Subgroups — #30875821

Order 17152.

716 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22561150	C₂	1	2	yes	maximal
2	#22560775	C₂	1	2	yes	maximal
3	#22560768	C₂	1	2	yes	maximal
4	#22560352	C₂	1	1	yes	maximal, characteristic
5	#22560352	C₂	1	1	yes	maximal, characteristic
6	#22560326	C₂	1	1	yes	maximal, characteristic
7	#22560084	C₂	1	2	yes	maximal
8	#22560062	C₂	1	1	yes	maximal, characteristic
9	#22559958	C₂	1	1	yes	maximal, characteristic
10	#22559955	C₂	1	1	yes	maximal, characteristic
11	C₄²×Q₈×C₆₇	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄⋊(C₆₇⋊C₈)	C₂²	1	2	yes	—
13	C₂×C₄⋊(C₆₇⋊C₈)	C₂²	1	2	yes	—
14	C₂×#14523954	C₂²	1	2	yes	—
15	C₂×#14523954	C₂²	1	2	yes	—
16	C₂×C₄×C₆₇⋊C₈	C₂²	1	2	yes	—
17	#16863151	C₂²	1	2	yes	—
18	#16863151	C₂²	1	2	yes	—
19	#16863151	C₂²	1	2	yes	—
20	#16863151	C₂²	1	2	yes	—
21	#16863151	C₂²	1	2	yes	—
22	#16863151	C₂²	1	2	yes	—
23	#16863151	C₂²	1	2	yes	—
24	#16863151	C₂²	1	1	yes	characteristic
25	#16863151	C₂²	1	1	yes	characteristic
26	#16863151	C₂²	1	1	yes	characteristic
27	#16863151	C₂²	1	1	yes	characteristic
28	C₂×C₄×Q₈×C₆₇	C₄	1	1	yes	characteristic
29	C₂×C₄×Q₈×C₆₇	C₄	1	1	yes	characteristic
30	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
31	C₄×C₄⋊C₄×C₆₇	C₄	1	1	yes	characteristic
32	C₄×C₄⋊C₄×C₆₇	C₄	1	1	yes	characteristic
33	C₄×C₄⋊C₄×C₆₇	C₄	1	1	yes	characteristic
34	C₄×C₄⋊C₄×C₆₇	C₄	1	1	yes	characteristic
35	C₄×C₄⋊C₄×C₆₇	C₄	1	1	yes	characteristic
36	C₄×C₄⋊C₄×C₆₇	C₄	1	1	yes	characteristic
37	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
38	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
39	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
40	C₄³×C₆₇	C₂²	1	1	yes	characteristic
41	C₄³×C₆₇	C₂²	1	1	yes	characteristic
42	C₄³×C₆₇	C₂²	1	1	yes	characteristic
43	C₂²×C₆₇⋊C₈	C₂³	1	2	yes	—
44	C₂²×C₆₇⋊C₈	C₂³	1	2	yes	—
45	C₂²×C₆₇⋊C₈	C₂³	1	2	yes	—
46	C₂²×C₆₇⋊C₈	C₂³	1	2	yes	—
47	C₄⋊(C₆₇⋊C₈)	—	2	4	no	—
48	C₄⋊(C₆₇⋊C₈)	—	2	4	no	—
49	#14523954	—	2	4	no	—
50	#14523954	—	2	4	no	—
51	C₄×C₆₇⋊C₈	—	2	4	no	—
52	C₂²×Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
53	C₄×Q₈×C₆₇	—	2	4	no	—
54	C₄×Q₈×C₆₇	—	2	4	no	—
55	C₄×Q₈×C₆₇	—	2	2	no	—
56	C₄×Q₈×C₆₇	—	2	2	no	—
57	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
62	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
63	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
64	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
68	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
69	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
70	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
71	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
72	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
73	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
74	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
75	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
76	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
78	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
79	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
80	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
81	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
82	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
83	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
84	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
85	#95×C₆₇	C₂×C₄	1	1	yes	characteristic
86	#95×C₆₇	C₂×C₄	1	1	yes	characteristic
87	#95×C₆₇	C₂×C₄	1	1	yes	characteristic
88	#95×C₆₇	C₂×C₄	1	1	yes	characteristic
89	#95×C₆₇	C₂×C₄	1	1	yes	characteristic
90	#95×C₆₇	C₂×C₄	1	1	yes	characteristic
91	C₂×C₆₇⋊C₈	—	2	2	no	—
92	C₂×C₆₇⋊C₈	—	2	2	no	—
93	C₂×C₆₇⋊C₈	—	2	2	no	—
94	C₂×C₆₇⋊C₈	—	2	2	no	—
95	C₂×C₆₇⋊C₈	—	2	2	no	—
96	C₂×C₆₇⋊C₈	—	2	2	no	—
97	C₂×C₆₇⋊C₈	—	2	2	no	—
98	C₂×C₆₇⋊C₈	—	2	2	no	—
99	C₂×C₆₇⋊C₈	—	2	2	no	—
100	C₂×C₆₇⋊C₈	—	2	2	no	—
101	C₂×C₆₇⋊C₈	—	2	2	no	—
102	C₂×C₆₇⋊C₈	#41	1	4	yes	—
103	C₂×Q₈×C₆₇	—	2	2	no	—
104	C₂×Q₈×C₆₇	—	2	2	no	—
105	C₂×Q₈×C₆₇	—	2	2	no	—
106	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
107	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
108	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
109	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
110	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
111	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
112	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
113	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
114	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
115	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
116	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
117	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
118	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
119	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
120	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
121	C₄⋊C₄×C₆₇	—	2	2	no	—
122	C₄⋊C₄×C₆₇	—	2	2	no	—
123	C₄⋊C₄×C₆₇	—	2	2	no	—
124	C₄⋊C₄×C₆₇	—	2	2	no	—
125	C₄⋊C₄×C₆₇	—	2	2	no	—
126	C₄⋊C₄×C₆₇	—	2	2	no	—
127	C₄⋊C₄×C₆₇	—	2	2	no	—
128	C₄⋊C₄×C₆₇	—	2	2	no	—
129	C₄⋊C₄×C₆₇	M₁₆	1	4	yes	—
130	C₄²×C₆₇	—	2	2	no	—
131	C₄²×C₆₇	—	2	2	no	—
132	C₄²×C₆₇	—	2	2	no	—
133	C₄²×C₆₇	—	2	2	no	—
134	C₄²×C₆₇	—	2	2	no	—
135	C₄²×C₆₇	—	2	2	no	—
136	C₄²×C₆₇	—	2	2	no	—
137	C₄²×C₆₇	—	2	2	no	—
138	C₄²×C₆₇	—	2	1	no	—
139	C₄²×C₆₇	—	2	1	no	—
140	C₄²×C₆₇	—	2	1	no	—
141	C₄²×C₆₇	—	2	1	no	—
142	C₄²×C₆₇	—	2	2	no	—
143	C₄²×C₆₇	—	2	2	no	—
144	C₄²×C₆₇	—	2	2	no	—
145	C₄²×C₆₇	—	2	2	no	—
146	C₄²×C₆₇	—	4	1	no	—
147	C₄²×C₆₇	—	4	1	no	—
148	C₄²×C₆₇	—	4	1	no	—
149	C₄²×C₆₇	M₁₆	1	4	yes	—
150	C₄²×C₆₇	#41	1	2	yes	—
151	C₄²×C₆₇	#41	1	2	yes	—
152	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
153	Q₈×C₆₇	—	2	8	no	—
154	C₂×C₄×C₆₇	—	2	1	no	—
155	C₂×C₄×C₆₇	—	2	1	no	—
156	C₂×C₄×C₆₇	—	2	1	no	—
157	C₂×C₄×C₆₇	—	2	1	no	—
158	C₂×C₄×C₆₇	—	2	1	no	—
159	C₂×C₄×C₆₇	—	2	1	no	—
160	C₂×C₄×C₆₇	—	2	1	no	—
161	C₂×C₄×C₆₇	—	2	1	no	—
162	C₂×C₄×C₆₇	—	2	1	no	—
163	C₂×C₄×C₆₇	—	2	1	no	—
164	C₂×C₄×C₆₇	—	2	1	no	—
165	C₂×C₄×C₆₇	—	2	1	no	—
166	C₂×C₄×C₆₇	—	2	1	no	—
167	C₂×C₄×C₆₇	—	2	1	no	—
168	C₂×C₄×C₆₇	—	2	1	no	—
169	C₂×C₄×C₆₇	—	2	1	no	—
170	C₂×C₄×C₆₇	—	2	1	no	—
171	C₂×C₄×C₆₇	—	2	1	no	—
172	C₂×C₄×C₆₇	—	2	1	no	—
173	C₂×C₄×C₆₇	—	2	1	no	—
174	C₂×C₄×C₆₇	—	2	1	no	—
175	C₂×C₄×C₆₇	—	2	1	no	—
176	C₂×C₄×C₆₇	—	2	1	no	—
177	C₂×C₄×C₆₇	—	2	1	no	—
178	C₂×C₄×C₆₇	—	2	1	no	—
179	C₂×C₄×C₆₇	—	2	1	no	—
180	C₂×C₄×C₆₇	—	2	1	no	—
181	C₂×C₄×C₆₇	—	2	1	no	—
182	C₂×C₄×C₆₇	—	2	1	no	—
183	C₂×C₄×C₆₇	—	2	1	no	—
184	C₂×C₄×C₆₇	—	2	1	no	—
185	C₂×C₄×C₆₇	—	2	1	no	—
186	C₂×C₄×C₆₇	—	2	1	no	—
187	C₂×C₄×C₆₇	#117	1	2	yes	—
188	C₂×C₄×C₆₇	#117	1	2	yes	—
189	C₂×C₄×C₆₇	C₂×M₁₆	1	2	yes	—
190	C₂×C₄×C₆₇	C₂×M₁₆	1	2	yes	—
191	C₂×C₄×C₆₇	C₂×M₁₆	1	2	yes	—
192	C₂×C₄×C₆₇	C₂×M₁₆	1	2	yes	—
193	C₂×C₄×C₆₇	C₂×M₁₆	1	2	yes	—
194	C₂×C₄×C₆₇	C₂×M₁₆	1	2	yes	—
195	C₂×C₄×C₆₇	#131	1	2	yes	—
196	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
197	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
198	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
199	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
200	C₆₇⋊C₈	—	2	4	no	—
201	C₆₇⋊C₈	—	4	2	no	—
202	C₆₇⋊C₈	—	4	2	no	—
203	C₆₇⋊C₈	—	4	2	no	—
204	C₂²×C₆₇	C₂×#117	1	1	yes	characteristic
205	C₂²×C₆₇	C₄×#41	1	1	yes	characteristic
206	C₂²×C₆₇	#519	1	1	yes	characteristic
207	C₂²×C₆₇	C₂²×M₁₆	1	1	yes	characteristic
208	C₂²×C₆₇	C₂²×M₁₆	1	1	yes	characteristic
209	C₂²×C₆₇	C₂×#131	1	1	yes	characteristic
210	C₂²×C₆₇	#568	1	1	yes	characteristic
211	C₄×C₆₇	—	2	2	no	—
212	C₄×C₆₇	—	2	2	no	—
213	C₄×C₆₇	—	2	2	no	—
214	C₄×C₆₇	—	2	2	no	—
215	C₄×C₆₇	—	2	2	no	—
216	C₄×C₆₇	—	2	2	no	—
217	C₄×C₆₇	—	2	2	no	—
218	C₄×C₆₇	—	2	2	no	—
219	C₄×C₆₇	—	2	2	no	—
220	C₄×C₆₇	—	4	1	no	—
221	C₄×C₆₇	—	4	1	no	—
222	C₄×C₆₇	—	4	1	no	—
223	C₄×C₆₇	—	4	1	no	—
224	C₄×C₆₇	—	4	1	no	—
225	C₄×C₆₇	#552	1	2	yes	—
226	C₄×C₆₇	#556	1	2	yes	—
227	#22830	—	67	1	no	maximal, Sylow
228	C₂×C₆₇	#2356	1	1	yes	characteristic
229	C₂×C₆₇	#2920	1	1	yes	characteristic
230	C₂×C₆₇	#2925	1	1	yes	characteristic
231	C₂×C₆₇	#2965	1	1	yes	characteristic
232	C₂×C₆₇	#2970	1	1	yes	characteristic
233	C₂×C₆₇	#2983	1	1	yes	characteristic
234	C₂×C₆₇	#2984	1	1	yes	characteristic
235	C₄²×Q₈	D₆₇	1	1	yes	characteristic
236	#1985	—	67	2	no	—
237	#1917	—	67	2	no	—
238	#1916	—	67	2	no	—
239	#1839	—	67	1	no	—
240	#1839	—	67	1	no	—
241	#1831	—	67	1	no	—
242	#1771	—	67	2	no	—
243	#1767	—	67	1	no	—
244	#1745	—	67	1	no	—
245	#1744	—	67	1	no	—
246	C₆₇	#22830	1	1	yes	characteristic, complemented, Sylow
247	C₂×C₄×Q₈	Dic₆₇	1	1	yes	characteristic
248	C₂×C₄×Q₈	Dic₆₇	1	1	yes	characteristic
249	C₂×C₄×Q₈	C₂×D₆₇	1	1	yes	characteristic
250	C₂×C₄⋊C₈	—	67	2	no	—
251	C₂×C₄⋊C₈	—	67	2	no	—
252	C₂×#97	—	67	2	no	—
253	C₂×#97	—	67	2	no	—
254	C₂×C₄×C₈	—	67	2	no	—
255	C₄×C₄⋊C₄	Dic₆₇	1	1	yes	characteristic
256	C₄×C₄⋊C₄	Dic₆₇	1	1	yes	characteristic
257	C₄×C₄⋊C₄	Dic₆₇	1	1	yes	characteristic
258	C₄×C₄⋊C₄	Dic₆₇	1	1	yes	characteristic
259	C₄×C₄⋊C₄	Dic₆₇	1	1	yes	characteristic
260	C₄×C₄⋊C₄	Dic₆₇	1	1	yes	characteristic
261	C₄×C₄⋊C₄	C₂×D₆₇	1	1	yes	characteristic
262	C₄×C₄⋊C₄	C₂×D₆₇	1	1	yes	characteristic
263	C₄×C₄⋊C₄	C₂×D₆₇	1	1	yes	characteristic
264	C₄³	C₂×D₆₇	1	1	yes	characteristic
265	C₄³	C₂×D₆₇	1	1	yes	characteristic
266	C₄³	C₂×D₆₇	1	1	yes	characteristic
267	#336	—	67	1	no	—
268	#336	—	67	1	no	—
269	#336	—	67	2	no	—
270	#336	—	67	1	no	—
271	#336	—	67	2	no	—
272	#336	—	67	2	no	—
273	#336	—	67	2	no	—
274	#336	—	67	2	no	—
275	#336	—	67	2	no	—
276	#336	—	67	2	no	—
277	#336	—	67	1	no	—
278	C₂²×Q₈	C₂×Dic₆₇	1	1	yes	characteristic
279	C₂²×C₈	—	67	2	no	—
280	C₂²×C₈	—	67	2	no	—
281	C₂²×C₈	—	67	2	no	—
282	C₂²×C₈	—	67	2	no	—
283	C₄×Q₈	—	2	4	no	—
284	C₄×Q₈	—	2	4	no	—
285	C₄×Q₈	—	2	2	no	—
286	C₄×Q₈	—	2	2	no	—
287	C₂×C₄⋊C₄	C₂×Dic₆₇	1	1	yes	characteristic
288	C₂×C₄⋊C₄	C₂×Dic₆₇	1	1	yes	characteristic
289	C₂×C₄⋊C₄	C₂×Dic₆₇	1	1	yes	characteristic
290	C₂×C₄⋊C₄	C₂×Dic₆₇	1	1	yes	characteristic
291	C₂×C₄⋊C₄	C₂×Dic₆₇	1	1	yes	characteristic
292	C₂×C₄⋊C₄	C₂×Dic₆₇	1	1	yes	characteristic
293	C₂×C₄⋊C₄	C₂×Dic₆₇	1	1	yes	characteristic
294	C₂×C₄⋊C₄	C₂×Dic₆₇	1	1	yes	characteristic
295	C₂×C₄⋊C₄	C₂×Dic₆₇	1	1	yes	characteristic
296	C₂×C₄²	C₂×Dic₆₇	1	1	yes	characteristic
297	C₂×C₄²	C₂×Dic₆₇	1	1	yes	characteristic
298	C₂×C₄²	C₂×Dic₆₇	1	1	yes	characteristic
299	C₂×C₄²	C₂×Dic₆₇	1	1	yes	characteristic
300	C₂×C₄²	C₂×Dic₆₇	1	1	yes	characteristic
301	C₂×C₄²	C₂×Dic₆₇	1	1	yes	characteristic
302	C₂×C₄²	C₂×Dic₆₇	1	1	yes	characteristic
303	C₂×C₄²	C₂×Dic₆₇	1	1	yes	characteristic
304	C₂×C₄²	C₂×Dic₆₇	1	1	yes	characteristic
305	C₂×C₄²	C₂×Dic₆₇	1	1	yes	characteristic
306	C₂×C₄²	C₂×Dic₆₇	1	1	yes	characteristic
307	C₂×C₄²	C₂×Dic₆₇	1	1	yes	characteristic
308	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
309	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
310	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
311	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
312	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
313	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
314	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
315	C₄⋊C₈	—	134	4	no	—
316	C₄⋊C₈	—	134	4	no	—
317	#97	—	134	4	no	—
318	#97	—	134	4	no	—
319	C₄×C₈	—	134	4	no	—
320	#95	C₂×Dic₆₇	1	1	yes	characteristic
321	#95	C₂×Dic₆₇	1	1	yes	characteristic
322	#95	C₂×Dic₆₇	1	1	yes	characteristic
323	#95	C₂×Dic₆₇	1	1	yes	characteristic
324	#95	C₂×Dic₆₇	1	1	yes	characteristic
325	#95	C₂×Dic₆₇	1	1	yes	characteristic
326	C₂×Q₈	—	2	2	no	—
327	C₂×Q₈	—	2	2	no	—
328	C₂×Q₈	—	2	2	no	—
329	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
330	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
331	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
332	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
333	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
334	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
335	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
336	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
337	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
338	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
339	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
340	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
341	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
342	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
343	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
344	C₂×C₈	—	67	4	no	—
345	C₂×C₈	—	134	2	no	—
346	C₂×C₈	—	134	2	no	—
347	C₂×C₈	—	134	2	no	—
348	C₂×C₈	—	134	2	no	—
349	C₂×C₈	—	134	2	no	—
350	C₂×C₈	—	134	2	no	—
351	C₂×C₈	—	134	2	no	—
352	C₂×C₈	—	134	2	no	—
353	C₂×C₈	—	134	2	no	—
354	C₂×C₈	—	134	2	no	—
355	C₂×C₈	—	134	2	no	—
356	C₄⋊C₄	—	2	2	no	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	#11761612	1	4	yes	—
365	C₄²	—	2	2	no	—
366	C₄²	—	2	2	no	—
367	C₄²	—	2	2	no	—
368	C₄²	—	2	2	no	—
369	C₄²	—	2	2	no	—
370	C₄²	—	2	2	no	—
371	C₄²	—	2	2	no	—
372	C₄²	—	2	2	no	—
373	C₄²	—	2	2	no	—
374	C₄²	—	2	2	no	—
375	C₄²	—	2	2	no	—
376	C₄²	—	2	1	no	—
377	C₄²	—	2	1	no	—
378	C₄²	—	2	1	no	—
379	C₄²	—	2	1	no	—
380	C₄²	—	2	2	no	—
381	C₄²	—	4	1	no	—
382	C₄²	—	4	1	no	—
383	C₄²	—	4	1	no	—
384	C₄²	#11761612	1	4	yes	—
385	C₄²	#11761628	1	2	yes	—
386	C₄²	#11761628	1	2	yes	—
387	C₂³	C₂³×Dic₆₇	1	1	yes	characteristic
388	Q₈	—	2	8	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	#14524002	1	2	yes	—
423	C₂×C₄	#14524002	1	2	yes	—
424	C₂×C₄	C₂×#11761612	1	2	yes	—
425	C₂×C₄	C₂×#11761612	1	2	yes	—
426	C₂×C₄	C₂×#11761612	1	2	yes	—
427	C₂×C₄	C₂×#11761612	1	2	yes	—
428	C₂×C₄	C₂×#11761612	1	2	yes	—
429	C₂×C₄	C₂×#11761612	1	2	yes	—
430	C₂×C₄	#14524050	1	2	yes	—
431	C₂×C₄	#41×D₆₇	1	2	yes	—
432	C₂×C₄	C₂×#11761628	1	1	yes	characteristic
433	C₂×C₄	C₂×#11761628	1	1	yes	characteristic
434	C₂×C₄	#14524091	1	2	yes	—
435	C₈	—	268	2	no	—
436	C₈	—	268	2	no	—
437	C₈	—	268	2	no	—
438	C₈	—	134	4	no	—
439	C₂²	C₂×#14524002	1	1	yes	characteristic
440	C₂²	#41×Dic₆₇	1	1	yes	characteristic
441	C₂²	#16863874	1	1	yes	characteristic
442	C₂²	C₂²×#11761612	1	1	yes	characteristic
443	C₂²	C₂²×#11761612	1	1	yes	characteristic
444	C₂²	C₂×#14524050	1	1	yes	characteristic
445	C₂²	#16864163	1	1	yes	characteristic
446	C₄	—	2	2	no	—
447	C₄	—	2	2	no	—
448	C₄	—	2	2	no	—
449	C₄	—	2	2	no	—
450	C₄	—	2	2	no	—
451	C₄	—	2	2	no	—
452	C₄	—	2	2	no	—
453	C₄	—	2	2	no	—
454	C₄	—	2	2	no	—
455	C₄	—	4	1	no	—
456	C₄	—	4	1	no	—
457	C₄	—	4	1	no	—
458	C₄	—	4	1	no	—
459	C₄	—	4	1	no	—
460	C₄	#16864087	1	2	yes	—
461	C₄	#16864118	1	2	yes	—
462	C₂	#22563174	1	1	yes	characteristic
463	C₂	#22568842	1	1	yes	characteristic
464	C₂	#22568875	1	1	yes	characteristic
465	C₂	#22569176	1	1	yes	characteristic
466	C₂	#22569223	1	1	yes	characteristic
467	C₂	#22569294	1	1	yes	characteristic
468	C₂	#22569298	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₆₇
commutator, socle, prime radical	C₂³×C₆₇	C₂³×C₄
Fitting	C₄²×Q₈×C₆₇	C₂
cosocle	C₂²×C₄×C₆₇	C₂⁴
hypercenter	C₄²×Q₈	D₆₇
hypocenter	C₆₇	#22830
LCS	G ▷ C₂³×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₄²×Q₈

Complements

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

N	H ≅ G/N	type
246. C₆₇	#22830	semidirect

Maximal subgroups

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

subgroup	index
#22561150	2
#22560775	2
#22560768	2
#22560352	2
#22560326	2
#22560084	2
#22560062	2
#22559958	2
#22559955	2
C₄²×Q₈×C₆₇	2
#22830	67