Subgroups — C₂×C₆₇×#2529 #30714047

Order 17152.

2074 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#2529	C₂	1	16	yes	maximal, direct product factor
2	C₂×#400×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#398×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#397×C₆₇	C₂	1	1	yes	maximal, characteristic
5	C₂×#396×C₆₇	C₂	1	1	yes	maximal, characteristic
6	C₂×#389×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#388×C₆₇	C₂	1	1	yes	maximal, characteristic
8	C₂×#388×C₆₇	C₂	1	1	yes	maximal, characteristic
9	C₂×#388×C₆₇	C₂	1	1	yes	maximal, characteristic
10	C₂×#388×C₆₇	C₂	1	1	yes	maximal, characteristic
11	C₂×#388×C₆₇	C₂	1	1	yes	maximal, characteristic
12	C₂×#387×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#387×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#382×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₄×C₄⋊C₄×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#376×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
18	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
19	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
20	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
21	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
22	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
23	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
24	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
25	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
26	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
27	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
28	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
29	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
30	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
31	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
32	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
33	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
34	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
35	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
36	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
37	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
38	#400×C₆₇	C₂²	1	8	yes	complemented
39	#398×C₆₇	C₂²	1	8	yes	complemented
40	#397×C₆₇	C₂²	1	8	yes	—
41	#396×C₆₇	C₂²	1	8	yes	—
42	#389×C₆₇	C₂²	1	8	yes	complemented
43	#388×C₆₇	C₂²	1	8	yes	—
44	#388×C₆₇	C₂²	1	8	yes	—
45	#388×C₆₇	C₂²	1	8	yes	—
46	#388×C₆₇	C₂²	1	8	yes	—
47	#388×C₆₇	C₂²	1	8	yes	—
48	#387×C₆₇	C₂²	1	8	yes	complemented
49	#387×C₆₇	C₂²	1	8	yes	complemented
50	#382×C₆₇	C₂²	1	8	yes	complemented
51	C₄×C₄⋊C₄×C₆₇	C₂²	1	8	yes	complemented
52	#376×C₆₇	C₂²	1	8	yes	complemented
53	C₂×#95×C₆₇	C₂²	1	1	yes	characteristic
54	C₂×#95×C₆₇	C₂²	1	1	yes	characteristic
55	C₂×#95×C₆₇	C₂²	1	1	yes	characteristic
56	C₂×#95×C₆₇	C₂²	1	1	yes	characteristic
57	C₂×#95×C₆₇	C₂²	1	1	yes	characteristic
58	C₂×#95×C₆₇	C₂²	1	1	yes	characteristic
59	C₂×#95×C₆₇	C₂²	1	1	yes	characteristic
60	C₂×#95×C₆₇	C₂²	1	1	yes	characteristic
61	C₂×#95×C₆₇	C₂²	1	1	yes	characteristic
62	C₂×#95×C₆₇	C₂²	1	1	yes	characteristic
63	C₂×#95×C₆₇	C₂²	1	1	yes	characteristic
64	C₂×#95×C₆₇	C₂²	1	1	yes	characteristic
65	C₂×#95×C₆₇	C₂²	1	1	yes	characteristic
66	C₂×#95×C₆₇	C₂²	1	1	yes	characteristic
67	C₂⁵×C₆₇	C₂³	1	1	yes	characteristic
68	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
69	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
70	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
71	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
72	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
73	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
75	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
76	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
77	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
78	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
79	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
80	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
81	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
82	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
83	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
84	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
85	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
86	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
87	C₂×C₄⋊C₄×C₆₇	—	4	2	no	—
88	C₂×C₄⋊C₄×C₆₇	—	4	2	no	—
89	C₂×C₄⋊C₄×C₆₇	—	4	2	no	—
90	C₂×C₄⋊C₄×C₆₇	—	4	2	no	—
91	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
92	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
93	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
94	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
95	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
96	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
97	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
98	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
99	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
100	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
101	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
102	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
103	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
104	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
105	C₂×C₂²⋊C₄×C₆₇	—	4	2	no	—
106	C₂×C₂²⋊C₄×C₆₇	—	4	2	no	—
107	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
108	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
109	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
110	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
111	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
112	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
113	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
114	C₂×C₄²×C₆₇	—	2	4	no	—
115	C₂×C₄²×C₆₇	—	2	4	no	—
116	C₂×C₄²×C₆₇	—	2	4	no	—
117	C₂×C₄²×C₆₇	—	2	4	no	—
118	C₂×C₄²×C₆₇	—	2	4	no	—
119	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
120	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
121	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
122	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
123	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
124	#95×C₆₇	C₂³	1	4	yes	—
125	#95×C₆₇	C₂³	1	4	yes	—
126	#95×C₆₇	C₂³	1	4	yes	—
127	#95×C₆₇	C₂³	1	4	yes	—
128	#95×C₆₇	C₂³	1	4	yes	—
129	#95×C₆₇	C₂³	1	4	yes	—
130	#95×C₆₇	C₂³	1	4	yes	—
131	#95×C₆₇	C₂³	1	4	yes	—
132	#95×C₆₇	C₂³	1	4	yes	—
133	#95×C₆₇	C₂³	1	4	yes	—
134	#95×C₆₇	C₂³	1	4	yes	—
135	#95×C₆₇	C₂³	1	4	yes	—
136	#95×C₆₇	C₂³	1	4	yes	—
137	#95×C₆₇	C₂³	1	4	yes	—
138	C₂⁴×C₆₇	—	2	2	no	—
139	C₂⁴×C₆₇	—	2	2	no	—
140	C₂⁴×C₆₇	—	2	2	no	—
141	C₂⁴×C₆₇	—	2	2	no	—
142	C₂⁴×C₆₇	—	2	2	no	—
143	C₂⁴×C₆₇	—	2	2	no	—
144	C₂⁴×C₆₇	—	2	2	no	—
145	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
146	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
147	C₂²×C₄×C₆₇	—	2	2	no	—
148	C₂²×C₄×C₆₇	—	2	2	no	—
149	C₂²×C₄×C₆₇	—	2	2	no	—
150	C₂²×C₄×C₆₇	—	2	2	no	—
151	C₂²×C₄×C₆₇	—	2	2	no	—
152	C₂²×C₄×C₆₇	—	2	2	no	—
153	C₂²×C₄×C₆₇	—	2	2	no	—
154	C₂²×C₄×C₆₇	—	2	2	no	—
155	C₂²×C₄×C₆₇	—	2	2	no	—
156	C₂²×C₄×C₆₇	—	2	2	no	—
157	C₂²×C₄×C₆₇	—	2	2	no	—
158	C₂²×C₄×C₆₇	—	2	2	no	—
159	C₂²×C₄×C₆₇	—	2	2	no	—
160	C₂²×C₄×C₆₇	—	2	2	no	—
161	C₂²×C₄×C₆₇	—	2	2	no	—
162	C₂²×C₄×C₆₇	—	2	2	no	—
163	C₂²×C₄×C₆₇	—	2	2	no	—
164	C₂²×C₄×C₆₇	—	2	2	no	—
165	C₂²×C₄×C₆₇	—	2	2	no	—
166	C₂²×C₄×C₆₇	—	2	2	no	—
167	C₂²×C₄×C₆₇	—	2	2	no	—
168	C₂²×C₄×C₆₇	—	2	2	no	—
169	C₂²×C₄×C₆₇	—	2	2	no	—
170	C₂²×C₄×C₆₇	—	2	2	no	—
171	C₂²×C₄×C₆₇	—	2	2	no	—
172	C₂²×C₄×C₆₇	—	2	2	no	—
173	C₂²×C₄×C₆₇	—	2	2	no	—
174	C₂²×C₄×C₆₇	—	2	2	no	—
175	C₂²×C₄×C₆₇	—	2	2	no	—
176	C₂²×C₄×C₆₇	—	2	2	no	—
177	C₂²×C₄×C₆₇	—	2	2	no	—
178	C₂²×C₄×C₆₇	—	2	2	no	—
179	C₂²×C₄×C₆₇	—	2	2	no	—
180	C₂²×C₄×C₆₇	—	2	2	no	—
181	C₂²×C₄×C₆₇	—	2	2	no	—
182	C₂²×C₄×C₆₇	—	2	2	no	—
183	C₂²×C₄×C₆₇	—	2	2	no	—
184	C₂²×C₄×C₆₇	#41	1	4	yes	—
185	C₂²×C₄×C₆₇	#41	1	4	yes	—
186	C₂²×C₄×C₆₇	#41	1	4	yes	—
187	C₂²×C₄×C₆₇	#41	1	4	yes	—
188	C₂²×C₄×C₆₇	#41	1	4	yes	—
189	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
190	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
191	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
192	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
193	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
194	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
195	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
196	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
197	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
198	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
199	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
200	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
201	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
202	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
203	C₄⋊C₄×C₆₇	—	2	8	no	—
204	C₄⋊C₄×C₆₇	—	2	8	no	—
205	C₄⋊C₄×C₆₇	—	2	8	no	—
206	C₄⋊C₄×C₆₇	—	2	8	no	—
207	C₄⋊C₄×C₆₇	—	2	8	no	—
208	C₄⋊C₄×C₆₇	—	4	4	no	—
209	C₄⋊C₄×C₆₇	—	4	4	no	—
210	C₄⋊C₄×C₆₇	—	4	4	no	—
211	C₄⋊C₄×C₆₇	—	4	4	no	—
212	C₂²⋊C₄×C₆₇	—	2	8	no	—
213	C₂²⋊C₄×C₆₇	—	2	8	no	—
214	C₂²⋊C₄×C₆₇	—	2	8	no	—
215	C₂²⋊C₄×C₆₇	—	2	8	no	—
216	C₂²⋊C₄×C₆₇	—	2	8	no	—
217	C₂²⋊C₄×C₆₇	—	4	4	no	—
218	C₂²⋊C₄×C₆₇	—	4	4	no	—
219	C₄²×C₆₇	—	2	8	no	—
220	C₄²×C₆₇	—	2	8	no	—
221	C₄²×C₆₇	—	2	8	no	—
222	C₄²×C₆₇	—	2	8	no	—
223	C₄²×C₆₇	—	2	8	no	—
224	C₂³×C₆₇	—	2	2	no	—
225	C₂³×C₆₇	—	2	2	no	—
226	C₂³×C₆₇	—	2	2	no	—
227	C₂³×C₆₇	—	2	2	no	—
228	C₂³×C₆₇	—	2	2	no	—
229	C₂³×C₆₇	—	2	2	no	—
230	C₂³×C₆₇	—	2	2	no	—
231	C₂³×C₆₇	—	4	4	no	—
232	C₂³×C₆₇	—	4	4	no	—
233	C₂³×C₆₇	—	4	4	no	—
234	C₂³×C₆₇	—	4	4	no	—
235	C₂³×C₆₇	—	4	4	no	—
236	C₂³×C₆₇	—	4	4	no	—
237	C₂³×C₆₇	—	4	4	no	—
238	C₂³×C₆₇	C₂×#41	1	2	yes	—
239	C₂³×C₆₇	C₂×#41	1	2	yes	—
240	C₂³×C₆₇	C₂×#41	1	2	yes	—
241	C₂³×C₆₇	C₂×#41	1	2	yes	—
242	C₂³×C₆₇	C₂×#41	1	2	yes	—
243	C₂³×C₆₇	H(5,𝔽₂)	1	2	yes	—
244	C₂³×C₆₇	2₋¹⁺⁴	1	2	yes	—
245	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
246	C₂×C₄×C₆₇	—	2	8	no	—
247	C₂×C₄×C₆₇	—	2	8	no	—
248	C₂×C₄×C₆₇	—	2	8	no	—
249	C₂×C₄×C₆₇	—	2	8	no	—
250	C₂×C₄×C₆₇	—	2	8	no	—
251	C₂×C₄×C₆₇	—	2	2	no	—
252	C₂×C₄×C₆₇	—	2	2	no	—
253	C₂×C₄×C₆₇	—	2	2	no	—
254	C₂×C₄×C₆₇	—	2	2	no	—
255	C₂×C₄×C₆₇	—	2	2	no	—
256	C₂×C₄×C₆₇	—	2	2	no	—
257	C₂×C₄×C₆₇	—	2	2	no	—
258	C₂×C₄×C₆₇	—	2	2	no	—
259	C₂×C₄×C₆₇	—	2	2	no	—
260	C₂×C₄×C₆₇	—	2	2	no	—
261	C₂×C₄×C₆₇	—	2	2	no	—
262	C₂×C₄×C₆₇	—	2	2	no	—
263	C₂×C₄×C₆₇	—	2	2	no	—
264	C₂×C₄×C₆₇	—	2	2	no	—
265	C₂×C₄×C₆₇	—	2	2	no	—
266	C₂×C₄×C₆₇	—	2	2	no	—
267	C₂×C₄×C₆₇	—	2	2	no	—
268	C₂×C₄×C₆₇	—	2	2	no	—
269	C₂×C₄×C₆₇	—	2	2	no	—
270	C₂×C₄×C₆₇	—	2	2	no	—
271	C₂×C₄×C₆₇	—	2	2	no	—
272	C₂×C₄×C₆₇	—	2	2	no	—
273	C₂×C₄×C₆₇	—	2	2	no	—
274	C₂×C₄×C₆₇	—	2	2	no	—
275	C₂×C₄×C₆₇	—	2	2	no	—
276	C₂×C₄×C₆₇	—	2	2	no	—
277	C₂×C₄×C₆₇	—	2	2	no	—
278	C₂×C₄×C₆₇	—	2	2	no	—
279	C₂×C₄×C₆₇	—	2	2	no	—
280	C₂×C₄×C₆₇	—	2	2	no	—
281	C₂×C₄×C₆₇	—	2	2	no	—
282	C₂×C₄×C₆₇	—	2	2	no	—
283	C₂×C₄×C₆₇	—	2	2	no	—
284	C₂×C₄×C₆₇	—	2	2	no	—
285	C₂×C₄×C₆₇	—	2	2	no	—
286	C₂×C₄×C₆₇	—	2	2	no	—
287	C₂×C₄×C₆₇	—	2	2	no	—
288	C₂×C₄×C₆₇	—	4	4	no	—
289	C₂×C₄×C₆₇	—	4	4	no	—
290	C₂×C₄×C₆₇	—	4	4	no	—
291	C₂×C₄×C₆₇	—	4	4	no	—
292	C₂×C₄×C₆₇	—	4	4	no	—
293	C₂×C₄×C₆₇	—	4	4	no	—
294	C₂×C₄×C₆₇	—	4	4	no	—
295	C₂×C₄×C₆₇	—	4	4	no	—
296	C₂×C₄×C₆₇	—	4	4	no	—
297	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
298	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
299	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
300	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
301	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
302	C₂²×C₆₇	—	4	2	no	—
303	C₂²×C₆₇	—	4	2	no	—
304	C₂²×C₆₇	—	4	2	no	—
305	C₂²×C₆₇	—	4	2	no	—
306	C₂²×C₆₇	—	4	2	no	—
307	C₂²×C₆₇	—	4	2	no	—
308	C₂²×C₆₇	—	4	2	no	—
309	C₂²×C₆₇	—	8	8	no	—
310	C₂²×C₆₇	#529	1	4	yes	—
311	C₂²×C₆₇	#529	1	4	yes	—
312	C₂²×C₆₇	#542	1	4	yes	—
313	C₂²×C₆₇	#552	1	4	yes	—
314	C₂²×C₆₇	#552	1	4	yes	—
315	C₂²×C₆₇	#553	1	4	yes	—
316	C₂²×C₆₇	#555	1	4	yes	—
317	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
318	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
319	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
320	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
321	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
322	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
323	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
324	C₄×C₆₇	—	2	4	no	—
325	C₄×C₆₇	—	2	4	no	—
326	C₄×C₆₇	—	2	4	no	—
327	C₄×C₆₇	—	2	4	no	—
328	C₄×C₆₇	—	2	4	no	—
329	C₄×C₆₇	—	4	2	no	—
330	C₄×C₆₇	—	4	2	no	—
331	C₄×C₆₇	—	4	2	no	—
332	C₄×C₆₇	—	4	2	no	—
333	C₄×C₆₇	—	4	2	no	—
334	C₄×C₆₇	—	4	2	no	—
335	C₄×C₆₇	—	4	2	no	—
336	C₄×C₆₇	—	4	2	no	—
337	C₄×C₆₇	—	4	2	no	—
338	C₂×#2529	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
339	C₂×C₆₇	—	8	2	no	—
340	C₂×C₆₇	#2529	1	8	yes	direct product factor
341	C₂×C₆₇	C₂×#529	1	1	yes	characteristic
342	C₂×C₆₇	C₂×#529	1	1	yes	characteristic
343	C₂×C₆₇	C₂×#542	1	1	yes	characteristic
344	C₂×C₆₇	C₂×#552	1	1	yes	characteristic
345	C₂×C₆₇	C₂×#552	1	1	yes	characteristic
346	C₂×C₆₇	C₂×#553	1	1	yes	characteristic
347	C₂×C₆₇	C₂×#555	1	1	yes	characteristic
348	#2529	C₂×C₆₇	1	16	yes	direct product factor
349	C₂×#400	C₂×C₆₇	1	1	yes	characteristic, complemented
350	C₂×#398	C₂×C₆₇	1	1	yes	characteristic, complemented
351	C₂×#397	C₂×C₆₇	1	1	yes	characteristic
352	C₂×#396	C₂×C₆₇	1	1	yes	characteristic
353	C₂×#389	C₂×C₆₇	1	1	yes	characteristic, complemented
354	C₂×#388	C₂×C₆₇	1	1	yes	characteristic
355	C₂×#388	C₂×C₆₇	1	1	yes	characteristic
356	C₂×#388	C₂×C₆₇	1	1	yes	characteristic
357	C₂×#388	C₂×C₆₇	1	1	yes	characteristic
358	C₂×#388	C₂×C₆₇	1	1	yes	characteristic
359	C₂×#387	C₂×C₆₇	1	1	yes	characteristic, complemented
360	C₂×#387	C₂×C₆₇	1	1	yes	characteristic, complemented
361	C₂×#382	C₂×C₆₇	1	1	yes	characteristic, complemented
362	C₂×C₄×C₄⋊C₄	C₂×C₆₇	1	1	yes	characteristic, complemented
363	C₂×#376	C₂×C₆₇	1	1	yes	characteristic, complemented
364	C₆₇	C₂×#2529	1	1	yes	characteristic, direct product factor, Sylow
365	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
366	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
367	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
368	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
369	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
370	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
371	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
372	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
373	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
374	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
375	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
376	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
377	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
378	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
379	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
380	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
381	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
382	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
383	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
384	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
385	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
386	#400	C₂²×C₆₇	1	8	yes	complemented
387	#398	C₂²×C₆₇	1	8	yes	complemented
388	#397	C₂²×C₆₇	1	8	yes	—
389	#396	C₂²×C₆₇	1	8	yes	—
390	#389	C₂²×C₆₇	1	8	yes	complemented
391	#388	C₂²×C₆₇	1	8	yes	—
392	#388	C₂²×C₆₇	1	8	yes	—
393	#388	C₂²×C₆₇	1	8	yes	—
394	#388	C₂²×C₆₇	1	8	yes	—
395	#388	C₂²×C₆₇	1	8	yes	—
396	#387	C₂²×C₆₇	1	8	yes	complemented
397	#387	C₂²×C₆₇	1	8	yes	complemented
398	#382	C₂²×C₆₇	1	8	yes	complemented
399	C₄×C₄⋊C₄	C₂²×C₆₇	1	8	yes	complemented
400	#376	C₂²×C₆₇	1	8	yes	complemented
401	C₂×#95	C₂²×C₆₇	1	1	yes	characteristic
402	C₂×#95	C₂²×C₆₇	1	1	yes	characteristic
403	C₂×#95	C₂²×C₆₇	1	1	yes	characteristic
404	C₂×#95	C₂²×C₆₇	1	1	yes	characteristic
405	C₂×#95	C₂²×C₆₇	1	1	yes	characteristic
406	C₂×#95	C₂²×C₆₇	1	1	yes	characteristic
407	C₂×#95	C₂²×C₆₇	1	1	yes	characteristic
408	C₂×#95	C₂²×C₆₇	1	1	yes	characteristic
409	C₂×#95	C₂²×C₆₇	1	1	yes	characteristic
410	C₂×#95	C₂²×C₆₇	1	1	yes	characteristic
411	C₂×#95	C₂²×C₆₇	1	1	yes	characteristic
412	C₂×#95	C₂²×C₆₇	1	1	yes	characteristic
413	C₂×#95	C₂²×C₆₇	1	1	yes	characteristic
414	C₂×#95	C₂²×C₆₇	1	1	yes	characteristic
415	C₂⁵	C₂³×C₆₇	1	1	yes	characteristic
416	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
417	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
418	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
419	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
420	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
421	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
422	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
423	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
424	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
425	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
426	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
427	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
428	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
429	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
430	C₂×C₄⋊C₄	—	2	4	no	—
431	C₂×C₄⋊C₄	—	2	4	no	—
432	C₂×C₄⋊C₄	—	2	4	no	—
433	C₂×C₄⋊C₄	—	2	4	no	—
434	C₂×C₄⋊C₄	—	2	4	no	—
435	C₂×C₄⋊C₄	—	4	2	no	—
436	C₂×C₄⋊C₄	—	4	2	no	—
437	C₂×C₄⋊C₄	—	4	2	no	—
438	C₂×C₄⋊C₄	—	4	2	no	—
439	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
440	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
441	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
442	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
443	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
444	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
445	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
446	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
447	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
448	C₂×C₂²⋊C₄	—	2	4	no	—
449	C₂×C₂²⋊C₄	—	2	4	no	—
450	C₂×C₂²⋊C₄	—	2	4	no	—
451	C₂×C₂²⋊C₄	—	2	4	no	—
452	C₂×C₂²⋊C₄	—	2	4	no	—
453	C₂×C₂²⋊C₄	—	4	2	no	—
454	C₂×C₂²⋊C₄	—	4	2	no	—
455	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
456	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
457	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
458	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
459	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
460	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
461	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
462	C₂×C₄²	—	2	4	no	—
463	C₂×C₄²	—	2	4	no	—
464	C₂×C₄²	—	2	4	no	—
465	C₂×C₄²	—	2	4	no	—
466	C₂×C₄²	—	2	4	no	—
467	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
468	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
469	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
470	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
471	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
472	#95	C₂³×C₆₇	1	4	yes	—
473	#95	C₂³×C₆₇	1	4	yes	—
474	#95	C₂³×C₆₇	1	4	yes	—
475	#95	C₂³×C₆₇	1	4	yes	—
476	#95	C₂³×C₆₇	1	4	yes	—
477	#95	C₂³×C₆₇	1	4	yes	—
478	#95	C₂³×C₆₇	1	4	yes	—
479	#95	C₂³×C₆₇	1	4	yes	—
480	#95	C₂³×C₆₇	1	4	yes	—
481	#95	C₂³×C₆₇	1	4	yes	—
482	#95	C₂³×C₆₇	1	4	yes	—
483	#95	C₂³×C₆₇	1	4	yes	—
484	#95	C₂³×C₆₇	1	4	yes	—
485	#95	C₂³×C₆₇	1	4	yes	—
486	C₂⁴	—	2	2	no	—
487	C₂⁴	—	2	2	no	—
488	C₂⁴	—	2	2	no	—
489	C₂⁴	—	2	2	no	—
490	C₂⁴	—	2	2	no	—
491	C₂⁴	—	2	2	no	—
492	C₂⁴	—	2	2	no	—
493	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
494	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
495	C₂²×C₄	—	2	2	no	—
496	C₂²×C₄	—	2	2	no	—
497	C₂²×C₄	—	2	2	no	—
498	C₂²×C₄	—	2	2	no	—
499	C₂²×C₄	—	2	2	no	—
500	C₂²×C₄	—	2	2	no	—
501	C₂²×C₄	—	2	2	no	—
502	C₂²×C₄	—	2	2	no	—
503	C₂²×C₄	—	2	2	no	—
504	C₂²×C₄	—	2	2	no	—
505	C₂²×C₄	—	2	2	no	—
506	C₂²×C₄	—	2	2	no	—
507	C₂²×C₄	—	2	2	no	—
508	C₂²×C₄	—	2	2	no	—
509	C₂²×C₄	—	2	2	no	—
510	C₂²×C₄	—	2	2	no	—
511	C₂²×C₄	—	2	2	no	—
512	C₂²×C₄	—	2	2	no	—
513	C₂²×C₄	—	2	2	no	—
514	C₂²×C₄	—	2	2	no	—
515	C₂²×C₄	—	2	2	no	—
516	C₂²×C₄	—	2	2	no	—
517	C₂²×C₄	—	2	2	no	—
518	C₂²×C₄	—	2	2	no	—
519	C₂²×C₄	—	2	2	no	—
520	C₂²×C₄	—	2	2	no	—
521	C₂²×C₄	—	2	2	no	—
522	C₂²×C₄	—	2	2	no	—
523	C₂²×C₄	—	2	2	no	—
524	C₂²×C₄	—	2	2	no	—
525	C₂²×C₄	—	2	2	no	—
526	C₂²×C₄	—	2	2	no	—
527	C₂²×C₄	—	2	2	no	—
528	C₂²×C₄	—	2	2	no	—
529	C₂²×C₄	—	2	2	no	—
530	C₂²×C₄	—	2	2	no	—
531	C₂²×C₄	—	2	2	no	—
532	C₂²×C₄	#41×C₆₇	1	4	yes	—
533	C₂²×C₄	#41×C₆₇	1	4	yes	—
534	C₂²×C₄	#41×C₆₇	1	4	yes	—
535	C₂²×C₄	#41×C₆₇	1	4	yes	—
536	C₂²×C₄	#41×C₆₇	1	4	yes	—
537	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
538	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
539	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
540	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
541	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
542	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
543	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
544	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
545	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
546	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
547	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
548	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
549	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
550	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
551	C₄⋊C₄	—	2	8	no	—
552	C₄⋊C₄	—	2	8	no	—
553	C₄⋊C₄	—	2	8	no	—
554	C₄⋊C₄	—	2	8	no	—
555	C₄⋊C₄	—	2	8	no	—
556	C₄⋊C₄	—	4	4	no	—
557	C₄⋊C₄	—	4	4	no	—
558	C₄⋊C₄	—	4	4	no	—
559	C₄⋊C₄	—	4	4	no	—
560	C₂²⋊C₄	—	2	8	no	—
561	C₂²⋊C₄	—	2	8	no	—
562	C₂²⋊C₄	—	2	8	no	—
563	C₂²⋊C₄	—	2	8	no	—
564	C₂²⋊C₄	—	2	8	no	—
565	C₂²⋊C₄	—	4	4	no	—
566	C₂²⋊C₄	—	4	4	no	—
567	C₄²	—	2	8	no	—
568	C₄²	—	2	8	no	—
569	C₄²	—	2	8	no	—
570	C₄²	—	2	8	no	—
571	C₄²	—	2	8	no	—
572	C₂³	—	2	2	no	—
573	C₂³	—	2	2	no	—
574	C₂³	—	2	2	no	—
575	C₂³	—	2	2	no	—
576	C₂³	—	2	2	no	—
577	C₂³	—	2	2	no	—
578	C₂³	—	2	2	no	—
579	C₂³	—	4	4	no	—
580	C₂³	—	4	4	no	—
581	C₂³	—	4	4	no	—
582	C₂³	—	4	4	no	—
583	C₂³	—	4	4	no	—
584	C₂³	—	4	4	no	—
585	C₂³	—	4	4	no	—
586	C₂³	C₂×#41×C₆₇	1	2	yes	—
587	C₂³	C₂×#41×C₆₇	1	2	yes	—
588	C₂³	C₂×#41×C₆₇	1	2	yes	—
589	C₂³	C₂×#41×C₆₇	1	2	yes	—
590	C₂³	C₂×#41×C₆₇	1	2	yes	—
591	C₂³	H(5,𝔽₂)×C₆₇	1	2	yes	—
592	C₂³	2₋¹⁺⁴×C₆₇	1	2	yes	—
593	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
594	C₂×C₄	—	2	8	no	—
595	C₂×C₄	—	2	8	no	—
596	C₂×C₄	—	2	8	no	—
597	C₂×C₄	—	2	8	no	—
598	C₂×C₄	—	2	8	no	—
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	2	2	no	—
601	C₂×C₄	—	2	2	no	—
602	C₂×C₄	—	2	2	no	—
603	C₂×C₄	—	2	2	no	—
604	C₂×C₄	—	2	2	no	—
605	C₂×C₄	—	2	2	no	—
606	C₂×C₄	—	2	2	no	—
607	C₂×C₄	—	2	2	no	—
608	C₂×C₄	—	2	2	no	—
609	C₂×C₄	—	2	2	no	—
610	C₂×C₄	—	2	2	no	—
611	C₂×C₄	—	2	2	no	—
612	C₂×C₄	—	2	2	no	—
613	C₂×C₄	—	2	2	no	—
614	C₂×C₄	—	2	2	no	—
615	C₂×C₄	—	2	2	no	—
616	C₂×C₄	—	2	2	no	—
617	C₂×C₄	—	2	2	no	—
618	C₂×C₄	—	2	2	no	—
619	C₂×C₄	—	2	2	no	—
620	C₂×C₄	—	2	2	no	—
621	C₂×C₄	—	2	2	no	—
622	C₂×C₄	—	2	2	no	—
623	C₂×C₄	—	2	2	no	—
624	C₂×C₄	—	2	2	no	—
625	C₂×C₄	—	2	2	no	—
626	C₂×C₄	—	2	2	no	—
627	C₂×C₄	—	2	2	no	—
628	C₂×C₄	—	2	2	no	—
629	C₂×C₄	—	2	2	no	—
630	C₂×C₄	—	2	2	no	—
631	C₂×C₄	—	2	2	no	—
632	C₂×C₄	—	2	2	no	—
633	C₂×C₄	—	2	2	no	—
634	C₂×C₄	—	2	2	no	—
635	C₂×C₄	—	2	2	no	—
636	C₂×C₄	—	4	4	no	—
637	C₂×C₄	—	4	4	no	—
638	C₂×C₄	—	4	4	no	—
639	C₂×C₄	—	4	4	no	—
640	C₂×C₄	—	4	4	no	—
641	C₂×C₄	—	4	4	no	—
642	C₂×C₄	—	4	4	no	—
643	C₂×C₄	—	4	4	no	—
644	C₂×C₄	—	4	4	no	—
645	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
646	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
647	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
648	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
649	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
650	C₂²	—	4	2	no	—
651	C₂²	—	4	2	no	—
652	C₂²	—	4	2	no	—
653	C₂²	—	4	2	no	—
654	C₂²	—	4	2	no	—
655	C₂²	—	4	2	no	—
656	C₂²	—	4	2	no	—
657	C₂²	—	8	8	no	—
658	C₂²	#529×C₆₇	1	4	yes	—
659	C₂²	#529×C₆₇	1	4	yes	—
660	C₂²	#542×C₆₇	1	4	yes	—
661	C₂²	#552×C₆₇	1	4	yes	—
662	C₂²	#552×C₆₇	1	4	yes	—
663	C₂²	#553×C₆₇	1	4	yes	—
664	C₂²	#555×C₆₇	1	4	yes	—
665	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
666	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
667	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
668	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
669	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
670	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
671	C₂²	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
672	C₄	—	2	4	no	—
673	C₄	—	2	4	no	—
674	C₄	—	2	4	no	—
675	C₄	—	2	4	no	—
676	C₄	—	2	4	no	—
677	C₄	—	4	2	no	—
678	C₄	—	4	2	no	—
679	C₄	—	4	2	no	—
680	C₄	—	4	2	no	—
681	C₄	—	4	2	no	—
682	C₄	—	4	2	no	—
683	C₄	—	4	2	no	—
684	C₄	—	4	2	no	—
685	C₄	—	4	2	no	—
686	C₂	—	8	2	no	—
687	C₂	C₆₇×#2529	1	8	yes	direct product factor
688	C₂	C₂×#529×C₆₇	1	1	yes	characteristic
689	C₂	C₂×#529×C₆₇	1	1	yes	characteristic
690	C₂	C₂×#542×C₆₇	1	1	yes	characteristic
691	C₂	C₂×#552×C₆₇	1	1	yes	characteristic
692	C₂	C₂×#552×C₆₇	1	1	yes	characteristic
693	C₂	C₂×#553×C₆₇	1	1	yes	characteristic
694	C₂	C₂×#555×C₆₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₆₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₇
prime radical	C₂⁵×C₆₇	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#2529	C₂	direct (N × H)
2. C₂×#400×C₆₇	C₂	semidirect
3. C₂×#398×C₆₇	C₂	semidirect
6. C₂×#389×C₆₇	C₂	semidirect
12. C₂×#387×C₆₇	C₂	semidirect
13. C₂×#387×C₆₇	C₂	semidirect
14. C₂×#382×C₆₇	C₂	semidirect
15. C₂×C₄×C₄⋊C₄×C₆₇	C₂	semidirect
16. C₂×#376×C₆₇	C₂	semidirect
38. #400×C₆₇	C₂²	semidirect
39. #398×C₆₇	C₂²	semidirect
42. #389×C₆₇	C₂²	semidirect
48. #387×C₆₇	C₂²	semidirect
49. #387×C₆₇	C₂²	semidirect
50. #382×C₆₇	C₂²	semidirect
51. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
52. #376×C₆₇	C₂²	semidirect
338. C₂×#2529	C₆₇	direct (N × H)
340. C₂×C₆₇	#2529	direct (N × H)
348. #2529	C₂×C₆₇	direct (N × H)
349. C₂×#400	C₂×C₆₇	semidirect
350. C₂×#398	C₂×C₆₇	semidirect
353. C₂×#389	C₂×C₆₇	semidirect
359. C₂×#387	C₂×C₆₇	semidirect
360. C₂×#387	C₂×C₆₇	semidirect
361. C₂×#382	C₂×C₆₇	semidirect
362. C₂×C₄×C₄⋊C₄	C₂×C₆₇	semidirect
363. C₂×#376	C₂×C₆₇	semidirect
364. C₆₇	C₂×#2529	direct (N × H)
386. #400	C₂²×C₆₇	semidirect
387. #398	C₂²×C₆₇	semidirect
390. #389	C₂²×C₆₇	semidirect
396. #387	C₂²×C₆₇	semidirect
397. #387	C₂²×C₆₇	semidirect
398. #382	C₂²×C₆₇	semidirect
399. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
400. #376	C₂²×C₆₇	semidirect
687. C₂	C₆₇×#2529	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×#2529	2
C₂×#400×C₆₇	2
C₂×#398×C₆₇	2
C₂×#397×C₆₇	2
C₂×#396×C₆₇	2
C₂×#389×C₆₇	2
C₂×#388×C₆₇	2
C₂×#387×C₆₇	2
C₂×#382×C₆₇	2
C₂×C₄×C₄⋊C₄×C₆₇	2
C₂×#376×C₆₇	2
C₂×#2529	67

Subgroups — C2×C67×#2529 #30714047

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₇×#2529 #30714047