Subgroups — C₆₇×#11127 #30690378

Order 17152.

1002 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#108×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#418×C₆₇	C₂	1	1	yes	maximal, characteristic
3	C₂²×#102×C₆₇	C₂	1	1	yes	maximal, characteristic
4	C₂²×#100×C₆₇	C₂	1	1	yes	maximal, characteristic
5	C₂×#343×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#1736	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#1729	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂³×D₄×C₆₇	C₂²	1	1	yes	characteristic
9	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
10	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
11	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
12	C₂³×C₈×C₆₇	C₂²	1	1	yes	characteristic
13	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
14	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
15	C₂×#108×C₆₇	—	2	2	no	—
16	C₂×#108×C₆₇	—	2	2	no	—
17	C₂×#108×C₆₇	—	2	2	no	—
18	#418×C₆₇	—	2	2	no	—
19	#418×C₆₇	—	2	2	no	—
20	C₂×#102×C₆₇	—	2	2	no	—
21	C₂×#102×C₆₇	—	2	2	no	—
22	C₂×#102×C₆₇	—	2	2	no	—
23	C₂×#102×C₆₇	C₄	1	4	yes	complemented
24	C₂×#100×C₆₇	—	2	2	no	—
25	C₂×#100×C₆₇	—	2	2	no	—
26	C₂×#100×C₆₇	—	2	2	no	—
27	#343×C₆₇	—	2	2	no	—
28	#340×C₆₇	—	2	2	no	—
29	#336×C₆₇	—	2	2	no	—
30	C₂⁵×C₆₇	—	2	1	no	—
31	C₂²×D₄×C₆₇	—	2	1	no	—
32	C₂²×D₄×C₆₇	—	2	1	no	—
33	C₂²×D₄×C₆₇	—	2	1	no	—
34	C₂²×D₄×C₆₇	—	2	1	no	—
35	C₂²×D₄×C₆₇	—	2	1	no	—
36	C₂²×D₄×C₆₇	—	2	1	no	—
37	C₂²×D₄×C₆₇	—	2	1	no	—
38	C₂²×D₄×C₆₇	—	2	1	no	—
39	C₂²×D₄×C₆₇	—	2	1	no	—
40	C₂²×D₄×C₆₇	—	2	1	no	—
41	C₂²×D₄×C₆₇	—	2	1	no	—
42	C₂²×D₄×C₆₇	C₂×C₄	1	2	yes	—
43	C₂²×D₄×C₆₇	D₄	1	2	yes	—
44	C₂²×D₄×C₆₇	Q₈	1	2	yes	—
45	C₂³×C₄×C₆₇	—	2	1	no	—
46	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
47	C₂×M₁₆×C₆₇	—	2	1	no	—
48	C₂×M₁₆×C₆₇	—	2	1	no	—
49	C₂×M₁₆×C₆₇	—	2	1	no	—
50	C₂×M₁₆×C₆₇	—	2	1	no	—
51	C₂×M₁₆×C₆₇	—	2	1	no	—
52	C₂×M₁₆×C₆₇	—	2	1	no	—
53	C₂×M₁₆×C₆₇	—	2	1	no	—
54	C₂×M₁₆×C₆₇	—	2	1	no	—
55	C₂×M₁₆×C₆₇	—	2	1	no	—
56	C₂×M₁₆×C₆₇	—	2	1	no	—
57	C₂×M₁₆×C₆₇	—	2	1	no	—
58	C₂×M₁₆×C₆₇	—	2	1	no	—
59	C₂×M₁₆×C₆₇	—	2	1	no	—
60	C₂×M₁₆×C₆₇	—	2	1	no	—
61	C₂×M₁₆×C₆₇	—	2	1	no	—
62	C₂×M₁₆×C₆₇	D₄	1	2	yes	—
63	C₂×M₁₆×C₆₇	D₄	1	2	yes	—
64	C₂×M₁₆×C₆₇	D₄	1	2	yes	—
65	C₂²×C₈×C₆₇	—	2	1	no	—
66	C₂²×C₈×C₆₇	—	2	1	no	—
67	C₂²×C₈×C₆₇	—	2	1	no	—
68	C₂²×C₈×C₆₇	—	2	1	no	—
69	C₂²×C₈×C₆₇	—	2	1	no	—
70	C₂²×C₈×C₆₇	—	2	1	no	—
71	C₂²×C₈×C₆₇	—	2	1	no	—
72	C₂²×C₈×C₆₇	C₂×C₄	1	2	yes	—
73	C₂²×C₈×C₆₇	D₄	1	2	yes	—
74	C₂²×C₈×C₆₇	D₄	1	2	yes	—
75	#117×C₆₇	—	2	1	no	—
76	#117×C₆₇	—	2	1	no	—
77	#117×C₆₇	—	2	1	no	—
78	#117×C₆₇	—	2	1	no	—
79	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
80	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
81	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
82	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
83	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
84	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
85	C₂×C₄⋊C₄×C₆₇	D₄	1	2	yes	—
86	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
87	C₂×C₄²×C₆₇	—	2	1	no	—
88	#108×C₆₇	—	2	8	no	—
89	#102×C₆₇	—	2	8	no	—
90	#102×C₆₇	—	2	8	no	—
91	#100×C₆₇	—	2	8	no	—
92	C₂⁴×C₆₇	—	2	2	no	—
93	C₂⁴×C₆₇	—	2	2	no	—
94	C₂⁴×C₆₇	—	2	2	no	—
95	C₂⁴×C₆₇	—	4	1	no	—
96	C₂⁴×C₆₇	—	4	1	no	—
97	C₂⁴×C₆₇	—	4	1	no	—
98	C₂⁴×C₆₇	—	4	1	no	—
99	C₂⁴×C₆₇	—	8	2	no	—
100	C₂⁴×C₆₇	—	8	2	no	—
101	C₂⁴×C₆₇	#41	1	1	yes	characteristic
102	C₂×D₄×C₆₇	—	2	2	no	—
103	C₂×D₄×C₆₇	—	2	2	no	—
104	C₂×D₄×C₆₇	—	2	2	no	—
105	C₂×D₄×C₆₇	—	2	2	no	—
106	C₂×D₄×C₆₇	—	2	2	no	—
107	C₂×D₄×C₆₇	—	2	2	no	—
108	C₂×D₄×C₆₇	—	2	2	no	—
109	C₂×D₄×C₆₇	—	2	2	no	—
110	C₂×D₄×C₆₇	—	2	2	no	—
111	C₂×D₄×C₆₇	—	2	2	no	—
112	C₂×D₄×C₆₇	—	2	2	no	—
113	C₂×D₄×C₆₇	—	2	2	no	—
114	C₂×D₄×C₆₇	—	2	2	no	—
115	C₂×D₄×C₆₇	—	2	2	no	—
116	C₂×D₄×C₆₇	—	2	2	no	—
117	C₂×D₄×C₆₇	—	4	1	no	—
118	C₂×D₄×C₆₇	—	4	1	no	—
119	C₂×D₄×C₆₇	—	4	1	no	—
120	C₂×D₄×C₆₇	—	4	1	no	—
121	C₂×D₄×C₆₇	—	4	1	no	—
122	C₂×D₄×C₆₇	—	4	1	no	—
123	C₂×D₄×C₆₇	—	4	1	no	—
124	C₂×D₄×C₆₇	—	4	1	no	—
125	C₂×D₄×C₆₇	—	4	1	no	—
126	C₂×D₄×C₆₇	—	4	1	no	—
127	C₂×D₄×C₆₇	—	4	1	no	—
128	C₂×D₄×C₆₇	—	4	1	no	—
129	C₂×D₄×C₆₇	C₄⋊C₄	1	4	yes	—
130	C₂²×C₄×C₆₇	—	2	2	no	—
131	C₂²×C₄×C₆₇	—	2	2	no	—
132	C₂²×C₄×C₆₇	—	4	1	no	—
133	C₂²×C₄×C₆₇	—	4	1	no	—
134	C₂²×C₄×C₆₇	—	8	2	no	—
135	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
136	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₆₇	C₂×Q₈	1	1	yes	characteristic
144	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
145	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
146	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
147	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
148	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
149	M₁₆×C₆₇	—	2	2	no	—
150	M₁₆×C₆₇	—	2	2	no	—
151	M₁₆×C₆₇	—	2	2	no	—
152	M₁₆×C₆₇	—	2	2	no	—
153	M₁₆×C₆₇	—	2	2	no	—
154	M₁₆×C₆₇	—	2	2	no	—
155	M₁₆×C₆₇	—	4	1	no	—
156	M₁₆×C₆₇	—	4	1	no	—
157	M₁₆×C₆₇	—	4	1	no	—
158	M₁₆×C₆₇	—	4	1	no	—
159	M₁₆×C₆₇	—	4	1	no	—
160	M₁₆×C₆₇	—	4	1	no	—
161	C₂×C₈×C₆₇	—	2	2	no	—
162	C₂×C₈×C₆₇	—	2	2	no	—
163	C₂×C₈×C₆₇	—	2	2	no	—
164	C₂×C₈×C₆₇	—	2	2	no	—
165	C₂×C₈×C₆₇	—	2	2	no	—
166	C₂×C₈×C₆₇	—	2	2	no	—
167	C₂×C₈×C₆₇	—	2	2	no	—
168	C₂×C₈×C₆₇	—	2	2	no	—
169	C₂×C₈×C₆₇	—	2	2	no	—
170	C₂×C₈×C₆₇	—	4	1	no	—
171	C₂×C₈×C₆₇	—	4	1	no	—
172	C₂×C₈×C₆₇	—	4	1	no	—
173	C₂×C₈×C₆₇	—	4	1	no	—
174	C₂×C₈×C₆₇	—	4	1	no	—
175	C₂×C₈×C₆₇	—	4	1	no	—
176	C₂×C₈×C₆₇	C₂²⋊C₄	1	4	yes	—
177	C₄⋊C₄×C₆₇	—	2	2	no	—
178	C₄⋊C₄×C₆₇	—	2	2	no	—
179	C₄⋊C₄×C₆₇	—	2	2	no	—
180	C₄⋊C₄×C₆₇	—	2	2	no	—
181	C₄⋊C₄×C₆₇	—	4	1	no	—
182	C₄⋊C₄×C₆₇	—	4	1	no	—
183	C₂²⋊C₄×C₆₇	—	4	1	no	—
184	C₂²⋊C₄×C₆₇	—	4	1	no	—
185	C₄²×C₆₇	—	4	1	no	—
186	C₄²×C₆₇	—	4	1	no	—
187	C₂³×C₆₇	—	2	2	no	—
188	C₂³×C₆₇	—	2	2	no	—
189	C₂³×C₆₇	—	2	4	no	—
190	C₂³×C₆₇	—	4	2	no	—
191	C₂³×C₆₇	—	4	2	no	—
192	C₂³×C₆₇	—	4	2	no	—
193	C₂³×C₆₇	—	4	2	no	—
194	C₂³×C₆₇	—	4	2	no	—
195	C₂³×C₆₇	—	4	2	no	—
196	C₂³×C₆₇	—	8	4	no	—
197	C₂³×C₆₇	—	8	4	no	—
198	C₂³×C₆₇	—	8	2	no	—
199	C₂³×C₆₇	—	8	2	no	—
200	C₂³×C₆₇	—	8	4	no	—
201	C₂³×C₆₇	—	8	4	no	—
202	C₂³×C₆₇	—	8	2	no	—
203	C₂³×C₆₇	—	8	2	no	—
204	C₂³×C₆₇	—	8	2	no	—
205	C₂³×C₆₇	—	8	2	no	—
206	C₂³×C₆₇	C₄×D₄	1	1	yes	characteristic
207	C₂³×C₆₇	#121	1	1	yes	characteristic
208	C₂³×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
209	C₂³×C₆₇	#123	1	1	yes	characteristic
210	C₂³×C₆₇	#124	1	1	yes	characteristic
211	C₂³×C₆₇	#124	1	1	yes	characteristic
212	C₂³×C₆₇	#126	1	1	yes	characteristic
213	D₄×C₆₇	—	2	4	no	—
214	D₄×C₆₇	—	2	4	no	—
215	D₄×C₆₇	—	4	2	no	—
216	D₄×C₆₇	—	4	2	no	—
217	D₄×C₆₇	—	4	2	no	—
218	D₄×C₆₇	—	4	2	no	—
219	D₄×C₆₇	—	4	2	no	—
220	D₄×C₆₇	—	4	2	no	—
221	C₂×C₄×C₆₇	—	4	2	no	—
222	C₂×C₄×C₆₇	—	4	2	no	—
223	C₂×C₄×C₆₇	—	4	2	no	—
224	C₂×C₄×C₆₇	—	4	2	no	—
225	C₂×C₄×C₆₇	—	8	2	no	—
226	C₂×C₄×C₆₇	—	8	2	no	—
227	C₂×C₄×C₆₇	—	8	2	no	—
228	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
229	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
230	C₂×C₄×C₆₇	#117	1	1	yes	characteristic
231	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
232	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
233	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
234	C₂×C₄×C₆₇	#120	1	1	yes	characteristic
235	C₂×C₄×C₆₇	#120	1	1	yes	characteristic
236	C₂×C₄×C₆₇	#120	1	1	yes	characteristic
237	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
238	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
239	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
240	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
241	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
242	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
243	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
244	C₂×C₄×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
245	C₂×C₄×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
246	C₂×C₄×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
247	C₂×C₄×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
248	C₂×C₄×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
249	C₂×C₄×C₆₇	#123	1	1	yes	characteristic
250	C₂×C₄×C₆₇	#123	1	1	yes	characteristic
251	C₂×C₄×C₆₇	#123	1	1	yes	characteristic
252	C₂×C₄×C₆₇	#123	1	1	yes	characteristic
253	C₂×C₄×C₆₇	#124	1	1	yes	characteristic
254	C₂×C₄×C₆₇	#126	1	1	yes	characteristic
255	C₂×C₄×C₆₇	#127	1	1	yes	characteristic
256	C₈×C₆₇	—	2	4	no	—
257	C₈×C₆₇	—	4	2	no	—
258	C₈×C₆₇	—	4	2	no	—
259	C₈×C₆₇	—	4	2	no	—
260	C₂²×C₆₇	—	2	2	no	—
261	C₂²×C₆₇	—	2	2	no	—
262	C₂²×C₆₇	—	2	2	no	—
263	C₂²×C₆₇	—	2	2	no	—
264	C₂²×C₆₇	—	2	1	no	—
265	C₂²×C₆₇	—	2	1	no	—
266	C₂²×C₆₇	—	2	1	no	—
267	C₂²×C₆₇	—	2	1	no	—
268	C₂²×C₆₇	—	4	4	no	—
269	C₂²×C₆₇	—	8	4	no	—
270	C₂²×C₆₇	—	8	4	no	—
271	C₂²×C₆₇	—	8	4	no	—
272	C₂²×C₆₇	—	8	4	no	—
273	C₂²×C₆₇	—	8	4	no	—
274	C₂²×C₆₇	—	8	4	no	—
275	C₂²×C₆₇	—	8	2	no	—
276	C₂²×C₆₇	—	8	2	no	—
277	C₂²×C₆₇	#385	1	1	yes	characteristic
278	C₂²×C₆₇	#388	1	1	yes	characteristic
279	C₂²×C₆₇	#390	1	1	yes	characteristic
280	C₂²×C₆₇	#393	1	1	yes	characteristic
281	C₂²×C₆₇	#394	1	1	yes	characteristic
282	C₂²×C₆₇	#396	1	1	yes	characteristic
283	C₂²×C₆₇	#397	1	1	yes	characteristic
284	C₂²×C₆₇	#471	1	2	yes	—
285	C₂²×C₆₇	#472	1	2	yes	—
286	C₄×C₆₇	—	8	2	no	—
287	C₄×C₆₇	—	8	2	no	—
288	C₄×C₆₇	#380	1	1	yes	characteristic
289	C₄×C₆₇	#385	1	1	yes	characteristic
290	C₄×C₆₇	#386	1	1	yes	characteristic
291	C₄×C₆₇	#388	1	1	yes	characteristic
292	C₄×C₆₇	#392	1	1	yes	characteristic
293	C₄×C₆₇	#394	1	1	yes	characteristic
294	C₄×C₆₇	#396	1	1	yes	characteristic
295	C₄×C₆₇	#399	1	1	yes	characteristic
296	#11127	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
297	C₂×C₆₇	—	2	1	no	—
298	C₂×C₆₇	—	2	1	no	—
299	C₂×C₆₇	—	2	1	no	—
300	C₂×C₆₇	—	2	1	no	—
301	C₂×C₆₇	—	8	4	no	—
302	C₂×C₆₇	#1439	1	1	yes	characteristic
303	C₂×C₆₇	#1977	1	1	yes	characteristic
304	C₂×C₆₇	#1978	1	1	yes	characteristic
305	C₂×C₆₇	#2051	1	2	yes	—
306	C₂×C₆₇	#2063	1	2	yes	—
307	C₂²×#108	C₂×C₆₇	1	1	yes	characteristic, complemented
308	C₂×#418	C₂×C₆₇	1	1	yes	characteristic
309	C₂²×#102	C₂×C₆₇	1	1	yes	characteristic
310	C₂²×#100	C₂×C₆₇	1	1	yes	characteristic
311	C₂×#343	C₂×C₆₇	1	1	yes	characteristic, complemented
312	#1736	C₂×C₆₇	1	1	yes	characteristic, complemented
313	#1729	C₂×C₆₇	1	1	yes	characteristic, complemented
314	C₆₇	#11127	1	1	yes	characteristic, direct product factor, Sylow
315	C₂³×D₄	C₂²×C₆₇	1	1	yes	characteristic
316	C₂²×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
317	C₂²×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
318	C₂²×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
319	C₂³×C₈	C₂²×C₆₇	1	1	yes	characteristic
320	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
321	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
322	C₂×#108	—	2	2	no	—
323	C₂×#108	—	2	2	no	—
324	C₂×#108	—	2	2	no	—
325	#418	—	2	2	no	—
326	#418	—	2	2	no	—
327	C₂×#102	—	2	2	no	—
328	C₂×#102	—	2	2	no	—
329	C₂×#102	—	2	2	no	—
330	C₂×#102	C₄×C₆₇	1	4	yes	complemented
331	C₂×#100	—	2	2	no	—
332	C₂×#100	—	2	2	no	—
333	C₂×#100	—	2	2	no	—
334	#343	—	2	2	no	—
335	#340	—	2	2	no	—
336	#336	—	2	2	no	—
337	C₂⁵	—	2	1	no	—
338	C₂²×D₄	—	2	1	no	—
339	C₂²×D₄	—	2	1	no	—
340	C₂²×D₄	—	2	1	no	—
341	C₂²×D₄	—	2	1	no	—
342	C₂²×D₄	—	2	1	no	—
343	C₂²×D₄	—	2	1	no	—
344	C₂²×D₄	—	2	1	no	—
345	C₂²×D₄	—	2	1	no	—
346	C₂²×D₄	—	2	1	no	—
347	C₂²×D₄	—	2	1	no	—
348	C₂²×D₄	—	2	1	no	—
349	C₂²×D₄	C₂×C₄×C₆₇	1	2	yes	—
350	C₂²×D₄	D₄×C₆₇	1	2	yes	—
351	C₂²×D₄	Q₈×C₆₇	1	2	yes	—
352	C₂³×C₄	—	2	1	no	—
353	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
354	C₂×M₁₆	—	2	1	no	—
355	C₂×M₁₆	—	2	1	no	—
356	C₂×M₁₆	—	2	1	no	—
357	C₂×M₁₆	—	2	1	no	—
358	C₂×M₁₆	—	2	1	no	—
359	C₂×M₁₆	—	2	1	no	—
360	C₂×M₁₆	—	2	1	no	—
361	C₂×M₁₆	—	2	1	no	—
362	C₂×M₁₆	—	2	1	no	—
363	C₂×M₁₆	—	2	1	no	—
364	C₂×M₁₆	—	2	1	no	—
365	C₂×M₁₆	—	2	1	no	—
366	C₂×M₁₆	—	2	1	no	—
367	C₂×M₁₆	—	2	1	no	—
368	C₂×M₁₆	—	2	1	no	—
369	C₂×M₁₆	D₄×C₆₇	1	2	yes	—
370	C₂×M₁₆	D₄×C₆₇	1	2	yes	—
371	C₂×M₁₆	D₄×C₆₇	1	2	yes	—
372	C₂²×C₈	—	2	1	no	—
373	C₂²×C₈	—	2	1	no	—
374	C₂²×C₈	—	2	1	no	—
375	C₂²×C₈	—	2	1	no	—
376	C₂²×C₈	—	2	1	no	—
377	C₂²×C₈	—	2	1	no	—
378	C₂²×C₈	—	2	1	no	—
379	C₂²×C₈	C₂×C₄×C₆₇	1	2	yes	—
380	C₂²×C₈	D₄×C₆₇	1	2	yes	—
381	C₂²×C₈	D₄×C₆₇	1	2	yes	—
382	#117	—	2	1	no	—
383	#117	—	2	1	no	—
384	#117	—	2	1	no	—
385	#117	—	2	1	no	—
386	C₂×C₄⋊C₄	—	2	1	no	—
387	C₂×C₄⋊C₄	—	2	1	no	—
388	C₂×C₄⋊C₄	—	2	1	no	—
389	C₂×C₄⋊C₄	—	2	1	no	—
390	C₂×C₄⋊C₄	—	2	1	no	—
391	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	2	yes	—
392	C₂×C₄⋊C₄	D₄×C₆₇	1	2	yes	—
393	C₂×C₂²⋊C₄	—	2	1	no	—
394	C₂×C₄²	—	2	1	no	—
395	#108	—	2	8	no	—
396	#102	—	2	8	no	—
397	#102	—	2	8	no	—
398	#100	—	2	8	no	—
399	C₂⁴	—	2	2	no	—
400	C₂⁴	—	2	2	no	—
401	C₂⁴	—	2	2	no	—
402	C₂⁴	—	4	1	no	—
403	C₂⁴	—	4	1	no	—
404	C₂⁴	—	4	1	no	—
405	C₂⁴	—	4	1	no	—
406	C₂⁴	—	8	2	no	—
407	C₂⁴	—	8	2	no	—
408	C₂⁴	#41×C₆₇	1	1	yes	characteristic
409	C₂×D₄	—	2	2	no	—
410	C₂×D₄	—	2	2	no	—
411	C₂×D₄	—	2	2	no	—
412	C₂×D₄	—	2	2	no	—
413	C₂×D₄	—	2	2	no	—
414	C₂×D₄	—	2	2	no	—
415	C₂×D₄	—	2	2	no	—
416	C₂×D₄	—	2	2	no	—
417	C₂×D₄	—	2	2	no	—
418	C₂×D₄	—	2	2	no	—
419	C₂×D₄	—	2	2	no	—
420	C₂×D₄	—	2	2	no	—
421	C₂×D₄	—	2	2	no	—
422	C₂×D₄	—	2	2	no	—
423	C₂×D₄	—	2	2	no	—
424	C₂×D₄	—	4	1	no	—
425	C₂×D₄	—	4	1	no	—
426	C₂×D₄	—	4	1	no	—
427	C₂×D₄	—	4	1	no	—
428	C₂×D₄	—	4	1	no	—
429	C₂×D₄	—	4	1	no	—
430	C₂×D₄	—	4	1	no	—
431	C₂×D₄	—	4	1	no	—
432	C₂×D₄	—	4	1	no	—
433	C₂×D₄	—	4	1	no	—
434	C₂×D₄	—	4	1	no	—
435	C₂×D₄	—	4	1	no	—
436	C₂×D₄	C₄⋊C₄×C₆₇	1	4	yes	—
437	C₂²×C₄	—	2	2	no	—
438	C₂²×C₄	—	2	2	no	—
439	C₂²×C₄	—	4	1	no	—
440	C₂²×C₄	—	4	1	no	—
441	C₂²×C₄	—	8	2	no	—
442	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
443	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
444	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
445	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
446	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
447	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
448	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
449	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
450	C₂²×C₄	C₂×Q₈×C₆₇	1	1	yes	characteristic
451	C₂²×C₄	#41×C₆₇	1	1	yes	characteristic
452	C₂²×C₄	#41×C₆₇	1	1	yes	characteristic
453	C₂²×C₄	#41×C₆₇	1	1	yes	characteristic
454	C₂²×C₄	#41×C₆₇	1	1	yes	characteristic
455	C₂²×C₄	#41×C₆₇	1	1	yes	characteristic
456	M₁₆	—	2	2	no	—
457	M₁₆	—	2	2	no	—
458	M₁₆	—	2	2	no	—
459	M₁₆	—	2	2	no	—
460	M₁₆	—	2	2	no	—
461	M₁₆	—	2	2	no	—
462	M₁₆	—	4	1	no	—
463	M₁₆	—	4	1	no	—
464	M₁₆	—	4	1	no	—
465	M₁₆	—	4	1	no	—
466	M₁₆	—	4	1	no	—
467	M₁₆	—	4	1	no	—
468	C₂×C₈	—	2	2	no	—
469	C₂×C₈	—	2	2	no	—
470	C₂×C₈	—	2	2	no	—
471	C₂×C₈	—	2	2	no	—
472	C₂×C₈	—	2	2	no	—
473	C₂×C₈	—	2	2	no	—
474	C₂×C₈	—	2	2	no	—
475	C₂×C₈	—	2	2	no	—
476	C₂×C₈	—	2	2	no	—
477	C₂×C₈	—	4	1	no	—
478	C₂×C₈	—	4	1	no	—
479	C₂×C₈	—	4	1	no	—
480	C₂×C₈	—	4	1	no	—
481	C₂×C₈	—	4	1	no	—
482	C₂×C₈	—	4	1	no	—
483	C₂×C₈	C₂²⋊C₄×C₆₇	1	4	yes	—
484	C₄⋊C₄	—	2	2	no	—
485	C₄⋊C₄	—	2	2	no	—
486	C₄⋊C₄	—	2	2	no	—
487	C₄⋊C₄	—	2	2	no	—
488	C₄⋊C₄	—	4	1	no	—
489	C₄⋊C₄	—	4	1	no	—
490	C₂²⋊C₄	—	4	1	no	—
491	C₂²⋊C₄	—	4	1	no	—
492	C₄²	—	4	1	no	—
493	C₄²	—	4	1	no	—
494	C₂³	—	2	2	no	—
495	C₂³	—	2	2	no	—
496	C₂³	—	2	4	no	—
497	C₂³	—	4	2	no	—
498	C₂³	—	4	2	no	—
499	C₂³	—	4	2	no	—
500	C₂³	—	4	2	no	—
501	C₂³	—	4	2	no	—
502	C₂³	—	4	2	no	—
503	C₂³	—	8	4	no	—
504	C₂³	—	8	4	no	—
505	C₂³	—	8	2	no	—
506	C₂³	—	8	2	no	—
507	C₂³	—	8	4	no	—
508	C₂³	—	8	4	no	—
509	C₂³	—	8	2	no	—
510	C₂³	—	8	2	no	—
511	C₂³	—	8	2	no	—
512	C₂³	—	8	2	no	—
513	C₂³	C₄×D₄×C₆₇	1	1	yes	characteristic
514	C₂³	#121×C₆₇	1	1	yes	characteristic
515	C₂³	C₂²⋊Q₈×C₆₇	1	1	yes	characteristic
516	C₂³	#123×C₆₇	1	1	yes	characteristic
517	C₂³	#124×C₆₇	1	1	yes	characteristic
518	C₂³	#124×C₆₇	1	1	yes	characteristic
519	C₂³	#126×C₆₇	1	1	yes	characteristic
520	D₄	—	2	4	no	—
521	D₄	—	2	4	no	—
522	D₄	—	4	2	no	—
523	D₄	—	4	2	no	—
524	D₄	—	4	2	no	—
525	D₄	—	4	2	no	—
526	D₄	—	4	2	no	—
527	D₄	—	4	2	no	—
528	C₂×C₄	—	4	2	no	—
529	C₂×C₄	—	4	2	no	—
530	C₂×C₄	—	4	2	no	—
531	C₂×C₄	—	4	2	no	—
532	C₂×C₄	—	8	2	no	—
533	C₂×C₄	—	8	2	no	—
534	C₂×C₄	—	8	2	no	—
535	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	1	yes	characteristic
536	C₂×C₄	C₂×C₄⋊C₄×C₆₇	1	1	yes	characteristic
537	C₂×C₄	#117×C₆₇	1	1	yes	characteristic
538	C₂×C₄	C₄×D₄×C₆₇	1	1	yes	characteristic
539	C₂×C₄	C₄×D₄×C₆₇	1	1	yes	characteristic
540	C₂×C₄	C₄×D₄×C₆₇	1	1	yes	characteristic
541	C₂×C₄	#120×C₆₇	1	1	yes	characteristic
542	C₂×C₄	#120×C₆₇	1	1	yes	characteristic
543	C₂×C₄	#120×C₆₇	1	1	yes	characteristic
544	C₂×C₄	#121×C₆₇	1	1	yes	characteristic
545	C₂×C₄	#121×C₆₇	1	1	yes	characteristic
546	C₂×C₄	#121×C₆₇	1	1	yes	characteristic
547	C₂×C₄	#121×C₆₇	1	1	yes	characteristic
548	C₂×C₄	#121×C₆₇	1	1	yes	characteristic
549	C₂×C₄	#121×C₆₇	1	1	yes	characteristic
550	C₂×C₄	#121×C₆₇	1	1	yes	characteristic
551	C₂×C₄	C₂²⋊Q₈×C₆₇	1	1	yes	characteristic
552	C₂×C₄	C₂²⋊Q₈×C₆₇	1	1	yes	characteristic
553	C₂×C₄	C₂²⋊Q₈×C₆₇	1	1	yes	characteristic
554	C₂×C₄	C₂²⋊Q₈×C₆₇	1	1	yes	characteristic
555	C₂×C₄	C₂²⋊Q₈×C₆₇	1	1	yes	characteristic
556	C₂×C₄	#123×C₆₇	1	1	yes	characteristic
557	C₂×C₄	#123×C₆₇	1	1	yes	characteristic
558	C₂×C₄	#123×C₆₇	1	1	yes	characteristic
559	C₂×C₄	#123×C₆₇	1	1	yes	characteristic
560	C₂×C₄	#124×C₆₇	1	1	yes	characteristic
561	C₂×C₄	#126×C₆₇	1	1	yes	characteristic
562	C₂×C₄	#127×C₆₇	1	1	yes	characteristic
563	C₈	—	2	4	no	—
564	C₈	—	4	2	no	—
565	C₈	—	4	2	no	—
566	C₈	—	4	2	no	—
567	C₂²	—	2	2	no	—
568	C₂²	—	2	2	no	—
569	C₂²	—	2	2	no	—
570	C₂²	—	2	2	no	—
571	C₂²	—	2	1	no	—
572	C₂²	—	2	1	no	—
573	C₂²	—	2	1	no	—
574	C₂²	—	2	1	no	—
575	C₂²	—	4	4	no	—
576	C₂²	—	8	4	no	—
577	C₂²	—	8	4	no	—
578	C₂²	—	8	4	no	—
579	C₂²	—	8	4	no	—
580	C₂²	—	8	4	no	—
581	C₂²	—	8	4	no	—
582	C₂²	—	8	2	no	—
583	C₂²	—	8	2	no	—
584	C₂²	#385×C₆₇	1	1	yes	characteristic
585	C₂²	#388×C₆₇	1	1	yes	characteristic
586	C₂²	#390×C₆₇	1	1	yes	characteristic
587	C₂²	#393×C₆₇	1	1	yes	characteristic
588	C₂²	#394×C₆₇	1	1	yes	characteristic
589	C₂²	#396×C₆₇	1	1	yes	characteristic
590	C₂²	#397×C₆₇	1	1	yes	characteristic
591	C₂²	#471×C₆₇	1	2	yes	—
592	C₂²	#472×C₆₇	1	2	yes	—
593	C₄	—	8	2	no	—
594	C₄	—	8	2	no	—
595	C₄	#380×C₆₇	1	1	yes	characteristic
596	C₄	#385×C₆₇	1	1	yes	characteristic
597	C₄	#386×C₆₇	1	1	yes	characteristic
598	C₄	#388×C₆₇	1	1	yes	characteristic
599	C₄	#392×C₆₇	1	1	yes	characteristic
600	C₄	#394×C₆₇	1	1	yes	characteristic
601	C₄	#396×C₆₇	1	1	yes	characteristic
602	C₄	#399×C₆₇	1	1	yes	characteristic
603	C₂	—	2	1	no	—
604	C₂	—	2	1	no	—
605	C₂	—	2	1	no	—
606	C₂	—	2	1	no	—
607	C₂	—	8	4	no	—
608	C₂	C₆₇×#1439	1	1	yes	characteristic
609	C₂	C₆₇×#1977	1	1	yes	characteristic
610	C₂	C₆₇×#1978	1	1	yes	characteristic
611	C₂	C₆₇×#2051	1	2	yes	—
612	C₂	C₆₇×#2063	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₆₇	#121
commutator	C₂²×C₄	C₂²×C₄×C₆₇
Frattini, cosocle	C₂³×C₄	C₂³×C₆₇
prime radical	C₂³×D₄×C₆₇	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ C₂³×C₄×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×#108×C₆₇	C₂	semidirect
5. C₂×#343×C₆₇	C₂	semidirect
6. C₆₇×#1736	C₂	semidirect
7. C₆₇×#1729	C₂	semidirect
23. C₂×#102×C₆₇	C₄	semidirect
296. #11127	C₆₇	direct (N × H)
307. C₂²×#108	C₂×C₆₇	semidirect
311. C₂×#343	C₂×C₆₇	semidirect
312. #1736	C₂×C₆₇	semidirect
313. #1729	C₂×C₆₇	semidirect
314. C₆₇	#11127	direct (N × H)
330. C₂×#102	C₄×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#108×C₆₇	2
C₂×#418×C₆₇	2
C₂²×#102×C₆₇	2
C₂²×#100×C₆₇	2
C₂×#343×C₆₇	2
C₆₇×#1736	2
C₆₇×#1729	2
#11127	67

Subgroups — C67×#11127 #30690378

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#11127 #30690378