Subgroups — C₆₇×#61475 #30740726

Order 17152.

1900 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3514	C₂	1	2	yes	maximal, complemented
2	C₆₇×#3396	C₂	1	1	yes	maximal, characteristic, complemented
3	Q₈×D₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#3373	C₂	1	2	yes	maximal, complemented
5	C₆₇×#3342	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#3341	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3324	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3319	C₂	1	4	yes	maximal, complemented
9	C₆₇×#3280	C₂	1	2	yes	maximal, complemented
10	D₄×D₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#3175	C₂	1	2	yes	maximal, complemented
12	C₆₇×#3169	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3118	C₂	1	4	yes	maximal, complemented
14	C₆₇×#3115	C₂	1	2	yes	maximal, complemented
15	C₆₇×#2966	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#2948	C₂	1	2	yes	maximal, complemented
17	C₄×#135×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic
19	C₂²×D₈×C₆₇	C₂²	1	2	yes	—
20	#559×C₆₇	C₂²	1	2	yes	complemented
21	#556×C₆₇	C₂²	1	2	yes	—
22	#555×C₆₇	C₂²	1	4	yes	complemented
23	#551×C₆₇	—	2	4	no	—
24	D₄×Q₈×C₆₇	C₂²	1	2	yes	complemented
25	#548×C₆₇	—	2	2	no	—
26	#546×C₆₇	—	2	2	no	—
27	#546×C₆₇	C₂²	1	4	yes	complemented
28	D₄²×C₆₇	C₂²	1	2	yes	—
29	#542×C₆₇	C₂²	1	4	yes	complemented
30	#538×C₆₇	—	2	4	no	—
31	#532×C₆₇	C₂²	1	2	yes	complemented
32	#529×C₆₇	—	2	2	no	—
33	#529×C₆₇	C₂²	1	1	yes	characteristic
34	C₂×#124×C₆₇	—	2	2	no	—
35	#518×C₆₇	C₂²	1	4	yes	complemented
36	C₄×#41×C₆₇	C₂²	1	2	yes	complemented
37	#500×C₆₇	C₂²	1	2	yes	complemented
38	#500×C₆₇	C₂²	1	1	yes	characteristic, complemented
39	#495×C₆₇	C₂²	1	2	yes	complemented
40	#493×C₆₇	C₂²	1	1	yes	characteristic
41	#489×C₆₇	C₂²	1	4	yes	complemented
42	#486×C₆₇	C₂²	1	2	yes	complemented
43	#485×C₆₇	C₂²	1	4	yes	complemented
44	#482×C₆₇	C₂²	1	4	yes	complemented
45	#482×C₆₇	C₂²	1	4	yes	complemented
46	#476×C₆₇	C₂²	1	4	yes	complemented
47	#475×C₆₇	C₂²	1	2	yes	complemented
48	#474×C₆₇	C₂²	1	4	yes	complemented
49	#474×C₆₇	C₂²	1	2	yes	complemented
50	#468×C₆₇	C₂²	1	4	yes	complemented
51	#467×C₆₇	C₂²	1	2	yes	complemented
52	#466×C₆₇	C₂²	1	2	yes	—
53	#466×C₆₇	C₂²	1	2	yes	complemented
54	#466×C₆₇	C₂²	1	2	yes	complemented
55	#463×C₆₇	C₂²	1	4	yes	complemented
56	#463×C₆₇	C₂²	1	4	yes	complemented
57	#460×C₆₇	C₂²	1	2	yes	complemented
58	#459×C₆₇	C₂²	1	2	yes	—
59	#450×C₆₇	C₂²	1	4	yes	complemented
60	#449×C₆₇	C₂²	1	4	yes	complemented
61	#447×C₆₇	C₂²	1	4	yes	—
62	#446×C₆₇	C₂²	1	1	yes	characteristic, complemented
63	C₈×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
64	#442×C₆₇	C₂²	1	4	yes	complemented
65	#442×C₆₇	C₂²	1	4	yes	complemented
66	#440×C₆₇	C₂²	1	4	yes	complemented
67	C₄×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
68	C₄×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
69	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
70	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
71	C₄×D₈×C₆₇	C₂²	1	1	yes	characteristic
72	C₄×D₈×C₆₇	C₂²	1	2	yes	—
73	C₄×D₈×C₆₇	C₂²	1	1	yes	characteristic
74	C₄×D₈×C₆₇	C₂²	1	2	yes	complemented
75	C₄×D₈×C₆₇	C₂²	1	2	yes	complemented
76	C₄×D₈×C₆₇	C₂²	1	2	yes	complemented
77	#436×C₆₇	C₂²	1	1	yes	characteristic
78	#435×C₆₇	C₂²	1	2	yes	complemented
79	C₈×D₄×C₆₇	C₂²	1	1	yes	characteristic
80	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
81	#433×C₆₇	C₂²	1	2	yes	complemented
82	#432×C₆₇	C₂²	1	1	yes	characteristic, complemented
83	#427×C₆₇	C₂²	1	1	yes	characteristic, complemented
84	#427×C₆₇	C₂²	1	2	yes	complemented
85	#418×C₆₇	C₂²	1	4	yes	complemented
86	#416×C₆₇	C₂²	1	2	yes	complemented
87	#405×C₆₇	C₂²	1	2	yes	complemented
88	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
89	C₂×#41×C₆₇	—	2	2	no	—
90	C₂×#41×C₆₇	C₂³	1	2	yes	—
91	C₂²×Q₈×C₆₇	—	2	2	no	—
92	C₂²×D₄×C₆₇	—	2	2	no	—
93	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
94	#135×C₆₇	—	2	4	no	—
95	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
96	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
97	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
98	C₂×D₈×C₆₇	—	2	8	no	—
99	C₂×D₈×C₆₇	C₂³	1	4	yes	—
100	C₂×D₈×C₆₇	C₂³	1	2	yes	—
101	C₂×D₈×C₆₇	C₂³	1	2	yes	—
102	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
103	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
104	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
105	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
106	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
107	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
108	C₄⋊Q₈×C₆₇	C₂³	1	4	yes	—
109	#127×C₆₇	C₂³	1	2	yes	—
110	#126×C₆₇	—	2	4	no	—
111	#126×C₆₇	—	2	4	no	—
112	#126×C₆₇	D₄	1	2	yes	—
113	#125×C₆₇	D₄	1	1	yes	characteristic
114	#124×C₆₇	—	2	2	no	—
115	#124×C₆₇	—	2	2	no	—
116	#124×C₆₇	—	2	4	no	—
117	#124×C₆₇	—	2	4	no	—
118	#124×C₆₇	—	2	4	no	—
119	#124×C₆₇	—	2	2	no	—
120	#124×C₆₇	D₄	1	1	yes	characteristic
121	#124×C₆₇	C₂³	1	4	yes	—
122	#123×C₆₇	—	2	4	no	—
123	#123×C₆₇	—	2	4	no	—
124	#123×C₆₇	—	2	4	no	—
125	#123×C₆₇	D₄	1	2	yes	—
126	C₂²⋊Q₈×C₆₇	—	2	2	no	—
127	C₂²⋊Q₈×C₆₇	—	2	4	no	—
128	C₂²⋊Q₈×C₆₇	—	2	4	no	—
129	C₂²⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
130	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
131	#121×C₆₇	—	2	4	no	—
132	#121×C₆₇	—	2	2	no	—
133	#121×C₆₇	—	2	2	no	—
134	#121×C₆₇	—	2	4	no	—
135	#121×C₆₇	D₄	1	1	yes	characteristic
136	#121×C₆₇	C₂³	1	4	yes	—
137	#121×C₆₇	C₂³	1	4	yes	—
138	#120×C₆₇	—	2	4	no	—
139	#120×C₆₇	—	2	4	no	—
140	C₄×Q₈×C₆₇	—	2	2	no	—
141	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
142	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
143	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
144	C₄×D₄×C₆₇	—	2	2	no	—
145	C₄×D₄×C₆₇	—	2	2	no	—
146	C₄×D₄×C₆₇	—	2	4	no	—
147	C₄×D₄×C₆₇	—	2	4	no	—
148	C₄×D₄×C₆₇	—	2	2	no	—
149	C₄×D₄×C₆₇	—	2	2	no	—
150	C₄×D₄×C₆₇	C₂³	1	2	yes	—
151	C₄×D₄×C₆₇	C₂³	1	4	yes	—
152	C₄×D₄×C₆₇	C₂³	1	4	yes	—
153	C₄×D₄×C₆₇	C₂³	1	2	yes	—
154	C₄×D₄×C₆₇	C₂³	1	4	yes	—
155	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
156	C₄×D₄×C₆₇	C₂³	1	2	yes	—
157	#117×C₆₇	—	2	4	no	—
158	#117×C₆₇	—	2	2	no	—
159	#117×C₆₇	C₂³	1	2	yes	—
160	#117×C₆₇	C₂³	1	4	yes	—
161	#117×C₆₇	C₂³	1	2	yes	—
162	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
163	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
164	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
165	C₂×C₄²×C₆₇	—	2	2	no	—
166	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
167	#107×C₆₇	C₂³	1	1	yes	characteristic
168	#107×C₆₇	C₂³	1	2	yes	—
169	#107×C₆₇	C₂³	1	2	yes	—
170	#107×C₆₇	C₂³	1	4	yes	—
171	#107×C₆₇	C₂³	1	1	yes	characteristic
172	#106×C₆₇	C₂³	1	4	yes	—
173	#106×C₆₇	C₂³	1	2	yes	—
174	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
175	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
176	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
177	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
178	#103×C₆₇	C₂³	1	4	yes	—
179	#103×C₆₇	C₂³	1	2	yes	—
180	#103×C₆₇	C₂³	1	2	yes	—
181	#102×C₆₇	C₂³	1	4	yes	—
182	#102×C₆₇	C₂³	1	4	yes	—
183	#102×C₆₇	C₂³	1	4	yes	—
184	#102×C₆₇	C₂³	1	4	yes	—
185	#102×C₆₇	C₂³	1	4	yes	—
186	#102×C₆₇	C₂³	1	2	yes	—
187	#102×C₆₇	C₂³	1	2	yes	—
188	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
189	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
190	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
191	#97×C₆₇	C₂³	1	2	yes	—
192	#97×C₆₇	C₂³	1	2	yes	—
193	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
194	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
195	C₄×C₈×C₆₇	C₂³	1	2	yes	—
196	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
197	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
198	C₂⁴×C₆₇	—	2	4	no	—
199	#41×C₆₇	—	2	4	no	—
200	#41×C₆₇	—	4	2	no	—
201	#41×C₆₇	—	8	4	no	—
202	C₂×Q₈×C₆₇	—	2	2	no	—
203	C₂×Q₈×C₆₇	—	2	4	no	—
204	C₂×Q₈×C₆₇	—	8	4	no	—
205	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
206	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
207	C₂×D₄×C₆₇	—	2	8	no	—
208	C₂×D₄×C₆₇	—	2	2	no	—
209	C₂×D₄×C₆₇	—	2	4	no	—
210	C₂×D₄×C₆₇	—	2	4	no	—
211	C₂×D₄×C₆₇	—	2	4	no	—
212	C₂×D₄×C₆₇	—	2	2	no	—
213	C₂×D₄×C₆₇	—	2	2	no	—
214	C₂×D₄×C₆₇	—	4	4	no	—
215	C₂×D₄×C₆₇	—	8	4	no	—
216	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
217	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
218	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
219	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
220	C₂²×C₄×C₆₇	—	2	2	no	—
221	C₂²×C₄×C₆₇	—	2	2	no	—
222	C₂²×C₄×C₆₇	—	2	2	no	—
223	C₂²×C₄×C₆₇	—	2	4	no	—
224	C₂²×C₄×C₆₇	—	2	4	no	—
225	C₂²×C₄×C₆₇	—	2	4	no	—
226	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
227	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
228	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
229	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
230	Q₁₆×C₆₇	—	2	2	no	—
231	SD₁₆×C₆₇	—	2	4	no	—
232	SD₁₆×C₆₇	—	4	4	no	—
233	D₈×C₆₇	—	2	8	no	—
234	D₈×C₆₇	—	2	4	no	—
235	D₈×C₆₇	—	4	2	no	—
236	D₈×C₆₇	#41	1	4	yes	complemented
237	M₁₆×C₆₇	—	4	2	no	—
238	C₂×C₈×C₆₇	—	2	4	no	—
239	C₂×C₈×C₆₇	—	2	2	no	—
240	C₂×C₈×C₆₇	—	4	1	no	—
241	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
242	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
243	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
244	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
245	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
246	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
247	C₄⋊C₄×C₆₇	—	2	2	no	—
248	C₄⋊C₄×C₆₇	—	2	2	no	—
249	C₄⋊C₄×C₆₇	—	2	4	no	—
250	C₄⋊C₄×C₆₇	—	2	2	no	—
251	C₄⋊C₄×C₆₇	—	2	4	no	—
252	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
253	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
254	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
255	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
256	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
257	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
258	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
259	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
260	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
261	C₂²⋊C₄×C₆₇	—	2	4	no	—
262	C₂²⋊C₄×C₆₇	—	2	4	no	—
263	C₂²⋊C₄×C₆₇	—	2	2	no	—
264	C₂²⋊C₄×C₆₇	—	2	2	no	—
265	C₂²⋊C₄×C₆₇	—	2	4	no	—
266	C₂²⋊C₄×C₆₇	—	2	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	2	no	—
271	C₂²⋊C₄×C₆₇	—	2	4	no	—
272	C₂²⋊C₄×C₆₇	—	2	4	no	—
273	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
274	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
275	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
276	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
277	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
278	C₄²×C₆₇	—	2	2	no	—
279	C₄²×C₆₇	—	2	2	no	—
280	C₄²×C₆₇	—	2	2	no	—
281	C₄²×C₆₇	—	2	4	no	—
282	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
283	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
284	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
285	C₄²×C₆₇	C₂⁴	1	2	yes	—
286	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
287	C₂³×C₆₇	—	2	2	no	—
288	C₂³×C₆₇	—	2	4	no	—
289	C₂³×C₆₇	—	4	8	no	—
290	C₂³×C₆₇	—	8	4	no	—
291	C₂³×C₆₇	—	8	4	no	—
292	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
293	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
294	Q₈×C₆₇	—	2	2	no	—
295	Q₈×C₆₇	—	2	2	no	—
296	Q₈×C₆₇	—	2	2	no	—
297	Q₈×C₆₇	—	4	4	no	—
298	Q₈×C₆₇	—	8	4	no	—
299	D₄×C₆₇	—	2	2	no	—
300	D₄×C₆₇	—	2	4	no	—
301	D₄×C₆₇	—	2	2	no	—
302	D₄×C₆₇	—	2	4	no	—
303	D₄×C₆₇	—	4	2	no	—
304	D₄×C₆₇	—	4	8	no	—
305	D₄×C₆₇	—	4	4	no	—
306	D₄×C₆₇	—	4	4	no	—
307	D₄×C₆₇	—	8	2	no	—
308	D₄×C₆₇	—	8	4	no	—
309	D₄×C₆₇	—	8	4	no	—
310	D₄×C₆₇	C₂×#41	1	4	yes	—
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	2	no	—
316	C₂×C₄×C₆₇	—	2	2	no	—
317	C₂×C₄×C₆₇	—	2	2	no	—
318	C₂×C₄×C₆₇	—	2	2	no	—
319	C₂×C₄×C₆₇	—	2	4	no	—
320	C₂×C₄×C₆₇	—	4	1	no	—
321	C₂×C₄×C₆₇	—	4	4	no	—
322	C₂×C₄×C₆₇	—	4	4	no	—
323	C₂×C₄×C₆₇	—	8	2	no	—
324	C₂×C₄×C₆₇	—	8	4	no	—
325	C₂×C₄×C₆₇	—	8	4	no	—
326	C₂×C₄×C₆₇	—	8	4	no	—
327	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
328	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
329	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
330	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
331	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
332	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
333	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
334	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
335	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
336	C₈×C₆₇	—	2	2	no	—
337	C₈×C₆₇	—	2	1	no	—
338	C₈×C₆₇	—	2	1	no	—
339	C₈×C₆₇	—	2	1	no	—
340	C₈×C₆₇	—	2	2	no	—
341	C₈×C₆₇	C₂×#41	1	2	yes	—
342	C₂²×C₆₇	—	2	1	no	—
343	C₂²×C₆₇	—	2	2	no	—
344	C₂²×C₆₇	—	2	1	no	—
345	C₂²×C₆₇	—	2	2	no	—
346	C₂²×C₆₇	—	2	4	no	—
347	C₂²×C₆₇	—	2	1	no	—
348	C₂²×C₆₇	—	2	2	no	—
349	C₂²×C₆₇	—	4	2	no	—
350	C₂²×C₆₇	—	4	2	no	—
351	C₂²×C₆₇	—	4	4	no	—
352	C₂²×C₆₇	—	4	4	no	—
353	C₂²×C₆₇	—	4	4	no	—
354	C₂²×C₆₇	—	16	8	no	—
355	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
356	C₄×C₆₇	—	2	1	no	—
357	C₄×C₆₇	—	2	1	no	—
358	C₄×C₆₇	—	2	2	no	—
359	C₄×C₆₇	—	2	1	no	—
360	C₄×C₆₇	—	2	2	no	—
361	C₄×C₆₇	—	2	1	no	—
362	C₄×C₆₇	—	2	2	no	—
363	C₄×C₆₇	—	4	2	no	—
364	C₄×C₆₇	—	4	2	no	—
365	C₄×C₆₇	—	4	2	no	—
366	C₄×C₆₇	—	4	4	no	—
367	C₄×C₆₇	#576	1	2	yes	—
368	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
369	C₄×C₆₇	#585	1	1	yes	characteristic
370	#61475	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
371	C₂×C₆₇	—	4	1	no	—
372	C₂×C₆₇	—	4	2	no	—
373	C₂×C₆₇	—	4	4	no	—
374	C₂×C₆₇	—	8	4	no	—
375	C₂×C₆₇	D₄×#41	1	1	yes	characteristic
376	C₂×C₆₇	C₂×#576	1	1	yes	characteristic
377	C₂×C₆₇	#3584	1	1	yes	characteristic
378	#3514	C₂×C₆₇	1	2	yes	complemented
379	#3396	C₂×C₆₇	1	1	yes	characteristic, complemented
380	Q₈×D₈	C₂×C₆₇	1	1	yes	characteristic, complemented
381	#3373	C₂×C₆₇	1	2	yes	complemented
382	#3342	C₂×C₆₇	1	1	yes	characteristic, complemented
383	#3341	C₂×C₆₇	1	2	yes	complemented
384	#3324	C₂×C₆₇	1	2	yes	complemented
385	#3319	C₂×C₆₇	1	4	yes	complemented
386	#3280	C₂×C₆₇	1	2	yes	complemented
387	D₄×D₈	C₂×C₆₇	1	1	yes	characteristic, complemented
388	#3175	C₂×C₆₇	1	2	yes	complemented
389	#3169	C₂×C₆₇	1	1	yes	characteristic, complemented
390	#3118	C₂×C₆₇	1	4	yes	complemented
391	#3115	C₂×C₆₇	1	2	yes	complemented
392	#2966	C₂×C₆₇	1	1	yes	characteristic, complemented
393	#2948	C₂×C₆₇	1	2	yes	complemented
394	C₄×#135	C₂×C₆₇	1	1	yes	characteristic, complemented
395	C₆₇	#61475	1	1	yes	characteristic, direct product factor, Sylow
396	C₂×#135	C₂²×C₆₇	1	1	yes	characteristic
397	C₂²×D₈	C₂²×C₆₇	1	2	yes	—
398	#559	C₂²×C₆₇	1	2	yes	complemented
399	#556	C₂²×C₆₇	1	2	yes	—
400	#555	C₂²×C₆₇	1	4	yes	complemented
401	#551	—	2	4	no	—
402	D₄×Q₈	C₂²×C₆₇	1	2	yes	complemented
403	#548	—	2	2	no	—
404	#546	—	2	2	no	—
405	#546	C₂²×C₆₇	1	4	yes	complemented
406	D₄²	C₂²×C₆₇	1	2	yes	—
407	#542	C₂²×C₆₇	1	4	yes	complemented
408	#538	—	2	4	no	—
409	#532	C₂²×C₆₇	1	2	yes	complemented
410	#529	—	2	2	no	—
411	#529	C₂²×C₆₇	1	1	yes	characteristic
412	C₂×#124	—	2	2	no	—
413	#518	C₂²×C₆₇	1	4	yes	complemented
414	C₄×#41	C₂²×C₆₇	1	2	yes	complemented
415	#500	C₂²×C₆₇	1	2	yes	complemented
416	#500	C₂²×C₆₇	1	1	yes	characteristic, complemented
417	#495	C₂²×C₆₇	1	2	yes	complemented
418	#493	C₂²×C₆₇	1	1	yes	characteristic
419	#489	C₂²×C₆₇	1	4	yes	complemented
420	#486	C₂²×C₆₇	1	2	yes	complemented
421	#485	C₂²×C₆₇	1	4	yes	complemented
422	#482	C₂²×C₆₇	1	4	yes	complemented
423	#482	C₂²×C₆₇	1	4	yes	complemented
424	#476	C₂²×C₆₇	1	4	yes	complemented
425	#475	C₂²×C₆₇	1	2	yes	complemented
426	#474	C₂²×C₆₇	1	2	yes	complemented
427	#474	C₂²×C₆₇	1	4	yes	complemented
428	#468	C₂²×C₆₇	1	4	yes	complemented
429	#467	C₂²×C₆₇	1	2	yes	complemented
430	#466	C₂²×C₆₇	1	2	yes	—
431	#466	C₂²×C₆₇	1	2	yes	complemented
432	#466	C₂²×C₆₇	1	2	yes	complemented
433	#463	C₂²×C₆₇	1	4	yes	complemented
434	#463	C₂²×C₆₇	1	4	yes	complemented
435	#460	C₂²×C₆₇	1	2	yes	complemented
436	#459	C₂²×C₆₇	1	2	yes	—
437	#450	C₂²×C₆₇	1	4	yes	complemented
438	#449	C₂²×C₆₇	1	4	yes	complemented
439	#447	C₂²×C₆₇	1	4	yes	—
440	#446	C₂²×C₆₇	1	1	yes	characteristic, complemented
441	C₈×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
442	#442	C₂²×C₆₇	1	4	yes	complemented
443	#442	C₂²×C₆₇	1	4	yes	complemented
444	#440	C₂²×C₆₇	1	4	yes	complemented
445	C₄×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
446	C₄×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
447	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
448	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
449	C₄×D₈	C₂²×C₆₇	1	1	yes	characteristic
450	C₄×D₈	C₂²×C₆₇	1	2	yes	—
451	C₄×D₈	C₂²×C₆₇	1	1	yes	characteristic
452	C₄×D₈	C₂²×C₆₇	1	2	yes	complemented
453	C₄×D₈	C₂²×C₆₇	1	2	yes	complemented
454	C₄×D₈	C₂²×C₆₇	1	2	yes	complemented
455	#436	C₂²×C₆₇	1	1	yes	characteristic
456	#435	C₂²×C₆₇	1	2	yes	complemented
457	C₈×D₄	C₂²×C₆₇	1	1	yes	characteristic
458	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
459	#433	C₂²×C₆₇	1	2	yes	complemented
460	#432	C₂²×C₆₇	1	1	yes	characteristic, complemented
461	#427	C₂²×C₆₇	1	1	yes	characteristic, complemented
462	#427	C₂²×C₆₇	1	2	yes	complemented
463	#418	C₂²×C₆₇	1	4	yes	complemented
464	#416	C₂²×C₆₇	1	2	yes	complemented
465	#405	C₂²×C₆₇	1	2	yes	complemented
466	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
467	C₂×#41	—	2	2	no	—
468	C₂×#41	C₂³×C₆₇	1	2	yes	—
469	C₂²×Q₈	—	2	2	no	—
470	C₂²×D₄	—	2	2	no	—
471	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
472	#135	—	2	4	no	—
473	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic
474	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
475	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
476	C₂×D₈	—	2	8	no	—
477	C₂×D₈	C₂³×C₆₇	1	2	yes	—
478	C₂×D₈	C₂³×C₆₇	1	4	yes	—
479	C₂×D₈	C₂³×C₆₇	1	2	yes	—
480	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic
481	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
482	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
483	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
484	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
485	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
486	C₄⋊Q₈	C₂³×C₆₇	1	4	yes	—
487	#127	C₂³×C₆₇	1	2	yes	—
488	#126	—	2	4	no	—
489	#126	—	2	4	no	—
490	#126	D₄×C₆₇	1	2	yes	—
491	#125	D₄×C₆₇	1	1	yes	characteristic
492	#124	—	2	2	no	—
493	#124	—	2	2	no	—
494	#124	—	2	4	no	—
495	#124	—	2	4	no	—
496	#124	—	2	4	no	—
497	#124	—	2	2	no	—
498	#124	D₄×C₆₇	1	1	yes	characteristic
499	#124	C₂³×C₆₇	1	4	yes	—
500	#123	—	2	4	no	—
501	#123	—	2	4	no	—
502	#123	—	2	4	no	—
503	#123	D₄×C₆₇	1	2	yes	—
504	C₂²⋊Q₈	—	2	2	no	—
505	C₂²⋊Q₈	—	2	4	no	—
506	C₂²⋊Q₈	—	2	4	no	—
507	C₂²⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
508	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
509	#121	—	2	4	no	—
510	#121	—	2	2	no	—
511	#121	—	2	2	no	—
512	#121	—	2	4	no	—
513	#121	D₄×C₆₇	1	1	yes	characteristic
514	#121	C₂³×C₆₇	1	4	yes	—
515	#121	C₂³×C₆₇	1	4	yes	—
516	#120	—	2	4	no	—
517	#120	—	2	4	no	—
518	C₄×Q₈	—	2	2	no	—
519	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
520	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
521	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
522	C₄×D₄	—	2	2	no	—
523	C₄×D₄	—	2	2	no	—
524	C₄×D₄	—	2	4	no	—
525	C₄×D₄	—	2	4	no	—
526	C₄×D₄	—	2	2	no	—
527	C₄×D₄	—	2	2	no	—
528	C₄×D₄	C₂³×C₆₇	1	2	yes	—
529	C₄×D₄	C₂³×C₆₇	1	2	yes	—
530	C₄×D₄	C₂³×C₆₇	1	4	yes	—
531	C₄×D₄	C₂³×C₆₇	1	4	yes	—
532	C₄×D₄	C₂³×C₆₇	1	4	yes	—
533	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
534	C₄×D₄	C₂³×C₆₇	1	2	yes	—
535	#117	—	2	4	no	—
536	#117	—	2	2	no	—
537	#117	C₂³×C₆₇	1	2	yes	—
538	#117	C₂³×C₆₇	1	4	yes	—
539	#117	C₂³×C₆₇	1	2	yes	—
540	C₂×C₂²⋊C₄	—	2	4	no	—
541	C₂×C₂²⋊C₄	—	2	4	no	—
542	C₂×C₂²⋊C₄	—	2	4	no	—
543	C₂×C₄²	—	2	2	no	—
544	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
545	#107	C₂³×C₆₇	1	1	yes	characteristic
546	#107	C₂³×C₆₇	1	2	yes	—
547	#107	C₂³×C₆₇	1	1	yes	characteristic
548	#107	C₂³×C₆₇	1	2	yes	—
549	#107	C₂³×C₆₇	1	4	yes	—
550	#106	C₂³×C₆₇	1	2	yes	—
551	#106	C₂³×C₆₇	1	4	yes	—
552	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
553	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
554	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
555	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
556	#103	C₂³×C₆₇	1	2	yes	—
557	#103	C₂³×C₆₇	1	2	yes	—
558	#103	C₂³×C₆₇	1	4	yes	—
559	#102	C₂³×C₆₇	1	2	yes	—
560	#102	C₂³×C₆₇	1	2	yes	—
561	#102	C₂³×C₆₇	1	4	yes	—
562	#102	C₂³×C₆₇	1	4	yes	—
563	#102	C₂³×C₆₇	1	4	yes	—
564	#102	C₂³×C₆₇	1	4	yes	—
565	#102	C₂³×C₆₇	1	4	yes	—
566	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
567	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
568	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
569	#97	C₂³×C₆₇	1	2	yes	—
570	#97	C₂³×C₆₇	1	2	yes	—
571	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
572	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
573	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
574	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
575	C₄×C₈	C₂³×C₆₇	1	2	yes	—
576	C₂⁴	—	2	4	no	—
577	#41	—	2	4	no	—
578	#41	—	4	2	no	—
579	#41	—	8	4	no	—
580	C₂×Q₈	—	2	2	no	—
581	C₂×Q₈	—	2	4	no	—
582	C₂×Q₈	—	8	4	no	—
583	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
584	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
585	C₂×D₄	—	2	8	no	—
586	C₂×D₄	—	2	2	no	—
587	C₂×D₄	—	2	4	no	—
588	C₂×D₄	—	2	4	no	—
589	C₂×D₄	—	2	4	no	—
590	C₂×D₄	—	2	2	no	—
591	C₂×D₄	—	2	2	no	—
592	C₂×D₄	—	4	4	no	—
593	C₂×D₄	—	8	4	no	—
594	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
595	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
596	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
597	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
598	C₂²×C₄	—	2	2	no	—
599	C₂²×C₄	—	2	2	no	—
600	C₂²×C₄	—	2	2	no	—
601	C₂²×C₄	—	2	4	no	—
602	C₂²×C₄	—	2	4	no	—
603	C₂²×C₄	—	2	4	no	—
604	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
605	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
606	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
607	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
608	Q₁₆	—	2	2	no	—
609	SD₁₆	—	2	4	no	—
610	SD₁₆	—	4	4	no	—
611	D₈	—	2	8	no	—
612	D₈	—	2	4	no	—
613	D₈	—	4	2	no	—
614	D₈	#41×C₆₇	1	4	yes	complemented
615	M₁₆	—	4	2	no	—
616	C₂×C₈	—	2	4	no	—
617	C₂×C₈	—	2	2	no	—
618	C₂×C₈	—	4	1	no	—
619	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
620	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
621	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
622	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
623	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
624	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
625	C₄⋊C₄	—	2	2	no	—
626	C₄⋊C₄	—	2	2	no	—
627	C₄⋊C₄	—	2	4	no	—
628	C₄⋊C₄	—	2	2	no	—
629	C₄⋊C₄	—	2	4	no	—
630	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
631	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
632	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
633	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
634	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
635	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
636	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
637	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
638	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
639	C₂²⋊C₄	—	2	4	no	—
640	C₂²⋊C₄	—	2	4	no	—
641	C₂²⋊C₄	—	2	2	no	—
642	C₂²⋊C₄	—	2	2	no	—
643	C₂²⋊C₄	—	2	4	no	—
644	C₂²⋊C₄	—	2	4	no	—
645	C₂²⋊C₄	—	2	4	no	—
646	C₂²⋊C₄	—	2	4	no	—
647	C₂²⋊C₄	—	2	4	no	—
648	C₂²⋊C₄	—	2	2	no	—
649	C₂²⋊C₄	—	2	4	no	—
650	C₂²⋊C₄	—	2	4	no	—
651	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
652	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
653	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
654	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
655	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
656	C₄²	—	2	2	no	—
657	C₄²	—	2	2	no	—
658	C₄²	—	2	2	no	—
659	C₄²	—	2	4	no	—
660	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
661	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
662	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
663	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
664	C₄²	C₂⁴×C₆₇	1	2	yes	—
665	C₂³	—	2	2	no	—
666	C₂³	—	2	4	no	—
667	C₂³	—	4	8	no	—
668	C₂³	—	8	4	no	—
669	C₂³	—	8	4	no	—
670	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
671	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
672	Q₈	—	2	2	no	—
673	Q₈	—	2	2	no	—
674	Q₈	—	2	2	no	—
675	Q₈	—	4	4	no	—
676	Q₈	—	8	4	no	—
677	D₄	—	2	2	no	—
678	D₄	—	2	4	no	—
679	D₄	—	2	2	no	—
680	D₄	—	2	4	no	—
681	D₄	—	4	2	no	—
682	D₄	—	4	8	no	—
683	D₄	—	4	4	no	—
684	D₄	—	4	4	no	—
685	D₄	—	8	2	no	—
686	D₄	—	8	4	no	—
687	D₄	—	8	4	no	—
688	D₄	C₂×#41×C₆₇	1	4	yes	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	1	no	—
692	C₂×C₄	—	2	1	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	4	no	—
698	C₂×C₄	—	4	1	no	—
699	C₂×C₄	—	4	4	no	—
700	C₂×C₄	—	4	4	no	—
701	C₂×C₄	—	8	4	no	—
702	C₂×C₄	—	8	4	no	—
703	C₂×C₄	—	8	2	no	—
704	C₂×C₄	—	8	4	no	—
705	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
706	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
707	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
708	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
709	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
710	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
711	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
712	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
713	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
714	C₈	—	2	2	no	—
715	C₈	—	2	1	no	—
716	C₈	—	2	1	no	—
717	C₈	—	2	1	no	—
718	C₈	—	2	2	no	—
719	C₈	C₂×#41×C₆₇	1	2	yes	—
720	C₂²	—	2	1	no	—
721	C₂²	—	2	2	no	—
722	C₂²	—	2	1	no	—
723	C₂²	—	2	2	no	—
724	C₂²	—	2	1	no	—
725	C₂²	—	2	2	no	—
726	C₂²	—	2	4	no	—
727	C₂²	—	4	2	no	—
728	C₂²	—	4	2	no	—
729	C₂²	—	4	4	no	—
730	C₂²	—	4	4	no	—
731	C₂²	—	4	4	no	—
732	C₂²	—	16	8	no	—
733	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
734	C₄	—	2	1	no	—
735	C₄	—	2	2	no	—
736	C₄	—	2	1	no	—
737	C₄	—	2	1	no	—
738	C₄	—	2	2	no	—
739	C₄	—	2	1	no	—
740	C₄	—	2	2	no	—
741	C₄	—	4	2	no	—
742	C₄	—	4	4	no	—
743	C₄	—	4	2	no	—
744	C₄	—	4	2	no	—
745	C₄	#576×C₆₇	1	2	yes	—
746	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
747	C₄	#585×C₆₇	1	1	yes	characteristic
748	C₂	—	4	2	no	—
749	C₂	—	4	1	no	—
750	C₂	—	4	4	no	—
751	C₂	—	8	4	no	—
752	C₂	D₄×#41×C₆₇	1	1	yes	characteristic
753	C₂	C₂×#576×C₆₇	1	1	yes	characteristic
754	C₂	C₆₇×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ #529×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3514	C₂	semidirect
2. C₆₇×#3396	C₂	semidirect
3. Q₈×D₈×C₆₇	C₂	semidirect
4. C₆₇×#3373	C₂	semidirect
5. C₆₇×#3342	C₂	semidirect
6. C₆₇×#3341	C₂	semidirect
7. C₆₇×#3324	C₂	semidirect
8. C₆₇×#3319	C₂	semidirect
9. C₆₇×#3280	C₂	semidirect
10. D₄×D₈×C₆₇	C₂	semidirect
11. C₆₇×#3175	C₂	semidirect
12. C₆₇×#3169	C₂	semidirect
13. C₆₇×#3118	C₂	semidirect
14. C₆₇×#3115	C₂	semidirect
15. C₆₇×#2966	C₂	semidirect
16. C₆₇×#2948	C₂	semidirect
17. C₄×#135×C₆₇	C₂	semidirect
20. #559×C₆₇	C₂²	semidirect
22. #555×C₆₇	C₂²	semidirect
24. D₄×Q₈×C₆₇	C₂²	semidirect
27. #546×C₆₇	C₂²	semidirect
29. #542×C₆₇	C₂²	semidirect
31. #532×C₆₇	C₂²	semidirect
35. #518×C₆₇	C₂²	semidirect
36. C₄×#41×C₆₇	C₂²	semidirect
37. #500×C₆₇	C₂²	semidirect
38. #500×C₆₇	C₂²	semidirect
39. #495×C₆₇	C₂²	semidirect
41. #489×C₆₇	C₂²	semidirect
42. #486×C₆₇	C₂²	semidirect
43. #485×C₆₇	C₂²	semidirect
44. #482×C₆₇	C₂²	semidirect
45. #482×C₆₇	C₂²	semidirect
46. #476×C₆₇	C₂²	semidirect
47. #475×C₆₇	C₂²	semidirect
48. #474×C₆₇	C₂²	semidirect
49. #474×C₆₇	C₂²	semidirect
50. #468×C₆₇	C₂²	semidirect
51. #467×C₆₇	C₂²	semidirect
53. #466×C₆₇	C₂²	semidirect
54. #466×C₆₇	C₂²	semidirect
55. #463×C₆₇	C₂²	semidirect
56. #463×C₆₇	C₂²	semidirect
57. #460×C₆₇	C₂²	semidirect
59. #450×C₆₇	C₂²	semidirect
60. #449×C₆₇	C₂²	semidirect
62. #446×C₆₇	C₂²	semidirect
63. C₈×Q₈×C₆₇	C₂²	semidirect
64. #442×C₆₇	C₂²	semidirect
65. #442×C₆₇	C₂²	semidirect
66. #440×C₆₇	C₂²	semidirect
67. C₄×Q₁₆×C₆₇	C₂²	semidirect
68. C₄×Q₁₆×C₆₇	C₂²	semidirect
69. C₄×SD₁₆×C₆₇	C₂²	semidirect
70. C₄×SD₁₆×C₆₇	C₂²	semidirect
74. C₄×D₈×C₆₇	C₂²	semidirect
75. C₄×D₈×C₆₇	C₂²	semidirect
76. C₄×D₈×C₆₇	C₂²	semidirect
78. #435×C₆₇	C₂²	semidirect
80. C₈×D₄×C₆₇	C₂²	semidirect
81. #433×C₆₇	C₂²	semidirect
82. #432×C₆₇	C₂²	semidirect
83. #427×C₆₇	C₂²	semidirect
84. #427×C₆₇	C₂²	semidirect
85. #418×C₆₇	C₂²	semidirect
86. #416×C₆₇	C₂²	semidirect
87. #405×C₆₇	C₂²	semidirect
88. C₂×C₄×C₈×C₆₇	C₂²	semidirect
236. D₈×C₆₇	#41	semidirect
370. #61475	C₆₇	direct (N × H)
378. #3514	C₂×C₆₇	semidirect
379. #3396	C₂×C₆₇	semidirect
380. Q₈×D₈	C₂×C₆₇	semidirect
381. #3373	C₂×C₆₇	semidirect
382. #3342	C₂×C₆₇	semidirect
383. #3341	C₂×C₆₇	semidirect
384. #3324	C₂×C₆₇	semidirect
385. #3319	C₂×C₆₇	semidirect
386. #3280	C₂×C₆₇	semidirect
387. D₄×D₈	C₂×C₆₇	semidirect
388. #3175	C₂×C₆₇	semidirect
389. #3169	C₂×C₆₇	semidirect
390. #3118	C₂×C₆₇	semidirect
391. #3115	C₂×C₆₇	semidirect
392. #2966	C₂×C₆₇	semidirect
393. #2948	C₂×C₆₇	semidirect
394. C₄×#135	C₂×C₆₇	semidirect
395. C₆₇	#61475	direct (N × H)
398. #559	C₂²×C₆₇	semidirect
400. #555	C₂²×C₆₇	semidirect
402. D₄×Q₈	C₂²×C₆₇	semidirect
405. #546	C₂²×C₆₇	semidirect
407. #542	C₂²×C₆₇	semidirect
409. #532	C₂²×C₆₇	semidirect
413. #518	C₂²×C₆₇	semidirect
414. C₄×#41	C₂²×C₆₇	semidirect
415. #500	C₂²×C₆₇	semidirect
416. #500	C₂²×C₆₇	semidirect
417. #495	C₂²×C₆₇	semidirect
419. #489	C₂²×C₆₇	semidirect
420. #486	C₂²×C₆₇	semidirect
421. #485	C₂²×C₆₇	semidirect
422. #482	C₂²×C₆₇	semidirect
423. #482	C₂²×C₆₇	semidirect
424. #476	C₂²×C₆₇	semidirect
425. #475	C₂²×C₆₇	semidirect
426. #474	C₂²×C₆₇	semidirect
427. #474	C₂²×C₆₇	semidirect
428. #468	C₂²×C₆₇	semidirect
429. #467	C₂²×C₆₇	semidirect
431. #466	C₂²×C₆₇	semidirect
432. #466	C₂²×C₆₇	semidirect
433. #463	C₂²×C₆₇	semidirect
434. #463	C₂²×C₆₇	semidirect
435. #460	C₂²×C₆₇	semidirect
437. #450	C₂²×C₆₇	semidirect
438. #449	C₂²×C₆₇	semidirect
440. #446	C₂²×C₆₇	semidirect
441. C₈×Q₈	C₂²×C₆₇	semidirect
442. #442	C₂²×C₆₇	semidirect
443. #442	C₂²×C₆₇	semidirect
444. #440	C₂²×C₆₇	semidirect
445. C₄×Q₁₆	C₂²×C₆₇	semidirect
446. C₄×Q₁₆	C₂²×C₆₇	semidirect
447. C₄×SD₁₆	C₂²×C₆₇	semidirect
448. C₄×SD₁₆	C₂²×C₆₇	semidirect
452. C₄×D₈	C₂²×C₆₇	semidirect
453. C₄×D₈	C₂²×C₆₇	semidirect
454. C₄×D₈	C₂²×C₆₇	semidirect
456. #435	C₂²×C₆₇	semidirect
458. C₈×D₄	C₂²×C₆₇	semidirect
459. #433	C₂²×C₆₇	semidirect
460. #432	C₂²×C₆₇	semidirect
461. #427	C₂²×C₆₇	semidirect
462. #427	C₂²×C₆₇	semidirect
463. #418	C₂²×C₆₇	semidirect
464. #416	C₂²×C₆₇	semidirect
465. #405	C₂²×C₆₇	semidirect
466. C₂×C₄×C₈	C₂²×C₆₇	semidirect
614. D₈	#41×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#3514	2
C₆₇×#3396	2
Q₈×D₈×C₆₇	2
C₆₇×#3373	2
C₆₇×#3342	2
C₆₇×#3341	2
C₆₇×#3324	2
C₆₇×#3319	2
C₆₇×#3280	2
D₄×D₈×C₆₇	2
C₆₇×#3175	2
C₆₇×#3169	2
C₆₇×#3118	2
C₆₇×#3115	2
C₆₇×#2966	2
C₆₇×#2948	2
C₄×#135×C₆₇	2
#61475	67

Subgroups — C67×#61475 #30740726

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61475 #30740726