Subgroups — C₆₇×#33039 #30712290

Order 17152.

884 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#479×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#460×C₆₇	C₂	1	1	yes	maximal, characteristic
3	C₆₇×#2641	C₂	1	1	yes	maximal, characteristic
4	C₆₇×#2276	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
7	C₆₇×#1926	C₂	1	2	yes	maximal, complemented
8	C₆₇×#1925	C₂	1	2	yes	maximal, complemented
9	C₆₇×#1880	C₂	1	2	yes	maximal, complemented
10	C₆₇×#1880	C₂	1	2	yes	maximal, complemented
11	C₆₇×#1832	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×SD₁₆×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×Q₈×C₆₇	C₂²	1	2	yes	—
16	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
17	#479×C₆₇	—	2	4	no	—
18	#460×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×#103×C₆₇	C₂²	1	1	yes	characteristic
24	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic
25	C₂×#102×C₆₇	C₂²	1	2	yes	—
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	—	2	2	no	—
34	C₄×C₄⋊C₄×C₆₇	—	2	1	no	—
35	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
36	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
37	#376×C₆₇	—	2	1	no	—
38	#376×C₆₇	C₂²	1	1	yes	characteristic
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×Q₈×C₆₇	C₂³	1	1	yes	characteristic
44	C₂²×D₄×C₆₇	—	2	1	no	—
45	C₂²×D₄×C₆₇	—	2	1	no	—
46	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
47	C₂×SD₁₆×C₆₇	—	2	4	no	—
48	C₂×SD₁₆×C₆₇	—	2	4	no	—
49	C₂×SD₁₆×C₆₇	—	2	4	no	—
50	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
51	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
53	#127×C₆₇	—	2	2	no	—
54	#127×C₆₇	—	2	2	no	—
55	#125×C₆₇	—	2	2	no	—
56	#125×C₆₇	—	2	2	no	—
57	C₄×Q₈×C₆₇	—	2	4	no	—
58	C₄×Q₈×C₆₇	—	2	4	no	—
59	C₄×Q₈×C₆₇	—	2	2	no	—
60	C₄×Q₈×C₆₇	D₄	1	4	yes	—
61	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
62	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
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	2	no	—
71	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
72	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
73	C₂×C₄²×C₆₇	—	2	2	no	—
74	C₂×C₄²×C₆₇	—	2	1	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	#103×C₆₇	—	2	2	no	—
84	#103×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	2	no	—
94	C₂×Q₈×C₆₇	—	2	1	no	—
95	C₂×Q₈×C₆₇	—	2	2	no	—
96	C₂×Q₈×C₆₇	C₂×D₄	1	2	yes	—
97	C₂×Q₈×C₆₇	#41	1	4	yes	—
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	—	2	2	no	—
104	C₂×D₄×C₆₇	—	4	2	no	—
105	C₂×D₄×C₆₇	—	4	2	no	—
106	C₂×D₄×C₆₇	—	8	1	no	—
107	C₂×D₄×C₆₇	—	8	2	no	—
108	C₂×D₄×C₆₇	—	8	1	no	—
109	C₂²×C₄×C₆₇	—	2	1	no	—
110	C₂²×C₄×C₆₇	—	2	1	no	—
111	C₂²×C₄×C₆₇	—	2	2	no	—
112	C₂²×C₄×C₆₇	—	2	1	no	—
113	C₂²×C₄×C₆₇	—	2	1	no	—
114	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
116	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
119	SD₁₆×C₆₇	—	4	8	no	—
120	C₂×C₈×C₆₇	—	2	2	no	—
121	C₂×C₈×C₆₇	—	2	1	no	—
122	C₂×C₈×C₆₇	—	2	1	no	—
123	C₂×C₈×C₆₇	—	2	2	no	—
124	C₂×C₈×C₆₇	—	2	2	no	—
125	C₂×C₈×C₆₇	—	2	2	no	—
126	C₂×C₈×C₆₇	—	2	2	no	—
127	C₄⋊C₄×C₆₇	—	2	8	no	—
128	C₄⋊C₄×C₆₇	—	2	4	no	—
129	C₄⋊C₄×C₆₇	—	2	1	no	—
130	C₄⋊C₄×C₆₇	—	2	2	no	—
131	C₄⋊C₄×C₆₇	—	2	1	no	—
132	C₄⋊C₄×C₆₇	—	2	1	no	—
133	C₄⋊C₄×C₆₇	—	2	1	no	—
134	C₄⋊C₄×C₆₇	—	2	1	no	—
135	C₄⋊C₄×C₆₇	—	4	2	no	—
136	C₄⋊C₄×C₆₇	—	4	2	no	—
137	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
138	C₄⋊C₄×C₆₇	#41	1	4	yes	—
139	C₂²⋊C₄×C₆₇	—	8	2	no	—
140	C₂²⋊C₄×C₆₇	—	8	2	no	—
141	C₂²⋊C₄×C₆₇	—	8	2	no	—
142	C₂²⋊C₄×C₆₇	—	8	2	no	—
143	C₄²×C₆₇	—	2	8	no	—
144	C₄²×C₆₇	—	2	4	no	—
145	C₄²×C₆₇	—	2	2	no	—
146	C₄²×C₆₇	—	2	2	no	—
147	C₄²×C₆₇	—	8	1	no	—
148	C₄²×C₆₇	—	8	2	no	—
149	C₄²×C₆₇	C₂×D₄	1	2	yes	—
150	C₄²×C₆₇	#41	1	2	yes	—
151	C₂³×C₆₇	—	4	2	no	—
152	C₂³×C₆₇	—	4	2	no	—
153	C₂³×C₆₇	—	4	2	no	—
154	C₂³×C₆₇	—	4	2	no	—
155	C₂³×C₆₇	—	4	2	no	—
156	C₂³×C₆₇	—	4	2	no	—
157	C₂³×C₆₇	—	4	2	no	—
158	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
159	Q₈×C₆₇	—	2	4	no	—
160	Q₈×C₆₇	—	2	2	no	—
161	Q₈×C₆₇	#124	1	4	yes	—
162	D₄×C₆₇	—	4	2	no	—
163	D₄×C₆₇	—	4	2	no	—
164	D₄×C₆₇	—	4	2	no	—
165	D₄×C₆₇	—	4	2	no	—
166	D₄×C₆₇	—	8	4	no	—
167	D₄×C₆₇	—	8	4	no	—
168	C₂×C₄×C₆₇	—	2	2	no	—
169	C₂×C₄×C₆₇	—	2	4	no	—
170	C₂×C₄×C₆₇	—	2	1	no	—
171	C₂×C₄×C₆₇	—	2	2	no	—
172	C₂×C₄×C₆₇	—	2	1	no	—
173	C₂×C₄×C₆₇	—	2	2	no	—
174	C₂×C₄×C₆₇	—	2	2	no	—
175	C₂×C₄×C₆₇	—	2	2	no	—
176	C₂×C₄×C₆₇	—	2	4	no	—
177	C₂×C₄×C₆₇	—	2	2	no	—
178	C₂×C₄×C₆₇	—	2	2	no	—
179	C₂×C₄×C₆₇	—	2	2	no	—
180	C₂×C₄×C₆₇	—	2	2	no	—
181	C₂×C₄×C₆₇	—	4	2	no	—
182	C₂×C₄×C₆₇	—	4	1	no	—
183	C₂×C₄×C₆₇	—	4	2	no	—
184	C₂×C₄×C₆₇	—	4	1	no	—
185	C₂×C₄×C₆₇	—	4	1	no	—
186	C₂×C₄×C₆₇	—	4	1	no	—
187	C₂×C₄×C₆₇	—	4	1	no	—
188	C₂×C₄×C₆₇	—	4	2	no	—
189	C₂×C₄×C₆₇	—	4	1	no	—
190	C₂×C₄×C₆₇	#121	1	2	yes	—
191	C₂×C₄×C₆₇	#121	1	2	yes	—
192	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
193	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
194	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
195	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
196	C₈×C₆₇	—	4	2	no	—
197	C₈×C₆₇	—	4	1	no	—
198	C₈×C₆₇	—	4	1	no	—
199	C₂²×C₆₇	—	8	2	no	—
200	C₂²×C₆₇	—	8	2	no	—
201	C₂²×C₆₇	—	8	2	no	—
202	C₂²×C₆₇	—	8	2	no	—
203	C₂²×C₆₇	—	8	2	no	—
204	C₂²×C₆₇	—	8	2	no	—
205	C₂²×C₆₇	—	8	2	no	—
206	C₂²×C₆₇	C₂×#121	1	1	yes	characteristic
207	C₂²×C₆₇	#525	1	2	yes	—
208	C₂²×C₆₇	#576	1	1	yes	characteristic
209	C₂²×C₆₇	#577	1	2	yes	—
210	C₂²×C₆₇	#577	1	1	yes	characteristic
211	C₄×C₆₇	—	2	4	no	—
212	C₄×C₆₇	—	2	2	no	—
213	C₄×C₆₇	—	2	2	no	—
214	C₄×C₆₇	—	4	2	no	—
215	C₄×C₆₇	—	4	4	no	—
216	C₄×C₆₇	—	4	2	no	—
217	C₄×C₆₇	—	4	2	no	—
218	C₄×C₆₇	—	8	1	no	—
219	C₄×C₆₇	—	8	1	no	—
220	C₄×C₆₇	C₂×#124	1	1	yes	characteristic
221	C₄×C₆₇	#529	1	2	yes	—
222	C₄×C₆₇	#532	1	1	yes	characteristic
223	#33039	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
224	C₂×C₆₇	—	16	2	no	—
225	C₂×C₆₇	#2850	1	1	yes	characteristic
226	C₂×C₆₇	#3043	1	1	yes	characteristic
227	C₂×C₆₇	#3045	1	1	yes	characteristic
228	C₂×C₆₇	#3119	1	2	yes	—
229	C₂×C₆₇	#3126	1	2	yes	—
230	C₂×#479	C₂×C₆₇	1	1	yes	characteristic, complemented
231	C₂×#460	C₂×C₆₇	1	1	yes	characteristic
232	#2641	C₂×C₆₇	1	1	yes	characteristic
233	#2276	C₂×C₆₇	1	1	yes	characteristic, complemented
234	#1989	C₂×C₆₇	1	1	yes	characteristic, complemented
235	#1982	C₂×C₆₇	1	1	yes	characteristic
236	#1926	C₂×C₆₇	1	2	yes	complemented
237	#1925	C₂×C₆₇	1	2	yes	complemented
238	#1880	C₂×C₆₇	1	2	yes	complemented
239	#1880	C₂×C₆₇	1	2	yes	complemented
240	#1832	C₂×C₆₇	1	1	yes	characteristic, complemented
241	C₆₇	#33039	1	1	yes	characteristic, direct product factor, Sylow
242	C₂²×SD₁₆	C₂²×C₆₇	1	2	yes	—
243	C₂×#127	C₂²×C₆₇	1	1	yes	characteristic
244	C₂×#125	C₂²×C₆₇	1	1	yes	characteristic
245	C₂×C₄×Q₈	C₂²×C₆₇	1	2	yes	—
246	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
247	#479	—	2	4	no	—
248	#460	—	2	4	no	—
249	C₂×#107	C₂²×C₆₇	1	1	yes	characteristic
250	C₂×#106	C₂²×C₆₇	1	1	yes	characteristic
251	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
252	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
253	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic
254	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic
255	C₂×#102	C₂²×C₆₇	1	2	yes	—
256	C₂×#102	C₂²×C₆₇	1	2	yes	—
257	C₂×#102	C₂²×C₆₇	1	2	yes	—
258	#394	—	2	1	no	—
259	#394	—	2	2	no	—
260	#394	—	2	1	no	—
261	#390	C₂²×C₆₇	1	2	yes	—
262	#390	C₂²×C₆₇	1	2	yes	—
263	C₄×C₄⋊C₄	—	2	2	no	—
264	C₄×C₄⋊C₄	—	2	1	no	—
265	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
266	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
267	#376	—	2	1	no	—
268	#376	C₂²×C₆₇	1	1	yes	characteristic
269	#340	C₂²×C₆₇	1	2	yes	—
270	#340	C₂²×C₆₇	1	2	yes	—
271	#336	C₂²×C₆₇	1	2	yes	—
272	#336	C₂²×C₆₇	1	2	yes	—
273	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
274	C₂²×D₄	—	2	1	no	—
275	C₂²×D₄	—	2	1	no	—
276	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
277	C₂×SD₁₆	—	2	4	no	—
278	C₂×SD₁₆	—	2	4	no	—
279	C₂×SD₁₆	—	2	4	no	—
280	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
281	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
282	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
283	#127	—	2	2	no	—
284	#127	—	2	2	no	—
285	#125	—	2	2	no	—
286	#125	—	2	2	no	—
287	C₄×Q₈	—	2	4	no	—
288	C₄×Q₈	—	2	4	no	—
289	C₄×Q₈	—	2	2	no	—
290	C₄×Q₈	D₄×C₆₇	1	4	yes	—
291	C₂×C₄⋊C₄	—	2	2	no	—
292	C₂×C₄⋊C₄	—	2	1	no	—
293	C₂×C₄⋊C₄	—	2	1	no	—
294	C₂×C₄⋊C₄	—	2	1	no	—
295	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
296	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
297	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
298	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
299	C₂×C₂²⋊C₄	—	2	2	no	—
300	C₂×C₂²⋊C₄	—	2	2	no	—
301	C₂×C₂²⋊C₄	—	2	2	no	—
302	C₂×C₂²⋊C₄	—	2	2	no	—
303	C₂×C₄²	—	2	2	no	—
304	C₂×C₄²	—	2	1	no	—
305	C₂×C₄²	—	2	2	no	—
306	C₂×C₄²	—	2	1	no	—
307	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
308	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
309	#107	—	2	2	no	—
310	#106	—	2	2	no	—
311	C₄⋊C₈	—	2	2	no	—
312	C₄⋊C₈	—	2	2	no	—
313	#103	—	2	2	no	—
314	#103	—	2	2	no	—
315	#102	—	2	4	no	—
316	#102	—	2	4	no	—
317	#102	—	2	4	no	—
318	#95	—	2	2	no	—
319	#95	—	2	1	no	—
320	#95	D₄×C₆₇	1	1	yes	characteristic
321	#95	D₄×C₆₇	1	2	yes	—
322	#95	D₄×C₆₇	1	1	yes	characteristic
323	C₂⁴	—	2	2	no	—
324	C₂×Q₈	—	2	1	no	—
325	C₂×Q₈	—	2	2	no	—
326	C₂×Q₈	C₂×D₄×C₆₇	1	2	yes	—
327	C₂×Q₈	#41×C₆₇	1	4	yes	—
328	C₂×D₄	—	2	2	no	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	2	2	no	—
331	C₂×D₄	—	2	2	no	—
332	C₂×D₄	—	2	2	no	—
333	C₂×D₄	—	2	2	no	—
334	C₂×D₄	—	4	2	no	—
335	C₂×D₄	—	4	2	no	—
336	C₂×D₄	—	8	1	no	—
337	C₂×D₄	—	8	2	no	—
338	C₂×D₄	—	8	1	no	—
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	2	1	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
345	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
346	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
347	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
348	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
349	SD₁₆	—	4	8	no	—
350	C₂×C₈	—	2	2	no	—
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	2	1	no	—
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	—	2	2	no	—
356	C₂×C₈	—	2	2	no	—
357	C₄⋊C₄	—	2	8	no	—
358	C₄⋊C₄	—	2	4	no	—
359	C₄⋊C₄	—	2	1	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	2	1	no	—
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	—	4	2	no	—
366	C₄⋊C₄	—	4	2	no	—
367	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
368	C₄⋊C₄	#41×C₆₇	1	4	yes	—
369	C₂²⋊C₄	—	8	2	no	—
370	C₂²⋊C₄	—	8	2	no	—
371	C₂²⋊C₄	—	8	2	no	—
372	C₂²⋊C₄	—	8	2	no	—
373	C₄²	—	2	8	no	—
374	C₄²	—	2	4	no	—
375	C₄²	—	2	2	no	—
376	C₄²	—	2	2	no	—
377	C₄²	—	8	1	no	—
378	C₄²	—	8	2	no	—
379	C₄²	C₂×D₄×C₆₇	1	2	yes	—
380	C₄²	#41×C₆₇	1	2	yes	—
381	C₂³	—	4	2	no	—
382	C₂³	—	4	2	no	—
383	C₂³	—	4	2	no	—
384	C₂³	—	4	2	no	—
385	C₂³	—	4	2	no	—
386	C₂³	—	4	2	no	—
387	C₂³	—	4	2	no	—
388	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
389	Q₈	—	2	4	no	—
390	Q₈	—	2	2	no	—
391	Q₈	#124×C₆₇	1	4	yes	—
392	D₄	—	4	2	no	—
393	D₄	—	4	2	no	—
394	D₄	—	4	2	no	—
395	D₄	—	4	2	no	—
396	D₄	—	8	4	no	—
397	D₄	—	8	4	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	4	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	4	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	4	1	no	—
417	C₂×C₄	—	4	1	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	1	no	—
420	C₂×C₄	#121×C₆₇	1	2	yes	—
421	C₂×C₄	#121×C₆₇	1	2	yes	—
422	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
423	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
424	C₂×C₄	C₂×#41×C₆₇	1	1	yes	characteristic
425	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
426	C₈	—	4	2	no	—
427	C₈	—	4	1	no	—
428	C₈	—	4	1	no	—
429	C₂²	—	8	2	no	—
430	C₂²	—	8	2	no	—
431	C₂²	—	8	2	no	—
432	C₂²	—	8	2	no	—
433	C₂²	—	8	2	no	—
434	C₂²	—	8	2	no	—
435	C₂²	—	8	2	no	—
436	C₂²	C₂×#121×C₆₇	1	1	yes	characteristic
437	C₂²	#525×C₆₇	1	2	yes	—
438	C₂²	#576×C₆₇	1	1	yes	characteristic
439	C₂²	#577×C₆₇	1	2	yes	—
440	C₂²	#577×C₆₇	1	1	yes	characteristic
441	C₄	—	2	2	no	—
442	C₄	—	2	2	no	—
443	C₄	—	2	4	no	—
444	C₄	—	4	2	no	—
445	C₄	—	4	2	no	—
446	C₄	—	4	4	no	—
447	C₄	—	4	2	no	—
448	C₄	—	8	1	no	—
449	C₄	—	8	1	no	—
450	C₄	C₂×#124×C₆₇	1	1	yes	characteristic
451	C₄	#529×C₆₇	1	2	yes	—
452	C₄	#532×C₆₇	1	1	yes	characteristic
453	C₂	—	16	2	no	—
454	C₂	C₆₇×#2850	1	1	yes	characteristic
455	C₂	C₆₇×#3043	1	1	yes	characteristic
456	C₂	C₆₇×#3045	1	1	yes	characteristic
457	C₂	C₆₇×#3119	1	2	yes	—
458	C₂	C₆₇×#3126	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₇
prime radical	C₂×#127×C₆₇	C₂²
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×#479×C₆₇	C₂	semidirect
4. C₆₇×#2276	C₂	semidirect
5. C₆₇×#1989	C₂	semidirect
7. C₆₇×#1926	C₂	semidirect
8. C₆₇×#1925	C₂	semidirect
9. C₆₇×#1880	C₂	semidirect
10. C₆₇×#1880	C₂	semidirect
11. C₆₇×#1832	C₂	semidirect
223. #33039	C₆₇	direct (N × H)
230. C₂×#479	C₂×C₆₇	semidirect
233. #2276	C₂×C₆₇	semidirect
234. #1989	C₂×C₆₇	semidirect
236. #1926	C₂×C₆₇	semidirect
237. #1925	C₂×C₆₇	semidirect
238. #1880	C₂×C₆₇	semidirect
239. #1880	C₂×C₆₇	semidirect
240. #1832	C₂×C₆₇	semidirect
241. C₆₇	#33039	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×#479×C₆₇	2
C₂×#460×C₆₇	2
C₆₇×#2641	2
C₆₇×#2276	2
C₆₇×#1989	2
C₆₇×#1982	2
C₆₇×#1926	2
C₆₇×#1925	2
C₆₇×#1880	2
C₆₇×#1832	2
#33039	67

Subgroups — C67×#33039 #30712290

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#33039 #30712290