Subgroups — #72259092

Order 2048.

At least 11325 conjugacy classes of subgroups; only the 1372 normal subgroups are shown.

The subgroup lattice has 531 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72259089	C₂	1	2	yes	maximal, complemented
2	#72259083	C₂	1	2	yes	maximal, complemented
3	#72236453	C₂	1	2	yes	maximal, complemented
4	#72236437	C₂	1	2	yes	maximal, complemented
5	C₂×#359428	C₂	1	1	yes	maximal, characteristic, complemented
6	#72218766	C₂	1	2	yes	maximal, complemented
7	#72217789	C₂	1	1	yes	maximal, characteristic, complemented
8	#72217511	C₂	1	1	yes	maximal, characteristic
9	C₂×#115690	C₂	1	2	yes	maximal, complemented
10	C₂×#62817	C₂²	1	1	yes	characteristic
11	C₂⁴×#120	C₂²	1	1	yes	characteristic
12	#7642273	C₄	1	2	yes	complemented
13	#7642244	C₄	1	2	yes	complemented
14	#7641845	C₂²	1	2	yes	—
15	C₂²×#2846	C₂²	1	2	yes	—
16	#7630944	C₄	1	2	yes	complemented
17	#7630939	C₄	1	2	yes	complemented
18	#7626202	C₂²	1	1	yes	characteristic
19	C₂³×#379	C₂²	1	1	yes	characteristic, complemented
20	C₂×#21746	C₂²	1	2	yes	—
21	C₂×#21746	C₂²	1	2	yes	complemented
22	C₂×#21746	C₂²	1	2	yes	complemented
23	C₂×#21746	C₂²	1	1	yes	characteristic, complemented
24	C₂×#21746	C₂²	1	1	yes	characteristic, complemented
25	C₂²×#1898	C₂²	1	2	yes	—
26	C₂²×#1898	C₂²	1	2	yes	complemented
27	C₂²×#1898	C₂²	1	2	yes	complemented
28	C₂×#14679	C₂²	1	1	yes	characteristic, complemented
29	C₂×#14679	C₂²	1	2	yes	complemented
30	#516383	C₂²	1	2	yes	complemented
31	C₂×#10735	C₂²	1	2	yes	complemented
32	C₂×#10725	C₂²	1	2	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	C₂⁵×D₄	C₂×C₄	1	1	yes	characteristic
37	C₂⁵×D₄	D₄	1	1	yes	characteristic
38	C₂⁵×D₄	D₄	1	1	yes	characteristic
39	C₂×#3490	C₂×C₄	1	2	yes	—
40	C₂×#3490	D₄	1	4	yes	—
41	C₂×#3484	C₂×C₄	1	2	yes	—
42	C₂×#3484	D₄	1	4	yes	—
43	C₂³×#120	C₂×C₄	1	1	yes	characteristic
44	C₂³×#120	C₂×C₄	1	1	yes	characteristic
45	C₂³×#120	D₄	1	4	yes	—
46	C₂³×#120	D₄	1	1	yes	characteristic
47	C₂³×#120	D₄	1	1	yes	characteristic
48	C₂³×#120	D₄	1	1	yes	characteristic
49	C₂³×#120	D₄	1	1	yes	characteristic
50	C₂³×#120	C₂³	1	1	yes	characteristic
51	C₂³×#120	C₂³	1	1	yes	characteristic
52	C₂³×#120	C₂³	1	2	yes	—
53	C₂⁴×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
54	C₂⁴×C₂²⋊C₄	D₄	1	1	yes	characteristic
55	C₂⁴×C₂²⋊C₄	D₄	1	1	yes	characteristic
56	C₂⁴×C₂²⋊C₄	C₂³	1	2	yes	—
57	#37436	D₄	1	8	yes	—
58	C₂×#2846	C₂×C₄	1	4	yes	—
59	C₂×#2846	C₂×C₄	1	4	yes	—
60	C₂×#2846	D₄	1	8	yes	—
61	#34992	C₂×C₄	1	4	yes	—
62	#34992	D₄	1	4	yes	—
63	#34980	C₂×C₄	1	4	yes	—
64	#34980	D₄	1	4	yes	—
65	#34356	D₄	1	8	yes	—
66	#34176	C₂×C₄	1	2	yes	—
67	#34171	C₂×C₄	1	2	yes	—
68	C₂²×#379	D₄	1	4	yes	—
69	C₂²×#379	C₂³	1	2	yes	—
70	C₂²×#379	C₂³	1	2	yes	—
71	C₂²×#379	C₂³	1	2	yes	—
72	C₂²×#379	C₂³	1	2	yes	—
73	C₂×#1898	D₄	1	8	yes	complemented
74	C₂×#1898	D₄	1	8	yes	complemented
75	C₂⁷	C₂²⋊C₄	1	1	yes	characteristic, complemented
76	C₂⁷	C₂²×C₄	1	1	yes	characteristic
77	C₂⁷	C₂²×C₄	1	1	yes	characteristic
78	C₂⁷	C₂×D₄	1	1	yes	characteristic
79	C₂⁷	C₂×D₄	1	4	yes	—
80	C₂⁷	C₂×D₄	1	1	yes	characteristic
81	C₂⁷	C₂×D₄	1	1	yes	characteristic
82	C₂⁷	C₂×D₄	1	1	yes	characteristic
83	C₂⁷	C₂×D₄	1	4	yes	—
84	C₂⁷	C₂⁴	1	1	yes	characteristic
85	C₂²×H(5,𝔽₂)	C₂²⋊C₄	1	2	yes	complemented
86	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic, complemented
87	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic, complemented
88	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic, complemented
89	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic, complemented
90	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic, complemented
91	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic, complemented
92	C₂⁴×D₄	C₂²×C₄	1	1	yes	characteristic
93	C₂⁴×D₄	C₂²×C₄	1	1	yes	characteristic
94	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
95	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
96	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
97	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
98	C₂⁴×D₄	C₂×D₄	1	2	yes	—
99	C₂⁴×D₄	C₂×D₄	1	2	yes	—
100	C₂⁴×D₄	C₂×D₄	1	2	yes	—
101	C₂⁵×C₄	C₂²⋊C₄	1	1	yes	characteristic, complemented
102	C₂⁵×C₄	C₂²⋊C₄	1	1	yes	characteristic, complemented
103	C₂⁵×C₄	C₂²⋊C₄	1	1	yes	characteristic, complemented
104	C₂×#543	C₂²⋊C₄	1	2	yes	complemented
105	C₂×#534	C₂²⋊C₄	1	4	yes	complemented
106	C₂×#534	C₂²⋊C₄	1	2	yes	complemented
107	C₂²×#120	C₂²⋊C₄	1	8	yes	complemented
108	C₂²×#120	C₂²⋊C₄	1	8	yes	complemented
109	C₂²×#120	C₂²×C₄	1	4	yes	—
110	C₂²×#120	C₂×D₄	1	4	yes	—
111	C₂²×#120	C₂×D₄	1	4	yes	—
112	C₂²×#120	C₂×D₄	1	4	yes	—
113	C₂²×#120	C₂×D₄	1	4	yes	—
114	C₂²×#120	C₂×D₄	1	4	yes	—
115	C₂²×#120	C₂×D₄	1	4	yes	—
116	C₂²×#120	C₂×D₄	1	4	yes	—
117	C₂²×#120	C₂×D₄	1	4	yes	—
118	C₂²×#120	C₂×D₄	1	4	yes	—
119	C₂²×#120	#41	1	4	yes	—
120	C₂²×#120	#41	1	4	yes	—
121	C₂×#518	C₂²⋊C₄	1	4	yes	complemented
122	C₂×#518	C₂²⋊C₄	1	2	yes	complemented
123	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic, complemented
124	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic, complemented
125	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic, complemented
126	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic, complemented
127	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic, complemented
128	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic, complemented
129	C₂³×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
130	C₂³×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
131	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
132	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
133	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
134	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
135	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
136	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
137	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
138	C₂³×C₂²⋊C₄	C₂×D₄	1	4	yes	—
139	C₂³×C₂²⋊C₄	C₂×D₄	1	4	yes	complemented
140	C₂³×C₂²⋊C₄	C₂×D₄	1	4	yes	complemented
141	#2483	C₂²⋊C₄	1	8	yes	complemented
142	#2405	C₂²⋊C₄	1	8	yes	complemented
143	#2405	C₂²⋊C₄	1	8	yes	complemented
144	#2403	C₂²⋊C₄	1	8	yes	complemented
145	#2312	C₂²⋊C₄	1	4	yes	complemented
146	#2312	C₂²⋊C₄	1	4	yes	complemented
147	#2309	C₂²⋊C₄	1	4	yes	complemented
148	#2308	C₂²⋊C₄	1	4	yes	complemented
149	C₂×#379	C₂²⋊C₄	1	8	yes	complemented
150	C₂×#379	C₂²⋊C₄	1	8	yes	complemented
151	C₂×#379	C₂²×C₄	1	4	yes	—
152	C₂×#379	C₂×D₄	1	4	yes	—
153	C₂×#379	C₂×D₄	1	4	yes	—
154	C₂×#379	C₂×D₄	1	4	yes	—
155	C₂×#379	C₂×D₄	1	4	yes	—
156	C₂×#379	C₂×D₄	1	4	yes	—
157	C₂×#379	C₂×D₄	1	4	yes	complemented
158	C₂×#379	C₂×D₄	1	4	yes	complemented
159	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
160	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
161	C₂⁶	C₂×C₂²⋊C₄	1	4	yes	—
162	C₂⁶	C₂×C₂²⋊C₄	1	4	yes	—
163	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
164	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
165	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
166	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
167	C₂⁶	#120	1	2	yes	—
168	C₂⁶	#120	1	2	yes	—
169	C₂⁶	#120	1	2	yes	—
170	C₂⁶	#120	1	4	yes	—
171	C₂⁶	#120	1	4	yes	—
172	C₂⁶	#120	1	2	yes	—
173	C₂⁶	#120	1	2	yes	—
174	C₂⁶	C₂³×C₄	1	1	yes	characteristic
175	C₂⁶	C₂²×D₄	1	1	yes	characteristic
176	C₂⁶	C₂²×D₄	1	2	yes	—
177	C₂⁶	C₂²×D₄	1	1	yes	characteristic
178	C₂⁶	C₂²×D₄	1	2	yes	—
179	C₂⁶	C₂²×D₄	1	2	yes	—
180	C₂⁶	C₂²×D₄	1	2	yes	—
181	C₂⁶	C₂²×D₄	1	2	yes	—
182	C₂⁶	C₂²×D₄	1	2	yes	—
183	C₂⁶	C₂²×D₄	1	2	yes	—
184	C₂⁶	C₂²×D₄	1	2	yes	—
185	C₂⁶	C₂×#41	1	2	yes	—
186	C₂⁶	C₂×#41	1	2	yes	—
187	C₂⁶	H(5,𝔽₂)	1	1	yes	characteristic
188	C₂⁶	H(5,𝔽₂)	1	2	yes	—
189	C₂⁶	H(5,𝔽₂)	1	1	yes	characteristic
190	C₂⁶	H(5,𝔽₂)	1	1	yes	characteristic
191	C₂⁶	H(5,𝔽₂)	1	1	yes	characteristic
192	C₂⁶	H(5,𝔽₂)	1	2	yes	—
193	C₂³×D₄	C₂×C₂²⋊C₄	1	4	yes	—
194	C₂³×D₄	C₂×C₂²⋊C₄	1	4	yes	—
195	C₂³×D₄	C₂×C₂²⋊C₄	1	4	yes	—
196	C₂³×D₄	C₂×C₂²⋊C₄	1	4	yes	—
197	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
198	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
199	C₂³×D₄	C₄×D₄	1	4	yes	—
200	C₂³×D₄	C₄×D₄	1	4	yes	—
201	C₂³×D₄	#120	1	2	yes	—
202	C₂³×D₄	#120	1	4	yes	—
203	C₂³×D₄	#120	1	4	yes	—
204	C₂³×D₄	#120	1	2	yes	—
205	C₂³×D₄	#120	1	4	yes	—
206	C₂³×D₄	#120	1	4	yes	—
207	C₂³×D₄	#120	1	4	yes	—
208	C₂³×D₄	#120	1	4	yes	—
209	C₂³×D₄	#120	1	2	yes	—
210	C₂³×D₄	#120	1	2	yes	—
211	C₂³×D₄	#121	1	4	yes	—
212	C₂³×D₄	#121	1	4	yes	—
213	C₂³×D₄	#123	1	2	yes	—
214	C₂³×D₄	#123	1	2	yes	—
215	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
216	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
217	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
218	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
219	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
220	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
221	C₂⁴×C₄	#120	1	2	yes	—
222	C₂⁴×C₄	#120	1	2	yes	—
223	C₂⁴×C₄	#120	1	2	yes	—
224	C₂×#120	#120	1	8	yes	—
225	C₂×#120	#121	1	8	yes	—
226	C₂×#120	#121	1	8	yes	—
227	C₂×#120	#121	1	8	yes	—
228	C₂×#120	#121	1	8	yes	—
229	C₂×#120	#123	1	8	yes	—
230	C₂×#120	#124	1	8	yes	—
231	C₂×#120	#127	1	8	yes	—
232	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	4	yes	—
233	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	4	yes	—
234	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	4	yes	—
235	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	4	yes	—
236	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
237	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
238	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	8	yes	—
239	C₂²×C₂²⋊C₄	C₄×D₄	1	4	yes	—
240	C₂²×C₂²⋊C₄	C₄×D₄	1	4	yes	—
241	C₂²×C₂²⋊C₄	#120	1	2	yes	—
242	C₂²×C₂²⋊C₄	#120	1	2	yes	—
243	C₂²×C₂²⋊C₄	#120	1	4	yes	—
244	C₂²×C₂²⋊C₄	#120	1	4	yes	—
245	C₂²×C₂²⋊C₄	#120	1	4	yes	—
246	C₂²×C₂²⋊C₄	#120	1	4	yes	—
247	C₂²×C₂²⋊C₄	#120	1	2	yes	—
248	C₂²×C₂²⋊C₄	#120	1	2	yes	—
249	C₂²×C₂²⋊C₄	#120	1	4	yes	—
250	C₂²×C₂²⋊C₄	#120	1	4	yes	—
251	C₂²×C₂²⋊C₄	#120	1	8	yes	—
252	C₂²×C₂²⋊C₄	#120	1	8	yes	—
253	C₂²×C₂²⋊C₄	#121	1	4	yes	—
254	C₂²×C₂²⋊C₄	#121	1	4	yes	—
255	C₂²×C₂²⋊C₄	#123	1	2	yes	—
256	C₂²×C₂²⋊C₄	#123	1	2	yes	—
257	#379	C₂×C₂²⋊C₄	1	8	yes	—
258	#379	C₂×C₂²⋊C₄	1	8	yes	—
259	#379	#120	1	8	yes	—
260	#379	#120	1	8	yes	—
261	C₂⁵	#379	1	2	yes	—
262	C₂⁵	#379	1	2	yes	—
263	C₂⁵	#379	1	2	yes	—
264	C₂⁵	#379	1	2	yes	—
265	C₂⁵	#379	1	4	yes	—
266	C₂⁵	#379	1	2	yes	—
267	C₂⁵	#379	1	2	yes	—
268	C₂⁵	#386	1	2	yes	—
269	C₂⁵	#386	1	2	yes	—
270	C₂⁵	B(4,𝔽₂)	1	4	yes	—
271	C₂⁵	#458	1	4	yes	—
272	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
273	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
274	C₂⁵	C₂²×C₂²⋊C₄	1	2	yes	—
275	C₂⁵	C₂²×C₂²⋊C₄	1	2	yes	—
276	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
277	C₂⁵	C₂×C₄×D₄	1	2	yes	—
278	C₂⁵	C₂×C₄×D₄	1	2	yes	—
279	C₂⁵	#518	1	1	yes	characteristic
280	C₂⁵	#518	1	1	yes	characteristic
281	C₂⁵	#518	1	1	yes	characteristic
282	C₂⁵	#518	1	1	yes	characteristic
283	C₂⁵	C₂×#120	1	2	yes	—
284	C₂⁵	C₂×#120	1	2	yes	—
285	C₂⁵	C₂×#120	1	1	yes	characteristic
286	C₂⁵	C₂×#120	1	2	yes	—
287	C₂⁵	C₂×#120	1	2	yes	—
288	C₂⁵	C₂×#120	1	2	yes	—
289	C₂⁵	C₂×#120	1	2	yes	—
290	C₂⁵	C₂×#120	1	1	yes	characteristic
291	C₂⁵	C₂×#120	1	1	yes	characteristic
292	C₂⁵	C₂×#120	1	2	yes	—
293	C₂⁵	C₂×#120	1	1	yes	characteristic
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	2	yes	—
298	C₂⁵	C₂×#120	1	1	yes	characteristic
299	C₂⁵	C₂×#120	1	2	yes	—
300	C₂⁵	C₂×#120	1	2	yes	—
301	C₂⁵	C₂×#120	1	1	yes	characteristic
302	C₂⁵	C₂×#121	1	2	yes	—
303	C₂⁵	C₂×#121	1	2	yes	—
304	C₂⁵	C₂×#121	1	2	yes	—
305	C₂⁵	C₂×#121	1	2	yes	—
306	C₂⁵	C₂×#121	1	2	yes	—
307	C₂⁵	C₂×#121	1	2	yes	—
308	C₂⁵	C₂×#123	1	1	yes	characteristic
309	C₂⁵	C₂×#123	1	1	yes	characteristic
310	C₂⁵	C₂×#123	1	2	yes	—
311	C₂⁵	C₂×#124	1	2	yes	—
312	C₂⁵	C₂×#127	1	2	yes	—
313	C₂⁵	#534	1	1	yes	characteristic
314	C₂⁵	#534	1	1	yes	characteristic
315	C₂⁵	#534	1	1	yes	characteristic
316	C₂⁵	#534	1	2	yes	—
317	C₂⁵	#534	1	2	yes	—
318	C₂⁵	#534	1	2	yes	—
319	C₂⁵	#534	1	2	yes	—
320	C₂⁵	#534	1	1	yes	characteristic
321	C₂⁵	#534	1	2	yes	—
322	C₂⁵	#534	1	2	yes	—
323	C₂⁵	#535	1	2	yes	—
324	C₂⁵	#535	1	2	yes	—
325	C₂⁵	#535	1	2	yes	—
326	C₂⁵	#535	1	2	yes	—
327	C₂⁵	D₄²	1	2	yes	—
328	C₂⁵	D₄²	1	2	yes	—
329	C₂⁵	D₄²	1	2	yes	—
330	C₂⁵	D₄²	1	2	yes	—
331	C₂⁵	D₄²	1	2	yes	—
332	C₂⁵	D₄²	1	2	yes	—
333	C₂⁵	D₄²	1	2	yes	—
334	C₂⁵	D₄²	1	2	yes	—
335	C₂⁵	D₄²	1	2	yes	—
336	C₂⁵	D₄²	1	2	yes	—
337	C₂⁵	D₄²	1	2	yes	—
338	C₂⁵	D₄²	1	2	yes	—
339	C₂⁵	D₄²	1	2	yes	—
340	C₂⁵	D₄²	1	2	yes	—
341	C₂⁵	D₄²	1	2	yes	—
342	C₂⁵	D₄²	1	2	yes	—
343	C₂⁵	#546	1	2	yes	—
344	C₂⁵	#546	1	2	yes	—
345	C₂⁵	#546	1	2	yes	—
346	C₂⁵	#546	1	2	yes	—
347	C₂⁵	#546	1	2	yes	—
348	C₂⁵	#546	1	2	yes	—
349	C₂⁵	#546	1	2	yes	—
350	C₂⁵	#546	1	2	yes	—
351	C₂⁵	#546	1	2	yes	—
352	C₂⁵	#546	1	2	yes	—
353	C₂⁵	#546	1	2	yes	—
354	C₂⁵	#546	1	2	yes	—
355	C₂⁵	#546	1	2	yes	—
356	C₂⁵	#546	1	2	yes	—
357	C₂⁵	#546	1	2	yes	—
358	C₂⁵	#546	1	2	yes	—
359	C₂²×D₄	#386	1	8	yes	—
360	C₂²×D₄	#390	1	8	yes	—
361	C₂²×D₄	#392	1	8	yes	—
362	C₂²×D₄	#392	1	8	yes	—
363	C₂²×D₄	#394	1	8	yes	—
364	C₂²×D₄	#394	1	8	yes	—
365	C₂³×C₄	#379	1	4	yes	—
366	C₂³×C₄	#379	1	4	yes	—
367	C₂³×C₄	#379	1	2	yes	—
368	C₂³×C₄	#379	1	2	yes	—
369	C₂³×C₄	#379	1	4	yes	—
370	C₂³×C₄	#379	1	2	yes	—
371	C₂³×C₄	#379	1	2	yes	—
372	C₂³×C₄	#379	1	2	yes	—
373	C₂³×C₄	#379	1	2	yes	—
374	C₂³×C₄	#386	1	2	yes	—
375	C₂³×C₄	#386	1	2	yes	—
376	C₂³×C₄	#386	1	2	yes	—
377	C₂³×C₄	#386	1	2	yes	—
378	C₂³×C₄	#386	1	2	yes	—
379	C₂³×C₄	#386	1	2	yes	—
380	C₂×C₂²⋊C₄	#379	1	16	yes	—
381	C₂×C₂²⋊C₄	#386	1	8	yes	—
382	C₂×C₂²⋊C₄	#390	1	8	yes	—
383	C₂×C₂²⋊C₄	#392	1	8	yes	—
384	C₂×C₂²⋊C₄	#392	1	8	yes	—
385	C₂×C₂²⋊C₄	#394	1	8	yes	—
386	C₂×C₂²⋊C₄	#394	1	8	yes	—
387	C₂⁴	#1438	1	4	yes	—
388	C₂⁴	#1790	1	4	yes	—
389	C₂⁴	#1790	1	4	yes	—
390	C₂⁴	C₂×#379	1	1	yes	characteristic
391	C₂⁴	C₂×#379	1	1	yes	characteristic
392	C₂⁴	C₂×#379	1	2	yes	—
393	C₂⁴	C₂×#379	1	2	yes	—
394	C₂⁴	C₂×#379	1	1	yes	characteristic
395	C₂⁴	C₂×#386	1	1	yes	characteristic
396	C₂⁴	C₂×#386	1	2	yes	—
397	C₂⁴	C₂×#386	1	1	yes	characteristic
398	C₂⁴	C₂×#390	1	2	yes	—
399	C₂⁴	#2308	1	1	yes	characteristic
400	C₂⁴	#2308	1	1	yes	characteristic
401	C₂⁴	#2308	1	1	yes	characteristic
402	C₂⁴	#2308	1	1	yes	characteristic
403	C₂⁴	#2309	1	1	yes	characteristic
404	C₂⁴	#2309	1	1	yes	characteristic
405	C₂⁴	D₄×C₂²⋊C₄	1	2	yes	—
406	C₂⁴	D₄×C₂²⋊C₄	1	2	yes	—
407	C₂⁴	D₄×C₂²⋊C₄	1	2	yes	—
408	C₂⁴	D₄×C₂²⋊C₄	1	2	yes	—
409	C₂⁴	D₄×C₂²⋊C₄	1	2	yes	—
410	C₂⁴	D₄×C₂²⋊C₄	1	2	yes	—
411	C₂⁴	D₄×C₂²⋊C₄	1	2	yes	—
412	C₂⁴	D₄×C₂²⋊C₄	1	2	yes	—
413	C₂⁴	C₂×#392	1	2	yes	—
414	C₂⁴	C₂×#392	1	2	yes	—
415	C₂⁴	C₂×#394	1	2	yes	—
416	C₂⁴	C₂×#394	1	2	yes	—
417	C₂⁴	#2403	1	2	yes	—
418	C₂⁴	#2403	1	2	yes	—
419	C₂⁴	#2403	1	2	yes	—
420	C₂⁴	#2403	1	1	yes	characteristic
421	C₂⁴	#2403	1	2	yes	—
422	C₂⁴	#2403	1	2	yes	—
423	C₂⁴	#2403	1	2	yes	—
424	C₂⁴	#2403	1	1	yes	characteristic
425	C₂⁴	#2403	1	1	yes	characteristic
426	C₂⁴	#2403	1	1	yes	characteristic
427	C₂⁴	#2405	1	2	yes	—
428	C₂⁴	#2405	1	1	yes	characteristic
429	C₂⁴	#2405	1	2	yes	—
430	C₂⁴	#2405	1	1	yes	characteristic
431	C₂⁴	#2405	1	2	yes	—
432	C₂⁴	#2405	1	2	yes	—
433	C₂⁴	#2405	1	1	yes	characteristic
434	C₂⁴	#2405	1	2	yes	—
435	C₂⁴	#2405	1	2	yes	—
436	C₂⁴	#2405	1	1	yes	characteristic
437	C₂⁴	#2408	1	2	yes	—
438	C₂⁴	#2408	1	2	yes	—
439	C₂⁴	#2408	1	2	yes	—
440	C₂⁴	#2408	1	2	yes	—
441	C₂⁴	#2408	1	2	yes	—
442	C₂⁴	#2408	1	2	yes	—
443	C₂⁴	#2408	1	2	yes	—
444	C₂⁴	#2408	1	2	yes	—
445	C₂⁴	#2410	1	2	yes	—
446	C₂⁴	#2410	1	2	yes	—
447	C₂⁴	#2410	1	2	yes	—
448	C₂⁴	#2410	1	2	yes	—
449	C₂⁴	#2410	1	2	yes	—
450	C₂⁴	#2410	1	2	yes	—
451	C₂⁴	#2410	1	2	yes	—
452	C₂⁴	#2410	1	2	yes	—
453	C₂⁴	#2410	1	2	yes	—
454	C₂⁴	#2410	1	2	yes	—
455	C₂⁴	#2410	1	2	yes	—
456	C₂⁴	#2410	1	2	yes	—
457	C₂⁴	#2410	1	2	yes	—
458	C₂⁴	#2410	1	2	yes	—
459	C₂⁴	#2410	1	2	yes	—
460	C₂⁴	#2410	1	2	yes	—
461	C₂⁴	#2433	1	2	yes	—
462	C₂⁴	#2433	1	2	yes	—
463	C₂⁴	#2433	1	2	yes	—
464	C₂⁴	#2433	1	2	yes	—
465	C₂⁴	#2435	1	2	yes	—
466	C₂⁴	#2435	1	2	yes	—
467	C₂⁴	#2435	1	2	yes	—
468	C₂⁴	#2435	1	2	yes	—
469	C₂⁴	#2613	1	2	yes	—
470	C₂⁴	#2613	1	2	yes	—
471	C₂⁴	#2613	1	2	yes	—
472	C₂⁴	#2613	1	2	yes	—
473	C₂⁴	#2846	1	2	yes	—
474	C₂⁴	#2846	1	2	yes	—
475	C₂⁴	#2846	1	2	yes	—
476	C₂⁴	#2846	1	2	yes	—
477	C₂⁴	C₂×B(4,𝔽₂)	1	2	yes	—
478	C₂⁴	C₂×#458	1	2	yes	—
479	C₂⁴	#3026	1	4	yes	—
480	C₂²×C₄	#1438	1	4	yes	—
481	C₂²×C₄	#1438	1	4	yes	—
482	C₂²×C₄	#1438	1	4	yes	—
483	C₂³	C₂×#1438	1	1	yes	characteristic
484	C₂³	#13867	1	2	yes	—
485	C₂³	#13867	1	1	yes	characteristic
486	C₂³	#13867	1	1	yes	characteristic
487	C₂³	#13867	1	1	yes	characteristic
488	C₂³	#13867	1	1	yes	characteristic
489	C₂³	#13867	1	2	yes	—
490	C₂³	#13902	1	2	yes	—
491	C₂³	#13902	1	2	yes	—
492	C₂³	#14335	1	1	yes	characteristic
493	C₂³	#14679	1	1	yes	characteristic
494	C₂³	#14715	1	2	yes	—
495	C₂³	#14715	1	2	yes	—
496	C₂³	#14715	1	2	yes	—
497	C₂³	#14715	1	2	yes	—
498	C₂³	#14724	1	2	yes	—
499	C₂³	#14724	1	2	yes	—
500	C₂³	#14724	1	2	yes	—
501	C₂³	#14724	1	2	yes	—
502	C₂³	C₂×#1790	1	2	yes	—
503	C₂³	#20609	1	2	yes	—
504	C₂³	#21776	1	4	yes	—
505	C₂³	#23895	1	4	yes	—
506	C₂³	#23900	1	1	yes	characteristic
507	C₂³	#23901	1	1	yes	characteristic
508	C₂³	#23903	1	2	yes	—
509	C₂³	#24056	1	2	yes	—
510	C₂³	#24058	1	2	yes	—
511	C₂³	#24404	1	4	yes	—
512	C₂³	#24405	1	4	yes	—
513	C₂³	#32898	1	4	yes	—
514	C₂³	#32900	1	4	yes	—
515	C₂²	#154094	1	1	yes	characteristic
516	C₂²	#359531	1	2	yes	—
517	C₂²	#359549	1	2	yes	—
518	C₂²	#359552	1	1	yes	characteristic
519	C₂²	#359554	1	1	yes	characteristic
520	C₂²	#359591	1	4	yes	—
521	C₂²	#382434	1	2	yes	—
522	C₂²	#392125	1	2	yes	—
523	C₂²	#394064	1	4	yes	—
524	C₂²	#394066	1	2	yes	—
525	C₂²	#394068	1	2	yes	—
526	C₂²	#395418	1	4	yes	—
527	C₂	#72225622	1	1	yes	characteristic
528	C₂	#72225808	1	1	yes	characteristic
529	C₂	#72240548	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	#154094
commutator	C₂⁶	C₂³×C₄
Frattini, cosocle	C₂⁷	C₂⁴
prime radical	#72217511	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. #72259089	C₂	semidirect
2. #72259083	C₂	semidirect
3. #72236453	C₂	semidirect
4. #72236437	C₂	semidirect
5. C₂×#359428	C₂	semidirect
6. #72218766	C₂	semidirect
7. #72217789	C₂	semidirect
9. C₂×#115690	C₂	semidirect
12. #7642273	C₄	semidirect
13. #7642244	C₄	semidirect
16. #7630944	C₄	semidirect
17. #7630939	C₄	semidirect
19. C₂³×#379	C₂²	semidirect
21. C₂×#21746	C₂²	semidirect
22. C₂×#21746	C₂²	semidirect
23. C₂×#21746	C₂²	semidirect
24. C₂×#21746	C₂²	semidirect
26. C₂²×#1898	C₂²	semidirect
27. C₂²×#1898	C₂²	semidirect
28. C₂×#14679	C₂²	semidirect
29. C₂×#14679	C₂²	semidirect
30. #516383	C₂²	semidirect
31. C₂×#10735	C₂²	semidirect
32. C₂×#10725	C₂²	semidirect
33. C₂×#8101	C₂²	semidirect
34. C₂×#8101	C₂²	semidirect
73. C₂×#1898	D₄	semidirect
74. C₂×#1898	D₄	semidirect
75. C₂⁷	C₂²⋊C₄	semidirect
85. C₂²×H(5,𝔽₂)	C₂²⋊C₄	semidirect
86. C₂⁴×D₄	C₂²⋊C₄	semidirect
87. C₂⁴×D₄	C₂²⋊C₄	semidirect
88. C₂⁴×D₄	C₂²⋊C₄	semidirect
89. C₂⁴×D₄	C₂²⋊C₄	semidirect
90. C₂⁴×D₄	C₂²⋊C₄	semidirect
91. C₂⁴×D₄	C₂²⋊C₄	semidirect
101. C₂⁵×C₄	C₂²⋊C₄	semidirect
102. C₂⁵×C₄	C₂²⋊C₄	semidirect
103. C₂⁵×C₄	C₂²⋊C₄	semidirect
104. C₂×#543	C₂²⋊C₄	semidirect
105. C₂×#534	C₂²⋊C₄	semidirect
106. C₂×#534	C₂²⋊C₄	semidirect
107. C₂²×#120	C₂²⋊C₄	semidirect
108. C₂²×#120	C₂²⋊C₄	semidirect
121. C₂×#518	C₂²⋊C₄	semidirect
122. C₂×#518	C₂²⋊C₄	semidirect
123. C₂³×C₂²⋊C₄	C₂²⋊C₄	semidirect
124. C₂³×C₂²⋊C₄	C₂²⋊C₄	semidirect
125. C₂³×C₂²⋊C₄	C₂²⋊C₄	semidirect
126. C₂³×C₂²⋊C₄	C₂²⋊C₄	semidirect
127. C₂³×C₂²⋊C₄	C₂²⋊C₄	semidirect
128. C₂³×C₂²⋊C₄	C₂²⋊C₄	semidirect
139. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
140. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
141. #2483	C₂²⋊C₄	semidirect
142. #2405	C₂²⋊C₄	semidirect
143. #2405	C₂²⋊C₄	semidirect
144. #2403	C₂²⋊C₄	semidirect
145. #2312	C₂²⋊C₄	semidirect
146. #2312	C₂²⋊C₄	semidirect
147. #2309	C₂²⋊C₄	semidirect
148. #2308	C₂²⋊C₄	semidirect
149. C₂×#379	C₂²⋊C₄	semidirect
150. C₂×#379	C₂²⋊C₄	semidirect
157. C₂×#379	C₂×D₄	semidirect
158. C₂×#379	C₂×D₄	semidirect

Maximal subgroups

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

subgroup	index
#72259089	2
#72259083	2
#72236453	2
#72236437	2
C₂×#359428	2
#72218766	2
#72217789	2
#72217511	2
C₂×#115690	2