Subgroups — C₂×C₆₇×#2606 #30714113

Order 17152.

1966 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#2606	C₂	1	16	yes	maximal, direct product factor
2	C₂×#398×C₆₇	C₂	1	2	yes	maximal
3	C₂×#398×C₆₇	C₂	1	2	yes	maximal
4	C₂×#389×C₆₇	C₂	1	2	yes	maximal
5	C₂×#389×C₆₇	C₂	1	2	yes	maximal
6	C₂×#387×C₆₇	C₂	1	2	yes	maximal
7	C₂×#387×C₆₇	C₂	1	2	yes	maximal
8	C₂×#383×C₆₇	C₂	1	1	yes	maximal, characteristic
9	C₂×C₄×C₄⋊C₄×C₆₇	C₂	1	1	yes	maximal, characteristic
10	C₂×#376×C₆₇	C₂	1	1	yes	maximal, characteristic
11	C₂²×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
12	C₂²×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
13	C₂²×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
14	C₂²×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
15	C₂²×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
16	C₂²×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
17	C₂²×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
18	C₂²×C₄²×C₆₇	C₂²	1	2	yes	—
19	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
20	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
21	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
22	#398×C₆₇	C₂²	1	16	yes	—
23	#398×C₆₇	C₂²	1	16	yes	—
24	#389×C₆₇	C₂²	1	16	yes	—
25	#389×C₆₇	C₂²	1	16	yes	—
26	#387×C₆₇	C₂²	1	16	yes	—
27	#387×C₆₇	C₂²	1	16	yes	—
28	#383×C₆₇	C₂²	1	8	yes	—
29	C₄×C₄⋊C₄×C₆₇	C₂²	1	8	yes	—
30	#376×C₆₇	C₂²	1	8	yes	—
31	C₂×#95×C₆₇	C₂²	1	2	yes	—
32	C₂×#95×C₆₇	C₂²	1	1	yes	characteristic
33	C₂×#95×C₆₇	C₂²	1	1	yes	characteristic
34	C₂×#95×C₆₇	C₂²	1	2	yes	—
35	C₂×#95×C₆₇	C₂²	1	1	yes	characteristic
36	C₂×#95×C₆₇	C₂²	1	2	yes	—
37	C₂×#95×C₆₇	C₂²	1	1	yes	characteristic
38	C₂×#95×C₆₇	C₂²	1	2	yes	—
39	C₂×#95×C₆₇	C₂²	1	2	yes	—
40	C₂×#95×C₆₇	C₂²	1	2	yes	—
41	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
42	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
43	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
44	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
45	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
47	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
48	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
49	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
50	C₂×C₄⋊C₄×C₆₇	—	2	8	no	—
51	C₂×C₄⋊C₄×C₆₇	—	2	8	no	—
52	C₂×C₄⋊C₄×C₆₇	—	2	8	no	—
53	C₂×C₄⋊C₄×C₆₇	—	2	8	no	—
54	C₂×C₄⋊C₄×C₆₇	—	2	8	no	—
55	C₂×C₄⋊C₄×C₆₇	—	4	4	no	—
56	C₂×C₄⋊C₄×C₆₇	—	4	4	no	—
57	C₂×C₄⋊C₄×C₆₇	C₂³	1	8	yes	—
58	C₂×C₄⋊C₄×C₆₇	C₂³	1	8	yes	—
59	C₂×C₄⋊C₄×C₆₇	C₂³	1	8	yes	—
60	C₂×C₄⋊C₄×C₆₇	C₂³	1	8	yes	—
61	C₂×C₄⋊C₄×C₆₇	C₂³	1	8	yes	—
62	C₂×C₄⋊C₄×C₆₇	C₂³	1	8	yes	—
63	C₂×C₄⋊C₄×C₆₇	C₂³	1	8	yes	—
64	C₂×C₄²×C₆₇	—	2	8	no	—
65	C₂×C₄²×C₆₇	—	4	2	no	—
66	C₂×C₄²×C₆₇	—	4	2	no	—
67	C₂×C₄²×C₆₇	Q₈	1	8	yes	—
68	C₂×C₄²×C₆₇	C₂³	1	8	yes	—
69	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
70	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
71	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
72	#95×C₆₇	C₂³	1	8	yes	—
73	#95×C₆₇	C₂³	1	4	yes	—
74	#95×C₆₇	C₂³	1	4	yes	—
75	#95×C₆₇	C₂³	1	8	yes	—
76	#95×C₆₇	C₂³	1	4	yes	—
77	#95×C₆₇	C₂³	1	8	yes	—
78	#95×C₆₇	C₂³	1	4	yes	—
79	#95×C₆₇	C₂³	1	8	yes	—
80	#95×C₆₇	C₂³	1	8	yes	—
81	#95×C₆₇	C₂³	1	8	yes	—
82	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
83	C₂²×C₄×C₆₇	—	2	4	no	—
84	C₂²×C₄×C₆₇	—	2	4	no	—
85	C₂²×C₄×C₆₇	—	2	4	no	—
86	C₂²×C₄×C₆₇	—	2	4	no	—
87	C₂²×C₄×C₆₇	—	2	2	no	—
88	C₂²×C₄×C₆₇	—	2	4	no	—
89	C₂²×C₄×C₆₇	—	2	2	no	—
90	C₂²×C₄×C₆₇	—	2	4	no	—
91	C₂²×C₄×C₆₇	—	2	4	no	—
92	C₂²×C₄×C₆₇	—	2	4	no	—
93	C₂²×C₄×C₆₇	—	2	4	no	—
94	C₂²×C₄×C₆₇	—	2	4	no	—
95	C₂²×C₄×C₆₇	—	2	4	no	—
96	C₂²×C₄×C₆₇	—	2	4	no	—
97	C₂²×C₄×C₆₇	—	2	4	no	—
98	C₂²×C₄×C₆₇	—	2	4	no	—
99	C₂²×C₄×C₆₇	—	2	4	no	—
100	C₂²×C₄×C₆₇	—	2	4	no	—
101	C₂²×C₄×C₆₇	—	2	4	no	—
102	C₂²×C₄×C₆₇	—	2	4	no	—
103	C₂²×C₄×C₆₇	C₂×Q₈	1	4	yes	—
104	C₂²×C₄×C₆₇	C₂×Q₈	1	4	yes	—
105	C₂²×C₄×C₆₇	C₂×Q₈	1	4	yes	—
106	C₂²×C₄×C₆₇	#41	1	8	yes	—
107	C₂²×C₄×C₆₇	#41	1	8	yes	—
108	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
109	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
110	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
111	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
112	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
113	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
114	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
115	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
116	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
117	C₄⋊C₄×C₆₇	—	2	16	no	—
118	C₄⋊C₄×C₆₇	—	2	16	no	—
119	C₄⋊C₄×C₆₇	—	2	16	no	—
120	C₄⋊C₄×C₆₇	—	2	16	no	—
121	C₄⋊C₄×C₆₇	—	2	16	no	—
122	C₄⋊C₄×C₆₇	—	4	8	no	—
123	C₄⋊C₄×C₆₇	—	4	8	no	—
124	C₄²×C₆₇	—	2	16	no	—
125	C₄²×C₆₇	—	4	4	no	—
126	C₄²×C₆₇	—	4	4	no	—
127	C₄²×C₆₇	C₂×Q₈	1	16	yes	—
128	C₂³×C₆₇	C₂²×Q₈	1	2	yes	—
129	C₂³×C₆₇	C₂×#41	1	4	yes	—
130	C₂³×C₆₇	C₂×#41	1	4	yes	—
131	C₂³×C₆₇	H(5,𝔽₂)	1	2	yes	—
132	C₂³×C₆₇	2₋¹⁺⁴	1	2	yes	—
133	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
134	C₂×C₄×C₆₇	—	2	8	no	—
135	C₂×C₄×C₆₇	—	2	8	no	—
136	C₂×C₄×C₆₇	—	2	8	no	—
137	C₂×C₄×C₆₇	—	2	16	no	—
138	C₂×C₄×C₆₇	—	2	16	no	—
139	C₂×C₄×C₆₇	—	2	4	no	—
140	C₂×C₄×C₆₇	—	2	4	no	—
141	C₂×C₄×C₆₇	—	2	4	no	—
142	C₂×C₄×C₆₇	—	2	4	no	—
143	C₂×C₄×C₆₇	—	2	2	no	—
144	C₂×C₄×C₆₇	—	2	4	no	—
145	C₂×C₄×C₆₇	—	2	2	no	—
146	C₂×C₄×C₆₇	—	2	4	no	—
147	C₂×C₄×C₆₇	—	2	4	no	—
148	C₂×C₄×C₆₇	—	2	4	no	—
149	C₂×C₄×C₆₇	—	2	4	no	—
150	C₂×C₄×C₆₇	—	2	4	no	—
151	C₂×C₄×C₆₇	—	2	4	no	—
152	C₂×C₄×C₆₇	—	2	4	no	—
153	C₂×C₄×C₆₇	—	2	4	no	—
154	C₂×C₄×C₆₇	—	2	4	no	—
155	C₂×C₄×C₆₇	—	2	4	no	—
156	C₂×C₄×C₆₇	—	2	4	no	—
157	C₂×C₄×C₆₇	—	2	4	no	—
158	C₂×C₄×C₆₇	—	2	4	no	—
159	C₂×C₄×C₆₇	—	4	8	no	—
160	C₂×C₄×C₆₇	—	4	8	no	—
161	C₂×C₄×C₆₇	—	4	8	no	—
162	C₂×C₄×C₆₇	—	4	8	no	—
163	C₂×C₄×C₆₇	C₂²×Q₈	1	4	yes	—
164	C₂×C₄×C₆₇	C₂²×Q₈	1	4	yes	—
165	C₂×C₄×C₆₇	C₂²×Q₈	1	4	yes	—
166	C₂×C₄×C₆₇	C₂×#41	1	8	yes	—
167	C₂×C₄×C₆₇	C₂×#41	1	8	yes	—
168	C₂²×C₆₇	#533	1	4	yes	—
169	C₂²×C₆₇	#533	1	4	yes	—
170	C₂²×C₆₇	#544	1	4	yes	—
171	C₂²×C₆₇	#552	1	8	yes	—
172	C₂²×C₆₇	#553	1	8	yes	—
173	C₂²×C₆₇	C₂³×Q₈	1	1	yes	characteristic
174	C₂²×C₆₇	C₂²×#41	1	2	yes	—
175	C₂²×C₆₇	C₂²×#41	1	2	yes	—
176	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
177	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
178	C₄×C₆₇	—	2	4	no	—
179	C₄×C₆₇	—	2	4	no	—
180	C₄×C₆₇	—	2	4	no	—
181	C₄×C₆₇	—	2	8	no	—
182	C₄×C₆₇	—	2	8	no	—
183	C₄×C₆₇	—	4	4	no	—
184	C₄×C₆₇	—	4	4	no	—
185	C₄×C₆₇	—	4	4	no	—
186	C₄×C₆₇	—	4	4	no	—
187	C₂×#2606	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
188	C₂×C₆₇	#2606	1	8	yes	direct product factor
189	C₂×C₆₇	C₂×#533	1	1	yes	characteristic
190	C₂×C₆₇	C₂×#533	1	1	yes	characteristic
191	C₂×C₆₇	C₂×#544	1	1	yes	characteristic
192	C₂×C₆₇	C₂×#552	1	2	yes	—
193	C₂×C₆₇	C₂×#553	1	2	yes	—
194	#2606	C₂×C₆₇	1	16	yes	direct product factor
195	C₂×#398	C₂×C₆₇	1	2	yes	—
196	C₂×#398	C₂×C₆₇	1	2	yes	—
197	C₂×#389	C₂×C₆₇	1	2	yes	—
198	C₂×#389	C₂×C₆₇	1	2	yes	—
199	C₂×#387	C₂×C₆₇	1	2	yes	—
200	C₂×#387	C₂×C₆₇	1	2	yes	—
201	C₂×#383	C₂×C₆₇	1	1	yes	characteristic
202	C₂×C₄×C₄⋊C₄	C₂×C₆₇	1	1	yes	characteristic
203	C₂×#376	C₂×C₆₇	1	1	yes	characteristic
204	C₆₇	C₂×#2606	1	1	yes	characteristic, direct product factor, Sylow
205	C₂²×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
206	C₂²×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
207	C₂²×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
208	C₂²×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
209	C₂²×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
210	C₂²×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
211	C₂²×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
212	C₂²×C₄²	C₂²×C₆₇	1	2	yes	—
213	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
214	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
215	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
216	#398	C₂²×C₆₇	1	16	yes	—
217	#398	C₂²×C₆₇	1	16	yes	—
218	#389	C₂²×C₆₇	1	16	yes	—
219	#389	C₂²×C₆₇	1	16	yes	—
220	#387	C₂²×C₆₇	1	16	yes	—
221	#387	C₂²×C₆₇	1	16	yes	—
222	#383	C₂²×C₆₇	1	8	yes	—
223	C₄×C₄⋊C₄	C₂²×C₆₇	1	8	yes	—
224	#376	C₂²×C₆₇	1	8	yes	—
225	C₂×#95	C₂²×C₆₇	1	1	yes	characteristic
226	C₂×#95	C₂²×C₆₇	1	1	yes	characteristic
227	C₂×#95	C₂²×C₆₇	1	2	yes	—
228	C₂×#95	C₂²×C₆₇	1	2	yes	—
229	C₂×#95	C₂²×C₆₇	1	2	yes	—
230	C₂×#95	C₂²×C₆₇	1	2	yes	—
231	C₂×#95	C₂²×C₆₇	1	2	yes	—
232	C₂×#95	C₂²×C₆₇	1	1	yes	characteristic
233	C₂×#95	C₂²×C₆₇	1	2	yes	—
234	C₂×#95	C₂²×C₆₇	1	1	yes	characteristic
235	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
236	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
237	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
238	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
239	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
240	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
241	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
242	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
243	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
244	C₂×C₄⋊C₄	—	2	8	no	—
245	C₂×C₄⋊C₄	—	2	8	no	—
246	C₂×C₄⋊C₄	—	2	8	no	—
247	C₂×C₄⋊C₄	—	2	8	no	—
248	C₂×C₄⋊C₄	—	2	8	no	—
249	C₂×C₄⋊C₄	—	4	4	no	—
250	C₂×C₄⋊C₄	—	4	4	no	—
251	C₂×C₄⋊C₄	C₂³×C₆₇	1	8	yes	—
252	C₂×C₄⋊C₄	C₂³×C₆₇	1	8	yes	—
253	C₂×C₄⋊C₄	C₂³×C₆₇	1	8	yes	—
254	C₂×C₄⋊C₄	C₂³×C₆₇	1	8	yes	—
255	C₂×C₄⋊C₄	C₂³×C₆₇	1	8	yes	—
256	C₂×C₄⋊C₄	C₂³×C₆₇	1	8	yes	—
257	C₂×C₄⋊C₄	C₂³×C₆₇	1	8	yes	—
258	C₂×C₄²	—	2	8	no	—
259	C₂×C₄²	—	4	2	no	—
260	C₂×C₄²	—	4	2	no	—
261	C₂×C₄²	Q₈×C₆₇	1	8	yes	—
262	C₂×C₄²	C₂³×C₆₇	1	8	yes	—
263	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
264	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
265	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
266	#95	C₂³×C₆₇	1	8	yes	—
267	#95	C₂³×C₆₇	1	4	yes	—
268	#95	C₂³×C₆₇	1	4	yes	—
269	#95	C₂³×C₆₇	1	8	yes	—
270	#95	C₂³×C₆₇	1	4	yes	—
271	#95	C₂³×C₆₇	1	8	yes	—
272	#95	C₂³×C₆₇	1	4	yes	—
273	#95	C₂³×C₆₇	1	8	yes	—
274	#95	C₂³×C₆₇	1	8	yes	—
275	#95	C₂³×C₆₇	1	8	yes	—
276	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
277	C₂²×C₄	—	2	4	no	—
278	C₂²×C₄	—	2	4	no	—
279	C₂²×C₄	—	2	4	no	—
280	C₂²×C₄	—	2	4	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	2	4	no	—
283	C₂²×C₄	—	2	2	no	—
284	C₂²×C₄	—	2	4	no	—
285	C₂²×C₄	—	2	4	no	—
286	C₂²×C₄	—	2	4	no	—
287	C₂²×C₄	—	2	4	no	—
288	C₂²×C₄	—	2	4	no	—
289	C₂²×C₄	—	2	4	no	—
290	C₂²×C₄	—	2	4	no	—
291	C₂²×C₄	—	2	4	no	—
292	C₂²×C₄	—	2	4	no	—
293	C₂²×C₄	—	2	4	no	—
294	C₂²×C₄	—	2	4	no	—
295	C₂²×C₄	—	2	4	no	—
296	C₂²×C₄	—	2	4	no	—
297	C₂²×C₄	C₂×Q₈×C₆₇	1	4	yes	—
298	C₂²×C₄	C₂×Q₈×C₆₇	1	4	yes	—
299	C₂²×C₄	C₂×Q₈×C₆₇	1	4	yes	—
300	C₂²×C₄	#41×C₆₇	1	8	yes	—
301	C₂²×C₄	#41×C₆₇	1	8	yes	—
302	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
303	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
304	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
305	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
306	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
307	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
308	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
309	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
310	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
311	C₄⋊C₄	—	2	16	no	—
312	C₄⋊C₄	—	2	16	no	—
313	C₄⋊C₄	—	2	16	no	—
314	C₄⋊C₄	—	2	16	no	—
315	C₄⋊C₄	—	2	16	no	—
316	C₄⋊C₄	—	4	8	no	—
317	C₄⋊C₄	—	4	8	no	—
318	C₄²	—	2	16	no	—
319	C₄²	—	4	4	no	—
320	C₄²	—	4	4	no	—
321	C₄²	C₂×Q₈×C₆₇	1	16	yes	—
322	C₂³	C₂²×Q₈×C₆₇	1	2	yes	—
323	C₂³	C₂×#41×C₆₇	1	4	yes	—
324	C₂³	C₂×#41×C₆₇	1	4	yes	—
325	C₂³	H(5,𝔽₂)×C₆₇	1	2	yes	—
326	C₂³	2₋¹⁺⁴×C₆₇	1	2	yes	—
327	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
328	C₂×C₄	—	2	8	no	—
329	C₂×C₄	—	2	8	no	—
330	C₂×C₄	—	2	8	no	—
331	C₂×C₄	—	2	16	no	—
332	C₂×C₄	—	2	16	no	—
333	C₂×C₄	—	2	4	no	—
334	C₂×C₄	—	2	4	no	—
335	C₂×C₄	—	2	4	no	—
336	C₂×C₄	—	2	4	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	4	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	4	no	—
341	C₂×C₄	—	2	4	no	—
342	C₂×C₄	—	2	4	no	—
343	C₂×C₄	—	2	4	no	—
344	C₂×C₄	—	2	4	no	—
345	C₂×C₄	—	2	4	no	—
346	C₂×C₄	—	2	4	no	—
347	C₂×C₄	—	2	4	no	—
348	C₂×C₄	—	2	4	no	—
349	C₂×C₄	—	2	4	no	—
350	C₂×C₄	—	2	4	no	—
351	C₂×C₄	—	2	4	no	—
352	C₂×C₄	—	2	4	no	—
353	C₂×C₄	—	4	8	no	—
354	C₂×C₄	—	4	8	no	—
355	C₂×C₄	—	4	8	no	—
356	C₂×C₄	—	4	8	no	—
357	C₂×C₄	C₂²×Q₈×C₆₇	1	4	yes	—
358	C₂×C₄	C₂²×Q₈×C₆₇	1	4	yes	—
359	C₂×C₄	C₂²×Q₈×C₆₇	1	4	yes	—
360	C₂×C₄	C₂×#41×C₆₇	1	8	yes	—
361	C₂×C₄	C₂×#41×C₆₇	1	8	yes	—
362	C₂²	#533×C₆₇	1	4	yes	—
363	C₂²	#533×C₆₇	1	4	yes	—
364	C₂²	#544×C₆₇	1	4	yes	—
365	C₂²	#552×C₆₇	1	8	yes	—
366	C₂²	#553×C₆₇	1	8	yes	—
367	C₂²	C₂³×Q₈×C₆₇	1	1	yes	characteristic
368	C₂²	C₂²×#41×C₆₇	1	2	yes	—
369	C₂²	C₂²×#41×C₆₇	1	2	yes	—
370	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
371	C₂²	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
372	C₄	—	2	4	no	—
373	C₄	—	2	4	no	—
374	C₄	—	2	4	no	—
375	C₄	—	2	8	no	—
376	C₄	—	2	8	no	—
377	C₄	—	4	4	no	—
378	C₄	—	4	4	no	—
379	C₄	—	4	4	no	—
380	C₄	—	4	4	no	—
381	C₂	C₆₇×#2606	1	8	yes	direct product factor
382	C₂	C₂×#533×C₆₇	1	1	yes	characteristic
383	C₂	C₂×#533×C₆₇	1	1	yes	characteristic
384	C₂	C₂×#544×C₆₇	1	1	yes	characteristic
385	C₂	C₂×#552×C₆₇	1	2	yes	—
386	C₂	C₂×#553×C₆₇	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₆₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₇
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×#2606	C₂	direct (N × H)
187. C₂×#2606	C₆₇	direct (N × H)
188. C₂×C₆₇	#2606	direct (N × H)
194. #2606	C₂×C₆₇	direct (N × H)
204. C₆₇	C₂×#2606	direct (N × H)
381. C₂	C₆₇×#2606	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×#2606	2
C₂×#398×C₆₇	2
C₂×#389×C₆₇	2
C₂×#387×C₆₇	2
C₂×#383×C₆₇	2
C₂×C₄×C₄⋊C₄×C₆₇	2
C₂×#376×C₆₇	2
C₂×#2606	67

Subgroups — C2×C67×#2606 #30714113

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₇×#2606 #30714113