Subgroups — C₆₇×#60289 #30739540

Order 17152.

1770 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×#529×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₆₇×#2995	C₂	1	4	yes	maximal, complemented
3	C₆₇×#2993	C₂	1	4	yes	maximal, complemented
4	C₆₇×#2984	C₂	1	2	yes	maximal, complemented
5	C₆₇×#2975	C₂	1	2	yes	maximal, complemented
6	C₆₇×#2974	C₂	1	2	yes	maximal, complemented
7	C₆₇×#2973	C₂	1	2	yes	maximal, complemented
8	C₆₇×#2969	C₂	1	4	yes	maximal, complemented
9	C₆₇×#2967	C₂	1	4	yes	maximal, complemented
10	C₆₇×#2924	C₂	1	4	yes	maximal, complemented
11	C₆₇×#2920	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#2920	C₂	1	1	yes	maximal, characteristic, complemented
13	#529×C₆₇	C₄	1	2	yes	—
14	#529×C₆₇	C₄	1	2	yes	—
15	#529×C₆₇	C₄	1	2	yes	—
16	#529×C₆₇	C₄	1	2	yes	—
17	#529×C₆₇	C₂²	1	2	yes	—
18	#529×C₆₇	C₂²	1	2	yes	—
19	#529×C₆₇	C₂²	1	2	yes	—
20	#529×C₆₇	C₂²	1	2	yes	—
21	C₂×#126×C₆₇	C₄	1	2	yes	—
22	C₂×#125×C₆₇	C₄	1	1	yes	characteristic
23	C₂×#124×C₆₇	C₄	1	1	yes	characteristic
24	C₂×#123×C₆₇	C₄	1	2	yes	—
25	C₂×C₂²⋊Q₈×C₆₇	C₄	1	1	yes	characteristic
26	C₂×#121×C₆₇	C₄	1	1	yes	characteristic
27	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
29	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
30	C₂×#117×C₆₇	C₂²	1	2	yes	—
31	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
32	#446×C₆₇	C₂²	1	8	yes	complemented
33	#446×C₆₇	C₂²	1	4	yes	complemented
34	C₈×Q₈×C₆₇	C₂²	1	4	yes	complemented
35	#436×C₆₇	C₂²	1	8	yes	complemented
36	#436×C₆₇	C₂²	1	4	yes	complemented
37	#436×C₆₇	C₂²	1	8	yes	complemented
38	#435×C₆₇	C₂²	1	8	yes	complemented
39	#435×C₆₇	C₂²	1	8	yes	complemented
40	#435×C₆₇	C₂²	1	8	yes	complemented
41	C₈×D₄×C₆₇	C₂²	1	4	yes	complemented
42	#433×C₆₇	C₂²	1	8	yes	complemented
43	#433×C₆₇	C₂²	1	8	yes	complemented
44	#432×C₆₇	C₂²	1	2	yes	—
45	#432×C₆₇	C₂²	1	2	yes	—
46	#432×C₆₇	C₂²	1	4	yes	—
47	#432×C₆₇	C₂²	1	2	yes	complemented
48	#432×C₆₇	C₂²	1	2	yes	complemented
49	#431×C₆₇	C₂²	1	2	yes	—
50	#431×C₆₇	C₂²	1	2	yes	—
51	#431×C₆₇	C₂²	1	4	yes	—
52	#431×C₆₇	C₂²	1	2	yes	complemented
53	#431×C₆₇	C₂²	1	2	yes	complemented
54	#424×C₆₇	C₂²	1	8	yes	complemented
55	#423×C₆₇	C₂²	1	2	yes	complemented
56	#423×C₆₇	C₂²	1	2	yes	complemented
57	#407×C₆₇	C₂²	1	1	yes	characteristic
58	#407×C₆₇	C₂²	1	2	yes	—
59	#407×C₆₇	C₂²	1	1	yes	characteristic
60	#407×C₆₇	C₂²	1	4	yes	—
61	C₂×C₂²⋊C₈×C₆₇	C₂²	1	4	yes	—
62	#405×C₆₇	C₂²	1	8	yes	complemented
63	C₄×M₁₆×C₆₇	C₂²	1	2	yes	complemented
64	C₄×M₁₆×C₆₇	C₂²	1	2	yes	complemented
65	C₂²×Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
66	C₂²×D₄×C₆₇	C₂×C₄	1	2	yes	—
67	C₂²×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
68	C₂³×C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
69	C₂³×C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
70	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
71	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
72	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
73	C₂×M₁₆×C₆₇	C₂³	1	4	yes	—
74	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
75	C₂×M₁₆×C₆₇	C₂³	1	8	yes	—
76	C₂²×C₈×C₆₇	C₂³	1	8	yes	—
77	#126×C₆₇	C₂×C₄	1	4	yes	—
78	#126×C₆₇	C₂×C₄	1	4	yes	—
79	#126×C₆₇	C₂×C₄	1	4	yes	—
80	#126×C₆₇	C₂×C₄	1	4	yes	—
81	#125×C₆₇	C₂×C₄	1	2	yes	—
82	#125×C₆₇	C₂×C₄	1	2	yes	—
83	#125×C₆₇	C₂×C₄	1	2	yes	—
84	#125×C₆₇	C₂×C₄	1	2	yes	—
85	#124×C₆₇	C₂×C₄	1	2	yes	—
86	#124×C₆₇	C₂×C₄	1	2	yes	—
87	#124×C₆₇	C₂×C₄	1	2	yes	—
88	#124×C₆₇	C₂×C₄	1	2	yes	—
89	#123×C₆₇	C₂×C₄	1	4	yes	—
90	#123×C₆₇	C₂×C₄	1	4	yes	—
91	#123×C₆₇	C₂×C₄	1	4	yes	—
92	#123×C₆₇	C₂×C₄	1	4	yes	—
93	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
94	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
95	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
96	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
97	#121×C₆₇	C₂×C₄	1	2	yes	—
98	#121×C₆₇	C₂×C₄	1	2	yes	—
99	#121×C₆₇	C₂×C₄	1	2	yes	—
100	#121×C₆₇	C₂×C₄	1	2	yes	—
101	C₄×Q₈×C₆₇	C₂×C₄	1	2	yes	—
102	C₄×Q₈×C₆₇	C₂×C₄	1	2	yes	—
103	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
104	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
105	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
106	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
107	C₄×D₄×C₆₇	C₂×C₄	1	4	yes	—
108	C₄×D₄×C₆₇	C₂×C₄	1	4	yes	—
109	C₄×D₄×C₆₇	C₂³	1	2	yes	—
110	C₄×D₄×C₆₇	C₂³	1	2	yes	—
111	C₄×D₄×C₆₇	C₂³	1	4	yes	—
112	C₄×D₄×C₆₇	C₂³	1	4	yes	—
113	#117×C₆₇	C₂×C₄	1	4	yes	—
114	#117×C₆₇	C₂×C₄	1	4	yes	—
115	#117×C₆₇	C₂³	1	4	yes	—
116	#117×C₆₇	C₂³	1	4	yes	—
117	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
118	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
119	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
120	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
121	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
122	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
123	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
124	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
125	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
126	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
127	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
128	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
129	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
130	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
131	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
132	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
133	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
134	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
135	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
136	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
137	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
138	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
139	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
140	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
141	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
142	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
143	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
144	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
145	C₄⋊C₈×C₆₇	C₂³	1	8	yes	—
146	C₄⋊C₈×C₆₇	C₂³	1	8	yes	—
147	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
148	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
149	C₂²⋊C₈×C₆₇	C₂³	1	8	yes	—
150	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
151	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
152	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
153	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
154	C₂²⋊C₈×C₆₇	C₂³	1	8	yes	—
155	#97×C₆₇	C₂³	1	4	yes	—
156	#97×C₆₇	C₂³	1	4	yes	—
157	#97×C₆₇	C₂³	1	8	yes	—
158	C₄×C₈×C₆₇	C₂³	1	4	yes	—
159	C₄×C₈×C₆₇	C₂³	1	4	yes	—
160	C₄×C₈×C₆₇	C₂³	1	8	yes	—
161	C₂⁴×C₆₇	C₂²×C₄	1	2	yes	—
162	C₂⁴×C₆₇	C₂²×C₄	1	1	yes	characteristic
163	C₂×Q₈×C₆₇	—	4	2	no	—
164	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
165	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
166	C₂×D₄×C₆₇	—	4	2	no	—
167	C₂×D₄×C₆₇	—	4	4	no	—
168	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
169	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
170	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
171	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
172	C₂²×C₄×C₆₇	—	4	2	no	—
173	C₂²×C₄×C₆₇	—	4	4	no	—
174	C₂²×C₄×C₆₇	—	4	2	no	—
175	C₂²×C₄×C₆₇	—	4	2	no	—
176	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
177	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
178	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
179	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
180	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
181	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
182	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
183	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
184	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
185	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
186	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
187	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
188	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
189	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
190	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
191	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
192	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
193	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
194	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
195	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
196	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
197	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
198	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
199	M₁₆×C₆₇	—	4	2	no	—
200	M₁₆×C₆₇	—	4	4	no	—
201	M₁₆×C₆₇	—	4	8	no	—
202	M₁₆×C₆₇	—	4	2	no	—
203	C₂×C₈×C₆₇	—	4	8	no	—
204	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
205	C₂×C₈×C₆₇	C₂⁴	1	8	yes	—
206	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
207	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
208	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
209	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
210	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
211	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
212	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
213	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
214	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
215	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
216	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
217	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
218	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
219	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
220	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
221	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
222	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
223	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
224	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
225	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
226	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
227	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
228	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
229	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
230	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
231	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
232	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
233	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
234	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
235	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
236	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
237	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
238	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
239	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
240	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
241	C₄²×C₆₇	C₂²×C₄	1	4	yes	—
242	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
243	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
244	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
245	C₄²×C₆₇	C₂⁴	1	4	yes	—
246	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
247	C₂³×C₆₇	—	2	2	no	—
248	C₂³×C₆₇	—	2	4	no	—
249	C₂³×C₆₇	—	4	1	no	—
250	C₂³×C₆₇	—	4	1	no	—
251	C₂³×C₆₇	—	4	2	no	—
252	C₂³×C₆₇	—	4	2	no	—
253	C₂³×C₆₇	C₂³×C₄	1	4	yes	—
254	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
255	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
256	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
257	Q₈×C₆₇	—	2	4	no	—
258	Q₈×C₆₇	—	4	2	no	—
259	D₄×C₆₇	—	2	4	no	—
260	D₄×C₆₇	—	4	2	no	—
261	D₄×C₆₇	—	4	4	no	—
262	D₄×C₆₇	—	4	4	no	—
263	C₂×C₄×C₆₇	—	2	2	no	—
264	C₂×C₄×C₆₇	—	2	2	no	—
265	C₂×C₄×C₆₇	—	2	4	no	—
266	C₂×C₄×C₆₇	—	2	2	no	—
267	C₂×C₄×C₆₇	—	2	2	no	—
268	C₂×C₄×C₆₇	—	2	2	no	—
269	C₂×C₄×C₆₇	—	2	8	no	—
270	C₂×C₄×C₆₇	—	2	2	no	—
271	C₂×C₄×C₆₇	—	2	2	no	—
272	C₂×C₄×C₆₇	—	2	2	no	—
273	C₂×C₄×C₆₇	—	4	1	no	—
274	C₂×C₄×C₆₇	—	4	1	no	—
275	C₂×C₄×C₆₇	—	4	4	no	—
276	C₂×C₄×C₆₇	—	4	1	no	—
277	C₂×C₄×C₆₇	—	4	2	no	—
278	C₂×C₄×C₆₇	—	4	1	no	—
279	C₂×C₄×C₆₇	—	4	1	no	—
280	C₂×C₄×C₆₇	—	4	1	no	—
281	C₂×C₄×C₆₇	—	4	1	no	—
282	C₂×C₄×C₆₇	—	4	1	no	—
283	C₂×C₄×C₆₇	—	4	1	no	—
284	C₂×C₄×C₆₇	—	4	1	no	—
285	C₂×C₄×C₆₇	—	4	2	no	—
286	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
287	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
288	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
289	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
290	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
291	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
292	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
293	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
294	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
295	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
296	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
297	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
298	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
299	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
300	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
301	C₈×C₆₇	—	2	4	no	—
302	C₈×C₆₇	—	2	8	no	—
303	C₈×C₆₇	—	2	4	no	—
304	C₂²×C₆₇	—	2	1	no	—
305	C₂²×C₆₇	—	2	1	no	—
306	C₂²×C₆₇	—	2	1	no	—
307	C₂²×C₆₇	—	2	1	no	—
308	C₂²×C₆₇	—	2	4	no	—
309	C₂²×C₆₇	—	2	1	no	—
310	C₂²×C₆₇	—	2	1	no	—
311	C₂²×C₆₇	—	2	1	no	—
312	C₂²×C₆₇	—	2	1	no	—
313	C₂²×C₆₇	—	2	4	no	—
314	C₂²×C₆₇	—	2	4	no	—
315	C₂²×C₆₇	—	4	4	no	—
316	C₂²×C₆₇	—	8	4	no	—
317	C₂²×C₆₇	#568	1	2	yes	—
318	C₂²×C₆₇	C₂⁴×C₄	1	1	yes	characteristic
319	C₄×C₆₇	—	2	1	no	—
320	C₄×C₆₇	—	2	4	no	—
321	C₄×C₆₇	—	2	1	no	—
322	C₄×C₆₇	—	2	1	no	—
323	C₄×C₆₇	—	2	1	no	—
324	C₄×C₆₇	—	2	1	no	—
325	C₄×C₆₇	—	2	1	no	—
326	C₄×C₆₇	—	2	1	no	—
327	C₄×C₆₇	—	2	1	no	—
328	C₄×C₆₇	—	2	1	no	—
329	C₄×C₆₇	—	2	1	no	—
330	C₄×C₆₇	—	2	4	no	—
331	C₄×C₆₇	—	2	4	no	—
332	C₄×C₆₇	#568	1	2	yes	—
333	C₄×C₆₇	#585	1	2	yes	—
334	#60289	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
335	C₂×C₆₇	—	2	2	no	—
336	C₂×C₆₇	—	4	1	no	—
337	C₂×C₆₇	—	4	1	no	—
338	C₂×C₆₇	—	4	4	no	—
339	C₂×C₆₇	#3428	1	1	yes	characteristic
340	C₂×C₆₇	C₂×#568	1	1	yes	characteristic
341	C₂×C₆₇	C₂×#568	1	1	yes	characteristic
342	C₂×#529	C₂×C₆₇	1	1	yes	characteristic
343	#2995	C₂×C₆₇	1	4	yes	complemented
344	#2993	C₂×C₆₇	1	4	yes	complemented
345	#2984	C₂×C₆₇	1	2	yes	complemented
346	#2975	C₂×C₆₇	1	2	yes	complemented
347	#2974	C₂×C₆₇	1	2	yes	complemented
348	#2973	C₂×C₆₇	1	2	yes	complemented
349	#2969	C₂×C₆₇	1	4	yes	complemented
350	#2967	C₂×C₆₇	1	4	yes	complemented
351	#2924	C₂×C₆₇	1	4	yes	complemented
352	#2920	C₂×C₆₇	1	1	yes	characteristic, complemented
353	#2920	C₂×C₆₇	1	1	yes	characteristic, complemented
354	C₆₇	#60289	1	1	yes	characteristic, direct product factor, Sylow
355	#529	C₄×C₆₇	1	2	yes	—
356	#529	C₄×C₆₇	1	2	yes	—
357	#529	C₄×C₆₇	1	2	yes	—
358	#529	C₄×C₆₇	1	2	yes	—
359	#529	C₂²×C₆₇	1	2	yes	—
360	#529	C₂²×C₆₇	1	2	yes	—
361	#529	C₂²×C₆₇	1	2	yes	—
362	#529	C₂²×C₆₇	1	2	yes	—
363	C₂×#126	C₄×C₆₇	1	2	yes	—
364	C₂×#125	C₄×C₆₇	1	1	yes	characteristic
365	C₂×#124	C₄×C₆₇	1	1	yes	characteristic
366	C₂×#123	C₄×C₆₇	1	2	yes	—
367	C₂×C₂²⋊Q₈	C₄×C₆₇	1	1	yes	characteristic
368	C₂×#121	C₄×C₆₇	1	1	yes	characteristic
369	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
370	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
371	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
372	C₂×#117	C₂²×C₆₇	1	2	yes	—
373	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
374	#446	C₂²×C₆₇	1	8	yes	complemented
375	#446	C₂²×C₆₇	1	4	yes	complemented
376	C₈×Q₈	C₂²×C₆₇	1	4	yes	complemented
377	#436	C₂²×C₆₇	1	8	yes	complemented
378	#436	C₂²×C₆₇	1	4	yes	complemented
379	#436	C₂²×C₆₇	1	8	yes	complemented
380	#435	C₂²×C₆₇	1	8	yes	complemented
381	#435	C₂²×C₆₇	1	8	yes	complemented
382	#435	C₂²×C₆₇	1	8	yes	complemented
383	C₈×D₄	C₂²×C₆₇	1	4	yes	complemented
384	#433	C₂²×C₆₇	1	8	yes	complemented
385	#433	C₂²×C₆₇	1	8	yes	complemented
386	#432	C₂²×C₆₇	1	2	yes	—
387	#432	C₂²×C₆₇	1	2	yes	—
388	#432	C₂²×C₆₇	1	4	yes	—
389	#432	C₂²×C₆₇	1	2	yes	complemented
390	#432	C₂²×C₆₇	1	2	yes	complemented
391	#431	C₂²×C₆₇	1	2	yes	—
392	#431	C₂²×C₆₇	1	2	yes	—
393	#431	C₂²×C₆₇	1	4	yes	—
394	#431	C₂²×C₆₇	1	2	yes	complemented
395	#431	C₂²×C₆₇	1	2	yes	complemented
396	#424	C₂²×C₆₇	1	8	yes	complemented
397	#423	C₂²×C₆₇	1	2	yes	complemented
398	#423	C₂²×C₆₇	1	2	yes	complemented
399	#407	C₂²×C₆₇	1	1	yes	characteristic
400	#407	C₂²×C₆₇	1	2	yes	—
401	#407	C₂²×C₆₇	1	1	yes	characteristic
402	#407	C₂²×C₆₇	1	4	yes	—
403	C₂×C₂²⋊C₈	C₂²×C₆₇	1	4	yes	—
404	#405	C₂²×C₆₇	1	8	yes	complemented
405	C₄×M₁₆	C₂²×C₆₇	1	2	yes	complemented
406	C₄×M₁₆	C₂²×C₆₇	1	2	yes	complemented
407	C₂²×Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
408	C₂²×D₄	C₂×C₄×C₆₇	1	2	yes	—
409	C₂²×D₄	C₂×C₄×C₆₇	1	1	yes	characteristic
410	C₂³×C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
411	C₂³×C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
412	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
413	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
414	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
415	C₂×M₁₆	C₂³×C₆₇	1	4	yes	—
416	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
417	C₂×M₁₆	C₂³×C₆₇	1	8	yes	—
418	C₂²×C₈	C₂³×C₆₇	1	8	yes	—
419	#126	C₂×C₄×C₆₇	1	4	yes	—
420	#126	C₂×C₄×C₆₇	1	4	yes	—
421	#126	C₂×C₄×C₆₇	1	4	yes	—
422	#126	C₂×C₄×C₆₇	1	4	yes	—
423	#125	C₂×C₄×C₆₇	1	2	yes	—
424	#125	C₂×C₄×C₆₇	1	2	yes	—
425	#125	C₂×C₄×C₆₇	1	2	yes	—
426	#125	C₂×C₄×C₆₇	1	2	yes	—
427	#124	C₂×C₄×C₆₇	1	2	yes	—
428	#124	C₂×C₄×C₆₇	1	2	yes	—
429	#124	C₂×C₄×C₆₇	1	2	yes	—
430	#124	C₂×C₄×C₆₇	1	2	yes	—
431	#123	C₂×C₄×C₆₇	1	4	yes	—
432	#123	C₂×C₄×C₆₇	1	4	yes	—
433	#123	C₂×C₄×C₆₇	1	4	yes	—
434	#123	C₂×C₄×C₆₇	1	4	yes	—
435	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
436	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
437	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
438	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
439	#121	C₂×C₄×C₆₇	1	2	yes	—
440	#121	C₂×C₄×C₆₇	1	2	yes	—
441	#121	C₂×C₄×C₆₇	1	2	yes	—
442	#121	C₂×C₄×C₆₇	1	2	yes	—
443	C₄×Q₈	C₂×C₄×C₆₇	1	2	yes	—
444	C₄×Q₈	C₂×C₄×C₆₇	1	2	yes	—
445	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
446	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
447	C₄×D₄	C₂×C₄×C₆₇	1	2	yes	—
448	C₄×D₄	C₂×C₄×C₆₇	1	2	yes	—
449	C₄×D₄	C₂×C₄×C₆₇	1	4	yes	—
450	C₄×D₄	C₂×C₄×C₆₇	1	4	yes	—
451	C₄×D₄	C₂³×C₆₇	1	2	yes	—
452	C₄×D₄	C₂³×C₆₇	1	2	yes	—
453	C₄×D₄	C₂³×C₆₇	1	4	yes	—
454	C₄×D₄	C₂³×C₆₇	1	4	yes	—
455	#117	C₂×C₄×C₆₇	1	4	yes	—
456	#117	C₂×C₄×C₆₇	1	4	yes	—
457	#117	C₂³×C₆₇	1	4	yes	—
458	#117	C₂³×C₆₇	1	4	yes	—
459	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	2	yes	—
460	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	2	yes	—
461	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
462	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	2	yes	—
463	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
464	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	2	yes	—
465	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	2	yes	—
466	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	2	yes	—
467	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	2	yes	—
468	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	2	yes	—
469	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	2	yes	—
470	C₂×C₄²	C₂×C₄×C₆₇	1	1	yes	characteristic
471	C₂×C₄²	C₂×C₄×C₆₇	1	1	yes	characteristic
472	C₂×C₄²	C₂×C₄×C₆₇	1	1	yes	characteristic
473	C₂×C₄²	C₂×C₄×C₆₇	1	1	yes	characteristic
474	C₂×C₄²	C₂×C₄×C₆₇	1	1	yes	characteristic
475	C₂×C₄²	C₂×C₄×C₆₇	1	1	yes	characteristic
476	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
477	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
478	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
479	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
480	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
481	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
482	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
483	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
484	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
485	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
486	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
487	C₄⋊C₈	C₂³×C₆₇	1	8	yes	—
488	C₄⋊C₈	C₂³×C₆₇	1	8	yes	—
489	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
490	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
491	C₂²⋊C₈	C₂³×C₆₇	1	8	yes	—
492	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
493	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
494	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
495	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
496	C₂²⋊C₈	C₂³×C₆₇	1	8	yes	—
497	#97	C₂³×C₆₇	1	4	yes	—
498	#97	C₂³×C₆₇	1	4	yes	—
499	#97	C₂³×C₆₇	1	8	yes	—
500	C₄×C₈	C₂³×C₆₇	1	4	yes	—
501	C₄×C₈	C₂³×C₆₇	1	4	yes	—
502	C₄×C₈	C₂³×C₆₇	1	8	yes	—
503	C₂⁴	C₂²×C₄×C₆₇	1	2	yes	—
504	C₂⁴	C₂²×C₄×C₆₇	1	1	yes	characteristic
505	C₂×Q₈	—	4	2	no	—
506	C₂×Q₈	C₂²×C₄×C₆₇	1	2	yes	—
507	C₂×Q₈	C₂²×C₄×C₆₇	1	2	yes	—
508	C₂×D₄	—	4	2	no	—
509	C₂×D₄	—	4	4	no	—
510	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
511	C₂×D₄	C₂²×C₄×C₆₇	1	4	yes	—
512	C₂×D₄	C₂²×C₄×C₆₇	1	4	yes	—
513	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
514	C₂²×C₄	—	4	2	no	—
515	C₂²×C₄	—	4	4	no	—
516	C₂²×C₄	—	4	2	no	—
517	C₂²×C₄	—	4	2	no	—
518	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
519	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
520	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
521	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
522	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
523	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
524	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
525	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
526	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
527	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
528	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
529	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
530	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
531	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
532	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
533	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
534	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
535	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
536	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
537	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
538	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
539	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
540	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
541	M₁₆	—	4	2	no	—
542	M₁₆	—	4	4	no	—
543	M₁₆	—	4	8	no	—
544	M₁₆	—	4	2	no	—
545	C₂×C₈	—	4	8	no	—
546	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
547	C₂×C₈	C₂⁴×C₆₇	1	8	yes	—
548	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
549	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
550	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
551	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
552	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
553	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
554	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
555	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
556	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
557	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
558	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
559	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
560	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
561	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
562	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
563	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
564	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
565	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
566	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
567	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
568	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
569	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
570	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
571	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
572	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
573	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
574	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
575	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
576	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
577	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
578	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
579	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
580	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
581	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
582	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
583	C₄²	C₂²×C₄×C₆₇	1	4	yes	—
584	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
585	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
586	C₄²	C₂⁴×C₆₇	1	4	yes	—
587	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
588	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
589	C₂³	—	2	2	no	—
590	C₂³	—	2	4	no	—
591	C₂³	—	4	1	no	—
592	C₂³	—	4	1	no	—
593	C₂³	—	4	2	no	—
594	C₂³	—	4	2	no	—
595	C₂³	C₂³×C₄×C₆₇	1	4	yes	—
596	C₂³	C₂³×C₄×C₆₇	1	1	yes	characteristic
597	C₂³	C₂³×C₄×C₆₇	1	1	yes	characteristic
598	C₂³	C₂³×C₄×C₆₇	1	1	yes	characteristic
599	Q₈	—	2	4	no	—
600	Q₈	—	4	2	no	—
601	D₄	—	2	4	no	—
602	D₄	—	4	2	no	—
603	D₄	—	4	4	no	—
604	D₄	—	4	4	no	—
605	C₂×C₄	—	2	2	no	—
606	C₂×C₄	—	2	2	no	—
607	C₂×C₄	—	2	4	no	—
608	C₂×C₄	—	2	2	no	—
609	C₂×C₄	—	2	2	no	—
610	C₂×C₄	—	2	2	no	—
611	C₂×C₄	—	2	8	no	—
612	C₂×C₄	—	2	2	no	—
613	C₂×C₄	—	2	2	no	—
614	C₂×C₄	—	2	2	no	—
615	C₂×C₄	—	4	1	no	—
616	C₂×C₄	—	4	1	no	—
617	C₂×C₄	—	4	1	no	—
618	C₂×C₄	—	4	1	no	—
619	C₂×C₄	—	4	1	no	—
620	C₂×C₄	—	4	1	no	—
621	C₂×C₄	—	4	1	no	—
622	C₂×C₄	—	4	1	no	—
623	C₂×C₄	—	4	1	no	—
624	C₂×C₄	—	4	4	no	—
625	C₂×C₄	—	4	1	no	—
626	C₂×C₄	—	4	2	no	—
627	C₂×C₄	—	4	2	no	—
628	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
629	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
630	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
631	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
632	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
633	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
634	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
635	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
636	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
637	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
638	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
639	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
640	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
641	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
642	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
643	C₈	—	2	4	no	—
644	C₈	—	2	8	no	—
645	C₈	—	2	4	no	—
646	C₂²	—	2	1	no	—
647	C₂²	—	2	1	no	—
648	C₂²	—	2	1	no	—
649	C₂²	—	2	1	no	—
650	C₂²	—	2	1	no	—
651	C₂²	—	2	1	no	—
652	C₂²	—	2	4	no	—
653	C₂²	—	2	4	no	—
654	C₂²	—	2	1	no	—
655	C₂²	—	2	1	no	—
656	C₂²	—	2	4	no	—
657	C₂²	—	4	4	no	—
658	C₂²	—	8	4	no	—
659	C₂²	#568×C₆₇	1	2	yes	—
660	C₂²	C₂⁴×C₄×C₆₇	1	1	yes	characteristic
661	C₄	—	2	1	no	—
662	C₄	—	2	1	no	—
663	C₄	—	2	1	no	—
664	C₄	—	2	1	no	—
665	C₄	—	2	1	no	—
666	C₄	—	2	1	no	—
667	C₄	—	2	1	no	—
668	C₄	—	2	4	no	—
669	C₄	—	2	4	no	—
670	C₄	—	2	1	no	—
671	C₄	—	2	4	no	—
672	C₄	—	2	1	no	—
673	C₄	—	2	1	no	—
674	C₄	#568×C₆₇	1	2	yes	—
675	C₄	#585×C₆₇	1	2	yes	—
676	C₂	—	2	2	no	—
677	C₂	—	4	1	no	—
678	C₂	—	4	1	no	—
679	C₂	—	4	4	no	—
680	C₂	C₆₇×#3428	1	1	yes	characteristic
681	C₂	C₂×#568×C₆₇	1	1	yes	characteristic
682	C₂	C₂×#568×C₆₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₆₇	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₆₇
Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
socle	C₂²×C₆₇	C₂⁴×C₄
prime radical	C₂×#121×C₆₇	C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₆₇×#2995	C₂	semidirect
3. C₆₇×#2993	C₂	semidirect
4. C₆₇×#2984	C₂	semidirect
5. C₆₇×#2975	C₂	semidirect
6. C₆₇×#2974	C₂	semidirect
7. C₆₇×#2973	C₂	semidirect
8. C₆₇×#2969	C₂	semidirect
9. C₆₇×#2967	C₂	semidirect
10. C₆₇×#2924	C₂	semidirect
11. C₆₇×#2920	C₂	semidirect
12. C₆₇×#2920	C₂	semidirect
32. #446×C₆₇	C₂²	semidirect
33. #446×C₆₇	C₂²	semidirect
34. C₈×Q₈×C₆₇	C₂²	semidirect
35. #436×C₆₇	C₂²	semidirect
36. #436×C₆₇	C₂²	semidirect
37. #436×C₆₇	C₂²	semidirect
38. #435×C₆₇	C₂²	semidirect
39. #435×C₆₇	C₂²	semidirect
40. #435×C₆₇	C₂²	semidirect
41. C₈×D₄×C₆₇	C₂²	semidirect
42. #433×C₆₇	C₂²	semidirect
43. #433×C₆₇	C₂²	semidirect
47. #432×C₆₇	C₂²	semidirect
48. #432×C₆₇	C₂²	semidirect
52. #431×C₆₇	C₂²	semidirect
53. #431×C₆₇	C₂²	semidirect
54. #424×C₆₇	C₂²	semidirect
55. #423×C₆₇	C₂²	semidirect
56. #423×C₆₇	C₂²	semidirect
62. #405×C₆₇	C₂²	semidirect
63. C₄×M₁₆×C₆₇	C₂²	semidirect
64. C₄×M₁₆×C₆₇	C₂²	semidirect
334. #60289	C₆₇	direct (N × H)
343. #2995	C₂×C₆₇	semidirect
344. #2993	C₂×C₆₇	semidirect
345. #2984	C₂×C₆₇	semidirect
346. #2975	C₂×C₆₇	semidirect
347. #2974	C₂×C₆₇	semidirect
348. #2973	C₂×C₆₇	semidirect
349. #2969	C₂×C₆₇	semidirect
350. #2967	C₂×C₆₇	semidirect
351. #2924	C₂×C₆₇	semidirect
352. #2920	C₂×C₆₇	semidirect
353. #2920	C₂×C₆₇	semidirect
354. C₆₇	#60289	direct (N × H)
374. #446	C₂²×C₆₇	semidirect
375. #446	C₂²×C₆₇	semidirect
376. C₈×Q₈	C₂²×C₆₇	semidirect
377. #436	C₂²×C₆₇	semidirect
378. #436	C₂²×C₆₇	semidirect
379. #436	C₂²×C₆₇	semidirect
380. #435	C₂²×C₆₇	semidirect
381. #435	C₂²×C₆₇	semidirect
382. #435	C₂²×C₆₇	semidirect
383. C₈×D₄	C₂²×C₆₇	semidirect
384. #433	C₂²×C₆₇	semidirect
385. #433	C₂²×C₆₇	semidirect
389. #432	C₂²×C₆₇	semidirect
390. #432	C₂²×C₆₇	semidirect
394. #431	C₂²×C₆₇	semidirect
395. #431	C₂²×C₆₇	semidirect
396. #424	C₂²×C₆₇	semidirect
397. #423	C₂²×C₆₇	semidirect
398. #423	C₂²×C₆₇	semidirect
404. #405	C₂²×C₆₇	semidirect
405. C₄×M₁₆	C₂²×C₆₇	semidirect
406. C₄×M₁₆	C₂²×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#529×C₆₇	2
C₆₇×#2995	2
C₆₇×#2993	2
C₆₇×#2984	2
C₆₇×#2975	2
C₆₇×#2974	2
C₆₇×#2973	2
C₆₇×#2969	2
C₆₇×#2967	2
C₆₇×#2924	2
C₆₇×#2920	2
#60289	67

Subgroups — C67×#60289 #30739540

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#60289 #30739540