Subgroups — #30874378

Order 17152.

944 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16863468	C₂	1	1	yes	maximal, characteristic
2	C₂×D₄×C₆₇⋊C₈	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	#22560394	C₂	1	1	yes	maximal, characteristic, complemented
6	#22560389	C₂	1	1	yes	maximal, characteristic, complemented
7	#22560389	C₂	1	1	yes	maximal, characteristic, complemented
8	#22560389	C₂	1	1	yes	maximal, characteristic, complemented
9	#22560329	C₂	1	1	yes	maximal, characteristic, complemented
10	#22560193	C₂	1	1	yes	maximal, characteristic, complemented
11	#22560189	C₂	1	1	yes	maximal, characteristic, complemented
12	#22560066	C₂	1	1	yes	maximal, characteristic, complemented
13	#22559906	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#16863151	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#2290	C₂	1	1	yes	maximal, characteristic
16	C₂²×#11761612	C₂²	1	1	yes	characteristic
17	C₂³×C₆₇⋊C₈	C₂²	1	1	yes	characteristic
18	C₂³×C₆₇⋊C₈	C₂²	1	1	yes	characteristic
19	C₂³×C₆₇⋊C₈	C₂²	1	1	yes	characteristic
20	#16863468	—	2	4	no	—
21	D₄×C₆₇⋊C₈	—	2	4	no	—
22	C₂×C₄⋊(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	C₂×C₄⋊(C₆₇⋊C₈)	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊(C₆₇⋊C₈)	C₂²	1	1	yes	characteristic
27	C₂×C₄⋊(C₆₇⋊C₈)	C₂²	1	1	yes	characteristic
28	C₂×C₄⋊(C₆₇⋊C₈)	C₂²	1	1	yes	characteristic
29	C₂×C₄⋊(C₆₇⋊C₈)	C₂²	1	1	yes	characteristic
30	C₂×C₂²⋊(C₆₇⋊C₈)	C₂²	1	1	yes	characteristic
31	C₂×C₂²⋊(C₆₇⋊C₈)	C₂²	1	1	yes	characteristic
32	C₂×C₂²⋊(C₆₇⋊C₈)	C₂²	1	1	yes	characteristic
33	C₂×C₂²⋊(C₆₇⋊C₈)	C₂²	1	1	yes	characteristic
34	C₂×#14523954	C₂²	1	1	yes	characteristic
35	C₂×C₄×C₆₇⋊C₈	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×C₄×D₄×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	#388×C₆₇	C₄	1	1	yes	characteristic
50	#388×C₆₇	C₄	1	1	yes	characteristic
51	#387×C₆₇	C₄	1	1	yes	characteristic
52	#387×C₆₇	C₄	1	1	yes	characteristic
53	#386×C₆₇	C₄	1	1	yes	characteristic
54	#386×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×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
59	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
60	#376×C₆₇	C₂²	1	1	yes	characteristic
61	C₂×#11761612	—	2	2	no	—
62	C₂×#11761612	—	2	2	no	—
63	C₂×#11761612	—	4	1	no	—
64	C₂²×C₆₇⋊C₈	—	2	2	no	—
65	C₂²×C₆₇⋊C₈	—	2	2	no	—
66	C₂²×C₆₇⋊C₈	—	2	2	no	—
67	C₂²×C₆₇⋊C₈	—	2	2	no	—
68	C₂²×C₆₇⋊C₈	—	2	2	no	—
69	C₂²×C₆₇⋊C₈	—	2	2	no	—
70	C₂²×C₆₇⋊C₈	—	4	1	no	—
71	C₂²×C₆₇⋊C₈	—	4	1	no	—
72	C₂²×C₆₇⋊C₈	—	4	1	no	—
73	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
74	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
75	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
76	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
77	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
78	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
79	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
80	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
81	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
82	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
83	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
84	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
85	C₄⋊(C₆₇⋊C₈)	—	4	1	no	—
86	C₄⋊(C₆₇⋊C₈)	—	4	1	no	—
87	C₄⋊(C₆₇⋊C₈)	—	4	1	no	—
88	C₄⋊(C₆₇⋊C₈)	—	4	1	no	—
89	C₂²⋊(C₆₇⋊C₈)	—	2	2	no	—
90	C₂²⋊(C₆₇⋊C₈)	—	2	2	no	—
91	C₂²⋊(C₆₇⋊C₈)	—	2	2	no	—
92	C₂²⋊(C₆₇⋊C₈)	—	2	2	no	—
93	#14523954	—	2	2	no	—
94	C₄×C₆₇⋊C₈	—	2	2	no	—
95	C₂²×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
96	C₂³×C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
97	C₂³×C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
98	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
99	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
100	C₄×D₄×C₆₇	D₄	1	4	yes	—
101	C₄×D₄×C₆₇	Q₈	1	4	yes	—
102	#117×C₆₇	—	4	1	no	—
103	#117×C₆₇	—	4	1	no	—
104	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
105	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
106	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
107	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
108	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
109	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
110	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	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×C₂²⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
114	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
115	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
116	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
117	C₂×C₄²×C₆₇	—	4	1	no	—
118	C₂×C₄²×C₆₇	—	4	1	no	—
119	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
120	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
121	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
122	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
123	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
124	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
125	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
126	#95×C₆₇	C₂×C₄	1	1	yes	characteristic
127	#95×C₆₇	C₂×C₄	1	1	yes	characteristic
128	#95×C₆₇	C₂×C₄	1	1	yes	characteristic
129	#95×C₆₇	C₂×C₄	1	1	yes	characteristic
130	#95×C₆₇	C₂×C₄	1	1	yes	characteristic
131	#95×C₆₇	C₂×C₄	1	1	yes	characteristic
132	#95×C₆₇	C₂×C₄	1	1	yes	characteristic
133	#95×C₆₇	C₂×C₄	1	1	yes	characteristic
134	#95×C₆₇	C₂×C₄	1	1	yes	characteristic
135	#95×C₆₇	C₂×C₄	1	1	yes	characteristic
136	#11761612	—	4	4	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	—	2	1	no	—
149	C₂×C₆₇⋊C₈	—	2	1	no	—
150	C₂×C₆₇⋊C₈	—	2	1	no	—
151	C₂×C₆₇⋊C₈	—	2	1	no	—
152	C₂×C₆₇⋊C₈	—	2	1	no	—
153	C₂×C₆₇⋊C₈	—	2	1	no	—
154	C₂×C₆₇⋊C₈	—	2	1	no	—
155	C₂×C₆₇⋊C₈	—	2	1	no	—
156	C₂×C₆₇⋊C₈	—	2	1	no	—
157	C₂×C₆₇⋊C₈	—	2	1	no	—
158	C₂×C₆₇⋊C₈	—	2	1	no	—
159	C₂×C₆₇⋊C₈	—	4	4	no	—
160	C₂×C₆₇⋊C₈	—	4	4	no	—
161	C₂×C₆₇⋊C₈	—	4	4	no	—
162	C₂×C₆₇⋊C₈	#41	1	2	yes	—
163	C₂×C₆₇⋊C₈	#41	1	2	yes	—
164	C₂⁴×C₆₇	C₂²×C₄	1	1	yes	characteristic
165	C₂⁴×C₆₇	C₂²×C₄	1	1	yes	characteristic
166	C₂×D₄×C₆₇	—	2	2	no	—
167	C₂×D₄×C₆₇	—	2	2	no	—
168	C₂×D₄×C₆₇	C₄⋊C₄	1	4	yes	—
169	C₂²×C₄×C₆₇	—	2	1	no	—
170	C₂²×C₄×C₆₇	—	2	1	no	—
171	C₂²×C₄×C₆₇	—	2	1	no	—
172	C₂²×C₄×C₆₇	—	2	1	no	—
173	C₂²×C₄×C₆₇	—	2	1	no	—
174	C₂²×C₄×C₆₇	—	2	1	no	—
175	C₂²×C₄×C₆₇	—	2	1	no	—
176	C₂²×C₄×C₆₇	—	2	1	no	—
177	C₂²×C₄×C₆₇	—	2	2	no	—
178	C₂²×C₄×C₆₇	—	2	2	no	—
179	C₂²×C₄×C₆₇	—	2	2	no	—
180	C₂²×C₄×C₆₇	—	4	1	no	—
181	C₂²×C₄×C₆₇	—	4	1	no	—
182	C₂²×C₄×C₆₇	—	4	1	no	—
183	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
184	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
185	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
186	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
187	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
188	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
189	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
190	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
191	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
192	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
193	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
194	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
195	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
196	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
197	C₂²×C₄×C₆₇	C₂×Q₈	1	2	yes	—
198	C₂²×C₄×C₆₇	C₂×Q₈	1	2	yes	—
199	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
200	C₄⋊C₄×C₆₇	—	2	2	no	—
201	C₄⋊C₄×C₆₇	—	4	1	no	—
202	C₄⋊C₄×C₆₇	—	4	1	no	—
203	C₄⋊C₄×C₆₇	—	4	1	no	—
204	C₄⋊C₄×C₆₇	C₄⋊C₄	1	4	yes	—
205	C₂²⋊C₄×C₆₇	—	2	2	no	—
206	C₂²⋊C₄×C₆₇	—	2	2	no	—
207	C₂²⋊C₄×C₆₇	—	2	2	no	—
208	C₂²⋊C₄×C₆₇	—	4	1	no	—
209	C₂²⋊C₄×C₆₇	—	4	1	no	—
210	C₂²⋊C₄×C₆₇	—	4	1	no	—
211	C₂²⋊C₄×C₆₇	C₄⋊C₄	1	4	yes	—
212	C₂²⋊C₄×C₆₇	C₄⋊C₄	1	4	yes	—
213	C₄²×C₆₇	—	2	1	no	—
214	C₄²×C₆₇	—	2	1	no	—
215	C₄²×C₆₇	—	2	1	no	—
216	C₄²×C₆₇	—	2	1	no	—
217	C₄²×C₆₇	—	2	1	no	—
218	C₄²×C₆₇	—	2	1	no	—
219	C₄²×C₆₇	—	2	1	no	—
220	C₄²×C₆₇	—	2	1	no	—
221	C₄²×C₆₇	—	4	1	no	—
222	C₄²×C₆₇	—	4	1	no	—
223	C₄²×C₆₇	C₂×D₄	1	2	yes	—
224	C₄²×C₆₇	C₂×Q₈	1	2	yes	—
225	C₂³×C₆₇	—	2	1	no	—
226	C₂³×C₆₇	—	2	1	no	—
227	C₂³×C₆₇	—	2	1	no	—
228	C₂³×C₆₇	—	2	1	no	—
229	C₂³×C₆₇	—	2	1	no	—
230	C₂³×C₆₇	—	2	1	no	—
231	C₂³×C₆₇	—	2	1	no	—
232	C₂³×C₆₇	—	2	1	no	—
233	C₂³×C₆₇	—	2	1	no	—
234	C₂³×C₆₇	—	2	1	no	—
235	C₂³×C₆₇	C₂×C₄⋊C₄	1	2	yes	—
236	C₂³×C₆₇	C₂×C₄⋊C₄	1	2	yes	—
237	C₂³×C₆₇	#131	1	2	yes	—
238	C₂³×C₆₇	#131	1	2	yes	—
239	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
240	D₄×C₆₇	—	2	8	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	2	no	—
252	C₂×C₄×C₆₇	—	2	2	no	—
253	C₂×C₄×C₆₇	—	2	2	no	—
254	C₂×C₄×C₆₇	—	2	2	no	—
255	C₂×C₄×C₆₇	—	2	2	no	—
256	C₂×C₄×C₆₇	—	2	2	no	—
257	C₂×C₄×C₆₇	—	2	2	no	—
258	C₂×C₄×C₆₇	—	2	2	no	—
259	C₂×C₄×C₆₇	—	2	1	no	—
260	C₂×C₄×C₆₇	—	2	1	no	—
261	C₂×C₄×C₆₇	—	2	1	no	—
262	C₂×C₄×C₆₇	—	2	1	no	—
263	C₂×C₄×C₆₇	—	2	1	no	—
264	C₂×C₄×C₆₇	—	2	1	no	—
265	C₂×C₄×C₆₇	—	2	1	no	—
266	C₂×C₄×C₆₇	—	2	1	no	—
267	C₂×C₄×C₆₇	—	2	1	no	—
268	C₂×C₄×C₆₇	—	2	1	no	—
269	C₂×C₄×C₆₇	—	2	1	no	—
270	C₂×C₄×C₆₇	—	2	1	no	—
271	C₂×C₄×C₆₇	—	2	1	no	—
272	C₂×C₄×C₆₇	—	2	1	no	—
273	C₂×C₄×C₆₇	—	2	1	no	—
274	C₂×C₄×C₆₇	—	2	1	no	—
275	C₂×C₄×C₆₇	—	2	1	no	—
276	C₂×C₄×C₆₇	—	2	1	no	—
277	C₂×C₄×C₆₇	—	2	1	no	—
278	C₂×C₄×C₆₇	—	2	1	no	—
279	C₂×C₄×C₆₇	—	2	1	no	—
280	C₂×C₄×C₆₇	—	4	4	no	—
281	C₂×C₄×C₆₇	—	4	4	no	—
282	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	2	yes	—
283	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	2	yes	—
284	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	2	yes	—
285	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	2	yes	—
286	C₂×C₄×C₆₇	#131	1	2	yes	—
287	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
288	C₂×C₄×C₆₇	C₂²×Q₈	1	1	yes	characteristic
289	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
290	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
291	C₂×C₄×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
292	C₂×C₄×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
293	C₆₇⋊C₈	—	2	2	no	—
294	C₆₇⋊C₈	—	2	2	no	—
295	C₆₇⋊C₈	—	4	1	no	—
296	C₆₇⋊C₈	—	4	1	no	—
297	C₆₇⋊C₈	—	4	1	no	—
298	C₆₇⋊C₈	—	4	1	no	—
299	C₆₇⋊C₈	—	4	1	no	—
300	C₆₇⋊C₈	—	4	1	no	—
301	C₂²×C₆₇	—	2	2	no	—
302	C₂²×C₆₇	—	2	2	no	—
303	C₂²×C₆₇	—	2	2	no	—
304	C₂²×C₆₇	—	2	2	no	—
305	C₂²×C₆₇	—	2	2	no	—
306	C₂²×C₆₇	—	2	2	no	—
307	C₂²×C₆₇	—	2	2	no	—
308	C₂²×C₆₇	—	2	2	no	—
309	C₂²×C₆₇	—	2	2	no	—
310	C₂²×C₆₇	—	4	1	no	—
311	C₂²×C₆₇	—	4	1	no	—
312	C₂²×C₆₇	—	4	1	no	—
313	C₂²×C₆₇	—	4	1	no	—
314	C₂²×C₆₇	#424	1	4	yes	—
315	C₂²×C₆₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
316	C₂²×C₆₇	C₄×#41	1	1	yes	characteristic
317	C₂²×C₆₇	#518	1	1	yes	characteristic
318	C₂²×C₆₇	C₂×#131	1	1	yes	characteristic
319	C₂²×C₆₇	C₂×#131	1	1	yes	characteristic
320	C₂²×C₆₇	C₂×#131	1	1	yes	characteristic
321	C₂²×C₆₇	#568	1	1	yes	characteristic
322	C₄×C₆₇	—	2	2	no	—
323	C₄×C₆₇	—	2	2	no	—
324	C₄×C₆₇	—	2	2	no	—
325	C₄×C₆₇	—	2	2	no	—
326	C₄×C₆₇	—	2	2	no	—
327	C₄×C₆₇	—	4	1	no	—
328	C₄×C₆₇	—	4	1	no	—
329	C₄×C₆₇	—	4	1	no	—
330	C₄×C₆₇	—	4	1	no	—
331	C₄×C₆₇	—	4	1	no	—
332	C₄×C₆₇	—	4	1	no	—
333	C₄×C₆₇	—	4	1	no	—
334	C₄×C₆₇	#546	1	1	yes	characteristic
335	C₄×C₆₇	#546	1	1	yes	characteristic
336	C₄×C₆₇	#554	1	1	yes	characteristic
337	C₄×C₆₇	#554	1	1	yes	characteristic
338	#22697	—	67	1	no	maximal, Sylow
339	C₂×C₆₇	—	2	4	no	—
340	C₂×C₆₇	—	4	2	no	—
341	C₂×C₆₇	#2349	1	1	yes	characteristic
342	C₂×C₆₇	C₂×#424	1	1	yes	characteristic
343	C₂×C₆₇	#2906	1	1	yes	characteristic
344	C₂×C₆₇	#2966	1	1	yes	characteristic
345	C₂×C₆₇	#2968	1	1	yes	characteristic
346	C₂×C₆₇	#2976	1	1	yes	characteristic
347	C₂×C₆₇	#2977	1	1	yes	characteristic
348	C₂×#435	—	67	1	no	—
349	C₂×C₈×D₄	—	67	1	no	—
350	#2290	D₆₇	1	1	yes	characteristic
351	#1940	—	67	1	no	—
352	#1939	—	67	1	no	—
353	#1851	—	67	1	no	—
354	#1850	—	67	1	no	—
355	#1850	—	67	1	no	—
356	#1850	—	67	1	no	—
357	#1832	—	67	1	no	—
358	#1798	—	67	1	no	—
359	#1797	—	67	1	no	—
360	#1768	—	67	1	no	—
361	#1729	—	67	1	no	—
362	C₂×#336	—	67	1	no	—
363	C₆₇	#22697	1	1	yes	characteristic, complemented, Sylow
364	C₂²×M₁₆	—	67	1	no	—
365	C₂³×C₈	—	67	1	no	—
366	C₂³×C₈	—	67	1	no	—
367	C₂³×C₈	—	67	1	no	—
368	C₂×C₄×D₄	C₂×D₆₇	1	1	yes	characteristic
369	C₂×#117	C₂×D₆₇	1	1	yes	characteristic
370	C₂²×C₄²	C₂×D₆₇	1	1	yes	characteristic
371	#435	—	134	4	no	—
372	C₈×D₄	—	134	4	no	—
373	C₂×C₄⋊C₈	—	67	1	no	—
374	C₂×C₄⋊C₈	—	67	1	no	—
375	C₂×C₄⋊C₈	—	67	1	no	—
376	C₂×C₄⋊C₈	—	67	1	no	—
377	C₂×C₄⋊C₈	—	67	1	no	—
378	C₂×C₄⋊C₈	—	67	1	no	—
379	C₂×C₄⋊C₈	—	67	1	no	—
380	C₂×C₄⋊C₈	—	67	1	no	—
381	C₂×C₂²⋊C₈	—	67	1	no	—
382	C₂×C₂²⋊C₈	—	67	1	no	—
383	C₂×C₂²⋊C₈	—	67	1	no	—
384	C₂×C₂²⋊C₈	—	67	1	no	—
385	C₂×#97	—	67	1	no	—
386	C₂×C₄×C₈	—	67	1	no	—
387	#388	Dic₆₇	1	1	yes	characteristic
388	#388	Dic₆₇	1	1	yes	characteristic
389	#387	Dic₆₇	1	1	yes	characteristic
390	#387	Dic₆₇	1	1	yes	characteristic
391	#386	Dic₆₇	1	1	yes	characteristic
392	#386	Dic₆₇	1	1	yes	characteristic
393	#385	Dic₆₇	1	1	yes	characteristic
394	#385	Dic₆₇	1	1	yes	characteristic
395	C₄×C₄⋊C₄	C₂×D₆₇	1	1	yes	characteristic
396	C₄×C₂²⋊C₄	C₂×D₆₇	1	1	yes	characteristic
397	C₄×C₂²⋊C₄	C₂×D₆₇	1	1	yes	characteristic
398	#376	C₂×D₆₇	1	1	yes	characteristic
399	#336	—	67	1	no	—
400	#336	—	67	1	no	—
401	#336	—	67	1	no	—
402	#336	—	67	1	no	—
403	#336	—	67	1	no	—
404	#336	—	67	1	no	—
405	#336	—	67	1	no	—
406	#336	—	67	1	no	—
407	#336	—	67	1	no	—
408	#336	—	67	1	no	—
409	C₂²×D₄	C₂×Dic₆₇	1	1	yes	characteristic
410	C₂³×C₄	C₂×Dic₆₇	1	1	yes	characteristic
411	C₂³×C₄	C₂×Dic₆₇	1	1	yes	characteristic
412	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
413	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
414	C₂×M₁₆	—	268	1	no	—
415	C₂×M₁₆	—	134	2	no	—
416	C₂×M₁₆	—	134	2	no	—
417	C₂²×C₈	—	268	1	no	—
418	C₂²×C₈	—	268	1	no	—
419	C₂²×C₈	—	268	1	no	—
420	C₂²×C₈	—	67	1	no	—
421	C₂²×C₈	—	67	1	no	—
422	C₂²×C₈	—	67	1	no	—
423	C₂²×C₈	—	67	1	no	—
424	C₂²×C₈	—	67	1	no	—
425	C₂²×C₈	—	67	1	no	—
426	C₂²×C₈	—	67	1	no	—
427	C₂²×C₈	—	67	1	no	—
428	C₂²×C₈	—	134	2	no	—
429	C₂²×C₈	—	134	2	no	—
430	C₂²×C₈	—	134	2	no	—
431	C₂²×C₈	—	134	2	no	—
432	C₂²×C₈	—	134	2	no	—
433	C₂²×C₈	—	134	2	no	—
434	C₄×D₄	Dic₁₃₄	1	4	yes	—
435	C₄×D₄	D₂₆₈	1	4	yes	—
436	#117	—	4	1	no	—
437	#117	—	4	1	no	—
438	C₂×C₄⋊C₄	C₂×Dic₆₇	1	1	yes	characteristic
439	C₂×C₄⋊C₄	C₂×Dic₆₇	1	1	yes	characteristic
440	C₂×C₄⋊C₄	C₂×Dic₆₇	1	1	yes	characteristic
441	C₂×C₄⋊C₄	C₂×Dic₆₇	1	1	yes	characteristic
442	C₂×C₄⋊C₄	C₂×Dic₆₇	1	1	yes	characteristic
443	C₂×C₂²⋊C₄	C₂×Dic₆₇	1	1	yes	characteristic
444	C₂×C₂²⋊C₄	C₂×Dic₆₇	1	1	yes	characteristic
445	C₂×C₂²⋊C₄	C₂×Dic₆₇	1	1	yes	characteristic
446	C₂×C₂²⋊C₄	C₂×Dic₆₇	1	1	yes	characteristic
447	C₂×C₂²⋊C₄	C₂×Dic₆₇	1	1	yes	characteristic
448	C₂×C₂²⋊C₄	C₂×Dic₆₇	1	1	yes	characteristic
449	C₂×C₂²⋊C₄	C₂×Dic₆₇	1	1	yes	characteristic
450	C₂×C₂²⋊C₄	C₂×Dic₆₇	1	1	yes	characteristic
451	C₂×C₄²	—	4	1	no	—
452	C₂×C₄²	—	4	1	no	—
453	C₂×C₄²	C₂×Dic₆₇	1	1	yes	characteristic
454	C₂×C₄²	C₂×Dic₆₇	1	1	yes	characteristic
455	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
456	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
457	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
458	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
459	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
460	C₄⋊C₈	—	268	1	no	—
461	C₄⋊C₈	—	268	1	no	—
462	C₄⋊C₈	—	268	1	no	—
463	C₄⋊C₈	—	268	1	no	—
464	C₄⋊C₈	—	134	2	no	—
465	C₄⋊C₈	—	134	2	no	—
466	C₄⋊C₈	—	134	2	no	—
467	C₄⋊C₈	—	134	2	no	—
468	C₂²⋊C₈	—	134	2	no	—
469	C₂²⋊C₈	—	134	2	no	—
470	C₂²⋊C₈	—	134	2	no	—
471	C₂²⋊C₈	—	134	2	no	—
472	#97	—	134	2	no	—
473	C₄×C₈	—	134	2	no	—
474	#95	C₂×Dic₆₇	1	1	yes	characteristic
475	#95	C₂×Dic₆₇	1	1	yes	characteristic
476	#95	C₂×Dic₆₇	1	1	yes	characteristic
477	#95	C₂×Dic₆₇	1	1	yes	characteristic
478	#95	C₂×Dic₆₇	1	1	yes	characteristic
479	#95	C₂×Dic₆₇	1	1	yes	characteristic
480	#95	C₂×Dic₆₇	1	1	yes	characteristic
481	#95	C₂×Dic₆₇	1	1	yes	characteristic
482	#95	C₂×Dic₆₇	1	1	yes	characteristic
483	#95	C₂×Dic₆₇	1	1	yes	characteristic
484	C₂⁴	C₂²×Dic₆₇	1	1	yes	characteristic
485	C₂⁴	C₂²×Dic₆₇	1	1	yes	characteristic
486	C₂×D₄	—	2	2	no	—
487	C₂×D₄	—	2	2	no	—
488	C₂×D₄	C₄⋊Dic₆₇	1	4	yes	—
489	C₂²×C₄	—	2	1	no	—
490	C₂²×C₄	—	2	1	no	—
491	C₂²×C₄	—	2	1	no	—
492	C₂²×C₄	—	2	1	no	—
493	C₂²×C₄	—	2	1	no	—
494	C₂²×C₄	—	2	1	no	—
495	C₂²×C₄	—	2	1	no	—
496	C₂²×C₄	—	2	1	no	—
497	C₂²×C₄	—	2	2	no	—
498	C₂²×C₄	—	2	2	no	—
499	C₂²×C₄	—	2	2	no	—
500	C₂²×C₄	—	4	1	no	—
501	C₂²×C₄	—	4	1	no	—
502	C₂²×C₄	—	4	1	no	—
503	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
504	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
505	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
506	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
507	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
508	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
509	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
510	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
511	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
512	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
513	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
514	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
515	C₂²×C₄	C₂×D₂₆₈	1	2	yes	—
516	C₂²×C₄	C₂×D₂₆₈	1	2	yes	—
517	C₂²×C₄	C₂×Dic₁₃₄	1	2	yes	—
518	C₂²×C₄	C₂×Dic₁₃₄	1	2	yes	—
519	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
520	M₁₆	—	268	4	no	—
521	C₂×C₈	—	268	4	no	—
522	C₂×C₈	—	268	4	no	—
523	C₂×C₈	—	268	4	no	—
524	C₂×C₈	—	67	2	no	—
525	C₂×C₈	—	67	2	no	—
526	C₂×C₈	—	134	1	no	—
527	C₂×C₈	—	134	1	no	—
528	C₂×C₈	—	134	1	no	—
529	C₂×C₈	—	134	1	no	—
530	C₂×C₈	—	134	1	no	—
531	C₂×C₈	—	134	1	no	—
532	C₂×C₈	—	134	1	no	—
533	C₂×C₈	—	134	1	no	—
534	C₂×C₈	—	134	1	no	—
535	C₂×C₈	—	134	1	no	—
536	C₂×C₈	—	134	1	no	—
537	C₂×C₈	—	134	1	no	—
538	C₂×C₈	—	134	1	no	—
539	C₂×C₈	—	134	1	no	—
540	C₂×C₈	—	134	1	no	—
541	C₂×C₈	—	134	1	no	—
542	C₂×C₈	—	134	1	no	—
543	C₂×C₈	—	134	1	no	—
544	C₂×C₈	—	134	1	no	—
545	C₂×C₈	—	134	1	no	—
546	C₂×C₈	—	134	1	no	—
547	C₂×C₈	—	134	1	no	—
548	C₄⋊C₄	—	2	2	no	—
549	C₄⋊C₄	—	4	1	no	—
550	C₄⋊C₄	—	4	1	no	—
551	C₄⋊C₄	—	4	1	no	—
552	C₄⋊C₄	C₄⋊Dic₆₇	1	4	yes	—
553	C₂²⋊C₄	—	2	2	no	—
554	C₂²⋊C₄	—	2	2	no	—
555	C₂²⋊C₄	—	2	2	no	—
556	C₂²⋊C₄	—	4	1	no	—
557	C₂²⋊C₄	—	4	1	no	—
558	C₂²⋊C₄	—	4	1	no	—
559	C₂²⋊C₄	C₄⋊Dic₆₇	1	4	yes	—
560	C₂²⋊C₄	C₄⋊Dic₆₇	1	4	yes	—
561	C₄²	—	2	1	no	—
562	C₄²	—	2	1	no	—
563	C₄²	—	2	1	no	—
564	C₄²	—	2	1	no	—
565	C₄²	—	2	1	no	—
566	C₄²	—	2	1	no	—
567	C₄²	—	2	1	no	—
568	C₄²	—	2	1	no	—
569	C₄²	—	4	1	no	—
570	C₄²	—	4	1	no	—
571	C₄²	C₂×D₂₆₈	1	2	yes	—
572	C₄²	C₂×Dic₁₃₄	1	2	yes	—
573	C₂³	—	2	1	no	—
574	C₂³	—	2	1	no	—
575	C₂³	—	2	1	no	—
576	C₂³	—	2	1	no	—
577	C₂³	—	2	1	no	—
578	C₂³	—	2	1	no	—
579	C₂³	—	2	1	no	—
580	C₂³	—	2	1	no	—
581	C₂³	—	2	1	no	—
582	C₂³	—	2	1	no	—
583	C₂³	C₂×C₄⋊Dic₆₇	1	2	yes	—
584	C₂³	C₂×C₄⋊Dic₆₇	1	2	yes	—
585	C₂³	#14524050	1	2	yes	—
586	C₂³	#14524050	1	2	yes	—
587	C₂³	C₂³×Dic₆₇	1	1	yes	characteristic
588	D₄	—	2	8	no	—
589	C₂×C₄	—	2	1	no	—
590	C₂×C₄	—	2	1	no	—
591	C₂×C₄	—	2	1	no	—
592	C₂×C₄	—	2	1	no	—
593	C₂×C₄	—	2	1	no	—
594	C₂×C₄	—	2	1	no	—
595	C₂×C₄	—	2	1	no	—
596	C₂×C₄	—	2	1	no	—
597	C₂×C₄	—	2	1	no	—
598	C₂×C₄	—	2	1	no	—
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	2	2	no	—
601	C₂×C₄	—	2	2	no	—
602	C₂×C₄	—	2	2	no	—
603	C₂×C₄	—	2	2	no	—
604	C₂×C₄	—	2	2	no	—
605	C₂×C₄	—	2	2	no	—
606	C₂×C₄	—	2	2	no	—
607	C₂×C₄	—	2	1	no	—
608	C₂×C₄	—	2	1	no	—
609	C₂×C₄	—	2	1	no	—
610	C₂×C₄	—	2	1	no	—
611	C₂×C₄	—	2	1	no	—
612	C₂×C₄	—	2	1	no	—
613	C₂×C₄	—	2	1	no	—
614	C₂×C₄	—	2	1	no	—
615	C₂×C₄	—	2	1	no	—
616	C₂×C₄	—	2	1	no	—
617	C₂×C₄	—	2	1	no	—
618	C₂×C₄	—	2	1	no	—
619	C₂×C₄	—	2	1	no	—
620	C₂×C₄	—	2	1	no	—
621	C₂×C₄	—	2	1	no	—
622	C₂×C₄	—	2	1	no	—
623	C₂×C₄	—	2	1	no	—
624	C₂×C₄	—	2	1	no	—
625	C₂×C₄	—	2	1	no	—
626	C₂×C₄	—	2	1	no	—
627	C₂×C₄	—	2	1	no	—
628	C₂×C₄	—	4	4	no	—
629	C₂×C₄	—	4	4	no	—
630	C₂×C₄	C₂×C₄⋊Dic₆₇	1	2	yes	—
631	C₂×C₄	C₂×C₄⋊Dic₆₇	1	2	yes	—
632	C₂×C₄	C₂×C₄⋊Dic₆₇	1	2	yes	—
633	C₂×C₄	C₂×C₄⋊Dic₆₇	1	2	yes	—
634	C₂×C₄	#14524050	1	2	yes	—
635	C₂×C₄	C₂²×D₂₆₈	1	1	yes	characteristic
636	C₂×C₄	C₂²×Dic₁₃₄	1	1	yes	characteristic
637	C₂×C₄	#41×D₆₇	1	1	yes	characteristic
638	C₂×C₄	#41×D₆₇	1	1	yes	characteristic
639	C₂×C₄	#14524088	1	1	yes	characteristic
640	C₂×C₄	#14524088	1	1	yes	characteristic
641	C₈	—	268	1	no	—
642	C₈	—	268	1	no	—
643	C₈	—	268	1	no	—
644	C₈	—	268	1	no	—
645	C₈	—	268	1	no	—
646	C₈	—	268	1	no	—
647	C₈	—	134	2	no	—
648	C₈	—	134	2	no	—
649	C₂²	—	2	2	no	—
650	C₂²	—	2	2	no	—
651	C₂²	—	2	2	no	—
652	C₂²	—	2	2	no	—
653	C₂²	—	2	2	no	—
654	C₂²	—	2	2	no	—
655	C₂²	—	2	2	no	—
656	C₂²	—	2	2	no	—
657	C₂²	—	2	2	no	—
658	C₂²	—	4	1	no	—
659	C₂²	—	4	1	no	—
660	C₂²	—	4	1	no	—
661	C₂²	—	4	1	no	—
662	C₂²	#16863423	1	4	yes	—
663	C₂²	C₂²×C₄⋊Dic₆₇	1	1	yes	characteristic
664	C₂²	#41×Dic₆₇	1	1	yes	characteristic
665	C₂²	#16863871	1	1	yes	characteristic
666	C₂²	C₂×#14524050	1	1	yes	characteristic
667	C₂²	C₂×#14524050	1	1	yes	characteristic
668	C₂²	C₂×#14524050	1	1	yes	characteristic
669	C₂²	#16864163	1	1	yes	characteristic
670	C₄	—	2	2	no	—
671	C₄	—	2	2	no	—
672	C₄	—	2	2	no	—
673	C₄	—	2	2	no	—
674	C₄	—	2	2	no	—
675	C₄	—	4	1	no	—
676	C₄	—	4	1	no	—
677	C₄	—	4	1	no	—
678	C₄	—	4	1	no	—
679	C₄	—	4	1	no	—
680	C₄	—	4	1	no	—
681	C₄	—	4	1	no	—
682	C₄	#16864041	1	1	yes	characteristic
683	C₄	#16864041	1	1	yes	characteristic
684	C₄	#16864105	1	1	yes	characteristic
685	C₄	#16864105	1	1	yes	characteristic
686	C₂	—	2	4	no	—
687	C₂	—	4	2	no	—
688	C₂	#22563119	1	1	yes	characteristic
689	C₂	C₂×#16863423	1	1	yes	characteristic
690	C₂	#22568777	1	1	yes	characteristic
691	C₂	#22569185	1	1	yes	characteristic
692	C₂	#22569205	1	1	yes	characteristic
693	C₂	#22569257	1	1	yes	characteristic
694	C₂	#22569265	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₆₇
commutator, socle	C₂³×C₆₇	C₂³×C₄
Fitting	C₆₇×#2290	C₂
prime radical	C₂²×D₄×C₆₇	C₂×C₄
cosocle	C₂²×C₄×C₆₇	C₂⁴
hypercenter	#2290	D₆₇
hypocenter	C₆₇	#22697
LCS	G ▷ C₂³×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂²×C₄ ◁ #2290

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. #22560394	C₂	semidirect
6. #22560389	C₂	semidirect
7. #22560389	C₂	semidirect
8. #22560389	C₂	semidirect
9. #22560329	C₂	semidirect
10. #22560193	C₂	semidirect
11. #22560189	C₂	semidirect
12. #22560066	C₂	semidirect
13. #22559906	C₂	semidirect
14. C₂×#16863151	C₂	semidirect
363. C₆₇	#22697	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16863468	2
C₂×D₄×C₆₇⋊C₈	2
#22560933	2
#22560928	2
#22560394	2
#22560389	2
#22560329	2
#22560193	2
#22560189	2
#22560066	2
#22559906	2
C₂×#16863151	2
C₆₇×#2290	2
#22697	67