Subgroups — #72313673

Order 2048.

At least 7150 conjugacy classes of subgroups; only the 1356 normal subgroups are shown.

The subgroup lattice has 641 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72313663	C₂	1	2	yes	maximal, complemented
2	#72313655	C₂	1	2	yes	maximal, complemented
3	#72313650	C₂	1	1	yes	maximal, characteristic, complemented
4	#99×#102	C₂	1	1	yes	maximal, characteristic, complemented
5	#72313599	C₂	1	2	yes	maximal, complemented
6	#72313570	C₂	1	1	yes	maximal, characteristic, complemented
7	#72313490	C₂	1	1	yes	maximal, characteristic, complemented
8	#72313444	C₂	1	2	yes	maximal, complemented
9	#72313406	C₂	1	2	yes	maximal, complemented
10	C₂×#267371	C₂	1	1	yes	maximal, characteristic
11	#72313358	C₂	1	1	yes	maximal, characteristic, complemented
12	#72313258	C₂	1	1	yes	maximal, characteristic, complemented
13	#72313124	C₂	1	1	yes	maximal, characteristic, complemented
14	#72311781	C₂	1	1	yes	maximal, characteristic, complemented
15	D₄×#1867	C₂	1	1	yes	maximal, characteristic, complemented
16	#72281648	C₂	1	1	yes	maximal, characteristic, complemented
17	#72281619	C₂	1	1	yes	maximal, characteristic, complemented
18	#72264298	C₂	1	2	yes	maximal, complemented
19	#72264243	C₂	1	1	yes	maximal, characteristic, complemented
20	#72264018	C₂	1	1	yes	maximal, characteristic, complemented
21	#72264008	C₂	1	2	yes	maximal, complemented
22	#72264002	C₂	1	2	yes	maximal, complemented
23	#72263993	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#61559	C₂²	1	1	yes	characteristic
25	C₂³×#442	C₂²	1	1	yes	characteristic, complemented
26	D₄×#518	C₂²	1	1	yes	characteristic
27	#7625796	C₂²	1	1	yes	characteristic
28	C₂×#25771	C₂²	1	1	yes	characteristic
29	C₂×#24354	C₂²	1	2	yes	—
30	C₂×#23848	C₂²	1	1	yes	characteristic
31	#6396090	C₂²	1	2	yes	—
32	#6394561	C₂²	1	2	yes	—
33	#6393452	C₂²	1	1	yes	characteristic
34	#6392651	C₂²	1	1	yes	characteristic
35	#6387593	C₂²	1	2	yes	—
36	C₂×#22858	C₂²	1	2	yes	—
37	C₂×D₄×#102	C₂²	1	1	yes	characteristic
38	C₂×D₄×#99	C₂²	1	1	yes	characteristic
39	#6370404	C₂²	1	1	yes	characteristic
40	#519711	C₂²	1	2	yes	complemented
41	#519568	C₂²	1	1	yes	characteristic
42	D₄×#385	C₂²	1	2	yes	complemented
43	D₄×#386	C₂²	1	1	yes	characteristic
44	#393055	C₂²	1	1	yes	characteristic
45	#392900	C₂²	1	1	yes	characteristic
46	#392817	C₂²	1	1	yes	characteristic, complemented
47	#392817	C₂²	1	2	yes	complemented
48	#392632	C₂²	1	2	yes	—
49	#392632	C₂²	1	1	yes	characteristic, complemented
50	#392585	C₂²	1	1	yes	characteristic, complemented
51	#392585	C₂²	1	2	yes	complemented
52	#373842	C₂²	1	1	yes	characteristic
53	#370088	C₂²	1	2	yes	complemented
54	#369052	C₂²	1	2	yes	complemented
55	#368434	C₂²	1	1	yes	characteristic, complemented
56	#368330	C₂²	1	2	yes	complemented
57	#368330	C₂²	1	2	yes	complemented
58	#368058	C₂²	1	1	yes	characteristic
59	#368007	C₂²	1	2	yes	complemented
60	#366572	C₂²	1	2	yes	complemented
61	#366548	C₂²	1	1	yes	characteristic, complemented
62	#366287	C₂²	1	2	yes	complemented
63	#365543	C₂²	1	2	yes	complemented
64	#364394	C₂²	1	1	yes	characteristic
65	#361664	C₂²	1	1	yes	characteristic
66	#360745	C₂²	1	1	yes	characteristic
67	#359487	C₂²	1	2	yes	complemented
68	#359487	C₂²	1	1	yes	characteristic, complemented
69	#356958	C₂²	1	2	yes	complemented
70	D₄×#342	C₂²	1	2	yes	complemented
71	C₄⋊C₄×#99	C₂²	1	1	yes	characteristic
72	C₂²⋊C₄×#102	C₂²	1	2	yes	complemented
73	#356085	C₂²	1	1	yes	characteristic, complemented
74	#354462	C₂²	1	2	yes	complemented
75	C₄×#1867	C₂²	1	1	yes	characteristic
76	#354290	C₂²	1	1	yes	characteristic
77	#267371	C₄	1	16	yes	complemented
78	C₂×#10564	C₂²	1	2	yes	—
79	C₂×#9946	C₂²	1	2	yes	—
80	C₂×#9468	C₂²	1	1	yes	characteristic
81	C₂×#9259	C₂²	1	2	yes	—
82	C₂×#9259	C₂²	1	2	yes	—
83	#195202	C₂²	1	2	yes	complemented
84	#194755	C₂²	1	1	yes	characteristic
85	#192366	C₂²	1	2	yes	complemented
86	C₂×#8851	C₂²	1	1	yes	characteristic
87	#185958	C₂²	1	1	yes	characteristic
88	C₂×#8375	C₂²	1	1	yes	characteristic
89	C₂×#8350	C₂²	1	1	yes	characteristic
90	C₂×C₈×#99	C₂²	1	1	yes	characteristic
91	#121601	C₂²	1	2	yes	complemented
92	#121510	C₂²	1	2	yes	complemented
93	#120504	C₂²	1	2	yes	complemented
94	#119893	C₂²	1	2	yes	complemented
95	#117591	C₂²	1	2	yes	complemented
96	#116309	C₂²	1	2	yes	complemented
97	#116073	C₂²	1	2	yes	complemented
98	#114963	C₂²	1	2	yes	—
99	#113914	C₂²	1	2	yes	complemented
100	#111444	C₂²	1	2	yes	—
101	#111179	C₂²	1	2	yes	complemented
102	#111110	C₂²	1	2	yes	complemented
103	#110427	C₂²	1	2	yes	complemented
104	#110425	C₂²	1	2	yes	complemented
105	#110425	C₂²	1	2	yes	complemented
106	#109899	C₂²	1	2	yes	complemented
107	#109648	C₂²	1	2	yes	complemented
108	#109648	C₂²	1	2	yes	complemented
109	#109585	C₂²	1	2	yes	complemented
110	#109581	C₂²	1	2	yes	complemented
111	#108575	C₂²	1	2	yes	complemented
112	#108186	C₂²	1	1	yes	characteristic
113	#108082	C₂²	1	2	yes	complemented
114	#108082	C₂²	1	2	yes	complemented
115	#106962	C₂²	1	2	yes	complemented
116	#106722	C₂²	1	1	yes	characteristic
117	#106610	C₂²	1	1	yes	characteristic
118	#106318	C₂²	1	1	yes	characteristic
119	#106314	C₂²	1	1	yes	characteristic
120	#106162	C₂²	1	2	yes	complemented
121	#106108	C₂²	1	1	yes	characteristic
122	#105986	C₂²	1	2	yes	complemented
123	#105305	C₂²	1	2	yes	complemented
124	C₂⁴×D₈	C₂³	1	1	yes	characteristic
125	C₂×#3496	C₂³	1	1	yes	characteristic
126	C₂²×D₄²	C₂³	1	1	yes	characteristic
127	C₂³×C₄×D₄	C₂³	1	1	yes	characteristic
128	C₂³×C₄×D₄	C₂³	1	1	yes	characteristic
129	#61559	C₂×C₄	1	8	yes	complemented
130	C₂×#3186	C₂³	1	2	yes	—
131	C₂²×#447	C₂³	1	1	yes	characteristic
132	C₂²×#447	C₂³	1	2	yes	—
133	C₂×#2972	C₂³	1	1	yes	characteristic
134	C₂²×#442	D₄	1	2	yes	complemented
135	C₂²×C₈×D₄	C₂³	1	1	yes	characteristic
136	C₂³×#106	C₂³	1	1	yes	characteristic
137	C₂³×#102	D₄	1	1	yes	characteristic, complemented
138	C₂³×#102	C₂³	1	1	yes	characteristic
139	C₂³×#102	C₂³	1	1	yes	characteristic
140	C₂³×#97	C₂³	1	1	yes	characteristic
141	C₂×#2433	C₂³	1	2	yes	—
142	C₂×#2408	C₂³	1	1	yes	characteristic
143	#34205	C₂³	1	2	yes	—
144	#34205	C₂³	1	2	yes	—
145	#34181	C₂³	1	1	yes	characteristic
146	C₂×#2361	C₂³	1	2	yes	—
147	C₂×D₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
148	C₂×D₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
149	C₂×D₄×C₂²⋊C₄	C₂³	1	2	yes	—
150	C₂×D₄×C₂²⋊C₄	C₂³	1	2	yes	—
151	C₄×#518	C₂³	1	1	yes	characteristic
152	#25771	C₂×C₄	1	8	yes	complemented
153	#24354	C₂×C₄	1	16	yes	complemented
154	#23848	C₂×C₄	1	8	yes	complemented
155	D₄×#99	C₂×C₄	1	8	yes	complemented
156	#21938	C₂³	1	2	yes	—
157	#21758	C₂³	1	2	yes	—
158	C₂×#1982	D₄	1	1	yes	characteristic, complemented
159	C₂×#1972	D₄	1	2	yes	complemented
160	C₂×#1964	C₂³	1	2	yes	—
161	C₂×#1964	C₂³	1	2	yes	—
162	C₂×#1964	C₂³	1	2	yes	—
163	C₂×#1957	D₄	1	1	yes	characteristic, complemented
164	C₂×#1936	D₄	1	2	yes	complemented
165	C₂×#1926	D₄	1	2	yes	complemented
166	C₂×#1893	D₄	1	1	yes	characteristic, complemented
167	C₂×#1893	C₂³	1	2	yes	—
168	C₂×#1893	C₂³	1	1	yes	characteristic
169	C₂×#1893	C₂³	1	1	yes	characteristic
170	C₂×#1893	C₂³	1	2	yes	—
171	C₂×#1879	D₄	1	2	yes	complemented
172	C₂×#1879	D₄	1	2	yes	complemented
173	C₂×#1874	D₄	1	1	yes	characteristic, complemented
174	C₂×#1874	C₂³	1	2	yes	—
175	C₂×#1874	C₂³	1	1	yes	characteristic
176	C₂×#1869	C₂³	1	1	yes	characteristic
177	C₂×#1867	D₄	1	1	yes	characteristic
178	C₂×#1867	D₄	1	1	yes	characteristic
179	C₂×#1864	D₄	1	2	yes	complemented
180	C₂×#1853	C₂³	1	2	yes	—
181	C₂×#1853	C₂³	1	1	yes	characteristic
182	C₂×#1850	C₂³	1	2	yes	—
183	C₂×#1802	D₄	1	1	yes	characteristic, complemented
184	C₂×#1799	C₂³	1	1	yes	characteristic
185	C₂×#1799	C₂³	1	1	yes	characteristic
186	C₂×#1786	D₄	1	1	yes	characteristic, complemented
187	C₂×#1786	C₂³	1	2	yes	—
188	C₂×#1786	C₂³	1	1	yes	characteristic
189	C₂×#1786	C₂³	1	2	yes	—
190	C₂×#1786	C₂³	1	1	yes	characteristic
191	C₂×#1786	C₂³	1	2	yes	—
192	C₂×#1786	C₂³	1	1	yes	characteristic
193	#20526	C₂³	1	2	yes	—
194	C₂×#1762	D₄	1	2	yes	complemented
195	C₂×C₄×#102	D₄	1	1	yes	characteristic, complemented
196	C₂×C₄×#99	C₂³	1	1	yes	characteristic
197	C₂×#1752	C₂³	1	1	yes	characteristic
198	C₂×#1752	C₂³	1	2	yes	—
199	C₂×C₈×C₂²⋊C₄	C₂³	1	2	yes	—
200	C₂×#1519	C₂³	1	2	yes	—
201	C₂×#1519	C₂³	1	2	yes	—
202	C₂×#1519	C₂³	1	2	yes	—
203	C₂×#1459	C₂³	1	1	yes	characteristic
204	#14698	C₂³	1	2	yes	—
205	#14698	C₂³	1	1	yes	characteristic
206	#14697	C₂³	1	1	yes	characteristic
207	#14697	C₂³	1	2	yes	—
208	#14137	C₂³	1	1	yes	characteristic
209	#14130	C₂³	1	2	yes	—
210	#13902	C₂³	1	2	yes	—
211	#13902	C₂³	1	1	yes	characteristic
212	#13880	C₂³	1	2	yes	—
213	#13872	C₂³	1	1	yes	characteristic
214	C₂²⋊C₄×C₄⋊C₄	C₂³	1	2	yes	—
215	C₂²⋊C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
216	C₄×#385	C₂³	1	2	yes	—
217	C₄×#386	C₂³	1	1	yes	characteristic
218	#10918	D₄	1	2	yes	—
219	#10918	D₄	1	2	yes	—
220	#10854	C₂³	1	2	yes	—
221	#10854	C₂³	1	2	yes	—
222	#10854	C₂³	1	2	yes	—
223	#10846	C₂³	1	2	yes	—
224	#10846	C₂³	1	2	yes	—
225	#10745	D₄	1	1	yes	characteristic
226	#10745	D₄	1	1	yes	characteristic
227	#10730	C₂³	1	2	yes	—
228	#10730	C₂³	1	1	yes	characteristic
229	#10730	C₂³	1	2	yes	—
230	#10730	C₂³	1	1	yes	characteristic
231	#10721	C₂³	1	1	yes	characteristic
232	#10721	C₂³	1	2	yes	—
233	#10721	C₂³	1	1	yes	characteristic
234	#10721	C₂³	1	2	yes	—
235	#10714	C₂³	1	1	yes	characteristic
236	#10714	C₂³	1	2	yes	—
237	#10712	C₂³	1	2	yes	—
238	#10712	C₂³	1	1	yes	characteristic
239	C₄×#342	C₂³	1	2	yes	—
240	#10564	C₂×C₄	1	16	yes	complemented
241	#9946	C₂×C₄	1	16	yes	complemented
242	#9468	C₂×C₄	1	8	yes	complemented
243	#9259	C₂×C₄	1	16	yes	complemented
244	#8851	C₂×C₄	1	8	yes	complemented
245	#8350	C₂×C₄	1	8	yes	complemented
246	#8023	C₂³	1	2	yes	—
247	#8023	C₂³	1	2	yes	—
248	#8023	C₂³	1	2	yes	—
249	C₂×#1289	C₂³	1	2	yes	—
250	C₂×#1289	C₂³	1	2	yes	—
251	C₂×#1289	C₂³	1	2	yes	—
252	C₂×#1282	C₂³	1	2	yes	—
253	C₂×#1282	C₂³	1	2	yes	—
254	C₂×#1282	C₂³	1	2	yes	—
255	#7907	C₂³	1	2	yes	—
256	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
257	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
258	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
259	C₂³×D₈	C₂²×C₄	1	4	yes	complemented
260	C₂³×D₈	C₂×D₄	1	2	yes	—
261	C₂³×D₈	C₂×D₄	1	2	yes	—
262	C₂⁴×C₈	C₂×D₄	1	1	yes	characteristic
263	C₂⁴×C₈	C₂⁴	1	1	yes	characteristic
264	C₂⁴×C₈	C₂⁴	1	1	yes	characteristic
265	#3496	C₂²×C₄	1	4	yes	—
266	C₂×D₄²	C₂²×C₄	1	4	yes	—
267	C₂×D₄²	#41	1	4	yes	—
268	C₂²×#127	C₂×D₄	1	1	yes	characteristic
269	C₂²×#121	C₂×D₄	1	1	yes	characteristic
270	C₂²×#121	C₂⁴	1	2	yes	—
271	C₂²×#121	C₂⁴	1	1	yes	characteristic
272	C₂×#518	C₂×D₄	1	1	yes	characteristic
273	C₂×#518	C₂×D₄	1	1	yes	characteristic
274	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
275	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
276	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
277	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
278	C₂²×C₄×D₄	C₂⁴	1	1	yes	characteristic
279	C₂³×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
280	C₂³×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
281	C₂³×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
282	C₂³×C₄²	C₂⁴	1	1	yes	characteristic
283	#3186	C₂²×C₄	1	8	yes	—
284	C₂×#447	C₂²×C₄	1	8	yes	—
285	C₂×#447	C₂²×C₄	1	4	yes	complemented
286	C₂×#447	#41	1	8	yes	—
287	#2972	C₂²×C₄	1	4	yes	—
288	C₂²×#106	C₂×D₄	1	2	yes	—
289	C₂²×#106	C₂×D₄	1	2	yes	—
290	C₂²×C₄⋊C₈	C₂×D₄	1	1	yes	characteristic
291	C₂²×#102	C₂×D₄	1	2	yes	—
292	C₂²×#102	C₂×D₄	1	2	yes	—
293	C₂²×#102	C₂×D₄	1	1	yes	characteristic
294	C₂²×#102	C₂×D₄	1	2	yes	—
295	C₂²×#102	C₂×D₄	1	1	yes	characteristic
296	C₂²×#102	C₂×D₄	1	1	yes	characteristic
297	C₂²×#102	C₂×D₄	1	1	yes	characteristic
298	C₂²×#102	C₂×D₄	1	1	yes	characteristic
299	C₂²×#102	C₂×D₄	1	2	yes	—
300	C₂²×#102	C₂×D₄	1	2	yes	—
301	C₂²×#102	C₂×D₄	1	1	yes	characteristic
302	C₂²×#102	C₂×D₄	1	1	yes	characteristic
303	C₂²×#102	C₂×D₄	1	1	yes	characteristic
304	C₂²×#102	C₂×D₄	1	1	yes	characteristic
305	C₂²×#102	C₂×D₄	1	1	yes	characteristic
306	C₂²×#102	C₂×D₄	1	1	yes	characteristic
307	C₂²×#102	C₂×D₄	1	2	yes	—
308	C₂²×#102	C₂×D₄	1	2	yes	—
309	C₂²×#102	C₂×D₄	1	1	yes	characteristic
310	C₂²×#102	C₂×D₄	1	2	yes	—
311	C₂²×#99	C₂×D₄	1	1	yes	characteristic
312	C₂²×#99	C₂×D₄	1	1	yes	characteristic
313	C₂²×C₂²⋊C₈	C₂×D₄	1	1	yes	characteristic
314	C₂²×C₂²⋊C₈	C₂⁴	1	2	yes	—
315	C₂²×C₂²⋊C₈	C₂⁴	1	1	yes	characteristic
316	C₂²×C₂²⋊C₈	C₂⁴	1	1	yes	characteristic
317	C₂²×C₂²⋊C₈	C₂⁴	1	2	yes	—
318	C₂²×#97	C₂×D₄	1	2	yes	—
319	C₂²×#97	C₂×D₄	1	2	yes	—
320	C₂²×C₄×C₈	C₂×D₄	1	1	yes	characteristic
321	#2433	C₂²×C₄	1	8	yes	complemented
322	#2408	C₂²×C₄	1	4	yes	—
323	D₄×C₂²⋊C₄	C₂²×C₄	1	8	yes	complemented
324	C₂×#390	C₂×D₄	1	2	yes	—
325	C₂×#390	C₂×D₄	1	2	yes	—
326	C₂×#390	C₂×D₄	1	2	yes	—
327	C₂×#389	C₂×D₄	1	2	yes	—
328	C₂×#386	C₂×D₄	1	1	yes	characteristic
329	C₂×#386	C₂×D₄	1	1	yes	characteristic
330	C₂×#385	C₂×D₄	1	2	yes	—
331	C₂×#385	C₂×D₄	1	2	yes	—
332	C₂×#384	C₂×D₄	1	1	yes	characteristic
333	C₂×#380	C₂×D₄	1	1	yes	characteristic
334	C₂×#380	C₂⁴	1	1	yes	characteristic
335	C₂×#380	C₂⁴	1	2	yes	—
336	C₂×#380	C₂⁴	1	2	yes	—
337	C₂×#380	C₂⁴	1	1	yes	characteristic
338	C₂×#380	C₂⁴	1	2	yes	—
339	C₂×#380	C₂⁴	1	1	yes	characteristic
340	#2273	C₂×D₄	1	2	yes	—
341	C₂×C₄×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
342	C₂×C₄×C₄⋊C₄	C₂×D₄	1	2	yes	—
343	C₂×C₄×C₂²⋊C₄	C₂⁴	1	1	yes	characteristic
344	C₂×C₄×C₂²⋊C₄	C₂⁴	1	2	yes	—
345	C₂×C₄×C₂²⋊C₄	C₂⁴	1	2	yes	—
346	#1964	C₂²×C₄	1	8	yes	complemented
347	#1964	C₂²×C₄	1	8	yes	complemented
348	#1893	C₂²×C₄	1	8	yes	complemented
349	#1893	C₂²×C₄	1	4	yes	complemented
350	#1869	C₂²×C₄	1	4	yes	—
351	#1850	C₂²×C₄	1	8	yes	complemented
352	#1799	C₂²×C₄	1	4	yes	—
353	#1786	C₂²×C₄	1	8	yes	complemented
354	#1786	C₂²×C₄	1	4	yes	complemented
355	C₄×#99	C₂²×C₄	1	4	yes	—
356	C₄×#99	#41	1	4	yes	—
357	C₂×#342	C₂×D₄	1	2	yes	—
358	C₂×#342	C₂×D₄	1	2	yes	—
359	C₂×#342	C₂×D₄	1	2	yes	—
360	C₂×#342	C₂×D₄	1	2	yes	—
361	C₂×#342	C₂×D₄	1	2	yes	—
362	C₂×#340	C₂×D₄	1	2	yes	—
363	C₂×#340	C₂×D₄	1	2	yes	—
364	C₂×#340	C₂×D₄	1	1	yes	characteristic
365	C₂×#340	C₂×D₄	1	1	yes	characteristic
366	C₂×#340	C₂×D₄	1	2	yes	—
367	C₂×#340	C₂×D₄	1	2	yes	—
368	C₂×#340	C₂×D₄	1	1	yes	characteristic
369	C₂×#340	C₂×D₄	1	1	yes	characteristic
370	C₂×#336	C₂×D₄	1	2	yes	—
371	C₂×#336	C₂×D₄	1	2	yes	—
372	#1519	C₂²×C₄	1	8	yes	complemented
373	C₂²⋊#95	C₂×D₄	1	1	yes	characteristic
374	C₂²⋊#95	C₂×D₄	1	2	yes	—
375	C₂²⋊#95	C₂×D₄	1	2	yes	—
376	C₂²⋊#95	C₂×D₄	1	1	yes	characteristic
377	#1289	C₂²×C₄	1	8	yes	complemented
378	#1282	C₂²×C₄	1	8	yes	complemented
379	C₂³×D₄	C₄×D₄	1	4	yes	complemented
380	C₂³×D₄	C₂³×C₄	1	2	yes	—
381	C₂³×D₄	C₂³×C₄	1	2	yes	—
382	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
383	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
384	C₂³×D₄	C₂²×D₄	1	2	yes	—
385	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
386	C₂³×D₄	C₂²×D₄	1	2	yes	—
387	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
388	C₂³×D₄	C₂²×D₄	1	2	yes	—
389	C₂³×D₄	C₂×#41	1	4	yes	—
390	C₂³×D₄	C₂×#41	1	2	yes	—
391	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
392	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
393	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
394	C₂⁴×C₄	C₂⁵	1	1	yes	characteristic
395	C₂²×D₈	C₄×D₄	1	8	yes	complemented
396	C₂²×D₈	C₄×D₄	1	8	yes	complemented
397	C₂³×C₈	C₂³×C₄	1	2	yes	—
398	C₂³×C₈	C₂²×D₄	1	2	yes	—
399	C₂³×C₈	C₂²×D₄	1	1	yes	characteristic
400	C₂³×C₈	C₂²×D₄	1	1	yes	characteristic
401	C₂³×C₈	C₂²×D₄	1	1	yes	characteristic
402	C₂³×C₈	C₂²×D₄	1	2	yes	—
403	C₂³×C₈	C₂²×D₄	1	2	yes	—
404	C₂³×C₈	C₂²×D₄	1	1	yes	characteristic
405	C₂³×C₈	C₂²×D₄	1	2	yes	—
406	C₂×#127	C₄×D₄	1	4	yes	complemented
407	C₂×#121	C₄×D₄	1	4	yes	complemented
408	C₂×#121	C₂³×C₄	1	2	yes	—
409	C₂×#121	C₂³×C₄	1	4	yes	—
410	C₂×#121	C₂×#41	1	2	yes	—
411	C₂×#121	C₂×#41	1	4	yes	—
412	C₂×C₄×D₄	C₄×D₄	1	4	yes	complemented
413	C₂×C₄×D₄	C₂³×C₄	1	2	yes	—
414	C₂×C₄×D₄	C₂×#41	1	2	yes	—
415	C₂×C₄×D₄	C₂×#41	1	2	yes	—
416	C₂×C₄×D₄	2₋¹⁺⁴	1	2	yes	—
417	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
418	C₂²×C₄⋊C₄	C₂²×D₄	1	2	yes	—
419	C₂²×C₄⋊C₄	C₂²×D₄	1	2	yes	—
420	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
421	C₂²×C₄⋊C₄	C₂²×D₄	1	2	yes	—
422	C₂²×C₄⋊C₄	C₂²×D₄	1	2	yes	—
423	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
424	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
425	C₂²×C₄⋊C₄	C₂²×D₄	1	2	yes	—
426	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
427	C₂²×C₄⋊C₄	H(5,𝔽₂)	1	1	yes	characteristic
428	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
429	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
430	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
431	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
432	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
433	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
434	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
435	C₂²×C₂²⋊C₄	H(5,𝔽₂)	1	1	yes	characteristic
436	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
437	C₂²×C₄²	C₂²×D₄	1	2	yes	—
438	C₂²×C₄²	C₂²×D₄	1	2	yes	—
439	C₂×#102	C₄×D₄	1	8	yes	complemented
440	C₂×#102	C₄×D₄	1	8	yes	complemented
441	C₂×#102	#120	1	2	yes	—
442	C₂×#102	#120	1	1	yes	characteristic
443	C₂×#102	#120	1	1	yes	characteristic
444	C₂×#102	#120	1	1	yes	characteristic
445	C₂×#102	#120	1	2	yes	—
446	C₂×#102	#120	1	2	yes	—
447	C₂×#102	#120	1	2	yes	—
448	C₂×#102	#120	1	2	yes	—
449	C₂×#102	#120	1	2	yes	—
450	C₂×#102	#120	1	1	yes	characteristic
451	C₂×#99	C₄×D₄	1	4	yes	—
452	C₂×#99	C₄×D₄	1	4	yes	—
453	C₂×#99	AGL(1,ℤ/8)	1	4	yes	—
454	C₂×#99	AGL(1,ℤ/8)	1	4	yes	—
455	C₂×C₂²⋊C₈	C₂³×C₄	1	2	yes	—
456	C₂×C₂²⋊C₈	C₂³×C₄	1	4	yes	—
457	C₂×C₂²⋊C₈	C₂×#41	1	4	yes	—
458	#380	C₂³×C₄	1	4	yes	—
459	#380	C₂³×C₄	1	2	yes	—
460	C₄×C₂²⋊C₄	C₂³×C₄	1	4	yes	—
461	C₄×C₂²⋊C₄	C₂×#41	1	4	yes	—
462	C₂×#95	H(5,𝔽₂)	1	2	yes	—
463	C₂×#95	H(5,𝔽₂)	1	2	yes	—
464	#342	C₄×D₄	1	8	yes	—
465	C₂⁵	D₄²	1	1	yes	characteristic
466	C₂⁵	C₂³×D₄	1	1	yes	characteristic
467	C₂²×D₄	C₂×C₄×D₄	1	2	yes	—
468	C₂²×D₄	C₂×C₄×D₄	1	4	yes	—
469	C₂²×D₄	C₂×C₄×D₄	1	2	yes	—
470	C₂²×D₄	C₂×C₄×D₄	1	4	yes	—
471	C₂²×D₄	C₂×C₄×D₄	1	2	yes	—
472	C₂²×D₄	C₂×C₄×D₄	1	2	yes	—
473	C₂²×D₄	C₂×C₄×D₄	1	4	yes	—
474	C₂²×D₄	C₂×#120	1	2	yes	—
475	C₂²×D₄	C₂×#120	1	1	yes	characteristic
476	C₂²×D₄	C₂×#120	1	1	yes	characteristic
477	C₂²×D₄	#525	1	2	yes	—
478	C₂²×D₄	#525	1	4	yes	—
479	C₂²×D₄	#525	1	2	yes	—
480	C₂²×D₄	#525	1	4	yes	—
481	C₂²×D₄	#548	1	2	yes	—
482	C₂²×D₄	C₂×AGL(1,ℤ/8)	1	2	yes	—
483	C₂²×D₄	C₂×AGL(1,ℤ/8)	1	2	yes	—
484	C₂²×D₄	#576	1	2	yes	—
485	C₂²×D₄	#577	1	2	yes	—
486	C₂³×C₄	C₂×C₄×D₄	1	2	yes	—
487	C₂³×C₄	D₄²	1	1	yes	characteristic
488	C₂³×C₄	D₄²	1	2	yes	—
489	C₂³×C₄	D₄²	1	2	yes	—
490	C₂³×C₄	D₄²	1	2	yes	—
491	C₂³×C₄	D₄²	1	2	yes	—
492	C₂³×C₄	D₄²	1	1	yes	characteristic
493	C₂³×C₄	D₄²	1	1	yes	characteristic
494	C₂³×C₄	#547	1	2	yes	—
495	C₂³×C₄	C₂⁴×C₄	1	1	yes	characteristic
496	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
497	C₂³×C₄	C₂³×D₄	1	2	yes	—
498	C₂³×C₄	C₂²×#41	1	1	yes	characteristic
499	C₂³×C₄	C₂²×#41	1	2	yes	—
500	C₂³×C₄	C₂²×#41	1	1	yes	characteristic
501	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
502	C₂³×C₄	C₂×H(5,𝔽₂)	1	2	yes	—
503	C₂³×C₄	C₂×2₋¹⁺⁴	1	1	yes	characteristic
504	C₂³×C₄	#585	1	2	yes	—
505	C₂²×C₈	C₂×C₄×D₄	1	4	yes	—
506	C₂²×C₈	C₂×C₄×D₄	1	4	yes	—
507	C₂²×C₈	C₂×#120	1	1	yes	characteristic
508	C₂²×C₈	C₂×#120	1	2	yes	—
509	C₂²×C₈	C₂×#120	1	1	yes	characteristic
510	C₂×C₄⋊C₄	C₂×C₄×D₄	1	2	yes	—
511	C₂×C₄⋊C₄	C₂×C₄×D₄	1	4	yes	—
512	C₂×C₄⋊C₄	#520	1	2	yes	—
513	C₂×C₄⋊C₄	C₂×#120	1	1	yes	characteristic
514	C₂×C₄⋊C₄	C₂×#120	1	2	yes	—
515	C₂×C₄⋊C₄	C₂×#120	1	1	yes	characteristic
516	C₂×C₄⋊C₄	#553	1	2	yes	—
517	C₂×C₂²⋊C₄	C₂×C₄×D₄	1	4	yes	—
518	C₂×C₂²⋊C₄	C₂×C₄×D₄	1	2	yes	—
519	C₂×C₂²⋊C₄	C₂×C₄×D₄	1	4	yes	—
520	C₂×C₂²⋊C₄	#520	1	2	yes	—
521	C₂×C₂²⋊C₄	#548	1	2	yes	—
522	C₂×C₂²⋊C₄	#553	1	2	yes	—
523	C₂×C₂²⋊C₄	C₂×AGL(1,ℤ/8)	1	4	yes	—
524	C₂×C₂²⋊C₄	C₂×AGL(1,ℤ/8)	1	4	yes	—
525	C₂×C₄²	C₂×C₄×D₄	1	2	yes	—
526	C₂×C₄²	#547	1	2	yes	—
527	#102	B(4,𝔽₂)	1	4	yes	complemented
528	#99	#442	1	16	yes	complemented
529	C₂⁴	#2361	1	2	yes	—
530	C₂⁴	#3272	1	2	yes	—
531	C₂⁴	#3274	1	2	yes	—
532	C₂⁴	C₂²×C₄×D₄	1	1	yes	characteristic
533	C₂⁴	C₂×D₄²	1	2	yes	—
534	C₂⁴	C₂×D₄²	1	1	yes	characteristic
535	C₂⁴	C₂×#548	1	1	yes	characteristic
536	C₂⁴	D₄×#41	1	2	yes	—
537	C₂⁴	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
538	C₂⁴	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
539	C₂⁴	C₂×#576	1	1	yes	characteristic
540	C₂⁴	C₂×#577	1	1	yes	characteristic
541	C₂⁴	#3585	1	2	yes	—
542	C₂⁴	#3585	1	2	yes	—
543	C₂×D₄	C₄×#120	1	2	yes	—
544	C₂×D₄	C₄×#120	1	4	yes	—
545	C₂×D₄	C₄×#120	1	2	yes	—
546	C₂×D₄	C₂×#442	1	4	yes	—
547	C₂×D₄	#2946	1	4	yes	—
548	C₂×D₄	C₂×B(4,𝔽₂)	1	2	yes	—
549	C₂×D₄	#3025	1	2	yes	—
550	C₂×D₄	#3366	1	4	yes	—
551	C₂×D₄	#3373	1	4	yes	—
552	C₂²×C₄	#2361	1	2	yes	—
553	C₂²×C₄	#2361	1	2	yes	—
554	C₂²×C₄	#2361	1	2	yes	—
555	C₂²×C₄	#3272	1	2	yes	—
556	C₂²×C₄	#3274	1	2	yes	—
557	C₂²×C₄	C₂²×C₄×D₄	1	1	yes	characteristic
558	C₂²×C₄	C₂²×C₄×D₄	1	2	yes	—
559	C₂²×C₄	C₂×#520	1	1	yes	characteristic
560	C₂²×C₄	C₄×H(5,𝔽₂)	1	2	yes	—
561	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
562	C₂²×C₄	C₂×#525	1	2	yes	—
563	C₂²×C₄	C₂×#525	1	1	yes	characteristic
564	C₂²×C₄	C₂×#547	1	1	yes	characteristic
565	C₂²×C₄	D₄×#41	1	2	yes	—
566	C₂²×C₄	C₂×#553	1	1	yes	characteristic
567	C₂²×C₄	#3481	1	2	yes	—
568	C₂²×C₄	#3484	1	2	yes	—
569	C₂²×C₄	#3484	1	1	yes	characteristic
570	C₂²×C₄	#3485	1	1	yes	characteristic
571	C₂²×C₄	#3489	1	2	yes	—
572	C₂²×C₄	#3505	1	2	yes	—
573	C₂²×C₄	#3513	1	2	yes	—
574	C₂²×C₄	#3520	1	2	yes	—
575	C₂×C₈	C₂×B(4,𝔽₂)	1	2	yes	—
576	C₄⋊C₄	C₂×B(4,𝔽₂)	1	2	yes	—
577	C₂²⋊C₄	C₂×#442	1	8	yes	complemented
578	C₂³	#23001	1	4	yes	complemented
579	C₂³	C₂×#2361	1	1	yes	characteristic
580	C₂³	C₄×D₄²	1	2	yes	—
581	C₂³	D₄×#120	1	1	yes	characteristic
582	C₂³	#36097	1	2	yes	—
583	C₂³	#36099	1	1	yes	characteristic
584	C₂³	C₂²×#442	1	1	yes	characteristic
585	C₂³	C₂×#2946	1	1	yes	characteristic
586	C₂³	#60176	1	2	yes	—
587	C₂³	C₂×#3272	1	1	yes	characteristic
588	C₂³	C₂×#3274	1	1	yes	characteristic
589	C₂³	#61058	1	1	yes	characteristic
590	C₂³	#61059	1	1	yes	characteristic
591	C₂³	D₄×AGL(1,ℤ/8)	1	2	yes	—
592	C₂³	D₄×AGL(1,ℤ/8)	1	2	yes	—
593	C₂³	#61071	1	2	yes	—
594	C₂³	#61072	1	2	yes	—
595	C₂³	C₂×#3366	1	1	yes	characteristic
596	C₂³	C₂×#3373	1	1	yes	characteristic
597	C₂³	#61332	1	2	yes	—
598	C₂³	#61451	1	2	yes	—
599	C₂³	#61451	1	2	yes	—
600	C₂³	#61519	1	2	yes	—
601	C₂³	#61522	1	2	yes	—
602	D₄	C₄×B(4,𝔽₂)	1	4	yes	complemented
603	C₂×C₄	#23001	1	4	yes	complemented
604	C₂×C₄	C₂×C₄×#120	1	1	yes	characteristic
605	C₂×C₄	#34264	1	1	yes	characteristic
606	C₂×C₄	#34288	1	2	yes	—
607	C₂×C₄	#36213	1	1	yes	characteristic
608	C₂×C₄	#36221	1	2	yes	—
609	C₂×C₄	#36317	1	1	yes	characteristic
610	C₂×C₄	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
611	C₂×C₄	C₂×#3025	1	1	yes	characteristic
612	C₂×C₄	#60399	1	1	yes	characteristic
613	C₂×C₄	#60401	1	1	yes	characteristic
614	C₂²	#519707	1	1	yes	characteristic
615	C₂²	C₂×#23001	1	1	yes	characteristic
616	C₂²	#6381891	1	1	yes	characteristic
617	C₂²	D₄×#442	1	2	yes	—
618	C₂²	#6383975	1	2	yes	—
619	C₂²	#6573500	1	1	yes	characteristic
620	C₂²	#6573502	1	1	yes	characteristic
621	C₂²	D₄×B(4,𝔽₂)	1	1	yes	characteristic
622	C₂²	#6573713	1	1	yes	characteristic
623	C₂²	#6573735	1	1	yes	characteristic
624	C₂²	#6573736	1	1	yes	characteristic
625	C₂²	#6576138	1	2	yes	—
626	C₂²	#6576140	1	2	yes	—
627	C₂²	#6577260	1	1	yes	characteristic
628	C₂²	#6577278	1	1	yes	characteristic
629	C₄	C₂×C₄×B(4,𝔽₂)	1	1	yes	characteristic
630	C₄	#6372733	1	1	yes	characteristic
631	C₄	#6596184	1	1	yes	characteristic
632	C₄	#6596186	1	1	yes	characteristic
633	C₂	#72264298	1	1	yes	characteristic
634	C₂	#72268291	1	1	yes	characteristic
635	C₂	#72268305	1	1	yes	characteristic
636	C₂	#72280919	1	1	yes	characteristic
637	C₂	#72311708	1	1	yes	characteristic
638	C₂	#72313079	1	1	yes	characteristic
639	C₂	#72313082	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³	D₄×#120
commutator	C₂³×C₄	C₂⁴×C₄
Frattini, cosocle	C₂⁴×C₄	C₂⁵
prime radical	C₂×#267371	C₂
LCS	G ▷ C₂³×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³ ◁ C₂⁴×C₄ ◁ G
LECS	G ▷ C₂⁴×C₄ ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72313663	C₂	semidirect
2. #72313655	C₂	semidirect
3. #72313650	C₂	semidirect
4. #99×#102	C₂	semidirect
5. #72313599	C₂	semidirect
6. #72313570	C₂	semidirect
7. #72313490	C₂	semidirect
8. #72313444	C₂	semidirect
9. #72313406	C₂	semidirect
11. #72313358	C₂	semidirect
12. #72313258	C₂	semidirect
13. #72313124	C₂	semidirect
14. #72311781	C₂	semidirect
15. D₄×#1867	C₂	semidirect
16. #72281648	C₂	semidirect
17. #72281619	C₂	semidirect
18. #72264298	C₂	semidirect
19. #72264243	C₂	semidirect
20. #72264018	C₂	semidirect
21. #72264008	C₂	semidirect
22. #72264002	C₂	semidirect
23. #72263993	C₂	semidirect
25. C₂³×#442	C₂²	semidirect
40. #519711	C₂²	semidirect
42. D₄×#385	C₂²	semidirect
46. #392817	C₂²	semidirect
47. #392817	C₂²	semidirect
49. #392632	C₂²	semidirect
50. #392585	C₂²	semidirect
51. #392585	C₂²	semidirect
53. #370088	C₂²	semidirect
54. #369052	C₂²	semidirect
55. #368434	C₂²	semidirect
56. #368330	C₂²	semidirect
57. #368330	C₂²	semidirect
59. #368007	C₂²	semidirect
60. #366572	C₂²	semidirect
61. #366548	C₂²	semidirect
62. #366287	C₂²	semidirect
63. #365543	C₂²	semidirect
67. #359487	C₂²	semidirect
68. #359487	C₂²	semidirect
69. #356958	C₂²	semidirect
70. D₄×#342	C₂²	semidirect
72. C₂²⋊C₄×#102	C₂²	semidirect
73. #356085	C₂²	semidirect
74. #354462	C₂²	semidirect
77. #267371	C₄	semidirect
83. #195202	C₂²	semidirect
85. #192366	C₂²	semidirect
91. #121601	C₂²	semidirect
92. #121510	C₂²	semidirect
93. #120504	C₂²	semidirect
94. #119893	C₂²	semidirect
95. #117591	C₂²	semidirect
96. #116309	C₂²	semidirect
97. #116073	C₂²	semidirect
99. #113914	C₂²	semidirect
101. #111179	C₂²	semidirect
102. #111110	C₂²	semidirect
103. #110427	C₂²	semidirect
104. #110425	C₂²	semidirect
105. #110425	C₂²	semidirect
106. #109899	C₂²	semidirect
107. #109648	C₂²	semidirect
108. #109648	C₂²	semidirect
109. #109585	C₂²	semidirect
110. #109581	C₂²	semidirect
111. #108575	C₂²	semidirect
113. #108082	C₂²	semidirect
114. #108082	C₂²	semidirect
115. #106962	C₂²	semidirect
120. #106162	C₂²	semidirect
122. #105986	C₂²	semidirect
123. #105305	C₂²	semidirect
129. #61559	C₂×C₄	semidirect
134. C₂²×#442	D₄	semidirect
137. C₂³×#102	D₄	semidirect
152. #25771	C₂×C₄	semidirect
153. #24354	C₂×C₄	semidirect
154. #23848	C₂×C₄	semidirect
155. D₄×#99	C₂×C₄	semidirect
158. C₂×#1982	D₄	semidirect
159. C₂×#1972	D₄	semidirect
163. C₂×#1957	D₄	semidirect
164. C₂×#1936	D₄	semidirect
165. C₂×#1926	D₄	semidirect
166. C₂×#1893	D₄	semidirect
171. C₂×#1879	D₄	semidirect
172. C₂×#1879	D₄	semidirect
173. C₂×#1874	D₄	semidirect
179. C₂×#1864	D₄	semidirect
183. C₂×#1802	D₄	semidirect
186. C₂×#1786	D₄	semidirect
194. C₂×#1762	D₄	semidirect
195. C₂×C₄×#102	D₄	semidirect
240. #10564	C₂×C₄	semidirect
241. #9946	C₂×C₄	semidirect
242. #9468	C₂×C₄	semidirect
243. #9259	C₂×C₄	semidirect
244. #8851	C₂×C₄	semidirect
245. #8350	C₂×C₄	semidirect
259. C₂³×D₈	C₂²×C₄	semidirect
285. C₂×#447	C₂²×C₄	semidirect
321. #2433	C₂²×C₄	semidirect
323. D₄×C₂²⋊C₄	C₂²×C₄	semidirect
346. #1964	C₂²×C₄	semidirect
347. #1964	C₂²×C₄	semidirect
348. #1893	C₂²×C₄	semidirect
349. #1893	C₂²×C₄	semidirect
351. #1850	C₂²×C₄	semidirect
353. #1786	C₂²×C₄	semidirect
354. #1786	C₂²×C₄	semidirect
372. #1519	C₂²×C₄	semidirect
377. #1289	C₂²×C₄	semidirect
378. #1282	C₂²×C₄	semidirect
379. C₂³×D₄	C₄×D₄	semidirect
395. C₂²×D₈	C₄×D₄	semidirect
396. C₂²×D₈	C₄×D₄	semidirect
406. C₂×#127	C₄×D₄	semidirect
407. C₂×#121	C₄×D₄	semidirect
412. C₂×C₄×D₄	C₄×D₄	semidirect
439. C₂×#102	C₄×D₄	semidirect
440. C₂×#102	C₄×D₄	semidirect
527. #102	B(4,𝔽₂)	semidirect
528. #99	#442	semidirect
577. C₂²⋊C₄	C₂×#442	semidirect
578. C₂³	#23001	semidirect
602. D₄	C₄×B(4,𝔽₂)	semidirect
603. C₂×C₄	#23001	semidirect

Maximal subgroups

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

subgroup	index
#72313663	2
#72313655	2
#72313650	2
#99×#102	2
#72313599	2
#72313570	2
#72313490	2
#72313444	2
#72313406	2
C₂×#267371	2
#72313358	2
#72313258	2
#72313124	2
#72311781	2
D₄×#1867	2
#72281648	2
#72281619	2
#72264298	2
#72264243	2
#72264018	2
#72264008	2
#72264002	2
#72263993	2