Subgroups — C₂×#72240984 #72344197

Order 6144.

At least 21805 conjugacy classes of subgroups; only the 691 normal subgroups are shown.

The subgroup lattice has 259 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×#72236796	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#72236824	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×#11714175	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#72236832	C₂	1	2	yes	maximal, complemented
5	C₂×#60401⋊C₃	C₂²	1	1	yes	characteristic, complemented
6	C₂×#72236805	C₂	1	2	yes	maximal, complemented
7	C₂×#11711590	C₂²	1	2	yes	complemented
8	C₂×#11710352	C₂²	1	1	yes	characteristic, complemented
9	C₂×#72236910	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#72236924	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#72236905	C₂	1	2	yes	maximal, complemented
12	C₂×#72215741	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#72236909	C₂	1	2	yes	maximal, complemented
14	C₂×#11710347	C₂²	1	1	yes	characteristic, complemented
15	C₂×#11715710	C₂²	1	2	yes	complemented
16	C₂×#11711639	C₂²	1	2	yes	complemented
17	C₂×#11711644	C₂²	1	2	yes	complemented
18	C₂²×#87522	C₂²	1	1	yes	characteristic, complemented
19	C₂×#11711588	C₂²	1	2	yes	complemented
20	C₂²×#3025⋊C₃	C₂²	1	1	yes	characteristic
21	C₂×#11711638	C₂²	1	2	yes	complemented
22	C₂×#72236781	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×#11711642	C₂²	1	2	yes	complemented
24	C₂×#11715709	C₂²	1	2	yes	complemented
25	C₂×#11715711	C₂²	1	2	yes	complemented
26	C₂×#11715661	C₂²	1	1	yes	characteristic, complemented
27	C₂×#11715708	C₂²	1	2	yes	complemented
28	C₂²×#87521	C₂²	1	1	yes	characteristic, complemented
29	C₂×#11715667	C₂²	1	1	yes	characteristic, complemented
30	C₂×#60398⋊C₃	C₂²	1	1	yes	characteristic, complemented
31	C₂×#11710937	C₂²	1	1	yes	characteristic, complemented
32	C₂×#10574874	D₃	1	1	yes	characteristic, complemented
33	#72240984	C₂	1	16	yes	maximal, direct product factor
34	#72236924	C₂²	1	8	yes	complemented
35	#72236910	C₂²	1	8	yes	complemented
36	#72236909	C₂²	1	16	yes	complemented
37	#72236905	C₂²	1	16	yes	complemented
38	#72236832	C₂²	1	16	yes	complemented
39	#72236824	C₂²	1	8	yes	complemented
40	#72236805	C₂²	1	16	yes	complemented
41	#72236796	C₂²	1	8	yes	complemented
42	C₂×#60399⋊C₃	C₂²	1	1	yes	characteristic, complemented
43	#72236781	C₂²	1	8	yes	complemented
44	C₂×#11714175	C₂²	1	2	yes	complemented
45	C₂×#11714175	C₂²	1	2	yes	complemented
46	C₂×#11714175	C₂²	1	8	yes	complemented
47	#72215741	C₂²	1	8	yes	complemented
48	C₂×#87521	C₂³	1	2	yes	—
49	C₂×#87521	C₂³	1	4	yes	complemented
50	C₂×#87522	C₂³	1	2	yes	—
51	C₂×#87522	C₂³	1	4	yes	complemented
52	#11715711	C₂³	1	8	yes	complemented
53	#11715710	C₂³	1	8	yes	complemented
54	#11715709	C₂³	1	8	yes	complemented
55	#11715708	C₂³	1	8	yes	complemented
56	#11715667	C₂³	1	4	yes	complemented
57	C₂×#85567	C₂³	1	2	yes	complemented
58	#11715661	C₂³	1	4	yes	complemented
59	C₂×#85566	C₂³	1	2	yes	complemented
60	#11714175	C₂³	1	8	yes	complemented
61	#11714175	C₂³	1	8	yes	complemented
62	#11711644	C₂³	1	8	yes	complemented
63	#11711642	C₂³	1	8	yes	complemented
64	#11711639	C₂³	1	8	yes	complemented
65	#11711638	C₂³	1	8	yes	complemented
66	#11711590	C₂³	1	8	yes	complemented
67	#11711588	C₂³	1	8	yes	complemented
68	#11710937	C₂³	1	4	yes	complemented
69	C₂×#87548	C₂³	1	1	yes	characteristic, complemented
70	C₂×#87547	C₂³	1	1	yes	characteristic, complemented
71	C₂²×#5950	C₂³	1	1	yes	characteristic
72	#11710352	C₂³	1	4	yes	complemented
73	#60401⋊C₃	C₂³	1	4	yes	complemented
74	#11710347	C₂³	1	4	yes	complemented
75	#60399⋊C₃	C₂³	1	4	yes	complemented
76	#60398⋊C₃	C₂³	1	4	yes	complemented
77	C₂×#3028⋊C₃	C₂³	1	1	yes	characteristic, complemented
78	C₂×#3027⋊C₃	C₂³	1	1	yes	characteristic, complemented
79	C₂×#3025⋊C₃	D₄	1	4	yes	complemented
80	C₂×#3025⋊C₃	D₄	1	1	yes	characteristic, complemented
81	C₂×#3025⋊C₃	D₄	1	1	yes	characteristic, complemented
82	C₂×#3025⋊C₃	C₂³	1	1	yes	characteristic
83	C₂×#3025⋊C₃	C₂³	1	1	yes	characteristic
84	C₂×#3025⋊C₃	C₂³	1	4	yes	—
85	C₂²×#458⋊C₃	D₄	1	1	yes	characteristic, complemented
86	C₂²×B(4,𝔽₂)⋊C₃	D₄	1	1	yes	characteristic, complemented
87	C₂×#63103	C₂×D₃	1	1	yes	characteristic, complemented
88	C₂×#60402	C₂×D₃	1	1	yes	characteristic, complemented
89	C₂×#60400	C₂×D₃	1	1	yes	characteristic, complemented
90	C₂×#60398	C₂×D₃	1	1	yes	characteristic, complemented
91	C₂²×#3025	C₂×D₃	1	1	yes	characteristic
92	#10574874	C₂×D₃	1	8	yes	complemented
93	C₂×#60401	C₂×D₃	1	1	yes	characteristic, complemented
94	C₂×#60399	C₂×D₃	1	1	yes	characteristic, complemented
95	#87548	C₂⁴	1	2	yes	complemented
96	#87547	C₂⁴	1	2	yes	complemented
97	C₂×#5950	C₂×D₄	1	1	yes	characteristic
98	C₂×#5950	C₂×D₄	1	2	yes	—
99	C₂×#5950	C₂⁴	1	1	yes	characteristic
100	C₂×#5950	C₂⁴	1	2	yes	—
101	C₂²×#997	C₂×D₄	1	1	yes	characteristic
102	#87522	C₂⁴	1	4	yes	—
103	#87521	C₂⁴	1	4	yes	—
104	#85567	C₂⁴	1	4	yes	complemented
105	#85566	C₂⁴	1	4	yes	complemented
106	#3028⋊C₃	C₂⁴	1	2	yes	complemented
107	#3027⋊C₃	C₂⁴	1	2	yes	complemented
108	#3025⋊C₃	C₂×D₄	1	4	yes	complemented
109	#3025⋊C₃	C₂×D₄	1	4	yes	complemented
110	#3025⋊C₃	C₂×D₄	1	2	yes	complemented
111	#3025⋊C₃	C₂×D₄	1	2	yes	complemented
112	#3025⋊C₃	C₂⁴	1	2	yes	—
113	#3025⋊C₃	C₂⁴	1	2	yes	—
114	C₂×#458⋊C₃	C₂×D₄	1	1	yes	characteristic, complemented
115	C₂×#458⋊C₃	C₂×D₄	1	1	yes	characteristic, complemented
116	C₂×#458⋊C₃	C₂×D₄	1	4	yes	complemented
117	C₂×B(4,𝔽₂)⋊C₃	C₂×D₄	1	1	yes	characteristic, complemented
118	C₂×B(4,𝔽₂)⋊C₃	C₂×D₄	1	1	yes	characteristic, complemented
119	C₂×B(4,𝔽₂)⋊C₃	C₂×D₄	1	4	yes	complemented
120	#63103	C₂²×D₃	1	4	yes	complemented
121	C₂×2₋¹⁺⁶	C₂²×D₃	1	1	yes	characteristic, complemented
122	C₂×H(7,𝔽₂)	C₂²×D₃	1	1	yes	characteristic, complemented
123	C₂²×#585	C₂²×D₃	1	1	yes	characteristic
124	C₂⁴×#41	S₄	1	1	yes	characteristic, complemented
125	#60402	C₂²×D₃	1	4	yes	complemented
126	#60401	C₂²×D₃	1	4	yes	complemented
127	#60400	C₂²×D₃	1	4	yes	complemented
128	#60399	C₂²×D₃	1	4	yes	complemented
129	#60398	C₂²×D₃	1	4	yes	complemented
130	C₂×#3028	C₂²×D₃	1	1	yes	characteristic, complemented
131	C₂×#3027	C₂²×D₃	1	1	yes	characteristic, complemented
132	C₂×#3025	#67	1	4	yes	—
133	C₂×#3025	#67	1	1	yes	characteristic
134	C₂×#3025	#67	1	1	yes	characteristic
135	C₂×#3025	C₂²×D₃	1	1	yes	characteristic
136	C₂×#3025	C₂²×D₃	1	1	yes	characteristic
137	C₂×#3025	C₂²×D₃	1	4	yes	—
138	C₂²×#458	#67	1	1	yes	characteristic
139	C₂²×B(4,𝔽₂)	#67	1	1	yes	characteristic
140	#5950	C₂²×D₄	1	2	yes	—
141	#5950	C₂²×D₄	1	1	yes	characteristic
142	#5950	C₂⁵	1	1	yes	characteristic
143	C₂×#997	C₂²×D₄	1	1	yes	characteristic
144	C₂×#997	C₂²×D₄	1	2	yes	—
145	#458⋊C₃	C₂²×D₄	1	2	yes	complemented
146	#458⋊C₃	C₂²×D₄	1	2	yes	complemented
147	B(4,𝔽₂)⋊C₃	C₂²×D₄	1	2	yes	complemented
148	B(4,𝔽₂)⋊C₃	C₂²×D₄	1	2	yes	complemented
149	2₋¹⁺⁶	C₂³×D₃	1	2	yes	complemented
150	H(7,𝔽₂)	C₂³×D₃	1	2	yes	complemented
151	C₂×#585	C₂×#67	1	1	yes	characteristic
152	C₂×#585	C₂×#67	1	2	yes	—
153	C₂×#585	C₂³×D₃	1	1	yes	characteristic
154	C₂×#585	C₂³×D₃	1	2	yes	—
155	C₂²×H(5,𝔽₂)	C₂×#67	1	1	yes	characteristic
156	C₂³×#41	C₂×S₄	1	1	yes	characteristic
157	C₂³×#41	C₂×S₄	1	1	yes	characteristic
158	C₂³×#41	C₂×S₄	1	1	yes	characteristic, complemented
159	C₂³×#41	C₂×S₄	1	1	yes	characteristic, complemented
160	C₂³×#41	C₂×S₄	1	8	yes	complemented
161	C₂⁴×Q₈	C₂×S₄	1	1	yes	characteristic, complemented
162	C₂⁴×D₄	C₂×S₄	1	1	yes	characteristic, complemented
163	C₂⁵×C₄	C₂×S₄	1	1	yes	characteristic
164	#3028	C₂³×D₃	1	2	yes	complemented
165	#3027	C₂³×D₃	1	2	yes	complemented
166	#3025	C₂×#67	1	4	yes	—
167	#3025	C₂×#67	1	4	yes	—
168	#3025	C₂×#67	1	2	yes	—
169	#3025	C₂×#67	1	2	yes	—
170	#3025	C₂³×D₃	1	2	yes	—
171	#3025	C₂³×D₃	1	2	yes	—
172	C₂×#458	C₂×#67	1	1	yes	characteristic
173	C₂×#458	C₂×#67	1	1	yes	characteristic
174	C₂×#458	C₂×#67	1	4	yes	—
175	C₂×B(4,𝔽₂)	C₂×#67	1	1	yes	characteristic
176	C₂×B(4,𝔽₂)	C₂×#67	1	1	yes	characteristic
177	C₂×B(4,𝔽₂)	C₂×#67	1	4	yes	—
178	#997	C₂³×D₄	1	1	yes	characteristic
179	C₂⁶	GL(2,ℤ/4)	1	1	yes	characteristic
180	#585	C₂²×#67	1	2	yes	—
181	#585	C₂²×#67	1	1	yes	characteristic
182	#585	C₂⁴×D₃	1	1	yes	characteristic
183	C₂×H(5,𝔽₂)	C₂²×#67	1	1	yes	characteristic
184	C₂×H(5,𝔽₂)	C₂²×#67	1	2	yes	—
185	C₂²×#41	C₂²×S₄	1	4	yes	—
186	C₂²×#41	C₂²×S₄	1	4	yes	—
187	C₂²×#41	C₂²×S₄	1	4	yes	complemented
188	C₂²×#41	C₂²×S₄	1	4	yes	complemented
189	C₂³×Q₈	C₂²×S₄	1	1	yes	characteristic
190	C₂³×Q₈	C₂²×S₄	1	1	yes	characteristic
191	C₂³×Q₈	C₂²×S₄	1	4	yes	complemented
192	C₂³×D₄	C₂²×S₄	1	1	yes	characteristic
193	C₂³×D₄	C₂²×S₄	1	1	yes	characteristic
194	C₂³×D₄	C₂²×S₄	1	4	yes	complemented
195	C₂⁴×C₄	GL(2,ℤ/4)	1	1	yes	characteristic
196	C₂⁴×C₄	GL(2,ℤ/4)	1	1	yes	characteristic
197	C₂⁴×C₄	GL(2,ℤ/4)	1	1	yes	characteristic
198	C₂⁴×C₄	GL(2,ℤ/4)	1	4	yes	—
199	C₂⁴×C₄	C₂²×S₄	1	1	yes	characteristic
200	C₂⁴×C₄	C₂²×S₄	1	1	yes	characteristic
201	C₂⁴×C₄	C₂²×S₄	1	1	yes	characteristic
202	C₂⁴×C₄	C₂²×S₄	1	4	yes	—
203	#458	C₂²×#67	1	2	yes	—
204	#458	C₂²×#67	1	2	yes	—
205	B(4,𝔽₂)	C₂²×#67	1	2	yes	—
206	B(4,𝔽₂)	C₂²×#67	1	2	yes	—
207	C₂⁵	C₂×GL(2,ℤ/4)	1	1	yes	characteristic
208	C₂⁵	C₂×GL(2,ℤ/4)	1	1	yes	characteristic
209	C₂⁵	C₂×GL(2,ℤ/4)	1	1	yes	characteristic
210	C₂⁵	C₂×GL(2,ℤ/4)	1	4	yes	—
211	H(5,𝔽₂)	C₂³×#67	1	1	yes	characteristic
212	C₂×#41	#1020⋊C₂	1	1	yes	characteristic
213	C₂²×Q₈	C₂³×S₄	1	2	yes	—
214	C₂²×Q₈	C₂³×S₄	1	2	yes	—
215	C₂²×D₄	C₂³×S₄	1	2	yes	—
216	C₂²×D₄	C₂³×S₄	1	2	yes	—
217	C₂³×C₄	C₂×GL(2,ℤ/4)	1	1	yes	characteristic
218	C₂³×C₄	C₂×GL(2,ℤ/4)	1	2	yes	—
219	C₂³×C₄	C₂×GL(2,ℤ/4)	1	1	yes	characteristic
220	C₂³×C₄	C₂×GL(2,ℤ/4)	1	1	yes	characteristic
221	C₂³×C₄	C₂×GL(2,ℤ/4)	1	4	yes	—
222	C₂³×C₄	C₂×GL(2,ℤ/4)	1	4	yes	—
223	C₂³×C₄	C₂×GL(2,ℤ/4)	1	2	yes	—
224	C₂³×C₄	C₂×GL(2,ℤ/4)	1	4	yes	—
225	C₂³×C₄	C₂×GL(2,ℤ/4)	1	2	yes	—
226	C₂³×C₄	C₂³×S₄	1	1	yes	characteristic
227	C₂³×C₄	C₂³×S₄	1	2	yes	—
228	C₂³×C₄	C₂³×S₄	1	2	yes	—
229	C₂³×C₄	C₂³×S₄	1	2	yes	—
230	C₂⁴	C₂²×GL(2,ℤ/4)	1	1	yes	characteristic
231	C₂⁴	C₂²×GL(2,ℤ/4)	1	2	yes	—
232	C₂⁴	C₂²×GL(2,ℤ/4)	1	2	yes	—
233	C₂⁴	C₂²×GL(2,ℤ/4)	1	2	yes	—
234	#41	C₂×#1020⋊C₂	1	4	yes	—
235	C₂×Q₈	C₂×#1020⋊C₂	1	1	yes	characteristic
236	C₂×D₄	C₂×#1020⋊C₂	1	1	yes	characteristic
237	C₂²×C₄	C₂×#1020⋊C₂	1	1	yes	characteristic
238	C₂²×C₄	C₂²×GL(2,ℤ/4)	1	2	yes	—
239	C₂²×C₄	C₂²×GL(2,ℤ/4)	1	1	yes	characteristic
240	C₂²×C₄	C₂²×GL(2,ℤ/4)	1	2	yes	—
241	C₂²×C₄	C₂²×GL(2,ℤ/4)	1	2	yes	—
242	C₂²×C₄	C₂⁴×S₄	1	1	yes	characteristic
243	C₂³	#11713201	1	1	yes	characteristic
244	C₂³	C₂³×GL(2,ℤ/4)	1	1	yes	characteristic
245	Q₈	C₂²×#1020⋊C₂	1	2	yes	—
246	D₄	C₂²×#1020⋊C₂	1	2	yes	—
247	C₂×C₄	#11713201	1	2	yes	—
248	C₂×C₄	#11713201	1	1	yes	characteristic
249	C₂×C₄	C₂²×#1020⋊C₂	1	2	yes	—
250	C₂×C₄	C₂²×#1020⋊C₂	1	1	yes	characteristic
251	C₂²	C₂×#11713201	1	2	yes	—
252	C₂²	C₂×#11713201	1	1	yes	characteristic
253	C₄	C₂³×#1020⋊C₂	1	1	yes	characteristic
254	C₄	C₂×#11713201	1	2	yes	—
255	C₄	C₂×#11713201	1	1	yes	characteristic
256	C₂	#72240984	1	2	yes	direct product factor
257	C₂	C₂²×#11713201	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂×#11713201
commutator, cosocle	#5950	C₂⁵
Frattini	C₂²×C₄	C₂⁴×S₄
Fitting	C₂×#10574874	D₃
hypercenter	C₂×#41	#1020⋊C₂
hypocenter	#997	C₂³×D₄
LCS	G ▷ #5950 ▷ #997
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#41

Complements

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

N	H ≅ G/N	type
1. C₂×#72236796	C₂	semidirect
2. C₂×#72236824	C₂	semidirect
3. C₂²×#11714175	C₂	semidirect
4. C₂×#72236832	C₂	semidirect
5. C₂×#60401⋊C₃	C₂²	semidirect
6. C₂×#72236805	C₂	semidirect
7. C₂×#11711590	C₂²	semidirect
8. C₂×#11710352	C₂²	semidirect
9. C₂×#72236910	C₂	semidirect
10. C₂×#72236924	C₂	semidirect
11. C₂×#72236905	C₂	semidirect
12. C₂×#72215741	C₂	semidirect
13. C₂×#72236909	C₂	semidirect
14. C₂×#11710347	C₂²	semidirect
15. C₂×#11715710	C₂²	semidirect
16. C₂×#11711639	C₂²	semidirect
17. C₂×#11711644	C₂²	semidirect
18. C₂²×#87522	C₂²	semidirect
19. C₂×#11711588	C₂²	semidirect
21. C₂×#11711638	C₂²	semidirect
22. C₂×#72236781	C₂	semidirect
23. C₂×#11711642	C₂²	semidirect
24. C₂×#11715709	C₂²	semidirect
25. C₂×#11715711	C₂²	semidirect
26. C₂×#11715661	C₂²	semidirect
27. C₂×#11715708	C₂²	semidirect
28. C₂²×#87521	C₂²	semidirect
29. C₂×#11715667	C₂²	semidirect
30. C₂×#60398⋊C₃	C₂²	semidirect
31. C₂×#11710937	C₂²	semidirect
32. C₂×#10574874	D₃	semidirect
33. #72240984	C₂	direct (N × H)
34. #72236924	C₂²	semidirect
35. #72236910	C₂²	semidirect
36. #72236909	C₂²	semidirect
37. #72236905	C₂²	semidirect
38. #72236832	C₂²	semidirect
39. #72236824	C₂²	semidirect
40. #72236805	C₂²	semidirect
41. #72236796	C₂²	semidirect
42. C₂×#60399⋊C₃	C₂²	semidirect
43. #72236781	C₂²	semidirect
44. C₂×#11714175	C₂²	semidirect
45. C₂×#11714175	C₂²	semidirect
46. C₂×#11714175	C₂²	semidirect
47. #72215741	C₂²	semidirect
49. C₂×#87521	C₂³	semidirect
51. C₂×#87522	C₂³	semidirect
52. #11715711	C₂³	semidirect
53. #11715710	C₂³	semidirect
54. #11715709	C₂³	semidirect
55. #11715708	C₂³	semidirect
56. #11715667	C₂³	semidirect
57. C₂×#85567	C₂³	semidirect
58. #11715661	C₂³	semidirect
59. C₂×#85566	C₂³	semidirect
60. #11714175	C₂³	semidirect
61. #11714175	C₂³	semidirect
62. #11711644	C₂³	semidirect
63. #11711642	C₂³	semidirect
64. #11711639	C₂³	semidirect
65. #11711638	C₂³	semidirect
66. #11711590	C₂³	semidirect
67. #11711588	C₂³	semidirect
68. #11710937	C₂³	semidirect
69. C₂×#87548	C₂³	semidirect
70. C₂×#87547	C₂³	semidirect
72. #11710352	C₂³	semidirect
73. #60401⋊C₃	C₂³	semidirect
74. #11710347	C₂³	semidirect
75. #60399⋊C₃	C₂³	semidirect
76. #60398⋊C₃	C₂³	semidirect
77. C₂×#3028⋊C₃	C₂³	semidirect
78. C₂×#3027⋊C₃	C₂³	semidirect
79. C₂×#3025⋊C₃	D₄	semidirect
80. C₂×#3025⋊C₃	D₄	semidirect
81. C₂×#3025⋊C₃	D₄	semidirect
85. C₂²×#458⋊C₃	D₄	semidirect
86. C₂²×B(4,𝔽₂)⋊C₃	D₄	semidirect
87. C₂×#63103	C₂×D₃	semidirect
88. C₂×#60402	C₂×D₃	semidirect
89. C₂×#60400	C₂×D₃	semidirect
90. C₂×#60398	C₂×D₃	semidirect
92. #10574874	C₂×D₃	semidirect
93. C₂×#60401	C₂×D₃	semidirect
94. C₂×#60399	C₂×D₃	semidirect
95. #87548	C₂⁴	semidirect
96. #87547	C₂⁴	semidirect
104. #85567	C₂⁴	semidirect
105. #85566	C₂⁴	semidirect
106. #3028⋊C₃	C₂⁴	semidirect
107. #3027⋊C₃	C₂⁴	semidirect
108. #3025⋊C₃	C₂×D₄	semidirect
109. #3025⋊C₃	C₂×D₄	semidirect
110. #3025⋊C₃	C₂×D₄	semidirect
111. #3025⋊C₃	C₂×D₄	semidirect
114. C₂×#458⋊C₃	C₂×D₄	semidirect
115. C₂×#458⋊C₃	C₂×D₄	semidirect
116. C₂×#458⋊C₃	C₂×D₄	semidirect
117. C₂×B(4,𝔽₂)⋊C₃	C₂×D₄	semidirect
118. C₂×B(4,𝔽₂)⋊C₃	C₂×D₄	semidirect
119. C₂×B(4,𝔽₂)⋊C₃	C₂×D₄	semidirect
120. #63103	C₂²×D₃	semidirect
121. C₂×2₋¹⁺⁶	C₂²×D₃	semidirect
122. C₂×H(7,𝔽₂)	C₂²×D₃	semidirect
124. C₂⁴×#41	S₄	semidirect
125. #60402	C₂²×D₃	semidirect
126. #60401	C₂²×D₃	semidirect
127. #60400	C₂²×D₃	semidirect
128. #60399	C₂²×D₃	semidirect
129. #60398	C₂²×D₃	semidirect
130. C₂×#3028	C₂²×D₃	semidirect
131. C₂×#3027	C₂²×D₃	semidirect
145. #458⋊C₃	C₂²×D₄	semidirect
146. #458⋊C₃	C₂²×D₄	semidirect
147. B(4,𝔽₂)⋊C₃	C₂²×D₄	semidirect
148. B(4,𝔽₂)⋊C₃	C₂²×D₄	semidirect
149. 2₋¹⁺⁶	C₂³×D₃	semidirect
150. H(7,𝔽₂)	C₂³×D₃	semidirect
158. C₂³×#41	C₂×S₄	semidirect
159. C₂³×#41	C₂×S₄	semidirect
160. C₂³×#41	C₂×S₄	semidirect
161. C₂⁴×Q₈	C₂×S₄	semidirect
162. C₂⁴×D₄	C₂×S₄	semidirect
164. #3028	C₂³×D₃	semidirect
165. #3027	C₂³×D₃	semidirect
187. C₂²×#41	C₂²×S₄	semidirect
188. C₂²×#41	C₂²×S₄	semidirect
191. C₂³×Q₈	C₂²×S₄	semidirect
194. C₂³×D₄	C₂²×S₄	semidirect
256. C₂	#72240984	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#85513	4
C₂×#72236796	2
C₂×#72236824	2
C₂²×#11714175	2
C₂×#72236832	2
C₂×#72236805	2
C₂×#72236910	2
C₂×#72236924	2
C₂×#72236905	2
C₂×#72215741	2
C₂×#72236909	2
C₂×#72236781	2
C₂×#72237529	3
#72240984	2

Subgroups — C2×#72240984 #72344197

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#72240984 #72344197