Subgroups — C₆₇×#34503 #30713754

Order 17152.

2140 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#555×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₆₇×#2381	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#2379	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#2377	C₂	1	2	yes	maximal, complemented
5	C₆₇×#2372	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#2367	C₂	1	2	yes	maximal, complemented
7	C₆₇×#2364	C₂	1	2	yes	maximal, complemented
8	C₆₇×#2353	C₂	1	2	yes	maximal, complemented
9	C₆₇×#2343	C₂	1	2	yes	maximal, complemented
10	C₆₇×#2343	C₂	1	2	yes	maximal, complemented
11	C₆₇×#2337	C₂	1	2	yes	maximal, complemented
12	C₆₇×#2333	C₂	1	2	yes	maximal, complemented
13	C₆₇×#2327	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#2326	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#2325	C₂	1	2	yes	maximal, complemented
16	C₆₇×#2318	C₂	1	2	yes	maximal, complemented
17	C₆₇×#2314	C₂	1	2	yes	maximal, complemented
18	C₄×#124×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₇×#2298	C₂	1	2	yes	maximal, complemented
20	#555×C₆₇	C₄	1	16	yes	complemented
21	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
22	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic
23	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic
24	C₂×#124×C₆₇	C₂²	1	2	yes	—
25	C₂×#121×C₆₇	C₂²	1	2	yes	—
26	C₂×#121×C₆₇	C₂²	1	2	yes	—
27	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
28	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
29	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
31	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
32	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
33	C₂×#117×C₆₇	C₂²	1	2	yes	—
34	C₂×#117×C₆₇	C₂²	1	2	yes	—
35	#391×C₆₇	C₂²	1	1	yes	characteristic
36	#391×C₆₇	C₂²	1	1	yes	characteristic
37	#391×C₆₇	C₂²	1	1	yes	characteristic
38	#391×C₆₇	C₂²	1	1	yes	characteristic
39	#391×C₆₇	C₂²	1	2	yes	—
40	#390×C₆₇	C₂²	1	1	yes	characteristic
41	#390×C₆₇	C₂²	1	1	yes	characteristic
42	#390×C₆₇	C₂²	1	2	yes	—
43	#388×C₆₇	C₂²	1	2	yes	—
44	#388×C₆₇	C₂²	1	2	yes	—
45	#388×C₆₇	C₂²	1	2	yes	—
46	#388×C₆₇	C₂²	1	2	yes	—
47	#388×C₆₇	C₂²	1	2	yes	—
48	#388×C₆₇	C₂²	1	2	yes	—
49	#388×C₆₇	C₂²	1	2	yes	—
50	#388×C₆₇	C₂²	1	2	yes	—
51	#388×C₆₇	C₂²	1	2	yes	—
52	#388×C₆₇	C₂²	1	2	yes	—
53	#388×C₆₇	C₂²	1	2	yes	—
54	#388×C₆₇	C₂²	1	2	yes	—
55	#387×C₆₇	C₂²	1	2	yes	—
56	#387×C₆₇	C₂²	1	2	yes	—
57	#387×C₆₇	C₂²	1	2	yes	—
58	#387×C₆₇	C₂²	1	2	yes	—
59	#387×C₆₇	C₂²	1	2	yes	—
60	#387×C₆₇	C₂²	1	2	yes	—
61	#387×C₆₇	C₂²	1	2	yes	—
62	#387×C₆₇	C₂²	1	2	yes	—
63	#387×C₆₇	C₂²	1	2	yes	—
64	#387×C₆₇	C₂²	1	2	yes	—
65	#387×C₆₇	C₂²	1	2	yes	—
66	#387×C₆₇	C₂²	1	2	yes	—
67	#386×C₆₇	C₂²	1	2	yes	—
68	#386×C₆₇	C₂²	1	2	yes	—
69	#386×C₆₇	C₂²	1	2	yes	—
70	#386×C₆₇	C₂²	1	2	yes	—
71	#386×C₆₇	C₂²	1	2	yes	—
72	#386×C₆₇	C₂²	1	2	yes	—
73	#386×C₆₇	C₂²	1	2	yes	—
74	#386×C₆₇	C₂²	1	2	yes	—
75	#385×C₆₇	C₂²	1	2	yes	—
76	#385×C₆₇	C₂²	1	2	yes	—
77	#385×C₆₇	C₂²	1	2	yes	—
78	#385×C₆₇	C₂²	1	2	yes	—
79	#385×C₆₇	C₂²	1	2	yes	—
80	#385×C₆₇	C₂²	1	2	yes	—
81	#384×C₆₇	C₂²	1	1	yes	characteristic
82	#383×C₆₇	C₂²	1	2	yes	—
83	#383×C₆₇	C₂²	1	2	yes	—
84	#382×C₆₇	C₂²	1	1	yes	characteristic
85	#382×C₆₇	C₂²	1	2	yes	—
86	#382×C₆₇	C₂²	1	1	yes	characteristic
87	#381×C₆₇	C₂²	1	2	yes	—
88	#381×C₆₇	C₂²	1	2	yes	—
89	#380×C₆₇	C₂²	1	2	yes	—
90	#380×C₆₇	C₂²	1	2	yes	—
91	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
92	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
93	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
94	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
95	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
96	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
97	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
98	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
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	#376×C₆₇	C₂²	1	2	yes	—
103	#376×C₆₇	C₂²	1	1	yes	characteristic
104	#376×C₆₇	C₂²	1	1	yes	characteristic
105	C₂×#95×C₆₇	C₂²	1	2	yes	—
106	C₂×#95×C₆₇	C₂²	1	2	yes	—
107	C₄³×C₆₇	C₂²	1	1	yes	characteristic
108	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
109	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
110	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
111	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
112	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
113	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
114	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
115	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
116	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
117	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
118	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
119	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
120	C₄⋊Q₈×C₆₇	C₂×C₄	1	8	yes	complemented
121	#124×C₆₇	C₂×C₄	1	8	yes	complemented
122	#124×C₆₇	C₂×C₄	1	8	yes	complemented
123	#124×C₆₇	C₂×C₄	1	16	yes	complemented
124	#121×C₆₇	C₂×C₄	1	16	yes	complemented
125	#121×C₆₇	C₂×C₄	1	16	yes	complemented
126	C₄×Q₈×C₆₇	—	4	2	no	—
127	C₄×Q₈×C₆₇	—	4	2	no	—
128	C₄×D₄×C₆₇	—	4	2	no	—
129	C₄×D₄×C₆₇	—	4	2	no	—
130	C₄×D₄×C₆₇	—	4	4	no	—
131	C₄×D₄×C₆₇	C₂×C₄	1	16	yes	complemented
132	#117×C₆₇	C₂×C₄	1	16	yes	complemented
133	#117×C₆₇	C₂×C₄	1	16	yes	complemented
134	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
135	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
136	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
137	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
138	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
139	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
140	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
141	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
142	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
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	2	yes	—
146	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
147	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
148	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
149	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
150	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
151	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
152	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
153	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
154	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
155	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	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	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×C₄²×C₆₇	C₂³	1	1	yes	characteristic
168	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
169	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
170	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
171	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
172	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
173	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
174	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
175	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
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	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
182	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
183	#95×C₆₇	C₂³	1	2	yes	—
184	#95×C₆₇	C₂³	1	2	yes	—
185	#95×C₆₇	C₂³	1	2	yes	—
186	#95×C₆₇	C₂³	1	2	yes	—
187	#95×C₆₇	C₂³	1	2	yes	—
188	#95×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	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
210	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
211	C₂×Q₈×C₆₇	—	4	1	no	—
212	C₂×Q₈×C₆₇	—	4	1	no	—
213	C₂×Q₈×C₆₇	—	4	1	no	—
214	C₂×Q₈×C₆₇	—	4	1	no	—
215	C₂×Q₈×C₆₇	C₂²×C₄	1	4	yes	—
216	C₂×Q₈×C₆₇	C₂²×C₄	1	4	yes	—
217	C₂×D₄×C₆₇	—	4	1	no	—
218	C₂×D₄×C₆₇	—	4	1	no	—
219	C₂×D₄×C₆₇	—	4	2	no	—
220	C₂×D₄×C₆₇	—	4	1	no	—
221	C₂×D₄×C₆₇	—	4	1	no	—
222	C₂×D₄×C₆₇	—	4	2	no	—
223	C₂×D₄×C₆₇	—	4	2	no	—
224	C₂×D₄×C₆₇	—	4	2	no	—
225	C₂×D₄×C₆₇	C₂²×C₄	1	8	yes	—
226	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
227	C₂×D₄×C₆₇	C₂²×C₄	1	8	yes	—
228	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
229	C₂²×C₄×C₆₇	—	2	4	no	—
230	C₂²×C₄×C₆₇	—	4	2	no	—
231	C₂²×C₄×C₆₇	—	4	2	no	—
232	C₂²×C₄×C₆₇	—	4	2	no	—
233	C₂²×C₄×C₆₇	—	4	2	no	—
234	C₂²×C₄×C₆₇	—	4	2	no	—
235	C₂²×C₄×C₆₇	—	4	2	no	—
236	C₂²×C₄×C₆₇	—	4	2	no	—
237	C₂²×C₄×C₆₇	—	4	2	no	—
238	C₂²×C₄×C₆₇	—	4	2	no	—
239	C₂²×C₄×C₆₇	—	4	2	no	—
240	C₂²×C₄×C₆₇	—	4	2	no	—
241	C₂²×C₄×C₆₇	—	4	2	no	—
242	C₂²×C₄×C₆₇	—	4	2	no	—
243	C₂²×C₄×C₆₇	—	4	2	no	—
244	C₂²×C₄×C₆₇	—	4	2	no	—
245	C₂²×C₄×C₆₇	C₂²×C₄	1	8	yes	—
246	C₂²×C₄×C₆₇	C₂²×C₄	1	8	yes	—
247	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
248	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
249	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
250	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
251	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
252	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
253	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
254	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
255	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
256	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
257	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
258	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
259	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
260	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
261	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
262	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
263	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
264	C₄⋊C₄×C₆₇	—	2	4	no	—
265	C₄⋊C₄×C₆₇	—	4	2	no	—
266	C₄⋊C₄×C₆₇	—	4	2	no	—
267	C₄⋊C₄×C₆₇	—	4	2	no	—
268	C₄⋊C₄×C₆₇	—	4	2	no	—
269	C₄⋊C₄×C₆₇	—	4	2	no	—
270	C₄⋊C₄×C₆₇	—	4	1	no	—
271	C₄⋊C₄×C₆₇	—	4	1	no	—
272	C₄⋊C₄×C₆₇	—	4	1	no	—
273	C₄⋊C₄×C₆₇	—	4	1	no	—
274	C₄⋊C₄×C₆₇	—	4	1	no	—
275	C₄⋊C₄×C₆₇	—	4	1	no	—
276	C₄⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
277	C₄⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
278	C₄⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
279	C₂²⋊C₄×C₆₇	—	2	4	no	—
280	C₂²⋊C₄×C₆₇	—	4	2	no	—
281	C₂²⋊C₄×C₆₇	—	4	2	no	—
282	C₂²⋊C₄×C₆₇	—	4	2	no	—
283	C₂²⋊C₄×C₆₇	—	4	2	no	—
284	C₂²⋊C₄×C₆₇	—	4	2	no	—
285	C₂²⋊C₄×C₆₇	—	4	2	no	—
286	C₂²⋊C₄×C₆₇	—	4	2	no	—
287	C₂²⋊C₄×C₆₇	—	4	2	no	—
288	C₂²⋊C₄×C₆₇	—	4	2	no	—
289	C₂²⋊C₄×C₆₇	—	4	2	no	—
290	C₂²⋊C₄×C₆₇	—	4	2	no	—
291	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
292	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
293	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
294	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
295	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
296	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
297	C₄²×C₆₇	—	2	2	no	—
298	C₄²×C₆₇	—	2	2	no	—
299	C₄²×C₆₇	—	2	2	no	—
300	C₄²×C₆₇	—	4	2	no	—
301	C₄²×C₆₇	—	4	2	no	—
302	C₄²×C₆₇	—	4	2	no	—
303	C₄²×C₆₇	—	4	2	no	—
304	C₄²×C₆₇	—	4	1	no	—
305	C₄²×C₆₇	—	4	1	no	—
306	C₄²×C₆₇	—	4	1	no	—
307	C₄²×C₆₇	—	4	2	no	—
308	C₄²×C₆₇	—	4	2	no	—
309	C₄²×C₆₇	C₂²×C₄	1	4	yes	—
310	C₄²×C₆₇	C₂²×C₄	1	4	yes	—
311	C₄²×C₆₇	C₂²×C₄	1	8	yes	—
312	C₄²×C₆₇	C₂²×C₄	1	4	yes	—
313	C₂³×C₆₇	—	2	2	no	—
314	C₂³×C₆₇	—	2	2	no	—
315	C₂³×C₆₇	—	2	2	no	—
316	C₂³×C₆₇	—	2	2	no	—
317	C₂³×C₆₇	—	2	2	no	—
318	C₂³×C₆₇	—	2	2	no	—
319	C₂³×C₆₇	—	2	2	no	—
320	C₂³×C₆₇	—	2	2	no	—
321	C₂³×C₆₇	—	2	2	no	—
322	C₂³×C₆₇	—	2	2	no	—
323	C₂³×C₆₇	—	2	2	no	—
324	C₂³×C₆₇	—	2	2	no	—
325	C₂³×C₆₇	C₂³×C₄	1	4	yes	—
326	C₂³×C₆₇	C₂³×C₄	1	4	yes	—
327	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
328	Q₈×C₆₇	—	4	4	no	—
329	Q₈×C₆₇	—	4	4	no	—
330	D₄×C₆₇	—	4	8	no	—
331	D₄×C₆₇	—	4	4	no	—
332	D₄×C₆₇	—	4	4	no	—
333	D₄×C₆₇	—	4	8	no	—
334	C₂×C₄×C₆₇	—	2	1	no	—
335	C₂×C₄×C₆₇	—	2	1	no	—
336	C₂×C₄×C₆₇	—	2	1	no	—
337	C₂×C₄×C₆₇	—	2	2	no	—
338	C₂×C₄×C₆₇	—	2	2	no	—
339	C₂×C₄×C₆₇	—	2	2	no	—
340	C₂×C₄×C₆₇	—	2	2	no	—
341	C₂×C₄×C₆₇	—	2	1	no	—
342	C₂×C₄×C₆₇	—	2	1	no	—
343	C₂×C₄×C₆₇	—	2	1	no	—
344	C₂×C₄×C₆₇	—	2	2	no	—
345	C₂×C₄×C₆₇	—	2	2	no	—
346	C₂×C₄×C₆₇	—	2	2	no	—
347	C₂×C₄×C₆₇	—	2	2	no	—
348	C₂×C₄×C₆₇	—	2	2	no	—
349	C₂×C₄×C₆₇	—	2	1	no	—
350	C₂×C₄×C₆₇	—	2	1	no	—
351	C₂×C₄×C₆₇	—	2	1	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	2	no	—
357	C₂×C₄×C₆₇	—	2	2	no	—
358	C₂×C₄×C₆₇	—	2	2	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	2	no	—
364	C₂×C₄×C₆₇	—	2	2	no	—
365	C₂×C₄×C₆₇	—	2	2	no	—
366	C₂×C₄×C₆₇	—	2	2	no	—
367	C₂×C₄×C₆₇	—	2	2	no	—
368	C₂×C₄×C₆₇	—	2	2	no	—
369	C₂×C₄×C₆₇	—	2	2	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	—	4	8	no	—
374	C₂×C₄×C₆₇	—	4	8	no	—
375	C₂×C₄×C₆₇	—	8	4	no	—
376	C₂×C₄×C₆₇	—	8	4	no	—
377	C₂×C₄×C₆₇	—	8	4	no	—
378	C₂×C₄×C₆₇	—	8	4	no	—
379	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
380	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
381	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
382	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
383	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
384	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
385	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
386	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
387	C₂²×C₆₇	—	2	4	no	—
388	C₂²×C₆₇	—	2	4	no	—
389	C₂²×C₆₇	—	2	4	no	—
390	C₂²×C₆₇	—	2	4	no	—
391	C₂²×C₆₇	—	2	4	no	—
392	C₂²×C₆₇	—	2	4	no	—
393	C₂²×C₆₇	—	4	2	no	—
394	C₂²×C₆₇	—	4	2	no	—
395	C₂²×C₆₇	—	4	2	no	—
396	C₂²×C₆₇	—	4	2	no	—
397	C₂²×C₆₇	—	4	2	no	—
398	C₂²×C₆₇	—	4	2	no	—
399	C₂²×C₆₇	—	4	2	no	—
400	C₂²×C₆₇	—	4	2	no	—
401	C₂²×C₆₇	C₂⁴×C₄	1	1	yes	characteristic
402	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
403	C₂²×C₆₇	#585	1	2	yes	—
404	C₂²×C₆₇	#585	1	2	yes	—
405	C₂²×C₆₇	#585	1	1	yes	characteristic
406	C₄×C₆₇	—	2	4	no	—
407	C₄×C₆₇	—	2	4	no	—
408	C₄×C₆₇	—	2	4	no	—
409	C₄×C₆₇	—	2	2	no	—
410	C₄×C₆₇	—	2	2	no	—
411	C₄×C₆₇	—	2	4	no	—
412	C₄×C₆₇	—	2	2	no	—
413	C₄×C₆₇	—	2	2	no	—
414	C₄×C₆₇	—	4	2	no	—
415	C₄×C₆₇	—	4	2	no	—
416	C₄×C₆₇	—	4	1	no	—
417	C₄×C₆₇	—	4	1	no	—
418	C₄×C₆₇	—	4	2	no	—
419	C₄×C₆₇	—	4	1	no	—
420	C₄×C₆₇	—	4	2	no	—
421	C₄×C₆₇	—	4	2	no	—
422	C₄×C₆₇	—	4	2	no	—
423	#34503	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
424	C₂×C₆₇	—	4	4	no	—
425	C₂×C₆₇	—	4	4	no	—
426	C₂×C₆₇	#3428	1	2	yes	—
427	C₂×C₆₇	C₄×H(5,𝔽₂)	1	1	yes	characteristic
428	C₂×C₆₇	#3545	1	1	yes	characteristic
429	C₂×C₆₇	#3551	1	1	yes	characteristic
430	C₂×C₆₇	#3566	1	2	yes	—
431	C₂×#555	C₂×C₆₇	1	1	yes	characteristic
432	#2381	C₂×C₆₇	1	1	yes	characteristic, complemented
433	#2379	C₂×C₆₇	1	1	yes	characteristic, complemented
434	#2377	C₂×C₆₇	1	2	yes	complemented
435	#2372	C₂×C₆₇	1	1	yes	characteristic, complemented
436	#2367	C₂×C₆₇	1	2	yes	complemented
437	#2364	C₂×C₆₇	1	2	yes	complemented
438	#2353	C₂×C₆₇	1	2	yes	complemented
439	#2343	C₂×C₆₇	1	2	yes	complemented
440	#2343	C₂×C₆₇	1	2	yes	complemented
441	#2337	C₂×C₆₇	1	2	yes	complemented
442	#2333	C₂×C₆₇	1	2	yes	complemented
443	#2327	C₂×C₆₇	1	1	yes	characteristic, complemented
444	#2326	C₂×C₆₇	1	1	yes	characteristic, complemented
445	#2325	C₂×C₆₇	1	2	yes	complemented
446	#2318	C₂×C₆₇	1	2	yes	complemented
447	#2314	C₂×C₆₇	1	2	yes	complemented
448	C₄×#124	C₂×C₆₇	1	1	yes	characteristic, complemented
449	#2298	C₂×C₆₇	1	2	yes	complemented
450	C₆₇	#34503	1	1	yes	characteristic, direct product factor, Sylow
451	#555	C₄×C₆₇	1	16	yes	complemented
452	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
453	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic
454	C₂×#124	C₂²×C₆₇	1	2	yes	—
455	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic
456	C₂×#121	C₂²×C₆₇	1	2	yes	—
457	C₂×#121	C₂²×C₆₇	1	2	yes	—
458	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
459	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
460	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
461	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
462	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
463	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
464	C₂×#117	C₂²×C₆₇	1	2	yes	—
465	C₂×#117	C₂²×C₆₇	1	2	yes	—
466	#391	C₂²×C₆₇	1	1	yes	characteristic
467	#391	C₂²×C₆₇	1	1	yes	characteristic
468	#391	C₂²×C₆₇	1	1	yes	characteristic
469	#391	C₂²×C₆₇	1	2	yes	—
470	#391	C₂²×C₆₇	1	1	yes	characteristic
471	#390	C₂²×C₆₇	1	1	yes	characteristic
472	#390	C₂²×C₆₇	1	2	yes	—
473	#390	C₂²×C₆₇	1	1	yes	characteristic
474	#388	C₂²×C₆₇	1	2	yes	—
475	#388	C₂²×C₆₇	1	2	yes	—
476	#388	C₂²×C₆₇	1	2	yes	—
477	#388	C₂²×C₆₇	1	2	yes	—
478	#388	C₂²×C₆₇	1	2	yes	—
479	#388	C₂²×C₆₇	1	2	yes	—
480	#388	C₂²×C₆₇	1	2	yes	—
481	#388	C₂²×C₆₇	1	2	yes	—
482	#388	C₂²×C₆₇	1	2	yes	—
483	#388	C₂²×C₆₇	1	2	yes	—
484	#388	C₂²×C₆₇	1	2	yes	—
485	#388	C₂²×C₆₇	1	2	yes	—
486	#387	C₂²×C₆₇	1	2	yes	—
487	#387	C₂²×C₆₇	1	2	yes	—
488	#387	C₂²×C₆₇	1	2	yes	—
489	#387	C₂²×C₆₇	1	2	yes	—
490	#387	C₂²×C₆₇	1	2	yes	—
491	#387	C₂²×C₆₇	1	2	yes	—
492	#387	C₂²×C₆₇	1	2	yes	—
493	#387	C₂²×C₆₇	1	2	yes	—
494	#387	C₂²×C₆₇	1	2	yes	—
495	#387	C₂²×C₆₇	1	2	yes	—
496	#387	C₂²×C₆₇	1	2	yes	—
497	#387	C₂²×C₆₇	1	2	yes	—
498	#386	C₂²×C₆₇	1	2	yes	—
499	#386	C₂²×C₆₇	1	2	yes	—
500	#386	C₂²×C₆₇	1	2	yes	—
501	#386	C₂²×C₆₇	1	2	yes	—
502	#386	C₂²×C₆₇	1	2	yes	—
503	#386	C₂²×C₆₇	1	2	yes	—
504	#386	C₂²×C₆₇	1	2	yes	—
505	#386	C₂²×C₆₇	1	2	yes	—
506	#385	C₂²×C₆₇	1	2	yes	—
507	#385	C₂²×C₆₇	1	2	yes	—
508	#385	C₂²×C₆₇	1	2	yes	—
509	#385	C₂²×C₆₇	1	2	yes	—
510	#385	C₂²×C₆₇	1	2	yes	—
511	#385	C₂²×C₆₇	1	2	yes	—
512	#384	C₂²×C₆₇	1	1	yes	characteristic
513	#383	C₂²×C₆₇	1	2	yes	—
514	#383	C₂²×C₆₇	1	2	yes	—
515	#382	C₂²×C₆₇	1	2	yes	—
516	#382	C₂²×C₆₇	1	1	yes	characteristic
517	#382	C₂²×C₆₇	1	1	yes	characteristic
518	#381	C₂²×C₆₇	1	2	yes	—
519	#381	C₂²×C₆₇	1	2	yes	—
520	#380	C₂²×C₆₇	1	2	yes	—
521	#380	C₂²×C₆₇	1	2	yes	—
522	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
523	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
524	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
525	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
526	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
527	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
528	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
529	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
530	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
531	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
532	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
533	#376	C₂²×C₆₇	1	1	yes	characteristic
534	#376	C₂²×C₆₇	1	1	yes	characteristic
535	#376	C₂²×C₆₇	1	2	yes	—
536	C₂×#95	C₂²×C₆₇	1	2	yes	—
537	C₂×#95	C₂²×C₆₇	1	2	yes	—
538	C₄³	C₂²×C₆₇	1	1	yes	characteristic
539	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
540	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
541	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
542	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
543	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
544	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
545	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
546	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
547	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
548	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
549	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
550	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
551	C₄⋊Q₈	C₂×C₄×C₆₇	1	8	yes	complemented
552	#124	C₂×C₄×C₆₇	1	8	yes	complemented
553	#124	C₂×C₄×C₆₇	1	16	yes	complemented
554	#124	C₂×C₄×C₆₇	1	8	yes	complemented
555	#121	C₂×C₄×C₆₇	1	16	yes	complemented
556	#121	C₂×C₄×C₆₇	1	16	yes	complemented
557	C₄×Q₈	—	4	2	no	—
558	C₄×Q₈	—	4	2	no	—
559	C₄×D₄	—	4	2	no	—
560	C₄×D₄	—	4	2	no	—
561	C₄×D₄	—	4	4	no	—
562	C₄×D₄	C₂×C₄×C₆₇	1	16	yes	complemented
563	#117	C₂×C₄×C₆₇	1	16	yes	complemented
564	#117	C₂×C₄×C₆₇	1	16	yes	complemented
565	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
566	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
567	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
568	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
569	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
570	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
571	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
572	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
573	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
574	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
575	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
576	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
577	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
578	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
579	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
580	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
581	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
582	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
583	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
584	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
585	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
586	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
587	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
588	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
589	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
590	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
591	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
592	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
593	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
594	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
595	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
596	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
597	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
598	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
599	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
600	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
601	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
602	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
603	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
604	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
605	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
606	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
607	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
608	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
609	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
610	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
611	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
612	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
613	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
614	#95	C₂³×C₆₇	1	2	yes	—
615	#95	C₂³×C₆₇	1	2	yes	—
616	#95	C₂³×C₆₇	1	2	yes	—
617	#95	C₂³×C₆₇	1	2	yes	—
618	#95	C₂³×C₆₇	1	2	yes	—
619	#95	C₂³×C₆₇	1	2	yes	—
620	#95	C₂³×C₆₇	1	2	yes	—
621	#95	C₂³×C₆₇	1	2	yes	—
622	#95	C₂³×C₆₇	1	2	yes	—
623	#95	C₂³×C₆₇	1	2	yes	—
624	#95	C₂³×C₆₇	1	2	yes	—
625	#95	C₂³×C₆₇	1	2	yes	—
626	#95	C₂³×C₆₇	1	2	yes	—
627	#95	C₂³×C₆₇	1	2	yes	—
628	#95	C₂³×C₆₇	1	2	yes	—
629	#95	C₂³×C₆₇	1	2	yes	—
630	#95	C₂³×C₆₇	1	2	yes	—
631	#95	C₂³×C₆₇	1	2	yes	—
632	#95	C₂³×C₆₇	1	2	yes	—
633	#95	C₂³×C₆₇	1	2	yes	—
634	#95	C₂³×C₆₇	1	2	yes	—
635	#95	C₂³×C₆₇	1	2	yes	—
636	#95	C₂³×C₆₇	1	2	yes	—
637	#95	C₂³×C₆₇	1	2	yes	—
638	#95	C₂³×C₆₇	1	2	yes	—
639	#95	C₂³×C₆₇	1	2	yes	—
640	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
641	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
642	C₂×Q₈	—	4	1	no	—
643	C₂×Q₈	—	4	1	no	—
644	C₂×Q₈	—	4	1	no	—
645	C₂×Q₈	—	4	1	no	—
646	C₂×Q₈	C₂²×C₄×C₆₇	1	4	yes	—
647	C₂×Q₈	C₂²×C₄×C₆₇	1	4	yes	—
648	C₂×D₄	—	4	1	no	—
649	C₂×D₄	—	4	1	no	—
650	C₂×D₄	—	4	2	no	—
651	C₂×D₄	—	4	1	no	—
652	C₂×D₄	—	4	1	no	—
653	C₂×D₄	—	4	2	no	—
654	C₂×D₄	—	4	2	no	—
655	C₂×D₄	—	4	2	no	—
656	C₂×D₄	C₂²×C₄×C₆₇	1	8	yes	—
657	C₂×D₄	C₂²×C₄×C₆₇	1	4	yes	—
658	C₂×D₄	C₂²×C₄×C₆₇	1	8	yes	—
659	C₂×D₄	C₂²×C₄×C₆₇	1	4	yes	—
660	C₂²×C₄	—	2	4	no	—
661	C₂²×C₄	—	4	2	no	—
662	C₂²×C₄	—	4	2	no	—
663	C₂²×C₄	—	4	2	no	—
664	C₂²×C₄	—	4	2	no	—
665	C₂²×C₄	—	4	2	no	—
666	C₂²×C₄	—	4	2	no	—
667	C₂²×C₄	—	4	2	no	—
668	C₂²×C₄	—	4	2	no	—
669	C₂²×C₄	—	4	2	no	—
670	C₂²×C₄	—	4	2	no	—
671	C₂²×C₄	—	4	2	no	—
672	C₂²×C₄	—	4	2	no	—
673	C₂²×C₄	—	4	2	no	—
674	C₂²×C₄	—	4	2	no	—
675	C₂²×C₄	—	4	2	no	—
676	C₂²×C₄	C₂²×C₄×C₆₇	1	8	yes	—
677	C₂²×C₄	C₂²×C₄×C₆₇	1	8	yes	—
678	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
679	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
680	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
681	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
682	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
683	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
684	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
685	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
686	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
687	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
688	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
689	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
690	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
691	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
692	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
693	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
694	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
695	C₄⋊C₄	—	2	4	no	—
696	C₄⋊C₄	—	4	1	no	—
697	C₄⋊C₄	—	4	1	no	—
698	C₄⋊C₄	—	4	1	no	—
699	C₄⋊C₄	—	4	1	no	—
700	C₄⋊C₄	—	4	1	no	—
701	C₄⋊C₄	—	4	1	no	—
702	C₄⋊C₄	—	4	2	no	—
703	C₄⋊C₄	—	4	2	no	—
704	C₄⋊C₄	—	4	2	no	—
705	C₄⋊C₄	—	4	2	no	—
706	C₄⋊C₄	—	4	2	no	—
707	C₄⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
708	C₄⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
709	C₄⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
710	C₂²⋊C₄	—	2	4	no	—
711	C₂²⋊C₄	—	4	2	no	—
712	C₂²⋊C₄	—	4	2	no	—
713	C₂²⋊C₄	—	4	2	no	—
714	C₂²⋊C₄	—	4	2	no	—
715	C₂²⋊C₄	—	4	2	no	—
716	C₂²⋊C₄	—	4	2	no	—
717	C₂²⋊C₄	—	4	2	no	—
718	C₂²⋊C₄	—	4	2	no	—
719	C₂²⋊C₄	—	4	2	no	—
720	C₂²⋊C₄	—	4	2	no	—
721	C₂²⋊C₄	—	4	2	no	—
722	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
723	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
724	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
725	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
726	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
727	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
728	C₄²	—	2	2	no	—
729	C₄²	—	2	2	no	—
730	C₄²	—	2	2	no	—
731	C₄²	—	4	2	no	—
732	C₄²	—	4	2	no	—
733	C₄²	—	4	2	no	—
734	C₄²	—	4	2	no	—
735	C₄²	—	4	2	no	—
736	C₄²	—	4	2	no	—
737	C₄²	—	4	1	no	—
738	C₄²	—	4	1	no	—
739	C₄²	—	4	1	no	—
740	C₄²	C₂²×C₄×C₆₇	1	4	yes	—
741	C₄²	C₂²×C₄×C₆₇	1	4	yes	—
742	C₄²	C₂²×C₄×C₆₇	1	8	yes	—
743	C₄²	C₂²×C₄×C₆₇	1	4	yes	—
744	C₂³	—	2	2	no	—
745	C₂³	—	2	2	no	—
746	C₂³	—	2	2	no	—
747	C₂³	—	2	2	no	—
748	C₂³	—	2	2	no	—
749	C₂³	—	2	2	no	—
750	C₂³	—	2	2	no	—
751	C₂³	—	2	2	no	—
752	C₂³	—	2	2	no	—
753	C₂³	—	2	2	no	—
754	C₂³	—	2	2	no	—
755	C₂³	—	2	2	no	—
756	C₂³	C₂³×C₄×C₆₇	1	4	yes	—
757	C₂³	C₂³×C₄×C₆₇	1	4	yes	—
758	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
759	Q₈	—	4	4	no	—
760	Q₈	—	4	4	no	—
761	D₄	—	4	8	no	—
762	D₄	—	4	4	no	—
763	D₄	—	4	4	no	—
764	D₄	—	4	8	no	—
765	C₂×C₄	—	2	1	no	—
766	C₂×C₄	—	2	1	no	—
767	C₂×C₄	—	2	1	no	—
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	1	no	—
773	C₂×C₄	—	2	1	no	—
774	C₂×C₄	—	2	1	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	2	2	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	2	no	—
780	C₂×C₄	—	2	1	no	—
781	C₂×C₄	—	2	1	no	—
782	C₂×C₄	—	2	1	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	2	2	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	2	2	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	2	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	2	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	2	no	—
797	C₂×C₄	—	2	2	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	2	2	no	—
804	C₂×C₄	—	4	8	no	—
805	C₂×C₄	—	4	8	no	—
806	C₂×C₄	—	8	4	no	—
807	C₂×C₄	—	8	4	no	—
808	C₂×C₄	—	8	4	no	—
809	C₂×C₄	—	8	4	no	—
810	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
811	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
812	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
813	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
814	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
815	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
816	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
817	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
818	C₂²	—	2	4	no	—
819	C₂²	—	2	4	no	—
820	C₂²	—	2	4	no	—
821	C₂²	—	2	4	no	—
822	C₂²	—	2	4	no	—
823	C₂²	—	2	4	no	—
824	C₂²	—	4	2	no	—
825	C₂²	—	4	2	no	—
826	C₂²	—	4	2	no	—
827	C₂²	—	4	2	no	—
828	C₂²	—	4	2	no	—
829	C₂²	—	4	2	no	—
830	C₂²	—	4	2	no	—
831	C₂²	—	4	2	no	—
832	C₂²	C₂⁴×C₄×C₆₇	1	1	yes	characteristic
833	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
834	C₂²	#585×C₆₇	1	2	yes	—
835	C₂²	#585×C₆₇	1	2	yes	—
836	C₂²	#585×C₆₇	1	1	yes	characteristic
837	C₄	—	2	2	no	—
838	C₄	—	2	4	no	—
839	C₄	—	2	4	no	—
840	C₄	—	2	4	no	—
841	C₄	—	2	2	no	—
842	C₄	—	2	2	no	—
843	C₄	—	2	4	no	—
844	C₄	—	2	2	no	—
845	C₄	—	4	2	no	—
846	C₄	—	4	2	no	—
847	C₄	—	4	1	no	—
848	C₄	—	4	2	no	—
849	C₄	—	4	1	no	—
850	C₄	—	4	1	no	—
851	C₄	—	4	2	no	—
852	C₄	—	4	2	no	—
853	C₄	—	4	2	no	—
854	C₂	—	4	4	no	—
855	C₂	—	4	4	no	—
856	C₂	C₆₇×#3428	1	2	yes	—
857	C₂	C₄×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
858	C₂	C₆₇×#3545	1	1	yes	characteristic
859	C₂	C₆₇×#3551	1	1	yes	characteristic
860	C₂	C₆₇×#3566	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₆₇
Frattini, cosocle	C₂³	C₂⁵×C₆₇
prime radical	C₂×#555×C₆₇	C₂
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×#2381	C₂	semidirect
3. C₆₇×#2379	C₂	semidirect
4. C₆₇×#2377	C₂	semidirect
5. C₆₇×#2372	C₂	semidirect
6. C₆₇×#2367	C₂	semidirect
7. C₆₇×#2364	C₂	semidirect
8. C₆₇×#2353	C₂	semidirect
9. C₆₇×#2343	C₂	semidirect
10. C₆₇×#2343	C₂	semidirect
11. C₆₇×#2337	C₂	semidirect
12. C₆₇×#2333	C₂	semidirect
13. C₆₇×#2327	C₂	semidirect
14. C₆₇×#2326	C₂	semidirect
15. C₆₇×#2325	C₂	semidirect
16. C₆₇×#2318	C₂	semidirect
17. C₆₇×#2314	C₂	semidirect
18. C₄×#124×C₆₇	C₂	semidirect
19. C₆₇×#2298	C₂	semidirect
20. #555×C₆₇	C₄	semidirect
120. C₄⋊Q₈×C₆₇	C₂×C₄	semidirect
121. #124×C₆₇	C₂×C₄	semidirect
122. #124×C₆₇	C₂×C₄	semidirect
123. #124×C₆₇	C₂×C₄	semidirect
124. #121×C₆₇	C₂×C₄	semidirect
125. #121×C₆₇	C₂×C₄	semidirect
131. C₄×D₄×C₆₇	C₂×C₄	semidirect
132. #117×C₆₇	C₂×C₄	semidirect
133. #117×C₆₇	C₂×C₄	semidirect
423. #34503	C₆₇	direct (N × H)
432. #2381	C₂×C₆₇	semidirect
433. #2379	C₂×C₆₇	semidirect
434. #2377	C₂×C₆₇	semidirect
435. #2372	C₂×C₆₇	semidirect
436. #2367	C₂×C₆₇	semidirect
437. #2364	C₂×C₆₇	semidirect
438. #2353	C₂×C₆₇	semidirect
439. #2343	C₂×C₆₇	semidirect
440. #2343	C₂×C₆₇	semidirect
441. #2337	C₂×C₆₇	semidirect
442. #2333	C₂×C₆₇	semidirect
443. #2327	C₂×C₆₇	semidirect
444. #2326	C₂×C₆₇	semidirect
445. #2325	C₂×C₆₇	semidirect
446. #2318	C₂×C₆₇	semidirect
447. #2314	C₂×C₆₇	semidirect
448. C₄×#124	C₂×C₆₇	semidirect
449. #2298	C₂×C₆₇	semidirect
450. C₆₇	#34503	direct (N × H)
451. #555	C₄×C₆₇	semidirect
551. C₄⋊Q₈	C₂×C₄×C₆₇	semidirect
552. #124	C₂×C₄×C₆₇	semidirect
553. #124	C₂×C₄×C₆₇	semidirect
554. #124	C₂×C₄×C₆₇	semidirect
555. #121	C₂×C₄×C₆₇	semidirect
556. #121	C₂×C₄×C₆₇	semidirect
562. C₄×D₄	C₂×C₄×C₆₇	semidirect
563. #117	C₂×C₄×C₆₇	semidirect
564. #117	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×#555×C₆₇	2
C₆₇×#2381	2
C₆₇×#2379	2
C₆₇×#2377	2
C₆₇×#2372	2
C₆₇×#2367	2
C₆₇×#2364	2
C₆₇×#2353	2
C₆₇×#2343	2
C₆₇×#2337	2
C₆₇×#2333	2
C₆₇×#2327	2
C₆₇×#2326	2
C₆₇×#2325	2
C₆₇×#2318	2
C₆₇×#2314	2
C₄×#124×C₆₇	2
C₆₇×#2298	2
#34503	67

Subgroups — C67×#34503 #30713754

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#34503 #30713754