Subgroups — #147248

Order 512.

652 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#367	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#107	C₂	1	1	yes	maximal, characteristic
3	C₂×#1380	C₂	1	1	yes	maximal, characteristic
4	C₂×#1380	C₂	1	1	yes	maximal, characteristic
5	C₂×#1380	C₂	1	1	yes	maximal, characteristic
6	C₂×#1374	C₂	1	1	yes	maximal, characteristic
7	#10862	C₂	1	1	yes	maximal, characteristic
8	C₂³×C₁₆	C₂²	1	1	yes	characteristic
9	C₂³×C₁₆	C₂²	1	1	yes	characteristic
10	C₂²×#107	C₂²	1	1	yes	characteristic
11	C₂²×#107	C₂²	1	1	yes	characteristic
12	C₂²×#107	C₂²	1	1	yes	characteristic
13	C₂²×#107	C₂²	1	1	yes	characteristic
14	C₂²×C₄×C₈	C₂²	1	1	yes	characteristic
15	C₂×C₄×C₄⋊C₄	—	2	1	no	—
16	C₂×#367	—	2	2	no	—
17	C₂×#367	—	2	2	no	—
18	C₂×#367	C₄	1	4	yes	complemented
19	C₄×#107	—	2	2	no	—
20	C₄×#107	—	2	2	no	—
21	C₂×#340	—	2	1	no	—
22	C₂×#340	—	2	1	no	—
23	C₄⋊#95	—	2	1	no	—
24	#1380	—	2	2	no	—
25	#1380	—	2	2	no	—
26	#1380	C₄	1	4	yes	complemented
27	#1374	C₄	1	4	yes	complemented
28	C₂³×C₈	D₄	1	1	yes	characteristic
29	C₂³×C₈	C₂³	1	1	yes	characteristic
30	C₂²×C₄⋊C₄	—	2	1	no	—
31	C₂²×C₄⋊C₄	—	2	1	no	—
32	C₂²×C₄⋊C₄	—	2	1	no	—
33	C₂²×C₄⋊C₄	—	2	1	no	—
34	C₂²×C₄²	—	4	1	no	—
35	C₂²×C₄²	D₄	1	1	yes	characteristic
36	C₂²×C₁₆	—	2	1	no	—
37	C₂²×C₁₆	—	2	1	no	—
38	C₂²×C₁₆	—	2	1	no	—
39	C₂²×C₁₆	—	2	1	no	—
40	C₂²×C₁₆	—	2	1	no	—
41	C₂²×C₁₆	—	2	1	no	—
42	C₂²×C₁₆	—	2	1	no	—
43	C₂²×C₁₆	—	2	1	no	—
44	C₂²×C₁₆	—	2	1	no	—
45	C₂²×C₁₆	—	2	1	no	—
46	C₂²×C₁₆	C₂×C₄	1	2	yes	—
47	C₂²×C₁₆	C₂×C₄	1	2	yes	—
48	C₂²×C₁₆	C₂×C₄	1	2	yes	—
49	C₂²×C₁₆	C₂×C₄	1	2	yes	—
50	C₂×#107	—	2	1	no	—
51	C₂×#107	—	2	1	no	—
52	C₂×#107	—	2	1	no	—
53	C₂×#107	—	2	1	no	—
54	C₂×#107	—	2	1	no	—
55	C₂×#107	—	2	1	no	—
56	C₂×#107	—	2	1	no	—
57	C₂×#107	—	2	1	no	—
58	C₂×#107	—	2	1	no	—
59	C₂×#107	—	2	1	no	—
60	C₂×#107	—	2	1	no	—
61	C₂×#107	—	2	1	no	—
62	C₂×#107	—	2	1	no	—
63	C₂×#107	—	2	1	no	—
64	C₂×#107	—	2	1	no	—
65	C₂×#107	—	2	1	no	—
66	C₂×#107	C₂×C₄	1	2	yes	—
67	C₂×#107	C₂×C₄	1	2	yes	—
68	C₂×#107	C₂×C₄	1	2	yes	—
69	C₂×#107	C₂×C₄	1	2	yes	—
70	C₂×#107	D₄	1	2	yes	—
71	C₂×#107	D₄	1	2	yes	—
72	C₂×#107	D₄	1	2	yes	—
73	C₂×#107	Q₈	1	2	yes	—
74	C₂×C₄×C₈	—	2	1	no	—
75	C₂×C₄×C₈	—	2	1	no	—
76	C₂×C₄×C₈	—	2	1	no	—
77	C₂×C₄×C₈	—	2	1	no	—
78	C₂×C₄×C₈	C₂×C₄	1	2	yes	—
79	C₂×C₄×C₈	Q₈	1	2	yes	—
80	C₄×C₄⋊C₄	—	2	4	no	—
81	C₄×C₄⋊C₄	—	4	2	no	—
82	C₂×#95	—	4	1	no	—
83	C₂×#95	—	4	1	no	—
84	C₂×#95	—	4	1	no	—
85	#367	—	2	8	no	—
86	#340	—	2	4	no	—
87	#340	—	4	2	no	—
88	C₂³×C₄	—	4	1	no	—
89	C₂³×C₄	—	4	1	no	—
90	C₂³×C₄	—	4	1	no	—
91	C₂³×C₄	—	4	1	no	—
92	C₂³×C₄	D₈	1	1	yes	characteristic
93	C₂³×C₄	D₈	1	1	yes	characteristic
94	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₈	—	2	1	no	—
96	C₂²×C₈	—	2	1	no	—
97	C₂²×C₈	—	2	1	no	—
98	C₂²×C₈	—	2	1	no	—
99	C₂²×C₈	—	2	1	no	—
100	C₂²×C₈	—	2	1	no	—
101	C₂²×C₈	C₄⋊C₄	1	2	yes	—
102	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₈	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₈	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₈	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₈	C₂×Q₈	1	1	yes	characteristic
109	C₂²×C₈	C₂×Q₈	1	1	yes	characteristic
110	C₂²×C₈	#41	1	1	yes	characteristic
111	C₂²×C₈	#41	1	1	yes	characteristic
112	C₂²×C₈	#41	1	1	yes	characteristic
113	C₂²×C₈	#41	1	1	yes	characteristic
114	C₂²×C₈	#41	1	1	yes	characteristic
115	C₂²×C₈	#41	1	1	yes	characteristic
116	C₂×C₄⋊C₄	—	2	2	no	—
117	C₂×C₄⋊C₄	—	2	2	no	—
118	C₂×C₄⋊C₄	—	2	2	no	—
119	C₂×C₄⋊C₄	—	2	2	no	—
120	C₂×C₄⋊C₄	—	2	2	no	—
121	C₂×C₄⋊C₄	—	2	2	no	—
122	C₂×C₄⋊C₄	—	2	2	no	—
123	C₂×C₄⋊C₄	—	2	2	no	—
124	C₂×C₄⋊C₄	—	4	1	no	—
125	C₂×C₄⋊C₄	—	4	1	no	—
126	C₂×C₄⋊C₄	—	4	1	no	—
127	C₂×C₄⋊C₄	—	4	1	no	—
128	C₂×C₄⋊C₄	—	4	1	no	—
129	C₂×C₄⋊C₄	—	4	1	no	—
130	C₂×C₄⋊C₄	—	4	1	no	—
131	C₂×C₄⋊C₄	—	4	1	no	—
132	C₂×C₄⋊C₄	—	4	1	no	—
133	C₂×C₄⋊C₄	—	4	1	no	—
134	C₂×C₄⋊C₄	—	4	1	no	—
135	C₂×C₄⋊C₄	—	4	1	no	—
136	C₂×C₄⋊C₄	—	4	1	no	—
137	C₂×C₄⋊C₄	—	4	1	no	—
138	C₂×C₄⋊C₄	—	4	1	no	—
139	C₂×C₄⋊C₄	—	4	1	no	—
140	C₂×C₄²	—	2	1	no	—
141	C₂×C₄²	—	2	1	no	—
142	C₂×C₄²	—	2	1	no	—
143	C₂×C₄²	—	2	1	no	—
144	C₂×C₄²	—	4	4	no	—
145	C₂×C₄²	—	8	2	no	—
146	C₂×C₄²	—	8	2	no	—
147	C₂×C₄²	C₄⋊C₄	1	2	yes	—
148	C₂×C₄²	Q₁₆	1	2	yes	—
149	C₂×C₁₆	—	2	2	no	—
150	C₂×C₁₆	—	2	2	no	—
151	C₂×C₁₆	—	2	2	no	—
152	C₂×C₁₆	—	2	2	no	—
153	C₂×C₁₆	—	2	2	no	—
154	C₂×C₁₆	—	2	2	no	—
155	C₂×C₁₆	—	2	2	no	—
156	C₂×C₁₆	—	2	2	no	—
157	C₂×C₁₆	—	2	2	no	—
158	C₂×C₁₆	—	4	1	no	—
159	C₂×C₁₆	—	4	1	no	—
160	C₂×C₁₆	—	4	1	no	—
161	C₂×C₁₆	—	4	1	no	—
162	C₂×C₁₆	C₄²	1	4	yes	complemented
163	#107	—	2	2	no	—
164	#107	—	2	2	no	—
165	#107	—	2	2	no	—
166	#107	—	2	2	no	—
167	#107	—	2	2	no	—
168	#107	—	2	2	no	—
169	#107	—	2	2	no	—
170	#107	—	2	2	no	—
171	#107	—	2	2	no	—
172	#107	—	2	2	no	—
173	#107	—	4	1	no	—
174	#107	—	4	1	no	—
175	#107	—	4	1	no	—
176	#107	—	4	1	no	—
177	#107	C₂²⋊C₄	1	4	yes	—
178	#107	C₄⋊C₄	1	4	yes	—
179	C₄×C₈	—	2	2	no	—
180	C₄×C₈	—	2	2	no	—
181	C₄×C₈	—	2	2	no	—
182	C₄×C₈	—	2	2	no	—
183	#95	—	4	4	no	—
184	#95	—	8	2	no	—
185	#95	—	8	2	no	—
186	C₂⁴	C₂×D₈	1	1	yes	characteristic
187	C₂²×C₄	—	2	1	no	—
188	C₂²×C₄	—	2	1	no	—
189	C₂²×C₄	—	2	1	no	—
190	C₂²×C₄	—	2	1	no	—
191	C₂²×C₄	—	2	1	no	—
192	C₂²×C₄	—	2	1	no	—
193	C₂²×C₄	—	2	1	no	—
194	C₂²×C₄	—	2	1	no	—
195	C₂²×C₄	—	2	1	no	—
196	C₂²×C₄	—	2	1	no	—
197	C₂²×C₄	—	4	2	no	—
198	C₂²×C₄	—	4	2	no	—
199	C₂²×C₄	—	4	2	no	—
200	C₂²×C₄	—	4	2	no	—
201	C₂²×C₄	—	4	2	no	—
202	C₂²×C₄	—	4	2	no	—
203	C₂²×C₄	—	4	2	no	—
204	C₂²×C₄	—	4	2	no	—
205	C₂²×C₄	—	8	1	no	—
206	C₂²×C₄	—	8	1	no	—
207	C₂²×C₄	—	8	1	no	—
208	C₂²×C₄	—	8	1	no	—
209	C₂²×C₄	—	8	1	no	—
210	C₂²×C₄	—	8	1	no	—
211	C₂²×C₄	—	8	1	no	—
212	C₂²×C₄	—	8	1	no	—
213	C₂²×C₄	—	8	1	no	—
214	C₂²×C₄	—	8	1	no	—
215	C₂²×C₄	—	8	1	no	—
216	C₂²×C₄	—	8	1	no	—
217	C₂²×C₄	—	8	1	no	—
218	C₂²×C₄	—	8	1	no	—
219	C₂²×C₄	—	8	1	no	—
220	C₂²×C₄	—	8	1	no	—
221	C₂²×C₄	—	8	1	no	—
222	C₂²×C₄	—	8	1	no	—
223	C₂²×C₄	—	8	1	no	—
224	C₂²×C₄	—	8	1	no	—
225	C₂²×C₄	#107	1	2	yes	—
226	C₂²×C₄	#107	1	2	yes	—
227	C₂²×C₄	SD₃₂	1	2	yes	—
228	C₂²×C₄	SD₃₂	1	2	yes	—
229	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
230	C₂²×C₄	C₄×D₄	1	1	yes	characteristic
231	C₂²×C₄	C₄×D₄	1	1	yes	characteristic
232	C₂²×C₄	#120	1	1	yes	characteristic
233	C₂²×C₄	#121	1	1	yes	characteristic
234	C₂²×C₄	C₂²⋊Q₈	1	1	yes	characteristic
235	C₂²×C₄	#123	1	1	yes	characteristic
236	C₂²×C₄	C₂×Q₁₆	1	1	yes	characteristic
237	C₂²×C₄	#135	1	1	yes	characteristic
238	C₂²×C₄	#135	1	1	yes	characteristic
239	C₂²×C₄	AGL(1,ℤ/8)	1	1	yes	characteristic
240	C₂²×C₄	AGL(1,ℤ/8)	1	1	yes	characteristic
241	C₂²×C₄	#137	1	1	yes	characteristic
242	C₂²×C₄	#137	1	1	yes	characteristic
243	C₂×C₈	—	2	2	no	—
244	C₂×C₈	—	2	2	no	—
245	C₂×C₈	—	2	2	no	—
246	C₂×C₈	—	4	1	no	—
247	C₂×C₈	—	4	1	no	—
248	C₂×C₈	—	4	1	no	—
249	C₂×C₈	—	4	1	no	—
250	C₂×C₈	C₂×C₄²	1	1	yes	characteristic
251	C₂×C₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
252	C₂×C₈	C₂×C₄⋊C₄	1	1	yes	characteristic
253	C₂×C₈	#117	1	1	yes	characteristic
254	C₂×C₈	#117	1	1	yes	characteristic
255	C₂×C₈	#117	1	1	yes	characteristic
256	C₂×C₈	C₄×D₄	1	1	yes	characteristic
257	C₂×C₈	C₄×D₄	1	1	yes	characteristic
258	C₂×C₈	C₄×D₄	1	1	yes	characteristic
259	C₂×C₈	C₄×D₄	1	1	yes	characteristic
260	C₂×C₈	C₄×D₄	1	1	yes	characteristic
261	C₂×C₈	C₄×D₄	1	1	yes	characteristic
262	C₂×C₈	C₄×Q₈	1	1	yes	characteristic
263	C₂×C₈	C₄×Q₈	1	1	yes	characteristic
264	C₂×C₈	C₄×Q₈	1	1	yes	characteristic
265	C₂×C₈	C₄×Q₈	1	1	yes	characteristic
266	C₂×C₈	#121	1	1	yes	characteristic
267	C₂×C₈	C₂²⋊Q₈	1	1	yes	characteristic
268	C₂×C₈	C₂²⋊Q₈	1	1	yes	characteristic
269	C₂×C₈	C₂²⋊Q₈	1	1	yes	characteristic
270	C₂×C₈	#123	1	1	yes	characteristic
271	C₂×C₈	#123	1	1	yes	characteristic
272	C₂×C₈	#124	1	1	yes	characteristic
273	C₂×C₈	#125	1	1	yes	characteristic
274	C₂×C₈	#125	1	1	yes	characteristic
275	C₂×C₈	#126	1	1	yes	characteristic
276	C₂×C₈	#126	1	1	yes	characteristic
277	C₂×C₈	C₄⋊Q₈	1	1	yes	characteristic
278	C₄⋊C₄	—	2	4	no	—
279	C₄⋊C₄	—	2	4	no	—
280	C₄⋊C₄	—	4	2	no	—
281	C₄⋊C₄	—	4	2	no	—
282	C₄⋊C₄	—	4	2	no	—
283	C₄⋊C₄	—	4	2	no	—
284	C₄⋊C₄	—	4	2	no	—
285	C₄⋊C₄	—	4	2	no	—
286	C₄⋊C₄	—	4	2	no	—
287	C₄⋊C₄	—	4	2	no	—
288	C₄⋊C₄	—	4	2	no	—
289	C₄⋊C₄	—	4	2	no	—
290	C₄⋊C₄	—	8	1	no	—
291	C₄⋊C₄	—	8	1	no	—
292	C₄⋊C₄	—	8	1	no	—
293	C₄⋊C₄	—	8	1	no	—
294	C₄²	—	2	2	no	—
295	C₄²	—	2	2	no	—
296	C₄²	—	2	2	no	—
297	C₄²	—	2	2	no	—
298	C₄²	—	8	8	no	—
299	C₁₆	—	2	4	no	—
300	C₁₆	—	4	2	no	—
301	C₂³	C₂×#107	1	1	yes	characteristic
302	C₂³	C₄×D₈	1	1	yes	characteristic
303	C₂³	C₄×D₈	1	1	yes	characteristic
304	C₂³	#447	1	1	yes	characteristic
305	C₂³	#459	1	1	yes	characteristic
306	C₂³	#474	1	1	yes	characteristic
307	C₂³	#480	1	1	yes	characteristic
308	C₂³	C₂×SD₃₂	1	1	yes	characteristic
309	C₂³	C₂×SD₃₂	1	1	yes	characteristic
310	C₂³	#508	1	1	yes	characteristic
311	C₂³	#508	1	1	yes	characteristic
312	C₂³	#509	1	1	yes	characteristic
313	C₂³	#509	1	1	yes	characteristic
314	C₂³	#510	1	1	yes	characteristic
315	C₂³	#510	1	1	yes	characteristic
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	4	1	no	—
326	C₂×C₄	—	4	1	no	—
327	C₂×C₄	—	4	1	no	—
328	C₂×C₄	—	4	1	no	—
329	C₂×C₄	—	4	4	no	—
330	C₂×C₄	—	4	4	no	—
331	C₂×C₄	—	8	2	no	—
332	C₂×C₄	—	8	2	no	—
333	C₂×C₄	—	8	2	no	—
334	C₂×C₄	—	8	2	no	—
335	C₂×C₄	—	8	2	no	—
336	C₂×C₄	—	8	2	no	—
337	C₂×C₄	—	8	2	no	—
338	C₂×C₄	—	8	2	no	—
339	C₂×C₄	—	8	2	no	—
340	C₂×C₄	—	8	2	no	—
341	C₂×C₄	—	8	2	no	—
342	C₂×C₄	—	8	2	no	—
343	C₂×C₄	—	8	2	no	—
344	C₂×C₄	—	8	2	no	—
345	C₂×C₄	—	8	2	no	—
346	C₂×C₄	—	8	2	no	—
347	C₂×C₄	—	8	2	no	—
348	C₂×C₄	—	8	2	no	—
349	C₂×C₄	—	16	1	no	—
350	C₂×C₄	—	16	1	no	—
351	C₂×C₄	—	16	1	no	—
352	C₂×C₄	—	16	1	no	—
353	C₂×C₄	—	16	1	no	—
354	C₂×C₄	—	16	1	no	—
355	C₂×C₄	—	16	1	no	—
356	C₂×C₄	—	16	1	no	—
357	C₂×C₄	#367	1	4	yes	complemented
358	C₂×C₄	C₄×C₄⋊C₄	1	1	yes	characteristic
359	C₂×C₄	#385	1	1	yes	characteristic
360	C₂×C₄	#385	1	1	yes	characteristic
361	C₂×C₄	#386	1	1	yes	characteristic
362	C₂×C₄	#387	1	1	yes	characteristic
363	C₂×C₄	#388	1	1	yes	characteristic
364	C₂×C₄	#389	1	1	yes	characteristic
365	C₂×C₄	#427	1	1	yes	characteristic
366	C₂×C₄	#428	1	1	yes	characteristic
367	C₂×C₄	#428	1	1	yes	characteristic
368	C₂×C₄	C₄×Q₁₆	1	1	yes	characteristic
369	C₂×C₄	C₄×Q₁₆	1	1	yes	characteristic
370	C₂×C₄	#440	1	1	yes	characteristic
371	C₂×C₄	#440	1	1	yes	characteristic
372	C₂×C₄	#441	1	1	yes	characteristic
373	C₂×C₄	#442	1	1	yes	characteristic
374	C₂×C₄	#449	1	1	yes	characteristic
375	C₂×C₄	#451	1	1	yes	characteristic
376	C₂×C₄	#452	1	1	yes	characteristic
377	C₂×C₄	#462	1	1	yes	characteristic
378	C₂×C₄	#463	1	1	yes	characteristic
379	C₂×C₄	#464	1	1	yes	characteristic
380	C₂×C₄	#477	1	1	yes	characteristic
381	C₂×C₄	#478	1	1	yes	characteristic
382	C₂×C₄	#479	1	1	yes	characteristic
383	C₂×C₄	#482	1	1	yes	characteristic
384	C₂×C₄	#484	1	1	yes	characteristic
385	C₂×C₄	#485	1	1	yes	characteristic
386	C₈	—	4	2	no	—
387	C₈	C₄×C₂²⋊C₄	1	1	yes	characteristic
388	C₈	C₄×C₄⋊C₄	1	1	yes	characteristic
389	C₈	#387	1	1	yes	characteristic
390	C₈	#387	1	1	yes	characteristic
391	C₈	#387	1	1	yes	characteristic
392	C₈	#388	1	1	yes	characteristic
393	C₈	#389	1	1	yes	characteristic
394	C₈	#391	1	1	yes	characteristic
395	C₂²	C₄×#107	1	1	yes	characteristic
396	C₂²	#1852	1	1	yes	characteristic
397	C₂²	#1862	1	1	yes	characteristic
398	C₂²	#1879	1	1	yes	characteristic
399	C₂²	#1918	1	1	yes	characteristic
400	C₂²	#1925	1	1	yes	characteristic
401	C₂²	#1947	1	1	yes	characteristic
402	C₂²	C₂×#367	1	1	yes	characteristic
403	C₂²	#2158	1	1	yes	characteristic
404	C₂²	#2159	1	1	yes	characteristic
405	C₂²	#2159	1	1	yes	characteristic
406	C₂²	C₄×SD₃₂	1	1	yes	characteristic
407	C₂²	C₄×SD₃₂	1	1	yes	characteristic
408	C₂²	C₄×SD₃₂	1	1	yes	characteristic
409	C₂²	C₄×SD₃₂	1	1	yes	characteristic
410	C₂²	#2175	1	1	yes	characteristic
411	C₂²	#2175	1	1	yes	characteristic
412	C₂²	#2176	1	1	yes	characteristic
413	C₂²	#2177	1	1	yes	characteristic
414	C₂²	#2185	1	1	yes	characteristic
415	C₂²	#2186	1	1	yes	characteristic
416	C₂²	#2187	1	1	yes	characteristic
417	C₂²	#2189	1	1	yes	characteristic
418	C₂²	#2207	1	1	yes	characteristic
419	C₂²	#2208	1	1	yes	characteristic
420	C₂²	#2210	1	1	yes	characteristic
421	C₂²	#2211	1	1	yes	characteristic
422	C₂²	#2225	1	1	yes	characteristic
423	C₂²	#2226	1	1	yes	characteristic
424	C₂²	#2228	1	1	yes	characteristic
425	C₂²	#2229	1	1	yes	characteristic
426	C₂²	#2233	1	1	yes	characteristic
427	C₂²	#2234	1	1	yes	characteristic
428	C₂²	#2235	1	1	yes	characteristic
429	C₂²	#2237	1	1	yes	characteristic
430	C₄	—	2	4	no	—
431	C₄	—	4	2	no	—
432	C₄	—	8	4	no	—
433	C₄	—	8	4	no	—
434	C₄	—	16	2	no	—
435	C₄	—	16	2	no	—
436	C₄	#1436	1	1	yes	characteristic
437	C₄	#1776	1	1	yes	characteristic
438	C₄	#1854	1	1	yes	characteristic
439	C₄	#1863	1	1	yes	characteristic
440	C₄	#1878	1	1	yes	characteristic
441	C₄	#1921	1	1	yes	characteristic
442	C₄	#1928	1	1	yes	characteristic
443	C₄	#1949	1	1	yes	characteristic
444	C₂	#10907	1	1	yes	characteristic
445	C₂	C₄×#367	1	1	yes	characteristic
446	C₂	#12674	1	1	yes	characteristic
447	C₂	#12920	1	1	yes	characteristic
448	C₂	#12921	1	1	yes	characteristic
449	C₂	#12937	1	1	yes	characteristic
450	C₂	#12938	1	1	yes	characteristic
451	C₂	#13013	1	1	yes	characteristic
452	C₂	#13014	1	1	yes	characteristic
453	C₂	#13110	1	1	yes	characteristic
454	C₂	#13111	1	1	yes	characteristic
455	C₂	#13131	1	1	yes	characteristic
456	C₂	#13132	1	1	yes	characteristic
457	C₂	#13177	1	1	yes	characteristic
458	C₂	#13178	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂⁴	C₂×D₈
commutator	C₂×C₈	C₂×C₄²
Frattini, cosocle	C₂³×C₈	C₂³
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄² ◁ C₂²×C₄×C₈ ◁ G
LECS	G ▷ C₂³×C₈ ▷ C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
18. C₂×#367	C₄	semidirect
26. #1380	C₄	semidirect
27. #1374	C₄	semidirect
162. C₂×C₁₆	C₄²	semidirect
357. C₂×C₄	#367	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#367	2
C₂×C₄×#107	2
C₂×#1380	2
C₂×#1374	2
#10862	2