Subgroups — C₂×#22573844 #31763714

Order 17152.

14438 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#14524088	C₂	1	1	yes	maximal, characteristic, complemented
2	#22573844	C₂	1	32	yes	maximal, direct product factor
3	C₂×#16864040	C₂	1	8	yes	maximal, complemented
4	C₂×D₄×C₂²⋊D₆₇	C₂	1	8	yes	maximal, complemented
5	C₂×#16863963	C₂	1	2	yes	maximal, complemented
6	C₂×#16863955	C₂	1	4	yes	maximal, complemented
7	C₂×#16863907	C₂	1	2	yes	maximal, complemented
8	C₂²×#14524012	C₂	1	4	yes	maximal, complemented
9	C₂×#16863871	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂⁴×D₄×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#14524088	—	2	16	no	—
12	C₂×#14524088	C₂²	1	16	yes	complemented
13	C₂²×#11761628	C₂²	1	2	yes	complemented
14	C₂²×#11761627	C₂²	1	4	yes	complemented
15	C₂³×C₂²⋊D₆₇	C₂²	1	4	yes	complemented
16	C₂³×C₂²⋊D₆₇	C₂²	1	8	yes	complemented
17	C₂²×D₄×D₆₇	C₂²	1	4	yes	complemented
18	#16864040	C₂²	1	128	yes	complemented
19	D₄×C₂²⋊D₆₇	C₂²	1	128	yes	complemented
20	#16863963	C₂²	1	32	yes	complemented
21	#16863955	C₂²	1	64	yes	complemented
22	C₂×#14524039	C₂²	1	4	yes	complemented
23	C₂×#14524030	C₂²	1	4	yes	complemented
24	#16863907	C₂²	1	32	yes	complemented
25	C₂×#14524026	C₂²	1	4	yes	complemented
26	C₂×#14524024	C₂²	1	8	yes	complemented
27	C₂×#14524022	C₂²	1	4	yes	complemented
28	C₂×#14524017	C₂²	1	4	yes	complemented
29	C₂×#14524015	C₂²	1	16	yes	complemented
30	C₂×#14524014	C₂²	1	8	yes	complemented
31	C₂×#14524012	C₂²	1	4	yes	complemented
32	C₂×#14524012	C₂²	1	16	yes	complemented
33	C₂×#14524012	C₂²	1	8	yes	complemented
34	C₂×#14524012	C₂²	1	64	yes	complemented
35	C₂×#14524011	C₂²	1	8	yes	complemented
36	#16863871	C₂²	1	16	yes	complemented
37	C₂×D₄×Dic₆₇	C₂²	1	8	yes	complemented
38	C₂×C₄×C₂²⋊D₆₇	C₂²	1	8	yes	complemented
39	C₂×#14524002	C₂²	1	2	yes	complemented
40	C₂²×C₂²⋊Dic₆₇	C₂²	1	4	yes	complemented
41	C₂²×C₂²⋊Dic₆₇	C₂²	1	8	yes	complemented
42	C₂⁶×C₆₇	C₂²	1	2	yes	complemented
43	C₂³×D₄×C₆₇	—	2	16	no	—
44	C₂³×D₄×C₆₇	C₂²	1	1	yes	characteristic
45	C₂³×D₄×C₆₇	C₂²	1	8	yes	complemented
46	C₂³×D₄×C₆₇	C₂²	1	2	yes	complemented
47	C₂³×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
48	C₂³×D₄×C₆₇	C₂²	1	16	yes	complemented
49	C₂⁴×C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
50	C₂⁴×D₆₇	C₂³	1	4	yes	complemented
51	#14524088	—	2	128	no	—
52	C₂×#11761628	—	2	16	no	—
53	C₂×#11761628	C₂³	1	16	yes	complemented
54	C₂×#11761627	—	2	32	no	—
55	C₂×#11761627	C₂³	1	32	yes	complemented
56	C₂²×Dic₁₃₄	C₂³	1	2	yes	complemented
57	C₂²×D₂₆₈	C₂³	1	2	yes	complemented
58	C₂²×C₂²⋊D₆₇	—	2	32	no	—
59	C₂²×C₂²⋊D₆₇	—	4	32	no	—
60	C₂²×C₂²⋊D₆₇	C₂³	1	8	yes	—
61	C₂²×C₂²⋊D₆₇	C₂³	1	4	yes	—
62	C₂²×C₂²⋊D₆₇	C₂³	1	8	yes	complemented
63	C₂²×C₂²⋊D₆₇	C₂³	1	16	yes	complemented
64	C₂²×C₂²⋊D₆₇	C₂³	1	32	yes	complemented
65	C₂²×C₂²⋊D₆₇	C₂³	1	64	yes	complemented
66	C₂×D₄×D₆₇	—	2	32	no	—
67	C₂×D₄×D₆₇	C₂³	1	32	yes	complemented
68	C₂³×Dic₆₇	C₂³	1	4	yes	complemented
69	C₂³×Dic₆₇	C₂³	1	8	yes	complemented
70	C₂²×C₄×D₆₇	C₂³	1	4	yes	complemented
71	#14524039	C₂³	1	32	yes	complemented
72	#14524030	C₂³	1	32	yes	complemented
73	#14524026	C₂³	1	32	yes	complemented
74	#14524024	C₂³	1	64	yes	complemented
75	#14524022	C₂³	1	32	yes	complemented
76	#14524017	C₂³	1	32	yes	complemented
77	#14524015	C₂³	1	128	yes	complemented
78	#14524014	C₂³	1	64	yes	complemented
79	#14524012	C₂³	1	32	yes	complemented
80	#14524012	C₂³	1	128	yes	complemented
81	#14524012	C₂³	1	64	yes	complemented
82	#14524011	C₂³	1	64	yes	complemented
83	D₄×Dic₆₇	C₂³	1	64	yes	complemented
84	C₄×C₂²⋊D₆₇	C₂³	1	64	yes	complemented
85	#14524002	C₂³	1	16	yes	complemented
86	C₂×C₄⋊Dic₆₇	C₂³	1	4	yes	complemented
87	C₂×Dic₆₇⋊C₄	C₂³	1	8	yes	complemented
88	C₂×C₂²⋊Dic₆₇	C₂³	1	4	yes	—
89	C₂×C₂²⋊Dic₆₇	C₂³	1	8	yes	—
90	C₂×C₂²⋊Dic₆₇	C₂³	1	64	yes	complemented
91	C₂×C₂²⋊Dic₆₇	C₂³	1	32	yes	complemented
92	C₂×C₂²⋊Dic₆₇	C₂³	1	8	yes	complemented
93	C₂×C₂²⋊Dic₆₇	C₂³	1	16	yes	complemented
94	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	8	yes	complemented
95	C₂×C₄×Dic₆₇	C₂³	1	4	yes	complemented
96	C₂⁵×C₆₇	—	2	16	no	—
97	C₂⁵×C₆₇	—	4	16	no	—
98	C₂⁵×C₆₇	C₂³	1	1	yes	characteristic
99	C₂⁵×C₆₇	C₂³	1	8	yes	—
100	C₂⁵×C₆₇	C₂³	1	2	yes	—
101	C₂⁵×C₆₇	C₂³	1	2	yes	—
102	C₂⁵×C₆₇	C₂³	1	16	yes	complemented
103	C₂²×D₄×C₆₇	—	2	16	no	—
104	C₂²×D₄×C₆₇	—	2	64	no	—
105	C₂²×D₄×C₆₇	—	2	128	no	—
106	C₂²×D₄×C₆₇	—	2	8	no	—
107	C₂²×D₄×C₆₇	D₄	1	16	yes	complemented
108	C₂²×D₄×C₆₇	C₂³	1	8	yes	—
109	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
110	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
111	C₂²×D₄×C₆₇	C₂³	1	8	yes	—
112	C₂²×D₄×C₆₇	C₂³	1	64	yes	complemented
113	C₂²×D₄×C₆₇	C₂³	1	16	yes	complemented
114	C₂²×D₄×C₆₇	C₂³	1	8	yes	complemented
115	C₂³×C₄×C₆₇	—	2	8	no	—
116	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
117	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
118	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
119	C₂³×C₄×C₆₇	C₂³	1	8	yes	complemented
120	C₂³×D₆₇	—	2	16	no	—
121	C₂³×D₆₇	—	4	16	no	—
122	C₂³×D₆₇	C₂⁴	1	4	yes	—
123	C₂³×D₆₇	C₂⁴	1	16	yes	complemented
124	#11761628	—	2	64	no	—
125	#11761627	—	2	128	no	—
126	C₂×Dic₁₃₄	—	2	8	no	—
127	C₂×Dic₁₃₄	C₂⁴	1	8	yes	complemented
128	C₂×D₂₆₈	—	2	8	no	—
129	C₂×D₂₆₈	C₂⁴	1	8	yes	complemented
130	C₂×C₂²⋊D₆₇	—	2	32	no	—
131	C₂×C₂²⋊D₆₇	—	2	16	no	—
132	C₂×C₂²⋊D₆₇	—	2	128	no	—
133	C₂×C₂²⋊D₆₇	—	2	32	no	—
134	C₂×C₂²⋊D₆₇	—	4	32	no	—
135	C₂×C₂²⋊D₆₇	—	4	128	no	—
136	C₂×C₂²⋊D₆₇	C₂⁴	1	32	yes	—
137	C₂×C₂²⋊D₆₇	C₂⁴	1	16	yes	—
138	C₂×C₂²⋊D₆₇	C₂⁴	1	32	yes	complemented
139	C₂×C₂²⋊D₆₇	C₂⁴	1	64	yes	complemented
140	D₄×D₆₇	—	2	128	no	—
141	C₂²×Dic₆₇	—	2	16	no	—
142	C₂²×Dic₆₇	—	4	16	no	—
143	C₂²×Dic₆₇	C₂⁴	1	8	yes	—
144	C₂²×Dic₆₇	C₂⁴	1	4	yes	—
145	C₂²×Dic₆₇	C₂⁴	1	16	yes	complemented
146	C₂²×Dic₆₇	C₂⁴	1	32	yes	complemented
147	C₂×C₄×D₆₇	—	2	16	no	—
148	C₂×C₄×D₆₇	C₂⁴	1	16	yes	complemented
149	C₄⋊Dic₆₇	C₂⁴	1	16	yes	complemented
150	Dic₆₇⋊C₄	C₂⁴	1	32	yes	complemented
151	C₂²⋊Dic₆₇	C₂⁴	1	16	yes	—
152	C₂²⋊Dic₆₇	C₂⁴	1	32	yes	—
153	C₂²⋊Dic₆₇	C₂⁴	1	32	yes	complemented
154	C₂²⋊Dic₆₇	C₂⁴	1	64	yes	complemented
155	(C₂×D₆₇)⋊C₄	C₂⁴	1	32	yes	complemented
156	C₄×Dic₆₇	C₂⁴	1	16	yes	complemented
157	C₂⁴×C₆₇	—	2	4	no	—
158	C₂⁴×C₆₇	—	2	8	no	—
159	C₂⁴×C₆₇	—	2	32	no	—
160	C₂⁴×C₆₇	—	2	8	no	—
161	C₂⁴×C₆₇	—	2	64	no	—
162	C₂⁴×C₆₇	—	2	32	no	—
163	C₂⁴×C₆₇	—	4	8	no	—
164	C₂⁴×C₆₇	—	4	16	no	—
165	C₂⁴×C₆₇	—	4	8	no	—
166	C₂⁴×C₆₇	—	4	64	no	—
167	C₂⁴×C₆₇	—	4	128	no	—
168	C₂⁴×C₆₇	C₂×D₄	1	16	yes	complemented
169	C₂⁴×C₆₇	C₂⁴	1	4	yes	—
170	C₂⁴×C₆₇	C₂⁴	1	4	yes	—
171	C₂⁴×C₆₇	C₂⁴	1	32	yes	—
172	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
173	C₂⁴×C₆₇	C₂⁴	1	4	yes	—
174	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
175	C₂⁴×C₆₇	C₂⁴	1	8	yes	—
176	C₂⁴×C₆₇	C₂⁴	1	8	yes	—
177	C₂×D₄×C₆₇	—	2	32	no	—
178	C₂×D₄×C₆₇	—	2	64	no	—
179	C₂×D₄×C₆₇	—	2	256	no	—
180	C₂×D₄×C₆₇	—	2	16	no	—
181	C₂×D₄×C₆₇	—	2	32	no	—
182	C₂×D₄×C₆₇	C₂×D₄	1	32	yes	complemented
183	C₂×D₄×C₆₇	C₂×D₄	1	64	yes	complemented
184	C₂×D₄×C₆₇	C₂⁴	1	32	yes	—
185	C₂×D₄×C₆₇	C₂⁴	1	16	yes	—
186	C₂×D₄×C₆₇	C₂⁴	1	16	yes	—
187	C₂²×C₄×C₆₇	—	2	4	no	—
188	C₂²×C₄×C₆₇	—	2	16	no	—
189	C₂²×C₄×C₆₇	—	2	32	no	—
190	C₂²×C₄×C₆₇	C₂×D₄	1	8	yes	complemented
191	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
192	C₂²×C₄×C₆₇	C₂⁴	1	16	yes	—
193	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
194	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
195	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
196	C₂³×C₆₇	—	2	32	no	—
197	C₂³×C₆₇	—	2	8	no	—
198	C₂³×C₆₇	—	2	4	no	—
199	C₂³×C₆₇	—	2	4	no	—
200	C₂³×C₆₇	—	2	4	no	—
201	C₂³×C₆₇	—	2	16	no	—
202	C₂³×C₆₇	—	2	16	no	—
203	C₂³×C₆₇	—	2	64	no	—
204	C₂³×C₆₇	—	2	16	no	—
205	C₂³×C₆₇	—	2	8	no	—
206	C₂³×C₆₇	—	2	16	no	—
207	C₂³×C₆₇	—	2	64	no	—
208	C₂³×C₆₇	—	4	32	no	—
209	C₂³×C₆₇	—	4	16	no	—
210	C₂³×C₆₇	—	4	32	no	—
211	C₂³×C₆₇	—	4	16	no	—
212	C₂³×C₆₇	—	4	128	no	—
213	C₂³×C₆₇	—	4	256	no	—
214	C₂³×C₆₇	—	4	32	no	—
215	C₂³×C₆₇	C₂²×D₄	1	4	yes	—
216	C₂³×C₆₇	C₂²×D₄	1	16	yes	—
217	C₂³×C₆₇	C₂²×D₄	1	32	yes	complemented
218	C₂³×C₆₇	H(5,𝔽₂)	1	8	yes	complemented
219	C₂³×C₆₇	C₂⁵	1	8	yes	—
220	C₂³×C₆₇	C₂⁵	1	2	yes	—
221	C₂³×C₆₇	C₂⁵	1	8	yes	—
222	C₂³×C₆₇	C₂⁵	1	4	yes	—
223	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
224	C₂²×D₆₇	—	2	8	no	—
225	C₂²×D₆₇	—	2	16	no	—
226	C₂²×D₆₇	—	2	32	no	—
227	C₂²×D₆₇	—	4	32	no	—
228	C₂²×D₆₇	—	8	32	no	—
229	C₂²×D₆₇	C₂⁵	1	8	yes	—
230	D₄×C₆₇	—	2	64	no	—
231	D₄×C₆₇	—	2	32	no	—
232	D₄×C₆₇	C₂²×D₄	1	64	yes	complemented
233	C₂×C₄×C₆₇	—	2	8	no	—
234	C₂×C₄×C₆₇	—	2	4	no	—
235	C₂×C₄×C₆₇	—	2	32	no	—
236	C₂×C₄×C₆₇	C₂²×D₄	1	8	yes	—
237	C₂×C₄×C₆₇	C₂²×D₄	1	16	yes	complemented
238	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
239	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
240	C₂²⋊D₆₇	—	2	64	no	—
241	C₂²⋊D₆₇	—	2	32	no	—
242	C₂²⋊D₆₇	—	2	64	no	—
243	C₂²⋊D₆₇	—	4	64	no	—
244	C₂×Dic₆₇	—	2	8	no	—
245	C₂×Dic₆₇	—	2	32	no	—
246	C₂×Dic₆₇	—	2	16	no	—
247	C₂×Dic₆₇	—	4	32	no	—
248	C₂×Dic₆₇	C₂⁵	1	16	yes	—
249	C₂×Dic₆₇	C₂⁵	1	8	yes	—
250	D₂₆₈	—	2	16	no	—
251	C₄×D₆₇	—	2	32	no	—
252	Dic₁₃₄	—	2	16	no	—
253	C₂²×C₆₇	—	2	32	no	—
254	C₂²×C₆₇	—	2	4	no	—
255	C₂²×C₆₇	—	2	16	no	—
256	C₂²×C₆₇	—	2	4	no	—
257	C₂²×C₆₇	—	2	4	no	—
258	C₂²×C₆₇	—	2	32	no	—
259	C₂²×C₆₇	—	2	8	no	—
260	C₂²×C₆₇	—	2	16	no	—
261	C₂²×C₆₇	—	2	8	no	—
262	C₂²×C₆₇	—	2	16	no	—
263	C₂²×C₆₇	—	4	32	no	—
264	C₂²×C₆₇	—	4	128	no	—
265	C₂²×C₆₇	—	4	32	no	—
266	C₂²×C₆₇	—	4	16	no	—
267	C₂²×C₆₇	C₂³×D₄	1	16	yes	—
268	C₂²×C₆₇	C₂³×D₄	1	4	yes	—
269	C₂²×C₆₇	C₂³×D₄	1	2	yes	—
270	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	4	yes	—
271	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	8	yes	complemented
272	C₂²×C₆₇	C₂⁶	1	1	yes	characteristic
273	C₂×D₆₇	—	2	8	no	—
274	C₂×D₆₇	—	2	16	no	—
275	C₂×D₆₇	—	4	16	no	—
276	C₂×D₆₇	—	8	32	no	—
277	C₄×C₆₇	—	2	4	no	—
278	C₄×C₆₇	C₂³×D₄	1	8	yes	—
279	Dic₆₇	—	2	8	no	—
280	Dic₆₇	—	2	16	no	—
281	C₂×#3484	—	67	1	no	maximal, Sylow
282	C₂×C₆₇	—	2	16	no	—
283	C₂×C₆₇	—	2	4	no	—
284	C₂×C₆₇	—	2	8	no	—
285	C₂×C₆₇	—	4	8	no	—
286	C₂×C₆₇	#3484	1	4	yes	complemented
287	C₂×C₆₇	C₂⁴×D₄	1	1	yes	characteristic
288	C₂×C₆₇	C₂²×H(5,𝔽₂)	1	2	yes	—
289	D₆₇	—	4	8	no	—
290	C₂²×H(5,𝔽₂)	—	67	1	no	—
291	C₂⁴×D₄	D₆₇	1	1	yes	characteristic, complemented
292	#3484	—	67	32	no	—
293	C₂×#546	—	67	8	no	—
294	C₂×D₄²	—	67	8	no	—
295	C₂×#535	—	67	2	no	—
296	C₂×#534	—	67	4	no	—
297	C₂×#525	—	67	2	no	—
298	C₂²×#120	—	67	4	no	—
299	C₂×#518	—	67	1	no	—
300	C₆₇	C₂×#3484	1	1	yes	characteristic, complemented, Sylow
301	C₂⁶	C₂×D₆₇	1	2	yes	complemented
302	C₂×H(5,𝔽₂)	—	67	16	no	—
303	C₂×H(5,𝔽₂)	—	134	16	no	—
304	C₂²×#41	—	67	4	no	—
305	C₂²×#41	—	67	2	no	—
306	C₂³×D₄	—	2	16	no	—
307	C₂³×D₄	—	67	8	no	—
308	C₂³×D₄	—	67	4	no	—
309	C₂³×D₄	—	67	4	no	—
310	C₂³×D₄	C₂×D₆₇	1	1	yes	characteristic
311	C₂³×D₄	C₂×D₆₇	1	2	yes	complemented
312	C₂³×D₄	C₂×D₆₇	1	1	yes	characteristic, complemented
313	C₂³×D₄	C₂×D₆₇	1	8	yes	complemented
314	C₂³×D₄	C₂×D₆₇	1	16	yes	complemented
315	C₂⁴×C₄	C₂×D₆₇	1	1	yes	characteristic, complemented
316	#546	—	67	128	no	—
317	D₄²	—	67	128	no	—
318	#535	—	67	32	no	—
319	#534	—	67	64	no	—
320	C₂×#127	—	67	4	no	—
321	C₂×#124	—	67	4	no	—
322	#525	—	67	32	no	—
323	C₂×#123	—	67	8	no	—
324	C₂×#123	—	67	4	no	—
325	C₂×C₂²⋊Q₈	—	67	4	no	—
326	C₂×#121	—	67	16	no	—
327	C₂×#121	—	67	8	no	—
328	C₂×#121	—	67	4	no	—
329	C₂×#120	—	67	4	no	—
330	C₂×#120	—	67	8	no	—
331	C₂×#120	—	67	16	no	—
332	C₂×#120	—	67	64	no	—
333	C₂×#120	—	67	8	no	—
334	#518	—	67	16	no	—
335	C₂×C₄×D₄	—	67	8	no	—
336	C₂×C₄×D₄	—	67	8	no	—
337	C₂×#117	—	67	2	no	—
338	C₂²×C₂²⋊C₄	—	67	4	no	—
339	C₂²×C₂²⋊C₄	—	67	8	no	—
340	C₂⁵	—	2	16	no	—
341	C₂⁵	—	4	16	no	—
342	C₂⁵	—	67	4	no	—
343	C₂⁵	C₂²×D₆₇	1	1	yes	characteristic
344	C₂⁵	C₂²×D₆₇	1	8	yes	—
345	C₂⁵	C₂²×D₆₇	1	2	yes	—
346	C₂⁵	C₂²×D₆₇	1	2	yes	—
347	C₂⁵	C₂²×D₆₇	1	16	yes	complemented
348	H(5,𝔽₂)	—	134	128	no	—
349	C₂×#41	—	67	32	no	—
350	C₂×#41	—	67	16	no	—
351	C₂×#41	—	134	32	no	—
352	C₂×#41	—	134	16	no	—
353	C₂²×Q₈	—	67	2	no	—
354	C₂²×D₄	—	2	16	no	—
355	C₂²×D₄	—	2	64	no	—
356	C₂²×D₄	—	2	128	no	—
357	C₂²×D₄	—	2	8	no	—
358	C₂²×D₄	—	268	32	no	—
359	C₂²×D₄	—	67	16	no	—
360	C₂²×D₄	—	67	64	no	—
361	C₂²×D₄	—	67	8	no	—
362	C₂²×D₄	—	67	4	no	—
363	C₂²×D₄	—	67	8	no	—
364	C₂²×D₄	—	67	32	no	—
365	C₂²×D₄	—	67	32	no	—
366	C₂²×D₄	—	67	2	no	—
367	C₂²×D₄	—	134	32	no	—
368	C₂²×D₄	—	134	32	no	—
369	C₂²×D₄	C₂²⋊D₆₇	1	16	yes	complemented
370	C₂²×D₄	C₂²×D₆₇	1	8	yes	—
371	C₂²×D₄	C₂²×D₆₇	1	4	yes	—
372	C₂²×D₄	C₂²×D₆₇	1	4	yes	—
373	C₂²×D₄	C₂²×D₆₇	1	8	yes	—
374	C₂²×D₄	C₂²×D₆₇	1	16	yes	complemented
375	C₂²×D₄	C₂²×D₆₇	1	8	yes	complemented
376	C₂²×D₄	C₂²×D₆₇	1	64	yes	complemented
377	C₂³×C₄	—	2	8	no	—
378	C₂³×C₄	—	67	8	no	—
379	C₂³×C₄	—	67	4	no	—
380	C₂³×C₄	—	67	4	no	—
381	C₂³×C₄	C₂²×D₆₇	1	4	yes	—
382	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
383	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
384	C₂³×C₄	C₂²×D₆₇	1	8	yes	complemented
385	#127	—	67	32	no	—
386	#124	—	67	32	no	—
387	#123	—	67	64	no	—
388	#123	—	67	32	no	—
389	C₂²⋊Q₈	—	67	32	no	—
390	#121	—	67	128	no	—
391	#121	—	67	64	no	—
392	#121	—	67	32	no	—
393	#120	—	67	32	no	—
394	#120	—	67	64	no	—
395	#120	—	67	128	no	—
396	#120	—	67	64	no	—
397	C₄×D₄	—	67	64	no	—
398	C₄×D₄	—	67	64	no	—
399	#117	—	67	16	no	—
400	C₂×C₄⋊C₄	—	67	4	no	—
401	C₂×C₄⋊C₄	—	67	8	no	—
402	C₂×C₂²⋊C₄	—	67	4	no	—
403	C₂×C₂²⋊C₄	—	67	8	no	—
404	C₂×C₂²⋊C₄	—	67	8	no	—
405	C₂×C₂²⋊C₄	—	67	32	no	—
406	C₂×C₂²⋊C₄	—	67	16	no	—
407	C₂×C₂²⋊C₄	—	67	64	no	—
408	C₂×C₂²⋊C₄	—	67	8	no	—
409	C₂×C₄²	—	67	4	no	—
410	C₂⁴	—	2	4	no	—
411	C₂⁴	—	2	8	no	—
412	C₂⁴	—	2	32	no	—
413	C₂⁴	—	2	8	no	—
414	C₂⁴	—	2	64	no	—
415	C₂⁴	—	2	32	no	—
416	C₂⁴	—	4	8	no	—
417	C₂⁴	—	4	16	no	—
418	C₂⁴	—	4	8	no	—
419	C₂⁴	—	4	64	no	—
420	C₂⁴	—	4	128	no	—
421	C₂⁴	—	268	16	no	—
422	C₂⁴	—	67	16	no	—
423	C₂⁴	—	67	4	no	—
424	C₂⁴	—	134	16	no	—
425	C₂⁴	C₂×C₂²⋊D₆₇	1	16	yes	complemented
426	C₂⁴	C₂³×D₆₇	1	4	yes	—
427	C₂⁴	C₂³×D₆₇	1	4	yes	—
428	C₂⁴	C₂³×D₆₇	1	32	yes	—
429	C₂⁴	C₂³×D₆₇	1	1	yes	characteristic
430	C₂⁴	C₂³×D₆₇	1	4	yes	—
431	C₂⁴	C₂³×D₆₇	1	2	yes	—
432	C₂⁴	C₂³×D₆₇	1	8	yes	—
433	C₂⁴	C₂³×D₆₇	1	8	yes	—
434	#41	—	134	128	no	—
435	#41	—	134	64	no	—
436	C₂×Q₈	—	67	8	no	—
437	C₂×Q₈	—	134	8	no	—
438	C₂×D₄	—	2	32	no	—
439	C₂×D₄	—	2	64	no	—
440	C₂×D₄	—	2	256	no	—
441	C₂×D₄	—	2	16	no	—
442	C₂×D₄	—	2	32	no	—
443	C₂×D₄	—	268	128	no	—
444	C₂×D₄	—	268	32	no	—
445	C₂×D₄	—	67	64	no	—
446	C₂×D₄	—	67	32	no	—
447	C₂×D₄	—	67	16	no	—
448	C₂×D₄	—	67	32	no	—
449	C₂×D₄	—	67	8	no	—
450	C₂×D₄	—	134	16	no	—
451	C₂×D₄	—	134	32	no	—
452	C₂×D₄	—	134	128	no	—
453	C₂×D₄	—	134	32	no	—
454	C₂×D₄	—	134	128	no	—
455	C₂×D₄	—	134	8	no	—
456	C₂×D₄	C₂×C₂²⋊D₆₇	1	32	yes	complemented
457	C₂×D₄	C₂×C₂²⋊D₆₇	1	64	yes	complemented
458	C₂×D₄	C₂³×D₆₇	1	32	yes	—
459	C₂×D₄	C₂³×D₆₇	1	16	yes	—
460	C₂×D₄	C₂³×D₆₇	1	16	yes	—
461	C₂²×C₄	—	2	4	no	—
462	C₂²×C₄	—	2	16	no	—
463	C₂²×C₄	—	2	32	no	—
464	C₂²×C₄	—	268	16	no	—
465	C₂²×C₄	—	67	32	no	—
466	C₂²×C₄	—	67	16	no	—
467	C₂²×C₄	—	67	8	no	—
468	C₂²×C₄	—	67	4	no	—
469	C₂²×C₄	—	67	16	no	—
470	C₂²×C₄	—	134	16	no	—
471	C₂²×C₄	—	134	16	no	—
472	C₂²×C₄	C₂×C₂²⋊D₆₇	1	8	yes	complemented
473	C₂²×C₄	C₂³×D₆₇	1	16	yes	—
474	C₂²×C₄	C₂³×D₆₇	1	4	yes	—
475	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
476	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
477	C₂²×C₄	C₂³×D₆₇	1	4	yes	—
478	C₄⋊C₄	—	67	16	no	—
479	C₄⋊C₄	—	67	32	no	—
480	C₂²⋊C₄	—	67	16	no	—
481	C₂²⋊C₄	—	67	32	no	—
482	C₂²⋊C₄	—	67	32	no	—
483	C₂²⋊C₄	—	67	64	no	—
484	C₂²⋊C₄	—	67	32	no	—
485	C₄²	—	67	16	no	—
486	C₂³	—	2	32	no	—
487	C₂³	—	2	8	no	—
488	C₂³	—	2	4	no	—
489	C₂³	—	2	16	no	—
490	C₂³	—	2	4	no	—
491	C₂³	—	2	4	no	—
492	C₂³	—	2	16	no	—
493	C₂³	—	2	64	no	—
494	C₂³	—	2	16	no	—
495	C₂³	—	2	8	no	—
496	C₂³	—	2	16	no	—
497	C₂³	—	2	64	no	—
498	C₂³	—	4	32	no	—
499	C₂³	—	4	16	no	—
500	C₂³	—	4	32	no	—
501	C₂³	—	4	16	no	—
502	C₂³	—	4	128	no	—
503	C₂³	—	4	256	no	—
504	C₂³	—	4	32	no	—
505	C₂³	—	268	32	no	—
506	C₂³	—	536	32	no	—
507	C₂³	—	67	8	no	—
508	C₂³	—	134	8	no	—
509	C₂³	—	134	16	no	—
510	C₂³	—	134	32	no	—
511	C₂³	C₂²×C₂²⋊D₆₇	1	4	yes	—
512	C₂³	C₂²×C₂²⋊D₆₇	1	16	yes	—
513	C₂³	C₂²×C₂²⋊D₆₇	1	32	yes	complemented
514	C₂³	#14524088	1	8	yes	complemented
515	C₂³	C₂⁴×D₆₇	1	8	yes	—
516	C₂³	C₂⁴×D₆₇	1	2	yes	—
517	C₂³	C₂⁴×D₆₇	1	8	yes	—
518	C₂³	C₂⁴×D₆₇	1	4	yes	—
519	C₂³	C₂⁴×D₆₇	1	1	yes	characteristic
520	Q₈	—	134	16	no	—
521	D₄	—	2	64	no	—
522	D₄	—	2	32	no	—
523	D₄	—	268	64	no	—
524	D₄	—	134	32	no	—
525	D₄	—	134	64	no	—
526	D₄	—	134	64	no	—
527	D₄	—	134	16	no	—
528	D₄	C₂²×C₂²⋊D₆₇	1	64	yes	complemented
529	C₂×C₄	—	2	8	no	—
530	C₂×C₄	—	2	4	no	—
531	C₂×C₄	—	2	32	no	—
532	C₂×C₄	—	268	32	no	—
533	C₂×C₄	—	67	16	no	—
534	C₂×C₄	—	67	8	no	—
535	C₂×C₄	—	134	8	no	—
536	C₂×C₄	—	134	32	no	—
537	C₂×C₄	—	134	16	no	—
538	C₂×C₄	—	134	32	no	—
539	C₂×C₄	C₂²×C₂²⋊D₆₇	1	8	yes	—
540	C₂×C₄	C₂²×C₂²⋊D₆₇	1	16	yes	complemented
541	C₂×C₄	C₂⁴×D₆₇	1	4	yes	—
542	C₂×C₄	C₂⁴×D₆₇	1	4	yes	—
543	C₂²	—	2	32	no	—
544	C₂²	—	2	8	no	—
545	C₂²	—	2	16	no	—
546	C₂²	—	2	32	no	—
547	C₂²	—	2	4	no	—
548	C₂²	—	2	16	no	—
549	C₂²	—	2	4	no	—
550	C₂²	—	2	4	no	—
551	C₂²	—	2	8	no	—
552	C₂²	—	2	16	no	—
553	C₂²	—	4	32	no	—
554	C₂²	—	4	128	no	—
555	C₂²	—	4	32	no	—
556	C₂²	—	4	16	no	—
557	C₂²	—	268	16	no	—
558	C₂²	—	536	32	no	—
559	C₂²	—	134	8	no	—
560	C₂²	—	134	16	no	—
561	C₂²	C₂³×C₂²⋊D₆₇	1	4	yes	—
562	C₂²	C₂³×C₂²⋊D₆₇	1	16	yes	—
563	C₂²	C₂³×C₂²⋊D₆₇	1	2	yes	—
564	C₂²	C₂×#14524088	1	4	yes	—
565	C₂²	C₂×#14524088	1	8	yes	complemented
566	C₂²	C₂⁵×D₆₇	1	1	yes	characteristic
567	C₄	—	2	4	no	—
568	C₄	—	134	8	no	—
569	C₄	—	134	16	no	—
570	C₄	C₂³×C₂²⋊D₆₇	1	8	yes	—
571	C₂	—	2	4	no	—
572	C₂	—	2	8	no	—
573	C₂	—	2	16	no	—
574	C₂	—	4	8	no	—
575	C₂	—	268	8	no	—
576	C₂	#22573844	1	4	yes	direct product factor
577	C₂	C₂⁴×C₂²⋊D₆₇	1	1	yes	characteristic
578	C₂	C₂²×#14524088	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂⁴×D₆₇
commutator, cosocle	C₂²×C₆₇	C₂⁶
Frattini	C₂²	C₂⁵×D₆₇
Fitting	C₂⁴×D₄×C₆₇	C₂
socle	C₂³×C₆₇	C₂⁵
hypercenter	C₂⁴×D₄	D₆₇
hypocenter	C₆₇	C₂×#3484
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂³ ◁ C₂⁴×D₄

Complements

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

N	H ≅ G/N	type
1. C₂²×#14524088	C₂	semidirect
2. #22573844	C₂	direct (N × H)
3. C₂×#16864040	C₂	semidirect
4. C₂×D₄×C₂²⋊D₆₇	C₂	semidirect
5. C₂×#16863963	C₂	semidirect
6. C₂×#16863955	C₂	semidirect
7. C₂×#16863907	C₂	semidirect
8. C₂²×#14524012	C₂	semidirect
9. C₂×#16863871	C₂	semidirect
10. C₂⁴×D₄×C₆₇	C₂	semidirect
12. C₂×#14524088	C₂²	semidirect
13. C₂²×#11761628	C₂²	semidirect
14. C₂²×#11761627	C₂²	semidirect
15. C₂³×C₂²⋊D₆₇	C₂²	semidirect
16. C₂³×C₂²⋊D₆₇	C₂²	semidirect
17. C₂²×D₄×D₆₇	C₂²	semidirect
18. #16864040	C₂²	semidirect
19. D₄×C₂²⋊D₆₇	C₂²	semidirect
20. #16863963	C₂²	semidirect
21. #16863955	C₂²	semidirect
22. C₂×#14524039	C₂²	semidirect
23. C₂×#14524030	C₂²	semidirect
24. #16863907	C₂²	semidirect
25. C₂×#14524026	C₂²	semidirect
26. C₂×#14524024	C₂²	semidirect
27. C₂×#14524022	C₂²	semidirect
28. C₂×#14524017	C₂²	semidirect
29. C₂×#14524015	C₂²	semidirect
30. C₂×#14524014	C₂²	semidirect
31. C₂×#14524012	C₂²	semidirect
32. C₂×#14524012	C₂²	semidirect
33. C₂×#14524012	C₂²	semidirect
34. C₂×#14524012	C₂²	semidirect
35. C₂×#14524011	C₂²	semidirect
36. #16863871	C₂²	semidirect
37. C₂×D₄×Dic₆₇	C₂²	semidirect
38. C₂×C₄×C₂²⋊D₆₇	C₂²	semidirect
39. C₂×#14524002	C₂²	semidirect
40. C₂²×C₂²⋊Dic₆₇	C₂²	semidirect
41. C₂²×C₂²⋊Dic₆₇	C₂²	semidirect
42. C₂⁶×C₆₇	C₂²	semidirect
45. C₂³×D₄×C₆₇	C₂²	semidirect
46. C₂³×D₄×C₆₇	C₂²	semidirect
47. C₂³×D₄×C₆₇	C₂²	semidirect
48. C₂³×D₄×C₆₇	C₂²	semidirect
49. C₂⁴×C₄×C₆₇	C₂²	semidirect
50. C₂⁴×D₆₇	C₂³	semidirect
53. C₂×#11761628	C₂³	semidirect
55. C₂×#11761627	C₂³	semidirect
56. C₂²×Dic₁₃₄	C₂³	semidirect
57. C₂²×D₂₆₈	C₂³	semidirect
62. C₂²×C₂²⋊D₆₇	C₂³	semidirect
63. C₂²×C₂²⋊D₆₇	C₂³	semidirect
64. C₂²×C₂²⋊D₆₇	C₂³	semidirect
65. C₂²×C₂²⋊D₆₇	C₂³	semidirect
67. C₂×D₄×D₆₇	C₂³	semidirect
68. C₂³×Dic₆₇	C₂³	semidirect
69. C₂³×Dic₆₇	C₂³	semidirect
70. C₂²×C₄×D₆₇	C₂³	semidirect
71. #14524039	C₂³	semidirect
72. #14524030	C₂³	semidirect
73. #14524026	C₂³	semidirect
74. #14524024	C₂³	semidirect
75. #14524022	C₂³	semidirect
76. #14524017	C₂³	semidirect
77. #14524015	C₂³	semidirect
78. #14524014	C₂³	semidirect
79. #14524012	C₂³	semidirect
80. #14524012	C₂³	semidirect
81. #14524012	C₂³	semidirect
82. #14524011	C₂³	semidirect
83. D₄×Dic₆₇	C₂³	semidirect
84. C₄×C₂²⋊D₆₇	C₂³	semidirect
85. #14524002	C₂³	semidirect
86. C₂×C₄⋊Dic₆₇	C₂³	semidirect
87. C₂×Dic₆₇⋊C₄	C₂³	semidirect
90. C₂×C₂²⋊Dic₆₇	C₂³	semidirect
91. C₂×C₂²⋊Dic₆₇	C₂³	semidirect
92. C₂×C₂²⋊Dic₆₇	C₂³	semidirect
93. C₂×C₂²⋊Dic₆₇	C₂³	semidirect
94. C₂×(C₂×D₆₇)⋊C₄	C₂³	semidirect
95. C₂×C₄×Dic₆₇	C₂³	semidirect
102. C₂⁵×C₆₇	C₂³	semidirect
107. C₂²×D₄×C₆₇	D₄	semidirect
112. C₂²×D₄×C₆₇	C₂³	semidirect
113. C₂²×D₄×C₆₇	C₂³	semidirect
114. C₂²×D₄×C₆₇	C₂³	semidirect
119. C₂³×C₄×C₆₇	C₂³	semidirect
123. C₂³×D₆₇	C₂⁴	semidirect
127. C₂×Dic₁₃₄	C₂⁴	semidirect
129. C₂×D₂₆₈	C₂⁴	semidirect
138. C₂×C₂²⋊D₆₇	C₂⁴	semidirect
139. C₂×C₂²⋊D₆₇	C₂⁴	semidirect
145. C₂²×Dic₆₇	C₂⁴	semidirect
146. C₂²×Dic₆₇	C₂⁴	semidirect
148. C₂×C₄×D₆₇	C₂⁴	semidirect
149. C₄⋊Dic₆₇	C₂⁴	semidirect
150. Dic₆₇⋊C₄	C₂⁴	semidirect
153. C₂²⋊Dic₆₇	C₂⁴	semidirect
154. C₂²⋊Dic₆₇	C₂⁴	semidirect
155. (C₂×D₆₇)⋊C₄	C₂⁴	semidirect
156. C₄×Dic₆₇	C₂⁴	semidirect
168. C₂⁴×C₆₇	C₂×D₄	semidirect
182. C₂×D₄×C₆₇	C₂×D₄	semidirect
183. C₂×D₄×C₆₇	C₂×D₄	semidirect
190. C₂²×C₄×C₆₇	C₂×D₄	semidirect
217. C₂³×C₆₇	C₂²×D₄	semidirect
218. C₂³×C₆₇	H(5,𝔽₂)	semidirect
232. D₄×C₆₇	C₂²×D₄	semidirect
237. C₂×C₄×C₆₇	C₂²×D₄	semidirect
271. C₂²×C₆₇	C₂×H(5,𝔽₂)	semidirect
286. C₂×C₆₇	#3484	semidirect
291. C₂⁴×D₄	D₆₇	semidirect
300. C₆₇	C₂×#3484	semidirect
301. C₂⁶	C₂×D₆₇	semidirect
311. C₂³×D₄	C₂×D₆₇	semidirect
312. C₂³×D₄	C₂×D₆₇	semidirect
313. C₂³×D₄	C₂×D₆₇	semidirect
314. C₂³×D₄	C₂×D₆₇	semidirect
315. C₂⁴×C₄	C₂×D₆₇	semidirect
347. C₂⁵	C₂²×D₆₇	semidirect
369. C₂²×D₄	C₂²⋊D₆₇	semidirect
374. C₂²×D₄	C₂²×D₆₇	semidirect
375. C₂²×D₄	C₂²×D₆₇	semidirect
376. C₂²×D₄	C₂²×D₆₇	semidirect
384. C₂³×C₄	C₂²×D₆₇	semidirect
425. C₂⁴	C₂×C₂²⋊D₆₇	semidirect
456. C₂×D₄	C₂×C₂²⋊D₆₇	semidirect
457. C₂×D₄	C₂×C₂²⋊D₆₇	semidirect
472. C₂²×C₄	C₂×C₂²⋊D₆₇	semidirect
513. C₂³	C₂²×C₂²⋊D₆₇	semidirect
514. C₂³	#14524088	semidirect
528. D₄	C₂²×C₂²⋊D₆₇	semidirect
540. C₂×C₄	C₂²×C₂²⋊D₆₇	semidirect
565. C₂²	C₂×#14524088	semidirect
576. C₂	#22573844	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#14524088	2
#22573844	2
C₂×#16864040	2
C₂×D₄×C₂²⋊D₆₇	2
C₂×#16863963	2
C₂×#16863955	2
C₂×#16863907	2
C₂²×#14524012	2
C₂×#16863871	2
C₂⁴×D₄×C₆₇	2
C₂×#3484	67

Subgroups — C2×#22573844 #31763714

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22573844 #31763714