Subgroups — C₄×#16840805 #30614517

Order 15616.

1046 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16840805	C₂	1	2	yes	maximal
2	C₄×#14519865	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#14519864	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×#14519847	C₂	1	1	yes	maximal, characteristic, complemented
5	#21461622	C₂	1	2	yes	maximal, complemented
6	#21461596	C₂	1	2	yes	maximal, complemented
7	#21461594	C₂	1	2	yes	maximal, complemented
8	C₄×#14519842	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×#14519841	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×C₈×#6923	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×#14519798	C₂	1	1	yes	maximal, characteristic
12	C₂×#14519865	C₂²	1	2	yes	—
13	C₂×#14519864	C₂²	1	2	yes	—
14	#16840805	C₄	1	16	yes	direct product factor
15	C₂×#14519847	C₂²	1	2	yes	—
16	C₂×#14519842	C₂²	1	2	yes	—
17	C₂×#14519841	C₂²	1	2	yes	—
18	#16840727	—	2	2	no	—
19	#16840727	C₂²	1	2	yes	—
20	#16840727	C₂²	1	2	yes	—
21	#16840726	—	2	2	no	—
22	C₄×#11758213	—	2	1	no	—
23	C₄×#11758213	C₂²	1	1	yes	characteristic
24	C₄×#11758213	C₂²	1	1	yes	characteristic
25	C₄×#11758217	—	2	1	no	—
26	C₄×D₆₁⋊C₈	—	2	1	no	—
27	C₄×D₆₁⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₄×#92420	—	2	1	no	—
29	C₂×C₈×#6923	C₂²	1	2	yes	—
30	C₂×C₈×#6923	C₂²	1	2	yes	—
31	C₄²×#6923	C₂²	1	1	yes	characteristic
32	#16840638	C₂²	1	2	yes	—
33	#16840632	C₂²	1	2	yes	—
34	#16840632	C₂²	1	2	yes	—
35	C₂×#14519798	C₂²	1	1	yes	characteristic
36	C₄×#11758226	C₂²	1	1	yes	characteristic
37	C₄×#11758224	C₂²	1	1	yes	characteristic
38	C₄×#11758202	C₄	1	1	yes	characteristic, complemented
39	#16839854	C₄	1	1	yes	characteristic, complemented
40	C₄×#11758190	C₄	1	1	yes	characteristic, complemented
41	SD₁₆×Dic₆₁	C₄	1	1	yes	characteristic, complemented
42	#16839849	C₄	1	1	yes	characteristic, complemented
43	C₄×#11758199	C₄	1	1	yes	characteristic, complemented
44	#16839842	C₄	1	1	yes	characteristic, complemented
45	#16839797	C₂²	1	1	yes	characteristic
46	#16839757	C₂²	1	1	yes	characteristic
47	#16839755	C₂²	1	1	yes	characteristic
48	C₄×C₈×D₆₁	C₂²	1	1	yes	characteristic
49	C₄×SD₁₆×C₆₁	C₄	1	1	yes	characteristic, complemented
50	#14519865	—	2	4	no	—
51	#14519865	C₂×C₄	1	8	yes	complemented
52	#14519864	—	2	4	no	—
53	#14519864	C₂×C₄	1	8	yes	complemented
54	C₂×#11758213	—	2	2	no	—
55	C₂×#11758213	C₂³	1	2	yes	—
56	C₂×#11758213	C₂³	1	2	yes	—
57	C₂×#11758217	—	2	2	no	—
58	C₂×D₆₁⋊C₈	—	2	2	no	—
59	C₂×D₆₁⋊C₈	C₂³	1	2	yes	—
60	C₂²×#92420	—	2	2	no	—
61	C₂×C₄×#6923	—	2	1	no	—
62	C₂×C₄×#6923	—	2	1	no	—
63	C₂×C₄×#6923	C₂³	1	2	yes	—
64	#14519847	C₂×C₄	1	8	yes	complemented
65	#14519842	C₂×C₄	1	8	yes	complemented
66	#14519841	C₂×C₄	1	8	yes	complemented
67	#14519832	—	2	2	no	—
68	#14519832	—	2	2	no	—
69	#14519832	—	2	1	no	—
70	#14519832	—	2	1	no	—
71	C₄×#92420	—	2	2	no	—
72	C₄×#92420	—	2	2	no	—
73	C₄×#92420	—	2	1	no	—
74	C₄×#92420	—	2	1	no	—
75	C₄×#92420	D₄	1	1	yes	characteristic
76	C₄×#92420	D₄	1	1	yes	characteristic
77	C₄×#92420	D₄	1	2	yes	—
78	C₈×#6923	—	2	4	no	—
79	C₈×#6923	C₂×C₄	1	8	yes	complemented
80	C₂×#11758226	C₂³	1	1	yes	characteristic
81	C₂×#11758224	C₂³	1	1	yes	characteristic
82	#14519798	C₂×C₄	1	8	yes	—
83	C₂×#11758202	C₂×C₄	1	1	yes	characteristic
84	C₂×#11758190	C₂×C₄	1	1	yes	characteristic
85	C₂×#11758199	C₂×C₄	1	1	yes	characteristic
86	C₂×C₈×D₆₁	C₂³	1	1	yes	characteristic
87	C₂×C₈×D₆₁	C₂³	1	1	yes	characteristic
88	Q₈×Dic₆₁	C₂×C₄	1	1	yes	characteristic
89	C₄×Dic₁₂₂	C₂×C₄	1	1	yes	characteristic
90	#14519742	C₂×C₄	1	1	yes	characteristic
91	C₄×D₂₄₄	—	2	1	no	—
92	C₄×D₂₄₄	C₂×C₄	1	1	yes	characteristic
93	D₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
94	#14519739	—	2	1	no	—
95	#14519739	C₂×C₄	1	1	yes	characteristic
96	C₄×C₂²⋊D₆₁	—	2	1	no	—
97	#14519737	—	2	1	no	—
98	#14519735	—	2	1	no	—
99	#14519735	C₂³	1	1	yes	characteristic
100	#14519735	C₂³	1	1	yes	characteristic
101	#14519733	—	2	1	no	—
102	C₂×C₄×Dic₆₁	—	2	1	no	—
103	C₄²×D₆₁	—	2	1	no	—
104	C₄²×D₆₁	C₂³	1	1	yes	characteristic
105	#14519710	C₂×C₄	1	1	yes	characteristic
106	#14519710	C₂×C₄	1	1	yes	characteristic
107	#14519709	C₂×C₄	1	1	yes	characteristic
108	#14519702	C₂×C₄	1	1	yes	characteristic
109	#14519701	C₂×C₄	1	1	yes	characteristic
110	#14519700	C₂×C₄	1	1	yes	characteristic
111	#14519699	C₂×C₄	1	1	yes	characteristic
112	#14519698	C₂×C₄	1	1	yes	characteristic
113	#14519697	C₂×C₄	1	1	yes	characteristic
114	C₄×#92418	C₂×C₄	1	1	yes	characteristic
115	C₈×Dic₆₁	C₂×C₄	1	1	yes	characteristic
116	C₈×Dic₆₁	C₂×C₄	1	1	yes	characteristic
117	C₂×SD₁₆×C₆₁	C₂×C₄	1	1	yes	characteristic
118	C₄×Q₈×C₆₁	C₂×C₄	1	1	yes	characteristic
119	C₄×D₄×C₆₁	C₂×C₄	1	1	yes	characteristic
120	#106×C₆₁	C₂×C₄	1	1	yes	characteristic
121	#103×C₆₁	C₂×C₄	1	1	yes	characteristic
122	#102×C₆₁	C₂×C₄	1	1	yes	characteristic
123	C₄×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
124	C₂²×#6923	—	2	2	no	—
125	C₂×Q₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
126	C₂×D₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
127	C₂²×C₄×C₆₁	—	2	1	no	—
128	C₂×C₂²⋊D₆₁	—	2	1	no	—
129	C₂²×Dic₆₁	—	2	1	no	—
130	C₂²×Dic₆₁	—	2	1	no	—
131	#11758226	—	2	2	no	—
132	#11758226	C₂²×C₄	1	4	yes	—
133	#11758224	—	2	2	no	—
134	#11758224	C₂²×C₄	1	4	yes	—
135	C₂×D₂₄₄	—	2	1	no	—
136	C₂×D₂₄₄	C₂²×C₄	1	1	yes	characteristic
137	C₂×C₄×D₆₁	—	2	1	no	—
138	C₂×C₄×D₆₁	—	2	1	no	—
139	C₂×C₄×D₆₁	—	2	1	no	—
140	C₂×C₄×D₆₁	#41	1	1	yes	characteristic
141	C₂×C₄×D₆₁	#41	1	1	yes	characteristic
142	C₂×C₄×D₆₁	C₂⁴	1	1	yes	characteristic
143	C₂×Dic₁₂₂	C₂²×C₄	1	1	yes	characteristic
144	#11758217	—	2	8	no	—
145	C₂×#92420	—	2	2	no	—
146	C₂×#92420	—	2	2	no	—
147	C₂×#92420	—	2	8	no	—
148	C₂×#92420	C₂×D₄	1	2	yes	—
149	C₂×#92420	C₂×D₄	1	2	yes	—
150	C₄×#6923	—	2	4	no	—
151	C₄×#6923	—	2	4	no	—
152	C₄×#6923	—	2	2	no	—
153	C₄×#6923	C₂²×C₄	1	4	yes	—
154	#11758213	—	2	2	no	—
155	#11758213	—	2	2	no	—
156	#11758213	—	2	8	no	—
157	#11758213	C₂²×C₄	1	4	yes	—
158	#11758213	C₂²×C₄	1	4	yes	—
159	D₆₁⋊C₈	—	2	8	no	—
160	D₆₁⋊C₈	C₂²×C₄	1	4	yes	—
161	D₆₁⋊C₈	#41	1	4	yes	—
162	SD₁₆×C₆₁	C₄²	1	4	yes	complemented
163	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
164	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
165	C₄⋊C₄×C₆₁	—	2	1	no	—
166	C₄⋊C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
167	C₄⋊C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
168	C₂²⋊C₄×C₆₁	—	2	1	no	—
169	C₄²×C₆₁	—	2	1	no	—
170	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
171	C₂²⋊Dic₆₁	—	2	1	no	—
172	#11758202	C₄²	1	4	yes	complemented
173	#11758199	C₄²	1	4	yes	complemented
174	#11758198	—	2	1	no	—
175	#11758198	—	2	1	no	—
176	#11758198	—	2	1	no	—
177	#11758198	—	2	1	no	—
178	C₄⋊Dic₆₁	—	2	1	no	—
179	C₄⋊Dic₆₁	C₂²×C₄	1	1	yes	characteristic
180	C₄⋊Dic₆₁	C₂²×C₄	1	1	yes	characteristic
181	#11758196	—	2	1	no	—
182	#11758196	—	2	1	no	—
183	C₄×Dic₆₁	—	2	1	no	—
184	C₄×Dic₆₁	—	2	1	no	—
185	C₄×Dic₆₁	—	2	1	no	—
186	C₄×Dic₆₁	—	2	1	no	—
187	C₄×Dic₆₁	—	2	1	no	—
188	C₄×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
189	C₄×Dic₆₁	C₂×D₄	1	1	yes	characteristic
190	C₄×Dic₆₁	C₂×D₄	1	1	yes	characteristic
191	C₂×#92418	C₂²×C₄	1	1	yes	characteristic
192	C₂×#92418	C₂²×C₄	1	1	yes	characteristic
193	#11758190	C₄²	1	4	yes	complemented
194	C₈×D₆₁	—	2	2	no	—
195	C₈×D₆₁	C₂²×C₄	1	4	yes	—
196	C₂³×C₆₁	—	2	1	no	—
197	C₂²×D₆₁	—	2	1	no	—
198	C₂²×D₆₁	C₂×#41	1	1	yes	characteristic
199	C₂×#6923	—	2	4	no	—
200	C₂×#6923	—	2	4	no	—
201	C₂×#6923	—	2	4	no	—
202	Q₈×C₆₁	—	2	1	no	—
203	Q₈×C₆₁	C₂×C₄²	1	2	yes	—
204	D₄×C₆₁	—	2	1	no	—
205	D₄×C₆₁	C₂×C₄²	1	2	yes	—
206	C₂×C₄×C₆₁	—	2	1	no	—
207	C₂×C₄×C₆₁	—	2	1	no	—
208	C₂×C₄×C₆₁	—	2	1	no	—
209	C₂×C₄×C₆₁	—	4	2	no	—
210	C₂×C₄×C₆₁	C₄×D₄	1	1	yes	characteristic
211	C₂×C₄×C₆₁	C₄×D₄	1	1	yes	characteristic
212	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
213	C₂²⋊D₆₁	—	2	4	no	—
214	C₂×Dic₆₁	—	2	1	no	—
215	C₂×Dic₆₁	—	2	4	no	—
216	C₂×Dic₆₁	—	2	1	no	—
217	C₂×Dic₆₁	—	2	1	no	—
218	C₂×Dic₆₁	—	4	2	no	—
219	C₂×Dic₆₁	C₄×D₄	1	1	yes	characteristic
220	C₂×Dic₆₁	C₄×D₄	1	1	yes	characteristic
221	C₂×Dic₆₁	C₂²×D₄	1	1	yes	characteristic
222	D₂₄₄	—	2	4	no	—
223	D₂₄₄	—	2	1	no	—
224	D₂₄₄	C₂×C₄²	1	2	yes	—
225	C₄×D₆₁	—	2	2	no	—
226	C₄×D₆₁	—	2	4	no	—
227	C₄×D₆₁	—	2	2	no	—
228	C₄×D₆₁	—	4	2	no	—
229	C₄×D₆₁	—	4	2	no	—
230	C₄×D₆₁	C₂³×C₄	1	2	yes	—
231	C₄×D₆₁	C₂×#41	1	2	yes	—
232	Dic₁₂₂	—	2	1	no	—
233	Dic₁₂₂	C₂×C₄²	1	2	yes	—
234	#92420	—	2	4	no	—
235	#92420	—	2	4	no	—
236	#92420	C₄×D₄	1	4	yes	—
237	#92420	C₄×D₄	1	4	yes	—
238	C₈×C₆₁	—	2	1	no	—
239	C₈×C₆₁	C₂×C₄²	1	2	yes	—
240	#92418	—	2	1	no	—
241	#92418	C₂×C₄²	1	2	yes	—
242	C₄×#443	—	61	1	no	maximal, Sylow
243	C₂²×C₆₁	—	2	2	no	—
244	C₂²×C₆₁	—	4	1	no	—
245	C₂²×C₆₁	—	4	1	no	—
246	C₂²×C₆₁	C₂×C₄×D₄	1	1	yes	characteristic
247	C₂×D₆₁	—	2	1	no	—
248	C₂×D₆₁	—	2	1	no	—
249	C₂×D₆₁	—	2	2	no	—
250	C₂×D₆₁	—	4	1	no	—
251	C₂×D₆₁	—	4	1	no	—
252	C₂×D₆₁	C₄×#41	1	2	yes	—
253	#6923	—	2	8	no	—
254	C₄×C₆₁	—	2	1	no	—
255	C₄×C₆₁	—	2	2	no	—
256	C₄×C₆₁	—	4	1	no	—
257	C₄×C₆₁	—	4	1	no	—
258	C₄×C₆₁	#443	1	2	yes	complemented
259	C₄×C₆₁	C₂²×C₄²	1	1	yes	characteristic
260	C₄×C₆₁	C₄×#41	1	1	yes	characteristic
261	Dic₆₁	—	2	1	no	—
262	Dic₆₁	—	2	2	no	—
263	Dic₆₁	—	4	1	no	—
264	Dic₆₁	—	4	1	no	—
265	Dic₆₁	#443	1	2	yes	complemented
266	Dic₆₁	C₂×C₄×D₄	1	2	yes	—
267	C₂×#443	—	61	2	no	—
268	C₄×#135	—	61	1	no	—
269	C₄×#131	—	61	1	no	—
270	C₄×#131	—	61	1	no	—
271	C₄×#108	—	61	1	no	—
272	#1772	—	61	2	no	—
273	#1764	—	61	2	no	—
274	#1764	—	61	2	no	—
275	C₄×#104	—	61	1	no	—
276	C₄×#104	—	61	1	no	—
277	C₄²×C₈	—	61	1	no	—
278	C₂×C₆₁	—	4	2	no	—
279	C₂×C₆₁	C₄²×D₄	1	1	yes	characteristic
280	C₂×C₆₁	C₂×#443	1	1	yes	characteristic
281	C₂×C₆₁	C₂×#443	1	1	yes	characteristic
282	D₆₁	—	2	2	no	—
283	D₆₁	—	4	2	no	—
284	C₂×#135	—	61	1	no	—
285	C₂×#131	—	61	2	no	—
286	C₂×#131	—	61	2	no	—
287	C₄×#41	—	61	1	no	—
288	C₄×#41	—	61	1	no	—
289	#443	—	61	16	no	—
290	C₄×Q₁₆	—	61	1	no	—
291	C₄×Q₁₆	—	61	1	no	—
292	C₄×SD₁₆	—	61	1	no	—
293	C₄×SD₁₆	—	61	1	no	—
294	C₄×SD₁₆	—	61	1	no	—
295	C₄×SD₁₆	#6923	1	1	yes	characteristic, complemented
296	C₄×D₈	—	61	1	no	—
297	C₄×D₈	—	61	1	no	—
298	C₂×#108	—	61	2	no	—
299	#427	—	61	1	no	—
300	C₂×#104	—	61	2	no	—
301	C₂×#104	—	61	2	no	—
302	#416	—	61	1	no	—
303	#416	—	61	1	no	—
304	#405	—	61	2	no	—
305	#405	—	61	2	no	—
306	#405	—	122	2	no	—
307	#405	—	122	2	no	—
308	C₄×M₁₆	—	61	1	no	—
309	C₄×M₁₆	—	61	1	no	—
310	C₄×M₁₆	—	122	1	no	—
311	C₄×M₁₆	—	122	1	no	—
312	C₂×C₄×C₈	—	61	2	no	—
313	C₂×C₄×C₈	—	61	1	no	—
314	C₂×C₄×C₈	—	61	1	no	—
315	C₂×C₄×C₈	—	61	2	no	—
316	C₂×C₄×C₈	—	122	1	no	—
317	C₂×C₄×C₈	—	122	1	no	—
318	C₄³	—	61	1	no	—
319	#341	—	61	2	no	—
320	#339	—	61	2	no	—
321	#339	—	61	2	no	—
322	C₆₁	C₄×#443	1	1	yes	characteristic, complemented, Sylow
323	C₂×#41	—	61	1	no	—
324	C₂×#41	—	61	1	no	—
325	#135	—	61	8	no	—
326	C₂×Q₁₆	—	61	1	no	—
327	C₂×SD₁₆	—	61	1	no	—
328	C₂×SD₁₆	C₂×#6923	1	1	yes	characteristic
329	C₂×D₈	—	61	1	no	—
330	#131	—	61	8	no	—
331	#131	—	61	8	no	—
332	#131	—	122	4	no	—
333	#131	—	122	4	no	—
334	C₂×M₁₆	—	61	2	no	—
335	C₂×M₁₆	—	61	2	no	—
336	C₂×M₁₆	—	122	2	no	—
337	C₂×M₁₆	—	122	2	no	—
338	C₂²×C₈	—	61	2	no	—
339	C₂²×C₈	—	61	1	no	—
340	C₂²×C₈	—	61	1	no	—
341	C₂²×C₈	—	122	2	no	—
342	C₂²×C₈	—	122	2	no	—
343	C₄×Q₈	—	61	1	no	—
344	C₄×Q₈	—	61	1	no	—
345	C₄×Q₈	—	61	1	no	—
346	C₄×Q₈	C₂×#6923	1	1	yes	characteristic
347	C₄×D₄	—	61	1	no	—
348	C₄×D₄	—	61	1	no	—
349	C₄×D₄	—	61	1	no	—
350	C₄×D₄	—	122	1	no	—
351	C₄×D₄	—	122	1	no	—
352	C₄×D₄	—	122	1	no	—
353	C₄×D₄	—	122	1	no	—
354	C₄×D₄	C₂×#6923	1	1	yes	characteristic
355	#117	—	61	1	no	—
356	#117	—	61	1	no	—
357	#117	—	122	1	no	—
358	#117	—	122	1	no	—
359	C₂×C₄²	—	61	1	no	—
360	C₂×C₄²	—	61	2	no	—
361	C₂×C₄²	—	122	1	no	—
362	C₂×C₄²	—	122	1	no	—
363	C₂×C₄²	—	122	1	no	—
364	C₂×C₄²	—	122	1	no	—
365	#108	—	61	8	no	—
366	#107	—	61	1	no	—
367	#107	—	61	1	no	—
368	#106	—	61	1	no	—
369	#106	C₂×#6923	1	1	yes	characteristic
370	#104	—	61	8	no	—
371	#104	—	61	8	no	—
372	#103	—	61	1	no	—
373	#103	—	61	1	no	—
374	#103	—	61	1	no	—
375	#103	C₂×#6923	1	1	yes	characteristic
376	#102	—	61	1	no	—
377	#102	—	61	1	no	—
378	#102	—	61	1	no	—
379	#102	C₂×#6923	1	1	yes	characteristic
380	#97	—	122	1	no	—
381	#97	—	122	1	no	—
382	#97	—	122	2	no	—
383	#97	—	122	2	no	—
384	C₄×C₈	—	61	8	no	—
385	C₄×C₈	—	61	1	no	—
386	C₄×C₈	—	61	1	no	—
387	C₄×C₈	—	61	2	no	—
388	C₄×C₈	—	61	1	no	—
389	C₄×C₈	—	61	1	no	—
390	C₄×C₈	—	61	1	no	—
391	C₄×C₈	—	122	1	no	—
392	C₄×C₈	—	122	1	no	—
393	C₄×C₈	—	122	4	no	—
394	C₄×C₈	—	122	2	no	—
395	C₄×C₈	—	122	2	no	—
396	C₄×C₈	C₂×#6923	1	1	yes	characteristic
397	#41	—	61	4	no	—
398	#41	—	61	4	no	—
399	#41	—	122	2	no	—
400	#41	—	122	2	no	—
401	C₂×Q₈	—	61	1	no	—
402	C₂×Q₈	C₂²×#6923	1	1	yes	characteristic
403	C₂×D₄	—	61	1	no	—
404	C₂×D₄	—	122	1	no	—
405	C₂×D₄	—	122	1	no	—
406	C₂×D₄	C₂²×#6923	1	1	yes	characteristic
407	C₂²×C₄	—	2	1	no	—
408	C₂²×C₄	—	61	1	no	—
409	C₂²×C₄	—	61	1	no	—
410	C₂²×C₄	—	61	1	no	—
411	C₂²×C₄	—	122	1	no	—
412	C₂²×C₄	—	122	1	no	—
413	C₂²×C₄	—	122	1	no	—
414	C₂²×C₄	—	122	1	no	—
415	C₂²×C₄	—	122	2	no	—
416	C₂²×C₄	—	122	1	no	—
417	Q₁₆	—	61	4	no	—
418	SD₁₆	—	61	4	no	—
419	SD₁₆	C₄×#6923	1	4	yes	complemented
420	D₈	—	61	4	no	—
421	M₁₆	—	61	4	no	—
422	M₁₆	—	61	4	no	—
423	M₁₆	—	122	8	no	—
424	M₁₆	—	122	8	no	—
425	M₁₆	—	122	2	no	—
426	M₁₆	—	122	2	no	—
427	C₂×C₈	—	61	2	no	—
428	C₂×C₈	—	61	2	no	—
429	C₂×C₈	—	61	4	no	—
430	C₂×C₈	—	61	4	no	—
431	C₂×C₈	—	61	1	no	—
432	C₂×C₈	—	61	4	no	—
433	C₂×C₈	—	61	1	no	—
434	C₂×C₈	—	122	2	no	—
435	C₂×C₈	—	122	8	no	—
436	C₂×C₈	—	122	8	no	—
437	C₂×C₈	—	122	2	no	—
438	C₂×C₈	—	122	2	no	—
439	C₂×C₈	C₂²×#6923	1	1	yes	characteristic
440	C₂×C₈	C₂²×#6923	1	1	yes	characteristic
441	C₄⋊C₄	—	2	1	no	—
442	C₄⋊C₄	—	61	1	no	—
443	C₄⋊C₄	—	61	1	no	—
444	C₄⋊C₄	—	122	1	no	—
445	C₄⋊C₄	—	122	1	no	—
446	C₄⋊C₄	—	122	1	no	—
447	C₄⋊C₄	C₂²×#6923	1	1	yes	characteristic
448	C₄⋊C₄	C₂²×#6923	1	1	yes	characteristic
449	C₂²⋊C₄	—	2	1	no	—
450	C₂²⋊C₄	—	122	1	no	—
451	C₂²⋊C₄	—	122	1	no	—
452	C₂²⋊C₄	—	122	1	no	—
453	C₂²⋊C₄	—	122	1	no	—
454	C₂²⋊C₄	—	122	1	no	—
455	C₄²	—	2	1	no	—
456	C₄²	—	61	1	no	—
457	C₄²	—	61	1	no	—
458	C₄²	—	61	1	no	—
459	C₄²	—	61	4	no	—
460	C₄²	—	122	1	no	—
461	C₄²	—	122	1	no	—
462	C₄²	—	122	1	no	—
463	C₄²	—	122	1	no	—
464	C₄²	—	122	2	no	—
465	C₄²	—	122	4	no	—
466	C₄²	—	122	4	no	—
467	C₄²	—	122	1	no	—
468	C₄²	C₂²×#6923	1	1	yes	characteristic
469	C₂³	—	2	1	no	—
470	C₂³	—	61	1	no	—
471	C₂³	—	122	1	no	—
472	Q₈	—	2	1	no	—
473	Q₈	—	61	2	no	—
474	Q₈	—	122	1	no	—
475	Q₈	C₂×C₄×#6923	1	2	yes	—
476	D₄	—	2	1	no	—
477	D₄	—	61	2	no	—
478	D₄	—	122	4	no	—
479	D₄	—	122	4	no	—
480	D₄	—	122	1	no	—
481	D₄	C₂×C₄×#6923	1	2	yes	—
482	C₂×C₄	—	2	1	no	—
483	C₂×C₄	—	2	1	no	—
484	C₂×C₄	—	2	1	no	—
485	C₂×C₄	—	4	2	no	—
486	C₂×C₄	—	61	1	no	—
487	C₂×C₄	—	61	1	no	—
488	C₂×C₄	—	61	2	no	—
489	C₂×C₄	—	61	2	no	—
490	C₂×C₄	—	61	1	no	—
491	C₂×C₄	—	122	2	no	—
492	C₂×C₄	—	122	4	no	—
493	C₂×C₄	—	122	4	no	—
494	C₂×C₄	—	122	4	no	—
495	C₂×C₄	—	122	4	no	—
496	C₂×C₄	—	122	4	no	—
497	C₂×C₄	—	122	1	no	—
498	C₂×C₄	—	122	2	no	—
499	C₂×C₄	—	122	1	no	—
500	C₂×C₄	—	122	1	no	—
501	C₂×C₄	—	244	2	no	—
502	C₂×C₄	—	244	2	no	—
503	C₂×C₄	—	244	2	no	—
504	C₂×C₄	D₄×#6923	1	1	yes	characteristic
505	C₂×C₄	D₄×#6923	1	1	yes	characteristic
506	C₂×C₄	C₂³×#6923	1	1	yes	characteristic
507	C₈	—	2	1	no	—
508	C₈	—	61	4	no	—
509	C₈	—	61	4	no	—
510	C₈	—	61	2	no	—
511	C₈	—	122	4	no	—
512	C₈	—	122	4	no	—
513	C₈	—	122	1	no	—
514	C₈	C₂×C₄×#6923	1	2	yes	—
515	C₂²	—	2	2	no	—
516	C₂²	—	4	1	no	—
517	C₂²	—	4	1	no	—
518	C₂²	—	61	2	no	—
519	C₂²	—	122	1	no	—
520	C₂²	—	122	1	no	—
521	C₂²	—	122	2	no	—
522	C₂²	—	244	1	no	—
523	C₂²	—	244	1	no	—
524	C₂²	C₂×D₄×#6923	1	1	yes	characteristic
525	C₄	—	2	1	no	—
526	C₄	—	2	2	no	—
527	C₄	—	4	1	no	—
528	C₄	—	4	1	no	—
529	C₄	—	61	2	no	—
530	C₄	—	61	2	no	—
531	C₄	—	122	8	no	—
532	C₄	—	122	1	no	—
533	C₄	—	122	2	no	—
534	C₄	—	244	1	no	—
535	C₄	—	244	1	no	—
536	C₄	#16840805	1	2	yes	direct product factor
537	C₄	C₂²×C₄×#6923	1	1	yes	characteristic
538	C₄	#41×#6923	1	1	yes	characteristic
539	C₂	—	4	2	no	—
540	C₂	—	122	2	no	—
541	C₂	—	244	2	no	—
542	C₂	C₄×D₄×#6923	1	1	yes	characteristic
543	C₂	C₂×#16840805	1	1	yes	characteristic
544	C₂	D₆₁⋊#443	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₄×#6923
commutator	C₄×C₆₁	C₂²×C₄²
Frattini	C₂×C₄	C₂³×#6923
Fitting	C₄×SD₁₆×C₆₁	C₄
socle	C₂²×C₆₁	C₂×C₄×D₄
prime radical	C₂×#14519798	C₂²
cosocle	C₂×C₄×D₆₁	C₂⁴
hypercenter	C₄×SD₁₆	#6923
hypocenter	C₆₁	C₄×#443
LCS	G ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×SD₁₆

Complements

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

N	H ≅ G/N	type
2. C₄×#14519865	C₂	semidirect
3. C₄×#14519864	C₂	semidirect
4. C₄×#14519847	C₂	semidirect
5. #21461622	C₂	semidirect
6. #21461596	C₂	semidirect
7. #21461594	C₂	semidirect
8. C₄×#14519842	C₂	semidirect
9. C₄×#14519841	C₂	semidirect
10. C₄×C₈×#6923	C₂	semidirect
14. #16840805	C₄	direct (N × H)
38. C₄×#11758202	C₄	semidirect
39. #16839854	C₄	semidirect
40. C₄×#11758190	C₄	semidirect
41. SD₁₆×Dic₆₁	C₄	semidirect
42. #16839849	C₄	semidirect
43. C₄×#11758199	C₄	semidirect
44. #16839842	C₄	semidirect
49. C₄×SD₁₆×C₆₁	C₄	semidirect
51. #14519865	C₂×C₄	semidirect
53. #14519864	C₂×C₄	semidirect
64. #14519847	C₂×C₄	semidirect
65. #14519842	C₂×C₄	semidirect
66. #14519841	C₂×C₄	semidirect
79. C₈×#6923	C₂×C₄	semidirect
162. SD₁₆×C₆₁	C₄²	semidirect
172. #11758202	C₄²	semidirect
173. #11758199	C₄²	semidirect
193. #11758190	C₄²	semidirect
258. C₄×C₆₁	#443	semidirect
265. Dic₆₁	#443	semidirect
295. C₄×SD₁₆	#6923	semidirect
322. C₆₁	C₄×#443	semidirect
419. SD₁₆	C₄×#6923	semidirect
536. C₄	#16840805	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#16840805	2
C₄×#14519865	2
C₄×#14519864	2
C₄×#14519847	2
#21461622	2
#21461596	2
#21461594	2
C₄×#14519842	2
C₄×#14519841	2
C₄×C₈×#6923	2
C₄×#14519798	2
C₄×#443	61

Subgroups — C4×#16840805 #30614517

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#16840805 #30614517