Subgroups — C₂×#22560449 #30856728

Order 17152.

1358 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16863444	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#16863419	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#16863413	C₂	1	1	yes	maximal, characteristic
4	C₂²×#14523970	C₂	1	1	yes	maximal, characteristic
5	#22560449	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×#568×C₆₇	C₂	1	1	yes	maximal, characteristic
9	C₂²×#11761612	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	#16863444	—	2	2	no	—
14	#16863444	C₂²	1	4	yes	complemented
15	C₂×#14523978	—	2	2	no	—
16	#16863419	—	2	2	no	—
17	#16863419	C₂²	1	4	yes	complemented
18	C₂×Dic₆₇⋊C₈	—	2	2	no	—
19	#16863413	—	2	2	no	—
20	#16863413	C₂²	1	4	yes	—
21	C₂×#14523970	—	2	2	no	—
22	C₂×#14523970	C₄	1	2	yes	complemented
23	C₂×#14523970	C₄	1	2	yes	complemented
24	C₂×#14523970	C₄	1	4	yes	complemented
25	C₂×#14523970	C₂²	1	4	yes	—
26	#16863167	C₂²	1	4	yes	complemented
27	#16863157	C₂²	1	4	yes	complemented
28	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
29	#568×C₆₇	—	2	2	no	—
30	#568×C₆₇	—	2	2	no	—
31	#568×C₆₇	—	2	2	no	—
32	#568×C₆₇	C₂²	1	4	yes	—
33	C₂×#131×C₆₇	—	2	2	no	—
34	C₂×#131×C₆₇	—	2	2	no	—
35	C₂²×M₁₆×C₆₇	—	2	2	no	—
36	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
37	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
38	C₂³×Dic₆₇	—	2	1	no	—
39	C₂×#11761612	—	2	1	no	—
40	C₂×#11761612	—	2	1	no	—
41	C₂×#11761612	—	2	1	no	—
42	C₂×#11761612	—	2	1	no	—
43	C₂×#11761612	—	2	1	no	—
44	C₂×#11761612	—	2	1	no	—
45	C₂×#11761612	—	2	1	no	—
46	C₂×#11761612	—	2	1	no	—
47	C₂×#11761612	C₂×C₄	1	2	yes	—
48	C₂×#11761612	C₂×C₄	1	2	yes	—
49	C₂×#11761612	C₂³	1	2	yes	—
50	C₂×#11761612	C₂³	1	2	yes	—
51	C₂²×C₆₇⋊C₈	—	2	1	no	—
52	C₂²×C₆₇⋊C₈	—	2	1	no	—
53	#14524002	—	2	1	no	—
54	#14524002	—	2	1	no	—
55	#14524002	—	2	1	no	—
56	#14524002	C₂³	1	2	yes	—
57	C₂×C₄⋊Dic₆₇	—	2	1	no	—
58	C₂×C₂²⋊Dic₆₇	—	2	1	no	—
59	C₂×C₄×Dic₆₇	—	2	1	no	—
60	C₂×C₄×Dic₆₇	—	2	1	no	—
61	C₂×C₄×Dic₆₇	—	2	1	no	—
62	C₂×C₄×Dic₆₇	—	2	1	no	—
63	C₂×C₄×Dic₆₇	C₂×C₄	1	1	yes	characteristic
64	C₂×C₄×Dic₆₇	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄×Dic₆₇	C₂×C₄	1	2	yes	—
66	C₂×C₄×Dic₆₇	C₂³	1	2	yes	—
67	#14523978	—	2	8	no	—
68	Dic₆₇⋊C₈	—	2	8	no	—
69	#14523970	—	2	8	no	—
70	#14523970	C₂×C₄	1	8	yes	complemented
71	#14523970	C₂×C₄	1	8	yes	complemented
72	C₂×#41×C₆₇	—	2	1	no	—
73	C₂×#41×C₆₇	—	2	1	no	—
74	C₂×#41×C₆₇	—	2	1	no	—
75	C₂×#41×C₆₇	—	2	1	no	—
76	C₂×#41×C₆₇	—	2	1	no	—
77	C₂×#41×C₆₇	—	2	1	no	—
78	C₂×#41×C₆₇	C₂×C₄	1	2	yes	—
79	C₂×#41×C₆₇	C₂×C₄	1	2	yes	—
80	C₂×#41×C₆₇	D₄	1	2	yes	—
81	C₂×#41×C₆₇	D₄	1	2	yes	—
82	C₂×#41×C₆₇	Q₈	1	2	yes	—
83	C₂×#41×C₆₇	C₂³	1	2	yes	—
84	C₂²×Q₈×C₆₇	Q₈	1	1	yes	characteristic
85	C₂²×D₄×C₆₇	—	2	1	no	—
86	C₂²×D₄×C₆₇	Q₈	1	1	yes	characteristic
87	C₂³×C₄×C₆₇	—	2	1	no	—
88	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
89	#131×C₆₇	—	2	8	no	—
90	#131×C₆₇	—	2	8	no	—
91	#131×C₆₇	—	2	8	no	—
92	#131×C₆₇	—	2	8	no	—
93	C₂×M₁₆×C₆₇	—	2	4	no	—
94	C₂×M₁₆×C₆₇	—	2	8	no	—
95	C₂×M₁₆×C₆₇	—	2	1	no	—
96	C₂×M₁₆×C₆₇	—	2	1	no	—
97	C₂×M₁₆×C₆₇	—	2	1	no	—
98	C₂×M₁₆×C₆₇	—	2	1	no	—
99	C₂×M₁₆×C₆₇	—	2	1	no	—
100	C₂×M₁₆×C₆₇	—	2	1	no	—
101	C₂×M₁₆×C₆₇	—	2	1	no	—
102	C₂×M₁₆×C₆₇	—	2	8	no	—
103	C₂×M₁₆×C₆₇	D₄	1	2	yes	—
104	C₂×M₁₆×C₆₇	D₄	1	2	yes	—
105	C₂×M₁₆×C₆₇	D₄	1	2	yes	—
106	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
107	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
108	C₂²×C₈×C₆₇	—	2	4	no	—
109	C₂²×C₈×C₆₇	—	2	1	no	—
110	C₂²×C₈×C₆₇	D₄	1	2	yes	—
111	C₂²×Dic₆₇	—	2	1	no	—
112	C₂²×Dic₆₇	—	2	2	no	—
113	C₂²×Dic₆₇	—	2	1	no	—
114	C₂²×Dic₆₇	—	2	2	no	—
115	C₂²×Dic₆₇	—	4	4	no	—
116	C₂²×Dic₆₇	—	4	1	no	—
117	#11761612	—	2	2	no	—
118	#11761612	—	2	2	no	—
119	#11761612	—	2	2	no	—
120	#11761612	—	2	2	no	—
121	#11761612	—	2	2	no	—
122	#11761612	—	4	1	no	—
123	#11761612	—	4	1	no	—
124	#11761612	C₂²×C₄	1	4	yes	—
125	C₂×C₆₇⋊C₈	—	2	2	no	—
126	C₂×C₆₇⋊C₈	—	2	2	no	—
127	C₂×C₆₇⋊C₈	—	2	2	no	—
128	C₂×C₆₇⋊C₈	—	2	2	no	—
129	C₂×C₆₇⋊C₈	—	4	1	no	—
130	C₂×C₆₇⋊C₈	—	4	1	no	—
131	C₄⋊Dic₆₇	—	2	2	no	—
132	C₄⋊Dic₆₇	—	4	1	no	—
133	C₂²⋊Dic₆₇	—	2	2	no	—
134	C₂²⋊Dic₆₇	—	4	1	no	—
135	C₄×Dic₆₇	—	2	1	no	—
136	C₄×Dic₆₇	—	2	2	no	—
137	C₄×Dic₆₇	—	2	1	no	—
138	C₄×Dic₆₇	—	2	2	no	—
139	C₄×Dic₆₇	—	2	2	no	—
140	C₄×Dic₆₇	—	4	1	no	—
141	C₄×Dic₆₇	C₂²×C₄	1	2	yes	—
142	C₄×Dic₆₇	C₂²×C₄	1	2	yes	—
143	C₂⁴×C₆₇	—	2	1	no	—
144	C₂⁴×C₆₇	#41	1	1	yes	characteristic
145	#41×C₆₇	—	2	2	no	—
146	#41×C₆₇	—	2	2	no	—
147	#41×C₆₇	—	2	2	no	—
148	#41×C₆₇	—	2	2	no	—
149	#41×C₆₇	—	2	2	no	—
150	#41×C₆₇	—	2	2	no	—
151	#41×C₆₇	—	2	2	no	—
152	#41×C₆₇	—	2	2	no	—
153	#41×C₆₇	—	2	2	no	—
154	#41×C₆₇	—	2	2	no	—
155	#41×C₆₇	—	2	2	no	—
156	#41×C₆₇	—	2	2	no	—
157	#41×C₆₇	C₄⋊C₄	1	4	yes	—
158	#41×C₆₇	C₄⋊C₄	1	4	yes	—
159	#41×C₆₇	C₂²×C₄	1	4	yes	—
160	#41×C₆₇	C₂×D₄	1	4	yes	—
161	C₂×Q₈×C₆₇	—	2	1	no	—
162	C₂×Q₈×C₆₇	—	2	1	no	—
163	C₂×Q₈×C₆₇	—	2	1	no	—
164	C₂×Q₈×C₆₇	C₄⋊C₄	1	2	yes	—
165	C₂×Q₈×C₆₇	C₄⋊C₄	1	2	yes	—
166	C₂×Q₈×C₆₇	C₂×Q₈	1	2	yes	—
167	C₂×D₄×C₆₇	—	2	2	no	—
168	C₂×D₄×C₆₇	—	2	2	no	—
169	C₂×D₄×C₆₇	—	2	2	no	—
170	C₂×D₄×C₆₇	—	2	2	no	—
171	C₂×D₄×C₆₇	—	2	2	no	—
172	C₂×D₄×C₆₇	—	2	2	no	—
173	C₂×D₄×C₆₇	—	2	1	no	—
174	C₂×D₄×C₆₇	—	2	1	no	—
175	C₂×D₄×C₆₇	—	2	1	no	—
176	C₂×D₄×C₆₇	C₄⋊C₄	1	2	yes	—
177	C₂×D₄×C₆₇	C₄⋊C₄	1	2	yes	—
178	C₂×D₄×C₆₇	C₂×Q₈	1	2	yes	—
179	C₂²×C₄×C₆₇	—	2	1	no	—
180	C₂²×C₄×C₆₇	—	2	2	no	—
181	C₂²×C₄×C₆₇	—	2	2	no	—
182	C₂²×C₄×C₆₇	—	2	2	no	—
183	C₂²×C₄×C₆₇	—	2	2	no	—
184	C₂²×C₄×C₆₇	—	2	2	no	—
185	C₂²×C₄×C₆₇	—	2	2	no	—
186	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
187	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
188	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
189	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
190	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
191	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
192	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
193	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
194	C₂²×C₄×C₆₇	C₂×Q₈	1	1	yes	characteristic
195	C₂²×C₄×C₆₇	C₂×Q₈	1	1	yes	characteristic
196	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
197	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
198	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
199	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
200	M₁₆×C₆₇	—	2	16	no	—
201	M₁₆×C₆₇	—	2	2	no	—
202	M₁₆×C₆₇	—	2	2	no	—
203	M₁₆×C₆₇	—	2	2	no	—
204	M₁₆×C₆₇	—	2	2	no	—
205	M₁₆×C₆₇	—	2	2	no	—
206	M₁₆×C₆₇	—	2	2	no	—
207	M₁₆×C₆₇	—	2	2	no	—
208	M₁₆×C₆₇	C₂×D₄	1	4	yes	—
209	C₂×C₈×C₆₇	—	2	16	no	—
210	C₂×C₈×C₆₇	—	2	2	no	—
211	C₂×C₈×C₆₇	—	2	2	no	—
212	C₂×C₈×C₆₇	—	2	2	no	—
213	C₂×C₈×C₆₇	—	2	2	no	—
214	C₂×C₈×C₆₇	—	2	2	no	—
215	C₂×C₈×C₆₇	C₂×D₄	1	4	yes	—
216	C₂³×C₆₇	—	2	2	no	—
217	C₂³×C₆₇	—	2	2	no	—
218	C₂³×C₆₇	—	2	2	no	—
219	C₂³×C₆₇	—	4	2	no	—
220	C₂³×C₆₇	—	8	2	no	—
221	C₂³×C₆₇	C₄×D₄	1	1	yes	characteristic
222	C₂³×C₆₇	C₄×D₄	1	1	yes	characteristic
223	C₂³×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
224	C₂³×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
225	C₂³×C₆₇	#123	1	1	yes	characteristic
226	C₂³×C₆₇	#123	1	1	yes	characteristic
227	C₂³×C₆₇	C₂×#41	1	1	yes	characteristic
228	Q₈×C₆₇	—	2	2	no	—
229	Q₈×C₆₇	—	2	2	no	—
230	Q₈×C₆₇	—	2	2	no	—
231	Q₈×C₆₇	C₂×C₄⋊C₄	1	4	yes	—
232	D₄×C₆₇	—	2	4	no	—
233	D₄×C₆₇	—	2	4	no	—
234	D₄×C₆₇	—	2	4	no	—
235	D₄×C₆₇	—	2	4	no	—
236	D₄×C₆₇	—	2	2	no	—
237	D₄×C₆₇	—	2	2	no	—
238	D₄×C₆₇	—	2	2	no	—
239	D₄×C₆₇	C₂×C₄⋊C₄	1	4	yes	—
240	C₂×C₄×C₆₇	—	2	2	no	—
241	C₂×C₄×C₆₇	—	2	2	no	—
242	C₂×C₄×C₆₇	—	2	2	no	—
243	C₂×C₄×C₆₇	—	2	4	no	—
244	C₂×C₄×C₆₇	—	2	4	no	—
245	C₂×C₄×C₆₇	—	2	4	no	—
246	C₂×C₄×C₆₇	—	2	4	no	—
247	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
248	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
249	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
250	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
251	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
252	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
253	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
254	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
255	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
256	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
257	C₂×C₄×C₆₇	#120	1	1	yes	characteristic
258	C₂×C₄×C₆₇	#120	1	1	yes	characteristic
259	C₂×C₄×C₆₇	#120	1	1	yes	characteristic
260	C₂×C₄×C₆₇	#120	1	1	yes	characteristic
261	C₂×C₄×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
262	C₂×C₄×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
263	C₂×C₄×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
264	C₂×C₄×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
265	C₂×C₄×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
266	C₂×C₄×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
267	C₂×C₄×C₆₇	#123	1	1	yes	characteristic
268	C₂×C₄×C₆₇	#123	1	1	yes	characteristic
269	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
270	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
271	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
272	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
273	C₂×C₄×C₆₇	C₂²×Q₈	1	1	yes	characteristic
274	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
275	C₂×Dic₆₇	—	2	4	no	—
276	C₂×Dic₆₇	—	2	2	no	—
277	C₂×Dic₆₇	—	2	2	no	—
278	C₂×Dic₆₇	—	4	4	no	—
279	C₂×Dic₆₇	—	4	4	no	—
280	C₂×Dic₆₇	—	4	2	no	—
281	C₂×Dic₆₇	—	4	2	no	—
282	C₂×Dic₆₇	—	8	2	no	—
283	C₈×C₆₇	—	2	4	no	—
284	C₈×C₆₇	—	2	4	no	—
285	C₆₇⋊C₈	—	2	4	no	—
286	C₆₇⋊C₈	—	4	2	no	—
287	C₂²×C₆₇	—	2	2	no	—
288	C₂²×C₆₇	—	2	2	no	—
289	C₂²×C₆₇	—	2	2	no	—
290	C₂²×C₆₇	—	2	4	no	—
291	C₂²×C₆₇	—	4	1	no	—
292	C₂²×C₆₇	—	4	1	no	—
293	C₂²×C₆₇	—	4	1	no	—
294	C₂²×C₆₇	—	4	1	no	—
295	C₂²×C₆₇	—	4	4	no	—
296	C₂²×C₆₇	—	8	2	no	—
297	C₂²×C₆₇	—	8	2	no	—
298	C₂²×C₆₇	#385	1	1	yes	characteristic
299	C₂²×C₆₇	#385	1	1	yes	characteristic
300	C₂²×C₆₇	#385	1	1	yes	characteristic
301	C₂²×C₆₇	#385	1	1	yes	characteristic
302	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
303	C₂²×C₆₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
304	C₂²×C₆₇	C₂×#123	1	1	yes	characteristic
305	C₄×C₆₇	—	2	4	no	—
306	C₄×C₆₇	#385	1	1	yes	characteristic
307	C₄×C₆₇	#385	1	1	yes	characteristic
308	C₄×C₆₇	#385	1	1	yes	characteristic
309	C₄×C₆₇	#385	1	1	yes	characteristic
310	C₄×C₆₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
311	C₄×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
312	C₄×C₆₇	C₂×#120	1	1	yes	characteristic
313	C₄×C₆₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
314	Dic₆₇	—	2	4	no	—
315	Dic₆₇	—	4	2	no	—
316	Dic₆₇	—	8	2	no	—
317	C₂×#1861	—	67	1	no	maximal, Sylow
318	C₂×C₆₇	—	2	1	no	—
319	C₂×C₆₇	—	2	1	no	—
320	C₂×C₆₇	—	2	1	no	—
321	C₂×C₆₇	—	2	1	no	—
322	C₂×C₆₇	—	2	1	no	—
323	C₂×C₆₇	—	2	1	no	—
324	C₂×C₆₇	—	4	4	no	—
325	C₂×C₆₇	#1861	1	2	yes	complemented
326	C₂×C₆₇	C₂×#385	1	1	yes	characteristic
327	C₂×#568	D₆₇	1	1	yes	characteristic
328	C₂×#430	—	67	1	no	—
329	C₂×#423	—	67	1	no	—
330	C₂×#421	—	67	1	no	—
331	C₂²×#104	—	67	1	no	—
332	#1861	—	67	8	no	—
333	C₂×#344	—	67	1	no	—
334	C₂×#339	—	67	1	no	—
335	C₆₇	C₂×#1861	1	1	yes	characteristic, complemented, Sylow
336	C₂²×#41	C₂×D₆₇	1	1	yes	characteristic
337	#568	—	2	2	no	—
338	#568	—	2	2	no	—
339	#568	—	2	2	no	—
340	#568	C₂×D₆₇	1	4	yes	—
341	C₂×#131	—	2	2	no	—
342	C₂×#131	—	2	2	no	—
343	C₂²×M₁₆	—	2	2	no	—
344	C₂²×M₁₆	—	67	1	no	—
345	C₂²×M₁₆	—	67	1	no	—
346	C₂²×M₁₆	C₂×D₆₇	1	1	yes	characteristic
347	C₂²×M₁₆	C₂×D₆₇	1	1	yes	characteristic
348	C₂×#117	—	67	1	no	—
349	C₂²×C₄²	—	67	1	no	—
350	#430	—	67	4	no	—
351	#430	—	134	2	no	—
352	C₂×#108	—	134	2	no	—
353	#423	—	67	4	no	—
354	#423	—	134	2	no	—
355	C₂×C₄⋊C₈	—	134	2	no	—
356	#421	—	67	4	no	—
357	#421	—	134	2	no	—
358	C₂×#104	—	67	2	no	—
359	C₂×#104	—	67	4	no	—
360	C₂×#104	—	67	2	no	—
361	C₂×#104	—	67	4	no	—
362	C₂×#104	—	134	2	no	—
363	#344	—	67	4	no	—
364	#339	—	67	4	no	—
365	C₂×#41	—	2	1	no	—
366	C₂×#41	—	2	1	no	—
367	C₂×#41	—	2	1	no	—
368	C₂×#41	—	2	1	no	—
369	C₂×#41	—	2	1	no	—
370	C₂×#41	—	2	1	no	—
371	C₂×#41	Dic₁₃₄	1	2	yes	—
372	C₂×#41	C₄×D₆₇	1	2	yes	—
373	C₂×#41	C₄×D₆₇	1	2	yes	—
374	C₂×#41	C₂²⋊D₆₇	1	2	yes	—
375	C₂×#41	C₂²⋊D₆₇	1	2	yes	—
376	C₂×#41	C₂²×D₆₇	1	2	yes	—
377	C₂²×Q₈	Dic₁₃₄	1	1	yes	characteristic
378	C₂²×D₄	—	2	1	no	—
379	C₂²×D₄	Dic₁₃₄	1	1	yes	characteristic
380	C₂³×C₄	—	2	1	no	—
381	C₂³×C₄	—	134	1	no	—
382	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
383	#131	—	2	8	no	—
384	#131	—	2	8	no	—
385	#131	—	2	8	no	—
386	#131	—	2	8	no	—
387	C₂×M₁₆	—	2	4	no	—
388	C₂×M₁₆	—	2	8	no	—
389	C₂×M₁₆	—	2	1	no	—
390	C₂×M₁₆	—	2	1	no	—
391	C₂×M₁₆	—	2	1	no	—
392	C₂×M₁₆	—	2	1	no	—
393	C₂×M₁₆	—	2	1	no	—
394	C₂×M₁₆	—	2	1	no	—
395	C₂×M₁₆	—	2	1	no	—
396	C₂×M₁₆	—	2	8	no	—
397	C₂×M₁₆	—	67	2	no	—
398	C₂×M₁₆	—	67	2	no	—
399	C₂×M₁₆	—	67	2	no	—
400	C₂×M₁₆	—	67	2	no	—
401	C₂×M₁₆	—	134	1	no	—
402	C₂×M₁₆	—	134	1	no	—
403	C₂×M₁₆	—	134	1	no	—
404	C₂×M₁₆	—	134	1	no	—
405	C₂×M₁₆	—	134	1	no	—
406	C₂×M₁₆	—	134	1	no	—
407	C₂×M₁₆	—	134	1	no	—
408	C₂×M₁₆	—	134	1	no	—
409	C₂×M₁₆	C₂²⋊D₆₇	1	2	yes	—
410	C₂×M₁₆	C₂²⋊D₆₇	1	2	yes	—
411	C₂×M₁₆	C₂²⋊D₆₇	1	2	yes	—
412	C₂×M₁₆	C₂²×D₆₇	1	2	yes	—
413	C₂×M₁₆	C₂²×D₆₇	1	2	yes	—
414	C₂²×C₈	—	2	4	no	—
415	C₂²×C₈	—	2	1	no	—
416	C₂²×C₈	—	134	1	no	—
417	C₂²×C₈	—	134	1	no	—
418	C₂²×C₈	C₂²⋊D₆₇	1	2	yes	—
419	#117	—	67	2	no	—
420	#117	—	134	1	no	—
421	#117	—	134	1	no	—
422	#117	—	134	1	no	—
423	C₂×C₄⋊C₄	—	134	1	no	—
424	C₂×C₂²⋊C₄	—	134	1	no	—
425	C₂×C₄²	—	67	1	no	—
426	C₂×C₄²	—	67	2	no	—
427	C₂×C₄²	—	67	1	no	—
428	C₂×C₄²	—	67	2	no	—
429	C₂×C₄²	—	134	1	no	—
430	C₂×C₄²	—	134	1	no	—
431	C₂×C₄²	—	134	1	no	—
432	C₂×C₄²	—	134	1	no	—
433	#108	—	134	8	no	—
434	C₄⋊C₈	—	134	8	no	—
435	#104	—	67	8	no	—
436	#104	—	67	8	no	—
437	#104	—	134	8	no	—
438	C₂⁴	—	2	1	no	—
439	C₂⁴	#11761628	1	1	yes	characteristic
440	#41	—	2	2	no	—
441	#41	—	2	2	no	—
442	#41	—	2	2	no	—
443	#41	—	2	2	no	—
444	#41	—	2	2	no	—
445	#41	—	2	2	no	—
446	#41	—	2	2	no	—
447	#41	—	2	2	no	—
448	#41	—	2	2	no	—
449	#41	—	2	2	no	—
450	#41	—	2	2	no	—
451	#41	—	2	2	no	—
452	#41	Dic₆₇⋊C₄	1	4	yes	—
453	#41	Dic₆₇⋊C₄	1	4	yes	—
454	#41	C₂×C₄×D₆₇	1	4	yes	—
455	#41	C₂×C₂²⋊D₆₇	1	4	yes	—
456	C₂×Q₈	—	2	1	no	—
457	C₂×Q₈	—	2	1	no	—
458	C₂×Q₈	—	2	1	no	—
459	C₂×Q₈	Dic₆₇⋊C₄	1	2	yes	—
460	C₂×Q₈	Dic₆₇⋊C₄	1	2	yes	—
461	C₂×Q₈	C₂×Dic₁₃₄	1	2	yes	—
462	C₂×D₄	—	2	2	no	—
463	C₂×D₄	—	2	2	no	—
464	C₂×D₄	—	2	2	no	—
465	C₂×D₄	—	2	2	no	—
466	C₂×D₄	—	2	2	no	—
467	C₂×D₄	—	2	2	no	—
468	C₂×D₄	—	2	1	no	—
469	C₂×D₄	—	2	1	no	—
470	C₂×D₄	—	2	1	no	—
471	C₂×D₄	Dic₆₇⋊C₄	1	2	yes	—
472	C₂×D₄	Dic₆₇⋊C₄	1	2	yes	—
473	C₂×D₄	C₂×Dic₁₃₄	1	2	yes	—
474	C₂²×C₄	—	2	1	no	—
475	C₂²×C₄	—	2	2	no	—
476	C₂²×C₄	—	2	2	no	—
477	C₂²×C₄	—	2	2	no	—
478	C₂²×C₄	—	2	2	no	—
479	C₂²×C₄	—	2	2	no	—
480	C₂²×C₄	—	2	2	no	—
481	C₂²×C₄	—	268	4	no	—
482	C₂²×C₄	—	268	1	no	—
483	C₂²×C₄	—	134	1	no	—
484	C₂²×C₄	—	134	2	no	—
485	C₂²×C₄	—	134	2	no	—
486	C₂²×C₄	—	134	1	no	—
487	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
488	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
489	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
490	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
491	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
492	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
493	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
494	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
495	C₂²×C₄	C₂×Dic₁₃₄	1	1	yes	characteristic
496	C₂²×C₄	C₂×Dic₁₃₄	1	1	yes	characteristic
497	C₂²×C₄	#11761628	1	1	yes	characteristic
498	C₂²×C₄	#11761628	1	1	yes	characteristic
499	C₂²×C₄	#11761628	1	1	yes	characteristic
500	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
501	M₁₆	—	2	16	no	—
502	M₁₆	—	2	2	no	—
503	M₁₆	—	2	2	no	—
504	M₁₆	—	2	2	no	—
505	M₁₆	—	2	2	no	—
506	M₁₆	—	2	2	no	—
507	M₁₆	—	2	2	no	—
508	M₁₆	—	2	2	no	—
509	M₁₆	—	268	1	no	—
510	M₁₆	—	268	1	no	—
511	M₁₆	—	67	4	no	—
512	M₁₆	—	134	2	no	—
513	M₁₆	—	134	2	no	—
514	M₁₆	—	134	2	no	—
515	M₁₆	—	134	2	no	—
516	M₁₆	—	134	2	no	—
517	M₁₆	C₂×C₂²⋊D₆₇	1	4	yes	—
518	C₂×C₈	—	2	16	no	—
519	C₂×C₈	—	2	2	no	—
520	C₂×C₈	—	2	2	no	—
521	C₂×C₈	—	2	2	no	—
522	C₂×C₈	—	2	2	no	—
523	C₂×C₈	—	2	2	no	—
524	C₂×C₈	—	268	1	no	—
525	C₂×C₈	—	268	1	no	—
526	C₂×C₈	—	134	2	no	—
527	C₂×C₈	—	134	2	no	—
528	C₂×C₈	—	134	2	no	—
529	C₂×C₈	—	134	2	no	—
530	C₂×C₈	C₂×C₂²⋊D₆₇	1	4	yes	—
531	C₄⋊C₄	—	268	1	no	—
532	C₄⋊C₄	—	134	2	no	—
533	C₂²⋊C₄	—	268	1	no	—
534	C₂²⋊C₄	—	134	2	no	—
535	C₄²	—	268	1	no	—
536	C₄²	—	67	2	no	—
537	C₄²	—	67	2	no	—
538	C₄²	—	134	2	no	—
539	C₄²	—	134	1	no	—
540	C₄²	—	134	2	no	—
541	C₄²	—	134	1	no	—
542	C₄²	—	134	2	no	—
543	C₂³	—	2	2	no	—
544	C₂³	—	2	2	no	—
545	C₂³	—	2	2	no	—
546	C₂³	—	4	2	no	—
547	C₂³	—	8	2	no	—
548	C₂³	C₄×C₂²⋊D₆₇	1	1	yes	characteristic
549	C₂³	C₄×C₂²⋊D₆₇	1	1	yes	characteristic
550	C₂³	#14524022	1	1	yes	characteristic
551	C₂³	#14524022	1	1	yes	characteristic
552	C₂³	#14524026	1	1	yes	characteristic
553	C₂³	#14524026	1	1	yes	characteristic
554	C₂³	C₂×#11761628	1	1	yes	characteristic
555	Q₈	—	2	2	no	—
556	Q₈	—	2	2	no	—
557	Q₈	—	2	2	no	—
558	Q₈	C₂×Dic₆₇⋊C₄	1	4	yes	—
559	D₄	—	2	4	no	—
560	D₄	—	2	4	no	—
561	D₄	—	2	4	no	—
562	D₄	—	2	4	no	—
563	D₄	—	2	2	no	—
564	D₄	—	2	2	no	—
565	D₄	—	2	2	no	—
566	D₄	C₂×Dic₆₇⋊C₄	1	4	yes	—
567	C₂×C₄	—	2	2	no	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	2	2	no	—
570	C₂×C₄	—	2	4	no	—
571	C₂×C₄	—	2	4	no	—
572	C₂×C₄	—	2	4	no	—
573	C₂×C₄	—	2	4	no	—
574	C₂×C₄	—	268	2	no	—
575	C₂×C₄	—	268	4	no	—
576	C₂×C₄	—	268	4	no	—
577	C₂×C₄	—	268	2	no	—
578	C₂×C₄	—	536	2	no	—
579	C₂×C₄	—	134	2	no	—
580	C₂×C₄	—	134	4	no	—
581	C₂×C₄	—	134	2	no	—
582	C₂×C₄	C₂×Dic₆₇⋊C₄	1	1	yes	characteristic
583	C₂×C₄	C₂×Dic₆₇⋊C₄	1	1	yes	characteristic
584	C₂×C₄	C₂×Dic₆₇⋊C₄	1	1	yes	characteristic
585	C₂×C₄	C₂×Dic₆₇⋊C₄	1	1	yes	characteristic
586	C₂×C₄	C₄×C₂²⋊D₆₇	1	1	yes	characteristic
587	C₂×C₄	C₄×C₂²⋊D₆₇	1	1	yes	characteristic
588	C₂×C₄	C₄×C₂²⋊D₆₇	1	1	yes	characteristic
589	C₂×C₄	C₄×C₂²⋊D₆₇	1	1	yes	characteristic
590	C₂×C₄	C₄×C₂²⋊D₆₇	1	1	yes	characteristic
591	C₂×C₄	C₄×C₂²⋊D₆₇	1	1	yes	characteristic
592	C₂×C₄	#14524012	1	1	yes	characteristic
593	C₂×C₄	#14524012	1	1	yes	characteristic
594	C₂×C₄	#14524012	1	1	yes	characteristic
595	C₂×C₄	#14524012	1	1	yes	characteristic
596	C₂×C₄	#14524022	1	1	yes	characteristic
597	C₂×C₄	#14524022	1	1	yes	characteristic
598	C₂×C₄	#14524022	1	1	yes	characteristic
599	C₂×C₄	#14524022	1	1	yes	characteristic
600	C₂×C₄	#14524022	1	1	yes	characteristic
601	C₂×C₄	#14524022	1	1	yes	characteristic
602	C₂×C₄	#14524026	1	1	yes	characteristic
603	C₂×C₄	#14524026	1	1	yes	characteristic
604	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
605	C₂×C₄	C₂²×C₂²⋊D₆₇	1	1	yes	characteristic
606	C₂×C₄	C₂²×C₂²⋊D₆₇	1	1	yes	characteristic
607	C₂×C₄	C₂²×C₂²⋊D₆₇	1	1	yes	characteristic
608	C₂×C₄	C₂²×Dic₁₃₄	1	1	yes	characteristic
609	C₂×C₄	C₂×#11761628	1	1	yes	characteristic
610	C₈	—	2	4	no	—
611	C₈	—	2	4	no	—
612	C₈	—	268	2	no	—
613	C₈	—	134	4	no	—
614	C₂²	—	2	2	no	—
615	C₂²	—	2	2	no	—
616	C₂²	—	2	2	no	—
617	C₂²	—	2	4	no	—
618	C₂²	—	4	1	no	—
619	C₂²	—	4	1	no	—
620	C₂²	—	4	1	no	—
621	C₂²	—	4	1	no	—
622	C₂²	—	4	4	no	—
623	C₂²	—	8	2	no	—
624	C₂²	—	8	2	no	—
625	C₂²	#16863269	1	1	yes	characteristic
626	C₂²	#16863269	1	1	yes	characteristic
627	C₂²	#16863269	1	1	yes	characteristic
628	C₂²	#16863269	1	1	yes	characteristic
629	C₂²	C₂×C₄×C₂²⋊D₆₇	1	1	yes	characteristic
630	C₂²	C₂×#14524022	1	1	yes	characteristic
631	C₂²	C₂×#14524026	1	1	yes	characteristic
632	C₄	—	2	4	no	—
633	C₄	—	268	2	no	—
634	C₄	—	536	2	no	—
635	C₄	—	134	4	no	—
636	C₄	#16863269	1	1	yes	characteristic
637	C₄	#16863269	1	1	yes	characteristic
638	C₄	#16863269	1	1	yes	characteristic
639	C₄	#16863269	1	1	yes	characteristic
640	C₄	C₂²×Dic₆₇⋊C₄	1	1	yes	characteristic
641	C₄	C₂×C₄×C₂²⋊D₆₇	1	1	yes	characteristic
642	C₄	C₂×#14524012	1	1	yes	characteristic
643	C₄	C₂×#14524022	1	1	yes	characteristic
644	C₂	—	2	1	no	—
645	C₂	—	2	1	no	—
646	C₂	—	2	1	no	—
647	C₂	—	2	1	no	—
648	C₂	—	2	1	no	—
649	C₂	—	2	1	no	—
650	C₂	—	4	4	no	—
651	C₂	#22560449	1	2	yes	direct product factor
652	C₂	C₂×#16863269	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#14524012
commutator	C₂×C₄×C₆₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₆₇
Fitting	C₂×#568×C₆₇	C₂
socle	C₂²×C₆₇	#385
prime radical	C₂²×#41×C₆₇	C₂²
cosocle	C₂²×C₄×C₆₇	C₂⁴
hypercenter	C₂×#568	D₆₇
hypocenter	C₆₇	C₂×#1861
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂×#568

Complements

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

N	H ≅ G/N	type
1. C₂×#16863444	C₂	semidirect
2. C₂×#16863419	C₂	semidirect
5. #22560449	C₂	direct (N × H)
6. C₂×#16863167	C₂	semidirect
7. C₂×#16863157	C₂	semidirect
14. #16863444	C₂²	semidirect
17. #16863419	C₂²	semidirect
22. C₂×#14523970	C₄	semidirect
23. C₂×#14523970	C₄	semidirect
24. C₂×#14523970	C₄	semidirect
26. #16863167	C₂²	semidirect
27. #16863157	C₂²	semidirect
70. #14523970	C₂×C₄	semidirect
71. #14523970	C₂×C₄	semidirect
325. C₂×C₆₇	#1861	semidirect
335. C₆₇	C₂×#1861	semidirect
651. C₂	#22560449	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×#16863444	2
C₂×#16863419	2
C₂×#16863413	2
C₂²×#14523970	2
#22560449	2
C₂×#16863167	2
C₂×#16863157	2
C₂×#568×C₆₇	2
C₂×#1861	67

Subgroups — C2×#22560449 #30856728

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22560449 #30856728