Subgroups — C₆₇×#60337 #30739588

Order 17152.

1700 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3482	C₂	1	1	yes	maximal, characteristic
2	C₆₇×#2995	C₂	1	4	yes	maximal, complemented
3	C₆₇×#2993	C₂	1	2	yes	maximal, complemented
4	C₆₇×#2991	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#2990	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#2989	C₂	1	2	yes	maximal, complemented
7	C₆₇×#2986	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#2985	C₂	1	2	yes	maximal, complemented
9	C₆₇×#2983	C₂	1	2	yes	maximal, complemented
10	C₆₇×#2971	C₂	1	2	yes	maximal, complemented
11	C₆₇×#2969	C₂	1	2	yes	maximal, complemented
12	C₆₇×#2967	C₂	1	4	yes	maximal, complemented
13	C₆₇×#2965	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#2965	C₂	1	1	yes	maximal, characteristic, complemented
15	Q₈×M₁₆×C₆₇	C₂	1	2	yes	maximal, complemented
16	C₆₇×#2962	C₂	1	2	yes	maximal, complemented
17	C₆₇×#2960	C₂	1	1	yes	maximal, characteristic, complemented
18	#557×C₆₇	C₄	1	1	yes	characteristic
19	#556×C₆₇	C₄	1	2	yes	—
20	#556×C₆₇	C₄	1	1	yes	characteristic
21	#552×C₆₇	C₄	1	2	yes	—
22	#552×C₆₇	C₄	1	4	yes	—
23	D₄×Q₈×C₆₇	C₄	1	1	yes	characteristic
24	#548×C₆₇	C₄	1	2	yes	—
25	#547×C₆₇	C₄	1	1	yes	characteristic
26	#547×C₆₇	C₄	1	2	yes	—
27	#533×C₆₇	C₂²	1	1	yes	characteristic
28	#533×C₆₇	C₂²	1	2	yes	—
29	#529×C₆₇	C₂²	1	4	yes	—
30	#529×C₆₇	C₂²	1	2	yes	—
31	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
32	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
33	C₄×#41×C₆₇	C₂²	1	2	yes	—
34	C₂×C₄×Q₈×C₆₇	C₂²	1	2	yes	—
35	#446×C₆₇	C₂²	1	2	yes	—
36	#446×C₆₇	C₂²	1	2	yes	—
37	#446×C₆₇	C₂²	1	1	yes	characteristic
38	#446×C₆₇	C₂²	1	4	yes	—
39	#446×C₆₇	C₂²	1	4	yes	—
40	#446×C₆₇	C₂²	1	2	yes	—
41	#446×C₆₇	C₂²	1	1	yes	characteristic
42	#446×C₆₇	C₂²	1	2	yes	—
43	#446×C₆₇	C₂²	1	4	yes	—
44	#446×C₆₇	C₂²	1	1	yes	characteristic
45	#446×C₆₇	C₂²	1	1	yes	characteristic
46	#446×C₆₇	C₂²	1	4	yes	—
47	#446×C₆₇	C₂²	1	2	yes	—
48	C₈×Q₈×C₆₇	C₂²	1	2	yes	—
49	C₈×Q₈×C₆₇	C₂²	1	2	yes	—
50	C₈×Q₈×C₆₇	C₂²	1	2	yes	—
51	C₈×Q₈×C₆₇	C₂²	1	2	yes	—
52	C₈×Q₈×C₆₇	C₂²	1	2	yes	—
53	#436×C₆₇	C₂²	1	1	yes	characteristic
54	#436×C₆₇	C₂²	1	1	yes	characteristic
55	#436×C₆₇	C₂²	1	1	yes	characteristic
56	#436×C₆₇	C₂²	1	1	yes	characteristic
57	#436×C₆₇	C₂²	1	4	yes	—
58	#436×C₆₇	C₂²	1	4	yes	—
59	#436×C₆₇	C₂²	1	2	yes	—
60	#436×C₆₇	C₂²	1	4	yes	—
61	#435×C₆₇	C₂²	1	2	yes	—
62	#435×C₆₇	C₂²	1	2	yes	—
63	#435×C₆₇	C₂²	1	2	yes	—
64	#435×C₆₇	C₂²	1	2	yes	—
65	#435×C₆₇	C₂²	1	4	yes	—
66	#435×C₆₇	C₂²	1	4	yes	—
67	#435×C₆₇	C₂²	1	4	yes	—
68	C₈×D₄×C₆₇	C₂²	1	2	yes	—
69	#433×C₆₇	C₂²	1	4	yes	—
70	#433×C₆₇	C₂²	1	4	yes	—
71	#433×C₆₇	C₂²	1	4	yes	—
72	#432×C₆₇	C₂²	1	4	yes	—
73	#432×C₆₇	C₂²	1	4	yes	—
74	#432×C₆₇	C₂²	1	2	yes	—
75	#431×C₆₇	C₂²	1	2	yes	—
76	#431×C₆₇	C₂²	1	2	yes	—
77	#431×C₆₇	C₂²	1	1	yes	characteristic
78	#431×C₆₇	C₂²	1	1	yes	characteristic
79	#431×C₆₇	C₂²	1	2	yes	—
80	#424×C₆₇	C₂²	1	2	yes	—
81	#424×C₆₇	C₂²	1	4	yes	—
82	#423×C₆₇	C₂²	1	1	yes	characteristic
83	#423×C₆₇	C₂²	1	4	yes	—
84	#423×C₆₇	C₂²	1	2	yes	—
85	C₂×C₄⋊C₈×C₆₇	C₂²	1	2	yes	—
86	#405×C₆₇	C₂²	1	2	yes	—
87	#405×C₆₇	C₂²	1	4	yes	—
88	C₄×M₁₆×C₆₇	C₂²	1	2	yes	—
89	C₄×M₁₆×C₆₇	C₂²	1	2	yes	—
90	C₄×M₁₆×C₆₇	C₂²	1	4	yes	—
91	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
92	C₂×#41×C₆₇	C₂×C₄	1	1	yes	characteristic
93	C₂×#41×C₆₇	C₂×C₄	1	2	yes	—
94	C₂×#41×C₆₇	C₂×C₄	1	1	yes	characteristic
95	C₂²×Q₈×C₆₇	C₂×C₄	1	2	yes	—
96	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
97	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
98	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
99	C₂×M₁₆×C₆₇	C₂³	1	4	yes	—
100	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
101	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
102	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
103	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
104	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
105	C₄⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
106	C₄⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
107	C₄⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
108	C₄⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
109	#126×C₆₇	C₂×C₄	1	4	yes	—
110	#126×C₆₇	C₂×C₄	1	4	yes	—
111	#126×C₆₇	C₂×C₄	1	4	yes	—
112	#125×C₆₇	C₂×C₄	1	4	yes	—
113	#125×C₆₇	C₂×C₄	1	2	yes	—
114	#125×C₆₇	C₂×C₄	1	2	yes	—
115	#125×C₆₇	C₂×C₄	1	4	yes	—
116	#124×C₆₇	C₂×C₄	1	2	yes	—
117	#124×C₆₇	C₂×C₄	1	4	yes	—
118	#123×C₆₇	C₂×C₄	1	4	yes	—
119	#123×C₆₇	C₂×C₄	1	4	yes	—
120	#123×C₆₇	C₂×C₄	1	4	yes	—
121	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
122	C₂²⋊Q₈×C₆₇	C₂×C₄	1	4	yes	—
123	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
124	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
125	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
126	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
127	C₂²⋊Q₈×C₆₇	C₂×C₄	1	4	yes	—
128	#121×C₆₇	C₂×C₄	1	2	yes	—
129	#121×C₆₇	C₂×C₄	1	4	yes	—
130	C₄×Q₈×C₆₇	C₂×C₄	1	2	yes	—
131	C₄×Q₈×C₆₇	C₂×C₄	1	2	yes	—
132	C₄×Q₈×C₆₇	C₂×C₄	1	4	yes	—
133	C₄×Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
134	C₄×Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
135	C₄×Q₈×C₆₇	C₂×C₄	1	2	yes	—
136	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
137	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
138	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
139	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
140	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
141	C₄×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
142	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
143	C₄×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
144	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
145	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
146	C₄×D₄×C₆₇	C₂×C₄	1	4	yes	—
147	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
148	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
149	C₄×D₄×C₆₇	C₂³	1	2	yes	—
150	C₄×D₄×C₆₇	C₂³	1	2	yes	—
151	C₄×D₄×C₆₇	C₂³	1	4	yes	—
152	#117×C₆₇	C₂×C₄	1	1	yes	characteristic
153	#117×C₆₇	C₂×C₄	1	2	yes	—
154	#117×C₆₇	C₂×C₄	1	2	yes	—
155	#117×C₆₇	C₂×C₄	1	4	yes	—
156	#117×C₆₇	C₂×C₄	1	1	yes	characteristic
157	#117×C₆₇	C₂×C₄	1	2	yes	—
158	#117×C₆₇	C₂³	1	2	yes	—
159	#117×C₆₇	C₂³	1	4	yes	—
160	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
161	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	4	yes	—
162	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
163	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
164	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
165	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
166	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
167	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
168	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
169	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
170	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
171	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
172	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
173	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
174	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
175	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
176	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
177	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
178	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
179	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
180	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
181	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
182	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
183	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
184	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
185	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
186	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
187	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
188	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
189	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
190	#97×C₆₇	C₂³	1	2	yes	—
191	#97×C₆₇	C₂³	1	2	yes	—
192	#97×C₆₇	C₂³	1	2	yes	—
193	#97×C₆₇	C₂³	1	4	yes	—
194	#97×C₆₇	C₂³	1	2	yes	—
195	#97×C₆₇	C₂³	1	4	yes	—
196	#97×C₆₇	C₂³	1	4	yes	—
197	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
198	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
199	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
200	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
201	C₄×C₈×C₆₇	C₂³	1	4	yes	—
202	C₄×C₈×C₆₇	C₂³	1	2	yes	—
203	C₄×C₈×C₆₇	C₂³	1	2	yes	—
204	C₄×C₈×C₆₇	C₂³	1	4	yes	—
205	C₄×C₈×C₆₇	C₂³	1	4	yes	—
206	#41×C₆₇	—	4	2	no	—
207	#41×C₆₇	—	4	2	no	—
208	#41×C₆₇	—	4	4	no	—
209	C₂×Q₈×C₆₇	—	4	4	no	—
210	C₂×Q₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
211	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
212	C₂×Q₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
213	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
214	C₂×Q₈×C₆₇	C₂²×C₄	1	4	yes	—
215	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
216	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
217	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
218	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
219	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
220	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
221	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
222	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
223	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
224	C₂²×C₄×C₆₇	C₂²×C₄	1	2	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	2	yes	—
228	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
229	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
230	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
231	M₁₆×C₆₇	—	2	4	no	—
232	M₁₆×C₆₇	—	2	4	no	—
233	M₁₆×C₆₇	—	4	2	no	—
234	M₁₆×C₆₇	—	4	2	no	—
235	M₁₆×C₆₇	—	4	2	no	—
236	M₁₆×C₆₇	—	4	4	no	—
237	C₂×C₈×C₆₇	—	2	2	no	—
238	C₂×C₈×C₆₇	—	4	4	no	—
239	C₂×C₈×C₆₇	—	4	1	no	—
240	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
241	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
242	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
243	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
244	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
245	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
246	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
247	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
248	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
249	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
250	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
251	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
252	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
253	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
254	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
255	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
256	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
257	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
258	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
259	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
260	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
261	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
262	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
263	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
264	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
265	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
266	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
267	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
268	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
269	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
270	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
271	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
272	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
273	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
274	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
275	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
276	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
277	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
278	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
279	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
280	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
281	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
282	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
283	C₄²×C₆₇	C₂²×C₄	1	4	yes	—
284	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
285	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
286	C₄²×C₆₇	C₂²×C₄	1	4	yes	—
287	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
288	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
289	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
290	C₄²×C₆₇	C₂⁴	1	2	yes	—
291	C₄²×C₆₇	C₂⁴	1	4	yes	—
292	C₄²×C₆₇	C₂⁴	1	2	yes	—
293	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
294	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
295	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
296	Q₈×C₆₇	—	2	2	no	—
297	Q₈×C₆₇	—	2	4	no	—
298	Q₈×C₆₇	—	2	2	no	—
299	Q₈×C₆₇	—	2	4	no	—
300	Q₈×C₆₇	—	4	4	no	—
301	D₄×C₆₇	—	2	2	no	—
302	D₄×C₆₇	—	2	2	no	—
303	D₄×C₆₇	—	4	2	no	—
304	D₄×C₆₇	—	4	2	no	—
305	D₄×C₆₇	—	4	4	no	—
306	C₂×C₄×C₆₇	—	2	4	no	—
307	C₂×C₄×C₆₇	—	2	2	no	—
308	C₂×C₄×C₆₇	—	2	2	no	—
309	C₂×C₄×C₆₇	—	2	4	no	—
310	C₂×C₄×C₆₇	—	2	1	no	—
311	C₂×C₄×C₆₇	—	2	2	no	—
312	C₂×C₄×C₆₇	—	2	2	no	—
313	C₂×C₄×C₆₇	—	2	2	no	—
314	C₂×C₄×C₆₇	—	2	1	no	—
315	C₂×C₄×C₆₇	—	2	2	no	—
316	C₂×C₄×C₆₇	—	4	4	no	—
317	C₂×C₄×C₆₇	—	4	2	no	—
318	C₂×C₄×C₆₇	—	4	2	no	—
319	C₂×C₄×C₆₇	—	4	4	no	—
320	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
321	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
322	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
323	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
324	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
325	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
326	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
327	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
328	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
329	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
330	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
331	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
332	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
333	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
334	C₈×C₆₇	—	2	1	no	—
335	C₈×C₆₇	—	2	2	no	—
336	C₈×C₆₇	—	2	2	no	—
337	C₈×C₆₇	—	2	2	no	—
338	C₈×C₆₇	—	2	4	no	—
339	C₈×C₆₇	—	2	1	no	—
340	C₈×C₆₇	—	2	1	no	—
341	C₈×C₆₇	—	2	2	no	—
342	C₈×C₆₇	2₋¹⁺⁴	1	2	yes	—
343	C₂²×C₆₇	—	2	1	no	—
344	C₂²×C₆₇	—	2	2	no	—
345	C₂²×C₆₇	—	2	2	no	—
346	C₂²×C₆₇	—	2	2	no	—
347	C₂²×C₆₇	—	2	1	no	—
348	C₂²×C₆₇	—	2	1	no	—
349	C₂²×C₆₇	—	2	2	no	—
350	C₂²×C₆₇	—	2	2	no	—
351	C₂²×C₆₇	—	2	2	no	—
352	C₂²×C₆₇	C₂⁴×C₄	1	1	yes	characteristic
353	C₄×C₆₇	—	2	1	no	—
354	C₄×C₆₇	—	2	2	no	—
355	C₄×C₆₇	—	2	2	no	—
356	C₄×C₆₇	—	2	1	no	—
357	C₄×C₆₇	—	2	2	no	—
358	C₄×C₆₇	—	2	1	no	—
359	C₄×C₆₇	—	2	2	no	—
360	C₄×C₆₇	—	2	2	no	—
361	C₄×C₆₇	—	2	2	no	—
362	C₄×C₆₇	—	2	4	no	—
363	C₄×C₆₇	—	2	4	no	—
364	C₄×C₆₇	#568	1	2	yes	—
365	C₄×C₆₇	#568	1	2	yes	—
366	C₄×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
367	C₄×C₆₇	#585	1	1	yes	characteristic
368	#60337	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
369	C₂×C₆₇	—	4	2	no	—
370	C₂×C₆₇	—	4	1	no	—
371	C₂×C₆₇	—	4	2	no	—
372	C₂×C₆₇	C₄×2₋¹⁺⁴	1	1	yes	characteristic
373	C₂×C₆₇	C₂×#568	1	1	yes	characteristic
374	C₂×C₆₇	C₂×#568	1	1	yes	characteristic
375	#3482	C₂×C₆₇	1	1	yes	characteristic
376	#2995	C₂×C₆₇	1	4	yes	complemented
377	#2993	C₂×C₆₇	1	2	yes	complemented
378	#2991	C₂×C₆₇	1	1	yes	characteristic, complemented
379	#2990	C₂×C₆₇	1	1	yes	characteristic, complemented
380	#2989	C₂×C₆₇	1	2	yes	complemented
381	#2986	C₂×C₆₇	1	1	yes	characteristic, complemented
382	#2985	C₂×C₆₇	1	2	yes	complemented
383	#2983	C₂×C₆₇	1	2	yes	complemented
384	#2971	C₂×C₆₇	1	2	yes	complemented
385	#2969	C₂×C₆₇	1	2	yes	complemented
386	#2967	C₂×C₆₇	1	4	yes	complemented
387	#2965	C₂×C₆₇	1	1	yes	characteristic, complemented
388	#2965	C₂×C₆₇	1	1	yes	characteristic, complemented
389	Q₈×M₁₆	C₂×C₆₇	1	2	yes	complemented
390	#2962	C₂×C₆₇	1	2	yes	complemented
391	#2960	C₂×C₆₇	1	1	yes	characteristic, complemented
392	C₆₇	#60337	1	1	yes	characteristic, direct product factor, Sylow
393	#557	C₄×C₆₇	1	1	yes	characteristic
394	#556	C₄×C₆₇	1	2	yes	—
395	#556	C₄×C₆₇	1	1	yes	characteristic
396	#552	C₄×C₆₇	1	2	yes	—
397	#552	C₄×C₆₇	1	4	yes	—
398	D₄×Q₈	C₄×C₆₇	1	1	yes	characteristic
399	#548	C₄×C₆₇	1	2	yes	—
400	#547	C₄×C₆₇	1	1	yes	characteristic
401	#547	C₄×C₆₇	1	2	yes	—
402	#533	C₂²×C₆₇	1	1	yes	characteristic
403	#533	C₂²×C₆₇	1	2	yes	—
404	#529	C₂²×C₆₇	1	4	yes	—
405	#529	C₂²×C₆₇	1	2	yes	—
406	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
407	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
408	C₄×#41	C₂²×C₆₇	1	2	yes	—
409	C₂×C₄×Q₈	C₂²×C₆₇	1	2	yes	—
410	#446	C₂²×C₆₇	1	2	yes	—
411	#446	C₂²×C₆₇	1	2	yes	—
412	#446	C₂²×C₆₇	1	1	yes	characteristic
413	#446	C₂²×C₆₇	1	4	yes	—
414	#446	C₂²×C₆₇	1	4	yes	—
415	#446	C₂²×C₆₇	1	2	yes	—
416	#446	C₂²×C₆₇	1	1	yes	characteristic
417	#446	C₂²×C₆₇	1	2	yes	—
418	#446	C₂²×C₆₇	1	4	yes	—
419	#446	C₂²×C₆₇	1	1	yes	characteristic
420	#446	C₂²×C₆₇	1	1	yes	characteristic
421	#446	C₂²×C₆₇	1	4	yes	—
422	#446	C₂²×C₆₇	1	2	yes	—
423	C₈×Q₈	C₂²×C₆₇	1	2	yes	—
424	C₈×Q₈	C₂²×C₆₇	1	2	yes	—
425	C₈×Q₈	C₂²×C₆₇	1	2	yes	—
426	C₈×Q₈	C₂²×C₆₇	1	2	yes	—
427	C₈×Q₈	C₂²×C₆₇	1	2	yes	—
428	#436	C₂²×C₆₇	1	1	yes	characteristic
429	#436	C₂²×C₆₇	1	1	yes	characteristic
430	#436	C₂²×C₆₇	1	1	yes	characteristic
431	#436	C₂²×C₆₇	1	1	yes	characteristic
432	#436	C₂²×C₆₇	1	4	yes	—
433	#436	C₂²×C₆₇	1	4	yes	—
434	#436	C₂²×C₆₇	1	2	yes	—
435	#436	C₂²×C₆₇	1	4	yes	—
436	#435	C₂²×C₆₇	1	2	yes	—
437	#435	C₂²×C₆₇	1	2	yes	—
438	#435	C₂²×C₆₇	1	2	yes	—
439	#435	C₂²×C₆₇	1	2	yes	—
440	#435	C₂²×C₆₇	1	4	yes	—
441	#435	C₂²×C₆₇	1	4	yes	—
442	#435	C₂²×C₆₇	1	4	yes	—
443	C₈×D₄	C₂²×C₆₇	1	2	yes	—
444	#433	C₂²×C₆₇	1	4	yes	—
445	#433	C₂²×C₆₇	1	4	yes	—
446	#433	C₂²×C₆₇	1	4	yes	—
447	#432	C₂²×C₆₇	1	4	yes	—
448	#432	C₂²×C₆₇	1	4	yes	—
449	#432	C₂²×C₆₇	1	2	yes	—
450	#431	C₂²×C₆₇	1	2	yes	—
451	#431	C₂²×C₆₇	1	2	yes	—
452	#431	C₂²×C₆₇	1	1	yes	characteristic
453	#431	C₂²×C₆₇	1	1	yes	characteristic
454	#431	C₂²×C₆₇	1	2	yes	—
455	#424	C₂²×C₆₇	1	2	yes	—
456	#424	C₂²×C₆₇	1	4	yes	—
457	#423	C₂²×C₆₇	1	1	yes	characteristic
458	#423	C₂²×C₆₇	1	4	yes	—
459	#423	C₂²×C₆₇	1	2	yes	—
460	C₂×C₄⋊C₈	C₂²×C₆₇	1	2	yes	—
461	#405	C₂²×C₆₇	1	2	yes	—
462	#405	C₂²×C₆₇	1	4	yes	—
463	C₄×M₁₆	C₂²×C₆₇	1	2	yes	—
464	C₄×M₁₆	C₂²×C₆₇	1	2	yes	—
465	C₄×M₁₆	C₂²×C₆₇	1	4	yes	—
466	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic
467	C₂×#41	C₂×C₄×C₆₇	1	1	yes	characteristic
468	C₂×#41	C₂×C₄×C₆₇	1	2	yes	—
469	C₂×#41	C₂×C₄×C₆₇	1	1	yes	characteristic
470	C₂²×Q₈	C₂×C₄×C₆₇	1	2	yes	—
471	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
472	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
473	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
474	C₂×M₁₆	C₂³×C₆₇	1	4	yes	—
475	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
476	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
477	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
478	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
479	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
480	C₄⋊Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
481	C₄⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
482	C₄⋊Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
483	C₄⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
484	#126	C₂×C₄×C₆₇	1	4	yes	—
485	#126	C₂×C₄×C₆₇	1	4	yes	—
486	#126	C₂×C₄×C₆₇	1	4	yes	—
487	#125	C₂×C₄×C₆₇	1	4	yes	—
488	#125	C₂×C₄×C₆₇	1	2	yes	—
489	#125	C₂×C₄×C₆₇	1	2	yes	—
490	#125	C₂×C₄×C₆₇	1	4	yes	—
491	#124	C₂×C₄×C₆₇	1	2	yes	—
492	#124	C₂×C₄×C₆₇	1	4	yes	—
493	#123	C₂×C₄×C₆₇	1	4	yes	—
494	#123	C₂×C₄×C₆₇	1	4	yes	—
495	#123	C₂×C₄×C₆₇	1	4	yes	—
496	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
497	C₂²⋊Q₈	C₂×C₄×C₆₇	1	4	yes	—
498	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
499	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
500	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
501	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
502	C₂²⋊Q₈	C₂×C₄×C₆₇	1	4	yes	—
503	#121	C₂×C₄×C₆₇	1	2	yes	—
504	#121	C₂×C₄×C₆₇	1	4	yes	—
505	C₄×Q₈	C₂×C₄×C₆₇	1	2	yes	—
506	C₄×Q₈	C₂×C₄×C₆₇	1	2	yes	—
507	C₄×Q₈	C₂×C₄×C₆₇	1	4	yes	—
508	C₄×Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
509	C₄×Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
510	C₄×Q₈	C₂×C₄×C₆₇	1	2	yes	—
511	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
512	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
513	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
514	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
515	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
516	C₄×D₄	C₂×C₄×C₆₇	1	1	yes	characteristic
517	C₄×D₄	C₂×C₄×C₆₇	1	2	yes	—
518	C₄×D₄	C₂×C₄×C₆₇	1	1	yes	characteristic
519	C₄×D₄	C₂×C₄×C₆₇	1	2	yes	—
520	C₄×D₄	C₂×C₄×C₆₇	1	2	yes	—
521	C₄×D₄	C₂×C₄×C₆₇	1	4	yes	—
522	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
523	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
524	C₄×D₄	C₂³×C₆₇	1	2	yes	—
525	C₄×D₄	C₂³×C₆₇	1	2	yes	—
526	C₄×D₄	C₂³×C₆₇	1	4	yes	—
527	#117	C₂×C₄×C₆₇	1	1	yes	characteristic
528	#117	C₂×C₄×C₆₇	1	2	yes	—
529	#117	C₂×C₄×C₆₇	1	2	yes	—
530	#117	C₂×C₄×C₆₇	1	4	yes	—
531	#117	C₂×C₄×C₆₇	1	1	yes	characteristic
532	#117	C₂×C₄×C₆₇	1	2	yes	—
533	#117	C₂³×C₆₇	1	2	yes	—
534	#117	C₂³×C₆₇	1	4	yes	—
535	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	2	yes	—
536	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	4	yes	—
537	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
538	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
539	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
540	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
541	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
542	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
543	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
544	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
545	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
546	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
547	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
548	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
549	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
550	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
551	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
552	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
553	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
554	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
555	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
556	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
557	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
558	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
559	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
560	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
561	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
562	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
563	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
564	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
565	#97	C₂³×C₆₇	1	2	yes	—
566	#97	C₂³×C₆₇	1	2	yes	—
567	#97	C₂³×C₆₇	1	2	yes	—
568	#97	C₂³×C₆₇	1	4	yes	—
569	#97	C₂³×C₆₇	1	2	yes	—
570	#97	C₂³×C₆₇	1	4	yes	—
571	#97	C₂³×C₆₇	1	4	yes	—
572	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
573	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
574	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
575	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
576	C₄×C₈	C₂³×C₆₇	1	4	yes	—
577	C₄×C₈	C₂³×C₆₇	1	2	yes	—
578	C₄×C₈	C₂³×C₆₇	1	2	yes	—
579	C₄×C₈	C₂³×C₆₇	1	4	yes	—
580	C₄×C₈	C₂³×C₆₇	1	4	yes	—
581	#41	—	4	2	no	—
582	#41	—	4	4	no	—
583	#41	—	4	2	no	—
584	C₂×Q₈	—	4	4	no	—
585	C₂×Q₈	C₂²×C₄×C₆₇	1	1	yes	characteristic
586	C₂×Q₈	C₂²×C₄×C₆₇	1	2	yes	—
587	C₂×Q₈	C₂²×C₄×C₆₇	1	1	yes	characteristic
588	C₂×Q₈	C₂²×C₄×C₆₇	1	2	yes	—
589	C₂×Q₈	C₂²×C₄×C₆₇	1	4	yes	—
590	C₂×D₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
591	C₂×D₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
592	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
593	C₂×D₄	C₂²×C₄×C₆₇	1	4	yes	—
594	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
595	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
596	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
597	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
598	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
599	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
600	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
601	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
602	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
603	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
604	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
605	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
606	M₁₆	—	2	4	no	—
607	M₁₆	—	2	4	no	—
608	M₁₆	—	4	2	no	—
609	M₁₆	—	4	2	no	—
610	M₁₆	—	4	2	no	—
611	M₁₆	—	4	4	no	—
612	C₂×C₈	—	2	2	no	—
613	C₂×C₈	—	4	4	no	—
614	C₂×C₈	—	4	1	no	—
615	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
616	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
617	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
618	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
619	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
620	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
621	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
622	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
623	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
624	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
625	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
626	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
627	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
628	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
629	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
630	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
631	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
632	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
633	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
634	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
635	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
636	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
637	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
638	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
639	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
640	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
641	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
642	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
643	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
644	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
645	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
646	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
647	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
648	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
649	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
650	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
651	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
652	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
653	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
654	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
655	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
656	C₄²	C₂²×C₄×C₆₇	1	2	yes	—
657	C₄²	C₂²×C₄×C₆₇	1	2	yes	—
658	C₄²	C₂²×C₄×C₆₇	1	4	yes	—
659	C₄²	C₂²×C₄×C₆₇	1	2	yes	—
660	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
661	C₄²	C₂²×C₄×C₆₇	1	4	yes	—
662	C₄²	C₂²×C₄×C₆₇	1	2	yes	—
663	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
664	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
665	C₄²	C₂⁴×C₆₇	1	4	yes	—
666	C₄²	C₂⁴×C₆₇	1	2	yes	—
667	C₄²	C₂⁴×C₆₇	1	2	yes	—
668	C₂³	C₂³×C₄×C₆₇	1	1	yes	characteristic
669	C₂³	C₂³×C₄×C₆₇	1	2	yes	—
670	C₂³	C₂³×C₄×C₆₇	1	2	yes	—
671	Q₈	—	2	2	no	—
672	Q₈	—	2	4	no	—
673	Q₈	—	2	2	no	—
674	Q₈	—	2	4	no	—
675	Q₈	—	4	4	no	—
676	D₄	—	2	2	no	—
677	D₄	—	2	2	no	—
678	D₄	—	4	2	no	—
679	D₄	—	4	2	no	—
680	D₄	—	4	4	no	—
681	C₂×C₄	—	2	4	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	4	no	—
685	C₂×C₄	—	2	1	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	2	1	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	4	4	no	—
692	C₂×C₄	—	4	2	no	—
693	C₂×C₄	—	4	2	no	—
694	C₂×C₄	—	4	4	no	—
695	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
696	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
697	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
698	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
699	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
700	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
701	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
702	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
703	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
704	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
705	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
706	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
707	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
708	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
709	C₈	—	2	1	no	—
710	C₈	—	2	2	no	—
711	C₈	—	2	2	no	—
712	C₈	—	2	2	no	—
713	C₈	—	2	4	no	—
714	C₈	—	2	1	no	—
715	C₈	—	2	1	no	—
716	C₈	—	2	2	no	—
717	C₈	2₋¹⁺⁴×C₆₇	1	2	yes	—
718	C₂²	—	2	2	no	—
719	C₂²	—	2	1	no	—
720	C₂²	—	2	1	no	—
721	C₂²	—	2	2	no	—
722	C₂²	—	2	2	no	—
723	C₂²	—	2	2	no	—
724	C₂²	—	2	1	no	—
725	C₂²	—	2	2	no	—
726	C₂²	—	2	2	no	—
727	C₂²	C₂⁴×C₄×C₆₇	1	1	yes	characteristic
728	C₄	—	2	1	no	—
729	C₄	—	2	2	no	—
730	C₄	—	2	1	no	—
731	C₄	—	2	2	no	—
732	C₄	—	2	2	no	—
733	C₄	—	2	2	no	—
734	C₄	—	2	4	no	—
735	C₄	—	2	4	no	—
736	C₄	—	2	1	no	—
737	C₄	—	2	2	no	—
738	C₄	—	2	2	no	—
739	C₄	#568×C₆₇	1	2	yes	—
740	C₄	#568×C₆₇	1	2	yes	—
741	C₄	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
742	C₄	#585×C₆₇	1	1	yes	characteristic
743	C₂	—	4	2	no	—
744	C₂	—	4	1	no	—
745	C₂	—	4	2	no	—
746	C₂	C₄×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
747	C₂	C₂×#568×C₆₇	1	1	yes	characteristic
748	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	C₆₇×#3482	C₂
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×#2991	C₂	semidirect
5. C₆₇×#2990	C₂	semidirect
6. C₆₇×#2989	C₂	semidirect
7. C₆₇×#2986	C₂	semidirect
8. C₆₇×#2985	C₂	semidirect
9. C₆₇×#2983	C₂	semidirect
10. C₆₇×#2971	C₂	semidirect
11. C₆₇×#2969	C₂	semidirect
12. C₆₇×#2967	C₂	semidirect
13. C₆₇×#2965	C₂	semidirect
14. C₆₇×#2965	C₂	semidirect
15. Q₈×M₁₆×C₆₇	C₂	semidirect
16. C₆₇×#2962	C₂	semidirect
17. C₆₇×#2960	C₂	semidirect
368. #60337	C₆₇	direct (N × H)
376. #2995	C₂×C₆₇	semidirect
377. #2993	C₂×C₆₇	semidirect
378. #2991	C₂×C₆₇	semidirect
379. #2990	C₂×C₆₇	semidirect
380. #2989	C₂×C₆₇	semidirect
381. #2986	C₂×C₆₇	semidirect
382. #2985	C₂×C₆₇	semidirect
383. #2983	C₂×C₆₇	semidirect
384. #2971	C₂×C₆₇	semidirect
385. #2969	C₂×C₆₇	semidirect
386. #2967	C₂×C₆₇	semidirect
387. #2965	C₂×C₆₇	semidirect
388. #2965	C₂×C₆₇	semidirect
389. Q₈×M₁₆	C₂×C₆₇	semidirect
390. #2962	C₂×C₆₇	semidirect
391. #2960	C₂×C₆₇	semidirect
392. C₆₇	#60337	direct (N × H)

Maximal subgroups

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

subgroup	index
C₆₇×#3482	2
C₆₇×#2995	2
C₆₇×#2993	2
C₆₇×#2991	2
C₆₇×#2990	2
C₆₇×#2989	2
C₆₇×#2986	2
C₆₇×#2985	2
C₆₇×#2983	2
C₆₇×#2971	2
C₆₇×#2969	2
C₆₇×#2967	2
C₆₇×#2965	2
Q₈×M₁₆×C₆₇	2
C₆₇×#2962	2
C₆₇×#2960	2
#60337	67

Subgroups — C67×#60337 #30739588

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#60337 #30739588