Subgroups — C₆₇×#25950 #30705201

Order 17152.

1206 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#474×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#102×C₆₇	C₂	1	1	yes	maximal, characteristic
3	C₆₇×#2440	C₂	1	1	yes	maximal, characteristic, complemented
4	D₄×C₂²⋊C₄×C₆₇	C₂	1	1	yes	maximal, characteristic
5	C₆₇×#2093	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#2067	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#2067	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#2023	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#1862	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#1862	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#1852	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#1850	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#1808	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#1802	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#1786	C₂	1	1	yes	maximal, characteristic
16	C₂³×D₄×C₆₇	C₂²	1	1	yes	characteristic
17	C₂³×C₈×C₆₇	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
19	C₂×C₂²⋊Q₈×C₆₇	—	2	1	no	—
20	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
22	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
23	C₂²×C₂²⋊C₄×C₆₇	—	2	1	no	—
24	#474×C₆₇	—	2	4	no	—
25	C₂×#107×C₆₇	C₂²	1	1	yes	characteristic, complemented
26	C₂×#107×C₆₇	C₂²	1	1	yes	characteristic, complemented
27	C₂×#107×C₆₇	C₂²	1	1	yes	characteristic, complemented
28	C₂×#107×C₆₇	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
31	C₂×#102×C₆₇	—	2	4	no	—
32	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
33	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
34	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
35	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
36	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
37	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
38	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
39	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
40	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
41	#398×C₆₇	—	2	1	no	—
42	#395×C₆₇	—	2	1	no	—
43	#390×C₆₇	C₂²	1	1	yes	characteristic
44	#390×C₆₇	C₂²	1	1	yes	characteristic
45	#389×C₆₇	C₂²	1	1	yes	characteristic, complemented
46	#389×C₆₇	C₂²	1	1	yes	characteristic, complemented
47	#386×C₆₇	—	2	1	no	—
48	#386×C₆₇	—	2	1	no	—
49	#385×C₆₇	—	2	1	no	—
50	#384×C₆₇	C₂²	1	1	yes	characteristic, complemented
51	#380×C₆₇	C₂²	1	1	yes	characteristic
52	#380×C₆₇	C₂²	1	1	yes	characteristic
53	#379×C₆₇	—	2	1	no	—
54	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
55	#340×C₆₇	C₂²	1	1	yes	characteristic, complemented
56	#340×C₆₇	C₂²	1	1	yes	characteristic, complemented
57	#340×C₆₇	C₂²	1	1	yes	characteristic, complemented
58	#340×C₆₇	C₂²	1	1	yes	characteristic, complemented
59	#336×C₆₇	C₂²	1	1	yes	characteristic, complemented
60	#336×C₆₇	C₂²	1	1	yes	characteristic, complemented
61	C₂⁵×C₆₇	—	2	1	no	—
62	C₂²×Q₈×C₆₇	—	2	1	no	—
63	C₂²×D₄×C₆₇	—	2	2	no	—
64	C₂²×D₄×C₆₇	—	2	2	no	—
65	C₂²×D₄×C₆₇	—	2	1	no	—
66	C₂²×D₄×C₆₇	—	2	2	no	—
67	C₂²×D₄×C₆₇	—	4	1	no	—
68	C₂²×D₄×C₆₇	—	4	1	no	—
69	C₂²×D₄×C₆₇	Q₈	1	4	yes	complemented
70	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
71	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
72	C₂³×C₄×C₆₇	—	2	1	no	—
73	C₂³×C₄×C₆₇	—	2	1	no	—
74	C₂³×C₄×C₆₇	—	2	1	no	—
75	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
76	C₂²×C₈×C₆₇	—	2	2	no	—
77	C₂²×C₈×C₆₇	—	2	2	no	—
78	C₂²×C₈×C₆₇	—	4	1	no	—
79	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
80	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
81	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
82	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
83	C₄⋊Q₈×C₆₇	—	2	2	no	—
84	C₄⋊Q₈×C₆₇	—	4	1	no	—
85	C₂²⋊Q₈×C₆₇	—	4	4	no	—
86	C₄×D₄×C₆₇	—	2	2	no	—
87	C₄×D₄×C₆₇	—	2	2	no	—
88	C₄×D₄×C₆₇	—	4	1	no	—
89	C₄×D₄×C₆₇	—	4	1	no	—
90	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
91	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
92	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
93	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
94	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
95	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
96	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
97	C₂×C₄⋊C₄×C₆₇	—	4	1	no	—
98	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
99	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
100	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
101	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
102	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
103	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
104	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
105	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
106	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
107	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
108	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
109	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
110	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
111	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
112	C₂×C₂²⋊C₄×C₆₇	—	4	4	no	—
113	C₂×C₂²⋊C₄×C₆₇	D₄	1	1	yes	characteristic
114	C₂×C₂²⋊C₄×C₆₇	D₄	1	1	yes	characteristic
115	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
116	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
117	#107×C₆₇	—	2	2	no	—
118	#107×C₆₇	—	2	2	no	—
119	#107×C₆₇	—	4	1	no	—
120	#107×C₆₇	—	4	1	no	—
121	C₄⋊C₈×C₆₇	—	2	2	no	—
122	C₄⋊C₈×C₆₇	—	4	1	no	—
123	#102×C₆₇	—	2	2	no	—
124	#102×C₆₇	—	2	2	no	—
125	#102×C₆₇	—	2	2	no	—
126	#102×C₆₇	—	2	2	no	—
127	#102×C₆₇	—	2	2	no	—
128	#102×C₆₇	—	4	1	no	—
129	#102×C₆₇	—	4	1	no	—
130	#102×C₆₇	D₄	1	4	yes	—
131	C₂²⋊C₈×C₆₇	—	2	2	no	—
132	#95×C₆₇	—	2	1	no	—
133	#95×C₆₇	—	2	1	no	—
134	#95×C₆₇	—	2	1	no	—
135	#95×C₆₇	—	2	1	no	—
136	#95×C₆₇	D₄	1	1	yes	characteristic
137	#95×C₆₇	D₄	1	1	yes	characteristic
138	C₂⁴×C₆₇	—	2	1	no	—
139	C₂⁴×C₆₇	—	2	1	no	—
140	C₂⁴×C₆₇	—	2	4	no	—
141	C₂⁴×C₆₇	—	4	2	no	—
142	C₂⁴×C₆₇	—	4	2	no	—
143	C₂⁴×C₆₇	—	4	2	no	—
144	C₂⁴×C₆₇	—	4	2	no	—
145	C₂⁴×C₆₇	—	8	1	no	—
146	C₂⁴×C₆₇	—	8	1	no	—
147	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
148	C₂×Q₈×C₆₇	—	4	2	no	—
149	C₂×Q₈×C₆₇	—	4	2	no	—
150	C₂×Q₈×C₆₇	—	8	1	no	—
151	C₂×D₄×C₆₇	—	2	8	no	—
152	C₂×D₄×C₆₇	—	2	4	no	—
153	C₂×D₄×C₆₇	—	2	1	no	—
154	C₂×D₄×C₆₇	—	2	1	no	—
155	C₂×D₄×C₆₇	—	2	1	no	—
156	C₂×D₄×C₆₇	—	2	1	no	—
157	C₂×D₄×C₆₇	—	2	1	no	—
158	C₂×D₄×C₆₇	—	2	1	no	—
159	C₂×D₄×C₆₇	—	2	1	no	—
160	C₂×D₄×C₆₇	—	2	1	no	—
161	C₂×D₄×C₆₇	—	4	4	no	—
162	C₂×D₄×C₆₇	—	4	4	no	—
163	C₂×D₄×C₆₇	—	4	4	no	—
164	C₂×D₄×C₆₇	—	4	2	no	—
165	C₂×D₄×C₆₇	—	4	2	no	—
166	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
167	C₂×D₄×C₆₇	C₂×Q₈	1	2	yes	—
168	C₂×D₄×C₆₇	C₂×Q₈	1	2	yes	—
169	C₂×D₄×C₆₇	#41	1	2	yes	—
170	C₂²×C₄×C₆₇	—	2	1	no	—
171	C₂²×C₄×C₆₇	—	2	1	no	—
172	C₂²×C₄×C₆₇	—	2	1	no	—
173	C₂²×C₄×C₆₇	—	2	1	no	—
174	C₂²×C₄×C₆₇	—	2	1	no	—
175	C₂²×C₄×C₆₇	—	2	1	no	—
176	C₂²×C₄×C₆₇	—	2	1	no	—
177	C₂²×C₄×C₆₇	—	2	1	no	—
178	C₂²×C₄×C₆₇	—	2	1	no	—
179	C₂²×C₄×C₆₇	—	2	1	no	—
180	C₂²×C₄×C₆₇	—	4	2	no	—
181	C₂²×C₄×C₆₇	—	4	2	no	—
182	C₂²×C₄×C₆₇	—	4	2	no	—
183	C₂²×C₄×C₆₇	—	4	2	no	—
184	C₂²×C₄×C₆₇	—	4	2	no	—
185	C₂²×C₄×C₆₇	—	4	2	no	—
186	C₂²×C₄×C₆₇	—	8	1	no	—
187	C₂²×C₄×C₆₇	—	8	1	no	—
188	C₂²×C₄×C₆₇	—	8	1	no	—
189	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
190	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
191	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
192	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
193	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
194	C₂²×C₄×C₆₇	C₂×Q₈	1	2	yes	—
195	C₂²×C₄×C₆₇	#41	1	2	yes	—
196	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
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	—	2	1	no	—
205	C₂×C₈×C₆₇	—	2	1	no	—
206	C₂×C₈×C₆₇	—	2	1	no	—
207	C₂×C₈×C₆₇	—	2	1	no	—
208	C₂×C₈×C₆₇	—	4	4	no	—
209	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
210	C₄⋊C₄×C₆₇	—	2	1	no	—
211	C₄⋊C₄×C₆₇	—	2	1	no	—
212	C₄⋊C₄×C₆₇	—	2	1	no	—
213	C₄⋊C₄×C₆₇	—	2	1	no	—
214	C₄⋊C₄×C₆₇	—	2	1	no	—
215	C₄⋊C₄×C₆₇	—	2	1	no	—
216	C₄⋊C₄×C₆₇	—	2	1	no	—
217	C₄⋊C₄×C₆₇	—	2	1	no	—
218	C₄⋊C₄×C₆₇	—	2	1	no	—
219	C₄⋊C₄×C₆₇	—	2	1	no	—
220	C₄⋊C₄×C₆₇	—	2	1	no	—
221	C₄⋊C₄×C₆₇	—	4	2	no	—
222	C₄⋊C₄×C₆₇	—	4	2	no	—
223	C₄⋊C₄×C₆₇	—	4	2	no	—
224	C₄⋊C₄×C₆₇	—	4	2	no	—
225	C₄⋊C₄×C₆₇	—	4	2	no	—
226	C₄⋊C₄×C₆₇	—	8	1	no	—
227	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
228	C₂²⋊C₄×C₆₇	—	2	2	no	—
229	C₂²⋊C₄×C₆₇	—	4	2	no	—
230	C₂²⋊C₄×C₆₇	—	4	2	no	—
231	C₂²⋊C₄×C₆₇	—	4	2	no	—
232	C₂²⋊C₄×C₆₇	—	4	2	no	—
233	C₂²⋊C₄×C₆₇	—	4	2	no	—
234	C₂²⋊C₄×C₆₇	—	4	2	no	—
235	C₂²⋊C₄×C₆₇	—	8	1	no	—
236	C₂²⋊C₄×C₆₇	—	8	1	no	—
237	C₂²⋊C₄×C₆₇	D₈	1	4	yes	—
238	C₄²×C₆₇	—	2	1	no	—
239	C₄²×C₆₇	—	2	1	no	—
240	C₄²×C₆₇	—	2	1	no	—
241	C₄²×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	2	no	—
247	C₂³×C₆₇	—	2	2	no	—
248	C₂³×C₆₇	—	2	2	no	—
249	C₂³×C₆₇	—	2	2	no	—
250	C₂³×C₆₇	—	4	8	no	—
251	C₂³×C₆₇	—	4	1	no	—
252	C₂³×C₆₇	—	4	1	no	—
253	C₂³×C₆₇	—	4	1	no	—
254	C₂³×C₆₇	—	4	1	no	—
255	C₂³×C₆₇	—	4	1	no	—
256	C₂³×C₆₇	—	4	1	no	—
257	C₂³×C₆₇	—	4	1	no	—
258	C₂³×C₆₇	—	4	1	no	—
259	C₂³×C₆₇	—	4	1	no	—
260	C₂³×C₆₇	—	4	1	no	—
261	C₂³×C₆₇	—	4	8	no	—
262	C₂³×C₆₇	—	8	4	no	—
263	C₂³×C₆₇	—	8	4	no	—
264	C₂³×C₆₇	—	8	4	no	—
265	C₂³×C₆₇	—	8	4	no	—
266	C₂³×C₆₇	—	8	4	no	—
267	C₂³×C₆₇	C₂²⋊Q₈	1	2	yes	—
268	C₂³×C₆₇	C₂×D₈	1	2	yes	—
269	C₂³×C₆₇	#137	1	2	yes	—
270	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
271	Q₈×C₆₇	—	8	4	no	—
272	D₄×C₆₇	—	2	2	no	—
273	D₄×C₆₇	—	2	2	no	—
274	D₄×C₆₇	—	2	2	no	—
275	D₄×C₆₇	—	2	2	no	—
276	D₄×C₆₇	—	2	2	no	—
277	D₄×C₆₇	—	4	8	no	—
278	D₄×C₆₇	—	4	1	no	—
279	D₄×C₆₇	—	4	1	no	—
280	D₄×C₆₇	C₂²⋊Q₈	1	4	yes	complemented
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	—	2	1	no	—
287	C₂×C₄×C₆₇	—	2	2	no	—
288	C₂×C₄×C₆₇	—	2	2	no	—
289	C₂×C₄×C₆₇	—	2	2	no	—
290	C₂×C₄×C₆₇	—	2	2	no	—
291	C₂×C₄×C₆₇	—	2	1	no	—
292	C₂×C₄×C₆₇	—	2	2	no	—
293	C₂×C₄×C₆₇	—	2	1	no	—
294	C₂×C₄×C₆₇	—	2	1	no	—
295	C₂×C₄×C₆₇	—	2	1	no	—
296	C₂×C₄×C₆₇	—	2	1	no	—
297	C₂×C₄×C₆₇	—	2	1	no	—
298	C₂×C₄×C₆₇	—	4	1	no	—
299	C₂×C₄×C₆₇	—	4	1	no	—
300	C₂×C₄×C₆₇	—	4	1	no	—
301	C₂×C₄×C₆₇	—	4	1	no	—
302	C₂×C₄×C₆₇	—	4	1	no	—
303	C₂×C₄×C₆₇	—	4	1	no	—
304	C₂×C₄×C₆₇	—	4	1	no	—
305	C₂×C₄×C₆₇	—	4	1	no	—
306	C₂×C₄×C₆₇	—	4	1	no	—
307	C₂×C₄×C₆₇	—	4	1	no	—
308	C₂×C₄×C₆₇	—	4	1	no	—
309	C₂×C₄×C₆₇	—	4	1	no	—
310	C₂×C₄×C₆₇	—	4	1	no	—
311	C₂×C₄×C₆₇	—	4	1	no	—
312	C₂×C₄×C₆₇	—	4	1	no	—
313	C₂×C₄×C₆₇	—	4	1	no	—
314	C₂×C₄×C₆₇	—	4	1	no	—
315	C₂×C₄×C₆₇	—	8	4	no	—
316	C₂×C₄×C₆₇	—	8	4	no	—
317	C₂×C₄×C₆₇	—	8	4	no	—
318	C₂×C₄×C₆₇	C₂²⋊Q₈	1	2	yes	—
319	C₂×C₄×C₆₇	C₂×D₈	1	2	yes	—
320	C₂×C₄×C₆₇	C₂×D₈	1	2	yes	—
321	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
322	C₂×C₄×C₆₇	C₂²×Q₈	1	1	yes	characteristic
323	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
324	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
325	C₂×C₄×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
326	C₂×C₄×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
327	C₈×C₆₇	—	2	2	no	—
328	C₈×C₆₇	—	4	1	no	—
329	C₈×C₆₇	—	4	1	no	—
330	C₈×C₆₇	—	4	1	no	—
331	C₂²×C₆₇	—	2	2	no	—
332	C₂²×C₆₇	—	2	2	no	—
333	C₂²×C₆₇	—	2	2	no	—
334	C₂²×C₆₇	—	2	2	no	—
335	C₂²×C₆₇	—	2	2	no	—
336	C₂²×C₆₇	—	2	2	no	—
337	C₂²×C₆₇	—	2	4	no	—
338	C₂²×C₆₇	—	4	2	no	—
339	C₂²×C₆₇	—	4	2	no	—
340	C₂²×C₆₇	—	4	2	no	—
341	C₂²×C₆₇	—	4	2	no	—
342	C₂²×C₆₇	—	4	2	no	—
343	C₂²×C₆₇	—	4	2	no	—
344	C₂²×C₆₇	—	4	2	no	—
345	C₂²×C₆₇	—	4	2	no	—
346	C₂²×C₆₇	—	4	2	no	—
347	C₂²×C₆₇	—	8	16	no	—
348	C₂²×C₆₇	—	8	1	no	—
349	C₂²×C₆₇	—	8	1	no	—
350	C₂²×C₆₇	—	8	1	no	—
351	C₂²×C₆₇	—	8	1	no	—
352	C₂²×C₆₇	#474	1	4	yes	complemented
353	C₂²×C₆₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
354	C₂²×C₆₇	D₄²	1	1	yes	characteristic
355	C₂²×C₆₇	#546	1	1	yes	characteristic
356	C₂²×C₆₇	C₂²×D₈	1	1	yes	characteristic
357	C₂²×C₆₇	C₂×#137	1	1	yes	characteristic
358	C₂²×C₆₇	#576	1	1	yes	characteristic
359	C₂²×C₆₇	#577	1	1	yes	characteristic
360	C₄×C₆₇	—	2	2	no	—
361	C₄×C₆₇	—	2	2	no	—
362	C₄×C₆₇	—	2	2	no	—
363	C₄×C₆₇	—	4	1	no	—
364	C₄×C₆₇	—	4	2	no	—
365	C₄×C₆₇	—	4	1	no	—
366	C₄×C₆₇	—	8	1	no	—
367	C₄×C₆₇	—	8	1	no	—
368	C₄×C₆₇	—	8	1	no	—
369	C₄×C₆₇	—	8	1	no	—
370	C₄×C₆₇	—	8	1	no	—
371	C₄×C₆₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
372	C₄×C₆₇	#543	1	1	yes	characteristic
373	C₄×C₆₇	#546	1	1	yes	characteristic
374	C₄×C₆₇	#551	1	1	yes	characteristic
375	#25950	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
376	C₂×C₆₇	—	2	4	no	—
377	C₂×C₆₇	—	4	4	no	—
378	C₂×C₆₇	—	8	2	no	—
379	C₂×C₆₇	#2437	1	1	yes	characteristic
380	C₂×C₆₇	C₂×#474	1	1	yes	characteristic
381	C₂×C₆₇	#3081	1	1	yes	characteristic
382	C₂×C₆₇	#3266	1	1	yes	characteristic
383	C₂×C₆₇	D₄×D₈	1	1	yes	characteristic
384	C₂×C₆₇	#3294	1	1	yes	characteristic
385	C₂×C₆₇	#3314	1	1	yes	characteristic
386	C₂×#474	C₂×C₆₇	1	1	yes	characteristic, complemented
387	C₂²×#102	C₂×C₆₇	1	1	yes	characteristic
388	#2440	C₂×C₆₇	1	1	yes	characteristic, complemented
389	D₄×C₂²⋊C₄	C₂×C₆₇	1	1	yes	characteristic
390	#2093	C₂×C₆₇	1	1	yes	characteristic, complemented
391	#2067	C₂×C₆₇	1	1	yes	characteristic, complemented
392	#2067	C₂×C₆₇	1	1	yes	characteristic, complemented
393	#2023	C₂×C₆₇	1	1	yes	characteristic, complemented
394	#1862	C₂×C₆₇	1	1	yes	characteristic, complemented
395	#1862	C₂×C₆₇	1	1	yes	characteristic, complemented
396	#1852	C₂×C₆₇	1	1	yes	characteristic, complemented
397	#1850	C₂×C₆₇	1	1	yes	characteristic, complemented
398	#1808	C₂×C₆₇	1	1	yes	characteristic, complemented
399	#1802	C₂×C₆₇	1	1	yes	characteristic, complemented
400	#1786	C₂×C₆₇	1	1	yes	characteristic
401	C₆₇	#25950	1	1	yes	characteristic, direct product factor, Sylow
402	C₂³×D₄	C₂²×C₆₇	1	1	yes	characteristic
403	C₂³×C₈	C₂²×C₆₇	1	1	yes	characteristic
404	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
405	C₂×C₂²⋊Q₈	—	2	1	no	—
406	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
407	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
408	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
409	C₂²×C₂²⋊C₄	—	2	1	no	—
410	#474	—	2	4	no	—
411	C₂×#107	C₂²×C₆₇	1	1	yes	characteristic, complemented
412	C₂×#107	C₂²×C₆₇	1	1	yes	characteristic, complemented
413	C₂×#107	C₂²×C₆₇	1	1	yes	characteristic, complemented
414	C₂×#107	C₂²×C₆₇	1	1	yes	characteristic, complemented
415	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
416	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
417	C₂×#102	—	2	4	no	—
418	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
419	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
420	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
421	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
422	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
423	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
424	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
425	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
426	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
427	#398	—	2	1	no	—
428	#395	—	2	1	no	—
429	#390	C₂²×C₆₇	1	1	yes	characteristic
430	#390	C₂²×C₆₇	1	1	yes	characteristic
431	#389	C₂²×C₆₇	1	1	yes	characteristic, complemented
432	#389	C₂²×C₆₇	1	1	yes	characteristic, complemented
433	#386	—	2	1	no	—
434	#386	—	2	1	no	—
435	#385	—	2	1	no	—
436	#384	C₂²×C₆₇	1	1	yes	characteristic, complemented
437	#380	C₂²×C₆₇	1	1	yes	characteristic
438	#380	C₂²×C₆₇	1	1	yes	characteristic
439	#379	—	2	1	no	—
440	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
441	#340	C₂²×C₆₇	1	1	yes	characteristic, complemented
442	#340	C₂²×C₆₇	1	1	yes	characteristic, complemented
443	#340	C₂²×C₆₇	1	1	yes	characteristic, complemented
444	#340	C₂²×C₆₇	1	1	yes	characteristic, complemented
445	#336	C₂²×C₆₇	1	1	yes	characteristic, complemented
446	#336	C₂²×C₆₇	1	1	yes	characteristic, complemented
447	C₂⁵	—	2	1	no	—
448	C₂²×Q₈	—	2	1	no	—
449	C₂²×D₄	—	2	2	no	—
450	C₂²×D₄	—	2	2	no	—
451	C₂²×D₄	—	2	1	no	—
452	C₂²×D₄	—	2	2	no	—
453	C₂²×D₄	—	4	1	no	—
454	C₂²×D₄	—	4	1	no	—
455	C₂²×D₄	Q₈×C₆₇	1	4	yes	complemented
456	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
457	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
458	C₂³×C₄	—	2	1	no	—
459	C₂³×C₄	—	2	1	no	—
460	C₂³×C₄	—	2	1	no	—
461	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
462	C₂²×C₈	—	2	2	no	—
463	C₂²×C₈	—	2	2	no	—
464	C₂²×C₈	—	4	1	no	—
465	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
466	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
467	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
468	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
469	C₄⋊Q₈	—	2	2	no	—
470	C₄⋊Q₈	—	4	1	no	—
471	C₂²⋊Q₈	—	4	4	no	—
472	C₄×D₄	—	2	2	no	—
473	C₄×D₄	—	2	2	no	—
474	C₄×D₄	—	4	1	no	—
475	C₄×D₄	—	4	1	no	—
476	C₂×C₄⋊C₄	—	2	2	no	—
477	C₂×C₄⋊C₄	—	2	1	no	—
478	C₂×C₄⋊C₄	—	2	1	no	—
479	C₂×C₄⋊C₄	—	2	1	no	—
480	C₂×C₄⋊C₄	—	2	1	no	—
481	C₂×C₄⋊C₄	—	2	1	no	—
482	C₂×C₄⋊C₄	—	2	1	no	—
483	C₂×C₄⋊C₄	—	4	1	no	—
484	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
485	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
486	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
487	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
488	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
489	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
490	C₂×C₂²⋊C₄	—	2	1	no	—
491	C₂×C₂²⋊C₄	—	2	1	no	—
492	C₂×C₂²⋊C₄	—	2	1	no	—
493	C₂×C₂²⋊C₄	—	2	1	no	—
494	C₂×C₂²⋊C₄	—	2	1	no	—
495	C₂×C₂²⋊C₄	—	2	1	no	—
496	C₂×C₂²⋊C₄	—	2	1	no	—
497	C₂×C₂²⋊C₄	—	2	1	no	—
498	C₂×C₂²⋊C₄	—	4	4	no	—
499	C₂×C₂²⋊C₄	D₄×C₆₇	1	1	yes	characteristic
500	C₂×C₂²⋊C₄	D₄×C₆₇	1	1	yes	characteristic
501	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
502	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
503	#107	—	2	2	no	—
504	#107	—	2	2	no	—
505	#107	—	4	1	no	—
506	#107	—	4	1	no	—
507	C₄⋊C₈	—	2	2	no	—
508	C₄⋊C₈	—	4	1	no	—
509	#102	—	2	2	no	—
510	#102	—	2	2	no	—
511	#102	—	2	2	no	—
512	#102	—	2	2	no	—
513	#102	—	2	2	no	—
514	#102	—	4	1	no	—
515	#102	—	4	1	no	—
516	#102	D₄×C₆₇	1	4	yes	—
517	C₂²⋊C₈	—	2	2	no	—
518	#95	—	2	1	no	—
519	#95	—	2	1	no	—
520	#95	—	2	1	no	—
521	#95	—	2	1	no	—
522	#95	D₄×C₆₇	1	1	yes	characteristic
523	#95	D₄×C₆₇	1	1	yes	characteristic
524	C₂⁴	—	2	1	no	—
525	C₂⁴	—	2	1	no	—
526	C₂⁴	—	2	4	no	—
527	C₂⁴	—	4	2	no	—
528	C₂⁴	—	4	2	no	—
529	C₂⁴	—	4	2	no	—
530	C₂⁴	—	4	2	no	—
531	C₂⁴	—	8	1	no	—
532	C₂⁴	—	8	1	no	—
533	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
534	C₂×Q₈	—	4	2	no	—
535	C₂×Q₈	—	4	2	no	—
536	C₂×Q₈	—	8	1	no	—
537	C₂×D₄	—	2	8	no	—
538	C₂×D₄	—	2	4	no	—
539	C₂×D₄	—	2	1	no	—
540	C₂×D₄	—	2	1	no	—
541	C₂×D₄	—	2	1	no	—
542	C₂×D₄	—	2	1	no	—
543	C₂×D₄	—	2	1	no	—
544	C₂×D₄	—	2	1	no	—
545	C₂×D₄	—	2	1	no	—
546	C₂×D₄	—	2	1	no	—
547	C₂×D₄	—	4	4	no	—
548	C₂×D₄	—	4	4	no	—
549	C₂×D₄	—	4	4	no	—
550	C₂×D₄	—	4	2	no	—
551	C₂×D₄	—	4	2	no	—
552	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
553	C₂×D₄	C₂×Q₈×C₆₇	1	2	yes	—
554	C₂×D₄	C₂×Q₈×C₆₇	1	2	yes	—
555	C₂×D₄	#41×C₆₇	1	2	yes	—
556	C₂²×C₄	—	2	1	no	—
557	C₂²×C₄	—	2	1	no	—
558	C₂²×C₄	—	2	1	no	—
559	C₂²×C₄	—	2	1	no	—
560	C₂²×C₄	—	2	1	no	—
561	C₂²×C₄	—	2	1	no	—
562	C₂²×C₄	—	2	1	no	—
563	C₂²×C₄	—	2	1	no	—
564	C₂²×C₄	—	2	1	no	—
565	C₂²×C₄	—	2	1	no	—
566	C₂²×C₄	—	4	2	no	—
567	C₂²×C₄	—	4	2	no	—
568	C₂²×C₄	—	4	2	no	—
569	C₂²×C₄	—	4	2	no	—
570	C₂²×C₄	—	4	2	no	—
571	C₂²×C₄	—	4	2	no	—
572	C₂²×C₄	—	8	1	no	—
573	C₂²×C₄	—	8	1	no	—
574	C₂²×C₄	—	8	1	no	—
575	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
576	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
577	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
578	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
579	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
580	C₂²×C₄	C₂×Q₈×C₆₇	1	2	yes	—
581	C₂²×C₄	#41×C₆₇	1	2	yes	—
582	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
583	C₂×C₈	—	2	1	no	—
584	C₂×C₈	—	2	1	no	—
585	C₂×C₈	—	2	1	no	—
586	C₂×C₈	—	2	1	no	—
587	C₂×C₈	—	2	1	no	—
588	C₂×C₈	—	2	1	no	—
589	C₂×C₈	—	2	1	no	—
590	C₂×C₈	—	2	1	no	—
591	C₂×C₈	—	2	1	no	—
592	C₂×C₈	—	2	1	no	—
593	C₂×C₈	—	2	1	no	—
594	C₂×C₈	—	4	4	no	—
595	C₂×C₈	C₂×D₄×C₆₇	1	2	yes	—
596	C₄⋊C₄	—	2	1	no	—
597	C₄⋊C₄	—	2	1	no	—
598	C₄⋊C₄	—	2	1	no	—
599	C₄⋊C₄	—	2	1	no	—
600	C₄⋊C₄	—	2	1	no	—
601	C₄⋊C₄	—	2	1	no	—
602	C₄⋊C₄	—	2	1	no	—
603	C₄⋊C₄	—	2	1	no	—
604	C₄⋊C₄	—	2	1	no	—
605	C₄⋊C₄	—	2	1	no	—
606	C₄⋊C₄	—	2	1	no	—
607	C₄⋊C₄	—	4	2	no	—
608	C₄⋊C₄	—	4	2	no	—
609	C₄⋊C₄	—	4	2	no	—
610	C₄⋊C₄	—	4	2	no	—
611	C₄⋊C₄	—	4	2	no	—
612	C₄⋊C₄	—	8	1	no	—
613	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
614	C₂²⋊C₄	—	2	2	no	—
615	C₂²⋊C₄	—	4	2	no	—
616	C₂²⋊C₄	—	4	2	no	—
617	C₂²⋊C₄	—	4	2	no	—
618	C₂²⋊C₄	—	4	2	no	—
619	C₂²⋊C₄	—	4	2	no	—
620	C₂²⋊C₄	—	4	2	no	—
621	C₂²⋊C₄	—	8	1	no	—
622	C₂²⋊C₄	—	8	1	no	—
623	C₂²⋊C₄	D₈×C₆₇	1	4	yes	—
624	C₄²	—	2	1	no	—
625	C₄²	—	2	1	no	—
626	C₄²	—	2	1	no	—
627	C₄²	—	2	1	no	—
628	C₂³	—	2	1	no	—
629	C₂³	—	2	1	no	—
630	C₂³	—	2	1	no	—
631	C₂³	—	2	1	no	—
632	C₂³	—	2	2	no	—
633	C₂³	—	2	2	no	—
634	C₂³	—	2	2	no	—
635	C₂³	—	2	2	no	—
636	C₂³	—	4	8	no	—
637	C₂³	—	4	1	no	—
638	C₂³	—	4	1	no	—
639	C₂³	—	4	1	no	—
640	C₂³	—	4	1	no	—
641	C₂³	—	4	8	no	—
642	C₂³	—	4	1	no	—
643	C₂³	—	4	1	no	—
644	C₂³	—	4	1	no	—
645	C₂³	—	4	1	no	—
646	C₂³	—	4	1	no	—
647	C₂³	—	4	1	no	—
648	C₂³	—	8	4	no	—
649	C₂³	—	8	4	no	—
650	C₂³	—	8	4	no	—
651	C₂³	—	8	4	no	—
652	C₂³	—	8	4	no	—
653	C₂³	C₂²⋊Q₈×C₆₇	1	2	yes	—
654	C₂³	C₂×D₈×C₆₇	1	2	yes	—
655	C₂³	#137×C₆₇	1	2	yes	—
656	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
657	Q₈	—	8	4	no	—
658	D₄	—	2	2	no	—
659	D₄	—	2	2	no	—
660	D₄	—	2	2	no	—
661	D₄	—	2	2	no	—
662	D₄	—	2	2	no	—
663	D₄	—	4	8	no	—
664	D₄	—	4	1	no	—
665	D₄	—	4	1	no	—
666	D₄	C₂²⋊Q₈×C₆₇	1	4	yes	complemented
667	C₂×C₄	—	2	1	no	—
668	C₂×C₄	—	2	1	no	—
669	C₂×C₄	—	2	1	no	—
670	C₂×C₄	—	2	1	no	—
671	C₂×C₄	—	2	1	no	—
672	C₂×C₄	—	2	1	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	2	2	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	1	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	1	no	—
680	C₂×C₄	—	2	1	no	—
681	C₂×C₄	—	2	1	no	—
682	C₂×C₄	—	2	1	no	—
683	C₂×C₄	—	2	1	no	—
684	C₂×C₄	—	4	1	no	—
685	C₂×C₄	—	4	1	no	—
686	C₂×C₄	—	4	1	no	—
687	C₂×C₄	—	4	1	no	—
688	C₂×C₄	—	4	1	no	—
689	C₂×C₄	—	4	1	no	—
690	C₂×C₄	—	4	1	no	—
691	C₂×C₄	—	4	1	no	—
692	C₂×C₄	—	4	1	no	—
693	C₂×C₄	—	4	1	no	—
694	C₂×C₄	—	4	1	no	—
695	C₂×C₄	—	4	1	no	—
696	C₂×C₄	—	4	1	no	—
697	C₂×C₄	—	4	1	no	—
698	C₂×C₄	—	4	1	no	—
699	C₂×C₄	—	4	1	no	—
700	C₂×C₄	—	4	1	no	—
701	C₂×C₄	—	8	4	no	—
702	C₂×C₄	—	8	4	no	—
703	C₂×C₄	—	8	4	no	—
704	C₂×C₄	C₂²⋊Q₈×C₆₇	1	2	yes	—
705	C₂×C₄	C₂×D₈×C₆₇	1	2	yes	—
706	C₂×C₄	C₂×D₈×C₆₇	1	2	yes	—
707	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
708	C₂×C₄	C₂²×Q₈×C₆₇	1	1	yes	characteristic
709	C₂×C₄	C₂×#41×C₆₇	1	1	yes	characteristic
710	C₂×C₄	C₂×#41×C₆₇	1	1	yes	characteristic
711	C₂×C₄	H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
712	C₂×C₄	H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
713	C₈	—	2	2	no	—
714	C₈	—	4	1	no	—
715	C₈	—	4	1	no	—
716	C₈	—	4	1	no	—
717	C₂²	—	2	2	no	—
718	C₂²	—	2	2	no	—
719	C₂²	—	2	2	no	—
720	C₂²	—	2	2	no	—
721	C₂²	—	2	2	no	—
722	C₂²	—	2	2	no	—
723	C₂²	—	2	4	no	—
724	C₂²	—	4	2	no	—
725	C₂²	—	4	2	no	—
726	C₂²	—	4	2	no	—
727	C₂²	—	4	2	no	—
728	C₂²	—	4	2	no	—
729	C₂²	—	4	2	no	—
730	C₂²	—	4	2	no	—
731	C₂²	—	4	2	no	—
732	C₂²	—	4	2	no	—
733	C₂²	—	8	16	no	—
734	C₂²	—	8	1	no	—
735	C₂²	—	8	1	no	—
736	C₂²	—	8	1	no	—
737	C₂²	—	8	1	no	—
738	C₂²	#474×C₆₇	1	4	yes	complemented
739	C₂²	C₂×C₂²⋊Q₈×C₆₇	1	1	yes	characteristic
740	C₂²	D₄²×C₆₇	1	1	yes	characteristic
741	C₂²	#546×C₆₇	1	1	yes	characteristic
742	C₂²	C₂²×D₈×C₆₇	1	1	yes	characteristic
743	C₂²	C₂×#137×C₆₇	1	1	yes	characteristic
744	C₂²	#576×C₆₇	1	1	yes	characteristic
745	C₂²	#577×C₆₇	1	1	yes	characteristic
746	C₄	—	2	2	no	—
747	C₄	—	2	2	no	—
748	C₄	—	2	2	no	—
749	C₄	—	4	1	no	—
750	C₄	—	4	2	no	—
751	C₄	—	4	1	no	—
752	C₄	—	8	1	no	—
753	C₄	—	8	1	no	—
754	C₄	—	8	1	no	—
755	C₄	—	8	1	no	—
756	C₄	—	8	1	no	—
757	C₄	C₂×C₂²⋊Q₈×C₆₇	1	1	yes	characteristic
758	C₄	#543×C₆₇	1	1	yes	characteristic
759	C₄	#546×C₆₇	1	1	yes	characteristic
760	C₄	#551×C₆₇	1	1	yes	characteristic
761	C₂	—	2	4	no	—
762	C₂	—	4	4	no	—
763	C₂	—	8	2	no	—
764	C₂	C₆₇×#2437	1	1	yes	characteristic
765	C₂	C₂×#474×C₆₇	1	1	yes	characteristic
766	C₂	C₆₇×#3081	1	1	yes	characteristic
767	C₂	C₆₇×#3266	1	1	yes	characteristic
768	C₂	D₄×D₈×C₆₇	1	1	yes	characteristic
769	C₂	C₆₇×#3294	1	1	yes	characteristic
770	C₂	C₆₇×#3314	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₇
prime radical	C₂³×D₄×C₆₇	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ C₄×C₂²⋊C₄×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#474×C₆₇	C₂	semidirect
3. C₆₇×#2440	C₂	semidirect
5. C₆₇×#2093	C₂	semidirect
6. C₆₇×#2067	C₂	semidirect
7. C₆₇×#2067	C₂	semidirect
8. C₆₇×#2023	C₂	semidirect
9. C₆₇×#1862	C₂	semidirect
10. C₆₇×#1862	C₂	semidirect
11. C₆₇×#1852	C₂	semidirect
12. C₆₇×#1850	C₂	semidirect
13. C₆₇×#1808	C₂	semidirect
14. C₆₇×#1802	C₂	semidirect
18. C₂×C₄⋊Q₈×C₆₇	C₂²	semidirect
25. C₂×#107×C₆₇	C₂²	semidirect
26. C₂×#107×C₆₇	C₂²	semidirect
27. C₂×#107×C₆₇	C₂²	semidirect
28. C₂×#107×C₆₇	C₂²	semidirect
29. C₂×C₄⋊C₈×C₆₇	C₂²	semidirect
30. C₂×C₄⋊C₈×C₆₇	C₂²	semidirect
45. #389×C₆₇	C₂²	semidirect
46. #389×C₆₇	C₂²	semidirect
50. #384×C₆₇	C₂²	semidirect
55. #340×C₆₇	C₂²	semidirect
56. #340×C₆₇	C₂²	semidirect
57. #340×C₆₇	C₂²	semidirect
58. #340×C₆₇	C₂²	semidirect
59. #336×C₆₇	C₂²	semidirect
60. #336×C₆₇	C₂²	semidirect
69. C₂²×D₄×C₆₇	Q₈	semidirect
280. D₄×C₆₇	C₂²⋊Q₈	semidirect
352. C₂²×C₆₇	#474	semidirect
375. #25950	C₆₇	direct (N × H)
386. C₂×#474	C₂×C₆₇	semidirect
388. #2440	C₂×C₆₇	semidirect
390. #2093	C₂×C₆₇	semidirect
391. #2067	C₂×C₆₇	semidirect
392. #2067	C₂×C₆₇	semidirect
393. #2023	C₂×C₆₇	semidirect
394. #1862	C₂×C₆₇	semidirect
395. #1862	C₂×C₆₇	semidirect
396. #1852	C₂×C₆₇	semidirect
397. #1850	C₂×C₆₇	semidirect
398. #1808	C₂×C₆₇	semidirect
399. #1802	C₂×C₆₇	semidirect
401. C₆₇	#25950	direct (N × H)
404. C₂×C₄⋊Q₈	C₂²×C₆₇	semidirect
411. C₂×#107	C₂²×C₆₇	semidirect
412. C₂×#107	C₂²×C₆₇	semidirect
413. C₂×#107	C₂²×C₆₇	semidirect
414. C₂×#107	C₂²×C₆₇	semidirect
415. C₂×C₄⋊C₈	C₂²×C₆₇	semidirect
416. C₂×C₄⋊C₈	C₂²×C₆₇	semidirect
431. #389	C₂²×C₆₇	semidirect
432. #389	C₂²×C₆₇	semidirect
436. #384	C₂²×C₆₇	semidirect
441. #340	C₂²×C₆₇	semidirect
442. #340	C₂²×C₆₇	semidirect
443. #340	C₂²×C₆₇	semidirect
444. #340	C₂²×C₆₇	semidirect
445. #336	C₂²×C₆₇	semidirect
446. #336	C₂²×C₆₇	semidirect
455. C₂²×D₄	Q₈×C₆₇	semidirect
666. D₄	C₂²⋊Q₈×C₆₇	semidirect
738. C₂²	#474×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#474×C₆₇	2
C₂²×#102×C₆₇	2
C₆₇×#2440	2
D₄×C₂²⋊C₄×C₆₇	2
C₆₇×#2093	2
C₆₇×#2067	2
C₆₇×#2023	2
C₆₇×#1862	2
C₆₇×#1852	2
C₆₇×#1850	2
C₆₇×#1808	2
C₆₇×#1802	2
C₆₇×#1786	2
#25950	67

Subgroups — C67×#25950 #30705201

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#25950 #30705201