Subgroups — #72341461

Order 2048.

At least 7765 conjugacy classes of subgroups; only the 988 normal subgroups are shown.

The subgroup lattice has 378 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72341457	C₂	1	4	yes	maximal, complemented
2	#72341454	C₂	1	4	yes	maximal, complemented
3	#72341453	C₂	1	1	yes	maximal, characteristic, complemented
4	#72341445	C₂	1	1	yes	maximal, characteristic, complemented
5	#72341435	C₂	1	1	yes	maximal, characteristic, complemented
6	#72341391	C₂	1	1	yes	maximal, characteristic, complemented
7	#72341312	C₂	1	2	yes	maximal, complemented
8	#72318605	C₂	1	8	yes	maximal, complemented
9	#72311608	C₂	1	1	yes	maximal, characteristic, complemented
10	#72311058	C₂	1	1	yes	maximal, characteristic, complemented
11	#72306419	C₂	1	2	yes	maximal, complemented
12	#72284724	C₂	1	1	yes	maximal, characteristic, complemented
13	#72234146	C₂	1	2	yes	maximal, complemented
14	#72233917	C₂	1	2	yes	maximal, complemented
15	C₂×#60388	C₂²	1	2	yes	complemented
16	#8968221	C₂²	1	2	yes	complemented
17	#8932958	C₂²	1	1	yes	characteristic
18	#8928621	C₂²	1	1	yes	characteristic
19	#8824175	C₂²	1	4	yes	complemented
20	#8362204	C₂²	1	2	yes	complemented
21	#7743195	C₂²	1	2	yes	—
22	#7737411	C₂²	1	2	yes	—
23	#7674604	C₂²	1	1	yes	characteristic
24	#6628902	C₂²	1	1	yes	characteristic, complemented
25	#6628897	C₂²	1	1	yes	characteristic, complemented
26	#6628896	C₂²	1	1	yes	characteristic
27	#6628896	C₂²	1	2	yes	complemented
28	#499849	C₂²	1	8	yes	complemented
29	#499843	C₂²	1	8	yes	complemented
30	#499838	C₂²	1	8	yes	complemented
31	#499832	C₂²	1	8	yes	complemented
32	#494682	C₂²	1	2	yes	—
33	#494682	C₂²	1	2	yes	complemented
34	#494682	C₂²	1	2	yes	complemented
35	#494681	C₂²	1	2	yes	complemented
36	#493430	C₂²	1	2	yes	complemented
37	#493430	C₂²	1	2	yes	complemented
38	#449493	C₂²	1	2	yes	complemented
39	#417817	C₂²	1	2	yes	complemented
40	#417566	C₂²	1	4	yes	complemented
41	#374010	C₂²	1	1	yes	characteristic, complemented
42	#359605	C₂²	1	2	yes	complemented
43	#251855	C₂²	1	4	yes	complemented
44	#251838	C₂²	1	4	yes	complemented
45	#245256	C₂²	1	4	yes	complemented
46	#245235	C₂²	1	4	yes	complemented
47	#213862	C₂²	1	1	yes	characteristic, complemented
48	#213862	C₂²	1	1	yes	characteristic, complemented
49	#213855	C₂²	1	1	yes	characteristic, complemented
50	#213854	C₂²	1	1	yes	characteristic
51	#213854	C₂²	1	2	yes	complemented
52	#134013	C₂²	1	2	yes	complemented
53	#133905	C₂²	1	4	yes	complemented
54	#133836	C₂²	1	2	yes	complemented
55	#133431	C₂²	1	4	yes	complemented
56	#133428	C₂²	1	4	yes	complemented
57	#133359	C₂²	1	8	yes	complemented
58	#133356	C₂²	1	8	yes	complemented
59	#133335	C₂²	1	8	yes	complemented
60	#133332	C₂²	1	8	yes	complemented
61	#133312	C₂²	1	4	yes	complemented
62	#133310	C₂²	1	4	yes	complemented
63	C₂×H(7,𝔽₂)	C₂³	1	1	yes	characteristic
64	C₂×#3500	D₄	1	2	yes	complemented
65	C₂×#3498	C₂³	1	2	yes	—
66	C₂²×D₄²	D₄	1	2	yes	complemented
67	C₂²×#560	D₄	1	2	yes	complemented
68	C₂×#3019	C₂³	1	4	yes	complemented
69	C₂²×#453	C₂³	1	4	yes	complemented
70	C₂×#2888	C₂³	1	2	yes	—
71	#59126	C₂³	1	4	yes	—
72	#59041	D₄	1	4	yes	complemented
73	#52013	D₄	1	4	yes	complemented
74	#52012	C₂³	1	4	yes	—
75	#52004	D₄	1	4	yes	complemented
76	#52004	C₂³	1	4	yes	—
77	#47563	C₂³	1	2	yes	—
78	#46997	C₂³	1	2	yes	—
79	#46388	D₄	1	2	yes	complemented
80	#46386	D₄	1	2	yes	complemented
81	#46385	D₄	1	4	yes	complemented
82	#46324	C₂³	1	4	yes	—
83	#46276	D₄	1	4	yes	complemented
84	#36967	C₂³	1	2	yes	—
85	#36955	D₄	1	2	yes	complemented
86	#36714	D₄	1	4	yes	complemented
87	#36702	D₄	1	2	yes	complemented
88	#36702	D₄	1	2	yes	complemented
89	#36702	D₄	1	2	yes	complemented
90	#35676	C₂³	1	1	yes	characteristic
91	#35616	C₂³	1	1	yes	characteristic
92	#35616	C₂³	1	2	yes	complemented
93	#35527	D₄	1	2	yes	complemented
94	#35451	C₂³	1	2	yes	—
95	#35446	C₂³	1	1	yes	characteristic
96	#35354	D₄	1	2	yes	complemented
97	#35350	D₄	1	2	yes	complemented
98	#35346	C₂³	1	1	yes	characteristic
99	#35346	C₂³	1	2	yes	—
100	#35327	D₄	1	2	yes	complemented
101	#35272	C₂³	1	2	yes	—
102	C₂×#2657	C₂³	1	1	yes	characteristic
103	#34364	D₄	1	2	yes	complemented
104	#34364	D₄	1	2	yes	complemented
105	#34070	D₄	1	2	yes	complemented
106	#32900	C₂³	1	4	yes	complemented
107	#32898	C₂³	1	4	yes	—
108	#32898	C₂³	1	8	yes	complemented
109	#20586	C₂³	1	1	yes	characteristic
110	#20586	C₂³	1	2	yes	complemented
111	#20585	C₂³	1	1	yes	characteristic
112	#20585	C₂³	1	2	yes	—
113	#20585	C₂³	1	1	yes	characteristic
114	#13082	C₂³	1	8	yes	—
115	#13082	C₂³	1	8	yes	complemented
116	#13082	C₂³	1	8	yes	complemented
117	#13080	C₂³	1	8	yes	complemented
118	#12696	C₂³	1	4	yes	complemented
119	#12696	C₂³	1	4	yes	complemented
120	#12693	C₂³	1	4	yes	complemented
121	#12693	C₂³	1	4	yes	complemented
122	#11167	C₂³	1	2	yes	complemented
123	#10989	C₂³	1	4	yes	complemented
124	#10982	C₂³	1	2	yes	complemented
125	#10975	C₂³	1	4	yes	complemented
126	#9501	C₂³	1	4	yes	complemented
127	#9497	C₂³	1	4	yes	—
128	#9497	C₂³	1	8	yes	complemented
129	#8748	C₂³	1	2	yes	complemented
130	#8748	C₂³	1	2	yes	complemented
131	#8544	C₂³	1	2	yes	complemented
132	#8544	C₂³	1	2	yes	complemented
133	C₂²×2₋¹⁺⁴	C₂×D₄	1	1	yes	characteristic, complemented
134	C₂²×H(5,𝔽₂)	C₂×D₄	1	2	yes	—
135	C₂²×H(5,𝔽₂)	C₂⁴	1	2	yes	—
136	C₂²×H(5,𝔽₂)	C₂⁴	1	1	yes	characteristic
137	C₂×#560	C₂×D₄	1	4	yes	complemented
138	C₂×#560	C₂×D₄	1	4	yes	complemented
139	C₂×D₄²	C₂×D₄	1	4	yes	complemented
140	C₂×D₄²	C₂×D₄	1	4	yes	complemented
141	C₂×#536	C₂×D₄	1	2	yes	—
142	C₂×#535	C₂×D₄	1	2	yes	—
143	C₂×#535	C₂×D₄	1	2	yes	—
144	C₂×#535	C₂×D₄	1	2	yes	—
145	C₂×#535	C₂×D₄	1	2	yes	—
146	C₂×#535	C₂×D₄	1	2	yes	—
147	C₂×#535	C₂×D₄	1	2	yes	complemented
148	C₂×#535	C₂⁴	1	2	yes	—
149	C₂×#534	C₂×D₄	1	2	yes	complemented
150	C₂×#532	C₂×D₄	1	2	yes	—
151	C₂×#532	C₂×D₄	1	2	yes	—
152	C₂×#532	C₂×D₄	1	2	yes	—
153	C₂²×#127	C₂×D₄	1	2	yes	—
154	C₂²×#127	C₂×D₄	1	2	yes	—
155	C₂²×#127	C₂×D₄	1	1	yes	characteristic, complemented
156	C₂²×#127	C₂⁴	1	2	yes	—
157	C₂²×#124	C₂×D₄	1	2	yes	complemented
158	C₂²×#124	C₂⁴	1	1	yes	characteristic
159	C₂²×#123	C₂×D₄	1	2	yes	—
160	C₂²×#123	C₂×D₄	1	1	yes	characteristic
161	C₂²×#120	C₂×D₄	1	2	yes	—
162	C₂²×#120	C₂×D₄	1	2	yes	—
163	C₂²×#120	C₂×D₄	1	2	yes	—
164	C₂²×#120	C₂×D₄	1	2	yes	—
165	C₂²×#120	C₂×D₄	1	1	yes	characteristic
166	C₂×#518	C₂×D₄	1	2	yes	complemented
167	C₂×C₄×#41	C₂×D₄	1	2	yes	—
168	C₂×C₄×#41	C₂×D₄	1	2	yes	complemented
169	C₂²×#100	C₂⁴	1	4	yes	—
170	#2842	C₂×D₄	1	2	yes	complemented
171	#2840	C₂×D₄	1	2	yes	complemented
172	#2717	C₂×D₄	1	4	yes	complemented
173	#2709	C₂×D₄	1	4	yes	complemented
174	#2684	C₂×D₄	1	4	yes	complemented
175	#2684	C₂×D₄	1	4	yes	complemented
176	#2684	C₂×D₄	1	4	yes	complemented
177	#2669	C₂×D₄	1	4	yes	complemented
178	#2669	C₂×D₄	1	4	yes	complemented
179	#2669	C₂×D₄	1	4	yes	complemented
180	#2483	C₂×D₄	1	2	yes	complemented
181	#2406	C₂×D₄	1	4	yes	—
182	#2405	C₂×D₄	1	2	yes	—
183	#2405	C₂×D₄	1	2	yes	—
184	#2405	C₂×D₄	1	2	yes	—
185	#2405	C₂×D₄	1	4	yes	—
186	#2405	C₂×D₄	1	2	yes	complemented
187	#2405	C₂×D₄	1	2	yes	complemented
188	#2405	C₂×D₄	1	4	yes	complemented
189	#2405	C₂⁴	1	2	yes	—
190	#2404	C₂×D₄	1	4	yes	—
191	#2404	C₂×D₄	1	4	yes	—
192	#2404	C₂×D₄	1	4	yes	—
193	#2403	C₂×D₄	1	2	yes	—
194	#2403	C₂×D₄	1	4	yes	—
195	#2403	C₂×D₄	1	2	yes	complemented
196	#2403	C₂⁴	1	2	yes	—
197	#2403	C₂⁴	1	4	yes	—
198	#2380	C₂×D₄	1	4	yes	complemented
199	#2380	C₂×D₄	1	4	yes	complemented
200	#2366	C₂×D₄	1	4	yes	complemented
201	#2366	C₂×D₄	1	4	yes	complemented
202	#2312	C₂×D₄	1	2	yes	complemented
203	#2312	C₂×D₄	1	2	yes	complemented
204	#2312	C₂×D₄	1	2	yes	complemented
205	#2310	C₂×D₄	1	1	yes	characteristic, complemented
206	#2309	C₂×D₄	1	4	yes	complemented
207	#2309	C₂×D₄	1	2	yes	complemented
208	#2309	C₂⁴	1	2	yes	—
209	#2309	C₂⁴	1	1	yes	characteristic
210	#2308	C₂×D₄	1	2	yes	—
211	#2308	C₂×D₄	1	2	yes	—
212	#2308	C₂×D₄	1	2	yes	—
213	#2308	C₂×D₄	1	2	yes	—
214	#2308	C₂×D₄	1	2	yes	—
215	#2308	C₂×D₄	1	1	yes	characteristic
216	#2308	C₂×D₄	1	1	yes	characteristic
217	#2308	C₂×D₄	1	2	yes	complemented
218	#2297	C₂×D₄	1	2	yes	—
219	#2297	C₂×D₄	1	2	yes	complemented
220	#2285	C₂×D₄	1	2	yes	complemented
221	C₂×#376	C₂×D₄	1	1	yes	characteristic, complemented
222	#1781	C₂⁴	1	4	yes	—
223	#1781	C₂⁴	1	2	yes	—
224	#1781	C₂⁴	1	2	yes	—
225	C₂⁶	#120	1	1	yes	characteristic
226	C₂⁶	#120	1	2	yes	—
227	C₂²×#41	#120	1	2	yes	—
228	C₂²×#41	#120	1	2	yes	—
229	C₂²×#41	C₂²×D₄	1	2	yes	—
230	C₂²×#41	C₂²×D₄	1	2	yes	—
231	C₂²×#41	C₂²×D₄	1	2	yes	—
232	C₂²×#41	C₂²×D₄	1	2	yes	—
233	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
234	C₂³×D₄	#120	1	2	yes	—
235	C₂³×D₄	#120	1	2	yes	—
236	C₂³×D₄	C₂²×D₄	1	2	yes	—
237	C₂³×D₄	C₂²×D₄	1	2	yes	—
238	C₂³×D₄	C₂²×D₄	1	2	yes	—
239	C₂³×D₄	C₂²×D₄	1	4	yes	—
240	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
241	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
242	C₂³×D₄	C₂²×D₄	1	2	yes	—
243	C₂³×D₄	C₂²×D₄	1	2	yes	—
244	C₂³×D₄	C₂⁵	1	1	yes	characteristic
245	C₂⁴×C₄	#120	1	1	yes	characteristic
246	C₂×C₄⋊Q₈	#120	1	2	yes	—
247	C₂×#127	#120	1	2	yes	—
248	C₂×#127	#120	1	2	yes	—
249	C₂×#127	#120	1	2	yes	—
250	C₂×#127	C₂²×D₄	1	2	yes	—
251	C₂×#127	C₂²×D₄	1	2	yes	—
252	C₂×#127	C₂²×D₄	1	2	yes	—
253	C₂×#127	C₂²×D₄	1	2	yes	—
254	C₂×#127	C₂²×D₄	1	2	yes	—
255	C₂×#127	C₂²×D₄	1	2	yes	—
256	C₂×#124	#120	1	2	yes	—
257	C₂×#124	#120	1	2	yes	—
258	C₂×#124	#120	1	2	yes	—
259	C₂×#124	#120	1	2	yes	—
260	C₂×#124	C₂²×D₄	1	2	yes	—
261	C₂×#124	C₂²×D₄	1	2	yes	—
262	C₂×#123	#120	1	4	yes	—
263	C₂×#123	#120	1	4	yes	—
264	C₂×#123	#120	1	4	yes	—
265	C₂×#123	C₂²×D₄	1	4	yes	—
266	C₂×#120	#120	1	4	yes	—
267	C₂×#120	#120	1	4	yes	—
268	C₂×#120	#120	1	4	yes	—
269	C₂×#120	C₂²×D₄	1	4	yes	—
270	C₂×#120	C₂²×D₄	1	4	yes	—
271	C₂×#120	C₂²×D₄	1	4	yes	—
272	C₂×#117	#120	1	2	yes	—
273	C₂×#117	#120	1	2	yes	—
274	C₂×#117	C₂²×D₄	1	2	yes	—
275	C₂×#117	C₂²×D₄	1	2	yes	—
276	C₂²×C₄⋊C₄	#120	1	2	yes	—
277	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
278	C₂²×C₂²⋊C₄	#120	1	2	yes	—
279	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
280	C₂²×C₂²⋊C₄	#120	1	2	yes	—
281	C₂²×C₂²⋊C₄	#120	1	4	yes	—
282	C₂²×C₂²⋊C₄	#120	1	2	yes	—
283	C₂²×C₂²⋊C₄	#120	1	2	yes	—
284	C₂²×C₂²⋊C₄	#120	1	2	yes	—
285	C₂²×C₂²⋊C₄	#120	1	2	yes	—
286	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
287	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
288	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
289	C₂²×C₄²	#120	1	2	yes	—
290	C₂²×C₄²	#120	1	2	yes	—
291	C₂²×C₄²	C₂²×D₄	1	2	yes	—
292	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
293	#386	#120	1	4	yes	—
294	#386	#120	1	4	yes	—
295	#386	#120	1	4	yes	—
296	#386	#120	1	4	yes	—
297	#386	#120	1	4	yes	—
298	#386	#120	1	4	yes	—
299	#386	C₂²×D₄	1	4	yes	—
300	#386	C₂²×D₄	1	4	yes	—
301	#386	C₂²×D₄	1	4	yes	—
302	#386	C₂²×D₄	1	4	yes	—
303	#381	#120	1	4	yes	—
304	#381	#120	1	2	yes	—
305	#381	#120	1	2	yes	—
306	#379	C₂²×D₄	1	2	yes	—
307	#379	C₂²×D₄	1	4	yes	—
308	#379	C₂²×D₄	1	2	yes	—
309	#379	C₂²×D₄	1	2	yes	—
310	#379	C₂²×D₄	1	2	yes	—
311	C₂⁵	C₂×#120	1	2	yes	—
312	C₂⁵	C₂×#120	1	1	yes	characteristic
313	C₂⁵	C₂×#120	1	1	yes	characteristic
314	C₂⁵	C₂×#120	1	2	yes	—
315	C₂⁵	C₂×#120	1	4	yes	—
316	C₂⁵	C₂³×D₄	1	1	yes	characteristic
317	C₂⁵	C₂³×D₄	1	1	yes	characteristic
318	C₂²×Q₈	C₂×#120	1	2	yes	—
319	C₂²×Q₈	C₂×#120	1	2	yes	—
320	C₂²×D₄	C₂×#120	1	2	yes	—
321	C₂²×D₄	C₂×#120	1	2	yes	—
322	C₂²×D₄	C₂×#120	1	2	yes	—
323	C₂²×D₄	C₂×#120	1	2	yes	—
324	C₂²×D₄	C₂×#120	1	2	yes	—
325	C₂²×D₄	C₂×#120	1	2	yes	—
326	C₂²×D₄	C₂×#120	1	2	yes	—
327	C₂²×D₄	C₂×#120	1	2	yes	—
328	C₂²×D₄	C₂×#120	1	2	yes	—
329	C₂²×D₄	C₂×#120	1	2	yes	—
330	C₂²×D₄	C₂³×D₄	1	2	yes	—
331	C₂²×D₄	C₂³×D₄	1	2	yes	—
332	C₂³×C₄	C₂×#120	1	2	yes	—
333	C₂³×C₄	C₂×#120	1	2	yes	—
334	C₂³×C₄	C₂×#120	1	2	yes	—
335	C₂³×C₄	C₂×#120	1	2	yes	—
336	C₂³×C₄	C₂×#120	1	2	yes	—
337	C₂³×C₄	C₂×#120	1	2	yes	—
338	C₂³×C₄	C₂×#120	1	4	yes	—
339	C₂³×C₄	C₂×#120	1	2	yes	—
340	C₂³×C₄	C₂×#120	1	1	yes	characteristic
341	C₂³×C₄	C₂×#120	1	2	yes	—
342	C₂³×C₄	C₂×#120	1	1	yes	characteristic
343	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
344	#127	B(4,𝔽₂)	1	8	yes	—
345	C₂×C₂²⋊C₄	C₂×#120	1	4	yes	—
346	C₂×C₂²⋊C₄	C₂×#120	1	4	yes	—
347	C₂×C₂²⋊C₄	C₂×#120	1	4	yes	—
348	C₂×C₂²⋊C₄	C₂×#120	1	4	yes	—
349	C₂×C₂²⋊C₄	C₂×#120	1	4	yes	—
350	C₂×C₄²	C₂×#120	1	2	yes	—
351	C₂×C₄²	C₂×#120	1	2	yes	—
352	C₂×C₄²	C₂×#120	1	2	yes	—
353	C₂×C₄²	C₂×#120	1	2	yes	—
354	C₂⁴	#2846	1	2	yes	—
355	C₂⁴	#2846	1	2	yes	—
356	C₂⁴	C₂²×#120	1	1	yes	characteristic
357	C₂⁴	C₂²×#120	1	2	yes	—
358	C₂⁴	C₂²×#120	1	1	yes	characteristic
359	C₂⁴	C₂²×#120	1	1	yes	characteristic
360	C₂×D₄	C₂×B(4,𝔽₂)	1	4	yes	—
361	C₂×D₄	C₂×B(4,𝔽₂)	1	4	yes	—
362	C₂×D₄	#3026	1	4	yes	—
363	C₂²×C₄	#2846	1	2	yes	—
364	C₂²×C₄	#2846	1	2	yes	—
365	C₂²×C₄	C₂²×#120	1	2	yes	—
366	C₄²	C₂×B(4,𝔽₂)	1	4	yes	—
367	C₂³	#32898	1	4	yes	—
368	C₂³	#32898	1	4	yes	—
369	C₂³	C₂×#2846	1	1	yes	characteristic
370	C₂³	#60399	1	2	yes	—
371	C₂×C₄	C₂²×B(4,𝔽₂)	1	2	yes	—
372	C₂×C₄	C₂×#3026	1	2	yes	—
373	C₂²	C₂×#32898	1	2	yes	—
374	C₂²	#6628896	1	1	yes	characteristic
375	C₂	#72216323	1	1	yes	characteristic
376	C₂	#72240648	1	2	yes	—

	subgroup	G/H
center, socle	C₂²	#6628896
commutator, Frattini, cosocle	C₂³×D₄	C₂⁵
LCS	G ▷ C₂³×D₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂⁴ ◁ #35616 ◁ 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. #72341457	C₂	semidirect
2. #72341454	C₂	semidirect
3. #72341453	C₂	semidirect
4. #72341445	C₂	semidirect
5. #72341435	C₂	semidirect
6. #72341391	C₂	semidirect
7. #72341312	C₂	semidirect
8. #72318605	C₂	semidirect
9. #72311608	C₂	semidirect
10. #72311058	C₂	semidirect
11. #72306419	C₂	semidirect
12. #72284724	C₂	semidirect
13. #72234146	C₂	semidirect
14. #72233917	C₂	semidirect
15. C₂×#60388	C₂²	semidirect
16. #8968221	C₂²	semidirect
19. #8824175	C₂²	semidirect
20. #8362204	C₂²	semidirect
24. #6628902	C₂²	semidirect
25. #6628897	C₂²	semidirect
27. #6628896	C₂²	semidirect
28. #499849	C₂²	semidirect
29. #499843	C₂²	semidirect
30. #499838	C₂²	semidirect
31. #499832	C₂²	semidirect
33. #494682	C₂²	semidirect
34. #494682	C₂²	semidirect
35. #494681	C₂²	semidirect
36. #493430	C₂²	semidirect
37. #493430	C₂²	semidirect
38. #449493	C₂²	semidirect
39. #417817	C₂²	semidirect
40. #417566	C₂²	semidirect
41. #374010	C₂²	semidirect
42. #359605	C₂²	semidirect
43. #251855	C₂²	semidirect
44. #251838	C₂²	semidirect
45. #245256	C₂²	semidirect
46. #245235	C₂²	semidirect
47. #213862	C₂²	semidirect
48. #213862	C₂²	semidirect
49. #213855	C₂²	semidirect
51. #213854	C₂²	semidirect
52. #134013	C₂²	semidirect
53. #133905	C₂²	semidirect
54. #133836	C₂²	semidirect
55. #133431	C₂²	semidirect
56. #133428	C₂²	semidirect
57. #133359	C₂²	semidirect
58. #133356	C₂²	semidirect
59. #133335	C₂²	semidirect
60. #133332	C₂²	semidirect
61. #133312	C₂²	semidirect
62. #133310	C₂²	semidirect
64. C₂×#3500	D₄	semidirect
66. C₂²×D₄²	D₄	semidirect
67. C₂²×#560	D₄	semidirect
68. C₂×#3019	C₂³	semidirect
69. C₂²×#453	C₂³	semidirect
72. #59041	D₄	semidirect
73. #52013	D₄	semidirect
75. #52004	D₄	semidirect
79. #46388	D₄	semidirect
80. #46386	D₄	semidirect
81. #46385	D₄	semidirect
83. #46276	D₄	semidirect
85. #36955	D₄	semidirect
86. #36714	D₄	semidirect
87. #36702	D₄	semidirect
88. #36702	D₄	semidirect
89. #36702	D₄	semidirect
92. #35616	C₂³	semidirect
93. #35527	D₄	semidirect
96. #35354	D₄	semidirect
97. #35350	D₄	semidirect
100. #35327	D₄	semidirect
103. #34364	D₄	semidirect
104. #34364	D₄	semidirect
105. #34070	D₄	semidirect
106. #32900	C₂³	semidirect
108. #32898	C₂³	semidirect
110. #20586	C₂³	semidirect
115. #13082	C₂³	semidirect
116. #13082	C₂³	semidirect
117. #13080	C₂³	semidirect
118. #12696	C₂³	semidirect
119. #12696	C₂³	semidirect
120. #12693	C₂³	semidirect
121. #12693	C₂³	semidirect
122. #11167	C₂³	semidirect
123. #10989	C₂³	semidirect
124. #10982	C₂³	semidirect
125. #10975	C₂³	semidirect
126. #9501	C₂³	semidirect
128. #9497	C₂³	semidirect
129. #8748	C₂³	semidirect
130. #8748	C₂³	semidirect
131. #8544	C₂³	semidirect
132. #8544	C₂³	semidirect
133. C₂²×2₋¹⁺⁴	C₂×D₄	semidirect
137. C₂×#560	C₂×D₄	semidirect
138. C₂×#560	C₂×D₄	semidirect
139. C₂×D₄²	C₂×D₄	semidirect
140. C₂×D₄²	C₂×D₄	semidirect
147. C₂×#535	C₂×D₄	semidirect
149. C₂×#534	C₂×D₄	semidirect
155. C₂²×#127	C₂×D₄	semidirect
157. C₂²×#124	C₂×D₄	semidirect
166. C₂×#518	C₂×D₄	semidirect
168. C₂×C₄×#41	C₂×D₄	semidirect
170. #2842	C₂×D₄	semidirect
171. #2840	C₂×D₄	semidirect
172. #2717	C₂×D₄	semidirect
173. #2709	C₂×D₄	semidirect
174. #2684	C₂×D₄	semidirect
175. #2684	C₂×D₄	semidirect
176. #2684	C₂×D₄	semidirect
177. #2669	C₂×D₄	semidirect
178. #2669	C₂×D₄	semidirect
179. #2669	C₂×D₄	semidirect
180. #2483	C₂×D₄	semidirect
186. #2405	C₂×D₄	semidirect
187. #2405	C₂×D₄	semidirect
188. #2405	C₂×D₄	semidirect
195. #2403	C₂×D₄	semidirect
198. #2380	C₂×D₄	semidirect
199. #2380	C₂×D₄	semidirect
200. #2366	C₂×D₄	semidirect
201. #2366	C₂×D₄	semidirect
202. #2312	C₂×D₄	semidirect
203. #2312	C₂×D₄	semidirect
204. #2312	C₂×D₄	semidirect
205. #2310	C₂×D₄	semidirect
206. #2309	C₂×D₄	semidirect
207. #2309	C₂×D₄	semidirect
217. #2308	C₂×D₄	semidirect
219. #2297	C₂×D₄	semidirect
220. #2285	C₂×D₄	semidirect
221. C₂×#376	C₂×D₄	semidirect

Maximal subgroups

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

subgroup	index
#72341457	2
#72341454	2
#72341453	2
#72341445	2
#72341435	2
#72341391	2
#72341312	2
#72318605	2
#72311608	2
#72311058	2
#72306419	2
#72284724	2
#72234146	2
#72233917	2