Subgroups — #1591×D₆₇ #30825569

Order 17152.

670 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#446×D₆₇	C₂	1	2	yes	maximal
2	C₄×Q₁₆×D₆₇	C₂	1	1	yes	maximal, characteristic
3	#22559107	C₂	1	1	yes	maximal, characteristic, complemented
4	#22559106	C₂	1	1	yes	maximal, characteristic, complemented
5	#22559105	C₂	1	1	yes	maximal, characteristic, complemented
6	#22559104	C₂	1	2	yes	maximal, complemented
7	#22559103	C₂	1	2	yes	maximal, complemented
8	#335×D₆₇	C₂	1	1	yes	maximal, characteristic
9	Q₈⋊C₈×D₆₇	C₂	1	2	yes	maximal
10	C₈²×D₆₇	C₂	1	1	yes	maximal, characteristic
11	C₆₇×#1591	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×Q₁₆×D₆₇	C₄	1	1	yes	characteristic
13	C₄×Q₈×D₆₇	C₂²	1	2	yes	—
14	#16863527	C₂²	1	2	yes	—
15	#16863526	C₂²	1	2	yes	—
16	#16863525	—	2	2	no	—
17	#16863524	—	2	2	no	—
18	#16863523	C₂²	1	2	yes	—
19	C₄×Dic₂₆₈	C₂²	1	1	yes	characteristic
20	Q₁₆×Dic₆₇	C₄	1	1	yes	characteristic
21	#16863490	C₄	1	1	yes	characteristic
22	C₄×#11761618	C₂²	1	2	yes	—
23	#16863488	C₄	1	2	yes	—
24	#107×D₆₇	C₄	1	1	yes	characteristic
25	C₄⋊C₈×D₆₇	—	2	2	no	—
26	C₄⋊C₈×D₆₇	C₂²	1	2	yes	—
27	#103×D₆₇	C₄	1	2	yes	—
28	#97×D₆₇	—	2	2	no	—
29	C₄×C₈×D₆₇	C₂²	1	1	yes	characteristic
30	C₄×C₈×D₆₇	C₂²	1	1	yes	characteristic
31	C₄×C₈×D₆₇	C₂²	1	1	yes	characteristic
32	#16863149	C₂²	1	1	yes	characteristic
33	#16863148	C₂²	1	2	yes	—
34	#16863128	C₂²	1	2	yes	—
35	Q₈⋊(C₆₇⋊C₈)	C₂²	1	2	yes	—
36	#16863126	C₂²	1	2	yes	—
37	C₈×C₆₇⋊C₈	C₂²	1	1	yes	characteristic
38	C₈×C₆₇⋊C₈	C₂²	1	1	yes	characteristic
39	C₈×C₆₇⋊C₈	C₂²	1	1	yes	characteristic
40	#446×C₆₇	C₂²	1	2	yes	—
41	C₄×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic
42	#335×C₆₇	C₂²	1	1	yes	characteristic
43	Q₈⋊C₈×C₆₇	C₂²	1	2	yes	—
44	C₈²×C₆₇	C₂²	1	1	yes	characteristic
45	C₂×Q₈×D₆₇	C₂×C₄	1	2	yes	—
46	C₂×Dic₂₆₈	C₂×C₄	1	1	yes	characteristic
47	C₂×#11761618	C₂×C₄	1	2	yes	—
48	Q₁₆×D₆₇	—	2	4	no	—
49	C₂×C₈×D₆₇	—	2	1	no	—
50	C₂×C₈×D₆₇	—	2	2	no	—
51	C₂×C₈×D₆₇	C₂×C₄	1	1	yes	characteristic
52	C₂×C₈×D₆₇	C₂×C₄	1	1	yes	characteristic
53	C₂×C₈×D₆₇	D₄	1	1	yes	characteristic
54	C₂×C₈×D₆₇	D₄	1	1	yes	characteristic
55	Q₈×Dic₆₇	C₂×C₄	1	2	yes	—
56	C₄×Dic₁₃₄	—	2	2	no	—
57	C₄×Dic₁₃₄	C₂³	1	2	yes	—
58	#14524008	—	2	2	no	—
59	#14524008	C₂×C₄	1	2	yes	—
60	C₄⋊C₄×D₆₇	—	2	2	no	—
61	C₄⋊C₄×D₆₇	C₂×C₄	1	2	yes	—
62	C₄²×D₆₇	—	2	2	no	—
63	C₄²×D₆₇	C₂³	1	1	yes	characteristic
64	#14523977	C₂×C₄	1	1	yes	characteristic
65	#14523976	C₂×C₄	1	2	yes	—
66	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
67	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
68	Dic₆₇⋊C₈	—	2	2	no	—
69	Dic₆₇⋊C₈	—	2	2	no	—
70	Dic₆₇⋊C₈	—	2	2	no	—
71	#14523968	C₂×C₄	1	2	yes	—
72	#14523967	C₂×C₄	1	2	yes	—
73	#14523966	C₂×C₄	1	2	yes	—
74	#14523954	—	2	2	no	—
75	#14523953	—	2	2	no	—
76	#14523953	—	2	2	no	—
77	C₄×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
78	C₄×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
79	C₄×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
80	C₈×Dic₆₇	—	2	1	no	—
81	C₈×Dic₆₇	C₂×C₄	1	1	yes	characteristic
82	C₈×Dic₆₇	C₂×C₄	1	1	yes	characteristic
83	C₈×Dic₆₇	D₄	1	1	yes	characteristic
84	C₈×Dic₆₇	D₄	1	1	yes	characteristic
85	C₂×Q₁₆×C₆₇	C₂×C₄	1	1	yes	characteristic
86	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
87	#107×C₆₇	C₂×C₄	1	1	yes	characteristic
88	C₄⋊C₈×C₆₇	—	2	2	no	—
89	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
90	#103×C₆₇	C₂×C₄	1	2	yes	—
91	#97×C₆₇	—	2	2	no	—
92	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
93	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
94	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
95	C₂×Dic₁₃₄	—	2	2	no	—
96	C₂×Dic₁₃₄	C₂²×C₄	1	2	yes	—
97	Q₈×D₆₇	—	2	4	no	—
98	Q₈×D₆₇	—	2	4	no	—
99	C₂×C₄×D₆₇	—	2	2	no	—
100	C₂×C₄×D₆₇	—	2	2	no	—
101	C₂×C₄×D₆₇	C₂²×C₄	1	1	yes	characteristic
102	C₂×C₄×D₆₇	C₂×D₄	1	1	yes	characteristic
103	C₂×C₄×D₆₇	#41	1	1	yes	characteristic
104	Dic₂₆₈	—	2	2	no	—
105	#11761618	—	2	4	no	—
106	C₂×C₆₇⋊C₈	—	2	1	no	—
107	C₂×C₆₇⋊C₈	—	2	2	no	—
108	C₂×C₆₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
109	C₂×C₆₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
110	C₂×C₆₇⋊C₈	C₂×D₄	1	1	yes	characteristic
111	C₂×C₆₇⋊C₈	C₂×D₄	1	1	yes	characteristic
112	C₈×D₆₇	—	2	4	no	—
113	C₈×D₆₇	—	2	2	no	—
114	C₈×D₆₇	—	2	2	no	—
115	C₈×D₆₇	—	4	4	no	—
116	C₈×D₆₇	M₁₆	1	4	yes	—
117	C₈×D₆₇	Q₁₆	1	4	yes	complemented
118	C₄⋊Dic₆₇	—	2	2	no	—
119	C₄⋊Dic₆₇	C₂²×C₄	1	2	yes	—
120	Dic₆₇⋊C₄	—	2	2	no	—
121	Dic₆₇⋊C₄	—	2	2	no	—
122	Dic₆₇⋊C₄	—	2	2	no	—
123	C₄×Dic₆₇	—	2	2	no	—
124	C₄×Dic₆₇	—	2	2	no	—
125	C₄×Dic₆₇	—	2	2	no	—
126	C₄×Dic₆₇	C₂²×C₄	1	1	yes	characteristic
127	C₄×Dic₆₇	C₂×D₄	1	1	yes	characteristic
128	C₄×Dic₆₇	#41	1	1	yes	characteristic
129	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
130	Q₁₆×C₆₇	—	2	2	no	—
131	C₂×C₈×C₆₇	—	2	1	no	—
132	C₂×C₈×C₆₇	—	2	2	no	—
133	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
134	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
136	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
137	C₄⋊C₄×C₆₇	—	2	2	no	—
138	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
139	C₄²×C₆₇	—	2	2	no	—
140	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
141	C₂²×D₆₇	C₄×D₄	1	1	yes	characteristic
142	Q₈×C₆₇	—	2	2	no	—
143	Q₈×C₆₇	—	2	2	no	—
144	C₂×C₄×C₆₇	—	2	2	no	—
145	C₂×C₄×C₆₇	—	2	2	no	—
146	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
147	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
148	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
149	C₂×Dic₆₇	—	2	2	no	—
150	C₂×Dic₆₇	—	2	2	no	—
151	C₂×Dic₆₇	C₄×D₄	1	1	yes	characteristic
152	C₂×Dic₆₇	C₄×D₄	1	1	yes	characteristic
153	C₂×Dic₆₇	C₄×D₄	1	1	yes	characteristic
154	C₄×D₆₇	—	2	2	no	—
155	C₄×D₆₇	—	4	4	no	—
156	C₄×D₆₇	—	4	4	no	—
157	C₄×D₆₇	C₂×M₁₆	1	2	yes	—
158	C₄×D₆₇	#131	1	2	yes	—
159	C₄×D₆₇	C₂×Q₁₆	1	2	yes	—
160	C₄×D₆₇	#135	1	2	yes	—
161	Dic₁₃₄	—	2	2	no	—
162	Dic₁₃₄	—	2	2	no	—
163	Dic₁₃₄	—	4	4	no	—
164	C₈×C₆₇	—	2	2	no	—
165	C₈×C₆₇	—	2	1	no	—
166	C₈×C₆₇	—	2	1	no	—
167	C₈×C₆₇	—	4	2	no	—
168	C₈×C₆₇	C₂×M₁₆	1	2	yes	—
169	C₈×C₆₇	C₂×Q₁₆	1	2	yes	complemented
170	C₆₇⋊C₈	—	2	2	no	—
171	C₆₇⋊C₈	—	2	1	no	—
172	C₆₇⋊C₈	—	2	1	no	—
173	C₆₇⋊C₈	—	4	2	no	—
174	C₆₇⋊C₈	C₂×M₁₆	1	2	yes	—
175	C₆₇⋊C₈	C₂×Q₁₆	1	2	yes	complemented
176	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
177	C₂×D₆₇	#436	1	2	yes	—
178	C₂×D₆₇	C₄×Q₁₆	1	2	yes	—
179	C₂×D₆₇	#443	1	2	yes	—
180	C₄×C₆₇	—	2	1	no	—
181	C₄×C₆₇	—	4	2	no	—
182	C₄×C₆₇	—	4	2	no	—
183	C₄×C₆₇	C₂²×M₁₆	1	1	yes	characteristic
184	C₄×C₆₇	C₂×#131	1	1	yes	characteristic
185	C₄×C₆₇	C₂²×Q₁₆	1	1	yes	characteristic
186	C₄×C₆₇	C₂×#135	1	1	yes	characteristic
187	Dic₆₇	—	2	1	no	—
188	Dic₆₇	—	4	2	no	—
189	Dic₆₇	—	4	2	no	—
190	Dic₆₇	#436	1	2	yes	—
191	Dic₆₇	C₄×Q₁₆	1	2	yes	—
192	C₂×#1591	—	67	1	no	maximal, Sylow
193	C₂×C₆₇	C₂×#436	1	1	yes	characteristic
194	C₂×C₆₇	C₂×C₄×Q₁₆	1	1	yes	characteristic
195	C₂×C₆₇	C₂×#443	1	1	yes	characteristic
196	D₆₇	#1591	1	4	yes	direct product factor
197	C₂×#446	—	67	2	no	—
198	C₂×C₄×Q₁₆	—	67	1	no	—
199	#1591	—	67	2	no	—
200	#1591	—	67	1	no	—
201	#1591	—	67	1	no	—
202	#1591	—	67	2	no	—
203	#1591	—	67	1	no	—
204	#1591	D₆₇	1	1	yes	characteristic, direct product factor
205	C₂×#335	—	67	1	no	—
206	C₂×Q₈⋊C₈	—	67	2	no	—
207	C₂×C₈²	—	67	1	no	—
208	C₆₇	C₂×#1591	1	1	yes	characteristic, complemented, Sylow
209	C₂²×Q₁₆	—	67	1	no	—
210	C₂×C₄×Q₈	—	67	2	no	—
211	#446	—	67	2	no	—
212	#446	—	67	2	no	—
213	#446	—	67	2	no	—
214	#446	—	134	2	no	—
215	#446	—	134	2	no	—
216	#446	C₂×D₆₇	1	2	yes	—
217	C₄×Q₁₆	—	67	1	no	—
218	C₄×Q₁₆	—	67	2	no	—
219	C₄×Q₁₆	—	67	1	no	—
220	C₄×Q₁₆	—	67	2	no	—
221	C₄×Q₁₆	—	67	1	no	—
222	C₄×Q₁₆	C₂×D₆₇	1	1	yes	characteristic
223	C₂×#107	—	67	1	no	—
224	C₂×C₄⋊C₈	—	67	2	no	—
225	C₂×C₄⋊C₈	—	134	2	no	—
226	C₂×#103	—	67	2	no	—
227	C₂×#97	—	134	2	no	—
228	C₂×C₄×C₈	—	67	1	no	—
229	C₂×C₄×C₈	—	67	1	no	—
230	C₂×C₄×C₈	—	67	1	no	—
231	#335	—	67	2	no	—
232	#335	—	67	1	no	—
233	#335	C₂×D₆₇	1	1	yes	characteristic
234	Q₈⋊C₈	—	67	2	no	—
235	Q₈⋊C₈	—	67	2	no	—
236	Q₈⋊C₈	—	67	2	no	—
237	Q₈⋊C₈	C₂×D₆₇	1	2	yes	—
238	C₈²	—	67	1	no	—
239	C₈²	—	67	1	no	—
240	C₈²	—	67	1	no	—
241	C₈²	C₂×D₆₇	1	1	yes	characteristic
242	C₂²×Q₈	—	67	2	no	—
243	C₂×Q₁₆	—	67	2	no	—
244	C₂×Q₁₆	—	67	1	no	—
245	C₂×Q₁₆	—	134	4	no	—
246	C₂×Q₁₆	C₄×D₆₇	1	1	yes	characteristic
247	C₂²×C₈	—	67	1	no	—
248	C₂²×C₈	—	67	1	no	—
249	C₂²×C₈	—	67	1	no	—
250	C₂²×C₈	—	67	1	no	—
251	C₂²×C₈	—	134	2	no	—
252	C₂²×C₈	—	134	1	no	—
253	C₄×Q₈	—	67	2	no	—
254	C₄×Q₈	—	67	2	no	—
255	C₄×Q₈	—	67	2	no	—
256	C₄×Q₈	—	134	2	no	—
257	C₄×Q₈	—	134	2	no	—
258	C₄×Q₈	C₂²×D₆₇	1	2	yes	—
259	C₂×C₄⋊C₄	—	67	2	no	—
260	C₂×C₄⋊C₄	—	134	2	no	—
261	C₂×C₄²	—	67	1	no	—
262	C₂×C₄²	—	134	2	no	—
263	#107	—	67	1	no	—
264	#107	—	67	2	no	—
265	#107	C₄×D₆₇	1	1	yes	characteristic
266	C₄⋊C₈	—	2	2	no	—
267	C₄⋊C₈	—	67	2	no	—
268	C₄⋊C₈	—	134	2	no	—
269	C₄⋊C₈	—	134	2	no	—
270	C₄⋊C₈	—	134	2	no	—
271	C₄⋊C₈	—	134	2	no	—
272	C₄⋊C₈	C₂²×D₆₇	1	2	yes	—
273	#103	—	67	2	no	—
274	#103	—	67	2	no	—
275	#103	—	67	2	no	—
276	#103	C₄×D₆₇	1	2	yes	—
277	#97	—	2	2	no	—
278	#97	—	134	2	no	—
279	#97	—	134	2	no	—
280	#97	—	134	2	no	—
281	C₄×C₈	—	67	1	no	—
282	C₄×C₈	—	67	1	no	—
283	C₄×C₈	—	67	1	no	—
284	C₄×C₈	—	67	1	no	—
285	C₄×C₈	—	67	1	no	—
286	C₄×C₈	—	67	1	no	—
287	C₄×C₈	—	67	1	no	—
288	C₄×C₈	—	134	1	no	—
289	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
290	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
291	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
292	C₂×Q₈	—	67	2	no	—
293	C₂×Q₈	—	134	2	no	—
294	C₂×Q₈	—	134	4	no	—
295	C₂×Q₈	—	134	4	no	—
296	C₂×Q₈	C₂×C₄×D₆₇	1	2	yes	—
297	C₂²×C₄	—	67	1	no	—
298	C₂²×C₄	—	67	1	no	—
299	C₂²×C₄	—	67	1	no	—
300	C₂²×C₄	—	134	2	no	—
301	C₂²×C₄	—	134	2	no	—
302	Q₁₆	—	2	2	no	—
303	Q₁₆	—	134	4	no	—
304	Q₁₆	—	134	2	no	—
305	C₂×C₈	—	2	1	no	—
306	C₂×C₈	—	2	2	no	—
307	C₂×C₈	—	268	4	no	—
308	C₂×C₈	—	67	1	no	—
309	C₂×C₈	—	67	1	no	—
310	C₂×C₈	—	67	4	no	—
311	C₂×C₈	—	67	4	no	—
312	C₂×C₈	—	67	1	no	—
313	C₂×C₈	—	67	1	no	—
314	C₂×C₈	—	134	2	no	—
315	C₂×C₈	—	134	2	no	—
316	C₂×C₈	—	134	4	no	—
317	C₂×C₈	—	134	2	no	—
318	C₂×C₈	—	134	1	no	—
319	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
320	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
321	C₂×C₈	D₄×D₆₇	1	1	yes	characteristic
322	C₂×C₈	D₄×D₆₇	1	1	yes	characteristic
323	C₄⋊C₄	—	2	2	no	—
324	C₄⋊C₄	—	67	2	no	—
325	C₄⋊C₄	—	134	2	no	—
326	C₄⋊C₄	—	134	2	no	—
327	C₄⋊C₄	—	134	2	no	—
328	C₄⋊C₄	—	134	2	no	—
329	C₄⋊C₄	C₂×C₄×D₆₇	1	2	yes	—
330	C₄²	—	2	2	no	—
331	C₄²	—	67	1	no	—
332	C₄²	—	67	1	no	—
333	C₄²	—	67	1	no	—
334	C₄²	—	134	2	no	—
335	C₄²	—	134	2	no	—
336	C₄²	—	134	2	no	—
337	C₄²	C₂³×D₆₇	1	1	yes	characteristic
338	C₂³	—	67	1	no	—
339	Q₈	—	2	2	no	—
340	Q₈	—	2	2	no	—
341	Q₈	—	268	4	no	—
342	Q₈	—	134	2	no	—
343	Q₈	—	134	2	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	268	4	no	—
347	C₂×C₄	—	268	4	no	—
348	C₂×C₄	—	67	1	no	—
349	C₂×C₄	—	67	1	no	—
350	C₂×C₄	—	67	2	no	—
351	C₂×C₄	—	67	2	no	—
352	C₂×C₄	—	67	2	no	—
353	C₂×C₄	—	67	2	no	—
354	C₂×C₄	—	67	1	no	—
355	C₂×C₄	—	134	2	no	—
356	C₂×C₄	—	134	2	no	—
357	C₂×C₄	—	134	2	no	—
358	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
359	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
360	C₂×C₄	#41×D₆₇	1	1	yes	characteristic
361	C₈	—	2	2	no	—
362	C₈	—	2	1	no	—
363	C₈	—	2	1	no	—
364	C₈	—	4	2	no	—
365	C₈	—	268	2	no	—
366	C₈	—	67	2	no	—
367	C₈	—	67	2	no	—
368	C₈	—	134	2	no	—
369	C₈	—	134	1	no	—
370	C₈	—	134	1	no	—
371	C₈	M₁₆×D₆₇	1	2	yes	—
372	C₈	Q₁₆×D₆₇	1	2	yes	complemented
373	C₂²	—	67	2	no	—
374	C₂²	—	67	2	no	—
375	C₂²	—	67	2	no	—
376	C₂²	C₄×D₄×D₆₇	1	1	yes	characteristic
377	C₄	—	2	1	no	—
378	C₄	—	4	2	no	—
379	C₄	—	4	2	no	—
380	C₄	—	268	2	no	—
381	C₄	—	268	2	no	—
382	C₄	—	67	2	no	—
383	C₄	—	67	2	no	—
384	C₄	—	134	1	no	—
385	C₄	C₂×M₁₆×D₆₇	1	1	yes	characteristic
386	C₄	#131×D₆₇	1	1	yes	characteristic
387	C₄	C₂×Q₁₆×D₆₇	1	1	yes	characteristic
388	C₄	#135×D₆₇	1	1	yes	characteristic
389	C₂	—	67	4	no	—
390	C₂	#436×D₆₇	1	1	yes	characteristic
391	C₂	C₄×Q₁₆×D₆₇	1	1	yes	characteristic
392	C₂	#443×D₆₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₆₇
commutator	C₂×C₄×C₆₇	C₂³×C₄
Frattini	C₄²	C₂³×D₆₇
Fitting	C₆₇×#1591	C₂
socle	C₂²×C₆₇	C₂×C₄×D₄
prime radical	C₂²×D₆₇	C₄×D₄
cosocle	C₄²×C₆₇	C₂⁴
hypercenter	#1591	D₆₇
hypocenter	C₆₇	C₂×#1591
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #1591

Complements

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

N	H ≅ G/N	type
3. #22559107	C₂	semidirect
4. #22559106	C₂	semidirect
5. #22559105	C₂	semidirect
6. #22559104	C₂	semidirect
7. #22559103	C₂	semidirect
11. C₆₇×#1591	C₂	semidirect
117. C₈×D₆₇	Q₁₆	semidirect
169. C₈×C₆₇	C₂×Q₁₆	semidirect
175. C₆₇⋊C₈	C₂×Q₁₆	semidirect
196. D₆₇	#1591	direct (N × H)
204. #1591	D₆₇	direct (N × H)
208. C₆₇	C₂×#1591	semidirect
372. C₈	Q₁₆×D₆₇	semidirect

Maximal subgroups

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

subgroup	index
#446×D₆₇	2
C₄×Q₁₆×D₆₇	2
#22559107	2
#22559106	2
#22559105	2
#22559104	2
#22559103	2
#335×D₆₇	2
Q₈⋊C₈×D₆₇	2
C₈²×D₆₇	2
C₆₇×#1591	2
C₂×#1591	67

Subgroups — #1591×D67 #30825569

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #1591×D₆₇ #30825569