Subgroups — #29651017

Order 15616.

662 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21455850	C₂	1	1	yes	maximal, characteristic
2	Q₈×#11758194	C₂	1	1	yes	maximal, characteristic, complemented
3	#21454562	C₂	1	1	yes	maximal, characteristic
4	#21444724	C₂	1	2	yes	maximal, complemented
5	#21444694	C₂	1	2	yes	maximal, complemented
6	#21444679	C₂	1	2	yes	maximal, complemented
7	#21444634	C₂	1	2	yes	maximal, complemented
8	#21444593	C₂	1	1	yes	maximal, characteristic, complemented
9	#21444271	C₂	1	1	yes	maximal, characteristic
10	#21444108	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₆₁×Q₈⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14519783	—	2	1	no	—
13	#16840312	C₂²	1	1	yes	characteristic
14	#16840080	C₄	1	2	yes	—
15	#16840047	C₄	1	1	yes	characteristic
16	#16840047	C₄	1	1	yes	characteristic
17	#16839962	C₄	1	1	yes	characteristic
18	#16839962	C₄	1	1	yes	characteristic
19	#16839901	C₄	1	2	yes	—
20	#16839893	—	2	2	no	—
21	#16839893	C₂²	1	2	yes	—
22	Q₈×#92418	C₂²	1	2	yes	—
23	C₄×#11758201	C₂²	1	2	yes	—
24	C₄×#11758201	C₂²	1	2	yes	—
25	#16839839	C₂²	1	2	yes	—
26	#16839832	—	2	2	no	—
27	#16839827	C₂²	1	2	yes	—
28	#16839815	C₂²	1	1	yes	characteristic
29	#16839786	—	2	1	no	—
30	#16839786	C₂²	1	1	yes	characteristic
31	#16839728	—	2	1	no	—
32	C₄×#11758194	—	2	1	no	—
33	C₄×#11758194	C₂²	1	1	yes	characteristic
34	#16839514	C₂²	1	2	yes	—
35	#16839514	C₂²	1	2	yes	—
36	#16839491	C₂²	1	2	yes	—
37	#16839491	C₂²	1	2	yes	—
38	#16839484	C₂²	1	2	yes	—
39	#16839483	C₂²	1	2	yes	—
40	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
41	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
42	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
43	C₆₁×Q₈⋊C₈	C₂²	1	1	yes	characteristic
44	C₆₁×Q₈⋊C₈	C₂²	1	1	yes	characteristic
45	C₆₁×Q₈⋊C₈	C₂²	1	1	yes	characteristic
46	C₆₁×Q₈⋊C₈	C₂²	1	1	yes	characteristic
47	C₂×#11758222	—	2	1	no	—
48	C₂×#11758201	C₂×C₄	1	2	yes	—
49	C₂×#11758201	C₂×C₄	1	2	yes	—
50	#14519783	—	4	4	no	—
51	C₂×#11758194	—	2	1	no	—
52	C₂×#11758194	D₄	1	1	yes	characteristic
53	C₂×#11758194	D₄	1	1	yes	characteristic
54	C₂×#11758189	—	2	2	no	—
55	C₂×C₈×D₆₁	—	2	2	no	—
56	#14519777	C₂×C₄	1	1	yes	characteristic
57	#14519774	C₂×C₄	1	1	yes	characteristic
58	#14519765	—	2	1	no	—
59	#14519751	—	2	1	no	—
60	#14519751	C₂×C₄	1	2	yes	—
61	C₄×D₂₄₄	—	2	1	no	—
62	C₄×D₂₄₄	C₂³	1	2	yes	—
63	#14519708	C₂×C₄	1	2	yes	—
64	#14519708	C₂×C₄	1	2	yes	—
65	C₄⋊#92418	—	2	1	no	—
66	C₄⋊#92418	—	2	2	no	—
67	C₄⋊#92418	—	2	2	no	—
68	C₄⋊#92418	C₂×C₄	1	1	yes	characteristic
69	C₄⋊#92418	C₂×C₄	1	1	yes	characteristic
70	C₄⋊#92418	C₂³	1	2	yes	—
71	#14519701	C₂×C₄	1	2	yes	—
72	#14519701	C₂×C₄	1	2	yes	—
73	#14519697	C₂×C₄	1	2	yes	—
74	#14519697	C₂×C₄	1	2	yes	—
75	C₂²⋊#92418	C₂×C₄	1	2	yes	—
76	#14519689	—	2	2	no	—
77	#14519689	—	2	2	no	—
78	#14519688	—	2	2	no	—
79	#14519688	D₄	1	2	yes	—
80	C₄×#92418	—	2	2	no	—
81	C₄×#92418	C₂³	1	2	yes	—
82	C₄×#92418	C₂³	1	2	yes	—
83	C₂²×Q₈×C₆₁	C₂×C₄	1	1	yes	characteristic
84	C₂²×C₈×C₆₁	—	2	1	no	—
85	C₂²×C₈×C₆₁	—	2	1	no	—
86	C₄×Q₈×C₆₁	—	2	1	no	—
87	C₄×Q₈×C₆₁	—	2	1	no	—
88	C₄×Q₈×C₆₁	C₂×C₄	1	1	yes	characteristic
89	C₄×Q₈×C₆₁	C₂×C₄	1	1	yes	characteristic
90	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
91	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
92	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
93	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
94	C₂×C₄²×C₆₁	—	2	1	no	—
95	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
96	C₄⋊C₈×C₆₁	—	2	1	no	—
97	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
98	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
99	C₄×C₈×C₆₁	—	2	1	no	—
100	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
101	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
102	C₂×Q₈×C₆₁	—	2	1	no	—
103	C₂×Q₈×C₆₁	—	2	2	no	—
104	C₂×Q₈×C₆₁	—	4	1	no	—
105	C₂×Q₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
106	C₂×Q₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
107	C₂²×C₄×C₆₁	—	2	1	no	—
108	C₂²×C₄×C₆₁	—	2	1	no	—
109	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
110	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₆₁	#41	1	1	yes	characteristic
112	C₂×C₂²⋊D₆₁	—	2	2	no	—
113	#11758222	—	4	2	no	—
114	#11758222	—	4	2	no	—
115	C₂×D₂₄₄	—	2	1	no	—
116	C₂×D₂₄₄	—	2	1	no	—
117	C₂×D₂₄₄	C₂²×C₄	1	2	yes	—
118	C₂×C₄×D₆₁	—	2	2	no	—
119	C₂×Dic₁₂₂	—	2	1	no	—
120	C₂×C₈×C₆₁	—	2	1	no	—
121	C₂×C₈×C₆₁	—	2	1	no	—
122	C₂×C₈×C₆₁	—	2	1	no	—
123	C₂×C₈×C₆₁	—	2	1	no	—
124	C₂×C₈×C₆₁	—	4	2	no	—
125	C₂×C₈×C₆₁	—	4	2	no	—
126	C₄⋊C₄×C₆₁	—	2	1	no	—
127	C₄⋊C₄×C₆₁	—	2	1	no	—
128	C₄⋊C₄×C₆₁	—	2	1	no	—
129	C₄⋊C₄×C₆₁	—	2	1	no	—
130	C₄⋊C₄×C₆₁	—	2	1	no	—
131	C₄⋊C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
132	C₄⋊C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
133	C₄²×C₆₁	—	2	1	no	—
134	C₄²×C₆₁	—	2	1	no	—
135	C₄²×C₆₁	—	2	1	no	—
136	C₄²×C₆₁	—	2	1	no	—
137	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
138	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
139	C₄²×C₆₁	#41	1	1	yes	characteristic
140	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
141	#11758201	—	2	4	no	—
142	#11758201	—	4	2	no	—
143	#11758198	—	2	2	no	—
144	#11758198	—	2	2	no	—
145	C₄⋊Dic₆₁	—	2	1	no	—
146	C₄⋊Dic₆₁	C₂²×C₄	1	2	yes	—
147	#11758194	—	2	2	no	—
148	#11758194	—	2	2	no	—
149	#11758194	—	4	2	no	—
150	C₂×#92418	—	2	2	no	—
151	C₂×#92418	C₂²×C₄	1	2	yes	—
152	C₂×#92418	C₂²×C₄	1	2	yes	—
153	C₂×#92418	C₂×D₄	1	2	yes	—
154	C₂×#92418	C₂×D₄	1	2	yes	—
155	#11758189	—	4	4	no	—
156	C₈×D₆₁	—	4	4	no	—
157	C₂³×C₆₁	C₄×D₄	1	1	yes	characteristic
158	C₂²×D₆₁	—	2	2	no	—
159	Q₈×C₆₁	—	2	1	no	—
160	Q₈×C₆₁	—	2	1	no	—
161	Q₈×C₆₁	—	2	1	no	—
162	Q₈×C₆₁	—	4	2	no	—
163	Q₈×C₆₁	#131	1	2	yes	complemented
164	C₂×C₄×C₆₁	—	2	1	no	—
165	C₂×C₄×C₆₁	—	2	1	no	—
166	C₂×C₄×C₆₁	—	2	1	no	—
167	C₂×C₄×C₆₁	—	2	1	no	—
168	C₂×C₄×C₆₁	—	2	1	no	—
169	C₂×C₄×C₆₁	—	2	1	no	—
170	C₂×C₄×C₆₁	—	4	1	no	—
171	C₂×C₄×C₆₁	—	4	2	no	—
172	C₂×C₄×C₆₁	—	8	1	no	—
173	C₂×C₄×C₆₁	C₄×D₄	1	1	yes	characteristic
174	C₂×C₄×C₆₁	C₄×D₄	1	1	yes	characteristic
175	C₂×C₄×C₆₁	C₄×D₄	1	1	yes	characteristic
176	C₂×C₄×C₆₁	AGL(1,ℤ/8)	1	2	yes	—
177	C₂×C₄×C₆₁	#137	1	2	yes	—
178	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
179	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
180	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
181	C₂²⋊D₆₁	—	4	4	no	—
182	C₂×Dic₆₁	—	2	2	no	—
183	D₂₄₄	—	2	2	no	—
184	D₂₄₄	—	2	2	no	—
185	D₂₄₄	—	4	2	no	—
186	D₂₄₄	—	8	1	no	—
187	C₄×D₆₁	—	4	2	no	—
188	C₄×D₆₁	—	4	2	no	—
189	Dic₁₂₂	—	4	2	no	—
190	C₈×C₆₁	—	2	2	no	—
191	C₈×C₆₁	—	4	1	no	—
192	C₈×C₆₁	—	4	1	no	—
193	C₈×C₆₁	—	4	1	no	—
194	#92418	—	2	2	no	—
195	#92418	—	2	2	no	—
196	#92418	—	2	2	no	—
197	#92418	—	2	2	no	—
198	#92418	—	4	2	no	—
199	#18004	—	61	1	no	maximal, Sylow
200	C₂²×C₆₁	—	2	1	no	—
201	C₂²×C₆₁	—	2	1	no	—
202	C₂²×C₆₁	#440	1	2	yes	—
203	C₂²×C₆₁	C₂×C₄×D₄	1	1	yes	characteristic
204	C₂×D₆₁	—	4	2	no	—
205	C₂×D₆₁	—	4	2	no	—
206	C₂×D₆₁	—	4	2	no	—
207	C₄×C₆₁	—	2	1	no	—
208	C₄×C₆₁	—	2	2	no	—
209	C₄×C₆₁	—	2	1	no	—
210	C₄×C₆₁	—	2	1	no	—
211	C₄×C₆₁	—	4	1	no	—
212	C₄×C₆₁	—	4	1	no	—
213	C₄×C₆₁	—	4	1	no	—
214	C₄×C₆₁	#440	1	2	yes	—
215	C₄×C₆₁	C₂×#131	1	1	yes	characteristic
216	C₄×C₆₁	#568	1	1	yes	characteristic
217	C₄×C₆₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
218	C₄×C₆₁	C₂×#137	1	1	yes	characteristic
219	Dic₆₁	—	4	2	no	—
220	#3103	—	61	1	no	—
221	Q₈×M₁₆	—	61	1	no	—
222	#2935	—	61	1	no	—
223	#1592	—	61	2	no	—
224	#1588	—	61	2	no	—
225	#1585	—	61	2	no	—
226	SD₁₆⋊C₈	—	61	2	no	—
227	#1571	—	61	1	no	—
228	#1492	—	61	1	no	—
229	C₂×Q₈⋊C₈	D₆₁	1	1	yes	characteristic, complemented
230	#1451	—	61	1	no	—
231	C₂×C₆₁	—	2	2	no	—
232	C₂×C₆₁	#2933	1	1	yes	characteristic
233	C₂×C₆₁	C₂×#440	1	1	yes	characteristic
234	C₂×C₆₁	#2956	1	1	yes	characteristic
235	D₆₁	—	8	2	no	—
236	C₂×#131	—	122	1	no	—
237	#532	—	61	1	no	—
238	C₂×C₄×Q₈	C₂×D₆₁	1	1	yes	characteristic
239	#481	—	61	2	no	—
240	#475	—	61	1	no	—
241	#475	—	61	1	no	—
242	#460	—	61	1	no	—
243	#460	—	61	1	no	—
244	#448	—	61	2	no	—
245	#446	—	61	2	no	—
246	#446	—	122	2	no	—
247	C₈×Q₈	—	61	2	no	—
248	C₄×SD₁₆	—	61	2	no	—
249	C₄×SD₁₆	—	61	2	no	—
250	#436	—	61	2	no	—
251	#435	—	122	2	no	—
252	C₈×D₄	—	61	2	no	—
253	#431	—	61	1	no	—
254	#423	—	61	1	no	—
255	#423	—	122	1	no	—
256	C₂×C₄⋊C₈	C₂×D₆₁	1	1	yes	characteristic
257	#408	—	122	1	no	—
258	C₄×M₁₆	—	61	1	no	—
259	C₄×M₁₆	—	122	1	no	—
260	C₂×C₄×C₈	C₂×D₆₁	1	1	yes	characteristic
261	#335	—	61	2	no	—
262	#335	—	61	2	no	—
263	Q₈⋊C₈	C₂×D₆₁	1	1	yes	characteristic
264	Q₈⋊C₈	C₂×D₆₁	1	1	yes	characteristic
265	Q₈⋊C₈	C₂×D₆₁	1	1	yes	characteristic
266	Q₈⋊C₈	C₂×D₆₁	1	1	yes	characteristic
267	D₄⋊C₈	—	61	2	no	—
268	D₄⋊C₈	—	61	2	no	—
269	#322	—	61	2	no	—
270	#322	—	61	2	no	—
271	C₆₁	#18004	1	1	yes	characteristic, complemented, Sylow
272	C₂×#41	—	122	1	no	—
273	C₂²×Q₈	C₄×D₆₁	1	1	yes	characteristic
274	C₂×SD₁₆	—	61	2	no	—
275	C₂×SD₁₆	—	61	2	no	—
276	#131	—	244	4	no	—
277	C₂×M₁₆	—	61	1	no	—
278	C₂×M₁₆	—	61	1	no	—
279	C₂×M₁₆	—	122	2	no	—
280	C₂×M₁₆	—	122	1	no	—
281	C₂²×C₈	—	2	1	no	—
282	C₂²×C₈	—	2	1	no	—
283	C₂²×C₈	—	122	2	no	—
284	C₄⋊Q₈	—	61	1	no	—
285	#127	—	61	1	no	—
286	#124	—	122	1	no	—
287	#121	—	61	2	no	—
288	#121	—	122	1	no	—
289	C₄×Q₈	—	2	1	no	—
290	C₄×Q₈	—	2	1	no	—
291	C₄×Q₈	C₄×D₆₁	1	1	yes	characteristic
292	C₄×Q₈	C₄×D₆₁	1	1	yes	characteristic
293	C₄×Q₈	C₂²×D₆₁	1	1	yes	characteristic
294	C₄×Q₈	C₂²×D₆₁	1	1	yes	characteristic
295	C₄×D₄	—	61	2	no	—
296	C₄×D₄	—	122	1	no	—
297	C₂×C₄⋊C₄	—	2	1	no	—
298	C₂×C₄⋊C₄	C₄×D₆₁	1	1	yes	characteristic
299	C₂×C₄²	—	2	1	no	—
300	C₂×C₄²	C₂²×D₆₁	1	1	yes	characteristic
301	#106	—	61	2	no	—
302	#106	—	61	2	no	—
303	C₄⋊C₈	—	2	1	no	—
304	C₄⋊C₈	—	61	1	no	—
305	C₄⋊C₈	—	61	1	no	—
306	C₄⋊C₈	—	61	2	no	—
307	C₄⋊C₈	—	122	2	no	—
308	C₄⋊C₈	—	122	2	no	—
309	C₄⋊C₈	—	122	1	no	—
310	C₄⋊C₈	C₂²×D₆₁	1	1	yes	characteristic
311	C₄⋊C₈	C₂²×D₆₁	1	1	yes	characteristic
312	#103	—	61	2	no	—
313	#103	—	61	2	no	—
314	#102	—	61	2	no	—
315	#102	—	61	2	no	—
316	C₂²⋊C₈	—	61	2	no	—
317	C₂²⋊C₈	—	122	2	no	—
318	C₂²⋊C₈	—	122	2	no	—
319	#97	—	61	2	no	—
320	#97	—	122	2	no	—
321	C₄×C₈	—	2	1	no	—
322	C₄×C₈	—	61	2	no	—
323	C₄×C₈	—	61	2	no	—
324	C₄×C₈	—	122	2	no	—
325	C₄×C₈	C₂²×D₆₁	1	1	yes	characteristic
326	C₄×C₈	C₂²×D₆₁	1	1	yes	characteristic
327	#41	—	244	2	no	—
328	#41	—	244	2	no	—
329	C₂×Q₈	—	2	1	no	—
330	C₂×Q₈	—	2	2	no	—
331	C₂×Q₈	—	4	1	no	—
332	C₂×Q₈	—	122	1	no	—
333	C₂×Q₈	C₂×C₄×D₆₁	1	1	yes	characteristic
334	C₂×Q₈	C₂×C₄×D₆₁	1	1	yes	characteristic
335	C₂×D₄	—	61	2	no	—
336	C₂×D₄	—	122	2	no	—
337	C₂×D₄	—	122	1	no	—
338	C₂×D₄	—	122	1	no	—
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	2	1	no	—
341	C₂²×C₄	—	122	2	no	—
342	C₂²×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
343	C₂²×C₄	D₄×D₆₁	1	1	yes	characteristic
344	C₂²×C₄	#11758224	1	1	yes	characteristic
345	SD₁₆	—	122	4	no	—
346	SD₁₆	—	244	2	no	—
347	M₁₆	—	122	2	no	—
348	M₁₆	—	122	2	no	—
349	M₁₆	—	244	4	no	—
350	M₁₆	—	244	2	no	—
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	2	1	no	—
353	C₂×C₈	—	2	1	no	—
354	C₂×C₈	—	2	1	no	—
355	C₂×C₈	—	4	2	no	—
356	C₂×C₈	—	4	2	no	—
357	C₂×C₈	—	61	2	no	—
358	C₂×C₈	—	61	2	no	—
359	C₂×C₈	—	61	2	no	—
360	C₂×C₈	—	61	2	no	—
361	C₂×C₈	—	122	2	no	—
362	C₂×C₈	—	244	4	no	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	—	2	1	no	—
366	C₄⋊C₄	—	2	1	no	—
367	C₄⋊C₄	—	2	1	no	—
368	C₄⋊C₄	—	61	2	no	—
369	C₄⋊C₄	—	122	1	no	—
370	C₄⋊C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
371	C₄⋊C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
372	C₂²⋊C₄	—	122	2	no	—
373	C₂²⋊C₄	—	122	2	no	—
374	C₄²	—	2	1	no	—
375	C₄²	—	2	1	no	—
376	C₄²	—	2	1	no	—
377	C₄²	—	2	1	no	—
378	C₄²	C₂×C₄×D₆₁	1	1	yes	characteristic
379	C₄²	D₄×D₆₁	1	1	yes	characteristic
380	C₄²	#11758224	1	1	yes	characteristic
381	C₄²	C₂³×D₆₁	1	1	yes	characteristic
382	C₂³	—	122	2	no	—
383	C₂³	#14519737	1	1	yes	characteristic
384	Q₈	—	2	1	no	—
385	Q₈	—	2	1	no	—
386	Q₈	—	2	1	no	—
387	Q₈	—	4	2	no	—
388	Q₈	—	244	2	no	—
389	Q₈	#14519783	1	2	yes	complemented
390	D₄	—	122	2	no	—
391	D₄	—	122	2	no	—
392	D₄	—	488	1	no	—
393	D₄	—	244	4	no	—
394	D₄	—	244	2	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	8	1	no	—
404	C₂×C₄	—	122	2	no	—
405	C₂×C₄	—	244	2	no	—
406	C₂×C₄	—	244	2	no	—
407	C₂×C₄	#14519737	1	1	yes	characteristic
408	C₂×C₄	#14519737	1	1	yes	characteristic
409	C₂×C₄	#14519737	1	1	yes	characteristic
410	C₂×C₄	#14519804	1	2	yes	—
411	C₂×C₄	#14519809	1	2	yes	—
412	C₂×C₄	C₂²×C₄×D₆₁	1	1	yes	characteristic
413	C₂×C₄	C₂×D₄×D₆₁	1	1	yes	characteristic
414	C₂×C₄	C₂×#11758224	1	1	yes	characteristic
415	C₈	—	2	2	no	—
416	C₈	—	4	1	no	—
417	C₈	—	4	1	no	—
418	C₈	—	4	1	no	—
419	C₈	—	122	2	no	—
420	C₈	—	122	2	no	—
421	C₈	—	122	2	no	—
422	C₈	—	122	2	no	—
423	C₈	—	244	2	no	—
424	C₂²	—	2	1	no	—
425	C₂²	—	2	1	no	—
426	C₂²	—	244	2	no	—
427	C₂²	—	244	2	no	—
428	C₂²	—	244	2	no	—
429	C₂²	#16839865	1	2	yes	—
430	C₂²	C₂×#14519737	1	1	yes	characteristic
431	C₄	—	2	1	no	—
432	C₄	—	2	1	no	—
433	C₄	—	2	1	no	—
434	C₄	—	2	2	no	—
435	C₄	—	4	1	no	—
436	C₄	—	4	1	no	—
437	C₄	—	4	1	no	—
438	C₄	—	244	2	no	—
439	C₄	#16839865	1	2	yes	—
440	C₄	C₂×#14519783	1	1	yes	characteristic
441	C₄	#16840528	1	1	yes	characteristic
442	C₄	C₂×#14519804	1	1	yes	characteristic
443	C₄	C₂×#14519809	1	1	yes	characteristic
444	C₂	—	2	2	no	—
445	C₂	—	488	2	no	—
446	C₂	#21454540	1	1	yes	characteristic
447	C₂	C₂×#16839865	1	1	yes	characteristic
448	C₂	#21454725	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₆₁
commutator	C₂×C₄×C₆₁	C₂³×C₄
Frattini	C₄²	C₂³×D₆₁
Fitting	C₂×C₆₁×Q₈⋊C₈	C₂
socle	C₂²×C₆₁	C₂×C₄×D₄
prime radical	#16840312	C₂²
cosocle	C₄²×C₆₁	C₂⁴
hypercenter	C₂×Q₈⋊C₈	D₆₁
hypocenter	C₆₁	#18004
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×Q₈⋊C₈

Complements

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

N	H ≅ G/N	type
2. Q₈×#11758194	C₂	semidirect
4. #21444724	C₂	semidirect
5. #21444694	C₂	semidirect
6. #21444679	C₂	semidirect
7. #21444634	C₂	semidirect
8. #21444593	C₂	semidirect
10. #21444108	C₂	semidirect
11. C₂×C₆₁×Q₈⋊C₈	C₂	semidirect
163. Q₈×C₆₁	#131	semidirect
229. C₂×Q₈⋊C₈	D₆₁	semidirect
271. C₆₁	#18004	semidirect
389. Q₈	#14519783	semidirect

Maximal subgroups

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

subgroup	index
#21455850	2
Q₈×#11758194	2
#21454562	2
#21444724	2
#21444694	2
#21444679	2
#21444634	2
#21444593	2
#21444271	2
#21444108	2
C₂×C₆₁×Q₈⋊C₈	2
#18004	61