Subgroups — C₆₇×#60210 #30739461

Order 17152.

1996 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3444	C₂	1	1	yes	maximal, characteristic
2	C₆₇×#2969	C₂	1	4	yes	maximal, complemented
3	C₆₇×#2968	C₂	1	4	yes	maximal, complemented
4	C₆₇×#2965	C₂	1	2	yes	maximal, complemented
5	C₆₇×#2965	C₂	1	4	yes	maximal, complemented
6	C₈×#41×C₆₇	C₂	1	2	yes	maximal, complemented
7	C₆₇×#2962	C₂	1	2	yes	maximal, complemented
8	C₆₇×#2935	C₂	1	2	yes	maximal, complemented
9	C₆₇×#2933	C₂	1	4	yes	maximal, complemented
10	C₆₇×#2922	C₂	1	2	yes	maximal, complemented
11	C₂×#431×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×#131×C₆₇	C₂	1	2	yes	maximal, complemented
13	C₂×C₄×M₁₆×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#131×C₆₇	C₂²	1	4	yes	—
15	C₂²×M₁₆×C₆₇	C₂²	1	2	yes	—
16	#533×C₆₇	C₄	1	1	yes	characteristic
17	#533×C₆₇	C₄	1	1	yes	characteristic
18	#533×C₆₇	C₂²	1	1	yes	characteristic
19	#532×C₆₇	C₄	1	1	yes	characteristic
20	#532×C₆₇	C₄	1	1	yes	characteristic
21	#532×C₆₇	C₂²	1	1	yes	characteristic
22	#529×C₆₇	C₄	1	2	yes	—
23	#529×C₆₇	C₄	1	2	yes	—
24	#529×C₆₇	C₄	1	2	yes	—
25	#529×C₆₇	C₄	1	2	yes	—
26	#529×C₆₇	C₂²	1	2	yes	—
27	#529×C₆₇	C₂²	1	2	yes	—
28	#525×C₆₇	C₄	1	2	yes	—
29	#525×C₆₇	C₄	1	2	yes	—
30	#525×C₆₇	C₂²	1	2	yes	—
31	C₄×#41×C₆₇	C₂²	1	2	yes	—
32	C₄×#41×C₆₇	C₂²	1	2	yes	—
33	C₄×#41×C₆₇	C₂²	1	2	yes	—
34	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
35	#446×C₆₇	C₂²	1	8	yes	complemented
36	#446×C₆₇	C₂²	1	4	yes	complemented
37	C₈×Q₈×C₆₇	C₂²	1	4	yes	complemented
38	#436×C₆₇	C₂²	1	8	yes	—
39	#436×C₆₇	C₂²	1	4	yes	complemented
40	#435×C₆₇	C₂²	1	8	yes	—
41	#435×C₆₇	C₂²	1	8	yes	—
42	#435×C₆₇	C₂²	1	8	yes	complemented
43	C₈×D₄×C₆₇	C₂²	1	8	yes	—
44	C₈×D₄×C₆₇	C₂²	1	4	yes	complemented
45	#433×C₆₇	C₂²	1	8	yes	complemented
46	#431×C₆₇	C₂²	1	1	yes	characteristic
47	#431×C₆₇	C₂²	1	2	yes	—
48	#431×C₆₇	C₂²	1	1	yes	characteristic
49	#431×C₆₇	C₂²	1	2	yes	—
50	#431×C₆₇	C₂²	1	2	yes	—
51	#431×C₆₇	C₂²	1	4	yes	complemented
52	#431×C₆₇	C₂²	1	4	yes	complemented
53	#424×C₆₇	C₂²	1	4	yes	—
54	C₂×C₄⋊C₈×C₆₇	C₂²	1	2	yes	—
55	#408×C₆₇	C₂²	1	4	yes	—
56	C₂×C₂²⋊C₈×C₆₇	C₂²	1	2	yes	—
57	#405×C₆₇	C₂²	1	4	yes	—
58	#405×C₆₇	C₂²	1	8	yes	complemented
59	C₄×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
60	C₄×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
61	C₄×M₁₆×C₆₇	C₂²	1	2	yes	—
62	C₄×M₁₆×C₆₇	C₂²	1	2	yes	—
63	C₄×M₁₆×C₆₇	C₂²	1	2	yes	—
64	C₄×M₁₆×C₆₇	C₂²	1	4	yes	complemented
65	C₂×#97×C₆₇	C₂²	1	2	yes	—
66	C₂×C₄×C₈×C₆₇	C₂²	1	2	yes	—
67	C₂×C₄×C₈×C₆₇	C₂²	1	2	yes	—
68	C₂×C₄×C₈×C₆₇	C₂²	1	4	yes	complemented
69	C₂×#41×C₆₇	C₂×C₄	1	2	yes	—
70	C₂×#41×C₆₇	C₂×C₄	1	2	yes	—
71	C₂×#41×C₆₇	C₂³	1	2	yes	—
72	C₂³×C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
73	C₂³×C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
74	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
75	#131×C₆₇	—	2	16	no	—
76	C₂×M₁₆×C₆₇	—	2	8	no	—
77	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
78	C₂×M₁₆×C₆₇	C₂³	1	4	yes	—
79	C₂×M₁₆×C₆₇	C₂³	1	8	yes	—
80	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
81	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
82	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
83	C₂²×C₈×C₆₇	C₂³	1	8	yes	—
84	C₄⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
85	C₄⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
86	C₄⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
87	#127×C₆₇	C₂×C₄	1	1	yes	characteristic
88	#126×C₆₇	C₂×C₄	1	4	yes	—
89	#126×C₆₇	C₂×C₄	1	4	yes	—
90	#125×C₆₇	C₂×C₄	1	2	yes	—
91	#125×C₆₇	C₂×C₄	1	2	yes	—
92	#125×C₆₇	C₂×C₄	1	2	yes	—
93	#124×C₆₇	C₂×C₄	1	2	yes	—
94	#124×C₆₇	C₂×C₄	1	2	yes	—
95	#124×C₆₇	C₂×C₄	1	2	yes	—
96	#123×C₆₇	C₂×C₄	1	4	yes	—
97	#123×C₆₇	C₂×C₄	1	4	yes	—
98	#123×C₆₇	C₂×C₄	1	4	yes	—
99	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
100	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
101	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
102	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
103	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
104	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
105	#121×C₆₇	C₂×C₄	1	2	yes	—
106	#121×C₆₇	C₂×C₄	1	2	yes	—
107	#121×C₆₇	C₂×C₄	1	2	yes	—
108	#121×C₆₇	C₂×C₄	1	2	yes	—
109	#121×C₆₇	C₂×C₄	1	2	yes	—
110	#121×C₆₇	C₂×C₄	1	2	yes	—
111	#120×C₆₇	C₂×C₄	1	4	yes	—
112	C₄×Q₈×C₆₇	C₂×C₄	1	2	yes	—
113	C₄×Q₈×C₆₇	C₂×C₄	1	2	yes	—
114	C₄×Q₈×C₆₇	C₂×C₄	1	2	yes	—
115	C₄×Q₈×C₆₇	C₂×C₄	1	2	yes	—
116	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
117	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
118	C₄×D₄×C₆₇	C₂×C₄	1	4	yes	—
119	C₄×D₄×C₆₇	C₂×C₄	1	4	yes	—
120	C₄×D₄×C₆₇	C₂×C₄	1	4	yes	—
121	C₄×D₄×C₆₇	C₂×C₄	1	4	yes	—
122	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
123	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
124	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
125	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
126	C₄×D₄×C₆₇	C₂³	1	4	yes	—
127	C₄×D₄×C₆₇	C₂³	1	4	yes	—
128	C₄×D₄×C₆₇	C₂³	1	2	yes	—
129	C₄×D₄×C₆₇	C₂³	1	2	yes	—
130	#117×C₆₇	C₂×C₄	1	2	yes	—
131	#117×C₆₇	C₂×C₄	1	2	yes	—
132	#117×C₆₇	C₂×C₄	1	4	yes	—
133	#117×C₆₇	C₂×C₄	1	4	yes	—
134	#117×C₆₇	C₂³	1	2	yes	—
135	#117×C₆₇	C₂³	1	4	yes	—
136	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
137	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
138	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
139	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
140	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
141	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
142	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
143	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
144	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
145	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
146	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
147	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
148	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
149	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
150	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
151	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
152	C₄⋊C₈×C₆₇	C₂³	1	8	yes	—
153	C₄⋊C₈×C₆₇	C₂³	1	8	yes	—
154	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
155	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
156	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
157	C₂²⋊C₈×C₆₇	C₂³	1	8	yes	—
158	C₂²⋊C₈×C₆₇	C₂³	1	8	yes	—
159	#97×C₆₇	C₂³	1	2	yes	—
160	#97×C₆₇	C₂³	1	2	yes	—
161	#97×C₆₇	C₂³	1	4	yes	—
162	#97×C₆₇	C₂³	1	8	yes	—
163	C₄×C₈×C₆₇	C₂³	1	4	yes	—
164	C₄×C₈×C₆₇	C₂³	1	4	yes	—
165	C₄×C₈×C₆₇	C₂³	1	8	yes	—
166	C₄×C₈×C₆₇	C₂³	1	2	yes	—
167	C₄×C₈×C₆₇	C₂³	1	2	yes	—
168	C₄×C₈×C₆₇	C₂³	1	2	yes	—
169	C₄×C₈×C₆₇	C₂³	1	2	yes	—
170	C₂⁴×C₆₇	C₂²×C₄	1	1	yes	characteristic
171	#41×C₆₇	—	2	8	no	—
172	#41×C₆₇	—	2	8	no	—
173	#41×C₆₇	—	4	4	no	—
174	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
175	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
176	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
177	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
178	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
179	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
180	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
181	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
182	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
183	C₂²×C₄×C₆₇	—	2	4	no	—
184	C₂²×C₄×C₆₇	—	2	4	no	—
185	C₂²×C₄×C₆₇	—	4	2	no	—
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	1	yes	characteristic
193	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
194	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
195	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
196	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
197	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
198	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
199	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
200	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
201	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
202	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
203	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
204	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
205	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
206	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
207	M₁₆×C₆₇	—	2	4	no	—
208	M₁₆×C₆₇	—	2	8	no	—
209	M₁₆×C₆₇	—	2	16	no	—
210	M₁₆×C₆₇	#41	1	8	yes	complemented
211	C₂×C₈×C₆₇	—	2	8	no	—
212	C₂×C₈×C₆₇	—	2	8	no	—
213	C₂×C₈×C₆₇	—	2	16	no	—
214	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
215	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
216	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
217	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
218	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
219	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
220	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
221	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
222	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
223	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
224	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
225	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
226	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
227	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
228	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
229	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
230	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
231	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
232	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
233	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
234	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
235	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
236	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
237	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
238	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
239	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
240	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
241	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
242	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
243	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
244	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
245	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
246	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
247	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
248	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
249	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
250	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
251	C₄²×C₆₇	C₂²×C₄	1	4	yes	—
252	C₄²×C₆₇	C₂²×C₄	1	4	yes	—
253	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
254	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
255	C₄²×C₆₇	C₂⁴	1	4	yes	—
256	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
257	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
258	C₂³×C₆₇	—	2	2	no	—
259	C₂³×C₆₇	—	2	2	no	—
260	C₂³×C₆₇	—	4	1	no	—
261	C₂³×C₆₇	C₂³×C₄	1	4	yes	—
262	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
263	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
264	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
265	Q₈×C₆₇	—	2	4	no	—
266	Q₈×C₆₇	—	2	4	no	—
267	Q₈×C₆₇	—	4	2	no	—
268	D₄×C₆₇	—	2	8	no	—
269	D₄×C₆₇	—	2	8	no	—
270	D₄×C₆₇	—	2	4	no	—
271	D₄×C₆₇	—	2	4	no	—
272	D₄×C₆₇	—	4	2	no	—
273	D₄×C₆₇	—	4	4	no	—
274	C₂×C₄×C₆₇	—	2	2	no	—
275	C₂×C₄×C₆₇	—	2	2	no	—
276	C₂×C₄×C₆₇	—	2	2	no	—
277	C₂×C₄×C₆₇	—	2	2	no	—
278	C₂×C₄×C₆₇	—	2	2	no	—
279	C₂×C₄×C₆₇	—	2	2	no	—
280	C₂×C₄×C₆₇	—	2	2	no	—
281	C₂×C₄×C₆₇	—	2	2	no	—
282	C₂×C₄×C₆₇	—	2	8	no	—
283	C₂×C₄×C₆₇	—	2	2	no	—
284	C₂×C₄×C₆₇	—	2	2	no	—
285	C₂×C₄×C₆₇	—	2	2	no	—
286	C₂×C₄×C₆₇	—	2	8	no	—
287	C₂×C₄×C₆₇	—	2	2	no	—
288	C₂×C₄×C₆₇	—	2	8	no	—
289	C₂×C₄×C₆₇	—	2	2	no	—
290	C₂×C₄×C₆₇	—	4	1	no	—
291	C₂×C₄×C₆₇	—	4	1	no	—
292	C₂×C₄×C₆₇	—	4	1	no	—
293	C₂×C₄×C₆₇	#131	1	4	yes	complemented
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	1	yes	characteristic
297	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
298	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
299	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
300	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
301	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
302	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
303	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
304	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
305	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
306	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
307	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
308	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
309	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
310	C₈×C₆₇	—	2	4	no	—
311	C₈×C₆₇	—	2	4	no	—
312	C₈×C₆₇	—	2	4	no	—
313	C₈×C₆₇	C₂×#41	1	8	yes	—
314	C₂²×C₆₇	—	2	1	no	—
315	C₂²×C₆₇	—	2	1	no	—
316	C₂²×C₆₇	—	2	1	no	—
317	C₂²×C₆₇	—	2	1	no	—
318	C₂²×C₆₇	—	2	1	no	—
319	C₂²×C₆₇	—	2	4	no	—
320	C₂²×C₆₇	—	2	1	no	—
321	C₂²×C₆₇	—	2	4	no	—
322	C₂²×C₆₇	—	2	1	no	—
323	C₂²×C₆₇	—	2	4	no	—
324	C₂²×C₆₇	—	4	4	no	—
325	C₂²×C₆₇	C₄×#41	1	2	yes	—
326	C₂²×C₆₇	C₂×#131	1	2	yes	—
327	C₂²×C₆₇	C₂⁴×C₄	1	1	yes	characteristic
328	C₄×C₆₇	—	2	1	no	—
329	C₄×C₆₇	—	2	1	no	—
330	C₄×C₆₇	—	2	4	no	—
331	C₄×C₆₇	—	2	1	no	—
332	C₄×C₆₇	—	2	1	no	—
333	C₄×C₆₇	—	2	4	no	—
334	C₄×C₆₇	—	2	1	no	—
335	C₄×C₆₇	—	2	1	no	—
336	C₄×C₆₇	—	2	1	no	—
337	C₄×C₆₇	—	2	4	no	—
338	C₄×C₆₇	C₄×#41	1	2	yes	—
339	C₄×C₆₇	C₂×#131	1	2	yes	—
340	C₄×C₆₇	C₂×#131	1	2	yes	—
341	C₄×C₆₇	#568	1	2	yes	—
342	C₄×C₆₇	C₂²×#41	1	2	yes	—
343	#60210	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
344	C₂×C₆₇	—	2	2	no	—
345	C₂×C₆₇	—	2	2	no	—
346	C₂×C₆₇	—	4	4	no	—
347	C₂×C₆₇	—	4	1	no	—
348	C₂×C₆₇	C₂×C₄×#41	1	1	yes	characteristic
349	C₂×C₆₇	C₂²×#131	1	1	yes	characteristic
350	C₂×C₆₇	C₂×#568	1	1	yes	characteristic
351	#3444	C₂×C₆₇	1	1	yes	characteristic
352	#2969	C₂×C₆₇	1	4	yes	complemented
353	#2968	C₂×C₆₇	1	4	yes	complemented
354	#2965	C₂×C₆₇	1	2	yes	complemented
355	#2965	C₂×C₆₇	1	4	yes	complemented
356	C₈×#41	C₂×C₆₇	1	2	yes	complemented
357	#2962	C₂×C₆₇	1	2	yes	complemented
358	#2935	C₂×C₆₇	1	2	yes	complemented
359	#2933	C₂×C₆₇	1	4	yes	complemented
360	#2922	C₂×C₆₇	1	2	yes	complemented
361	C₂×#431	C₂×C₆₇	1	1	yes	characteristic, complemented
362	C₄×#131	C₂×C₆₇	1	2	yes	complemented
363	C₂×C₄×M₁₆	C₂×C₆₇	1	1	yes	characteristic, complemented
364	C₆₇	#60210	1	1	yes	characteristic, direct product factor, Sylow
365	C₂×#131	C₂²×C₆₇	1	4	yes	—
366	C₂²×M₁₆	C₂²×C₆₇	1	2	yes	—
367	#533	C₄×C₆₇	1	1	yes	characteristic
368	#533	C₄×C₆₇	1	1	yes	characteristic
369	#533	C₂²×C₆₇	1	1	yes	characteristic
370	#532	C₄×C₆₇	1	1	yes	characteristic
371	#532	C₄×C₆₇	1	1	yes	characteristic
372	#532	C₂²×C₆₇	1	1	yes	characteristic
373	#529	C₄×C₆₇	1	2	yes	—
374	#529	C₄×C₆₇	1	2	yes	—
375	#529	C₄×C₆₇	1	2	yes	—
376	#529	C₄×C₆₇	1	2	yes	—
377	#529	C₂²×C₆₇	1	2	yes	—
378	#529	C₂²×C₆₇	1	2	yes	—
379	#525	C₄×C₆₇	1	2	yes	—
380	#525	C₄×C₆₇	1	2	yes	—
381	#525	C₂²×C₆₇	1	2	yes	—
382	C₄×#41	C₂²×C₆₇	1	2	yes	—
383	C₄×#41	C₂²×C₆₇	1	2	yes	—
384	C₄×#41	C₂²×C₆₇	1	2	yes	—
385	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
386	#446	C₂²×C₆₇	1	8	yes	complemented
387	#446	C₂²×C₆₇	1	4	yes	complemented
388	C₈×Q₈	C₂²×C₆₇	1	4	yes	complemented
389	#436	C₂²×C₆₇	1	8	yes	—
390	#436	C₂²×C₆₇	1	4	yes	complemented
391	#435	C₂²×C₆₇	1	8	yes	—
392	#435	C₂²×C₆₇	1	8	yes	—
393	#435	C₂²×C₆₇	1	8	yes	complemented
394	C₈×D₄	C₂²×C₆₇	1	8	yes	—
395	C₈×D₄	C₂²×C₆₇	1	4	yes	complemented
396	#433	C₂²×C₆₇	1	8	yes	complemented
397	#431	C₂²×C₆₇	1	1	yes	characteristic
398	#431	C₂²×C₆₇	1	2	yes	—
399	#431	C₂²×C₆₇	1	1	yes	characteristic
400	#431	C₂²×C₆₇	1	2	yes	—
401	#431	C₂²×C₆₇	1	2	yes	—
402	#431	C₂²×C₆₇	1	4	yes	complemented
403	#431	C₂²×C₆₇	1	4	yes	complemented
404	#424	C₂²×C₆₇	1	4	yes	—
405	C₂×C₄⋊C₈	C₂²×C₆₇	1	2	yes	—
406	#408	C₂²×C₆₇	1	4	yes	—
407	C₂×C₂²⋊C₈	C₂²×C₆₇	1	2	yes	—
408	#405	C₂²×C₆₇	1	4	yes	—
409	#405	C₂²×C₆₇	1	8	yes	complemented
410	C₄×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
411	C₄×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
412	C₄×M₁₆	C₂²×C₆₇	1	2	yes	—
413	C₄×M₁₆	C₂²×C₆₇	1	2	yes	—
414	C₄×M₁₆	C₂²×C₆₇	1	2	yes	—
415	C₄×M₁₆	C₂²×C₆₇	1	4	yes	complemented
416	C₂×#97	C₂²×C₆₇	1	2	yes	—
417	C₂×C₄×C₈	C₂²×C₆₇	1	2	yes	—
418	C₂×C₄×C₈	C₂²×C₆₇	1	2	yes	—
419	C₂×C₄×C₈	C₂²×C₆₇	1	4	yes	complemented
420	C₂×#41	C₂×C₄×C₆₇	1	2	yes	—
421	C₂×#41	C₂×C₄×C₆₇	1	2	yes	—
422	C₂×#41	C₂³×C₆₇	1	2	yes	—
423	C₂³×C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
424	C₂³×C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
425	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
426	#131	—	2	16	no	—
427	C₂×M₁₆	—	2	8	no	—
428	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
429	C₂×M₁₆	C₂³×C₆₇	1	4	yes	—
430	C₂×M₁₆	C₂³×C₆₇	1	8	yes	—
431	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
432	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
433	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
434	C₂²×C₈	C₂³×C₆₇	1	8	yes	—
435	C₄⋊Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
436	C₄⋊Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
437	C₄⋊Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
438	#127	C₂×C₄×C₆₇	1	1	yes	characteristic
439	#126	C₂×C₄×C₆₇	1	4	yes	—
440	#126	C₂×C₄×C₆₇	1	4	yes	—
441	#125	C₂×C₄×C₆₇	1	2	yes	—
442	#125	C₂×C₄×C₆₇	1	2	yes	—
443	#125	C₂×C₄×C₆₇	1	2	yes	—
444	#124	C₂×C₄×C₆₇	1	2	yes	—
445	#124	C₂×C₄×C₆₇	1	2	yes	—
446	#124	C₂×C₄×C₆₇	1	2	yes	—
447	#123	C₂×C₄×C₆₇	1	4	yes	—
448	#123	C₂×C₄×C₆₇	1	4	yes	—
449	#123	C₂×C₄×C₆₇	1	4	yes	—
450	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
451	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
452	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
453	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
454	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
455	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
456	#121	C₂×C₄×C₆₇	1	2	yes	—
457	#121	C₂×C₄×C₆₇	1	2	yes	—
458	#121	C₂×C₄×C₆₇	1	2	yes	—
459	#121	C₂×C₄×C₆₇	1	2	yes	—
460	#121	C₂×C₄×C₆₇	1	2	yes	—
461	#121	C₂×C₄×C₆₇	1	2	yes	—
462	#120	C₂×C₄×C₆₇	1	4	yes	—
463	C₄×Q₈	C₂×C₄×C₆₇	1	2	yes	—
464	C₄×Q₈	C₂×C₄×C₆₇	1	2	yes	—
465	C₄×Q₈	C₂×C₄×C₆₇	1	2	yes	—
466	C₄×Q₈	C₂×C₄×C₆₇	1	2	yes	—
467	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
468	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
469	C₄×D₄	C₂×C₄×C₆₇	1	4	yes	—
470	C₄×D₄	C₂×C₄×C₆₇	1	4	yes	—
471	C₄×D₄	C₂×C₄×C₆₇	1	4	yes	—
472	C₄×D₄	C₂×C₄×C₆₇	1	4	yes	—
473	C₄×D₄	C₂×C₄×C₆₇	1	2	yes	—
474	C₄×D₄	C₂×C₄×C₆₇	1	2	yes	—
475	C₄×D₄	C₂×C₄×C₆₇	1	2	yes	—
476	C₄×D₄	C₂×C₄×C₆₇	1	2	yes	—
477	C₄×D₄	C₂³×C₆₇	1	4	yes	—
478	C₄×D₄	C₂³×C₆₇	1	4	yes	—
479	C₄×D₄	C₂³×C₆₇	1	2	yes	—
480	C₄×D₄	C₂³×C₆₇	1	2	yes	—
481	#117	C₂×C₄×C₆₇	1	2	yes	—
482	#117	C₂×C₄×C₆₇	1	2	yes	—
483	#117	C₂×C₄×C₆₇	1	4	yes	—
484	#117	C₂×C₄×C₆₇	1	4	yes	—
485	#117	C₂³×C₆₇	1	2	yes	—
486	#117	C₂³×C₆₇	1	4	yes	—
487	C₂×C₄²	C₂×C₄×C₆₇	1	1	yes	characteristic
488	C₂×C₄²	C₂×C₄×C₆₇	1	1	yes	characteristic
489	C₂×C₄²	C₂×C₄×C₆₇	1	1	yes	characteristic
490	C₂×C₄²	C₂×C₄×C₆₇	1	1	yes	characteristic
491	C₂×C₄²	C₂×C₄×C₆₇	1	1	yes	characteristic
492	C₂×C₄²	C₂×C₄×C₆₇	1	1	yes	characteristic
493	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
494	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
495	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
496	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
497	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
498	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
499	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
500	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
501	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
502	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
503	C₄⋊C₈	C₂³×C₆₇	1	8	yes	—
504	C₄⋊C₈	C₂³×C₆₇	1	8	yes	—
505	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
506	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
507	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
508	C₂²⋊C₈	C₂³×C₆₇	1	8	yes	—
509	C₂²⋊C₈	C₂³×C₆₇	1	8	yes	—
510	#97	C₂³×C₆₇	1	2	yes	—
511	#97	C₂³×C₆₇	1	2	yes	—
512	#97	C₂³×C₆₇	1	4	yes	—
513	#97	C₂³×C₆₇	1	8	yes	—
514	C₄×C₈	C₂³×C₆₇	1	2	yes	—
515	C₄×C₈	C₂³×C₆₇	1	2	yes	—
516	C₄×C₈	C₂³×C₆₇	1	2	yes	—
517	C₄×C₈	C₂³×C₆₇	1	4	yes	—
518	C₄×C₈	C₂³×C₆₇	1	2	yes	—
519	C₄×C₈	C₂³×C₆₇	1	4	yes	—
520	C₄×C₈	C₂³×C₆₇	1	8	yes	—
521	C₂⁴	C₂²×C₄×C₆₇	1	1	yes	characteristic
522	#41	—	2	8	no	—
523	#41	—	2	8	no	—
524	#41	—	4	4	no	—
525	C₂×Q₈	C₂²×C₄×C₆₇	1	2	yes	—
526	C₂×Q₈	C₂²×C₄×C₆₇	1	2	yes	—
527	C₂×Q₈	C₂²×C₄×C₆₇	1	2	yes	—
528	C₂×D₄	C₂²×C₄×C₆₇	1	4	yes	—
529	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
530	C₂×D₄	C₂²×C₄×C₆₇	1	4	yes	—
531	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
532	C₂×D₄	C₂²×C₄×C₆₇	1	4	yes	—
533	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
534	C₂²×C₄	—	2	4	no	—
535	C₂²×C₄	—	2	4	no	—
536	C₂²×C₄	—	4	2	no	—
537	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
538	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
539	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
540	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
541	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
542	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
543	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
544	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
545	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
546	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
547	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
548	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
549	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
550	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
551	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
552	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
553	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
554	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
555	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
556	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
557	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
558	M₁₆	—	2	4	no	—
559	M₁₆	—	2	8	no	—
560	M₁₆	—	2	16	no	—
561	M₁₆	#41×C₆₇	1	8	yes	complemented
562	C₂×C₈	—	2	8	no	—
563	C₂×C₈	—	2	8	no	—
564	C₂×C₈	—	2	16	no	—
565	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
566	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
567	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
568	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
569	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
570	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
571	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
572	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
573	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
574	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
575	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
576	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
577	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
578	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
579	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
580	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
581	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
582	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
583	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
584	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
585	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
586	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
587	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
588	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
589	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
590	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
591	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
592	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
593	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
594	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
595	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
596	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
597	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
598	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
599	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
600	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
601	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
602	C₄²	C₂²×C₄×C₆₇	1	4	yes	—
603	C₄²	C₂²×C₄×C₆₇	1	4	yes	—
604	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
605	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
606	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
607	C₄²	C₂⁴×C₆₇	1	4	yes	—
608	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
609	C₂³	—	2	2	no	—
610	C₂³	—	2	2	no	—
611	C₂³	—	4	1	no	—
612	C₂³	C₂³×C₄×C₆₇	1	4	yes	—
613	C₂³	C₂³×C₄×C₆₇	1	1	yes	characteristic
614	C₂³	C₂³×C₄×C₆₇	1	1	yes	characteristic
615	C₂³	C₂³×C₄×C₆₇	1	1	yes	characteristic
616	Q₈	—	2	4	no	—
617	Q₈	—	2	4	no	—
618	Q₈	—	4	2	no	—
619	D₄	—	2	8	no	—
620	D₄	—	2	8	no	—
621	D₄	—	2	4	no	—
622	D₄	—	2	4	no	—
623	D₄	—	4	2	no	—
624	D₄	—	4	4	no	—
625	C₂×C₄	—	2	2	no	—
626	C₂×C₄	—	2	2	no	—
627	C₂×C₄	—	2	2	no	—
628	C₂×C₄	—	2	2	no	—
629	C₂×C₄	—	2	2	no	—
630	C₂×C₄	—	2	2	no	—
631	C₂×C₄	—	2	2	no	—
632	C₂×C₄	—	2	2	no	—
633	C₂×C₄	—	2	8	no	—
634	C₂×C₄	—	2	2	no	—
635	C₂×C₄	—	2	2	no	—
636	C₂×C₄	—	2	2	no	—
637	C₂×C₄	—	2	8	no	—
638	C₂×C₄	—	2	2	no	—
639	C₂×C₄	—	2	8	no	—
640	C₂×C₄	—	2	2	no	—
641	C₂×C₄	—	4	1	no	—
642	C₂×C₄	—	4	1	no	—
643	C₂×C₄	—	4	1	no	—
644	C₂×C₄	#131×C₆₇	1	4	yes	complemented
645	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
646	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
647	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
648	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
649	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
650	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
651	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
652	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
653	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
654	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
655	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
656	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
657	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
658	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
659	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
660	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
661	C₈	—	2	4	no	—
662	C₈	—	2	4	no	—
663	C₈	—	2	4	no	—
664	C₈	C₂×#41×C₆₇	1	8	yes	—
665	C₂²	—	2	1	no	—
666	C₂²	—	2	1	no	—
667	C₂²	—	2	1	no	—
668	C₂²	—	2	1	no	—
669	C₂²	—	2	1	no	—
670	C₂²	—	2	4	no	—
671	C₂²	—	2	1	no	—
672	C₂²	—	2	4	no	—
673	C₂²	—	2	1	no	—
674	C₂²	—	2	4	no	—
675	C₂²	—	4	4	no	—
676	C₂²	C₄×#41×C₆₇	1	2	yes	—
677	C₂²	C₂×#131×C₆₇	1	2	yes	—
678	C₂²	C₂⁴×C₄×C₆₇	1	1	yes	characteristic
679	C₄	—	2	1	no	—
680	C₄	—	2	1	no	—
681	C₄	—	2	4	no	—
682	C₄	—	2	1	no	—
683	C₄	—	2	1	no	—
684	C₄	—	2	1	no	—
685	C₄	—	2	4	no	—
686	C₄	—	2	1	no	—
687	C₄	—	2	1	no	—
688	C₄	—	2	4	no	—
689	C₄	C₄×#41×C₆₇	1	2	yes	—
690	C₄	C₂×#131×C₆₇	1	2	yes	—
691	C₄	C₂×#131×C₆₇	1	2	yes	—
692	C₄	#568×C₆₇	1	2	yes	—
693	C₄	C₂²×#41×C₆₇	1	2	yes	—
694	C₂	—	2	2	no	—
695	C₂	—	2	2	no	—
696	C₂	—	4	1	no	—
697	C₂	—	4	4	no	—
698	C₂	C₂×C₄×#41×C₆₇	1	1	yes	characteristic
699	C₂	C₂²×#131×C₆₇	1	1	yes	characteristic
700	C₂	C₂×#568×C₆₇	1	1	yes	characteristic

	subgroup	G/H
center	C₄²×C₆₇	C₂⁴
commutator	C₂²	C₂⁴×C₄×C₆₇
Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
socle	C₂²×C₆₇	C₂⁴×C₄
prime radical	C₆₇×#3444	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₄²×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₆₇×#2969	C₂	semidirect
3. C₆₇×#2968	C₂	semidirect
4. C₆₇×#2965	C₂	semidirect
5. C₆₇×#2965	C₂	semidirect
6. C₈×#41×C₆₇	C₂	semidirect
7. C₆₇×#2962	C₂	semidirect
8. C₆₇×#2935	C₂	semidirect
9. C₆₇×#2933	C₂	semidirect
10. C₆₇×#2922	C₂	semidirect
11. C₂×#431×C₆₇	C₂	semidirect
12. C₄×#131×C₆₇	C₂	semidirect
13. C₂×C₄×M₁₆×C₆₇	C₂	semidirect
35. #446×C₆₇	C₂²	semidirect
36. #446×C₆₇	C₂²	semidirect
37. C₈×Q₈×C₆₇	C₂²	semidirect
39. #436×C₆₇	C₂²	semidirect
42. #435×C₆₇	C₂²	semidirect
44. C₈×D₄×C₆₇	C₂²	semidirect
45. #433×C₆₇	C₂²	semidirect
51. #431×C₆₇	C₂²	semidirect
52. #431×C₆₇	C₂²	semidirect
58. #405×C₆₇	C₂²	semidirect
64. C₄×M₁₆×C₆₇	C₂²	semidirect
68. C₂×C₄×C₈×C₆₇	C₂²	semidirect
210. M₁₆×C₆₇	#41	semidirect
293. C₂×C₄×C₆₇	#131	semidirect
343. #60210	C₆₇	direct (N × H)
352. #2969	C₂×C₆₇	semidirect
353. #2968	C₂×C₆₇	semidirect
354. #2965	C₂×C₆₇	semidirect
355. #2965	C₂×C₆₇	semidirect
356. C₈×#41	C₂×C₆₇	semidirect
357. #2962	C₂×C₆₇	semidirect
358. #2935	C₂×C₆₇	semidirect
359. #2933	C₂×C₆₇	semidirect
360. #2922	C₂×C₆₇	semidirect
361. C₂×#431	C₂×C₆₇	semidirect
362. C₄×#131	C₂×C₆₇	semidirect
363. C₂×C₄×M₁₆	C₂×C₆₇	semidirect
364. C₆₇	#60210	direct (N × H)
386. #446	C₂²×C₆₇	semidirect
387. #446	C₂²×C₆₇	semidirect
388. C₈×Q₈	C₂²×C₆₇	semidirect
390. #436	C₂²×C₆₇	semidirect
393. #435	C₂²×C₆₇	semidirect
395. C₈×D₄	C₂²×C₆₇	semidirect
396. #433	C₂²×C₆₇	semidirect
402. #431	C₂²×C₆₇	semidirect
403. #431	C₂²×C₆₇	semidirect
409. #405	C₂²×C₆₇	semidirect
415. C₄×M₁₆	C₂²×C₆₇	semidirect
419. C₂×C₄×C₈	C₂²×C₆₇	semidirect
561. M₁₆	#41×C₆₇	semidirect
644. C₂×C₄	#131×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#3444	2
C₆₇×#2969	2
C₆₇×#2968	2
C₆₇×#2965	2
C₈×#41×C₆₇	2
C₆₇×#2962	2
C₆₇×#2935	2
C₆₇×#2933	2
C₆₇×#2922	2
C₂×#431×C₆₇	2
C₄×#131×C₆₇	2
C₂×C₄×M₁₆×C₆₇	2
#60210	67

Subgroups — C67×#60210 #30739461

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#60210 #30739461