Subgroups — C₆₇×#59814 #30739065

Order 17152.

3566 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#546×C₆₇	C₂	1	4	yes	maximal, complemented
2	C₆₇×#2683	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#2682	C₂	1	2	yes	maximal, complemented
4	C₆₇×#2679	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#2555	C₂	1	2	yes	maximal, complemented
6	C₆₇×#2534	C₂	1	4	yes	maximal, complemented
7	C₆₇×#2461	C₂	1	4	yes	maximal, complemented
8	C₆₇×#2424	C₂	1	4	yes	maximal, complemented
9	C₆₇×#2406	C₂	1	2	yes	maximal, complemented
10	C₆₇×#2403	C₂	1	2	yes	maximal, complemented
11	C₆₇×#2358	C₂	1	2	yes	maximal, complemented
12	C₄×#121×C₆₇	C₂	1	2	yes	maximal, complemented
13	C₂×#390×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²×#41×C₆₇	C₂²	1	2	yes	—
15	C₂³×D₄×C₆₇	C₂²	1	1	yes	characteristic
16	C₂³×D₄×C₆₇	C₂²	1	2	yes	complemented
17	#546×C₆₇	—	2	32	no	—
18	C₂×#124×C₆₇	C₂²	1	4	yes	complemented
19	C₂×#123×C₆₇	C₂²	1	4	yes	complemented
20	C₂×#123×C₆₇	C₂²	1	4	yes	complemented
21	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	4	yes	complemented
22	C₂×#121×C₆₇	C₂²	1	2	yes	—
23	C₂×#121×C₆₇	C₂²	1	4	yes	complemented
24	C₂×#121×C₆₇	C₂²	1	4	yes	complemented
25	C₂×#120×C₆₇	C₂²	1	4	yes	—
26	C₂×#120×C₆₇	C₂²	1	2	yes	—
27	C₂×#120×C₆₇	C₂²	1	4	yes	complemented
28	C₂×#120×C₆₇	C₂²	1	2	yes	complemented
29	C₂×C₄×D₄×C₆₇	C₂²	1	4	yes	complemented
30	C₂×C₄×D₄×C₆₇	C₂²	1	4	yes	complemented
31	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
32	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
33	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	4	yes	complemented
34	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	4	yes	complemented
35	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic, complemented
36	#396×C₆₇	C₂²	1	4	yes	complemented
37	#396×C₆₇	C₂²	1	4	yes	complemented
38	#395×C₆₇	C₂²	1	2	yes	complemented
39	#395×C₆₇	C₂²	1	2	yes	complemented
40	#394×C₆₇	C₂²	1	4	yes	complemented
41	#394×C₆₇	C₂²	1	4	yes	complemented
42	#394×C₆₇	C₂²	1	2	yes	complemented
43	#394×C₆₇	C₂²	1	2	yes	complemented
44	#392×C₆₇	C₂²	1	4	yes	—
45	#392×C₆₇	C₂²	1	4	yes	complemented
46	#390×C₆₇	C₂²	1	1	yes	characteristic
47	#390×C₆₇	C₂²	1	1	yes	characteristic
48	#390×C₆₇	C₂²	1	1	yes	characteristic, complemented
49	#390×C₆₇	C₂²	1	4	yes	complemented
50	#390×C₆₇	C₂²	1	1	yes	characteristic, complemented
51	#390×C₆₇	C₂²	1	2	yes	complemented
52	#389×C₆₇	C₂²	1	2	yes	complemented
53	#388×C₆₇	C₂²	1	4	yes	complemented
54	#388×C₆₇	C₂²	1	4	yes	complemented
55	#388×C₆₇	C₂²	1	4	yes	complemented
56	#386×C₆₇	C₂²	1	2	yes	—
57	#386×C₆₇	C₂²	1	4	yes	complemented
58	#386×C₆₇	C₂²	1	4	yes	complemented
59	#386×C₆₇	C₂²	1	4	yes	complemented
60	#386×C₆₇	C₂²	1	2	yes	complemented
61	#385×C₆₇	C₂²	1	4	yes	complemented
62	#385×C₆₇	C₂²	1	4	yes	complemented
63	#381×C₆₇	C₂²	1	2	yes	complemented
64	#380×C₆₇	C₂²	1	2	yes	complemented
65	#379×C₆₇	C₂²	1	2	yes	complemented
66	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	complemented
67	C₄×C₂²⋊C₄×C₆₇	C₂²	1	4	yes	complemented
68	C₂⁵×C₆₇	C₂³	1	2	yes	—
69	C₂⁵×C₆₇	C₂³	1	2	yes	—
70	C₂×#41×C₆₇	—	2	16	no	—
71	C₂×#41×C₆₇	—	4	4	no	—
72	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
73	C₂²×D₄×C₆₇	—	2	16	no	—
74	C₂²×D₄×C₆₇	—	2	4	no	—
75	C₂²×D₄×C₆₇	—	4	2	no	—
76	C₂²×D₄×C₆₇	—	4	2	no	—
77	C₂²×D₄×C₆₇	—	4	4	no	—
78	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
79	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
80	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
81	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
82	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
83	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
84	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
85	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
86	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
89	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
90	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
91	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
92	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
93	#124×C₆₇	—	2	16	no	—
94	#123×C₆₇	—	2	16	no	—
95	#123×C₆₇	—	2	16	no	—
96	C₂²⋊Q₈×C₆₇	—	2	16	no	—
97	#121×C₆₇	—	2	16	no	—
98	#121×C₆₇	—	2	16	no	—
99	#121×C₆₇	D₄	1	16	yes	complemented
100	#120×C₆₇	—	2	16	no	—
101	#120×C₆₇	—	2	16	no	—
102	#120×C₆₇	—	2	8	no	—
103	#120×C₆₇	—	4	4	no	—
104	C₄×D₄×C₆₇	—	2	16	no	—
105	C₄×D₄×C₆₇	—	2	16	no	—
106	C₄×D₄×C₆₇	—	4	4	no	—
107	C₂×C₄⋊C₄×C₆₇	—	4	2	no	—
108	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
109	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
110	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
111	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
112	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
113	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
114	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
115	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
116	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
117	C₂×C₂²⋊C₄×C₆₇	—	2	16	no	—
118	C₂×C₂²⋊C₄×C₆₇	—	2	16	no	—
119	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
120	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
121	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
122	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
123	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
124	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
125	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
126	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
127	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
128	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
129	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
130	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
131	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
132	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
133	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
134	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
135	C₂×C₄²×C₆₇	—	4	2	no	—
136	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
137	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
138	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
139	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
140	#95×C₆₇	C₂³	1	4	yes	—
141	#95×C₆₇	C₂³	1	4	yes	—
142	#95×C₆₇	C₂³	1	4	yes	—
143	#95×C₆₇	C₂³	1	4	yes	—
144	#95×C₆₇	C₂³	1	2	yes	—
145	#95×C₆₇	C₂³	1	2	yes	—
146	C₂⁴×C₆₇	—	2	4	no	—
147	C₂⁴×C₆₇	—	2	8	no	—
148	C₂⁴×C₆₇	—	2	8	no	—
149	C₂⁴×C₆₇	—	2	4	no	—
150	C₂⁴×C₆₇	—	2	4	no	—
151	C₂⁴×C₆₇	—	4	2	no	—
152	C₂⁴×C₆₇	—	4	2	no	—
153	C₂⁴×C₆₇	—	4	4	no	—
154	C₂⁴×C₆₇	—	4	4	no	—
155	C₂⁴×C₆₇	—	4	2	no	—
156	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
157	C₂⁴×C₆₇	C₂⁴	1	4	yes	—
158	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
159	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
160	#41×C₆₇	—	4	32	no	—
161	C₂×Q₈×C₆₇	—	2	8	no	—
162	C₂×Q₈×C₆₇	—	4	2	no	—
163	C₂×D₄×C₆₇	—	2	8	no	—
164	C₂×D₄×C₆₇	—	2	8	no	—
165	C₂×D₄×C₆₇	—	2	8	no	—
166	C₂×D₄×C₆₇	—	2	8	no	—
167	C₂×D₄×C₆₇	—	2	8	no	—
168	C₂×D₄×C₆₇	—	2	8	no	—
169	C₂×D₄×C₆₇	—	2	4	no	—
170	C₂×D₄×C₆₇	—	2	8	no	—
171	C₂×D₄×C₆₇	—	2	8	no	—
172	C₂×D₄×C₆₇	—	2	2	no	—
173	C₂×D₄×C₆₇	—	2	4	no	—
174	C₂×D₄×C₆₇	—	4	2	no	—
175	C₂×D₄×C₆₇	—	4	1	no	—
176	C₂×D₄×C₆₇	—	4	1	no	—
177	C₂×D₄×C₆₇	—	4	1	no	—
178	C₂×D₄×C₆₇	—	4	2	no	—
179	C₂×D₄×C₆₇	—	4	1	no	—
180	C₂×D₄×C₆₇	—	4	4	no	—
181	C₂×D₄×C₆₇	—	4	2	no	—
182	C₂×D₄×C₆₇	—	4	4	no	—
183	C₂×D₄×C₆₇	—	4	2	no	—
184	C₂×D₄×C₆₇	—	4	16	no	—
185	C₂×D₄×C₆₇	—	4	4	no	—
186	C₂×D₄×C₆₇	—	4	4	no	—
187	C₂×D₄×C₆₇	—	4	32	no	—
188	C₂×D₄×C₆₇	C₂×D₄	1	16	yes	—
189	C₂×D₄×C₆₇	C₂×D₄	1	8	yes	complemented
190	C₂×D₄×C₆₇	#41	1	4	yes	complemented
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	8	no	—
195	C₂²×C₄×C₆₇	—	2	8	no	—
196	C₂²×C₄×C₆₇	—	2	4	no	—
197	C₂²×C₄×C₆₇	—	2	8	no	—
198	C₂²×C₄×C₆₇	—	2	8	no	—
199	C₂²×C₄×C₆₇	—	2	8	no	—
200	C₂²×C₄×C₆₇	—	4	2	no	—
201	C₂²×C₄×C₆₇	—	4	2	no	—
202	C₂²×C₄×C₆₇	—	4	2	no	—
203	C₂²×C₄×C₆₇	—	4	4	no	—
204	C₂²×C₄×C₆₇	—	4	4	no	—
205	C₂²×C₄×C₆₇	—	4	4	no	—
206	C₂²×C₄×C₆₇	C₂×D₄	1	8	yes	—
207	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
208	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
209	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
210	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
211	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
212	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
213	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
214	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
215	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
216	C₄⋊C₄×C₆₇	—	2	8	no	—
217	C₄⋊C₄×C₆₇	—	2	8	no	—
218	C₄⋊C₄×C₆₇	—	2	8	no	—
219	C₄⋊C₄×C₆₇	—	4	1	no	—
220	C₄⋊C₄×C₆₇	—	4	2	no	—
221	C₄⋊C₄×C₆₇	—	4	1	no	—
222	C₄⋊C₄×C₆₇	—	4	2	no	—
223	C₄⋊C₄×C₆₇	—	4	2	no	—
224	C₄⋊C₄×C₆₇	C₂×D₄	1	8	yes	complemented
225	C₂²⋊C₄×C₆₇	—	2	8	no	—
226	C₂²⋊C₄×C₆₇	—	2	8	no	—
227	C₂²⋊C₄×C₆₇	—	2	8	no	—
228	C₂²⋊C₄×C₆₇	—	2	4	no	—
229	C₂²⋊C₄×C₆₇	—	2	8	no	—
230	C₂²⋊C₄×C₆₇	—	2	8	no	—
231	C₂²⋊C₄×C₆₇	—	2	8	no	—
232	C₂²⋊C₄×C₆₇	—	2	8	no	—
233	C₂²⋊C₄×C₆₇	—	2	8	no	—
234	C₂²⋊C₄×C₆₇	—	2	8	no	—
235	C₂²⋊C₄×C₆₇	—	2	8	no	—
236	C₂²⋊C₄×C₆₇	—	2	8	no	—
237	C₂²⋊C₄×C₆₇	—	2	8	no	—
238	C₂²⋊C₄×C₆₇	—	4	4	no	—
239	C₂²⋊C₄×C₆₇	—	4	2	no	—
240	C₂²⋊C₄×C₆₇	C₂×D₄	1	16	yes	complemented
241	C₄²×C₆₇	—	2	8	no	—
242	C₄²×C₆₇	—	2	4	no	—
243	C₄²×C₆₇	—	4	1	no	—
244	C₄²×C₆₇	—	4	1	no	—
245	C₂³×C₆₇	—	2	1	no	—
246	C₂³×C₆₇	—	2	1	no	—
247	C₂³×C₆₇	—	2	2	no	—
248	C₂³×C₆₇	—	2	4	no	—
249	C₂³×C₆₇	—	2	4	no	—
250	C₂³×C₆₇	—	2	4	no	—
251	C₂³×C₆₇	—	2	4	no	—
252	C₂³×C₆₇	—	2	2	no	—
253	C₂³×C₆₇	—	2	4	no	—
254	C₂³×C₆₇	—	2	2	no	—
255	C₂³×C₆₇	—	2	4	no	—
256	C₂³×C₆₇	—	2	4	no	—
257	C₂³×C₆₇	—	2	4	no	—
258	C₂³×C₆₇	—	2	4	no	—
259	C₂³×C₆₇	—	2	2	no	—
260	C₂³×C₆₇	—	2	2	no	—
261	C₂³×C₆₇	—	2	2	no	—
262	C₂³×C₆₇	—	2	4	no	—
263	C₂³×C₆₇	—	4	8	no	—
264	C₂³×C₆₇	—	4	8	no	—
265	C₂³×C₆₇	—	4	16	no	—
266	C₂³×C₆₇	—	4	16	no	—
267	C₂³×C₆₇	—	4	8	no	—
268	C₂³×C₆₇	—	8	8	no	—
269	C₂³×C₆₇	—	8	4	no	—
270	C₂³×C₆₇	—	8	4	no	—
271	C₂³×C₆₇	—	8	8	no	—
272	C₂³×C₆₇	—	8	4	no	—
273	C₂³×C₆₇	C₂²×D₄	1	8	yes	—
274	C₂³×C₆₇	C₂²×D₄	1	4	yes	—
275	C₂³×C₆₇	C₂×#41	1	4	yes	—
276	C₂³×C₆₇	H(5,𝔽₂)	1	2	yes	—
277	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
278	Q₈×C₆₇	—	4	8	no	—
279	D₄×C₆₇	—	2	32	no	—
280	D₄×C₆₇	—	4	4	no	—
281	D₄×C₆₇	—	4	8	no	—
282	D₄×C₆₇	—	4	16	no	—
283	D₄×C₆₇	—	4	8	no	—
284	D₄×C₆₇	—	4	4	no	—
285	D₄×C₆₇	—	4	16	no	—
286	D₄×C₆₇	—	4	8	no	—
287	D₄×C₆₇	—	8	8	no	—
288	C₂×C₄×C₆₇	—	2	8	no	—
289	C₂×C₄×C₆₇	—	2	4	no	—
290	C₂×C₄×C₆₇	—	2	1	no	—
291	C₂×C₄×C₆₇	—	2	2	no	—
292	C₂×C₄×C₆₇	—	2	2	no	—
293	C₂×C₄×C₆₇	—	2	1	no	—
294	C₂×C₄×C₆₇	—	2	1	no	—
295	C₂×C₄×C₆₇	—	2	1	no	—
296	C₂×C₄×C₆₇	—	2	4	no	—
297	C₂×C₄×C₆₇	—	2	2	no	—
298	C₂×C₄×C₆₇	—	2	2	no	—
299	C₂×C₄×C₆₇	—	2	4	no	—
300	C₂×C₄×C₆₇	—	2	4	no	—
301	C₂×C₄×C₆₇	—	2	4	no	—
302	C₂×C₄×C₆₇	—	2	4	no	—
303	C₂×C₄×C₆₇	—	2	4	no	—
304	C₂×C₄×C₆₇	—	2	4	no	—
305	C₂×C₄×C₆₇	—	2	2	no	—
306	C₂×C₄×C₆₇	—	2	2	no	—
307	C₂×C₄×C₆₇	—	2	4	no	—
308	C₂×C₄×C₆₇	—	2	4	no	—
309	C₂×C₄×C₆₇	—	4	8	no	—
310	C₂×C₄×C₆₇	—	4	8	no	—
311	C₂×C₄×C₆₇	—	4	16	no	—
312	C₂×C₄×C₆₇	—	4	8	no	—
313	C₂×C₄×C₆₇	—	8	8	no	—
314	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
315	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
316	C₂×C₄×C₆₇	C₂²×D₄	1	8	yes	—
317	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
318	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
319	C₂²×C₆₇	—	2	4	no	—
320	C₂²×C₆₇	—	2	2	no	—
321	C₂²×C₆₇	—	2	4	no	—
322	C₂²×C₆₇	—	2	2	no	—
323	C₂²×C₆₇	—	2	8	no	—
324	C₂²×C₆₇	—	2	8	no	—
325	C₂²×C₆₇	—	2	8	no	—
326	C₂²×C₆₇	—	2	4	no	—
327	C₂²×C₆₇	—	2	8	no	—
328	C₂²×C₆₇	—	4	2	no	—
329	C₂²×C₆₇	—	4	4	no	—
330	C₂²×C₆₇	—	4	4	no	—
331	C₂²×C₆₇	—	4	4	no	—
332	C₂²×C₆₇	—	4	4	no	—
333	C₂²×C₆₇	—	4	4	no	—
334	C₂²×C₆₇	—	4	2	no	—
335	C₂²×C₆₇	—	4	2	no	—
336	C₂²×C₆₇	—	4	4	no	—
337	C₂²×C₆₇	—	4	2	no	—
338	C₂²×C₆₇	—	4	4	no	—
339	C₂²×C₆₇	—	4	2	no	—
340	C₂²×C₆₇	—	8	16	no	—
341	C₂²×C₆₇	—	8	16	no	—
342	C₂²×C₆₇	D₄²	1	4	yes	—
343	C₂²×C₆₇	C₂³×D₄	1	2	yes	—
344	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
345	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
346	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
347	C₂²×C₆₇	#585	1	2	yes	—
348	C₄×C₆₇	—	2	8	no	—
349	C₄×C₆₇	—	2	2	no	—
350	C₄×C₆₇	—	2	2	no	—
351	C₄×C₆₇	—	2	4	no	—
352	C₄×C₆₇	—	2	4	no	—
353	C₄×C₆₇	—	4	2	no	—
354	C₄×C₆₇	—	4	2	no	—
355	C₄×C₆₇	—	4	4	no	—
356	C₄×C₆₇	—	4	4	no	—
357	#59814	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
358	C₂×C₆₇	—	2	4	no	—
359	C₂×C₆₇	—	4	8	no	—
360	C₂×C₆₇	—	4	4	no	—
361	C₂×C₆₇	—	8	2	no	—
362	C₂×C₆₇	C₂×D₄²	1	1	yes	characteristic
363	C₂×C₆₇	D₄×#41	1	2	yes	—
364	C₂×C₆₇	#3490	1	1	yes	characteristic
365	C₂×C₆₇	#3496	1	2	yes	—
366	C₂×C₆₇	#3545	1	1	yes	characteristic
367	C₂×#546	C₂×C₆₇	1	4	yes	complemented
368	#2683	C₂×C₆₇	1	1	yes	characteristic, complemented
369	#2682	C₂×C₆₇	1	2	yes	complemented
370	#2679	C₂×C₆₇	1	1	yes	characteristic, complemented
371	#2555	C₂×C₆₇	1	2	yes	complemented
372	#2534	C₂×C₆₇	1	4	yes	complemented
373	#2461	C₂×C₆₇	1	4	yes	complemented
374	#2424	C₂×C₆₇	1	4	yes	complemented
375	#2406	C₂×C₆₇	1	2	yes	complemented
376	#2403	C₂×C₆₇	1	2	yes	complemented
377	#2358	C₂×C₆₇	1	2	yes	complemented
378	C₄×#121	C₂×C₆₇	1	2	yes	complemented
379	C₂×#390	C₂×C₆₇	1	1	yes	characteristic, complemented
380	C₆₇	#59814	1	1	yes	characteristic, direct product factor, Sylow
381	C₂²×#41	C₂²×C₆₇	1	2	yes	—
382	C₂³×D₄	C₂²×C₆₇	1	1	yes	characteristic
383	C₂³×D₄	C₂²×C₆₇	1	2	yes	complemented
384	#546	—	2	32	no	—
385	C₂×#124	C₂²×C₆₇	1	4	yes	complemented
386	C₂×#123	C₂²×C₆₇	1	4	yes	complemented
387	C₂×#123	C₂²×C₆₇	1	4	yes	complemented
388	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	4	yes	complemented
389	C₂×#121	C₂²×C₆₇	1	2	yes	—
390	C₂×#121	C₂²×C₆₇	1	4	yes	complemented
391	C₂×#121	C₂²×C₆₇	1	4	yes	complemented
392	C₂×#120	C₂²×C₆₇	1	2	yes	—
393	C₂×#120	C₂²×C₆₇	1	4	yes	—
394	C₂×#120	C₂²×C₆₇	1	4	yes	complemented
395	C₂×#120	C₂²×C₆₇	1	2	yes	complemented
396	C₂×C₄×D₄	C₂²×C₆₇	1	4	yes	complemented
397	C₂×C₄×D₄	C₂²×C₆₇	1	4	yes	complemented
398	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
399	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
400	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	4	yes	complemented
401	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	4	yes	complemented
402	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic, complemented
403	#396	C₂²×C₆₇	1	4	yes	complemented
404	#396	C₂²×C₆₇	1	4	yes	complemented
405	#395	C₂²×C₆₇	1	2	yes	complemented
406	#395	C₂²×C₆₇	1	2	yes	complemented
407	#394	C₂²×C₆₇	1	2	yes	complemented
408	#394	C₂²×C₆₇	1	2	yes	complemented
409	#394	C₂²×C₆₇	1	4	yes	complemented
410	#394	C₂²×C₆₇	1	4	yes	complemented
411	#392	C₂²×C₆₇	1	4	yes	—
412	#392	C₂²×C₆₇	1	4	yes	complemented
413	#390	C₂²×C₆₇	1	1	yes	characteristic
414	#390	C₂²×C₆₇	1	1	yes	characteristic
415	#390	C₂²×C₆₇	1	2	yes	complemented
416	#390	C₂²×C₆₇	1	4	yes	complemented
417	#390	C₂²×C₆₇	1	1	yes	characteristic, complemented
418	#390	C₂²×C₆₇	1	1	yes	characteristic, complemented
419	#389	C₂²×C₆₇	1	2	yes	complemented
420	#388	C₂²×C₆₇	1	4	yes	complemented
421	#388	C₂²×C₆₇	1	4	yes	complemented
422	#388	C₂²×C₆₇	1	4	yes	complemented
423	#386	C₂²×C₆₇	1	2	yes	—
424	#386	C₂²×C₆₇	1	4	yes	complemented
425	#386	C₂²×C₆₇	1	4	yes	complemented
426	#386	C₂²×C₆₇	1	2	yes	complemented
427	#386	C₂²×C₆₇	1	4	yes	complemented
428	#385	C₂²×C₆₇	1	4	yes	complemented
429	#385	C₂²×C₆₇	1	4	yes	complemented
430	#381	C₂²×C₆₇	1	2	yes	complemented
431	#380	C₂²×C₆₇	1	2	yes	complemented
432	#379	C₂²×C₆₇	1	2	yes	complemented
433	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	complemented
434	C₄×C₂²⋊C₄	C₂²×C₆₇	1	4	yes	complemented
435	C₂⁵	C₂³×C₆₇	1	2	yes	—
436	C₂⁵	C₂³×C₆₇	1	2	yes	—
437	C₂×#41	—	2	16	no	—
438	C₂×#41	—	4	4	no	—
439	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
440	C₂²×D₄	—	2	16	no	—
441	C₂²×D₄	—	2	4	no	—
442	C₂²×D₄	—	4	2	no	—
443	C₂²×D₄	—	4	2	no	—
444	C₂²×D₄	—	4	4	no	—
445	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
446	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
447	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
448	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
449	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
450	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
451	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
452	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
453	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
454	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
455	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
456	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
457	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
458	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
459	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
460	#124	—	2	16	no	—
461	#123	—	2	16	no	—
462	#123	—	2	16	no	—
463	C₂²⋊Q₈	—	2	16	no	—
464	#121	—	2	16	no	—
465	#121	—	2	16	no	—
466	#121	D₄×C₆₇	1	16	yes	complemented
467	#120	—	2	16	no	—
468	#120	—	2	16	no	—
469	#120	—	2	8	no	—
470	#120	—	4	4	no	—
471	C₄×D₄	—	2	16	no	—
472	C₄×D₄	—	2	16	no	—
473	C₄×D₄	—	4	4	no	—
474	C₂×C₄⋊C₄	—	4	2	no	—
475	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
476	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
477	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
478	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
479	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
480	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
481	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
482	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
483	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
484	C₂×C₂²⋊C₄	—	2	16	no	—
485	C₂×C₂²⋊C₄	—	2	16	no	—
486	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
487	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
488	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
489	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
490	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
491	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
492	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
493	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
494	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
495	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
496	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
497	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
498	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
499	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
500	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
501	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
502	C₂×C₄²	—	4	2	no	—
503	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
504	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
505	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
506	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
507	#95	C₂³×C₆₇	1	4	yes	—
508	#95	C₂³×C₆₇	1	4	yes	—
509	#95	C₂³×C₆₇	1	4	yes	—
510	#95	C₂³×C₆₇	1	4	yes	—
511	#95	C₂³×C₆₇	1	2	yes	—
512	#95	C₂³×C₆₇	1	2	yes	—
513	C₂⁴	—	2	4	no	—
514	C₂⁴	—	2	8	no	—
515	C₂⁴	—	2	8	no	—
516	C₂⁴	—	2	4	no	—
517	C₂⁴	—	2	4	no	—
518	C₂⁴	—	4	2	no	—
519	C₂⁴	—	4	2	no	—
520	C₂⁴	—	4	4	no	—
521	C₂⁴	—	4	4	no	—
522	C₂⁴	—	4	2	no	—
523	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
524	C₂⁴	C₂⁴×C₆₇	1	4	yes	—
525	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
526	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
527	#41	—	4	32	no	—
528	C₂×Q₈	—	2	8	no	—
529	C₂×Q₈	—	4	2	no	—
530	C₂×D₄	—	2	8	no	—
531	C₂×D₄	—	2	8	no	—
532	C₂×D₄	—	2	8	no	—
533	C₂×D₄	—	2	8	no	—
534	C₂×D₄	—	2	8	no	—
535	C₂×D₄	—	2	8	no	—
536	C₂×D₄	—	2	4	no	—
537	C₂×D₄	—	2	8	no	—
538	C₂×D₄	—	2	8	no	—
539	C₂×D₄	—	2	2	no	—
540	C₂×D₄	—	2	4	no	—
541	C₂×D₄	—	4	2	no	—
542	C₂×D₄	—	4	1	no	—
543	C₂×D₄	—	4	1	no	—
544	C₂×D₄	—	4	1	no	—
545	C₂×D₄	—	4	2	no	—
546	C₂×D₄	—	4	1	no	—
547	C₂×D₄	—	4	4	no	—
548	C₂×D₄	—	4	2	no	—
549	C₂×D₄	—	4	2	no	—
550	C₂×D₄	—	4	4	no	—
551	C₂×D₄	—	4	16	no	—
552	C₂×D₄	—	4	4	no	—
553	C₂×D₄	—	4	4	no	—
554	C₂×D₄	—	4	32	no	—
555	C₂×D₄	C₂×D₄×C₆₇	1	16	yes	—
556	C₂×D₄	C₂×D₄×C₆₇	1	8	yes	complemented
557	C₂×D₄	#41×C₆₇	1	4	yes	complemented
558	C₂²×C₄	—	2	2	no	—
559	C₂²×C₄	—	2	2	no	—
560	C₂²×C₄	—	2	2	no	—
561	C₂²×C₄	—	2	8	no	—
562	C₂²×C₄	—	2	8	no	—
563	C₂²×C₄	—	2	4	no	—
564	C₂²×C₄	—	2	8	no	—
565	C₂²×C₄	—	2	8	no	—
566	C₂²×C₄	—	2	8	no	—
567	C₂²×C₄	—	4	2	no	—
568	C₂²×C₄	—	4	2	no	—
569	C₂²×C₄	—	4	4	no	—
570	C₂²×C₄	—	4	2	no	—
571	C₂²×C₄	—	4	4	no	—
572	C₂²×C₄	—	4	4	no	—
573	C₂²×C₄	C₂×D₄×C₆₇	1	8	yes	—
574	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
575	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
576	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
577	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
578	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
579	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
580	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
581	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
582	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
583	C₄⋊C₄	—	2	8	no	—
584	C₄⋊C₄	—	2	8	no	—
585	C₄⋊C₄	—	2	8	no	—
586	C₄⋊C₄	—	4	1	no	—
587	C₄⋊C₄	—	4	2	no	—
588	C₄⋊C₄	—	4	1	no	—
589	C₄⋊C₄	—	4	2	no	—
590	C₄⋊C₄	—	4	2	no	—
591	C₄⋊C₄	C₂×D₄×C₆₇	1	8	yes	complemented
592	C₂²⋊C₄	—	2	8	no	—
593	C₂²⋊C₄	—	2	8	no	—
594	C₂²⋊C₄	—	2	8	no	—
595	C₂²⋊C₄	—	2	4	no	—
596	C₂²⋊C₄	—	2	8	no	—
597	C₂²⋊C₄	—	2	8	no	—
598	C₂²⋊C₄	—	2	8	no	—
599	C₂²⋊C₄	—	2	8	no	—
600	C₂²⋊C₄	—	2	8	no	—
601	C₂²⋊C₄	—	2	8	no	—
602	C₂²⋊C₄	—	2	8	no	—
603	C₂²⋊C₄	—	2	8	no	—
604	C₂²⋊C₄	—	2	8	no	—
605	C₂²⋊C₄	—	4	2	no	—
606	C₂²⋊C₄	—	4	4	no	—
607	C₂²⋊C₄	C₂×D₄×C₆₇	1	16	yes	complemented
608	C₄²	—	2	8	no	—
609	C₄²	—	2	4	no	—
610	C₄²	—	4	1	no	—
611	C₄²	—	4	1	no	—
612	C₂³	—	2	1	no	—
613	C₂³	—	2	1	no	—
614	C₂³	—	2	2	no	—
615	C₂³	—	2	4	no	—
616	C₂³	—	2	4	no	—
617	C₂³	—	2	4	no	—
618	C₂³	—	2	4	no	—
619	C₂³	—	2	2	no	—
620	C₂³	—	2	4	no	—
621	C₂³	—	2	2	no	—
622	C₂³	—	2	4	no	—
623	C₂³	—	2	4	no	—
624	C₂³	—	2	4	no	—
625	C₂³	—	2	4	no	—
626	C₂³	—	2	2	no	—
627	C₂³	—	2	2	no	—
628	C₂³	—	2	2	no	—
629	C₂³	—	2	4	no	—
630	C₂³	—	4	8	no	—
631	C₂³	—	4	8	no	—
632	C₂³	—	4	16	no	—
633	C₂³	—	4	16	no	—
634	C₂³	—	4	8	no	—
635	C₂³	—	8	4	no	—
636	C₂³	—	8	8	no	—
637	C₂³	—	8	4	no	—
638	C₂³	—	8	8	no	—
639	C₂³	—	8	4	no	—
640	C₂³	C₂²×D₄×C₆₇	1	8	yes	—
641	C₂³	C₂²×D₄×C₆₇	1	4	yes	—
642	C₂³	C₂×#41×C₆₇	1	4	yes	—
643	C₂³	H(5,𝔽₂)×C₆₇	1	2	yes	—
644	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
645	Q₈	—	4	8	no	—
646	D₄	—	2	32	no	—
647	D₄	—	4	4	no	—
648	D₄	—	4	8	no	—
649	D₄	—	4	16	no	—
650	D₄	—	4	8	no	—
651	D₄	—	4	4	no	—
652	D₄	—	4	8	no	—
653	D₄	—	4	16	no	—
654	D₄	—	8	8	no	—
655	C₂×C₄	—	2	8	no	—
656	C₂×C₄	—	2	4	no	—
657	C₂×C₄	—	2	1	no	—
658	C₂×C₄	—	2	2	no	—
659	C₂×C₄	—	2	2	no	—
660	C₂×C₄	—	2	1	no	—
661	C₂×C₄	—	2	1	no	—
662	C₂×C₄	—	2	1	no	—
663	C₂×C₄	—	2	4	no	—
664	C₂×C₄	—	2	2	no	—
665	C₂×C₄	—	2	2	no	—
666	C₂×C₄	—	2	4	no	—
667	C₂×C₄	—	2	4	no	—
668	C₂×C₄	—	2	4	no	—
669	C₂×C₄	—	2	4	no	—
670	C₂×C₄	—	2	4	no	—
671	C₂×C₄	—	2	4	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	2	4	no	—
675	C₂×C₄	—	2	4	no	—
676	C₂×C₄	—	4	8	no	—
677	C₂×C₄	—	4	8	no	—
678	C₂×C₄	—	4	16	no	—
679	C₂×C₄	—	4	8	no	—
680	C₂×C₄	—	8	8	no	—
681	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
682	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
683	C₂×C₄	C₂²×D₄×C₆₇	1	8	yes	—
684	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
685	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
686	C₂²	—	2	2	no	—
687	C₂²	—	2	4	no	—
688	C₂²	—	2	2	no	—
689	C₂²	—	2	4	no	—
690	C₂²	—	2	8	no	—
691	C₂²	—	2	8	no	—
692	C₂²	—	2	8	no	—
693	C₂²	—	2	4	no	—
694	C₂²	—	2	8	no	—
695	C₂²	—	4	2	no	—
696	C₂²	—	4	4	no	—
697	C₂²	—	4	2	no	—
698	C₂²	—	4	4	no	—
699	C₂²	—	4	4	no	—
700	C₂²	—	4	4	no	—
701	C₂²	—	4	4	no	—
702	C₂²	—	4	2	no	—
703	C₂²	—	4	2	no	—
704	C₂²	—	4	4	no	—
705	C₂²	—	4	2	no	—
706	C₂²	—	4	4	no	—
707	C₂²	—	8	16	no	—
708	C₂²	—	8	16	no	—
709	C₂²	D₄²×C₆₇	1	4	yes	—
710	C₂²	C₂³×D₄×C₆₇	1	2	yes	—
711	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
712	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
713	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
714	C₂²	#585×C₆₇	1	2	yes	—
715	C₄	—	2	8	no	—
716	C₄	—	2	2	no	—
717	C₄	—	2	2	no	—
718	C₄	—	2	4	no	—
719	C₄	—	2	4	no	—
720	C₄	—	4	2	no	—
721	C₄	—	4	2	no	—
722	C₄	—	4	4	no	—
723	C₄	—	4	4	no	—
724	C₂	—	2	4	no	—
725	C₂	—	4	4	no	—
726	C₂	—	4	8	no	—
727	C₂	—	8	2	no	—
728	C₂	C₂×D₄²×C₆₇	1	1	yes	characteristic
729	C₂	D₄×#41×C₆₇	1	2	yes	—
730	C₂	C₆₇×#3490	1	1	yes	characteristic
731	C₂	C₆₇×#3496	1	2	yes	—
732	C₂	C₆₇×#3545	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₇
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#546×C₆₇	C₂	semidirect
2. C₆₇×#2683	C₂	semidirect
3. C₆₇×#2682	C₂	semidirect
4. C₆₇×#2679	C₂	semidirect
5. C₆₇×#2555	C₂	semidirect
6. C₆₇×#2534	C₂	semidirect
7. C₆₇×#2461	C₂	semidirect
8. C₆₇×#2424	C₂	semidirect
9. C₆₇×#2406	C₂	semidirect
10. C₆₇×#2403	C₂	semidirect
11. C₆₇×#2358	C₂	semidirect
12. C₄×#121×C₆₇	C₂	semidirect
13. C₂×#390×C₆₇	C₂	semidirect
16. C₂³×D₄×C₆₇	C₂²	semidirect
18. C₂×#124×C₆₇	C₂²	semidirect
19. C₂×#123×C₆₇	C₂²	semidirect
20. C₂×#123×C₆₇	C₂²	semidirect
21. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
23. C₂×#121×C₆₇	C₂²	semidirect
24. C₂×#121×C₆₇	C₂²	semidirect
27. C₂×#120×C₆₇	C₂²	semidirect
28. C₂×#120×C₆₇	C₂²	semidirect
29. C₂×C₄×D₄×C₆₇	C₂²	semidirect
30. C₂×C₄×D₄×C₆₇	C₂²	semidirect
31. C₂×C₄×D₄×C₆₇	C₂²	semidirect
32. C₂²×C₄⋊C₄×C₆₇	C₂²	semidirect
33. C₂²×C₂²⋊C₄×C₆₇	C₂²	semidirect
34. C₂²×C₂²⋊C₄×C₆₇	C₂²	semidirect
35. C₂²×C₄²×C₆₇	C₂²	semidirect
36. #396×C₆₇	C₂²	semidirect
37. #396×C₆₇	C₂²	semidirect
38. #395×C₆₇	C₂²	semidirect
39. #395×C₆₇	C₂²	semidirect
40. #394×C₆₇	C₂²	semidirect
41. #394×C₆₇	C₂²	semidirect
42. #394×C₆₇	C₂²	semidirect
43. #394×C₆₇	C₂²	semidirect
45. #392×C₆₇	C₂²	semidirect
48. #390×C₆₇	C₂²	semidirect
49. #390×C₆₇	C₂²	semidirect
50. #390×C₆₇	C₂²	semidirect
51. #390×C₆₇	C₂²	semidirect
52. #389×C₆₇	C₂²	semidirect
53. #388×C₆₇	C₂²	semidirect
54. #388×C₆₇	C₂²	semidirect
55. #388×C₆₇	C₂²	semidirect
57. #386×C₆₇	C₂²	semidirect
58. #386×C₆₇	C₂²	semidirect
59. #386×C₆₇	C₂²	semidirect
60. #386×C₆₇	C₂²	semidirect
61. #385×C₆₇	C₂²	semidirect
62. #385×C₆₇	C₂²	semidirect
63. #381×C₆₇	C₂²	semidirect
64. #380×C₆₇	C₂²	semidirect
65. #379×C₆₇	C₂²	semidirect
66. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
67. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
99. #121×C₆₇	D₄	semidirect
189. C₂×D₄×C₆₇	C₂×D₄	semidirect
190. C₂×D₄×C₆₇	#41	semidirect
224. C₄⋊C₄×C₆₇	C₂×D₄	semidirect
240. C₂²⋊C₄×C₆₇	C₂×D₄	semidirect
357. #59814	C₆₇	direct (N × H)
367. C₂×#546	C₂×C₆₇	semidirect
368. #2683	C₂×C₆₇	semidirect
369. #2682	C₂×C₆₇	semidirect
370. #2679	C₂×C₆₇	semidirect
371. #2555	C₂×C₆₇	semidirect
372. #2534	C₂×C₆₇	semidirect
373. #2461	C₂×C₆₇	semidirect
374. #2424	C₂×C₆₇	semidirect
375. #2406	C₂×C₆₇	semidirect
376. #2403	C₂×C₆₇	semidirect
377. #2358	C₂×C₆₇	semidirect
378. C₄×#121	C₂×C₆₇	semidirect
379. C₂×#390	C₂×C₆₇	semidirect
380. C₆₇	#59814	direct (N × H)
383. C₂³×D₄	C₂²×C₆₇	semidirect
385. C₂×#124	C₂²×C₆₇	semidirect
386. C₂×#123	C₂²×C₆₇	semidirect
387. C₂×#123	C₂²×C₆₇	semidirect
388. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
390. C₂×#121	C₂²×C₆₇	semidirect
391. C₂×#121	C₂²×C₆₇	semidirect
394. C₂×#120	C₂²×C₆₇	semidirect
395. C₂×#120	C₂²×C₆₇	semidirect
396. C₂×C₄×D₄	C₂²×C₆₇	semidirect
397. C₂×C₄×D₄	C₂²×C₆₇	semidirect
398. C₂×C₄×D₄	C₂²×C₆₇	semidirect
399. C₂²×C₄⋊C₄	C₂²×C₆₇	semidirect
400. C₂²×C₂²⋊C₄	C₂²×C₆₇	semidirect
401. C₂²×C₂²⋊C₄	C₂²×C₆₇	semidirect
402. C₂²×C₄²	C₂²×C₆₇	semidirect
403. #396	C₂²×C₆₇	semidirect
404. #396	C₂²×C₆₇	semidirect
405. #395	C₂²×C₆₇	semidirect
406. #395	C₂²×C₆₇	semidirect
407. #394	C₂²×C₆₇	semidirect
408. #394	C₂²×C₆₇	semidirect
409. #394	C₂²×C₆₇	semidirect
410. #394	C₂²×C₆₇	semidirect
412. #392	C₂²×C₆₇	semidirect
415. #390	C₂²×C₆₇	semidirect
416. #390	C₂²×C₆₇	semidirect
417. #390	C₂²×C₆₇	semidirect
418. #390	C₂²×C₆₇	semidirect
419. #389	C₂²×C₆₇	semidirect
420. #388	C₂²×C₆₇	semidirect
421. #388	C₂²×C₆₇	semidirect
422. #388	C₂²×C₆₇	semidirect
424. #386	C₂²×C₆₇	semidirect
425. #386	C₂²×C₆₇	semidirect
426. #386	C₂²×C₆₇	semidirect
427. #386	C₂²×C₆₇	semidirect
428. #385	C₂²×C₆₇	semidirect
429. #385	C₂²×C₆₇	semidirect
430. #381	C₂²×C₆₇	semidirect
431. #380	C₂²×C₆₇	semidirect
432. #379	C₂²×C₆₇	semidirect
433. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
434. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
466. #121	D₄×C₆₇	semidirect
556. C₂×D₄	C₂×D₄×C₆₇	semidirect
557. C₂×D₄	#41×C₆₇	semidirect
591. C₄⋊C₄	C₂×D₄×C₆₇	semidirect
607. C₂²⋊C₄	C₂×D₄×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#546×C₆₇	2
C₆₇×#2683	2
C₆₇×#2682	2
C₆₇×#2679	2
C₆₇×#2555	2
C₆₇×#2534	2
C₆₇×#2461	2
C₆₇×#2424	2
C₆₇×#2406	2
C₆₇×#2403	2
C₆₇×#2358	2
C₄×#121×C₆₇	2
C₂×#390×C₆₇	2
#59814	67

Subgroups — C67×#59814 #30739065

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#59814 #30739065