Subgroups — C₆₇×#33200 #30712451

Order 17152.

810 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	C₂×#479×C₆₇	C₂	1	2	yes	maximal
2	C₆₇×#2859	C₂	1	1	yes	maximal, characteristic
3	C₄²×Q₈×C₆₇	C₂	1	1	yes	maximal, characteristic
4	C₆₇×#1989	C₂	1	2	yes	maximal
5	C₆₇×#1949	C₂	1	2	yes	maximal
6	C₆₇×#1948	C₂	1	1	yes	maximal, characteristic
7	C₆₇×#1947	C₂	1	1	yes	maximal, characteristic
8	C₆₇×#1842	C₂	1	1	yes	maximal, characteristic
9	C₆₇×#1805	C₂	1	2	yes	maximal
10	C₆₇×#1803	C₂	1	1	yes	maximal, characteristic
11	C₆₇×#1803	C₂	1	1	yes	maximal, characteristic
12	C₂×#125×C₆₇	C₂²	1	2	yes	—
13	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
15	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
16	#479×C₆₇	—	2	8	no	—
17	C₂×#107×C₆₇	C₂²	1	2	yes	—
18	C₂×#106×C₆₇	C₂²	1	2	yes	—
19	C₂×C₄⋊C₈×C₆₇	C₂²	1	2	yes	—
20	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊C₈×C₆₇	C₂²	1	2	yes	—
23	C₂×#103×C₆₇	C₂²	1	2	yes	—
24	C₂×#103×C₆₇	C₂²	1	2	yes	—
25	#389×C₆₇	—	2	1	no	—
26	#389×C₆₇	—	2	1	no	—
27	#389×C₆₇	—	2	1	no	—
28	#389×C₆₇	—	2	1	no	—
29	#384×C₆₇	C₂²	1	1	yes	characteristic
30	#384×C₆₇	C₂²	1	1	yes	characteristic
31	#382×C₆₇	C₂²	1	2	yes	—
32	C₄×C₄⋊C₄×C₆₇	—	2	1	no	—
33	C₄×C₄⋊C₄×C₆₇	—	2	1	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	1	yes	characteristic
37	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
38	C₄³×C₆₇	—	2	1	no	—
39	C₄³×C₆₇	C₂²	1	1	yes	characteristic
40	#340×C₆₇	C₂²	1	2	yes	—
41	#340×C₆₇	C₂²	1	2	yes	—
42	#340×C₆₇	C₂²	1	2	yes	—
43	#340×C₆₇	C₂²	1	2	yes	—
44	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
45	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
46	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
47	#125×C₆₇	—	2	4	no	—
48	#125×C₆₇	—	2	4	no	—
49	C₄×Q₈×C₆₇	—	2	2	no	—
50	C₄×Q₈×C₆₇	—	2	2	no	—
51	C₄×Q₈×C₆₇	—	2	2	no	—
52	C₄×Q₈×C₆₇	D₄	1	4	yes	—
53	C₄×Q₈×C₆₇	Q₈	1	4	yes	—
54	C₄×Q₈×C₆₇	Q₈	1	4	yes	—
55	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
56	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
57	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
58	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
59	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
60	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
61	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
62	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
63	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
64	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
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	1	yes	characteristic
68	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
69	C₂×C₄²×C₆₇	—	2	1	no	—
70	C₂×C₄²×C₆₇	—	2	1	no	—
71	C₂×C₄²×C₆₇	—	2	1	no	—
72	C₂×C₄²×C₆₇	—	2	1	no	—
73	C₂×C₄²×C₆₇	—	2	1	no	—
74	C₂×C₄²×C₆₇	—	2	1	no	—
75	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
76	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
77	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
78	C₂×C₄²×C₆₇	D₄	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	#107×C₆₇	—	2	4	no	—
83	#106×C₆₇	—	2	4	no	—
84	C₄⋊C₈×C₆₇	—	2	4	no	—
85	C₄⋊C₈×C₆₇	—	2	2	no	—
86	C₄⋊C₈×C₆₇	—	2	2	no	—
87	C₄⋊C₈×C₆₇	—	2	4	no	—
88	#103×C₆₇	—	2	4	no	—
89	#103×C₆₇	—	2	4	no	—
90	#95×C₆₇	—	2	1	no	—
91	#95×C₆₇	—	2	1	no	—
92	#95×C₆₇	—	2	1	no	—
93	#95×C₆₇	—	2	2	no	—
94	#95×C₆₇	—	2	2	no	—
95	C₂×Q₈×C₆₇	—	2	1	no	—
96	C₂×Q₈×C₆₇	—	2	1	no	—
97	C₂×Q₈×C₆₇	—	2	1	no	—
98	C₂×Q₈×C₆₇	C₂×D₄	1	2	yes	—
99	C₂×Q₈×C₆₇	C₂×Q₈	1	2	yes	—
100	C₂×Q₈×C₆₇	C₂×Q₈	1	2	yes	—
101	C₂²×C₄×C₆₇	—	2	1	no	—
102	C₂²×C₄×C₆₇	—	2	1	no	—
103	C₂²×C₄×C₆₇	—	2	1	no	—
104	C₂²×C₄×C₆₇	—	2	1	no	—
105	C₂²×C₄×C₆₇	—	2	2	no	—
106	C₂²×C₄×C₆₇	—	2	2	no	—
107	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
114	C₂×C₈×C₆₇	—	2	2	no	—
115	C₂×C₈×C₆₇	—	2	2	no	—
116	C₂×C₈×C₆₇	—	2	2	no	—
117	C₂×C₈×C₆₇	—	2	2	no	—
118	C₂×C₈×C₆₇	—	2	2	no	—
119	C₂×C₈×C₆₇	—	2	2	no	—
120	C₄⋊C₄×C₆₇	—	2	4	no	—
121	C₄⋊C₄×C₆₇	—	2	4	no	—
122	C₄⋊C₄×C₆₇	—	2	4	no	—
123	C₄⋊C₄×C₆₇	—	2	1	no	—
124	C₄⋊C₄×C₆₇	—	2	1	no	—
125	C₄⋊C₄×C₆₇	—	2	1	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	—	2	2	no	—
130	C₄⋊C₄×C₆₇	—	4	2	no	—
131	C₄⋊C₄×C₆₇	—	4	2	no	—
132	C₄⋊C₄×C₆₇	—	4	4	no	—
133	C₄⋊C₄×C₆₇	—	4	4	no	—
134	C₄⋊C₄×C₆₇	—	4	2	no	—
135	C₄⋊C₄×C₆₇	—	4	2	no	—
136	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
137	C₄⋊C₄×C₆₇	C₂×Q₈	1	2	yes	—
138	C₄⋊C₄×C₆₇	C₂×Q₈	1	2	yes	—
139	C₄²×C₆₇	—	2	4	no	—
140	C₄²×C₆₇	—	2	4	no	—
141	C₄²×C₆₇	—	2	4	no	—
142	C₄²×C₆₇	—	2	2	no	—
143	C₄²×C₆₇	—	2	2	no	—
144	C₄²×C₆₇	—	4	1	no	—
145	C₄²×C₆₇	—	4	1	no	—
146	C₄²×C₆₇	—	4	2	no	—
147	C₄²×C₆₇	—	4	2	no	—
148	C₄²×C₆₇	—	4	2	no	—
149	C₄²×C₆₇	C₂×D₄	1	2	yes	—
150	C₄²×C₆₇	C₂×Q₈	1	2	yes	—
151	C₄²×C₆₇	C₂×Q₈	1	2	yes	—
152	C₄²×C₆₇	#41	1	2	yes	—
153	C₄²×C₆₇	#41	1	2	yes	—
154	C₄²×C₆₇	#41	1	2	yes	—
155	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
156	Q₈×C₆₇	—	2	2	no	—
157	Q₈×C₆₇	—	2	2	no	—
158	Q₈×C₆₇	—	2	2	no	—
159	Q₈×C₆₇	C₄⋊Q₈	1	4	yes	—
160	C₂×C₄×C₆₇	—	2	2	no	—
161	C₂×C₄×C₆₇	—	2	2	no	—
162	C₂×C₄×C₆₇	—	2	2	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	2	no	—
174	C₂×C₄×C₆₇	—	2	2	no	—
175	C₂×C₄×C₆₇	—	2	2	no	—
176	C₂×C₄×C₆₇	—	4	1	no	—
177	C₂×C₄×C₆₇	—	4	1	no	—
178	C₂×C₄×C₆₇	—	4	1	no	—
179	C₂×C₄×C₆₇	—	4	1	no	—
180	C₂×C₄×C₆₇	—	4	1	no	—
181	C₂×C₄×C₆₇	—	4	1	no	—
182	C₂×C₄×C₆₇	—	4	2	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	—	4	2	no	—
188	C₂×C₄×C₆₇	#121	1	2	yes	—
189	C₂×C₄×C₆₇	#121	1	2	yes	—
190	C₂×C₄×C₆₇	C₂²⋊Q₈	1	2	yes	—
191	C₂×C₄×C₆₇	C₂²⋊Q₈	1	2	yes	—
192	C₂×C₄×C₆₇	C₂²⋊Q₈	1	2	yes	—
193	C₂×C₄×C₆₇	C₂²⋊Q₈	1	2	yes	—
194	C₂×C₄×C₆₇	#135	1	2	yes	—
195	C₂×C₄×C₆₇	#137	1	2	yes	—
196	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
197	C₂×C₄×C₆₇	C₂²×Q₈	1	1	yes	characteristic
198	C₂×C₄×C₆₇	C₂²×Q₈	1	1	yes	characteristic
199	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
200	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
201	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
202	C₈×C₆₇	—	4	2	no	—
203	C₈×C₆₇	—	4	2	no	—
204	C₂²×C₆₇	C₂×#121	1	1	yes	characteristic
205	C₂²×C₆₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
206	C₂²×C₆₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
207	C₂²×C₆₇	C₂×#135	1	1	yes	characteristic
208	C₂²×C₆₇	C₂×#137	1	1	yes	characteristic
209	C₂²×C₆₇	#575	1	1	yes	characteristic
210	C₂²×C₆₇	#575	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	4	no	—
215	C₄×C₆₇	—	2	2	no	—
216	C₄×C₆₇	—	2	2	no	—
217	C₄×C₆₇	—	4	2	no	—
218	C₄×C₆₇	—	4	2	no	—
219	C₄×C₆₇	—	4	2	no	—
220	C₄×C₆₇	—	8	2	no	—
221	C₄×C₆₇	—	8	2	no	—
222	C₄×C₆₇	#479	1	4	yes	complemented
223	C₄×C₆₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
224	C₄×C₆₇	#532	1	1	yes	characteristic
225	C₄×C₆₇	#533	1	1	yes	characteristic
226	C₄×C₆₇	#533	1	1	yes	characteristic
227	#33200	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
228	C₂×C₆₇	#2857	1	1	yes	characteristic
229	C₂×C₆₇	#3035	1	1	yes	characteristic
230	C₂×C₆₇	#3037	1	1	yes	characteristic
231	C₂×C₆₇	C₂×#479	1	1	yes	characteristic
232	C₂×C₆₇	#3076	1	1	yes	characteristic
233	C₂×C₆₇	#3078	1	1	yes	characteristic
234	C₂×C₆₇	#3080	1	1	yes	characteristic
235	C₂×#479	C₂×C₆₇	1	2	yes	—
236	#2859	C₂×C₆₇	1	1	yes	characteristic
237	C₄²×Q₈	C₂×C₆₇	1	1	yes	characteristic
238	#1989	C₂×C₆₇	1	2	yes	—
239	#1949	C₂×C₆₇	1	2	yes	—
240	#1948	C₂×C₆₇	1	1	yes	characteristic
241	#1947	C₂×C₆₇	1	1	yes	characteristic
242	#1842	C₂×C₆₇	1	1	yes	characteristic
243	#1805	C₂×C₆₇	1	2	yes	—
244	#1803	C₂×C₆₇	1	1	yes	characteristic
245	#1803	C₂×C₆₇	1	1	yes	characteristic
246	C₆₇	#33200	1	1	yes	characteristic, direct product factor, Sylow
247	C₂×#125	C₂²×C₆₇	1	2	yes	—
248	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
249	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
250	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
251	#479	—	2	8	no	—
252	C₂×#107	C₂²×C₆₇	1	2	yes	—
253	C₂×#106	C₂²×C₆₇	1	2	yes	—
254	C₂×C₄⋊C₈	C₂²×C₆₇	1	2	yes	—
255	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
256	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
257	C₂×C₄⋊C₈	C₂²×C₆₇	1	2	yes	—
258	C₂×#103	C₂²×C₆₇	1	2	yes	—
259	C₂×#103	C₂²×C₆₇	1	2	yes	—
260	#389	—	2	1	no	—
261	#389	—	2	1	no	—
262	#389	—	2	1	no	—
263	#389	—	2	1	no	—
264	#384	C₂²×C₆₇	1	1	yes	characteristic
265	#384	C₂²×C₆₇	1	1	yes	characteristic
266	#382	C₂²×C₆₇	1	2	yes	—
267	C₄×C₄⋊C₄	—	2	1	no	—
268	C₄×C₄⋊C₄	—	2	1	no	—
269	C₄×C₄⋊C₄	—	2	1	no	—
270	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
271	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
272	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
273	C₄³	—	2	1	no	—
274	C₄³	C₂²×C₆₇	1	1	yes	characteristic
275	#340	C₂²×C₆₇	1	2	yes	—
276	#340	C₂²×C₆₇	1	2	yes	—
277	#340	C₂²×C₆₇	1	2	yes	—
278	#340	C₂²×C₆₇	1	2	yes	—
279	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
280	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
281	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
282	#125	—	2	4	no	—
283	#125	—	2	4	no	—
284	C₄×Q₈	—	2	2	no	—
285	C₄×Q₈	—	2	2	no	—
286	C₄×Q₈	—	2	2	no	—
287	C₄×Q₈	D₄×C₆₇	1	4	yes	—
288	C₄×Q₈	Q₈×C₆₇	1	4	yes	—
289	C₄×Q₈	Q₈×C₆₇	1	4	yes	—
290	C₂×C₄⋊C₄	—	2	1	no	—
291	C₂×C₄⋊C₄	—	2	1	no	—
292	C₂×C₄⋊C₄	—	2	1	no	—
293	C₂×C₄⋊C₄	—	2	2	no	—
294	C₂×C₄⋊C₄	—	2	2	no	—
295	C₂×C₄⋊C₄	—	2	1	no	—
296	C₂×C₄⋊C₄	—	2	1	no	—
297	C₂×C₄⋊C₄	—	2	1	no	—
298	C₂×C₄⋊C₄	—	2	1	no	—
299	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
300	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
301	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
302	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
303	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
304	C₂×C₄²	—	2	1	no	—
305	C₂×C₄²	—	2	1	no	—
306	C₂×C₄²	—	2	1	no	—
307	C₂×C₄²	—	2	1	no	—
308	C₂×C₄²	—	2	1	no	—
309	C₂×C₄²	—	2	1	no	—
310	C₂×C₄²	D₄×C₆₇	1	1	yes	characteristic
311	C₂×C₄²	D₄×C₆₇	1	1	yes	characteristic
312	C₂×C₄²	D₄×C₆₇	1	1	yes	characteristic
313	C₂×C₄²	D₄×C₆₇	1	1	yes	characteristic
314	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
315	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
316	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
317	#107	—	2	4	no	—
318	#106	—	2	4	no	—
319	C₄⋊C₈	—	2	4	no	—
320	C₄⋊C₈	—	2	2	no	—
321	C₄⋊C₈	—	2	2	no	—
322	C₄⋊C₈	—	2	4	no	—
323	#103	—	2	4	no	—
324	#103	—	2	4	no	—
325	#95	—	2	1	no	—
326	#95	—	2	1	no	—
327	#95	—	2	1	no	—
328	#95	—	2	2	no	—
329	#95	—	2	2	no	—
330	C₂×Q₈	—	2	1	no	—
331	C₂×Q₈	—	2	1	no	—
332	C₂×Q₈	—	2	1	no	—
333	C₂×Q₈	C₂×D₄×C₆₇	1	2	yes	—
334	C₂×Q₈	C₂×Q₈×C₆₇	1	2	yes	—
335	C₂×Q₈	C₂×Q₈×C₆₇	1	2	yes	—
336	C₂²×C₄	—	2	1	no	—
337	C₂²×C₄	—	2	1	no	—
338	C₂²×C₄	—	2	1	no	—
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
343	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
344	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
345	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
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	C₂×C₈	—	2	2	no	—
350	C₂×C₈	—	2	2	no	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	—	2	2	no	—
355	C₄⋊C₄	—	2	4	no	—
356	C₄⋊C₄	—	2	4	no	—
357	C₄⋊C₄	—	2	4	no	—
358	C₄⋊C₄	—	2	1	no	—
359	C₄⋊C₄	—	2	1	no	—
360	C₄⋊C₄	—	2	1	no	—
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	—	4	2	no	—
366	C₄⋊C₄	—	4	2	no	—
367	C₄⋊C₄	—	4	4	no	—
368	C₄⋊C₄	—	4	4	no	—
369	C₄⋊C₄	—	4	2	no	—
370	C₄⋊C₄	—	4	2	no	—
371	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
372	C₄⋊C₄	C₂×Q₈×C₆₇	1	2	yes	—
373	C₄⋊C₄	C₂×Q₈×C₆₇	1	2	yes	—
374	C₄²	—	2	4	no	—
375	C₄²	—	2	4	no	—
376	C₄²	—	2	4	no	—
377	C₄²	—	2	2	no	—
378	C₄²	—	2	2	no	—
379	C₄²	—	4	1	no	—
380	C₄²	—	4	1	no	—
381	C₄²	—	4	2	no	—
382	C₄²	—	4	2	no	—
383	C₄²	—	4	2	no	—
384	C₄²	C₂×D₄×C₆₇	1	2	yes	—
385	C₄²	C₂×Q₈×C₆₇	1	2	yes	—
386	C₄²	C₂×Q₈×C₆₇	1	2	yes	—
387	C₄²	#41×C₆₇	1	2	yes	—
388	C₄²	#41×C₆₇	1	2	yes	—
389	C₄²	#41×C₆₇	1	2	yes	—
390	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
391	Q₈	—	2	2	no	—
392	Q₈	—	2	2	no	—
393	Q₈	—	2	2	no	—
394	Q₈	C₄⋊Q₈×C₆₇	1	4	yes	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	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	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	4	1	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	4	1	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	#121×C₆₇	1	2	yes	—
424	C₂×C₄	#121×C₆₇	1	2	yes	—
425	C₂×C₄	C₂²⋊Q₈×C₆₇	1	2	yes	—
426	C₂×C₄	C₂²⋊Q₈×C₆₇	1	2	yes	—
427	C₂×C₄	C₂²⋊Q₈×C₆₇	1	2	yes	—
428	C₂×C₄	C₂²⋊Q₈×C₆₇	1	2	yes	—
429	C₂×C₄	#135×C₆₇	1	2	yes	—
430	C₂×C₄	#137×C₆₇	1	2	yes	—
431	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
432	C₂×C₄	C₂²×Q₈×C₆₇	1	1	yes	characteristic
433	C₂×C₄	C₂²×Q₈×C₆₇	1	1	yes	characteristic
434	C₂×C₄	C₂×#41×C₆₇	1	1	yes	characteristic
435	C₂×C₄	C₂×#41×C₆₇	1	1	yes	characteristic
436	C₂×C₄	C₂×#41×C₆₇	1	1	yes	characteristic
437	C₈	—	4	2	no	—
438	C₈	—	4	2	no	—
439	C₂²	C₂×#121×C₆₇	1	1	yes	characteristic
440	C₂²	C₂×C₂²⋊Q₈×C₆₇	1	1	yes	characteristic
441	C₂²	C₂×C₂²⋊Q₈×C₆₇	1	1	yes	characteristic
442	C₂²	C₂×#135×C₆₇	1	1	yes	characteristic
443	C₂²	C₂×#137×C₆₇	1	1	yes	characteristic
444	C₂²	#575×C₆₇	1	1	yes	characteristic
445	C₂²	#575×C₆₇	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	4	no	—
452	C₄	—	4	2	no	—
453	C₄	—	4	2	no	—
454	C₄	—	4	2	no	—
455	C₄	—	8	2	no	—
456	C₄	—	8	2	no	—
457	C₄	#479×C₆₇	1	4	yes	complemented
458	C₄	C₂×C₄⋊Q₈×C₆₇	1	1	yes	characteristic
459	C₄	#532×C₆₇	1	1	yes	characteristic
460	C₄	#533×C₆₇	1	1	yes	characteristic
461	C₄	#533×C₆₇	1	1	yes	characteristic
462	C₂	C₆₇×#2857	1	1	yes	characteristic
463	C₂	C₆₇×#3035	1	1	yes	characteristic
464	C₂	C₆₇×#3037	1	1	yes	characteristic
465	C₂	C₂×#479×C₆₇	1	1	yes	characteristic
466	C₂	C₆₇×#3076	1	1	yes	characteristic
467	C₂	C₆₇×#3078	1	1	yes	characteristic
468	C₂	C₆₇×#3080	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₆₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₇
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ C₄³×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
222. C₄×C₆₇	#479	semidirect
227. #33200	C₆₇	direct (N × H)
246. C₆₇	#33200	direct (N × H)
457. C₄	#479×C₆₇	semidirect

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
C₆₇×#2859	2
C₄²×Q₈×C₆₇	2
C₆₇×#1989	2
C₆₇×#1949	2
C₆₇×#1948	2
C₆₇×#1947	2
C₆₇×#1842	2
C₆₇×#1805	2
C₆₇×#1803	2
#33200	67

Subgroups — C67×#33200 #30712451

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#33200 #30712451