Subgroups — C₆₇×#33035 #30712286

Order 17152.

842 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#477×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#464×C₆₇	C₂	1	1	yes	maximal, characteristic
3	C₆₇×#2640	C₂	1	1	yes	maximal, characteristic
4	C₆₇×#2276	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#1988	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#1983	C₂	1	1	yes	maximal, characteristic
7	C₆₇×#1928	C₂	1	2	yes	maximal, complemented
8	C₆₇×#1925	C₂	1	2	yes	maximal
9	C₆₇×#1880	C₂	1	2	yes	maximal
10	C₆₇×#1878	C₂	1	2	yes	maximal, complemented
11	C₆₇×#1832	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic
13	C₂²×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
15	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic
16	C₂×C₄×Q₈×C₆₇	C₂²	1	2	yes	—
17	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
18	#477×C₆₇	—	2	4	no	—
19	#464×C₆₇	—	2	4	no	—
20	C₂×#107×C₆₇	C₂²	1	2	yes	—
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	2	yes	—
25	C₂×#103×C₆₇	C₂²	1	2	yes	—
26	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
27	C₂×#102×C₆₇	C₂²	1	2	yes	—
28	#397×C₆₇	—	2	1	no	—
29	#397×C₆₇	—	2	1	no	—
30	#393×C₆₇	—	2	2	no	—
31	#391×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	—	2	1	no	—
44	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
45	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
46	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
47	C₂×Q₁₆×C₆₇	—	2	2	no	—
48	C₂×Q₁₆×C₆₇	—	2	4	no	—
49	C₂×SD₁₆×C₆₇	—	2	2	no	—
50	C₂×SD₁₆×C₆₇	—	2	4	no	—
51	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
53	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
54	C₄⋊Q₈×C₆₇	—	2	2	no	—
55	C₄⋊Q₈×C₆₇	—	2	2	no	—
56	#124×C₆₇	—	2	2	no	—
57	#124×C₆₇	—	2	2	no	—
58	C₄×Q₈×C₆₇	—	2	4	no	—
59	C₄×Q₈×C₆₇	—	2	4	no	—
60	C₄×Q₈×C₆₇	—	2	2	no	—
61	C₄×Q₈×C₆₇	D₄	1	4	yes	—
62	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
63	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
64	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
65	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
66	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
67	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
68	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
69	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
70	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
71	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
72	C₂×C₄²×C₆₇	—	2	2	no	—
73	C₂×C₄²×C₆₇	—	2	1	no	—
74	C₂×C₄²×C₆₇	—	2	2	no	—
75	C₂×C₄²×C₆₇	—	2	1	no	—
76	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
77	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
78	#107×C₆₇	—	2	4	no	—
79	C₄⋊C₈×C₆₇	—	2	2	no	—
80	C₄⋊C₈×C₆₇	—	2	2	no	—
81	#103×C₆₇	—	2	4	no	—
82	#103×C₆₇	—	2	2	no	—
83	#103×C₆₇	—	2	4	no	—
84	#102×C₆₇	—	2	2	no	—
85	#102×C₆₇	—	2	4	no	—
86	#95×C₆₇	—	2	2	no	—
87	#95×C₆₇	—	2	1	no	—
88	#95×C₆₇	—	2	2	no	—
89	#95×C₆₇	—	2	2	no	—
90	#95×C₆₇	D₄	1	1	yes	characteristic
91	#95×C₆₇	D₄	1	2	yes	—
92	#95×C₆₇	D₄	1	1	yes	characteristic
93	C₂⁴×C₆₇	—	2	1	no	—
94	C₂×Q₈×C₆₇	—	2	1	no	—
95	C₂×Q₈×C₆₇	—	2	2	no	—
96	C₂×Q₈×C₆₇	—	2	1	no	—
97	C₂×Q₈×C₆₇	—	2	2	no	—
98	C₂×Q₈×C₆₇	—	2	1	no	—
99	C₂×Q₈×C₆₇	—	2	2	no	—
100	C₂×Q₈×C₆₇	—	4	2	no	—
101	C₂×Q₈×C₆₇	—	8	1	no	—
102	C₂×Q₈×C₆₇	—	8	1	no	—
103	C₂×Q₈×C₆₇	C₂×D₄	1	2	yes	—
104	C₂×Q₈×C₆₇	#41	1	4	yes	—
105	C₂×D₄×C₆₇	—	2	1	no	—
106	C₂×D₄×C₆₇	—	2	2	no	—
107	C₂×D₄×C₆₇	—	2	1	no	—
108	C₂×D₄×C₆₇	—	2	2	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	2	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	Q₁₆×C₆₇	—	4	4	no	—
120	SD₁₆×C₆₇	—	4	4	no	—
121	C₂×C₈×C₆₇	—	2	1	no	—
122	C₂×C₈×C₆₇	—	2	2	no	—
123	C₂×C₈×C₆₇	—	2	1	no	—
124	C₂×C₈×C₆₇	—	2	2	no	—
125	C₂×C₈×C₆₇	—	2	2	no	—
126	C₂×C₈×C₆₇	—	2	2	no	—
127	C₂×C₈×C₆₇	—	2	2	no	—
128	C₄⋊C₄×C₆₇	—	2	8	no	—
129	C₄⋊C₄×C₆₇	—	2	4	no	—
130	C₄⋊C₄×C₆₇	—	2	1	no	—
131	C₄⋊C₄×C₆₇	—	2	2	no	—
132	C₄⋊C₄×C₆₇	—	2	2	no	—
133	C₄⋊C₄×C₆₇	—	2	2	no	—
134	C₄⋊C₄×C₆₇	—	4	2	no	—
135	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
136	C₄⋊C₄×C₆₇	#41	1	4	yes	—
137	C₂²⋊C₄×C₆₇	—	4	2	no	—
138	C₂²⋊C₄×C₆₇	—	4	2	no	—
139	C₂²⋊C₄×C₆₇	—	8	2	no	—
140	C₂²⋊C₄×C₆₇	—	8	2	no	—
141	C₄²×C₆₇	—	2	8	no	—
142	C₄²×C₆₇	—	2	4	no	—
143	C₄²×C₆₇	—	2	2	no	—
144	C₄²×C₆₇	—	2	2	no	—
145	C₄²×C₆₇	—	8	1	no	—
146	C₄²×C₆₇	—	8	2	no	—
147	C₄²×C₆₇	C₂×D₄	1	2	yes	—
148	C₄²×C₆₇	#41	1	2	yes	—
149	C₂³×C₆₇	—	4	1	no	—
150	C₂³×C₆₇	—	4	2	no	—
151	C₂³×C₆₇	—	4	1	no	—
152	C₂³×C₆₇	—	4	1	no	—
153	C₂³×C₆₇	—	4	2	no	—
154	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
155	Q₈×C₆₇	—	2	4	no	—
156	Q₈×C₆₇	—	2	2	no	—
157	Q₈×C₆₇	—	4	1	no	—
158	Q₈×C₆₇	—	4	2	no	—
159	Q₈×C₆₇	—	4	1	no	—
160	Q₈×C₆₇	—	8	4	no	—
161	Q₈×C₆₇	#124	1	4	yes	—
162	D₄×C₆₇	—	4	1	no	—
163	D₄×C₆₇	—	4	2	no	—
164	D₄×C₆₇	—	4	1	no	—
165	C₂×C₄×C₆₇	—	2	2	no	—
166	C₂×C₄×C₆₇	—	2	4	no	—
167	C₂×C₄×C₆₇	—	2	1	no	—
168	C₂×C₄×C₆₇	—	2	1	no	—
169	C₂×C₄×C₆₇	—	2	2	no	—
170	C₂×C₄×C₆₇	—	2	2	no	—
171	C₂×C₄×C₆₇	—	2	2	no	—
172	C₂×C₄×C₆₇	—	2	2	no	—
173	C₂×C₄×C₆₇	—	2	4	no	—
174	C₂×C₄×C₆₇	—	2	2	no	—
175	C₂×C₄×C₆₇	—	2	2	no	—
176	C₂×C₄×C₆₇	—	2	2	no	—
177	C₂×C₄×C₆₇	—	2	2	no	—
178	C₂×C₄×C₆₇	—	4	2	no	—
179	C₂×C₄×C₆₇	—	4	1	no	—
180	C₂×C₄×C₆₇	—	4	1	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	2	no	—
185	C₂×C₄×C₆₇	—	4	2	no	—
186	C₂×C₄×C₆₇	—	4	2	no	—
187	C₂×C₄×C₆₇	#121	1	2	yes	—
188	C₂×C₄×C₆₇	#121	1	2	yes	—
189	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
190	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
191	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
192	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
193	C₈×C₆₇	—	4	1	no	—
194	C₈×C₆₇	—	4	1	no	—
195	C₈×C₆₇	—	4	2	no	—
196	C₂²×C₆₇	—	8	1	no	—
197	C₂²×C₆₇	—	8	2	no	—
198	C₂²×C₆₇	—	8	2	no	—
199	C₂²×C₆₇	—	8	1	no	—
200	C₂²×C₆₇	—	8	1	no	—
201	C₂²×C₆₇	C₂×#121	1	1	yes	characteristic
202	C₂²×C₆₇	#525	1	2	yes	—
203	C₂²×C₆₇	#576	1	1	yes	characteristic
204	C₂²×C₆₇	#577	1	1	yes	characteristic
205	C₂²×C₆₇	#578	1	2	yes	—
206	C₄×C₆₇	—	2	4	no	—
207	C₄×C₆₇	—	2	2	no	—
208	C₄×C₆₇	—	2	2	no	—
209	C₄×C₆₇	—	4	2	no	—
210	C₄×C₆₇	—	4	2	no	—
211	C₄×C₆₇	—	4	4	no	—
212	C₄×C₆₇	—	4	2	no	—
213	C₄×C₆₇	—	8	1	no	—
214	C₄×C₆₇	—	8	2	no	—
215	C₄×C₆₇	C₂×#124	1	1	yes	characteristic
216	C₄×C₆₇	#529	1	2	yes	—
217	C₄×C₆₇	#532	1	1	yes	characteristic
218	#33035	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
219	C₂×C₆₇	—	16	1	no	—
220	C₂×C₆₇	#2850	1	1	yes	characteristic
221	C₂×C₆₇	#3044	1	1	yes	characteristic
222	C₂×C₆₇	#3045	1	1	yes	characteristic
223	C₂×C₆₇	#3121	1	2	yes	—
224	C₂×C₆₇	#3124	1	2	yes	—
225	C₂×#477	C₂×C₆₇	1	1	yes	characteristic, complemented
226	C₂×#464	C₂×C₆₇	1	1	yes	characteristic
227	#2640	C₂×C₆₇	1	1	yes	characteristic
228	#2276	C₂×C₆₇	1	1	yes	characteristic, complemented
229	#1988	C₂×C₆₇	1	1	yes	characteristic, complemented
230	#1983	C₂×C₆₇	1	1	yes	characteristic
231	#1928	C₂×C₆₇	1	2	yes	complemented
232	#1925	C₂×C₆₇	1	2	yes	—
233	#1880	C₂×C₆₇	1	2	yes	—
234	#1878	C₂×C₆₇	1	2	yes	complemented
235	#1832	C₂×C₆₇	1	1	yes	characteristic, complemented
236	C₆₇	#33035	1	1	yes	characteristic, direct product factor, Sylow
237	C₂²×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic
238	C₂²×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic
239	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
240	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic
241	C₂×C₄×Q₈	C₂²×C₆₇	1	2	yes	—
242	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
243	#477	—	2	4	no	—
244	#464	—	2	4	no	—
245	C₂×#107	C₂²×C₆₇	1	2	yes	—
246	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
247	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
248	C₂×#103	C₂²×C₆₇	1	2	yes	—
249	C₂×#103	C₂²×C₆₇	1	2	yes	—
250	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic
251	C₂×#102	C₂²×C₆₇	1	2	yes	—
252	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
253	#397	—	2	1	no	—
254	#397	—	2	1	no	—
255	#393	—	2	2	no	—
256	#391	C₂²×C₆₇	1	2	yes	—
257	#390	C₂²×C₆₇	1	2	yes	—
258	C₄×C₄⋊C₄	—	2	2	no	—
259	C₄×C₄⋊C₄	—	2	1	no	—
260	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
261	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
262	#376	—	2	1	no	—
263	#376	C₂²×C₆₇	1	1	yes	characteristic
264	#340	C₂²×C₆₇	1	2	yes	—
265	#340	C₂²×C₆₇	1	2	yes	—
266	#336	C₂²×C₆₇	1	2	yes	—
267	#336	C₂²×C₆₇	1	2	yes	—
268	C₂²×Q₈	—	2	1	no	—
269	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
270	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
271	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
272	C₂×Q₁₆	—	2	2	no	—
273	C₂×Q₁₆	—	2	4	no	—
274	C₂×SD₁₆	—	2	2	no	—
275	C₂×SD₁₆	—	2	4	no	—
276	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
277	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
278	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
279	C₄⋊Q₈	—	2	2	no	—
280	C₄⋊Q₈	—	2	2	no	—
281	#124	—	2	2	no	—
282	#124	—	2	2	no	—
283	C₄×Q₈	—	2	4	no	—
284	C₄×Q₈	—	2	4	no	—
285	C₄×Q₈	—	2	2	no	—
286	C₄×Q₈	D₄×C₆₇	1	4	yes	—
287	C₂×C₄⋊C₄	—	2	2	no	—
288	C₂×C₄⋊C₄	—	2	1	no	—
289	C₂×C₄⋊C₄	—	2	1	no	—
290	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
291	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
292	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
293	C₂×C₂²⋊C₄	—	2	1	no	—
294	C₂×C₂²⋊C₄	—	2	1	no	—
295	C₂×C₂²⋊C₄	—	2	2	no	—
296	C₂×C₂²⋊C₄	—	2	2	no	—
297	C₂×C₄²	—	2	2	no	—
298	C₂×C₄²	—	2	1	no	—
299	C₂×C₄²	—	2	2	no	—
300	C₂×C₄²	—	2	1	no	—
301	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
302	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
303	#107	—	2	4	no	—
304	C₄⋊C₈	—	2	2	no	—
305	C₄⋊C₈	—	2	2	no	—
306	#103	—	2	4	no	—
307	#103	—	2	2	no	—
308	#103	—	2	4	no	—
309	#102	—	2	2	no	—
310	#102	—	2	4	no	—
311	#95	—	2	2	no	—
312	#95	—	2	1	no	—
313	#95	—	2	2	no	—
314	#95	—	2	2	no	—
315	#95	D₄×C₆₇	1	1	yes	characteristic
316	#95	D₄×C₆₇	1	2	yes	—
317	#95	D₄×C₆₇	1	1	yes	characteristic
318	C₂⁴	—	2	1	no	—
319	C₂×Q₈	—	2	1	no	—
320	C₂×Q₈	—	2	2	no	—
321	C₂×Q₈	—	2	1	no	—
322	C₂×Q₈	—	2	2	no	—
323	C₂×Q₈	—	2	1	no	—
324	C₂×Q₈	—	2	2	no	—
325	C₂×Q₈	—	4	2	no	—
326	C₂×Q₈	—	8	1	no	—
327	C₂×Q₈	—	8	1	no	—
328	C₂×Q₈	C₂×D₄×C₆₇	1	2	yes	—
329	C₂×Q₈	#41×C₆₇	1	4	yes	—
330	C₂×D₄	—	2	1	no	—
331	C₂×D₄	—	2	2	no	—
332	C₂×D₄	—	2	1	no	—
333	C₂×D₄	—	2	2	no	—
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	1	no	—
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
340	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
341	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
342	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
343	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
344	Q₁₆	—	4	4	no	—
345	SD₁₆	—	4	4	no	—
346	C₂×C₈	—	2	1	no	—
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	—	2	1	no	—
349	C₂×C₈	—	2	2	no	—
350	C₂×C₈	—	2	2	no	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	—	2	2	no	—
353	C₄⋊C₄	—	2	8	no	—
354	C₄⋊C₄	—	2	4	no	—
355	C₄⋊C₄	—	2	1	no	—
356	C₄⋊C₄	—	2	2	no	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	4	2	no	—
360	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
361	C₄⋊C₄	#41×C₆₇	1	4	yes	—
362	C₂²⋊C₄	—	4	2	no	—
363	C₂²⋊C₄	—	4	2	no	—
364	C₂²⋊C₄	—	8	2	no	—
365	C₂²⋊C₄	—	8	2	no	—
366	C₄²	—	2	8	no	—
367	C₄²	—	2	4	no	—
368	C₄²	—	2	2	no	—
369	C₄²	—	2	2	no	—
370	C₄²	—	8	1	no	—
371	C₄²	—	8	2	no	—
372	C₄²	C₂×D₄×C₆₇	1	2	yes	—
373	C₄²	#41×C₆₇	1	2	yes	—
374	C₂³	—	4	1	no	—
375	C₂³	—	4	2	no	—
376	C₂³	—	4	1	no	—
377	C₂³	—	4	1	no	—
378	C₂³	—	4	2	no	—
379	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
380	Q₈	—	2	4	no	—
381	Q₈	—	2	2	no	—
382	Q₈	—	4	1	no	—
383	Q₈	—	4	2	no	—
384	Q₈	—	4	1	no	—
385	Q₈	—	8	4	no	—
386	Q₈	#124×C₆₇	1	4	yes	—
387	D₄	—	4	1	no	—
388	D₄	—	4	2	no	—
389	D₄	—	4	1	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	4	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	4	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	#121×C₆₇	1	2	yes	—
413	C₂×C₄	#121×C₆₇	1	2	yes	—
414	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
415	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
416	C₂×C₄	C₂×#41×C₆₇	1	1	yes	characteristic
417	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
418	C₈	—	4	1	no	—
419	C₈	—	4	1	no	—
420	C₈	—	4	2	no	—
421	C₂²	—	8	1	no	—
422	C₂²	—	8	1	no	—
423	C₂²	—	8	1	no	—
424	C₂²	—	8	2	no	—
425	C₂²	—	8	2	no	—
426	C₂²	C₂×#121×C₆₇	1	1	yes	characteristic
427	C₂²	#525×C₆₇	1	2	yes	—
428	C₂²	#576×C₆₇	1	1	yes	characteristic
429	C₂²	#577×C₆₇	1	1	yes	characteristic
430	C₂²	#578×C₆₇	1	2	yes	—
431	C₄	—	2	2	no	—
432	C₄	—	2	2	no	—
433	C₄	—	2	4	no	—
434	C₄	—	4	2	no	—
435	C₄	—	4	2	no	—
436	C₄	—	4	2	no	—
437	C₄	—	4	4	no	—
438	C₄	—	8	2	no	—
439	C₄	—	8	1	no	—
440	C₄	C₂×#124×C₆₇	1	1	yes	characteristic
441	C₄	#529×C₆₇	1	2	yes	—
442	C₄	#532×C₆₇	1	1	yes	characteristic
443	C₂	—	16	1	no	—
444	C₂	C₆₇×#2850	1	1	yes	characteristic
445	C₂	C₆₇×#3044	1	1	yes	characteristic
446	C₂	C₆₇×#3045	1	1	yes	characteristic
447	C₂	C₆₇×#3121	1	2	yes	—
448	C₂	C₆₇×#3124	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₇
prime radical	C₂²×D₄×C₆₇	C₂³
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×#477×C₆₇	C₂	semidirect
4. C₆₇×#2276	C₂	semidirect
5. C₆₇×#1988	C₂	semidirect
7. C₆₇×#1928	C₂	semidirect
10. C₆₇×#1878	C₂	semidirect
11. C₆₇×#1832	C₂	semidirect
218. #33035	C₆₇	direct (N × H)
225. C₂×#477	C₂×C₆₇	semidirect
228. #2276	C₂×C₆₇	semidirect
229. #1988	C₂×C₆₇	semidirect
231. #1928	C₂×C₆₇	semidirect
234. #1878	C₂×C₆₇	semidirect
235. #1832	C₂×C₆₇	semidirect
236. C₆₇	#33035	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×#477×C₆₇	2
C₂×#464×C₆₇	2
C₆₇×#2640	2
C₆₇×#2276	2
C₆₇×#1988	2
C₆₇×#1983	2
C₆₇×#1928	2
C₆₇×#1925	2
C₆₇×#1880	2
C₆₇×#1878	2
C₆₇×#1832	2
#33035	67

Subgroups — C67×#33035 #30712286

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#33035 #30712286