Subgroups — C₆₇×#34738 #30713989

Order 17152.

5570 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#41×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#532×C₆₇	C₂	1	2	yes	maximal, complemented
3	C₂×#525×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#2436	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#2435	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#2434	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#2433	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#2432	C₂	1	2	yes	maximal, complemented
9	C₆₇×#2431	C₂	1	2	yes	maximal, complemented
10	C₆₇×#2430	C₂	1	4	yes	maximal, complemented
11	C₆₇×#2410	C₂	1	4	yes	maximal, complemented
12	C₆₇×#2388	C₂	1	4	yes	maximal, complemented
13	C₄×#120×C₆₇	C₂	1	4	yes	maximal, complemented
14	C₆₇×#2297	C₂	1	2	yes	maximal, complemented
15	C₂×C₄×C₂²⋊C₄×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₆₇	—	2	16	no	—
17	C₂²×#41×C₆₇	—	2	8	no	—
18	C₂²×#41×C₆₇	C₂²	1	2	yes	—
19	C₂²×#41×C₆₇	C₂²	1	2	yes	—
20	C₂²×#41×C₆₇	C₂²	1	2	yes	—
21	C₂²×#41×C₆₇	C₂²	1	2	yes	—
22	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic, complemented
23	C₂³×Q₈×C₆₇	C₂²	1	1	yes	characteristic
24	C₂³×D₄×C₆₇	C₂²	1	2	yes	—
25	C₂³×D₄×C₆₇	C₂²	1	1	yes	characteristic
26	C₂⁴×C₄×C₆₇	C₂²	1	2	yes	—
27	C₂⁴×C₄×C₆₇	C₂²	1	1	yes	characteristic
28	#532×C₆₇	—	2	16	no	—
29	C₂×C₄⋊Q₈×C₆₇	C₂²	1	2	yes	complemented
30	C₂×#127×C₆₇	C₂²	1	2	yes	complemented
31	C₂×#124×C₆₇	C₂²	1	2	yes	complemented
32	C₂×#124×C₆₇	C₂²	1	2	yes	complemented
33	#525×C₆₇	—	2	8	no	—
34	C₂×#123×C₆₇	C₂²	1	2	yes	complemented
35	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
36	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
37	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
38	C₂×#121×C₆₇	C₂²	1	8	yes	complemented
39	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic, complemented
40	C₂×#120×C₆₇	C₂²	1	4	yes	—
41	C₂×#120×C₆₇	C₂²	1	2	yes	—
42	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
43	C₂×C₄×D₄×C₆₇	C₂²	1	8	yes	complemented
44	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
45	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic, complemented
46	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
47	C₂²×C₄²×C₆₇	C₂²	1	2	yes	complemented
48	#395×C₆₇	C₂²	1	4	yes	complemented
49	#394×C₆₇	C₂²	1	8	yes	complemented
50	#394×C₆₇	C₂²	1	4	yes	complemented
51	#393×C₆₇	C₂²	1	4	yes	complemented
52	#392×C₆₇	C₂²	1	8	yes	complemented
53	#392×C₆₇	C₂²	1	4	yes	complemented
54	#391×C₆₇	C₂²	1	2	yes	complemented
55	#391×C₆₇	C₂²	1	2	yes	complemented
56	#390×C₆₇	C₂²	1	2	yes	complemented
57	#390×C₆₇	C₂²	1	2	yes	complemented
58	#386×C₆₇	C₂²	1	4	yes	—
59	#386×C₆₇	C₂²	1	8	yes	complemented
60	#386×C₆₇	C₂²	1	8	yes	complemented
61	#385×C₆₇	C₂²	1	4	yes	—
62	#385×C₆₇	C₂²	1	8	yes	complemented
63	#379×C₆₇	C₂²	1	4	yes	—
64	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
65	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
66	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
67	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
68	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
69	C₄×C₂²⋊C₄×C₆₇	C₂²	1	8	yes	complemented
70	C₂×#95×C₆₇	C₂²	1	2	yes	complemented
71	C₂⁵×C₆₇	C₂³	1	2	yes	—
72	C₂⁵×C₆₇	C₂³	1	1	yes	characteristic
73	C₂×#41×C₆₇	—	2	128	no	—
74	C₂×#41×C₆₇	—	2	8	no	—
75	C₂×#41×C₆₇	—	2	16	no	—
76	C₂×#41×C₆₇	—	2	8	no	—
77	C₂×#41×C₆₇	—	2	16	no	—
78	C₂×#41×C₆₇	—	2	8	no	—
79	C₂×#41×C₆₇	—	2	8	no	—
80	C₂×#41×C₆₇	—	2	8	no	—
81	C₂×#41×C₆₇	—	2	8	no	—
82	C₂×#41×C₆₇	—	2	8	no	—
83	C₂×#41×C₆₇	—	2	4	no	—
84	C₂×#41×C₆₇	—	2	8	no	—
85	C₂×#41×C₆₇	D₄	1	16	yes	complemented
86	C₂²×Q₈×C₆₇	—	2	8	no	—
87	C₂²×Q₈×C₆₇	—	2	4	no	—
88	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
89	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
90	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
91	C₂²×D₄×C₆₇	—	2	8	no	—
92	C₂²×D₄×C₆₇	—	2	16	no	—
93	C₂²×D₄×C₆₇	—	2	8	no	—
94	C₂²×D₄×C₆₇	—	2	4	no	—
95	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
96	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
97	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
98	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
99	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
100	C₂²×D₄×C₆₇	C₂³	1	8	yes	—
101	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
102	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
103	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
104	C₂³×C₄×C₆₇	—	2	8	no	—
105	C₂³×C₄×C₆₇	—	2	16	no	—
106	C₂³×C₄×C₆₇	—	2	8	no	—
107	C₂³×C₄×C₆₇	D₄	1	8	yes	complemented
108	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
109	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
110	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
111	C₂³×C₄×C₆₇	C₂³	1	4	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	4	yes	—
117	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
118	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
119	C₄⋊Q₈×C₆₇	—	2	8	no	—
120	#127×C₆₇	—	2	8	no	—
121	#124×C₆₇	—	2	8	no	—
122	#124×C₆₇	—	2	8	no	—
123	#123×C₆₇	—	2	8	no	—
124	C₂²⋊Q₈×C₆₇	—	2	4	no	—
125	C₂²⋊Q₈×C₆₇	—	2	4	no	—
126	#121×C₆₇	—	2	32	no	—
127	#121×C₆₇	—	2	4	no	—
128	#121×C₆₇	—	2	4	no	—
129	#120×C₆₇	—	2	8	no	—
130	#120×C₆₇	—	2	16	no	—
131	C₄×D₄×C₆₇	—	2	8	no	—
132	C₄×D₄×C₆₇	—	2	8	no	—
133	C₄×D₄×C₆₇	—	2	32	no	—
134	#117×C₆₇	—	2	4	no	—
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	2	yes	—
138	C₂×C₄⋊C₄×C₆₇	C₂³	1	8	yes	—
139	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
140	C₂×C₂²⋊C₄×C₆₇	—	2	8	no	—
141	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
142	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
143	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
144	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
145	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
146	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
147	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
148	C₂×C₂²⋊C₄×C₆₇	C₂³	1	8	yes	—
149	C₂×C₂²⋊C₄×C₆₇	C₂³	1	8	yes	—
150	C₂×C₂²⋊C₄×C₆₇	C₂³	1	8	yes	—
151	C₂×C₂²⋊C₄×C₆₇	C₂³	1	8	yes	—
152	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
153	C₂×C₄²×C₆₇	—	2	8	no	—
154	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
155	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
156	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
157	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
158	#95×C₆₇	C₂³	1	4	yes	—
159	#95×C₆₇	C₂³	1	2	yes	—
160	#95×C₆₇	C₂³	1	2	yes	—
161	#95×C₆₇	C₂³	1	8	yes	—
162	#95×C₆₇	C₂³	1	8	yes	—
163	C₂⁴×C₆₇	—	2	8	no	—
164	C₂⁴×C₆₇	—	2	4	no	—
165	C₂⁴×C₆₇	—	2	4	no	—
166	C₂⁴×C₆₇	—	2	4	no	—
167	C₂⁴×C₆₇	—	2	8	no	—
168	C₂⁴×C₆₇	—	4	2	no	—
169	C₂⁴×C₆₇	—	4	4	no	—
170	C₂⁴×C₆₇	C₂×D₄	1	4	yes	—
171	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
172	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
173	C₂⁴×C₆₇	C₂⁴	1	4	yes	—
174	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
175	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
176	#41×C₆₇	—	2	64	no	—
177	#41×C₆₇	—	2	64	no	—
178	#41×C₆₇	—	2	64	no	—
179	#41×C₆₇	—	2	64	no	—
180	#41×C₆₇	—	4	16	no	—
181	C₂×Q₈×C₆₇	—	2	32	no	—
182	C₂×Q₈×C₆₇	—	2	8	no	—
183	C₂×Q₈×C₆₇	—	2	4	no	—
184	C₂×Q₈×C₆₇	—	2	4	no	—
185	C₂×Q₈×C₆₇	—	2	4	no	—
186	C₂×Q₈×C₆₇	—	2	2	no	—
187	C₂×Q₈×C₆₇	—	2	4	no	—
188	C₂×Q₈×C₆₇	C₂×D₄	1	8	yes	—
189	C₂×D₄×C₆₇	—	2	64	no	—
190	C₂×D₄×C₆₇	—	2	32	no	—
191	C₂×D₄×C₆₇	—	2	8	no	—
192	C₂×D₄×C₆₇	—	2	8	no	—
193	C₂×D₄×C₆₇	—	2	8	no	—
194	C₂×D₄×C₆₇	—	2	8	no	—
195	C₂×D₄×C₆₇	—	2	8	no	—
196	C₂×D₄×C₆₇	—	2	4	no	—
197	C₂×D₄×C₆₇	—	2	4	no	—
198	C₂×D₄×C₆₇	—	2	16	no	—
199	C₂×D₄×C₆₇	—	2	4	no	—
200	C₂×D₄×C₆₇	—	2	8	no	—
201	C₂×D₄×C₆₇	—	2	8	no	—
202	C₂×D₄×C₆₇	—	2	8	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	2	no	—
207	C₂×D₄×C₆₇	—	2	4	no	—
208	C₂×D₄×C₆₇	—	2	16	no	—
209	C₂×D₄×C₆₇	—	4	8	no	—
210	C₂×D₄×C₆₇	—	4	4	no	—
211	C₂×D₄×C₆₇	C₂×D₄	1	16	yes	—
212	C₂×D₄×C₆₇	C₂×D₄	1	8	yes	—
213	C₂²×C₄×C₆₇	—	2	64	no	—
214	C₂²×C₄×C₆₇	—	2	4	no	—
215	C₂²×C₄×C₆₇	—	2	8	no	—
216	C₂²×C₄×C₆₇	—	2	4	no	—
217	C₂²×C₄×C₆₇	—	2	32	no	—
218	C₂²×C₄×C₆₇	—	2	4	no	—
219	C₂²×C₄×C₆₇	—	2	8	no	—
220	C₂²×C₄×C₆₇	—	2	4	no	—
221	C₂²×C₄×C₆₇	—	2	8	no	—
222	C₂²×C₄×C₆₇	—	2	8	no	—
223	C₂²×C₄×C₆₇	—	2	4	no	—
224	C₂²×C₄×C₆₇	—	2	8	no	—
225	C₂²×C₄×C₆₇	—	2	8	no	—
226	C₂²×C₄×C₆₇	—	2	4	no	—
227	C₂²×C₄×C₆₇	—	2	8	no	—
228	C₂²×C₄×C₆₇	—	2	4	no	—
229	C₂²×C₄×C₆₇	—	2	8	no	—
230	C₂²×C₄×C₆₇	—	2	8	no	—
231	C₂²×C₄×C₆₇	—	4	4	no	—
232	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
233	C₂²×C₄×C₆₇	C₂×D₄	1	16	yes	—
234	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
235	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
236	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
237	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
238	C₂²×C₄×C₆₇	C₂×D₄	1	8	yes	—
239	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
240	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
241	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
242	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
243	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
244	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
245	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
246	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
247	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
248	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
249	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
250	C₄⋊C₄×C₆₇	—	2	2	no	—
251	C₄⋊C₄×C₆₇	—	2	2	no	—
252	C₄⋊C₄×C₆₇	—	2	16	no	—
253	C₄⋊C₄×C₆₇	—	2	4	no	—
254	C₄⋊C₄×C₆₇	—	2	4	no	—
255	C₂²⋊C₄×C₆₇	—	2	4	no	—
256	C₂²⋊C₄×C₆₇	—	2	4	no	—
257	C₂²⋊C₄×C₆₇	—	2	4	no	—
258	C₂²⋊C₄×C₆₇	—	2	16	no	—
259	C₂²⋊C₄×C₆₇	—	2	4	no	—
260	C₂²⋊C₄×C₆₇	—	2	4	no	—
261	C₂²⋊C₄×C₆₇	—	2	4	no	—
262	C₂²⋊C₄×C₆₇	—	2	16	no	—
263	C₂²⋊C₄×C₆₇	—	2	8	no	—
264	C₂²⋊C₄×C₆₇	—	2	16	no	—
265	C₂²⋊C₄×C₆₇	—	4	8	no	—
266	C₂²⋊C₄×C₆₇	#41	1	8	yes	complemented
267	C₄²×C₆₇	—	2	8	no	—
268	C₄²×C₆₇	—	2	4	no	—
269	C₄²×C₆₇	—	2	4	no	—
270	C₄²×C₆₇	—	2	4	no	—
271	C₂³×C₆₇	—	2	2	no	—
272	C₂³×C₆₇	—	2	2	no	—
273	C₂³×C₆₇	—	2	2	no	—
274	C₂³×C₆₇	—	2	2	no	—
275	C₂³×C₆₇	—	2	16	no	—
276	C₂³×C₆₇	—	2	8	no	—
277	C₂³×C₆₇	—	2	8	no	—
278	C₂³×C₆₇	—	2	4	no	—
279	C₂³×C₆₇	—	2	4	no	—
280	C₂³×C₆₇	—	2	2	no	—
281	C₂³×C₆₇	—	2	2	no	—
282	C₂³×C₆₇	—	2	8	no	—
283	C₂³×C₆₇	—	2	8	no	—
284	C₂³×C₆₇	—	2	2	no	—
285	C₂³×C₆₇	—	2	2	no	—
286	C₂³×C₆₇	—	2	4	no	—
287	C₂³×C₆₇	—	2	4	no	—
288	C₂³×C₆₇	—	2	4	no	—
289	C₂³×C₆₇	—	4	4	no	—
290	C₂³×C₆₇	—	4	16	no	—
291	C₂³×C₆₇	—	4	32	no	—
292	C₂³×C₆₇	—	4	8	no	—
293	C₂³×C₆₇	—	4	8	no	—
294	C₂³×C₆₇	C₂²×D₄	1	8	yes	—
295	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
296	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
297	C₂³×C₆₇	C₂²×D₄	1	4	yes	—
298	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
299	C₂³×C₆₇	C₂×#41	1	4	yes	—
300	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
301	Q₈×C₆₇	—	2	16	no	—
302	Q₈×C₆₇	—	2	16	no	—
303	Q₈×C₆₇	—	4	4	no	—
304	D₄×C₆₇	—	2	32	no	—
305	D₄×C₆₇	—	2	16	no	—
306	D₄×C₆₇	—	2	32	no	—
307	D₄×C₆₇	—	2	16	no	—
308	D₄×C₆₇	—	4	32	no	—
309	D₄×C₆₇	—	4	8	no	—
310	D₄×C₆₇	—	4	8	no	—
311	D₄×C₆₇	—	4	8	no	—
312	D₄×C₆₇	—	4	4	no	—
313	C₂×C₄×C₆₇	—	2	16	no	—
314	C₂×C₄×C₆₇	—	2	32	no	—
315	C₂×C₄×C₆₇	—	2	8	no	—
316	C₂×C₄×C₆₇	—	2	4	no	—
317	C₂×C₄×C₆₇	—	2	2	no	—
318	C₂×C₄×C₆₇	—	2	4	no	—
319	C₂×C₄×C₆₇	—	2	4	no	—
320	C₂×C₄×C₆₇	—	2	2	no	—
321	C₂×C₄×C₆₇	—	2	4	no	—
322	C₂×C₄×C₆₇	—	2	8	no	—
323	C₂×C₄×C₆₇	—	2	8	no	—
324	C₂×C₄×C₆₇	—	2	8	no	—
325	C₂×C₄×C₆₇	—	2	32	no	—
326	C₂×C₄×C₆₇	—	2	8	no	—
327	C₂×C₄×C₆₇	—	2	4	no	—
328	C₂×C₄×C₆₇	—	2	2	no	—
329	C₂×C₄×C₆₇	—	2	2	no	—
330	C₂×C₄×C₆₇	—	2	2	no	—
331	C₂×C₄×C₆₇	—	2	4	no	—
332	C₂×C₄×C₆₇	—	2	4	no	—
333	C₂×C₄×C₆₇	—	2	4	no	—
334	C₂×C₄×C₆₇	—	2	4	no	—
335	C₂×C₄×C₆₇	—	2	4	no	—
336	C₂×C₄×C₆₇	—	4	16	no	—
337	C₂×C₄×C₆₇	—	4	8	no	—
338	C₂×C₄×C₆₇	#120	1	16	yes	complemented
339	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
340	C₂×C₄×C₆₇	C₂²×D₄	1	8	yes	—
341	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
342	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
343	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
344	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
345	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
346	C₂×C₄×C₆₇	C₂×#41	1	8	yes	complemented
347	C₂²×C₆₇	—	2	2	no	—
348	C₂²×C₆₇	—	2	2	no	—
349	C₂²×C₆₇	—	2	2	no	—
350	C₂²×C₆₇	—	2	2	no	—
351	C₂²×C₆₇	—	2	8	no	—
352	C₂²×C₆₇	—	2	8	no	—
353	C₂²×C₆₇	—	2	8	no	—
354	C₂²×C₆₇	—	2	2	no	—
355	C₂²×C₆₇	—	2	2	no	—
356	C₂²×C₆₇	—	2	2	no	—
357	C₂²×C₆₇	—	2	16	no	—
358	C₂²×C₆₇	—	4	16	no	—
359	C₂²×C₆₇	—	4	32	no	—
360	C₂²×C₆₇	—	4	4	no	—
361	C₂²×C₆₇	—	4	4	no	—
362	C₂²×C₆₇	—	4	4	no	—
363	C₂²×C₆₇	—	4	8	no	—
364	C₂²×C₆₇	—	4	2	no	—
365	C₂²×C₆₇	—	4	2	no	—
366	C₂²×C₆₇	—	4	2	no	—
367	C₂²×C₆₇	—	4	8	no	—
368	C₂²×C₆₇	C₂×#120	1	4	yes	—
369	C₂²×C₆₇	#532	1	4	yes	complemented
370	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
371	C₂²×C₆₇	C₂³×D₄	1	2	yes	—
372	C₂²×C₆₇	C₂²×#41	1	2	yes	—
373	C₂²×C₆₇	#585	1	2	yes	—
374	C₄×C₆₇	—	2	2	no	—
375	C₄×C₆₇	—	2	8	no	—
376	C₄×C₆₇	—	2	2	no	—
377	C₄×C₆₇	—	2	8	no	—
378	C₄×C₆₇	—	4	2	no	—
379	C₄×C₆₇	—	4	2	no	—
380	C₄×C₆₇	—	4	2	no	—
381	C₄×C₆₇	—	4	4	no	—
382	C₄×C₆₇	C₂×#120	1	4	yes	—
383	C₄×C₆₇	C₂×#120	1	4	yes	—
384	#34738	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
385	C₂×C₆₇	—	2	4	no	—
386	C₂×C₆₇	—	2	4	no	—
387	C₂×C₆₇	—	4	2	no	—
388	C₂×C₆₇	—	4	8	no	—
389	C₂×C₆₇	—	8	2	no	—
390	C₂×C₆₇	C₂²×#120	1	1	yes	characteristic
391	C₂×C₆₇	C₂×#532	1	1	yes	characteristic
392	C₂×C₆₇	#3449	1	1	yes	characteristic
393	C₂×C₆₇	D₄×#41	1	4	yes	—
394	C₂³×#41	C₂×C₆₇	1	1	yes	characteristic, complemented
395	C₂×#532	C₂×C₆₇	1	2	yes	complemented
396	C₂×#525	C₂×C₆₇	1	1	yes	characteristic, complemented
397	#2436	C₂×C₆₇	1	1	yes	characteristic, complemented
398	#2435	C₂×C₆₇	1	1	yes	characteristic, complemented
399	#2434	C₂×C₆₇	1	1	yes	characteristic, complemented
400	#2433	C₂×C₆₇	1	1	yes	characteristic, complemented
401	#2432	C₂×C₆₇	1	2	yes	complemented
402	#2431	C₂×C₆₇	1	2	yes	complemented
403	#2430	C₂×C₆₇	1	4	yes	complemented
404	#2410	C₂×C₆₇	1	4	yes	complemented
405	#2388	C₂×C₆₇	1	4	yes	complemented
406	C₄×#120	C₂×C₆₇	1	4	yes	complemented
407	#2297	C₂×C₆₇	1	2	yes	complemented
408	C₂×C₄×C₂²⋊C₄	C₂×C₆₇	1	1	yes	characteristic, complemented
409	C₆₇	#34738	1	1	yes	characteristic, direct product factor, Sylow
410	C₂²×#41	—	2	16	no	—
411	C₂²×#41	—	2	8	no	—
412	C₂²×#41	C₂²×C₆₇	1	2	yes	—
413	C₂²×#41	C₂²×C₆₇	1	2	yes	—
414	C₂²×#41	C₂²×C₆₇	1	2	yes	—
415	C₂²×#41	C₂²×C₆₇	1	2	yes	—
416	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic, complemented
417	C₂³×Q₈	C₂²×C₆₇	1	1	yes	characteristic
418	C₂³×D₄	C₂²×C₆₇	1	2	yes	—
419	C₂³×D₄	C₂²×C₆₇	1	1	yes	characteristic
420	C₂⁴×C₄	C₂²×C₆₇	1	2	yes	—
421	C₂⁴×C₄	C₂²×C₆₇	1	1	yes	characteristic
422	#532	—	2	16	no	—
423	C₂×C₄⋊Q₈	C₂²×C₆₇	1	2	yes	complemented
424	C₂×#127	C₂²×C₆₇	1	2	yes	complemented
425	C₂×#124	C₂²×C₆₇	1	2	yes	complemented
426	C₂×#124	C₂²×C₆₇	1	2	yes	complemented
427	#525	—	2	8	no	—
428	C₂×#123	C₂²×C₆₇	1	2	yes	complemented
429	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
430	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
431	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
432	C₂×#121	C₂²×C₆₇	1	8	yes	complemented
433	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic, complemented
434	C₂×#120	C₂²×C₆₇	1	2	yes	—
435	C₂×#120	C₂²×C₆₇	1	4	yes	—
436	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
437	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
438	C₂×C₄×D₄	C₂²×C₆₇	1	8	yes	complemented
439	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic, complemented
440	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
441	C₂²×C₄²	C₂²×C₆₇	1	2	yes	complemented
442	#395	C₂²×C₆₇	1	4	yes	complemented
443	#394	C₂²×C₆₇	1	8	yes	complemented
444	#394	C₂²×C₆₇	1	4	yes	complemented
445	#393	C₂²×C₆₇	1	4	yes	complemented
446	#392	C₂²×C₆₇	1	8	yes	complemented
447	#392	C₂²×C₆₇	1	4	yes	complemented
448	#391	C₂²×C₆₇	1	2	yes	complemented
449	#391	C₂²×C₆₇	1	2	yes	complemented
450	#390	C₂²×C₆₇	1	2	yes	complemented
451	#390	C₂²×C₆₇	1	2	yes	complemented
452	#386	C₂²×C₆₇	1	4	yes	—
453	#386	C₂²×C₆₇	1	8	yes	complemented
454	#386	C₂²×C₆₇	1	8	yes	complemented
455	#385	C₂²×C₆₇	1	4	yes	—
456	#385	C₂²×C₆₇	1	8	yes	complemented
457	#379	C₂²×C₆₇	1	4	yes	—
458	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
459	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
460	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
461	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
462	C₄×C₂²⋊C₄	C₂²×C₆₇	1	8	yes	complemented
463	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
464	C₂×#95	C₂²×C₆₇	1	2	yes	complemented
465	C₂⁵	C₂³×C₆₇	1	2	yes	—
466	C₂⁵	C₂³×C₆₇	1	1	yes	characteristic
467	C₂×#41	—	2	128	no	—
468	C₂×#41	—	2	8	no	—
469	C₂×#41	—	2	16	no	—
470	C₂×#41	—	2	8	no	—
471	C₂×#41	—	2	16	no	—
472	C₂×#41	—	2	8	no	—
473	C₂×#41	—	2	8	no	—
474	C₂×#41	—	2	8	no	—
475	C₂×#41	—	2	8	no	—
476	C₂×#41	—	2	8	no	—
477	C₂×#41	—	2	4	no	—
478	C₂×#41	—	2	8	no	—
479	C₂×#41	D₄×C₆₇	1	16	yes	complemented
480	C₂²×Q₈	—	2	8	no	—
481	C₂²×Q₈	—	2	4	no	—
482	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
483	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
484	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
485	C₂²×D₄	—	2	8	no	—
486	C₂²×D₄	—	2	16	no	—
487	C₂²×D₄	—	2	8	no	—
488	C₂²×D₄	—	2	4	no	—
489	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
490	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
491	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
492	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
493	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
494	C₂²×D₄	C₂³×C₆₇	1	8	yes	—
495	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
496	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
497	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
498	C₂³×C₄	—	2	8	no	—
499	C₂³×C₄	—	2	16	no	—
500	C₂³×C₄	—	2	8	no	—
501	C₂³×C₄	D₄×C₆₇	1	8	yes	complemented
502	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
503	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
504	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
505	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
506	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
507	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
508	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
509	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
510	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
511	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
512	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
513	C₄⋊Q₈	—	2	8	no	—
514	#127	—	2	8	no	—
515	#124	—	2	8	no	—
516	#124	—	2	8	no	—
517	#123	—	2	8	no	—
518	C₂²⋊Q₈	—	2	4	no	—
519	C₂²⋊Q₈	—	2	4	no	—
520	#121	—	2	32	no	—
521	#121	—	2	4	no	—
522	#121	—	2	4	no	—
523	#120	—	2	8	no	—
524	#120	—	2	16	no	—
525	C₄×D₄	—	2	8	no	—
526	C₄×D₄	—	2	8	no	—
527	C₄×D₄	—	2	32	no	—
528	#117	—	2	4	no	—
529	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
530	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
531	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
532	C₂×C₄⋊C₄	C₂³×C₆₇	1	8	yes	—
533	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
534	C₂×C₂²⋊C₄	—	2	8	no	—
535	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
536	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
537	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
538	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
539	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
540	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
541	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
542	C₂×C₂²⋊C₄	C₂³×C₆₇	1	8	yes	—
543	C₂×C₂²⋊C₄	C₂³×C₆₇	1	8	yes	—
544	C₂×C₂²⋊C₄	C₂³×C₆₇	1	8	yes	—
545	C₂×C₂²⋊C₄	C₂³×C₆₇	1	8	yes	—
546	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
547	C₂×C₄²	—	2	8	no	—
548	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
549	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
550	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
551	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
552	#95	C₂³×C₆₇	1	4	yes	—
553	#95	C₂³×C₆₇	1	2	yes	—
554	#95	C₂³×C₆₇	1	2	yes	—
555	#95	C₂³×C₆₇	1	8	yes	—
556	#95	C₂³×C₆₇	1	8	yes	—
557	C₂⁴	—	2	8	no	—
558	C₂⁴	—	2	4	no	—
559	C₂⁴	—	2	4	no	—
560	C₂⁴	—	2	4	no	—
561	C₂⁴	—	2	8	no	—
562	C₂⁴	—	4	2	no	—
563	C₂⁴	—	4	4	no	—
564	C₂⁴	C₂×D₄×C₆₇	1	4	yes	—
565	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
566	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
567	C₂⁴	C₂⁴×C₆₇	1	4	yes	—
568	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
569	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
570	#41	—	2	64	no	—
571	#41	—	2	64	no	—
572	#41	—	2	64	no	—
573	#41	—	2	64	no	—
574	#41	—	4	16	no	—
575	C₂×Q₈	—	2	32	no	—
576	C₂×Q₈	—	2	8	no	—
577	C₂×Q₈	—	2	4	no	—
578	C₂×Q₈	—	2	4	no	—
579	C₂×Q₈	—	2	4	no	—
580	C₂×Q₈	—	2	2	no	—
581	C₂×Q₈	—	2	4	no	—
582	C₂×Q₈	C₂×D₄×C₆₇	1	8	yes	—
583	C₂×D₄	—	2	64	no	—
584	C₂×D₄	—	2	32	no	—
585	C₂×D₄	—	2	8	no	—
586	C₂×D₄	—	2	8	no	—
587	C₂×D₄	—	2	8	no	—
588	C₂×D₄	—	2	8	no	—
589	C₂×D₄	—	2	8	no	—
590	C₂×D₄	—	2	4	no	—
591	C₂×D₄	—	2	4	no	—
592	C₂×D₄	—	2	16	no	—
593	C₂×D₄	—	2	4	no	—
594	C₂×D₄	—	2	8	no	—
595	C₂×D₄	—	2	8	no	—
596	C₂×D₄	—	2	8	no	—
597	C₂×D₄	—	2	4	no	—
598	C₂×D₄	—	2	4	no	—
599	C₂×D₄	—	2	4	no	—
600	C₂×D₄	—	2	2	no	—
601	C₂×D₄	—	2	4	no	—
602	C₂×D₄	—	2	16	no	—
603	C₂×D₄	—	4	8	no	—
604	C₂×D₄	—	4	4	no	—
605	C₂×D₄	C₂×D₄×C₆₇	1	16	yes	—
606	C₂×D₄	C₂×D₄×C₆₇	1	8	yes	—
607	C₂²×C₄	—	2	64	no	—
608	C₂²×C₄	—	2	4	no	—
609	C₂²×C₄	—	2	8	no	—
610	C₂²×C₄	—	2	4	no	—
611	C₂²×C₄	—	2	32	no	—
612	C₂²×C₄	—	2	4	no	—
613	C₂²×C₄	—	2	8	no	—
614	C₂²×C₄	—	2	4	no	—
615	C₂²×C₄	—	2	8	no	—
616	C₂²×C₄	—	2	8	no	—
617	C₂²×C₄	—	2	4	no	—
618	C₂²×C₄	—	2	8	no	—
619	C₂²×C₄	—	2	8	no	—
620	C₂²×C₄	—	2	4	no	—
621	C₂²×C₄	—	2	8	no	—
622	C₂²×C₄	—	2	4	no	—
623	C₂²×C₄	—	2	8	no	—
624	C₂²×C₄	—	2	8	no	—
625	C₂²×C₄	—	4	4	no	—
626	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
627	C₂²×C₄	C₂×D₄×C₆₇	1	16	yes	—
628	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
629	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
630	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
631	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
632	C₂²×C₄	C₂×D₄×C₆₇	1	8	yes	—
633	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
634	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
635	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
636	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
637	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
638	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
639	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
640	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
641	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
642	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
643	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
644	C₄⋊C₄	—	2	2	no	—
645	C₄⋊C₄	—	2	2	no	—
646	C₄⋊C₄	—	2	16	no	—
647	C₄⋊C₄	—	2	4	no	—
648	C₄⋊C₄	—	2	4	no	—
649	C₂²⋊C₄	—	2	4	no	—
650	C₂²⋊C₄	—	2	4	no	—
651	C₂²⋊C₄	—	2	4	no	—
652	C₂²⋊C₄	—	2	16	no	—
653	C₂²⋊C₄	—	2	4	no	—
654	C₂²⋊C₄	—	2	4	no	—
655	C₂²⋊C₄	—	2	4	no	—
656	C₂²⋊C₄	—	2	16	no	—
657	C₂²⋊C₄	—	2	8	no	—
658	C₂²⋊C₄	—	2	16	no	—
659	C₂²⋊C₄	—	4	8	no	—
660	C₂²⋊C₄	#41×C₆₇	1	8	yes	complemented
661	C₄²	—	2	8	no	—
662	C₄²	—	2	4	no	—
663	C₄²	—	2	4	no	—
664	C₄²	—	2	4	no	—
665	C₂³	—	2	2	no	—
666	C₂³	—	2	2	no	—
667	C₂³	—	2	2	no	—
668	C₂³	—	2	2	no	—
669	C₂³	—	2	16	no	—
670	C₂³	—	2	8	no	—
671	C₂³	—	2	8	no	—
672	C₂³	—	2	4	no	—
673	C₂³	—	2	4	no	—
674	C₂³	—	2	2	no	—
675	C₂³	—	2	2	no	—
676	C₂³	—	2	8	no	—
677	C₂³	—	2	8	no	—
678	C₂³	—	2	2	no	—
679	C₂³	—	2	2	no	—
680	C₂³	—	2	4	no	—
681	C₂³	—	2	4	no	—
682	C₂³	—	2	4	no	—
683	C₂³	—	4	4	no	—
684	C₂³	—	4	16	no	—
685	C₂³	—	4	32	no	—
686	C₂³	—	4	8	no	—
687	C₂³	—	4	8	no	—
688	C₂³	C₂²×D₄×C₆₇	1	8	yes	—
689	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
690	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
691	C₂³	C₂²×D₄×C₆₇	1	4	yes	—
692	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
693	C₂³	C₂×#41×C₆₇	1	4	yes	—
694	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
695	Q₈	—	2	16	no	—
696	Q₈	—	2	16	no	—
697	Q₈	—	4	4	no	—
698	D₄	—	2	32	no	—
699	D₄	—	2	16	no	—
700	D₄	—	2	32	no	—
701	D₄	—	2	16	no	—
702	D₄	—	4	32	no	—
703	D₄	—	4	8	no	—
704	D₄	—	4	8	no	—
705	D₄	—	4	8	no	—
706	D₄	—	4	4	no	—
707	C₂×C₄	—	2	16	no	—
708	C₂×C₄	—	2	32	no	—
709	C₂×C₄	—	2	8	no	—
710	C₂×C₄	—	2	4	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	4	no	—
713	C₂×C₄	—	2	4	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	4	no	—
716	C₂×C₄	—	2	8	no	—
717	C₂×C₄	—	2	8	no	—
718	C₂×C₄	—	2	8	no	—
719	C₂×C₄	—	2	32	no	—
720	C₂×C₄	—	2	8	no	—
721	C₂×C₄	—	2	4	no	—
722	C₂×C₄	—	2	2	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	2	no	—
725	C₂×C₄	—	2	4	no	—
726	C₂×C₄	—	2	4	no	—
727	C₂×C₄	—	2	4	no	—
728	C₂×C₄	—	2	4	no	—
729	C₂×C₄	—	2	4	no	—
730	C₂×C₄	—	4	16	no	—
731	C₂×C₄	—	4	8	no	—
732	C₂×C₄	#120×C₆₇	1	16	yes	complemented
733	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
734	C₂×C₄	C₂²×D₄×C₆₇	1	8	yes	—
735	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
736	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
737	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
738	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
739	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
740	C₂×C₄	C₂×#41×C₆₇	1	8	yes	complemented
741	C₂²	—	2	2	no	—
742	C₂²	—	2	2	no	—
743	C₂²	—	2	2	no	—
744	C₂²	—	2	2	no	—
745	C₂²	—	2	8	no	—
746	C₂²	—	2	8	no	—
747	C₂²	—	2	8	no	—
748	C₂²	—	2	2	no	—
749	C₂²	—	2	2	no	—
750	C₂²	—	2	2	no	—
751	C₂²	—	2	16	no	—
752	C₂²	—	4	16	no	—
753	C₂²	—	4	32	no	—
754	C₂²	—	4	4	no	—
755	C₂²	—	4	4	no	—
756	C₂²	—	4	4	no	—
757	C₂²	—	4	8	no	—
758	C₂²	—	4	2	no	—
759	C₂²	—	4	2	no	—
760	C₂²	—	4	2	no	—
761	C₂²	—	4	8	no	—
762	C₂²	C₂×#120×C₆₇	1	4	yes	—
763	C₂²	#532×C₆₇	1	4	yes	complemented
764	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
765	C₂²	C₂³×D₄×C₆₇	1	2	yes	—
766	C₂²	C₂²×#41×C₆₇	1	2	yes	—
767	C₂²	#585×C₆₇	1	2	yes	—
768	C₄	—	2	2	no	—
769	C₄	—	2	8	no	—
770	C₄	—	2	2	no	—
771	C₄	—	2	8	no	—
772	C₄	—	4	2	no	—
773	C₄	—	4	2	no	—
774	C₄	—	4	2	no	—
775	C₄	—	4	4	no	—
776	C₄	C₂×#120×C₆₇	1	4	yes	—
777	C₄	C₂×#120×C₆₇	1	4	yes	—
778	C₂	—	2	4	no	—
779	C₂	—	2	4	no	—
780	C₂	—	4	2	no	—
781	C₂	—	4	8	no	—
782	C₂	—	8	2	no	—
783	C₂	C₂²×#120×C₆₇	1	1	yes	characteristic
784	C₂	C₂×#532×C₆₇	1	1	yes	characteristic
785	C₂	C₆₇×#3449	1	1	yes	characteristic
786	C₂	D₄×#41×C₆₇	1	4	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. C₂³×#41×C₆₇	C₂	semidirect
2. C₂×#532×C₆₇	C₂	semidirect
3. C₂×#525×C₆₇	C₂	semidirect
4. C₆₇×#2436	C₂	semidirect
5. C₆₇×#2435	C₂	semidirect
6. C₆₇×#2434	C₂	semidirect
7. C₆₇×#2433	C₂	semidirect
8. C₆₇×#2432	C₂	semidirect
9. C₆₇×#2431	C₂	semidirect
10. C₆₇×#2430	C₂	semidirect
11. C₆₇×#2410	C₂	semidirect
12. C₆₇×#2388	C₂	semidirect
13. C₄×#120×C₆₇	C₂	semidirect
14. C₆₇×#2297	C₂	semidirect
15. C₂×C₄×C₂²⋊C₄×C₆₇	C₂	semidirect
22. C₂²×#41×C₆₇	C₂²	semidirect
29. C₂×C₄⋊Q₈×C₆₇	C₂²	semidirect
30. C₂×#127×C₆₇	C₂²	semidirect
31. C₂×#124×C₆₇	C₂²	semidirect
32. C₂×#124×C₆₇	C₂²	semidirect
34. C₂×#123×C₆₇	C₂²	semidirect
36. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
38. C₂×#121×C₆₇	C₂²	semidirect
39. C₂×#121×C₆₇	C₂²	semidirect
43. C₂×C₄×D₄×C₆₇	C₂²	semidirect
44. C₂×C₄×D₄×C₆₇	C₂²	semidirect
45. C₂×#117×C₆₇	C₂²	semidirect
47. C₂²×C₄²×C₆₇	C₂²	semidirect
48. #395×C₆₇	C₂²	semidirect
49. #394×C₆₇	C₂²	semidirect
50. #394×C₆₇	C₂²	semidirect
51. #393×C₆₇	C₂²	semidirect
52. #392×C₆₇	C₂²	semidirect
53. #392×C₆₇	C₂²	semidirect
54. #391×C₆₇	C₂²	semidirect
55. #391×C₆₇	C₂²	semidirect
56. #390×C₆₇	C₂²	semidirect
57. #390×C₆₇	C₂²	semidirect
59. #386×C₆₇	C₂²	semidirect
60. #386×C₆₇	C₂²	semidirect
62. #385×C₆₇	C₂²	semidirect
67. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
68. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
69. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
70. C₂×#95×C₆₇	C₂²	semidirect
85. C₂×#41×C₆₇	D₄	semidirect
107. C₂³×C₄×C₆₇	D₄	semidirect
266. C₂²⋊C₄×C₆₇	#41	semidirect
338. C₂×C₄×C₆₇	#120	semidirect
346. C₂×C₄×C₆₇	C₂×#41	semidirect
369. C₂²×C₆₇	#532	semidirect
384. #34738	C₆₇	direct (N × H)
394. C₂³×#41	C₂×C₆₇	semidirect
395. C₂×#532	C₂×C₆₇	semidirect
396. C₂×#525	C₂×C₆₇	semidirect
397. #2436	C₂×C₆₇	semidirect
398. #2435	C₂×C₆₇	semidirect
399. #2434	C₂×C₆₇	semidirect
400. #2433	C₂×C₆₇	semidirect
401. #2432	C₂×C₆₇	semidirect
402. #2431	C₂×C₆₇	semidirect
403. #2430	C₂×C₆₇	semidirect
404. #2410	C₂×C₆₇	semidirect
405. #2388	C₂×C₆₇	semidirect
406. C₄×#120	C₂×C₆₇	semidirect
407. #2297	C₂×C₆₇	semidirect
408. C₂×C₄×C₂²⋊C₄	C₂×C₆₇	semidirect
409. C₆₇	#34738	direct (N × H)
416. C₂²×#41	C₂²×C₆₇	semidirect
423. C₂×C₄⋊Q₈	C₂²×C₆₇	semidirect
424. C₂×#127	C₂²×C₆₇	semidirect
425. C₂×#124	C₂²×C₆₇	semidirect
426. C₂×#124	C₂²×C₆₇	semidirect
428. C₂×#123	C₂²×C₆₇	semidirect
430. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
432. C₂×#121	C₂²×C₆₇	semidirect
433. C₂×#121	C₂²×C₆₇	semidirect
437. C₂×C₄×D₄	C₂²×C₆₇	semidirect
438. C₂×C₄×D₄	C₂²×C₆₇	semidirect
439. C₂×#117	C₂²×C₆₇	semidirect
441. C₂²×C₄²	C₂²×C₆₇	semidirect
442. #395	C₂²×C₆₇	semidirect
443. #394	C₂²×C₆₇	semidirect
444. #394	C₂²×C₆₇	semidirect
445. #393	C₂²×C₆₇	semidirect
446. #392	C₂²×C₆₇	semidirect
447. #392	C₂²×C₆₇	semidirect
448. #391	C₂²×C₆₇	semidirect
449. #391	C₂²×C₆₇	semidirect
450. #390	C₂²×C₆₇	semidirect
451. #390	C₂²×C₆₇	semidirect
453. #386	C₂²×C₆₇	semidirect
454. #386	C₂²×C₆₇	semidirect
456. #385	C₂²×C₆₇	semidirect
461. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
462. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
463. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
464. C₂×#95	C₂²×C₆₇	semidirect
479. C₂×#41	D₄×C₆₇	semidirect
501. C₂³×C₄	D₄×C₆₇	semidirect
660. C₂²⋊C₄	#41×C₆₇	semidirect
732. C₂×C₄	#120×C₆₇	semidirect
740. C₂×C₄	C₂×#41×C₆₇	semidirect
763. C₂²	#532×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂³×#41×C₆₇	2
C₂×#532×C₆₇	2
C₂×#525×C₆₇	2
C₆₇×#2436	2
C₆₇×#2435	2
C₆₇×#2434	2
C₆₇×#2433	2
C₆₇×#2432	2
C₆₇×#2431	2
C₆₇×#2430	2
C₆₇×#2410	2
C₆₇×#2388	2
C₄×#120×C₆₇	2
C₆₇×#2297	2
C₂×C₄×C₂²⋊C₄×C₆₇	2
#34738	67

Subgroups — C67×#34738 #30713989

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#34738 #30713989