Subgroups — #7622703

Order 512.

1225 conjugacy classes of subgroups.

The subgroup lattice has 421 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#2960	C₂	1	1	yes	maximal, characteristic
2	#33501	C₂	1	4	yes	maximal, complemented
3	#33499	C₂	1	4	yes	maximal, complemented
4	#33498	C₂	1	4	yes	maximal, complemented
5	#33497	C₂	1	4	yes	maximal, complemented
6	#33476	C₂	1	4	yes	maximal, complemented
7	#33475	C₂	1	4	yes	maximal, complemented
8	#33422	C₂	1	4	yes	maximal
9	#33418	C₂	1	1	yes	maximal, characteristic
10	C₂×#2163	C₂	1	1	yes	maximal, characteristic
11	C₂×#533	C₄	1	1	yes	characteristic
12	#2960	C₄	1	2	yes	—
13	#2960	C₄	1	2	yes	—
14	#2960	C₄	1	2	yes	—
15	#2960	C₄	1	2	yes	—
16	#2960	C₂²	1	2	yes	—
17	#2960	C₂²	1	2	yes	—
18	#2960	C₂²	1	2	yes	—
19	#2960	C₂²	1	2	yes	—
20	C₂×#446	C₄	1	2	yes	—
21	C₂×#446	C₄	1	2	yes	—
22	C₂×C₈×Q₈	C₂²	1	2	yes	—
23	C₂×C₈×Q₈	C₂²	1	2	yes	—
24	C₂×#424	C₄	1	2	yes	—
25	C₂×#423	C₄	1	1	yes	characteristic
26	C₂×#405	C₂²	1	2	yes	—
27	C₂²×C₄×C₈	C₂²	1	1	yes	characteristic
28	#2183	C₂²	1	16	yes	complemented
29	#2183	C₂²	1	16	yes	complemented
30	#2183	C₂²	1	16	yes	complemented
31	#2183	C₂²	1	8	yes	complemented
32	Q₈×C₁₆	C₂²	1	8	yes	complemented
33	#2164	C₂²	1	16	yes	—
34	#2163	C₂²	1	2	yes	—
35	#2163	C₂²	1	2	yes	—
36	#2163	C₂²	1	2	yes	—
37	#2163	C₂²	1	2	yes	—
38	#2163	C₂²	1	2	yes	—
39	#2163	C₂²	1	2	yes	—
40	#2163	C₂²	1	8	yes	—
41	#2162	C₂²	1	2	yes	—
42	#2162	C₂²	1	2	yes	—
43	#2162	C₂²	1	8	yes	—
44	#2151	C₂²	1	8	yes	—
45	#2150	C₂²	1	2	yes	—
46	C₂×C₄⋊C₁₆	C₂²	1	2	yes	—
47	#2112	C₂²	1	2	yes	—
48	C₂×C₂²⋊C₁₆	C₂²	1	2	yes	—
49	#2108	C₂²	1	8	yes	—
50	C₄×M₃₂	C₂²	1	2	yes	—
51	C₂×#346	C₂²	1	2	yes	—
52	C₂²×M₁₆	C₂×C₄	1	2	yes	—
53	C₂³×C₈	C₂×C₄	1	1	yes	characteristic
54	C₂³×C₈	C₂³	1	1	yes	characteristic
55	#533	C₈	1	2	yes	—
56	#533	C₈	1	2	yes	—
57	#533	C₈	1	2	yes	—
58	#533	C₈	1	2	yes	—
59	#533	C₂×C₄	1	2	yes	—
60	#533	C₂×C₄	1	2	yes	—
61	#533	C₂×C₄	1	2	yes	—
62	#533	C₂×C₄	1	2	yes	—
63	C₂×C₄⋊Q₈	C₈	1	1	yes	characteristic
64	C₂×C₄⋊Q₈	C₈	1	1	yes	characteristic
65	C₂×#125	C₈	1	2	yes	—
66	C₂×C₂²⋊Q₈	C₈	1	2	yes	—
67	C₂×C₂²⋊Q₈	C₈	1	2	yes	—
68	C₂×C₄×Q₈	C₂×C₄	1	2	yes	—
69	C₂×C₄×Q₈	C₂×C₄	1	2	yes	—
70	C₂×#117	C₂×C₄	1	2	yes	—
71	C₂²×C₄²	C₂×C₄	1	1	yes	characteristic
72	C₂×M₃₂	C₂³	1	4	yes	—
73	C₂²×C₁₆	C₂³	1	4	yes	—
74	#446	C₂×C₄	1	4	yes	—
75	#446	C₂×C₄	1	4	yes	—
76	#446	C₂×C₄	1	4	yes	—
77	#446	C₂×C₄	1	4	yes	—
78	#446	C₂×C₄	1	4	yes	—
79	#446	C₂×C₄	1	4	yes	—
80	#446	C₂×C₄	1	4	yes	—
81	#446	C₂×C₄	1	4	yes	—
82	C₈×Q₈	C₂×C₄	1	4	yes	—
83	C₈×Q₈	C₂×C₄	1	4	yes	—
84	C₈×Q₈	C₂×C₄	1	4	yes	—
85	C₈×Q₈	C₂×C₄	1	4	yes	—
86	C₈×Q₈	C₂³	1	4	yes	—
87	C₈×Q₈	C₂³	1	4	yes	—
88	C₈×Q₈	C₂³	1	4	yes	—
89	C₈×Q₈	C₂³	1	4	yes	—
90	#424	C₂×C₄	1	4	yes	—
91	#424	C₂×C₄	1	4	yes	—
92	#424	C₂×C₄	1	4	yes	—
93	#424	C₂×C₄	1	4	yes	—
94	#423	C₂×C₄	1	2	yes	—
95	#423	C₂×C₄	1	2	yes	—
96	#423	C₂×C₄	1	2	yes	—
97	#423	C₂×C₄	1	2	yes	—
98	C₂×C₄⋊C₈	C₂×C₄	1	2	yes	—
99	C₂×C₄⋊C₈	C₂×C₄	1	2	yes	—
100	C₂×C₄⋊C₈	C₂×C₄	1	4	yes	—
101	C₂×C₄⋊C₈	C₂×C₄	1	4	yes	—
102	#405	C₂×C₄	1	4	yes	—
103	#405	C₂×C₄	1	4	yes	—
104	#405	C₂³	1	4	yes	—
105	#405	C₂³	1	4	yes	—
106	C₂×#97	C₂×C₄	1	4	yes	—
107	C₂×C₄×C₈	C₂×C₄	1	1	yes	characteristic
108	C₂×C₄×C₈	C₂×C₄	1	1	yes	characteristic
109	C₂×C₄×C₈	C₂×C₄	1	1	yes	characteristic
110	C₂×C₄×C₈	C₂×C₄	1	1	yes	characteristic
111	C₂×C₄×C₈	C₂×C₄	1	1	yes	characteristic
112	C₂×C₄×C₈	C₂×C₄	1	1	yes	characteristic
113	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
114	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
115	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
116	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
117	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
118	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
119	C₂×C₄×C₈	C₂³	1	4	yes	—
120	C₄⋊C₁₆	C₂³	1	4	yes	—
121	C₄⋊C₁₆	C₂³	1	4	yes	—
122	C₄⋊C₁₆	C₂³	1	4	yes	—
123	C₄⋊C₁₆	C₂³	1	4	yes	—
124	C₄⋊C₁₆	C₂³	1	16	yes	—
125	C₄⋊C₁₆	C₂³	1	16	yes	—
126	C₂²⋊C₁₆	C₂³	1	4	yes	—
127	C₂²⋊C₁₆	C₂³	1	4	yes	—
128	C₂²⋊C₁₆	C₂³	1	4	yes	—
129	C₂²⋊C₁₆	C₂³	1	4	yes	—
130	#346	C₂³	1	4	yes	—
131	#346	C₂³	1	4	yes	—
132	#346	C₂³	1	4	yes	—
133	#346	C₂³	1	16	yes	—
134	C₄×C₁₆	C₂³	1	4	yes	—
135	C₄×C₁₆	C₂³	1	16	yes	—
136	C₂²×Q₈	C₂×C₈	1	2	yes	—
137	C₂²×Q₈	C₂×C₈	1	2	yes	—
138	C₂³×C₄	C₂×C₈	1	1	yes	characteristic
139	C₂³×C₄	C₂×C₈	1	1	yes	characteristic
140	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
141	C₂×M₁₆	—	4	4	no	—
142	C₂×M₁₆	C₂²×C₄	1	4	yes	—
143	C₂×M₁₆	C₂²×C₄	1	4	yes	—
144	C₂²×C₈	—	2	4	no	—
145	C₂²×C₈	—	4	2	no	—
146	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
147	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
148	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
149	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
150	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
151	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
152	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
153	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
154	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
155	C₂²×C₈	C₂²×C₄	1	4	yes	—
156	C₂²×C₈	C₂⁴	1	1	yes	characteristic
157	C₂²×C₈	C₂⁴	1	1	yes	characteristic
158	C₂²×C₈	C₂⁴	1	1	yes	characteristic
159	C₄⋊Q₈	C₂×C₈	1	2	yes	—
160	C₄⋊Q₈	C₂×C₈	1	2	yes	—
161	C₄⋊Q₈	C₂×C₈	1	2	yes	—
162	C₄⋊Q₈	C₂×C₈	1	2	yes	—
163	C₄⋊Q₈	C₂×C₈	1	2	yes	—
164	C₄⋊Q₈	C₂×C₈	1	2	yes	—
165	C₄⋊Q₈	C₂×C₈	1	2	yes	—
166	C₄⋊Q₈	C₂×C₈	1	2	yes	—
167	#125	C₂×C₈	1	4	yes	—
168	#125	C₂×C₈	1	4	yes	—
169	#125	C₂×C₈	1	4	yes	—
170	#125	C₂×C₈	1	4	yes	—
171	C₂²⋊Q₈	C₂×C₈	1	4	yes	—
172	C₂²⋊Q₈	C₂×C₈	1	4	yes	—
173	C₂²⋊Q₈	C₂×C₈	1	4	yes	—
174	C₂²⋊Q₈	C₂×C₈	1	4	yes	—
175	C₂²⋊Q₈	C₂×C₈	1	4	yes	—
176	C₂²⋊Q₈	C₂×C₈	1	4	yes	—
177	C₂²⋊Q₈	C₂×C₈	1	4	yes	—
178	C₂²⋊Q₈	C₂×C₈	1	4	yes	—
179	C₄×Q₈	C₂×C₈	1	4	yes	—
180	C₄×Q₈	C₂×C₈	1	4	yes	—
181	C₄×Q₈	C₂×C₈	1	4	yes	—
182	C₄×Q₈	C₂×C₈	1	4	yes	—
183	C₄×Q₈	C₂²×C₄	1	4	yes	—
184	C₄×Q₈	C₂²×C₄	1	4	yes	—
185	C₄×Q₈	C₂²×C₄	1	4	yes	—
186	C₄×Q₈	C₂²×C₄	1	4	yes	—
187	#117	C₂×C₈	1	4	yes	—
188	#117	C₂×C₈	1	4	yes	—
189	#117	C₂²×C₄	1	4	yes	—
190	#117	C₂²×C₄	1	4	yes	—
191	C₂×C₄⋊C₄	C₂×C₈	1	2	yes	—
192	C₂×C₄⋊C₄	C₂×C₈	1	2	yes	—
193	C₂×C₄⋊C₄	C₂×C₈	1	4	yes	—
194	C₂×C₄⋊C₄	C₂×C₈	1	4	yes	—
195	C₂×C₄⋊C₄	C₂×C₈	1	2	yes	—
196	C₂×C₄⋊C₄	C₂×C₈	1	2	yes	—
197	C₂×C₂²⋊C₄	C₂×C₈	1	4	yes	—
198	C₂×C₄²	C₂×C₈	1	1	yes	characteristic
199	C₂×C₄²	C₂×C₈	1	1	yes	characteristic
200	C₂×C₄²	C₂×C₈	1	1	yes	characteristic
201	C₂×C₄²	C₂×C₈	1	1	yes	characteristic
202	C₂×C₄²	C₂×C₈	1	1	yes	characteristic
203	C₂×C₄²	C₂×C₈	1	1	yes	characteristic
204	C₂×C₄²	C₂²×C₄	1	4	yes	—
205	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
206	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
207	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
208	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
209	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
210	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
211	M₃₂	—	2	8	no	—
212	C₂×C₁₆	—	2	8	no	—
213	C₂×C₁₆	C₂⁴	1	8	yes	—
214	C₂×C₁₆	C₂⁴	1	8	yes	—
215	C₄⋊C₈	C₂²×C₄	1	4	yes	—
216	C₄⋊C₈	C₂²×C₄	1	4	yes	—
217	C₄⋊C₈	C₂²×C₄	1	4	yes	—
218	C₄⋊C₈	C₂²×C₄	1	4	yes	—
219	C₄⋊C₈	C₂²×C₄	1	8	yes	—
220	C₄⋊C₈	C₂²×C₄	1	8	yes	—
221	C₄⋊C₈	C₂²×C₄	1	8	yes	—
222	C₄⋊C₈	C₂²×C₄	1	8	yes	—
223	#97	C₂²×C₄	1	8	yes	—
224	#97	C₂²×C₄	1	8	yes	—
225	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
226	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
227	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
228	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
229	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
230	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
231	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
232	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
233	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
234	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
235	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
236	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
237	C₄×C₈	C₂²×C₄	1	8	yes	—
238	C₄×C₈	C₂⁴	1	1	yes	characteristic
239	C₄×C₈	C₂⁴	1	8	yes	—
240	C₄×C₈	C₂⁴	1	1	yes	characteristic
241	C₄×C₈	C₂⁴	1	1	yes	characteristic
242	C₄×C₈	C₂⁴	1	1	yes	characteristic
243	C₂⁴	C₂²×C₈	1	1	yes	characteristic
244	C₂×Q₈	—	4	4	no	—
245	C₂×Q₈	—	4	4	no	—
246	C₂×Q₈	C₂²×C₈	1	4	yes	—
247	C₂×Q₈	C₂²×C₈	1	4	yes	—
248	C₂×Q₈	C₂²×C₈	1	4	yes	—
249	C₂×Q₈	C₂²×C₈	1	4	yes	—
250	C₂²×C₄	—	2	2	no	—
251	C₂²×C₄	—	2	2	no	—
252	C₂²×C₄	—	4	2	no	—
253	C₂²×C₄	—	4	2	no	—
254	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
255	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
256	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
257	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
258	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
259	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
260	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
261	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
262	C₂²×C₄	C₂²×C₈	1	4	yes	—
263	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
264	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
265	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
266	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
267	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
268	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
269	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
270	C₂²×C₄	C₂²×C₈	1	4	yes	—
271	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
272	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
273	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
274	M₁₆	—	2	8	no	—
275	M₁₆	—	4	4	no	—
276	C₂×C₈	—	2	2	no	—
277	C₂×C₈	—	2	2	no	—
278	C₂×C₈	—	2	2	no	—
279	C₂×C₈	—	2	2	no	—
280	C₂×C₈	—	2	2	no	—
281	C₂×C₈	—	2	2	no	—
282	C₂×C₈	—	2	2	no	—
283	C₂×C₈	—	4	1	no	—
284	C₂×C₈	—	4	1	no	—
285	C₂×C₈	—	4	1	no	—
286	C₂×C₈	—	4	1	no	—
287	C₂×C₈	—	4	4	no	—
288	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
289	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
290	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
291	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
292	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
293	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
294	C₂×C₈	C₂³×C₄	1	8	yes	—
295	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
296	C₂×C₈	2₋¹⁺⁴	1	4	yes	—
297	C₂×C₈	C₂⁵	1	1	yes	characteristic
298	C₄⋊C₄	C₂²×C₈	1	4	yes	—
299	C₄⋊C₄	C₂²×C₈	1	4	yes	—
300	C₄⋊C₄	C₂²×C₈	1	4	yes	—
301	C₄⋊C₄	C₂²×C₈	1	4	yes	—
302	C₄⋊C₄	C₂²×C₈	1	8	yes	—
303	C₄⋊C₄	C₂²×C₈	1	8	yes	—
304	C₄⋊C₄	C₂²×C₈	1	8	yes	—
305	C₄⋊C₄	C₂²×C₈	1	8	yes	—
306	C₄⋊C₄	C₂²×C₈	1	4	yes	—
307	C₄⋊C₄	C₂²×C₈	1	4	yes	—
308	C₄⋊C₄	C₂²×C₈	1	4	yes	—
309	C₄⋊C₄	C₂²×C₈	1	4	yes	—
310	C₂²⋊C₄	C₂²×C₈	1	8	yes	—
311	C₂²⋊C₄	C₂²×C₈	1	8	yes	—
312	C₄²	C₂²×C₈	1	1	yes	characteristic
313	C₄²	C₂²×C₈	1	1	yes	characteristic
314	C₄²	C₂²×C₈	1	1	yes	characteristic
315	C₄²	C₂²×C₈	1	1	yes	characteristic
316	C₄²	C₂²×C₈	1	1	yes	characteristic
317	C₄²	C₂²×C₈	1	1	yes	characteristic
318	C₄²	C₂²×C₈	1	1	yes	characteristic
319	C₄²	C₂²×C₈	1	1	yes	characteristic
320	C₄²	C₂²×C₈	1	1	yes	characteristic
321	C₄²	C₂²×C₈	1	1	yes	characteristic
322	C₄²	C₂²×C₈	1	1	yes	characteristic
323	C₄²	C₂²×C₈	1	1	yes	characteristic
324	C₄²	C₂²×C₈	1	8	yes	—
325	C₄²	C₂³×C₄	1	1	yes	characteristic
326	C₄²	C₂³×C₄	1	1	yes	characteristic
327	C₄²	C₂³×C₄	1	1	yes	characteristic
328	C₄²	C₂³×C₄	1	1	yes	characteristic
329	C₄²	C₂³×C₄	1	8	yes	—
330	C₁₆	—	2	8	no	—
331	C₁₆	—	2	8	no	—
332	C₂³	—	2	2	no	—
333	C₂³	—	2	2	no	—
334	C₂³	—	4	1	no	—
335	C₂³	C₂³×C₈	1	1	yes	characteristic
336	C₂³	C₂³×C₈	1	1	yes	characteristic
337	C₂³	C₂³×C₈	1	1	yes	characteristic
338	Q₈	—	2	8	no	—
339	Q₈	—	4	4	no	—
340	Q₈	—	4	4	no	—
341	Q₈	—	4	4	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	8	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	4	1	no	—
356	C₂×C₄	—	4	1	no	—
357	C₂×C₄	—	4	1	no	—
358	C₂×C₄	—	4	1	no	—
359	C₂×C₄	—	4	1	no	—
360	C₂×C₄	—	4	1	no	—
361	C₂×C₄	—	4	1	no	—
362	C₂×C₄	—	4	4	no	—
363	C₂×C₄	#519	1	2	yes	—
364	C₂×C₄	C₂³×C₈	1	1	yes	characteristic
365	C₂×C₄	C₂³×C₈	1	1	yes	characteristic
366	C₂×C₄	C₂³×C₈	1	1	yes	characteristic
367	C₂×C₄	C₂³×C₈	1	1	yes	characteristic
368	C₂×C₄	C₂³×C₈	1	1	yes	characteristic
369	C₂×C₄	C₂³×C₈	1	1	yes	characteristic
370	C₂×C₄	C₂³×C₈	1	1	yes	characteristic
371	C₂×C₄	C₂³×C₈	1	1	yes	characteristic
372	C₂×C₄	C₂³×C₈	1	1	yes	characteristic
373	C₂×C₄	C₂³×C₈	1	8	yes	—
374	C₂×C₄	C₂³×C₈	1	8	yes	—
375	C₂×C₄	C₂³×C₈	1	1	yes	characteristic
376	C₂×C₄	C₂³×C₈	1	1	yes	characteristic
377	C₂×C₄	#568	1	2	yes	—
378	C₂×C₄	C₂⁴×C₄	1	1	yes	characteristic
379	C₈	—	2	1	no	—
380	C₈	—	2	1	no	—
381	C₈	—	2	1	no	—
382	C₈	—	2	1	no	—
383	C₈	—	2	1	no	—
384	C₈	—	2	1	no	—
385	C₈	—	2	8	no	—
386	C₈	#519	1	2	yes	—
387	C₈	C₂×2₋¹⁺⁴	1	2	yes	—
388	C₂²	—	2	1	no	—
389	C₂²	—	2	1	no	—
390	C₂²	—	2	1	no	—
391	C₂²	—	2	1	no	—
392	C₂²	—	2	1	no	—
393	C₂²	—	2	1	no	—
394	C₂²	—	2	1	no	—
395	C₂²	—	4	4	no	—
396	C₂²	#2982	1	2	yes	—
397	C₂²	#3407	1	2	yes	—
398	C₂²	C₂⁴×C₈	1	1	yes	characteristic
399	C₄	—	2	1	no	—
400	C₄	—	2	1	no	—
401	C₄	—	2	1	no	—
402	C₄	—	2	1	no	—
403	C₄	—	2	1	no	—
404	C₄	—	2	1	no	—
405	C₄	—	2	1	no	—
406	C₄	—	2	1	no	—
407	C₄	—	2	1	no	—
408	C₄	—	2	8	no	—
409	C₄	—	2	8	no	—
410	C₄	#2982	1	2	yes	—
411	C₄	#3407	1	2	yes	—
412	C₄	C₂×#519	1	1	yes	characteristic
413	C₄	C₂×#568	1	1	yes	characteristic
414	C₂	—	2	2	no	—
415	C₂	—	2	2	no	—
416	C₂	—	4	1	no	—
417	C₂	C₂×#2982	1	1	yes	characteristic
418	C₂	C₂×#3407	1	1	yes	characteristic
419	C₂	C₂×#3407	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, cosocle	C₂×C₈	C₂⁵
commutator, socle	C₂²	C₂⁴×C₈
prime radical	C₂⁴	C₂²×C₈
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₈ ◁ G
LECS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
2. #33501	C₂	semidirect
3. #33499	C₂	semidirect
4. #33498	C₂	semidirect
5. #33497	C₂	semidirect
6. #33476	C₂	semidirect
7. #33475	C₂	semidirect
28. #2183	C₂²	semidirect
29. #2183	C₂²	semidirect
30. #2183	C₂²	semidirect
31. #2183	C₂²	semidirect
32. Q₈×C₁₆	C₂²	semidirect

Maximal subgroups

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

subgroup	index
C₂×#2960	2
#33501	2
#33499	2
#33498	2
#33497	2
#33476	2
#33475	2
#33422	2
#33418	2
C₂×#2163	2