Subgroups — #72287251

Order 2048.

At least 6420 conjugacy classes of subgroups; only the 530 normal subgroups are shown.

The subgroup lattice has 343 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72287221	C₂	1	1	yes	maximal, characteristic
2	#72287157	C₂	1	1	yes	maximal, characteristic, complemented
3	#72287053	C₂	1	2	yes	maximal, complemented
4	#72286951	C₂	1	2	yes	maximal, complemented
5	#72286622	C₂	1	2	yes	maximal, complemented
6	#72286294	C₂	1	2	yes	maximal, complemented
7	#72284902	C₂	1	1	yes	maximal, characteristic, complemented
8	#72284779	C₂	1	1	yes	maximal, characteristic, complemented
9	#72284566	C₂	1	1	yes	maximal, characteristic, complemented
10	#72284408	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#7622467	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#62852	C₂²	1	1	yes	characteristic
13	#10574842	C₄	1	1	yes	characteristic, complemented
14	C₂×#33361	C₂²	1	2	yes	—
15	C₂×#33359	C₂²	1	2	yes	—
16	C₂×#33358	C₂²	1	1	yes	characteristic
17	C₂×#33358	C₂²	1	1	yes	characteristic
18	#6437623	C₄	1	1	yes	characteristic, complemented
19	C₂×#23873	C₄	1	1	yes	characteristic, complemented
20	C₂×#23873	C₂²	1	1	yes	characteristic
21	C₂×#23872	C₄	1	1	yes	characteristic, complemented
22	C₂×#23872	C₂²	1	1	yes	characteristic
23	#6437444	C₂²	1	1	yes	characteristic
24	#512578	C₂²	1	2	yes	complemented
25	#512564	C₂²	1	2	yes	complemented
26	#392134	C₄	1	1	yes	characteristic, complemented
27	#359671	C₄	1	1	yes	characteristic, complemented
28	#359671	C₂²	1	1	yes	characteristic
29	#359669	C₄	1	1	yes	characteristic, complemented
30	#359669	C₂²	1	1	yes	characteristic
31	#359471	C₂²	1	1	yes	characteristic
32	#359444	C₄	1	1	yes	characteristic, complemented
33	#187807	C₂²	1	1	yes	characteristic
34	#187807	C₂²	1	1	yes	characteristic
35	#187135	C₂²	1	2	yes	—
36	#187081	C₂²	1	2	yes	—
37	#151816	C₂²	1	2	yes	complemented
38	#151814	C₂²	1	2	yes	complemented
39	#151806	C₂²	1	2	yes	complemented
40	#151794	C₂²	1	2	yes	complemented
41	#151784	C₂²	1	2	yes	complemented
42	#151782	C₂²	1	2	yes	complemented
43	C₂²×#585	C₂×C₄	1	1	yes	characteristic
44	C₂³×H(5,𝔽₂)	D₄	1	1	yes	characteristic
45	C₂×#3586	C₂×C₄	1	1	yes	characteristic, complemented
46	C₂×#3585	C₂×C₄	1	1	yes	characteristic, complemented
47	#62811	C₂×C₄	1	1	yes	characteristic, complemented
48	C₂×#3500	C₂×C₄	1	1	yes	characteristic
49	C₂×#3500	D₄	1	1	yes	characteristic
50	C₂×#3500	D₄	1	1	yes	characteristic
51	C₂×#3500	C₂³	1	1	yes	characteristic
52	C₂×#3498	C₂×C₄	1	1	yes	characteristic
53	C₂×#3498	D₄	1	1	yes	characteristic
54	C₂×#3498	D₄	1	1	yes	characteristic
55	C₂×#3498	C₂³	1	1	yes	characteristic
56	C₂×#3449	D₄	1	1	yes	characteristic
57	C₂×#3449	C₂³	1	1	yes	characteristic
58	C₂²×#535	C₂×C₄	1	1	yes	characteristic
59	C₂²×#535	D₄	1	1	yes	characteristic
60	C₂×#3428	D₄	1	1	yes	characteristic
61	C₂×#3027	C₂×C₄	1	1	yes	characteristic, complemented
62	C₂×#3027	C₂×C₄	1	1	yes	characteristic, complemented
63	C₂×#3018	C₂×C₄	1	1	yes	characteristic, complemented
64	C₂×#3018	C₂³	1	1	yes	characteristic
65	#60088	C₂×C₄	1	1	yes	characteristic, complemented
66	#60087	C₂×C₄	1	1	yes	characteristic, complemented
67	#60064	C₂×C₄	1	1	yes	characteristic, complemented
68	#33361	D₄	1	8	yes	complemented
69	#33359	D₄	1	8	yes	complemented
70	C₂×#2129	D₄	1	2	yes	complemented
71	C₂×#2128	D₄	1	2	yes	complemented
72	C₂×#2127	D₄	1	2	yes	complemented
73	C₂×#2127	D₄	1	2	yes	complemented
74	C₂×#2126	C₂³	1	2	yes	—
75	C₂×#2126	C₂³	1	2	yes	—
76	C₂×#1914	C₂×C₄	1	1	yes	characteristic, complemented
77	C₂×#1914	C₂×C₄	1	1	yes	characteristic, complemented
78	C₂×#1914	C₂×C₄	1	1	yes	characteristic, complemented
79	C₂×#1914	C₂×C₄	1	1	yes	characteristic, complemented
80	#20961	C₂×C₄	1	1	yes	characteristic, complemented
81	#20961	C₂×C₄	1	1	yes	characteristic, complemented
82	#20952	C₂×C₄	1	1	yes	characteristic, complemented
83	#20952	C₂³	1	1	yes	characteristic
84	C₂×#1884	C₂×C₄	1	1	yes	characteristic, complemented
85	C₂×#1884	C₂×C₄	1	1	yes	characteristic, complemented
86	C₂×#1884	C₂³	1	1	yes	characteristic
87	C₂×#1884	C₂³	1	1	yes	characteristic
88	C₂×#1796	C₂×C₄	1	1	yes	characteristic, complemented
89	C₂×#1796	C₂×C₄	1	1	yes	characteristic, complemented
90	C₂×#1795	C₂×C₄	1	1	yes	characteristic, complemented
91	C₂×#1795	C₂×C₄	1	1	yes	characteristic, complemented
92	#20591	C₂×C₄	1	1	yes	characteristic, complemented
93	#20584	C₂×C₄	1	1	yes	characteristic, complemented
94	#17738	C₂³	1	2	yes	—
95	#17663	C₂³	1	2	yes	—
96	C₂×#585	C₂²×C₄	1	1	yes	characteristic, complemented
97	C₂²×2₋¹⁺⁴	C₂²⋊C₄	1	1	yes	characteristic
98	C₂²×2₋¹⁺⁴	C₂²×C₄	1	1	yes	characteristic
99	C₂²×H(5,𝔽₂)	C₂²⋊C₄	1	1	yes	characteristic
100	C₂²×H(5,𝔽₂)	C₂²⋊C₄	1	1	yes	characteristic
101	C₂²×H(5,𝔽₂)	C₂²⋊C₄	1	1	yes	characteristic
102	C₂²×H(5,𝔽₂)	C₂²×C₄	1	1	yes	characteristic
103	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
104	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
105	C₂³×#41	C₂²⋊C₄	1	1	yes	characteristic
106	C₂³×#41	C₂²⋊C₄	1	1	yes	characteristic
107	C₂³×#41	C₂²×C₄	1	1	yes	characteristic
108	C₂³×#41	C₂×D₄	1	1	yes	characteristic
109	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
110	C₂×#568	C₂²×C₄	1	1	yes	characteristic, complemented
111	C₂×#568	C₂²×C₄	1	1	yes	characteristic, complemented
112	#3500	C₂×D₄	1	4	yes	—
113	#3500	#41	1	4	yes	—
114	#3498	C₂×D₄	1	4	yes	—
115	#3498	#41	1	4	yes	—
116	C₂×#536	C₂²⋊C₄	1	1	yes	characteristic
117	C₂×#536	C₂×D₄	1	1	yes	characteristic
118	C₂×#536	C₂×D₄	1	1	yes	characteristic
119	C₂×#536	#41	1	1	yes	characteristic
120	C₂×#536	#41	1	1	yes	characteristic
121	C₂×#536	#41	1	1	yes	characteristic
122	C₂×#535	C₂²⋊C₄	1	1	yes	characteristic
123	C₂×#535	C₂²⋊C₄	1	1	yes	characteristic
124	C₂×#535	C₂²⋊C₄	1	1	yes	characteristic
125	C₂×#535	C₂²×C₄	1	1	yes	characteristic
126	C₂×#535	C₂²×C₄	1	1	yes	characteristic
127	C₂×#535	C₂×D₄	1	1	yes	characteristic
128	C₂×#535	C₂×D₄	1	1	yes	characteristic
129	C₂×#535	C₂×D₄	1	1	yes	characteristic
130	C₂×#535	C₂×D₄	1	1	yes	characteristic
131	C₂×#535	#41	1	1	yes	characteristic
132	C₂×#532	C₂²×C₄	1	1	yes	characteristic
133	C₂×#532	C₂×D₄	1	1	yes	characteristic
134	C₂×#532	C₂×D₄	1	1	yes	characteristic
135	C₂×#532	C₂⁴	1	1	yes	characteristic
136	C₂²×#127	C₂²⋊C₄	1	1	yes	characteristic
137	C₂²×#127	C₂×D₄	1	1	yes	characteristic
138	C₂²×#124	C₂²⋊C₄	1	1	yes	characteristic
139	C₂²×#124	C₂×D₄	1	1	yes	characteristic
140	#3428	C₂²×C₄	1	1	yes	characteristic, complemented
141	C₂×C₄×#41	C₂²⋊C₄	1	1	yes	characteristic
142	C₂×C₄×#41	C₂²⋊C₄	1	1	yes	characteristic
143	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
144	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
145	C₂²×#117	C₂²⋊C₄	1	1	yes	characteristic
146	C₂²×#117	C₂×D₄	1	1	yes	characteristic
147	C₂×#413	C₂²×C₄	1	1	yes	characteristic, complemented
148	C₂×#413	C₂²×C₄	1	1	yes	characteristic, complemented
149	C₂×#410	C₂²×C₄	1	1	yes	characteristic, complemented
150	C₂×#410	C₂²×C₄	1	1	yes	characteristic, complemented
151	#2126	C₂×D₄	1	4	yes	—
152	#2126	C₂×D₄	1	4	yes	—
153	#2126	C₂×D₄	1	4	yes	—
154	#2126	C₂×D₄	1	4	yes	—
155	C₂×#354	C₂×D₄	1	4	yes	—
156	C₂×#353	C₂×D₄	1	4	yes	—
157	C₂⁶	#99	1	2	yes	—
158	C₂×2₋¹⁺⁴	C₄×D₄	1	4	yes	—
159	C₂×H(5,𝔽₂)	#99	1	4	yes	—
160	C₂×H(5,𝔽₂)	#99	1	4	yes	—
161	C₂×H(5,𝔽₂)	C₄×D₄	1	4	yes	—
162	C₂×H(5,𝔽₂)	#120	1	2	yes	—
163	C₂×H(5,𝔽₂)	#120	1	2	yes	—
164	C₂×H(5,𝔽₂)	#123	1	2	yes	—
165	C₂×H(5,𝔽₂)	#123	1	2	yes	—
166	C₂²×#41	#99	1	1	yes	characteristic
167	C₂²×#41	#99	1	1	yes	characteristic
168	C₂²×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
169	C₂²×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
170	C₂²×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
171	C₂²×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
172	C₂²×#41	C₄×D₄	1	1	yes	characteristic
173	C₂²×#41	C₄×D₄	1	1	yes	characteristic
174	C₂²×#41	#120	1	1	yes	characteristic
175	C₂²×#41	#123	1	1	yes	characteristic
176	C₂²×#41	C₂³×C₄	1	1	yes	characteristic
177	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
178	C₂³×Q₈	#99	1	1	yes	characteristic
179	C₂³×Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
180	C₂³×Q₈	C₄×D₄	1	1	yes	characteristic
181	C₂³×Q₈	#123	1	1	yes	characteristic
182	C₂³×D₄	#99	1	1	yes	characteristic
183	C₂³×D₄	#99	1	2	yes	—
184	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
185	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
186	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
187	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
188	C₂³×D₄	#120	1	1	yes	characteristic
189	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
190	#536	#120	1	2	yes	—
191	#536	#123	1	2	yes	—
192	#535	C₄×D₄	1	4	yes	—
193	#535	C₄×D₄	1	4	yes	—
194	#535	#120	1	2	yes	—
195	#535	#123	1	2	yes	—
196	#532	C₂²×D₄	1	2	yes	—
197	#532	C₂²×D₄	1	2	yes	—
198	#532	C₂×#41	1	2	yes	—
199	#532	C₂×#41	1	2	yes	—
200	C₂×C₄⋊Q₈	C₄×D₄	1	1	yes	characteristic
201	C₂×C₄⋊Q₈	#121	1	1	yes	characteristic
202	C₂×C₄⋊Q₈	#123	1	1	yes	characteristic
203	C₂×C₄⋊Q₈	C₂×#41	1	1	yes	characteristic
204	C₂×#127	C₄×D₄	1	1	yes	characteristic
205	C₂×#127	#120	1	1	yes	characteristic
206	C₂×#127	#121	1	1	yes	characteristic
207	C₂×#127	#121	1	4	yes	—
208	C₂×#127	C₂²×D₄	1	1	yes	characteristic
209	C₂×#124	C₄×D₄	1	1	yes	characteristic
210	C₂×#124	C₄×D₄	1	1	yes	characteristic
211	C₂×#124	#120	1	1	yes	characteristic
212	C₂×#124	#121	1	4	yes	—
213	C₂×#124	#121	1	1	yes	characteristic
214	C₂×#124	#121	1	1	yes	characteristic
215	C₂×#124	#123	1	1	yes	characteristic
216	C₂×#124	C₂²×D₄	1	1	yes	characteristic
217	C₂×#124	C₂×#41	1	1	yes	characteristic
218	C₄×#41	#121	1	4	yes	—
219	C₄×#41	#121	1	4	yes	—
220	C₂×#117	C₂×C₂²⋊C₄	1	1	yes	characteristic
221	C₂×#117	C₂×C₂²⋊C₄	1	1	yes	characteristic
222	C₂×#117	#121	1	1	yes	characteristic
223	C₂×#117	#121	1	1	yes	characteristic
224	C₂×#117	#121	1	1	yes	characteristic
225	C₂×#117	#121	1	1	yes	characteristic
226	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
227	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
228	#354	#120	1	8	yes	complemented
229	#353	#120	1	8	yes	complemented
230	C₂⁵	C₂×#99	1	1	yes	characteristic
231	C₂⁵	C₂×#99	1	2	yes	—
232	C₂⁵	C₂×#99	1	2	yes	—
233	C₂×#41	#386	1	2	yes	—
234	C₂×#41	#386	1	2	yes	—
235	C₂×#41	C₂×#99	1	2	yes	—
236	C₂×#41	C₂×#99	1	2	yes	—
237	C₂×#41	C₂×#99	1	2	yes	—
238	C₂×#41	C₂×#99	1	2	yes	—
239	C₂×#41	C₂×C₄×D₄	1	2	yes	—
240	C₂×#41	C₂×C₄×D₄	1	2	yes	—
241	C₂×#41	C₂×#120	1	1	yes	characteristic
242	C₂×#41	C₂×#120	1	1	yes	characteristic
243	C₂×#41	C₂×#123	1	1	yes	characteristic
244	C₂×#41	C₂×#123	1	1	yes	characteristic
245	C₂²×Q₈	#386	1	1	yes	characteristic
246	C₂²×Q₈	#386	1	2	yes	—
247	C₂²×Q₈	#386	1	1	yes	characteristic
248	C₂²×Q₈	C₂×#99	1	1	yes	characteristic
249	C₂²×Q₈	C₂×#99	1	1	yes	characteristic
250	C₂²×Q₈	C₂×C₄×D₄	1	1	yes	characteristic
251	C₂²×Q₈	C₂×#123	1	1	yes	characteristic
252	C₂²×D₄	AΣL(1,𝔽₁₆)	1	4	yes	—
253	C₂²×D₄	#386	1	1	yes	characteristic
254	C₂²×D₄	#386	1	2	yes	—
255	C₂²×D₄	#386	1	2	yes	—
256	C₂²×D₄	#386	1	2	yes	—
257	C₂²×D₄	#386	1	1	yes	characteristic
258	C₂²×D₄	C₂×#99	1	2	yes	—
259	C₂²×D₄	C₂×#99	1	2	yes	—
260	C₂²×D₄	C₂×#99	1	1	yes	characteristic
261	C₂²×D₄	C₂×#99	1	1	yes	characteristic
262	C₂²×D₄	C₂×C₄×D₄	1	1	yes	characteristic
263	C₂²×D₄	C₂×#120	1	1	yes	characteristic
264	C₂³×C₄	#386	1	1	yes	characteristic
265	C₂³×C₄	#386	1	1	yes	characteristic
266	C₂³×C₄	C₂×#99	1	1	yes	characteristic
267	C₂³×C₄	C₂×#99	1	1	yes	characteristic
268	C₂³×C₄	C₂×#99	1	1	yes	characteristic
269	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
270	C₄⋊Q₈	#525	1	2	yes	—
271	C₄⋊Q₈	#525	1	2	yes	—
272	#127	C₂×#120	1	2	yes	—
273	#127	#525	1	2	yes	—
274	#124	C₂×#120	1	2	yes	—
275	#124	#525	1	2	yes	—
276	#124	#525	1	2	yes	—
277	#124	#525	1	2	yes	—
278	#117	#386	1	2	yes	—
279	#117	#386	1	2	yes	—
280	C₂×C₄²	#386	1	1	yes	characteristic
281	C₂×C₄²	#386	1	1	yes	characteristic
282	C₂×C₄²	C₂×#121	1	1	yes	characteristic
283	C₂×C₄²	C₂×#121	1	1	yes	characteristic
284	C₂×C₄²	C₂×#121	1	2	yes	—
285	C₂×C₄²	C₂×#121	1	2	yes	—
286	C₂⁴	#1898	1	1	yes	characteristic
287	C₂⁴	#1898	1	1	yes	characteristic
288	C₂⁴	#1898	1	4	yes	—
289	C₂⁴	#1898	1	4	yes	—
290	C₂⁴	C₂²×#99	1	1	yes	characteristic
291	C₂×Q₈	#1898	1	2	yes	—
292	C₂×Q₈	#1898	1	2	yes	—
293	C₂×Q₈	#1898	1	2	yes	—
294	C₂×Q₈	C₄×#120	1	2	yes	—
295	C₂×Q₈	#2849	1	1	yes	characteristic
296	C₂×Q₈	#2849	1	1	yes	characteristic
297	C₂×D₄	#1898	1	2	yes	—
298	C₂×D₄	#1898	1	2	yes	—
299	C₂×D₄	#1898	1	2	yes	—
300	C₂×D₄	C₂×AΣL(1,𝔽₁₆)	1	2	yes	—
301	C₂×D₄	C₂×AΣL(1,𝔽₁₆)	1	2	yes	—
302	C₂×D₄	#2121	1	2	yes	—
303	C₂×D₄	#2121	1	2	yes	—
304	C₂×D₄	C₄×#120	1	2	yes	—
305	C₂×D₄	#2846	1	1	yes	characteristic
306	C₂×D₄	#2849	1	1	yes	characteristic
307	C₂²×C₄	#1898	1	1	yes	characteristic
308	C₂²×C₄	#1898	1	1	yes	characteristic
309	C₂²×C₄	C₂×AΣL(1,𝔽₁₆)	1	2	yes	—
310	C₂²×C₄	#2121	1	2	yes	—
311	C₂²×C₄	C₂×#386	1	1	yes	characteristic
312	C₂²×C₄	C₂×#386	1	1	yes	characteristic
313	C₂²×C₄	C₂×#386	1	1	yes	characteristic
314	C₂²×C₄	C₂²×#99	1	1	yes	characteristic
315	C₂²×C₄	C₂²×#99	1	1	yes	characteristic
316	C₂²×C₄	C₂²×#99	1	1	yes	characteristic
317	C₄²	#2847	1	2	yes	—
318	C₄²	#2847	1	2	yes	—
319	C₂³	#13086	1	2	yes	—
320	C₂³	C₂×#1898	1	1	yes	characteristic
321	C₂³	C₂×#1898	1	1	yes	characteristic
322	C₂³	C₂×#1898	1	1	yes	characteristic
323	D₄	#13086	1	4	yes	—
324	D₄	#13086	1	4	yes	—
325	C₂×C₄	#13086	1	2	yes	—
326	C₂×C₄	#14694	1	1	yes	characteristic
327	C₂×C₄	C₂×#1898	1	1	yes	characteristic
328	C₂×C₄	C₂×#1898	1	1	yes	characteristic
329	C₂×C₄	C₂×#1898	1	1	yes	characteristic
330	C₂×C₄	C₂²×AΣL(1,𝔽₁₆)	1	1	yes	characteristic
331	C₂×C₄	C₂×#2121	1	1	yes	characteristic
332	C₂×C₄	C₂×#2121	1	1	yes	characteristic
333	C₂×C₄	C₂×#2121	1	1	yes	characteristic
334	C₂²	#392675	1	1	yes	characteristic
335	C₂²	C₂×#13086	1	1	yes	characteristic
336	C₂²	#494695	1	1	yes	characteristic
337	C₄	C₂×#13086	1	1	yes	characteristic
338	C₄	C₂×#13086	1	1	yes	characteristic
339	C₄	#494695	1	1	yes	characteristic
340	C₄	#494695	1	1	yes	characteristic
341	C₂	#72280502	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂	#72280502
commutator	C₂²×#41	C₂³×C₄
Frattini, cosocle	C₂×#532	C₂⁴
prime radical	#72287221	C₂
LCS	G ▷ C₂²×#41 ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ C₂³×#41 ◁ C₂×#62852 ◁ G
LECS	G ▷ C₂×#532 ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
2. #72287157	C₂	semidirect
3. #72287053	C₂	semidirect
4. #72286951	C₂	semidirect
5. #72286622	C₂	semidirect
6. #72286294	C₂	semidirect
7. #72284902	C₂	semidirect
8. #72284779	C₂	semidirect
9. #72284566	C₂	semidirect
10. #72284408	C₂	semidirect
11. C₂×#7622467	C₂	semidirect
13. #10574842	C₄	semidirect
18. #6437623	C₄	semidirect
19. C₂×#23873	C₄	semidirect
21. C₂×#23872	C₄	semidirect
24. #512578	C₂²	semidirect
25. #512564	C₂²	semidirect
26. #392134	C₄	semidirect
27. #359671	C₄	semidirect
29. #359669	C₄	semidirect
32. #359444	C₄	semidirect
37. #151816	C₂²	semidirect
38. #151814	C₂²	semidirect
39. #151806	C₂²	semidirect
40. #151794	C₂²	semidirect
41. #151784	C₂²	semidirect
42. #151782	C₂²	semidirect
45. C₂×#3586	C₂×C₄	semidirect
46. C₂×#3585	C₂×C₄	semidirect
47. #62811	C₂×C₄	semidirect
61. C₂×#3027	C₂×C₄	semidirect
62. C₂×#3027	C₂×C₄	semidirect
63. C₂×#3018	C₂×C₄	semidirect
65. #60088	C₂×C₄	semidirect
66. #60087	C₂×C₄	semidirect
67. #60064	C₂×C₄	semidirect
68. #33361	D₄	semidirect
69. #33359	D₄	semidirect
70. C₂×#2129	D₄	semidirect
71. C₂×#2128	D₄	semidirect
72. C₂×#2127	D₄	semidirect
73. C₂×#2127	D₄	semidirect
76. C₂×#1914	C₂×C₄	semidirect
77. C₂×#1914	C₂×C₄	semidirect
78. C₂×#1914	C₂×C₄	semidirect
79. C₂×#1914	C₂×C₄	semidirect
80. #20961	C₂×C₄	semidirect
81. #20961	C₂×C₄	semidirect
82. #20952	C₂×C₄	semidirect
84. C₂×#1884	C₂×C₄	semidirect
85. C₂×#1884	C₂×C₄	semidirect
88. C₂×#1796	C₂×C₄	semidirect
89. C₂×#1796	C₂×C₄	semidirect
90. C₂×#1795	C₂×C₄	semidirect
91. C₂×#1795	C₂×C₄	semidirect
92. #20591	C₂×C₄	semidirect
93. #20584	C₂×C₄	semidirect
96. C₂×#585	C₂²×C₄	semidirect
110. C₂×#568	C₂²×C₄	semidirect
111. C₂×#568	C₂²×C₄	semidirect
140. #3428	C₂²×C₄	semidirect
147. C₂×#413	C₂²×C₄	semidirect
148. C₂×#413	C₂²×C₄	semidirect
149. C₂×#410	C₂²×C₄	semidirect
150. C₂×#410	C₂²×C₄	semidirect
228. #354	#120	semidirect
229. #353	#120	semidirect

Maximal subgroups

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

subgroup	index
#72287221	2
#72287157	2
#72287053	2
#72286951	2
#72286622	2
#72286294	2
#72284902	2
#72284779	2
#72284566	2
#72284408	2
C₂×#7622467	2