Subgroups — #72262689

Order 2048.

At least 8460 conjugacy classes of subgroups; only the 1240 normal subgroups are shown.

The subgroup lattice has 530 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72262592	C₂	1	2	yes	maximal, complemented
2	#72262566	C₂	1	4	yes	maximal, complemented
3	#72262465	C₂	1	8	yes	maximal, complemented
4	#72256581	C₂	1	1	yes	maximal, characteristic
5	#72235794	C₂	1	2	yes	maximal, complemented
6	#72235727	C₂	1	4	yes	maximal, complemented
7	C₂×#188087	C₂	1	1	yes	maximal, characteristic, complemented
8	#72232735	C₂	1	4	yes	maximal, complemented
9	#72232723	C₂	1	4	yes	maximal, complemented
10	C₂×#188035	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂³×D₄²	C₂²	1	1	yes	characteristic
12	C₂³×#535	C₄	1	1	yes	characteristic, complemented
13	C₂×#35250	C₂²	1	1	yes	characteristic
14	C₂×#34736	C₄	1	1	yes	characteristic, complemented
15	C₂×#21746	C₂²	1	2	yes	complemented
16	C₂×#17396	C₂²	1	2	yes	complemented
17	#686207	C₄	1	4	yes	complemented
18	#686207	C₂²	1	4	yes	—
19	#649042	C₄	1	2	yes	complemented
20	#649042	C₂²	1	2	yes	—
21	#649038	C₄	1	2	yes	complemented
22	#649038	C₂²	1	2	yes	—
23	#617709	C₄	1	2	yes	complemented
24	#617709	C₂²	1	2	yes	—
25	#616961	C₄	1	2	yes	complemented
26	#616961	C₂²	1	2	yes	—
27	#517415	C₄	1	1	yes	characteristic, complemented
28	#516385	C₂²	1	1	yes	characteristic
29	#514052	C₄	1	1	yes	characteristic, complemented
30	#482549	C₂²	1	8	yes	complemented
31	#188087	C₂²	1	4	yes	—
32	#188087	C₂²	1	4	yes	complemented
33	C₂×#8549	C₂²	1	2	yes	—
34	C₂×#8547	C₂²	1	2	yes	complemented
35	#188035	C₂²	1	4	yes	—
36	#188035	C₂²	1	4	yes	complemented
37	C₂×#8542	C₂²	1	2	yes	—
38	C₂×#8542	C₂²	1	2	yes	complemented
39	#139504	C₂²	1	16	yes	complemented
40	#139486	C₂²	1	16	yes	complemented
41	#139472	C₂²	1	16	yes	complemented
42	#139434	C₂²	1	16	yes	complemented
43	#135485	C₂²	1	8	yes	complemented
44	#135479	C₂²	1	8	yes	complemented
45	#133222	C₂²	1	4	yes	complemented
46	#133121	C₂²	1	8	yes	complemented
47	#133093	C₂²	1	4	yes	complemented
48	#127215	C₂²	1	8	yes	complemented
49	C₂⁴×#41	C₂×C₄	1	1	yes	characteristic, complemented
50	C₂⁵×D₄	C₂×C₄	1	1	yes	characteristic
51	C₂⁵×D₄	D₄	1	1	yes	characteristic
52	C₂⁵×D₄	D₄	1	1	yes	characteristic
53	C₂⁵×D₄	D₄	1	1	yes	characteristic
54	C₂²×D₄²	C₂×C₄	1	2	yes	—
55	C₂²×D₄²	C₂×C₄	1	2	yes	—
56	C₂²×D₄²	D₄	1	2	yes	—
57	C₂²×D₄²	D₄	1	2	yes	—
58	C₂²×D₄²	D₄	1	2	yes	—
59	C₂²×D₄²	D₄	1	2	yes	—
60	C₂²×D₄²	C₂³	1	2	yes	—
61	C₂²×D₄²	C₂³	1	2	yes	—
62	C₂²×#535	C₂×C₄	1	2	yes	—
63	C₂²×#535	C₂×C₄	1	2	yes	complemented
64	C₂²×#535	C₂×C₄	1	4	yes	complemented
65	C₂³×#127	C₂×C₄	1	2	yes	complemented
66	C₂³×#127	D₄	1	1	yes	characteristic
67	C₂³×#124	C₂×C₄	1	2	yes	complemented
68	C₂³×#121	C₂×C₄	1	1	yes	characteristic
69	C₂³×#121	D₄	1	1	yes	characteristic
70	C₂³×#121	C₂³	1	1	yes	characteristic
71	C₂³×#121	C₂³	1	1	yes	characteristic
72	C₂³×#120	C₂×C₄	1	1	yes	characteristic
73	C₂³×#120	D₄	1	1	yes	characteristic
74	C₂³×#120	D₄	1	1	yes	characteristic
75	C₂³×#120	C₂³	1	1	yes	characteristic
76	C₂³×C₄×D₄	C₂×C₄	1	1	yes	characteristic
77	C₂³×C₄×D₄	D₄	1	1	yes	characteristic
78	C₂³×#117	C₂×C₄	1	1	yes	characteristic, complemented
79	C₂×#2406	C₂×C₄	1	2	yes	complemented
80	C₂×#2404	C₂×C₄	1	2	yes	—
81	C₂×#2404	C₂×C₄	1	2	yes	complemented
82	C₂×#2404	C₂³	1	2	yes	—
83	C₂×#2436	C₂×C₄	1	1	yes	characteristic, complemented
84	C₂×#2436	C₂³	1	1	yes	characteristic
85	C₂×#2409	C₂×C₄	1	2	yes	complemented
86	C₂×#2433	C₂×C₄	1	1	yes	characteristic, complemented
87	C₂×#2433	C₂³	1	1	yes	characteristic
88	C₂×#2408	C₂×C₄	1	2	yes	complemented
89	C₂×#2615	C₂×C₄	1	2	yes	complemented
90	C₂×#2615	C₂³	1	2	yes	—
91	C₂×#2388	C₂×C₄	1	4	yes	complemented
92	C₂×#2280	C₂×C₄	1	1	yes	characteristic, complemented
93	C₂×#2280	C₂×C₄	1	1	yes	characteristic, complemented
94	#21746	C₂³	1	8	yes	—
95	C₂×#1819	C₂³	1	4	yes	—
96	#17396	C₂³	1	8	yes	—
97	C₂×#1462	C₂³	1	4	yes	—
98	#15673	C₂×C₄	1	4	yes	complemented
99	#15673	C₂×C₄	1	4	yes	complemented
100	#15673	C₂×C₄	1	4	yes	complemented
101	#15673	C₂³	1	4	yes	—
102	#15310	C₂×C₄	1	4	yes	complemented
103	#15310	C₂×C₄	1	4	yes	complemented
104	#15310	C₂×C₄	1	4	yes	complemented
105	#15310	C₂³	1	4	yes	—
106	#15259	C₂×C₄	1	4	yes	—
107	#15259	C₂×C₄	1	4	yes	complemented
108	#15259	C₂×C₄	1	4	yes	complemented
109	#15259	C₂³	1	4	yes	—
110	#15258	C₂×C₄	1	4	yes	—
111	#15258	C₂×C₄	1	4	yes	complemented
112	#15258	C₂×C₄	1	4	yes	complemented
113	#15258	C₂³	1	4	yes	—
114	#14698	C₂×C₄	1	2	yes	complemented
115	#14698	C₂³	1	2	yes	—
116	#14335	C₂×C₄	1	2	yes	—
117	#14335	C₂×C₄	1	2	yes	complemented
118	#14136	C₂×C₄	1	2	yes	complemented
119	#14136	C₂³	1	2	yes	—
120	#13902	C₂×C₄	1	2	yes	complemented
121	#13902	C₂×C₄	1	2	yes	complemented
122	#13902	C₂×C₄	1	4	yes	complemented
123	#13871	C₂×C₄	1	4	yes	complemented
124	#13870	C₂×C₄	1	2	yes	complemented
125	#13868	C₂×C₄	1	2	yes	—
126	#13868	C₂×C₄	1	2	yes	complemented
127	#13868	C₂³	1	2	yes	—
128	C₄×#386	C₂×C₄	1	2	yes	complemented
129	C₄×#386	C₂×C₄	1	2	yes	complemented
130	#11808	C₂³	1	16	yes	complemented
131	#11796	C₂³	1	16	yes	complemented
132	#8549	C₂³	1	4	yes	—
133	#8549	C₂³	1	4	yes	—
134	#8547	C₂³	1	8	yes	—
135	#8542	C₂³	1	4	yes	—
136	#8542	C₂³	1	4	yes	—
137	#8542	C₂³	1	8	yes	—
138	#7213	C₂³	1	32	yes	complemented
139	C₂⁷	C₂²⋊C₄	1	1	yes	characteristic
140	C₂⁷	C₂²⋊C₄	1	1	yes	characteristic
141	C₂⁷	C₂²⋊C₄	1	1	yes	characteristic
142	C₂⁷	C₂×D₄	1	1	yes	characteristic
143	C₂³×#41	C₂²×C₄	1	2	yes	—
144	C₂³×#41	C₂²×C₄	1	2	yes	complemented
145	C₂⁴×Q₈	C₂²×C₄	1	1	yes	characteristic, complemented
146	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
147	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
148	C₂⁴×D₄	C₂²⋊C₄	1	2	yes	—
149	C₂⁴×D₄	C₂²⋊C₄	1	2	yes	—
150	C₂⁴×D₄	C₂²⋊C₄	1	2	yes	—
151	C₂⁴×D₄	C₂²⋊C₄	1	2	yes	—
152	C₂⁴×D₄	C₂²⋊C₄	1	2	yes	—
153	C₂⁴×D₄	C₂²⋊C₄	1	2	yes	—
154	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
155	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
156	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
157	C₂⁴×D₄	C₂²⋊C₄	1	2	yes	—
158	C₂⁴×D₄	C₂²⋊C₄	1	2	yes	—
159	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
160	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
161	C₂⁴×D₄	C₂²×C₄	1	1	yes	characteristic
162	C₂⁴×D₄	C₂²×C₄	1	1	yes	characteristic
163	C₂⁴×D₄	C₂²×C₄	1	2	yes	—
164	C₂⁴×D₄	C₂²×C₄	1	2	yes	—
165	C₂⁴×D₄	C₂²×C₄	1	1	yes	characteristic, complemented
166	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
167	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
168	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
169	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
170	C₂⁴×D₄	C₂×D₄	1	2	yes	—
171	C₂⁴×D₄	C₂×D₄	1	2	yes	—
172	C₂⁴×D₄	C₂×D₄	1	2	yes	—
173	C₂⁴×D₄	C₂×D₄	1	2	yes	—
174	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
175	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
176	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
177	C₂⁴×D₄	C₂×D₄	1	2	yes	—
178	C₂⁴×D₄	C₂×D₄	1	2	yes	—
179	C₂⁵×C₄	C₂²⋊C₄	1	1	yes	characteristic
180	C₂⁵×C₄	C₂²⋊C₄	1	1	yes	characteristic
181	C₂⁵×C₄	C₂²×C₄	1	1	yes	characteristic
182	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
183	C₂²×#127	C₂²⋊C₄	1	2	yes	—
184	C₂²×#127	C₂²⋊C₄	1	2	yes	—
185	C₂²×#127	C₂²×C₄	1	4	yes	—
186	C₂²×#127	C₂²×C₄	1	4	yes	complemented
187	C₂²×#127	C₂×D₄	1	2	yes	—
188	C₂²×#127	C₂×D₄	1	2	yes	—
189	C₂²×#124	C₂²×C₄	1	4	yes	—
190	C₂²×#124	C₂²×C₄	1	4	yes	complemented
191	C₂²×#121	C₂²⋊C₄	1	2	yes	—
192	C₂²×#121	C₂²⋊C₄	1	2	yes	—
193	C₂²×#121	C₂²⋊C₄	1	2	yes	—
194	C₂²×#121	C₂²⋊C₄	1	2	yes	—
195	C₂²×#121	C₂²×C₄	1	2	yes	—
196	C₂²×#121	C₂²×C₄	1	2	yes	—
197	C₂²×#121	C₂²×C₄	1	2	yes	—
198	C₂²×#121	C₂²×C₄	1	1	yes	characteristic
199	C₂²×#121	C₂²×C₄	1	1	yes	characteristic
200	C₂²×#121	C₂×D₄	1	1	yes	characteristic
201	C₂²×#121	C₂×D₄	1	1	yes	characteristic
202	C₂²×#121	C₂×D₄	1	2	yes	—
203	C₂²×#121	C₂×D₄	1	1	yes	characteristic
204	C₂²×#121	C₂×D₄	1	1	yes	characteristic
205	C₂²×#121	C₂×D₄	1	2	yes	—
206	C₂²×#121	C₂×D₄	1	2	yes	—
207	C₂²×#121	C₂×D₄	1	2	yes	—
208	C₂²×#121	C₂⁴	1	1	yes	characteristic
209	C₂²×#121	C₂⁴	1	1	yes	characteristic
210	C₂²×#121	C₂⁴	1	2	yes	—
211	C₂²×#120	C₂²⋊C₄	1	2	yes	—
212	C₂²×#120	C₂²⋊C₄	1	2	yes	—
213	C₂²×#120	C₂²⋊C₄	1	2	yes	—
214	C₂²×#120	C₂²⋊C₄	1	2	yes	—
215	C₂²×#120	C₂²⋊C₄	1	2	yes	—
216	C₂²×#120	C₂²⋊C₄	1	2	yes	—
217	C₂²×#120	C₂²×C₄	1	2	yes	—
218	C₂²×#120	C₂²×C₄	1	2	yes	—
219	C₂²×#120	C₂²×C₄	1	2	yes	—
220	C₂²×#120	C₂×D₄	1	2	yes	—
221	C₂²×#120	C₂×D₄	1	2	yes	—
222	C₂²×#120	C₂×D₄	1	2	yes	—
223	C₂²×#120	C₂×D₄	1	2	yes	—
224	C₂²×#120	C₂×D₄	1	2	yes	—
225	C₂²×#120	C₂×D₄	1	2	yes	—
226	C₂²×#120	C₂⁴	1	2	yes	—
227	C₂²×C₄×D₄	C₂²⋊C₄	1	2	yes	—
228	C₂²×C₄×D₄	C₂²⋊C₄	1	2	yes	—
229	C₂²×C₄×D₄	C₂²⋊C₄	1	2	yes	—
230	C₂²×C₄×D₄	C₂²⋊C₄	1	2	yes	—
231	C₂²×C₄×D₄	C₂²×C₄	1	2	yes	—
232	C₂²×C₄×D₄	C₂²×C₄	1	2	yes	—
233	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
234	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
235	C₂²×#117	C₂²×C₄	1	2	yes	—
236	C₂²×#117	C₂²×C₄	1	2	yes	complemented
237	C₂³×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
238	C₂³×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
239	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
240	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
241	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
242	C₂³×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
243	C₂³×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
244	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
245	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
246	C₂³×C₂²⋊C₄	C₂⁴	1	1	yes	characteristic
247	C₂³×C₄²	C₂²⋊C₄	1	1	yes	characteristic
248	C₂³×C₄²	C₂²×C₄	1	2	yes	complemented
249	C₂×#395	C₂²×C₄	1	4	yes	complemented
250	C₂×#394	C₂²×C₄	1	4	yes	complemented
251	C₂×#393	C₂²×C₄	1	2	yes	—
252	C₂×#393	C₂²×C₄	1	4	yes	—
253	C₂×#393	C₂²×C₄	1	2	yes	complemented
254	C₂×#393	C₂²×C₄	1	2	yes	complemented
255	C₂×#393	C₂⁴	1	2	yes	—
256	C₂×#392	C₂²×C₄	1	2	yes	—
257	C₂×#392	C₂²×C₄	1	4	yes	—
258	C₂×#392	C₂²×C₄	1	2	yes	complemented
259	C₂×#392	C₂²×C₄	1	2	yes	complemented
260	C₂×#392	C₂⁴	1	2	yes	—
261	C₂×#381	C₂²×C₄	1	2	yes	—
262	C₂×#381	C₂²×C₄	1	2	yes	—
263	C₂×#380	C₂²×C₄	1	2	yes	complemented
264	C₂×#380	C₂²×C₄	1	2	yes	complemented
265	C₂×C₄×C₂²⋊C₄	C₂²×C₄	1	2	yes	complemented
266	C₂×C₄×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic, complemented
267	C₂×C₄×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic, complemented
268	#1819	C₂⁴	1	8	yes	—
269	#1462	C₂⁴	1	8	yes	—
270	#1438	C₂²×C₄	1	4	yes	—
271	#1438	C₂²×C₄	1	4	yes	—
272	#1438	C₂²×C₄	1	4	yes	complemented
273	#1438	C₂²×C₄	1	4	yes	complemented
274	#1437	C₂²×C₄	1	4	yes	—
275	#1437	C₂²×C₄	1	4	yes	—
276	#1437	C₂²×C₄	1	4	yes	—
277	#1437	C₂²×C₄	1	4	yes	complemented
278	#1437	C₂²×C₄	1	4	yes	complemented
279	#1437	C₂⁴	1	4	yes	—
280	#1436	C₂²×C₄	1	4	yes	complemented
281	#1436	C₂²×C₄	1	4	yes	complemented
282	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
283	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
284	C₂⁶	C₂×C₂²⋊C₄	1	2	yes	—
285	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
286	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
287	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
288	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
289	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
290	C₂⁶	C₂×C₂²⋊C₄	1	2	yes	—
291	C₂⁶	C₂×C₂²⋊C₄	1	2	yes	—
292	C₂⁶	C₂×C₂²⋊C₄	1	2	yes	—
293	C₂⁶	C₂×C₂²⋊C₄	1	2	yes	—
294	C₂⁶	C₂×C₂²⋊C₄	1	2	yes	—
295	C₂⁶	C₂×C₂²⋊C₄	1	2	yes	—
296	C₂⁶	C₂²×D₄	1	2	yes	—
297	C₂⁶	C₂²×D₄	1	1	yes	characteristic
298	C₂³×Q₈	C₂³×C₄	1	2	yes	—
299	C₂³×D₄	#99	1	1	yes	characteristic
300	C₂³×D₄	#99	1	1	yes	characteristic
301	C₂³×D₄	#99	1	2	yes	—
302	C₂³×D₄	#99	1	2	yes	—
303	C₂³×D₄	#99	1	2	yes	—
304	C₂³×D₄	#99	1	2	yes	—
305	C₂³×D₄	#99	1	1	yes	characteristic
306	C₂³×D₄	#99	1	2	yes	—
307	C₂³×D₄	#99	1	2	yes	—
308	C₂³×D₄	#99	1	1	yes	characteristic
309	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
310	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
311	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
312	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
313	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
314	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
315	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
316	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
317	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
318	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
319	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
320	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
321	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
322	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
323	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
324	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
325	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
326	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
327	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
328	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
329	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
330	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
331	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
332	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
333	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
334	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
335	C₂³×D₄	C₂³×C₄	1	2	yes	—
336	C₂³×D₄	C₂³×C₄	1	2	yes	—
337	C₂³×D₄	C₂³×C₄	1	2	yes	—
338	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
339	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
340	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
341	C₂³×D₄	C₂²×D₄	1	2	yes	—
342	C₂³×D₄	C₂²×D₄	1	2	yes	—
343	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
344	C₂³×D₄	C₂²×D₄	1	2	yes	—
345	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
346	C₂³×D₄	C₂²×D₄	1	2	yes	—
347	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
348	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
349	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
350	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
351	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
352	C₂⁴×C₄	C₂×C₂²⋊C₄	1	2	yes	—
353	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
354	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
355	C₂⁴×C₄	C₂×C₂²⋊C₄	1	2	yes	—
356	C₂⁴×C₄	C₂×C₂²⋊C₄	1	2	yes	—
357	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
358	C₂⁴×C₄	C₂×C₂²⋊C₄	1	2	yes	—
359	C₂⁴×C₄	C₂×C₂²⋊C₄	1	2	yes	—
360	C₂⁴×C₄	C₂³×C₄	1	1	yes	characteristic
361	C₂⁴×C₄	C₂³×C₄	1	1	yes	characteristic
362	C₂⁴×C₄	C₂³×C₄	1	1	yes	characteristic
363	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
364	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
365	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
366	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
367	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
368	C₂²×C₄⋊C₄	C₂³×C₄	1	2	yes	—
369	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
370	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
371	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
372	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
373	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
374	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
375	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
376	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
377	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
378	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
379	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
380	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
381	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
382	C₂²×C₂²⋊C₄	C₂³×C₄	1	2	yes	—
383	C₂²×C₂²⋊C₄	C₂³×C₄	1	1	yes	characteristic
384	C₂²×C₂²⋊C₄	C₂³×C₄	1	1	yes	characteristic
385	C₂²×C₂²⋊C₄	C₂³×C₄	1	1	yes	characteristic
386	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
387	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
388	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
389	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
390	C₂²×C₂²⋊C₄	H(5,𝔽₂)	1	4	yes	—
391	C₂²×C₂²⋊C₄	H(5,𝔽₂)	1	4	yes	—
392	C₂²×C₂²⋊C₄	C₂⁵	1	1	yes	characteristic
393	C₂²×C₄²	C₂×C₂²⋊C₄	1	2	yes	—
394	C₂²×C₄²	C₂×C₂²⋊C₄	1	2	yes	—
395	C₂²×C₄²	C₂³×C₄	1	4	yes	—
396	C₂×#95	C₂³×C₄	1	2	yes	—
397	C₂×#95	C₂³×C₄	1	2	yes	—
398	C₂×#95	C₂³×C₄	1	4	yes	—
399	C₂⁵	C₂×#99	1	1	yes	characteristic
400	C₂⁵	C₂×#99	1	1	yes	characteristic
401	C₂⁵	C₂×#99	1	1	yes	characteristic
402	C₂⁵	C₂×#99	1	2	yes	—
403	C₂⁵	C₂×#99	1	2	yes	—
404	C₂⁵	C₂×#99	1	2	yes	—
405	C₂⁵	C₂×#99	1	2	yes	—
406	C₂⁵	C₂×#99	1	2	yes	—
407	C₂⁵	C₂×#99	1	1	yes	characteristic
408	C₂⁵	C₂×#99	1	1	yes	characteristic
409	C₂⁵	C₂×#99	1	1	yes	characteristic
410	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
411	C₂⁵	C₂²×C₂²⋊C₄	1	2	yes	—
412	C₂⁵	C₂²×C₂²⋊C₄	1	2	yes	—
413	C₂⁵	C₂²×C₂²⋊C₄	1	2	yes	—
414	C₂⁵	C₂²×C₂²⋊C₄	1	2	yes	—
415	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
416	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
417	C₂⁵	C₂²×C₂²⋊C₄	1	2	yes	—
418	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
419	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
420	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
421	C₂⁵	#534	1	2	yes	—
422	C₂⁵	#534	1	2	yes	—
423	C₂⁵	C₂³×D₄	1	1	yes	characteristic
424	C₂²×D₄	AΣL(1,𝔽₁₆)	1	8	yes	—
425	C₂²×D₄	C₂×#99	1	2	yes	—
426	C₂²×D₄	C₂×#99	1	2	yes	—
427	C₂²×D₄	C₂×#99	1	2	yes	—
428	C₂²×D₄	C₂×#99	1	2	yes	—
429	C₂²×D₄	C₂×#99	1	2	yes	—
430	C₂²×D₄	C₂×#99	1	2	yes	—
431	C₂²×D₄	C₂×#99	1	2	yes	—
432	C₂²×D₄	C₂×#99	1	2	yes	—
433	C₂²×D₄	C₂×#99	1	2	yes	—
434	C₂²×D₄	C₂×#99	1	2	yes	—
435	C₂²×D₄	C₂×#99	1	2	yes	—
436	C₂²×D₄	C₂×#99	1	2	yes	—
437	C₂²×D₄	C₂×#99	1	2	yes	—
438	C₂²×D₄	C₂×#99	1	2	yes	—
439	C₂²×D₄	C₂×#99	1	2	yes	—
440	C₂²×D₄	C₂×#99	1	2	yes	—
441	C₂³×C₄	C₂×#99	1	1	yes	characteristic
442	C₂³×C₄	C₂×#99	1	1	yes	characteristic
443	C₂³×C₄	C₂×#99	1	1	yes	characteristic
444	C₂³×C₄	C₂×#99	1	2	yes	—
445	C₂³×C₄	C₂×#99	1	1	yes	characteristic
446	C₂³×C₄	C₂×#99	1	1	yes	characteristic
447	C₂³×C₄	C₂×#99	1	1	yes	characteristic
448	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
449	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
450	C₂³×C₄	C₂²×C₂²⋊C₄	1	2	yes	—
451	C₂³×C₄	C₂²×C₂²⋊C₄	1	2	yes	—
452	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
453	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
454	C₂³×C₄	C₂²×C₂²⋊C₄	1	2	yes	—
455	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
456	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
457	C₂³×C₄	#518	1	2	yes	—
458	C₂³×C₄	#518	1	2	yes	—
459	C₂³×C₄	#534	1	2	yes	—
460	C₂³×C₄	#534	1	2	yes	—
461	C₂³×C₄	C₂⁴×C₄	1	1	yes	characteristic
462	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
463	C₂×C₂²⋊C₄	#518	1	4	yes	—
464	C₂×C₂²⋊C₄	#534	1	4	yes	—
465	C₂×C₂²⋊C₄	#534	1	4	yes	—
466	C₂×C₂²⋊C₄	C₂×H(5,𝔽₂)	1	4	yes	—
467	C₂⁴	C₂×AΣL(1,𝔽₁₆)	1	4	yes	—
468	C₂⁴	C₂×AΣL(1,𝔽₁₆)	1	4	yes	—
469	C₂⁴	#2308	1	1	yes	characteristic
470	C₂⁴	#2308	1	1	yes	characteristic
471	C₂⁴	#2308	1	2	yes	—
472	C₂⁴	C₂²×#99	1	1	yes	characteristic
473	C₂⁴	C₂²×#99	1	1	yes	characteristic
474	C₂⁴	C₂²×#99	1	2	yes	—
475	C₂⁴	C₂²×#99	1	2	yes	—
476	C₂⁴	C₂²×#99	1	2	yes	—
477	C₂⁴	C₂²×#99	1	2	yes	—
478	C₂⁴	C₂²×#99	1	2	yes	—
479	C₂⁴	C₂²×#99	1	2	yes	—
480	C₂⁴	C₂²×#99	1	2	yes	—
481	C₂⁴	C₂²×#99	1	2	yes	—
482	C₂⁴	C₂²×#99	1	1	yes	characteristic
483	C₂⁴	C₂²×#99	1	1	yes	characteristic
484	C₂⁴	C₂³×C₂²⋊C₄	1	1	yes	characteristic
485	C₂⁴	C₂×#534	1	2	yes	—
486	C₂×D₄	C₂×AΣL(1,𝔽₁₆)	1	8	yes	—
487	C₂×D₄	C₂×AΣL(1,𝔽₁₆)	1	8	yes	—
488	C₂×D₄	#2127	1	8	yes	—
489	C₂²×C₄	C₂×AΣL(1,𝔽₁₆)	1	4	yes	—
490	C₂²×C₄	#2121	1	4	yes	—
491	C₂²×C₄	#2308	1	2	yes	—
492	C₂²×C₄	#2308	1	2	yes	—
493	C₂²×C₄	C₂²×#99	1	2	yes	—
494	C₂²×C₄	C₂²×#99	1	1	yes	characteristic
495	C₂²×C₄	C₂²×#99	1	1	yes	characteristic
496	C₂²×C₄	C₂²×#99	1	1	yes	characteristic
497	C₂²×C₄	C₂²×#99	1	1	yes	characteristic
498	C₂²×C₄	C₂²×#99	1	2	yes	—
499	C₂²×C₄	C₂×#518	1	2	yes	—
500	C₂²×C₄	C₂×#534	1	2	yes	—
501	C₂³	#21746	1	1	yes	characteristic
502	C₂³	#21746	1	1	yes	characteristic
503	C₂³	#21746	1	1	yes	characteristic
504	C₂³	#21746	1	1	yes	characteristic
505	C₂³	C₂²×AΣL(1,𝔽₁₆)	1	4	yes	—
506	C₂³	C₂²×AΣL(1,𝔽₁₆)	1	4	yes	—
507	C₂³	C₂²×AΣL(1,𝔽₁₆)	1	2	yes	—
508	C₂³	C₂×#2121	1	2	yes	—
509	C₂³	C₂×#2127	1	4	yes	—
510	C₂³	C₂×#2127	1	4	yes	—
511	C₂³	C₂×#2308	1	1	yes	characteristic
512	C₂³	C₂³×#99	1	1	yes	characteristic
513	C₂³	C₂³×#99	1	1	yes	characteristic
514	C₂×C₄	C₂²×AΣL(1,𝔽₁₆)	1	2	yes	—
515	C₂×C₄	C₂²×AΣL(1,𝔽₁₆)	1	2	yes	—
516	C₂×C₄	C₂×#2121	1	2	yes	—
517	C₂×C₄	C₂×#2121	1	2	yes	—
518	C₂×C₄	C₂×#2127	1	4	yes	—
519	C₂²	#496225	1	2	yes	—
520	C₂²	#496225	1	2	yes	—
521	C₂²	C₂×#21746	1	1	yes	characteristic
522	C₂²	#6374206	1	2	yes	—
523	C₂²	C₂³×AΣL(1,𝔽₁₆)	1	1	yes	characteristic
524	C₂²	C₂²×#2121	1	1	yes	characteristic
525	C₂²	C₂²×#2127	1	2	yes	—
526	C₂	C₂×#496225	1	1	yes	characteristic
527	C₂	#72236704	1	1	yes	characteristic
528	C₂	#72256081	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂×#21746
commutator	C₂³×C₄	C₂⁴×C₄
Frattini, cosocle	C₂²×C₂²⋊C₄	C₂⁵
prime radical	#72256581	C₂
LCS	G ▷ C₂³×C₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂⁵ ◁ C₂³×D₄² ◁ G
LECS	G ▷ C₂²×C₂²⋊C₄ ▷ C₂³ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72262592	C₂	semidirect
2. #72262566	C₂	semidirect
3. #72262465	C₂	semidirect
5. #72235794	C₂	semidirect
6. #72235727	C₂	semidirect
7. C₂×#188087	C₂	semidirect
8. #72232735	C₂	semidirect
9. #72232723	C₂	semidirect
10. C₂×#188035	C₂	semidirect
12. C₂³×#535	C₄	semidirect
14. C₂×#34736	C₄	semidirect
15. C₂×#21746	C₂²	semidirect
16. C₂×#17396	C₂²	semidirect
17. #686207	C₄	semidirect
19. #649042	C₄	semidirect
21. #649038	C₄	semidirect
23. #617709	C₄	semidirect
25. #616961	C₄	semidirect
27. #517415	C₄	semidirect
29. #514052	C₄	semidirect
30. #482549	C₂²	semidirect
32. #188087	C₂²	semidirect
34. C₂×#8547	C₂²	semidirect
36. #188035	C₂²	semidirect
38. C₂×#8542	C₂²	semidirect
39. #139504	C₂²	semidirect
40. #139486	C₂²	semidirect
41. #139472	C₂²	semidirect
42. #139434	C₂²	semidirect
43. #135485	C₂²	semidirect
44. #135479	C₂²	semidirect
45. #133222	C₂²	semidirect
46. #133121	C₂²	semidirect
47. #133093	C₂²	semidirect
48. #127215	C₂²	semidirect
49. C₂⁴×#41	C₂×C₄	semidirect
63. C₂²×#535	C₂×C₄	semidirect
64. C₂²×#535	C₂×C₄	semidirect
65. C₂³×#127	C₂×C₄	semidirect
67. C₂³×#124	C₂×C₄	semidirect
78. C₂³×#117	C₂×C₄	semidirect
79. C₂×#2406	C₂×C₄	semidirect
81. C₂×#2404	C₂×C₄	semidirect
83. C₂×#2436	C₂×C₄	semidirect
85. C₂×#2409	C₂×C₄	semidirect
86. C₂×#2433	C₂×C₄	semidirect
88. C₂×#2408	C₂×C₄	semidirect
89. C₂×#2615	C₂×C₄	semidirect
91. C₂×#2388	C₂×C₄	semidirect
92. C₂×#2280	C₂×C₄	semidirect
93. C₂×#2280	C₂×C₄	semidirect
98. #15673	C₂×C₄	semidirect
99. #15673	C₂×C₄	semidirect
100. #15673	C₂×C₄	semidirect
102. #15310	C₂×C₄	semidirect
103. #15310	C₂×C₄	semidirect
104. #15310	C₂×C₄	semidirect
107. #15259	C₂×C₄	semidirect
108. #15259	C₂×C₄	semidirect
111. #15258	C₂×C₄	semidirect
112. #15258	C₂×C₄	semidirect
114. #14698	C₂×C₄	semidirect
117. #14335	C₂×C₄	semidirect
118. #14136	C₂×C₄	semidirect
120. #13902	C₂×C₄	semidirect
121. #13902	C₂×C₄	semidirect
122. #13902	C₂×C₄	semidirect
123. #13871	C₂×C₄	semidirect
124. #13870	C₂×C₄	semidirect
126. #13868	C₂×C₄	semidirect
128. C₄×#386	C₂×C₄	semidirect
129. C₄×#386	C₂×C₄	semidirect
130. #11808	C₂³	semidirect
131. #11796	C₂³	semidirect
138. #7213	C₂³	semidirect
144. C₂³×#41	C₂²×C₄	semidirect
145. C₂⁴×Q₈	C₂²×C₄	semidirect
165. C₂⁴×D₄	C₂²×C₄	semidirect
186. C₂²×#127	C₂²×C₄	semidirect
190. C₂²×#124	C₂²×C₄	semidirect
236. C₂²×#117	C₂²×C₄	semidirect
248. C₂³×C₄²	C₂²×C₄	semidirect
249. C₂×#395	C₂²×C₄	semidirect
250. C₂×#394	C₂²×C₄	semidirect
253. C₂×#393	C₂²×C₄	semidirect
254. C₂×#393	C₂²×C₄	semidirect
258. C₂×#392	C₂²×C₄	semidirect
259. C₂×#392	C₂²×C₄	semidirect
263. C₂×#380	C₂²×C₄	semidirect
264. C₂×#380	C₂²×C₄	semidirect
265. C₂×C₄×C₂²⋊C₄	C₂²×C₄	semidirect
266. C₂×C₄×C₂²⋊C₄	C₂²×C₄	semidirect
267. C₂×C₄×C₂²⋊C₄	C₂²×C₄	semidirect
272. #1438	C₂²×C₄	semidirect
273. #1438	C₂²×C₄	semidirect
277. #1437	C₂²×C₄	semidirect
278. #1437	C₂²×C₄	semidirect
280. #1436	C₂²×C₄	semidirect
281. #1436	C₂²×C₄	semidirect

Maximal subgroups

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

subgroup	index
#72262592	2
#72262566	2
#72262465	2
#72256581	2
#72235794	2
#72235727	2
C₂×#188087	2
#72232735	2
#72232723	2
C₂×#188035	2