Subgroups — #30873413

Order 17152.

780 conjugacy classes of subgroups.

The subgroup lattice has 628 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	C₂×#16863453	C₂	1	1	yes	maximal, characteristic
3	#22560933	C₂	1	1	yes	maximal, characteristic, complemented
4	#22560928	C₂	1	1	yes	maximal, characteristic, complemented
5	#22560775	C₂	1	1	yes	maximal, characteristic, complemented
6	#22560775	C₂	1	1	yes	maximal, characteristic, complemented
7	#22560775	C₂	1	1	yes	maximal, characteristic, complemented
8	#22560768	C₂	1	1	yes	maximal, characteristic, complemented
9	#22560280	C₂	1	1	yes	maximal, characteristic
10	#22560277	C₂	1	1	yes	maximal, characteristic
11	#22560193	C₂	1	1	yes	maximal, characteristic
12	#22560084	C₂	1	1	yes	maximal, characteristic, complemented
13	#22560078	C₂	1	1	yes	maximal, characteristic, complemented
14	#22559975	C₂	1	1	yes	maximal, characteristic
15	C₆₇×#2296	C₂	1	1	yes	maximal, characteristic
16	#16863457	—	2	4	no	—
17	#16863453	—	2	4	no	—
18	C₂×C₄⋊(C₆₇⋊C₈)	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊(C₆₇⋊C₈)	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊(C₆₇⋊C₈)	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊(C₆₇⋊C₈)	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊(C₆₇⋊C₈)	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊(C₆₇⋊C₈)	C₂²	1	1	yes	characteristic
24	C₂×C₂²⋊(C₆₇⋊C₈)	C₂²	1	1	yes	characteristic
25	C₂×C₂²⋊(C₆₇⋊C₈)	C₂²	1	1	yes	characteristic
26	C₂×C₂²⋊(C₆₇⋊C₈)	C₂²	1	1	yes	characteristic
27	C₂×C₂²⋊(C₆₇⋊C₈)	C₂²	1	1	yes	characteristic
28	C₂×#14523954	C₂²	1	1	yes	characteristic
29	C₂×#14523954	C₂²	1	1	yes	characteristic
30	C₂×#14523954	C₂²	1	1	yes	characteristic
31	C₂×#14523954	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₆₇⋊C₈	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₆₇⋊C₈	C₂²	1	1	yes	characteristic
34	#16863151	C₂²	1	1	yes	characteristic
35	#16863151	C₂²	1	1	yes	characteristic
36	#16863151	C₂²	1	1	yes	characteristic
37	#16863151	C₂²	1	1	yes	characteristic
38	#16863151	C₂²	1	1	yes	characteristic
39	#16863151	C₂²	1	1	yes	characteristic
40	#16863151	C₂²	1	1	yes	characteristic
41	#16863151	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	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
47	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
48	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
49	#389×C₆₇	C₄	1	1	yes	characteristic
50	#389×C₆₇	C₄	1	1	yes	characteristic
51	#389×C₆₇	C₄	1	1	yes	characteristic
52	#389×C₆₇	C₄	1	1	yes	characteristic
53	#385×C₆₇	C₄	1	1	yes	characteristic
54	#385×C₆₇	C₄	1	1	yes	characteristic
55	#385×C₆₇	C₄	1	1	yes	characteristic
56	#385×C₆₇	C₄	1	1	yes	characteristic
57	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
58	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
59	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
60	C₄×C₄⋊C₄×C₆₇	C₂²	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	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	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
69	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
70	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
71	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
72	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
73	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
74	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
75	C₂²⋊(C₆₇⋊C₈)	—	2	2	no	—
76	C₂²⋊(C₆₇⋊C₈)	—	2	2	no	—
77	C₂²⋊(C₆₇⋊C₈)	—	2	2	no	—
78	C₂²⋊(C₆₇⋊C₈)	D₄	1	4	yes	—
79	#14523954	—	2	2	no	—
80	#14523954	—	2	2	no	—
81	#14523954	—	2	2	no	—
82	#14523954	—	2	2	no	—
83	C₄×C₆₇⋊C₈	—	2	2	no	—
84	C₄×C₆₇⋊C₈	—	2	2	no	—
85	C₂³×C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
86	C₂³×C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
87	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
88	#117×C₆₇	—	2	2	no	—
89	#117×C₆₇	—	2	2	no	—
90	#117×C₆₇	—	2	2	no	—
91	#117×C₆₇	—	2	2	no	—
92	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
93	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
94	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
95	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
96	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
97	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
98	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
99	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
100	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
101	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
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×C₂²⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
107	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
108	C₂×C₄²×C₆₇	—	2	2	no	—
109	C₂×C₄²×C₆₇	—	2	2	no	—
110	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
111	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
112	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
113	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
114	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
115	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
116	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
117	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
118	#95×C₆₇	C₂×C₄	1	1	yes	characteristic
119	#95×C₆₇	C₂×C₄	1	1	yes	characteristic
120	#95×C₆₇	C₂×C₄	1	1	yes	characteristic
121	#95×C₆₇	C₂×C₄	1	1	yes	characteristic
122	#95×C₆₇	C₂×C₄	1	1	yes	characteristic
123	#95×C₆₇	C₂×C₄	1	1	yes	characteristic
124	#95×C₆₇	C₂×C₄	1	1	yes	characteristic
125	#95×C₆₇	C₂×C₄	1	1	yes	characteristic
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	—	2	1	no	—
130	C₂×C₆₇⋊C₈	—	2	1	no	—
131	C₂×C₆₇⋊C₈	—	2	1	no	—
132	C₂×C₆₇⋊C₈	—	2	1	no	—
133	C₂×C₆₇⋊C₈	—	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	—	2	1	no	—
145	C₂×C₆₇⋊C₈	—	2	1	no	—
146	C₂×C₆₇⋊C₈	—	2	1	no	—
147	C₂×C₆₇⋊C₈	—	2	1	no	—
148	C₂×C₆₇⋊C₈	C₂×D₄	1	2	yes	—
149	C₂×C₆₇⋊C₈	C₂×D₄	1	2	yes	—
150	C₂⁴×C₆₇	C₂²×C₄	1	1	yes	characteristic
151	C₂²×C₄×C₆₇	—	2	1	no	—
152	C₂²×C₄×C₆₇	—	2	1	no	—
153	C₂²×C₄×C₆₇	—	2	1	no	—
154	C₂²×C₄×C₆₇	—	2	1	no	—
155	C₂²×C₄×C₆₇	—	2	2	no	—
156	C₂²×C₄×C₆₇	—	2	2	no	—
157	C₂²×C₄×C₆₇	—	2	2	no	—
158	C₂²×C₄×C₆₇	—	4	1	no	—
159	C₂²×C₄×C₆₇	—	4	1	no	—
160	C₂²×C₄×C₆₇	—	4	1	no	—
161	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
162	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
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	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	C₂²×C₄	1	1	yes	characteristic
174	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
175	C₂²×C₄×C₆₇	#41	1	2	yes	—
176	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
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	—	2	2	no	—
182	C₄⋊C₄×C₆₇	—	2	2	no	—
183	C₄⋊C₄×C₆₇	—	4	1	no	—
184	C₄⋊C₄×C₆₇	—	4	1	no	—
185	C₄⋊C₄×C₆₇	—	4	1	no	—
186	C₄⋊C₄×C₆₇	—	4	1	no	—
187	C₄⋊C₄×C₆₇	—	4	1	no	—
188	C₄⋊C₄×C₆₇	—	4	1	no	—
189	C₂²⋊C₄×C₆₇	—	2	2	no	—
190	C₂²⋊C₄×C₆₇	—	2	2	no	—
191	C₂²⋊C₄×C₆₇	—	2	2	no	—
192	C₂²⋊C₄×C₆₇	—	2	2	no	—
193	C₄²×C₆₇	—	2	2	no	—
194	C₄²×C₆₇	—	2	2	no	—
195	C₄²×C₆₇	—	2	1	no	—
196	C₄²×C₆₇	—	2	1	no	—
197	C₄²×C₆₇	—	2	1	no	—
198	C₄²×C₆₇	—	2	1	no	—
199	C₄²×C₆₇	—	2	1	no	—
200	C₄²×C₆₇	—	2	1	no	—
201	C₄²×C₆₇	—	2	1	no	—
202	C₄²×C₆₇	—	2	1	no	—
203	C₄²×C₆₇	—	2	1	no	—
204	C₄²×C₆₇	—	2	1	no	—
205	C₄²×C₆₇	#41	1	2	yes	—
206	C₄²×C₆₇	#41	1	2	yes	—
207	C₂³×C₆₇	—	2	1	no	—
208	C₂³×C₆₇	—	2	1	no	—
209	C₂³×C₆₇	—	2	1	no	—
210	C₂³×C₆₇	—	2	1	no	—
211	C₂³×C₆₇	—	2	1	no	—
212	C₂³×C₆₇	—	2	1	no	—
213	C₂³×C₆₇	C₄×D₄	1	2	yes	—
214	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
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	—	2	1	no	—
222	C₂×C₄×C₆₇	—	2	1	no	—
223	C₂×C₄×C₆₇	—	2	2	no	—
224	C₂×C₄×C₆₇	—	2	2	no	—
225	C₂×C₄×C₆₇	—	2	2	no	—
226	C₂×C₄×C₆₇	—	2	2	no	—
227	C₂×C₄×C₆₇	—	2	1	no	—
228	C₂×C₄×C₆₇	—	2	1	no	—
229	C₂×C₄×C₆₇	—	2	1	no	—
230	C₂×C₄×C₆₇	—	2	1	no	—
231	C₂×C₄×C₆₇	—	2	1	no	—
232	C₂×C₄×C₆₇	—	2	1	no	—
233	C₂×C₄×C₆₇	—	2	1	no	—
234	C₂×C₄×C₆₇	—	2	1	no	—
235	C₂×C₄×C₆₇	—	2	1	no	—
236	C₂×C₄×C₆₇	—	2	1	no	—
237	C₂×C₄×C₆₇	—	2	1	no	—
238	C₂×C₄×C₆₇	—	2	1	no	—
239	C₂×C₄×C₆₇	—	2	1	no	—
240	C₂×C₄×C₆₇	—	2	1	no	—
241	C₂×C₄×C₆₇	—	2	1	no	—
242	C₂×C₄×C₆₇	—	2	1	no	—
243	C₂×C₄×C₆₇	—	2	1	no	—
244	C₂×C₄×C₆₇	—	2	1	no	—
245	C₂×C₄×C₆₇	—	2	1	no	—
246	C₂×C₄×C₆₇	—	2	1	no	—
247	C₂×C₄×C₆₇	—	2	1	no	—
248	C₂×C₄×C₆₇	—	2	1	no	—
249	C₂×C₄×C₆₇	—	2	1	no	—
250	C₂×C₄×C₆₇	—	2	1	no	—
251	C₂×C₄×C₆₇	—	2	1	no	—
252	C₂×C₄×C₆₇	—	2	1	no	—
253	C₂×C₄×C₆₇	—	2	1	no	—
254	C₂×C₄×C₆₇	—	4	4	no	—
255	C₂×C₄×C₆₇	—	4	4	no	—
256	C₂×C₄×C₆₇	#117	1	2	yes	—
257	C₂×C₄×C₆₇	#117	1	2	yes	—
258	C₂×C₄×C₆₇	C₄×D₄	1	2	yes	—
259	C₂×C₄×C₆₇	#131	1	2	yes	—
260	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
261	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
262	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
263	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
264	C₂×C₄×C₆₇	2₋¹⁺⁴	1	1	yes	characteristic
265	C₂×C₄×C₆₇	2₋¹⁺⁴	1	1	yes	characteristic
266	C₆₇⋊C₈	—	2	2	no	—
267	C₆₇⋊C₈	—	2	2	no	—
268	C₆₇⋊C₈	—	4	1	no	—
269	C₆₇⋊C₈	—	4	1	no	—
270	C₆₇⋊C₈	—	4	1	no	—
271	C₆₇⋊C₈	—	4	1	no	—
272	C₆₇⋊C₈	—	4	1	no	—
273	C₆₇⋊C₈	—	4	1	no	—
274	C₂²×C₆₇	—	2	2	no	—
275	C₂²×C₆₇	—	2	2	no	—
276	C₂²×C₆₇	—	2	2	no	—
277	C₂²×C₆₇	—	4	1	no	—
278	C₂²×C₆₇	—	4	1	no	—
279	C₂²×C₆₇	—	4	1	no	—
280	C₂²×C₆₇	—	4	1	no	—
281	C₂²×C₆₇	C₂×#117	1	1	yes	characteristic
282	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
283	C₂²×C₆₇	#519	1	1	yes	characteristic
284	C₂²×C₆₇	C₂×#131	1	1	yes	characteristic
285	C₂²×C₆₇	#568	1	1	yes	characteristic
286	C₂²×C₆₇	#568	1	1	yes	characteristic
287	C₂²×C₆₇	#568	1	1	yes	characteristic
288	C₄×C₆₇	—	2	2	no	—
289	C₄×C₆₇	—	2	2	no	—
290	C₄×C₆₇	—	2	2	no	—
291	C₄×C₆₇	—	2	2	no	—
292	C₄×C₆₇	—	4	1	no	—
293	C₄×C₆₇	—	4	1	no	—
294	C₄×C₆₇	—	4	1	no	—
295	C₄×C₆₇	—	4	1	no	—
296	C₄×C₆₇	—	4	1	no	—
297	C₄×C₆₇	—	4	1	no	—
298	C₄×C₆₇	—	4	1	no	—
299	C₄×C₆₇	—	4	1	no	—
300	C₄×C₆₇	—	4	1	no	—
301	C₄×C₆₇	#547	1	1	yes	characteristic
302	C₄×C₆₇	#547	1	1	yes	characteristic
303	C₄×C₆₇	#552	1	1	yes	characteristic
304	C₄×C₆₇	#552	1	1	yes	characteristic
305	#22605	—	67	1	no	maximal, Sylow
306	C₂×C₆₇	—	4	2	no	—
307	C₂×C₆₇	#2344	1	1	yes	characteristic
308	C₂×C₆₇	#2923	1	1	yes	characteristic
309	C₂×C₆₇	#2925	1	1	yes	characteristic
310	C₂×C₆₇	#2930	1	1	yes	characteristic
311	C₂×C₆₇	#2933	1	1	yes	characteristic
312	C₂×C₆₇	#2985	1	1	yes	characteristic
313	C₂×C₆₇	#2987	1	1	yes	characteristic
314	C₂×#433	—	67	1	no	—
315	C₂×#432	—	67	1	no	—
316	#2296	D₆₇	1	1	yes	characteristic
317	#1940	—	67	1	no	—
318	#1939	—	67	1	no	—
319	#1917	—	67	1	no	—
320	#1917	—	67	1	no	—
321	#1917	—	67	1	no	—
322	#1916	—	67	1	no	—
323	#1818	—	67	1	no	—
324	#1817	—	67	1	no	—
325	#1798	—	67	1	no	—
326	#1771	—	67	1	no	—
327	#1770	—	67	1	no	—
328	#1750	—	67	1	no	—
329	C₆₇	#22605	1	1	yes	characteristic, complemented, Sylow
330	C₂×#117	C₂×D₆₇	1	1	yes	characteristic
331	C₂×#117	C₂×D₆₇	1	1	yes	characteristic
332	C₂²×C₄²	C₂×D₆₇	1	1	yes	characteristic
333	#433	—	134	4	no	—
334	#432	—	134	4	no	—
335	C₂×C₄⋊C₈	—	67	1	no	—
336	C₂×C₄⋊C₈	—	67	1	no	—
337	C₂×C₄⋊C₈	—	67	1	no	—
338	C₂×C₄⋊C₈	—	67	1	no	—
339	C₂×C₄⋊C₈	—	67	1	no	—
340	C₂×C₄⋊C₈	—	67	1	no	—
341	C₂×C₂²⋊C₈	—	67	1	no	—
342	C₂×C₂²⋊C₈	—	67	1	no	—
343	C₂×C₂²⋊C₈	—	67	1	no	—
344	C₂×C₂²⋊C₈	—	67	1	no	—
345	C₂×#97	—	67	1	no	—
346	C₂×#97	—	67	1	no	—
347	C₂×#97	—	67	1	no	—
348	C₂×#97	—	67	1	no	—
349	C₂×C₄×C₈	—	67	1	no	—
350	C₂×C₄×C₈	—	67	1	no	—
351	#389	Dic₆₇	1	1	yes	characteristic
352	#389	Dic₆₇	1	1	yes	characteristic
353	#389	Dic₆₇	1	1	yes	characteristic
354	#389	Dic₆₇	1	1	yes	characteristic
355	#385	Dic₆₇	1	1	yes	characteristic
356	#385	Dic₆₇	1	1	yes	characteristic
357	#385	Dic₆₇	1	1	yes	characteristic
358	#385	Dic₆₇	1	1	yes	characteristic
359	C₄×C₄⋊C₄	C₂×D₆₇	1	1	yes	characteristic
360	C₄×C₄⋊C₄	C₂×D₆₇	1	1	yes	characteristic
361	C₄×C₄⋊C₄	C₂×D₆₇	1	1	yes	characteristic
362	C₄×C₄⋊C₄	C₂×D₆₇	1	1	yes	characteristic
363	#336	—	67	1	no	—
364	#336	—	67	1	no	—
365	#336	—	67	1	no	—
366	#336	—	67	1	no	—
367	#336	—	67	1	no	—
368	#336	—	67	1	no	—
369	#336	—	67	1	no	—
370	#336	—	67	1	no	—
371	#336	—	67	1	no	—
372	#336	—	67	1	no	—
373	#336	—	67	1	no	—
374	#336	—	67	1	no	—
375	C₂³×C₄	C₂×Dic₆₇	1	1	yes	characteristic
376	C₂³×C₄	C₂×Dic₆₇	1	1	yes	characteristic
377	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
378	C₂²×C₈	—	67	1	no	—
379	C₂²×C₈	—	67	1	no	—
380	C₂²×C₈	—	67	1	no	—
381	C₂²×C₈	—	67	1	no	—
382	C₂²×C₈	—	67	1	no	—
383	C₂²×C₈	—	67	1	no	—
384	C₂²×C₈	—	67	1	no	—
385	C₂²×C₈	—	67	1	no	—
386	#117	—	2	2	no	—
387	#117	—	2	2	no	—
388	#117	—	2	2	no	—
389	#117	—	2	2	no	—
390	C₂×C₄⋊C₄	C₂×Dic₆₇	1	1	yes	characteristic
391	C₂×C₄⋊C₄	C₂×Dic₆₇	1	1	yes	characteristic
392	C₂×C₄⋊C₄	C₂×Dic₆₇	1	1	yes	characteristic
393	C₂×C₄⋊C₄	C₂×Dic₆₇	1	1	yes	characteristic
394	C₂×C₄⋊C₄	C₂×Dic₆₇	1	1	yes	characteristic
395	C₂×C₄⋊C₄	C₂×Dic₆₇	1	1	yes	characteristic
396	C₂×C₄⋊C₄	C₂×Dic₆₇	1	1	yes	characteristic
397	C₂×C₄⋊C₄	C₂×Dic₆₇	1	1	yes	characteristic
398	C₂×C₄⋊C₄	C₂×Dic₆₇	1	1	yes	characteristic
399	C₂×C₄⋊C₄	C₂×Dic₆₇	1	1	yes	characteristic
400	C₂×C₄⋊C₄	C₂×Dic₆₇	1	1	yes	characteristic
401	C₂×C₄⋊C₄	C₂×Dic₆₇	1	1	yes	characteristic
402	C₂×C₂²⋊C₄	C₂×Dic₆₇	1	1	yes	characteristic
403	C₂×C₂²⋊C₄	C₂×Dic₆₇	1	1	yes	characteristic
404	C₂×C₂²⋊C₄	C₂×Dic₆₇	1	1	yes	characteristic
405	C₂×C₂²⋊C₄	C₂×Dic₆₇	1	1	yes	characteristic
406	C₂×C₄²	—	2	2	no	—
407	C₂×C₄²	—	2	2	no	—
408	C₂×C₄²	C₂×Dic₆₇	1	1	yes	characteristic
409	C₂×C₄²	C₂×Dic₆₇	1	1	yes	characteristic
410	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
411	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
412	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
413	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
414	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
415	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
416	C₄⋊C₈	—	134	2	no	—
417	C₄⋊C₈	—	134	2	no	—
418	C₄⋊C₈	—	134	2	no	—
419	C₄⋊C₈	—	134	2	no	—
420	C₄⋊C₈	—	134	2	no	—
421	C₄⋊C₈	—	134	2	no	—
422	C₂²⋊C₈	—	67	4	no	—
423	C₂²⋊C₈	—	134	2	no	—
424	C₂²⋊C₈	—	134	2	no	—
425	C₂²⋊C₈	—	134	2	no	—
426	#97	—	134	2	no	—
427	#97	—	134	2	no	—
428	#97	—	134	2	no	—
429	#97	—	134	2	no	—
430	C₄×C₈	—	134	2	no	—
431	C₄×C₈	—	134	2	no	—
432	#95	C₂×Dic₆₇	1	1	yes	characteristic
433	#95	C₂×Dic₆₇	1	1	yes	characteristic
434	#95	C₂×Dic₆₇	1	1	yes	characteristic
435	#95	C₂×Dic₆₇	1	1	yes	characteristic
436	#95	C₂×Dic₆₇	1	1	yes	characteristic
437	#95	C₂×Dic₆₇	1	1	yes	characteristic
438	#95	C₂×Dic₆₇	1	1	yes	characteristic
439	#95	C₂×Dic₆₇	1	1	yes	characteristic
440	C₂⁴	C₂²×Dic₆₇	1	1	yes	characteristic
441	C₂²×C₄	—	2	1	no	—
442	C₂²×C₄	—	2	1	no	—
443	C₂²×C₄	—	2	1	no	—
444	C₂²×C₄	—	2	1	no	—
445	C₂²×C₄	—	2	2	no	—
446	C₂²×C₄	—	2	2	no	—
447	C₂²×C₄	—	2	2	no	—
448	C₂²×C₄	—	4	1	no	—
449	C₂²×C₄	—	4	1	no	—
450	C₂²×C₄	—	4	1	no	—
451	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
452	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
453	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
454	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
455	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
456	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
457	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
458	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
459	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
460	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
461	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
462	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
463	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
464	C₂²×C₄	D₄×D₆₇	1	2	yes	—
465	C₂²×C₄	#11761627	1	2	yes	—
466	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
467	C₂×C₈	—	67	2	no	—
468	C₂×C₈	—	67	2	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	—	134	1	no	—
475	C₂×C₈	—	134	1	no	—
476	C₂×C₈	—	134	1	no	—
477	C₂×C₈	—	134	1	no	—
478	C₂×C₈	—	134	1	no	—
479	C₂×C₈	—	134	1	no	—
480	C₂×C₈	—	134	1	no	—
481	C₂×C₈	—	134	1	no	—
482	C₂×C₈	—	134	1	no	—
483	C₂×C₈	—	134	1	no	—
484	C₂×C₈	—	134	1	no	—
485	C₂×C₈	—	134	1	no	—
486	C₂×C₈	—	134	1	no	—
487	C₂×C₈	—	134	1	no	—
488	C₂×C₈	—	134	1	no	—
489	C₂×C₈	—	134	1	no	—
490	C₂×C₈	—	134	1	no	—
491	C₄⋊C₄	—	2	2	no	—
492	C₄⋊C₄	—	2	2	no	—
493	C₄⋊C₄	—	2	2	no	—
494	C₄⋊C₄	—	2	2	no	—
495	C₄⋊C₄	—	2	2	no	—
496	C₄⋊C₄	—	2	2	no	—
497	C₄⋊C₄	—	4	1	no	—
498	C₄⋊C₄	—	4	1	no	—
499	C₄⋊C₄	—	4	1	no	—
500	C₄⋊C₄	—	4	1	no	—
501	C₄⋊C₄	—	4	1	no	—
502	C₄⋊C₄	—	4	1	no	—
503	C₂²⋊C₄	—	2	2	no	—
504	C₂²⋊C₄	—	2	2	no	—
505	C₂²⋊C₄	—	2	2	no	—
506	C₂²⋊C₄	—	2	2	no	—
507	C₄²	—	2	2	no	—
508	C₄²	—	2	2	no	—
509	C₄²	—	2	1	no	—
510	C₄²	—	2	1	no	—
511	C₄²	—	2	1	no	—
512	C₄²	—	2	1	no	—
513	C₄²	—	2	1	no	—
514	C₄²	—	2	1	no	—
515	C₄²	—	2	1	no	—
516	C₄²	—	2	1	no	—
517	C₄²	—	2	1	no	—
518	C₄²	—	2	1	no	—
519	C₄²	#11761628	1	2	yes	—
520	C₄²	#11761628	1	2	yes	—
521	C₂³	—	2	1	no	—
522	C₂³	—	2	1	no	—
523	C₂³	—	2	1	no	—
524	C₂³	—	2	1	no	—
525	C₂³	—	2	1	no	—
526	C₂³	—	2	1	no	—
527	C₂³	D₄×Dic₆₇	1	2	yes	—
528	C₂³	C₂³×Dic₆₇	1	1	yes	characteristic
529	C₂×C₄	—	2	1	no	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	2	no	—
538	C₂×C₄	—	2	2	no	—
539	C₂×C₄	—	2	2	no	—
540	C₂×C₄	—	2	2	no	—
541	C₂×C₄	—	2	1	no	—
542	C₂×C₄	—	2	1	no	—
543	C₂×C₄	—	2	1	no	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	2	1	no	—
551	C₂×C₄	—	2	1	no	—
552	C₂×C₄	—	2	1	no	—
553	C₂×C₄	—	2	1	no	—
554	C₂×C₄	—	2	1	no	—
555	C₂×C₄	—	2	1	no	—
556	C₂×C₄	—	2	1	no	—
557	C₂×C₄	—	2	1	no	—
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	1	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	2	1	no	—
563	C₂×C₄	—	2	1	no	—
564	C₂×C₄	—	2	1	no	—
565	C₂×C₄	—	2	1	no	—
566	C₂×C₄	—	2	1	no	—
567	C₂×C₄	—	2	1	no	—
568	C₂×C₄	—	4	4	no	—
569	C₂×C₄	—	4	4	no	—
570	C₂×C₄	#14524002	1	2	yes	—
571	C₂×C₄	#14524002	1	2	yes	—
572	C₂×C₄	D₄×Dic₆₇	1	2	yes	—
573	C₂×C₄	#14524050	1	2	yes	—
574	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
575	C₂×C₄	C₂×#11761627	1	1	yes	characteristic
576	C₂×C₄	C₂×#11761628	1	1	yes	characteristic
577	C₂×C₄	C₂×#11761628	1	1	yes	characteristic
578	C₂×C₄	#14524091	1	1	yes	characteristic
579	C₂×C₄	#14524091	1	1	yes	characteristic
580	C₈	—	268	1	no	—
581	C₈	—	268	1	no	—
582	C₈	—	268	1	no	—
583	C₈	—	268	1	no	—
584	C₈	—	268	1	no	—
585	C₈	—	268	1	no	—
586	C₈	—	134	2	no	—
587	C₈	—	134	2	no	—
588	C₂²	—	2	2	no	—
589	C₂²	—	2	2	no	—
590	C₂²	—	2	2	no	—
591	C₂²	—	4	1	no	—
592	C₂²	—	4	1	no	—
593	C₂²	—	4	1	no	—
594	C₂²	—	4	1	no	—
595	C₂²	C₂×#14524002	1	1	yes	characteristic
596	C₂²	C₂×D₄×Dic₆₇	1	1	yes	characteristic
597	C₂²	#16863874	1	1	yes	characteristic
598	C₂²	C₂×#14524050	1	1	yes	characteristic
599	C₂²	#16864163	1	1	yes	characteristic
600	C₂²	#16864163	1	1	yes	characteristic
601	C₂²	#16864163	1	1	yes	characteristic
602	C₄	—	2	2	no	—
603	C₄	—	2	2	no	—
604	C₄	—	2	2	no	—
605	C₄	—	2	2	no	—
606	C₄	—	4	1	no	—
607	C₄	—	4	1	no	—
608	C₄	—	4	1	no	—
609	C₄	—	4	1	no	—
610	C₄	—	4	1	no	—
611	C₄	—	4	1	no	—
612	C₄	—	4	1	no	—
613	C₄	—	4	1	no	—
614	C₄	—	4	1	no	—
615	C₄	#16864047	1	1	yes	characteristic
616	C₄	#16864047	1	1	yes	characteristic
617	C₄	#16864081	1	1	yes	characteristic
618	C₄	#16864081	1	1	yes	characteristic
619	C₂	—	4	2	no	—
620	C₂	#22563078	1	1	yes	characteristic
621	C₂	#22568860	1	1	yes	characteristic
622	C₂	#22568875	1	1	yes	characteristic
623	C₂	#22568913	1	1	yes	characteristic
624	C₂	#22568936	1	1	yes	characteristic
625	C₂	#22569304	1	1	yes	characteristic
626	C₂	#22569315	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₆₇
commutator, socle	C₂³×C₆₇	C₂³×C₄
Fitting	C₆₇×#2296	C₂
prime radical	C₂⁴×C₆₇	C₂²×C₄
cosocle	C₂²×C₄×C₆₇	C₂⁴
hypercenter	#2296	D₆₇
hypocenter	C₆₇	#22605
LCS	G ▷ C₂³×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂²×C₄ ◁ #2296

Complements

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

N	H ≅ G/N	type
3. #22560933	C₂	semidirect
4. #22560928	C₂	semidirect
5. #22560775	C₂	semidirect
6. #22560775	C₂	semidirect
7. #22560775	C₂	semidirect
8. #22560768	C₂	semidirect
12. #22560084	C₂	semidirect
13. #22560078	C₂	semidirect
329. C₆₇	#22605	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
C₂×#16863453	2
#22560933	2
#22560928	2
#22560775	2
#22560768	2
#22560280	2
#22560277	2
#22560193	2
#22560084	2
#22560078	2
#22559975	2
C₆₇×#2296	2
#22605	67