Subgroups — #498784

Order 512.

451 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×#126	C₂	1	1	yes	maximal, characteristic
2	#13160	C₂	1	1	yes	maximal, characteristic, complemented
3	#13159	C₂	1	1	yes	maximal, characteristic, complemented
4	#13159	C₂	1	1	yes	maximal, characteristic, complemented
5	#13121	C₂	1	1	yes	maximal, characteristic
6	#13120	C₂	1	1	yes	maximal, characteristic
7	#13120	C₂	1	1	yes	maximal, characteristic
8	#13105	C₂	1	1	yes	maximal, characteristic, complemented
9	#13104	C₂	1	1	yes	maximal, characteristic, complemented
10	#13104	C₂	1	1	yes	maximal, characteristic, complemented
11	#12913	C₂	1	1	yes	maximal, characteristic
12	#12913	C₂	1	1	yes	maximal, characteristic
13	#12913	C₂	1	1	yes	maximal, characteristic
14	#12898	C₂	1	1	yes	maximal, characteristic, complemented
15	#12894	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×M₃₂	C₂²	1	1	yes	characteristic
17	C₄×#126	C₄	1	1	yes	characteristic
18	C₂×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
27	C₂×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
29	C₂×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
30	C₂×#346	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₁₆	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₁₆	C₂²	1	1	yes	characteristic
33	#1923	C₄	1	1	yes	characteristic
34	#1923	C₄	1	1	yes	characteristic
35	#1923	C₄	1	1	yes	characteristic
36	#1916	C₄	1	1	yes	characteristic
37	#1916	C₄	1	1	yes	characteristic
38	#1916	C₄	1	1	yes	characteristic
39	#1839	C₄	1	1	yes	characteristic
40	C₈×C₄⋊C₄	C₂²	1	1	yes	characteristic
41	C₈×C₄⋊C₄	C₂²	1	1	yes	characteristic
42	C₈×C₄⋊C₄	C₂²	1	1	yes	characteristic
43	C₈×C₂²⋊C₄	C₂²	1	1	yes	characteristic
44	C₈×C₂²⋊C₄	C₂²	1	1	yes	characteristic
45	C₈×C₂²⋊C₄	C₂²	1	1	yes	characteristic
46	C₄²×C₈	C₂²	1	1	yes	characteristic
47	#1374	C₂²	1	1	yes	characteristic
48	#1374	C₂²	1	1	yes	characteristic
49	#1374	C₂²	1	1	yes	characteristic
50	#1374	C₂²	1	1	yes	characteristic
51	#1374	C₂²	1	1	yes	characteristic
52	#1374	C₂²	1	1	yes	characteristic
53	#1374	C₂²	1	1	yes	characteristic
54	#1374	C₂²	1	1	yes	characteristic
55	#1374	C₂²	1	1	yes	characteristic
56	#1374	C₂²	1	1	yes	characteristic
57	#1374	C₂²	1	1	yes	characteristic
58	#1374	C₂²	1	1	yes	characteristic
59	C₂³×C₈	C₂³	1	1	yes	characteristic
60	C₂×#126	C₈	1	1	yes	characteristic
61	C₂×M₃₂	—	4	1	no	—
62	C₂×M₃₂	—	4	1	no	—
63	C₂×M₃₂	—	4	1	no	—
64	C₂²×C₁₆	C₂³	1	1	yes	characteristic
65	C₂²×C₁₆	C₂³	1	1	yes	characteristic
66	C₂²×C₁₆	C₂³	1	1	yes	characteristic
67	C₂²×C₁₆	C₂³	1	1	yes	characteristic
68	C₂²×C₁₆	C₂³	1	1	yes	characteristic
69	C₂²×C₁₆	C₂³	1	1	yes	characteristic
70	C₂²×C₁₆	C₂³	1	1	yes	characteristic
71	C₂²×C₁₆	C₂³	1	1	yes	characteristic
72	C₂×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
73	C₂×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
74	C₂×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
75	C₂×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
76	C₂×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
77	C₂×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
78	C₂×C₄×C₈	C₂×C₄	1	1	yes	characteristic
79	C₂×C₄×C₈	C₂×C₄	1	1	yes	characteristic
80	C₂×C₄×C₈	C₂×C₄	1	1	yes	characteristic
81	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
82	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
83	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
84	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
85	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
86	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
87	#388	C₈	1	1	yes	characteristic
88	#388	C₈	1	1	yes	characteristic
89	#388	C₈	1	1	yes	characteristic
90	#387	C₈	1	1	yes	characteristic
91	#387	C₈	1	1	yes	characteristic
92	#387	C₈	1	1	yes	characteristic
93	#383	C₈	1	1	yes	characteristic
94	C₄×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
95	C₄×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
96	C₄×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
97	C₄×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
98	C₄×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
99	C₄×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
100	C₄³	C₂×C₄	1	1	yes	characteristic
101	C₄⋊C₁₆	—	4	1	no	—
102	C₄⋊C₁₆	—	4	1	no	—
103	C₄⋊C₁₆	—	4	1	no	—
104	C₄⋊C₁₆	—	4	1	no	—
105	C₄⋊C₁₆	—	4	1	no	—
106	C₄⋊C₁₆	—	4	1	no	—
107	C₄⋊C₁₆	—	4	1	no	—
108	C₄⋊C₁₆	—	4	1	no	—
109	C₄⋊C₁₆	—	4	1	no	—
110	C₂²⋊C₁₆	—	4	1	no	—
111	C₂²⋊C₁₆	—	4	1	no	—
112	C₂²⋊C₁₆	—	4	1	no	—
113	#346	—	4	1	no	—
114	C₄×C₁₆	—	4	1	no	—
115	C₄×C₁₆	—	4	1	no	—
116	#336	C₂×C₄	1	1	yes	characteristic
117	#336	C₂×C₄	1	1	yes	characteristic
118	#336	C₂×C₄	1	1	yes	characteristic
119	#336	C₂×C₄	1	1	yes	characteristic
120	#336	C₂×C₄	1	1	yes	characteristic
121	#336	C₂×C₄	1	1	yes	characteristic
122	#336	C₂×C₄	1	1	yes	characteristic
123	#336	C₂×C₄	1	1	yes	characteristic
124	#336	C₂×C₄	1	1	yes	characteristic
125	#336	C₂×C₄	1	1	yes	characteristic
126	#336	C₂×C₄	1	1	yes	characteristic
127	#336	C₂×C₄	1	1	yes	characteristic
128	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
129	C₂²×C₈	—	2	1	no	—
130	C₂²×C₈	—	2	1	no	—
131	C₂²×C₈	—	2	1	no	—
132	C₂²×C₈	—	2	1	no	—
133	C₂²×C₈	—	2	1	no	—
134	C₂²×C₈	—	2	1	no	—
135	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
136	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
137	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
138	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
139	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
140	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
141	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
142	C₂²×C₈	C₂⁴	1	1	yes	characteristic
143	#126	—	2	4	no	—
144	C₂×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
145	C₂×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
146	C₂×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
147	C₂×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
148	C₂×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
149	C₂×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
150	C₂×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
151	C₂×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
152	C₂×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
153	C₂×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
154	C₂×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
155	C₂×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
156	C₂×C₄²	C₂×C₈	1	1	yes	characteristic
157	C₂×C₄²	C₂×C₈	1	1	yes	characteristic
158	C₂×C₄²	C₂×C₈	1	1	yes	characteristic
159	C₂×C₄²	C₂×C₈	1	1	yes	characteristic
160	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
161	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
162	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
163	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
164	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
165	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
166	M₃₂	—	4	4	no	—
167	C₂×C₁₆	—	2	1	no	—
168	C₂×C₁₆	—	2	1	no	—
169	C₂×C₁₆	—	2	1	no	—
170	C₂×C₁₆	—	2	1	no	—
171	C₂×C₁₆	—	2	1	no	—
172	C₂×C₁₆	—	2	1	no	—
173	C₂×C₁₆	—	2	1	no	—
174	C₂×C₁₆	—	2	1	no	—
175	C₂×C₁₆	—	2	1	no	—
176	C₂×C₁₆	—	2	1	no	—
177	C₂×C₁₆	—	2	1	no	—
178	C₂×C₁₆	—	2	1	no	—
179	C₂×C₁₆	—	2	1	no	—
180	C₂×C₁₆	—	2	1	no	—
181	C₂×C₁₆	—	2	1	no	—
182	C₂×C₁₆	—	2	1	no	—
183	C₂×C₁₆	—	2	1	no	—
184	C₂×C₁₆	—	2	1	no	—
185	C₂×C₁₆	—	2	1	no	—
186	C₂×C₁₆	—	2	1	no	—
187	C₂×C₁₆	—	2	1	no	—
188	C₂×C₁₆	—	2	1	no	—
189	C₂×C₁₆	—	2	1	no	—
190	C₂×C₁₆	—	2	1	no	—
191	C₄⋊C₈	—	4	1	no	—
192	C₄⋊C₈	—	4	1	no	—
193	C₄⋊C₈	—	4	1	no	—
194	C₂²⋊C₈	—	4	1	no	—
195	C₂²⋊C₈	—	4	1	no	—
196	C₂²⋊C₈	—	4	1	no	—
197	C₄×C₈	—	2	1	no	—
198	C₄×C₈	—	2	1	no	—
199	C₄×C₈	—	2	1	no	—
200	C₄×C₈	—	2	1	no	—
201	C₄×C₈	—	2	1	no	—
202	C₄×C₈	—	2	1	no	—
203	C₄×C₈	—	2	1	no	—
204	C₄×C₈	—	2	1	no	—
205	C₄×C₈	—	2	1	no	—
206	C₄×C₈	—	2	1	no	—
207	C₄×C₈	—	2	1	no	—
208	C₄×C₈	—	2	1	no	—
209	C₄×C₈	—	4	1	no	—
210	C₄×C₈	—	4	1	no	—
211	C₄×C₈	—	4	1	no	—
212	#95	C₂×C₈	1	1	yes	characteristic
213	#95	C₂×C₈	1	1	yes	characteristic
214	#95	C₂×C₈	1	1	yes	characteristic
215	#95	C₂×C₈	1	1	yes	characteristic
216	#95	C₂×C₈	1	1	yes	characteristic
217	#95	C₂×C₈	1	1	yes	characteristic
218	#95	C₂×C₈	1	1	yes	characteristic
219	#95	C₂×C₈	1	1	yes	characteristic
220	#95	C₂×C₈	1	1	yes	characteristic
221	#95	C₂×C₈	1	1	yes	characteristic
222	#95	C₂×C₈	1	1	yes	characteristic
223	#95	C₂×C₈	1	1	yes	characteristic
224	C₂⁴	C₂²×C₈	1	1	yes	characteristic
225	C₂²×C₄	—	2	1	no	—
226	C₂²×C₄	—	2	1	no	—
227	C₂²×C₄	—	2	1	no	—
228	C₂²×C₄	—	2	1	no	—
229	C₂²×C₄	—	2	1	no	—
230	C₂²×C₄	—	2	1	no	—
231	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
232	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
233	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
234	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
235	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
236	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
237	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
238	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
239	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
240	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
241	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
242	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
243	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
244	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
245	C₂×C₈	—	2	1	no	—
246	C₂×C₈	—	2	1	no	—
247	C₂×C₈	—	2	1	no	—
248	C₂×C₈	—	2	1	no	—
249	C₂×C₈	—	2	1	no	—
250	C₂×C₈	—	2	1	no	—
251	C₂×C₈	—	2	1	no	—
252	C₂×C₈	—	2	1	no	—
253	C₂×C₈	—	2	1	no	—
254	C₂×C₈	—	2	1	no	—
255	C₂×C₈	—	2	1	no	—
256	C₂×C₈	—	2	1	no	—
257	C₂×C₈	—	2	1	no	—
258	C₂×C₈	—	2	1	no	—
259	C₂×C₈	—	2	1	no	—
260	C₂×C₈	—	2	1	no	—
261	C₂×C₈	—	2	1	no	—
262	C₂×C₈	—	2	1	no	—
263	C₂×C₈	—	2	1	no	—
264	C₂×C₈	—	2	1	no	—
265	C₂×C₈	—	2	1	no	—
266	C₂×C₈	—	4	1	no	—
267	C₂×C₈	—	4	1	no	—
268	C₂×C₈	—	4	1	no	—
269	C₂×C₈	—	4	1	no	—
270	C₂×C₈	H(5,𝔽₂)	1	1	yes	characteristic
271	C₂×C₈	H(5,𝔽₂)	1	1	yes	characteristic
272	C₂×C₈	H(5,𝔽₂)	1	1	yes	characteristic
273	C₂×C₈	2₋¹⁺⁴	1	1	yes	characteristic
274	C₂×C₈	2₋¹⁺⁴	1	1	yes	characteristic
275	C₂×C₈	2₋¹⁺⁴	1	1	yes	characteristic
276	C₄⋊C₄	—	2	2	no	—
277	C₄⋊C₄	—	2	2	no	—
278	C₄⋊C₄	—	2	2	no	—
279	C₄⋊C₄	—	2	2	no	—
280	C₄⋊C₄	—	4	1	no	—
281	C₄⋊C₄	M₃₂	1	4	yes	complemented
282	C₂²⋊C₄	—	2	2	no	—
283	C₂²⋊C₄	—	2	2	no	—
284	C₂²⋊C₄	—	2	2	no	—
285	C₂²⋊C₄	—	2	2	no	—
286	C₂²⋊C₄	—	2	2	no	—
287	C₂²⋊C₄	—	4	1	no	—
288	C₄²	—	2	1	no	—
289	C₄²	—	2	1	no	—
290	C₄²	—	2	1	no	—
291	C₄²	—	2	1	no	—
292	C₄²	—	2	1	no	—
293	C₄²	—	2	1	no	—
294	C₄²	—	2	1	no	—
295	C₄²	—	2	1	no	—
296	C₄²	—	2	1	no	—
297	C₄²	—	2	1	no	—
298	C₄²	—	2	1	no	—
299	C₄²	—	2	1	no	—
300	C₄²	—	2	2	no	—
301	C₄²	—	2	2	no	—
302	C₄²	—	2	2	no	—
303	C₄²	—	4	1	no	—
304	C₁₆	—	4	1	no	—
305	C₁₆	—	4	1	no	—
306	C₁₆	—	4	1	no	—
307	C₁₆	—	4	1	no	—
308	C₁₆	—	4	1	no	—
309	C₁₆	—	4	1	no	—
310	C₁₆	—	4	1	no	—
311	C₁₆	—	4	1	no	—
312	C₂³	—	2	1	no	—
313	C₂³	—	2	1	no	—
314	C₂³	—	2	1	no	—
315	C₂³	—	2	1	no	—
316	C₂³	—	2	1	no	—
317	C₂³	—	2	1	no	—
318	C₂³	—	2	1	no	—
319	C₂³	C₂³×C₈	1	1	yes	characteristic
320	C₂×C₄	—	2	1	no	—
321	C₂×C₄	—	2	1	no	—
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	2	1	no	—
327	C₂×C₄	—	2	1	no	—
328	C₂×C₄	—	2	1	no	—
329	C₂×C₄	—	2	1	no	—
330	C₂×C₄	—	2	1	no	—
331	C₂×C₄	—	2	1	no	—
332	C₂×C₄	—	2	1	no	—
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	4	1	no	—
355	C₂×C₄	—	4	1	no	—
356	C₂×C₄	—	4	1	no	—
357	C₂×C₄	—	4	1	no	—
358	C₂×C₄	C₂×M₃₂	1	2	yes	—
359	C₂×C₄	C₂×M₃₂	1	2	yes	—
360	C₂×C₄	C₂×M₃₂	1	2	yes	—
361	C₂×C₄	#504	1	2	yes	—
362	C₂×C₄	#504	1	2	yes	—
363	C₂×C₄	#520	1	1	yes	characteristic
364	C₂×C₄	#520	1	1	yes	characteristic
365	C₂×C₄	#520	1	1	yes	characteristic
366	C₂×C₄	#568	1	1	yes	characteristic
367	C₂×C₄	#568	1	1	yes	characteristic
368	C₂×C₄	#568	1	1	yes	characteristic
369	C₈	—	4	1	no	—
370	C₈	—	4	1	no	—
371	C₈	—	4	1	no	—
372	C₈	—	4	1	no	—
373	C₈	—	4	1	no	—
374	C₈	—	4	1	no	—
375	C₈	—	4	1	no	—
376	C₈	#560	1	1	yes	characteristic
377	C₈	#563	1	1	yes	characteristic
378	C₈	#563	1	1	yes	characteristic
379	C₈	#563	1	1	yes	characteristic
380	C₂²	—	4	1	no	—
381	C₂²	—	4	1	no	—
382	C₂²	—	4	1	no	—
383	C₂²	—	4	1	no	—
384	C₂²	—	4	1	no	—
385	C₂²	—	4	1	no	—
386	C₂²	—	4	1	no	—
387	C₂²	#2988	1	1	yes	characteristic
388	C₂²	#2988	1	1	yes	characteristic
389	C₂²	#2988	1	1	yes	characteristic
390	C₂²	C₂²×M₃₂	1	1	yes	characteristic
391	C₂²	C₂×#504	1	1	yes	characteristic
392	C₂²	C₂×#504	1	1	yes	characteristic
393	C₂²	#3407	1	1	yes	characteristic
394	C₄	—	2	2	no	—
395	C₄	—	2	2	no	—
396	C₄	—	2	2	no	—
397	C₄	—	2	2	no	—
398	C₄	—	2	2	no	—
399	C₄	—	4	1	no	—
400	C₄	—	4	1	no	—
401	C₄	—	4	1	no	—
402	C₄	—	4	1	no	—
403	C₄	—	4	1	no	—
404	C₄	—	4	1	no	—
405	C₄	—	4	1	no	—
406	C₄	—	4	1	no	—
407	C₄	#2383	1	1	yes	characteristic
408	C₄	#2995	1	1	yes	characteristic
409	C₄	#2995	1	1	yes	characteristic
410	C₄	#2995	1	1	yes	characteristic
411	C₂	—	8	1	no	—
412	C₂	#23375	1	1	yes	characteristic
413	C₂	#33503	1	1	yes	characteristic
414	C₂	#33504	1	1	yes	characteristic
415	C₂	#33505	1	1	yes	characteristic
416	C₂	#33506	1	1	yes	characteristic
417	C₂	#33507	1	1	yes	characteristic
418	C₂	#33508	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. #13160	C₂	semidirect
3. #13159	C₂	semidirect
4. #13159	C₂	semidirect
8. #13105	C₂	semidirect
9. #13104	C₂	semidirect
10. #13104	C₂	semidirect
14. #12898	C₂	semidirect
15. #12894	C₂	semidirect
281. C₄⋊C₄	M₃₂	semidirect

Maximal subgroups

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

subgroup	index
C₈×#126	2
#13160	2
#13159	2
#13121	2
#13120	2
#13105	2
#13104	2
#12913	2
#12898	2
#12894	2