Subgroups — #31008469

Order 17152.

826 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#14523982	C₂	1	1	yes	maximal, characteristic
2	C₂×M₃₂×D₆₇	C₂	1	1	yes	maximal, characteristic
3	#405×D₆₇	C₂	1	1	yes	maximal, characteristic
4	#22561808	C₂	1	1	yes	maximal, characteristic, complemented
5	#22561807	C₂	1	2	yes	maximal, complemented
6	#22561806	C₂	1	1	yes	maximal, characteristic, complemented
7	#22561805	C₂	1	1	yes	maximal, characteristic, complemented
8	#22561804	C₂	1	2	yes	maximal, complemented
9	#22561802	C₂	1	2	yes	maximal, complemented
10	C₄×#14523982	C₂	1	2	yes	maximal, complemented
11	C₆₇×#2108	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×M₁₆×D₆₇	C₄	1	1	yes	characteristic
13	C₂²×C₈×D₆₇	C₂²	1	1	yes	characteristic
14	#117×D₆₇	C₄	1	1	yes	characteristic
15	C₂×#14523983	C₂²	1	1	yes	characteristic
16	C₂×#14523982	C₄	1	8	yes	complemented
17	C₂×#14523982	C₂²	1	1	yes	characteristic
18	C₂×#14523982	C₂²	1	2	yes	—
19	C₂×#14523982	C₂²	1	1	yes	characteristic
20	C₂×#14523982	C₂²	1	1	yes	characteristic
21	C₂×#14523982	C₂²	1	1	yes	characteristic
22	M₃₂×D₆₇	C₄	1	8	yes	complemented
23	C₂²×C₆₇⋊C₁₆	C₂²	1	1	yes	characteristic
24	C₂×C₁₆×D₆₇	C₂²	1	2	yes	—
25	#16863354	C₄	1	1	yes	characteristic
26	#16863353	C₄	1	2	yes	—
27	#16863352	C₄	1	1	yes	characteristic
28	#16863351	C₂²	1	1	yes	characteristic
29	#16863350	C₂²	1	2	yes	—
30	#97×D₆₇	C₄	1	2	yes	—
31	C₄×C₈×D₆₇	C₂²	1	2	yes	—
32	#16863172	C₂²	1	2	yes	complemented
33	#16863171	C₂²	1	2	yes	complemented
34	#16863171	C₂²	1	2	yes	complemented
35	C₄×C₆₇⋊C₁₆	C₂²	1	2	yes	complemented
36	C₁₆×Dic₆₇	C₂²	1	2	yes	complemented
37	C₁₆×Dic₆₇	C₂²	1	2	yes	complemented
38	C₂×M₃₂×C₆₇	C₂²	1	1	yes	characteristic
39	C₂²×C₁₆×C₆₇	C₂²	1	1	yes	characteristic
40	#405×C₆₇	C₂²	1	1	yes	characteristic
41	#346×C₆₇	C₂²	1	2	yes	complemented
42	C₄×C₁₆×C₆₇	C₂²	1	2	yes	complemented
43	C₂²×C₄×D₆₇	C₂×C₄	1	1	yes	characteristic
44	C₂×#11761612	C₂×C₄	1	1	yes	characteristic
45	C₂×#11761611	C₂×C₄	1	2	yes	—
46	M₁₆×D₆₇	C₈	1	8	yes	—
47	C₂²×C₆₇⋊C₈	C₂×C₄	1	1	yes	characteristic
48	C₂×C₈×D₆₇	C₂×C₄	1	1	yes	characteristic
49	C₂×C₈×D₆₇	C₂×C₄	1	1	yes	characteristic
50	C₂×C₈×D₆₇	C₂×C₄	1	4	yes	—
51	C₂×C₈×D₆₇	C₂×C₄	1	4	yes	—
52	C₂×C₈×D₆₇	C₂×C₄	1	2	yes	—
53	C₂×C₈×D₆₇	C₂³	1	1	yes	characteristic
54	C₂×C₈×D₆₇	C₂³	1	1	yes	characteristic
55	#14524002	C₂×C₄	1	1	yes	characteristic
56	#14524001	C₈	1	2	yes	—
57	#14524000	C₂×C₄	1	2	yes	—
58	#14523999	C₈	1	2	yes	—
59	C₄⋊C₄×D₆₇	C₈	1	2	yes	—
60	C₂²⋊C₄×D₆₇	C₈	1	2	yes	—
61	C₄²×D₆₇	C₂×C₄	1	2	yes	—
62	#14523983	C₂×C₄	1	4	yes	complemented
63	#14523982	C₂×C₄	1	8	yes	—
64	#14523982	C₂×C₄	1	4	yes	—
65	#14523982	C₂×C₄	1	4	yes	—
66	#14523982	C₂×C₄	1	4	yes	complemented
67	#14523982	C₂×C₄	1	4	yes	complemented
68	C₂×C₆₇⋊C₁₆	C₂×C₄	1	4	yes	complemented
69	C₂×C₆₇⋊C₁₆	C₂³	1	2	yes	—
70	C₂×C₆₇⋊C₁₆	C₂³	1	1	yes	characteristic
71	C₂×C₆₇⋊C₁₆	C₂³	1	1	yes	characteristic
72	C₁₆×D₆₇	C₂×C₄	1	8	yes	complemented
73	#14523954	C₂×C₄	1	2	yes	—
74	#14523953	C₂×C₄	1	2	yes	—
75	#14523953	C₂×C₄	1	2	yes	—
76	C₄×C₆₇⋊C₈	C₂×C₄	1	2	yes	—
77	C₈×Dic₆₇	C₂×C₄	1	2	yes	—
78	C₈×Dic₆₇	C₂³	1	2	yes	—
79	C₂×M₁₆×C₆₇	C₂×C₄	1	1	yes	characteristic
80	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
81	#117×C₆₇	C₂×C₄	1	1	yes	characteristic
82	M₃₂×C₆₇	C₂×C₄	1	4	yes	complemented
83	C₂×C₁₆×C₆₇	C₂×C₄	1	4	yes	complemented
84	C₂×C₁₆×C₆₇	C₂³	1	1	yes	characteristic
85	C₂×C₁₆×C₆₇	C₂³	1	1	yes	characteristic
86	C₂×C₁₆×C₆₇	C₂³	1	2	yes	—
87	#97×C₆₇	C₂×C₄	1	2	yes	—
88	C₄×C₈×C₆₇	C₂³	1	2	yes	—
89	C₂³×D₆₇	C₂×C₈	1	1	yes	characteristic
90	C₂²×Dic₆₇	C₂×C₈	1	1	yes	characteristic
91	C₂×C₄×D₆₇	C₄²	1	4	yes	—
92	C₂×C₄×D₆₇	C₂×C₈	1	4	yes	—
93	C₂×C₄×D₆₇	C₂×C₈	1	1	yes	characteristic
94	C₂×C₄×D₆₇	C₂×C₈	1	1	yes	characteristic
95	C₂×C₄×D₆₇	C₂×C₈	1	4	yes	—
96	C₂×C₄×D₆₇	C₂²×C₄	1	1	yes	characteristic
97	C₂×C₄×D₆₇	C₂²×C₄	1	1	yes	characteristic
98	#11761612	C₂×C₈	1	4	yes	—
99	#11761611	C₂×C₈	1	8	yes	—
100	C₂×C₆₇⋊C₈	C₄²	1	4	yes	—
101	C₂×C₆₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
102	C₂×C₆₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
103	C₂×C₆₇⋊C₈	C₂²×C₄	1	2	yes	—
104	C₈×D₆₇	C₄²	1	4	yes	—
105	C₈×D₆₇	C₄²	1	4	yes	—
106	C₈×D₆₇	C₂×C₈	1	8	yes	—
107	C₈×D₆₇	C₂²×C₄	1	2	yes	—
108	C₈×D₆₇	C₂²×C₄	1	2	yes	—
109	C₈×D₆₇	C₂²×C₄	1	2	yes	—
110	C₈×D₆₇	C₂²×C₄	1	2	yes	—
111	C₄⋊Dic₆₇	C₂×C₈	1	2	yes	—
112	Dic₆₇⋊C₄	C₂×C₈	1	4	yes	—
113	C₂²⋊Dic₆₇	C₂×C₈	1	2	yes	—
114	(C₂×D₆₇)⋊C₄	C₂×C₈	1	4	yes	—
115	C₄×Dic₆₇	C₂×C₈	1	4	yes	—
116	C₄×Dic₆₇	C₂²×C₄	1	2	yes	—
117	C₆₇⋊C₁₆	C₂²×C₄	1	4	yes	—
118	C₆₇⋊C₁₆	C₂²×C₄	1	2	yes	—
119	C₆₇⋊C₁₆	C₂²×C₄	1	2	yes	—
120	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
121	M₁₆×C₆₇	C₂×C₈	1	4	yes	—
122	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
123	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
124	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
125	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
126	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
127	C₄⋊C₄×C₆₇	C₂×C₈	1	2	yes	—
128	C₂²⋊C₄×C₆₇	C₂×C₈	1	2	yes	—
129	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
130	C₁₆×C₆₇	C₂²×C₄	1	2	yes	—
131	C₁₆×C₆₇	C₂²×C₄	1	2	yes	—
132	C₁₆×C₆₇	C₂²×C₄	1	4	yes	—
133	C₂³×C₆₇	C₂²×C₈	1	1	yes	characteristic
134	C₂²×D₆₇	—	4	2	no	—
135	C₂²×D₆₇	C₄×C₈	1	4	yes	—
136	C₂²×D₆₇	C₂²×C₈	1	1	yes	characteristic
137	C₂²×D₆₇	C₂²×C₈	1	1	yes	characteristic
138	C₂×C₄×C₆₇	C₂×C₄²	1	2	yes	—
139	C₂×C₄×C₆₇	C₂²×C₈	1	4	yes	—
140	C₂×C₄×C₆₇	C₂²×C₈	1	2	yes	—
141	C₂×C₄×C₆₇	C₂²×C₈	1	1	yes	characteristic
142	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
143	C₂×Dic₆₇	C₄×C₈	1	4	yes	—
144	C₂×Dic₆₇	C₂²×C₈	1	4	yes	—
145	C₂×Dic₆₇	C₂²×C₈	1	1	yes	characteristic
146	C₂×Dic₆₇	C₂²×C₈	1	1	yes	characteristic
147	C₄×D₆₇	—	4	4	no	—
148	C₄×D₆₇	C₄×C₈	1	4	yes	—
149	C₄×D₆₇	C₄×C₈	1	4	yes	—
150	C₄×D₆₇	C₂×C₄²	1	2	yes	—
151	C₄×D₆₇	C₂×C₄²	1	2	yes	—
152	C₄×D₆₇	C₂²×C₈	1	2	yes	—
153	C₄×D₆₇	C₂²×C₈	1	2	yes	—
154	C₈×C₆₇	C₂×C₄²	1	2	yes	—
155	C₈×C₆₇	C₂²×C₈	1	4	yes	—
156	C₈×C₆₇	C₂³×C₄	1	1	yes	characteristic
157	C₈×C₆₇	C₂³×C₄	1	1	yes	characteristic
158	C₆₇⋊C₈	C₂×C₄²	1	2	yes	—
159	C₆₇⋊C₈	C₂×C₄²	1	2	yes	—
160	C₆₇⋊C₈	C₂²×C₈	1	4	yes	—
161	C₂²×C₆₇	—	2	2	no	—
162	C₂²×C₆₇	C₂×C₄×C₈	1	2	yes	—
163	C₂²×C₆₇	C₂³×C₈	1	1	yes	characteristic
164	C₂×D₆₇	—	2	2	no	—
165	C₂×D₆₇	—	2	2	no	—
166	C₂×D₆₇	—	4	4	no	—
167	C₂×D₆₇	C₂×C₄×C₈	1	2	yes	—
168	C₂×D₆₇	C₂×C₄×C₈	1	2	yes	—
169	C₄×C₆₇	—	2	4	no	—
170	C₄×C₆₇	C₂×C₄×C₈	1	2	yes	—
171	C₄×C₆₇	C₂²×C₄²	1	1	yes	characteristic
172	C₄×C₆₇	C₂³×C₈	1	1	yes	characteristic
173	Dic₆₇	—	2	4	no	—
174	Dic₆₇	C₂×C₄×C₈	1	2	yes	—
175	Dic₆₇	C₂×C₄×C₈	1	2	yes	—
176	#33324	—	67	1	no	maximal, Sylow
177	C₂×C₆₇	—	2	2	no	—
178	C₂×C₆₇	C₂²×C₄×C₈	1	1	yes	characteristic
179	C₂×C₆₇	#3407	1	2	yes	—
180	D₆₇	—	2	2	no	—
181	D₆₇	—	2	2	no	—
182	C₂²×M₃₂	—	67	1	no	—
183	C₂²×M₃₂	—	67	1	no	—
184	C₂×#405	—	67	1	no	—
185	#2108	—	67	1	no	—
186	#2108	—	67	1	no	—
187	#2108	—	67	1	no	—
188	#2108	—	67	2	no	—
189	#2108	—	67	2	no	—
190	#2108	D₆₇	1	1	yes	characteristic, complemented
191	C₄×M₃₂	—	67	2	no	—
192	C₄×M₃₂	—	67	2	no	—
193	C₆₇	#33324	1	1	yes	characteristic, complemented, Sylow
194	C₂²×M₁₆	—	67	1	no	—
195	C₂³×C₈	—	67	1	no	—
196	C₂×#117	—	67	1	no	—
197	C₂×M₃₂	—	67	1	no	—
198	C₂×M₃₂	—	67	8	no	—
199	C₂×M₃₂	—	67	8	no	—
200	C₂×M₃₂	—	67	1	no	—
201	C₂×M₃₂	—	67	2	no	—
202	C₂×M₃₂	—	67	1	no	—
203	C₂×M₃₂	—	67	1	no	—
204	C₂×M₃₂	—	67	1	no	—
205	C₂×M₃₂	C₂×D₆₇	1	1	yes	characteristic
206	C₂²×C₁₆	—	67	1	no	—
207	C₂²×C₁₆	—	67	2	no	—
208	C₂²×C₁₆	C₂×D₆₇	1	1	yes	characteristic
209	#405	—	67	1	no	—
210	#405	—	67	1	no	—
211	#405	—	67	1	no	—
212	#405	—	67	2	no	—
213	#405	—	67	2	no	—
214	#405	C₂×D₆₇	1	1	yes	characteristic
215	C₂×#97	—	67	2	no	—
216	C₂×C₄×C₈	—	67	2	no	—
217	#346	—	67	2	no	—
218	#346	—	67	2	no	—
219	#346	—	67	2	no	—
220	#346	C₂×D₆₇	1	2	yes	complemented
221	C₄×C₁₆	—	67	2	no	—
222	C₄×C₁₆	—	67	2	no	—
223	C₄×C₁₆	—	67	2	no	—
224	C₄×C₁₆	C₂×D₆₇	1	2	yes	complemented
225	C₂³×C₄	—	67	1	no	—
226	C₂×M₁₆	—	67	1	no	—
227	C₂×M₁₆	—	67	8	no	—
228	C₂×M₁₆	—	67	2	no	—
229	C₂×M₁₆	C₄×D₆₇	1	1	yes	characteristic
230	C₂²×C₈	—	67	1	no	—
231	C₂²×C₈	—	67	1	no	—
232	C₂²×C₈	—	67	1	no	—
233	C₂²×C₈	—	67	4	no	—
234	C₂²×C₈	—	67	4	no	—
235	C₂²×C₈	—	67	2	no	—
236	C₂²×C₈	—	67	1	no	—
237	C₂²×C₈	—	67	1	no	—
238	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
239	#117	—	67	1	no	—
240	#117	—	67	2	no	—
241	#117	—	67	2	no	—
242	#117	—	67	2	no	—
243	#117	C₄×D₆₇	1	1	yes	characteristic
244	C₂×C₄⋊C₄	—	67	2	no	—
245	C₂×C₂²⋊C₄	—	67	2	no	—
246	C₂×C₄²	—	67	2	no	—
247	M₃₂	—	67	4	no	—
248	M₃₂	—	67	8	no	—
249	M₃₂	—	67	4	no	—
250	M₃₂	—	67	4	no	—
251	M₃₂	—	67	4	no	—
252	M₃₂	—	67	4	no	—
253	M₃₂	C₄×D₆₇	1	4	yes	complemented
254	C₂×C₁₆	—	67	4	no	—
255	C₂×C₁₆	—	67	2	no	—
256	C₂×C₁₆	—	67	1	no	—
257	C₂×C₁₆	—	67	1	no	—
258	C₂×C₁₆	—	67	8	no	—
259	C₂×C₁₆	C₄×D₆₇	1	4	yes	complemented
260	C₂×C₁₆	C₂²×D₆₇	1	1	yes	characteristic
261	C₂×C₁₆	C₂²×D₆₇	1	2	yes	—
262	C₂×C₁₆	C₂²×D₆₇	1	1	yes	characteristic
263	#97	—	67	2	no	—
264	#97	—	67	2	no	—
265	#97	—	67	2	no	—
266	#97	C₄×D₆₇	1	2	yes	—
267	C₄×C₈	—	67	2	no	—
268	C₄×C₈	—	67	2	no	—
269	C₄×C₈	—	67	2	no	—
270	C₄×C₈	C₂²×D₆₇	1	2	yes	—
271	C₂⁴	—	67	1	no	—
272	C₂²×C₄	—	67	4	no	—
273	C₂²×C₄	—	67	1	no	—
274	C₂²×C₄	—	67	4	no	—
275	C₂²×C₄	—	67	1	no	—
276	C₂²×C₄	—	67	1	no	—
277	C₂²×C₄	—	67	4	no	—
278	C₂²×C₄	—	67	1	no	—
279	C₂²×C₄	—	67	1	no	—
280	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
281	M₁₆	—	67	4	no	—
282	M₁₆	—	67	8	no	—
283	M₁₆	C₈×D₆₇	1	4	yes	—
284	C₂×C₈	—	67	4	no	—
285	C₂×C₈	—	67	1	no	—
286	C₂×C₈	—	67	2	no	—
287	C₂×C₈	—	67	1	no	—
288	C₂×C₈	—	67	4	no	—
289	C₂×C₈	—	67	4	no	—
290	C₂×C₈	—	67	8	no	—
291	C₂×C₈	—	67	2	no	—
292	C₂×C₈	—	67	2	no	—
293	C₂×C₈	—	67	2	no	—
294	C₂×C₈	—	67	2	no	—
295	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
296	C₂×C₈	C₂×C₄×D₆₇	1	2	yes	—
297	C₂×C₈	C₂×C₄×D₆₇	1	2	yes	—
298	C₂×C₈	C₂×C₄×D₆₇	1	2	yes	—
299	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
300	C₄⋊C₄	—	67	4	no	—
301	C₄⋊C₄	—	67	2	no	—
302	C₄⋊C₄	C₈×D₆₇	1	2	yes	—
303	C₂²⋊C₄	—	67	2	no	—
304	C₂²⋊C₄	—	67	4	no	—
305	C₂²⋊C₄	C₈×D₆₇	1	2	yes	—
306	C₄²	—	67	4	no	—
307	C₄²	—	67	2	no	—
308	C₄²	C₂×C₄×D₆₇	1	2	yes	—
309	C₁₆	—	67	2	no	—
310	C₁₆	—	67	2	no	—
311	C₁₆	—	67	4	no	—
312	C₁₆	C₂×C₄×D₆₇	1	4	yes	—
313	C₁₆	C₂×C₄×D₆₇	1	2	yes	—
314	C₁₆	C₂×C₄×D₆₇	1	2	yes	—
315	C₂³	—	268	2	no	—
316	C₂³	—	67	4	no	—
317	C₂³	—	67	1	no	—
318	C₂³	—	67	1	no	—
319	C₂³	C₂×C₈×D₆₇	1	1	yes	characteristic
320	C₂×C₄	—	268	4	no	—
321	C₂×C₄	—	67	4	no	—
322	C₂×C₄	—	67	1	no	—
323	C₂×C₄	—	67	1	no	—
324	C₂×C₄	—	67	2	no	—
325	C₂×C₄	—	67	2	no	—
326	C₂×C₄	—	67	4	no	—
327	C₂×C₄	—	67	4	no	—
328	C₂×C₄	—	67	2	no	—
329	C₂×C₄	—	67	2	no	—
330	C₂×C₄	—	67	4	no	—
331	C₂×C₄	C₄²×D₆₇	1	2	yes	—
332	C₂×C₄	C₂×C₈×D₆₇	1	4	yes	—
333	C₂×C₄	C₂×C₈×D₆₇	1	1	yes	characteristic
334	C₂×C₄	C₂×C₈×D₆₇	1	2	yes	—
335	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
336	C₈	—	67	2	no	—
337	C₈	—	67	2	no	—
338	C₈	—	67	4	no	—
339	C₈	C₄²×D₆₇	1	2	yes	—
340	C₈	C₂×C₈×D₆₇	1	4	yes	—
341	C₈	C₂²×C₄×D₆₇	1	1	yes	characteristic
342	C₈	C₂²×C₄×D₆₇	1	1	yes	characteristic
343	C₂²	—	2	2	no	—
344	C₂²	—	268	4	no	—
345	C₂²	—	67	2	no	—
346	C₂²	—	67	2	no	—
347	C₂²	—	134	2	no	—
348	C₂²	—	134	2	no	—
349	C₂²	C₄×C₈×D₆₇	1	2	yes	—
350	C₂²	C₂²×C₈×D₆₇	1	1	yes	characteristic
351	C₄	—	2	4	no	—
352	C₄	—	67	2	no	—
353	C₄	—	67	2	no	—
354	C₄	—	134	4	no	—
355	C₄	C₄×C₈×D₆₇	1	2	yes	—
356	C₄	C₂×C₄²×D₆₇	1	1	yes	characteristic
357	C₄	C₂²×C₈×D₆₇	1	1	yes	characteristic
358	C₂	—	2	2	no	—
359	C₂	—	134	2	no	—
360	C₂	—	134	2	no	—
361	C₂	C₂×C₄×C₈×D₆₇	1	1	yes	characteristic
362	C₂	#22573310	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₆₇
commutator	C₂×C₆₇	C₂²×C₄×C₈
Fitting	C₆₇×#2108	C₂
socle	C₂²×C₆₇	C₂³×C₈
prime radical	C₂³×D₆₇	C₂×C₈
cosocle	C₂×C₈×C₆₇	C₂⁴
hypercenter	#2108	D₆₇
hypocenter	C₆₇	#33324
LCS	G ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₈ ◁ #2108

Complements

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

N	H ≅ G/N	type
4. #22561808	C₂	semidirect
5. #22561807	C₂	semidirect
6. #22561806	C₂	semidirect
7. #22561805	C₂	semidirect
8. #22561804	C₂	semidirect
9. #22561802	C₂	semidirect
10. C₄×#14523982	C₂	semidirect
11. C₆₇×#2108	C₂	semidirect
16. C₂×#14523982	C₄	semidirect
22. M₃₂×D₆₇	C₄	semidirect
32. #16863172	C₂²	semidirect
33. #16863171	C₂²	semidirect
34. #16863171	C₂²	semidirect
35. C₄×C₆₇⋊C₁₆	C₂²	semidirect
36. C₁₆×Dic₆₇	C₂²	semidirect
37. C₁₆×Dic₆₇	C₂²	semidirect
41. #346×C₆₇	C₂²	semidirect
42. C₄×C₁₆×C₆₇	C₂²	semidirect
62. #14523983	C₂×C₄	semidirect
66. #14523982	C₂×C₄	semidirect
67. #14523982	C₂×C₄	semidirect
68. C₂×C₆₇⋊C₁₆	C₂×C₄	semidirect
72. C₁₆×D₆₇	C₂×C₄	semidirect
82. M₃₂×C₆₇	C₂×C₄	semidirect
83. C₂×C₁₆×C₆₇	C₂×C₄	semidirect
190. #2108	D₆₇	semidirect
193. C₆₇	#33324	semidirect
220. #346	C₂×D₆₇	semidirect
224. C₄×C₁₆	C₂×D₆₇	semidirect
253. M₃₂	C₄×D₆₇	semidirect
259. C₂×C₁₆	C₄×D₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#14523982	2
C₂×M₃₂×D₆₇	2
#405×D₆₇	2
#22561808	2
#22561807	2
#22561806	2
#22561805	2
#22561804	2
#22561802	2
C₄×#14523982	2
C₆₇×#2108	2
#33324	67