Subgroups — C₆₇×#60087 #30739338

Order 17152.

5154 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×H(5,𝔽₂)×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₂×#568×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3428	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#2897	C₂	1	16	yes	maximal, complemented
5	C₆₇×#2896	C₂	1	6	yes	maximal, complemented
6	C₂×#418×C₆₇	C₂	1	6	yes	maximal, complemented
7	C₂×H(5,𝔽₂)×C₆₇	—	2	8	no	—
8	C₂×H(5,𝔽₂)×C₆₇	—	2	4	no	—
9	C₂×H(5,𝔽₂)×C₆₇	C₄	1	16	yes	complemented
10	C₂×H(5,𝔽₂)×C₆₇	C₂²	1	8	yes	—
11	C₂²×#41×C₆₇	—	2	1	no	—
12	C₂²×#41×C₆₇	C₂²	1	3	yes	—
13	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
14	C₂³×D₄×C₆₇	—	2	3	no	—
15	C₂³×D₄×C₆₇	C₂²	1	3	yes	—
16	#568×C₆₇	—	2	8	no	—
17	C₂×#131×C₆₇	C₂²	1	8	yes	complemented
18	C₂²×M₁₆×C₆₇	C₂²	1	6	yes	complemented
19	#520×C₆₇	C₂²	1	8	yes	complemented
20	#519×C₆₇	—	2	1	no	—
21	#518×C₆₇	—	2	3	no	—
22	C₄×#41×C₆₇	—	2	4	no	—
23	C₂×#117×C₆₇	C₂²	1	6	yes	complemented
24	#419×C₆₇	C₂²	1	4	yes	complemented
25	#418×C₆₇	C₂²	1	12	yes	complemented
26	#418×C₆₇	C₂²	1	24	yes	complemented
27	#417×C₆₇	C₂²	1	24	yes	complemented
28	#416×C₆₇	C₂²	1	24	yes	complemented
29	C₂×#102×C₆₇	C₂²	1	24	yes	complemented
30	C₂⁵×C₆₇	—	2	3	no	—
31	H(5,𝔽₂)×C₆₇	—	2	64	no	—
32	H(5,𝔽₂)×C₆₇	—	2	32	no	—
33	H(5,𝔽₂)×C₆₇	C₂×C₄	1	64	yes	complemented
34	C₂×#41×C₆₇	—	2	16	no	—
35	C₂×#41×C₆₇	—	2	8	no	—
36	C₂×#41×C₆₇	—	2	12	no	—
37	C₂×#41×C₆₇	—	2	6	no	—
38	C₂×#41×C₆₇	C₂×C₄	1	8	yes	—
39	C₂×#41×C₆₇	C₂×C₄	1	24	yes	complemented
40	C₂×#41×C₆₇	D₄	1	8	yes	—
41	C₂×#41×C₆₇	D₄	1	4	yes	—
42	C₂×#41×C₆₇	C₂³	1	12	yes	—
43	C₂×#41×C₆₇	C₂³	1	4	yes	—
44	C₂²×Q₈×C₆₇	D₄	1	1	yes	characteristic
45	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
46	C₂²×D₄×C₆₇	—	2	3	no	—
47	C₂²×D₄×C₆₇	—	2	48	no	—
48	C₂²×D₄×C₆₇	—	2	24	no	—
49	C₂²×D₄×C₆₇	—	2	3	no	—
50	C₂²×D₄×C₆₇	—	2	6	no	—
51	C₂²×D₄×C₆₇	—	2	12	no	—
52	C₂²×D₄×C₆₇	C₂×C₄	1	24	yes	complemented
53	C₂²×D₄×C₆₇	D₄	1	3	yes	—
54	C₂²×D₄×C₆₇	C₂³	1	3	yes	—
55	C₂²×D₄×C₆₇	C₂³	1	12	yes	—
56	C₂³×C₄×C₆₇	—	2	3	no	—
57	C₂³×C₄×C₆₇	C₂³	1	3	yes	—
58	#131×C₆₇	—	2	32	no	—
59	C₂×M₁₆×C₆₇	—	2	24	no	—
60	C₂×M₁₆×C₆₇	C₂³	1	4	yes	—
61	C₂×M₁₆×C₆₇	C₂³	1	12	yes	complemented
62	C₂²×C₈×C₆₇	C₂³	1	12	yes	complemented
63	C₄×Q₈×C₆₇	—	2	8	no	—
64	C₄×D₄×C₆₇	—	2	24	no	—
65	#117×C₆₇	—	2	6	no	—
66	#117×C₆₇	—	2	6	no	—
67	#117×C₆₇	C₂³	1	4	yes	—
68	#117×C₆₇	C₂³	1	12	yes	complemented
69	C₂×C₄⋊C₄×C₆₇	C₂³	1	12	yes	complemented
70	C₂×C₂²⋊C₄×C₆₇	—	2	6	no	—
71	C₂×C₄²×C₆₇	—	2	6	no	—
72	#103×C₆₇	C₂³	1	16	yes	complemented
73	#102×C₆₇	C₂³	1	48	yes	complemented
74	C₂⁴×C₆₇	—	2	3	no	—
75	C₂⁴×C₆₇	—	2	24	no	—
76	C₂⁴×C₆₇	—	2	12	no	—
77	C₂⁴×C₆₇	—	8	12	no	—
78	C₂⁴×C₆₇	C₂×D₄	1	3	yes	—
79	#41×C₆₇	—	2	64	no	—
80	#41×C₆₇	—	2	48	no	—
81	#41×C₆₇	—	2	24	no	—
82	#41×C₆₇	C₂²⋊C₄	1	32	yes	—
83	#41×C₆₇	C₂²×C₄	1	48	yes	—
84	#41×C₆₇	C₂²×C₄	1	16	yes	—
85	#41×C₆₇	C₂×D₄	1	16	yes	—
86	C₂×Q₈×C₆₇	—	2	2	no	—
87	C₂×Q₈×C₆₇	—	2	1	no	—
88	C₂×Q₈×C₆₇	C₂²⋊C₄	1	8	yes	—
89	C₂×Q₈×C₆₇	C₂²×C₄	1	4	yes	—
90	C₂×Q₈×C₆₇	C₂×D₄	1	4	yes	—
91	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
92	C₂×D₄×C₆₇	—	2	24	no	—
93	C₂×D₄×C₆₇	—	2	12	no	—
94	C₂×D₄×C₆₇	—	2	192	no	—
95	C₂×D₄×C₆₇	—	2	24	no	—
96	C₂×D₄×C₆₇	—	2	48	no	—
97	C₂×D₄×C₆₇	—	2	3	no	—
98	C₂×D₄×C₆₇	—	2	12	no	—
99	C₂×D₄×C₆₇	—	2	6	no	—
100	C₂×D₄×C₆₇	—	2	24	no	—
101	C₂×D₄×C₆₇	C₂²⋊C₄	1	24	yes	—
102	C₂×D₄×C₆₇	C₂²×C₄	1	12	yes	—
103	C₂×D₄×C₆₇	C₂²×C₄	1	48	yes	—
104	C₂×D₄×C₆₇	C₂×D₄	1	12	yes	—
105	C₂×D₄×C₆₇	C₂⁴	1	6	yes	—
106	C₂²×C₄×C₆₇	—	2	1	no	—
107	C₂²×C₄×C₆₇	—	2	24	no	—
108	C₂²×C₄×C₆₇	—	2	12	no	—
109	C₂²×C₄×C₆₇	—	2	12	no	—
110	C₂²×C₄×C₆₇	C₂²×C₄	1	12	yes	—
111	C₂²×C₄×C₆₇	C₂×D₄	1	6	yes	—
112	C₂²×C₄×C₆₇	C₂×D₄	1	3	yes	—
113	C₂²×C₄×C₆₇	C₂×D₄	1	12	yes	—
114	C₂²×C₄×C₆₇	C₂⁴	1	6	yes	—
115	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
116	M₁₆×C₆₇	—	2	8	no	—
117	M₁₆×C₆₇	—	2	24	no	—
118	C₂×C₈×C₆₇	—	2	24	no	—
119	C₂×C₈×C₆₇	C₂⁴	1	8	yes	—
120	C₄⋊C₄×C₆₇	—	2	12	no	—
121	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
122	C₂²⋊C₄×C₆₇	—	2	4	no	—
123	C₂²⋊C₄×C₆₇	—	2	12	no	—
124	C₄²×C₆₇	—	2	4	no	—
125	C₄²×C₆₇	—	2	12	no	—
126	C₂³×C₆₇	—	2	12	no	—
127	C₂³×C₆₇	—	2	6	no	—
128	C₂³×C₆₇	—	2	48	no	—
129	C₂³×C₆₇	—	4	6	no	—
130	C₂³×C₆₇	—	4	12	no	—
131	C₂³×C₆₇	—	8	24	no	—
132	C₂³×C₆₇	—	8	48	no	—
133	C₂³×C₆₇	C₂×C₂²⋊C₄	1	12	yes	—
134	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
135	C₂³×C₆₇	C₂²×D₄	1	6	yes	—
136	Q₈×C₆₇	—	2	4	no	—
137	Q₈×C₆₇	—	2	2	no	—
138	Q₈×C₆₇	C₂×C₂²⋊C₄	1	16	yes	—
139	Q₈×C₆₇	C₂³×C₄	1	4	yes	—
140	D₄×C₆₇	—	2	48	no	—
141	D₄×C₆₇	—	2	48	no	—
142	D₄×C₆₇	—	2	12	no	—
143	D₄×C₆₇	—	2	6	no	—
144	D₄×C₆₇	C₂×C₂²⋊C₄	1	48	yes	—
145	D₄×C₆₇	C₂³×C₄	1	12	yes	—
146	C₂×C₄×C₆₇	—	2	4	no	—
147	C₂×C₄×C₆₇	—	2	2	no	—
148	C₂×C₄×C₆₇	—	2	48	no	—
149	C₂×C₄×C₆₇	—	2	8	no	—
150	C₂×C₄×C₆₇	—	8	12	no	—
151	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	12	yes	—
152	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	24	yes	—
153	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
154	C₂×C₄×C₆₇	C₂³×C₄	1	12	yes	—
155	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
156	C₂×C₄×C₆₇	C₂²×D₄	1	6	yes	—
157	C₂×C₄×C₆₇	C₂²×D₄	1	12	yes	—
158	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
159	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
160	C₈×C₆₇	—	2	8	no	—
161	C₂²×C₆₇	—	2	12	no	—
162	C₂²×C₆₇	—	2	2	no	—
163	C₂²×C₆₇	—	2	12	no	—
164	C₂²×C₆₇	—	4	12	no	—
165	C₂²×C₆₇	—	4	24	no	—
166	C₂²×C₆₇	—	4	12	no	—
167	C₂²×C₆₇	—	8	48	no	—
168	C₂²×C₆₇	C₂²×C₂²⋊C₄	1	2	yes	—
169	C₂²×C₆₇	C₂²×C₂²⋊C₄	1	12	yes	—
170	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
171	C₄×C₆₇	—	2	4	no	—
172	C₄×C₆₇	—	4	8	no	—
173	C₄×C₆₇	C₂²×C₂²⋊C₄	1	12	yes	—
174	C₄×C₆₇	C₂²×C₂²⋊C₄	1	2	yes	—
175	C₄×C₆₇	C₂⁴×C₄	1	1	yes	characteristic
176	C₄×C₆₇	C₂³×D₄	1	1	yes	characteristic
177	#60087	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
178	C₂×C₆₇	—	2	2	no	—
179	C₂×C₆₇	—	2	12	no	—
180	C₂×C₆₇	—	4	12	no	—
181	C₂×C₆₇	C₂³×C₂²⋊C₄	1	1	yes	characteristic
182	C₂×C₆₇	#3585	1	2	yes	—
183	C₂²×H(5,𝔽₂)	C₂×C₆₇	1	1	yes	characteristic
184	C₂×#568	C₂×C₆₇	1	1	yes	characteristic, complemented
185	#3428	C₂×C₆₇	1	1	yes	characteristic, complemented
186	#2897	C₂×C₆₇	1	16	yes	complemented
187	#2896	C₂×C₆₇	1	6	yes	complemented
188	C₂×#418	C₂×C₆₇	1	6	yes	complemented
189	C₆₇	#60087	1	1	yes	characteristic, direct product factor, Sylow
190	C₂×H(5,𝔽₂)	—	2	8	no	—
191	C₂×H(5,𝔽₂)	—	2	4	no	—
192	C₂×H(5,𝔽₂)	C₄×C₆₇	1	16	yes	complemented
193	C₂×H(5,𝔽₂)	C₂²×C₆₇	1	8	yes	—
194	C₂²×#41	—	2	1	no	—
195	C₂²×#41	C₂²×C₆₇	1	3	yes	—
196	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
197	C₂³×D₄	—	2	3	no	—
198	C₂³×D₄	C₂²×C₆₇	1	3	yes	—
199	#568	—	2	8	no	—
200	C₂×#131	C₂²×C₆₇	1	8	yes	complemented
201	C₂²×M₁₆	C₂²×C₆₇	1	6	yes	complemented
202	#520	C₂²×C₆₇	1	8	yes	complemented
203	#519	—	2	1	no	—
204	#518	—	2	3	no	—
205	C₄×#41	—	2	4	no	—
206	C₂×#117	C₂²×C₆₇	1	6	yes	complemented
207	#419	C₂²×C₆₇	1	4	yes	complemented
208	#418	C₂²×C₆₇	1	12	yes	complemented
209	#418	C₂²×C₆₇	1	24	yes	complemented
210	#417	C₂²×C₆₇	1	24	yes	complemented
211	#416	C₂²×C₆₇	1	24	yes	complemented
212	C₂×#102	C₂²×C₆₇	1	24	yes	complemented
213	C₂⁵	—	2	3	no	—
214	H(5,𝔽₂)	—	2	64	no	—
215	H(5,𝔽₂)	—	2	32	no	—
216	H(5,𝔽₂)	C₂×C₄×C₆₇	1	64	yes	complemented
217	C₂×#41	—	2	16	no	—
218	C₂×#41	—	2	8	no	—
219	C₂×#41	—	2	12	no	—
220	C₂×#41	—	2	6	no	—
221	C₂×#41	C₂×C₄×C₆₇	1	8	yes	—
222	C₂×#41	C₂×C₄×C₆₇	1	24	yes	complemented
223	C₂×#41	D₄×C₆₇	1	8	yes	—
224	C₂×#41	D₄×C₆₇	1	4	yes	—
225	C₂×#41	C₂³×C₆₇	1	12	yes	—
226	C₂×#41	C₂³×C₆₇	1	4	yes	—
227	C₂²×Q₈	D₄×C₆₇	1	1	yes	characteristic
228	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
229	C₂²×D₄	—	2	3	no	—
230	C₂²×D₄	—	2	48	no	—
231	C₂²×D₄	—	2	24	no	—
232	C₂²×D₄	—	2	3	no	—
233	C₂²×D₄	—	2	6	no	—
234	C₂²×D₄	—	2	12	no	—
235	C₂²×D₄	C₂×C₄×C₆₇	1	24	yes	complemented
236	C₂²×D₄	D₄×C₆₇	1	3	yes	—
237	C₂²×D₄	C₂³×C₆₇	1	3	yes	—
238	C₂²×D₄	C₂³×C₆₇	1	12	yes	—
239	C₂³×C₄	—	2	3	no	—
240	C₂³×C₄	C₂³×C₆₇	1	3	yes	—
241	#131	—	2	32	no	—
242	C₂×M₁₆	—	2	24	no	—
243	C₂×M₁₆	C₂³×C₆₇	1	4	yes	—
244	C₂×M₁₆	C₂³×C₆₇	1	12	yes	complemented
245	C₂²×C₈	C₂³×C₆₇	1	12	yes	complemented
246	C₄×Q₈	—	2	8	no	—
247	C₄×D₄	—	2	24	no	—
248	#117	—	2	6	no	—
249	#117	—	2	6	no	—
250	#117	C₂³×C₆₇	1	4	yes	—
251	#117	C₂³×C₆₇	1	12	yes	complemented
252	C₂×C₄⋊C₄	C₂³×C₆₇	1	12	yes	complemented
253	C₂×C₂²⋊C₄	—	2	6	no	—
254	C₂×C₄²	—	2	6	no	—
255	#103	C₂³×C₆₇	1	16	yes	complemented
256	#102	C₂³×C₆₇	1	48	yes	complemented
257	C₂⁴	—	2	3	no	—
258	C₂⁴	—	2	24	no	—
259	C₂⁴	—	2	12	no	—
260	C₂⁴	—	8	12	no	—
261	C₂⁴	C₂×D₄×C₆₇	1	3	yes	—
262	#41	—	2	64	no	—
263	#41	—	2	48	no	—
264	#41	—	2	24	no	—
265	#41	C₂²⋊C₄×C₆₇	1	32	yes	—
266	#41	C₂²×C₄×C₆₇	1	48	yes	—
267	#41	C₂²×C₄×C₆₇	1	16	yes	—
268	#41	C₂×D₄×C₆₇	1	16	yes	—
269	C₂×Q₈	—	2	2	no	—
270	C₂×Q₈	—	2	1	no	—
271	C₂×Q₈	C₂²⋊C₄×C₆₇	1	8	yes	—
272	C₂×Q₈	C₂²×C₄×C₆₇	1	4	yes	—
273	C₂×Q₈	C₂×D₄×C₆₇	1	4	yes	—
274	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
275	C₂×D₄	—	2	24	no	—
276	C₂×D₄	—	2	12	no	—
277	C₂×D₄	—	2	192	no	—
278	C₂×D₄	—	2	24	no	—
279	C₂×D₄	—	2	48	no	—
280	C₂×D₄	—	2	3	no	—
281	C₂×D₄	—	2	12	no	—
282	C₂×D₄	—	2	6	no	—
283	C₂×D₄	—	2	24	no	—
284	C₂×D₄	C₂²⋊C₄×C₆₇	1	24	yes	—
285	C₂×D₄	C₂²×C₄×C₆₇	1	12	yes	—
286	C₂×D₄	C₂²×C₄×C₆₇	1	48	yes	—
287	C₂×D₄	C₂×D₄×C₆₇	1	12	yes	—
288	C₂×D₄	C₂⁴×C₆₇	1	6	yes	—
289	C₂²×C₄	—	2	1	no	—
290	C₂²×C₄	—	2	24	no	—
291	C₂²×C₄	—	2	12	no	—
292	C₂²×C₄	—	2	12	no	—
293	C₂²×C₄	C₂²×C₄×C₆₇	1	12	yes	—
294	C₂²×C₄	C₂×D₄×C₆₇	1	6	yes	—
295	C₂²×C₄	C₂×D₄×C₆₇	1	3	yes	—
296	C₂²×C₄	C₂×D₄×C₆₇	1	12	yes	—
297	C₂²×C₄	C₂⁴×C₆₇	1	6	yes	—
298	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
299	M₁₆	—	2	8	no	—
300	M₁₆	—	2	24	no	—
301	C₂×C₈	—	2	24	no	—
302	C₂×C₈	C₂⁴×C₆₇	1	8	yes	—
303	C₄⋊C₄	—	2	12	no	—
304	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
305	C₂²⋊C₄	—	2	4	no	—
306	C₂²⋊C₄	—	2	12	no	—
307	C₄²	—	2	4	no	—
308	C₄²	—	2	12	no	—
309	C₂³	—	2	12	no	—
310	C₂³	—	2	6	no	—
311	C₂³	—	2	48	no	—
312	C₂³	—	4	6	no	—
313	C₂³	—	4	12	no	—
314	C₂³	—	8	24	no	—
315	C₂³	—	8	48	no	—
316	C₂³	C₂×C₂²⋊C₄×C₆₇	1	12	yes	—
317	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
318	C₂³	C₂²×D₄×C₆₇	1	6	yes	—
319	Q₈	—	2	4	no	—
320	Q₈	—	2	2	no	—
321	Q₈	C₂×C₂²⋊C₄×C₆₇	1	16	yes	—
322	Q₈	C₂³×C₄×C₆₇	1	4	yes	—
323	D₄	—	2	48	no	—
324	D₄	—	2	48	no	—
325	D₄	—	2	12	no	—
326	D₄	—	2	6	no	—
327	D₄	C₂×C₂²⋊C₄×C₆₇	1	48	yes	—
328	D₄	C₂³×C₄×C₆₇	1	12	yes	—
329	C₂×C₄	—	2	4	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	48	no	—
332	C₂×C₄	—	2	8	no	—
333	C₂×C₄	—	8	12	no	—
334	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	12	yes	—
335	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	24	yes	—
336	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
337	C₂×C₄	C₂³×C₄×C₆₇	1	12	yes	—
338	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
339	C₂×C₄	C₂²×D₄×C₆₇	1	6	yes	—
340	C₂×C₄	C₂²×D₄×C₆₇	1	12	yes	—
341	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
342	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
343	C₈	—	2	8	no	—
344	C₂²	—	2	12	no	—
345	C₂²	—	2	2	no	—
346	C₂²	—	2	12	no	—
347	C₂²	—	4	12	no	—
348	C₂²	—	4	24	no	—
349	C₂²	—	4	12	no	—
350	C₂²	—	8	48	no	—
351	C₂²	C₂²×C₂²⋊C₄×C₆₇	1	2	yes	—
352	C₂²	C₂²×C₂²⋊C₄×C₆₇	1	12	yes	—
353	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
354	C₄	—	2	4	no	—
355	C₄	—	4	8	no	—
356	C₄	C₂²×C₂²⋊C₄×C₆₇	1	12	yes	—
357	C₄	C₂²×C₂²⋊C₄×C₆₇	1	2	yes	—
358	C₄	C₂⁴×C₄×C₆₇	1	1	yes	characteristic
359	C₄	C₂³×D₄×C₆₇	1	1	yes	characteristic
360	C₂	—	2	2	no	—
361	C₂	—	2	12	no	—
362	C₂	—	4	12	no	—
363	C₂	C₂³×C₂²⋊C₄×C₆₇	1	1	yes	characteristic
364	C₂	C₆₇×#3585	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂³×D₄
commutator	C₄	C₂⁴×C₄×C₆₇
Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
prime radical	C₂²×H(5,𝔽₂)×C₆₇	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ C₂²×#41×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#568×C₆₇	C₂	semidirect
3. C₆₇×#3428	C₂	semidirect
4. C₆₇×#2897	C₂	semidirect
5. C₆₇×#2896	C₂	semidirect
6. C₂×#418×C₆₇	C₂	semidirect
9. C₂×H(5,𝔽₂)×C₆₇	C₄	semidirect
17. C₂×#131×C₆₇	C₂²	semidirect
18. C₂²×M₁₆×C₆₇	C₂²	semidirect
19. #520×C₆₇	C₂²	semidirect
23. C₂×#117×C₆₇	C₂²	semidirect
24. #419×C₆₇	C₂²	semidirect
25. #418×C₆₇	C₂²	semidirect
26. #418×C₆₇	C₂²	semidirect
27. #417×C₆₇	C₂²	semidirect
28. #416×C₆₇	C₂²	semidirect
29. C₂×#102×C₆₇	C₂²	semidirect
33. H(5,𝔽₂)×C₆₇	C₂×C₄	semidirect
39. C₂×#41×C₆₇	C₂×C₄	semidirect
52. C₂²×D₄×C₆₇	C₂×C₄	semidirect
61. C₂×M₁₆×C₆₇	C₂³	semidirect
62. C₂²×C₈×C₆₇	C₂³	semidirect
68. #117×C₆₇	C₂³	semidirect
69. C₂×C₄⋊C₄×C₆₇	C₂³	semidirect
72. #103×C₆₇	C₂³	semidirect
73. #102×C₆₇	C₂³	semidirect
177. #60087	C₆₇	direct (N × H)
184. C₂×#568	C₂×C₆₇	semidirect
185. #3428	C₂×C₆₇	semidirect
186. #2897	C₂×C₆₇	semidirect
187. #2896	C₂×C₆₇	semidirect
188. C₂×#418	C₂×C₆₇	semidirect
189. C₆₇	#60087	direct (N × H)
192. C₂×H(5,𝔽₂)	C₄×C₆₇	semidirect
200. C₂×#131	C₂²×C₆₇	semidirect
201. C₂²×M₁₆	C₂²×C₆₇	semidirect
202. #520	C₂²×C₆₇	semidirect
206. C₂×#117	C₂²×C₆₇	semidirect
207. #419	C₂²×C₆₇	semidirect
208. #418	C₂²×C₆₇	semidirect
209. #418	C₂²×C₆₇	semidirect
210. #417	C₂²×C₆₇	semidirect
211. #416	C₂²×C₆₇	semidirect
212. C₂×#102	C₂²×C₆₇	semidirect
216. H(5,𝔽₂)	C₂×C₄×C₆₇	semidirect
222. C₂×#41	C₂×C₄×C₆₇	semidirect
235. C₂²×D₄	C₂×C₄×C₆₇	semidirect
244. C₂×M₁₆	C₂³×C₆₇	semidirect
245. C₂²×C₈	C₂³×C₆₇	semidirect
251. #117	C₂³×C₆₇	semidirect
252. C₂×C₄⋊C₄	C₂³×C₆₇	semidirect
255. #103	C₂³×C₆₇	semidirect
256. #102	C₂³×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂²×H(5,𝔽₂)×C₆₇	2
C₂×#568×C₆₇	2
C₆₇×#3428	2
C₆₇×#2897	2
C₆₇×#2896	2
C₂×#418×C₆₇	2
#60087	67

Subgroups — C67×#60087 #30739338

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#60087 #30739338