Subgroups — C₆₇×#61051 #30740302

Order 17152.

2734 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#576×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#135×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3485	C₂	1	2	yes	maximal, complemented
4	C₆₇×#3283	C₂	1	4	yes	maximal, complemented
5	C₆₇×#3280	C₂	1	4	yes	maximal, complemented
6	C₆₇×#3267	C₂	1	8	yes	maximal, complemented
7	C₆₇×#3156	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#3059	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#3050	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#3042	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3009	C₂	1	2	yes	maximal, complemented
12	C₆₇×#3005	C₂	1	2	yes	maximal, complemented
13	C₆₇×#2948	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#2929	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×H(5,𝔽₂)×C₆₇	C₂²	1	2	yes	—
16	C₂²×#41×C₆₇	C₂²	1	2	yes	complemented
17	#576×C₆₇	—	2	8	no	—
18	C₂×#137×C₆₇	C₂²	1	2	yes	complemented
19	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	2	yes	—
20	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	4	yes	complemented
21	C₂×#135×C₆₇	—	2	8	no	—
22	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic
23	C₂×#135×C₆₇	C₂²	1	4	yes	complemented
24	C₂×#135×C₆₇	C₂²	1	4	yes	complemented
25	C₂×#135×C₆₇	C₂²	1	2	yes	complemented
26	C₂²×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
27	C₂²×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
28	C₂²×D₈×C₆₇	C₂²	1	1	yes	characteristic
29	C₂²×D₈×C₆₇	C₂²	1	2	yes	complemented
30	C₂×#131×C₆₇	C₂²	1	1	yes	characteristic
31	C₂³×C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
32	#547×C₆₇	—	2	4	no	—
33	#547×C₆₇	C₂²	1	8	yes	complemented
34	#546×C₆₇	—	2	4	no	—
35	#546×C₆₇	C₂²	1	8	yes	complemented
36	#536×C₆₇	C₂²	1	2	yes	—
37	#536×C₆₇	C₂²	1	2	yes	complemented
38	#534×C₆₇	—	2	4	no	—
39	#525×C₆₇	C₂²	1	1	yes	characteristic
40	#525×C₆₇	C₂²	1	2	yes	complemented
41	C₂×#123×C₆₇	—	2	4	no	—
42	#518×C₆₇	C₂²	1	2	yes	complemented
43	#497×C₆₇	C₂²	1	4	yes	complemented
44	#495×C₆₇	C₂²	1	2	yes	complemented
45	#494×C₆₇	C₂²	1	2	yes	complemented
46	#470×C₆₇	C₂²	1	4	yes	complemented
47	#467×C₆₇	C₂²	1	4	yes	complemented
48	#467×C₆₇	C₂²	1	2	yes	complemented
49	#466×C₆₇	C₂²	1	2	yes	complemented
50	#465×C₆₇	C₂²	1	4	yes	complemented
51	#463×C₆₇	C₂²	1	8	yes	complemented
52	#461×C₆₇	C₂²	1	8	yes	complemented
53	#452×C₆₇	C₂²	1	8	yes	complemented
54	#452×C₆₇	C₂²	1	8	yes	complemented
55	#450×C₆₇	C₂²	1	8	yes	complemented
56	#449×C₆₇	C₂²	1	8	yes	complemented
57	#442×C₆₇	C₂²	1	4	yes	complemented
58	C₄×D₈×C₆₇	C₂²	1	4	yes	complemented
59	#435×C₆₇	C₂²	1	4	yes	complemented
60	C₈×D₄×C₆₇	C₂²	1	4	yes	complemented
61	#427×C₆₇	C₂²	1	1	yes	characteristic, complemented
62	#424×C₆₇	C₂²	1	1	yes	characteristic, complemented
63	#419×C₆₇	C₂²	1	2	yes	complemented
64	#418×C₆₇	C₂²	1	2	yes	complemented
65	#416×C₆₇	C₂²	1	2	yes	complemented
66	#408×C₆₇	C₂²	1	1	yes	characteristic
67	#407×C₆₇	C₂²	1	1	yes	characteristic, complemented
68	#405×C₆₇	C₂²	1	1	yes	characteristic, complemented
69	H(5,𝔽₂)×C₆₇	—	2	8	no	—
70	H(5,𝔽₂)×C₆₇	—	4	4	no	—
71	C₂×#41×C₆₇	—	2	2	no	—
72	C₂×#41×C₆₇	—	2	4	no	—
73	C₂×#41×C₆₇	—	2	8	no	—
74	C₂×#41×C₆₇	—	4	4	no	—
75	C₂×#41×C₆₇	C₂³	1	2	yes	—
76	C₂×#41×C₆₇	C₂³	1	8	yes	—
77	C₂×#41×C₆₇	C₂³	1	4	yes	—
78	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
79	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
80	C₂²×D₄×C₆₇	—	2	2	no	—
81	C₂²×D₄×C₆₇	—	2	4	no	—
82	C₂²×D₄×C₆₇	—	2	2	no	—
83	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
84	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
85	C₂³×C₄×C₆₇	—	2	2	no	—
86	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
87	#137×C₆₇	—	4	4	no	—
88	AGL(1,ℤ/8)×C₆₇	—	2	8	no	—
89	AGL(1,ℤ/8)×C₆₇	—	2	16	no	—
90	#135×C₆₇	—	2	16	no	—
91	#135×C₆₇	—	2	16	no	—
92	#135×C₆₇	—	2	8	no	—
93	#135×C₆₇	—	2	4	no	—
94	C₂×Q₁₆×C₆₇	—	2	4	no	—
95	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
96	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
97	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
98	C₂×Q₁₆×C₆₇	C₂³	1	4	yes	—
99	C₂×SD₁₆×C₆₇	—	2	8	no	—
100	C₂×SD₁₆×C₆₇	C₂³	1	8	yes	—
101	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
102	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
103	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
104	C₂×D₈×C₆₇	—	2	8	no	—
105	C₂×D₈×C₆₇	D₄	1	8	yes	complemented
106	C₂×D₈×C₆₇	C₂³	1	4	yes	—
107	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
108	C₂×D₈×C₆₇	C₂³	1	2	yes	—
109	C₂×D₈×C₆₇	C₂³	1	2	yes	—
110	#131×C₆₇	—	2	4	no	—
111	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
112	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
113	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
114	C₂²×C₈×C₆₇	—	2	4	no	—
115	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
116	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
117	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
118	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
119	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
120	C₄⋊Q₈×C₆₇	—	2	2	no	—
121	C₄⋊Q₈×C₆₇	C₂³	1	4	yes	—
122	#124×C₆₇	—	2	2	no	—
123	#124×C₆₇	C₂³	1	4	yes	—
124	#123×C₆₇	—	2	4	no	—
125	#123×C₆₇	—	2	2	no	—
126	#123×C₆₇	—	2	8	no	—
127	#123×C₆₇	—	2	4	no	—
128	#123×C₆₇	—	2	8	no	—
129	#123×C₆₇	—	2	8	no	—
130	#123×C₆₇	D₄	1	2	yes	—
131	C₂²⋊Q₈×C₆₇	—	2	4	no	—
132	C₂²⋊Q₈×C₆₇	D₄	1	2	yes	—
133	C₂²⋊Q₈×C₆₇	C₂³	1	8	yes	—
134	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
135	#121×C₆₇	—	2	8	no	—
136	#121×C₆₇	—	2	8	no	—
137	#121×C₆₇	D₄	1	2	yes	—
138	#121×C₆₇	C₂³	1	4	yes	—
139	#120×C₆₇	—	2	2	no	—
140	#120×C₆₇	—	2	8	no	—
141	#120×C₆₇	D₄	1	2	yes	—
142	C₄×D₄×C₆₇	—	2	4	no	—
143	C₄×D₄×C₆₇	—	2	4	no	—
144	C₄×D₄×C₆₇	C₂³	1	8	yes	—
145	C₄×D₄×C₆₇	C₂³	1	4	yes	—
146	#117×C₆₇	C₂³	1	2	yes	—
147	#117×C₆₇	C₂³	1	1	yes	characteristic
148	C₂×C₄⋊C₄×C₆₇	—	2	8	no	—
149	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
150	C₂×C₂²⋊C₄×C₆₇	—	2	8	no	—
151	#107×C₆₇	C₂³	1	2	yes	—
152	#106×C₆₇	C₂³	1	2	yes	—
153	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
154	#103×C₆₇	C₂³	1	8	yes	—
155	#103×C₆₇	C₂³	1	4	yes	—
156	#102×C₆₇	C₂³	1	8	yes	—
157	#102×C₆₇	C₂³	1	4	yes	—
158	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
159	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
160	#97×C₆₇	C₂³	1	2	yes	—
161	C₄×C₈×C₆₇	C₂³	1	2	yes	—
162	C₂⁴×C₆₇	—	2	2	no	—
163	C₂⁴×C₆₇	—	2	4	no	—
164	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
165	#41×C₆₇	—	2	2	no	—
166	#41×C₆₇	—	2	2	no	—
167	#41×C₆₇	—	2	16	no	—
168	#41×C₆₇	—	2	8	no	—
169	#41×C₆₇	—	2	4	no	—
170	#41×C₆₇	—	2	4	no	—
171	#41×C₆₇	—	4	8	no	—
172	#41×C₆₇	—	4	4	no	—
173	#41×C₆₇	—	4	16	no	—
174	#41×C₆₇	—	4	8	no	—
175	C₂×Q₈×C₆₇	—	2	2	no	—
176	C₂×Q₈×C₆₇	—	2	4	no	—
177	C₂×Q₈×C₆₇	—	2	4	no	—
178	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
179	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
180	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
181	C₂×D₄×C₆₇	—	2	8	no	—
182	C₂×D₄×C₆₇	—	2	8	no	—
183	C₂×D₄×C₆₇	—	2	2	no	—
184	C₂×D₄×C₆₇	—	2	4	no	—
185	C₂×D₄×C₆₇	—	2	4	no	—
186	C₂×D₄×C₆₇	—	2	2	no	—
187	C₂×D₄×C₆₇	—	2	4	no	—
188	C₂×D₄×C₆₇	—	2	4	no	—
189	C₂×D₄×C₆₇	—	4	4	no	—
190	C₂×D₄×C₆₇	—	4	8	no	—
191	C₂×D₄×C₆₇	—	4	16	no	—
192	C₂×D₄×C₆₇	—	4	8	no	—
193	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
194	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
195	C₂×D₄×C₆₇	C₂×D₄	1	8	yes	—
196	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	—
197	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
198	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
199	C₂²×C₄×C₆₇	—	2	2	no	—
200	C₂²×C₄×C₆₇	—	2	2	no	—
201	C₂²×C₄×C₆₇	—	2	2	no	—
202	C₂²×C₄×C₆₇	—	2	8	no	—
203	C₂²×C₄×C₆₇	—	2	4	no	—
204	C₂²×C₄×C₆₇	—	2	2	no	—
205	C₂²×C₄×C₆₇	—	2	8	no	—
206	C₂²×C₄×C₆₇	—	4	8	no	—
207	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
208	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
209	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
210	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
211	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
212	Q₁₆×C₆₇	—	2	4	no	—
213	Q₁₆×C₆₇	—	2	4	no	—
214	Q₁₆×C₆₇	—	2	2	no	—
215	Q₁₆×C₆₇	—	4	4	no	—
216	SD₁₆×C₆₇	—	2	16	no	—
217	SD₁₆×C₆₇	—	2	8	no	—
218	SD₁₆×C₆₇	—	2	4	no	—
219	SD₁₆×C₆₇	—	4	4	no	—
220	D₈×C₆₇	—	2	8	no	—
221	D₈×C₆₇	—	2	2	no	—
222	D₈×C₆₇	C₂×D₄	1	8	yes	—
223	D₈×C₆₇	C₂×D₄	1	8	yes	—
224	M₁₆×C₆₇	—	2	2	no	—
225	M₁₆×C₆₇	—	2	2	no	—
226	M₁₆×C₆₇	—	2	4	no	—
227	C₂×C₈×C₆₇	—	2	2	no	—
228	C₂×C₈×C₆₇	—	2	4	no	—
229	C₂×C₈×C₆₇	—	2	4	no	—
230	C₂×C₈×C₆₇	—	2	4	no	—
231	C₂×C₈×C₆₇	C₂×D₄	1	4	yes	—
232	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
233	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
234	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
235	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
236	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
237	C₄⋊C₄×C₆₇	—	2	4	no	—
238	C₄⋊C₄×C₆₇	—	2	8	no	—
239	C₄⋊C₄×C₆₇	—	2	8	no	—
240	C₄⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
241	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
242	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
243	C₂²⋊C₄×C₆₇	—	2	2	no	—
244	C₂²⋊C₄×C₆₇	—	2	8	no	—
245	C₂²⋊C₄×C₆₇	—	2	4	no	—
246	C₂²⋊C₄×C₆₇	—	2	4	no	—
247	C₂²⋊C₄×C₆₇	—	2	8	no	—
248	C₂²⋊C₄×C₆₇	—	2	8	no	—
249	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
250	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
251	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
252	C₄²×C₆₇	—	2	2	no	—
253	C₄²×C₆₇	C₂⁴	1	2	yes	—
254	C₂³×C₆₇	—	2	2	no	—
255	C₂³×C₆₇	—	2	4	no	—
256	C₂³×C₆₇	—	2	8	no	—
257	C₂³×C₆₇	—	2	2	no	—
258	C₂³×C₆₇	—	4	2	no	—
259	C₂³×C₆₇	—	4	8	no	—
260	C₂³×C₆₇	—	8	4	no	—
261	C₂³×C₆₇	—	8	8	no	—
262	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
263	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
264	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
265	Q₈×C₆₇	—	2	2	no	—
266	Q₈×C₆₇	—	2	2	no	—
267	Q₈×C₆₇	—	2	4	no	—
268	Q₈×C₆₇	—	2	4	no	—
269	Q₈×C₆₇	—	2	2	no	—
270	Q₈×C₆₇	—	4	4	no	—
271	D₄×C₆₇	—	2	4	no	—
272	D₄×C₆₇	—	2	8	no	—
273	D₄×C₆₇	—	2	2	no	—
274	D₄×C₆₇	—	2	2	no	—
275	D₄×C₆₇	—	2	4	no	—
276	D₄×C₆₇	—	2	2	no	—
277	D₄×C₆₇	—	4	4	no	—
278	D₄×C₆₇	—	4	8	no	—
279	D₄×C₆₇	—	4	8	no	—
280	D₄×C₆₇	—	4	16	no	—
281	D₄×C₆₇	—	4	4	no	—
282	D₄×C₆₇	—	8	4	no	—
283	D₄×C₆₇	C₂²×D₄	1	8	yes	—
284	C₂×C₄×C₆₇	—	2	2	no	—
285	C₂×C₄×C₆₇	—	2	4	no	—
286	C₂×C₄×C₆₇	—	2	2	no	—
287	C₂×C₄×C₆₇	—	2	2	no	—
288	C₂×C₄×C₆₇	—	2	2	no	—
289	C₂×C₄×C₆₇	—	2	2	no	—
290	C₂×C₄×C₆₇	—	2	4	no	—
291	C₂×C₄×C₆₇	—	2	4	no	—
292	C₂×C₄×C₆₇	—	2	2	no	—
293	C₂×C₄×C₆₇	—	4	16	no	—
294	C₂×C₄×C₆₇	—	4	8	no	—
295	C₂×C₄×C₆₇	—	4	4	no	—
296	C₂×C₄×C₆₇	—	4	4	no	—
297	C₂×C₄×C₆₇	—	8	8	no	—
298	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
299	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
300	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
301	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
302	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
303	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
304	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
305	C₈×C₆₇	—	2	2	no	—
306	C₈×C₆₇	—	2	2	no	—
307	C₈×C₆₇	—	2	2	no	—
308	C₈×C₆₇	C₂²×D₄	1	2	yes	—
309	C₈×C₆₇	C₂²×D₄	1	2	yes	—
310	C₂²×C₆₇	—	2	2	no	—
311	C₂²×C₆₇	—	2	2	no	—
312	C₂²×C₆₇	—	2	4	no	—
313	C₂²×C₆₇	—	2	2	no	—
314	C₂²×C₆₇	—	2	2	no	—
315	C₂²×C₆₇	—	2	2	no	—
316	C₂²×C₆₇	—	2	8	no	—
317	C₂²×C₆₇	—	4	4	no	—
318	C₂²×C₆₇	—	4	8	no	—
319	C₂²×C₆₇	—	4	4	no	—
320	C₂²×C₆₇	—	4	2	no	—
321	C₂²×C₆₇	—	8	8	no	—
322	C₂²×C₆₇	—	16	8	no	—
323	C₂²×C₆₇	D₄²	1	2	yes	—
324	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
325	C₄×C₆₇	—	2	4	no	—
326	C₄×C₆₇	—	2	2	no	—
327	C₄×C₆₇	—	2	2	no	—
328	C₄×C₆₇	—	4	4	no	—
329	C₄×C₆₇	—	4	2	no	—
330	C₄×C₆₇	—	4	4	no	—
331	C₄×C₆₇	D₄²	1	2	yes	—
332	C₄×C₆₇	C₂³×D₄	1	1	yes	characteristic
333	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
334	#61051	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
335	C₂×C₆₇	—	2	2	no	—
336	C₂×C₆₇	—	4	2	no	—
337	C₂×C₆₇	—	4	2	no	—
338	C₂×C₆₇	—	4	8	no	—
339	C₂×C₆₇	—	8	2	no	—
340	C₂×C₆₇	C₂×D₄²	1	1	yes	characteristic
341	C₂×C₆₇	#3584	1	2	yes	—
342	C₂×#576	C₂×C₆₇	1	1	yes	characteristic, complemented
343	C₂²×#135	C₂×C₆₇	1	1	yes	characteristic, complemented
344	#3485	C₂×C₆₇	1	2	yes	complemented
345	#3283	C₂×C₆₇	1	4	yes	complemented
346	#3280	C₂×C₆₇	1	4	yes	complemented
347	#3267	C₂×C₆₇	1	8	yes	complemented
348	#3156	C₂×C₆₇	1	1	yes	characteristic, complemented
349	#3059	C₂×C₆₇	1	1	yes	characteristic, complemented
350	#3050	C₂×C₆₇	1	1	yes	characteristic, complemented
351	#3042	C₂×C₆₇	1	2	yes	complemented
352	#3009	C₂×C₆₇	1	2	yes	complemented
353	#3005	C₂×C₆₇	1	2	yes	complemented
354	#2948	C₂×C₆₇	1	1	yes	characteristic, complemented
355	#2929	C₂×C₆₇	1	1	yes	characteristic, complemented
356	C₆₇	#61051	1	1	yes	characteristic, direct product factor, Sylow
357	C₂×H(5,𝔽₂)	C₂²×C₆₇	1	2	yes	—
358	C₂²×#41	C₂²×C₆₇	1	2	yes	complemented
359	#576	—	2	8	no	—
360	C₂×#137	C₂²×C₆₇	1	2	yes	complemented
361	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	—
362	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	4	yes	complemented
363	C₂×#135	—	2	8	no	—
364	C₂×#135	C₂²×C₆₇	1	1	yes	characteristic
365	C₂×#135	C₂²×C₆₇	1	4	yes	complemented
366	C₂×#135	C₂²×C₆₇	1	4	yes	complemented
367	C₂×#135	C₂²×C₆₇	1	2	yes	complemented
368	C₂²×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
369	C₂²×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
370	C₂²×D₈	C₂²×C₆₇	1	1	yes	characteristic
371	C₂²×D₈	C₂²×C₆₇	1	2	yes	complemented
372	C₂×#131	C₂²×C₆₇	1	1	yes	characteristic
373	C₂³×C₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
374	#547	—	2	4	no	—
375	#547	C₂²×C₆₇	1	8	yes	complemented
376	#546	—	2	4	no	—
377	#546	C₂²×C₆₇	1	8	yes	complemented
378	#536	C₂²×C₆₇	1	2	yes	—
379	#536	C₂²×C₆₇	1	2	yes	complemented
380	#534	—	2	4	no	—
381	#525	C₂²×C₆₇	1	1	yes	characteristic
382	#525	C₂²×C₆₇	1	2	yes	complemented
383	C₂×#123	—	2	4	no	—
384	#518	C₂²×C₆₇	1	2	yes	complemented
385	#497	C₂²×C₆₇	1	4	yes	complemented
386	#495	C₂²×C₆₇	1	2	yes	complemented
387	#494	C₂²×C₆₇	1	2	yes	complemented
388	#470	C₂²×C₆₇	1	4	yes	complemented
389	#467	C₂²×C₆₇	1	4	yes	complemented
390	#467	C₂²×C₆₇	1	2	yes	complemented
391	#466	C₂²×C₆₇	1	2	yes	complemented
392	#465	C₂²×C₆₇	1	4	yes	complemented
393	#463	C₂²×C₆₇	1	8	yes	complemented
394	#461	C₂²×C₆₇	1	8	yes	complemented
395	#452	C₂²×C₆₇	1	8	yes	complemented
396	#452	C₂²×C₆₇	1	8	yes	complemented
397	#450	C₂²×C₆₇	1	8	yes	complemented
398	#449	C₂²×C₆₇	1	8	yes	complemented
399	#442	C₂²×C₆₇	1	4	yes	complemented
400	C₄×D₈	C₂²×C₆₇	1	4	yes	complemented
401	#435	C₂²×C₆₇	1	4	yes	complemented
402	C₈×D₄	C₂²×C₆₇	1	4	yes	complemented
403	#427	C₂²×C₆₇	1	1	yes	characteristic, complemented
404	#424	C₂²×C₆₇	1	1	yes	characteristic, complemented
405	#419	C₂²×C₆₇	1	2	yes	complemented
406	#418	C₂²×C₆₇	1	2	yes	complemented
407	#416	C₂²×C₆₇	1	2	yes	complemented
408	#408	C₂²×C₆₇	1	1	yes	characteristic
409	#407	C₂²×C₆₇	1	1	yes	characteristic, complemented
410	#405	C₂²×C₆₇	1	1	yes	characteristic, complemented
411	H(5,𝔽₂)	—	2	8	no	—
412	H(5,𝔽₂)	—	4	4	no	—
413	C₂×#41	—	2	2	no	—
414	C₂×#41	—	2	4	no	—
415	C₂×#41	—	2	8	no	—
416	C₂×#41	—	4	4	no	—
417	C₂×#41	C₂³×C₆₇	1	2	yes	—
418	C₂×#41	C₂³×C₆₇	1	8	yes	—
419	C₂×#41	C₂³×C₆₇	1	4	yes	—
420	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
421	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
422	C₂²×D₄	—	2	2	no	—
423	C₂²×D₄	—	2	4	no	—
424	C₂²×D₄	—	2	2	no	—
425	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
426	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
427	C₂³×C₄	—	2	2	no	—
428	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
429	#137	—	4	4	no	—
430	AGL(1,ℤ/8)	—	2	8	no	—
431	AGL(1,ℤ/8)	—	2	16	no	—
432	#135	—	2	16	no	—
433	#135	—	2	16	no	—
434	#135	—	2	8	no	—
435	#135	—	2	4	no	—
436	C₂×Q₁₆	—	2	4	no	—
437	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
438	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
439	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic
440	C₂×Q₁₆	C₂³×C₆₇	1	4	yes	—
441	C₂×SD₁₆	—	2	8	no	—
442	C₂×SD₁₆	C₂³×C₆₇	1	8	yes	—
443	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
444	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
445	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
446	C₂×D₈	—	2	8	no	—
447	C₂×D₈	D₄×C₆₇	1	8	yes	complemented
448	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic
449	C₂×D₈	C₂³×C₆₇	1	4	yes	—
450	C₂×D₈	C₂³×C₆₇	1	2	yes	—
451	C₂×D₈	C₂³×C₆₇	1	2	yes	—
452	#131	—	2	4	no	—
453	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
454	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
455	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
456	C₂²×C₈	—	2	4	no	—
457	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
458	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
459	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
460	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
461	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
462	C₄⋊Q₈	—	2	2	no	—
463	C₄⋊Q₈	C₂³×C₆₇	1	4	yes	—
464	#124	—	2	2	no	—
465	#124	C₂³×C₆₇	1	4	yes	—
466	#123	—	2	4	no	—
467	#123	—	2	2	no	—
468	#123	—	2	8	no	—
469	#123	—	2	4	no	—
470	#123	—	2	8	no	—
471	#123	—	2	8	no	—
472	#123	D₄×C₆₇	1	2	yes	—
473	C₂²⋊Q₈	—	2	4	no	—
474	C₂²⋊Q₈	D₄×C₆₇	1	2	yes	—
475	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
476	C₂²⋊Q₈	C₂³×C₆₇	1	8	yes	—
477	#121	—	2	8	no	—
478	#121	—	2	8	no	—
479	#121	D₄×C₆₇	1	2	yes	—
480	#121	C₂³×C₆₇	1	4	yes	—
481	#120	—	2	2	no	—
482	#120	—	2	8	no	—
483	#120	D₄×C₆₇	1	2	yes	—
484	C₄×D₄	—	2	4	no	—
485	C₄×D₄	—	2	4	no	—
486	C₄×D₄	C₂³×C₆₇	1	8	yes	—
487	C₄×D₄	C₂³×C₆₇	1	4	yes	—
488	#117	C₂³×C₆₇	1	2	yes	—
489	#117	C₂³×C₆₇	1	1	yes	characteristic
490	C₂×C₄⋊C₄	—	2	8	no	—
491	C₂×C₂²⋊C₄	—	2	4	no	—
492	C₂×C₂²⋊C₄	—	2	8	no	—
493	#107	C₂³×C₆₇	1	2	yes	—
494	#106	C₂³×C₆₇	1	2	yes	—
495	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
496	#103	C₂³×C₆₇	1	4	yes	—
497	#103	C₂³×C₆₇	1	8	yes	—
498	#102	C₂³×C₆₇	1	4	yes	—
499	#102	C₂³×C₆₇	1	8	yes	—
500	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
501	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
502	#97	C₂³×C₆₇	1	2	yes	—
503	C₄×C₈	C₂³×C₆₇	1	2	yes	—
504	C₂⁴	—	2	2	no	—
505	C₂⁴	—	2	4	no	—
506	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
507	#41	—	2	2	no	—
508	#41	—	2	2	no	—
509	#41	—	2	16	no	—
510	#41	—	2	8	no	—
511	#41	—	2	4	no	—
512	#41	—	2	4	no	—
513	#41	—	4	8	no	—
514	#41	—	4	4	no	—
515	#41	—	4	16	no	—
516	#41	—	4	8	no	—
517	C₂×Q₈	—	2	2	no	—
518	C₂×Q₈	—	2	4	no	—
519	C₂×Q₈	—	2	4	no	—
520	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
521	C₂×Q₈	C₂⁴×C₆₇	1	4	yes	—
522	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
523	C₂×D₄	—	2	8	no	—
524	C₂×D₄	—	2	8	no	—
525	C₂×D₄	—	2	2	no	—
526	C₂×D₄	—	2	4	no	—
527	C₂×D₄	—	2	4	no	—
528	C₂×D₄	—	2	2	no	—
529	C₂×D₄	—	2	4	no	—
530	C₂×D₄	—	2	4	no	—
531	C₂×D₄	—	4	4	no	—
532	C₂×D₄	—	4	8	no	—
533	C₂×D₄	—	4	16	no	—
534	C₂×D₄	—	4	8	no	—
535	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
536	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
537	C₂×D₄	C₂×D₄×C₆₇	1	8	yes	—
538	C₂×D₄	C₂×D₄×C₆₇	1	4	yes	—
539	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
540	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
541	C₂²×C₄	—	2	2	no	—
542	C₂²×C₄	—	2	2	no	—
543	C₂²×C₄	—	2	2	no	—
544	C₂²×C₄	—	2	8	no	—
545	C₂²×C₄	—	2	4	no	—
546	C₂²×C₄	—	2	2	no	—
547	C₂²×C₄	—	2	8	no	—
548	C₂²×C₄	—	4	8	no	—
549	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
550	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
551	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
552	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
553	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
554	Q₁₆	—	2	4	no	—
555	Q₁₆	—	2	4	no	—
556	Q₁₆	—	2	2	no	—
557	Q₁₆	—	4	4	no	—
558	SD₁₆	—	2	16	no	—
559	SD₁₆	—	2	8	no	—
560	SD₁₆	—	2	4	no	—
561	SD₁₆	—	4	4	no	—
562	D₈	—	2	8	no	—
563	D₈	—	2	2	no	—
564	D₈	C₂×D₄×C₆₇	1	8	yes	—
565	D₈	C₂×D₄×C₆₇	1	8	yes	—
566	M₁₆	—	2	2	no	—
567	M₁₆	—	2	2	no	—
568	M₁₆	—	2	4	no	—
569	C₂×C₈	—	2	2	no	—
570	C₂×C₈	—	2	4	no	—
571	C₂×C₈	—	2	4	no	—
572	C₂×C₈	—	2	4	no	—
573	C₂×C₈	C₂×D₄×C₆₇	1	4	yes	—
574	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
575	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
576	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
577	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
578	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
579	C₄⋊C₄	—	2	4	no	—
580	C₄⋊C₄	—	2	8	no	—
581	C₄⋊C₄	—	2	8	no	—
582	C₄⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
583	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
584	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
585	C₂²⋊C₄	—	2	2	no	—
586	C₂²⋊C₄	—	2	8	no	—
587	C₂²⋊C₄	—	2	4	no	—
588	C₂²⋊C₄	—	2	4	no	—
589	C₂²⋊C₄	—	2	8	no	—
590	C₂²⋊C₄	—	2	8	no	—
591	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
592	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
593	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
594	C₄²	—	2	2	no	—
595	C₄²	C₂⁴×C₆₇	1	2	yes	—
596	C₂³	—	2	2	no	—
597	C₂³	—	2	4	no	—
598	C₂³	—	2	8	no	—
599	C₂³	—	2	2	no	—
600	C₂³	—	4	2	no	—
601	C₂³	—	4	8	no	—
602	C₂³	—	8	4	no	—
603	C₂³	—	8	8	no	—
604	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
605	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
606	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
607	Q₈	—	2	2	no	—
608	Q₈	—	2	2	no	—
609	Q₈	—	2	4	no	—
610	Q₈	—	2	4	no	—
611	Q₈	—	2	2	no	—
612	Q₈	—	4	4	no	—
613	D₄	—	2	4	no	—
614	D₄	—	2	8	no	—
615	D₄	—	2	2	no	—
616	D₄	—	2	2	no	—
617	D₄	—	2	4	no	—
618	D₄	—	2	2	no	—
619	D₄	—	4	4	no	—
620	D₄	—	4	8	no	—
621	D₄	—	4	8	no	—
622	D₄	—	4	16	no	—
623	D₄	—	4	4	no	—
624	D₄	—	8	4	no	—
625	D₄	C₂²×D₄×C₆₇	1	8	yes	—
626	C₂×C₄	—	2	2	no	—
627	C₂×C₄	—	2	4	no	—
628	C₂×C₄	—	2	2	no	—
629	C₂×C₄	—	2	2	no	—
630	C₂×C₄	—	2	2	no	—
631	C₂×C₄	—	2	2	no	—
632	C₂×C₄	—	2	4	no	—
633	C₂×C₄	—	2	4	no	—
634	C₂×C₄	—	2	2	no	—
635	C₂×C₄	—	4	16	no	—
636	C₂×C₄	—	4	8	no	—
637	C₂×C₄	—	4	4	no	—
638	C₂×C₄	—	4	4	no	—
639	C₂×C₄	—	8	8	no	—
640	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
641	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
642	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
643	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
644	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
645	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
646	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
647	C₈	—	2	2	no	—
648	C₈	—	2	2	no	—
649	C₈	—	2	2	no	—
650	C₈	C₂²×D₄×C₆₇	1	2	yes	—
651	C₈	C₂²×D₄×C₆₇	1	2	yes	—
652	C₂²	—	2	2	no	—
653	C₂²	—	2	2	no	—
654	C₂²	—	2	4	no	—
655	C₂²	—	2	2	no	—
656	C₂²	—	2	2	no	—
657	C₂²	—	2	2	no	—
658	C₂²	—	2	8	no	—
659	C₂²	—	4	4	no	—
660	C₂²	—	4	8	no	—
661	C₂²	—	4	4	no	—
662	C₂²	—	4	2	no	—
663	C₂²	—	8	8	no	—
664	C₂²	—	16	8	no	—
665	C₂²	D₄²×C₆₇	1	2	yes	—
666	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
667	C₄	—	2	4	no	—
668	C₄	—	2	2	no	—
669	C₄	—	2	2	no	—
670	C₄	—	4	4	no	—
671	C₄	—	4	2	no	—
672	C₄	—	4	4	no	—
673	C₄	D₄²×C₆₇	1	2	yes	—
674	C₄	C₂³×D₄×C₆₇	1	1	yes	characteristic
675	C₄	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
676	C₂	—	2	2	no	—
677	C₂	—	4	2	no	—
678	C₂	—	4	2	no	—
679	C₂	—	4	8	no	—
680	C₂	—	8	2	no	—
681	C₂	C₂×D₄²×C₆₇	1	1	yes	characteristic
682	C₂	C₆₇×#3584	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ #525×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#576×C₆₇	C₂	semidirect
2. C₂²×#135×C₆₇	C₂	semidirect
3. C₆₇×#3485	C₂	semidirect
4. C₆₇×#3283	C₂	semidirect
5. C₆₇×#3280	C₂	semidirect
6. C₆₇×#3267	C₂	semidirect
7. C₆₇×#3156	C₂	semidirect
8. C₆₇×#3059	C₂	semidirect
9. C₆₇×#3050	C₂	semidirect
10. C₆₇×#3042	C₂	semidirect
11. C₆₇×#3009	C₂	semidirect
12. C₆₇×#3005	C₂	semidirect
13. C₆₇×#2948	C₂	semidirect
14. C₆₇×#2929	C₂	semidirect
16. C₂²×#41×C₆₇	C₂²	semidirect
18. C₂×#137×C₆₇	C₂²	semidirect
20. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
23. C₂×#135×C₆₇	C₂²	semidirect
24. C₂×#135×C₆₇	C₂²	semidirect
25. C₂×#135×C₆₇	C₂²	semidirect
26. C₂²×Q₁₆×C₆₇	C₂²	semidirect
27. C₂²×SD₁₆×C₆₇	C₂²	semidirect
29. C₂²×D₈×C₆₇	C₂²	semidirect
31. C₂³×C₈×C₆₇	C₂²	semidirect
33. #547×C₆₇	C₂²	semidirect
35. #546×C₆₇	C₂²	semidirect
37. #536×C₆₇	C₂²	semidirect
40. #525×C₆₇	C₂²	semidirect
42. #518×C₆₇	C₂²	semidirect
43. #497×C₆₇	C₂²	semidirect
44. #495×C₆₇	C₂²	semidirect
45. #494×C₆₇	C₂²	semidirect
46. #470×C₆₇	C₂²	semidirect
47. #467×C₆₇	C₂²	semidirect
48. #467×C₆₇	C₂²	semidirect
49. #466×C₆₇	C₂²	semidirect
50. #465×C₆₇	C₂²	semidirect
51. #463×C₆₇	C₂²	semidirect
52. #461×C₆₇	C₂²	semidirect
53. #452×C₆₇	C₂²	semidirect
54. #452×C₆₇	C₂²	semidirect
55. #450×C₆₇	C₂²	semidirect
56. #449×C₆₇	C₂²	semidirect
57. #442×C₆₇	C₂²	semidirect
58. C₄×D₈×C₆₇	C₂²	semidirect
59. #435×C₆₇	C₂²	semidirect
60. C₈×D₄×C₆₇	C₂²	semidirect
61. #427×C₆₇	C₂²	semidirect
62. #424×C₆₇	C₂²	semidirect
63. #419×C₆₇	C₂²	semidirect
64. #418×C₆₇	C₂²	semidirect
65. #416×C₆₇	C₂²	semidirect
67. #407×C₆₇	C₂²	semidirect
68. #405×C₆₇	C₂²	semidirect
105. C₂×D₈×C₆₇	D₄	semidirect
334. #61051	C₆₇	direct (N × H)
342. C₂×#576	C₂×C₆₇	semidirect
343. C₂²×#135	C₂×C₆₇	semidirect
344. #3485	C₂×C₆₇	semidirect
345. #3283	C₂×C₆₇	semidirect
346. #3280	C₂×C₆₇	semidirect
347. #3267	C₂×C₆₇	semidirect
348. #3156	C₂×C₆₇	semidirect
349. #3059	C₂×C₆₇	semidirect
350. #3050	C₂×C₆₇	semidirect
351. #3042	C₂×C₆₇	semidirect
352. #3009	C₂×C₆₇	semidirect
353. #3005	C₂×C₆₇	semidirect
354. #2948	C₂×C₆₇	semidirect
355. #2929	C₂×C₆₇	semidirect
356. C₆₇	#61051	direct (N × H)
358. C₂²×#41	C₂²×C₆₇	semidirect
360. C₂×#137	C₂²×C₆₇	semidirect
362. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
365. C₂×#135	C₂²×C₆₇	semidirect
366. C₂×#135	C₂²×C₆₇	semidirect
367. C₂×#135	C₂²×C₆₇	semidirect
368. C₂²×Q₁₆	C₂²×C₆₇	semidirect
369. C₂²×SD₁₆	C₂²×C₆₇	semidirect
371. C₂²×D₈	C₂²×C₆₇	semidirect
373. C₂³×C₈	C₂²×C₆₇	semidirect
375. #547	C₂²×C₆₇	semidirect
377. #546	C₂²×C₆₇	semidirect
379. #536	C₂²×C₆₇	semidirect
382. #525	C₂²×C₆₇	semidirect
384. #518	C₂²×C₆₇	semidirect
385. #497	C₂²×C₆₇	semidirect
386. #495	C₂²×C₆₇	semidirect
387. #494	C₂²×C₆₇	semidirect
388. #470	C₂²×C₆₇	semidirect
389. #467	C₂²×C₆₇	semidirect
390. #467	C₂²×C₆₇	semidirect
391. #466	C₂²×C₆₇	semidirect
392. #465	C₂²×C₆₇	semidirect
393. #463	C₂²×C₆₇	semidirect
394. #461	C₂²×C₆₇	semidirect
395. #452	C₂²×C₆₇	semidirect
396. #452	C₂²×C₆₇	semidirect
397. #450	C₂²×C₆₇	semidirect
398. #449	C₂²×C₆₇	semidirect
399. #442	C₂²×C₆₇	semidirect
400. C₄×D₈	C₂²×C₆₇	semidirect
401. #435	C₂²×C₆₇	semidirect
402. C₈×D₄	C₂²×C₆₇	semidirect
403. #427	C₂²×C₆₇	semidirect
404. #424	C₂²×C₆₇	semidirect
405. #419	C₂²×C₆₇	semidirect
406. #418	C₂²×C₆₇	semidirect
407. #416	C₂²×C₆₇	semidirect
409. #407	C₂²×C₆₇	semidirect
410. #405	C₂²×C₆₇	semidirect
447. C₂×D₈	D₄×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#576×C₆₇	2
C₂²×#135×C₆₇	2
C₆₇×#3485	2
C₆₇×#3283	2
C₆₇×#3280	2
C₆₇×#3267	2
C₆₇×#3156	2
C₆₇×#3059	2
C₆₇×#3050	2
C₆₇×#3042	2
C₆₇×#3009	2
C₆₇×#3005	2
C₆₇×#2948	2
C₆₇×#2929	2
#61051	67

Subgroups — C67×#61051 #30740302

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61051 #30740302