Subgroups — C₆₇×#34562 #30713813

Order 17152.

2982 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#525×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₄×D₄×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#2638	C₂	1	2	yes	maximal, complemented
4	C₆₇×#2635	C₂	1	2	yes	maximal, complemented
5	C₆₇×#2630	C₂	1	4	yes	maximal, complemented
6	C₆₇×#2627	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#2626	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#2622	C₂	1	2	yes	maximal, complemented
9	C₆₇×#2618	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#2617	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#2613	C₂	1	2	yes	maximal, complemented
12	C₆₇×#2395	C₂	1	2	yes	maximal, complemented
13	C₆₇×#2392	C₂	1	4	yes	maximal, complemented
14	C₆₇×#2388	C₂	1	2	yes	maximal, complemented
15	C₄×#123×C₆₇	C₂	1	2	yes	maximal, complemented
16	C₄×#120×C₆₇	C₂	1	2	yes	maximal, complemented
17	C₆₇×#2280	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic, complemented
19	C₂³×D₄×C₆₇	C₂²	1	1	yes	characteristic
20	C₂⁴×C₄×C₆₇	C₂²	1	1	yes	characteristic
21	C₂⁴×C₄×C₆₇	C₂²	1	1	yes	characteristic
22	#525×C₆₇	—	2	8	no	—
23	C₂×#123×C₆₇	C₂²	1	2	yes	—
24	C₂×#123×C₆₇	C₂²	1	2	yes	complemented
25	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
26	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
27	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
28	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic, complemented
29	C₂×#120×C₆₇	C₂²	1	2	yes	—
30	C₂×#120×C₆₇	C₂²	1	2	yes	—
31	C₂×C₄×D₄×C₆₇	—	2	8	no	—
32	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
33	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
34	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
35	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
36	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
37	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
38	C₂×C₄×D₄×C₆₇	C₂²	1	4	yes	complemented
39	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic, complemented
40	C₂×#117×C₆₇	C₂²	1	2	yes	complemented
41	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
42	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
43	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
44	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
45	#400×C₆₇	C₂²	1	2	yes	complemented
46	#399×C₆₇	C₂²	1	2	yes	complemented
47	#398×C₆₇	C₂²	1	2	yes	complemented
48	#398×C₆₇	C₂²	1	4	yes	complemented
49	#397×C₆₇	C₂²	1	2	yes	complemented
50	#397×C₆₇	C₂²	1	4	yes	complemented
51	#397×C₆₇	C₂²	1	4	yes	complemented
52	#396×C₆₇	C₂²	1	4	yes	complemented
53	#396×C₆₇	C₂²	1	4	yes	complemented
54	#395×C₆₇	C₂²	1	2	yes	complemented
55	#394×C₆₇	C₂²	1	4	yes	—
56	#394×C₆₇	C₂²	1	4	yes	—
57	#394×C₆₇	C₂²	1	4	yes	complemented
58	#394×C₆₇	C₂²	1	2	yes	complemented
59	#394×C₆₇	C₂²	1	4	yes	complemented
60	#394×C₆₇	C₂²	1	4	yes	complemented
61	#393×C₆₇	C₂²	1	2	yes	complemented
62	#392×C₆₇	C₂²	1	4	yes	—
63	#392×C₆₇	C₂²	1	4	yes	—
64	#392×C₆₇	C₂²	1	2	yes	complemented
65	#388×C₆₇	C₂²	1	4	yes	complemented
66	#387×C₆₇	C₂²	1	4	yes	complemented
67	#386×C₆₇	C₂²	1	2	yes	—
68	#386×C₆₇	C₂²	1	2	yes	—
69	#386×C₆₇	C₂²	1	4	yes	complemented
70	#385×C₆₇	C₂²	1	2	yes	—
71	#385×C₆₇	C₂²	1	2	yes	—
72	#385×C₆₇	C₂²	1	4	yes	complemented
73	#381×C₆₇	C₂²	1	2	yes	—
74	#381×C₆₇	C₂²	1	2	yes	complemented
75	#380×C₆₇	C₂²	1	1	yes	characteristic
76	#380×C₆₇	C₂²	1	1	yes	characteristic
77	#380×C₆₇	C₂²	1	2	yes	complemented
78	#379×C₆₇	C₂²	1	2	yes	—
79	#379×C₆₇	C₂²	1	2	yes	—
80	C₄×C₄⋊C₄×C₆₇	C₂²	1	4	yes	complemented
81	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
82	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
83	C₄×C₂²⋊C₄×C₆₇	C₂²	1	4	yes	complemented
84	C₄×C₂²⋊C₄×C₆₇	C₂²	1	4	yes	complemented
85	C₂⁵×C₆₇	C₂³	1	1	yes	characteristic
86	C₂⁵×C₆₇	C₂³	1	1	yes	characteristic
87	C₂×#41×C₆₇	—	2	4	no	—
88	C₂×#41×C₆₇	—	4	4	no	—
89	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
90	C₂²×D₄×C₆₇	—	2	4	no	—
91	C₂²×D₄×C₆₇	—	2	4	no	—
92	C₂²×D₄×C₆₇	—	2	4	no	—
93	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
94	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
95	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
96	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
97	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
98	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
99	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
100	C₂³×C₄×C₆₇	—	2	4	no	—
101	C₂³×C₄×C₆₇	—	4	4	no	—
102	C₂³×C₄×C₆₇	—	4	4	no	—
103	C₂³×C₄×C₆₇	D₄	1	8	yes	complemented
104	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
105	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
106	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
107	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
108	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
109	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
110	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
111	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
112	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
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	#123×C₆₇	—	2	8	no	—
117	#123×C₆₇	—	2	8	no	—
118	C₂²⋊Q₈×C₆₇	—	2	4	no	—
119	C₂²⋊Q₈×C₆₇	—	2	4	no	—
120	#121×C₆₇	—	2	4	no	—
121	#121×C₆₇	—	2	4	no	—
122	#120×C₆₇	—	2	8	no	—
123	#120×C₆₇	—	2	8	no	—
124	C₄×D₄×C₆₇	—	2	8	no	—
125	C₄×D₄×C₆₇	—	2	8	no	—
126	C₄×D₄×C₆₇	—	2	8	no	—
127	C₄×D₄×C₆₇	—	2	8	no	—
128	C₄×D₄×C₆₇	—	2	8	no	—
129	C₄×D₄×C₆₇	—	2	8	no	—
130	C₄×D₄×C₆₇	—	4	8	no	—
131	#117×C₆₇	—	2	4	no	—
132	#117×C₆₇	—	4	4	no	—
133	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
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	1	yes	characteristic
137	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
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	4	yes	—
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	4	yes	—
144	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
145	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
146	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
147	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
148	C₂×C₂²⋊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	4	yes	—
158	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	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	4	yes	—
162	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
163	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
164	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
165	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
166	C₂×C₄²×C₆₇	—	2	4	no	—
167	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
168	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
169	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
170	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
171	#95×C₆₇	C₂³	1	4	yes	—
172	#95×C₆₇	C₂³	1	2	yes	—
173	#95×C₆₇	C₂³	1	2	yes	—
174	#95×C₆₇	C₂³	1	4	yes	—
175	#95×C₆₇	C₂³	1	4	yes	—
176	#95×C₆₇	C₂³	1	4	yes	—
177	#95×C₆₇	C₂³	1	4	yes	—
178	#95×C₆₇	C₂³	1	4	yes	—
179	#95×C₆₇	C₂³	1	4	yes	—
180	C₂⁴×C₆₇	—	2	2	no	—
181	C₂⁴×C₆₇	—	2	2	no	—
182	C₂⁴×C₆₇	—	2	2	no	—
183	C₂⁴×C₆₇	—	2	2	no	—
184	C₂⁴×C₆₇	—	4	2	no	—
185	C₂⁴×C₆₇	—	4	2	no	—
186	C₂⁴×C₆₇	—	4	2	no	—
187	C₂⁴×C₆₇	—	4	2	no	—
188	C₂⁴×C₆₇	C₂×D₄	1	4	yes	—
189	C₂⁴×C₆₇	#41	1	4	yes	complemented
190	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
191	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
192	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
193	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
194	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
195	#41×C₆₇	—	4	16	no	—
196	C₂×Q₈×C₆₇	—	2	2	no	—
197	C₂×Q₈×C₆₇	—	4	2	no	—
198	C₂×D₄×C₆₇	—	2	32	no	—
199	C₂×D₄×C₆₇	—	2	4	no	—
200	C₂×D₄×C₆₇	—	2	4	no	—
201	C₂×D₄×C₆₇	—	2	4	no	—
202	C₂×D₄×C₆₇	—	2	4	no	—
203	C₂×D₄×C₆₇	—	2	4	no	—
204	C₂×D₄×C₆₇	—	2	4	no	—
205	C₂×D₄×C₆₇	—	2	4	no	—
206	C₂×D₄×C₆₇	—	2	8	no	—
207	C₂×D₄×C₆₇	—	2	4	no	—
208	C₂×D₄×C₆₇	—	2	4	no	—
209	C₂×D₄×C₆₇	—	2	2	no	—
210	C₂×D₄×C₆₇	—	2	4	no	—
211	C₂×D₄×C₆₇	—	2	4	no	—
212	C₂×D₄×C₆₇	—	4	4	no	—
213	C₂×D₄×C₆₇	—	4	4	no	—
214	C₂×D₄×C₆₇	—	4	4	no	—
215	C₂×D₄×C₆₇	—	4	2	no	—
216	C₂×D₄×C₆₇	—	4	4	no	—
217	C₂²×C₄×C₆₇	—	2	2	no	—
218	C₂²×C₄×C₆₇	—	2	2	no	—
219	C₂²×C₄×C₆₇	—	2	4	no	—
220	C₂²×C₄×C₆₇	—	2	4	no	—
221	C₂²×C₄×C₆₇	—	2	4	no	—
222	C₂²×C₄×C₆₇	—	2	2	no	—
223	C₂²×C₄×C₆₇	—	2	2	no	—
224	C₂²×C₄×C₆₇	—	2	4	no	—
225	C₂²×C₄×C₆₇	—	2	4	no	—
226	C₂²×C₄×C₆₇	—	2	4	no	—
227	C₂²×C₄×C₆₇	—	2	8	no	—
228	C₂²×C₄×C₆₇	—	2	8	no	—
229	C₂²×C₄×C₆₇	—	4	16	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	4	no	—
234	C₂²×C₄×C₆₇	—	4	2	no	—
235	C₂²×C₄×C₆₇	—	4	2	no	—
236	C₂²×C₄×C₆₇	—	4	16	no	—
237	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
238	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
239	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
240	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
241	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
242	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
243	C₂²×C₄×C₆₇	#41	1	4	yes	complemented
244	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
245	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
246	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
247	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
248	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
249	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
250	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
251	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
252	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
253	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
254	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
255	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
256	C₄⋊C₄×C₆₇	—	2	4	no	—
257	C₄⋊C₄×C₆₇	—	2	4	no	—
258	C₄⋊C₄×C₆₇	—	2	2	no	—
259	C₄⋊C₄×C₆₇	—	2	2	no	—
260	C₄⋊C₄×C₆₇	—	2	4	no	—
261	C₄⋊C₄×C₆₇	—	2	4	no	—
262	C₄⋊C₄×C₆₇	—	2	8	no	—
263	C₄⋊C₄×C₆₇	—	4	4	no	—
264	C₄⋊C₄×C₆₇	—	4	2	no	—
265	C₄⋊C₄×C₆₇	—	4	2	no	—
266	C₄⋊C₄×C₆₇	—	4	4	no	—
267	C₂²⋊C₄×C₆₇	—	2	4	no	—
268	C₂²⋊C₄×C₆₇	—	2	4	no	—
269	C₂²⋊C₄×C₆₇	—	2	4	no	—
270	C₂²⋊C₄×C₆₇	—	2	4	no	—
271	C₂²⋊C₄×C₆₇	—	2	4	no	—
272	C₂²⋊C₄×C₆₇	—	2	8	no	—
273	C₂²⋊C₄×C₆₇	—	2	4	no	—
274	C₂²⋊C₄×C₆₇	—	2	4	no	—
275	C₂²⋊C₄×C₆₇	—	2	4	no	—
276	C₂²⋊C₄×C₆₇	—	2	4	no	—
277	C₂²⋊C₄×C₆₇	—	2	4	no	—
278	C₂²⋊C₄×C₆₇	—	2	4	no	—
279	C₂²⋊C₄×C₆₇	—	2	8	no	—
280	C₂²⋊C₄×C₆₇	—	4	4	no	—
281	C₂²⋊C₄×C₆₇	—	4	4	no	—
282	C₂²⋊C₄×C₆₇	—	4	4	no	—
283	C₂²⋊C₄×C₆₇	—	4	4	no	—
284	C₂²⋊C₄×C₆₇	—	4	4	no	—
285	C₂²⋊C₄×C₆₇	—	4	4	no	—
286	C₄²×C₆₇	—	2	4	no	—
287	C₄²×C₆₇	—	2	4	no	—
288	C₄²×C₆₇	—	2	4	no	—
289	C₄²×C₆₇	—	2	8	no	—
290	C₂³×C₆₇	—	2	2	no	—
291	C₂³×C₆₇	—	2	2	no	—
292	C₂³×C₆₇	—	2	8	no	—
293	C₂³×C₆₇	—	2	8	no	—
294	C₂³×C₆₇	—	2	2	no	—
295	C₂³×C₆₇	—	2	1	no	—
296	C₂³×C₆₇	—	2	1	no	—
297	C₂³×C₆₇	—	2	1	no	—
298	C₂³×C₆₇	—	2	1	no	—
299	C₂³×C₆₇	—	2	2	no	—
300	C₂³×C₆₇	—	2	2	no	—
301	C₂³×C₆₇	—	2	4	no	—
302	C₂³×C₆₇	—	2	2	no	—
303	C₂³×C₆₇	—	2	2	no	—
304	C₂³×C₆₇	—	2	4	no	—
305	C₂³×C₆₇	—	2	2	no	—
306	C₂³×C₆₇	—	2	2	no	—
307	C₂³×C₆₇	—	2	2	no	—
308	C₂³×C₆₇	—	2	2	no	—
309	C₂³×C₆₇	—	2	4	no	—
310	C₂³×C₆₇	—	2	4	no	—
311	C₂³×C₆₇	—	4	4	no	—
312	C₂³×C₆₇	—	4	4	no	—
313	C₂³×C₆₇	—	4	8	no	—
314	C₂³×C₆₇	—	4	4	no	—
315	C₂³×C₆₇	—	4	4	no	—
316	C₂³×C₆₇	—	4	8	no	—
317	C₂³×C₆₇	—	4	8	no	—
318	C₂³×C₆₇	—	4	8	no	—
319	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
320	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
321	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
322	C₂³×C₆₇	C₂×#41	1	4	yes	—
323	C₂³×C₆₇	C₂×#41	1	2	yes	—
324	C₂³×C₆₇	C₂×#41	1	2	yes	—
325	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
326	Q₈×C₆₇	—	4	4	no	—
327	D₄×C₆₇	—	2	16	no	—
328	D₄×C₆₇	—	2	16	no	—
329	D₄×C₆₇	—	4	4	no	—
330	D₄×C₆₇	—	4	8	no	—
331	D₄×C₆₇	—	4	16	no	—
332	D₄×C₆₇	—	4	8	no	—
333	D₄×C₆₇	—	4	8	no	—
334	C₂×C₄×C₆₇	—	2	8	no	—
335	C₂×C₄×C₆₇	—	2	2	no	—
336	C₂×C₄×C₆₇	—	2	2	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	8	no	—
341	C₂×C₄×C₆₇	—	2	8	no	—
342	C₂×C₄×C₆₇	—	2	8	no	—
343	C₂×C₄×C₆₇	—	2	2	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	4	no	—
349	C₂×C₄×C₆₇	—	2	2	no	—
350	C₂×C₄×C₆₇	—	2	4	no	—
351	C₂×C₄×C₆₇	—	2	2	no	—
352	C₂×C₄×C₆₇	—	2	4	no	—
353	C₂×C₄×C₆₇	—	2	4	no	—
354	C₂×C₄×C₆₇	—	2	4	no	—
355	C₂×C₄×C₆₇	—	2	4	no	—
356	C₂×C₄×C₆₇	—	2	4	no	—
357	C₂×C₄×C₆₇	—	2	4	no	—
358	C₂×C₄×C₆₇	—	2	4	no	—
359	C₂×C₄×C₆₇	—	2	4	no	—
360	C₂×C₄×C₆₇	—	4	4	no	—
361	C₂×C₄×C₆₇	—	4	4	no	—
362	C₂×C₄×C₆₇	—	4	4	no	—
363	C₂×C₄×C₆₇	—	4	8	no	—
364	C₂×C₄×C₆₇	—	4	4	no	—
365	C₂×C₄×C₆₇	—	4	4	no	—
366	C₂×C₄×C₆₇	—	4	8	no	—
367	C₂×C₄×C₆₇	—	4	8	no	—
368	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
369	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
370	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
371	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
372	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
373	C₂×C₄×C₆₇	H(5,𝔽₂)	1	4	yes	—
374	C₂²×C₆₇	—	2	2	no	—
375	C₂²×C₆₇	—	2	2	no	—
376	C₂²×C₆₇	—	2	4	no	—
377	C₂²×C₆₇	—	2	4	no	—
378	C₂²×C₆₇	—	2	2	no	—
379	C₂²×C₆₇	—	2	2	no	—
380	C₂²×C₆₇	—	2	4	no	—
381	C₂²×C₆₇	—	2	2	no	—
382	C₂²×C₆₇	—	2	2	no	—
383	C₂²×C₆₇	—	2	2	no	—
384	C₂²×C₆₇	—	2	2	no	—
385	C₂²×C₆₇	—	2	8	no	—
386	C₂²×C₆₇	—	4	16	no	—
387	C₂²×C₆₇	—	4	16	no	—
388	C₂²×C₆₇	—	4	2	no	—
389	C₂²×C₆₇	—	4	2	no	—
390	C₂²×C₆₇	—	4	2	no	—
391	C₂²×C₆₇	—	4	2	no	—
392	C₂²×C₆₇	—	4	2	no	—
393	C₂²×C₆₇	—	4	4	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	4	no	—
399	C₂²×C₆₇	—	4	4	no	—
400	C₂²×C₆₇	#525	1	4	yes	—
401	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
402	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
403	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
404	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
405	C₂²×C₆₇	#585	1	2	yes	—
406	C₄×C₆₇	—	2	4	no	—
407	C₄×C₆₇	—	2	2	no	—
408	C₄×C₆₇	—	2	2	no	—
409	C₄×C₆₇	—	2	2	no	—
410	C₄×C₆₇	—	4	2	no	—
411	C₄×C₆₇	—	4	2	no	—
412	C₄×C₆₇	—	4	2	no	—
413	C₄×C₆₇	—	4	2	no	—
414	C₄×C₆₇	—	4	2	no	—
415	C₄×C₆₇	—	4	4	no	—
416	C₄×C₆₇	—	4	4	no	—
417	C₄×C₆₇	#534	1	4	yes	—
418	#34562	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
419	C₂×C₆₇	—	2	4	no	—
420	C₂×C₆₇	—	4	2	no	—
421	C₂×C₆₇	—	4	2	no	—
422	C₂×C₆₇	—	4	4	no	—
423	C₂×C₆₇	—	8	2	no	—
424	C₂×C₆₇	C₂×#525	1	1	yes	characteristic
425	C₂×C₆₇	C₂×#534	1	1	yes	characteristic
426	C₂×C₆₇	#3449	1	1	yes	characteristic
427	C₂×C₆₇	#3459	1	2	yes	—
428	C₂×C₆₇	#3460	1	2	yes	—
429	C₂×#525	C₂×C₆₇	1	1	yes	characteristic, complemented
430	C₂²×C₄×D₄	C₂×C₆₇	1	1	yes	characteristic, complemented
431	#2638	C₂×C₆₇	1	2	yes	complemented
432	#2635	C₂×C₆₇	1	2	yes	complemented
433	#2630	C₂×C₆₇	1	4	yes	complemented
434	#2627	C₂×C₆₇	1	1	yes	characteristic, complemented
435	#2626	C₂×C₆₇	1	1	yes	characteristic, complemented
436	#2622	C₂×C₆₇	1	2	yes	complemented
437	#2618	C₂×C₆₇	1	1	yes	characteristic, complemented
438	#2617	C₂×C₆₇	1	1	yes	characteristic, complemented
439	#2613	C₂×C₆₇	1	2	yes	complemented
440	#2395	C₂×C₆₇	1	2	yes	complemented
441	#2392	C₂×C₆₇	1	4	yes	complemented
442	#2388	C₂×C₆₇	1	2	yes	complemented
443	C₄×#123	C₂×C₆₇	1	2	yes	complemented
444	C₄×#120	C₂×C₆₇	1	2	yes	complemented
445	#2280	C₂×C₆₇	1	1	yes	characteristic, complemented
446	C₆₇	#34562	1	1	yes	characteristic, direct product factor, Sylow
447	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic, complemented
448	C₂³×D₄	C₂²×C₆₇	1	1	yes	characteristic
449	C₂⁴×C₄	C₂²×C₆₇	1	1	yes	characteristic
450	C₂⁴×C₄	C₂²×C₆₇	1	1	yes	characteristic
451	#525	—	2	8	no	—
452	C₂×#123	C₂²×C₆₇	1	2	yes	—
453	C₂×#123	C₂²×C₆₇	1	2	yes	complemented
454	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
455	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
456	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
457	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic, complemented
458	C₂×#120	C₂²×C₆₇	1	2	yes	—
459	C₂×#120	C₂²×C₆₇	1	2	yes	—
460	C₂×C₄×D₄	—	2	8	no	—
461	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
462	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
463	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
464	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
465	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
466	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
467	C₂×C₄×D₄	C₂²×C₆₇	1	4	yes	complemented
468	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic, complemented
469	C₂×#117	C₂²×C₆₇	1	2	yes	complemented
470	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
471	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
472	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
473	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
474	#400	C₂²×C₆₇	1	2	yes	complemented
475	#399	C₂²×C₆₇	1	2	yes	complemented
476	#398	C₂²×C₆₇	1	2	yes	complemented
477	#398	C₂²×C₆₇	1	4	yes	complemented
478	#397	C₂²×C₆₇	1	2	yes	complemented
479	#397	C₂²×C₆₇	1	4	yes	complemented
480	#397	C₂²×C₆₇	1	4	yes	complemented
481	#396	C₂²×C₆₇	1	4	yes	complemented
482	#396	C₂²×C₆₇	1	4	yes	complemented
483	#395	C₂²×C₆₇	1	2	yes	complemented
484	#394	C₂²×C₆₇	1	4	yes	—
485	#394	C₂²×C₆₇	1	4	yes	—
486	#394	C₂²×C₆₇	1	4	yes	complemented
487	#394	C₂²×C₆₇	1	2	yes	complemented
488	#394	C₂²×C₆₇	1	4	yes	complemented
489	#394	C₂²×C₆₇	1	4	yes	complemented
490	#393	C₂²×C₆₇	1	2	yes	complemented
491	#392	C₂²×C₆₇	1	4	yes	—
492	#392	C₂²×C₆₇	1	4	yes	—
493	#392	C₂²×C₆₇	1	2	yes	complemented
494	#388	C₂²×C₆₇	1	4	yes	complemented
495	#387	C₂²×C₆₇	1	4	yes	complemented
496	#386	C₂²×C₆₇	1	2	yes	—
497	#386	C₂²×C₆₇	1	2	yes	—
498	#386	C₂²×C₆₇	1	4	yes	complemented
499	#385	C₂²×C₆₇	1	2	yes	—
500	#385	C₂²×C₆₇	1	2	yes	—
501	#385	C₂²×C₆₇	1	4	yes	complemented
502	#381	C₂²×C₆₇	1	2	yes	—
503	#381	C₂²×C₆₇	1	2	yes	complemented
504	#380	C₂²×C₆₇	1	1	yes	characteristic
505	#380	C₂²×C₆₇	1	1	yes	characteristic
506	#380	C₂²×C₆₇	1	2	yes	complemented
507	#379	C₂²×C₆₇	1	2	yes	—
508	#379	C₂²×C₆₇	1	2	yes	—
509	C₄×C₄⋊C₄	C₂²×C₆₇	1	4	yes	complemented
510	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
511	C₄×C₂²⋊C₄	C₂²×C₆₇	1	4	yes	complemented
512	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
513	C₄×C₂²⋊C₄	C₂²×C₆₇	1	4	yes	complemented
514	C₂⁵	C₂³×C₆₇	1	1	yes	characteristic
515	C₂⁵	C₂³×C₆₇	1	1	yes	characteristic
516	C₂×#41	—	2	4	no	—
517	C₂×#41	—	4	4	no	—
518	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
519	C₂²×D₄	—	2	4	no	—
520	C₂²×D₄	—	2	4	no	—
521	C₂²×D₄	—	2	4	no	—
522	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
523	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
524	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
525	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
526	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
527	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
528	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
529	C₂³×C₄	—	2	4	no	—
530	C₂³×C₄	—	4	4	no	—
531	C₂³×C₄	—	4	4	no	—
532	C₂³×C₄	D₄×C₆₇	1	8	yes	complemented
533	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
534	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
535	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
536	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
537	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
538	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
539	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
540	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
541	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
542	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
543	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
544	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
545	#123	—	2	8	no	—
546	#123	—	2	8	no	—
547	C₂²⋊Q₈	—	2	4	no	—
548	C₂²⋊Q₈	—	2	4	no	—
549	#121	—	2	4	no	—
550	#121	—	2	4	no	—
551	#120	—	2	8	no	—
552	#120	—	2	8	no	—
553	C₄×D₄	—	2	8	no	—
554	C₄×D₄	—	2	8	no	—
555	C₄×D₄	—	2	8	no	—
556	C₄×D₄	—	2	8	no	—
557	C₄×D₄	—	2	8	no	—
558	C₄×D₄	—	2	8	no	—
559	C₄×D₄	—	4	8	no	—
560	#117	—	2	4	no	—
561	#117	—	4	4	no	—
562	C₂×C₄⋊C₄	—	2	4	no	—
563	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
564	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
565	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
566	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
567	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
568	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
569	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
570	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
571	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
572	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
573	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
574	C₂×C₂²⋊C₄	—	2	4	no	—
575	C₂×C₂²⋊C₄	—	2	4	no	—
576	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
577	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
578	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
579	C₂×C₂²⋊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	4	yes	—
587	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
588	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
589	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
590	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
591	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
592	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
593	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
594	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
595	C₂×C₄²	—	2	4	no	—
596	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
597	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
598	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
599	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
600	#95	C₂³×C₆₇	1	4	yes	—
601	#95	C₂³×C₆₇	1	2	yes	—
602	#95	C₂³×C₆₇	1	2	yes	—
603	#95	C₂³×C₆₇	1	4	yes	—
604	#95	C₂³×C₆₇	1	4	yes	—
605	#95	C₂³×C₆₇	1	4	yes	—
606	#95	C₂³×C₆₇	1	4	yes	—
607	#95	C₂³×C₆₇	1	4	yes	—
608	#95	C₂³×C₆₇	1	4	yes	—
609	C₂⁴	—	2	2	no	—
610	C₂⁴	—	2	2	no	—
611	C₂⁴	—	2	2	no	—
612	C₂⁴	—	2	2	no	—
613	C₂⁴	—	4	2	no	—
614	C₂⁴	—	4	2	no	—
615	C₂⁴	—	4	2	no	—
616	C₂⁴	—	4	2	no	—
617	C₂⁴	C₂×D₄×C₆₇	1	4	yes	—
618	C₂⁴	#41×C₆₇	1	4	yes	complemented
619	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
620	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
621	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
622	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
623	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
624	#41	—	4	16	no	—
625	C₂×Q₈	—	2	2	no	—
626	C₂×Q₈	—	4	2	no	—
627	C₂×D₄	—	2	32	no	—
628	C₂×D₄	—	2	4	no	—
629	C₂×D₄	—	2	4	no	—
630	C₂×D₄	—	2	4	no	—
631	C₂×D₄	—	2	4	no	—
632	C₂×D₄	—	2	4	no	—
633	C₂×D₄	—	2	4	no	—
634	C₂×D₄	—	2	4	no	—
635	C₂×D₄	—	2	8	no	—
636	C₂×D₄	—	2	4	no	—
637	C₂×D₄	—	2	4	no	—
638	C₂×D₄	—	2	2	no	—
639	C₂×D₄	—	2	4	no	—
640	C₂×D₄	—	2	4	no	—
641	C₂×D₄	—	4	4	no	—
642	C₂×D₄	—	4	2	no	—
643	C₂×D₄	—	4	4	no	—
644	C₂×D₄	—	4	4	no	—
645	C₂×D₄	—	4	4	no	—
646	C₂²×C₄	—	2	2	no	—
647	C₂²×C₄	—	2	2	no	—
648	C₂²×C₄	—	2	4	no	—
649	C₂²×C₄	—	2	4	no	—
650	C₂²×C₄	—	2	4	no	—
651	C₂²×C₄	—	2	2	no	—
652	C₂²×C₄	—	2	2	no	—
653	C₂²×C₄	—	2	4	no	—
654	C₂²×C₄	—	2	4	no	—
655	C₂²×C₄	—	2	4	no	—
656	C₂²×C₄	—	2	8	no	—
657	C₂²×C₄	—	2	8	no	—
658	C₂²×C₄	—	4	16	no	—
659	C₂²×C₄	—	4	2	no	—
660	C₂²×C₄	—	4	2	no	—
661	C₂²×C₄	—	4	2	no	—
662	C₂²×C₄	—	4	4	no	—
663	C₂²×C₄	—	4	2	no	—
664	C₂²×C₄	—	4	2	no	—
665	C₂²×C₄	—	4	16	no	—
666	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
667	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
668	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
669	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
670	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
671	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
672	C₂²×C₄	#41×C₆₇	1	4	yes	complemented
673	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
674	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
675	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
676	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
677	C₂²×C₄	C₂⁴×C₆₇	1	2	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	1	yes	characteristic
682	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
683	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
684	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
685	C₄⋊C₄	—	2	4	no	—
686	C₄⋊C₄	—	2	4	no	—
687	C₄⋊C₄	—	2	2	no	—
688	C₄⋊C₄	—	2	2	no	—
689	C₄⋊C₄	—	2	4	no	—
690	C₄⋊C₄	—	2	4	no	—
691	C₄⋊C₄	—	2	8	no	—
692	C₄⋊C₄	—	4	2	no	—
693	C₄⋊C₄	—	4	2	no	—
694	C₄⋊C₄	—	4	4	no	—
695	C₄⋊C₄	—	4	4	no	—
696	C₂²⋊C₄	—	2	4	no	—
697	C₂²⋊C₄	—	2	4	no	—
698	C₂²⋊C₄	—	2	4	no	—
699	C₂²⋊C₄	—	2	4	no	—
700	C₂²⋊C₄	—	2	4	no	—
701	C₂²⋊C₄	—	2	8	no	—
702	C₂²⋊C₄	—	2	4	no	—
703	C₂²⋊C₄	—	2	4	no	—
704	C₂²⋊C₄	—	2	4	no	—
705	C₂²⋊C₄	—	2	4	no	—
706	C₂²⋊C₄	—	2	4	no	—
707	C₂²⋊C₄	—	2	4	no	—
708	C₂²⋊C₄	—	2	8	no	—
709	C₂²⋊C₄	—	4	4	no	—
710	C₂²⋊C₄	—	4	4	no	—
711	C₂²⋊C₄	—	4	4	no	—
712	C₂²⋊C₄	—	4	4	no	—
713	C₂²⋊C₄	—	4	4	no	—
714	C₂²⋊C₄	—	4	4	no	—
715	C₄²	—	2	4	no	—
716	C₄²	—	2	4	no	—
717	C₄²	—	2	4	no	—
718	C₄²	—	2	8	no	—
719	C₂³	—	2	2	no	—
720	C₂³	—	2	2	no	—
721	C₂³	—	2	8	no	—
722	C₂³	—	2	8	no	—
723	C₂³	—	2	2	no	—
724	C₂³	—	2	1	no	—
725	C₂³	—	2	1	no	—
726	C₂³	—	2	1	no	—
727	C₂³	—	2	1	no	—
728	C₂³	—	2	2	no	—
729	C₂³	—	2	2	no	—
730	C₂³	—	2	4	no	—
731	C₂³	—	2	2	no	—
732	C₂³	—	2	2	no	—
733	C₂³	—	2	4	no	—
734	C₂³	—	2	2	no	—
735	C₂³	—	2	2	no	—
736	C₂³	—	2	2	no	—
737	C₂³	—	2	2	no	—
738	C₂³	—	2	4	no	—
739	C₂³	—	2	4	no	—
740	C₂³	—	4	4	no	—
741	C₂³	—	4	4	no	—
742	C₂³	—	4	8	no	—
743	C₂³	—	4	4	no	—
744	C₂³	—	4	4	no	—
745	C₂³	—	4	8	no	—
746	C₂³	—	4	8	no	—
747	C₂³	—	4	8	no	—
748	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
749	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
750	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
751	C₂³	C₂×#41×C₆₇	1	4	yes	—
752	C₂³	C₂×#41×C₆₇	1	2	yes	—
753	C₂³	C₂×#41×C₆₇	1	2	yes	—
754	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
755	Q₈	—	4	4	no	—
756	D₄	—	2	16	no	—
757	D₄	—	2	16	no	—
758	D₄	—	4	4	no	—
759	D₄	—	4	8	no	—
760	D₄	—	4	8	no	—
761	D₄	—	4	16	no	—
762	D₄	—	4	8	no	—
763	C₂×C₄	—	2	8	no	—
764	C₂×C₄	—	2	2	no	—
765	C₂×C₄	—	2	2	no	—
766	C₂×C₄	—	2	2	no	—
767	C₂×C₄	—	2	2	no	—
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	2	8	no	—
770	C₂×C₄	—	2	8	no	—
771	C₂×C₄	—	2	8	no	—
772	C₂×C₄	—	2	2	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	2	4	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	4	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	4	no	—
782	C₂×C₄	—	2	4	no	—
783	C₂×C₄	—	2	4	no	—
784	C₂×C₄	—	2	4	no	—
785	C₂×C₄	—	2	4	no	—
786	C₂×C₄	—	2	4	no	—
787	C₂×C₄	—	2	4	no	—
788	C₂×C₄	—	2	4	no	—
789	C₂×C₄	—	4	4	no	—
790	C₂×C₄	—	4	4	no	—
791	C₂×C₄	—	4	4	no	—
792	C₂×C₄	—	4	8	no	—
793	C₂×C₄	—	4	4	no	—
794	C₂×C₄	—	4	4	no	—
795	C₂×C₄	—	4	8	no	—
796	C₂×C₄	—	4	8	no	—
797	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
798	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
799	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
800	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
801	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
802	C₂×C₄	H(5,𝔽₂)×C₆₇	1	4	yes	—
803	C₂²	—	2	2	no	—
804	C₂²	—	2	2	no	—
805	C₂²	—	2	4	no	—
806	C₂²	—	2	4	no	—
807	C₂²	—	2	2	no	—
808	C₂²	—	2	2	no	—
809	C₂²	—	2	4	no	—
810	C₂²	—	2	2	no	—
811	C₂²	—	2	2	no	—
812	C₂²	—	2	2	no	—
813	C₂²	—	2	2	no	—
814	C₂²	—	2	8	no	—
815	C₂²	—	4	16	no	—
816	C₂²	—	4	16	no	—
817	C₂²	—	4	2	no	—
818	C₂²	—	4	2	no	—
819	C₂²	—	4	2	no	—
820	C₂²	—	4	2	no	—
821	C₂²	—	4	2	no	—
822	C₂²	—	4	4	no	—
823	C₂²	—	4	2	no	—
824	C₂²	—	4	2	no	—
825	C₂²	—	4	2	no	—
826	C₂²	—	4	2	no	—
827	C₂²	—	4	4	no	—
828	C₂²	—	4	4	no	—
829	C₂²	#525×C₆₇	1	4	yes	—
830	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
831	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
832	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
833	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	2	yes	—
834	C₂²	#585×C₆₇	1	2	yes	—
835	C₄	—	2	4	no	—
836	C₄	—	2	2	no	—
837	C₄	—	2	2	no	—
838	C₄	—	2	2	no	—
839	C₄	—	4	2	no	—
840	C₄	—	4	2	no	—
841	C₄	—	4	2	no	—
842	C₄	—	4	2	no	—
843	C₄	—	4	2	no	—
844	C₄	—	4	4	no	—
845	C₄	—	4	4	no	—
846	C₄	#534×C₆₇	1	4	yes	—
847	C₂	—	2	4	no	—
848	C₂	—	4	2	no	—
849	C₂	—	4	2	no	—
850	C₂	—	4	4	no	—
851	C₂	—	8	2	no	—
852	C₂	C₂×#525×C₆₇	1	1	yes	characteristic
853	C₂	C₂×#534×C₆₇	1	1	yes	characteristic
854	C₂	C₆₇×#3449	1	1	yes	characteristic
855	C₂	C₆₇×#3459	1	2	yes	—
856	C₂	C₆₇×#3460	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₂×#525×C₆₇	C₂	semidirect
2. C₂²×C₄×D₄×C₆₇	C₂	semidirect
3. C₆₇×#2638	C₂	semidirect
4. C₆₇×#2635	C₂	semidirect
5. C₆₇×#2630	C₂	semidirect
6. C₆₇×#2627	C₂	semidirect
7. C₆₇×#2626	C₂	semidirect
8. C₆₇×#2622	C₂	semidirect
9. C₆₇×#2618	C₂	semidirect
10. C₆₇×#2617	C₂	semidirect
11. C₆₇×#2613	C₂	semidirect
12. C₆₇×#2395	C₂	semidirect
13. C₆₇×#2392	C₂	semidirect
14. C₆₇×#2388	C₂	semidirect
15. C₄×#123×C₆₇	C₂	semidirect
16. C₄×#120×C₆₇	C₂	semidirect
17. C₆₇×#2280	C₂	semidirect
18. C₂²×#41×C₆₇	C₂²	semidirect
24. C₂×#123×C₆₇	C₂²	semidirect
26. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
28. C₂×#121×C₆₇	C₂²	semidirect
37. C₂×C₄×D₄×C₆₇	C₂²	semidirect
38. C₂×C₄×D₄×C₆₇	C₂²	semidirect
39. C₂×#117×C₆₇	C₂²	semidirect
40. C₂×#117×C₆₇	C₂²	semidirect
45. #400×C₆₇	C₂²	semidirect
46. #399×C₆₇	C₂²	semidirect
47. #398×C₆₇	C₂²	semidirect
48. #398×C₆₇	C₂²	semidirect
49. #397×C₆₇	C₂²	semidirect
50. #397×C₆₇	C₂²	semidirect
51. #397×C₆₇	C₂²	semidirect
52. #396×C₆₇	C₂²	semidirect
53. #396×C₆₇	C₂²	semidirect
54. #395×C₆₇	C₂²	semidirect
57. #394×C₆₇	C₂²	semidirect
58. #394×C₆₇	C₂²	semidirect
59. #394×C₆₇	C₂²	semidirect
60. #394×C₆₇	C₂²	semidirect
61. #393×C₆₇	C₂²	semidirect
64. #392×C₆₇	C₂²	semidirect
65. #388×C₆₇	C₂²	semidirect
66. #387×C₆₇	C₂²	semidirect
69. #386×C₆₇	C₂²	semidirect
72. #385×C₆₇	C₂²	semidirect
74. #381×C₆₇	C₂²	semidirect
77. #380×C₆₇	C₂²	semidirect
80. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
82. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
83. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
84. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
103. C₂³×C₄×C₆₇	D₄	semidirect
189. C₂⁴×C₆₇	#41	semidirect
243. C₂²×C₄×C₆₇	#41	semidirect
418. #34562	C₆₇	direct (N × H)
429. C₂×#525	C₂×C₆₇	semidirect
430. C₂²×C₄×D₄	C₂×C₆₇	semidirect
431. #2638	C₂×C₆₇	semidirect
432. #2635	C₂×C₆₇	semidirect
433. #2630	C₂×C₆₇	semidirect
434. #2627	C₂×C₆₇	semidirect
435. #2626	C₂×C₆₇	semidirect
436. #2622	C₂×C₆₇	semidirect
437. #2618	C₂×C₆₇	semidirect
438. #2617	C₂×C₆₇	semidirect
439. #2613	C₂×C₆₇	semidirect
440. #2395	C₂×C₆₇	semidirect
441. #2392	C₂×C₆₇	semidirect
442. #2388	C₂×C₆₇	semidirect
443. C₄×#123	C₂×C₆₇	semidirect
444. C₄×#120	C₂×C₆₇	semidirect
445. #2280	C₂×C₆₇	semidirect
446. C₆₇	#34562	direct (N × H)
447. C₂²×#41	C₂²×C₆₇	semidirect
453. C₂×#123	C₂²×C₆₇	semidirect
455. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
457. C₂×#121	C₂²×C₆₇	semidirect
466. C₂×C₄×D₄	C₂²×C₆₇	semidirect
467. C₂×C₄×D₄	C₂²×C₆₇	semidirect
468. C₂×#117	C₂²×C₆₇	semidirect
469. C₂×#117	C₂²×C₆₇	semidirect
474. #400	C₂²×C₆₇	semidirect
475. #399	C₂²×C₆₇	semidirect
476. #398	C₂²×C₆₇	semidirect
477. #398	C₂²×C₆₇	semidirect
478. #397	C₂²×C₆₇	semidirect
479. #397	C₂²×C₆₇	semidirect
480. #397	C₂²×C₆₇	semidirect
481. #396	C₂²×C₆₇	semidirect
482. #396	C₂²×C₆₇	semidirect
483. #395	C₂²×C₆₇	semidirect
486. #394	C₂²×C₆₇	semidirect
487. #394	C₂²×C₆₇	semidirect
488. #394	C₂²×C₆₇	semidirect
489. #394	C₂²×C₆₇	semidirect
490. #393	C₂²×C₆₇	semidirect
493. #392	C₂²×C₆₇	semidirect
494. #388	C₂²×C₆₇	semidirect
495. #387	C₂²×C₆₇	semidirect
498. #386	C₂²×C₆₇	semidirect
501. #385	C₂²×C₆₇	semidirect
503. #381	C₂²×C₆₇	semidirect
506. #380	C₂²×C₆₇	semidirect
509. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
511. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
512. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
513. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
532. C₂³×C₄	D₄×C₆₇	semidirect
618. C₂⁴	#41×C₆₇	semidirect
672. C₂²×C₄	#41×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#525×C₆₇	2
C₂²×C₄×D₄×C₆₇	2
C₆₇×#2638	2
C₆₇×#2635	2
C₆₇×#2630	2
C₆₇×#2627	2
C₆₇×#2626	2
C₆₇×#2622	2
C₆₇×#2618	2
C₆₇×#2617	2
C₆₇×#2613	2
C₆₇×#2395	2
C₆₇×#2392	2
C₆₇×#2388	2
C₄×#123×C₆₇	2
C₄×#120×C₆₇	2
C₆₇×#2280	2
#34562	67

Subgroups — C67×#34562 #30713813

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#34562 #30713813