Subgroups — C₂×C₆₇×#3290 #30740352

Order 17152.

2650 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#578×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#577×C₆₇	C₂	1	2	yes	maximal, complemented
3	C₂×#576×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#3290	C₂	1	16	yes	maximal, direct product factor
5	C₂×#495×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#473×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#472×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#471×C₆₇	C₂	1	2	yes	maximal, complemented
9	C₂×#454×C₆₇	C₂	1	2	yes	maximal, complemented
10	C₂×#455×C₆₇	C₂	1	2	yes	maximal, complemented
11	C₂×#443×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#443×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×2₋¹⁺⁴×C₆₇	C₂²	1	2	yes	complemented
14	C₂×H(5,𝔽₂)×C₆₇	C₂²	1	2	yes	—
15	#578×C₆₇	—	2	4	no	—
16	#578×C₆₇	C₂²	1	8	yes	complemented
17	#577×C₆₇	—	2	8	no	—
18	#577×C₆₇	C₂²	1	16	yes	complemented
19	#576×C₆₇	—	2	4	no	—
20	#576×C₆₇	C₂²	1	8	yes	complemented
21	C₂×#137×C₆₇	—	2	2	no	—
22	C₂×#137×C₆₇	—	2	2	no	—
23	C₂×#137×C₆₇	C₂²	1	2	yes	—
24	C₂×#137×C₆₇	C₂²	1	2	yes	complemented
25	C₂×AGL(1,ℤ/8)×C₆₇	—	2	2	no	—
26	C₂×AGL(1,ℤ/8)×C₆₇	—	2	2	no	—
27	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	2	yes	—
28	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	2	yes	complemented
29	C₂×#135×C₆₇	—	2	1	no	—
30	C₂×#135×C₆₇	—	2	2	no	—
31	C₂×#135×C₆₇	—	2	1	no	—
32	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic
33	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic
34	C₂²×Q₁₆×C₆₇	—	2	1	no	—
35	C₂²×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
36	C₂²×SD₁₆×C₆₇	—	2	2	no	—
37	C₂²×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
38	C₂²×D₈×C₆₇	—	2	1	no	—
39	C₂²×D₈×C₆₇	C₂²	1	1	yes	characteristic
40	C₂×#131×C₆₇	C₂²	1	1	yes	characteristic
41	C₂×#131×C₆₇	C₂²	1	2	yes	complemented
42	C₂×#131×C₆₇	C₂²	1	1	yes	characteristic, complemented
43	C₂×#124×C₆₇	C₂²	1	2	yes	complemented
44	#495×C₆₇	C₂²	1	8	yes	complemented
45	#473×C₆₇	C₂²	1	8	yes	complemented
46	#472×C₆₇	C₂²	1	8	yes	complemented
47	#471×C₆₇	C₂²	1	16	yes	complemented
48	#455×C₆₇	C₂²	1	16	yes	complemented
49	#454×C₆₇	C₂²	1	16	yes	complemented
50	#443×C₆₇	C₂²	1	8	yes	complemented
51	#443×C₆₇	C₂²	1	8	yes	complemented
52	C₂×#108×C₆₇	C₂²	1	1	yes	characteristic, complemented
53	C₂×#108×C₆₇	C₂²	1	1	yes	characteristic, complemented
54	C₂×#104×C₆₇	C₂²	1	1	yes	characteristic
55	C₂×#104×C₆₇	C₂²	1	2	yes	complemented
56	C₂×#104×C₆₇	C₂²	1	1	yes	characteristic, complemented
57	C₂×#101×C₆₇	C₂²	1	2	yes	complemented
58	C₂×#100×C₆₇	C₂²	1	2	yes	complemented
59	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
60	2₋¹⁺⁴×C₆₇	—	2	4	no	—
61	2₋¹⁺⁴×C₆₇	—	2	4	no	—
62	2₋¹⁺⁴×C₆₇	—	4	2	no	—
63	2₋¹⁺⁴×C₆₇	C₂³	1	8	yes	complemented
64	H(5,𝔽₂)×C₆₇	—	2	4	no	—
65	H(5,𝔽₂)×C₆₇	—	2	4	no	—
66	H(5,𝔽₂)×C₆₇	—	4	2	no	—
67	H(5,𝔽₂)×C₆₇	C₂³	1	8	yes	—
68	C₂×#41×C₆₇	—	2	2	no	—
69	C₂×#41×C₆₇	—	2	2	no	—
70	C₂×#41×C₆₇	—	2	2	no	—
71	C₂×#41×C₆₇	—	2	2	no	—
72	C₂×#41×C₆₇	—	4	2	no	—
73	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
74	C₂×#41×C₆₇	C₂³	1	2	yes	—
75	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
76	C₂²×Q₈×C₆₇	—	2	2	no	—
77	C₂²×Q₈×C₆₇	—	2	2	no	—
78	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
79	C₂²×D₄×C₆₇	—	2	2	no	—
80	C₂²×D₄×C₆₇	—	2	2	no	—
81	C₂²×D₄×C₆₇	—	4	2	no	—
82	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
83	#137×C₆₇	—	2	4	no	—
84	#137×C₆₇	—	2	4	no	—
85	#137×C₆₇	—	2	16	no	—
86	#137×C₆₇	—	2	16	no	—
87	#137×C₆₇	C₂³	1	8	yes	—
88	#137×C₆₇	C₂³	1	8	yes	complemented
89	AGL(1,ℤ/8)×C₆₇	—	2	4	no	—
90	AGL(1,ℤ/8)×C₆₇	—	2	4	no	—
91	AGL(1,ℤ/8)×C₆₇	—	2	16	no	—
92	AGL(1,ℤ/8)×C₆₇	—	2	16	no	—
93	AGL(1,ℤ/8)×C₆₇	C₂³	1	8	yes	—
94	AGL(1,ℤ/8)×C₆₇	C₂³	1	8	yes	complemented
95	#135×C₆₇	—	2	8	no	—
96	#135×C₆₇	—	2	16	no	—
97	#135×C₆₇	—	2	8	no	—
98	#135×C₆₇	D₄	1	4	yes	—
99	#135×C₆₇	D₄	1	4	yes	—
100	#135×C₆₇	C₂³	1	4	yes	—
101	#135×C₆₇	C₂³	1	4	yes	—
102	C₂×Q₁₆×C₆₇	—	2	2	no	—
103	C₂×Q₁₆×C₆₇	—	2	2	no	—
104	C₂×Q₁₆×C₆₇	—	2	8	no	—
105	C₂×Q₁₆×C₆₇	—	2	1	no	—
106	C₂×Q₁₆×C₆₇	—	2	1	no	—
107	C₂×Q₁₆×C₆₇	—	2	2	no	—
108	C₂×Q₁₆×C₆₇	D₄	1	1	yes	characteristic
109	C₂×Q₁₆×C₆₇	D₄	1	1	yes	characteristic
110	C₂×Q₁₆×C₆₇	C₂³	1	4	yes	complemented
111	C₂×SD₁₆×C₆₇	—	2	2	no	—
112	C₂×SD₁₆×C₆₇	—	2	2	no	—
113	C₂×SD₁₆×C₆₇	—	2	2	no	—
114	C₂×SD₁₆×C₆₇	—	2	2	no	—
115	C₂×SD₁₆×C₆₇	—	2	16	no	—
116	C₂×SD₁₆×C₆₇	—	2	2	no	—
117	C₂×SD₁₆×C₆₇	—	2	2	no	—
118	C₂×SD₁₆×C₆₇	—	2	4	no	—
119	C₂×SD₁₆×C₆₇	D₄	1	1	yes	characteristic
120	C₂×SD₁₆×C₆₇	D₄	1	1	yes	characteristic
121	C₂×SD₁₆×C₆₇	D₄	1	2	yes	—
122	C₂×SD₁₆×C₆₇	C₂³	1	8	yes	complemented
123	C₂×D₈×C₆₇	—	2	2	no	—
124	C₂×D₈×C₆₇	—	2	2	no	—
125	C₂×D₈×C₆₇	—	2	8	no	—
126	C₂×D₈×C₆₇	—	2	1	no	—
127	C₂×D₈×C₆₇	—	2	1	no	—
128	C₂×D₈×C₆₇	—	2	2	no	—
129	C₂×D₈×C₆₇	D₄	1	1	yes	characteristic
130	C₂×D₈×C₆₇	D₄	1	1	yes	characteristic
131	C₂×D₈×C₆₇	C₂³	1	4	yes	—
132	#131×C₆₇	—	2	2	no	—
133	#131×C₆₇	—	2	4	no	—
134	#131×C₆₇	—	2	2	no	—
135	#131×C₆₇	C₂³	1	4	yes	—
136	#131×C₆₇	C₂³	1	8	yes	complemented
137	#131×C₆₇	C₂³	1	4	yes	complemented
138	C₂×M₁₆×C₆₇	—	2	1	no	—
139	C₂×M₁₆×C₆₇	—	2	2	no	—
140	C₂×M₁₆×C₆₇	—	2	1	no	—
141	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
142	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
143	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
144	C₂²×C₈×C₆₇	—	2	1	no	—
145	C₂²×C₈×C₆₇	—	2	2	no	—
146	C₂²×C₈×C₆₇	—	2	1	no	—
147	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
148	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
149	#124×C₆₇	—	4	2	no	—
150	#124×C₆₇	C₂³	1	8	yes	complemented
151	C₂×C₂²⋊C₄×C₆₇	—	4	2	no	—
152	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
153	#108×C₆₇	C₂³	1	4	yes	complemented
154	#108×C₆₇	C₂³	1	4	yes	complemented
155	#104×C₆₇	C₂³	1	4	yes	—
156	#104×C₆₇	C₂³	1	4	yes	complemented
157	#104×C₆₇	C₂³	1	8	yes	complemented
158	#101×C₆₇	C₂³	1	8	yes	complemented
159	#100×C₆₇	C₂³	1	8	yes	complemented
160	C₄×C₈×C₆₇	C₂³	1	4	yes	complemented
161	C₂⁴×C₆₇	—	2	2	no	—
162	C₂⁴×C₆₇	—	4	2	no	—
163	#41×C₆₇	—	2	1	no	—
164	#41×C₆₇	—	2	2	no	—
165	#41×C₆₇	—	2	1	no	—
166	#41×C₆₇	—	2	1	no	—
167	#41×C₆₇	—	2	2	no	—
168	#41×C₆₇	—	2	1	no	—
169	#41×C₆₇	—	2	8	no	—
170	#41×C₆₇	—	2	8	no	—
171	#41×C₆₇	—	2	8	no	—
172	#41×C₆₇	—	2	8	no	—
173	#41×C₆₇	—	4	8	no	—
174	#41×C₆₇	—	4	4	no	—
175	#41×C₆₇	—	4	4	no	—
176	#41×C₆₇	—	4	4	no	—
177	#41×C₆₇	—	4	4	no	—
178	#41×C₆₇	—	4	8	no	—
179	#41×C₆₇	C₂×D₄	1	2	yes	—
180	#41×C₆₇	C₂×D₄	1	4	yes	—
181	#41×C₆₇	C₂×D₄	1	2	yes	—
182	#41×C₆₇	C₂⁴	1	2	yes	—
183	#41×C₆₇	C₂⁴	1	4	yes	—
184	#41×C₆₇	C₂⁴	1	2	yes	—
185	C₂×Q₈×C₆₇	—	2	2	no	—
186	C₂×Q₈×C₆₇	—	2	8	no	—
187	C₂×Q₈×C₆₇	—	2	8	no	—
188	C₂×Q₈×C₆₇	—	2	2	no	—
189	C₂×Q₈×C₆₇	—	2	2	no	—
190	C₂×Q₈×C₆₇	—	2	2	no	—
191	C₂×Q₈×C₆₇	—	2	2	no	—
192	C₂×Q₈×C₆₇	—	4	2	no	—
193	C₂×Q₈×C₆₇	—	4	4	no	—
194	C₂×Q₈×C₆₇	—	4	4	no	—
195	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
196	C₂×Q₈×C₆₇	C₂×D₄	1	2	yes	—
197	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
198	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
199	C₂×D₄×C₆₇	—	2	1	no	—
200	C₂×D₄×C₆₇	—	2	2	no	—
201	C₂×D₄×C₆₇	—	2	1	no	—
202	C₂×D₄×C₆₇	—	2	8	no	—
203	C₂×D₄×C₆₇	—	2	8	no	—
204	C₂×D₄×C₆₇	—	2	2	no	—
205	C₂×D₄×C₆₇	—	2	2	no	—
206	C₂×D₄×C₆₇	—	2	2	no	—
207	C₂×D₄×C₆₇	—	2	2	no	—
208	C₂×D₄×C₆₇	—	2	2	no	—
209	C₂×D₄×C₆₇	—	4	4	no	—
210	C₂×D₄×C₆₇	—	4	4	no	—
211	C₂×D₄×C₆₇	—	4	2	no	—
212	C₂×D₄×C₆₇	—	4	2	no	—
213	C₂×D₄×C₆₇	—	4	8	no	—
214	C₂×D₄×C₆₇	—	4	8	no	—
215	C₂×D₄×C₆₇	—	4	2	no	—
216	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
217	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
218	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
219	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
220	C₂²×C₄×C₆₇	—	2	1	no	—
221	C₂²×C₄×C₆₇	—	2	2	no	—
222	C₂²×C₄×C₆₇	—	2	1	no	—
223	C₂²×C₄×C₆₇	—	2	1	no	—
224	C₂²×C₄×C₆₇	—	2	2	no	—
225	C₂²×C₄×C₆₇	—	4	2	no	—
226	C₂²×C₄×C₆₇	—	4	2	no	—
227	C₂²×C₄×C₆₇	—	4	2	no	—
228	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
229	Q₁₆×C₆₇	—	2	8	no	—
230	Q₁₆×C₆₇	—	2	8	no	—
231	Q₁₆×C₆₇	—	2	4	no	—
232	Q₁₆×C₆₇	—	2	4	no	—
233	Q₁₆×C₆₇	C₂×D₄	1	4	yes	—
234	Q₁₆×C₆₇	C₂×D₄	1	4	yes	—
235	SD₁₆×C₆₇	—	2	8	no	—
236	SD₁₆×C₆₇	—	2	8	no	—
237	SD₁₆×C₆₇	—	2	8	no	—
238	SD₁₆×C₆₇	—	2	8	no	—
239	SD₁₆×C₆₇	—	2	8	no	—
240	SD₁₆×C₆₇	—	2	8	no	—
241	SD₁₆×C₆₇	C₂×D₄	1	4	yes	—
242	SD₁₆×C₆₇	C₂×D₄	1	4	yes	—
243	SD₁₆×C₆₇	C₂×D₄	1	8	yes	—
244	D₈×C₆₇	—	2	8	no	—
245	D₈×C₆₇	—	2	8	no	—
246	D₈×C₆₇	—	2	4	no	—
247	D₈×C₆₇	—	2	4	no	—
248	D₈×C₆₇	C₂×D₄	1	4	yes	—
249	D₈×C₆₇	C₂×D₄	1	4	yes	—
250	M₁₆×C₆₇	—	2	1	no	—
251	M₁₆×C₆₇	—	2	2	no	—
252	M₁₆×C₆₇	—	2	1	no	—
253	M₁₆×C₆₇	—	2	4	no	—
254	M₁₆×C₆₇	—	2	8	no	—
255	M₁₆×C₆₇	—	2	4	no	—
256	M₁₆×C₆₇	C₂⁴	1	2	yes	—
257	M₁₆×C₆₇	C₂⁴	1	4	yes	—
258	M₁₆×C₆₇	C₂⁴	1	2	yes	—
259	C₂×C₈×C₆₇	—	2	1	no	—
260	C₂×C₈×C₆₇	—	2	2	no	—
261	C₂×C₈×C₆₇	—	2	1	no	—
262	C₂×C₈×C₆₇	—	2	4	no	—
263	C₂×C₈×C₆₇	—	2	8	no	—
264	C₂×C₈×C₆₇	—	2	4	no	—
265	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
266	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
267	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
268	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
269	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
270	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
271	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
272	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
273	C₂²⋊C₄×C₆₇	—	4	8	no	—
274	C₄²×C₆₇	—	2	1	no	—
275	C₄²×C₆₇	C₂⁴	1	2	yes	—
276	C₂³×C₆₇	—	2	1	no	—
277	C₂³×C₆₇	—	2	2	no	—
278	C₂³×C₆₇	—	2	1	no	—
279	C₂³×C₆₇	—	2	4	no	—
280	C₂³×C₆₇	—	4	8	no	—
281	C₂³×C₆₇	—	4	2	no	—
282	C₂³×C₆₇	—	4	2	no	—
283	C₂³×C₆₇	—	8	4	no	—
284	C₂³×C₆₇	—	16	4	no	—
285	C₂³×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
286	Q₈×C₆₇	—	2	1	no	—
287	Q₈×C₆₇	—	2	2	no	—
288	Q₈×C₆₇	—	2	1	no	—
289	Q₈×C₆₇	—	2	4	no	—
290	Q₈×C₆₇	—	2	4	no	—
291	Q₈×C₆₇	—	4	8	no	—
292	Q₈×C₆₇	—	4	2	no	—
293	Q₈×C₆₇	—	4	2	no	—
294	Q₈×C₆₇	C₂²×D₄	1	2	yes	—
295	Q₈×C₆₇	C₂²×D₄	1	4	yes	—
296	Q₈×C₆₇	C₂²×D₄	1	2	yes	—
297	D₄×C₆₇	—	2	2	no	—
298	D₄×C₆₇	—	2	4	no	—
299	D₄×C₆₇	—	2	2	no	—
300	D₄×C₆₇	—	2	2	no	—
301	D₄×C₆₇	—	2	4	no	—
302	D₄×C₆₇	—	2	2	no	—
303	D₄×C₆₇	—	2	1	no	—
304	D₄×C₆₇	—	2	2	no	—
305	D₄×C₆₇	—	2	1	no	—
306	D₄×C₆₇	—	2	4	no	—
307	D₄×C₆₇	—	2	4	no	—
308	D₄×C₆₇	—	4	8	no	—
309	D₄×C₆₇	—	4	8	no	—
310	D₄×C₆₇	—	4	8	no	—
311	D₄×C₆₇	—	4	2	no	—
312	D₄×C₆₇	—	4	2	no	—
313	D₄×C₆₇	C₂²×D₄	1	2	yes	—
314	D₄×C₆₇	C₂²×D₄	1	4	yes	—
315	D₄×C₆₇	C₂²×D₄	1	2	yes	—
316	C₂×C₄×C₆₇	—	2	1	no	—
317	C₂×C₄×C₆₇	—	2	2	no	—
318	C₂×C₄×C₆₇	—	2	1	no	—
319	C₂×C₄×C₆₇	—	2	2	no	—
320	C₂×C₄×C₆₇	—	2	4	no	—
321	C₂×C₄×C₆₇	—	2	2	no	—
322	C₂×C₄×C₆₇	—	2	2	no	—
323	C₂×C₄×C₆₇	—	2	4	no	—
324	C₂×C₄×C₆₇	—	2	2	no	—
325	C₂×C₄×C₆₇	—	2	2	no	—
326	C₂×C₄×C₆₇	—	2	4	no	—
327	C₂×C₄×C₆₇	—	4	8	no	—
328	C₂×C₄×C₆₇	—	4	8	no	—
329	C₂×C₄×C₆₇	—	4	8	no	—
330	C₂×C₄×C₆₇	—	4	2	no	—
331	C₂×C₄×C₆₇	—	4	2	no	—
332	C₂×C₄×C₆₇	—	4	2	no	—
333	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
334	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
335	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
336	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
337	C₂×C₄×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
338	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
339	C₈×C₆₇	—	2	2	no	—
340	C₈×C₆₇	—	2	4	no	—
341	C₈×C₆₇	—	2	2	no	—
342	C₈×C₆₇	C₂²×D₄	1	2	yes	—
343	C₈×C₆₇	C₂²×D₄	1	2	yes	—
344	C₈×C₆₇	C₂²×D₄	1	2	yes	—
345	C₈×C₆₇	C₂²×D₄	1	2	yes	—
346	C₂²×C₆₇	—	2	2	no	—
347	C₂²×C₆₇	—	2	2	no	—
348	C₂²×C₆₇	—	2	4	no	—
349	C₂²×C₆₇	—	2	2	no	—
350	C₂²×C₆₇	—	4	2	no	—
351	C₂²×C₆₇	—	4	4	no	—
352	C₂²×C₆₇	—	4	2	no	—
353	C₂²×C₆₇	—	4	4	no	—
354	C₂²×C₆₇	—	8	4	no	—
355	C₂²×C₆₇	—	8	4	no	—
356	C₂²×C₆₇	—	16	2	no	—
357	C₂²×C₆₇	—	16	8	no	—
358	C₂²×C₆₇	D₄²	1	1	yes	characteristic
359	C₂²×C₆₇	D₄²	1	1	yes	characteristic
360	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
361	C₄×C₆₇	—	2	2	no	—
362	C₄×C₆₇	—	2	4	no	—
363	C₄×C₆₇	—	2	2	no	—
364	C₄×C₆₇	—	4	2	no	—
365	C₄×C₆₇	—	4	4	no	—
366	C₄×C₆₇	D₄²	1	1	yes	characteristic
367	C₄×C₆₇	D₄²	1	1	yes	characteristic
368	C₄×C₆₇	C₂³×D₄	1	1	yes	characteristic
369	C₄×C₆₇	C₂³×D₄	1	1	yes	characteristic
370	C₂×#3290	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
371	C₂×C₆₇	—	2	1	no	—
372	C₂×C₆₇	—	2	1	no	—
373	C₂×C₆₇	—	4	2	no	—
374	C₂×C₆₇	—	4	4	no	—
375	C₂×C₆₇	—	4	2	no	—
376	C₂×C₆₇	—	8	4	no	—
377	C₂×C₆₇	#3290	1	2	yes	direct product factor
378	C₂×C₆₇	C₂×D₄²	1	1	yes	characteristic
379	C₂×#578	C₂×C₆₇	1	1	yes	characteristic, complemented
380	C₂×#577	C₂×C₆₇	1	2	yes	complemented
381	C₂×#576	C₂×C₆₇	1	1	yes	characteristic, complemented
382	#3290	C₂×C₆₇	1	16	yes	direct product factor
383	C₂×#495	C₂×C₆₇	1	1	yes	characteristic, complemented
384	C₂×#473	C₂×C₆₇	1	1	yes	characteristic, complemented
385	C₂×#472	C₂×C₆₇	1	1	yes	characteristic, complemented
386	C₂×#471	C₂×C₆₇	1	2	yes	complemented
387	C₂×#454	C₂×C₆₇	1	2	yes	complemented
388	C₂×#455	C₂×C₆₇	1	2	yes	complemented
389	C₂×#443	C₂×C₆₇	1	1	yes	characteristic, complemented
390	C₂×#443	C₂×C₆₇	1	1	yes	characteristic, complemented
391	C₆₇	C₂×#3290	1	1	yes	characteristic, direct product factor, Sylow
392	C₂×2₋¹⁺⁴	C₂²×C₆₇	1	2	yes	complemented
393	C₂×H(5,𝔽₂)	C₂²×C₆₇	1	2	yes	—
394	#578	—	2	4	no	—
395	#578	C₂²×C₆₇	1	8	yes	complemented
396	#577	—	2	8	no	—
397	#577	C₂²×C₆₇	1	16	yes	complemented
398	#576	—	2	4	no	—
399	#576	C₂²×C₆₇	1	8	yes	complemented
400	C₂×#137	—	2	2	no	—
401	C₂×#137	—	2	2	no	—
402	C₂×#137	C₂²×C₆₇	1	2	yes	—
403	C₂×#137	C₂²×C₆₇	1	2	yes	complemented
404	C₂×AGL(1,ℤ/8)	—	2	2	no	—
405	C₂×AGL(1,ℤ/8)	—	2	2	no	—
406	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	—
407	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	complemented
408	C₂×#135	—	2	1	no	—
409	C₂×#135	—	2	2	no	—
410	C₂×#135	—	2	1	no	—
411	C₂×#135	C₂²×C₆₇	1	1	yes	characteristic
412	C₂×#135	C₂²×C₆₇	1	1	yes	characteristic
413	C₂²×Q₁₆	—	2	1	no	—
414	C₂²×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
415	C₂²×SD₁₆	—	2	2	no	—
416	C₂²×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
417	C₂²×D₈	—	2	1	no	—
418	C₂²×D₈	C₂²×C₆₇	1	1	yes	characteristic
419	C₂×#131	C₂²×C₆₇	1	1	yes	characteristic
420	C₂×#131	C₂²×C₆₇	1	2	yes	complemented
421	C₂×#131	C₂²×C₆₇	1	1	yes	characteristic, complemented
422	C₂×#124	C₂²×C₆₇	1	2	yes	complemented
423	#495	C₂²×C₆₇	1	8	yes	complemented
424	#473	C₂²×C₆₇	1	8	yes	complemented
425	#472	C₂²×C₆₇	1	8	yes	complemented
426	#471	C₂²×C₆₇	1	16	yes	complemented
427	#455	C₂²×C₆₇	1	16	yes	complemented
428	#454	C₂²×C₆₇	1	16	yes	complemented
429	#443	C₂²×C₆₇	1	8	yes	complemented
430	#443	C₂²×C₆₇	1	8	yes	complemented
431	C₂×#108	C₂²×C₆₇	1	1	yes	characteristic, complemented
432	C₂×#108	C₂²×C₆₇	1	1	yes	characteristic, complemented
433	C₂×#104	C₂²×C₆₇	1	1	yes	characteristic
434	C₂×#104	C₂²×C₆₇	1	2	yes	complemented
435	C₂×#104	C₂²×C₆₇	1	1	yes	characteristic, complemented
436	C₂×#101	C₂²×C₆₇	1	2	yes	complemented
437	C₂×#100	C₂²×C₆₇	1	2	yes	complemented
438	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
439	2₋¹⁺⁴	—	2	4	no	—
440	2₋¹⁺⁴	—	2	4	no	—
441	2₋¹⁺⁴	—	4	2	no	—
442	2₋¹⁺⁴	C₂³×C₆₇	1	8	yes	complemented
443	H(5,𝔽₂)	—	2	4	no	—
444	H(5,𝔽₂)	—	2	4	no	—
445	H(5,𝔽₂)	—	4	2	no	—
446	H(5,𝔽₂)	C₂³×C₆₇	1	8	yes	—
447	C₂×#41	—	2	2	no	—
448	C₂×#41	—	2	2	no	—
449	C₂×#41	—	2	2	no	—
450	C₂×#41	—	2	2	no	—
451	C₂×#41	—	4	2	no	—
452	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
453	C₂×#41	C₂³×C₆₇	1	2	yes	—
454	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
455	C₂²×Q₈	—	2	2	no	—
456	C₂²×Q₈	—	2	2	no	—
457	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
458	C₂²×D₄	—	2	2	no	—
459	C₂²×D₄	—	2	2	no	—
460	C₂²×D₄	—	4	2	no	—
461	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
462	#137	—	2	4	no	—
463	#137	—	2	4	no	—
464	#137	—	2	16	no	—
465	#137	—	2	16	no	—
466	#137	C₂³×C₆₇	1	8	yes	—
467	#137	C₂³×C₆₇	1	8	yes	complemented
468	AGL(1,ℤ/8)	—	2	4	no	—
469	AGL(1,ℤ/8)	—	2	4	no	—
470	AGL(1,ℤ/8)	—	2	16	no	—
471	AGL(1,ℤ/8)	—	2	16	no	—
472	AGL(1,ℤ/8)	C₂³×C₆₇	1	8	yes	—
473	AGL(1,ℤ/8)	C₂³×C₆₇	1	8	yes	complemented
474	#135	—	2	8	no	—
475	#135	—	2	16	no	—
476	#135	—	2	8	no	—
477	#135	D₄×C₆₇	1	4	yes	—
478	#135	D₄×C₆₇	1	4	yes	—
479	#135	C₂³×C₆₇	1	4	yes	—
480	#135	C₂³×C₆₇	1	4	yes	—
481	C₂×Q₁₆	—	2	2	no	—
482	C₂×Q₁₆	—	2	2	no	—
483	C₂×Q₁₆	—	2	8	no	—
484	C₂×Q₁₆	—	2	1	no	—
485	C₂×Q₁₆	—	2	1	no	—
486	C₂×Q₁₆	—	2	2	no	—
487	C₂×Q₁₆	D₄×C₆₇	1	1	yes	characteristic
488	C₂×Q₁₆	D₄×C₆₇	1	1	yes	characteristic
489	C₂×Q₁₆	C₂³×C₆₇	1	4	yes	complemented
490	C₂×SD₁₆	—	2	2	no	—
491	C₂×SD₁₆	—	2	2	no	—
492	C₂×SD₁₆	—	2	2	no	—
493	C₂×SD₁₆	—	2	2	no	—
494	C₂×SD₁₆	—	2	16	no	—
495	C₂×SD₁₆	—	2	2	no	—
496	C₂×SD₁₆	—	2	2	no	—
497	C₂×SD₁₆	—	2	4	no	—
498	C₂×SD₁₆	D₄×C₆₇	1	1	yes	characteristic
499	C₂×SD₁₆	D₄×C₆₇	1	1	yes	characteristic
500	C₂×SD₁₆	D₄×C₆₇	1	2	yes	—
501	C₂×SD₁₆	C₂³×C₆₇	1	8	yes	complemented
502	C₂×D₈	—	2	2	no	—
503	C₂×D₈	—	2	2	no	—
504	C₂×D₈	—	2	8	no	—
505	C₂×D₈	—	2	1	no	—
506	C₂×D₈	—	2	1	no	—
507	C₂×D₈	—	2	2	no	—
508	C₂×D₈	D₄×C₆₇	1	1	yes	characteristic
509	C₂×D₈	D₄×C₆₇	1	1	yes	characteristic
510	C₂×D₈	C₂³×C₆₇	1	4	yes	—
511	#131	—	2	2	no	—
512	#131	—	2	4	no	—
513	#131	—	2	2	no	—
514	#131	C₂³×C₆₇	1	4	yes	—
515	#131	C₂³×C₆₇	1	8	yes	complemented
516	#131	C₂³×C₆₇	1	4	yes	complemented
517	C₂×M₁₆	—	2	1	no	—
518	C₂×M₁₆	—	2	2	no	—
519	C₂×M₁₆	—	2	1	no	—
520	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
521	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
522	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
523	C₂²×C₈	—	2	1	no	—
524	C₂²×C₈	—	2	2	no	—
525	C₂²×C₈	—	2	1	no	—
526	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
527	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
528	#124	—	4	2	no	—
529	#124	C₂³×C₆₇	1	8	yes	complemented
530	C₂×C₂²⋊C₄	—	4	2	no	—
531	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
532	#108	C₂³×C₆₇	1	4	yes	complemented
533	#108	C₂³×C₆₇	1	4	yes	complemented
534	#104	C₂³×C₆₇	1	4	yes	—
535	#104	C₂³×C₆₇	1	4	yes	complemented
536	#104	C₂³×C₆₇	1	8	yes	complemented
537	#101	C₂³×C₆₇	1	8	yes	complemented
538	#100	C₂³×C₆₇	1	8	yes	complemented
539	C₄×C₈	C₂³×C₆₇	1	4	yes	complemented
540	C₂⁴	—	2	2	no	—
541	C₂⁴	—	4	2	no	—
542	#41	—	2	1	no	—
543	#41	—	2	2	no	—
544	#41	—	2	1	no	—
545	#41	—	2	1	no	—
546	#41	—	2	2	no	—
547	#41	—	2	1	no	—
548	#41	—	2	8	no	—
549	#41	—	2	8	no	—
550	#41	—	2	8	no	—
551	#41	—	2	8	no	—
552	#41	—	4	8	no	—
553	#41	—	4	4	no	—
554	#41	—	4	4	no	—
555	#41	—	4	4	no	—
556	#41	—	4	4	no	—
557	#41	—	4	8	no	—
558	#41	C₂×D₄×C₆₇	1	2	yes	—
559	#41	C₂×D₄×C₆₇	1	4	yes	—
560	#41	C₂×D₄×C₆₇	1	2	yes	—
561	#41	C₂⁴×C₆₇	1	2	yes	—
562	#41	C₂⁴×C₆₇	1	4	yes	—
563	#41	C₂⁴×C₆₇	1	2	yes	—
564	C₂×Q₈	—	2	2	no	—
565	C₂×Q₈	—	2	8	no	—
566	C₂×Q₈	—	2	8	no	—
567	C₂×Q₈	—	2	2	no	—
568	C₂×Q₈	—	2	2	no	—
569	C₂×Q₈	—	2	2	no	—
570	C₂×Q₈	—	2	2	no	—
571	C₂×Q₈	—	4	2	no	—
572	C₂×Q₈	—	4	4	no	—
573	C₂×Q₈	—	4	4	no	—
574	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
575	C₂×Q₈	C₂×D₄×C₆₇	1	2	yes	—
576	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
577	C₂×Q₈	C₂⁴×C₆₇	1	4	yes	—
578	C₂×D₄	—	2	1	no	—
579	C₂×D₄	—	2	2	no	—
580	C₂×D₄	—	2	1	no	—
581	C₂×D₄	—	2	8	no	—
582	C₂×D₄	—	2	8	no	—
583	C₂×D₄	—	2	2	no	—
584	C₂×D₄	—	2	2	no	—
585	C₂×D₄	—	2	2	no	—
586	C₂×D₄	—	2	2	no	—
587	C₂×D₄	—	2	2	no	—
588	C₂×D₄	—	4	4	no	—
589	C₂×D₄	—	4	4	no	—
590	C₂×D₄	—	4	2	no	—
591	C₂×D₄	—	4	2	no	—
592	C₂×D₄	—	4	8	no	—
593	C₂×D₄	—	4	8	no	—
594	C₂×D₄	—	4	2	no	—
595	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
596	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
597	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
598	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
599	C₂²×C₄	—	2	1	no	—
600	C₂²×C₄	—	2	2	no	—
601	C₂²×C₄	—	2	1	no	—
602	C₂²×C₄	—	2	1	no	—
603	C₂²×C₄	—	2	2	no	—
604	C₂²×C₄	—	4	2	no	—
605	C₂²×C₄	—	4	2	no	—
606	C₂²×C₄	—	4	2	no	—
607	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
608	Q₁₆	—	2	8	no	—
609	Q₁₆	—	2	8	no	—
610	Q₁₆	—	2	4	no	—
611	Q₁₆	—	2	4	no	—
612	Q₁₆	C₂×D₄×C₆₇	1	4	yes	—
613	Q₁₆	C₂×D₄×C₆₇	1	4	yes	—
614	SD₁₆	—	2	8	no	—
615	SD₁₆	—	2	8	no	—
616	SD₁₆	—	2	8	no	—
617	SD₁₆	—	2	8	no	—
618	SD₁₆	—	2	8	no	—
619	SD₁₆	—	2	8	no	—
620	SD₁₆	C₂×D₄×C₆₇	1	4	yes	—
621	SD₁₆	C₂×D₄×C₆₇	1	4	yes	—
622	SD₁₆	C₂×D₄×C₆₇	1	8	yes	—
623	D₈	—	2	8	no	—
624	D₈	—	2	8	no	—
625	D₈	—	2	4	no	—
626	D₈	—	2	4	no	—
627	D₈	C₂×D₄×C₆₇	1	4	yes	—
628	D₈	C₂×D₄×C₆₇	1	4	yes	—
629	M₁₆	—	2	1	no	—
630	M₁₆	—	2	2	no	—
631	M₁₆	—	2	1	no	—
632	M₁₆	—	2	4	no	—
633	M₁₆	—	2	8	no	—
634	M₁₆	—	2	4	no	—
635	M₁₆	C₂⁴×C₆₇	1	2	yes	—
636	M₁₆	C₂⁴×C₆₇	1	4	yes	—
637	M₁₆	C₂⁴×C₆₇	1	2	yes	—
638	C₂×C₈	—	2	1	no	—
639	C₂×C₈	—	2	2	no	—
640	C₂×C₈	—	2	1	no	—
641	C₂×C₈	—	2	4	no	—
642	C₂×C₈	—	2	8	no	—
643	C₂×C₈	—	2	4	no	—
644	C₂×C₈	C₂×D₄×C₆₇	1	1	yes	characteristic
645	C₂×C₈	C₂×D₄×C₆₇	1	1	yes	characteristic
646	C₂×C₈	C₂×D₄×C₆₇	1	1	yes	characteristic
647	C₂×C₈	C₂×D₄×C₆₇	1	1	yes	characteristic
648	C₂×C₈	C₂×D₄×C₆₇	1	2	yes	—
649	C₂×C₈	C₂×D₄×C₆₇	1	2	yes	—
650	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
651	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
652	C₂²⋊C₄	—	4	8	no	—
653	C₄²	—	2	1	no	—
654	C₄²	C₂⁴×C₆₇	1	2	yes	—
655	C₂³	—	2	1	no	—
656	C₂³	—	2	2	no	—
657	C₂³	—	2	1	no	—
658	C₂³	—	2	4	no	—
659	C₂³	—	4	8	no	—
660	C₂³	—	4	2	no	—
661	C₂³	—	4	2	no	—
662	C₂³	—	8	4	no	—
663	C₂³	—	16	4	no	—
664	C₂³	H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
665	Q₈	—	2	1	no	—
666	Q₈	—	2	2	no	—
667	Q₈	—	2	1	no	—
668	Q₈	—	2	4	no	—
669	Q₈	—	2	4	no	—
670	Q₈	—	4	8	no	—
671	Q₈	—	4	2	no	—
672	Q₈	—	4	2	no	—
673	Q₈	C₂²×D₄×C₆₇	1	2	yes	—
674	Q₈	C₂²×D₄×C₆₇	1	4	yes	—
675	Q₈	C₂²×D₄×C₆₇	1	2	yes	—
676	D₄	—	2	2	no	—
677	D₄	—	2	4	no	—
678	D₄	—	2	2	no	—
679	D₄	—	2	2	no	—
680	D₄	—	2	4	no	—
681	D₄	—	2	2	no	—
682	D₄	—	2	1	no	—
683	D₄	—	2	2	no	—
684	D₄	—	2	1	no	—
685	D₄	—	2	4	no	—
686	D₄	—	2	4	no	—
687	D₄	—	4	8	no	—
688	D₄	—	4	8	no	—
689	D₄	—	4	8	no	—
690	D₄	—	4	2	no	—
691	D₄	—	4	2	no	—
692	D₄	C₂²×D₄×C₆₇	1	2	yes	—
693	D₄	C₂²×D₄×C₆₇	1	4	yes	—
694	D₄	C₂²×D₄×C₆₇	1	2	yes	—
695	C₂×C₄	—	2	1	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	1	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	4	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	4	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	4	no	—
706	C₂×C₄	—	4	8	no	—
707	C₂×C₄	—	4	8	no	—
708	C₂×C₄	—	4	8	no	—
709	C₂×C₄	—	4	2	no	—
710	C₂×C₄	—	4	2	no	—
711	C₂×C₄	—	4	2	no	—
712	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
713	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
714	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
715	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
716	C₂×C₄	H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
717	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
718	C₈	—	2	2	no	—
719	C₈	—	2	4	no	—
720	C₈	—	2	2	no	—
721	C₈	C₂²×D₄×C₆₇	1	2	yes	—
722	C₈	C₂²×D₄×C₆₇	1	2	yes	—
723	C₈	C₂²×D₄×C₆₇	1	2	yes	—
724	C₈	C₂²×D₄×C₆₇	1	2	yes	—
725	C₂²	—	2	2	no	—
726	C₂²	—	2	2	no	—
727	C₂²	—	2	4	no	—
728	C₂²	—	2	2	no	—
729	C₂²	—	4	2	no	—
730	C₂²	—	4	4	no	—
731	C₂²	—	4	2	no	—
732	C₂²	—	4	4	no	—
733	C₂²	—	8	4	no	—
734	C₂²	—	8	4	no	—
735	C₂²	—	16	2	no	—
736	C₂²	—	16	8	no	—
737	C₂²	D₄²×C₆₇	1	1	yes	characteristic
738	C₂²	D₄²×C₆₇	1	1	yes	characteristic
739	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
740	C₄	—	2	2	no	—
741	C₄	—	2	4	no	—
742	C₄	—	2	2	no	—
743	C₄	—	4	2	no	—
744	C₄	—	4	4	no	—
745	C₄	D₄²×C₆₇	1	1	yes	characteristic
746	C₄	D₄²×C₆₇	1	1	yes	characteristic
747	C₄	C₂³×D₄×C₆₇	1	1	yes	characteristic
748	C₄	C₂³×D₄×C₆₇	1	1	yes	characteristic
749	C₂	—	2	1	no	—
750	C₂	—	2	1	no	—
751	C₂	—	4	2	no	—
752	C₂	—	4	4	no	—
753	C₂	—	4	2	no	—
754	C₂	—	8	4	no	—
755	C₂	C₆₇×#3290	1	2	yes	direct product factor
756	C₂	C₂×D₄²×C₆₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₇	D₄²
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ C₂²×C₄×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#578×C₆₇	C₂	semidirect
2. C₂×#577×C₆₇	C₂	semidirect
3. C₂×#576×C₆₇	C₂	semidirect
4. C₆₇×#3290	C₂	direct (N × H)
5. C₂×#495×C₆₇	C₂	semidirect
6. C₂×#473×C₆₇	C₂	semidirect
7. C₂×#472×C₆₇	C₂	semidirect
8. C₂×#471×C₆₇	C₂	semidirect
9. C₂×#454×C₆₇	C₂	semidirect
10. C₂×#455×C₆₇	C₂	semidirect
11. C₂×#443×C₆₇	C₂	semidirect
12. C₂×#443×C₆₇	C₂	semidirect
13. C₂×2₋¹⁺⁴×C₆₇	C₂²	semidirect
16. #578×C₆₇	C₂²	semidirect
18. #577×C₆₇	C₂²	semidirect
20. #576×C₆₇	C₂²	semidirect
24. C₂×#137×C₆₇	C₂²	semidirect
28. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
35. C₂²×Q₁₆×C₆₇	C₂²	semidirect
37. C₂²×SD₁₆×C₆₇	C₂²	semidirect
41. C₂×#131×C₆₇	C₂²	semidirect
42. C₂×#131×C₆₇	C₂²	semidirect
43. C₂×#124×C₆₇	C₂²	semidirect
44. #495×C₆₇	C₂²	semidirect
45. #473×C₆₇	C₂²	semidirect
46. #472×C₆₇	C₂²	semidirect
47. #471×C₆₇	C₂²	semidirect
48. #455×C₆₇	C₂²	semidirect
49. #454×C₆₇	C₂²	semidirect
50. #443×C₆₇	C₂²	semidirect
51. #443×C₆₇	C₂²	semidirect
52. C₂×#108×C₆₇	C₂²	semidirect
53. C₂×#108×C₆₇	C₂²	semidirect
55. C₂×#104×C₆₇	C₂²	semidirect
56. C₂×#104×C₆₇	C₂²	semidirect
57. C₂×#101×C₆₇	C₂²	semidirect
58. C₂×#100×C₆₇	C₂²	semidirect
59. C₂×C₄×C₈×C₆₇	C₂²	semidirect
63. 2₋¹⁺⁴×C₆₇	C₂³	semidirect
88. #137×C₆₇	C₂³	semidirect
94. AGL(1,ℤ/8)×C₆₇	C₂³	semidirect
110. C₂×Q₁₆×C₆₇	C₂³	semidirect
122. C₂×SD₁₆×C₆₇	C₂³	semidirect
136. #131×C₆₇	C₂³	semidirect
137. #131×C₆₇	C₂³	semidirect
150. #124×C₆₇	C₂³	semidirect
153. #108×C₆₇	C₂³	semidirect
154. #108×C₆₇	C₂³	semidirect
156. #104×C₆₇	C₂³	semidirect
157. #104×C₆₇	C₂³	semidirect
158. #101×C₆₇	C₂³	semidirect
159. #100×C₆₇	C₂³	semidirect
160. C₄×C₈×C₆₇	C₂³	semidirect
370. C₂×#3290	C₆₇	direct (N × H)
377. C₂×C₆₇	#3290	direct (N × H)
379. C₂×#578	C₂×C₆₇	semidirect
380. C₂×#577	C₂×C₆₇	semidirect
381. C₂×#576	C₂×C₆₇	semidirect
382. #3290	C₂×C₆₇	direct (N × H)
383. C₂×#495	C₂×C₆₇	semidirect
384. C₂×#473	C₂×C₆₇	semidirect
385. C₂×#472	C₂×C₆₇	semidirect
386. C₂×#471	C₂×C₆₇	semidirect
387. C₂×#454	C₂×C₆₇	semidirect
388. C₂×#455	C₂×C₆₇	semidirect
389. C₂×#443	C₂×C₆₇	semidirect
390. C₂×#443	C₂×C₆₇	semidirect
391. C₆₇	C₂×#3290	direct (N × H)
392. C₂×2₋¹⁺⁴	C₂²×C₆₇	semidirect
395. #578	C₂²×C₆₇	semidirect
397. #577	C₂²×C₆₇	semidirect
399. #576	C₂²×C₆₇	semidirect
403. C₂×#137	C₂²×C₆₇	semidirect
407. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
414. C₂²×Q₁₆	C₂²×C₆₇	semidirect
416. C₂²×SD₁₆	C₂²×C₆₇	semidirect
420. C₂×#131	C₂²×C₆₇	semidirect
421. C₂×#131	C₂²×C₆₇	semidirect
422. C₂×#124	C₂²×C₆₇	semidirect
423. #495	C₂²×C₆₇	semidirect
424. #473	C₂²×C₆₇	semidirect
425. #472	C₂²×C₆₇	semidirect
426. #471	C₂²×C₆₇	semidirect
427. #455	C₂²×C₆₇	semidirect
428. #454	C₂²×C₆₇	semidirect
429. #443	C₂²×C₆₇	semidirect
430. #443	C₂²×C₆₇	semidirect
431. C₂×#108	C₂²×C₆₇	semidirect
432. C₂×#108	C₂²×C₆₇	semidirect
434. C₂×#104	C₂²×C₆₇	semidirect
435. C₂×#104	C₂²×C₆₇	semidirect
436. C₂×#101	C₂²×C₆₇	semidirect
437. C₂×#100	C₂²×C₆₇	semidirect
438. C₂×C₄×C₈	C₂²×C₆₇	semidirect
442. 2₋¹⁺⁴	C₂³×C₆₇	semidirect
467. #137	C₂³×C₆₇	semidirect
473. AGL(1,ℤ/8)	C₂³×C₆₇	semidirect
489. C₂×Q₁₆	C₂³×C₆₇	semidirect
501. C₂×SD₁₆	C₂³×C₆₇	semidirect
515. #131	C₂³×C₆₇	semidirect
516. #131	C₂³×C₆₇	semidirect
529. #124	C₂³×C₆₇	semidirect
532. #108	C₂³×C₆₇	semidirect
533. #108	C₂³×C₆₇	semidirect
535. #104	C₂³×C₆₇	semidirect
536. #104	C₂³×C₆₇	semidirect
537. #101	C₂³×C₆₇	semidirect
538. #100	C₂³×C₆₇	semidirect
539. C₄×C₈	C₂³×C₆₇	semidirect
755. C₂	C₆₇×#3290	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×#578×C₆₇	2
C₂×#577×C₆₇	2
C₂×#576×C₆₇	2
C₆₇×#3290	2
C₂×#495×C₆₇	2
C₂×#473×C₆₇	2
C₂×#472×C₆₇	2
C₂×#471×C₆₇	2
C₂×#454×C₆₇	2
C₂×#455×C₆₇	2
C₂×#443×C₆₇	2
C₂×#3290	67

Subgroups — C2×C67×#3290 #30740352

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₇×#3290 #30740352