Subgroups — C₂×#22560877 #30858411

Order 17152.

1046 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16863412	C₂	1	1	yes	maximal, characteristic
2	C₂²×#14523969	C₂	1	1	yes	maximal, characteristic
3	C₂×#16863378	C₂	1	1	yes	maximal, characteristic
4	C₂×M₁₆×Dic₆₇	C₂	1	1	yes	maximal, characteristic, complemented
5	#22560877	C₂	1	8	yes	maximal, direct product factor
6	C₂×#16863167	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#16863157	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#430×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#11761628	C₂²	1	1	yes	characteristic
10	C₂²×#11761612	C₂²	1	1	yes	characteristic
11	C₂×#14524002	C₂²	1	1	yes	characteristic
12	C₂²×C₄×Dic₆₇	C₂²	1	1	yes	characteristic
13	#16863412	—	2	2	no	—
14	#16863412	C₂²	1	4	yes	—
15	C₂×#14523969	—	2	1	no	—
16	C₂×#14523969	—	2	1	no	—
17	C₂×#14523969	—	2	2	no	—
18	C₂×#14523969	—	2	2	no	—
19	C₂×#14523969	C₂²	1	4	yes	—
20	#16863378	C₄	1	4	yes	complemented
21	#16863378	C₂²	1	4	yes	—
22	C₂×#14523961	C₄	1	2	yes	complemented
23	C₂×#14523959	C₄	1	2	yes	complemented
24	M₁₆×Dic₆₇	—	2	2	no	—
25	M₁₆×Dic₆₇	C₂²	1	4	yes	complemented
26	C₂×#14523953	—	2	1	no	—
27	C₂×C₈×Dic₆₇	—	2	1	no	—
28	#16863167	C₂²	1	4	yes	complemented
29	#16863157	C₂²	1	4	yes	complemented
30	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
31	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
32	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
33	#430×C₆₇	—	2	2	no	—
34	#430×C₆₇	C₂²	1	4	yes	complemented
35	C₂×#108×C₆₇	—	2	2	no	—
36	C₂×#11761628	—	2	1	no	—
37	C₂×#11761628	—	2	1	no	—
38	C₂×#11761628	—	2	1	no	—
39	C₂×#11761628	—	2	1	no	—
40	C₂×#11761628	—	2	1	no	—
41	C₂×#11761628	—	2	1	no	—
42	C₂×#11761628	—	2	1	no	—
43	C₂×#11761628	—	2	1	no	—
44	C₂×#11761628	—	2	1	no	—
45	C₂×#11761628	—	2	1	no	—
46	C₂×#11761628	C₂×C₄	1	2	yes	—
47	C₂×#11761628	C₂³	1	2	yes	—
48	C₂²×Dic₁₃₄	C₂×C₄	1	1	yes	characteristic
49	C₂²×D₂₆₈	C₂×C₄	1	1	yes	characteristic
50	C₂²×C₂²⋊D₆₇	—	2	1	no	—
51	C₂³×Dic₆₇	—	2	1	no	—
52	C₂²×C₄×D₆₇	—	2	1	no	—
53	C₂×#11761612	—	2	1	no	—
54	C₂×#11761612	—	2	1	no	—
55	C₂×#11761612	—	2	1	no	—
56	C₂×#11761612	C₂×C₄	1	2	yes	—
57	C₂×#11761612	C₂×C₄	1	2	yes	—
58	C₂×#11761612	C₂³	1	2	yes	—
59	C₂²×C₆₇⋊C₈	—	2	1	no	—
60	#14524002	—	2	1	no	—
61	#14524002	—	2	1	no	—
62	#14524002	—	2	1	no	—
63	#14524002	C₂³	1	2	yes	—
64	C₂×C₄⋊Dic₆₇	—	2	1	no	—
65	C₂×C₂²⋊Dic₆₇	—	2	1	no	—
66	C₂×C₄×Dic₆₇	—	2	1	no	—
67	C₂×C₄×Dic₆₇	—	2	1	no	—
68	C₂×C₄×Dic₆₇	—	2	1	no	—
69	C₂×C₄×Dic₆₇	—	2	1	no	—
70	C₂×C₄×Dic₆₇	D₄	1	1	yes	characteristic
71	C₂×C₄×Dic₆₇	D₄	1	1	yes	characteristic
72	C₂×C₄×Dic₆₇	D₄	1	2	yes	—
73	C₂×C₄×Dic₆₇	C₂³	1	2	yes	—
74	#14523969	—	2	4	no	—
75	#14523969	—	2	4	no	—
76	#14523969	—	2	8	no	—
77	#14523961	C₂×C₄	1	8	yes	complemented
78	#14523959	C₂×C₄	1	8	yes	complemented
79	#14523953	—	2	4	no	—
80	C₈×Dic₆₇	—	2	4	no	—
81	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
82	C₂×M₁₆×C₆₇	—	2	1	no	—
83	C₂×M₁₆×C₆₇	—	2	1	no	—
84	C₂×M₁₆×C₆₇	—	2	1	no	—
85	C₂×M₁₆×C₆₇	—	2	1	no	—
86	C₂×M₁₆×C₆₇	—	2	1	no	—
87	C₂×M₁₆×C₆₇	—	2	1	no	—
88	C₂×M₁₆×C₆₇	—	2	1	no	—
89	C₂×M₁₆×C₆₇	—	2	1	no	—
90	C₂×M₁₆×C₆₇	—	2	1	no	—
91	C₂×M₁₆×C₆₇	—	2	1	no	—
92	C₂×M₁₆×C₆₇	—	2	1	no	—
93	C₂×M₁₆×C₆₇	C₂×C₄	1	2	yes	—
94	C₂×M₁₆×C₆₇	C₂×C₄	1	2	yes	—
95	C₂×M₁₆×C₆₇	D₄	1	2	yes	—
96	C₂×M₁₆×C₆₇	D₄	1	2	yes	—
97	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
98	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
99	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
100	C₂²×C₈×C₆₇	—	2	1	no	—
101	C₂²×C₈×C₆₇	—	2	1	no	—
102	C₂²×C₈×C₆₇	—	2	1	no	—
103	#108×C₆₇	—	2	8	no	—
104	C₂³×D₆₇	—	2	1	no	—
105	#11761628	—	2	2	no	—
106	#11761628	—	2	2	no	—
107	#11761628	—	2	2	no	—
108	#11761628	—	2	2	no	—
109	#11761628	—	2	2	no	—
110	#11761628	—	2	2	no	—
111	#11761628	—	2	2	no	—
112	#11761628	—	2	2	no	—
113	#11761628	—	4	1	no	—
114	#11761628	—	4	1	no	—
115	#11761628	—	4	1	no	—
116	#11761628	—	4	1	no	—
117	#11761628	—	4	1	no	—
118	#11761628	—	4	1	no	—
119	#11761628	—	4	1	no	—
120	#11761628	—	4	1	no	—
121	C₂×Dic₁₃₄	—	2	1	no	—
122	C₂×Dic₁₃₄	—	2	1	no	—
123	C₂×Dic₁₃₄	—	2	1	no	—
124	C₂×Dic₁₃₄	—	2	1	no	—
125	C₂×Dic₁₃₄	—	2	1	no	—
126	C₂×Dic₁₃₄	C₂²×C₄	1	2	yes	—
127	C₂×D₂₆₈	—	2	1	no	—
128	C₂×D₂₆₈	—	2	1	no	—
129	C₂×D₂₆₈	—	2	1	no	—
130	C₂×D₂₆₈	—	2	1	no	—
131	C₂×D₂₆₈	—	2	1	no	—
132	C₂×D₂₆₈	C₂²×C₄	1	2	yes	—
133	C₂×C₂²⋊D₆₇	—	2	2	no	—
134	C₂×C₂²⋊D₆₇	—	2	2	no	—
135	C₂×C₂²⋊D₆₇	—	4	1	no	—
136	C₂×C₂²⋊D₆₇	—	4	1	no	—
137	C₂×C₂²⋊D₆₇	—	4	1	no	—
138	C₂×C₂²⋊D₆₇	—	4	1	no	—
139	C₂²×Dic₆₇	—	2	1	no	—
140	C₂²×Dic₆₇	—	2	1	no	—
141	C₂²×Dic₆₇	—	2	2	no	—
142	C₂²×Dic₆₇	—	2	1	no	—
143	C₂²×Dic₆₇	—	2	2	no	—
144	C₂²×Dic₆₇	—	4	4	no	—
145	C₂²×Dic₆₇	—	4	1	no	—
146	C₂×C₄×D₆₇	—	2	2	no	—
147	C₂×C₄×D₆₇	—	2	2	no	—
148	C₂×C₄×D₆₇	—	4	1	no	—
149	C₂×C₄×D₆₇	—	4	1	no	—
150	C₂×C₄×D₆₇	—	4	1	no	—
151	C₂×C₄×D₆₇	—	4	1	no	—
152	#11761612	—	2	2	no	—
153	#11761612	—	2	2	no	—
154	#11761612	—	2	2	no	—
155	#11761612	C₂²×C₄	1	4	yes	—
156	C₂×C₆₇⋊C₈	—	2	2	no	—
157	C₂×C₆₇⋊C₈	—	2	2	no	—
158	C₂×C₆₇⋊C₈	—	2	2	no	—
159	C₄⋊Dic₆₇	—	2	2	no	—
160	C₄⋊Dic₆₇	—	4	1	no	—
161	C₂²⋊Dic₆₇	—	2	2	no	—
162	C₂²⋊Dic₆₇	—	4	1	no	—
163	C₄×Dic₆₇	—	2	1	no	—
164	C₄×Dic₆₇	—	2	2	no	—
165	C₄×Dic₆₇	—	2	1	no	—
166	C₄×Dic₆₇	—	2	2	no	—
167	C₄×Dic₆₇	—	2	2	no	—
168	C₄×Dic₆₇	—	4	1	no	—
169	C₄×Dic₆₇	C₂×D₄	1	2	yes	—
170	C₄×Dic₆₇	C₂×D₄	1	2	yes	—
171	C₂⁴×C₆₇	#41	1	1	yes	characteristic
172	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
173	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
174	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
175	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
176	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
177	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
178	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
179	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
180	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
181	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
182	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
183	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
184	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
185	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
186	M₁₆×C₆₇	—	2	2	no	—
187	M₁₆×C₆₇	—	2	2	no	—
188	M₁₆×C₆₇	—	2	2	no	—
189	M₁₆×C₆₇	—	2	2	no	—
190	M₁₆×C₆₇	—	2	2	no	—
191	M₁₆×C₆₇	—	2	2	no	—
192	M₁₆×C₆₇	—	2	2	no	—
193	M₁₆×C₆₇	—	2	2	no	—
194	M₁₆×C₆₇	—	4	1	no	—
195	M₁₆×C₆₇	—	4	1	no	—
196	M₁₆×C₆₇	C₂²×C₄	1	4	yes	—
197	M₁₆×C₆₇	C₂×D₄	1	4	yes	—
198	C₂×C₈×C₆₇	—	2	2	no	—
199	C₂×C₈×C₆₇	—	2	2	no	—
200	C₂×C₈×C₆₇	—	2	2	no	—
201	C₂×C₈×C₆₇	—	2	2	no	—
202	C₂×C₈×C₆₇	—	2	2	no	—
203	C₂×C₈×C₆₇	—	2	2	no	—
204	C₂×C₈×C₆₇	—	2	2	no	—
205	C₂×C₈×C₆₇	—	4	1	no	—
206	C₂×C₈×C₆₇	—	4	1	no	—
207	C₂³×C₆₇	—	4	2	no	—
208	C₂³×C₆₇	#117	1	1	yes	characteristic
209	C₂³×C₆₇	#117	1	1	yes	characteristic
210	C₂³×C₆₇	#123	1	1	yes	characteristic
211	C₂³×C₆₇	#123	1	1	yes	characteristic
212	C₂³×C₆₇	#124	1	1	yes	characteristic
213	C₂³×C₆₇	#124	1	1	yes	characteristic
214	C₂³×C₆₇	C₂×#41	1	1	yes	characteristic
215	C₂²×D₆₇	—	2	2	no	—
216	C₂²×D₆₇	—	4	1	no	—
217	C₂²×D₆₇	—	4	1	no	—
218	C₂²×D₆₇	—	8	2	no	—
219	C₂×C₄×C₆₇	#117	1	1	yes	characteristic
220	C₂×C₄×C₆₇	#117	1	1	yes	characteristic
221	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
222	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
223	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
224	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
225	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
226	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
227	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
228	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
229	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
230	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
231	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
232	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
233	C₂×C₄×C₆₇	#123	1	1	yes	characteristic
234	C₂×C₄×C₆₇	#123	1	1	yes	characteristic
235	C₂×C₄×C₆₇	#124	1	1	yes	characteristic
236	C₂×C₄×C₆₇	#124	1	1	yes	characteristic
237	C₂×C₄×C₆₇	#126	1	1	yes	characteristic
238	C₂×C₄×C₆₇	#126	1	1	yes	characteristic
239	C₂×C₄×C₆₇	#126	1	1	yes	characteristic
240	C₂×C₄×C₆₇	#126	1	1	yes	characteristic
241	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
242	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
243	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
244	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
245	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
246	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
247	C₂²⋊D₆₇	—	4	2	no	—
248	C₂²⋊D₆₇	—	4	2	no	—
249	C₂²⋊D₆₇	—	4	2	no	—
250	C₂²⋊D₆₇	—	4	2	no	—
251	C₂×Dic₆₇	—	2	4	no	—
252	C₂×Dic₆₇	—	2	2	no	—
253	C₂×Dic₆₇	—	2	2	no	—
254	C₂×Dic₆₇	—	2	2	no	—
255	C₂×Dic₆₇	—	4	4	no	—
256	C₂×Dic₆₇	—	4	4	no	—
257	C₂×Dic₆₇	—	4	2	no	—
258	C₂×Dic₆₇	—	4	1	no	—
259	C₂×Dic₆₇	—	4	1	no	—
260	C₂×Dic₆₇	—	4	2	no	—
261	C₂×Dic₆₇	—	8	2	no	—
262	D₂₆₈	—	2	2	no	—
263	D₂₆₈	—	2	2	no	—
264	D₂₆₈	—	4	1	no	—
265	D₂₆₈	—	4	1	no	—
266	C₄×D₆₇	—	4	2	no	—
267	C₄×D₆₇	—	4	2	no	—
268	C₄×D₆₇	—	4	2	no	—
269	C₄×D₆₇	—	4	2	no	—
270	Dic₁₃₄	—	2	2	no	—
271	Dic₁₃₄	—	2	2	no	—
272	Dic₁₃₄	—	4	1	no	—
273	Dic₁₃₄	—	4	1	no	—
274	C₈×C₆₇	—	2	4	no	—
275	C₈×C₆₇	—	2	4	no	—
276	C₈×C₆₇	—	4	2	no	—
277	C₆₇⋊C₈	—	2	4	no	—
278	C₂²×C₆₇	—	2	2	no	—
279	C₂²×C₆₇	—	2	2	no	—
280	C₂²×C₆₇	—	2	2	no	—
281	C₂²×C₆₇	—	4	1	no	—
282	C₂²×C₆₇	—	4	1	no	—
283	C₂²×C₆₇	—	4	1	no	—
284	C₂²×C₆₇	—	4	1	no	—
285	C₂²×C₆₇	#388	1	1	yes	characteristic
286	C₂²×C₆₇	#388	1	1	yes	characteristic
287	C₂²×C₆₇	#388	1	1	yes	characteristic
288	C₂²×C₆₇	#388	1	1	yes	characteristic
289	C₂²×C₆₇	C₂×#117	1	1	yes	characteristic
290	C₂²×C₆₇	C₂×#123	1	1	yes	characteristic
291	C₂²×C₆₇	C₂×#124	1	1	yes	characteristic
292	C₂×D₆₇	—	4	2	no	—
293	C₂×D₆₇	—	8	2	no	—
294	C₂×D₆₇	—	8	2	no	—
295	C₂×D₆₇	—	8	2	no	—
296	C₄×C₆₇	#388	1	1	yes	characteristic
297	C₄×C₆₇	#388	1	1	yes	characteristic
298	C₄×C₆₇	#388	1	1	yes	characteristic
299	C₄×C₆₇	#388	1	1	yes	characteristic
300	C₄×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
301	C₄×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
302	C₄×C₆₇	C₂×#121	1	1	yes	characteristic
303	C₄×C₆₇	C₂×#126	1	1	yes	characteristic
304	Dic₆₇	—	2	4	no	—
305	Dic₆₇	—	4	2	no	—
306	Dic₆₇	—	4	2	no	—
307	Dic₆₇	—	8	2	no	—
308	C₂×#1932	—	67	1	no	maximal, Sylow
309	C₂×C₆₇	—	2	1	no	—
310	C₂×C₆₇	—	2	1	no	—
311	C₂×C₆₇	—	2	1	no	—
312	C₂×C₆₇	—	2	1	no	—
313	C₂×C₆₇	—	2	1	no	—
314	C₂×C₆₇	—	2	1	no	—
315	C₂×C₆₇	#1932	1	2	yes	complemented
316	C₂×C₆₇	C₂×#388	1	1	yes	characteristic
317	D₆₇	—	8	2	no	—
318	C₂×#430	D₆₇	1	1	yes	characteristic, complemented
319	C₂×#421	—	67	1	no	—
320	C₂²×#104	—	67	1	no	—
321	C₂×#413	—	67	1	no	—
322	C₂×C₄×M₁₆	—	67	1	no	—
323	#1932	—	67	8	no	—
324	C₂×#344	—	67	1	no	—
325	C₂×#339	—	67	1	no	—
326	C₆₇	C₂×#1932	1	1	yes	characteristic, complemented, Sylow
327	C₂²×#41	—	67	1	no	—
328	C₂²×M₁₆	—	67	1	no	—
329	C₂²×M₁₆	C₂×D₆₇	1	1	yes	characteristic
330	C₂²×M₁₆	C₂×D₆₇	1	1	yes	characteristic
331	C₂²×M₁₆	C₂×D₆₇	1	1	yes	characteristic
332	C₂×#117	—	67	1	no	—
333	C₂²×C₄²	—	67	1	no	—
334	#430	—	2	2	no	—
335	#430	C₂×D₆₇	1	4	yes	complemented
336	C₂×#108	—	2	2	no	—
337	#421	—	67	4	no	—
338	#421	—	134	2	no	—
339	C₂×#104	—	67	4	no	—
340	C₂×#104	—	134	1	no	—
341	C₂×#104	—	134	1	no	—
342	C₂×#104	—	134	2	no	—
343	C₂×#104	—	134	2	no	—
344	#413	—	67	4	no	—
345	#413	—	67	4	no	—
346	C₂×#101	—	67	2	no	—
347	C₂×#100	—	67	2	no	—
348	C₄×M₁₆	—	67	4	no	—
349	C₄×M₁₆	—	134	2	no	—
350	C₂×#97	—	134	1	no	—
351	C₂×C₄×C₈	—	134	1	no	—
352	#344	—	67	4	no	—
353	#339	—	67	4	no	—
354	C₂×#41	—	67	2	no	—
355	C₂×#41	—	67	2	no	—
356	C₂×#41	—	134	1	no	—
357	C₂×#41	—	134	1	no	—
358	C₂×#41	—	134	1	no	—
359	C₂×#41	—	134	1	no	—
360	C₂×#41	—	134	1	no	—
361	C₂×#41	—	134	1	no	—
362	C₂×#41	—	134	1	no	—
363	C₂×#41	—	134	1	no	—
364	C₂×#41	—	134	1	no	—
365	C₂×#41	—	134	1	no	—
366	C₂²×Q₈	—	67	1	no	—
367	C₂²×D₄	—	67	1	no	—
368	C₂²×D₄	—	134	1	no	—
369	C₂³×C₄	—	134	1	no	—
370	C₂³×C₄	—	134	1	no	—
371	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
372	C₂×M₁₆	—	2	1	no	—
373	C₂×M₁₆	—	2	1	no	—
374	C₂×M₁₆	—	2	1	no	—
375	C₂×M₁₆	—	2	1	no	—
376	C₂×M₁₆	—	2	1	no	—
377	C₂×M₁₆	—	2	1	no	—
378	C₂×M₁₆	—	2	1	no	—
379	C₂×M₁₆	—	2	1	no	—
380	C₂×M₁₆	—	2	1	no	—
381	C₂×M₁₆	—	2	1	no	—
382	C₂×M₁₆	—	2	1	no	—
383	C₂×M₁₆	—	67	2	no	—
384	C₂×M₁₆	—	67	2	no	—
385	C₂×M₁₆	—	67	2	no	—
386	C₂×M₁₆	—	134	1	no	—
387	C₂×M₁₆	—	134	1	no	—
388	C₂×M₁₆	—	134	1	no	—
389	C₂×M₁₆	C₄×D₆₇	1	2	yes	—
390	C₂×M₁₆	C₄×D₆₇	1	2	yes	—
391	C₂×M₁₆	C₂²⋊D₆₇	1	2	yes	—
392	C₂×M₁₆	C₂²⋊D₆₇	1	2	yes	—
393	C₂×M₁₆	C₂²×D₆₇	1	2	yes	—
394	C₂×M₁₆	C₂²×D₆₇	1	2	yes	—
395	C₂×M₁₆	C₂²×D₆₇	1	2	yes	—
396	C₂²×C₈	—	2	1	no	—
397	C₂²×C₈	—	2	1	no	—
398	C₂²×C₈	—	2	1	no	—
399	C₂²×C₈	—	134	1	no	—
400	#117	—	67	2	no	—
401	#117	—	134	1	no	—
402	#117	—	134	1	no	—
403	#117	—	134	1	no	—
404	C₂×C₄⋊C₄	—	134	1	no	—
405	C₂×C₂²⋊C₄	—	134	1	no	—
406	C₂×C₄²	—	67	1	no	—
407	C₂×C₄²	—	67	1	no	—
408	C₂×C₄²	—	67	2	no	—
409	C₂×C₄²	—	67	2	no	—
410	C₂×C₄²	—	134	1	no	—
411	C₂×C₄²	—	134	1	no	—
412	C₂×C₄²	—	134	1	no	—
413	C₂×C₄²	—	134	1	no	—
414	#108	—	2	8	no	—
415	#104	—	134	4	no	—
416	#104	—	134	4	no	—
417	#104	—	134	8	no	—
418	#101	—	67	8	no	—
419	#100	—	67	8	no	—
420	#97	—	134	4	no	—
421	C₄×C₈	—	134	4	no	—
422	C₂⁴	—	134	1	no	—
423	C₂⁴	#11761629	1	1	yes	characteristic
424	#41	—	268	1	no	—
425	#41	—	268	1	no	—
426	#41	—	268	1	no	—
427	#41	—	268	1	no	—
428	#41	—	268	1	no	—
429	#41	—	268	1	no	—
430	#41	—	268	1	no	—
431	#41	—	268	1	no	—
432	#41	—	134	2	no	—
433	#41	—	134	2	no	—
434	#41	—	134	2	no	—
435	#41	—	134	2	no	—
436	#41	—	134	2	no	—
437	#41	—	134	2	no	—
438	#41	—	134	2	no	—
439	#41	—	134	2	no	—
440	C₂×Q₈	—	67	2	no	—
441	C₂×Q₈	—	134	1	no	—
442	C₂×Q₈	—	134	1	no	—
443	C₂×Q₈	—	134	1	no	—
444	C₂×Q₈	—	134	1	no	—
445	C₂×Q₈	—	134	1	no	—
446	C₂×D₄	—	268	1	no	—
447	C₂×D₄	—	268	1	no	—
448	C₂×D₄	—	268	1	no	—
449	C₂×D₄	—	268	1	no	—
450	C₂×D₄	—	67	2	no	—
451	C₂×D₄	—	134	2	no	—
452	C₂×D₄	—	134	2	no	—
453	C₂×D₄	—	134	1	no	—
454	C₂×D₄	—	134	1	no	—
455	C₂×D₄	—	134	1	no	—
456	C₂×D₄	—	134	1	no	—
457	C₂×D₄	—	134	1	no	—
458	C₂²×C₄	—	268	4	no	—
459	C₂²×C₄	—	268	1	no	—
460	C₂²×C₄	—	268	1	no	—
461	C₂²×C₄	—	268	1	no	—
462	C₂²×C₄	—	268	1	no	—
463	C₂²×C₄	—	268	1	no	—
464	C₂²×C₄	—	134	1	no	—
465	C₂²×C₄	—	134	1	no	—
466	C₂²×C₄	—	134	2	no	—
467	C₂²×C₄	—	134	2	no	—
468	C₂²×C₄	—	134	2	no	—
469	C₂²×C₄	—	134	2	no	—
470	C₂²×C₄	—	134	1	no	—
471	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
472	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
473	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
474	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
475	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
476	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
477	C₂²×C₄	#11761627	1	1	yes	characteristic
478	C₂²×C₄	#11761627	1	1	yes	characteristic
479	C₂²×C₄	#11761628	1	1	yes	characteristic
480	C₂²×C₄	#11761628	1	1	yes	characteristic
481	C₂²×C₄	#11761629	1	1	yes	characteristic
482	C₂²×C₄	#11761629	1	1	yes	characteristic
483	C₂²×C₄	#11761629	1	1	yes	characteristic
484	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
485	M₁₆	—	2	2	no	—
486	M₁₆	—	2	2	no	—
487	M₁₆	—	2	2	no	—
488	M₁₆	—	2	2	no	—
489	M₁₆	—	2	2	no	—
490	M₁₆	—	2	2	no	—
491	M₁₆	—	2	2	no	—
492	M₁₆	—	2	2	no	—
493	M₁₆	—	4	1	no	—
494	M₁₆	—	4	1	no	—
495	M₁₆	—	67	4	no	—
496	M₁₆	—	134	2	no	—
497	M₁₆	—	134	2	no	—
498	M₁₆	—	134	2	no	—
499	M₁₆	C₂×C₄×D₆₇	1	4	yes	—
500	M₁₆	C₂×C₂²⋊D₆₇	1	4	yes	—
501	C₂×C₈	—	2	2	no	—
502	C₂×C₈	—	2	2	no	—
503	C₂×C₈	—	2	2	no	—
504	C₂×C₈	—	2	2	no	—
505	C₂×C₈	—	2	2	no	—
506	C₂×C₈	—	2	2	no	—
507	C₂×C₈	—	2	2	no	—
508	C₂×C₈	—	4	1	no	—
509	C₂×C₈	—	4	1	no	—
510	C₂×C₈	—	134	2	no	—
511	C₂×C₈	—	134	2	no	—
512	C₂×C₈	—	134	2	no	—
513	C₄⋊C₄	—	268	1	no	—
514	C₄⋊C₄	—	134	2	no	—
515	C₂²⋊C₄	—	268	1	no	—
516	C₂²⋊C₄	—	134	2	no	—
517	C₄²	—	268	1	no	—
518	C₄²	—	67	2	no	—
519	C₄²	—	67	2	no	—
520	C₄²	—	134	2	no	—
521	C₄²	—	134	1	no	—
522	C₄²	—	134	2	no	—
523	C₄²	—	134	1	no	—
524	C₄²	—	134	2	no	—
525	C₂³	—	4	2	no	—
526	C₂³	—	268	1	no	—
527	C₂³	—	268	1	no	—
528	C₂³	—	536	2	no	—
529	C₂³	—	134	2	no	—
530	C₂³	#14524001	1	1	yes	characteristic
531	C₂³	#14524001	1	1	yes	characteristic
532	C₂³	#14524028	1	1	yes	characteristic
533	C₂³	#14524028	1	1	yes	characteristic
534	C₂³	#14524032	1	1	yes	characteristic
535	C₂³	#14524032	1	1	yes	characteristic
536	C₂³	C₂×#11761629	1	1	yes	characteristic
537	Q₈	—	268	1	no	—
538	Q₈	—	268	1	no	—
539	Q₈	—	134	2	no	—
540	Q₈	—	134	2	no	—
541	D₄	—	268	2	no	—
542	D₄	—	268	2	no	—
543	D₄	—	268	2	no	—
544	D₄	—	268	2	no	—
545	D₄	—	268	1	no	—
546	D₄	—	268	1	no	—
547	D₄	—	134	2	no	—
548	D₄	—	134	2	no	—
549	C₂×C₄	—	268	2	no	—
550	C₂×C₄	—	268	1	no	—
551	C₂×C₄	—	268	1	no	—
552	C₂×C₄	—	268	4	no	—
553	C₂×C₄	—	268	4	no	—
554	C₂×C₄	—	268	2	no	—
555	C₂×C₄	—	268	2	no	—
556	C₂×C₄	—	268	2	no	—
557	C₂×C₄	—	268	2	no	—
558	C₂×C₄	—	268	2	no	—
559	C₂×C₄	—	536	2	no	—
560	C₂×C₄	—	134	2	no	—
561	C₂×C₄	—	134	2	no	—
562	C₂×C₄	—	134	4	no	—
563	C₂×C₄	—	134	2	no	—
564	C₂×C₄	#14524001	1	1	yes	characteristic
565	C₂×C₄	#14524001	1	1	yes	characteristic
566	C₂×C₄	C₄×C₂²⋊D₆₇	1	1	yes	characteristic
567	C₂×C₄	C₄×C₂²⋊D₆₇	1	1	yes	characteristic
568	C₂×C₄	C₄×C₂²⋊D₆₇	1	1	yes	characteristic
569	C₂×C₄	C₄×C₂²⋊D₆₇	1	1	yes	characteristic
570	C₂×C₄	#14524005	1	1	yes	characteristic
571	C₂×C₄	#14524005	1	1	yes	characteristic
572	C₂×C₄	#14524005	1	1	yes	characteristic
573	C₂×C₄	#14524005	1	1	yes	characteristic
574	C₂×C₄	#14524015	1	1	yes	characteristic
575	C₂×C₄	#14524015	1	1	yes	characteristic
576	C₂×C₄	#14524015	1	1	yes	characteristic
577	C₂×C₄	#14524015	1	1	yes	characteristic
578	C₂×C₄	#14524028	1	1	yes	characteristic
579	C₂×C₄	#14524028	1	1	yes	characteristic
580	C₂×C₄	#14524032	1	1	yes	characteristic
581	C₂×C₄	#14524032	1	1	yes	characteristic
582	C₂×C₄	#14524038	1	1	yes	characteristic
583	C₂×C₄	#14524038	1	1	yes	characteristic
584	C₂×C₄	#14524038	1	1	yes	characteristic
585	C₂×C₄	#14524038	1	1	yes	characteristic
586	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
587	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
588	C₂×C₄	C₂²×C₂²⋊D₆₇	1	1	yes	characteristic
589	C₂×C₄	C₂×#11761627	1	1	yes	characteristic
590	C₂×C₄	C₂×#11761628	1	1	yes	characteristic
591	C₂×C₄	C₂×#11761629	1	1	yes	characteristic
592	C₈	—	2	4	no	—
593	C₈	—	2	4	no	—
594	C₈	—	4	2	no	—
595	C₈	—	134	4	no	—
596	C₂²	—	2	2	no	—
597	C₂²	—	2	2	no	—
598	C₂²	—	2	2	no	—
599	C₂²	—	4	1	no	—
600	C₂²	—	4	1	no	—
601	C₂²	—	4	1	no	—
602	C₂²	—	4	1	no	—
603	C₂²	—	268	2	no	—
604	C₂²	—	536	2	no	—
605	C₂²	—	536	2	no	—
606	C₂²	—	536	2	no	—
607	C₂²	#16863286	1	1	yes	characteristic
608	C₂²	#16863286	1	1	yes	characteristic
609	C₂²	#16863286	1	1	yes	characteristic
610	C₂²	#16863286	1	1	yes	characteristic
611	C₂²	C₂×#14524001	1	1	yes	characteristic
612	C₂²	C₂×#14524028	1	1	yes	characteristic
613	C₂²	C₂×#14524032	1	1	yes	characteristic
614	C₄	—	268	2	no	—
615	C₄	—	268	2	no	—
616	C₄	—	536	2	no	—
617	C₄	—	134	4	no	—
618	C₄	#16863286	1	1	yes	characteristic
619	C₄	#16863286	1	1	yes	characteristic
620	C₄	#16863286	1	1	yes	characteristic
621	C₄	#16863286	1	1	yes	characteristic
622	C₄	C₂×C₄×C₂²⋊D₆₇	1	1	yes	characteristic
623	C₄	C₂×#14524005	1	1	yes	characteristic
624	C₄	C₂×#14524015	1	1	yes	characteristic
625	C₄	C₂×#14524038	1	1	yes	characteristic
626	C₂	—	2	1	no	—
627	C₂	—	2	1	no	—
628	C₂	—	2	1	no	—
629	C₂	—	2	1	no	—
630	C₂	—	2	1	no	—
631	C₂	—	2	1	no	—
632	C₂	—	536	2	no	—
633	C₂	#22560877	1	2	yes	direct product factor
634	C₂	C₂×#16863286	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#14524015
commutator	C₂×C₄×C₆₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₆₇
Fitting	C₂×#430×C₆₇	C₂
socle	C₂²×C₆₇	#388
prime radical	C₂²×#11761628	C₂²
cosocle	C₂²×C₄×C₆₇	C₂⁴
hypercenter	C₂×#430	D₆₇
hypocenter	C₆₇	C₂×#1932
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂×#430

Complements

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

N	H ≅ G/N	type
4. C₂×M₁₆×Dic₆₇	C₂	semidirect
5. #22560877	C₂	direct (N × H)
6. C₂×#16863167	C₂	semidirect
7. C₂×#16863157	C₂	semidirect
8. C₂×#430×C₆₇	C₂	semidirect
20. #16863378	C₄	semidirect
22. C₂×#14523961	C₄	semidirect
23. C₂×#14523959	C₄	semidirect
25. M₁₆×Dic₆₇	C₂²	semidirect
28. #16863167	C₂²	semidirect
29. #16863157	C₂²	semidirect
34. #430×C₆₇	C₂²	semidirect
77. #14523961	C₂×C₄	semidirect
78. #14523959	C₂×C₄	semidirect
315. C₂×C₆₇	#1932	semidirect
318. C₂×#430	D₆₇	semidirect
326. C₆₇	C₂×#1932	semidirect
335. #430	C₂×D₆₇	semidirect
633. C₂	#22560877	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×#16863412	2
C₂²×#14523969	2
C₂×#16863378	2
C₂×M₁₆×Dic₆₇	2
#22560877	2
C₂×#16863167	2
C₂×#16863157	2
C₂×#430×C₆₇	2
C₂×#1932	67

Subgroups — C2×#22560877 #30858411

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22560877 #30858411