Subgroups — #72337502

Order 2048.

At least 8674 conjugacy classes of subgroups; only the 1288 normal subgroups are shown.

The subgroup lattice has 604 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	C₂×#6629051	C₂	1	1	yes	maximal, characteristic, complemented
3	#72337497	C₂	1	1	yes	maximal, characteristic, complemented
4	#72337494	C₂	1	1	yes	maximal, characteristic, complemented
5	#72337435	C₂	1	8	yes	maximal, complemented
6	#72337423	C₂	1	8	yes	maximal, complemented
7	#72312755	C₂	1	1	yes	maximal, characteristic, complemented
8	#72312697	C₂	1	1	yes	maximal, characteristic, complemented
9	#72312687	C₂	1	1	yes	maximal, characteristic, complemented
10	#72312359	C₂	1	1	yes	maximal, characteristic, complemented
11	#72312304	C₂	1	1	yes	maximal, characteristic, complemented
12	#72303813	C₂	1	1	yes	maximal, characteristic, complemented
13	#72303727	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#498943	C₂	1	1	yes	maximal, characteristic, complemented
15	#72256636	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#33553	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×#12755	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#63076	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	C₂²×#3027	C₂²	1	1	yes	characteristic
23	C₂²×#3025	C₂²	1	1	yes	characteristic
24	C₂×#60387	C₂²	1	1	yes	characteristic, complemented
25	C₂²×#3021	C₂²	1	1	yes	characteristic
26	#7634872	C₂²	1	1	yes	characteristic
27	C₂×#33553	C₂²	1	8	yes	—
28	C₂²×#2134	C₂²	1	1	yes	characteristic
29	C₂×#33358	C₂²	1	1	yes	characteristic, complemented
30	C₂²×#2128	C₂²	1	1	yes	characteristic
31	C₂×#33347	C₂²	1	1	yes	characteristic, complemented
32	C₂²×#2122	C₂²	1	1	yes	characteristic
33	C₂²×#2122	C₂²	1	1	yes	characteristic
34	C₂²×#2120	C₂²	1	1	yes	characteristic
35	C₂²×#2120	C₂²	1	1	yes	characteristic
36	C₂×#32951	C₂²	1	4	yes	complemented
37	C₂×#32950	C₂²	1	4	yes	complemented
38	#6500196	C₂²	1	4	yes	complemented
39	#6500186	C₂²	1	4	yes	complemented
40	#6374164	C₂²	1	1	yes	characteristic
41	C₂×#21017	C₂²	1	1	yes	characteristic, complemented
42	C₂²×#1914	C₂²	1	1	yes	characteristic
43	C₂²×#1910	C₂²	1	1	yes	characteristic
44	#6371484	C₂²	1	1	yes	characteristic
45	C₂²×#1891	C₂²	1	1	yes	characteristic
46	#6371364	C₂²	1	1	yes	characteristic
47	C₂×#20673	C₂²	1	1	yes	characteristic, complemented
48	C₂×#20612	C₂²	1	1	yes	characteristic, complemented
49	#6370734	C₂²	1	1	yes	characteristic, complemented
50	C₂×#13355	C₂²	1	4	yes	complemented
51	C₂×#13353	C₂²	1	4	yes	complemented
52	#498930	C₂²	1	4	yes	complemented
53	#498929	C₂²	1	4	yes	complemented
54	C₂×#12755	C₂²	1	8	yes	complemented
55	C₂×#12589	C₂²	1	1	yes	characteristic, complemented
56	C₂×#12589	C₂²	1	1	yes	characteristic, complemented
57	#492906	C₂²	1	1	yes	characteristic, complemented
58	#492886	C₂²	1	1	yes	characteristic, complemented
59	#392717	C₂²	1	8	yes	complemented
60	#392665	C₂²	1	8	yes	complemented
61	#353434	C₂²	1	1	yes	characteristic, complemented
62	#353422	C₂²	1	1	yes	characteristic, complemented
63	#353340	C₂²	1	1	yes	characteristic, complemented
64	#353326	C₂²	1	1	yes	characteristic, complemented
65	#148474	C₂²	1	8	yes	complemented
66	#148021	C₂²	1	8	yes	complemented
67	#148014	C₂²	1	8	yes	complemented
68	#147856	C₂²	1	4	yes	complemented
69	#147855	C₂²	1	4	yes	complemented
70	#147818	C₂²	1	4	yes	complemented
71	#147817	C₂²	1	4	yes	complemented
72	#147755	C₂²	1	8	yes	complemented
73	#147726	C₂²	1	4	yes	complemented
74	#147725	C₂²	1	4	yes	complemented
75	C₂²×#585	C₂³	1	1	yes	characteristic
76	C₂³×AGL(1,ℤ/8)	D₄	1	1	yes	characteristic, complemented
77	C₂×#3573	C₂³	1	4	yes	complemented
78	C₂²×#568	C₂³	1	1	yes	characteristic
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×#3027	D₄	1	8	yes	complemented
92	C₂×#3027	C₂³	1	4	yes	—
93	C₂×#3025	D₄	1	4	yes	—
94	C₂×#3025	C₂³	1	4	yes	—
95	C₂²×#458	D₄	1	2	yes	—
96	C₂²×B(4,𝔽₂)	D₄	1	2	yes	—
97	C₂×#3022	C₂³	1	2	yes	complemented
98	C₂×#3021	D₄	1	8	yes	complemented
99	C₂×#3021	C₂³	1	4	yes	—
100	C₂×#3021	C₂³	1	2	yes	complemented
101	C₂×#2911	D₄	1	1	yes	characteristic, complemented
102	C₂×#2896	D₄	1	1	yes	characteristic, complemented
103	C₂²×#418	D₄	1	1	yes	characteristic, complemented
104	C₂²×#418	D₄	1	1	yes	characteristic, complemented
105	C₂²×#418	D₄	1	1	yes	characteristic, complemented
106	C₂²×#413	C₂³	1	1	yes	characteristic
107	C₂²×#413	C₂³	1	1	yes	characteristic
108	C₂²×#413	C₂³	1	1	yes	characteristic
109	C₂²×#410	C₂³	1	1	yes	characteristic
110	C₂²×#410	C₂³	1	1	yes	characteristic
111	C₂²×#410	C₂³	1	1	yes	characteristic
112	C₂×#2879	C₂³	1	1	yes	characteristic
113	C₂²×#407	D₄	1	1	yes	characteristic, complemented
114	C₂²×#407	D₄	1	1	yes	characteristic, complemented
115	#37374	C₂³	1	2	yes	—
116	#37269	C₂³	1	2	yes	—
117	#34044	C₂³	1	1	yes	characteristic
118	C₂×#2134	C₂³	1	4	yes	—
119	C₂×#2129	C₂³	1	2	yes	complemented
120	C₂×#2128	C₂³	1	4	yes	—
121	C₂×#2128	C₂³	1	2	yes	complemented
122	C₂×#2123	C₂³	1	2	yes	complemented
123	C₂×#2122	C₂³	1	4	yes	—
124	C₂×#2122	C₂³	1	4	yes	—
125	C₂×#2122	C₂³	1	2	yes	complemented
126	C₂×#2120	C₂³	1	4	yes	—
127	C₂×#2120	C₂³	1	4	yes	—
128	#21770	C₂³	1	4	yes	—
129	C₂×#1915	C₂³	1	2	yes	complemented
130	C₂×#1914	D₄	1	8	yes	complemented
131	C₂×#1914	C₂³	1	4	yes	—
132	C₂×#1914	C₂³	1	2	yes	complemented
133	C₂×#1910	C₂³	1	4	yes	—
134	#20975	D₄	1	4	yes	complemented
135	#20975	C₂³	1	4	yes	—
136	C₂×#1891	C₂³	1	4	yes	—
137	#20899	D₄	1	4	yes	complemented
138	#20899	C₂³	1	4	yes	—
139	C₂×#1813	C₂³	1	4	yes	complemented
140	C₂×#1791	C₂³	1	4	yes	complemented
141	#20610	C₂³	1	4	yes	complemented
142	#20347	D₄	1	1	yes	characteristic, complemented
143	#20347	D₄	1	1	yes	characteristic, complemented
144	#20335	D₄	1	1	yes	characteristic, complemented
145	#20335	D₄	1	1	yes	characteristic, complemented
146	C₂×#1395	C₂³	1	4	yes	complemented
147	C₂×#1395	C₂³	1	4	yes	complemented
148	#12587	C₂³	1	4	yes	complemented
149	#12575	C₂³	1	4	yes	complemented
150	#10764	C₂³	1	4	yes	complemented
151	#10759	C₂³	1	4	yes	complemented
152	#10748	C₂³	1	4	yes	complemented
153	#10742	C₂³	1	4	yes	complemented
154	C₂×#585	C₂×D₄	1	4	yes	—
155	C₂×#585	C₂×D₄	1	4	yes	—
156	C₂×#585	C₂×D₄	1	2	yes	—
157	C₂×#585	C₂⁴	1	2	yes	—
158	C₂²×H(5,𝔽₂)	C₂×D₄	1	2	yes	—
159	C₂³×#41	C₂×D₄	1	1	yes	characteristic
160	C₂³×#41	C₂⁴	1	1	yes	characteristic
161	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
162	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
163	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
164	C₂³×SD₁₆	C₂×D₄	1	2	yes	complemented
165	C₂³×D₈	C₂×D₄	1	2	yes	complemented
166	C₂×#568	C₂×D₄	1	4	yes	—
167	C₂×#568	C₂⁴	1	2	yes	—
168	C₂²×#131	C₂×D₄	1	2	yes	—
169	C₂²×#131	C₂×D₄	1	2	yes	—
170	C₂²×#131	C₂×D₄	1	2	yes	—
171	C₂²×#131	C₂⁴	1	2	yes	—
172	C₂³×M₁₆	C₂×D₄	1	1	yes	characteristic
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	C₂×#536	C₂×D₄	1	1	yes	characteristic
181	C₂×#536	C₂⁴	1	1	yes	characteristic
182	C₂×#535	C₂×D₄	1	4	yes	—
183	C₂×#535	C₂×D₄	1	4	yes	—
184	C₂×#535	C₂×D₄	1	4	yes	—
185	C₂×#535	C₂×D₄	1	1	yes	characteristic
186	C₂×#535	C₂×D₄	1	2	yes	—
187	C₂×#535	C₂×D₄	1	2	yes	—
188	C₂×#535	#41	1	4	yes	—
189	C₂×#535	C₂⁴	1	1	yes	characteristic
190	C₂×#535	C₂⁴	1	2	yes	—
191	C₂×#535	C₂⁴	1	2	yes	—
192	C₂×#525	C₂×D₄	1	2	yes	—
193	C₂×#525	C₂×D₄	1	2	yes	—
194	C₂×#525	#41	1	2	yes	—
195	C₂×#525	C₂⁴	1	2	yes	—
196	C₂²×#123	C₂×D₄	1	1	yes	characteristic
197	C₂²×#123	#41	1	1	yes	characteristic
198	C₂²×#120	C₂×D₄	1	1	yes	characteristic
199	C₂²×#120	#41	1	1	yes	characteristic
200	C₂²×#117	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	#3027	C₂×D₄	1	16	yes	—
207	C₂×#458	C₂×D₄	1	8	yes	—
208	C₂×B(4,𝔽₂)	C₂×D₄	1	8	yes	—
209	#3021	C₂×D₄	1	16	yes	—
210	C₂×#427	C₂×D₄	1	2	yes	complemented
211	C₂×#427	C₂×D₄	1	2	yes	complemented
212	C₂×#419	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	2	yes	complemented
216	C₂×#418	C₂×D₄	1	4	yes	complemented
217	C₂²×#102	C₂×D₄	1	4	yes	complemented
218	C₂×#413	C₂×D₄	1	4	yes	—
219	C₂×#413	C₂×D₄	1	4	yes	—
220	C₂×#413	C₂⁴	1	2	yes	—
221	C₂×#413	C₂⁴	1	2	yes	—
222	C₂×#413	C₂⁴	1	2	yes	—
223	C₂×#410	C₂×D₄	1	4	yes	—
224	C₂×#410	C₂×D₄	1	2	yes	—
225	C₂×#410	C₂⁴	1	2	yes	—
226	C₂×#410	C₂⁴	1	2	yes	—
227	C₂×#410	C₂⁴	1	2	yes	—
228	C₂²×#99	C₂×D₄	1	2	yes	—
229	C₂×#408	C₂×D₄	1	2	yes	—
230	C₂×#408	C₂⁴	1	2	yes	—
231	C₂×#407	C₂×D₄	1	4	yes	complemented
232	C₂²×C₂²⋊C₈	C₂×D₄	1	4	yes	complemented
233	#2311	C₂×D₄	1	2	yes	—
234	#2311	C₂⁴	1	2	yes	—
235	#1914	C₂×D₄	1	16	yes	complemented
236	#1736	C₂×D₄	1	4	yes	complemented
237	#1735	C₂×D₄	1	4	yes	complemented
238	#1729	C₂×D₄	1	4	yes	complemented
239	#1729	C₂×D₄	1	4	yes	complemented
240	C₂⁶	#121	1	1	yes	characteristic
241	#585	#120	1	8	yes	—
242	#585	C₂²×D₄	1	4	yes	—
243	#585	C₂²×D₄	1	4	yes	—
244	C₂×H(5,𝔽₂)	#120	1	8	yes	—
245	C₂×H(5,𝔽₂)	C₂²×D₄	1	4	yes	—
246	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
247	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
248	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
249	C₂²×#41	C₂²×D₄	1	2	yes	—
250	C₂²×#41	C₂²×D₄	1	2	yes	—
251	C₂²×#41	C₂²×D₄	1	2	yes	—
252	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
253	C₂²×#41	C₂×#41	1	1	yes	characteristic
254	C₂²×#41	C₂×#41	1	2	yes	—
255	C₂²×#41	H(5,𝔽₂)	1	2	yes	—
256	C₂²×#41	H(5,𝔽₂)	1	2	yes	—
257	C₂²×#41	H(5,𝔽₂)	1	2	yes	—
258	C₂²×#41	H(5,𝔽₂)	1	1	yes	characteristic
259	C₂²×#41	H(5,𝔽₂)	1	2	yes	—
260	C₂²×#41	H(5,𝔽₂)	1	1	yes	characteristic
261	C₂²×#41	C₂⁵	1	1	yes	characteristic
262	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
263	C₂³×Q₈	H(5,𝔽₂)	1	1	yes	characteristic
264	C₂³×D₄	#120	1	4	yes	—
265	C₂³×D₄	#121	1	4	yes	—
266	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
267	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
268	C₂³×D₄	C₂²×D₄	1	2	yes	—
269	C₂³×D₄	C₂²×D₄	1	2	yes	—
270	C₂³×D₄	C₂×#41	1	1	yes	characteristic
271	C₂³×D₄	H(5,𝔽₂)	1	1	yes	characteristic
272	C₂⁴×C₄	#121	1	1	yes	characteristic
273	C₂⁴×C₄	#121	1	2	yes	—
274	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
275	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
276	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
277	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
278	#568	C₂²×D₄	1	4	yes	—
279	C₂²×M₁₆	#120	1	2	yes	—
280	C₂²×M₁₆	#120	1	1	yes	characteristic
281	C₂²×M₁₆	#120	1	1	yes	characteristic
282	C₂²×M₁₆	#120	1	2	yes	—
283	C₂²×M₁₆	#120	1	2	yes	—
284	C₂²×M₁₆	#120	1	1	yes	characteristic
285	C₂²×M₁₆	#120	1	1	yes	characteristic
286	C₂²×M₁₆	C₂²×D₄	1	2	yes	—
287	C₂²×M₁₆	C₂²×D₄	1	2	yes	—
288	C₂²×M₁₆	C₂²×D₄	1	2	yes	—
289	C₂²×M₁₆	C₂²×D₄	1	2	yes	—
290	C₂³×C₈	#120	1	2	yes	—
291	C₂³×C₈	#120	1	2	yes	—
292	C₂³×C₈	#120	1	2	yes	—
293	C₂³×C₈	C₂²×D₄	1	2	yes	—
294	C₂³×C₈	C₂²×D₄	1	2	yes	—
295	C₂³×C₈	C₂²×D₄	1	2	yes	—
296	C₂³×C₈	C₂²×D₄	1	2	yes	—
297	#535	#120	1	8	yes	—
298	#535	#121	1	8	yes	—
299	#535	C₂²×D₄	1	4	yes	—
300	#535	C₂²×D₄	1	4	yes	—
301	#535	C₂²×D₄	1	4	yes	—
302	#535	C₂×#41	1	4	yes	—
303	C₂×#123	#121	1	2	yes	—
304	C₂×#123	#121	1	2	yes	—
305	C₂×#123	C₂²×D₄	1	2	yes	—
306	C₂×#123	C₂×#41	1	2	yes	—
307	C₂×#120	#121	1	2	yes	—
308	C₂×#120	#121	1	2	yes	—
309	C₂×#120	C₂²×D₄	1	2	yes	—
310	C₂×#120	C₂×#41	1	2	yes	—
311	C₂×#117	#120	1	4	yes	—
312	C₂×#117	#121	1	4	yes	—
313	C₂×#117	#121	1	2	yes	—
314	C₂×#117	C₂²×D₄	1	1	yes	characteristic
315	C₂×#117	C₂²×D₄	1	1	yes	characteristic
316	C₂×#117	C₂²×D₄	1	2	yes	—
317	C₂×#117	C₂²×D₄	1	2	yes	—
318	C₂×#117	C₂²×D₄	1	2	yes	—
319	C₂×#117	C₂²×D₄	1	2	yes	—
320	C₂²×C₄⋊C₄	C₂²×D₄	1	2	yes	—
321	C₂²×C₂²⋊C₄	#121	1	1	yes	characteristic
322	C₂²×C₂²⋊C₄	#121	1	1	yes	characteristic
323	#413	C₂²×D₄	1	4	yes	—
324	#413	C₂²×D₄	1	4	yes	—
325	#410	C₂²×D₄	1	4	yes	—
326	C₂×#99	C₂²×D₄	1	4	yes	—
327	C₂⁵	C₂×#121	1	1	yes	characteristic
328	C₂⁵	C₂×#121	1	2	yes	—
329	C₂⁵	D₄²	1	1	yes	characteristic
330	C₂⁵	#546	1	1	yes	characteristic
331	H(5,𝔽₂)	C₂×#120	1	8	yes	—
332	C₂×#41	C₂×#120	1	2	yes	—
333	C₂×#41	C₂×#120	1	2	yes	—
334	C₂×#41	C₂×#121	1	2	yes	—
335	C₂×#41	#525	1	2	yes	—
336	C₂×#41	#534	1	2	yes	—
337	C₂×#41	#534	1	2	yes	—
338	C₂×#41	#534	1	2	yes	—
339	C₂×#41	#534	1	2	yes	—
340	C₂×#41	#535	1	2	yes	—
341	C₂×#41	#535	1	2	yes	—
342	C₂×#41	#538	1	2	yes	—
343	C₂×#41	#538	1	2	yes	—
344	C₂×#41	D₄²	1	2	yes	—
345	C₂×#41	D₄²	1	2	yes	—
346	C₂×#41	D₄²	1	2	yes	—
347	C₂×#41	D₄²	1	2	yes	—
348	C₂×#41	D₄²	1	2	yes	—
349	C₂×#41	D₄²	1	2	yes	—
350	C₂×#41	D₄²	1	2	yes	—
351	C₂×#41	D₄²	1	2	yes	—
352	C₂×#41	#546	1	2	yes	—
353	C₂×#41	#546	1	2	yes	—
354	C₂×#41	#546	1	2	yes	—
355	C₂×#41	#546	1	2	yes	—
356	C₂×#41	#546	1	2	yes	—
357	C₂×#41	#546	1	2	yes	—
358	C₂×#41	#560	1	2	yes	—
359	C₂×#41	#560	1	2	yes	—
360	C₂×#41	C₂³×D₄	1	1	yes	characteristic
361	C₂×#41	C₂³×D₄	1	1	yes	characteristic
362	C₂×#41	C₂³×D₄	1	1	yes	characteristic
363	C₂×#41	C₂²×#41	1	1	yes	characteristic
364	C₂×#41	C₂×H(5,𝔽₂)	1	1	yes	characteristic
365	C₂×#41	C₂×H(5,𝔽₂)	1	1	yes	characteristic
366	C₂×#41	C₂×H(5,𝔽₂)	1	1	yes	characteristic
367	C₂×#41	C₂×H(5,𝔽₂)	1	1	yes	characteristic
368	C₂²×Q₈	#534	1	2	yes	—
369	C₂²×Q₈	#535	1	1	yes	characteristic
370	C₂²×Q₈	#538	1	2	yes	—
371	C₂²×Q₈	D₄²	1	2	yes	—
372	C₂²×Q₈	D₄²	1	1	yes	characteristic
373	C₂²×Q₈	#546	1	1	yes	characteristic
374	C₂²×Q₈	#560	1	2	yes	—
375	C₂²×Q₈	C₂×H(5,𝔽₂)	1	1	yes	characteristic
376	C₂²×D₄	C₂×#120	1	2	yes	—
377	C₂²×D₄	C₂×#120	1	4	yes	—
378	C₂²×D₄	C₂×#121	1	1	yes	characteristic
379	C₂²×D₄	C₂×#121	1	1	yes	characteristic
380	C₂²×D₄	C₂×#121	1	4	yes	—
381	C₂²×D₄	#525	1	2	yes	—
382	C₂²×D₄	#534	1	2	yes	—
383	C₂²×D₄	#534	1	2	yes	—
384	C₂²×D₄	#535	1	2	yes	—
385	C₂²×D₄	#535	1	1	yes	characteristic
386	C₂²×D₄	#538	1	2	yes	—
387	C₂²×D₄	D₄²	1	2	yes	—
388	C₂²×D₄	D₄²	1	1	yes	characteristic
389	C₂²×D₄	D₄²	1	1	yes	characteristic
390	C₂²×D₄	D₄²	1	1	yes	characteristic
391	C₂²×D₄	#546	1	1	yes	characteristic
392	C₂²×D₄	#546	1	1	yes	characteristic
393	C₂²×D₄	#546	1	2	yes	—
394	C₂²×D₄	#546	1	2	yes	—
395	C₂²×D₄	#546	1	2	yes	—
396	C₂²×D₄	#546	1	2	yes	—
397	C₂²×D₄	#546	1	1	yes	characteristic
398	C₂²×D₄	#560	1	2	yes	—
399	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
400	C₂²×D₄	C₂²×#41	1	1	yes	characteristic
401	C₂²×D₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
402	C₂³×C₄	C₂×#120	1	2	yes	—
403	C₂³×C₄	C₂×#120	1	1	yes	characteristic
404	C₂³×C₄	C₂×#120	1	1	yes	characteristic
405	C₂³×C₄	C₂×#120	1	1	yes	characteristic
406	C₂³×C₄	C₂×#120	1	1	yes	characteristic
407	C₂³×C₄	C₂×#121	1	2	yes	—
408	C₂³×C₄	C₂×#121	1	1	yes	characteristic
409	C₂³×C₄	C₂×#121	1	2	yes	—
410	C₂³×C₄	#534	1	2	yes	—
411	C₂³×C₄	#535	1	2	yes	—
412	C₂³×C₄	#535	1	1	yes	characteristic
413	C₂³×C₄	#535	1	1	yes	characteristic
414	C₂³×C₄	D₄²	1	2	yes	—
415	C₂³×C₄	D₄²	1	1	yes	characteristic
416	C₂³×C₄	D₄²	1	1	yes	characteristic
417	C₂³×C₄	D₄²	1	2	yes	—
418	C₂³×C₄	D₄²	1	2	yes	—
419	C₂³×C₄	D₄²	1	2	yes	—
420	C₂³×C₄	D₄²	1	2	yes	—
421	C₂³×C₄	D₄²	1	1	yes	characteristic
422	C₂³×C₄	D₄²	1	2	yes	—
423	C₂³×C₄	#546	1	1	yes	characteristic
424	C₂³×C₄	#546	1	2	yes	—
425	C₂³×C₄	#546	1	2	yes	—
426	C₂³×C₄	#546	1	1	yes	characteristic
427	C₂³×C₄	#546	1	1	yes	characteristic
428	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
429	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
430	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
431	C₂×M₁₆	B(4,𝔽₂)	1	2	yes	—
432	C₂×M₁₆	B(4,𝔽₂)	1	2	yes	—
433	C₂×M₁₆	B(4,𝔽₂)	1	4	yes	—
434	C₂²×C₈	C₂×#120	1	2	yes	—
435	C₂²×C₈	C₂×#120	1	2	yes	—
436	C₂²×C₈	C₂×#120	1	2	yes	—
437	C₂²×C₈	C₂×#120	1	2	yes	—
438	#117	C₂×#120	1	4	yes	—
439	#117	C₂×#121	1	4	yes	—
440	C₂×C₂²⋊C₄	C₂×#121	1	2	yes	—
441	C₂×C₂²⋊C₄	C₂×#121	1	2	yes	—
442	C₂⁴	#2404	1	2	yes	—
443	C₂⁴	#2408	1	1	yes	characteristic
444	C₂⁴	#2408	1	1	yes	characteristic
445	C₂⁴	#2408	1	1	yes	characteristic
446	C₂⁴	#2408	1	1	yes	characteristic
447	C₂⁴	#2410	1	2	yes	—
448	C₂⁴	#2410	1	2	yes	—
449	C₂⁴	#2424	1	2	yes	—
450	C₂⁴	#2668	1	2	yes	—
451	C₂⁴	#2669	1	2	yes	—
452	C₂⁴	C₂²×#121	1	1	yes	characteristic
453	C₂⁴	C₂×D₄²	1	1	yes	characteristic
454	C₂⁴	C₂×#546	1	1	yes	characteristic
455	C₂×Q₈	#2403	1	2	yes	—
456	C₂×Q₈	#2424	1	2	yes	—
457	C₂×Q₈	#2668	1	2	yes	—
458	C₂×Q₈	#2669	1	2	yes	—
459	C₂×Q₈	#2678	1	2	yes	—
460	C₂×Q₈	#2678	1	2	yes	—
461	C₂×Q₈	C₂×#534	1	1	yes	characteristic
462	C₂×Q₈	C₂×#538	1	1	yes	characteristic
463	C₂×Q₈	C₂×D₄²	1	1	yes	characteristic
464	C₂×Q₈	C₂×#560	1	1	yes	characteristic
465	C₂×D₄	#2403	1	2	yes	—
466	C₂×D₄	#2404	1	2	yes	—
467	C₂×D₄	#2404	1	2	yes	—
468	C₂×D₄	#2410	1	2	yes	—
469	C₂×D₄	#2410	1	2	yes	—
470	C₂×D₄	#2410	1	2	yes	—
471	C₂×D₄	#2410	1	2	yes	—
472	C₂×D₄	#2424	1	2	yes	—
473	C₂×D₄	#2424	1	2	yes	—
474	C₂×D₄	#2424	1	2	yes	—
475	C₂×D₄	#2668	1	2	yes	—
476	C₂×D₄	#2668	1	2	yes	—
477	C₂×D₄	#2668	1	2	yes	—
478	C₂×D₄	#2669	1	2	yes	—
479	C₂×D₄	#2669	1	2	yes	—
480	C₂×D₄	#2669	1	2	yes	—
481	C₂×D₄	#2678	1	2	yes	—
482	C₂×D₄	#2678	1	2	yes	—
483	C₂×D₄	C₂²×#120	1	1	yes	characteristic
484	C₂×D₄	C₂×#525	1	1	yes	characteristic
485	C₂×D₄	C₂×#534	1	1	yes	characteristic
486	C₂×D₄	C₂×#534	1	1	yes	characteristic
487	C₂×D₄	C₂×#535	1	1	yes	characteristic
488	C₂×D₄	C₂×#538	1	1	yes	characteristic
489	C₂×D₄	C₂×D₄²	1	1	yes	characteristic
490	C₂×D₄	C₂×#546	1	1	yes	characteristic
491	C₂×D₄	C₂×#546	1	1	yes	characteristic
492	C₂×D₄	C₂×#546	1	1	yes	characteristic
493	C₂×D₄	C₂×#546	1	1	yes	characteristic
494	C₂×D₄	C₂×#560	1	1	yes	characteristic
495	C₂²×C₄	#2403	1	2	yes	—
496	C₂²×C₄	#2403	1	2	yes	—
497	C₂²×C₄	#2403	1	2	yes	—
498	C₂²×C₄	#2403	1	2	yes	—
499	C₂²×C₄	#2403	1	2	yes	—
500	C₂²×C₄	#2403	1	2	yes	—
501	C₂²×C₄	#2404	1	2	yes	—
502	C₂²×C₄	#2408	1	2	yes	—
503	C₂²×C₄	#2408	1	2	yes	—
504	C₂²×C₄	#2408	1	2	yes	—
505	C₂²×C₄	#2408	1	1	yes	characteristic
506	C₂²×C₄	#2408	1	1	yes	characteristic
507	C₂²×C₄	#2408	1	1	yes	characteristic
508	C₂²×C₄	#2408	1	2	yes	—
509	C₂²×C₄	#2408	1	1	yes	characteristic
510	C₂²×C₄	#2410	1	2	yes	—
511	C₂²×C₄	#2410	1	2	yes	—
512	C₂²×C₄	#2424	1	2	yes	—
513	C₂²×C₄	#2424	1	2	yes	—
514	C₂²×C₄	#2424	1	2	yes	—
515	C₂²×C₄	#2668	1	2	yes	—
516	C₂²×C₄	#2668	1	2	yes	—
517	C₂²×C₄	#2668	1	2	yes	—
518	C₂²×C₄	#2669	1	2	yes	—
519	C₂²×C₄	#2669	1	2	yes	—
520	C₂²×C₄	#2669	1	2	yes	—
521	C₂²×C₄	#2678	1	2	yes	—
522	C₂²×C₄	#2678	1	2	yes	—
523	C₂²×C₄	#2678	1	2	yes	—
524	C₂²×C₄	#2678	1	2	yes	—
525	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
526	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
527	C₂²×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
528	C₂²×C₄	#3025	1	1	yes	characteristic
529	C₂²×C₄	#3025	1	2	yes	—
530	C₂²×C₄	#3025	1	1	yes	characteristic
531	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
532	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
533	C₂²×C₄	C₂²×#121	1	1	yes	characteristic
534	C₂²×C₄	C₂×#534	1	1	yes	characteristic
535	C₂²×C₄	C₂×#535	1	1	yes	characteristic
536	C₂²×C₄	C₂×#535	1	1	yes	characteristic
537	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
538	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
539	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
540	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
541	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
542	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
543	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
544	C₂²×C₄	C₂×#546	1	1	yes	characteristic
545	C₂²×C₄	C₂×#546	1	1	yes	characteristic
546	C₂²×C₄	C₂×#546	1	1	yes	characteristic
547	C₂×C₈	C₂×B(4,𝔽₂)	1	4	yes	—
548	C₂×C₈	C₂×B(4,𝔽₂)	1	4	yes	—
549	C₂³	#15257	1	2	yes	—
550	C₂³	#15257	1	2	yes	—
551	C₂³	#15257	1	2	yes	—
552	C₂³	#15257	1	2	yes	—
553	C₂³	#24260	1	1	yes	characteristic
554	C₂³	#24260	1	1	yes	characteristic
555	C₂³	#24260	1	2	yes	—
556	C₂³	C₂×#2410	1	1	yes	characteristic
557	C₂³	C₂×#2410	1	1	yes	characteristic
558	C₂³	C₂×#2424	1	1	yes	characteristic
559	C₂³	C₂×#2408	1	1	yes	characteristic
560	C₂³	C₂×#2404	1	1	yes	characteristic
561	C₂³	C₂×#2668	1	1	yes	characteristic
562	C₂³	C₂×#2669	1	1	yes	characteristic
563	C₂×C₄	#15257	1	2	yes	—
564	C₂×C₄	#15257	1	2	yes	—
565	C₂×C₄	#15257	1	2	yes	—
566	C₂×C₄	#15257	1	2	yes	—
567	C₂×C₄	#23900	1	2	yes	—
568	C₂×C₄	#23900	1	2	yes	—
569	C₂×C₄	#23902	1	2	yes	—
570	C₂×C₄	#23902	1	2	yes	—
571	C₂×C₄	#24260	1	2	yes	—
572	C₂×C₄	#24260	1	2	yes	—
573	C₂×C₄	#24260	1	2	yes	—
574	C₂×C₄	#24260	1	2	yes	—
575	C₂×C₄	#24260	1	2	yes	—
576	C₂×C₄	#24260	1	1	yes	characteristic
577	C₂×C₄	#24260	1	1	yes	characteristic
578	C₂×C₄	C₂×#2403	1	1	yes	characteristic
579	C₂×C₄	C₂×#2403	1	1	yes	characteristic
580	C₂×C₄	C₂×#2424	1	1	yes	characteristic
581	C₂×C₄	C₂×#2408	1	1	yes	characteristic
582	C₂×C₄	C₂×#2668	1	1	yes	characteristic
583	C₂×C₄	C₂×#2669	1	1	yes	characteristic
584	C₂×C₄	C₂×#2678	1	1	yes	characteristic
585	C₂×C₄	C₂×#2678	1	1	yes	characteristic
586	C₂×C₄	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
587	C₂×C₄	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
588	C₂×C₄	C₂×#3025	1	1	yes	characteristic
589	C₂×C₄	C₂×#3025	1	1	yes	characteristic
590	C₂²	#417526	1	2	yes	—
591	C₂²	#417526	1	2	yes	—
592	C₂²	C₂×#15257	1	1	yes	characteristic
593	C₂²	C₂×#24260	1	1	yes	characteristic
594	C₂²	C₂×#24260	1	1	yes	characteristic
595	C₄	#417526	1	2	yes	—
596	C₄	#417526	1	2	yes	—
597	C₄	C₂×#23900	1	1	yes	characteristic
598	C₄	C₂×#23902	1	1	yes	characteristic
599	C₄	C₂×#24260	1	1	yes	characteristic
600	C₄	C₂×#24260	1	1	yes	characteristic
601	C₂	#72236890	1	2	yes	—
602	C₂	C₂×#417526	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂×#24260
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. C₂×#6629051	C₂	semidirect
3. #72337497	C₂	semidirect
4. #72337494	C₂	semidirect
5. #72337435	C₂	semidirect
6. #72337423	C₂	semidirect
7. #72312755	C₂	semidirect
8. #72312697	C₂	semidirect
9. #72312687	C₂	semidirect
10. #72312359	C₂	semidirect
11. #72312304	C₂	semidirect
12. #72303813	C₂	semidirect
13. #72303727	C₂	semidirect
14. C₂×#498943	C₂	semidirect
15. #72256636	C₂	semidirect
16. C₂²×#33553	C₂	semidirect
17. C₂²×#12755	C₂	semidirect
18. C₂×#63076	C₂²	semidirect
24. C₂×#60387	C₂²	semidirect
29. C₂×#33358	C₂²	semidirect
31. C₂×#33347	C₂²	semidirect
36. C₂×#32951	C₂²	semidirect
37. C₂×#32950	C₂²	semidirect
38. #6500196	C₂²	semidirect
39. #6500186	C₂²	semidirect
41. C₂×#21017	C₂²	semidirect
47. C₂×#20673	C₂²	semidirect
48. C₂×#20612	C₂²	semidirect
49. #6370734	C₂²	semidirect
50. C₂×#13355	C₂²	semidirect
51. C₂×#13353	C₂²	semidirect
52. #498930	C₂²	semidirect
53. #498929	C₂²	semidirect
54. C₂×#12755	C₂²	semidirect
55. C₂×#12589	C₂²	semidirect
56. C₂×#12589	C₂²	semidirect
57. #492906	C₂²	semidirect
58. #492886	C₂²	semidirect
59. #392717	C₂²	semidirect
60. #392665	C₂²	semidirect
61. #353434	C₂²	semidirect
62. #353422	C₂²	semidirect
63. #353340	C₂²	semidirect
64. #353326	C₂²	semidirect
65. #148474	C₂²	semidirect
66. #148021	C₂²	semidirect
67. #148014	C₂²	semidirect
68. #147856	C₂²	semidirect
69. #147855	C₂²	semidirect
70. #147818	C₂²	semidirect
71. #147817	C₂²	semidirect
72. #147755	C₂²	semidirect
73. #147726	C₂²	semidirect
74. #147725	C₂²	semidirect
76. C₂³×AGL(1,ℤ/8)	D₄	semidirect
77. C₂×#3573	C₂³	semidirect
87. C₂×#3058	D₄	semidirect
89. C₂×#3057	D₄	semidirect
91. C₂×#3027	D₄	semidirect
97. C₂×#3022	C₂³	semidirect
98. C₂×#3021	D₄	semidirect
100. C₂×#3021	C₂³	semidirect
101. C₂×#2911	D₄	semidirect
102. C₂×#2896	D₄	semidirect
103. C₂²×#418	D₄	semidirect
104. C₂²×#418	D₄	semidirect
105. C₂²×#418	D₄	semidirect
113. C₂²×#407	D₄	semidirect
114. C₂²×#407	D₄	semidirect
119. C₂×#2129	C₂³	semidirect
121. C₂×#2128	C₂³	semidirect
122. C₂×#2123	C₂³	semidirect
125. C₂×#2122	C₂³	semidirect
129. C₂×#1915	C₂³	semidirect
130. C₂×#1914	D₄	semidirect
132. C₂×#1914	C₂³	semidirect
134. #20975	D₄	semidirect
137. #20899	D₄	semidirect
139. C₂×#1813	C₂³	semidirect
140. C₂×#1791	C₂³	semidirect
141. #20610	C₂³	semidirect
142. #20347	D₄	semidirect
143. #20347	D₄	semidirect
144. #20335	D₄	semidirect
145. #20335	D₄	semidirect
146. C₂×#1395	C₂³	semidirect
147. C₂×#1395	C₂³	semidirect
148. #12587	C₂³	semidirect
149. #12575	C₂³	semidirect
150. #10764	C₂³	semidirect
151. #10759	C₂³	semidirect
152. #10748	C₂³	semidirect
153. #10742	C₂³	semidirect
164. C₂³×SD₁₆	C₂×D₄	semidirect
165. C₂³×D₈	C₂×D₄	semidirect
210. C₂×#427	C₂×D₄	semidirect
211. C₂×#427	C₂×D₄	semidirect
212. C₂×#419	C₂×D₄	semidirect
213. C₂×#418	C₂×D₄	semidirect
214. C₂×#418	C₂×D₄	semidirect
215. C₂×#418	C₂×D₄	semidirect
216. C₂×#418	C₂×D₄	semidirect
217. C₂²×#102	C₂×D₄	semidirect
231. C₂×#407	C₂×D₄	semidirect
232. C₂²×C₂²⋊C₈	C₂×D₄	semidirect
235. #1914	C₂×D₄	semidirect
236. #1736	C₂×D₄	semidirect
237. #1735	C₂×D₄	semidirect
238. #1729	C₂×D₄	semidirect
239. #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
C₂×#6629051	2
#72337497	2
#72337494	2
#72337435	2
#72337423	2
#72312755	2
#72312697	2
#72312687	2
#72312359	2
#72312304	2
#72303813	2
#72303727	2
C₂×#498943	2
#72256636	2
C₂²×#33553	2
C₂²×#12755	2