Subgroups — C₆₇×#19114 #30698365

Order 17152.

714 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3147	C₂	1	1	yes	maximal, characteristic
2	C₆₇×#3103	C₂	1	2	yes	maximal, complemented
3	C₂×C₈×Q₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#1670	C₂	1	2	yes	maximal, complemented
5	C₆₇×#1668	C₂	1	2	yes	maximal, complemented
6	C₆₇×#1666	C₂	1	4	yes	maximal, complemented
7	C₆₇×#1564	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#1540	C₂	1	2	yes	maximal, complemented
9	C₂×#135×C₆₇	—	2	1	no	—
10	C₂×#135×C₆₇	—	2	1	no	—
11	#532×C₆₇	C₂²	1	2	yes	—
12	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
13	#495×C₆₇	—	2	1	no	—
14	#495×C₆₇	—	2	1	no	—
15	#494×C₆₇	C₂²	1	1	yes	characteristic
16	#493×C₆₇	C₂²	1	1	yes	characteristic
17	#492×C₆₇	C₂²	1	2	yes	—
18	#481×C₆₇	—	2	2	no	—
19	#475×C₆₇	C₂²	1	4	yes	—
20	#460×C₆₇	C₂²	1	4	yes	—
21	#448×C₆₇	—	2	2	no	—
22	C₈×Q₈×C₆₇	—	2	1	no	—
23	C₈×Q₈×C₆₇	—	2	1	no	—
24	C₈×Q₈×C₆₇	C₂²	1	2	yes	—
25	C₈×Q₈×C₆₇	C₂²	1	2	yes	—
26	C₄×SD₁₆×C₆₇	—	2	4	no	—
27	#431×C₆₇	C₂²	1	2	yes	—
28	C₂×C₄⋊C₈×C₆₇	—	2	1	no	—
29	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₈×C₆₇	—	2	1	no	—
31	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
32	#335×C₆₇	C₂²	1	2	yes	—
33	#334×C₆₇	C₂²	1	2	yes	—
34	#332×C₆₇	C₂²	1	4	yes	—
35	#331×C₆₇	C₂²	1	4	yes	—
36	C₂×#41×C₆₇	—	2	2	no	—
37	C₂²×Q₈×C₆₇	D₄	1	1	yes	characteristic
38	#135×C₆₇	—	4	4	no	—
39	#135×C₆₇	—	4	4	no	—
40	C₂×Q₁₆×C₆₇	—	2	1	no	—
41	C₂×Q₁₆×C₆₇	—	2	1	no	—
42	C₂×SD₁₆×C₆₇	—	2	4	no	—
43	C₂×SD₁₆×C₆₇	—	2	2	no	—
44	C₂×SD₁₆×C₆₇	—	2	2	no	—
45	C₂×D₈×C₆₇	—	2	1	no	—
46	C₂×D₈×C₆₇	—	2	1	no	—
47	C₂²×C₈×C₆₇	—	2	1	no	—
48	C₂²×C₈×C₆₇	D₄	1	1	yes	characteristic
49	C₂²×C₈×C₆₇	D₄	1	1	yes	characteristic
50	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
51	#127×C₆₇	C₂³	1	2	yes	—
52	#124×C₆₇	—	2	2	no	—
53	#121×C₆₇	—	2	2	no	—
54	#121×C₆₇	—	2	2	no	—
55	C₄×Q₈×C₆₇	—	2	1	no	—
56	C₄×Q₈×C₆₇	—	2	1	no	—
57	C₄×Q₈×C₆₇	D₄	1	2	yes	—
58	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
59	C₄×D₄×C₆₇	—	2	2	no	—
60	C₄×D₄×C₆₇	—	2	2	no	—
61	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
62	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
63	C₂×C₄²×C₆₇	—	2	1	no	—
64	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
65	#106×C₆₇	—	2	4	no	—
66	C₄⋊C₈×C₆₇	—	2	2	no	—
67	C₄⋊C₈×C₆₇	—	2	2	no	—
68	C₄⋊C₈×C₆₇	—	2	1	no	—
69	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
70	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
71	#103×C₆₇	—	2	4	no	—
72	#102×C₆₇	—	2	4	no	—
73	C₂²⋊C₈×C₆₇	—	2	2	no	—
74	C₄×C₈×C₆₇	—	2	2	no	—
75	C₄×C₈×C₆₇	—	2	2	no	—
76	C₄×C₈×C₆₇	—	2	2	no	—
77	C₄×C₈×C₆₇	D₄	1	1	yes	characteristic
78	C₄×C₈×C₆₇	D₄	1	1	yes	characteristic
79	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
80	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
81	#41×C₆₇	—	4	4	no	—
82	#41×C₆₇	—	4	4	no	—
83	C₂×Q₈×C₆₇	—	2	4	no	—
84	C₂×Q₈×C₆₇	—	2	1	no	—
85	C₂×Q₈×C₆₇	—	2	2	no	—
86	C₂×Q₈×C₆₇	C₂×D₄	1	2	yes	—
87	C₂×D₄×C₆₇	—	2	2	no	—
88	C₂×D₄×C₆₇	—	2	2	no	—
89	C₂×D₄×C₆₇	—	2	2	no	—
90	C₂×D₄×C₆₇	—	4	2	no	—
91	C₂²×C₄×C₆₇	—	2	1	no	—
92	C₂²×C₄×C₆₇	—	2	1	no	—
93	C₂²×C₄×C₆₇	—	4	2	no	—
94	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
97	Q₁₆×C₆₇	—	4	2	no	—
98	Q₁₆×C₆₇	—	4	2	no	—
99	SD₁₆×C₆₇	—	4	4	no	—
100	SD₁₆×C₆₇	—	4	8	no	—
101	SD₁₆×C₆₇	—	4	4	no	—
102	D₈×C₆₇	—	4	2	no	—
103	D₈×C₆₇	—	4	2	no	—
104	C₂×C₈×C₆₇	—	2	2	no	—
105	C₂×C₈×C₆₇	—	2	4	no	—
106	C₂×C₈×C₆₇	—	2	2	no	—
107	C₂×C₈×C₆₇	—	4	2	no	—
108	C₂×C₈×C₆₇	SD₁₆	1	4	yes	complemented
109	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
110	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
111	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
112	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
113	C₄⋊C₄×C₆₇	—	2	2	no	—
114	C₄⋊C₄×C₆₇	—	2	1	no	—
115	C₄⋊C₄×C₆₇	—	2	2	no	—
116	C₄⋊C₄×C₆₇	—	2	2	no	—
117	C₄⋊C₄×C₆₇	—	2	2	no	—
118	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
119	C₂²⋊C₄×C₆₇	—	4	2	no	—
120	C₂²⋊C₄×C₆₇	—	4	2	no	—
121	C₄²×C₆₇	—	2	2	no	—
122	C₄²×C₆₇	—	2	2	no	—
123	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
124	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
125	C₄²×C₆₇	#41	1	1	yes	characteristic
126	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
127	C₂³×C₆₇	—	4	2	no	—
128	C₂³×C₆₇	#121	1	1	yes	characteristic
129	Q₈×C₆₇	—	2	4	no	—
130	Q₈×C₆₇	—	2	2	no	—
131	Q₈×C₆₇	—	4	2	no	—
132	Q₈×C₆₇	—	4	2	no	—
133	Q₈×C₆₇	#135	1	4	yes	complemented
134	D₄×C₆₇	—	4	2	no	—
135	D₄×C₆₇	—	4	4	no	—
136	D₄×C₆₇	—	4	2	no	—
137	D₄×C₆₇	—	8	2	no	—
138	D₄×C₆₇	—	8	4	no	—
139	C₂×C₄×C₆₇	—	2	4	no	—
140	C₂×C₄×C₆₇	—	2	2	no	—
141	C₂×C₄×C₆₇	—	2	2	no	—
142	C₂×C₄×C₆₇	—	2	2	no	—
143	C₂×C₄×C₆₇	—	4	1	no	—
144	C₂×C₄×C₆₇	—	4	2	no	—
145	C₂×C₄×C₆₇	—	4	2	no	—
146	C₂×C₄×C₆₇	—	8	4	no	—
147	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
148	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
149	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
150	C₂×C₄×C₆₇	C₂×SD₁₆	1	2	yes	—
151	C₂×C₄×C₆₇	AGL(1,ℤ/8)	1	2	yes	—
152	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
153	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
154	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
155	C₈×C₆₇	—	2	1	no	—
156	C₈×C₆₇	—	2	1	no	—
157	C₈×C₆₇	—	4	4	no	—
158	C₈×C₆₇	—	4	2	no	—
159	C₈×C₆₇	C₂×SD₁₆	1	2	yes	—
160	C₈×C₆₇	C₂×SD₁₆	1	2	yes	—
161	C₂²×C₆₇	—	2	1	no	—
162	C₂²×C₆₇	—	2	1	no	—
163	C₂²×C₆₇	—	8	2	no	—
164	C₂²×C₆₇	—	8	2	no	—
165	C₂²×C₆₇	—	8	2	no	—
166	C₂²×C₆₇	#460	1	2	yes	—
167	C₂²×C₆₇	C₂×#121	1	1	yes	characteristic
168	C₄×C₆₇	—	2	4	no	—
169	C₄×C₆₇	—	2	1	no	—
170	C₄×C₆₇	—	2	1	no	—
171	C₄×C₆₇	—	2	1	no	—
172	C₄×C₆₇	—	4	2	no	—
173	C₄×C₆₇	—	8	2	no	—
174	C₄×C₆₇	#460	1	2	yes	—
175	C₄×C₆₇	C₂²×SD₁₆	1	1	yes	characteristic
176	C₄×C₆₇	C₂×#135	1	2	yes	—
177	C₄×C₆₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
178	#19114	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
179	C₂×C₆₇	—	2	2	no	—
180	C₂×C₆₇	—	16	2	no	—
181	C₂×C₆₇	C₂×#460	1	1	yes	characteristic
182	C₂×C₆₇	#3050	1	1	yes	characteristic
183	C₂×C₆₇	#3067	1	1	yes	characteristic
184	#3147	C₂×C₆₇	1	1	yes	characteristic
185	#3103	C₂×C₆₇	1	2	yes	complemented
186	C₂×C₈×Q₈	C₂×C₆₇	1	1	yes	characteristic, complemented
187	#1670	C₂×C₆₇	1	2	yes	complemented
188	#1668	C₂×C₆₇	1	2	yes	complemented
189	#1666	C₂×C₆₇	1	4	yes	complemented
190	#1564	C₂×C₆₇	1	1	yes	characteristic, complemented
191	#1540	C₂×C₆₇	1	2	yes	complemented
192	C₆₇	#19114	1	1	yes	characteristic, direct product factor, Sylow
193	C₂×#135	—	2	1	no	—
194	C₂×#135	—	2	1	no	—
195	#532	C₂²×C₆₇	1	2	yes	—
196	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
197	#495	—	2	1	no	—
198	#495	—	2	1	no	—
199	#494	C₂²×C₆₇	1	1	yes	characteristic
200	#493	C₂²×C₆₇	1	1	yes	characteristic
201	#492	C₂²×C₆₇	1	2	yes	—
202	#481	—	2	2	no	—
203	#475	C₂²×C₆₇	1	4	yes	—
204	#460	C₂²×C₆₇	1	4	yes	—
205	#448	—	2	2	no	—
206	C₈×Q₈	—	2	1	no	—
207	C₈×Q₈	—	2	1	no	—
208	C₈×Q₈	C₂²×C₆₇	1	2	yes	—
209	C₈×Q₈	C₂²×C₆₇	1	2	yes	—
210	C₄×SD₁₆	—	2	4	no	—
211	#431	C₂²×C₆₇	1	2	yes	—
212	C₂×C₄⋊C₈	—	2	1	no	—
213	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
214	C₂×C₄×C₈	—	2	1	no	—
215	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic
216	#335	C₂²×C₆₇	1	2	yes	—
217	#334	C₂²×C₆₇	1	2	yes	—
218	#332	C₂²×C₆₇	1	4	yes	—
219	#331	C₂²×C₆₇	1	4	yes	—
220	C₂×#41	—	2	2	no	—
221	C₂²×Q₈	D₄×C₆₇	1	1	yes	characteristic
222	#135	—	4	4	no	—
223	#135	—	4	4	no	—
224	C₂×Q₁₆	—	2	1	no	—
225	C₂×Q₁₆	—	2	1	no	—
226	C₂×SD₁₆	—	2	4	no	—
227	C₂×SD₁₆	—	2	2	no	—
228	C₂×SD₁₆	—	2	2	no	—
229	C₂×D₈	—	2	1	no	—
230	C₂×D₈	—	2	1	no	—
231	C₂²×C₈	—	2	1	no	—
232	C₂²×C₈	D₄×C₆₇	1	1	yes	characteristic
233	C₂²×C₈	D₄×C₆₇	1	1	yes	characteristic
234	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
235	#127	C₂³×C₆₇	1	2	yes	—
236	#124	—	2	2	no	—
237	#121	—	2	2	no	—
238	#121	—	2	2	no	—
239	C₄×Q₈	—	2	1	no	—
240	C₄×Q₈	—	2	1	no	—
241	C₄×Q₈	D₄×C₆₇	1	2	yes	—
242	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
243	C₄×D₄	—	2	2	no	—
244	C₄×D₄	—	2	2	no	—
245	C₂×C₄⋊C₄	—	2	1	no	—
246	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
247	C₂×C₄²	—	2	1	no	—
248	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
249	#106	—	2	4	no	—
250	C₄⋊C₈	—	2	2	no	—
251	C₄⋊C₈	—	2	2	no	—
252	C₄⋊C₈	—	2	1	no	—
253	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
254	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
255	#103	—	2	4	no	—
256	#102	—	2	4	no	—
257	C₂²⋊C₈	—	2	2	no	—
258	C₄×C₈	—	2	2	no	—
259	C₄×C₈	—	2	2	no	—
260	C₄×C₈	—	2	2	no	—
261	C₄×C₈	D₄×C₆₇	1	1	yes	characteristic
262	C₄×C₈	D₄×C₆₇	1	1	yes	characteristic
263	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
264	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
265	#41	—	4	4	no	—
266	#41	—	4	4	no	—
267	C₂×Q₈	—	2	4	no	—
268	C₂×Q₈	—	2	1	no	—
269	C₂×Q₈	—	2	2	no	—
270	C₂×Q₈	C₂×D₄×C₆₇	1	2	yes	—
271	C₂×D₄	—	2	2	no	—
272	C₂×D₄	—	2	2	no	—
273	C₂×D₄	—	2	2	no	—
274	C₂×D₄	—	4	2	no	—
275	C₂²×C₄	—	2	1	no	—
276	C₂²×C₄	—	2	1	no	—
277	C₂²×C₄	—	4	2	no	—
278	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
279	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
280	C₂²×C₄	#41×C₆₇	1	1	yes	characteristic
281	Q₁₆	—	4	2	no	—
282	Q₁₆	—	4	2	no	—
283	SD₁₆	—	4	4	no	—
284	SD₁₆	—	4	8	no	—
285	SD₁₆	—	4	4	no	—
286	D₈	—	4	2	no	—
287	D₈	—	4	2	no	—
288	C₂×C₈	—	2	2	no	—
289	C₂×C₈	—	2	2	no	—
290	C₂×C₈	—	2	4	no	—
291	C₂×C₈	—	4	2	no	—
292	C₂×C₈	SD₁₆×C₆₇	1	4	yes	complemented
293	C₂×C₈	C₂×D₄×C₆₇	1	1	yes	characteristic
294	C₂×C₈	C₂×D₄×C₆₇	1	1	yes	characteristic
295	C₂×C₈	C₂×D₄×C₆₇	1	1	yes	characteristic
296	C₂×C₈	C₂×D₄×C₆₇	1	1	yes	characteristic
297	C₄⋊C₄	—	2	2	no	—
298	C₄⋊C₄	—	2	1	no	—
299	C₄⋊C₄	—	2	2	no	—
300	C₄⋊C₄	—	2	2	no	—
301	C₄⋊C₄	—	2	2	no	—
302	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
303	C₂²⋊C₄	—	4	2	no	—
304	C₂²⋊C₄	—	4	2	no	—
305	C₄²	—	2	2	no	—
306	C₄²	—	2	2	no	—
307	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
308	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
309	C₄²	#41×C₆₇	1	1	yes	characteristic
310	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
311	C₂³	—	4	2	no	—
312	C₂³	#121×C₆₇	1	1	yes	characteristic
313	Q₈	—	2	4	no	—
314	Q₈	—	2	2	no	—
315	Q₈	—	4	2	no	—
316	Q₈	—	4	2	no	—
317	Q₈	#135×C₆₇	1	4	yes	complemented
318	D₄	—	4	2	no	—
319	D₄	—	4	4	no	—
320	D₄	—	4	2	no	—
321	D₄	—	8	2	no	—
322	D₄	—	8	4	no	—
323	C₂×C₄	—	2	4	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	4	1	no	—
328	C₂×C₄	—	4	2	no	—
329	C₂×C₄	—	4	2	no	—
330	C₂×C₄	—	8	4	no	—
331	C₂×C₄	#121×C₆₇	1	1	yes	characteristic
332	C₂×C₄	#121×C₆₇	1	1	yes	characteristic
333	C₂×C₄	#121×C₆₇	1	1	yes	characteristic
334	C₂×C₄	C₂×SD₁₆×C₆₇	1	2	yes	—
335	C₂×C₄	AGL(1,ℤ/8)×C₆₇	1	2	yes	—
336	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
337	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
338	C₂×C₄	C₂×#41×C₆₇	1	1	yes	characteristic
339	C₈	—	2	1	no	—
340	C₈	—	2	1	no	—
341	C₈	—	4	4	no	—
342	C₈	—	4	2	no	—
343	C₈	C₂×SD₁₆×C₆₇	1	2	yes	—
344	C₈	C₂×SD₁₆×C₆₇	1	2	yes	—
345	C₂²	—	2	1	no	—
346	C₂²	—	2	1	no	—
347	C₂²	—	8	2	no	—
348	C₂²	—	8	2	no	—
349	C₂²	—	8	2	no	—
350	C₂²	#460×C₆₇	1	2	yes	—
351	C₂²	C₂×#121×C₆₇	1	1	yes	characteristic
352	C₄	—	2	4	no	—
353	C₄	—	2	1	no	—
354	C₄	—	2	1	no	—
355	C₄	—	2	1	no	—
356	C₄	—	4	2	no	—
357	C₄	—	8	2	no	—
358	C₄	#460×C₆₇	1	2	yes	—
359	C₄	C₂²×SD₁₆×C₆₇	1	1	yes	characteristic
360	C₄	C₂×#135×C₆₇	1	2	yes	—
361	C₄	C₂×AGL(1,ℤ/8)×C₆₇	1	1	yes	characteristic
362	C₂	—	2	2	no	—
363	C₂	—	16	2	no	—
364	C₂	C₂×#460×C₆₇	1	1	yes	characteristic
365	C₂	C₆₇×#3050	1	1	yes	characteristic
366	C₂	C₆₇×#3067	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₆₇	#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₆₇
socle	C₂²×C₆₇	C₂×#121
prime radical	C₆₇×#3147	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₆₇ ◁ C₂×C₄²×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₆₇×#3103	C₂	semidirect
3. C₂×C₈×Q₈×C₆₇	C₂	semidirect
4. C₆₇×#1670	C₂	semidirect
5. C₆₇×#1668	C₂	semidirect
6. C₆₇×#1666	C₂	semidirect
7. C₆₇×#1564	C₂	semidirect
8. C₆₇×#1540	C₂	semidirect
108. C₂×C₈×C₆₇	SD₁₆	semidirect
133. Q₈×C₆₇	#135	semidirect
178. #19114	C₆₇	direct (N × H)
185. #3103	C₂×C₆₇	semidirect
186. C₂×C₈×Q₈	C₂×C₆₇	semidirect
187. #1670	C₂×C₆₇	semidirect
188. #1668	C₂×C₆₇	semidirect
189. #1666	C₂×C₆₇	semidirect
190. #1564	C₂×C₆₇	semidirect
191. #1540	C₂×C₆₇	semidirect
192. C₆₇	#19114	direct (N × H)
292. C₂×C₈	SD₁₆×C₆₇	semidirect
317. Q₈	#135×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#3147	2
C₆₇×#3103	2
C₂×C₈×Q₈×C₆₇	2
C₆₇×#1670	2
C₆₇×#1668	2
C₆₇×#1666	2
C₆₇×#1564	2
C₆₇×#1540	2
#19114	67

Subgroups — C67×#19114 #30698365

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#19114 #30698365