Subgroups — C₆₇×#61087 #30740338

Order 17152.

2786 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#577×C₆₇	C₂	1	2	yes	maximal, complemented
2	C₆₇×#3499	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3498	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#3284	C₂	1	4	yes	maximal, complemented
5	D₄×SD₁₆×C₆₇	C₂	1	4	yes	maximal, complemented
6	C₆₇×#3278	C₂	1	4	yes	maximal, complemented
7	C₆₇×#3272	C₂	1	4	yes	maximal, complemented
8	C₂×#492×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#3057	C₂	1	2	yes	maximal, complemented
10	C₆₇×#3039	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#3038	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#3010	C₂	1	2	yes	maximal, complemented
13	C₆₇×#3009	C₂	1	2	yes	maximal, complemented
14	C₄×#135×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#2931	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×2₋¹⁺⁴×C₆₇	C₂²	1	2	yes	complemented
17	C₂×H(5,𝔽₂)×C₆₇	C₂²	1	2	yes	—
18	#577×C₆₇	—	2	16	no	—
19	C₂×#137×C₆₇	C₂²	1	2	yes	—
20	C₂×#137×C₆₇	C₂²	1	4	yes	complemented
21	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	2	yes	complemented
22	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	4	yes	complemented
23	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic
24	C₂×#135×C₆₇	C₂²	1	4	yes	complemented
25	C₂²×SD₁₆×C₆₇	C₂²	1	4	yes	complemented
26	C₂²×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
27	C₂²×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
28	C₂×#131×C₆₇	C₂²	1	2	yes	complemented
29	#550×C₆₇	C₂²	1	4	yes	—
30	D₄×Q₈×C₆₇	C₂²	1	4	yes	complemented
31	#547×C₆₇	—	2	4	no	—
32	#547×C₆₇	C₂²	1	4	yes	complemented
33	D₄²×C₆₇	—	2	4	no	—
34	D₄²×C₆₇	C₂²	1	4	yes	—
35	#536×C₆₇	—	2	2	no	—
36	#536×C₆₇	C₂²	1	2	yes	complemented
37	#535×C₆₇	—	2	2	no	—
38	#535×C₆₇	C₂²	1	2	yes	—
39	#532×C₆₇	—	2	1	no	—
40	#532×C₆₇	—	2	1	no	—
41	#532×C₆₇	C₂²	1	1	yes	characteristic
42	C₂×C₄⋊Q₈×C₆₇	—	2	1	no	—
43	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
44	C₂×#127×C₆₇	—	2	1	no	—
45	C₂×#127×C₆₇	C₂²	1	1	yes	characteristic
46	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
47	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic, complemented
48	#492×C₆₇	C₂²	1	4	yes	complemented
49	#492×C₆₇	C₂²	1	4	yes	complemented
50	#468×C₆₇	C₂²	1	8	yes	complemented
51	#465×C₆₇	C₂²	1	8	yes	complemented
52	#462×C₆₇	C₂²	1	4	yes	complemented
53	#461×C₆₇	C₂²	1	4	yes	complemented
54	#460×C₆₇	C₂²	1	4	yes	complemented
55	#459×C₆₇	C₂²	1	4	yes	complemented
56	#452×C₆₇	C₂²	1	8	yes	complemented
57	#450×C₆₇	C₂²	1	8	yes	complemented
58	#449×C₆₇	C₂²	1	8	yes	complemented
59	#448×C₆₇	C₂²	1	8	yes	complemented
60	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	complemented
61	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
62	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
63	C₄×D₈×C₆₇	C₂²	1	2	yes	complemented
64	#436×C₆₇	C₂²	1	4	yes	complemented
65	C₈×D₄×C₆₇	C₂²	1	4	yes	complemented
66	#427×C₆₇	C₂²	1	1	yes	characteristic, complemented
67	#423×C₆₇	C₂²	1	1	yes	characteristic, complemented
68	#419×C₆₇	C₂²	1	2	yes	complemented
69	#418×C₆₇	C₂²	1	2	yes	complemented
70	#416×C₆₇	C₂²	1	1	yes	characteristic
71	#416×C₆₇	C₂²	1	1	yes	characteristic, complemented
72	#408×C₆₇	C₂²	1	2	yes	complemented
73	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
74	2₋¹⁺⁴×C₆₇	—	2	8	no	—
75	2₋¹⁺⁴×C₆₇	—	4	4	no	—
76	H(5,𝔽₂)×C₆₇	—	2	8	no	—
77	H(5,𝔽₂)×C₆₇	—	4	4	no	—
78	C₂×#41×C₆₇	—	2	2	no	—
79	C₂×#41×C₆₇	—	2	2	no	—
80	C₂×#41×C₆₇	—	2	4	no	—
81	C₂×#41×C₆₇	C₂³	1	4	yes	—
82	C₂×#41×C₆₇	C₂³	1	4	yes	—
83	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
84	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
85	C₂×#41×C₆₇	C₂³	1	2	yes	—
86	C₂²×Q₈×C₆₇	—	2	2	no	—
87	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
88	C₂²×Q₈×C₆₇	C₂³	1	4	yes	—
89	C₂²×D₄×C₆₇	—	2	2	no	—
90	C₂²×D₄×C₆₇	—	2	4	no	—
91	C₂²×D₄×C₆₇	—	2	4	no	—
92	C₂²×D₄×C₆₇	—	2	2	no	—
93	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
94	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
95	#137×C₆₇	—	2	8	no	—
96	#137×C₆₇	—	2	16	no	—
97	AGL(1,ℤ/8)×C₆₇	—	2	8	no	—
98	AGL(1,ℤ/8)×C₆₇	—	2	16	no	—
99	#135×C₆₇	—	2	16	no	—
100	#135×C₆₇	D₄	1	8	yes	complemented
101	C₂×Q₁₆×C₆₇	C₂³	1	4	yes	—
102	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
103	C₂×SD₁₆×C₆₇	—	2	16	no	—
104	C₂×SD₁₆×C₆₇	—	2	8	no	—
105	C₂×SD₁₆×C₆₇	—	4	4	no	—
106	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
107	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
108	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
109	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
110	C₂×SD₁₆×C₆₇	C₂³	1	8	yes	—
111	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
112	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
113	C₂×D₈×C₆₇	C₂³	1	4	yes	—
114	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
115	#131×C₆₇	—	2	8	no	—
116	C₂×M₁₆×C₆₇	C₂³	1	4	yes	—
117	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
118	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
119	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
120	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
121	C₄⋊Q₈×C₆₇	—	2	2	no	—
122	C₄⋊Q₈×C₆₇	—	2	4	no	—
123	C₄⋊Q₈×C₆₇	—	2	1	no	—
124	C₄⋊Q₈×C₆₇	—	2	1	no	—
125	C₄⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
126	C₄⋊Q₈×C₆₇	C₂³	1	4	yes	—
127	#127×C₆₇	—	2	2	no	—
128	#127×C₆₇	—	2	4	no	—
129	#127×C₆₇	—	2	1	no	—
130	#127×C₆₇	—	2	1	no	—
131	#127×C₆₇	D₄	1	1	yes	characteristic
132	#127×C₆₇	C₂³	1	4	yes	—
133	#124×C₆₇	—	2	2	no	—
134	#124×C₆₇	—	2	2	no	—
135	#124×C₆₇	D₄	1	2	yes	—
136	#123×C₆₇	—	2	4	no	—
137	#123×C₆₇	—	2	8	no	—
138	C₂²⋊Q₈×C₆₇	—	2	8	no	—
139	C₂²⋊Q₈×C₆₇	C₂³	1	8	yes	—
140	#121×C₆₇	—	2	4	no	—
141	#121×C₆₇	—	2	4	no	—
142	#121×C₆₇	—	2	8	no	—
143	#121×C₆₇	D₄	1	4	yes	—
144	#121×C₆₇	C₂³	1	8	yes	—
145	#120×C₆₇	—	2	4	no	—
146	#120×C₆₇	—	2	8	no	—
147	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
148	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
149	C₄×D₄×C₆₇	—	2	4	no	—
150	C₄×D₄×C₆₇	—	2	2	no	—
151	C₄×D₄×C₆₇	—	2	2	no	—
152	C₄×D₄×C₆₇	—	2	4	no	—
153	C₄×D₄×C₆₇	C₂³	1	2	yes	—
154	C₄×D₄×C₆₇	C₂³	1	2	yes	—
155	C₄×D₄×C₆₇	C₂³	1	4	yes	—
156	#117×C₆₇	—	2	1	no	—
157	#117×C₆₇	—	2	1	no	—
158	#117×C₆₇	C₂³	1	1	yes	characteristic
159	#117×C₆₇	C₂³	1	1	yes	characteristic
160	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
161	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
162	C₂×C₄²×C₆₇	—	2	1	no	—
163	C₂×C₄²×C₆₇	—	2	1	no	—
164	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
165	#107×C₆₇	C₂³	1	2	yes	—
166	#106×C₆₇	C₂³	1	2	yes	—
167	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
168	#103×C₆₇	C₂³	1	2	yes	—
169	#103×C₆₇	C₂³	1	8	yes	—
170	#103×C₆₇	C₂³	1	2	yes	—
171	#102×C₆₇	C₂³	1	2	yes	—
172	#102×C₆₇	C₂³	1	2	yes	—
173	#102×C₆₇	C₂³	1	8	yes	—
174	C₂²⋊C₈×C₆₇	C₂³	1	8	yes	—
175	C₄×C₈×C₆₇	C₂³	1	2	yes	—
176	C₄×C₈×C₆₇	C₂³	1	2	yes	—
177	C₂⁴×C₆₇	—	2	4	no	—
178	C₂⁴×C₆₇	—	2	2	no	—
179	#41×C₆₇	—	2	4	no	—
180	#41×C₆₇	—	2	2	no	—
181	#41×C₆₇	—	2	4	no	—
182	#41×C₆₇	—	2	2	no	—
183	#41×C₆₇	—	2	8	no	—
184	#41×C₆₇	—	2	8	no	—
185	#41×C₆₇	—	4	4	no	—
186	#41×C₆₇	—	4	4	no	—
187	#41×C₆₇	—	4	8	no	—
188	#41×C₆₇	—	4	8	no	—
189	#41×C₆₇	—	4	16	no	—
190	#41×C₆₇	C₂×D₄	1	4	yes	—
191	#41×C₆₇	C₂×D₄	1	4	yes	complemented
192	C₂×Q₈×C₆₇	—	2	4	no	—
193	C₂×Q₈×C₆₇	—	2	2	no	—
194	C₂×Q₈×C₆₇	—	2	8	no	—
195	C₂×Q₈×C₆₇	—	2	4	no	—
196	C₂×Q₈×C₆₇	—	2	4	no	—
197	C₂×Q₈×C₆₇	—	4	4	no	—
198	C₂×Q₈×C₆₇	—	4	8	no	—
199	C₂×Q₈×C₆₇	C₂×D₄	1	2	yes	—
200	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
201	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
202	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
203	C₂×D₄×C₆₇	—	2	1	no	—
204	C₂×D₄×C₆₇	—	2	1	no	—
205	C₂×D₄×C₆₇	—	2	8	no	—
206	C₂×D₄×C₆₇	—	2	4	no	—
207	C₂×D₄×C₆₇	—	2	4	no	—
208	C₂×D₄×C₆₇	—	2	8	no	—
209	C₂×D₄×C₆₇	—	2	4	no	—
210	C₂×D₄×C₆₇	—	2	4	no	—
211	C₂×D₄×C₆₇	—	2	4	no	—
212	C₂×D₄×C₆₇	—	2	2	no	—
213	C₂×D₄×C₆₇	—	2	4	no	—
214	C₂×D₄×C₆₇	—	2	4	no	—
215	C₂×D₄×C₆₇	—	4	4	no	—
216	C₂×D₄×C₆₇	—	4	8	no	—
217	C₂×D₄×C₆₇	—	4	16	no	—
218	C₂×D₄×C₆₇	—	8	4	no	—
219	C₂×D₄×C₆₇	—	8	8	no	—
220	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	—
221	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	—
222	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
223	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
224	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
225	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
226	C₂²×C₄×C₆₇	—	2	1	no	—
227	C₂²×C₄×C₆₇	—	2	1	no	—
228	C₂²×C₄×C₆₇	—	2	2	no	—
229	C₂²×C₄×C₆₇	—	2	4	no	—
230	C₂²×C₄×C₆₇	—	2	2	no	—
231	C₂²×C₄×C₆₇	—	2	2	no	—
232	C₂²×C₄×C₆₇	—	2	4	no	—
233	C₂²×C₄×C₆₇	—	2	4	no	—
234	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
235	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
236	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
237	Q₁₆×C₆₇	—	2	8	no	—
238	Q₁₆×C₆₇	C₂×D₄	1	4	yes	complemented
239	SD₁₆×C₆₇	—	2	8	no	—
240	SD₁₆×C₆₇	—	2	8	no	—
241	SD₁₆×C₆₇	—	2	8	no	—
242	SD₁₆×C₆₇	—	2	8	no	—
243	SD₁₆×C₆₇	—	4	8	no	—
244	SD₁₆×C₆₇	C₂×D₄	1	4	yes	complemented
245	SD₁₆×C₆₇	C₂×D₄	1	4	yes	complemented
246	D₈×C₆₇	—	2	8	no	—
247	D₈×C₆₇	C₂×D₄	1	4	yes	complemented
248	M₁₆×C₆₇	—	2	4	no	—
249	M₁₆×C₆₇	—	2	8	no	—
250	C₂×C₈×C₆₇	—	2	2	no	—
251	C₂×C₈×C₆₇	—	2	8	no	—
252	C₂×C₈×C₆₇	C₂×D₄	1	4	yes	complemented
253	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
254	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
255	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
256	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
257	C₄⋊C₄×C₆₇	—	2	4	no	—
258	C₄⋊C₄×C₆₇	—	2	4	no	—
259	C₄⋊C₄×C₆₇	—	2	8	no	—
260	C₄⋊C₄×C₆₇	—	2	2	no	—
261	C₄⋊C₄×C₆₇	—	2	2	no	—
262	C₄⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
263	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
264	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
265	C₂²⋊C₄×C₆₇	—	2	1	no	—
266	C₂²⋊C₄×C₆₇	—	2	1	no	—
267	C₂²⋊C₄×C₆₇	—	2	8	no	—
268	C₂²⋊C₄×C₆₇	—	2	2	no	—
269	C₂²⋊C₄×C₆₇	—	2	2	no	—
270	C₂²⋊C₄×C₆₇	—	2	8	no	—
271	C₂²⋊C₄×C₆₇	C₂×D₄	1	8	yes	—
272	C₄²×C₆₇	—	2	1	no	—
273	C₄²×C₆₇	—	2	1	no	—
274	C₄²×C₆₇	—	2	2	no	—
275	C₄²×C₆₇	—	2	2	no	—
276	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
277	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
278	C₄²×C₆₇	C₂⁴	1	2	yes	—
279	C₂³×C₆₇	—	2	1	no	—
280	C₂³×C₆₇	—	2	1	no	—
281	C₂³×C₆₇	—	2	4	no	—
282	C₂³×C₆₇	—	4	8	no	—
283	C₂³×C₆₇	—	4	4	no	—
284	C₂³×C₆₇	—	8	4	no	—
285	C₂³×C₆₇	—	8	8	no	—
286	C₂³×C₆₇	C₂²×D₄	1	4	yes	—
287	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
288	Q₈×C₆₇	—	2	4	no	—
289	Q₈×C₆₇	—	2	1	no	—
290	Q₈×C₆₇	—	2	1	no	—
291	Q₈×C₆₇	—	2	4	no	—
292	Q₈×C₆₇	—	2	4	no	—
293	Q₈×C₆₇	—	4	8	no	—
294	Q₈×C₆₇	—	4	4	no	—
295	Q₈×C₆₇	C₂²×D₄	1	2	yes	—
296	Q₈×C₆₇	C₂²×D₄	1	2	yes	—
297	D₄×C₆₇	—	2	4	no	—
298	D₄×C₆₇	—	2	4	no	—
299	D₄×C₆₇	—	2	8	no	—
300	D₄×C₆₇	—	2	4	no	—
301	D₄×C₆₇	—	2	8	no	—
302	D₄×C₆₇	—	2	4	no	—
303	D₄×C₆₇	—	2	1	no	—
304	D₄×C₆₇	—	2	1	no	—
305	D₄×C₆₇	—	2	4	no	—
306	D₄×C₆₇	—	4	8	no	—
307	D₄×C₆₇	—	4	8	no	—
308	D₄×C₆₇	—	4	8	no	—
309	D₄×C₆₇	—	4	4	no	—
310	D₄×C₆₇	—	4	8	no	—
311	D₄×C₆₇	—	8	4	no	—
312	D₄×C₆₇	—	8	8	no	—
313	D₄×C₆₇	C₂²×D₄	1	2	yes	—
314	D₄×C₆₇	C₂²×D₄	1	2	yes	—
315	C₂×C₄×C₆₇	—	2	1	no	—
316	C₂×C₄×C₆₇	—	2	1	no	—
317	C₂×C₄×C₆₇	—	2	4	no	—
318	C₂×C₄×C₆₇	—	2	4	no	—
319	C₂×C₄×C₆₇	—	2	4	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	2	no	—
324	C₂×C₄×C₆₇	—	2	4	no	—
325	C₂×C₄×C₆₇	—	4	8	no	—
326	C₂×C₄×C₆₇	—	4	8	no	—
327	C₂×C₄×C₆₇	—	4	8	no	—
328	C₂×C₄×C₆₇	—	4	4	no	—
329	C₂×C₄×C₆₇	—	4	4	no	—
330	C₂×C₄×C₆₇	—	4	4	no	—
331	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
332	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
333	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
334	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
335	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
336	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
337	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
338	C₈×C₆₇	—	2	4	no	—
339	C₈×C₆₇	—	2	2	no	—
340	C₈×C₆₇	C₂²×D₄	1	2	yes	—
341	C₈×C₆₇	C₂²×D₄	1	2	yes	—
342	C₂²×C₆₇	—	2	2	no	—
343	C₂²×C₆₇	—	2	2	no	—
344	C₂²×C₆₇	—	2	4	no	—
345	C₂²×C₆₇	—	2	2	no	—
346	C₂²×C₆₇	—	2	8	no	—
347	C₂²×C₆₇	—	4	2	no	—
348	C₂²×C₆₇	—	4	2	no	—
349	C₂²×C₆₇	—	4	4	no	—
350	C₂²×C₆₇	—	4	8	no	—
351	C₂²×C₆₇	—	16	4	no	—
352	C₂²×C₆₇	—	16	8	no	—
353	C₂²×C₆₇	D₄²	1	2	yes	—
354	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
355	C₄×C₆₇	—	2	2	no	—
356	C₄×C₆₇	—	2	2	no	—
357	C₄×C₆₇	—	2	4	no	—
358	C₄×C₆₇	—	2	2	no	—
359	C₄×C₆₇	—	4	4	no	—
360	C₄×C₆₇	—	4	2	no	—
361	C₄×C₆₇	—	4	2	no	—
362	C₄×C₆₇	D₄²	1	2	yes	—
363	C₄×C₆₇	#577	1	4	yes	complemented
364	C₄×C₆₇	C₂³×D₄	1	1	yes	characteristic
365	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
366	#61087	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
367	C₂×C₆₇	—	2	2	no	—
368	C₂×C₆₇	—	4	4	no	—
369	C₂×C₆₇	—	4	2	no	—
370	C₂×C₆₇	—	4	2	no	—
371	C₂×C₆₇	—	8	4	no	—
372	C₂×C₆₇	C₂×D₄²	1	1	yes	characteristic
373	C₂×C₆₇	C₂×#577	1	2	yes	—
374	C₂×#577	C₂×C₆₇	1	2	yes	complemented
375	#3499	C₂×C₆₇	1	1	yes	characteristic, complemented
376	#3498	C₂×C₆₇	1	1	yes	characteristic, complemented
377	#3284	C₂×C₆₇	1	4	yes	complemented
378	D₄×SD₁₆	C₂×C₆₇	1	4	yes	complemented
379	#3278	C₂×C₆₇	1	4	yes	complemented
380	#3272	C₂×C₆₇	1	4	yes	complemented
381	C₂×#492	C₂×C₆₇	1	1	yes	characteristic, complemented
382	#3057	C₂×C₆₇	1	2	yes	complemented
383	#3039	C₂×C₆₇	1	1	yes	characteristic, complemented
384	#3038	C₂×C₆₇	1	1	yes	characteristic, complemented
385	#3010	C₂×C₆₇	1	2	yes	complemented
386	#3009	C₂×C₆₇	1	2	yes	complemented
387	C₄×#135	C₂×C₆₇	1	1	yes	characteristic, complemented
388	#2931	C₂×C₆₇	1	1	yes	characteristic, complemented
389	C₆₇	#61087	1	1	yes	characteristic, direct product factor, Sylow
390	C₂×2₋¹⁺⁴	C₂²×C₆₇	1	2	yes	complemented
391	C₂×H(5,𝔽₂)	C₂²×C₆₇	1	2	yes	—
392	#577	—	2	16	no	—
393	C₂×#137	C₂²×C₆₇	1	2	yes	—
394	C₂×#137	C₂²×C₆₇	1	4	yes	complemented
395	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	complemented
396	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	4	yes	complemented
397	C₂×#135	C₂²×C₆₇	1	1	yes	characteristic
398	C₂×#135	C₂²×C₆₇	1	4	yes	complemented
399	C₂²×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
400	C₂²×SD₁₆	C₂²×C₆₇	1	4	yes	complemented
401	C₂²×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
402	C₂×#131	C₂²×C₆₇	1	2	yes	complemented
403	#550	C₂²×C₆₇	1	4	yes	—
404	D₄×Q₈	C₂²×C₆₇	1	4	yes	complemented
405	#547	—	2	4	no	—
406	#547	C₂²×C₆₇	1	4	yes	complemented
407	D₄²	—	2	4	no	—
408	D₄²	C₂²×C₆₇	1	4	yes	—
409	#536	—	2	2	no	—
410	#536	C₂²×C₆₇	1	2	yes	complemented
411	#535	—	2	2	no	—
412	#535	C₂²×C₆₇	1	2	yes	—
413	#532	—	2	1	no	—
414	#532	—	2	1	no	—
415	#532	C₂²×C₆₇	1	1	yes	characteristic
416	C₂×C₄⋊Q₈	—	2	1	no	—
417	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
418	C₂×#127	—	2	1	no	—
419	C₂×#127	C₂²×C₆₇	1	1	yes	characteristic
420	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
421	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic, complemented
422	#492	C₂²×C₆₇	1	4	yes	complemented
423	#492	C₂²×C₆₇	1	4	yes	complemented
424	#468	C₂²×C₆₇	1	8	yes	complemented
425	#465	C₂²×C₆₇	1	8	yes	complemented
426	#462	C₂²×C₆₇	1	4	yes	complemented
427	#461	C₂²×C₆₇	1	4	yes	complemented
428	#460	C₂²×C₆₇	1	4	yes	complemented
429	#459	C₂²×C₆₇	1	4	yes	complemented
430	#452	C₂²×C₆₇	1	8	yes	complemented
431	#450	C₂²×C₆₇	1	8	yes	complemented
432	#449	C₂²×C₆₇	1	8	yes	complemented
433	#448	C₂²×C₆₇	1	8	yes	complemented
434	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	complemented
435	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
436	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
437	C₄×D₈	C₂²×C₆₇	1	2	yes	complemented
438	#436	C₂²×C₆₇	1	4	yes	complemented
439	C₈×D₄	C₂²×C₆₇	1	4	yes	complemented
440	#427	C₂²×C₆₇	1	1	yes	characteristic, complemented
441	#423	C₂²×C₆₇	1	1	yes	characteristic, complemented
442	#419	C₂²×C₆₇	1	2	yes	complemented
443	#418	C₂²×C₆₇	1	2	yes	complemented
444	#416	C₂²×C₆₇	1	1	yes	characteristic
445	#416	C₂²×C₆₇	1	1	yes	characteristic, complemented
446	#408	C₂²×C₆₇	1	2	yes	complemented
447	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
448	2₋¹⁺⁴	—	2	8	no	—
449	2₋¹⁺⁴	—	4	4	no	—
450	H(5,𝔽₂)	—	2	8	no	—
451	H(5,𝔽₂)	—	4	4	no	—
452	C₂×#41	—	2	2	no	—
453	C₂×#41	—	2	2	no	—
454	C₂×#41	—	2	4	no	—
455	C₂×#41	C₂³×C₆₇	1	4	yes	—
456	C₂×#41	C₂³×C₆₇	1	4	yes	—
457	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
458	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
459	C₂×#41	C₂³×C₆₇	1	2	yes	—
460	C₂²×Q₈	—	2	2	no	—
461	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
462	C₂²×Q₈	C₂³×C₆₇	1	4	yes	—
463	C₂²×D₄	—	2	2	no	—
464	C₂²×D₄	—	2	4	no	—
465	C₂²×D₄	—	2	4	no	—
466	C₂²×D₄	—	2	2	no	—
467	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
468	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
469	#137	—	2	8	no	—
470	#137	—	2	16	no	—
471	AGL(1,ℤ/8)	—	2	8	no	—
472	AGL(1,ℤ/8)	—	2	16	no	—
473	#135	—	2	16	no	—
474	#135	D₄×C₆₇	1	8	yes	complemented
475	C₂×Q₁₆	C₂³×C₆₇	1	4	yes	—
476	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic
477	C₂×SD₁₆	—	2	16	no	—
478	C₂×SD₁₆	—	2	8	no	—
479	C₂×SD₁₆	—	4	4	no	—
480	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
481	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
482	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
483	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
484	C₂×SD₁₆	C₂³×C₆₇	1	8	yes	—
485	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
486	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
487	C₂×D₈	C₂³×C₆₇	1	4	yes	—
488	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic
489	#131	—	2	8	no	—
490	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
491	C₂×M₁₆	C₂³×C₆₇	1	4	yes	—
492	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
493	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
494	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
495	C₄⋊Q₈	—	2	2	no	—
496	C₄⋊Q₈	—	2	4	no	—
497	C₄⋊Q₈	—	2	1	no	—
498	C₄⋊Q₈	—	2	1	no	—
499	C₄⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
500	C₄⋊Q₈	C₂³×C₆₇	1	4	yes	—
501	#127	—	2	2	no	—
502	#127	—	2	4	no	—
503	#127	—	2	1	no	—
504	#127	—	2	1	no	—
505	#127	D₄×C₆₇	1	1	yes	characteristic
506	#127	C₂³×C₆₇	1	4	yes	—
507	#124	—	2	2	no	—
508	#124	—	2	2	no	—
509	#124	D₄×C₆₇	1	2	yes	—
510	#123	—	2	4	no	—
511	#123	—	2	8	no	—
512	C₂²⋊Q₈	—	2	8	no	—
513	C₂²⋊Q₈	C₂³×C₆₇	1	8	yes	—
514	#121	—	2	4	no	—
515	#121	—	2	4	no	—
516	#121	—	2	8	no	—
517	#121	D₄×C₆₇	1	4	yes	—
518	#121	C₂³×C₆₇	1	8	yes	—
519	#120	—	2	4	no	—
520	#120	—	2	8	no	—
521	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
522	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
523	C₄×D₄	—	2	4	no	—
524	C₄×D₄	—	2	2	no	—
525	C₄×D₄	—	2	2	no	—
526	C₄×D₄	—	2	4	no	—
527	C₄×D₄	C₂³×C₆₇	1	2	yes	—
528	C₄×D₄	C₂³×C₆₇	1	2	yes	—
529	C₄×D₄	C₂³×C₆₇	1	4	yes	—
530	#117	—	2	1	no	—
531	#117	—	2	1	no	—
532	#117	C₂³×C₆₇	1	1	yes	characteristic
533	#117	C₂³×C₆₇	1	1	yes	characteristic
534	C₂×C₄⋊C₄	—	2	2	no	—
535	C₂×C₄⋊C₄	—	2	4	no	—
536	C₂×C₄²	—	2	1	no	—
537	C₂×C₄²	—	2	1	no	—
538	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
539	#107	C₂³×C₆₇	1	2	yes	—
540	#106	C₂³×C₆₇	1	2	yes	—
541	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
542	#103	C₂³×C₆₇	1	2	yes	—
543	#103	C₂³×C₆₇	1	2	yes	—
544	#103	C₂³×C₆₇	1	8	yes	—
545	#102	C₂³×C₆₇	1	2	yes	—
546	#102	C₂³×C₆₇	1	2	yes	—
547	#102	C₂³×C₆₇	1	8	yes	—
548	C₂²⋊C₈	C₂³×C₆₇	1	8	yes	—
549	C₄×C₈	C₂³×C₆₇	1	2	yes	—
550	C₄×C₈	C₂³×C₆₇	1	2	yes	—
551	C₂⁴	—	2	4	no	—
552	C₂⁴	—	2	2	no	—
553	#41	—	2	4	no	—
554	#41	—	2	2	no	—
555	#41	—	2	4	no	—
556	#41	—	2	2	no	—
557	#41	—	2	8	no	—
558	#41	—	2	8	no	—
559	#41	—	4	4	no	—
560	#41	—	4	4	no	—
561	#41	—	4	8	no	—
562	#41	—	4	8	no	—
563	#41	—	4	16	no	—
564	#41	C₂×D₄×C₆₇	1	4	yes	—
565	#41	C₂×D₄×C₆₇	1	4	yes	complemented
566	C₂×Q₈	—	2	4	no	—
567	C₂×Q₈	—	2	2	no	—
568	C₂×Q₈	—	2	8	no	—
569	C₂×Q₈	—	2	4	no	—
570	C₂×Q₈	—	2	4	no	—
571	C₂×Q₈	—	4	4	no	—
572	C₂×Q₈	—	4	8	no	—
573	C₂×Q₈	C₂×D₄×C₆₇	1	2	yes	—
574	C₂×Q₈	C₂⁴×C₆₇	1	4	yes	—
575	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
576	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
577	C₂×D₄	—	2	1	no	—
578	C₂×D₄	—	2	1	no	—
579	C₂×D₄	—	2	8	no	—
580	C₂×D₄	—	2	4	no	—
581	C₂×D₄	—	2	4	no	—
582	C₂×D₄	—	2	8	no	—
583	C₂×D₄	—	2	4	no	—
584	C₂×D₄	—	2	4	no	—
585	C₂×D₄	—	2	4	no	—
586	C₂×D₄	—	2	2	no	—
587	C₂×D₄	—	2	4	no	—
588	C₂×D₄	—	2	4	no	—
589	C₂×D₄	—	4	4	no	—
590	C₂×D₄	—	4	8	no	—
591	C₂×D₄	—	4	16	no	—
592	C₂×D₄	—	8	4	no	—
593	C₂×D₄	—	8	8	no	—
594	C₂×D₄	C₂×D₄×C₆₇	1	4	yes	—
595	C₂×D₄	C₂×D₄×C₆₇	1	4	yes	—
596	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
597	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
598	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
599	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
600	C₂²×C₄	—	2	1	no	—
601	C₂²×C₄	—	2	1	no	—
602	C₂²×C₄	—	2	2	no	—
603	C₂²×C₄	—	2	4	no	—
604	C₂²×C₄	—	2	2	no	—
605	C₂²×C₄	—	2	2	no	—
606	C₂²×C₄	—	2	4	no	—
607	C₂²×C₄	—	2	4	no	—
608	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
609	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
610	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
611	Q₁₆	—	2	8	no	—
612	Q₁₆	C₂×D₄×C₆₇	1	4	yes	complemented
613	SD₁₆	—	2	8	no	—
614	SD₁₆	—	2	8	no	—
615	SD₁₆	—	2	8	no	—
616	SD₁₆	—	2	8	no	—
617	SD₁₆	—	4	8	no	—
618	SD₁₆	C₂×D₄×C₆₇	1	4	yes	complemented
619	SD₁₆	C₂×D₄×C₆₇	1	4	yes	complemented
620	D₈	—	2	8	no	—
621	D₈	C₂×D₄×C₆₇	1	4	yes	complemented
622	M₁₆	—	2	4	no	—
623	M₁₆	—	2	8	no	—
624	C₂×C₈	—	2	2	no	—
625	C₂×C₈	—	2	8	no	—
626	C₂×C₈	C₂×D₄×C₆₇	1	4	yes	complemented
627	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
628	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
629	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
630	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
631	C₄⋊C₄	—	2	4	no	—
632	C₄⋊C₄	—	2	4	no	—
633	C₄⋊C₄	—	2	8	no	—
634	C₄⋊C₄	—	2	2	no	—
635	C₄⋊C₄	—	2	2	no	—
636	C₄⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
637	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
638	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
639	C₂²⋊C₄	—	2	1	no	—
640	C₂²⋊C₄	—	2	1	no	—
641	C₂²⋊C₄	—	2	8	no	—
642	C₂²⋊C₄	—	2	2	no	—
643	C₂²⋊C₄	—	2	2	no	—
644	C₂²⋊C₄	—	2	8	no	—
645	C₂²⋊C₄	C₂×D₄×C₆₇	1	8	yes	—
646	C₄²	—	2	1	no	—
647	C₄²	—	2	1	no	—
648	C₄²	—	2	2	no	—
649	C₄²	—	2	2	no	—
650	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
651	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
652	C₄²	C₂⁴×C₆₇	1	2	yes	—
653	C₂³	—	2	1	no	—
654	C₂³	—	2	1	no	—
655	C₂³	—	2	4	no	—
656	C₂³	—	4	8	no	—
657	C₂³	—	4	4	no	—
658	C₂³	—	8	4	no	—
659	C₂³	—	8	8	no	—
660	C₂³	C₂²×D₄×C₆₇	1	4	yes	—
661	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
662	Q₈	—	2	4	no	—
663	Q₈	—	2	1	no	—
664	Q₈	—	2	1	no	—
665	Q₈	—	2	4	no	—
666	Q₈	—	2	4	no	—
667	Q₈	—	4	8	no	—
668	Q₈	—	4	4	no	—
669	Q₈	C₂²×D₄×C₆₇	1	2	yes	—
670	Q₈	C₂²×D₄×C₆₇	1	2	yes	—
671	D₄	—	2	4	no	—
672	D₄	—	2	4	no	—
673	D₄	—	2	8	no	—
674	D₄	—	2	4	no	—
675	D₄	—	2	8	no	—
676	D₄	—	2	4	no	—
677	D₄	—	2	1	no	—
678	D₄	—	2	1	no	—
679	D₄	—	2	4	no	—
680	D₄	—	4	8	no	—
681	D₄	—	4	8	no	—
682	D₄	—	4	8	no	—
683	D₄	—	4	4	no	—
684	D₄	—	4	8	no	—
685	D₄	—	8	4	no	—
686	D₄	—	8	8	no	—
687	D₄	C₂²×D₄×C₆₇	1	2	yes	—
688	D₄	C₂²×D₄×C₆₇	1	2	yes	—
689	C₂×C₄	—	2	1	no	—
690	C₂×C₄	—	2	1	no	—
691	C₂×C₄	—	2	4	no	—
692	C₂×C₄	—	2	4	no	—
693	C₂×C₄	—	2	4	no	—
694	C₂×C₄	—	2	4	no	—
695	C₂×C₄	—	2	4	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	4	no	—
699	C₂×C₄	—	4	8	no	—
700	C₂×C₄	—	4	8	no	—
701	C₂×C₄	—	4	8	no	—
702	C₂×C₄	—	4	4	no	—
703	C₂×C₄	—	4	4	no	—
704	C₂×C₄	—	4	4	no	—
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	1	yes	characteristic
708	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
709	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
710	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
711	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
712	C₈	—	2	4	no	—
713	C₈	—	2	2	no	—
714	C₈	C₂²×D₄×C₆₇	1	2	yes	—
715	C₈	C₂²×D₄×C₆₇	1	2	yes	—
716	C₂²	—	2	2	no	—
717	C₂²	—	2	8	no	—
718	C₂²	—	2	2	no	—
719	C₂²	—	2	4	no	—
720	C₂²	—	2	2	no	—
721	C₂²	—	4	2	no	—
722	C₂²	—	4	2	no	—
723	C₂²	—	4	8	no	—
724	C₂²	—	4	4	no	—
725	C₂²	—	16	4	no	—
726	C₂²	—	16	8	no	—
727	C₂²	D₄²×C₆₇	1	2	yes	—
728	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
729	C₄	—	2	2	no	—
730	C₄	—	2	2	no	—
731	C₄	—	2	2	no	—
732	C₄	—	2	4	no	—
733	C₄	—	4	2	no	—
734	C₄	—	4	2	no	—
735	C₄	—	4	4	no	—
736	C₄	D₄²×C₆₇	1	2	yes	—
737	C₄	#577×C₆₇	1	4	yes	complemented
738	C₄	C₂³×D₄×C₆₇	1	1	yes	characteristic
739	C₄	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
740	C₂	—	2	2	no	—
741	C₂	—	4	4	no	—
742	C₂	—	4	2	no	—
743	C₂	—	4	2	no	—
744	C₂	—	8	4	no	—
745	C₂	C₂×D₄²×C₆₇	1	1	yes	characteristic
746	C₂	C₂×#577×C₆₇	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 ◁ #532×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#577×C₆₇	C₂	semidirect
2. C₆₇×#3499	C₂	semidirect
3. C₆₇×#3498	C₂	semidirect
4. C₆₇×#3284	C₂	semidirect
5. D₄×SD₁₆×C₆₇	C₂	semidirect
6. C₆₇×#3278	C₂	semidirect
7. C₆₇×#3272	C₂	semidirect
8. C₂×#492×C₆₇	C₂	semidirect
9. C₆₇×#3057	C₂	semidirect
10. C₆₇×#3039	C₂	semidirect
11. C₆₇×#3038	C₂	semidirect
12. C₆₇×#3010	C₂	semidirect
13. C₆₇×#3009	C₂	semidirect
14. C₄×#135×C₆₇	C₂	semidirect
15. C₆₇×#2931	C₂	semidirect
16. C₂×2₋¹⁺⁴×C₆₇	C₂²	semidirect
20. C₂×#137×C₆₇	C₂²	semidirect
21. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
22. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
24. C₂×#135×C₆₇	C₂²	semidirect
25. C₂²×SD₁₆×C₆₇	C₂²	semidirect
26. C₂²×SD₁₆×C₆₇	C₂²	semidirect
27. C₂²×SD₁₆×C₆₇	C₂²	semidirect
28. C₂×#131×C₆₇	C₂²	semidirect
30. D₄×Q₈×C₆₇	C₂²	semidirect
32. #547×C₆₇	C₂²	semidirect
36. #536×C₆₇	C₂²	semidirect
43. C₂×C₄⋊Q₈×C₆₇	C₂²	semidirect
47. C₄×#41×C₆₇	C₂²	semidirect
48. #492×C₆₇	C₂²	semidirect
49. #492×C₆₇	C₂²	semidirect
50. #468×C₆₇	C₂²	semidirect
51. #465×C₆₇	C₂²	semidirect
52. #462×C₆₇	C₂²	semidirect
53. #461×C₆₇	C₂²	semidirect
54. #460×C₆₇	C₂²	semidirect
55. #459×C₆₇	C₂²	semidirect
56. #452×C₆₇	C₂²	semidirect
57. #450×C₆₇	C₂²	semidirect
58. #449×C₆₇	C₂²	semidirect
59. #448×C₆₇	C₂²	semidirect
60. C₄×Q₁₆×C₆₇	C₂²	semidirect
61. C₄×SD₁₆×C₆₇	C₂²	semidirect
62. C₄×SD₁₆×C₆₇	C₂²	semidirect
63. C₄×D₈×C₆₇	C₂²	semidirect
64. #436×C₆₇	C₂²	semidirect
65. C₈×D₄×C₆₇	C₂²	semidirect
66. #427×C₆₇	C₂²	semidirect
67. #423×C₆₇	C₂²	semidirect
68. #419×C₆₇	C₂²	semidirect
69. #418×C₆₇	C₂²	semidirect
71. #416×C₆₇	C₂²	semidirect
72. #408×C₆₇	C₂²	semidirect
73. C₂×C₄×C₈×C₆₇	C₂²	semidirect
100. #135×C₆₇	D₄	semidirect
191. #41×C₆₇	C₂×D₄	semidirect
238. Q₁₆×C₆₇	C₂×D₄	semidirect
244. SD₁₆×C₆₇	C₂×D₄	semidirect
245. SD₁₆×C₆₇	C₂×D₄	semidirect
247. D₈×C₆₇	C₂×D₄	semidirect
252. C₂×C₈×C₆₇	C₂×D₄	semidirect
363. C₄×C₆₇	#577	semidirect
366. #61087	C₆₇	direct (N × H)
374. C₂×#577	C₂×C₆₇	semidirect
375. #3499	C₂×C₆₇	semidirect
376. #3498	C₂×C₆₇	semidirect
377. #3284	C₂×C₆₇	semidirect
378. D₄×SD₁₆	C₂×C₆₇	semidirect
379. #3278	C₂×C₆₇	semidirect
380. #3272	C₂×C₆₇	semidirect
381. C₂×#492	C₂×C₆₇	semidirect
382. #3057	C₂×C₆₇	semidirect
383. #3039	C₂×C₆₇	semidirect
384. #3038	C₂×C₆₇	semidirect
385. #3010	C₂×C₆₇	semidirect
386. #3009	C₂×C₆₇	semidirect
387. C₄×#135	C₂×C₆₇	semidirect
388. #2931	C₂×C₆₇	semidirect
389. C₆₇	#61087	direct (N × H)
390. C₂×2₋¹⁺⁴	C₂²×C₆₇	semidirect
394. C₂×#137	C₂²×C₆₇	semidirect
395. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
396. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
398. C₂×#135	C₂²×C₆₇	semidirect
399. C₂²×SD₁₆	C₂²×C₆₇	semidirect
400. C₂²×SD₁₆	C₂²×C₆₇	semidirect
401. C₂²×SD₁₆	C₂²×C₆₇	semidirect
402. C₂×#131	C₂²×C₆₇	semidirect
404. D₄×Q₈	C₂²×C₆₇	semidirect
406. #547	C₂²×C₆₇	semidirect
410. #536	C₂²×C₆₇	semidirect
417. C₂×C₄⋊Q₈	C₂²×C₆₇	semidirect
421. C₄×#41	C₂²×C₆₇	semidirect
422. #492	C₂²×C₆₇	semidirect
423. #492	C₂²×C₆₇	semidirect
424. #468	C₂²×C₆₇	semidirect
425. #465	C₂²×C₆₇	semidirect
426. #462	C₂²×C₆₇	semidirect
427. #461	C₂²×C₆₇	semidirect
428. #460	C₂²×C₆₇	semidirect
429. #459	C₂²×C₆₇	semidirect
430. #452	C₂²×C₆₇	semidirect
431. #450	C₂²×C₆₇	semidirect
432. #449	C₂²×C₆₇	semidirect
433. #448	C₂²×C₆₇	semidirect
434. C₄×Q₁₆	C₂²×C₆₇	semidirect
435. C₄×SD₁₆	C₂²×C₆₇	semidirect
436. C₄×SD₁₆	C₂²×C₆₇	semidirect
437. C₄×D₈	C₂²×C₆₇	semidirect
438. #436	C₂²×C₆₇	semidirect
439. C₈×D₄	C₂²×C₆₇	semidirect
440. #427	C₂²×C₆₇	semidirect
441. #423	C₂²×C₆₇	semidirect
442. #419	C₂²×C₆₇	semidirect
443. #418	C₂²×C₆₇	semidirect
445. #416	C₂²×C₆₇	semidirect
446. #408	C₂²×C₆₇	semidirect
447. C₂×C₄×C₈	C₂²×C₆₇	semidirect
474. #135	D₄×C₆₇	semidirect
565. #41	C₂×D₄×C₆₇	semidirect
612. Q₁₆	C₂×D₄×C₆₇	semidirect
618. SD₁₆	C₂×D₄×C₆₇	semidirect
619. SD₁₆	C₂×D₄×C₆₇	semidirect
621. D₈	C₂×D₄×C₆₇	semidirect
626. C₂×C₈	C₂×D₄×C₆₇	semidirect
737. C₄	#577×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#577×C₆₇	2
C₆₇×#3499	2
C₆₇×#3498	2
C₆₇×#3284	2
D₄×SD₁₆×C₆₇	2
C₆₇×#3278	2
C₆₇×#3272	2
C₂×#492×C₆₇	2
C₆₇×#3057	2
C₆₇×#3039	2
C₆₇×#3038	2
C₆₇×#3010	2
C₆₇×#3009	2
C₄×#135×C₆₇	2
C₆₇×#2931	2
#61087	67

Subgroups — C67×#61087 #30740338

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61087 #30740338