Subgroups — C₂×C₆₇×#2933 #30739388

Order 17152.

2926 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#131×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×M₁₆×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#525×C₆₇	C₂	1	1	yes	maximal, characteristic
4	C₆₇×#2933	C₂	1	16	yes	maximal, direct product factor
5	C₂×#436×C₆₇	C₂	1	2	yes	maximal, complemented
6	C₂×#435×C₆₇	C₂	1	2	yes	maximal, complemented
7	C₂×#435×C₆₇	C₂	1	2	yes	maximal, complemented
8	C₂×C₈×D₄×C₆₇	C₂	1	2	yes	maximal, complemented
9	C₂×#424×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#408×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×C₂²⋊C₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#405×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
14	C₂⁴×C₄×C₆₇	C₂²	1	1	yes	characteristic
15	C₂×#131×C₆₇	—	2	8	no	—
16	C₂×#131×C₆₇	C₂²	1	8	yes	complemented
17	C₂²×M₁₆×C₆₇	—	2	8	no	—
18	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
19	C₂²×M₁₆×C₆₇	C₂²	1	2	yes	—
20	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
21	C₂²×M₁₆×C₆₇	C₂²	1	8	yes	complemented
22	C₂²×M₁₆×C₆₇	C₂²	1	2	yes	complemented
23	C₂³×C₈×C₆₇	C₂²	1	2	yes	—
24	C₂³×C₈×C₆₇	C₂²	1	1	yes	characteristic
25	C₂³×C₈×C₆₇	C₂²	1	1	yes	characteristic
26	C₂³×C₈×C₆₇	C₂²	1	2	yes	complemented
27	#525×C₆₇	C₄	1	8	yes	—
28	#525×C₆₇	C₂²	1	8	yes	—
29	C₂×#123×C₆₇	C₄	1	2	yes	—
30	C₂×C₂²⋊Q₈×C₆₇	C₄	1	1	yes	characteristic
31	C₂×C₂²⋊Q₈×C₆₇	C₄	1	1	yes	characteristic
32	C₂×#121×C₆₇	C₄	1	1	yes	characteristic
33	C₂×#121×C₆₇	C₄	1	1	yes	characteristic
34	C₂×#120×C₆₇	C₄	1	2	yes	—
35	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
36	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
37	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
38	#436×C₆₇	C₂²	1	16	yes	complemented
39	#435×C₆₇	C₂²	1	16	yes	complemented
40	#435×C₆₇	C₂²	1	16	yes	complemented
41	C₈×D₄×C₆₇	C₂²	1	16	yes	complemented
42	#424×C₆₇	C₂²	1	8	yes	complemented
43	C₂×C₄⋊C₈×C₆₇	C₂²	1	2	yes	complemented
44	C₂×C₄⋊C₈×C₆₇	C₂²	1	2	yes	complemented
45	#408×C₆₇	C₂²	1	8	yes	complemented
46	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
47	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
48	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
49	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
50	C₂×C₂²⋊C₈×C₆₇	C₂²	1	8	yes	complemented
51	C₂×C₂²⋊C₈×C₆₇	C₂²	1	2	yes	complemented
52	C₂×C₂²⋊C₈×C₆₇	C₂²	1	2	yes	complemented
53	#405×C₆₇	C₂²	1	8	yes	complemented
54	C₂×#97×C₆₇	C₂²	1	2	yes	complemented
55	C₂×C₄×C₈×C₆₇	C₂²	1	2	yes	complemented
56	C₂⁵×C₆₇	C₂×C₄	1	1	yes	characteristic
57	C₂×#41×C₆₇	—	2	4	no	—
58	C₂×#41×C₆₇	—	2	4	no	—
59	C₂×#41×C₆₇	C₂×C₄	1	4	yes	—
60	C₂×#41×C₆₇	C₂³	1	4	yes	—
61	C₂²×Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
62	C₂²×D₄×C₆₇	C₂×C₄	1	2	yes	—
63	C₂²×D₄×C₆₇	C₂×C₄	1	2	yes	—
64	C₂²×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
65	C₂²×D₄×C₆₇	C₂×C₄	1	2	yes	—
66	C₂³×C₄×C₆₇	—	2	4	no	—
67	C₂³×C₄×C₆₇	—	2	4	no	—
68	C₂³×C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
69	C₂³×C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
70	C₂³×C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
71	C₂³×C₄×C₆₇	C₂×C₄	1	4	yes	—
72	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
73	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
75	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
76	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
77	#131×C₆₇	—	2	32	no	—
78	C₂×M₁₆×C₆₇	—	2	4	no	—
79	C₂×M₁₆×C₆₇	—	2	32	no	—
80	C₂×M₁₆×C₆₇	—	2	8	no	—
81	C₂×M₁₆×C₆₇	—	2	8	no	—
82	C₂×M₁₆×C₆₇	D₄	1	8	yes	complemented
83	C₂×M₁₆×C₆₇	C₂³	1	4	yes	—
84	C₂×M₁₆×C₆₇	C₂³	1	8	yes	—
85	C₂×M₁₆×C₆₇	C₂³	1	4	yes	—
86	C₂×M₁₆×C₆₇	C₂³	1	8	yes	complemented
87	C₂²×C₈×C₆₇	—	2	4	no	—
88	C₂²×C₈×C₆₇	—	2	4	no	—
89	C₂²×C₈×C₆₇	—	2	8	no	—
90	C₂²×C₈×C₆₇	—	2	8	no	—
91	C₂²×C₈×C₆₇	C₂³	1	8	yes	—
92	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
93	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
94	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
95	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
96	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
97	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
98	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
99	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
100	C₂²×C₈×C₆₇	C₂³	1	8	yes	complemented
101	#123×C₆₇	C₂×C₄	1	16	yes	—
102	C₂²⋊Q₈×C₆₇	C₂×C₄	1	8	yes	—
103	C₂²⋊Q₈×C₆₇	C₂×C₄	1	8	yes	—
104	#121×C₆₇	C₂×C₄	1	8	yes	—
105	#121×C₆₇	C₂×C₄	1	8	yes	—
106	#120×C₆₇	C₂×C₄	1	16	yes	—
107	C₄×D₄×C₆₇	C₂×C₄	1	8	yes	—
108	C₄×D₄×C₆₇	C₂×C₄	1	8	yes	—
109	C₄×D₄×C₆₇	C₂³	1	8	yes	—
110	C₄×D₄×C₆₇	C₂³	1	8	yes	—
111	#117×C₆₇	C₂×C₄	1	4	yes	—
112	#117×C₆₇	C₂³	1	4	yes	—
113	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
114	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
115	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
116	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
117	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
118	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
119	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
120	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
121	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
122	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
123	C₄⋊C₈×C₆₇	C₂³	1	8	yes	complemented
124	C₄⋊C₈×C₆₇	C₂³	1	8	yes	complemented
125	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
126	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
127	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
128	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
129	C₂²⋊C₈×C₆₇	C₂³	1	8	yes	complemented
130	C₂²⋊C₈×C₆₇	C₂³	1	8	yes	complemented
131	#97×C₆₇	C₂³	1	8	yes	complemented
132	C₄×C₈×C₆₇	C₂³	1	8	yes	complemented
133	C₂⁴×C₆₇	—	2	4	no	—
134	C₂⁴×C₆₇	—	2	4	no	—
135	C₂⁴×C₆₇	—	4	2	no	—
136	C₂⁴×C₆₇	C₂²×C₄	1	1	yes	characteristic
137	C₂⁴×C₆₇	C₂²×C₄	1	2	yes	—
138	C₂⁴×C₆₇	C₂²×C₄	1	4	yes	—
139	C₂⁴×C₆₇	C₂²×C₄	1	1	yes	characteristic
140	C₂⁴×C₆₇	C₂²×C₄	1	1	yes	characteristic
141	#41×C₆₇	—	2	16	no	—
142	#41×C₆₇	—	2	8	no	—
143	#41×C₆₇	—	2	8	no	—
144	C₂×Q₈×C₆₇	—	2	4	no	—
145	C₂×Q₈×C₆₇	C₂²×C₄	1	4	yes	—
146	C₂×D₄×C₆₇	—	2	8	no	—
147	C₂×D₄×C₆₇	—	2	8	no	—
148	C₂×D₄×C₆₇	—	2	4	no	—
149	C₂×D₄×C₆₇	—	4	4	no	—
150	C₂×D₄×C₆₇	C₂²×C₄	1	8	yes	—
151	C₂×D₄×C₆₇	C₂²×C₄	1	8	yes	—
152	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
153	C₂×D₄×C₆₇	C₂²×C₄	1	8	yes	—
154	C₂²×C₄×C₆₇	—	2	4	no	—
155	C₂²×C₄×C₆₇	—	2	4	no	—
156	C₂²×C₄×C₆₇	—	2	4	no	—
157	C₂²×C₄×C₆₇	—	2	16	no	—
158	C₂²×C₄×C₆₇	—	2	2	no	—
159	C₂²×C₄×C₆₇	—	2	4	no	—
160	C₂²×C₄×C₆₇	—	2	8	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	8	no	—
165	C₂²×C₄×C₆₇	—	2	4	no	—
166	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
167	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
168	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
169	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
170	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
171	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
172	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
173	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
174	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
175	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
176	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
177	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
178	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
179	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
180	C₂²×C₄×C₆₇	#41	1	4	yes	—
181	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
182	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
183	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
184	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
185	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
186	M₁₆×C₆₇	—	2	8	no	—
187	M₁₆×C₆₇	—	2	16	no	—
188	M₁₆×C₆₇	—	2	16	no	—
189	M₁₆×C₆₇	C₂×D₄	1	16	yes	complemented
190	C₂×C₈×C₆₇	—	2	2	no	—
191	C₂×C₈×C₆₇	—	2	2	no	—
192	C₂×C₈×C₆₇	—	2	4	no	—
193	C₂×C₈×C₆₇	—	2	8	no	—
194	C₂×C₈×C₆₇	—	2	2	no	—
195	C₂×C₈×C₆₇	—	2	2	no	—
196	C₂×C₈×C₆₇	—	2	8	no	—
197	C₂×C₈×C₆₇	—	2	16	no	—
198	C₂×C₈×C₆₇	—	2	16	no	—
199	C₂×C₈×C₆₇	C₂×D₄	1	8	yes	—
200	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
201	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
202	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
203	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
204	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
205	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
206	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
207	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
208	C₄⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
209	C₄⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
210	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
211	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
212	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
213	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
214	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
215	C₄²×C₆₇	C₂²×C₄	1	4	yes	—
216	C₄²×C₆₇	C₂⁴	1	4	yes	—
217	C₂³×C₆₇	—	2	2	no	—
218	C₂³×C₆₇	—	2	2	no	—
219	C₂³×C₆₇	—	2	2	no	—
220	C₂³×C₆₇	—	2	2	no	—
221	C₂³×C₆₇	—	2	8	no	—
222	C₂³×C₆₇	—	2	2	no	—
223	C₂³×C₆₇	—	2	4	no	—
224	C₂³×C₆₇	—	2	4	no	—
225	C₂³×C₆₇	—	2	2	no	—
226	C₂³×C₆₇	—	2	8	no	—
227	C₂³×C₆₇	—	2	2	no	—
228	C₂³×C₆₇	—	2	4	no	—
229	C₂³×C₆₇	—	4	4	no	—
230	C₂³×C₆₇	—	4	16	no	—
231	C₂³×C₆₇	C₄×D₄	1	4	yes	—
232	C₂³×C₆₇	#131	1	4	yes	complemented
233	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
234	C₂³×C₆₇	C₂³×C₄	1	4	yes	—
235	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
236	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
237	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
238	Q₈×C₆₇	—	2	8	no	—
239	D₄×C₆₇	—	2	16	no	—
240	D₄×C₆₇	—	2	16	no	—
241	D₄×C₆₇	—	2	8	no	—
242	D₄×C₆₇	—	4	8	no	—
243	C₂×C₄×C₆₇	—	2	8	no	—
244	C₂×C₄×C₆₇	—	2	2	no	—
245	C₂×C₄×C₆₇	—	2	2	no	—
246	C₂×C₄×C₆₇	—	2	4	no	—
247	C₂×C₄×C₆₇	—	2	4	no	—
248	C₂×C₄×C₆₇	—	2	4	no	—
249	C₂×C₄×C₆₇	—	2	4	no	—
250	C₂×C₄×C₆₇	—	2	4	no	—
251	C₂×C₄×C₆₇	—	2	8	no	—
252	C₂×C₄×C₆₇	—	2	8	no	—
253	C₂×C₄×C₆₇	—	2	8	no	—
254	C₂×C₄×C₆₇	—	2	2	no	—
255	C₂×C₄×C₆₇	—	2	4	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	4	no	—
260	C₂×C₄×C₆₇	C₄×D₄	1	4	yes	—
261	C₂×C₄×C₆₇	C₄×D₄	1	8	yes	—
262	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
263	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
264	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
265	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
266	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
267	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
268	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
269	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
270	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
271	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
272	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
273	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
274	C₈×C₆₇	—	2	2	no	—
275	C₈×C₆₇	—	2	2	no	—
276	C₈×C₆₇	—	2	4	no	—
277	C₈×C₆₇	—	2	2	no	—
278	C₈×C₆₇	—	2	2	no	—
279	C₈×C₆₇	C₂²×D₄	1	8	yes	—
280	C₂²×C₆₇	—	2	2	no	—
281	C₂²×C₆₇	—	2	8	no	—
282	C₂²×C₆₇	—	2	8	no	—
283	C₂²×C₆₇	—	2	2	no	—
284	C₂²×C₆₇	—	2	2	no	—
285	C₂²×C₆₇	—	2	2	no	—
286	C₂²×C₆₇	—	2	2	no	—
287	C₂²×C₆₇	—	2	4	no	—
288	C₂²×C₆₇	—	2	4	no	—
289	C₂²×C₆₇	—	2	2	no	—
290	C₂²×C₆₇	—	2	2	no	—
291	C₂²×C₆₇	—	2	4	no	—
292	C₂²×C₆₇	—	4	16	no	—
293	C₂²×C₆₇	—	4	8	no	—
294	C₂²×C₆₇	—	4	4	no	—
295	C₂²×C₆₇	C₂×C₄×D₄	1	4	yes	—
296	C₂²×C₆₇	C₂×C₄×D₄	1	2	yes	—
297	C₂²×C₆₇	C₂×#131	1	2	yes	—
298	C₂²×C₆₇	C₂×#131	1	4	yes	complemented
299	C₂²×C₆₇	#568	1	2	yes	—
300	C₂²×C₆₇	C₂⁴×C₄	1	1	yes	characteristic
301	C₄×C₆₇	—	2	2	no	—
302	C₄×C₆₇	—	2	2	no	—
303	C₄×C₆₇	—	2	4	no	—
304	C₄×C₆₇	—	2	4	no	—
305	C₄×C₆₇	—	2	4	no	—
306	C₄×C₆₇	C₂×C₄×D₄	1	2	yes	—
307	C₄×C₆₇	C₂×C₄×D₄	1	4	yes	—
308	C₄×C₆₇	C₂³×D₄	1	1	yes	characteristic
309	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
310	C₂×#2933	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
311	C₂×C₆₇	—	2	4	no	—
312	C₂×C₆₇	—	2	4	no	—
313	C₂×C₆₇	—	4	4	no	—
314	C₂×C₆₇	—	4	2	no	—
315	C₂×C₆₇	#2933	1	4	yes	direct product factor
316	C₂×C₆₇	C₂²×C₄×D₄	1	1	yes	characteristic
317	C₂×C₆₇	C₂²×#131	1	1	yes	characteristic
318	C₂×C₆₇	C₂×#568	1	1	yes	characteristic
319	C₂²×#131	C₂×C₆₇	1	1	yes	characteristic, complemented
320	C₂³×M₁₆	C₂×C₆₇	1	1	yes	characteristic, complemented
321	C₂×#525	C₂×C₆₇	1	1	yes	characteristic
322	#2933	C₂×C₆₇	1	16	yes	direct product factor
323	C₂×#436	C₂×C₆₇	1	2	yes	complemented
324	C₂×#435	C₂×C₆₇	1	2	yes	complemented
325	C₂×#435	C₂×C₆₇	1	2	yes	complemented
326	C₂×C₈×D₄	C₂×C₆₇	1	2	yes	complemented
327	C₂×#424	C₂×C₆₇	1	1	yes	characteristic, complemented
328	C₂×#408	C₂×C₆₇	1	1	yes	characteristic, complemented
329	C₂²×C₂²⋊C₈	C₂×C₆₇	1	1	yes	characteristic, complemented
330	C₂×#405	C₂×C₆₇	1	1	yes	characteristic, complemented
331	C₆₇	C₂×#2933	1	1	yes	characteristic, direct product factor, Sylow
332	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
333	C₂⁴×C₄	C₂²×C₆₇	1	1	yes	characteristic
334	C₂×#131	—	2	8	no	—
335	C₂×#131	C₂²×C₆₇	1	8	yes	complemented
336	C₂²×M₁₆	—	2	8	no	—
337	C₂²×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
338	C₂²×M₁₆	C₂²×C₆₇	1	2	yes	—
339	C₂²×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
340	C₂²×M₁₆	C₂²×C₆₇	1	8	yes	complemented
341	C₂²×M₁₆	C₂²×C₆₇	1	2	yes	complemented
342	C₂³×C₈	C₂²×C₆₇	1	1	yes	characteristic
343	C₂³×C₈	C₂²×C₆₇	1	1	yes	characteristic
344	C₂³×C₈	C₂²×C₆₇	1	2	yes	—
345	C₂³×C₈	C₂²×C₆₇	1	2	yes	complemented
346	#525	C₄×C₆₇	1	8	yes	—
347	#525	C₂²×C₆₇	1	8	yes	—
348	C₂×#123	C₄×C₆₇	1	2	yes	—
349	C₂×C₂²⋊Q₈	C₄×C₆₇	1	1	yes	characteristic
350	C₂×C₂²⋊Q₈	C₄×C₆₇	1	1	yes	characteristic
351	C₂×#121	C₄×C₆₇	1	1	yes	characteristic
352	C₂×#121	C₄×C₆₇	1	1	yes	characteristic
353	C₂×#120	C₄×C₆₇	1	2	yes	—
354	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
355	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
356	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
357	#436	C₂²×C₆₇	1	16	yes	complemented
358	#435	C₂²×C₆₇	1	16	yes	complemented
359	#435	C₂²×C₆₇	1	16	yes	complemented
360	C₈×D₄	C₂²×C₆₇	1	16	yes	complemented
361	#424	C₂²×C₆₇	1	8	yes	complemented
362	C₂×C₄⋊C₈	C₂²×C₆₇	1	2	yes	complemented
363	C₂×C₄⋊C₈	C₂²×C₆₇	1	2	yes	complemented
364	#408	C₂²×C₆₇	1	8	yes	complemented
365	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
366	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
367	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
368	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
369	C₂×C₂²⋊C₈	C₂²×C₆₇	1	8	yes	complemented
370	C₂×C₂²⋊C₈	C₂²×C₆₇	1	2	yes	complemented
371	C₂×C₂²⋊C₈	C₂²×C₆₇	1	2	yes	complemented
372	#405	C₂²×C₆₇	1	8	yes	complemented
373	C₂×#97	C₂²×C₆₇	1	2	yes	complemented
374	C₂×C₄×C₈	C₂²×C₆₇	1	2	yes	complemented
375	C₂⁵	C₂×C₄×C₆₇	1	1	yes	characteristic
376	C₂×#41	—	2	4	no	—
377	C₂×#41	—	2	4	no	—
378	C₂×#41	C₂×C₄×C₆₇	1	4	yes	—
379	C₂×#41	C₂³×C₆₇	1	4	yes	—
380	C₂²×Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
381	C₂²×D₄	C₂×C₄×C₆₇	1	2	yes	—
382	C₂²×D₄	C₂×C₄×C₆₇	1	2	yes	—
383	C₂²×D₄	C₂×C₄×C₆₇	1	1	yes	characteristic
384	C₂²×D₄	C₂×C₄×C₆₇	1	2	yes	—
385	C₂³×C₄	—	2	4	no	—
386	C₂³×C₄	—	2	4	no	—
387	C₂³×C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
388	C₂³×C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
389	C₂³×C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
390	C₂³×C₄	C₂×C₄×C₆₇	1	4	yes	—
391	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
392	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
393	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
394	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
395	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
396	#131	—	2	32	no	—
397	C₂×M₁₆	—	2	4	no	—
398	C₂×M₁₆	—	2	32	no	—
399	C₂×M₁₆	—	2	8	no	—
400	C₂×M₁₆	—	2	8	no	—
401	C₂×M₁₆	D₄×C₆₇	1	8	yes	complemented
402	C₂×M₁₆	C₂³×C₆₇	1	4	yes	—
403	C₂×M₁₆	C₂³×C₆₇	1	8	yes	—
404	C₂×M₁₆	C₂³×C₆₇	1	4	yes	—
405	C₂×M₁₆	C₂³×C₆₇	1	8	yes	complemented
406	C₂²×C₈	—	2	4	no	—
407	C₂²×C₈	—	2	4	no	—
408	C₂²×C₈	—	2	8	no	—
409	C₂²×C₈	—	2	8	no	—
410	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
411	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
412	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
413	C₂²×C₈	C₂³×C₆₇	1	8	yes	—
414	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
415	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
416	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
417	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
418	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
419	C₂²×C₈	C₂³×C₆₇	1	8	yes	complemented
420	#123	C₂×C₄×C₆₇	1	16	yes	—
421	C₂²⋊Q₈	C₂×C₄×C₆₇	1	8	yes	—
422	C₂²⋊Q₈	C₂×C₄×C₆₇	1	8	yes	—
423	#121	C₂×C₄×C₆₇	1	8	yes	—
424	#121	C₂×C₄×C₆₇	1	8	yes	—
425	#120	C₂×C₄×C₆₇	1	16	yes	—
426	C₄×D₄	C₂×C₄×C₆₇	1	8	yes	—
427	C₄×D₄	C₂×C₄×C₆₇	1	8	yes	—
428	C₄×D₄	C₂³×C₆₇	1	8	yes	—
429	C₄×D₄	C₂³×C₆₇	1	8	yes	—
430	#117	C₂×C₄×C₆₇	1	4	yes	—
431	#117	C₂³×C₆₇	1	4	yes	—
432	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
433	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
434	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	2	yes	—
435	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	2	yes	—
436	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	2	yes	—
437	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	2	yes	—
438	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	2	yes	—
439	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	2	yes	—
440	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	2	yes	—
441	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
442	C₄⋊C₈	C₂³×C₆₇	1	8	yes	complemented
443	C₄⋊C₈	C₂³×C₆₇	1	8	yes	complemented
444	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
445	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
446	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
447	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
448	C₂²⋊C₈	C₂³×C₆₇	1	8	yes	complemented
449	C₂²⋊C₈	C₂³×C₆₇	1	8	yes	complemented
450	#97	C₂³×C₆₇	1	8	yes	complemented
451	C₄×C₈	C₂³×C₆₇	1	8	yes	complemented
452	C₂⁴	—	2	4	no	—
453	C₂⁴	—	2	4	no	—
454	C₂⁴	—	4	2	no	—
455	C₂⁴	C₂²×C₄×C₆₇	1	1	yes	characteristic
456	C₂⁴	C₂²×C₄×C₆₇	1	2	yes	—
457	C₂⁴	C₂²×C₄×C₆₇	1	4	yes	—
458	C₂⁴	C₂²×C₄×C₆₇	1	1	yes	characteristic
459	C₂⁴	C₂²×C₄×C₆₇	1	1	yes	characteristic
460	#41	—	2	16	no	—
461	#41	—	2	8	no	—
462	#41	—	2	8	no	—
463	C₂×Q₈	—	2	4	no	—
464	C₂×Q₈	C₂²×C₄×C₆₇	1	4	yes	—
465	C₂×D₄	—	2	8	no	—
466	C₂×D₄	—	2	8	no	—
467	C₂×D₄	—	2	4	no	—
468	C₂×D₄	—	4	4	no	—
469	C₂×D₄	C₂²×C₄×C₆₇	1	8	yes	—
470	C₂×D₄	C₂²×C₄×C₆₇	1	8	yes	—
471	C₂×D₄	C₂²×C₄×C₆₇	1	4	yes	—
472	C₂×D₄	C₂²×C₄×C₆₇	1	8	yes	—
473	C₂²×C₄	—	2	4	no	—
474	C₂²×C₄	—	2	4	no	—
475	C₂²×C₄	—	2	4	no	—
476	C₂²×C₄	—	2	16	no	—
477	C₂²×C₄	—	2	2	no	—
478	C₂²×C₄	—	2	4	no	—
479	C₂²×C₄	—	2	8	no	—
480	C₂²×C₄	—	2	2	no	—
481	C₂²×C₄	—	2	2	no	—
482	C₂²×C₄	—	2	2	no	—
483	C₂²×C₄	—	2	8	no	—
484	C₂²×C₄	—	2	4	no	—
485	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
486	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
487	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
488	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
489	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
490	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
491	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
492	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
493	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
494	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
495	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
496	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
497	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
498	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
499	C₂²×C₄	#41×C₆₇	1	4	yes	—
500	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
501	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
502	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
503	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
504	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
505	M₁₆	—	2	8	no	—
506	M₁₆	—	2	16	no	—
507	M₁₆	—	2	16	no	—
508	M₁₆	C₂×D₄×C₆₇	1	16	yes	complemented
509	C₂×C₈	—	2	2	no	—
510	C₂×C₈	—	2	2	no	—
511	C₂×C₈	—	2	4	no	—
512	C₂×C₈	—	2	8	no	—
513	C₂×C₈	—	2	2	no	—
514	C₂×C₈	—	2	2	no	—
515	C₂×C₈	—	2	8	no	—
516	C₂×C₈	—	2	16	no	—
517	C₂×C₈	—	2	16	no	—
518	C₂×C₈	C₂×D₄×C₆₇	1	8	yes	—
519	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
520	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
521	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
522	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
523	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
524	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
525	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
526	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
527	C₄⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
528	C₄⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
529	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
530	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
531	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
532	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
533	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
534	C₄²	C₂²×C₄×C₆₇	1	4	yes	—
535	C₄²	C₂⁴×C₆₇	1	4	yes	—
536	C₂³	—	2	2	no	—
537	C₂³	—	2	2	no	—
538	C₂³	—	2	2	no	—
539	C₂³	—	2	2	no	—
540	C₂³	—	2	8	no	—
541	C₂³	—	2	2	no	—
542	C₂³	—	2	4	no	—
543	C₂³	—	2	4	no	—
544	C₂³	—	2	2	no	—
545	C₂³	—	2	8	no	—
546	C₂³	—	2	2	no	—
547	C₂³	—	2	4	no	—
548	C₂³	—	4	4	no	—
549	C₂³	—	4	16	no	—
550	C₂³	C₄×D₄×C₆₇	1	4	yes	—
551	C₂³	#131×C₆₇	1	4	yes	complemented
552	C₂³	C₂³×C₄×C₆₇	1	2	yes	—
553	C₂³	C₂³×C₄×C₆₇	1	4	yes	—
554	C₂³	C₂³×C₄×C₆₇	1	2	yes	—
555	C₂³	C₂³×C₄×C₆₇	1	2	yes	—
556	C₂³	C₂³×C₄×C₆₇	1	1	yes	characteristic
557	Q₈	—	2	8	no	—
558	D₄	—	2	16	no	—
559	D₄	—	2	16	no	—
560	D₄	—	2	8	no	—
561	D₄	—	4	8	no	—
562	C₂×C₄	—	2	8	no	—
563	C₂×C₄	—	2	2	no	—
564	C₂×C₄	—	2	2	no	—
565	C₂×C₄	—	2	4	no	—
566	C₂×C₄	—	2	4	no	—
567	C₂×C₄	—	2	4	no	—
568	C₂×C₄	—	2	4	no	—
569	C₂×C₄	—	2	4	no	—
570	C₂×C₄	—	2	8	no	—
571	C₂×C₄	—	2	8	no	—
572	C₂×C₄	—	2	8	no	—
573	C₂×C₄	—	2	2	no	—
574	C₂×C₄	—	2	4	no	—
575	C₂×C₄	—	2	2	no	—
576	C₂×C₄	—	2	2	no	—
577	C₂×C₄	—	2	2	no	—
578	C₂×C₄	—	2	4	no	—
579	C₂×C₄	C₄×D₄×C₆₇	1	4	yes	—
580	C₂×C₄	C₄×D₄×C₆₇	1	8	yes	—
581	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
582	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
583	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
584	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
585	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
586	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
587	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
588	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
589	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
590	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
591	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
592	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
593	C₈	—	2	2	no	—
594	C₈	—	2	2	no	—
595	C₈	—	2	4	no	—
596	C₈	—	2	2	no	—
597	C₈	—	2	2	no	—
598	C₈	C₂²×D₄×C₆₇	1	8	yes	—
599	C₂²	—	2	2	no	—
600	C₂²	—	2	2	no	—
601	C₂²	—	2	2	no	—
602	C₂²	—	2	2	no	—
603	C₂²	—	2	8	no	—
604	C₂²	—	2	8	no	—
605	C₂²	—	2	4	no	—
606	C₂²	—	2	2	no	—
607	C₂²	—	2	2	no	—
608	C₂²	—	2	4	no	—
609	C₂²	—	2	2	no	—
610	C₂²	—	2	4	no	—
611	C₂²	—	4	16	no	—
612	C₂²	—	4	4	no	—
613	C₂²	—	4	8	no	—
614	C₂²	C₂×C₄×D₄×C₆₇	1	4	yes	—
615	C₂²	C₂×C₄×D₄×C₆₇	1	2	yes	—
616	C₂²	C₂×#131×C₆₇	1	2	yes	—
617	C₂²	C₂×#131×C₆₇	1	4	yes	complemented
618	C₂²	#568×C₆₇	1	2	yes	—
619	C₂²	C₂⁴×C₄×C₆₇	1	1	yes	characteristic
620	C₄	—	2	4	no	—
621	C₄	—	2	4	no	—
622	C₄	—	2	2	no	—
623	C₄	—	2	2	no	—
624	C₄	—	2	4	no	—
625	C₄	C₂×C₄×D₄×C₆₇	1	2	yes	—
626	C₄	C₂×C₄×D₄×C₆₇	1	4	yes	—
627	C₄	C₂³×D₄×C₆₇	1	1	yes	characteristic
628	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
629	C₂	—	2	4	no	—
630	C₂	—	2	4	no	—
631	C₂	—	4	2	no	—
632	C₂	—	4	4	no	—
633	C₂	C₆₇×#2933	1	4	yes	direct product factor
634	C₂	C₂²×C₄×D₄×C₆₇	1	1	yes	characteristic
635	C₂	C₂²×#131×C₆₇	1	1	yes	characteristic
636	C₂	C₂×#568×C₆₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₆₇	C₂⁴
commutator	C₂²	C₂⁴×C₄×C₆₇
Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
socle	C₂³×C₆₇	C₂³×C₄
prime radical	C₂×#525×C₆₇	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×#131×C₆₇	C₂	semidirect
2. C₂³×M₁₆×C₆₇	C₂	semidirect
4. C₆₇×#2933	C₂	direct (N × H)
5. C₂×#436×C₆₇	C₂	semidirect
6. C₂×#435×C₆₇	C₂	semidirect
7. C₂×#435×C₆₇	C₂	semidirect
8. C₂×C₈×D₄×C₆₇	C₂	semidirect
9. C₂×#424×C₆₇	C₂	semidirect
10. C₂×#408×C₆₇	C₂	semidirect
11. C₂²×C₂²⋊C₈×C₆₇	C₂	semidirect
12. C₂×#405×C₆₇	C₂	semidirect
16. C₂×#131×C₆₇	C₂²	semidirect
21. C₂²×M₁₆×C₆₇	C₂²	semidirect
22. C₂²×M₁₆×C₆₇	C₂²	semidirect
26. C₂³×C₈×C₆₇	C₂²	semidirect
38. #436×C₆₇	C₂²	semidirect
39. #435×C₆₇	C₂²	semidirect
40. #435×C₆₇	C₂²	semidirect
41. C₈×D₄×C₆₇	C₂²	semidirect
42. #424×C₆₇	C₂²	semidirect
43. C₂×C₄⋊C₈×C₆₇	C₂²	semidirect
44. C₂×C₄⋊C₈×C₆₇	C₂²	semidirect
45. #408×C₆₇	C₂²	semidirect
50. C₂×C₂²⋊C₈×C₆₇	C₂²	semidirect
51. C₂×C₂²⋊C₈×C₆₇	C₂²	semidirect
52. C₂×C₂²⋊C₈×C₆₇	C₂²	semidirect
53. #405×C₆₇	C₂²	semidirect
54. C₂×#97×C₆₇	C₂²	semidirect
55. C₂×C₄×C₈×C₆₇	C₂²	semidirect
82. C₂×M₁₆×C₆₇	D₄	semidirect
86. C₂×M₁₆×C₆₇	C₂³	semidirect
100. C₂²×C₈×C₆₇	C₂³	semidirect
123. C₄⋊C₈×C₆₇	C₂³	semidirect
124. C₄⋊C₈×C₆₇	C₂³	semidirect
129. C₂²⋊C₈×C₆₇	C₂³	semidirect
130. C₂²⋊C₈×C₆₇	C₂³	semidirect
131. #97×C₆₇	C₂³	semidirect
132. C₄×C₈×C₆₇	C₂³	semidirect
189. M₁₆×C₆₇	C₂×D₄	semidirect
232. C₂³×C₆₇	#131	semidirect
298. C₂²×C₆₇	C₂×#131	semidirect
310. C₂×#2933	C₆₇	direct (N × H)
315. C₂×C₆₇	#2933	direct (N × H)
319. C₂²×#131	C₂×C₆₇	semidirect
320. C₂³×M₁₆	C₂×C₆₇	semidirect
322. #2933	C₂×C₆₇	direct (N × H)
323. C₂×#436	C₂×C₆₇	semidirect
324. C₂×#435	C₂×C₆₇	semidirect
325. C₂×#435	C₂×C₆₇	semidirect
326. C₂×C₈×D₄	C₂×C₆₇	semidirect
327. C₂×#424	C₂×C₆₇	semidirect
328. C₂×#408	C₂×C₆₇	semidirect
329. C₂²×C₂²⋊C₈	C₂×C₆₇	semidirect
330. C₂×#405	C₂×C₆₇	semidirect
331. C₆₇	C₂×#2933	direct (N × H)
335. C₂×#131	C₂²×C₆₇	semidirect
340. C₂²×M₁₆	C₂²×C₆₇	semidirect
341. C₂²×M₁₆	C₂²×C₆₇	semidirect
345. C₂³×C₈	C₂²×C₆₇	semidirect
357. #436	C₂²×C₆₇	semidirect
358. #435	C₂²×C₆₇	semidirect
359. #435	C₂²×C₆₇	semidirect
360. C₈×D₄	C₂²×C₆₇	semidirect
361. #424	C₂²×C₆₇	semidirect
362. C₂×C₄⋊C₈	C₂²×C₆₇	semidirect
363. C₂×C₄⋊C₈	C₂²×C₆₇	semidirect
364. #408	C₂²×C₆₇	semidirect
369. C₂×C₂²⋊C₈	C₂²×C₆₇	semidirect
370. C₂×C₂²⋊C₈	C₂²×C₆₇	semidirect
371. C₂×C₂²⋊C₈	C₂²×C₆₇	semidirect
372. #405	C₂²×C₆₇	semidirect
373. C₂×#97	C₂²×C₆₇	semidirect
374. C₂×C₄×C₈	C₂²×C₆₇	semidirect
401. C₂×M₁₆	D₄×C₆₇	semidirect
405. C₂×M₁₆	C₂³×C₆₇	semidirect
419. C₂²×C₈	C₂³×C₆₇	semidirect
442. C₄⋊C₈	C₂³×C₆₇	semidirect
443. C₄⋊C₈	C₂³×C₆₇	semidirect
448. C₂²⋊C₈	C₂³×C₆₇	semidirect
449. C₂²⋊C₈	C₂³×C₆₇	semidirect
450. #97	C₂³×C₆₇	semidirect
451. C₄×C₈	C₂³×C₆₇	semidirect
508. M₁₆	C₂×D₄×C₆₇	semidirect
551. C₂³	#131×C₆₇	semidirect
617. C₂²	C₂×#131×C₆₇	semidirect
633. C₂	C₆₇×#2933	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#131×C₆₇	2
C₂³×M₁₆×C₆₇	2
C₂×#525×C₆₇	2
C₆₇×#2933	2
C₂×#436×C₆₇	2
C₂×#435×C₆₇	2
C₂×C₈×D₄×C₆₇	2
C₂×#424×C₆₇	2
C₂×#408×C₆₇	2
C₂²×C₂²⋊C₈×C₆₇	2
C₂×#405×C₆₇	2
C₂×#2933	67

Subgroups — C2×C67×#2933 #30739388

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₇×#2933 #30739388