Subgroups — C₂×#22560263 #30855493

Order 17152.

1330 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#14523979	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#16863434	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#16863413	C₂	1	2	yes	maximal
4	#22560263	C₂	1	8	yes	maximal, direct product factor
5	C₂×#16863168	C₂	1	2	yes	maximal, complemented
6	C₂²×#131×C₆₇	C₂	1	1	yes	maximal, characteristic
7	C₂²×#11761612	C₂²	1	2	yes	—
8	C₂×#14524002	C₂²	1	2	yes	—
9	C₂×#14523979	—	2	1	no	—
10	C₂×#14523979	—	2	1	no	—
11	C₂×#14523979	—	2	2	no	—
12	C₂×#14523979	C₂²	1	4	yes	complemented
13	#16863434	—	2	2	no	—
14	#16863434	C₂²	1	4	yes	complemented
15	C₂×#14523977	—	2	1	no	—
16	C₂×#14523975	—	2	1	no	—
17	#16863413	—	2	4	no	—
18	#16863413	C₂²	1	8	yes	—
19	C₂×#14523970	—	2	4	no	—
20	#16863168	C₂²	1	8	yes	complemented
21	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
22	C₂×#131×C₆₇	—	2	1	no	—
23	C₂×#131×C₆₇	—	2	1	no	—
24	C₂×#131×C₆₇	—	2	2	no	—
25	C₂×#131×C₆₇	—	2	2	no	—
26	C₂×#131×C₆₇	C₄	1	2	yes	complemented
27	C₂×#131×C₆₇	C₄	1	2	yes	complemented
28	C₂×#131×C₆₇	C₄	1	4	yes	complemented
29	C₂×#131×C₆₇	C₂²	1	4	yes	—
30	C₂²×M₁₆×C₆₇	—	2	1	no	—
31	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
32	C₂³×C₈×C₆₇	—	2	1	no	—
33	C₂³×C₈×C₆₇	C₂²	1	1	yes	characteristic
34	C₂×#11761612	—	2	2	no	—
35	C₂×#11761612	—	2	2	no	—
36	C₂×#11761612	—	2	2	no	—
37	C₂×#11761612	—	2	2	no	—
38	C₂×#11761612	—	2	2	no	—
39	C₂×#11761612	C₂³	1	4	yes	—
40	C₂²×C₆₇⋊C₈	—	2	2	no	—
41	#14524002	—	2	2	no	—
42	#14524002	—	2	2	no	—
43	#14524002	—	2	2	no	—
44	#14524002	C₂³	1	4	yes	—
45	C₂×C₄⋊Dic₆₇	—	2	2	no	—
46	C₂×C₂²⋊Dic₆₇	—	2	2	no	—
47	C₂×C₄×Dic₆₇	—	2	2	no	—
48	#14523979	—	2	4	no	—
49	#14523979	—	2	4	no	—
50	#14523977	—	2	4	no	—
51	#14523975	—	2	4	no	—
52	#14523970	—	2	16	no	—
53	C₂×#41×C₆₇	—	2	1	no	—
54	C₂×#41×C₆₇	—	2	1	no	—
55	C₂×#41×C₆₇	—	2	1	no	—
56	C₂×#41×C₆₇	—	2	1	no	—
57	C₂×#41×C₆₇	—	2	1	no	—
58	C₂×#41×C₆₇	—	2	1	no	—
59	C₂×#41×C₆₇	C₂×C₄	1	2	yes	—
60	C₂×#41×C₆₇	C₂×C₄	1	2	yes	—
61	C₂×#41×C₆₇	D₄	1	2	yes	—
62	C₂×#41×C₆₇	D₄	1	2	yes	—
63	C₂×#41×C₆₇	Q₈	1	2	yes	—
64	C₂×#41×C₆₇	C₂³	1	2	yes	—
65	C₂²×Q₈×C₆₇	Q₈	1	1	yes	characteristic
66	C₂²×D₄×C₆₇	—	2	1	no	—
67	C₂²×D₄×C₆₇	Q₈	1	1	yes	characteristic
68	C₂³×C₄×C₆₇	—	2	1	no	—
69	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
70	#131×C₆₇	—	2	4	no	—
71	#131×C₆₇	—	2	4	no	—
72	#131×C₆₇	—	2	4	no	—
73	#131×C₆₇	—	2	4	no	—
74	#131×C₆₇	—	2	4	no	—
75	#131×C₆₇	—	2	4	no	—
76	#131×C₆₇	C₂×C₄	1	8	yes	complemented
77	#131×C₆₇	C₂×C₄	1	8	yes	complemented
78	C₂×M₁₆×C₆₇	—	2	1	no	—
79	C₂×M₁₆×C₆₇	—	2	1	no	—
80	C₂×M₁₆×C₆₇	—	2	1	no	—
81	C₂×M₁₆×C₆₇	—	2	2	no	—
82	C₂×M₁₆×C₆₇	—	2	2	no	—
83	C₂×M₁₆×C₆₇	—	2	4	no	—
84	C₂×M₁₆×C₆₇	—	2	4	no	—
85	C₂×M₁₆×C₆₇	C₂×C₄	1	2	yes	—
86	C₂×M₁₆×C₆₇	C₂×C₄	1	2	yes	—
87	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
88	C₂²×C₈×C₆₇	—	2	1	no	—
89	C₂²×C₈×C₆₇	—	2	2	no	—
90	C₂²×C₈×C₆₇	—	2	2	no	—
91	C₂²×C₈×C₆₇	—	2	4	no	—
92	C₂²×C₈×C₆₇	—	2	4	no	—
93	C₂²×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
94	C₂²×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
95	C₂²×C₈×C₆₇	C₂×C₄	1	2	yes	—
96	C₂²×C₈×C₆₇	D₄	1	1	yes	characteristic
97	C₂²×C₈×C₆₇	D₄	1	1	yes	characteristic
98	C₂²×C₈×C₆₇	D₄	1	1	yes	characteristic
99	C₂²×C₈×C₆₇	D₄	1	1	yes	characteristic
100	C₂²×C₈×C₆₇	D₄	1	2	yes	—
101	C₂²×C₈×C₆₇	D₄	1	2	yes	—
102	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
103	C₂²×Dic₆₇	—	4	2	no	—
104	#11761612	—	2	4	no	—
105	#11761612	—	2	4	no	—
106	#11761612	—	4	2	no	—
107	#11761612	—	4	2	no	—
108	C₂×C₆₇⋊C₈	—	2	4	no	—
109	C₂×C₆₇⋊C₈	—	4	2	no	—
110	C₂×C₆₇⋊C₈	—	4	2	no	—
111	C₄⋊Dic₆₇	—	2	4	no	—
112	C₄⋊Dic₆₇	—	4	2	no	—
113	C₂²⋊Dic₆₇	—	2	4	no	—
114	C₂²⋊Dic₆₇	—	4	2	no	—
115	C₄×Dic₆₇	—	2	4	no	—
116	C₄×Dic₆₇	—	4	2	no	—
117	C₂⁴×C₆₇	—	2	1	no	—
118	C₂⁴×C₆₇	#41	1	1	yes	characteristic
119	#41×C₆₇	—	2	2	no	—
120	#41×C₆₇	—	2	2	no	—
121	#41×C₆₇	—	2	2	no	—
122	#41×C₆₇	—	2	2	no	—
123	#41×C₆₇	—	2	2	no	—
124	#41×C₆₇	—	2	2	no	—
125	#41×C₆₇	—	2	2	no	—
126	#41×C₆₇	—	2	2	no	—
127	#41×C₆₇	—	2	2	no	—
128	#41×C₆₇	—	2	2	no	—
129	#41×C₆₇	—	2	2	no	—
130	#41×C₆₇	—	2	2	no	—
131	#41×C₆₇	C₄⋊C₄	1	4	yes	—
132	#41×C₆₇	C₄⋊C₄	1	4	yes	—
133	#41×C₆₇	C₂²×C₄	1	4	yes	—
134	#41×C₆₇	C₂×D₄	1	4	yes	—
135	C₂×Q₈×C₆₇	—	2	1	no	—
136	C₂×Q₈×C₆₇	—	2	1	no	—
137	C₂×Q₈×C₆₇	—	2	1	no	—
138	C₂×Q₈×C₆₇	C₄⋊C₄	1	2	yes	—
139	C₂×Q₈×C₆₇	C₄⋊C₄	1	2	yes	—
140	C₂×Q₈×C₆₇	C₂×Q₈	1	2	yes	—
141	C₂×D₄×C₆₇	—	2	2	no	—
142	C₂×D₄×C₆₇	—	2	2	no	—
143	C₂×D₄×C₆₇	—	2	2	no	—
144	C₂×D₄×C₆₇	—	2	2	no	—
145	C₂×D₄×C₆₇	—	2	2	no	—
146	C₂×D₄×C₆₇	—	2	2	no	—
147	C₂×D₄×C₆₇	—	2	1	no	—
148	C₂×D₄×C₆₇	—	2	1	no	—
149	C₂×D₄×C₆₇	—	2	1	no	—
150	C₂×D₄×C₆₇	C₄⋊C₄	1	2	yes	—
151	C₂×D₄×C₆₇	C₄⋊C₄	1	2	yes	—
152	C₂×D₄×C₆₇	C₂×Q₈	1	2	yes	—
153	C₂²×C₄×C₆₇	—	2	1	no	—
154	C₂²×C₄×C₆₇	—	2	2	no	—
155	C₂²×C₄×C₆₇	—	2	2	no	—
156	C₂²×C₄×C₆₇	—	2	2	no	—
157	C₂²×C₄×C₆₇	—	2	2	no	—
158	C₂²×C₄×C₆₇	—	2	2	no	—
159	C₂²×C₄×C₆₇	—	2	2	no	—
160	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
161	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
162	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₆₇	C₂×Q₈	1	1	yes	characteristic
169	C₂²×C₄×C₆₇	C₂×Q₈	1	1	yes	characteristic
170	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
171	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
172	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
173	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
174	M₁₆×C₆₇	—	2	2	no	—
175	M₁₆×C₆₇	—	2	2	no	—
176	M₁₆×C₆₇	—	2	2	no	—
177	M₁₆×C₆₇	—	2	8	no	—
178	M₁₆×C₆₇	—	2	8	no	—
179	M₁₆×C₆₇	C₂²×C₄	1	4	yes	—
180	C₂×C₈×C₆₇	—	2	2	no	—
181	C₂×C₈×C₆₇	—	2	2	no	—
182	C₂×C₈×C₆₇	—	2	2	no	—
183	C₂×C₈×C₆₇	—	2	8	no	—
184	C₂×C₈×C₆₇	—	2	8	no	—
185	C₂×C₈×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
186	C₂×C₈×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
187	C₂×C₈×C₆₇	C₂²⋊C₄	1	2	yes	—
188	C₂×C₈×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
189	C₂×C₈×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
190	C₂×C₈×C₆₇	C₂²⋊C₄	1	2	yes	—
191	C₂×C₈×C₆₇	C₂²⋊C₄	1	2	yes	—
192	C₂×C₈×C₆₇	C₂²⋊C₄	1	2	yes	—
193	C₂×C₈×C₆₇	C₂²⋊C₄	1	2	yes	—
194	C₂×C₈×C₆₇	C₂²⋊C₄	1	2	yes	—
195	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
196	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
197	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
198	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
199	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
200	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
201	C₂³×C₆₇	—	2	2	no	—
202	C₂³×C₆₇	—	2	2	no	—
203	C₂³×C₆₇	—	2	2	no	—
204	C₂³×C₆₇	—	4	2	no	—
205	C₂³×C₆₇	—	4	4	no	—
206	C₂³×C₆₇	#117	1	1	yes	characteristic
207	C₂³×C₆₇	#117	1	1	yes	characteristic
208	C₂³×C₆₇	#121	1	1	yes	characteristic
209	C₂³×C₆₇	#121	1	1	yes	characteristic
210	C₂³×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
211	C₂³×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
212	C₂³×C₆₇	C₂×#41	1	1	yes	characteristic
213	Q₈×C₆₇	—	2	2	no	—
214	Q₈×C₆₇	—	2	2	no	—
215	Q₈×C₆₇	—	2	2	no	—
216	Q₈×C₆₇	C₂×C₄⋊C₄	1	4	yes	—
217	D₄×C₆₇	—	2	4	no	—
218	D₄×C₆₇	—	2	4	no	—
219	D₄×C₆₇	—	2	4	no	—
220	D₄×C₆₇	—	2	4	no	—
221	D₄×C₆₇	—	2	2	no	—
222	D₄×C₆₇	—	2	2	no	—
223	D₄×C₆₇	—	2	2	no	—
224	D₄×C₆₇	C₂×C₄⋊C₄	1	4	yes	—
225	C₂×C₄×C₆₇	—	2	2	no	—
226	C₂×C₄×C₆₇	—	2	2	no	—
227	C₂×C₄×C₆₇	—	2	2	no	—
228	C₂×C₄×C₆₇	—	2	4	no	—
229	C₂×C₄×C₆₇	—	2	4	no	—
230	C₂×C₄×C₆₇	—	2	4	no	—
231	C₂×C₄×C₆₇	—	2	4	no	—
232	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
233	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
234	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
235	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
236	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
237	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
238	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
239	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
240	C₂×C₄×C₆₇	#117	1	1	yes	characteristic
241	C₂×C₄×C₆₇	#117	1	1	yes	characteristic
242	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
243	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
244	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
245	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
246	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
247	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
248	C₂×C₄×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
249	C₂×C₄×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
250	C₂×C₄×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
251	C₂×C₄×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
252	C₂×C₄×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
253	C₂×C₄×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
254	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
255	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
256	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
257	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
258	C₂×C₄×C₆₇	C₂²×Q₈	1	1	yes	characteristic
259	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
260	C₂×Dic₆₇	—	4	4	no	—
261	C₂×Dic₆₇	—	8	4	no	—
262	C₈×C₆₇	—	2	4	no	—
263	C₈×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
264	C₈×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
265	C₈×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
266	C₈×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
267	C₆₇⋊C₈	—	4	4	no	—
268	C₂²×C₆₇	—	2	2	no	—
269	C₂²×C₆₇	—	2	2	no	—
270	C₂²×C₆₇	—	2	2	no	—
271	C₂²×C₆₇	—	2	4	no	—
272	C₂²×C₆₇	—	4	1	no	—
273	C₂²×C₆₇	—	4	1	no	—
274	C₂²×C₆₇	—	4	1	no	—
275	C₂²×C₆₇	—	4	1	no	—
276	C₂²×C₆₇	—	4	4	no	—
277	C₂²×C₆₇	—	4	4	no	—
278	C₂²×C₆₇	—	4	4	no	—
279	C₂²×C₆₇	#380	1	1	yes	characteristic
280	C₂²×C₆₇	#380	1	1	yes	characteristic
281	C₂²×C₆₇	#380	1	1	yes	characteristic
282	C₂²×C₆₇	#380	1	1	yes	characteristic
283	C₂²×C₆₇	C₂×#117	1	1	yes	characteristic
284	C₂²×C₆₇	C₂×#121	1	1	yes	characteristic
285	C₂²×C₆₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
286	C₄×C₆₇	—	2	4	no	—
287	C₄×C₆₇	#380	1	1	yes	characteristic
288	C₄×C₆₇	#380	1	1	yes	characteristic
289	C₄×C₆₇	#380	1	1	yes	characteristic
290	C₄×C₆₇	#380	1	1	yes	characteristic
291	C₄×C₆₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
292	C₄×C₆₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
293	C₄×C₆₇	C₂×#121	1	1	yes	characteristic
294	C₄×C₆₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
295	Dic₆₇	—	8	4	no	—
296	C₂×#1814	—	67	1	no	maximal, Sylow
297	C₂×C₆₇	—	2	1	no	—
298	C₂×C₆₇	—	2	1	no	—
299	C₂×C₆₇	—	2	1	no	—
300	C₂×C₆₇	—	2	1	no	—
301	C₂×C₆₇	—	2	1	no	—
302	C₂×C₆₇	—	2	1	no	—
303	C₂×C₆₇	—	4	4	no	—
304	C₂×C₆₇	#1814	1	2	yes	complemented
305	C₂×C₆₇	C₂×#380	1	1	yes	characteristic
306	C₂²×#131	D₆₇	1	1	yes	characteristic
307	C₂²×#108	—	67	1	no	—
308	C₂×#427	—	67	1	no	—
309	C₂×#421	—	67	2	no	—
310	#1814	—	67	8	no	—
311	C₂×#344	—	67	2	no	—
312	C₆₇	C₂×#1814	1	1	yes	characteristic, complemented, Sylow
313	C₂²×#41	C₂×D₆₇	1	1	yes	characteristic
314	C₂×#131	—	2	1	no	—
315	C₂×#131	—	2	1	no	—
316	C₂×#131	—	2	2	no	—
317	C₂×#131	—	2	2	no	—
318	C₂×#131	Dic₆₇	1	2	yes	complemented
319	C₂×#131	Dic₆₇	1	2	yes	complemented
320	C₂×#131	Dic₆₇	1	4	yes	complemented
321	C₂×#131	C₂×D₆₇	1	4	yes	—
322	C₂²×M₁₆	—	2	1	no	—
323	C₂²×M₁₆	—	67	2	no	—
324	C₂²×M₁₆	C₂×D₆₇	1	1	yes	characteristic
325	C₂³×C₈	—	2	1	no	—
326	C₂³×C₈	C₂×D₆₇	1	1	yes	characteristic
327	C₂×#117	—	67	2	no	—
328	C₂×#108	—	67	4	no	—
329	C₂×#108	—	134	1	no	—
330	C₂×#108	—	134	1	no	—
331	C₂×#108	—	134	2	no	—
332	#427	—	67	4	no	—
333	#427	—	134	2	no	—
334	C₂×#107	—	134	1	no	—
335	C₂×#106	—	134	1	no	—
336	#421	—	67	8	no	—
337	#421	—	134	4	no	—
338	C₂×#104	—	134	4	no	—
339	#344	—	67	8	no	—
340	C₂×#41	—	2	1	no	—
341	C₂×#41	—	2	1	no	—
342	C₂×#41	—	2	1	no	—
343	C₂×#41	—	2	1	no	—
344	C₂×#41	—	2	1	no	—
345	C₂×#41	—	2	1	no	—
346	C₂×#41	Dic₁₃₄	1	2	yes	—
347	C₂×#41	D₂₆₈	1	2	yes	—
348	C₂×#41	D₂₆₈	1	2	yes	—
349	C₂×#41	C₂×Dic₆₇	1	2	yes	—
350	C₂×#41	C₂×Dic₆₇	1	2	yes	—
351	C₂×#41	C₂²×D₆₇	1	2	yes	—
352	C₂²×Q₈	Dic₁₃₄	1	1	yes	characteristic
353	C₂²×D₄	—	2	1	no	—
354	C₂²×D₄	Dic₁₃₄	1	1	yes	characteristic
355	C₂³×C₄	—	2	1	no	—
356	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
357	#131	—	2	4	no	—
358	#131	—	2	4	no	—
359	#131	—	2	4	no	—
360	#131	—	2	4	no	—
361	#131	—	2	4	no	—
362	#131	—	2	4	no	—
363	#131	C₂×Dic₆₇	1	8	yes	complemented
364	#131	C₂×Dic₆₇	1	8	yes	complemented
365	C₂×M₁₆	—	2	1	no	—
366	C₂×M₁₆	—	2	1	no	—
367	C₂×M₁₆	—	2	1	no	—
368	C₂×M₁₆	—	2	2	no	—
369	C₂×M₁₆	—	2	2	no	—
370	C₂×M₁₆	—	2	4	no	—
371	C₂×M₁₆	—	2	4	no	—
372	C₂×M₁₆	—	67	4	no	—
373	C₂×M₁₆	—	134	2	no	—
374	C₂×M₁₆	—	134	2	no	—
375	C₂×M₁₆	—	134	2	no	—
376	C₂×M₁₆	—	134	2	no	—
377	C₂×M₁₆	—	134	2	no	—
378	C₂×M₁₆	C₂×Dic₆₇	1	2	yes	—
379	C₂×M₁₆	C₂×Dic₆₇	1	2	yes	—
380	C₂×M₁₆	C₂²×D₆₇	1	2	yes	—
381	C₂²×C₈	—	2	1	no	—
382	C₂²×C₈	—	2	2	no	—
383	C₂²×C₈	—	2	2	no	—
384	C₂²×C₈	—	2	4	no	—
385	C₂²×C₈	—	2	4	no	—
386	C₂²×C₈	—	134	2	no	—
387	C₂²×C₈	C₂×Dic₆₇	1	1	yes	characteristic
388	C₂²×C₈	C₂×Dic₆₇	1	1	yes	characteristic
389	C₂²×C₈	C₂×Dic₆₇	1	2	yes	—
390	C₂²×C₈	C₂²⋊D₆₇	1	1	yes	characteristic
391	C₂²×C₈	C₂²⋊D₆₇	1	1	yes	characteristic
392	C₂²×C₈	C₂²⋊D₆₇	1	1	yes	characteristic
393	C₂²×C₈	C₂²⋊D₆₇	1	1	yes	characteristic
394	C₂²×C₈	C₂²⋊D₆₇	1	2	yes	—
395	C₂²×C₈	C₂²⋊D₆₇	1	2	yes	—
396	C₂²×C₈	C₂²×D₆₇	1	2	yes	—
397	#117	—	67	4	no	—
398	#117	—	134	2	no	—
399	#117	—	134	2	no	—
400	#117	—	134	2	no	—
401	C₂×C₄⋊C₄	—	134	2	no	—
402	C₂×C₂²⋊C₄	—	134	2	no	—
403	C₂×C₄²	—	134	2	no	—
404	#108	—	134	4	no	—
405	#108	—	134	4	no	—
406	#107	—	134	4	no	—
407	#106	—	134	4	no	—
408	#104	—	134	16	no	—
409	C₂⁴	—	2	1	no	—
410	C₂⁴	#11761628	1	1	yes	characteristic
411	#41	—	2	2	no	—
412	#41	—	2	2	no	—
413	#41	—	2	2	no	—
414	#41	—	2	2	no	—
415	#41	—	2	2	no	—
416	#41	—	2	2	no	—
417	#41	—	2	2	no	—
418	#41	—	2	2	no	—
419	#41	—	2	2	no	—
420	#41	—	2	2	no	—
421	#41	—	2	2	no	—
422	#41	—	2	2	no	—
423	#41	C₄⋊Dic₆₇	1	4	yes	—
424	#41	C₄⋊Dic₆₇	1	4	yes	—
425	#41	C₂²×Dic₆₇	1	4	yes	—
426	#41	C₂×D₂₆₈	1	4	yes	—
427	C₂×Q₈	—	2	1	no	—
428	C₂×Q₈	—	2	1	no	—
429	C₂×Q₈	—	2	1	no	—
430	C₂×Q₈	C₄⋊Dic₆₇	1	2	yes	—
431	C₂×Q₈	C₄⋊Dic₆₇	1	2	yes	—
432	C₂×Q₈	C₂×Dic₁₃₄	1	2	yes	—
433	C₂×D₄	—	2	2	no	—
434	C₂×D₄	—	2	2	no	—
435	C₂×D₄	—	2	2	no	—
436	C₂×D₄	—	2	2	no	—
437	C₂×D₄	—	2	2	no	—
438	C₂×D₄	—	2	2	no	—
439	C₂×D₄	—	2	1	no	—
440	C₂×D₄	—	2	1	no	—
441	C₂×D₄	—	2	1	no	—
442	C₂×D₄	C₄⋊Dic₆₇	1	2	yes	—
443	C₂×D₄	C₄⋊Dic₆₇	1	2	yes	—
444	C₂×D₄	C₂×Dic₁₃₄	1	2	yes	—
445	C₂²×C₄	—	2	1	no	—
446	C₂²×C₄	—	2	2	no	—
447	C₂²×C₄	—	2	2	no	—
448	C₂²×C₄	—	2	2	no	—
449	C₂²×C₄	—	2	2	no	—
450	C₂²×C₄	—	2	2	no	—
451	C₂²×C₄	—	2	2	no	—
452	C₂²×C₄	—	268	2	no	—
453	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
454	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
455	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
456	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
457	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
458	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
459	C₂²×C₄	C₂×D₂₆₈	1	1	yes	characteristic
460	C₂²×C₄	C₂×D₂₆₈	1	1	yes	characteristic
461	C₂²×C₄	C₂×Dic₁₃₄	1	1	yes	characteristic
462	C₂²×C₄	C₂×Dic₁₃₄	1	1	yes	characteristic
463	C₂²×C₄	#11761628	1	1	yes	characteristic
464	C₂²×C₄	#11761628	1	1	yes	characteristic
465	C₂²×C₄	#11761628	1	1	yes	characteristic
466	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
467	M₁₆	—	2	2	no	—
468	M₁₆	—	2	2	no	—
469	M₁₆	—	2	2	no	—
470	M₁₆	—	2	8	no	—
471	M₁₆	—	2	8	no	—
472	M₁₆	—	268	2	no	—
473	M₁₆	—	268	2	no	—
474	M₁₆	—	134	4	no	—
475	M₁₆	—	134	4	no	—
476	M₁₆	C₂²×Dic₆₇	1	4	yes	—
477	C₂×C₈	—	2	2	no	—
478	C₂×C₈	—	2	2	no	—
479	C₂×C₈	—	2	2	no	—
480	C₂×C₈	—	2	8	no	—
481	C₂×C₈	—	2	8	no	—
482	C₂×C₈	—	268	2	no	—
483	C₂×C₈	—	268	2	no	—
484	C₂×C₈	—	134	4	no	—
485	C₂×C₈	C₂²⋊Dic₆₇	1	1	yes	characteristic
486	C₂×C₈	C₂²⋊Dic₆₇	1	1	yes	characteristic
487	C₂×C₈	C₂²⋊Dic₆₇	1	2	yes	—
488	C₂×C₈	C₂²⋊Dic₆₇	1	1	yes	characteristic
489	C₂×C₈	C₂²⋊Dic₆₇	1	1	yes	characteristic
490	C₂×C₈	C₂²⋊Dic₆₇	1	2	yes	—
491	C₂×C₈	C₂²⋊Dic₆₇	1	2	yes	—
492	C₂×C₈	C₂²⋊Dic₆₇	1	2	yes	—
493	C₂×C₈	C₂²⋊Dic₆₇	1	2	yes	—
494	C₂×C₈	C₂²⋊Dic₆₇	1	2	yes	—
495	C₂×C₈	C₂²×Dic₆₇	1	2	yes	—
496	C₂×C₈	C₂²×Dic₆₇	1	2	yes	—
497	C₂×C₈	C₂×C₂²⋊D₆₇	1	2	yes	—
498	C₂×C₈	C₂×C₂²⋊D₆₇	1	2	yes	—
499	C₂×C₈	C₂×C₂²⋊D₆₇	1	2	yes	—
500	C₂×C₈	C₂×C₂²⋊D₆₇	1	2	yes	—
501	C₄⋊C₄	—	268	2	no	—
502	C₄⋊C₄	—	134	4	no	—
503	C₂²⋊C₄	—	268	2	no	—
504	C₂²⋊C₄	—	134	4	no	—
505	C₄²	—	268	2	no	—
506	C₄²	—	134	4	no	—
507	C₂³	—	2	2	no	—
508	C₂³	—	2	2	no	—
509	C₂³	—	2	2	no	—
510	C₂³	—	4	2	no	—
511	C₂³	—	4	4	no	—
512	C₂³	#14524002	1	1	yes	characteristic
513	C₂³	#14524002	1	1	yes	characteristic
514	C₂³	#14524017	1	1	yes	characteristic
515	C₂³	#14524017	1	1	yes	characteristic
516	C₂³	#14524022	1	1	yes	characteristic
517	C₂³	#14524022	1	1	yes	characteristic
518	C₂³	C₂×#11761628	1	1	yes	characteristic
519	Q₈	—	2	2	no	—
520	Q₈	—	2	2	no	—
521	Q₈	—	2	2	no	—
522	Q₈	C₂×C₄⋊Dic₆₇	1	4	yes	—
523	D₄	—	2	4	no	—
524	D₄	—	2	4	no	—
525	D₄	—	2	4	no	—
526	D₄	—	2	4	no	—
527	D₄	—	2	2	no	—
528	D₄	—	2	2	no	—
529	D₄	—	2	2	no	—
530	D₄	C₂×C₄⋊Dic₆₇	1	4	yes	—
531	C₂×C₄	—	2	2	no	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	2	2	no	—
534	C₂×C₄	—	2	4	no	—
535	C₂×C₄	—	2	4	no	—
536	C₂×C₄	—	2	4	no	—
537	C₂×C₄	—	2	4	no	—
538	C₂×C₄	—	268	4	no	—
539	C₂×C₄	—	536	4	no	—
540	C₂×C₄	C₂×C₂²⋊Dic₆₇	1	1	yes	characteristic
541	C₂×C₄	C₂×C₂²⋊Dic₆₇	1	1	yes	characteristic
542	C₂×C₄	C₂×C₂²⋊Dic₆₇	1	1	yes	characteristic
543	C₂×C₄	C₂×C₂²⋊Dic₆₇	1	1	yes	characteristic
544	C₂×C₄	C₂×C₄⋊Dic₆₇	1	1	yes	characteristic
545	C₂×C₄	C₂×C₄⋊Dic₆₇	1	1	yes	characteristic
546	C₂×C₄	C₂×C₄⋊Dic₆₇	1	1	yes	characteristic
547	C₂×C₄	C₂×C₄⋊Dic₆₇	1	1	yes	characteristic
548	C₂×C₄	#14524002	1	1	yes	characteristic
549	C₂×C₄	#14524002	1	1	yes	characteristic
550	C₂×C₄	#14524017	1	1	yes	characteristic
551	C₂×C₄	#14524017	1	1	yes	characteristic
552	C₂×C₄	#14524017	1	1	yes	characteristic
553	C₂×C₄	#14524017	1	1	yes	characteristic
554	C₂×C₄	#14524017	1	1	yes	characteristic
555	C₂×C₄	#14524017	1	1	yes	characteristic
556	C₂×C₄	#14524022	1	1	yes	characteristic
557	C₂×C₄	#14524022	1	1	yes	characteristic
558	C₂×C₄	#14524022	1	1	yes	characteristic
559	C₂×C₄	#14524022	1	1	yes	characteristic
560	C₂×C₄	#14524022	1	1	yes	characteristic
561	C₂×C₄	#14524022	1	1	yes	characteristic
562	C₂×C₄	C₂³×Dic₆₇	1	1	yes	characteristic
563	C₂×C₄	C₂²×C₂²⋊D₆₇	1	1	yes	characteristic
564	C₂×C₄	C₂²×C₂²⋊D₆₇	1	1	yes	characteristic
565	C₂×C₄	C₂²×D₂₆₈	1	1	yes	characteristic
566	C₂×C₄	C₂²×Dic₁₃₄	1	1	yes	characteristic
567	C₂×C₄	C₂×#11761628	1	1	yes	characteristic
568	C₈	—	2	4	no	—
569	C₈	—	268	4	no	—
570	C₈	C₂×C₂²⋊Dic₆₇	1	2	yes	—
571	C₈	C₂×C₂²⋊Dic₆₇	1	2	yes	—
572	C₈	C₂×C₂²⋊Dic₆₇	1	2	yes	—
573	C₈	C₂×C₂²⋊Dic₆₇	1	2	yes	—
574	C₂²	—	2	2	no	—
575	C₂²	—	2	2	no	—
576	C₂²	—	2	2	no	—
577	C₂²	—	2	4	no	—
578	C₂²	—	4	1	no	—
579	C₂²	—	4	1	no	—
580	C₂²	—	4	1	no	—
581	C₂²	—	4	1	no	—
582	C₂²	—	4	4	no	—
583	C₂²	—	4	4	no	—
584	C₂²	—	4	4	no	—
585	C₂²	#16863256	1	1	yes	characteristic
586	C₂²	#16863256	1	1	yes	characteristic
587	C₂²	#16863256	1	1	yes	characteristic
588	C₂²	#16863256	1	1	yes	characteristic
589	C₂²	C₂×#14524002	1	1	yes	characteristic
590	C₂²	C₂×#14524017	1	1	yes	characteristic
591	C₂²	C₂×#14524022	1	1	yes	characteristic
592	C₄	—	2	4	no	—
593	C₄	—	536	4	no	—
594	C₄	#16863256	1	1	yes	characteristic
595	C₄	#16863256	1	1	yes	characteristic
596	C₄	#16863256	1	1	yes	characteristic
597	C₄	#16863256	1	1	yes	characteristic
598	C₄	C₂²×C₂²⋊Dic₆₇	1	1	yes	characteristic
599	C₄	C₂²×C₄⋊Dic₆₇	1	1	yes	characteristic
600	C₄	C₂×#14524017	1	1	yes	characteristic
601	C₄	C₂×#14524022	1	1	yes	characteristic
602	C₂	—	2	1	no	—
603	C₂	—	2	1	no	—
604	C₂	—	2	1	no	—
605	C₂	—	2	1	no	—
606	C₂	—	2	1	no	—
607	C₂	—	2	1	no	—
608	C₂	—	4	4	no	—
609	C₂	#22560263	1	2	yes	direct product factor
610	C₂	C₂×#16863256	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#14524017
commutator	C₂×C₄×C₆₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₆₇
Fitting	C₂²×#131×C₆₇	C₂
socle	C₂²×C₆₇	#380
prime radical	C₂²×#41×C₆₇	C₂²
cosocle	C₂²×C₄×C₆₇	C₂⁴
hypercenter	C₂²×#131	D₆₇
hypocenter	C₆₇	C₂×#1814
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂²×#131

Complements

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

N	H ≅ G/N	type
1. C₂²×#14523979	C₂	semidirect
2. C₂×#16863434	C₂	semidirect
4. #22560263	C₂	direct (N × H)
5. C₂×#16863168	C₂	semidirect
12. C₂×#14523979	C₂²	semidirect
14. #16863434	C₂²	semidirect
20. #16863168	C₂²	semidirect
26. C₂×#131×C₆₇	C₄	semidirect
27. C₂×#131×C₆₇	C₄	semidirect
28. C₂×#131×C₆₇	C₄	semidirect
76. #131×C₆₇	C₂×C₄	semidirect
77. #131×C₆₇	C₂×C₄	semidirect
304. C₂×C₆₇	#1814	semidirect
312. C₆₇	C₂×#1814	semidirect
318. C₂×#131	Dic₆₇	semidirect
319. C₂×#131	Dic₆₇	semidirect
320. C₂×#131	Dic₆₇	semidirect
363. #131	C₂×Dic₆₇	semidirect
364. #131	C₂×Dic₆₇	semidirect
609. C₂	#22560263	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#14523979	2
C₂×#16863434	2
C₂×#16863413	2
#22560263	2
C₂×#16863168	2
C₂²×#131×C₆₇	2
C₂×#1814	67

Subgroups — C2×#22560263 #30855493

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22560263 #30855493