Subgroups — #72340650

Order 2048.

At least 8876 conjugacy classes of subgroups; only the 774 normal subgroups are shown.

The subgroup lattice has 373 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72340647	C₂	1	1	yes	maximal, characteristic, complemented
2	#72340644	C₂	1	1	yes	maximal, characteristic, complemented
3	#72340642	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#152745	C₂	1	1	yes	maximal, characteristic, complemented
5	#72340633	C₂	1	1	yes	maximal, characteristic, complemented
6	#72340630	C₂	1	1	yes	maximal, characteristic, complemented
7	#72340629	C₂	1	1	yes	maximal, characteristic, complemented
8	#72340626	C₂	1	1	yes	maximal, characteristic, complemented
9	#72340625	C₂	1	1	yes	maximal, characteristic, complemented
10	#72340623	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#7514140	C₂	1	1	yes	maximal, characteristic, complemented
12	#72340549	C₂	1	1	yes	maximal, characteristic, complemented
13	#72340538	C₂	1	1	yes	maximal, characteristic, complemented
14	#72337673	C₂	1	8	yes	maximal, complemented
15	#72286309	C₂	1	1	yes	maximal, characteristic, complemented
16	#72283294	C₂	1	1	yes	maximal, characteristic, complemented
17	#72209905	C₂	1	8	yes	maximal, complemented
18	#10586704	C₂²	1	1	yes	characteristic, complemented
19	C₂×#61110	C₂²	1	1	yes	characteristic, complemented
20	C₂×#60388	C₂²	1	1	yes	characteristic
21	#7622914	C₂²	1	4	yes	complemented
22	#7622913	C₂²	1	4	yes	complemented
23	#7622903	C₂²	1	1	yes	characteristic
24	#7622903	C₂²	1	1	yes	characteristic
25	#7622903	C₂²	1	1	yes	characteristic, complemented
26	#7622903	C₂²	1	1	yes	characteristic, complemented
27	#7622903	C₂²	1	1	yes	characteristic, complemented
28	#7622874	C₂²	1	1	yes	characteristic, complemented
29	C₂×#33373	C₂²	1	1	yes	characteristic, complemented
30	#7514140	C₂²	1	8	yes	complemented
31	C₂×#31076	C₂²	1	1	yes	characteristic, complemented
32	C₂×#30496	C₂²	1	1	yes	characteristic, complemented
33	C₂×#25747	C₂²	1	1	yes	characteristic
34	C₂×#23872	C₂²	1	1	yes	characteristic
35	C₂×#22899	C₂²	1	1	yes	characteristic, complemented
36	#6351563	C₂²	1	1	yes	characteristic, complemented
37	#6348452	C₂²	1	1	yes	characteristic, complemented
38	#512900	C₂²	1	8	yes	complemented
39	#512886	C₂²	1	4	yes	complemented
40	#512885	C₂²	1	4	yes	complemented
41	C₂×#13591	C₂²	1	1	yes	characteristic, complemented
42	C₂×#13579	C₂²	1	1	yes	characteristic, complemented
43	#512585	C₂²	1	1	yes	characteristic, complemented
44	#512585	C₂²	1	1	yes	characteristic, complemented
45	#512578	C₂²	1	1	yes	characteristic, complemented
46	#512571	C₂²	1	1	yes	characteristic, complemented
47	#512571	C₂²	1	1	yes	characteristic, complemented
48	#512564	C₂²	1	1	yes	characteristic, complemented
49	#511838	C₂²	1	4	yes	complemented
50	#511836	C₂²	1	4	yes	complemented
51	#493605	C₂²	1	1	yes	characteristic, complemented
52	#493600	C₂²	1	1	yes	characteristic, complemented
53	C₂×#12718	C₂²	1	1	yes	characteristic, complemented
54	#346947	C₂²	1	4	yes	complemented
55	#346946	C₂²	1	4	yes	complemented
56	#187896	C₂²	1	1	yes	characteristic, complemented
57	#187081	C₂²	1	1	yes	characteristic, complemented
58	#186594	C₂²	1	1	yes	characteristic, complemented
59	#153180	C₂²	1	4	yes	complemented
60	#153179	C₂²	1	4	yes	complemented
61	#153149	C₂²	1	8	yes	complemented
62	#153134	C₂²	1	4	yes	complemented
63	#153133	C₂²	1	4	yes	complemented
64	#153125	C₂²	1	8	yes	complemented
65	#152745	C₂²	1	8	yes	complemented
66	#152707	C₂²	1	8	yes	complemented
67	#152571	C₂²	1	4	yes	complemented
68	#152570	C₂²	1	4	yes	complemented
69	#152557	C₂²	1	8	yes	complemented
70	#152027	C₂²	1	8	yes	complemented
71	C₂×#7497	C₂²	1	1	yes	characteristic, complemented
72	C₂×#7501	C₂²	1	1	yes	characteristic, complemented
73	#151820	C₂²	1	1	yes	characteristic, complemented
74	#151812	C₂²	1	1	yes	characteristic, complemented
75	C₂×H(7,𝔽₂)	D₄	1	1	yes	characteristic, complemented
76	C₂×#3585	D₄	1	1	yes	characteristic
77	#63040	C₂³	1	2	yes	complemented
78	#63035	C₂³	1	2	yes	complemented
79	C₂×#3498	C₂³	1	1	yes	characteristic
80	#62759	C₂³	1	1	yes	characteristic
81	#62759	C₂³	1	1	yes	characteristic
82	#61110	C₂³	1	4	yes	—
83	C₂×#3151	C₂³	1	1	yes	characteristic
84	C₂×#3038	D₄	1	1	yes	characteristic, complemented
85	C₂×#3027	D₄	1	1	yes	characteristic
86	#60388	D₄	1	4	yes	complemented
87	#60388	C₂³	1	4	yes	—
88	C₂×#3021	D₄	1	1	yes	characteristic, complemented
89	C₂×#3021	D₄	1	1	yes	characteristic, complemented
90	C₂×#3018	C₂³	1	1	yes	characteristic
91	C₂×#3018	C₂³	1	1	yes	characteristic
92	C₂×#3018	C₂³	1	1	yes	characteristic
93	C₂×#2888	D₄	1	1	yes	characteristic, complemented
94	C₂×#2867	D₄	1	1	yes	characteristic, complemented
95	#33571	D₄	1	2	yes	complemented
96	#33571	C₂³	1	2	yes	—
97	#33571	C₂³	1	2	yes	complemented
98	#33570	D₄	1	2	yes	complemented
99	#33570	C₂³	1	2	yes	—
100	#33570	C₂³	1	2	yes	complemented
101	#33569	D₄	1	4	yes	complemented
102	#33568	D₄	1	4	yes	complemented
103	#33567	C₂³	1	4	yes	—
104	#33567	C₂³	1	4	yes	complemented
105	#33567	C₂³	1	4	yes	complemented
106	#33564	D₄	1	4	yes	complemented
107	#33561	C₂³	1	2	yes	complemented
108	#33559	C₂³	1	2	yes	complemented
109	#33373	C₂³	1	4	yes	complemented
110	C₂×#2132	C₂³	1	1	yes	characteristic
111	C₂×#2132	C₂³	1	1	yes	characteristic
112	C₂×#2132	C₂³	1	1	yes	characteristic
113	C₂×#2126	C₂³	1	1	yes	characteristic
114	#31076	C₂³	1	4	yes	—
115	#30496	C₂³	1	4	yes	—
116	#25747	D₄	1	4	yes	complemented
117	#25747	C₂³	1	4	yes	—
118	#23872	D₄	1	4	yes	—
119	#23872	C₂³	1	4	yes	—
120	#22899	C₂³	1	4	yes	—
121	C₂×#1965	D₄	1	1	yes	characteristic, complemented
122	C₂×#1962	C₂³	1	1	yes	characteristic
123	C₂×#1914	D₄	1	1	yes	characteristic
124	C₂×#1884	C₂³	1	1	yes	characteristic
125	C₂×#1795	D₄	1	1	yes	characteristic
126	C₂×C₄×#104	D₄	1	1	yes	characteristic, complemented
127	#19077	C₂³	1	2	yes	complemented
128	#19073	C₂³	1	2	yes	complemented
129	#18548	C₂³	1	4	yes	complemented
130	#17738	C₂³	1	1	yes	characteristic
131	#17663	C₂³	1	1	yes	characteristic
132	#13591	C₂³	1	4	yes	complemented
133	#13579	C₂³	1	4	yes	complemented
134	#13574	C₂³	1	4	yes	—
135	#13574	C₂³	1	4	yes	complemented
136	#13568	C₂³	1	4	yes	—
137	#13564	C₂³	1	4	yes	complemented
138	#13564	C₂³	1	4	yes	complemented
139	#13562	C₂³	1	4	yes	complemented
140	#12773	C₂³	1	4	yes	complemented
141	#12771	C₂³	1	2	yes	complemented
142	#12769	C₂³	1	2	yes	complemented
143	#12718	C₂³	1	4	yes	complemented
144	#8531	C₂³	1	2	yes	complemented
145	#8530	C₂³	1	2	yes	complemented
146	#8469	C₂³	1	4	yes	complemented
147	#8441	C₂³	1	4	yes	complemented
148	#7501	C₂³	1	4	yes	complemented
149	#7497	C₂³	1	4	yes	complemented
150	#7496	C₂³	1	4	yes	complemented
151	#7492	C₂³	1	4	yes	complemented
152	H(7,𝔽₂)	C₂×D₄	1	4	yes	—
153	C₂×#585	C₂×D₄	1	1	yes	characteristic
154	C₂×#585	C₂×D₄	1	1	yes	characteristic
155	C₂×#585	C₂×D₄	1	1	yes	characteristic
156	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
157	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
158	#3585	C₂×D₄	1	4	yes	—
159	C₂×#568	C₂×D₄	1	1	yes	characteristic
160	#3550	C₂×D₄	1	1	yes	characteristic, complemented
161	#3550	C₂⁴	1	1	yes	characteristic
162	#3549	C₂×D₄	1	1	yes	characteristic, complemented
163	#3549	C₂⁴	1	1	yes	characteristic
164	#3545	C₂×D₄	1	2	yes	complemented
165	#3544	C₂×D₄	1	2	yes	complemented
166	#3529	C₂×D₄	1	2	yes	complemented
167	#3498	C₂×D₄	1	2	yes	—
168	#3498	C₂×D₄	1	2	yes	—
169	#3498	C₂×D₄	1	2	yes	—
170	#3498	C₂⁴	1	2	yes	—
171	#3483	C₂⁴	1	2	yes	—
172	C₂×#535	C₂×D₄	1	1	yes	characteristic
173	C₂×#535	C₂×D₄	1	1	yes	characteristic
174	C₂×#532	C₂⁴	1	1	yes	characteristic
175	C₂²×#127	C₂×D₄	1	1	yes	characteristic
176	C₂²×#127	C₂×D₄	1	1	yes	characteristic
177	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
178	#3151	C₂×D₄	1	2	yes	—
179	#3151	C₂⁴	1	2	yes	—
180	#3038	C₂×D₄	1	4	yes	—
181	#3027	C₂×D₄	1	4	yes	—
182	#3021	C₂×D₄	1	4	yes	—
183	#3021	C₂×D₄	1	4	yes	—
184	#3018	C₂×D₄	1	2	yes	—
185	#3018	C₂×D₄	1	2	yes	—
186	#3018	C₂×D₄	1	2	yes	—
187	#3018	C₂×D₄	1	2	yes	—
188	#3018	C₂×D₄	1	2	yes	—
189	#3018	C₂⁴	1	2	yes	—
190	#3018	C₂⁴	1	2	yes	—
191	#3018	C₂⁴	1	2	yes	—
192	C₂×#456	C₂×D₄	1	2	yes	—
193	C₂×#454	C₂×D₄	1	2	yes	—
194	C₂×#423	C₂×D₄	1	1	yes	characteristic
195	#2888	C₂×D₄	1	4	yes	—
196	C₂×#413	C₂×D₄	1	1	yes	characteristic
197	C₂×#413	C₂×D₄	1	1	yes	characteristic
198	C₂×#413	C₂×D₄	1	1	yes	characteristic
199	C₂×#410	C₂×D₄	1	1	yes	characteristic
200	C₂×C₄×M₁₆	C₂×D₄	1	1	yes	characteristic
201	#2867	C₂×D₄	1	4	yes	—
202	C₂×C₄³	C₂×D₄	1	1	yes	characteristic
203	#2205	C₂×D₄	1	8	yes	complemented
204	#2204	C₂×D₄	1	8	yes	complemented
205	#2203	C₂×D₄	1	8	yes	complemented
206	#2202	C₂×D₄	1	8	yes	complemented
207	#2132	C₂×D₄	1	2	yes	complemented
208	#2132	C₂×D₄	1	2	yes	complemented
209	#2132	C₂⁴	1	2	yes	—
210	#2132	C₂⁴	1	2	yes	—
211	#2132	C₂⁴	1	2	yes	—
212	C₂×#356	C₂×D₄	1	2	yes	complemented
213	C₂×#355	C₂×D₄	1	2	yes	complemented
214	#2126	C₂⁴	1	2	yes	—
215	#1965	C₂×D₄	1	4	yes	—
216	#1962	C₂×D₄	1	2	yes	—
217	#1962	C₂⁴	1	2	yes	—
218	#1914	C₂×D₄	1	4	yes	—
219	#1884	C₂×D₄	1	2	yes	—
220	#1884	C₂⁴	1	2	yes	—
221	#1795	C₂×D₄	1	4	yes	—
222	C₄×#104	C₂×D₄	1	4	yes	—
223	#1560	C₂⁴	1	2	yes	—
224	#1525	C₂⁴	1	2	yes	—
225	#585	#120	1	2	yes	—
226	#585	C₂²×D₄	1	2	yes	—
227	#585	C₂²×D₄	1	2	yes	—
228	#585	C₂²×D₄	1	2	yes	—
229	C₂×2₋¹⁺⁴	#120	1	2	yes	—
230	C₂×H(5,𝔽₂)	#120	1	2	yes	—
231	C₂×H(5,𝔽₂)	#120	1	2	yes	—
232	C₂×H(5,𝔽₂)	C₂²×D₄	1	2	yes	—
233	C₂×H(5,𝔽₂)	C₂²×D₄	1	2	yes	—
234	C₂²×#41	#120	1	1	yes	characteristic
235	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
236	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
237	C₂³×D₄	#120	1	1	yes	characteristic
238	C₂³×D₄	#120	1	1	yes	characteristic
239	#568	C₂²×D₄	1	2	yes	—
240	#563	C₂²×D₄	1	2	yes	complemented
241	H(3,𝔽₄)	C₂²×D₄	1	2	yes	complemented
242	Q₈²	C₂²×D₄	1	2	yes	complemented
243	#555	C₂²×D₄	1	2	yes	complemented
244	#535	#120	1	2	yes	—
245	#535	#120	1	2	yes	—
246	#535	C₂²×D₄	1	2	yes	—
247	#535	C₂²×D₄	1	2	yes	—
248	#532	C₂²×D₄	1	1	yes	characteristic
249	#532	C₂²×D₄	1	1	yes	characteristic
250	#532	C₂²×D₄	1	1	yes	characteristic
251	#532	C₂²×D₄	1	1	yes	characteristic
252	#532	C₂²×D₄	1	1	yes	characteristic
253	#532	H(5,𝔽₂)	1	1	yes	characteristic
254	#532	H(5,𝔽₂)	1	1	yes	characteristic
255	#532	C₂⁵	1	1	yes	characteristic
256	C₂×C₄⋊Q₈	C₂²×D₄	1	1	yes	characteristic
257	C₂×#127	#120	1	2	yes	—
258	C₂×#127	C₂²×D₄	1	2	yes	—
259	C₂×#127	C₂²×D₄	1	2	yes	—
260	C₂×#127	H(5,𝔽₂)	1	1	yes	characteristic
261	C₂×#124	C₂²×D₄	1	1	yes	characteristic
262	C₂×#124	H(5,𝔽₂)	1	1	yes	characteristic
263	C₄×#41	#120	1	2	yes	—
264	C₄×#41	C₂²×D₄	1	2	yes	—
265	C₂×#117	#120	1	1	yes	characteristic
266	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
267	#456	#120	1	4	yes	—
268	#456	C₂²×D₄	1	4	yes	—
269	#454	#120	1	4	yes	—
270	#454	C₂²×D₄	1	4	yes	—
271	#423	C₂²×D₄	1	2	yes	—
272	#413	#120	1	2	yes	—
273	#413	C₂²×D₄	1	2	yes	—
274	#413	C₂²×D₄	1	2	yes	—
275	#413	C₂²×D₄	1	2	yes	—
276	C₂×#101	#120	1	2	yes	—
277	#410	C₂²×D₄	1	2	yes	—
278	C₄×M₁₆	C₂²×D₄	1	2	yes	—
279	C₄³	C₂²×D₄	1	2	yes	—
280	#356	C₂²×D₄	1	4	yes	complemented
281	#355	C₂²×D₄	1	4	yes	complemented
282	C₂⁵	B(4,𝔽₂)	1	2	yes	—
283	2₋¹⁺⁴	C₂×#120	1	4	yes	—
284	C₂×#41	B(4,𝔽₂)	1	2	yes	—
285	C₂×#41	C₂×#120	1	1	yes	characteristic
286	C₂×#41	C₂×#120	1	1	yes	characteristic
287	C₂×#41	C₂×#120	1	1	yes	characteristic
288	C₂×#41	C₂×#120	1	2	yes	—
289	C₂×#41	#534	1	1	yes	characteristic
290	C₂×#41	D₄²	1	1	yes	characteristic
291	C₂×#41	D₄²	1	1	yes	characteristic
292	C₂×#41	C₂³×D₄	1	1	yes	characteristic
293	C₂×#41	C₂³×D₄	1	1	yes	characteristic
294	C₂²×Q₈	B(4,𝔽₂)	1	1	yes	characteristic
295	C₂²×Q₈	C₂×#120	1	1	yes	characteristic
296	C₂²×Q₈	D₄²	1	1	yes	characteristic
297	C₂²×D₄	B(4,𝔽₂)	1	2	yes	—
298	C₂²×D₄	B(4,𝔽₂)	1	1	yes	characteristic
299	C₂²×D₄	C₂×#120	1	2	yes	—
300	C₂²×D₄	C₂×#120	1	2	yes	—
301	C₂²×D₄	#534	1	1	yes	characteristic
302	C₂²×D₄	D₄²	1	1	yes	characteristic
303	C₂³×C₄	C₂×#120	1	1	yes	characteristic
304	C₄⋊Q₈	C₂×#120	1	1	yes	characteristic
305	C₄⋊Q₈	D₄²	1	1	yes	characteristic
306	C₄⋊Q₈	D₄²	1	1	yes	characteristic
307	C₄⋊Q₈	C₂³×D₄	1	1	yes	characteristic
308	#127	#534	1	1	yes	characteristic
309	#127	D₄²	1	1	yes	characteristic
310	#127	D₄²	1	1	yes	characteristic
311	#127	C₂×H(5,𝔽₂)	1	1	yes	characteristic
312	#124	C₂×#120	1	1	yes	characteristic
313	#124	#534	1	1	yes	characteristic
314	#124	D₄²	1	1	yes	characteristic
315	#124	D₄²	1	1	yes	characteristic
316	#124	D₄²	1	1	yes	characteristic
317	#124	D₄²	1	1	yes	characteristic
318	#124	C₂³×D₄	1	1	yes	characteristic
319	#124	C₂×H(5,𝔽₂)	1	1	yes	characteristic
320	#117	C₂×#120	1	2	yes	—
321	C₂×C₄²	C₂×#120	1	1	yes	characteristic
322	C₂×C₄²	D₄²	1	1	yes	characteristic
323	C₂×C₄²	D₄²	1	1	yes	characteristic
324	C₂×C₄²	D₄²	1	1	yes	characteristic
325	C₂×C₄²	D₄²	1	1	yes	characteristic
326	C₂×C₄²	C₂³×D₄	1	1	yes	characteristic
327	#101	C₂×#120	1	4	yes	—
328	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
329	C₂⁴	C₂×B(4,𝔽₂)	1	4	yes	—
330	C₂×Q₈	#2196	1	2	yes	—
331	C₂×Q₈	#2196	1	2	yes	—
332	C₂×Q₈	#2403	1	1	yes	characteristic
333	C₂×Q₈	#2403	1	1	yes	characteristic
334	C₂×Q₈	C₂×B(4,𝔽₂)	1	2	yes	—
335	C₂×Q₈	C₂²×#120	1	1	yes	characteristic
336	C₂×Q₈	C₂×D₄²	1	1	yes	characteristic
337	C₂×D₄	#2403	1	1	yes	characteristic
338	C₂×D₄	#2403	1	1	yes	characteristic
339	C₂×D₄	C₂×B(4,𝔽₂)	1	2	yes	—
340	C₂×D₄	C₂×#534	1	1	yes	characteristic
341	C₂×D₄	C₂×D₄²	1	1	yes	characteristic
342	C₂²×C₄	#2403	1	1	yes	characteristic
343	C₂²×C₄	#2403	1	1	yes	characteristic
344	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
345	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
346	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
347	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
348	C₄²	#2403	1	1	yes	characteristic
349	C₄²	#2403	1	1	yes	characteristic
350	C₄²	C₂×D₄²	1	1	yes	characteristic
351	C₄²	C₂×D₄²	1	1	yes	characteristic
352	C₂³	#23900	1	1	yes	characteristic
353	C₂³	#23900	1	1	yes	characteristic
354	C₂³	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
355	Q₈	C₂×#2196	1	4	yes	—
356	C₂×C₄	#23900	1	1	yes	characteristic
357	C₂×C₄	#23900	1	1	yes	characteristic
358	C₂×C₄	C₂×#2196	1	1	yes	characteristic
359	C₂×C₄	C₂×#2196	1	1	yes	characteristic
360	C₂×C₄	#33551	1	1	yes	characteristic
361	C₂×C₄	#33551	1	1	yes	characteristic
362	C₂×C₄	C₂×#2403	1	1	yes	characteristic
363	C₂×C₄	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
364	C₂²	#499787	1	1	yes	characteristic
365	C₂²	#499787	1	1	yes	characteristic
366	C₂²	C₂×#23900	1	1	yes	characteristic
367	C₄	#499787	1	1	yes	characteristic
368	C₄	#499787	1	1	yes	characteristic
369	C₄	C₂²×#2196	1	1	yes	characteristic
370	C₄	C₂×#33551	1	1	yes	characteristic
371	C₂	C₂×#499787	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂	C₂×#499787
commutator, Frattini, cosocle	#532	C₂⁵
LCS	G ▷ #532 ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ C₂²×#41 ◁ C₂×#3498 ◁ G
LECS	G ▷ #532 ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72340647	C₂	semidirect
2. #72340644	C₂	semidirect
3. #72340642	C₂	semidirect
4. C₂×#152745	C₂	semidirect
5. #72340633	C₂	semidirect
6. #72340630	C₂	semidirect
7. #72340629	C₂	semidirect
8. #72340626	C₂	semidirect
9. #72340625	C₂	semidirect
10. #72340623	C₂	semidirect
11. C₂×#7514140	C₂	semidirect
12. #72340549	C₂	semidirect
13. #72340538	C₂	semidirect
14. #72337673	C₂	semidirect
15. #72286309	C₂	semidirect
16. #72283294	C₂	semidirect
17. #72209905	C₂	semidirect
18. #10586704	C₂²	semidirect
19. C₂×#61110	C₂²	semidirect
21. #7622914	C₂²	semidirect
22. #7622913	C₂²	semidirect
25. #7622903	C₂²	semidirect
26. #7622903	C₂²	semidirect
27. #7622903	C₂²	semidirect
28. #7622874	C₂²	semidirect
29. C₂×#33373	C₂²	semidirect
30. #7514140	C₂²	semidirect
31. C₂×#31076	C₂²	semidirect
32. C₂×#30496	C₂²	semidirect
35. C₂×#22899	C₂²	semidirect
36. #6351563	C₂²	semidirect
37. #6348452	C₂²	semidirect
38. #512900	C₂²	semidirect
39. #512886	C₂²	semidirect
40. #512885	C₂²	semidirect
41. C₂×#13591	C₂²	semidirect
42. C₂×#13579	C₂²	semidirect
43. #512585	C₂²	semidirect
44. #512585	C₂²	semidirect
45. #512578	C₂²	semidirect
46. #512571	C₂²	semidirect
47. #512571	C₂²	semidirect
48. #512564	C₂²	semidirect
49. #511838	C₂²	semidirect
50. #511836	C₂²	semidirect
51. #493605	C₂²	semidirect
52. #493600	C₂²	semidirect
53. C₂×#12718	C₂²	semidirect
54. #346947	C₂²	semidirect
55. #346946	C₂²	semidirect
56. #187896	C₂²	semidirect
57. #187081	C₂²	semidirect
58. #186594	C₂²	semidirect
59. #153180	C₂²	semidirect
60. #153179	C₂²	semidirect
61. #153149	C₂²	semidirect
62. #153134	C₂²	semidirect
63. #153133	C₂²	semidirect
64. #153125	C₂²	semidirect
65. #152745	C₂²	semidirect
66. #152707	C₂²	semidirect
67. #152571	C₂²	semidirect
68. #152570	C₂²	semidirect
69. #152557	C₂²	semidirect
70. #152027	C₂²	semidirect
71. C₂×#7497	C₂²	semidirect
72. C₂×#7501	C₂²	semidirect
73. #151820	C₂²	semidirect
74. #151812	C₂²	semidirect
75. C₂×H(7,𝔽₂)	D₄	semidirect
77. #63040	C₂³	semidirect
78. #63035	C₂³	semidirect
84. C₂×#3038	D₄	semidirect
86. #60388	D₄	semidirect
88. C₂×#3021	D₄	semidirect
89. C₂×#3021	D₄	semidirect
93. C₂×#2888	D₄	semidirect
94. C₂×#2867	D₄	semidirect
95. #33571	D₄	semidirect
97. #33571	C₂³	semidirect
98. #33570	D₄	semidirect
100. #33570	C₂³	semidirect
101. #33569	D₄	semidirect
102. #33568	D₄	semidirect
104. #33567	C₂³	semidirect
105. #33567	C₂³	semidirect
106. #33564	D₄	semidirect
107. #33561	C₂³	semidirect
108. #33559	C₂³	semidirect
109. #33373	C₂³	semidirect
116. #25747	D₄	semidirect
121. C₂×#1965	D₄	semidirect
126. C₂×C₄×#104	D₄	semidirect
127. #19077	C₂³	semidirect
128. #19073	C₂³	semidirect
129. #18548	C₂³	semidirect
132. #13591	C₂³	semidirect
133. #13579	C₂³	semidirect
135. #13574	C₂³	semidirect
137. #13564	C₂³	semidirect
138. #13564	C₂³	semidirect
139. #13562	C₂³	semidirect
140. #12773	C₂³	semidirect
141. #12771	C₂³	semidirect
142. #12769	C₂³	semidirect
143. #12718	C₂³	semidirect
144. #8531	C₂³	semidirect
145. #8530	C₂³	semidirect
146. #8469	C₂³	semidirect
147. #8441	C₂³	semidirect
148. #7501	C₂³	semidirect
149. #7497	C₂³	semidirect
150. #7496	C₂³	semidirect
151. #7492	C₂³	semidirect
160. #3550	C₂×D₄	semidirect
162. #3549	C₂×D₄	semidirect
164. #3545	C₂×D₄	semidirect
165. #3544	C₂×D₄	semidirect
166. #3529	C₂×D₄	semidirect
203. #2205	C₂×D₄	semidirect
204. #2204	C₂×D₄	semidirect
205. #2203	C₂×D₄	semidirect
206. #2202	C₂×D₄	semidirect
207. #2132	C₂×D₄	semidirect
208. #2132	C₂×D₄	semidirect
212. C₂×#356	C₂×D₄	semidirect
213. C₂×#355	C₂×D₄	semidirect
240. #563	C₂²×D₄	semidirect
241. H(3,𝔽₄)	C₂²×D₄	semidirect
242. Q₈²	C₂²×D₄	semidirect
243. #555	C₂²×D₄	semidirect
280. #356	C₂²×D₄	semidirect
281. #355	C₂²×D₄	semidirect

Maximal subgroups

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

subgroup	index
#72340647	2
#72340644	2
#72340642	2
C₂×#152745	2
#72340633	2
#72340630	2
#72340629	2
#72340626	2
#72340625	2
#72340623	2
C₂×#7514140	2
#72340549	2
#72340538	2
#72337673	2
#72286309	2
#72283294	2
#72209905	2