Subgroups — #72259029

Order 2048.

At least 7720 conjugacy classes of subgroups; only the 1420 normal subgroups are shown.

The subgroup lattice has 452 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72259021	C₂	1	2	yes	maximal, complemented
2	#72259008	C₂	1	1	yes	maximal, characteristic, complemented
3	#72259002	C₂	1	2	yes	maximal, complemented
4	#72237398	C₂	1	2	yes	maximal, complemented
5	#72235847	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#7670203	C₂	1	1	yes	maximal, characteristic
7	#72218451	C₂	1	2	yes	maximal, complemented
8	#72217789	C₂	1	2	yes	maximal, complemented
9	C₂×#115690	C₂	1	2	yes	maximal, complemented
10	C₂²×#3484	C₄	1	1	yes	characteristic, complemented
11	C₂²×#3484	C₂²	1	1	yes	characteristic
12	C₂⁴×#120	C₂²	1	1	yes	characteristic
13	C₂⁴×#120	C₂²	1	1	yes	characteristic
14	C₂²×#2846	C₂²	1	1	yes	characteristic
15	C₂×#35390	C₄	1	1	yes	characteristic, complemented
16	C₂×#35348	C₄	1	1	yes	characteristic, complemented
17	C₂×#35348	C₄	1	1	yes	characteristic, complemented
18	C₂×#35346	C₄	1	1	yes	characteristic, complemented
19	C₂×#34981	C₄	1	1	yes	characteristic, complemented
20	C₂×#34981	C₂²	1	1	yes	characteristic
21	C₂×#34980	C₄	1	1	yes	characteristic, complemented
22	C₂×#34980	C₂²	1	1	yes	characteristic
23	C₂×#34198	C₄	1	1	yes	characteristic, complemented
24	C₂×#34198	C₂²	1	1	yes	characteristic
25	C₂×#21746	C₂²	1	4	yes	—
26	C₂×#21746	C₂²	1	4	yes	complemented
27	C₂×#21746	C₂²	1	2	yes	complemented
28	C₂×#21746	C₂²	1	2	yes	complemented
29	C₂²×#1781	C₂²	1	2	yes	complemented
30	C₂×#14679	C₂²	1	4	yes	complemented
31	#517411	C₂²	1	2	yes	complemented
32	C₂×#10735	C₂²	1	4	yes	complemented
33	C₂×#8101	C₂²	1	2	yes	complemented
34	C₂×#8101	C₂²	1	2	yes	complemented
35	C₂⁸	C₂³	1	1	yes	characteristic
36	C₂³×H(5,𝔽₂)	C₂×C₄	1	1	yes	characteristic
37	C₂⁵×D₄	C₂×C₄	1	1	yes	characteristic
38	C₂⁵×D₄	D₄	1	2	yes	—
39	C₂⁵×D₄	C₂³	1	1	yes	characteristic
40	C₂×#3484	D₄	1	8	yes	—
41	C₂²×#534	C₂×C₄	1	1	yes	characteristic
42	C₂²×#534	C₂×C₄	1	1	yes	characteristic
43	C₂²×#534	C₂×C₄	1	1	yes	characteristic
44	C₂²×#534	C₂×C₄	1	1	yes	characteristic
45	C₂²×#534	C₂×C₄	1	1	yes	characteristic
46	C₂³×#120	C₂×C₄	1	1	yes	characteristic
47	C₂³×#120	C₂×C₄	1	1	yes	characteristic
48	C₂³×#120	C₂×C₄	1	1	yes	characteristic
49	C₂³×#120	C₂×C₄	1	1	yes	characteristic
50	C₂³×#120	C₂×C₄	1	1	yes	characteristic
51	C₂³×#120	C₂×C₄	1	1	yes	characteristic
52	C₂³×#120	C₂×C₄	1	1	yes	characteristic
53	C₂³×#120	C₂×C₄	1	1	yes	characteristic
54	C₂³×#120	D₄	1	8	yes	—
55	C₂³×#120	D₄	1	2	yes	—
56	C₂³×#120	D₄	1	2	yes	—
57	C₂³×#120	C₂³	1	1	yes	characteristic
58	C₂³×#120	C₂³	1	1	yes	characteristic
59	C₂³×#120	C₂³	1	1	yes	characteristic
60	C₂²×#518	C₂×C₄	1	1	yes	characteristic
61	C₂²×#518	C₂×C₄	1	1	yes	characteristic
62	C₂⁴×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
63	C₂⁴×C₂²⋊C₄	D₄	1	2	yes	—
64	C₂⁴×C₂²⋊C₄	C₂³	1	1	yes	characteristic
65	C₂×#2849	D₄	1	2	yes	—
66	C₂×#2846	D₄	1	2	yes	—
67	C₂×#2846	D₄	1	8	yes	—
68	C₂×#2412	D₄	1	4	yes	—
69	C₂×#2410	D₄	1	4	yes	—
70	C₂×#2613	D₄	1	2	yes	—
71	C₂×#2613	D₄	1	2	yes	—
72	#34198	D₄	1	8	yes	—
73	C₂×#2315	C₂×C₄	1	1	yes	characteristic
74	C₂×#2315	C₂×C₄	1	1	yes	characteristic
75	C₂×#2308	C₂×C₄	1	1	yes	characteristic
76	C₂×#2308	C₂×C₄	1	1	yes	characteristic
77	C₂×#2308	C₂×C₄	1	1	yes	characteristic
78	C₂×#2308	C₂×C₄	1	1	yes	characteristic
79	C₂×#2308	C₂×C₄	1	1	yes	characteristic
80	C₂²×#379	C₂×C₄	1	1	yes	characteristic
81	C₂²×#379	C₂×C₄	1	1	yes	characteristic
82	C₂²×#379	C₂³	1	4	yes	—
83	C₂²×#379	C₂³	1	1	yes	characteristic
84	C₂²×#379	C₂³	1	4	yes	—
85	C₂×#2273	C₂×C₄	1	1	yes	characteristic
86	C₂×#1898	D₄	1	16	yes	complemented
87	C₂⁷	C₂²⋊C₄	1	1	yes	characteristic, complemented
88	C₂⁷	C₂²×C₄	1	1	yes	characteristic
89	C₂⁷	C₂²×C₄	1	1	yes	characteristic
90	C₂⁷	C₂×D₄	1	4	yes	—
91	C₂⁷	C₂×D₄	1	2	yes	—
92	C₂⁷	C₂×D₄	1	2	yes	—
93	C₂⁷	C₂×D₄	1	1	yes	characteristic
94	C₂⁷	C₂×D₄	1	4	yes	—
95	C₂⁷	C₂⁴	1	1	yes	characteristic
96	C₂²×H(5,𝔽₂)	C₂²⋊C₄	1	4	yes	complemented
97	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic, complemented
98	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic, complemented
99	C₂⁴×D₄	C₂²⋊C₄	1	2	yes	complemented
100	C₂⁴×D₄	C₂²⋊C₄	1	2	yes	complemented
101	C₂⁴×D₄	C₂²×C₄	1	1	yes	characteristic
102	C₂⁴×D₄	C₂²×C₄	1	1	yes	characteristic
103	C₂⁴×D₄	C₂²×C₄	1	1	yes	characteristic
104	C₂⁴×D₄	C₂²×C₄	1	1	yes	characteristic
105	C₂⁴×D₄	C₂²×C₄	1	1	yes	characteristic
106	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
107	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
108	C₂⁴×D₄	C₂×D₄	1	2	yes	—
109	C₂⁴×D₄	C₂×D₄	1	2	yes	—
110	C₂⁴×D₄	C₂×D₄	1	2	yes	—
111	C₂⁴×D₄	C₂×D₄	1	4	yes	—
112	C₂⁴×D₄	C₂×D₄	1	4	yes	—
113	C₂⁵×C₄	C₂²⋊C₄	1	1	yes	characteristic, complemented
114	C₂⁵×C₄	C₂²⋊C₄	1	2	yes	complemented
115	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
116	C₂×#534	C₂²⋊C₄	1	4	yes	complemented
117	C₂×#534	C₂²⋊C₄	1	4	yes	complemented
118	C₂²×#123	C₂²⋊C₄	1	2	yes	complemented
119	C₂²×#123	C₂²⋊C₄	1	2	yes	complemented
120	C₂²×#123	C₂²⋊C₄	1	2	yes	complemented
121	C₂²×#120	C₂²⋊C₄	1	4	yes	—
122	C₂²×#120	C₂²⋊C₄	1	4	yes	—
123	C₂²×#120	C₂²⋊C₄	1	4	yes	—
124	C₂²×#120	C₂²⋊C₄	1	4	yes	—
125	C₂²×#120	C₂²⋊C₄	1	4	yes	complemented
126	C₂²×#120	C₂²⋊C₄	1	2	yes	complemented
127	C₂²×#120	C₂²⋊C₄	1	2	yes	complemented
128	C₂²×#120	C₂²⋊C₄	1	4	yes	complemented
129	C₂²×#120	C₂²⋊C₄	1	2	yes	complemented
130	C₂²×#120	C₂×D₄	1	4	yes	—
131	C₂²×#120	C₂×D₄	1	4	yes	—
132	C₂²×#120	C₂×D₄	1	2	yes	—
133	C₂²×#120	C₂×D₄	1	4	yes	—
134	C₂²×#120	C₂×D₄	1	2	yes	—
135	C₂²×#120	C₂×D₄	1	4	yes	—
136	C₂²×#120	C₂×D₄	1	4	yes	—
137	C₂²×#120	C₂×D₄	1	8	yes	—
138	C₂²×#120	#41	1	8	yes	—
139	C₂×#518	C₂²⋊C₄	1	4	yes	complemented
140	C₂×#518	C₂²⋊C₄	1	4	yes	complemented
141	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	complemented
142	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	complemented
143	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	complemented
144	C₂³×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
145	C₂³×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
146	C₂³×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
147	C₂³×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
148	C₂³×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
149	C₂³×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
150	C₂³×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
151	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
152	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
153	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
154	C₂³×C₂²⋊C₄	C₂×D₄	1	4	yes	—
155	C₂³×C₂²⋊C₄	C₂×D₄	1	4	yes	—
156	C₂³×C₂²⋊C₄	C₂×D₄	1	4	yes	—
157	C₂³×C₂²⋊C₄	C₂×D₄	1	8	yes	complemented
158	#2315	C₂²⋊C₄	1	4	yes	complemented
159	#2308	C₂²⋊C₄	1	4	yes	complemented
160	C₂×#386	C₂²⋊C₄	1	4	yes	complemented
161	C₂×#385	C₂²⋊C₄	1	4	yes	complemented
162	C₂×#381	C₂²⋊C₄	1	2	yes	complemented
163	C₂×#381	C₂²⋊C₄	1	2	yes	complemented
164	C₂×#381	C₂²⋊C₄	1	2	yes	complemented
165	C₂×#379	C₂²⋊C₄	1	4	yes	complemented
166	C₂×#379	C₂²⋊C₄	1	4	yes	complemented
167	C₂×#379	C₂²⋊C₄	1	2	yes	complemented
168	C₂×#379	C₂²⋊C₄	1	2	yes	complemented
169	C₂×#379	C₂²⋊C₄	1	2	yes	complemented
170	C₂×#379	C₂×D₄	1	2	yes	—
171	C₂×#379	C₂×D₄	1	2	yes	—
172	C₂×#379	C₂×D₄	1	4	yes	—
173	C₂×#379	C₂×D₄	1	4	yes	—
174	C₂×#379	C₂×D₄	1	8	yes	complemented
175	#2273	C₂²⋊C₄	1	4	yes	complemented
176	C₂⁶	C₂×C₂²⋊C₄	1	2	yes	—
177	C₂⁶	C₂×C₂²⋊C₄	1	2	yes	—
178	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
179	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
180	C₂⁶	C₂×C₂²⋊C₄	1	2	yes	—
181	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
182	C₂⁶	C₂×C₂²⋊C₄	1	2	yes	—
183	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
184	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
185	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
186	C₂⁶	C₂×C₂²⋊C₄	1	2	yes	—
187	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
188	C₂⁶	#120	1	8	yes	—
189	C₂⁶	#120	1	4	yes	—
190	C₂⁶	#120	1	8	yes	—
191	C₂⁶	C₂³×C₄	1	1	yes	characteristic
192	C₂⁶	C₂²×D₄	1	2	yes	—
193	C₂⁶	C₂²×D₄	1	1	yes	characteristic
194	C₂⁶	C₂²×D₄	1	2	yes	—
195	C₂⁶	C₂²×D₄	1	2	yes	—
196	C₂⁶	C₂²×D₄	1	4	yes	—
197	C₂⁶	C₂²×D₄	1	2	yes	—
198	C₂⁶	C₂²×D₄	1	2	yes	—
199	C₂⁶	C₂²×D₄	1	2	yes	—
200	C₂⁶	C₂²×D₄	1	1	yes	characteristic
201	C₂⁶	C₂×#41	1	4	yes	—
202	C₂⁶	H(5,𝔽₂)	1	4	yes	—
203	C₂⁶	H(5,𝔽₂)	1	4	yes	—
204	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
205	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
206	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
207	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
208	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
209	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
210	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
211	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
212	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
213	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
214	C₂³×D₄	C₄×D₄	1	8	yes	—
215	C₂³×D₄	#120	1	4	yes	—
216	C₂³×D₄	#120	1	4	yes	—
217	C₂³×D₄	#120	1	4	yes	—
218	C₂³×D₄	#120	1	4	yes	—
219	C₂³×D₄	#120	1	8	yes	—
220	C₂³×D₄	#120	1	8	yes	—
221	C₂³×D₄	#120	1	4	yes	—
222	C₂³×D₄	#121	1	8	yes	—
223	C₂³×D₄	#123	1	4	yes	—
224	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
225	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
226	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
227	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
228	C₂⁴×C₄	C₂×C₂²⋊C₄	1	2	yes	—
229	C₂⁴×C₄	C₂×C₂²⋊C₄	1	2	yes	—
230	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
231	C₂⁴×C₄	C₂×C₂²⋊C₄	1	2	yes	—
232	C₂⁴×C₄	#120	1	4	yes	—
233	C₂×#120	#99	1	16	yes	complemented
234	C₂×#120	#120	1	8	yes	—
235	C₂×#120	#121	1	16	yes	—
236	C₂×#120	#121	1	16	yes	—
237	C₂×#120	#123	1	8	yes	—
238	C₂×#120	#124	1	8	yes	—
239	C₂×#120	#127	1	8	yes	—
240	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
241	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
242	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
243	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
244	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
245	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
246	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
247	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
248	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
249	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
250	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
251	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
252	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
253	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
254	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
255	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
256	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
257	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
258	C₂²×C₂²⋊C₄	C₄×D₄	1	8	yes	—
259	C₂²×C₂²⋊C₄	#120	1	4	yes	—
260	C₂²×C₂²⋊C₄	#120	1	4	yes	—
261	C₂²×C₂²⋊C₄	#120	1	8	yes	—
262	C₂²×C₂²⋊C₄	#120	1	4	yes	—
263	C₂²×C₂²⋊C₄	#120	1	8	yes	—
264	C₂²×C₂²⋊C₄	#120	1	16	yes	—
265	C₂²×C₂²⋊C₄	#121	1	8	yes	—
266	C₂²×C₂²⋊C₄	#123	1	4	yes	—
267	#379	#120	1	8	yes	—
268	#379	#120	1	8	yes	—
269	C₂⁵	#379	1	4	yes	—
270	C₂⁵	#379	1	2	yes	—
271	C₂⁵	#379	1	2	yes	—
272	C₂⁵	#379	1	2	yes	—
273	C₂⁵	#379	1	2	yes	—
274	C₂⁵	#379	1	2	yes	—
275	C₂⁵	#379	1	2	yes	—
276	C₂⁵	#379	1	2	yes	—
277	C₂⁵	#386	1	4	yes	—
278	C₂⁵	C₂×#99	1	8	yes	—
279	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
280	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
281	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
282	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
283	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
284	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
285	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
286	C₂⁵	C₂×C₄×D₄	1	4	yes	—
287	C₂⁵	#518	1	4	yes	—
288	C₂⁵	C₂×#120	1	2	yes	—
289	C₂⁵	C₂×#120	1	2	yes	—
290	C₂⁵	C₂×#120	1	4	yes	—
291	C₂⁵	C₂×#120	1	4	yes	—
292	C₂⁵	C₂×#120	1	2	yes	—
293	C₂⁵	C₂×#120	1	2	yes	—
294	C₂⁵	C₂×#120	1	2	yes	—
295	C₂⁵	C₂×#120	1	2	yes	—
296	C₂⁵	C₂×#120	1	2	yes	—
297	C₂⁵	C₂×#120	1	4	yes	—
298	C₂⁵	C₂×#120	1	4	yes	—
299	C₂⁵	C₂×#120	1	2	yes	—
300	C₂⁵	C₂×#121	1	4	yes	—
301	C₂⁵	C₂×#121	1	4	yes	—
302	C₂⁵	C₂×#121	1	4	yes	—
303	C₂⁵	C₂×#123	1	2	yes	—
304	C₂⁵	C₂×#123	1	2	yes	—
305	C₂⁵	C₂×#124	1	2	yes	—
306	C₂⁵	C₂×#127	1	2	yes	—
307	C₂⁵	#534	1	2	yes	—
308	C₂⁵	#534	1	4	yes	—
309	C₂⁵	#534	1	2	yes	—
310	C₂⁵	#534	1	2	yes	—
311	C₂⁵	#534	1	4	yes	—
312	C₂⁵	#534	1	2	yes	—
313	C₂⁵	#535	1	2	yes	—
314	C₂⁵	#535	1	4	yes	—
315	C₂⁵	#535	1	2	yes	—
316	C₂⁵	D₄²	1	4	yes	—
317	C₂⁵	D₄²	1	4	yes	—
318	C₂⁵	D₄²	1	4	yes	—
319	C₂⁵	D₄²	1	4	yes	—
320	C₂⁵	D₄²	1	4	yes	—
321	C₂⁵	D₄²	1	4	yes	—
322	C₂⁵	D₄²	1	4	yes	—
323	C₂⁵	D₄²	1	4	yes	—
324	C₂⁵	#546	1	4	yes	—
325	C₂⁵	#546	1	4	yes	—
326	C₂⁵	#546	1	4	yes	—
327	C₂⁵	#546	1	4	yes	—
328	C₂⁵	#546	1	4	yes	—
329	C₂⁵	#546	1	4	yes	—
330	C₂⁵	#546	1	4	yes	—
331	C₂⁵	#546	1	4	yes	—
332	C₂²×D₄	#386	1	8	yes	—
333	C₂²×D₄	#390	1	8	yes	—
334	C₂²×D₄	#392	1	16	yes	—
335	C₂²×D₄	#394	1	16	yes	—
336	C₂²×D₄	C₂×#99	1	8	yes	—
337	C₂³×C₄	#379	1	2	yes	—
338	C₂³×C₄	#379	1	2	yes	—
339	C₂³×C₄	#379	1	4	yes	—
340	C₂³×C₄	#379	1	2	yes	—
341	C₂³×C₄	#379	1	2	yes	—
342	C₂³×C₄	#379	1	4	yes	—
343	C₂³×C₄	#379	1	2	yes	—
344	C₂³×C₄	#379	1	4	yes	—
345	C₂³×C₄	#386	1	4	yes	—
346	C₂³×C₄	#386	1	4	yes	—
347	C₂³×C₄	#386	1	4	yes	—
348	C₂×C₂²⋊C₄	#379	1	4	yes	—
349	C₂×C₂²⋊C₄	#379	1	4	yes	—
350	C₂×C₂²⋊C₄	#379	1	4	yes	—
351	C₂×C₂²⋊C₄	#379	1	4	yes	—
352	C₂×C₂²⋊C₄	#386	1	8	yes	—
353	C₂×C₂²⋊C₄	#390	1	8	yes	—
354	C₂×C₂²⋊C₄	#392	1	16	yes	—
355	C₂×C₂²⋊C₄	#394	1	16	yes	—
356	C₂×C₂²⋊C₄	C₂×#99	1	8	yes	—
357	C₂⁴	#1438	1	4	yes	—
358	C₂⁴	#1781	1	4	yes	—
359	C₂⁴	#1781	1	4	yes	—
360	C₂⁴	#1781	1	4	yes	complemented
361	C₂⁴	C₂×#379	1	1	yes	characteristic
362	C₂⁴	C₂×#379	1	1	yes	characteristic
363	C₂⁴	C₂×#379	1	1	yes	characteristic
364	C₂⁴	C₂×#379	1	1	yes	characteristic
365	C₂⁴	C₂×#379	1	1	yes	characteristic
366	C₂⁴	C₂×#379	1	1	yes	characteristic
367	C₂⁴	C₂×#379	1	1	yes	characteristic
368	C₂⁴	C₂×#386	1	2	yes	—
369	C₂⁴	C₂×#386	1	2	yes	—
370	C₂⁴	C₂×#390	1	2	yes	—
371	C₂⁴	#2308	1	2	yes	—
372	C₂⁴	#2308	1	2	yes	—
373	C₂⁴	#2309	1	2	yes	—
374	C₂⁴	D₄×C₂²⋊C₄	1	4	yes	—
375	C₂⁴	D₄×C₂²⋊C₄	1	4	yes	—
376	C₂⁴	D₄×C₂²⋊C₄	1	4	yes	—
377	C₂⁴	D₄×C₂²⋊C₄	1	4	yes	—
378	C₂⁴	C₂×#392	1	4	yes	—
379	C₂⁴	C₂×#394	1	4	yes	—
380	C₂⁴	#2403	1	2	yes	—
381	C₂⁴	#2403	1	4	yes	—
382	C₂⁴	#2403	1	2	yes	—
383	C₂⁴	#2403	1	4	yes	—
384	C₂⁴	#2403	1	2	yes	—
385	C₂⁴	#2403	1	2	yes	—
386	C₂⁴	#2405	1	2	yes	—
387	C₂⁴	#2405	1	2	yes	—
388	C₂⁴	#2405	1	4	yes	—
389	C₂⁴	#2405	1	2	yes	—
390	C₂⁴	#2405	1	2	yes	—
391	C₂⁴	#2405	1	4	yes	—
392	C₂⁴	#2408	1	4	yes	—
393	C₂⁴	#2408	1	4	yes	—
394	C₂⁴	#2408	1	4	yes	—
395	C₂⁴	#2408	1	4	yes	—
396	C₂⁴	#2410	1	4	yes	—
397	C₂⁴	#2410	1	4	yes	—
398	C₂⁴	#2410	1	4	yes	—
399	C₂⁴	#2410	1	4	yes	—
400	C₂⁴	#2410	1	4	yes	—
401	C₂⁴	#2410	1	4	yes	—
402	C₂⁴	#2410	1	4	yes	—
403	C₂⁴	#2410	1	4	yes	—
404	C₂⁴	#2433	1	4	yes	—
405	C₂⁴	#2433	1	2	yes	—
406	C₂⁴	#2433	1	2	yes	—
407	C₂⁴	#2435	1	4	yes	—
408	C₂⁴	#2435	1	2	yes	—
409	C₂⁴	#2435	1	2	yes	—
410	C₂⁴	#2613	1	4	yes	—
411	C₂⁴	#2613	1	4	yes	—
412	C₂⁴	#2846	1	4	yes	—
413	C₂⁴	#2846	1	4	yes	—
414	C₂⁴	C₂²×#99	1	4	yes	—
415	C₂⁴	#2883	1	4	yes	—
416	C₂²×C₄	#1438	1	8	yes	—
417	C₂²×C₄	#1438	1	4	yes	—
418	C₂²×C₄	#1781	1	4	yes	complemented
419	C₂²⋊C₄	#1781	1	8	yes	complemented
420	C₂³	C₂×#1438	1	1	yes	characteristic
421	C₂³	#13867	1	2	yes	—
422	C₂³	#13867	1	2	yes	—
423	C₂³	#13867	1	2	yes	—
424	C₂³	#13867	1	2	yes	—
425	C₂³	#13902	1	2	yes	—
426	C₂³	#13902	1	2	yes	—
427	C₂³	#14335	1	1	yes	characteristic
428	C₂³	#14679	1	1	yes	characteristic
429	C₂³	#14715	1	4	yes	—
430	C₂³	#14715	1	4	yes	—
431	C₂³	#14724	1	4	yes	—
432	C₂³	#14724	1	4	yes	—
433	C₂³	C₂×#1781	1	2	yes	—
434	C₂³	C₂×#1781	1	2	yes	—
435	C₂³	C₂×#1781	1	2	yes	—
436	C₂³	#20585	1	2	yes	—
437	C₂³	#20585	1	2	yes	—
438	C₂³	#20586	1	2	yes	—
439	C₂³	D₄×#99	1	16	yes	—
440	C₂³	#23895	1	8	yes	—
441	C₂²	#154094	1	1	yes	characteristic
442	C₂²	#359549	1	4	yes	—
443	C₂²	#359579	1	4	yes	—
444	C₂²	#359579	1	4	yes	—
445	C₂²	#361622	1	4	yes	—
446	C₂²	#392109	1	1	yes	characteristic
447	C₂²	#392111	1	1	yes	characteristic
448	C₂²	#394064	1	8	yes	—
449	C₂	#72225621	1	1	yes	characteristic
450	C₂	#72240548	1	2	yes	—

	subgroup	G/H
center, socle	C₂²	#154094
commutator	C₂⁶	C₂³×C₄
Frattini, cosocle	C₂⁷	C₂⁴
prime radical	C₂×#7670203	C₂
LCS	G ▷ C₂⁶ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂⁷ ◁ G
LECS	G ▷ C₂⁷ ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72259021	C₂	semidirect
2. #72259008	C₂	semidirect
3. #72259002	C₂	semidirect
4. #72237398	C₂	semidirect
5. #72235847	C₂	semidirect
7. #72218451	C₂	semidirect
8. #72217789	C₂	semidirect
9. C₂×#115690	C₂	semidirect
10. C₂²×#3484	C₄	semidirect
15. C₂×#35390	C₄	semidirect
16. C₂×#35348	C₄	semidirect
17. C₂×#35348	C₄	semidirect
18. C₂×#35346	C₄	semidirect
19. C₂×#34981	C₄	semidirect
21. C₂×#34980	C₄	semidirect
23. C₂×#34198	C₄	semidirect
26. C₂×#21746	C₂²	semidirect
27. C₂×#21746	C₂²	semidirect
28. C₂×#21746	C₂²	semidirect
29. C₂²×#1781	C₂²	semidirect
30. C₂×#14679	C₂²	semidirect
31. #517411	C₂²	semidirect
32. C₂×#10735	C₂²	semidirect
33. C₂×#8101	C₂²	semidirect
34. C₂×#8101	C₂²	semidirect
86. C₂×#1898	D₄	semidirect
87. C₂⁷	C₂²⋊C₄	semidirect
96. C₂²×H(5,𝔽₂)	C₂²⋊C₄	semidirect
97. C₂⁴×D₄	C₂²⋊C₄	semidirect
98. C₂⁴×D₄	C₂²⋊C₄	semidirect
99. C₂⁴×D₄	C₂²⋊C₄	semidirect
100. C₂⁴×D₄	C₂²⋊C₄	semidirect
113. C₂⁵×C₄	C₂²⋊C₄	semidirect
114. C₂⁵×C₄	C₂²⋊C₄	semidirect
116. C₂×#534	C₂²⋊C₄	semidirect
117. C₂×#534	C₂²⋊C₄	semidirect
118. C₂²×#123	C₂²⋊C₄	semidirect
119. C₂²×#123	C₂²⋊C₄	semidirect
120. C₂²×#123	C₂²⋊C₄	semidirect
125. C₂²×#120	C₂²⋊C₄	semidirect
126. C₂²×#120	C₂²⋊C₄	semidirect
127. C₂²×#120	C₂²⋊C₄	semidirect
128. C₂²×#120	C₂²⋊C₄	semidirect
129. C₂²×#120	C₂²⋊C₄	semidirect
139. C₂×#518	C₂²⋊C₄	semidirect
140. C₂×#518	C₂²⋊C₄	semidirect
141. C₂³×C₂²⋊C₄	C₂²⋊C₄	semidirect
142. C₂³×C₂²⋊C₄	C₂²⋊C₄	semidirect
143. C₂³×C₂²⋊C₄	C₂²⋊C₄	semidirect
157. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
158. #2315	C₂²⋊C₄	semidirect
159. #2308	C₂²⋊C₄	semidirect
160. C₂×#386	C₂²⋊C₄	semidirect
161. C₂×#385	C₂²⋊C₄	semidirect
162. C₂×#381	C₂²⋊C₄	semidirect
163. C₂×#381	C₂²⋊C₄	semidirect
164. C₂×#381	C₂²⋊C₄	semidirect
165. C₂×#379	C₂²⋊C₄	semidirect
166. C₂×#379	C₂²⋊C₄	semidirect
167. C₂×#379	C₂²⋊C₄	semidirect
168. C₂×#379	C₂²⋊C₄	semidirect
169. C₂×#379	C₂²⋊C₄	semidirect
174. C₂×#379	C₂×D₄	semidirect
175. #2273	C₂²⋊C₄	semidirect
233. C₂×#120	#99	semidirect
360. C₂⁴	#1781	semidirect
418. C₂²×C₄	#1781	semidirect
419. C₂²⋊C₄	#1781	semidirect

Maximal subgroups

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

subgroup	index
#72259021	2
#72259008	2
#72259002	2
#72237398	2
#72235847	2
C₂×#7670203	2
#72218451	2
#72217789	2
C₂×#115690	2