Subgroups — C₂×#22569126 #31720152

Order 17152.

2642 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16864163	C₂	1	2	yes	maximal, complemented
2	#22569126	C₂	1	16	yes	maximal, direct product factor
3	C₂×#16863518	C₂	1	4	yes	maximal, complemented
4	C₂×#16863513	C₂	1	4	yes	maximal, complemented
5	C₂²×#14523979	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#16863413	C₂	1	2	yes	maximal, complemented
7	C₂×#16863351	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#135×C₆₇	C₂	1	1	yes	maximal, characteristic
9	#16864163	—	2	8	no	—
10	#16864163	C₂²	1	16	yes	complemented
11	C₂×#14524050	—	2	4	no	—
12	C₂×#14524050	C₂²	1	8	yes	complemented
13	C₂²×#11761612	—	2	4	no	—
14	C₂²×#11761612	C₂²	1	2	yes	—
15	C₂²×#11761612	C₂²	1	1	yes	characteristic
16	C₂×#14524002	C₂²	1	1	yes	characteristic
17	#16863518	C₂²	1	32	yes	complemented
18	#16863513	C₂²	1	32	yes	complemented
19	C₂×#14523979	C₂²	1	2	yes	complemented
20	C₂×#14523979	C₂²	1	2	yes	complemented
21	C₂×#14523979	C₂²	1	8	yes	complemented
22	#16863413	C₂²	1	16	yes	complemented
23	C₂×#14523970	C₂²	1	8	yes	complemented
24	#16863351	C₂²	1	8	yes	complemented
25	C₂×#14523953	C₂²	1	2	yes	complemented
26	C₂×C₈×Dic₆₇	C₂²	1	2	yes	complemented
27	C₂²×#41×C₆₇	C₂²	1	2	yes	—
28	C₂×#135×C₆₇	C₄	1	2	yes	complemented
29	C₂×#135×C₆₇	C₄	1	2	yes	complemented
30	C₂×#135×C₆₇	C₄	1	8	yes	complemented
31	C₂×#135×C₆₇	C₂²	1	2	yes	—
32	C₂×#135×C₆₇	C₂²	1	2	yes	—
33	C₂×#135×C₆₇	C₂²	1	8	yes	—
34	C₂²×Q₁₆×C₆₇	C₄	1	1	yes	characteristic, complemented
35	C₂²×SD₁₆×C₆₇	C₄	1	2	yes	complemented
36	C₂²×D₈×C₆₇	C₄	1	1	yes	characteristic, complemented
37	C₂³×C₈×C₆₇	C₂²	1	1	yes	characteristic
38	#14524050	—	2	32	no	—
39	#14524050	—	2	16	no	—
40	#14524050	C₂³	1	32	yes	complemented
41	C₂×#11761612	—	2	32	no	—
42	C₂×#11761612	—	2	8	no	—
43	C₂×#11761612	—	2	2	no	—
44	C₂×#11761612	—	2	4	no	—
45	C₂×#11761612	D₄	1	2	yes	—
46	C₂×#11761612	D₄	1	2	yes	—
47	C₂×#11761612	D₄	1	4	yes	—
48	C₂×#11761612	C₂³	1	4	yes	—
49	C₂×#11761612	C₂³	1	8	yes	—
50	C₂×#11761612	C₂³	1	4	yes	—
51	C₂²×C₆₇⋊C₈	—	2	8	no	—
52	C₂²×C₆₇⋊C₈	—	2	2	no	—
53	C₂²×C₆₇⋊C₈	C₂³	1	2	yes	—
54	#14524002	—	2	2	no	—
55	#14524002	C₂³	1	4	yes	—
56	C₂×C₄⋊Dic₆₇	—	2	1	no	—
57	C₂×C₂²⋊Dic₆₇	—	2	1	no	—
58	C₂×C₄×Dic₆₇	C₂³	1	2	yes	—
59	#14523979	C₂³	1	8	yes	complemented
60	#14523979	C₂³	1	8	yes	complemented
61	#14523970	C₂³	1	32	yes	complemented
62	#14523953	C₂³	1	8	yes	complemented
63	C₈×Dic₆₇	C₂³	1	8	yes	complemented
64	C₂×#41×C₆₇	—	2	2	no	—
65	C₂×#41×C₆₇	—	2	4	no	—
66	C₂×#41×C₆₇	—	2	2	no	—
67	C₂×#41×C₆₇	—	2	4	no	—
68	C₂×#41×C₆₇	C₂×C₄	1	4	yes	—
69	C₂×#41×C₆₇	C₂×C₄	1	8	yes	—
70	C₂×#41×C₆₇	C₂³	1	4	yes	—
71	C₂×#41×C₆₇	C₂³	1	8	yes	—
72	C₂²×Q₈×C₆₇	C₂×C₄	1	2	yes	—
73	C₂²×D₄×C₆₇	—	2	2	no	—
74	C₂²×D₄×C₆₇	C₂×C₄	1	2	yes	—
75	C₂³×C₄×C₆₇	—	2	2	no	—
76	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
77	#135×C₆₇	C₂×C₄	1	8	yes	—
78	#135×C₆₇	C₂×C₄	1	8	yes	—
79	#135×C₆₇	C₂×C₄	1	16	yes	complemented
80	#135×C₆₇	C₂×C₄	1	16	yes	complemented
81	#135×C₆₇	C₂³	1	8	yes	—
82	#135×C₆₇	C₂³	1	8	yes	—
83	C₂×Q₁₆×C₆₇	C₂×C₄	1	2	yes	—
84	C₂×Q₁₆×C₆₇	C₂×C₄	1	2	yes	—
85	C₂×Q₁₆×C₆₇	C₂×C₄	1	8	yes	complemented
86	C₂×SD₁₆×C₆₇	C₂×C₄	1	4	yes	—
87	C₂×SD₁₆×C₆₇	C₂×C₄	1	4	yes	—
88	C₂×SD₁₆×C₆₇	C₂×C₄	1	16	yes	complemented
89	C₂×D₈×C₆₇	C₂×C₄	1	2	yes	—
90	C₂×D₈×C₆₇	C₂×C₄	1	2	yes	—
91	C₂×D₈×C₆₇	C₂×C₄	1	8	yes	complemented
92	C₂²×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
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	1	yes	characteristic
96	C₂²×C₈×C₆₇	C₂×C₄	1	4	yes	—
97	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
98	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
99	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
100	C₂²×Dic₆₇	—	2	2	no	—
101	#11761612	—	2	8	no	—
102	#11761612	—	2	4	no	—
103	#11761612	—	2	32	no	—
104	#11761612	C₂×D₄	1	8	yes	—
105	#11761612	C₂×D₄	1	8	yes	—
106	#11761612	C₂⁴	1	8	yes	—
107	C₂×C₆₇⋊C₈	—	2	4	no	—
108	C₂×C₆₇⋊C₈	—	2	8	no	—
109	C₂×C₆₇⋊C₈	—	2	32	no	—
110	C₂×C₆₇⋊C₈	C₂×D₄	1	4	yes	—
111	C₂×C₆₇⋊C₈	C₂×D₄	1	4	yes	—
112	C₂×C₆₇⋊C₈	C₂⁴	1	4	yes	—
113	C₄⋊Dic₆₇	—	2	4	no	—
114	C₂²⋊Dic₆₇	—	2	4	no	—
115	C₄×Dic₆₇	—	2	2	no	—
116	C₄×Dic₆₇	C₂⁴	1	4	yes	—
117	C₂⁴×C₆₇	—	2	2	no	—
118	C₂⁴×C₆₇	#41	1	1	yes	characteristic
119	#41×C₆₇	—	2	8	no	—
120	#41×C₆₇	—	2	8	no	—
121	#41×C₆₇	—	2	8	no	—
122	#41×C₆₇	—	2	8	no	—
123	#41×C₆₇	—	2	4	no	—
124	#41×C₆₇	—	2	4	no	—
125	#41×C₆₇	—	2	8	no	—
126	#41×C₆₇	C₂²×C₄	1	8	yes	—
127	#41×C₆₇	C₂²×C₄	1	16	yes	—
128	#41×C₆₇	C₂⁴	1	8	yes	—
129	C₂×Q₈×C₆₇	—	2	2	no	—
130	C₂×Q₈×C₆₇	—	2	4	no	—
131	C₂×Q₈×C₆₇	C₂²×C₄	1	4	yes	—
132	C₂×Q₈×C₆₇	C₂²×C₄	1	8	yes	—
133	C₂×D₄×C₆₇	—	2	4	no	—
134	C₂×D₄×C₆₇	—	2	8	no	—
135	C₂×D₄×C₆₇	—	2	4	no	—
136	C₂×D₄×C₆₇	—	2	8	no	—
137	C₂×D₄×C₆₇	—	2	2	no	—
138	C₂×D₄×C₆₇	—	2	4	no	—
139	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
140	C₂×D₄×C₆₇	C₂²×C₄	1	8	yes	—
141	C₂²×C₄×C₆₇	—	2	2	no	—
142	C₂²×C₄×C₆₇	—	2	4	no	—
143	C₂²×C₄×C₆₇	—	2	8	no	—
144	C₂²×C₄×C₆₇	—	2	4	no	—
145	C₂²×C₄×C₆₇	—	2	8	no	—
146	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
147	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
148	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
149	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
152	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
153	C₂²×C₄×C₆₇	#41	1	2	yes	—
154	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
155	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
156	Q₁₆×C₆₇	C₂²×C₄	1	8	yes	—
157	Q₁₆×C₆₇	C₂²×C₄	1	8	yes	—
158	SD₁₆×C₆₇	C₂²×C₄	1	16	yes	—
159	SD₁₆×C₆₇	C₂²×C₄	1	16	yes	—
160	D₈×C₆₇	C₂²×C₄	1	8	yes	—
161	D₈×C₆₇	C₂²×C₄	1	8	yes	—
162	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
163	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
164	C₂×C₈×C₆₇	C₂²×C₄	1	4	yes	—
165	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
166	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
167	C₂×C₈×C₆₇	C₂²×C₄	1	4	yes	—
168	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
169	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
170	C₂×C₈×C₆₇	C₂²×C₄	1	4	yes	—
171	C₂×C₈×C₆₇	C₂²×C₄	1	4	yes	—
172	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
173	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
174	C₂³×C₆₇	—	2	4	no	—
175	C₂³×C₆₇	—	2	8	no	—
176	C₂³×C₆₇	—	4	2	no	—
177	C₂³×C₆₇	—	8	4	no	—
178	C₂³×C₆₇	C₄×D₄	1	1	yes	characteristic
179	C₂³×C₆₇	C₄×D₄	1	1	yes	characteristic
180	C₂³×C₆₇	C₄×D₄	1	2	yes	—
181	C₂³×C₆₇	C₂×#41	1	1	yes	characteristic
182	C₂³×C₆₇	C₂×#41	1	2	yes	—
183	Q₈×C₆₇	—	2	4	no	—
184	Q₈×C₆₇	—	2	8	no	—
185	Q₈×C₆₇	C₂³×C₄	1	8	yes	—
186	D₄×C₆₇	—	2	8	no	—
187	D₄×C₆₇	—	2	16	no	—
188	D₄×C₆₇	—	2	8	no	—
189	D₄×C₆₇	—	2	4	no	—
190	D₄×C₆₇	—	2	8	no	—
191	D₄×C₆₇	C₂³×C₄	1	8	yes	—
192	C₂×C₄×C₆₇	—	2	8	no	—
193	C₂×C₄×C₆₇	—	2	4	no	—
194	C₂×C₄×C₆₇	—	2	8	no	—
195	C₂×C₄×C₆₇	—	2	16	no	—
196	C₂×C₄×C₆₇	—	2	8	no	—
197	C₂×C₄×C₆₇	C₄×D₄	1	2	yes	—
198	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
199	C₂×C₄×C₆₇	C₄×D₄	1	2	yes	—
200	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
201	C₂×C₄×C₆₇	C₄×D₄	1	2	yes	—
202	C₂×C₄×C₆₇	C₄×D₄	1	2	yes	—
203	C₂×C₄×C₆₇	C₄×D₄	1	2	yes	—
204	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
205	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
206	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
207	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
208	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
209	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
210	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
211	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
212	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
213	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
214	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
215	C₂×Dic₆₇	—	2	4	no	—
216	C₂×Dic₆₇	—	4	4	no	—
217	C₈×C₆₇	C₂³×C₄	1	2	yes	—
218	C₈×C₆₇	C₂³×C₄	1	2	yes	—
219	C₈×C₆₇	C₂³×C₄	1	2	yes	—
220	C₈×C₆₇	C₂³×C₄	1	2	yes	—
221	C₆₇⋊C₈	—	2	8	no	—
222	C₆₇⋊C₈	C₂²×D₄	1	8	yes	—
223	C₂²×C₆₇	—	2	2	no	—
224	C₂²×C₆₇	—	2	2	no	—
225	C₂²×C₆₇	—	2	2	no	—
226	C₂²×C₆₇	—	2	8	no	—
227	C₂²×C₆₇	—	4	2	no	—
228	C₂²×C₆₇	—	4	2	no	—
229	C₂²×C₆₇	—	4	8	no	—
230	C₂²×C₆₇	—	8	8	no	—
231	C₂²×C₆₇	C₂×C₄×D₄	1	2	yes	—
232	C₂²×C₆₇	C₂×C₄×D₄	1	2	yes	—
233	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
234	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
235	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
236	C₄×C₆₇	—	2	8	no	—
237	C₄×C₆₇	C₂×C₄×D₄	1	2	yes	—
238	C₄×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
239	C₄×C₆₇	C₂×C₄×D₄	1	2	yes	—
240	C₄×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
241	C₄×C₆₇	C₂⁴×C₄	1	1	yes	characteristic
242	C₄×C₆₇	C₂³×D₄	1	1	yes	characteristic
243	Dic₆₇	—	4	4	no	—
244	C₂×#2957	—	67	1	no	maximal, Sylow
245	C₂×C₆₇	—	2	1	no	—
246	C₂×C₆₇	—	2	2	no	—
247	C₂×C₆₇	—	2	1	no	—
248	C₂×C₆₇	—	2	2	no	—
249	C₂×C₆₇	—	4	8	no	—
250	C₂×C₆₇	#2957	1	2	yes	complemented
251	C₂×C₆₇	C₂²×C₄×D₄	1	1	yes	characteristic
252	C₂²×#135	D₆₇	1	1	yes	characteristic
253	C₂×#568	—	67	2	no	—
254	#2957	—	67	16	no	—
255	C₂×#444	—	67	4	no	—
256	C₂×#443	—	67	4	no	—
257	C₂²×#108	—	67	1	no	—
258	C₂×#421	—	67	2	no	—
259	C₂×#405	—	67	1	no	—
260	C₆₇	C₂×#2957	1	1	yes	characteristic, complemented, Sylow
261	C₂²×#41	C₂×D₆₇	1	2	yes	—
262	C₂×#135	Dic₆₇	1	2	yes	complemented
263	C₂×#135	Dic₆₇	1	2	yes	complemented
264	C₂×#135	Dic₆₇	1	8	yes	complemented
265	C₂×#135	C₂×D₆₇	1	2	yes	—
266	C₂×#135	C₂×D₆₇	1	2	yes	—
267	C₂×#135	C₂×D₆₇	1	8	yes	—
268	C₂²×Q₁₆	Dic₆₇	1	1	yes	characteristic, complemented
269	C₂²×SD₁₆	Dic₆₇	1	2	yes	complemented
270	C₂²×D₈	Dic₆₇	1	1	yes	characteristic, complemented
271	#568	—	67	16	no	—
272	#568	—	134	8	no	—
273	C₂×#131	—	67	8	no	—
274	C₂×#131	—	134	4	no	—
275	C₂²×M₁₆	—	67	1	no	—
276	C₂²×M₁₆	—	67	2	no	—
277	C₂²×M₁₆	—	134	4	no	—
278	C₂³×C₈	C₂×D₆₇	1	1	yes	characteristic
279	C₂×#117	—	67	1	no	—
280	#444	—	67	32	no	—
281	#443	—	67	32	no	—
282	C₂×#108	—	67	2	no	—
283	C₂×#108	—	67	2	no	—
284	C₂×#108	—	67	8	no	—
285	#421	—	67	16	no	—
286	C₂×#104	—	67	8	no	—
287	#405	—	67	8	no	—
288	C₂×#97	—	67	2	no	—
289	C₂×C₄×C₈	—	67	2	no	—
290	C₂×#41	—	2	2	no	—
291	C₂×#41	—	2	4	no	—
292	C₂×#41	—	2	2	no	—
293	C₂×#41	—	2	4	no	—
294	C₂×#41	C₂×Dic₆₇	1	4	yes	—
295	C₂×#41	C₂×Dic₆₇	1	8	yes	—
296	C₂×#41	C₂²×D₆₇	1	4	yes	—
297	C₂×#41	C₂²×D₆₇	1	8	yes	—
298	C₂²×Q₈	C₂×Dic₆₇	1	2	yes	—
299	C₂²×D₄	—	2	2	no	—
300	C₂²×D₄	C₂×Dic₆₇	1	2	yes	—
301	C₂³×C₄	—	2	2	no	—
302	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
303	#135	C₂×Dic₆₇	1	8	yes	—
304	#135	C₂×Dic₆₇	1	8	yes	—
305	#135	C₂×Dic₆₇	1	16	yes	complemented
306	#135	C₂×Dic₆₇	1	16	yes	complemented
307	#135	C₂²×D₆₇	1	8	yes	—
308	#135	C₂²×D₆₇	1	8	yes	—
309	C₂×Q₁₆	C₂×Dic₆₇	1	2	yes	—
310	C₂×Q₁₆	C₂×Dic₆₇	1	2	yes	—
311	C₂×Q₁₆	C₂×Dic₆₇	1	8	yes	complemented
312	C₂×SD₁₆	C₂×Dic₆₇	1	4	yes	—
313	C₂×SD₁₆	C₂×Dic₆₇	1	4	yes	—
314	C₂×SD₁₆	C₂×Dic₆₇	1	16	yes	complemented
315	C₂×D₈	C₂×Dic₆₇	1	2	yes	—
316	C₂×D₈	C₂×Dic₆₇	1	2	yes	—
317	C₂×D₈	C₂×Dic₆₇	1	8	yes	complemented
318	#131	—	67	32	no	—
319	#131	—	134	16	no	—
320	#131	—	134	32	no	—
321	C₂×M₁₆	—	67	2	no	—
322	C₂×M₁₆	—	67	2	no	—
323	C₂×M₁₆	—	67	4	no	—
324	C₂×M₁₆	—	67	4	no	—
325	C₂×M₁₆	—	67	4	no	—
326	C₂×M₁₆	—	67	8	no	—
327	C₂×M₁₆	—	134	8	no	—
328	C₂×M₁₆	—	134	32	no	—
329	C₂×M₁₆	—	134	2	no	—
330	C₂×M₁₆	—	134	4	no	—
331	C₂²×C₈	—	67	2	no	—
332	C₂²×C₈	—	134	8	no	—
333	C₂²×C₈	—	134	2	no	—
334	C₂²×C₈	C₂×Dic₆₇	1	1	yes	characteristic
335	C₂²×C₈	C₂×Dic₆₇	1	1	yes	characteristic
336	C₂²×C₈	C₂×Dic₆₇	1	1	yes	characteristic
337	C₂²×C₈	C₂×Dic₆₇	1	1	yes	characteristic
338	C₂²×C₈	C₂×Dic₆₇	1	4	yes	—
339	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
340	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
341	C₂²×C₈	C₂²×D₆₇	1	4	yes	—
342	#117	—	67	4	no	—
343	#117	—	134	2	no	—
344	C₂×C₄⋊C₄	—	134	1	no	—
345	C₂×C₂²⋊C₄	—	134	1	no	—
346	C₂×C₄²	—	67	2	no	—
347	#108	—	67	8	no	—
348	#108	—	67	8	no	—
349	#104	—	67	32	no	—
350	#97	—	67	8	no	—
351	C₄×C₈	—	67	8	no	—
352	C₂⁴	—	2	2	no	—
353	C₂⁴	#11761627	1	1	yes	characteristic
354	#41	—	2	8	no	—
355	#41	—	2	8	no	—
356	#41	—	2	8	no	—
357	#41	—	2	4	no	—
358	#41	—	2	8	no	—
359	#41	—	2	4	no	—
360	#41	—	2	8	no	—
361	#41	C₂²×Dic₆₇	1	8	yes	—
362	#41	C₂²×Dic₆₇	1	16	yes	—
363	#41	C₂³×D₆₇	1	8	yes	—
364	C₂×Q₈	—	2	2	no	—
365	C₂×Q₈	—	2	4	no	—
366	C₂×Q₈	C₂²×Dic₆₇	1	4	yes	—
367	C₂×Q₈	C₂²×Dic₆₇	1	8	yes	—
368	C₂×D₄	—	2	4	no	—
369	C₂×D₄	—	2	8	no	—
370	C₂×D₄	—	2	4	no	—
371	C₂×D₄	—	2	8	no	—
372	C₂×D₄	—	2	2	no	—
373	C₂×D₄	—	2	4	no	—
374	C₂×D₄	C₂²×Dic₆₇	1	4	yes	—
375	C₂×D₄	C₂²×Dic₆₇	1	8	yes	—
376	C₂²×C₄	—	2	2	no	—
377	C₂²×C₄	—	2	4	no	—
378	C₂²×C₄	—	2	8	no	—
379	C₂²×C₄	—	2	8	no	—
380	C₂²×C₄	—	2	4	no	—
381	C₂²×C₄	—	134	2	no	—
382	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
383	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
384	C₂²×C₄	C₂²×Dic₆₇	1	2	yes	—
385	C₂²×C₄	D₄×D₆₇	1	2	yes	—
386	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
387	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
388	C₂²×C₄	#11761627	1	1	yes	characteristic
389	C₂²×C₄	#11761627	1	2	yes	—
390	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
391	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
392	Q₁₆	C₂²×Dic₆₇	1	8	yes	—
393	Q₁₆	C₂²×Dic₆₇	1	8	yes	—
394	SD₁₆	C₂²×Dic₆₇	1	16	yes	—
395	SD₁₆	C₂²×Dic₆₇	1	16	yes	—
396	D₈	C₂²×Dic₆₇	1	8	yes	—
397	D₈	C₂²×Dic₆₇	1	8	yes	—
398	M₁₆	—	67	8	no	—
399	M₁₆	—	67	8	no	—
400	M₁₆	—	67	8	no	—
401	M₁₆	—	134	32	no	—
402	M₁₆	—	134	8	no	—
403	M₁₆	—	134	4	no	—
404	C₂×C₈	—	67	4	no	—
405	C₂×C₈	—	67	4	no	—
406	C₂×C₈	—	67	4	no	—
407	C₂×C₈	—	134	32	no	—
408	C₂×C₈	—	134	8	no	—
409	C₂×C₈	—	134	4	no	—
410	C₂×C₈	C₂²×Dic₆₇	1	1	yes	characteristic
411	C₂×C₈	C₂²×Dic₆₇	1	1	yes	characteristic
412	C₂×C₈	C₂²×Dic₆₇	1	4	yes	—
413	C₂×C₈	C₂²×Dic₆₇	1	1	yes	characteristic
414	C₂×C₈	C₂²×Dic₆₇	1	1	yes	characteristic
415	C₂×C₈	C₂²×Dic₆₇	1	4	yes	—
416	C₂×C₈	C₂²×Dic₆₇	1	2	yes	—
417	C₂×C₈	C₂²×Dic₆₇	1	2	yes	—
418	C₂×C₈	C₂²×Dic₆₇	1	4	yes	—
419	C₂×C₈	C₂²×Dic₆₇	1	4	yes	—
420	C₂×C₈	C₂³×D₆₇	1	2	yes	—
421	C₂×C₈	C₂³×D₆₇	1	2	yes	—
422	C₄⋊C₄	—	134	4	no	—
423	C₂²⋊C₄	—	134	4	no	—
424	C₄²	—	67	4	no	—
425	C₄²	—	134	2	no	—
426	C₂³	—	2	4	no	—
427	C₂³	—	2	8	no	—
428	C₂³	—	4	2	no	—
429	C₂³	—	8	4	no	—
430	C₂³	D₄×Dic₆₇	1	1	yes	characteristic
431	C₂³	D₄×Dic₆₇	1	1	yes	characteristic
432	C₂³	D₄×Dic₆₇	1	2	yes	—
433	C₂³	C₂×#11761627	1	1	yes	characteristic
434	C₂³	C₂×#11761627	1	2	yes	—
435	Q₈	—	2	4	no	—
436	Q₈	—	2	8	no	—
437	Q₈	C₂³×Dic₆₇	1	8	yes	—
438	D₄	—	2	8	no	—
439	D₄	—	2	16	no	—
440	D₄	—	2	8	no	—
441	D₄	—	2	4	no	—
442	D₄	—	2	8	no	—
443	D₄	C₂³×Dic₆₇	1	8	yes	—
444	C₂×C₄	—	2	8	no	—
445	C₂×C₄	—	2	4	no	—
446	C₂×C₄	—	2	16	no	—
447	C₂×C₄	—	2	8	no	—
448	C₂×C₄	—	2	8	no	—
449	C₂×C₄	—	268	4	no	—
450	C₂×C₄	—	134	4	no	—
451	C₂×C₄	D₄×Dic₆₇	1	1	yes	characteristic
452	C₂×C₄	D₄×Dic₆₇	1	2	yes	—
453	C₂×C₄	D₄×Dic₆₇	1	2	yes	—
454	C₂×C₄	D₄×Dic₆₇	1	1	yes	characteristic
455	C₂×C₄	D₄×Dic₆₇	1	2	yes	—
456	C₂×C₄	D₄×Dic₆₇	1	2	yes	—
457	C₂×C₄	D₄×Dic₆₇	1	2	yes	—
458	C₂×C₄	C₂³×Dic₆₇	1	2	yes	—
459	C₂×C₄	C₂³×Dic₆₇	1	1	yes	characteristic
460	C₂×C₄	C₂³×Dic₆₇	1	2	yes	—
461	C₂×C₄	C₂³×Dic₆₇	1	1	yes	characteristic
462	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
463	C₂×C₄	C₂×D₄×D₆₇	1	2	yes	—
464	C₂×C₄	C₂×D₄×D₆₇	1	2	yes	—
465	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
466	C₂×C₄	C₂×#11761627	1	1	yes	characteristic
467	C₂×C₄	C₂×#11761627	1	2	yes	—
468	C₂×C₄	C₂⁴×D₆₇	1	1	yes	characteristic
469	C₈	—	67	8	no	—
470	C₈	—	134	8	no	—
471	C₈	C₂³×Dic₆₇	1	2	yes	—
472	C₈	C₂³×Dic₆₇	1	2	yes	—
473	C₈	C₂³×Dic₆₇	1	2	yes	—
474	C₈	C₂³×Dic₆₇	1	2	yes	—
475	C₂²	—	2	2	no	—
476	C₂²	—	2	2	no	—
477	C₂²	—	2	2	no	—
478	C₂²	—	2	8	no	—
479	C₂²	—	4	2	no	—
480	C₂²	—	4	2	no	—
481	C₂²	—	4	8	no	—
482	C₂²	—	8	8	no	—
483	C₂²	C₂×D₄×Dic₆₇	1	2	yes	—
484	C₂²	C₂×D₄×Dic₆₇	1	1	yes	characteristic
485	C₂²	C₂×D₄×Dic₆₇	1	2	yes	—
486	C₂²	C₂×D₄×Dic₆₇	1	1	yes	characteristic
487	C₂²	C₂²×#11761627	1	1	yes	characteristic
488	C₄	—	2	8	no	—
489	C₄	—	268	4	no	—
490	C₄	C₂×D₄×Dic₆₇	1	2	yes	—
491	C₄	C₂×D₄×Dic₆₇	1	1	yes	characteristic
492	C₄	C₂×D₄×Dic₆₇	1	1	yes	characteristic
493	C₄	C₂×D₄×Dic₆₇	1	2	yes	—
494	C₄	C₂⁴×Dic₆₇	1	1	yes	characteristic
495	C₄	C₂²×D₄×D₆₇	1	1	yes	characteristic
496	C₂	—	2	1	no	—
497	C₂	—	2	2	no	—
498	C₂	—	2	1	no	—
499	C₂	—	2	2	no	—
500	C₂	—	4	8	no	—
501	C₂	#22569126	1	2	yes	direct product factor
502	C₂	C₂²×D₄×Dic₆₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₆₇
commutator	C₄×C₆₇	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₆₇
Fitting, prime radical	C₂²×#135×C₆₇	C₂
socle	C₂²×C₆₇	C₂×C₄×D₄
cosocle	C₂×C₄×C₆₇	C₂⁵
hypercenter	C₂²×#135	D₆₇
hypocenter	C₆₇	C₂×#2957
LCS	G ▷ C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂²×#135

Complements

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

N	H ≅ G/N	type
1. C₂×#16864163	C₂	semidirect
2. #22569126	C₂	direct (N × H)
3. C₂×#16863518	C₂	semidirect
4. C₂×#16863513	C₂	semidirect
5. C₂²×#14523979	C₂	semidirect
6. C₂×#16863413	C₂	semidirect
7. C₂×#16863351	C₂	semidirect
10. #16864163	C₂²	semidirect
12. C₂×#14524050	C₂²	semidirect
17. #16863518	C₂²	semidirect
18. #16863513	C₂²	semidirect
19. C₂×#14523979	C₂²	semidirect
20. C₂×#14523979	C₂²	semidirect
21. C₂×#14523979	C₂²	semidirect
22. #16863413	C₂²	semidirect
23. C₂×#14523970	C₂²	semidirect
24. #16863351	C₂²	semidirect
25. C₂×#14523953	C₂²	semidirect
26. C₂×C₈×Dic₆₇	C₂²	semidirect
28. C₂×#135×C₆₇	C₄	semidirect
29. C₂×#135×C₆₇	C₄	semidirect
30. C₂×#135×C₆₇	C₄	semidirect
34. C₂²×Q₁₆×C₆₇	C₄	semidirect
35. C₂²×SD₁₆×C₆₇	C₄	semidirect
36. C₂²×D₈×C₆₇	C₄	semidirect
40. #14524050	C₂³	semidirect
59. #14523979	C₂³	semidirect
60. #14523979	C₂³	semidirect
61. #14523970	C₂³	semidirect
62. #14523953	C₂³	semidirect
63. C₈×Dic₆₇	C₂³	semidirect
79. #135×C₆₇	C₂×C₄	semidirect
80. #135×C₆₇	C₂×C₄	semidirect
85. C₂×Q₁₆×C₆₇	C₂×C₄	semidirect
88. C₂×SD₁₆×C₆₇	C₂×C₄	semidirect
91. C₂×D₈×C₆₇	C₂×C₄	semidirect
250. C₂×C₆₇	#2957	semidirect
260. C₆₇	C₂×#2957	semidirect
262. C₂×#135	Dic₆₇	semidirect
263. C₂×#135	Dic₆₇	semidirect
264. C₂×#135	Dic₆₇	semidirect
268. C₂²×Q₁₆	Dic₆₇	semidirect
269. C₂²×SD₁₆	Dic₆₇	semidirect
270. C₂²×D₈	Dic₆₇	semidirect
305. #135	C₂×Dic₆₇	semidirect
306. #135	C₂×Dic₆₇	semidirect
311. C₂×Q₁₆	C₂×Dic₆₇	semidirect
314. C₂×SD₁₆	C₂×Dic₆₇	semidirect
317. C₂×D₈	C₂×Dic₆₇	semidirect
501. C₂	#22569126	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×#16864163	2
#22569126	2
C₂×#16863518	2
C₂×#16863513	2
C₂²×#14523979	2
C₂×#16863413	2
C₂×#16863351	2
C₂²×#135×C₆₇	2
C₂×#2957	67

Subgroups — C2×#22569126 #31720152

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22569126 #31720152