Subgroups — #72266700

Order 2048.

At least 7826 conjugacy classes of subgroups; only the 360 normal subgroups are shown.

The subgroup lattice has 334 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72266699	C₂	1	2	yes	maximal, complemented
2	#72266698	C₂	1	2	yes	maximal, complemented
3	#72266041	C₂	1	1	yes	maximal, characteristic, complemented
4	#72263135	C₂	1	2	yes	maximal, complemented
5	#72258912	C₂	1	1	yes	maximal, characteristic
6	#72238446	C₂	1	1	yes	maximal, characteristic, complemented
7	#72233645	C₂	1	2	yes	maximal, complemented
8	#72232723	C₂	1	1	yes	maximal, characteristic, complemented
9	#72232723	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#139716	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#139716	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#21746	C₂²	1	1	yes	characteristic
13	C₂×#21746	C₂²	1	1	yes	characteristic
14	#5063443	C₄	1	1	yes	characteristic, complemented
15	#5063443	C₂²	1	1	yes	characteristic
16	#5063442	C₄	1	1	yes	characteristic, complemented
17	#5063442	C₂²	1	1	yes	characteristic
18	#4464171	C₄	1	1	yes	characteristic, complemented
19	#2356274	C₄	1	1	yes	characteristic, complemented
20	#2356274	C₂²	1	1	yes	characteristic
21	#2108839	C₄	1	1	yes	characteristic, complemented
22	#2108839	C₂²	1	1	yes	characteristic
23	#616961	C₄	1	1	yes	characteristic, complemented
24	#616961	C₂²	1	1	yes	characteristic
25	C₂×#15947	C₂²	1	1	yes	characteristic
26	#556752	C₄	1	1	yes	characteristic, complemented
27	#556752	C₂²	1	1	yes	characteristic
28	#552671	C₄	1	1	yes	characteristic, complemented
29	C₂×#8547	C₂²	1	1	yes	characteristic
30	C₂×#8547	C₂²	1	1	yes	characteristic
31	#139716	C₂²	1	2	yes	—
32	#139716	C₂²	1	2	yes	—
33	#139716	C₂²	1	2	yes	—
34	#139716	C₂²	1	2	yes	—
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	#135561	C₂²	1	2	yes	complemented
41	#119550	C₂²	1	2	yes	complemented
42	#119550	C₂²	1	2	yes	complemented
43	C₂²×#535	C₂×C₄	1	1	yes	characteristic
44	C₂³×#120	C₂×C₄	1	1	yes	characteristic
45	C₂³×#120	D₄	1	1	yes	characteristic
46	C₂³×#120	D₄	1	1	yes	characteristic
47	C₂³×#120	C₂³	1	1	yes	characteristic
48	C₂×#2404	D₄	1	1	yes	characteristic
49	C₂×#2404	D₄	1	1	yes	characteristic
50	C₂²×#379	D₄	1	1	yes	characteristic
51	C₂²×#379	D₄	1	1	yes	characteristic
52	#21746	C₂³	1	2	yes	—
53	#21746	C₂³	1	2	yes	—
54	#17271	C₂×C₄	1	1	yes	characteristic, complemented
55	#17271	C₂×C₄	1	1	yes	characteristic, complemented
56	#17137	C₂×C₄	1	1	yes	characteristic, complemented
57	#17137	C₂×C₄	1	1	yes	characteristic, complemented
58	#15947	C₂×C₄	1	1	yes	characteristic
59	#15947	C₂×C₄	1	1	yes	characteristic
60	#15947	D₄	1	1	yes	characteristic
61	#15947	D₄	1	1	yes	characteristic
62	#15947	D₄	1	1	yes	characteristic
63	#15947	D₄	1	1	yes	characteristic
64	#15947	C₂³	1	1	yes	characteristic
65	#15947	C₂³	1	1	yes	characteristic
66	#15259	C₂×C₄	1	1	yes	characteristic
67	#15259	C₂×C₄	1	1	yes	characteristic, complemented
68	#15259	C₂×C₄	1	1	yes	characteristic, complemented
69	#15259	D₄	1	1	yes	characteristic
70	#15259	D₄	1	1	yes	characteristic
71	#15259	C₂³	1	1	yes	characteristic
72	#15258	C₂×C₄	1	1	yes	characteristic
73	#15258	C₂×C₄	1	1	yes	characteristic, complemented
74	#15258	C₂×C₄	1	1	yes	characteristic, complemented
75	#15258	D₄	1	1	yes	characteristic
76	#15258	D₄	1	1	yes	characteristic
77	#15258	C₂³	1	1	yes	characteristic
78	#14657	C₂×C₄	1	1	yes	characteristic, complemented
79	#14657	C₂×C₄	1	1	yes	characteristic, complemented
80	#14492	C₂×C₄	1	1	yes	characteristic, complemented
81	#14492	C₂×C₄	1	1	yes	characteristic, complemented
82	#14419	C₂×C₄	1	1	yes	characteristic, complemented
83	#14419	C₂×C₄	1	1	yes	characteristic, complemented
84	#14341	D₄	1	1	yes	characteristic
85	#14341	D₄	1	1	yes	characteristic
86	#14335	C₂×C₄	1	1	yes	characteristic
87	#14335	C₂×C₄	1	1	yes	characteristic
88	#14335	C₂×C₄	1	1	yes	characteristic
89	#14255	C₂×C₄	1	1	yes	characteristic
90	#14255	C₂×C₄	1	1	yes	characteristic
91	#14255	D₄	1	1	yes	characteristic
92	#14255	D₄	1	1	yes	characteristic
93	#14255	D₄	1	1	yes	characteristic
94	#14255	D₄	1	1	yes	characteristic
95	#14255	C₂³	1	1	yes	characteristic
96	#14255	C₂³	1	1	yes	characteristic
97	#14134	C₂×C₄	1	1	yes	characteristic, complemented
98	#14134	C₂×C₄	1	1	yes	characteristic, complemented
99	#13868	D₄	1	1	yes	characteristic
100	#13868	D₄	1	1	yes	characteristic
101	C₂×#1438	C₂×C₄	1	1	yes	characteristic
102	C₂×#1438	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	C₂⁷	C₂×D₄	1	1	yes	characteristic
108	C₂³×#41	C₂²⋊C₄	1	1	yes	characteristic
109	C₂⁴×D₄	C₂²×C₄	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×#124	C₂²⋊C₄	1	1	yes	characteristic
115	C₂²×#124	C₂²×C₄	1	1	yes	characteristic
116	C₂²×#120	C₂²⋊C₄	1	1	yes	characteristic
117	C₂²×#120	C₂²⋊C₄	1	1	yes	characteristic
118	C₂²×#120	C₂²⋊C₄	1	1	yes	characteristic
119	C₂²×#120	C₂²⋊C₄	1	1	yes	characteristic
120	C₂²×#120	C₂²⋊C₄	1	1	yes	characteristic
121	C₂²×#120	C₂²⋊C₄	1	1	yes	characteristic
122	C₂²×#120	C₂²×C₄	1	1	yes	characteristic
123	C₂²×#120	C₂²×C₄	1	1	yes	characteristic
124	C₂²×#120	C₂²×C₄	1	1	yes	characteristic
125	C₂²×#120	C₂×D₄	1	1	yes	characteristic
126	C₂²×#120	C₂×D₄	1	1	yes	characteristic
127	C₂²×#120	C₂×D₄	1	1	yes	characteristic
128	C₂²×#120	C₂×D₄	1	1	yes	characteristic
129	C₂²×#120	C₂×D₄	1	1	yes	characteristic
130	C₂²×#120	C₂×D₄	1	1	yes	characteristic
131	C₂²×#120	C₂×D₄	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	C₂⁴	1	1	yes	characteristic
136	C₂²×#117	C₂²⋊C₄	1	1	yes	characteristic
137	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
138	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
139	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
140	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
141	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
142	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
143	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
144	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
145	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
146	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
147	C₂×#393	C₂²⋊C₄	1	1	yes	characteristic
148	C₂×#393	C₂²⋊C₄	1	1	yes	characteristic
149	C₂×#393	C₂×D₄	1	1	yes	characteristic
150	C₂×#393	C₂×D₄	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	C₂×D₄	1	1	yes	characteristic
154	C₂×#392	C₂×D₄	1	1	yes	characteristic
155	C₂×#381	C₂²⋊C₄	1	1	yes	characteristic
156	C₂×#381	C₂²⋊C₄	1	1	yes	characteristic
157	C₂×#379	C₂²⋊C₄	1	1	yes	characteristic
158	C₂×#379	C₂²⋊C₄	1	1	yes	characteristic
159	C₂×#379	C₂²⋊C₄	1	1	yes	characteristic
160	C₂×#379	C₂²⋊C₄	1	1	yes	characteristic
161	C₂×#379	C₂²⋊C₄	1	1	yes	characteristic
162	C₂×#379	C₂²⋊C₄	1	1	yes	characteristic
163	C₂×#379	C₂×D₄	1	1	yes	characteristic
164	C₂×#379	C₂×D₄	1	1	yes	characteristic
165	#1440	C₂²⋊C₄	1	1	yes	characteristic
166	#1440	C₂²⋊C₄	1	1	yes	characteristic
167	#1440	C₂²⋊C₄	1	1	yes	characteristic
168	#1440	C₂²⋊C₄	1	1	yes	characteristic
169	#1440	C₂×D₄	1	1	yes	characteristic
170	#1440	C₂×D₄	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	C₂×C₂²⋊C₄	1	1	yes	characteristic
210	C₂⁶	#120	1	1	yes	characteristic
211	C₂⁶	#120	1	1	yes	characteristic
212	C₂⁶	#120	1	1	yes	characteristic
213	C₂⁶	#120	1	1	yes	characteristic
214	C₂⁶	C₂²×D₄	1	1	yes	characteristic
215	C₂³×Q₈	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	C₂×C₂²⋊C₄	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	C₂³×C₄	1	1	yes	characteristic
227	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
228	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
229	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
230	C₂⁴×C₄	#120	1	1	yes	characteristic
231	C₂⁴×C₄	#120	1	1	yes	characteristic
232	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
233	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
234	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
235	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
236	C₂²×C₂²⋊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	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	#120	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	#120	1	1	yes	characteristic
253	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
254	C₂²×C₂²⋊C₄	#120	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×C₂²⋊C₄	C₂²×D₄	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	#379	1	1	yes	characteristic
269	C₂⁵	#410	1	1	yes	characteristic
270	C₂⁵	#410	1	1	yes	characteristic
271	C₂⁵	#410	1	1	yes	characteristic
272	C₂⁵	#410	1	1	yes	characteristic
273	C₂⁵	B(4,𝔽₂)	1	1	yes	characteristic
274	C₂⁵	B(4,𝔽₂)	1	1	yes	characteristic
275	C₂⁵	B(4,𝔽₂)	1	1	yes	characteristic
276	C₂⁵	B(4,𝔽₂)	1	1	yes	characteristic
277	C₂⁵	#458	1	1	yes	characteristic
278	C₂⁵	#458	1	1	yes	characteristic
279	C₂⁵	#458	1	1	yes	characteristic
280	C₂⁵	#458	1	1	yes	characteristic
281	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
282	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
283	C₂⁵	C₂×#120	1	1	yes	characteristic
284	C₂⁵	C₂×#120	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	C₂²×C₂²⋊C₄	1	1	yes	characteristic
289	C₂³×C₄	C₂×#120	1	1	yes	characteristic
290	C₂³×C₄	C₂×#120	1	1	yes	characteristic
291	C₂⁴	#1782	1	1	yes	characteristic
292	C₂⁴	#1782	1	1	yes	characteristic
293	C₂⁴	#1782	1	1	yes	characteristic
294	C₂⁴	#1782	1	1	yes	characteristic
295	C₂⁴	#1790	1	1	yes	characteristic
296	C₂⁴	#1790	1	1	yes	characteristic
297	C₂⁴	#1790	1	1	yes	characteristic
298	C₂⁴	#1790	1	1	yes	characteristic
299	C₂⁴	#1790	1	1	yes	characteristic
300	C₂⁴	#1790	1	1	yes	characteristic
301	C₂⁴	#1790	1	1	yes	characteristic
302	C₂⁴	#1790	1	1	yes	characteristic
303	C₂⁴	C₂×#379	1	1	yes	characteristic
304	C₂⁴	C₂×#410	1	1	yes	characteristic
305	C₂⁴	C₂×#410	1	1	yes	characteristic
306	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
307	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
308	C₂⁴	C₂×#458	1	1	yes	characteristic
309	C₂⁴	C₂×#458	1	1	yes	characteristic
310	C₂³	#8535	1	1	yes	characteristic
311	C₂³	#8535	1	1	yes	characteristic
312	C₂³	#8535	1	1	yes	characteristic
313	C₂³	#8535	1	1	yes	characteristic
314	C₂³	#12725	1	2	yes	—
315	C₂³	#12725	1	2	yes	—
316	C₂³	#12753	1	2	yes	—
317	C₂³	C₂×#1782	1	1	yes	characteristic
318	C₂³	C₂×#1790	1	1	yes	characteristic
319	C₂³	C₂×#1790	1	1	yes	characteristic
320	C₂³	#33551	1	2	yes	—
321	C₂²	#133422	1	2	yes	—
322	C₂²	#133422	1	2	yes	—
323	C₂²	C₂×#8535	1	1	yes	characteristic
324	C₂²	C₂×#12725	1	1	yes	characteristic
325	C₂²	C₂×#12725	1	1	yes	characteristic
326	C₂²	C₂×#12753	1	1	yes	characteristic
327	C₂²	#493562	1	1	yes	characteristic
328	C₂²	#493582	1	1	yes	characteristic
329	C₂²	#493594	1	1	yes	characteristic
330	C₂	#72265770	1	1	yes	characteristic
331	C₂	#72265773	1	1	yes	characteristic
332	C₂	C₂×#133422	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂×#8535
commutator	C₂³×D₄	C₂³×C₄
Frattini, cosocle	C₂²×#120	C₂⁴
prime radical	#72258912	C₂
LCS	G ▷ C₂³×D₄ ▷ C₂⁴ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂⁵ ◁ C₂³×#120 ◁ 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. #72266699	C₂	semidirect
2. #72266698	C₂	semidirect
3. #72266041	C₂	semidirect
4. #72263135	C₂	semidirect
6. #72238446	C₂	semidirect
7. #72233645	C₂	semidirect
8. #72232723	C₂	semidirect
9. #72232723	C₂	semidirect
10. C₂×#139716	C₂	semidirect
11. C₂×#139716	C₂	semidirect
14. #5063443	C₄	semidirect
16. #5063442	C₄	semidirect
18. #4464171	C₄	semidirect
19. #2356274	C₄	semidirect
21. #2108839	C₄	semidirect
23. #616961	C₄	semidirect
26. #556752	C₄	semidirect
28. #552671	C₄	semidirect
35. #139504	C₂²	semidirect
36. #139504	C₂²	semidirect
37. #139486	C₂²	semidirect
38. #139486	C₂²	semidirect
39. #135561	C₂²	semidirect
40. #135561	C₂²	semidirect
41. #119550	C₂²	semidirect
42. #119550	C₂²	semidirect
54. #17271	C₂×C₄	semidirect
55. #17271	C₂×C₄	semidirect
56. #17137	C₂×C₄	semidirect
57. #17137	C₂×C₄	semidirect
67. #15259	C₂×C₄	semidirect
68. #15259	C₂×C₄	semidirect
73. #15258	C₂×C₄	semidirect
74. #15258	C₂×C₄	semidirect
78. #14657	C₂×C₄	semidirect
79. #14657	C₂×C₄	semidirect
80. #14492	C₂×C₄	semidirect
81. #14492	C₂×C₄	semidirect
82. #14419	C₂×C₄	semidirect
83. #14419	C₂×C₄	semidirect
97. #14134	C₂×C₄	semidirect
98. #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
#72266699	2
#72266698	2
#72266041	2
#72263135	2
#72258912	2
#72238446	2
#72233645	2
#72232723	2
C₂×#139716	2