Subgroups — #72263318

Order 2048.

At least 7717 conjugacy classes of subgroups; only the 358 normal subgroups are shown.

The subgroup lattice has 326 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72263156	C₂	1	1	yes	maximal, characteristic, complemented
2	#72262837	C₂	1	2	yes	maximal, complemented
3	#72262522	C₂	1	2	yes	maximal, complemented
4	#72237598	C₂	1	2	yes	maximal, complemented
5	#72234783	C₂	1	1	yes	maximal, characteristic
6	#72234778	C₂	1	1	yes	maximal, characteristic, complemented
7	#72233243	C₂	1	1	yes	maximal, characteristic, complemented
8	#72232808	C₂	1	2	yes	maximal, complemented
9	#72232743	C₂	1	1	yes	maximal, characteristic, complemented
10	#72232735	C₂	1	1	yes	maximal, characteristic, complemented
11	#72219461	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#57971	C₄	1	1	yes	characteristic, complemented
13	C₂×#37644	C₂²	1	1	yes	characteristic
14	#6385971	C₂²	1	1	yes	characteristic, complemented
15	#4599081	C₄	1	1	yes	characteristic, complemented
16	#4466055	C₂²	1	1	yes	characteristic
17	#4435227	C₂²	1	1	yes	characteristic
18	#4418479	C₂²	1	1	yes	characteristic
19	#4378714	C₄	1	1	yes	characteristic, complemented
20	#2805719	C₂²	1	1	yes	characteristic
21	#2032088	C₄	1	1	yes	characteristic, complemented
22	#1465620	C₄	1	1	yes	characteristic, complemented
23	#1460307	C₂²	1	1	yes	characteristic
24	#649038	C₂²	1	1	yes	characteristic
25	#648360	C₄	1	1	yes	characteristic, complemented
26	#634305	C₄	1	1	yes	characteristic, complemented
27	#534229	C₄	1	1	yes	characteristic, complemented
28	#188087	C₂²	1	1	yes	characteristic, complemented
29	#188035	C₂²	1	1	yes	characteristic, complemented
30	#188035	C₂²	1	1	yes	characteristic, complemented
31	#139720	C₂²	1	2	yes	complemented
32	#139718	C₂²	1	2	yes	complemented
33	#139718	C₂²	1	2	yes	complemented
34	#139718	C₂²	1	2	yes	complemented
35	#139504	C₂²	1	2	yes	complemented
36	#139504	C₂²	1	2	yes	complemented
37	#139504	C₂²	1	2	yes	complemented
38	#139486	C₂²	1	2	yes	complemented
39	#133893	C₂²	1	2	yes	complemented
40	#133825	C₂²	1	2	yes	complemented
41	#115631	C₂²	1	2	yes	complemented
42	#115163	C₂²	1	2	yes	complemented
43	C₂²×D₄²	C₂³	1	1	yes	characteristic
44	C₂²×#534	D₄	1	1	yes	characteristic
45	C₂³×#127	D₄	1	1	yes	characteristic
46	C₂³×#120	D₄	1	1	yes	characteristic
47	C₂³×#120	D₄	1	1	yes	characteristic
48	C₂×#2760	C₂×C₄	1	1	yes	characteristic, complemented
49	C₂×#2670	C₂×C₄	1	1	yes	characteristic, complemented
50	C₂×#2815	C₂×C₄	1	1	yes	characteristic, complemented
51	C₂×#2846	C₂×C₄	1	1	yes	characteristic
52	C₂×#2539	D₄	1	1	yes	characteristic
53	C₂×#2534	C₂×C₄	1	1	yes	characteristic
54	C₂×#2433	D₄	1	1	yes	characteristic
55	C₂×#2408	C₂×C₄	1	1	yes	characteristic
56	C₂×#2412	C₂×C₄	1	1	yes	characteristic
57	C₂×#2405	D₄	1	1	yes	characteristic
58	C₂×#2410	C₂³	1	1	yes	characteristic
59	C₂×#2403	C₂×C₄	1	1	yes	characteristic, complemented
60	C₂×#2403	D₄	1	1	yes	characteristic
61	C₂×#2657	D₄	1	1	yes	characteristic
62	C₂×#2631	C₂×C₄	1	1	yes	characteristic
63	C₂×#2631	D₄	1	1	yes	characteristic
64	C₂×#2617	D₄	1	1	yes	characteristic
65	C₂×#2613	C₂³	1	1	yes	characteristic
66	C₂×D₄×C₂²⋊C₄	D₄	1	1	yes	characteristic
67	C₂×#2321	C₂×C₄	1	1	yes	characteristic
68	#21746	C₂³	1	2	yes	—
69	#21746	C₂³	1	2	yes	—
70	#15635	C₂×C₄	1	1	yes	characteristic, complemented
71	#15622	C₂×C₄	1	1	yes	characteristic, complemented
72	#15467	C₂×C₄	1	1	yes	characteristic, complemented
73	#15420	C₂×C₄	1	1	yes	characteristic, complemented
74	#15420	C₂×C₄	1	1	yes	characteristic, complemented
75	#15310	D₄	1	1	yes	characteristic
76	#15310	D₄	1	1	yes	characteristic
77	#15310	D₄	1	1	yes	characteristic
78	#15310	D₄	1	1	yes	characteristic
79	#15267	C₂×C₄	1	1	yes	characteristic, complemented
80	#15267	C₂×C₄	1	1	yes	characteristic, complemented
81	#15267	C₂×C₄	1	1	yes	characteristic, complemented
82	#15259	C₂×C₄	1	1	yes	characteristic
83	#15259	D₄	1	1	yes	characteristic
84	#15259	D₄	1	1	yes	characteristic
85	#15259	C₂³	1	1	yes	characteristic
86	#15258	C₂×C₄	1	1	yes	characteristic
87	#15258	C₂×C₄	1	1	yes	characteristic
88	#15258	C₂×C₄	1	1	yes	characteristic
89	#15258	D₄	1	1	yes	characteristic
90	#15258	D₄	1	1	yes	characteristic
91	#15258	C₂³	1	1	yes	characteristic
92	#15258	C₂³	1	1	yes	characteristic
93	#15258	C₂³	1	1	yes	characteristic
94	#14698	D₄	1	1	yes	characteristic
95	#14661	D₄	1	1	yes	characteristic
96	#14507	C₂×C₄	1	1	yes	characteristic, complemented
97	#14365	C₂×C₄	1	1	yes	characteristic, complemented
98	#13959	C₂×C₄	1	1	yes	characteristic
99	#13959	D₄	1	1	yes	characteristic
100	#13902	D₄	1	1	yes	characteristic
101	#13807	C₂×C₄	1	1	yes	characteristic, complemented
102	C₂²⋊C₄²	C₂×C₄	1	1	yes	characteristic, complemented
103	C₄×#386	C₂×C₄	1	1	yes	characteristic
104	#8547	C₂³	1	2	yes	—
105	#8541	C₂³	1	2	yes	—
106	C₂⁷	C₂²⋊C₄	1	1	yes	characteristic
107	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
108	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
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
112	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
113	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
114	C₂²×#127	C₂²⋊C₄	1	1	yes	characteristic
115	C₂²×#127	C₂²⋊C₄	1	1	yes	characteristic
116	C₂²×#127	C₂²⋊C₄	1	1	yes	characteristic
117	C₂²×#127	C₂×D₄	1	1	yes	characteristic
118	C₂²×#127	C₂×D₄	1	1	yes	characteristic
119	C₂²×#127	C₂×D₄	1	1	yes	characteristic
120	C₂²×#127	C₂×D₄	1	1	yes	characteristic
121	C₂²×#124	C₂²⋊C₄	1	1	yes	characteristic
122	C₂²×#124	C₂²⋊C₄	1	1	yes	characteristic
123	C₂²×#124	C₂×D₄	1	1	yes	characteristic
124	C₂²×#123	C₂²⋊C₄	1	1	yes	characteristic
125	C₂²×#123	C₂²⋊C₄	1	1	yes	characteristic
126	C₂²×#123	C₂×D₄	1	1	yes	characteristic
127	C₂²×#121	C₂×D₄	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	1	yes	characteristic
131	C₂²×#120	C₂²⋊C₄	1	1	yes	characteristic
132	C₂²×#120	C₂²⋊C₄	1	1	yes	characteristic
133	C₂²×#120	C₂²⋊C₄	1	1	yes	characteristic
134	C₂²×#120	C₂²⋊C₄	1	1	yes	characteristic
135	C₂²×#120	C₂²×C₄	1	1	yes	characteristic
136	C₂²×#120	C₂×D₄	1	1	yes	characteristic
137	C₂²×#120	C₂×D₄	1	1	yes	characteristic
138	C₂²×#120	C₂×D₄	1	1	yes	characteristic
139	C₂²×#120	C₂×D₄	1	1	yes	characteristic
140	C₂²×#120	C₂⁴	1	1	yes	characteristic
141	C₂²×C₄×D₄	C₂²×C₄	1	1	yes	characteristic
142	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
143	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
144	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
145	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
146	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
147	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
148	C₂³×C₄²	C₂²⋊C₄	1	1	yes	characteristic
149	C₂×#394	C₂²⋊C₄	1	1	yes	characteristic
150	C₂×#394	C₂²⋊C₄	1	1	yes	characteristic
151	C₂×#393	C₂²⋊C₄	1	1	yes	characteristic
152	C₂×#393	C₂²⋊C₄	1	1	yes	characteristic
153	C₂×#393	C₂²×C₄	1	1	yes	characteristic
154	C₂×#393	C₂×D₄	1	1	yes	characteristic
155	C₂×#392	C₂²⋊C₄	1	1	yes	characteristic
156	C₂×#392	C₂²⋊C₄	1	1	yes	characteristic
157	C₂×#392	C₂²⋊C₄	1	1	yes	characteristic
158	C₂×#392	C₂²⋊C₄	1	1	yes	characteristic
159	C₂×#392	C₂²×C₄	1	1	yes	characteristic
160	C₂×#392	C₂²×C₄	1	1	yes	characteristic
161	C₂×#392	C₂²×C₄	1	1	yes	characteristic
162	C₂×#392	C₂×D₄	1	1	yes	characteristic
163	C₂×#392	C₂×D₄	1	1	yes	characteristic
164	C₂×#392	C₂×D₄	1	1	yes	characteristic
165	C₂×#386	C₂²⋊C₄	1	1	yes	characteristic
166	C₂×#386	C₂²⋊C₄	1	1	yes	characteristic
167	C₂×#386	C₂×D₄	1	1	yes	characteristic
168	C₂×#385	C₂²×C₄	1	1	yes	characteristic
169	C₂×#383	C₂²⋊C₄	1	1	yes	characteristic
170	C₂×#383	C₂²⋊C₄	1	1	yes	characteristic
171	C₂×#381	C₂²×C₄	1	1	yes	characteristic
172	C₂×#380	C₂²⋊C₄	1	1	yes	characteristic
173	C₂×#380	C₂²⋊C₄	1	1	yes	characteristic
174	C₂×#379	C₂²⋊C₄	1	1	yes	characteristic
175	C₂×#379	C₂²×C₄	1	1	yes	characteristic
176	C₂×#379	C₂²×C₄	1	1	yes	characteristic
177	C₂×#379	C₂×D₄	1	1	yes	characteristic
178	C₂×C₄×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
179	C₂×C₄×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
180	C₂×#376	C₂²⋊C₄	1	1	yes	characteristic
181	#1438	C₂²⋊C₄	1	1	yes	characteristic
182	#1438	C₂²⋊C₄	1	1	yes	characteristic
183	#1438	C₂²⋊C₄	1	1	yes	characteristic
184	#1438	C₂²⋊C₄	1	1	yes	characteristic
185	#1438	C₂×D₄	1	1	yes	characteristic
186	#1438	C₂×D₄	1	1	yes	characteristic
187	#1438	C₂×D₄	1	1	yes	characteristic
188	#1438	C₂×D₄	1	1	yes	characteristic
189	#1437	C₂²⋊C₄	1	1	yes	characteristic
190	#1437	C₂²⋊C₄	1	1	yes	characteristic
191	#1437	C₂²⋊C₄	1	1	yes	characteristic
192	#1437	C₂²⋊C₄	1	1	yes	characteristic
193	#1437	C₂²⋊C₄	1	1	yes	characteristic
194	#1437	C₂²⋊C₄	1	1	yes	characteristic
195	#1437	C₂²×C₄	1	1	yes	characteristic
196	#1437	C₂²×C₄	1	1	yes	characteristic
197	#1437	C₂²×C₄	1	1	yes	characteristic
198	#1437	C₂²×C₄	1	1	yes	characteristic
199	#1437	C₂×D₄	1	1	yes	characteristic
200	#1437	C₂×D₄	1	1	yes	characteristic
201	#1437	C₂×D₄	1	1	yes	characteristic
202	#1437	C₂×D₄	1	1	yes	characteristic
203	#1436	C₂²⋊C₄	1	1	yes	characteristic
204	#1436	C₂²⋊C₄	1	1	yes	characteristic
205	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
206	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
207	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
208	C₂⁶	#120	1	1	yes	characteristic
209	C₂⁶	#120	1	1	yes	characteristic
210	C₂⁶	C₂²×D₄	1	1	yes	characteristic
211	C₂³×Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
212	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
213	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
214	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
215	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
216	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
217	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
218	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
219	C₂³×D₄	#120	1	1	yes	characteristic
220	C₂³×D₄	#120	1	1	yes	characteristic
221	C₂³×D₄	#120	1	1	yes	characteristic
222	C₂³×D₄	#120	1	1	yes	characteristic
223	C₂³×D₄	#120	1	1	yes	characteristic
224	C₂³×D₄	#120	1	1	yes	characteristic
225	C₂³×D₄	#120	1	1	yes	characteristic
226	C₂³×D₄	#120	1	1	yes	characteristic
227	C₂³×D₄	#120	1	1	yes	characteristic
228	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
229	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
230	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
231	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
232	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
233	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
234	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
235	C₂⁴×C₄	#120	1	1	yes	characteristic
236	C₂⁴×C₄	#120	1	1	yes	characteristic
237	C₂×#123	#99	1	2	yes	—
238	C₂×#123	#99	1	2	yes	—
239	C₂×#120	#99	1	2	yes	—
240	C₂×#120	#99	1	2	yes	—
241	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
242	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
243	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
244	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
245	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
246	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
247	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
248	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
249	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
250	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
251	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
252	C₂²×C₂²⋊C₄	C₂³×C₄	1	1	yes	characteristic
253	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
254	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
255	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
256	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
257	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
258	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
259	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
260	C₂×#95	C₂×C₂²⋊C₄	1	1	yes	characteristic
261	C₂×#95	C₂×C₂²⋊C₄	1	1	yes	characteristic
262	C₂×#95	C₂×C₂²⋊C₄	1	1	yes	characteristic
263	C₂×#95	C₂×C₂²⋊C₄	1	1	yes	characteristic
264	C₂×#95	C₂×C₂²⋊C₄	1	1	yes	characteristic
265	C₂×#95	C₂×C₂²⋊C₄	1	1	yes	characteristic
266	C₂×#95	C₂×C₂²⋊C₄	1	1	yes	characteristic
267	C₂×#95	C₂×C₂²⋊C₄	1	1	yes	characteristic
268	C₂⁵	#379	1	1	yes	characteristic
269	C₂⁵	#379	1	1	yes	characteristic
270	C₂⁵	#379	1	1	yes	characteristic
271	C₂⁵	#379	1	1	yes	characteristic
272	C₂⁵	C₂×#99	1	2	yes	—
273	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
274	C₂⁵	C₂×#120	1	1	yes	characteristic
275	C₂⁵	C₂×#120	1	1	yes	characteristic
276	C₂⁵	C₂×#120	1	1	yes	characteristic
277	C₂²×D₄	C₂×#99	1	1	yes	characteristic
278	C₂²×D₄	C₂×#99	1	1	yes	characteristic
279	C₂²×D₄	C₂×#99	1	1	yes	characteristic
280	C₂²×D₄	C₂×#99	1	1	yes	characteristic
281	C₂²×D₄	B(4,𝔽₂)	1	1	yes	characteristic
282	C₂²×D₄	B(4,𝔽₂)	1	1	yes	characteristic
283	C₂²×D₄	#458	1	1	yes	characteristic
284	C₂²×D₄	#458	1	1	yes	characteristic
285	C₂³×C₄	#379	1	1	yes	characteristic
286	C₂³×C₄	#379	1	1	yes	characteristic
287	C₂³×C₄	#379	1	1	yes	characteristic
288	C₂³×C₄	#379	1	1	yes	characteristic
289	C₂³×C₄	C₂×#99	1	2	yes	—
290	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
291	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
292	C₂³×C₄	C₂×#120	1	1	yes	characteristic
293	C₂×C₂²⋊C₄	C₂×#99	1	2	yes	—
294	C₂×C₂²⋊C₄	C₂×#99	1	2	yes	—
295	C₂⁴	#1781	1	1	yes	characteristic
296	C₂⁴	#1781	1	1	yes	characteristic
297	C₂⁴	#1790	1	1	yes	characteristic
298	C₂⁴	#1790	1	1	yes	characteristic
299	C₂⁴	C₂×#379	1	1	yes	characteristic
300	C₂⁴	C₂²×#99	1	1	yes	characteristic
301	C₂⁴	C₂²×#99	1	1	yes	characteristic
302	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
303	C₂⁴	C₂×#458	1	1	yes	characteristic
304	C₂⁴	#3026	1	2	yes	—
305	C₂²×C₄	#1781	1	1	yes	characteristic
306	C₂²×C₄	#1781	1	1	yes	characteristic
307	C₂²×C₄	#1790	1	1	yes	characteristic
308	C₂²×C₄	#1790	1	1	yes	characteristic
309	C₂³	#12707	1	2	yes	—
310	C₂³	#12753	1	2	yes	—
311	C₂³	C₂×#1781	1	1	yes	characteristic
312	C₂³	C₂×#1790	1	1	yes	characteristic
313	C₂³	#20609	1	1	yes	characteristic
314	C₂³	#33359	1	2	yes	—
315	C₂²	#187928	1	1	yes	characteristic
316	C₂²	C₂×#12707	1	1	yes	characteristic
317	C₂²	#493430	1	1	yes	characteristic
318	C₂²	C₂×#12753	1	1	yes	characteristic
319	C₂²	#493594	1	1	yes	characteristic
320	C₂²	#493635	1	1	yes	characteristic
321	C₂²	#493635	1	1	yes	characteristic
322	C₂	#72232810	1	1	yes	characteristic
323	C₂	#72233333	1	1	yes	characteristic
324	C₂	#72255769	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	#187928
commutator	C₂²×C₂²⋊C₄	C₂³×C₄
Frattini, cosocle	C₂²×#120	C₂⁴
prime radical	#72234783	C₂
LCS	G ▷ C₂²×C₂²⋊C₄ ▷ C₂⁴ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂⁴ ◁ C₂²×D₄² ◁ G
LECS	G ▷ C₂²×#120 ▷ C₂⁴ ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72263156	C₂	semidirect
2. #72262837	C₂	semidirect
3. #72262522	C₂	semidirect
4. #72237598	C₂	semidirect
6. #72234778	C₂	semidirect
7. #72233243	C₂	semidirect
8. #72232808	C₂	semidirect
9. #72232743	C₂	semidirect
10. #72232735	C₂	semidirect
11. #72219461	C₂	semidirect
12. C₂×#57971	C₄	semidirect
14. #6385971	C₂²	semidirect
15. #4599081	C₄	semidirect
19. #4378714	C₄	semidirect
21. #2032088	C₄	semidirect
22. #1465620	C₄	semidirect
25. #648360	C₄	semidirect
26. #634305	C₄	semidirect
27. #534229	C₄	semidirect
28. #188087	C₂²	semidirect
29. #188035	C₂²	semidirect
30. #188035	C₂²	semidirect
31. #139720	C₂²	semidirect
32. #139718	C₂²	semidirect
33. #139718	C₂²	semidirect
34. #139718	C₂²	semidirect
35. #139504	C₂²	semidirect
36. #139504	C₂²	semidirect
37. #139504	C₂²	semidirect
38. #139486	C₂²	semidirect
39. #133893	C₂²	semidirect
40. #133825	C₂²	semidirect
41. #115631	C₂²	semidirect
42. #115163	C₂²	semidirect
48. C₂×#2760	C₂×C₄	semidirect
49. C₂×#2670	C₂×C₄	semidirect
50. C₂×#2815	C₂×C₄	semidirect
59. C₂×#2403	C₂×C₄	semidirect
70. #15635	C₂×C₄	semidirect
71. #15622	C₂×C₄	semidirect
72. #15467	C₂×C₄	semidirect
73. #15420	C₂×C₄	semidirect
74. #15420	C₂×C₄	semidirect
79. #15267	C₂×C₄	semidirect
80. #15267	C₂×C₄	semidirect
81. #15267	C₂×C₄	semidirect
96. #14507	C₂×C₄	semidirect
97. #14365	C₂×C₄	semidirect
101. #13807	C₂×C₄	semidirect
102. C₂²⋊C₄²	C₂×C₄	semidirect

Maximal subgroups

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

subgroup	index
#72263156	2
#72262837	2
#72262522	2
#72237598	2
#72234783	2
#72234778	2
#72233243	2
#72232808	2
#72232743	2
#72232735	2
#72219461	2