Subgroups — #21460385

Order 7808.

1032 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16840511	C₂	1	2	yes	maximal, complemented
2	#16840508	C₂	1	2	yes	maximal, complemented
3	#16840486	C₂	1	1	yes	maximal, characteristic, complemented
4	#16840484	C₂	1	1	yes	maximal, characteristic, complemented
5	#16840441	C₂	1	2	yes	maximal, complemented
6	#16840439	C₂	1	2	yes	maximal, complemented
7	Q₈×C₂²⋊D₆₁	C₂	1	1	yes	maximal, characteristic, complemented
8	#16840423	C₂	1	1	yes	maximal, characteristic, complemented
9	#16840422	C₂	1	1	yes	maximal, characteristic, complemented
10	#16840408	C₂	1	1	yes	maximal, characteristic, complemented
11	#16840403	C₂	1	1	yes	maximal, characteristic, complemented
12	#16840387	C₂	1	2	yes	maximal, complemented
13	#16840386	C₂	1	2	yes	maximal, complemented
14	#16840385	C₂	1	1	yes	maximal, characteristic, complemented
15	#16840384	C₂	1	1	yes	maximal, characteristic, complemented
16	#16840382	C₂	1	2	yes	maximal, complemented
17	#16840345	C₂	1	2	yes	maximal, complemented
18	#16840337	C₂	1	1	yes	maximal, characteristic, complemented
19	#16840336	C₂	1	1	yes	maximal, characteristic, complemented
20	#16840314	C₂	1	1	yes	maximal, characteristic, complemented
21	#16840292	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#14519766	C₂	1	1	yes	maximal, characteristic, complemented
23	D₄×Q₈×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#11758226	C₂²	1	1	yes	characteristic
25	C₂×#11758222	C₂²	1	1	yes	characteristic
26	C₂×Q₈×D₆₁	C₂²	1	1	yes	characteristic, complemented
27	C₂²×D₂₄₄	C₂²	1	1	yes	characteristic
28	#14519776	C₂²	1	1	yes	characteristic, complemented
29	#14519775	C₂²	1	1	yes	characteristic, complemented
30	#14519775	C₂²	1	2	yes	complemented
31	#14519775	C₂²	1	1	yes	characteristic, complemented
32	#14519772	C₂²	1	2	yes	complemented
33	#14519772	C₂²	1	2	yes	complemented
34	#14519772	C₂²	1	2	yes	complemented
35	#14519772	C₂²	1	2	yes	complemented
36	#14519772	C₂²	1	1	yes	characteristic, complemented
37	#14519771	C₂²	1	2	yes	complemented
38	#14519771	C₂²	1	2	yes	complemented
39	#14519770	C₂²	1	1	yes	characteristic, complemented
40	#14519767	C₂²	1	2	yes	complemented
41	#14519767	C₂²	1	1	yes	characteristic, complemented
42	#14519766	C₂²	1	1	yes	characteristic
43	#14519766	C₂²	1	1	yes	characteristic
44	#14519766	C₂²	1	1	yes	characteristic
45	#14519766	C₂²	1	2	yes	—
46	#14519766	C₂²	1	1	yes	characteristic
47	#14519766	C₂²	1	1	yes	characteristic
48	#14519766	C₂²	1	2	yes	—
49	#14519766	C₂²	1	2	yes	complemented
50	#14519765	C₂²	1	1	yes	characteristic
51	#14519765	C₂²	1	2	yes	complemented
52	#14519763	C₂²	1	1	yes	characteristic, complemented
53	#14519763	C₂²	1	2	yes	complemented
54	#14519763	C₂²	1	2	yes	complemented
55	#14519762	C₂²	1	2	yes	—
56	#14519762	C₂²	1	2	yes	—
57	#14519762	C₂²	1	2	yes	complemented
58	#14519762	C₂²	1	2	yes	complemented
59	#14519762	C₂²	1	2	yes	complemented
60	#14519761	C₂²	1	1	yes	characteristic
61	#14519760	C₂²	1	2	yes	complemented
62	#14519760	C₂²	1	2	yes	complemented
63	#14519759	C₂²	1	2	yes	complemented
64	#14519758	C₂²	1	1	yes	characteristic
65	#14519757	C₂²	1	2	yes	complemented
66	#14519757	C₂²	1	2	yes	complemented
67	#14519756	C₂²	1	1	yes	characteristic
68	#14519756	C₂²	1	2	yes	—
69	#14519755	C₂²	1	2	yes	complemented
70	#14519755	C₂²	1	2	yes	complemented
71	#14519755	C₂²	1	2	yes	complemented
72	#14519755	C₂²	1	2	yes	complemented
73	#14519755	C₂²	1	2	yes	complemented
74	#14519754	C₂²	1	1	yes	characteristic
75	#14519754	C₂²	1	2	yes	—
76	#14519753	C₂²	1	2	yes	complemented
77	#14519753	C₂²	1	2	yes	complemented
78	#14519753	C₂²	1	2	yes	complemented
79	#14519753	C₂²	1	2	yes	complemented
80	#14519753	C₂²	1	1	yes	characteristic, complemented
81	#14519752	C₂²	1	2	yes	—
82	#14519752	C₂²	1	1	yes	characteristic
83	#14519751	C₂²	1	1	yes	characteristic
84	#14519751	C₂²	1	2	yes	complemented
85	#14519750	C₂²	1	2	yes	—
86	#14519750	C₂²	1	2	yes	complemented
87	#14519749	C₂²	1	1	yes	characteristic
88	#14519747	C₂²	1	2	yes	—
89	#14519745	C₂²	1	2	yes	—
90	Q₈×Dic₆₁	C₂²	1	1	yes	characteristic, complemented
91	Q₈×Dic₆₁	C₂²	1	1	yes	characteristic, complemented
92	C₄×Dic₁₂₂	C₂²	1	1	yes	characteristic, complemented
93	#14519742	C₂²	1	1	yes	characteristic, complemented
94	#14519742	C₂²	1	2	yes	complemented
95	C₄×D₂₄₄	C₂²	1	1	yes	characteristic
96	#14519739	C₂²	1	1	yes	characteristic
97	#14519739	C₂²	1	2	yes	complemented
98	C₄×C₂²⋊D₆₁	C₂²	1	1	yes	characteristic
99	C₄×C₂²⋊D₆₁	C₂²	1	2	yes	—
100	C₄×C₂²⋊D₆₁	C₂²	1	1	yes	characteristic, complemented
101	C₄×C₂²⋊D₆₁	C₂²	1	2	yes	complemented
102	#14519736	C₂²	1	1	yes	characteristic, complemented
103	#14519735	C₂²	1	2	yes	complemented
104	#14519734	C₂²	1	2	yes	complemented
105	#14519734	C₂²	1	1	yes	characteristic, complemented
106	#14519733	C₂²	1	2	yes	—
107	C₂×#11758198	C₂²	1	2	yes	—
108	C₂×#11758198	C₂²	1	2	yes	—
109	C₂²⋊C₄×D₆₁	C₂²	1	2	yes	—
110	C₂²⋊C₄×D₆₁	C₂²	1	2	yes	—
111	C₂×C₄×Dic₆₁	C₂²	1	1	yes	characteristic
112	C₂²×Q₈×C₆₁	C₂²	1	1	yes	characteristic
113	C₂²×Q₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
114	C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
115	C₄⋊Q₈×C₆₁	C₂²	1	2	yes	complemented
116	C₂²⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
117	C₂²⋊Q₈×C₆₁	C₂²	1	2	yes	—
118	C₂²⋊Q₈×C₆₁	C₂²	1	2	yes	complemented
119	C₂²⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
120	C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
121	C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
122	C₄×D₄×C₆₁	C₂²	1	2	yes	—
123	C₂³×D₆₁	C₂³	1	2	yes	—
124	C₂×Q₈×C₆₁	—	4	2	no	—
125	C₂×Q₈×C₆₁	—	4	2	no	—
126	C₂×Q₈×C₆₁	C₂³	1	1	yes	characteristic
127	C₂×Q₈×C₆₁	C₂³	1	1	yes	characteristic
128	C₂×Q₈×C₆₁	C₂³	1	1	yes	characteristic
129	C₂×Q₈×C₆₁	C₂³	1	2	yes	—
130	C₂×Q₈×C₆₁	C₂³	1	2	yes	—
131	C₂×D₄×C₆₁	C₂³	1	1	yes	characteristic
132	C₂²×C₄×C₆₁	C₂³	1	1	yes	characteristic
133	C₂²×C₄×C₆₁	C₂³	1	1	yes	characteristic
134	C₂²×C₄×C₆₁	C₂³	1	2	yes	—
135	C₂²×C₄×C₆₁	C₂³	1	2	yes	—
136	C₂×C₂²⋊D₆₁	C₂³	1	1	yes	characteristic
137	C₂×C₂²⋊D₆₁	C₂³	1	2	yes	—
138	C₂×C₂²⋊D₆₁	C₂³	1	2	yes	—
139	C₂×C₂²⋊D₆₁	C₂³	1	1	yes	characteristic
140	C₂²×Dic₆₁	C₂³	1	1	yes	characteristic
141	C₂²×Dic₆₁	C₂³	1	1	yes	characteristic
142	#11758226	—	4	2	no	—
143	Q₈×D₆₁	—	4	2	no	—
144	#11758222	—	4	2	no	—
145	C₂×D₂₄₄	—	4	2	no	—
146	C₂×D₂₄₄	C₂³	1	1	yes	characteristic
147	C₂×D₂₄₄	C₂³	1	1	yes	characteristic
148	C₂×D₂₄₄	C₂³	1	2	yes	—
149	C₂×D₂₄₄	C₂³	1	2	yes	—
150	C₂×D₂₄₄	C₂³	1	2	yes	—
151	C₂×C₄×D₆₁	C₂³	1	1	yes	characteristic
152	C₂×C₄×D₆₁	C₂³	1	2	yes	—
153	C₂×C₄×D₆₁	C₂³	1	2	yes	—
154	C₂×C₄×D₆₁	C₂³	1	2	yes	—
155	C₂×C₄×D₆₁	C₂³	1	2	yes	—
156	C₂×C₄×D₆₁	C₂³	1	2	yes	—
157	C₂×Dic₁₂₂	C₂³	1	1	yes	characteristic
158	C₂×Dic₁₂₂	C₂³	1	2	yes	—
159	C₂×Dic₁₂₂	C₂³	1	2	yes	—
160	C₂×Dic₁₂₂	C₂³	1	1	yes	characteristic
161	C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
162	C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
163	C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
164	C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
165	C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
166	C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
167	C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
168	C₂²⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
169	C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
170	C₂²⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
171	C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
172	C₄²×C₆₁	C₂³	1	1	yes	characteristic
173	C₄²×C₆₁	C₂³	1	2	yes	—
174	C₂²⋊Dic₆₁	C₂³	1	1	yes	characteristic
175	C₂²⋊Dic₆₁	C₂³	1	2	yes	—
176	C₂²⋊Dic₆₁	C₂³	1	1	yes	characteristic
177	C₂²⋊Dic₆₁	C₂³	1	1	yes	characteristic
178	C₂²⋊Dic₆₁	C₂³	1	1	yes	characteristic
179	#11758198	C₂³	1	2	yes	—
180	#11758198	C₂³	1	2	yes	—
181	#11758198	C₂³	1	2	yes	—
182	#11758198	C₂³	1	2	yes	—
183	#11758198	C₂³	1	2	yes	—
184	#11758198	C₂³	1	2	yes	—
185	#11758198	C₂³	1	2	yes	—
186	#11758198	C₂³	1	2	yes	—
187	#11758198	C₂³	1	2	yes	—
188	#11758198	C₂³	1	2	yes	—
189	#11758198	C₂³	1	2	yes	—
190	#11758198	C₂³	1	2	yes	—
191	#11758198	C₂³	1	2	yes	—
192	#11758198	C₂³	1	1	yes	characteristic
193	#11758198	C₂³	1	1	yes	characteristic
194	#11758198	C₂³	1	2	yes	—
195	#11758198	C₂³	1	2	yes	—
196	#11758198	C₂³	1	1	yes	characteristic
197	#11758198	C₂³	1	1	yes	characteristic
198	#11758198	C₂³	1	2	yes	—
199	#11758198	C₂³	1	2	yes	—
200	C₄⋊Dic₆₁	C₂³	1	1	yes	characteristic
201	C₄⋊Dic₆₁	C₂³	1	1	yes	characteristic
202	C₄⋊Dic₆₁	C₂³	1	1	yes	characteristic
203	C₄⋊Dic₆₁	C₂³	1	1	yes	characteristic
204	C₄⋊Dic₆₁	C₂³	1	2	yes	—
205	C₄⋊Dic₆₁	C₂³	1	2	yes	—
206	#11758196	C₂³	1	2	yes	—
207	#11758196	C₂³	1	2	yes	—
208	#11758196	C₂³	1	1	yes	characteristic
209	#11758196	C₂³	1	2	yes	—
210	#11758196	C₂³	1	1	yes	characteristic
211	#11758196	C₂³	1	1	yes	characteristic
212	#11758196	C₂³	1	2	yes	—
213	#11758196	C₂³	1	1	yes	characteristic
214	#11758196	C₂³	1	1	yes	characteristic
215	#11758196	C₂³	1	2	yes	—
216	#11758196	C₂³	1	2	yes	—
217	#11758196	C₂³	1	2	yes	—
218	#11758196	C₂³	1	2	yes	—
219	#11758196	C₂³	1	1	yes	characteristic
220	C₄×Dic₆₁	C₂³	1	1	yes	characteristic
221	C₄×Dic₆₁	C₂³	1	1	yes	characteristic
222	C₄×Dic₆₁	C₂³	1	1	yes	characteristic
223	C₄×Dic₆₁	C₂³	1	1	yes	characteristic
224	C₄×Dic₆₁	C₂³	1	2	yes	—
225	C₄×Dic₆₁	C₂³	1	2	yes	—
226	C₄×Dic₆₁	C₂³	1	2	yes	—
227	C₄×Dic₆₁	C₂³	1	1	yes	characteristic
228	C₂³×C₆₁	C₂⁴	1	1	yes	characteristic
229	C₂³×C₆₁	C₂⁴	1	1	yes	characteristic
230	C₂²×D₆₁	—	2	4	no	—
231	C₂²×D₆₁	—	4	2	no	—
232	C₂²×D₆₁	—	4	2	no	—
233	C₂²×D₆₁	C₂⁴	1	2	yes	—
234	C₂²×D₆₁	C₂⁴	1	2	yes	—
235	C₂²×D₆₁	C₂⁴	1	1	yes	characteristic
236	Q₈×C₆₁	—	2	2	no	—
237	Q₈×C₆₁	—	2	2	no	—
238	Q₈×C₆₁	—	2	2	no	—
239	Q₈×C₆₁	—	4	2	no	—
240	Q₈×C₆₁	—	4	2	no	—
241	D₄×C₆₁	—	2	2	no	—
242	C₂×C₄×C₆₁	—	2	2	no	—
243	C₂×C₄×C₆₁	—	2	2	no	—
244	C₂×C₄×C₆₁	—	4	2	no	—
245	C₂×C₄×C₆₁	—	4	2	no	—
246	C₂×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
247	C₂×C₄×C₆₁	C₂⁴	1	2	yes	—
248	C₂×C₄×C₆₁	C₂⁴	1	2	yes	—
249	C₂×C₄×C₆₁	C₂⁴	1	2	yes	—
250	C₂×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
251	C₂×C₄×C₆₁	C₂⁴	1	2	yes	—
252	C₂×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
253	C₂×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
254	C₂×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
255	C₂²⋊D₆₁	—	2	2	no	—
256	C₂²⋊D₆₁	—	4	2	no	—
257	C₂²⋊D₆₁	—	4	2	no	—
258	C₂²⋊D₆₁	—	4	1	no	—
259	C₂×Dic₆₁	—	2	2	no	—
260	C₂×Dic₆₁	—	4	1	no	—
261	C₂×Dic₆₁	C₂⁴	1	1	yes	characteristic
262	C₂×Dic₆₁	C₂⁴	1	1	yes	characteristic
263	C₂×Dic₆₁	C₂⁴	1	1	yes	characteristic
264	C₂×Dic₆₁	C₂⁴	1	1	yes	characteristic
265	C₂×Dic₆₁	C₂⁴	1	2	yes	—
266	C₂×Dic₆₁	C₂⁴	1	1	yes	characteristic
267	C₂×Dic₆₁	C₂⁴	1	2	yes	—
268	C₂×Dic₆₁	C₂⁴	1	1	yes	characteristic
269	C₂×Dic₆₁	C₂⁴	1	1	yes	characteristic
270	D₂₄₄	—	2	2	no	—
271	D₂₄₄	—	2	2	no	—
272	D₂₄₄	—	4	2	no	—
273	D₂₄₄	—	4	2	no	—
274	D₂₄₄	—	4	2	no	—
275	C₄×D₆₁	—	2	2	no	—
276	C₄×D₆₁	—	4	2	no	—
277	C₄×D₆₁	—	4	2	no	—
278	C₄×D₆₁	—	4	2	no	—
279	C₄×D₆₁	—	4	2	no	—
280	C₄×D₆₁	—	4	2	no	—
281	Dic₁₂₂	—	2	2	no	—
282	Dic₁₂₂	—	4	2	no	—
283	Dic₁₂₂	—	4	1	no	—
284	Dic₁₂₂	—	4	2	no	—
285	C₂²×C₆₁	—	2	1	no	—
286	C₂²×C₆₁	—	2	1	no	—
287	C₂²×C₆₁	—	2	1	no	—
288	C₂²×C₆₁	—	2	1	no	—
289	C₂²×C₆₁	—	2	1	no	—
290	C₂²×C₆₁	2₋¹⁺⁴	1	2	yes	—
291	C₂²×C₆₁	C₂⁵	1	1	yes	characteristic
292	C₂×D₆₁	—	2	1	no	—
293	C₂×D₆₁	—	2	2	no	—
294	C₂×D₆₁	—	2	2	no	—
295	C₂×D₆₁	—	2	1	no	—
296	C₂×D₆₁	—	2	2	no	—
297	C₂×D₆₁	—	2	2	no	—
298	C₂×D₆₁	—	2	2	no	—
299	C₂×D₆₁	—	2	2	no	—
300	C₂×D₆₁	—	2	1	no	—
301	C₂×D₆₁	—	8	4	no	—
302	C₄×C₆₁	—	2	2	no	—
303	C₄×C₆₁	—	2	1	no	—
304	C₄×C₆₁	—	2	2	no	—
305	C₄×C₆₁	—	2	1	no	—
306	C₄×C₆₁	—	2	2	no	—
307	C₄×C₆₁	—	2	1	no	—
308	C₄×C₆₁	—	2	1	no	—
309	C₄×C₆₁	—	2	2	no	—
310	C₄×C₆₁	H(5,𝔽₂)	1	2	yes	—
311	Dic₆₁	—	2	2	no	—
312	Dic₆₁	—	2	1	no	—
313	Dic₆₁	—	2	1	no	—
314	Dic₆₁	—	2	1	no	—
315	Dic₆₁	—	2	1	no	—
316	Dic₆₁	—	2	1	no	—
317	Dic₆₁	—	2	1	no	—
318	Dic₆₁	—	2	2	no	—
319	Dic₆₁	—	2	1	no	—
320	#3561	—	61	1	no	maximal, Sylow
321	C₂×C₆₁	—	2	2	no	—
322	C₂×C₆₁	—	4	1	no	—
323	C₂×C₆₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
324	C₂×C₆₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
325	C₂×C₆₁	#585	1	1	yes	characteristic
326	D₆₁	—	4	1	no	—
327	D₆₁	—	4	2	no	—
328	D₆₁	—	4	2	no	—
329	#563	—	61	2	no	—
330	#562	—	61	2	no	—
331	#556	—	61	1	no	—
332	#556	—	61	1	no	—
333	#551	—	61	2	no	—
334	#551	—	61	2	no	—
335	D₄×Q₈	—	61	1	no	—
336	D₄×Q₈	D₆₁	1	1	yes	characteristic, complemented
337	#548	—	61	1	no	—
338	#548	—	61	1	no	—
339	#546	—	61	1	no	—
340	#546	—	61	1	no	—
341	#543	—	61	2	no	—
342	#542	—	61	2	no	—
343	#542	—	61	2	no	—
344	#542	—	61	1	no	—
345	#542	—	61	1	no	—
346	#538	—	61	2	no	—
347	#536	—	61	1	no	—
348	#536	—	61	1	no	—
349	#533	—	61	1	no	—
350	#529	—	61	1	no	—
351	C₂×#124	—	61	1	no	—
352	C₆₁	#3561	1	1	yes	characteristic, complemented, Sylow
353	C₂×#41	—	61	1	no	—
354	C₂×#41	—	61	1	no	—
355	C₂²×Q₈	—	61	1	no	—
356	C₂²×Q₈	C₂×D₆₁	1	1	yes	characteristic
357	C₂²×Q₈	C₂×D₆₁	1	1	yes	characteristic, complemented
358	C₂²×D₄	—	61	1	no	—
359	C₄⋊Q₈	—	61	1	no	—
360	C₄⋊Q₈	—	61	1	no	—
361	C₄⋊Q₈	—	61	2	no	—
362	C₄⋊Q₈	—	61	1	no	—
363	C₄⋊Q₈	C₂×D₆₁	1	1	yes	characteristic, complemented
364	C₄⋊Q₈	C₂×D₆₁	1	2	yes	complemented
365	#126	—	61	1	no	—
366	#126	—	61	2	no	—
367	#126	—	61	2	no	—
368	#126	—	61	2	no	—
369	#126	—	61	2	no	—
370	#126	—	61	1	no	—
371	#126	—	61	2	no	—
372	#126	—	61	2	no	—
373	#125	—	61	1	no	—
374	#125	—	61	2	no	—
375	#124	—	61	1	no	—
376	#124	—	61	1	no	—
377	#124	—	61	2	no	—
378	#124	—	61	1	no	—
379	#124	—	61	1	no	—
380	#124	—	61	2	no	—
381	#124	—	61	1	no	—
382	#124	—	61	2	no	—
383	#124	—	61	1	no	—
384	#124	—	61	2	no	—
385	#124	—	61	2	no	—
386	#124	—	61	1	no	—
387	#124	—	61	2	no	—
388	#123	—	61	1	no	—
389	#123	—	61	2	no	—
390	#123	—	61	2	no	—
391	#123	—	61	2	no	—
392	#123	—	61	2	no	—
393	#123	—	61	2	no	—
394	#123	—	61	2	no	—
395	#123	—	61	2	no	—
396	#123	—	61	1	no	—
397	#123	—	61	2	no	—
398	C₂²⋊Q₈	—	61	2	no	—
399	C₂²⋊Q₈	—	61	2	no	—
400	C₂²⋊Q₈	—	61	1	no	—
401	C₂²⋊Q₈	—	61	2	no	—
402	C₂²⋊Q₈	—	61	2	no	—
403	C₂²⋊Q₈	—	61	1	no	—
404	C₂²⋊Q₈	—	61	2	no	—
405	C₂²⋊Q₈	—	61	2	no	—
406	C₂²⋊Q₈	—	61	2	no	—
407	C₂²⋊Q₈	—	61	2	no	—
408	C₂²⋊Q₈	—	61	2	no	—
409	C₂²⋊Q₈	—	61	2	no	—
410	C₂²⋊Q₈	—	61	2	no	—
411	C₂²⋊Q₈	—	61	2	no	—
412	C₂²⋊Q₈	—	61	1	no	—
413	C₂²⋊Q₈	—	61	2	no	—
414	C₂²⋊Q₈	C₂×D₆₁	1	1	yes	characteristic
415	C₂²⋊Q₈	C₂×D₆₁	1	2	yes	—
416	C₂²⋊Q₈	C₂×D₆₁	1	1	yes	characteristic, complemented
417	C₂²⋊Q₈	C₂×D₆₁	1	2	yes	complemented
418	#121	—	61	1	no	—
419	#121	—	61	2	no	—
420	#121	—	61	1	no	—
421	#121	—	61	1	no	—
422	#121	—	61	2	no	—
423	#121	—	61	2	no	—
424	#121	—	61	2	no	—
425	#120	—	61	2	no	—
426	#120	—	61	2	no	—
427	C₄×Q₈	—	61	1	no	—
428	C₄×Q₈	—	61	1	no	—
429	C₄×Q₈	—	61	2	no	—
430	C₄×Q₈	—	61	1	no	—
431	C₄×Q₈	—	61	1	no	—
432	C₄×Q₈	C₂×D₆₁	1	1	yes	characteristic, complemented
433	C₄×D₄	—	61	1	no	—
434	C₄×D₄	—	61	1	no	—
435	C₄×D₄	—	61	2	no	—
436	C₄×D₄	—	61	2	no	—
437	C₄×D₄	—	61	1	no	—
438	C₄×D₄	—	61	2	no	—
439	C₄×D₄	—	61	1	no	—
440	C₄×D₄	C₂×D₆₁	1	1	yes	characteristic
441	C₄×D₄	C₂×D₆₁	1	2	yes	—
442	#117	—	61	1	no	—
443	#117	—	61	2	no	—
444	#117	—	61	2	no	—
445	#117	—	61	1	no	—
446	#117	—	61	2	no	—
447	C₂×C₂²⋊C₄	—	61	2	no	—
448	C₂×C₂²⋊C₄	—	61	2	no	—
449	C₂×C₂²⋊C₄	—	61	2	no	—
450	C₂×C₂²⋊C₄	—	61	2	no	—
451	C₂×C₄²	—	61	1	no	—
452	C₂⁴	—	61	2	no	—
453	#41	—	244	2	no	—
454	#41	—	244	2	no	—
455	C₂×Q₈	—	4	2	no	—
456	C₂×Q₈	—	4	2	no	—
457	C₂×Q₈	—	61	1	no	—
458	C₂×Q₈	—	61	1	no	—
459	C₂×Q₈	—	61	2	no	—
460	C₂×Q₈	—	61	2	no	—
461	C₂×Q₈	—	244	2	no	—
462	C₂×Q₈	C₂²×D₆₁	1	1	yes	characteristic
463	C₂×Q₈	C₂²×D₆₁	1	1	yes	characteristic
464	C₂×Q₈	C₂²×D₆₁	1	1	yes	characteristic
465	C₂×Q₈	C₂²×D₆₁	1	2	yes	—
466	C₂×Q₈	C₂²×D₆₁	1	2	yes	—
467	C₂×D₄	—	61	1	no	—
468	C₂×D₄	—	61	2	no	—
469	C₂×D₄	—	61	1	no	—
470	C₂×D₄	—	61	2	no	—
471	C₂×D₄	—	61	1	no	—
472	C₂×D₄	—	61	1	no	—
473	C₂×D₄	—	61	2	no	—
474	C₂×D₄	—	61	2	no	—
475	C₂×D₄	—	61	2	no	—
476	C₂×D₄	—	244	2	no	—
477	C₂×D₄	C₂²×D₆₁	1	1	yes	characteristic
478	C₂²×C₄	—	61	1	no	—
479	C₂²×C₄	—	61	1	no	—
480	C₂²×C₄	—	61	1	no	—
481	C₂²×C₄	—	61	2	no	—
482	C₂²×C₄	—	61	2	no	—
483	C₂²×C₄	—	61	2	no	—
484	C₂²×C₄	—	61	2	no	—
485	C₂²×C₄	—	61	2	no	—
486	C₂²×C₄	C₂²×D₆₁	1	1	yes	characteristic
487	C₂²×C₄	C₂²×D₆₁	1	1	yes	characteristic
488	C₂²×C₄	C₂²×D₆₁	1	2	yes	—
489	C₂²×C₄	C₂²×D₆₁	1	2	yes	—
490	C₄⋊C₄	—	61	1	no	—
491	C₄⋊C₄	—	61	1	no	—
492	C₄⋊C₄	—	61	2	no	—
493	C₄⋊C₄	—	61	2	no	—
494	C₄⋊C₄	—	61	1	no	—
495	C₄⋊C₄	—	61	2	no	—
496	C₄⋊C₄	—	61	1	no	—
497	C₄⋊C₄	—	61	2	no	—
498	C₄⋊C₄	—	61	2	no	—
499	C₄⋊C₄	—	61	1	no	—
500	C₄⋊C₄	—	61	2	no	—
501	C₄⋊C₄	—	61	2	no	—
502	C₄⋊C₄	—	61	1	no	—
503	C₄⋊C₄	—	61	2	no	—
504	C₄⋊C₄	—	61	1	no	—
505	C₄⋊C₄	—	61	1	no	—
506	C₄⋊C₄	—	61	1	no	—
507	C₄⋊C₄	—	61	1	no	—
508	C₄⋊C₄	—	61	2	no	—
509	C₄⋊C₄	—	61	2	no	—
510	C₄⋊C₄	C₂²×D₆₁	1	2	yes	—
511	C₄⋊C₄	C₂²×D₆₁	1	1	yes	characteristic
512	C₄⋊C₄	C₂²×D₆₁	1	2	yes	—
513	C₄⋊C₄	C₂²×D₆₁	1	2	yes	—
514	C₄⋊C₄	C₂²×D₆₁	1	1	yes	characteristic
515	C₄⋊C₄	C₂²×D₆₁	1	2	yes	—
516	C₄⋊C₄	C₂²×D₆₁	1	2	yes	—
517	C₂²⋊C₄	—	61	1	no	—
518	C₂²⋊C₄	—	61	2	no	—
519	C₂²⋊C₄	—	61	1	no	—
520	C₂²⋊C₄	—	61	1	no	—
521	C₂²⋊C₄	—	61	1	no	—
522	C₂²⋊C₄	—	61	2	no	—
523	C₂²⋊C₄	—	61	2	no	—
524	C₂²⋊C₄	—	61	2	no	—
525	C₂²⋊C₄	—	61	2	no	—
526	C₂²⋊C₄	—	61	2	no	—
527	C₂²⋊C₄	—	61	2	no	—
528	C₂²⋊C₄	—	61	2	no	—
529	C₂²⋊C₄	—	61	2	no	—
530	C₂²⋊C₄	—	61	2	no	—
531	C₂²⋊C₄	—	61	2	no	—
532	C₂²⋊C₄	—	61	2	no	—
533	C₂²⋊C₄	—	61	2	no	—
534	C₂²⋊C₄	—	61	2	no	—
535	C₂²⋊C₄	—	61	2	no	—
536	C₂²⋊C₄	—	61	1	no	—
537	C₂²⋊C₄	—	61	1	no	—
538	C₂²⋊C₄	—	61	1	no	—
539	C₂²⋊C₄	—	61	2	no	—
540	C₂²⋊C₄	—	61	2	no	—
541	C₂²⋊C₄	—	61	1	no	—
542	C₂²⋊C₄	—	61	2	no	—
543	C₂²⋊C₄	C₂²×D₆₁	1	1	yes	characteristic
544	C₂²⋊C₄	C₂²×D₆₁	1	2	yes	—
545	C₂²⋊C₄	C₂²×D₆₁	1	1	yes	characteristic
546	C₂²⋊C₄	C₂²×D₆₁	1	2	yes	—
547	C₄²	—	61	1	no	—
548	C₄²	—	61	1	no	—
549	C₄²	—	61	1	no	—
550	C₄²	—	61	1	no	—
551	C₄²	—	61	2	no	—
552	C₄²	—	61	2	no	—
553	C₄²	—	61	1	no	—
554	C₄²	—	61	2	no	—
555	C₄²	C₂²×D₆₁	1	1	yes	characteristic
556	C₄²	C₂²×D₆₁	1	2	yes	—
557	C₂³	—	61	2	no	—
558	C₂³	—	61	2	no	—
559	C₂³	—	61	1	no	—
560	C₂³	—	122	4	no	—
561	C₂³	—	244	2	no	—
562	C₂³	—	244	2	no	—
563	C₂³	C₂³×D₆₁	1	1	yes	characteristic
564	C₂³	C₂³×D₆₁	1	1	yes	characteristic
565	Q₈	—	2	2	no	—
566	Q₈	—	2	2	no	—
567	Q₈	—	2	2	no	—
568	Q₈	—	4	2	no	—
569	Q₈	—	4	2	no	—
570	Q₈	—	122	2	no	—
571	Q₈	—	244	1	no	—
572	Q₈	—	244	2	no	—
573	Q₈	—	244	2	no	—
574	D₄	—	2	2	no	—
575	D₄	—	122	2	no	—
576	D₄	—	122	2	no	—
577	D₄	—	122	2	no	—
578	D₄	—	244	2	no	—
579	D₄	—	244	2	no	—
580	D₄	—	244	2	no	—
581	D₄	—	244	2	no	—
582	D₄	—	244	1	no	—
583	D₄	—	244	2	no	—
584	C₂×C₄	—	2	2	no	—
585	C₂×C₄	—	2	2	no	—
586	C₂×C₄	—	4	2	no	—
587	C₂×C₄	—	4	2	no	—
588	C₂×C₄	—	61	1	no	—
589	C₂×C₄	—	61	1	no	—
590	C₂×C₄	—	61	1	no	—
591	C₂×C₄	—	61	1	no	—
592	C₂×C₄	—	61	1	no	—
593	C₂×C₄	—	61	2	no	—
594	C₂×C₄	—	61	1	no	—
595	C₂×C₄	—	61	2	no	—
596	C₂×C₄	—	61	1	no	—
597	C₂×C₄	—	122	2	no	—
598	C₂×C₄	—	122	2	no	—
599	C₂×C₄	—	244	2	no	—
600	C₂×C₄	—	244	2	no	—
601	C₂×C₄	—	244	2	no	—
602	C₂×C₄	—	244	2	no	—
603	C₂×C₄	—	244	2	no	—
604	C₂×C₄	—	244	1	no	—
605	C₂×C₄	C₂³×D₆₁	1	1	yes	characteristic
606	C₂×C₄	C₂³×D₆₁	1	2	yes	—
607	C₂×C₄	C₂³×D₆₁	1	2	yes	—
608	C₂×C₄	C₂³×D₆₁	1	2	yes	—
609	C₂×C₄	C₂³×D₆₁	1	1	yes	characteristic
610	C₂×C₄	C₂³×D₆₁	1	2	yes	—
611	C₂×C₄	C₂³×D₆₁	1	1	yes	characteristic
612	C₂×C₄	C₂³×D₆₁	1	1	yes	characteristic
613	C₂×C₄	C₂³×D₆₁	1	1	yes	characteristic
614	C₂²	—	2	1	no	—
615	C₂²	—	2	1	no	—
616	C₂²	—	2	1	no	—
617	C₂²	—	2	1	no	—
618	C₂²	—	2	1	no	—
619	C₂²	—	122	1	no	—
620	C₂²	—	122	2	no	—
621	C₂²	—	122	2	no	—
622	C₂²	—	122	1	no	—
623	C₂²	—	122	2	no	—
624	C₂²	—	122	2	no	—
625	C₂²	—	122	2	no	—
626	C₂²	—	122	2	no	—
627	C₂²	—	122	1	no	—
628	C₂²	—	488	4	no	—
629	C₂²	#14519825	1	2	yes	—
630	C₂²	C₂⁴×D₆₁	1	1	yes	characteristic
631	C₄	—	2	1	no	—
632	C₄	—	2	1	no	—
633	C₄	—	2	2	no	—
634	C₄	—	2	2	no	—
635	C₄	—	2	2	no	—
636	C₄	—	2	1	no	—
637	C₄	—	2	1	no	—
638	C₄	—	2	2	no	—
639	C₄	—	122	1	no	—
640	C₄	—	122	2	no	—
641	C₄	—	122	1	no	—
642	C₄	—	122	1	no	—
643	C₄	—	122	1	no	—
644	C₄	—	122	1	no	—
645	C₄	—	122	2	no	—
646	C₄	—	122	1	no	—
647	C₄	—	122	1	no	—
648	C₄	#14519822	1	2	yes	—
649	C₂	—	2	2	no	—
650	C₂	—	4	1	no	—
651	C₂	—	244	2	no	—
652	C₂	—	244	2	no	—
653	C₂	—	244	1	no	—
654	C₂	C₂×#14519822	1	1	yes	characteristic
655	C₂	C₂×#14519825	1	1	yes	characteristic
656	C₂	#16840599	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₆₁
commutator, socle	C₂²×C₆₁	C₂⁵
Fitting	D₄×Q₈×C₆₁	C₂
hypercenter	D₄×Q₈	D₆₁
hypocenter	C₆₁	#3561
LCS	G ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ D₄×Q₈

Complements

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

N	H ≅ G/N	type
1. #16840511	C₂	semidirect
2. #16840508	C₂	semidirect
3. #16840486	C₂	semidirect
4. #16840484	C₂	semidirect
5. #16840441	C₂	semidirect
6. #16840439	C₂	semidirect
7. Q₈×C₂²⋊D₆₁	C₂	semidirect
8. #16840423	C₂	semidirect
9. #16840422	C₂	semidirect
10. #16840408	C₂	semidirect
11. #16840403	C₂	semidirect
12. #16840387	C₂	semidirect
13. #16840386	C₂	semidirect
14. #16840385	C₂	semidirect
15. #16840384	C₂	semidirect
16. #16840382	C₂	semidirect
17. #16840345	C₂	semidirect
18. #16840337	C₂	semidirect
19. #16840336	C₂	semidirect
20. #16840314	C₂	semidirect
21. #16840292	C₂	semidirect
22. C₂×#14519766	C₂	semidirect
23. D₄×Q₈×C₆₁	C₂	semidirect
26. C₂×Q₈×D₆₁	C₂²	semidirect
28. #14519776	C₂²	semidirect
29. #14519775	C₂²	semidirect
30. #14519775	C₂²	semidirect
31. #14519775	C₂²	semidirect
32. #14519772	C₂²	semidirect
33. #14519772	C₂²	semidirect
34. #14519772	C₂²	semidirect
35. #14519772	C₂²	semidirect
36. #14519772	C₂²	semidirect
37. #14519771	C₂²	semidirect
38. #14519771	C₂²	semidirect
39. #14519770	C₂²	semidirect
40. #14519767	C₂²	semidirect
41. #14519767	C₂²	semidirect
49. #14519766	C₂²	semidirect
51. #14519765	C₂²	semidirect
52. #14519763	C₂²	semidirect
53. #14519763	C₂²	semidirect
54. #14519763	C₂²	semidirect
57. #14519762	C₂²	semidirect
58. #14519762	C₂²	semidirect
59. #14519762	C₂²	semidirect
61. #14519760	C₂²	semidirect
62. #14519760	C₂²	semidirect
63. #14519759	C₂²	semidirect
65. #14519757	C₂²	semidirect
66. #14519757	C₂²	semidirect
69. #14519755	C₂²	semidirect
70. #14519755	C₂²	semidirect
71. #14519755	C₂²	semidirect
72. #14519755	C₂²	semidirect
73. #14519755	C₂²	semidirect
76. #14519753	C₂²	semidirect
77. #14519753	C₂²	semidirect
78. #14519753	C₂²	semidirect
79. #14519753	C₂²	semidirect
80. #14519753	C₂²	semidirect
84. #14519751	C₂²	semidirect
86. #14519750	C₂²	semidirect
90. Q₈×Dic₆₁	C₂²	semidirect
91. Q₈×Dic₆₁	C₂²	semidirect
92. C₄×Dic₁₂₂	C₂²	semidirect
93. #14519742	C₂²	semidirect
94. #14519742	C₂²	semidirect
97. #14519739	C₂²	semidirect
100. C₄×C₂²⋊D₆₁	C₂²	semidirect
101. C₄×C₂²⋊D₆₁	C₂²	semidirect
102. #14519736	C₂²	semidirect
103. #14519735	C₂²	semidirect
104. #14519734	C₂²	semidirect
105. #14519734	C₂²	semidirect
113. C₂²×Q₈×C₆₁	C₂²	semidirect
114. C₄⋊Q₈×C₆₁	C₂²	semidirect
115. C₄⋊Q₈×C₆₁	C₂²	semidirect
118. C₂²⋊Q₈×C₆₁	C₂²	semidirect
119. C₂²⋊Q₈×C₆₁	C₂²	semidirect
120. C₄×Q₈×C₆₁	C₂²	semidirect
336. D₄×Q₈	D₆₁	semidirect
352. C₆₁	#3561	semidirect
357. C₂²×Q₈	C₂×D₆₁	semidirect
363. C₄⋊Q₈	C₂×D₆₁	semidirect
364. C₄⋊Q₈	C₂×D₆₁	semidirect
416. C₂²⋊Q₈	C₂×D₆₁	semidirect
417. C₂²⋊Q₈	C₂×D₆₁	semidirect
432. C₄×Q₈	C₂×D₆₁	semidirect