Subgroups — C₂×C₆₇×#3018 #30739633

Order 17152.

4850 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#585×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#575×C₆₇	C₂	1	2	yes	maximal, complemented
3	C₂×#532×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#3018	C₂	1	16	yes	maximal, direct product factor
5	C₂×#456×C₆₇	C₂	1	2	yes	maximal, complemented
6	C₂×#454×C₆₇	C₂	1	2	yes	maximal, complemented
7	C₂×#455×C₆₇	C₂	1	2	yes	maximal, complemented
8	C₂×#453×C₆₇	C₂	1	2	yes	maximal, complemented
9	C₂²×#104×C₆₇	C₂	1	2	yes	maximal, complemented
10	C₂×#413×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
11	#585×C₆₇	—	2	4	no	—
12	#585×C₆₇	—	2	8	no	—
13	#585×C₆₇	C₂²	1	8	yes	complemented
14	C₂×2₋¹⁺⁴×C₆₇	—	2	2	no	—
15	C₂×2₋¹⁺⁴×C₆₇	C₂²	1	2	yes	—
16	C₂×H(5,𝔽₂)×C₆₇	—	2	2	no	—
17	C₂×H(5,𝔽₂)×C₆₇	—	2	2	no	—
18	C₂×H(5,𝔽₂)×C₆₇	C₂²	1	2	yes	—
19	C₂²×#41×C₆₇	—	2	4	no	—
20	C₂²×#41×C₆₇	—	2	2	no	—
21	C₂²×#41×C₆₇	C₂²	1	2	yes	—
22	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
23	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic, complemented
24	#575×C₆₇	—	2	8	no	—
25	#575×C₆₇	C₂²	1	16	yes	complemented
26	C₂×#137×C₆₇	—	2	2	no	—
27	C₂×#137×C₆₇	C₂²	1	4	yes	complemented
28	C₂×AGL(1,ℤ/8)×C₆₇	—	2	2	no	—
29	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	4	yes	complemented
30	C₂×#135×C₆₇	—	2	4	no	—
31	C₂²×M₁₆×C₆₇	C₂²	1	2	yes	complemented
32	#532×C₆₇	—	2	4	no	—
33	#532×C₆₇	C₂²	1	8	yes	complemented
34	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
35	C₂×#127×C₆₇	C₂²	1	1	yes	characteristic, complemented
36	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic, complemented
37	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic, complemented
38	C₂×#121×C₆₇	—	2	2	no	—
39	C₂×C₄×D₄×C₆₇	—	2	2	no	—
40	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic, complemented
41	#456×C₆₇	C₂²	1	16	yes	complemented
42	#455×C₆₇	C₂²	1	16	yes	complemented
43	#454×C₆₇	C₂²	1	16	yes	complemented
44	#453×C₆₇	C₂²	1	16	yes	complemented
45	C₂×#104×C₆₇	C₂²	1	4	yes	complemented
46	C₂×#104×C₆₇	C₂²	1	4	yes	complemented
47	C₂×#104×C₆₇	C₂²	1	16	yes	complemented
48	#413×C₆₇	C₂²	1	8	yes	complemented
49	C₂×#101×C₆₇	C₂²	1	2	yes	complemented
50	C₂×#100×C₆₇	C₂²	1	2	yes	complemented
51	2₋¹⁺⁴×C₆₇	—	2	16	no	—
52	2₋¹⁺⁴×C₆₇	—	2	8	no	—
53	2₋¹⁺⁴×C₆₇	—	2	4	no	—
54	2₋¹⁺⁴×C₆₇	—	2	16	no	—
55	2₋¹⁺⁴×C₆₇	C₂³	1	8	yes	—
56	H(5,𝔽₂)×C₆₇	—	2	16	no	—
57	H(5,𝔽₂)×C₆₇	—	2	16	no	—
58	H(5,𝔽₂)×C₆₇	—	2	8	no	—
59	H(5,𝔽₂)×C₆₇	—	2	16	no	—
60	H(5,𝔽₂)×C₆₇	—	2	4	no	—
61	H(5,𝔽₂)×C₆₇	—	2	16	no	—
62	H(5,𝔽₂)×C₆₇	C₂³	1	8	yes	—
63	C₂×#41×C₆₇	—	2	4	no	—
64	C₂×#41×C₆₇	—	2	8	no	—
65	C₂×#41×C₆₇	—	2	4	no	—
66	C₂×#41×C₆₇	—	2	32	no	—
67	C₂×#41×C₆₇	—	2	16	no	—
68	C₂×#41×C₆₇	—	2	32	no	—
69	C₂×#41×C₆₇	—	2	4	no	—
70	C₂×#41×C₆₇	—	2	4	no	—
71	C₂×#41×C₆₇	—	2	2	no	—
72	C₂×#41×C₆₇	—	2	2	no	—
73	C₂×#41×C₆₇	—	2	4	no	—
74	C₂×#41×C₆₇	—	2	16	no	—
75	C₂×#41×C₆₇	—	2	2	no	—
76	C₂×#41×C₆₇	—	2	2	no	—
77	C₂×#41×C₆₇	—	2	4	no	—
78	C₂×#41×C₆₇	—	2	4	no	—
79	C₂×#41×C₆₇	—	2	4	no	—
80	C₂×#41×C₆₇	—	2	2	no	—
81	C₂×#41×C₆₇	—	2	2	no	—
82	C₂×#41×C₆₇	—	2	2	no	—
83	C₂×#41×C₆₇	—	2	4	no	—
84	C₂×#41×C₆₇	D₄	1	4	yes	—
85	C₂×#41×C₆₇	D₄	1	4	yes	complemented
86	C₂×#41×C₆₇	D₄	1	8	yes	complemented
87	C₂×#41×C₆₇	C₂³	1	4	yes	—
88	C₂×#41×C₆₇	C₂³	1	8	yes	—
89	C₂×#41×C₆₇	C₂³	1	4	yes	—
90	C₂×#41×C₆₇	C₂³	1	4	yes	complemented
91	C₂²×Q₈×C₆₇	—	2	2	no	—
92	C₂²×Q₈×C₆₇	—	2	4	no	—
93	C₂²×Q₈×C₆₇	D₄	1	2	yes	complemented
94	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
95	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
96	C₂²×D₄×C₆₇	—	2	8	no	—
97	C₂²×D₄×C₆₇	—	2	2	no	—
98	C₂²×D₄×C₆₇	—	2	4	no	—
99	C₂²×D₄×C₆₇	—	2	2	no	—
100	C₂²×D₄×C₆₇	—	2	4	no	—
101	C₂²×D₄×C₆₇	—	2	2	no	—
102	C₂²×D₄×C₆₇	—	2	1	no	—
103	C₂²×D₄×C₆₇	D₄	1	2	yes	—
104	C₂²×D₄×C₆₇	D₄	1	2	yes	complemented
105	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
106	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
107	C₂³×C₄×C₆₇	—	2	4	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	D₄	1	2	yes	—
112	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
113	#137×C₆₇	—	2	8	no	—
114	#137×C₆₇	—	2	16	no	—
115	#137×C₆₇	C₂³	1	16	yes	complemented
116	AGL(1,ℤ/8)×C₆₇	—	2	8	no	—
117	AGL(1,ℤ/8)×C₆₇	—	2	16	no	—
118	AGL(1,ℤ/8)×C₆₇	C₂³	1	16	yes	complemented
119	#135×C₆₇	—	2	32	no	—
120	C₂×Q₁₆×C₆₇	—	2	4	no	—
121	C₂×SD₁₆×C₆₇	—	2	4	no	—
122	C₂×SD₁₆×C₆₇	—	2	4	no	—
123	C₂×D₈×C₆₇	—	2	4	no	—
124	C₂×M₁₆×C₆₇	—	2	2	no	—
125	C₂×M₁₆×C₆₇	—	2	4	no	—
126	C₂×M₁₆×C₆₇	C₂³	1	4	yes	—
127	C₂×M₁₆×C₆₇	C₂³	1	8	yes	complemented
128	C₂²×C₈×C₆₇	—	2	2	no	—
129	C₄⋊Q₈×C₆₇	—	2	2	no	—
130	C₄⋊Q₈×C₆₇	C₂³	1	4	yes	complemented
131	#127×C₆₇	—	2	2	no	—
132	#127×C₆₇	C₂³	1	4	yes	complemented
133	#124×C₆₇	—	2	2	no	—
134	#124×C₆₇	—	2	2	no	—
135	#124×C₆₇	C₂³	1	4	yes	complemented
136	#124×C₆₇	C₂³	1	4	yes	complemented
137	#121×C₆₇	—	2	16	no	—
138	C₄×D₄×C₆₇	—	2	16	no	—
139	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
140	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
141	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
142	C₂×C₄²×C₆₇	—	2	1	no	—
143	C₂×C₄²×C₆₇	—	2	2	no	—
144	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
145	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
146	C₂×C₄²×C₆₇	C₂³	1	4	yes	complemented
147	#104×C₆₇	C₂³	1	16	yes	complemented
148	#104×C₆₇	C₂³	1	16	yes	complemented
149	#101×C₆₇	C₂³	1	8	yes	complemented
150	#100×C₆₇	C₂³	1	8	yes	complemented
151	C₂⁴×C₆₇	—	2	4	no	—
152	C₂⁴×C₆₇	—	2	2	no	—
153	C₂⁴×C₆₇	—	2	1	no	—
154	C₂⁴×C₆₇	C₂×D₄	1	2	yes	—
155	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
156	#41×C₆₇	—	2	32	no	—
157	#41×C₆₇	—	2	64	no	—
158	#41×C₆₇	—	2	16	no	—
159	#41×C₆₇	—	2	16	no	—
160	#41×C₆₇	—	2	16	no	—
161	#41×C₆₇	—	2	32	no	—
162	#41×C₆₇	—	2	16	no	—
163	#41×C₆₇	—	2	16	no	—
164	#41×C₆₇	—	2	8	no	—
165	#41×C₆₇	—	2	8	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	—	2	16	no	—
172	#41×C₆₇	—	2	4	no	—
173	#41×C₆₇	—	2	8	no	—
174	#41×C₆₇	—	2	4	no	—
175	#41×C₆₇	—	2	8	no	—
176	#41×C₆₇	—	2	8	no	—
177	#41×C₆₇	—	2	8	no	—
178	#41×C₆₇	—	4	4	no	—
179	#41×C₆₇	—	4	4	no	—
180	#41×C₆₇	C₂×D₄	1	8	yes	—
181	#41×C₆₇	C₂×D₄	1	16	yes	complemented
182	#41×C₆₇	C₂⁴	1	8	yes	—
183	C₂×Q₈×C₆₇	—	2	4	no	—
184	C₂×Q₈×C₆₇	—	2	16	no	—
185	C₂×Q₈×C₆₇	—	2	16	no	—
186	C₂×Q₈×C₆₇	—	2	16	no	—
187	C₂×Q₈×C₆₇	—	2	2	no	—
188	C₂×Q₈×C₆₇	—	2	4	no	—
189	C₂×Q₈×C₆₇	—	2	2	no	—
190	C₂×Q₈×C₆₇	—	2	2	no	—
191	C₂×Q₈×C₆₇	—	2	1	no	—
192	C₂×Q₈×C₆₇	—	2	2	no	—
193	C₂×Q₈×C₆₇	—	2	2	no	—
194	C₂×Q₈×C₆₇	C₂×D₄	1	4	yes	—
195	C₂×Q₈×C₆₇	C₂×D₄	1	2	yes	—
196	C₂×Q₈×C₆₇	C₂×D₄	1	8	yes	complemented
197	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
198	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
199	C₂×D₄×C₆₇	—	2	8	no	—
200	C₂×D₄×C₆₇	—	2	4	no	—
201	C₂×D₄×C₆₇	—	2	16	no	—
202	C₂×D₄×C₆₇	—	2	64	no	—
203	C₂×D₄×C₆₇	—	2	16	no	—
204	C₂×D₄×C₆₇	—	2	16	no	—
205	C₂×D₄×C₆₇	—	2	4	no	—
206	C₂×D₄×C₆₇	—	2	4	no	—
207	C₂×D₄×C₆₇	—	2	8	no	—
208	C₂×D₄×C₆₇	—	2	4	no	—
209	C₂×D₄×C₆₇	—	2	4	no	—
210	C₂×D₄×C₆₇	—	2	16	no	—
211	C₂×D₄×C₆₇	—	2	8	no	—
212	C₂×D₄×C₆₇	—	2	16	no	—
213	C₂×D₄×C₆₇	—	2	8	no	—
214	C₂×D₄×C₆₇	—	2	4	no	—
215	C₂×D₄×C₆₇	—	2	2	no	—
216	C₂×D₄×C₆₇	—	2	4	no	—
217	C₂×D₄×C₆₇	—	2	2	no	—
218	C₂×D₄×C₆₇	—	2	2	no	—
219	C₂×D₄×C₆₇	—	2	2	no	—
220	C₂×D₄×C₆₇	—	2	2	no	—
221	C₂×D₄×C₆₇	—	2	1	no	—
222	C₂×D₄×C₆₇	—	4	8	no	—
223	C₂×D₄×C₆₇	—	4	2	no	—
224	C₂×D₄×C₆₇	—	4	2	no	—
225	C₂×D₄×C₆₇	C₂×D₄	1	8	yes	—
226	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
227	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	—
228	C₂×D₄×C₆₇	C₂×D₄	1	8	yes	complemented
229	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
230	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
231	C₂²×C₄×C₆₇	—	2	4	no	—
232	C₂²×C₄×C₆₇	—	2	8	no	—
233	C₂²×C₄×C₆₇	—	2	32	no	—
234	C₂²×C₄×C₆₇	—	2	2	no	—
235	C₂²×C₄×C₆₇	—	2	1	no	—
236	C₂²×C₄×C₆₇	—	2	8	no	—
237	C₂²×C₄×C₆₇	—	2	2	no	—
238	C₂²×C₄×C₆₇	—	2	4	no	—
239	C₂²×C₄×C₆₇	—	2	4	no	—
240	C₂²×C₄×C₆₇	—	2	2	no	—
241	C₂²×C₄×C₆₇	—	2	4	no	—
242	C₂²×C₄×C₆₇	—	2	8	no	—
243	C₂²×C₄×C₆₇	—	2	1	no	—
244	C₂²×C₄×C₆₇	—	2	4	no	—
245	C₂²×C₄×C₆₇	—	2	1	no	—
246	C₂²×C₄×C₆₇	—	2	4	no	—
247	C₂²×C₄×C₆₇	—	4	4	no	—
248	C₂²×C₄×C₆₇	—	4	1	no	—
249	C₂²×C₄×C₆₇	—	4	2	no	—
250	C₂²×C₄×C₆₇	—	4	1	no	—
251	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
252	C₂²×C₄×C₆₇	C₂×D₄	1	8	yes	—
253	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
254	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
255	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
256	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
257	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
258	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
259	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
260	Q₁₆×C₆₇	—	2	16	no	—
261	SD₁₆×C₆₇	—	2	16	no	—
262	SD₁₆×C₆₇	—	2	16	no	—
263	D₈×C₆₇	—	2	16	no	—
264	M₁₆×C₆₇	—	2	4	no	—
265	M₁₆×C₆₇	—	2	8	no	—
266	M₁₆×C₆₇	C₂⁴	1	8	yes	—
267	C₂×C₈×C₆₇	—	2	4	no	—
268	C₂×C₈×C₆₇	—	2	8	no	—
269	C₄⋊C₄×C₆₇	—	2	8	no	—
270	C₂²⋊C₄×C₆₇	—	2	8	no	—
271	C₂²⋊C₄×C₆₇	—	2	8	no	—
272	C₄²×C₆₇	—	2	1	no	—
273	C₄²×C₆₇	—	2	1	no	—
274	C₄²×C₆₇	—	2	4	no	—
275	C₄²×C₆₇	C₂⁴	1	2	yes	—
276	C₄²×C₆₇	C₂⁴	1	2	yes	—
277	C₂³×C₆₇	—	2	16	no	—
278	C₂³×C₆₇	—	2	2	no	—
279	C₂³×C₆₇	—	2	4	no	—
280	C₂³×C₆₇	—	2	2	no	—
281	C₂³×C₆₇	—	2	8	no	—
282	C₂³×C₆₇	—	2	2	no	—
283	C₂³×C₆₇	—	4	2	no	—
284	C₂³×C₆₇	—	4	4	no	—
285	C₂³×C₆₇	—	4	4	no	—
286	C₂³×C₆₇	—	4	1	no	—
287	C₂³×C₆₇	—	4	1	no	—
288	C₂³×C₆₇	—	8	4	no	—
289	C₂³×C₆₇	—	8	8	no	—
290	C₂³×C₆₇	#120	1	2	yes	—
291	C₂³×C₆₇	#120	1	2	yes	—
292	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
293	C₂³×C₆₇	C₂²×D₄	1	4	yes	—
294	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
295	Q₈×C₆₇	—	2	16	no	—
296	Q₈×C₆₇	—	2	4	no	—
297	Q₈×C₆₇	—	2	4	no	—
298	Q₈×C₆₇	—	2	8	no	—
299	Q₈×C₆₇	—	2	4	no	—
300	Q₈×C₆₇	—	2	4	no	—
301	Q₈×C₆₇	—	4	2	no	—
302	Q₈×C₆₇	C₂²×D₄	1	8	yes	—
303	D₄×C₆₇	—	2	32	no	—
304	D₄×C₆₇	—	2	16	no	—
305	D₄×C₆₇	—	2	8	no	—
306	D₄×C₆₇	—	2	16	no	—
307	D₄×C₆₇	—	2	16	no	—
308	D₄×C₆₇	—	2	8	no	—
309	D₄×C₆₇	—	2	4	no	—
310	D₄×C₆₇	—	2	4	no	—
311	D₄×C₆₇	—	2	8	no	—
312	D₄×C₆₇	—	2	4	no	—
313	D₄×C₆₇	—	2	4	no	—
314	D₄×C₆₇	—	4	16	no	—
315	D₄×C₆₇	—	4	8	no	—
316	D₄×C₆₇	—	4	2	no	—
317	D₄×C₆₇	C₂²×D₄	1	8	yes	—
318	C₂×C₄×C₆₇	—	2	16	no	—
319	C₂×C₄×C₆₇	—	2	32	no	—
320	C₂×C₄×C₆₇	—	2	4	no	—
321	C₂×C₄×C₆₇	—	2	4	no	—
322	C₂×C₄×C₆₇	—	2	2	no	—
323	C₂×C₄×C₆₇	—	2	8	no	—
324	C₂×C₄×C₆₇	—	2	2	no	—
325	C₂×C₄×C₆₇	—	2	2	no	—
326	C₂×C₄×C₆₇	—	2	16	no	—
327	C₂×C₄×C₆₇	—	2	8	no	—
328	C₂×C₄×C₆₇	—	2	8	no	—
329	C₂×C₄×C₆₇	—	2	8	no	—
330	C₂×C₄×C₆₇	—	2	8	no	—
331	C₂×C₄×C₆₇	—	2	2	no	—
332	C₂×C₄×C₆₇	—	2	2	no	—
333	C₂×C₄×C₆₇	—	4	8	no	—
334	C₂×C₄×C₆₇	—	4	2	no	—
335	C₂×C₄×C₆₇	—	4	1	no	—
336	C₂×C₄×C₆₇	—	4	1	no	—
337	C₂×C₄×C₆₇	—	4	4	no	—
338	C₂×C₄×C₆₇	—	4	4	no	—
339	C₂×C₄×C₆₇	#120	1	1	yes	characteristic
340	C₂×C₄×C₆₇	#120	1	2	yes	—
341	C₂×C₄×C₆₇	#120	1	4	yes	—
342	C₂×C₄×C₆₇	#120	1	4	yes	—
343	C₂×C₄×C₆₇	#120	1	1	yes	characteristic
344	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
345	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
346	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
347	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
348	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
349	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
350	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
351	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
352	C₈×C₆₇	—	2	8	no	—
353	C₂²×C₆₇	—	2	2	no	—
354	C₂²×C₆₇	—	2	4	no	—
355	C₂²×C₆₇	—	2	4	no	—
356	C₂²×C₆₇	—	2	8	no	—
357	C₂²×C₆₇	—	4	2	no	—
358	C₂²×C₆₇	—	4	2	no	—
359	C₂²×C₆₇	—	4	4	no	—
360	C₂²×C₆₇	—	4	4	no	—
361	C₂²×C₆₇	—	4	4	no	—
362	C₂²×C₆₇	—	4	8	no	—
363	C₂²×C₆₇	—	4	2	no	—
364	C₂²×C₆₇	—	8	2	no	—
365	C₂²×C₆₇	—	8	8	no	—
366	C₂²×C₆₇	—	8	2	no	—
367	C₂²×C₆₇	—	8	16	no	—
368	C₂²×C₆₇	—	8	2	no	—
369	C₂²×C₆₇	C₂×#120	1	1	yes	characteristic
370	C₂²×C₆₇	C₂×#120	1	4	yes	—
371	C₂²×C₆₇	C₂×#120	1	1	yes	characteristic
372	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
373	C₄×C₆₇	—	2	4	no	—
374	C₄×C₆₇	—	2	8	no	—
375	C₄×C₆₇	—	2	4	no	—
376	C₄×C₆₇	—	4	2	no	—
377	C₄×C₆₇	—	4	2	no	—
378	C₄×C₆₇	C₂×#120	1	2	yes	—
379	C₄×C₆₇	C₂×#120	1	2	yes	—
380	C₄×C₆₇	C₂×#120	1	2	yes	—
381	C₄×C₆₇	C₂³×D₄	1	2	yes	—
382	C₂×#3018	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
383	C₂×C₆₇	—	2	1	no	—
384	C₂×C₆₇	—	2	1	no	—
385	C₂×C₆₇	—	2	4	no	—
386	C₂×C₆₇	—	4	4	no	—
387	C₂×C₆₇	—	4	8	no	—
388	C₂×C₆₇	—	8	2	no	—
389	C₂×C₆₇	#3018	1	2	yes	direct product factor
390	C₂×C₆₇	C₂²×#120	1	1	yes	characteristic
391	C₂×#585	C₂×C₆₇	1	1	yes	characteristic, complemented
392	C₂×#575	C₂×C₆₇	1	2	yes	complemented
393	C₂×#532	C₂×C₆₇	1	1	yes	characteristic, complemented
394	#3018	C₂×C₆₇	1	16	yes	direct product factor
395	C₂×#456	C₂×C₆₇	1	2	yes	complemented
396	C₂×#454	C₂×C₆₇	1	2	yes	complemented
397	C₂×#455	C₂×C₆₇	1	2	yes	complemented
398	C₂×#453	C₂×C₆₇	1	2	yes	complemented
399	C₂²×#104	C₂×C₆₇	1	2	yes	complemented
400	C₂×#413	C₂×C₆₇	1	1	yes	characteristic, complemented
401	C₆₇	C₂×#3018	1	1	yes	characteristic, direct product factor, Sylow
402	#585	—	2	4	no	—
403	#585	—	2	8	no	—
404	#585	C₂²×C₆₇	1	8	yes	complemented
405	C₂×2₋¹⁺⁴	—	2	2	no	—
406	C₂×2₋¹⁺⁴	C₂²×C₆₇	1	2	yes	—
407	C₂×H(5,𝔽₂)	—	2	2	no	—
408	C₂×H(5,𝔽₂)	—	2	2	no	—
409	C₂×H(5,𝔽₂)	C₂²×C₆₇	1	2	yes	—
410	C₂²×#41	—	2	4	no	—
411	C₂²×#41	—	2	2	no	—
412	C₂²×#41	C₂²×C₆₇	1	2	yes	—
413	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
414	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic, complemented
415	#575	—	2	8	no	—
416	#575	C₂²×C₆₇	1	16	yes	complemented
417	C₂×#137	—	2	2	no	—
418	C₂×#137	C₂²×C₆₇	1	4	yes	complemented
419	C₂×AGL(1,ℤ/8)	—	2	2	no	—
420	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	4	yes	complemented
421	C₂×#135	—	2	4	no	—
422	C₂²×M₁₆	C₂²×C₆₇	1	2	yes	complemented
423	#532	—	2	4	no	—
424	#532	C₂²×C₆₇	1	8	yes	complemented
425	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
426	C₂×#127	C₂²×C₆₇	1	1	yes	characteristic, complemented
427	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic, complemented
428	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic, complemented
429	C₂×#121	—	2	2	no	—
430	C₂×C₄×D₄	—	2	2	no	—
431	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic, complemented
432	#456	C₂²×C₆₇	1	16	yes	complemented
433	#455	C₂²×C₆₇	1	16	yes	complemented
434	#454	C₂²×C₆₇	1	16	yes	complemented
435	#453	C₂²×C₆₇	1	16	yes	complemented
436	C₂×#104	C₂²×C₆₇	1	4	yes	complemented
437	C₂×#104	C₂²×C₆₇	1	4	yes	complemented
438	C₂×#104	C₂²×C₆₇	1	16	yes	complemented
439	#413	C₂²×C₆₇	1	8	yes	complemented
440	C₂×#101	C₂²×C₆₇	1	2	yes	complemented
441	C₂×#100	C₂²×C₆₇	1	2	yes	complemented
442	2₋¹⁺⁴	—	2	16	no	—
443	2₋¹⁺⁴	—	2	8	no	—
444	2₋¹⁺⁴	—	2	4	no	—
445	2₋¹⁺⁴	—	2	16	no	—
446	2₋¹⁺⁴	C₂³×C₆₇	1	8	yes	—
447	H(5,𝔽₂)	—	2	16	no	—
448	H(5,𝔽₂)	—	2	16	no	—
449	H(5,𝔽₂)	—	2	8	no	—
450	H(5,𝔽₂)	—	2	16	no	—
451	H(5,𝔽₂)	—	2	4	no	—
452	H(5,𝔽₂)	—	2	16	no	—
453	H(5,𝔽₂)	C₂³×C₆₇	1	8	yes	—
454	C₂×#41	—	2	4	no	—
455	C₂×#41	—	2	8	no	—
456	C₂×#41	—	2	4	no	—
457	C₂×#41	—	2	32	no	—
458	C₂×#41	—	2	16	no	—
459	C₂×#41	—	2	32	no	—
460	C₂×#41	—	2	4	no	—
461	C₂×#41	—	2	4	no	—
462	C₂×#41	—	2	2	no	—
463	C₂×#41	—	2	2	no	—
464	C₂×#41	—	2	4	no	—
465	C₂×#41	—	2	16	no	—
466	C₂×#41	—	2	2	no	—
467	C₂×#41	—	2	2	no	—
468	C₂×#41	—	2	4	no	—
469	C₂×#41	—	2	4	no	—
470	C₂×#41	—	2	4	no	—
471	C₂×#41	—	2	2	no	—
472	C₂×#41	—	2	2	no	—
473	C₂×#41	—	2	2	no	—
474	C₂×#41	—	2	4	no	—
475	C₂×#41	D₄×C₆₇	1	4	yes	—
476	C₂×#41	D₄×C₆₇	1	4	yes	complemented
477	C₂×#41	D₄×C₆₇	1	8	yes	complemented
478	C₂×#41	C₂³×C₆₇	1	4	yes	—
479	C₂×#41	C₂³×C₆₇	1	8	yes	—
480	C₂×#41	C₂³×C₆₇	1	4	yes	—
481	C₂×#41	C₂³×C₆₇	1	4	yes	complemented
482	C₂²×Q₈	—	2	2	no	—
483	C₂²×Q₈	—	2	4	no	—
484	C₂²×Q₈	D₄×C₆₇	1	2	yes	complemented
485	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
486	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
487	C₂²×D₄	—	2	8	no	—
488	C₂²×D₄	—	2	2	no	—
489	C₂²×D₄	—	2	4	no	—
490	C₂²×D₄	—	2	2	no	—
491	C₂²×D₄	—	2	4	no	—
492	C₂²×D₄	—	2	2	no	—
493	C₂²×D₄	—	2	1	no	—
494	C₂²×D₄	D₄×C₆₇	1	2	yes	—
495	C₂²×D₄	D₄×C₆₇	1	2	yes	complemented
496	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
497	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
498	C₂³×C₄	—	2	4	no	—
499	C₂³×C₄	—	2	2	no	—
500	C₂³×C₄	—	2	1	no	—
501	C₂³×C₄	—	2	1	no	—
502	C₂³×C₄	D₄×C₆₇	1	2	yes	—
503	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
504	#137	—	2	8	no	—
505	#137	—	2	16	no	—
506	#137	C₂³×C₆₇	1	16	yes	complemented
507	AGL(1,ℤ/8)	—	2	8	no	—
508	AGL(1,ℤ/8)	—	2	16	no	—
509	AGL(1,ℤ/8)	C₂³×C₆₇	1	16	yes	complemented
510	#135	—	2	32	no	—
511	C₂×Q₁₆	—	2	4	no	—
512	C₂×SD₁₆	—	2	4	no	—
513	C₂×SD₁₆	—	2	4	no	—
514	C₂×D₈	—	2	4	no	—
515	C₂×M₁₆	—	2	2	no	—
516	C₂×M₁₆	—	2	4	no	—
517	C₂×M₁₆	C₂³×C₆₇	1	4	yes	—
518	C₂×M₁₆	C₂³×C₆₇	1	8	yes	complemented
519	C₂²×C₈	—	2	2	no	—
520	C₄⋊Q₈	—	2	2	no	—
521	C₄⋊Q₈	C₂³×C₆₇	1	4	yes	complemented
522	#127	—	2	2	no	—
523	#127	C₂³×C₆₇	1	4	yes	complemented
524	#124	—	2	2	no	—
525	#124	—	2	2	no	—
526	#124	C₂³×C₆₇	1	4	yes	complemented
527	#124	C₂³×C₆₇	1	4	yes	complemented
528	#121	—	2	16	no	—
529	C₄×D₄	—	2	16	no	—
530	C₂×C₄⋊C₄	—	2	2	no	—
531	C₂×C₂²⋊C₄	—	2	2	no	—
532	C₂×C₂²⋊C₄	—	2	2	no	—
533	C₂×C₄²	—	2	1	no	—
534	C₂×C₄²	—	2	2	no	—
535	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
536	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
537	C₂×C₄²	C₂³×C₆₇	1	4	yes	complemented
538	#104	C₂³×C₆₇	1	16	yes	complemented
539	#104	C₂³×C₆₇	1	16	yes	complemented
540	#101	C₂³×C₆₇	1	8	yes	complemented
541	#100	C₂³×C₆₇	1	8	yes	complemented
542	C₂⁴	—	2	4	no	—
543	C₂⁴	—	2	2	no	—
544	C₂⁴	—	2	1	no	—
545	C₂⁴	C₂×D₄×C₆₇	1	2	yes	—
546	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
547	#41	—	2	32	no	—
548	#41	—	2	64	no	—
549	#41	—	2	16	no	—
550	#41	—	2	16	no	—
551	#41	—	2	16	no	—
552	#41	—	2	32	no	—
553	#41	—	2	16	no	—
554	#41	—	2	16	no	—
555	#41	—	2	8	no	—
556	#41	—	2	8	no	—
557	#41	—	2	8	no	—
558	#41	—	2	8	no	—
559	#41	—	2	8	no	—
560	#41	—	2	8	no	—
561	#41	—	2	8	no	—
562	#41	—	2	16	no	—
563	#41	—	2	4	no	—
564	#41	—	2	8	no	—
565	#41	—	2	4	no	—
566	#41	—	2	8	no	—
567	#41	—	2	8	no	—
568	#41	—	2	8	no	—
569	#41	—	4	4	no	—
570	#41	—	4	4	no	—
571	#41	C₂×D₄×C₆₇	1	8	yes	—
572	#41	C₂×D₄×C₆₇	1	16	yes	complemented
573	#41	C₂⁴×C₆₇	1	8	yes	—
574	C₂×Q₈	—	2	4	no	—
575	C₂×Q₈	—	2	16	no	—
576	C₂×Q₈	—	2	16	no	—
577	C₂×Q₈	—	2	16	no	—
578	C₂×Q₈	—	2	2	no	—
579	C₂×Q₈	—	2	4	no	—
580	C₂×Q₈	—	2	2	no	—
581	C₂×Q₈	—	2	2	no	—
582	C₂×Q₈	—	2	1	no	—
583	C₂×Q₈	—	2	2	no	—
584	C₂×Q₈	—	2	2	no	—
585	C₂×Q₈	C₂×D₄×C₆₇	1	4	yes	—
586	C₂×Q₈	C₂×D₄×C₆₇	1	2	yes	—
587	C₂×Q₈	C₂×D₄×C₆₇	1	8	yes	complemented
588	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
589	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
590	C₂×D₄	—	2	8	no	—
591	C₂×D₄	—	2	4	no	—
592	C₂×D₄	—	2	16	no	—
593	C₂×D₄	—	2	64	no	—
594	C₂×D₄	—	2	16	no	—
595	C₂×D₄	—	2	16	no	—
596	C₂×D₄	—	2	4	no	—
597	C₂×D₄	—	2	4	no	—
598	C₂×D₄	—	2	8	no	—
599	C₂×D₄	—	2	4	no	—
600	C₂×D₄	—	2	4	no	—
601	C₂×D₄	—	2	16	no	—
602	C₂×D₄	—	2	8	no	—
603	C₂×D₄	—	2	16	no	—
604	C₂×D₄	—	2	8	no	—
605	C₂×D₄	—	2	4	no	—
606	C₂×D₄	—	2	2	no	—
607	C₂×D₄	—	2	4	no	—
608	C₂×D₄	—	2	2	no	—
609	C₂×D₄	—	2	2	no	—
610	C₂×D₄	—	2	2	no	—
611	C₂×D₄	—	2	2	no	—
612	C₂×D₄	—	2	1	no	—
613	C₂×D₄	—	4	8	no	—
614	C₂×D₄	—	4	2	no	—
615	C₂×D₄	—	4	2	no	—
616	C₂×D₄	C₂×D₄×C₆₇	1	8	yes	—
617	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
618	C₂×D₄	C₂×D₄×C₆₇	1	4	yes	—
619	C₂×D₄	C₂×D₄×C₆₇	1	8	yes	complemented
620	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
621	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
622	C₂²×C₄	—	2	4	no	—
623	C₂²×C₄	—	2	8	no	—
624	C₂²×C₄	—	2	32	no	—
625	C₂²×C₄	—	2	2	no	—
626	C₂²×C₄	—	2	1	no	—
627	C₂²×C₄	—	2	4	no	—
628	C₂²×C₄	—	2	2	no	—
629	C₂²×C₄	—	2	8	no	—
630	C₂²×C₄	—	2	2	no	—
631	C₂²×C₄	—	2	4	no	—
632	C₂²×C₄	—	2	4	no	—
633	C₂²×C₄	—	2	8	no	—
634	C₂²×C₄	—	2	1	no	—
635	C₂²×C₄	—	2	4	no	—
636	C₂²×C₄	—	2	1	no	—
637	C₂²×C₄	—	2	4	no	—
638	C₂²×C₄	—	4	4	no	—
639	C₂²×C₄	—	4	1	no	—
640	C₂²×C₄	—	4	1	no	—
641	C₂²×C₄	—	4	2	no	—
642	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
643	C₂²×C₄	C₂×D₄×C₆₇	1	8	yes	—
644	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
645	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
646	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
647	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
648	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
649	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
650	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
651	Q₁₆	—	2	16	no	—
652	SD₁₆	—	2	16	no	—
653	SD₁₆	—	2	16	no	—
654	D₈	—	2	16	no	—
655	M₁₆	—	2	4	no	—
656	M₁₆	—	2	8	no	—
657	M₁₆	C₂⁴×C₆₇	1	8	yes	—
658	C₂×C₈	—	2	4	no	—
659	C₂×C₈	—	2	8	no	—
660	C₄⋊C₄	—	2	8	no	—
661	C₂²⋊C₄	—	2	8	no	—
662	C₂²⋊C₄	—	2	8	no	—
663	C₄²	—	2	1	no	—
664	C₄²	—	2	1	no	—
665	C₄²	—	2	4	no	—
666	C₄²	C₂⁴×C₆₇	1	2	yes	—
667	C₄²	C₂⁴×C₆₇	1	2	yes	—
668	C₂³	—	2	16	no	—
669	C₂³	—	2	2	no	—
670	C₂³	—	2	4	no	—
671	C₂³	—	2	2	no	—
672	C₂³	—	2	8	no	—
673	C₂³	—	2	2	no	—
674	C₂³	—	4	2	no	—
675	C₂³	—	4	4	no	—
676	C₂³	—	4	4	no	—
677	C₂³	—	4	1	no	—
678	C₂³	—	4	1	no	—
679	C₂³	—	8	4	no	—
680	C₂³	—	8	8	no	—
681	C₂³	#120×C₆₇	1	2	yes	—
682	C₂³	#120×C₆₇	1	2	yes	—
683	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
684	C₂³	C₂²×D₄×C₆₇	1	4	yes	—
685	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
686	Q₈	—	2	16	no	—
687	Q₈	—	2	4	no	—
688	Q₈	—	2	4	no	—
689	Q₈	—	2	8	no	—
690	Q₈	—	2	4	no	—
691	Q₈	—	2	4	no	—
692	Q₈	—	4	2	no	—
693	Q₈	C₂²×D₄×C₆₇	1	8	yes	—
694	D₄	—	2	32	no	—
695	D₄	—	2	16	no	—
696	D₄	—	2	8	no	—
697	D₄	—	2	16	no	—
698	D₄	—	2	16	no	—
699	D₄	—	2	8	no	—
700	D₄	—	2	4	no	—
701	D₄	—	2	4	no	—
702	D₄	—	2	8	no	—
703	D₄	—	2	4	no	—
704	D₄	—	2	4	no	—
705	D₄	—	4	16	no	—
706	D₄	—	4	8	no	—
707	D₄	—	4	2	no	—
708	D₄	C₂²×D₄×C₆₇	1	8	yes	—
709	C₂×C₄	—	2	16	no	—
710	C₂×C₄	—	2	32	no	—
711	C₂×C₄	—	2	4	no	—
712	C₂×C₄	—	2	4	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	8	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	16	no	—
718	C₂×C₄	—	2	8	no	—
719	C₂×C₄	—	2	8	no	—
720	C₂×C₄	—	2	8	no	—
721	C₂×C₄	—	2	8	no	—
722	C₂×C₄	—	2	2	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	4	8	no	—
725	C₂×C₄	—	4	2	no	—
726	C₂×C₄	—	4	1	no	—
727	C₂×C₄	—	4	1	no	—
728	C₂×C₄	—	4	4	no	—
729	C₂×C₄	—	4	4	no	—
730	C₂×C₄	#120×C₆₇	1	1	yes	characteristic
731	C₂×C₄	#120×C₆₇	1	1	yes	characteristic
732	C₂×C₄	#120×C₆₇	1	2	yes	—
733	C₂×C₄	#120×C₆₇	1	4	yes	—
734	C₂×C₄	#120×C₆₇	1	4	yes	—
735	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
736	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
737	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
738	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
739	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
740	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
741	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
742	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
743	C₈	—	2	8	no	—
744	C₂²	—	2	2	no	—
745	C₂²	—	2	4	no	—
746	C₂²	—	2	4	no	—
747	C₂²	—	2	8	no	—
748	C₂²	—	4	2	no	—
749	C₂²	—	4	2	no	—
750	C₂²	—	4	4	no	—
751	C₂²	—	4	4	no	—
752	C₂²	—	4	4	no	—
753	C₂²	—	4	8	no	—
754	C₂²	—	4	2	no	—
755	C₂²	—	8	2	no	—
756	C₂²	—	8	8	no	—
757	C₂²	—	8	2	no	—
758	C₂²	—	8	16	no	—
759	C₂²	—	8	2	no	—
760	C₂²	C₂×#120×C₆₇	1	1	yes	characteristic
761	C₂²	C₂×#120×C₆₇	1	4	yes	—
762	C₂²	C₂×#120×C₆₇	1	1	yes	characteristic
763	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
764	C₄	—	2	4	no	—
765	C₄	—	2	8	no	—
766	C₄	—	2	4	no	—
767	C₄	—	4	2	no	—
768	C₄	—	4	2	no	—
769	C₄	C₂×#120×C₆₇	1	2	yes	—
770	C₄	C₂×#120×C₆₇	1	2	yes	—
771	C₄	C₂×#120×C₆₇	1	2	yes	—
772	C₄	C₂³×D₄×C₆₇	1	2	yes	—
773	C₂	—	2	1	no	—
774	C₂	—	2	1	no	—
775	C₂	—	2	4	no	—
776	C₂	—	4	4	no	—
777	C₂	—	4	8	no	—
778	C₂	—	8	2	no	—
779	C₂	C₆₇×#3018	1	2	yes	direct product factor
780	C₂	C₂²×#120×C₆₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₆₇	#120
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
socle	C₂²×C₆₇	C₂×#120
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₆₇ ◁ C₂³×C₄×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#585×C₆₇	C₂	semidirect
2. C₂×#575×C₆₇	C₂	semidirect
3. C₂×#532×C₆₇	C₂	semidirect
4. C₆₇×#3018	C₂	direct (N × H)
5. C₂×#456×C₆₇	C₂	semidirect
6. C₂×#454×C₆₇	C₂	semidirect
7. C₂×#455×C₆₇	C₂	semidirect
8. C₂×#453×C₆₇	C₂	semidirect
9. C₂²×#104×C₆₇	C₂	semidirect
10. C₂×#413×C₆₇	C₂	semidirect
13. #585×C₆₇	C₂²	semidirect
23. C₂²×#41×C₆₇	C₂²	semidirect
25. #575×C₆₇	C₂²	semidirect
27. C₂×#137×C₆₇	C₂²	semidirect
29. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
31. C₂²×M₁₆×C₆₇	C₂²	semidirect
33. #532×C₆₇	C₂²	semidirect
34. C₂×C₄⋊Q₈×C₆₇	C₂²	semidirect
35. C₂×#127×C₆₇	C₂²	semidirect
36. C₂×#124×C₆₇	C₂²	semidirect
37. C₂×#124×C₆₇	C₂²	semidirect
40. C₂²×C₄²×C₆₇	C₂²	semidirect
41. #456×C₆₇	C₂²	semidirect
42. #455×C₆₇	C₂²	semidirect
43. #454×C₆₇	C₂²	semidirect
44. #453×C₆₇	C₂²	semidirect
45. C₂×#104×C₆₇	C₂²	semidirect
46. C₂×#104×C₆₇	C₂²	semidirect
47. C₂×#104×C₆₇	C₂²	semidirect
48. #413×C₆₇	C₂²	semidirect
49. C₂×#101×C₆₇	C₂²	semidirect
50. C₂×#100×C₆₇	C₂²	semidirect
85. C₂×#41×C₆₇	D₄	semidirect
86. C₂×#41×C₆₇	D₄	semidirect
90. C₂×#41×C₆₇	C₂³	semidirect
93. C₂²×Q₈×C₆₇	D₄	semidirect
104. C₂²×D₄×C₆₇	D₄	semidirect
115. #137×C₆₇	C₂³	semidirect
118. AGL(1,ℤ/8)×C₆₇	C₂³	semidirect
127. C₂×M₁₆×C₆₇	C₂³	semidirect
130. C₄⋊Q₈×C₆₇	C₂³	semidirect
132. #127×C₆₇	C₂³	semidirect
135. #124×C₆₇	C₂³	semidirect
136. #124×C₆₇	C₂³	semidirect
146. C₂×C₄²×C₆₇	C₂³	semidirect
147. #104×C₆₇	C₂³	semidirect
148. #104×C₆₇	C₂³	semidirect
149. #101×C₆₇	C₂³	semidirect
150. #100×C₆₇	C₂³	semidirect
181. #41×C₆₇	C₂×D₄	semidirect
196. C₂×Q₈×C₆₇	C₂×D₄	semidirect
228. C₂×D₄×C₆₇	C₂×D₄	semidirect
382. C₂×#3018	C₆₇	direct (N × H)
389. C₂×C₆₇	#3018	direct (N × H)
391. C₂×#585	C₂×C₆₇	semidirect
392. C₂×#575	C₂×C₆₇	semidirect
393. C₂×#532	C₂×C₆₇	semidirect
394. #3018	C₂×C₆₇	direct (N × H)
395. C₂×#456	C₂×C₆₇	semidirect
396. C₂×#454	C₂×C₆₇	semidirect
397. C₂×#455	C₂×C₆₇	semidirect
398. C₂×#453	C₂×C₆₇	semidirect
399. C₂²×#104	C₂×C₆₇	semidirect
400. C₂×#413	C₂×C₆₇	semidirect
401. C₆₇	C₂×#3018	direct (N × H)
404. #585	C₂²×C₆₇	semidirect
414. C₂²×#41	C₂²×C₆₇	semidirect
416. #575	C₂²×C₆₇	semidirect
418. C₂×#137	C₂²×C₆₇	semidirect
420. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
422. C₂²×M₁₆	C₂²×C₆₇	semidirect
424. #532	C₂²×C₆₇	semidirect
425. C₂×C₄⋊Q₈	C₂²×C₆₇	semidirect
426. C₂×#127	C₂²×C₆₇	semidirect
427. C₂×#124	C₂²×C₆₇	semidirect
428. C₂×#124	C₂²×C₆₇	semidirect
431. C₂²×C₄²	C₂²×C₆₇	semidirect
432. #456	C₂²×C₆₇	semidirect
433. #455	C₂²×C₆₇	semidirect
434. #454	C₂²×C₆₇	semidirect
435. #453	C₂²×C₆₇	semidirect
436. C₂×#104	C₂²×C₆₇	semidirect
437. C₂×#104	C₂²×C₆₇	semidirect
438. C₂×#104	C₂²×C₆₇	semidirect
439. #413	C₂²×C₆₇	semidirect
440. C₂×#101	C₂²×C₆₇	semidirect
441. C₂×#100	C₂²×C₆₇	semidirect
476. C₂×#41	D₄×C₆₇	semidirect
477. C₂×#41	D₄×C₆₇	semidirect
481. C₂×#41	C₂³×C₆₇	semidirect
484. C₂²×Q₈	D₄×C₆₇	semidirect
495. C₂²×D₄	D₄×C₆₇	semidirect
506. #137	C₂³×C₆₇	semidirect
509. AGL(1,ℤ/8)	C₂³×C₆₇	semidirect
518. C₂×M₁₆	C₂³×C₆₇	semidirect
521. C₄⋊Q₈	C₂³×C₆₇	semidirect
523. #127	C₂³×C₆₇	semidirect
526. #124	C₂³×C₆₇	semidirect
527. #124	C₂³×C₆₇	semidirect
537. C₂×C₄²	C₂³×C₆₇	semidirect
538. #104	C₂³×C₆₇	semidirect
539. #104	C₂³×C₆₇	semidirect
540. #101	C₂³×C₆₇	semidirect
541. #100	C₂³×C₆₇	semidirect
572. #41	C₂×D₄×C₆₇	semidirect
587. C₂×Q₈	C₂×D₄×C₆₇	semidirect
619. C₂×D₄	C₂×D₄×C₆₇	semidirect
779. C₂	C₆₇×#3018	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×#585×C₆₇	2
C₂×#575×C₆₇	2
C₂×#532×C₆₇	2
C₆₇×#3018	2
C₂×#456×C₆₇	2
C₂×#454×C₆₇	2
C₂×#455×C₆₇	2
C₂×#453×C₆₇	2
C₂²×#104×C₆₇	2
C₂×#413×C₆₇	2
C₂×#3018	67

Subgroups — C2×C67×#3018 #30739633

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₇×#3018 #30739633