Subgroups — C₆₇×#33006 #30712257

Order 17152.

1408 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#41×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#482×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#449×C₆₇	C₂	1	1	yes	maximal, characteristic
4	C₆₇×#2854	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#1880	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#1880	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#1879	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#1879	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#1865	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#1864	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#1863	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#1862	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#1825	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#1817	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#1788	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
17	C₂²×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic
18	C₂²×D₈×C₆₇	C₂²	1	1	yes	characteristic
19	C₂×#123×C₆₇	—	2	1	no	—
20	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
21	C₄×#41×C₆₇	—	2	4	no	—
22	C₄×#41×C₆₇	—	2	4	no	—
23	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
24	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₄×C₆₇	—	2	1	no	—
26	C₂×C₄×D₄×C₆₇	—	2	1	no	—
27	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
29	C₂×#117×C₆₇	—	2	1	no	—
30	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
31	C₂²×C₄²×C₆₇	—	2	1	no	—
32	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
33	#482×C₆₇	—	2	4	no	—
34	#449×C₆₇	—	2	4	no	—
35	C₂×#107×C₆₇	C₂²	1	1	yes	characteristic
36	C₂×#106×C₆₇	C₂²	1	1	yes	characteristic
37	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic
38	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic
39	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic
40	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
41	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
42	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
43	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
44	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
45	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
46	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
47	#390×C₆₇	C₂²	1	1	yes	characteristic
48	#390×C₆₇	C₂²	1	1	yes	characteristic
49	#389×C₆₇	C₂²	1	1	yes	characteristic
50	#389×C₆₇	C₂²	1	1	yes	characteristic
51	#388×C₆₇	—	2	1	no	—
52	#388×C₆₇	—	2	1	no	—
53	#386×C₆₇	—	2	1	no	—
54	#380×C₆₇	C₂²	1	1	yes	characteristic
55	#340×C₆₇	C₂²	1	1	yes	characteristic
56	#340×C₆₇	C₂²	1	1	yes	characteristic
57	#340×C₆₇	C₂²	1	1	yes	characteristic
58	#340×C₆₇	C₂²	1	1	yes	characteristic
59	#336×C₆₇	C₂²	1	1	yes	characteristic
60	#336×C₆₇	C₂²	1	1	yes	characteristic
61	#336×C₆₇	C₂²	1	1	yes	characteristic
62	#336×C₆₇	C₂²	1	1	yes	characteristic
63	C₂×#41×C₆₇	—	2	2	no	—
64	C₂×#41×C₆₇	—	2	2	no	—
65	C₂×#41×C₆₇	—	2	2	no	—
66	C₂×#41×C₆₇	—	2	2	no	—
67	C₂×#41×C₆₇	—	2	2	no	—
68	C₂×#41×C₆₇	D₄	1	4	yes	—
69	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
70	C₂²×D₄×C₆₇	—	2	1	no	—
71	C₂²×D₄×C₆₇	—	2	1	no	—
72	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
73	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₆₇	—	2	1	no	—
75	C₂³×C₄×C₆₇	—	2	1	no	—
76	C₂³×C₄×C₆₇	—	2	1	no	—
77	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
78	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
79	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
80	C₂×SD₁₆×C₆₇	—	2	2	no	—
81	C₂×SD₁₆×C₆₇	—	2	2	no	—
82	C₂×SD₁₆×C₆₇	—	2	2	no	—
83	C₂×D₈×C₆₇	—	2	2	no	—
84	C₂×D₈×C₆₇	—	2	2	no	—
85	C₂×D₈×C₆₇	—	2	2	no	—
86	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
87	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
88	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
89	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
90	#123×C₆₇	—	4	4	no	—
91	#121×C₆₇	—	2	2	no	—
92	#121×C₆₇	—	2	2	no	—
93	C₄×Q₈×C₆₇	—	2	2	no	—
94	C₄×Q₈×C₆₇	—	2	2	no	—
95	C₄×Q₈×C₆₇	—	2	2	no	—
96	C₄×Q₈×C₆₇	—	2	2	no	—
97	C₄×D₄×C₆₇	—	2	8	no	—
98	C₄×D₄×C₆₇	—	2	8	no	—
99	C₄×D₄×C₆₇	—	2	2	no	—
100	C₄×D₄×C₆₇	—	2	2	no	—
101	C₄×D₄×C₆₇	—	2	2	no	—
102	C₄×D₄×C₆₇	—	2	2	no	—
103	#117×C₆₇	—	2	8	no	—
104	#117×C₆₇	—	2	2	no	—
105	#117×C₆₇	D₄	1	4	yes	—
106	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
107	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
108	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
109	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
110	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
111	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
112	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
113	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
114	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
115	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
116	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
117	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
118	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
119	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
120	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
121	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
122	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
123	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
124	C₂×C₄²×C₆₇	—	2	8	no	—
125	C₂×C₄²×C₆₇	—	2	1	no	—
126	C₂×C₄²×C₆₇	—	2	1	no	—
127	C₂×C₄²×C₆₇	—	2	1	no	—
128	C₂×C₄²×C₆₇	—	2	2	no	—
129	C₂×C₄²×C₆₇	—	2	2	no	—
130	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
131	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
132	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
133	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
134	#107×C₆₇	—	2	2	no	—
135	#106×C₆₇	—	2	2	no	—
136	#103×C₆₇	—	2	2	no	—
137	#103×C₆₇	—	2	2	no	—
138	#103×C₆₇	—	2	2	no	—
139	#102×C₆₇	—	2	2	no	—
140	#102×C₆₇	—	2	2	no	—
141	#102×C₆₇	—	2	2	no	—
142	#102×C₆₇	—	2	2	no	—
143	#102×C₆₇	—	2	2	no	—
144	C₂²⋊C₈×C₆₇	—	2	2	no	—
145	C₂²⋊C₈×C₆₇	—	2	2	no	—
146	#95×C₆₇	—	2	1	no	—
147	#95×C₆₇	—	2	1	no	—
148	#95×C₆₇	—	2	1	no	—
149	C₂⁴×C₆₇	—	2	1	no	—
150	C₂⁴×C₆₇	—	2	1	no	—
151	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
152	#41×C₆₇	—	2	8	no	—
153	#41×C₆₇	—	2	8	no	—
154	#41×C₆₇	—	2	8	no	—
155	#41×C₆₇	—	2	8	no	—
156	C₂×Q₈×C₆₇	—	2	1	no	—
157	C₂×Q₈×C₆₇	—	2	1	no	—
158	C₂×Q₈×C₆₇	—	2	1	no	—
159	C₂×Q₈×C₆₇	C₂×D₄	1	2	yes	—
160	C₂×Q₈×C₆₇	#41	1	2	yes	—
161	C₂×Q₈×C₆₇	#41	1	2	yes	—
162	C₂×D₄×C₆₇	—	2	4	no	—
163	C₂×D₄×C₆₇	—	2	4	no	—
164	C₂×D₄×C₆₇	—	2	4	no	—
165	C₂×D₄×C₆₇	—	2	1	no	—
166	C₂×D₄×C₆₇	—	2	1	no	—
167	C₂×D₄×C₆₇	—	2	1	no	—
168	C₂×D₄×C₆₇	—	2	1	no	—
169	C₂×D₄×C₆₇	—	2	1	no	—
170	C₂×D₄×C₆₇	—	2	1	no	—
171	C₂×D₄×C₆₇	—	2	1	no	—
172	C₂×D₄×C₆₇	—	2	1	no	—
173	C₂×D₄×C₆₇	—	2	1	no	—
174	C₂×D₄×C₆₇	—	4	2	no	—
175	C₂×D₄×C₆₇	—	4	2	no	—
176	C₂×D₄×C₆₇	—	4	2	no	—
177	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
178	C₂×D₄×C₆₇	#41	1	2	yes	—
179	C₂×D₄×C₆₇	#41	1	2	yes	—
180	C₂²×C₄×C₆₇	—	2	4	no	—
181	C₂²×C₄×C₆₇	—	2	4	no	—
182	C₂²×C₄×C₆₇	—	2	1	no	—
183	C₂²×C₄×C₆₇	—	2	4	no	—
184	C₂²×C₄×C₆₇	—	2	1	no	—
185	C₂²×C₄×C₆₇	—	2	1	no	—
186	C₂²×C₄×C₆₇	—	2	1	no	—
187	C₂²×C₄×C₆₇	—	2	1	no	—
188	C₂²×C₄×C₆₇	—	2	4	no	—
189	C₂²×C₄×C₆₇	—	2	4	no	—
190	C₂²×C₄×C₆₇	—	2	2	no	—
191	C₂²×C₄×C₆₇	—	2	2	no	—
192	C₂²×C₄×C₆₇	—	2	1	no	—
193	C₂²×C₄×C₆₇	—	2	1	no	—
194	C₂²×C₄×C₆₇	—	2	2	no	—
195	C₂²×C₄×C₆₇	—	2	2	no	—
196	C₂²×C₄×C₆₇	—	2	1	no	—
197	C₂²×C₄×C₆₇	—	2	1	no	—
198	C₂²×C₄×C₆₇	—	2	1	no	—
199	C₂²×C₄×C₆₇	—	4	1	no	—
200	C₂²×C₄×C₆₇	—	4	1	no	—
201	C₂²×C₄×C₆₇	—	4	2	no	—
202	C₂²×C₄×C₆₇	—	4	2	no	—
203	C₂²×C₄×C₆₇	—	4	2	no	—
204	C₂²×C₄×C₆₇	—	4	2	no	—
205	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
206	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
207	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
208	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
209	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
210	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
211	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
212	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
213	SD₁₆×C₆₇	—	4	4	no	—
214	D₈×C₆₇	—	4	4	no	—
215	C₂×C₈×C₆₇	—	2	1	no	—
216	C₂×C₈×C₆₇	—	2	1	no	—
217	C₂×C₈×C₆₇	—	2	1	no	—
218	C₂×C₈×C₆₇	—	2	1	no	—
219	C₂×C₈×C₆₇	—	2	1	no	—
220	C₂×C₈×C₆₇	—	2	1	no	—
221	C₂×C₈×C₆₇	—	2	1	no	—
222	C₂×C₈×C₆₇	—	2	1	no	—
223	C₂×C₈×C₆₇	—	2	1	no	—
224	C₂×C₈×C₆₇	—	2	1	no	—
225	C₂×C₈×C₆₇	—	2	1	no	—
226	C₂×C₈×C₆₇	—	2	1	no	—
227	C₄⋊C₄×C₆₇	—	2	4	no	—
228	C₄⋊C₄×C₆₇	—	2	4	no	—
229	C₄⋊C₄×C₆₇	—	2	1	no	—
230	C₄⋊C₄×C₆₇	—	2	1	no	—
231	C₄⋊C₄×C₆₇	—	2	1	no	—
232	C₄⋊C₄×C₆₇	—	2	1	no	—
233	C₄⋊C₄×C₆₇	—	2	1	no	—
234	C₄⋊C₄×C₆₇	—	2	1	no	—
235	C₄⋊C₄×C₆₇	—	2	1	no	—
236	C₄⋊C₄×C₆₇	—	2	1	no	—
237	C₄⋊C₄×C₆₇	—	4	2	no	—
238	C₄⋊C₄×C₆₇	—	4	2	no	—
239	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
240	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
241	C₂²⋊C₄×C₆₇	—	2	4	no	—
242	C₂²⋊C₄×C₆₇	—	2	4	no	—
243	C₂²⋊C₄×C₆₇	—	2	4	no	—
244	C₂²⋊C₄×C₆₇	—	4	2	no	—
245	C₂²⋊C₄×C₆₇	—	4	2	no	—
246	C₂²⋊C₄×C₆₇	—	4	2	no	—
247	C₂²⋊C₄×C₆₇	—	4	2	no	—
248	C₂²⋊C₄×C₆₇	—	4	2	no	—
249	C₂²⋊C₄×C₆₇	—	4	2	no	—
250	C₄²×C₆₇	—	2	4	no	—
251	C₄²×C₆₇	—	2	4	no	—
252	C₄²×C₆₇	—	2	2	no	—
253	C₄²×C₆₇	—	2	4	no	—
254	C₄²×C₆₇	—	2	2	no	—
255	C₄²×C₆₇	—	2	1	no	—
256	C₄²×C₆₇	—	2	1	no	—
257	C₄²×C₆₇	—	2	1	no	—
258	C₄²×C₆₇	—	2	1	no	—
259	C₂³×C₆₇	—	2	2	no	—
260	C₂³×C₆₇	—	2	1	no	—
261	C₂³×C₆₇	—	2	1	no	—
262	C₂³×C₆₇	—	2	2	no	—
263	C₂³×C₆₇	—	2	2	no	—
264	C₂³×C₆₇	—	2	1	no	—
265	C₂³×C₆₇	—	2	1	no	—
266	C₂³×C₆₇	—	2	1	no	—
267	C₂³×C₆₇	—	2	1	no	—
268	C₂³×C₆₇	—	4	1	no	—
269	C₂³×C₆₇	—	4	1	no	—
270	C₂³×C₆₇	—	4	1	no	—
271	C₂³×C₆₇	—	4	1	no	—
272	C₂³×C₆₇	—	4	1	no	—
273	C₂³×C₆₇	—	4	1	no	—
274	C₂³×C₆₇	—	4	1	no	—
275	C₂³×C₆₇	—	4	1	no	—
276	C₂³×C₆₇	—	4	1	no	—
277	C₂³×C₆₇	—	4	1	no	—
278	C₂³×C₆₇	—	4	1	no	—
279	C₂³×C₆₇	#120	1	2	yes	—
280	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
281	Q₈×C₆₇	—	2	2	no	—
282	Q₈×C₆₇	—	2	2	no	—
283	Q₈×C₆₇	—	2	2	no	—
284	Q₈×C₆₇	#123	1	4	yes	complemented
285	D₄×C₆₇	—	2	16	no	—
286	D₄×C₆₇	—	2	2	no	—
287	D₄×C₆₇	—	2	2	no	—
288	D₄×C₆₇	—	2	2	no	—
289	D₄×C₆₇	—	4	1	no	—
290	D₄×C₆₇	—	4	1	no	—
291	D₄×C₆₇	—	4	1	no	—
292	D₄×C₆₇	—	4	1	no	—
293	D₄×C₆₇	—	8	4	no	—
294	D₄×C₆₇	#123	1	4	yes	complemented
295	C₂×C₄×C₆₇	—	2	16	no	—
296	C₂×C₄×C₆₇	—	2	1	no	—
297	C₂×C₄×C₆₇	—	2	1	no	—
298	C₂×C₄×C₆₇	—	2	2	no	—
299	C₂×C₄×C₆₇	—	2	1	no	—
300	C₂×C₄×C₆₇	—	2	1	no	—
301	C₂×C₄×C₆₇	—	2	2	no	—
302	C₂×C₄×C₆₇	—	2	2	no	—
303	C₂×C₄×C₆₇	—	2	1	no	—
304	C₂×C₄×C₆₇	—	2	1	no	—
305	C₂×C₄×C₆₇	—	2	2	no	—
306	C₂×C₄×C₆₇	—	2	2	no	—
307	C₂×C₄×C₆₇	—	2	2	no	—
308	C₂×C₄×C₆₇	—	2	2	no	—
309	C₂×C₄×C₆₇	—	2	1	no	—
310	C₂×C₄×C₆₇	—	2	1	no	—
311	C₂×C₄×C₆₇	—	2	2	no	—
312	C₂×C₄×C₆₇	—	2	2	no	—
313	C₂×C₄×C₆₇	—	2	1	no	—
314	C₂×C₄×C₆₇	—	2	1	no	—
315	C₂×C₄×C₆₇	—	2	1	no	—
316	C₂×C₄×C₆₇	—	2	1	no	—
317	C₂×C₄×C₆₇	—	4	4	no	—
318	C₂×C₄×C₆₇	—	4	4	no	—
319	C₂×C₄×C₆₇	—	4	8	no	—
320	C₂×C₄×C₆₇	—	4	8	no	—
321	C₂×C₄×C₆₇	—	4	1	no	—
322	C₂×C₄×C₆₇	—	4	1	no	—
323	C₂×C₄×C₆₇	—	4	1	no	—
324	C₂×C₄×C₆₇	—	4	1	no	—
325	C₂×C₄×C₆₇	—	4	1	no	—
326	C₂×C₄×C₆₇	—	4	1	no	—
327	C₂×C₄×C₆₇	—	4	1	no	—
328	C₂×C₄×C₆₇	—	4	1	no	—
329	C₂×C₄×C₆₇	—	4	1	no	—
330	C₂×C₄×C₆₇	—	4	1	no	—
331	C₂×C₄×C₆₇	—	4	1	no	—
332	C₂×C₄×C₆₇	—	4	1	no	—
333	C₂×C₄×C₆₇	—	4	1	no	—
334	C₂×C₄×C₆₇	#120	1	2	yes	—
335	C₂×C₄×C₆₇	#135	1	2	yes	—
336	C₂×C₄×C₆₇	AGL(1,ℤ/8)	1	2	yes	—
337	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
338	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
339	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
340	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
341	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
342	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
343	C₈×C₆₇	—	4	1	no	—
344	C₈×C₆₇	—	4	1	no	—
345	C₈×C₆₇	—	4	1	no	—
346	C₈×C₆₇	—	4	1	no	—
347	C₂²×C₆₇	—	2	2	no	—
348	C₂²×C₆₇	—	2	4	no	—
349	C₂²×C₆₇	—	2	2	no	—
350	C₂²×C₆₇	—	2	2	no	—
351	C₂²×C₆₇	—	4	1	no	—
352	C₂²×C₆₇	—	4	2	no	—
353	C₂²×C₆₇	—	4	1	no	—
354	C₂²×C₆₇	—	4	2	no	—
355	C₂²×C₆₇	—	4	1	no	—
356	C₂²×C₆₇	—	4	2	no	—
357	C₂²×C₆₇	—	4	1	no	—
358	C₂²×C₆₇	—	4	2	no	—
359	C₂²×C₆₇	—	4	2	no	—
360	C₂²×C₆₇	—	4	2	no	—
361	C₂²×C₆₇	—	8	1	no	—
362	C₂²×C₆₇	—	8	1	no	—
363	C₂²×C₆₇	—	8	1	no	—
364	C₂²×C₆₇	—	8	1	no	—
365	C₂²×C₆₇	—	8	1	no	—
366	C₂²×C₆₇	—	8	1	no	—
367	C₂²×C₆₇	—	8	1	no	—
368	C₂²×C₆₇	C₂×#120	1	1	yes	characteristic
369	C₂²×C₆₇	#525	1	1	yes	characteristic
370	C₂²×C₆₇	#525	1	1	yes	characteristic
371	C₂²×C₆₇	C₂×#135	1	1	yes	characteristic
372	C₂²×C₆₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
373	C₂²×C₆₇	#575	1	1	yes	characteristic
374	C₂²×C₆₇	#575	1	1	yes	characteristic
375	C₄×C₆₇	—	2	2	no	—
376	C₄×C₆₇	—	2	4	no	—
377	C₄×C₆₇	—	2	2	no	—
378	C₄×C₆₇	—	2	2	no	—
379	C₄×C₆₇	—	4	1	no	—
380	C₄×C₆₇	—	4	2	no	—
381	C₄×C₆₇	—	4	1	no	—
382	C₄×C₆₇	—	4	2	no	—
383	C₄×C₆₇	—	8	1	no	—
384	C₄×C₆₇	—	8	1	no	—
385	C₄×C₆₇	—	8	1	no	—
386	C₄×C₆₇	C₂×#123	1	1	yes	characteristic
387	C₄×C₆₇	C₂×#123	1	1	yes	characteristic
388	C₄×C₆₇	#525	1	1	yes	characteristic
389	C₄×C₆₇	#525	1	1	yes	characteristic
390	#33006	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
391	C₂×C₆₇	—	4	2	no	—
392	C₂×C₆₇	—	4	4	no	—
393	C₂×C₆₇	—	16	1	no	—
394	C₂×C₆₇	#2849	1	1	yes	characteristic
395	C₂×C₆₇	#3002	1	1	yes	characteristic
396	C₂×C₆₇	#3006	1	1	yes	characteristic
397	C₂×C₆₇	#3102	1	1	yes	characteristic
398	C₂×C₆₇	#3106	1	1	yes	characteristic
399	C₂×C₆₇	#3111	1	1	yes	characteristic
400	C₂×C₆₇	#3115	1	1	yes	characteristic
401	C₂×C₄×#41	C₂×C₆₇	1	1	yes	characteristic, complemented
402	C₂×#482	C₂×C₆₇	1	1	yes	characteristic, complemented
403	C₂×#449	C₂×C₆₇	1	1	yes	characteristic
404	#2854	C₂×C₆₇	1	1	yes	characteristic, complemented
405	#1880	C₂×C₆₇	1	1	yes	characteristic, complemented
406	#1880	C₂×C₆₇	1	1	yes	characteristic, complemented
407	#1879	C₂×C₆₇	1	1	yes	characteristic, complemented
408	#1879	C₂×C₆₇	1	1	yes	characteristic, complemented
409	#1865	C₂×C₆₇	1	1	yes	characteristic, complemented
410	#1864	C₂×C₆₇	1	1	yes	characteristic, complemented
411	#1863	C₂×C₆₇	1	1	yes	characteristic, complemented
412	#1862	C₂×C₆₇	1	1	yes	characteristic, complemented
413	#1825	C₂×C₆₇	1	1	yes	characteristic, complemented
414	#1817	C₂×C₆₇	1	1	yes	characteristic, complemented
415	#1788	C₂×C₆₇	1	1	yes	characteristic, complemented
416	C₆₇	#33006	1	1	yes	characteristic, direct product factor, Sylow
417	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
418	C₂²×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic
419	C₂²×D₈	C₂²×C₆₇	1	1	yes	characteristic
420	C₂×#123	—	2	1	no	—
421	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
422	C₄×#41	—	2	4	no	—
423	C₄×#41	—	2	4	no	—
424	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
425	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
426	C₂×C₄×D₄	—	2	1	no	—
427	C₂×C₄×D₄	—	2	1	no	—
428	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
429	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
430	C₂×#117	—	2	1	no	—
431	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
432	C₂²×C₄²	—	2	1	no	—
433	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
434	#482	—	2	4	no	—
435	#449	—	2	4	no	—
436	C₂×#107	C₂²×C₆₇	1	1	yes	characteristic
437	C₂×#106	C₂²×C₆₇	1	1	yes	characteristic
438	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic
439	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic
440	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic
441	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
442	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
443	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
444	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
445	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
446	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
447	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
448	#390	C₂²×C₆₇	1	1	yes	characteristic
449	#390	C₂²×C₆₇	1	1	yes	characteristic
450	#389	C₂²×C₆₇	1	1	yes	characteristic
451	#389	C₂²×C₆₇	1	1	yes	characteristic
452	#388	—	2	1	no	—
453	#388	—	2	1	no	—
454	#386	—	2	1	no	—
455	#380	C₂²×C₆₇	1	1	yes	characteristic
456	#340	C₂²×C₆₇	1	1	yes	characteristic
457	#340	C₂²×C₆₇	1	1	yes	characteristic
458	#340	C₂²×C₆₇	1	1	yes	characteristic
459	#340	C₂²×C₆₇	1	1	yes	characteristic
460	#336	C₂²×C₆₇	1	1	yes	characteristic
461	#336	C₂²×C₆₇	1	1	yes	characteristic
462	#336	C₂²×C₆₇	1	1	yes	characteristic
463	#336	C₂²×C₆₇	1	1	yes	characteristic
464	C₂×#41	—	2	2	no	—
465	C₂×#41	—	2	2	no	—
466	C₂×#41	—	2	2	no	—
467	C₂×#41	—	2	2	no	—
468	C₂×#41	—	2	2	no	—
469	C₂×#41	D₄×C₆₇	1	4	yes	—
470	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
471	C₂²×D₄	—	2	1	no	—
472	C₂²×D₄	—	2	1	no	—
473	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
474	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
475	C₂³×C₄	—	2	1	no	—
476	C₂³×C₄	—	2	1	no	—
477	C₂³×C₄	—	2	1	no	—
478	C₂³×C₄	D₄×C₆₇	1	1	yes	characteristic
479	C₂³×C₄	D₄×C₆₇	1	1	yes	characteristic
480	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
481	C₂×SD₁₆	—	2	2	no	—
482	C₂×SD₁₆	—	2	2	no	—
483	C₂×SD₁₆	—	2	2	no	—
484	C₂×D₈	—	2	2	no	—
485	C₂×D₈	—	2	2	no	—
486	C₂×D₈	—	2	2	no	—
487	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
488	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
489	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
490	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
491	#123	—	4	4	no	—
492	#121	—	2	2	no	—
493	#121	—	2	2	no	—
494	C₄×Q₈	—	2	2	no	—
495	C₄×Q₈	—	2	2	no	—
496	C₄×Q₈	—	2	2	no	—
497	C₄×Q₈	—	2	2	no	—
498	C₄×D₄	—	2	8	no	—
499	C₄×D₄	—	2	8	no	—
500	C₄×D₄	—	2	2	no	—
501	C₄×D₄	—	2	2	no	—
502	C₄×D₄	—	2	2	no	—
503	C₄×D₄	—	2	2	no	—
504	#117	—	2	8	no	—
505	#117	—	2	2	no	—
506	#117	D₄×C₆₇	1	4	yes	—
507	C₂×C₄⋊C₄	—	2	1	no	—
508	C₂×C₄⋊C₄	—	2	1	no	—
509	C₂×C₄⋊C₄	—	2	1	no	—
510	C₂×C₄⋊C₄	—	2	1	no	—
511	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
512	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
513	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
514	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
515	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
516	C₂×C₂²⋊C₄	—	2	1	no	—
517	C₂×C₂²⋊C₄	—	2	1	no	—
518	C₂×C₂²⋊C₄	—	2	1	no	—
519	C₂×C₂²⋊C₄	—	2	1	no	—
520	C₂×C₂²⋊C₄	—	2	1	no	—
521	C₂×C₂²⋊C₄	—	2	1	no	—
522	C₂×C₂²⋊C₄	—	2	1	no	—
523	C₂×C₂²⋊C₄	—	2	1	no	—
524	C₂×C₂²⋊C₄	—	2	1	no	—
525	C₂×C₄²	—	2	8	no	—
526	C₂×C₄²	—	2	1	no	—
527	C₂×C₄²	—	2	1	no	—
528	C₂×C₄²	—	2	1	no	—
529	C₂×C₄²	—	2	2	no	—
530	C₂×C₄²	—	2	2	no	—
531	C₂×C₄²	D₄×C₆₇	1	1	yes	characteristic
532	C₂×C₄²	D₄×C₆₇	1	1	yes	characteristic
533	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
534	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
535	#107	—	2	2	no	—
536	#106	—	2	2	no	—
537	#103	—	2	2	no	—
538	#103	—	2	2	no	—
539	#103	—	2	2	no	—
540	#102	—	2	2	no	—
541	#102	—	2	2	no	—
542	#102	—	2	2	no	—
543	#102	—	2	2	no	—
544	#102	—	2	2	no	—
545	C₂²⋊C₈	—	2	2	no	—
546	C₂²⋊C₈	—	2	2	no	—
547	#95	—	2	1	no	—
548	#95	—	2	1	no	—
549	#95	—	2	1	no	—
550	C₂⁴	—	2	1	no	—
551	C₂⁴	—	2	1	no	—
552	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
553	#41	—	2	8	no	—
554	#41	—	2	8	no	—
555	#41	—	2	8	no	—
556	#41	—	2	8	no	—
557	C₂×Q₈	—	2	1	no	—
558	C₂×Q₈	—	2	1	no	—
559	C₂×Q₈	—	2	1	no	—
560	C₂×Q₈	C₂×D₄×C₆₇	1	2	yes	—
561	C₂×Q₈	#41×C₆₇	1	2	yes	—
562	C₂×Q₈	#41×C₆₇	1	2	yes	—
563	C₂×D₄	—	2	4	no	—
564	C₂×D₄	—	2	4	no	—
565	C₂×D₄	—	2	4	no	—
566	C₂×D₄	—	2	1	no	—
567	C₂×D₄	—	2	1	no	—
568	C₂×D₄	—	2	1	no	—
569	C₂×D₄	—	2	1	no	—
570	C₂×D₄	—	2	1	no	—
571	C₂×D₄	—	2	1	no	—
572	C₂×D₄	—	2	1	no	—
573	C₂×D₄	—	2	1	no	—
574	C₂×D₄	—	2	1	no	—
575	C₂×D₄	—	4	2	no	—
576	C₂×D₄	—	4	2	no	—
577	C₂×D₄	—	4	2	no	—
578	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
579	C₂×D₄	#41×C₆₇	1	2	yes	—
580	C₂×D₄	#41×C₆₇	1	2	yes	—
581	C₂²×C₄	—	2	4	no	—
582	C₂²×C₄	—	2	4	no	—
583	C₂²×C₄	—	2	1	no	—
584	C₂²×C₄	—	2	4	no	—
585	C₂²×C₄	—	2	1	no	—
586	C₂²×C₄	—	2	1	no	—
587	C₂²×C₄	—	2	1	no	—
588	C₂²×C₄	—	2	1	no	—
589	C₂²×C₄	—	2	4	no	—
590	C₂²×C₄	—	2	4	no	—
591	C₂²×C₄	—	2	2	no	—
592	C₂²×C₄	—	2	2	no	—
593	C₂²×C₄	—	2	1	no	—
594	C₂²×C₄	—	2	1	no	—
595	C₂²×C₄	—	2	2	no	—
596	C₂²×C₄	—	2	2	no	—
597	C₂²×C₄	—	2	1	no	—
598	C₂²×C₄	—	2	1	no	—
599	C₂²×C₄	—	2	1	no	—
600	C₂²×C₄	—	4	1	no	—
601	C₂²×C₄	—	4	1	no	—
602	C₂²×C₄	—	4	2	no	—
603	C₂²×C₄	—	4	2	no	—
604	C₂²×C₄	—	4	2	no	—
605	C₂²×C₄	—	4	2	no	—
606	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
607	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
608	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
609	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
610	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
611	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
612	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
613	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
614	SD₁₆	—	4	4	no	—
615	D₈	—	4	4	no	—
616	C₂×C₈	—	2	1	no	—
617	C₂×C₈	—	2	1	no	—
618	C₂×C₈	—	2	1	no	—
619	C₂×C₈	—	2	1	no	—
620	C₂×C₈	—	2	1	no	—
621	C₂×C₈	—	2	1	no	—
622	C₂×C₈	—	2	1	no	—
623	C₂×C₈	—	2	1	no	—
624	C₂×C₈	—	2	1	no	—
625	C₂×C₈	—	2	1	no	—
626	C₂×C₈	—	2	1	no	—
627	C₂×C₈	—	2	1	no	—
628	C₄⋊C₄	—	2	4	no	—
629	C₄⋊C₄	—	2	4	no	—
630	C₄⋊C₄	—	2	1	no	—
631	C₄⋊C₄	—	2	1	no	—
632	C₄⋊C₄	—	2	1	no	—
633	C₄⋊C₄	—	2	1	no	—
634	C₄⋊C₄	—	2	1	no	—
635	C₄⋊C₄	—	2	1	no	—
636	C₄⋊C₄	—	2	1	no	—
637	C₄⋊C₄	—	2	1	no	—
638	C₄⋊C₄	—	4	2	no	—
639	C₄⋊C₄	—	4	2	no	—
640	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
641	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
642	C₂²⋊C₄	—	2	4	no	—
643	C₂²⋊C₄	—	2	4	no	—
644	C₂²⋊C₄	—	2	4	no	—
645	C₂²⋊C₄	—	4	2	no	—
646	C₂²⋊C₄	—	4	2	no	—
647	C₂²⋊C₄	—	4	2	no	—
648	C₂²⋊C₄	—	4	2	no	—
649	C₂²⋊C₄	—	4	2	no	—
650	C₂²⋊C₄	—	4	2	no	—
651	C₄²	—	2	4	no	—
652	C₄²	—	2	4	no	—
653	C₄²	—	2	2	no	—
654	C₄²	—	2	4	no	—
655	C₄²	—	2	2	no	—
656	C₄²	—	2	1	no	—
657	C₄²	—	2	1	no	—
658	C₄²	—	2	1	no	—
659	C₄²	—	2	1	no	—
660	C₂³	—	2	2	no	—
661	C₂³	—	2	1	no	—
662	C₂³	—	2	1	no	—
663	C₂³	—	2	2	no	—
664	C₂³	—	2	2	no	—
665	C₂³	—	2	1	no	—
666	C₂³	—	2	1	no	—
667	C₂³	—	2	1	no	—
668	C₂³	—	2	1	no	—
669	C₂³	—	4	1	no	—
670	C₂³	—	4	1	no	—
671	C₂³	—	4	1	no	—
672	C₂³	—	4	1	no	—
673	C₂³	—	4	1	no	—
674	C₂³	—	4	1	no	—
675	C₂³	—	4	1	no	—
676	C₂³	—	4	1	no	—
677	C₂³	—	4	1	no	—
678	C₂³	—	4	1	no	—
679	C₂³	—	4	1	no	—
680	C₂³	#120×C₆₇	1	2	yes	—
681	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
682	Q₈	—	2	2	no	—
683	Q₈	—	2	2	no	—
684	Q₈	—	2	2	no	—
685	Q₈	#123×C₆₇	1	4	yes	complemented
686	D₄	—	2	16	no	—
687	D₄	—	2	2	no	—
688	D₄	—	2	2	no	—
689	D₄	—	2	2	no	—
690	D₄	—	4	1	no	—
691	D₄	—	4	1	no	—
692	D₄	—	4	1	no	—
693	D₄	—	4	1	no	—
694	D₄	—	8	4	no	—
695	D₄	#123×C₆₇	1	4	yes	complemented
696	C₂×C₄	—	2	16	no	—
697	C₂×C₄	—	2	1	no	—
698	C₂×C₄	—	2	1	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	1	no	—
701	C₂×C₄	—	2	1	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	1	no	—
705	C₂×C₄	—	2	1	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	1	no	—
711	C₂×C₄	—	2	1	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	1	no	—
715	C₂×C₄	—	2	1	no	—
716	C₂×C₄	—	2	1	no	—
717	C₂×C₄	—	2	1	no	—
718	C₂×C₄	—	4	4	no	—
719	C₂×C₄	—	4	4	no	—
720	C₂×C₄	—	4	8	no	—
721	C₂×C₄	—	4	8	no	—
722	C₂×C₄	—	4	1	no	—
723	C₂×C₄	—	4	1	no	—
724	C₂×C₄	—	4	1	no	—
725	C₂×C₄	—	4	1	no	—
726	C₂×C₄	—	4	1	no	—
727	C₂×C₄	—	4	1	no	—
728	C₂×C₄	—	4	1	no	—
729	C₂×C₄	—	4	1	no	—
730	C₂×C₄	—	4	1	no	—
731	C₂×C₄	—	4	1	no	—
732	C₂×C₄	—	4	1	no	—
733	C₂×C₄	—	4	1	no	—
734	C₂×C₄	—	4	1	no	—
735	C₂×C₄	#120×C₆₇	1	2	yes	—
736	C₂×C₄	#135×C₆₇	1	2	yes	—
737	C₂×C₄	AGL(1,ℤ/8)×C₆₇	1	2	yes	—
738	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
739	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
740	C₂×C₄	C₂×#41×C₆₇	1	1	yes	characteristic
741	C₂×C₄	C₂×#41×C₆₇	1	1	yes	characteristic
742	C₂×C₄	C₂×#41×C₆₇	1	1	yes	characteristic
743	C₂×C₄	C₂×#41×C₆₇	1	1	yes	characteristic
744	C₈	—	4	1	no	—
745	C₈	—	4	1	no	—
746	C₈	—	4	1	no	—
747	C₈	—	4	1	no	—
748	C₂²	—	2	2	no	—
749	C₂²	—	2	4	no	—
750	C₂²	—	2	2	no	—
751	C₂²	—	2	2	no	—
752	C₂²	—	4	1	no	—
753	C₂²	—	4	2	no	—
754	C₂²	—	4	1	no	—
755	C₂²	—	4	2	no	—
756	C₂²	—	4	1	no	—
757	C₂²	—	4	2	no	—
758	C₂²	—	4	1	no	—
759	C₂²	—	4	2	no	—
760	C₂²	—	4	2	no	—
761	C₂²	—	4	2	no	—
762	C₂²	—	8	1	no	—
763	C₂²	—	8	1	no	—
764	C₂²	—	8	1	no	—
765	C₂²	—	8	1	no	—
766	C₂²	—	8	1	no	—
767	C₂²	—	8	1	no	—
768	C₂²	—	8	1	no	—
769	C₂²	C₂×#120×C₆₇	1	1	yes	characteristic
770	C₂²	#525×C₆₇	1	1	yes	characteristic
771	C₂²	#525×C₆₇	1	1	yes	characteristic
772	C₂²	C₂×#135×C₆₇	1	1	yes	characteristic
773	C₂²	C₂×AGL(1,ℤ/8)×C₆₇	1	1	yes	characteristic
774	C₂²	#575×C₆₇	1	1	yes	characteristic
775	C₂²	#575×C₆₇	1	1	yes	characteristic
776	C₄	—	2	2	no	—
777	C₄	—	2	4	no	—
778	C₄	—	2	2	no	—
779	C₄	—	2	2	no	—
780	C₄	—	4	1	no	—
781	C₄	—	4	2	no	—
782	C₄	—	4	1	no	—
783	C₄	—	4	2	no	—
784	C₄	—	8	1	no	—
785	C₄	—	8	1	no	—
786	C₄	—	8	1	no	—
787	C₄	C₂×#123×C₆₇	1	1	yes	characteristic
788	C₄	C₂×#123×C₆₇	1	1	yes	characteristic
789	C₄	#525×C₆₇	1	1	yes	characteristic
790	C₄	#525×C₆₇	1	1	yes	characteristic
791	C₂	—	4	2	no	—
792	C₂	—	4	4	no	—
793	C₂	—	16	1	no	—
794	C₂	C₆₇×#2849	1	1	yes	characteristic
795	C₂	C₆₇×#3002	1	1	yes	characteristic
796	C₂	C₆₇×#3006	1	1	yes	characteristic
797	C₂	C₆₇×#3102	1	1	yes	characteristic
798	C₂	C₆₇×#3106	1	1	yes	characteristic
799	C₂	C₆₇×#3111	1	1	yes	characteristic
800	C₂	C₆₇×#3115	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₇
prime radical	C₂×#449×C₆₇	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ C₂²×C₄²×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄×#41×C₆₇	C₂	semidirect
2. C₂×#482×C₆₇	C₂	semidirect
4. C₆₇×#2854	C₂	semidirect
5. C₆₇×#1880	C₂	semidirect
6. C₆₇×#1880	C₂	semidirect
7. C₆₇×#1879	C₂	semidirect
8. C₆₇×#1879	C₂	semidirect
9. C₆₇×#1865	C₂	semidirect
10. C₆₇×#1864	C₂	semidirect
11. C₆₇×#1863	C₂	semidirect
12. C₆₇×#1862	C₂	semidirect
13. C₆₇×#1825	C₂	semidirect
14. C₆₇×#1817	C₂	semidirect
15. C₆₇×#1788	C₂	semidirect
284. Q₈×C₆₇	#123	semidirect
294. D₄×C₆₇	#123	semidirect
390. #33006	C₆₇	direct (N × H)
401. C₂×C₄×#41	C₂×C₆₇	semidirect
402. C₂×#482	C₂×C₆₇	semidirect
404. #2854	C₂×C₆₇	semidirect
405. #1880	C₂×C₆₇	semidirect
406. #1880	C₂×C₆₇	semidirect
407. #1879	C₂×C₆₇	semidirect
408. #1879	C₂×C₆₇	semidirect
409. #1865	C₂×C₆₇	semidirect
410. #1864	C₂×C₆₇	semidirect
411. #1863	C₂×C₆₇	semidirect
412. #1862	C₂×C₆₇	semidirect
413. #1825	C₂×C₆₇	semidirect
414. #1817	C₂×C₆₇	semidirect
415. #1788	C₂×C₆₇	semidirect
416. C₆₇	#33006	direct (N × H)
685. Q₈	#123×C₆₇	semidirect
695. D₄	#123×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×#41×C₆₇	2
C₂×#482×C₆₇	2
C₂×#449×C₆₇	2
C₆₇×#2854	2
C₆₇×#1880	2
C₆₇×#1879	2
C₆₇×#1865	2
C₆₇×#1864	2
C₆₇×#1863	2
C₆₇×#1862	2
C₆₇×#1825	2
C₆₇×#1817	2
C₆₇×#1788	2
#33006	67

Subgroups — C67×#33006 #30712257

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#33006 #30712257