Subgroups — C₂×C₆₇×#3008 #30739611

Order 17152.

5254 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×H(5,𝔽₂)×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×AGL(1,ℤ/8)×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂³×D₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#535×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#3008	C₂	1	16	yes	maximal, direct product factor
6	C₂×#449×C₆₇	C₂	1	4	yes	maximal, complemented
7	C₂×#447×C₆₇	C₂	1	4	yes	maximal, complemented
8	C₂×#418×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#416×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#408×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×H(5,𝔽₂)×C₆₇	—	2	4	no	—
12	C₂×H(5,𝔽₂)×C₆₇	—	2	8	no	—
13	C₂×H(5,𝔽₂)×C₆₇	—	2	8	no	—
14	C₂×H(5,𝔽₂)×C₆₇	C₂²	1	8	yes	complemented
15	C₂²×#41×C₆₇	—	2	1	no	—
16	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
17	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
18	C₂²×#41×C₆₇	C₂²	1	2	yes	complemented
19	C₂³×D₄×C₆₇	—	2	1	no	—
20	C₂³×D₄×C₆₇	—	2	2	no	—
21	C₂³×D₄×C₆₇	C₂²	1	1	yes	characteristic
22	C₂³×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
23	C₂³×D₄×C₆₇	C₂²	1	2	yes	complemented
24	C₂×AGL(1,ℤ/8)×C₆₇	—	2	8	no	—
25	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	8	yes	complemented
26	C₂²×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
27	C₂²×D₈×C₆₇	—	2	8	no	—
28	C₂²×D₈×C₆₇	C₂²	1	4	yes	complemented
29	C₂²×D₈×C₆₇	C₂²	1	2	yes	complemented
30	C₂²×D₈×C₆₇	C₂²	1	8	yes	complemented
31	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
32	C₂³×C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
33	#535×C₆₇	—	2	4	no	—
34	#535×C₆₇	C₂²	1	8	yes	complemented
35	C₂×#127×C₆₇	—	2	1	no	—
36	C₂×#124×C₆₇	—	2	1	no	—
37	C₂×#121×C₆₇	C₂²	1	4	yes	complemented
38	C₂×#120×C₆₇	—	2	2	no	—
39	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic, complemented
40	#449×C₆₇	C₂²	1	32	yes	complemented
41	#447×C₆₇	C₂²	1	32	yes	complemented
42	#418×C₆₇	C₂²	1	8	yes	complemented
43	#416×C₆₇	C₂²	1	8	yes	complemented
44	C₂×#103×C₆₇	C₂²	1	2	yes	complemented
45	C₂×#102×C₆₇	C₂²	1	2	yes	complemented
46	C₂×#102×C₆₇	C₂²	1	4	yes	complemented
47	#408×C₆₇	C₂²	1	8	yes	complemented
48	C₂×C₂²⋊C₈×C₆₇	C₂²	1	4	yes	complemented
49	C₂⁵×C₆₇	—	2	1	no	—
50	C₂⁵×C₆₇	—	2	2	no	—
51	C₂⁵×C₆₇	—	2	1	no	—
52	H(5,𝔽₂)×C₆₇	—	2	64	no	—
53	H(5,𝔽₂)×C₆₇	—	2	32	no	—
54	H(5,𝔽₂)×C₆₇	—	2	32	no	—
55	C₂×#41×C₆₇	—	2	16	no	—
56	C₂×#41×C₆₇	—	2	8	no	—
57	C₂×#41×C₆₇	—	2	8	no	—
58	C₂×#41×C₆₇	—	2	8	no	—
59	C₂×#41×C₆₇	—	2	4	no	—
60	C₂×#41×C₆₇	—	2	2	no	—
61	C₂×#41×C₆₇	—	2	4	no	—
62	C₂×#41×C₆₇	—	2	4	no	—
63	C₂×#41×C₆₇	—	2	4	no	—
64	C₂×#41×C₆₇	D₄	1	4	yes	—
65	C₂×#41×C₆₇	D₄	1	8	yes	complemented
66	C₂×#41×C₆₇	C₂³	1	4	yes	—
67	C₂×#41×C₆₇	C₂³	1	4	yes	—
68	C₂×#41×C₆₇	C₂³	1	8	yes	complemented
69	C₂²×Q₈×C₆₇	D₄	1	1	yes	characteristic
70	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
71	C₂²×D₄×C₆₇	—	2	32	no	—
72	C₂²×D₄×C₆₇	—	2	16	no	—
73	C₂²×D₄×C₆₇	—	2	1	no	—
74	C₂²×D₄×C₆₇	—	2	2	no	—
75	C₂²×D₄×C₆₇	—	2	8	no	—
76	C₂²×D₄×C₆₇	—	2	16	no	—
77	C₂²×D₄×C₆₇	—	2	8	no	—
78	C₂²×D₄×C₆₇	—	2	8	no	—
79	C₂²×D₄×C₆₇	—	2	4	no	—
80	C₂²×D₄×C₆₇	—	2	1	no	—
81	C₂²×D₄×C₆₇	—	2	2	no	—
82	C₂²×D₄×C₆₇	—	2	2	no	—
83	C₂²×D₄×C₆₇	—	2	4	no	—
84	C₂²×D₄×C₆₇	—	2	4	no	—
85	C₂²×D₄×C₆₇	—	2	4	no	—
86	C₂²×D₄×C₆₇	—	2	4	no	—
87	C₂²×D₄×C₆₇	—	2	1	no	—
88	C₂²×D₄×C₆₇	—	2	2	no	—
89	C₂²×D₄×C₆₇	D₄	1	2	yes	—
90	C₂²×D₄×C₆₇	D₄	1	1	yes	characteristic
91	C₂²×D₄×C₆₇	D₄	1	8	yes	complemented
92	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
93	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
94	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
95	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
96	C₂²×D₄×C₆₇	C₂³	1	4	yes	complemented
97	C₂²×D₄×C₆₇	C₂³	1	8	yes	complemented
98	C₂³×C₄×C₆₇	—	2	1	no	—
99	C₂³×C₄×C₆₇	—	2	2	no	—
100	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
101	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
102	AGL(1,ℤ/8)×C₆₇	—	2	32	no	—
103	C₂×SD₁₆×C₆₇	—	2	8	no	—
104	C₂×SD₁₆×C₆₇	C₂³	1	8	yes	complemented
105	C₂×D₈×C₆₇	—	2	16	no	—
106	C₂×D₈×C₆₇	—	2	8	no	—
107	C₂×D₈×C₆₇	—	2	32	no	—
108	C₂×D₈×C₆₇	C₂³	1	16	yes	complemented
109	C₂×D₈×C₆₇	C₂³	1	8	yes	complemented
110	C₂×M₁₆×C₆₇	—	2	4	no	—
111	C₂×M₁₆×C₆₇	C₂³	1	4	yes	complemented
112	C₂²×C₈×C₆₇	—	2	4	no	—
113	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
114	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
115	C₂²×C₈×C₆₇	C₂³	1	4	yes	complemented
116	#127×C₆₇	—	2	8	no	—
117	#124×C₆₇	—	2	8	no	—
118	#121×C₆₇	—	2	8	no	—
119	#121×C₆₇	C₂³	1	16	yes	complemented
120	#120×C₆₇	—	2	16	no	—
121	#117×C₆₇	—	2	2	no	—
122	#117×C₆₇	C₂³	1	4	yes	complemented
123	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
124	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
125	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
126	C₂×C₄²×C₆₇	—	2	1	no	—
127	#103×C₆₇	C₂³	1	8	yes	complemented
128	#102×C₆₇	C₂³	1	16	yes	complemented
129	#102×C₆₇	C₂³	1	8	yes	complemented
130	C₂²⋊C₈×C₆₇	C₂³	1	16	yes	complemented
131	C₂⁴×C₆₇	—	2	16	no	—
132	C₂⁴×C₆₇	—	2	1	no	—
133	C₂⁴×C₆₇	—	2	2	no	—
134	C₂⁴×C₆₇	—	2	8	no	—
135	C₂⁴×C₆₇	—	2	4	no	—
136	C₂⁴×C₆₇	—	2	8	no	—
137	C₂⁴×C₆₇	—	2	2	no	—
138	C₂⁴×C₆₇	—	2	4	no	—
139	C₂⁴×C₆₇	—	4	4	no	—
140	C₂⁴×C₆₇	—	8	4	no	—
141	C₂⁴×C₆₇	—	8	4	no	—
142	C₂⁴×C₆₇	—	8	8	no	—
143	C₂⁴×C₆₇	C₂×D₄	1	2	yes	—
144	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
145	#41×C₆₇	—	2	64	no	—
146	#41×C₆₇	—	2	32	no	—
147	#41×C₆₇	—	2	16	no	—
148	#41×C₆₇	—	2	16	no	—
149	#41×C₆₇	—	2	16	no	—
150	#41×C₆₇	—	2	16	no	—
151	#41×C₆₇	—	2	8	no	—
152	#41×C₆₇	—	2	8	no	—
153	#41×C₆₇	—	2	8	no	—
154	#41×C₆₇	C₂×D₄	1	16	yes	complemented
155	C₂×Q₈×C₆₇	—	2	4	no	—
156	C₂×Q₈×C₆₇	—	2	2	no	—
157	C₂×Q₈×C₆₇	—	2	1	no	—
158	C₂×Q₈×C₆₇	C₂×D₄	1	4	yes	—
159	C₂×Q₈×C₆₇	C₂×D₄	1	4	yes	—
160	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
161	C₂×D₄×C₆₇	—	2	16	no	—
162	C₂×D₄×C₆₇	—	2	16	no	—
163	C₂×D₄×C₆₇	—	2	128	no	—
164	C₂×D₄×C₆₇	—	2	64	no	—
165	C₂×D₄×C₆₇	—	2	32	no	—
166	C₂×D₄×C₆₇	—	2	8	no	—
167	C₂×D₄×C₆₇	—	2	8	no	—
168	C₂×D₄×C₆₇	—	2	4	no	—
169	C₂×D₄×C₆₇	—	2	8	no	—
170	C₂×D₄×C₆₇	—	2	16	no	—
171	C₂×D₄×C₆₇	—	2	16	no	—
172	C₂×D₄×C₆₇	—	2	16	no	—
173	C₂×D₄×C₆₇	—	2	4	no	—
174	C₂×D₄×C₆₇	—	2	8	no	—
175	C₂×D₄×C₆₇	—	2	16	no	—
176	C₂×D₄×C₆₇	—	2	4	no	—
177	C₂×D₄×C₆₇	—	2	2	no	—
178	C₂×D₄×C₆₇	—	2	1	no	—
179	C₂×D₄×C₆₇	—	2	4	no	—
180	C₂×D₄×C₆₇	—	2	2	no	—
181	C₂×D₄×C₆₇	—	2	8	no	—
182	C₂×D₄×C₆₇	—	2	8	no	—
183	C₂×D₄×C₆₇	—	2	4	no	—
184	C₂×D₄×C₆₇	—	2	8	no	—
185	C₂×D₄×C₆₇	—	2	4	no	—
186	C₂×D₄×C₆₇	—	2	8	no	—
187	C₂×D₄×C₆₇	—	2	2	no	—
188	C₂×D₄×C₆₇	—	2	4	no	—
189	C₂×D₄×C₆₇	—	4	4	no	—
190	C₂×D₄×C₆₇	—	4	8	no	—
191	C₂×D₄×C₆₇	—	8	8	no	—
192	C₂×D₄×C₆₇	C₂×D₄	1	8	yes	—
193	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	—
194	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	—
195	C₂×D₄×C₆₇	C₂×D₄	1	8	yes	—
196	C₂×D₄×C₆₇	C₂×D₄	1	16	yes	complemented
197	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
198	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
199	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
200	C₂²×C₄×C₆₇	—	2	16	no	—
201	C₂²×C₄×C₆₇	—	2	1	no	—
202	C₂²×C₄×C₆₇	—	2	8	no	—
203	C₂²×C₄×C₆₇	—	2	4	no	—
204	C₂²×C₄×C₆₇	—	2	8	no	—
205	C₂²×C₄×C₆₇	—	2	4	no	—
206	C₂²×C₄×C₆₇	—	2	4	no	—
207	C₂²×C₄×C₆₇	—	2	2	no	—
208	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
209	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
210	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
211	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
212	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
213	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
214	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
215	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
216	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
217	SD₁₆×C₆₇	—	2	16	no	—
218	D₈×C₆₇	—	2	32	no	—
219	D₈×C₆₇	—	2	16	no	—
220	M₁₆×C₆₇	—	2	8	no	—
221	C₂×C₈×C₆₇	—	2	4	no	—
222	C₂×C₈×C₆₇	—	2	8	no	—
223	C₂×C₈×C₆₇	—	2	4	no	—
224	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
225	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
226	C₄⋊C₄×C₆₇	—	2	2	no	—
227	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
228	C₂²⋊C₄×C₆₇	—	2	4	no	—
229	C₂²⋊C₄×C₆₇	—	2	16	no	—
230	C₄²×C₆₇	—	2	4	no	—
231	C₂³×C₆₇	—	2	4	no	—
232	C₂³×C₆₇	—	2	32	no	—
233	C₂³×C₆₇	—	2	4	no	—
234	C₂³×C₆₇	—	2	8	no	—
235	C₂³×C₆₇	—	2	4	no	—
236	C₂³×C₆₇	—	2	8	no	—
237	C₂³×C₆₇	—	2	2	no	—
238	C₂³×C₆₇	—	2	4	no	—
239	C₂³×C₆₇	—	2	16	no	—
240	C₂³×C₆₇	—	2	4	no	—
241	C₂³×C₆₇	—	4	8	no	—
242	C₂³×C₆₇	—	4	4	no	—
243	C₂³×C₆₇	—	4	8	no	—
244	C₂³×C₆₇	—	4	4	no	—
245	C₂³×C₆₇	—	4	8	no	—
246	C₂³×C₆₇	—	8	16	no	—
247	C₂³×C₆₇	—	8	8	no	—
248	C₂³×C₆₇	—	8	8	no	—
249	C₂³×C₆₇	—	8	16	no	—
250	C₂³×C₆₇	—	8	16	no	—
251	C₂³×C₆₇	—	8	32	no	—
252	C₂³×C₆₇	#120	1	4	yes	—
253	C₂³×C₆₇	C₂²×D₄	1	4	yes	—
254	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
255	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
256	Q₈×C₆₇	—	2	4	no	—
257	Q₈×C₆₇	—	2	8	no	—
258	Q₈×C₆₇	—	2	2	no	—
259	Q₈×C₆₇	C₂²×D₄	1	4	yes	—
260	D₄×C₆₇	—	2	32	no	—
261	D₄×C₆₇	—	2	32	no	—
262	D₄×C₆₇	—	2	16	no	—
263	D₄×C₆₇	—	2	16	no	—
264	D₄×C₆₇	—	2	8	no	—
265	D₄×C₆₇	—	2	4	no	—
266	D₄×C₆₇	—	2	8	no	—
267	D₄×C₆₇	—	2	16	no	—
268	D₄×C₆₇	—	2	4	no	—
269	D₄×C₆₇	—	2	2	no	—
270	D₄×C₆₇	—	2	4	no	—
271	D₄×C₆₇	—	2	4	no	—
272	D₄×C₆₇	—	4	4	no	—
273	D₄×C₆₇	—	4	8	no	—
274	D₄×C₆₇	—	8	16	no	—
275	D₄×C₆₇	C₂²×D₄	1	4	yes	—
276	D₄×C₆₇	C₂²×D₄	1	8	yes	—
277	C₂×C₄×C₆₇	—	2	32	no	—
278	C₂×C₄×C₆₇	—	2	4	no	—
279	C₂×C₄×C₆₇	—	2	4	no	—
280	C₂×C₄×C₆₇	—	2	2	no	—
281	C₂×C₄×C₆₇	—	2	16	no	—
282	C₂×C₄×C₆₇	—	2	8	no	—
283	C₂×C₄×C₆₇	—	2	4	no	—
284	C₂×C₄×C₆₇	—	2	4	no	—
285	C₂×C₄×C₆₇	—	2	4	no	—
286	C₂×C₄×C₆₇	—	4	4	no	—
287	C₂×C₄×C₆₇	#120	1	4	yes	—
288	C₂×C₄×C₆₇	#120	1	8	yes	—
289	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
290	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
291	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
292	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
293	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
294	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
295	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
296	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
297	C₈×C₆₇	—	2	4	no	—
298	C₈×C₆₇	—	2	4	no	—
299	C₂²×C₆₇	—	2	8	no	—
300	C₂²×C₆₇	—	2	4	no	—
301	C₂²×C₆₇	—	2	4	no	—
302	C₂²×C₆₇	—	2	8	no	—
303	C₂²×C₆₇	—	2	4	no	—
304	C₂²×C₆₇	—	2	8	no	—
305	C₂²×C₆₇	—	4	8	no	—
306	C₂²×C₆₇	—	4	16	no	—
307	C₂²×C₆₇	—	4	8	no	—
308	C₂²×C₆₇	—	4	8	no	—
309	C₂²×C₆₇	—	4	4	no	—
310	C₂²×C₆₇	—	4	4	no	—
311	C₂²×C₆₇	—	4	8	no	—
312	C₂²×C₆₇	—	8	16	no	—
313	C₂²×C₆₇	—	8	16	no	—
314	C₂²×C₆₇	—	8	32	no	—
315	C₂²×C₆₇	—	8	8	no	—
316	C₂²×C₆₇	C₂×#120	1	4	yes	—
317	C₂²×C₆₇	C₂×#120	1	2	yes	—
318	C₂²×C₆₇	#576	1	4	yes	—
319	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
320	C₄×C₆₇	—	2	4	no	—
321	C₄×C₆₇	—	2	4	no	—
322	C₄×C₆₇	—	4	4	no	—
323	C₄×C₆₇	C₂×#120	1	4	yes	—
324	C₄×C₆₇	C₂×#120	1	2	yes	—
325	C₄×C₆₇	C₂³×D₄	1	1	yes	characteristic
326	C₄×C₆₇	C₂³×D₄	1	1	yes	characteristic
327	C₂×#3008	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
328	C₂×C₆₇	—	2	4	no	—
329	C₂×C₆₇	—	4	4	no	—
330	C₂×C₆₇	—	4	8	no	—
331	C₂×C₆₇	—	4	4	no	—
332	C₂×C₆₇	—	8	4	no	—
333	C₂×C₆₇	#3008	1	4	yes	direct product factor
334	C₂×C₆₇	C₂²×#120	1	1	yes	characteristic
335	C₂×C₆₇	C₂×#576	1	2	yes	—
336	C₂²×H(5,𝔽₂)	C₂×C₆₇	1	1	yes	characteristic, complemented
337	C₂²×AGL(1,ℤ/8)	C₂×C₆₇	1	1	yes	characteristic, complemented
338	C₂³×D₈	C₂×C₆₇	1	1	yes	characteristic, complemented
339	C₂×#535	C₂×C₆₇	1	1	yes	characteristic, complemented
340	#3008	C₂×C₆₇	1	16	yes	direct product factor
341	C₂×#449	C₂×C₆₇	1	4	yes	complemented
342	C₂×#447	C₂×C₆₇	1	4	yes	complemented
343	C₂×#418	C₂×C₆₇	1	1	yes	characteristic, complemented
344	C₂×#416	C₂×C₆₇	1	1	yes	characteristic, complemented
345	C₂×#408	C₂×C₆₇	1	1	yes	characteristic, complemented
346	C₆₇	C₂×#3008	1	1	yes	characteristic, direct product factor, Sylow
347	C₂×H(5,𝔽₂)	—	2	4	no	—
348	C₂×H(5,𝔽₂)	—	2	8	no	—
349	C₂×H(5,𝔽₂)	—	2	8	no	—
350	C₂×H(5,𝔽₂)	C₂²×C₆₇	1	8	yes	complemented
351	C₂²×#41	—	2	1	no	—
352	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
353	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
354	C₂²×#41	C₂²×C₆₇	1	2	yes	complemented
355	C₂³×D₄	—	2	1	no	—
356	C₂³×D₄	—	2	2	no	—
357	C₂³×D₄	C₂²×C₆₇	1	1	yes	characteristic
358	C₂³×D₄	C₂²×C₆₇	1	2	yes	complemented
359	C₂³×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
360	C₂×AGL(1,ℤ/8)	—	2	8	no	—
361	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	8	yes	complemented
362	C₂²×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
363	C₂²×D₈	—	2	8	no	—
364	C₂²×D₈	C₂²×C₆₇	1	2	yes	complemented
365	C₂²×D₈	C₂²×C₆₇	1	4	yes	complemented
366	C₂²×D₈	C₂²×C₆₇	1	8	yes	complemented
367	C₂²×M₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
368	C₂³×C₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
369	#535	—	2	4	no	—
370	#535	C₂²×C₆₇	1	8	yes	complemented
371	C₂×#127	—	2	1	no	—
372	C₂×#124	—	2	1	no	—
373	C₂×#121	C₂²×C₆₇	1	4	yes	complemented
374	C₂×#120	—	2	2	no	—
375	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic, complemented
376	#449	C₂²×C₆₇	1	32	yes	complemented
377	#447	C₂²×C₆₇	1	32	yes	complemented
378	#418	C₂²×C₆₇	1	8	yes	complemented
379	#416	C₂²×C₆₇	1	8	yes	complemented
380	C₂×#103	C₂²×C₆₇	1	2	yes	complemented
381	C₂×#102	C₂²×C₆₇	1	2	yes	complemented
382	C₂×#102	C₂²×C₆₇	1	4	yes	complemented
383	#408	C₂²×C₆₇	1	8	yes	complemented
384	C₂×C₂²⋊C₈	C₂²×C₆₇	1	4	yes	complemented
385	C₂⁵	—	2	1	no	—
386	C₂⁵	—	2	2	no	—
387	C₂⁵	—	2	1	no	—
388	H(5,𝔽₂)	—	2	64	no	—
389	H(5,𝔽₂)	—	2	32	no	—
390	H(5,𝔽₂)	—	2	32	no	—
391	C₂×#41	—	2	16	no	—
392	C₂×#41	—	2	8	no	—
393	C₂×#41	—	2	8	no	—
394	C₂×#41	—	2	8	no	—
395	C₂×#41	—	2	4	no	—
396	C₂×#41	—	2	2	no	—
397	C₂×#41	—	2	4	no	—
398	C₂×#41	—	2	4	no	—
399	C₂×#41	—	2	4	no	—
400	C₂×#41	D₄×C₆₇	1	4	yes	—
401	C₂×#41	D₄×C₆₇	1	8	yes	complemented
402	C₂×#41	C₂³×C₆₇	1	4	yes	—
403	C₂×#41	C₂³×C₆₇	1	4	yes	—
404	C₂×#41	C₂³×C₆₇	1	8	yes	complemented
405	C₂²×Q₈	D₄×C₆₇	1	1	yes	characteristic
406	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
407	C₂²×D₄	—	2	32	no	—
408	C₂²×D₄	—	2	16	no	—
409	C₂²×D₄	—	2	1	no	—
410	C₂²×D₄	—	2	2	no	—
411	C₂²×D₄	—	2	8	no	—
412	C₂²×D₄	—	2	16	no	—
413	C₂²×D₄	—	2	8	no	—
414	C₂²×D₄	—	2	8	no	—
415	C₂²×D₄	—	2	4	no	—
416	C₂²×D₄	—	2	1	no	—
417	C₂²×D₄	—	2	2	no	—
418	C₂²×D₄	—	2	2	no	—
419	C₂²×D₄	—	2	4	no	—
420	C₂²×D₄	—	2	4	no	—
421	C₂²×D₄	—	2	4	no	—
422	C₂²×D₄	—	2	4	no	—
423	C₂²×D₄	—	2	1	no	—
424	C₂²×D₄	—	2	2	no	—
425	C₂²×D₄	D₄×C₆₇	1	2	yes	—
426	C₂²×D₄	D₄×C₆₇	1	1	yes	characteristic
427	C₂²×D₄	D₄×C₆₇	1	8	yes	complemented
428	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
429	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
430	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
431	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
432	C₂²×D₄	C₂³×C₆₇	1	4	yes	complemented
433	C₂²×D₄	C₂³×C₆₇	1	8	yes	complemented
434	C₂³×C₄	—	2	1	no	—
435	C₂³×C₄	—	2	2	no	—
436	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
437	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
438	AGL(1,ℤ/8)	—	2	32	no	—
439	C₂×SD₁₆	—	2	8	no	—
440	C₂×SD₁₆	C₂³×C₆₇	1	8	yes	complemented
441	C₂×D₈	—	2	16	no	—
442	C₂×D₈	—	2	8	no	—
443	C₂×D₈	—	2	32	no	—
444	C₂×D₈	C₂³×C₆₇	1	16	yes	complemented
445	C₂×D₈	C₂³×C₆₇	1	8	yes	complemented
446	C₂×M₁₆	—	2	4	no	—
447	C₂×M₁₆	C₂³×C₆₇	1	4	yes	complemented
448	C₂²×C₈	—	2	4	no	—
449	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
450	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
451	C₂²×C₈	C₂³×C₆₇	1	4	yes	complemented
452	#127	—	2	8	no	—
453	#124	—	2	8	no	—
454	#121	—	2	8	no	—
455	#121	C₂³×C₆₇	1	16	yes	complemented
456	#120	—	2	16	no	—
457	#117	—	2	2	no	—
458	#117	C₂³×C₆₇	1	4	yes	complemented
459	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
460	C₂×C₂²⋊C₄	—	2	1	no	—
461	C₂×C₂²⋊C₄	—	2	4	no	—
462	C₂×C₄²	—	2	1	no	—
463	#103	C₂³×C₆₇	1	8	yes	complemented
464	#102	C₂³×C₆₇	1	8	yes	complemented
465	#102	C₂³×C₆₇	1	16	yes	complemented
466	C₂²⋊C₈	C₂³×C₆₇	1	16	yes	complemented
467	C₂⁴	—	2	16	no	—
468	C₂⁴	—	2	1	no	—
469	C₂⁴	—	2	2	no	—
470	C₂⁴	—	2	8	no	—
471	C₂⁴	—	2	4	no	—
472	C₂⁴	—	2	8	no	—
473	C₂⁴	—	2	2	no	—
474	C₂⁴	—	2	4	no	—
475	C₂⁴	—	4	4	no	—
476	C₂⁴	—	8	4	no	—
477	C₂⁴	—	8	4	no	—
478	C₂⁴	—	8	8	no	—
479	C₂⁴	C₂×D₄×C₆₇	1	2	yes	—
480	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
481	#41	—	2	64	no	—
482	#41	—	2	32	no	—
483	#41	—	2	16	no	—
484	#41	—	2	16	no	—
485	#41	—	2	16	no	—
486	#41	—	2	16	no	—
487	#41	—	2	8	no	—
488	#41	—	2	8	no	—
489	#41	—	2	8	no	—
490	#41	C₂×D₄×C₆₇	1	16	yes	complemented
491	C₂×Q₈	—	2	4	no	—
492	C₂×Q₈	—	2	2	no	—
493	C₂×Q₈	—	2	1	no	—
494	C₂×Q₈	C₂×D₄×C₆₇	1	4	yes	—
495	C₂×Q₈	C₂×D₄×C₆₇	1	4	yes	—
496	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
497	C₂×D₄	—	2	16	no	—
498	C₂×D₄	—	2	16	no	—
499	C₂×D₄	—	2	128	no	—
500	C₂×D₄	—	2	64	no	—
501	C₂×D₄	—	2	32	no	—
502	C₂×D₄	—	2	8	no	—
503	C₂×D₄	—	2	8	no	—
504	C₂×D₄	—	2	4	no	—
505	C₂×D₄	—	2	8	no	—
506	C₂×D₄	—	2	16	no	—
507	C₂×D₄	—	2	16	no	—
508	C₂×D₄	—	2	16	no	—
509	C₂×D₄	—	2	4	no	—
510	C₂×D₄	—	2	8	no	—
511	C₂×D₄	—	2	16	no	—
512	C₂×D₄	—	2	4	no	—
513	C₂×D₄	—	2	2	no	—
514	C₂×D₄	—	2	1	no	—
515	C₂×D₄	—	2	4	no	—
516	C₂×D₄	—	2	2	no	—
517	C₂×D₄	—	2	8	no	—
518	C₂×D₄	—	2	8	no	—
519	C₂×D₄	—	2	4	no	—
520	C₂×D₄	—	2	8	no	—
521	C₂×D₄	—	2	4	no	—
522	C₂×D₄	—	2	8	no	—
523	C₂×D₄	—	2	2	no	—
524	C₂×D₄	—	2	4	no	—
525	C₂×D₄	—	4	4	no	—
526	C₂×D₄	—	4	8	no	—
527	C₂×D₄	—	8	8	no	—
528	C₂×D₄	C₂×D₄×C₆₇	1	8	yes	—
529	C₂×D₄	C₂×D₄×C₆₇	1	4	yes	—
530	C₂×D₄	C₂×D₄×C₆₇	1	4	yes	—
531	C₂×D₄	C₂×D₄×C₆₇	1	8	yes	—
532	C₂×D₄	C₂×D₄×C₆₇	1	16	yes	complemented
533	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
534	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
535	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
536	C₂²×C₄	—	2	16	no	—
537	C₂²×C₄	—	2	1	no	—
538	C₂²×C₄	—	2	8	no	—
539	C₂²×C₄	—	2	4	no	—
540	C₂²×C₄	—	2	8	no	—
541	C₂²×C₄	—	2	4	no	—
542	C₂²×C₄	—	2	4	no	—
543	C₂²×C₄	—	2	2	no	—
544	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
545	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
546	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
547	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
548	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
549	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
550	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
551	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
552	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
553	SD₁₆	—	2	16	no	—
554	D₈	—	2	32	no	—
555	D₈	—	2	16	no	—
556	M₁₆	—	2	8	no	—
557	C₂×C₈	—	2	4	no	—
558	C₂×C₈	—	2	8	no	—
559	C₂×C₈	—	2	4	no	—
560	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
561	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
562	C₄⋊C₄	—	2	2	no	—
563	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
564	C₂²⋊C₄	—	2	4	no	—
565	C₂²⋊C₄	—	2	16	no	—
566	C₄²	—	2	4	no	—
567	C₂³	—	2	4	no	—
568	C₂³	—	2	32	no	—
569	C₂³	—	2	4	no	—
570	C₂³	—	2	8	no	—
571	C₂³	—	2	4	no	—
572	C₂³	—	2	8	no	—
573	C₂³	—	2	2	no	—
574	C₂³	—	2	4	no	—
575	C₂³	—	2	16	no	—
576	C₂³	—	2	4	no	—
577	C₂³	—	4	8	no	—
578	C₂³	—	4	4	no	—
579	C₂³	—	4	8	no	—
580	C₂³	—	4	4	no	—
581	C₂³	—	4	8	no	—
582	C₂³	—	8	8	no	—
583	C₂³	—	8	8	no	—
584	C₂³	—	8	16	no	—
585	C₂³	—	8	16	no	—
586	C₂³	—	8	16	no	—
587	C₂³	—	8	32	no	—
588	C₂³	#120×C₆₇	1	4	yes	—
589	C₂³	C₂²×D₄×C₆₇	1	4	yes	—
590	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
591	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
592	Q₈	—	2	4	no	—
593	Q₈	—	2	8	no	—
594	Q₈	—	2	2	no	—
595	Q₈	C₂²×D₄×C₆₇	1	4	yes	—
596	D₄	—	2	32	no	—
597	D₄	—	2	32	no	—
598	D₄	—	2	16	no	—
599	D₄	—	2	16	no	—
600	D₄	—	2	8	no	—
601	D₄	—	2	4	no	—
602	D₄	—	2	8	no	—
603	D₄	—	2	16	no	—
604	D₄	—	2	4	no	—
605	D₄	—	2	2	no	—
606	D₄	—	2	4	no	—
607	D₄	—	2	4	no	—
608	D₄	—	4	4	no	—
609	D₄	—	4	8	no	—
610	D₄	—	8	16	no	—
611	D₄	C₂²×D₄×C₆₇	1	4	yes	—
612	D₄	C₂²×D₄×C₆₇	1	8	yes	—
613	C₂×C₄	—	2	32	no	—
614	C₂×C₄	—	2	4	no	—
615	C₂×C₄	—	2	4	no	—
616	C₂×C₄	—	2	2	no	—
617	C₂×C₄	—	2	16	no	—
618	C₂×C₄	—	2	8	no	—
619	C₂×C₄	—	2	4	no	—
620	C₂×C₄	—	2	4	no	—
621	C₂×C₄	—	2	4	no	—
622	C₂×C₄	—	4	4	no	—
623	C₂×C₄	#120×C₆₇	1	4	yes	—
624	C₂×C₄	#120×C₆₇	1	8	yes	—
625	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
626	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
627	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
628	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
629	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
630	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
631	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
632	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
633	C₈	—	2	4	no	—
634	C₈	—	2	4	no	—
635	C₂²	—	2	4	no	—
636	C₂²	—	2	8	no	—
637	C₂²	—	2	8	no	—
638	C₂²	—	2	4	no	—
639	C₂²	—	2	8	no	—
640	C₂²	—	2	4	no	—
641	C₂²	—	4	8	no	—
642	C₂²	—	4	4	no	—
643	C₂²	—	4	8	no	—
644	C₂²	—	4	16	no	—
645	C₂²	—	4	8	no	—
646	C₂²	—	4	8	no	—
647	C₂²	—	4	4	no	—
648	C₂²	—	8	16	no	—
649	C₂²	—	8	16	no	—
650	C₂²	—	8	32	no	—
651	C₂²	—	8	8	no	—
652	C₂²	C₂×#120×C₆₇	1	4	yes	—
653	C₂²	C₂×#120×C₆₇	1	2	yes	—
654	C₂²	#576×C₆₇	1	4	yes	—
655	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
656	C₄	—	2	4	no	—
657	C₄	—	2	4	no	—
658	C₄	—	4	4	no	—
659	C₄	C₂×#120×C₆₇	1	4	yes	—
660	C₄	C₂×#120×C₆₇	1	2	yes	—
661	C₄	C₂³×D₄×C₆₇	1	1	yes	characteristic
662	C₄	C₂³×D₄×C₆₇	1	1	yes	characteristic
663	C₂	—	2	4	no	—
664	C₂	—	4	4	no	—
665	C₂	—	4	8	no	—
666	C₂	—	4	4	no	—
667	C₂	—	8	4	no	—
668	C₂	C₆₇×#3008	1	4	yes	direct product factor
669	C₂	C₂²×#120×C₆₇	1	1	yes	characteristic
670	C₂	C₂×#576×C₆₇	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ C₂²×#41×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×H(5,𝔽₂)×C₆₇	C₂	semidirect
2. C₂²×AGL(1,ℤ/8)×C₆₇	C₂	semidirect
3. C₂³×D₈×C₆₇	C₂	semidirect
4. C₂×#535×C₆₇	C₂	semidirect
5. C₆₇×#3008	C₂	direct (N × H)
6. C₂×#449×C₆₇	C₂	semidirect
7. C₂×#447×C₆₇	C₂	semidirect
8. C₂×#418×C₆₇	C₂	semidirect
9. C₂×#416×C₆₇	C₂	semidirect
10. C₂×#408×C₆₇	C₂	semidirect
14. C₂×H(5,𝔽₂)×C₆₇	C₂²	semidirect
18. C₂²×#41×C₆₇	C₂²	semidirect
22. C₂³×D₄×C₆₇	C₂²	semidirect
23. C₂³×D₄×C₆₇	C₂²	semidirect
25. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
26. C₂²×SD₁₆×C₆₇	C₂²	semidirect
28. C₂²×D₈×C₆₇	C₂²	semidirect
29. C₂²×D₈×C₆₇	C₂²	semidirect
30. C₂²×D₈×C₆₇	C₂²	semidirect
31. C₂²×M₁₆×C₆₇	C₂²	semidirect
32. C₂³×C₈×C₆₇	C₂²	semidirect
34. #535×C₆₇	C₂²	semidirect
37. C₂×#121×C₆₇	C₂²	semidirect
39. C₂×#117×C₆₇	C₂²	semidirect
40. #449×C₆₇	C₂²	semidirect
41. #447×C₆₇	C₂²	semidirect
42. #418×C₆₇	C₂²	semidirect
43. #416×C₆₇	C₂²	semidirect
44. C₂×#103×C₆₇	C₂²	semidirect
45. C₂×#102×C₆₇	C₂²	semidirect
46. C₂×#102×C₆₇	C₂²	semidirect
47. #408×C₆₇	C₂²	semidirect
48. C₂×C₂²⋊C₈×C₆₇	C₂²	semidirect
65. C₂×#41×C₆₇	D₄	semidirect
68. C₂×#41×C₆₇	C₂³	semidirect
91. C₂²×D₄×C₆₇	D₄	semidirect
96. C₂²×D₄×C₆₇	C₂³	semidirect
97. C₂²×D₄×C₆₇	C₂³	semidirect
104. C₂×SD₁₆×C₆₇	C₂³	semidirect
108. C₂×D₈×C₆₇	C₂³	semidirect
109. C₂×D₈×C₆₇	C₂³	semidirect
111. C₂×M₁₆×C₆₇	C₂³	semidirect
115. C₂²×C₈×C₆₇	C₂³	semidirect
119. #121×C₆₇	C₂³	semidirect
122. #117×C₆₇	C₂³	semidirect
127. #103×C₆₇	C₂³	semidirect
128. #102×C₆₇	C₂³	semidirect
129. #102×C₆₇	C₂³	semidirect
130. C₂²⋊C₈×C₆₇	C₂³	semidirect
154. #41×C₆₇	C₂×D₄	semidirect
196. C₂×D₄×C₆₇	C₂×D₄	semidirect
327. C₂×#3008	C₆₇	direct (N × H)
333. C₂×C₆₇	#3008	direct (N × H)
336. C₂²×H(5,𝔽₂)	C₂×C₆₇	semidirect
337. C₂²×AGL(1,ℤ/8)	C₂×C₆₇	semidirect
338. C₂³×D₈	C₂×C₆₇	semidirect
339. C₂×#535	C₂×C₆₇	semidirect
340. #3008	C₂×C₆₇	direct (N × H)
341. C₂×#449	C₂×C₆₇	semidirect
342. C₂×#447	C₂×C₆₇	semidirect
343. C₂×#418	C₂×C₆₇	semidirect
344. C₂×#416	C₂×C₆₇	semidirect
345. C₂×#408	C₂×C₆₇	semidirect
346. C₆₇	C₂×#3008	direct (N × H)
350. C₂×H(5,𝔽₂)	C₂²×C₆₇	semidirect
354. C₂²×#41	C₂²×C₆₇	semidirect
358. C₂³×D₄	C₂²×C₆₇	semidirect
359. C₂³×D₄	C₂²×C₆₇	semidirect
361. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
362. C₂²×SD₁₆	C₂²×C₆₇	semidirect
364. C₂²×D₈	C₂²×C₆₇	semidirect
365. C₂²×D₈	C₂²×C₆₇	semidirect
366. C₂²×D₈	C₂²×C₆₇	semidirect
367. C₂²×M₁₆	C₂²×C₆₇	semidirect
368. C₂³×C₈	C₂²×C₆₇	semidirect
370. #535	C₂²×C₆₇	semidirect
373. C₂×#121	C₂²×C₆₇	semidirect
375. C₂×#117	C₂²×C₆₇	semidirect
376. #449	C₂²×C₆₇	semidirect
377. #447	C₂²×C₆₇	semidirect
378. #418	C₂²×C₆₇	semidirect
379. #416	C₂²×C₆₇	semidirect
380. C₂×#103	C₂²×C₆₇	semidirect
381. C₂×#102	C₂²×C₆₇	semidirect
382. C₂×#102	C₂²×C₆₇	semidirect
383. #408	C₂²×C₆₇	semidirect
384. C₂×C₂²⋊C₈	C₂²×C₆₇	semidirect
401. C₂×#41	D₄×C₆₇	semidirect
404. C₂×#41	C₂³×C₆₇	semidirect
427. C₂²×D₄	D₄×C₆₇	semidirect
432. C₂²×D₄	C₂³×C₆₇	semidirect
433. C₂²×D₄	C₂³×C₆₇	semidirect
440. C₂×SD₁₆	C₂³×C₆₇	semidirect
444. C₂×D₈	C₂³×C₆₇	semidirect
445. C₂×D₈	C₂³×C₆₇	semidirect
447. C₂×M₁₆	C₂³×C₆₇	semidirect
451. C₂²×C₈	C₂³×C₆₇	semidirect
455. #121	C₂³×C₆₇	semidirect
458. #117	C₂³×C₆₇	semidirect
463. #103	C₂³×C₆₇	semidirect
464. #102	C₂³×C₆₇	semidirect
465. #102	C₂³×C₆₇	semidirect
466. C₂²⋊C₈	C₂³×C₆₇	semidirect
490. #41	C₂×D₄×C₆₇	semidirect
532. C₂×D₄	C₂×D₄×C₆₇	semidirect
668. C₂	C₆₇×#3008	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×H(5,𝔽₂)×C₆₇	2
C₂²×AGL(1,ℤ/8)×C₆₇	2
C₂³×D₈×C₆₇	2
C₂×#535×C₆₇	2
C₆₇×#3008	2
C₂×#449×C₆₇	2
C₂×#447×C₆₇	2
C₂×#418×C₆₇	2
C₂×#416×C₆₇	2
C₂×#408×C₆₇	2
C₂×#3008	67

Subgroups — C2×C67×#3008 #30739611

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₇×#3008 #30739611