Subgroups — C₂×#585×D₆₇ #31769722

Order 17152.

60366 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16864233	C₂	1	6	yes	maximal, complemented
2	C₂×#16864232	C₂	1	15	yes	maximal, complemented
3	C₂×#16864231	C₂	1	10	yes	maximal, complemented
4	#585×D₆₇	C₂	1	64	yes	maximal, direct product factor
5	C₂×2₋¹⁺⁴×D₆₇	C₂	1	6	yes	maximal, complemented
6	C₂×H(5,𝔽₂)×D₆₇	C₂	1	10	yes	maximal, complemented
7	C₂²×#41×D₆₇	C₂	1	15	yes	maximal, complemented
8	C₂×#585×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
9	#16864233	C₂²	1	192	yes	complemented
10	#16864232	C₂²	1	480	yes	complemented
11	#16864231	C₂²	1	320	yes	complemented
12	C₂×#14524091	C₂²	1	30	yes	complemented
13	C₂×#14524090	C₂²	1	60	yes	complemented
14	2₋¹⁺⁴×D₆₇	C₂²	1	192	yes	complemented
15	C₂×#14524089	C₂²	1	60	yes	complemented
16	C₂×#14524088	C₂²	1	90	yes	complemented
17	H(5,𝔽₂)×D₆₇	C₂²	1	320	yes	complemented
18	C₂²×#11761629	C₂²	1	15	yes	complemented
19	C₂²×#11761628	C₂²	1	45	yes	complemented
20	C₂²×#11761627	C₂²	1	45	yes	complemented
21	C₂×#41×D₆₇	C₂²	1	20	yes	complemented
22	C₂×#41×D₆₇	C₂²	1	60	yes	complemented
23	C₂×#41×D₆₇	C₂²	1	480	yes	complemented
24	C₂×#41×D₆₇	C₂²	1	60	yes	complemented
25	C₂×#41×D₆₇	C₂²	1	60	yes	complemented
26	C₂²×Q₈×D₆₇	C₂²	1	15	yes	complemented
27	C₂²×D₄×D₆₇	C₂²	1	45	yes	complemented
28	C₂³×C₄×D₆₇	C₂²	1	15	yes	complemented
29	#585×C₆₇	C₂²	1	32	yes	complemented
30	C₂×2₋¹⁺⁴×C₆₇	C₂²	1	6	yes	complemented
31	C₂×H(5,𝔽₂)×C₆₇	C₂²	1	10	yes	complemented
32	C₂²×#41×C₆₇	C₂²	1	15	yes	complemented
33	C₂⁴×D₆₇	C₂³	1	15	yes	—
34	#14524091	C₂³	1	480	yes	complemented
35	#14524090	C₂³	1	960	yes	complemented
36	#14524089	C₂³	1	960	yes	complemented
37	#14524088	C₂³	1	1440	yes	complemented
38	C₂×#11761629	C₂³	1	20	yes	complemented
39	C₂×#11761629	C₂³	1	60	yes	complemented
40	C₂×#11761629	C₂³	1	240	yes	complemented
41	C₂×#11761628	C₂³	1	60	yes	complemented
42	C₂×#11761628	C₂³	1	180	yes	complemented
43	C₂×#11761628	C₂³	1	720	yes	complemented
44	C₂×#11761627	C₂³	1	60	yes	complemented
45	C₂×#11761627	C₂³	1	180	yes	complemented
46	C₂×#11761627	C₂³	1	720	yes	complemented
47	#41×D₆₇	C₂³	1	320	yes	complemented
48	#41×D₆₇	C₂³	1	960	yes	complemented
49	#41×D₆₇	C₂³	1	960	yes	complemented
50	#41×D₆₇	C₂³	1	960	yes	complemented
51	C₂²×Dic₁₃₄	C₂³	1	45	yes	complemented
52	C₂×Q₈×D₆₇	C₂³	1	20	yes	—
53	C₂×Q₈×D₆₇	C₂³	1	60	yes	complemented
54	C₂×Q₈×D₆₇	C₂³	1	240	yes	complemented
55	C₂²×D₂₆₈	C₂³	1	45	yes	complemented
56	C₂²×C₂²⋊D₆₇	C₂³	1	90	yes	complemented
57	C₂×D₄×D₆₇	C₂³	1	60	yes	—
58	C₂×D₄×D₆₇	C₂³	1	180	yes	complemented
59	C₂×D₄×D₆₇	C₂³	1	720	yes	complemented
60	C₂³×Dic₆₇	C₂³	1	15	yes	complemented
61	C₂²×C₄×D₆₇	C₂³	1	15	yes	—
62	C₂²×C₄×D₆₇	C₂³	1	45	yes	—
63	C₂²×C₄×D₆₇	C₂³	1	45	yes	complemented
64	C₂²×C₄×D₆₇	C₂³	1	45	yes	complemented
65	C₂²×C₄×D₆₇	C₂³	1	240	yes	complemented
66	2₋¹⁺⁴×C₆₇	C₂³	1	96	yes	complemented
67	H(5,𝔽₂)×C₆₇	C₂³	1	160	yes	complemented
68	C₂×#41×C₆₇	C₂³	1	20	yes	complemented
69	C₂×#41×C₆₇	C₂³	1	60	yes	complemented
70	C₂×#41×C₆₇	C₂³	1	240	yes	complemented
71	C₂²×Q₈×C₆₇	C₂³	1	15	yes	complemented
72	C₂²×D₄×C₆₇	C₂³	1	45	yes	complemented
73	C₂³×C₄×C₆₇	C₂³	1	15	yes	complemented
74	C₂³×D₆₇	—	4	60	no	—
75	C₂³×D₆₇	C₂⁴	1	15	yes	—
76	C₂³×D₆₇	C₂⁴	1	120	yes	—
77	C₂³×D₆₇	C₂⁴	1	45	yes	—
78	#11761629	C₂⁴	1	160	yes	complemented
79	#11761629	C₂⁴	1	480	yes	complemented
80	#11761628	C₂⁴	1	480	yes	complemented
81	#11761628	C₂⁴	1	1440	yes	complemented
82	#11761627	C₂⁴	1	480	yes	complemented
83	#11761627	C₂⁴	1	1440	yes	complemented
84	C₂×Dic₁₃₄	C₂⁴	1	60	yes	—
85	C₂×Dic₁₃₄	C₂⁴	1	360	yes	complemented
86	Q₈×D₆₇	C₂⁴	1	160	yes	—
87	Q₈×D₆₇	C₂⁴	1	480	yes	complemented
88	C₂×D₂₆₈	C₂⁴	1	60	yes	—
89	C₂×D₂₆₈	C₂⁴	1	360	yes	complemented
90	C₂×C₂²⋊D₆₇	C₂⁴	1	120	yes	—
91	C₂×C₂²⋊D₆₇	C₂⁴	1	720	yes	complemented
92	D₄×D₆₇	C₂⁴	1	480	yes	—
93	D₄×D₆₇	C₂⁴	1	1440	yes	complemented
94	C₂²×Dic₆₇	C₂⁴	1	15	yes	—
95	C₂²×Dic₆₇	C₂⁴	1	45	yes	—
96	C₂²×Dic₆₇	C₂⁴	1	120	yes	complemented
97	C₂×C₄×D₆₇	C₂⁴	1	1	yes	characteristic
98	C₂×C₄×D₆₇	C₂⁴	1	15	yes	—
99	C₂×C₄×D₆₇	C₂⁴	1	120	yes	—
100	C₂×C₄×D₆₇	C₂⁴	1	15	yes	—
101	C₂×C₄×D₆₇	C₂⁴	1	15	yes	—
102	C₂×C₄×D₆₇	C₂⁴	1	360	yes	—
103	C₂×C₄×D₆₇	C₂⁴	1	90	yes	—
104	C₂×C₄×D₆₇	C₂⁴	1	360	yes	complemented
105	C₂×C₄×D₆₇	C₂⁴	1	360	yes	complemented
106	C₂⁴×C₆₇	C₂⁴	1	15	yes	—
107	#41×C₆₇	C₂⁴	1	160	yes	complemented
108	#41×C₆₇	C₂⁴	1	480	yes	complemented
109	C₂×Q₈×C₆₇	C₂⁴	1	20	yes	—
110	C₂×Q₈×C₆₇	C₂⁴	1	120	yes	complemented
111	C₂×D₄×C₆₇	C₂⁴	1	60	yes	—
112	C₂×D₄×C₆₇	C₂⁴	1	360	yes	complemented
113	C₂²×C₄×C₆₇	C₂⁴	1	15	yes	—
114	C₂²×C₄×C₆₇	C₂⁴	1	45	yes	—
115	C₂²×C₄×C₆₇	C₂⁴	1	120	yes	complemented
116	C₂³×C₆₇	—	4	30	no	—
117	C₂³×C₆₇	C₂⁵	1	15	yes	—
118	C₂³×C₆₇	C₂⁵	1	60	yes	—
119	C₂²×D₆₇	—	2	60	no	—
120	C₂²×D₆₇	—	4	240	no	—
121	C₂²×D₆₇	—	4	90	no	—
122	C₂²×D₆₇	C₂⁵	1	60	yes	—
123	C₂²×D₆₇	C₂⁵	1	15	yes	—
124	C₂²×D₆₇	C₂⁵	1	180	yes	—
125	C₂²×D₆₇	C₂⁵	1	1	yes	characteristic
126	Q₈×C₆₇	C₂⁵	1	80	yes	—
127	D₄×C₆₇	C₂⁵	1	240	yes	—
128	C₂×C₄×C₆₇	C₂⁵	1	15	yes	—
129	C₂×C₄×C₆₇	C₂⁵	1	60	yes	—
130	C₂×C₄×C₆₇	C₂⁵	1	180	yes	—
131	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
132	C₂²⋊D₆₇	C₂⁵	1	480	yes	—
133	C₂×Dic₆₇	C₂⁵	1	1	yes	characteristic
134	C₂×Dic₆₇	C₂⁵	1	15	yes	—
135	C₂×Dic₆₇	C₂⁵	1	60	yes	—
136	C₂×Dic₆₇	C₂⁵	1	180	yes	—
137	D₂₆₈	C₂⁵	1	240	yes	—
138	C₄×D₆₇	C₂⁵	1	4	yes	—
139	C₄×D₆₇	C₂⁵	1	60	yes	—
140	C₄×D₆₇	C₂⁵	1	60	yes	—
141	C₄×D₆₇	C₂⁵	1	60	yes	—
142	C₄×D₆₇	C₂⁵	1	360	yes	—
143	Dic₁₃₄	C₂⁵	1	240	yes	—
144	C₂²×C₆₇	—	2	30	no	—
145	C₂²×C₆₇	—	4	60	no	—
146	C₂²×C₆₇	C₂⁶	1	30	yes	—
147	C₂²×C₆₇	C₂⁶	1	1	yes	characteristic
148	C₂×D₆₇	—	2	30	no	—
149	C₂×D₆₇	—	2	120	no	—
150	C₂×D₆₇	—	4	180	no	—
151	C₂×D₆₇	#585	1	4	yes	direct product factor
152	C₂×D₆₇	C₂⁶	1	30	yes	—
153	C₂×D₆₇	C₂⁶	1	2	yes	—
154	C₄×C₆₇	C₂⁶	1	30	yes	—
155	C₄×C₆₇	C₂⁶	1	2	yes	—
156	Dic₆₇	C₂⁶	1	30	yes	—
157	Dic₆₇	C₂⁶	1	2	yes	—
158	C₂²×#585	—	67	1	no	maximal, Sylow
159	C₂×C₆₇	—	2	30	no	—
160	C₂×C₆₇	C₂×#585	1	2	yes	complemented
161	C₂×C₆₇	C₂⁷	1	1	yes	characteristic
162	D₆₇	—	2	30	no	—
163	D₆₇	C₂×#585	1	4	yes	direct product factor
164	C₂×#585	—	67	64	no	—
165	C₂×#585	—	67	6	no	—
166	C₂×#585	—	67	10	no	—
167	C₂×#585	—	67	15	no	—
168	C₂×#585	D₆₇	1	1	yes	characteristic, direct product factor
169	C₂²×2₋¹⁺⁴	—	67	6	no	—
170	C₂²×H(5,𝔽₂)	—	67	10	no	—
171	C₂³×#41	—	67	15	no	—
172	C₆₇	C₂²×#585	1	1	yes	characteristic, complemented, Sylow
173	#585	—	67	192	no	—
174	#585	—	67	320	no	—
175	#585	—	67	480	no	—
176	#585	C₂×D₆₇	1	32	yes	direct product factor
177	C₂×2₋¹⁺⁴	—	67	192	no	—
178	C₂×2₋¹⁺⁴	—	67	60	no	—
179	C₂×2₋¹⁺⁴	—	67	30	no	—
180	C₂×2₋¹⁺⁴	C₂×D₆₇	1	6	yes	complemented
181	C₂×H(5,𝔽₂)	—	67	320	no	—
182	C₂×H(5,𝔽₂)	—	67	60	no	—
183	C₂×H(5,𝔽₂)	—	67	90	no	—
184	C₂×H(5,𝔽₂)	C₂×D₆₇	1	10	yes	complemented
185	C₂²×#41	—	67	20	no	—
186	C₂²×#41	—	67	60	no	—
187	C₂²×#41	—	67	60	no	—
188	C₂²×#41	—	67	60	no	—
189	C₂²×#41	—	67	480	no	—
190	C₂²×#41	—	67	15	no	—
191	C₂²×#41	—	67	45	no	—
192	C₂²×#41	—	67	45	no	—
193	C₂²×#41	C₂×D₆₇	1	15	yes	complemented
194	C₂³×Q₈	—	67	15	no	—
195	C₂³×D₄	—	67	45	no	—
196	C₂⁴×C₄	—	67	15	no	—
197	C₂⁵	—	67	15	no	—
198	2₋¹⁺⁴	—	67	960	no	—
199	2₋¹⁺⁴	—	67	480	no	—
200	2₋¹⁺⁴	C₂²×D₆₇	1	96	yes	complemented
201	H(5,𝔽₂)	—	67	960	no	—
202	H(5,𝔽₂)	—	67	1440	no	—
203	H(5,𝔽₂)	C₂²×D₆₇	1	160	yes	complemented
204	C₂×#41	—	67	320	no	—
205	C₂×#41	—	67	960	no	—
206	C₂×#41	—	67	960	no	—
207	C₂×#41	—	67	960	no	—
208	C₂×#41	—	67	20	no	—
209	C₂×#41	—	67	60	no	—
210	C₂×#41	—	67	240	no	—
211	C₂×#41	—	67	60	no	—
212	C₂×#41	—	67	180	no	—
213	C₂×#41	—	67	720	no	—
214	C₂×#41	—	67	60	no	—
215	C₂×#41	—	67	180	no	—
216	C₂×#41	—	67	720	no	—
217	C₂×#41	C₂²×D₆₇	1	20	yes	complemented
218	C₂×#41	C₂²×D₆₇	1	60	yes	complemented
219	C₂×#41	C₂²×D₆₇	1	240	yes	complemented
220	C₂²×Q₈	—	67	20	no	—
221	C₂²×Q₈	—	67	60	no	—
222	C₂²×Q₈	—	67	240	no	—
223	C₂²×Q₈	—	67	45	no	—
224	C₂²×Q₈	C₂²×D₆₇	1	15	yes	complemented
225	C₂²×D₄	—	67	90	no	—
226	C₂²×D₄	—	67	60	no	—
227	C₂²×D₄	—	67	180	no	—
228	C₂²×D₄	—	67	720	no	—
229	C₂²×D₄	—	67	45	no	—
230	C₂²×D₄	C₂²×D₆₇	1	45	yes	complemented
231	C₂³×C₄	—	67	15	no	—
232	C₂³×C₄	—	67	15	no	—
233	C₂³×C₄	—	67	45	no	—
234	C₂³×C₄	—	67	45	no	—
235	C₂³×C₄	—	67	45	no	—
236	C₂³×C₄	—	67	240	no	—
237	C₂³×C₄	C₂²×D₆₇	1	15	yes	complemented
238	C₂⁴	—	268	60	no	—
239	C₂⁴	—	67	45	no	—
240	C₂⁴	—	67	120	no	—
241	C₂⁴	—	67	15	no	—
242	C₂⁴	C₂³×D₆₇	1	15	yes	—
243	#41	—	67	160	no	—
244	#41	—	67	480	no	—
245	#41	—	67	480	no	—
246	#41	—	67	1440	no	—
247	#41	—	67	480	no	—
248	#41	—	67	1440	no	—
249	#41	C₂³×D₆₇	1	160	yes	complemented
250	#41	C₂³×D₆₇	1	480	yes	complemented
251	C₂×Q₈	—	67	160	no	—
252	C₂×Q₈	—	67	480	no	—
253	C₂×Q₈	—	67	60	no	—
254	C₂×Q₈	—	67	360	no	—
255	C₂×Q₈	C₂³×D₆₇	1	20	yes	—
256	C₂×Q₈	C₂³×D₆₇	1	120	yes	complemented
257	C₂×D₄	—	67	120	no	—
258	C₂×D₄	—	67	720	no	—
259	C₂×D₄	—	67	480	no	—
260	C₂×D₄	—	67	1440	no	—
261	C₂×D₄	—	67	60	no	—
262	C₂×D₄	—	67	360	no	—
263	C₂×D₄	C₂³×D₆₇	1	60	yes	—
264	C₂×D₄	C₂³×D₆₇	1	360	yes	complemented
265	C₂²×C₄	—	67	15	no	—
266	C₂²×C₄	—	67	45	no	—
267	C₂²×C₄	—	67	120	no	—
268	C₂²×C₄	—	67	15	no	—
269	C₂²×C₄	—	67	15	no	—
270	C₂²×C₄	—	67	120	no	—
271	C₂²×C₄	—	67	90	no	—
272	C₂²×C₄	—	67	360	no	—
273	C₂²×C₄	—	67	360	no	—
274	C₂²×C₄	—	67	360	no	—
275	C₂²×C₄	—	67	1	no	—
276	C₂²×C₄	—	67	15	no	—
277	C₂²×C₄	C₂³×D₆₇	1	45	yes	—
278	C₂²×C₄	C₂³×D₆₇	1	15	yes	—
279	C₂²×C₄	C₂³×D₆₇	1	120	yes	complemented
280	C₂³	—	4	30	no	—
281	C₂³	—	268	90	no	—
282	C₂³	—	268	240	no	—
283	C₂³	—	67	180	no	—
284	C₂³	—	67	1	no	—
285	C₂³	—	67	60	no	—
286	C₂³	—	67	15	no	—
287	C₂³	—	134	60	no	—
288	C₂³	C₂⁴×D₆₇	1	15	yes	—
289	C₂³	C₂⁴×D₆₇	1	60	yes	—
290	Q₈	—	67	240	no	—
291	Q₈	C₂⁴×D₆₇	1	80	yes	—
292	D₄	—	67	480	no	—
293	D₄	—	67	240	no	—
294	D₄	C₂⁴×D₆₇	1	240	yes	—
295	C₂×C₄	—	67	1	no	—
296	C₂×C₄	—	67	15	no	—
297	C₂×C₄	—	67	60	no	—
298	C₂×C₄	—	67	180	no	—
299	C₂×C₄	—	67	4	no	—
300	C₂×C₄	—	67	60	no	—
301	C₂×C₄	—	67	60	no	—
302	C₂×C₄	—	67	60	no	—
303	C₂×C₄	—	67	360	no	—
304	C₂×C₄	C₂⁴×D₆₇	1	15	yes	—
305	C₂×C₄	C₂⁴×D₆₇	1	60	yes	—
306	C₂×C₄	C₂⁴×D₆₇	1	180	yes	—
307	C₂×C₄	C₂⁴×D₆₇	1	1	yes	characteristic
308	C₂²	—	2	30	no	—
309	C₂²	—	4	60	no	—
310	C₂²	—	268	180	no	—
311	C₂²	—	67	4	no	—
312	C₂²	—	67	2	no	—
313	C₂²	—	67	30	no	—
314	C₂²	—	134	120	no	—
315	C₂²	—	134	30	no	—
316	C₂²	C₂⁵×D₆₇	1	30	yes	—
317	C₂²	C₂⁵×D₆₇	1	1	yes	characteristic
318	C₄	—	67	2	no	—
319	C₄	—	67	30	no	—
320	C₄	C₂⁵×D₆₇	1	2	yes	—
321	C₄	C₂⁵×D₆₇	1	30	yes	—
322	C₂	—	2	30	no	—
323	C₂	—	67	4	no	—
324	C₂	—	134	30	no	—
325	C₂	#585×D₆₇	1	2	yes	direct product factor
326	C₂	C₂⁶×D₆₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂⁴×D₆₇
commutator, cosocle	C₂×C₆₇	C₂⁷
Frattini	C₂	C₂⁶×D₆₇
Fitting	C₂×#585×C₆₇	C₂
socle	C₂²×C₆₇	C₂⁶
hypercenter	C₂×#585	D₆₇
hypocenter	C₆₇	C₂²×#585
LCS	G ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×#585

Complements

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

N	H ≅ G/N	type
1. C₂×#16864233	C₂	semidirect
2. C₂×#16864232	C₂	semidirect
3. C₂×#16864231	C₂	semidirect
4. #585×D₆₇	C₂	direct (N × H)
5. C₂×2₋¹⁺⁴×D₆₇	C₂	semidirect
6. C₂×H(5,𝔽₂)×D₆₇	C₂	semidirect
7. C₂²×#41×D₆₇	C₂	semidirect
8. C₂×#585×C₆₇	C₂	semidirect
9. #16864233	C₂²	semidirect
10. #16864232	C₂²	semidirect
11. #16864231	C₂²	semidirect
12. C₂×#14524091	C₂²	semidirect
13. C₂×#14524090	C₂²	semidirect
14. 2₋¹⁺⁴×D₆₇	C₂²	semidirect
15. C₂×#14524089	C₂²	semidirect
16. C₂×#14524088	C₂²	semidirect
17. H(5,𝔽₂)×D₆₇	C₂²	semidirect
18. C₂²×#11761629	C₂²	semidirect
19. C₂²×#11761628	C₂²	semidirect
20. C₂²×#11761627	C₂²	semidirect
21. C₂×#41×D₆₇	C₂²	semidirect
22. C₂×#41×D₆₇	C₂²	semidirect
23. C₂×#41×D₆₇	C₂²	semidirect
24. C₂×#41×D₆₇	C₂²	semidirect
25. C₂×#41×D₆₇	C₂²	semidirect
26. C₂²×Q₈×D₆₇	C₂²	semidirect
27. C₂²×D₄×D₆₇	C₂²	semidirect
28. C₂³×C₄×D₆₇	C₂²	semidirect
29. #585×C₆₇	C₂²	semidirect
30. C₂×2₋¹⁺⁴×C₆₇	C₂²	semidirect
31. C₂×H(5,𝔽₂)×C₆₇	C₂²	semidirect
32. C₂²×#41×C₆₇	C₂²	semidirect
34. #14524091	C₂³	semidirect
35. #14524090	C₂³	semidirect
36. #14524089	C₂³	semidirect
37. #14524088	C₂³	semidirect
38. C₂×#11761629	C₂³	semidirect
39. C₂×#11761629	C₂³	semidirect
40. C₂×#11761629	C₂³	semidirect
41. C₂×#11761628	C₂³	semidirect
42. C₂×#11761628	C₂³	semidirect
43. C₂×#11761628	C₂³	semidirect
44. C₂×#11761627	C₂³	semidirect
45. C₂×#11761627	C₂³	semidirect
46. C₂×#11761627	C₂³	semidirect
47. #41×D₆₇	C₂³	semidirect
48. #41×D₆₇	C₂³	semidirect
49. #41×D₆₇	C₂³	semidirect
50. #41×D₆₇	C₂³	semidirect
51. C₂²×Dic₁₃₄	C₂³	semidirect
53. C₂×Q₈×D₆₇	C₂³	semidirect
54. C₂×Q₈×D₆₇	C₂³	semidirect
55. C₂²×D₂₆₈	C₂³	semidirect
56. C₂²×C₂²⋊D₆₇	C₂³	semidirect
58. C₂×D₄×D₆₇	C₂³	semidirect
59. C₂×D₄×D₆₇	C₂³	semidirect
60. C₂³×Dic₆₇	C₂³	semidirect
63. C₂²×C₄×D₆₇	C₂³	semidirect
64. C₂²×C₄×D₆₇	C₂³	semidirect
65. C₂²×C₄×D₆₇	C₂³	semidirect
66. 2₋¹⁺⁴×C₆₇	C₂³	semidirect
67. H(5,𝔽₂)×C₆₇	C₂³	semidirect
68. C₂×#41×C₆₇	C₂³	semidirect
69. C₂×#41×C₆₇	C₂³	semidirect
70. C₂×#41×C₆₇	C₂³	semidirect
71. C₂²×Q₈×C₆₇	C₂³	semidirect
72. C₂²×D₄×C₆₇	C₂³	semidirect
73. C₂³×C₄×C₆₇	C₂³	semidirect
78. #11761629	C₂⁴	semidirect
79. #11761629	C₂⁴	semidirect
80. #11761628	C₂⁴	semidirect
81. #11761628	C₂⁴	semidirect
82. #11761627	C₂⁴	semidirect
83. #11761627	C₂⁴	semidirect
85. C₂×Dic₁₃₄	C₂⁴	semidirect
87. Q₈×D₆₇	C₂⁴	semidirect
89. C₂×D₂₆₈	C₂⁴	semidirect
91. C₂×C₂²⋊D₆₇	C₂⁴	semidirect
93. D₄×D₆₇	C₂⁴	semidirect
96. C₂²×Dic₆₇	C₂⁴	semidirect
104. C₂×C₄×D₆₇	C₂⁴	semidirect
105. C₂×C₄×D₆₇	C₂⁴	semidirect
107. #41×C₆₇	C₂⁴	semidirect
108. #41×C₆₇	C₂⁴	semidirect
110. C₂×Q₈×C₆₇	C₂⁴	semidirect
112. C₂×D₄×C₆₇	C₂⁴	semidirect
115. C₂²×C₄×C₆₇	C₂⁴	semidirect
151. C₂×D₆₇	#585	direct (N × H)
160. C₂×C₆₇	C₂×#585	semidirect
163. D₆₇	C₂×#585	direct (N × H)
168. C₂×#585	D₆₇	direct (N × H)
172. C₆₇	C₂²×#585	semidirect
176. #585	C₂×D₆₇	direct (N × H)
180. C₂×2₋¹⁺⁴	C₂×D₆₇	semidirect
184. C₂×H(5,𝔽₂)	C₂×D₆₇	semidirect
193. C₂²×#41	C₂×D₆₇	semidirect
200. 2₋¹⁺⁴	C₂²×D₆₇	semidirect
203. H(5,𝔽₂)	C₂²×D₆₇	semidirect
217. C₂×#41	C₂²×D₆₇	semidirect
218. C₂×#41	C₂²×D₆₇	semidirect
219. C₂×#41	C₂²×D₆₇	semidirect
224. C₂²×Q₈	C₂²×D₆₇	semidirect
230. C₂²×D₄	C₂²×D₆₇	semidirect
237. C₂³×C₄	C₂²×D₆₇	semidirect
249. #41	C₂³×D₆₇	semidirect
250. #41	C₂³×D₆₇	semidirect
256. C₂×Q₈	C₂³×D₆₇	semidirect
264. C₂×D₄	C₂³×D₆₇	semidirect
279. C₂²×C₄	C₂³×D₆₇	semidirect
325. C₂	#585×D₆₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#16864233	2
C₂×#16864232	2
C₂×#16864231	2
#585×D₆₇	2
C₂×2₋¹⁺⁴×D₆₇	2
C₂×H(5,𝔽₂)×D₆₇	2
C₂²×#41×D₆₇	2
C₂×#585×C₆₇	2
C₂²×#585	67

Subgroups — C2×#585×D67 #31769722

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#585×D₆₇ #31769722