Subgroups — #72234147

Order 2048.

At least 6591 conjugacy classes of subgroups; only the 806 normal subgroups are shown.

The subgroup lattice has 299 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72234144	C₂	1	4	yes	maximal, complemented
2	#72234143	C₂	1	4	yes	maximal, complemented
3	#72234142	C₂	1	4	yes	maximal, complemented
4	#72234141	C₂	1	4	yes	maximal, complemented
5	#72234140	C₂	1	1	yes	maximal, characteristic, complemented
6	#72234139	C₂	1	2	yes	maximal, complemented
7	#72234119	C₂	1	1	yes	maximal, characteristic, complemented
8	#72233675	C₂	1	1	yes	maximal, characteristic, complemented
9	#72232736	C₂	1	2	yes	maximal, complemented
10	#72231479	C₂	1	4	yes	maximal, complemented
11	C₂×#511771	C₂	1	2	yes	maximal, complemented
12	#72216323	C₂	1	2	yes	maximal, complemented
13	#10586472	C₂²	1	1	yes	characteristic, complemented
14	C₂³×D₄²	C₂²	1	1	yes	characteristic, complemented
15	C₂×D₄×#127	C₂²	1	1	yes	characteristic
16	#6516740	C₂²	1	2	yes	complemented
17	#6512701	C₂²	1	2	yes	complemented
18	#6499992	C₂²	1	2	yes	complemented
19	#6499837	C₂²	1	2	yes	complemented
20	#6470019	C₂²	1	2	yes	complemented
21	C₂×#23900	C₂²	1	4	yes	complemented
22	C₂×#23906	C₂²	1	2	yes	—
23	#6385983	C₂²	1	1	yes	characteristic, complemented
24	#1420272	C₂²	1	2	yes	complemented
25	#1418385	C₂²	1	2	yes	complemented
26	#846057	C₂²	1	2	yes	complemented
27	#674656	C₂²	1	2	yes	complemented
28	#674141	C₂²	1	2	yes	complemented
29	#647656	C₂²	1	2	yes	—
30	#531766	C₂²	1	1	yes	characteristic, complemented
31	#511771	C₂²	1	8	yes	complemented
32	#511771	C₂²	1	8	yes	complemented
33	#496189	C₂²	1	2	yes	complemented
34	C₂×#12693	C₂²	1	2	yes	complemented
35	C₂×#12687	C₂²	1	4	yes	complemented
36	#347047	C₂²	1	8	yes	complemented
37	#347043	C₂²	1	8	yes	complemented
38	#188035	C₂²	1	2	yes	complemented
39	#187928	C₂²	1	4	yes	complemented
40	#144404	C₂²	1	16	yes	complemented
41	#144386	C₂²	1	16	yes	complemented
42	#139790	C₂²	1	8	yes	complemented
43	#139776	C₂²	1	8	yes	complemented
44	#139713	C₂²	1	8	yes	complemented
45	#139706	C₂²	1	8	yes	complemented
46	#134009	C₂²	1	2	yes	complemented
47	#133876	C₂²	1	2	yes	complemented
48	#133853	C₂²	1	2	yes	complemented
49	#133828	C₂²	1	2	yes	complemented
50	#128073	C₂²	1	4	yes	complemented
51	#62832	C₂³	1	2	yes	complemented
52	#62818	C₂³	1	2	yes	complemented
53	C₂×#3484	C₂³	1	2	yes	—
54	C₂²×D₄²	D₄	1	1	yes	characteristic, complemented
55	C₂²×D₄²	C₂³	1	1	yes	characteristic
56	C₂²×D₄²	C₂³	1	2	yes	complemented
57	C₂²×D₄²	C₂³	1	2	yes	complemented
58	C₂³×#127	D₄	1	1	yes	characteristic, complemented
59	C₂³×#127	C₂³	1	1	yes	characteristic
60	C₂³×#120	D₄	1	2	yes	complemented
61	C₂³×#120	C₂³	1	2	yes	—
62	C₂²×#453	D₄	1	4	yes	complemented
63	C₂×#2867	C₂³	1	1	yes	characteristic
64	C₂×#2856	D₄	1	1	yes	characteristic, complemented
65	C₂×#2856	C₂³	1	1	yes	characteristic
66	C₂×#2846	D₄	1	2	yes	complemented
67	C₂×#2541	D₄	1	1	yes	characteristic, complemented
68	C₂×#2541	C₂³	1	1	yes	characteristic
69	C₂×#2433	D₄	1	1	yes	characteristic, complemented
70	C₂×#2433	D₄	1	1	yes	characteristic, complemented
71	C₂×#2433	C₂³	1	1	yes	characteristic
72	C₂×#2433	C₂³	1	1	yes	characteristic
73	C₂×C₄×#127	D₄	1	1	yes	characteristic, complemented
74	C₂×C₄²×D₄	D₄	1	1	yes	characteristic, complemented
75	#24018	C₂³	1	4	yes	complemented
76	#23906	D₄	1	8	yes	complemented
77	#23906	C₂³	1	4	yes	—
78	#23906	C₂³	1	4	yes	—
79	#23906	C₂³	1	4	yes	complemented
80	#23900	C₂³	1	16	yes	—
81	#21797	C₂³	1	2	yes	complemented
82	#21752	C₂³	1	2	yes	complemented
83	C₂×#1887	D₄	1	4	yes	complemented
84	C₂×#1783	C₂³	1	2	yes	—
85	C₂×#1781	C₂³	1	4	yes	—
86	#15947	D₄	1	4	yes	complemented
87	#15281	C₂³	1	4	yes	complemented
88	#15258	C₂³	1	4	yes	—
89	#15258	C₂³	1	4	yes	complemented
90	#15257	D₄	1	4	yes	complemented
91	#15257	C₂³	1	4	yes	—
92	#14419	C₂³	1	2	yes	complemented
93	#14154	C₂³	1	2	yes	complemented
94	#14134	D₄	1	2	yes	complemented
95	#13867	D₄	1	2	yes	complemented
96	#13867	C₂³	1	2	yes	—
97	#12856	C₂³	1	4	yes	complemented
98	#12693	C₂³	1	4	yes	complemented
99	#12693	C₂³	1	4	yes	complemented
100	#12693	C₂³	1	4	yes	complemented
101	#12687	C₂³	1	16	yes	complemented
102	#8546	C₂³	1	4	yes	complemented
103	#8542	C₂³	1	4	yes	complemented
104	#8534	C₂³	1	16	yes	complemented
105	#7304	C₂³	1	16	yes	complemented
106	C₂⁷	C₂×D₄	1	2	yes	—
107	C₂²×H(5,𝔽₂)	C₂×D₄	1	2	yes	complemented
108	C₂⁴×D₄	C₂×D₄	1	2	yes	—
109	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
110	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
111	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic, complemented
112	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
113	#3484	C₂×D₄	1	4	yes	complemented
114	#3484	C₂⁴	1	4	yes	—
115	C₂²×#127	C₂×D₄	1	1	yes	characteristic
116	C₂²×#127	C₂×D₄	1	4	yes	—
117	C₂²×#127	C₂×D₄	1	1	yes	characteristic
118	C₂²×#127	C₂×D₄	1	1	yes	characteristic
119	C₂²×#127	C₂×D₄	1	4	yes	—
120	C₂²×#127	C₂×D₄	1	1	yes	characteristic, complemented
121	C₂²×#127	C₂×D₄	1	1	yes	characteristic, complemented
122	C₂²×#127	C₂×D₄	1	1	yes	characteristic, complemented
123	C₂²×#127	C₂×D₄	1	1	yes	characteristic, complemented
124	C₂²×#127	C₂⁴	1	1	yes	characteristic
125	C₂²×#127	C₂⁴	1	1	yes	characteristic
126	C₂²×#127	C₂⁴	1	1	yes	characteristic
127	C₂²×#127	C₂⁴	1	1	yes	characteristic
128	C₂²×#121	C₂×D₄	1	1	yes	characteristic
129	C₂²×#121	C₂×D₄	1	1	yes	characteristic
130	C₂²×#121	C₂×D₄	1	2	yes	—
131	C₂²×#121	C₂×D₄	1	1	yes	characteristic, complemented
132	C₂²×#121	C₂⁴	1	1	yes	characteristic
133	C₂²×#120	C₂×D₄	1	4	yes	—
134	C₂²×#120	C₂×D₄	1	2	yes	—
135	C₂²×#120	C₂×D₄	1	2	yes	—
136	C₂²×#120	C₂×D₄	1	4	yes	complemented
137	C₂²×#120	C₂×D₄	1	4	yes	complemented
138	C₂²×#120	C₂×D₄	1	4	yes	complemented
139	C₂²×#120	C₂⁴	1	4	yes	—
140	C₂×#518	C₂×D₄	1	2	yes	complemented
141	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic, complemented
144	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
145	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
146	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic
147	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic, complemented
148	C₂×#453	C₂×D₄	1	8	yes	complemented
149	C₂×#453	C₂×D₄	1	8	yes	complemented
150	C₂²×#100	C₂×D₄	1	4	yes	complemented
151	C₂×#390	C₂×D₄	1	1	yes	characteristic
152	C₂×#390	C₂×D₄	1	1	yes	characteristic, complemented
153	C₂×#390	C₂×D₄	1	1	yes	characteristic, complemented
154	C₂×#390	C₂×D₄	1	1	yes	characteristic, complemented
155	C₂×#390	C₂×D₄	1	1	yes	characteristic, complemented
156	C₂×#390	C₂⁴	1	1	yes	characteristic
157	C₂×#384	C₂×D₄	1	1	yes	characteristic, complemented
158	C₂×#379	C₂×D₄	1	2	yes	—
159	C₂×#379	C₂×D₄	1	4	yes	complemented
160	C₂×C₄×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
161	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
162	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
163	C₂×C₄³	C₂×D₄	1	1	yes	characteristic, complemented
164	#1887	C₂×D₄	1	8	yes	complemented
165	#1887	C₂×D₄	1	8	yes	complemented
166	#1783	C₂×D₄	1	4	yes	complemented
167	#1783	C₂⁴	1	4	yes	—
168	#1781	C₂⁴	1	8	yes	—
169	#1440	C₂×D₄	1	4	yes	complemented
170	#1438	C₂×D₄	1	4	yes	—
171	#1438	C₂×D₄	1	4	yes	complemented
172	#1438	C₂×D₄	1	4	yes	complemented
173	#1438	C₂×D₄	1	4	yes	complemented
174	#1438	C₂⁴	1	4	yes	—
175	C₂⁶	#120	1	2	yes	—
176	C₂⁶	C₂²×D₄	1	2	yes	—
177	C₂⁶	C₂²×D₄	1	4	yes	—
178	C₂×H(5,𝔽₂)	C₂²×D₄	1	4	yes	—
179	C₂³×D₄	#120	1	1	yes	characteristic
180	C₂³×D₄	#120	1	2	yes	—
181	C₂³×D₄	#120	1	2	yes	—
182	C₂³×D₄	#120	1	4	yes	—
183	C₂³×D₄	C₂²×D₄	1	2	yes	—
184	C₂³×D₄	C₂²×D₄	1	2	yes	—
185	C₂³×D₄	C₂²×D₄	1	2	yes	—
186	C₂³×D₄	C₂²×D₄	1	2	yes	—
187	C₂³×D₄	C₂²×D₄	1	2	yes	—
188	C₂³×D₄	C₂²×D₄	1	2	yes	—
189	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
190	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
191	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
192	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
193	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
194	C₂³×D₄	H(5,𝔽₂)	1	4	yes	—
195	C₂³×D₄	C₂⁵	1	1	yes	characteristic
196	C₂⁴×C₄	#120	1	2	yes	—
197	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
198	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
199	C₂×#127	#120	1	2	yes	—
200	C₂×#127	#120	1	2	yes	—
201	C₂×#127	#120	1	2	yes	—
202	C₂×#127	#120	1	2	yes	—
203	C₂×#127	C₂²×D₄	1	4	yes	—
204	C₂×#127	C₂²×D₄	1	4	yes	—
205	#518	C₂²×D₄	1	4	yes	—
206	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
207	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
208	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
209	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
210	C₂²×C₂²⋊C₄	#120	1	2	yes	—
211	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
212	C₂²×C₂²⋊C₄	#120	1	2	yes	—
213	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
214	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
215	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
216	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
217	C₂²×C₄²	#120	1	4	yes	—
218	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
219	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
220	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
221	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
222	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
223	C₂×#100	C₂²×D₄	1	8	yes	—
224	C₂⁵	C₂×#120	1	2	yes	—
225	C₂⁵	C₂×#120	1	1	yes	characteristic
226	C₂⁵	C₂×#120	1	2	yes	—
227	C₂⁵	C₂×#120	1	1	yes	characteristic
228	C₂⁵	D₄²	1	4	yes	—
229	C₂⁵	D₄²	1	4	yes	—
230	C₂⁵	C₂³×D₄	1	2	yes	—
231	C₂²×D₄	B(4,𝔽₂)	1	1	yes	characteristic
232	C₂²×D₄	B(4,𝔽₂)	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	C₂×#120	1	2	yes	—
236	C₂²×D₄	C₂×#120	1	1	yes	characteristic
237	C₂²×D₄	C₂×#120	1	2	yes	—
238	C₂²×D₄	C₂×#120	1	1	yes	characteristic
239	C₂²×D₄	#534	1	2	yes	—
240	C₂²×D₄	D₄²	1	4	yes	—
241	C₂²×D₄	D₄²	1	4	yes	—
242	C₂²×D₄	C₂³×D₄	1	2	yes	—
243	C₂²×D₄	C₂×H(5,𝔽₂)	1	2	yes	—
244	C₂³×C₄	C₂×#120	1	2	yes	—
245	C₂³×C₄	C₂×#120	1	1	yes	characteristic
246	C₂³×C₄	C₂×#120	1	2	yes	—
247	C₂³×C₄	C₂×#120	1	1	yes	characteristic
248	C₂³×C₄	C₂×#120	1	1	yes	characteristic
249	C₂³×C₄	C₂×#120	1	1	yes	characteristic
250	C₂³×C₄	#534	1	2	yes	—
251	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
252	#127	B(4,𝔽₂)	1	8	yes	complemented
253	C₂×C₂²⋊C₄	B(4,𝔽₂)	1	4	yes	—
254	C₂×C₄²	C₂×#120	1	2	yes	—
255	C₂×C₄²	C₂×#120	1	2	yes	—
256	C₂⁴	#2403	1	2	yes	—
257	C₂⁴	#2403	1	2	yes	—
258	C₂⁴	#2403	1	2	yes	—
259	C₂⁴	C₂×B(4,𝔽₂)	1	2	yes	—
260	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
261	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
262	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
263	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
264	C₂⁴	C₂²×#120	1	1	yes	characteristic
265	C₂⁴	C₂×D₄²	1	4	yes	—
266	C₂×D₄	#2196	1	4	yes	complemented
267	C₂×D₄	C₂×B(4,𝔽₂)	1	4	yes	—
268	C₂×D₄	C₂×B(4,𝔽₂)	1	4	yes	complemented
269	C₂²×C₄	#2403	1	2	yes	—
270	C₂²×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
271	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
272	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
273	C₂²×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
274	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
275	C₂²×C₄	C₂×#534	1	1	yes	characteristic
276	C₄²	C₂×B(4,𝔽₂)	1	4	yes	complemented
277	C₂³	#23900	1	2	yes	—
278	C₂³	#23900	1	2	yes	—
279	C₂³	#23900	1	4	yes	—
280	C₂³	C₂×#2196	1	2	yes	—
281	C₂³	C₂×#2196	1	2	yes	complemented
282	C₂³	#33557	1	2	yes	—
283	C₂³	C₂×#2403	1	1	yes	characteristic
284	C₂³	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
285	C₂³	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
286	C₂×C₄	C₂×#2196	1	2	yes	complemented
287	C₂×C₄	C₂²×B(4,𝔽₂)	1	2	yes	—
288	C₂²	#499843	1	4	yes	—
289	C₂²	C₂×#23900	1	1	yes	characteristic
290	C₂²	C₂×#23900	1	1	yes	characteristic
291	C₂²	#6437629	1	1	yes	characteristic
292	C₂²	C₂²×#2196	1	1	yes	characteristic
293	C₂²	C₂×#33557	1	1	yes	characteristic
294	C₂²	#7622880	1	2	yes	—
295	C₂	#72233348	1	1	yes	characteristic
296	C₂	C₂×#499843	1	1	yes	characteristic
297	C₂	#72234146	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂×#23900
commutator, Frattini, cosocle	C₂³×D₄	C₂⁵
LCS	G ▷ C₂³×D₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂⁵ ◁ C₂²×D₄² ◁ G
LECS	G ▷ C₂³×D₄ ▷ C₂³ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72234144	C₂	semidirect
2. #72234143	C₂	semidirect
3. #72234142	C₂	semidirect
4. #72234141	C₂	semidirect
5. #72234140	C₂	semidirect
6. #72234139	C₂	semidirect
7. #72234119	C₂	semidirect
8. #72233675	C₂	semidirect
9. #72232736	C₂	semidirect
10. #72231479	C₂	semidirect
11. C₂×#511771	C₂	semidirect
12. #72216323	C₂	semidirect
13. #10586472	C₂²	semidirect
14. C₂³×D₄²	C₂²	semidirect
16. #6516740	C₂²	semidirect
17. #6512701	C₂²	semidirect
18. #6499992	C₂²	semidirect
19. #6499837	C₂²	semidirect
20. #6470019	C₂²	semidirect
21. C₂×#23900	C₂²	semidirect
23. #6385983	C₂²	semidirect
24. #1420272	C₂²	semidirect
25. #1418385	C₂²	semidirect
26. #846057	C₂²	semidirect
27. #674656	C₂²	semidirect
28. #674141	C₂²	semidirect
30. #531766	C₂²	semidirect
31. #511771	C₂²	semidirect
32. #511771	C₂²	semidirect
33. #496189	C₂²	semidirect
34. C₂×#12693	C₂²	semidirect
35. C₂×#12687	C₂²	semidirect
36. #347047	C₂²	semidirect
37. #347043	C₂²	semidirect
38. #188035	C₂²	semidirect
39. #187928	C₂²	semidirect
40. #144404	C₂²	semidirect
41. #144386	C₂²	semidirect
42. #139790	C₂²	semidirect
43. #139776	C₂²	semidirect
44. #139713	C₂²	semidirect
45. #139706	C₂²	semidirect
46. #134009	C₂²	semidirect
47. #133876	C₂²	semidirect
48. #133853	C₂²	semidirect
49. #133828	C₂²	semidirect
50. #128073	C₂²	semidirect
51. #62832	C₂³	semidirect
52. #62818	C₂³	semidirect
54. C₂²×D₄²	D₄	semidirect
56. C₂²×D₄²	C₂³	semidirect
57. C₂²×D₄²	C₂³	semidirect
58. C₂³×#127	D₄	semidirect
60. C₂³×#120	D₄	semidirect
62. C₂²×#453	D₄	semidirect
64. C₂×#2856	D₄	semidirect
66. C₂×#2846	D₄	semidirect
67. C₂×#2541	D₄	semidirect
69. C₂×#2433	D₄	semidirect
70. C₂×#2433	D₄	semidirect
73. C₂×C₄×#127	D₄	semidirect
74. C₂×C₄²×D₄	D₄	semidirect
75. #24018	C₂³	semidirect
76. #23906	D₄	semidirect
79. #23906	C₂³	semidirect
81. #21797	C₂³	semidirect
82. #21752	C₂³	semidirect
83. C₂×#1887	D₄	semidirect
86. #15947	D₄	semidirect
87. #15281	C₂³	semidirect
89. #15258	C₂³	semidirect
90. #15257	D₄	semidirect
92. #14419	C₂³	semidirect
93. #14154	C₂³	semidirect
94. #14134	D₄	semidirect
95. #13867	D₄	semidirect
97. #12856	C₂³	semidirect
98. #12693	C₂³	semidirect
99. #12693	C₂³	semidirect
100. #12693	C₂³	semidirect
101. #12687	C₂³	semidirect
102. #8546	C₂³	semidirect
103. #8542	C₂³	semidirect
104. #8534	C₂³	semidirect
105. #7304	C₂³	semidirect
107. C₂²×H(5,𝔽₂)	C₂×D₄	semidirect
111. C₂⁴×D₄	C₂×D₄	semidirect
113. #3484	C₂×D₄	semidirect
120. C₂²×#127	C₂×D₄	semidirect
121. C₂²×#127	C₂×D₄	semidirect
122. C₂²×#127	C₂×D₄	semidirect
123. C₂²×#127	C₂×D₄	semidirect
131. C₂²×#121	C₂×D₄	semidirect
136. C₂²×#120	C₂×D₄	semidirect
137. C₂²×#120	C₂×D₄	semidirect
138. C₂²×#120	C₂×D₄	semidirect
140. C₂×#518	C₂×D₄	semidirect
143. C₂²×C₄×D₄	C₂×D₄	semidirect
147. C₂³×C₄²	C₂×D₄	semidirect
148. C₂×#453	C₂×D₄	semidirect
149. C₂×#453	C₂×D₄	semidirect
150. C₂²×#100	C₂×D₄	semidirect
152. C₂×#390	C₂×D₄	semidirect
153. C₂×#390	C₂×D₄	semidirect
154. C₂×#390	C₂×D₄	semidirect
155. C₂×#390	C₂×D₄	semidirect
157. C₂×#384	C₂×D₄	semidirect
159. C₂×#379	C₂×D₄	semidirect
160. C₂×C₄×C₄⋊C₄	C₂×D₄	semidirect
162. C₂×C₄×C₂²⋊C₄	C₂×D₄	semidirect
163. C₂×C₄³	C₂×D₄	semidirect
164. #1887	C₂×D₄	semidirect
165. #1887	C₂×D₄	semidirect
166. #1783	C₂×D₄	semidirect
169. #1440	C₂×D₄	semidirect
171. #1438	C₂×D₄	semidirect
172. #1438	C₂×D₄	semidirect
173. #1438	C₂×D₄	semidirect
252. #127	B(4,𝔽₂)	semidirect
266. C₂×D₄	#2196	semidirect
268. C₂×D₄	C₂×B(4,𝔽₂)	semidirect
276. C₄²	C₂×B(4,𝔽₂)	semidirect
281. C₂³	C₂×#2196	semidirect
286. C₂×C₄	C₂×#2196	semidirect

Maximal subgroups

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

subgroup	index
#72234144	2
#72234143	2
#72234142	2
#72234141	2
#72234140	2
#72234139	2
#72234119	2
#72233675	2
#72232736	2
#72231479	2
C₂×#511771	2
#72216323	2