Subgroups — C₆₇×#61049 #30740300

Order 17152.

3074 conjugacy classes of subgroups.

The subgroup lattice has 708 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	C₂³×D₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3484	C₂	1	2	yes	maximal, complemented
4	C₆₇×#3280	C₂	1	4	yes	maximal, complemented
5	D₄×D₈×C₆₇	C₂	1	4	yes	maximal, complemented
6	C₆₇×#3264	C₂	1	8	yes	maximal, complemented
7	C₆₇×#3155	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#3058	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#3050	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#3041	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3008	C₂	1	2	yes	maximal, complemented
12	C₆₇×#3003	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	complemented
16	C₂³×D₄×C₆₇	C₂²	1	2	yes	complemented
17	#576×C₆₇	—	2	8	no	—
18	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	2	yes	complemented
19	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	2	yes	complemented
20	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	4	yes	complemented
21	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic, complemented
22	C₂×#135×C₆₇	C₂²	1	2	yes	complemented
23	C₂²×D₈×C₆₇	—	2	8	no	—
24	C₂²×D₈×C₆₇	C₂²	1	1	yes	characteristic
25	C₂²×D₈×C₆₇	C₂²	1	4	yes	complemented
26	C₂²×D₈×C₆₇	C₂²	1	2	yes	complemented
27	C₂²×D₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
28	C₂²×D₈×C₆₇	C₂²	1	4	yes	complemented
29	C₂²×D₈×C₆₇	C₂²	1	2	yes	complemented
30	C₂×#131×C₆₇	C₂²	1	1	yes	characteristic, complemented
31	C₂³×C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
32	#546×C₆₇	—	2	4	no	—
33	#546×C₆₇	C₂²	1	8	yes	complemented
34	D₄²×C₆₇	—	2	4	no	—
35	D₄²×C₆₇	C₂²	1	8	yes	complemented
36	#535×C₆₇	C₂²	1	2	yes	complemented
37	#535×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×#120×C₆₇	—	2	4	no	—
42	#518×C₆₇	C₂²	1	2	yes	complemented
43	#496×C₆₇	C₂²	1	4	yes	complemented
44	#495×C₆₇	C₂²	1	2	yes	complemented
45	#493×C₆₇	C₂²	1	2	yes	complemented
46	#469×C₆₇	C₂²	1	4	yes	complemented
47	#467×C₆₇	C₂²	1	2	yes	complemented
48	#466×C₆₇	C₂²	1	2	yes	complemented
49	#466×C₆₇	C₂²	1	4	yes	complemented
50	#465×C₆₇	C₂²	1	4	yes	complemented
51	#463×C₆₇	C₂²	1	8	yes	complemented
52	#459×C₆₇	C₂²	1	8	yes	complemented
53	#450×C₆₇	C₂²	1	8	yes	complemented
54	#449×C₆₇	C₂²	1	8	yes	complemented
55	#447×C₆₇	C₂²	1	8	yes	complemented
56	#447×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	#418×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, complemented
67	#407×C₆₇	C₂²	1	1	yes	characteristic, complemented
68	#405×C₆₇	C₂²	1	1	yes	characteristic, complemented
69	C₂⁵×C₆₇	—	2	2	no	—
70	H(5,𝔽₂)×C₆₇	—	2	8	no	—
71	H(5,𝔽₂)×C₆₇	—	4	4	no	—
72	C₂×#41×C₆₇	—	2	2	no	—
73	C₂×#41×C₆₇	C₂³	1	2	yes	—
74	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
75	C₂×#41×C₆₇	C₂³	1	4	yes	complemented
76	C₂²×D₄×C₆₇	—	2	8	no	—
77	C₂²×D₄×C₆₇	—	2	4	no	—
78	C₂²×D₄×C₆₇	—	2	2	no	—
79	C₂²×D₄×C₆₇	—	2	8	no	—
80	C₂²×D₄×C₆₇	—	2	2	no	—
81	C₂²×D₄×C₆₇	—	2	4	no	—
82	C₂²×D₄×C₆₇	—	4	4	no	—
83	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
84	C₂²×D₄×C₆₇	C₂³	1	8	yes	—
85	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
86	C₂²×D₄×C₆₇	C₂³	1	4	yes	complemented
87	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
88	AGL(1,ℤ/8)×C₆₇	—	2	8	no	—
89	AGL(1,ℤ/8)×C₆₇	—	2	16	no	—
90	AGL(1,ℤ/8)×C₆₇	—	4	4	no	—
91	#135×C₆₇	—	2	8	no	—
92	#135×C₆₇	—	2	4	no	—
93	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic, complemented
94	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	complemented
95	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	complemented
96	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	complemented
97	C₂×D₈×C₆₇	—	2	8	no	—
98	C₂×D₈×C₆₇	—	2	16	no	—
99	C₂×D₈×C₆₇	—	2	16	no	—
100	C₂×D₈×C₆₇	—	2	8	no	—
101	C₂×D₈×C₆₇	—	2	4	no	—
102	C₂×D₈×C₆₇	D₄	1	8	yes	complemented
103	C₂×D₈×C₆₇	C₂³	1	8	yes	—
104	C₂×D₈×C₆₇	C₂³	1	2	yes	—
105	C₂×D₈×C₆₇	C₂³	1	2	yes	—
106	C₂×D₈×C₆₇	C₂³	1	2	yes	—
107	C₂×D₈×C₆₇	C₂³	1	2	yes	—
108	C₂×D₈×C₆₇	C₂³	1	4	yes	complemented
109	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic, complemented
110	C₂×D₈×C₆₇	C₂³	1	4	yes	complemented
111	#131×C₆₇	—	2	4	no	—
112	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
113	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
114	C₂×M₁₆×C₆₇	C₂³	1	2	yes	complemented
115	C₂²×C₈×C₆₇	—	2	4	no	—
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	C₂²×C₈×C₆₇	C₂³	1	2	yes	complemented
121	#127×C₆₇	—	2	2	no	—
122	#127×C₆₇	C₂³	1	4	yes	complemented
123	#124×C₆₇	—	2	2	no	—
124	#124×C₆₇	C₂³	1	4	yes	complemented
125	#123×C₆₇	—	2	2	no	—
126	#123×C₆₇	—	2	8	no	—
127	#123×C₆₇	D₄	1	2	yes	—
128	C₂²⋊Q₈×C₆₇	D₄	1	2	yes	—
129	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
130	#121×C₆₇	—	2	8	no	—
131	#121×C₆₇	—	2	4	no	—
132	#121×C₆₇	—	2	8	no	—
133	#121×C₆₇	D₄	1	2	yes	—
134	#121×C₆₇	C₂³	1	4	yes	—
135	#121×C₆₇	C₂³	1	8	yes	complemented
136	#120×C₆₇	—	2	2	no	—
137	#120×C₆₇	—	2	4	no	—
138	#120×C₆₇	—	2	8	no	—
139	#120×C₆₇	—	2	4	no	—
140	#120×C₆₇	—	2	8	no	—
141	#120×C₆₇	—	2	8	no	—
142	#120×C₆₇	D₄	1	2	yes	—
143	C₄×D₄×C₆₇	—	2	4	no	—
144	C₄×D₄×C₆₇	—	2	4	no	—
145	C₄×D₄×C₆₇	C₂³	1	4	yes	—
146	C₄×D₄×C₆₇	C₂³	1	8	yes	complemented
147	#117×C₆₇	C₂³	1	2	yes	—
148	#117×C₆₇	C₂³	1	1	yes	characteristic
149	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
150	C₂×C₂²⋊C₄×C₆₇	—	2	8	no	—
151	#107×C₆₇	C₂³	1	2	yes	complemented
152	#106×C₆₇	C₂³	1	2	yes	complemented
153	C₄⋊C₈×C₆₇	C₂³	1	4	yes	complemented
154	#103×C₆₇	C₂³	1	4	yes	complemented
155	#102×C₆₇	C₂³	1	8	yes	complemented
156	#102×C₆₇	C₂³	1	8	yes	complemented
157	#102×C₆₇	C₂³	1	4	yes	complemented
158	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
159	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	complemented
160	#97×C₆₇	C₂³	1	2	yes	complemented
161	C₄×C₈×C₆₇	C₂³	1	2	yes	complemented
162	C₂⁴×C₆₇	—	2	2	no	—
163	C₂⁴×C₆₇	—	2	8	no	—
164	C₂⁴×C₆₇	—	2	2	no	—
165	C₂⁴×C₆₇	—	2	4	no	—
166	C₂⁴×C₆₇	—	4	8	no	—
167	C₂⁴×C₆₇	—	8	8	no	—
168	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
169	#41×C₆₇	—	2	2	no	—
170	#41×C₆₇	—	2	2	no	—
171	#41×C₆₇	—	2	8	no	—
172	#41×C₆₇	—	2	4	no	—
173	#41×C₆₇	—	2	4	no	—
174	#41×C₆₇	—	4	4	no	—
175	#41×C₆₇	—	4	8	no	—
176	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
177	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
178	C₂×D₄×C₆₇	—	2	16	no	—
179	C₂×D₄×C₆₇	—	2	8	no	—
180	C₂×D₄×C₆₇	—	2	4	no	—
181	C₂×D₄×C₆₇	—	2	2	no	—
182	C₂×D₄×C₆₇	—	2	4	no	—
183	C₂×D₄×C₆₇	—	2	8	no	—
184	C₂×D₄×C₆₇	—	2	2	no	—
185	C₂×D₄×C₆₇	—	2	4	no	—
186	C₂×D₄×C₆₇	—	2	4	no	—
187	C₂×D₄×C₆₇	—	2	8	no	—
188	C₂×D₄×C₆₇	—	2	2	no	—
189	C₂×D₄×C₆₇	—	2	8	no	—
190	C₂×D₄×C₆₇	—	2	4	no	—
191	C₂×D₄×C₆₇	—	2	4	no	—
192	C₂×D₄×C₆₇	—	4	8	no	—
193	C₂×D₄×C₆₇	—	4	4	no	—
194	C₂×D₄×C₆₇	—	4	16	no	—
195	C₂×D₄×C₆₇	—	4	8	no	—
196	C₂×D₄×C₆₇	—	4	8	no	—
197	C₂×D₄×C₆₇	—	4	16	no	—
198	C₂×D₄×C₆₇	—	8	16	no	—
199	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	—
200	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
201	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
202	C₂×D₄×C₆₇	C₂×D₄	1	8	yes	complemented
203	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
204	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
205	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
206	C₂²×C₄×C₆₇	—	2	2	no	—
207	C₂²×C₄×C₆₇	—	2	2	no	—
208	C₂²×C₄×C₆₇	—	2	4	no	—
209	C₂²×C₄×C₆₇	—	2	2	no	—
210	C₂²×C₄×C₆₇	—	2	8	no	—
211	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
212	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
213	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
214	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
215	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
216	Q₁₆×C₆₇	—	2	2	no	—
217	SD₁₆×C₆₇	—	2	8	no	—
218	SD₁₆×C₆₇	—	2	4	no	—
219	SD₁₆×C₆₇	—	4	4	no	—
220	D₈×C₆₇	—	2	16	no	—
221	D₈×C₆₇	—	2	8	no	—
222	D₈×C₆₇	—	2	4	no	—
223	D₈×C₆₇	—	2	4	no	—
224	D₈×C₆₇	—	2	2	no	—
225	D₈×C₆₇	—	4	4	no	—
226	D₈×C₆₇	C₂×D₄	1	8	yes	complemented
227	D₈×C₆₇	C₂×D₄	1	8	yes	complemented
228	M₁₆×C₆₇	—	2	2	no	—
229	M₁₆×C₆₇	—	2	2	no	—
230	M₁₆×C₆₇	—	2	4	no	—
231	C₂×C₈×C₆₇	—	2	2	no	—
232	C₂×C₈×C₆₇	—	2	4	no	—
233	C₂×C₈×C₆₇	—	2	4	no	—
234	C₂×C₈×C₆₇	—	2	4	no	—
235	C₂×C₈×C₆₇	C₂×D₄	1	4	yes	complemented
236	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
237	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
238	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
239	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
240	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
241	C₄⋊C₄×C₆₇	—	2	4	no	—
242	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
243	C₄⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
244	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
245	C₂²⋊C₄×C₆₇	—	2	2	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	—	2	8	no	—
250	C₂²⋊C₄×C₆₇	—	2	4	no	—
251	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
252	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
253	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
254	C₄²×C₆₇	—	2	2	no	—
255	C₄²×C₆₇	C₂⁴	1	2	yes	—
256	C₂³×C₆₇	—	2	2	no	—
257	C₂³×C₆₇	—	2	4	no	—
258	C₂³×C₆₇	—	2	4	no	—
259	C₂³×C₆₇	—	2	8	no	—
260	C₂³×C₆₇	—	2	4	no	—
261	C₂³×C₆₇	—	2	2	no	—
262	C₂³×C₆₇	—	4	16	no	—
263	C₂³×C₆₇	—	4	8	no	—
264	C₂³×C₆₇	—	4	4	no	—
265	C₂³×C₆₇	—	4	16	no	—
266	C₂³×C₆₇	—	8	4	no	—
267	C₂³×C₆₇	—	8	8	no	—
268	C₂³×C₆₇	—	8	4	no	—
269	C₂³×C₆₇	—	8	8	no	—
270	C₂³×C₆₇	—	8	32	no	—
271	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
272	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
273	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
274	Q₈×C₆₇	—	2	2	no	—
275	Q₈×C₆₇	—	2	2	no	—
276	Q₈×C₆₇	—	2	2	no	—
277	D₄×C₆₇	—	2	4	no	—
278	D₄×C₆₇	—	2	8	no	—
279	D₄×C₆₇	—	2	8	no	—
280	D₄×C₆₇	—	2	2	no	—
281	D₄×C₆₇	—	2	4	no	—
282	D₄×C₆₇	—	2	2	no	—
283	D₄×C₆₇	—	2	4	no	—
284	D₄×C₆₇	—	2	2	no	—
285	D₄×C₆₇	—	2	4	no	—
286	D₄×C₆₇	—	4	16	no	—
287	D₄×C₆₇	—	4	8	no	—
288	D₄×C₆₇	—	4	8	no	—
289	D₄×C₆₇	—	4	4	no	—
290	D₄×C₆₇	—	4	8	no	—
291	D₄×C₆₇	—	4	4	no	—
292	D₄×C₆₇	—	8	8	no	—
293	D₄×C₆₇	—	8	8	no	—
294	D₄×C₆₇	C₂²×D₄	1	8	yes	—
295	C₂×C₄×C₆₇	—	2	2	no	—
296	C₂×C₄×C₆₇	—	2	4	no	—
297	C₂×C₄×C₆₇	—	2	2	no	—
298	C₂×C₄×C₆₇	—	2	2	no	—
299	C₂×C₄×C₆₇	—	2	2	no	—
300	C₂×C₄×C₆₇	—	2	2	no	—
301	C₂×C₄×C₆₇	—	2	4	no	—
302	C₂×C₄×C₆₇	—	2	2	no	—
303	C₂×C₄×C₆₇	—	4	8	no	—
304	C₂×C₄×C₆₇	—	4	4	no	—
305	C₂×C₄×C₆₇	—	8	8	no	—
306	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
307	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
308	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
309	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
310	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
311	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
312	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
313	C₈×C₆₇	—	2	2	no	—
314	C₈×C₆₇	—	2	2	no	—
315	C₈×C₆₇	—	2	2	no	—
316	C₈×C₆₇	C₂²×D₄	1	2	yes	—
317	C₈×C₆₇	C₂²×D₄	1	2	yes	—
318	C₂²×C₆₇	—	2	8	no	—
319	C₂²×C₆₇	—	2	2	no	—
320	C₂²×C₆₇	—	2	2	no	—
321	C₂²×C₆₇	—	2	2	no	—
322	C₂²×C₆₇	—	2	2	no	—
323	C₂²×C₆₇	—	2	8	no	—
324	C₂²×C₆₇	—	2	4	no	—
325	C₂²×C₆₇	—	4	8	no	—
326	C₂²×C₆₇	—	4	2	no	—
327	C₂²×C₆₇	—	4	4	no	—
328	C₂²×C₆₇	—	4	4	no	—
329	C₂²×C₆₇	—	4	8	no	—
330	C₂²×C₆₇	—	8	8	no	—
331	C₂²×C₆₇	—	8	32	no	—
332	C₂²×C₆₇	—	8	8	no	—
333	C₂²×C₆₇	—	16	8	no	—
334	C₂²×C₆₇	D₄²	1	2	yes	—
335	C₂²×C₆₇	#576	1	4	yes	complemented
336	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
337	C₄×C₆₇	—	2	2	no	—
338	C₄×C₆₇	—	2	2	no	—
339	C₄×C₆₇	—	2	4	no	—
340	C₄×C₆₇	—	4	2	no	—
341	C₄×C₆₇	—	4	4	no	—
342	C₄×C₆₇	D₄²	1	2	yes	—
343	C₄×C₆₇	C₂³×D₄	1	1	yes	characteristic
344	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
345	#61049	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
346	C₂×C₆₇	—	2	2	no	—
347	C₂×C₆₇	—	2	4	no	—
348	C₂×C₆₇	—	4	2	no	—
349	C₂×C₆₇	—	4	8	no	—
350	C₂×C₆₇	—	8	4	no	—
351	C₂×C₆₇	—	8	2	no	—
352	C₂×C₆₇	C₂×D₄²	1	1	yes	characteristic
353	C₂×C₆₇	C₂×#576	1	2	yes	—
354	C₂×#576	C₂×C₆₇	1	1	yes	characteristic, complemented
355	C₂³×D₈	C₂×C₆₇	1	1	yes	characteristic, complemented
356	#3484	C₂×C₆₇	1	2	yes	complemented
357	#3280	C₂×C₆₇	1	4	yes	complemented
358	D₄×D₈	C₂×C₆₇	1	4	yes	complemented
359	#3264	C₂×C₆₇	1	8	yes	complemented
360	#3155	C₂×C₆₇	1	1	yes	characteristic, complemented
361	#3058	C₂×C₆₇	1	1	yes	characteristic, complemented
362	#3050	C₂×C₆₇	1	1	yes	characteristic, complemented
363	#3041	C₂×C₆₇	1	2	yes	complemented
364	#3008	C₂×C₆₇	1	2	yes	complemented
365	#3003	C₂×C₆₇	1	2	yes	complemented
366	#2948	C₂×C₆₇	1	1	yes	characteristic, complemented
367	#2929	C₂×C₆₇	1	1	yes	characteristic, complemented
368	C₆₇	#61049	1	1	yes	characteristic, direct product factor, Sylow
369	C₂×H(5,𝔽₂)	C₂²×C₆₇	1	2	yes	complemented
370	C₂³×D₄	C₂²×C₆₇	1	2	yes	complemented
371	#576	—	2	8	no	—
372	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	complemented
373	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	complemented
374	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	4	yes	complemented
375	C₂×#135	C₂²×C₆₇	1	1	yes	characteristic, complemented
376	C₂×#135	C₂²×C₆₇	1	2	yes	complemented
377	C₂²×D₈	—	2	8	no	—
378	C₂²×D₈	C₂²×C₆₇	1	1	yes	characteristic
379	C₂²×D₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
380	C₂²×D₈	C₂²×C₆₇	1	2	yes	complemented
381	C₂²×D₈	C₂²×C₆₇	1	4	yes	complemented
382	C₂²×D₈	C₂²×C₆₇	1	4	yes	complemented
383	C₂²×D₈	C₂²×C₆₇	1	2	yes	complemented
384	C₂×#131	C₂²×C₆₇	1	1	yes	characteristic, complemented
385	C₂³×C₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
386	#546	—	2	4	no	—
387	#546	C₂²×C₆₇	1	8	yes	complemented
388	D₄²	—	2	4	no	—
389	D₄²	C₂²×C₆₇	1	8	yes	complemented
390	#535	C₂²×C₆₇	1	2	yes	complemented
391	#535	C₂²×C₆₇	1	2	yes	complemented
392	#534	—	2	4	no	—
393	#525	C₂²×C₆₇	1	1	yes	characteristic
394	#525	C₂²×C₆₇	1	2	yes	complemented
395	C₂×#120	—	2	4	no	—
396	#518	C₂²×C₆₇	1	2	yes	complemented
397	#496	C₂²×C₆₇	1	4	yes	complemented
398	#495	C₂²×C₆₇	1	2	yes	complemented
399	#493	C₂²×C₆₇	1	2	yes	complemented
400	#469	C₂²×C₆₇	1	4	yes	complemented
401	#467	C₂²×C₆₇	1	2	yes	complemented
402	#466	C₂²×C₆₇	1	2	yes	complemented
403	#466	C₂²×C₆₇	1	4	yes	complemented
404	#465	C₂²×C₆₇	1	4	yes	complemented
405	#463	C₂²×C₆₇	1	8	yes	complemented
406	#459	C₂²×C₆₇	1	8	yes	complemented
407	#450	C₂²×C₆₇	1	8	yes	complemented
408	#449	C₂²×C₆₇	1	8	yes	complemented
409	#447	C₂²×C₆₇	1	8	yes	complemented
410	#447	C₂²×C₆₇	1	8	yes	complemented
411	#442	C₂²×C₆₇	1	4	yes	complemented
412	C₄×D₈	C₂²×C₆₇	1	4	yes	complemented
413	#435	C₂²×C₆₇	1	4	yes	complemented
414	C₈×D₄	C₂²×C₆₇	1	4	yes	complemented
415	#427	C₂²×C₆₇	1	1	yes	characteristic, complemented
416	#424	C₂²×C₆₇	1	1	yes	characteristic, complemented
417	#418	C₂²×C₆₇	1	2	yes	complemented
418	#418	C₂²×C₆₇	1	2	yes	complemented
419	#416	C₂²×C₆₇	1	2	yes	complemented
420	#408	C₂²×C₆₇	1	1	yes	characteristic, complemented
421	#407	C₂²×C₆₇	1	1	yes	characteristic, complemented
422	#405	C₂²×C₆₇	1	1	yes	characteristic, complemented
423	C₂⁵	—	2	2	no	—
424	H(5,𝔽₂)	—	2	8	no	—
425	H(5,𝔽₂)	—	4	4	no	—
426	C₂×#41	—	2	2	no	—
427	C₂×#41	C₂³×C₆₇	1	2	yes	—
428	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
429	C₂×#41	C₂³×C₆₇	1	4	yes	complemented
430	C₂²×D₄	—	2	8	no	—
431	C₂²×D₄	—	2	4	no	—
432	C₂²×D₄	—	2	2	no	—
433	C₂²×D₄	—	2	8	no	—
434	C₂²×D₄	—	2	2	no	—
435	C₂²×D₄	—	2	4	no	—
436	C₂²×D₄	—	4	4	no	—
437	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
438	C₂²×D₄	C₂³×C₆₇	1	8	yes	—
439	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
440	C₂²×D₄	C₂³×C₆₇	1	4	yes	complemented
441	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
442	AGL(1,ℤ/8)	—	2	8	no	—
443	AGL(1,ℤ/8)	—	2	16	no	—
444	AGL(1,ℤ/8)	—	4	4	no	—
445	#135	—	2	8	no	—
446	#135	—	2	4	no	—
447	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic, complemented
448	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	complemented
449	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	complemented
450	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	complemented
451	C₂×D₈	—	2	8	no	—
452	C₂×D₈	—	2	16	no	—
453	C₂×D₈	—	2	16	no	—
454	C₂×D₈	—	2	8	no	—
455	C₂×D₈	—	2	4	no	—
456	C₂×D₈	D₄×C₆₇	1	8	yes	complemented
457	C₂×D₈	C₂³×C₆₇	1	8	yes	—
458	C₂×D₈	C₂³×C₆₇	1	2	yes	—
459	C₂×D₈	C₂³×C₆₇	1	2	yes	—
460	C₂×D₈	C₂³×C₆₇	1	2	yes	—
461	C₂×D₈	C₂³×C₆₇	1	2	yes	—
462	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic, complemented
463	C₂×D₈	C₂³×C₆₇	1	4	yes	complemented
464	C₂×D₈	C₂³×C₆₇	1	4	yes	complemented
465	#131	—	2	4	no	—
466	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
467	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
468	C₂×M₁₆	C₂³×C₆₇	1	2	yes	complemented
469	C₂²×C₈	—	2	4	no	—
470	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
471	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
472	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
473	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
474	C₂²×C₈	C₂³×C₆₇	1	2	yes	complemented
475	#127	—	2	2	no	—
476	#127	C₂³×C₆₇	1	4	yes	complemented
477	#124	—	2	2	no	—
478	#124	C₂³×C₆₇	1	4	yes	complemented
479	#123	—	2	2	no	—
480	#123	—	2	8	no	—
481	#123	D₄×C₆₇	1	2	yes	—
482	C₂²⋊Q₈	D₄×C₆₇	1	2	yes	—
483	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
484	#121	—	2	8	no	—
485	#121	—	2	4	no	—
486	#121	—	2	8	no	—
487	#121	D₄×C₆₇	1	2	yes	—
488	#121	C₂³×C₆₇	1	4	yes	—
489	#121	C₂³×C₆₇	1	8	yes	complemented
490	#120	—	2	2	no	—
491	#120	—	2	4	no	—
492	#120	—	2	8	no	—
493	#120	—	2	4	no	—
494	#120	—	2	8	no	—
495	#120	—	2	8	no	—
496	#120	D₄×C₆₇	1	2	yes	—
497	C₄×D₄	—	2	4	no	—
498	C₄×D₄	—	2	4	no	—
499	C₄×D₄	C₂³×C₆₇	1	4	yes	—
500	C₄×D₄	C₂³×C₆₇	1	8	yes	complemented
501	#117	C₂³×C₆₇	1	2	yes	—
502	#117	C₂³×C₆₇	1	1	yes	characteristic
503	C₂×C₂²⋊C₄	—	2	4	no	—
504	C₂×C₂²⋊C₄	—	2	8	no	—
505	#107	C₂³×C₆₇	1	2	yes	complemented
506	#106	C₂³×C₆₇	1	2	yes	complemented
507	C₄⋊C₈	C₂³×C₆₇	1	4	yes	complemented
508	#103	C₂³×C₆₇	1	4	yes	complemented
509	#102	C₂³×C₆₇	1	4	yes	complemented
510	#102	C₂³×C₆₇	1	8	yes	complemented
511	#102	C₂³×C₆₇	1	8	yes	complemented
512	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
513	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	complemented
514	#97	C₂³×C₆₇	1	2	yes	complemented
515	C₄×C₈	C₂³×C₆₇	1	2	yes	complemented
516	C₂⁴	—	2	2	no	—
517	C₂⁴	—	2	8	no	—
518	C₂⁴	—	2	2	no	—
519	C₂⁴	—	2	4	no	—
520	C₂⁴	—	4	8	no	—
521	C₂⁴	—	8	8	no	—
522	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
523	#41	—	2	2	no	—
524	#41	—	2	2	no	—
525	#41	—	2	8	no	—
526	#41	—	2	4	no	—
527	#41	—	2	4	no	—
528	#41	—	4	4	no	—
529	#41	—	4	8	no	—
530	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
531	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
532	C₂×D₄	—	2	16	no	—
533	C₂×D₄	—	2	8	no	—
534	C₂×D₄	—	2	4	no	—
535	C₂×D₄	—	2	2	no	—
536	C₂×D₄	—	2	4	no	—
537	C₂×D₄	—	2	8	no	—
538	C₂×D₄	—	2	2	no	—
539	C₂×D₄	—	2	4	no	—
540	C₂×D₄	—	2	4	no	—
541	C₂×D₄	—	2	8	no	—
542	C₂×D₄	—	2	2	no	—
543	C₂×D₄	—	2	8	no	—
544	C₂×D₄	—	2	4	no	—
545	C₂×D₄	—	2	4	no	—
546	C₂×D₄	—	4	8	no	—
547	C₂×D₄	—	4	4	no	—
548	C₂×D₄	—	4	16	no	—
549	C₂×D₄	—	4	8	no	—
550	C₂×D₄	—	4	8	no	—
551	C₂×D₄	—	4	16	no	—
552	C₂×D₄	—	8	16	no	—
553	C₂×D₄	C₂×D₄×C₆₇	1	4	yes	—
554	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
555	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
556	C₂×D₄	C₂×D₄×C₆₇	1	8	yes	complemented
557	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
558	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
559	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
560	C₂²×C₄	—	2	2	no	—
561	C₂²×C₄	—	2	2	no	—
562	C₂²×C₄	—	2	4	no	—
563	C₂²×C₄	—	2	2	no	—
564	C₂²×C₄	—	2	8	no	—
565	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
566	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
567	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
568	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
569	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
570	Q₁₆	—	2	2	no	—
571	SD₁₆	—	2	8	no	—
572	SD₁₆	—	2	4	no	—
573	SD₁₆	—	4	4	no	—
574	D₈	—	2	16	no	—
575	D₈	—	2	8	no	—
576	D₈	—	2	4	no	—
577	D₈	—	2	4	no	—
578	D₈	—	2	2	no	—
579	D₈	—	4	4	no	—
580	D₈	C₂×D₄×C₆₇	1	8	yes	complemented
581	D₈	C₂×D₄×C₆₇	1	8	yes	complemented
582	M₁₆	—	2	2	no	—
583	M₁₆	—	2	2	no	—
584	M₁₆	—	2	4	no	—
585	C₂×C₈	—	2	2	no	—
586	C₂×C₈	—	2	4	no	—
587	C₂×C₈	—	2	4	no	—
588	C₂×C₈	—	2	4	no	—
589	C₂×C₈	C₂×D₄×C₆₇	1	4	yes	complemented
590	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
591	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
592	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
593	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
594	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
595	C₄⋊C₄	—	2	4	no	—
596	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
597	C₄⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
598	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
599	C₂²⋊C₄	—	2	2	no	—
600	C₂²⋊C₄	—	2	4	no	—
601	C₂²⋊C₄	—	2	8	no	—
602	C₂²⋊C₄	—	2	8	no	—
603	C₂²⋊C₄	—	2	8	no	—
604	C₂²⋊C₄	—	2	4	no	—
605	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
606	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
607	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
608	C₄²	—	2	2	no	—
609	C₄²	C₂⁴×C₆₇	1	2	yes	—
610	C₂³	—	2	2	no	—
611	C₂³	—	2	4	no	—
612	C₂³	—	2	4	no	—
613	C₂³	—	2	8	no	—
614	C₂³	—	2	4	no	—
615	C₂³	—	2	2	no	—
616	C₂³	—	4	16	no	—
617	C₂³	—	4	8	no	—
618	C₂³	—	4	4	no	—
619	C₂³	—	4	16	no	—
620	C₂³	—	8	4	no	—
621	C₂³	—	8	8	no	—
622	C₂³	—	8	4	no	—
623	C₂³	—	8	8	no	—
624	C₂³	—	8	32	no	—
625	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
626	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
627	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
628	Q₈	—	2	2	no	—
629	Q₈	—	2	2	no	—
630	Q₈	—	2	2	no	—
631	D₄	—	2	4	no	—
632	D₄	—	2	8	no	—
633	D₄	—	2	8	no	—
634	D₄	—	2	2	no	—
635	D₄	—	2	4	no	—
636	D₄	—	2	2	no	—
637	D₄	—	2	4	no	—
638	D₄	—	2	2	no	—
639	D₄	—	2	4	no	—
640	D₄	—	4	16	no	—
641	D₄	—	4	8	no	—
642	D₄	—	4	8	no	—
643	D₄	—	4	4	no	—
644	D₄	—	4	8	no	—
645	D₄	—	4	4	no	—
646	D₄	—	8	8	no	—
647	D₄	—	8	8	no	—
648	D₄	C₂²×D₄×C₆₇	1	8	yes	—
649	C₂×C₄	—	2	2	no	—
650	C₂×C₄	—	2	4	no	—
651	C₂×C₄	—	2	2	no	—
652	C₂×C₄	—	2	2	no	—
653	C₂×C₄	—	2	2	no	—
654	C₂×C₄	—	2	2	no	—
655	C₂×C₄	—	2	4	no	—
656	C₂×C₄	—	2	2	no	—
657	C₂×C₄	—	4	8	no	—
658	C₂×C₄	—	4	4	no	—
659	C₂×C₄	—	8	8	no	—
660	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
661	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
662	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
663	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
664	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
665	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
666	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
667	C₈	—	2	2	no	—
668	C₈	—	2	2	no	—
669	C₈	—	2	2	no	—
670	C₈	C₂²×D₄×C₆₇	1	2	yes	—
671	C₈	C₂²×D₄×C₆₇	1	2	yes	—
672	C₂²	—	2	8	no	—
673	C₂²	—	2	2	no	—
674	C₂²	—	2	2	no	—
675	C₂²	—	2	2	no	—
676	C₂²	—	2	4	no	—
677	C₂²	—	2	2	no	—
678	C₂²	—	2	8	no	—
679	C₂²	—	4	8	no	—
680	C₂²	—	4	4	no	—
681	C₂²	—	4	8	no	—
682	C₂²	—	4	2	no	—
683	C₂²	—	4	4	no	—
684	C₂²	—	8	8	no	—
685	C₂²	—	8	32	no	—
686	C₂²	—	8	8	no	—
687	C₂²	—	16	8	no	—
688	C₂²	D₄²×C₆₇	1	2	yes	—
689	C₂²	#576×C₆₇	1	4	yes	complemented
690	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
691	C₄	—	2	4	no	—
692	C₄	—	2	2	no	—
693	C₄	—	2	2	no	—
694	C₄	—	4	4	no	—
695	C₄	—	4	2	no	—
696	C₄	D₄²×C₆₇	1	2	yes	—
697	C₄	C₂³×D₄×C₆₇	1	1	yes	characteristic
698	C₄	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
699	C₂	—	2	2	no	—
700	C₂	—	2	4	no	—
701	C₂	—	4	2	no	—
702	C₂	—	4	8	no	—
703	C₂	—	8	4	no	—
704	C₂	—	8	2	no	—
705	C₂	C₂×D₄²×C₆₇	1	1	yes	characteristic
706	C₂	C₂×#576×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 ◁ #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. C₂³×D₈×C₆₇	C₂	semidirect
3. C₆₇×#3484	C₂	semidirect
4. C₆₇×#3280	C₂	semidirect
5. D₄×D₈×C₆₇	C₂	semidirect
6. C₆₇×#3264	C₂	semidirect
7. C₆₇×#3155	C₂	semidirect
8. C₆₇×#3058	C₂	semidirect
9. C₆₇×#3050	C₂	semidirect
10. C₆₇×#3041	C₂	semidirect
11. C₆₇×#3008	C₂	semidirect
12. C₆₇×#3003	C₂	semidirect
13. C₆₇×#2948	C₂	semidirect
14. C₆₇×#2929	C₂	semidirect
15. C₂×H(5,𝔽₂)×C₆₇	C₂²	semidirect
16. C₂³×D₄×C₆₇	C₂²	semidirect
18. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
19. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
20. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
21. C₂×#135×C₆₇	C₂²	semidirect
22. C₂×#135×C₆₇	C₂²	semidirect
25. C₂²×D₈×C₆₇	C₂²	semidirect
26. C₂²×D₈×C₆₇	C₂²	semidirect
27. C₂²×D₈×C₆₇	C₂²	semidirect
28. C₂²×D₈×C₆₇	C₂²	semidirect
29. C₂²×D₈×C₆₇	C₂²	semidirect
30. C₂×#131×C₆₇	C₂²	semidirect
31. C₂³×C₈×C₆₇	C₂²	semidirect
33. #546×C₆₇	C₂²	semidirect
35. D₄²×C₆₇	C₂²	semidirect
36. #535×C₆₇	C₂²	semidirect
37. #535×C₆₇	C₂²	semidirect
40. #525×C₆₇	C₂²	semidirect
42. #518×C₆₇	C₂²	semidirect
43. #496×C₆₇	C₂²	semidirect
44. #495×C₆₇	C₂²	semidirect
45. #493×C₆₇	C₂²	semidirect
46. #469×C₆₇	C₂²	semidirect
47. #467×C₆₇	C₂²	semidirect
48. #466×C₆₇	C₂²	semidirect
49. #466×C₆₇	C₂²	semidirect
50. #465×C₆₇	C₂²	semidirect
51. #463×C₆₇	C₂²	semidirect
52. #459×C₆₇	C₂²	semidirect
53. #450×C₆₇	C₂²	semidirect
54. #449×C₆₇	C₂²	semidirect
55. #447×C₆₇	C₂²	semidirect
56. #447×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. #418×C₆₇	C₂²	semidirect
64. #418×C₆₇	C₂²	semidirect
65. #416×C₆₇	C₂²	semidirect
66. #408×C₆₇	C₂²	semidirect
67. #407×C₆₇	C₂²	semidirect
68. #405×C₆₇	C₂²	semidirect
75. C₂×#41×C₆₇	C₂³	semidirect
86. C₂²×D₄×C₆₇	C₂³	semidirect
93. C₂×Q₁₆×C₆₇	C₂³	semidirect
94. C₂×SD₁₆×C₆₇	C₂³	semidirect
95. C₂×SD₁₆×C₆₇	C₂³	semidirect
96. C₂×SD₁₆×C₆₇	C₂³	semidirect
102. C₂×D₈×C₆₇	D₄	semidirect
108. C₂×D₈×C₆₇	C₂³	semidirect
109. C₂×D₈×C₆₇	C₂³	semidirect
110. C₂×D₈×C₆₇	C₂³	semidirect
114. C₂×M₁₆×C₆₇	C₂³	semidirect
120. C₂²×C₈×C₆₇	C₂³	semidirect
122. #127×C₆₇	C₂³	semidirect
124. #124×C₆₇	C₂³	semidirect
135. #121×C₆₇	C₂³	semidirect
146. C₄×D₄×C₆₇	C₂³	semidirect
151. #107×C₆₇	C₂³	semidirect
152. #106×C₆₇	C₂³	semidirect
153. C₄⋊C₈×C₆₇	C₂³	semidirect
154. #103×C₆₇	C₂³	semidirect
155. #102×C₆₇	C₂³	semidirect
156. #102×C₆₇	C₂³	semidirect
157. #102×C₆₇	C₂³	semidirect
159. C₂²⋊C₈×C₆₇	C₂³	semidirect
160. #97×C₆₇	C₂³	semidirect
161. C₄×C₈×C₆₇	C₂³	semidirect
202. C₂×D₄×C₆₇	C₂×D₄	semidirect
226. D₈×C₆₇	C₂×D₄	semidirect
227. D₈×C₆₇	C₂×D₄	semidirect
235. C₂×C₈×C₆₇	C₂×D₄	semidirect
335. C₂²×C₆₇	#576	semidirect
345. #61049	C₆₇	direct (N × H)
354. C₂×#576	C₂×C₆₇	semidirect
355. C₂³×D₈	C₂×C₆₇	semidirect
356. #3484	C₂×C₆₇	semidirect
357. #3280	C₂×C₆₇	semidirect
358. D₄×D₈	C₂×C₆₇	semidirect
359. #3264	C₂×C₆₇	semidirect
360. #3155	C₂×C₆₇	semidirect
361. #3058	C₂×C₆₇	semidirect
362. #3050	C₂×C₆₇	semidirect
363. #3041	C₂×C₆₇	semidirect
364. #3008	C₂×C₆₇	semidirect
365. #3003	C₂×C₆₇	semidirect
366. #2948	C₂×C₆₇	semidirect
367. #2929	C₂×C₆₇	semidirect
368. C₆₇	#61049	direct (N × H)
369. C₂×H(5,𝔽₂)	C₂²×C₆₇	semidirect
370. C₂³×D₄	C₂²×C₆₇	semidirect
372. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
373. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
374. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
375. C₂×#135	C₂²×C₆₇	semidirect
376. C₂×#135	C₂²×C₆₇	semidirect
379. C₂²×D₈	C₂²×C₆₇	semidirect
380. C₂²×D₈	C₂²×C₆₇	semidirect
381. C₂²×D₈	C₂²×C₆₇	semidirect
382. C₂²×D₈	C₂²×C₆₇	semidirect
383. C₂²×D₈	C₂²×C₆₇	semidirect
384. C₂×#131	C₂²×C₆₇	semidirect
385. C₂³×C₈	C₂²×C₆₇	semidirect
387. #546	C₂²×C₆₇	semidirect
389. D₄²	C₂²×C₆₇	semidirect
390. #535	C₂²×C₆₇	semidirect
391. #535	C₂²×C₆₇	semidirect
394. #525	C₂²×C₆₇	semidirect
396. #518	C₂²×C₆₇	semidirect
397. #496	C₂²×C₆₇	semidirect
398. #495	C₂²×C₆₇	semidirect
399. #493	C₂²×C₆₇	semidirect
400. #469	C₂²×C₆₇	semidirect
401. #467	C₂²×C₆₇	semidirect
402. #466	C₂²×C₆₇	semidirect
403. #466	C₂²×C₆₇	semidirect
404. #465	C₂²×C₆₇	semidirect
405. #463	C₂²×C₆₇	semidirect
406. #459	C₂²×C₆₇	semidirect
407. #450	C₂²×C₆₇	semidirect
408. #449	C₂²×C₆₇	semidirect
409. #447	C₂²×C₆₇	semidirect
410. #447	C₂²×C₆₇	semidirect
411. #442	C₂²×C₆₇	semidirect
412. C₄×D₈	C₂²×C₆₇	semidirect
413. #435	C₂²×C₆₇	semidirect
414. C₈×D₄	C₂²×C₆₇	semidirect
415. #427	C₂²×C₆₇	semidirect
416. #424	C₂²×C₆₇	semidirect
417. #418	C₂²×C₆₇	semidirect
418. #418	C₂²×C₆₇	semidirect
419. #416	C₂²×C₆₇	semidirect
420. #408	C₂²×C₆₇	semidirect
421. #407	C₂²×C₆₇	semidirect
422. #405	C₂²×C₆₇	semidirect
429. C₂×#41	C₂³×C₆₇	semidirect
440. C₂²×D₄	C₂³×C₆₇	semidirect
447. C₂×Q₁₆	C₂³×C₆₇	semidirect
448. C₂×SD₁₆	C₂³×C₆₇	semidirect
449. C₂×SD₁₆	C₂³×C₆₇	semidirect
450. C₂×SD₁₆	C₂³×C₆₇	semidirect
456. C₂×D₈	D₄×C₆₇	semidirect
462. C₂×D₈	C₂³×C₆₇	semidirect
463. C₂×D₈	C₂³×C₆₇	semidirect
464. C₂×D₈	C₂³×C₆₇	semidirect
468. C₂×M₁₆	C₂³×C₆₇	semidirect
474. C₂²×C₈	C₂³×C₆₇	semidirect
476. #127	C₂³×C₆₇	semidirect
478. #124	C₂³×C₆₇	semidirect
489. #121	C₂³×C₆₇	semidirect
500. C₄×D₄	C₂³×C₆₇	semidirect
505. #107	C₂³×C₆₇	semidirect
506. #106	C₂³×C₆₇	semidirect
507. C₄⋊C₈	C₂³×C₆₇	semidirect
508. #103	C₂³×C₆₇	semidirect
509. #102	C₂³×C₆₇	semidirect
510. #102	C₂³×C₆₇	semidirect
511. #102	C₂³×C₆₇	semidirect
513. C₂²⋊C₈	C₂³×C₆₇	semidirect
514. #97	C₂³×C₆₇	semidirect
515. C₄×C₈	C₂³×C₆₇	semidirect
556. C₂×D₄	C₂×D₄×C₆₇	semidirect
580. D₈	C₂×D₄×C₆₇	semidirect
581. D₈	C₂×D₄×C₆₇	semidirect
589. C₂×C₈	C₂×D₄×C₆₇	semidirect
689. C₂²	#576×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
C₂³×D₈×C₆₇	2
C₆₇×#3484	2
C₆₇×#3280	2
D₄×D₈×C₆₇	2
C₆₇×#3264	2
C₆₇×#3155	2
C₆₇×#3058	2
C₆₇×#3050	2
C₆₇×#3041	2
C₆₇×#3008	2
C₆₇×#3003	2
C₆₇×#2948	2
C₆₇×#2929	2
#61049	67

Subgroups — C67×#61049 #30740300

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61049 #30740300