Subgroups — C₆₇×#59412 #30738663

Order 17152.

3744 conjugacy classes of subgroups.

The subgroup lattice has 930 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#550×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#546×C₆₇	C₂	1	2	yes	maximal, complemented
3	C₂×D₄²×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#2678	C₂	1	4	yes	maximal, complemented
5	C₆₇×#2538	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#2537	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#2535	C₂	1	2	yes	maximal, complemented
8	C₆₇×#2433	C₂	1	2	yes	maximal, complemented
9	C₆₇×#2428	C₂	1	2	yes	maximal, complemented
10	C₆₇×#2424	C₂	1	4	yes	maximal, complemented
11	C₆₇×#2422	C₂	1	2	yes	maximal, complemented
12	C₆₇×#2408	C₂	1	2	yes	maximal, complemented
13	C₆₇×#2407	C₂	1	2	yes	maximal, complemented
14	D₄×C₂²⋊C₄×C₆₇	C₂	1	2	yes	maximal, complemented
15	C₄×#127×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×#127×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×#124×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×#41×C₆₇	C₂²	1	2	yes	complemented
19	C₂³×D₄×C₆₇	C₂²	1	2	yes	—
20	C₂³×D₄×C₆₇	C₂²	1	2	yes	—
21	#550×C₆₇	—	2	8	no	—
22	#546×C₆₇	—	2	16	no	—
23	D₄²×C₆₇	—	2	8	no	—
24	C₂×#127×C₆₇	C₂²	1	1	yes	characteristic
25	C₂×#127×C₆₇	C₂²	1	1	yes	characteristic
26	C₂×#127×C₆₇	C₂²	1	2	yes	complemented
27	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic
28	C₂×#123×C₆₇	C₂²	1	4	yes	complemented
29	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	complemented
30	C₂×#121×C₆₇	C₂²	1	2	yes	—
31	C₂×#121×C₆₇	C₂²	1	2	yes	—
32	C₂×#121×C₆₇	C₂²	1	2	yes	—
33	C₂×#121×C₆₇	C₂²	1	2	yes	complemented
34	C₂×#121×C₆₇	C₂²	1	4	yes	complemented
35	C₂×#121×C₆₇	C₂²	1	4	yes	complemented
36	C₂×#121×C₆₇	C₂²	1	2	yes	complemented
37	C₂×#120×C₆₇	C₂²	1	4	yes	—
38	C₂×#120×C₆₇	C₂²	1	4	yes	complemented
39	C₂×#120×C₆₇	C₂²	1	4	yes	complemented
40	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
43	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
44	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
45	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
46	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
47	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
48	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
49	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
50	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	4	yes	complemented
51	#397×C₆₇	C₂²	1	4	yes	complemented
52	#396×C₆₇	C₂²	1	4	yes	complemented
53	#394×C₆₇	C₂²	1	4	yes	complemented
54	#394×C₆₇	C₂²	1	4	yes	complemented
55	#394×C₆₇	C₂²	1	4	yes	complemented
56	#392×C₆₇	C₂²	1	4	yes	complemented
57	#392×C₆₇	C₂²	1	4	yes	complemented
58	#392×C₆₇	C₂²	1	4	yes	complemented
59	#391×C₆₇	C₂²	1	1	yes	characteristic, complemented
60	#390×C₆₇	C₂²	1	2	yes	—
61	#390×C₆₇	C₂²	1	1	yes	characteristic
62	#390×C₆₇	C₂²	1	1	yes	characteristic
63	#390×C₆₇	C₂²	1	2	yes	complemented
64	#390×C₆₇	C₂²	1	2	yes	complemented
65	#390×C₆₇	C₂²	1	2	yes	complemented
66	#390×C₆₇	C₂²	1	2	yes	complemented
67	#390×C₆₇	C₂²	1	2	yes	complemented
68	#390×C₆₇	C₂²	1	1	yes	characteristic, complemented
69	#389×C₆₇	C₂²	1	2	yes	complemented
70	#388×C₆₇	C₂²	1	2	yes	complemented
71	#388×C₆₇	C₂²	1	2	yes	complemented
72	#386×C₆₇	C₂²	1	4	yes	complemented
73	#386×C₆₇	C₂²	1	4	yes	complemented
74	#386×C₆₇	C₂²	1	4	yes	complemented
75	#385×C₆₇	C₂²	1	4	yes	complemented
76	#384×C₆₇	C₂²	1	1	yes	characteristic, complemented
77	#384×C₆₇	C₂²	1	1	yes	characteristic, complemented
78	#382×C₆₇	C₂²	1	1	yes	characteristic, complemented
79	#380×C₆₇	C₂²	1	2	yes	complemented
80	#380×C₆₇	C₂²	1	2	yes	complemented
81	#380×C₆₇	C₂²	1	2	yes	complemented
82	#379×C₆₇	C₂²	1	4	yes	complemented
83	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
84	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
85	C₄³×C₆₇	C₂²	1	1	yes	characteristic, complemented
86	C₂⁵×C₆₇	C₂³	1	4	yes	—
87	C₂×#41×C₆₇	—	2	8	no	—
88	C₂×#41×C₆₇	—	2	8	no	—
89	C₂×#41×C₆₇	—	4	4	no	—
90	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
91	C₂²×D₄×C₆₇	—	2	8	no	—
92	C₂²×D₄×C₆₇	—	2	8	no	—
93	C₂²×D₄×C₆₇	—	2	8	no	—
94	C₂²×D₄×C₆₇	—	2	8	no	—
95	C₂²×D₄×C₆₇	—	4	4	no	—
96	C₂²×D₄×C₆₇	—	4	4	no	—
97	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
98	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
99	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
100	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
101	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
102	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
103	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
104	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
105	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
106	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
107	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
108	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
109	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
110	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
111	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
112	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
113	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
114	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
115	#127×C₆₇	—	2	8	no	—
116	#127×C₆₇	—	2	4	no	—
117	#127×C₆₇	D₄	1	8	yes	complemented
118	#124×C₆₇	D₄	1	8	yes	complemented
119	#123×C₆₇	—	2	16	no	—
120	C₂²⋊Q₈×C₆₇	—	2	8	no	—
121	#121×C₆₇	—	2	8	no	—
122	#121×C₆₇	—	2	8	no	—
123	#121×C₆₇	—	2	8	no	—
124	#121×C₆₇	—	2	8	no	—
125	#121×C₆₇	—	2	16	no	—
126	#121×C₆₇	—	2	16	no	—
127	#121×C₆₇	—	4	4	no	—
128	#120×C₆₇	—	2	16	no	—
129	#120×C₆₇	—	2	16	no	—
130	#120×C₆₇	—	4	8	no	—
131	C₄×Q₈×C₆₇	—	2	4	no	—
132	C₄×D₄×C₆₇	—	2	8	no	—
133	C₄×D₄×C₆₇	—	2	4	no	—
134	C₄×D₄×C₆₇	—	2	4	no	—
135	C₄×D₄×C₆₇	—	2	4	no	—
136	C₄×D₄×C₆₇	—	2	8	no	—
137	C₄×D₄×C₆₇	—	2	8	no	—
138	C₄×D₄×C₆₇	—	4	4	no	—
139	C₄×D₄×C₆₇	—	4	4	no	—
140	C₄×D₄×C₆₇	—	4	4	no	—
141	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
142	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
143	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
144	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
145	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
146	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
147	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
148	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
149	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
150	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
151	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
152	C₂×C₂²⋊C₄×C₆₇	—	2	16	no	—
153	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
154	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
155	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
156	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
157	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
158	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
159	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
160	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
161	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
162	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
163	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
164	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
165	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
166	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
167	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
168	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
169	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
170	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
171	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
172	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
173	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
174	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
175	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
176	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
177	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
178	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
179	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
180	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
181	#95×C₆₇	C₂³	1	2	yes	—
182	#95×C₆₇	C₂³	1	2	yes	—
183	#95×C₆₇	C₂³	1	2	yes	—
184	#95×C₆₇	C₂³	1	2	yes	—
185	#95×C₆₇	C₂³	1	4	yes	—
186	#95×C₆₇	C₂³	1	4	yes	—
187	C₂⁴×C₆₇	—	2	8	no	—
188	C₂⁴×C₆₇	—	2	8	no	—
189	C₂⁴×C₆₇	—	2	8	no	—
190	C₂⁴×C₆₇	—	4	4	no	—
191	C₂⁴×C₆₇	—	4	4	no	—
192	C₂⁴×C₆₇	—	4	4	no	—
193	C₂⁴×C₆₇	—	4	4	no	—
194	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
195	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
196	C₂⁴×C₆₇	C₂⁴	1	4	yes	—
197	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
198	#41×C₆₇	—	4	32	no	—
199	C₂×Q₈×C₆₇	—	2	2	no	—
200	C₂×Q₈×C₆₇	—	2	2	no	—
201	C₂×Q₈×C₆₇	C₂×D₄	1	4	yes	complemented
202	C₂×D₄×C₆₇	—	2	8	no	—
203	C₂×D₄×C₆₇	—	2	8	no	—
204	C₂×D₄×C₆₇	—	2	8	no	—
205	C₂×D₄×C₆₇	—	2	8	no	—
206	C₂×D₄×C₆₇	—	2	4	no	—
207	C₂×D₄×C₆₇	—	2	4	no	—
208	C₂×D₄×C₆₇	—	2	8	no	—
209	C₂×D₄×C₆₇	—	2	8	no	—
210	C₂×D₄×C₆₇	—	2	8	no	—
211	C₂×D₄×C₆₇	—	2	2	no	—
212	C₂×D₄×C₆₇	—	2	2	no	—
213	C₂×D₄×C₆₇	—	2	4	no	—
214	C₂×D₄×C₆₇	—	2	4	no	—
215	C₂×D₄×C₆₇	—	2	2	no	—
216	C₂×D₄×C₆₇	—	2	8	no	—
217	C₂×D₄×C₆₇	—	2	4	no	—
218	C₂×D₄×C₆₇	—	2	2	no	—
219	C₂×D₄×C₆₇	—	2	4	no	—
220	C₂×D₄×C₆₇	—	2	2	no	—
221	C₂×D₄×C₆₇	—	2	2	no	—
222	C₂×D₄×C₆₇	—	2	4	no	—
223	C₂×D₄×C₆₇	—	2	4	no	—
224	C₂×D₄×C₆₇	—	2	2	no	—
225	C₂×D₄×C₆₇	—	4	2	no	—
226	C₂×D₄×C₆₇	—	4	2	no	—
227	C₂×D₄×C₆₇	—	4	4	no	—
228	C₂×D₄×C₆₇	—	4	4	no	—
229	C₂×D₄×C₆₇	—	4	2	no	—
230	C₂×D₄×C₆₇	—	4	2	no	—
231	C₂×D₄×C₆₇	—	4	4	no	—
232	C₂×D₄×C₆₇	—	4	4	no	—
233	C₂×D₄×C₆₇	—	4	4	no	—
234	C₂×D₄×C₆₇	—	4	4	no	—
235	C₂×D₄×C₆₇	—	4	4	no	—
236	C₂×D₄×C₆₇	—	4	32	no	—
237	C₂×D₄×C₆₇	—	4	32	no	—
238	C₂×D₄×C₆₇	C₂×D₄	1	8	yes	—
239	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	—
240	C₂×D₄×C₆₇	C₂×D₄	1	8	yes	—
241	C₂×D₄×C₆₇	C₂×D₄	1	8	yes	—
242	C₂×D₄×C₆₇	#41	1	4	yes	complemented
243	C₂²×C₄×C₆₇	—	2	8	no	—
244	C₂²×C₄×C₆₇	—	2	8	no	—
245	C₂²×C₄×C₆₇	—	2	4	no	—
246	C₂²×C₄×C₆₇	—	2	4	no	—
247	C₂²×C₄×C₆₇	—	2	4	no	—
248	C₂²×C₄×C₆₇	—	2	4	no	—
249	C₂²×C₄×C₆₇	—	2	4	no	—
250	C₂²×C₄×C₆₇	—	2	4	no	—
251	C₂²×C₄×C₆₇	—	2	4	no	—
252	C₂²×C₄×C₆₇	—	2	4	no	—
253	C₂²×C₄×C₆₇	—	2	4	no	—
254	C₂²×C₄×C₆₇	—	2	8	no	—
255	C₂²×C₄×C₆₇	—	4	4	no	—
256	C₂²×C₄×C₆₇	—	4	4	no	—
257	C₂²×C₄×C₆₇	—	4	4	no	—
258	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
259	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
260	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
261	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
262	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
263	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
264	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
265	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
266	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
267	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
268	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
269	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
270	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
271	C₄⋊C₄×C₆₇	—	2	2	no	—
272	C₄⋊C₄×C₆₇	—	2	2	no	—
273	C₄⋊C₄×C₆₇	—	2	2	no	—
274	C₄⋊C₄×C₆₇	—	2	4	no	—
275	C₄⋊C₄×C₆₇	—	2	4	no	—
276	C₄⋊C₄×C₆₇	—	2	4	no	—
277	C₄⋊C₄×C₆₇	—	2	2	no	—
278	C₄⋊C₄×C₆₇	—	2	8	no	—
279	C₄⋊C₄×C₆₇	—	2	4	no	—
280	C₄⋊C₄×C₆₇	—	4	2	no	—
281	C₄⋊C₄×C₆₇	—	4	2	no	—
282	C₂²⋊C₄×C₆₇	—	2	8	no	—
283	C₂²⋊C₄×C₆₇	—	2	8	no	—
284	C₂²⋊C₄×C₆₇	—	2	8	no	—
285	C₂²⋊C₄×C₆₇	—	2	4	no	—
286	C₂²⋊C₄×C₆₇	—	2	8	no	—
287	C₂²⋊C₄×C₆₇	—	2	4	no	—
288	C₂²⋊C₄×C₆₇	—	2	4	no	—
289	C₂²⋊C₄×C₆₇	—	2	8	no	—
290	C₂²⋊C₄×C₆₇	—	2	4	no	—
291	C₂²⋊C₄×C₆₇	—	2	4	no	—
292	C₂²⋊C₄×C₆₇	—	2	8	no	—
293	C₂²⋊C₄×C₆₇	—	2	4	no	—
294	C₂²⋊C₄×C₆₇	—	4	2	no	—
295	C₂²⋊C₄×C₆₇	—	4	4	no	—
296	C₂²⋊C₄×C₆₇	—	4	2	no	—
297	C₂²⋊C₄×C₆₇	—	4	2	no	—
298	C₂²⋊C₄×C₆₇	—	4	4	no	—
299	C₂²⋊C₄×C₆₇	—	4	4	no	—
300	C₂²⋊C₄×C₆₇	C₂×D₄	1	8	yes	complemented
301	C₂²⋊C₄×C₆₇	C₂×D₄	1	8	yes	complemented
302	C₄²×C₆₇	—	2	4	no	—
303	C₄²×C₆₇	—	2	2	no	—
304	C₄²×C₆₇	—	2	2	no	—
305	C₄²×C₆₇	—	2	2	no	—
306	C₄²×C₆₇	—	2	2	no	—
307	C₄²×C₆₇	—	4	1	no	—
308	C₄²×C₆₇	C₂×D₄	1	4	yes	—
309	C₄²×C₆₇	C₂×D₄	1	4	yes	complemented
310	C₂³×C₆₇	—	2	2	no	—
311	C₂³×C₆₇	—	2	4	no	—
312	C₂³×C₆₇	—	2	2	no	—
313	C₂³×C₆₇	—	2	2	no	—
314	C₂³×C₆₇	—	2	2	no	—
315	C₂³×C₆₇	—	2	4	no	—
316	C₂³×C₆₇	—	2	4	no	—
317	C₂³×C₆₇	—	2	2	no	—
318	C₂³×C₆₇	—	2	2	no	—
319	C₂³×C₆₇	—	2	2	no	—
320	C₂³×C₆₇	—	2	4	no	—
321	C₂³×C₆₇	—	2	2	no	—
322	C₂³×C₆₇	—	2	4	no	—
323	C₂³×C₆₇	—	2	2	no	—
324	C₂³×C₆₇	—	2	2	no	—
325	C₂³×C₆₇	—	2	2	no	—
326	C₂³×C₆₇	—	2	4	no	—
327	C₂³×C₆₇	—	2	2	no	—
328	C₂³×C₆₇	—	2	2	no	—
329	C₂³×C₆₇	—	2	2	no	—
330	C₂³×C₆₇	—	2	2	no	—
331	C₂³×C₆₇	—	2	2	no	—
332	C₂³×C₆₇	—	2	2	no	—
333	C₂³×C₆₇	—	2	2	no	—
334	C₂³×C₆₇	—	2	2	no	—
335	C₂³×C₆₇	—	4	16	no	—
336	C₂³×C₆₇	—	4	16	no	—
337	C₂³×C₆₇	—	4	16	no	—
338	C₂³×C₆₇	—	8	8	no	—
339	C₂³×C₆₇	—	8	8	no	—
340	C₂³×C₆₇	—	8	8	no	—
341	C₂³×C₆₇	—	8	8	no	—
342	C₂³×C₆₇	C₂²×D₄	1	4	yes	—
343	C₂³×C₆₇	C₂²×D₄	1	8	yes	—
344	C₂³×C₆₇	C₂×#41	1	4	yes	—
345	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
346	Q₈×C₆₇	—	2	8	no	—
347	D₄×C₆₇	—	2	8	no	—
348	D₄×C₆₇	—	2	16	no	—
349	D₄×C₆₇	—	2	8	no	—
350	D₄×C₆₇	—	2	16	no	—
351	D₄×C₆₇	—	4	8	no	—
352	D₄×C₆₇	—	4	8	no	—
353	D₄×C₆₇	—	4	8	no	—
354	D₄×C₆₇	—	4	16	no	—
355	D₄×C₆₇	—	4	16	no	—
356	D₄×C₆₇	—	4	16	no	—
357	D₄×C₆₇	—	4	4	no	—
358	D₄×C₆₇	—	8	8	no	—
359	D₄×C₆₇	—	8	8	no	—
360	C₂×C₄×C₆₇	—	2	2	no	—
361	C₂×C₄×C₆₇	—	2	1	no	—
362	C₂×C₄×C₆₇	—	2	1	no	—
363	C₂×C₄×C₆₇	—	2	1	no	—
364	C₂×C₄×C₆₇	—	2	1	no	—
365	C₂×C₄×C₆₇	—	2	1	no	—
366	C₂×C₄×C₆₇	—	2	1	no	—
367	C₂×C₄×C₆₇	—	2	2	no	—
368	C₂×C₄×C₆₇	—	2	1	no	—
369	C₂×C₄×C₆₇	—	2	1	no	—
370	C₂×C₄×C₆₇	—	2	2	no	—
371	C₂×C₄×C₆₇	—	2	4	no	—
372	C₂×C₄×C₆₇	—	2	2	no	—
373	C₂×C₄×C₆₇	—	2	2	no	—
374	C₂×C₄×C₆₇	—	2	2	no	—
375	C₂×C₄×C₆₇	—	2	2	no	—
376	C₂×C₄×C₆₇	—	2	2	no	—
377	C₂×C₄×C₆₇	—	2	2	no	—
378	C₂×C₄×C₆₇	—	2	1	no	—
379	C₂×C₄×C₆₇	—	2	1	no	—
380	C₂×C₄×C₆₇	—	2	2	no	—
381	C₂×C₄×C₆₇	—	2	4	no	—
382	C₂×C₄×C₆₇	—	2	4	no	—
383	C₂×C₄×C₆₇	—	2	2	no	—
384	C₂×C₄×C₆₇	—	2	2	no	—
385	C₂×C₄×C₆₇	—	2	2	no	—
386	C₂×C₄×C₆₇	—	2	1	no	—
387	C₂×C₄×C₆₇	—	2	2	no	—
388	C₂×C₄×C₆₇	—	4	16	no	—
389	C₂×C₄×C₆₇	—	4	8	no	—
390	C₂×C₄×C₆₇	—	4	8	no	—
391	C₂×C₄×C₆₇	—	4	8	no	—
392	C₂×C₄×C₆₇	—	8	8	no	—
393	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
394	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
395	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
396	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
397	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
398	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
399	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
400	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
401	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
402	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
403	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
404	C₂²×C₆₇	—	2	8	no	—
405	C₂²×C₆₇	—	2	4	no	—
406	C₂²×C₆₇	—	2	4	no	—
407	C₂²×C₆₇	—	2	8	no	—
408	C₂²×C₆₇	—	2	4	no	—
409	C₂²×C₆₇	—	2	4	no	—
410	C₂²×C₆₇	—	2	8	no	—
411	C₂²×C₆₇	—	2	4	no	—
412	C₂²×C₆₇	—	2	4	no	—
413	C₂²×C₆₇	—	4	2	no	—
414	C₂²×C₆₇	—	4	2	no	—
415	C₂²×C₆₇	—	4	4	no	—
416	C₂²×C₆₇	—	4	2	no	—
417	C₂²×C₆₇	—	4	2	no	—
418	C₂²×C₆₇	—	4	4	no	—
419	C₂²×C₆₇	—	4	2	no	—
420	C₂²×C₆₇	—	4	4	no	—
421	C₂²×C₆₇	—	4	2	no	—
422	C₂²×C₆₇	—	4	4	no	—
423	C₂²×C₆₇	—	4	2	no	—
424	C₂²×C₆₇	—	4	2	no	—
425	C₂²×C₆₇	—	4	2	no	—
426	C₂²×C₆₇	—	4	2	no	—
427	C₂²×C₆₇	—	4	2	no	—
428	C₂²×C₆₇	—	4	2	no	—
429	C₂²×C₆₇	—	4	2	no	—
430	C₂²×C₆₇	—	4	2	no	—
431	C₂²×C₆₇	—	4	2	no	—
432	C₂²×C₆₇	—	8	32	no	—
433	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
434	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
435	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
436	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
437	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
438	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
439	C₂²×C₆₇	#585	1	1	yes	characteristic
440	C₄×C₆₇	—	2	4	no	—
441	C₄×C₆₇	—	2	2	no	—
442	C₄×C₆₇	—	2	2	no	—
443	C₄×C₆₇	—	2	2	no	—
444	C₄×C₆₇	—	2	2	no	—
445	C₄×C₆₇	—	4	2	no	—
446	C₄×C₆₇	—	4	2	no	—
447	C₄×C₆₇	—	4	2	no	—
448	C₄×C₆₇	—	4	2	no	—
449	C₄×C₆₇	—	4	4	no	—
450	C₄×C₆₇	—	4	1	no	—
451	C₄×C₆₇	D₄²	1	4	yes	—
452	C₄×C₆₇	#546	1	4	yes	complemented
453	#59412	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
454	C₂×C₆₇	—	4	8	no	—
455	C₂×C₆₇	—	4	4	no	—
456	C₂×C₆₇	—	4	4	no	—
457	C₂×C₆₇	—	8	2	no	—
458	C₂×C₆₇	C₂×D₄²	1	1	yes	characteristic
459	C₂×C₆₇	C₂×#546	1	1	yes	characteristic
460	C₂×C₆₇	D₄×#41	1	1	yes	characteristic
461	C₂×C₆₇	#3496	1	1	yes	characteristic
462	C₂×C₆₇	#3498	1	1	yes	characteristic
463	C₂×C₆₇	#3519	1	1	yes	characteristic
464	C₂×C₆₇	#3546	1	1	yes	characteristic
465	C₂×#550	C₂×C₆₇	1	1	yes	characteristic, complemented
466	C₂×#546	C₂×C₆₇	1	2	yes	complemented
467	C₂×D₄²	C₂×C₆₇	1	1	yes	characteristic, complemented
468	#2678	C₂×C₆₇	1	4	yes	complemented
469	#2538	C₂×C₆₇	1	1	yes	characteristic, complemented
470	#2537	C₂×C₆₇	1	1	yes	characteristic, complemented
471	#2535	C₂×C₆₇	1	2	yes	complemented
472	#2433	C₂×C₆₇	1	2	yes	complemented
473	#2428	C₂×C₆₇	1	2	yes	complemented
474	#2424	C₂×C₆₇	1	4	yes	complemented
475	#2422	C₂×C₆₇	1	2	yes	complemented
476	#2408	C₂×C₆₇	1	2	yes	complemented
477	#2407	C₂×C₆₇	1	2	yes	complemented
478	D₄×C₂²⋊C₄	C₂×C₆₇	1	2	yes	complemented
479	C₄×#127	C₂×C₆₇	1	1	yes	characteristic, complemented
480	C₄×#127	C₂×C₆₇	1	1	yes	characteristic, complemented
481	C₄×#124	C₂×C₆₇	1	1	yes	characteristic, complemented
482	C₆₇	#59412	1	1	yes	characteristic, direct product factor, Sylow
483	C₂²×#41	C₂²×C₆₇	1	2	yes	complemented
484	C₂³×D₄	C₂²×C₆₇	1	2	yes	—
485	C₂³×D₄	C₂²×C₆₇	1	2	yes	—
486	#550	—	2	8	no	—
487	#546	—	2	16	no	—
488	D₄²	—	2	8	no	—
489	C₂×#127	C₂²×C₆₇	1	1	yes	characteristic
490	C₂×#127	C₂²×C₆₇	1	1	yes	characteristic
491	C₂×#127	C₂²×C₆₇	1	2	yes	complemented
492	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic
493	C₂×#123	C₂²×C₆₇	1	4	yes	complemented
494	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	complemented
495	C₂×#121	C₂²×C₆₇	1	2	yes	—
496	C₂×#121	C₂²×C₆₇	1	2	yes	—
497	C₂×#121	C₂²×C₆₇	1	2	yes	—
498	C₂×#121	C₂²×C₆₇	1	2	yes	complemented
499	C₂×#121	C₂²×C₆₇	1	4	yes	complemented
500	C₂×#121	C₂²×C₆₇	1	4	yes	complemented
501	C₂×#121	C₂²×C₆₇	1	2	yes	complemented
502	C₂×#120	C₂²×C₆₇	1	4	yes	—
503	C₂×#120	C₂²×C₆₇	1	4	yes	complemented
504	C₂×#120	C₂²×C₆₇	1	4	yes	complemented
505	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
506	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
507	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
508	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
509	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
510	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
511	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
512	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
513	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
514	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
515	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	4	yes	complemented
516	#397	C₂²×C₆₇	1	4	yes	complemented
517	#396	C₂²×C₆₇	1	4	yes	complemented
518	#394	C₂²×C₆₇	1	4	yes	complemented
519	#394	C₂²×C₆₇	1	4	yes	complemented
520	#394	C₂²×C₆₇	1	4	yes	complemented
521	#392	C₂²×C₆₇	1	4	yes	complemented
522	#392	C₂²×C₆₇	1	4	yes	complemented
523	#392	C₂²×C₆₇	1	4	yes	complemented
524	#391	C₂²×C₆₇	1	1	yes	characteristic, complemented
525	#390	C₂²×C₆₇	1	1	yes	characteristic
526	#390	C₂²×C₆₇	1	2	yes	—
527	#390	C₂²×C₆₇	1	1	yes	characteristic
528	#390	C₂²×C₆₇	1	2	yes	complemented
529	#390	C₂²×C₆₇	1	2	yes	complemented
530	#390	C₂²×C₆₇	1	2	yes	complemented
531	#390	C₂²×C₆₇	1	2	yes	complemented
532	#390	C₂²×C₆₇	1	2	yes	complemented
533	#390	C₂²×C₆₇	1	1	yes	characteristic, complemented
534	#389	C₂²×C₆₇	1	2	yes	complemented
535	#388	C₂²×C₆₇	1	2	yes	complemented
536	#388	C₂²×C₆₇	1	2	yes	complemented
537	#386	C₂²×C₆₇	1	4	yes	complemented
538	#386	C₂²×C₆₇	1	4	yes	complemented
539	#386	C₂²×C₆₇	1	4	yes	complemented
540	#385	C₂²×C₆₇	1	4	yes	complemented
541	#384	C₂²×C₆₇	1	1	yes	characteristic, complemented
542	#384	C₂²×C₆₇	1	1	yes	characteristic, complemented
543	#382	C₂²×C₆₇	1	1	yes	characteristic, complemented
544	#380	C₂²×C₆₇	1	2	yes	complemented
545	#380	C₂²×C₆₇	1	2	yes	complemented
546	#380	C₂²×C₆₇	1	2	yes	complemented
547	#379	C₂²×C₆₇	1	4	yes	complemented
548	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
549	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
550	C₄³	C₂²×C₆₇	1	1	yes	characteristic, complemented
551	C₂⁵	C₂³×C₆₇	1	4	yes	—
552	C₂×#41	—	2	8	no	—
553	C₂×#41	—	2	8	no	—
554	C₂×#41	—	4	4	no	—
555	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
556	C₂²×D₄	—	2	8	no	—
557	C₂²×D₄	—	2	8	no	—
558	C₂²×D₄	—	2	8	no	—
559	C₂²×D₄	—	2	8	no	—
560	C₂²×D₄	—	4	4	no	—
561	C₂²×D₄	—	4	4	no	—
562	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
563	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
564	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
565	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
566	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
567	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
568	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
569	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
570	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
571	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
572	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
573	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
574	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
575	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
576	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
577	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
578	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
579	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
580	#127	—	2	8	no	—
581	#127	—	2	4	no	—
582	#127	D₄×C₆₇	1	8	yes	complemented
583	#124	D₄×C₆₇	1	8	yes	complemented
584	#123	—	2	16	no	—
585	C₂²⋊Q₈	—	2	8	no	—
586	#121	—	2	8	no	—
587	#121	—	2	8	no	—
588	#121	—	2	8	no	—
589	#121	—	2	8	no	—
590	#121	—	2	16	no	—
591	#121	—	2	16	no	—
592	#121	—	4	4	no	—
593	#120	—	2	16	no	—
594	#120	—	2	16	no	—
595	#120	—	4	8	no	—
596	C₄×Q₈	—	2	4	no	—
597	C₄×D₄	—	2	8	no	—
598	C₄×D₄	—	2	4	no	—
599	C₄×D₄	—	2	4	no	—
600	C₄×D₄	—	2	4	no	—
601	C₄×D₄	—	2	8	no	—
602	C₄×D₄	—	2	8	no	—
603	C₄×D₄	—	4	4	no	—
604	C₄×D₄	—	4	4	no	—
605	C₄×D₄	—	4	4	no	—
606	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
607	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
608	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
609	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
610	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
611	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
612	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
613	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
614	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
615	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
616	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
617	C₂×C₂²⋊C₄	—	2	16	no	—
618	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
619	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
620	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
621	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
622	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
623	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
624	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
625	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
626	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
627	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
628	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
629	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
630	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
631	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
632	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
633	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
634	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
635	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
636	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
637	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
638	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
639	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
640	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
641	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
642	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
643	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
644	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
645	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
646	#95	C₂³×C₆₇	1	2	yes	—
647	#95	C₂³×C₆₇	1	2	yes	—
648	#95	C₂³×C₆₇	1	2	yes	—
649	#95	C₂³×C₆₇	1	2	yes	—
650	#95	C₂³×C₆₇	1	4	yes	—
651	#95	C₂³×C₆₇	1	4	yes	—
652	C₂⁴	—	2	8	no	—
653	C₂⁴	—	2	8	no	—
654	C₂⁴	—	2	8	no	—
655	C₂⁴	—	4	4	no	—
656	C₂⁴	—	4	4	no	—
657	C₂⁴	—	4	4	no	—
658	C₂⁴	—	4	4	no	—
659	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
660	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
661	C₂⁴	C₂⁴×C₆₇	1	4	yes	—
662	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
663	#41	—	4	32	no	—
664	C₂×Q₈	—	2	2	no	—
665	C₂×Q₈	—	2	2	no	—
666	C₂×Q₈	C₂×D₄×C₆₇	1	4	yes	complemented
667	C₂×D₄	—	2	8	no	—
668	C₂×D₄	—	2	8	no	—
669	C₂×D₄	—	2	8	no	—
670	C₂×D₄	—	2	8	no	—
671	C₂×D₄	—	2	4	no	—
672	C₂×D₄	—	2	4	no	—
673	C₂×D₄	—	2	8	no	—
674	C₂×D₄	—	2	8	no	—
675	C₂×D₄	—	2	8	no	—
676	C₂×D₄	—	2	2	no	—
677	C₂×D₄	—	2	2	no	—
678	C₂×D₄	—	2	4	no	—
679	C₂×D₄	—	2	4	no	—
680	C₂×D₄	—	2	2	no	—
681	C₂×D₄	—	2	8	no	—
682	C₂×D₄	—	2	4	no	—
683	C₂×D₄	—	2	2	no	—
684	C₂×D₄	—	2	4	no	—
685	C₂×D₄	—	2	2	no	—
686	C₂×D₄	—	2	2	no	—
687	C₂×D₄	—	2	4	no	—
688	C₂×D₄	—	2	4	no	—
689	C₂×D₄	—	2	2	no	—
690	C₂×D₄	—	4	2	no	—
691	C₂×D₄	—	4	2	no	—
692	C₂×D₄	—	4	4	no	—
693	C₂×D₄	—	4	4	no	—
694	C₂×D₄	—	4	4	no	—
695	C₂×D₄	—	4	2	no	—
696	C₂×D₄	—	4	2	no	—
697	C₂×D₄	—	4	4	no	—
698	C₂×D₄	—	4	4	no	—
699	C₂×D₄	—	4	4	no	—
700	C₂×D₄	—	4	4	no	—
701	C₂×D₄	—	4	32	no	—
702	C₂×D₄	—	4	32	no	—
703	C₂×D₄	C₂×D₄×C₆₇	1	8	yes	—
704	C₂×D₄	C₂×D₄×C₆₇	1	4	yes	—
705	C₂×D₄	C₂×D₄×C₆₇	1	8	yes	—
706	C₂×D₄	C₂×D₄×C₆₇	1	8	yes	—
707	C₂×D₄	#41×C₆₇	1	4	yes	complemented
708	C₂²×C₄	—	2	8	no	—
709	C₂²×C₄	—	2	8	no	—
710	C₂²×C₄	—	2	4	no	—
711	C₂²×C₄	—	2	4	no	—
712	C₂²×C₄	—	2	4	no	—
713	C₂²×C₄	—	2	4	no	—
714	C₂²×C₄	—	2	4	no	—
715	C₂²×C₄	—	2	4	no	—
716	C₂²×C₄	—	2	4	no	—
717	C₂²×C₄	—	2	4	no	—
718	C₂²×C₄	—	2	4	no	—
719	C₂²×C₄	—	2	8	no	—
720	C₂²×C₄	—	4	4	no	—
721	C₂²×C₄	—	4	4	no	—
722	C₂²×C₄	—	4	4	no	—
723	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
724	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
725	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
726	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
727	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
728	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
729	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
730	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
731	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
732	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
733	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
734	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
735	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
736	C₄⋊C₄	—	2	2	no	—
737	C₄⋊C₄	—	2	2	no	—
738	C₄⋊C₄	—	2	2	no	—
739	C₄⋊C₄	—	2	4	no	—
740	C₄⋊C₄	—	2	4	no	—
741	C₄⋊C₄	—	2	4	no	—
742	C₄⋊C₄	—	2	2	no	—
743	C₄⋊C₄	—	2	8	no	—
744	C₄⋊C₄	—	2	4	no	—
745	C₄⋊C₄	—	4	2	no	—
746	C₄⋊C₄	—	4	2	no	—
747	C₂²⋊C₄	—	2	8	no	—
748	C₂²⋊C₄	—	2	8	no	—
749	C₂²⋊C₄	—	2	8	no	—
750	C₂²⋊C₄	—	2	4	no	—
751	C₂²⋊C₄	—	2	8	no	—
752	C₂²⋊C₄	—	2	4	no	—
753	C₂²⋊C₄	—	2	4	no	—
754	C₂²⋊C₄	—	2	8	no	—
755	C₂²⋊C₄	—	2	4	no	—
756	C₂²⋊C₄	—	2	4	no	—
757	C₂²⋊C₄	—	2	8	no	—
758	C₂²⋊C₄	—	2	4	no	—
759	C₂²⋊C₄	—	4	4	no	—
760	C₂²⋊C₄	—	4	2	no	—
761	C₂²⋊C₄	—	4	2	no	—
762	C₂²⋊C₄	—	4	4	no	—
763	C₂²⋊C₄	—	4	4	no	—
764	C₂²⋊C₄	—	4	2	no	—
765	C₂²⋊C₄	C₂×D₄×C₆₇	1	8	yes	complemented
766	C₂²⋊C₄	C₂×D₄×C₆₇	1	8	yes	complemented
767	C₄²	—	2	4	no	—
768	C₄²	—	2	2	no	—
769	C₄²	—	2	2	no	—
770	C₄²	—	2	2	no	—
771	C₄²	—	2	2	no	—
772	C₄²	—	4	1	no	—
773	C₄²	C₂×D₄×C₆₇	1	4	yes	—
774	C₄²	C₂×D₄×C₆₇	1	4	yes	complemented
775	C₂³	—	2	2	no	—
776	C₂³	—	2	4	no	—
777	C₂³	—	2	2	no	—
778	C₂³	—	2	2	no	—
779	C₂³	—	2	2	no	—
780	C₂³	—	2	4	no	—
781	C₂³	—	2	4	no	—
782	C₂³	—	2	2	no	—
783	C₂³	—	2	2	no	—
784	C₂³	—	2	2	no	—
785	C₂³	—	2	4	no	—
786	C₂³	—	2	2	no	—
787	C₂³	—	2	4	no	—
788	C₂³	—	2	2	no	—
789	C₂³	—	2	2	no	—
790	C₂³	—	2	2	no	—
791	C₂³	—	2	4	no	—
792	C₂³	—	2	2	no	—
793	C₂³	—	2	2	no	—
794	C₂³	—	2	2	no	—
795	C₂³	—	2	2	no	—
796	C₂³	—	2	2	no	—
797	C₂³	—	2	2	no	—
798	C₂³	—	2	2	no	—
799	C₂³	—	2	2	no	—
800	C₂³	—	4	16	no	—
801	C₂³	—	4	16	no	—
802	C₂³	—	4	16	no	—
803	C₂³	—	8	8	no	—
804	C₂³	—	8	8	no	—
805	C₂³	—	8	8	no	—
806	C₂³	—	8	8	no	—
807	C₂³	C₂²×D₄×C₆₇	1	4	yes	—
808	C₂³	C₂²×D₄×C₆₇	1	8	yes	—
809	C₂³	C₂×#41×C₆₇	1	4	yes	—
810	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
811	Q₈	—	2	8	no	—
812	D₄	—	2	8	no	—
813	D₄	—	2	16	no	—
814	D₄	—	2	8	no	—
815	D₄	—	2	16	no	—
816	D₄	—	4	8	no	—
817	D₄	—	4	16	no	—
818	D₄	—	4	8	no	—
819	D₄	—	4	8	no	—
820	D₄	—	4	16	no	—
821	D₄	—	4	16	no	—
822	D₄	—	4	4	no	—
823	D₄	—	8	8	no	—
824	D₄	—	8	8	no	—
825	C₂×C₄	—	2	2	no	—
826	C₂×C₄	—	2	1	no	—
827	C₂×C₄	—	2	1	no	—
828	C₂×C₄	—	2	1	no	—
829	C₂×C₄	—	2	1	no	—
830	C₂×C₄	—	2	1	no	—
831	C₂×C₄	—	2	1	no	—
832	C₂×C₄	—	2	2	no	—
833	C₂×C₄	—	2	1	no	—
834	C₂×C₄	—	2	1	no	—
835	C₂×C₄	—	2	2	no	—
836	C₂×C₄	—	2	4	no	—
837	C₂×C₄	—	2	2	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	2	no	—
841	C₂×C₄	—	2	2	no	—
842	C₂×C₄	—	2	2	no	—
843	C₂×C₄	—	2	1	no	—
844	C₂×C₄	—	2	1	no	—
845	C₂×C₄	—	2	2	no	—
846	C₂×C₄	—	2	4	no	—
847	C₂×C₄	—	2	4	no	—
848	C₂×C₄	—	2	2	no	—
849	C₂×C₄	—	2	2	no	—
850	C₂×C₄	—	2	2	no	—
851	C₂×C₄	—	2	1	no	—
852	C₂×C₄	—	2	2	no	—
853	C₂×C₄	—	4	16	no	—
854	C₂×C₄	—	4	8	no	—
855	C₂×C₄	—	4	8	no	—
856	C₂×C₄	—	4	8	no	—
857	C₂×C₄	—	8	8	no	—
858	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
859	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
860	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
861	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
862	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
863	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
864	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
865	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
866	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
867	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
868	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
869	C₂²	—	2	8	no	—
870	C₂²	—	2	4	no	—
871	C₂²	—	2	4	no	—
872	C₂²	—	2	8	no	—
873	C₂²	—	2	4	no	—
874	C₂²	—	2	4	no	—
875	C₂²	—	2	8	no	—
876	C₂²	—	2	4	no	—
877	C₂²	—	2	4	no	—
878	C₂²	—	4	2	no	—
879	C₂²	—	4	2	no	—
880	C₂²	—	4	4	no	—
881	C₂²	—	4	2	no	—
882	C₂²	—	4	2	no	—
883	C₂²	—	4	4	no	—
884	C₂²	—	4	2	no	—
885	C₂²	—	4	2	no	—
886	C₂²	—	4	4	no	—
887	C₂²	—	4	2	no	—
888	C₂²	—	4	2	no	—
889	C₂²	—	4	4	no	—
890	C₂²	—	4	2	no	—
891	C₂²	—	4	2	no	—
892	C₂²	—	4	2	no	—
893	C₂²	—	4	2	no	—
894	C₂²	—	4	2	no	—
895	C₂²	—	4	2	no	—
896	C₂²	—	4	2	no	—
897	C₂²	—	8	32	no	—
898	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
899	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
900	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
901	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
902	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
903	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
904	C₂²	#585×C₆₇	1	1	yes	characteristic
905	C₄	—	2	4	no	—
906	C₄	—	2	2	no	—
907	C₄	—	2	2	no	—
908	C₄	—	2	2	no	—
909	C₄	—	2	2	no	—
910	C₄	—	4	1	no	—
911	C₄	—	4	2	no	—
912	C₄	—	4	2	no	—
913	C₄	—	4	2	no	—
914	C₄	—	4	2	no	—
915	C₄	—	4	4	no	—
916	C₄	D₄²×C₆₇	1	4	yes	—
917	C₄	#546×C₆₇	1	4	yes	complemented
918	C₂	—	4	4	no	—
919	C₂	—	4	4	no	—
920	C₂	—	4	8	no	—
921	C₂	—	8	2	no	—
922	C₂	C₂×D₄²×C₆₇	1	1	yes	characteristic
923	C₂	C₂×#546×C₆₇	1	1	yes	characteristic
924	C₂	D₄×#41×C₆₇	1	1	yes	characteristic
925	C₂	C₆₇×#3496	1	1	yes	characteristic
926	C₂	C₆₇×#3498	1	1	yes	characteristic
927	C₂	C₆₇×#3519	1	1	yes	characteristic
928	C₂	C₆₇×#3546	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₇
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#550×C₆₇	C₂	semidirect
2. C₂×#546×C₆₇	C₂	semidirect
3. C₂×D₄²×C₆₇	C₂	semidirect
4. C₆₇×#2678	C₂	semidirect
5. C₆₇×#2538	C₂	semidirect
6. C₆₇×#2537	C₂	semidirect
7. C₆₇×#2535	C₂	semidirect
8. C₆₇×#2433	C₂	semidirect
9. C₆₇×#2428	C₂	semidirect
10. C₆₇×#2424	C₂	semidirect
11. C₆₇×#2422	C₂	semidirect
12. C₆₇×#2408	C₂	semidirect
13. C₆₇×#2407	C₂	semidirect
14. D₄×C₂²⋊C₄×C₆₇	C₂	semidirect
15. C₄×#127×C₆₇	C₂	semidirect
16. C₄×#127×C₆₇	C₂	semidirect
17. C₄×#124×C₆₇	C₂	semidirect
18. C₂²×#41×C₆₇	C₂²	semidirect
26. C₂×#127×C₆₇	C₂²	semidirect
28. C₂×#123×C₆₇	C₂²	semidirect
29. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
33. C₂×#121×C₆₇	C₂²	semidirect
34. C₂×#121×C₆₇	C₂²	semidirect
35. C₂×#121×C₆₇	C₂²	semidirect
36. C₂×#121×C₆₇	C₂²	semidirect
38. C₂×#120×C₆₇	C₂²	semidirect
39. C₂×#120×C₆₇	C₂²	semidirect
40. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
43. C₂×C₄×D₄×C₆₇	C₂²	semidirect
44. C₂×C₄×D₄×C₆₇	C₂²	semidirect
45. C₂×C₄×D₄×C₆₇	C₂²	semidirect
46. C₂×C₄×D₄×C₆₇	C₂²	semidirect
47. C₂×C₄×D₄×C₆₇	C₂²	semidirect
48. C₂×C₄×D₄×C₆₇	C₂²	semidirect
49. C₂×C₄×D₄×C₆₇	C₂²	semidirect
50. C₂²×C₂²⋊C₄×C₆₇	C₂²	semidirect
51. #397×C₆₇	C₂²	semidirect
52. #396×C₆₇	C₂²	semidirect
53. #394×C₆₇	C₂²	semidirect
54. #394×C₆₇	C₂²	semidirect
55. #394×C₆₇	C₂²	semidirect
56. #392×C₆₇	C₂²	semidirect
57. #392×C₆₇	C₂²	semidirect
58. #392×C₆₇	C₂²	semidirect
59. #391×C₆₇	C₂²	semidirect
63. #390×C₆₇	C₂²	semidirect
64. #390×C₆₇	C₂²	semidirect
65. #390×C₆₇	C₂²	semidirect
66. #390×C₆₇	C₂²	semidirect
67. #390×C₆₇	C₂²	semidirect
68. #390×C₆₇	C₂²	semidirect
69. #389×C₆₇	C₂²	semidirect
70. #388×C₆₇	C₂²	semidirect
71. #388×C₆₇	C₂²	semidirect
72. #386×C₆₇	C₂²	semidirect
73. #386×C₆₇	C₂²	semidirect
74. #386×C₆₇	C₂²	semidirect
75. #385×C₆₇	C₂²	semidirect
76. #384×C₆₇	C₂²	semidirect
77. #384×C₆₇	C₂²	semidirect
78. #382×C₆₇	C₂²	semidirect
79. #380×C₆₇	C₂²	semidirect
80. #380×C₆₇	C₂²	semidirect
81. #380×C₆₇	C₂²	semidirect
82. #379×C₆₇	C₂²	semidirect
83. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
84. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
85. C₄³×C₆₇	C₂²	semidirect
117. #127×C₆₇	D₄	semidirect
118. #124×C₆₇	D₄	semidirect
201. C₂×Q₈×C₆₇	C₂×D₄	semidirect
242. C₂×D₄×C₆₇	#41	semidirect
300. C₂²⋊C₄×C₆₇	C₂×D₄	semidirect
301. C₂²⋊C₄×C₆₇	C₂×D₄	semidirect
309. C₄²×C₆₇	C₂×D₄	semidirect
452. C₄×C₆₇	#546	semidirect
453. #59412	C₆₇	direct (N × H)
465. C₂×#550	C₂×C₆₇	semidirect
466. C₂×#546	C₂×C₆₇	semidirect
467. C₂×D₄²	C₂×C₆₇	semidirect
468. #2678	C₂×C₆₇	semidirect
469. #2538	C₂×C₆₇	semidirect
470. #2537	C₂×C₆₇	semidirect
471. #2535	C₂×C₆₇	semidirect
472. #2433	C₂×C₆₇	semidirect
473. #2428	C₂×C₆₇	semidirect
474. #2424	C₂×C₆₇	semidirect
475. #2422	C₂×C₆₇	semidirect
476. #2408	C₂×C₆₇	semidirect
477. #2407	C₂×C₆₇	semidirect
478. D₄×C₂²⋊C₄	C₂×C₆₇	semidirect
479. C₄×#127	C₂×C₆₇	semidirect
480. C₄×#127	C₂×C₆₇	semidirect
481. C₄×#124	C₂×C₆₇	semidirect
482. C₆₇	#59412	direct (N × H)
483. C₂²×#41	C₂²×C₆₇	semidirect
491. C₂×#127	C₂²×C₆₇	semidirect
493. C₂×#123	C₂²×C₆₇	semidirect
494. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
498. C₂×#121	C₂²×C₆₇	semidirect
499. C₂×#121	C₂²×C₆₇	semidirect
500. C₂×#121	C₂²×C₆₇	semidirect
501. C₂×#121	C₂²×C₆₇	semidirect
503. C₂×#120	C₂²×C₆₇	semidirect
504. C₂×#120	C₂²×C₆₇	semidirect
505. C₂×C₄×Q₈	C₂²×C₆₇	semidirect
508. C₂×C₄×D₄	C₂²×C₆₇	semidirect
509. C₂×C₄×D₄	C₂²×C₆₇	semidirect
510. C₂×C₄×D₄	C₂²×C₆₇	semidirect
511. C₂×C₄×D₄	C₂²×C₆₇	semidirect
512. C₂×C₄×D₄	C₂²×C₆₇	semidirect
513. C₂×C₄×D₄	C₂²×C₆₇	semidirect
514. C₂×C₄×D₄	C₂²×C₆₇	semidirect
515. C₂²×C₂²⋊C₄	C₂²×C₆₇	semidirect
516. #397	C₂²×C₆₇	semidirect
517. #396	C₂²×C₆₇	semidirect
518. #394	C₂²×C₆₇	semidirect
519. #394	C₂²×C₆₇	semidirect
520. #394	C₂²×C₆₇	semidirect
521. #392	C₂²×C₆₇	semidirect
522. #392	C₂²×C₆₇	semidirect
523. #392	C₂²×C₆₇	semidirect
524. #391	C₂²×C₆₇	semidirect
528. #390	C₂²×C₆₇	semidirect
529. #390	C₂²×C₆₇	semidirect
530. #390	C₂²×C₆₇	semidirect
531. #390	C₂²×C₆₇	semidirect
532. #390	C₂²×C₆₇	semidirect
533. #390	C₂²×C₆₇	semidirect
534. #389	C₂²×C₆₇	semidirect
535. #388	C₂²×C₆₇	semidirect
536. #388	C₂²×C₆₇	semidirect
537. #386	C₂²×C₆₇	semidirect
538. #386	C₂²×C₆₇	semidirect
539. #386	C₂²×C₆₇	semidirect
540. #385	C₂²×C₆₇	semidirect
541. #384	C₂²×C₆₇	semidirect
542. #384	C₂²×C₆₇	semidirect
543. #382	C₂²×C₆₇	semidirect
544. #380	C₂²×C₆₇	semidirect
545. #380	C₂²×C₆₇	semidirect
546. #380	C₂²×C₆₇	semidirect
547. #379	C₂²×C₆₇	semidirect
548. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
549. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
550. C₄³	C₂²×C₆₇	semidirect
582. #127	D₄×C₆₇	semidirect
583. #124	D₄×C₆₇	semidirect
666. C₂×Q₈	C₂×D₄×C₆₇	semidirect
707. C₂×D₄	#41×C₆₇	semidirect
765. C₂²⋊C₄	C₂×D₄×C₆₇	semidirect
766. C₂²⋊C₄	C₂×D₄×C₆₇	semidirect
774. C₄²	C₂×D₄×C₆₇	semidirect
917. C₄	#546×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#550×C₆₇	2
C₂×#546×C₆₇	2
C₂×D₄²×C₆₇	2
C₆₇×#2678	2
C₆₇×#2538	2
C₆₇×#2537	2
C₆₇×#2535	2
C₆₇×#2433	2
C₆₇×#2428	2
C₆₇×#2424	2
C₆₇×#2422	2
C₆₇×#2408	2
C₆₇×#2407	2
D₄×C₂²⋊C₄×C₆₇	2
C₄×#127×C₆₇	2
C₄×#124×C₆₇	2
#59412	67

Subgroups — C67×#59412 #30738663

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#59412 #30738663