Subgroups — C₆₇×#11077 #30690328

Order 17152.

1050 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄⋊C₈×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₂²×#103×C₆₇	C₂	1	2	yes	maximal
3	C₂×#391×C₆₇	C₂	1	1	yes	maximal, characteristic
4	C₂×#340×C₆₇	C₂	1	2	yes	maximal
5	C₆₇×C₄⋊#95	C₂	1	1	yes	maximal, characteristic
6	C₂³×Q₈×C₆₇	C₂²	1	1	yes	characteristic
7	C₂³×C₈×C₆₇	C₂²	1	2	yes	—
8	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
9	C₂²×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
10	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊C₈×C₆₇	—	2	4	no	—
12	C₂×C₄⋊C₈×C₆₇	—	2	2	no	—
13	C₂×#103×C₆₇	—	2	4	no	—
14	C₂×#103×C₆₇	—	2	4	no	—
15	C₂×#103×C₆₇	—	2	4	no	—
16	#391×C₆₇	—	2	2	no	—
17	#391×C₆₇	C₄	1	4	yes	complemented
18	C₂×#95×C₆₇	—	2	1	no	—
19	C₂×#95×C₆₇	—	2	1	no	—
20	C₂×#95×C₆₇	—	2	1	no	—
21	C₂×#95×C₆₇	—	2	1	no	—
22	#340×C₆₇	—	2	4	no	—
23	C₂²×Q₈×C₆₇	—	2	1	no	—
24	C₂²×Q₈×C₆₇	—	2	1	no	—
25	C₂²×Q₈×C₆₇	—	2	1	no	—
26	C₂²×Q₈×C₆₇	—	2	2	no	—
27	C₂²×Q₈×C₆₇	—	2	2	no	—
28	C₂²×Q₈×C₆₇	—	2	2	no	—
29	C₂²×Q₈×C₆₇	—	2	2	no	—
30	C₂²×Q₈×C₆₇	C₂×C₄	1	2	yes	—
31	C₂²×Q₈×C₆₇	D₄	1	2	yes	—
32	C₂²×Q₈×C₆₇	Q₈	1	2	yes	—
33	C₂³×C₄×C₆₇	—	2	1	no	—
34	C₂³×C₄×C₆₇	—	2	1	no	—
35	C₂³×C₄×C₆₇	—	2	2	no	—
36	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
37	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
38	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
39	C₂²×C₈×C₆₇	—	2	2	no	—
40	C₂²×C₈×C₆₇	—	2	2	no	—
41	C₂²×C₈×C₆₇	—	2	2	no	—
42	C₂²×C₈×C₆₇	—	2	2	no	—
43	C₂²×C₈×C₆₇	—	2	2	no	—
44	C₂²×C₈×C₆₇	—	2	2	no	—
45	C₂²×C₈×C₆₇	D₄	1	4	yes	—
46	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
47	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
48	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
49	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
50	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
51	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
52	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
53	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
54	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
55	C₂×C₄⋊C₄×C₆₇	D₄	1	4	yes	—
56	C₂×C₄²×C₆₇	—	2	2	no	—
57	C₂×C₄²×C₆₇	—	2	2	no	—
58	C₂×C₄²×C₆₇	C₂×C₄	1	2	yes	—
59	C₂×C₄²×C₆₇	D₄	1	2	yes	—
60	C₄⋊C₈×C₆₇	—	2	8	no	—
61	#103×C₆₇	—	2	16	no	—
62	#95×C₆₇	—	2	4	no	—
63	#95×C₆₇	—	2	4	no	—
64	#95×C₆₇	—	4	2	no	—
65	#95×C₆₇	—	4	2	no	—
66	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
67	C₂×Q₈×C₆₇	—	2	2	no	—
68	C₂×Q₈×C₆₇	—	2	2	no	—
69	C₂×Q₈×C₆₇	—	2	2	no	—
70	C₂×Q₈×C₆₇	—	2	4	no	—
71	C₂×Q₈×C₆₇	—	2	4	no	—
72	C₂×Q₈×C₆₇	—	2	4	no	—
73	C₂×Q₈×C₆₇	—	2	4	no	—
74	C₂×Q₈×C₆₇	—	2	4	no	—
75	C₂×Q₈×C₆₇	—	2	4	no	—
76	C₂×Q₈×C₆₇	—	4	1	no	—
77	C₂×Q₈×C₆₇	—	4	2	no	—
78	C₂×Q₈×C₆₇	—	4	1	no	—
79	C₂×Q₈×C₆₇	—	4	2	no	—
80	C₂×Q₈×C₆₇	—	4	1	no	—
81	C₂×Q₈×C₆₇	—	4	2	no	—
82	C₂×Q₈×C₆₇	—	4	2	no	—
83	C₂×Q₈×C₆₇	—	4	1	no	—
84	C₂×Q₈×C₆₇	C₄⋊C₄	1	4	yes	—
85	C₂²×C₄×C₆₇	—	2	2	no	—
86	C₂²×C₄×C₆₇	—	2	2	no	—
87	C₂²×C₄×C₆₇	—	2	2	no	—
88	C₂²×C₄×C₆₇	—	2	2	no	—
89	C₂²×C₄×C₆₇	—	2	2	no	—
90	C₂²×C₄×C₆₇	—	2	2	no	—
91	C₂²×C₄×C₆₇	—	2	1	no	—
92	C₂²×C₄×C₆₇	—	2	1	no	—
93	C₂²×C₄×C₆₇	—	2	2	no	—
94	C₂²×C₄×C₆₇	—	2	2	no	—
95	C₂²×C₄×C₆₇	—	2	4	no	—
96	C₂²×C₄×C₆₇	—	4	2	no	—
97	C₂²×C₄×C₆₇	—	4	2	no	—
98	C₂²×C₄×C₆₇	—	4	2	no	—
99	C₂²×C₄×C₆₇	—	4	2	no	—
100	C₂²×C₄×C₆₇	—	4	2	no	—
101	C₂²×C₄×C₆₇	—	4	2	no	—
102	C₂²×C₄×C₆₇	—	4	2	no	—
103	C₂²×C₄×C₆₇	—	4	2	no	—
104	C₂²×C₄×C₆₇	—	4	1	no	—
105	C₂²×C₄×C₆₇	—	4	2	no	—
106	C₂²×C₄×C₆₇	—	4	1	no	—
107	C₂²×C₄×C₆₇	—	4	2	no	—
108	C₂²×C₄×C₆₇	C₂²⋊C₄	1	2	yes	—
109	C₂²×C₄×C₆₇	C₂²⋊C₄	1	2	yes	—
110	C₂²×C₄×C₆₇	SD₁₆	1	2	yes	—
111	C₂²×C₄×C₆₇	Q₁₆	1	2	yes	—
112	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
113	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
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×Q₈	1	1	yes	characteristic
118	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
119	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
120	C₂²×C₄×C₆₇	#41	1	2	yes	—
121	C₂²×C₄×C₆₇	#41	1	2	yes	—
122	C₂×C₈×C₆₇	—	2	4	no	—
123	C₂×C₈×C₆₇	—	2	4	no	—
124	C₂×C₈×C₆₇	—	2	4	no	—
125	C₂×C₈×C₆₇	—	4	2	no	—
126	C₂×C₈×C₆₇	—	4	2	no	—
127	C₂×C₈×C₆₇	—	4	2	no	—
128	C₂×C₈×C₆₇	—	4	2	no	—
129	C₄⋊C₄×C₆₇	—	2	4	no	—
130	C₄⋊C₄×C₆₇	—	2	4	no	—
131	C₄⋊C₄×C₆₇	—	2	4	no	—
132	C₄⋊C₄×C₆₇	—	4	2	no	—
133	C₄⋊C₄×C₆₇	—	4	1	no	—
134	C₄⋊C₄×C₆₇	—	4	2	no	—
135	C₄⋊C₄×C₆₇	—	4	1	no	—
136	C₄²×C₆₇	—	2	4	no	—
137	C₄²×C₆₇	—	2	2	no	—
138	C₄²×C₆₇	—	2	2	no	—
139	C₂³×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
140	C₂³×C₆₇	#121	1	1	yes	characteristic
141	C₂³×C₆₇	#121	1	2	yes	—
142	C₂³×C₆₇	#121	1	2	yes	—
143	C₂³×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
144	C₂³×C₆₇	C₂×SD₁₆	1	1	yes	characteristic
145	C₂³×C₆₇	C₂×Q₁₆	1	1	yes	characteristic
146	C₂³×C₆₇	#135	1	2	yes	—
147	C₂³×C₆₇	AGL(1,ℤ/8)	1	1	yes	characteristic
148	C₂³×C₆₇	#137	1	1	yes	characteristic
149	C₂³×C₆₇	#137	1	2	yes	—
150	Q₈×C₆₇	—	2	8	no	—
151	Q₈×C₆₇	—	4	4	no	—
152	Q₈×C₆₇	—	4	2	no	—
153	Q₈×C₆₇	—	4	2	no	—
154	Q₈×C₆₇	—	4	2	no	—
155	Q₈×C₆₇	—	4	2	no	—
156	C₂×C₄×C₆₇	—	2	2	no	—
157	C₂×C₄×C₆₇	—	2	2	no	—
158	C₂×C₄×C₆₇	—	2	4	no	—
159	C₂×C₄×C₆₇	—	2	4	no	—
160	C₂×C₄×C₆₇	—	2	4	no	—
161	C₂×C₄×C₆₇	—	2	2	no	—
162	C₂×C₄×C₆₇	—	2	2	no	—
163	C₂×C₄×C₆₇	—	2	2	no	—
164	C₂×C₄×C₆₇	—	4	2	no	—
165	C₂×C₄×C₆₇	—	4	2	no	—
166	C₂×C₄×C₆₇	—	4	4	no	—
167	C₂×C₄×C₆₇	—	4	4	no	—
168	C₂×C₄×C₆₇	—	4	2	no	—
169	C₂×C₄×C₆₇	—	4	2	no	—
170	C₂×C₄×C₆₇	—	4	2	no	—
171	C₂×C₄×C₆₇	—	4	4	no	—
172	C₂×C₄×C₆₇	—	4	2	no	—
173	C₂×C₄×C₆₇	—	4	2	no	—
174	C₂×C₄×C₆₇	—	4	4	no	—
175	C₂×C₄×C₆₇	—	4	4	no	—
176	C₂×C₄×C₆₇	—	8	2	no	—
177	C₂×C₄×C₆₇	—	8	2	no	—
178	C₂×C₄×C₆₇	—	8	2	no	—
179	C₂×C₄×C₆₇	—	8	2	no	—
180	C₂×C₄×C₆₇	—	8	2	no	—
181	C₂×C₄×C₆₇	—	8	2	no	—
182	C₂×C₄×C₆₇	#103	1	4	yes	complemented
183	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
184	C₂×C₄×C₆₇	#117	1	1	yes	characteristic
185	C₂×C₄×C₆₇	C₄×D₄	1	2	yes	—
186	C₂×C₄×C₆₇	C₄×D₄	1	2	yes	—
187	C₂×C₄×C₆₇	#120	1	2	yes	—
188	C₂×C₄×C₆₇	#120	1	1	yes	characteristic
189	C₂×C₄×C₆₇	#121	1	2	yes	—
190	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
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	1	yes	characteristic
194	C₂×C₄×C₆₇	#123	1	2	yes	—
195	C₂×C₄×C₆₇	#123	1	2	yes	—
196	C₂×C₄×C₆₇	#123	1	1	yes	characteristic
197	C₂×C₄×C₆₇	#124	1	2	yes	—
198	C₂×C₄×C₆₇	#124	1	1	yes	characteristic
199	C₂×C₄×C₆₇	#126	1	2	yes	—
200	C₂×C₄×C₆₇	#127	1	1	yes	characteristic
201	C₈×C₆₇	—	4	4	no	—
202	C₂²×C₆₇	#380	1	1	yes	characteristic
203	C₂²×C₆₇	#386	1	1	yes	characteristic
204	C₂²×C₆₇	#390	1	1	yes	characteristic
205	C₂²×C₆₇	#394	1	2	yes	—
206	C₂²×C₆₇	#396	1	2	yes	—
207	C₂²×C₆₇	C₂×#103	1	1	yes	characteristic
208	C₂²×C₆₇	#416	1	1	yes	characteristic
209	C₂²×C₆₇	#417	1	1	yes	characteristic
210	C₂²×C₆₇	#419	1	1	yes	characteristic
211	C₂²×C₆₇	#460	1	1	yes	characteristic
212	C₂²×C₆₇	#461	1	2	yes	—
213	C₂²×C₆₇	#462	1	1	yes	characteristic
214	C₂²×C₆₇	#462	1	2	yes	—
215	C₂²×C₆₇	#463	1	2	yes	—
216	C₂²×C₆₇	#464	1	2	yes	—
217	C₂²×C₆₇	#464	1	2	yes	—
218	C₂²×C₆₇	#465	1	2	yes	—
219	C₂²×C₆₇	#467	1	2	yes	—
220	C₂²×C₆₇	#468	1	2	yes	—
221	C₂²×C₆₇	#470	1	2	yes	—
222	C₂²×C₆₇	#475	1	1	yes	characteristic
223	C₂²×C₆₇	#477	1	1	yes	characteristic
224	C₂²×C₆₇	#479	1	2	yes	—
225	C₄×C₆₇	—	2	4	no	—
226	C₄×C₆₇	—	4	2	no	—
227	C₄×C₆₇	—	4	4	no	—
228	C₄×C₆₇	—	8	4	no	—
229	C₄×C₆₇	—	8	2	no	—
230	C₄×C₆₇	#385	1	2	yes	—
231	C₄×C₆₇	#388	1	2	yes	—
232	C₄×C₆₇	#392	1	1	yes	characteristic
233	C₄×C₆₇	#393	1	1	yes	characteristic
234	C₄×C₆₇	#397	1	1	yes	characteristic
235	C₄×C₆₇	#399	1	1	yes	characteristic
236	#11077	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
237	C₂×C₆₇	#1439	1	1	yes	characteristic
238	C₂×C₆₇	#1803	1	1	yes	characteristic
239	C₂×C₆₇	#1805	1	1	yes	characteristic
240	C₂×C₆₇	#1892	1	1	yes	characteristic
241	C₂×C₆₇	#1894	1	1	yes	characteristic
242	C₂×C₆₇	#1981	1	1	yes	characteristic
243	C₂×C₆₇	#1983	1	1	yes	characteristic
244	C₂×C₆₇	#2055	1	2	yes	—
245	C₂×C₆₇	#2056	1	2	yes	—
246	C₂×C₆₇	#2066	1	2	yes	—
247	C₂×C₆₇	#2068	1	2	yes	—
248	C₂²×C₄⋊C₈	C₂×C₆₇	1	1	yes	characteristic
249	C₂²×#103	C₂×C₆₇	1	2	yes	—
250	C₂×#391	C₂×C₆₇	1	1	yes	characteristic
251	C₂×#340	C₂×C₆₇	1	2	yes	—
252	C₄⋊#95	C₂×C₆₇	1	1	yes	characteristic
253	C₆₇	#11077	1	1	yes	characteristic, direct product factor, Sylow
254	C₂³×Q₈	C₂²×C₆₇	1	1	yes	characteristic
255	C₂³×C₈	C₂²×C₆₇	1	2	yes	—
256	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
257	C₂²×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
258	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
259	C₂×C₄⋊C₈	—	2	4	no	—
260	C₂×C₄⋊C₈	—	2	2	no	—
261	C₂×#103	—	2	4	no	—
262	C₂×#103	—	2	4	no	—
263	C₂×#103	—	2	4	no	—
264	#391	—	2	2	no	—
265	#391	C₄×C₆₇	1	4	yes	complemented
266	C₂×#95	—	2	1	no	—
267	C₂×#95	—	2	1	no	—
268	C₂×#95	—	2	1	no	—
269	C₂×#95	—	2	1	no	—
270	#340	—	2	4	no	—
271	C₂²×Q₈	—	2	1	no	—
272	C₂²×Q₈	—	2	1	no	—
273	C₂²×Q₈	—	2	1	no	—
274	C₂²×Q₈	—	2	2	no	—
275	C₂²×Q₈	—	2	2	no	—
276	C₂²×Q₈	—	2	2	no	—
277	C₂²×Q₈	—	2	2	no	—
278	C₂²×Q₈	C₂×C₄×C₆₇	1	2	yes	—
279	C₂²×Q₈	D₄×C₆₇	1	2	yes	—
280	C₂²×Q₈	Q₈×C₆₇	1	2	yes	—
281	C₂³×C₄	—	2	1	no	—
282	C₂³×C₄	—	2	1	no	—
283	C₂³×C₄	—	2	2	no	—
284	C₂³×C₄	D₄×C₆₇	1	1	yes	characteristic
285	C₂³×C₄	D₄×C₆₇	1	1	yes	characteristic
286	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
287	C₂²×C₈	—	2	2	no	—
288	C₂²×C₈	—	2	2	no	—
289	C₂²×C₈	—	2	2	no	—
290	C₂²×C₈	—	2	2	no	—
291	C₂²×C₈	—	2	2	no	—
292	C₂²×C₈	—	2	2	no	—
293	C₂²×C₈	D₄×C₆₇	1	4	yes	—
294	C₂×C₄⋊C₄	—	2	2	no	—
295	C₂×C₄⋊C₄	—	2	2	no	—
296	C₂×C₄⋊C₄	—	2	2	no	—
297	C₂×C₄⋊C₄	—	2	2	no	—
298	C₂×C₄⋊C₄	—	2	2	no	—
299	C₂×C₄⋊C₄	—	2	2	no	—
300	C₂×C₄⋊C₄	—	2	1	no	—
301	C₂×C₄⋊C₄	—	2	2	no	—
302	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	2	yes	—
303	C₂×C₄⋊C₄	D₄×C₆₇	1	4	yes	—
304	C₂×C₄²	—	2	2	no	—
305	C₂×C₄²	—	2	2	no	—
306	C₂×C₄²	C₂×C₄×C₆₇	1	2	yes	—
307	C₂×C₄²	D₄×C₆₇	1	2	yes	—
308	C₄⋊C₈	—	2	8	no	—
309	#103	—	2	16	no	—
310	#95	—	2	4	no	—
311	#95	—	2	4	no	—
312	#95	—	4	2	no	—
313	#95	—	4	2	no	—
314	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
315	C₂×Q₈	—	2	2	no	—
316	C₂×Q₈	—	2	2	no	—
317	C₂×Q₈	—	2	2	no	—
318	C₂×Q₈	—	2	4	no	—
319	C₂×Q₈	—	2	4	no	—
320	C₂×Q₈	—	2	4	no	—
321	C₂×Q₈	—	2	4	no	—
322	C₂×Q₈	—	2	4	no	—
323	C₂×Q₈	—	2	4	no	—
324	C₂×Q₈	—	4	1	no	—
325	C₂×Q₈	—	4	2	no	—
326	C₂×Q₈	—	4	1	no	—
327	C₂×Q₈	—	4	2	no	—
328	C₂×Q₈	—	4	1	no	—
329	C₂×Q₈	—	4	2	no	—
330	C₂×Q₈	—	4	2	no	—
331	C₂×Q₈	—	4	1	no	—
332	C₂×Q₈	C₄⋊C₄×C₆₇	1	4	yes	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	2	1	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	2	4	no	—
344	C₂²×C₄	—	4	2	no	—
345	C₂²×C₄	—	4	2	no	—
346	C₂²×C₄	—	4	2	no	—
347	C₂²×C₄	—	4	2	no	—
348	C₂²×C₄	—	4	2	no	—
349	C₂²×C₄	—	4	2	no	—
350	C₂²×C₄	—	4	2	no	—
351	C₂²×C₄	—	4	2	no	—
352	C₂²×C₄	—	4	2	no	—
353	C₂²×C₄	—	4	1	no	—
354	C₂²×C₄	—	4	2	no	—
355	C₂²×C₄	—	4	1	no	—
356	C₂²×C₄	C₂²⋊C₄×C₆₇	1	2	yes	—
357	C₂²×C₄	C₂²⋊C₄×C₆₇	1	2	yes	—
358	C₂²×C₄	SD₁₆×C₆₇	1	2	yes	—
359	C₂²×C₄	Q₁₆×C₆₇	1	2	yes	—
360	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
361	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
362	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
363	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
364	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
365	C₂²×C₄	C₂×Q₈×C₆₇	1	1	yes	characteristic
366	C₂²×C₄	#41×C₆₇	1	1	yes	characteristic
367	C₂²×C₄	#41×C₆₇	1	1	yes	characteristic
368	C₂²×C₄	#41×C₆₇	1	2	yes	—
369	C₂²×C₄	#41×C₆₇	1	2	yes	—
370	C₂×C₈	—	2	4	no	—
371	C₂×C₈	—	2	4	no	—
372	C₂×C₈	—	2	4	no	—
373	C₂×C₈	—	4	2	no	—
374	C₂×C₈	—	4	2	no	—
375	C₂×C₈	—	4	2	no	—
376	C₂×C₈	—	4	2	no	—
377	C₄⋊C₄	—	2	4	no	—
378	C₄⋊C₄	—	2	4	no	—
379	C₄⋊C₄	—	2	4	no	—
380	C₄⋊C₄	—	4	2	no	—
381	C₄⋊C₄	—	4	1	no	—
382	C₄⋊C₄	—	4	2	no	—
383	C₄⋊C₄	—	4	1	no	—
384	C₄²	—	2	4	no	—
385	C₄²	—	2	2	no	—
386	C₄²	—	2	2	no	—
387	C₂³	C₂×C₂²⋊C₄×C₆₇	1	1	yes	characteristic
388	C₂³	#121×C₆₇	1	1	yes	characteristic
389	C₂³	#121×C₆₇	1	2	yes	—
390	C₂³	#121×C₆₇	1	2	yes	—
391	C₂³	C₂²⋊Q₈×C₆₇	1	1	yes	characteristic
392	C₂³	C₂×SD₁₆×C₆₇	1	1	yes	characteristic
393	C₂³	C₂×Q₁₆×C₆₇	1	1	yes	characteristic
394	C₂³	#135×C₆₇	1	2	yes	—
395	C₂³	AGL(1,ℤ/8)×C₆₇	1	1	yes	characteristic
396	C₂³	#137×C₆₇	1	2	yes	—
397	C₂³	#137×C₆₇	1	1	yes	characteristic
398	Q₈	—	2	8	no	—
399	Q₈	—	4	4	no	—
400	Q₈	—	4	2	no	—
401	Q₈	—	4	2	no	—
402	Q₈	—	4	2	no	—
403	Q₈	—	4	2	no	—
404	C₂×C₄	—	2	4	no	—
405	C₂×C₄	—	2	4	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	4	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	4	no	—
417	C₂×C₄	—	4	4	no	—
418	C₂×C₄	—	4	4	no	—
419	C₂×C₄	—	4	4	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	4	4	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	8	2	no	—
425	C₂×C₄	—	8	2	no	—
426	C₂×C₄	—	8	2	no	—
427	C₂×C₄	—	8	2	no	—
428	C₂×C₄	—	8	2	no	—
429	C₂×C₄	—	8	2	no	—
430	C₂×C₄	#103×C₆₇	1	4	yes	complemented
431	C₂×C₄	C₂×C₄⋊C₄×C₆₇	1	1	yes	characteristic
432	C₂×C₄	#117×C₆₇	1	1	yes	characteristic
433	C₂×C₄	C₄×D₄×C₆₇	1	2	yes	—
434	C₂×C₄	C₄×D₄×C₆₇	1	2	yes	—
435	C₂×C₄	#120×C₆₇	1	2	yes	—
436	C₂×C₄	#120×C₆₇	1	1	yes	characteristic
437	C₂×C₄	#121×C₆₇	1	2	yes	—
438	C₂×C₄	#121×C₆₇	1	1	yes	characteristic
439	C₂×C₄	C₂²⋊Q₈×C₆₇	1	2	yes	—
440	C₂×C₄	C₂²⋊Q₈×C₆₇	1	2	yes	—
441	C₂×C₄	C₂²⋊Q₈×C₆₇	1	1	yes	characteristic
442	C₂×C₄	#123×C₆₇	1	2	yes	—
443	C₂×C₄	#123×C₆₇	1	2	yes	—
444	C₂×C₄	#123×C₆₇	1	1	yes	characteristic
445	C₂×C₄	#124×C₆₇	1	2	yes	—
446	C₂×C₄	#124×C₆₇	1	1	yes	characteristic
447	C₂×C₄	#126×C₆₇	1	2	yes	—
448	C₂×C₄	#127×C₆₇	1	1	yes	characteristic
449	C₈	—	4	4	no	—
450	C₂²	#380×C₆₇	1	1	yes	characteristic
451	C₂²	#386×C₆₇	1	1	yes	characteristic
452	C₂²	#390×C₆₇	1	1	yes	characteristic
453	C₂²	#394×C₆₇	1	2	yes	—
454	C₂²	#396×C₆₇	1	2	yes	—
455	C₂²	C₂×#103×C₆₇	1	1	yes	characteristic
456	C₂²	#416×C₆₇	1	1	yes	characteristic
457	C₂²	#417×C₆₇	1	1	yes	characteristic
458	C₂²	#419×C₆₇	1	1	yes	characteristic
459	C₂²	#460×C₆₇	1	1	yes	characteristic
460	C₂²	#461×C₆₇	1	2	yes	—
461	C₂²	#462×C₆₇	1	1	yes	characteristic
462	C₂²	#462×C₆₇	1	2	yes	—
463	C₂²	#463×C₆₇	1	2	yes	—
464	C₂²	#464×C₆₇	1	2	yes	—
465	C₂²	#464×C₆₇	1	2	yes	—
466	C₂²	#465×C₆₇	1	2	yes	—
467	C₂²	#467×C₆₇	1	2	yes	—
468	C₂²	#468×C₆₇	1	2	yes	—
469	C₂²	#470×C₆₇	1	2	yes	—
470	C₂²	#475×C₆₇	1	1	yes	characteristic
471	C₂²	#477×C₆₇	1	1	yes	characteristic
472	C₂²	#479×C₆₇	1	2	yes	—
473	C₄	—	2	4	no	—
474	C₄	—	4	2	no	—
475	C₄	—	4	4	no	—
476	C₄	—	8	4	no	—
477	C₄	—	8	2	no	—
478	C₄	#385×C₆₇	1	2	yes	—
479	C₄	#388×C₆₇	1	2	yes	—
480	C₄	#392×C₆₇	1	1	yes	characteristic
481	C₄	#393×C₆₇	1	1	yes	characteristic
482	C₄	#397×C₆₇	1	1	yes	characteristic
483	C₄	#399×C₆₇	1	1	yes	characteristic
484	C₂	C₆₇×#1439	1	1	yes	characteristic
485	C₂	C₆₇×#1803	1	1	yes	characteristic
486	C₂	C₆₇×#1805	1	1	yes	characteristic
487	C₂	C₆₇×#1892	1	1	yes	characteristic
488	C₂	C₆₇×#1894	1	1	yes	characteristic
489	C₂	C₆₇×#1981	1	1	yes	characteristic
490	C₂	C₆₇×#1983	1	1	yes	characteristic
491	C₂	C₆₇×#2055	1	2	yes	—
492	C₂	C₆₇×#2056	1	2	yes	—
493	C₂	C₆₇×#2066	1	2	yes	—
494	C₂	C₆₇×#2068	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₆₇	C₂×D₄
commutator	C₂²×C₄	C₂²×C₄×C₆₇
Frattini, cosocle	C₂³×C₄	C₂³×C₆₇
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₆₇ ◁ C₂²×C₄²×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
17. #391×C₆₇	C₄	semidirect
182. C₂×C₄×C₆₇	#103	semidirect
236. #11077	C₆₇	direct (N × H)
253. C₆₇	#11077	direct (N × H)
265. #391	C₄×C₆₇	semidirect
430. C₂×C₄	#103×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄⋊C₈×C₆₇	2
C₂²×#103×C₆₇	2
C₂×#391×C₆₇	2
C₂×#340×C₆₇	2
C₆₇×C₄⋊#95	2
#11077	67

Subgroups — C67×#11077 #30690328

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#11077 #30690328