Subgroups — #72343385

Order 4096.

At least 9017 conjugacy classes of subgroups; only the 563 normal subgroups are shown.

The subgroup lattice has 562 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72343278	C₂	1	1	yes	maximal, characteristic, complemented
2	#72343256	C₂	1	1	yes	maximal, characteristic, complemented
3	#72343254	C₂	1	1	yes	maximal, characteristic, complemented
4	#72343103	C₂	1	1	yes	maximal, characteristic, complemented
5	#72321495	C₂	1	1	yes	maximal, characteristic
6	#72321467	C₄	1	1	yes	characteristic
7	#72321395	C₄	1	1	yes	characteristic
8	#72321240	C₄	1	1	yes	characteristic
9	#72321082	C₄	1	1	yes	characteristic
10	#72320832	C₄	1	1	yes	characteristic
11	#72320832	C₄	1	1	yes	characteristic
12	#72320734	C₄	1	1	yes	characteristic
13	#72320734	C₄	1	1	yes	characteristic
14	#72319036	C₂	1	1	yes	maximal, characteristic, complemented
15	#72287615	C₂	1	1	yes	maximal, characteristic, complemented
16	#72287606	C₂²	1	1	yes	characteristic, complemented
17	#72287606	C₂²	1	1	yes	characteristic, complemented
18	#72287460	C₂	1	1	yes	maximal, characteristic, complemented
19	#72287432	C₂	1	1	yes	maximal, characteristic, complemented
20	#72287431	C₂	1	1	yes	maximal, characteristic
21	#72287376	C₂²	1	1	yes	characteristic
22	#72287368	C₂²	1	1	yes	characteristic
23	#72287291	C₂²	1	1	yes	characteristic
24	#72287154	C₂²	1	1	yes	characteristic
25	#72286411	C₂	1	1	yes	maximal, characteristic, complemented
26	#72286336	C₂²	1	1	yes	characteristic, complemented
27	#72286336	C₂²	1	1	yes	characteristic, complemented
28	#72286279	C₂²	1	1	yes	characteristic
29	#72286252	C₂	1	1	yes	maximal, characteristic, complemented
30	#72286160	C₂²	1	1	yes	characteristic, complemented
31	#72286160	C₂²	1	1	yes	characteristic, complemented
32	#72286130	C₂²	1	1	yes	characteristic
33	#72286130	C₂²	1	1	yes	characteristic
34	#72286111	C₂²	1	1	yes	characteristic, complemented
35	#72286111	C₂²	1	1	yes	characteristic, complemented
36	#72286070	C₂²	1	1	yes	characteristic
37	#72225122	C₂	1	1	yes	maximal, characteristic, complemented
38	#72225121	C₂	1	1	yes	maximal, characteristic, complemented
39	#72225045	C₂	1	1	yes	maximal, characteristic
40	#72225043	C₂²	1	1	yes	characteristic
41	#72225042	C₂²	1	1	yes	characteristic
42	#72225041	C₂²	1	1	yes	characteristic
43	#72225037	C₂²	1	1	yes	characteristic
44	#72225025	C₂²	1	1	yes	characteristic, complemented
45	#72225025	C₂²	1	1	yes	characteristic, complemented
46	#72224991	C₂²	1	1	yes	characteristic
47	#72224991	C₂²	1	1	yes	characteristic
48	#72224979	C₂²	1	1	yes	characteristic, complemented
49	#72224979	C₂²	1	1	yes	characteristic, complemented
50	#72224951	C₂²	1	1	yes	characteristic, complemented
51	#72224951	C₂²	1	1	yes	characteristic, complemented
52	#72217274	C₂²	1	1	yes	characteristic
53	#72217219	C₂²	1	1	yes	characteristic, complemented
54	#72217215	C₂²	1	1	yes	characteristic, complemented
55	#72217181	C₂²	1	1	yes	characteristic
56	#72216759	C₂²	1	1	yes	characteristic
57	#72216752	C₂²	1	1	yes	characteristic
58	#72216687	C₂²	1	1	yes	characteristic
59	#7623973	Q₈	1	1	yes	characteristic
60	#7623937	Q₈	1	1	yes	characteristic
61	#7623852	C₂×C₄	1	1	yes	characteristic
62	#7623818	C₂×C₄	1	1	yes	characteristic
63	#7623818	Q₈	1	1	yes	characteristic
64	#7623634	C₂×C₄	1	1	yes	characteristic
65	#7623604	C₂×C₄	1	1	yes	characteristic
66	#7623604	Q₈	1	1	yes	characteristic
67	#7623252	D₄	1	1	yes	characteristic
68	#7623252	C₂³	1	1	yes	characteristic
69	#7623243	D₄	1	1	yes	characteristic
70	#7622738	D₄	1	1	yes	characteristic
71	#7622660	C₂³	1	1	yes	characteristic
72	#7622620	D₄	1	1	yes	characteristic
73	#7622620	C₂³	1	1	yes	characteristic
74	C₂²×#2177	D₄	1	1	yes	characteristic
75	#6342500	D₄	1	1	yes	characteristic
76	#512736	C₂³	1	1	yes	characteristic
77	#512736	C₂³	1	1	yes	characteristic
78	#512736	C₂³	1	1	yes	characteristic
79	#512548	C₂³	1	1	yes	characteristic
80	#494212	C₂³	1	1	yes	characteristic
81	#494212	C₂³	1	1	yes	characteristic
82	#483996	D₄	1	1	yes	characteristic
83	#483996	D₄	1	1	yes	characteristic
84	#483993	D₄	1	1	yes	characteristic
85	#483993	D₄	1	1	yes	characteristic
86	#483992	D₄	1	1	yes	characteristic
87	#483992	D₄	1	1	yes	characteristic
88	#483989	D₄	1	1	yes	characteristic
89	#483989	D₄	1	1	yes	characteristic
90	#483844	D₄	1	1	yes	characteristic
91	#483843	D₄	1	1	yes	characteristic
92	#483836	D₄	1	1	yes	characteristic
93	C₂×#12089	D₄	1	1	yes	characteristic
94	#483597	D₄	1	1	yes	characteristic
95	#483596	D₄	1	1	yes	characteristic
96	#483589	D₄	1	1	yes	characteristic
97	C₂×#12067	D₄	1	1	yes	characteristic
98	#483449	D₄	1	1	yes	characteristic
99	#483449	D₄	1	1	yes	characteristic
100	#483446	D₄	1	1	yes	characteristic
101	#483444	D₄	1	1	yes	characteristic
102	#483414	C₂³	1	1	yes	characteristic
103	#483399	C₂³	1	1	yes	characteristic
104	#483399	C₂³	1	1	yes	characteristic
105	#483327	C₂³	1	1	yes	characteristic
106	#479976	D₄	1	1	yes	characteristic
107	#479976	D₄	1	1	yes	characteristic
108	#479960	C₂³	1	1	yes	characteristic
109	#479960	C₂³	1	1	yes	characteristic
110	#152372	C₂×C₄	1	1	yes	characteristic
111	#152372	C₂×C₄	1	1	yes	characteristic
112	#152371	C₂×C₄	1	1	yes	characteristic
113	#152371	C₂×C₄	1	1	yes	characteristic
114	#152171	C₂×C₄	1	1	yes	characteristic
115	#152171	C₂×C₄	1	1	yes	characteristic
116	#152169	C₂×C₄	1	1	yes	characteristic
117	#152169	C₂×C₄	1	1	yes	characteristic
118	#150883	C₂×C₄	1	1	yes	characteristic
119	#150883	C₂×C₄	1	1	yes	characteristic
120	#150881	C₂×C₄	1	1	yes	characteristic
121	#150881	C₂×C₄	1	1	yes	characteristic
122	#150879	C₂×C₄	1	1	yes	characteristic
123	#150879	C₂×C₄	1	1	yes	characteristic
124	#150878	C₂×C₄	1	1	yes	characteristic
125	#150878	C₂×C₄	1	1	yes	characteristic
126	#149672	C₂×C₄	1	1	yes	characteristic
127	#149672	C₂×C₄	1	1	yes	characteristic
128	#149669	C₂×C₄	1	1	yes	characteristic
129	#149669	C₂×C₄	1	1	yes	characteristic
130	#134778	C₂×C₄	1	1	yes	characteristic
131	#134776	C₂×C₄	1	1	yes	characteristic
132	#134773	C₂×C₄	1	1	yes	characteristic
133	#134773	C₂×C₄	1	1	yes	characteristic
134	C₂×#3415	C₄⋊C₄	1	1	yes	characteristic
135	C₂×#3415	C₂²×C₄	1	1	yes	characteristic
136	C₂³×D₁₆	C₄⋊C₄	1	1	yes	characteristic
137	#60204	C₂×D₄	1	1	yes	characteristic
138	#33750	C₂×D₄	1	1	yes	characteristic
139	#33750	C₂×D₄	1	1	yes	characteristic
140	#33748	C₂×D₄	1	1	yes	characteristic
141	#33748	C₂×D₄	1	1	yes	characteristic
142	#33742	#41	1	1	yes	characteristic
143	#33742	#41	1	1	yes	characteristic
144	#33740	#41	1	1	yes	characteristic
145	#33740	#41	1	1	yes	characteristic
146	#33730	C₄⋊C₄	1	1	yes	characteristic
147	#33730	C₂×Q₈	1	1	yes	characteristic
148	#33728	C₄⋊C₄	1	1	yes	characteristic
149	#33720	C₄⋊C₄	1	1	yes	characteristic
150	#33720	C₂×Q₈	1	1	yes	characteristic
151	#33716	C₄⋊C₄	1	1	yes	characteristic
152	#33611	C₄⋊C₄	1	1	yes	characteristic
153	#33611	C₂²×C₄	1	1	yes	characteristic
154	#33607	C₄⋊C₄	1	1	yes	characteristic
155	#33607	C₂²×C₄	1	1	yes	characteristic
156	#33600	C₄⋊C₄	1	1	yes	characteristic
157	#33600	C₄⋊C₄	1	1	yes	characteristic
158	#33475	C₂×Q₈	1	1	yes	characteristic
159	#33475	#41	1	1	yes	characteristic
160	#33460	C₄⋊C₄	1	1	yes	characteristic
161	#33460	C₂×Q₈	1	1	yes	characteristic
162	#33460	#41	1	1	yes	characteristic
163	#33460	#41	1	1	yes	characteristic
164	#33456	C₄⋊C₄	1	1	yes	characteristic
165	#33456	C₂×Q₈	1	1	yes	characteristic
166	#33456	#41	1	1	yes	characteristic
167	#33456	#41	1	1	yes	characteristic
168	#33451	C₂×D₄	1	1	yes	characteristic
169	#33451	C₂×D₄	1	1	yes	characteristic
170	#33451	C₂×D₄	1	1	yes	characteristic
171	#33451	C₂×D₄	1	1	yes	characteristic
172	C₂×#2177	C₄⋊C₄	1	1	yes	characteristic
173	C₂×#2177	C₄⋊C₄	1	1	yes	characteristic
174	C₂×#2177	C₂×D₄	1	1	yes	characteristic
175	C₂×#2177	C₂×D₄	1	1	yes	characteristic
176	C₂×#2177	C₂×D₄	1	1	yes	characteristic
177	C₂×#2177	C₂×D₄	1	1	yes	characteristic
178	#33435	C₂²×C₄	1	1	yes	characteristic
179	#33435	#41	1	1	yes	characteristic
180	#33432	C₂²×C₄	1	1	yes	characteristic
181	#33432	C₂×Q₈	1	1	yes	characteristic
182	#33432	#41	1	1	yes	characteristic
183	#33432	#41	1	1	yes	characteristic
184	#33421	C₂×D₄	1	1	yes	characteristic
185	#33421	C₂×D₄	1	1	yes	characteristic
186	#33421	C₂×D₄	1	1	yes	characteristic
187	#33421	C₂×D₄	1	1	yes	characteristic
188	#33418	C₂×D₄	1	1	yes	characteristic
189	#33411	C₄⋊C₄	1	1	yes	characteristic
190	#33411	C₂²×C₄	1	1	yes	characteristic
191	C₂²×#367	C₄⋊C₄	1	1	yes	characteristic
192	#33326	C₂×D₄	1	1	yes	characteristic
193	#33326	C₂⁴	1	1	yes	characteristic
194	C₂²×#346	C₂×D₄	1	1	yes	characteristic
195	#17342	SD₁₆	1	1	yes	characteristic
196	#17342	SD₁₆	1	1	yes	characteristic
197	#17336	C₂×D₄	1	1	yes	characteristic
198	#17336	C₂×D₄	1	1	yes	characteristic
199	M₁₆²	SD₁₆	1	1	yes	characteristic
200	#17325	SD₁₆	1	1	yes	characteristic
201	#13556	C₂²×C₄	1	1	yes	characteristic
202	#13556	C₂²×C₄	1	1	yes	characteristic
203	#13556	C₂²×C₄	1	1	yes	characteristic
204	#13556	C₂²×C₄	1	1	yes	characteristic
205	#12840	C₂²×C₄	1	1	yes	characteristic
206	#12840	C₂²×C₄	1	1	yes	characteristic
207	#12839	C₂²×C₄	1	1	yes	characteristic
208	#12839	C₂²×C₄	1	1	yes	characteristic
209	#12021	C₂×D₄	1	1	yes	characteristic
210	#12021	C₂×D₄	1	1	yes	characteristic
211	#12021	C₂×D₄	1	1	yes	characteristic
212	#12021	C₂×D₄	1	1	yes	characteristic
213	#12020	C₂×D₄	1	1	yes	characteristic
214	#12020	C₂×D₄	1	1	yes	characteristic
215	#12020	C₂×D₄	1	1	yes	characteristic
216	#12020	C₂×D₄	1	1	yes	characteristic
217	#11999	C₂×D₄	1	1	yes	characteristic
218	#11999	C₂×D₄	1	1	yes	characteristic
219	C₂×#1368	C₂×D₄	1	1	yes	characteristic
220	C₂×#1368	C₂×D₄	1	1	yes	characteristic
221	#11405	C₂×D₄	1	1	yes	characteristic
222	#11405	C₂×D₄	1	1	yes	characteristic
223	#11405	C₂×D₄	1	1	yes	characteristic
224	#11405	C₂×D₄	1	1	yes	characteristic
225	#11404	C₂×D₄	1	1	yes	characteristic
226	#11404	C₂×D₄	1	1	yes	characteristic
227	C₂×#1313	C₂×D₄	1	1	yes	characteristic
228	C₂×#1313	C₂×D₄	1	1	yes	characteristic
229	#3444	AGL(1,ℤ/8)	1	1	yes	characteristic
230	C₂×#508	C₂×C₄⋊C₄	1	1	yes	characteristic
231	C₂×#508	C₂×C₄⋊C₄	1	1	yes	characteristic
232	C₂×#508	C₄×D₄	1	1	yes	characteristic
233	C₂×#508	C₄×D₄	1	1	yes	characteristic
234	C₂²×D₁₆	C₂×C₄⋊C₄	1	1	yes	characteristic
235	C₂²×D₁₆	C₂×C₄⋊C₄	1	1	yes	characteristic
236	C₂²×D₁₆	C₄×D₄	1	1	yes	characteristic
237	C₂²×D₁₆	C₄×D₄	1	1	yes	characteristic
238	C₂×#504	C₂×C₄⋊C₄	1	1	yes	characteristic
239	C₂×#504	#123	1	1	yes	characteristic
240	C₂×#504	C₂³×C₄	1	1	yes	characteristic
241	C₂×#504	C₂×#41	1	1	yes	characteristic
242	C₂³×C₁₆	C₂×C₄⋊C₄	1	1	yes	characteristic
243	C₂³×C₁₆	#123	1	1	yes	characteristic
244	#2960	C₂²⋊Q₈	1	1	yes	characteristic
245	#2960	#135	1	1	yes	characteristic
246	#2931	C₄×D₄	1	1	yes	characteristic
247	#2931	AGL(1,ℤ/8)	1	1	yes	characteristic
248	#2929	C₄×D₄	1	1	yes	characteristic
249	#2929	C₂²⋊Q₈	1	1	yes	characteristic
250	#2929	#135	1	1	yes	characteristic
251	#2929	AGL(1,ℤ/8)	1	1	yes	characteristic
252	#2922	C₂×SD₁₆	1	1	yes	characteristic
253	#2922	AGL(1,ℤ/8)	1	1	yes	characteristic
254	#2920	C₂×SD₁₆	1	1	yes	characteristic
255	C₄×#131	#120	1	1	yes	characteristic
256	C₄×#131	C₂²×D₄	1	1	yes	characteristic
257	C₂²×C₄×C₈	#120	1	1	yes	characteristic
258	#2254	C₂²⋊Q₈	1	1	yes	characteristic
259	#2254	C₂²⋊Q₈	1	1	yes	characteristic
260	#2253	C₂²⋊Q₈	1	1	yes	characteristic
261	#2253	C₂²⋊Q₈	1	1	yes	characteristic
262	#2249	C₂²⋊Q₈	1	1	yes	characteristic
263	#2249	C₂²⋊Q₈	1	1	yes	characteristic
264	#2246	C₂²⋊Q₈	1	1	yes	characteristic
265	#2246	C₂²⋊Q₈	1	1	yes	characteristic
266	#2219	C₄×D₄	1	1	yes	characteristic
267	#2219	C₄×D₄	1	1	yes	characteristic
268	#2218	C₄×D₄	1	1	yes	characteristic
269	#2218	C₄×D₄	1	1	yes	characteristic
270	#2218	C₄×D₄	1	1	yes	characteristic
271	#2218	C₄×D₄	1	1	yes	characteristic
272	#2218	C₄×D₄	1	1	yes	characteristic
273	#2218	C₄×D₄	1	1	yes	characteristic
274	#2177	#120	1	1	yes	characteristic
275	#2177	#120	1	1	yes	characteristic
276	#2177	#120	1	1	yes	characteristic
277	#2177	#120	1	1	yes	characteristic
278	#2177	#120	1	1	yes	characteristic
279	#2177	#120	1	1	yes	characteristic
280	#2177	C₂²⋊Q₈	1	1	yes	characteristic
281	#2177	C₂²⋊Q₈	1	1	yes	characteristic
282	#2177	C₂²⋊Q₈	1	1	yes	characteristic
283	#2177	C₂²⋊Q₈	1	1	yes	characteristic
284	#2177	C₂²⋊Q₈	1	1	yes	characteristic
285	#2177	C₂²⋊Q₈	1	1	yes	characteristic
286	#2177	#123	1	1	yes	characteristic
287	#2177	#123	1	1	yes	characteristic
288	#2177	#123	1	1	yes	characteristic
289	#2177	#123	1	1	yes	characteristic
290	#2177	#123	1	1	yes	characteristic
291	#2177	#123	1	1	yes	characteristic
292	#2176	#120	1	1	yes	characteristic
293	#2176	#120	1	1	yes	characteristic
294	#2176	C₂²⋊Q₈	1	1	yes	characteristic
295	#2176	C₂²⋊Q₈	1	1	yes	characteristic
296	#2176	#123	1	1	yes	characteristic
297	#2176	#123	1	1	yes	characteristic
298	#2158	C₂×C₄⋊C₄	1	1	yes	characteristic
299	#2158	C₂×C₄⋊C₄	1	1	yes	characteristic
300	#2158	C₄×D₄	1	1	yes	characteristic
301	#2158	C₄×D₄	1	1	yes	characteristic
302	C₂×#367	C₂×C₄⋊C₄	1	1	yes	characteristic
303	C₂×#367	C₂×C₄⋊C₄	1	1	yes	characteristic
304	C₂×#367	C₄×D₄	1	1	yes	characteristic
305	C₂×#367	C₄×D₄	1	1	yes	characteristic
306	#2151	C₄×D₄	1	1	yes	characteristic
307	#2151	C₂²⋊Q₈	1	1	yes	characteristic
308	#2151	C₂²⋊Q₈	1	1	yes	characteristic
309	#2151	C₂²⋊Q₈	1	1	yes	characteristic
310	#2150	C₄×D₄	1	1	yes	characteristic
311	#2150	C₂²⋊Q₈	1	1	yes	characteristic
312	#2113	C₄×D₄	1	1	yes	characteristic
313	#2113	C₄×D₄	1	1	yes	characteristic
314	#2113	C₄×D₄	1	1	yes	characteristic
315	#2113	C₂²⋊Q₈	1	1	yes	characteristic
316	#2112	C₄×D₄	1	1	yes	characteristic
317	#2112	C₂²⋊Q₈	1	1	yes	characteristic
318	#2108	C₂×C₄⋊C₄	1	1	yes	characteristic
319	#2108	#123	1	1	yes	characteristic
320	#2108	C₂²×Q₈	1	1	yes	characteristic
321	#2108	C₂×#41	1	1	yes	characteristic
322	#2108	C₂×#41	1	1	yes	characteristic
323	#2108	C₂×#41	1	1	yes	characteristic
324	#2108	C₂×#41	1	1	yes	characteristic
325	#2108	C₂×#41	1	1	yes	characteristic
326	C₄×M₃₂	#120	1	1	yes	characteristic
327	C₄×M₃₂	#120	1	1	yes	characteristic
328	C₄×M₃₂	#120	1	1	yes	characteristic
329	C₄×M₃₂	C₂²×D₄	1	1	yes	characteristic
330	C₄×M₃₂	C₂²×D₄	1	1	yes	characteristic
331	C₄×M₃₂	C₂²×D₄	1	1	yes	characteristic
332	C₂×#346	C₂×C₄⋊C₄	1	1	yes	characteristic
333	C₂×#346	#120	1	1	yes	characteristic
334	C₂×#346	#120	1	1	yes	characteristic
335	C₂×#346	#120	1	1	yes	characteristic
336	C₂×#346	#123	1	1	yes	characteristic
337	C₂×#346	C₂²×D₄	1	1	yes	characteristic
338	C₂×#346	C₂²×D₄	1	1	yes	characteristic
339	C₂×#346	C₂²×D₄	1	1	yes	characteristic
340	#1455	C₂×SD₁₆	1	1	yes	characteristic
341	#1455	C₂×SD₁₆	1	1	yes	characteristic
342	#1455	AGL(1,ℤ/8)	1	1	yes	characteristic
343	#1455	AGL(1,ℤ/8)	1	1	yes	characteristic
344	#1453	C₂×SD₁₆	1	1	yes	characteristic
345	#1453	C₂×SD₁₆	1	1	yes	characteristic
346	#1453	AGL(1,ℤ/8)	1	1	yes	characteristic
347	#1453	AGL(1,ℤ/8)	1	1	yes	characteristic
348	#1450	#120	1	1	yes	characteristic
349	#1450	#120	1	1	yes	characteristic
350	C₂×#322	#120	1	1	yes	characteristic
351	C₂×#322	#120	1	1	yes	characteristic
352	#1368	#120	1	1	yes	characteristic
353	#1368	#120	1	1	yes	characteristic
354	#1368	#120	1	1	yes	characteristic
355	#1368	#120	1	1	yes	characteristic
356	#1368	#120	1	1	yes	characteristic
357	#1368	#120	1	1	yes	characteristic
358	#1368	#120	1	1	yes	characteristic
359	#1368	#120	1	1	yes	characteristic
360	C₂×#131	#385	1	1	yes	characteristic
361	C₂×#131	#449	1	1	yes	characteristic
362	C₂×#131	C₂×C₄×D₄	1	1	yes	characteristic
363	C₂×#131	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
364	C₂³×C₈	#385	1	1	yes	characteristic
365	C₂³×C₈	#449	1	1	yes	characteristic
366	#533	#478	1	1	yes	characteristic
367	#532	#442	1	1	yes	characteristic
368	#525	#442	1	1	yes	characteristic
369	#525	#478	1	1	yes	characteristic
370	C₄×#41	#450	1	1	yes	characteristic
371	C₄×#41	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
372	C₂²×C₄²	#450	1	1	yes	characteristic
373	C₂×Q₃₂	#385	1	1	yes	characteristic
374	C₂×Q₃₂	#385	1	1	yes	characteristic
375	C₂×D₁₆	#385	1	1	yes	characteristic
376	C₂×D₁₆	#385	1	1	yes	characteristic
377	C₂×D₁₆	#385	1	1	yes	characteristic
378	C₂×D₁₆	#385	1	1	yes	characteristic
379	C₂×D₁₆	#385	1	1	yes	characteristic
380	C₂×D₁₆	#385	1	1	yes	characteristic
381	C₂×M₃₂	#385	1	1	yes	characteristic
382	C₂×M₃₂	#385	1	1	yes	characteristic
383	C₂×M₃₂	C₂×C₄×D₄	1	1	yes	characteristic
384	C₂×M₃₂	C₂×C₄×D₄	1	1	yes	characteristic
385	C₂×M₃₂	C₂×C₄×D₄	1	1	yes	characteristic
386	C₂×M₃₂	C₂×C₂²⋊Q₈	1	1	yes	characteristic
387	C₂×M₃₂	#525	1	1	yes	characteristic
388	C₂×M₃₂	#525	1	1	yes	characteristic
389	C₂²×C₁₆	#385	1	1	yes	characteristic
390	C₂²×C₁₆	#385	1	1	yes	characteristic
391	C₂²×C₁₆	C₂²×C₄⋊C₄	1	1	yes	characteristic
392	C₂²×C₁₆	C₂×C₄×D₄	1	1	yes	characteristic
393	C₂²×C₁₆	C₂×C₄×D₄	1	1	yes	characteristic
394	C₂²×C₁₆	C₂×#123	1	1	yes	characteristic
395	C₂²×C₁₆	#525	1	1	yes	characteristic
396	C₂²×C₁₆	#525	1	1	yes	characteristic
397	#424	C₄×SD₁₆	1	1	yes	characteristic
398	#424	#476	1	1	yes	characteristic
399	#424	#478	1	1	yes	characteristic
400	#424	#478	1	1	yes	characteristic
401	#423	C₄×SD₁₆	1	1	yes	characteristic
402	#423	#476	1	1	yes	characteristic
403	#408	C₄×SD₁₆	1	1	yes	characteristic
404	#408	#442	1	1	yes	characteristic
405	#408	#442	1	1	yes	characteristic
406	#408	#476	1	1	yes	characteristic
407	#407	C₄×SD₁₆	1	1	yes	characteristic
408	#407	#476	1	1	yes	characteristic
409	#405	#385	1	1	yes	characteristic
410	#405	#449	1	1	yes	characteristic
411	#405	C₂×C₂²⋊Q₈	1	1	yes	characteristic
412	#405	#525	1	1	yes	characteristic
413	#405	#525	1	1	yes	characteristic
414	#405	C₂×#135	1	1	yes	characteristic
415	#405	#575	1	1	yes	characteristic
416	#405	#575	1	1	yes	characteristic
417	C₄×M₁₆	#450	1	1	yes	characteristic
418	C₄×M₁₆	C₂²×SD₁₆	1	1	yes	characteristic
419	C₄×M₁₆	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
420	C₄×M₁₆	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
421	C₂×C₄×C₈	#385	1	1	yes	characteristic
422	C₂×C₄×C₈	#449	1	1	yes	characteristic
423	C₂×C₄×C₈	#450	1	1	yes	characteristic
424	C₂×C₄×C₈	C₂×#120	1	1	yes	characteristic
425	C₂×C₄×C₈	C₂×#120	1	1	yes	characteristic
426	C₂×C₄×C₈	C₂×#120	1	1	yes	characteristic
427	#367	#385	1	1	yes	characteristic
428	#367	#385	1	1	yes	characteristic
429	#367	#385	1	1	yes	characteristic
430	#367	#385	1	1	yes	characteristic
431	#367	#385	1	1	yes	characteristic
432	#367	#385	1	1	yes	characteristic
433	#367	#385	1	1	yes	characteristic
434	#367	#385	1	1	yes	characteristic
435	#346	C₂×#120	1	1	yes	characteristic
436	#346	C₂×#120	1	1	yes	characteristic
437	#346	C₂×#120	1	1	yes	characteristic
438	#346	C₂×#120	1	1	yes	characteristic
439	#346	C₂×C₂²⋊Q₈	1	1	yes	characteristic
440	#346	C₂×C₂²⋊Q₈	1	1	yes	characteristic
441	#346	C₂×#123	1	1	yes	characteristic
442	#346	C₂×#123	1	1	yes	characteristic
443	#346	#525	1	1	yes	characteristic
444	#346	#525	1	1	yes	characteristic
445	C₄×C₁₆	C₂×C₂²⋊Q₈	1	1	yes	characteristic
446	C₄×C₁₆	C₂×C₂²⋊Q₈	1	1	yes	characteristic
447	C₄×C₁₆	#525	1	1	yes	characteristic
448	C₄×C₁₆	#525	1	1	yes	characteristic
449	C₄×C₁₆	#525	1	1	yes	characteristic
450	C₄×C₁₆	#525	1	1	yes	characteristic
451	#322	#450	1	1	yes	characteristic
452	#322	#450	1	1	yes	characteristic
453	#322	#450	1	1	yes	characteristic
454	#322	#450	1	1	yes	characteristic
455	C₈²	#450	1	1	yes	characteristic
456	C₈²	#450	1	1	yes	characteristic
457	C₈²	#450	1	1	yes	characteristic
458	C₈²	#450	1	1	yes	characteristic
459	C₂×#41	#1864	1	1	yes	characteristic
460	C₂×#41	C₂×#442	1	1	yes	characteristic
461	C₂³×C₄	#1864	1	1	yes	characteristic
462	C₂×M₁₆	#1864	1	1	yes	characteristic
463	C₂×M₁₆	#1864	1	1	yes	characteristic
464	C₂×M₁₆	C₂×C₄×SD₁₆	1	1	yes	characteristic
465	C₂×M₁₆	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
466	C₂×M₁₆	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
467	C₂×M₁₆	C₂×#476	1	1	yes	characteristic
468	C₂×M₁₆	#3109	1	1	yes	characteristic
469	C₂×M₁₆	#3109	1	1	yes	characteristic
470	C₂²×C₈	#1864	1	1	yes	characteristic
471	C₂²×C₈	#1864	1	1	yes	characteristic
472	C₂²×C₈	C₂×#385	1	1	yes	characteristic
473	C₂²×C₈	C₄×#120	1	1	yes	characteristic
474	C₂²×C₈	C₄×#120	1	1	yes	characteristic
475	C₂²×C₈	C₂×#449	1	1	yes	characteristic
476	C₂²×C₈	#3006	1	1	yes	characteristic
477	C₂²×C₈	#3006	1	1	yes	characteristic
478	C₄⋊Q₈	AGL(1,ℤ/16)	1	1	yes	characteristic
479	#127	AGL(1,ℤ/16)	1	1	yes	characteristic
480	#124	AGL(1,ℤ/16)	1	1	yes	characteristic
481	#124	AGL(1,ℤ/16)	1	1	yes	characteristic
482	#123	AGL(1,ℤ/16)	1	1	yes	characteristic
483	#123	AGL(1,ℤ/16)	1	1	yes	characteristic
484	#120	AGL(1,ℤ/16)	1	1	yes	characteristic
485	#120	AGL(1,ℤ/16)	1	1	yes	characteristic
486	#117	#1864	1	1	yes	characteristic
487	#117	C₂×#478	1	1	yes	characteristic
488	#117	#3114	1	1	yes	characteristic
489	#117	#3114	1	1	yes	characteristic
490	C₂×C₄²	#1864	1	1	yes	characteristic
491	C₂×C₄²	C₂×#450	1	1	yes	characteristic
492	C₂×C₄²	#3003	1	1	yes	characteristic
493	C₂×C₄²	#3003	1	1	yes	characteristic
494	D₁₆	#1868	1	2	yes	—
495	C₂×C₁₆	C₂×#385	1	1	yes	characteristic
496	C₂×C₁₆	C₂×#385	1	1	yes	characteristic
497	C₂×C₁₆	C₄×#120	1	1	yes	characteristic
498	C₂×C₁₆	C₄×#120	1	1	yes	characteristic
499	C₂×C₁₆	#2848	1	1	yes	characteristic
500	C₂×C₁₆	#2848	1	1	yes	characteristic
501	C₂×C₁₆	#2849	1	1	yes	characteristic
502	C₂×C₁₆	#2849	1	1	yes	characteristic
503	#97	#3077	1	1	yes	characteristic
504	#97	#3077	1	1	yes	characteristic
505	#97	#3101	1	1	yes	characteristic
506	#97	#3101	1	1	yes	characteristic
507	#97	#3105	1	1	yes	characteristic
508	#97	#3105	1	1	yes	characteristic
509	C₄×C₈	#2846	1	1	yes	characteristic
510	C₄×C₈	#2848	1	1	yes	characteristic
511	C₄×C₈	#2848	1	1	yes	characteristic
512	C₄×C₈	#2849	1	1	yes	characteristic
513	C₄×C₈	C₂×#450	1	1	yes	characteristic
514	C₄×C₈	C₂×#450	1	1	yes	characteristic
515	C₄×C₈	#3002	1	1	yes	characteristic
516	C₄×C₈	#3002	1	1	yes	characteristic
517	C₄×C₈	#3003	1	1	yes	characteristic
518	C₄×C₈	#3005	1	1	yes	characteristic
519	C₂⁴	#12956	1	1	yes	characteristic
520	C₂×Q₈	#12956	1	1	yes	characteristic
521	C₂×Q₈	C₂×AGL(1,ℤ/16)	1	1	yes	characteristic
522	C₂×D₄	#12956	1	1	yes	characteristic
523	C₂×D₄	C₂×AGL(1,ℤ/16)	1	1	yes	characteristic
524	C₂×D₄	C₂×AGL(1,ℤ/16)	1	1	yes	characteristic
525	C₂×D₄	C₂×AGL(1,ℤ/16)	1	1	yes	characteristic
526	C₂²×C₄	#12956	1	1	yes	characteristic
527	C₂²×C₄	C₂×#1864	1	1	yes	characteristic
528	C₂²×C₄	#21452	1	1	yes	characteristic
529	C₂²×C₄	#21452	1	1	yes	characteristic
530	C₂×C₈	#14693	1	1	yes	characteristic
531	C₂×C₈	#20873	1	1	yes	characteristic
532	C₂×C₈	C₄×#450	1	1	yes	characteristic
533	C₂×C₈	C₄×#450	1	1	yes	characteristic
534	C₂×C₈	#32880	1	1	yes	characteristic
535	C₂×C₈	#32956	1	1	yes	characteristic
536	C₂×C₈	#32956	1	1	yes	characteristic
537	C₂×C₈	#33004	1	1	yes	characteristic
538	C₂²⋊C₄	#12956	1	1	yes	characteristic
539	C₂²⋊C₄	#12956	1	1	yes	characteristic
540	C₄²	#12956	1	1	yes	characteristic
541	C₄²	#12956	1	1	yes	characteristic
542	C₄²	#32881	1	1	yes	characteristic
543	C₄²	#32959	1	1	yes	characteristic
544	C₄²	#32959	1	1	yes	characteristic
545	C₄²	#33007	1	1	yes	characteristic
546	C₁₆	C₂×#1868	1	1	yes	characteristic
547	C₁₆	#20892	1	1	yes	characteristic
548	C₂³	C₂×#12956	1	1	yes	characteristic
549	C₂³	#495725	1	1	yes	characteristic
550	C₂³	#495725	1	1	yes	characteristic
551	C₂×C₄	#392585	1	1	yes	characteristic
552	C₂×C₄	C₂×#12956	1	1	yes	characteristic
553	C₂×C₄	#495725	1	1	yes	characteristic
554	C₂×C₄	#495725	1	1	yes	characteristic
555	C₈	#392597	1	1	yes	characteristic
556	C₈	#392605	1	1	yes	characteristic
557	C₂²	#72231308	1	1	yes	characteristic
558	C₄	#72320672	1	1	yes	characteristic
559	C₄	#72343137	1	1	yes	characteristic
560	C₂	#72343251	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂	#72343251
commutator	C₂×#504	C₂³×C₄
Frattini, cosocle	#33326	C₂⁴
prime radical	#72216687	C₂²
LCS	G ▷ C₂×#504 ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×#131 ◁ #72287154 ◁ G
LECS	G ▷ #33326 ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72343278	C₂	semidirect
2. #72343256	C₂	semidirect
3. #72343254	C₂	semidirect
4. #72343103	C₂	semidirect
14. #72319036	C₂	semidirect
15. #72287615	C₂	semidirect
16. #72287606	C₂²	semidirect
17. #72287606	C₂²	semidirect
18. #72287460	C₂	semidirect
19. #72287432	C₂	semidirect
25. #72286411	C₂	semidirect
26. #72286336	C₂²	semidirect
27. #72286336	C₂²	semidirect
29. #72286252	C₂	semidirect
30. #72286160	C₂²	semidirect
31. #72286160	C₂²	semidirect
34. #72286111	C₂²	semidirect
35. #72286111	C₂²	semidirect
37. #72225122	C₂	semidirect
38. #72225121	C₂	semidirect
44. #72225025	C₂²	semidirect
45. #72225025	C₂²	semidirect
48. #72224979	C₂²	semidirect
49. #72224979	C₂²	semidirect
50. #72224951	C₂²	semidirect
51. #72224951	C₂²	semidirect
53. #72217219	C₂²	semidirect
54. #72217215	C₂²	semidirect

Maximal subgroups

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

subgroup	index
#72343278	2
#72343256	2
#72343254	2
#72343103	2
#72321495	2
#72319036	2
#72287615	2
#72287460	2
#72287432	2
#72287431	2
#72286411	2
#72286252	2
#72225122	2
#72225121	2
#72225045	2