Subgroups — #31008937

Order 17152.

600 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#405×D₆₇	C₂	1	1	yes	maximal, characteristic
2	#22562015	C₂	1	2	yes	maximal, complemented
3	#22562015	C₂	1	2	yes	maximal, complemented
4	#22562011	C₂	1	2	yes	maximal, complemented
5	#22562007	C₂	1	2	yes	maximal, complemented
6	#22561968	C₂	1	1	yes	maximal, characteristic, complemented
7	#22561819	C₂	1	1	yes	maximal, characteristic
8	C₂×(C₂×D₆₇)⋊C₁₆	C₂	1	1	yes	maximal, characteristic
9	#22561808	C₂	1	1	yes	maximal, characteristic, complemented
10	#22561805	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#2151	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	C₂²×C₆₇⋊C₁₆	C₂²	1	1	yes	characteristic
17	#16863354	C₄	1	1	yes	characteristic
18	#16863353	C₄	1	2	yes	—
19	#16863352	C₄	1	1	yes	characteristic
20	#16863351	C₂²	1	1	yes	characteristic
21	#16863350	C₂²	1	2	yes	—
22	#97×D₆₇	C₄	1	2	yes	—
23	C₄×C₈×D₆₇	C₂²	1	2	yes	—
24	C₄⋊(C₆₇⋊C₁₆)	C₂²	1	2	yes	complemented
25	C₄⋊(C₆₇⋊C₁₆)	C₂²	1	2	yes	complemented
26	(C₂×D₆₇)⋊C₁₆	C₂²	1	1	yes	characteristic
27	(C₂×D₆₇)⋊C₁₆	C₂²	1	1	yes	characteristic
28	(C₂×D₆₇)⋊C₁₆	C₂²	1	1	yes	characteristic
29	(C₂×D₆₇)⋊C₁₆	C₂²	1	1	yes	characteristic
30	(C₂×D₆₇)⋊C₁₆	C₂²	1	2	yes	—
31	(C₂×D₆₇)⋊C₁₆	C₂²	1	2	yes	—
32	#16863171	C₂²	1	2	yes	complemented
33	#16863171	C₂²	1	2	yes	complemented
34	C₁₆×Dic₆₇	C₂²	1	2	yes	complemented
35	C₁₆×Dic₆₇	C₂²	1	2	yes	complemented
36	C₂×M₃₂×C₆₇	C₂²	1	1	yes	characteristic
37	C₂²×C₁₆×C₆₇	C₂²	1	1	yes	characteristic
38	#405×C₆₇	C₂²	1	1	yes	characteristic
39	C₄⋊C₁₆×C₆₇	C₂²	1	2	yes	complemented
40	C₄⋊C₁₆×C₆₇	C₂²	1	2	yes	complemented
41	C₂²×C₄×D₆₇	C₂×C₄	1	1	yes	characteristic
42	C₂×#11761612	C₂×C₄	1	1	yes	characteristic
43	C₂×#11761611	C₂×C₄	1	2	yes	—
44	M₁₆×D₆₇	—	2	4	no	—
45	C₂²×C₆₇⋊C₈	C₂×C₄	1	1	yes	characteristic
46	C₂×C₈×D₆₇	—	2	2	no	—
47	C₂×C₈×D₆₇	—	2	2	no	—
48	C₂×C₈×D₆₇	C₂×C₄	1	2	yes	—
49	C₂×C₈×D₆₇	C₂×C₄	1	1	yes	characteristic
50	C₂×C₈×D₆₇	C₂×C₄	1	1	yes	characteristic
51	C₂×C₈×D₆₇	C₂³	1	1	yes	characteristic
52	C₂×C₈×D₆₇	C₂³	1	1	yes	characteristic
53	#14524002	C₂×C₄	1	1	yes	characteristic
54	#14524001	C₈	1	1	yes	characteristic
55	#14524001	C₈	1	1	yes	characteristic
56	#14524000	C₂×C₄	1	2	yes	—
57	#14523999	C₈	1	2	yes	—
58	C₄⋊C₄×D₆₇	C₈	1	1	yes	characteristic
59	C₄⋊C₄×D₆₇	C₈	1	1	yes	characteristic
60	C₂²⋊C₄×D₆₇	C₈	1	2	yes	—
61	C₄²×D₆₇	C₂×C₄	1	2	yes	—
62	#14523983	—	2	2	no	—
63	C₂×C₆₇⋊C₁₆	—	2	2	no	—
64	C₂×C₆₇⋊C₁₆	C₂³	1	1	yes	characteristic
65	C₂×C₆₇⋊C₁₆	C₂³	1	1	yes	characteristic
66	C₂×C₆₇⋊C₁₆	C₂³	1	2	yes	—
67	#14523954	C₂×C₄	1	2	yes	—
68	#14523953	C₂×C₄	1	2	yes	—
69	#14523953	C₂×C₄	1	2	yes	—
70	C₄×C₆₇⋊C₈	C₂×C₄	1	2	yes	—
71	C₈×Dic₆₇	C₂×C₄	1	2	yes	—
72	C₈×Dic₆₇	C₂³	1	2	yes	—
73	C₂×M₁₆×C₆₇	C₂×C₄	1	1	yes	characteristic
74	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
75	#117×C₆₇	C₂×C₄	1	1	yes	characteristic
76	M₃₂×C₆₇	—	2	2	no	—
77	C₂×C₁₆×C₆₇	—	2	2	no	—
78	C₂×C₁₆×C₆₇	C₂³	1	1	yes	characteristic
79	C₂×C₁₆×C₆₇	C₂³	1	1	yes	characteristic
80	C₂×C₁₆×C₆₇	C₂³	1	2	yes	—
81	#97×C₆₇	C₂×C₄	1	2	yes	—
82	C₄×C₈×C₆₇	C₂³	1	2	yes	—
83	C₂³×D₆₇	C₂×C₈	1	1	yes	characteristic
84	C₂²×Dic₆₇	C₂×C₈	1	1	yes	characteristic
85	C₂×C₄×D₆₇	—	2	2	no	—
86	C₂×C₄×D₆₇	—	2	2	no	—
87	C₂×C₄×D₆₇	C₂×C₈	1	2	yes	—
88	C₂×C₄×D₆₇	C₂×C₈	1	1	yes	characteristic
89	C₂×C₄×D₆₇	C₂×C₈	1	1	yes	characteristic
90	C₂×C₄×D₆₇	C₂×C₈	1	2	yes	—
91	C₂×C₄×D₆₇	C₂²×C₄	1	1	yes	characteristic
92	C₂×C₄×D₆₇	C₂²×C₄	1	1	yes	characteristic
93	#11761612	M₁₆	1	4	yes	—
94	#11761611	—	2	4	no	—
95	C₂×C₆₇⋊C₈	—	2	2	no	—
96	C₂×C₆₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
97	C₂×C₆₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
98	C₂×C₆₇⋊C₈	C₂²×C₄	1	2	yes	—
99	C₈×D₆₇	—	2	2	no	—
100	C₈×D₆₇	—	2	2	no	—
101	C₈×D₆₇	—	2	1	no	—
102	C₈×D₆₇	—	2	1	no	—
103	C₈×D₆₇	—	2	1	no	—
104	C₈×D₆₇	—	2	1	no	—
105	C₈×D₆₇	—	2	4	no	—
106	C₄⋊Dic₆₇	C₂×C₈	1	1	yes	characteristic
107	C₄⋊Dic₆₇	C₂×C₈	1	1	yes	characteristic
108	Dic₆₇⋊C₄	C₂×C₈	1	2	yes	—
109	Dic₆₇⋊C₄	C₂×C₈	1	2	yes	—
110	C₂²⋊Dic₆₇	C₂×C₈	1	2	yes	—
111	(C₂×D₆₇)⋊C₄	C₂×C₈	1	2	yes	—
112	(C₂×D₆₇)⋊C₄	C₂×C₈	1	2	yes	—
113	C₄×Dic₆₇	C₂×C₈	1	2	yes	—
114	C₄×Dic₆₇	C₂×C₈	1	2	yes	—
115	C₄×Dic₆₇	C₂²×C₄	1	2	yes	—
116	C₆₇⋊C₁₆	—	2	1	no	—
117	C₆₇⋊C₁₆	—	2	1	no	—
118	C₆₇⋊C₁₆	—	2	2	no	—
119	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
120	M₁₆×C₆₇	—	2	2	no	—
121	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
122	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
123	C₂×C₈×C₆₇	#41	1	2	yes	—
124	C₂×C₈×C₆₇	#41	1	2	yes	—
125	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
126	C₄⋊C₄×C₆₇	C₂×C₈	1	1	yes	characteristic
127	C₄⋊C₄×C₆₇	C₂×C₈	1	1	yes	characteristic
128	C₂²⋊C₄×C₆₇	C₂×C₈	1	2	yes	—
129	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
130	C₁₆×C₆₇	—	2	1	no	—
131	C₁₆×C₆₇	—	2	1	no	—
132	C₁₆×C₆₇	—	2	2	no	—
133	C₂³×C₆₇	C₂²×C₈	1	1	yes	characteristic
134	C₂²×D₆₇	—	2	2	no	—
135	C₂²×D₆₇	—	2	2	no	—
136	C₂²×D₆₇	—	4	1	no	—
137	C₂²×D₆₇	C₂²×C₈	1	1	yes	characteristic
138	C₂²×D₆₇	C₂²×C₈	1	1	yes	characteristic
139	C₂×C₄×C₆₇	#117	1	2	yes	—
140	C₂×C₄×C₆₇	C₂²×C₈	1	2	yes	—
141	C₂×C₄×C₆₇	C₂²×C₈	1	2	yes	—
142	C₂×C₄×C₆₇	C₂²×C₈	1	1	yes	characteristic
143	C₂×C₄×C₆₇	C₂×M₁₆	1	2	yes	—
144	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
145	C₂×Dic₆₇	—	2	2	no	—
146	C₂×Dic₆₇	C₂²×C₈	1	1	yes	characteristic
147	C₂×Dic₆₇	C₂²×C₈	1	2	yes	—
148	C₂×Dic₆₇	C₂²×C₈	1	2	yes	—
149	C₂×Dic₆₇	C₂²×C₈	1	1	yes	characteristic
150	C₄×D₆₇	—	2	4	no	—
151	C₄×D₆₇	—	2	1	no	—
152	C₄×D₆₇	—	2	1	no	—
153	C₄×D₆₇	—	2	1	no	—
154	C₄×D₆₇	—	2	1	no	—
155	C₄×D₆₇	—	2	2	no	—
156	C₄×D₆₇	—	2	2	no	—
157	C₄×D₆₇	—	4	2	no	—
158	C₈×C₆₇	—	2	2	no	—
159	C₈×C₆₇	#117	1	2	yes	—
160	C₈×C₆₇	C₂×#41	1	1	yes	characteristic
161	C₈×C₆₇	C₂×#41	1	1	yes	characteristic
162	C₆₇⋊C₈	—	2	1	no	—
163	C₆₇⋊C₈	—	2	1	no	—
164	C₆₇⋊C₈	C₂×M₁₆	1	4	yes	—
165	C₂²×C₆₇	—	2	1	no	—
166	C₂²×C₆₇	—	2	1	no	—
167	C₂²×C₆₇	#431	1	2	yes	—
168	C₂²×C₆₇	C₂³×C₈	1	1	yes	characteristic
169	C₂×D₆₇	—	2	1	no	—
170	C₂×D₆₇	—	2	1	no	—
171	C₂×D₆₇	—	2	1	no	—
172	C₂×D₆₇	—	2	1	no	—
173	C₂×D₆₇	—	2	1	no	—
174	C₂×D₆₇	—	4	4	no	—
175	C₂×D₆₇	#504	1	2	yes	—
176	C₄×C₆₇	—	2	2	no	—
177	C₄×C₆₇	—	2	2	no	—
178	C₄×C₆₇	#431	1	2	yes	—
179	C₄×C₆₇	C₂×#117	1	1	yes	characteristic
180	C₄×C₆₇	C₂²×M₁₆	1	1	yes	characteristic
181	Dic₆₇	—	2	2	no	—
182	Dic₆₇	—	2	2	no	—
183	Dic₆₇	—	2	1	no	—
184	Dic₆₇	—	2	1	no	—
185	#33422	—	67	1	no	maximal, Sylow
186	C₂×C₆₇	—	2	2	no	—
187	C₂×C₆₇	C₂×#431	1	1	yes	characteristic
188	C₂×C₆₇	C₂×#504	1	1	yes	characteristic
189	C₂×C₆₇	#3407	1	1	yes	characteristic
190	D₆₇	—	2	2	no	—
191	D₆₇	—	4	1	no	—
192	C₂×#405	—	67	1	no	—
193	#2164	—	67	2	no	—
194	#2164	—	67	2	no	—
195	#2163	—	67	2	no	—
196	#2162	—	67	2	no	—
197	#2151	—	67	1	no	—
198	#2151	D₆₇	1	1	yes	characteristic, complemented
199	#2112	—	67	1	no	—
200	C₂×C₂²⋊C₁₆	—	67	1	no	—
201	#2108	—	67	1	no	—
202	#2108	—	67	1	no	—
203	C₆₇	#33422	1	1	yes	characteristic, complemented, Sylow
204	C₂²×M₁₆	—	67	1	no	—
205	C₂³×C₈	—	67	1	no	—
206	C₂×#117	—	67	1	no	—
207	C₂×M₃₂	—	67	1	no	—
208	C₂×M₃₂	C₂×D₆₇	1	1	yes	characteristic
209	C₂²×C₁₆	—	67	1	no	—
210	C₂²×C₁₆	C₂×D₆₇	1	1	yes	characteristic
211	#405	—	67	1	no	—
212	#405	—	67	1	no	—
213	#405	—	67	1	no	—
214	#405	—	67	2	no	—
215	#405	—	67	2	no	—
216	#405	C₂×D₆₇	1	1	yes	characteristic
217	C₂×#97	—	67	2	no	—
218	C₂×C₄×C₈	—	67	2	no	—
219	C₄⋊C₁₆	—	67	2	no	—
220	C₄⋊C₁₆	—	67	2	no	—
221	C₄⋊C₁₆	C₂×D₆₇	1	2	yes	complemented
222	C₄⋊C₁₆	C₂×D₆₇	1	2	yes	complemented
223	C₂²⋊C₁₆	—	67	1	no	—
224	C₂²⋊C₁₆	—	67	1	no	—
225	C₂²⋊C₁₆	—	67	1	no	—
226	C₂²⋊C₁₆	—	67	1	no	—
227	C₂²⋊C₁₆	—	67	2	no	—
228	C₂²⋊C₁₆	—	67	2	no	—
229	#346	—	67	2	no	—
230	#346	—	67	2	no	—
231	C₄×C₁₆	—	67	2	no	—
232	C₄×C₁₆	—	67	2	no	—
233	C₂³×C₄	—	67	1	no	—
234	C₂×M₁₆	—	67	1	no	—
235	C₂×M₁₆	—	67	2	no	—
236	C₂×M₁₆	—	134	4	no	—
237	C₂×M₁₆	C₄×D₆₇	1	1	yes	characteristic
238	C₂²×C₈	—	67	1	no	—
239	C₂²×C₈	—	67	1	no	—
240	C₂²×C₈	—	67	1	no	—
241	C₂²×C₈	—	67	2	no	—
242	C₂²×C₈	—	67	1	no	—
243	C₂²×C₈	—	67	1	no	—
244	C₂²×C₈	—	134	2	no	—
245	C₂²×C₈	—	134	2	no	—
246	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
247	#117	—	67	1	no	—
248	#117	—	67	1	no	—
249	#117	—	67	1	no	—
250	#117	—	67	2	no	—
251	#117	—	67	2	no	—
252	#117	C₄×D₆₇	1	1	yes	characteristic
253	C₂×C₄⋊C₄	—	67	1	no	—
254	C₂×C₄⋊C₄	—	67	1	no	—
255	C₂×C₂²⋊C₄	—	67	2	no	—
256	C₂×C₄²	—	67	2	no	—
257	M₃₂	—	2	2	no	—
258	M₃₂	—	134	2	no	—
259	C₂×C₁₆	—	2	2	no	—
260	C₂×C₁₆	—	67	1	no	—
261	C₂×C₁₆	—	67	2	no	—
262	C₂×C₁₆	—	67	1	no	—
263	C₂×C₁₆	—	134	2	no	—
264	C₂×C₁₆	C₂²×D₆₇	1	1	yes	characteristic
265	C₂×C₁₆	C₂²×D₆₇	1	2	yes	—
266	C₂×C₁₆	C₂²×D₆₇	1	1	yes	characteristic
267	#97	—	67	2	no	—
268	#97	—	67	2	no	—
269	#97	—	67	2	no	—
270	#97	C₄×D₆₇	1	2	yes	—
271	C₄×C₈	—	67	2	no	—
272	C₄×C₈	—	67	2	no	—
273	C₄×C₈	—	67	2	no	—
274	C₄×C₈	C₂²×D₆₇	1	2	yes	—
275	C₂⁴	—	67	1	no	—
276	C₂²×C₄	—	67	2	no	—
277	C₂²×C₄	—	67	1	no	—
278	C₂²×C₄	—	67	2	no	—
279	C₂²×C₄	—	67	1	no	—
280	C₂²×C₄	—	67	1	no	—
281	C₂²×C₄	—	67	1	no	—
282	C₂²×C₄	—	67	1	no	—
283	C₂²×C₄	—	134	2	no	—
284	C₂²×C₄	—	134	2	no	—
285	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
286	M₁₆	—	2	2	no	—
287	M₁₆	—	67	4	no	—
288	M₁₆	—	134	4	no	—
289	C₂×C₈	—	67	2	no	—
290	C₂×C₈	—	67	1	no	—
291	C₂×C₈	—	67	1	no	—
292	C₂×C₈	—	134	4	no	—
293	C₂×C₈	—	134	2	no	—
294	C₂×C₈	—	134	2	no	—
295	C₂×C₈	—	134	2	no	—
296	C₂×C₈	—	134	1	no	—
297	C₂×C₈	—	134	1	no	—
298	C₂×C₈	—	134	1	no	—
299	C₂×C₈	—	134	1	no	—
300	C₂×C₈	C₂×C₄×D₆₇	1	2	yes	—
301	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
302	C₂×C₈	#11761627	1	2	yes	—
303	C₂×C₈	#11761629	1	2	yes	—
304	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
305	C₄⋊C₄	—	67	2	no	—
306	C₄⋊C₄	—	67	2	no	—
307	C₄⋊C₄	—	67	1	no	—
308	C₄⋊C₄	—	67	1	no	—
309	C₄⋊C₄	C₈×D₆₇	1	1	yes	characteristic
310	C₄⋊C₄	C₈×D₆₇	1	1	yes	characteristic
311	C₂²⋊C₄	—	67	2	no	—
312	C₂²⋊C₄	—	67	2	no	—
313	C₂²⋊C₄	—	67	2	no	—
314	C₂²⋊C₄	C₈×D₆₇	1	2	yes	—
315	C₄²	—	67	2	no	—
316	C₄²	—	67	2	no	—
317	C₄²	—	67	2	no	—
318	C₄²	C₂×C₄×D₆₇	1	2	yes	—
319	C₁₆	—	2	1	no	—
320	C₁₆	—	2	1	no	—
321	C₁₆	—	2	2	no	—
322	C₁₆	—	134	1	no	—
323	C₁₆	—	134	1	no	—
324	C₁₆	—	134	2	no	—
325	C₂³	—	268	1	no	—
326	C₂³	—	67	1	no	—
327	C₂³	—	67	1	no	—
328	C₂³	—	134	2	no	—
329	C₂³	—	134	2	no	—
330	C₂³	C₂×C₈×D₆₇	1	1	yes	characteristic
331	C₂×C₄	—	268	2	no	—
332	C₂×C₄	—	67	1	no	—
333	C₂×C₄	—	67	2	no	—
334	C₂×C₄	—	67	2	no	—
335	C₂×C₄	—	67	1	no	—
336	C₂×C₄	—	134	4	no	—
337	C₂×C₄	—	134	2	no	—
338	C₂×C₄	—	134	1	no	—
339	C₂×C₄	—	134	1	no	—
340	C₂×C₄	—	134	1	no	—
341	C₂×C₄	—	134	1	no	—
342	C₂×C₄	—	134	2	no	—
343	C₂×C₄	—	134	2	no	—
344	C₂×C₄	#14524001	1	2	yes	—
345	C₂×C₄	C₂×C₈×D₆₇	1	2	yes	—
346	C₂×C₄	C₂×C₈×D₆₇	1	2	yes	—
347	C₂×C₄	C₂×C₈×D₆₇	1	1	yes	characteristic
348	C₂×C₄	M₁₆×D₆₇	1	2	yes	—
349	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
350	C₈	—	2	2	no	—
351	C₈	—	67	4	no	—
352	C₈	—	134	1	no	—
353	C₈	—	134	1	no	—
354	C₈	#14524001	1	2	yes	—
355	C₈	C₂×#11761627	1	1	yes	characteristic
356	C₈	C₂×#11761629	1	1	yes	characteristic
357	C₂²	—	2	1	no	—
358	C₂²	—	2	1	no	—
359	C₂²	—	268	4	no	—
360	C₂²	—	67	2	no	—
361	C₂²	—	134	1	no	—
362	C₂²	—	134	1	no	—
363	C₂²	—	134	1	no	—
364	C₂²	—	134	1	no	—
365	C₂²	—	134	1	no	—
366	C₂²	#16863448	1	2	yes	—
367	C₂²	C₂²×C₈×D₆₇	1	1	yes	characteristic
368	C₄	—	2	2	no	—
369	C₄	—	2	2	no	—
370	C₄	—	134	1	no	—
371	C₄	—	134	1	no	—
372	C₄	—	134	2	no	—
373	C₄	—	134	2	no	—
374	C₄	#16863448	1	2	yes	—
375	C₄	C₂×#14524001	1	1	yes	characteristic
376	C₄	C₂×M₁₆×D₆₇	1	1	yes	characteristic
377	C₂	—	2	2	no	—
378	C₂	—	268	1	no	—
379	C₂	—	134	2	no	—
380	C₂	C₂×#16863448	1	1	yes	characteristic
381	C₂	#504×D₆₇	1	1	yes	characteristic
382	C₂	#22573310	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₆₇
commutator, socle	C₂²×C₆₇	C₂³×C₈
Fitting	C₆₇×#2151	C₂
prime radical	C₂³×D₆₇	C₂×C₈
cosocle	C₂×C₈×C₆₇	C₂⁴
hypercenter	#2151	D₆₇
hypocenter	C₆₇	#33422
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₈ ◁ #2151

Complements

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

N	H ≅ G/N	type
2. #22562015	C₂	semidirect
3. #22562015	C₂	semidirect
4. #22562011	C₂	semidirect
5. #22562007	C₂	semidirect
6. #22561968	C₂	semidirect
9. #22561808	C₂	semidirect
10. #22561805	C₂	semidirect
11. C₆₇×#2151	C₂	semidirect
24. C₄⋊(C₆₇⋊C₁₆)	C₂²	semidirect
25. C₄⋊(C₆₇⋊C₁₆)	C₂²	semidirect
32. #16863171	C₂²	semidirect
33. #16863171	C₂²	semidirect
34. C₁₆×Dic₆₇	C₂²	semidirect
35. C₁₆×Dic₆₇	C₂²	semidirect
39. C₄⋊C₁₆×C₆₇	C₂²	semidirect
40. C₄⋊C₁₆×C₆₇	C₂²	semidirect
198. #2151	D₆₇	semidirect
203. C₆₇	#33422	semidirect
221. C₄⋊C₁₆	C₂×D₆₇	semidirect
222. C₄⋊C₁₆	C₂×D₆₇	semidirect

Maximal subgroups

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

subgroup	index
#405×D₆₇	2
#22562015	2
#22562011	2
#22562007	2
#22561968	2
#22561819	2
C₂×(C₂×D₆₇)⋊C₁₆	2
#22561808	2
#22561805	2
C₆₇×#2151	2
#33422	67