Subgroups — #72340523

Order 4096.

At least 8987 conjugacy classes of subgroups; only the 605 normal subgroups are shown.

The subgroup lattice has 310 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72340522	C₂	1	1	yes	maximal, characteristic, complemented
2	#72340520	C₂	1	2	yes	maximal, complemented
3	#72340518	C₂	1	1	yes	maximal, characteristic, complemented
4	#72337710	C₂	1	2	yes	maximal, complemented
5	#72337709	C₂	1	2	yes	maximal, complemented
6	#72337708	C₂	1	2	yes	maximal, complemented
7	#72337707	C₂	1	2	yes	maximal, complemented
8	#72337706	C₂	1	2	yes	maximal, complemented
9	#72337705	C₂	1	2	yes	maximal, complemented
10	#72337704	C₂	1	2	yes	maximal, complemented
11	#72337703	C₂²	1	2	yes	complemented
12	#72337703	C₂²	1	2	yes	complemented
13	#72337702	C₂	1	2	yes	maximal, complemented
14	#72337701	C₂²	1	2	yes	complemented
15	#72337695	C₂	1	1	yes	maximal, characteristic, complemented
16	#72337694	C₂²	1	2	yes	complemented
17	#72337685	C₂	1	1	yes	maximal, characteristic, complemented
18	#72337684	C₂²	1	1	yes	characteristic, complemented
19	#72337683	C₂²	1	1	yes	characteristic, complemented
20	#72337679	C₂²	1	1	yes	characteristic, complemented
21	#72337678	C₂	1	2	yes	maximal, complemented
22	#72337670	C₂	1	2	yes	maximal, complemented
23	#72337667	C₂²	1	2	yes	complemented
24	#72337665	C₂²	1	2	yes	complemented
25	#72337664	C₂²	1	2	yes	complemented
26	#72337661	C₂²	1	2	yes	complemented
27	#72337661	C₂²	1	2	yes	complemented
28	#72337660	C₂	1	2	yes	maximal, complemented
29	#72337659	C₂²	1	2	yes	—
30	#72337659	C₂²	1	2	yes	complemented
31	#72337659	C₂²	1	2	yes	complemented
32	#72337656	C₂²	1	2	yes	complemented
33	#72337655	C₂²	1	2	yes	complemented
34	#72337654	C₂²	1	2	yes	complemented
35	#72337652	C₂²	1	2	yes	complemented
36	#72337650	C₂²	1	2	yes	complemented
37	#72337649	C₂²	1	2	yes	complemented
38	#72337648	C₂²	1	2	yes	complemented
39	#72337648	C₂²	1	2	yes	complemented
40	#72337648	C₂²	1	2	yes	complemented
41	#72337647	C₂²	1	2	yes	complemented
42	#72337645	C₂²	1	2	yes	complemented
43	#72337644	C₂²	1	2	yes	complemented
44	#72337637	C₂²	1	2	yes	complemented
45	#72337636	C₂²	1	2	yes	complemented
46	#72337636	C₂²	1	2	yes	complemented
47	#72337635	C₂²	1	2	yes	complemented
48	#72337635	C₂²	1	2	yes	complemented
49	#72337629	C₂²	1	2	yes	complemented
50	#72337629	C₂²	1	2	yes	complemented
51	#72337627	C₂²	1	2	yes	complemented
52	#72337625	C₂²	1	2	yes	complemented
53	#72337625	C₂²	1	2	yes	complemented
54	#72319263	C₂²	1	2	yes	complemented
55	#72319263	C₂²	1	2	yes	complemented
56	#72318569	C₂²	1	2	yes	complemented
57	#72318569	C₂²	1	2	yes	complemented
58	#72310971	C₂²	1	2	yes	complemented
59	#72252378	C₂²	1	2	yes	complemented
60	#72241344	C₂²	1	2	yes	complemented
61	#72241344	C₂²	1	2	yes	complemented
62	#72241344	C₂²	1	2	yes	complemented
63	#72241323	C₂	1	1	yes	maximal, characteristic, complemented
64	#72241322	C₂²	1	2	yes	complemented
65	#72241322	C₂²	1	2	yes	complemented
66	#72236986	C₂	1	1	yes	maximal, characteristic, complemented
67	#72236979	C₂²	1	1	yes	characteristic, complemented
68	#72236975	C₂²	1	1	yes	characteristic, complemented
69	#72236975	C₂²	1	1	yes	characteristic, complemented
70	#72236189	C₂²	1	1	yes	characteristic, complemented
71	#72227941	C₂²	1	2	yes	complemented
72	#72227940	C₂²	1	2	yes	complemented
73	#72227940	C₂²	1	2	yes	complemented
74	#72227940	C₂²	1	2	yes	complemented
75	#72227940	C₂²	1	2	yes	complemented
76	#72227940	C₂²	1	2	yes	complemented
77	#72227940	C₂²	1	2	yes	complemented
78	#72213269	C₂²	1	2	yes	complemented
79	#72213269	C₂²	1	1	yes	characteristic, complemented
80	#72213260	C₂²	1	2	yes	complemented
81	#72213260	C₂²	1	1	yes	characteristic, complemented
82	#72210591	C₂	1	1	yes	maximal, characteristic, complemented
83	#72210572	C₂²	1	2	yes	complemented
84	#72210572	C₂²	1	2	yes	complemented
85	#72210569	C₂²	1	2	yes	complemented
86	#72210563	C₂²	1	2	yes	complemented
87	#72210559	C₂²	1	2	yes	—
88	#72210559	C₂²	1	2	yes	—
89	#72210559	C₂²	1	2	yes	complemented
90	#72210559	C₂²	1	2	yes	complemented
91	#72210549	C₂²	1	1	yes	characteristic, complemented
92	#72210539	C₂²	1	1	yes	characteristic, complemented
93	#72210529	C₂²	1	1	yes	characteristic, complemented
94	#72210529	C₂²	1	1	yes	characteristic, complemented
95	#72210524	C₂²	1	1	yes	characteristic
96	#72210498	C₂²	1	2	yes	—
97	#72210498	C₂²	1	2	yes	—
98	#72210498	C₂²	1	2	yes	complemented
99	#72210498	C₂²	1	2	yes	complemented
100	#72210498	C₂²	1	2	yes	complemented
101	#72210498	C₂²	1	1	yes	characteristic, complemented
102	#72210483	C₂²	1	1	yes	characteristic, complemented
103	#72210439	C₂²	1	1	yes	characteristic
104	#72210439	C₂²	1	1	yes	characteristic
105	#72210439	C₂²	1	1	yes	characteristic, complemented
106	#72210015	C₂²	1	2	yes	complemented
107	#8934366	C₂³	1	1	yes	characteristic
108	#8934366	C₂³	1	2	yes	—
109	#8934366	C₂³	1	1	yes	characteristic
110	#8934366	C₂³	1	1	yes	characteristic, complemented
111	#8933848	C₂³	1	1	yes	characteristic, complemented
112	#7672751	C₂³	1	1	yes	characteristic
113	#7672751	C₂³	1	2	yes	—
114	#6628901	C₂³	1	1	yes	characteristic
115	#6628896	D₄	1	2	yes	complemented
116	#6470231	D₄	1	4	yes	complemented
117	#6432958	C₂³	1	2	yes	—
118	#449527	C₂³	1	2	yes	—
119	#449492	C₂³	1	1	yes	characteristic
120	#449492	C₂³	1	2	yes	—
121	#449492	C₂³	1	1	yes	characteristic
122	#418114	C₂³	1	2	yes	—
123	#417807	C₂³	1	1	yes	characteristic
124	#417807	C₂³	1	2	yes	—
125	#417807	C₂³	1	1	yes	characteristic
126	#391714	C₂³	1	2	yes	—
127	#374009	C₂³	1	1	yes	characteristic
128	#346282	C₂³	1	2	yes	complemented
129	#251830	D₄	1	4	yes	complemented
130	#251828	D₄	1	2	yes	complemented
131	#251828	D₄	1	2	yes	complemented
132	#251828	D₄	1	4	yes	complemented
133	#245234	C₂³	1	2	yes	—
134	#245234	C₂³	1	2	yes	—
135	#245234	C₂³	1	2	yes	—
136	#245234	C₂³	1	2	yes	—
137	#245234	C₂³	1	2	yes	complemented
138	#245234	C₂³	1	2	yes	complemented
139	#245233	C₂³	1	2	yes	—
140	#245233	C₂³	1	2	yes	—
141	#245233	C₂³	1	2	yes	—
142	#245233	C₂³	1	2	yes	—
143	#245233	C₂³	1	2	yes	—
144	#245233	C₂³	1	2	yes	—
145	#245233	C₂³	1	2	yes	—
146	#245233	C₂³	1	2	yes	—
147	#245233	C₂³	1	2	yes	complemented
148	#213865	C₂³	1	2	yes	complemented
149	#213861	C₂³	1	2	yes	—
150	#213861	C₂³	1	2	yes	—
151	#213861	C₂³	1	1	yes	characteristic, complemented
152	#213861	C₂³	1	2	yes	complemented
153	#213860	C₂³	1	1	yes	characteristic
154	#213860	C₂³	1	1	yes	characteristic
155	#213860	C₂³	1	1	yes	characteristic, complemented
156	#213854	D₄	1	2	yes	complemented
157	#213829	D₄	1	4	yes	complemented
158	#134009	C₂³	1	2	yes	—
159	#134009	C₂³	1	2	yes	—
160	#134009	C₂³	1	2	yes	—
161	#133936	C₂³	1	2	yes	complemented
162	#133835	C₂³	1	2	yes	—
163	#133835	C₂³	1	2	yes	—
164	#133835	C₂³	1	2	yes	—
165	#133835	C₂³	1	2	yes	complemented
166	#133835	C₂³	1	1	yes	characteristic, complemented
167	#133835	C₂³	1	1	yes	characteristic, complemented
168	#133309	C₂³	1	2	yes	complemented
169	#133309	C₂³	1	2	yes	complemented
170	#133308	C₂³	1	2	yes	—
171	#133308	C₂³	1	2	yes	—
172	#133308	C₂³	1	2	yes	—
173	#133308	C₂³	1	2	yes	—
174	#133308	C₂³	1	2	yes	—
175	#133308	C₂³	1	2	yes	—
176	#133308	C₂³	1	2	yes	—
177	#133308	C₂³	1	2	yes	—
178	#133308	C₂³	1	2	yes	—
179	#133308	C₂³	1	2	yes	—
180	#133308	C₂³	1	2	yes	—
181	#133308	C₂³	1	2	yes	—
182	#133308	C₂³	1	2	yes	complemented
183	#133308	C₂³	1	2	yes	complemented
184	#133308	C₂³	1	2	yes	complemented
185	#133308	C₂³	1	2	yes	complemented
186	#97466	C₂³	1	2	yes	complemented
187	#97460	C₂³	1	2	yes	complemented
188	#97460	C₂³	1	1	yes	characteristic, complemented
189	#97460	C₂³	1	1	yes	characteristic, complemented
190	#93146	C₂³	1	2	yes	complemented
191	#93146	C₂³	1	2	yes	complemented
192	#93146	C₂³	1	2	yes	complemented
193	#93139	C₂³	1	2	yes	complemented
194	#93139	C₂³	1	2	yes	complemented
195	#93139	C₂³	1	2	yes	complemented
196	#93113	C₂³	1	2	yes	complemented
197	#93113	C₂³	1	2	yes	complemented
198	#93113	C₂³	1	2	yes	complemented
199	#93113	C₂³	1	2	yes	complemented
200	#93113	C₂³	1	2	yes	complemented
201	#93113	C₂³	1	2	yes	complemented
202	C₂×H(7,𝔽₂)	C₂×D₄	1	1	yes	characteristic
203	#62842	C₂×D₄	1	2	yes	complemented
204	#46384	C₂×D₄	1	2	yes	—
205	#46384	C₂×D₄	1	4	yes	—
206	C₂×#2867	C₂⁴	1	1	yes	characteristic
207	#35554	C₂⁴	1	2	yes	—
208	#35527	C₂⁴	1	1	yes	characteristic
209	#35527	C₂⁴	1	1	yes	characteristic
210	#35527	C₂⁴	1	2	yes	—
211	#35527	C₂⁴	1	2	yes	—
212	#35527	C₂⁴	1	1	yes	characteristic
213	#35527	C₂⁴	1	1	yes	characteristic
214	#35527	C₂⁴	1	2	yes	—
215	#35346	C₂×D₄	1	2	yes	—
216	#35346	C₂×D₄	1	4	yes	—
217	#33020	C₂×D₄	1	4	yes	—
218	#33020	C₂×D₄	1	4	yes	complemented
219	#32898	C₂×D₄	1	4	yes	—
220	#32898	C₂×D₄	1	4	yes	—
221	#32898	C₂×D₄	1	4	yes	—
222	#32898	C₂×D₄	1	4	yes	complemented
223	#20690	C₂×D₄	1	2	yes	complemented
224	#20586	C₂×D₄	1	1	yes	characteristic
225	#20586	C₂×D₄	1	1	yes	characteristic
226	#20586	C₂×D₄	1	1	yes	characteristic
227	#20586	C₂×D₄	1	4	yes	complemented
228	#20586	C₂×D₄	1	2	yes	complemented
229	#20586	C₂×D₄	1	2	yes	complemented
230	#20585	C₂×D₄	1	2	yes	—
231	#10981	C₂⁴	1	2	yes	—
232	#10981	C₂⁴	1	1	yes	characteristic
233	#10981	C₂⁴	1	1	yes	characteristic
234	#10981	C₂⁴	1	2	yes	—
235	#9497	C₂×D₄	1	4	yes	—
236	#9497	C₂×D₄	1	4	yes	—
237	#9497	C₂×D₄	1	4	yes	—
238	#9497	C₂×D₄	1	4	yes	—
239	#9497	C₂×D₄	1	4	yes	complemented
240	#9497	C₂×D₄	1	4	yes	complemented
241	#8748	C₂×D₄	1	2	yes	—
242	#8748	C₂×D₄	1	4	yes	complemented
243	#8546	C₂⁴	1	2	yes	—
244	#8546	C₂⁴	1	2	yes	—
245	#8546	C₂⁴	1	2	yes	—
246	#8546	C₂⁴	1	2	yes	—
247	#8546	C₂⁴	1	2	yes	—
248	#8546	C₂⁴	1	2	yes	—
249	C₂²×H(5,𝔽₂)	C₂²×D₄	1	1	yes	characteristic
250	C₂²×H(5,𝔽₂)	C₂²×D₄	1	2	yes	—
251	C₂²×H(5,𝔽₂)	C₂²×D₄	1	1	yes	characteristic
252	C₂²×H(5,𝔽₂)	C₂²×D₄	1	1	yes	characteristic
253	C₂²×H(5,𝔽₂)	C₂²×D₄	1	2	yes	—
254	C₂²×H(5,𝔽₂)	H(5,𝔽₂)	1	2	yes	—
255	C₂²×H(5,𝔽₂)	H(5,𝔽₂)	1	1	yes	characteristic
256	C₂²×#127	H(5,𝔽₂)	1	1	yes	characteristic
257	C₂²×#127	C₂⁵	1	1	yes	characteristic
258	C₂²×#120	#120	1	2	yes	—
259	C₂×#518	C₂²×D₄	1	2	yes	—
260	#2842	#120	1	2	yes	—
261	#2403	#120	1	4	yes	—
262	#2403	#120	1	2	yes	—
263	#2403	C₂²×D₄	1	4	yes	—
264	#2403	C₂²×D₄	1	4	yes	—
265	#2403	C₂²×D₄	1	4	yes	—
266	#2309	C₂²×D₄	1	1	yes	characteristic
267	#2309	C₂²×D₄	1	2	yes	—
268	#2309	C₂²×D₄	1	2	yes	—
269	#2309	C₂²×D₄	1	1	yes	characteristic
270	#2309	C₂²×D₄	1	2	yes	—
271	#2309	C₂²×D₄	1	1	yes	characteristic
272	#2309	H(5,𝔽₂)	1	2	yes	—
273	#2309	H(5,𝔽₂)	1	1	yes	characteristic
274	#2308	#120	1	4	yes	—
275	#2308	#120	1	2	yes	—
276	C₂×C₄³	H(5,𝔽₂)	1	1	yes	characteristic
277	#1781	C₂²×D₄	1	4	yes	—
278	#1781	C₂²×D₄	1	4	yes	—
279	#1781	C₂²×D₄	1	4	yes	—
280	C₂⁶	B(4,𝔽₂)	1	2	yes	—
281	C₂³×D₄	C₂×#120	1	2	yes	—
282	C₂³×D₄	C₂×#120	1	4	yes	—
283	C₂³×D₄	C₂³×D₄	1	1	yes	characteristic
284	C₂³×D₄	C₂³×D₄	1	2	yes	—
285	C₂³×D₄	C₂×H(5,𝔽₂)	1	2	yes	—
286	C₂³×D₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
287	C₂²×C₂²⋊C₄	B(4,𝔽₂)	1	2	yes	—
288	C₂²×C₂²⋊C₄	B(4,𝔽₂)	1	4	yes	—
289	C₂²×C₄²	C₂×H(5,𝔽₂)	1	1	yes	characteristic
290	#379	C₂×#120	1	4	yes	—
291	#379	C₂×#120	1	2	yes	—
292	C₂⁵	C₂×B(4,𝔽₂)	1	2	yes	—
293	C₂⁵	C₂×B(4,𝔽₂)	1	4	yes	—
294	C₂⁵	C₂²×#120	1	1	yes	characteristic
295	C₂⁵	#3484	1	2	yes	—
296	C₂⁵	#3484	1	1	yes	characteristic
297	C₂³×C₄	C₂×B(4,𝔽₂)	1	4	yes	—
298	C₂³×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
299	C₂³×C₄	#3484	1	2	yes	—
300	C₂³×C₄	#3484	1	1	yes	characteristic
301	C₂⁴	#35346	1	1	yes	characteristic
302	C₂⁴	C₂²×B(4,𝔽₂)	1	2	yes	—
303	C₂³	#6499867	1	1	yes	characteristic
304	C₂³	#6499874	1	1	yes	characteristic
305	C₂³	#6499874	1	1	yes	characteristic
306	C₂²	#72216396	1	1	yes	characteristic
307	C₂	#72216398	1	1	yes	characteristic
308	C₂	#72262472	1	2	yes	—

	subgroup	G/H
center, socle	C₂²	#72216396
commutator, Frattini, cosocle	C₂²×#127	C₂⁵
LCS	G ▷ C₂²×#127 ▷ C₂⁴ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂⁴ ◁ C₂²×#127 ◁ G
LECS	G ▷ C₂²×#127 ▷ C₂⁴ ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72340522	C₂	semidirect
2. #72340520	C₂	semidirect
3. #72340518	C₂	semidirect
4. #72337710	C₂	semidirect
5. #72337709	C₂	semidirect
6. #72337708	C₂	semidirect
7. #72337707	C₂	semidirect
8. #72337706	C₂	semidirect
9. #72337705	C₂	semidirect
10. #72337704	C₂	semidirect
11. #72337703	C₂²	semidirect
12. #72337703	C₂²	semidirect
13. #72337702	C₂	semidirect
14. #72337701	C₂²	semidirect
15. #72337695	C₂	semidirect
16. #72337694	C₂²	semidirect
17. #72337685	C₂	semidirect
18. #72337684	C₂²	semidirect
19. #72337683	C₂²	semidirect
20. #72337679	C₂²	semidirect
21. #72337678	C₂	semidirect
22. #72337670	C₂	semidirect
23. #72337667	C₂²	semidirect
24. #72337665	C₂²	semidirect
25. #72337664	C₂²	semidirect
26. #72337661	C₂²	semidirect
27. #72337661	C₂²	semidirect
28. #72337660	C₂	semidirect
30. #72337659	C₂²	semidirect
31. #72337659	C₂²	semidirect
32. #72337656	C₂²	semidirect
33. #72337655	C₂²	semidirect
34. #72337654	C₂²	semidirect
35. #72337652	C₂²	semidirect
36. #72337650	C₂²	semidirect
37. #72337649	C₂²	semidirect
38. #72337648	C₂²	semidirect
39. #72337648	C₂²	semidirect
40. #72337648	C₂²	semidirect
41. #72337647	C₂²	semidirect
42. #72337645	C₂²	semidirect
43. #72337644	C₂²	semidirect
44. #72337637	C₂²	semidirect
45. #72337636	C₂²	semidirect
46. #72337636	C₂²	semidirect
47. #72337635	C₂²	semidirect
48. #72337635	C₂²	semidirect
49. #72337629	C₂²	semidirect
50. #72337629	C₂²	semidirect
51. #72337627	C₂²	semidirect
52. #72337625	C₂²	semidirect
53. #72337625	C₂²	semidirect
54. #72319263	C₂²	semidirect
55. #72319263	C₂²	semidirect
56. #72318569	C₂²	semidirect
57. #72318569	C₂²	semidirect
58. #72310971	C₂²	semidirect
59. #72252378	C₂²	semidirect
60. #72241344	C₂²	semidirect
61. #72241344	C₂²	semidirect
62. #72241344	C₂²	semidirect
63. #72241323	C₂	semidirect
64. #72241322	C₂²	semidirect
65. #72241322	C₂²	semidirect
66. #72236986	C₂	semidirect
67. #72236979	C₂²	semidirect
68. #72236975	C₂²	semidirect
69. #72236975	C₂²	semidirect
70. #72236189	C₂²	semidirect
71. #72227941	C₂²	semidirect
72. #72227940	C₂²	semidirect
73. #72227940	C₂²	semidirect
74. #72227940	C₂²	semidirect
75. #72227940	C₂²	semidirect
76. #72227940	C₂²	semidirect
77. #72227940	C₂²	semidirect
78. #72213269	C₂²	semidirect
79. #72213269	C₂²	semidirect
80. #72213260	C₂²	semidirect
81. #72213260	C₂²	semidirect
82. #72210591	C₂	semidirect
83. #72210572	C₂²	semidirect
84. #72210572	C₂²	semidirect
85. #72210569	C₂²	semidirect
86. #72210563	C₂²	semidirect
89. #72210559	C₂²	semidirect
90. #72210559	C₂²	semidirect
91. #72210549	C₂²	semidirect
92. #72210539	C₂²	semidirect
93. #72210529	C₂²	semidirect
94. #72210529	C₂²	semidirect
98. #72210498	C₂²	semidirect
99. #72210498	C₂²	semidirect
100. #72210498	C₂²	semidirect
101. #72210498	C₂²	semidirect
102. #72210483	C₂²	semidirect
105. #72210439	C₂²	semidirect
106. #72210015	C₂²	semidirect
110. #8934366	C₂³	semidirect
111. #8933848	C₂³	semidirect
115. #6628896	D₄	semidirect
116. #6470231	D₄	semidirect
128. #346282	C₂³	semidirect
129. #251830	D₄	semidirect
130. #251828	D₄	semidirect
131. #251828	D₄	semidirect
132. #251828	D₄	semidirect
137. #245234	C₂³	semidirect
138. #245234	C₂³	semidirect
147. #245233	C₂³	semidirect
148. #213865	C₂³	semidirect
151. #213861	C₂³	semidirect
152. #213861	C₂³	semidirect
155. #213860	C₂³	semidirect
156. #213854	D₄	semidirect
157. #213829	D₄	semidirect
161. #133936	C₂³	semidirect
165. #133835	C₂³	semidirect
166. #133835	C₂³	semidirect
167. #133835	C₂³	semidirect
168. #133309	C₂³	semidirect
169. #133309	C₂³	semidirect
182. #133308	C₂³	semidirect
183. #133308	C₂³	semidirect
184. #133308	C₂³	semidirect
185. #133308	C₂³	semidirect
186. #97466	C₂³	semidirect
187. #97460	C₂³	semidirect
188. #97460	C₂³	semidirect
189. #97460	C₂³	semidirect
190. #93146	C₂³	semidirect
191. #93146	C₂³	semidirect
192. #93146	C₂³	semidirect
193. #93139	C₂³	semidirect
194. #93139	C₂³	semidirect
195. #93139	C₂³	semidirect
196. #93113	C₂³	semidirect
197. #93113	C₂³	semidirect
198. #93113	C₂³	semidirect
199. #93113	C₂³	semidirect
200. #93113	C₂³	semidirect
201. #93113	C₂³	semidirect
203. #62842	C₂×D₄	semidirect
218. #33020	C₂×D₄	semidirect
222. #32898	C₂×D₄	semidirect
223. #20690	C₂×D₄	semidirect
227. #20586	C₂×D₄	semidirect
228. #20586	C₂×D₄	semidirect
229. #20586	C₂×D₄	semidirect
239. #9497	C₂×D₄	semidirect
240. #9497	C₂×D₄	semidirect
242. #8748	C₂×D₄	semidirect

Maximal subgroups

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

subgroup	index
#72340522	2
#72340520	2
#72340518	2
#72337710	2
#72337709	2
#72337708	2
#72337707	2
#72337706	2
#72337705	2
#72337704	2
#72337702	2
#72337695	2
#72337685	2
#72337678	2
#72337670	2
#72337660	2
#72241323	2
#72236986	2
#72210591	2