Subgroups — C₆₇×#33839 #30713090

Order 17152.

712 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#509×C₆₇	C₂	1	2	yes	maximal, complemented
2	C₆₇×#3280	C₂	1	2	yes	maximal, complemented
3	C₆₇×#2249	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#2220	C₂	1	2	yes	maximal, complemented
5	C₆₇×#2210	C₂	1	2	yes	maximal, complemented
6	C₆₇×#2189	C₂	1	2	yes	maximal, complemented
7	C₆₇×#2184	C₂	1	2	yes	maximal, complemented
8	C₄×D₁₆×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#2169	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#135×C₆₇	C₂²	1	2	yes	—
11	C₂²×D₈×C₆₇	C₂²	1	2	yes	complemented
12	#546×C₆₇	—	2	2	no	—
13	#509×C₆₇	—	2	8	no	—
14	C₂×Q₃₂×C₆₇	C₂²	1	1	yes	characteristic, complemented
15	C₂×SD₃₂×C₆₇	C₂²	1	2	yes	complemented
16	C₂×SD₃₂×C₆₇	C₂²	1	2	yes	complemented
17	C₂×D₁₆×C₆₇	C₂²	1	2	yes	—
18	C₂×D₁₆×C₆₇	C₂²	1	1	yes	characteristic
19	C₂×D₁₆×C₆₇	C₂²	1	1	yes	characteristic
20	C₂×M₃₂×C₆₇	C₂²	1	2	yes	complemented
21	#495×C₆₇	C₂²	1	2	yes	complemented
22	#467×C₆₇	C₂²	1	2	yes	complemented
23	#466×C₆₇	C₂²	1	2	yes	—
24	#463×C₆₇	—	2	2	no	—
25	#450×C₆₇	—	2	2	no	—
26	#449×C₆₇	—	2	2	no	—
27	C₄×D₈×C₆₇	C₂²	1	2	yes	complemented
28	C₈×D₄×C₆₇	C₂²	1	1	yes	characteristic
29	#366×C₆₇	C₂²	1	1	yes	characteristic, complemented
30	C₄⋊C₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
31	#358×C₆₇	C₂²	1	2	yes	complemented
32	#357×C₆₇	C₂²	1	2	yes	complemented
33	#357×C₆₇	C₂²	1	2	yes	complemented
34	C₂²⋊C₁₆×C₆₇	C₂²	1	2	yes	complemented
35	C₄×C₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
36	C₂×#41×C₆₇	—	2	2	no	—
37	C₂²×D₄×C₆₇	—	2	2	no	—
38	#135×C₆₇	—	2	4	no	—
39	#135×C₆₇	—	4	2	no	—
40	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
41	C₂×SD₁₆×C₆₇	—	2	2	no	—
42	C₂×SD₁₆×C₆₇	—	2	2	no	—
43	C₂×D₈×C₆₇	—	2	4	no	—
44	C₂×D₈×C₆₇	—	2	2	no	—
45	C₂×D₈×C₆₇	—	4	2	no	—
46	C₂×D₈×C₆₇	C₂³	1	2	yes	—
47	C₂×D₈×C₆₇	C₂³	1	2	yes	—
48	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
49	#124×C₆₇	—	2	2	no	—
50	#123×C₆₇	—	4	2	no	—
51	C₂²⋊Q₈×C₆₇	—	2	2	no	—
52	#121×C₆₇	—	2	2	no	—
53	#121×C₆₇	—	4	2	no	—
54	#120×C₆₇	—	4	2	no	—
55	C₄×D₄×C₆₇	—	2	2	no	—
56	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
57	C₂×C₂²⋊C₄×C₆₇	—	4	2	no	—
58	Q₃₂×C₆₇	—	4	1	no	—
59	SD₃₂×C₆₇	—	2	4	no	—
60	SD₃₂×C₆₇	—	2	4	no	—
61	D₁₆×C₆₇	—	2	4	no	—
62	D₁₆×C₆₇	—	4	1	no	—
63	D₁₆×C₆₇	D₄	1	4	yes	complemented
64	M₃₂×C₆₇	—	2	4	no	—
65	C₂×C₁₆×C₆₇	C₂³	1	2	yes	—
66	C₂×C₁₆×C₆₇	C₂³	1	1	yes	characteristic
67	C₂×C₁₆×C₆₇	C₂³	1	1	yes	characteristic
68	#107×C₆₇	C₂³	1	2	yes	—
69	C₄⋊C₈×C₆₇	D₄	1	1	yes	characteristic
70	#103×C₆₇	—	2	2	no	—
71	#102×C₆₇	—	2	2	no	—
72	#102×C₆₇	—	2	2	no	—
73	C₂²⋊C₈×C₆₇	D₄	1	2	yes	—
74	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
75	C₂⁴×C₆₇	—	4	2	no	—
76	#41×C₆₇	—	4	4	no	—
77	#41×C₆₇	—	8	2	no	—
78	C₂×Q₈×C₆₇	—	2	2	no	—
79	C₂×D₄×C₆₇	—	2	2	no	—
80	C₂×D₄×C₆₇	—	2	2	no	—
81	C₂×D₄×C₆₇	—	4	4	no	—
82	C₂×D₄×C₆₇	—	4	2	no	—
83	C₂×D₄×C₆₇	—	4	2	no	—
84	C₂×D₄×C₆₇	—	4	2	no	—
85	C₂×D₄×C₆₇	—	8	2	no	—
86	C₂×D₄×C₆₇	D₈	1	1	yes	characteristic
87	C₂²×C₄×C₆₇	—	4	2	no	—
88	C₂²×C₄×C₆₇	—	4	2	no	—
89	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
90	Q₁₆×C₆₇	—	2	2	no	—
91	Q₁₆×C₆₇	—	2	2	no	—
92	SD₁₆×C₆₇	—	4	4	no	—
93	SD₁₆×C₆₇	—	8	2	no	—
94	D₈×C₆₇	—	2	2	no	—
95	D₈×C₆₇	—	2	2	no	—
96	D₈×C₆₇	—	2	2	no	—
97	D₈×C₆₇	—	4	4	no	—
98	D₈×C₆₇	C₂×D₄	1	4	yes	—
99	C₂×C₈×C₆₇	—	2	2	no	—
100	C₂×C₈×C₆₇	—	2	2	no	—
101	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
102	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
103	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
104	C₄⋊C₄×C₆₇	—	2	2	no	—
105	C₄⋊C₄×C₆₇	—	4	2	no	—
106	C₄⋊C₄×C₆₇	D₈	1	1	yes	characteristic
107	C₂²⋊C₄×C₆₇	—	4	2	no	—
108	C₂²⋊C₄×C₆₇	—	4	2	no	—
109	C₂²⋊C₄×C₆₇	—	4	2	no	—
110	C₂²⋊C₄×C₆₇	—	4	2	no	—
111	C₂²⋊C₄×C₆₇	—	4	2	no	—
112	C₂²⋊C₄×C₆₇	D₈	1	2	yes	—
113	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
114	C₁₆×C₆₇	—	2	2	no	—
115	C₁₆×C₆₇	—	2	1	no	—
116	C₁₆×C₆₇	C₂×D₄	1	2	yes	—
117	C₂³×C₆₇	—	4	2	no	—
118	C₂³×C₆₇	—	4	2	no	—
119	C₂³×C₆₇	—	8	4	no	—
120	C₂³×C₆₇	—	8	4	no	—
121	C₂³×C₆₇	—	16	2	no	—
122	C₂³×C₆₇	C₂×D₈	1	2	yes	—
123	Q₈×C₆₇	—	4	2	no	—
124	Q₈×C₆₇	—	4	2	no	—
125	D₄×C₆₇	—	2	4	no	—
126	D₄×C₆₇	—	4	1	no	—
127	D₄×C₆₇	—	4	2	no	—
128	D₄×C₆₇	—	4	2	no	—
129	D₄×C₆₇	—	4	2	no	—
130	D₄×C₆₇	—	8	4	no	—
131	D₄×C₆₇	—	8	4	no	—
132	D₄×C₆₇	—	16	2	no	—
133	C₂×C₄×C₆₇	—	2	2	no	—
134	C₂×C₄×C₆₇	—	2	2	no	—
135	C₂×C₄×C₆₇	—	4	2	no	—
136	C₂×C₄×C₆₇	—	4	2	no	—
137	C₂×C₄×C₆₇	—	8	4	no	—
138	C₂×C₄×C₆₇	—	16	2	no	—
139	C₂×C₄×C₆₇	C₂×D₈	1	1	yes	characteristic
140	C₂×C₄×C₆₇	C₂×D₈	1	1	yes	characteristic
141	C₂×C₄×C₆₇	C₂×D₈	1	2	yes	—
142	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
143	C₈×C₆₇	—	2	2	no	—
144	C₈×C₆₇	—	2	1	no	—
145	C₈×C₆₇	C₂²×D₄	1	1	yes	characteristic
146	C₈×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
147	C₂²×C₆₇	—	2	2	no	—
148	C₂²×C₆₇	—	2	2	no	—
149	C₂²×C₆₇	—	2	2	no	—
150	C₂²×C₆₇	—	4	4	no	—
151	C₂²×C₆₇	—	8	2	no	—
152	C₂²×C₆₇	—	8	2	no	—
153	C₂²×C₆₇	—	8	2	no	—
154	C₂²×C₆₇	—	8	2	no	—
155	C₂²×C₆₇	—	8	2	no	—
156	C₂²×C₆₇	—	16	8	no	—
157	C₂²×C₆₇	C₂²×D₈	1	1	yes	characteristic
158	C₄×C₆₇	—	2	1	no	—
159	C₄×C₆₇	—	2	1	no	—
160	C₄×C₆₇	—	2	2	no	—
161	C₄×C₆₇	—	8	2	no	—
162	C₄×C₆₇	—	8	2	no	—
163	C₄×C₆₇	D₄²	1	1	yes	characteristic
164	C₄×C₆₇	#576	1	1	yes	characteristic
165	#33839	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
166	C₂×C₆₇	—	4	2	no	—
167	C₂×C₆₇	—	8	4	no	—
168	C₂×C₆₇	—	16	2	no	—
169	C₂×C₆₇	D₄×D₈	1	1	yes	characteristic
170	C₂×C₆₇	#3414	1	1	yes	characteristic
171	C₂×C₆₇	#3415	1	1	yes	characteristic
172	C₂×#509	C₂×C₆₇	1	2	yes	complemented
173	#3280	C₂×C₆₇	1	2	yes	complemented
174	#2249	C₂×C₆₇	1	1	yes	characteristic, complemented
175	#2220	C₂×C₆₇	1	2	yes	complemented
176	#2210	C₂×C₆₇	1	2	yes	complemented
177	#2189	C₂×C₆₇	1	2	yes	complemented
178	#2184	C₂×C₆₇	1	2	yes	complemented
179	C₄×D₁₆	C₂×C₆₇	1	1	yes	characteristic, complemented
180	#2169	C₂×C₆₇	1	1	yes	characteristic, complemented
181	C₆₇	#33839	1	1	yes	characteristic, direct product factor, Sylow
182	C₂×#135	C₂²×C₆₇	1	2	yes	—
183	C₂²×D₈	C₂²×C₆₇	1	2	yes	complemented
184	#546	—	2	2	no	—
185	#509	—	2	8	no	—
186	C₂×Q₃₂	C₂²×C₆₇	1	1	yes	characteristic, complemented
187	C₂×SD₃₂	C₂²×C₆₇	1	2	yes	complemented
188	C₂×SD₃₂	C₂²×C₆₇	1	2	yes	complemented
189	C₂×D₁₆	C₂²×C₆₇	1	2	yes	—
190	C₂×D₁₆	C₂²×C₆₇	1	1	yes	characteristic
191	C₂×D₁₆	C₂²×C₆₇	1	1	yes	characteristic
192	C₂×M₃₂	C₂²×C₆₇	1	2	yes	complemented
193	#495	C₂²×C₆₇	1	2	yes	complemented
194	#467	C₂²×C₆₇	1	2	yes	complemented
195	#466	C₂²×C₆₇	1	2	yes	—
196	#463	—	2	2	no	—
197	#450	—	2	2	no	—
198	#449	—	2	2	no	—
199	C₄×D₈	C₂²×C₆₇	1	2	yes	complemented
200	C₈×D₄	C₂²×C₆₇	1	1	yes	characteristic
201	#366	C₂²×C₆₇	1	1	yes	characteristic, complemented
202	C₄⋊C₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
203	#358	C₂²×C₆₇	1	2	yes	complemented
204	#357	C₂²×C₆₇	1	2	yes	complemented
205	#357	C₂²×C₆₇	1	2	yes	complemented
206	C₂²⋊C₁₆	C₂²×C₆₇	1	2	yes	complemented
207	C₄×C₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
208	C₂×#41	—	2	2	no	—
209	C₂²×D₄	—	2	2	no	—
210	#135	—	2	4	no	—
211	#135	—	4	2	no	—
212	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
213	C₂×SD₁₆	—	2	2	no	—
214	C₂×SD₁₆	—	2	2	no	—
215	C₂×D₈	—	2	4	no	—
216	C₂×D₈	—	2	2	no	—
217	C₂×D₈	—	4	2	no	—
218	C₂×D₈	C₂³×C₆₇	1	2	yes	—
219	C₂×D₈	C₂³×C₆₇	1	2	yes	—
220	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
221	#124	—	2	2	no	—
222	#123	—	4	2	no	—
223	C₂²⋊Q₈	—	2	2	no	—
224	#121	—	2	2	no	—
225	#121	—	4	2	no	—
226	#120	—	4	2	no	—
227	C₄×D₄	—	2	2	no	—
228	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
229	C₂×C₂²⋊C₄	—	4	2	no	—
230	Q₃₂	—	4	1	no	—
231	SD₃₂	—	2	4	no	—
232	SD₃₂	—	2	4	no	—
233	D₁₆	—	2	4	no	—
234	D₁₆	—	4	1	no	—
235	D₁₆	D₄×C₆₇	1	4	yes	complemented
236	M₃₂	—	2	4	no	—
237	C₂×C₁₆	C₂³×C₆₇	1	1	yes	characteristic
238	C₂×C₁₆	C₂³×C₆₇	1	2	yes	—
239	C₂×C₁₆	C₂³×C₆₇	1	1	yes	characteristic
240	#107	C₂³×C₆₇	1	2	yes	—
241	C₄⋊C₈	D₄×C₆₇	1	1	yes	characteristic
242	#103	—	2	2	no	—
243	#102	—	2	2	no	—
244	#102	—	2	2	no	—
245	C₂²⋊C₈	D₄×C₆₇	1	2	yes	—
246	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
247	C₂⁴	—	4	2	no	—
248	#41	—	4	4	no	—
249	#41	—	8	2	no	—
250	C₂×Q₈	—	2	2	no	—
251	C₂×D₄	—	2	2	no	—
252	C₂×D₄	—	2	2	no	—
253	C₂×D₄	—	4	4	no	—
254	C₂×D₄	—	4	2	no	—
255	C₂×D₄	—	4	2	no	—
256	C₂×D₄	—	4	2	no	—
257	C₂×D₄	—	8	2	no	—
258	C₂×D₄	D₈×C₆₇	1	1	yes	characteristic
259	C₂²×C₄	—	4	2	no	—
260	C₂²×C₄	—	4	2	no	—
261	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
262	Q₁₆	—	2	2	no	—
263	Q₁₆	—	2	2	no	—
264	SD₁₆	—	4	4	no	—
265	SD₁₆	—	8	2	no	—
266	D₈	—	2	2	no	—
267	D₈	—	2	2	no	—
268	D₈	—	2	2	no	—
269	D₈	—	4	4	no	—
270	D₈	C₂×D₄×C₆₇	1	4	yes	—
271	C₂×C₈	—	2	2	no	—
272	C₂×C₈	—	2	2	no	—
273	C₂×C₈	C₂×D₄×C₆₇	1	1	yes	characteristic
274	C₂×C₈	C₂×D₄×C₆₇	1	2	yes	—
275	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
276	C₄⋊C₄	—	2	2	no	—
277	C₄⋊C₄	—	4	2	no	—
278	C₄⋊C₄	D₈×C₆₇	1	1	yes	characteristic
279	C₂²⋊C₄	—	4	2	no	—
280	C₂²⋊C₄	—	4	2	no	—
281	C₂²⋊C₄	—	4	2	no	—
282	C₂²⋊C₄	—	4	2	no	—
283	C₂²⋊C₄	—	4	2	no	—
284	C₂²⋊C₄	D₈×C₆₇	1	2	yes	—
285	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
286	C₁₆	—	2	2	no	—
287	C₁₆	—	2	1	no	—
288	C₁₆	C₂×D₄×C₆₇	1	2	yes	—
289	C₂³	—	4	2	no	—
290	C₂³	—	4	2	no	—
291	C₂³	—	8	4	no	—
292	C₂³	—	8	4	no	—
293	C₂³	—	16	2	no	—
294	C₂³	C₂×D₈×C₆₇	1	2	yes	—
295	Q₈	—	4	2	no	—
296	Q₈	—	4	2	no	—
297	D₄	—	2	4	no	—
298	D₄	—	4	1	no	—
299	D₄	—	4	2	no	—
300	D₄	—	4	2	no	—
301	D₄	—	4	2	no	—
302	D₄	—	8	4	no	—
303	D₄	—	8	4	no	—
304	D₄	—	16	2	no	—
305	C₂×C₄	—	2	2	no	—
306	C₂×C₄	—	2	2	no	—
307	C₂×C₄	—	4	2	no	—
308	C₂×C₄	—	4	2	no	—
309	C₂×C₄	—	8	4	no	—
310	C₂×C₄	—	16	2	no	—
311	C₂×C₄	C₂×D₈×C₆₇	1	1	yes	characteristic
312	C₂×C₄	C₂×D₈×C₆₇	1	1	yes	characteristic
313	C₂×C₄	C₂×D₈×C₆₇	1	2	yes	—
314	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
315	C₈	—	2	2	no	—
316	C₈	—	2	1	no	—
317	C₈	C₂²×D₄×C₆₇	1	1	yes	characteristic
318	C₈	H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
319	C₂²	—	2	2	no	—
320	C₂²	—	2	2	no	—
321	C₂²	—	2	2	no	—
322	C₂²	—	4	4	no	—
323	C₂²	—	8	2	no	—
324	C₂²	—	8	2	no	—
325	C₂²	—	8	2	no	—
326	C₂²	—	8	2	no	—
327	C₂²	—	8	2	no	—
328	C₂²	—	16	8	no	—
329	C₂²	C₂²×D₈×C₆₇	1	1	yes	characteristic
330	C₄	—	2	2	no	—
331	C₄	—	2	1	no	—
332	C₄	—	2	1	no	—
333	C₄	—	8	2	no	—
334	C₄	—	8	2	no	—
335	C₄	D₄²×C₆₇	1	1	yes	characteristic
336	C₄	#576×C₆₇	1	1	yes	characteristic
337	C₂	—	4	2	no	—
338	C₂	—	8	4	no	—
339	C₂	—	16	2	no	—
340	C₂	D₄×D₈×C₆₇	1	1	yes	characteristic
341	C₂	C₆₇×#3414	1	1	yes	characteristic
342	C₂	C₆₇×#3415	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₆₇
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ C₄×D₄×C₆₇ ◁ C₈×D₄×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#509×C₆₇	C₂	semidirect
2. C₆₇×#3280	C₂	semidirect
3. C₆₇×#2249	C₂	semidirect
4. C₆₇×#2220	C₂	semidirect
5. C₆₇×#2210	C₂	semidirect
6. C₆₇×#2189	C₂	semidirect
7. C₆₇×#2184	C₂	semidirect
8. C₄×D₁₆×C₆₇	C₂	semidirect
9. C₆₇×#2169	C₂	semidirect
11. C₂²×D₈×C₆₇	C₂²	semidirect
14. C₂×Q₃₂×C₆₇	C₂²	semidirect
15. C₂×SD₃₂×C₆₇	C₂²	semidirect
16. C₂×SD₃₂×C₆₇	C₂²	semidirect
20. C₂×M₃₂×C₆₇	C₂²	semidirect
21. #495×C₆₇	C₂²	semidirect
22. #467×C₆₇	C₂²	semidirect
27. C₄×D₈×C₆₇	C₂²	semidirect
29. #366×C₆₇	C₂²	semidirect
30. C₄⋊C₁₆×C₆₇	C₂²	semidirect
31. #358×C₆₇	C₂²	semidirect
32. #357×C₆₇	C₂²	semidirect
33. #357×C₆₇	C₂²	semidirect
34. C₂²⋊C₁₆×C₆₇	C₂²	semidirect
35. C₄×C₁₆×C₆₇	C₂²	semidirect
63. D₁₆×C₆₇	D₄	semidirect
165. #33839	C₆₇	direct (N × H)
172. C₂×#509	C₂×C₆₇	semidirect
173. #3280	C₂×C₆₇	semidirect
174. #2249	C₂×C₆₇	semidirect
175. #2220	C₂×C₆₇	semidirect
176. #2210	C₂×C₆₇	semidirect
177. #2189	C₂×C₆₇	semidirect
178. #2184	C₂×C₆₇	semidirect
179. C₄×D₁₆	C₂×C₆₇	semidirect
180. #2169	C₂×C₆₇	semidirect
181. C₆₇	#33839	direct (N × H)
183. C₂²×D₈	C₂²×C₆₇	semidirect
186. C₂×Q₃₂	C₂²×C₆₇	semidirect
187. C₂×SD₃₂	C₂²×C₆₇	semidirect
188. C₂×SD₃₂	C₂²×C₆₇	semidirect
192. C₂×M₃₂	C₂²×C₆₇	semidirect
193. #495	C₂²×C₆₇	semidirect
194. #467	C₂²×C₆₇	semidirect
199. C₄×D₈	C₂²×C₆₇	semidirect
201. #366	C₂²×C₆₇	semidirect
202. C₄⋊C₁₆	C₂²×C₆₇	semidirect
203. #358	C₂²×C₆₇	semidirect
204. #357	C₂²×C₆₇	semidirect
205. #357	C₂²×C₆₇	semidirect
206. C₂²⋊C₁₆	C₂²×C₆₇	semidirect
207. C₄×C₁₆	C₂²×C₆₇	semidirect
235. D₁₆	D₄×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#509×C₆₇	2
C₆₇×#3280	2
C₆₇×#2249	2
C₆₇×#2220	2
C₆₇×#2210	2
C₆₇×#2189	2
C₆₇×#2184	2
C₄×D₁₆×C₆₇	2
C₆₇×#2169	2
#33839	67

Subgroups — C67×#33839 #30713090

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#33839 #30713090