Subgroups — C₆₇×#33038 #30712289

Order 17152.

960 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#478×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#459×C₆₇	C₂	1	1	yes	maximal, characteristic
3	C₆₇×#2641	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#2275	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#1989	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#1982	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#1926	C₂	1	2	yes	maximal, complemented
8	C₆₇×#1925	C₂	1	2	yes	maximal, complemented
9	C₆₇×#1879	C₂	1	2	yes	maximal, complemented
10	C₆₇×#1879	C₂	1	2	yes	maximal, complemented
11	C₆₇×#1832	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×D₈×C₆₇	C₂²	1	2	yes	—
13	C₂×#127×C₆₇	C₂²	1	1	yes	characteristic
14	C₂×#125×C₆₇	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
16	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
17	#478×C₆₇	—	2	4	no	—
18	#459×C₆₇	—	2	4	no	—
19	C₂×#107×C₆₇	C₂²	1	1	yes	characteristic
20	C₂×#106×C₆₇	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
23	C₂×#102×C₆₇	C₂²	1	2	yes	—
24	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
25	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
26	C₂×#102×C₆₇	C₂²	1	2	yes	—
27	C₂×#102×C₆₇	C₂²	1	2	yes	—
28	#394×C₆₇	—	2	1	no	—
29	#394×C₆₇	—	2	1	no	—
30	#394×C₆₇	—	2	2	no	—
31	#390×C₆₇	C₂²	1	2	yes	—
32	#390×C₆₇	C₂²	1	2	yes	—
33	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
34	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
35	C₄×C₂²⋊C₄×C₆₇	—	2	1	no	—
36	C₄×C₂²⋊C₄×C₆₇	—	2	2	no	—
37	#376×C₆₇	C₂²	1	1	yes	characteristic
38	C₂×#95×C₆₇	—	2	1	no	—
39	#340×C₆₇	C₂²	1	2	yes	—
40	#340×C₆₇	C₂²	1	2	yes	—
41	#336×C₆₇	C₂²	1	2	yes	—
42	#336×C₆₇	C₂²	1	2	yes	—
43	C₂²×D₄×C₆₇	—	2	1	no	—
44	C₂²×D₄×C₆₇	—	2	1	no	—
45	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
46	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
47	C₂³×C₄×C₆₇	—	2	2	no	—
48	C₂³×C₄×C₆₇	—	2	1	no	—
49	C₂×D₈×C₆₇	—	2	4	no	—
50	C₂×D₈×C₆₇	—	2	4	no	—
51	C₂×D₈×C₆₇	—	2	4	no	—
52	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
53	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
55	#127×C₆₇	—	2	2	no	—
56	#127×C₆₇	—	2	2	no	—
57	#125×C₆₇	—	2	2	no	—
58	#125×C₆₇	—	2	2	no	—
59	C₄×D₄×C₆₇	—	2	4	no	—
60	C₄×D₄×C₆₇	—	2	4	no	—
61	C₄×D₄×C₆₇	—	2	2	no	—
62	C₄×D₄×C₆₇	D₄	1	4	yes	—
63	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
64	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
65	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
66	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
67	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
68	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
69	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
70	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
71	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
72	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
73	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
74	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
75	C₂×C₄²×C₆₇	—	2	2	no	—
76	C₂×C₄²×C₆₇	—	2	1	no	—
77	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
78	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
79	#107×C₆₇	—	2	2	no	—
80	#106×C₆₇	—	2	2	no	—
81	C₄⋊C₈×C₆₇	—	2	2	no	—
82	C₄⋊C₈×C₆₇	—	2	2	no	—
83	#102×C₆₇	—	2	2	no	—
84	#102×C₆₇	—	2	2	no	—
85	#102×C₆₇	—	2	4	no	—
86	#102×C₆₇	—	2	4	no	—
87	#102×C₆₇	—	2	4	no	—
88	#95×C₆₇	—	2	2	no	—
89	#95×C₆₇	—	2	1	no	—
90	#95×C₆₇	D₄	1	1	yes	characteristic
91	#95×C₆₇	D₄	1	1	yes	characteristic
92	#95×C₆₇	D₄	1	2	yes	—
93	C₂⁴×C₆₇	—	2	1	no	—
94	C₂⁴×C₆₇	—	2	2	no	—
95	C₂×D₄×C₆₇	—	2	2	no	—
96	C₂×D₄×C₆₇	—	2	1	no	—
97	C₂×D₄×C₆₇	—	2	2	no	—
98	C₂×D₄×C₆₇	—	2	2	no	—
99	C₂×D₄×C₆₇	—	2	2	no	—
100	C₂×D₄×C₆₇	—	2	2	no	—
101	C₂×D₄×C₆₇	—	2	2	no	—
102	C₂×D₄×C₆₇	—	2	2	no	—
103	C₂×D₄×C₆₇	—	4	2	no	—
104	C₂×D₄×C₆₇	—	4	2	no	—
105	C₂×D₄×C₆₇	—	8	1	no	—
106	C₂×D₄×C₆₇	—	8	2	no	—
107	C₂×D₄×C₆₇	—	8	1	no	—
108	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
109	C₂×D₄×C₆₇	#41	1	4	yes	—
110	C₂²×C₄×C₆₇	—	2	1	no	—
111	C₂²×C₄×C₆₇	—	2	2	no	—
112	C₂²×C₄×C₆₇	—	2	8	no	—
113	C₂²×C₄×C₆₇	—	2	4	no	—
114	C₂²×C₄×C₆₇	—	2	1	no	—
115	C₂²×C₄×C₆₇	—	2	1	no	—
116	C₂²×C₄×C₆₇	—	8	2	no	—
117	C₂²×C₄×C₆₇	—	8	2	no	—
118	C₂²×C₄×C₆₇	—	8	2	no	—
119	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
120	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
121	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
124	D₈×C₆₇	—	4	8	no	—
125	C₂×C₈×C₆₇	—	2	1	no	—
126	C₂×C₈×C₆₇	—	2	1	no	—
127	C₂×C₈×C₆₇	—	2	2	no	—
128	C₂×C₈×C₆₇	—	2	2	no	—
129	C₂×C₈×C₆₇	—	2	2	no	—
130	C₂×C₈×C₆₇	—	2	2	no	—
131	C₂×C₈×C₆₇	—	2	2	no	—
132	C₄⋊C₄×C₆₇	—	2	1	no	—
133	C₄⋊C₄×C₆₇	—	2	2	no	—
134	C₄⋊C₄×C₆₇	—	2	1	no	—
135	C₄⋊C₄×C₆₇	—	2	1	no	—
136	C₄⋊C₄×C₆₇	—	2	1	no	—
137	C₄⋊C₄×C₆₇	—	2	1	no	—
138	C₄⋊C₄×C₆₇	—	4	2	no	—
139	C₄⋊C₄×C₆₇	—	4	2	no	—
140	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
141	C₄⋊C₄×C₆₇	#41	1	4	yes	—
142	C₂²⋊C₄×C₆₇	—	2	8	no	—
143	C₂²⋊C₄×C₆₇	—	2	4	no	—
144	C₂²⋊C₄×C₆₇	—	8	2	no	—
145	C₂²⋊C₄×C₆₇	—	8	2	no	—
146	C₂²⋊C₄×C₆₇	—	8	2	no	—
147	C₂²⋊C₄×C₆₇	—	8	2	no	—
148	C₄²×C₆₇	—	2	2	no	—
149	C₄²×C₆₇	—	2	2	no	—
150	C₄²×C₆₇	—	8	1	no	—
151	C₄²×C₆₇	—	8	2	no	—
152	C₄²×C₆₇	C₂×D₄	1	2	yes	—
153	C₄²×C₆₇	#41	1	2	yes	—
154	C₂³×C₆₇	—	2	2	no	—
155	C₂³×C₆₇	—	2	4	no	—
156	C₂³×C₆₇	—	4	2	no	—
157	C₂³×C₆₇	—	4	1	no	—
158	C₂³×C₆₇	—	4	1	no	—
159	C₂³×C₆₇	—	4	2	no	—
160	C₂³×C₆₇	—	4	2	no	—
161	C₂³×C₆₇	—	4	2	no	—
162	C₂³×C₆₇	—	4	2	no	—
163	C₂³×C₆₇	—	4	2	no	—
164	C₂³×C₆₇	—	4	2	no	—
165	C₂³×C₆₇	—	4	2	no	—
166	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
167	D₄×C₆₇	—	2	4	no	—
168	D₄×C₆₇	—	2	2	no	—
169	D₄×C₆₇	—	4	2	no	—
170	D₄×C₆₇	—	4	2	no	—
171	D₄×C₆₇	—	4	2	no	—
172	D₄×C₆₇	—	4	2	no	—
173	D₄×C₆₇	—	8	4	no	—
174	D₄×C₆₇	—	8	4	no	—
175	D₄×C₆₇	#124	1	4	yes	—
176	C₂×C₄×C₆₇	—	2	1	no	—
177	C₂×C₄×C₆₇	—	2	2	no	—
178	C₂×C₄×C₆₇	—	2	1	no	—
179	C₂×C₄×C₆₇	—	2	2	no	—
180	C₂×C₄×C₆₇	—	2	2	no	—
181	C₂×C₄×C₆₇	—	2	2	no	—
182	C₂×C₄×C₆₇	—	2	4	no	—
183	C₂×C₄×C₆₇	—	2	2	no	—
184	C₂×C₄×C₆₇	—	2	2	no	—
185	C₂×C₄×C₆₇	—	2	2	no	—
186	C₂×C₄×C₆₇	—	2	2	no	—
187	C₂×C₄×C₆₇	—	4	2	no	—
188	C₂×C₄×C₆₇	—	4	2	no	—
189	C₂×C₄×C₆₇	—	4	2	no	—
190	C₂×C₄×C₆₇	—	4	1	no	—
191	C₂×C₄×C₆₇	—	4	1	no	—
192	C₂×C₄×C₆₇	—	4	2	no	—
193	C₂×C₄×C₆₇	—	4	1	no	—
194	C₂×C₄×C₆₇	—	4	1	no	—
195	C₂×C₄×C₆₇	—	8	4	no	—
196	C₂×C₄×C₆₇	—	8	8	no	—
197	C₂×C₄×C₆₇	#121	1	2	yes	—
198	C₂×C₄×C₆₇	#121	1	2	yes	—
199	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
200	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
201	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
202	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
203	C₈×C₆₇	—	4	2	no	—
204	C₈×C₆₇	—	4	1	no	—
205	C₈×C₆₇	—	4	1	no	—
206	C₂²×C₆₇	—	2	4	no	—
207	C₂²×C₆₇	—	4	4	no	—
208	C₂²×C₆₇	—	4	4	no	—
209	C₂²×C₆₇	—	4	2	no	—
210	C₂²×C₆₇	—	4	2	no	—
211	C₂²×C₆₇	—	8	2	no	—
212	C₂²×C₆₇	—	8	2	no	—
213	C₂²×C₆₇	—	8	2	no	—
214	C₂²×C₆₇	—	8	2	no	—
215	C₂²×C₆₇	—	8	2	no	—
216	C₂²×C₆₇	—	8	2	no	—
217	C₂²×C₆₇	—	8	2	no	—
218	C₂²×C₆₇	C₂×#121	1	1	yes	characteristic
219	C₂²×C₆₇	#525	1	2	yes	—
220	C₂²×C₆₇	#576	1	2	yes	—
221	C₂²×C₆₇	#576	1	1	yes	characteristic
222	C₂²×C₆₇	#577	1	1	yes	characteristic
223	C₄×C₆₇	—	2	2	no	—
224	C₄×C₆₇	—	2	2	no	—
225	C₄×C₆₇	—	4	2	no	—
226	C₄×C₆₇	—	4	2	no	—
227	C₄×C₆₇	—	4	4	no	—
228	C₄×C₆₇	—	4	2	no	—
229	C₄×C₆₇	—	8	1	no	—
230	C₄×C₆₇	—	8	1	no	—
231	C₄×C₆₇	C₂×#124	1	1	yes	characteristic
232	C₄×C₆₇	#529	1	2	yes	—
233	C₄×C₆₇	#532	1	1	yes	characteristic
234	#33038	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
235	C₂×C₆₇	—	4	4	no	—
236	C₂×C₆₇	—	16	2	no	—
237	C₂×C₆₇	#2850	1	1	yes	characteristic
238	C₂×C₆₇	#3041	1	1	yes	characteristic
239	C₂×C₆₇	#3045	1	1	yes	characteristic
240	C₂×C₆₇	#3119	1	2	yes	—
241	C₂×C₆₇	#3122	1	2	yes	—
242	C₂×#478	C₂×C₆₇	1	1	yes	characteristic, complemented
243	C₂×#459	C₂×C₆₇	1	1	yes	characteristic
244	#2641	C₂×C₆₇	1	1	yes	characteristic, complemented
245	#2275	C₂×C₆₇	1	1	yes	characteristic, complemented
246	#1989	C₂×C₆₇	1	1	yes	characteristic, complemented
247	#1982	C₂×C₆₇	1	1	yes	characteristic, complemented
248	#1926	C₂×C₆₇	1	2	yes	complemented
249	#1925	C₂×C₆₇	1	2	yes	complemented
250	#1879	C₂×C₆₇	1	2	yes	complemented
251	#1879	C₂×C₆₇	1	2	yes	complemented
252	#1832	C₂×C₆₇	1	1	yes	characteristic, complemented
253	C₆₇	#33038	1	1	yes	characteristic, direct product factor, Sylow
254	C₂²×D₈	C₂²×C₆₇	1	2	yes	—
255	C₂×#127	C₂²×C₆₇	1	1	yes	characteristic
256	C₂×#125	C₂²×C₆₇	1	1	yes	characteristic
257	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
258	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
259	#478	—	2	4	no	—
260	#459	—	2	4	no	—
261	C₂×#107	C₂²×C₆₇	1	1	yes	characteristic
262	C₂×#106	C₂²×C₆₇	1	1	yes	characteristic
263	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
264	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
265	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
266	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
267	C₂×#102	C₂²×C₆₇	1	2	yes	—
268	C₂×#102	C₂²×C₆₇	1	2	yes	—
269	C₂×#102	C₂²×C₆₇	1	2	yes	—
270	#394	—	2	1	no	—
271	#394	—	2	2	no	—
272	#394	—	2	1	no	—
273	#390	C₂²×C₆₇	1	2	yes	—
274	#390	C₂²×C₆₇	1	2	yes	—
275	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
276	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
277	C₄×C₂²⋊C₄	—	2	2	no	—
278	C₄×C₂²⋊C₄	—	2	1	no	—
279	#376	C₂²×C₆₇	1	1	yes	characteristic
280	C₂×#95	—	2	1	no	—
281	#340	C₂²×C₆₇	1	2	yes	—
282	#340	C₂²×C₆₇	1	2	yes	—
283	#336	C₂²×C₆₇	1	2	yes	—
284	#336	C₂²×C₆₇	1	2	yes	—
285	C₂²×D₄	—	2	1	no	—
286	C₂²×D₄	—	2	1	no	—
287	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
288	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
289	C₂³×C₄	—	2	2	no	—
290	C₂³×C₄	—	2	1	no	—
291	C₂×D₈	—	2	4	no	—
292	C₂×D₈	—	2	4	no	—
293	C₂×D₈	—	2	4	no	—
294	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
295	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
296	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
297	#127	—	2	2	no	—
298	#127	—	2	2	no	—
299	#125	—	2	2	no	—
300	#125	—	2	2	no	—
301	C₄×D₄	—	2	4	no	—
302	C₄×D₄	—	2	4	no	—
303	C₄×D₄	—	2	2	no	—
304	C₄×D₄	D₄×C₆₇	1	4	yes	—
305	C₂×C₄⋊C₄	—	2	1	no	—
306	C₂×C₄⋊C₄	—	2	1	no	—
307	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
308	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
309	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
310	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
311	C₂×C₂²⋊C₄	—	2	2	no	—
312	C₂×C₂²⋊C₄	—	2	1	no	—
313	C₂×C₂²⋊C₄	—	2	2	no	—
314	C₂×C₂²⋊C₄	—	2	2	no	—
315	C₂×C₂²⋊C₄	—	2	2	no	—
316	C₂×C₂²⋊C₄	—	2	2	no	—
317	C₂×C₄²	—	2	2	no	—
318	C₂×C₄²	—	2	1	no	—
319	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
320	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
321	#107	—	2	2	no	—
322	#106	—	2	2	no	—
323	C₄⋊C₈	—	2	2	no	—
324	C₄⋊C₈	—	2	2	no	—
325	#102	—	2	2	no	—
326	#102	—	2	2	no	—
327	#102	—	2	4	no	—
328	#102	—	2	4	no	—
329	#102	—	2	4	no	—
330	#95	—	2	2	no	—
331	#95	—	2	1	no	—
332	#95	D₄×C₆₇	1	1	yes	characteristic
333	#95	D₄×C₆₇	1	2	yes	—
334	#95	D₄×C₆₇	1	1	yes	characteristic
335	C₂⁴	—	2	1	no	—
336	C₂⁴	—	2	2	no	—
337	C₂×D₄	—	2	2	no	—
338	C₂×D₄	—	2	1	no	—
339	C₂×D₄	—	2	2	no	—
340	C₂×D₄	—	2	2	no	—
341	C₂×D₄	—	2	2	no	—
342	C₂×D₄	—	2	2	no	—
343	C₂×D₄	—	2	2	no	—
344	C₂×D₄	—	2	2	no	—
345	C₂×D₄	—	4	2	no	—
346	C₂×D₄	—	4	2	no	—
347	C₂×D₄	—	8	1	no	—
348	C₂×D₄	—	8	2	no	—
349	C₂×D₄	—	8	1	no	—
350	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
351	C₂×D₄	#41×C₆₇	1	4	yes	—
352	C₂²×C₄	—	2	1	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	8	no	—
355	C₂²×C₄	—	2	4	no	—
356	C₂²×C₄	—	2	1	no	—
357	C₂²×C₄	—	2	1	no	—
358	C₂²×C₄	—	8	2	no	—
359	C₂²×C₄	—	8	2	no	—
360	C₂²×C₄	—	8	2	no	—
361	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
362	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
363	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
364	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
365	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
366	D₈	—	4	8	no	—
367	C₂×C₈	—	2	1	no	—
368	C₂×C₈	—	2	1	no	—
369	C₂×C₈	—	2	2	no	—
370	C₂×C₈	—	2	2	no	—
371	C₂×C₈	—	2	2	no	—
372	C₂×C₈	—	2	2	no	—
373	C₂×C₈	—	2	2	no	—
374	C₄⋊C₄	—	2	1	no	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	2	1	no	—
377	C₄⋊C₄	—	2	1	no	—
378	C₄⋊C₄	—	2	1	no	—
379	C₄⋊C₄	—	2	1	no	—
380	C₄⋊C₄	—	4	2	no	—
381	C₄⋊C₄	—	4	2	no	—
382	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
383	C₄⋊C₄	#41×C₆₇	1	4	yes	—
384	C₂²⋊C₄	—	2	8	no	—
385	C₂²⋊C₄	—	2	4	no	—
386	C₂²⋊C₄	—	8	2	no	—
387	C₂²⋊C₄	—	8	2	no	—
388	C₂²⋊C₄	—	8	2	no	—
389	C₂²⋊C₄	—	8	2	no	—
390	C₄²	—	2	2	no	—
391	C₄²	—	2	2	no	—
392	C₄²	—	8	1	no	—
393	C₄²	—	8	2	no	—
394	C₄²	C₂×D₄×C₆₇	1	2	yes	—
395	C₄²	#41×C₆₇	1	2	yes	—
396	C₂³	—	2	2	no	—
397	C₂³	—	2	4	no	—
398	C₂³	—	4	2	no	—
399	C₂³	—	4	1	no	—
400	C₂³	—	4	1	no	—
401	C₂³	—	4	2	no	—
402	C₂³	—	4	2	no	—
403	C₂³	—	4	2	no	—
404	C₂³	—	4	2	no	—
405	C₂³	—	4	2	no	—
406	C₂³	—	4	2	no	—
407	C₂³	—	4	2	no	—
408	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
409	D₄	—	2	4	no	—
410	D₄	—	2	2	no	—
411	D₄	—	4	2	no	—
412	D₄	—	4	2	no	—
413	D₄	—	4	2	no	—
414	D₄	—	4	2	no	—
415	D₄	—	8	4	no	—
416	D₄	—	8	4	no	—
417	D₄	#124×C₆₇	1	4	yes	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	4	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	4	2	no	—
432	C₂×C₄	—	4	1	no	—
433	C₂×C₄	—	4	1	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	—	4	1	no	—
436	C₂×C₄	—	4	1	no	—
437	C₂×C₄	—	8	4	no	—
438	C₂×C₄	—	8	8	no	—
439	C₂×C₄	#121×C₆₇	1	2	yes	—
440	C₂×C₄	#121×C₆₇	1	2	yes	—
441	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
442	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
443	C₂×C₄	C₂×#41×C₆₇	1	1	yes	characteristic
444	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
445	C₈	—	4	2	no	—
446	C₈	—	4	1	no	—
447	C₈	—	4	1	no	—
448	C₂²	—	2	4	no	—
449	C₂²	—	4	2	no	—
450	C₂²	—	4	2	no	—
451	C₂²	—	4	4	no	—
452	C₂²	—	4	4	no	—
453	C₂²	—	8	2	no	—
454	C₂²	—	8	2	no	—
455	C₂²	—	8	2	no	—
456	C₂²	—	8	2	no	—
457	C₂²	—	8	2	no	—
458	C₂²	—	8	2	no	—
459	C₂²	—	8	2	no	—
460	C₂²	C₂×#121×C₆₇	1	1	yes	characteristic
461	C₂²	#525×C₆₇	1	2	yes	—
462	C₂²	#576×C₆₇	1	2	yes	—
463	C₂²	#576×C₆₇	1	1	yes	characteristic
464	C₂²	#577×C₆₇	1	1	yes	characteristic
465	C₄	—	2	2	no	—
466	C₄	—	2	2	no	—
467	C₄	—	4	2	no	—
468	C₄	—	4	2	no	—
469	C₄	—	4	2	no	—
470	C₄	—	4	4	no	—
471	C₄	—	8	1	no	—
472	C₄	—	8	1	no	—
473	C₄	C₂×#124×C₆₇	1	1	yes	characteristic
474	C₄	#529×C₆₇	1	2	yes	—
475	C₄	#532×C₆₇	1	1	yes	characteristic
476	C₂	—	4	4	no	—
477	C₂	—	16	2	no	—
478	C₂	C₆₇×#2850	1	1	yes	characteristic
479	C₂	C₆₇×#3041	1	1	yes	characteristic
480	C₂	C₆₇×#3045	1	1	yes	characteristic
481	C₂	C₆₇×#3119	1	2	yes	—
482	C₂	C₆₇×#3122	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₇
prime radical	C₂×#459×C₆₇	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ #376×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#478×C₆₇	C₂	semidirect
3. C₆₇×#2641	C₂	semidirect
4. C₆₇×#2275	C₂	semidirect
5. C₆₇×#1989	C₂	semidirect
6. C₆₇×#1982	C₂	semidirect
7. C₆₇×#1926	C₂	semidirect
8. C₆₇×#1925	C₂	semidirect
9. C₆₇×#1879	C₂	semidirect
10. C₆₇×#1879	C₂	semidirect
11. C₆₇×#1832	C₂	semidirect
234. #33038	C₆₇	direct (N × H)
242. C₂×#478	C₂×C₆₇	semidirect
244. #2641	C₂×C₆₇	semidirect
245. #2275	C₂×C₆₇	semidirect
246. #1989	C₂×C₆₇	semidirect
247. #1982	C₂×C₆₇	semidirect
248. #1926	C₂×C₆₇	semidirect
249. #1925	C₂×C₆₇	semidirect
250. #1879	C₂×C₆₇	semidirect
251. #1879	C₂×C₆₇	semidirect
252. #1832	C₂×C₆₇	semidirect
253. C₆₇	#33038	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#478×C₆₇	2
C₂×#459×C₆₇	2
C₆₇×#2641	2
C₆₇×#2275	2
C₆₇×#1989	2
C₆₇×#1982	2
C₆₇×#1926	2
C₆₇×#1925	2
C₆₇×#1879	2
C₆₇×#1832	2
#33038	67

Subgroups — C67×#33038 #30712289

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#33038 #30712289