Subgroups — #72337449

Order 2048.

At least 9754 conjugacy classes of subgroups; only the 1000 normal subgroups are shown.

The subgroup lattice has 552 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72337447	C₂	1	1	yes	maximal, characteristic, complemented
2	#72337443	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#6573703	C₂	1	1	yes	maximal, characteristic, complemented
4	#72337439	C₂	1	1	yes	maximal, characteristic, complemented
5	#72337437	C₂	1	2	yes	maximal, complemented
6	#72337435	C₂	1	2	yes	maximal, complemented
7	#72337434	C₂	1	2	yes	maximal, complemented
8	#72337433	C₂	1	2	yes	maximal, complemented
9	#72337431	C₂	1	1	yes	maximal, characteristic, complemented
10	#72337430	C₂	1	1	yes	maximal, characteristic, complemented
11	#72337428	C₂	1	1	yes	maximal, characteristic, complemented
12	#72315278	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#499889	C₂	1	1	yes	maximal, characteristic, complemented
14	#72313178	C₂	1	2	yes	maximal, complemented
15	#72313143	C₂	1	2	yes	maximal, complemented
16	#72312259	C₂	1	2	yes	maximal, complemented
17	#72312095	C₂	1	1	yes	maximal, characteristic, complemented
18	#72312034	C₂	1	1	yes	maximal, characteristic, complemented
19	#72311838	C₂	1	1	yes	maximal, characteristic, complemented
20	#72306416	C₂	1	1	yes	maximal, characteristic, complemented
21	#72280900	C₂	1	2	yes	maximal, complemented
22	C₂×#7622880	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×#511819	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#63092	C₂²	1	1	yes	characteristic, complemented
25	C₂×#63011	C₂²	1	1	yes	characteristic, complemented
26	C₂×#61664	C₂²	1	1	yes	characteristic, complemented
27	C₂×#61087	C₂²	1	1	yes	characteristic
28	C₂×#60399	C₂²	1	2	yes	—
29	C₂×#60391	C₂²	1	1	yes	characteristic, complemented
30	C₂×#60388	C₂²	1	1	yes	characteristic
31	#7739315	C₂²	1	1	yes	characteristic, complemented
32	C₂×#33570	C₂²	1	1	yes	characteristic, complemented
33	C₂×#33559	C₂²	1	1	yes	characteristic
34	C₂×#33559	C₂²	1	1	yes	characteristic, complemented
35	C₂×#33553	C₂²	1	2	yes	—
36	C₂×#33553	C₂²	1	2	yes	complemented
37	C₂×#33553	C₂²	1	2	yes	complemented
38	C₂×#33546	C₂²	1	1	yes	characteristic
39	C₂×#33546	C₂²	1	1	yes	characteristic, complemented
40	C₂×#33546	C₂²	1	1	yes	characteristic, complemented
41	C₂×#33359	C₂²	1	1	yes	characteristic, complemented
42	C₂×#33348	C₂²	1	2	yes	complemented
43	C₂×#32950	C₂²	1	1	yes	characteristic, complemented
44	#6628899	C₂²	1	2	yes	complemented
45	C₂×#32895	C₂²	1	1	yes	characteristic, complemented
46	C₂×#32895	C₂²	1	2	yes	complemented
47	C₂×#32896	C₂²	1	1	yes	characteristic, complemented
48	#6500196	C₂²	1	2	yes	complemented
49	#6499824	C₂²	1	2	yes	complemented
50	#6470214	C₂²	1	2	yes	complemented
51	C₂×#25798	C₂²	1	1	yes	characteristic, complemented
52	C₂×#24287	C₂²	1	1	yes	characteristic, complemented
53	C₂×#24422	C₂²	1	1	yes	characteristic, complemented
54	C₂×#24421	C₂²	1	1	yes	characteristic, complemented
55	C₂×#23875	C₂²	1	1	yes	characteristic, complemented
56	C₂×#23872	C₂²	1	1	yes	characteristic
57	C₂×#23882	C₂²	1	2	yes	—
58	#6437564	C₂²	1	2	yes	—
59	#6393497	C₂²	1	1	yes	characteristic, complemented
60	#6393353	C₂²	1	1	yes	characteristic, complemented
61	#6386055	C₂²	1	1	yes	characteristic, complemented
62	C₂×#22459	C₂²	1	1	yes	characteristic, complemented
63	C₂×#21477	C₂²	1	1	yes	characteristic, complemented
64	C₂×#13355	C₂²	1	2	yes	complemented
65	#498930	C₂²	1	2	yes	complemented
66	#498930	C₂²	1	2	yes	complemented
67	C₂×#13361	C₂²	1	2	yes	complemented
68	C₂×#13351	C₂²	1	2	yes	complemented
69	#498889	C₂²	1	2	yes	complemented
70	C₂×#13100	C₂²	1	2	yes	complemented
71	C₂×#13098	C₂²	1	2	yes	complemented
72	#494684	C₂²	1	2	yes	complemented
73	#494619	C₂²	1	1	yes	characteristic, complemented
74	C₂×#13054	C₂²	1	1	yes	characteristic, complemented
75	C₂×#13054	C₂²	1	1	yes	characteristic, complemented
76	C₂×#13051	C₂²	1	1	yes	characteristic, complemented
77	#494598	C₂²	1	1	yes	characteristic, complemented
78	#494598	C₂²	1	1	yes	characteristic, complemented
79	C₂×#12778	C₂²	1	1	yes	characteristic, complemented
80	C₂×#12765	C₂²	1	1	yes	characteristic, complemented
81	C₂×#12755	C₂²	1	2	yes	complemented
82	#493432	C₂²	1	1	yes	characteristic, complemented
83	C₂×#12718	C₂²	1	1	yes	characteristic, complemented
84	C₂×#12717	C₂²	1	1	yes	characteristic, complemented
85	C₂×#12711	C₂²	1	2	yes	complemented
86	#394091	C₂²	1	2	yes	complemented
87	#394081	C₂²	1	2	yes	complemented
88	#394044	C₂²	1	2	yes	complemented
89	#393939	C₂²	1	2	yes	complemented
90	#392717	C₂²	1	2	yes	complemented
91	#392665	C₂²	1	2	yes	complemented
92	#392141	C₂²	1	2	yes	complemented
93	#359611	C₂²	1	2	yes	complemented
94	#359546	C₂²	1	2	yes	complemented
95	#148474	C₂²	1	2	yes	complemented
96	#148265	C₂²	1	2	yes	complemented
97	#148260	C₂²	1	2	yes	complemented
98	#148021	C₂²	1	2	yes	complemented
99	#148014	C₂²	1	2	yes	complemented
100	#147856	C₂²	1	2	yes	complemented
101	#147818	C₂²	1	2	yes	complemented
102	#147764	C₂²	1	2	yes	complemented
103	#147764	C₂²	1	2	yes	complemented
104	#147762	C₂²	1	2	yes	complemented
105	#147759	C₂²	1	2	yes	complemented
106	#147755	C₂²	1	2	yes	complemented
107	#147755	C₂²	1	2	yes	complemented
108	#147751	C₂²	1	2	yes	complemented
109	#147751	C₂²	1	2	yes	complemented
110	#147751	C₂²	1	2	yes	complemented
111	#147726	C₂²	1	2	yes	complemented
112	#147586	C₂²	1	2	yes	complemented
113	#147586	C₂²	1	2	yes	complemented
114	#147574	C₂²	1	2	yes	complemented
115	#147517	C₂²	1	2	yes	complemented
116	#147498	C₂²	1	2	yes	complemented
117	#146724	C₂²	1	1	yes	characteristic, complemented
118	#146713	C₂²	1	1	yes	characteristic, complemented
119	#146646	C₂²	1	1	yes	characteristic, complemented
120	#146637	C₂²	1	1	yes	characteristic, complemented
121	#146591	C₂²	1	2	yes	complemented
122	#146587	C₂²	1	2	yes	complemented
123	C₂×2₋¹⁺⁶	C₂³	1	1	yes	characteristic, complemented
124	C₂×H(7,𝔽₂)	C₂³	1	1	yes	characteristic
125	C₂×#3586	C₂³	1	1	yes	characteristic, complemented
126	C₂×#3585	C₂³	1	1	yes	characteristic
127	C₂×#3584	C₂³	1	1	yes	characteristic, complemented
128	C₂²×#577	D₄	1	1	yes	characteristic, complemented
129	C₂²×#577	C₂³	1	1	yes	characteristic
130	C₂×#3573	C₂³	1	1	yes	characteristic, complemented
131	C₂×#3499	C₂³	1	1	yes	characteristic
132	C₂×#3498	C₂³	1	1	yes	characteristic
133	C₂×#3484	C₂³	1	2	yes	—
134	C₂×#3549	C₂³	1	1	yes	characteristic
135	C₂×#3537	C₂³	1	2	yes	—
136	C₂×#3481	C₂³	1	1	yes	characteristic
137	C₂×#3200	C₂³	1	2	yes	—
138	C₂²×#492	D₄	1	1	yes	characteristic, complemented
139	C₂×#3057	D₄	1	1	yes	characteristic, complemented
140	C₂×#3057	C₂³	1	1	yes	characteristic
141	C₂×#3039	D₄	1	1	yes	characteristic, complemented
142	C₂×#3038	D₄	1	1	yes	characteristic, complemented
143	C₂×#3028	C₂³	1	1	yes	characteristic, complemented
144	C₂×#3027	C₂³	1	2	yes	—
145	C₂×#3027	C₂³	1	2	yes	—
146	C₂×#3027	C₂³	1	1	yes	characteristic
147	C₂×#3025	C₂³	1	2	yes	—
148	C₂×#3025	C₂³	1	2	yes	—
149	C₂×#3025	C₂³	1	2	yes	—
150	#60388	D₄	1	8	yes	complemented
151	C₂×#3022	C₂³	1	1	yes	characteristic, complemented
152	C₂×#3022	C₂³	1	1	yes	characteristic, complemented
153	C₂×#3021	C₂³	1	1	yes	characteristic
154	C₂×#3021	C₂³	1	1	yes	characteristic
155	C₂×#3021	C₂³	1	2	yes	—
156	C₂×#3018	C₂³	1	1	yes	characteristic
157	C₂×#3018	C₂³	1	1	yes	characteristic
158	C₂×#3018	C₂³	1	1	yes	characteristic
159	C₂×#3010	D₄	1	1	yes	characteristic, complemented
160	C₂×#3010	C₂³	1	1	yes	characteristic
161	C₂×#3010	C₂³	1	2	yes	—
162	C₂×#3009	D₄	1	1	yes	characteristic, complemented
163	C₂×#3009	C₂³	1	1	yes	characteristic
164	C₂×#3003	D₄	1	2	yes	complemented
165	C₂²×#450	D₄	1	2	yes	complemented
166	C₂×#2979	C₂³	1	1	yes	characteristic
167	C₂×C₄×#135	D₄	1	1	yes	characteristic, complemented
168	C₂×#2931	C₂³	1	1	yes	characteristic
169	C₂×#2889	C₂³	1	1	yes	characteristic, complemented
170	C₂×#2888	C₂³	1	1	yes	characteristic
171	C₂×#2883	C₂³	1	2	yes	—
172	#37374	C₂³	1	2	yes	—
173	#35659	C₂³	1	2	yes	—
174	#34368	C₂³	1	1	yes	characteristic
175	#33559	D₄	1	8	yes	complemented
176	C₂×#2198	D₄	1	2	yes	complemented
177	C₂×#2197	D₄	1	4	yes	complemented
178	C₂×#2196	D₄	1	2	yes	complemented
179	C₂×#2134	C₂³	1	2	yes	—
180	C₂×#2132	C₂³	1	1	yes	characteristic
181	C₂×#2129	C₂³	1	2	yes	complemented
182	C₂×#2128	C₂³	1	2	yes	—
183	C₂×#2128	C₂³	1	2	yes	—
184	C₂×#2126	C₂³	1	1	yes	characteristic
185	C₂×#2126	C₂³	1	1	yes	characteristic
186	C₂×#2126	C₂³	1	1	yes	characteristic
187	C₂×#2123	C₂³	1	2	yes	complemented
188	C₂×#2122	C₂³	1	2	yes	—
189	C₂×#2122	C₂³	1	2	yes	—
190	C₂×#2122	C₂³	1	2	yes	—
191	C₂×#2120	C₂³	1	2	yes	—
192	C₂×#2120	C₂³	1	2	yes	—
193	C₂×#2120	C₂³	1	2	yes	—
194	C₂×#2120	C₂³	1	2	yes	—
195	#23872	D₄	1	8	yes	complemented
196	#23426	D₄	1	2	yes	complemented
197	#23423	D₄	1	2	yes	complemented
198	#23392	D₄	1	2	yes	complemented
199	#23386	D₄	1	2	yes	complemented
200	#21770	C₂³	1	2	yes	—
201	#21770	C₂³	1	2	yes	—
202	#21744	C₂³	1	2	yes	—
203	C₂×#1915	C₂³	1	1	yes	characteristic, complemented
204	C₂×#1914	C₂³	1	1	yes	characteristic
205	C₂×#1910	C₂³	1	2	yes	—
206	#20975	C₂³	1	2	yes	—
207	C₂×#1891	C₂³	1	2	yes	—
208	C₂×#1884	C₂³	1	1	yes	characteristic
209	#20933	D₄	1	2	yes	complemented
210	#20929	D₄	1	2	yes	complemented
211	#20899	C₂³	1	2	yes	—
212	C₂×#1858	C₂³	1	1	yes	characteristic, complemented
213	C₂×#1813	C₂³	1	1	yes	characteristic, complemented
214	C₂×#1796	C₂³	1	1	yes	characteristic, complemented
215	C₂×#1796	C₂³	1	2	yes	complemented
216	C₂×#1795	C₂³	1	2	yes	—
217	C₂×#1795	C₂³	1	1	yes	characteristic
218	C₂×#1794	C₂³	1	1	yes	characteristic, complemented
219	C₂×#1794	C₂³	1	2	yes	complemented
220	C₂×#1794	C₂³	1	2	yes	complemented
221	#20618	C₂³	1	2	yes	complemented
222	C₂×#1791	C₂³	1	1	yes	characteristic, complemented
223	C₂×#1791	C₂³	1	1	yes	characteristic, complemented
224	C₂×#1791	C₂³	1	2	yes	complemented
225	#20610	C₂³	1	2	yes	complemented
226	#20610	C₂³	1	2	yes	complemented
227	#20602	C₂³	1	2	yes	—
228	#20587	C₂³	1	2	yes	complemented
229	C₂×#1757	C₂³	1	1	yes	characteristic, complemented
230	C₂×#1395	C₂³	1	2	yes	complemented
231	C₂×#1395	C₂³	1	2	yes	complemented
232	C₂×#1395	C₂³	1	2	yes	complemented
233	#12587	C₂³	1	2	yes	complemented
234	#12583	C₂³	1	2	yes	complemented
235	C₂×#1392	C₂³	1	2	yes	complemented
236	C₂×#1391	C₂³	1	2	yes	complemented
237	C₂×#1391	C₂³	1	2	yes	complemented
238	#12575	C₂³	1	2	yes	complemented
239	#12575	C₂³	1	2	yes	complemented
240	#10764	C₂³	1	2	yes	complemented
241	#10759	C₂³	1	2	yes	complemented
242	#10748	C₂³	1	2	yes	complemented
243	#10742	C₂³	1	2	yes	complemented
244	H(7,𝔽₂)	C₂×D₄	1	4	yes	—
245	C₂×#585	C₂⁴	1	1	yes	characteristic
246	C₂×#585	C₂⁴	1	1	yes	characteristic
247	C₂×#585	C₂⁴	1	1	yes	characteristic
248	C₂²×2₋¹⁺⁴	C₂×D₄	1	1	yes	characteristic, complemented
249	C₂²×2₋¹⁺⁴	C₂⁴	1	1	yes	characteristic
250	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
251	C₂²×H(5,𝔽₂)	C₂⁴	1	1	yes	characteristic
252	C₂⁴×D₄	C₂×D₄	1	2	yes	—
253	#3585	C₂×D₄	1	4	yes	—
254	C₂²×#137	C₂×D₄	1	1	yes	characteristic
255	C₂²×#137	C₂×D₄	1	1	yes	characteristic
256	C₂²×#137	C₂×D₄	1	2	yes	—
257	C₂²×AGL(1,ℤ/8)	C₂×D₄	1	2	yes	—
258	C₂²×AGL(1,ℤ/8)	C₂×D₄	1	1	yes	characteristic
259	C₂²×AGL(1,ℤ/8)	C₂×D₄	1	1	yes	characteristic, complemented
260	C₂²×AGL(1,ℤ/8)	C₂×D₄	1	2	yes	complemented
261	C₂²×#135	C₂×D₄	1	1	yes	characteristic
262	C₂²×#135	C₂×D₄	1	2	yes	—
263	C₂³×SD₁₆	C₂×D₄	1	2	yes	—
264	C₂³×SD₁₆	C₂×D₄	1	1	yes	characteristic
265	C₂³×SD₁₆	C₂×D₄	1	1	yes	characteristic
266	C₂³×SD₁₆	C₂×D₄	1	1	yes	characteristic, complemented
267	C₂³×SD₁₆	C₂×D₄	1	2	yes	complemented
268	C₂³×SD₁₆	C₂×D₄	1	1	yes	characteristic, complemented
269	C₂×#568	C₂⁴	1	1	yes	characteristic
270	C₂²×#131	C₂×D₄	1	1	yes	characteristic, complemented
271	C₂²×#131	C₂⁴	1	1	yes	characteristic
272	#3549	C₂×D₄	1	4	yes	—
273	#3498	C₂×D₄	1	4	yes	—
274	#3498	C₂×D₄	1	4	yes	—
275	C₂×#559	C₂×D₄	1	1	yes	characteristic
276	C₂×#551	C₂×D₄	1	2	yes	—
277	C₂×D₄²	C₂×D₄	1	1	yes	characteristic
278	C₂×#536	C₂×D₄	1	1	yes	characteristic, complemented
279	C₂×#536	C₂⁴	1	1	yes	characteristic
280	C₂×#535	C₂×D₄	1	2	yes	—
281	C₂×#535	C₂×D₄	1	1	yes	characteristic
282	C₂×#535	C₂⁴	1	1	yes	characteristic
283	C₂×#535	C₂⁴	1	2	yes	—
284	C₂×#532	C₂⁴	1	1	yes	characteristic
285	C₂²×C₄⋊Q₈	C₂×D₄	1	1	yes	characteristic, complemented
286	C₂²×#127	C₂×D₄	1	1	yes	characteristic
287	C₂×#525	C₂×D₄	1	2	yes	—
288	C₂×#525	C₂×D₄	1	2	yes	complemented
289	C₂×#525	C₂⁴	1	2	yes	—
290	C₂²×C₂²⋊Q₈	C₂×D₄	1	2	yes	complemented
291	C₂×#518	C₂×D₄	1	2	yes	—
292	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
293	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic, complemented
294	#3027	C₂×D₄	1	8	yes	—
295	#3027	C₂×D₄	1	4	yes	complemented
296	C₂×#458	C₂×D₄	1	4	yes	—
297	C₂×B(4,𝔽₂)	C₂×D₄	1	4	yes	—
298	#3021	C₂×D₄	1	4	yes	—
299	#3021	C₂×D₄	1	4	yes	—
300	#3018	C₂×D₄	1	4	yes	—
301	#3018	C₂×D₄	1	4	yes	—
302	#3018	C₂×D₄	1	4	yes	—
303	#3018	C₂×D₄	1	4	yes	complemented
304	C₂×#455	C₂×D₄	1	2	yes	—
305	C₂×#453	C₂×D₄	1	2	yes	—
306	C₂×#427	C₂×D₄	1	1	yes	characteristic, complemented
307	C₂×#423	C₂×D₄	1	1	yes	characteristic, complemented
308	C₂×#417	C₂×D₄	1	2	yes	—
309	C₂×#419	C₂×D₄	1	1	yes	characteristic, complemented
310	C₂×#419	C₂×D₄	1	2	yes	complemented
311	C₂×#419	C₂×D₄	1	1	yes	characteristic, complemented
312	C₂×#418	C₂×D₄	1	1	yes	characteristic
313	C₂×#418	C₂×D₄	1	2	yes	—
314	C₂×#418	C₂×D₄	1	1	yes	characteristic, complemented
315	C₂×#418	C₂×D₄	1	2	yes	complemented
316	C₂×#416	C₂×D₄	1	1	yes	characteristic
317	C₂×#416	C₂×D₄	1	2	yes	—
318	C₂×#416	C₂×D₄	1	2	yes	complemented
319	C₂×#416	C₂×D₄	1	1	yes	characteristic, complemented
320	C₂²×#102	C₂×D₄	1	2	yes	—
321	C₂²×#102	C₂×D₄	1	2	yes	complemented
322	#2888	C₂×D₄	1	4	yes	—
323	C₂×#413	C₂⁴	1	2	yes	—
324	C₂×#413	C₂⁴	1	1	yes	characteristic
325	C₂×#413	C₂⁴	1	1	yes	characteristic
326	C₂×#413	C₂⁴	1	1	yes	characteristic
327	C₂×#410	C₂⁴	1	2	yes	—
328	C₂×#410	C₂⁴	1	2	yes	—
329	C₂×#410	C₂⁴	1	1	yes	characteristic
330	C₂×#410	C₂⁴	1	2	yes	—
331	C₂×#408	C₂×D₄	1	1	yes	characteristic, complemented
332	C₂×#408	C₂⁴	1	1	yes	characteristic
333	C₂×#408	C₂⁴	1	2	yes	—
334	C₂×#407	C₂×D₄	1	2	yes	complemented
335	C₂²×C₂²⋊C₈	C₂×D₄	1	2	yes	complemented
336	C₂²×C₄×C₈	C₂×D₄	1	1	yes	characteristic, complemented
337	#2311	C₂×D₄	1	2	yes	complemented
338	#2311	C₂⁴	1	2	yes	—
339	#2310	C₂×D₄	1	2	yes	complemented
340	#2126	C₂×D₄	1	4	yes	—
341	C₂×#354	C₂×D₄	1	2	yes	—
342	C₂×#353	C₂×D₄	1	2	yes	—
343	#2122	C₂×D₄	1	8	yes	—
344	C₂×#352	C₂×D₄	1	4	yes	—
345	C₂×AΣL(1,𝔽₁₆)	C₂×D₄	1	4	yes	—
346	#1914	C₂×D₄	1	4	yes	complemented
347	#1884	C₂×D₄	1	4	yes	complemented
348	#1795	C₂×D₄	1	4	yes	—
349	#1736	C₂×D₄	1	2	yes	complemented
350	#1735	C₂×D₄	1	2	yes	complemented
351	#1729	C₂×D₄	1	2	yes	complemented
352	#1729	C₂×D₄	1	2	yes	complemented
353	#585	C₂²×D₄	1	2	yes	—
354	#585	C₂²×D₄	1	2	yes	—
355	#585	C₂²×D₄	1	2	yes	—
356	#585	C₂²×D₄	1	2	yes	—
357	C₂×H(5,𝔽₂)	#120	1	4	yes	—
358	C₂×H(5,𝔽₂)	C₂²×D₄	1	2	yes	—
359	C₂×H(5,𝔽₂)	C₂²×D₄	1	2	yes	—
360	C₂×H(5,𝔽₂)	C₂²×D₄	1	2	yes	—
361	C₂×H(5,𝔽₂)	H(5,𝔽₂)	1	4	yes	—
362	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
363	C₂²×#41	C₂²×D₄	1	2	yes	—
364	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
365	C₂²×#41	C₂²×D₄	1	2	yes	—
366	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
367	C₂²×#41	C₂⁵	1	1	yes	characteristic
368	C₂³×Q₈	C₂²×D₄	1	2	yes	—
369	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
370	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
371	C₂³×D₄	C₂²×D₄	1	2	yes	—
372	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
373	C₂³×D₄	C₂²×D₄	1	2	yes	—
374	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
375	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
376	C₂²×Q₁₆	#120	1	1	yes	characteristic
377	C₂²×Q₁₆	#120	1	2	yes	—
378	C₂²×SD₁₆	#120	1	2	yes	—
379	C₂²×SD₁₆	#120	1	1	yes	characteristic
380	C₂²×SD₁₆	#120	1	2	yes	—
381	C₂²×SD₁₆	#120	1	2	yes	—
382	C₂²×SD₁₆	#120	1	2	yes	—
383	C₂²×SD₁₆	#120	1	1	yes	characteristic
384	C₂²×D₈	#120	1	2	yes	—
385	C₂²×D₈	#120	1	1	yes	characteristic
386	#568	C₂²×D₄	1	2	yes	—
387	C₂²×M₁₆	C₂²×D₄	1	2	yes	—
388	C₂²×M₁₆	C₂²×D₄	1	1	yes	characteristic
389	C₂²×M₁₆	C₂²×D₄	1	2	yes	—
390	C₂²×M₁₆	C₂²×D₄	1	1	yes	characteristic
391	C₂³×C₈	C₂²×D₄	1	1	yes	characteristic
392	C₂³×C₈	C₂²×D₄	1	2	yes	—
393	C₂³×C₈	C₂²×D₄	1	1	yes	characteristic
394	C₂³×C₈	C₂²×D₄	1	2	yes	—
395	#535	#120	1	4	yes	—
396	#535	C₂²×D₄	1	2	yes	—
397	#535	C₂²×D₄	1	2	yes	—
398	#535	C₂²×D₄	1	4	yes	—
399	#535	H(5,𝔽₂)	1	4	yes	—
400	#532	C₂²×D₄	1	2	yes	—
401	#532	C₂²×D₄	1	2	yes	—
402	#532	C₂²×D₄	1	2	yes	—
403	#532	H(5,𝔽₂)	1	2	yes	—
404	C₂×C₄⋊Q₈	H(5,𝔽₂)	1	1	yes	characteristic
405	C₂×#127	#120	1	4	yes	—
406	C₂×#127	C₂²×D₄	1	1	yes	characteristic
407	C₂×#124	C₂²×D₄	1	1	yes	characteristic
408	C₂×#124	H(5,𝔽₂)	1	1	yes	characteristic
409	C₂×#123	C₂²×D₄	1	2	yes	—
410	C₂×#123	H(5,𝔽₂)	1	2	yes	—
411	C₂×#120	C₂²×D₄	1	2	yes	—
412	C₂×#120	H(5,𝔽₂)	1	2	yes	—
413	C₄×#41	#120	1	4	yes	—
414	C₂×#117	C₂²×D₄	1	1	yes	characteristic
415	C₂×#117	C₂²×D₄	1	1	yes	characteristic
416	C₂×#117	C₂²×D₄	1	2	yes	—
417	C₂×#117	C₂²×D₄	1	2	yes	—
418	C₂×#117	C₂²×D₄	1	2	yes	—
419	C₂²×C₄⋊C₄	C₂²×D₄	1	2	yes	—
420	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
421	#455	#120	1	8	yes	—
422	#453	#120	1	8	yes	—
423	#413	C₂²×D₄	1	2	yes	—
424	#413	C₂²×D₄	1	2	yes	—
425	#413	C₂²×D₄	1	2	yes	—
426	#413	C₂²×D₄	1	2	yes	—
427	C₂×#100	C₂²×D₄	1	2	yes	—
428	#410	C₂²×D₄	1	2	yes	—
429	#410	C₂²×D₄	1	4	yes	—
430	C₂×#99	C₂²×D₄	1	4	yes	—
431	C₂⁵	D₄²	1	2	yes	—
432	H(5,𝔽₂)	C₂×#120	1	4	yes	—
433	C₂×#41	C₂×#120	1	2	yes	—
434	C₂×#41	C₂×#120	1	2	yes	—
435	C₂×#41	#534	1	2	yes	—
436	C₂×#41	D₄²	1	4	yes	—
437	C₂×#41	D₄²	1	4	yes	—
438	C₂×#41	D₄²	1	2	yes	—
439	C₂×#41	C₂³×D₄	1	1	yes	characteristic
440	C₂×#41	C₂³×D₄	1	1	yes	characteristic
441	C₂×#41	C₂³×D₄	1	1	yes	characteristic
442	C₂×#41	C₂×H(5,𝔽₂)	1	2	yes	—
443	C₂×#41	C₂×H(5,𝔽₂)	1	1	yes	characteristic
444	C₂×#41	C₂×H(5,𝔽₂)	1	2	yes	—
445	C₂²×Q₈	C₂×#120	1	2	yes	—
446	C₂²×Q₈	C₂×#120	1	1	yes	characteristic
447	C₂²×Q₈	C₂×#120	1	1	yes	characteristic
448	C₂²×Q₈	D₄²	1	1	yes	characteristic
449	C₂²×Q₈	C₂×H(5,𝔽₂)	1	1	yes	characteristic
450	C₂²×D₄	C₂×#120	1	2	yes	—
451	C₂²×D₄	C₂×#120	1	2	yes	—
452	C₂²×D₄	C₂×#120	1	2	yes	—
453	C₂²×D₄	C₂×#120	1	1	yes	characteristic
454	C₂²×D₄	C₂×#120	1	1	yes	characteristic
455	C₂²×D₄	#534	1	2	yes	—
456	C₂²×D₄	D₄²	1	4	yes	—
457	C₂²×D₄	D₄²	1	4	yes	—
458	C₂²×D₄	D₄²	1	4	yes	—
459	C₂²×D₄	D₄²	1	1	yes	characteristic
460	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
461	C₂²×D₄	C₂×H(5,𝔽₂)	1	2	yes	—
462	C₂³×C₄	D₄²	1	2	yes	—
463	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
464	C₂³×C₄	C₂³×D₄	1	2	yes	—
465	C₂×SD₁₆	B(4,𝔽₂)	1	2	yes	—
466	C₂×SD₁₆	B(4,𝔽₂)	1	2	yes	—
467	C₂×D₈	B(4,𝔽₂)	1	4	yes	—
468	C₂²×C₈	C₂×#120	1	2	yes	—
469	C₂²×C₈	C₂×#120	1	1	yes	characteristic
470	C₂²×C₈	C₂×#120	1	1	yes	characteristic
471	C₄⋊Q₈	#534	1	2	yes	—
472	C₄⋊Q₈	D₄²	1	2	yes	—
473	#127	C₂×#120	1	2	yes	—
474	#127	D₄²	1	2	yes	—
475	#124	C₂×#120	1	2	yes	—
476	#124	#534	1	2	yes	—
477	#124	D₄²	1	2	yes	—
478	#124	D₄²	1	2	yes	—
479	#117	C₂×#120	1	2	yes	—
480	#117	D₄²	1	4	yes	—
481	C₂×C₂²⋊C₄	D₄²	1	2	yes	—
482	C₂×C₂²⋊C₄	D₄²	1	2	yes	—
483	C₂×C₄²	C₂×#120	1	2	yes	—
484	C₂×C₄²	D₄²	1	1	yes	characteristic
485	C₂×C₄²	D₄²	1	1	yes	characteristic
486	C₂×C₄²	D₄²	1	2	yes	—
487	#100	C₂×#120	1	4	yes	—
488	C₂⁴	C₂×D₄²	1	2	yes	—
489	C₂⁴	#3484	1	1	yes	characteristic
490	C₂×Q₈	#2403	1	2	yes	—
491	C₂×Q₈	#2403	1	2	yes	—
492	C₂×Q₈	C₂×B(4,𝔽₂)	1	2	yes	—
493	C₂×Q₈	C₂×#534	1	1	yes	characteristic
494	C₂×Q₈	C₂×D₄²	1	1	yes	characteristic
495	C₂×Q₈	#3532	1	2	yes	—
496	C₂×D₄	#2403	1	4	yes	—
497	C₂×D₄	#2403	1	2	yes	—
498	C₂×D₄	#2403	1	2	yes	—
499	C₂×D₄	C₂×B(4,𝔽₂)	1	2	yes	—
500	C₂×D₄	C₂×B(4,𝔽₂)	1	2	yes	—
501	C₂×D₄	C₂×B(4,𝔽₂)	1	2	yes	—
502	C₂×D₄	C₂²×#120	1	1	yes	characteristic
503	C₂×D₄	C₂×D₄²	1	1	yes	characteristic
504	C₂×D₄	#3484	1	2	yes	—
505	C₂×D₄	#3484	1	2	yes	—
506	C₂×D₄	#3484	1	2	yes	—
507	C₂×D₄	#3484	1	2	yes	—
508	C₂×D₄	#3532	1	2	yes	—
509	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
510	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
511	C₂²×C₄	C₂×#534	1	1	yes	characteristic
512	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
513	C₂²×C₄	C₂×D₄²	1	2	yes	—
514	C₂²×C₄	C₂×D₄²	1	2	yes	—
515	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
516	C₂²×C₄	C₂×D₄²	1	2	yes	—
517	C₂²×C₄	#3484	1	2	yes	—
518	C₂²×C₄	#3484	1	1	yes	characteristic
519	C₂²×C₄	#3484	1	2	yes	—
520	C₂×C₈	C₂×B(4,𝔽₂)	1	1	yes	characteristic
521	C₂×C₈	C₂×B(4,𝔽₂)	1	1	yes	characteristic
522	C₂×C₈	C₂×B(4,𝔽₂)	1	2	yes	—
523	C₄²	#2403	1	2	yes	—
524	C₄²	#2403	1	2	yes	—
525	C₂³	#35346	1	1	yes	characteristic
526	C₂³	D₄×#120	1	1	yes	characteristic
527	C₂³	D₄×#120	1	2	yes	—
528	C₂³	#37644	1	1	yes	characteristic
529	C₂³	#58990	1	2	yes	—
530	D₄	#23900	1	4	yes	—
531	C₂×C₄	C₂×#2403	1	1	yes	characteristic
532	C₂×C₄	C₂×#2403	1	1	yes	characteristic
533	C₂×C₄	D₄×#120	1	1	yes	characteristic
534	C₂×C₄	#37644	1	1	yes	characteristic
535	C₂×C₄	#37644	1	2	yes	—
536	C₂×C₄	#58990	1	2	yes	—
537	C₂×C₄	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
538	C₂×C₄	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
539	C₂×C₄	#60399	1	1	yes	characteristic
540	C₂×C₄	#60399	1	1	yes	characteristic
541	C₂²	#647656	1	1	yes	characteristic
542	C₂²	D₄×B(4,𝔽₂)	1	1	yes	characteristic
543	C₂²	D₄×B(4,𝔽₂)	1	1	yes	characteristic
544	C₄	C₂×#23900	1	1	yes	characteristic
545	C₄	#6437632	1	1	yes	characteristic
546	C₄	D₄×B(4,𝔽₂)	1	1	yes	characteristic
547	C₄	D₄×B(4,𝔽₂)	1	1	yes	characteristic
548	C₂	#72216660	1	1	yes	characteristic
549	C₂	#72236997	1	1	yes	characteristic
550	C₂	#72237525	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	D₄×B(4,𝔽₂)
commutator, Frattini, cosocle	C₂²×#41	C₂⁵
LCS	G ▷ C₂²×#41 ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×#577 ◁ G
LECS	G ▷ C₂²×#41 ▷ C₂² ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72337447	C₂	semidirect
2. #72337443	C₂	semidirect
3. C₂×#6573703	C₂	semidirect
4. #72337439	C₂	semidirect
5. #72337437	C₂	semidirect
6. #72337435	C₂	semidirect
7. #72337434	C₂	semidirect
8. #72337433	C₂	semidirect
9. #72337431	C₂	semidirect
10. #72337430	C₂	semidirect
11. #72337428	C₂	semidirect
12. #72315278	C₂	semidirect
13. C₂×#499889	C₂	semidirect
14. #72313178	C₂	semidirect
15. #72313143	C₂	semidirect
16. #72312259	C₂	semidirect
17. #72312095	C₂	semidirect
18. #72312034	C₂	semidirect
19. #72311838	C₂	semidirect
20. #72306416	C₂	semidirect
21. #72280900	C₂	semidirect
22. C₂×#7622880	C₂	semidirect
23. C₂×#511819	C₂	semidirect
24. C₂×#63092	C₂²	semidirect
25. C₂×#63011	C₂²	semidirect
26. C₂×#61664	C₂²	semidirect
29. C₂×#60391	C₂²	semidirect
31. #7739315	C₂²	semidirect
32. C₂×#33570	C₂²	semidirect
34. C₂×#33559	C₂²	semidirect
36. C₂×#33553	C₂²	semidirect
37. C₂×#33553	C₂²	semidirect
39. C₂×#33546	C₂²	semidirect
40. C₂×#33546	C₂²	semidirect
41. C₂×#33359	C₂²	semidirect
42. C₂×#33348	C₂²	semidirect
43. C₂×#32950	C₂²	semidirect
44. #6628899	C₂²	semidirect
45. C₂×#32895	C₂²	semidirect
46. C₂×#32895	C₂²	semidirect
47. C₂×#32896	C₂²	semidirect
48. #6500196	C₂²	semidirect
49. #6499824	C₂²	semidirect
50. #6470214	C₂²	semidirect
51. C₂×#25798	C₂²	semidirect
52. C₂×#24287	C₂²	semidirect
53. C₂×#24422	C₂²	semidirect
54. C₂×#24421	C₂²	semidirect
55. C₂×#23875	C₂²	semidirect
59. #6393497	C₂²	semidirect
60. #6393353	C₂²	semidirect
61. #6386055	C₂²	semidirect
62. C₂×#22459	C₂²	semidirect
63. C₂×#21477	C₂²	semidirect
64. C₂×#13355	C₂²	semidirect
65. #498930	C₂²	semidirect
66. #498930	C₂²	semidirect
67. C₂×#13361	C₂²	semidirect
68. C₂×#13351	C₂²	semidirect
69. #498889	C₂²	semidirect
70. C₂×#13100	C₂²	semidirect
71. C₂×#13098	C₂²	semidirect
72. #494684	C₂²	semidirect
73. #494619	C₂²	semidirect
74. C₂×#13054	C₂²	semidirect
75. C₂×#13054	C₂²	semidirect
76. C₂×#13051	C₂²	semidirect
77. #494598	C₂²	semidirect
78. #494598	C₂²	semidirect
79. C₂×#12778	C₂²	semidirect
80. C₂×#12765	C₂²	semidirect
81. C₂×#12755	C₂²	semidirect
82. #493432	C₂²	semidirect
83. C₂×#12718	C₂²	semidirect
84. C₂×#12717	C₂²	semidirect
85. C₂×#12711	C₂²	semidirect
86. #394091	C₂²	semidirect
87. #394081	C₂²	semidirect
88. #394044	C₂²	semidirect
89. #393939	C₂²	semidirect
90. #392717	C₂²	semidirect
91. #392665	C₂²	semidirect
92. #392141	C₂²	semidirect
93. #359611	C₂²	semidirect
94. #359546	C₂²	semidirect
95. #148474	C₂²	semidirect
96. #148265	C₂²	semidirect
97. #148260	C₂²	semidirect
98. #148021	C₂²	semidirect
99. #148014	C₂²	semidirect
100. #147856	C₂²	semidirect
101. #147818	C₂²	semidirect
102. #147764	C₂²	semidirect
103. #147764	C₂²	semidirect
104. #147762	C₂²	semidirect
105. #147759	C₂²	semidirect
106. #147755	C₂²	semidirect
107. #147755	C₂²	semidirect
108. #147751	C₂²	semidirect
109. #147751	C₂²	semidirect
110. #147751	C₂²	semidirect
111. #147726	C₂²	semidirect
112. #147586	C₂²	semidirect
113. #147586	C₂²	semidirect
114. #147574	C₂²	semidirect
115. #147517	C₂²	semidirect
116. #147498	C₂²	semidirect
117. #146724	C₂²	semidirect
118. #146713	C₂²	semidirect
119. #146646	C₂²	semidirect
120. #146637	C₂²	semidirect
121. #146591	C₂²	semidirect
122. #146587	C₂²	semidirect
123. C₂×2₋¹⁺⁶	C₂³	semidirect
125. C₂×#3586	C₂³	semidirect
127. C₂×#3584	C₂³	semidirect
128. C₂²×#577	D₄	semidirect
130. C₂×#3573	C₂³	semidirect
138. C₂²×#492	D₄	semidirect
139. C₂×#3057	D₄	semidirect
141. C₂×#3039	D₄	semidirect
142. C₂×#3038	D₄	semidirect
143. C₂×#3028	C₂³	semidirect
150. #60388	D₄	semidirect
151. C₂×#3022	C₂³	semidirect
152. C₂×#3022	C₂³	semidirect
159. C₂×#3010	D₄	semidirect
162. C₂×#3009	D₄	semidirect
164. C₂×#3003	D₄	semidirect
165. C₂²×#450	D₄	semidirect
167. C₂×C₄×#135	D₄	semidirect
169. C₂×#2889	C₂³	semidirect
175. #33559	D₄	semidirect
176. C₂×#2198	D₄	semidirect
177. C₂×#2197	D₄	semidirect
178. C₂×#2196	D₄	semidirect
181. C₂×#2129	C₂³	semidirect
187. C₂×#2123	C₂³	semidirect
195. #23872	D₄	semidirect
196. #23426	D₄	semidirect
197. #23423	D₄	semidirect
198. #23392	D₄	semidirect
199. #23386	D₄	semidirect
203. C₂×#1915	C₂³	semidirect
209. #20933	D₄	semidirect
210. #20929	D₄	semidirect
212. C₂×#1858	C₂³	semidirect
213. C₂×#1813	C₂³	semidirect
214. C₂×#1796	C₂³	semidirect
215. C₂×#1796	C₂³	semidirect
218. C₂×#1794	C₂³	semidirect
219. C₂×#1794	C₂³	semidirect
220. C₂×#1794	C₂³	semidirect
221. #20618	C₂³	semidirect
222. C₂×#1791	C₂³	semidirect
223. C₂×#1791	C₂³	semidirect
224. C₂×#1791	C₂³	semidirect
225. #20610	C₂³	semidirect
226. #20610	C₂³	semidirect
228. #20587	C₂³	semidirect
229. C₂×#1757	C₂³	semidirect
230. C₂×#1395	C₂³	semidirect
231. C₂×#1395	C₂³	semidirect
232. C₂×#1395	C₂³	semidirect
233. #12587	C₂³	semidirect
234. #12583	C₂³	semidirect
235. C₂×#1392	C₂³	semidirect
236. C₂×#1391	C₂³	semidirect
237. C₂×#1391	C₂³	semidirect
238. #12575	C₂³	semidirect
239. #12575	C₂³	semidirect
240. #10764	C₂³	semidirect
241. #10759	C₂³	semidirect
242. #10748	C₂³	semidirect
243. #10742	C₂³	semidirect
248. C₂²×2₋¹⁺⁴	C₂×D₄	semidirect
259. C₂²×AGL(1,ℤ/8)	C₂×D₄	semidirect
260. C₂²×AGL(1,ℤ/8)	C₂×D₄	semidirect
266. C₂³×SD₁₆	C₂×D₄	semidirect
267. C₂³×SD₁₆	C₂×D₄	semidirect
268. C₂³×SD₁₆	C₂×D₄	semidirect
270. C₂²×#131	C₂×D₄	semidirect
278. C₂×#536	C₂×D₄	semidirect
285. C₂²×C₄⋊Q₈	C₂×D₄	semidirect
288. C₂×#525	C₂×D₄	semidirect
290. C₂²×C₂²⋊Q₈	C₂×D₄	semidirect
293. C₂×C₄×#41	C₂×D₄	semidirect
295. #3027	C₂×D₄	semidirect
303. #3018	C₂×D₄	semidirect
306. C₂×#427	C₂×D₄	semidirect
307. C₂×#423	C₂×D₄	semidirect
309. C₂×#419	C₂×D₄	semidirect
310. C₂×#419	C₂×D₄	semidirect
311. C₂×#419	C₂×D₄	semidirect
314. C₂×#418	C₂×D₄	semidirect
315. C₂×#418	C₂×D₄	semidirect
318. C₂×#416	C₂×D₄	semidirect
319. C₂×#416	C₂×D₄	semidirect
321. C₂²×#102	C₂×D₄	semidirect
331. C₂×#408	C₂×D₄	semidirect
334. C₂×#407	C₂×D₄	semidirect
335. C₂²×C₂²⋊C₈	C₂×D₄	semidirect
336. C₂²×C₄×C₈	C₂×D₄	semidirect
337. #2311	C₂×D₄	semidirect
339. #2310	C₂×D₄	semidirect
346. #1914	C₂×D₄	semidirect
347. #1884	C₂×D₄	semidirect
349. #1736	C₂×D₄	semidirect
350. #1735	C₂×D₄	semidirect
351. #1729	C₂×D₄	semidirect
352. #1729	C₂×D₄	semidirect

Maximal subgroups

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

subgroup	index
#72337447	2
#72337443	2
C₂×#6573703	2
#72337439	2
#72337437	2
#72337435	2
#72337434	2
#72337433	2
#72337431	2
#72337430	2
#72337428	2
#72315278	2
C₂×#499889	2
#72313178	2
#72313143	2
#72312259	2
#72312095	2
#72312034	2
#72311838	2
#72306416	2
#72280900	2
C₂×#7622880	2
C₂×#511819	2