Subgroups — C₆₇×#18054 #30697305

Order 17152.

726 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#2974	C₂	1	2	yes	maximal, complemented
2	C₂×C₄×D₈×C₆₇	C₂	1	1	yes	maximal, characteristic
3	C₆₇×#1589	C₂	1	2	yes	maximal, complemented
4	C₆₇×#1586	C₂	1	4	yes	maximal, complemented
5	C₈×D₈×C₆₇	C₂	1	2	yes	maximal, complemented
6	C₆₇×#1568	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#1490	C₂	1	2	yes	maximal, complemented
8	C₈×M₁₆×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×D₈×C₆₇	C₄	1	1	yes	characteristic
10	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
11	C₄×D₈×C₆₇	C₄	1	1	yes	characteristic
12	C₄×D₈×C₆₇	C₄	1	2	yes	—
13	C₄×D₈×C₆₇	C₄	1	1	yes	characteristic
14	C₄×D₈×C₆₇	C₂²	1	1	yes	characteristic
15	C₄×D₈×C₆₇	C₂²	1	2	yes	—
16	C₄×D₈×C₆₇	C₂²	1	1	yes	characteristic
17	#436×C₆₇	C₂²	1	4	yes	complemented
18	#435×C₆₇	—	2	4	no	—
19	C₈×D₄×C₆₇	C₂²	1	4	yes	complemented
20	#432×C₆₇	C₂²	1	2	yes	—
21	#431×C₆₇	C₂²	1	1	yes	characteristic
22	C₂×#107×C₆₇	C₄	1	1	yes	characteristic
23	C₂×#102×C₆₇	C₄	1	2	yes	—
24	#407×C₆₇	—	2	2	no	—
25	C₂×C₂²⋊C₈×C₆₇	—	2	2	no	—
26	C₄×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
28	#335×C₆₇	C₂²	1	2	yes	complemented
29	#334×C₆₇	C₂²	1	2	yes	complemented
30	D₄⋊C₈×C₆₇	C₂²	1	4	yes	complemented
31	D₄⋊C₈×C₆₇	C₂²	1	4	yes	complemented
32	#322×C₆₇	C₂²	1	2	yes	complemented
33	C₈²×C₆₇	C₂²	1	2	yes	complemented
34	C₂²×D₄×C₆₇	C₂×C₄	1	2	yes	—
35	C₂³×C₄×C₆₇	—	2	2	no	—
36	C₂×D₈×C₆₇	—	2	4	no	—
37	C₂×D₈×C₆₇	C₂×C₄	1	2	yes	—
38	C₂×D₈×C₆₇	C₂×C₄	1	1	yes	characteristic
39	C₂×D₈×C₆₇	C₂×C₄	1	1	yes	characteristic
40	C₂×M₁₆×C₆₇	—	2	1	no	—
41	C₂×M₁₆×C₆₇	—	2	4	no	—
42	C₂²×C₈×C₆₇	—	2	4	no	—
43	C₂²×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
44	C₂²×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
45	C₄×D₄×C₆₇	—	2	2	no	—
46	C₄×D₄×C₆₇	—	2	2	no	—
47	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
48	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
49	C₄×D₄×C₆₇	C₂³	1	2	yes	—
50	C₄×D₄×C₆₇	C₂³	1	2	yes	—
51	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
52	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
53	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
54	#107×C₆₇	C₂×C₄	1	2	yes	—
55	#107×C₆₇	C₂×C₄	1	1	yes	characteristic
56	#107×C₆₇	C₂×C₄	1	1	yes	characteristic
57	C₄⋊C₈×C₆₇	D₄	1	2	yes	—
58	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
59	#102×C₆₇	C₂×C₄	1	2	yes	—
60	#102×C₆₇	C₂×C₄	1	2	yes	—
61	#102×C₆₇	C₂×C₄	1	2	yes	—
62	#102×C₆₇	C₂×C₄	1	2	yes	—
63	C₂²⋊C₈×C₆₇	—	2	2	no	—
64	C₂²⋊C₈×C₆₇	—	2	4	no	—
65	C₂²⋊C₈×C₆₇	—	2	4	no	—
66	C₂²⋊C₈×C₆₇	D₄	1	1	yes	characteristic
67	C₂²⋊C₈×C₆₇	D₄	1	1	yes	characteristic
68	#97×C₆₇	—	2	2	no	—
69	#97×C₆₇	—	2	1	no	—
70	C₄×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
71	C₄×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
72	C₄×C₈×C₆₇	C₂³	1	2	yes	—
73	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
74	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
75	C₄×C₈×C₆₇	C₂³	1	2	yes	—
76	C₂⁴×C₆₇	—	2	2	no	—
77	C₂×D₄×C₆₇	—	2	4	no	—
78	C₂×D₄×C₆₇	—	2	2	no	—
79	C₂×D₄×C₆₇	—	4	2	no	—
80	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
81	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
82	C₂²×C₄×C₆₇	—	2	2	no	—
83	C₂²×C₄×C₆₇	—	2	2	no	—
84	C₂²×C₄×C₆₇	—	2	2	no	—
85	C₂²×C₄×C₆₇	—	2	2	no	—
86	C₂²×C₄×C₆₇	—	2	2	no	—
87	C₂²×C₄×C₆₇	—	8	4	no	—
88	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
91	D₈×C₆₇	—	2	4	no	—
92	D₈×C₆₇	—	2	2	no	—
93	D₈×C₆₇	M₁₆	1	4	yes	complemented
94	M₁₆×C₆₇	—	2	4	no	—
95	M₁₆×C₆₇	—	8	4	no	—
96	C₂×C₈×C₆₇	—	2	2	no	—
97	C₂×C₈×C₆₇	—	2	2	no	—
98	C₂×C₈×C₆₇	—	2	4	no	—
99	C₂×C₈×C₆₇	—	4	1	no	—
100	C₂×C₈×C₆₇	—	8	4	no	—
101	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
102	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
103	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
104	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
105	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
106	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
107	C₄⋊C₄×C₆₇	—	2	2	no	—
108	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
109	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
110	C₂²⋊C₄×C₆₇	—	2	2	no	—
111	C₂²⋊C₄×C₆₇	—	2	2	no	—
112	C₂²⋊C₄×C₆₇	—	2	2	no	—
113	C₂²⋊C₄×C₆₇	—	2	2	no	—
114	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
115	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
116	C₄²×C₆₇	#41	1	1	yes	characteristic
117	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
118	C₂³×C₆₇	—	2	2	no	—
119	C₂³×C₆₇	—	2	2	no	—
120	C₂³×C₆₇	—	4	4	no	—
121	C₂³×C₆₇	—	4	4	no	—
122	C₂³×C₆₇	—	8	2	no	—
123	C₂³×C₆₇	C₄×D₄	1	1	yes	characteristic
124	D₄×C₆₇	—	2	2	no	—
125	D₄×C₆₇	—	2	2	no	—
126	D₄×C₆₇	—	2	2	no	—
127	D₄×C₆₇	—	4	4	no	—
128	D₄×C₆₇	C₂×M₁₆	1	4	yes	—
129	C₂×C₄×C₆₇	—	2	2	no	—
130	C₂×C₄×C₆₇	—	2	1	no	—
131	C₂×C₄×C₆₇	—	2	1	no	—
132	C₂×C₄×C₆₇	—	2	2	no	—
133	C₂×C₄×C₆₇	—	2	2	no	—
134	C₂×C₄×C₆₇	—	2	2	no	—
135	C₂×C₄×C₆₇	—	4	4	no	—
136	C₂×C₄×C₆₇	—	4	4	no	—
137	C₂×C₄×C₆₇	—	8	2	no	—
138	C₂×C₄×C₆₇	—	8	2	no	—
139	C₂×C₄×C₆₇	—	8	2	no	—
140	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
141	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
142	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
143	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
144	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
145	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
146	C₈×C₆₇	—	2	4	no	—
147	C₈×C₆₇	—	2	1	no	—
148	C₈×C₆₇	—	2	1	no	—
149	C₈×C₆₇	—	2	1	no	—
150	C₈×C₆₇	—	2	2	no	—
151	C₈×C₆₇	—	2	2	no	—
152	C₈×C₆₇	—	4	4	no	—
153	C₈×C₆₇	C₂×M₁₆	1	2	yes	—
154	C₂²×C₆₇	—	2	1	no	—
155	C₂²×C₆₇	—	2	1	no	—
156	C₂²×C₆₇	—	2	4	no	—
157	C₂²×C₆₇	—	4	2	no	—
158	C₂²×C₆₇	—	4	2	no	—
159	C₂²×C₆₇	—	4	2	no	—
160	C₂²×C₆₇	—	4	2	no	—
161	C₂²×C₆₇	—	4	2	no	—
162	C₂²×C₆₇	—	8	8	no	—
163	C₂²×C₆₇	#443	1	2	yes	—
164	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
165	C₄×C₆₇	—	2	1	no	—
166	C₄×C₆₇	—	2	1	no	—
167	C₄×C₆₇	—	2	1	no	—
168	C₄×C₆₇	—	2	1	no	—
169	C₄×C₆₇	—	4	2	no	—
170	C₄×C₆₇	—	4	2	no	—
171	C₄×C₆₇	C₂²×M₁₆	1	1	yes	characteristic
172	C₄×C₆₇	#568	1	1	yes	characteristic
173	C₄×C₆₇	#576	1	2	yes	—
174	#18054	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
175	C₂×C₆₇	—	2	2	no	—
176	C₂×C₆₇	—	4	4	no	—
177	C₂×C₆₇	—	8	2	no	—
178	C₂×C₆₇	D₄×M₁₆	1	1	yes	characteristic
179	C₂×C₆₇	#2948	1	1	yes	characteristic
180	C₂×C₆₇	C₂×#443	1	1	yes	characteristic
181	#2974	C₂×C₆₇	1	2	yes	complemented
182	C₂×C₄×D₈	C₂×C₆₇	1	1	yes	characteristic
183	#1589	C₂×C₆₇	1	2	yes	complemented
184	#1586	C₂×C₆₇	1	4	yes	complemented
185	C₈×D₈	C₂×C₆₇	1	2	yes	complemented
186	#1568	C₂×C₆₇	1	1	yes	characteristic, complemented
187	#1490	C₂×C₆₇	1	2	yes	complemented
188	C₈×M₁₆	C₂×C₆₇	1	1	yes	characteristic, complemented
189	C₆₇	#18054	1	1	yes	characteristic, direct product factor, Sylow
190	C₂²×D₈	C₄×C₆₇	1	1	yes	characteristic
191	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
192	C₄×D₈	C₄×C₆₇	1	2	yes	—
193	C₄×D₈	C₄×C₆₇	1	1	yes	characteristic
194	C₄×D₈	C₄×C₆₇	1	1	yes	characteristic
195	C₄×D₈	C₂²×C₆₇	1	1	yes	characteristic
196	C₄×D₈	C₂²×C₆₇	1	2	yes	—
197	C₄×D₈	C₂²×C₆₇	1	1	yes	characteristic
198	#436	C₂²×C₆₇	1	4	yes	complemented
199	#435	—	2	4	no	—
200	C₈×D₄	C₂²×C₆₇	1	4	yes	complemented
201	#432	C₂²×C₆₇	1	2	yes	—
202	#431	C₂²×C₆₇	1	1	yes	characteristic
203	C₂×#107	C₄×C₆₇	1	1	yes	characteristic
204	C₂×#102	C₄×C₆₇	1	2	yes	—
205	#407	—	2	2	no	—
206	C₂×C₂²⋊C₈	—	2	2	no	—
207	C₄×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
208	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic
209	#335	C₂²×C₆₇	1	2	yes	complemented
210	#334	C₂²×C₆₇	1	2	yes	complemented
211	D₄⋊C₈	C₂²×C₆₇	1	4	yes	complemented
212	D₄⋊C₈	C₂²×C₆₇	1	4	yes	complemented
213	#322	C₂²×C₆₇	1	2	yes	complemented
214	C₈²	C₂²×C₆₇	1	2	yes	complemented
215	C₂²×D₄	C₂×C₄×C₆₇	1	2	yes	—
216	C₂³×C₄	—	2	2	no	—
217	C₂×D₈	—	2	4	no	—
218	C₂×D₈	C₂×C₄×C₆₇	1	2	yes	—
219	C₂×D₈	C₂×C₄×C₆₇	1	1	yes	characteristic
220	C₂×D₈	C₂×C₄×C₆₇	1	1	yes	characteristic
221	C₂×M₁₆	—	2	1	no	—
222	C₂×M₁₆	—	2	4	no	—
223	C₂²×C₈	—	2	4	no	—
224	C₂²×C₈	C₂×C₄×C₆₇	1	1	yes	characteristic
225	C₂²×C₈	C₂×C₄×C₆₇	1	1	yes	characteristic
226	C₄×D₄	—	2	2	no	—
227	C₄×D₄	—	2	2	no	—
228	C₄×D₄	C₂×C₄×C₆₇	1	2	yes	—
229	C₄×D₄	C₂×C₄×C₆₇	1	2	yes	—
230	C₄×D₄	C₂³×C₆₇	1	2	yes	—
231	C₄×D₄	C₂³×C₆₇	1	2	yes	—
232	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	2	yes	—
233	C₂×C₂²⋊C₄	—	2	2	no	—
234	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
235	#107	C₂×C₄×C₆₇	1	2	yes	—
236	#107	C₂×C₄×C₆₇	1	1	yes	characteristic
237	#107	C₂×C₄×C₆₇	1	1	yes	characteristic
238	C₄⋊C₈	D₄×C₆₇	1	2	yes	—
239	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
240	#102	C₂×C₄×C₆₇	1	2	yes	—
241	#102	C₂×C₄×C₆₇	1	2	yes	—
242	#102	C₂×C₄×C₆₇	1	2	yes	—
243	#102	C₂×C₄×C₆₇	1	2	yes	—
244	C₂²⋊C₈	—	2	2	no	—
245	C₂²⋊C₈	—	2	4	no	—
246	C₂²⋊C₈	—	2	4	no	—
247	C₂²⋊C₈	D₄×C₆₇	1	1	yes	characteristic
248	C₂²⋊C₈	D₄×C₆₇	1	1	yes	characteristic
249	#97	—	2	2	no	—
250	#97	—	2	1	no	—
251	C₄×C₈	C₂×C₄×C₆₇	1	1	yes	characteristic
252	C₄×C₈	C₂×C₄×C₆₇	1	1	yes	characteristic
253	C₄×C₈	C₂³×C₆₇	1	2	yes	—
254	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
255	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
256	C₄×C₈	C₂³×C₆₇	1	2	yes	—
257	C₂⁴	—	2	2	no	—
258	C₂×D₄	—	2	4	no	—
259	C₂×D₄	—	2	2	no	—
260	C₂×D₄	—	4	2	no	—
261	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
262	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
263	C₂²×C₄	—	2	2	no	—
264	C₂²×C₄	—	2	2	no	—
265	C₂²×C₄	—	2	2	no	—
266	C₂²×C₄	—	2	2	no	—
267	C₂²×C₄	—	2	2	no	—
268	C₂²×C₄	—	8	4	no	—
269	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
270	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
271	C₂²×C₄	#41×C₆₇	1	1	yes	characteristic
272	D₈	—	2	4	no	—
273	D₈	—	2	2	no	—
274	D₈	M₁₆×C₆₇	1	4	yes	complemented
275	M₁₆	—	2	4	no	—
276	M₁₆	—	8	4	no	—
277	C₂×C₈	—	2	2	no	—
278	C₂×C₈	—	2	2	no	—
279	C₂×C₈	—	2	4	no	—
280	C₂×C₈	—	4	1	no	—
281	C₂×C₈	—	8	4	no	—
282	C₂×C₈	C₂²×C₄×C₆₇	1	1	yes	characteristic
283	C₂×C₈	C₂²×C₄×C₆₇	1	1	yes	characteristic
284	C₂×C₈	C₂²×C₄×C₆₇	1	1	yes	characteristic
285	C₂×C₈	C₂²×C₄×C₆₇	1	1	yes	characteristic
286	C₂×C₈	C₂×D₄×C₆₇	1	2	yes	—
287	C₂×C₈	C₂×D₄×C₆₇	1	2	yes	—
288	C₄⋊C₄	—	2	2	no	—
289	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
290	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
291	C₂²⋊C₄	—	2	2	no	—
292	C₂²⋊C₄	—	2	2	no	—
293	C₂²⋊C₄	—	2	2	no	—
294	C₂²⋊C₄	—	2	2	no	—
295	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
296	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
297	C₄²	#41×C₆₇	1	1	yes	characteristic
298	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
299	C₂³	—	2	2	no	—
300	C₂³	—	2	2	no	—
301	C₂³	—	4	4	no	—
302	C₂³	—	4	4	no	—
303	C₂³	—	8	2	no	—
304	C₂³	C₄×D₄×C₆₇	1	1	yes	characteristic
305	D₄	—	2	2	no	—
306	D₄	—	2	2	no	—
307	D₄	—	2	2	no	—
308	D₄	—	4	4	no	—
309	D₄	C₂×M₁₆×C₆₇	1	4	yes	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	1	no	—
312	C₂×C₄	—	2	1	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	4	4	no	—
317	C₂×C₄	—	4	4	no	—
318	C₂×C₄	—	8	2	no	—
319	C₂×C₄	—	8	2	no	—
320	C₂×C₄	—	8	2	no	—
321	C₂×C₄	C₄×D₄×C₆₇	1	1	yes	characteristic
322	C₂×C₄	C₄×D₄×C₆₇	1	1	yes	characteristic
323	C₂×C₄	C₄×D₄×C₆₇	1	1	yes	characteristic
324	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
325	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
326	C₂×C₄	C₂×#41×C₆₇	1	1	yes	characteristic
327	C₈	—	2	4	no	—
328	C₈	—	2	1	no	—
329	C₈	—	2	1	no	—
330	C₈	—	2	1	no	—
331	C₈	—	2	2	no	—
332	C₈	—	2	2	no	—
333	C₈	—	4	4	no	—
334	C₈	C₂×M₁₆×C₆₇	1	2	yes	—
335	C₂²	—	2	1	no	—
336	C₂²	—	2	1	no	—
337	C₂²	—	2	4	no	—
338	C₂²	—	4	2	no	—
339	C₂²	—	4	2	no	—
340	C₂²	—	4	2	no	—
341	C₂²	—	4	2	no	—
342	C₂²	—	4	2	no	—
343	C₂²	—	8	8	no	—
344	C₂²	#443×C₆₇	1	2	yes	—
345	C₂²	C₂×C₄×D₄×C₆₇	1	1	yes	characteristic
346	C₄	—	2	1	no	—
347	C₄	—	2	1	no	—
348	C₄	—	2	1	no	—
349	C₄	—	2	1	no	—
350	C₄	—	4	2	no	—
351	C₄	—	4	2	no	—
352	C₄	C₂²×M₁₆×C₆₇	1	1	yes	characteristic
353	C₄	#568×C₆₇	1	1	yes	characteristic
354	C₄	#576×C₆₇	1	2	yes	—
355	C₂	—	2	2	no	—
356	C₂	—	4	4	no	—
357	C₂	—	8	2	no	—
358	C₂	D₄×M₁₆×C₆₇	1	1	yes	characteristic
359	C₂	C₆₇×#2948	1	1	yes	characteristic
360	C₂	C₂×#443×C₆₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₆₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₆₇
Frattini, cosocle	C₄²	C₂⁴×C₆₇
socle	C₂²×C₆₇	C₂×C₄×D₄
prime radical	C₂²×D₈×C₆₇	C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₆₇ ◁ #431×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#2974	C₂	semidirect
3. C₆₇×#1589	C₂	semidirect
4. C₆₇×#1586	C₂	semidirect
5. C₈×D₈×C₆₇	C₂	semidirect
6. C₆₇×#1568	C₂	semidirect
7. C₆₇×#1490	C₂	semidirect
8. C₈×M₁₆×C₆₇	C₂	semidirect
17. #436×C₆₇	C₂²	semidirect
19. C₈×D₄×C₆₇	C₂²	semidirect
28. #335×C₆₇	C₂²	semidirect
29. #334×C₆₇	C₂²	semidirect
30. D₄⋊C₈×C₆₇	C₂²	semidirect
31. D₄⋊C₈×C₆₇	C₂²	semidirect
32. #322×C₆₇	C₂²	semidirect
33. C₈²×C₆₇	C₂²	semidirect
93. D₈×C₆₇	M₁₆	semidirect
174. #18054	C₆₇	direct (N × H)
181. #2974	C₂×C₆₇	semidirect
183. #1589	C₂×C₆₇	semidirect
184. #1586	C₂×C₆₇	semidirect
185. C₈×D₈	C₂×C₆₇	semidirect
186. #1568	C₂×C₆₇	semidirect
187. #1490	C₂×C₆₇	semidirect
188. C₈×M₁₆	C₂×C₆₇	semidirect
189. C₆₇	#18054	direct (N × H)
198. #436	C₂²×C₆₇	semidirect
200. C₈×D₄	C₂²×C₆₇	semidirect
209. #335	C₂²×C₆₇	semidirect
210. #334	C₂²×C₆₇	semidirect
211. D₄⋊C₈	C₂²×C₆₇	semidirect
212. D₄⋊C₈	C₂²×C₆₇	semidirect
213. #322	C₂²×C₆₇	semidirect
214. C₈²	C₂²×C₆₇	semidirect
274. D₈	M₁₆×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#2974	2
C₂×C₄×D₈×C₆₇	2
C₆₇×#1589	2
C₆₇×#1586	2
C₈×D₈×C₆₇	2
C₆₇×#1568	2
C₆₇×#1490	2
C₈×M₁₆×C₆₇	2
#18054	67

Subgroups — C67×#18054 #30697305

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#18054 #30697305