Subgroups — #72339110

Order 4096.

At least 9041 conjugacy classes of subgroups; only the 671 normal subgroups are shown.

The subgroup lattice has 314 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72339100	C₂	1	1	yes	maximal, characteristic, complemented
2	#72339098	C₂	1	1	yes	maximal, characteristic, complemented
3	#72339009	C₂	1	1	yes	maximal, characteristic, complemented
4	#72339003	C₂	1	2	yes	maximal, complemented
5	#72339003	C₂	1	2	yes	maximal, complemented
6	#72338964	C₂	1	1	yes	maximal, characteristic, complemented
7	#72338962	C₂²	1	2	yes	complemented
8	#72338961	C₂²	1	1	yes	characteristic, complemented
9	#72338879	C₂	1	2	yes	maximal, complemented
10	#72338878	C₂²	1	2	yes	complemented
11	#72338878	C₂²	1	2	yes	complemented
12	C₂×#72210569	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#93146	C₂²	1	1	yes	characteristic, complemented
14	C₂×#72210559	C₂	1	2	yes	maximal, complemented
15	C₂×#133308	C₂²	1	2	yes	—
16	C₂×#133308	C₂²	1	2	yes	—
17	C₂×#133308	C₂²	1	2	yes	complemented
18	C₂×#417807	C₂²	1	2	yes	—
19	#72338811	C₂	1	2	yes	maximal, complemented
20	#72338801	C₂	1	2	yes	maximal, complemented
21	#72338787	C₂²	1	2	yes	complemented
22	#72338486	C₂	1	1	yes	maximal, characteristic, complemented
23	#72338476	C₂²	1	1	yes	characteristic
24	#72338476	C₂²	1	1	yes	characteristic
25	#72338476	C₂²	1	2	yes	complemented
26	#72337708	C₂	1	2	yes	maximal, complemented
27	#72337669	C₂	1	4	yes	maximal, complemented
28	#72337665	C₂²	1	2	yes	complemented
29	#72337662	C₂²	1	1	yes	characteristic, complemented
30	#72337662	C₂²	1	2	yes	complemented
31	#72337654	C₂²	1	2	yes	complemented
32	#72337652	C₂²	1	2	yes	complemented
33	#72337652	C₂²	1	2	yes	complemented
34	#72310971	C₂²	1	1	yes	characteristic, complemented
35	C₂×#7672751	C₂²	1	1	yes	characteristic
36	#72266236	C₂	1	1	yes	maximal, characteristic, complemented
37	#72266199	C₂²	1	1	yes	characteristic, complemented
38	#72266169	C₂²	1	1	yes	characteristic
39	#72266169	C₂²	1	1	yes	characteristic
40	#72266169	C₂²	1	2	yes	complemented
41	#72252381	C₂	1	4	yes	maximal, complemented
42	#72252379	C₂²	1	4	yes	complemented
43	#72252378	C₂²	1	2	yes	complemented
44	#72241387	C₂²	1	2	yes	complemented
45	#72241387	C₂²	1	1	yes	characteristic, complemented
46	#72241346	C₂	1	2	yes	maximal, complemented
47	#72241344	C₂²	1	2	yes	complemented
48	#72241343	C₂²	1	2	yes	complemented
49	#72241342	C₂²	1	1	yes	characteristic, complemented
50	#72241322	C₂²	1	4	yes	complemented
51	#72241322	C₂²	1	4	yes	complemented
52	#72241322	C₂²	1	4	yes	complemented
53	#72241322	C₂²	1	4	yes	complemented
54	C₂×#134009	C₂²	1	1	yes	characteristic
55	C₂×#134009	C₂²	1	2	yes	—
56	C₂×#134009	C₂²	1	1	yes	characteristic
57	#72240077	C₂²	1	4	yes	complemented
58	#72236979	C₂²	1	2	yes	complemented
59	#72236979	C₂²	1	2	yes	complemented
60	C₂×#245233	C₂²	1	2	yes	—
61	C₂×#245233	C₂²	1	2	yes	—
62	C₂×#245233	C₂²	1	1	yes	characteristic, complemented
63	#72227941	C₂²	1	4	yes	complemented
64	#72227941	C₂²	1	2	yes	complemented
65	#72227941	C₂²	1	2	yes	complemented
66	#72227940	C₂²	1	4	yes	complemented
67	#72227940	C₂²	1	4	yes	complemented
68	#72227940	C₂²	1	4	yes	complemented
69	#72227940	C₂²	1	4	yes	complemented
70	#72227556	C₂²	1	2	yes	complemented
71	#72213260	C₂²	1	4	yes	complemented
72	#72213260	C₂²	1	4	yes	complemented
73	#72210569	C₂²	1	4	yes	complemented
74	#72210569	C₂²	1	2	yes	complemented
75	#72210569	C₂²	1	2	yes	complemented
76	#72210559	C₂²	1	4	yes	complemented
77	#72210559	C₂²	1	4	yes	complemented
78	#72210559	C₂²	1	4	yes	complemented
79	#72210559	C₂²	1	4	yes	complemented
80	#72210539	C₂²	1	4	yes	complemented
81	#72210539	C₂²	1	4	yes	complemented
82	#72210015	C₂²	1	2	yes	complemented
83	#7672751	C₂³	1	2	yes	—
84	#7672751	C₂³	1	2	yes	—
85	C₂²×#2867	C₂³	1	1	yes	characteristic
86	C₂×#35527	C₂³	1	1	yes	characteristic
87	C₂×#35527	C₂³	1	2	yes	—
88	C₂×#35527	C₂³	1	1	yes	characteristic
89	C₂×#32898	D₄	1	4	yes	complemented
90	#6370693	D₄	1	2	yes	complemented
91	#417807	C₂³	1	4	yes	—
92	#417807	C₂³	1	4	yes	—
93	C₂×#10981	C₂³	1	2	yes	—
94	#346283	C₂³	1	1	yes	characteristic, complemented
95	#346283	C₂³	1	2	yes	complemented
96	#346282	C₂³	1	1	yes	characteristic, complemented
97	#245233	D₄	1	4	yes	complemented
98	#245233	D₄	1	4	yes	complemented
99	#245233	C₂³	1	4	yes	—
100	#245233	C₂³	1	4	yes	—
101	#245233	C₂³	1	2	yes	—
102	#245233	C₂³	1	2	yes	—
103	#245233	C₂³	1	2	yes	—
104	#245233	C₂³	1	2	yes	—
105	#245233	C₂³	1	1	yes	characteristic, complemented
106	#245233	C₂³	1	1	yes	characteristic, complemented
107	#245233	C₂³	1	2	yes	complemented
108	#213861	D₄	1	2	yes	complemented
109	#213861	C₂³	1	1	yes	characteristic
110	#213861	C₂³	1	1	yes	characteristic
111	#213861	C₂³	1	2	yes	—
112	#213861	C₂³	1	2	yes	complemented
113	#213861	C₂³	1	2	yes	complemented
114	#213860	D₄	1	2	yes	complemented
115	#213860	C₂³	1	1	yes	characteristic
116	#213860	C₂³	1	1	yes	characteristic
117	#213860	C₂³	1	2	yes	—
118	#213860	C₂³	1	2	yes	complemented
119	#213860	C₂³	1	2	yes	complemented
120	C₂×#9497	D₄	1	4	yes	complemented
121	#190117	D₄	1	2	yes	complemented
122	C₂×#8546	C₂³	1	1	yes	characteristic
123	C₂×#8546	C₂³	1	2	yes	—
124	C₂×#8546	C₂³	1	1	yes	characteristic
125	C₂×#8546	C₂³	1	2	yes	—
126	C₂×#8546	C₂³	1	1	yes	characteristic
127	C₂×#8546	C₂³	1	1	yes	characteristic
128	#134009	C₂³	1	2	yes	—
129	#134009	C₂³	1	2	yes	—
130	#134009	C₂³	1	4	yes	—
131	#134009	C₂³	1	4	yes	—
132	#134009	C₂³	1	2	yes	—
133	#134009	C₂³	1	2	yes	—
134	#133835	C₂³	1	2	yes	—
135	#133835	C₂³	1	2	yes	—
136	#133835	C₂³	1	2	yes	—
137	#133835	C₂³	1	2	yes	—
138	#133835	C₂³	1	4	yes	complemented
139	#133835	C₂³	1	4	yes	complemented
140	#133308	C₂³	1	4	yes	—
141	#133308	C₂³	1	4	yes	—
142	#133308	C₂³	1	4	yes	—
143	#133308	C₂³	1	4	yes	—
144	#133308	C₂³	1	4	yes	complemented
145	#133308	C₂³	1	4	yes	complemented
146	#93146	C₂³	1	2	yes	complemented
147	#93146	C₂³	1	2	yes	complemented
148	#93139	C₂³	1	2	yes	complemented
149	#93139	C₂³	1	4	yes	complemented
150	#93139	C₂³	1	4	yes	complemented
151	#93139	C₂³	1	2	yes	complemented
152	#93113	C₂³	1	4	yes	complemented
153	#93113	C₂³	1	4	yes	complemented
154	#93113	C₂³	1	4	yes	complemented
155	#93113	C₂³	1	4	yes	complemented
156	C₂³×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
157	C₂³×H(5,𝔽₂)	C₂×D₄	1	2	yes	—
158	C₂³×H(5,𝔽₂)	#41	1	1	yes	characteristic, complemented
159	C₂³×#127	#41	1	1	yes	characteristic, complemented
160	C₂³×#127	C₂⁴	1	1	yes	characteristic
161	C₂×#2867	#41	1	2	yes	complemented
162	C₂×#2867	C₂⁴	1	2	yes	—
163	#35527	C₂×D₄	1	4	yes	—
164	#35527	C₂×D₄	1	2	yes	—
165	#35527	C₂×D₄	1	2	yes	—
166	#35527	C₂×D₄	1	1	yes	characteristic
167	#35527	C₂×D₄	1	1	yes	characteristic
168	#35527	#41	1	2	yes	complemented
169	#35527	C₂⁴	1	2	yes	—
170	#35527	C₂⁴	1	2	yes	—
171	#35527	C₂⁴	1	1	yes	characteristic
172	#35527	C₂⁴	1	1	yes	characteristic
173	#35527	C₂⁴	1	2	yes	—
174	C₂×#2403	C₂×D₄	1	4	yes	—
175	C₂×#2309	C₂×D₄	1	2	yes	—
176	C₂×#2309	C₂×D₄	1	1	yes	characteristic
177	C₂×#2309	#41	1	1	yes	characteristic, complemented
178	C₂²×C₄³	#41	1	1	yes	characteristic, complemented
179	#32898	C₂×D₄	1	4	yes	complemented
180	#32898	C₂×D₄	1	4	yes	complemented
181	#32898	C₂×D₄	1	4	yes	complemented
182	#32898	C₂×D₄	1	4	yes	complemented
183	#20586	C₂×D₄	1	2	yes	complemented
184	#20586	C₂×D₄	1	2	yes	complemented
185	#20585	C₂×D₄	1	2	yes	complemented
186	#20585	C₂×D₄	1	2	yes	complemented
187	C₂×#1781	C₂×D₄	1	4	yes	—
188	C₂×#1781	C₂×D₄	1	2	yes	—
189	C₂×#1781	C₂×D₄	1	2	yes	—
190	#10981	C₂⁴	1	4	yes	—
191	#9497	C₂×D₄	1	4	yes	complemented
192	#9497	C₂×D₄	1	4	yes	complemented
193	#9497	C₂×D₄	1	4	yes	complemented
194	#9497	C₂×D₄	1	4	yes	complemented
195	#8748	C₂×D₄	1	2	yes	complemented
196	#8748	C₂×D₄	1	2	yes	complemented
197	#8748	C₂×D₄	1	2	yes	complemented
198	#8748	C₂×D₄	1	2	yes	complemented
199	#8546	C₂×D₄	1	2	yes	—
200	#8546	C₂×D₄	1	4	yes	—
201	#8546	C₂×D₄	1	2	yes	—
202	#8546	C₂⁴	1	2	yes	—
203	#8546	C₂⁴	1	2	yes	—
204	#8546	C₂⁴	1	4	yes	—
205	#8546	C₂⁴	1	1	yes	characteristic
206	#8546	C₂⁴	1	1	yes	characteristic
207	#8546	C₂⁴	1	1	yes	characteristic
208	#8546	C₂⁴	1	1	yes	characteristic
209	#8546	C₂⁴	1	2	yes	—
210	#8546	C₂⁴	1	2	yes	—
211	C₂²×H(5,𝔽₂)	#120	1	2	yes	—
212	C₂²×H(5,𝔽₂)	C₂²×D₄	1	1	yes	characteristic
213	C₂²×H(5,𝔽₂)	C₂²×D₄	1	1	yes	characteristic
214	C₂²×H(5,𝔽₂)	C₂²×D₄	1	2	yes	—
215	C₂²×H(5,𝔽₂)	C₂²×D₄	1	2	yes	—
216	C₂²×H(5,𝔽₂)	C₂×#41	1	2	yes	—
217	C₂⁴×D₄	#120	1	2	yes	—
218	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
219	C₂⁴×D₄	C₂²×D₄	1	2	yes	—
220	C₂⁴×D₄	C₂×#41	1	1	yes	characteristic
221	C₂⁴×D₄	H(5,𝔽₂)	1	2	yes	—
222	C₂²×#127	C₂²×D₄	1	1	yes	characteristic
223	C₂²×#127	C₂²×D₄	1	2	yes	—
224	C₂²×#127	C₂×#41	1	2	yes	—
225	C₂²×#127	C₂×#41	1	1	yes	characteristic
226	C₂²×#127	C₂×#41	1	1	yes	characteristic
227	C₂²×#127	H(5,𝔽₂)	1	2	yes	—
228	C₂²×#127	C₂⁵	1	1	yes	characteristic
229	C₂³×C₄²	C₂×#41	1	1	yes	characteristic
230	#2403	#120	1	4	yes	—
231	#2403	#120	1	4	yes	—
232	#2403	C₂²×D₄	1	4	yes	—
233	#2403	C₂²×D₄	1	4	yes	—
234	#2309	#120	1	2	yes	—
235	#2309	C₂²×D₄	1	2	yes	—
236	#2309	C₂²×D₄	1	2	yes	—
237	#2309	C₂²×D₄	1	1	yes	characteristic
238	#2309	C₂²×D₄	1	1	yes	characteristic
239	#2309	C₂×#41	1	2	yes	—
240	C₂×#379	#120	1	2	yes	—
241	C₂×C₄³	C₂×#41	1	2	yes	—
242	#1781	C₂²×D₄	1	2	yes	—
243	#1781	C₂²×D₄	1	2	yes	—
244	#1781	C₂²×D₄	1	4	yes	—
245	#1781	C₂²×D₄	1	4	yes	—
246	#1781	C₂²×D₄	1	2	yes	—
247	#1781	C₂²×D₄	1	2	yes	—
248	C₂⁶	B(4,𝔽₂)	1	2	yes	—
249	C₂⁶	C₂×#120	1	1	yes	characteristic
250	C₂⁶	#535	1	1	yes	characteristic
251	C₂⁶	#546	1	2	yes	—
252	C₂³×D₄	B(4,𝔽₂)	1	2	yes	—
253	C₂³×D₄	B(4,𝔽₂)	1	2	yes	—
254	C₂³×D₄	C₂×#120	1	2	yes	—
255	C₂³×D₄	C₂×#120	1	1	yes	characteristic
256	C₂³×D₄	C₂×#120	1	2	yes	—
257	C₂³×D₄	C₂×#120	1	2	yes	—
258	C₂³×D₄	#525	1	1	yes	characteristic
259	C₂³×D₄	#525	1	1	yes	characteristic
260	C₂³×D₄	#535	1	1	yes	characteristic
261	C₂³×D₄	#535	1	2	yes	—
262	C₂³×D₄	#546	1	2	yes	—
263	C₂³×D₄	#546	1	2	yes	—
264	C₂³×D₄	#546	1	2	yes	—
265	C₂³×D₄	#546	1	2	yes	—
266	C₂³×D₄	#546	1	2	yes	—
267	C₂³×D₄	C₂³×D₄	1	1	yes	characteristic
268	C₂³×D₄	C₂³×D₄	1	2	yes	—
269	C₂³×D₄	C₂²×#41	1	1	yes	characteristic
270	C₂³×D₄	C₂×H(5,𝔽₂)	1	2	yes	—
271	C₂⁴×C₄	B(4,𝔽₂)	1	2	yes	—
272	C₂⁴×C₄	#525	1	1	yes	characteristic
273	C₂⁴×C₄	#546	1	2	yes	—
274	C₂²×C₄²	#525	1	1	yes	characteristic
275	C₂²×C₄²	#546	1	2	yes	—
276	C₂²×C₄²	C₂²×#41	1	1	yes	characteristic
277	#379	C₂×#120	1	2	yes	—
278	#379	C₂×#120	1	2	yes	—
279	C₂⁵	#2404	1	2	yes	—
280	C₂⁵	#2404	1	1	yes	characteristic
281	C₂⁵	#2404	1	1	yes	characteristic
282	C₂⁵	#2404	1	1	yes	characteristic
283	C₂⁵	C₂×B(4,𝔽₂)	1	2	yes	—
284	C₂⁵	C₂×B(4,𝔽₂)	1	2	yes	—
285	C₂⁵	C₂×B(4,𝔽₂)	1	2	yes	—
286	C₂⁵	C₂×B(4,𝔽₂)	1	2	yes	—
287	C₂⁵	C₂²×#120	1	1	yes	characteristic
288	C₂⁵	C₂×#535	1	1	yes	characteristic
289	C₂⁵	C₂×#546	1	2	yes	—
290	C₂³×C₄	#2404	1	1	yes	characteristic
291	C₂³×C₄	#2404	1	2	yes	—
292	C₂³×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
293	C₂³×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
294	C₂³×C₄	C₂×#525	1	1	yes	characteristic
295	C₂³×C₄	C₂×#546	1	2	yes	—
296	C₂⁴	#23984	1	1	yes	characteristic
297	C₂⁴	#23984	1	1	yes	characteristic
298	C₂⁴	#23984	1	2	yes	—
299	C₂⁴	#23996	1	2	yes	—
300	C₂⁴	#23996	1	2	yes	—
301	C₂⁴	C₂×#2404	1	1	yes	characteristic
302	C₂⁴	C₂²×B(4,𝔽₂)	1	2	yes	—
303	C₂³	#251827	1	1	yes	characteristic
304	C₂³	#251827	1	2	yes	—
305	C₂³	#251827	1	1	yes	characteristic
306	C₂³	C₂×#23996	1	2	yes	—
307	C₂³	C₂×#23984	1	1	yes	characteristic
308	C₂²	#72216336	1	4	yes	—
309	C₂²	#72216370	1	2	yes	—
310	C₂²	C₂×#251827	1	1	yes	characteristic
311	C₂	C₂×#72216370	1	1	yes	characteristic
312	C₂	C₂×#72216336	1	2	yes	—

	subgroup	G/H
center, socle	C₂²	C₂×#251827
commutator, Frattini, cosocle	C₂²×#127	C₂⁵
LCS	G ▷ C₂²×#127 ▷ C₂⁴ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂⁵ ◁ C₂³×#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. #72339100	C₂	semidirect
2. #72339098	C₂	semidirect
3. #72339009	C₂	semidirect
4. #72339003	C₂	semidirect
5. #72339003	C₂	semidirect
6. #72338964	C₂	semidirect
7. #72338962	C₂²	semidirect
8. #72338961	C₂²	semidirect
9. #72338879	C₂	semidirect
10. #72338878	C₂²	semidirect
11. #72338878	C₂²	semidirect
12. C₂×#72210569	C₂	semidirect
13. C₂×#93146	C₂²	semidirect
14. C₂×#72210559	C₂	semidirect
17. C₂×#133308	C₂²	semidirect
19. #72338811	C₂	semidirect
20. #72338801	C₂	semidirect
21. #72338787	C₂²	semidirect
22. #72338486	C₂	semidirect
25. #72338476	C₂²	semidirect
26. #72337708	C₂	semidirect
27. #72337669	C₂	semidirect
28. #72337665	C₂²	semidirect
29. #72337662	C₂²	semidirect
30. #72337662	C₂²	semidirect
31. #72337654	C₂²	semidirect
32. #72337652	C₂²	semidirect
33. #72337652	C₂²	semidirect
34. #72310971	C₂²	semidirect
36. #72266236	C₂	semidirect
37. #72266199	C₂²	semidirect
40. #72266169	C₂²	semidirect
41. #72252381	C₂	semidirect
42. #72252379	C₂²	semidirect
43. #72252378	C₂²	semidirect
44. #72241387	C₂²	semidirect
45. #72241387	C₂²	semidirect
46. #72241346	C₂	semidirect
47. #72241344	C₂²	semidirect
48. #72241343	C₂²	semidirect
49. #72241342	C₂²	semidirect
50. #72241322	C₂²	semidirect
51. #72241322	C₂²	semidirect
52. #72241322	C₂²	semidirect
53. #72241322	C₂²	semidirect
57. #72240077	C₂²	semidirect
58. #72236979	C₂²	semidirect
59. #72236979	C₂²	semidirect
62. C₂×#245233	C₂²	semidirect
63. #72227941	C₂²	semidirect
64. #72227941	C₂²	semidirect
65. #72227941	C₂²	semidirect
66. #72227940	C₂²	semidirect
67. #72227940	C₂²	semidirect
68. #72227940	C₂²	semidirect
69. #72227940	C₂²	semidirect
70. #72227556	C₂²	semidirect
71. #72213260	C₂²	semidirect
72. #72213260	C₂²	semidirect
73. #72210569	C₂²	semidirect
74. #72210569	C₂²	semidirect
75. #72210569	C₂²	semidirect
76. #72210559	C₂²	semidirect
77. #72210559	C₂²	semidirect
78. #72210559	C₂²	semidirect
79. #72210559	C₂²	semidirect
80. #72210539	C₂²	semidirect
81. #72210539	C₂²	semidirect
82. #72210015	C₂²	semidirect
89. C₂×#32898	D₄	semidirect
90. #6370693	D₄	semidirect
94. #346283	C₂³	semidirect
95. #346283	C₂³	semidirect
96. #346282	C₂³	semidirect
97. #245233	D₄	semidirect
98. #245233	D₄	semidirect
105. #245233	C₂³	semidirect
106. #245233	C₂³	semidirect
107. #245233	C₂³	semidirect
108. #213861	D₄	semidirect
112. #213861	C₂³	semidirect
113. #213861	C₂³	semidirect
114. #213860	D₄	semidirect
118. #213860	C₂³	semidirect
119. #213860	C₂³	semidirect
120. C₂×#9497	D₄	semidirect
121. #190117	D₄	semidirect
138. #133835	C₂³	semidirect
139. #133835	C₂³	semidirect
144. #133308	C₂³	semidirect
145. #133308	C₂³	semidirect
146. #93146	C₂³	semidirect
147. #93146	C₂³	semidirect
148. #93139	C₂³	semidirect
149. #93139	C₂³	semidirect
150. #93139	C₂³	semidirect
151. #93139	C₂³	semidirect
152. #93113	C₂³	semidirect
153. #93113	C₂³	semidirect
154. #93113	C₂³	semidirect
155. #93113	C₂³	semidirect
158. C₂³×H(5,𝔽₂)	#41	semidirect
159. C₂³×#127	#41	semidirect
161. C₂×#2867	#41	semidirect
168. #35527	#41	semidirect
177. C₂×#2309	#41	semidirect
178. C₂²×C₄³	#41	semidirect
179. #32898	C₂×D₄	semidirect
180. #32898	C₂×D₄	semidirect
181. #32898	C₂×D₄	semidirect
182. #32898	C₂×D₄	semidirect
183. #20586	C₂×D₄	semidirect
184. #20586	C₂×D₄	semidirect
185. #20585	C₂×D₄	semidirect
186. #20585	C₂×D₄	semidirect
191. #9497	C₂×D₄	semidirect
192. #9497	C₂×D₄	semidirect
193. #9497	C₂×D₄	semidirect
194. #9497	C₂×D₄	semidirect
195. #8748	C₂×D₄	semidirect
196. #8748	C₂×D₄	semidirect
197. #8748	C₂×D₄	semidirect
198. #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
#72339100	2
#72339098	2
#72339009	2
#72339003	2
#72338964	2
#72338879	2
C₂×#72210569	2
C₂×#72210559	2
#72338811	2
#72338801	2
#72338486	2
#72337708	2
#72337669	2
#72266236	2
#72252381	2
#72241346	2