Subgroups — #72263243

Order 2048.

At least 6964 conjugacy classes of subgroups; only the 342 normal subgroups are shown.

The subgroup lattice has 318 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72263241	C₂	1	1	yes	maximal, characteristic
2	#72263135	C₂	1	2	yes	maximal, complemented
3	#72262841	C₂	1	2	yes	maximal, complemented
4	#72262519	C₂	1	2	yes	maximal, complemented
5	#72234778	C₂	1	1	yes	maximal, characteristic, complemented
6	#72234778	C₂	1	1	yes	maximal, characteristic, complemented
7	#72233241	C₂	1	1	yes	maximal, characteristic, complemented
8	#72233060	C₂	1	1	yes	maximal, characteristic, complemented
9	#72232741	C₂	1	1	yes	maximal, characteristic, complemented
10	#72232741	C₂	1	1	yes	maximal, characteristic, complemented
11	#72219512	C₂	1	2	yes	maximal, complemented
12	#6385971	C₂²	1	1	yes	characteristic, complemented
13	#6385971	C₂²	1	1	yes	characteristic, complemented
14	#5486612	C₄	1	1	yes	characteristic, complemented
15	#5486439	C₄	1	1	yes	characteristic, complemented
16	#5236488	C₄	1	1	yes	characteristic, complemented
17	#5065227	C₂²	1	1	yes	characteristic
18	#4607564	C₂²	1	1	yes	characteristic
19	#4467031	C₄	1	1	yes	characteristic, complemented
20	#4418479	C₄	1	1	yes	characteristic, complemented
21	#4418479	C₂²	1	1	yes	characteristic
22	#4111277	C₄	1	1	yes	characteristic, complemented
23	#2356274	C₂²	1	1	yes	characteristic
24	#2032505	C₄	1	1	yes	characteristic, complemented
25	#1418393	C₂²	1	1	yes	characteristic
26	#687584	C₂²	1	1	yes	characteristic
27	#647656	C₄	1	1	yes	characteristic, complemented
28	#647656	C₂²	1	1	yes	characteristic
29	#188087	C₂²	1	1	yes	characteristic, complemented
30	#188087	C₂²	1	1	yes	characteristic, complemented
31	#139716	C₂²	1	2	yes	—
32	#139716	C₂²	1	2	yes	—
33	#139716	C₂²	1	2	yes	complemented
34	#139716	C₂²	1	2	yes	complemented
35	#139504	C₂²	1	2	yes	complemented
36	#139504	C₂²	1	2	yes	complemented
37	#139486	C₂²	1	2	yes	complemented
38	#139486	C₂²	1	2	yes	complemented
39	#135561	C₂²	1	2	yes	complemented
40	#134083	C₂²	1	2	yes	complemented
41	#119550	C₂²	1	2	yes	complemented
42	#115163	C₂²	1	2	yes	complemented
43	C₂²×D₄²	C₂×C₄	1	1	yes	characteristic, complemented
44	C₂²×D₄²	C₂³	1	1	yes	characteristic
45	C₂²×#534	D₄	1	1	yes	characteristic
46	C₂³×#120	D₄	1	1	yes	characteristic
47	C₂³×#120	D₄	1	1	yes	characteristic
48	C₂×#2684	C₂×C₄	1	1	yes	characteristic, complemented
49	C₂×#2846	C₂×C₄	1	1	yes	characteristic
50	C₂×#2410	C₂³	1	1	yes	characteristic
51	C₂×#2403	D₄	1	1	yes	characteristic
52	C₂×#2657	C₂×C₄	1	1	yes	characteristic
53	C₂×#2631	D₄	1	1	yes	characteristic
54	C₂×#2631	D₄	1	1	yes	characteristic
55	#21746	C₂³	1	2	yes	—
56	#21746	C₂³	1	2	yes	—
57	#17272	C₂×C₄	1	1	yes	characteristic, complemented
58	#17271	C₂×C₄	1	1	yes	characteristic, complemented
59	#15950	D₄	1	1	yes	characteristic
60	#15948	C₂×C₄	1	1	yes	characteristic
61	#15947	C₂×C₄	1	1	yes	characteristic
62	#15947	C₂×C₄	1	1	yes	characteristic, complemented
63	#15947	C₂³	1	1	yes	characteristic
64	#15947	C₂³	1	1	yes	characteristic
65	#15313	C₂×C₄	1	1	yes	characteristic, complemented
66	#15266	C₂×C₄	1	1	yes	characteristic, complemented
67	#15261	C₂×C₄	1	1	yes	characteristic
68	#15260	D₄	1	1	yes	characteristic
69	#15259	C₂×C₄	1	1	yes	characteristic
70	#15259	C₂×C₄	1	1	yes	characteristic, complemented
71	#15259	C₂×C₄	1	1	yes	characteristic, complemented
72	#15259	D₄	1	1	yes	characteristic
73	#15259	D₄	1	1	yes	characteristic
74	#15259	C₂³	1	1	yes	characteristic
75	#15258	C₂×C₄	1	1	yes	characteristic
76	#15258	C₂×C₄	1	1	yes	characteristic
77	#15258	C₂×C₄	1	1	yes	characteristic
78	#15258	C₂×C₄	1	1	yes	characteristic
79	#15258	C₂×C₄	1	1	yes	characteristic, complemented
80	#15258	D₄	1	1	yes	characteristic
81	#15258	D₄	1	1	yes	characteristic
82	#15258	C₂³	1	1	yes	characteristic
83	#15257	D₄	1	1	yes	characteristic
84	#15257	D₄	1	1	yes	characteristic
85	#15257	D₄	1	1	yes	characteristic
86	#15257	D₄	1	1	yes	characteristic
87	#15257	D₄	1	1	yes	characteristic
88	#15257	D₄	1	1	yes	characteristic
89	#14666	C₂×C₄	1	1	yes	characteristic, complemented
90	#14661	C₂×C₄	1	1	yes	characteristic
91	#14661	C₂×C₄	1	1	yes	characteristic, complemented
92	#14492	C₂×C₄	1	1	yes	characteristic, complemented
93	#14358	C₂×C₄	1	1	yes	characteristic, complemented
94	#14358	C₂×C₄	1	1	yes	characteristic, complemented
95	#14255	C₂³	1	1	yes	characteristic
96	#14134	C₂×C₄	1	1	yes	characteristic
97	#14134	C₂×C₄	1	1	yes	characteristic, complemented
98	#13959	D₄	1	1	yes	characteristic
99	#13959	D₄	1	1	yes	characteristic
100	#13867	D₄	1	1	yes	characteristic
101	#13867	D₄	1	1	yes	characteristic
102	#13867	D₄	1	1	yes	characteristic
103	C₂×#1438	D₄	1	1	yes	characteristic
104	#8547	C₂³	1	2	yes	—
105	#8547	C₂³	1	2	yes	—
106	C₂⁷	C₂²⋊C₄	1	1	yes	characteristic
107	C₂⁴×D₄	C₂×D₄	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	C₂²×#127	C₂²⋊C₄	1	1	yes	characteristic
113	C₂²×#127	C₂²×C₄	1	1	yes	characteristic
114	C₂²×#127	C₂²×C₄	1	1	yes	characteristic
115	C₂²×#124	C₂²⋊C₄	1	1	yes	characteristic
116	C₂²×#124	C₂²⋊C₄	1	1	yes	characteristic
117	C₂²×#124	C₂²×C₄	1	1	yes	characteristic
118	C₂²×#123	C₂²⋊C₄	1	1	yes	characteristic
119	C₂²×#123	C₂²⋊C₄	1	1	yes	characteristic
120	C₂²×#121	C₂×D₄	1	1	yes	characteristic
121	C₂²×#121	C₂×D₄	1	1	yes	characteristic
122	C₂²×#121	C₂×D₄	1	1	yes	characteristic
123	C₂²×#121	C₂×D₄	1	1	yes	characteristic
124	C₂²×#120	C₂²⋊C₄	1	1	yes	characteristic
125	C₂²×#120	C₂²⋊C₄	1	1	yes	characteristic
126	C₂²×#120	C₂²⋊C₄	1	1	yes	characteristic
127	C₂²×#120	C₂²⋊C₄	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	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	C₂×D₄	1	1	yes	characteristic
141	C₂²×#120	C₂×D₄	1	1	yes	characteristic
142	C₂²×#120	C₂⁴	1	1	yes	characteristic
143	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×D₄	C₂×D₄	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×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
149	C₂×#393	C₂²⋊C₄	1	1	yes	characteristic
150	C₂×#393	C₂²⋊C₄	1	1	yes	characteristic
151	C₂×#393	C₂×D₄	1	1	yes	characteristic
152	C₂×#393	C₂×D₄	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×#386	C₂²⋊C₄	1	1	yes	characteristic
158	C₂×#386	C₂²⋊C₄	1	1	yes	characteristic
159	C₂×#386	C₂²×C₄	1	1	yes	characteristic
160	C₂×#385	C₂×D₄	1	1	yes	characteristic
161	C₂×#383	C₂²⋊C₄	1	1	yes	characteristic
162	C₂×#383	C₂²⋊C₄	1	1	yes	characteristic
163	C₂×#379	C₂²⋊C₄	1	1	yes	characteristic
164	C₂×#379	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×#379	C₂×D₄	1	1	yes	characteristic
168	C₂×#376	C₂²⋊C₄	1	1	yes	characteristic
169	#1440	C₂²⋊C₄	1	1	yes	characteristic
170	#1440	C₂²⋊C₄	1	1	yes	characteristic
171	#1440	C₂×D₄	1	1	yes	characteristic
172	#1440	C₂×D₄	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	C₂²⋊C₄	1	1	yes	characteristic
184	#1438	C₂²⋊C₄	1	1	yes	characteristic
185	#1438	C₂²⋊C₄	1	1	yes	characteristic
186	#1438	C₂²⋊C₄	1	1	yes	characteristic
187	#1438	C₂²×C₄	1	1	yes	characteristic
188	#1438	C₂²×C₄	1	1	yes	characteristic
189	#1438	C₂²×C₄	1	1	yes	characteristic
190	#1438	C₂²×C₄	1	1	yes	characteristic
191	#1438	C₂²×C₄	1	1	yes	characteristic
192	#1438	C₂²×C₄	1	1	yes	characteristic
193	#1438	C₂×D₄	1	1	yes	characteristic
194	#1438	C₂×D₄	1	1	yes	characteristic
195	#1438	C₂×D₄	1	1	yes	characteristic
196	#1438	C₂×D₄	1	1	yes	characteristic
197	#1437	C₂²⋊C₄	1	1	yes	characteristic
198	#1437	C₂²⋊C₄	1	1	yes	characteristic
199	#1437	C₂²⋊C₄	1	1	yes	characteristic
200	#1437	C₂²⋊C₄	1	1	yes	characteristic
201	#1437	C₂×D₄	1	1	yes	characteristic
202	#1437	C₂×D₄	1	1	yes	characteristic
203	#1437	C₂×D₄	1	1	yes	characteristic
204	#1437	C₂×D₄	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	C₂×C₂²⋊C₄	1	1	yes	characteristic
209	C₂⁶	#120	1	1	yes	characteristic
210	C₂⁶	#120	1	1	yes	characteristic
211	C₂⁶	C₂²×D₄	1	1	yes	characteristic
212	C₂³×Q₈	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	C₂×C₂²⋊C₄	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	C₂³×C₄	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	#120	1	1	yes	characteristic
232	C₂⁴×C₄	#120	1	1	yes	characteristic
233	C₂⁴×C₄	#120	1	1	yes	characteristic
234	C₂⁴×C₄	#120	1	1	yes	characteristic
235	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
236	C₂²×C₄⋊C₄	#120	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	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	C₂×C₂²⋊C₄	1	1	yes	characteristic
251	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
252	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
253	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
254	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
255	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
256	C₂²×C₂²⋊C₄	C₂²×D₄	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	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	C₂²×C₂²⋊C₄	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	C₂×#120	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	C₂²×C₄	#1790	1	1	yes	characteristic
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	C₂³	#12753	1	2	yes	—
302	C₂³	#12753	1	2	yes	—
303	C₂³	#20585	1	1	yes	characteristic
304	C₂³	C₂×#1790	1	1	yes	characteristic
305	C₂³	C₂×#1790	1	1	yes	characteristic
306	C₂³	#33551	1	2	yes	—
307	C₂²	#187940	1	1	yes	characteristic
308	C₂²	#493474	1	1	yes	characteristic
309	C₂²	#493478	1	1	yes	characteristic
310	C₂²	C₂×#12753	1	1	yes	characteristic
311	C₂²	C₂×#12753	1	1	yes	characteristic
312	C₂²	#493582	1	1	yes	characteristic
313	C₂²	#493594	1	1	yes	characteristic
314	C₂	#72232777	1	1	yes	characteristic
315	C₂	#72249372	1	1	yes	characteristic
316	C₂	#72255723	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	#187940
commutator	C₂³×D₄	C₂³×C₄
Frattini, cosocle	C₂²×#120	C₂⁴
prime radical	#72263241	C₂
LCS	G ▷ C₂³×D₄ ▷ 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
2. #72263135	C₂	semidirect
3. #72262841	C₂	semidirect
4. #72262519	C₂	semidirect
5. #72234778	C₂	semidirect
6. #72234778	C₂	semidirect
7. #72233241	C₂	semidirect
8. #72233060	C₂	semidirect
9. #72232741	C₂	semidirect
10. #72232741	C₂	semidirect
11. #72219512	C₂	semidirect
12. #6385971	C₂²	semidirect
13. #6385971	C₂²	semidirect
14. #5486612	C₄	semidirect
15. #5486439	C₄	semidirect
16. #5236488	C₄	semidirect
19. #4467031	C₄	semidirect
20. #4418479	C₄	semidirect
22. #4111277	C₄	semidirect
24. #2032505	C₄	semidirect
27. #647656	C₄	semidirect
29. #188087	C₂²	semidirect
30. #188087	C₂²	semidirect
33. #139716	C₂²	semidirect
34. #139716	C₂²	semidirect
35. #139504	C₂²	semidirect
36. #139504	C₂²	semidirect
37. #139486	C₂²	semidirect
38. #139486	C₂²	semidirect
39. #135561	C₂²	semidirect
40. #134083	C₂²	semidirect
41. #119550	C₂²	semidirect
42. #115163	C₂²	semidirect
43. C₂²×D₄²	C₂×C₄	semidirect
48. C₂×#2684	C₂×C₄	semidirect
57. #17272	C₂×C₄	semidirect
58. #17271	C₂×C₄	semidirect
62. #15947	C₂×C₄	semidirect
65. #15313	C₂×C₄	semidirect
66. #15266	C₂×C₄	semidirect
70. #15259	C₂×C₄	semidirect
71. #15259	C₂×C₄	semidirect
79. #15258	C₂×C₄	semidirect
89. #14666	C₂×C₄	semidirect
91. #14661	C₂×C₄	semidirect
92. #14492	C₂×C₄	semidirect
93. #14358	C₂×C₄	semidirect
94. #14358	C₂×C₄	semidirect
97. #14134	C₂×C₄	semidirect

Maximal subgroups

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

subgroup	index
#72263241	2
#72263135	2
#72262841	2
#72262519	2
#72234778	2
#72233241	2
#72233060	2
#72232741	2
#72219512	2