Subgroups — C₂×C₆₇×#2826 #30715906

Order 17152.

2542 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#2826	C₂	1	16	yes	maximal, direct product factor
2	C₂×#400×C₆₇	C₂	1	2	yes	maximal, complemented
3	C₂×#399×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#397×C₆₇	C₂	1	2	yes	maximal, complemented
5	C₂×#396×C₆₇	C₂	1	2	yes	maximal, complemented
6	C₂×#394×C₆₇	C₂	1	2	yes	maximal, complemented
7	C₂×#394×C₆₇	C₂	1	2	yes	maximal, complemented
8	C₂×#392×C₆₇	C₂	1	1	yes	maximal, characteristic
9	C₂×#386×C₆₇	C₂	1	2	yes	maximal, complemented
10	C₂×#385×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂³×D₄×C₆₇	C₂²	1	2	yes	—
12	C₂³×D₄×C₆₇	C₂²	1	1	yes	characteristic
13	C₂⁴×C₄×C₆₇	C₂²	1	1	yes	characteristic
14	C₂²×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
15	C₂²×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
16	C₂²×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
17	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
18	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
19	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
20	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
21	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
22	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
23	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
24	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
25	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
26	#400×C₆₇	C₂²	1	16	yes	complemented
27	#399×C₆₇	C₂²	1	8	yes	complemented
28	#397×C₆₇	C₂²	1	16	yes	complemented
29	#396×C₆₇	C₂²	1	16	yes	complemented
30	#394×C₆₇	C₂²	1	16	yes	complemented
31	#394×C₆₇	C₂²	1	16	yes	complemented
32	#392×C₆₇	C₂²	1	8	yes	—
33	#386×C₆₇	C₂²	1	16	yes	complemented
34	#385×C₆₇	C₂²	1	8	yes	complemented
35	C₂×#95×C₆₇	C₂²	1	2	yes	—
36	C₂×#95×C₆₇	C₂²	1	2	yes	—
37	C₂×#95×C₆₇	C₂²	1	2	yes	—
38	C₂×#95×C₆₇	C₂²	1	1	yes	characteristic
39	C₂×#95×C₆₇	C₂²	1	2	yes	—
40	C₂×#95×C₆₇	C₂²	1	1	yes	characteristic
41	C₂⁵×C₆₇	C₂³	1	2	yes	—
42	C₂⁵×C₆₇	C₂³	1	1	yes	characteristic
43	C₂²×D₄×C₆₇	—	2	8	no	—
44	C₂²×D₄×C₆₇	—	4	4	no	—
45	C₂²×D₄×C₆₇	—	4	2	no	—
46	C₂²×D₄×C₆₇	—	4	4	no	—
47	C₂²×D₄×C₆₇	—	4	4	no	—
48	C₂²×D₄×C₆₇	C₂³	1	8	yes	—
49	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
50	C₂³×C₄×C₆₇	—	4	2	no	—
51	C₂³×C₄×C₆₇	—	4	4	no	—
52	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
53	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
54	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
55	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
56	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
57	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
58	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
59	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
60	C₂×C₄⋊C₄×C₆₇	—	4	2	no	—
61	C₂×C₄⋊C₄×C₆₇	—	4	4	no	—
62	C₂×C₄⋊C₄×C₆₇	—	4	4	no	—
63	C₂×C₄⋊C₄×C₆₇	—	4	4	no	—
64	C₂×C₄⋊C₄×C₆₇	C₂³	1	8	yes	—
65	C₂×C₄⋊C₄×C₆₇	C₂³	1	8	yes	—
66	C₂×C₄⋊C₄×C₆₇	C₂³	1	8	yes	—
67	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
68	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
69	C₂×C₂²⋊C₄×C₆₇	—	4	4	no	—
70	C₂×C₂²⋊C₄×C₆₇	—	4	4	no	—
71	C₂×C₂²⋊C₄×C₆₇	—	4	4	no	—
72	C₂×C₂²⋊C₄×C₆₇	—	4	4	no	—
73	C₂×C₂²⋊C₄×C₆₇	—	4	4	no	—
74	C₂×C₂²⋊C₄×C₆₇	—	4	2	no	—
75	C₂×C₂²⋊C₄×C₆₇	—	4	4	no	—
76	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
77	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
78	C₂×C₂²⋊C₄×C₆₇	C₂³	1	8	yes	—
79	C₂×C₂²⋊C₄×C₆₇	C₂³	1	8	yes	—
80	C₂×C₂²⋊C₄×C₆₇	C₂³	1	8	yes	—
81	C₂×C₂²⋊C₄×C₆₇	C₂³	1	8	yes	—
82	C₂×C₂²⋊C₄×C₆₇	C₂³	1	8	yes	—
83	C₂×C₂²⋊C₄×C₆₇	C₂³	1	8	yes	—
84	#95×C₆₇	C₂³	1	8	yes	—
85	#95×C₆₇	C₂³	1	8	yes	—
86	#95×C₆₇	C₂³	1	8	yes	—
87	#95×C₆₇	C₂³	1	4	yes	—
88	#95×C₆₇	C₂³	1	8	yes	—
89	#95×C₆₇	C₂³	1	4	yes	—
90	C₂⁴×C₆₇	—	2	2	no	—
91	C₂⁴×C₆₇	—	2	4	no	—
92	C₂⁴×C₆₇	—	2	4	no	—
93	C₂⁴×C₆₇	—	2	2	no	—
94	C₂⁴×C₆₇	—	2	4	no	—
95	C₂⁴×C₆₇	—	2	4	no	—
96	C₂⁴×C₆₇	—	2	4	no	—
97	C₂⁴×C₆₇	—	2	4	no	—
98	C₂⁴×C₆₇	—	2	4	no	—
99	C₂⁴×C₆₇	—	2	4	no	—
100	C₂⁴×C₆₇	—	2	4	no	—
101	C₂⁴×C₆₇	#41	1	4	yes	—
102	C₂⁴×C₆₇	C₂⁴	1	4	yes	—
103	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
104	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
105	C₂×D₄×C₆₇	—	2	16	no	—
106	C₂×D₄×C₆₇	—	4	8	no	—
107	C₂×D₄×C₆₇	—	4	4	no	—
108	C₂×D₄×C₆₇	—	4	8	no	—
109	C₂×D₄×C₆₇	—	4	8	no	—
110	C₂×D₄×C₆₇	—	4	32	no	—
111	C₂×D₄×C₆₇	—	4	16	no	—
112	C₂²×C₄×C₆₇	—	2	4	no	—
113	C₂²×C₄×C₆₇	—	2	4	no	—
114	C₂²×C₄×C₆₇	—	2	4	no	—
115	C₂²×C₄×C₆₇	—	2	4	no	—
116	C₂²×C₄×C₆₇	—	2	4	no	—
117	C₂²×C₄×C₆₇	—	2	4	no	—
118	C₂²×C₄×C₆₇	—	2	4	no	—
119	C₂²×C₄×C₆₇	—	2	4	no	—
120	C₂²×C₄×C₆₇	—	2	2	no	—
121	C₂²×C₄×C₆₇	—	2	4	no	—
122	C₂²×C₄×C₆₇	—	2	4	no	—
123	C₂²×C₄×C₆₇	—	2	4	no	—
124	C₂²×C₄×C₆₇	—	2	4	no	—
125	C₂²×C₄×C₆₇	—	2	2	no	—
126	C₂²×C₄×C₆₇	—	2	4	no	—
127	C₂²×C₄×C₆₇	—	2	4	no	—
128	C₂²×C₄×C₆₇	—	2	4	no	—
129	C₂²×C₄×C₆₇	—	2	4	no	—
130	C₂²×C₄×C₆₇	—	2	4	no	—
131	C₂²×C₄×C₆₇	—	4	4	no	—
132	C₂²×C₄×C₆₇	—	4	8	no	—
133	C₂²×C₄×C₆₇	—	4	16	no	—
134	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
135	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
136	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
137	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
138	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
139	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
140	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
141	C₄⋊C₄×C₆₇	—	4	4	no	—
142	C₄⋊C₄×C₆₇	—	4	8	no	—
143	C₄⋊C₄×C₆₇	—	4	8	no	—
144	C₄⋊C₄×C₆₇	—	4	8	no	—
145	C₂²⋊C₄×C₆₇	—	2	8	no	—
146	C₂²⋊C₄×C₆₇	—	4	8	no	—
147	C₂²⋊C₄×C₆₇	—	4	8	no	—
148	C₂²⋊C₄×C₆₇	—	4	8	no	—
149	C₂²⋊C₄×C₆₇	—	4	8	no	—
150	C₂²⋊C₄×C₆₇	—	4	8	no	—
151	C₂²⋊C₄×C₆₇	—	4	4	no	—
152	C₂²⋊C₄×C₆₇	—	4	8	no	—
153	C₂³×C₆₇	—	2	16	no	—
154	C₂³×C₆₇	—	2	8	no	—
155	C₂³×C₆₇	—	2	2	no	—
156	C₂³×C₆₇	—	2	4	no	—
157	C₂³×C₆₇	—	2	4	no	—
158	C₂³×C₆₇	—	2	2	no	—
159	C₂³×C₆₇	—	2	4	no	—
160	C₂³×C₆₇	—	2	4	no	—
161	C₂³×C₆₇	—	2	4	no	—
162	C₂³×C₆₇	—	2	4	no	—
163	C₂³×C₆₇	—	2	4	no	—
164	C₂³×C₆₇	—	2	4	no	—
165	C₂³×C₆₇	—	2	4	no	—
166	C₂³×C₆₇	—	4	4	no	—
167	C₂³×C₆₇	—	4	4	no	—
168	C₂³×C₆₇	—	4	8	no	—
169	C₂³×C₆₇	—	4	8	no	—
170	C₂³×C₆₇	—	4	8	no	—
171	C₂³×C₆₇	—	4	8	no	—
172	C₂³×C₆₇	—	4	8	no	—
173	C₂³×C₆₇	—	4	8	no	—
174	C₂³×C₆₇	—	4	8	no	—
175	C₂³×C₆₇	—	4	8	no	—
176	C₂³×C₆₇	C₂×#41	1	4	yes	—
177	C₂³×C₆₇	C₂×#41	1	2	yes	—
178	C₂³×C₆₇	H(5,𝔽₂)	1	4	yes	—
179	C₂³×C₆₇	H(5,𝔽₂)	1	4	yes	—
180	C₂³×C₆₇	H(5,𝔽₂)	1	2	yes	—
181	C₂³×C₆₇	2₋¹⁺⁴	1	2	yes	—
182	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
183	D₄×C₆₇	—	4	32	no	—
184	D₄×C₆₇	—	4	16	no	—
185	C₂×C₄×C₆₇	—	2	4	no	—
186	C₂×C₄×C₆₇	—	2	4	no	—
187	C₂×C₄×C₆₇	—	2	4	no	—
188	C₂×C₄×C₆₇	—	2	4	no	—
189	C₂×C₄×C₆₇	—	2	4	no	—
190	C₂×C₄×C₆₇	—	2	4	no	—
191	C₂×C₄×C₆₇	—	2	4	no	—
192	C₂×C₄×C₆₇	—	2	4	no	—
193	C₂×C₄×C₆₇	—	2	2	no	—
194	C₂×C₄×C₆₇	—	2	4	no	—
195	C₂×C₄×C₆₇	—	2	4	no	—
196	C₂×C₄×C₆₇	—	2	4	no	—
197	C₂×C₄×C₆₇	—	2	4	no	—
198	C₂×C₄×C₆₇	—	2	2	no	—
199	C₂×C₄×C₆₇	—	2	4	no	—
200	C₂×C₄×C₆₇	—	2	4	no	—
201	C₂×C₄×C₆₇	—	2	4	no	—
202	C₂×C₄×C₆₇	—	2	4	no	—
203	C₂×C₄×C₆₇	—	2	4	no	—
204	C₂×C₄×C₆₇	—	4	16	no	—
205	C₂×C₄×C₆₇	—	4	8	no	—
206	C₂×C₄×C₆₇	—	4	8	no	—
207	C₂×C₄×C₆₇	—	4	8	no	—
208	C₂×C₄×C₆₇	—	4	4	no	—
209	C₂×C₄×C₆₇	—	4	8	no	—
210	C₂×C₄×C₆₇	—	4	4	no	—
211	C₂×C₄×C₆₇	—	4	8	no	—
212	C₂²×C₆₇	—	2	8	no	—
213	C₂²×C₆₇	—	2	4	no	—
214	C₂²×C₆₇	—	4	16	no	—
215	C₂²×C₆₇	—	4	2	no	—
216	C₂²×C₆₇	—	4	2	no	—
217	C₂²×C₆₇	—	4	4	no	—
218	C₂²×C₆₇	—	4	4	no	—
219	C₂²×C₆₇	—	4	4	no	—
220	C₂²×C₆₇	—	4	4	no	—
221	C₂²×C₆₇	—	4	4	no	—
222	C₂²×C₆₇	—	4	4	no	—
223	C₂²×C₆₇	—	4	4	no	—
224	C₂²×C₆₇	—	4	4	no	—
225	C₂²×C₆₇	—	8	16	no	—
226	C₂²×C₆₇	#538	1	8	yes	—
227	C₂²×C₆₇	#539	1	4	yes	—
228	C₂²×C₆₇	#560	1	4	yes	—
229	C₂²×C₆₇	#560	1	4	yes	—
230	C₂²×C₆₇	#562	1	8	yes	—
231	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
232	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
233	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
234	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
235	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
236	C₄×C₆₇	—	4	4	no	—
237	C₄×C₆₇	—	4	4	no	—
238	C₄×C₆₇	—	4	4	no	—
239	C₄×C₆₇	—	4	2	no	—
240	C₄×C₆₇	—	4	4	no	—
241	C₄×C₆₇	—	4	2	no	—
242	C₄×C₆₇	—	4	4	no	—
243	C₂×#2826	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
244	C₂×C₆₇	—	4	4	no	—
245	C₂×C₆₇	—	8	4	no	—
246	C₂×C₆₇	#2826	1	8	yes	direct product factor
247	C₂×C₆₇	C₂×#538	1	2	yes	—
248	C₂×C₆₇	C₂×#539	1	1	yes	characteristic
249	C₂×C₆₇	C₂×#560	1	1	yes	characteristic
250	C₂×C₆₇	C₂×#560	1	1	yes	characteristic
251	C₂×C₆₇	C₂×#562	1	2	yes	—
252	#2826	C₂×C₆₇	1	16	yes	direct product factor
253	C₂×#400	C₂×C₆₇	1	2	yes	complemented
254	C₂×#399	C₂×C₆₇	1	1	yes	characteristic, complemented
255	C₂×#397	C₂×C₆₇	1	2	yes	complemented
256	C₂×#396	C₂×C₆₇	1	2	yes	complemented
257	C₂×#394	C₂×C₆₇	1	2	yes	complemented
258	C₂×#394	C₂×C₆₇	1	2	yes	complemented
259	C₂×#392	C₂×C₆₇	1	1	yes	characteristic
260	C₂×#386	C₂×C₆₇	1	2	yes	complemented
261	C₂×#385	C₂×C₆₇	1	1	yes	characteristic, complemented
262	C₆₇	C₂×#2826	1	1	yes	characteristic, direct product factor, Sylow
263	C₂³×D₄	C₂²×C₆₇	1	2	yes	—
264	C₂³×D₄	C₂²×C₆₇	1	1	yes	characteristic
265	C₂⁴×C₄	C₂²×C₆₇	1	1	yes	characteristic
266	C₂²×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
267	C₂²×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
268	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
269	C₂²×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
270	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
271	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
272	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
273	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
274	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
275	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
276	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
277	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
278	#400	C₂²×C₆₇	1	16	yes	complemented
279	#399	C₂²×C₆₇	1	8	yes	complemented
280	#397	C₂²×C₆₇	1	16	yes	complemented
281	#396	C₂²×C₆₇	1	16	yes	complemented
282	#394	C₂²×C₆₇	1	16	yes	complemented
283	#394	C₂²×C₆₇	1	16	yes	complemented
284	#392	C₂²×C₆₇	1	8	yes	—
285	#386	C₂²×C₆₇	1	16	yes	complemented
286	#385	C₂²×C₆₇	1	8	yes	complemented
287	C₂×#95	C₂²×C₆₇	1	1	yes	characteristic
288	C₂×#95	C₂²×C₆₇	1	2	yes	—
289	C₂×#95	C₂²×C₆₇	1	2	yes	—
290	C₂×#95	C₂²×C₆₇	1	2	yes	—
291	C₂×#95	C₂²×C₆₇	1	1	yes	characteristic
292	C₂×#95	C₂²×C₆₇	1	2	yes	—
293	C₂⁵	C₂³×C₆₇	1	2	yes	—
294	C₂⁵	C₂³×C₆₇	1	1	yes	characteristic
295	C₂²×D₄	—	2	8	no	—
296	C₂²×D₄	—	4	4	no	—
297	C₂²×D₄	—	4	2	no	—
298	C₂²×D₄	—	4	4	no	—
299	C₂²×D₄	—	4	4	no	—
300	C₂²×D₄	C₂³×C₆₇	1	8	yes	—
301	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
302	C₂³×C₄	—	4	2	no	—
303	C₂³×C₄	—	4	4	no	—
304	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
305	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
306	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
307	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
308	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
309	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
310	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
311	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
312	C₂×C₄⋊C₄	—	4	2	no	—
313	C₂×C₄⋊C₄	—	4	4	no	—
314	C₂×C₄⋊C₄	—	4	4	no	—
315	C₂×C₄⋊C₄	—	4	4	no	—
316	C₂×C₄⋊C₄	C₂³×C₆₇	1	8	yes	—
317	C₂×C₄⋊C₄	C₂³×C₆₇	1	8	yes	—
318	C₂×C₄⋊C₄	C₂³×C₆₇	1	8	yes	—
319	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
320	C₂×C₂²⋊C₄	—	2	4	no	—
321	C₂×C₂²⋊C₄	—	4	4	no	—
322	C₂×C₂²⋊C₄	—	4	4	no	—
323	C₂×C₂²⋊C₄	—	4	4	no	—
324	C₂×C₂²⋊C₄	—	4	4	no	—
325	C₂×C₂²⋊C₄	—	4	4	no	—
326	C₂×C₂²⋊C₄	—	4	2	no	—
327	C₂×C₂²⋊C₄	—	4	4	no	—
328	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
329	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
330	C₂×C₂²⋊C₄	C₂³×C₆₇	1	8	yes	—
331	C₂×C₂²⋊C₄	C₂³×C₆₇	1	8	yes	—
332	C₂×C₂²⋊C₄	C₂³×C₆₇	1	8	yes	—
333	C₂×C₂²⋊C₄	C₂³×C₆₇	1	8	yes	—
334	C₂×C₂²⋊C₄	C₂³×C₆₇	1	8	yes	—
335	C₂×C₂²⋊C₄	C₂³×C₆₇	1	8	yes	—
336	#95	C₂³×C₆₇	1	8	yes	—
337	#95	C₂³×C₆₇	1	8	yes	—
338	#95	C₂³×C₆₇	1	8	yes	—
339	#95	C₂³×C₆₇	1	4	yes	—
340	#95	C₂³×C₆₇	1	8	yes	—
341	#95	C₂³×C₆₇	1	4	yes	—
342	C₂⁴	—	2	2	no	—
343	C₂⁴	—	2	4	no	—
344	C₂⁴	—	2	4	no	—
345	C₂⁴	—	2	2	no	—
346	C₂⁴	—	2	4	no	—
347	C₂⁴	—	2	4	no	—
348	C₂⁴	—	2	4	no	—
349	C₂⁴	—	2	4	no	—
350	C₂⁴	—	2	4	no	—
351	C₂⁴	—	2	4	no	—
352	C₂⁴	—	2	4	no	—
353	C₂⁴	#41×C₆₇	1	4	yes	—
354	C₂⁴	C₂⁴×C₆₇	1	4	yes	—
355	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
356	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
357	C₂×D₄	—	2	16	no	—
358	C₂×D₄	—	4	8	no	—
359	C₂×D₄	—	4	4	no	—
360	C₂×D₄	—	4	8	no	—
361	C₂×D₄	—	4	8	no	—
362	C₂×D₄	—	4	32	no	—
363	C₂×D₄	—	4	16	no	—
364	C₂²×C₄	—	2	4	no	—
365	C₂²×C₄	—	2	4	no	—
366	C₂²×C₄	—	2	4	no	—
367	C₂²×C₄	—	2	4	no	—
368	C₂²×C₄	—	2	4	no	—
369	C₂²×C₄	—	2	4	no	—
370	C₂²×C₄	—	2	4	no	—
371	C₂²×C₄	—	2	4	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	2	4	no	—
374	C₂²×C₄	—	2	4	no	—
375	C₂²×C₄	—	2	4	no	—
376	C₂²×C₄	—	2	4	no	—
377	C₂²×C₄	—	2	2	no	—
378	C₂²×C₄	—	2	4	no	—
379	C₂²×C₄	—	2	4	no	—
380	C₂²×C₄	—	2	4	no	—
381	C₂²×C₄	—	2	4	no	—
382	C₂²×C₄	—	2	4	no	—
383	C₂²×C₄	—	4	4	no	—
384	C₂²×C₄	—	4	8	no	—
385	C₂²×C₄	—	4	16	no	—
386	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
387	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
388	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
389	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
390	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
391	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
392	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
393	C₄⋊C₄	—	4	4	no	—
394	C₄⋊C₄	—	4	8	no	—
395	C₄⋊C₄	—	4	8	no	—
396	C₄⋊C₄	—	4	8	no	—
397	C₂²⋊C₄	—	2	8	no	—
398	C₂²⋊C₄	—	4	8	no	—
399	C₂²⋊C₄	—	4	8	no	—
400	C₂²⋊C₄	—	4	8	no	—
401	C₂²⋊C₄	—	4	8	no	—
402	C₂²⋊C₄	—	4	8	no	—
403	C₂²⋊C₄	—	4	4	no	—
404	C₂²⋊C₄	—	4	8	no	—
405	C₂³	—	2	16	no	—
406	C₂³	—	2	8	no	—
407	C₂³	—	2	2	no	—
408	C₂³	—	2	4	no	—
409	C₂³	—	2	4	no	—
410	C₂³	—	2	2	no	—
411	C₂³	—	2	4	no	—
412	C₂³	—	2	4	no	—
413	C₂³	—	2	4	no	—
414	C₂³	—	2	4	no	—
415	C₂³	—	2	4	no	—
416	C₂³	—	2	4	no	—
417	C₂³	—	2	4	no	—
418	C₂³	—	4	4	no	—
419	C₂³	—	4	4	no	—
420	C₂³	—	4	8	no	—
421	C₂³	—	4	8	no	—
422	C₂³	—	4	8	no	—
423	C₂³	—	4	8	no	—
424	C₂³	—	4	8	no	—
425	C₂³	—	4	8	no	—
426	C₂³	—	4	8	no	—
427	C₂³	—	4	8	no	—
428	C₂³	C₂×#41×C₆₇	1	4	yes	—
429	C₂³	C₂×#41×C₆₇	1	2	yes	—
430	C₂³	H(5,𝔽₂)×C₆₇	1	4	yes	—
431	C₂³	H(5,𝔽₂)×C₆₇	1	4	yes	—
432	C₂³	H(5,𝔽₂)×C₆₇	1	2	yes	—
433	C₂³	2₋¹⁺⁴×C₆₇	1	2	yes	—
434	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
435	D₄	—	4	32	no	—
436	D₄	—	4	16	no	—
437	C₂×C₄	—	2	4	no	—
438	C₂×C₄	—	2	4	no	—
439	C₂×C₄	—	2	4	no	—
440	C₂×C₄	—	2	4	no	—
441	C₂×C₄	—	2	4	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	4	no	—
444	C₂×C₄	—	2	4	no	—
445	C₂×C₄	—	2	4	no	—
446	C₂×C₄	—	2	4	no	—
447	C₂×C₄	—	2	4	no	—
448	C₂×C₄	—	2	4	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	4	no	—
451	C₂×C₄	—	2	4	no	—
452	C₂×C₄	—	2	4	no	—
453	C₂×C₄	—	2	4	no	—
454	C₂×C₄	—	2	4	no	—
455	C₂×C₄	—	2	4	no	—
456	C₂×C₄	—	4	16	no	—
457	C₂×C₄	—	4	8	no	—
458	C₂×C₄	—	4	8	no	—
459	C₂×C₄	—	4	8	no	—
460	C₂×C₄	—	4	4	no	—
461	C₂×C₄	—	4	8	no	—
462	C₂×C₄	—	4	4	no	—
463	C₂×C₄	—	4	8	no	—
464	C₂²	—	2	8	no	—
465	C₂²	—	2	4	no	—
466	C₂²	—	4	2	no	—
467	C₂²	—	4	2	no	—
468	C₂²	—	4	4	no	—
469	C₂²	—	4	16	no	—
470	C₂²	—	4	4	no	—
471	C₂²	—	4	4	no	—
472	C₂²	—	4	4	no	—
473	C₂²	—	4	4	no	—
474	C₂²	—	4	4	no	—
475	C₂²	—	4	4	no	—
476	C₂²	—	4	4	no	—
477	C₂²	—	8	16	no	—
478	C₂²	#538×C₆₇	1	8	yes	—
479	C₂²	#539×C₆₇	1	4	yes	—
480	C₂²	#560×C₆₇	1	4	yes	—
481	C₂²	#560×C₆₇	1	4	yes	—
482	C₂²	#562×C₆₇	1	8	yes	—
483	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
484	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
485	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	2	yes	—
486	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	2	yes	—
487	C₂²	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
488	C₄	—	4	4	no	—
489	C₄	—	4	2	no	—
490	C₄	—	4	4	no	—
491	C₄	—	4	2	no	—
492	C₄	—	4	4	no	—
493	C₄	—	4	4	no	—
494	C₄	—	4	4	no	—
495	C₂	—	4	4	no	—
496	C₂	—	8	4	no	—
497	C₂	C₆₇×#2826	1	8	yes	direct product factor
498	C₂	C₂×#538×C₆₇	1	2	yes	—
499	C₂	C₂×#539×C₆₇	1	1	yes	characteristic
500	C₂	C₂×#560×C₆₇	1	1	yes	characteristic
501	C₂	C₂×#560×C₆₇	1	1	yes	characteristic
502	C₂	C₂×#562×C₆₇	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₆₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₇
prime radical	C₂×#392×C₆₇	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#2826	C₂	direct (N × H)
2. C₂×#400×C₆₇	C₂	semidirect
3. C₂×#399×C₆₇	C₂	semidirect
4. C₂×#397×C₆₇	C₂	semidirect
5. C₂×#396×C₆₇	C₂	semidirect
6. C₂×#394×C₆₇	C₂	semidirect
7. C₂×#394×C₆₇	C₂	semidirect
9. C₂×#386×C₆₇	C₂	semidirect
10. C₂×#385×C₆₇	C₂	semidirect
26. #400×C₆₇	C₂²	semidirect
27. #399×C₆₇	C₂²	semidirect
28. #397×C₆₇	C₂²	semidirect
29. #396×C₆₇	C₂²	semidirect
30. #394×C₆₇	C₂²	semidirect
31. #394×C₆₇	C₂²	semidirect
33. #386×C₆₇	C₂²	semidirect
34. #385×C₆₇	C₂²	semidirect
243. C₂×#2826	C₆₇	direct (N × H)
246. C₂×C₆₇	#2826	direct (N × H)
252. #2826	C₂×C₆₇	direct (N × H)
253. C₂×#400	C₂×C₆₇	semidirect
254. C₂×#399	C₂×C₆₇	semidirect
255. C₂×#397	C₂×C₆₇	semidirect
256. C₂×#396	C₂×C₆₇	semidirect
257. C₂×#394	C₂×C₆₇	semidirect
258. C₂×#394	C₂×C₆₇	semidirect
260. C₂×#386	C₂×C₆₇	semidirect
261. C₂×#385	C₂×C₆₇	semidirect
262. C₆₇	C₂×#2826	direct (N × H)
278. #400	C₂²×C₆₇	semidirect
279. #399	C₂²×C₆₇	semidirect
280. #397	C₂²×C₆₇	semidirect
281. #396	C₂²×C₆₇	semidirect
282. #394	C₂²×C₆₇	semidirect
283. #394	C₂²×C₆₇	semidirect
285. #386	C₂²×C₆₇	semidirect
286. #385	C₂²×C₆₇	semidirect
497. C₂	C₆₇×#2826	direct (N × H)

Maximal subgroups

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

subgroup	index
C₆₇×#2826	2
C₂×#400×C₆₇	2
C₂×#399×C₆₇	2
C₂×#397×C₆₇	2
C₂×#396×C₆₇	2
C₂×#394×C₆₇	2
C₂×#392×C₆₇	2
C₂×#386×C₆₇	2
C₂×#385×C₆₇	2
C₂×#2826	67

Subgroups — C2×C67×#2826 #30715906

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₇×#2826 #30715906