Subgroups — C₆₇×#22333 #30701584

Order 17152.

884 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#121×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₆₇×#1955	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#1954	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#1923	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#1923	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#1917	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#1916	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#1870	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#1870	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#1869	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#1869	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#1817	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#1753	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈×C₂²⋊C₄×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₂²⋊C₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
17	C₂³×C₈×C₆₇	C₂²	1	1	yes	characteristic
18	C₂×#121×C₆₇	C₄	1	1	yes	characteristic
19	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
22	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
25	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
26	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
27	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
29	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
30	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
31	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
32	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
33	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
34	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
35	C₂×#97×C₆₇	C₂²	1	1	yes	characteristic
36	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
39	#390×C₆₇	C₄	1	1	yes	characteristic
40	#389×C₆₇	C₄	1	1	yes	characteristic
41	#388×C₆₇	C₄	1	1	yes	characteristic
42	#388×C₆₇	C₄	1	1	yes	characteristic
43	#386×C₆₇	C₄	1	1	yes	characteristic
44	#386×C₆₇	C₄	1	1	yes	characteristic
45	#380×C₆₇	C₄	1	1	yes	characteristic
46	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
47	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
48	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
49	#336×C₆₇	C₂²	1	1	yes	characteristic
50	#336×C₆₇	C₂²	1	1	yes	characteristic
51	#336×C₆₇	C₂²	1	1	yes	characteristic
52	#336×C₆₇	C₂²	1	1	yes	characteristic
53	#336×C₆₇	C₂²	1	1	yes	characteristic
54	#336×C₆₇	C₂²	1	1	yes	characteristic
55	#336×C₆₇	C₂²	1	1	yes	characteristic
56	#336×C₆₇	C₂²	1	1	yes	characteristic
57	#336×C₆₇	C₂²	1	1	yes	characteristic
58	#336×C₆₇	C₂²	1	1	yes	characteristic
59	C₂²×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
60	C₂²×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
61	C₂²×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
62	C₂³×C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
63	C₂³×C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
64	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
65	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
67	C₂×M₁₆×C₆₇	—	2	2	no	—
68	C₂×M₁₆×C₆₇	—	4	1	no	—
69	C₂×M₁₆×C₆₇	—	4	1	no	—
70	C₂²×C₈×C₆₇	—	2	2	no	—
71	C₂²×C₈×C₆₇	—	4	1	no	—
72	C₂²×C₈×C₆₇	—	4	1	no	—
73	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
75	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
76	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
77	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
78	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
79	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
80	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
81	#121×C₆₇	—	2	4	no	—
82	C₄×D₄×C₆₇	—	4	1	no	—
83	C₄×D₄×C₆₇	—	4	1	no	—
84	C₄×D₄×C₆₇	—	4	1	no	—
85	C₄×D₄×C₆₇	—	4	1	no	—
86	C₄×D₄×C₆₇	—	4	1	no	—
87	C₄×D₄×C₆₇	—	4	1	no	—
88	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
89	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
90	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
91	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
92	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
93	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
94	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
95	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
96	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
97	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
98	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
99	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
100	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
101	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
102	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
103	C₂×C₄²×C₆₇	—	4	1	no	—
104	C₂×C₄²×C₆₇	—	4	1	no	—
105	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
106	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
107	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
108	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
109	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
110	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
111	C₄⋊C₈×C₆₇	—	4	1	no	—
112	C₄⋊C₈×C₆₇	—	4	1	no	—
113	C₂²⋊C₈×C₆₇	—	2	2	no	—
114	C₂²⋊C₈×C₆₇	—	2	2	no	—
115	C₂²⋊C₈×C₆₇	—	2	2	no	—
116	C₂²⋊C₈×C₆₇	—	2	2	no	—
117	C₂²⋊C₈×C₆₇	—	4	1	no	—
118	C₂²⋊C₈×C₆₇	—	4	1	no	—
119	C₂²⋊C₈×C₆₇	—	4	1	no	—
120	C₂²⋊C₈×C₆₇	—	4	1	no	—
121	C₂²⋊C₈×C₆₇	—	4	1	no	—
122	C₂²⋊C₈×C₆₇	—	4	1	no	—
123	#97×C₆₇	—	4	1	no	—
124	C₄×C₈×C₆₇	—	4	1	no	—
125	C₄×C₈×C₆₇	—	4	1	no	—
126	C₄×C₈×C₆₇	—	4	1	no	—
127	#95×C₆₇	C₂×C₄	1	1	yes	characteristic
128	#95×C₆₇	C₂×C₄	1	1	yes	characteristic
129	#95×C₆₇	C₂×C₄	1	1	yes	characteristic
130	#95×C₆₇	C₂×C₄	1	1	yes	characteristic
131	#95×C₆₇	C₂×C₄	1	1	yes	characteristic
132	#95×C₆₇	C₂×C₄	1	1	yes	characteristic
133	C₂⁴×C₆₇	C₂²×C₄	1	1	yes	characteristic
134	C₂⁴×C₆₇	C₂²×C₄	1	1	yes	characteristic
135	C₂⁴×C₆₇	C₂²×C₄	1	1	yes	characteristic
136	C₂×D₄×C₆₇	—	2	2	no	—
137	C₂×D₄×C₆₇	—	2	2	no	—
138	C₂×D₄×C₆₇	—	2	2	no	—
139	C₂×D₄×C₆₇	—	2	2	no	—
140	C₂×D₄×C₆₇	—	2	2	no	—
141	C₂×D₄×C₆₇	—	2	2	no	—
142	C₂×D₄×C₆₇	—	4	1	no	—
143	C₂×D₄×C₆₇	—	4	1	no	—
144	C₂×D₄×C₆₇	—	4	1	no	—
145	C₂²×C₄×C₆₇	—	2	2	no	—
146	C₂²×C₄×C₆₇	—	2	2	no	—
147	C₂²×C₄×C₆₇	—	2	2	no	—
148	C₂²×C₄×C₆₇	—	2	2	no	—
149	C₂²×C₄×C₆₇	—	2	1	no	—
150	C₂²×C₄×C₆₇	—	2	1	no	—
151	C₂²×C₄×C₆₇	—	2	1	no	—
152	C₂²×C₄×C₆₇	—	2	1	no	—
153	C₂²×C₄×C₆₇	—	2	1	no	—
154	C₂²×C₄×C₆₇	—	2	1	no	—
155	C₂²×C₄×C₆₇	—	2	1	no	—
156	C₂²×C₄×C₆₇	—	2	1	no	—
157	C₂²×C₄×C₆₇	—	2	1	no	—
158	C₂²×C₄×C₆₇	—	2	1	no	—
159	C₂²×C₄×C₆₇	—	2	1	no	—
160	C₂²×C₄×C₆₇	—	2	1	no	—
161	C₂²×C₄×C₆₇	—	2	1	no	—
162	C₂²×C₄×C₆₇	—	2	1	no	—
163	C₂²×C₄×C₆₇	—	2	1	no	—
164	C₂²×C₄×C₆₇	—	2	1	no	—
165	C₂²×C₄×C₆₇	—	2	1	no	—
166	C₂²×C₄×C₆₇	—	2	1	no	—
167	C₂²×C₄×C₆₇	—	4	1	no	—
168	C₂²×C₄×C₆₇	—	4	1	no	—
169	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
170	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
171	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
172	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
173	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
174	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
175	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
176	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
177	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
178	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
179	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
180	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
181	M₁₆×C₆₇	—	4	4	no	—
182	C₂×C₈×C₆₇	—	2	1	no	—
183	C₂×C₈×C₆₇	—	2	1	no	—
184	C₂×C₈×C₆₇	—	2	1	no	—
185	C₂×C₈×C₆₇	—	2	1	no	—
186	C₂×C₈×C₆₇	—	2	1	no	—
187	C₂×C₈×C₆₇	—	2	1	no	—
188	C₂×C₈×C₆₇	—	2	1	no	—
189	C₂×C₈×C₆₇	—	2	1	no	—
190	C₂×C₈×C₆₇	—	2	1	no	—
191	C₂×C₈×C₆₇	—	2	1	no	—
192	C₂×C₈×C₆₇	—	2	1	no	—
193	C₂×C₈×C₆₇	—	2	1	no	—
194	C₂×C₈×C₆₇	—	2	1	no	—
195	C₂×C₈×C₆₇	—	2	1	no	—
196	C₂×C₈×C₆₇	—	2	1	no	—
197	C₂×C₈×C₆₇	—	2	1	no	—
198	C₂×C₈×C₆₇	—	2	1	no	—
199	C₂×C₈×C₆₇	—	2	1	no	—
200	C₂×C₈×C₆₇	—	2	1	no	—
201	C₂×C₈×C₆₇	—	2	1	no	—
202	C₂×C₈×C₆₇	—	2	1	no	—
203	C₂×C₈×C₆₇	—	2	1	no	—
204	C₂×C₈×C₆₇	—	4	4	no	—
205	C₂×C₈×C₆₇	#41	1	2	yes	—
206	C₂×C₈×C₆₇	#41	1	2	yes	—
207	C₄⋊C₄×C₆₇	—	2	2	no	—
208	C₄⋊C₄×C₆₇	—	2	2	no	—
209	C₄⋊C₄×C₆₇	—	4	1	no	—
210	C₄⋊C₄×C₆₇	—	4	1	no	—
211	C₄⋊C₄×C₆₇	—	4	1	no	—
212	C₂²⋊C₄×C₆₇	—	2	2	no	—
213	C₂²⋊C₄×C₆₇	—	2	2	no	—
214	C₂²⋊C₄×C₆₇	—	2	2	no	—
215	C₂²⋊C₄×C₆₇	—	4	1	no	—
216	C₂²⋊C₄×C₆₇	—	4	1	no	—
217	C₂²⋊C₄×C₆₇	—	4	1	no	—
218	C₂²⋊C₄×C₆₇	—	4	1	no	—
219	C₂²⋊C₄×C₆₇	—	4	1	no	—
220	C₂²⋊C₄×C₆₇	—	4	1	no	—
221	C₂²⋊C₄×C₆₇	M₁₆	1	4	yes	complemented
222	C₄²×C₆₇	—	2	1	no	—
223	C₄²×C₆₇	—	2	1	no	—
224	C₄²×C₆₇	—	2	1	no	—
225	C₄²×C₆₇	—	2	1	no	—
226	C₄²×C₆₇	—	2	1	no	—
227	C₄²×C₆₇	—	2	1	no	—
228	C₄²×C₆₇	—	2	1	no	—
229	C₄²×C₆₇	—	2	1	no	—
230	C₄²×C₆₇	—	4	1	no	—
231	C₄²×C₆₇	—	4	1	no	—
232	C₂³×C₆₇	—	2	1	no	—
233	C₂³×C₆₇	—	2	1	no	—
234	C₂³×C₆₇	—	2	1	no	—
235	C₂³×C₆₇	—	2	1	no	—
236	C₂³×C₆₇	—	2	1	no	—
237	C₂³×C₆₇	—	2	1	no	—
238	C₂³×C₆₇	—	2	1	no	—
239	C₂³×C₆₇	—	2	1	no	—
240	C₂³×C₆₇	—	2	1	no	—
241	C₂³×C₆₇	—	2	1	no	—
242	C₂³×C₆₇	—	2	1	no	—
243	C₂³×C₆₇	—	2	1	no	—
244	C₂³×C₆₇	—	2	1	no	—
245	C₂³×C₆₇	—	2	1	no	—
246	C₂³×C₆₇	—	2	1	no	—
247	C₂³×C₆₇	—	2	1	no	—
248	C₂³×C₆₇	—	2	1	no	—
249	C₂³×C₆₇	—	2	1	no	—
250	C₂³×C₆₇	—	2	1	no	—
251	C₂³×C₆₇	C₂×M₁₆	1	2	yes	—
252	C₂³×C₆₇	#131	1	2	yes	—
253	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
254	D₄×C₆₇	—	4	4	no	—
255	D₄×C₆₇	—	4	4	no	—
256	D₄×C₆₇	—	4	4	no	—
257	C₂×C₄×C₆₇	—	2	1	no	—
258	C₂×C₄×C₆₇	—	2	1	no	—
259	C₂×C₄×C₆₇	—	2	1	no	—
260	C₂×C₄×C₆₇	—	2	1	no	—
261	C₂×C₄×C₆₇	—	2	1	no	—
262	C₂×C₄×C₆₇	—	2	1	no	—
263	C₂×C₄×C₆₇	—	2	1	no	—
264	C₂×C₄×C₆₇	—	2	1	no	—
265	C₂×C₄×C₆₇	—	2	1	no	—
266	C₂×C₄×C₆₇	—	2	1	no	—
267	C₂×C₄×C₆₇	—	2	1	no	—
268	C₂×C₄×C₆₇	—	2	1	no	—
269	C₂×C₄×C₆₇	—	2	1	no	—
270	C₂×C₄×C₆₇	—	2	1	no	—
271	C₂×C₄×C₆₇	—	2	1	no	—
272	C₂×C₄×C₆₇	—	2	1	no	—
273	C₂×C₄×C₆₇	—	2	1	no	—
274	C₂×C₄×C₆₇	—	2	1	no	—
275	C₂×C₄×C₆₇	—	2	1	no	—
276	C₂×C₄×C₆₇	—	2	1	no	—
277	C₂×C₄×C₆₇	—	2	1	no	—
278	C₂×C₄×C₆₇	—	2	1	no	—
279	C₂×C₄×C₆₇	—	2	1	no	—
280	C₂×C₄×C₆₇	—	2	1	no	—
281	C₂×C₄×C₆₇	—	2	1	no	—
282	C₂×C₄×C₆₇	—	2	1	no	—
283	C₂×C₄×C₆₇	—	2	1	no	—
284	C₂×C₄×C₆₇	—	2	1	no	—
285	C₂×C₄×C₆₇	—	2	1	no	—
286	C₂×C₄×C₆₇	—	4	4	no	—
287	C₂×C₄×C₆₇	—	4	4	no	—
288	C₂×C₄×C₆₇	—	4	1	no	—
289	C₂×C₄×C₆₇	—	4	1	no	—
290	C₂×C₄×C₆₇	—	4	1	no	—
291	C₂×C₄×C₆₇	—	4	1	no	—
292	C₂×C₄×C₆₇	—	4	1	no	—
293	C₂×C₄×C₆₇	—	4	1	no	—
294	C₂×C₄×C₆₇	—	4	1	no	—
295	C₂×C₄×C₆₇	—	4	1	no	—
296	C₂×C₄×C₆₇	—	4	1	no	—
297	C₂×C₄×C₆₇	—	4	1	no	—
298	C₂×C₄×C₆₇	—	4	1	no	—
299	C₂×C₄×C₆₇	—	4	1	no	—
300	C₂×C₄×C₆₇	C₂×M₁₆	1	2	yes	—
301	C₂×C₄×C₆₇	C₂×M₁₆	1	2	yes	—
302	C₂×C₄×C₆₇	#131	1	2	yes	—
303	C₂×C₄×C₆₇	#131	1	2	yes	—
304	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
305	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
306	C₂×C₄×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
307	C₂×C₄×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
308	C₂×C₄×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
309	C₂×C₄×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
310	C₈×C₆₇	—	2	2	no	—
311	C₈×C₆₇	—	2	2	no	—
312	C₈×C₆₇	—	4	1	no	—
313	C₈×C₆₇	—	4	1	no	—
314	C₈×C₆₇	—	4	1	no	—
315	C₈×C₆₇	—	4	1	no	—
316	C₈×C₆₇	—	4	1	no	—
317	C₈×C₆₇	—	4	1	no	—
318	C₂²×C₆₇	—	2	2	no	—
319	C₂²×C₆₇	—	2	2	no	—
320	C₂²×C₆₇	—	2	2	no	—
321	C₂²×C₆₇	—	2	2	no	—
322	C₂²×C₆₇	—	2	2	no	—
323	C₂²×C₆₇	—	2	2	no	—
324	C₂²×C₆₇	—	4	1	no	—
325	C₂²×C₆₇	—	4	1	no	—
326	C₂²×C₆₇	—	4	1	no	—
327	C₂²×C₆₇	—	4	1	no	—
328	C₂²×C₆₇	—	4	1	no	—
329	C₂²×C₆₇	—	4	1	no	—
330	C₂²×C₆₇	—	4	1	no	—
331	C₂²×C₆₇	—	4	1	no	—
332	C₂²×C₆₇	—	4	1	no	—
333	C₂²×C₆₇	—	4	1	no	—
334	C₂²×C₆₇	—	4	1	no	—
335	C₂²×C₆₇	—	4	1	no	—
336	C₂²×C₆₇	—	4	1	no	—
337	C₂²×C₆₇	—	4	1	no	—
338	C₂²×C₆₇	—	4	1	no	—
339	C₂²×C₆₇	C₄×#41	1	1	yes	characteristic
340	C₂²×C₆₇	#518	1	1	yes	characteristic
341	C₂²×C₆₇	#518	1	1	yes	characteristic
342	C₂²×C₆₇	C₂²×M₁₆	1	1	yes	characteristic
343	C₂²×C₆₇	C₂×#131	1	1	yes	characteristic
344	C₂²×C₆₇	C₂×#131	1	1	yes	characteristic
345	C₂²×C₆₇	C₂×#131	1	1	yes	characteristic
346	C₄×C₆₇	—	2	2	no	—
347	C₄×C₆₇	—	2	2	no	—
348	C₄×C₆₇	—	2	2	no	—
349	C₄×C₆₇	—	2	2	no	—
350	C₄×C₆₇	—	4	1	no	—
351	C₄×C₆₇	—	4	1	no	—
352	C₄×C₆₇	—	4	1	no	—
353	C₄×C₆₇	—	4	1	no	—
354	C₄×C₆₇	—	4	1	no	—
355	C₄×C₆₇	—	4	1	no	—
356	C₄×C₆₇	—	4	1	no	—
357	C₄×C₆₇	#538	1	1	yes	characteristic
358	C₄×C₆₇	#538	1	1	yes	characteristic
359	C₄×C₆₇	#540	1	1	yes	characteristic
360	C₄×C₆₇	#540	1	1	yes	characteristic
361	#22333	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
362	C₂×C₆₇	—	4	2	no	—
363	C₂×C₆₇	—	4	2	no	—
364	C₂×C₆₇	—	8	1	no	—
365	C₂×C₆₇	#2333	1	1	yes	characteristic
366	C₂×C₆₇	#2965	1	1	yes	characteristic
367	C₂×C₆₇	#2966	1	1	yes	characteristic
368	C₂×C₆₇	#2974	1	1	yes	characteristic
369	C₂×C₆₇	#2974	1	1	yes	characteristic
370	C₂×C₆₇	#2977	1	1	yes	characteristic
371	C₂×C₆₇	#2979	1	1	yes	characteristic
372	C₄×#121	C₂×C₆₇	1	1	yes	characteristic
373	#1955	C₂×C₆₇	1	1	yes	characteristic, complemented
374	#1954	C₂×C₆₇	1	1	yes	characteristic, complemented
375	#1923	C₂×C₆₇	1	1	yes	characteristic, complemented
376	#1923	C₂×C₆₇	1	1	yes	characteristic, complemented
377	#1917	C₂×C₆₇	1	1	yes	characteristic, complemented
378	#1916	C₂×C₆₇	1	1	yes	characteristic, complemented
379	#1870	C₂×C₆₇	1	1	yes	characteristic, complemented
380	#1870	C₂×C₆₇	1	1	yes	characteristic, complemented
381	#1869	C₂×C₆₇	1	1	yes	characteristic, complemented
382	#1869	C₂×C₆₇	1	1	yes	characteristic, complemented
383	#1817	C₂×C₆₇	1	1	yes	characteristic, complemented
384	#1753	C₂×C₆₇	1	1	yes	characteristic, complemented
385	C₈×C₂²⋊C₄	C₂×C₆₇	1	1	yes	characteristic, complemented
386	C₄×C₂²⋊C₈	C₂×C₆₇	1	1	yes	characteristic, complemented
387	C₆₇	#22333	1	1	yes	characteristic, direct product factor, Sylow
388	C₂²×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
389	C₂³×C₈	C₂²×C₆₇	1	1	yes	characteristic
390	C₂×#121	C₄×C₆₇	1	1	yes	characteristic
391	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
392	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
393	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
394	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
395	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
396	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
397	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
398	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
399	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
400	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
401	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
402	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
403	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
404	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
405	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
406	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
407	C₂×#97	C₂²×C₆₇	1	1	yes	characteristic
408	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic
409	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic
410	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic
411	#390	C₄×C₆₇	1	1	yes	characteristic
412	#389	C₄×C₆₇	1	1	yes	characteristic
413	#388	C₄×C₆₇	1	1	yes	characteristic
414	#388	C₄×C₆₇	1	1	yes	characteristic
415	#386	C₄×C₆₇	1	1	yes	characteristic
416	#386	C₄×C₆₇	1	1	yes	characteristic
417	#380	C₄×C₆₇	1	1	yes	characteristic
418	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
419	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
420	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
421	#336	C₂²×C₆₇	1	1	yes	characteristic
422	#336	C₂²×C₆₇	1	1	yes	characteristic
423	#336	C₂²×C₆₇	1	1	yes	characteristic
424	#336	C₂²×C₆₇	1	1	yes	characteristic
425	#336	C₂²×C₆₇	1	1	yes	characteristic
426	#336	C₂²×C₆₇	1	1	yes	characteristic
427	#336	C₂²×C₆₇	1	1	yes	characteristic
428	#336	C₂²×C₆₇	1	1	yes	characteristic
429	#336	C₂²×C₆₇	1	1	yes	characteristic
430	#336	C₂²×C₆₇	1	1	yes	characteristic
431	C₂²×D₄	C₂×C₄×C₆₇	1	1	yes	characteristic
432	C₂²×D₄	C₂×C₄×C₆₇	1	1	yes	characteristic
433	C₂²×D₄	C₂×C₄×C₆₇	1	1	yes	characteristic
434	C₂³×C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
435	C₂³×C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
436	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
437	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
438	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
439	C₂×M₁₆	—	2	2	no	—
440	C₂×M₁₆	—	4	1	no	—
441	C₂×M₁₆	—	4	1	no	—
442	C₂²×C₈	—	2	2	no	—
443	C₂²×C₈	—	4	1	no	—
444	C₂²×C₈	—	4	1	no	—
445	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
446	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
447	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
448	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
449	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
450	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
451	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
452	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
453	#121	—	2	4	no	—
454	C₄×D₄	—	4	1	no	—
455	C₄×D₄	—	4	1	no	—
456	C₄×D₄	—	4	1	no	—
457	C₄×D₄	—	4	1	no	—
458	C₄×D₄	—	4	1	no	—
459	C₄×D₄	—	4	1	no	—
460	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
461	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
462	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
463	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
464	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
465	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
466	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
467	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
468	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
469	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
470	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
471	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
472	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
473	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
474	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
475	C₂×C₄²	—	4	1	no	—
476	C₂×C₄²	—	4	1	no	—
477	C₂×C₄²	C₂×C₄×C₆₇	1	1	yes	characteristic
478	C₂×C₄²	C₂×C₄×C₆₇	1	1	yes	characteristic
479	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
480	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
481	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
482	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
483	C₄⋊C₈	—	4	1	no	—
484	C₄⋊C₈	—	4	1	no	—
485	C₂²⋊C₈	—	2	2	no	—
486	C₂²⋊C₈	—	2	2	no	—
487	C₂²⋊C₈	—	2	2	no	—
488	C₂²⋊C₈	—	2	2	no	—
489	C₂²⋊C₈	—	4	1	no	—
490	C₂²⋊C₈	—	4	1	no	—
491	C₂²⋊C₈	—	4	1	no	—
492	C₂²⋊C₈	—	4	1	no	—
493	C₂²⋊C₈	—	4	1	no	—
494	C₂²⋊C₈	—	4	1	no	—
495	#97	—	4	1	no	—
496	C₄×C₈	—	4	1	no	—
497	C₄×C₈	—	4	1	no	—
498	C₄×C₈	—	4	1	no	—
499	#95	C₂×C₄×C₆₇	1	1	yes	characteristic
500	#95	C₂×C₄×C₆₇	1	1	yes	characteristic
501	#95	C₂×C₄×C₆₇	1	1	yes	characteristic
502	#95	C₂×C₄×C₆₇	1	1	yes	characteristic
503	#95	C₂×C₄×C₆₇	1	1	yes	characteristic
504	#95	C₂×C₄×C₆₇	1	1	yes	characteristic
505	C₂⁴	C₂²×C₄×C₆₇	1	1	yes	characteristic
506	C₂⁴	C₂²×C₄×C₆₇	1	1	yes	characteristic
507	C₂⁴	C₂²×C₄×C₆₇	1	1	yes	characteristic
508	C₂×D₄	—	2	2	no	—
509	C₂×D₄	—	2	2	no	—
510	C₂×D₄	—	2	2	no	—
511	C₂×D₄	—	2	2	no	—
512	C₂×D₄	—	2	2	no	—
513	C₂×D₄	—	2	2	no	—
514	C₂×D₄	—	4	1	no	—
515	C₂×D₄	—	4	1	no	—
516	C₂×D₄	—	4	1	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	1	no	—
522	C₂²×C₄	—	2	1	no	—
523	C₂²×C₄	—	2	1	no	—
524	C₂²×C₄	—	2	1	no	—
525	C₂²×C₄	—	2	1	no	—
526	C₂²×C₄	—	2	1	no	—
527	C₂²×C₄	—	2	1	no	—
528	C₂²×C₄	—	2	1	no	—
529	C₂²×C₄	—	2	1	no	—
530	C₂²×C₄	—	2	1	no	—
531	C₂²×C₄	—	2	1	no	—
532	C₂²×C₄	—	2	1	no	—
533	C₂²×C₄	—	2	1	no	—
534	C₂²×C₄	—	2	1	no	—
535	C₂²×C₄	—	2	1	no	—
536	C₂²×C₄	—	2	1	no	—
537	C₂²×C₄	—	2	1	no	—
538	C₂²×C₄	—	2	1	no	—
539	C₂²×C₄	—	4	1	no	—
540	C₂²×C₄	—	4	1	no	—
541	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
542	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
543	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
544	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
545	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
546	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
547	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
548	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
549	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
550	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
551	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
552	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
553	M₁₆	—	4	4	no	—
554	C₂×C₈	—	2	1	no	—
555	C₂×C₈	—	2	1	no	—
556	C₂×C₈	—	2	1	no	—
557	C₂×C₈	—	2	1	no	—
558	C₂×C₈	—	2	1	no	—
559	C₂×C₈	—	2	1	no	—
560	C₂×C₈	—	2	1	no	—
561	C₂×C₈	—	2	1	no	—
562	C₂×C₈	—	2	1	no	—
563	C₂×C₈	—	2	1	no	—
564	C₂×C₈	—	2	1	no	—
565	C₂×C₈	—	2	1	no	—
566	C₂×C₈	—	2	1	no	—
567	C₂×C₈	—	2	1	no	—
568	C₂×C₈	—	2	1	no	—
569	C₂×C₈	—	2	1	no	—
570	C₂×C₈	—	2	1	no	—
571	C₂×C₈	—	2	1	no	—
572	C₂×C₈	—	2	1	no	—
573	C₂×C₈	—	2	1	no	—
574	C₂×C₈	—	2	1	no	—
575	C₂×C₈	—	2	1	no	—
576	C₂×C₈	—	4	4	no	—
577	C₂×C₈	#41×C₆₇	1	2	yes	—
578	C₂×C₈	#41×C₆₇	1	2	yes	—
579	C₄⋊C₄	—	2	2	no	—
580	C₄⋊C₄	—	2	2	no	—
581	C₄⋊C₄	—	4	1	no	—
582	C₄⋊C₄	—	4	1	no	—
583	C₄⋊C₄	—	4	1	no	—
584	C₂²⋊C₄	—	2	2	no	—
585	C₂²⋊C₄	—	2	2	no	—
586	C₂²⋊C₄	—	2	2	no	—
587	C₂²⋊C₄	—	4	1	no	—
588	C₂²⋊C₄	—	4	1	no	—
589	C₂²⋊C₄	—	4	1	no	—
590	C₂²⋊C₄	—	4	1	no	—
591	C₂²⋊C₄	—	4	1	no	—
592	C₂²⋊C₄	—	4	1	no	—
593	C₂²⋊C₄	M₁₆×C₆₇	1	4	yes	complemented
594	C₄²	—	2	1	no	—
595	C₄²	—	2	1	no	—
596	C₄²	—	2	1	no	—
597	C₄²	—	2	1	no	—
598	C₄²	—	2	1	no	—
599	C₄²	—	2	1	no	—
600	C₄²	—	2	1	no	—
601	C₄²	—	2	1	no	—
602	C₄²	—	4	1	no	—
603	C₄²	—	4	1	no	—
604	C₂³	—	2	1	no	—
605	C₂³	—	2	1	no	—
606	C₂³	—	2	1	no	—
607	C₂³	—	2	1	no	—
608	C₂³	—	2	1	no	—
609	C₂³	—	2	1	no	—
610	C₂³	—	2	1	no	—
611	C₂³	—	2	1	no	—
612	C₂³	—	2	1	no	—
613	C₂³	—	2	1	no	—
614	C₂³	—	2	1	no	—
615	C₂³	—	2	1	no	—
616	C₂³	—	2	1	no	—
617	C₂³	—	2	1	no	—
618	C₂³	—	2	1	no	—
619	C₂³	—	2	1	no	—
620	C₂³	—	2	1	no	—
621	C₂³	—	2	1	no	—
622	C₂³	—	2	1	no	—
623	C₂³	C₂×M₁₆×C₆₇	1	2	yes	—
624	C₂³	#131×C₆₇	1	2	yes	—
625	C₂³	C₂³×C₄×C₆₇	1	1	yes	characteristic
626	D₄	—	4	4	no	—
627	D₄	—	4	4	no	—
628	D₄	—	4	4	no	—
629	C₂×C₄	—	2	1	no	—
630	C₂×C₄	—	2	1	no	—
631	C₂×C₄	—	2	1	no	—
632	C₂×C₄	—	2	1	no	—
633	C₂×C₄	—	2	1	no	—
634	C₂×C₄	—	2	1	no	—
635	C₂×C₄	—	2	1	no	—
636	C₂×C₄	—	2	1	no	—
637	C₂×C₄	—	2	1	no	—
638	C₂×C₄	—	2	1	no	—
639	C₂×C₄	—	2	1	no	—
640	C₂×C₄	—	2	1	no	—
641	C₂×C₄	—	2	1	no	—
642	C₂×C₄	—	2	1	no	—
643	C₂×C₄	—	2	1	no	—
644	C₂×C₄	—	2	1	no	—
645	C₂×C₄	—	2	1	no	—
646	C₂×C₄	—	2	1	no	—
647	C₂×C₄	—	2	1	no	—
648	C₂×C₄	—	2	1	no	—
649	C₂×C₄	—	2	1	no	—
650	C₂×C₄	—	2	1	no	—
651	C₂×C₄	—	2	1	no	—
652	C₂×C₄	—	2	1	no	—
653	C₂×C₄	—	2	1	no	—
654	C₂×C₄	—	2	1	no	—
655	C₂×C₄	—	2	1	no	—
656	C₂×C₄	—	2	1	no	—
657	C₂×C₄	—	2	1	no	—
658	C₂×C₄	—	4	4	no	—
659	C₂×C₄	—	4	4	no	—
660	C₂×C₄	—	4	1	no	—
661	C₂×C₄	—	4	1	no	—
662	C₂×C₄	—	4	1	no	—
663	C₂×C₄	—	4	1	no	—
664	C₂×C₄	—	4	1	no	—
665	C₂×C₄	—	4	1	no	—
666	C₂×C₄	—	4	1	no	—
667	C₂×C₄	—	4	1	no	—
668	C₂×C₄	—	4	1	no	—
669	C₂×C₄	—	4	1	no	—
670	C₂×C₄	—	4	1	no	—
671	C₂×C₄	—	4	1	no	—
672	C₂×C₄	C₂×M₁₆×C₆₇	1	2	yes	—
673	C₂×C₄	C₂×M₁₆×C₆₇	1	2	yes	—
674	C₂×C₄	#131×C₆₇	1	2	yes	—
675	C₂×C₄	#131×C₆₇	1	2	yes	—
676	C₂×C₄	C₂×#41×C₆₇	1	1	yes	characteristic
677	C₂×C₄	C₂×#41×C₆₇	1	1	yes	characteristic
678	C₂×C₄	H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
679	C₂×C₄	H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
680	C₂×C₄	H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
681	C₂×C₄	H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
682	C₈	—	2	2	no	—
683	C₈	—	2	2	no	—
684	C₈	—	4	1	no	—
685	C₈	—	4	1	no	—
686	C₈	—	4	1	no	—
687	C₈	—	4	1	no	—
688	C₈	—	4	1	no	—
689	C₈	—	4	1	no	—
690	C₂²	—	2	2	no	—
691	C₂²	—	2	2	no	—
692	C₂²	—	2	2	no	—
693	C₂²	—	2	2	no	—
694	C₂²	—	2	2	no	—
695	C₂²	—	2	2	no	—
696	C₂²	—	4	1	no	—
697	C₂²	—	4	1	no	—
698	C₂²	—	4	1	no	—
699	C₂²	—	4	1	no	—
700	C₂²	—	4	1	no	—
701	C₂²	—	4	1	no	—
702	C₂²	—	4	1	no	—
703	C₂²	—	4	1	no	—
704	C₂²	—	4	1	no	—
705	C₂²	—	4	1	no	—
706	C₂²	—	4	1	no	—
707	C₂²	—	4	1	no	—
708	C₂²	—	4	1	no	—
709	C₂²	—	4	1	no	—
710	C₂²	—	4	1	no	—
711	C₂²	C₄×#41×C₆₇	1	1	yes	characteristic
712	C₂²	#518×C₆₇	1	1	yes	characteristic
713	C₂²	#518×C₆₇	1	1	yes	characteristic
714	C₂²	C₂²×M₁₆×C₆₇	1	1	yes	characteristic
715	C₂²	C₂×#131×C₆₇	1	1	yes	characteristic
716	C₂²	C₂×#131×C₆₇	1	1	yes	characteristic
717	C₂²	C₂×#131×C₆₇	1	1	yes	characteristic
718	C₄	—	2	2	no	—
719	C₄	—	2	2	no	—
720	C₄	—	2	2	no	—
721	C₄	—	2	2	no	—
722	C₄	—	4	1	no	—
723	C₄	—	4	1	no	—
724	C₄	—	4	1	no	—
725	C₄	—	4	1	no	—
726	C₄	—	4	1	no	—
727	C₄	—	4	1	no	—
728	C₄	—	4	1	no	—
729	C₄	#538×C₆₇	1	1	yes	characteristic
730	C₄	#538×C₆₇	1	1	yes	characteristic
731	C₄	#540×C₆₇	1	1	yes	characteristic
732	C₄	#540×C₆₇	1	1	yes	characteristic
733	C₂	—	4	2	no	—
734	C₂	—	4	2	no	—
735	C₂	—	8	1	no	—
736	C₂	C₆₇×#2333	1	1	yes	characteristic
737	C₂	C₆₇×#2965	1	1	yes	characteristic
738	C₂	C₆₇×#2966	1	1	yes	characteristic
739	C₂	C₆₇×#2974	1	1	yes	characteristic
740	C₂	C₆₇×#2974	1	1	yes	characteristic
741	C₂	C₆₇×#2977	1	1	yes	characteristic
742	C₂	C₆₇×#2979	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₆₇	C₂⁴
commutator	C₂³	C₂³×C₄×C₆₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₇
socle	C₂³×C₆₇	C₂³×C₄
prime radical	C₂×#121×C₆₇	C₄
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₆₇×#1955	C₂	semidirect
3. C₆₇×#1954	C₂	semidirect
4. C₆₇×#1923	C₂	semidirect
5. C₆₇×#1923	C₂	semidirect
6. C₆₇×#1917	C₂	semidirect
7. C₆₇×#1916	C₂	semidirect
8. C₆₇×#1870	C₂	semidirect
9. C₆₇×#1870	C₂	semidirect
10. C₆₇×#1869	C₂	semidirect
11. C₆₇×#1869	C₂	semidirect
12. C₆₇×#1817	C₂	semidirect
13. C₆₇×#1753	C₂	semidirect
14. C₈×C₂²⋊C₄×C₆₇	C₂	semidirect
15. C₄×C₂²⋊C₈×C₆₇	C₂	semidirect
221. C₂²⋊C₄×C₆₇	M₁₆	semidirect
361. #22333	C₆₇	direct (N × H)
373. #1955	C₂×C₆₇	semidirect
374. #1954	C₂×C₆₇	semidirect
375. #1923	C₂×C₆₇	semidirect
376. #1923	C₂×C₆₇	semidirect
377. #1917	C₂×C₆₇	semidirect
378. #1916	C₂×C₆₇	semidirect
379. #1870	C₂×C₆₇	semidirect
380. #1870	C₂×C₆₇	semidirect
381. #1869	C₂×C₆₇	semidirect
382. #1869	C₂×C₆₇	semidirect
383. #1817	C₂×C₆₇	semidirect
384. #1753	C₂×C₆₇	semidirect
385. C₈×C₂²⋊C₄	C₂×C₆₇	semidirect
386. C₄×C₂²⋊C₈	C₂×C₆₇	semidirect
387. C₆₇	#22333	direct (N × H)
593. C₂²⋊C₄	M₁₆×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₄×#121×C₆₇	2
C₆₇×#1955	2
C₆₇×#1954	2
C₆₇×#1923	2
C₆₇×#1917	2
C₆₇×#1916	2
C₆₇×#1870	2
C₆₇×#1869	2
C₆₇×#1817	2
C₆₇×#1753	2
C₈×C₂²⋊C₄×C₆₇	2
C₄×C₂²⋊C₈×C₆₇	2
#22333	67

Subgroups — C67×#22333 #30701584

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#22333 #30701584