Subgroups — #72281378

Order 2048.

At least 10308 conjugacy classes of subgroups; only the 1400 normal subgroups are shown.

The subgroup lattice has 551 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#493402	C₂	1	1	yes	maximal, characteristic, complemented
2	#72281167	C₂	1	2	yes	maximal, complemented
3	C₂×#493410	C₂	1	2	yes	maximal, complemented
4	#72280621	C₂	1	2	yes	maximal, complemented
5	#72267978	C₂	1	2	yes	maximal, complemented
6	C₂×#493396	C₂	1	1	yes	maximal, characteristic, complemented
7	#72240229	C₂	1	2	yes	maximal, complemented
8	#72239419	C₂	1	1	yes	maximal, characteristic
9	#72237193	C₂	1	2	yes	maximal, complemented
10	C₂×#62811	C₄	1	1	yes	characteristic, complemented
11	C₂×#62811	C₂²	1	1	yes	characteristic
12	C₂×#62811	C₂²	1	1	yes	characteristic
13	C₂×#62811	C₂²	1	1	yes	characteristic
14	#7629122	C₄	1	1	yes	characteristic, complemented
15	#7629122	C₄	1	1	yes	characteristic, complemented
16	#7629122	C₄	1	1	yes	characteristic, complemented
17	#7629122	C₂²	1	1	yes	characteristic
18	#7629121	C₄	1	1	yes	characteristic, complemented
19	#7629121	C₂²	1	1	yes	characteristic
20	C₂×#34936	C₄	1	1	yes	characteristic, complemented
21	C₂×#34736	C₄	1	1	yes	characteristic, complemented
22	C₂×#34736	C₂²	1	1	yes	characteristic
23	#7625567	C₄	1	1	yes	characteristic, complemented
24	#7625567	C₂²	1	1	yes	characteristic
25	C₂×#33369	C₂²	1	2	yes	—
26	C₂×#33369	C₂²	1	2	yes	complemented
27	C₂×#33358	C₂²	1	2	yes	—
28	C₂×#33358	C₂²	1	2	yes	complemented
29	C₂²×#2120	C₂²	1	4	yes	complemented
30	C₂×#20623	C₂²	1	4	yes	complemented
31	C₂×#20591	C₂²	1	2	yes	complemented
32	C₂×#20584	C₂²	1	2	yes	complemented
33	C₂×#12573	C₂²	1	4	yes	complemented
34	#353324	C₂²	1	4	yes	complemented
35	C₂²×#585	C₂×C₄	1	1	yes	characteristic
36	C₂²×#585	C₂³	1	1	yes	characteristic
37	C₂⁴×#41	C₂×C₄	1	1	yes	characteristic
38	C₂⁴×#41	C₂³	1	1	yes	characteristic
39	C₂×#3487	D₄	1	2	yes	—
40	C₂×#3487	D₄	1	2	yes	—
41	C₂×#3486	D₄	1	2	yes	—
42	C₂×#3486	D₄	1	2	yes	—
43	C₂×#3485	D₄	1	2	yes	—
44	C₂×#3485	D₄	1	2	yes	—
45	C₂×#3484	D₄	1	2	yes	—
46	C₂×#3484	D₄	1	2	yes	—
47	C₂×#3449	C₂×C₄	1	1	yes	characteristic
48	C₂×#3449	C₂×C₄	1	1	yes	characteristic
49	C₂×#3449	C₂×C₄	1	1	yes	characteristic
50	C₂×#3449	C₂×C₄	1	1	yes	characteristic
51	C₂×#3449	D₄	1	4	yes	—
52	C₂×#3449	C₂³	1	1	yes	characteristic
53	C₂×#3449	C₂³	1	1	yes	characteristic
54	C₂²×#532	C₂×C₄	1	1	yes	characteristic
55	C₂²×#525	C₂×C₄	1	1	yes	characteristic
56	C₂²×#525	C₂×C₄	1	1	yes	characteristic
57	C₂²×#525	C₂×C₄	1	1	yes	characteristic
58	C₂²×#525	C₂×C₄	1	1	yes	characteristic
59	C₂²×#525	C₂×C₄	1	1	yes	characteristic
60	C₂²×#525	C₂×C₄	1	1	yes	characteristic
61	C₂²×#525	C₂×C₄	1	1	yes	characteristic
62	C₂²×#525	D₄	1	4	yes	—
63	C₂²×#525	C₂³	1	1	yes	characteristic
64	C₂×#3428	C₂×C₄	1	1	yes	characteristic
65	C₂×#3428	C₂×C₄	1	1	yes	characteristic
66	C₂×#3428	C₂×C₄	1	1	yes	characteristic
67	C₂×#3428	C₂³	1	1	yes	characteristic
68	C₂³×C₄×D₄	C₂×C₄	1	1	yes	characteristic
69	C₂²×#413	C₂³	1	4	yes	—
70	C₂²×#410	C₂³	1	4	yes	—
71	#35676	D₄	1	2	yes	—
72	#35666	D₄	1	2	yes	—
73	#35616	D₄	1	2	yes	—
74	#35527	D₄	1	2	yes	—
75	#34743	D₄	1	4	yes	—
76	#34743	D₄	1	4	yes	—
77	C₂×#2406	D₄	1	2	yes	—
78	C₂×#2404	D₄	1	2	yes	—
79	C₂×#2405	D₄	1	2	yes	—
80	C₂×#2403	D₄	1	2	yes	—
81	#34070	D₄	1	4	yes	—
82	#34052	C₂×C₄	1	1	yes	characteristic
83	#34052	C₂×C₄	1	1	yes	characteristic
84	#34044	C₂×C₄	1	1	yes	characteristic
85	#34044	C₂×C₄	1	1	yes	characteristic
86	C₄×#532	D₄	1	4	yes	—
87	C₂×#2297	C₂×C₄	1	1	yes	characteristic
88	C₂×#2297	C₂×C₄	1	1	yes	characteristic
89	C₂×#2297	C₂×C₄	1	1	yes	characteristic
90	C₂×#2297	C₂³	1	1	yes	characteristic
91	C₂×#2280	C₂×C₄	1	1	yes	characteristic
92	C₂×#2280	C₂×C₄	1	1	yes	characteristic
93	C₂×C₄×#117	C₂×C₄	1	1	yes	characteristic
94	#33369	D₄	1	8	yes	complemented
95	#33358	D₄	1	8	yes	complemented
96	C₂²×2₋¹⁺⁴	C₂²⋊C₄	1	2	yes	—
97	C₂²×2₋¹⁺⁴	C₂×D₄	1	2	yes	—
98	C₂²×2₋¹⁺⁴	C₂×D₄	1	2	yes	—
99	C₂²×H(5,𝔽₂)	C₂²⋊C₄	1	2	yes	—
100	C₂²×H(5,𝔽₂)	C₂×D₄	1	2	yes	—
101	C₂²×H(5,𝔽₂)	C₂×D₄	1	2	yes	—
102	C₂³×#41	C₂²⋊C₄	1	1	yes	characteristic, complemented
103	C₂³×#41	C₂²⋊C₄	1	1	yes	characteristic, complemented
104	C₂³×#41	C₂²×C₄	1	1	yes	characteristic
105	C₂³×#41	C₂²×C₄	1	1	yes	characteristic
106	C₂³×#41	C₂²×C₄	1	1	yes	characteristic
107	C₂³×#41	C₂²×C₄	1	1	yes	characteristic
108	C₂³×#41	C₂²×C₄	1	1	yes	characteristic
109	C₂³×#41	C₂×D₄	1	4	yes	—
110	C₂³×#41	C₂×D₄	1	2	yes	—
111	C₂³×#41	C₂×D₄	1	1	yes	characteristic
112	C₂³×#41	C₂×D₄	1	2	yes	—
113	C₂³×#41	C₂×D₄	1	1	yes	characteristic
114	C₂³×#41	C₂⁴	1	1	yes	characteristic
115	C₂⁴×Q₈	C₂²⋊C₄	1	1	yes	characteristic, complemented
116	C₂⁴×Q₈	C₂×D₄	1	1	yes	characteristic
117	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
118	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic, complemented
119	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
120	C₂⁴×D₄	C₂×D₄	1	2	yes	—
121	C₂⁵×C₄	C₂²×C₄	1	1	yes	characteristic
122	C₂⁵×C₄	C₂²×C₄	1	1	yes	characteristic
123	C₂⁵×C₄	C₂×D₄	1	2	yes	—
124	#3449	C₂×D₄	1	4	yes	—
125	#3449	C₂×D₄	1	4	yes	—
126	#3449	#41	1	4	yes	—
127	#3449	#41	1	4	yes	—
128	C₂×#536	C₂²⋊C₄	1	2	yes	complemented
129	C₂×#536	C₂²⋊C₄	1	2	yes	complemented
130	C₂×#536	C₂×D₄	1	2	yes	—
131	C₂×#536	C₂×D₄	1	2	yes	—
132	C₂×#536	C₂×D₄	1	2	yes	—
133	C₂×#536	C₂×D₄	1	2	yes	—
134	C₂×#535	C₂²⋊C₄	1	2	yes	complemented
135	C₂×#535	C₂²⋊C₄	1	2	yes	complemented
136	C₂×#535	C₂×D₄	1	2	yes	—
137	C₂×#535	C₂×D₄	1	2	yes	—
138	C₂×#535	C₂×D₄	1	2	yes	—
139	C₂×#535	C₂×D₄	1	2	yes	—
140	C₂×#532	C₂×D₄	1	4	yes	—
141	C₂×#532	C₂×D₄	1	4	yes	—
142	C₂²×C₄⋊Q₈	C₂²⋊C₄	1	1	yes	characteristic, complemented
143	C₂²×#127	C₂²⋊C₄	1	1	yes	characteristic, complemented
144	C₂²×#124	C₂²⋊C₄	1	1	yes	characteristic, complemented
145	C₂²×#124	C₂²⋊C₄	1	1	yes	characteristic, complemented
146	C₂×#525	C₂²⋊C₄	1	4	yes	—
147	C₂×#525	C₂²⋊C₄	1	2	yes	—
148	C₂×#525	C₂²⋊C₄	1	2	yes	—
149	C₂×#525	C₂²⋊C₄	1	2	yes	—
150	C₂×#525	C₂²⋊C₄	1	2	yes	—
151	C₂×#525	C₂²⋊C₄	1	2	yes	—
152	C₂×#525	C₂²⋊C₄	1	2	yes	—
153	C₂×#525	C₂²⋊C₄	1	2	yes	—
154	C₂×#525	C₂²⋊C₄	1	2	yes	—
155	C₂×#525	C₂²⋊C₄	1	4	yes	—
156	C₂×#525	C₂²⋊C₄	1	2	yes	complemented
157	C₂×#525	C₂²⋊C₄	1	2	yes	complemented
158	C₂×#525	C₂²⋊C₄	1	2	yes	complemented
159	C₂×#525	C₂²⋊C₄	1	2	yes	complemented
160	C₂×#525	C₂×D₄	1	2	yes	—
161	C₂×#525	C₂×D₄	1	2	yes	—
162	C₂×#525	C₂×D₄	1	2	yes	—
163	C₂×#525	C₂×D₄	1	2	yes	—
164	C₂²×#123	C₂²⋊C₄	1	2	yes	—
165	C₂²×#123	C₂×D₄	1	2	yes	—
166	C₂²×#120	C₂²⋊C₄	1	2	yes	—
167	C₂²×#120	C₂×D₄	1	2	yes	—
168	C₂×#519	C₂²⋊C₄	1	2	yes	—
169	C₂×#519	C₂²⋊C₄	1	2	yes	complemented
170	C₂×#518	C₂²⋊C₄	1	2	yes	—
171	C₂×#518	C₂²⋊C₄	1	2	yes	complemented
172	C₂×C₄×#41	C₂²⋊C₄	1	4	yes	complemented
173	C₂×C₄×#41	C₂×D₄	1	4	yes	—
174	C₂×C₄×#41	C₂×D₄	1	4	yes	—
175	C₂²×#117	C₂²×C₄	1	1	yes	characteristic
176	C₂²×#117	C₂²×C₄	1	1	yes	characteristic
177	C₂²×#117	C₂²×C₄	1	1	yes	characteristic
178	C₂²×#117	C₂²×C₄	1	1	yes	characteristic
179	C₂²×#117	C₂²×C₄	1	1	yes	characteristic
180	C₂²×#117	C₂²×C₄	1	1	yes	characteristic
181	C₂²×#117	C₂×D₄	1	4	yes	—
182	C₂³×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
183	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
184	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
185	C₂³×C₄²	C₂²×C₄	1	1	yes	characteristic
186	C₂×#413	C₂×D₄	1	8	yes	complemented
187	C₂×#410	C₂×D₄	1	8	yes	complemented
188	#2310	C₂²⋊C₄	1	2	yes	complemented
189	#2309	C₂²⋊C₄	1	2	yes	complemented
190	#2297	C₂²⋊C₄	1	2	yes	complemented
191	#2297	C₂²⋊C₄	1	2	yes	complemented
192	#2297	C₂²⋊C₄	1	2	yes	complemented
193	#2297	C₂²⋊C₄	1	2	yes	complemented
194	#2297	C₂²⋊C₄	1	4	yes	complemented
195	#2297	C₂×D₄	1	2	yes	—
196	#2297	C₂×D₄	1	2	yes	—
197	#2297	C₂×D₄	1	2	yes	—
198	#2297	C₂×D₄	1	2	yes	—
199	#2296	C₂²⋊C₄	1	4	yes	complemented
200	C₂×#386	C₂²⋊C₄	1	2	yes	—
201	C₂×#386	C₂²⋊C₄	1	2	yes	—
202	C₂×#386	C₂×D₄	1	2	yes	—
203	C₂×#386	C₂×D₄	1	2	yes	—
204	#2285	C₂²⋊C₄	1	4	yes	complemented
205	C₂×#381	C₂²⋊C₄	1	2	yes	—
206	C₂×#379	C₂²⋊C₄	1	2	yes	—
207	C₂×C₄×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	complemented
208	C₂×C₄×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	complemented
209	C₂×#376	C₂²⋊C₄	1	2	yes	complemented
210	C₂×C₄³	C₂²⋊C₄	1	2	yes	complemented
211	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
212	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
213	C₂⁶	#120	1	2	yes	—
214	C₂²×#41	C₂×C₂²⋊C₄	1	2	yes	—
215	C₂²×#41	C₂×C₂²⋊C₄	1	2	yes	—
216	C₂²×#41	C₂×C₂²⋊C₄	1	2	yes	—
217	C₂²×#41	C₂×C₂²⋊C₄	1	2	yes	—
218	C₂²×#41	C₂×C₂²⋊C₄	1	2	yes	—
219	C₂²×#41	C₂×C₂²⋊C₄	1	2	yes	—
220	C₂²×#41	C₂×C₂²⋊C₄	1	2	yes	—
221	C₂²×#41	C₂×C₂²⋊C₄	1	2	yes	—
222	C₂²×#41	C₄×D₄	1	4	yes	—
223	C₂²×#41	C₄×D₄	1	4	yes	—
224	C₂²×#41	#120	1	4	yes	—
225	C₂²×#41	#120	1	4	yes	—
226	C₂²×#41	C₂²×D₄	1	2	yes	—
227	C₂²×#41	C₂²×D₄	1	2	yes	—
228	C₂²×#41	C₂²×D₄	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	C₂×#41	1	2	yes	—
233	C₂²×#41	C₂×#41	1	2	yes	—
234	C₂²×#41	H(5,𝔽₂)	1	4	yes	—
235	C₂²×#41	H(5,𝔽₂)	1	4	yes	—
236	C₂³×Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
237	C₂³×Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
238	C₂³×Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
239	C₂³×Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
240	C₂³×Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
241	C₂³×Q₈	#120	1	4	yes	—
242	C₂³×Q₈	#120	1	2	yes	—
243	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
244	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
245	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
246	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
247	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
248	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
249	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
250	C₂³×D₄	#120	1	2	yes	—
251	C₂³×D₄	#120	1	4	yes	—
252	C₂³×D₄	#120	1	2	yes	—
253	C₂³×D₄	#120	1	2	yes	—
254	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
255	C₂³×D₄	C₂²×D₄	1	2	yes	—
256	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
257	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
258	C₂⁴×C₄	C₂×C₂²⋊C₄	1	2	yes	—
259	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
260	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
261	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
262	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
263	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
264	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
265	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
266	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
267	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
268	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
269	C₂⁴×C₄	#120	1	2	yes	—
270	C₂⁴×C₄	#120	1	2	yes	—
271	C₂⁴×C₄	#120	1	2	yes	—
272	C₂⁴×C₄	C₂³×C₄	1	1	yes	characteristic
273	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
274	#536	#120	1	4	yes	—
275	#536	#120	1	4	yes	—
276	#536	#121	1	4	yes	—
277	#536	#121	1	8	yes	—
278	#536	#121	1	4	yes	—
279	#536	#123	1	4	yes	—
280	#536	#123	1	4	yes	—
281	#535	#120	1	4	yes	—
282	#535	#120	1	4	yes	—
283	#535	#121	1	4	yes	—
284	#535	#121	1	8	yes	—
285	#535	#121	1	4	yes	—
286	#535	#123	1	4	yes	—
287	#535	#123	1	4	yes	—
288	#532	#121	1	8	yes	—
289	#532	#121	1	8	yes	—
290	#532	#124	1	8	yes	—
291	#532	#127	1	8	yes	—
292	C₂×C₄⋊Q₈	#120	1	4	yes	—
293	C₂×C₄⋊Q₈	#120	1	4	yes	—
294	C₂×#127	#120	1	4	yes	—
295	C₂×#127	#120	1	4	yes	—
296	C₂×#124	#120	1	4	yes	—
297	C₂×#124	#120	1	4	yes	—
298	C₂×#124	#120	1	4	yes	—
299	C₂×#124	#120	1	4	yes	—
300	#525	#99	1	16	yes	—
301	C₂×#123	#120	1	4	yes	—
302	C₂×#123	#120	1	4	yes	—
303	C₂×#120	#120	1	4	yes	—
304	C₂×#120	#120	1	4	yes	—
305	C₂×#117	C₂×C₂²⋊C₄	1	2	yes	—
306	C₂×#117	C₂×C₂²⋊C₄	1	2	yes	—
307	C₂×#117	C₂×C₂²⋊C₄	1	2	yes	—
308	C₂×#117	C₂×C₂²⋊C₄	1	2	yes	—
309	C₂×#117	C₂×C₂²⋊C₄	1	2	yes	—
310	C₂×#117	C₂×C₂²⋊C₄	1	2	yes	—
311	C₂×#117	C₂×C₂²⋊C₄	1	2	yes	—
312	C₂×#117	C₂×C₂²⋊C₄	1	2	yes	—
313	C₂×#117	C₂×C₂²⋊C₄	1	2	yes	—
314	C₂×#117	C₂×C₂²⋊C₄	1	2	yes	—
315	C₂×#117	C₂×C₂²⋊C₄	1	2	yes	—
316	C₂×#117	C₂×C₂²⋊C₄	1	2	yes	—
317	C₂×#117	C₄×D₄	1	4	yes	—
318	C₂×#117	C₄×D₄	1	4	yes	—
319	C₂×#117	#120	1	8	yes	—
320	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
321	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
322	C₂²×C₄²	C₂×C₂²⋊C₄	1	2	yes	—
323	C₂²×C₄²	C₂×C₂²⋊C₄	1	2	yes	—
324	C₂²×C₄²	C₂×C₂²⋊C₄	1	2	yes	—
325	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
326	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
327	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
328	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
329	C₂²×C₄²	C₂×C₂²⋊C₄	1	2	yes	—
330	C₂²×C₄²	#120	1	8	yes	—
331	#386	#120	1	4	yes	—
332	#386	#120	1	4	yes	—
333	#386	#120	1	4	yes	—
334	#386	#120	1	4	yes	—
335	C₂⁵	#379	1	1	yes	characteristic
336	C₂⁵	#379	1	1	yes	characteristic
337	C₂⁵	#379	1	2	yes	—
338	C₂⁵	#379	1	1	yes	characteristic
339	C₂⁵	#379	1	1	yes	characteristic
340	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
341	C₂⁵	C₂×#120	1	2	yes	—
342	C₂×#41	#386	1	4	yes	—
343	C₂×#41	#386	1	4	yes	—
344	C₂×#41	#390	1	8	yes	—
345	C₂×#41	C₂×#99	1	8	yes	—
346	C₂×#41	C₂×#120	1	2	yes	—
347	C₂×#41	C₂×#121	1	2	yes	—
348	C₂×#41	C₂×#121	1	2	yes	—
349	C₂×#41	C₂×#121	1	2	yes	—
350	C₂×#41	C₂×#121	1	2	yes	—
351	C₂×#41	C₂×#123	1	2	yes	—
352	C₂×#41	C₂×#124	1	2	yes	—
353	C₂×#41	C₂×#127	1	2	yes	—
354	C₂×#41	#534	1	4	yes	—
355	C₂×#41	#534	1	4	yes	—
356	C₂×#41	#535	1	4	yes	—
357	C₂×#41	#535	1	4	yes	—
358	C₂×#41	D₄²	1	4	yes	—
359	C₂×#41	D₄²	1	4	yes	—
360	C₂×#41	D₄²	1	4	yes	—
361	C₂×#41	D₄²	1	4	yes	—
362	C₂×#41	#546	1	4	yes	—
363	C₂×#41	#546	1	4	yes	—
364	C₂×#41	#546	1	4	yes	—
365	C₂×#41	#546	1	4	yes	—
366	C₂²×Q₈	#379	1	2	yes	—
367	C₂²×Q₈	#379	1	2	yes	—
368	C₂²×Q₈	#379	1	2	yes	—
369	C₂²×Q₈	#379	1	2	yes	—
370	C₂²×Q₈	#386	1	4	yes	—
371	C₂²×Q₈	C₂×#120	1	2	yes	—
372	C₂²×Q₈	C₂×#120	1	2	yes	—
373	C₂²×Q₈	C₂×#120	1	1	yes	characteristic
374	C₂²×Q₈	C₂×#121	1	2	yes	—
375	C₂²×Q₈	C₂×#123	1	1	yes	characteristic
376	C₂²×Q₈	#534	1	2	yes	—
377	C₂²×Q₈	#534	1	2	yes	—
378	C₂²×D₄	#379	1	2	yes	—
379	C₂²×D₄	#379	1	2	yes	—
380	C₂²×D₄	#379	1	2	yes	—
381	C₂²×D₄	#379	1	2	yes	—
382	C₂²×D₄	#386	1	4	yes	—
383	C₂²×D₄	C₂×#120	1	4	yes	—
384	C₂²×D₄	C₂×#120	1	4	yes	—
385	C₂²×D₄	C₂×#120	1	2	yes	—
386	C₂²×D₄	C₂×#120	1	2	yes	—
387	C₂²×D₄	C₂×#120	1	1	yes	characteristic
388	C₂²×D₄	C₂×#121	1	2	yes	—
389	C₂²×D₄	C₂×#123	1	1	yes	characteristic
390	C₂²×D₄	#534	1	2	yes	—
391	C₂²×D₄	#534	1	2	yes	—
392	C₂²×D₄	D₄²	1	4	yes	—
393	C₂²×D₄	D₄²	1	4	yes	—
394	C₂²×D₄	#546	1	4	yes	—
395	C₂²×D₄	#546	1	4	yes	—
396	C₂³×C₄	#379	1	1	yes	characteristic
397	C₂³×C₄	#379	1	1	yes	characteristic
398	C₂³×C₄	#379	1	2	yes	—
399	C₂³×C₄	#379	1	1	yes	characteristic
400	C₂³×C₄	#379	1	1	yes	characteristic
401	C₂³×C₄	#379	1	1	yes	characteristic
402	C₂³×C₄	#379	1	1	yes	characteristic
403	C₂³×C₄	#379	1	1	yes	characteristic
404	C₂³×C₄	#379	1	1	yes	characteristic
405	C₂³×C₄	C₂×#99	1	8	yes	—
406	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
407	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
408	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
409	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
410	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
411	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
412	C₂³×C₄	C₂×C₄×D₄	1	2	yes	—
413	C₂³×C₄	C₂×C₄×D₄	1	2	yes	—
414	C₂³×C₄	#518	1	2	yes	—
415	C₂³×C₄	#518	1	2	yes	—
416	C₂³×C₄	C₂×#120	1	2	yes	—
417	C₂³×C₄	C₂×#120	1	4	yes	—
418	C₂³×C₄	C₂×#120	1	4	yes	—
419	C₂³×C₄	D₄²	1	4	yes	—
420	C₂³×C₄	D₄²	1	4	yes	—
421	C₂³×C₄	#546	1	4	yes	—
422	C₂³×C₄	#546	1	4	yes	—
423	C₄⋊Q₈	#392	1	8	yes	—
424	C₄⋊Q₈	#394	1	8	yes	—
425	#127	#392	1	8	yes	—
426	#127	#394	1	8	yes	—
427	#124	#392	1	8	yes	—
428	#124	#392	1	8	yes	—
429	#124	#394	1	8	yes	—
430	#124	#394	1	8	yes	—
431	#117	#386	1	4	yes	—
432	#117	#386	1	4	yes	—
433	#117	#386	1	4	yes	—
434	#117	#386	1	4	yes	—
435	#117	C₂×#99	1	8	yes	—
436	C₂×C₂²⋊C₄	#379	1	4	yes	—
437	C₂×C₂²⋊C₄	#379	1	4	yes	—
438	C₂×C₄²	#379	1	4	yes	—
439	C₂×C₄²	#379	1	4	yes	—
440	C₂×C₄²	#379	1	4	yes	—
441	C₂×C₄²	#379	1	4	yes	—
442	C₂×C₄²	#390	1	8	yes	—
443	C₂⁴	#1781	1	4	yes	—
444	C₂⁴	C₂×#379	1	1	yes	characteristic
445	C₂⁴	C₂×#379	1	1	yes	characteristic
446	C₂⁴	C₂×#379	1	1	yes	characteristic
447	C₂⁴	D₄×C₂²⋊C₄	1	2	yes	—
448	C₂⁴	D₄×C₂²⋊C₄	1	2	yes	—
449	C₂⁴	#2403	1	2	yes	—
450	C₂⁴	#2405	1	2	yes	—
451	C₂⁴	#2410	1	4	yes	—
452	C₂⁴	#2846	1	4	yes	—
453	C₂×Q₈	#1438	1	4	yes	—
454	C₂×Q₈	#1781	1	4	yes	—
455	C₂×Q₈	C₂×#392	1	2	yes	—
456	C₂×Q₈	C₂×#394	1	2	yes	—
457	C₂×Q₈	#2403	1	2	yes	—
458	C₂×Q₈	#2405	1	2	yes	—
459	C₂×Q₈	#2410	1	4	yes	—
460	C₂×Q₈	#2613	1	4	yes	—
461	C₂×D₄	#1438	1	4	yes	—
462	C₂×D₄	#1781	1	4	yes	—
463	C₂×D₄	C₂×#392	1	2	yes	—
464	C₂×D₄	C₂×#394	1	2	yes	—
465	C₂×D₄	#2403	1	2	yes	—
466	C₂×D₄	#2403	1	4	yes	—
467	C₂×D₄	#2405	1	2	yes	—
468	C₂×D₄	#2405	1	4	yes	—
469	C₂×D₄	#2408	1	4	yes	—
470	C₂×D₄	#2408	1	4	yes	—
471	C₂×D₄	#2410	1	4	yes	—
472	C₂×D₄	#2410	1	4	yes	—
473	C₂×D₄	#2410	1	4	yes	—
474	C₂×D₄	#2433	1	4	yes	—
475	C₂×D₄	#2435	1	4	yes	—
476	C₂×D₄	#2613	1	4	yes	—
477	C₂²×C₄	#1781	1	4	yes	—
478	C₂²×C₄	C₂×#379	1	1	yes	characteristic
479	C₂²×C₄	C₂×#379	1	1	yes	characteristic
480	C₂²×C₄	C₂×#379	1	1	yes	characteristic
481	C₂²×C₄	C₂×#379	1	1	yes	characteristic
482	C₂²×C₄	C₂×#386	1	1	yes	characteristic
483	C₂²×C₄	C₂×#386	1	1	yes	characteristic
484	C₂²×C₄	C₂×#386	1	2	yes	—
485	C₂²×C₄	C₂×#390	1	2	yes	—
486	C₂²×C₄	#2308	1	2	yes	—
487	C₂²×C₄	#2308	1	1	yes	characteristic
488	C₂²×C₄	#2308	1	1	yes	characteristic
489	C₂²×C₄	#2309	1	2	yes	—
490	C₂²×C₄	D₄×C₂²⋊C₄	1	2	yes	—
491	C₂²×C₄	D₄×C₂²⋊C₄	1	2	yes	—
492	C₂²×C₄	D₄×C₂²⋊C₄	1	2	yes	—
493	C₂²×C₄	D₄×C₂²⋊C₄	1	2	yes	—
494	C₂²×C₄	D₄×C₂²⋊C₄	1	2	yes	—
495	C₂²×C₄	D₄×C₂²⋊C₄	1	2	yes	—
496	C₂²×C₄	#2403	1	4	yes	—
497	C₂²×C₄	#2403	1	2	yes	—
498	C₂²×C₄	#2405	1	4	yes	—
499	C₂²×C₄	#2405	1	2	yes	—
500	C₂²×C₄	#2408	1	4	yes	—
501	C₂²×C₄	#2408	1	4	yes	—
502	C₂²×C₄	#2410	1	4	yes	—
503	C₂²×C₄	#2410	1	4	yes	—
504	C₂²×C₄	#2410	1	4	yes	—
505	C₂²×C₄	#2433	1	4	yes	—
506	C₂²×C₄	#2435	1	4	yes	—
507	C₂²×C₄	#2846	1	4	yes	—
508	C₂²×C₄	C₂²×#99	1	4	yes	—
509	C₂²×C₄	#2883	1	2	yes	—
510	C₂²×C₄	#2883	1	2	yes	—
511	C₄²	#1438	1	8	yes	—
512	C₄²	#1781	1	8	yes	—
513	C₂³	#13867	1	2	yes	—
514	C₂³	#13867	1	1	yes	characteristic
515	C₂³	#13867	1	1	yes	characteristic
516	C₂³	#13902	1	2	yes	—
517	C₂³	#14679	1	1	yes	characteristic
518	C₂³	#14715	1	4	yes	—
519	C₂³	#14724	1	4	yes	—
520	C₂³	C₂×#1781	1	2	yes	—
521	C₂³	#20585	1	2	yes	—
522	C₂×C₄	C₂×#1438	1	1	yes	characteristic
523	C₂×C₄	#13867	1	1	yes	characteristic
524	C₂×C₄	#13867	1	1	yes	characteristic
525	C₂×C₄	#13867	1	2	yes	—
526	C₂×C₄	#13902	1	2	yes	—
527	C₂×C₄	#14335	1	1	yes	characteristic
528	C₂×C₄	#14715	1	4	yes	—
529	C₂×C₄	#14724	1	4	yes	—
530	C₂×C₄	C₂×#1781	1	2	yes	—
531	C₂×C₄	C₂×#1781	1	2	yes	—
532	C₂×C₄	#20585	1	2	yes	—
533	C₂×C₄	#20586	1	1	yes	characteristic
534	C₂×C₄	#20586	1	1	yes	characteristic
535	C₂×C₄	D₄×#99	1	4	yes	—
536	C₂×C₄	D₄×#99	1	4	yes	—
537	C₂×C₄	D₄×#99	1	4	yes	—
538	C₂×C₄	D₄×#99	1	4	yes	—
539	C₂²	#154094	1	1	yes	characteristic
540	C₂²	#359579	1	2	yes	—
541	C₂²	#359579	1	2	yes	—
542	C₂²	#392109	1	1	yes	characteristic
543	C₂²	#392111	1	1	yes	characteristic
544	C₄	#359579	1	4	yes	—
545	C₄	#361622	1	2	yes	—
546	C₄	#361622	1	2	yes	—
547	C₂	#72225621	1	1	yes	characteristic
548	C₂	#72280637	1	1	yes	characteristic
549	C₂	#72280847	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#20586
commutator	C₂⁴×C₄	C₂³×C₄
Frattini, cosocle	C₂³×#41	C₂⁴
socle	C₂²	#392111
prime radical	#72239419	C₂
LCS	G ▷ C₂⁴×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂×#62811 ◁ G
LECS	G ▷ C₂³×#41 ▷ C₂² ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. C₂×#493402	C₂	semidirect
2. #72281167	C₂	semidirect
3. C₂×#493410	C₂	semidirect
4. #72280621	C₂	semidirect
5. #72267978	C₂	semidirect
6. C₂×#493396	C₂	semidirect
7. #72240229	C₂	semidirect
9. #72237193	C₂	semidirect
10. C₂×#62811	C₄	semidirect
14. #7629122	C₄	semidirect
15. #7629122	C₄	semidirect
16. #7629122	C₄	semidirect
18. #7629121	C₄	semidirect
20. C₂×#34936	C₄	semidirect
21. C₂×#34736	C₄	semidirect
23. #7625567	C₄	semidirect
26. C₂×#33369	C₂²	semidirect
28. C₂×#33358	C₂²	semidirect
29. C₂²×#2120	C₂²	semidirect
30. C₂×#20623	C₂²	semidirect
31. C₂×#20591	C₂²	semidirect
32. C₂×#20584	C₂²	semidirect
33. C₂×#12573	C₂²	semidirect
34. #353324	C₂²	semidirect
94. #33369	D₄	semidirect
95. #33358	D₄	semidirect
102. C₂³×#41	C₂²⋊C₄	semidirect
103. C₂³×#41	C₂²⋊C₄	semidirect
115. C₂⁴×Q₈	C₂²⋊C₄	semidirect
118. C₂⁴×D₄	C₂²⋊C₄	semidirect
128. C₂×#536	C₂²⋊C₄	semidirect
129. C₂×#536	C₂²⋊C₄	semidirect
134. C₂×#535	C₂²⋊C₄	semidirect
135. C₂×#535	C₂²⋊C₄	semidirect
142. C₂²×C₄⋊Q₈	C₂²⋊C₄	semidirect
143. C₂²×#127	C₂²⋊C₄	semidirect
144. C₂²×#124	C₂²⋊C₄	semidirect
145. C₂²×#124	C₂²⋊C₄	semidirect
156. C₂×#525	C₂²⋊C₄	semidirect
157. C₂×#525	C₂²⋊C₄	semidirect
158. C₂×#525	C₂²⋊C₄	semidirect
159. C₂×#525	C₂²⋊C₄	semidirect
169. C₂×#519	C₂²⋊C₄	semidirect
171. C₂×#518	C₂²⋊C₄	semidirect
172. C₂×C₄×#41	C₂²⋊C₄	semidirect
186. C₂×#413	C₂×D₄	semidirect
187. C₂×#410	C₂×D₄	semidirect
188. #2310	C₂²⋊C₄	semidirect
189. #2309	C₂²⋊C₄	semidirect
190. #2297	C₂²⋊C₄	semidirect
191. #2297	C₂²⋊C₄	semidirect
192. #2297	C₂²⋊C₄	semidirect
193. #2297	C₂²⋊C₄	semidirect
194. #2297	C₂²⋊C₄	semidirect
199. #2296	C₂²⋊C₄	semidirect
204. #2285	C₂²⋊C₄	semidirect
207. C₂×C₄×C₂²⋊C₄	C₂²⋊C₄	semidirect
208. C₂×C₄×C₂²⋊C₄	C₂²⋊C₄	semidirect
209. C₂×#376	C₂²⋊C₄	semidirect
210. C₂×C₄³	C₂²⋊C₄	semidirect

Maximal subgroups

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

subgroup	index
C₂×#493402	2
#72281167	2
C₂×#493410	2
#72280621	2
#72267978	2
C₂×#493396	2
#72240229	2
#72239419	2
#72237193	2