Subgroups — #30854013

Order 17152.

950 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16863457	C₂	1	1	yes	maximal, characteristic
2	#117×Dic₆₇	C₂	1	1	yes	maximal, characteristic
3	#22560068	C₂	1	1	yes	maximal, characteristic, complemented
4	#22560068	C₂	1	1	yes	maximal, characteristic, complemented
5	#22560064	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄⋊C₈×Dic₆₇	C₂	1	1	yes	maximal, characteristic, complemented
7	#22559977	C₂	1	1	yes	maximal, characteristic
8	#22559977	C₂	1	1	yes	maximal, characteristic
9	#22559973	C₂	1	1	yes	maximal, characteristic
10	C₂²⋊C₈×Dic₆₇	C₂	1	1	yes	maximal, characteristic
11	#22559957	C₂	1	1	yes	maximal, characteristic, complemented
12	#22559954	C₂	1	1	yes	maximal, characteristic, complemented
13	#22559897	C₂	1	1	yes	maximal, characteristic, complemented
14	#22559895	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#433×C₆₇	C₂	1	1	yes	maximal, characteristic
16	C₂×#14524002	C₂²	1	1	yes	characteristic
17	C₂²×C₄×Dic₆₇	C₂²	1	1	yes	characteristic
18	#16863457	C₄	1	8	yes	complemented
19	C₂×C₄⋊(C₆₇⋊C₈)	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊(C₆₇⋊C₈)	C₂²	1	1	yes	characteristic
21	C₂×C₂²⋊(C₆₇⋊C₈)	C₂²	1	1	yes	characteristic
22	C₂×C₂²⋊(C₆₇⋊C₈)	C₂²	1	1	yes	characteristic
23	C₂×#14523954	C₂²	1	1	yes	characteristic
24	C₂×#14523953	C₂²	1	1	yes	characteristic
25	C₂×#14523953	C₂²	1	1	yes	characteristic
26	C₂×#14523953	C₂²	1	1	yes	characteristic
27	C₂×#14523953	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₆₇⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₈×Dic₆₇	C₂²	1	1	yes	characteristic
30	C₂×C₈×Dic₆₇	C₂²	1	1	yes	characteristic
31	C₂×C₈×Dic₆₇	C₂²	1	1	yes	characteristic
32	C₂×C₈×Dic₆₇	C₂²	1	1	yes	characteristic
33	C₄⋊C₄×Dic₆₇	C₄	1	2	yes	—
34	C₄⋊C₄×Dic₆₇	C₄	1	2	yes	—
35	C₂²⋊C₄×Dic₆₇	C₄	1	2	yes	—
36	C₂²⋊C₄×Dic₆₇	C₄	1	2	yes	—
37	#16863242	C₂²	1	1	yes	characteristic
38	#16863242	C₂²	1	1	yes	characteristic
39	C₄²×Dic₆₇	C₂²	1	1	yes	characteristic
40	C₄²×Dic₆₇	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	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
50	#433×C₆₇	C₄	1	8	yes	complemented
51	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
52	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
53	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
54	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
55	C₂×#97×C₆₇	C₂²	1	1	yes	characteristic
56	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
57	C₂³×Dic₆₇	C₂×C₄	1	2	yes	—
58	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
59	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
60	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
61	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
62	#14524002	—	2	2	no	—
63	#14524002	—	2	2	no	—
64	C₂×C₄⋊Dic₆₇	C₂×C₄	1	2	yes	—
65	C₂×C₂²⋊Dic₆₇	C₂×C₄	1	2	yes	—
66	C₂×C₄×Dic₆₇	—	2	2	no	—
67	C₂×C₄×Dic₆₇	—	2	2	no	—
68	C₂×C₄×Dic₆₇	C₂×C₄	1	2	yes	—
69	C₂×C₄×Dic₆₇	C₂×C₄	1	2	yes	—
70	C₂×C₄×Dic₆₇	C₂×C₄	1	2	yes	—
71	C₂×C₄×Dic₆₇	C₂×C₄	1	2	yes	—
72	C₂×C₄×Dic₆₇	C₂×C₄	1	2	yes	—
73	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
74	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
75	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
76	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
77	C₄⋊(C₆₇⋊C₈)	C₂×C₄	1	4	yes	complemented
78	C₄⋊(C₆₇⋊C₈)	C₂×C₄	1	4	yes	complemented
79	C₂²⋊(C₆₇⋊C₈)	C₂×C₄	1	4	yes	—
80	C₂²⋊(C₆₇⋊C₈)	C₂×C₄	1	4	yes	—
81	#14523954	C₂×C₄	1	4	yes	complemented
82	#14523953	—	2	2	no	—
83	#14523953	—	2	2	no	—
84	#14523953	—	2	2	no	—
85	#14523953	—	2	2	no	—
86	C₄×C₆₇⋊C₈	C₂×C₄	1	4	yes	complemented
87	C₈×Dic₆₇	—	2	2	no	—
88	C₈×Dic₆₇	—	2	2	no	—
89	C₈×Dic₆₇	—	2	2	no	—
90	C₈×Dic₆₇	—	2	2	no	—
91	C₆₇⋊#95	C₂×C₄	1	2	yes	—
92	C₆₇⋊#95	C₂×C₄	1	2	yes	—
93	C₆₇⋊#95	C₂×C₄	1	2	yes	—
94	C₆₇⋊#95	C₂×C₄	1	2	yes	—
95	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
96	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
97	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
98	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
99	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
100	#117×C₆₇	C₂×C₄	1	4	yes	—
101	#117×C₆₇	C₂×C₄	1	4	yes	—
102	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
103	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
104	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
105	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
106	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
107	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
108	C₄⋊C₈×C₆₇	C₂×C₄	1	4	yes	complemented
109	C₄⋊C₈×C₆₇	C₂×C₄	1	4	yes	complemented
110	C₂²⋊C₈×C₆₇	C₂×C₄	1	4	yes	—
111	C₂²⋊C₈×C₆₇	C₂×C₄	1	4	yes	—
112	#97×C₆₇	C₂×C₄	1	4	yes	complemented
113	C₄×C₈×C₆₇	C₂×C₄	1	4	yes	complemented
114	C₂²×Dic₆₇	—	2	4	no	—
115	C₂²×Dic₆₇	—	2	4	no	—
116	C₂²×Dic₆₇	—	4	2	no	—
117	C₂²×Dic₆₇	C₂²×C₄	1	2	yes	—
118	C₂²×Dic₆₇	C₂²×C₄	1	2	yes	—
119	C₂²×Dic₆₇	C₂²×C₄	1	2	yes	—
120	C₂²×Dic₆₇	C₂²×C₄	1	2	yes	—
121	C₂×C₆₇⋊C₈	—	2	1	no	—
122	C₂×C₆₇⋊C₈	—	2	1	no	—
123	C₂×C₆₇⋊C₈	—	2	1	no	—
124	C₂×C₆₇⋊C₈	—	2	1	no	—
125	C₂×C₆₇⋊C₈	—	2	1	no	—
126	C₂×C₆₇⋊C₈	—	2	1	no	—
127	C₂×C₆₇⋊C₈	—	2	1	no	—
128	C₂×C₆₇⋊C₈	—	2	1	no	—
129	C₂×C₆₇⋊C₈	C₂²×C₄	1	2	yes	—
130	C₂×C₆₇⋊C₈	C₂²×C₄	1	2	yes	—
131	C₂×C₆₇⋊C₈	C₂²×C₄	1	2	yes	—
132	C₂×C₆₇⋊C₈	C₂²×C₄	1	2	yes	—
133	C₄⋊Dic₆₇	—	2	4	no	—
134	C₂²⋊Dic₆₇	—	2	4	no	—
135	C₄×Dic₆₇	—	2	1	no	—
136	C₄×Dic₆₇	—	2	1	no	—
137	C₄×Dic₆₇	—	2	1	no	—
138	C₄×Dic₆₇	—	2	1	no	—
139	C₄×Dic₆₇	—	2	4	no	—
140	C₄×Dic₆₇	—	2	4	no	—
141	C₄×Dic₆₇	—	2	4	no	—
142	C₄×Dic₆₇	—	4	2	no	—
143	C₄×Dic₆₇	—	4	2	no	—
144	C₄×Dic₆₇	#41	1	2	yes	—
145	C₄×Dic₆₇	#41	1	2	yes	—
146	C₄×Dic₆₇	#41	1	2	yes	—
147	C₄×Dic₆₇	#41	1	2	yes	—
148	C₂⁴×C₆₇	C₂²×C₄	1	1	yes	characteristic
149	C₂²×C₄×C₆₇	—	2	1	no	—
150	C₂²×C₄×C₆₇	—	2	1	no	—
151	C₂²×C₄×C₆₇	—	2	1	no	—
152	C₂²×C₄×C₆₇	—	2	1	no	—
153	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
154	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
155	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
156	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
157	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
158	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
159	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
160	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
161	C₂×C₈×C₆₇	—	2	1	no	—
162	C₂×C₈×C₆₇	—	2	1	no	—
163	C₂×C₈×C₆₇	—	2	1	no	—
164	C₂×C₈×C₆₇	—	2	1	no	—
165	C₂×C₈×C₆₇	—	2	1	no	—
166	C₂×C₈×C₆₇	—	2	1	no	—
167	C₂×C₈×C₆₇	—	2	1	no	—
168	C₂×C₈×C₆₇	—	2	1	no	—
169	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
170	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
171	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
172	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
173	C₄⋊C₄×C₆₇	C₄²	1	4	yes	—
174	C₄⋊C₄×C₆₇	C₄²	1	4	yes	—
175	C₂²⋊C₄×C₆₇	C₄²	1	4	yes	—
176	C₂²⋊C₄×C₆₇	C₄²	1	4	yes	—
177	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
178	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
179	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
180	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
181	C₂³×C₆₇	—	2	1	no	—
182	C₂³×C₆₇	—	2	1	no	—
183	C₂³×C₆₇	—	2	2	no	—
184	C₂³×C₆₇	—	2	2	no	—
185	C₂³×C₆₇	C₂×C₄²	1	2	yes	—
186	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
187	C₂×C₄×C₆₇	—	2	1	no	—
188	C₂×C₄×C₆₇	—	2	1	no	—
189	C₂×C₄×C₆₇	—	2	2	no	—
190	C₂×C₄×C₆₇	—	2	2	no	—
191	C₂×C₄×C₆₇	—	2	2	no	—
192	C₂×C₄×C₆₇	—	2	2	no	—
193	C₂×C₄×C₆₇	—	2	2	no	—
194	C₂×C₄×C₆₇	—	2	2	no	—
195	C₂×C₄×C₆₇	—	2	2	no	—
196	C₂×C₄×C₆₇	—	2	2	no	—
197	C₂×C₄×C₆₇	C₂×C₄²	1	2	yes	—
198	C₂×C₄×C₆₇	C₂×C₄²	1	2	yes	—
199	C₂×C₄×C₆₇	C₂×C₄²	1	2	yes	—
200	C₂×C₄×C₆₇	C₂×C₄²	1	2	yes	—
201	C₂×C₄×C₆₇	C₂×C₄²	1	2	yes	—
202	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
203	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
204	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
205	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
206	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
207	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
208	C₂×Dic₆₇	—	2	2	no	—
209	C₂×Dic₆₇	—	2	2	no	—
210	C₂×Dic₆₇	—	2	2	no	—
211	C₂×Dic₆₇	—	2	2	no	—
212	C₂×Dic₆₇	—	2	2	no	—
213	C₂×Dic₆₇	—	2	2	no	—
214	C₂×Dic₆₇	—	2	2	no	—
215	C₂×Dic₆₇	—	2	2	no	—
216	C₂×Dic₆₇	—	2	2	no	—
217	C₂×Dic₆₇	—	4	8	no	—
218	C₂×Dic₆₇	#117	1	4	yes	—
219	C₂×Dic₆₇	#117	1	4	yes	—
220	C₂×Dic₆₇	#131	1	4	yes	—
221	C₈×C₆₇	—	2	2	no	—
222	C₈×C₆₇	—	2	2	no	—
223	C₈×C₆₇	—	2	2	no	—
224	C₈×C₆₇	—	2	2	no	—
225	C₆₇⋊C₈	—	2	2	no	—
226	C₆₇⋊C₈	—	2	2	no	—
227	C₆₇⋊C₈	—	2	2	no	—
228	C₆₇⋊C₈	—	2	2	no	—
229	C₂²×C₆₇	—	2	2	no	—
230	C₂²×C₆₇	—	2	2	no	—
231	C₂²×C₆₇	—	2	2	no	—
232	C₂²×C₆₇	—	4	2	no	—
233	C₂²×C₆₇	—	4	2	no	—
234	C₂²×C₆₇	C₂²×C₄²	1	1	yes	characteristic
235	C₂²×C₆₇	C₂×#117	1	1	yes	characteristic
236	C₂²×C₆₇	C₂×#117	1	1	yes	characteristic
237	C₂²×C₆₇	C₂×#131	1	2	yes	—
238	C₂²×C₆₇	#568	1	2	yes	—
239	C₄×C₆₇	—	2	2	no	—
240	C₄×C₆₇	—	2	2	no	—
241	C₄×C₆₇	—	2	2	no	—
242	C₄×C₆₇	—	2	2	no	—
243	C₄×C₆₇	—	2	2	no	—
244	C₄×C₆₇	C₄×#41	1	1	yes	characteristic
245	C₄×C₆₇	C₄×#41	1	1	yes	characteristic
246	C₄×C₆₇	C₄×#41	1	1	yes	characteristic
247	C₄×C₆₇	C₄×#41	1	1	yes	characteristic
248	Dic₆₇	—	2	4	no	—
249	Dic₆₇	—	2	4	no	—
250	Dic₆₇	—	2	4	no	—
251	Dic₆₇	—	4	2	no	—
252	#20468	—	67	1	no	maximal, Sylow
253	C₂×C₆₇	—	4	2	no	—
254	C₂×C₆₇	C₄×#117	1	1	yes	characteristic
255	C₂×C₆₇	C₄×#131	1	1	yes	characteristic
256	C₂×C₆₇	#2875	1	1	yes	characteristic
257	C₂×C₆₇	#2924	1	2	yes	—
258	C₂×C₆₇	#2925	1	2	yes	—
259	C₂×#433	—	67	1	no	—
260	C₂×#433	D₆₇	1	1	yes	characteristic
261	C₄×#117	—	67	1	no	—
262	#1768	—	67	1	no	—
263	#1768	—	67	1	no	—
264	#1767	—	67	1	no	—
265	C₄×C₄⋊C₈	—	67	1	no	—
266	#1750	—	67	1	no	—
267	#1750	—	67	1	no	—
268	#1749	—	67	1	no	—
269	C₄×C₂²⋊C₈	—	67	1	no	—
270	#1745	—	67	1	no	—
271	#1744	—	67	1	no	—
272	#1726	—	67	1	no	—
273	#1726	—	67	1	no	—
274	C₆₇	#20468	1	1	yes	characteristic, complemented, Sylow
275	C₂×#117	—	67	1	no	—
276	C₂×#117	C₂×D₆₇	1	1	yes	characteristic
277	C₂²×C₄²	—	67	1	no	—
278	#433	—	67	8	no	—
279	#433	Dic₆₇	1	8	yes	complemented
280	C₂×C₄⋊C₈	—	67	1	no	—
281	C₂×C₄⋊C₈	—	67	1	no	—
282	C₂×C₄⋊C₈	C₂×D₆₇	1	1	yes	characteristic
283	C₂×C₄⋊C₈	C₂×D₆₇	1	1	yes	characteristic
284	C₂×C₂²⋊C₈	—	67	1	no	—
285	C₂×C₂²⋊C₈	—	67	1	no	—
286	C₂×C₂²⋊C₈	C₂×D₆₇	1	1	yes	characteristic
287	C₂×C₂²⋊C₈	C₂×D₆₇	1	1	yes	characteristic
288	C₂×#97	—	67	1	no	—
289	C₂×#97	—	67	1	no	—
290	C₂×#97	—	67	1	no	—
291	C₂×#97	—	67	1	no	—
292	C₂×#97	—	67	1	no	—
293	C₂×#97	C₂×D₆₇	1	1	yes	characteristic
294	C₂×C₄×C₈	—	67	1	no	—
295	C₂×C₄×C₈	—	67	1	no	—
296	C₂×C₄×C₈	—	67	1	no	—
297	C₂×C₄×C₈	—	67	1	no	—
298	C₂×C₄×C₈	—	67	1	no	—
299	C₂×C₄×C₈	C₂×D₆₇	1	1	yes	characteristic
300	C₄×C₄⋊C₄	—	67	2	no	—
301	C₄×C₄⋊C₄	—	67	2	no	—
302	C₄×C₂²⋊C₄	—	67	2	no	—
303	C₄×C₂²⋊C₄	—	67	2	no	—
304	#376	—	67	1	no	—
305	#376	—	67	1	no	—
306	C₄³	—	67	1	no	—
307	C₄³	—	67	1	no	—
308	#336	—	67	1	no	—
309	#336	—	67	1	no	—
310	#336	—	67	1	no	—
311	#336	—	67	1	no	—
312	#336	—	67	1	no	—
313	#336	—	67	1	no	—
314	#336	—	67	1	no	—
315	#336	—	67	1	no	—
316	C₂³×C₄	—	67	2	no	—
317	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
318	C₂²×C₈	—	67	1	no	—
319	C₂²×C₈	—	67	1	no	—
320	C₂²×C₈	—	67	1	no	—
321	C₂²×C₈	—	67	1	no	—
322	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
323	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
324	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
325	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
326	#117	—	134	2	no	—
327	#117	—	134	2	no	—
328	#117	C₄×D₆₇	1	4	yes	—
329	#117	C₂×Dic₆₇	1	4	yes	—
330	C₂×C₄⋊C₄	—	67	2	no	—
331	C₂×C₄⋊C₄	C₄×D₆₇	1	1	yes	characteristic
332	C₂×C₄⋊C₄	C₄×D₆₇	1	1	yes	characteristic
333	C₂×C₂²⋊C₄	—	67	2	no	—
334	C₂×C₂²⋊C₄	C₄×D₆₇	1	1	yes	characteristic
335	C₂×C₂²⋊C₄	C₄×D₆₇	1	1	yes	characteristic
336	C₂×C₄²	—	67	2	no	—
337	C₂×C₄²	—	67	2	no	—
338	C₂×C₄²	—	67	1	no	—
339	C₂×C₄²	—	67	1	no	—
340	C₂×C₄²	—	67	2	no	—
341	C₂×C₄²	—	67	2	no	—
342	C₂×C₄²	—	67	2	no	—
343	C₂×C₄²	—	67	1	no	—
344	C₂×C₄²	—	67	1	no	—
345	C₂×C₄²	—	134	2	no	—
346	C₂×C₄²	—	134	2	no	—
347	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
348	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
349	C₄⋊C₈	—	67	4	no	—
350	C₄⋊C₈	—	67	4	no	—
351	C₄⋊C₈	C₂×Dic₆₇	1	4	yes	complemented
352	C₄⋊C₈	C₂×Dic₆₇	1	4	yes	complemented
353	C₂²⋊C₈	—	67	4	no	—
354	C₂²⋊C₈	—	67	4	no	—
355	C₂²⋊C₈	C₂×Dic₆₇	1	4	yes	—
356	C₂²⋊C₈	C₂×Dic₆₇	1	4	yes	—
357	#97	—	67	4	no	—
358	#97	—	134	2	no	—
359	#97	—	134	2	no	—
360	#97	—	134	2	no	—
361	#97	—	134	2	no	—
362	#97	C₂×Dic₆₇	1	4	yes	complemented
363	C₄×C₈	—	67	4	no	—
364	C₄×C₈	—	134	2	no	—
365	C₄×C₈	—	134	2	no	—
366	C₄×C₈	—	134	2	no	—
367	C₄×C₈	—	134	2	no	—
368	C₄×C₈	C₂×Dic₆₇	1	4	yes	complemented
369	#95	—	67	2	no	—
370	#95	—	67	2	no	—
371	#95	—	67	2	no	—
372	#95	—	67	2	no	—
373	C₂⁴	C₂×C₄×D₆₇	1	1	yes	characteristic
374	C₂²×C₄	—	2	1	no	—
375	C₂²×C₄	—	2	1	no	—
376	C₂²×C₄	—	2	1	no	—
377	C₂²×C₄	—	2	1	no	—
378	C₂²×C₄	—	268	2	no	—
379	C₂²×C₄	—	67	2	no	—
380	C₂²×C₄	—	67	2	no	—
381	C₂²×C₄	—	67	2	no	—
382	C₂²×C₄	—	67	2	no	—
383	C₂²×C₄	—	134	4	no	—
384	C₂²×C₄	—	134	4	no	—
385	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
386	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
387	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
388	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
389	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
390	C₂²×C₄	C₂×C₄×D₆₇	1	2	yes	—
391	C₂²×C₄	C₂²×Dic₆₇	1	2	yes	—
392	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
393	C₂×C₈	—	2	1	no	—
394	C₂×C₈	—	2	1	no	—
395	C₂×C₈	—	2	1	no	—
396	C₂×C₈	—	2	1	no	—
397	C₂×C₈	—	2	1	no	—
398	C₂×C₈	—	2	1	no	—
399	C₂×C₈	—	2	1	no	—
400	C₂×C₈	—	2	1	no	—
401	C₂×C₈	—	67	2	no	—
402	C₂×C₈	—	67	2	no	—
403	C₂×C₈	—	67	2	no	—
404	C₂×C₈	—	67	2	no	—
405	C₂×C₈	—	134	1	no	—
406	C₂×C₈	—	134	1	no	—
407	C₂×C₈	—	134	1	no	—
408	C₂×C₈	—	134	1	no	—
409	C₂×C₈	—	134	1	no	—
410	C₂×C₈	—	134	1	no	—
411	C₂×C₈	—	134	1	no	—
412	C₂×C₈	—	134	1	no	—
413	C₂×C₈	C₂²×Dic₆₇	1	2	yes	—
414	C₂×C₈	C₂²×Dic₆₇	1	2	yes	—
415	C₂×C₈	C₂²×Dic₆₇	1	2	yes	—
416	C₂×C₈	C₂²×Dic₆₇	1	2	yes	—
417	C₄⋊C₄	—	134	4	no	—
418	C₄⋊C₄	C₄×Dic₆₇	1	4	yes	—
419	C₄⋊C₄	C₄×Dic₆₇	1	4	yes	—
420	C₂²⋊C₄	—	134	4	no	—
421	C₂²⋊C₄	C₄×Dic₆₇	1	4	yes	—
422	C₂²⋊C₄	C₄×Dic₆₇	1	4	yes	—
423	C₄²	—	268	2	no	—
424	C₄²	—	268	2	no	—
425	C₄²	—	67	2	no	—
426	C₄²	—	67	2	no	—
427	C₄²	—	67	2	no	—
428	C₄²	—	67	2	no	—
429	C₄²	—	134	4	no	—
430	C₄²	—	134	4	no	—
431	C₄²	—	134	4	no	—
432	C₄²	—	134	1	no	—
433	C₄²	—	134	1	no	—
434	C₄²	—	134	1	no	—
435	C₄²	—	134	1	no	—
436	C₄²	C₂×C₄×D₆₇	1	2	yes	—
437	C₄²	C₂×C₄×D₆₇	1	2	yes	—
438	C₄²	C₂²×Dic₆₇	1	2	yes	—
439	C₄²	C₂²×Dic₆₇	1	2	yes	—
440	C₂³	—	2	1	no	—
441	C₂³	—	2	1	no	—
442	C₂³	—	2	2	no	—
443	C₂³	—	2	2	no	—
444	C₂³	C₂×C₄×Dic₆₇	1	2	yes	—
445	C₂³	C₂²×C₄×D₆₇	1	1	yes	characteristic
446	C₂×C₄	—	2	1	no	—
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	268	8	no	—
457	C₂×C₄	—	67	4	no	—
458	C₂×C₄	—	67	4	no	—
459	C₂×C₄	—	67	4	no	—
460	C₂×C₄	—	134	2	no	—
461	C₂×C₄	—	134	2	no	—
462	C₂×C₄	—	134	2	no	—
463	C₂×C₄	—	134	2	no	—
464	C₂×C₄	—	134	2	no	—
465	C₂×C₄	—	134	2	no	—
466	C₂×C₄	—	134	2	no	—
467	C₂×C₄	—	134	2	no	—
468	C₂×C₄	—	134	2	no	—
469	C₂×C₄	C₂×C₄×Dic₆₇	1	2	yes	—
470	C₂×C₄	C₂×C₄×Dic₆₇	1	2	yes	—
471	C₂×C₄	C₂×C₄×Dic₆₇	1	2	yes	—
472	C₂×C₄	C₂×C₄×Dic₆₇	1	2	yes	—
473	C₂×C₄	C₂×C₄×Dic₆₇	1	2	yes	—
474	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
475	C₂×C₄	C₂³×Dic₆₇	1	1	yes	characteristic
476	C₂×C₄	#41×D₆₇	1	1	yes	characteristic
477	C₂×C₄	#41×D₆₇	1	1	yes	characteristic
478	C₂×C₄	#41×D₆₇	1	1	yes	characteristic
479	C₂×C₄	#41×D₆₇	1	1	yes	characteristic
480	C₈	—	2	2	no	—
481	C₈	—	2	2	no	—
482	C₈	—	2	2	no	—
483	C₈	—	2	2	no	—
484	C₈	—	134	2	no	—
485	C₈	—	134	2	no	—
486	C₈	—	134	2	no	—
487	C₈	—	134	2	no	—
488	C₂²	—	2	2	no	—
489	C₂²	—	2	2	no	—
490	C₂²	—	2	2	no	—
491	C₂²	—	4	2	no	—
492	C₂²	—	4	2	no	—
493	C₂²	C₂²×C₄×Dic₆₇	1	1	yes	characteristic
494	C₂²	#117×D₆₇	1	1	yes	characteristic
495	C₂²	#117×D₆₇	1	1	yes	characteristic
496	C₂²	#131×D₆₇	1	2	yes	—
497	C₂²	#16864161	1	2	yes	—
498	C₄	—	2	2	no	—
499	C₄	—	2	2	no	—
500	C₄	—	2	2	no	—
501	C₄	—	2	2	no	—
502	C₄	—	2	2	no	—
503	C₄	—	268	2	no	—
504	C₄	—	134	4	no	—
505	C₄	—	134	4	no	—
506	C₄	—	134	4	no	—
507	C₄	#16863864	1	1	yes	characteristic
508	C₄	#16863864	1	1	yes	characteristic
509	C₄	#41×Dic₆₇	1	1	yes	characteristic
510	C₄	#41×Dic₆₇	1	1	yes	characteristic
511	C₂	—	4	2	no	—
512	C₂	#117×Dic₆₇	1	1	yes	characteristic
513	C₂	#131×Dic₆₇	1	1	yes	characteristic
514	C₂	#22568635	1	1	yes	characteristic
515	C₂	#22568865	1	2	yes	—
516	C₂	#22568872	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₆₇
commutator	C₂²×C₆₇	C₂²×C₄²
Fitting	C₂×#433×C₆₇	C₂
socle	C₂³×C₆₇	C₂³×C₄
prime radical	C₂⁴×C₆₇	C₂²×C₄
cosocle	C₂²×C₄×C₆₇	C₂⁴
hypercenter	C₂×#433	D₆₇
hypocenter	C₆₇	#20468
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#433

Complements

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

N	H ≅ G/N	type
3. #22560068	C₂	semidirect
4. #22560068	C₂	semidirect
5. #22560064	C₂	semidirect
6. C₄⋊C₈×Dic₆₇	C₂	semidirect
11. #22559957	C₂	semidirect
12. #22559954	C₂	semidirect
13. #22559897	C₂	semidirect
14. #22559895	C₂	semidirect
18. #16863457	C₄	semidirect
50. #433×C₆₇	C₄	semidirect
77. C₄⋊(C₆₇⋊C₈)	C₂×C₄	semidirect
78. C₄⋊(C₆₇⋊C₈)	C₂×C₄	semidirect
81. #14523954	C₂×C₄	semidirect
86. C₄×C₆₇⋊C₈	C₂×C₄	semidirect
108. C₄⋊C₈×C₆₇	C₂×C₄	semidirect
109. C₄⋊C₈×C₆₇	C₂×C₄	semidirect
112. #97×C₆₇	C₂×C₄	semidirect
113. C₄×C₈×C₆₇	C₂×C₄	semidirect
274. C₆₇	#20468	semidirect
279. #433	Dic₆₇	semidirect
351. C₄⋊C₈	C₂×Dic₆₇	semidirect
352. C₄⋊C₈	C₂×Dic₆₇	semidirect
362. #97	C₂×Dic₆₇	semidirect
368. C₄×C₈	C₂×Dic₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16863457	2
#117×Dic₆₇	2
#22560068	2
#22560064	2
C₄⋊C₈×Dic₆₇	2
#22559977	2
#22559973	2
C₂²⋊C₈×Dic₆₇	2
#22559957	2
#22559954	2
#22559897	2
#22559895	2
C₂×#433×C₆₇	2
#20468	67