Subgroups — C₆₇×#61342 #30740593

Order 17152.

1724 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3509	C₂	1	1	yes	maximal, characteristic
2	C₆₇×#3502	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3377	C₂	1	4	yes	maximal, complemented
4	C₆₇×#3374	C₂	1	2	yes	maximal, complemented
5	C₆₇×#3374	C₂	1	4	yes	maximal, complemented
6	C₆₇×#3369	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3364	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3363	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3139	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#3137	C₂	1	2	yes	maximal
11	C₆₇×#3082	C₂	1	2	yes	maximal, complemented
12	C₆₇×#3076	C₂	1	1	yes	maximal, characteristic
13	C₆₇×#3044	C₂	1	2	yes	maximal
14	C₂×#462×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#2962	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#2950	C₂	1	2	yes	maximal, complemented
17	C₄×#137×C₆₇	C₂	1	1	yes	maximal, characteristic
18	C₂×#137×C₆₇	C₂²	1	1	yes	characteristic
19	C₂²×Q₁₆×C₆₇	C₂²	1	2	yes	—
20	Q₈²×C₆₇	—	2	1	no	—
21	Q₈²×C₆₇	C₂²	1	2	yes	—
22	#557×C₆₇	—	2	1	no	—
23	#557×C₆₇	—	2	2	no	—
24	#557×C₆₇	C₂²	1	2	yes	—
25	#557×C₆₇	C₂²	1	2	yes	—
26	#557×C₆₇	C₂²	1	2	yes	—
27	#557×C₆₇	C₂²	1	4	yes	—
28	#556×C₆₇	C₂²	1	2	yes	—
29	#556×C₆₇	C₂²	1	2	yes	—
30	#552×C₆₇	—	2	2	no	—
31	#552×C₆₇	—	2	2	no	—
32	#544×C₆₇	—	2	2	no	—
33	#544×C₆₇	C₂²	1	2	yes	—
34	#541×C₆₇	—	2	2	no	—
35	#536×C₆₇	C₂²	1	2	yes	—
36	#533×C₆₇	—	2	1	no	—
37	#533×C₆₇	—	2	1	no	—
38	#533×C₆₇	—	2	2	no	—
39	#533×C₆₇	C₂²	1	1	yes	characteristic
40	#533×C₆₇	C₂²	1	1	yes	characteristic
41	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
42	#519×C₆₇	C₂²	1	2	yes	—
43	#519×C₆₇	C₂²	1	2	yes	—
44	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
45	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
46	#491×C₆₇	C₂²	1	4	yes	—
47	#491×C₆₇	C₂²	1	4	yes	—
48	#489×C₆₇	C₂²	1	4	yes	—
49	#488×C₆₇	C₂²	1	4	yes	—
50	#487×C₆₇	C₂²	1	2	yes	—
51	#487×C₆₇	C₂²	1	4	yes	—
52	#487×C₆₇	C₂²	1	2	yes	—
53	#479×C₆₇	C₂²	1	2	yes	—
54	#479×C₆₇	C₂²	1	4	yes	—
55	#479×C₆₇	C₂²	1	4	yes	—
56	#478×C₆₇	C₂²	1	2	yes	—
57	#477×C₆₇	C₂²	1	1	yes	characteristic
58	#477×C₆₇	C₂²	1	4	yes	—
59	#476×C₆₇	C₂²	1	1	yes	characteristic
60	#475×C₆₇	C₂²	1	1	yes	characteristic
61	#475×C₆₇	C₂²	1	4	yes	—
62	#474×C₆₇	C₂²	1	1	yes	characteristic
63	#464×C₆₇	C₂²	1	4	yes	—
64	#464×C₆₇	C₂²	1	4	yes	—
65	#462×C₆₇	C₂²	1	2	yes	—
66	#462×C₆₇	C₂²	1	2	yes	—
67	#462×C₆₇	C₂²	1	4	yes	—
68	#462×C₆₇	C₂²	1	4	yes	—
69	#462×C₆₇	C₂²	1	4	yes	—
70	#446×C₆₇	C₂²	1	2	yes	—
71	#446×C₆₇	C₂²	1	4	yes	—
72	C₈×Q₈×C₆₇	C₂²	1	2	yes	—
73	#441×C₆₇	C₂²	1	4	yes	—
74	#441×C₆₇	C₂²	1	2	yes	—
75	#441×C₆₇	C₂²	1	4	yes	—
76	#440×C₆₇	C₂²	1	2	yes	—
77	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	—
78	C₄×Q₁₆×C₆₇	C₂²	1	4	yes	—
79	C₄×Q₁₆×C₆₇	C₂²	1	4	yes	—
80	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	—
81	#428×C₆₇	C₂²	1	1	yes	characteristic
82	#427×C₆₇	C₂²	1	2	yes	—
83	#424×C₆₇	C₂²	1	2	yes	—
84	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
85	#419×C₆₇	C₂²	1	2	yes	—
86	#419×C₆₇	C₂²	1	2	yes	—
87	#419×C₆₇	C₂²	1	1	yes	characteristic
88	#417×C₆₇	C₂²	1	1	yes	characteristic
89	#416×C₆₇	C₂²	1	2	yes	—
90	C₂×#103×C₆₇	C₂²	1	2	yes	—
91	#405×C₆₇	C₂²	1	2	yes	—
92	C₄×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
93	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
94	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
95	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
96	#137×C₆₇	—	2	4	no	—
97	C₂×Q₁₆×C₆₇	—	2	8	no	—
98	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
99	C₂×Q₁₆×C₆₇	C₂³	1	4	yes	—
100	C₂×Q₁₆×C₆₇	C₂³	1	4	yes	—
101	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
102	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
103	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
104	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
105	C₄⋊Q₈×C₆₇	—	2	2	no	—
106	C₄⋊Q₈×C₆₇	—	2	4	no	—
107	C₄⋊Q₈×C₆₇	—	2	2	no	—
108	C₄⋊Q₈×C₆₇	—	2	4	no	—
109	C₄⋊Q₈×C₆₇	—	2	2	no	—
110	C₄⋊Q₈×C₆₇	—	2	1	no	—
111	C₄⋊Q₈×C₆₇	—	2	1	no	—
112	C₄⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
113	C₄⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
114	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
115	C₄⋊Q₈×C₆₇	C₂³	1	4	yes	—
116	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
117	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
118	C₄⋊Q₈×C₆₇	C₂³	1	4	yes	—
119	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
120	#126×C₆₇	—	2	4	no	—
121	#126×C₆₇	—	2	4	no	—
122	#125×C₆₇	—	2	2	no	—
123	#125×C₆₇	—	2	2	no	—
124	#125×C₆₇	—	2	4	no	—
125	#125×C₆₇	—	2	4	no	—
126	#125×C₆₇	—	2	4	no	—
127	#125×C₆₇	—	2	4	no	—
128	#125×C₆₇	—	2	4	no	—
129	#125×C₆₇	—	2	2	no	—
130	#125×C₆₇	D₄	1	2	yes	—
131	#125×C₆₇	C₂³	1	2	yes	—
132	#125×C₆₇	C₂³	1	4	yes	—
133	#124×C₆₇	C₂³	1	4	yes	—
134	#123×C₆₇	—	2	4	no	—
135	C₂²⋊Q₈×C₆₇	—	2	2	no	—
136	C₂²⋊Q₈×C₆₇	—	2	2	no	—
137	C₂²⋊Q₈×C₆₇	—	2	1	no	—
138	C₂²⋊Q₈×C₆₇	—	2	1	no	—
139	C₂²⋊Q₈×C₆₇	—	2	2	no	—
140	C₂²⋊Q₈×C₆₇	—	2	2	no	—
141	C₂²⋊Q₈×C₆₇	—	2	4	no	—
142	C₂²⋊Q₈×C₆₇	D₄	1	2	yes	—
143	C₂²⋊Q₈×C₆₇	D₄	1	2	yes	—
144	C₄×Q₈×C₆₇	—	2	2	no	—
145	C₄×Q₈×C₆₇	—	2	2	no	—
146	C₄×Q₈×C₆₇	—	2	2	no	—
147	C₄×Q₈×C₆₇	—	2	2	no	—
148	C₄×Q₈×C₆₇	—	2	2	no	—
149	C₄×Q₈×C₆₇	—	2	2	no	—
150	C₄×Q₈×C₆₇	—	2	2	no	—
151	C₄×Q₈×C₆₇	—	2	4	no	—
152	C₄×Q₈×C₆₇	—	2	2	no	—
153	C₄×Q₈×C₆₇	—	2	1	no	—
154	C₄×Q₈×C₆₇	—	2	1	no	—
155	C₄×Q₈×C₆₇	—	2	1	no	—
156	C₄×Q₈×C₆₇	—	2	1	no	—
157	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
158	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
159	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
160	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
161	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
162	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
163	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
164	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
165	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
166	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
167	C₄×D₄×C₆₇	—	2	1	no	—
168	C₄×D₄×C₆₇	—	2	1	no	—
169	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
170	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
171	#117×C₆₇	—	2	2	no	—
172	#117×C₆₇	—	2	2	no	—
173	#117×C₆₇	—	2	4	no	—
174	#117×C₆₇	—	2	4	no	—
175	#117×C₆₇	—	2	1	no	—
176	#117×C₆₇	C₂³	1	1	yes	characteristic
177	#117×C₆₇	C₂³	1	2	yes	—
178	#117×C₆₇	C₂³	1	2	yes	—
179	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
180	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
181	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
182	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
183	C₂×C₄²×C₆₇	—	2	1	no	—
184	C₂×C₄²×C₆₇	—	2	1	no	—
185	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
186	#107×C₆₇	C₂³	1	2	yes	—
187	#107×C₆₇	C₂³	1	2	yes	—
188	#107×C₆₇	C₂³	1	2	yes	—
189	#106×C₆₇	C₂³	1	2	yes	—
190	#106×C₆₇	C₂³	1	2	yes	—
191	#106×C₆₇	C₂³	1	2	yes	—
192	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
193	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
194	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
195	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
196	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
197	#103×C₆₇	C₂³	1	4	yes	—
198	#103×C₆₇	C₂³	1	2	yes	—
199	#103×C₆₇	C₂³	1	2	yes	—
200	#103×C₆₇	C₂³	1	4	yes	—
201	#103×C₆₇	C₂³	1	4	yes	—
202	#103×C₆₇	C₂³	1	4	yes	—
203	#103×C₆₇	C₂³	1	4	yes	—
204	#103×C₆₇	C₂³	1	2	yes	—
205	#103×C₆₇	C₂³	1	4	yes	—
206	#103×C₆₇	C₂³	1	2	yes	—
207	#103×C₆₇	C₂³	1	2	yes	—
208	#102×C₆₇	C₂³	1	2	yes	—
209	#102×C₆₇	C₂³	1	2	yes	—
210	#102×C₆₇	C₂³	1	2	yes	—
211	#97×C₆₇	C₂³	1	4	yes	—
212	#97×C₆₇	C₂³	1	2	yes	—
213	C₄×C₈×C₆₇	C₂³	1	2	yes	—
214	C₄×C₈×C₆₇	C₂³	1	4	yes	—
215	#41×C₆₇	—	2	2	no	—
216	#41×C₆₇	—	2	2	no	—
217	C₂×Q₈×C₆₇	—	2	1	no	—
218	C₂×Q₈×C₆₇	—	2	1	no	—
219	C₂×Q₈×C₆₇	—	2	2	no	—
220	C₂×Q₈×C₆₇	—	2	1	no	—
221	C₂×Q₈×C₆₇	—	2	4	no	—
222	C₂×Q₈×C₆₇	—	2	2	no	—
223	C₂×Q₈×C₆₇	—	2	4	no	—
224	C₂×Q₈×C₆₇	—	2	4	no	—
225	C₂×Q₈×C₆₇	C₂×D₄	1	2	yes	—
226	C₂×Q₈×C₆₇	C₂×D₄	1	2	yes	—
227	C₂×Q₈×C₆₇	#41	1	4	yes	—
228	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
229	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
230	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
231	C₂×D₄×C₆₇	—	2	1	no	—
232	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
233	C₂²×C₄×C₆₇	—	2	1	no	—
234	C₂²×C₄×C₆₇	—	2	2	no	—
235	C₂²×C₄×C₆₇	—	2	1	no	—
236	C₂²×C₄×C₆₇	—	2	1	no	—
237	C₂²×C₄×C₆₇	—	2	1	no	—
238	C₂²×C₄×C₆₇	—	2	1	no	—
239	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
240	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
241	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
242	Q₁₆×C₆₇	—	2	8	no	—
243	Q₁₆×C₆₇	—	2	8	no	—
244	Q₁₆×C₆₇	—	2	4	no	—
245	SD₁₆×C₆₇	—	2	4	no	—
246	M₁₆×C₆₇	—	2	2	no	—
247	M₁₆×C₆₇	—	2	2	no	—
248	C₂×C₈×C₆₇	—	2	4	no	—
249	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
250	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
251	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
252	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
253	C₄⋊C₄×C₆₇	—	2	2	no	—
254	C₄⋊C₄×C₆₇	—	2	2	no	—
255	C₄⋊C₄×C₆₇	—	2	2	no	—
256	C₄⋊C₄×C₆₇	—	2	2	no	—
257	C₄⋊C₄×C₆₇	—	2	2	no	—
258	C₄⋊C₄×C₆₇	—	2	2	no	—
259	C₄⋊C₄×C₆₇	—	2	1	no	—
260	C₄⋊C₄×C₆₇	—	2	1	no	—
261	C₄⋊C₄×C₆₇	—	2	1	no	—
262	C₄⋊C₄×C₆₇	—	2	4	no	—
263	C₄⋊C₄×C₆₇	—	2	4	no	—
264	C₄⋊C₄×C₆₇	—	2	4	no	—
265	C₄⋊C₄×C₆₇	—	2	4	no	—
266	C₄⋊C₄×C₆₇	—	2	2	no	—
267	C₄⋊C₄×C₆₇	—	2	1	no	—
268	C₄⋊C₄×C₆₇	—	2	4	no	—
269	C₄⋊C₄×C₆₇	—	2	4	no	—
270	C₄⋊C₄×C₆₇	—	2	1	no	—
271	C₄⋊C₄×C₆₇	—	2	4	no	—
272	C₄⋊C₄×C₆₇	—	2	4	no	—
273	C₄⋊C₄×C₆₇	—	2	2	no	—
274	C₄⋊C₄×C₆₇	—	2	4	no	—
275	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
276	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
277	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
278	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
279	C₄⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
280	C₄⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
281	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
282	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
283	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
284	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
285	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
286	C₂²⋊C₄×C₆₇	—	2	1	no	—
287	C₂²⋊C₄×C₆₇	—	2	2	no	—
288	C₂²⋊C₄×C₆₇	—	2	1	no	—
289	C₂²⋊C₄×C₆₇	—	2	1	no	—
290	C₂²⋊C₄×C₆₇	—	2	4	no	—
291	C₂²⋊C₄×C₆₇	—	2	4	no	—
292	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
293	C₄²×C₆₇	—	2	1	no	—
294	C₄²×C₆₇	—	2	1	no	—
295	C₄²×C₆₇	—	2	1	no	—
296	C₄²×C₆₇	—	2	2	no	—
297	C₄²×C₆₇	—	2	2	no	—
298	C₄²×C₆₇	—	2	4	no	—
299	C₄²×C₆₇	—	2	4	no	—
300	C₄²×C₆₇	—	2	4	no	—
301	C₄²×C₆₇	—	2	4	no	—
302	C₄²×C₆₇	—	2	2	no	—
303	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
304	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
305	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
306	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
307	C₄²×C₆₇	C₂⁴	1	4	yes	—
308	C₂³×C₆₇	—	2	1	no	—
309	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
310	Q₈×C₆₇	—	2	4	no	—
311	Q₈×C₆₇	—	2	4	no	—
312	Q₈×C₆₇	—	2	2	no	—
313	Q₈×C₆₇	—	2	4	no	—
314	Q₈×C₆₇	—	2	1	no	—
315	Q₈×C₆₇	—	2	4	no	—
316	Q₈×C₆₇	—	2	1	no	—
317	Q₈×C₆₇	—	4	2	no	—
318	Q₈×C₆₇	—	4	4	no	—
319	Q₈×C₆₇	—	4	2	no	—
320	Q₈×C₆₇	—	8	1	no	—
321	Q₈×C₆₇	—	8	4	no	—
322	Q₈×C₆₇	C₂×#41	1	4	yes	—
323	D₄×C₆₇	—	2	1	no	—
324	D₄×C₆₇	—	2	1	no	—
325	D₄×C₆₇	—	4	2	no	—
326	C₂×C₄×C₆₇	—	2	4	no	—
327	C₂×C₄×C₆₇	—	2	2	no	—
328	C₂×C₄×C₆₇	—	2	2	no	—
329	C₂×C₄×C₆₇	—	2	1	no	—
330	C₂×C₄×C₆₇	—	2	1	no	—
331	C₂×C₄×C₆₇	—	2	2	no	—
332	C₂×C₄×C₆₇	—	2	2	no	—
333	C₂×C₄×C₆₇	—	2	4	no	—
334	C₂×C₄×C₆₇	—	2	1	no	—
335	C₂×C₄×C₆₇	—	2	2	no	—
336	C₂×C₄×C₆₇	—	4	1	no	—
337	C₂×C₄×C₆₇	—	4	2	no	—
338	C₂×C₄×C₆₇	—	4	4	no	—
339	C₂×C₄×C₆₇	—	4	2	no	—
340	C₂×C₄×C₆₇	—	4	2	no	—
341	C₂×C₄×C₆₇	—	8	1	no	—
342	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
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	1	yes	characteristic
346	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
347	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
348	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
349	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
350	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
351	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
352	C₈×C₆₇	—	2	2	no	—
353	C₈×C₆₇	—	2	2	no	—
354	C₈×C₆₇	—	2	2	no	—
355	C₈×C₆₇	—	2	2	no	—
356	C₂²×C₆₇	—	2	1	no	—
357	C₂²×C₆₇	—	2	1	no	—
358	C₂²×C₆₇	—	4	1	no	—
359	C₂²×C₆₇	—	4	1	no	—
360	C₂²×C₆₇	—	4	1	no	—
361	C₂²×C₆₇	#548	1	2	yes	—
362	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
363	C₄×C₆₇	—	2	1	no	—
364	C₄×C₆₇	—	2	1	no	—
365	C₄×C₆₇	—	2	4	no	—
366	C₄×C₆₇	—	2	4	no	—
367	C₄×C₆₇	—	2	1	no	—
368	C₄×C₆₇	—	2	4	no	—
369	C₄×C₆₇	—	4	1	no	—
370	C₄×C₆₇	—	4	2	no	—
371	C₄×C₆₇	—	4	2	no	—
372	C₄×C₆₇	—	4	1	no	—
373	C₄×C₆₇	—	4	4	no	—
374	C₄×C₆₇	—	4	1	no	—
375	C₄×C₆₇	—	4	2	no	—
376	C₄×C₆₇	#548	1	2	yes	—
377	C₄×C₆₇	#578	1	2	yes	—
378	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
379	C₄×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
380	#61342	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
381	C₂×C₆₇	—	2	2	no	—
382	C₂×C₆₇	—	8	1	no	—
383	C₂×C₆₇	C₂×#548	1	1	yes	characteristic
384	C₂×C₆₇	C₂×#578	1	1	yes	characteristic
385	C₂×C₆₇	#3586	1	1	yes	characteristic
386	#3509	C₂×C₆₇	1	1	yes	characteristic
387	#3502	C₂×C₆₇	1	1	yes	characteristic, complemented
388	#3377	C₂×C₆₇	1	4	yes	complemented
389	#3374	C₂×C₆₇	1	2	yes	complemented
390	#3374	C₂×C₆₇	1	4	yes	complemented
391	#3369	C₂×C₆₇	1	2	yes	complemented
392	#3364	C₂×C₆₇	1	2	yes	complemented
393	#3363	C₂×C₆₇	1	2	yes	complemented
394	#3139	C₂×C₆₇	1	1	yes	characteristic, complemented
395	#3137	C₂×C₆₇	1	2	yes	—
396	#3082	C₂×C₆₇	1	2	yes	complemented
397	#3076	C₂×C₆₇	1	1	yes	characteristic
398	#3044	C₂×C₆₇	1	2	yes	—
399	C₂×#462	C₂×C₆₇	1	1	yes	characteristic, complemented
400	#2962	C₂×C₆₇	1	1	yes	characteristic, complemented
401	#2950	C₂×C₆₇	1	2	yes	complemented
402	C₄×#137	C₂×C₆₇	1	1	yes	characteristic
403	C₆₇	#61342	1	1	yes	characteristic, direct product factor, Sylow
404	C₂×#137	C₂²×C₆₇	1	1	yes	characteristic
405	C₂²×Q₁₆	C₂²×C₆₇	1	2	yes	—
406	Q₈²	—	2	1	no	—
407	Q₈²	C₂²×C₆₇	1	2	yes	—
408	#557	—	2	1	no	—
409	#557	—	2	2	no	—
410	#557	C₂²×C₆₇	1	2	yes	—
411	#557	C₂²×C₆₇	1	2	yes	—
412	#557	C₂²×C₆₇	1	2	yes	—
413	#557	C₂²×C₆₇	1	4	yes	—
414	#556	C₂²×C₆₇	1	2	yes	—
415	#556	C₂²×C₆₇	1	2	yes	—
416	#552	—	2	2	no	—
417	#552	—	2	2	no	—
418	#544	—	2	2	no	—
419	#544	C₂²×C₆₇	1	2	yes	—
420	#541	—	2	2	no	—
421	#536	C₂²×C₆₇	1	2	yes	—
422	#533	—	2	1	no	—
423	#533	—	2	1	no	—
424	#533	—	2	2	no	—
425	#533	C₂²×C₆₇	1	1	yes	characteristic
426	#533	C₂²×C₆₇	1	1	yes	characteristic
427	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
428	#519	C₂²×C₆₇	1	2	yes	—
429	#519	C₂²×C₆₇	1	2	yes	—
430	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
431	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
432	#491	C₂²×C₆₇	1	4	yes	—
433	#491	C₂²×C₆₇	1	4	yes	—
434	#489	C₂²×C₆₇	1	4	yes	—
435	#488	C₂²×C₆₇	1	4	yes	—
436	#487	C₂²×C₆₇	1	2	yes	—
437	#487	C₂²×C₆₇	1	4	yes	—
438	#487	C₂²×C₆₇	1	2	yes	—
439	#479	C₂²×C₆₇	1	2	yes	—
440	#479	C₂²×C₆₇	1	4	yes	—
441	#479	C₂²×C₆₇	1	4	yes	—
442	#478	C₂²×C₆₇	1	2	yes	—
443	#477	C₂²×C₆₇	1	1	yes	characteristic
444	#477	C₂²×C₆₇	1	4	yes	—
445	#476	C₂²×C₆₇	1	1	yes	characteristic
446	#475	C₂²×C₆₇	1	1	yes	characteristic
447	#475	C₂²×C₆₇	1	4	yes	—
448	#474	C₂²×C₆₇	1	1	yes	characteristic
449	#464	C₂²×C₆₇	1	4	yes	—
450	#464	C₂²×C₆₇	1	4	yes	—
451	#462	C₂²×C₆₇	1	2	yes	—
452	#462	C₂²×C₆₇	1	4	yes	—
453	#462	C₂²×C₆₇	1	2	yes	—
454	#462	C₂²×C₆₇	1	4	yes	—
455	#462	C₂²×C₆₇	1	4	yes	—
456	#446	C₂²×C₆₇	1	2	yes	—
457	#446	C₂²×C₆₇	1	4	yes	—
458	C₈×Q₈	C₂²×C₆₇	1	2	yes	—
459	#441	C₂²×C₆₇	1	4	yes	—
460	#441	C₂²×C₆₇	1	2	yes	—
461	#441	C₂²×C₆₇	1	4	yes	—
462	#440	C₂²×C₆₇	1	2	yes	—
463	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	—
464	C₄×Q₁₆	C₂²×C₆₇	1	4	yes	—
465	C₄×Q₁₆	C₂²×C₆₇	1	4	yes	—
466	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	—
467	#428	C₂²×C₆₇	1	1	yes	characteristic
468	#427	C₂²×C₆₇	1	2	yes	—
469	#424	C₂²×C₆₇	1	2	yes	—
470	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
471	#419	C₂²×C₆₇	1	2	yes	—
472	#419	C₂²×C₆₇	1	2	yes	—
473	#419	C₂²×C₆₇	1	1	yes	characteristic
474	#417	C₂²×C₆₇	1	1	yes	characteristic
475	#416	C₂²×C₆₇	1	2	yes	—
476	C₂×#103	C₂²×C₆₇	1	2	yes	—
477	#405	C₂²×C₆₇	1	2	yes	—
478	C₄×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
479	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
480	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
481	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
482	#137	—	2	4	no	—
483	C₂×Q₁₆	—	2	8	no	—
484	C₂×Q₁₆	C₂³×C₆₇	1	4	yes	—
485	C₂×Q₁₆	C₂³×C₆₇	1	4	yes	—
486	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
487	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
488	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
489	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
490	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
491	C₄⋊Q₈	—	2	2	no	—
492	C₄⋊Q₈	—	2	4	no	—
493	C₄⋊Q₈	—	2	2	no	—
494	C₄⋊Q₈	—	2	4	no	—
495	C₄⋊Q₈	—	2	2	no	—
496	C₄⋊Q₈	—	2	1	no	—
497	C₄⋊Q₈	—	2	1	no	—
498	C₄⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
499	C₄⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
500	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
501	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
502	C₄⋊Q₈	C₂³×C₆₇	1	4	yes	—
503	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
504	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
505	C₄⋊Q₈	C₂³×C₆₇	1	4	yes	—
506	#126	—	2	4	no	—
507	#126	—	2	4	no	—
508	#125	—	2	2	no	—
509	#125	—	2	2	no	—
510	#125	—	2	4	no	—
511	#125	—	2	4	no	—
512	#125	—	2	4	no	—
513	#125	—	2	4	no	—
514	#125	—	2	4	no	—
515	#125	—	2	2	no	—
516	#125	D₄×C₆₇	1	2	yes	—
517	#125	C₂³×C₆₇	1	2	yes	—
518	#125	C₂³×C₆₇	1	4	yes	—
519	#124	C₂³×C₆₇	1	4	yes	—
520	#123	—	2	4	no	—
521	C₂²⋊Q₈	—	2	2	no	—
522	C₂²⋊Q₈	—	2	2	no	—
523	C₂²⋊Q₈	—	2	1	no	—
524	C₂²⋊Q₈	—	2	1	no	—
525	C₂²⋊Q₈	—	2	2	no	—
526	C₂²⋊Q₈	—	2	2	no	—
527	C₂²⋊Q₈	—	2	4	no	—
528	C₂²⋊Q₈	D₄×C₆₇	1	2	yes	—
529	C₂²⋊Q₈	D₄×C₆₇	1	2	yes	—
530	C₄×Q₈	—	2	2	no	—
531	C₄×Q₈	—	2	2	no	—
532	C₄×Q₈	—	2	2	no	—
533	C₄×Q₈	—	2	2	no	—
534	C₄×Q₈	—	2	2	no	—
535	C₄×Q₈	—	2	2	no	—
536	C₄×Q₈	—	2	2	no	—
537	C₄×Q₈	—	2	4	no	—
538	C₄×Q₈	—	2	2	no	—
539	C₄×Q₈	—	2	1	no	—
540	C₄×Q₈	—	2	1	no	—
541	C₄×Q₈	—	2	1	no	—
542	C₄×Q₈	—	2	1	no	—
543	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
544	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
545	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
546	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
547	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
548	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
549	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
550	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
551	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
552	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
553	C₄×D₄	—	2	1	no	—
554	C₄×D₄	—	2	1	no	—
555	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
556	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
557	#117	—	2	2	no	—
558	#117	—	2	2	no	—
559	#117	—	2	4	no	—
560	#117	—	2	4	no	—
561	#117	—	2	1	no	—
562	#117	C₂³×C₆₇	1	1	yes	characteristic
563	#117	C₂³×C₆₇	1	2	yes	—
564	#117	C₂³×C₆₇	1	2	yes	—
565	C₂×C₄⋊C₄	—	2	1	no	—
566	C₂×C₄⋊C₄	—	2	1	no	—
567	C₂×C₄⋊C₄	—	2	1	no	—
568	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
569	C₂×C₄²	—	2	1	no	—
570	C₂×C₄²	—	2	1	no	—
571	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
572	#107	C₂³×C₆₇	1	2	yes	—
573	#107	C₂³×C₆₇	1	2	yes	—
574	#107	C₂³×C₆₇	1	2	yes	—
575	#106	C₂³×C₆₇	1	2	yes	—
576	#106	C₂³×C₆₇	1	2	yes	—
577	#106	C₂³×C₆₇	1	2	yes	—
578	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
579	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
580	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
581	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
582	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
583	#103	C₂³×C₆₇	1	4	yes	—
584	#103	C₂³×C₆₇	1	4	yes	—
585	#103	C₂³×C₆₇	1	2	yes	—
586	#103	C₂³×C₆₇	1	2	yes	—
587	#103	C₂³×C₆₇	1	2	yes	—
588	#103	C₂³×C₆₇	1	2	yes	—
589	#103	C₂³×C₆₇	1	2	yes	—
590	#103	C₂³×C₆₇	1	4	yes	—
591	#103	C₂³×C₆₇	1	4	yes	—
592	#103	C₂³×C₆₇	1	4	yes	—
593	#103	C₂³×C₆₇	1	4	yes	—
594	#102	C₂³×C₆₇	1	2	yes	—
595	#102	C₂³×C₆₇	1	2	yes	—
596	#102	C₂³×C₆₇	1	2	yes	—
597	#97	C₂³×C₆₇	1	2	yes	—
598	#97	C₂³×C₆₇	1	4	yes	—
599	C₄×C₈	C₂³×C₆₇	1	2	yes	—
600	C₄×C₈	C₂³×C₆₇	1	4	yes	—
601	#41	—	2	2	no	—
602	#41	—	2	2	no	—
603	C₂×Q₈	—	2	1	no	—
604	C₂×Q₈	—	2	1	no	—
605	C₂×Q₈	—	2	2	no	—
606	C₂×Q₈	—	2	1	no	—
607	C₂×Q₈	—	2	4	no	—
608	C₂×Q₈	—	2	2	no	—
609	C₂×Q₈	—	2	4	no	—
610	C₂×Q₈	—	2	4	no	—
611	C₂×Q₈	C₂×D₄×C₆₇	1	2	yes	—
612	C₂×Q₈	C₂×D₄×C₆₇	1	2	yes	—
613	C₂×Q₈	#41×C₆₇	1	4	yes	—
614	C₂×Q₈	C₂⁴×C₆₇	1	4	yes	—
615	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
616	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
617	C₂×D₄	—	2	1	no	—
618	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
619	C₂²×C₄	—	2	1	no	—
620	C₂²×C₄	—	2	2	no	—
621	C₂²×C₄	—	2	1	no	—
622	C₂²×C₄	—	2	1	no	—
623	C₂²×C₄	—	2	1	no	—
624	C₂²×C₄	—	2	1	no	—
625	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
626	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
627	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
628	Q₁₆	—	2	8	no	—
629	Q₁₆	—	2	8	no	—
630	Q₁₆	—	2	4	no	—
631	SD₁₆	—	2	4	no	—
632	M₁₆	—	2	2	no	—
633	M₁₆	—	2	2	no	—
634	C₂×C₈	—	2	4	no	—
635	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
636	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
637	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
638	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
639	C₄⋊C₄	—	2	2	no	—
640	C₄⋊C₄	—	2	2	no	—
641	C₄⋊C₄	—	2	2	no	—
642	C₄⋊C₄	—	2	2	no	—
643	C₄⋊C₄	—	2	2	no	—
644	C₄⋊C₄	—	2	2	no	—
645	C₄⋊C₄	—	2	1	no	—
646	C₄⋊C₄	—	2	1	no	—
647	C₄⋊C₄	—	2	1	no	—
648	C₄⋊C₄	—	2	4	no	—
649	C₄⋊C₄	—	2	4	no	—
650	C₄⋊C₄	—	2	4	no	—
651	C₄⋊C₄	—	2	4	no	—
652	C₄⋊C₄	—	2	2	no	—
653	C₄⋊C₄	—	2	1	no	—
654	C₄⋊C₄	—	2	4	no	—
655	C₄⋊C₄	—	2	4	no	—
656	C₄⋊C₄	—	2	1	no	—
657	C₄⋊C₄	—	2	4	no	—
658	C₄⋊C₄	—	2	4	no	—
659	C₄⋊C₄	—	2	2	no	—
660	C₄⋊C₄	—	2	4	no	—
661	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
662	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
663	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
664	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
665	C₄⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
666	C₄⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
667	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
668	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
669	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
670	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
671	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
672	C₂²⋊C₄	—	2	1	no	—
673	C₂²⋊C₄	—	2	2	no	—
674	C₂²⋊C₄	—	2	1	no	—
675	C₂²⋊C₄	—	2	1	no	—
676	C₂²⋊C₄	—	2	4	no	—
677	C₂²⋊C₄	—	2	4	no	—
678	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
679	C₄²	—	2	1	no	—
680	C₄²	—	2	1	no	—
681	C₄²	—	2	1	no	—
682	C₄²	—	2	2	no	—
683	C₄²	—	2	2	no	—
684	C₄²	—	2	4	no	—
685	C₄²	—	2	4	no	—
686	C₄²	—	2	4	no	—
687	C₄²	—	2	4	no	—
688	C₄²	—	2	2	no	—
689	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
690	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
691	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
692	C₄²	C₂⁴×C₆₇	1	4	yes	—
693	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
694	C₂³	—	2	1	no	—
695	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
696	Q₈	—	2	4	no	—
697	Q₈	—	2	4	no	—
698	Q₈	—	2	2	no	—
699	Q₈	—	2	4	no	—
700	Q₈	—	2	1	no	—
701	Q₈	—	2	4	no	—
702	Q₈	—	2	1	no	—
703	Q₈	—	4	2	no	—
704	Q₈	—	4	4	no	—
705	Q₈	—	4	2	no	—
706	Q₈	—	8	1	no	—
707	Q₈	—	8	4	no	—
708	Q₈	C₂×#41×C₆₇	1	4	yes	—
709	D₄	—	2	1	no	—
710	D₄	—	2	1	no	—
711	D₄	—	4	2	no	—
712	C₂×C₄	—	2	4	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	1	no	—
716	C₂×C₄	—	2	1	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	2	4	no	—
720	C₂×C₄	—	2	1	no	—
721	C₂×C₄	—	2	2	no	—
722	C₂×C₄	—	4	1	no	—
723	C₂×C₄	—	4	2	no	—
724	C₂×C₄	—	4	4	no	—
725	C₂×C₄	—	4	2	no	—
726	C₂×C₄	—	4	2	no	—
727	C₂×C₄	—	8	1	no	—
728	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
729	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
730	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
731	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
732	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
733	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
734	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
735	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
736	C₂×C₄	2₋¹⁺⁴×C₆₇	1	2	yes	—
737	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
738	C₈	—	2	2	no	—
739	C₈	—	2	2	no	—
740	C₈	—	2	2	no	—
741	C₈	—	2	2	no	—
742	C₂²	—	2	1	no	—
743	C₂²	—	2	1	no	—
744	C₂²	—	4	1	no	—
745	C₂²	—	4	1	no	—
746	C₂²	—	4	1	no	—
747	C₂²	#548×C₆₇	1	2	yes	—
748	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
749	C₄	—	2	1	no	—
750	C₄	—	2	4	no	—
751	C₄	—	2	1	no	—
752	C₄	—	2	1	no	—
753	C₄	—	2	4	no	—
754	C₄	—	2	4	no	—
755	C₄	—	4	1	no	—
756	C₄	—	4	2	no	—
757	C₄	—	4	1	no	—
758	C₄	—	4	2	no	—
759	C₄	—	4	2	no	—
760	C₄	—	4	1	no	—
761	C₄	—	4	4	no	—
762	C₄	#548×C₆₇	1	2	yes	—
763	C₄	#578×C₆₇	1	2	yes	—
764	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
765	C₄	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
766	C₂	—	2	2	no	—
767	C₂	—	8	1	no	—
768	C₂	C₂×#548×C₆₇	1	1	yes	characteristic
769	C₂	C₂×#578×C₆₇	1	1	yes	characteristic
770	C₂	C₆₇×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
prime radical	C₂×#41×C₆₇	C₂³
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ #533×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₆₇×#3502	C₂	semidirect
3. C₆₇×#3377	C₂	semidirect
4. C₆₇×#3374	C₂	semidirect
5. C₆₇×#3374	C₂	semidirect
6. C₆₇×#3369	C₂	semidirect
7. C₆₇×#3364	C₂	semidirect
8. C₆₇×#3363	C₂	semidirect
9. C₆₇×#3139	C₂	semidirect
11. C₆₇×#3082	C₂	semidirect
14. C₂×#462×C₆₇	C₂	semidirect
15. C₆₇×#2962	C₂	semidirect
16. C₆₇×#2950	C₂	semidirect
380. #61342	C₆₇	direct (N × H)
387. #3502	C₂×C₆₇	semidirect
388. #3377	C₂×C₆₇	semidirect
389. #3374	C₂×C₆₇	semidirect
390. #3374	C₂×C₆₇	semidirect
391. #3369	C₂×C₆₇	semidirect
392. #3364	C₂×C₆₇	semidirect
393. #3363	C₂×C₆₇	semidirect
394. #3139	C₂×C₆₇	semidirect
396. #3082	C₂×C₆₇	semidirect
399. C₂×#462	C₂×C₆₇	semidirect
400. #2962	C₂×C₆₇	semidirect
401. #2950	C₂×C₆₇	semidirect
403. C₆₇	#61342	direct (N × H)

Maximal subgroups

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

subgroup	index
C₆₇×#3509	2
C₆₇×#3502	2
C₆₇×#3377	2
C₆₇×#3374	2
C₆₇×#3369	2
C₆₇×#3364	2
C₆₇×#3363	2
C₆₇×#3139	2
C₆₇×#3137	2
C₆₇×#3082	2
C₆₇×#3076	2
C₆₇×#3044	2
C₂×#462×C₆₇	2
C₆₇×#2962	2
C₆₇×#2950	2
C₄×#137×C₆₇	2
#61342	67

Subgroups — C67×#61342 #30740593

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61342 #30740593