Subgroups — #72286117

Order 2048.

At least 7966 conjugacy classes of subgroups; only the 774 normal subgroups are shown.

The subgroup lattice has 306 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72286108	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#511813	C₂	1	1	yes	maximal, characteristic, complemented
3	#72286083	C₂	1	2	yes	maximal, complemented
4	#72286072	C₂	1	2	yes	maximal, complemented
5	#72286062	C₂	1	2	yes	maximal, complemented
6	#72286052	C₂	1	8	yes	maximal, complemented
7	#72286041	C₂	1	8	yes	maximal, complemented
8	#72284670	C₂	1	1	yes	maximal, characteristic, complemented
9	#72279927	C₂	1	2	yes	maximal, complemented
10	C₂×#152710	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#152020	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#7622875	C₂	1	1	yes	maximal, characteristic, complemented
13	#72226694	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#62862	C₂²	1	1	yes	characteristic, complemented
15	C₂×#61109	C₂²	1	1	yes	characteristic, complemented
16	C₂²×#3019	C₂²	1	1	yes	characteristic
17	C₂×#33568	C₂²	1	2	yes	complemented
18	#7622875	C₂²	1	8	yes	complemented
19	C₂×#33558	C₂²	1	2	yes	—
20	C₂×#33558	C₂²	1	2	yes	complemented
21	C₂²×#2127	C₂²	1	1	yes	characteristic, complemented
22	#7514192	C₂²	1	4	yes	complemented
23	#7514191	C₂²	1	4	yes	complemented
24	#7503375	C₂²	1	1	yes	characteristic, complemented
25	#7500909	C₂²	1	1	yes	characteristic, complemented
26	#6443103	C₂²	1	1	yes	characteristic
27	C₂×#23915	C₂²	1	1	yes	characteristic
28	#6381476	C₂²	1	1	yes	characteristic, complemented
29	#6351559	C₂²	1	2	yes	complemented
30	#512877	C₂²	1	8	yes	complemented
31	#512876	C₂²	1	8	yes	complemented
32	C₂×#13578	C₂²	1	2	yes	complemented
33	C₂×#13569	C₂²	1	2	yes	complemented
34	C₂×#13565	C₂²	1	2	yes	complemented
35	C₂×#13565	C₂²	1	2	yes	complemented
36	#511813	C₂²	1	8	yes	complemented
37	C₂×#12781	C₂²	1	2	yes	complemented
38	C₂×#12703	C₂²	1	1	yes	characteristic, complemented
39	#347164	C₂²	1	4	yes	complemented
40	#347154	C₂²	1	4	yes	complemented
41	#187883	C₂²	1	2	yes	complemented
42	C₂×#8522	C₂²	1	1	yes	characteristic, complemented
43	#153168	C₂²	1	8	yes	complemented
44	#153167	C₂²	1	8	yes	complemented
45	#153132	C₂²	1	16	yes	complemented
46	#152764	C₂²	1	4	yes	complemented
47	#152762	C₂²	1	4	yes	complemented
48	#152710	C₂²	1	8	yes	complemented
49	#152568	C₂²	1	16	yes	complemented
50	#152020	C₂²	1	8	yes	complemented
51	#151861	C₂²	1	2	yes	complemented
52	C₂×#7481	C₂²	1	2	yes	complemented
53	C₂³×H(5,𝔽₂)	D₄	1	1	yes	characteristic
54	#62862	C₂³	1	4	yes	—
55	C₂×#3487	D₄	1	1	yes	characteristic, complemented
56	C₂×#3545	C₂³	1	2	yes	—
57	C₂²×#535	C₂³	1	1	yes	characteristic
58	C₂×#3289	C₂³	1	2	yes	complemented
59	C₂×#3288	C₂³	1	2	yes	complemented
60	C₂×#3153	C₂³	1	1	yes	characteristic
61	C₂×#3151	D₄	1	1	yes	characteristic, complemented
62	C₂×#3019	D₄	1	4	yes	—
63	C₂×#3019	C₂³	1	4	yes	—
64	C₂²×#454	D₄	1	1	yes	characteristic, complemented
65	C₂²×#454	C₂³	1	1	yes	characteristic
66	C₂²×#455	C₂³	1	1	yes	characteristic
67	C₂²×#455	C₂³	1	1	yes	characteristic
68	C₂²×#453	D₄	1	1	yes	characteristic
69	C₂²×#453	D₄	1	1	yes	characteristic
70	C₂³×#100	D₄	1	1	yes	characteristic
71	#34633	D₄	1	1	yes	characteristic, complemented
72	#33568	C₂³	1	8	yes	complemented
73	#33558	D₄	1	8	yes	complemented
74	#33558	C₂³	1	8	yes	—
75	#33558	C₂³	1	8	yes	—
76	C₂×#2201	D₄	1	4	yes	complemented
77	C₂×#2199	D₄	1	4	yes	complemented
78	C₂²×#355	C₂³	1	2	yes	—
79	C₂×#2127	C₂³	1	4	yes	—
80	C₂²×#354	C₂³	1	2	yes	—
81	#31072	C₂³	1	4	yes	complemented
82	#30492	C₂³	1	2	yes	complemented
83	#30491	C₂³	1	2	yes	complemented
84	#25734	D₄	1	2	yes	complemented
85	#25734	C₂³	1	2	yes	—
86	#25732	D₄	1	2	yes	complemented
87	#25732	C₂³	1	2	yes	—
88	#23915	D₄	1	4	yes	complemented
89	#23915	C₂³	1	4	yes	—
90	#22896	C₂³	1	4	yes	complemented
91	#21204	C₂³	1	1	yes	characteristic
92	#21203	D₄	1	1	yes	characteristic, complemented
93	C₂×#1888	D₄	1	1	yes	characteristic, complemented
94	C₂×#1888	C₂³	1	1	yes	characteristic
95	C₂×#1785	D₄	1	1	yes	characteristic, complemented
96	#20377	D₄	1	1	yes	characteristic, complemented
97	#19051	C₂³	1	4	yes	complemented
98	#19050	C₂³	1	4	yes	complemented
99	C₂×#1533	C₂³	1	2	yes	—
100	C₂×#1407	C₂³	1	4	yes	complemented
101	C₂×#1406	C₂³	1	4	yes	complemented
102	#13569	C₂³	1	8	yes	complemented
103	#13565	C₂³	1	8	yes	complemented
104	#13565	C₂³	1	8	yes	complemented
105	#12781	C₂³	1	8	yes	complemented
106	#12703	C₂³	1	4	yes	—
107	#8528	C₂³	1	8	yes	complemented
108	#8522	C₂³	1	4	yes	—
109	#7502	C₂³	1	8	yes	complemented
110	#7481	C₂³	1	8	yes	complemented
111	C₂²×2₋¹⁺⁴	C₂×D₄	1	1	yes	characteristic, complemented
112	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
113	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
114	C₂²×H(5,𝔽₂)	C₂×D₄	1	4	yes	—
115	C₂³×#41	C₂×D₄	1	1	yes	characteristic
116	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
117	#3545	C₂×D₄	1	4	yes	complemented
118	#3545	C₂⁴	1	4	yes	—
119	C₂×#563	C₂×D₄	1	2	yes	complemented
120	C₂×H(3,𝔽₄)	C₂×D₄	1	2	yes	complemented
121	#3487	C₂×D₄	1	4	yes	complemented
122	C₂×#535	C₂×D₄	1	2	yes	—
123	C₂×#535	C₂×D₄	1	2	yes	—
124	C₂×#535	C₂×D₄	1	2	yes	—
125	C₂×#535	C₂⁴	1	2	yes	—
126	C₂×#532	C₂×D₄	1	1	yes	characteristic, complemented
127	C₂²×#127	C₂×D₄	1	1	yes	characteristic
128	C₂²×#127	C₂×D₄	1	1	yes	characteristic
129	C₂²×#124	C₂×D₄	1	1	yes	characteristic
130	C₂²×#124	C₂⁴	1	1	yes	characteristic
131	C₂×#519	C₂×D₄	1	1	yes	characteristic, complemented
132	C₂²×#117	C₂×D₄	1	1	yes	characteristic
133	C₂×#497	C₂×D₄	1	1	yes	characteristic, complemented
134	C₂×#497	C₂⁴	1	1	yes	characteristic
135	C₂×#496	C₂×D₄	1	1	yes	characteristic, complemented
136	C₂×#496	C₂⁴	1	1	yes	characteristic
137	C₂×#493	C₂×D₄	1	2	yes	complemented
138	C₂×#492	C₂×D₄	1	2	yes	complemented
139	C₂×#454	C₂×D₄	1	2	yes	complemented
140	C₂×#454	C₂×D₄	1	4	yes	complemented
141	C₂×#454	C₂⁴	1	2	yes	—
142	C₂×#455	C₂×D₄	1	4	yes	—
143	C₂×#455	C₂×D₄	1	4	yes	—
144	C₂×#455	C₂×D₄	1	2	yes	—
145	C₂×#455	C₂×D₄	1	2	yes	—
146	C₂×#455	C₂⁴	1	2	yes	—
147	C₂×#455	C₂⁴	1	2	yes	—
148	C₂×#453	C₂×D₄	1	4	yes	—
149	C₂×#453	C₂×D₄	1	4	yes	—
150	C₂²×#101	C₂×D₄	1	1	yes	characteristic, complemented
151	C₂²×#101	C₂×D₄	1	1	yes	characteristic, complemented
152	C₂²×#100	C₂×D₄	1	1	yes	characteristic
153	C₂²×#100	C₂×D₄	1	4	yes	—
154	C₂²×#100	C₂×D₄	1	1	yes	characteristic
155	C₂×C₄×M₁₆	C₂×D₄	1	1	yes	characteristic, complemented
156	C₂×C₄×M₁₆	C₂×D₄	1	1	yes	characteristic, complemented
157	#2621	C₂×D₄	1	2	yes	complemented
158	#2619	C₂×D₄	1	2	yes	complemented
159	#2285	C₂×D₄	1	1	yes	characteristic, complemented
160	#2201	C₂×D₄	1	16	yes	complemented
161	#2199	C₂×D₄	1	16	yes	complemented
162	C₂×#355	C₂⁴	1	4	yes	—
163	C₂×#354	C₂×D₄	1	4	yes	complemented
164	C₂×#354	C₂×D₄	1	4	yes	complemented
165	C₂×#354	C₂⁴	1	4	yes	—
166	#1961	C₂×D₄	1	2	yes	complemented
167	#1961	C₂×D₄	1	2	yes	complemented
168	#1958	C₂×D₄	1	2	yes	complemented
169	#1958	C₂⁴	1	2	yes	—
170	#1888	C₂×D₄	1	2	yes	complemented
171	#1888	C₂×D₄	1	4	yes	complemented
172	#1888	C₂⁴	1	2	yes	—
173	#1785	C₂×D₄	1	4	yes	complemented
174	#1750	C₂×D₄	1	2	yes	complemented
175	#1750	C₂×D₄	1	2	yes	complemented
176	#1533	C₂⁴	1	4	yes	—
177	C₂×2₋¹⁺⁴	C₂²×D₄	1	2	yes	complemented
178	C₂×H(5,𝔽₂)	#120	1	2	yes	—
179	C₂×H(5,𝔽₂)	#120	1	2	yes	—
180	C₂×H(5,𝔽₂)	C₂²×D₄	1	2	yes	—
181	C₂×H(5,𝔽₂)	C₂²×D₄	1	2	yes	—
182	C₂²×#41	#120	1	2	yes	—
183	C₂²×#41	C₂²×D₄	1	2	yes	—
184	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
185	C₂³×D₄	#120	1	1	yes	characteristic
186	C₂³×D₄	#120	1	2	yes	—
187	C₂³×D₄	#120	1	1	yes	characteristic
188	C₂³×D₄	C₂²×D₄	1	2	yes	—
189	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
190	C₂⁴×C₄	#120	1	1	yes	characteristic
191	#563	C₂²×D₄	1	4	yes	—
192	H(3,𝔽₄)	C₂²×D₄	1	4	yes	—
193	C₂×C₄⋊Q₈	C₂²×D₄	1	1	yes	characteristic, complemented
194	C₂×#127	#120	1	2	yes	—
195	C₂×#127	#120	1	2	yes	—
196	C₂×#127	C₂²×D₄	1	2	yes	—
197	C₂×#127	C₂²×D₄	1	2	yes	—
198	C₂×#127	C₂²×D₄	1	1	yes	characteristic, complemented
199	C₂×#124	#120	1	2	yes	—
200	C₂×#124	C₂²×D₄	1	2	yes	—
201	C₂×#124	C₂²×D₄	1	1	yes	characteristic
202	C₂×#124	C₂²×D₄	1	1	yes	characteristic
203	C₂×#124	C₂²×D₄	1	2	yes	—
204	C₂×#124	C₂²×D₄	1	2	yes	—
205	C₂×#124	C₂²×D₄	1	1	yes	characteristic
206	C₂×#124	H(5,𝔽₂)	1	2	yes	—
207	C₂×#124	H(5,𝔽₂)	1	2	yes	—
208	C₂×#124	C₂⁵	1	1	yes	characteristic
209	#519	C₂²×D₄	1	2	yes	complemented
210	C₂×#117	#120	1	2	yes	—
211	C₂×#117	C₂²×D₄	1	2	yes	—
212	C₂²×C₄²	#120	1	1	yes	characteristic
213	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
214	#455	#120	1	8	yes	—
215	#455	C₂²×D₄	1	8	yes	—
216	C₂×#101	C₂²×D₄	1	2	yes	complemented
217	C₂×#101	C₂²×D₄	1	2	yes	complemented
218	C₂×#100	#120	1	2	yes	—
219	C₂×#100	#120	1	2	yes	—
220	C₂×#100	C₂²×D₄	1	2	yes	—
221	C₂×#100	C₂²×D₄	1	2	yes	—
222	C₂×#97	C₂²×D₄	1	1	yes	characteristic, complemented
223	C₂×#97	C₂²×D₄	1	1	yes	characteristic, complemented
224	C₂×C₄×C₈	C₂²×D₄	1	2	yes	complemented
225	#382	C₂²×D₄	1	2	yes	complemented
226	#354	C₂²×D₄	1	8	yes	—
227	C₂⁵	B(4,𝔽₂)	1	1	yes	characteristic
228	H(5,𝔽₂)	C₂×#120	1	4	yes	—
229	C₂²×Q₈	C₂×#120	1	1	yes	characteristic
230	C₂²×Q₈	D₄²	1	2	yes	—
231	C₂²×Q₈	D₄²	1	2	yes	—
232	C₂²×Q₈	C₂³×D₄	1	1	yes	characteristic
233	C₂²×D₄	B(4,𝔽₂)	1	1	yes	characteristic
234	C₂²×D₄	B(4,𝔽₂)	1	1	yes	characteristic
235	C₂²×D₄	B(4,𝔽₂)	1	2	yes	—
236	C₂²×D₄	C₂×#120	1	1	yes	characteristic
237	C₂²×D₄	C₂×#120	1	1	yes	characteristic
238	C₂²×D₄	C₂×#120	1	2	yes	—
239	C₂²×D₄	C₂×#120	1	1	yes	characteristic
240	C₂²×D₄	C₂×#120	1	2	yes	—
241	C₂²×D₄	#534	1	1	yes	characteristic
242	C₂²×D₄	#534	1	1	yes	characteristic
243	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
244	C₂³×C₄	B(4,𝔽₂)	1	1	yes	characteristic
245	C₂³×C₄	B(4,𝔽₂)	1	2	yes	—
246	C₂³×C₄	C₂×#120	1	2	yes	—
247	C₂³×C₄	C₂×#120	1	1	yes	characteristic
248	#124	C₂×#120	1	2	yes	—
249	#124	#534	1	2	yes	—
250	#124	D₄²	1	2	yes	—
251	#124	D₄²	1	2	yes	—
252	#124	D₄²	1	2	yes	—
253	#124	D₄²	1	2	yes	—
254	#124	C₂³×D₄	1	2	yes	—
255	#124	C₂×H(5,𝔽₂)	1	2	yes	—
256	C₂×C₄²	C₂×#120	1	2	yes	—
257	C₂×C₄²	C₂×#120	1	1	yes	characteristic
258	C₂×C₄²	D₄²	1	2	yes	—
259	C₂×C₄²	D₄²	1	2	yes	—
260	C₂×C₄²	C₂³×D₄	1	1	yes	characteristic
261	#100	C₂×#120	1	4	yes	—
262	C₂⁴	#2196	1	2	yes	—
263	C₂⁴	#2196	1	1	yes	characteristic
264	C₂⁴	#2196	1	1	yes	characteristic
265	C₂⁴	C₂×B(4,𝔽₂)	1	2	yes	—
266	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
267	C₂×Q₈	#2403	1	2	yes	—
268	C₂×Q₈	C₂×D₄²	1	2	yes	—
269	C₂×D₄	#2403	1	1	yes	characteristic
270	C₂×D₄	#2403	1	1	yes	characteristic
271	C₂×D₄	C₂×B(4,𝔽₂)	1	2	yes	—
272	C₂×D₄	C₂×B(4,𝔽₂)	1	2	yes	—
273	C₂×D₄	C₂²×#120	1	1	yes	characteristic
274	C₂×D₄	C₂×#534	1	1	yes	characteristic
275	C₂²×C₄	#2403	1	1	yes	characteristic
276	C₂²×C₄	#2403	1	1	yes	characteristic
277	C₂²×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
278	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
279	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
280	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
281	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
282	C₄²	#2403	1	2	yes	—
283	C₄²	C₂×D₄²	1	2	yes	—
284	C₂³	#23900	1	1	yes	characteristic
285	C₂³	#23900	1	1	yes	characteristic
286	C₂³	C₂×#2196	1	2	yes	—
287	C₂³	C₂×#2196	1	2	yes	—
288	C₂³	C₂×#2196	1	1	yes	characteristic
289	C₂³	C₂×#2196	1	1	yes	characteristic
290	C₂³	#33551	1	1	yes	characteristic
291	C₂³	#33551	1	1	yes	characteristic
292	C₂³	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
293	C₂×C₄	#23900	1	1	yes	characteristic
294	C₂×C₄	#23900	1	1	yes	characteristic
295	C₂×C₄	C₂×#2403	1	1	yes	characteristic
296	C₂×C₄	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
297	C₂²	#499787	1	1	yes	characteristic
298	C₂²	#499787	1	1	yes	characteristic
299	C₂²	#499787	1	1	yes	characteristic
300	C₂²	#499787	1	1	yes	characteristic
301	C₂²	C₂×#23900	1	1	yes	characteristic
302	C₂²	C₂²×#2196	1	1	yes	characteristic
303	C₂²	C₂×#33551	1	1	yes	characteristic
304	C₂	C₂×#499787	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂	C₂×#499787
commutator, Frattini, cosocle	C₂×#124	C₂⁵
LCS	G ▷ C₂×#124 ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂ ◁ C₂⁴ ◁ C₂⁴×C₄ ◁ C₂²×#535 ◁ G
LECS	G ▷ C₂×#124 ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72286108	C₂	semidirect
2. C₂×#511813	C₂	semidirect
3. #72286083	C₂	semidirect
4. #72286072	C₂	semidirect
5. #72286062	C₂	semidirect
6. #72286052	C₂	semidirect
7. #72286041	C₂	semidirect
8. #72284670	C₂	semidirect
9. #72279927	C₂	semidirect
10. C₂×#152710	C₂	semidirect
11. C₂×#152020	C₂	semidirect
12. C₂×#7622875	C₂	semidirect
13. #72226694	C₂	semidirect
14. C₂×#62862	C₂²	semidirect
15. C₂×#61109	C₂²	semidirect
17. C₂×#33568	C₂²	semidirect
18. #7622875	C₂²	semidirect
20. C₂×#33558	C₂²	semidirect
21. C₂²×#2127	C₂²	semidirect
22. #7514192	C₂²	semidirect
23. #7514191	C₂²	semidirect
24. #7503375	C₂²	semidirect
25. #7500909	C₂²	semidirect
28. #6381476	C₂²	semidirect
29. #6351559	C₂²	semidirect
30. #512877	C₂²	semidirect
31. #512876	C₂²	semidirect
32. C₂×#13578	C₂²	semidirect
33. C₂×#13569	C₂²	semidirect
34. C₂×#13565	C₂²	semidirect
35. C₂×#13565	C₂²	semidirect
36. #511813	C₂²	semidirect
37. C₂×#12781	C₂²	semidirect
38. C₂×#12703	C₂²	semidirect
39. #347164	C₂²	semidirect
40. #347154	C₂²	semidirect
41. #187883	C₂²	semidirect
42. C₂×#8522	C₂²	semidirect
43. #153168	C₂²	semidirect
44. #153167	C₂²	semidirect
45. #153132	C₂²	semidirect
46. #152764	C₂²	semidirect
47. #152762	C₂²	semidirect
48. #152710	C₂²	semidirect
49. #152568	C₂²	semidirect
50. #152020	C₂²	semidirect
51. #151861	C₂²	semidirect
52. C₂×#7481	C₂²	semidirect
55. C₂×#3487	D₄	semidirect
58. C₂×#3289	C₂³	semidirect
59. C₂×#3288	C₂³	semidirect
61. C₂×#3151	D₄	semidirect
64. C₂²×#454	D₄	semidirect
71. #34633	D₄	semidirect
72. #33568	C₂³	semidirect
73. #33558	D₄	semidirect
76. C₂×#2201	D₄	semidirect
77. C₂×#2199	D₄	semidirect
81. #31072	C₂³	semidirect
82. #30492	C₂³	semidirect
83. #30491	C₂³	semidirect
84. #25734	D₄	semidirect
86. #25732	D₄	semidirect
88. #23915	D₄	semidirect
90. #22896	C₂³	semidirect
92. #21203	D₄	semidirect
93. C₂×#1888	D₄	semidirect
95. C₂×#1785	D₄	semidirect
96. #20377	D₄	semidirect
97. #19051	C₂³	semidirect
98. #19050	C₂³	semidirect
100. C₂×#1407	C₂³	semidirect
101. C₂×#1406	C₂³	semidirect
102. #13569	C₂³	semidirect
103. #13565	C₂³	semidirect
104. #13565	C₂³	semidirect
105. #12781	C₂³	semidirect
107. #8528	C₂³	semidirect
109. #7502	C₂³	semidirect
110. #7481	C₂³	semidirect
111. C₂²×2₋¹⁺⁴	C₂×D₄	semidirect
117. #3545	C₂×D₄	semidirect
119. C₂×#563	C₂×D₄	semidirect
120. C₂×H(3,𝔽₄)	C₂×D₄	semidirect
121. #3487	C₂×D₄	semidirect
126. C₂×#532	C₂×D₄	semidirect
131. C₂×#519	C₂×D₄	semidirect
133. C₂×#497	C₂×D₄	semidirect
135. C₂×#496	C₂×D₄	semidirect
137. C₂×#493	C₂×D₄	semidirect
138. C₂×#492	C₂×D₄	semidirect
139. C₂×#454	C₂×D₄	semidirect
140. C₂×#454	C₂×D₄	semidirect
150. C₂²×#101	C₂×D₄	semidirect
151. C₂²×#101	C₂×D₄	semidirect
155. C₂×C₄×M₁₆	C₂×D₄	semidirect
156. C₂×C₄×M₁₆	C₂×D₄	semidirect
157. #2621	C₂×D₄	semidirect
158. #2619	C₂×D₄	semidirect
159. #2285	C₂×D₄	semidirect
160. #2201	C₂×D₄	semidirect
161. #2199	C₂×D₄	semidirect
163. C₂×#354	C₂×D₄	semidirect
164. C₂×#354	C₂×D₄	semidirect
166. #1961	C₂×D₄	semidirect
167. #1961	C₂×D₄	semidirect
168. #1958	C₂×D₄	semidirect
170. #1888	C₂×D₄	semidirect
171. #1888	C₂×D₄	semidirect
173. #1785	C₂×D₄	semidirect
174. #1750	C₂×D₄	semidirect
175. #1750	C₂×D₄	semidirect
177. C₂×2₋¹⁺⁴	C₂²×D₄	semidirect
193. C₂×C₄⋊Q₈	C₂²×D₄	semidirect
198. C₂×#127	C₂²×D₄	semidirect
209. #519	C₂²×D₄	semidirect
216. C₂×#101	C₂²×D₄	semidirect
217. C₂×#101	C₂²×D₄	semidirect
222. C₂×#97	C₂²×D₄	semidirect
223. C₂×#97	C₂²×D₄	semidirect
224. C₂×C₄×C₈	C₂²×D₄	semidirect
225. #382	C₂²×D₄	semidirect

Maximal subgroups

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

subgroup	index
#72286108	2
C₂×#511813	2
#72286083	2
#72286072	2
#72286062	2
#72286052	2
#72286041	2
#72284670	2
#72279927	2
C₂×#152710	2
C₂×#152020	2
C₂×#7622875	2
#72226694	2