Subgroups — #72337503

Order 2048.

At least 10485 conjugacy classes of subgroups; only the 1392 normal subgroups are shown.

The subgroup lattice has 624 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72337500	C₂	1	1	yes	maximal, characteristic, complemented
2	#72337497	C₂	1	1	yes	maximal, characteristic, complemented
3	#72337490	C₂	1	1	yes	maximal, characteristic, complemented
4	#72337437	C₂	1	8	yes	maximal, complemented
5	#72337424	C₂	1	8	yes	maximal, complemented
6	#72312860	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#498916	C₂	1	1	yes	maximal, characteristic, complemented
8	#72312313	C₂	1	1	yes	maximal, characteristic, complemented
9	#72303790	C₂	1	1	yes	maximal, characteristic, complemented
10	#72303787	C₂	1	1	yes	maximal, characteristic, complemented
11	#72280881	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#498898	C₂	1	1	yes	maximal, characteristic, complemented
13	#72279215	C₂	1	1	yes	maximal, characteristic, complemented
14	#72256636	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#6443344	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#33553	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×#33553	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#63090	C₂²	1	1	yes	characteristic, complemented
19	C₂²×#3537	C₂²	1	1	yes	characteristic
20	C₂×#60753	C₂²	1	1	yes	characteristic
21	C₂×#60454	C₂²	1	1	yes	characteristic
22	C₂×#60398	C₂²	1	1	yes	characteristic, complemented
23	C₂²×#3027	C₂²	1	1	yes	characteristic
24	C₂²×#3027	C₂²	1	1	yes	characteristic
25	C₂²×#3025	C₂²	1	1	yes	characteristic
26	C₂²×#3025	C₂²	1	1	yes	characteristic
27	C₂×#60387	C₂²	1	1	yes	characteristic, complemented
28	C₂²×#3021	C₂²	1	1	yes	characteristic
29	C₂²×#3021	C₂²	1	1	yes	characteristic
30	#7634872	C₂²	1	1	yes	characteristic
31	C₂×#33553	C₂²	1	8	yes	complemented
32	C₂×#33553	C₂²	1	8	yes	complemented
33	C₂×#33358	C₂²	1	1	yes	characteristic, complemented
34	C₂²×#2128	C₂²	1	1	yes	characteristic
35	C₂²×#2128	C₂²	1	1	yes	characteristic
36	C₂×#33347	C₂²	1	1	yes	characteristic, complemented
37	C₂²×#2122	C₂²	1	1	yes	characteristic
38	C₂²×#2122	C₂²	1	1	yes	characteristic
39	C₂²×#2120	C₂²	1	1	yes	characteristic
40	C₂²×#2120	C₂²	1	1	yes	characteristic
41	#6500196	C₂²	1	4	yes	complemented
42	#6500186	C₂²	1	4	yes	complemented
43	C₂×#25799	C₂²	1	4	yes	complemented
44	C₂×#25798	C₂²	1	4	yes	complemented
45	#6374164	C₂²	1	1	yes	characteristic
46	#6371484	C₂²	1	1	yes	characteristic
47	#6371364	C₂²	1	1	yes	characteristic
48	C₂×#20620	C₂²	1	1	yes	characteristic, complemented
49	C₂×#20620	C₂²	1	1	yes	characteristic, complemented
50	#6370746	C₂²	1	1	yes	characteristic, complemented
51	#6370734	C₂²	1	1	yes	characteristic, complemented
52	C₂×#20401	C₂²	1	1	yes	characteristic, complemented
53	#498930	C₂²	1	4	yes	complemented
54	#498929	C₂²	1	4	yes	complemented
55	C₂×#13361	C₂²	1	4	yes	complemented
56	C₂×#13360	C₂²	1	4	yes	complemented
57	C₂×#13351	C₂²	1	4	yes	complemented
58	C₂×#13350	C₂²	1	4	yes	complemented
59	#498889	C₂²	1	4	yes	complemented
60	#498888	C₂²	1	4	yes	complemented
61	#492899	C₂²	1	1	yes	characteristic, complemented
62	C₂×#12579	C₂²	1	1	yes	characteristic, complemented
63	C₂×#12577	C₂²	1	1	yes	characteristic, complemented
64	#492886	C₂²	1	1	yes	characteristic, complemented
65	#394044	C₂²	1	8	yes	complemented
66	#393939	C₂²	1	8	yes	complemented
67	#353340	C₂²	1	1	yes	characteristic, complemented
68	#353326	C₂²	1	1	yes	characteristic, complemented
69	#147764	C₂²	1	8	yes	complemented
70	#147759	C₂²	1	8	yes	complemented
71	#147726	C₂²	1	4	yes	complemented
72	#147725	C₂²	1	4	yes	complemented
73	#147517	C₂²	1	8	yes	complemented
74	#147498	C₂²	1	8	yes	complemented
75	C₂²×#585	C₂³	1	1	yes	characteristic
76	C₂²×#585	C₂³	1	1	yes	characteristic
77	C₂×#3584	C₂³	1	4	yes	complemented
78	C₂³×AGL(1,ℤ/8)	D₄	1	1	yes	characteristic, complemented
79	C₂²×#568	C₂³	1	1	yes	characteristic
80	C₂×#3537	C₂³	1	4	yes	—
81	C₂×#3449	C₂³	1	1	yes	characteristic
82	C₂²×#535	C₂³	1	1	yes	characteristic
83	C₂²×#535	C₂³	1	1	yes	characteristic
84	C₂²×#525	C₂³	1	1	yes	characteristic
85	C₂×#3200	C₂³	1	2	yes	—
86	C₂×#3199	C₂³	1	2	yes	—
87	C₂×#3058	D₄	1	2	yes	complemented
88	C₂×#3058	C₂³	1	2	yes	—
89	C₂×#3057	D₄	1	2	yes	complemented
90	C₂×#3057	C₂³	1	2	yes	—
91	C₂×#3028	C₂³	1	2	yes	complemented
92	C₂×#3027	D₄	1	8	yes	complemented
93	C₂×#3027	C₂³	1	4	yes	—
94	C₂×#3027	C₂³	1	4	yes	—
95	C₂×#3027	C₂³	1	2	yes	complemented
96	C₂×#3025	C₂³	1	4	yes	—
97	C₂×#3025	C₂³	1	4	yes	—
98	C₂×#3022	C₂³	1	2	yes	complemented
99	C₂×#3021	D₄	1	8	yes	complemented
100	C₂×#3021	C₂³	1	4	yes	—
101	C₂×#3021	C₂³	1	4	yes	—
102	C₂×#3021	C₂³	1	2	yes	complemented
103	C₂×#2911	D₄	1	1	yes	characteristic, complemented
104	C₂×#2896	D₄	1	1	yes	characteristic, complemented
105	C₂²×#418	D₄	1	1	yes	characteristic, complemented
106	C₂²×#418	D₄	1	1	yes	characteristic, complemented
107	C₂²×#418	D₄	1	1	yes	characteristic, complemented
108	C₂²×#413	C₂³	1	1	yes	characteristic
109	C₂²×#413	C₂³	1	1	yes	characteristic
110	C₂²×#410	C₂³	1	1	yes	characteristic
111	C₂²×#410	C₂³	1	1	yes	characteristic
112	C₂²×#410	C₂³	1	1	yes	characteristic
113	C₂²×#410	C₂³	1	1	yes	characteristic
114	C₂×#2879	C₂³	1	1	yes	characteristic
115	C₂²×#407	D₄	1	1	yes	characteristic, complemented
116	C₂²×#407	D₄	1	1	yes	characteristic, complemented
117	#37374	C₂³	1	2	yes	—
118	#37269	C₂³	1	2	yes	—
119	#34044	C₂³	1	1	yes	characteristic
120	C₂×#2129	C₂³	1	2	yes	complemented
121	C₂×#2128	D₄	1	8	yes	complemented
122	C₂×#2128	C₂³	1	4	yes	—
123	C₂×#2128	C₂³	1	4	yes	—
124	C₂×#2128	C₂³	1	2	yes	complemented
125	C₂×#2123	C₂³	1	2	yes	complemented
126	C₂×#2122	D₄	1	8	yes	complemented
127	C₂×#2122	C₂³	1	4	yes	—
128	C₂×#2122	C₂³	1	4	yes	—
129	C₂×#2122	C₂³	1	2	yes	complemented
130	C₂×#2120	D₄	1	4	yes	complemented
131	C₂×#2120	D₄	1	4	yes	complemented
132	C₂×#2120	C₂³	1	4	yes	—
133	C₂×#2120	C₂³	1	4	yes	—
134	C₂²×#352	D₄	1	2	yes	complemented
135	C₂²×#352	D₄	1	2	yes	complemented
136	C₂²×AΣL(1,𝔽₁₆)	D₄	1	2	yes	complemented
137	C₂²×AΣL(1,𝔽₁₆)	D₄	1	2	yes	complemented
138	#21770	C₂³	1	4	yes	—
139	#20975	D₄	1	4	yes	complemented
140	#20975	C₂³	1	4	yes	—
141	#20899	D₄	1	4	yes	complemented
142	#20899	C₂³	1	4	yes	—
143	C₂×#1794	C₂³	1	4	yes	complemented
144	C₂×#1794	C₂³	1	4	yes	complemented
145	#20618	C₂³	1	4	yes	complemented
146	#20610	C₂³	1	4	yes	complemented
147	C₂×#1757	C₂³	1	4	yes	complemented
148	#20347	D₄	1	1	yes	characteristic, complemented
149	#20347	D₄	1	1	yes	characteristic, complemented
150	#20335	D₄	1	1	yes	characteristic, complemented
151	#20335	D₄	1	1	yes	characteristic, complemented
152	#12583	C₂³	1	4	yes	complemented
153	C₂×#1392	C₂³	1	4	yes	complemented
154	C₂×#1391	C₂³	1	4	yes	complemented
155	#12575	C₂³	1	4	yes	complemented
156	#10764	C₂³	1	4	yes	complemented
157	#10759	C₂³	1	4	yes	complemented
158	C₂×#585	C₂×D₄	1	4	yes	—
159	C₂×#585	C₂×D₄	1	4	yes	—
160	C₂×#585	C₂⁴	1	2	yes	—
161	C₂×#585	C₂⁴	1	2	yes	—
162	C₂³×#41	C₂×D₄	1	1	yes	characteristic
163	C₂³×#41	C₂⁴	1	1	yes	characteristic
164	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
165	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
166	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
167	C₂³×SD₁₆	C₂×D₄	1	2	yes	complemented
168	C₂³×D₈	C₂×D₄	1	2	yes	complemented
169	C₂²×#131	C₂×D₄	1	2	yes	—
170	C₂²×#131	C₂×D₄	1	2	yes	—
171	C₂²×#131	C₂×D₄	1	2	yes	—
172	C₂²×#131	C₂⁴	1	2	yes	—
173	C₂³×M₁₆	C₂×D₄	1	1	yes	characteristic
174	C₂³×M₁₆	C₂×D₄	1	1	yes	characteristic
175	C₂³×M₁₆	C₂×D₄	1	1	yes	characteristic
176	C₂³×M₁₆	C₂×D₄	1	1	yes	characteristic
177	C₂³×M₁₆	C₂×D₄	1	1	yes	characteristic
178	C₂³×M₁₆	C₂×D₄	1	1	yes	characteristic
179	C₂³×M₁₆	C₂×D₄	1	1	yes	characteristic
180	C₂³×M₁₆	C₂×D₄	1	1	yes	characteristic
181	C₂×#536	C₂×D₄	1	1	yes	characteristic
182	C₂×#536	C₂⁴	1	1	yes	characteristic
183	C₂×#535	C₂×D₄	1	4	yes	—
184	C₂×#535	C₂×D₄	1	4	yes	—
185	C₂×#535	C₂×D₄	1	4	yes	—
186	C₂×#535	C₂×D₄	1	4	yes	—
187	C₂×#535	C₂×D₄	1	1	yes	characteristic
188	C₂×#535	C₂×D₄	1	2	yes	—
189	C₂×#535	C₂×D₄	1	2	yes	—
190	C₂×#535	C₂⁴	1	1	yes	characteristic
191	C₂×#535	C₂⁴	1	2	yes	—
192	C₂×#535	C₂⁴	1	2	yes	—
193	C₂×#525	C₂×D₄	1	2	yes	—
194	C₂×#525	C₂×D₄	1	2	yes	—
195	C₂×#525	C₂×D₄	1	2	yes	—
196	C₂×#525	C₂⁴	1	2	yes	—
197	C₂²×#123	C₂×D₄	1	1	yes	characteristic
198	C₂²×#123	C₂×D₄	1	1	yes	characteristic
199	C₂²×#120	C₂×D₄	1	1	yes	characteristic
200	C₂²×#120	C₂×D₄	1	1	yes	characteristic
201	C₂²×#117	C₂×D₄	1	1	yes	characteristic
202	C₂²×#117	C₂×D₄	1	1	yes	characteristic
203	C₂²×#117	C₂×D₄	1	1	yes	characteristic
204	C₂²×#117	C₂×D₄	1	1	yes	characteristic
205	C₂²×#117	C₂×D₄	1	1	yes	characteristic
206	C₂²×#117	C₂×D₄	1	1	yes	characteristic
207	#3027	C₂×D₄	1	16	yes	complemented
208	#3021	C₂×D₄	1	16	yes	complemented
209	C₂×#427	C₂×D₄	1	2	yes	complemented
210	C₂×#427	C₂×D₄	1	2	yes	complemented
211	C₂×#419	C₂×D₄	1	2	yes	complemented
212	C₂×#418	C₂×D₄	1	2	yes	complemented
213	C₂×#418	C₂×D₄	1	2	yes	complemented
214	C₂×#418	C₂×D₄	1	2	yes	complemented
215	C₂×#418	C₂×D₄	1	4	yes	complemented
216	C₂²×#102	C₂×D₄	1	4	yes	complemented
217	C₂×#413	C₂×D₄	1	4	yes	—
218	C₂×#413	C₂×D₄	1	4	yes	—
219	C₂×#413	C₂×D₄	1	2	yes	—
220	C₂×#413	C₂×D₄	1	2	yes	—
221	C₂×#413	C₂⁴	1	2	yes	—
222	C₂×#413	C₂⁴	1	2	yes	—
223	C₂²×#100	C₂×D₄	1	2	yes	—
224	C₂²×#100	C₂×D₄	1	2	yes	—
225	C₂×#410	C₂×D₄	1	4	yes	—
226	C₂×#410	C₂×D₄	1	4	yes	—
227	C₂×#410	C₂×D₄	1	4	yes	—
228	C₂×#410	C₂×D₄	1	4	yes	—
229	C₂×#410	C₂×D₄	1	2	yes	—
230	C₂×#410	C₂×D₄	1	2	yes	—
231	C₂×#410	C₂⁴	1	2	yes	—
232	C₂×#410	C₂⁴	1	2	yes	—
233	C₂×#410	C₂⁴	1	2	yes	—
234	C₂×#410	C₂⁴	1	2	yes	—
235	C₂²×#99	C₂×D₄	1	2	yes	—
236	C₂²×#99	C₂×D₄	1	2	yes	—
237	C₂×#408	C₂×D₄	1	2	yes	—
238	C₂×#408	C₂⁴	1	2	yes	—
239	C₂×#407	C₂×D₄	1	4	yes	complemented
240	C₂²×C₂²⋊C₈	C₂×D₄	1	4	yes	complemented
241	#2311	C₂×D₄	1	2	yes	—
242	#2311	C₂⁴	1	2	yes	—
243	#2128	C₂×D₄	1	16	yes	complemented
244	#2122	C₂×D₄	1	16	yes	complemented
245	C₂×#352	C₂×D₄	1	8	yes	complemented
246	C₂×#352	C₂×D₄	1	8	yes	complemented
247	C₂×AΣL(1,𝔽₁₆)	C₂×D₄	1	8	yes	complemented
248	C₂×AΣL(1,𝔽₁₆)	C₂×D₄	1	8	yes	complemented
249	#1736	C₂×D₄	1	4	yes	complemented
250	#1735	C₂×D₄	1	4	yes	complemented
251	#1729	C₂×D₄	1	4	yes	complemented
252	#1729	C₂×D₄	1	4	yes	complemented
253	C₂⁶	#127	1	1	yes	characteristic
254	#585	C₂²×D₄	1	4	yes	—
255	#585	C₂²×D₄	1	4	yes	—
256	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
257	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
258	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
259	C₂²×#41	C₂²×D₄	1	2	yes	—
260	C₂²×#41	C₂²×D₄	1	2	yes	—
261	C₂²×#41	C₂²×D₄	1	2	yes	—
262	C₂²×#41	C₂²×D₄	1	2	yes	—
263	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
264	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
265	C₂²×#41	H(5,𝔽₂)	1	2	yes	—
266	C₂²×#41	H(5,𝔽₂)	1	2	yes	—
267	C₂²×#41	H(5,𝔽₂)	1	2	yes	—
268	C₂²×#41	H(5,𝔽₂)	1	1	yes	characteristic
269	C₂²×#41	H(5,𝔽₂)	1	2	yes	—
270	C₂²×#41	H(5,𝔽₂)	1	1	yes	characteristic
271	C₂²×#41	C₂⁵	1	1	yes	characteristic
272	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
273	C₂³×Q₈	H(5,𝔽₂)	1	1	yes	characteristic
274	C₂³×D₄	#120	1	4	yes	—
275	C₂³×D₄	#127	1	4	yes	—
276	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
277	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
278	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
279	C₂³×D₄	C₂²×D₄	1	2	yes	—
280	C₂³×D₄	C₂²×D₄	1	2	yes	—
281	C₂³×D₄	H(5,𝔽₂)	1	1	yes	characteristic
282	C₂⁴×C₄	#127	1	1	yes	characteristic
283	C₂⁴×C₄	#127	1	2	yes	—
284	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
285	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
286	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
287	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
288	C₂²×M₁₆	#120	1	2	yes	—
289	C₂²×M₁₆	#120	1	1	yes	characteristic
290	C₂²×M₁₆	#120	1	1	yes	characteristic
291	C₂²×M₁₆	#120	1	2	yes	—
292	C₂²×M₁₆	#120	1	2	yes	—
293	C₂²×M₁₆	#120	1	1	yes	characteristic
294	C₂²×M₁₆	#120	1	1	yes	characteristic
295	C₂²×M₁₆	C₂²×D₄	1	2	yes	—
296	C₂²×M₁₆	C₂²×D₄	1	2	yes	—
297	C₂²×M₁₆	C₂²×D₄	1	2	yes	—
298	C₂²×M₁₆	C₂²×D₄	1	2	yes	—
299	C₂³×C₈	#120	1	2	yes	—
300	C₂³×C₈	#120	1	2	yes	—
301	C₂³×C₈	#120	1	2	yes	—
302	C₂³×C₈	C₂²×D₄	1	2	yes	—
303	C₂³×C₈	C₂²×D₄	1	2	yes	—
304	C₂³×C₈	C₂²×D₄	1	2	yes	—
305	C₂³×C₈	C₂²×D₄	1	2	yes	—
306	#535	#120	1	8	yes	—
307	#535	#127	1	8	yes	—
308	#535	C₂²×D₄	1	4	yes	—
309	#535	C₂²×D₄	1	4	yes	—
310	#535	C₂²×D₄	1	4	yes	—
311	#535	C₂²×D₄	1	4	yes	—
312	C₂×#123	#127	1	2	yes	—
313	C₂×#123	#127	1	2	yes	—
314	C₂×#123	C₂²×D₄	1	2	yes	—
315	C₂×#123	C₂²×D₄	1	2	yes	—
316	C₂×#120	#127	1	2	yes	—
317	C₂×#120	#127	1	2	yes	—
318	C₂×#120	C₂²×D₄	1	2	yes	—
319	C₂×#120	C₂²×D₄	1	2	yes	—
320	C₂×#117	#120	1	4	yes	—
321	C₂×#117	#127	1	4	yes	—
322	C₂×#117	#127	1	2	yes	—
323	C₂×#117	C₂²×D₄	1	1	yes	characteristic
324	C₂×#117	C₂²×D₄	1	1	yes	characteristic
325	C₂×#117	C₂²×D₄	1	2	yes	—
326	C₂×#117	C₂²×D₄	1	2	yes	—
327	C₂×#117	C₂²×D₄	1	2	yes	—
328	C₂×#117	C₂²×D₄	1	2	yes	—
329	C₂²×C₄⋊C₄	C₂²×D₄	1	2	yes	—
330	C₂²×C₂²⋊C₄	#127	1	1	yes	characteristic
331	C₂²×C₂²⋊C₄	#127	1	1	yes	characteristic
332	#413	#120	1	8	yes	—
333	#413	C₂²×D₄	1	4	yes	—
334	#413	C₂²×D₄	1	4	yes	—
335	C₂×#100	#120	1	8	yes	—
336	C₂×#100	C₂²×D₄	1	4	yes	—
337	C₂×#100	C₂²×D₄	1	4	yes	—
338	#410	#120	1	8	yes	—
339	#410	C₂²×D₄	1	4	yes	—
340	#410	C₂²×D₄	1	4	yes	—
341	#410	C₂²×D₄	1	4	yes	—
342	#410	C₂²×D₄	1	4	yes	—
343	C₂×#99	#120	1	8	yes	—
344	C₂×#99	C₂²×D₄	1	4	yes	—
345	C₂×#99	C₂²×D₄	1	4	yes	—
346	C₂⁵	C₂×#127	1	1	yes	characteristic
347	C₂⁵	C₂×#127	1	2	yes	—
348	C₂⁵	D₄²	1	1	yes	characteristic
349	C₂⁵	D₄²	1	1	yes	characteristic
350	C₂×#41	C₂×#120	1	2	yes	—
351	C₂×#41	C₂×#120	1	2	yes	—
352	C₂×#41	C₂×#120	1	2	yes	—
353	C₂×#41	C₂×#127	1	2	yes	—
354	C₂×#41	#534	1	2	yes	—
355	C₂×#41	#534	1	2	yes	—
356	C₂×#41	#534	1	2	yes	—
357	C₂×#41	#535	1	2	yes	—
358	C₂×#41	#535	1	2	yes	—
359	C₂×#41	#535	1	2	yes	—
360	C₂×#41	#535	1	2	yes	—
361	C₂×#41	#535	1	2	yes	—
362	C₂×#41	D₄²	1	2	yes	—
363	C₂×#41	D₄²	1	2	yes	—
364	C₂×#41	D₄²	1	2	yes	—
365	C₂×#41	D₄²	1	2	yes	—
366	C₂×#41	D₄²	1	2	yes	—
367	C₂×#41	D₄²	1	2	yes	—
368	C₂×#41	D₄²	1	2	yes	—
369	C₂×#41	D₄²	1	2	yes	—
370	C₂×#41	D₄²	1	2	yes	—
371	C₂×#41	D₄²	1	2	yes	—
372	C₂×#41	D₄²	1	2	yes	—
373	C₂×#41	D₄²	1	2	yes	—
374	C₂×#41	D₄²	1	2	yes	—
375	C₂×#41	D₄²	1	2	yes	—
376	C₂×#41	#560	1	2	yes	—
377	C₂×#41	#560	1	2	yes	—
378	C₂×#41	C₂³×D₄	1	1	yes	characteristic
379	C₂×#41	C₂³×D₄	1	1	yes	characteristic
380	C₂×#41	C₂³×D₄	1	1	yes	characteristic
381	C₂×#41	C₂³×D₄	1	1	yes	characteristic
382	C₂×#41	C₂×H(5,𝔽₂)	1	1	yes	characteristic
383	C₂×#41	C₂×H(5,𝔽₂)	1	1	yes	characteristic
384	C₂×#41	C₂×H(5,𝔽₂)	1	1	yes	characteristic
385	C₂×#41	C₂×H(5,𝔽₂)	1	1	yes	characteristic
386	C₂²×Q₈	#534	1	2	yes	—
387	C₂²×Q₈	#535	1	2	yes	—
388	C₂²×Q₈	#535	1	1	yes	characteristic
389	C₂²×Q₈	D₄²	1	2	yes	—
390	C₂²×Q₈	D₄²	1	1	yes	characteristic
391	C₂²×Q₈	D₄²	1	1	yes	characteristic
392	C₂²×Q₈	#560	1	2	yes	—
393	C₂²×Q₈	C₂×H(5,𝔽₂)	1	1	yes	characteristic
394	C₂²×D₄	C₂×#120	1	2	yes	—
395	C₂²×D₄	C₂×#120	1	4	yes	—
396	C₂²×D₄	C₂×#120	1	2	yes	—
397	C₂²×D₄	C₂×#127	1	4	yes	—
398	C₂²×D₄	C₂×#127	1	1	yes	characteristic
399	C₂²×D₄	C₂×#127	1	1	yes	characteristic
400	C₂²×D₄	#534	1	2	yes	—
401	C₂²×D₄	#535	1	2	yes	—
402	C₂²×D₄	#535	1	2	yes	—
403	C₂²×D₄	#535	1	2	yes	—
404	C₂²×D₄	#535	1	1	yes	characteristic
405	C₂²×D₄	D₄²	1	2	yes	—
406	C₂²×D₄	D₄²	1	2	yes	—
407	C₂²×D₄	D₄²	1	2	yes	—
408	C₂²×D₄	D₄²	1	2	yes	—
409	C₂²×D₄	D₄²	1	1	yes	characteristic
410	C₂²×D₄	D₄²	1	1	yes	characteristic
411	C₂²×D₄	D₄²	1	1	yes	characteristic
412	C₂²×D₄	D₄²	1	1	yes	characteristic
413	C₂²×D₄	D₄²	1	2	yes	—
414	C₂²×D₄	D₄²	1	1	yes	characteristic
415	C₂²×D₄	D₄²	1	1	yes	characteristic
416	C₂²×D₄	#560	1	2	yes	—
417	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
418	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
419	C₂²×D₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
420	C₂³×C₄	C₂×#120	1	2	yes	—
421	C₂³×C₄	C₂×#120	1	1	yes	characteristic
422	C₂³×C₄	C₂×#120	1	1	yes	characteristic
423	C₂³×C₄	C₂×#120	1	1	yes	characteristic
424	C₂³×C₄	C₂×#120	1	1	yes	characteristic
425	C₂³×C₄	C₂×#127	1	2	yes	—
426	C₂³×C₄	C₂×#127	1	1	yes	characteristic
427	C₂³×C₄	C₂×#127	1	2	yes	—
428	C₂³×C₄	#534	1	2	yes	—
429	C₂³×C₄	#535	1	1	yes	characteristic
430	C₂³×C₄	#535	1	1	yes	characteristic
431	C₂³×C₄	#535	1	2	yes	—
432	C₂³×C₄	D₄²	1	1	yes	characteristic
433	C₂³×C₄	D₄²	1	1	yes	characteristic
434	C₂³×C₄	D₄²	1	2	yes	—
435	C₂³×C₄	D₄²	1	2	yes	—
436	C₂³×C₄	D₄²	1	2	yes	—
437	C₂³×C₄	D₄²	1	1	yes	characteristic
438	C₂³×C₄	D₄²	1	2	yes	—
439	C₂³×C₄	D₄²	1	2	yes	—
440	C₂³×C₄	D₄²	1	2	yes	—
441	C₂³×C₄	D₄²	1	1	yes	characteristic
442	C₂³×C₄	D₄²	1	1	yes	characteristic
443	C₂³×C₄	D₄²	1	2	yes	—
444	C₂³×C₄	D₄²	1	2	yes	—
445	C₂³×C₄	D₄²	1	1	yes	characteristic
446	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
447	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
448	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
449	C₂×M₁₆	B(4,𝔽₂)	1	2	yes	—
450	C₂×M₁₆	B(4,𝔽₂)	1	2	yes	—
451	C₂×M₁₆	B(4,𝔽₂)	1	4	yes	—
452	C₂²×C₈	C₂×#120	1	2	yes	—
453	C₂²×C₈	C₂×#120	1	2	yes	—
454	C₂²×C₈	C₂×#120	1	2	yes	—
455	C₂²×C₈	C₂×#120	1	2	yes	—
456	#117	C₂×#120	1	4	yes	—
457	#117	C₂×#127	1	4	yes	—
458	C₂×C₂²⋊C₄	C₂×#127	1	2	yes	—
459	C₂×C₂²⋊C₄	C₂×#127	1	2	yes	—
460	#100	C₂×#120	1	8	yes	—
461	#99	C₂×#120	1	8	yes	—
462	C₂⁴	#2403	1	2	yes	—
463	C₂⁴	#2433	1	1	yes	characteristic
464	C₂⁴	#2433	1	1	yes	characteristic
465	C₂⁴	#2433	1	1	yes	characteristic
466	C₂⁴	#2433	1	2	yes	—
467	C₂⁴	#2433	1	2	yes	—
468	C₂⁴	#2433	1	2	yes	—
469	C₂⁴	#2433	1	1	yes	characteristic
470	C₂⁴	#2669	1	2	yes	—
471	C₂⁴	#2669	1	2	yes	—
472	C₂⁴	C₂²×#127	1	1	yes	characteristic
473	C₂⁴	C₂×D₄²	1	1	yes	characteristic
474	C₂⁴	C₂×D₄²	1	1	yes	characteristic
475	C₂×Q₈	#2403	1	2	yes	—
476	C₂×Q₈	#2433	1	2	yes	—
477	C₂×Q₈	#2669	1	2	yes	—
478	C₂×Q₈	#2669	1	2	yes	—
479	C₂×Q₈	#2669	1	2	yes	—
480	C₂×Q₈	#2669	1	2	yes	—
481	C₂×Q₈	C₂×#534	1	1	yes	characteristic
482	C₂×Q₈	C₂×#535	1	1	yes	characteristic
483	C₂×Q₈	C₂×D₄²	1	1	yes	characteristic
484	C₂×Q₈	C₂×#560	1	1	yes	characteristic
485	C₂×D₄	#2403	1	2	yes	—
486	C₂×D₄	#2403	1	2	yes	—
487	C₂×D₄	#2403	1	2	yes	—
488	C₂×D₄	#2433	1	2	yes	—
489	C₂×D₄	#2433	1	2	yes	—
490	C₂×D₄	#2433	1	2	yes	—
491	C₂×D₄	#2433	1	2	yes	—
492	C₂×D₄	#2433	1	2	yes	—
493	C₂×D₄	#2433	1	2	yes	—
494	C₂×D₄	#2433	1	2	yes	—
495	C₂×D₄	#2669	1	2	yes	—
496	C₂×D₄	#2669	1	2	yes	—
497	C₂×D₄	#2669	1	2	yes	—
498	C₂×D₄	#2669	1	2	yes	—
499	C₂×D₄	#2669	1	2	yes	—
500	C₂×D₄	#2669	1	2	yes	—
501	C₂×D₄	#2669	1	2	yes	—
502	C₂×D₄	#2669	1	2	yes	—
503	C₂×D₄	C₂²×#120	1	1	yes	characteristic
504	C₂×D₄	C₂²×#120	1	1	yes	characteristic
505	C₂×D₄	C₂×#534	1	1	yes	characteristic
506	C₂×D₄	C₂×#535	1	1	yes	characteristic
507	C₂×D₄	C₂×#535	1	1	yes	characteristic
508	C₂×D₄	C₂×#535	1	1	yes	characteristic
509	C₂×D₄	C₂×D₄²	1	1	yes	characteristic
510	C₂×D₄	C₂×D₄²	1	1	yes	characteristic
511	C₂×D₄	C₂×D₄²	1	1	yes	characteristic
512	C₂×D₄	C₂×D₄²	1	1	yes	characteristic
513	C₂×D₄	C₂×D₄²	1	1	yes	characteristic
514	C₂×D₄	C₂×#560	1	1	yes	characteristic
515	C₂²×C₄	#2403	1	2	yes	—
516	C₂²×C₄	#2403	1	2	yes	—
517	C₂²×C₄	#2403	1	2	yes	—
518	C₂²×C₄	#2403	1	2	yes	—
519	C₂²×C₄	#2403	1	2	yes	—
520	C₂²×C₄	#2403	1	2	yes	—
521	C₂²×C₄	#2403	1	2	yes	—
522	C₂²×C₄	#2433	1	2	yes	—
523	C₂²×C₄	#2433	1	2	yes	—
524	C₂²×C₄	#2433	1	2	yes	—
525	C₂²×C₄	#2433	1	2	yes	—
526	C₂²×C₄	#2433	1	2	yes	—
527	C₂²×C₄	#2433	1	1	yes	characteristic
528	C₂²×C₄	#2433	1	1	yes	characteristic
529	C₂²×C₄	#2433	1	1	yes	characteristic
530	C₂²×C₄	#2433	1	2	yes	—
531	C₂²×C₄	#2433	1	2	yes	—
532	C₂²×C₄	#2433	1	2	yes	—
533	C₂²×C₄	#2433	1	2	yes	—
534	C₂²×C₄	#2433	1	1	yes	characteristic
535	C₂²×C₄	#2669	1	2	yes	—
536	C₂²×C₄	#2669	1	2	yes	—
537	C₂²×C₄	#2669	1	2	yes	—
538	C₂²×C₄	#2669	1	2	yes	—
539	C₂²×C₄	#2669	1	2	yes	—
540	C₂²×C₄	#2669	1	2	yes	—
541	C₂²×C₄	#2669	1	2	yes	—
542	C₂²×C₄	#2669	1	2	yes	—
543	C₂²×C₄	#2669	1	2	yes	—
544	C₂²×C₄	#2669	1	2	yes	—
545	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
546	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
547	C₂²×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
548	C₂²×C₄	#3027	1	1	yes	characteristic
549	C₂²×C₄	#3027	1	1	yes	characteristic
550	C₂²×C₄	#3027	1	2	yes	—
551	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
552	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
553	C₂²×C₄	C₂²×#127	1	1	yes	characteristic
554	C₂²×C₄	C₂×#534	1	1	yes	characteristic
555	C₂²×C₄	C₂×#535	1	1	yes	characteristic
556	C₂²×C₄	C₂×#535	1	1	yes	characteristic
557	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
558	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
559	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
560	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
561	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
562	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
563	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
564	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
565	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
566	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
567	C₂×C₈	C₂×B(4,𝔽₂)	1	4	yes	—
568	C₂×C₈	C₂×B(4,𝔽₂)	1	4	yes	—
569	C₂³	#15258	1	2	yes	—
570	C₂³	#15258	1	2	yes	—
571	C₂³	#15258	1	2	yes	—
572	C₂³	#15258	1	2	yes	—
573	C₂³	#25771	1	1	yes	characteristic
574	C₂³	#25771	1	1	yes	characteristic
575	C₂³	#25771	1	2	yes	—
576	C₂³	C₂×#2403	1	1	yes	characteristic
577	C₂³	C₂×#2433	1	1	yes	characteristic
578	C₂³	C₂×#2433	1	1	yes	characteristic
579	C₂³	C₂×#2433	1	1	yes	characteristic
580	C₂³	C₂×#2433	1	1	yes	characteristic
581	C₂³	C₂×#2669	1	1	yes	characteristic
582	C₂³	C₂×#2669	1	1	yes	characteristic
583	C₂×C₄	#15258	1	2	yes	—
584	C₂×C₄	#15258	1	2	yes	—
585	C₂×C₄	#15258	1	2	yes	—
586	C₂×C₄	#15258	1	2	yes	—
587	C₂×C₄	#23900	1	2	yes	—
588	C₂×C₄	#23900	1	2	yes	—
589	C₂×C₄	#23904	1	2	yes	—
590	C₂×C₄	#23904	1	2	yes	—
591	C₂×C₄	#25771	1	2	yes	—
592	C₂×C₄	#25771	1	1	yes	characteristic
593	C₂×C₄	#25771	1	1	yes	characteristic
594	C₂×C₄	#25771	1	2	yes	—
595	C₂×C₄	#25771	1	2	yes	—
596	C₂×C₄	#25771	1	2	yes	—
597	C₂×C₄	#25771	1	2	yes	—
598	C₂×C₄	C₂×#2403	1	1	yes	characteristic
599	C₂×C₄	C₂×#2403	1	1	yes	characteristic
600	C₂×C₄	C₂×#2433	1	1	yes	characteristic
601	C₂×C₄	C₂×#2433	1	1	yes	characteristic
602	C₂×C₄	C₂×#2669	1	1	yes	characteristic
603	C₂×C₄	C₂×#2669	1	1	yes	characteristic
604	C₂×C₄	C₂×#2669	1	1	yes	characteristic
605	C₂×C₄	C₂×#2669	1	1	yes	characteristic
606	C₂×C₄	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
607	C₂×C₄	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
608	C₂×C₄	C₂×#3027	1	1	yes	characteristic
609	C₂×C₄	C₂×#3027	1	1	yes	characteristic
610	C₂²	#417821	1	2	yes	—
611	C₂²	#417821	1	2	yes	—
612	C₂²	C₂×#15258	1	1	yes	characteristic
613	C₂²	C₂×#25771	1	1	yes	characteristic
614	C₂²	C₂×#25771	1	1	yes	characteristic
615	C₄	#417821	1	2	yes	—
616	C₄	#417821	1	2	yes	—
617	C₄	C₂×#23900	1	1	yes	characteristic
618	C₄	C₂×#23904	1	1	yes	characteristic
619	C₄	C₂×#25771	1	1	yes	characteristic
620	C₄	C₂×#25771	1	1	yes	characteristic
621	C₂	#72237546	1	2	yes	—
622	C₂	C₂×#417821	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂×#25771
commutator, Frattini, cosocle	C₂²×#41	C₂⁵
LCS	G ▷ C₂²×#41 ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂²×#568 ◁ 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. #72337500	C₂	semidirect
2. #72337497	C₂	semidirect
3. #72337490	C₂	semidirect
4. #72337437	C₂	semidirect
5. #72337424	C₂	semidirect
6. #72312860	C₂	semidirect
7. C₂×#498916	C₂	semidirect
8. #72312313	C₂	semidirect
9. #72303790	C₂	semidirect
10. #72303787	C₂	semidirect
11. #72280881	C₂	semidirect
12. C₂×#498898	C₂	semidirect
13. #72279215	C₂	semidirect
14. #72256636	C₂	semidirect
15. C₂×#6443344	C₂	semidirect
16. C₂²×#33553	C₂	semidirect
17. C₂²×#33553	C₂	semidirect
18. C₂×#63090	C₂²	semidirect
22. C₂×#60398	C₂²	semidirect
27. C₂×#60387	C₂²	semidirect
31. C₂×#33553	C₂²	semidirect
32. C₂×#33553	C₂²	semidirect
33. C₂×#33358	C₂²	semidirect
36. C₂×#33347	C₂²	semidirect
41. #6500196	C₂²	semidirect
42. #6500186	C₂²	semidirect
43. C₂×#25799	C₂²	semidirect
44. C₂×#25798	C₂²	semidirect
48. C₂×#20620	C₂²	semidirect
49. C₂×#20620	C₂²	semidirect
50. #6370746	C₂²	semidirect
51. #6370734	C₂²	semidirect
52. C₂×#20401	C₂²	semidirect
53. #498930	C₂²	semidirect
54. #498929	C₂²	semidirect
55. C₂×#13361	C₂²	semidirect
56. C₂×#13360	C₂²	semidirect
57. C₂×#13351	C₂²	semidirect
58. C₂×#13350	C₂²	semidirect
59. #498889	C₂²	semidirect
60. #498888	C₂²	semidirect
61. #492899	C₂²	semidirect
62. C₂×#12579	C₂²	semidirect
63. C₂×#12577	C₂²	semidirect
64. #492886	C₂²	semidirect
65. #394044	C₂²	semidirect
66. #393939	C₂²	semidirect
67. #353340	C₂²	semidirect
68. #353326	C₂²	semidirect
69. #147764	C₂²	semidirect
70. #147759	C₂²	semidirect
71. #147726	C₂²	semidirect
72. #147725	C₂²	semidirect
73. #147517	C₂²	semidirect
74. #147498	C₂²	semidirect
77. C₂×#3584	C₂³	semidirect
78. C₂³×AGL(1,ℤ/8)	D₄	semidirect
87. C₂×#3058	D₄	semidirect
89. C₂×#3057	D₄	semidirect
91. C₂×#3028	C₂³	semidirect
92. C₂×#3027	D₄	semidirect
95. C₂×#3027	C₂³	semidirect
98. C₂×#3022	C₂³	semidirect
99. C₂×#3021	D₄	semidirect
102. C₂×#3021	C₂³	semidirect
103. C₂×#2911	D₄	semidirect
104. C₂×#2896	D₄	semidirect
105. C₂²×#418	D₄	semidirect
106. C₂²×#418	D₄	semidirect
107. C₂²×#418	D₄	semidirect
115. C₂²×#407	D₄	semidirect
116. C₂²×#407	D₄	semidirect
120. C₂×#2129	C₂³	semidirect
121. C₂×#2128	D₄	semidirect
124. C₂×#2128	C₂³	semidirect
125. C₂×#2123	C₂³	semidirect
126. C₂×#2122	D₄	semidirect
129. C₂×#2122	C₂³	semidirect
130. C₂×#2120	D₄	semidirect
131. C₂×#2120	D₄	semidirect
134. C₂²×#352	D₄	semidirect
135. C₂²×#352	D₄	semidirect
136. C₂²×AΣL(1,𝔽₁₆)	D₄	semidirect
137. C₂²×AΣL(1,𝔽₁₆)	D₄	semidirect
139. #20975	D₄	semidirect
141. #20899	D₄	semidirect
143. C₂×#1794	C₂³	semidirect
144. C₂×#1794	C₂³	semidirect
145. #20618	C₂³	semidirect
146. #20610	C₂³	semidirect
147. C₂×#1757	C₂³	semidirect
148. #20347	D₄	semidirect
149. #20347	D₄	semidirect
150. #20335	D₄	semidirect
151. #20335	D₄	semidirect
152. #12583	C₂³	semidirect
153. C₂×#1392	C₂³	semidirect
154. C₂×#1391	C₂³	semidirect
155. #12575	C₂³	semidirect
156. #10764	C₂³	semidirect
157. #10759	C₂³	semidirect
167. C₂³×SD₁₆	C₂×D₄	semidirect
168. C₂³×D₈	C₂×D₄	semidirect
207. #3027	C₂×D₄	semidirect
208. #3021	C₂×D₄	semidirect
209. C₂×#427	C₂×D₄	semidirect
210. C₂×#427	C₂×D₄	semidirect
211. C₂×#419	C₂×D₄	semidirect
212. C₂×#418	C₂×D₄	semidirect
213. C₂×#418	C₂×D₄	semidirect
214. C₂×#418	C₂×D₄	semidirect
215. C₂×#418	C₂×D₄	semidirect
216. C₂²×#102	C₂×D₄	semidirect
239. C₂×#407	C₂×D₄	semidirect
240. C₂²×C₂²⋊C₈	C₂×D₄	semidirect
243. #2128	C₂×D₄	semidirect
244. #2122	C₂×D₄	semidirect
245. C₂×#352	C₂×D₄	semidirect
246. C₂×#352	C₂×D₄	semidirect
247. C₂×AΣL(1,𝔽₁₆)	C₂×D₄	semidirect
248. C₂×AΣL(1,𝔽₁₆)	C₂×D₄	semidirect
249. #1736	C₂×D₄	semidirect
250. #1735	C₂×D₄	semidirect
251. #1729	C₂×D₄	semidirect
252. #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
#72337500	2
#72337497	2
#72337490	2
#72337437	2
#72337424	2
#72312860	2
C₂×#498916	2
#72312313	2
#72303790	2
#72303787	2
#72280881	2
C₂×#498898	2
#72279215	2
#72256636	2
C₂×#6443344	2
C₂²×#33553	2