Subgroups — #72260662

Order 2048.

At least 8056 conjugacy classes of subgroups; only the 800 normal subgroups are shown.

The subgroup lattice has 347 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72260584	C₂	1	2	yes	maximal, complemented
2	#72260537	C₂	1	2	yes	maximal, complemented
3	#72260512	C₂	1	4	yes	maximal, complemented
4	#72260395	C₂	1	4	yes	maximal, complemented
5	#72240132	C₂	1	1	yes	maximal, characteristic, complemented
6	#72237608	C₂	1	1	yes	maximal, characteristic, complemented
7	#72233441	C₂	1	2	yes	maximal, complemented
8	#72233433	C₂	1	4	yes	maximal, complemented
9	#72232592	C₂	1	1	yes	maximal, characteristic, complemented
10	#72231950	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#139716	C₂	1	1	yes	maximal, characteristic, complemented
12	#72219266	C₂	1	1	yes	maximal, characteristic, complemented
13	#72219040	C₂	1	2	yes	maximal, complemented
14	C₂×#347042	C₂	1	1	yes	maximal, characteristic, complemented
15	#72213719	C₂	1	4	yes	maximal, complemented
16	C₂×#62817	C₂²	1	1	yes	characteristic, complemented
17	C₂²×#3532	C₂²	1	1	yes	characteristic, complemented
18	C₂×#34981	C₂²	1	1	yes	characteristic
19	#6500011	C₂²	1	4	yes	complemented
20	#6500010	C₂²	1	4	yes	complemented
21	#6440460	C₂²	1	2	yes	complemented
22	#6437621	C₂²	1	2	yes	—
23	C₂×#23900	C₂²	1	2	yes	—
24	#6437445	C₂²	1	2	yes	—
25	C₂×#21746	C₂²	1	1	yes	characteristic, complemented
26	#4941163	C₂²	1	2	yes	complemented
27	#4941159	C₂²	1	2	yes	complemented
28	#1422022	C₂²	1	2	yes	complemented
29	#1418393	C₂²	1	2	yes	complemented
30	#763514	C₂²	1	1	yes	characteristic, complemented
31	#617161	C₂²	1	1	yes	characteristic, complemented
32	#616961	C₂²	1	1	yes	characteristic
33	C₂×#15947	C₂²	1	1	yes	characteristic
34	#552677	C₂²	1	1	yes	characteristic, complemented
35	#511776	C₂²	1	4	yes	complemented
36	#511775	C₂²	1	4	yes	complemented
37	#511772	C₂²	1	4	yes	complemented
38	#511771	C₂²	1	4	yes	complemented
39	#493879	C₂²	1	2	yes	complemented
40	#493370	C₂²	1	2	yes	complemented
41	#493357	C₂²	1	2	yes	complemented
42	C₂×#12687	C₂²	1	2	yes	complemented
43	#347042	C₂²	1	4	yes	—
44	#347042	C₂²	1	4	yes	complemented
45	#346456	C₂²	1	4	yes	complemented
46	#346446	C₂²	1	4	yes	complemented
47	C₂×#8547	C₂²	1	1	yes	characteristic, complemented
48	C₂×#8541	C₂²	1	1	yes	characteristic, complemented
49	C₂×#8534	C₂²	1	2	yes	complemented
50	#186835	C₂²	1	2	yes	complemented
51	#144415	C₂²	1	8	yes	complemented
52	#144414	C₂²	1	8	yes	complemented
53	#144412	C₂²	1	8	yes	complemented
54	#144412	C₂²	1	8	yes	complemented
55	#139774	C₂²	1	8	yes	complemented
56	#139773	C₂²	1	8	yes	complemented
57	#139720	C₂²	1	4	yes	complemented
58	#139718	C₂²	1	4	yes	complemented
59	#139716	C₂²	1	4	yes	complemented
60	#139716	C₂²	1	4	yes	complemented
61	#133895	C₂²	1	4	yes	complemented
62	#133893	C₂²	1	4	yes	complemented
63	C₂×#7304	C₂²	1	2	yes	complemented
64	#128009	C₂²	1	2	yes	complemented
65	#62817	C₂³	1	4	yes	—
66	C₂×#3484	C₂³	1	2	yes	—
67	C₂²×#551	C₂³	1	1	yes	characteristic, complemented
68	C₂²×D₄²	C₂³	1	1	yes	characteristic, complemented
69	C₂²×H(3,𝔽₄)	C₂³	1	1	yes	characteristic, complemented
70	C₂²×#560	C₂³	1	1	yes	characteristic, complemented
71	C₂²×#535	C₂³	1	1	yes	characteristic
72	C₂²×#534	C₂³	1	1	yes	characteristic
73	C₂³×#120	D₄	1	2	yes	complemented
74	C₂³×#120	D₄	1	1	yes	characteristic, complemented
75	C₂³×#120	C₂³	1	1	yes	characteristic
76	C₂³×#120	C₂³	1	1	yes	characteristic
77	C₂⁴×C₂²⋊C₄	D₄	1	1	yes	characteristic, complemented
78	C₂×#3026	D₄	1	4	yes	complemented
79	C₂×#2404	D₄	1	2	yes	complemented
80	C₂×#2412	D₄	1	2	yes	complemented
81	C₂×#2412	C₂³	1	2	yes	—
82	C₂×#2410	D₄	1	2	yes	complemented
83	C₂×#2410	C₂³	1	2	yes	—
84	C₂×#2315	D₄	1	1	yes	characteristic, complemented
85	C₂×#2308	D₄	1	1	yes	characteristic, complemented
86	C₂×#2308	C₂³	1	1	yes	characteristic
87	#24056	C₂³	1	8	yes	—
88	#23907	C₂³	1	4	yes	—
89	#23906	C₂³	1	4	yes	—
90	#23903	D₄	1	8	yes	complemented
91	#23901	C₂³	1	4	yes	—
92	#23900	C₂³	1	4	yes	—
93	#23900	C₂³	1	4	yes	—
94	#23900	C₂³	1	4	yes	—
95	#21746	C₂³	1	4	yes	—
96	#20960	D₄	1	4	yes	complemented
97	C₂×#1783	C₂³	1	2	yes	—
98	C₂×#1781	C₂³	1	2	yes	—
99	C₂×#1781	C₂³	1	2	yes	—
100	#15947	D₄	1	1	yes	characteristic, complemented
101	#15947	D₄	1	1	yes	characteristic, complemented
102	#15947	D₄	1	1	yes	characteristic, complemented
103	#15947	D₄	1	1	yes	characteristic, complemented
104	#15947	C₂³	1	2	yes	—
105	#15947	C₂³	1	2	yes	—
106	#15784	C₂³	1	2	yes	complemented
107	#15313	C₂³	1	2	yes	complemented
108	#15266	C₂³	1	2	yes	complemented
109	#15266	C₂³	1	2	yes	complemented
110	#15259	D₄	1	1	yes	characteristic, complemented
111	#15259	D₄	1	1	yes	characteristic, complemented
112	#15259	C₂³	1	2	yes	—
113	#15258	D₄	1	1	yes	characteristic, complemented
114	#15258	D₄	1	1	yes	characteristic, complemented
115	#15258	C₂³	1	2	yes	—
116	#14506	C₂³	1	2	yes	complemented
117	#14358	C₂³	1	2	yes	complemented
118	#14335	C₂³	1	1	yes	characteristic
119	#13868	D₄	1	2	yes	complemented
120	C₂×#1438	D₄	1	2	yes	complemented
121	C₂×#1438	C₂³	1	1	yes	characteristic
122	#12852	C₂³	1	8	yes	complemented
123	#12694	C₂³	1	4	yes	complemented
124	#12693	C₂³	1	4	yes	complemented
125	#12688	C₂³	1	4	yes	complemented
126	#12687	C₂³	1	4	yes	complemented
127	#12687	C₂³	1	4	yes	complemented
128	#12687	C₂³	1	4	yes	complemented
129	#8547	C₂³	1	4	yes	—
130	#8541	C₂³	1	4	yes	—
131	#8534	C₂³	1	8	yes	—
132	#8453	C₂³	1	8	yes	—
133	#7307	C₂³	1	8	yes	complemented
134	#7304	C₂³	1	8	yes	complemented
135	C₂⁷	C₂×D₄	1	1	yes	characteristic
136	C₂⁷	C₂×D₄	1	1	yes	characteristic
137	C₂²×H(5,𝔽₂)	C₂×D₄	1	2	yes	—
138	C₂³×#41	C₂×D₄	1	1	yes	characteristic
139	C₂⁴×D₄	C₂×D₄	1	2	yes	—
140	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
141	C₂⁴×D₄	C₂×D₄	1	2	yes	complemented
142	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
143	#3484	C₂×D₄	1	4	yes	—
144	#3484	C₂⁴	1	4	yes	—
145	C₂×#534	C₂×D₄	1	4	yes	—
146	C₂×#534	C₂×D₄	1	4	yes	—
147	C₂²×#127	C₂×D₄	1	1	yes	characteristic
148	C₂²×#127	C₂⁴	1	1	yes	characteristic
149	C₂²×#124	C₂×D₄	1	1	yes	characteristic
150	C₂²×#124	C₂⁴	1	1	yes	characteristic
151	C₂²×#123	C₂×D₄	1	1	yes	characteristic
152	C₂²×#123	C₂⁴	1	1	yes	characteristic
153	C₂²×#120	C₂×D₄	1	1	yes	characteristic
154	C₂²×#120	C₂×D₄	1	1	yes	characteristic
155	C₂²×#120	C₂×D₄	1	1	yes	characteristic
156	C₂²×#120	C₂×D₄	1	2	yes	—
157	C₂²×#120	C₂×D₄	1	2	yes	—
158	C₂²×#120	C₂×D₄	1	2	yes	—
159	C₂²×#120	C₂×D₄	1	2	yes	—
160	C₂²×#120	C₂×D₄	1	1	yes	characteristic
161	C₂²×#120	C₂×D₄	1	1	yes	characteristic
162	C₂²×#120	C₂×D₄	1	2	yes	—
163	C₂²×#120	C₂×D₄	1	1	yes	characteristic
164	C₂²×#120	C₂×D₄	1	1	yes	characteristic
165	C₂²×#120	C₂⁴	1	1	yes	characteristic
166	C₂²×#120	C₂⁴	1	1	yes	characteristic
167	C₂²×#120	C₂⁴	1	1	yes	characteristic
168	C₂²×#120	C₂⁴	1	2	yes	—
169	C₂×#518	C₂×D₄	1	2	yes	—
170	C₂²×#117	C₂×D₄	1	1	yes	characteristic
171	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
172	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
173	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
174	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
175	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
176	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
177	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
178	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	complemented
179	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	complemented
180	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	complemented
181	C₂×#458	C₂×D₄	1	8	yes	complemented
182	C₂×B(4,𝔽₂)	C₂×D₄	1	8	yes	complemented
183	C₂²×#99	C₂×D₄	1	4	yes	—
184	C₂×#393	C₂×D₄	1	2	yes	complemented
185	C₂×#393	C₂×D₄	1	2	yes	complemented
186	C₂×#392	C₂×D₄	1	2	yes	complemented
187	C₂×#392	C₂×D₄	1	2	yes	complemented
188	C₂×#386	C₂×D₄	1	2	yes	—
189	C₂×#386	C₂⁴	1	2	yes	—
190	C₂×#385	C₂×D₄	1	2	yes	complemented
191	C₂×#385	C₂×D₄	1	2	yes	complemented
192	C₂×#381	C₂×D₄	1	2	yes	—
193	C₂×#381	C₂×D₄	1	2	yes	complemented
194	C₂×#379	C₂×D₄	1	2	yes	complemented
195	#1890	C₂×D₄	1	8	yes	complemented
196	#1889	C₂×D₄	1	8	yes	complemented
197	#1783	C₂⁴	1	4	yes	—
198	#1781	C₂×D₄	1	4	yes	—
199	#1781	C₂⁴	1	4	yes	—
200	#1781	C₂⁴	1	4	yes	—
201	#1438	C₂×D₄	1	1	yes	characteristic
202	#1438	C₂×D₄	1	1	yes	characteristic
203	#1438	C₂×D₄	1	2	yes	—
204	#1438	C₂×D₄	1	2	yes	—
205	#1438	C₂×D₄	1	2	yes	—
206	#1438	C₂×D₄	1	2	yes	—
207	#1438	C₂×D₄	1	1	yes	characteristic
208	#1438	C₂×D₄	1	1	yes	characteristic
209	#1438	C₂⁴	1	2	yes	—
210	#1438	C₂⁴	1	2	yes	—
211	#1437	C₂×D₄	1	2	yes	complemented
212	#1437	C₂×D₄	1	2	yes	complemented
213	#1437	C₂×D₄	1	2	yes	complemented
214	#1437	C₂×D₄	1	2	yes	complemented
215	C₂⁶	#120	1	1	yes	characteristic
216	C₂⁶	#120	1	1	yes	characteristic
217	C₂⁶	#120	1	2	yes	—
218	C₂⁶	C₂²×D₄	1	1	yes	characteristic
219	C₂⁶	C₂²×D₄	1	2	yes	—
220	C₂⁶	C₂²×D₄	1	1	yes	characteristic
221	C₂⁶	C₂²×D₄	1	1	yes	characteristic
222	C₂⁶	C₂²×D₄	1	1	yes	characteristic
223	C₂⁶	C₂²×D₄	1	1	yes	characteristic
224	C₂×H(5,𝔽₂)	C₂²×D₄	1	4	yes	—
225	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
226	C₂³×D₄	#120	1	2	yes	—
227	C₂³×D₄	#120	1	2	yes	—
228	C₂³×D₄	#120	1	2	yes	—
229	C₂³×D₄	#120	1	2	yes	—
230	C₂³×D₄	C₂²×D₄	1	2	yes	—
231	C₂³×D₄	C₂²×D₄	1	2	yes	—
232	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
233	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
234	C₂³×D₄	C₂²×D₄	1	2	yes	—
235	C₂³×D₄	C₂²×D₄	1	2	yes	—
236	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
237	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
238	C₂³×D₄	H(5,𝔽₂)	1	2	yes	—
239	C₂³×D₄	H(5,𝔽₂)	1	2	yes	—
240	C₂³×D₄	C₂⁵	1	1	yes	characteristic
241	C₂⁴×C₄	#120	1	2	yes	—
242	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
243	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
244	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
245	C₂×#123	#120	1	4	yes	—
246	C₂×#123	C₂²×D₄	1	4	yes	—
247	C₂×#120	#120	1	4	yes	—
248	C₂×#120	C₂²×D₄	1	4	yes	—
249	#518	C₂²×D₄	1	4	yes	—
250	C₂²×C₂²⋊C₄	#120	1	2	yes	—
251	C₂²×C₂²⋊C₄	#120	1	2	yes	—
252	C₂²×C₂²⋊C₄	#120	1	2	yes	—
253	C₂²×C₂²⋊C₄	#120	1	2	yes	—
254	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
255	C₂²×C₂²⋊C₄	#120	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×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
259	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
260	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
261	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
262	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
263	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
264	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
265	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
266	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
267	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
268	C₂×#99	C₂²×D₄	1	8	yes	—
269	C₂×#95	C₂²×D₄	1	2	yes	—
270	C₂×#95	C₂²×D₄	1	2	yes	—
271	C₂⁵	B(4,𝔽₂)	1	2	yes	—
272	C₂⁵	B(4,𝔽₂)	1	2	yes	—
273	C₂⁵	B(4,𝔽₂)	1	2	yes	—
274	C₂⁵	B(4,𝔽₂)	1	2	yes	—
275	C₂⁵	C₂×#120	1	1	yes	characteristic
276	C₂⁵	C₂×#120	1	2	yes	—
277	C₂⁵	C₂×#120	1	1	yes	characteristic
278	C₂⁵	C₂×#120	1	1	yes	characteristic
279	C₂⁵	C₂×#120	1	2	yes	—
280	C₂⁵	C₂×#120	1	1	yes	characteristic
281	C₂⁵	C₂×#120	1	2	yes	—
282	C₂⁵	C₂×#120	1	1	yes	characteristic
283	C₂⁵	#534	1	1	yes	characteristic
284	C₂⁵	#534	1	1	yes	characteristic
285	C₂⁵	D₄²	1	2	yes	—
286	C₂⁵	D₄²	1	2	yes	—
287	C₂⁵	C₂³×D₄	1	1	yes	characteristic
288	C₂⁵	C₂³×D₄	1	1	yes	characteristic
289	C₂²×D₄	C₂×#120	1	2	yes	—
290	C₂²×D₄	#534	1	2	yes	—
291	C₂²×D₄	D₄²	1	2	yes	—
292	C₂²×D₄	D₄²	1	2	yes	—
293	C₂²×D₄	D₄²	1	2	yes	—
294	C₂²×D₄	D₄²	1	2	yes	—
295	C₂²×D₄	C₂³×D₄	1	2	yes	—
296	C₂²×D₄	C₂×H(5,𝔽₂)	1	2	yes	—
297	C₂³×C₄	C₂×#120	1	2	yes	—
298	C₂³×C₄	C₂×#120	1	2	yes	—
299	C₂³×C₄	C₂×#120	1	2	yes	—
300	C₂³×C₄	C₂×#120	1	1	yes	characteristic
301	C₂³×C₄	D₄²	1	2	yes	—
302	C₂³×C₄	D₄²	1	2	yes	—
303	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
304	C₂×C₂²⋊C₄	B(4,𝔽₂)	1	8	yes	complemented
305	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
306	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
307	C₂⁴	#2403	1	2	yes	—
308	C₂⁴	#2403	1	1	yes	characteristic
309	C₂⁴	#2403	1	1	yes	characteristic
310	C₂⁴	#2403	1	1	yes	characteristic
311	C₂⁴	#2403	1	1	yes	characteristic
312	C₂⁴	C₂×B(4,𝔽₂)	1	2	yes	—
313	C₂⁴	C₂×B(4,𝔽₂)	1	2	yes	—
314	C₂⁴	C₂×B(4,𝔽₂)	1	2	yes	—
315	C₂⁴	C₂×B(4,𝔽₂)	1	2	yes	—
316	C₂⁴	C₂×B(4,𝔽₂)	1	2	yes	—
317	C₂⁴	C₂×B(4,𝔽₂)	1	2	yes	—
318	C₂⁴	C₂×B(4,𝔽₂)	1	4	yes	—
319	C₂⁴	C₂²×#120	1	1	yes	characteristic
320	C₂⁴	C₂²×#120	1	1	yes	characteristic
321	C₂⁴	C₂×#534	1	1	yes	characteristic
322	C₂⁴	C₂×D₄²	1	2	yes	—
323	C₂²×C₄	#2403	1	2	yes	—
324	C₂²×C₄	C₂×D₄²	1	2	yes	—
325	C₂²⋊C₄	C₂×B(4,𝔽₂)	1	4	yes	complemented
326	C₂²⋊C₄	C₂×B(4,𝔽₂)	1	4	yes	complemented
327	C₂³	#23896	1	2	yes	—
328	C₂³	#23900	1	2	yes	—
329	C₂³	#23900	1	1	yes	characteristic
330	C₂³	#23900	1	1	yes	characteristic
331	C₂³	#23900	1	2	yes	—
332	C₂³	#23900	1	2	yes	—
333	C₂³	#33551	1	4	yes	complemented
334	C₂³	C₂×#2403	1	1	yes	characteristic
335	C₂³	C₂²×B(4,𝔽₂)	1	2	yes	—
336	C₂³	C₂²×B(4,𝔽₂)	1	2	yes	—
337	C₂²	#245229	1	2	yes	—
338	C₂²	#245229	1	2	yes	—
339	C₂²	C₂×#23900	1	1	yes	characteristic
340	C₂²	C₂×#23900	1	1	yes	characteristic
341	C₂²	C₂×#23896	1	1	yes	characteristic
342	C₂²	C₂×#33551	1	2	yes	—
343	C₂²	#7622875	1	2	yes	—
344	C₂	#72233116	1	2	yes	—
345	C₂	C₂×#245229	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂×#23900
commutator, Frattini, cosocle	C₂³×D₄	C₂⁵
LCS	G ▷ C₂³×D₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂⁵ ◁ C₂³×#120 ◁ G
LECS	G ▷ C₂³×D₄ ▷ C₂³ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72260584	C₂	semidirect
2. #72260537	C₂	semidirect
3. #72260512	C₂	semidirect
4. #72260395	C₂	semidirect
5. #72240132	C₂	semidirect
6. #72237608	C₂	semidirect
7. #72233441	C₂	semidirect
8. #72233433	C₂	semidirect
9. #72232592	C₂	semidirect
10. #72231950	C₂	semidirect
11. C₂×#139716	C₂	semidirect
12. #72219266	C₂	semidirect
13. #72219040	C₂	semidirect
14. C₂×#347042	C₂	semidirect
15. #72213719	C₂	semidirect
16. C₂×#62817	C₂²	semidirect
17. C₂²×#3532	C₂²	semidirect
19. #6500011	C₂²	semidirect
20. #6500010	C₂²	semidirect
21. #6440460	C₂²	semidirect
25. C₂×#21746	C₂²	semidirect
26. #4941163	C₂²	semidirect
27. #4941159	C₂²	semidirect
28. #1422022	C₂²	semidirect
29. #1418393	C₂²	semidirect
30. #763514	C₂²	semidirect
31. #617161	C₂²	semidirect
34. #552677	C₂²	semidirect
35. #511776	C₂²	semidirect
36. #511775	C₂²	semidirect
37. #511772	C₂²	semidirect
38. #511771	C₂²	semidirect
39. #493879	C₂²	semidirect
40. #493370	C₂²	semidirect
41. #493357	C₂²	semidirect
42. C₂×#12687	C₂²	semidirect
44. #347042	C₂²	semidirect
45. #346456	C₂²	semidirect
46. #346446	C₂²	semidirect
47. C₂×#8547	C₂²	semidirect
48. C₂×#8541	C₂²	semidirect
49. C₂×#8534	C₂²	semidirect
50. #186835	C₂²	semidirect
51. #144415	C₂²	semidirect
52. #144414	C₂²	semidirect
53. #144412	C₂²	semidirect
54. #144412	C₂²	semidirect
55. #139774	C₂²	semidirect
56. #139773	C₂²	semidirect
57. #139720	C₂²	semidirect
58. #139718	C₂²	semidirect
59. #139716	C₂²	semidirect
60. #139716	C₂²	semidirect
61. #133895	C₂²	semidirect
62. #133893	C₂²	semidirect
63. C₂×#7304	C₂²	semidirect
64. #128009	C₂²	semidirect
67. C₂²×#551	C₂³	semidirect
68. C₂²×D₄²	C₂³	semidirect
69. C₂²×H(3,𝔽₄)	C₂³	semidirect
70. C₂²×#560	C₂³	semidirect
73. C₂³×#120	D₄	semidirect
74. C₂³×#120	D₄	semidirect
77. C₂⁴×C₂²⋊C₄	D₄	semidirect
78. C₂×#3026	D₄	semidirect
79. C₂×#2404	D₄	semidirect
80. C₂×#2412	D₄	semidirect
82. C₂×#2410	D₄	semidirect
84. C₂×#2315	D₄	semidirect
85. C₂×#2308	D₄	semidirect
90. #23903	D₄	semidirect
96. #20960	D₄	semidirect
100. #15947	D₄	semidirect
101. #15947	D₄	semidirect
102. #15947	D₄	semidirect
103. #15947	D₄	semidirect
106. #15784	C₂³	semidirect
107. #15313	C₂³	semidirect
108. #15266	C₂³	semidirect
109. #15266	C₂³	semidirect
110. #15259	D₄	semidirect
111. #15259	D₄	semidirect
113. #15258	D₄	semidirect
114. #15258	D₄	semidirect
116. #14506	C₂³	semidirect
117. #14358	C₂³	semidirect
119. #13868	D₄	semidirect
120. C₂×#1438	D₄	semidirect
122. #12852	C₂³	semidirect
123. #12694	C₂³	semidirect
124. #12693	C₂³	semidirect
125. #12688	C₂³	semidirect
126. #12687	C₂³	semidirect
127. #12687	C₂³	semidirect
128. #12687	C₂³	semidirect
133. #7307	C₂³	semidirect
134. #7304	C₂³	semidirect
141. C₂⁴×D₄	C₂×D₄	semidirect
178. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
179. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
180. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
181. C₂×#458	C₂×D₄	semidirect
182. C₂×B(4,𝔽₂)	C₂×D₄	semidirect
184. C₂×#393	C₂×D₄	semidirect
185. C₂×#393	C₂×D₄	semidirect
186. C₂×#392	C₂×D₄	semidirect
187. C₂×#392	C₂×D₄	semidirect
190. C₂×#385	C₂×D₄	semidirect
191. C₂×#385	C₂×D₄	semidirect
193. C₂×#381	C₂×D₄	semidirect
194. C₂×#379	C₂×D₄	semidirect
195. #1890	C₂×D₄	semidirect
196. #1889	C₂×D₄	semidirect
211. #1437	C₂×D₄	semidirect
212. #1437	C₂×D₄	semidirect
213. #1437	C₂×D₄	semidirect
214. #1437	C₂×D₄	semidirect
304. C₂×C₂²⋊C₄	B(4,𝔽₂)	semidirect
325. C₂²⋊C₄	C₂×B(4,𝔽₂)	semidirect
326. C₂²⋊C₄	C₂×B(4,𝔽₂)	semidirect
333. C₂³	#33551	semidirect

Maximal subgroups

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

subgroup	index
#72260584	2
#72260537	2
#72260512	2
#72260395	2
#72240132	2
#72237608	2
#72233441	2
#72233433	2
#72232592	2
#72231950	2
C₂×#139716	2
#72219266	2
#72219040	2
C₂×#347042	2
#72213719	2