Subgroups — C₆₇×#60372 #30739623

Order 17152.

5126 conjugacy classes of subgroups.

The subgroup lattice has 674 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	C₂×#576×C₆₇	C₂	1	2	yes	maximal, complemented
3	C₆₇×#3488	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#3012	C₂	1	6	yes	maximal, complemented
5	C₆₇×#3008	C₂	1	6	yes	maximal, complemented
6	C₆₇×#3006	C₂	1	3	yes	maximal, complemented
7	C₆₇×#3003	C₂	1	3	yes	maximal, complemented
8	C₆₇×#3002	C₂	1	3	yes	maximal, complemented
9	C₂×#447×C₆₇	C₂	1	3	yes	maximal, complemented
10	C₆₇×#2897	C₂	1	2	yes	maximal, complemented
11	C₆₇×#2880	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×H(5,𝔽₂)×C₆₇	—	2	16	no	—
13	C₂×H(5,𝔽₂)×C₆₇	—	2	3	no	—
14	C₂×H(5,𝔽₂)×C₆₇	—	2	1	no	—
15	C₂×H(5,𝔽₂)×C₆₇	C₂²	1	2	yes	—
16	C₂×H(5,𝔽₂)×C₆₇	C₂²	1	6	yes	complemented
17	C₂×H(5,𝔽₂)×C₆₇	C₂²	1	1	yes	characteristic, complemented
18	C₂²×#41×C₆₇	—	2	1	no	—
19	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
20	C₂²×#41×C₆₇	C₂²	1	3	yes	complemented
21	C₂³×D₄×C₆₇	—	2	3	no	—
22	C₂³×D₄×C₆₇	C₂²	1	3	yes	complemented
23	#576×C₆₇	—	2	16	no	—
24	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	6	yes	complemented
25	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	6	yes	complemented
26	C₂×#135×C₆₇	C₂²	1	6	yes	complemented
27	C₂²×D₈×C₆₇	C₂²	1	6	yes	complemented
28	C₂×#131×C₆₇	C₂²	1	2	yes	complemented
29	#550×C₆₇	—	2	1	no	—
30	#548×C₆₇	—	2	1	no	—
31	#546×C₆₇	—	2	3	no	—
32	D₄²×C₆₇	—	2	3	no	—
33	#537×C₆₇	C₂²	1	3	yes	complemented
34	#535×C₆₇	C₂²	1	3	yes	complemented
35	#525×C₆₇	C₂²	1	3	yes	complemented
36	C₂×#121×C₆₇	C₂²	1	3	yes	complemented
37	#520×C₆₇	C₂²	1	1	yes	characteristic, complemented
38	#452×C₆₇	C₂²	1	6	yes	complemented
39	#451×C₆₇	C₂²	1	1	yes	characteristic, complemented
40	#450×C₆₇	C₂²	1	3	yes	complemented
41	#450×C₆₇	C₂²	1	6	yes	complemented
42	#449×C₆₇	C₂²	1	12	yes	complemented
43	#449×C₆₇	C₂²	1	6	yes	complemented
44	#448×C₆₇	C₂²	1	3	yes	complemented
45	#447×C₆₇	C₂²	1	3	yes	complemented
46	#447×C₆₇	C₂²	1	6	yes	complemented
47	#447×C₆₇	C₂²	1	12	yes	complemented
48	#447×C₆₇	C₂²	1	6	yes	complemented
49	#418×C₆₇	C₂²	1	6	yes	complemented
50	#417×C₆₇	C₂²	1	6	yes	complemented
51	#416×C₆₇	C₂²	1	6	yes	complemented
52	C₂×#102×C₆₇	C₂²	1	6	yes	complemented
53	#408×C₆₇	C₂²	1	6	yes	complemented
54	#407×C₆₇	C₂²	1	3	yes	complemented
55	C₂×C₂²⋊C₈×C₆₇	C₂²	1	3	yes	complemented
56	C₂⁵×C₆₇	—	2	3	no	—
57	H(5,𝔽₂)×C₆₇	—	2	16	no	—
58	H(5,𝔽₂)×C₆₇	—	2	48	no	—
59	H(5,𝔽₂)×C₆₇	—	2	8	no	—
60	H(5,𝔽₂)×C₆₇	—	2	24	no	—
61	H(5,𝔽₂)×C₆₇	—	2	24	no	—
62	H(5,𝔽₂)×C₆₇	—	2	8	no	—
63	H(5,𝔽₂)×C₆₇	D₄	1	16	yes	complemented
64	C₂×#41×C₆₇	—	2	16	no	—
65	C₂×#41×C₆₇	—	2	8	no	—
66	C₂×#41×C₆₇	—	2	24	no	—
67	C₂×#41×C₆₇	—	2	2	no	—
68	C₂×#41×C₆₇	—	2	6	no	—
69	C₂×#41×C₆₇	—	2	1	no	—
70	C₂×#41×C₆₇	—	2	3	no	—
71	C₂×#41×C₆₇	—	2	3	no	—
72	C₂×#41×C₆₇	D₄	1	3	yes	—
73	C₂×#41×C₆₇	D₄	1	1	yes	characteristic
74	C₂×#41×C₆₇	C₂³	1	6	yes	—
75	C₂×#41×C₆₇	C₂³	1	6	yes	—
76	C₂×#41×C₆₇	C₂³	1	3	yes	—
77	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
78	C₂×#41×C₆₇	C₂³	1	3	yes	complemented
79	C₂²×Q₈×C₆₇	D₄	1	1	yes	characteristic
80	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
81	C₂²×D₄×C₆₇	—	2	48	no	—
82	C₂²×D₄×C₆₇	—	2	3	no	—
83	C₂²×D₄×C₆₇	—	2	6	no	—
84	C₂²×D₄×C₆₇	—	2	12	no	—
85	C₂²×D₄×C₆₇	—	2	6	no	—
86	C₂²×D₄×C₆₇	—	2	24	no	—
87	C₂²×D₄×C₆₇	—	2	3	no	—
88	C₂²×D₄×C₆₇	—	2	3	no	—
89	C₂²×D₄×C₆₇	—	2	3	no	—
90	C₂²×D₄×C₆₇	—	2	3	no	—
91	C₂²×D₄×C₆₇	—	2	3	no	—
92	C₂²×D₄×C₆₇	D₄	1	3	yes	—
93	C₂²×D₄×C₆₇	C₂³	1	3	yes	—
94	C₂²×D₄×C₆₇	C₂³	1	6	yes	—
95	C₂²×D₄×C₆₇	C₂³	1	6	yes	—
96	C₂²×D₄×C₆₇	C₂³	1	3	yes	complemented
97	C₂³×C₄×C₆₇	—	2	3	no	—
98	C₂³×C₄×C₆₇	C₂³	1	3	yes	—
99	AGL(1,ℤ/8)×C₆₇	—	2	24	no	—
100	AGL(1,ℤ/8)×C₆₇	—	2	24	no	—
101	#135×C₆₇	—	2	24	no	—
102	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	complemented
103	C₂×SD₁₆×C₆₇	C₂³	1	6	yes	complemented
104	C₂×SD₁₆×C₆₇	C₂³	1	6	yes	complemented
105	C₂×D₈×C₆₇	—	2	24	no	—
106	C₂×D₈×C₆₇	C₂³	1	6	yes	complemented
107	C₂×D₈×C₆₇	C₂³	1	12	yes	complemented
108	#131×C₆₇	—	2	8	no	—
109	C₂×M₁₆×C₆₇	C₂³	1	6	yes	complemented
110	C₂²×C₈×C₆₇	C₂³	1	6	yes	complemented
111	#127×C₆₇	—	2	3	no	—
112	#124×C₆₇	—	2	3	no	—
113	#123×C₆₇	—	2	3	no	—
114	C₂²⋊Q₈×C₆₇	—	2	3	no	—
115	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
116	C₂²⋊Q₈×C₆₇	C₂³	1	3	yes	complemented
117	#121×C₆₇	—	2	6	no	—
118	#121×C₆₇	—	2	3	no	—
119	#121×C₆₇	—	2	3	no	—
120	#121×C₆₇	—	2	3	no	—
121	#121×C₆₇	C₂³	1	3	yes	—
122	#121×C₆₇	C₂³	1	6	yes	complemented
123	#121×C₆₇	C₂³	1	3	yes	complemented
124	#120×C₆₇	—	2	3	no	—
125	#120×C₆₇	—	2	6	no	—
126	C₄×Q₈×C₆₇	—	2	1	no	—
127	C₄×D₄×C₆₇	—	2	3	no	—
128	C₄×D₄×C₆₇	—	2	3	no	—
129	C₄×D₄×C₆₇	—	2	3	no	—
130	#117×C₆₇	C₂³	1	3	yes	complemented
131	C₂×C₄⋊C₄×C₆₇	C₂³	1	3	yes	complemented
132	C₂×C₂²⋊C₄×C₆₇	—	2	3	no	—
133	#103×C₆₇	C₂³	1	6	yes	complemented
134	#103×C₆₇	C₂³	1	2	yes	complemented
135	#102×C₆₇	C₂³	1	12	yes	complemented
136	#102×C₆₇	C₂³	1	6	yes	complemented
137	#102×C₆₇	C₂³	1	6	yes	complemented
138	C₂²⋊C₈×C₆₇	C₂³	1	3	yes	—
139	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
140	C₂²⋊C₈×C₆₇	C₂³	1	6	yes	complemented
141	C₂²⋊C₈×C₆₇	C₂³	1	6	yes	complemented
142	C₂⁴×C₆₇	—	2	24	no	—
143	C₂⁴×C₆₇	—	2	3	no	—
144	C₂⁴×C₆₇	—	2	6	no	—
145	C₂⁴×C₆₇	—	2	6	no	—
146	C₂⁴×C₆₇	—	2	3	no	—
147	C₂⁴×C₆₇	—	8	6	no	—
148	C₂⁴×C₆₇	—	8	6	no	—
149	C₂⁴×C₆₇	C₂×D₄	1	3	yes	—
150	#41×C₆₇	—	2	24	no	—
151	#41×C₆₇	—	2	48	no	—
152	#41×C₆₇	—	2	24	no	—
153	#41×C₆₇	—	2	16	no	—
154	#41×C₆₇	—	2	4	no	—
155	#41×C₆₇	—	2	12	no	—
156	#41×C₆₇	—	2	12	no	—
157	#41×C₆₇	—	2	12	no	—
158	#41×C₆₇	—	2	12	no	—
159	#41×C₆₇	—	2	12	no	—
160	#41×C₆₇	—	2	12	no	—
161	#41×C₆₇	—	4	4	no	—
162	#41×C₆₇	C₂×D₄	1	8	yes	—
163	#41×C₆₇	C₂×D₄	1	24	yes	complemented
164	C₂×Q₈×C₆₇	—	2	4	no	—
165	C₂×Q₈×C₆₇	—	2	4	no	—
166	C₂×Q₈×C₆₇	—	2	1	no	—
167	C₂×Q₈×C₆₇	C₂×D₄	1	3	yes	—
168	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
169	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
170	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
171	C₂×D₄×C₆₇	—	2	24	no	—
172	C₂×D₄×C₆₇	—	2	24	no	—
173	C₂×D₄×C₆₇	—	2	96	no	—
174	C₂×D₄×C₆₇	—	2	24	no	—
175	C₂×D₄×C₆₇	—	2	48	no	—
176	C₂×D₄×C₆₇	—	2	24	no	—
177	C₂×D₄×C₆₇	—	2	6	no	—
178	C₂×D₄×C₆₇	—	2	6	no	—
179	C₂×D₄×C₆₇	—	2	12	no	—
180	C₂×D₄×C₆₇	—	2	48	no	—
181	C₂×D₄×C₆₇	—	2	12	no	—
182	C₂×D₄×C₆₇	—	2	24	no	—
183	C₂×D₄×C₆₇	—	2	3	no	—
184	C₂×D₄×C₆₇	—	2	3	no	—
185	C₂×D₄×C₆₇	—	2	3	no	—
186	C₂×D₄×C₆₇	—	2	6	no	—
187	C₂×D₄×C₆₇	—	2	6	no	—
188	C₂×D₄×C₆₇	—	2	3	no	—
189	C₂×D₄×C₆₇	—	2	6	no	—
190	C₂×D₄×C₆₇	—	2	12	no	—
191	C₂×D₄×C₆₇	—	2	12	no	—
192	C₂×D₄×C₆₇	—	2	3	no	—
193	C₂×D₄×C₆₇	—	4	12	no	—
194	C₂×D₄×C₆₇	—	8	6	no	—
195	C₂×D₄×C₆₇	C₂×D₄	1	6	yes	—
196	C₂×D₄×C₆₇	C₂×D₄	1	3	yes	—
197	C₂×D₄×C₆₇	C₂×D₄	1	3	yes	—
198	C₂×D₄×C₆₇	C₂×D₄	1	24	yes	complemented
199	C₂×D₄×C₆₇	C₂⁴	1	3	yes	—
200	C₂×D₄×C₆₇	C₂⁴	1	6	yes	—
201	C₂²×C₄×C₆₇	—	2	24	no	—
202	C₂²×C₄×C₆₇	—	2	1	no	—
203	C₂²×C₄×C₆₇	—	2	6	no	—
204	C₂²×C₄×C₆₇	—	2	6	no	—
205	C₂²×C₄×C₆₇	—	2	12	no	—
206	C₂²×C₄×C₆₇	—	2	3	no	—
207	C₂²×C₄×C₆₇	—	2	3	no	—
208	C₂²×C₄×C₆₇	C₂×D₄	1	3	yes	—
209	C₂²×C₄×C₆₇	C₂×D₄	1	3	yes	—
210	C₂²×C₄×C₆₇	C₂×D₄	1	3	yes	—
211	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
212	C₂²×C₄×C₆₇	C₂⁴	1	3	yes	—
213	C₂²×C₄×C₆₇	C₂⁴	1	3	yes	—
214	Q₁₆×C₆₇	—	2	4	no	—
215	SD₁₆×C₆₇	—	2	12	no	—
216	SD₁₆×C₆₇	—	2	12	no	—
217	D₈×C₆₇	—	2	12	no	—
218	D₈×C₆₇	—	2	24	no	—
219	M₁₆×C₆₇	—	2	12	no	—
220	C₂×C₈×C₆₇	—	2	12	no	—
221	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
222	C₂×C₈×C₆₇	C₂⁴	1	6	yes	—
223	C₄⋊C₄×C₆₇	—	2	3	no	—
224	C₄⋊C₄×C₆₇	—	2	1	no	—
225	C₄⋊C₄×C₆₇	—	2	3	no	—
226	C₄⋊C₄×C₆₇	C₂⁴	1	3	yes	—
227	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
228	C₂²⋊C₄×C₆₇	—	2	3	no	—
229	C₂²⋊C₄×C₆₇	—	2	1	no	—
230	C₂²⋊C₄×C₆₇	—	2	3	no	—
231	C₂²⋊C₄×C₆₇	—	2	3	no	—
232	C₂²⋊C₄×C₆₇	—	2	6	no	—
233	C₂²⋊C₄×C₆₇	—	2	3	no	—
234	C₄²×C₆₇	—	2	3	no	—
235	C₂³×C₆₇	—	2	12	no	—
236	C₂³×C₆₇	—	2	24	no	—
237	C₂³×C₆₇	—	2	6	no	—
238	C₂³×C₆₇	—	2	6	no	—
239	C₂³×C₆₇	—	2	6	no	—
240	C₂³×C₆₇	—	2	24	no	—
241	C₂³×C₆₇	—	2	3	no	—
242	C₂³×C₆₇	—	4	3	no	—
243	C₂³×C₆₇	—	4	6	no	—
244	C₂³×C₆₇	—	4	6	no	—
245	C₂³×C₆₇	—	4	6	no	—
246	C₂³×C₆₇	—	8	6	no	—
247	C₂³×C₆₇	—	8	6	no	—
248	C₂³×C₆₇	—	8	6	no	—
249	C₂³×C₆₇	—	8	6	no	—
250	C₂³×C₆₇	—	8	3	no	—
251	C₂³×C₆₇	—	8	3	no	—
252	C₂³×C₆₇	—	8	48	no	—
253	C₂³×C₆₇	C₂²×D₄	1	3	yes	—
254	C₂³×C₆₇	C₂²×D₄	1	3	yes	—
255	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
256	Q₈×C₆₇	—	2	4	no	—
257	Q₈×C₆₇	—	2	6	no	—
258	Q₈×C₆₇	—	2	2	no	—
259	Q₈×C₆₇	—	2	2	no	—
260	Q₈×C₆₇	#120	1	4	yes	—
261	Q₈×C₆₇	C₂²×D₄	1	4	yes	—
262	D₄×C₆₇	—	2	24	no	—
263	D₄×C₆₇	—	2	24	no	—
264	D₄×C₆₇	—	2	12	no	—
265	D₄×C₆₇	—	2	24	no	—
266	D₄×C₆₇	—	2	12	no	—
267	D₄×C₆₇	—	2	6	no	—
268	D₄×C₆₇	—	2	24	no	—
269	D₄×C₆₇	—	2	6	no	—
270	D₄×C₆₇	—	2	6	no	—
271	D₄×C₆₇	—	4	6	no	—
272	D₄×C₆₇	—	4	6	no	—
273	D₄×C₆₇	—	4	6	no	—
274	D₄×C₆₇	—	8	3	no	—
275	D₄×C₆₇	—	8	6	no	—
276	D₄×C₆₇	#120	1	12	yes	—
277	D₄×C₆₇	C₂²×D₄	1	12	yes	—
278	C₂×C₄×C₆₇	—	2	4	no	—
279	C₂×C₄×C₆₇	—	2	24	no	—
280	C₂×C₄×C₆₇	—	2	6	no	—
281	C₂×C₄×C₆₇	—	2	2	no	—
282	C₂×C₄×C₆₇	—	2	6	no	—
283	C₂×C₄×C₆₇	—	2	24	no	—
284	C₂×C₄×C₆₇	—	2	6	no	—
285	C₂×C₄×C₆₇	—	2	2	no	—
286	C₂×C₄×C₆₇	—	2	6	no	—
287	C₂×C₄×C₆₇	—	2	1	no	—
288	C₂×C₄×C₆₇	—	2	3	no	—
289	C₂×C₄×C₆₇	—	2	1	no	—
290	C₂×C₄×C₆₇	—	4	6	no	—
291	C₂×C₄×C₆₇	—	8	3	no	—
292	C₂×C₄×C₆₇	C₂²×D₄	1	3	yes	—
293	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
294	C₂×C₄×C₆₇	C₂²×D₄	1	3	yes	—
295	C₂×C₄×C₆₇	C₂²×D₄	1	12	yes	—
296	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
297	C₈×C₆₇	—	2	2	no	—
298	C₈×C₆₇	—	2	6	no	—
299	C₂²×C₆₇	—	2	1	no	—
300	C₂²×C₆₇	—	2	3	no	—
301	C₂²×C₆₇	—	2	1	no	—
302	C₂²×C₆₇	—	2	3	no	—
303	C₂²×C₆₇	—	2	3	no	—
304	C₂²×C₆₇	—	2	3	no	—
305	C₂²×C₆₇	—	2	12	no	—
306	C₂²×C₆₇	—	2	3	no	—
307	C₂²×C₆₇	—	4	12	no	—
308	C₂²×C₆₇	—	4	24	no	—
309	C₂²×C₆₇	—	4	6	no	—
310	C₂²×C₆₇	—	4	6	no	—
311	C₂²×C₆₇	—	4	3	no	—
312	C₂²×C₆₇	—	4	3	no	—
313	C₂²×C₆₇	—	4	3	no	—
314	C₂²×C₆₇	—	8	24	no	—
315	C₂²×C₆₇	—	8	24	no	—
316	C₂²×C₆₇	—	16	6	no	—
317	C₂²×C₆₇	C₂×#120	1	6	yes	—
318	C₂²×C₆₇	#576	1	2	yes	complemented
319	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
320	C₄×C₆₇	—	2	4	no	—
321	C₄×C₆₇	—	2	3	no	—
322	C₄×C₆₇	—	2	1	no	—
323	C₄×C₆₇	—	4	1	no	—
324	C₄×C₆₇	—	4	1	no	—
325	C₄×C₆₇	—	4	3	no	—
326	C₄×C₆₇	C₂×#120	1	6	yes	—
327	C₄×C₆₇	C₂³×D₄	1	2	yes	—
328	#60372	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
329	C₂×C₆₇	—	2	2	no	—
330	C₂×C₆₇	—	2	6	no	—
331	C₂×C₆₇	—	4	3	no	—
332	C₂×C₆₇	—	4	12	no	—
333	C₂×C₆₇	—	8	3	no	—
334	C₂×C₆₇	C₂²×#120	1	1	yes	characteristic
335	C₂×C₆₇	C₂×#576	1	1	yes	characteristic
336	C₂×C₆₇	#3585	1	1	yes	characteristic
337	C₂²×H(5,𝔽₂)	C₂×C₆₇	1	1	yes	characteristic, complemented
338	C₂×#576	C₂×C₆₇	1	2	yes	complemented
339	#3488	C₂×C₆₇	1	1	yes	characteristic, complemented
340	#3012	C₂×C₆₇	1	6	yes	complemented
341	#3008	C₂×C₆₇	1	6	yes	complemented
342	#3006	C₂×C₆₇	1	3	yes	complemented
343	#3003	C₂×C₆₇	1	3	yes	complemented
344	#3002	C₂×C₆₇	1	3	yes	complemented
345	C₂×#447	C₂×C₆₇	1	3	yes	complemented
346	#2897	C₂×C₆₇	1	2	yes	complemented
347	#2880	C₂×C₆₇	1	1	yes	characteristic, complemented
348	C₆₇	#60372	1	1	yes	characteristic, direct product factor, Sylow
349	C₂×H(5,𝔽₂)	—	2	16	no	—
350	C₂×H(5,𝔽₂)	—	2	3	no	—
351	C₂×H(5,𝔽₂)	—	2	1	no	—
352	C₂×H(5,𝔽₂)	C₂²×C₆₇	1	2	yes	—
353	C₂×H(5,𝔽₂)	C₂²×C₆₇	1	6	yes	complemented
354	C₂×H(5,𝔽₂)	C₂²×C₆₇	1	1	yes	characteristic, complemented
355	C₂²×#41	—	2	1	no	—
356	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
357	C₂²×#41	C₂²×C₆₇	1	3	yes	complemented
358	C₂³×D₄	—	2	3	no	—
359	C₂³×D₄	C₂²×C₆₇	1	3	yes	complemented
360	#576	—	2	16	no	—
361	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	6	yes	complemented
362	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	6	yes	complemented
363	C₂×#135	C₂²×C₆₇	1	6	yes	complemented
364	C₂²×D₈	C₂²×C₆₇	1	6	yes	complemented
365	C₂×#131	C₂²×C₆₇	1	2	yes	complemented
366	#550	—	2	1	no	—
367	#548	—	2	1	no	—
368	#546	—	2	3	no	—
369	D₄²	—	2	3	no	—
370	#537	C₂²×C₆₇	1	3	yes	complemented
371	#535	C₂²×C₆₇	1	3	yes	complemented
372	#525	C₂²×C₆₇	1	3	yes	complemented
373	C₂×#121	C₂²×C₆₇	1	3	yes	complemented
374	#520	C₂²×C₆₇	1	1	yes	characteristic, complemented
375	#452	C₂²×C₆₇	1	6	yes	complemented
376	#451	C₂²×C₆₇	1	1	yes	characteristic, complemented
377	#450	C₂²×C₆₇	1	3	yes	complemented
378	#450	C₂²×C₆₇	1	6	yes	complemented
379	#449	C₂²×C₆₇	1	6	yes	complemented
380	#449	C₂²×C₆₇	1	12	yes	complemented
381	#448	C₂²×C₆₇	1	3	yes	complemented
382	#447	C₂²×C₆₇	1	3	yes	complemented
383	#447	C₂²×C₆₇	1	6	yes	complemented
384	#447	C₂²×C₆₇	1	12	yes	complemented
385	#447	C₂²×C₆₇	1	6	yes	complemented
386	#418	C₂²×C₆₇	1	6	yes	complemented
387	#417	C₂²×C₆₇	1	6	yes	complemented
388	#416	C₂²×C₆₇	1	6	yes	complemented
389	C₂×#102	C₂²×C₆₇	1	6	yes	complemented
390	#408	C₂²×C₆₇	1	6	yes	complemented
391	#407	C₂²×C₆₇	1	3	yes	complemented
392	C₂×C₂²⋊C₈	C₂²×C₆₇	1	3	yes	complemented
393	C₂⁵	—	2	3	no	—
394	H(5,𝔽₂)	—	2	16	no	—
395	H(5,𝔽₂)	—	2	48	no	—
396	H(5,𝔽₂)	—	2	8	no	—
397	H(5,𝔽₂)	—	2	24	no	—
398	H(5,𝔽₂)	—	2	24	no	—
399	H(5,𝔽₂)	—	2	8	no	—
400	H(5,𝔽₂)	D₄×C₆₇	1	16	yes	complemented
401	C₂×#41	—	2	16	no	—
402	C₂×#41	—	2	8	no	—
403	C₂×#41	—	2	24	no	—
404	C₂×#41	—	2	2	no	—
405	C₂×#41	—	2	6	no	—
406	C₂×#41	—	2	1	no	—
407	C₂×#41	—	2	3	no	—
408	C₂×#41	—	2	3	no	—
409	C₂×#41	D₄×C₆₇	1	3	yes	—
410	C₂×#41	D₄×C₆₇	1	1	yes	characteristic
411	C₂×#41	C₂³×C₆₇	1	6	yes	—
412	C₂×#41	C₂³×C₆₇	1	6	yes	—
413	C₂×#41	C₂³×C₆₇	1	3	yes	—
414	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
415	C₂×#41	C₂³×C₆₇	1	3	yes	complemented
416	C₂²×Q₈	D₄×C₆₇	1	1	yes	characteristic
417	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
418	C₂²×D₄	—	2	48	no	—
419	C₂²×D₄	—	2	3	no	—
420	C₂²×D₄	—	2	6	no	—
421	C₂²×D₄	—	2	12	no	—
422	C₂²×D₄	—	2	6	no	—
423	C₂²×D₄	—	2	24	no	—
424	C₂²×D₄	—	2	3	no	—
425	C₂²×D₄	—	2	3	no	—
426	C₂²×D₄	—	2	3	no	—
427	C₂²×D₄	—	2	3	no	—
428	C₂²×D₄	—	2	3	no	—
429	C₂²×D₄	D₄×C₆₇	1	3	yes	—
430	C₂²×D₄	C₂³×C₆₇	1	3	yes	—
431	C₂²×D₄	C₂³×C₆₇	1	6	yes	—
432	C₂²×D₄	C₂³×C₆₇	1	6	yes	—
433	C₂²×D₄	C₂³×C₆₇	1	3	yes	complemented
434	C₂³×C₄	—	2	3	no	—
435	C₂³×C₄	C₂³×C₆₇	1	3	yes	—
436	AGL(1,ℤ/8)	—	2	24	no	—
437	AGL(1,ℤ/8)	—	2	24	no	—
438	#135	—	2	24	no	—
439	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	complemented
440	C₂×SD₁₆	C₂³×C₆₇	1	6	yes	complemented
441	C₂×SD₁₆	C₂³×C₆₇	1	6	yes	complemented
442	C₂×D₈	—	2	24	no	—
443	C₂×D₈	C₂³×C₆₇	1	6	yes	complemented
444	C₂×D₈	C₂³×C₆₇	1	12	yes	complemented
445	#131	—	2	8	no	—
446	C₂×M₁₆	C₂³×C₆₇	1	6	yes	complemented
447	C₂²×C₈	C₂³×C₆₇	1	6	yes	complemented
448	#127	—	2	3	no	—
449	#124	—	2	3	no	—
450	#123	—	2	3	no	—
451	C₂²⋊Q₈	—	2	3	no	—
452	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
453	C₂²⋊Q₈	C₂³×C₆₇	1	3	yes	complemented
454	#121	—	2	6	no	—
455	#121	—	2	3	no	—
456	#121	—	2	3	no	—
457	#121	—	2	3	no	—
458	#121	C₂³×C₆₇	1	3	yes	—
459	#121	C₂³×C₆₇	1	6	yes	complemented
460	#121	C₂³×C₆₇	1	3	yes	complemented
461	#120	—	2	3	no	—
462	#120	—	2	6	no	—
463	C₄×Q₈	—	2	1	no	—
464	C₄×D₄	—	2	3	no	—
465	C₄×D₄	—	2	3	no	—
466	C₄×D₄	—	2	3	no	—
467	#117	C₂³×C₆₇	1	3	yes	complemented
468	C₂×C₄⋊C₄	C₂³×C₆₇	1	3	yes	complemented
469	C₂×C₂²⋊C₄	—	2	3	no	—
470	#103	C₂³×C₆₇	1	2	yes	complemented
471	#103	C₂³×C₆₇	1	6	yes	complemented
472	#102	C₂³×C₆₇	1	6	yes	complemented
473	#102	C₂³×C₆₇	1	12	yes	complemented
474	#102	C₂³×C₆₇	1	6	yes	complemented
475	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
476	C₂²⋊C₈	C₂³×C₆₇	1	3	yes	—
477	C₂²⋊C₈	C₂³×C₆₇	1	6	yes	complemented
478	C₂²⋊C₈	C₂³×C₆₇	1	6	yes	complemented
479	C₂⁴	—	2	24	no	—
480	C₂⁴	—	2	3	no	—
481	C₂⁴	—	2	6	no	—
482	C₂⁴	—	2	6	no	—
483	C₂⁴	—	2	3	no	—
484	C₂⁴	—	8	6	no	—
485	C₂⁴	—	8	6	no	—
486	C₂⁴	C₂×D₄×C₆₇	1	3	yes	—
487	#41	—	2	24	no	—
488	#41	—	2	48	no	—
489	#41	—	2	24	no	—
490	#41	—	2	16	no	—
491	#41	—	2	4	no	—
492	#41	—	2	12	no	—
493	#41	—	2	12	no	—
494	#41	—	2	12	no	—
495	#41	—	2	12	no	—
496	#41	—	2	12	no	—
497	#41	—	2	12	no	—
498	#41	—	4	4	no	—
499	#41	C₂×D₄×C₆₇	1	8	yes	—
500	#41	C₂×D₄×C₆₇	1	24	yes	complemented
501	C₂×Q₈	—	2	4	no	—
502	C₂×Q₈	—	2	4	no	—
503	C₂×Q₈	—	2	1	no	—
504	C₂×Q₈	C₂×D₄×C₆₇	1	3	yes	—
505	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
506	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
507	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
508	C₂×D₄	—	2	24	no	—
509	C₂×D₄	—	2	24	no	—
510	C₂×D₄	—	2	96	no	—
511	C₂×D₄	—	2	24	no	—
512	C₂×D₄	—	2	48	no	—
513	C₂×D₄	—	2	24	no	—
514	C₂×D₄	—	2	6	no	—
515	C₂×D₄	—	2	6	no	—
516	C₂×D₄	—	2	12	no	—
517	C₂×D₄	—	2	48	no	—
518	C₂×D₄	—	2	12	no	—
519	C₂×D₄	—	2	24	no	—
520	C₂×D₄	—	2	3	no	—
521	C₂×D₄	—	2	3	no	—
522	C₂×D₄	—	2	3	no	—
523	C₂×D₄	—	2	6	no	—
524	C₂×D₄	—	2	6	no	—
525	C₂×D₄	—	2	3	no	—
526	C₂×D₄	—	2	6	no	—
527	C₂×D₄	—	2	12	no	—
528	C₂×D₄	—	2	12	no	—
529	C₂×D₄	—	2	3	no	—
530	C₂×D₄	—	4	12	no	—
531	C₂×D₄	—	8	6	no	—
532	C₂×D₄	C₂×D₄×C₆₇	1	6	yes	—
533	C₂×D₄	C₂×D₄×C₆₇	1	3	yes	—
534	C₂×D₄	C₂×D₄×C₆₇	1	3	yes	—
535	C₂×D₄	C₂×D₄×C₆₇	1	24	yes	complemented
536	C₂×D₄	C₂⁴×C₆₇	1	3	yes	—
537	C₂×D₄	C₂⁴×C₆₇	1	6	yes	—
538	C₂²×C₄	—	2	24	no	—
539	C₂²×C₄	—	2	1	no	—
540	C₂²×C₄	—	2	6	no	—
541	C₂²×C₄	—	2	6	no	—
542	C₂²×C₄	—	2	12	no	—
543	C₂²×C₄	—	2	3	no	—
544	C₂²×C₄	—	2	3	no	—
545	C₂²×C₄	C₂×D₄×C₆₇	1	3	yes	—
546	C₂²×C₄	C₂×D₄×C₆₇	1	3	yes	—
547	C₂²×C₄	C₂×D₄×C₆₇	1	3	yes	—
548	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
549	C₂²×C₄	C₂⁴×C₆₇	1	3	yes	—
550	C₂²×C₄	C₂⁴×C₆₇	1	3	yes	—
551	Q₁₆	—	2	4	no	—
552	SD₁₆	—	2	12	no	—
553	SD₁₆	—	2	12	no	—
554	D₈	—	2	12	no	—
555	D₈	—	2	24	no	—
556	M₁₆	—	2	12	no	—
557	C₂×C₈	—	2	12	no	—
558	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
559	C₂×C₈	C₂⁴×C₆₇	1	6	yes	—
560	C₄⋊C₄	—	2	3	no	—
561	C₄⋊C₄	—	2	1	no	—
562	C₄⋊C₄	—	2	3	no	—
563	C₄⋊C₄	C₂⁴×C₆₇	1	3	yes	—
564	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
565	C₂²⋊C₄	—	2	3	no	—
566	C₂²⋊C₄	—	2	1	no	—
567	C₂²⋊C₄	—	2	3	no	—
568	C₂²⋊C₄	—	2	3	no	—
569	C₂²⋊C₄	—	2	6	no	—
570	C₂²⋊C₄	—	2	3	no	—
571	C₄²	—	2	3	no	—
572	C₂³	—	2	12	no	—
573	C₂³	—	2	24	no	—
574	C₂³	—	2	6	no	—
575	C₂³	—	2	6	no	—
576	C₂³	—	2	6	no	—
577	C₂³	—	2	24	no	—
578	C₂³	—	2	3	no	—
579	C₂³	—	4	3	no	—
580	C₂³	—	4	6	no	—
581	C₂³	—	4	6	no	—
582	C₂³	—	4	6	no	—
583	C₂³	—	8	6	no	—
584	C₂³	—	8	6	no	—
585	C₂³	—	8	6	no	—
586	C₂³	—	8	6	no	—
587	C₂³	—	8	3	no	—
588	C₂³	—	8	3	no	—
589	C₂³	—	8	48	no	—
590	C₂³	C₂²×D₄×C₆₇	1	3	yes	—
591	C₂³	C₂²×D₄×C₆₇	1	3	yes	—
592	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
593	Q₈	—	2	4	no	—
594	Q₈	—	2	6	no	—
595	Q₈	—	2	2	no	—
596	Q₈	—	2	2	no	—
597	Q₈	#120×C₆₇	1	4	yes	—
598	Q₈	C₂²×D₄×C₆₇	1	4	yes	—
599	D₄	—	2	24	no	—
600	D₄	—	2	24	no	—
601	D₄	—	2	12	no	—
602	D₄	—	2	24	no	—
603	D₄	—	2	12	no	—
604	D₄	—	2	6	no	—
605	D₄	—	2	24	no	—
606	D₄	—	2	6	no	—
607	D₄	—	2	6	no	—
608	D₄	—	4	6	no	—
609	D₄	—	4	6	no	—
610	D₄	—	4	6	no	—
611	D₄	—	8	6	no	—
612	D₄	—	8	3	no	—
613	D₄	#120×C₆₇	1	12	yes	—
614	D₄	C₂²×D₄×C₆₇	1	12	yes	—
615	C₂×C₄	—	2	4	no	—
616	C₂×C₄	—	2	24	no	—
617	C₂×C₄	—	2	6	no	—
618	C₂×C₄	—	2	2	no	—
619	C₂×C₄	—	2	6	no	—
620	C₂×C₄	—	2	24	no	—
621	C₂×C₄	—	2	6	no	—
622	C₂×C₄	—	2	2	no	—
623	C₂×C₄	—	2	6	no	—
624	C₂×C₄	—	2	1	no	—
625	C₂×C₄	—	2	3	no	—
626	C₂×C₄	—	2	1	no	—
627	C₂×C₄	—	4	6	no	—
628	C₂×C₄	—	8	3	no	—
629	C₂×C₄	C₂²×D₄×C₆₇	1	3	yes	—
630	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
631	C₂×C₄	C₂²×D₄×C₆₇	1	3	yes	—
632	C₂×C₄	C₂²×D₄×C₆₇	1	12	yes	—
633	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
634	C₈	—	2	2	no	—
635	C₈	—	2	6	no	—
636	C₂²	—	2	3	no	—
637	C₂²	—	2	1	no	—
638	C₂²	—	2	3	no	—
639	C₂²	—	2	1	no	—
640	C₂²	—	2	3	no	—
641	C₂²	—	2	3	no	—
642	C₂²	—	2	3	no	—
643	C₂²	—	2	12	no	—
644	C₂²	—	4	12	no	—
645	C₂²	—	4	24	no	—
646	C₂²	—	4	6	no	—
647	C₂²	—	4	6	no	—
648	C₂²	—	4	3	no	—
649	C₂²	—	4	3	no	—
650	C₂²	—	4	3	no	—
651	C₂²	—	8	24	no	—
652	C₂²	—	8	24	no	—
653	C₂²	—	16	6	no	—
654	C₂²	C₂×#120×C₆₇	1	6	yes	—
655	C₂²	#576×C₆₇	1	2	yes	complemented
656	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
657	C₄	—	2	4	no	—
658	C₄	—	2	3	no	—
659	C₄	—	2	1	no	—
660	C₄	—	4	3	no	—
661	C₄	—	4	1	no	—
662	C₄	—	4	1	no	—
663	C₄	C₂×#120×C₆₇	1	6	yes	—
664	C₄	C₂³×D₄×C₆₇	1	2	yes	—
665	C₂	—	2	2	no	—
666	C₂	—	2	6	no	—
667	C₂	—	4	3	no	—
668	C₂	—	4	12	no	—
669	C₂	—	8	3	no	—
670	C₂	C₂²×#120×C₆₇	1	1	yes	characteristic
671	C₂	C₂×#576×C₆₇	1	1	yes	characteristic
672	C₂	C₆₇×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×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. C₂×#576×C₆₇	C₂	semidirect
3. C₆₇×#3488	C₂	semidirect
4. C₆₇×#3012	C₂	semidirect
5. C₆₇×#3008	C₂	semidirect
6. C₆₇×#3006	C₂	semidirect
7. C₆₇×#3003	C₂	semidirect
8. C₆₇×#3002	C₂	semidirect
9. C₂×#447×C₆₇	C₂	semidirect
10. C₆₇×#2897	C₂	semidirect
11. C₆₇×#2880	C₂	semidirect
16. C₂×H(5,𝔽₂)×C₆₇	C₂²	semidirect
17. C₂×H(5,𝔽₂)×C₆₇	C₂²	semidirect
20. C₂²×#41×C₆₇	C₂²	semidirect
22. C₂³×D₄×C₆₇	C₂²	semidirect
24. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
25. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
26. C₂×#135×C₆₇	C₂²	semidirect
27. C₂²×D₈×C₆₇	C₂²	semidirect
28. C₂×#131×C₆₇	C₂²	semidirect
33. #537×C₆₇	C₂²	semidirect
34. #535×C₆₇	C₂²	semidirect
35. #525×C₆₇	C₂²	semidirect
36. C₂×#121×C₆₇	C₂²	semidirect
37. #520×C₆₇	C₂²	semidirect
38. #452×C₆₇	C₂²	semidirect
39. #451×C₆₇	C₂²	semidirect
40. #450×C₆₇	C₂²	semidirect
41. #450×C₆₇	C₂²	semidirect
42. #449×C₆₇	C₂²	semidirect
43. #449×C₆₇	C₂²	semidirect
44. #448×C₆₇	C₂²	semidirect
45. #447×C₆₇	C₂²	semidirect
46. #447×C₆₇	C₂²	semidirect
47. #447×C₆₇	C₂²	semidirect
48. #447×C₆₇	C₂²	semidirect
49. #418×C₆₇	C₂²	semidirect
50. #417×C₆₇	C₂²	semidirect
51. #416×C₆₇	C₂²	semidirect
52. C₂×#102×C₆₇	C₂²	semidirect
53. #408×C₆₇	C₂²	semidirect
54. #407×C₆₇	C₂²	semidirect
55. C₂×C₂²⋊C₈×C₆₇	C₂²	semidirect
63. H(5,𝔽₂)×C₆₇	D₄	semidirect
78. C₂×#41×C₆₇	C₂³	semidirect
96. C₂²×D₄×C₆₇	C₂³	semidirect
102. C₂×Q₁₆×C₆₇	C₂³	semidirect
103. C₂×SD₁₆×C₆₇	C₂³	semidirect
104. C₂×SD₁₆×C₆₇	C₂³	semidirect
106. C₂×D₈×C₆₇	C₂³	semidirect
107. C₂×D₈×C₆₇	C₂³	semidirect
109. C₂×M₁₆×C₆₇	C₂³	semidirect
110. C₂²×C₈×C₆₇	C₂³	semidirect
116. C₂²⋊Q₈×C₆₇	C₂³	semidirect
122. #121×C₆₇	C₂³	semidirect
123. #121×C₆₇	C₂³	semidirect
130. #117×C₆₇	C₂³	semidirect
131. C₂×C₄⋊C₄×C₆₇	C₂³	semidirect
133. #103×C₆₇	C₂³	semidirect
134. #103×C₆₇	C₂³	semidirect
135. #102×C₆₇	C₂³	semidirect
136. #102×C₆₇	C₂³	semidirect
137. #102×C₆₇	C₂³	semidirect
140. C₂²⋊C₈×C₆₇	C₂³	semidirect
141. C₂²⋊C₈×C₆₇	C₂³	semidirect
163. #41×C₆₇	C₂×D₄	semidirect
198. C₂×D₄×C₆₇	C₂×D₄	semidirect
318. C₂²×C₆₇	#576	semidirect
328. #60372	C₆₇	direct (N × H)
337. C₂²×H(5,𝔽₂)	C₂×C₆₇	semidirect
338. C₂×#576	C₂×C₆₇	semidirect
339. #3488	C₂×C₆₇	semidirect
340. #3012	C₂×C₆₇	semidirect
341. #3008	C₂×C₆₇	semidirect
342. #3006	C₂×C₆₇	semidirect
343. #3003	C₂×C₆₇	semidirect
344. #3002	C₂×C₆₇	semidirect
345. C₂×#447	C₂×C₆₇	semidirect
346. #2897	C₂×C₆₇	semidirect
347. #2880	C₂×C₆₇	semidirect
348. C₆₇	#60372	direct (N × H)
353. C₂×H(5,𝔽₂)	C₂²×C₆₇	semidirect
354. C₂×H(5,𝔽₂)	C₂²×C₆₇	semidirect
357. C₂²×#41	C₂²×C₆₇	semidirect
359. C₂³×D₄	C₂²×C₆₇	semidirect
361. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
362. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
363. C₂×#135	C₂²×C₆₇	semidirect
364. C₂²×D₈	C₂²×C₆₇	semidirect
365. C₂×#131	C₂²×C₆₇	semidirect
370. #537	C₂²×C₆₇	semidirect
371. #535	C₂²×C₆₇	semidirect
372. #525	C₂²×C₆₇	semidirect
373. C₂×#121	C₂²×C₆₇	semidirect
374. #520	C₂²×C₆₇	semidirect
375. #452	C₂²×C₆₇	semidirect
376. #451	C₂²×C₆₇	semidirect
377. #450	C₂²×C₆₇	semidirect
378. #450	C₂²×C₆₇	semidirect
379. #449	C₂²×C₆₇	semidirect
380. #449	C₂²×C₆₇	semidirect
381. #448	C₂²×C₆₇	semidirect
382. #447	C₂²×C₆₇	semidirect
383. #447	C₂²×C₆₇	semidirect
384. #447	C₂²×C₆₇	semidirect
385. #447	C₂²×C₆₇	semidirect
386. #418	C₂²×C₆₇	semidirect
387. #417	C₂²×C₆₇	semidirect
388. #416	C₂²×C₆₇	semidirect
389. C₂×#102	C₂²×C₆₇	semidirect
390. #408	C₂²×C₆₇	semidirect
391. #407	C₂²×C₆₇	semidirect
392. C₂×C₂²⋊C₈	C₂²×C₆₇	semidirect
400. H(5,𝔽₂)	D₄×C₆₇	semidirect
415. C₂×#41	C₂³×C₆₇	semidirect
433. C₂²×D₄	C₂³×C₆₇	semidirect
439. C₂×Q₁₆	C₂³×C₆₇	semidirect
440. C₂×SD₁₆	C₂³×C₆₇	semidirect
441. C₂×SD₁₆	C₂³×C₆₇	semidirect
443. C₂×D₈	C₂³×C₆₇	semidirect
444. C₂×D₈	C₂³×C₆₇	semidirect
446. C₂×M₁₆	C₂³×C₆₇	semidirect
447. C₂²×C₈	C₂³×C₆₇	semidirect
453. C₂²⋊Q₈	C₂³×C₆₇	semidirect
459. #121	C₂³×C₆₇	semidirect
460. #121	C₂³×C₆₇	semidirect
467. #117	C₂³×C₆₇	semidirect
468. C₂×C₄⋊C₄	C₂³×C₆₇	semidirect
470. #103	C₂³×C₆₇	semidirect
471. #103	C₂³×C₆₇	semidirect
472. #102	C₂³×C₆₇	semidirect
473. #102	C₂³×C₆₇	semidirect
474. #102	C₂³×C₆₇	semidirect
477. C₂²⋊C₈	C₂³×C₆₇	semidirect
478. C₂²⋊C₈	C₂³×C₆₇	semidirect
500. #41	C₂×D₄×C₆₇	semidirect
535. C₂×D₄	C₂×D₄×C₆₇	semidirect
655. C₂²	#576×C₆₇	semidirect

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
C₂×#576×C₆₇	2
C₆₇×#3488	2
C₆₇×#3012	2
C₆₇×#3008	2
C₆₇×#3006	2
C₆₇×#3003	2
C₆₇×#3002	2
C₂×#447×C₆₇	2
C₆₇×#2897	2
C₆₇×#2880	2
#60372	67

Subgroups — C67×#60372 #30739623

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#60372 #30739623