Subgroups — #30864101

Order 17152.

682 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22563510	C₂	1	1	yes	maximal, characteristic
2	#22560823	C₂	1	1	yes	maximal, characteristic
3	#22560814	C₂	1	1	yes	maximal, characteristic
4	#22560813	C₂	1	1	yes	maximal, characteristic
5	#22560770	C₂	1	1	yes	maximal, characteristic, complemented
6	#22560768	C₂	1	1	yes	maximal, characteristic, complemented
7	#22560765	C₂	1	1	yes	maximal, characteristic, complemented
8	#22560353	C₂	1	1	yes	maximal, characteristic, complemented
9	#22560085	C₂	1	1	yes	maximal, characteristic, complemented
10	#22560076	C₂	1	1	yes	maximal, characteristic, complemented
11	#22559986	C₂	1	1	yes	maximal, characteristic
12	#22559986	C₂	1	1	yes	maximal, characteristic
13	C₈×(C₂×D₆₇)⋊C₄	C₂	1	1	yes	maximal, characteristic
14	#22559897	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#1771	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₈×D₆₇	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊(C₆₇⋊C₈)	C₂²	1	1	yes	characteristic
18	C₂×Dic₆₇⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×(C₂×D₆₇)⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×(C₂×D₆₇)⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×(C₂×D₆₇)⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×#14523953	C₂²	1	1	yes	characteristic
23	C₂×#14523953	C₂²	1	1	yes	characteristic
24	C₂×#14523953	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₆₇⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₈×Dic₆₇	C₂²	1	1	yes	characteristic
27	C₂×C₈×Dic₆₇	C₂²	1	1	yes	characteristic
28	C₆₇⋊#401	C₄	1	1	yes	characteristic
29	#16863338	C₄	1	1	yes	characteristic
30	#16863335	C₄	1	1	yes	characteristic
31	#16863334	C₄	1	1	yes	characteristic
32	#16863325	C₄	1	1	yes	characteristic
33	#16863323	C₄	1	1	yes	characteristic
34	#16863322	C₄	1	1	yes	characteristic
35	#16863318	C₄	1	1	yes	characteristic
36	C₄×Dic₆₇⋊C₄	C₂²	1	1	yes	characteristic
37	C₄×C₄⋊Dic₆₇	C₂²	1	1	yes	characteristic
38	C₄×(C₂×D₆₇)⋊C₄	C₂²	1	1	yes	characteristic
39	C₄×(C₂×D₆₇)⋊C₄	C₂²	1	1	yes	characteristic
40	C₄×(C₂×D₆₇)⋊C₄	C₂²	1	1	yes	characteristic
41	#16863242	C₂²	1	1	yes	characteristic
42	#16863151	C₂²	1	1	yes	characteristic
43	#16863151	C₂²	1	1	yes	characteristic
44	#16863151	C₂²	1	1	yes	characteristic
45	#16863151	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	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
53	C₂×#97×C₆₇	C₂²	1	1	yes	characteristic
54	C₂×#97×C₆₇	C₂²	1	1	yes	characteristic
55	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
56	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
57	#336×C₆₇	C₂²	1	1	yes	characteristic
58	#336×C₆₇	C₂²	1	1	yes	characteristic
59	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
60	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
61	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
62	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
63	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
64	C₂×C₈×D₆₇	—	2	2	no	—
65	C₂×C₈×D₆₇	—	2	2	no	—
66	C₂×C₈×D₆₇	—	2	2	no	—
67	C₂×C₄⋊Dic₆₇	C₂×C₄	1	1	yes	characteristic
68	C₂×C₄⋊Dic₆₇	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×(C₂×D₆₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
72	C₂×(C₂×D₆₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
73	C₂×(C₂×D₆₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
74	C₂×(C₂×D₆₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
75	C₂×(C₂×D₆₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
76	C₂×(C₂×D₆₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
78	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
79	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
80	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
81	Dic₆₇⋊C₈	—	2	2	no	—
82	(C₂×D₆₇)⋊C₈	—	2	2	no	—
83	(C₂×D₆₇)⋊C₈	—	2	2	no	—
84	(C₂×D₆₇)⋊C₈	—	2	2	no	—
85	#14523953	—	2	2	no	—
86	#14523953	—	2	2	no	—
87	#14523953	—	2	2	no	—
88	C₄×C₆₇⋊C₈	—	2	2	no	—
89	C₈×Dic₆₇	—	2	2	no	—
90	C₈×Dic₆₇	—	2	2	no	—
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	C₆₇⋊#95	C₂×C₄	1	1	yes	characteristic
104	C₆₇⋊#95	C₂×C₄	1	1	yes	characteristic
105	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
106	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
107	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
108	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
109	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
110	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
111	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
112	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
113	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
114	C₄⋊C₈×C₆₇	—	2	2	no	—
115	#97×C₆₇	—	2	2	no	—
116	#97×C₆₇	—	2	2	no	—
117	C₄×C₈×C₆₇	—	2	2	no	—
118	#95×C₆₇	C₂×C₄	1	1	yes	characteristic
119	#95×C₆₇	C₂×C₄	1	1	yes	characteristic
120	C₂³×D₆₇	C₂²×C₄	1	1	yes	characteristic
121	C₂²×Dic₆₇	C₂²×C₄	1	1	yes	characteristic
122	C₂²×Dic₆₇	C₂²×C₄	1	1	yes	characteristic
123	C₂²×Dic₆₇	C₂²×C₄	1	1	yes	characteristic
124	C₂²×Dic₆₇	C₂²×C₄	1	1	yes	characteristic
125	C₂²×Dic₆₇	C₂²×C₄	1	1	yes	characteristic
126	C₂²×Dic₆₇	C₂²×C₄	1	1	yes	characteristic
127	C₂²×Dic₆₇	C₂²×C₄	1	1	yes	characteristic
128	C₂×C₄×D₆₇	—	2	1	no	—
129	C₂×C₄×D₆₇	—	2	1	no	—
130	C₂×C₄×D₆₇	—	2	1	no	—
131	C₂×C₄×D₆₇	—	2	1	no	—
132	C₂×C₄×D₆₇	—	2	1	no	—
133	C₂×C₄×D₆₇	—	2	1	no	—
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	#41	1	2	yes	—
145	C₂×C₆₇⋊C₈	#41	1	2	yes	—
146	C₈×D₆₇	—	4	4	no	—
147	C₄⋊Dic₆₇	—	2	2	no	—
148	C₄⋊Dic₆₇	—	4	1	no	—
149	Dic₆₇⋊C₄	—	4	1	no	—
150	Dic₆₇⋊C₄	—	4	1	no	—
151	(C₂×D₆₇)⋊C₄	—	2	2	no	—
152	(C₂×D₆₇)⋊C₄	—	2	2	no	—
153	(C₂×D₆₇)⋊C₄	—	2	2	no	—
154	(C₂×D₆₇)⋊C₄	—	2	2	no	—
155	(C₂×D₆₇)⋊C₄	—	4	1	no	—
156	(C₂×D₆₇)⋊C₄	—	4	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	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
164	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
165	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
166	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
167	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
168	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
169	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
170	C₂×C₈×C₆₇	—	2	1	no	—
171	C₂×C₈×C₆₇	—	2	1	no	—
172	C₂×C₈×C₆₇	—	2	1	no	—
173	C₂×C₈×C₆₇	—	2	1	no	—
174	C₂×C₈×C₆₇	—	2	1	no	—
175	C₂×C₈×C₆₇	—	2	1	no	—
176	C₂×C₈×C₆₇	—	2	1	no	—
177	C₂×C₈×C₆₇	—	2	1	no	—
178	C₂×C₈×C₆₇	#41	1	2	yes	—
179	C₂×C₈×C₆₇	#41	1	2	yes	—
180	C₂×C₈×C₆₇	#41	1	2	yes	—
181	C₂×C₈×C₆₇	#41	1	2	yes	—
182	C₄⋊C₄×C₆₇	—	2	2	no	—
183	C₄⋊C₄×C₆₇	—	4	1	no	—
184	C₄²×C₆₇	—	2	1	no	—
185	C₄²×C₆₇	—	2	1	no	—
186	C₄²×C₆₇	—	2	1	no	—
187	C₄²×C₆₇	—	2	1	no	—
188	C₄²×C₆₇	—	2	1	no	—
189	C₄²×C₆₇	—	2	1	no	—
190	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
191	C₂²×D₆₇	—	2	1	no	—
192	C₂²×D₆₇	—	2	1	no	—
193	C₂²×D₆₇	—	2	1	no	—
194	C₂²×D₆₇	—	2	1	no	—
195	C₂²×D₆₇	—	2	1	no	—
196	C₂²×D₆₇	—	2	1	no	—
197	C₂²×D₆₇	#131	1	2	yes	—
198	C₂×C₄×C₆₇	—	2	1	no	—
199	C₂×C₄×C₆₇	—	2	1	no	—
200	C₂×C₄×C₆₇	—	2	1	no	—
201	C₂×C₄×C₆₇	—	2	1	no	—
202	C₂×C₄×C₆₇	—	2	1	no	—
203	C₂×C₄×C₆₇	—	2	1	no	—
204	C₂×C₄×C₆₇	—	2	1	no	—
205	C₂×C₄×C₆₇	—	2	1	no	—
206	C₂×C₄×C₆₇	—	2	1	no	—
207	C₂×C₄×C₆₇	—	2	1	no	—
208	C₂×C₄×C₆₇	—	2	1	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	#131	1	2	yes	—
216	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
217	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
218	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
219	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
220	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
221	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
222	C₂×Dic₆₇	—	2	1	no	—
223	C₂×Dic₆₇	—	2	1	no	—
224	C₂×Dic₆₇	—	2	1	no	—
225	C₂×Dic₆₇	—	2	1	no	—
226	C₂×Dic₆₇	—	2	1	no	—
227	C₂×Dic₆₇	—	2	1	no	—
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	C₄×D₆₇	—	4	1	no	—
244	C₄×D₆₇	—	4	1	no	—
245	C₄×D₆₇	—	4	1	no	—
246	C₄×D₆₇	—	4	1	no	—
247	C₈×C₆₇	—	2	2	no	—
248	C₈×C₆₇	—	4	1	no	—
249	C₈×C₆₇	—	4	1	no	—
250	C₈×C₆₇	#126	1	4	yes	—
251	C₆₇⋊C₈	—	2	2	no	—
252	C₆₇⋊C₈	—	2	2	no	—
253	C₆₇⋊C₈	—	4	1	no	—
254	C₆₇⋊C₈	—	4	1	no	—
255	C₂²×C₆₇	C₄×#41	1	1	yes	characteristic
256	C₂²×C₆₇	C₄×#41	1	1	yes	characteristic
257	C₂²×C₆₇	C₄×#41	1	1	yes	characteristic
258	C₂²×C₆₇	C₂×#131	1	1	yes	characteristic
259	C₂²×C₆₇	C₂×#131	1	1	yes	characteristic
260	C₂²×C₆₇	#568	1	1	yes	characteristic
261	C₂²×C₆₇	#568	1	1	yes	characteristic
262	C₂×D₆₇	—	2	2	no	—
263	C₂×D₆₇	—	2	2	no	—
264	C₂×D₆₇	—	2	2	no	—
265	C₂×D₆₇	—	4	1	no	—
266	C₂×D₆₇	—	4	1	no	—
267	C₂×D₆₇	—	4	1	no	—
268	C₂×D₆₇	—	4	1	no	—
269	C₄×C₆₇	—	2	2	no	—
270	C₄×C₆₇	—	4	1	no	—
271	C₄×C₆₇	—	4	1	no	—
272	C₄×C₆₇	—	4	1	no	—
273	C₄×C₆₇	—	4	1	no	—
274	C₄×C₆₇	—	4	1	no	—
275	C₄×C₆₇	C₂×#126	1	1	yes	characteristic
276	C₄×C₆₇	#529	1	1	yes	characteristic
277	C₄×C₆₇	#529	1	1	yes	characteristic
278	C₄×C₆₇	#529	1	1	yes	characteristic
279	Dic₆₇	—	4	1	no	—
280	Dic₆₇	—	4	1	no	—
281	Dic₆₇	—	4	1	no	—
282	Dic₆₇	—	4	1	no	—
283	Dic₆₇	—	4	1	no	—
284	Dic₆₇	—	4	1	no	—
285	Dic₆₇	—	4	1	no	—
286	#21669	—	67	1	no	maximal, Sylow
287	C₂×C₆₇	C₄×#126	1	1	yes	characteristic
288	C₂×C₆₇	#2966	1	1	yes	characteristic
289	C₂×C₆₇	#2967	1	1	yes	characteristic
290	C₂×C₆₇	#2968	1	1	yes	characteristic
291	C₂×C₆₇	#2968	1	1	yes	characteristic
292	C₂×C₆₇	#2968	1	1	yes	characteristic
293	C₂×C₆₇	#2969	1	1	yes	characteristic
294	D₆₇	—	4	2	no	—
295	#2401	—	67	1	no	—
296	#1924	—	67	1	no	—
297	#1923	—	67	1	no	—
298	#1923	—	67	1	no	—
299	#1917	—	67	1	no	—
300	#1916	—	67	1	no	—
301	#1916	—	67	1	no	—
302	#1840	—	67	1	no	—
303	#1771	—	67	1	no	—
304	#1771	D₆₇	1	1	yes	characteristic, complemented
305	#1770	—	67	1	no	—
306	#1752	—	67	1	no	—
307	#1752	—	67	1	no	—
308	C₈×C₂²⋊C₄	—	67	1	no	—
309	#1726	—	67	1	no	—
310	C₆₇	#21669	1	1	yes	characteristic, complemented, Sylow
311	C₂³×C₈	—	67	1	no	—
312	C₂×C₄⋊C₈	—	67	1	no	—
313	C₂×C₄⋊C₈	—	67	1	no	—
314	C₂×C₄⋊C₈	C₂×D₆₇	1	1	yes	characteristic
315	C₂×C₂²⋊C₈	—	67	1	no	—
316	C₂×C₂²⋊C₈	—	67	1	no	—
317	C₂×C₂²⋊C₈	—	67	1	no	—
318	C₂×#97	—	67	1	no	—
319	C₂×#97	—	67	1	no	—
320	C₂×#97	—	67	1	no	—
321	C₂×#97	C₂×D₆₇	1	1	yes	characteristic
322	C₂×#97	C₂×D₆₇	1	1	yes	characteristic
323	C₂×C₄×C₈	—	67	1	no	—
324	C₂×C₄×C₈	—	67	1	no	—
325	C₂×C₄×C₈	—	67	1	no	—
326	C₂×C₄×C₈	C₂×D₆₇	1	1	yes	characteristic
327	#401	—	67	1	no	—
328	#400	—	67	1	no	—
329	#400	—	67	1	no	—
330	#400	—	67	1	no	—
331	#397	—	67	1	no	—
332	#397	—	67	1	no	—
333	#397	—	67	1	no	—
334	#396	—	67	1	no	—
335	C₄×C₄⋊C₄	—	67	1	no	—
336	C₄×C₄⋊C₄	—	67	1	no	—
337	C₄×C₄⋊C₄	C₂×D₆₇	1	1	yes	characteristic
338	C₄×C₂²⋊C₄	—	67	1	no	—
339	C₄×C₂²⋊C₄	—	67	1	no	—
340	C₄×C₂²⋊C₄	—	67	1	no	—
341	#376	—	67	1	no	—
342	#336	—	67	1	no	—
343	#336	—	67	1	no	—
344	#336	—	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	C₂×D₆₇	1	1	yes	characteristic
353	#336	C₂×D₆₇	1	1	yes	characteristic
354	C₂³×C₄	—	67	1	no	—
355	C₂²×C₈	—	67	1	no	—
356	C₂²×C₈	—	67	1	no	—
357	C₂²×C₈	—	67	1	no	—
358	C₂²×C₈	—	67	1	no	—
359	C₂²×C₈	—	134	2	no	—
360	C₂²×C₈	—	134	2	no	—
361	C₂²×C₈	—	134	2	no	—
362	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
363	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
364	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
365	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
366	C₂×C₄⋊C₄	—	67	1	no	—
367	C₂×C₄⋊C₄	—	67	1	no	—
368	C₂×C₄⋊C₄	—	67	1	no	—
369	C₂×C₄⋊C₄	—	67	1	no	—
370	C₂×C₄⋊C₄	C₄×D₆₇	1	1	yes	characteristic
371	C₂×C₄⋊C₄	C₄×D₆₇	1	1	yes	characteristic
372	C₂×C₂²⋊C₄	—	67	1	no	—
373	C₂×C₂²⋊C₄	—	67	1	no	—
374	C₂×C₂²⋊C₄	—	67	1	no	—
375	C₂×C₂²⋊C₄	—	67	1	no	—
376	C₂×C₂²⋊C₄	—	67	1	no	—
377	C₂×C₂²⋊C₄	—	67	1	no	—
378	C₂×C₄²	—	67	1	no	—
379	C₂×C₄²	—	67	1	no	—
380	C₂×C₄²	—	67	1	no	—
381	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
382	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
383	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
384	C₄⋊C₈	—	2	2	no	—
385	C₄⋊C₈	—	134	2	no	—
386	C₄⋊C₈	—	134	2	no	—
387	C₂²⋊C₈	—	134	2	no	—
388	C₂²⋊C₈	—	134	2	no	—
389	C₂²⋊C₈	—	134	2	no	—
390	#97	—	2	2	no	—
391	#97	—	2	2	no	—
392	#97	—	134	2	no	—
393	#97	—	134	2	no	—
394	#97	—	134	2	no	—
395	C₄×C₈	—	2	2	no	—
396	C₄×C₈	—	134	2	no	—
397	C₄×C₈	—	134	2	no	—
398	C₄×C₈	—	134	2	no	—
399	#95	—	67	1	no	—
400	#95	—	67	1	no	—
401	#95	—	67	1	no	—
402	#95	—	67	1	no	—
403	#95	—	67	1	no	—
404	#95	—	67	1	no	—
405	#95	—	67	1	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	C₄×D₆₇	1	1	yes	characteristic
414	#95	C₄×D₆₇	1	1	yes	characteristic
415	C₂⁴	—	67	1	no	—
416	C₂²×C₄	—	67	1	no	—
417	C₂²×C₄	—	67	1	no	—
418	C₂²×C₄	—	67	1	no	—
419	C₂²×C₄	—	67	1	no	—
420	C₂²×C₄	—	67	1	no	—
421	C₂²×C₄	—	67	1	no	—
422	C₂²×C₄	—	67	1	no	—
423	C₂²×C₄	—	134	1	no	—
424	C₂²×C₄	—	134	1	no	—
425	C₂²×C₄	—	134	1	no	—
426	C₂²×C₄	—	134	1	no	—
427	C₂²×C₄	—	134	1	no	—
428	C₂²×C₄	—	134	1	no	—
429	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
430	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
431	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
432	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
433	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
434	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
435	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
436	C₂×C₈	—	2	1	no	—
437	C₂×C₈	—	2	1	no	—
438	C₂×C₈	—	2	1	no	—
439	C₂×C₈	—	2	1	no	—
440	C₂×C₈	—	2	1	no	—
441	C₂×C₈	—	2	1	no	—
442	C₂×C₈	—	2	1	no	—
443	C₂×C₈	—	2	1	no	—
444	C₂×C₈	—	268	4	no	—
445	C₂×C₈	—	67	2	no	—
446	C₂×C₈	—	67	2	no	—
447	C₂×C₈	—	134	1	no	—
448	C₂×C₈	—	134	1	no	—
449	C₂×C₈	—	134	1	no	—
450	C₂×C₈	—	134	1	no	—
451	C₂×C₈	—	134	1	no	—
452	C₂×C₈	—	134	1	no	—
453	C₂×C₈	—	134	1	no	—
454	C₂×C₈	—	134	1	no	—
455	C₂×C₈	—	134	1	no	—
456	C₂×C₈	—	134	1	no	—
457	C₂×C₈	#11761627	1	2	yes	—
458	C₂×C₈	#11761628	1	2	yes	—
459	C₂×C₈	#11761628	1	2	yes	—
460	C₂×C₈	#11761629	1	2	yes	—
461	C₄⋊C₄	—	2	2	no	—
462	C₄⋊C₄	—	4	1	no	—
463	C₄⋊C₄	—	268	1	no	—
464	C₄⋊C₄	—	268	1	no	—
465	C₄⋊C₄	—	268	1	no	—
466	C₄⋊C₄	—	134	2	no	—
467	C₂²⋊C₄	—	268	1	no	—
468	C₂²⋊C₄	—	268	1	no	—
469	C₂²⋊C₄	—	134	2	no	—
470	C₂²⋊C₄	—	134	2	no	—
471	C₂²⋊C₄	—	134	2	no	—
472	C₂²⋊C₄	—	134	2	no	—
473	C₄²	—	2	1	no	—
474	C₄²	—	2	1	no	—
475	C₄²	—	2	1	no	—
476	C₄²	—	2	1	no	—
477	C₄²	—	2	1	no	—
478	C₄²	—	2	1	no	—
479	C₄²	—	134	1	no	—
480	C₄²	—	134	1	no	—
481	C₄²	—	134	1	no	—
482	C₄²	—	134	1	no	—
483	C₄²	—	134	1	no	—
484	C₄²	—	134	1	no	—
485	C₂³	—	67	2	no	—
486	C₂³	—	134	1	no	—
487	C₂³	—	134	1	no	—
488	C₂³	—	134	1	no	—
489	C₂³	—	134	1	no	—
490	C₂³	—	134	1	no	—
491	C₂³	—	134	1	no	—
492	C₂³	C₂²×C₄×D₆₇	1	1	yes	characteristic
493	C₂×C₄	—	2	1	no	—
494	C₂×C₄	—	2	1	no	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	1	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	268	1	no	—
511	C₂×C₄	—	268	1	no	—
512	C₂×C₄	—	268	1	no	—
513	C₂×C₄	—	268	1	no	—
514	C₂×C₄	—	134	1	no	—
515	C₂×C₄	—	134	1	no	—
516	C₂×C₄	—	134	1	no	—
517	C₂×C₄	—	134	1	no	—
518	C₂×C₄	—	134	1	no	—
519	C₂×C₄	—	134	1	no	—
520	C₂×C₄	—	134	1	no	—
521	C₂×C₄	—	134	1	no	—
522	C₂×C₄	—	134	1	no	—
523	C₂×C₄	—	134	1	no	—
524	C₂×C₄	—	134	1	no	—
525	C₂×C₄	—	134	1	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	#14524051	1	2	yes	—
536	C₂×C₄	#41×D₆₇	1	1	yes	characteristic
537	C₂×C₄	#41×D₆₇	1	1	yes	characteristic
538	C₂×C₄	C₂×#11761627	1	1	yes	characteristic
539	C₂×C₄	C₂×#11761628	1	1	yes	characteristic
540	C₂×C₄	C₂×#11761628	1	1	yes	characteristic
541	C₂×C₄	C₂×#11761629	1	1	yes	characteristic
542	C₈	—	2	2	no	—
543	C₈	—	4	1	no	—
544	C₈	—	4	1	no	—
545	C₈	—	268	1	no	—
546	C₈	—	268	1	no	—
547	C₈	—	134	2	no	—
548	C₈	—	134	2	no	—
549	C₈	#14524038	1	4	yes	—
550	C₂²	—	268	1	no	—
551	C₂²	—	268	1	no	—
552	C₂²	—	268	1	no	—
553	C₂²	—	268	1	no	—
554	C₂²	—	134	2	no	—
555	C₂²	—	134	2	no	—
556	C₂²	—	134	2	no	—
557	C₂²	C₄×#11761627	1	1	yes	characteristic
558	C₂²	C₄×#11761628	1	1	yes	characteristic
559	C₂²	C₄×#11761629	1	1	yes	characteristic
560	C₂²	#131×D₆₇	1	1	yes	characteristic
561	C₂²	C₂×#14524051	1	1	yes	characteristic
562	C₂²	#16864161	1	1	yes	characteristic
563	C₂²	#16864162	1	1	yes	characteristic
564	C₄	—	2	2	no	—
565	C₄	—	4	1	no	—
566	C₄	—	4	1	no	—
567	C₄	—	4	1	no	—
568	C₄	—	4	1	no	—
569	C₄	—	4	1	no	—
570	C₄	—	268	1	no	—
571	C₄	—	268	1	no	—
572	C₄	—	268	1	no	—
573	C₄	—	268	1	no	—
574	C₄	—	268	1	no	—
575	C₄	—	268	1	no	—
576	C₄	—	268	1	no	—
577	C₄	C₂×#14524038	1	1	yes	characteristic
578	C₄	#16863924	1	1	yes	characteristic
579	C₄	#16863926	1	1	yes	characteristic
580	C₄	#16863933	1	1	yes	characteristic
581	C₂	—	268	2	no	—
582	C₂	C₄×#14524038	1	1	yes	characteristic
583	C₂	#22569183	1	1	yes	characteristic
584	C₂	#22569193	1	1	yes	characteristic
585	C₂	#22569199	1	1	yes	characteristic
586	C₂	#22569200	1	1	yes	characteristic
587	C₂	#22569204	1	1	yes	characteristic
588	C₂	#22569213	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₆₇
commutator, socle	C₂³×C₆₇	C₂³×C₄
Fitting	C₆₇×#1771	C₂
prime radical	C₂³×D₆₇	C₂²×C₄
cosocle	C₂²×C₄×C₆₇	C₂⁴
hypercenter	#1771	D₆₇
hypocenter	C₆₇	#21669
LCS	G ▷ C₂³×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂²×C₄ ◁ #1771

Complements

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

N	H ≅ G/N	type
5. #22560770	C₂	semidirect
6. #22560768	C₂	semidirect
7. #22560765	C₂	semidirect
8. #22560353	C₂	semidirect
9. #22560085	C₂	semidirect
10. #22560076	C₂	semidirect
14. #22559897	C₂	semidirect
15. C₆₇×#1771	C₂	semidirect
304. #1771	D₆₇	semidirect
310. C₆₇	#21669	semidirect

Maximal subgroups

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

subgroup	index
#22563510	2
#22560823	2
#22560814	2
#22560813	2
#22560770	2
#22560768	2
#22560765	2
#22560353	2
#22560085	2
#22560076	2
#22559986	2
C₈×(C₂×D₆₇)⋊C₄	2
#22559897	2
C₆₇×#1771	2
#21669	67