Subgroups — #109836

Order 512.

780 conjugacy classes of subgroups.

The subgroup lattice has 563 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#1948	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
3	#10849	C₂	1	1	yes	maximal, characteristic
4	#10841	C₂	1	1	yes	maximal, characteristic
5	C₂×#1296	C₂	1	1	yes	maximal, characteristic
6	C₂×#1296	C₂	1	1	yes	maximal, characteristic
7	C₂×#1277	C₂	1	1	yes	maximal, characteristic
8	C₂²×#106	—	2	1	no	—
9	C₂²×C₄⋊C₈	C₂²	1	1	yes	characteristic
10	C₂²×C₄⋊C₈	C₂²	1	1	yes	characteristic
11	C₂²×C₄⋊C₈	C₂²	1	1	yes	characteristic
12	C₂²×C₄×C₈	—	2	1	no	—
13	C₂²×C₄×C₈	C₂²	1	1	yes	characteristic
14	C₂×#384	C₂²	1	1	yes	characteristic
15	C₂×#384	C₂²	1	1	yes	characteristic
16	C₂×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
17	#1948	—	2	2	no	—
18	#1948	C₄	1	4	yes	complemented
19	C₈×C₄⋊C₄	—	2	2	no	—
20	C₈×C₄⋊C₄	—	2	2	no	—
21	C₂×#340	—	2	1	no	—
22	C₂×#340	—	2	1	no	—
23	C₂×#340	—	2	1	no	—
24	C₂×#340	—	2	1	no	—
25	C₂×#340	—	2	1	no	—
26	C₂×#336	—	2	1	no	—
27	#1296	—	2	2	no	—
28	#1296	C₄	1	4	yes	complemented
29	#1277	C₄	1	4	yes	complemented
30	C₂³×C₈	—	2	1	no	—
31	C₂³×C₈	—	2	1	no	—
32	C₂³×C₈	—	2	1	no	—
33	C₂³×C₈	D₄	1	1	yes	characteristic
34	C₂³×C₈	D₄	1	1	yes	characteristic
35	C₂²×C₄⋊C₄	—	2	1	no	—
36	C₂²×C₄⋊C₄	—	2	1	no	—
37	C₂²×C₄⋊C₄	—	2	1	no	—
38	C₂²×C₄⋊C₄	—	2	1	no	—
39	C₂²×C₄⋊C₄	—	2	1	no	—
40	C₂²×C₄⋊C₄	—	2	1	no	—
41	C₂²×C₄⋊C₄	D₄	1	1	yes	characteristic
42	C₂²×C₄⋊C₄	D₄	1	1	yes	characteristic
43	C₂²×C₄²	—	2	1	no	—
44	C₂²×C₄²	C₂³	1	1	yes	characteristic
45	C₂×#106	—	2	4	no	—
46	C₂×#106	—	4	2	no	—
47	C₂×#106	—	4	2	no	—
48	C₂×C₄⋊C₈	—	2	1	no	—
49	C₂×C₄⋊C₈	—	2	1	no	—
50	C₂×C₄⋊C₈	—	2	1	no	—
51	C₂×C₄⋊C₈	—	2	1	no	—
52	C₂×C₄⋊C₈	—	2	1	no	—
53	C₂×C₄⋊C₈	—	2	1	no	—
54	C₂×C₄⋊C₈	—	2	1	no	—
55	C₂×C₄⋊C₈	—	2	1	no	—
56	C₂×C₄⋊C₈	—	2	1	no	—
57	C₂×C₄⋊C₈	—	2	1	no	—
58	C₂×C₄⋊C₈	—	2	1	no	—
59	C₂×C₄⋊C₈	C₂×C₄	1	2	yes	—
60	C₂×C₄⋊C₈	C₂×C₄	1	2	yes	—
61	C₂×C₄⋊C₈	C₂×C₄	1	2	yes	—
62	C₂×C₄⋊C₈	C₂×C₄	1	2	yes	—
63	C₂×C₄⋊C₈	C₂×C₄	1	2	yes	—
64	C₂×C₄⋊C₈	D₄	1	2	yes	—
65	C₂×C₄⋊C₈	Q₈	1	2	yes	—
66	C₂×C₄×C₈	—	2	1	no	—
67	C₂×C₄×C₈	—	2	1	no	—
68	C₂×C₄×C₈	—	2	1	no	—
69	C₂×C₄×C₈	—	2	1	no	—
70	C₂×C₄×C₈	—	2	4	no	—
71	C₂×C₄×C₈	—	4	2	no	—
72	C₂×C₄×C₈	—	4	2	no	—
73	C₂×C₄×C₈	C₂×C₄	1	2	yes	—
74	C₂×C₄×C₈	Q₈	1	2	yes	—
75	#384	—	2	1	no	—
76	#384	—	2	1	no	—
77	#384	—	2	1	no	—
78	#384	—	2	1	no	—
79	#384	—	2	1	no	—
80	#384	—	2	1	no	—
81	#384	C₂×C₄	1	2	yes	—
82	#384	C₂×C₄	1	2	yes	—
83	C₄×C₄⋊C₄	—	2	1	no	—
84	C₄×C₄⋊C₄	—	2	1	no	—
85	C₄×C₄⋊C₄	C₂×C₄	1	2	yes	—
86	C₄×C₄⋊C₄	D₄	1	2	yes	—
87	C₂×#95	—	2	1	no	—
88	#340	—	2	4	no	—
89	#340	—	4	2	no	—
90	#340	—	4	2	no	—
91	#340	—	4	2	no	—
92	#340	—	4	2	no	—
93	#336	—	2	4	no	—
94	C₂³×C₄	—	2	1	no	—
95	C₂³×C₄	—	2	1	no	—
96	C₂³×C₄	—	4	1	no	—
97	C₂³×C₄	—	4	1	no	—
98	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
99	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
100	C₂³×C₄	#41	1	1	yes	characteristic
101	C₂²×C₈	—	2	1	no	—
102	C₂²×C₈	—	2	1	no	—
103	C₂²×C₈	—	2	1	no	—
104	C₂²×C₈	—	2	1	no	—
105	C₂²×C₈	—	2	2	no	—
106	C₂²×C₈	—	2	2	no	—
107	C₂²×C₈	—	2	2	no	—
108	C₂²×C₈	—	2	2	no	—
109	C₂²×C₈	—	2	2	no	—
110	C₂²×C₈	—	2	1	no	—
111	C₂²×C₈	—	2	2	no	—
112	C₂²×C₈	—	2	1	no	—
113	C₂²×C₈	—	2	1	no	—
114	C₂²×C₈	—	2	1	no	—
115	C₂²×C₈	—	2	1	no	—
116	C₂²×C₈	—	2	1	no	—
117	C₂²×C₈	—	2	2	no	—
118	C₂²×C₈	—	4	1	no	—
119	C₂²×C₈	—	4	1	no	—
120	C₂²×C₈	—	4	1	no	—
121	C₂²×C₈	—	4	1	no	—
122	C₂²×C₈	—	4	1	no	—
123	C₂²×C₈	—	4	1	no	—
124	C₂²×C₈	—	4	1	no	—
125	C₂²×C₈	—	4	1	no	—
126	C₂²×C₈	—	4	1	no	—
127	C₂²×C₈	—	4	1	no	—
128	C₂²×C₈	—	4	1	no	—
129	C₂²×C₈	—	4	1	no	—
130	C₂²×C₈	—	4	1	no	—
131	C₂²×C₈	—	4	1	no	—
132	C₂²×C₈	C₄⋊C₄	1	2	yes	—
133	C₂²×C₈	C₄⋊C₄	1	2	yes	—
134	C₂²×C₈	SD₁₆	1	2	yes	—
135	C₂²×C₈	SD₁₆	1	2	yes	—
136	C₂×C₄⋊C₄	—	2	1	no	—
137	C₂×C₄⋊C₄	—	2	1	no	—
138	C₂×C₄⋊C₄	—	2	1	no	—
139	C₂×C₄⋊C₄	—	2	1	no	—
140	C₂×C₄⋊C₄	—	2	1	no	—
141	C₂×C₄⋊C₄	—	2	1	no	—
142	C₂×C₄⋊C₄	—	2	2	no	—
143	C₂×C₄⋊C₄	—	2	2	no	—
144	C₂×C₄⋊C₄	—	2	2	no	—
145	C₂×C₄⋊C₄	—	2	2	no	—
146	C₂×C₄⋊C₄	—	2	2	no	—
147	C₂×C₄⋊C₄	—	2	2	no	—
148	C₂×C₄⋊C₄	—	4	1	no	—
149	C₂×C₄⋊C₄	—	4	1	no	—
150	C₂×C₄⋊C₄	—	4	1	no	—
151	C₂×C₄⋊C₄	—	4	1	no	—
152	C₂×C₄⋊C₄	—	4	1	no	—
153	C₂×C₄⋊C₄	—	4	1	no	—
154	C₂×C₄⋊C₄	—	4	1	no	—
155	C₂×C₄⋊C₄	—	4	1	no	—
156	C₂×C₄⋊C₄	—	4	1	no	—
157	C₂×C₄⋊C₄	—	4	1	no	—
158	C₂×C₄⋊C₄	—	4	1	no	—
159	C₂×C₄⋊C₄	—	4	1	no	—
160	C₂×C₄⋊C₄	—	4	1	no	—
161	C₂×C₄⋊C₄	—	4	1	no	—
162	C₂×C₄⋊C₄	—	4	1	no	—
163	C₂×C₄⋊C₄	—	4	1	no	—
164	C₂×C₄⋊C₄	—	4	1	no	—
165	C₂×C₄⋊C₄	—	4	1	no	—
166	C₂×C₄⋊C₄	—	4	1	no	—
167	C₂×C₄⋊C₄	—	4	1	no	—
168	C₂×C₄⋊C₄	—	4	1	no	—
169	C₂×C₄⋊C₄	—	4	1	no	—
170	C₂×C₄⋊C₄	—	8	1	no	—
171	C₂×C₄⋊C₄	—	8	1	no	—
172	C₂×C₄⋊C₄	—	8	1	no	—
173	C₂×C₄⋊C₄	—	8	1	no	—
174	C₂×C₄⋊C₄	C₂²⋊C₄	1	2	yes	—
175	C₂×C₄⋊C₄	C₂²⋊C₄	1	2	yes	—
176	C₂×C₄⋊C₄	D₈	1	2	yes	—
177	C₂×C₄⋊C₄	SD₁₆	1	2	yes	—
178	C₂×C₄⋊C₄	SD₁₆	1	2	yes	—
179	C₂×C₄⋊C₄	Q₁₆	1	2	yes	—
180	C₂×C₄²	—	2	2	no	—
181	C₂×C₄²	—	2	2	no	—
182	C₂×C₄²	—	4	1	no	—
183	C₂×C₄²	—	4	1	no	—
184	C₂×C₄²	—	4	1	no	—
185	C₂×C₄²	—	4	1	no	—
186	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
187	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
188	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
189	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
190	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
191	C₂×C₄²	C₂×Q₈	1	1	yes	characteristic
192	C₂×C₄²	C₂×Q₈	1	1	yes	characteristic
193	C₂×C₄²	#41	1	1	yes	characteristic
194	C₂×C₄²	#41	1	1	yes	characteristic
195	C₂×C₄²	#41	1	1	yes	characteristic
196	C₂×C₄²	#41	1	1	yes	characteristic
197	C₂×C₄²	#41	1	1	yes	characteristic
198	#106	—	4	8	no	—
199	C₄⋊C₈	—	2	2	no	—
200	C₄⋊C₈	—	2	2	no	—
201	C₄⋊C₈	—	2	2	no	—
202	C₄⋊C₈	—	2	2	no	—
203	C₄⋊C₈	—	2	2	no	—
204	C₄⋊C₈	—	2	2	no	—
205	C₄⋊C₈	—	2	2	no	—
206	C₄⋊C₈	—	2	2	no	—
207	C₄⋊C₈	—	4	1	no	—
208	C₄⋊C₈	—	4	1	no	—
209	C₄⋊C₈	C₄²	1	4	yes	—
210	C₄⋊C₈	C₄⋊C₄	1	4	yes	—
211	C₄×C₈	—	2	2	no	—
212	C₄×C₈	—	2	2	no	—
213	C₄×C₈	—	2	2	no	—
214	C₄×C₈	—	2	2	no	—
215	C₄×C₈	—	4	8	no	—
216	#95	—	2	2	no	—
217	#95	—	2	2	no	—
218	C₂⁴	#121	1	1	yes	characteristic
219	C₂²×C₄	—	2	1	no	—
220	C₂²×C₄	—	2	1	no	—
221	C₂²×C₄	—	2	1	no	—
222	C₂²×C₄	—	2	1	no	—
223	C₂²×C₄	—	2	2	no	—
224	C₂²×C₄	—	2	2	no	—
225	C₂²×C₄	—	2	2	no	—
226	C₂²×C₄	—	2	2	no	—
227	C₂²×C₄	—	2	2	no	—
228	C₂²×C₄	—	2	2	no	—
229	C₂²×C₄	—	4	1	no	—
230	C₂²×C₄	—	4	1	no	—
231	C₂²×C₄	—	4	1	no	—
232	C₂²×C₄	—	4	1	no	—
233	C₂²×C₄	—	4	1	no	—
234	C₂²×C₄	—	4	1	no	—
235	C₂²×C₄	—	4	1	no	—
236	C₂²×C₄	—	4	1	no	—
237	C₂²×C₄	—	4	2	no	—
238	C₂²×C₄	—	4	2	no	—
239	C₂²×C₄	—	8	1	no	—
240	C₂²×C₄	—	8	1	no	—
241	C₂²×C₄	—	8	1	no	—
242	C₂²×C₄	—	8	1	no	—
243	C₂²×C₄	—	8	1	no	—
244	C₂²×C₄	—	8	1	no	—
245	C₂²×C₄	—	8	1	no	—
246	C₂²×C₄	—	8	1	no	—
247	C₂²×C₄	—	8	1	no	—
248	C₂²×C₄	—	8	1	no	—
249	C₂²×C₄	—	8	1	no	—
250	C₂²×C₄	—	8	1	no	—
251	C₂²×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
252	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
253	C₂²×C₄	#117	1	1	yes	characteristic
254	C₂²×C₄	C₄×D₄	1	1	yes	characteristic
255	C₂²×C₄	C₄×D₄	1	1	yes	characteristic
256	C₂²×C₄	C₄×D₄	1	1	yes	characteristic
257	C₂²×C₄	C₄×D₄	1	1	yes	characteristic
258	C₂²×C₄	C₄×D₄	1	1	yes	characteristic
259	C₂²×C₄	C₄×Q₈	1	1	yes	characteristic
260	C₂²×C₄	#120	1	1	yes	characteristic
261	C₂²×C₄	#121	1	1	yes	characteristic
262	C₂²×C₄	C₂²⋊Q₈	1	1	yes	characteristic
263	C₂²×C₄	#123	1	1	yes	characteristic
264	C₂²×C₄	#123	1	1	yes	characteristic
265	C₂²×C₄	#124	1	1	yes	characteristic
266	C₂²×C₄	#125	1	1	yes	characteristic
267	C₂²×C₄	#126	1	1	yes	characteristic
268	C₂²×C₄	C₄⋊Q₈	1	1	yes	characteristic
269	C₂²×C₄	C₂×D₈	1	1	yes	characteristic
270	C₂²×C₄	C₂×SD₁₆	1	1	yes	characteristic
271	C₂²×C₄	C₂×SD₁₆	1	1	yes	characteristic
272	C₂²×C₄	C₂×SD₁₆	1	1	yes	characteristic
273	C₂²×C₄	C₂×SD₁₆	1	1	yes	characteristic
274	C₂²×C₄	C₂×Q₁₆	1	1	yes	characteristic
275	C₂²×C₄	#135	1	1	yes	characteristic
276	C₂²×C₄	#135	1	1	yes	characteristic
277	C₂²×C₄	#135	1	1	yes	characteristic
278	C₂²×C₄	#135	1	1	yes	characteristic
279	C₂²×C₄	#135	1	1	yes	characteristic
280	C₂²×C₄	#135	1	1	yes	characteristic
281	C₂²×C₄	AGL(1,ℤ/8)	1	1	yes	characteristic
282	C₂²×C₄	AGL(1,ℤ/8)	1	1	yes	characteristic
283	C₂²×C₄	#137	1	1	yes	characteristic
284	C₂²×C₄	#137	1	1	yes	characteristic
285	C₂×C₈	—	2	2	no	—
286	C₂×C₈	—	2	2	no	—
287	C₂×C₈	—	2	2	no	—
288	C₂×C₈	—	2	2	no	—
289	C₂×C₈	—	2	2	no	—
290	C₂×C₈	—	2	2	no	—
291	C₂×C₈	—	2	4	no	—
292	C₂×C₈	—	2	2	no	—
293	C₂×C₈	—	2	4	no	—
294	C₂×C₈	—	2	2	no	—
295	C₂×C₈	—	2	2	no	—
296	C₂×C₈	—	4	2	no	—
297	C₂×C₈	—	4	2	no	—
298	C₂×C₈	—	4	2	no	—
299	C₂×C₈	—	4	2	no	—
300	C₂×C₈	—	4	2	no	—
301	C₂×C₈	—	4	2	no	—
302	C₂×C₈	—	4	2	no	—
303	C₂×C₈	—	4	2	no	—
304	C₂×C₈	—	4	1	no	—
305	C₂×C₈	—	4	2	no	—
306	C₂×C₈	—	4	2	no	—
307	C₂×C₈	—	4	1	no	—
308	C₂×C₈	—	4	2	no	—
309	C₂×C₈	—	4	2	no	—
310	C₂×C₈	—	4	1	no	—
311	C₂×C₈	—	4	1	no	—
312	C₂×C₈	—	4	2	no	—
313	C₂×C₈	—	4	2	no	—
314	C₂×C₈	—	4	2	no	—
315	C₂×C₈	—	8	1	no	—
316	C₂×C₈	—	8	1	no	—
317	C₂×C₈	—	8	1	no	—
318	C₂×C₈	—	8	1	no	—
319	C₂×C₈	#106	1	4	yes	complemented
320	C₄⋊C₄	—	2	2	no	—
321	C₄⋊C₄	—	2	2	no	—
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	—	2	2	no	—
324	C₄⋊C₄	—	2	2	no	—
325	C₄⋊C₄	—	2	2	no	—
326	C₄⋊C₄	—	4	2	no	—
327	C₄⋊C₄	—	4	2	no	—
328	C₄⋊C₄	—	4	2	no	—
329	C₄⋊C₄	—	4	2	no	—
330	C₄⋊C₄	—	4	2	no	—
331	C₄⋊C₄	—	4	2	no	—
332	C₄⋊C₄	—	4	2	no	—
333	C₄⋊C₄	—	4	2	no	—
334	C₄⋊C₄	—	8	2	no	—
335	C₄⋊C₄	—	8	2	no	—
336	C₄⋊C₄	—	8	2	no	—
337	C₄⋊C₄	—	8	2	no	—
338	C₄⋊C₄	—	8	1	no	—
339	C₄⋊C₄	—	8	1	no	—
340	C₄⋊C₄	—	8	1	no	—
341	C₄⋊C₄	—	8	1	no	—
342	C₄⋊C₄	—	8	1	no	—
343	C₄⋊C₄	—	8	1	no	—
344	C₄⋊C₄	—	8	1	no	—
345	C₄⋊C₄	—	8	1	no	—
346	C₄⋊C₄	#102	1	4	yes	—
347	C₄⋊C₄	#103	1	4	yes	—
348	C₄²	—	4	2	no	—
349	C₄²	—	4	2	no	—
350	C₄²	—	4	2	no	—
351	C₄²	—	4	2	no	—
352	C₄²	C₂×C₄²	1	1	yes	characteristic
353	C₄²	C₂×C₄⋊C₄	1	1	yes	characteristic
354	C₄²	#117	1	1	yes	characteristic
355	C₄²	#117	1	1	yes	characteristic
356	C₄²	C₄×D₄	1	1	yes	characteristic
357	C₄²	C₄×D₄	1	1	yes	characteristic
358	C₄²	C₄×D₄	1	1	yes	characteristic
359	C₄²	C₄×Q₈	1	1	yes	characteristic
360	C₄²	C₄×Q₈	1	1	yes	characteristic
361	C₄²	C₄×Q₈	1	1	yes	characteristic
362	C₄²	C₂²⋊Q₈	1	1	yes	characteristic
363	C₄²	C₂²⋊Q₈	1	1	yes	characteristic
364	C₄²	C₂²⋊Q₈	1	1	yes	characteristic
365	C₄²	#123	1	1	yes	characteristic
366	C₄²	#125	1	1	yes	characteristic
367	C₄²	#126	1	1	yes	characteristic
368	C₂³	#386	1	1	yes	characteristic
369	C₂³	#388	1	1	yes	characteristic
370	C₂³	#389	1	1	yes	characteristic
371	C₂³	#460	1	1	yes	characteristic
372	C₂³	#461	1	1	yes	characteristic
373	C₂³	#463	1	1	yes	characteristic
374	C₂³	#464	1	1	yes	characteristic
375	C₂³	#465	1	1	yes	characteristic
376	C₂³	#465	1	1	yes	characteristic
377	C₂³	#466	1	1	yes	characteristic
378	C₂³	#467	1	1	yes	characteristic
379	C₂³	#471	1	1	yes	characteristic
380	C₂³	#471	1	1	yes	characteristic
381	C₂³	#472	1	1	yes	characteristic
382	C₂³	#473	1	1	yes	characteristic
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	4	no	—
396	C₂×C₄	—	2	4	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	8	2	no	—
410	C₂×C₄	—	8	2	no	—
411	C₂×C₄	—	8	2	no	—
412	C₂×C₄	—	8	2	no	—
413	C₂×C₄	—	8	2	no	—
414	C₂×C₄	—	8	2	no	—
415	C₂×C₄	—	16	1	no	—
416	C₂×C₄	—	16	1	no	—
417	C₂×C₄	—	16	1	no	—
418	C₂×C₄	—	16	1	no	—
419	C₂×C₄	—	16	1	no	—
420	C₂×C₄	—	16	1	no	—
421	C₂×C₄	—	16	1	no	—
422	C₂×C₄	—	16	1	no	—
423	C₂×C₄	C₄×C₂²⋊C₄	1	1	yes	characteristic
424	C₂×C₄	C₄×C₄⋊C₄	1	1	yes	characteristic
425	C₂×C₄	C₄×C₄⋊C₄	1	1	yes	characteristic
426	C₂×C₄	#385	1	1	yes	characteristic
427	C₂×C₄	#385	1	1	yes	characteristic
428	C₂×C₄	#387	1	1	yes	characteristic
429	C₂×C₄	#387	1	1	yes	characteristic
430	C₂×C₄	#387	1	1	yes	characteristic
431	C₂×C₄	#387	1	1	yes	characteristic
432	C₂×C₄	#388	1	1	yes	characteristic
433	C₂×C₄	#389	1	1	yes	characteristic
434	C₂×C₄	#391	1	1	yes	characteristic
435	C₂×C₄	C₂×#102	1	1	yes	characteristic
436	C₂×C₄	C₂×#103	1	1	yes	characteristic
437	C₂×C₄	#416	1	1	yes	characteristic
438	C₂×C₄	#416	1	1	yes	characteristic
439	C₂×C₄	C₂×#106	1	1	yes	characteristic
440	C₂×C₄	#427	1	1	yes	characteristic
441	C₂×C₄	#428	1	1	yes	characteristic
442	C₂×C₄	#428	1	1	yes	characteristic
443	C₂×C₄	C₄×D₈	1	1	yes	characteristic
444	C₂×C₄	C₄×D₈	1	1	yes	characteristic
445	C₂×C₄	C₄×SD₁₆	1	1	yes	characteristic
446	C₂×C₄	C₄×SD₁₆	1	1	yes	characteristic
447	C₂×C₄	C₄×SD₁₆	1	1	yes	characteristic
448	C₂×C₄	C₄×SD₁₆	1	1	yes	characteristic
449	C₂×C₄	C₄×SD₁₆	1	1	yes	characteristic
450	C₂×C₄	C₄×SD₁₆	1	1	yes	characteristic
451	C₂×C₄	C₄×SD₁₆	1	1	yes	characteristic
452	C₂×C₄	C₄×SD₁₆	1	1	yes	characteristic
453	C₂×C₄	C₄×Q₁₆	1	1	yes	characteristic
454	C₂×C₄	C₄×Q₁₆	1	1	yes	characteristic
455	C₂×C₄	#440	1	1	yes	characteristic
456	C₂×C₄	#440	1	1	yes	characteristic
457	C₂×C₄	#441	1	1	yes	characteristic
458	C₂×C₄	#442	1	1	yes	characteristic
459	C₂×C₄	#448	1	1	yes	characteristic
460	C₂×C₄	#449	1	1	yes	characteristic
461	C₂×C₄	#450	1	1	yes	characteristic
462	C₂×C₄	#452	1	1	yes	characteristic
463	C₂×C₄	#465	1	1	yes	characteristic
464	C₂×C₄	#465	1	1	yes	characteristic
465	C₂×C₄	#466	1	1	yes	characteristic
466	C₂×C₄	#467	1	1	yes	characteristic
467	C₂×C₄	#475	1	1	yes	characteristic
468	C₂×C₄	#476	1	1	yes	characteristic
469	C₂×C₄	#478	1	1	yes	characteristic
470	C₂×C₄	#479	1	1	yes	characteristic
471	C₂×C₄	#481	1	1	yes	characteristic
472	C₂×C₄	#482	1	1	yes	characteristic
473	C₂×C₄	#483	1	1	yes	characteristic
474	C₂×C₄	#485	1	1	yes	characteristic
475	C₂×C₄	#486	1	1	yes	characteristic
476	C₂×C₄	#487	1	1	yes	characteristic
477	C₂×C₄	#488	1	1	yes	characteristic
478	C₂×C₄	#488	1	1	yes	characteristic
479	C₂×C₄	#498	1	1	yes	characteristic
480	C₂×C₄	#499	1	1	yes	characteristic
481	C₂×C₄	#499	1	1	yes	characteristic
482	C₂×C₄	#500	1	1	yes	characteristic
483	C₈	—	2	4	no	—
484	C₈	—	4	2	no	—
485	C₈	—	4	4	no	—
486	C₈	—	4	4	no	—
487	C₈	—	8	2	no	—
488	C₂²	#1436	1	1	yes	characteristic
489	C₂²	#1666	1	1	yes	characteristic
490	C₂²	#1666	1	1	yes	characteristic
491	C₂²	#1668	1	1	yes	characteristic
492	C₂²	#1670	1	1	yes	characteristic
493	C₂²	#1671	1	1	yes	characteristic
494	C₂²	#1671	1	1	yes	characteristic
495	C₂²	#1673	1	1	yes	characteristic
496	C₂²	#1675	1	1	yes	characteristic
497	C₂²	#1677	1	1	yes	characteristic
498	C₂²	#1678	1	1	yes	characteristic
499	C₂²	#1679	1	1	yes	characteristic
500	C₂²	#1680	1	1	yes	characteristic
501	C₂²	#1681	1	1	yes	characteristic
502	C₂²	#1682	1	1	yes	characteristic
503	C₂²	#1683	1	1	yes	characteristic
504	C₂²	#1684	1	1	yes	characteristic
505	C₂²	#1877	1	1	yes	characteristic
506	C₂²	#1880	1	1	yes	characteristic
507	C₂²	#1892	1	1	yes	characteristic
508	C₂²	#1893	1	1	yes	characteristic
509	C₂²	#1907	1	1	yes	characteristic
510	C₂²	#1908	1	1	yes	characteristic
511	C₂²	#1926	1	1	yes	characteristic
512	C₂²	#1927	1	1	yes	characteristic
513	C₂²	#1930	1	1	yes	characteristic
514	C₂²	#1931	1	1	yes	characteristic
515	C₂²	#1933	1	1	yes	characteristic
516	C₂²	#1934	1	1	yes	characteristic
517	C₂²	#1941	1	1	yes	characteristic
518	C₂²	#1942	1	1	yes	characteristic
519	C₂²	#1948	1	1	yes	characteristic
520	C₂²	#1949	1	1	yes	characteristic
521	C₂²	#1951	1	1	yes	characteristic
522	C₂²	#1952	1	1	yes	characteristic
523	C₄	—	2	1	no	—
524	C₄	—	2	1	no	—
525	C₄	—	2	1	no	—
526	C₄	—	2	1	no	—
527	C₄	—	4	4	no	—
528	C₄	—	4	4	no	—
529	C₄	—	16	2	no	—
530	C₄	—	16	2	no	—
531	C₄	C₄×#102	1	1	yes	characteristic
532	C₄	C₄×#103	1	1	yes	characteristic
533	C₄	C₄×#106	1	1	yes	characteristic
534	C₄	#1776	1	1	yes	characteristic
535	C₄	#1853	1	1	yes	characteristic
536	C₄	#1854	1	1	yes	characteristic
537	C₄	#1864	1	1	yes	characteristic
538	C₄	#1865	1	1	yes	characteristic
539	C₄	#1919	1	1	yes	characteristic
540	C₄	#1920	1	1	yes	characteristic
541	C₄	#1933	1	1	yes	characteristic
542	C₄	#1934	1	1	yes	characteristic
543	C₄	#1941	1	1	yes	characteristic
544	C₄	#1942	1	1	yes	characteristic
545	C₄	#1990	1	1	yes	characteristic
546	C₄	#1991	1	1	yes	characteristic
547	C₂	#9215	1	1	yes	characteristic
548	C₂	#9217	1	1	yes	characteristic
549	C₂	#9220	1	1	yes	characteristic
550	C₂	#9222	1	1	yes	characteristic
551	C₂	#9562	1	1	yes	characteristic
552	C₂	#9564	1	1	yes	characteristic
553	C₂	#9565	1	1	yes	characteristic
554	C₂	#9567	1	1	yes	characteristic
555	C₂	#9612	1	1	yes	characteristic
556	C₂	#9613	1	1	yes	characteristic
557	C₂	#9615	1	1	yes	characteristic
558	C₂	#9616	1	1	yes	characteristic
559	C₂	#10880	1	1	yes	characteristic
560	C₂	#10896	1	1	yes	characteristic
561	C₂	#10908	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂⁴	#121
commutator	C₄²	C₂×C₄²
Frattini, cosocle	C₂²×C₄²	C₂³
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄² ◁ G
LECS	G ▷ C₂²×C₄² ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
18. #1948	C₄	semidirect
28. #1296	C₄	semidirect
29. #1277	C₄	semidirect
319. C₂×C₈	#106	semidirect

Maximal subgroups

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

subgroup	index
C₂×#1948	2
C₂×C₈×C₄⋊C₄	2
#10849	2
#10841	2
C₂×#1296	2
C₂×#1277	2