Subgroups — C₂×#72237002 #72343867

Order 6144.

At least 18767 conjugacy classes of subgroups; only the 603 normal subgroups are shown.

The subgroup lattice has 256 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×#72236829	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#72236805	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#72236787	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#72236804	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#72236801	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#11711590	C₂²	1	1	yes	characteristic, complemented
7	C₂×#11714179	C₂²	1	1	yes	characteristic, complemented
8	C₂×#72236799	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#21484⋊C₃	C₂²	1	1	yes	characteristic, complemented
10	C₂×#11710352	C₂²	1	1	yes	characteristic, complemented
11	C₂×#72236891	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#72236871	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#72236853	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#11715688	C₂²	1	1	yes	characteristic, complemented
15	C₂×#72236895	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#11711589	C₂²	1	1	yes	characteristic, complemented
17	C₂×#72215654	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#11715710	C₂²	1	1	yes	characteristic, complemented
19	C₂×#11715738	C₂²	1	1	yes	characteristic, complemented
20	C₂×#72236850	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂×#11711638	C₂²	1	1	yes	characteristic, complemented
22	C₂×#11711638	C₂²	1	1	yes	characteristic, complemented
23	C₂×#11715736	C₂²	1	1	yes	characteristic, complemented
24	C₂×#32948⋊C₃	C₂²	1	1	yes	characteristic, complemented
25	C₂×#72236763	C₂	1	1	yes	maximal, characteristic, complemented
26	C₂×#11711643	C₂²	1	1	yes	characteristic, complemented
27	C₂×#11711642	C₂²	1	1	yes	characteristic, complemented
28	C₂×#11715709	C₂²	1	1	yes	characteristic, complemented
29	C₂×#32894⋊C₃	C₂²	1	1	yes	characteristic, complemented
30	C₂×#72236743	C₂	1	1	yes	maximal, characteristic, complemented
31	C₂×#11711647	C₂²	1	1	yes	characteristic, complemented
32	C₂×#11715711	C₂²	1	1	yes	characteristic, complemented
33	C₂×#11711646	C₂²	1	1	yes	characteristic, complemented
34	C₂×#32895⋊C₃	C₂²	1	1	yes	characteristic, complemented
35	C₂×#11711596	C₂²	1	1	yes	characteristic, complemented
36	C₂×#11715831	C₂²	1	1	yes	characteristic, complemented
37	C₂×#11715712	C₂²	1	1	yes	characteristic, complemented
38	C₂×#11710899	C₂²	1	1	yes	characteristic, complemented
39	C₂×#11715842	C₂²	1	1	yes	characteristic, complemented
40	C₂×#11714178	C₂²	1	1	yes	characteristic, complemented
41	C₂×#6573736	D₃	1	1	yes	characteristic, complemented
42	#72237002	C₂	1	16	yes	maximal, direct product factor
43	#72236895	C₂²	1	8	yes	complemented
44	#72236891	C₂²	1	8	yes	complemented
45	#72236871	C₂²	1	8	yes	complemented
46	#72236853	C₂²	1	8	yes	complemented
47	#72236850	C₂²	1	8	yes	complemented
48	#72236829	C₂²	1	8	yes	complemented
49	C₂×#72217027	C₂	1	1	yes	maximal, characteristic, complemented
50	#72236805	C₂²	1	8	yes	complemented
51	#72236804	C₂²	1	8	yes	complemented
52	#72236801	C₂²	1	8	yes	complemented
53	#72236799	C₂²	1	8	yes	complemented
54	C₂×#60399⋊C₃	C₂²	1	1	yes	characteristic, complemented
55	#72236787	C₂²	1	8	yes	complemented
56	C₂×#11714174	C₂²	1	1	yes	characteristic, complemented
57	#72236763	C₂²	1	8	yes	complemented
58	C₂×#11714184	C₂²	1	1	yes	characteristic
59	C₂×#11714184	C₂²	1	1	yes	characteristic, complemented
60	#72236743	C₂²	1	8	yes	complemented
61	C₂×#11714162	C₂²	1	1	yes	characteristic
62	C₂×#11714175	C₂²	1	1	yes	characteristic, complemented
63	C₂×#11715681	C₂²	1	1	yes	characteristic, complemented
64	C₂×#11715839	C₂²	1	1	yes	characteristic, complemented
65	#72217027	C₂²	1	8	yes	complemented
66	#72215654	C₂²	1	8	yes	complemented
67	C₂×#11715828	C₂²	1	1	yes	characteristic
68	#11715842	C₂³	1	4	yes	complemented
69	#11715839	C₂³	1	4	yes	complemented
70	C₂×#87521	C₂³	1	1	yes	characteristic
71	C₂×#87521	C₂³	1	1	yes	characteristic, complemented
72	C₂×#87519	C₂³	1	1	yes	characteristic
73	#11715831	C₂³	1	4	yes	complemented
74	#11715828	C₂³	1	4	yes	—
75	C₂×#87518	C₂³	1	1	yes	characteristic, complemented
76	C₂×#87522	C₂³	1	1	yes	characteristic
77	C₂×#87520	C₂³	1	1	yes	characteristic
78	#11715738	C₂³	1	4	yes	complemented
79	#11715736	C₂³	1	4	yes	complemented
80	#11715712	C₂³	1	4	yes	complemented
81	#11715711	C₂³	1	4	yes	complemented
82	#11715710	C₂³	1	4	yes	complemented
83	#11715709	C₂³	1	4	yes	complemented
84	#11715688	C₂³	1	4	yes	complemented
85	#11715681	C₂³	1	4	yes	complemented
86	C₂×#85567	C₂³	1	1	yes	characteristic, complemented
87	C₂×#85566	C₂³	1	1	yes	characteristic, complemented
88	#11714184	C₂³	1	4	yes	—
89	#11714184	C₂³	1	4	yes	complemented
90	#11714179	C₂³	1	4	yes	complemented
91	#11714178	C₂³	1	4	yes	complemented
92	#11714175	C₂³	1	4	yes	complemented
93	#11714174	C₂³	1	4	yes	complemented
94	#11714162	D₄	1	4	yes	complemented
95	#11714162	C₂³	1	4	yes	—
96	C₂×#73031	D₄	1	1	yes	characteristic, complemented
97	C₂×#73025	D₄	1	1	yes	characteristic, complemented
98	C₂×#73030	D₄	1	1	yes	characteristic, complemented
99	C₂×#73026	D₄	1	1	yes	characteristic, complemented
100	#11711647	C₂³	1	4	yes	complemented
101	#11711646	C₂³	1	4	yes	complemented
102	#11711643	C₂³	1	4	yes	complemented
103	#11711642	C₂³	1	4	yes	complemented
104	#11711638	C₂³	1	4	yes	complemented
105	#11711638	C₂³	1	4	yes	complemented
106	#11711596	C₂³	1	4	yes	complemented
107	#11711590	C₂³	1	4	yes	complemented
108	#11711589	C₂³	1	4	yes	complemented
109	C₂×#87548	C₂³	1	1	yes	characteristic, complemented
110	C₂×#87547	C₂³	1	1	yes	characteristic
111	#11710899	C₂³	1	4	yes	complemented
112	C₂×#85666	C₂³	1	1	yes	characteristic, complemented
113	#11710352	C₂³	1	4	yes	complemented
114	#60399⋊C₃	C₂³	1	4	yes	complemented
115	C₂×#3027⋊C₃	C₂³	1	1	yes	characteristic
116	C₂×#3027⋊C₃	C₂³	1	1	yes	characteristic, complemented
117	C₂×#3025⋊C₃	C₂³	1	1	yes	characteristic
118	#32948⋊C₃	C₂³	1	4	yes	complemented
119	#32895⋊C₃	C₂³	1	4	yes	complemented
120	#32894⋊C₃	C₂³	1	4	yes	complemented
121	#21484⋊C₃	C₂³	1	4	yes	complemented
122	C₂×#1791⋊C₃	C₂³	1	1	yes	characteristic, complemented
123	C₂×#63092	C₂×D₃	1	1	yes	characteristic, complemented
124	C₂×#60402	C₂×D₃	1	1	yes	characteristic, complemented
125	C₂×#60399	C₂×D₃	1	1	yes	characteristic, complemented
126	C₂×#32948	C₂×D₃	1	1	yes	characteristic, complemented
127	C₂×#32895	C₂×D₃	1	1	yes	characteristic, complemented
128	C₂×#32894	C₂×D₃	1	1	yes	characteristic, complemented
129	#6573736	C₂×D₃	1	8	yes	complemented
130	C₂×#21484	C₂×D₃	1	1	yes	characteristic, complemented
131	#87548	C₂⁴	1	2	yes	complemented
132	#87547	C₂⁴	1	2	yes	—
133	C₂×#5950	C₂⁴	1	1	yes	characteristic
134	#87522	C₂⁴	1	2	yes	—
135	#87521	C₂⁴	1	2	yes	—
136	#87521	C₂⁴	1	2	yes	complemented
137	#87520	C₂×D₄	1	2	yes	—
138	#87520	C₂⁴	1	2	yes	—
139	#87519	C₂×D₄	1	2	yes	—
140	#87519	C₂⁴	1	2	yes	—
141	#87518	C₂⁴	1	2	yes	complemented
142	C₂×#5935	C₂×D₄	1	1	yes	characteristic
143	C₂×#5934	C₂×D₄	1	1	yes	characteristic
144	C₂×#5933	C₂×D₄	1	1	yes	characteristic
145	C₂×#5932	C₂×D₄	1	1	yes	characteristic
146	#85666	C₂⁴	1	2	yes	complemented
147	#85567	C₂⁴	1	2	yes	complemented
148	#85566	C₂⁴	1	2	yes	complemented
149	#3027⋊C₃	C₂⁴	1	2	yes	—
150	#3027⋊C₃	C₂⁴	1	2	yes	complemented
151	#3025⋊C₃	C₂×D₄	1	2	yes	—
152	#3025⋊C₃	C₂⁴	1	2	yes	—
153	C₂×#458⋊C₃	C₂×D₄	1	1	yes	characteristic
154	C₂×B(4,𝔽₂)⋊C₃	C₂×D₄	1	1	yes	characteristic
155	#73031	C₂×D₄	1	4	yes	complemented
156	#73030	C₂×D₄	1	4	yes	complemented
157	#73026	C₂×D₄	1	4	yes	complemented
158	#73025	C₂×D₄	1	4	yes	complemented
159	#1791⋊C₃	C₂⁴	1	2	yes	complemented
160	C₂×2₋¹⁺⁶	C₂²×D₃	1	1	yes	characteristic, complemented
161	C₂×H(7,𝔽₂)	C₂²×D₃	1	1	yes	characteristic
162	#63092	C₂²×D₃	1	4	yes	complemented
163	C₂³×AGL(1,ℤ/8)	S₄	1	1	yes	characteristic, complemented
164	C₂×#3573	C₂²×D₃	1	1	yes	characteristic, complemented
165	#60402	C₂²×D₃	1	4	yes	complemented
166	#60399	C₂²×D₃	1	4	yes	complemented
167	C₂×#3027	C₂²×D₃	1	1	yes	characteristic
168	C₂×#3027	C₂²×D₃	1	1	yes	characteristic, complemented
169	C₂×#3025	C₂²×D₃	1	1	yes	characteristic
170	#32948	C₂²×D₃	1	4	yes	complemented
171	#32895	C₂²×D₃	1	4	yes	complemented
172	#32894	C₂²×D₃	1	4	yes	complemented
173	#21484	C₂²×D₃	1	4	yes	complemented
174	C₂×#1791	C₂²×D₃	1	1	yes	characteristic, complemented
175	#5950	C₂²×D₄	1	1	yes	characteristic
176	#5950	C₂⁵	1	1	yes	characteristic
177	C₂×#997	C₂²×D₄	1	1	yes	characteristic
178	#5935	C₂²×D₄	1	2	yes	—
179	#5934	C₂²×D₄	1	2	yes	—
180	#5933	C₂²×D₄	1	2	yes	—
181	#5932	C₂²×D₄	1	2	yes	—
182	#458⋊C₃	C₂²×D₄	1	2	yes	—
183	B(4,𝔽₂)⋊C₃	C₂²×D₄	1	2	yes	—
184	2₋¹⁺⁶	C₂³×D₃	1	2	yes	complemented
185	H(7,𝔽₂)	C₂³×D₃	1	2	yes	—
186	C₂×#585	C₂³×D₃	1	1	yes	characteristic
187	C₂³×#41	C₂×S₄	1	1	yes	characteristic, complemented
188	C₂⁴×D₄	C₂×S₄	1	1	yes	characteristic
189	C₂²×AGL(1,ℤ/8)	C₂×S₄	1	8	yes	complemented
190	C₂³×SD₁₆	C₂×S₄	1	1	yes	characteristic
191	C₂³×SD₁₆	C₂×S₄	1	1	yes	characteristic, complemented
192	C₂³×D₈	C₂×S₄	1	1	yes	characteristic
193	C₂³×D₈	C₂×S₄	1	1	yes	characteristic, complemented
194	#3573	C₂³×D₃	1	2	yes	complemented
195	C₂³×M₁₆	C₂×S₄	1	1	yes	characteristic, complemented
196	#3027	C₂³×D₃	1	2	yes	—
197	#3027	C₂³×D₃	1	2	yes	complemented
198	#3025	D₃×D₄	1	2	yes	—
199	#3025	C₂³×D₃	1	2	yes	—
200	C₂×#458	D₃×D₄	1	1	yes	characteristic
201	C₂×B(4,𝔽₂)	D₃×D₄	1	1	yes	characteristic
202	#1791	C₂³×D₃	1	2	yes	complemented
203	#997	C₂³×D₄	1	1	yes	characteristic
204	#585	C₂×D₃×D₄	1	1	yes	characteristic
205	#585	C₂⁴×D₃	1	1	yes	characteristic
206	C₂×H(5,𝔽₂)	C₂×D₃×D₄	1	1	yes	characteristic
207	C₂²×#41	C₂²×S₄	1	4	yes	complemented
208	C₂³×Q₈	C₂²×S₄	1	1	yes	characteristic
209	C₂³×D₄	C₂²×S₄	1	1	yes	characteristic
210	C₂³×D₄	C₂²×S₄	1	1	yes	characteristic
211	C₂³×D₄	C₂²×S₄	1	1	yes	characteristic
212	C₂³×D₄	C₂²×S₄	1	4	yes	—
213	C₂⁴×C₄	C₂²×S₄	1	1	yes	characteristic
214	C₂²×SD₁₆	C₂²×S₄	1	4	yes	—
215	C₂²×SD₁₆	C₂²×S₄	1	4	yes	complemented
216	C₂²×D₈	C₂²×S₄	1	4	yes	—
217	C₂²×D₈	C₂²×S₄	1	4	yes	complemented
218	C₂²×M₁₆	C₂²×S₄	1	4	yes	complemented
219	C₂³×C₈	C₂²×S₄	1	1	yes	characteristic
220	C₂³×C₈	C₂²×S₄	1	1	yes	characteristic
221	#458	C₂×D₃×D₄	1	2	yes	—
222	B(4,𝔽₂)	C₂×D₃×D₄	1	2	yes	—
223	C₂⁵	D₄×S₄	1	1	yes	characteristic
224	H(5,𝔽₂)	C₂²×D₃×D₄	1	1	yes	characteristic
225	C₂²×Q₈	C₂³×S₄	1	2	yes	—
226	C₂²×D₄	C₂³×S₄	1	2	yes	—
227	C₂²×D₄	C₂³×S₄	1	2	yes	—
228	C₂²×D₄	C₂³×S₄	1	2	yes	—
229	C₂³×C₄	D₄×S₄	1	1	yes	characteristic
230	C₂³×C₄	D₄×S₄	1	2	yes	—
231	C₂³×C₄	C₂³×S₄	1	1	yes	characteristic
232	C₂³×C₄	C₂³×S₄	1	2	yes	—
233	C₂×SD₁₆	#1020⋊C₂	1	1	yes	characteristic
234	C₂²×C₈	C₂³×S₄	1	2	yes	—
235	C₂²×C₈	C₂³×S₄	1	2	yes	—
236	C₂⁴	C₂×D₄×S₄	1	1	yes	characteristic
237	C₂⁴	C₂×D₄×S₄	1	2	yes	—
238	C₂×Q₈	C₂×#1020⋊C₂	1	1	yes	characteristic
239	C₂×D₄	C₂×#1020⋊C₂	1	1	yes	characteristic
240	C₂²×C₄	C₂×D₄×S₄	1	1	yes	characteristic
241	C₂²×C₄	C₂×D₄×S₄	1	2	yes	—
242	C₂²×C₄	C₂⁴×S₄	1	1	yes	characteristic
243	SD₁₆	C₂×#1020⋊C₂	1	4	yes	—
244	C₂×C₈	C₂×#1020⋊C₂	1	1	yes	characteristic
245	C₂³	C₂²×D₄×S₄	1	1	yes	characteristic
246	Q₈	C₂²×#1020⋊C₂	1	2	yes	—
247	D₄	C₂²×#1020⋊C₂	1	2	yes	—
248	C₂×C₄	C₂²×#1020⋊C₂	1	1	yes	characteristic
249	C₈	C₂²×#1020⋊C₂	1	2	yes	—
250	C₂²	D₄×#1020⋊C₂	1	1	yes	characteristic
251	C₄	D₄×#1020⋊C₂	1	1	yes	characteristic
252	C₄	C₂³×#1020⋊C₂	1	1	yes	characteristic
253	C₂	#72237002	1	2	yes	direct product factor
254	C₂	C₂×D₄×#1020⋊C₂	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	D₄×#1020⋊C₂
commutator, cosocle	#5950	C₂⁵
Frattini	C₂²×C₄	C₂⁴×S₄
Fitting	C₂×#6573736	D₃
hypercenter	C₂×SD₁₆	#1020⋊C₂
hypocenter	#997	C₂³×D₄
LCS	G ▷ #5950 ▷ #997
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×SD₁₆

Complements

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

N	H ≅ G/N	type
1. C₂×#72236829	C₂	semidirect
2. C₂×#72236805	C₂	semidirect
3. C₂×#72236787	C₂	semidirect
4. C₂×#72236804	C₂	semidirect
5. C₂×#72236801	C₂	semidirect
6. C₂×#11711590	C₂²	semidirect
7. C₂×#11714179	C₂²	semidirect
8. C₂×#72236799	C₂	semidirect
9. C₂×#21484⋊C₃	C₂²	semidirect
10. C₂×#11710352	C₂²	semidirect
11. C₂×#72236891	C₂	semidirect
12. C₂×#72236871	C₂	semidirect
13. C₂×#72236853	C₂	semidirect
14. C₂×#11715688	C₂²	semidirect
15. C₂×#72236895	C₂	semidirect
16. C₂×#11711589	C₂²	semidirect
17. C₂×#72215654	C₂	semidirect
18. C₂×#11715710	C₂²	semidirect
19. C₂×#11715738	C₂²	semidirect
20. C₂×#72236850	C₂	semidirect
21. C₂×#11711638	C₂²	semidirect
22. C₂×#11711638	C₂²	semidirect
23. C₂×#11715736	C₂²	semidirect
24. C₂×#32948⋊C₃	C₂²	semidirect
25. C₂×#72236763	C₂	semidirect
26. C₂×#11711643	C₂²	semidirect
27. C₂×#11711642	C₂²	semidirect
28. C₂×#11715709	C₂²	semidirect
29. C₂×#32894⋊C₃	C₂²	semidirect
30. C₂×#72236743	C₂	semidirect
31. C₂×#11711647	C₂²	semidirect
32. C₂×#11715711	C₂²	semidirect
33. C₂×#11711646	C₂²	semidirect
34. C₂×#32895⋊C₃	C₂²	semidirect
35. C₂×#11711596	C₂²	semidirect
36. C₂×#11715831	C₂²	semidirect
37. C₂×#11715712	C₂²	semidirect
38. C₂×#11710899	C₂²	semidirect
39. C₂×#11715842	C₂²	semidirect
40. C₂×#11714178	C₂²	semidirect
41. C₂×#6573736	D₃	semidirect
42. #72237002	C₂	direct (N × H)
43. #72236895	C₂²	semidirect
44. #72236891	C₂²	semidirect
45. #72236871	C₂²	semidirect
46. #72236853	C₂²	semidirect
47. #72236850	C₂²	semidirect
48. #72236829	C₂²	semidirect
49. C₂×#72217027	C₂	semidirect
50. #72236805	C₂²	semidirect
51. #72236804	C₂²	semidirect
52. #72236801	C₂²	semidirect
53. #72236799	C₂²	semidirect
54. C₂×#60399⋊C₃	C₂²	semidirect
55. #72236787	C₂²	semidirect
56. C₂×#11714174	C₂²	semidirect
57. #72236763	C₂²	semidirect
59. C₂×#11714184	C₂²	semidirect
60. #72236743	C₂²	semidirect
62. C₂×#11714175	C₂²	semidirect
63. C₂×#11715681	C₂²	semidirect
64. C₂×#11715839	C₂²	semidirect
65. #72217027	C₂²	semidirect
66. #72215654	C₂²	semidirect
68. #11715842	C₂³	semidirect
69. #11715839	C₂³	semidirect
71. C₂×#87521	C₂³	semidirect
73. #11715831	C₂³	semidirect
75. C₂×#87518	C₂³	semidirect
78. #11715738	C₂³	semidirect
79. #11715736	C₂³	semidirect
80. #11715712	C₂³	semidirect
81. #11715711	C₂³	semidirect
82. #11715710	C₂³	semidirect
83. #11715709	C₂³	semidirect
84. #11715688	C₂³	semidirect
85. #11715681	C₂³	semidirect
86. C₂×#85567	C₂³	semidirect
87. C₂×#85566	C₂³	semidirect
89. #11714184	C₂³	semidirect
90. #11714179	C₂³	semidirect
91. #11714178	C₂³	semidirect
92. #11714175	C₂³	semidirect
93. #11714174	C₂³	semidirect
94. #11714162	D₄	semidirect
96. C₂×#73031	D₄	semidirect
97. C₂×#73025	D₄	semidirect
98. C₂×#73030	D₄	semidirect
99. C₂×#73026	D₄	semidirect
100. #11711647	C₂³	semidirect
101. #11711646	C₂³	semidirect
102. #11711643	C₂³	semidirect
103. #11711642	C₂³	semidirect
104. #11711638	C₂³	semidirect
105. #11711638	C₂³	semidirect
106. #11711596	C₂³	semidirect
107. #11711590	C₂³	semidirect
108. #11711589	C₂³	semidirect
109. C₂×#87548	C₂³	semidirect
111. #11710899	C₂³	semidirect
112. C₂×#85666	C₂³	semidirect
113. #11710352	C₂³	semidirect
114. #60399⋊C₃	C₂³	semidirect
116. C₂×#3027⋊C₃	C₂³	semidirect
118. #32948⋊C₃	C₂³	semidirect
119. #32895⋊C₃	C₂³	semidirect
120. #32894⋊C₃	C₂³	semidirect
121. #21484⋊C₃	C₂³	semidirect
122. C₂×#1791⋊C₃	C₂³	semidirect
123. C₂×#63092	C₂×D₃	semidirect
124. C₂×#60402	C₂×D₃	semidirect
125. C₂×#60399	C₂×D₃	semidirect
126. C₂×#32948	C₂×D₃	semidirect
127. C₂×#32895	C₂×D₃	semidirect
128. C₂×#32894	C₂×D₃	semidirect
129. #6573736	C₂×D₃	semidirect
130. C₂×#21484	C₂×D₃	semidirect
131. #87548	C₂⁴	semidirect
136. #87521	C₂⁴	semidirect
141. #87518	C₂⁴	semidirect
146. #85666	C₂⁴	semidirect
147. #85567	C₂⁴	semidirect
148. #85566	C₂⁴	semidirect
150. #3027⋊C₃	C₂⁴	semidirect
155. #73031	C₂×D₄	semidirect
156. #73030	C₂×D₄	semidirect
157. #73026	C₂×D₄	semidirect
158. #73025	C₂×D₄	semidirect
159. #1791⋊C₃	C₂⁴	semidirect
160. C₂×2₋¹⁺⁶	C₂²×D₃	semidirect
162. #63092	C₂²×D₃	semidirect
163. C₂³×AGL(1,ℤ/8)	S₄	semidirect
164. C₂×#3573	C₂²×D₃	semidirect
165. #60402	C₂²×D₃	semidirect
166. #60399	C₂²×D₃	semidirect
168. C₂×#3027	C₂²×D₃	semidirect
170. #32948	C₂²×D₃	semidirect
171. #32895	C₂²×D₃	semidirect
172. #32894	C₂²×D₃	semidirect
173. #21484	C₂²×D₃	semidirect
174. C₂×#1791	C₂²×D₃	semidirect
184. 2₋¹⁺⁶	C₂³×D₃	semidirect
187. C₂³×#41	C₂×S₄	semidirect
189. C₂²×AGL(1,ℤ/8)	C₂×S₄	semidirect
191. C₂³×SD₁₆	C₂×S₄	semidirect
193. C₂³×D₈	C₂×S₄	semidirect
194. #3573	C₂³×D₃	semidirect
195. C₂³×M₁₆	C₂×S₄	semidirect
197. #3027	C₂³×D₃	semidirect
202. #1791	C₂³×D₃	semidirect
207. C₂²×#41	C₂²×S₄	semidirect
215. C₂²×SD₁₆	C₂²×S₄	semidirect
217. C₂²×D₈	C₂²×S₄	semidirect
218. C₂²×M₁₆	C₂²×S₄	semidirect
253. C₂	#72237002	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×#72236829	2
C₂×#72236805	2
C₂×#72236787	2
C₂×#72236804	2
C₂×#72236801	2
C₂×#72236799	2
C₂×#72236891	2
C₂×#72236871	2
C₂×#72236853	2
C₂×#72236895	2
C₂×#72215654	2
C₂×#72236850	2
C₂×#72236763	2
C₂×#72236743	2
C₂×#72236997	3
#72237002	2
C₂×#72217027	2
C₂×S₄×AGL(1,ℤ/8)	4

Subgroups — C2×#72237002 #72343867

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#72237002 #72343867