Subgroups — #30873293

Order 17152.

736 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22562603	C₂	1	1	yes	maximal, characteristic
2	#22560773	C₂	1	1	yes	maximal, characteristic, complemented
3	#22560773	C₂	1	1	yes	maximal, characteristic, complemented
4	#22560764	C₂	1	1	yes	maximal, characteristic, complemented
5	#22560764	C₂	1	1	yes	maximal, characteristic, complemented
6	#22560387	C₂	1	1	yes	maximal, characteristic
7	#22560386	C₂	1	1	yes	maximal, characteristic
8	#22560353	C₂	1	1	yes	maximal, characteristic, complemented
9	#22560327	C₂	1	1	yes	maximal, characteristic, complemented
10	#22560275	C₂	1	1	yes	maximal, characteristic
11	#22560069	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²⋊C₄×C₆₇⋊C₈	C₂	1	1	yes	maximal, characteristic
13	#22559962	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#16863150	C₂	1	1	yes	maximal, characteristic
15	C₆₇×#1752	C₂	1	1	yes	maximal, characteristic
16	C₂³×C₆₇⋊C₈	C₂²	1	1	yes	characteristic
17	C₂²×C₄×Dic₆₇	C₂²	1	1	yes	characteristic
18	C₂×Dic₆₇⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×Dic₆₇⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×Dic₆₇⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×Dic₆₇⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₂²⋊(C₆₇⋊C₈)	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₆₇⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₆₇⋊C₈	C₂²	1	1	yes	characteristic
25	#16863263	C₄	1	1	yes	characteristic
26	#16863263	C₄	1	1	yes	characteristic
27	#16863260	C₄	1	1	yes	characteristic
28	#16863260	C₄	1	1	yes	characteristic
29	#16863257	C₄	1	1	yes	characteristic
30	#16863257	C₄	1	1	yes	characteristic
31	#16863254	C₄	1	1	yes	characteristic
32	#16863254	C₄	1	1	yes	characteristic
33	C₄×Dic₆₇⋊C₄	C₂²	1	1	yes	characteristic
34	C₄×Dic₆₇⋊C₄	C₂²	1	1	yes	characteristic
35	C₄×C₂²⋊Dic₆₇	C₂²	1	1	yes	characteristic
36	#16863242	C₂²	1	1	yes	characteristic
37	#16863242	C₂²	1	1	yes	characteristic
38	#16863151	C₂²	1	1	yes	characteristic
39	#16863151	C₂²	1	1	yes	characteristic
40	#16863150	C₂²	1	1	yes	characteristic
41	#16863150	C₂²	1	1	yes	characteristic
42	#16863150	C₂²	1	1	yes	characteristic
43	#16863150	C₂²	1	1	yes	characteristic
44	#16863150	C₂²	1	1	yes	characteristic
45	#16863150	C₂²	1	1	yes	characteristic
46	#16863150	C₂²	1	1	yes	characteristic
47	#16863150	C₂²	1	1	yes	characteristic
48	#16863150	C₂²	1	1	yes	characteristic
49	#16863150	C₂²	1	1	yes	characteristic
50	#16863150	C₂²	1	1	yes	characteristic
51	#16863150	C₂²	1	1	yes	characteristic
52	C₂³×C₈×C₆₇	C₂²	1	1	yes	characteristic
53	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
54	C₂×#97×C₆₇	C₂²	1	1	yes	characteristic
55	C₂×#97×C₆₇	C₂²	1	1	yes	characteristic
56	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
57	#336×C₆₇	C₂²	1	1	yes	characteristic
58	#336×C₆₇	C₂²	1	1	yes	characteristic
59	C₂³×Dic₆₇	C₂×C₄	1	1	yes	characteristic
60	C₂³×Dic₆₇	C₂×C₄	1	1	yes	characteristic
61	C₂²×C₆₇⋊C₈	—	2	2	no	—
62	C₂²×C₆₇⋊C₈	—	2	2	no	—
63	C₂²×C₆₇⋊C₈	—	4	1	no	—
64	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
65	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
66	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
67	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
68	C₂×Dic₆₇⋊C₄	C₂×C₄	1	1	yes	characteristic
69	C₂×Dic₆₇⋊C₄	C₂×C₄	1	1	yes	characteristic
70	C₂×Dic₆₇⋊C₄	C₂×C₄	1	1	yes	characteristic
71	C₂×Dic₆₇⋊C₄	C₂×C₄	1	1	yes	characteristic
72	C₂×C₂²⋊Dic₆₇	C₂×C₄	1	1	yes	characteristic
73	C₂×C₂²⋊Dic₆₇	C₂×C₄	1	1	yes	characteristic
74	C₂×C₄×Dic₆₇	—	2	2	no	—
75	C₂×C₄×Dic₆₇	—	2	2	no	—
76	C₂×C₄×Dic₆₇	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄×Dic₆₇	C₂×C₄	1	1	yes	characteristic
78	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
79	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
80	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
81	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
82	Dic₆₇⋊C₈	—	2	2	no	—
83	Dic₆₇⋊C₈	—	2	2	no	—
84	Dic₆₇⋊C₈	—	4	1	no	—
85	Dic₆₇⋊C₈	—	4	1	no	—
86	C₂²⋊(C₆₇⋊C₈)	—	2	2	no	—
87	C₄×C₆₇⋊C₈	—	2	2	no	—
88	C₄×C₆₇⋊C₈	—	4	1	no	—
89	C₆₇⋊#95	C₂×C₄	1	1	yes	characteristic
90	C₆₇⋊#95	C₂×C₄	1	1	yes	characteristic
91	C₆₇⋊#95	C₂×C₄	1	1	yes	characteristic
92	C₆₇⋊#95	C₂×C₄	1	1	yes	characteristic
93	C₆₇⋊#95	C₂×C₄	1	1	yes	characteristic
94	C₆₇⋊#95	C₂×C₄	1	1	yes	characteristic
95	C₆₇⋊#95	C₂×C₄	1	1	yes	characteristic
96	C₆₇⋊#95	C₂×C₄	1	1	yes	characteristic
97	C₆₇⋊#95	C₂×C₄	1	1	yes	characteristic
98	C₆₇⋊#95	C₂×C₄	1	1	yes	characteristic
99	C₆₇⋊#95	C₂×C₄	1	1	yes	characteristic
100	C₆₇⋊#95	C₂×C₄	1	1	yes	characteristic
101	C₆₇⋊#95	C₂×C₄	1	1	yes	characteristic
102	C₆₇⋊#95	C₂×C₄	1	1	yes	characteristic
103	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
104	C₂²×C₈×C₆₇	—	2	2	no	—
105	C₂²×C₈×C₆₇	—	2	2	no	—
106	C₂²×C₈×C₆₇	—	4	1	no	—
107	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
108	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
109	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
110	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
111	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
112	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
113	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
114	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
115	C₂²⋊C₈×C₆₇	—	2	2	no	—
116	#97×C₆₇	—	2	2	no	—
117	#97×C₆₇	—	4	1	no	—
118	#95×C₆₇	C₂×C₄	1	1	yes	characteristic
119	#95×C₆₇	C₂×C₄	1	1	yes	characteristic
120	C₂²×Dic₆₇	—	2	2	no	—
121	C₂²×Dic₆₇	—	2	2	no	—
122	C₂²×Dic₆₇	—	2	2	no	—
123	C₂²×Dic₆₇	—	2	2	no	—
124	C₂²×Dic₆₇	—	2	2	no	—
125	C₂²×Dic₆₇	—	4	1	no	—
126	C₂²×Dic₆₇	C₂²×C₄	1	1	yes	characteristic
127	C₂²×Dic₆₇	C₂²×C₄	1	1	yes	characteristic
128	C₂²×Dic₆₇	C₂²×C₄	1	1	yes	characteristic
129	C₂²×Dic₆₇	C₂²×C₄	1	1	yes	characteristic
130	C₂²×Dic₆₇	C₂²×C₄	1	1	yes	characteristic
131	C₂²×Dic₆₇	C₂²×C₄	1	1	yes	characteristic
132	C₂²×Dic₆₇	C₂²×C₄	1	1	yes	characteristic
133	C₂²×Dic₆₇	C₂²×C₄	1	1	yes	characteristic
134	C₂×C₆₇⋊C₈	—	2	1	no	—
135	C₂×C₆₇⋊C₈	—	2	1	no	—
136	C₂×C₆₇⋊C₈	—	2	1	no	—
137	C₂×C₆₇⋊C₈	—	2	1	no	—
138	C₂×C₆₇⋊C₈	—	2	1	no	—
139	C₂×C₆₇⋊C₈	—	2	1	no	—
140	C₂×C₆₇⋊C₈	—	2	1	no	—
141	C₂×C₆₇⋊C₈	—	2	1	no	—
142	C₂×C₆₇⋊C₈	—	2	1	no	—
143	C₂×C₆₇⋊C₈	—	2	1	no	—
144	C₂×C₆₇⋊C₈	—	2	1	no	—
145	C₂×C₆₇⋊C₈	—	4	4	no	—
146	C₂×C₆₇⋊C₈	#41	1	2	yes	—
147	Dic₆₇⋊C₄	—	2	2	no	—
148	Dic₆₇⋊C₄	—	2	2	no	—
149	Dic₆₇⋊C₄	—	4	1	no	—
150	Dic₆₇⋊C₄	—	4	1	no	—
151	C₂²⋊Dic₆₇	—	2	2	no	—
152	C₂²⋊Dic₆₇	—	2	2	no	—
153	C₄×Dic₆₇	—	2	2	no	—
154	C₄×Dic₆₇	—	2	2	no	—
155	C₄×Dic₆₇	—	2	1	no	—
156	C₄×Dic₆₇	—	2	1	no	—
157	C₄×Dic₆₇	—	2	1	no	—
158	C₄×Dic₆₇	—	2	1	no	—
159	C₄×Dic₆₇	—	2	1	no	—
160	C₄×Dic₆₇	—	2	1	no	—
161	C₄×Dic₆₇	—	2	1	no	—
162	C₄×Dic₆₇	—	2	1	no	—
163	C₂⁴×C₆₇	C₂²×C₄	1	1	yes	characteristic
164	C₂²×C₄×C₆₇	—	2	1	no	—
165	C₂²×C₄×C₆₇	—	2	1	no	—
166	C₂²×C₄×C₆₇	—	2	1	no	—
167	C₂²×C₄×C₆₇	—	2	1	no	—
168	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
169	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
170	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
171	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
172	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
173	C₂²×C₄×C₆₇	#41	1	2	yes	—
174	C₂²×C₄×C₆₇	#41	1	2	yes	—
175	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
176	C₂×C₈×C₆₇	—	2	1	no	—
177	C₂×C₈×C₆₇	—	2	1	no	—
178	C₂×C₈×C₆₇	—	2	1	no	—
179	C₂×C₈×C₆₇	—	2	1	no	—
180	C₂×C₈×C₆₇	—	2	1	no	—
181	C₂×C₈×C₆₇	—	2	1	no	—
182	C₂×C₈×C₆₇	—	2	1	no	—
183	C₂×C₈×C₆₇	—	2	1	no	—
184	C₂×C₈×C₆₇	—	2	1	no	—
185	C₂×C₈×C₆₇	—	2	1	no	—
186	C₂×C₈×C₆₇	—	2	1	no	—
187	C₂×C₈×C₆₇	—	4	4	no	—
188	C₂×C₈×C₆₇	#41	1	2	yes	—
189	C₂²⋊C₄×C₆₇	—	2	2	no	—
190	C₂²⋊C₄×C₆₇	—	2	2	no	—
191	C₄²×C₆₇	—	2	1	no	—
192	C₄²×C₆₇	—	2	1	no	—
193	C₄²×C₆₇	—	2	1	no	—
194	C₄²×C₆₇	—	2	1	no	—
195	C₂³×C₆₇	—	2	1	no	—
196	C₂³×C₆₇	—	2	1	no	—
197	C₂³×C₆₇	—	2	1	no	—
198	C₂³×C₆₇	—	2	1	no	—
199	C₂³×C₆₇	#117	1	2	yes	—
200	C₂³×C₆₇	#131	1	2	yes	—
201	C₂³×C₆₇	#131	1	2	yes	—
202	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
203	C₂×C₄×C₆₇	—	2	1	no	—
204	C₂×C₄×C₆₇	—	2	1	no	—
205	C₂×C₄×C₆₇	—	2	2	no	—
206	C₂×C₄×C₆₇	—	2	2	no	—
207	C₂×C₄×C₆₇	—	2	2	no	—
208	C₂×C₄×C₆₇	—	2	2	no	—
209	C₂×C₄×C₆₇	—	2	1	no	—
210	C₂×C₄×C₆₇	—	2	1	no	—
211	C₂×C₄×C₆₇	—	2	1	no	—
212	C₂×C₄×C₆₇	—	2	1	no	—
213	C₂×C₄×C₆₇	—	2	1	no	—
214	C₂×C₄×C₆₇	—	2	1	no	—
215	C₂×C₄×C₆₇	—	2	1	no	—
216	C₂×C₄×C₆₇	—	2	1	no	—
217	C₂×C₄×C₆₇	—	2	1	no	—
218	C₂×C₄×C₆₇	—	2	1	no	—
219	C₂×C₄×C₆₇	—	2	1	no	—
220	C₂×C₄×C₆₇	—	2	1	no	—
221	C₂×C₄×C₆₇	#117	1	2	yes	—
222	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
223	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
224	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
225	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
226	C₂×C₄×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
227	C₂×C₄×C₆₇	2₋¹⁺⁴	1	1	yes	characteristic
228	C₂×Dic₆₇	—	2	1	no	—
229	C₂×Dic₆₇	—	2	1	no	—
230	C₂×Dic₆₇	—	2	1	no	—
231	C₂×Dic₆₇	—	2	1	no	—
232	C₂×Dic₆₇	—	2	1	no	—
233	C₂×Dic₆₇	—	2	1	no	—
234	C₂×Dic₆₇	—	2	1	no	—
235	C₂×Dic₆₇	—	2	1	no	—
236	C₂×Dic₆₇	—	2	1	no	—
237	C₂×Dic₆₇	—	2	1	no	—
238	C₂×Dic₆₇	—	2	1	no	—
239	C₂×Dic₆₇	—	2	1	no	—
240	C₂×Dic₆₇	—	2	1	no	—
241	C₂×Dic₆₇	—	2	1	no	—
242	C₂×Dic₆₇	—	2	1	no	—
243	C₂×Dic₆₇	—	2	1	no	—
244	C₂×Dic₆₇	—	2	1	no	—
245	C₂×Dic₆₇	—	2	1	no	—
246	C₂×Dic₆₇	—	2	1	no	—
247	C₂×Dic₆₇	—	2	1	no	—
248	C₂×Dic₆₇	—	2	1	no	—
249	C₂×Dic₆₇	—	2	1	no	—
250	C₂×Dic₆₇	—	2	1	no	—
251	C₂×Dic₆₇	—	4	4	no	—
252	C₂×Dic₆₇	—	4	4	no	—
253	C₂×Dic₆₇	#131	1	2	yes	—
254	C₈×C₆₇	—	2	2	no	—
255	C₈×C₆₇	—	4	1	no	—
256	C₈×C₆₇	—	4	1	no	—
257	C₈×C₆₇	—	4	1	no	—
258	C₆₇⋊C₈	—	2	2	no	—
259	C₆₇⋊C₈	—	4	1	no	—
260	C₆₇⋊C₈	—	4	1	no	—
261	C₆₇⋊C₈	—	4	1	no	—
262	C₂²×C₆₇	—	2	2	no	—
263	C₂²×C₆₇	—	2	2	no	—
264	C₂²×C₆₇	—	2	2	no	—
265	C₂²×C₆₇	—	2	2	no	—
266	C₂²×C₆₇	—	2	2	no	—
267	C₂²×C₆₇	—	2	2	no	—
268	C₂²×C₆₇	#433	1	4	yes	—
269	C₂²×C₆₇	C₂×#117	1	1	yes	characteristic
270	C₂²×C₆₇	C₄×#41	1	1	yes	characteristic
271	C₂²×C₆₇	#520	1	1	yes	characteristic
272	C₂²×C₆₇	C₂×#131	1	1	yes	characteristic
273	C₂²×C₆₇	C₂×#131	1	1	yes	characteristic
274	C₂²×C₆₇	C₂×#131	1	1	yes	characteristic
275	C₂²×C₆₇	#568	1	1	yes	characteristic
276	C₄×C₆₇	—	2	2	no	—
277	C₄×C₆₇	—	4	1	no	—
278	C₄×C₆₇	—	4	1	no	—
279	C₄×C₆₇	—	4	1	no	—
280	C₄×C₆₇	—	4	1	no	—
281	C₄×C₆₇	#551	1	1	yes	characteristic
282	C₄×C₆₇	#551	1	1	yes	characteristic
283	C₄×C₆₇	#552	1	1	yes	characteristic
284	C₄×C₆₇	#552	1	1	yes	characteristic
285	Dic₆₇	—	2	2	no	—
286	Dic₆₇	—	4	1	no	—
287	Dic₆₇	—	4	1	no	—
288	Dic₆₇	—	4	1	no	—
289	Dic₆₇	—	4	1	no	—
290	Dic₆₇	—	4	1	no	—
291	Dic₆₇	—	4	1	no	—
292	Dic₆₇	—	4	1	no	—
293	#22595	—	67	1	no	maximal, Sylow
294	C₂×C₆₇	—	2	4	no	—
295	C₂×C₆₇	#2343	1	1	yes	characteristic
296	C₂×C₆₇	C₂×#433	1	1	yes	characteristic
297	C₂×C₆₇	#2924	1	1	yes	characteristic
298	C₂×C₆₇	#2966	1	1	yes	characteristic
299	C₂×C₆₇	#2968	1	1	yes	characteristic
300	C₂×C₆₇	#2992	1	1	yes	characteristic
301	C₂×C₆₇	#2994	1	1	yes	characteristic
302	#2283	—	67	1	no	—
303	#1917	—	67	1	no	—
304	#1917	—	67	1	no	—
305	#1916	—	67	1	no	—
306	#1916	—	67	1	no	—
307	#1850	—	67	1	no	—
308	#1850	—	67	1	no	—
309	#1840	—	67	1	no	—
310	#1832	—	67	1	no	—
311	#1817	—	67	1	no	—
312	#1768	—	67	1	no	—
313	#1752	D₆₇	1	1	yes	characteristic
314	C₈×C₂²⋊C₄	—	67	1	no	—
315	#1746	—	67	1	no	—
316	C₂×#336	—	67	1	no	—
317	C₆₇	#22595	1	1	yes	characteristic, complemented, Sylow
318	C₂³×C₈	—	67	1	no	—
319	C₂³×C₈	C₂×D₆₇	1	1	yes	characteristic
320	C₂²×C₄²	—	67	1	no	—
321	C₂×C₄⋊C₈	—	67	1	no	—
322	C₂×C₄⋊C₈	—	67	1	no	—
323	C₂×C₄⋊C₈	—	67	1	no	—
324	C₂×C₄⋊C₈	—	67	1	no	—
325	C₂×C₂²⋊C₈	—	67	1	no	—
326	C₂×C₂²⋊C₈	C₂×D₆₇	1	1	yes	characteristic
327	C₂×#97	C₂×D₆₇	1	1	yes	characteristic
328	C₂×#97	C₂×D₆₇	1	1	yes	characteristic
329	C₂×C₄×C₈	—	67	1	no	—
330	C₂×C₄×C₈	—	67	1	no	—
331	#383	—	67	1	no	—
332	#383	—	67	1	no	—
333	#382	—	67	1	no	—
334	#382	—	67	1	no	—
335	#381	—	67	1	no	—
336	#381	—	67	1	no	—
337	#380	—	67	1	no	—
338	#380	—	67	1	no	—
339	C₄×C₄⋊C₄	—	67	1	no	—
340	C₄×C₄⋊C₄	—	67	1	no	—
341	C₄×C₂²⋊C₄	—	67	1	no	—
342	C₄×C₂²⋊C₄	C₂×D₆₇	1	1	yes	characteristic
343	#376	—	67	1	no	—
344	#376	—	67	1	no	—
345	#336	—	67	1	no	—
346	#336	—	67	1	no	—
347	#336	—	67	1	no	—
348	#336	—	67	1	no	—
349	#336	—	67	1	no	—
350	#336	—	67	1	no	—
351	#336	—	67	1	no	—
352	#336	—	67	1	no	—
353	#336	—	67	1	no	—
354	#336	—	67	1	no	—
355	#336	—	67	1	no	—
356	#336	—	67	1	no	—
357	#336	—	67	1	no	—
358	#336	—	67	1	no	—
359	#336	C₂×D₆₇	1	1	yes	characteristic
360	#336	C₂×D₆₇	1	1	yes	characteristic
361	C₂³×C₄	—	67	1	no	—
362	C₂³×C₄	—	67	1	no	—
363	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
364	C₂²×C₈	—	2	2	no	—
365	C₂²×C₈	—	2	2	no	—
366	C₂²×C₈	—	4	1	no	—
367	C₂²×C₈	—	268	1	no	—
368	C₂²×C₈	—	67	1	no	—
369	C₂²×C₈	—	67	1	no	—
370	C₂²×C₈	—	67	1	no	—
371	C₂²×C₈	—	67	1	no	—
372	C₂²×C₈	—	134	2	no	—
373	C₂²×C₈	—	134	2	no	—
374	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
375	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
376	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
377	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
378	C₂×C₄⋊C₄	—	67	1	no	—
379	C₂×C₄⋊C₄	—	67	1	no	—
380	C₂×C₄⋊C₄	—	67	1	no	—
381	C₂×C₄⋊C₄	—	67	1	no	—
382	C₂×C₂²⋊C₄	—	67	1	no	—
383	C₂×C₂²⋊C₄	—	67	1	no	—
384	C₂×C₂²⋊C₄	C₄×D₆₇	1	1	yes	characteristic
385	C₂×C₂²⋊C₄	C₄×D₆₇	1	1	yes	characteristic
386	C₂×C₄²	—	67	1	no	—
387	C₂×C₄²	—	67	1	no	—
388	C₂×C₄²	—	67	1	no	—
389	C₂×C₄²	—	67	1	no	—
390	C₂×C₄²	—	67	1	no	—
391	C₂×C₄²	—	67	1	no	—
392	C₂×C₄²	—	134	2	no	—
393	C₂×C₄²	—	134	2	no	—
394	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
395	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
396	C₄⋊C₈	—	268	1	no	—
397	C₄⋊C₈	—	268	1	no	—
398	C₄⋊C₈	—	134	2	no	—
399	C₄⋊C₈	—	134	2	no	—
400	C₂²⋊C₈	—	2	2	no	—
401	C₂²⋊C₈	—	134	2	no	—
402	#97	—	2	2	no	—
403	#97	—	4	1	no	—
404	C₄×C₈	—	268	1	no	—
405	C₄×C₈	—	134	2	no	—
406	#95	—	67	1	no	—
407	#95	—	67	1	no	—
408	#95	—	67	1	no	—
409	#95	—	67	1	no	—
410	#95	—	67	1	no	—
411	#95	—	67	1	no	—
412	#95	—	67	1	no	—
413	#95	—	67	1	no	—
414	#95	—	67	1	no	—
415	#95	—	67	1	no	—
416	#95	—	67	1	no	—
417	#95	—	67	1	no	—
418	#95	—	67	1	no	—
419	#95	—	67	1	no	—
420	#95	C₄×D₆₇	1	1	yes	characteristic
421	#95	C₄×D₆₇	1	1	yes	characteristic
422	C₂⁴	C₂×C₄×D₆₇	1	1	yes	characteristic
423	C₂²×C₄	—	2	1	no	—
424	C₂²×C₄	—	2	1	no	—
425	C₂²×C₄	—	2	1	no	—
426	C₂²×C₄	—	2	1	no	—
427	C₂²×C₄	—	268	1	no	—
428	C₂²×C₄	—	67	1	no	—
429	C₂²×C₄	—	67	1	no	—
430	C₂²×C₄	—	67	1	no	—
431	C₂²×C₄	—	67	1	no	—
432	C₂²×C₄	—	67	1	no	—
433	C₂²×C₄	—	67	1	no	—
434	C₂²×C₄	—	67	1	no	—
435	C₂²×C₄	—	67	1	no	—
436	C₂²×C₄	—	134	2	no	—
437	C₂²×C₄	—	134	2	no	—
438	C₂²×C₄	—	134	2	no	—
439	C₂²×C₄	—	134	2	no	—
440	C₂²×C₄	—	134	2	no	—
441	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
442	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
443	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
444	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
445	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
446	C₂²×C₄	#11761628	1	2	yes	—
447	C₂²×C₄	#11761628	1	2	yes	—
448	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
449	C₂×C₈	—	2	1	no	—
450	C₂×C₈	—	2	1	no	—
451	C₂×C₈	—	2	1	no	—
452	C₂×C₈	—	2	1	no	—
453	C₂×C₈	—	2	1	no	—
454	C₂×C₈	—	2	1	no	—
455	C₂×C₈	—	2	1	no	—
456	C₂×C₈	—	2	1	no	—
457	C₂×C₈	—	2	1	no	—
458	C₂×C₈	—	2	1	no	—
459	C₂×C₈	—	2	1	no	—
460	C₂×C₈	—	4	4	no	—
461	C₂×C₈	—	268	4	no	—
462	C₂×C₈	—	67	2	no	—
463	C₂×C₈	—	134	1	no	—
464	C₂×C₈	—	134	1	no	—
465	C₂×C₈	—	134	1	no	—
466	C₂×C₈	—	134	1	no	—
467	C₂×C₈	—	134	1	no	—
468	C₂×C₈	—	134	1	no	—
469	C₂×C₈	—	134	1	no	—
470	C₂×C₈	—	134	1	no	—
471	C₂×C₈	—	134	1	no	—
472	C₂×C₈	—	134	1	no	—
473	C₂×C₈	—	134	1	no	—
474	C₂×C₈	#11761627	1	2	yes	—
475	C₄⋊C₄	—	268	1	no	—
476	C₄⋊C₄	—	268	1	no	—
477	C₄⋊C₄	—	134	2	no	—
478	C₄⋊C₄	—	134	2	no	—
479	C₂²⋊C₄	—	2	2	no	—
480	C₂²⋊C₄	—	2	2	no	—
481	C₂²⋊C₄	—	134	2	no	—
482	C₂²⋊C₄	—	134	2	no	—
483	C₄²	—	2	1	no	—
484	C₄²	—	2	1	no	—
485	C₄²	—	2	1	no	—
486	C₄²	—	2	1	no	—
487	C₄²	—	134	2	no	—
488	C₄²	—	134	2	no	—
489	C₄²	—	134	1	no	—
490	C₄²	—	134	1	no	—
491	C₄²	—	134	1	no	—
492	C₄²	—	134	1	no	—
493	C₄²	—	134	1	no	—
494	C₄²	—	134	1	no	—
495	C₄²	—	134	1	no	—
496	C₄²	—	134	1	no	—
497	C₂³	—	2	1	no	—
498	C₂³	—	2	1	no	—
499	C₂³	—	2	1	no	—
500	C₂³	—	2	1	no	—
501	C₂³	#14524000	1	2	yes	—
502	C₂³	#14524051	1	2	yes	—
503	C₂³	#14524051	1	2	yes	—
504	C₂³	C₂²×C₄×D₆₇	1	1	yes	characteristic
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	2	2	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	268	4	no	—
524	C₂×C₄	—	268	4	no	—
525	C₂×C₄	—	67	2	no	—
526	C₂×C₄	—	134	1	no	—
527	C₂×C₄	—	134	1	no	—
528	C₂×C₄	—	134	1	no	—
529	C₂×C₄	—	134	1	no	—
530	C₂×C₄	—	134	1	no	—
531	C₂×C₄	—	134	1	no	—
532	C₂×C₄	—	134	1	no	—
533	C₂×C₄	—	134	1	no	—
534	C₂×C₄	—	134	1	no	—
535	C₂×C₄	—	134	1	no	—
536	C₂×C₄	—	134	1	no	—
537	C₂×C₄	—	134	1	no	—
538	C₂×C₄	—	134	1	no	—
539	C₂×C₄	—	134	1	no	—
540	C₂×C₄	—	134	1	no	—
541	C₂×C₄	—	134	1	no	—
542	C₂×C₄	—	134	1	no	—
543	C₂×C₄	—	134	1	no	—
544	C₂×C₄	—	134	1	no	—
545	C₂×C₄	—	134	1	no	—
546	C₂×C₄	—	134	1	no	—
547	C₂×C₄	—	134	1	no	—
548	C₂×C₄	—	134	1	no	—
549	C₂×C₄	#14524000	1	2	yes	—
550	C₂×C₄	#41×D₆₇	1	1	yes	characteristic
551	C₂×C₄	C₂×#11761627	1	1	yes	characteristic
552	C₂×C₄	C₂×#11761628	1	1	yes	characteristic
553	C₂×C₄	C₂×#11761628	1	1	yes	characteristic
554	C₂×C₄	#14524088	1	1	yes	characteristic
555	C₂×C₄	#14524090	1	1	yes	characteristic
556	C₈	—	2	2	no	—
557	C₈	—	4	1	no	—
558	C₈	—	4	1	no	—
559	C₈	—	4	1	no	—
560	C₈	—	268	1	no	—
561	C₈	—	268	1	no	—
562	C₈	—	268	1	no	—
563	C₈	—	134	2	no	—
564	C₂²	—	2	2	no	—
565	C₂²	—	2	2	no	—
566	C₂²	—	2	2	no	—
567	C₂²	—	2	2	no	—
568	C₂²	—	2	2	no	—
569	C₂²	—	2	2	no	—
570	C₂²	#16863458	1	4	yes	—
571	C₂²	C₂×#14524000	1	1	yes	characteristic
572	C₂²	C₄×#11761627	1	1	yes	characteristic
573	C₂²	#16863875	1	1	yes	characteristic
574	C₂²	#131×D₆₇	1	1	yes	characteristic
575	C₂²	C₂×#14524051	1	1	yes	characteristic
576	C₂²	C₂×#14524051	1	1	yes	characteristic
577	C₂²	#16864161	1	1	yes	characteristic
578	C₄	—	2	2	no	—
579	C₄	—	4	1	no	—
580	C₄	—	4	1	no	—
581	C₄	—	4	1	no	—
582	C₄	—	4	1	no	—
583	C₄	—	268	1	no	—
584	C₄	—	268	1	no	—
585	C₄	—	268	1	no	—
586	C₄	—	268	1	no	—
587	C₄	—	268	1	no	—
588	C₄	—	268	1	no	—
589	C₄	—	268	1	no	—
590	C₄	—	134	2	no	—
591	C₄	#16864072	1	1	yes	characteristic
592	C₄	#16864075	1	1	yes	characteristic
593	C₄	#16864079	1	1	yes	characteristic
594	C₄	#16864086	1	1	yes	characteristic
595	C₂	—	2	4	no	—
596	C₂	#22563063	1	1	yes	characteristic
597	C₂	C₂×#16863458	1	1	yes	characteristic
598	C₂	#22568864	1	1	yes	characteristic
599	C₂	#22569179	1	1	yes	characteristic
600	C₂	#22569204	1	1	yes	characteristic
601	C₂	#22569349	1	1	yes	characteristic
602	C₂	#22569362	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₆₇
commutator, socle	C₂³×C₆₇	C₂³×C₄
Fitting	C₆₇×#1752	C₂
prime radical	C₂⁴×C₆₇	C₂²×C₄
cosocle	C₂²×C₄×C₆₇	C₂⁴
hypercenter	#1752	D₆₇
hypocenter	C₆₇	#22595
LCS	G ▷ C₂³×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂²×C₄ ◁ #1752

Complements

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

N	H ≅ G/N	type
2. #22560773	C₂	semidirect
3. #22560773	C₂	semidirect
4. #22560764	C₂	semidirect
5. #22560764	C₂	semidirect
8. #22560353	C₂	semidirect
9. #22560327	C₂	semidirect
11. #22560069	C₂	semidirect
13. #22559962	C₂	semidirect
317. C₆₇	#22595	semidirect

Maximal subgroups

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

subgroup	index
#22562603	2
#22560773	2
#22560764	2
#22560387	2
#22560386	2
#22560353	2
#22560327	2
#22560275	2
#22560069	2
C₂²⋊C₄×C₆₇⋊C₈	2
#22559962	2
C₂×#16863150	2
C₆₇×#1752	2
#22595	67