Subgroups — C₂×C₆₇×#3013 #30739616

Order 17152.

4782 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×2₋¹⁺⁴×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#137×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×#135×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#537×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#3013	C₂	1	16	yes	maximal, direct product factor
6	C₂×#452×C₆₇	C₂	1	2	yes	maximal, complemented
7	C₂×#449×C₆₇	C₂	1	2	yes	maximal, complemented
8	C₂×#451×C₆₇	C₂	1	2	yes	maximal, complemented
9	C₂×#448×C₆₇	C₂	1	2	yes	maximal, complemented
10	C₂×#417×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×#103×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#408×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×2₋¹⁺⁴×C₆₇	—	2	4	no	—
14	C₂×2₋¹⁺⁴×C₆₇	—	2	8	no	—
15	C₂×2₋¹⁺⁴×C₆₇	—	2	8	no	—
16	C₂×2₋¹⁺⁴×C₆₇	C₂²	1	8	yes	complemented
17	C₂²×#41×C₆₇	—	2	1	no	—
18	C₂²×#41×C₆₇	—	2	2	no	—
19	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
20	C₂²×#41×C₆₇	C₂²	1	2	yes	—
21	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
22	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
23	C₂³×Q₈×C₆₇	—	2	1	no	—
24	C₂³×Q₈×C₆₇	C₂²	1	2	yes	—
25	C₂³×Q₈×C₆₇	C₂²	1	1	yes	characteristic
26	C₂×#137×C₆₇	—	2	8	no	—
27	C₂×#137×C₆₇	C₂²	1	8	yes	complemented
28	C₂×#135×C₆₇	—	2	8	no	—
29	C₂×#135×C₆₇	C₂²	1	8	yes	complemented
30	C₂²×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic
31	C₂²×Q₁₆×C₆₇	C₂²	1	2	yes	—
32	C₂²×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic
33	C₂²×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic
34	C₂²×SD₁₆×C₆₇	C₂²	1	2	yes	—
35	C₂²×D₈×C₆₇	C₂²	1	1	yes	characteristic
36	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
37	C₂³×C₈×C₆₇	C₂²	1	1	yes	characteristic
38	#537×C₆₇	—	2	4	no	—
39	#537×C₆₇	C₂²	1	8	yes	complemented
40	C₂×C₂²⋊Q₈×C₆₇	—	2	1	no	—
41	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
42	C₂×#121×C₆₇	—	2	1	no	—
43	C₂×#121×C₆₇	—	2	2	no	—
44	C₂×#121×C₆₇	C₂²	1	2	yes	—
45	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
46	#452×C₆₇	C₂²	1	16	yes	complemented
47	#451×C₆₇	C₂²	1	16	yes	complemented
48	#449×C₆₇	C₂²	1	16	yes	complemented
49	#448×C₆₇	C₂²	1	16	yes	complemented
50	#417×C₆₇	C₂²	1	8	yes	complemented
51	C₂×#103×C₆₇	C₂²	1	2	yes	—
52	C₂×#103×C₆₇	C₂²	1	2	yes	—
53	C₂×#103×C₆₇	C₂²	1	2	yes	—
54	C₂×#103×C₆₇	C₂²	1	8	yes	complemented
55	C₂×#102×C₆₇	C₂²	1	2	yes	—
56	#408×C₆₇	C₂²	1	8	yes	complemented
57	C₂×C₂²⋊C₈×C₆₇	C₂²	1	2	yes	—
58	C₂×C₂²⋊C₈×C₆₇	C₂²	1	2	yes	—
59	2₋¹⁺⁴×C₆₇	—	2	64	no	—
60	2₋¹⁺⁴×C₆₇	—	2	32	no	—
61	2₋¹⁺⁴×C₆₇	—	2	32	no	—
62	C₂×#41×C₆₇	—	2	32	no	—
63	C₂×#41×C₆₇	—	2	16	no	—
64	C₂×#41×C₆₇	—	2	8	no	—
65	C₂×#41×C₆₇	—	2	8	no	—
66	C₂×#41×C₆₇	—	2	16	no	—
67	C₂×#41×C₆₇	—	2	8	no	—
68	C₂×#41×C₆₇	—	2	4	no	—
69	C₂×#41×C₆₇	—	2	4	no	—
70	C₂×#41×C₆₇	—	2	2	no	—
71	C₂×#41×C₆₇	—	2	4	no	—
72	C₂×#41×C₆₇	—	2	4	no	—
73	C₂×#41×C₆₇	—	2	2	no	—
74	C₂×#41×C₆₇	—	2	4	no	—
75	C₂×#41×C₆₇	—	2	4	no	—
76	C₂×#41×C₆₇	D₄	1	4	yes	—
77	C₂×#41×C₆₇	D₄	1	8	yes	complemented
78	C₂×#41×C₆₇	C₂³	1	8	yes	—
79	C₂×#41×C₆₇	C₂³	1	4	yes	—
80	C₂×#41×C₆₇	C₂³	1	4	yes	—
81	C₂×#41×C₆₇	C₂³	1	4	yes	—
82	C₂²×Q₈×C₆₇	—	2	16	no	—
83	C₂²×Q₈×C₆₇	—	2	8	no	—
84	C₂²×Q₈×C₆₇	—	2	8	no	—
85	C₂²×Q₈×C₆₇	—	2	8	no	—
86	C₂²×Q₈×C₆₇	—	2	2	no	—
87	C₂²×Q₈×C₆₇	—	2	1	no	—
88	C₂²×Q₈×C₆₇	—	2	4	no	—
89	C₂²×Q₈×C₆₇	—	2	4	no	—
90	C₂²×Q₈×C₆₇	—	2	2	no	—
91	C₂²×Q₈×C₆₇	D₄	1	1	yes	characteristic
92	C₂²×Q₈×C₆₇	D₄	1	8	yes	complemented
93	C₂²×Q₈×C₆₇	C₂³	1	8	yes	—
94	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
95	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
96	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
97	C₂²×Q₈×C₆₇	C₂³	1	4	yes	—
98	C₂²×D₄×C₆₇	—	2	2	no	—
99	C₂²×D₄×C₆₇	—	2	1	no	—
100	C₂²×D₄×C₆₇	—	2	1	no	—
101	C₂²×D₄×C₆₇	—	2	2	no	—
102	C₂²×D₄×C₆₇	D₄	1	2	yes	—
103	C₂²×D₄×C₆₇	D₄	1	1	yes	characteristic
104	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
105	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
106	C₂³×C₄×C₆₇	—	2	2	no	—
107	C₂³×C₄×C₆₇	—	2	1	no	—
108	C₂³×C₄×C₆₇	—	2	2	no	—
109	C₂³×C₄×C₆₇	—	2	1	no	—
110	C₂³×C₄×C₆₇	—	2	1	no	—
111	C₂³×C₄×C₆₇	—	2	1	no	—
112	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
113	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
114	#137×C₆₇	—	2	32	no	—
115	#135×C₆₇	—	2	32	no	—
116	C₂×Q₁₆×C₆₇	—	2	4	no	—
117	C₂×Q₁₆×C₆₇	—	2	8	no	—
118	C₂×Q₁₆×C₆₇	C₂³	1	4	yes	—
119	C₂×Q₁₆×C₆₇	C₂³	1	8	yes	—
120	C₂×SD₁₆×C₆₇	—	2	4	no	—
121	C₂×SD₁₆×C₆₇	—	2	8	no	—
122	C₂×SD₁₆×C₆₇	—	2	4	no	—
123	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
124	C₂×SD₁₆×C₆₇	C₂³	1	8	yes	—
125	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
126	C₂×D₈×C₆₇	—	2	4	no	—
127	C₂×D₈×C₆₇	C₂³	1	4	yes	—
128	C₂×M₁₆×C₆₇	—	2	4	no	—
129	C₂×M₁₆×C₆₇	C₂³	1	4	yes	—
130	C₂²×C₈×C₆₇	—	2	4	no	—
131	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
132	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
133	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
134	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
135	C₂²⋊Q₈×C₆₇	—	2	8	no	—
136	C₂²⋊Q₈×C₆₇	—	2	4	no	—
137	C₂²⋊Q₈×C₆₇	C₂³	1	8	yes	—
138	#121×C₆₇	—	2	8	no	—
139	#121×C₆₇	—	2	16	no	—
140	#121×C₆₇	—	2	4	no	—
141	#121×C₆₇	C₂³	1	8	yes	—
142	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
143	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
144	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
145	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
146	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
147	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
148	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
149	#103×C₆₇	C₂³	1	8	yes	—
150	#103×C₆₇	C₂³	1	8	yes	—
151	#103×C₆₇	C₂³	1	8	yes	—
152	#102×C₆₇	C₂³	1	8	yes	—
153	C₂²⋊C₈×C₆₇	C₂³	1	8	yes	—
154	C₂²⋊C₈×C₆₇	C₂³	1	8	yes	—
155	C₂⁴×C₆₇	—	2	1	no	—
156	C₂⁴×C₆₇	—	2	1	no	—
157	C₂⁴×C₆₇	C₂×D₄	1	2	yes	—
158	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
159	#41×C₆₇	—	2	128	no	—
160	#41×C₆₇	—	2	64	no	—
161	#41×C₆₇	—	2	32	no	—
162	#41×C₆₇	—	2	16	no	—
163	#41×C₆₇	—	2	16	no	—
164	#41×C₆₇	—	2	16	no	—
165	#41×C₆₇	—	2	16	no	—
166	#41×C₆₇	—	2	8	no	—
167	#41×C₆₇	—	2	8	no	—
168	#41×C₆₇	—	2	8	no	—
169	#41×C₆₇	—	2	8	no	—
170	#41×C₆₇	—	2	8	no	—
171	#41×C₆₇	—	4	8	no	—
172	#41×C₆₇	C₂×D₄	1	16	yes	complemented
173	C₂×Q₈×C₆₇	—	2	16	no	—
174	C₂×Q₈×C₆₇	—	2	64	no	—
175	C₂×Q₈×C₆₇	—	2	32	no	—
176	C₂×Q₈×C₆₇	—	2	16	no	—
177	C₂×Q₈×C₆₇	—	2	16	no	—
178	C₂×Q₈×C₆₇	—	2	4	no	—
179	C₂×Q₈×C₆₇	—	2	8	no	—
180	C₂×Q₈×C₆₇	—	2	16	no	—
181	C₂×Q₈×C₆₇	—	2	2	no	—
182	C₂×Q₈×C₆₇	—	2	4	no	—
183	C₂×Q₈×C₆₇	—	2	8	no	—
184	C₂×Q₈×C₆₇	—	2	4	no	—
185	C₂×Q₈×C₆₇	—	2	1	no	—
186	C₂×Q₈×C₆₇	—	2	2	no	—
187	C₂×Q₈×C₆₇	—	2	8	no	—
188	C₂×Q₈×C₆₇	—	2	1	no	—
189	C₂×Q₈×C₆₇	—	2	2	no	—
190	C₂×Q₈×C₆₇	—	2	2	no	—
191	C₂×Q₈×C₆₇	C₂×D₄	1	4	yes	—
192	C₂×Q₈×C₆₇	C₂×D₄	1	8	yes	—
193	C₂×Q₈×C₆₇	C₂×D₄	1	4	yes	—
194	C₂×Q₈×C₆₇	C₂×D₄	1	16	yes	complemented
195	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
196	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
197	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
198	C₂×D₄×C₆₇	—	2	16	no	—
199	C₂×D₄×C₆₇	—	2	8	no	—
200	C₂×D₄×C₆₇	—	2	8	no	—
201	C₂×D₄×C₆₇	—	2	8	no	—
202	C₂×D₄×C₆₇	—	2	4	no	—
203	C₂×D₄×C₆₇	—	2	4	no	—
204	C₂×D₄×C₆₇	—	2	8	no	—
205	C₂×D₄×C₆₇	—	2	4	no	—
206	C₂×D₄×C₆₇	—	2	1	no	—
207	C₂×D₄×C₆₇	—	2	2	no	—
208	C₂×D₄×C₆₇	—	2	2	no	—
209	C₂×D₄×C₆₇	—	2	2	no	—
210	C₂×D₄×C₆₇	—	2	1	no	—
211	C₂×D₄×C₆₇	—	4	4	no	—
212	C₂×D₄×C₆₇	—	8	4	no	—
213	C₂×D₄×C₆₇	C₂×D₄	1	8	yes	—
214	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	—
215	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	—
216	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
217	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
218	C₂²×C₄×C₆₇	—	2	16	no	—
219	C₂²×C₄×C₆₇	—	2	16	no	—
220	C₂²×C₄×C₆₇	—	2	8	no	—
221	C₂²×C₄×C₆₇	—	2	8	no	—
222	C₂²×C₄×C₆₇	—	2	4	no	—
223	C₂²×C₄×C₆₇	—	2	2	no	—
224	C₂²×C₄×C₆₇	—	2	1	no	—
225	C₂²×C₄×C₆₇	—	2	8	no	—
226	C₂²×C₄×C₆₇	—	2	8	no	—
227	C₂²×C₄×C₆₇	—	2	4	no	—
228	C₂²×C₄×C₆₇	—	2	4	no	—
229	C₂²×C₄×C₆₇	—	2	4	no	—
230	C₂²×C₄×C₆₇	—	2	2	no	—
231	C₂²×C₄×C₆₇	—	2	1	no	—
232	C₂²×C₄×C₆₇	—	2	4	no	—
233	C₂²×C₄×C₆₇	—	2	4	no	—
234	C₂²×C₄×C₆₇	—	4	4	no	—
235	C₂²×C₄×C₆₇	—	8	2	no	—
236	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
237	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
238	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
239	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
240	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
241	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
242	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
243	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
244	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
245	Q₁₆×C₆₇	—	2	8	no	—
246	Q₁₆×C₆₇	—	2	16	no	—
247	SD₁₆×C₆₇	—	2	8	no	—
248	SD₁₆×C₆₇	—	2	16	no	—
249	SD₁₆×C₆₇	—	2	8	no	—
250	D₈×C₆₇	—	2	8	no	—
251	M₁₆×C₆₇	—	2	8	no	—
252	C₂×C₈×C₆₇	—	2	2	no	—
253	C₂×C₈×C₆₇	—	2	2	no	—
254	C₂×C₈×C₆₇	—	2	8	no	—
255	C₂×C₈×C₆₇	—	2	4	no	—
256	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
257	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
258	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
259	C₄⋊C₄×C₆₇	—	2	4	no	—
260	C₄⋊C₄×C₆₇	—	2	2	no	—
261	C₄⋊C₄×C₆₇	—	2	8	no	—
262	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
263	C₂²⋊C₄×C₆₇	—	2	8	no	—
264	C₂²⋊C₄×C₆₇	—	2	8	no	—
265	C₂³×C₆₇	—	2	2	no	—
266	C₂³×C₆₇	—	2	2	no	—
267	C₂³×C₆₇	—	2	4	no	—
268	C₂³×C₆₇	—	2	4	no	—
269	C₂³×C₆₇	—	2	4	no	—
270	C₂³×C₆₇	—	2	4	no	—
271	C₂³×C₆₇	—	2	2	no	—
272	C₂³×C₆₇	—	2	2	no	—
273	C₂³×C₆₇	—	4	2	no	—
274	C₂³×C₆₇	—	4	2	no	—
275	C₂³×C₆₇	—	4	2	no	—
276	C₂³×C₆₇	—	4	2	no	—
277	C₂³×C₆₇	—	4	2	no	—
278	C₂³×C₆₇	#120	1	4	yes	—
279	C₂³×C₆₇	C₂²×D₄	1	4	yes	—
280	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
281	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
282	Q₈×C₆₇	—	2	32	no	—
283	Q₈×C₆₇	—	2	4	no	—
284	Q₈×C₆₇	—	2	8	no	—
285	Q₈×C₆₇	—	2	8	no	—
286	Q₈×C₆₇	—	2	16	no	—
287	Q₈×C₆₇	—	2	2	no	—
288	Q₈×C₆₇	—	2	4	no	—
289	Q₈×C₆₇	—	2	2	no	—
290	Q₈×C₆₇	—	2	2	no	—
291	Q₈×C₆₇	—	4	2	no	—
292	Q₈×C₆₇	C₂²×D₄	1	4	yes	—
293	Q₈×C₆₇	C₂²×D₄	1	8	yes	—
294	D₄×C₆₇	—	2	32	no	—
295	D₄×C₆₇	—	2	16	no	—
296	D₄×C₆₇	—	2	16	no	—
297	D₄×C₆₇	—	2	8	no	—
298	D₄×C₆₇	—	2	4	no	—
299	D₄×C₆₇	—	2	2	no	—
300	D₄×C₆₇	—	2	2	no	—
301	D₄×C₆₇	—	2	2	no	—
302	D₄×C₆₇	—	4	8	no	—
303	D₄×C₆₇	—	4	2	no	—
304	D₄×C₆₇	—	8	8	no	—
305	D₄×C₆₇	C₂²×D₄	1	4	yes	—
306	C₂×C₄×C₆₇	—	2	32	no	—
307	C₂×C₄×C₆₇	—	2	32	no	—
308	C₂×C₄×C₆₇	—	2	8	no	—
309	C₂×C₄×C₆₇	—	2	4	no	—
310	C₂×C₄×C₆₇	—	2	4	no	—
311	C₂×C₄×C₆₇	—	2	16	no	—
312	C₂×C₄×C₆₇	—	2	4	no	—
313	C₂×C₄×C₆₇	—	2	2	no	—
314	C₂×C₄×C₆₇	—	2	16	no	—
315	C₂×C₄×C₆₇	—	2	8	no	—
316	C₂×C₄×C₆₇	—	2	4	no	—
317	C₂×C₄×C₆₇	—	2	4	no	—
318	C₂×C₄×C₆₇	—	2	4	no	—
319	C₂×C₄×C₆₇	—	2	2	no	—
320	C₂×C₄×C₆₇	—	4	2	no	—
321	C₂×C₄×C₆₇	—	4	4	no	—
322	C₂×C₄×C₆₇	—	4	8	no	—
323	C₂×C₄×C₆₇	—	8	4	no	—
324	C₂×C₄×C₆₇	#120	1	4	yes	—
325	C₂×C₄×C₆₇	#120	1	8	yes	—
326	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
327	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
328	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
329	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
330	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
331	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
332	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
333	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
334	C₈×C₆₇	—	2	2	no	—
335	C₈×C₆₇	—	2	2	no	—
336	C₈×C₆₇	—	2	4	no	—
337	C₂²×C₆₇	—	2	8	no	—
338	C₂²×C₆₇	—	2	2	no	—
339	C₂²×C₆₇	—	2	2	no	—
340	C₂²×C₆₇	—	2	4	no	—
341	C₂²×C₆₇	—	2	4	no	—
342	C₂²×C₆₇	—	2	4	no	—
343	C₂²×C₆₇	—	2	4	no	—
344	C₂²×C₆₇	—	4	8	no	—
345	C₂²×C₆₇	—	4	8	no	—
346	C₂²×C₆₇	—	4	2	no	—
347	C₂²×C₆₇	—	4	2	no	—
348	C₂²×C₆₇	—	4	2	no	—
349	C₂²×C₆₇	—	4	2	no	—
350	C₂²×C₆₇	—	4	2	no	—
351	C₂²×C₆₇	—	8	4	no	—
352	C₂²×C₆₇	C₂×#120	1	4	yes	—
353	C₂²×C₆₇	C₂×#120	1	2	yes	—
354	C₂²×C₆₇	#577	1	2	yes	—
355	C₂²×C₆₇	#578	1	2	yes	—
356	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
357	C₄×C₆₇	—	2	8	no	—
358	C₄×C₆₇	—	2	4	no	—
359	C₄×C₆₇	—	2	4	no	—
360	C₄×C₆₇	—	4	2	no	—
361	C₄×C₆₇	—	4	4	no	—
362	C₄×C₆₇	C₂×#120	1	4	yes	—
363	C₄×C₆₇	C₂×#120	1	2	yes	—
364	C₄×C₆₇	C₂³×D₄	1	1	yes	characteristic
365	C₄×C₆₇	C₂³×D₄	1	1	yes	characteristic
366	C₂×#3013	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
367	C₂×C₆₇	—	2	4	no	—
368	C₂×C₆₇	—	4	4	no	—
369	C₂×C₆₇	—	4	4	no	—
370	C₂×C₆₇	—	8	2	no	—
371	C₂×C₆₇	#3013	1	4	yes	direct product factor
372	C₂×C₆₇	C₂²×#120	1	1	yes	characteristic
373	C₂×C₆₇	C₂×#577	1	1	yes	characteristic
374	C₂×C₆₇	C₂×#578	1	1	yes	characteristic
375	C₂²×2₋¹⁺⁴	C₂×C₆₇	1	1	yes	characteristic, complemented
376	C₂²×#137	C₂×C₆₇	1	1	yes	characteristic, complemented
377	C₂²×#135	C₂×C₆₇	1	1	yes	characteristic, complemented
378	C₂×#537	C₂×C₆₇	1	1	yes	characteristic, complemented
379	#3013	C₂×C₆₇	1	16	yes	direct product factor
380	C₂×#452	C₂×C₆₇	1	2	yes	complemented
381	C₂×#449	C₂×C₆₇	1	2	yes	complemented
382	C₂×#451	C₂×C₆₇	1	2	yes	complemented
383	C₂×#448	C₂×C₆₇	1	2	yes	complemented
384	C₂×#417	C₂×C₆₇	1	1	yes	characteristic, complemented
385	C₂²×#103	C₂×C₆₇	1	1	yes	characteristic, complemented
386	C₂×#408	C₂×C₆₇	1	1	yes	characteristic, complemented
387	C₆₇	C₂×#3013	1	1	yes	characteristic, direct product factor, Sylow
388	C₂×2₋¹⁺⁴	—	2	4	no	—
389	C₂×2₋¹⁺⁴	—	2	8	no	—
390	C₂×2₋¹⁺⁴	—	2	8	no	—
391	C₂×2₋¹⁺⁴	C₂²×C₆₇	1	8	yes	complemented
392	C₂²×#41	—	2	1	no	—
393	C₂²×#41	—	2	2	no	—
394	C₂²×#41	C₂²×C₆₇	1	2	yes	—
395	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
396	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
397	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
398	C₂³×Q₈	—	2	1	no	—
399	C₂³×Q₈	C₂²×C₆₇	1	2	yes	—
400	C₂³×Q₈	C₂²×C₆₇	1	1	yes	characteristic
401	C₂×#137	—	2	8	no	—
402	C₂×#137	C₂²×C₆₇	1	8	yes	complemented
403	C₂×#135	—	2	8	no	—
404	C₂×#135	C₂²×C₆₇	1	8	yes	complemented
405	C₂²×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic
406	C₂²×Q₁₆	C₂²×C₆₇	1	2	yes	—
407	C₂²×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic
408	C₂²×SD₁₆	C₂²×C₆₇	1	2	yes	—
409	C₂²×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic
410	C₂²×D₈	C₂²×C₆₇	1	1	yes	characteristic
411	C₂²×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
412	C₂³×C₈	C₂²×C₆₇	1	1	yes	characteristic
413	#537	—	2	4	no	—
414	#537	C₂²×C₆₇	1	8	yes	complemented
415	C₂×C₂²⋊Q₈	—	2	1	no	—
416	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
417	C₂×#121	—	2	1	no	—
418	C₂×#121	—	2	2	no	—
419	C₂×#121	C₂²×C₆₇	1	2	yes	—
420	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
421	#452	C₂²×C₆₇	1	16	yes	complemented
422	#451	C₂²×C₆₇	1	16	yes	complemented
423	#449	C₂²×C₆₇	1	16	yes	complemented
424	#448	C₂²×C₆₇	1	16	yes	complemented
425	#417	C₂²×C₆₇	1	8	yes	complemented
426	C₂×#103	C₂²×C₆₇	1	2	yes	—
427	C₂×#103	C₂²×C₆₇	1	2	yes	—
428	C₂×#103	C₂²×C₆₇	1	2	yes	—
429	C₂×#103	C₂²×C₆₇	1	8	yes	complemented
430	C₂×#102	C₂²×C₆₇	1	2	yes	—
431	#408	C₂²×C₆₇	1	8	yes	complemented
432	C₂×C₂²⋊C₈	C₂²×C₆₇	1	2	yes	—
433	C₂×C₂²⋊C₈	C₂²×C₆₇	1	2	yes	—
434	2₋¹⁺⁴	—	2	64	no	—
435	2₋¹⁺⁴	—	2	32	no	—
436	2₋¹⁺⁴	—	2	32	no	—
437	C₂×#41	—	2	32	no	—
438	C₂×#41	—	2	16	no	—
439	C₂×#41	—	2	8	no	—
440	C₂×#41	—	2	8	no	—
441	C₂×#41	—	2	16	no	—
442	C₂×#41	—	2	8	no	—
443	C₂×#41	—	2	4	no	—
444	C₂×#41	—	2	4	no	—
445	C₂×#41	—	2	2	no	—
446	C₂×#41	—	2	4	no	—
447	C₂×#41	—	2	4	no	—
448	C₂×#41	—	2	2	no	—
449	C₂×#41	—	2	4	no	—
450	C₂×#41	—	2	4	no	—
451	C₂×#41	D₄×C₆₇	1	4	yes	—
452	C₂×#41	D₄×C₆₇	1	8	yes	complemented
453	C₂×#41	C₂³×C₆₇	1	4	yes	—
454	C₂×#41	C₂³×C₆₇	1	8	yes	—
455	C₂×#41	C₂³×C₆₇	1	4	yes	—
456	C₂×#41	C₂³×C₆₇	1	4	yes	—
457	C₂²×Q₈	—	2	16	no	—
458	C₂²×Q₈	—	2	8	no	—
459	C₂²×Q₈	—	2	8	no	—
460	C₂²×Q₈	—	2	8	no	—
461	C₂²×Q₈	—	2	2	no	—
462	C₂²×Q₈	—	2	1	no	—
463	C₂²×Q₈	—	2	4	no	—
464	C₂²×Q₈	—	2	4	no	—
465	C₂²×Q₈	—	2	2	no	—
466	C₂²×Q₈	D₄×C₆₇	1	1	yes	characteristic
467	C₂²×Q₈	D₄×C₆₇	1	8	yes	complemented
468	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
469	C₂²×Q₈	C₂³×C₆₇	1	8	yes	—
470	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
471	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
472	C₂²×Q₈	C₂³×C₆₇	1	4	yes	—
473	C₂²×D₄	—	2	2	no	—
474	C₂²×D₄	—	2	1	no	—
475	C₂²×D₄	—	2	1	no	—
476	C₂²×D₄	—	2	2	no	—
477	C₂²×D₄	D₄×C₆₇	1	2	yes	—
478	C₂²×D₄	D₄×C₆₇	1	1	yes	characteristic
479	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
480	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
481	C₂³×C₄	—	2	2	no	—
482	C₂³×C₄	—	2	1	no	—
483	C₂³×C₄	—	2	2	no	—
484	C₂³×C₄	—	2	1	no	—
485	C₂³×C₄	—	2	1	no	—
486	C₂³×C₄	—	2	1	no	—
487	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
488	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
489	#137	—	2	32	no	—
490	#135	—	2	32	no	—
491	C₂×Q₁₆	—	2	4	no	—
492	C₂×Q₁₆	—	2	8	no	—
493	C₂×Q₁₆	C₂³×C₆₇	1	4	yes	—
494	C₂×Q₁₆	C₂³×C₆₇	1	8	yes	—
495	C₂×SD₁₆	—	2	4	no	—
496	C₂×SD₁₆	—	2	8	no	—
497	C₂×SD₁₆	—	2	4	no	—
498	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
499	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
500	C₂×SD₁₆	C₂³×C₆₇	1	8	yes	—
501	C₂×D₈	—	2	4	no	—
502	C₂×D₈	C₂³×C₆₇	1	4	yes	—
503	C₂×M₁₆	—	2	4	no	—
504	C₂×M₁₆	C₂³×C₆₇	1	4	yes	—
505	C₂²×C₈	—	2	4	no	—
506	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
507	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
508	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
509	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
510	C₂²⋊Q₈	—	2	8	no	—
511	C₂²⋊Q₈	—	2	4	no	—
512	C₂²⋊Q₈	C₂³×C₆₇	1	8	yes	—
513	#121	—	2	8	no	—
514	#121	—	2	16	no	—
515	#121	—	2	4	no	—
516	#121	C₂³×C₆₇	1	8	yes	—
517	C₂×C₄⋊C₄	—	2	1	no	—
518	C₂×C₄⋊C₄	—	2	2	no	—
519	C₂×C₄⋊C₄	—	2	2	no	—
520	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
521	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
522	C₂×C₂²⋊C₄	—	2	2	no	—
523	C₂×C₂²⋊C₄	—	2	2	no	—
524	#103	C₂³×C₆₇	1	8	yes	—
525	#103	C₂³×C₆₇	1	8	yes	—
526	#103	C₂³×C₆₇	1	8	yes	—
527	#102	C₂³×C₆₇	1	8	yes	—
528	C₂²⋊C₈	C₂³×C₆₇	1	8	yes	—
529	C₂²⋊C₈	C₂³×C₆₇	1	8	yes	—
530	C₂⁴	—	2	1	no	—
531	C₂⁴	—	2	1	no	—
532	C₂⁴	C₂×D₄×C₆₇	1	2	yes	—
533	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
534	#41	—	2	128	no	—
535	#41	—	2	64	no	—
536	#41	—	2	32	no	—
537	#41	—	2	16	no	—
538	#41	—	2	16	no	—
539	#41	—	2	16	no	—
540	#41	—	2	16	no	—
541	#41	—	2	8	no	—
542	#41	—	2	8	no	—
543	#41	—	2	8	no	—
544	#41	—	2	8	no	—
545	#41	—	2	8	no	—
546	#41	—	4	8	no	—
547	#41	C₂×D₄×C₆₇	1	16	yes	complemented
548	C₂×Q₈	—	2	16	no	—
549	C₂×Q₈	—	2	64	no	—
550	C₂×Q₈	—	2	32	no	—
551	C₂×Q₈	—	2	16	no	—
552	C₂×Q₈	—	2	16	no	—
553	C₂×Q₈	—	2	4	no	—
554	C₂×Q₈	—	2	8	no	—
555	C₂×Q₈	—	2	16	no	—
556	C₂×Q₈	—	2	2	no	—
557	C₂×Q₈	—	2	4	no	—
558	C₂×Q₈	—	2	8	no	—
559	C₂×Q₈	—	2	4	no	—
560	C₂×Q₈	—	2	1	no	—
561	C₂×Q₈	—	2	2	no	—
562	C₂×Q₈	—	2	8	no	—
563	C₂×Q₈	—	2	1	no	—
564	C₂×Q₈	—	2	2	no	—
565	C₂×Q₈	—	2	2	no	—
566	C₂×Q₈	C₂×D₄×C₆₇	1	4	yes	—
567	C₂×Q₈	C₂×D₄×C₆₇	1	8	yes	—
568	C₂×Q₈	C₂×D₄×C₆₇	1	4	yes	—
569	C₂×Q₈	C₂×D₄×C₆₇	1	16	yes	complemented
570	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
571	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
572	C₂×Q₈	C₂⁴×C₆₇	1	4	yes	—
573	C₂×D₄	—	2	16	no	—
574	C₂×D₄	—	2	8	no	—
575	C₂×D₄	—	2	8	no	—
576	C₂×D₄	—	2	8	no	—
577	C₂×D₄	—	2	4	no	—
578	C₂×D₄	—	2	4	no	—
579	C₂×D₄	—	2	8	no	—
580	C₂×D₄	—	2	4	no	—
581	C₂×D₄	—	2	1	no	—
582	C₂×D₄	—	2	2	no	—
583	C₂×D₄	—	2	2	no	—
584	C₂×D₄	—	2	2	no	—
585	C₂×D₄	—	2	1	no	—
586	C₂×D₄	—	4	4	no	—
587	C₂×D₄	—	8	4	no	—
588	C₂×D₄	C₂×D₄×C₆₇	1	8	yes	—
589	C₂×D₄	C₂×D₄×C₆₇	1	4	yes	—
590	C₂×D₄	C₂×D₄×C₆₇	1	4	yes	—
591	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
592	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
593	C₂²×C₄	—	2	16	no	—
594	C₂²×C₄	—	2	16	no	—
595	C₂²×C₄	—	2	8	no	—
596	C₂²×C₄	—	2	2	no	—
597	C₂²×C₄	—	2	1	no	—
598	C₂²×C₄	—	2	8	no	—
599	C₂²×C₄	—	2	4	no	—
600	C₂²×C₄	—	2	8	no	—
601	C₂²×C₄	—	2	8	no	—
602	C₂²×C₄	—	2	4	no	—
603	C₂²×C₄	—	2	4	no	—
604	C₂²×C₄	—	2	4	no	—
605	C₂²×C₄	—	2	2	no	—
606	C₂²×C₄	—	2	1	no	—
607	C₂²×C₄	—	2	4	no	—
608	C₂²×C₄	—	2	4	no	—
609	C₂²×C₄	—	4	4	no	—
610	C₂²×C₄	—	8	2	no	—
611	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
612	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
613	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
614	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
615	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
616	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
617	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
618	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
619	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
620	Q₁₆	—	2	8	no	—
621	Q₁₆	—	2	16	no	—
622	SD₁₆	—	2	8	no	—
623	SD₁₆	—	2	16	no	—
624	SD₁₆	—	2	8	no	—
625	D₈	—	2	8	no	—
626	M₁₆	—	2	8	no	—
627	C₂×C₈	—	2	2	no	—
628	C₂×C₈	—	2	2	no	—
629	C₂×C₈	—	2	8	no	—
630	C₂×C₈	—	2	4	no	—
631	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
632	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
633	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
634	C₄⋊C₄	—	2	4	no	—
635	C₄⋊C₄	—	2	2	no	—
636	C₄⋊C₄	—	2	8	no	—
637	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
638	C₂²⋊C₄	—	2	8	no	—
639	C₂²⋊C₄	—	2	8	no	—
640	C₂³	—	2	2	no	—
641	C₂³	—	2	2	no	—
642	C₂³	—	2	4	no	—
643	C₂³	—	2	4	no	—
644	C₂³	—	2	4	no	—
645	C₂³	—	2	4	no	—
646	C₂³	—	2	2	no	—
647	C₂³	—	2	2	no	—
648	C₂³	—	4	2	no	—
649	C₂³	—	4	2	no	—
650	C₂³	—	4	2	no	—
651	C₂³	—	4	2	no	—
652	C₂³	—	4	2	no	—
653	C₂³	#120×C₆₇	1	4	yes	—
654	C₂³	C₂²×D₄×C₆₇	1	4	yes	—
655	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
656	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
657	Q₈	—	2	32	no	—
658	Q₈	—	2	4	no	—
659	Q₈	—	2	8	no	—
660	Q₈	—	2	8	no	—
661	Q₈	—	2	16	no	—
662	Q₈	—	2	2	no	—
663	Q₈	—	2	4	no	—
664	Q₈	—	2	2	no	—
665	Q₈	—	2	2	no	—
666	Q₈	—	4	2	no	—
667	Q₈	C₂²×D₄×C₆₇	1	4	yes	—
668	Q₈	C₂²×D₄×C₆₇	1	8	yes	—
669	D₄	—	2	32	no	—
670	D₄	—	2	16	no	—
671	D₄	—	2	16	no	—
672	D₄	—	2	8	no	—
673	D₄	—	2	4	no	—
674	D₄	—	2	2	no	—
675	D₄	—	2	2	no	—
676	D₄	—	2	2	no	—
677	D₄	—	4	8	no	—
678	D₄	—	4	2	no	—
679	D₄	—	8	8	no	—
680	D₄	C₂²×D₄×C₆₇	1	4	yes	—
681	C₂×C₄	—	2	32	no	—
682	C₂×C₄	—	2	32	no	—
683	C₂×C₄	—	2	8	no	—
684	C₂×C₄	—	2	4	no	—
685	C₂×C₄	—	2	4	no	—
686	C₂×C₄	—	2	16	no	—
687	C₂×C₄	—	2	4	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	2	16	no	—
690	C₂×C₄	—	2	8	no	—
691	C₂×C₄	—	2	4	no	—
692	C₂×C₄	—	2	4	no	—
693	C₂×C₄	—	2	4	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	4	2	no	—
696	C₂×C₄	—	4	4	no	—
697	C₂×C₄	—	4	8	no	—
698	C₂×C₄	—	8	4	no	—
699	C₂×C₄	#120×C₆₇	1	4	yes	—
700	C₂×C₄	#120×C₆₇	1	8	yes	—
701	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
702	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
703	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
704	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
705	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
706	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
707	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
708	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
709	C₈	—	2	2	no	—
710	C₈	—	2	2	no	—
711	C₈	—	2	4	no	—
712	C₂²	—	2	8	no	—
713	C₂²	—	2	2	no	—
714	C₂²	—	2	2	no	—
715	C₂²	—	2	4	no	—
716	C₂²	—	2	4	no	—
717	C₂²	—	2	4	no	—
718	C₂²	—	2	4	no	—
719	C₂²	—	4	8	no	—
720	C₂²	—	4	8	no	—
721	C₂²	—	4	2	no	—
722	C₂²	—	4	2	no	—
723	C₂²	—	4	2	no	—
724	C₂²	—	4	2	no	—
725	C₂²	—	4	2	no	—
726	C₂²	—	8	4	no	—
727	C₂²	C₂×#120×C₆₇	1	4	yes	—
728	C₂²	C₂×#120×C₆₇	1	2	yes	—
729	C₂²	#577×C₆₇	1	2	yes	—
730	C₂²	#578×C₆₇	1	2	yes	—
731	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
732	C₄	—	2	8	no	—
733	C₄	—	2	4	no	—
734	C₄	—	2	4	no	—
735	C₄	—	4	4	no	—
736	C₄	—	4	2	no	—
737	C₄	C₂×#120×C₆₇	1	4	yes	—
738	C₄	C₂×#120×C₆₇	1	2	yes	—
739	C₄	C₂³×D₄×C₆₇	1	1	yes	characteristic
740	C₄	C₂³×D₄×C₆₇	1	1	yes	characteristic
741	C₂	—	2	4	no	—
742	C₂	—	4	4	no	—
743	C₂	—	4	4	no	—
744	C₂	—	8	2	no	—
745	C₂	C₆₇×#3013	1	4	yes	direct product factor
746	C₂	C₂²×#120×C₆₇	1	1	yes	characteristic
747	C₂	C₂×#577×C₆₇	1	1	yes	characteristic
748	C₂	C₂×#578×C₆₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ C₂²×#41×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×2₋¹⁺⁴×C₆₇	C₂	semidirect
2. C₂²×#137×C₆₇	C₂	semidirect
3. C₂²×#135×C₆₇	C₂	semidirect
4. C₂×#537×C₆₇	C₂	semidirect
5. C₆₇×#3013	C₂	direct (N × H)
6. C₂×#452×C₆₇	C₂	semidirect
7. C₂×#449×C₆₇	C₂	semidirect
8. C₂×#451×C₆₇	C₂	semidirect
9. C₂×#448×C₆₇	C₂	semidirect
10. C₂×#417×C₆₇	C₂	semidirect
11. C₂²×#103×C₆₇	C₂	semidirect
12. C₂×#408×C₆₇	C₂	semidirect
16. C₂×2₋¹⁺⁴×C₆₇	C₂²	semidirect
27. C₂×#137×C₆₇	C₂²	semidirect
29. C₂×#135×C₆₇	C₂²	semidirect
39. #537×C₆₇	C₂²	semidirect
46. #452×C₆₇	C₂²	semidirect
47. #451×C₆₇	C₂²	semidirect
48. #449×C₆₇	C₂²	semidirect
49. #448×C₆₇	C₂²	semidirect
50. #417×C₆₇	C₂²	semidirect
54. C₂×#103×C₆₇	C₂²	semidirect
56. #408×C₆₇	C₂²	semidirect
77. C₂×#41×C₆₇	D₄	semidirect
92. C₂²×Q₈×C₆₇	D₄	semidirect
172. #41×C₆₇	C₂×D₄	semidirect
194. C₂×Q₈×C₆₇	C₂×D₄	semidirect
366. C₂×#3013	C₆₇	direct (N × H)
371. C₂×C₆₇	#3013	direct (N × H)
375. C₂²×2₋¹⁺⁴	C₂×C₆₇	semidirect
376. C₂²×#137	C₂×C₆₇	semidirect
377. C₂²×#135	C₂×C₆₇	semidirect
378. C₂×#537	C₂×C₆₇	semidirect
379. #3013	C₂×C₆₇	direct (N × H)
380. C₂×#452	C₂×C₆₇	semidirect
381. C₂×#449	C₂×C₆₇	semidirect
382. C₂×#451	C₂×C₆₇	semidirect
383. C₂×#448	C₂×C₆₇	semidirect
384. C₂×#417	C₂×C₆₇	semidirect
385. C₂²×#103	C₂×C₆₇	semidirect
386. C₂×#408	C₂×C₆₇	semidirect
387. C₆₇	C₂×#3013	direct (N × H)
391. C₂×2₋¹⁺⁴	C₂²×C₆₇	semidirect
402. C₂×#137	C₂²×C₆₇	semidirect
404. C₂×#135	C₂²×C₆₇	semidirect
414. #537	C₂²×C₆₇	semidirect
421. #452	C₂²×C₆₇	semidirect
422. #451	C₂²×C₆₇	semidirect
423. #449	C₂²×C₆₇	semidirect
424. #448	C₂²×C₆₇	semidirect
425. #417	C₂²×C₆₇	semidirect
429. C₂×#103	C₂²×C₆₇	semidirect
431. #408	C₂²×C₆₇	semidirect
452. C₂×#41	D₄×C₆₇	semidirect
467. C₂²×Q₈	D₄×C₆₇	semidirect
547. #41	C₂×D₄×C₆₇	semidirect
569. C₂×Q₈	C₂×D₄×C₆₇	semidirect
745. C₂	C₆₇×#3013	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×2₋¹⁺⁴×C₆₇	2
C₂²×#137×C₆₇	2
C₂²×#135×C₆₇	2
C₂×#537×C₆₇	2
C₆₇×#3013	2
C₂×#452×C₆₇	2
C₂×#449×C₆₇	2
C₂×#451×C₆₇	2
C₂×#448×C₆₇	2
C₂×#417×C₆₇	2
C₂²×#103×C₆₇	2
C₂×#408×C₆₇	2
C₂×#3013	67

Subgroups — C2×C67×#3013 #30739616

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₇×#3013 #30739616