Subgroups — C₆₇×#20612 #30699863

Order 17152.

3640 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#585×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₂×#413×C₆₇	C₂	1	3	yes	maximal, complemented
3	C₆₇×#2879	C₂	1	3	yes	maximal, complemented
4	C₆₇×#1791	C₂	1	8	yes	maximal, complemented
5	#585×C₆₇	—	2	6	no	—
6	#585×C₆₇	—	2	6	no	—
7	#585×C₆₇	C₄	1	4	yes	—
8	#585×C₆₇	C₂²	1	4	yes	—
9	C₂×2₋¹⁺⁴×C₆₇	—	2	3	no	—
10	C₂×H(5,𝔽₂)×C₆₇	—	2	3	no	—
11	C₂×H(5,𝔽₂)×C₆₇	C₄	1	4	yes	—
12	C₂²×#41×C₆₇	—	2	6	no	—
13	C₂²×#41×C₆₇	C₂²	1	3	yes	—
14	C₂²×M₁₆×C₆₇	C₂²	1	3	yes	complemented
15	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
16	#413×C₆₇	—	2	6	no	—
17	#413×C₆₇	C₂²	1	12	yes	complemented
18	C₂×#101×C₆₇	—	2	3	no	—
19	C₂×#100×C₆₇	—	2	3	no	—
20	#408×C₆₇	—	2	6	no	—
21	#408×C₆₇	C₂²	1	12	yes	complemented
22	#407×C₆₇	—	2	6	no	—
23	2₋¹⁺⁴×C₆₇	—	2	24	no	—
24	2₋¹⁺⁴×C₆₇	—	2	12	no	—
25	2₋¹⁺⁴×C₆₇	—	2	12	no	—
26	H(5,𝔽₂)×C₆₇	—	2	24	no	—
27	H(5,𝔽₂)×C₆₇	—	2	12	no	—
28	H(5,𝔽₂)×C₆₇	—	2	24	no	—
29	H(5,𝔽₂)×C₆₇	—	2	12	no	—
30	H(5,𝔽₂)×C₆₇	C₂×C₄	1	16	yes	—
31	C₂×#41×C₆₇	—	2	4	no	—
32	C₂×#41×C₆₇	—	2	12	no	—
33	C₂×#41×C₆₇	—	2	24	no	—
34	C₂×#41×C₆₇	—	2	24	no	—
35	C₂×#41×C₆₇	—	2	12	no	—
36	C₂×#41×C₆₇	—	2	24	no	—
37	C₂×#41×C₆₇	—	2	6	no	—
38	C₂×#41×C₆₇	—	2	24	no	—
39	C₂×#41×C₆₇	—	2	6	no	—
40	C₂×#41×C₆₇	—	2	6	no	—
41	C₂×#41×C₆₇	—	2	6	no	—
42	C₂×#41×C₆₇	C₂×C₄	1	6	yes	—
43	C₂×#41×C₆₇	D₄	1	6	yes	—
44	C₂×#41×C₆₇	D₄	1	6	yes	—
45	C₂×#41×C₆₇	C₂³	1	6	yes	—
46	C₂²×Q₈×C₆₇	—	2	6	no	—
47	C₂²×Q₈×C₆₇	D₄	1	3	yes	—
48	C₂²×D₄×C₆₇	—	2	6	no	—
49	C₂²×D₄×C₆₇	—	2	12	no	—
50	C₂²×D₄×C₆₇	C₂×C₄	1	6	yes	—
51	C₂²×D₄×C₆₇	D₄	1	3	yes	—
52	C₂³×C₄×C₆₇	—	2	4	no	—
53	C₂³×C₄×C₆₇	D₄	1	6	yes	—
54	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
55	C₂×M₁₆×C₆₇	—	2	3	no	—
56	C₂×M₁₆×C₆₇	—	2	3	no	—
57	C₂×M₁₆×C₆₇	—	2	3	no	—
58	C₂×M₁₆×C₆₇	—	2	6	no	—
59	C₂×M₁₆×C₆₇	—	2	6	no	—
60	C₂×M₁₆×C₆₇	C₂³	1	6	yes	complemented
61	C₂²×C₈×C₆₇	—	2	3	no	—
62	C₂²×C₈×C₆₇	C₂³	1	2	yes	complemented
63	#101×C₆₇	—	2	12	no	—
64	#100×C₆₇	—	2	12	no	—
65	C₂²⋊C₈×C₆₇	—	2	24	no	—
66	C₂⁴×C₆₇	—	2	4	no	—
67	C₂⁴×C₆₇	C₂²⋊C₄	1	6	yes	—
68	C₂⁴×C₆₇	C₂²×C₄	1	1	yes	characteristic
69	#41×C₆₇	—	2	16	no	—
70	#41×C₆₇	—	2	16	no	—
71	#41×C₆₇	—	2	48	no	—
72	#41×C₆₇	—	2	48	no	—
73	#41×C₆₇	—	2	48	no	—
74	#41×C₆₇	—	2	12	no	—
75	#41×C₆₇	—	2	48	no	—
76	#41×C₆₇	—	2	12	no	—
77	#41×C₆₇	—	2	12	no	—
78	#41×C₆₇	—	2	12	no	—
79	#41×C₆₇	—	2	12	no	—
80	#41×C₆₇	—	2	12	no	—
81	#41×C₆₇	—	2	12	no	—
82	#41×C₆₇	—	2	12	no	—
83	C₂×Q₈×C₆₇	—	2	4	no	—
84	C₂×Q₈×C₆₇	—	2	24	no	—
85	C₂×Q₈×C₆₇	—	2	24	no	—
86	C₂×Q₈×C₆₇	—	2	6	no	—
87	C₂×Q₈×C₆₇	—	2	6	no	—
88	C₂×Q₈×C₆₇	C₂²⋊C₄	1	6	yes	—
89	C₂×Q₈×C₆₇	C₂×D₄	1	6	yes	—
90	C₂×D₄×C₆₇	—	2	12	no	—
91	C₂×D₄×C₆₇	—	2	48	no	—
92	C₂×D₄×C₆₇	—	2	24	no	—
93	C₂×D₄×C₆₇	—	2	24	no	—
94	C₂×D₄×C₆₇	—	2	12	no	—
95	C₂×D₄×C₆₇	—	2	48	no	—
96	C₂×D₄×C₆₇	—	2	12	no	—
97	C₂×D₄×C₆₇	—	2	6	no	—
98	C₂×D₄×C₆₇	—	2	6	no	—
99	C₂×D₄×C₆₇	C₂²⋊C₄	1	12	yes	—
100	C₂×D₄×C₆₇	C₂²⋊C₄	1	6	yes	—
101	C₂×D₄×C₆₇	C₂²×C₄	1	12	yes	—
102	C₂×D₄×C₆₇	C₂×D₄	1	6	yes	—
103	C₂²×C₄×C₆₇	—	2	12	no	—
104	C₂²×C₄×C₆₇	—	2	16	no	—
105	C₂²×C₄×C₆₇	—	2	16	no	—
106	C₂²×C₄×C₆₇	—	2	6	no	—
107	C₂²×C₄×C₆₇	—	2	6	no	—
108	C₂²×C₄×C₆₇	—	2	6	no	—
109	C₂²×C₄×C₆₇	—	2	6	no	—
110	C₂²×C₄×C₆₇	C₂²⋊C₄	1	6	yes	—
111	C₂²×C₄×C₆₇	C₂²⋊C₄	1	12	yes	—
112	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
113	C₂²×C₄×C₆₇	C₂×D₄	1	12	yes	—
114	C₂²×C₄×C₆₇	C₂×D₄	1	3	yes	—
115	C₂²×C₄×C₆₇	C₂×D₄	1	3	yes	—
116	C₂²×C₄×C₆₇	C₂×D₄	1	3	yes	—
117	C₂²×C₄×C₆₇	C₂×D₄	1	3	yes	—
118	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
119	M₁₆×C₆₇	—	2	12	no	—
120	M₁₆×C₆₇	—	4	3	no	—
121	M₁₆×C₆₇	—	4	3	no	—
122	M₁₆×C₆₇	—	4	1	no	—
123	M₁₆×C₆₇	—	4	3	no	—
124	C₂×C₈×C₆₇	—	2	6	no	—
125	C₂×C₈×C₆₇	—	2	6	no	—
126	C₂×C₈×C₆₇	—	4	6	no	—
127	C₂³×C₆₇	—	2	16	no	—
128	C₂³×C₆₇	—	2	6	no	—
129	C₂³×C₆₇	—	2	6	no	—
130	C₂³×C₆₇	—	8	1	no	—
131	C₂³×C₆₇	—	8	6	no	—
132	C₂³×C₆₇	—	8	8	no	—
133	C₂³×C₆₇	C₂×C₂²⋊C₄	1	12	yes	—
134	C₂³×C₆₇	C₂×C₂²⋊C₄	1	3	yes	—
135	C₂³×C₆₇	C₂×C₂²⋊C₄	1	3	yes	—
136	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
137	Q₈×C₆₇	—	2	16	no	—
138	Q₈×C₆₇	—	2	12	no	—
139	Q₈×C₆₇	—	2	12	no	—
140	D₄×C₆₇	—	2	48	no	—
141	D₄×C₆₇	—	2	24	no	—
142	D₄×C₆₇	—	2	24	no	—
143	D₄×C₆₇	—	2	12	no	—
144	D₄×C₆₇	—	2	12	no	—
145	C₂×C₄×C₆₇	—	2	48	no	—
146	C₂×C₄×C₆₇	—	2	6	no	—
147	C₂×C₄×C₆₇	—	2	6	no	—
148	C₂×C₄×C₆₇	—	2	12	no	—
149	C₂×C₄×C₆₇	—	2	12	no	—
150	C₂×C₄×C₆₇	—	2	12	no	—
151	C₂×C₄×C₆₇	—	2	12	no	—
152	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	12	yes	—
153	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	3	yes	—
154	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	3	yes	—
155	C₂×C₄×C₆₇	#120	1	6	yes	—
156	C₂×C₄×C₆₇	#120	1	3	yes	—
157	C₂×C₄×C₆₇	#120	1	3	yes	—
158	C₂×C₄×C₆₇	#120	1	1	yes	characteristic
159	C₂×C₄×C₆₇	#120	1	3	yes	—
160	C₂×C₄×C₆₇	C₂²×D₄	1	3	yes	—
161	C₂×C₄×C₆₇	C₂²×D₄	1	3	yes	—
162	C₈×C₆₇	—	4	6	no	—
163	C₈×C₆₇	—	4	2	no	—
164	C₂²×C₆₇	—	2	12	no	—
165	C₂²×C₆₇	—	4	3	no	—
166	C₂²×C₆₇	—	4	3	no	—
167	C₂²×C₆₇	—	4	1	no	—
168	C₂²×C₆₇	—	4	12	no	—
169	C₂²×C₆₇	—	4	12	no	—
170	C₂²×C₆₇	—	8	6	no	—
171	C₂²×C₆₇	—	8	16	no	—
172	C₂²×C₆₇	#379	1	1	yes	characteristic
173	C₂²×C₆₇	#379	1	3	yes	—
174	C₂²×C₆₇	C₂²×C₂²⋊C₄	1	3	yes	—
175	C₄×C₆₇	—	2	12	no	—
176	C₄×C₆₇	#379	1	1	yes	characteristic
177	C₄×C₆₇	#379	1	3	yes	—
178	C₄×C₆₇	C₂×#120	1	3	yes	—
179	C₄×C₆₇	C₂×#120	1	1	yes	characteristic
180	#20612	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
181	C₂×C₆₇	—	2	1	no	—
182	C₂×C₆₇	—	2	3	no	—
183	C₂×C₆₇	—	2	3	no	—
184	C₂×C₆₇	—	4	12	no	—
185	C₂×C₆₇	C₂×#379	1	1	yes	characteristic
186	C₂×#585	C₂×C₆₇	1	1	yes	characteristic
187	C₂×#413	C₂×C₆₇	1	3	yes	complemented
188	#2879	C₂×C₆₇	1	3	yes	complemented
189	#1791	C₂×C₆₇	1	8	yes	complemented
190	C₆₇	#20612	1	1	yes	characteristic, direct product factor, Sylow
191	#585	—	2	6	no	—
192	#585	—	2	6	no	—
193	#585	C₄×C₆₇	1	4	yes	—
194	#585	C₂²×C₆₇	1	4	yes	—
195	C₂×2₋¹⁺⁴	—	2	3	no	—
196	C₂×H(5,𝔽₂)	—	2	3	no	—
197	C₂×H(5,𝔽₂)	C₄×C₆₇	1	4	yes	—
198	C₂²×#41	—	2	6	no	—
199	C₂²×#41	C₂²×C₆₇	1	3	yes	—
200	C₂²×M₁₆	C₂²×C₆₇	1	3	yes	complemented
201	C₂²×M₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
202	#413	—	2	6	no	—
203	#413	C₂²×C₆₇	1	12	yes	complemented
204	C₂×#101	—	2	3	no	—
205	C₂×#100	—	2	3	no	—
206	#408	—	2	6	no	—
207	#408	C₂²×C₆₇	1	12	yes	complemented
208	#407	—	2	6	no	—
209	2₋¹⁺⁴	—	2	24	no	—
210	2₋¹⁺⁴	—	2	12	no	—
211	2₋¹⁺⁴	—	2	12	no	—
212	H(5,𝔽₂)	—	2	24	no	—
213	H(5,𝔽₂)	—	2	12	no	—
214	H(5,𝔽₂)	—	2	24	no	—
215	H(5,𝔽₂)	—	2	12	no	—
216	H(5,𝔽₂)	C₂×C₄×C₆₇	1	16	yes	—
217	C₂×#41	—	2	4	no	—
218	C₂×#41	—	2	12	no	—
219	C₂×#41	—	2	24	no	—
220	C₂×#41	—	2	24	no	—
221	C₂×#41	—	2	12	no	—
222	C₂×#41	—	2	24	no	—
223	C₂×#41	—	2	6	no	—
224	C₂×#41	—	2	24	no	—
225	C₂×#41	—	2	6	no	—
226	C₂×#41	—	2	6	no	—
227	C₂×#41	—	2	6	no	—
228	C₂×#41	C₂×C₄×C₆₇	1	6	yes	—
229	C₂×#41	D₄×C₆₇	1	6	yes	—
230	C₂×#41	D₄×C₆₇	1	6	yes	—
231	C₂×#41	C₂³×C₆₇	1	6	yes	—
232	C₂²×Q₈	—	2	6	no	—
233	C₂²×Q₈	D₄×C₆₇	1	3	yes	—
234	C₂²×D₄	—	2	6	no	—
235	C₂²×D₄	—	2	12	no	—
236	C₂²×D₄	C₂×C₄×C₆₇	1	6	yes	—
237	C₂²×D₄	D₄×C₆₇	1	3	yes	—
238	C₂³×C₄	—	2	4	no	—
239	C₂³×C₄	D₄×C₆₇	1	6	yes	—
240	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
241	C₂×M₁₆	—	2	3	no	—
242	C₂×M₁₆	—	2	3	no	—
243	C₂×M₁₆	—	2	3	no	—
244	C₂×M₁₆	—	2	6	no	—
245	C₂×M₁₆	—	2	6	no	—
246	C₂×M₁₆	C₂³×C₆₇	1	6	yes	complemented
247	C₂²×C₈	—	2	3	no	—
248	C₂²×C₈	C₂³×C₆₇	1	2	yes	complemented
249	#101	—	2	12	no	—
250	#100	—	2	12	no	—
251	C₂²⋊C₈	—	2	24	no	—
252	C₂⁴	—	2	4	no	—
253	C₂⁴	C₂²⋊C₄×C₆₇	1	6	yes	—
254	C₂⁴	C₂²×C₄×C₆₇	1	1	yes	characteristic
255	#41	—	2	16	no	—
256	#41	—	2	16	no	—
257	#41	—	2	48	no	—
258	#41	—	2	48	no	—
259	#41	—	2	48	no	—
260	#41	—	2	12	no	—
261	#41	—	2	48	no	—
262	#41	—	2	12	no	—
263	#41	—	2	12	no	—
264	#41	—	2	12	no	—
265	#41	—	2	12	no	—
266	#41	—	2	12	no	—
267	#41	—	2	12	no	—
268	#41	—	2	12	no	—
269	C₂×Q₈	—	2	4	no	—
270	C₂×Q₈	—	2	24	no	—
271	C₂×Q₈	—	2	24	no	—
272	C₂×Q₈	—	2	6	no	—
273	C₂×Q₈	—	2	6	no	—
274	C₂×Q₈	C₂²⋊C₄×C₆₇	1	6	yes	—
275	C₂×Q₈	C₂×D₄×C₆₇	1	6	yes	—
276	C₂×D₄	—	2	12	no	—
277	C₂×D₄	—	2	48	no	—
278	C₂×D₄	—	2	24	no	—
279	C₂×D₄	—	2	24	no	—
280	C₂×D₄	—	2	12	no	—
281	C₂×D₄	—	2	48	no	—
282	C₂×D₄	—	2	12	no	—
283	C₂×D₄	—	2	6	no	—
284	C₂×D₄	—	2	6	no	—
285	C₂×D₄	C₂²⋊C₄×C₆₇	1	12	yes	—
286	C₂×D₄	C₂²⋊C₄×C₆₇	1	6	yes	—
287	C₂×D₄	C₂²×C₄×C₆₇	1	12	yes	—
288	C₂×D₄	C₂×D₄×C₆₇	1	6	yes	—
289	C₂²×C₄	—	2	12	no	—
290	C₂²×C₄	—	2	16	no	—
291	C₂²×C₄	—	2	16	no	—
292	C₂²×C₄	—	2	6	no	—
293	C₂²×C₄	—	2	6	no	—
294	C₂²×C₄	—	2	6	no	—
295	C₂²×C₄	—	2	6	no	—
296	C₂²×C₄	C₂²⋊C₄×C₆₇	1	6	yes	—
297	C₂²×C₄	C₂²⋊C₄×C₆₇	1	12	yes	—
298	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
299	C₂²×C₄	C₂×D₄×C₆₇	1	12	yes	—
300	C₂²×C₄	C₂×D₄×C₆₇	1	3	yes	—
301	C₂²×C₄	C₂×D₄×C₆₇	1	3	yes	—
302	C₂²×C₄	C₂×D₄×C₆₇	1	3	yes	—
303	C₂²×C₄	C₂×D₄×C₆₇	1	3	yes	—
304	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
305	M₁₆	—	2	12	no	—
306	M₁₆	—	4	1	no	—
307	M₁₆	—	4	3	no	—
308	M₁₆	—	4	3	no	—
309	M₁₆	—	4	3	no	—
310	C₂×C₈	—	2	6	no	—
311	C₂×C₈	—	2	6	no	—
312	C₂×C₈	—	4	6	no	—
313	C₂³	—	2	16	no	—
314	C₂³	—	2	6	no	—
315	C₂³	—	2	6	no	—
316	C₂³	—	8	1	no	—
317	C₂³	—	8	6	no	—
318	C₂³	—	8	8	no	—
319	C₂³	C₂×C₂²⋊C₄×C₆₇	1	12	yes	—
320	C₂³	C₂×C₂²⋊C₄×C₆₇	1	3	yes	—
321	C₂³	C₂×C₂²⋊C₄×C₆₇	1	3	yes	—
322	C₂³	C₂³×C₄×C₆₇	1	1	yes	characteristic
323	Q₈	—	2	16	no	—
324	Q₈	—	2	12	no	—
325	Q₈	—	2	12	no	—
326	D₄	—	2	48	no	—
327	D₄	—	2	24	no	—
328	D₄	—	2	24	no	—
329	D₄	—	2	12	no	—
330	D₄	—	2	12	no	—
331	C₂×C₄	—	2	48	no	—
332	C₂×C₄	—	2	6	no	—
333	C₂×C₄	—	2	6	no	—
334	C₂×C₄	—	2	12	no	—
335	C₂×C₄	—	2	12	no	—
336	C₂×C₄	—	2	12	no	—
337	C₂×C₄	—	2	12	no	—
338	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	12	yes	—
339	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	3	yes	—
340	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	3	yes	—
341	C₂×C₄	#120×C₆₇	1	6	yes	—
342	C₂×C₄	#120×C₆₇	1	1	yes	characteristic
343	C₂×C₄	#120×C₆₇	1	3	yes	—
344	C₂×C₄	#120×C₆₇	1	3	yes	—
345	C₂×C₄	#120×C₆₇	1	3	yes	—
346	C₂×C₄	C₂²×D₄×C₆₇	1	3	yes	—
347	C₂×C₄	C₂²×D₄×C₆₇	1	3	yes	—
348	C₈	—	4	2	no	—
349	C₈	—	4	6	no	—
350	C₂²	—	2	12	no	—
351	C₂²	—	4	3	no	—
352	C₂²	—	4	3	no	—
353	C₂²	—	4	1	no	—
354	C₂²	—	4	12	no	—
355	C₂²	—	4	12	no	—
356	C₂²	—	8	6	no	—
357	C₂²	—	8	16	no	—
358	C₂²	#379×C₆₇	1	1	yes	characteristic
359	C₂²	#379×C₆₇	1	3	yes	—
360	C₂²	C₂²×C₂²⋊C₄×C₆₇	1	3	yes	—
361	C₄	—	2	12	no	—
362	C₄	#379×C₆₇	1	1	yes	characteristic
363	C₄	#379×C₆₇	1	3	yes	—
364	C₄	C₂×#120×C₆₇	1	1	yes	characteristic
365	C₄	C₂×#120×C₆₇	1	3	yes	—
366	C₂	—	2	1	no	—
367	C₂	—	2	3	no	—
368	C₂	—	2	3	no	—
369	C₂	—	4	12	no	—
370	C₂	C₂×#379×C₆₇	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₆₇	C₂×#120
commutator	C₂³	C₂³×C₄×C₆₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₇
socle	C₂×C₆₇	C₂×#379
prime radical	C₂×#585×C₆₇	C₂
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₆₇ ◁ C₂³×C₄×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#413×C₆₇	C₂	semidirect
3. C₆₇×#2879	C₂	semidirect
4. C₆₇×#1791	C₂	semidirect
14. C₂²×M₁₆×C₆₇	C₂²	semidirect
15. C₂²×M₁₆×C₆₇	C₂²	semidirect
17. #413×C₆₇	C₂²	semidirect
21. #408×C₆₇	C₂²	semidirect
60. C₂×M₁₆×C₆₇	C₂³	semidirect
62. C₂²×C₈×C₆₇	C₂³	semidirect
180. #20612	C₆₇	direct (N × H)
187. C₂×#413	C₂×C₆₇	semidirect
188. #2879	C₂×C₆₇	semidirect
189. #1791	C₂×C₆₇	semidirect
190. C₆₇	#20612	direct (N × H)
200. C₂²×M₁₆	C₂²×C₆₇	semidirect
201. C₂²×M₁₆	C₂²×C₆₇	semidirect
203. #413	C₂²×C₆₇	semidirect
207. #408	C₂²×C₆₇	semidirect
246. C₂×M₁₆	C₂³×C₆₇	semidirect
248. C₂²×C₈	C₂³×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#585×C₆₇	2
C₂×#413×C₆₇	2
C₆₇×#2879	2
C₆₇×#1791	2
#20612	67

Subgroups — C67×#20612 #30699863

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#20612 #30699863