Subgroups — C₆₇×#34433 #30713684

Order 17152.

2234 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#543×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₆₇×#2378	C₂	1	2	yes	maximal, complemented
3	C₆₇×#2378	C₂	1	2	yes	maximal, complemented
4	C₆₇×#2368	C₂	1	2	yes	maximal, complemented
5	C₆₇×#2362	C₂	1	2	yes	maximal, complemented
6	C₆₇×#2362	C₂	1	2	yes	maximal, complemented
7	C₆₇×#2360	C₂	1	2	yes	maximal, complemented
8	C₆₇×#2342	C₂	1	2	yes	maximal
9	C₆₇×#2342	C₂	1	2	yes	maximal
10	C₆₇×#2332	C₂	1	2	yes	maximal, complemented
11	C₆₇×#2332	C₂	1	2	yes	maximal, complemented
12	C₆₇×#2329	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#2329	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#2323	C₂	1	2	yes	maximal, complemented
15	C₆₇×#2323	C₂	1	2	yes	maximal, complemented
16	C₆₇×#2312	C₂	1	1	yes	maximal, characteristic
17	C₄×C₂²⋊Q₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×C₂²⋊Q₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×#388×C₆₇	C₂	1	1	yes	maximal, characteristic
20	#543×C₆₇	C₄	1	16	yes	complemented
21	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
22	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
23	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
24	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
25	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
26	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
27	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
28	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₄×Q₈×C₆₇	C₂²	1	2	yes	complemented
31	C₂×#117×C₆₇	C₂²	1	2	yes	—
32	C₂×#117×C₆₇	C₂²	1	2	yes	—
33	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
34	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
35	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
36	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
37	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
38	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
39	#391×C₆₇	C₂²	1	1	yes	characteristic, complemented
40	#391×C₆₇	C₂²	1	1	yes	characteristic, complemented
41	#391×C₆₇	C₂²	1	2	yes	complemented
42	#391×C₆₇	C₂²	1	2	yes	complemented
43	#391×C₆₇	C₂²	1	2	yes	complemented
44	#391×C₆₇	C₂²	1	2	yes	complemented
45	#391×C₆₇	C₂²	1	2	yes	complemented
46	#389×C₆₇	C₂²	1	1	yes	characteristic, complemented
47	#389×C₆₇	C₂²	1	1	yes	characteristic, complemented
48	#389×C₆₇	C₂²	1	2	yes	complemented
49	#389×C₆₇	C₂²	1	2	yes	complemented
50	#389×C₆₇	C₂²	1	2	yes	complemented
51	#389×C₆₇	C₂²	1	2	yes	complemented
52	#389×C₆₇	C₂²	1	2	yes	complemented
53	#388×C₆₇	C₂²	1	2	yes	—
54	#388×C₆₇	C₂²	1	2	yes	—
55	#388×C₆₇	C₂²	1	2	yes	—
56	#388×C₆₇	C₂²	1	2	yes	—
57	#388×C₆₇	C₂²	1	2	yes	—
58	#388×C₆₇	C₂²	1	2	yes	—
59	#388×C₆₇	C₂²	1	2	yes	—
60	#388×C₆₇	C₂²	1	2	yes	—
61	#388×C₆₇	C₂²	1	2	yes	—
62	#388×C₆₇	C₂²	1	2	yes	—
63	#388×C₆₇	C₂²	1	2	yes	—
64	#388×C₆₇	C₂²	1	2	yes	—
65	#388×C₆₇	C₂²	1	2	yes	—
66	#388×C₆₇	C₂²	1	2	yes	—
67	#388×C₆₇	C₂²	1	2	yes	—
68	#388×C₆₇	C₂²	1	2	yes	—
69	#387×C₆₇	C₂²	1	2	yes	complemented
70	#387×C₆₇	C₂²	1	2	yes	complemented
71	#387×C₆₇	C₂²	1	2	yes	complemented
72	#387×C₆₇	C₂²	1	2	yes	complemented
73	#387×C₆₇	C₂²	1	2	yes	complemented
74	#387×C₆₇	C₂²	1	2	yes	complemented
75	#387×C₆₇	C₂²	1	2	yes	complemented
76	#387×C₆₇	C₂²	1	2	yes	complemented
77	#387×C₆₇	C₂²	1	2	yes	complemented
78	#387×C₆₇	C₂²	1	2	yes	complemented
79	#387×C₆₇	C₂²	1	2	yes	complemented
80	#387×C₆₇	C₂²	1	2	yes	complemented
81	#385×C₆₇	C₂²	1	2	yes	—
82	#385×C₆₇	C₂²	1	2	yes	—
83	#385×C₆₇	C₂²	1	2	yes	—
84	#385×C₆₇	C₂²	1	2	yes	—
85	#381×C₆₇	C₂²	1	2	yes	—
86	#381×C₆₇	C₂²	1	2	yes	—
87	#380×C₆₇	C₂²	1	1	yes	characteristic
88	#380×C₆₇	C₂²	1	1	yes	characteristic
89	#380×C₆₇	C₂²	1	2	yes	—
90	#380×C₆₇	C₂²	1	2	yes	—
91	#379×C₆₇	C₂²	1	2	yes	—
92	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	complemented
93	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
94	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
95	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	complemented
96	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	complemented
97	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	complemented
98	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	complemented
99	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
100	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
101	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
102	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
103	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
104	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
105	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
106	C₂×#95×C₆₇	C₂²	1	1	yes	characteristic
107	C₂×#95×C₆₇	C₂²	1	1	yes	characteristic
108	C₂⁵×C₆₇	C₂³	1	1	yes	characteristic
109	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
110	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
111	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
112	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
113	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
114	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
115	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
116	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
117	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
118	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
119	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
120	C₂²⋊Q₈×C₆₇	C₂×C₄	1	8	yes	—
121	C₂²⋊Q₈×C₆₇	C₂×C₄	1	8	yes	—
122	C₂²⋊Q₈×C₆₇	C₂×C₄	1	16	yes	—
123	C₂²⋊Q₈×C₆₇	C₂×C₄	1	16	yes	complemented
124	C₂²⋊Q₈×C₆₇	C₂×C₄	1	16	yes	complemented
125	C₂²⋊Q₈×C₆₇	C₂×C₄	1	16	yes	complemented
126	C₂²⋊Q₈×C₆₇	C₂×C₄	1	16	yes	complemented
127	C₄×Q₈×C₆₇	—	4	2	no	—
128	C₄×Q₈×C₆₇	—	4	2	no	—
129	C₄×Q₈×C₆₇	—	4	4	no	—
130	#117×C₆₇	—	4	4	no	—
131	#117×C₆₇	—	4	4	no	—
132	C₂×C₄⋊C₄×C₆₇	—	4	2	no	—
133	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
134	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
135	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
136	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
137	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
138	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
139	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
140	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
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	2	yes	—
144	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
145	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
146	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
147	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
148	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
149	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
150	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
151	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
152	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
153	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
154	C₂×C₂²⋊C₄×C₆₇	—	4	2	no	—
155	C₂×C₂²⋊C₄×C₆₇	—	4	2	no	—
156	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	16	yes	—
157	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	8	yes	—
158	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
159	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
160	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	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	2	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	2	yes	—
167	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
168	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
169	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	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×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
174	C₂×C₄²×C₆₇	—	4	2	no	—
175	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
176	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
177	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
178	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
179	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
180	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
181	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
182	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
183	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
184	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
185	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
186	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
187	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
188	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
189	#95×C₆₇	C₂³	1	2	yes	—
190	#95×C₆₇	C₂³	1	2	yes	—
191	#95×C₆₇	C₂³	1	2	yes	—
192	#95×C₆₇	C₂³	1	2	yes	—
193	#95×C₆₇	C₂³	1	2	yes	—
194	#95×C₆₇	C₂³	1	2	yes	—
195	#95×C₆₇	C₂³	1	2	yes	—
196	#95×C₆₇	C₂³	1	2	yes	—
197	#95×C₆₇	C₂³	1	2	yes	—
198	#95×C₆₇	C₂³	1	2	yes	—
199	#95×C₆₇	C₂³	1	2	yes	—
200	#95×C₆₇	C₂³	1	2	yes	—
201	#95×C₆₇	C₂³	1	2	yes	—
202	#95×C₆₇	C₂³	1	2	yes	—
203	#95×C₆₇	C₂³	1	2	yes	—
204	#95×C₆₇	C₂³	1	2	yes	—
205	#95×C₆₇	C₂³	1	2	yes	—
206	#95×C₆₇	C₂³	1	2	yes	—
207	#95×C₆₇	C₂³	1	2	yes	—
208	#95×C₆₇	C₂³	1	2	yes	—
209	#95×C₆₇	C₂³	1	2	yes	—
210	#95×C₆₇	C₂³	1	2	yes	—
211	#95×C₆₇	C₂³	1	2	yes	—
212	#95×C₆₇	C₂³	1	2	yes	—
213	C₂⁴×C₆₇	—	2	2	no	—
214	C₂⁴×C₆₇	—	2	2	no	—
215	C₂⁴×C₆₇	—	4	1	no	—
216	C₂⁴×C₆₇	—	4	1	no	—
217	C₂⁴×C₆₇	—	4	1	no	—
218	C₂⁴×C₆₇	—	4	1	no	—
219	C₂⁴×C₆₇	C₂²×C₄	1	4	yes	—
220	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
221	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
222	C₂×Q₈×C₆₇	—	4	1	no	—
223	C₂×Q₈×C₆₇	—	4	1	no	—
224	C₂×Q₈×C₆₇	—	4	2	no	—
225	C₂×Q₈×C₆₇	—	4	2	no	—
226	C₂×Q₈×C₆₇	—	4	1	no	—
227	C₂×Q₈×C₆₇	—	4	1	no	—
228	C₂×Q₈×C₆₇	C₂²×C₄	1	4	yes	—
229	C₂×Q₈×C₆₇	C₂²×C₄	1	4	yes	—
230	C₂×Q₈×C₆₇	C₂²×C₄	1	8	yes	—
231	C₂²×C₄×C₆₇	—	2	2	no	—
232	C₂²×C₄×C₆₇	—	2	2	no	—
233	C₂²×C₄×C₆₇	—	2	2	no	—
234	C₂²×C₄×C₆₇	—	2	2	no	—
235	C₂²×C₄×C₆₇	—	2	2	no	—
236	C₂²×C₄×C₆₇	—	2	2	no	—
237	C₂²×C₄×C₆₇	—	4	1	no	—
238	C₂²×C₄×C₆₇	—	4	1	no	—
239	C₂²×C₄×C₆₇	—	4	1	no	—
240	C₂²×C₄×C₆₇	—	4	2	no	—
241	C₂²×C₄×C₆₇	—	4	2	no	—
242	C₂²×C₄×C₆₇	—	4	1	no	—
243	C₂²×C₄×C₆₇	—	4	1	no	—
244	C₂²×C₄×C₆₇	—	4	2	no	—
245	C₂²×C₄×C₆₇	—	4	2	no	—
246	C₂²×C₄×C₆₇	—	4	1	no	—
247	C₂²×C₄×C₆₇	—	4	1	no	—
248	C₂²×C₄×C₆₇	—	4	1	no	—
249	C₂²×C₄×C₆₇	—	4	1	no	—
250	C₂²×C₄×C₆₇	—	4	1	no	—
251	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
252	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
253	C₂²×C₄×C₆₇	C₂²×C₄	1	8	yes	—
254	C₂²×C₄×C₆₇	C₂²×C₄	1	8	yes	—
255	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
256	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
257	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
258	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
259	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
260	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
261	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
262	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
263	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
264	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
265	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
266	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
267	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
268	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
269	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
270	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
271	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
272	C₄⋊C₄×C₆₇	—	2	4	no	—
273	C₄⋊C₄×C₆₇	—	2	4	no	—
274	C₄⋊C₄×C₆₇	—	2	4	no	—
275	C₄⋊C₄×C₆₇	—	4	2	no	—
276	C₄⋊C₄×C₆₇	—	4	1	no	—
277	C₄⋊C₄×C₆₇	—	4	2	no	—
278	C₄⋊C₄×C₆₇	—	4	2	no	—
279	C₄⋊C₄×C₆₇	—	4	1	no	—
280	C₄⋊C₄×C₆₇	—	4	2	no	—
281	C₄⋊C₄×C₆₇	—	4	2	no	—
282	C₄⋊C₄×C₆₇	—	4	2	no	—
283	C₄⋊C₄×C₆₇	—	4	1	no	—
284	C₄⋊C₄×C₆₇	—	4	1	no	—
285	C₄⋊C₄×C₆₇	—	4	2	no	—
286	C₄⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
287	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
288	C₄⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
289	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
290	C₄⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
291	C₄⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
292	C₄⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
293	C₂²⋊C₄×C₆₇	—	2	4	no	—
294	C₂²⋊C₄×C₆₇	—	2	4	no	—
295	C₂²⋊C₄×C₆₇	—	2	4	no	—
296	C₂²⋊C₄×C₆₇	—	2	4	no	—
297	C₂²⋊C₄×C₆₇	—	4	2	no	—
298	C₂²⋊C₄×C₆₇	—	4	2	no	—
299	C₂²⋊C₄×C₆₇	—	4	2	no	—
300	C₂²⋊C₄×C₆₇	—	4	2	no	—
301	C₂²⋊C₄×C₆₇	—	4	2	no	—
302	C₂²⋊C₄×C₆₇	—	4	2	no	—
303	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
304	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
305	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
306	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
307	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
308	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
309	C₄²×C₆₇	—	2	2	no	—
310	C₄²×C₆₇	—	2	2	no	—
311	C₄²×C₆₇	—	2	4	no	—
312	C₄²×C₆₇	—	2	4	no	—
313	C₄²×C₆₇	—	4	1	no	—
314	C₄²×C₆₇	—	4	1	no	—
315	C₄²×C₆₇	—	4	2	no	—
316	C₄²×C₆₇	—	4	2	no	—
317	C₄²×C₆₇	—	4	2	no	—
318	C₄²×C₆₇	—	4	2	no	—
319	C₄²×C₆₇	—	4	2	no	—
320	C₄²×C₆₇	—	4	2	no	—
321	C₄²×C₆₇	—	4	2	no	—
322	C₄²×C₆₇	—	4	2	no	—
323	C₂³×C₆₇	—	2	1	no	—
324	C₂³×C₆₇	—	2	1	no	—
325	C₂³×C₆₇	—	2	1	no	—
326	C₂³×C₆₇	—	2	1	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	8	no	—
334	C₂³×C₆₇	—	4	4	no	—
335	C₂³×C₆₇	—	4	4	no	—
336	C₂³×C₆₇	—	8	2	no	—
337	C₂³×C₆₇	—	8	2	no	—
338	C₂³×C₆₇	—	8	2	no	—
339	C₂³×C₆₇	—	8	2	no	—
340	C₂³×C₆₇	C₂³×C₄	1	4	yes	—
341	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
342	C₂³×C₆₇	2₋¹⁺⁴	1	2	yes	—
343	C₂³×C₆₇	2₋¹⁺⁴	1	2	yes	—
344	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
345	Q₈×C₆₇	—	4	4	no	—
346	Q₈×C₆₇	—	4	4	no	—
347	Q₈×C₆₇	—	4	8	no	—
348	C₂×C₄×C₆₇	—	2	1	no	—
349	C₂×C₄×C₆₇	—	2	1	no	—
350	C₂×C₄×C₆₇	—	2	1	no	—
351	C₂×C₄×C₆₇	—	2	2	no	—
352	C₂×C₄×C₆₇	—	2	2	no	—
353	C₂×C₄×C₆₇	—	2	2	no	—
354	C₂×C₄×C₆₇	—	2	2	no	—
355	C₂×C₄×C₆₇	—	2	2	no	—
356	C₂×C₄×C₆₇	—	2	1	no	—
357	C₂×C₄×C₆₇	—	2	1	no	—
358	C₂×C₄×C₆₇	—	2	1	no	—
359	C₂×C₄×C₆₇	—	2	2	no	—
360	C₂×C₄×C₆₇	—	2	2	no	—
361	C₂×C₄×C₆₇	—	2	2	no	—
362	C₂×C₄×C₆₇	—	2	2	no	—
363	C₂×C₄×C₆₇	—	2	1	no	—
364	C₂×C₄×C₆₇	—	2	2	no	—
365	C₂×C₄×C₆₇	—	2	1	no	—
366	C₂×C₄×C₆₇	—	2	2	no	—
367	C₂×C₄×C₆₇	—	2	1	no	—
368	C₂×C₄×C₆₇	—	2	2	no	—
369	C₂×C₄×C₆₇	—	2	1	no	—
370	C₂×C₄×C₆₇	—	2	2	no	—
371	C₂×C₄×C₆₇	—	2	2	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	1	no	—
376	C₂×C₄×C₆₇	—	2	2	no	—
377	C₂×C₄×C₆₇	—	2	2	no	—
378	C₂×C₄×C₆₇	—	2	2	no	—
379	C₂×C₄×C₆₇	—	2	2	no	—
380	C₂×C₄×C₆₇	—	2	1	no	—
381	C₂×C₄×C₆₇	—	2	1	no	—
382	C₂×C₄×C₆₇	—	2	2	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	2	no	—
387	C₂×C₄×C₆₇	—	2	2	no	—
388	C₂×C₄×C₆₇	—	2	2	no	—
389	C₂×C₄×C₆₇	—	2	1	no	—
390	C₂×C₄×C₆₇	—	4	4	no	—
391	C₂×C₄×C₆₇	—	4	4	no	—
392	C₂×C₄×C₆₇	—	4	8	no	—
393	C₂×C₄×C₆₇	—	4	8	no	—
394	C₂×C₄×C₆₇	—	4	4	no	—
395	C₂×C₄×C₆₇	—	4	4	no	—
396	C₂×C₄×C₆₇	—	8	2	no	—
397	C₂×C₄×C₆₇	—	8	2	no	—
398	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
399	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
400	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
401	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
402	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
403	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
404	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
405	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
406	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
407	C₂²×C₆₇	—	2	2	no	—
408	C₂²×C₆₇	—	2	2	no	—
409	C₂²×C₆₇	—	2	2	no	—
410	C₂²×C₆₇	—	2	2	no	—
411	C₂²×C₆₇	—	2	2	no	—
412	C₂²×C₆₇	—	2	2	no	—
413	C₂²×C₆₇	—	2	4	no	—
414	C₂²×C₆₇	—	2	4	no	—
415	C₂²×C₆₇	—	2	4	no	—
416	C₂²×C₆₇	—	4	2	no	—
417	C₂²×C₆₇	—	4	2	no	—
418	C₂²×C₆₇	—	4	2	no	—
419	C₂²×C₆₇	—	4	2	no	—
420	C₂²×C₆₇	—	8	8	no	—
421	C₂²×C₆₇	#519	1	4	yes	—
422	C₂²×C₆₇	C₂⁴×C₄	1	1	yes	characteristic
423	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
424	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
425	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
426	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
427	C₂²×C₆₇	#585	1	1	yes	characteristic
428	C₂²×C₆₇	#585	1	1	yes	characteristic
429	C₄×C₆₇	—	2	2	no	—
430	C₄×C₆₇	—	2	2	no	—
431	C₄×C₆₇	—	2	4	no	—
432	C₄×C₆₇	—	2	4	no	—
433	C₄×C₆₇	—	2	4	no	—
434	C₄×C₆₇	—	2	4	no	—
435	C₄×C₆₇	—	2	4	no	—
436	C₄×C₆₇	—	2	2	no	—
437	C₄×C₆₇	—	2	2	no	—
438	C₄×C₆₇	—	4	2	no	—
439	C₄×C₆₇	—	4	1	no	—
440	C₄×C₆₇	—	4	2	no	—
441	C₄×C₆₇	—	4	1	no	—
442	C₄×C₆₇	—	4	2	no	—
443	C₄×C₆₇	—	4	2	no	—
444	C₄×C₆₇	—	4	2	no	—
445	C₄×C₆₇	—	4	2	no	—
446	#34433	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
447	C₂×C₆₇	—	2	4	no	—
448	C₂×C₆₇	—	4	4	no	—
449	C₂×C₆₇	C₂×#519	1	1	yes	characteristic
450	C₂×C₆₇	C₄×H(5,𝔽₂)	1	1	yes	characteristic
451	C₂×C₆₇	C₄×H(5,𝔽₂)	1	1	yes	characteristic
452	C₂×C₆₇	#3535	1	1	yes	characteristic
453	C₂×C₆₇	#3536	1	1	yes	characteristic
454	C₂×C₆₇	#3561	1	1	yes	characteristic
455	C₂×C₆₇	#3564	1	1	yes	characteristic
456	C₂×#543	C₂×C₆₇	1	1	yes	characteristic
457	#2378	C₂×C₆₇	1	2	yes	complemented
458	#2378	C₂×C₆₇	1	2	yes	complemented
459	#2368	C₂×C₆₇	1	2	yes	complemented
460	#2362	C₂×C₆₇	1	2	yes	complemented
461	#2362	C₂×C₆₇	1	2	yes	complemented
462	#2360	C₂×C₆₇	1	2	yes	complemented
463	#2342	C₂×C₆₇	1	2	yes	—
464	#2342	C₂×C₆₇	1	2	yes	—
465	#2332	C₂×C₆₇	1	2	yes	complemented
466	#2332	C₂×C₆₇	1	2	yes	complemented
467	#2329	C₂×C₆₇	1	1	yes	characteristic, complemented
468	#2329	C₂×C₆₇	1	1	yes	characteristic, complemented
469	#2323	C₂×C₆₇	1	2	yes	complemented
470	#2323	C₂×C₆₇	1	2	yes	complemented
471	#2312	C₂×C₆₇	1	1	yes	characteristic
472	C₄×C₂²⋊Q₈	C₂×C₆₇	1	1	yes	characteristic, complemented
473	C₄×C₂²⋊Q₈	C₂×C₆₇	1	1	yes	characteristic, complemented
474	C₂×#388	C₂×C₆₇	1	1	yes	characteristic
475	C₆₇	#34433	1	1	yes	characteristic, direct product factor, Sylow
476	#543	C₄×C₆₇	1	16	yes	complemented
477	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
478	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
479	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
480	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
481	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
482	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
483	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
484	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
485	C₂×C₄×Q₈	C₂²×C₆₇	1	2	yes	complemented
486	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
487	C₂×#117	C₂²×C₆₇	1	2	yes	—
488	C₂×#117	C₂²×C₆₇	1	2	yes	—
489	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
490	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
491	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
492	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
493	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
494	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
495	#391	C₂²×C₆₇	1	2	yes	complemented
496	#391	C₂²×C₆₇	1	2	yes	complemented
497	#391	C₂²×C₆₇	1	2	yes	complemented
498	#391	C₂²×C₆₇	1	1	yes	characteristic, complemented
499	#391	C₂²×C₆₇	1	2	yes	complemented
500	#391	C₂²×C₆₇	1	2	yes	complemented
501	#391	C₂²×C₆₇	1	1	yes	characteristic, complemented
502	#389	C₂²×C₆₇	1	2	yes	complemented
503	#389	C₂²×C₆₇	1	1	yes	characteristic, complemented
504	#389	C₂²×C₆₇	1	2	yes	complemented
505	#389	C₂²×C₆₇	1	2	yes	complemented
506	#389	C₂²×C₆₇	1	2	yes	complemented
507	#389	C₂²×C₆₇	1	2	yes	complemented
508	#389	C₂²×C₆₇	1	1	yes	characteristic, complemented
509	#388	C₂²×C₆₇	1	2	yes	—
510	#388	C₂²×C₆₇	1	2	yes	—
511	#388	C₂²×C₆₇	1	2	yes	—
512	#388	C₂²×C₆₇	1	2	yes	—
513	#388	C₂²×C₆₇	1	2	yes	—
514	#388	C₂²×C₆₇	1	2	yes	—
515	#388	C₂²×C₆₇	1	2	yes	—
516	#388	C₂²×C₆₇	1	2	yes	—
517	#388	C₂²×C₆₇	1	2	yes	—
518	#388	C₂²×C₆₇	1	2	yes	—
519	#388	C₂²×C₆₇	1	2	yes	—
520	#388	C₂²×C₆₇	1	2	yes	—
521	#388	C₂²×C₆₇	1	2	yes	—
522	#388	C₂²×C₆₇	1	2	yes	—
523	#388	C₂²×C₆₇	1	2	yes	—
524	#388	C₂²×C₆₇	1	2	yes	—
525	#387	C₂²×C₆₇	1	2	yes	complemented
526	#387	C₂²×C₆₇	1	2	yes	complemented
527	#387	C₂²×C₆₇	1	2	yes	complemented
528	#387	C₂²×C₆₇	1	2	yes	complemented
529	#387	C₂²×C₆₇	1	2	yes	complemented
530	#387	C₂²×C₆₇	1	2	yes	complemented
531	#387	C₂²×C₆₇	1	2	yes	complemented
532	#387	C₂²×C₆₇	1	2	yes	complemented
533	#387	C₂²×C₆₇	1	2	yes	complemented
534	#387	C₂²×C₆₇	1	2	yes	complemented
535	#387	C₂²×C₆₇	1	2	yes	complemented
536	#387	C₂²×C₆₇	1	2	yes	complemented
537	#385	C₂²×C₆₇	1	2	yes	—
538	#385	C₂²×C₆₇	1	2	yes	—
539	#385	C₂²×C₆₇	1	2	yes	—
540	#385	C₂²×C₆₇	1	2	yes	—
541	#381	C₂²×C₆₇	1	2	yes	—
542	#381	C₂²×C₆₇	1	2	yes	—
543	#380	C₂²×C₆₇	1	1	yes	characteristic
544	#380	C₂²×C₆₇	1	1	yes	characteristic
545	#380	C₂²×C₆₇	1	2	yes	—
546	#380	C₂²×C₆₇	1	2	yes	—
547	#379	C₂²×C₆₇	1	2	yes	—
548	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	complemented
549	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	complemented
550	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
551	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	complemented
552	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	complemented
553	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
554	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	complemented
555	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
556	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
557	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
558	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
559	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
560	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
561	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
562	C₂×#95	C₂²×C₆₇	1	1	yes	characteristic
563	C₂×#95	C₂²×C₆₇	1	1	yes	characteristic
564	C₂⁵	C₂³×C₆₇	1	1	yes	characteristic
565	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
566	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
567	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
568	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
569	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
570	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
571	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
572	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
573	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
574	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
575	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
576	C₂²⋊Q₈	C₂×C₄×C₆₇	1	8	yes	—
577	C₂²⋊Q₈	C₂×C₄×C₆₇	1	8	yes	—
578	C₂²⋊Q₈	C₂×C₄×C₆₇	1	16	yes	—
579	C₂²⋊Q₈	C₂×C₄×C₆₇	1	16	yes	complemented
580	C₂²⋊Q₈	C₂×C₄×C₆₇	1	16	yes	complemented
581	C₂²⋊Q₈	C₂×C₄×C₆₇	1	16	yes	complemented
582	C₂²⋊Q₈	C₂×C₄×C₆₇	1	16	yes	complemented
583	C₄×Q₈	—	4	2	no	—
584	C₄×Q₈	—	4	2	no	—
585	C₄×Q₈	—	4	4	no	—
586	#117	—	4	4	no	—
587	#117	—	4	4	no	—
588	C₂×C₄⋊C₄	—	4	2	no	—
589	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
590	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
591	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
592	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
593	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
594	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
595	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
596	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
597	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
598	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
599	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
600	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
601	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
602	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
603	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
604	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
605	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
606	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
607	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
608	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
609	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
610	C₂×C₂²⋊C₄	—	4	2	no	—
611	C₂×C₂²⋊C₄	—	4	2	no	—
612	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	16	yes	—
613	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	8	yes	—
614	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
615	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
616	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
617	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
618	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
619	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
620	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	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	2	yes	—
624	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
625	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	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	2	yes	—
629	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
630	C₂×C₄²	—	4	2	no	—
631	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
632	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
633	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
634	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
635	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
636	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
637	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
638	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
639	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
640	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
641	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
642	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
643	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
644	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
645	#95	C₂³×C₆₇	1	2	yes	—
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	2	yes	—
651	#95	C₂³×C₆₇	1	2	yes	—
652	#95	C₂³×C₆₇	1	2	yes	—
653	#95	C₂³×C₆₇	1	2	yes	—
654	#95	C₂³×C₆₇	1	2	yes	—
655	#95	C₂³×C₆₇	1	2	yes	—
656	#95	C₂³×C₆₇	1	2	yes	—
657	#95	C₂³×C₆₇	1	2	yes	—
658	#95	C₂³×C₆₇	1	2	yes	—
659	#95	C₂³×C₆₇	1	2	yes	—
660	#95	C₂³×C₆₇	1	2	yes	—
661	#95	C₂³×C₆₇	1	2	yes	—
662	#95	C₂³×C₆₇	1	2	yes	—
663	#95	C₂³×C₆₇	1	2	yes	—
664	#95	C₂³×C₆₇	1	2	yes	—
665	#95	C₂³×C₆₇	1	2	yes	—
666	#95	C₂³×C₆₇	1	2	yes	—
667	#95	C₂³×C₆₇	1	2	yes	—
668	#95	C₂³×C₆₇	1	2	yes	—
669	C₂⁴	—	2	2	no	—
670	C₂⁴	—	2	2	no	—
671	C₂⁴	—	4	1	no	—
672	C₂⁴	—	4	1	no	—
673	C₂⁴	—	4	1	no	—
674	C₂⁴	—	4	1	no	—
675	C₂⁴	C₂²×C₄×C₆₇	1	4	yes	—
676	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
677	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
678	C₂×Q₈	—	4	1	no	—
679	C₂×Q₈	—	4	1	no	—
680	C₂×Q₈	—	4	2	no	—
681	C₂×Q₈	—	4	2	no	—
682	C₂×Q₈	—	4	1	no	—
683	C₂×Q₈	—	4	1	no	—
684	C₂×Q₈	C₂²×C₄×C₆₇	1	4	yes	—
685	C₂×Q₈	C₂²×C₄×C₆₇	1	4	yes	—
686	C₂×Q₈	C₂²×C₄×C₆₇	1	8	yes	—
687	C₂²×C₄	—	2	2	no	—
688	C₂²×C₄	—	2	2	no	—
689	C₂²×C₄	—	2	2	no	—
690	C₂²×C₄	—	2	2	no	—
691	C₂²×C₄	—	2	2	no	—
692	C₂²×C₄	—	2	2	no	—
693	C₂²×C₄	—	4	1	no	—
694	C₂²×C₄	—	4	1	no	—
695	C₂²×C₄	—	4	1	no	—
696	C₂²×C₄	—	4	2	no	—
697	C₂²×C₄	—	4	2	no	—
698	C₂²×C₄	—	4	1	no	—
699	C₂²×C₄	—	4	1	no	—
700	C₂²×C₄	—	4	2	no	—
701	C₂²×C₄	—	4	2	no	—
702	C₂²×C₄	—	4	1	no	—
703	C₂²×C₄	—	4	1	no	—
704	C₂²×C₄	—	4	1	no	—
705	C₂²×C₄	—	4	1	no	—
706	C₂²×C₄	—	4	1	no	—
707	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
708	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
709	C₂²×C₄	C₂²×C₄×C₆₇	1	8	yes	—
710	C₂²×C₄	C₂²×C₄×C₆₇	1	8	yes	—
711	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
712	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
713	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
714	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
715	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
716	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
717	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
718	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
719	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
720	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
721	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
722	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
723	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
724	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
725	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
726	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
727	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
728	C₄⋊C₄	—	2	4	no	—
729	C₄⋊C₄	—	2	4	no	—
730	C₄⋊C₄	—	2	4	no	—
731	C₄⋊C₄	—	4	2	no	—
732	C₄⋊C₄	—	4	2	no	—
733	C₄⋊C₄	—	4	2	no	—
734	C₄⋊C₄	—	4	2	no	—
735	C₄⋊C₄	—	4	1	no	—
736	C₄⋊C₄	—	4	1	no	—
737	C₄⋊C₄	—	4	2	no	—
738	C₄⋊C₄	—	4	1	no	—
739	C₄⋊C₄	—	4	2	no	—
740	C₄⋊C₄	—	4	2	no	—
741	C₄⋊C₄	—	4	1	no	—
742	C₄⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
743	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
744	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
745	C₄⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
746	C₄⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
747	C₄⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
748	C₄⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
749	C₂²⋊C₄	—	2	4	no	—
750	C₂²⋊C₄	—	2	4	no	—
751	C₂²⋊C₄	—	2	4	no	—
752	C₂²⋊C₄	—	2	4	no	—
753	C₂²⋊C₄	—	4	2	no	—
754	C₂²⋊C₄	—	4	2	no	—
755	C₂²⋊C₄	—	4	2	no	—
756	C₂²⋊C₄	—	4	2	no	—
757	C₂²⋊C₄	—	4	2	no	—
758	C₂²⋊C₄	—	4	2	no	—
759	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
760	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
761	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
762	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
763	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
764	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
765	C₄²	—	2	2	no	—
766	C₄²	—	2	2	no	—
767	C₄²	—	2	4	no	—
768	C₄²	—	2	4	no	—
769	C₄²	—	4	1	no	—
770	C₄²	—	4	1	no	—
771	C₄²	—	4	2	no	—
772	C₄²	—	4	2	no	—
773	C₄²	—	4	2	no	—
774	C₄²	—	4	2	no	—
775	C₄²	—	4	2	no	—
776	C₄²	—	4	2	no	—
777	C₄²	—	4	2	no	—
778	C₄²	—	4	2	no	—
779	C₂³	—	2	1	no	—
780	C₂³	—	2	1	no	—
781	C₂³	—	2	1	no	—
782	C₂³	—	2	1	no	—
783	C₂³	—	2	2	no	—
784	C₂³	—	2	2	no	—
785	C₂³	—	2	2	no	—
786	C₂³	—	2	2	no	—
787	C₂³	—	2	2	no	—
788	C₂³	—	2	2	no	—
789	C₂³	—	2	8	no	—
790	C₂³	—	4	4	no	—
791	C₂³	—	4	4	no	—
792	C₂³	—	8	2	no	—
793	C₂³	—	8	2	no	—
794	C₂³	—	8	2	no	—
795	C₂³	—	8	2	no	—
796	C₂³	C₂³×C₄×C₆₇	1	4	yes	—
797	C₂³	C₂³×C₄×C₆₇	1	2	yes	—
798	C₂³	2₋¹⁺⁴×C₆₇	1	2	yes	—
799	C₂³	2₋¹⁺⁴×C₆₇	1	2	yes	—
800	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
801	Q₈	—	4	4	no	—
802	Q₈	—	4	4	no	—
803	Q₈	—	4	8	no	—
804	C₂×C₄	—	2	1	no	—
805	C₂×C₄	—	2	1	no	—
806	C₂×C₄	—	2	1	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	1	no	—
813	C₂×C₄	—	2	1	no	—
814	C₂×C₄	—	2	1	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	1	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	1	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	2	1	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	1	no	—
826	C₂×C₄	—	2	2	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	2	2	no	—
830	C₂×C₄	—	2	2	no	—
831	C₂×C₄	—	2	1	no	—
832	C₂×C₄	—	2	2	no	—
833	C₂×C₄	—	2	2	no	—
834	C₂×C₄	—	2	2	no	—
835	C₂×C₄	—	2	2	no	—
836	C₂×C₄	—	2	1	no	—
837	C₂×C₄	—	2	1	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	2	no	—
844	C₂×C₄	—	2	2	no	—
845	C₂×C₄	—	2	1	no	—
846	C₂×C₄	—	4	4	no	—
847	C₂×C₄	—	4	4	no	—
848	C₂×C₄	—	4	8	no	—
849	C₂×C₄	—	4	8	no	—
850	C₂×C₄	—	4	4	no	—
851	C₂×C₄	—	4	4	no	—
852	C₂×C₄	—	8	2	no	—
853	C₂×C₄	—	8	2	no	—
854	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
855	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
856	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
857	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
858	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
859	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
860	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
861	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
862	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
863	C₂²	—	2	2	no	—
864	C₂²	—	2	2	no	—
865	C₂²	—	2	2	no	—
866	C₂²	—	2	2	no	—
867	C₂²	—	2	2	no	—
868	C₂²	—	2	2	no	—
869	C₂²	—	2	4	no	—
870	C₂²	—	2	4	no	—
871	C₂²	—	2	4	no	—
872	C₂²	—	4	2	no	—
873	C₂²	—	4	2	no	—
874	C₂²	—	4	2	no	—
875	C₂²	—	4	2	no	—
876	C₂²	—	8	8	no	—
877	C₂²	#519×C₆₇	1	4	yes	—
878	C₂²	C₂⁴×C₄×C₆₇	1	1	yes	characteristic
879	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
880	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
881	C₂²	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
882	C₂²	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
883	C₂²	#585×C₆₇	1	1	yes	characteristic
884	C₂²	#585×C₆₇	1	1	yes	characteristic
885	C₄	—	2	2	no	—
886	C₄	—	2	2	no	—
887	C₄	—	2	2	no	—
888	C₄	—	2	2	no	—
889	C₄	—	2	4	no	—
890	C₄	—	2	4	no	—
891	C₄	—	2	4	no	—
892	C₄	—	2	4	no	—
893	C₄	—	2	4	no	—
894	C₄	—	4	1	no	—
895	C₄	—	4	2	no	—
896	C₄	—	4	1	no	—
897	C₄	—	4	2	no	—
898	C₄	—	4	2	no	—
899	C₄	—	4	2	no	—
900	C₄	—	4	2	no	—
901	C₄	—	4	2	no	—
902	C₂	—	2	4	no	—
903	C₂	—	4	4	no	—
904	C₂	C₂×#519×C₆₇	1	1	yes	characteristic
905	C₂	C₄×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
906	C₂	C₄×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
907	C₂	C₆₇×#3535	1	1	yes	characteristic
908	C₂	C₆₇×#3536	1	1	yes	characteristic
909	C₂	C₆₇×#3561	1	1	yes	characteristic
910	C₂	C₆₇×#3564	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₆₇
Frattini, cosocle	C₂³	C₂⁵×C₆₇
prime radical	C₂⁵×C₆₇	C₂³
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₆₇×#2378	C₂	semidirect
3. C₆₇×#2378	C₂	semidirect
4. C₆₇×#2368	C₂	semidirect
5. C₆₇×#2362	C₂	semidirect
6. C₆₇×#2362	C₂	semidirect
7. C₆₇×#2360	C₂	semidirect
10. C₆₇×#2332	C₂	semidirect
11. C₆₇×#2332	C₂	semidirect
12. C₆₇×#2329	C₂	semidirect
13. C₆₇×#2329	C₂	semidirect
14. C₆₇×#2323	C₂	semidirect
15. C₆₇×#2323	C₂	semidirect
17. C₄×C₂²⋊Q₈×C₆₇	C₂	semidirect
18. C₄×C₂²⋊Q₈×C₆₇	C₂	semidirect
20. #543×C₆₇	C₄	semidirect
28. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
29. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
30. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
39. #391×C₆₇	C₂²	semidirect
40. #391×C₆₇	C₂²	semidirect
41. #391×C₆₇	C₂²	semidirect
42. #391×C₆₇	C₂²	semidirect
43. #391×C₆₇	C₂²	semidirect
44. #391×C₆₇	C₂²	semidirect
45. #391×C₆₇	C₂²	semidirect
46. #389×C₆₇	C₂²	semidirect
47. #389×C₆₇	C₂²	semidirect
48. #389×C₆₇	C₂²	semidirect
49. #389×C₆₇	C₂²	semidirect
50. #389×C₆₇	C₂²	semidirect
51. #389×C₆₇	C₂²	semidirect
52. #389×C₆₇	C₂²	semidirect
69. #387×C₆₇	C₂²	semidirect
70. #387×C₆₇	C₂²	semidirect
71. #387×C₆₇	C₂²	semidirect
72. #387×C₆₇	C₂²	semidirect
73. #387×C₆₇	C₂²	semidirect
74. #387×C₆₇	C₂²	semidirect
75. #387×C₆₇	C₂²	semidirect
76. #387×C₆₇	C₂²	semidirect
77. #387×C₆₇	C₂²	semidirect
78. #387×C₆₇	C₂²	semidirect
79. #387×C₆₇	C₂²	semidirect
80. #387×C₆₇	C₂²	semidirect
92. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
93. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
94. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
95. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
96. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
97. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
98. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
123. C₂²⋊Q₈×C₆₇	C₂×C₄	semidirect
124. C₂²⋊Q₈×C₆₇	C₂×C₄	semidirect
125. C₂²⋊Q₈×C₆₇	C₂×C₄	semidirect
126. C₂²⋊Q₈×C₆₇	C₂×C₄	semidirect
446. #34433	C₆₇	direct (N × H)
457. #2378	C₂×C₆₇	semidirect
458. #2378	C₂×C₆₇	semidirect
459. #2368	C₂×C₆₇	semidirect
460. #2362	C₂×C₆₇	semidirect
461. #2362	C₂×C₆₇	semidirect
462. #2360	C₂×C₆₇	semidirect
465. #2332	C₂×C₆₇	semidirect
466. #2332	C₂×C₆₇	semidirect
467. #2329	C₂×C₆₇	semidirect
468. #2329	C₂×C₆₇	semidirect
469. #2323	C₂×C₆₇	semidirect
470. #2323	C₂×C₆₇	semidirect
472. C₄×C₂²⋊Q₈	C₂×C₆₇	semidirect
473. C₄×C₂²⋊Q₈	C₂×C₆₇	semidirect
475. C₆₇	#34433	direct (N × H)
476. #543	C₄×C₆₇	semidirect
484. C₂×C₄×Q₈	C₂²×C₆₇	semidirect
485. C₂×C₄×Q₈	C₂²×C₆₇	semidirect
486. C₂×C₄×Q₈	C₂²×C₆₇	semidirect
495. #391	C₂²×C₆₇	semidirect
496. #391	C₂²×C₆₇	semidirect
497. #391	C₂²×C₆₇	semidirect
498. #391	C₂²×C₆₇	semidirect
499. #391	C₂²×C₆₇	semidirect
500. #391	C₂²×C₆₇	semidirect
501. #391	C₂²×C₆₇	semidirect
502. #389	C₂²×C₆₇	semidirect
503. #389	C₂²×C₆₇	semidirect
504. #389	C₂²×C₆₇	semidirect
505. #389	C₂²×C₆₇	semidirect
506. #389	C₂²×C₆₇	semidirect
507. #389	C₂²×C₆₇	semidirect
508. #389	C₂²×C₆₇	semidirect
525. #387	C₂²×C₆₇	semidirect
526. #387	C₂²×C₆₇	semidirect
527. #387	C₂²×C₆₇	semidirect
528. #387	C₂²×C₆₇	semidirect
529. #387	C₂²×C₆₇	semidirect
530. #387	C₂²×C₆₇	semidirect
531. #387	C₂²×C₆₇	semidirect
532. #387	C₂²×C₆₇	semidirect
533. #387	C₂²×C₆₇	semidirect
534. #387	C₂²×C₆₇	semidirect
535. #387	C₂²×C₆₇	semidirect
536. #387	C₂²×C₆₇	semidirect
548. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
549. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
550. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
551. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
552. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
553. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
554. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
579. C₂²⋊Q₈	C₂×C₄×C₆₇	semidirect
580. C₂²⋊Q₈	C₂×C₄×C₆₇	semidirect
581. C₂²⋊Q₈	C₂×C₄×C₆₇	semidirect
582. C₂²⋊Q₈	C₂×C₄×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#543×C₆₇	2
C₆₇×#2378	2
C₆₇×#2368	2
C₆₇×#2362	2
C₆₇×#2360	2
C₆₇×#2342	2
C₆₇×#2332	2
C₆₇×#2329	2
C₆₇×#2323	2
C₆₇×#2312	2
C₄×C₂²⋊Q₈×C₆₇	2
C₂×#388×C₆₇	2
#34433	67

Subgroups — C67×#34433 #30713684

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#34433 #30713684