Subgroups — #446×#6923 #30614549

Order 15616.

958 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	D₆₁⋊#446	C₂	1	1	yes	maximal, characteristic
2	C₄×Q₈×#6923	C₂	1	1	yes	maximal, characteristic
3	#21461620	C₂	1	2	yes	maximal
4	#21461617	C₂	1	2	yes	maximal
5	#21461616	C₂	1	1	yes	maximal, characteristic
6	#21461613	C₂	1	1	yes	maximal, characteristic
7	C₄⋊C₈×#6923	C₂	1	2	yes	maximal
8	C₄⋊C₈×#6923	C₂	1	1	yes	maximal, characteristic
9	#97×#6923	C₂	1	2	yes	maximal
10	C₄×C₈×#6923	C₂	1	1	yes	maximal, characteristic
11	#446×D₆₁	C₂	1	1	yes	maximal, characteristic
12	C₂×Q₈×#6923	C₄	1	2	yes	—
13	#16840814	C₄	1	4	yes	complemented
14	#16840813	C₄	1	2	yes	complemented
15	#16840812	C₄	1	2	yes	complemented
16	D₆₁⋊(C₄⋊C₈)	C₂²	1	1	yes	characteristic
17	D₆₁⋊(C₄⋊C₈)	C₂²	1	2	yes	—
18	#16840721	C₂²	1	2	yes	—
19	C₂×#14519831	C₂²	1	2	yes	—
20	C₂×#14519831	C₂²	1	2	yes	—
21	C₄×D₆₁⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₈×#6923	C₂²	1	1	yes	characteristic
23	C₂×C₈×#6923	C₂²	1	2	yes	—
24	C₂×C₈×#6923	C₂²	1	1	yes	characteristic
25	C₂×C₈×#6923	C₂²	1	1	yes	characteristic
26	C₂×C₈×#6923	C₂²	1	1	yes	characteristic
27	C₄⋊C₄×#6923	C₄	1	4	yes	—
28	C₄⋊C₄×#6923	C₄	1	2	yes	—
29	C₄×C₄⋊#6923	C₂²	1	1	yes	characteristic
30	C₄×C₄⋊#6923	C₂²	1	2	yes	—
31	C₄²×#6923	C₂²	1	1	yes	characteristic
32	C₄²×#6923	C₂²	1	2	yes	—
33	(C₂×#6923)⋊C₈	C₂²	1	2	yes	—
34	(C₂×#6923)⋊C₈	C₂²	1	2	yes	—
35	(C₂×#6923)⋊C₈	C₂²	1	2	yes	—
36	C₄×Q₈×D₆₁	C₂²	1	1	yes	characteristic
37	#16839893	C₄	1	1	yes	characteristic, complemented
38	#16839892	C₄	1	1	yes	characteristic, complemented
39	#16839891	C₄	1	2	yes	complemented
40	#16839890	C₄	1	2	yes	complemented
41	#16839889	C₄	1	1	yes	characteristic, complemented
42	C₄⋊C₈×D₆₁	C₂²	1	1	yes	characteristic
43	C₄⋊C₈×D₆₁	C₂²	1	2	yes	—
44	#97×D₆₁	C₂²	1	2	yes	—
45	C₄×C₈×D₆₁	C₂²	1	1	yes	characteristic
46	C₆₁×#446	C₄	1	1	yes	characteristic, complemented
47	C₂×D₆₁⋊C₈	C₂³	1	1	yes	characteristic
48	C₂×D₆₁⋊C₈	C₂³	1	2	yes	—
49	C₂×D₆₁⋊C₈	C₂³	1	1	yes	characteristic
50	Q₈×#6923	—	2	8	no	—
51	C₂×C₄⋊#6923	C₂×C₄	1	4	yes	—
52	C₂×C₄⋊#6923	C₂×C₄	1	2	yes	—
53	C₂×C₄×#6923	C₂×C₄	1	4	yes	—
54	C₂×C₄×#6923	C₂×C₄	1	4	yes	—
55	C₂×C₄×#6923	C₂×C₄	1	2	yes	—
56	C₂×C₄×#6923	C₂×C₄	1	2	yes	—
57	C₂×C₄×#6923	C₂³	1	1	yes	characteristic
58	C₂×C₄×#6923	C₂³	1	2	yes	—
59	C₂×C₄×#6923	C₂³	1	1	yes	characteristic
60	#14519844	C₂×C₄	1	4	yes	—
61	#14519844	C₂×C₄	1	2	yes	—
62	C₄⋊#92420	C₂×C₄	1	2	yes	—
63	C₄⋊#92420	C₂×C₄	1	4	yes	—
64	#14519832	C₂×C₄	1	4	yes	—
65	#14519832	C₂×C₄	1	4	yes	—
66	#14519831	—	2	4	no	—
67	#14519831	—	2	4	no	—
68	C₄×#92420	C₂×C₄	1	2	yes	—
69	C₄×#92420	C₂×C₄	1	2	yes	—
70	C₈×#6923	—	2	2	no	—
71	C₈×#6923	—	2	4	no	—
72	C₈×#6923	—	2	2	no	—
73	C₈×#6923	—	2	2	no	—
74	C₈×#6923	Q₈	1	4	yes	complemented
75	(C₂×#6923)⋊C₄	C₂×C₄	1	2	yes	—
76	(C₂×#6923)⋊C₄	C₂×C₄	1	4	yes	—
77	C₂×Q₈×D₆₁	C₂×C₄	1	1	yes	characteristic
78	C₂×C₈×D₆₁	C₂³	1	1	yes	characteristic
79	C₂×C₈×D₆₁	C₂³	1	2	yes	—
80	C₂×C₈×D₆₁	C₂³	1	1	yes	characteristic
81	Q₈×Dic₆₁	C₂×C₄	1	1	yes	characteristic
82	C₄×Dic₁₂₂	C₂×C₄	1	1	yes	characteristic
83	C₄×Dic₁₂₂	C₂×C₄	1	2	yes	—
84	#14519742	C₂×C₄	1	1	yes	characteristic
85	#14519742	C₂×C₄	1	2	yes	—
86	C₄⋊C₄×D₆₁	C₂×C₄	1	2	yes	—
87	C₄⋊C₄×D₆₁	C₂×C₄	1	1	yes	characteristic
88	C₄²×D₆₁	C₂³	1	1	yes	characteristic
89	C₄²×D₆₁	C₂³	1	2	yes	—
90	C₄⋊#92418	C₂×C₄	1	2	yes	—
91	C₄⋊#92418	C₂×C₄	1	1	yes	characteristic
92	#14519706	C₂×C₄	1	2	yes	—
93	#14519706	C₂×C₄	1	2	yes	—
94	#14519706	C₂×C₄	1	2	yes	—
95	#14519688	C₂×C₄	1	2	yes	—
96	#14519687	C₂×C₄	1	2	yes	—
97	#14519687	C₂×C₄	1	2	yes	—
98	C₄×#92418	C₂×C₄	1	1	yes	characteristic
99	C₈×Dic₆₁	C₂×C₄	1	1	yes	characteristic
100	C₈×Dic₆₁	C₂×C₄	1	1	yes	characteristic
101	C₄×Q₈×C₆₁	C₂×C₄	1	1	yes	characteristic
102	C₄⋊C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
103	C₄⋊C₈×C₆₁	C₂×C₄	1	2	yes	—
104	#97×C₆₁	C₂×C₄	1	2	yes	—
105	C₄×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
106	C₂²×#6923	C₂²×C₄	1	4	yes	—
107	C₂²×#6923	C₂²×C₄	1	2	yes	—
108	C₂²×#6923	C₂²×C₄	1	2	yes	—
109	C₂×Q₈×C₆₁	C₄²	1	1	yes	characteristic
110	Q₈×D₆₁	—	2	4	no	—
111	C₂×C₄×D₆₁	C₂²×C₄	1	2	yes	—
112	C₂×C₄×D₆₁	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₄×D₆₁	C₂²×C₄	1	2	yes	—
114	C₂×C₄×D₆₁	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₄×D₆₁	C₂⁴	1	1	yes	characteristic
116	C₂×Dic₁₂₂	C₄²	1	1	yes	characteristic
117	C₂×Dic₁₂₂	C₄²	1	2	yes	—
118	C₂×#92420	C₂²×C₄	1	2	yes	—
119	C₂×#92420	C₂²×C₄	1	4	yes	—
120	C₂×#92420	C₂²×C₄	1	2	yes	—
121	C₄⋊#6923	—	2	8	no	—
122	C₄⋊#6923	—	2	4	no	—
123	C₄×#6923	—	2	8	no	—
124	C₄×#6923	—	2	4	no	—
125	C₄×#6923	—	2	8	no	—
126	C₄×#6923	—	2	1	no	—
127	C₄×#6923	—	2	1	no	—
128	C₄×#6923	—	2	2	no	—
129	C₄×#6923	—	2	2	no	—
130	C₄×#6923	M₁₆	1	8	yes	—
131	C₄×#6923	C₂×Q₈	1	2	yes	—
132	C₄×#6923	#41	1	2	yes	—
133	D₆₁⋊C₈	—	2	1	no	—
134	D₆₁⋊C₈	—	2	1	no	—
135	D₆₁⋊C₈	—	2	2	no	—
136	D₆₁⋊C₈	—	2	2	no	—
137	D₆₁⋊C₈	C₂×Q₈	1	2	yes	—
138	D₆₁⋊C₈	#41	1	2	yes	—
139	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
140	C₂×C₈×C₆₁	C₂²×C₄	1	2	yes	—
141	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
142	C₄⋊C₄×C₆₁	C₄²	1	2	yes	—
143	C₄⋊C₄×C₆₁	C₄²	1	1	yes	characteristic
144	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
145	C₄²×C₆₁	C₂²×C₄	1	2	yes	—
146	C₄⋊Dic₆₁	C₄²	1	2	yes	—
147	C₄⋊Dic₆₁	C₄²	1	1	yes	characteristic
148	#11758196	C₄²	1	2	yes	—
149	#11758196	C₄²	1	2	yes	—
150	#11758196	C₄²	1	2	yes	—
151	C₄×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
152	C₄×Dic₆₁	C₂²×C₄	1	2	yes	—
153	C₄×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
154	C₄×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
155	C₄×Dic₆₁	C₂²×C₄	1	2	yes	—
156	C₄×Dic₆₁	C₂²×C₄	1	2	yes	—
157	C₂×#92418	C₂²×C₄	1	1	yes	characteristic
158	C₂×#92418	C₂²×C₄	1	2	yes	—
159	C₂×#92418	C₂²×C₄	1	1	yes	characteristic
160	C₈×D₆₁	—	2	1	no	—
161	C₈×D₆₁	—	2	1	no	—
162	C₈×D₆₁	—	2	2	no	—
163	C₈×D₆₁	—	2	2	no	—
164	C₈×D₆₁	C₂×Q₈	1	2	yes	—
165	C₈×D₆₁	#41	1	2	yes	—
166	C₂²×D₆₁	C₂³×C₄	1	1	yes	characteristic
167	C₂×#6923	—	2	2	no	—
168	C₂×#6923	—	2	2	no	—
169	C₂×#6923	—	2	4	no	—
170	C₂×#6923	—	2	4	no	—
171	C₂×#6923	—	2	4	no	—
172	C₂×#6923	C₄×Q₈	1	4	yes	—
173	C₂×#6923	C₂×M₁₆	1	4	yes	—
174	C₂×#6923	C₂×M₁₆	1	4	yes	—
175	C₂×#6923	#131	1	4	yes	—
176	Q₈×C₆₁	—	2	2	no	—
177	C₂×C₄×C₆₁	C₂×C₄²	1	1	yes	characteristic
178	C₂×C₄×C₆₁	C₂×C₄²	1	2	yes	—
179	C₂×C₄×C₆₁	C₂×C₄²	1	2	yes	—
180	C₂×C₄×C₆₁	C₂×C₄²	1	1	yes	characteristic
181	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
182	C₂×Dic₆₁	C₂×C₄²	1	1	yes	characteristic
183	C₂×Dic₆₁	C₂×C₄²	1	2	yes	—
184	C₂×Dic₆₁	C₂×C₄²	1	2	yes	—
185	C₂×Dic₆₁	C₂×C₄²	1	1	yes	characteristic
186	C₂×Dic₆₁	C₂³×C₄	1	1	yes	characteristic
187	C₄×D₆₁	—	2	4	no	—
188	C₄×D₆₁	—	2	2	no	—
189	C₄×D₆₁	—	2	4	no	—
190	C₄×D₆₁	C₂×M₁₆	1	4	yes	—
191	C₄×D₆₁	C₂²×Q₈	1	1	yes	characteristic
192	C₄×D₆₁	C₂×#41	1	1	yes	characteristic
193	C₄×D₆₁	C₂×#41	1	1	yes	characteristic
194	C₄×D₆₁	C₂×#41	1	1	yes	characteristic
195	Dic₁₂₂	—	2	2	no	—
196	Dic₁₂₂	—	2	4	no	—
197	#92420	—	2	2	no	—
198	#92420	—	2	4	no	—
199	#92420	C₄×Q₈	1	4	yes	complemented
200	C₈×C₆₁	—	2	1	no	—
201	C₈×C₆₁	—	2	2	no	—
202	C₈×C₆₁	C₄×Q₈	1	2	yes	complemented
203	#92418	—	2	1	no	—
204	#92418	—	2	2	no	—
205	#92418	C₄×Q₈	1	2	yes	complemented
206	C₄×#446	—	61	1	no	maximal, Sylow
207	C₂²×C₆₁	C₂²×C₄²	1	1	yes	characteristic
208	C₂×D₆₁	C₂×C₄×Q₈	1	1	yes	characteristic
209	C₂×D₆₁	C₄×#41	1	1	yes	characteristic
210	C₂×D₆₁	C₂²×M₁₆	1	2	yes	—
211	C₂×D₆₁	C₂×#131	1	2	yes	—
212	#6923	—	2	4	no	—
213	#6923	—	4	4	no	—
214	#6923	#446	1	8	yes	direct product factor
215	C₄×C₆₁	—	2	2	no	—
216	C₄×C₆₁	—	2	1	no	—
217	C₄×C₆₁	—	2	2	no	—
218	C₄×C₆₁	C₄×M₁₆	1	2	yes	—
219	C₄×C₆₁	C₂×C₄×Q₈	1	1	yes	characteristic
220	C₄×C₆₁	C₄×#41	1	1	yes	characteristic
221	Dic₆₁	—	2	2	no	—
222	Dic₆₁	—	2	1	no	—
223	Dic₆₁	—	2	2	no	—
224	Dic₆₁	C₄×M₁₆	1	2	yes	—
225	Dic₆₁	C₂×C₄×Q₈	1	1	yes	characteristic
226	Dic₆₁	C₄×#41	1	1	yes	characteristic
227	C₂×#446	—	61	1	no	—
228	C₂×#446	—	61	1	no	—
229	C₄²×Q₈	—	61	1	no	—
230	#1771	—	61	2	no	—
231	#1771	—	61	2	no	—
232	#1770	—	61	1	no	—
233	#1770	—	61	1	no	—
234	C₄×C₄⋊C₈	—	61	2	no	—
235	C₄×C₄⋊C₈	—	61	1	no	—
236	C₄×#97	—	61	2	no	—
237	C₄²×C₈	—	61	1	no	—
238	C₂×C₆₁	C₄²×Q₈	1	1	yes	characteristic
239	C₂×C₆₁	C₂×C₄×M₁₆	1	1	yes	characteristic
240	C₂×C₆₁	C₄×#131	1	1	yes	characteristic
241	D₆₁	C₂×#446	1	2	yes	—
242	D₆₁	#2965	1	2	yes	—
243	C₂×C₄×Q₈	—	61	1	no	—
244	C₂×C₄×Q₈	—	61	2	no	—
245	#446	—	61	2	no	—
246	#446	—	61	2	no	—
247	#446	—	61	4	no	—
248	#446	—	61	1	no	—
249	#446	—	61	1	no	—
250	#446	—	61	2	no	—
251	#446	—	61	2	no	—
252	#446	—	61	1	no	—
253	#446	#6923	1	1	yes	characteristic, direct product factor
254	C₂×C₄⋊C₈	—	61	1	no	—
255	C₂×C₄⋊C₈	—	61	2	no	—
256	C₂×C₄⋊C₈	—	61	1	no	—
257	C₂×C₄⋊C₈	—	61	2	no	—
258	C₂×#97	—	61	2	no	—
259	C₂×#97	—	61	2	no	—
260	C₂×#97	—	61	2	no	—
261	C₂×#97	—	61	2	no	—
262	C₂×C₄×C₈	—	61	1	no	—
263	C₂×C₄×C₈	—	61	1	no	—
264	C₂×C₄×C₈	—	61	1	no	—
265	C₂×C₄×C₈	—	61	1	no	—
266	C₂×C₄×C₈	—	61	1	no	—
267	C₂×C₄×C₈	—	61	1	no	—
268	C₂×C₄×C₈	—	61	2	no	—
269	C₄×C₄⋊C₄	—	61	1	no	—
270	C₄×C₄⋊C₄	—	61	2	no	—
271	C₄×C₄⋊C₄	—	61	2	no	—
272	C₄×C₄⋊C₄	—	61	4	no	—
273	C₄³	—	61	1	no	—
274	C₄³	—	61	2	no	—
275	#336	—	61	2	no	—
276	#336	—	61	2	no	—
277	#336	—	61	2	no	—
278	C₆₁	C₄×#446	1	1	yes	characteristic, complemented, Sylow
279	C₂²×Q₈	—	61	1	no	—
280	C₂²×C₈	—	61	1	no	—
281	C₂²×C₈	—	61	1	no	—
282	C₂²×C₈	—	61	1	no	—
283	C₂²×C₈	—	61	2	no	—
284	C₂²×C₈	—	61	1	no	—
285	C₂²×C₈	—	61	2	no	—
286	C₄×Q₈	—	61	1	no	—
287	C₄×Q₈	—	61	1	no	—
288	C₄×Q₈	—	61	2	no	—
289	C₄×Q₈	—	61	2	no	—
290	C₄×Q₈	—	61	1	no	—
291	C₄×Q₈	—	122	8	no	—
292	C₄×Q₈	C₂×#6923	1	1	yes	characteristic
293	C₂×C₄⋊C₄	—	61	1	no	—
294	C₂×C₄⋊C₄	—	61	2	no	—
295	C₂×C₄⋊C₄	—	61	2	no	—
296	C₂×C₄⋊C₄	—	61	4	no	—
297	C₂×C₄²	—	61	2	no	—
298	C₂×C₄²	—	61	1	no	—
299	C₂×C₄²	—	61	1	no	—
300	C₂×C₄²	—	61	2	no	—
301	C₂×C₄²	—	61	4	no	—
302	C₂×C₄²	—	61	2	no	—
303	C₂×C₄²	—	61	4	no	—
304	C₂×C₄²	—	61	1	no	—
305	C₂×C₄²	—	61	2	no	—
306	C₄⋊C₈	—	61	2	no	—
307	C₄⋊C₈	—	61	4	no	—
308	C₄⋊C₈	—	61	2	no	—
309	C₄⋊C₈	—	61	4	no	—
310	C₄⋊C₈	—	61	2	no	—
311	C₄⋊C₈	—	61	2	no	—
312	C₄⋊C₈	—	61	2	no	—
313	C₄⋊C₈	—	61	1	no	—
314	C₄⋊C₈	—	61	2	no	—
315	C₄⋊C₈	C₂×#6923	1	1	yes	characteristic
316	C₄⋊C₈	C₂×#6923	1	2	yes	—
317	#97	—	61	4	no	—
318	#97	—	61	4	no	—
319	#97	—	61	2	no	—
320	#97	—	61	2	no	—
321	#97	—	61	2	no	—
322	#97	—	122	4	no	—
323	#97	—	122	4	no	—
324	#97	C₂×#6923	1	2	yes	—
325	C₄×C₈	—	61	4	no	—
326	C₄×C₈	—	61	2	no	—
327	C₄×C₈	—	61	2	no	—
328	C₄×C₈	—	61	1	no	—
329	C₄×C₈	—	61	1	no	—
330	C₄×C₈	—	61	1	no	—
331	C₄×C₈	—	122	2	no	—
332	C₄×C₈	—	122	4	no	—
333	C₄×C₈	—	122	2	no	—
334	C₄×C₈	—	122	2	no	—
335	C₄×C₈	C₂×#6923	1	1	yes	characteristic
336	#95	—	61	4	no	—
337	#95	—	61	2	no	—
338	C₂×Q₈	—	61	2	no	—
339	C₂×Q₈	—	61	1	no	—
340	C₂×Q₈	—	122	4	no	—
341	C₂×Q₈	C₄×#6923	1	1	yes	characteristic
342	C₂²×C₄	—	61	2	no	—
343	C₂²×C₄	—	61	1	no	—
344	C₂²×C₄	—	61	1	no	—
345	C₂²×C₄	—	61	2	no	—
346	C₂²×C₄	—	61	1	no	—
347	C₂²×C₄	—	61	2	no	—
348	C₂²×C₄	—	61	2	no	—
349	C₂²×C₄	—	61	4	no	—
350	C₂×C₈	—	61	2	no	—
351	C₂×C₈	—	61	2	no	—
352	C₂×C₈	—	61	2	no	—
353	C₂×C₈	—	61	1	no	—
354	C₂×C₈	—	61	2	no	—
355	C₂×C₈	—	61	2	no	—
356	C₂×C₈	—	61	2	no	—
357	C₂×C₈	—	61	4	no	—
358	C₂×C₈	—	61	1	no	—
359	C₂×C₈	—	61	2	no	—
360	C₂×C₈	—	122	1	no	—
361	C₂×C₈	—	122	2	no	—
362	C₂×C₈	—	122	1	no	—
363	C₂×C₈	—	122	2	no	—
364	C₂×C₈	—	122	1	no	—
365	C₂×C₈	—	122	1	no	—
366	C₂×C₈	—	122	2	no	—
367	C₂×C₈	—	122	2	no	—
368	C₂×C₈	C₂²×#6923	1	1	yes	characteristic
369	C₂×C₈	C₂²×#6923	1	2	yes	—
370	C₂×C₈	C₂²×#6923	1	1	yes	characteristic
371	C₄⋊C₄	—	61	2	no	—
372	C₄⋊C₄	—	61	2	no	—
373	C₄⋊C₄	—	61	2	no	—
374	C₄⋊C₄	—	61	2	no	—
375	C₄⋊C₄	—	61	1	no	—
376	C₄⋊C₄	—	122	4	no	—
377	C₄⋊C₄	—	122	8	no	—
378	C₄⋊C₄	C₄×#6923	1	2	yes	—
379	C₄⋊C₄	C₄×#6923	1	1	yes	characteristic
380	C₄²	—	61	2	no	—
381	C₄²	—	61	2	no	—
382	C₄²	—	61	8	no	—
383	C₄²	—	61	1	no	—
384	C₄²	—	61	1	no	—
385	C₄²	—	61	2	no	—
386	C₄²	—	61	2	no	—
387	C₄²	—	61	1	no	—
388	C₄²	—	61	2	no	—
389	C₄²	—	122	1	no	—
390	C₄²	—	122	1	no	—
391	C₄²	—	122	2	no	—
392	C₄²	—	122	2	no	—
393	C₄²	—	122	8	no	—
394	C₄²	—	122	4	no	—
395	C₄²	—	122	8	no	—
396	C₄²	C₂²×#6923	1	1	yes	characteristic
397	C₄²	C₂²×#6923	1	2	yes	—
398	C₂³	—	61	1	no	—
399	Q₈	—	2	2	no	—
400	Q₈	—	122	4	no	—
401	Q₈	—	122	2	no	—
402	C₂×C₄	—	61	4	no	—
403	C₂×C₄	—	61	4	no	—
404	C₂×C₄	—	61	4	no	—
405	C₂×C₄	—	61	1	no	—
406	C₂×C₄	—	61	1	no	—
407	C₂×C₄	—	61	4	no	—
408	C₂×C₄	—	61	1	no	—
409	C₂×C₄	—	61	1	no	—
410	C₂×C₄	—	61	1	no	—
411	C₂×C₄	—	61	1	no	—
412	C₂×C₄	—	61	4	no	—
413	C₂×C₄	—	61	1	no	—
414	C₂×C₄	—	61	2	no	—
415	C₂×C₄	—	61	2	no	—
416	C₂×C₄	—	122	4	no	—
417	C₂×C₄	—	122	2	no	—
418	C₂×C₄	—	122	4	no	—
419	C₂×C₄	—	122	2	no	—
420	C₂×C₄	—	122	2	no	—
421	C₂×C₄	—	122	4	no	—
422	C₂×C₄	—	122	4	no	—
423	C₂×C₄	—	122	4	no	—
424	C₂×C₄	C₂×C₄×#6923	1	1	yes	characteristic
425	C₂×C₄	C₂×C₄×#6923	1	2	yes	—
426	C₂×C₄	C₂×C₄×#6923	1	2	yes	—
427	C₂×C₄	C₂×C₄×#6923	1	1	yes	characteristic
428	C₂×C₄	C₂³×#6923	1	1	yes	characteristic
429	C₈	—	2	1	no	—
430	C₈	—	2	2	no	—
431	C₈	—	61	4	no	—
432	C₈	—	61	2	no	—
433	C₈	—	122	2	no	—
434	C₈	—	122	4	no	—
435	C₈	—	122	1	no	—
436	C₈	—	122	2	no	—
437	C₈	Q₈×#6923	1	2	yes	complemented
438	C₂²	—	61	2	no	—
439	C₂²	—	61	2	no	—
440	C₂²	—	61	1	no	—
441	C₂²	—	61	1	no	—
442	C₂²	C₂²×C₄×#6923	1	1	yes	characteristic
443	C₄	—	2	2	no	—
444	C₄	—	2	1	no	—
445	C₄	—	2	2	no	—
446	C₄	—	61	8	no	—
447	C₄	—	61	2	no	—
448	C₄	—	61	1	no	—
449	C₄	—	61	1	no	—
450	C₄	—	122	4	no	—
451	C₄	—	122	2	no	—
452	C₄	—	122	1	no	—
453	C₄	—	122	2	no	—
454	C₄	—	244	4	no	—
455	C₄	M₁₆×#6923	1	2	yes	—
456	C₄	C₂×Q₈×#6923	1	1	yes	characteristic
457	C₄	#41×#6923	1	1	yes	characteristic
458	C₂	—	61	2	no	—
459	C₂	—	61	2	no	—
460	C₂	C₄×Q₈×#6923	1	1	yes	characteristic
461	C₂	C₂×M₁₆×#6923	1	1	yes	characteristic
462	C₂	#131×#6923	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×#6923
commutator, socle	C₂²×C₆₁	C₂²×C₄²
Fitting	C₆₁×#446	C₄
prime radical	C₂²×D₆₁	C₂³×C₄
cosocle	C₂×C₄×D₆₁	C₂⁴
hypercenter	#446	#6923
hypocenter	C₆₁	C₄×#446
LCS	G ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄ ◁ #446

Complements

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

N	H ≅ G/N	type
13. #16840814	C₄	semidirect
14. #16840813	C₄	semidirect
15. #16840812	C₄	semidirect
37. #16839893	C₄	semidirect
38. #16839892	C₄	semidirect
39. #16839891	C₄	semidirect
40. #16839890	C₄	semidirect
41. #16839889	C₄	semidirect
46. C₆₁×#446	C₄	semidirect
74. C₈×#6923	Q₈	semidirect
199. #92420	C₄×Q₈	semidirect
202. C₈×C₆₁	C₄×Q₈	semidirect
205. #92418	C₄×Q₈	semidirect
214. #6923	#446	direct (N × H)
253. #446	#6923	direct (N × H)
278. C₆₁	C₄×#446	semidirect
437. C₈	Q₈×#6923	semidirect

Maximal subgroups

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

subgroup	index
D₆₁⋊#446	2
C₄×Q₈×#6923	2
#21461620	2
#21461617	2
#21461616	2
#21461613	2
C₄⋊C₈×#6923	2
#97×#6923	2
C₄×C₈×#6923	2
#446×D₆₁	2
C₄×#446	61