Subgroups — C₆₇×#61570 #30740821

Order 17152.

2234 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3501	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#546×C₆₇	C₂	1	1	yes	maximal, characteristic
3	C₆₇×#3314	C₂	1	8	yes	maximal, complemented
4	C₆₇×#3266	C₂	1	8	yes	maximal, complemented
5	C₆₇×#3215	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3193	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3189	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3110	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3007	C₂	1	2	yes	maximal, complemented
10	C₂×#450×C₆₇	C₂	1	2	yes	maximal, complemented
11	C₆₇×#2973	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
13	C₂³×D₄×C₆₇	C₂²	1	1	yes	characteristic
14	C₂×#137×C₆₇	C₂²	1	4	yes	complemented
15	C₂²×SD₁₆×C₆₇	C₂²	1	4	yes	complemented
16	#554×C₆₇	—	2	4	no	—
17	#554×C₆₇	C₂²	1	4	yes	complemented
18	D₄×Q₈×C₆₇	C₂²	1	4	yes	complemented
19	#546×C₆₇	—	2	4	no	—
20	#546×C₆₇	C₂²	1	8	yes	—
21	#544×C₆₇	—	2	1	no	—
22	#543×C₆₇	—	2	1	no	—
23	#543×C₆₇	—	2	1	no	—
24	#533×C₆₇	C₂²	1	2	yes	complemented
25	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic
26	C₂×#123×C₆₇	—	2	1	no	—
27	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
29	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	complemented
30	C₂×#121×C₆₇	—	2	1	no	—
31	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
32	C₂×#120×C₆₇	—	2	1	no	—
33	#518×C₆₇	—	2	1	no	—
34	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
35	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
36	C₂²×C₂²⋊C₄×C₆₇	—	2	1	no	—
37	#497×C₆₇	C₂²	1	4	yes	complemented
38	#489×C₆₇	C₂²	1	4	yes	complemented
39	#484×C₆₇	C₂²	1	4	yes	complemented
40	#484×C₆₇	C₂²	1	4	yes	complemented
41	#480×C₆₇	C₂²	1	4	yes	complemented
42	#474×C₆₇	C₂²	1	4	yes	complemented
43	#468×C₆₇	C₂²	1	8	yes	complemented
44	#467×C₆₇	C₂²	1	8	yes	complemented
45	#464×C₆₇	C₂²	1	8	yes	complemented
46	#461×C₆₇	C₂²	1	4	yes	complemented
47	#452×C₆₇	C₂²	1	8	yes	complemented
48	#451×C₆₇	C₂²	1	4	yes	complemented
49	#451×C₆₇	C₂²	1	4	yes	complemented
50	#450×C₆₇	C₂²	1	4	yes	—
51	#450×C₆₇	C₂²	1	4	yes	—
52	#450×C₆₇	C₂²	1	8	yes	complemented
53	#448×C₆₇	C₂²	1	4	yes	complemented
54	#440×C₆₇	C₂²	1	8	yes	complemented
55	#435×C₆₇	C₂²	1	8	yes	complemented
56	#432×C₆₇	C₂²	1	2	yes	complemented
57	#417×C₆₇	C₂²	1	4	yes	complemented
58	C₂×#102×C₆₇	C₂²	1	4	yes	complemented
59	#407×C₆₇	C₂²	1	2	yes	complemented
60	C₂×C₂²⋊C₈×C₆₇	C₂²	1	2	yes	—
61	C₂⁵×C₆₇	—	2	1	no	—
62	C₂×#41×C₆₇	—	2	2	no	—
63	C₂×#41×C₆₇	—	4	4	no	—
64	C₂×#41×C₆₇	C₂³	1	4	yes	—
65	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
66	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
67	C₂²×Q₈×C₆₇	C₂³	1	2	yes	complemented
68	C₂²×D₄×C₆₇	—	2	1	no	—
69	C₂²×D₄×C₆₇	—	2	1	no	—
70	C₂²×D₄×C₆₇	—	2	1	no	—
71	C₂²×D₄×C₆₇	—	2	2	no	—
72	C₂²×D₄×C₆₇	—	4	4	no	—
73	C₂²×D₄×C₆₇	D₄	1	1	yes	characteristic
74	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
75	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
76	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
77	C₂³×C₄×C₆₇	—	2	1	no	—
78	C₂³×C₄×C₆₇	—	2	1	no	—
79	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
80	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
81	#137×C₆₇	—	4	8	no	—
82	C₂×Q₁₆×C₆₇	C₂³	1	8	yes	complemented
83	C₂×SD₁₆×C₆₇	—	4	8	no	—
84	C₂×SD₁₆×C₆₇	C₂³	1	8	yes	—
85	C₂×SD₁₆×C₆₇	C₂³	1	8	yes	—
86	C₂×M₁₆×C₆₇	C₂³	1	4	yes	complemented
87	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
88	C₄⋊Q₈×C₆₇	—	2	4	no	—
89	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	complemented
90	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	complemented
91	#125×C₆₇	—	2	4	no	—
92	#125×C₆₇	—	2	2	no	—
93	#124×C₆₇	—	2	2	no	—
94	#124×C₆₇	C₂³	1	4	yes	—
95	#123×C₆₇	—	2	8	no	—
96	C₂²⋊Q₈×C₆₇	—	2	2	no	—
97	C₂²⋊Q₈×C₆₇	—	2	2	no	—
98	C₂²⋊Q₈×C₆₇	—	2	2	no	—
99	C₂²⋊Q₈×C₆₇	—	2	2	no	—
100	C₂²⋊Q₈×C₆₇	—	2	2	no	—
101	C₂²⋊Q₈×C₆₇	—	2	2	no	—
102	C₂²⋊Q₈×C₆₇	—	2	4	no	—
103	C₂²⋊Q₈×C₆₇	—	2	4	no	—
104	C₂²⋊Q₈×C₆₇	—	2	4	no	—
105	C₂²⋊Q₈×C₆₇	—	2	4	no	—
106	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
107	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
108	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
109	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	complemented
110	#121×C₆₇	—	2	2	no	—
111	#121×C₆₇	—	2	8	no	—
112	#121×C₆₇	C₂³	1	4	yes	—
113	#120×C₆₇	—	2	8	no	—
114	C₄×Q₈×C₆₇	—	2	2	no	—
115	C₄×Q₈×C₆₇	C₂³	1	4	yes	complemented
116	C₄×D₄×C₆₇	—	2	4	no	—
117	C₄×D₄×C₆₇	—	2	4	no	—
118	C₄×D₄×C₆₇	—	2	2	no	—
119	C₄×D₄×C₆₇	D₄	1	4	yes	—
120	C₄×D₄×C₆₇	C₂³	1	4	yes	—
121	C₄×D₄×C₆₇	C₂³	1	4	yes	—
122	#117×C₆₇	—	2	2	no	—
123	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
124	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
125	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
126	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
127	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
128	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
129	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	complemented
130	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
131	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
132	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
133	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
134	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
135	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
136	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
137	C₂×C₂²⋊C₄×C₆₇	—	2	8	no	—
138	C₂×C₂²⋊C₄×C₆₇	D₄	1	1	yes	characteristic
139	C₂×C₂²⋊C₄×C₆₇	D₄	1	1	yes	characteristic
140	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
141	#107×C₆₇	C₂³	1	8	yes	complemented
142	C₄⋊C₈×C₆₇	C₂³	1	4	yes	complemented
143	#103×C₆₇	C₂³	1	8	yes	complemented
144	#103×C₆₇	C₂³	1	8	yes	complemented
145	#102×C₆₇	C₂³	1	8	yes	—
146	#102×C₆₇	C₂³	1	8	yes	—
147	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
148	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
149	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	complemented
150	#97×C₆₇	C₂³	1	4	yes	complemented
151	C₂⁴×C₆₇	—	2	1	no	—
152	C₂⁴×C₆₇	—	2	1	no	—
153	C₂⁴×C₆₇	—	2	4	no	—
154	C₂⁴×C₆₇	—	4	4	no	—
155	C₂⁴×C₆₇	—	4	4	no	—
156	C₂⁴×C₆₇	—	8	2	no	—
157	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
158	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
159	#41×C₆₇	—	2	8	no	—
160	#41×C₆₇	—	4	4	no	—
161	#41×C₆₇	—	4	8	no	—
162	C₂×Q₈×C₆₇	—	2	1	no	—
163	C₂×Q₈×C₆₇	—	2	2	no	—
164	C₂×Q₈×C₆₇	—	2	2	no	—
165	C₂×Q₈×C₆₇	—	2	2	no	—
166	C₂×Q₈×C₆₇	—	4	2	no	—
167	C₂×Q₈×C₆₇	—	4	4	no	—
168	C₂×Q₈×C₆₇	—	4	4	no	—
169	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
170	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
171	C₂×D₄×C₆₇	—	2	4	no	—
172	C₂×D₄×C₆₇	—	2	4	no	—
173	C₂×D₄×C₆₇	—	2	8	no	—
174	C₂×D₄×C₆₇	—	2	4	no	—
175	C₂×D₄×C₆₇	—	2	4	no	—
176	C₂×D₄×C₆₇	—	2	1	no	—
177	C₂×D₄×C₆₇	—	2	4	no	—
178	C₂×D₄×C₆₇	—	2	1	no	—
179	C₂×D₄×C₆₇	—	4	4	no	—
180	C₂×D₄×C₆₇	—	4	2	no	—
181	C₂×D₄×C₆₇	—	4	8	no	—
182	C₂×D₄×C₆₇	—	4	4	no	—
183	C₂×D₄×C₆₇	—	4	4	no	—
184	C₂×D₄×C₆₇	—	8	2	no	—
185	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	—
186	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
187	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
188	C₂²×C₄×C₆₇	—	2	1	no	—
189	C₂²×C₄×C₆₇	—	2	1	no	—
190	C₂²×C₄×C₆₇	—	2	2	no	—
191	C₂²×C₄×C₆₇	—	2	2	no	—
192	C₂²×C₄×C₆₇	—	2	2	no	—
193	C₂²×C₄×C₆₇	—	2	2	no	—
194	C₂²×C₄×C₆₇	—	2	4	no	—
195	C₂²×C₄×C₆₇	—	2	4	no	—
196	C₂²×C₄×C₆₇	—	4	2	no	—
197	C₂²×C₄×C₆₇	—	4	2	no	—
198	C₂²×C₄×C₆₇	—	4	4	no	—
199	C₂²×C₄×C₆₇	—	8	2	no	—
200	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
201	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
202	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
203	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
204	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
205	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
206	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
207	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
208	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
209	Q₁₆×C₆₇	—	4	8	no	—
210	SD₁₆×C₆₇	—	2	16	no	—
211	SD₁₆×C₆₇	—	4	8	no	—
212	M₁₆×C₆₇	—	4	4	no	—
213	C₂×C₈×C₆₇	—	4	4	no	—
214	C₂×C₈×C₆₇	C₂⁴	1	8	yes	—
215	C₄⋊C₄×C₆₇	—	2	4	no	—
216	C₄⋊C₄×C₆₇	—	2	4	no	—
217	C₄⋊C₄×C₆₇	—	2	4	no	—
218	C₄⋊C₄×C₆₇	—	2	4	no	—
219	C₄⋊C₄×C₆₇	—	2	1	no	—
220	C₄⋊C₄×C₆₇	—	2	2	no	—
221	C₄⋊C₄×C₆₇	—	2	2	no	—
222	C₄⋊C₄×C₆₇	—	2	2	no	—
223	C₄⋊C₄×C₆₇	—	2	2	no	—
224	C₄⋊C₄×C₆₇	—	2	2	no	—
225	C₄⋊C₄×C₆₇	—	2	4	no	—
226	C₄⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
227	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
228	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
229	C₂²⋊C₄×C₆₇	—	2	4	no	—
230	C₂²⋊C₄×C₆₇	—	2	4	no	—
231	C₂²⋊C₄×C₆₇	—	2	4	no	—
232	C₂²⋊C₄×C₆₇	—	2	4	no	—
233	C₂²⋊C₄×C₆₇	—	2	4	no	—
234	C₂²⋊C₄×C₆₇	—	2	4	no	—
235	C₂²⋊C₄×C₆₇	—	2	4	no	—
236	C₂²⋊C₄×C₆₇	—	2	4	no	—
237	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
238	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
239	C₄²×C₆₇	—	2	4	no	—
240	C₄²×C₆₇	C₂×D₄	1	2	yes	—
241	C₄²×C₆₇	C₂⁴	1	2	yes	—
242	C₂³×C₆₇	—	2	4	no	—
243	C₂³×C₆₇	—	2	2	no	—
244	C₂³×C₆₇	—	2	2	no	—
245	C₂³×C₆₇	—	2	2	no	—
246	C₂³×C₆₇	—	4	1	no	—
247	C₂³×C₆₇	—	4	1	no	—
248	C₂³×C₆₇	—	4	1	no	—
249	C₂³×C₆₇	—	4	1	no	—
250	C₂³×C₆₇	—	4	8	no	—
251	C₂³×C₆₇	—	4	2	no	—
252	C₂³×C₆₇	—	4	2	no	—
253	C₂³×C₆₇	—	4	2	no	—
254	C₂³×C₆₇	—	4	2	no	—
255	C₂³×C₆₇	—	4	8	no	—
256	C₂³×C₆₇	—	4	2	no	—
257	C₂³×C₆₇	—	8	4	no	—
258	C₂³×C₆₇	—	8	16	no	—
259	C₂³×C₆₇	#137	1	4	yes	complemented
260	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
261	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
262	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
263	Q₈×C₆₇	—	2	8	no	—
264	Q₈×C₆₇	—	2	4	no	—
265	Q₈×C₆₇	—	4	2	no	—
266	Q₈×C₆₇	—	8	2	no	—
267	Q₈×C₆₇	—	8	2	no	—
268	Q₈×C₆₇	—	8	2	no	—
269	D₄×C₆₇	—	2	4	no	—
270	D₄×C₆₇	—	2	8	no	—
271	D₄×C₆₇	—	2	2	no	—
272	D₄×C₆₇	—	2	4	no	—
273	D₄×C₆₇	—	4	8	no	—
274	D₄×C₆₇	—	4	2	no	—
275	D₄×C₆₇	—	4	8	no	—
276	D₄×C₆₇	—	8	4	no	—
277	D₄×C₆₇	H(5,𝔽₂)	1	4	yes	—
278	C₂×C₄×C₆₇	—	2	2	no	—
279	C₂×C₄×C₆₇	—	2	4	no	—
280	C₂×C₄×C₆₇	—	2	4	no	—
281	C₂×C₄×C₆₇	—	2	2	no	—
282	C₂×C₄×C₆₇	—	2	4	no	—
283	C₂×C₄×C₆₇	—	2	4	no	—
284	C₂×C₄×C₆₇	—	2	2	no	—
285	C₂×C₄×C₆₇	—	2	2	no	—
286	C₂×C₄×C₆₇	—	4	1	no	—
287	C₂×C₄×C₆₇	—	4	2	no	—
288	C₂×C₄×C₆₇	—	4	1	no	—
289	C₂×C₄×C₆₇	—	4	2	no	—
290	C₂×C₄×C₆₇	—	4	1	no	—
291	C₂×C₄×C₆₇	—	4	8	no	—
292	C₂×C₄×C₆₇	—	4	2	no	—
293	C₂×C₄×C₆₇	—	4	2	no	—
294	C₂×C₄×C₆₇	—	8	4	no	—
295	C₂×C₄×C₆₇	—	8	2	no	—
296	C₂×C₄×C₆₇	—	8	2	no	—
297	C₂×C₄×C₆₇	—	8	2	no	—
298	C₂×C₄×C₆₇	—	8	2	no	—
299	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
300	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
301	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
302	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
303	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
304	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
305	C₈×C₆₇	—	2	8	no	—
306	C₂²×C₆₇	—	2	1	no	—
307	C₂²×C₆₇	—	2	2	no	—
308	C₂²×C₆₇	—	2	1	no	—
309	C₂²×C₆₇	—	2	2	no	—
310	C₂²×C₆₇	—	2	2	no	—
311	C₂²×C₆₇	—	2	2	no	—
312	C₂²×C₆₇	—	2	4	no	—
313	C₂²×C₆₇	—	2	2	no	—
314	C₂²×C₆₇	—	4	4	no	—
315	C₂²×C₆₇	—	4	8	no	—
316	C₂²×C₆₇	—	4	2	no	—
317	C₂²×C₆₇	—	4	2	no	—
318	C₂²×C₆₇	—	4	2	no	—
319	C₂²×C₆₇	—	4	2	no	—
320	C₂²×C₆₇	—	4	2	no	—
321	C₂²×C₆₇	—	8	2	no	—
322	C₂²×C₆₇	—	8	16	no	—
323	C₂²×C₆₇	—	8	4	no	—
324	C₂²×C₆₇	C₂×#137	1	2	yes	—
325	C₂²×C₆₇	C₂×#137	1	4	yes	—
326	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
327	C₄×C₆₇	—	2	2	no	—
328	C₄×C₆₇	—	2	2	no	—
329	C₄×C₆₇	—	2	1	no	—
330	C₄×C₆₇	—	2	2	no	—
331	C₄×C₆₇	—	2	2	no	—
332	C₄×C₆₇	—	4	2	no	—
333	C₄×C₆₇	—	4	4	no	—
334	C₄×C₆₇	—	4	2	no	—
335	C₄×C₆₇	—	4	4	no	—
336	C₄×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
337	#61570	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
338	C₂×C₆₇	—	2	2	no	—
339	C₂×C₆₇	—	2	4	no	—
340	C₂×C₆₇	—	4	2	no	—
341	C₂×C₆₇	—	4	4	no	—
342	C₂×C₆₇	—	8	2	no	—
343	C₂×C₆₇	#3484	1	1	yes	characteristic
344	C₂×C₆₇	C₂²×#137	1	1	yes	characteristic
345	C₂×C₆₇	#3585	1	1	yes	characteristic
346	#3501	C₂×C₆₇	1	1	yes	characteristic, complemented
347	C₂×#546	C₂×C₆₇	1	1	yes	characteristic
348	#3314	C₂×C₆₇	1	8	yes	complemented
349	#3266	C₂×C₆₇	1	8	yes	complemented
350	#3215	C₂×C₆₇	1	2	yes	complemented
351	#3193	C₂×C₆₇	1	2	yes	complemented
352	#3189	C₂×C₆₇	1	2	yes	complemented
353	#3110	C₂×C₆₇	1	2	yes	complemented
354	#3007	C₂×C₆₇	1	2	yes	complemented
355	C₂×#450	C₂×C₆₇	1	2	yes	complemented
356	#2973	C₂×C₆₇	1	1	yes	characteristic, complemented
357	C₆₇	#61570	1	1	yes	characteristic, direct product factor, Sylow
358	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
359	C₂³×D₄	C₂²×C₆₇	1	1	yes	characteristic
360	C₂×#137	C₂²×C₆₇	1	4	yes	complemented
361	C₂²×SD₁₆	C₂²×C₆₇	1	4	yes	complemented
362	#554	—	2	4	no	—
363	#554	C₂²×C₆₇	1	4	yes	complemented
364	D₄×Q₈	C₂²×C₆₇	1	4	yes	complemented
365	#546	—	2	4	no	—
366	#546	C₂²×C₆₇	1	8	yes	—
367	#544	—	2	1	no	—
368	#543	—	2	1	no	—
369	#543	—	2	1	no	—
370	#533	C₂²×C₆₇	1	2	yes	complemented
371	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic
372	C₂×#123	—	2	1	no	—
373	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
374	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
375	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	complemented
376	C₂×#121	—	2	1	no	—
377	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
378	C₂×#120	—	2	1	no	—
379	#518	—	2	1	no	—
380	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
381	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
382	C₂²×C₂²⋊C₄	—	2	1	no	—
383	#497	C₂²×C₆₇	1	4	yes	complemented
384	#489	C₂²×C₆₇	1	4	yes	complemented
385	#484	C₂²×C₆₇	1	4	yes	complemented
386	#484	C₂²×C₆₇	1	4	yes	complemented
387	#480	C₂²×C₆₇	1	4	yes	complemented
388	#474	C₂²×C₆₇	1	4	yes	complemented
389	#468	C₂²×C₆₇	1	8	yes	complemented
390	#467	C₂²×C₆₇	1	8	yes	complemented
391	#464	C₂²×C₆₇	1	8	yes	complemented
392	#461	C₂²×C₆₇	1	4	yes	complemented
393	#452	C₂²×C₆₇	1	8	yes	complemented
394	#451	C₂²×C₆₇	1	4	yes	complemented
395	#451	C₂²×C₆₇	1	4	yes	complemented
396	#450	C₂²×C₆₇	1	4	yes	—
397	#450	C₂²×C₆₇	1	4	yes	—
398	#450	C₂²×C₆₇	1	8	yes	complemented
399	#448	C₂²×C₆₇	1	4	yes	complemented
400	#440	C₂²×C₆₇	1	8	yes	complemented
401	#435	C₂²×C₆₇	1	8	yes	complemented
402	#432	C₂²×C₆₇	1	2	yes	complemented
403	#417	C₂²×C₆₇	1	4	yes	complemented
404	C₂×#102	C₂²×C₆₇	1	4	yes	complemented
405	#407	C₂²×C₆₇	1	2	yes	complemented
406	C₂×C₂²⋊C₈	C₂²×C₆₇	1	2	yes	—
407	C₂⁵	—	2	1	no	—
408	C₂×#41	—	2	2	no	—
409	C₂×#41	—	4	4	no	—
410	C₂×#41	C₂³×C₆₇	1	4	yes	—
411	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
412	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
413	C₂²×Q₈	C₂³×C₆₇	1	2	yes	complemented
414	C₂²×D₄	—	2	1	no	—
415	C₂²×D₄	—	2	1	no	—
416	C₂²×D₄	—	2	1	no	—
417	C₂²×D₄	—	2	2	no	—
418	C₂²×D₄	—	4	4	no	—
419	C₂²×D₄	D₄×C₆₇	1	1	yes	characteristic
420	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
421	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
422	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
423	C₂³×C₄	—	2	1	no	—
424	C₂³×C₄	—	2	1	no	—
425	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
426	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
427	#137	—	4	8	no	—
428	C₂×Q₁₆	C₂³×C₆₇	1	8	yes	complemented
429	C₂×SD₁₆	—	4	8	no	—
430	C₂×SD₁₆	C₂³×C₆₇	1	8	yes	—
431	C₂×SD₁₆	C₂³×C₆₇	1	8	yes	—
432	C₂×M₁₆	C₂³×C₆₇	1	4	yes	complemented
433	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
434	C₄⋊Q₈	—	2	4	no	—
435	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	complemented
436	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	complemented
437	#125	—	2	4	no	—
438	#125	—	2	2	no	—
439	#124	—	2	2	no	—
440	#124	C₂³×C₆₇	1	4	yes	—
441	#123	—	2	8	no	—
442	C₂²⋊Q₈	—	2	2	no	—
443	C₂²⋊Q₈	—	2	2	no	—
444	C₂²⋊Q₈	—	2	2	no	—
445	C₂²⋊Q₈	—	2	2	no	—
446	C₂²⋊Q₈	—	2	2	no	—
447	C₂²⋊Q₈	—	2	2	no	—
448	C₂²⋊Q₈	—	2	4	no	—
449	C₂²⋊Q₈	—	2	4	no	—
450	C₂²⋊Q₈	—	2	4	no	—
451	C₂²⋊Q₈	—	2	4	no	—
452	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
453	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
454	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
455	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	complemented
456	#121	—	2	2	no	—
457	#121	—	2	8	no	—
458	#121	C₂³×C₆₇	1	4	yes	—
459	#120	—	2	8	no	—
460	C₄×Q₈	—	2	2	no	—
461	C₄×Q₈	C₂³×C₆₇	1	4	yes	complemented
462	C₄×D₄	—	2	4	no	—
463	C₄×D₄	—	2	4	no	—
464	C₄×D₄	—	2	2	no	—
465	C₄×D₄	D₄×C₆₇	1	4	yes	—
466	C₄×D₄	C₂³×C₆₇	1	4	yes	—
467	C₄×D₄	C₂³×C₆₇	1	4	yes	—
468	#117	—	2	2	no	—
469	C₂×C₄⋊C₄	—	2	1	no	—
470	C₂×C₄⋊C₄	—	2	2	no	—
471	C₂×C₄⋊C₄	—	2	2	no	—
472	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
473	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
474	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
475	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	complemented
476	C₂×C₂²⋊C₄	—	2	1	no	—
477	C₂×C₂²⋊C₄	—	2	2	no	—
478	C₂×C₂²⋊C₄	—	2	2	no	—
479	C₂×C₂²⋊C₄	—	2	1	no	—
480	C₂×C₂²⋊C₄	—	2	1	no	—
481	C₂×C₂²⋊C₄	—	2	1	no	—
482	C₂×C₂²⋊C₄	—	2	1	no	—
483	C₂×C₂²⋊C₄	—	2	8	no	—
484	C₂×C₂²⋊C₄	D₄×C₆₇	1	1	yes	characteristic
485	C₂×C₂²⋊C₄	D₄×C₆₇	1	1	yes	characteristic
486	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
487	#107	C₂³×C₆₇	1	8	yes	complemented
488	C₄⋊C₈	C₂³×C₆₇	1	4	yes	complemented
489	#103	C₂³×C₆₇	1	8	yes	complemented
490	#103	C₂³×C₆₇	1	8	yes	complemented
491	#102	C₂³×C₆₇	1	8	yes	—
492	#102	C₂³×C₆₇	1	8	yes	—
493	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
494	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
495	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	complemented
496	#97	C₂³×C₆₇	1	4	yes	complemented
497	C₂⁴	—	2	1	no	—
498	C₂⁴	—	2	1	no	—
499	C₂⁴	—	2	4	no	—
500	C₂⁴	—	4	4	no	—
501	C₂⁴	—	4	4	no	—
502	C₂⁴	—	8	2	no	—
503	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
504	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
505	#41	—	2	8	no	—
506	#41	—	4	4	no	—
507	#41	—	4	8	no	—
508	C₂×Q₈	—	2	1	no	—
509	C₂×Q₈	—	2	2	no	—
510	C₂×Q₈	—	2	2	no	—
511	C₂×Q₈	—	2	2	no	—
512	C₂×Q₈	—	4	2	no	—
513	C₂×Q₈	—	4	4	no	—
514	C₂×Q₈	—	4	4	no	—
515	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
516	C₂×Q₈	C₂⁴×C₆₇	1	4	yes	—
517	C₂×D₄	—	2	4	no	—
518	C₂×D₄	—	2	4	no	—
519	C₂×D₄	—	2	8	no	—
520	C₂×D₄	—	2	4	no	—
521	C₂×D₄	—	2	4	no	—
522	C₂×D₄	—	2	1	no	—
523	C₂×D₄	—	2	4	no	—
524	C₂×D₄	—	2	1	no	—
525	C₂×D₄	—	4	4	no	—
526	C₂×D₄	—	4	2	no	—
527	C₂×D₄	—	4	8	no	—
528	C₂×D₄	—	4	4	no	—
529	C₂×D₄	—	4	4	no	—
530	C₂×D₄	—	8	2	no	—
531	C₂×D₄	C₂×D₄×C₆₇	1	4	yes	—
532	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
533	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
534	C₂²×C₄	—	2	1	no	—
535	C₂²×C₄	—	2	1	no	—
536	C₂²×C₄	—	2	2	no	—
537	C₂²×C₄	—	2	2	no	—
538	C₂²×C₄	—	2	2	no	—
539	C₂²×C₄	—	2	2	no	—
540	C₂²×C₄	—	2	4	no	—
541	C₂²×C₄	—	2	4	no	—
542	C₂²×C₄	—	4	2	no	—
543	C₂²×C₄	—	4	2	no	—
544	C₂²×C₄	—	4	4	no	—
545	C₂²×C₄	—	8	2	no	—
546	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
547	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
548	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
549	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
550	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
551	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
552	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
553	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
554	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
555	Q₁₆	—	4	8	no	—
556	SD₁₆	—	2	16	no	—
557	SD₁₆	—	4	8	no	—
558	M₁₆	—	4	4	no	—
559	C₂×C₈	—	4	4	no	—
560	C₂×C₈	C₂⁴×C₆₇	1	8	yes	—
561	C₄⋊C₄	—	2	4	no	—
562	C₄⋊C₄	—	2	4	no	—
563	C₄⋊C₄	—	2	4	no	—
564	C₄⋊C₄	—	2	4	no	—
565	C₄⋊C₄	—	2	1	no	—
566	C₄⋊C₄	—	2	2	no	—
567	C₄⋊C₄	—	2	2	no	—
568	C₄⋊C₄	—	2	2	no	—
569	C₄⋊C₄	—	2	2	no	—
570	C₄⋊C₄	—	2	2	no	—
571	C₄⋊C₄	—	2	4	no	—
572	C₄⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
573	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
574	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
575	C₂²⋊C₄	—	2	4	no	—
576	C₂²⋊C₄	—	2	4	no	—
577	C₂²⋊C₄	—	2	4	no	—
578	C₂²⋊C₄	—	2	4	no	—
579	C₂²⋊C₄	—	2	4	no	—
580	C₂²⋊C₄	—	2	4	no	—
581	C₂²⋊C₄	—	2	4	no	—
582	C₂²⋊C₄	—	2	4	no	—
583	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
584	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
585	C₄²	—	2	4	no	—
586	C₄²	C₂×D₄×C₆₇	1	2	yes	—
587	C₄²	C₂⁴×C₆₇	1	2	yes	—
588	C₂³	—	2	4	no	—
589	C₂³	—	2	2	no	—
590	C₂³	—	2	2	no	—
591	C₂³	—	2	2	no	—
592	C₂³	—	4	1	no	—
593	C₂³	—	4	1	no	—
594	C₂³	—	4	1	no	—
595	C₂³	—	4	1	no	—
596	C₂³	—	4	8	no	—
597	C₂³	—	4	2	no	—
598	C₂³	—	4	2	no	—
599	C₂³	—	4	2	no	—
600	C₂³	—	4	2	no	—
601	C₂³	—	4	8	no	—
602	C₂³	—	4	2	no	—
603	C₂³	—	8	4	no	—
604	C₂³	—	8	16	no	—
605	C₂³	#137×C₆₇	1	4	yes	complemented
606	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
607	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
608	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
609	Q₈	—	2	8	no	—
610	Q₈	—	2	4	no	—
611	Q₈	—	4	2	no	—
612	Q₈	—	8	2	no	—
613	Q₈	—	8	2	no	—
614	Q₈	—	8	2	no	—
615	D₄	—	2	4	no	—
616	D₄	—	2	8	no	—
617	D₄	—	2	2	no	—
618	D₄	—	2	4	no	—
619	D₄	—	4	8	no	—
620	D₄	—	4	2	no	—
621	D₄	—	4	8	no	—
622	D₄	—	8	4	no	—
623	D₄	H(5,𝔽₂)×C₆₇	1	4	yes	—
624	C₂×C₄	—	2	2	no	—
625	C₂×C₄	—	2	4	no	—
626	C₂×C₄	—	2	4	no	—
627	C₂×C₄	—	2	2	no	—
628	C₂×C₄	—	2	4	no	—
629	C₂×C₄	—	2	4	no	—
630	C₂×C₄	—	2	2	no	—
631	C₂×C₄	—	2	2	no	—
632	C₂×C₄	—	4	1	no	—
633	C₂×C₄	—	4	2	no	—
634	C₂×C₄	—	4	1	no	—
635	C₂×C₄	—	4	2	no	—
636	C₂×C₄	—	4	1	no	—
637	C₂×C₄	—	4	8	no	—
638	C₂×C₄	—	4	2	no	—
639	C₂×C₄	—	4	2	no	—
640	C₂×C₄	—	8	4	no	—
641	C₂×C₄	—	8	2	no	—
642	C₂×C₄	—	8	2	no	—
643	C₂×C₄	—	8	2	no	—
644	C₂×C₄	—	8	2	no	—
645	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
646	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
647	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
648	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
649	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
650	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
651	C₈	—	2	8	no	—
652	C₂²	—	2	1	no	—
653	C₂²	—	2	2	no	—
654	C₂²	—	2	1	no	—
655	C₂²	—	2	2	no	—
656	C₂²	—	2	2	no	—
657	C₂²	—	2	2	no	—
658	C₂²	—	2	2	no	—
659	C₂²	—	2	4	no	—
660	C₂²	—	4	4	no	—
661	C₂²	—	4	8	no	—
662	C₂²	—	4	2	no	—
663	C₂²	—	4	2	no	—
664	C₂²	—	4	2	no	—
665	C₂²	—	4	2	no	—
666	C₂²	—	4	2	no	—
667	C₂²	—	8	2	no	—
668	C₂²	—	8	16	no	—
669	C₂²	—	8	4	no	—
670	C₂²	C₂×#137×C₆₇	1	2	yes	—
671	C₂²	C₂×#137×C₆₇	1	4	yes	—
672	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
673	C₄	—	2	2	no	—
674	C₄	—	2	2	no	—
675	C₄	—	2	2	no	—
676	C₄	—	2	1	no	—
677	C₄	—	2	2	no	—
678	C₄	—	4	2	no	—
679	C₄	—	4	4	no	—
680	C₄	—	4	2	no	—
681	C₄	—	4	4	no	—
682	C₄	C₂×H(5,𝔽₂)×C₆₇	1	2	yes	—
683	C₂	—	2	2	no	—
684	C₂	—	2	4	no	—
685	C₂	—	4	2	no	—
686	C₂	—	4	4	no	—
687	C₂	—	8	2	no	—
688	C₂	C₆₇×#3484	1	1	yes	characteristic
689	C₂	C₂²×#137×C₆₇	1	1	yes	characteristic
690	C₂	C₆₇×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
prime radical	C₂×#546×C₆₇	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ C₂×C₄×D₄×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3501	C₂	semidirect
3. C₆₇×#3314	C₂	semidirect
4. C₆₇×#3266	C₂	semidirect
5. C₆₇×#3215	C₂	semidirect
6. C₆₇×#3193	C₂	semidirect
7. C₆₇×#3189	C₂	semidirect
8. C₆₇×#3110	C₂	semidirect
9. C₆₇×#3007	C₂	semidirect
10. C₂×#450×C₆₇	C₂	semidirect
11. C₆₇×#2973	C₂	semidirect
14. C₂×#137×C₆₇	C₂²	semidirect
15. C₂²×SD₁₆×C₆₇	C₂²	semidirect
17. #554×C₆₇	C₂²	semidirect
18. D₄×Q₈×C₆₇	C₂²	semidirect
24. #533×C₆₇	C₂²	semidirect
29. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
37. #497×C₆₇	C₂²	semidirect
38. #489×C₆₇	C₂²	semidirect
39. #484×C₆₇	C₂²	semidirect
40. #484×C₆₇	C₂²	semidirect
41. #480×C₆₇	C₂²	semidirect
42. #474×C₆₇	C₂²	semidirect
43. #468×C₆₇	C₂²	semidirect
44. #467×C₆₇	C₂²	semidirect
45. #464×C₆₇	C₂²	semidirect
46. #461×C₆₇	C₂²	semidirect
47. #452×C₆₇	C₂²	semidirect
48. #451×C₆₇	C₂²	semidirect
49. #451×C₆₇	C₂²	semidirect
52. #450×C₆₇	C₂²	semidirect
53. #448×C₆₇	C₂²	semidirect
54. #440×C₆₇	C₂²	semidirect
55. #435×C₆₇	C₂²	semidirect
56. #432×C₆₇	C₂²	semidirect
57. #417×C₆₇	C₂²	semidirect
58. C₂×#102×C₆₇	C₂²	semidirect
59. #407×C₆₇	C₂²	semidirect
67. C₂²×Q₈×C₆₇	C₂³	semidirect
82. C₂×Q₁₆×C₆₇	C₂³	semidirect
86. C₂×M₁₆×C₆₇	C₂³	semidirect
89. C₄⋊Q₈×C₆₇	C₂³	semidirect
90. C₄⋊Q₈×C₆₇	C₂³	semidirect
109. C₂²⋊Q₈×C₆₇	C₂³	semidirect
115. C₄×Q₈×C₆₇	C₂³	semidirect
129. C₂×C₄⋊C₄×C₆₇	C₂³	semidirect
141. #107×C₆₇	C₂³	semidirect
142. C₄⋊C₈×C₆₇	C₂³	semidirect
143. #103×C₆₇	C₂³	semidirect
144. #103×C₆₇	C₂³	semidirect
149. C₂²⋊C₈×C₆₇	C₂³	semidirect
150. #97×C₆₇	C₂³	semidirect
259. C₂³×C₆₇	#137	semidirect
337. #61570	C₆₇	direct (N × H)
346. #3501	C₂×C₆₇	semidirect
348. #3314	C₂×C₆₇	semidirect
349. #3266	C₂×C₆₇	semidirect
350. #3215	C₂×C₆₇	semidirect
351. #3193	C₂×C₆₇	semidirect
352. #3189	C₂×C₆₇	semidirect
353. #3110	C₂×C₆₇	semidirect
354. #3007	C₂×C₆₇	semidirect
355. C₂×#450	C₂×C₆₇	semidirect
356. #2973	C₂×C₆₇	semidirect
357. C₆₇	#61570	direct (N × H)
360. C₂×#137	C₂²×C₆₇	semidirect
361. C₂²×SD₁₆	C₂²×C₆₇	semidirect
363. #554	C₂²×C₆₇	semidirect
364. D₄×Q₈	C₂²×C₆₇	semidirect
370. #533	C₂²×C₆₇	semidirect
375. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
383. #497	C₂²×C₆₇	semidirect
384. #489	C₂²×C₆₇	semidirect
385. #484	C₂²×C₆₇	semidirect
386. #484	C₂²×C₆₇	semidirect
387. #480	C₂²×C₆₇	semidirect
388. #474	C₂²×C₆₇	semidirect
389. #468	C₂²×C₆₇	semidirect
390. #467	C₂²×C₆₇	semidirect
391. #464	C₂²×C₆₇	semidirect
392. #461	C₂²×C₆₇	semidirect
393. #452	C₂²×C₆₇	semidirect
394. #451	C₂²×C₆₇	semidirect
395. #451	C₂²×C₆₇	semidirect
398. #450	C₂²×C₆₇	semidirect
399. #448	C₂²×C₆₇	semidirect
400. #440	C₂²×C₆₇	semidirect
401. #435	C₂²×C₆₇	semidirect
402. #432	C₂²×C₆₇	semidirect
403. #417	C₂²×C₆₇	semidirect
404. C₂×#102	C₂²×C₆₇	semidirect
405. #407	C₂²×C₆₇	semidirect
413. C₂²×Q₈	C₂³×C₆₇	semidirect
428. C₂×Q₁₆	C₂³×C₆₇	semidirect
432. C₂×M₁₆	C₂³×C₆₇	semidirect
435. C₄⋊Q₈	C₂³×C₆₇	semidirect
436. C₄⋊Q₈	C₂³×C₆₇	semidirect
455. C₂²⋊Q₈	C₂³×C₆₇	semidirect
461. C₄×Q₈	C₂³×C₆₇	semidirect
475. C₂×C₄⋊C₄	C₂³×C₆₇	semidirect
487. #107	C₂³×C₆₇	semidirect
488. C₄⋊C₈	C₂³×C₆₇	semidirect
489. #103	C₂³×C₆₇	semidirect
490. #103	C₂³×C₆₇	semidirect
495. C₂²⋊C₈	C₂³×C₆₇	semidirect
496. #97	C₂³×C₆₇	semidirect
605. C₂³	#137×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#3501	2
C₂×#546×C₆₇	2
C₆₇×#3314	2
C₆₇×#3266	2
C₆₇×#3215	2
C₆₇×#3193	2
C₆₇×#3189	2
C₆₇×#3110	2
C₆₇×#3007	2
C₂×#450×C₆₇	2
C₆₇×#2973	2
#61570	67

Subgroups — C67×#61570 #30740821

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61570 #30740821