes	—
542	C₂²×C₄	C₂×#534	1	2	yes	—
543	C₂²×C₄	C₂×#534	1	1	yes	characteristic
544	C₂²×C₄	C₂×#534	1	1	yes	characteristic
545	C₂²×C₄	C₂×#534	1	1	yes	characteristic
546	C₂²×C₄	C₂×#534	1	1	yes	characteristic
547	C₂²×C₄	C₂×#535	1	1	yes	characteristic
548	C₂²×C₄	C₂×#535	1	1	yes	characteristic
549	C₂²×C₄	C₂×#538	1	1	yes	characteristic
550	C₂²×C₄	C₂×#538	1	1	yes	characteristic
551	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
552	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
553	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
554	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
555	C₂²×C₄	C₂×D₄²	1	4	yes	—
556	C₂²×C₄	C₂×D₄²	1	4	yes	—
557	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
558	C₂²×C₄	C₂×#546	1	4	yes	—
559	C₂²×C₄	C₂×#546	1	1	yes	characteristic
560	C₂²×C₄	C₂×#546	1	1	yes	characteristic
561	C₂²×C₄	C₂×#546	1	1	yes	characteristic
562	C₂²×C₄	#3484	1	4	yes	—
563	C₂²×C₄	#3484	1	4	yes	—
564	C₂²×C₄	#3484	1	4	yes	—
565	C₂²×C₄	#3484	1	4	yes	—
566	C₂²×C₄	#3484	1	2	yes	—
567	C₂²×C₄	#3484	1	2	yes	—
568	C₂²×C₄	#3484	1	4	yes	—
569	C₂²×C₄	#3484	1	2	yes	—
570	C₂²×C₄	#3484	1	2	yes	—
571	C₂²×C₄	#3484	1	4	yes	—
572	C₂²×C₄	#3484	1	4	yes	—
573	C₂²×C₄	#3484	1	4	yes	—
574	C₂²×C₄	#3484	1	4	yes	—
575	C₂²×C₄	#3484	1	4	yes	—
576	C₂²×C₄	#3490	1	4	yes	—
577	C₂²×C₄	C₂×#560	1	1	yes	characteristic
578	C₂²×C₄	C₂×#560	1	1	yes	characteristic
579	C₂²×C₄	C₂×#560	1	1	yes	characteristic
580	C₂²×C₄	C₂×H(3,𝔽₄)	1	1	yes	characteristic
581	C₂²×C₄	#3532	1	4	yes	—
582	C₂²×C₄	#3532	1	4	yes	—
583	C₂²×C₄	#3532	1	4	yes	—
584	C₂²×C₄	#3532	1	4	yes	—
585	C₂²×C₄	#3532	1	4	yes	—
586	C₂²×C₄	#3532	1	4	yes	—
587	C₂²×C₄	#3532	1	4	yes	—
588	C₂²×C₄	#3532	1	4	yes	—
589	C₂×C₈	C₂×#379	1	8	yes	—
590	C₂³	#14357	1	4	yes	—
591	C₂³	#14357	1	4	yes	—
592	C₂³	#30434	1	8	yes	—
593	C₂³	C₂×#2321	1	1	yes	characteristic
594	C₂³	C₂×D₄×C₂²⋊C₄	1	1	yes	characteristic
595	C₂³	C₂×D₄×C₂²⋊C₄	1	2	yes	—
596	C₂³	C₂×#2358	1	1	yes	characteristic
597	C₂³	#34198	1	2	yes	—
598	C₂³	#36152	1	2	yes	—
599	C₂³	#36152	1	2	yes	—
600	C₂³	#37660	1	4	yes	—
601	C₂³	#37660	1	4	yes	—
602	C₂³	#37832	1	2	yes	—
603	C₂³	#37832	1	2	yes	—
604	C₂³	C₂×#2668	1	1	yes	characteristic
605	C₂³	C₂×#2678	1	1	yes	characteristic
606	C₂³	C₂×#2684	1	1	yes	characteristic
607	C₂³	C₂×#2697	1	1	yes	characteristic
608	C₂³	#58991	1	4	yes	—
609	C₂³	#59006	1	4	yes	—
610	C₂×C₄	#14357	1	4	yes	—
611	C₂×C₄	#14357	1	4	yes	—
612	C₂×C₄	C₂²×#379	1	1	yes	characteristic
613	C₂×C₄	C₂×#2308	1	1	yes	characteristic
614	C₂×C₄	C₂×#2308	1	1	yes	characteristic
615	C₂×C₄	C₂×#2321	1	1	yes	characteristic
616	C₂×C₄	C₂×D₄×C₂²⋊C₄	1	2	yes	—
617	C₂×C₄	C₂×D₄×C₂²⋊C₄	1	1	yes	characteristic
618	C₂×C₄	#34171	1	1	yes	characteristic
619	C₂×C₄	#34171	1	2	yes	—
620	C₂×C₄	#34171	1	2	yes	—
621	C₂×C₄	#34171	1	2	yes	—
622	C₂×C₄	#34171	1	2	yes	—
623	C₂×C₄	#34171	1	1	yes	characteristic
624	C₂×C₄	#34198	1	2	yes	—
625	C₂×C₄	C₂×#2375	1	1	yes	characteristic
626	C₂×C₄	#34356	1	2	yes	—
627	C₂×C₄	#34356	1	2	yes	—
628	C₂×C₄	#34356	1	2	yes	—
629	C₂×C₄	#34356	1	2	yes	—
630	C₂×C₄	#34980	1	2	yes	—
631	C₂×C₄	#34980	1	2	yes	—
632	C₂×C₄	#34980	1	2	yes	—
633	C₂×C₄	#34980	1	2	yes	—
634	C₂×C₄	D₄×#120	1	2	yes	—
635	C₂×C₄	D₄×#120	1	2	yes	—
636	C₂×C₄	D₄×#120	1	2	yes	—
637	C₂×C₄	D₄×#120	1	2	yes	—
638	C₂×C₄	#36152	1	2	yes	—
639	C₂×C₄	#36152	1	2	yes	—
640	C₂×C₄	#36702	1	2	yes	—
641	C₂×C₄	#36702	1	2	yes	—
642	C₂×C₄	#36714	1	2	yes	—
643	C₂×C₄	#36714	1	2	yes	—
644	C₂×C₄	#37644	1	4	yes	—
645	C₂×C₄	#37644	1	2	yes	—
646	C₂×C₄	#37644	1	2	yes	—
647	C₂×C₄	#37644	1	2	yes	—
648	C₂×C₄	#37644	1	4	yes	—
649	C₂×C₄	#37644	1	2	yes	—
650	C₂×C₄	#37645	1	4	yes	—
651	C₂×C₄	#37645	1	4	yes	—
652	C₂×C₄	#37660	1	4	yes	—
653	C₂×C₄	#37660	1	4	yes	—
654	C₂×C₄	#37832	1	2	yes	—
655	C₂×C₄	#37832	1	2	yes	—
656	C₂×C₄	#45438	1	4	yes	—
657	C₂×C₄	#45438	1	4	yes	—
658	C₂×C₄	#45438	1	4	yes	—
659	C₂×C₄	#45439	1	4	yes	—
660	C₂×C₄	C₂×#2668	1	1	yes	characteristic
661	C₂×C₄	C₂×#2669	1	1	yes	characteristic
662	C₂×C₄	C₂×#2678	1	1	yes	characteristic
663	C₂×C₄	C₂×#2679	1	1	yes	characteristic
664	C₂×C₄	#58990	1	4	yes	—
665	C₂×C₄	#58991	1	4	yes	—
666	C₂²	#383145	1	8	yes	complemented
667	C₂²	D₄×#379	1	1	yes	characteristic
668	C₂²	C₂×#14357	1	1	yes	characteristic
669	C₂²	#521311	1	1	yes	characteristic
670	C₂²	#530231	1	2	yes	—
671	C₂²	#531607	1	2	yes	—
672	C₂²	#845309	1	2	yes	—
673	C₂²	#845677	1	2	yes	—
674	C₂²	#846041	1	2	yes	—
675	C₂²	#846389	1	2	yes	—
676	C₂²	C₂×#30434	1	4	yes	—
677	C₄	#517411	1	1	yes	characteristic
678	C₄	D₄×#379	1	1	yes	characteristic
679	C₄	#521311	1	1	yes	characteristic
680	C₄	#530231	1	2	yes	—
681	C₄	#555894	1	1	yes	characteristic
682	C₄	#559835	1	2	yes	—
683	C₄	#845297	1	2	yes	—
684	C₄	#845309	1	2	yes	—
685	C₄	#846041	1	2	yes	—
686	C₄	#846057	1	2	yes	—
687	C₂	#72215520	1	4	yes	—
688	C₂	C₂×#383145	1	2	yes	—
689	C₂	#72252072	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³	C₂×#2668
commutator	C₂³×C₄	C₂⁴×C₄
Frattini, cosocle	C₂⁴×C₄	C₂⁵
prime radical	C₂³×#3003	C₂
LCS	G ▷ C₂³×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ C₂⁵×C₄ ◁ G
LECS	G ▷ C₂⁴×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72262716	C₂	semidirect
2. #72256427	C₂	semidirect
3. #72255991	C₂	semidirect
4. #72255959	C₂	semidirect
5. #72255720	C₂	semidirect
6. #72255679	C₂	semidirect
7. #72255631	C₂	semidirect
8. #72255601	C₂	semidirect
9. #72252150	C₂	semidirect
10. #72252132	C₂	semidirect
11. #72252112	C₂	semidirect
12. #72237236	C₂	semidirect
13. C₂×#359476	C₂	semidirect
14. C₂×#383145	C₂	semidirect
15. #72236779	C₂	semidirect
16. C₂×#392113	C₂	semidirect
17. C₂×#359507	C₂	semidirect
19. #72231771	C₂	semidirect
24. C₂²×#3003	C₄	semidirect
29. C₂×#60064	C₂²	semidirect
33. C₂×#21249	C₂²	semidirect
34. C₂×#21249	C₂²	semidirect
35. C₂×#21005	C₂²	semidirect
36. C₂²×#1903	C₂²	semidirect
37. C₂²×#1903	C₂²	semidirect
38. C₂²×#1891	C₂²	semidirect
39. C₂×#20667	C₂²	semidirect
40. C₂×#20605	C₂²	semidirect
41. #6370715	C₂²	semidirect
46. C₂×#20598	C₂²	semidirect
47. C₂×#20598	C₂²	semidirect
48. C₂×#20591	C₂²	semidirect
53. C₂²×#1783	C₂²	semidirect
54. C₂²×#1783	C₂²	semidirect
58. #6369812	C₂²	semidirect
60. C₂×#11187	C₂²	semidirect
61. C₂×#11181	C₂²	semidirect
62. C₂×#11133	C₂²	semidirect
63. C₂×#11101	C₂²	semidirect
64. C₂×#11034	C₂²	semidirect
65. C₂×#11034	C₂²	semidirect
66. #357581	C₂²	semidirect
67. C₂×#11014	C₂²	semidirect
68. C₂×#11014	C₂²	semidirect
69. C₂×#10994	C₂²	semidirect
70. C₂×#10994	C₂²	semidirect
71. #357541	C₂²	semidirect
72. #357541	C₂²	semidirect
73. C₂×#10993	C₂²	semidirect
74. C₂×#10953	C₂²	semidirect
75. C₂×#10937	C₂²	semidirect
76. #353416	C₂²	semidirect
77. C₂×#10738	C₂²	semidirect
78. C₂×#10738	C₂²	semidirect
79. C₂×#10737	C₂²	semidirect
80. #353403	C₂²	semidirect
81. #353403	C₂²	semidirect
82. #353386	C₂²	semidirect
83. C₂×#10729	C₂²	semidirect
84. C₂×C₂²⋊#338	C₂²	semidirect
85. C₂×#10716	C₂²	semidirect
86. #123644	C₂²	semidirect
87. #123628	C₂²	semidirect
88. #123619	C₂²	semidirect
89. #123619	C₂²	semidirect
90. #123535	C₂²	semidirect
91. #123532	C₂²	semidirect
112. C₂²×#568	C₂³	semidirect
124. C₂²×#430	C₂³	semidirect
125. C₂²×#421	C₂³	semidirect
126. C₂²×#421	C₂³	semidirect
127. C₂×#2896	C₂³	semidirect
128. C₂×#2896	C₂³	semidirect
141. C₂²×#413	C₂³	semidirect
142. C₂²×#413	C₂³	semidirect
149. C₂×#2879	C₂³	semidirect
162. C₂×#2873	C₂³	semidirect
166. C₂×#1786	D₄	semidirect
168. C₂²×#344	C₂³	semidirect
169. C₂²×#344	C₂³	semidirect
170. C₂²×#344	C₂³	semidirect
171. C₂²×#344	C₂³	semidirect
172. C₂²×#344	C₂³	semidirect
173. C₂×#1742	C₂³	semidirect
174. C₂×#1738	C₂³	semidirect
175. C₂×#1738	C₂³	semidirect
176. C₂×#1738	C₂³	semidirect
177. C₂×#1733	C₂³	semidirect
178. C₂²×#338	C₂³	semidirect
179. C₂²×#338	C₂³	semidirect
180. C₂²×H(3,ℤ/4)	C₂³	semidirect
181. #20335	C₂³	semidirect
210. C₂²×AGL(1,ℤ/8)	C₂²⋊C₄	semidirect
211. C₂²×AGL(1,ℤ/8)	C₂²⋊C₄	semidirect
224. C₂³×SD₁₆	C₂²⋊C₄	semidirect
229. C₂³×D₈	C₂²⋊C₄	semidirect
255. #3003	C₂²⋊C₄	semidirect
262. C₂²×#102	C₂×D₄	semidirect
466. C₂×SD₁₆	#379	semidirect
467. C₂×D₈	#379	semidirect
666. C₂²	#383145	semidirect

Maximal subgroups

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

subgroup	index
#72262716	2
#72256427	2
#72255991	2
#72255959	2
#72255720	2
#72255679	2
#72255631	2
#72255601	2
#72252150	2
#72252132	2
#72252112	2
#72237236	2
C₂×#359476	2
C₂×#383145	2
#72236779	2
C₂×#392113	2
C₂×#359507	2
C₂³×#3003	2
#72231771	2