Subgroups — C₆₇×#2703 #22557134

Order 8576.

612 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#123×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#121×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	#400×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
4	#397×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
5	#394×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
6	#392×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
7	#392×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
8	#392×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
9	#390×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
10	#388×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
11	#388×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
12	#386×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
13	#386×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
14	#386×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
15	#380×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×D₄×C₆₇	C₂²	1	1	yes	characteristic
17	C₂²×D₄×C₆₇	C₂²	1	1	yes	characteristic
18	C₂²×D₄×C₆₇	C₂²	1	1	yes	characteristic
19	C₂²×D₄×C₆₇	C₂²	1	1	yes	characteristic
20	C₂²×D₄×C₆₇	C₂²	1	1	yes	characteristic
21	C₂²×D₄×C₆₇	C₂²	1	1	yes	characteristic
22	C₂³×C₄×C₆₇	C₂²	1	1	yes	characteristic
23	C₂³×C₄×C₆₇	C₂²	1	1	yes	characteristic
24	#123×C₆₇	—	2	4	no	—
25	#121×C₆₇	—	2	4	no	—
26	C₂×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
27	C₂×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
28	C₂×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
29	C₂×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
30	C₂×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
31	C₂×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
32	C₂×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
33	C₂×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
34	C₂×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
35	C₂×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
36	C₂×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
37	C₂×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
38	C₂×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
39	C₂×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
40	C₂×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
41	C₂×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
42	C₂×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
43	C₂×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
44	C₂×C₄²×C₆₇	C₂²	1	1	yes	characteristic
45	#95×C₆₇	C₂²	1	1	yes	characteristic
46	#95×C₆₇	C₂²	1	1	yes	characteristic
47	#95×C₆₇	C₂²	1	1	yes	characteristic
48	#95×C₆₇	C₂²	1	1	yes	characteristic
49	#95×C₆₇	C₂²	1	1	yes	characteristic
50	#95×C₆₇	C₂²	1	1	yes	characteristic
51	#95×C₆₇	C₂²	1	1	yes	characteristic
52	#95×C₆₇	C₂²	1	1	yes	characteristic
53	C₂⁴×C₆₇	C₂³	1	1	yes	characteristic
54	C₂⁴×C₆₇	C₂³	1	1	yes	characteristic
55	C₂⁴×C₆₇	C₂³	1	1	yes	characteristic
56	C₂⁴×C₆₇	C₂³	1	1	yes	characteristic
57	C₂×D₄×C₆₇	—	2	2	no	—
58	C₂×D₄×C₆₇	—	2	2	no	—
59	C₂×D₄×C₆₇	—	2	2	no	—
60	C₂×D₄×C₆₇	—	2	2	no	—
61	C₂×D₄×C₆₇	—	2	2	no	—
62	C₂×D₄×C₆₇	—	2	2	no	—
63	C₂×D₄×C₆₇	—	2	2	no	—
64	C₂×D₄×C₆₇	—	2	2	no	—
65	C₂×D₄×C₆₇	—	4	1	no	—
66	C₂×D₄×C₆₇	—	4	1	no	—
67	C₂×D₄×C₆₇	—	4	1	no	—
68	C₂×D₄×C₆₇	—	4	1	no	—
69	C₂×D₄×C₆₇	—	4	1	no	—
70	C₂×D₄×C₆₇	—	4	1	no	—
71	C₂×D₄×C₆₇	—	4	1	no	—
72	C₂×D₄×C₆₇	—	4	1	no	—
73	C₂×D₄×C₆₇	—	4	1	no	—
74	C₂×D₄×C₆₇	—	4	1	no	—
75	C₂²×C₄×C₆₇	—	2	2	no	—
76	C₂²×C₄×C₆₇	—	2	2	no	—
77	C₂²×C₄×C₆₇	—	2	2	no	—
78	C₂²×C₄×C₆₇	—	4	1	no	—
79	C₂²×C₄×C₆₇	—	4	1	no	—
80	C₂²×C₄×C₆₇	—	4	1	no	—
81	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
82	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
83	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
84	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
85	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
86	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
87	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
88	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
89	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
90	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
91	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
92	C₄⋊C₄×C₆₇	—	2	2	no	—
93	C₄⋊C₄×C₆₇	—	2	2	no	—
94	C₄⋊C₄×C₆₇	—	2	2	no	—
95	C₄⋊C₄×C₆₇	—	4	1	no	—
96	C₂²⋊C₄×C₆₇	—	2	2	no	—
97	C₂²⋊C₄×C₆₇	—	2	2	no	—
98	C₂²⋊C₄×C₆₇	—	2	2	no	—
99	C₂²⋊C₄×C₆₇	—	2	2	no	—
100	C₂²⋊C₄×C₆₇	—	4	1	no	—
101	C₂²⋊C₄×C₆₇	—	4	1	no	—
102	C₂²⋊C₄×C₆₇	—	4	1	no	—
103	C₂²⋊C₄×C₆₇	—	4	1	no	—
104	C₂²⋊C₄×C₆₇	—	4	1	no	—
105	C₂²⋊C₄×C₆₇	—	4	1	no	—
106	C₂²⋊C₄×C₆₇	—	4	1	no	—
107	C₂²⋊C₄×C₆₇	—	4	1	no	—
108	C₂²⋊C₄×C₆₇	—	4	1	no	—
109	C₂²⋊C₄×C₆₇	D₄	1	4	yes	complemented
110	C₄²×C₆₇	—	4	1	no	—
111	C₂³×C₆₇	—	2	1	no	—
112	C₂³×C₆₇	—	2	1	no	—
113	C₂³×C₆₇	—	2	1	no	—
114	C₂³×C₆₇	—	2	1	no	—
115	C₂³×C₆₇	—	2	1	no	—
116	C₂³×C₆₇	—	2	1	no	—
117	C₂³×C₆₇	—	2	1	no	—
118	C₂³×C₆₇	—	2	1	no	—
119	C₂³×C₆₇	—	2	1	no	—
120	C₂³×C₆₇	—	2	1	no	—
121	C₂³×C₆₇	—	2	1	no	—
122	C₂³×C₆₇	—	2	1	no	—
123	C₂³×C₆₇	—	2	1	no	—
124	C₂³×C₆₇	—	2	1	no	—
125	C₂³×C₆₇	—	2	1	no	—
126	C₂³×C₆₇	—	2	1	no	—
127	C₂³×C₆₇	—	2	1	no	—
128	C₂³×C₆₇	—	2	1	no	—
129	C₂³×C₆₇	—	2	1	no	—
130	C₂³×C₆₇	—	2	1	no	—
131	C₂³×C₆₇	—	2	1	no	—
132	C₂³×C₆₇	—	2	1	no	—
133	C₂³×C₆₇	—	2	1	no	—
134	C₂³×C₆₇	—	2	1	no	—
135	C₂³×C₆₇	—	2	1	no	—
136	C₂³×C₆₇	—	2	1	no	—
137	C₂³×C₆₇	C₂×D₄	1	2	yes	—
138	C₂³×C₆₇	#41	1	2	yes	—
139	C₂³×C₆₇	C₂⁴	1	1	yes	characteristic
140	D₄×C₆₇	—	4	4	no	—
141	D₄×C₆₇	—	4	4	no	—
142	D₄×C₆₇	—	4	4	no	—
143	D₄×C₆₇	—	4	4	no	—
144	D₄×C₆₇	—	4	4	no	—
145	D₄×C₆₇	—	4	4	no	—
146	C₂×C₄×C₆₇	—	2	1	no	—
147	C₂×C₄×C₆₇	—	2	1	no	—
148	C₂×C₄×C₆₇	—	2	1	no	—
149	C₂×C₄×C₆₇	—	2	1	no	—
150	C₂×C₄×C₆₇	—	2	1	no	—
151	C₂×C₄×C₆₇	—	2	1	no	—
152	C₂×C₄×C₆₇	—	2	1	no	—
153	C₂×C₄×C₆₇	—	2	1	no	—
154	C₂×C₄×C₆₇	—	2	1	no	—
155	C₂×C₄×C₆₇	—	2	1	no	—
156	C₂×C₄×C₆₇	—	2	1	no	—
157	C₂×C₄×C₆₇	—	2	1	no	—
158	C₂×C₄×C₆₇	—	2	1	no	—
159	C₂×C₄×C₆₇	—	2	1	no	—
160	C₂×C₄×C₆₇	—	2	1	no	—
161	C₂×C₄×C₆₇	—	2	1	no	—
162	C₂×C₄×C₆₇	—	2	1	no	—
163	C₂×C₄×C₆₇	—	2	1	no	—
164	C₂×C₄×C₆₇	—	2	1	no	—
165	C₂×C₄×C₆₇	—	2	1	no	—
166	C₂×C₄×C₆₇	—	2	1	no	—
167	C₂×C₄×C₆₇	—	2	1	no	—
168	C₂×C₄×C₆₇	—	2	1	no	—
169	C₂×C₄×C₆₇	—	2	1	no	—
170	C₂×C₄×C₆₇	—	2	1	no	—
171	C₂×C₄×C₆₇	—	2	1	no	—
172	C₂×C₄×C₆₇	—	2	1	no	—
173	C₂×C₄×C₆₇	—	2	1	no	—
174	C₂×C₄×C₆₇	—	2	1	no	—
175	C₂×C₄×C₆₇	—	2	1	no	—
176	C₂×C₄×C₆₇	—	4	4	no	—
177	C₂×C₄×C₆₇	—	4	4	no	—
178	C₂×C₄×C₆₇	C₂×D₄	1	2	yes	—
179	C₂×C₄×C₆₇	C₂×D₄	1	2	yes	—
180	C₂×C₄×C₆₇	#41	1	2	yes	—
181	C₂²×C₆₇	—	2	2	no	—
182	C₂²×C₆₇	—	2	2	no	—
183	C₂²×C₆₇	—	2	2	no	—
184	C₂²×C₆₇	—	2	2	no	—
185	C₂²×C₆₇	—	2	2	no	—
186	C₂²×C₆₇	—	2	2	no	—
187	C₂²×C₆₇	—	4	1	no	—
188	C₂²×C₆₇	—	4	1	no	—
189	C₂²×C₆₇	—	4	1	no	—
190	C₂²×C₆₇	—	4	1	no	—
191	C₂²×C₆₇	—	4	1	no	—
192	C₂²×C₆₇	—	4	1	no	—
193	C₂²×C₆₇	—	4	1	no	—
194	C₂²×C₆₇	—	4	1	no	—
195	C₂²×C₆₇	—	4	1	no	—
196	C₂²×C₆₇	—	4	1	no	—
197	C₂²×C₆₇	—	4	1	no	—
198	C₂²×C₆₇	—	4	1	no	—
199	C₂²×C₆₇	—	4	1	no	—
200	C₂²×C₆₇	—	4	1	no	—
201	C₂²×C₆₇	—	4	1	no	—
202	C₂²×C₆₇	—	4	1	no	—
203	C₂²×C₆₇	—	4	1	no	—
204	C₂²×C₆₇	—	4	1	no	—
205	C₂²×C₆₇	—	4	1	no	—
206	C₂²×C₆₇	—	4	1	no	—
207	C₂²×C₆₇	—	4	1	no	—
208	C₂²×C₆₇	—	4	1	no	—
209	C₂²×C₆₇	C₂²×D₄	1	1	yes	characteristic
210	C₂²×C₆₇	C₂×#41	1	1	yes	characteristic
211	C₂²×C₆₇	C₂×#41	1	1	yes	characteristic
212	C₂²×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
213	C₂²×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
214	C₂²×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
215	C₂²×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
216	C₄×C₆₇	—	2	2	no	—
217	C₄×C₆₇	—	2	2	no	—
218	C₄×C₆₇	—	2	2	no	—
219	C₄×C₆₇	—	4	1	no	—
220	C₄×C₆₇	—	4	1	no	—
221	C₄×C₆₇	—	4	1	no	—
222	C₄×C₆₇	—	4	1	no	—
223	C₄×C₆₇	—	4	1	no	—
224	C₄×C₆₇	—	4	1	no	—
225	C₄×C₆₇	—	4	1	no	—
226	C₄×C₆₇	—	4	1	no	—
227	C₂×C₆₇	—	4	2	no	—
228	C₂×C₆₇	—	4	2	no	—
229	C₂×C₆₇	—	8	1	no	—
230	C₂×C₆₇	—	8	1	no	—
231	C₂×C₆₇	#535	1	1	yes	characteristic
232	C₂×C₆₇	#538	1	1	yes	characteristic
233	C₂×C₆₇	#540	1	1	yes	characteristic
234	C₂×C₆₇	#546	1	1	yes	characteristic
235	C₂×C₆₇	#546	1	1	yes	characteristic
236	C₂×C₆₇	#553	1	1	yes	characteristic
237	C₂×C₆₇	#560	1	1	yes	characteristic
238	#2703	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
239	C₆₇	#2703	1	1	yes	characteristic, direct product factor, Sylow
240	C₂×#123	C₂×C₆₇	1	1	yes	characteristic, complemented
241	C₂×#121	C₂×C₆₇	1	1	yes	characteristic, complemented
242	#400	C₂×C₆₇	1	1	yes	characteristic, complemented
243	#397	C₂×C₆₇	1	1	yes	characteristic, complemented
244	#394	C₂×C₆₇	1	1	yes	characteristic, complemented
245	#392	C₂×C₆₇	1	1	yes	characteristic, complemented
246	#392	C₂×C₆₇	1	1	yes	characteristic, complemented
247	#392	C₂×C₆₇	1	1	yes	characteristic, complemented
248	#390	C₂×C₆₇	1	1	yes	characteristic, complemented
249	#388	C₂×C₆₇	1	1	yes	characteristic, complemented
250	#388	C₂×C₆₇	1	1	yes	characteristic, complemented
251	#386	C₂×C₆₇	1	1	yes	characteristic, complemented
252	#386	C₂×C₆₇	1	1	yes	characteristic, complemented
253	#386	C₂×C₆₇	1	1	yes	characteristic, complemented
254	#380	C₂×C₆₇	1	1	yes	characteristic, complemented
255	C₂²×D₄	C₂²×C₆₇	1	1	yes	characteristic
256	C₂²×D₄	C₂²×C₆₇	1	1	yes	characteristic
257	C₂²×D₄	C₂²×C₆₇	1	1	yes	characteristic
258	C₂²×D₄	C₂²×C₆₇	1	1	yes	characteristic
259	C₂²×D₄	C₂²×C₆₇	1	1	yes	characteristic
260	C₂²×D₄	C₂²×C₆₇	1	1	yes	characteristic
261	C₂³×C₄	C₂²×C₆₇	1	1	yes	characteristic
262	C₂³×C₄	C₂²×C₆₇	1	1	yes	characteristic
263	#123	—	2	4	no	—
264	#121	—	2	4	no	—
265	C₂×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
266	C₂×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
267	C₂×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
268	C₂×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
269	C₂×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
270	C₂×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
271	C₂×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
272	C₂×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
273	C₂×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
274	C₂×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
275	C₂×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
276	C₂×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
277	C₂×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
278	C₂×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
279	C₂×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
280	C₂×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
281	C₂×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
282	C₂×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
283	C₂×C₄²	C₂²×C₆₇	1	1	yes	characteristic
284	#95	C₂²×C₆₇	1	1	yes	characteristic
285	#95	C₂²×C₆₇	1	1	yes	characteristic
286	#95	C₂²×C₆₇	1	1	yes	characteristic
287	#95	C₂²×C₆₇	1	1	yes	characteristic
288	#95	C₂²×C₆₇	1	1	yes	characteristic
289	#95	C₂²×C₆₇	1	1	yes	characteristic
290	#95	C₂²×C₆₇	1	1	yes	characteristic
291	#95	C₂²×C₆₇	1	1	yes	characteristic
292	C₂⁴	C₂³×C₆₇	1	1	yes	characteristic
293	C₂⁴	C₂³×C₆₇	1	1	yes	characteristic
294	C₂⁴	C₂³×C₆₇	1	1	yes	characteristic
295	C₂⁴	C₂³×C₆₇	1	1	yes	characteristic
296	C₂×D₄	—	2	2	no	—
297	C₂×D₄	—	2	2	no	—
298	C₂×D₄	—	2	2	no	—
299	C₂×D₄	—	2	2	no	—
300	C₂×D₄	—	2	2	no	—
301	C₂×D₄	—	2	2	no	—
302	C₂×D₄	—	2	2	no	—
303	C₂×D₄	—	2	2	no	—
304	C₂×D₄	—	4	1	no	—
305	C₂×D₄	—	4	1	no	—
306	C₂×D₄	—	4	1	no	—
307	C₂×D₄	—	4	1	no	—
308	C₂×D₄	—	4	1	no	—
309	C₂×D₄	—	4	1	no	—
310	C₂×D₄	—	4	1	no	—
311	C₂×D₄	—	4	1	no	—
312	C₂×D₄	—	4	1	no	—
313	C₂×D₄	—	4	1	no	—
314	C₂²×C₄	—	2	2	no	—
315	C₂²×C₄	—	2	2	no	—
316	C₂²×C₄	—	2	2	no	—
317	C₂²×C₄	—	4	1	no	—
318	C₂²×C₄	—	4	1	no	—
319	C₂²×C₄	—	4	1	no	—
320	C₂²×C₄	C₂³×C₆₇	1	1	yes	characteristic
321	C₂²×C₄	C₂³×C₆₇	1	1	yes	characteristic
322	C₂²×C₄	C₂³×C₆₇	1	1	yes	characteristic
323	C₂²×C₄	C₂³×C₆₇	1	1	yes	characteristic
324	C₂²×C₄	C₂³×C₆₇	1	1	yes	characteristic
325	C₂²×C₄	C₂³×C₆₇	1	1	yes	characteristic
326	C₂²×C₄	C₂³×C₆₇	1	1	yes	characteristic
327	C₂²×C₄	C₂³×C₆₇	1	1	yes	characteristic
328	C₂²×C₄	C₂³×C₆₇	1	1	yes	characteristic
329	C₂²×C₄	C₂³×C₆₇	1	1	yes	characteristic
330	C₂²×C₄	C₂³×C₆₇	1	1	yes	characteristic
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	2	2	no	—
333	C₄⋊C₄	—	2	2	no	—
334	C₄⋊C₄	—	4	1	no	—
335	C₂²⋊C₄	—	2	2	no	—
336	C₂²⋊C₄	—	2	2	no	—
337	C₂²⋊C₄	—	2	2	no	—
338	C₂²⋊C₄	—	2	2	no	—
339	C₂²⋊C₄	—	4	1	no	—
340	C₂²⋊C₄	—	4	1	no	—
341	C₂²⋊C₄	—	4	1	no	—
342	C₂²⋊C₄	—	4	1	no	—
343	C₂²⋊C₄	—	4	1	no	—
344	C₂²⋊C₄	—	4	1	no	—
345	C₂²⋊C₄	—	4	1	no	—
346	C₂²⋊C₄	—	4	1	no	—
347	C₂²⋊C₄	—	4	1	no	—
348	C₂²⋊C₄	D₄×C₆₇	1	4	yes	complemented
349	C₄²	—	4	1	no	—
350	C₂³	—	2	1	no	—
351	C₂³	—	2	1	no	—
352	C₂³	—	2	1	no	—
353	C₂³	—	2	1	no	—
354	C₂³	—	2	1	no	—
355	C₂³	—	2	1	no	—
356	C₂³	—	2	1	no	—
357	C₂³	—	2	1	no	—
358	C₂³	—	2	1	no	—
359	C₂³	—	2	1	no	—
360	C₂³	—	2	1	no	—
361	C₂³	—	2	1	no	—
362	C₂³	—	2	1	no	—
363	C₂³	—	2	1	no	—
364	C₂³	—	2	1	no	—
365	C₂³	—	2	1	no	—
366	C₂³	—	2	1	no	—
367	C₂³	—	2	1	no	—
368	C₂³	—	2	1	no	—
369	C₂³	—	2	1	no	—
370	C₂³	—	2	1	no	—
371	C₂³	—	2	1	no	—
372	C₂³	—	2	1	no	—
373	C₂³	—	2	1	no	—
374	C₂³	—	2	1	no	—
375	C₂³	—	2	1	no	—
376	C₂³	C₂×D₄×C₆₇	1	2	yes	—
377	C₂³	#41×C₆₇	1	2	yes	—
378	C₂³	C₂⁴×C₆₇	1	1	yes	characteristic
379	D₄	—	4	4	no	—
380	D₄	—	4	4	no	—
381	D₄	—	4	4	no	—
382	D₄	—	4	4	no	—
383	D₄	—	4	4	no	—
384	D₄	—	4	4	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	4	4	no	—
416	C₂×C₄	—	4	4	no	—
417	C₂×C₄	C₂×D₄×C₆₇	1	2	yes	—
418	C₂×C₄	C₂×D₄×C₆₇	1	2	yes	—
419	C₂×C₄	#41×C₆₇	1	2	yes	—
420	C₂²	—	2	2	no	—
421	C₂²	—	2	2	no	—
422	C₂²	—	2	2	no	—
423	C₂²	—	2	2	no	—
424	C₂²	—	2	2	no	—
425	C₂²	—	2	2	no	—
426	C₂²	—	4	1	no	—
427	C₂²	—	4	1	no	—
428	C₂²	—	4	1	no	—
429	C₂²	—	4	1	no	—
430	C₂²	—	4	1	no	—
431	C₂²	—	4	1	no	—
432	C₂²	—	4	1	no	—
433	C₂²	—	4	1	no	—
434	C₂²	—	4	1	no	—
435	C₂²	—	4	1	no	—
436	C₂²	—	4	1	no	—
437	C₂²	—	4	1	no	—
438	C₂²	—	4	1	no	—
439	C₂²	—	4	1	no	—
440	C₂²	—	4	1	no	—
441	C₂²	—	4	1	no	—
442	C₂²	—	4	1	no	—
443	C₂²	—	4	1	no	—
444	C₂²	—	4	1	no	—
445	C₂²	—	4	1	no	—
446	C₂²	—	4	1	no	—
447	C₂²	—	4	1	no	—
448	C₂²	C₂²×D₄×C₆₇	1	1	yes	characteristic
449	C₂²	C₂×#41×C₆₇	1	1	yes	characteristic
450	C₂²	C₂×#41×C₆₇	1	1	yes	characteristic
451	C₂²	H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
452	C₂²	H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
453	C₂²	H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
454	C₂²	H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
455	C₄	—	2	2	no	—
456	C₄	—	2	2	no	—
457	C₄	—	2	2	no	—
458	C₄	—	4	1	no	—
459	C₄	—	4	1	no	—
460	C₄	—	4	1	no	—
461	C₄	—	4	1	no	—
462	C₄	—	4	1	no	—
463	C₄	—	4	1	no	—
464	C₄	—	4	1	no	—
465	C₄	—	4	1	no	—
466	C₂	—	4	2	no	—
467	C₂	—	4	2	no	—
468	C₂	—	8	1	no	—
469	C₂	—	8	1	no	—
470	C₂	#535×C₆₇	1	1	yes	characteristic
471	C₂	#538×C₆₇	1	1	yes	characteristic
472	C₂	#540×C₆₇	1	1	yes	characteristic
473	C₂	#546×C₆₇	1	1	yes	characteristic
474	C₂	#546×C₆₇	1	1	yes	characteristic
475	C₂	#553×C₆₇	1	1	yes	characteristic
476	C₂	#560×C₆₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₆₇
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#123×C₆₇	C₂	semidirect
2. C₂×#121×C₆₇	C₂	semidirect
3. #400×C₆₇	C₂	semidirect
4. #397×C₆₇	C₂	semidirect
5. #394×C₆₇	C₂	semidirect
6. #392×C₆₇	C₂	semidirect
7. #392×C₆₇	C₂	semidirect
8. #392×C₆₇	C₂	semidirect
9. #390×C₆₇	C₂	semidirect
10. #388×C₆₇	C₂	semidirect
11. #388×C₆₇	C₂	semidirect
12. #386×C₆₇	C₂	semidirect
13. #386×C₆₇	C₂	semidirect
14. #386×C₆₇	C₂	semidirect
15. #380×C₆₇	C₂	semidirect
109. C₂²⋊C₄×C₆₇	D₄	semidirect
238. #2703	C₆₇	direct (N × H)
239. C₆₇	#2703	direct (N × H)
240. C₂×#123	C₂×C₆₇	semidirect
241. C₂×#121	C₂×C₆₇	semidirect
242. #400	C₂×C₆₇	semidirect
243. #397	C₂×C₆₇	semidirect
244. #394	C₂×C₆₇	semidirect
245. #392	C₂×C₆₇	semidirect
246. #392	C₂×C₆₇	semidirect
247. #392	C₂×C₆₇	semidirect
248. #390	C₂×C₆₇	semidirect
249. #388	C₂×C₆₇	semidirect
250. #388	C₂×C₆₇	semidirect
251. #386	C₂×C₆₇	semidirect
252. #386	C₂×C₆₇	semidirect
253. #386	C₂×C₆₇	semidirect
254. #380	C₂×C₆₇	semidirect
348. C₂²⋊C₄	D₄×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#123×C₆₇	2
C₂×#121×C₆₇	2
#400×C₆₇	2
#397×C₆₇	2
#394×C₆₇	2
#392×C₆₇	2
#390×C₆₇	2
#388×C₆₇	2
#386×C₆₇	2
#380×C₆₇	2
#2703	67

Subgroups — C67×#2703 #22557134

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#2703 #22557134