Subgroups — #72338206

Order 2048.

At least 11134 conjugacy classes of subgroups; only the 2656 normal subgroups are shown.

The subgroup lattice has 714 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72338205	C₂	1	2	yes	maximal, complemented
2	#72338204	C₂	1	2	yes	maximal, complemented
3	#72338203	C₂	1	1	yes	maximal, characteristic, complemented
4	#72338202	C₂	1	1	yes	maximal, characteristic, complemented
5	#72310282	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#359679	C₂	1	2	yes	maximal, complemented
7	C₂×#394133	C₂	1	2	yes	maximal, complemented
8	#72251201	C₂	1	1	yes	maximal, characteristic, complemented
9	#72251201	C₂	1	1	yes	maximal, characteristic, complemented
10	#72251128	C₂	1	2	yes	maximal, complemented
11	#72250500	C₂	1	2	yes	maximal, complemented
12	#72239627	C₂	1	1	yes	maximal, characteristic, complemented
13	#72238744	C₂	1	2	yes	maximal, complemented
14	#72237518	C₂	1	2	yes	maximal, complemented
15	#72237511	C₂	1	2	yes	maximal, complemented
16	#72237507	C₂	1	2	yes	maximal, complemented
17	C₂×#10574840	C₂	1	2	yes	maximal, complemented
18	#72231691	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×#394108	C₂	1	2	yes	maximal, complemented
20	C₂⁴×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
21	C₂²×#3585	C₂²	1	2	yes	—
22	C₂²×#3585	C₂²	1	2	yes	complemented
23	C₂×#62811	C₂²	1	2	yes	complemented
24	#10574839	C₂²	1	2	yes	complemented
25	C₂×#60367	C₂²	1	2	yes	—
26	C₂×#60367	C₂²	1	2	yes	—
27	C₂×#60367	C₂²	1	2	yes	complemented
28	C₂×#60367	C₂²	1	2	yes	complemented
29	C₂×#60387	C₂²	1	2	yes	complemented
30	C₂×#60359	C₂²	1	2	yes	—
31	C₂×#60359	C₂²	1	2	yes	—
32	C₂²×#3003	C₂²	1	2	yes	complemented
33	C₂²×#3003	C₂²	1	2	yes	complemented
34	C₂×#60064	C₂²	1	2	yes	complemented
35	C₂×#60087	C₂²	1	2	yes	—
36	C₂×#60087	C₂²	1	2	yes	complemented
37	C₂×#23443	C₂²	1	1	yes	characteristic, complemented
38	C₂×#23443	C₂²	1	1	yes	characteristic, complemented
39	C₂×#23439	C₂²	1	2	yes	complemented
40	C₂×#23439	C₂²	1	2	yes	complemented
41	#6431766	C₂²	1	1	yes	characteristic, complemented
42	#6431766	C₂²	1	1	yes	characteristic, complemented
43	C₂×#23414	C₂²	1	2	yes	complemented
44	C₂²×#2010	C₂²	1	2	yes	complemented
45	C₂×#23412	C₂²	1	2	yes	complemented
46	C₂×#23412	C₂²	1	2	yes	complemented
47	C₂×#23407	C₂²	1	1	yes	characteristic, complemented
48	C₂×#23407	C₂²	1	1	yes	characteristic, complemented
49	#6431722	C₂²	1	2	yes	complemented
50	#6371536	C₂²	1	2	yes	complemented
51	C₂×#21000	C₂²	1	2	yes	complemented
52	C₂×#20998	C₂²	1	2	yes	complemented
53	C₂×#20995	C₂²	1	2	yes	complemented
54	C₂×#20939	C₂²	1	2	yes	complemented
55	#6371397	C₂²	1	2	yes	complemented
56	C₂×#20623	C₂²	1	2	yes	complemented
57	C₂×#20620	C₂²	1	2	yes	complemented
58	C₂×#20616	C₂²	1	1	yes	characteristic
59	C₂×#20616	C₂²	1	1	yes	characteristic
60	C₂×#20616	C₂²	1	2	yes	complemented
61	C₂×#20616	C₂²	1	2	yes	complemented
62	C₂×#20616	C₂²	1	1	yes	characteristic, complemented
63	C₂×#20616	C₂²	1	1	yes	characteristic, complemented
64	C₂×#20605	C₂²	1	2	yes	complemented
65	#6370715	C₂²	1	2	yes	complemented
66	C₂²×#1783	C₂²	1	1	yes	characteristic, complemented
67	#517415	C₂²	1	1	yes	characteristic, complemented
68	C₂×#11037	C₂²	1	2	yes	complemented
69	C₂×#11034	C₂²	1	2	yes	complemented
70	C₂×#11034	C₂²	1	2	yes	complemented
71	C₂×#11032	C₂²	1	2	yes	complemented
72	C₂×#11030	C₂²	1	2	yes	complemented
73	C₂×#11030	C₂²	1	2	yes	complemented
74	#357575	C₂²	1	2	yes	complemented
75	C₂×#11014	C₂²	1	2	yes	complemented
76	C₂×#11014	C₂²	1	2	yes	complemented
77	C₂×#11012	C₂²	1	2	yes	complemented
78	C₂×#11012	C₂²	1	2	yes	complemented
79	#357561	C₂²	1	2	yes	complemented
80	C₂×#11003	C₂²	1	2	yes	complemented
81	C₂×#11000	C₂²	1	2	yes	complemented
82	C₂×#10994	C₂²	1	2	yes	complemented
83	C₂×#10994	C₂²	1	2	yes	complemented
84	#357544	C₂²	1	2	yes	complemented
85	C₂×#10993	C₂²	1	2	yes	complemented
86	C₂×#10993	C₂²	1	2	yes	complemented
87	#357475	C₂²	1	2	yes	complemented
88	C₂×#10787	C₂²	1	2	yes	complemented
89	#353468	C₂²	1	2	yes	complemented
90	#353462	C₂²	1	2	yes	complemented
91	C₂×#10793	C₂²	1	2	yes	complemented
92	C₂×#10792	C₂²	1	2	yes	complemented
93	C₂×#10778	C₂²	1	2	yes	complemented
94	#123619	C₂²	1	2	yes	complemented
95	#123619	C₂²	1	2	yes	complemented
96	#123611	C₂²	1	2	yes	complemented
97	#123604	C₂²	1	2	yes	complemented
98	#123563	C₂²	1	2	yes	complemented
99	#123560	C₂²	1	1	yes	characteristic, complemented
100	#123560	C₂²	1	1	yes	characteristic, complemented
101	#123556	C₂²	1	2	yes	complemented
102	#123547	C₂²	1	1	yes	characteristic, complemented
103	#123547	C₂²	1	1	yes	characteristic, complemented
104	#123535	C₂²	1	1	yes	characteristic, complemented
105	#123535	C₂²	1	1	yes	characteristic, complemented
106	#123532	C₂²	1	2	yes	complemented
107	C₂²×#585	C₂³	1	2	yes	—
108	C₂³×H(5,𝔽₂)	D₄	1	8	yes	complemented
109	C₂³×H(5,𝔽₂)	C₂³	1	2	yes	—
110	C₂³×H(5,𝔽₂)	C₂³	1	1	yes	characteristic
111	C₂³×H(5,𝔽₂)	C₂³	1	1	yes	characteristic
112	C₂⁴×#41	C₂³	1	2	yes	—
113	C₂⁵×D₄	C₂³	1	1	yes	characteristic
114	C₂²×#577	D₄	1	8	yes	complemented
115	C₂²×#576	D₄	1	8	yes	complemented
116	C₂²×#575	C₂³	1	2	yes	—
117	C₂²×#575	C₂³	1	2	yes	—
118	C₂²×#575	C₂³	1	2	yes	—
119	C₂²×#575	C₂³	1	2	yes	—
120	C₂²×#575	C₂³	1	2	yes	complemented
121	C₂³×AGL(1,ℤ/8)	C₂³	1	2	yes	—
122	C₂³×AGL(1,ℤ/8)	C₂³	1	2	yes	—
123	C₂³×AGL(1,ℤ/8)	C₂³	1	2	yes	—
124	C₂³×AGL(1,ℤ/8)	C₂³	1	2	yes	—
125	C₂²×#568	C₂³	1	2	yes	—
126	C₂²×#568	C₂³	1	2	yes	—
127	C₂×#3449	C₂³	1	2	yes	—
128	C₂×#3449	C₂³	1	2	yes	—
129	C₂×#3449	C₂³	1	1	yes	characteristic, complemented
130	C₂×#3449	C₂³	1	1	yes	characteristic, complemented
131	C₂²×#525	C₂³	1	2	yes	—
132	C₂²×#525	C₂³	1	2	yes	—
133	C₂×#3428	C₂³	1	2	yes	—
134	#60367	D₄	1	16	yes	complemented
135	C₂×#3009	D₄	1	8	yes	complemented
136	C₂×#3008	D₄	1	8	yes	complemented
137	#60359	D₄	1	16	yes	complemented
138	C₂×#3005	D₄	1	4	yes	complemented
139	C₂×#3005	D₄	1	4	yes	complemented
140	C₂×#3004	D₄	1	4	yes	complemented
141	C₂×#3003	D₄	1	4	yes	complemented
142	C₂²×#421	C₂³	1	2	yes	—
143	C₂²×#421	C₂³	1	2	yes	—
144	C₂²×#421	C₂³	1	2	yes	—
145	C₂²×#421	C₂³	1	2	yes	—
146	C₂²×#421	C₂³	1	2	yes	complemented
147	C₂²×#421	C₂³	1	2	yes	complemented
148	C₂²×#421	C₂³	1	2	yes	complemented
149	C₂²×#421	C₂³	1	2	yes	complemented
150	#60087	D₄	1	16	yes	complemented
151	C₂×#2896	C₂³	1	2	yes	—
152	C₂×#2896	C₂³	1	2	yes	—
153	C₂×#2896	C₂³	1	2	yes	—
154	C₂×#2896	C₂³	1	2	yes	—
155	C₂×#2896	C₂³	1	2	yes	—
156	C₂×#2896	C₂³	1	2	yes	—
157	C₂×#2896	C₂³	1	2	yes	—
158	C₂×#2896	C₂³	1	2	yes	—
159	C₂×#2896	C₂³	1	2	yes	complemented
160	C₂×#2896	C₂³	1	2	yes	complemented
161	C₂²×#418	C₂³	1	2	yes	—
162	C₂²×#418	C₂³	1	2	yes	—
163	C₂²×#418	C₂³	1	2	yes	—
164	C₂²×#418	C₂³	1	2	yes	—
165	C₂²×#413	C₂³	1	2	yes	complemented
166	C₂²×#413	C₂³	1	2	yes	complemented
167	C₂³×#100	C₂³	1	2	yes	—
168	C₂³×#100	C₂³	1	1	yes	characteristic
169	C₂³×#100	C₂³	1	1	yes	characteristic
170	C₂²×#410	C₂³	1	2	yes	complemented
171	C₂²×#410	C₂³	1	2	yes	complemented
172	C₂×#2879	C₂³	1	2	yes	—
173	C₂×#2879	C₂³	1	2	yes	—
174	C₂×#2879	C₂³	1	2	yes	complemented
175	C₂×#2879	C₂³	1	2	yes	complemented
176	C₂²×#407	C₂³	1	2	yes	—
177	C₂²×#407	C₂³	1	2	yes	—
178	C₂²×#407	C₂³	1	2	yes	—
179	C₂×#2309	C₂³	1	1	yes	characteristic
180	C₂×#2309	C₂³	1	1	yes	characteristic
181	C₂×#2309	C₂³	1	1	yes	characteristic
182	C₂×#2309	C₂³	1	1	yes	characteristic
183	C₂×#2280	C₂³	1	1	yes	characteristic
184	C₂×#2280	C₂³	1	1	yes	characteristic
185	C₂×#1792	D₄	1	8	yes	complemented
186	C₂²×#344	C₂³	1	2	yes	complemented
187	C₂²×#344	C₂³	1	2	yes	complemented
188	C₂²×#344	C₂³	1	2	yes	complemented
189	C₂²×#344	C₂³	1	2	yes	complemented
190	C₂²×#344	C₂³	1	2	yes	complemented
191	C₂²×#344	C₂³	1	2	yes	complemented
192	C₂×#1742	C₂³	1	1	yes	characteristic, complemented
193	C₂×#1742	C₂³	1	1	yes	characteristic, complemented
194	C₂×#1740	C₂³	1	1	yes	characteristic, complemented
195	C₂×#1740	C₂³	1	1	yes	characteristic, complemented
196	C₂×#1738	C₂³	1	2	yes	complemented
197	C₂×#1738	C₂³	1	2	yes	complemented
198	C₂×#1738	C₂³	1	2	yes	complemented
199	C₂×#1733	C₂³	1	2	yes	complemented
200	C₂×#1733	C₂³	1	2	yes	complemented
201	C₂²×#338	C₂³	1	2	yes	complemented
202	C₂²×H(3,ℤ/4)	C₂³	1	2	yes	complemented
203	C₂²×H(3,ℤ/4)	C₂³	1	2	yes	complemented
204	C₂²×H(3,ℤ/4)	C₂³	1	2	yes	complemented
205	#20335	C₂³	1	1	yes	characteristic, complemented
206	#20335	C₂³	1	1	yes	characteristic, complemented
207	C₂²×2₋¹⁺⁴	C₂×D₄	1	4	yes	complemented
208	C₂²×H(5,𝔽₂)	C₂×D₄	1	8	yes	—
209	C₂²×H(5,𝔽₂)	C₂×D₄	1	8	yes	—
210	C₂²×H(5,𝔽₂)	C₂×D₄	1	8	yes	—
211	C₂²×H(5,𝔽₂)	C₂×D₄	1	4	yes	—
212	C₂²×H(5,𝔽₂)	C₂×D₄	1	8	yes	—
213	C₂²×H(5,𝔽₂)	C₂×D₄	1	4	yes	—
214	C₂²×H(5,𝔽₂)	C₂×D₄	1	4	yes	—
215	C₂²×H(5,𝔽₂)	C₂×D₄	1	8	yes	—
216	C₂²×H(5,𝔽₂)	C₂×D₄	1	4	yes	complemented
217	C₂²×H(5,𝔽₂)	#41	1	4	yes	—
218	C₂³×#41	C₂×D₄	1	8	yes	—
219	C₂³×#41	C₂×D₄	1	8	yes	—
220	C₂³×#41	C₂×D₄	1	2	yes	—
221	C₂³×#41	C₂×D₄	1	2	yes	—
222	C₂³×#41	C₂⁴	1	2	yes	—
223	C₂³×#41	C₂⁴	1	2	yes	—
224	C₂³×#41	C₂⁴	1	2	yes	—
225	C₂³×#41	C₂⁴	1	2	yes	—
226	C₂⁴×Q₈	C₂×D₄	1	2	yes	—
227	C₂⁴×D₄	C₂×D₄	1	2	yes	—
228	C₂⁴×D₄	C₂×D₄	1	4	yes	—
229	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
230	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
231	C₂⁵×C₄	C₂⁴	1	1	yes	characteristic
232	C₂×#575	C₂×D₄	1	8	yes	—
233	C₂×#575	C₂×D₄	1	8	yes	—
234	C₂×#575	C₂×D₄	1	8	yes	—
235	C₂²×#137	C₂×D₄	1	4	yes	—
236	C₂²×#137	C₂×D₄	1	4	yes	—
237	C₂²×#137	C₂×D₄	1	4	yes	—
238	C₂²×#137	C₂×D₄	1	4	yes	—
239	C₂²×AGL(1,ℤ/8)	C₂×D₄	1	4	yes	—
240	C₂²×AGL(1,ℤ/8)	C₂×D₄	1	4	yes	—
241	C₂²×AGL(1,ℤ/8)	C₂×D₄	1	4	yes	—
242	C₂²×AGL(1,ℤ/8)	C₂×D₄	1	4	yes	—
243	C₂²×AGL(1,ℤ/8)	C₂×D₄	1	8	yes	complemented
244	C₂²×AGL(1,ℤ/8)	C₂×D₄	1	8	yes	complemented
245	C₂²×#135	C₂×D₄	1	8	yes	—
246	C₂³×SD₁₆	C₂×D₄	1	4	yes	complemented
247	C₂³×SD₁₆	C₂×D₄	1	4	yes	complemented
248	C₂³×D₈	C₂×D₄	1	4	yes	complemented
249	C₂³×D₈	C₂×D₄	1	4	yes	complemented
250	C₂×#568	C₂×D₄	1	8	yes	complemented
251	C₂²×#131	C₂×D₄	1	8	yes	complemented
252	C₂³×M₁₆	C₂⁴	1	2	yes	—
253	C₂³×M₁₆	C₂⁴	1	2	yes	—
254	C₂³×M₁₆	C₂⁴	1	2	yes	—
255	C₂³×M₁₆	C₂⁴	1	2	yes	—
256	C₂³×M₁₆	C₂⁴	1	2	yes	—
257	C₂³×M₁₆	C₂⁴	1	2	yes	—
258	#3449	C₂×D₄	1	8	yes	complemented
259	C₂×#536	C₂×D₄	1	4	yes	complemented
260	C₂×#535	C₂×D₄	1	4	yes	complemented
261	C₂×#525	C₂×D₄	1	8	yes	—
262	C₂×#525	C₂×D₄	1	4	yes	—
263	C₂×#525	C₂×D₄	1	4	yes	—
264	#3428	C₂×D₄	1	8	yes	complemented
265	C₂²×#117	C₂⁴	1	1	yes	characteristic
266	C₂²×#117	C₂⁴	1	1	yes	characteristic
267	C₂²×#117	C₂⁴	1	1	yes	characteristic
268	C₂²×#117	C₂⁴	1	2	yes	—
269	C₂²×#117	C₂⁴	1	2	yes	—
270	C₂²×#117	C₂⁴	1	1	yes	characteristic
271	C₂²×#104	C₂×D₄	1	8	yes	complemented
272	#2896	C₂×D₄	1	8	yes	—
273	#2896	C₂×D₄	1	8	yes	—
274	#2896	C₂×D₄	1	8	yes	—
275	#2896	C₂×D₄	1	8	yes	—
276	#2896	C₂×D₄	1	8	yes	—
277	C₂×#417	C₂×D₄	1	8	yes	complemented
278	C₂×#419	C₂×D₄	1	4	yes	—
279	C₂×#419	C₂×D₄	1	4	yes	—
280	C₂×#418	C₂×D₄	1	4	yes	—
281	C₂×#418	C₂×D₄	1	4	yes	—
282	C₂×#418	C₂×D₄	1	8	yes	complemented
283	C₂×#418	C₂×D₄	1	8	yes	complemented
284	C₂×#418	C₂×D₄	1	8	yes	complemented
285	C₂×#418	C₂×D₄	1	8	yes	complemented
286	C₂×#416	C₂×D₄	1	8	yes	—
287	C₂²×#100	C₂×D₄	1	4	yes	complemented
288	#2879	C₂×D₄	1	8	yes	complemented
289	C₂×#408	C₂×D₄	1	8	yes	complemented
290	C₂×#407	C₂×D₄	1	4	yes	—
291	C₂×#407	C₂×D₄	1	4	yes	—
292	C₂×#407	C₂×D₄	1	8	yes	—
293	C₂×#390	C₂×D₄	1	4	yes	complemented
294	C₂⁶	H(5,𝔽₂)	1	1	yes	characteristic
295	C₂×H(5,𝔽₂)	#120	1	32	yes	—
296	C₂×H(5,𝔽₂)	#120	1	16	yes	—
297	C₂×H(5,𝔽₂)	#120	1	32	yes	—
298	C₂×H(5,𝔽₂)	#121	1	16	yes	—
299	C₂×H(5,𝔽₂)	#121	1	32	yes	—
300	C₂×H(5,𝔽₂)	#127	1	16	yes	—
301	C₂²×#41	#120	1	8	yes	—
302	C₂²×#41	#120	1	8	yes	—
303	C₂²×#41	C₂²×D₄	1	4	yes	—
304	C₂²×#41	C₂²×D₄	1	4	yes	—
305	C₂²×#41	C₂²×D₄	1	4	yes	—
306	C₂²×#41	C₂²×D₄	1	4	yes	—
307	C₂²×#41	C₂²×D₄	1	4	yes	—
308	C₂²×#41	C₂²×D₄	1	4	yes	—
309	C₂²×#41	C₂²×D₄	1	4	yes	—
310	C₂²×#41	C₂²×D₄	1	4	yes	—
311	C₂²×#41	C₂²×D₄	1	4	yes	—
312	C₂²×#41	C₂²×D₄	1	4	yes	—
313	C₂²×#41	C₂²×D₄	1	4	yes	—
314	C₂²×#41	C₂²×D₄	1	4	yes	—
315	C₂²×#41	C₂²×D₄	1	4	yes	—
316	C₂²×#41	C₂²×D₄	1	4	yes	—
317	C₂²×#41	C₂²×D₄	1	4	yes	—
318	C₂²×#41	C₂²×D₄	1	4	yes	—
319	C₂²×#41	C₂²×D₄	1	4	yes	—
320	C₂²×#41	C₂×#41	1	4	yes	—
321	C₂²×#41	H(5,𝔽₂)	1	4	yes	—
322	C₂²×#41	H(5,𝔽₂)	1	4	yes	—
323	C₂²×#41	H(5,𝔽₂)	1	4	yes	—
324	C₂²×#41	H(5,𝔽₂)	1	4	yes	—
325	C₂²×#41	H(5,𝔽₂)	1	4	yes	—
326	C₂²×#41	H(5,𝔽₂)	1	4	yes	—
327	C₂³×Q₈	#120	1	8	yes	—
328	C₂³×Q₈	C₂²×D₄	1	2	yes	—
329	C₂³×Q₈	C₂²×D₄	1	2	yes	—
330	C₂³×Q₈	C₂²×D₄	1	2	yes	—
331	C₂³×Q₈	C₂²×D₄	1	2	yes	—
332	C₂³×D₄	#120	1	8	yes	—
333	C₂³×D₄	C₂²×D₄	1	2	yes	—
334	C₂³×D₄	C₂²×D₄	1	2	yes	—
335	C₂³×D₄	C₂²×D₄	1	4	yes	—
336	C₂³×D₄	C₂²×D₄	1	2	yes	—
337	C₂³×D₄	C₂²×D₄	1	2	yes	—
338	C₂³×D₄	C₂²×D₄	1	4	yes	—
339	C₂³×D₄	C₂²×D₄	1	2	yes	—
340	C₂³×D₄	C₂²×D₄	1	2	yes	—
341	C₂³×D₄	C₂²×D₄	1	4	yes	—
342	C₂³×D₄	C₂²×D₄	1	4	yes	—
343	C₂³×D₄	C₂²×D₄	1	2	yes	—
344	C₂³×D₄	C₂×#41	1	2	yes	—
345	C₂³×D₄	H(5,𝔽₂)	1	2	yes	—
346	C₂³×D₄	H(5,𝔽₂)	1	2	yes	—
347	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
348	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
349	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
350	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
351	C₂⁴×C₄	H(5,𝔽₂)	1	1	yes	characteristic
352	C₂⁴×C₄	H(5,𝔽₂)	1	2	yes	—
353	C₂⁴×C₄	C₂⁵	1	1	yes	characteristic
354	C₂×#137	#120	1	16	yes	—
355	C₂×AGL(1,ℤ/8)	#120	1	16	yes	—
356	C₂²×Q₁₆	#120	1	8	yes	—
357	C₂²×SD₁₆	#120	1	8	yes	—
358	C₂²×SD₁₆	#120	1	8	yes	—
359	C₂²×D₈	#120	1	8	yes	—
360	C₂²×M₁₆	C₂²×D₄	1	4	yes	—
361	C₂²×M₁₆	C₂²×D₄	1	4	yes	—
362	C₂²×M₁₆	C₂²×D₄	1	4	yes	—
363	C₂²×M₁₆	C₂²×D₄	1	4	yes	—
364	C₂²×M₁₆	C₂²×D₄	1	4	yes	—
365	C₂²×M₁₆	C₂²×D₄	1	4	yes	—
366	C₂²×M₁₆	C₂²×D₄	1	4	yes	—
367	C₂²×M₁₆	C₂²×D₄	1	4	yes	—
368	C₂²×M₁₆	C₂²×D₄	1	4	yes	—
369	C₂²×M₁₆	C₂²×D₄	1	4	yes	—
370	C₂²×M₁₆	C₂²×D₄	1	4	yes	—
371	C₂³×C₈	C₂²×D₄	1	4	yes	—
372	C₂³×C₈	C₂²×D₄	1	4	yes	—
373	C₂×#117	C₂²×D₄	1	4	yes	—
374	C₂×#117	C₂²×D₄	1	4	yes	—
375	C₂×#117	C₂²×D₄	1	4	yes	—
376	C₂×#117	C₂²×D₄	1	4	yes	—
377	C₂×#117	C₂²×D₄	1	4	yes	—
378	C₂×#117	C₂²×D₄	1	4	yes	—
379	C₂²×C₄⋊C₄	C₂²×D₄	1	2	yes	—
380	C₂²×C₄²	C₂²×D₄	1	2	yes	—
381	#419	#120	1	16	yes	—
382	#418	#120	1	16	yes	—
383	#416	#120	1	32	yes	—
384	C₂⁵	#534	1	2	yes	—
385	C₂⁵	D₄²	1	1	yes	characteristic
386	C₂⁵	D₄²	1	1	yes	characteristic
387	C₂⁵	D₄²	1	2	yes	—
388	C₂⁵	C₂×H(5,𝔽₂)	1	1	yes	characteristic
389	H(5,𝔽₂)	#392	1	64	yes	—
390	C₂×#41	C₂×#120	1	8	yes	—
391	C₂×#41	C₂×#120	1	8	yes	—
392	C₂×#41	C₂×#120	1	8	yes	—
393	C₂×#41	C₂×#120	1	8	yes	—
394	C₂×#41	C₂×#120	1	8	yes	—
395	C₂×#41	C₂×#120	1	8	yes	—
396	C₂×#41	C₂×#120	1	8	yes	—
397	C₂×#41	C₂×#121	1	8	yes	—
398	C₂×#41	C₂×#121	1	8	yes	—
399	C₂×#41	C₂×#121	1	8	yes	—
400	C₂×#41	C₂×#127	1	8	yes	—
401	C₂×#41	#534	1	8	yes	—
402	C₂×#41	#534	1	8	yes	—
403	C₂×#41	#534	1	8	yes	—
404	C₂×#41	#534	1	8	yes	—
405	C₂×#41	#534	1	8	yes	—
406	C₂×#41	#535	1	8	yes	—
407	C₂×#41	#535	1	8	yes	—
408	C₂×#41	D₄²	1	8	yes	—
409	C₂×#41	D₄²	1	8	yes	—
410	C₂×#41	D₄²	1	8	yes	—
411	C₂×#41	D₄²	1	8	yes	—
412	C₂×#41	D₄²	1	8	yes	—
413	C₂×#41	D₄²	1	8	yes	—
414	C₂×#41	D₄²	1	8	yes	—
415	C₂×#41	D₄²	1	8	yes	—
416	C₂×#41	D₄²	1	8	yes	—
417	C₂×#41	D₄²	1	8	yes	—
418	C₂×#41	D₄²	1	8	yes	—
419	C₂×#41	#546	1	8	yes	—
420	C₂×#41	#546	1	8	yes	—
421	C₂×#41	#546	1	8	yes	—
422	C₂²×Q₈	C₂×#120	1	4	yes	—
423	C₂²×Q₈	C₂×#120	1	4	yes	—
424	C₂²×Q₈	C₂×#120	1	4	yes	—
425	C₂²×Q₈	C₂×#120	1	4	yes	—
426	C₂²×Q₈	C₂×#120	1	4	yes	—
427	C₂²×Q₈	C₂×#120	1	4	yes	—
428	C₂²×Q₈	D₄²	1	4	yes	—
429	C₂²×Q₈	D₄²	1	4	yes	—
430	C₂²×Q₈	D₄²	1	4	yes	—
431	C₂²×Q₈	D₄²	1	4	yes	—
432	C₂²×Q₈	D₄²	1	4	yes	—
433	C₂²×Q₈	#546	1	4	yes	—
434	C₂²×D₄	C₂×#120	1	4	yes	—
435	C₂²×D₄	C₂×#120	1	4	yes	—
436	C₂²×D₄	C₂×#120	1	4	yes	—
437	C₂²×D₄	C₂×#120	1	8	yes	—
438	C₂²×D₄	C₂×#120	1	4	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×#121	1	8	yes	—
444	C₂²×D₄	C₂×#121	1	4	yes	—
445	C₂²×D₄	C₂×#127	1	4	yes	—
446	C₂²×D₄	#534	1	4	yes	—
447	C₂²×D₄	D₄²	1	4	yes	—
448	C₂²×D₄	D₄²	1	4	yes	—
449	C₂²×D₄	D₄²	1	4	yes	—
450	C₂²×D₄	D₄²	1	8	yes	—
451	C₂²×D₄	D₄²	1	4	yes	—
452	C₂²×D₄	D₄²	1	4	yes	—
453	C₂²×D₄	D₄²	1	4	yes	—
454	C₂²×D₄	D₄²	1	4	yes	—
455	C₂²×D₄	#546	1	4	yes	—
456	C₂³×C₄	C₂×#120	1	4	yes	—
457	C₂³×C₄	C₂×#120	1	4	yes	—
458	C₂³×C₄	#534	1	2	yes	—
459	C₂³×C₄	D₄²	1	2	yes	—
460	C₂³×C₄	D₄²	1	2	yes	—
461	C₂³×C₄	D₄²	1	4	yes	—
462	C₂³×C₄	D₄²	1	4	yes	—
463	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
464	C₂³×C₄	C₂³×D₄	1	2	yes	—
465	C₂³×C₄	C₂³×D₄	1	2	yes	—
466	C₂³×C₄	C₂³×D₄	1	2	yes	—
467	C₂³×C₄	C₂³×D₄	1	2	yes	—
468	C₂³×C₄	C₂³×D₄	1	2	yes	—
469	C₂³×C₄	C₂³×D₄	1	2	yes	—
470	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
471	C₂³×C₄	C₂²×#41	1	1	yes	characteristic
472	C₂³×C₄	C₂×H(5,𝔽₂)	1	2	yes	—
473	C₂³×C₄	C₂×H(5,𝔽₂)	1	2	yes	—
474	C₂³×C₄	C₂×H(5,𝔽₂)	1	2	yes	—
475	C₂³×C₄	C₂×H(5,𝔽₂)	1	2	yes	—
476	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
477	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
478	C₂³×C₄	C₂×H(5,𝔽₂)	1	2	yes	—
479	C₂³×C₄	C₂×H(5,𝔽₂)	1	2	yes	—
480	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
481	C₂×M₁₆	C₂×#120	1	8	yes	—
482	C₂×M₁₆	C₂×#120	1	8	yes	—
483	C₂²×C₈	C₂×#120	1	8	yes	—
484	C₂²×C₈	C₂×#120	1	8	yes	—
485	#117	C₂×#120	1	8	yes	—
486	#117	C₂×#120	1	8	yes	—
487	C₂⁴	#2403	1	2	yes	—
488	C₂⁴	#2403	1	2	yes	—
489	C₂⁴	C₂×#534	1	1	yes	characteristic
490	C₂⁴	C₂×D₄²	1	1	yes	characteristic
491	C₂⁴	C₂×D₄²	1	1	yes	characteristic
492	C₂⁴	#3484	1	2	yes	—
493	C₂⁴	#3484	1	2	yes	—
494	C₂⁴	#3484	1	1	yes	characteristic
495	C₂⁴	#3484	1	2	yes	—
496	C₂⁴	#3484	1	2	yes	—
497	C₂⁴	#3490	1	1	yes	characteristic
498	C₂⁴	#3532	1	1	yes	characteristic
499	C₂⁴	#3532	1	1	yes	characteristic
500	#41	C₂×#392	1	16	yes	—
501	#41	#2403	1	16	yes	—
502	#41	#2403	1	16	yes	—
503	#41	#2408	1	16	yes	—
504	#41	#2410	1	16	yes	—
505	#41	#2410	1	16	yes	—
506	#41	#2433	1	16	yes	—
507	#41	#2613	1	16	yes	—
508	C₂×Q₈	#2403	1	8	yes	—
509	C₂×Q₈	#2403	1	8	yes	—
510	C₂×Q₈	#2403	1	8	yes	—
511	C₂×Q₈	#2408	1	8	yes	—
512	C₂×Q₈	#2410	1	8	yes	—
513	C₂×Q₈	#2410	1	8	yes	—
514	C₂×Q₈	#2433	1	8	yes	—
515	C₂×Q₈	#2846	1	8	yes	—
516	C₂×D₄	C₂×#392	1	8	yes	—
517	C₂×D₄	#2403	1	8	yes	—
518	C₂×D₄	#2403	1	8	yes	—
519	C₂×D₄	#2403	1	8	yes	—
520	C₂×D₄	#2403	1	8	yes	—
521	C₂×D₄	#2408	1	8	yes	—
522	C₂×D₄	#2410	1	8	yes	—
523	C₂×D₄	#2410	1	8	yes	—
524	C₂×D₄	#2433	1	8	yes	—
525	C₂×D₄	#2846	1	8	yes	—
526	C₂²×C₄	#2403	1	4	yes	—
527	C₂²×C₄	C₂²×#120	1	2	yes	—
528	C₂²×C₄	C₂²×#120	1	2	yes	—
529	C₂²×C₄	C₂²×#120	1	2	yes	—
530	C₂²×C₄	C₂²×#120	1	2	yes	—
531	C₂²×C₄	C₂²×#120	1	2	yes	—
532	C₂²×C₄	C₂²×#120	1	2	yes	—
533	C₂²×C₄	C₂²×#120	1	2	yes	—
534	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
535	C₂²×C₄	C₂²×#121	1	2	yes	—
536	C₂²×C₄	C₂²×#121	1	1	yes	characteristic
537	C₂²×C₄	C₂²×#127	1	1	yes	characteristic
538	C₂²×C₄	C₂×#534	1	2	yes	—
539	C₂²×C₄	C₂×#534	1	2	yes	—
540	C₂²×C₄	C₂×#534	1	2	yes	—
541	C₂²×C₄	C₂×#534	1	2	yes	—
542	C₂²×C₄	C₂×#534	1	1	yes	characteristic
543	C₂²×C₄	C₂×#534	1	2	yes	—
544	C₂²×C₄	C₂×#535	1	2	yes	—
545	C₂²×C₄	C₂×#535	1	2	yes	—
546	C₂²×C₄	C₂×D₄²	1	2	yes	—
547	C₂²×C₄	C₂×D₄²	1	2	yes	—
548	C₂²×C₄	C₂×D₄²	1	2	yes	—
549	C₂²×C₄	C₂×D₄²	1	2	yes	—
550	C₂²×C₄	C₂×D₄²	1	2	yes	—
551	C₂²×C₄	C₂×D₄²	1	2	yes	—
552	C₂²×C₄	C₂×D₄²	1	2	yes	—
553	C₂²×C₄	C₂×D₄²	1	2	yes	—
554	C₂²×C₄	C₂×D₄²	1	2	yes	—
555	C₂²×C₄	C₂×D₄²	1	2	yes	—
556	C₂²×C₄	C₂×D₄²	1	2	yes	—
557	C₂²×C₄	C₂×D₄²	1	2	yes	—
558	C₂²×C₄	C₂×D₄²	1	2	yes	—
559	C₂²×C₄	C₂×D₄²	1	2	yes	—
560	C₂²×C₄	C₂×D₄²	1	2	yes	—
561	C₂²×C₄	C₂×D₄²	1	2	yes	—
562	C₂²×C₄	C₂×D₄²	1	2	yes	—
563	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
564	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
565	C₂²×C₄	C₂×D₄²	1	2	yes	—
566	C₂²×C₄	C₂×#546	1	2	yes	—
567	C₂²×C₄	C₂×#546	1	2	yes	—
568	C₂²×C₄	C₂×#546	1	2	yes	—
569	C₂²×C₄	C₂×#546	1	2	yes	—
570	C₂²×C₄	#3484	1	2	yes	—
571	C₂²×C₄	#3484	1	2	yes	—
572	C₂²×C₄	#3484	1	2	yes	—
573	C₂²×C₄	#3484	1	2	yes	—
574	C₂²×C₄	#3484	1	2	yes	—
575	C₂²×C₄	#3484	1	2	yes	—
576	C₂²×C₄	#3484	1	2	yes	—
577	C₂²×C₄	#3484	1	2	yes	—
578	C₂²×C₄	#3484	1	2	yes	—
579	C₂²×C₄	#3484	1	2	yes	—
580	C₂²×C₄	#3484	1	2	yes	—
581	C₂²×C₄	#3484	1	2	yes	—
582	C₂²×C₄	#3484	1	2	yes	—
583	C₂²×C₄	#3484	1	2	yes	—
584	C₂²×C₄	#3484	1	2	yes	—
585	C₂²×C₄	#3484	1	2	yes	—
586	C₂²×C₄	#3484	1	2	yes	—
587	C₂²×C₄	#3484	1	2	yes	—
588	C₂²×C₄	#3484	1	2	yes	—
589	C₂²×C₄	#3484	1	2	yes	—
590	C₂²×C₄	#3484	1	1	yes	characteristic
591	C₂²×C₄	#3484	1	1	yes	characteristic
592	C₂²×C₄	#3484	1	1	yes	characteristic
593	C₂²×C₄	#3490	1	1	yes	characteristic
594	C₂²×C₄	#3490	1	2	yes	—
595	C₂²×C₄	#3532	1	2	yes	—
596	C₂²×C₄	#3532	1	1	yes	characteristic
597	C₂²×C₄	#3532	1	1	yes	characteristic
598	C₂²×C₄	#3532	1	2	yes	—
599	C₂²×C₄	#3532	1	2	yes	—
600	C₂²×C₄	#3532	1	2	yes	—
601	C₂²×C₄	#3532	1	2	yes	—
602	C₂²×C₄	#3532	1	2	yes	—
603	C₂³	C₂×#2403	1	1	yes	characteristic
604	C₂³	#34980	1	2	yes	—
605	C₂³	#34980	1	2	yes	—
606	C₂³	#34981	1	1	yes	characteristic
607	C₂³	#35346	1	1	yes	characteristic
608	C₂³	#35348	1	2	yes	—
609	C₂³	#35390	1	1	yes	characteristic
610	C₂³	D₄×#120	1	2	yes	—
611	C₂³	D₄×#120	1	2	yes	—
612	C₂³	D₄×#120	1	2	yes	—
613	C₂³	D₄×#120	1	2	yes	—
614	C₂³	#37436	1	1	yes	characteristic
615	C₂³	#37644	1	2	yes	—
616	C₂³	#37644	1	2	yes	—
617	C₂³	#37645	1	2	yes	—
618	C₂³	#37645	1	2	yes	—
619	C₂³	#58990	1	1	yes	characteristic
620	C₂³	#58990	1	1	yes	characteristic
621	C₂³	#58990	1	1	yes	characteristic
622	C₂³	#58990	1	1	yes	characteristic
623	C₂³	#58991	1	1	yes	characteristic
624	C₂³	#58991	1	1	yes	characteristic
625	C₂³	#58991	1	2	yes	—
626	Q₈	#14715	1	16	yes	—
627	D₄	#14715	1	16	yes	—
628	C₂×C₄	C₂²×#392	1	1	yes	characteristic
629	C₂×C₄	C₂×#2613	1	2	yes	—
630	C₂×C₄	C₂×#2403	1	1	yes	characteristic
631	C₂×C₄	C₂×#2403	1	2	yes	—
632	C₂×C₄	C₂×#2403	1	2	yes	—
633	C₂×C₄	C₂×#2403	1	2	yes	—
634	C₂×C₄	C₂×#2403	1	2	yes	—
635	C₂×C₄	C₂×#2403	1	2	yes	—
636	C₂×C₄	C₂×#2410	1	2	yes	—
637	C₂×C₄	C₂×#2410	1	2	yes	—
638	C₂×C₄	C₂×#2410	1	2	yes	—
639	C₂×C₄	C₂×#2410	1	2	yes	—
640	C₂×C₄	C₂×#2408	1	2	yes	—
641	C₂×C₄	C₂×#2408	1	2	yes	—
642	C₂×C₄	C₂×#2433	1	2	yes	—
643	C₂×C₄	C₂×#2433	1	2	yes	—
644	C₂×C₄	#34980	1	2	yes	—
645	C₂×C₄	#34980	1	2	yes	—
646	C₂×C₄	#34980	1	2	yes	—
647	C₂×C₄	#34980	1	2	yes	—
648	C₂×C₄	#34981	1	1	yes	characteristic
649	C₂×C₄	#35346	1	1	yes	characteristic
650	C₂×C₄	#35348	1	2	yes	—
651	C₂×C₄	#35390	1	1	yes	characteristic
652	C₂×C₄	D₄×#120	1	2	yes	—
653	C₂×C₄	D₄×#120	1	2	yes	—
654	C₂×C₄	D₄×#120	1	2	yes	—
655	C₂×C₄	D₄×#120	1	2	yes	—
656	C₂×C₄	D₄×#120	1	2	yes	—
657	C₂×C₄	D₄×#120	1	2	yes	—
658	C₂×C₄	D₄×#120	1	2	yes	—
659	C₂×C₄	D₄×#120	1	2	yes	—
660	C₂×C₄	D₄×#120	1	2	yes	—
661	C₂×C₄	D₄×#120	1	2	yes	—
662	C₂×C₄	D₄×#120	1	2	yes	—
663	C₂×C₄	D₄×#120	1	2	yes	—
664	C₂×C₄	C₂×#2846	1	2	yes	—
665	C₂×C₄	#37436	1	1	yes	characteristic
666	C₂×C₄	#37436	1	2	yes	—
667	C₂×C₄	#37644	1	2	yes	—
668	C₂×C₄	#37644	1	2	yes	—
669	C₂×C₄	#37644	1	2	yes	—
670	C₂×C₄	#37644	1	2	yes	—
671	C₂×C₄	#37644	1	2	yes	—
672	C₂×C₄	#37644	1	2	yes	—
673	C₂×C₄	#37645	1	2	yes	—
674	C₂×C₄	#37645	1	2	yes	—
675	C₂×C₄	#37645	1	2	yes	—
676	C₂×C₄	#37645	1	2	yes	—
677	C₂×C₄	#37645	1	2	yes	—
678	C₂×C₄	#37645	1	2	yes	—
679	C₂×C₄	#58990	1	2	yes	—
680	C₂×C₄	#58990	1	2	yes	—
681	C₂×C₄	#58990	1	2	yes	—
682	C₂×C₄	#58990	1	2	yes	—
683	C₂×C₄	#58990	1	2	yes	—
684	C₂×C₄	#58990	1	2	yes	—
685	C₂×C₄	#58991	1	2	yes	—
686	C₂×C₄	#58991	1	1	yes	characteristic
687	C₂×C₄	#58991	1	1	yes	characteristic
688	C₂×C₄	#58991	1	2	yes	—
689	C₂×C₄	#58991	1	2	yes	—
690	C₂×C₄	#58991	1	2	yes	—
691	C₂×C₄	#58991	1	2	yes	—
692	C₂²	#612424	1	2	yes	—
693	C₂²	#635984	1	2	yes	—
694	C₂²	#647656	1	1	yes	characteristic
695	C₂²	#647656	1	1	yes	characteristic
696	C₂²	#647670	1	2	yes	—
697	C₂²	#647670	1	2	yes	—
698	C₂²	#648360	1	1	yes	characteristic
699	C₂²	#648360	1	1	yes	characteristic
700	C₂²	#759288	1	1	yes	characteristic
701	C₂²	#759288	1	1	yes	characteristic
702	C₂²	#5955303	1	1	yes	characteristic
703	C₄	C₂×#14715	1	2	yes	—
704	C₄	#612424	1	2	yes	—
705	C₄	#635984	1	2	yes	—
706	C₄	#647656	1	2	yes	—
707	C₄	#647670	1	2	yes	—
708	C₄	#647670	1	2	yes	—
709	C₄	#648360	1	2	yes	—
710	C₄	#759288	1	2	yes	—
711	C₂	#72216112	1	2	yes	—
712	C₂	#72236727	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	#647656
commutator, Frattini, cosocle	C₂⁴×C₄	C₂⁵
LCS	G ▷ C₂⁴×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂⁴×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. #72338205	C₂	semidirect
2. #72338204	C₂	semidirect
3. #72338203	C₂	semidirect
4. #72338202	C₂	semidirect
5. #72310282	C₂	semidirect
6. C₂×#359679	C₂	semidirect
7. C₂×#394133	C₂	semidirect
8. #72251201	C₂	semidirect
9. #72251201	C₂	semidirect
10. #72251128	C₂	semidirect
11. #72250500	C₂	semidirect
12. #72239627	C₂	semidirect
13. #72238744	C₂	semidirect
14. #72237518	C₂	semidirect
15. #72237511	C₂	semidirect
16. #72237507	C₂	semidirect
17. C₂×#10574840	C₂	semidirect
18. #72231691	C₂	semidirect
19. C₂×#394108	C₂	semidirect
22. C₂²×#3585	C₂²	semidirect
23. C₂×#62811	C₂²	semidirect
24. #10574839	C₂²	semidirect
27. C₂×#60367	C₂²	semidirect
28. C₂×#60367	C₂²	semidirect
29. C₂×#60387	C₂²	semidirect
32. C₂²×#3003	C₂²	semidirect
33. C₂²×#3003	C₂²	semidirect
34. C₂×#60064	C₂²	semidirect
36. C₂×#60087	C₂²	semidirect
37. C₂×#23443	C₂²	semidirect
38. C₂×#23443	C₂²	semidirect
39. C₂×#23439	C₂²	semidirect
40. C₂×#23439	C₂²	semidirect
41. #6431766	C₂²	semidirect
42. #6431766	C₂²	semidirect
43. C₂×#23414	C₂²	semidirect
44. C₂²×#2010	C₂²	semidirect
45. C₂×#23412	C₂²	semidirect
46. C₂×#23412	C₂²	semidirect
47. C₂×#23407	C₂²	semidirect
48. C₂×#23407	C₂²	semidirect
49. #6431722	C₂²	semidirect
50. #6371536	C₂²	semidirect
51. C₂×#21000	C₂²	semidirect
52. C₂×#20998	C₂²	semidirect
53. C₂×#20995	C₂²	semidirect
54. C₂×#20939	C₂²	semidirect
55. #6371397	C₂²	semidirect
56. C₂×#20623	C₂²	semidirect
57. C₂×#20620	C₂²	semidirect
60. C₂×#20616	C₂²	semidirect
61. C₂×#20616	C₂²	semidirect
62. C₂×#20616	C₂²	semidirect
63. C₂×#20616	C₂²	semidirect
64. C₂×#20605	C₂²	semidirect
65. #6370715	C₂²	semidirect
66. C₂²×#1783	C₂²	semidirect
67. #517415	C₂²	semidirect
68. C₂×#11037	C₂²	semidirect
69. C₂×#11034	C₂²	semidirect
70. C₂×#11034	C₂²	semidirect
71. C₂×#11032	C₂²	semidirect
72. C₂×#11030	C₂²	semidirect
73. C₂×#11030	C₂²	semidirect
74. #357575	C₂²	semidirect
75. C₂×#11014	C₂²	semidirect
76. C₂×#11014	C₂²	semidirect
77. C₂×#11012	C₂²	semidirect
78. C₂×#11012	C₂²	semidirect
79. #357561	C₂²	semidirect
80. C₂×#11003	C₂²	semidirect
81. C₂×#11000	C₂²	semidirect
82. C₂×#10994	C₂²	semidirect
83. C₂×#10994	C₂²	semidirect
84. #357544	C₂²	semidirect
85. C₂×#10993	C₂²	semidirect
86. C₂×#10993	C₂²	semidirect
87. #357475	C₂²	semidirect
88. C₂×#10787	C₂²	semidirect
89. #353468	C₂²	semidirect
90. #353462	C₂²	semidirect
91. C₂×#10793	C₂²	semidirect
92. C₂×#10792	C₂²	semidirect
93. C₂×#10778	C₂²	semidirect
94. #123619	C₂²	semidirect
95. #123619	C₂²	semidirect
96. #123611	C₂²	semidirect
97. #123604	C₂²	semidirect
98. #123563	C₂²	semidirect
99. #123560	C₂²	semidirect
100. #123560	C₂²	semidirect
101. #123556	C₂²	semidirect
102. #123547	C₂²	semidirect
103. #123547	C₂²	semidirect
104. #123535	C₂²	semidirect
105. #123535	C₂²	semidirect
106. #123532	C₂²	semidirect
108. C₂³×H(5,𝔽₂)	D₄	semidirect
114. C₂²×#577	D₄	semidirect
115. C₂²×#576	D₄	semidirect
120. C₂²×#575	C₂³	semidirect
129. C₂×#3449	C₂³	semidirect
130. C₂×#3449	C₂³	semidirect
134. #60367	D₄	semidirect
135. C₂×#3009	D₄	semidirect
136. C₂×#3008	D₄	semidirect
137. #60359	D₄	semidirect
138. C₂×#3005	D₄	semidirect
139. C₂×#3005	D₄	semidirect
140. C₂×#3004	D₄	semidirect
141. C₂×#3003	D₄	semidirect
146. C₂²×#421	C₂³	semidirect
147. C₂²×#421	C₂³	semidirect
148. C₂²×#421	C₂³	semidirect
149. C₂²×#421	C₂³	semidirect
150. #60087	D₄	semidirect
159. C₂×#2896	C₂³	semidirect
160. C₂×#2896	C₂³	semidirect
165. C₂²×#413	C₂³	semidirect
166. C₂²×#413	C₂³	semidirect
170. C₂²×#410	C₂³	semidirect
171. C₂²×#410	C₂³	semidirect
174. C₂×#2879	C₂³	semidirect
175. C₂×#2879	C₂³	semidirect
185. C₂×#1792	D₄	semidirect
186. C₂²×#344	C₂³	semidirect
187. C₂²×#344	C₂³	semidirect
188. C₂²×#344	C₂³	semidirect
189. C₂²×#344	C₂³	semidirect
190. C₂²×#344	C₂³	semidirect
191. C₂²×#344	C₂³	semidirect
192. C₂×#1742	C₂³	semidirect
193. C₂×#1742	C₂³	semidirect
194. C₂×#1740	C₂³	semidirect
195. C₂×#1740	C₂³	semidirect
196. C₂×#1738	C₂³	semidirect
197. C₂×#1738	C₂³	semidirect
198. C₂×#1738	C₂³	semidirect
199. C₂×#1733	C₂³	semidirect
200. C₂×#1733	C₂³	semidirect
201. C₂²×#338	C₂³	semidirect
202. C₂²×H(3,ℤ/4)	C₂³	semidirect
203. C₂²×H(3,ℤ/4)	C₂³	semidirect
204. C₂²×H(3,ℤ/4)	C₂³	semidirect
205. #20335	C₂³	semidirect
206. #20335	C₂³	semidirect
207. C₂²×2₋¹⁺⁴	C₂×D₄	semidirect
216. C₂²×H(5,𝔽₂)	C₂×D₄	semidirect
243. C₂²×AGL(1,ℤ/8)	C₂×D₄	semidirect
244. C₂²×AGL(1,ℤ/8)	C₂×D₄	semidirect
246. C₂³×SD₁₆	C₂×D₄	semidirect
247. C₂³×SD₁₆	C₂×D₄	semidirect
248. C₂³×D₈	C₂×D₄	semidirect
249. C₂³×D₈	C₂×D₄	semidirect
250. C₂×#568	C₂×D₄	semidirect
251. C₂²×#131	C₂×D₄	semidirect
258. #3449	C₂×D₄	semidirect
259. C₂×#536	C₂×D₄	semidirect
260. C₂×#535	C₂×D₄	semidirect
264. #3428	C₂×D₄	semidirect
271. C₂²×#104	C₂×D₄	semidirect
277. C₂×#417	C₂×D₄	semidirect
282. C₂×#418	C₂×D₄	semidirect
283. C₂×#418	C₂×D₄	semidirect
284. C₂×#418	C₂×D₄	semidirect
285. C₂×#418	C₂×D₄	semidirect
287. C₂²×#100	C₂×D₄	semidirect
288. #2879	C₂×D₄	semidirect
289. C₂×#408	C₂×D₄	semidirect
293. C₂×#390	C₂×D₄	semidirect

Maximal subgroups

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

subgroup	index
#72338205	2
#72338204	2
#72338203	2
#72338202	2
#72310282	2
C₂×#359679	2
C₂×#394133	2
#72251201	2
#72251128	2
#72250500	2
#72239627	2
#72238744	2
#72237518	2
#72237511	2
#72237507	2
C₂×#10574840	2
#72231691	2
C₂×#394108	2