Subgroups — #413417

Order 512.

717 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#2103	C₂	1	2	yes	maximal
2	#21177	C₂	1	1	yes	maximal, characteristic
3	#20793	C₂	1	1	yes	maximal, characteristic
4	#11264	C₂	1	2	yes	maximal
5	#11264	C₂	1	2	yes	maximal
6	#11237	C₂	1	2	yes	maximal
7	#10856	C₂	1	1	yes	maximal, characteristic
8	#10853	C₂	1	1	yes	maximal, characteristic
9	#10853	C₂	1	1	yes	maximal, characteristic
10	C₄⋊#338	C₂	1	1	yes	maximal, characteristic
11	C₄×#344	C₂	1	1	yes	maximal, characteristic
12	C₂×#430	C₂²	1	2	yes	—
13	C₂×#424	C₂²	1	2	yes	—
14	C₂×#424	C₂²	1	2	yes	—
15	C₂×#423	C₂²	1	1	yes	characteristic
16	C₂×#423	C₂²	1	1	yes	characteristic
17	C₂×#423	C₂²	1	1	yes	characteristic
18	C₂²×C₄⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₄×M₁₆	C₂²	1	1	yes	characteristic
20	C₂×C₄×M₁₆	C₂²	1	1	yes	characteristic
21	C₄×#117	C₂²	1	1	yes	characteristic
22	#2103	—	2	8	no	—
23	#1950	—	2	2	no	—
24	#1950	—	2	2	no	—
25	#1843	—	2	2	no	—
26	#1842	—	2	2	no	—
27	C₂×#344	C₂²	1	1	yes	characteristic
28	C₂×#344	C₂²	1	2	yes	—
29	C₂×#344	C₂²	1	2	yes	—
30	C₂×#344	C₂²	1	1	yes	characteristic
31	C₂×#344	C₂²	1	1	yes	characteristic
32	C₂×#344	C₂²	1	1	yes	characteristic
33	#1738	C₂²	1	2	yes	—
34	C₂×#341	C₂²	1	2	yes	—
35	C₂×#341	C₂²	1	2	yes	—
36	C₂×#341	C₂²	1	2	yes	—
37	C₂×#341	C₂²	1	2	yes	—
38	C₂×#338	C₂²	1	2	yes	—
39	C₂×#338	C₂²	1	2	yes	—
40	C₂²×M₁₆	C₂³	1	2	yes	—
41	C₂²×M₁₆	C₂³	1	2	yes	—
42	C₂²×M₁₆	C₂³	1	1	yes	characteristic
43	C₂²×M₁₆	C₂³	1	1	yes	characteristic
44	C₂²×M₁₆	C₂³	1	1	yes	characteristic
45	C₂²×M₁₆	C₂³	1	1	yes	characteristic
46	C₂²×M₁₆	C₂³	1	2	yes	—
47	C₂³×C₈	C₂³	1	2	yes	—
48	C₂×#117	C₂³	1	1	yes	characteristic
49	C₂×#117	C₂³	1	1	yes	characteristic
50	C₂²×C₄²	C₂³	1	1	yes	characteristic
51	#430	—	2	4	no	—
52	#430	—	4	2	no	—
53	C₂×#108	—	2	4	no	—
54	#424	—	2	4	no	—
55	#424	—	2	4	no	—
56	#424	—	4	2	no	—
57	#424	—	4	2	no	—
58	#423	—	2	1	no	—
59	#423	—	2	1	no	—
60	#423	—	2	1	no	—
61	#423	—	2	1	no	—
62	#423	—	2	1	no	—
63	#423	—	2	1	no	—
64	#423	—	2	1	no	—
65	#423	—	2	1	no	—
66	#423	—	2	1	no	—
67	#423	—	2	1	no	—
68	#423	—	2	1	no	—
69	#423	—	2	1	no	—
70	C₂×C₄⋊C₈	—	2	4	no	—
71	C₂×C₄⋊C₈	—	2	4	no	—
72	C₂×C₄⋊C₈	—	2	1	no	—
73	C₂×C₄⋊C₈	—	2	1	no	—
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	—	2	1	no	—
79	C₂×C₄⋊C₈	—	2	1	no	—
80	C₂×C₄⋊C₈	—	2	1	no	—
81	C₂×C₄⋊C₈	—	2	1	no	—
82	C₂×C₄⋊C₈	D₄	1	2	yes	—
83	C₂×C₄⋊C₈	D₄	1	2	yes	—
84	C₄×M₁₆	—	2	1	no	—
85	C₄×M₁₆	—	2	1	no	—
86	C₄×M₁₆	—	2	1	no	—
87	C₄×M₁₆	—	2	1	no	—
88	C₄×M₁₆	—	2	1	no	—
89	C₄×M₁₆	—	2	1	no	—
90	C₄×M₁₆	—	2	1	no	—
91	C₄×M₁₆	—	2	1	no	—
92	C₂×#97	—	2	1	no	—
93	C₂×#97	—	2	1	no	—
94	C₂×C₄×C₈	—	2	1	no	—
95	C₂×C₄×C₈	—	2	1	no	—
96	C₄×C₄⋊C₄	—	2	1	no	—
97	C₄×C₄⋊C₄	—	2	1	no	—
98	C₄×C₂²⋊C₄	Q₈	1	2	yes	—
99	C₄×C₂²⋊C₄	Q₈	1	2	yes	—
100	#376	—	2	1	no	—
101	C₄³	—	2	1	no	—
102	#344	—	2	4	no	—
103	#344	—	2	2	no	—
104	#344	—	2	4	no	—
105	#344	—	2	2	no	—
106	#344	D₄	1	4	yes	—
107	#344	Q₈	1	4	yes	—
108	#341	—	2	4	no	—
109	#341	—	2	4	no	—
110	#341	—	2	4	no	—
111	#341	—	4	2	no	—
112	#341	—	4	2	no	—
113	#338	—	2	4	no	—
114	#338	—	4	2	no	—
115	C₂³×C₄	C₂×Q₈	1	1	yes	characteristic
116	C₂³×C₄	C₂×Q₈	1	1	yes	characteristic
117	C₂³×C₄	C₂⁴	1	1	yes	characteristic
118	C₂×M₁₆	—	2	2	no	—
119	C₂×M₁₆	—	2	1	no	—
120	C₂×M₁₆	—	2	1	no	—
121	C₂×M₁₆	—	2	2	no	—
122	C₂×M₁₆	—	2	2	no	—
123	C₂×M₁₆	—	2	2	no	—
124	C₂×M₁₆	—	2	1	no	—
125	C₂×M₁₆	—	2	2	no	—
126	C₂×M₁₆	—	2	2	no	—
127	C₂×M₁₆	—	2	1	no	—
128	C₂×M₁₆	—	2	1	no	—
129	C₂×M₁₆	—	2	1	no	—
130	C₂×M₁₆	—	2	1	no	—
131	C₂×M₁₆	—	2	1	no	—
132	C₂×M₁₆	—	2	1	no	—
133	C₂×M₁₆	—	2	1	no	—
134	C₂×M₁₆	—	2	1	no	—
135	C₂×M₁₆	—	2	1	no	—
136	C₂×M₁₆	—	2	1	no	—
137	C₂×M₁₆	—	2	1	no	—
138	C₂×M₁₆	—	2	1	no	—
139	C₂×M₁₆	—	2	1	no	—
140	C₂×M₁₆	—	2	1	no	—
141	C₂×M₁₆	—	2	1	no	—
142	C₂×M₁₆	—	2	1	no	—
143	C₂×M₁₆	—	2	1	no	—
144	C₂×M₁₆	—	2	2	no	—
145	C₂×M₁₆	—	2	2	no	—
146	C₂×M₁₆	—	2	2	no	—
147	C₂×M₁₆	—	2	2	no	—
148	C₂×M₁₆	—	2	2	no	—
149	C₂×M₁₆	—	2	2	no	—
150	C₂×M₁₆	—	2	2	no	—
151	C₂×M₁₆	—	2	2	no	—
152	C₂×M₁₆	—	2	2	no	—
153	C₂×M₁₆	—	2	2	no	—
154	C₂×M₁₆	—	2	2	no	—
155	C₂×M₁₆	—	2	2	no	—
156	C₂×M₁₆	C₂×D₄	1	2	yes	—
157	C₂×M₁₆	C₂×D₄	1	2	yes	—
158	C₂×M₁₆	C₂×Q₈	1	2	yes	—
159	C₂×M₁₆	C₂×Q₈	1	2	yes	—
160	C₂²×C₈	—	2	1	no	—
161	C₂²×C₈	—	2	1	no	—
162	C₂²×C₈	—	2	1	no	—
163	C₂²×C₈	—	2	1	no	—
164	C₂²×C₈	—	2	2	no	—
165	C₂²×C₈	—	2	2	no	—
166	C₂²×C₈	—	2	2	no	—
167	C₂²×C₈	—	2	2	no	—
168	C₂²×C₈	—	2	2	no	—
169	C₂²×C₈	—	2	2	no	—
170	C₂²×C₈	—	2	2	no	—
171	C₂²×C₈	—	2	2	no	—
172	C₂²×C₈	—	2	2	no	—
173	C₂²×C₈	C₂×D₄	1	4	yes	—
174	#117	—	2	1	no	—
175	#117	—	2	1	no	—
176	#117	—	2	1	no	—
177	#117	—	2	1	no	—
178	#117	C₂×D₄	1	2	yes	—
179	#117	C₂×Q₈	1	2	yes	—
180	#117	#41	1	2	yes	—
181	#117	#41	1	2	yes	—
182	C₂×C₄⋊C₄	—	2	1	no	—
183	C₂×C₄⋊C₄	—	2	1	no	—
184	C₂×C₂²⋊C₄	C₂×Q₈	1	2	yes	—
185	C₂×C₂²⋊C₄	C₂×Q₈	1	2	yes	—
186	C₂×C₄²	—	2	1	no	—
187	C₂×C₄²	—	2	1	no	—
188	C₂×C₄²	—	2	2	no	—
189	C₂×C₄²	—	2	2	no	—
190	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
191	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
192	C₂×C₄²	#41	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	C₂×C₄²	#41	1	1	yes	characteristic
199	C₂×C₄²	#41	1	1	yes	characteristic
200	C₂×C₄²	#41	1	1	yes	characteristic
201	C₂×C₄²	#41	1	1	yes	characteristic
202	#108	—	4	8	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	8	no	—
208	C₄⋊C₈	—	4	8	no	—
209	C₄⋊C₈	—	4	1	no	—
210	C₄⋊C₈	—	4	1	no	—
211	C₄⋊C₈	—	4	1	no	—
212	C₄⋊C₈	—	4	1	no	—
213	C₄⋊C₈	—	4	1	no	—
214	C₄⋊C₈	—	4	1	no	—
215	C₄⋊C₈	—	4	1	no	—
216	C₄⋊C₈	—	4	1	no	—
217	C₄⋊C₈	—	4	1	no	—
218	C₄⋊C₈	—	4	1	no	—
219	C₄⋊C₈	—	4	1	no	—
220	C₄⋊C₈	—	4	1	no	—
221	#97	—	4	1	no	—
222	#97	—	4	1	no	—
223	#97	—	4	1	no	—
224	#97	—	4	1	no	—
225	C₄×C₈	—	4	1	no	—
226	C₄×C₈	—	4	1	no	—
227	C₄×C₈	—	4	1	no	—
228	C₄×C₈	—	4	1	no	—
229	#95	—	2	2	no	—
230	#95	—	2	2	no	—
231	C₂⁴	C₂²×Q₈	1	1	yes	characteristic
232	C₂²×C₄	—	2	2	no	—
233	C₂²×C₄	—	2	2	no	—
234	C₂²×C₄	—	4	2	no	—
235	C₂²×C₄	—	8	1	no	—
236	C₂²×C₄	C₂²⋊Q₈	1	1	yes	characteristic
237	C₂²×C₄	C₂²⋊Q₈	1	1	yes	characteristic
238	C₂²×C₄	C₂²⋊Q₈	1	1	yes	characteristic
239	C₂²×C₄	C₂²⋊Q₈	1	1	yes	characteristic
240	C₂²×C₄	#125	1	1	yes	characteristic
241	C₂²×C₄	#125	1	1	yes	characteristic
242	C₂²×C₄	#125	1	1	yes	characteristic
243	C₂²×C₄	#125	1	1	yes	characteristic
244	C₂²×C₄	#125	1	1	yes	characteristic
245	C₂²×C₄	#125	1	1	yes	characteristic
246	C₂²×C₄	#125	1	1	yes	characteristic
247	C₂²×C₄	#125	1	1	yes	characteristic
248	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
249	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
250	C₂²×C₄	C₂²×Q₈	1	1	yes	characteristic
251	C₂²×C₄	C₂×#41	1	1	yes	characteristic
252	C₂²×C₄	C₂×#41	1	1	yes	characteristic
253	C₂²×C₄	C₂×#41	1	1	yes	characteristic
254	C₂²×C₄	C₂×#41	1	1	yes	characteristic
255	C₂²×C₄	C₂×#41	1	1	yes	characteristic
256	C₂²×C₄	C₂×#41	1	1	yes	characteristic
257	C₂²×C₄	C₂×#41	1	1	yes	characteristic
258	C₂²×C₄	H(5,𝔽₂)	1	1	yes	characteristic
259	C₂²×C₄	H(5,𝔽₂)	1	1	yes	characteristic
260	C₂²×C₄	2₋¹⁺⁴	1	1	yes	characteristic
261	C₂²×C₄	2₋¹⁺⁴	1	1	yes	characteristic
262	M₁₆	—	2	2	no	—
263	M₁₆	—	2	2	no	—
264	M₁₆	—	2	2	no	—
265	M₁₆	—	2	2	no	—
266	M₁₆	—	2	2	no	—
267	M₁₆	—	2	2	no	—
268	M₁₆	—	2	2	no	—
269	M₁₆	—	2	2	no	—
270	M₁₆	—	4	2	no	—
271	M₁₆	—	4	2	no	—
272	M₁₆	—	4	1	no	—
273	M₁₆	—	4	1	no	—
274	M₁₆	—	4	1	no	—
275	M₁₆	—	4	1	no	—
276	M₁₆	—	4	2	no	—
277	M₁₆	—	4	1	no	—
278	M₁₆	—	4	1	no	—
279	M₁₆	—	4	1	no	—
280	M₁₆	—	4	1	no	—
281	M₁₆	—	4	2	no	—
282	M₁₆	—	4	2	no	—
283	M₁₆	—	4	2	no	—
284	M₁₆	—	4	2	no	—
285	M₁₆	—	4	2	no	—
286	M₁₆	—	4	2	no	—
287	M₁₆	—	4	2	no	—
288	M₁₆	—	4	2	no	—
289	M₁₆	—	4	2	no	—
290	C₂×C₈	—	2	4	no	—
291	C₂×C₈	—	2	2	no	—
292	C₂×C₈	—	2	2	no	—
293	C₂×C₈	—	2	4	no	—
294	C₂×C₈	—	2	4	no	—
295	C₂×C₈	—	2	2	no	—
296	C₂×C₈	—	2	2	no	—
297	C₂×C₈	—	4	1	no	—
298	C₂×C₈	—	4	1	no	—
299	C₂×C₈	—	4	1	no	—
300	C₂×C₈	—	4	1	no	—
301	C₂×C₈	—	4	1	no	—
302	C₂×C₈	—	4	1	no	—
303	C₂×C₈	—	4	1	no	—
304	C₂×C₈	—	4	1	no	—
305	C₂×C₈	—	4	2	no	—
306	C₂×C₈	—	4	2	no	—
307	C₂×C₈	—	4	2	no	—
308	C₂×C₈	—	4	2	no	—
309	C₂×C₈	—	4	2	no	—
310	C₂×C₈	—	4	2	no	—
311	C₂×C₈	—	4	2	no	—
312	C₂×C₈	—	4	2	no	—
313	C₂×C₈	—	4	2	no	—
314	C₂×C₈	—	4	2	no	—
315	C₂×C₈	—	4	2	no	—
316	C₂×C₈	—	4	2	no	—
317	C₂×C₈	—	4	2	no	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	2	2	no	—
320	C₄⋊C₄	—	2	2	no	—
321	C₄⋊C₄	—	2	2	no	—
322	C₂²⋊C₄	—	2	2	no	—
323	C₂²⋊C₄	—	2	2	no	—
324	C₂²⋊C₄	#125	1	4	yes	—
325	C₂²⋊C₄	C₄⋊Q₈	1	4	yes	—
326	C₄²	—	2	2	no	—
327	C₄²	—	2	2	no	—
328	C₄²	—	2	2	no	—
329	C₄²	—	2	2	no	—
330	C₄²	—	4	4	no	—
331	C₄²	—	8	2	no	—
332	C₄²	#123	1	1	yes	characteristic
333	C₄²	#123	1	1	yes	characteristic
334	C₄²	#123	1	1	yes	characteristic
335	C₄²	#123	1	1	yes	characteristic
336	C₄²	#124	1	1	yes	characteristic
337	C₄²	#124	1	1	yes	characteristic
338	C₄²	#124	1	1	yes	characteristic
339	C₄²	#124	1	1	yes	characteristic
340	C₄²	#126	1	1	yes	characteristic
341	C₄²	#126	1	1	yes	characteristic
342	C₄²	#126	1	1	yes	characteristic
343	C₄²	#126	1	1	yes	characteristic
344	C₄²	#126	1	1	yes	characteristic
345	C₄²	#126	1	1	yes	characteristic
346	C₄²	#126	1	1	yes	characteristic
347	C₄²	#126	1	1	yes	characteristic
348	C₂³	—	4	1	no	—
349	C₂³	—	4	1	no	—
350	C₂³	C₂×C₂²⋊Q₈	1	1	yes	characteristic
351	C₂³	C₂×#125	1	1	yes	characteristic
352	C₂³	C₂×#125	1	1	yes	characteristic
353	C₂³	C₂×#125	1	1	yes	characteristic
354	C₂³	C₂×C₄⋊Q₈	1	1	yes	characteristic
355	C₂³	#544	1	1	yes	characteristic
356	C₂³	#544	1	1	yes	characteristic
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	4	no	—
361	C₂×C₄	—	2	4	no	—
362	C₂×C₄	—	4	1	no	—
363	C₂×C₄	—	4	1	no	—
364	C₂×C₄	—	4	1	no	—
365	C₂×C₄	—	4	1	no	—
366	C₂×C₄	—	4	1	no	—
367	C₂×C₄	—	4	1	no	—
368	C₂×C₄	—	4	1	no	—
369	C₂×C₄	—	4	1	no	—
370	C₂×C₄	—	4	1	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	#400	1	1	yes	characteristic
376	C₂×C₄	#400	1	1	yes	characteristic
377	C₂×C₄	#400	1	1	yes	characteristic
378	C₂×C₄	#400	1	1	yes	characteristic
379	C₂×C₄	#400	1	1	yes	characteristic
380	C₂×C₄	#400	1	1	yes	characteristic
381	C₂×C₄	#400	1	1	yes	characteristic
382	C₂×C₄	#400	1	1	yes	characteristic
383	C₂×C₄	C₂×#123	1	1	yes	characteristic
384	C₂×C₄	C₂×#124	1	1	yes	characteristic
385	C₂×C₄	C₂×#126	1	1	yes	characteristic
386	C₂×C₄	C₂×#126	1	1	yes	characteristic
387	C₂×C₄	#532	1	1	yes	characteristic
388	C₂×C₄	#532	1	1	yes	characteristic
389	C₂×C₄	#533	1	1	yes	characteristic
390	C₂×C₄	#533	1	1	yes	characteristic
391	C₂×C₄	#540	1	1	yes	characteristic
392	C₂×C₄	#541	1	1	yes	characteristic
393	C₂×C₄	#542	1	1	yes	characteristic
394	C₂×C₄	#542	1	1	yes	characteristic
395	C₂×C₄	D₄²	1	1	yes	characteristic
396	C₂×C₄	#546	1	1	yes	characteristic
397	C₂×C₄	#547	1	1	yes	characteristic
398	C₂×C₄	#547	1	1	yes	characteristic
399	C₂×C₄	#548	1	1	yes	characteristic
400	C₂×C₄	D₄×Q₈	1	1	yes	characteristic
401	C₂×C₄	#550	1	1	yes	characteristic
402	C₂×C₄	#552	1	1	yes	characteristic
403	C₂×C₄	#553	1	1	yes	characteristic
404	C₂×C₄	#554	1	1	yes	characteristic
405	C₂×C₄	#554	1	1	yes	characteristic
406	C₂×C₄	#555	1	1	yes	characteristic
407	C₂×C₄	#556	1	1	yes	characteristic
408	C₂×C₄	#556	1	1	yes	characteristic
409	C₂×C₄	#557	1	1	yes	characteristic
410	C₂×C₄	#559	1	1	yes	characteristic
411	C₈	—	4	4	no	—
412	C₈	—	4	2	no	—
413	C₈	—	4	2	no	—
414	C₈	—	4	2	no	—
415	C₈	—	4	2	no	—
416	C₈	—	8	2	no	—
417	C₈	—	8	2	no	—
418	C₈	—	8	2	no	—
419	C₂²	—	2	1	no	—
420	C₂²	—	2	1	no	—
421	C₂²	—	2	1	no	—
422	C₂²	—	2	1	no	—
423	C₂²	—	2	1	no	—
424	C₂²	—	2	1	no	—
425	C₂²	—	4	1	no	—
426	C₂²	—	4	1	no	—
427	C₂²	—	4	1	no	—
428	C₂²	—	4	1	no	—
429	C₂²	C₂×#400	1	1	yes	characteristic
430	C₂²	#2440	1	1	yes	characteristic
431	C₂²	#2442	1	1	yes	characteristic
432	C₂²	#2552	1	1	yes	characteristic
433	C₂²	#2571	1	1	yes	characteristic
434	C₂²	#2647	1	1	yes	characteristic
435	C₂²	#2859	1	1	yes	characteristic
436	C₄	—	2	1	no	—
437	C₄	—	2	1	no	—
438	C₄	—	2	1	no	—
439	C₄	—	2	1	no	—
440	C₄	—	2	1	no	—
441	C₄	—	2	1	no	—
442	C₄	—	2	1	no	—
443	C₄	—	4	4	no	—
444	C₄	—	4	4	no	—
445	C₄	#2103	1	2	yes	complemented
446	C₄	#2445	1	1	yes	characteristic
447	C₄	#2446	1	1	yes	characteristic
448	C₄	#2491	1	1	yes	characteristic
449	C₄	#2492	1	1	yes	characteristic
450	C₄	#2496	1	1	yes	characteristic
451	C₄	#2497	1	1	yes	characteristic
452	C₄	#2511	1	1	yes	characteristic
453	C₄	#2512	1	1	yes	characteristic
454	C₂	—	2	1	no	—
455	C₂	—	2	1	no	—
456	C₂	—	2	1	no	—
457	C₂	—	2	1	no	—
458	C₂	—	2	1	no	—
459	C₂	—	2	1	no	—
460	C₂	#15146	1	1	yes	characteristic
461	C₂	C₂×#2103	1	1	yes	characteristic
462	C₂	#23753	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×#124
commutator, Frattini, cosocle	C₂³×C₄	C₂⁴
socle	C₂²	C₂×#400
prime radical	C₂⁴	C₂²×Q₈
LCS	G ▷ C₂³×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄² ◁ G
LECS	G ▷ C₂³×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
445. C₄	#2103	semidirect

Maximal subgroups

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

subgroup	index
C₂×#2103	2
#21177	2
#20793	2
#11264	2
#11237	2
#10856	2
#10853	2
C₄⋊#338	2
C₄×#344	2