Subgroups — #72263061

Order 2048.

At least 7561 conjugacy classes of subgroups; only the 350 normal subgroups are shown.

The subgroup lattice has 321 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72263060	C₂	1	2	yes	maximal, complemented
2	#72263059	C₂	1	1	yes	maximal, characteristic
3	#72262516	C₂	1	2	yes	maximal, complemented
4	#72233277	C₂	1	1	yes	maximal, characteristic, complemented
5	#72233277	C₂	1	1	yes	maximal, characteristic, complemented
6	#72233244	C₂	1	1	yes	maximal, characteristic, complemented
7	#72233060	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	#72232743	C₂	1	1	yes	maximal, characteristic, complemented
11	#72219507	C₂	1	2	yes	maximal, complemented
12	#6385971	C₂²	1	1	yes	characteristic, complemented
13	#6385971	C₂²	1	1	yes	characteristic, complemented
14	#4122222	C₄	1	1	yes	characteristic, complemented
15	#4122222	C₄	1	1	yes	characteristic, complemented
16	#4037130	C₄	1	1	yes	characteristic, complemented
17	#4035351	C₄	1	1	yes	characteristic, complemented
18	#2805719	C₂²	1	1	yes	characteristic
19	#2108865	C₂²	1	1	yes	characteristic
20	#2080819	C₂²	1	1	yes	characteristic
21	#2065520	C₄	1	1	yes	characteristic, complemented
22	#2032444	C₄	1	1	yes	characteristic, complemented
23	#1494104	C₂²	1	1	yes	characteristic
24	#687584	C₂²	1	1	yes	characteristic
25	#675267	C₄	1	1	yes	characteristic, complemented
26	#652666	C₄	1	1	yes	characteristic, complemented
27	#649038	C₂²	1	1	yes	characteristic
28	#649038	C₂²	1	1	yes	characteristic
29	#188151	C₂²	1	1	yes	characteristic, complemented
30	#188035	C₂²	1	1	yes	characteristic, complemented
31	#139718	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	#139504	C₂²	1	2	yes	complemented
39	#135507	C₂²	1	2	yes	complemented
40	#133893	C₂²	1	2	yes	complemented
41	#119550	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×#127	D₄	1	1	yes	characteristic
47	C₂×#2675	C₂×C₄	1	1	yes	characteristic, complemented
48	C₂×#2433	C₂×C₄	1	1	yes	characteristic
49	C₂×#2433	C₂×C₄	1	1	yes	characteristic
50	C₂×#2408	D₄	1	1	yes	characteristic
51	C₂×#2408	D₄	1	1	yes	characteristic
52	C₂×#2410	C₂³	1	1	yes	characteristic
53	C₂×#2403	C₂×C₄	1	1	yes	characteristic, complemented
54	C₂×#2403	D₄	1	1	yes	characteristic
55	#21746	C₂³	1	2	yes	—
56	#21746	C₂³	1	2	yes	—
57	#17102	C₂×C₄	1	1	yes	characteristic, complemented
58	#17102	C₂×C₄	1	1	yes	characteristic, complemented
59	#15950	C₂×C₄	1	1	yes	characteristic
60	#15948	D₄	1	1	yes	characteristic
61	#15947	D₄	1	1	yes	characteristic
62	#15649	C₂×C₄	1	1	yes	characteristic, complemented
63	#15636	C₂×C₄	1	1	yes	characteristic, complemented
64	#15635	C₂×C₄	1	1	yes	characteristic, complemented
65	#15420	C₂×C₄	1	1	yes	characteristic, complemented
66	#15310	C₂×C₄	1	1	yes	characteristic
67	#15310	C₂×C₄	1	1	yes	characteristic
68	#15310	C₂×C₄	1	1	yes	characteristic
69	#15310	C₂×C₄	1	1	yes	characteristic
70	#15310	D₄	1	1	yes	characteristic
71	#15310	D₄	1	1	yes	characteristic
72	#15310	D₄	1	1	yes	characteristic
73	#15310	D₄	1	1	yes	characteristic
74	#15267	C₂×C₄	1	1	yes	characteristic, complemented
75	#15267	C₂×C₄	1	1	yes	characteristic, complemented
76	#15261	D₄	1	1	yes	characteristic
77	#15260	C₂×C₄	1	1	yes	characteristic
78	#15258	D₄	1	1	yes	characteristic
79	#15258	D₄	1	1	yes	characteristic
80	#15258	D₄	1	1	yes	characteristic
81	#15258	D₄	1	1	yes	characteristic
82	#15258	D₄	1	1	yes	characteristic
83	#15258	C₂³	1	1	yes	characteristic
84	#15258	C₂³	1	1	yes	characteristic
85	#15258	C₂³	1	1	yes	characteristic
86	#15258	C₂³	1	1	yes	characteristic
87	#15257	C₂×C₄	1	1	yes	characteristic
88	#15257	C₂×C₄	1	1	yes	characteristic
89	#14698	C₂×C₄	1	1	yes	characteristic
90	#14698	C₂×C₄	1	1	yes	characteristic
91	#14567	C₂×C₄	1	1	yes	characteristic, complemented
92	#14533	C₂×C₄	1	1	yes	characteristic, complemented
93	#14365	C₂×C₄	1	1	yes	characteristic, complemented
94	#14255	C₂³	1	1	yes	characteristic
95	#14207	C₂×C₄	1	1	yes	characteristic, complemented
96	#14207	C₂×C₄	1	1	yes	characteristic, complemented
97	#13902	D₄	1	1	yes	characteristic
98	#13902	D₄	1	1	yes	characteristic
99	#13867	D₄	1	1	yes	characteristic
100	C₂×#1438	D₄	1	1	yes	characteristic
101	#13823	C₂×C₄	1	1	yes	characteristic, complemented
102	C₄×#386	D₄	1	1	yes	characteristic
103	C₄×#386	D₄	1	1	yes	characteristic
104	#8547	C₂³	1	2	yes	—
105	#8541	C₂³	1	2	yes	—
106	C₂⁴×D₄	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	C₂²×#127	C₂²⋊C₄	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×#127	C₂×D₄	1	1	yes	characteristic
122	C₂²×#123	C₂²⋊C₄	1	1	yes	characteristic
123	C₂²×#123	C₂²⋊C₄	1	1	yes	characteristic
124	C₂²×#121	C₂²×C₄	1	1	yes	characteristic
125	C₂²×#121	C₂²×C₄	1	1	yes	characteristic
126	C₂²×#121	C₂×D₄	1	1	yes	characteristic
127	C₂²×#121	C₂×D₄	1	1	yes	characteristic
128	C₂²×#120	C₂²⋊C₄	1	1	yes	characteristic
129	C₂²×#120	C₂²⋊C₄	1	1	yes	characteristic
130	C₂²×#120	C₂²⋊C₄	1	1	yes	characteristic
131	C₂²×#120	C₂²⋊C₄	1	1	yes	characteristic
132	C₂²×#120	C₂×D₄	1	1	yes	characteristic
133	C₂²×#120	C₂×D₄	1	1	yes	characteristic
134	C₂²×#120	C₂×D₄	1	1	yes	characteristic
135	C₂²×#120	C₂×D₄	1	1	yes	characteristic
136	C₂²×#120	C₂⁴	1	1	yes	characteristic
137	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
139	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
140	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
141	C₂³×C₄²	C₂²⋊C₄	1	1	yes	characteristic
142	C₂³×C₄²	C₂²⋊C₄	1	1	yes	characteristic
143	C₂×#394	C₂²⋊C₄	1	1	yes	characteristic
144	C₂×#394	C₂²⋊C₄	1	1	yes	characteristic
145	C₂×#394	C₂²⋊C₄	1	1	yes	characteristic
146	C₂×#394	C₂²⋊C₄	1	1	yes	characteristic
147	C₂×#392	C₂²⋊C₄	1	1	yes	characteristic
148	C₂×#392	C₂²⋊C₄	1	1	yes	characteristic
149	C₂×#392	C₂²⋊C₄	1	1	yes	characteristic
150	C₂×#392	C₂²⋊C₄	1	1	yes	characteristic
151	C₂×#392	C₂²×C₄	1	1	yes	characteristic
152	C₂×#392	C₂²×C₄	1	1	yes	characteristic
153	C₂×#392	C₂²×C₄	1	1	yes	characteristic
154	C₂×#392	C₂²×C₄	1	1	yes	characteristic
155	C₂×#392	C₂×D₄	1	1	yes	characteristic
156	C₂×#392	C₂×D₄	1	1	yes	characteristic
157	C₂×#392	C₂×D₄	1	1	yes	characteristic
158	C₂×#392	C₂×D₄	1	1	yes	characteristic
159	C₂×#386	C₂²⋊C₄	1	1	yes	characteristic
160	C₂×#386	C₂²⋊C₄	1	1	yes	characteristic
161	C₂×#386	C₂×D₄	1	1	yes	characteristic
162	C₂×#385	C₂²×C₄	1	1	yes	characteristic
163	C₂×#380	C₂²⋊C₄	1	1	yes	characteristic
164	C₂×#380	C₂²⋊C₄	1	1	yes	characteristic
165	C₂×#379	C₂²×C₄	1	1	yes	characteristic
166	C₂×#379	C₂×D₄	1	1	yes	characteristic
167	C₂×C₄×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
168	C₂×C₄×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
169	#1440	C₂²×C₄	1	1	yes	characteristic
170	#1440	C₂²×C₄	1	1	yes	characteristic
171	#1438	C₂²⋊C₄	1	1	yes	characteristic
172	#1438	C₂²⋊C₄	1	1	yes	characteristic
173	#1438	C₂²⋊C₄	1	1	yes	characteristic
174	#1438	C₂²⋊C₄	1	1	yes	characteristic
175	#1438	C₂²⋊C₄	1	1	yes	characteristic
176	#1438	C₂²⋊C₄	1	1	yes	characteristic
177	#1438	C₂²⋊C₄	1	1	yes	characteristic
178	#1438	C₂²⋊C₄	1	1	yes	characteristic
179	#1438	C₂²⋊C₄	1	1	yes	characteristic
180	#1438	C₂²⋊C₄	1	1	yes	characteristic
181	#1438	C₂²⋊C₄	1	1	yes	characteristic
182	#1438	C₂²⋊C₄	1	1	yes	characteristic
183	#1438	C₂×D₄	1	1	yes	characteristic
184	#1438	C₂×D₄	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	C₂×D₄	1	1	yes	characteristic
198	#1437	C₂×D₄	1	1	yes	characteristic
199	#1437	C₂×D₄	1	1	yes	characteristic
200	#1437	C₂×D₄	1	1	yes	characteristic
201	#1436	C₂²⋊C₄	1	1	yes	characteristic
202	#1436	C₂²⋊C₄	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	#120	1	1	yes	characteristic
207	C₂⁶	#120	1	1	yes	characteristic
208	C₂⁶	#120	1	1	yes	characteristic
209	C₂⁶	C₂²×D₄	1	1	yes	characteristic
210	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
211	C₂³×D₄	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	C₂×C₂²⋊C₄	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	C₂²×D₄	1	1	yes	characteristic
228	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
229	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
230	C₂⁴×C₄	C₂×C₂²⋊C₄	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	#120	1	1	yes	characteristic
234	C₂⁴×C₄	#120	1	1	yes	characteristic
235	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
236	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
237	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
238	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
239	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
240	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
241	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
242	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	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	#120	1	1	yes	characteristic
246	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
247	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
248	C₂²×C₂²⋊C₄	C₂³×C₄	1	1	yes	characteristic
249	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
250	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
251	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
252	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
253	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
254	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
255	C₂²×C₄²	#120	1	1	yes	characteristic
256	C₂×#95	C₂×C₂²⋊C₄	1	1	yes	characteristic
257	C₂×#95	C₂×C₂²⋊C₄	1	1	yes	characteristic
258	C₂×#95	C₂×C₂²⋊C₄	1	1	yes	characteristic
259	C₂×#95	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	C₂⁵	#379	1	1	yes	characteristic
265	C₂⁵	#379	1	1	yes	characteristic
266	C₂⁵	#379	1	1	yes	characteristic
267	C₂⁵	#379	1	1	yes	characteristic
268	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
269	C₂⁵	C₂×#120	1	1	yes	characteristic
270	C₂⁵	C₂×#120	1	1	yes	characteristic
271	C₂⁵	C₂×#120	1	1	yes	characteristic
272	C₂²×D₄	B(4,𝔽₂)	1	1	yes	characteristic
273	C₂²×D₄	B(4,𝔽₂)	1	1	yes	characteristic
274	C₂²×D₄	B(4,𝔽₂)	1	1	yes	characteristic
275	C₂²×D₄	B(4,𝔽₂)	1	1	yes	characteristic
276	C₂²×D₄	#458	1	1	yes	characteristic
277	C₂²×D₄	#458	1	1	yes	characteristic
278	C₂²×D₄	#458	1	1	yes	characteristic
279	C₂²×D₄	#458	1	1	yes	characteristic
280	C₂³×C₄	#379	1	1	yes	characteristic
281	C₂³×C₄	#379	1	1	yes	characteristic
282	C₂³×C₄	#379	1	1	yes	characteristic
283	C₂³×C₄	#379	1	1	yes	characteristic
284	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
285	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
286	C₂³×C₄	C₂×#120	1	1	yes	characteristic
287	C₂⁴	#1790	1	1	yes	characteristic
288	C₂⁴	#1790	1	1	yes	characteristic
289	C₂⁴	#1790	1	1	yes	characteristic
290	C₂⁴	#1790	1	1	yes	characteristic
291	C₂⁴	C₂×#379	1	1	yes	characteristic
292	C₂⁴	#2883	1	2	yes	—
293	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
294	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
295	C₂⁴	C₂×#458	1	1	yes	characteristic
296	C₂⁴	C₂×#458	1	1	yes	characteristic
297	C₂×D₄	#2196	1	4	yes	—
298	C₂²×C₄	#1790	1	1	yes	characteristic
299	C₂²×C₄	#1790	1	1	yes	characteristic
300	C₂²×C₄	#1790	1	1	yes	characteristic
301	C₂²×C₄	#1790	1	1	yes	characteristic
302	C₂³	#12753	1	2	yes	—
303	C₂³	#12759	1	2	yes	—
304	C₂³	#20585	1	1	yes	characteristic
305	C₂³	C₂×#1790	1	1	yes	characteristic
306	C₂³	C₂×#1790	1	1	yes	characteristic
307	C₂³	C₂×#2196	1	2	yes	—
308	C₂×C₄	#12759	1	2	yes	—
309	C₂×C₄	#12767	1	2	yes	—
310	C₂²	#187940	1	1	yes	characteristic
311	C₂²	#493480	1	1	yes	characteristic
312	C₂²	#493484	1	1	yes	characteristic
313	C₂²	C₂×#12753	1	1	yes	characteristic
314	C₂²	#493562	1	1	yes	characteristic
315	C₂²	C₂×#12759	1	1	yes	characteristic
316	C₂²	C₂×#12767	1	1	yes	characteristic
317	C₂	#72232749	1	1	yes	characteristic
318	C₂	#72232779	1	1	yes	characteristic
319	C₂	#72255738	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	#187940
commutator	C₂²×C₂²⋊C₄	C₂³×C₄
Frattini, cosocle	C₂²×#120	C₂⁴
prime radical	#72263059	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. #72263060	C₂	semidirect
3. #72262516	C₂	semidirect
4. #72233277	C₂	semidirect
5. #72233277	C₂	semidirect
6. #72233244	C₂	semidirect
7. #72233060	C₂	semidirect
8. #72232808	C₂	semidirect
9. #72232743	C₂	semidirect
10. #72232743	C₂	semidirect
11. #72219507	C₂	semidirect
12. #6385971	C₂²	semidirect
13. #6385971	C₂²	semidirect
14. #4122222	C₄	semidirect
15. #4122222	C₄	semidirect
16. #4037130	C₄	semidirect
17. #4035351	C₄	semidirect
21. #2065520	C₄	semidirect
22. #2032444	C₄	semidirect
25. #675267	C₄	semidirect
26. #652666	C₄	semidirect
29. #188151	C₂²	semidirect
30. #188035	C₂²	semidirect
31. #139718	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. #139504	C₂²	semidirect
39. #135507	C₂²	semidirect
40. #133893	C₂²	semidirect
41. #119550	C₂²	semidirect
42. #115163	C₂²	semidirect
47. C₂×#2675	C₂×C₄	semidirect
53. C₂×#2403	C₂×C₄	semidirect
57. #17102	C₂×C₄	semidirect
58. #17102	C₂×C₄	semidirect
62. #15649	C₂×C₄	semidirect
63. #15636	C₂×C₄	semidirect
64. #15635	C₂×C₄	semidirect
65. #15420	C₂×C₄	semidirect
74. #15267	C₂×C₄	semidirect
75. #15267	C₂×C₄	semidirect
91. #14567	C₂×C₄	semidirect
92. #14533	C₂×C₄	semidirect
93. #14365	C₂×C₄	semidirect
95. #14207	C₂×C₄	semidirect
96. #14207	C₂×C₄	semidirect
101. #13823	C₂×C₄	semidirect

Maximal subgroups

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

subgroup	index
#72263060	2
#72263059	2
#72262516	2
#72233277	2
#72233244	2
#72233060	2
#72232808	2
#72232743	2
#72219507	2