Subgroups — #435×#6923 #30614444

Order 15616.

1282 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₆₁⋊#435	C₂	1	1	yes	maximal, characteristic
2	C₂×M₁₆×#6923	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₈×#6923	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×D₄×#6923	C₂	1	1	yes	maximal, characteristic
5	#21461620	C₂	1	1	yes	maximal, characteristic, complemented
6	#21461617	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄⋊C₈×#6923	C₂	1	1	yes	maximal, characteristic, complemented
8	#21461562	C₂	1	1	yes	maximal, characteristic, complemented
9	#21461559	C₂	1	1	yes	maximal, characteristic, complemented
10	#21461558	C₂	1	1	yes	maximal, characteristic, complemented
11	#21461555	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²⋊C₈×#6923	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²⋊C₈×#6923	C₂	1	1	yes	maximal, characteristic, complemented
14	#97×#6923	C₂	1	1	yes	maximal, characteristic, complemented
15	#435×D₆₁	C₂	1	1	yes	maximal, characteristic
16	C₂×D₆₁⋊M₁₆	C₂²	1	1	yes	characteristic
17	C₂²×D₆₁⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×D₄×#6923	C₄	1	2	yes	—
19	C₂²×C₄×#6923	C₂²	1	1	yes	characteristic
20	C₂²×C₄×#6923	C₂²	1	1	yes	characteristic
21	#16840794	C₄	1	2	yes	complemented
22	#16840793	C₄	1	2	yes	complemented
23	#16840792	C₄	1	2	yes	complemented
24	#16840791	C₄	1	2	yes	complemented
25	D₆₁⋊(C₄⋊C₈)	C₂²	1	1	yes	characteristic
26	D₆₁⋊(C₂²⋊C₈)	C₂²	1	1	yes	characteristic
27	D₆₁⋊(C₂²⋊C₈)	C₂²	1	1	yes	characteristic
28	M₁₆×#6923	—	2	4	no	—
29	#16840721	C₂²	1	1	yes	characteristic
30	C₂×#14519831	C₂²	1	1	yes	characteristic
31	C₂×#14519831	C₂²	1	1	yes	characteristic
32	C₂×#14519831	C₂²	1	1	yes	characteristic
33	C₂×#14519831	C₂²	1	1	yes	characteristic
34	C₂×C₈×#6923	—	2	4	no	—
35	C₂×C₈×#6923	C₂²	1	1	yes	characteristic
36	C₂×C₈×#6923	C₂²	1	1	yes	characteristic
37	C₂×C₈×#6923	C₂²	1	1	yes	characteristic
38	C₂×C₈×#6923	C₂²	1	1	yes	characteristic
39	C₂×C₈×#6923	C₂²	1	1	yes	characteristic
40	C₂×C₈×#6923	C₂²	1	1	yes	characteristic
41	C₄⋊C₄×#6923	C₄	1	2	yes	—
42	C₄×C₄⋊#6923	C₂²	1	1	yes	characteristic
43	C₂²⋊C₄×#6923	C₄	1	2	yes	—
44	C₂²⋊C₄×#6923	C₄	1	2	yes	—
45	C₄×C₂²⋊#6923	C₂²	1	1	yes	characteristic
46	C₄×C₂²⋊#6923	C₂²	1	1	yes	characteristic
47	C₄²×#6923	C₂²	1	1	yes	characteristic
48	(C₂×#6923)⋊C₈	C₂²	1	1	yes	characteristic
49	(C₂×#6923)⋊C₈	C₂²	1	1	yes	characteristic
50	(C₂×#6923)⋊C₈	C₂²	1	1	yes	characteristic
51	(C₂×#6923)⋊C₈	C₂²	1	1	yes	characteristic
52	(C₂×#6923)⋊C₈	C₂²	1	1	yes	characteristic
53	(C₂×#6923)⋊C₈	C₂²	1	1	yes	characteristic
54	C₂×M₁₆×D₆₁	C₂²	1	1	yes	characteristic
55	C₂²×C₈×D₆₁	C₂²	1	1	yes	characteristic
56	C₄×D₄×D₆₁	C₂²	1	1	yes	characteristic
57	#16839836	C₄	1	1	yes	characteristic, complemented
58	#16839835	C₄	1	1	yes	characteristic, complemented
59	#16839834	C₄	1	1	yes	characteristic, complemented
60	#16839833	C₄	1	1	yes	characteristic, complemented
61	#16839832	C₄	1	1	yes	characteristic, complemented
62	#16839831	C₄	1	1	yes	characteristic, complemented
63	#16839830	C₄	1	1	yes	characteristic, complemented
64	C₄⋊C₈×D₆₁	C₂²	1	1	yes	characteristic
65	C₂²⋊C₈×D₆₁	C₂²	1	1	yes	characteristic
66	C₂²⋊C₈×D₆₁	C₂²	1	1	yes	characteristic
67	#97×D₆₁	C₂²	1	1	yes	characteristic
68	C₆₁×#435	C₄	1	1	yes	characteristic, complemented
69	C₂³×#6923	C₂×C₄	1	2	yes	—
70	C₂³×#6923	C₂×C₄	1	2	yes	—
71	C₂×#11758213	C₂×C₄	1	2	yes	complemented
72	D₆₁⋊M₁₆	—	2	2	no	—
73	D₆₁⋊M₁₆	—	2	2	no	—
74	C₂×#11758217	C₂×C₄	1	2	yes	complemented
75	C₂×D₆₁⋊C₈	—	2	2	no	—
76	C₂×D₆₁⋊C₈	—	2	2	no	—
77	C₂×D₆₁⋊C₈	C₂×C₄	1	2	yes	complemented
78	C₂×D₆₁⋊C₈	C₂³	1	1	yes	characteristic
79	C₂×D₆₁⋊C₈	C₂³	1	1	yes	characteristic
80	C₂×D₆₁⋊C₈	C₂³	1	1	yes	characteristic
81	C₂×D₆₁⋊C₈	C₂³	1	1	yes	characteristic
82	C₂²×#92420	C₂×C₄	1	2	yes	complemented
83	D₄×#6923	—	2	8	no	—
84	C₂×C₄⋊#6923	C₂×C₄	1	2	yes	—
85	C₂×C₂²⋊#6923	C₂×C₄	1	2	yes	—
86	C₂×C₂²⋊#6923	C₂×C₄	1	2	yes	—
87	C₂×C₄×#6923	—	2	2	no	—
88	C₂×C₄×#6923	—	2	2	no	—
89	C₂×C₄×#6923	—	2	2	no	—
90	C₂×C₄×#6923	—	2	2	no	—
91	C₂×C₄×#6923	C₂×C₄	1	2	yes	—
92	C₂×C₄×#6923	C₂×C₄	1	2	yes	—
93	C₂×C₄×#6923	C₂×C₄	1	2	yes	—
94	C₂×C₄×#6923	C₂×C₄	1	2	yes	—
95	C₂×C₄×#6923	C₂³	1	1	yes	characteristic
96	C₂×C₄×#6923	C₂³	1	1	yes	characteristic
97	C₂×C₄×#6923	C₂³	1	1	yes	characteristic
98	C₂×C₄×#6923	C₂³	1	1	yes	characteristic
99	#14519844	C₂×C₄	1	2	yes	complemented
100	C₄⋊#92420	C₂×C₄	1	2	yes	complemented
101	#14519834	C₂×C₄	1	2	yes	complemented
102	#14519834	C₂×C₄	1	2	yes	complemented
103	C₂²⋊#92420	C₂×C₄	1	2	yes	complemented
104	C₂²⋊#92420	C₂×C₄	1	2	yes	complemented
105	#14519832	C₂×C₄	1	2	yes	complemented
106	#14519832	C₂×C₄	1	2	yes	complemented
107	#14519831	—	2	2	no	—
108	#14519831	—	2	2	no	—
109	#14519831	—	2	2	no	—
110	#14519831	—	2	2	no	—
111	C₈×#6923	—	2	2	no	—
112	C₈×#6923	—	2	2	no	—
113	C₈×#6923	—	2	2	no	—
114	C₈×#6923	—	2	2	no	—
115	C₈×#6923	—	2	2	no	—
116	C₈×#6923	D₄	1	4	yes	complemented
117	(C₂×#6923)⋊C₄	C₂×C₄	1	2	yes	—
118	(C₂×#6923)⋊C₄	C₂×C₄	1	2	yes	—
119	(C₂×#6923)⋊C₄	C₂×C₄	1	2	yes	—
120	C₂×D₄×D₆₁	C₂×C₄	1	1	yes	characteristic
121	C₂²×C₄×D₆₁	C₂³	1	1	yes	characteristic
122	C₂²×C₄×D₆₁	C₂³	1	1	yes	characteristic
123	C₂×#11758194	C₂×C₄	1	1	yes	characteristic, complemented
124	C₂×#11758189	C₂×C₄	1	1	yes	characteristic, complemented
125	C₂×#11758189	C₂×C₄	1	1	yes	characteristic, complemented
126	M₁₆×D₆₁	—	2	2	no	—
127	M₁₆×D₆₁	—	2	2	no	—
128	C₂²×#92418	C₂×C₄	1	1	yes	characteristic, complemented
129	C₂×C₈×D₆₁	—	2	2	no	—
130	C₂×C₈×D₆₁	—	2	2	no	—
131	C₂×C₈×D₆₁	C₂×C₄	1	1	yes	characteristic, complemented
132	C₂×C₈×D₆₁	C₂×C₄	1	1	yes	characteristic, complemented
133	C₂×C₈×D₆₁	C₂³	1	1	yes	characteristic
134	C₂×C₈×D₆₁	C₂³	1	1	yes	characteristic
135	C₂×C₈×D₆₁	C₂³	1	1	yes	characteristic
136	C₂×C₈×D₆₁	C₂³	1	1	yes	characteristic
137	C₄×D₂₄₄	C₂×C₄	1	1	yes	characteristic
138	D₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
139	#14519739	C₂×C₄	1	1	yes	characteristic
140	C₄×C₂²⋊D₆₁	C₂×C₄	1	1	yes	characteristic
141	C₄×C₂²⋊D₆₁	C₂×C₄	1	1	yes	characteristic
142	#14519737	C₂×C₄	1	1	yes	characteristic
143	#14519737	C₂×C₄	1	1	yes	characteristic
144	C₄⋊C₄×D₆₁	C₂×C₄	1	1	yes	characteristic
145	C₂²⋊C₄×D₆₁	C₂×C₄	1	1	yes	characteristic
146	C₂²⋊C₄×D₆₁	C₂×C₄	1	1	yes	characteristic
147	C₄²×D₆₁	C₂³	1	1	yes	characteristic
148	C₄⋊#92418	C₂×C₄	1	1	yes	characteristic, complemented
149	#14519706	C₂×C₄	1	1	yes	characteristic, complemented
150	#14519706	C₂×C₄	1	1	yes	characteristic, complemented
151	C₂²⋊#92418	C₂×C₄	1	1	yes	characteristic, complemented
152	C₂²⋊#92418	C₂×C₄	1	1	yes	characteristic, complemented
153	#14519689	C₂×C₄	1	1	yes	characteristic, complemented
154	#14519689	C₂×C₄	1	1	yes	characteristic, complemented
155	#14519689	C₂×C₄	1	1	yes	characteristic, complemented
156	#14519689	C₂×C₄	1	1	yes	characteristic, complemented
157	#14519688	C₂×C₄	1	1	yes	characteristic, complemented
158	#14519687	C₂×C₄	1	1	yes	characteristic, complemented
159	#14519687	C₂×C₄	1	1	yes	characteristic, complemented
160	C₂×M₁₆×C₆₁	C₂×C₄	1	1	yes	characteristic, complemented
161	C₂²×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic, complemented
162	C₄×D₄×C₆₁	C₂×C₄	1	1	yes	characteristic
163	C₄⋊C₈×C₆₁	C₂×C₄	1	1	yes	characteristic, complemented
164	C₂²⋊C₈×C₆₁	C₂×C₄	1	1	yes	characteristic, complemented
165	C₂²⋊C₈×C₆₁	C₂×C₄	1	1	yes	characteristic, complemented
166	#97×C₆₁	C₂×C₄	1	1	yes	characteristic, complemented
167	C₂³×D₆₁	C₂²×C₄	1	1	yes	characteristic
168	C₂³×D₆₁	C₂²×C₄	1	1	yes	characteristic
169	C₂²×#6923	—	2	4	no	—
170	C₂²×#6923	—	2	4	no	—
171	C₂²×#6923	—	2	4	no	—
172	C₂²×#6923	—	2	4	no	—
173	C₂²×#6923	—	2	4	no	—
174	C₂²×#6923	M₁₆	1	8	yes	complemented
175	C₂²×#6923	C₂²×C₄	1	2	yes	—
176	C₂²×#6923	C₂²×C₄	1	2	yes	—
177	C₂²×#6923	C₂²×C₄	1	2	yes	—
178	C₂²×#6923	C₂²×C₄	1	2	yes	—
179	C₂×D₄×C₆₁	C₄²	1	1	yes	characteristic
180	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
181	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
182	C₂×C₂²⋊D₆₁	C₄²	1	1	yes	characteristic
183	C₂×C₂²⋊D₆₁	C₄²	1	1	yes	characteristic
184	C₂²×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
185	C₂²×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
186	D₄×D₆₁	—	2	4	no	—
187	C₂×D₂₄₄	C₄²	1	1	yes	characteristic
188	C₂×C₄×D₆₁	—	2	1	no	—
189	C₂×C₄×D₆₁	—	2	1	no	—
190	C₂×C₄×D₆₁	—	2	1	no	—
191	C₂×C₄×D₆₁	—	2	1	no	—
192	C₂×C₄×D₆₁	—	2	1	no	—
193	C₂×C₄×D₆₁	—	2	1	no	—
194	C₂×C₄×D₆₁	—	2	1	no	—
195	C₂×C₄×D₆₁	—	2	1	no	—
196	C₂×C₄×D₆₁	C₂²×C₄	1	1	yes	characteristic
197	C₂×C₄×D₆₁	C₂²×C₄	1	1	yes	characteristic
198	C₂×C₄×D₆₁	C₂²×C₄	1	1	yes	characteristic
199	C₂×C₄×D₆₁	C₂²×C₄	1	1	yes	characteristic
200	C₂×C₄×D₆₁	C₂²×C₄	1	1	yes	characteristic
201	C₂×C₄×D₆₁	C₂²×C₄	1	1	yes	characteristic
202	C₂×C₄×D₆₁	C₂²×C₄	1	1	yes	characteristic
203	C₂×C₄×D₆₁	C₂²×C₄	1	1	yes	characteristic
204	C₂×C₄×D₆₁	C₂⁴	1	1	yes	characteristic
205	C₂²⋊#6923	—	2	4	no	—
206	C₂²⋊#6923	—	2	4	no	—
207	#11758217	—	2	4	no	—
208	C₂×#92420	—	2	4	no	—
209	C₂×#92420	C₂²×C₄	1	2	yes	—
210	C₂×#92420	C₂²×C₄	1	2	yes	—
211	C₂×#92420	C₂²×C₄	1	2	yes	—
212	C₂×#92420	C₂²×C₄	1	2	yes	—
213	C₄⋊#6923	—	2	4	no	—
214	C₄×#6923	—	2	4	no	—
215	C₄×#6923	—	2	4	no	—
216	C₄×#6923	—	2	4	no	—
217	C₄×#6923	—	2	4	no	—
218	C₄×#6923	—	2	1	no	—
219	C₄×#6923	—	2	1	no	—
220	C₄×#6923	—	2	1	no	—
221	C₄×#6923	—	2	1	no	—
222	C₄×#6923	—	2	1	no	—
223	C₄×#6923	—	2	1	no	—
224	C₄×#6923	C₂×D₄	1	2	yes	—
225	C₄×#6923	#41	1	2	yes	—
226	#11758213	—	2	4	no	—
227	D₆₁⋊C₈	—	2	1	no	—
228	D₆₁⋊C₈	—	2	1	no	—
229	D₆₁⋊C₈	—	2	1	no	—
230	D₆₁⋊C₈	—	2	1	no	—
231	D₆₁⋊C₈	—	2	1	no	—
232	D₆₁⋊C₈	—	2	1	no	—
233	D₆₁⋊C₈	—	2	4	no	—
234	D₆₁⋊C₈	C₂×D₄	1	2	yes	—
235	D₆₁⋊C₈	#41	1	2	yes	—
236	M₁₆×C₆₁	—	2	2	no	—
237	C₂×C₈×C₆₁	—	2	2	no	—
238	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
239	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
240	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
241	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
242	C₄⋊C₄×C₆₁	C₄²	1	1	yes	characteristic
243	C₂²⋊C₄×C₆₁	C₄²	1	1	yes	characteristic
244	C₂²⋊C₄×C₆₁	C₄²	1	1	yes	characteristic
245	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
246	C₂²⋊Dic₆₁	C₄²	1	1	yes	characteristic
247	C₂²⋊Dic₆₁	C₄²	1	1	yes	characteristic
248	#11758198	C₄²	1	1	yes	characteristic
249	#11758198	C₄²	1	1	yes	characteristic
250	#11758198	C₄²	1	1	yes	characteristic
251	#11758198	C₄²	1	1	yes	characteristic
252	C₄⋊Dic₆₁	C₄²	1	1	yes	characteristic
253	#11758196	C₄²	1	1	yes	characteristic
254	#11758196	C₄²	1	1	yes	characteristic
255	C₄×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
256	C₄×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
257	C₄×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
258	#11758194	—	2	2	no	—
259	C₂×#92418	—	2	2	no	—
260	C₂×#92418	C₂²×C₄	1	1	yes	characteristic
261	C₂×#92418	C₂²×C₄	1	1	yes	characteristic
262	C₂×#92418	C₂²×C₄	1	1	yes	characteristic
263	C₂×#92418	C₂²×C₄	1	1	yes	characteristic
264	#11758189	—	2	2	no	—
265	#11758189	—	2	2	no	—
266	C₈×D₆₁	—	2	1	no	—
267	C₈×D₆₁	—	2	1	no	—
268	C₈×D₆₁	—	2	1	no	—
269	C₈×D₆₁	—	2	1	no	—
270	C₈×D₆₁	—	2	1	no	—
271	C₈×D₆₁	—	2	1	no	—
272	C₈×D₆₁	—	2	2	no	—
273	C₈×D₆₁	—	2	2	no	—
274	C₈×D₆₁	C₂×D₄	1	2	yes	—
275	C₈×D₆₁	#41	1	2	yes	—
276	C₂³×C₆₁	C₂×C₄²	1	1	yes	characteristic
277	C₂³×C₆₁	C₂×C₄²	1	1	yes	characteristic
278	C₂²×D₆₁	—	2	1	no	—
279	C₂²×D₆₁	—	2	1	no	—
280	C₂²×D₆₁	—	2	2	no	—
281	C₂²×D₆₁	—	2	1	no	—
282	C₂²×D₆₁	—	2	1	no	—
283	C₂²×D₆₁	—	2	2	no	—
284	C₂²×D₆₁	—	2	2	no	—
285	C₂²×D₆₁	C₂×C₄²	1	1	yes	characteristic
286	C₂²×D₆₁	C₂×C₄²	1	1	yes	characteristic
287	C₂²×D₆₁	C₂×M₁₆	1	4	yes	—
288	C₂²×D₆₁	C₂³×C₄	1	1	yes	characteristic
289	C₂×#6923	—	2	2	no	—
290	C₂×#6923	—	2	2	no	—
291	C₂×#6923	—	2	16	no	—
292	C₂×#6923	—	2	2	no	—
293	C₂×#6923	—	2	2	no	—
294	C₂×#6923	—	2	2	no	—
295	C₂×#6923	—	2	2	no	—
296	C₂×#6923	—	2	2	no	—
297	C₂×#6923	—	2	2	no	—
298	C₂×#6923	—	4	8	no	—
299	C₂×#6923	C₄×D₄	1	4	yes	—
300	C₂×#6923	C₂×M₁₆	1	4	yes	—
301	C₂×#6923	C₂×M₁₆	1	4	yes	—
302	C₂×#6923	#131	1	4	yes	—
303	D₄×C₆₁	—	2	2	no	—
304	C₂×C₄×C₆₁	—	2	1	no	—
305	C₂×C₄×C₆₁	—	2	1	no	—
306	C₂×C₄×C₆₁	—	2	1	no	—
307	C₂×C₄×C₆₁	—	2	1	no	—
308	C₂×C₄×C₆₁	C₂×C₄²	1	1	yes	characteristic
309	C₂×C₄×C₆₁	C₂×C₄²	1	1	yes	characteristic
310	C₂×C₄×C₆₁	C₂×C₄²	1	1	yes	characteristic
311	C₂×C₄×C₆₁	C₂×C₄²	1	1	yes	characteristic
312	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
313	C₂²⋊D₆₁	—	2	2	no	—
314	C₂²⋊D₆₁	—	2	2	no	—
315	C₂×Dic₆₁	—	2	1	no	—
316	C₂×Dic₆₁	—	2	1	no	—
317	C₂×Dic₆₁	—	2	1	no	—
318	C₂×Dic₆₁	—	2	1	no	—
319	C₂×Dic₆₁	C₂×C₄²	1	1	yes	characteristic
320	C₂×Dic₆₁	C₂×C₄²	1	1	yes	characteristic
321	C₂×Dic₆₁	C₂×C₄²	1	1	yes	characteristic
322	C₂×Dic₆₁	C₂×C₄²	1	1	yes	characteristic
323	C₂×Dic₆₁	C₂³×C₄	1	1	yes	characteristic
324	D₂₄₄	—	2	2	no	—
325	C₄×D₆₁	—	2	1	no	—
326	C₄×D₆₁	—	2	1	no	—
327	C₄×D₆₁	—	2	1	no	—
328	C₄×D₆₁	—	2	1	no	—
329	C₄×D₆₁	—	2	2	no	—
330	C₄×D₆₁	—	2	2	no	—
331	C₄×D₆₁	—	2	1	no	—
332	C₄×D₆₁	—	2	1	no	—
333	C₄×D₆₁	—	2	1	no	—
334	C₄×D₆₁	—	2	1	no	—
335	C₄×D₆₁	—	2	1	no	—
336	C₄×D₆₁	—	2	1	no	—
337	C₄×D₆₁	—	2	1	no	—
338	C₄×D₆₁	—	2	1	no	—
339	C₄×D₆₁	C₂²×D₄	1	1	yes	characteristic
340	C₄×D₆₁	C₂×#41	1	1	yes	characteristic
341	C₄×D₆₁	C₂×#41	1	1	yes	characteristic
342	C₄×D₆₁	C₂×#41	1	1	yes	characteristic
343	#92420	—	2	2	no	—
344	#92420	—	2	2	no	—
345	#92420	—	2	2	no	—
346	#92420	C₄×D₄	1	4	yes	complemented
347	C₈×C₆₁	—	2	1	no	—
348	C₈×C₆₁	—	2	1	no	—
349	C₈×C₆₁	—	2	1	no	—
350	C₈×C₆₁	C₄×D₄	1	2	yes	complemented
351	#92418	—	2	1	no	—
352	#92418	—	2	1	no	—
353	#92418	—	2	1	no	—
354	#92418	C₄×D₄	1	2	yes	complemented
355	C₄×#435	—	61	1	no	maximal, Sylow
356	C₂²×C₆₁	—	2	1	no	—
357	C₂²×C₆₁	—	2	1	no	—
358	C₂²×C₆₁	—	2	1	no	—
359	C₂²×C₆₁	—	2	1	no	—
360	C₂²×C₆₁	—	2	1	no	—
361	C₂²×C₆₁	C₄×M₁₆	1	2	yes	complemented
362	C₂²×C₆₁	C₂²×C₄²	1	1	yes	characteristic
363	C₂×D₆₁	—	2	1	no	—
364	C₂×D₆₁	—	2	1	no	—
365	C₂×D₆₁	—	2	4	no	—
366	C₂×D₆₁	—	2	4	no	—
367	C₂×D₆₁	—	2	1	no	—
368	C₂×D₆₁	—	2	1	no	—
369	C₂×D₆₁	—	2	1	no	—
370	C₂×D₆₁	—	4	2	no	—
371	C₂×D₆₁	—	4	2	no	—
372	C₂×D₆₁	C₄×M₁₆	1	2	yes	complemented
373	C₂×D₆₁	C₂×C₄×D₄	1	1	yes	characteristic
374	C₂×D₆₁	C₄×#41	1	1	yes	characteristic
375	C₂×D₆₁	C₂²×M₁₆	1	2	yes	—
376	C₂×D₆₁	C₂×#131	1	2	yes	—
377	#6923	—	2	4	no	—
378	#6923	—	4	2	no	—
379	#6923	—	4	2	no	—
380	#6923	#435	1	8	yes	direct product factor
381	C₄×C₆₁	—	2	1	no	—
382	C₄×C₆₁	—	2	1	no	—
383	C₄×C₆₁	—	2	1	no	—
384	C₄×C₆₁	—	2	1	no	—
385	C₄×C₆₁	C₂×C₄×D₄	1	1	yes	characteristic
386	C₄×C₆₁	C₄×#41	1	1	yes	characteristic
387	Dic₆₁	—	2	1	no	—
388	Dic₆₁	—	2	1	no	—
389	Dic₆₁	—	2	1	no	—
390	Dic₆₁	—	2	1	no	—
391	Dic₆₁	C₂×C₄×D₄	1	1	yes	characteristic
392	Dic₆₁	C₄×#41	1	1	yes	characteristic
393	C₂×#435	—	61	1	no	—
394	C₂×#435	—	61	1	no	—
395	C₂×C₄×M₁₆	—	61	1	no	—
396	C₂²×C₄×C₈	—	61	1	no	—
397	C₄²×D₄	—	61	1	no	—
398	#1771	—	61	1	no	—
399	#1771	—	61	1	no	—
400	C₄×C₄⋊C₈	—	61	1	no	—
401	#1753	—	61	1	no	—
402	#1753	—	61	1	no	—
403	#1752	—	61	1	no	—
404	#1752	—	61	1	no	—
405	C₄×C₂²⋊C₈	—	61	1	no	—
406	C₄×C₂²⋊C₈	—	61	1	no	—
407	C₄×#97	—	61	1	no	—
408	C₂×C₆₁	—	2	2	no	—
409	C₂×C₆₁	—	4	1	no	—
410	C₂×C₆₁	C₄²×D₄	1	1	yes	characteristic
411	C₂×C₆₁	C₂×C₄×M₁₆	1	1	yes	characteristic
412	C₂×C₆₁	C₄×#131	1	1	yes	characteristic
413	D₆₁	—	2	2	no	—
414	D₆₁	—	4	1	no	—
415	D₆₁	C₂×#435	1	2	yes	—
416	D₆₁	#2965	1	2	yes	—
417	C₂²×M₁₆	—	61	1	no	—
418	C₂²×M₁₆	—	61	1	no	—
419	C₂³×C₈	—	61	1	no	—
420	C₂³×C₈	—	61	1	no	—
421	C₂×C₄×D₄	—	61	1	no	—
422	C₂×C₄×D₄	—	61	2	no	—
423	C₂²×C₄²	—	61	1	no	—
424	C₂²×C₄²	—	61	1	no	—
425	#435	—	61	2	no	—
426	#435	—	61	2	no	—
427	#435	—	61	2	no	—
428	#435	—	61	2	no	—
429	#435	—	61	1	no	—
430	#435	—	61	1	no	—
431	#435	—	61	1	no	—
432	#435	—	61	1	no	—
433	#435	—	61	1	no	—
434	#435	—	61	1	no	—
435	#435	—	61	1	no	—
436	#435	#6923	1	1	yes	characteristic, direct product factor
437	C₂×C₄⋊C₈	—	61	1	no	—
438	C₂×C₄⋊C₈	—	61	1	no	—
439	C₂×C₂²⋊C₈	—	61	1	no	—
440	C₂×C₂²⋊C₈	—	61	1	no	—
441	C₂×C₂²⋊C₈	—	61	1	no	—
442	C₂×C₂²⋊C₈	—	61	1	no	—
443	C₄×M₁₆	—	122	4	no	—
444	C₂×#97	—	61	1	no	—
445	C₂×#97	—	61	1	no	—
446	C₂×#97	—	61	1	no	—
447	C₂×#97	—	61	1	no	—
448	C₂×#97	—	61	1	no	—
449	C₂×#97	—	61	1	no	—
450	C₂×C₄×C₈	—	61	1	no	—
451	C₂×C₄×C₈	—	61	1	no	—
452	C₂×C₄×C₈	—	61	1	no	—
453	C₂×C₄×C₈	—	61	1	no	—
454	C₂×C₄×C₈	—	61	1	no	—
455	C₂×C₄×C₈	—	61	1	no	—
456	C₂×C₄×C₈	—	122	4	no	—
457	C₄×C₄⋊C₄	—	61	1	no	—
458	C₄×C₄⋊C₄	—	61	2	no	—
459	C₄×C₂²⋊C₄	—	61	1	no	—
460	C₄×C₂²⋊C₄	—	61	1	no	—
461	C₄×C₂²⋊C₄	—	61	2	no	—
462	C₄×C₂²⋊C₄	—	61	2	no	—
463	C₄³	—	61	1	no	—
464	#336	—	61	1	no	—
465	#336	—	61	1	no	—
466	#336	—	61	1	no	—
467	#336	—	61	1	no	—
468	#336	—	61	1	no	—
469	#336	—	61	1	no	—
470	C₆₁	C₄×#435	1	1	yes	characteristic, complemented, Sylow
471	C₂²×D₄	—	61	1	no	—
472	C₂³×C₄	—	61	2	no	—
473	C₂³×C₄	—	61	1	no	—
474	C₂³×C₄	—	61	1	no	—
475	C₂³×C₄	—	61	2	no	—
476	C₂×M₁₆	—	61	2	no	—
477	C₂×M₁₆	—	61	2	no	—
478	C₂×M₁₆	—	61	1	no	—
479	C₂×M₁₆	—	61	1	no	—
480	C₂×M₁₆	—	61	1	no	—
481	C₂×M₁₆	—	122	2	no	—
482	C₂×M₁₆	—	122	2	no	—
483	C₂×M₁₆	—	122	2	no	—
484	C₂×M₁₆	—	122	2	no	—
485	C₂×M₁₆	C₂×#6923	1	1	yes	characteristic, complemented
486	C₂²×C₈	—	61	1	no	—
487	C₂²×C₈	—	61	1	no	—
488	C₂²×C₈	—	61	2	no	—
489	C₂²×C₈	—	61	2	no	—
490	C₂²×C₈	—	61	1	no	—
491	C₂²×C₈	—	61	1	no	—
492	C₂²×C₈	—	61	1	no	—
493	C₂²×C₈	—	61	1	no	—
494	C₂²×C₈	—	61	1	no	—
495	C₂²×C₈	—	61	1	no	—
496	C₂²×C₈	—	61	1	no	—
497	C₂²×C₈	—	61	1	no	—
498	C₂²×C₈	—	61	1	no	—
499	C₂²×C₈	—	122	2	no	—
500	C₂²×C₈	—	122	2	no	—
501	C₂²×C₈	—	122	2	no	—
502	C₂²×C₈	—	122	2	no	—
503	C₂²×C₈	C₂×#6923	1	1	yes	characteristic, complemented
504	C₄×D₄	—	61	1	no	—
505	C₄×D₄	—	61	1	no	—
506	C₄×D₄	—	61	1	no	—
507	C₄×D₄	—	61	1	no	—
508	C₄×D₄	—	61	1	no	—
509	C₄×D₄	—	61	1	no	—
510	C₄×D₄	—	61	1	no	—
511	C₄×D₄	—	122	8	no	—
512	C₄×D₄	C₂×#6923	1	1	yes	characteristic
513	C₂×C₄⋊C₄	—	61	1	no	—
514	C₂×C₄⋊C₄	—	61	2	no	—
515	C₂×C₂²⋊C₄	—	61	1	no	—
516	C₂×C₂²⋊C₄	—	61	1	no	—
517	C₂×C₂²⋊C₄	—	61	2	no	—
518	C₂×C₂²⋊C₄	—	61	2	no	—
519	C₂×C₄²	—	61	1	no	—
520	C₂×C₄²	—	61	1	no	—
521	C₂×C₄²	—	61	2	no	—
522	C₂×C₄²	—	61	2	no	—
523	C₂×C₄²	—	61	2	no	—
524	C₂×C₄²	—	61	2	no	—
525	C₂×C₄²	—	61	1	no	—
526	C₂×C₄²	—	61	1	no	—
527	C₂×C₄²	—	61	1	no	—
528	C₂×C₄²	—	122	2	no	—
529	C₂×C₄²	—	122	2	no	—
530	C₂×C₄²	—	122	2	no	—
531	C₂×C₄²	—	122	2	no	—
532	C₄⋊C₈	—	61	2	no	—
533	C₄⋊C₈	—	61	2	no	—
534	C₄⋊C₈	—	61	1	no	—
535	C₄⋊C₈	—	61	1	no	—
536	C₄⋊C₈	—	61	1	no	—
537	C₄⋊C₈	C₂×#6923	1	1	yes	characteristic, complemented
538	C₂²⋊C₈	—	61	2	no	—
539	C₂²⋊C₈	—	61	2	no	—
540	C₂²⋊C₈	—	61	2	no	—
541	C₂²⋊C₈	—	61	2	no	—
542	C₂²⋊C₈	—	61	1	no	—
543	C₂²⋊C₈	—	61	1	no	—
544	C₂²⋊C₈	—	61	1	no	—
545	C₂²⋊C₈	—	61	1	no	—
546	C₂²⋊C₈	—	61	1	no	—
547	C₂²⋊C₈	—	61	1	no	—
548	C₂²⋊C₈	C₂×#6923	1	1	yes	characteristic, complemented
549	C₂²⋊C₈	C₂×#6923	1	1	yes	characteristic, complemented
550	#97	—	61	2	no	—
551	#97	—	61	2	no	—
552	#97	—	61	1	no	—
553	#97	—	61	1	no	—
554	#97	—	61	1	no	—
555	#97	—	122	2	no	—
556	#97	—	122	2	no	—
557	#97	—	122	2	no	—
558	#97	—	122	2	no	—
559	#97	C₂×#6923	1	1	yes	characteristic, complemented
560	C₄×C₈	—	61	4	no	—
561	C₄×C₈	—	122	2	no	—
562	C₄×C₈	—	122	2	no	—
563	C₄×C₈	—	122	2	no	—
564	C₄×C₈	—	122	2	no	—
565	C₄×C₈	—	122	2	no	—
566	#95	—	61	2	no	—
567	#95	—	61	2	no	—
568	#95	—	61	2	no	—
569	C₂⁴	—	61	1	no	—
570	C₂⁴	—	61	1	no	—
571	C₂×D₄	—	61	1	no	—
572	C₂×D₄	—	61	1	no	—
573	C₂×D₄	—	61	1	no	—
574	C₂×D₄	—	122	4	no	—
575	C₂×D₄	C₄×#6923	1	1	yes	characteristic
576	C₂²×C₄	—	61	2	no	—
577	C₂²×C₄	—	61	1	no	—
578	C₂²×C₄	—	61	2	no	—
579	C₂²×C₄	—	61	8	no	—
580	C₂²×C₄	—	61	1	no	—
581	C₂²×C₄	—	61	1	no	—
582	C₂²×C₄	—	61	1	no	—
583	C₂²×C₄	—	61	1	no	—
584	C₂²×C₄	—	61	1	no	—
585	C₂²×C₄	—	61	1	no	—
586	C₂²×C₄	—	61	1	no	—
587	C₂²×C₄	—	61	1	no	—
588	C₂²×C₄	—	61	1	no	—
589	C₂²×C₄	—	61	1	no	—
590	C₂²×C₄	—	61	2	no	—
591	C₂²×C₄	—	61	2	no	—
592	C₂²×C₄	—	122	1	no	—
593	C₂²×C₄	—	122	1	no	—
594	C₂²×C₄	—	122	1	no	—
595	C₂²×C₄	—	122	1	no	—
596	C₂²×C₄	—	122	1	no	—
597	C₂²×C₄	—	122	1	no	—
598	C₂²×C₄	—	122	1	no	—
599	C₂²×C₄	—	122	1	no	—
600	C₂²×C₄	—	122	4	no	—
601	C₂²×C₄	—	122	4	no	—
602	C₂²×C₄	—	122	4	no	—
603	C₂²×C₄	—	122	4	no	—
604	C₂²×C₄	—	122	4	no	—
605	C₂²×C₄	C₂²×#6923	1	1	yes	characteristic
606	C₂²×C₄	C₂²×#6923	1	1	yes	characteristic
607	M₁₆	—	2	2	no	—
608	M₁₆	—	122	2	no	—
609	M₁₆	—	122	2	no	—
610	M₁₆	—	122	4	no	—
611	M₁₆	—	122	4	no	—
612	M₁₆	—	122	2	no	—
613	C₂×C₈	—	2	2	no	—
614	C₂×C₈	—	61	2	no	—
615	C₂×C₈	—	61	2	no	—
616	C₂×C₈	—	61	2	no	—
617	C₂×C₈	—	61	1	no	—
618	C₂×C₈	—	61	2	no	—
619	C₂×C₈	—	61	2	no	—
620	C₂×C₈	—	61	2	no	—
621	C₂×C₈	—	61	2	no	—
622	C₂×C₈	—	61	2	no	—
623	C₂×C₈	—	61	1	no	—
624	C₂×C₈	—	61	1	no	—
625	C₂×C₈	—	61	1	no	—
626	C₂×C₈	—	122	2	no	—
627	C₂×C₈	—	122	1	no	—
628	C₂×C₈	—	122	1	no	—
629	C₂×C₈	—	122	1	no	—
630	C₂×C₈	—	122	1	no	—
631	C₂×C₈	—	122	1	no	—
632	C₂×C₈	—	122	1	no	—
633	C₂×C₈	—	122	2	no	—
634	C₂×C₈	—	122	4	no	—
635	C₂×C₈	—	122	4	no	—
636	C₂×C₈	—	122	1	no	—
637	C₂×C₈	—	122	1	no	—
638	C₂×C₈	—	122	1	no	—
639	C₂×C₈	—	122	1	no	—
640	C₂×C₈	—	122	1	no	—
641	C₂×C₈	—	122	1	no	—
642	C₂×C₈	—	122	2	no	—
643	C₂×C₈	C₂²×#6923	1	1	yes	characteristic
644	C₂×C₈	C₂²×#6923	1	1	yes	characteristic
645	C₂×C₈	C₂²×#6923	1	1	yes	characteristic
646	C₂×C₈	C₂²×#6923	1	1	yes	characteristic
647	C₄⋊C₄	—	61	1	no	—
648	C₄⋊C₄	—	61	1	no	—
649	C₄⋊C₄	—	61	1	no	—
650	C₄⋊C₄	—	122	4	no	—
651	C₄⋊C₄	C₄×#6923	1	1	yes	characteristic
652	C₂²⋊C₄	—	61	1	no	—
653	C₂²⋊C₄	—	61	1	no	—
654	C₂²⋊C₄	—	61	1	no	—
655	C₂²⋊C₄	—	61	1	no	—
656	C₂²⋊C₄	—	61	1	no	—
657	C₂²⋊C₄	—	61	1	no	—
658	C₂²⋊C₄	—	122	4	no	—
659	C₂²⋊C₄	—	122	4	no	—
660	C₂²⋊C₄	C₄×#6923	1	1	yes	characteristic
661	C₂²⋊C₄	C₄×#6923	1	1	yes	characteristic
662	C₄²	—	61	2	no	—
663	C₄²	—	61	2	no	—
664	C₄²	—	61	1	no	—
665	C₄²	—	61	1	no	—
666	C₄²	—	61	1	no	—
667	C₄²	—	122	1	no	—
668	C₄²	—	122	1	no	—
669	C₄²	—	122	1	no	—
670	C₄²	—	122	1	no	—
671	C₄²	—	122	4	no	—
672	C₄²	—	122	4	no	—
673	C₄²	—	122	1	no	—
674	C₄²	—	122	1	no	—
675	C₄²	—	122	4	no	—
676	C₄²	—	122	4	no	—
677	C₄²	C₂²×#6923	1	1	yes	characteristic
678	C₂³	—	61	1	no	—
679	C₂³	—	61	4	no	—
680	C₂³	—	61	1	no	—
681	C₂³	—	61	1	no	—
682	C₂³	—	122	1	no	—
683	C₂³	—	122	2	no	—
684	C₂³	—	122	1	no	—
685	C₂³	—	122	2	no	—
686	C₂³	—	122	1	no	—
687	C₂³	—	122	2	no	—
688	C₂³	—	122	1	no	—
689	C₂³	C₂×C₄×#6923	1	1	yes	characteristic
690	C₂³	C₂×C₄×#6923	1	1	yes	characteristic
691	D₄	—	2	2	no	—
692	D₄	—	122	2	no	—
693	D₄	—	122	2	no	—
694	D₄	—	122	2	no	—
695	C₂×C₄	—	2	1	no	—
696	C₂×C₄	—	2	1	no	—
697	C₂×C₄	—	2	1	no	—
698	C₂×C₄	—	2	1	no	—
699	C₂×C₄	—	61	4	no	—
700	C₂×C₄	—	61	4	no	—
701	C₂×C₄	—	61	4	no	—
702	C₂×C₄	—	61	1	no	—
703	C₂×C₄	—	61	1	no	—
704	C₂×C₄	—	61	1	no	—
705	C₂×C₄	—	61	1	no	—
706	C₂×C₄	—	61	1	no	—
707	C₂×C₄	—	61	4	no	—
708	C₂×C₄	—	61	1	no	—
709	C₂×C₄	—	61	1	no	—
710	C₂×C₄	—	61	1	no	—
711	C₂×C₄	—	61	1	no	—
712	C₂×C₄	—	122	1	no	—
713	C₂×C₄	—	122	1	no	—
714	C₂×C₄	—	122	1	no	—
715	C₂×C₄	—	122	1	no	—
716	C₂×C₄	—	122	1	no	—
717	C₂×C₄	—	122	1	no	—
718	C₂×C₄	—	122	2	no	—
719	C₂×C₄	—	122	2	no	—
720	C₂×C₄	—	122	1	no	—
721	C₂×C₄	—	122	1	no	—
722	C₂×C₄	—	122	1	no	—
723	C₂×C₄	—	122	1	no	—
724	C₂×C₄	—	122	1	no	—
725	C₂×C₄	—	122	1	no	—
726	C₂×C₄	—	122	16	no	—
727	C₂×C₄	—	122	2	no	—
728	C₂×C₄	—	122	2	no	—
729	C₂×C₄	—	122	1	no	—
730	C₂×C₄	—	122	1	no	—
731	C₂×C₄	—	122	1	no	—
732	C₂×C₄	—	122	1	no	—
733	C₂×C₄	—	122	2	no	—
734	C₂×C₄	—	122	2	no	—
735	C₂×C₄	—	122	2	no	—
736	C₂×C₄	—	122	2	no	—
737	C₂×C₄	—	122	2	no	—
738	C₂×C₄	—	122	2	no	—
739	C₂×C₄	—	244	8	no	—
740	C₂×C₄	C₂×C₄×#6923	1	1	yes	characteristic
741	C₂×C₄	C₂×C₄×#6923	1	1	yes	characteristic
742	C₂×C₄	C₂×C₄×#6923	1	1	yes	characteristic
743	C₂×C₄	C₂×C₄×#6923	1	1	yes	characteristic
744	C₂×C₄	C₂³×#6923	1	1	yes	characteristic
745	C₈	—	2	1	no	—
746	C₈	—	2	1	no	—
747	C₈	—	2	1	no	—
748	C₈	—	61	4	no	—
749	C₈	—	61	2	no	—
750	C₈	—	122	2	no	—
751	C₈	—	122	2	no	—
752	C₈	—	122	2	no	—
753	C₈	—	122	1	no	—
754	C₈	—	122	1	no	—
755	C₈	—	122	1	no	—
756	C₈	D₄×#6923	1	2	yes	complemented
757	C₂²	—	2	1	no	—
758	C₂²	—	2	1	no	—
759	C₂²	—	2	1	no	—
760	C₂²	—	2	1	no	—
761	C₂²	—	2	1	no	—
762	C₂²	—	61	2	no	—
763	C₂²	—	61	2	no	—
764	C₂²	—	61	1	no	—
765	C₂²	—	61	1	no	—
766	C₂²	—	61	2	no	—
767	C₂²	—	122	4	no	—
768	C₂²	—	122	4	no	—
769	C₂²	—	122	1	no	—
770	C₂²	—	122	1	no	—
771	C₂²	—	122	1	no	—
772	C₂²	—	122	1	no	—
773	C₂²	—	122	1	no	—
774	C₂²	—	244	2	no	—
775	C₂²	—	244	2	no	—
776	C₂²	M₁₆×#6923	1	2	yes	complemented
777	C₂²	C₂²×C₄×#6923	1	1	yes	characteristic
778	C₄	—	2	1	no	—
779	C₄	—	2	1	no	—
780	C₄	—	2	1	no	—
781	C₄	—	2	1	no	—
782	C₄	—	61	8	no	—
783	C₄	—	61	1	no	—
784	C₄	—	61	1	no	—
785	C₄	—	122	4	no	—
786	C₄	—	122	1	no	—
787	C₄	—	122	1	no	—
788	C₄	—	122	1	no	—
789	C₄	—	122	1	no	—
790	C₄	—	244	2	no	—
791	C₄	—	244	2	no	—
792	C₄	C₂×D₄×#6923	1	1	yes	characteristic
793	C₄	#41×#6923	1	1	yes	characteristic
794	C₂	—	2	2	no	—
795	C₂	—	4	1	no	—
796	C₂	—	61	2	no	—
797	C₂	—	61	2	no	—
798	C₂	—	122	2	no	—
799	C₂	—	244	1	no	—
800	C₂	C₄×D₄×#6923	1	1	yes	characteristic
801	C₂	C₂×M₁₆×#6923	1	1	yes	characteristic
802	C₂	#131×#6923	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×#6923
commutator, socle	C₂²×C₆₁	C₂²×C₄²
Fitting	C₆₁×#435	C₄
prime radical	C₂×D₄×D₆₁	C₂×C₄
cosocle	C₂×C₄×D₆₁	C₂⁴
hypercenter	#435	#6923
hypocenter	C₆₁	C₄×#435
LCS	G ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄ ◁ #435

Complements

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

N	H ≅ G/N	type
2. C₂×M₁₆×#6923	C₂	semidirect
3. C₂²×C₈×#6923	C₂	semidirect
5. #21461620	C₂	semidirect
6. #21461617	C₂	semidirect
7. C₄⋊C₈×#6923	C₂	semidirect
8. #21461562	C₂	semidirect
9. #21461559	C₂	semidirect
10. #21461558	C₂	semidirect
11. #21461555	C₂	semidirect
12. C₂²⋊C₈×#6923	C₂	semidirect
13. C₂²⋊C₈×#6923	C₂	semidirect
14. #97×#6923	C₂	semidirect
21. #16840794	C₄	semidirect
22. #16840793	C₄	semidirect
23. #16840792	C₄	semidirect
24. #16840791	C₄	semidirect
57. #16839836	C₄	semidirect
58. #16839835	C₄	semidirect
59. #16839834	C₄	semidirect
60. #16839833	C₄	semidirect
61. #16839832	C₄	semidirect
62. #16839831	C₄	semidirect
63. #16839830	C₄	semidirect
68. C₆₁×#435	C₄	semidirect
71. C₂×#11758213	C₂×C₄	semidirect
74. C₂×#11758217	C₂×C₄	semidirect
77. C₂×D₆₁⋊C₈	C₂×C₄	semidirect
82. C₂²×#92420	C₂×C₄	semidirect
99. #14519844	C₂×C₄	semidirect
100. C₄⋊#92420	C₂×C₄	semidirect
101. #14519834	C₂×C₄	semidirect
102. #14519834	C₂×C₄	semidirect
103. C₂²⋊#92420	C₂×C₄	semidirect
104. C₂²⋊#92420	C₂×C₄	semidirect
105. #14519832	C₂×C₄	semidirect
106. #14519832	C₂×C₄	semidirect
116. C₈×#6923	D₄	semidirect
123. C₂×#11758194	C₂×C₄	semidirect
124. C₂×#11758189	C₂×C₄	semidirect
125. C₂×#11758189	C₂×C₄	semidirect
128. C₂²×#92418	C₂×C₄	semidirect
131. C₂×C₈×D₆₁	C₂×C₄	semidirect
132. C₂×C₈×D₆₁	C₂×C₄	semidirect
148. C₄⋊#92418	C₂×C₄	semidirect
149. #14519706	C₂×C₄	semidirect
150. #14519706	C₂×C₄	semidirect
151. C₂²⋊#92418	C₂×C₄	semidirect
152. C₂²⋊#92418	C₂×C₄	semidirect
153. #14519689	C₂×C₄	semidirect
154. #14519689	C₂×C₄	semidirect
155. #14519689	C₂×C₄	semidirect
156. #14519689	C₂×C₄	semidirect
157. #14519688	C₂×C₄	semidirect
158. #14519687	C₂×C₄	semidirect
159. #14519687	C₂×C₄	semidirect
160. C₂×M₁₆×C₆₁	C₂×C₄	semidirect
161. C₂²×C₈×C₆₁	C₂×C₄	semidirect
163. C₄⋊C₈×C₆₁	C₂×C₄	semidirect
164. C₂²⋊C₈×C₆₁	C₂×C₄	semidirect
165. C₂²⋊C₈×C₆₁	C₂×C₄	semidirect
166. #97×C₆₁	C₂×C₄	semidirect
174. C₂²×#6923	M₁₆	semidirect
346. #92420	C₄×D₄	semidirect
350. C₈×C₆₁	C₄×D₄	semidirect
354. #92418	C₄×D₄	semidirect
361. C₂²×C₆₁	C₄×M₁₆	semidirect
372. C₂×D₆₁	C₄×M₁₆	semidirect
380. #6923	#435	direct (N × H)
436. #435	#6923	direct (N × H)
470. C₆₁	C₄×#435	semidirect
485. C₂×M₁₆	C₂×#6923	semidirect
503. C₂²×C₈	C₂×#6923	semidirect
537. C₄⋊C₈	C₂×#6923	semidirect
548. C₂²⋊C₈	C₂×#6923	semidirect
549. C₂²⋊C₈	C₂×#6923	semidirect
559. #97	C₂×#6923	semidirect
756. C₈	D₄×#6923	semidirect
776. C₂²	M₁₆×#6923	semidirect

Maximal subgroups

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

subgroup	index
D₆₁⋊#435	2
C₂×M₁₆×#6923	2
C₂²×C₈×#6923	2
C₄×D₄×#6923	2
#21461620	2
#21461617	2
C₄⋊C₈×#6923	2
#21461562	2
#21461559	2
#21461558	2
#21461555	2
C₂²⋊C₈×#6923	2
#97×#6923	2
#435×D₆₁	2
C₄×#435	61