Subgroups — C₂×C₆₇×#1939 #30700392

Order 17152.

1246 conjugacy classes of subgroups.

The subgroup lattice has 348 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	2	yes	maximal
2	C₂²×C₄⋊C₈×C₆₇	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₄×C₈×C₆₇	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×C₄⋊C₄×C₆₇	C₂	1	1	yes	maximal, characteristic
5	C₆₇×#1939	C₂	1	8	yes	maximal, direct product factor
6	C₂×#336×C₆₇	C₂	1	2	yes	maximal
7	C₂³×C₈×C₆₇	C₂²	1	2	yes	—
8	C₂³×C₈×C₆₇	C₂²	1	1	yes	characteristic
9	C₂³×C₈×C₆₇	C₂²	1	1	yes	characteristic
10	C₂²×C₄⋊C₄×C₆₇	C₄	1	1	yes	characteristic
11	C₂²×C₄⋊C₄×C₆₇	C₄	1	1	yes	characteristic
12	C₂²×C₄²×C₆₇	C₂²	1	2	yes	—
13	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊C₈×C₆₇	—	2	8	no	—
15	C₂×C₄⋊C₈×C₆₇	—	2	4	no	—
16	C₂×C₄⋊C₈×C₆₇	C₂²	1	8	yes	—
17	C₂×C₄⋊C₈×C₆₇	C₂²	1	4	yes	—
18	C₂×C₄×C₈×C₆₇	—	2	4	no	—
19	C₂×C₄×C₈×C₆₇	C₂²	1	4	yes	—
20	C₄×C₄⋊C₄×C₆₇	C₄	1	4	yes	—
21	C₄×C₄⋊C₄×C₆₇	C₂²	1	4	yes	—
22	C₂×#95×C₆₇	C₄	1	2	yes	—
23	#336×C₆₇	C₂²	1	8	yes	—
24	C₂³×C₄×C₆₇	C₂×C₄	1	2	yes	—
25	C₂³×C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
26	C₂³×C₄×C₆₇	C₂×C₄	1	2	yes	—
27	C₂³×C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
28	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
29	C₂²×C₈×C₆₇	—	2	2	no	—
30	C₂²×C₈×C₆₇	—	2	2	no	—
31	C₂²×C₈×C₆₇	—	2	2	no	—
32	C₂²×C₈×C₆₇	—	2	2	no	—
33	C₂²×C₈×C₆₇	—	2	4	no	—
34	C₂²×C₈×C₆₇	—	2	4	no	—
35	C₂²×C₈×C₆₇	—	2	4	no	—
36	C₂²×C₈×C₆₇	D₄	1	4	yes	—
37	C₂²×C₈×C₆₇	Q₈	1	4	yes	—
38	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
39	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
40	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
41	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
42	C₂×C₄⋊C₄×C₆₇	C₈	1	8	yes	complemented
43	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	4	yes	—
44	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	4	yes	—
45	C₂×C₄²×C₆₇	—	2	4	no	—
46	C₂×C₄²×C₆₇	—	2	4	no	—
47	C₂×C₄²×C₆₇	C₂×C₄	1	4	yes	—
48	C₂×C₄²×C₆₇	C₂×C₄	1	2	yes	—
49	C₂×C₄²×C₆₇	D₄	1	4	yes	—
50	C₂×C₄²×C₆₇	Q₈	1	4	yes	—
51	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
52	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
53	C₄⋊C₈×C₆₇	—	2	16	no	—
54	C₄⋊C₈×C₆₇	—	2	8	no	—
55	C₄×C₈×C₆₇	—	2	8	no	—
56	#95×C₆₇	C₂×C₄	1	8	yes	—
57	C₂⁴×C₆₇	C₂²×C₄	1	1	yes	characteristic
58	C₂²×C₄×C₆₇	—	2	4	no	—
59	C₂²×C₄×C₆₇	—	2	2	no	—
60	C₂²×C₄×C₆₇	—	2	2	no	—
61	C₂²×C₄×C₆₇	—	2	4	no	—
62	C₂²×C₄×C₆₇	—	2	4	no	—
63	C₂²×C₄×C₆₇	—	2	4	no	—
64	C₂²×C₄×C₆₇	—	2	4	no	—
65	C₂²×C₄×C₆₇	C₄⋊C₄	1	4	yes	—
66	C₂²×C₄×C₆₇	C₄⋊C₄	1	4	yes	—
67	C₂²×C₄×C₆₇	C₂×C₈	1	8	yes	—
68	C₂²×C₄×C₆₇	C₂×C₈	1	4	yes	—
69	C₂²×C₄×C₆₇	M₁₆	1	4	yes	—
70	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
71	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
72	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
73	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
74	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
75	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
76	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
77	C₂²×C₄×C₆₇	C₂×Q₈	1	2	yes	—
78	C₂²×C₄×C₆₇	C₂×Q₈	1	2	yes	—
79	C₂²×C₄×C₆₇	#41	1	2	yes	—
80	C₂²×C₄×C₆₇	#41	1	2	yes	—
81	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
82	C₂×C₈×C₆₇	—	2	8	no	—
83	C₂×C₈×C₆₇	—	2	8	no	—
84	C₂×C₈×C₆₇	—	2	2	no	—
85	C₂×C₈×C₆₇	—	2	2	no	—
86	C₂×C₈×C₆₇	—	2	2	no	—
87	C₂×C₈×C₆₇	—	2	2	no	—
88	C₂×C₈×C₆₇	—	2	4	no	—
89	C₂×C₈×C₆₇	—	2	4	no	—
90	C₂×C₈×C₆₇	—	2	4	no	—
91	C₂×C₈×C₆₇	—	4	8	no	—
92	C₂×C₈×C₆₇	C₂×D₄	1	4	yes	—
93	C₂×C₈×C₆₇	C₂×Q₈	1	4	yes	—
94	C₄⋊C₄×C₆₇	—	2	8	no	—
95	C₄⋊C₄×C₆₇	C₂×C₈	1	16	yes	complemented
96	C₄²×C₆₇	—	2	8	no	—
97	C₄²×C₆₇	—	2	4	no	—
98	C₄²×C₆₇	—	2	4	no	—
99	C₄²×C₆₇	C₄⋊C₄	1	8	yes	—
100	C₄²×C₆₇	C₂×D₄	1	4	yes	—
101	C₄²×C₆₇	C₂×Q₈	1	4	yes	—
102	C₂³×C₆₇	C₂×C₄⋊C₄	1	2	yes	—
103	C₂³×C₆₇	C₄×D₄	1	2	yes	—
104	C₂³×C₆₇	C₄×Q₈	1	2	yes	—
105	C₂³×C₆₇	C₂²×C₈	1	2	yes	—
106	C₂³×C₆₇	C₂×M₁₆	1	2	yes	—
107	C₂³×C₆₇	#131	1	2	yes	—
108	C₂³×C₆₇	#131	1	2	yes	—
109	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
110	C₂×C₄×C₆₇	—	2	4	no	—
111	C₂×C₄×C₆₇	—	2	2	no	—
112	C₂×C₄×C₆₇	—	2	2	no	—
113	C₂×C₄×C₆₇	—	2	4	no	—
114	C₂×C₄×C₆₇	—	2	8	no	—
115	C₂×C₄×C₆₇	—	2	16	no	—
116	C₂×C₄×C₆₇	—	2	4	no	—
117	C₂×C₄×C₆₇	—	2	4	no	—
118	C₂×C₄×C₆₇	—	2	4	no	—
119	C₂×C₄×C₆₇	—	4	8	no	—
120	C₂×C₄×C₆₇	C₄⋊C₈	1	16	yes	complemented
121	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	4	yes	—
122	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	2	yes	—
123	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	4	yes	—
124	C₂×C₄×C₆₇	C₄×D₄	1	2	yes	—
125	C₂×C₄×C₆₇	C₄×Q₈	1	2	yes	—
126	C₂×C₄×C₆₇	#121	1	4	yes	—
127	C₂×C₄×C₆₇	C₂²⋊Q₈	1	4	yes	—
128	C₂×C₄×C₆₇	#125	1	4	yes	—
129	C₂×C₄×C₆₇	C₄⋊Q₈	1	4	yes	—
130	C₂×C₄×C₆₇	C₂²×C₈	1	8	yes	—
131	C₂×C₄×C₆₇	C₂²×C₈	1	4	yes	—
132	C₂×C₄×C₆₇	C₂×M₁₆	1	4	yes	—
133	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
134	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
135	C₂×C₄×C₆₇	C₂²×Q₈	1	1	yes	characteristic
136	C₂×C₄×C₆₇	C₂²×Q₈	1	1	yes	characteristic
137	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
138	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
139	C₈×C₆₇	—	2	4	no	—
140	C₈×C₆₇	—	2	4	no	—
141	C₈×C₆₇	—	4	4	no	—
142	C₂²×C₆₇	#389	1	4	yes	—
143	C₂²×C₆₇	C₂×C₄⋊C₈	1	4	yes	—
144	C₂²×C₆₇	#424	1	4	yes	—
145	C₂²×C₆₇	C₈×D₄	1	4	yes	—
146	C₂²×C₆₇	#436	1	4	yes	—
147	C₂²×C₆₇	C₈×Q₈	1	4	yes	—
148	C₂²×C₆₇	#446	1	4	yes	—
149	C₂²×C₆₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
150	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
151	C₂²×C₆₇	C₂×C₄×Q₈	1	1	yes	characteristic
152	C₂²×C₆₇	C₂³×C₈	1	1	yes	characteristic
153	C₂²×C₆₇	C₂²×M₁₆	1	1	yes	characteristic
154	C₂²×C₆₇	C₂×#131	1	1	yes	characteristic
155	C₂²×C₆₇	C₂×#131	1	1	yes	characteristic
156	C₄×C₆₇	—	2	4	no	—
157	C₄×C₆₇	—	2	8	no	—
158	C₄×C₆₇	—	4	4	no	—
159	C₄×C₆₇	#389	1	4	yes	—
160	C₄×C₆₇	C₂×C₄⋊C₈	1	8	yes	complemented
161	C₄×C₆₇	C₂×#121	1	1	yes	characteristic
162	C₄×C₆₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
163	C₄×C₆₇	C₂×#125	1	1	yes	characteristic
164	C₄×C₆₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
165	C₂×#1939	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
166	C₂×C₆₇	#1939	1	8	yes	direct product factor
167	C₂×C₆₇	C₂×#389	1	1	yes	characteristic
168	C₂×C₆₇	C₂²×C₄⋊C₈	1	1	yes	characteristic
169	C₂×C₆₇	C₂×#424	1	1	yes	characteristic
170	C₂×C₆₇	C₂×C₈×D₄	1	1	yes	characteristic
171	C₂×C₆₇	C₂×#436	1	1	yes	characteristic
172	C₂×C₆₇	C₂×C₈×Q₈	1	1	yes	characteristic
173	C₂×C₆₇	C₂×#446	1	1	yes	characteristic
174	C₂²×C₄⋊C₈	C₂×C₆₇	1	1	yes	characteristic
175	C₂²×C₄⋊C₈	C₂×C₆₇	1	2	yes	—
176	C₂²×C₄×C₈	C₂×C₆₇	1	1	yes	characteristic
177	C₂×C₄×C₄⋊C₄	C₂×C₆₇	1	1	yes	characteristic
178	#1939	C₂×C₆₇	1	8	yes	direct product factor
179	C₂×#336	C₂×C₆₇	1	2	yes	—
180	C₆₇	C₂×#1939	1	1	yes	characteristic, direct product factor, Sylow
181	C₂³×C₈	C₂²×C₆₇	1	2	yes	—
182	C₂³×C₈	C₂²×C₆₇	1	1	yes	characteristic
183	C₂³×C₈	C₂²×C₆₇	1	1	yes	characteristic
184	C₂²×C₄⋊C₄	C₄×C₆₇	1	1	yes	characteristic
185	C₂²×C₄⋊C₄	C₄×C₆₇	1	1	yes	characteristic
186	C₂²×C₄²	C₂²×C₆₇	1	2	yes	—
187	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
188	C₂×C₄⋊C₈	—	2	8	no	—
189	C₂×C₄⋊C₈	—	2	4	no	—
190	C₂×C₄⋊C₈	C₂²×C₆₇	1	8	yes	—
191	C₂×C₄⋊C₈	C₂²×C₆₇	1	4	yes	—
192	C₂×C₄×C₈	—	2	4	no	—
193	C₂×C₄×C₈	C₂²×C₆₇	1	4	yes	—
194	C₄×C₄⋊C₄	C₄×C₆₇	1	4	yes	—
195	C₄×C₄⋊C₄	C₂²×C₆₇	1	4	yes	—
196	C₂×#95	C₄×C₆₇	1	2	yes	—
197	#336	C₂²×C₆₇	1	8	yes	—
198	C₂³×C₄	C₂×C₄×C₆₇	1	2	yes	—
199	C₂³×C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
200	C₂³×C₄	C₂×C₄×C₆₇	1	2	yes	—
201	C₂³×C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
202	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
203	C₂²×C₈	—	2	2	no	—
204	C₂²×C₈	—	2	2	no	—
205	C₂²×C₈	—	2	2	no	—
206	C₂²×C₈	—	2	2	no	—
207	C₂²×C₈	—	2	4	no	—
208	C₂²×C₈	—	2	4	no	—
209	C₂²×C₈	—	2	4	no	—
210	C₂²×C₈	D₄×C₆₇	1	4	yes	—
211	C₂²×C₈	Q₈×C₆₇	1	4	yes	—
212	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
213	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
214	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
215	C₂×C₄⋊C₄	—	2	4	no	—
216	C₂×C₄⋊C₄	C₈×C₆₇	1	8	yes	complemented
217	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	4	yes	—
218	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	4	yes	—
219	C₂×C₄²	—	2	4	no	—
220	C₂×C₄²	—	2	4	no	—
221	C₂×C₄²	C₂×C₄×C₆₇	1	4	yes	—
222	C₂×C₄²	C₂×C₄×C₆₇	1	2	yes	—
223	C₂×C₄²	D₄×C₆₇	1	4	yes	—
224	C₂×C₄²	Q₈×C₆₇	1	4	yes	—
225	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
226	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
227	C₄⋊C₈	—	2	16	no	—
228	C₄⋊C₈	—	2	8	no	—
229	C₄×C₈	—	2	8	no	—
230	#95	C₂×C₄×C₆₇	1	8	yes	—
231	C₂⁴	C₂²×C₄×C₆₇	1	1	yes	characteristic
232	C₂²×C₄	—	2	4	no	—
233	C₂²×C₄	—	2	2	no	—
234	C₂²×C₄	—	2	2	no	—
235	C₂²×C₄	—	2	4	no	—
236	C₂²×C₄	—	2	4	no	—
237	C₂²×C₄	—	2	4	no	—
238	C₂²×C₄	—	2	4	no	—
239	C₂²×C₄	C₄⋊C₄×C₆₇	1	4	yes	—
240	C₂²×C₄	C₄⋊C₄×C₆₇	1	4	yes	—
241	C₂²×C₄	C₂×C₈×C₆₇	1	8	yes	—
242	C₂²×C₄	C₂×C₈×C₆₇	1	4	yes	—
243	C₂²×C₄	M₁₆×C₆₇	1	4	yes	—
244	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
245	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
246	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
247	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
248	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
249	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
250	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
251	C₂²×C₄	C₂×Q₈×C₆₇	1	2	yes	—
252	C₂²×C₄	C₂×Q₈×C₆₇	1	2	yes	—
253	C₂²×C₄	#41×C₆₇	1	2	yes	—
254	C₂²×C₄	#41×C₆₇	1	2	yes	—
255	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
256	C₂×C₈	—	2	8	no	—
257	C₂×C₈	—	2	8	no	—
258	C₂×C₈	—	2	2	no	—
259	C₂×C₈	—	2	2	no	—
260	C₂×C₈	—	2	2	no	—
261	C₂×C₈	—	2	2	no	—
262	C₂×C₈	—	2	4	no	—
263	C₂×C₈	—	2	4	no	—
264	C₂×C₈	—	2	4	no	—
265	C₂×C₈	—	4	8	no	—
266	C₂×C₈	C₂×D₄×C₆₇	1	4	yes	—
267	C₂×C₈	C₂×Q₈×C₆₇	1	4	yes	—
268	C₄⋊C₄	—	2	8	no	—
269	C₄⋊C₄	C₂×C₈×C₆₇	1	16	yes	complemented
270	C₄²	—	2	8	no	—
271	C₄²	—	2	4	no	—
272	C₄²	—	2	4	no	—
273	C₄²	C₄⋊C₄×C₆₇	1	8	yes	—
274	C₄²	C₂×D₄×C₆₇	1	4	yes	—
275	C₄²	C₂×Q₈×C₆₇	1	4	yes	—
276	C₂³	C₂×C₄⋊C₄×C₆₇	1	2	yes	—
277	C₂³	C₄×D₄×C₆₇	1	2	yes	—
278	C₂³	C₄×Q₈×C₆₇	1	2	yes	—
279	C₂³	C₂²×C₈×C₆₇	1	2	yes	—
280	C₂³	C₂×M₁₆×C₆₇	1	2	yes	—
281	C₂³	#131×C₆₇	1	2	yes	—
282	C₂³	#131×C₆₇	1	2	yes	—
283	C₂³	C₂³×C₄×C₆₇	1	1	yes	characteristic
284	C₂×C₄	—	2	4	no	—
285	C₂×C₄	—	2	2	no	—
286	C₂×C₄	—	2	2	no	—
287	C₂×C₄	—	2	4	no	—
288	C₂×C₄	—	2	8	no	—
289	C₂×C₄	—	2	16	no	—
290	C₂×C₄	—	2	4	no	—
291	C₂×C₄	—	2	4	no	—
292	C₂×C₄	—	2	4	no	—
293	C₂×C₄	—	4	8	no	—
294	C₂×C₄	C₄⋊C₈×C₆₇	1	16	yes	complemented
295	C₂×C₄	C₂×C₄⋊C₄×C₆₇	1	4	yes	—
296	C₂×C₄	C₂×C₄⋊C₄×C₆₇	1	2	yes	—
297	C₂×C₄	C₂×C₄⋊C₄×C₆₇	1	4	yes	—
298	C₂×C₄	C₄×D₄×C₆₇	1	2	yes	—
299	C₂×C₄	C₄×Q₈×C₆₇	1	2	yes	—
300	C₂×C₄	#121×C₆₇	1	4	yes	—
301	C₂×C₄	C₂²⋊Q₈×C₆₇	1	4	yes	—
302	C₂×C₄	#125×C₆₇	1	4	yes	—
303	C₂×C₄	C₄⋊Q₈×C₆₇	1	4	yes	—
304	C₂×C₄	C₂²×C₈×C₆₇	1	8	yes	—
305	C₂×C₄	C₂²×C₈×C₆₇	1	4	yes	—
306	C₂×C₄	C₂×M₁₆×C₆₇	1	4	yes	—
307	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
308	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
309	C₂×C₄	C₂²×Q₈×C₆₇	1	1	yes	characteristic
310	C₂×C₄	C₂²×Q₈×C₆₇	1	1	yes	characteristic
311	C₂×C₄	C₂×#41×C₆₇	1	1	yes	characteristic
312	C₂×C₄	C₂×#41×C₆₇	1	1	yes	characteristic
313	C₈	—	2	4	no	—
314	C₈	—	2	4	no	—
315	C₈	—	4	4	no	—
316	C₂²	#389×C₆₇	1	4	yes	—
317	C₂²	C₂×C₄⋊C₈×C₆₇	1	4	yes	—
318	C₂²	#424×C₆₇	1	4	yes	—
319	C₂²	C₈×D₄×C₆₇	1	4	yes	—
320	C₂²	#436×C₆₇	1	4	yes	—
321	C₂²	C₈×Q₈×C₆₇	1	4	yes	—
322	C₂²	#446×C₆₇	1	4	yes	—
323	C₂²	C₂²×C₄⋊C₄×C₆₇	1	1	yes	characteristic
324	C₂²	C₂×C₄×D₄×C₆₇	1	1	yes	characteristic
325	C₂²	C₂×C₄×Q₈×C₆₇	1	1	yes	characteristic
326	C₂²	C₂³×C₈×C₆₇	1	1	yes	characteristic
327	C₂²	C₂²×M₁₆×C₆₇	1	1	yes	characteristic
328	C₂²	C₂×#131×C₆₇	1	1	yes	characteristic
329	C₂²	C₂×#131×C₆₇	1	1	yes	characteristic
330	C₄	—	2	4	no	—
331	C₄	—	2	8	no	—
332	C₄	—	4	4	no	—
333	C₄	#389×C₆₇	1	4	yes	—
334	C₄	C₂×C₄⋊C₈×C₆₇	1	8	yes	complemented
335	C₄	C₂×#121×C₆₇	1	1	yes	characteristic
336	C₄	C₂×C₂²⋊Q₈×C₆₇	1	1	yes	characteristic
337	C₄	C₂×#125×C₆₇	1	1	yes	characteristic
338	C₄	C₂×C₄⋊Q₈×C₆₇	1	1	yes	characteristic
339	C₂	C₆₇×#1939	1	8	yes	direct product factor
340	C₂	C₂×#389×C₆₇	1	1	yes	characteristic
341	C₂	C₂²×C₄⋊C₈×C₆₇	1	1	yes	characteristic
342	C₂	C₂×#424×C₆₇	1	1	yes	characteristic
343	C₂	C₂×C₈×D₄×C₆₇	1	1	yes	characteristic
344	C₂	C₂×#436×C₆₇	1	1	yes	characteristic
345	C₂	C₂×C₈×Q₈×C₆₇	1	1	yes	characteristic
346	C₂	C₂×#446×C₆₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₄×C₆₇	C₂³
commutator	C₂²	C₂³×C₈×C₆₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₇
socle, prime radical	C₂⁴×C₆₇	C₂²×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₄×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
5. C₆₇×#1939	C₂	direct (N × H)
42. C₂×C₄⋊C₄×C₆₇	C₈	semidirect
95. C₄⋊C₄×C₆₇	C₂×C₈	semidirect
120. C₂×C₄×C₆₇	C₄⋊C₈	semidirect
160. C₄×C₆₇	C₂×C₄⋊C₈	semidirect
165. C₂×#1939	C₆₇	direct (N × H)
166. C₂×C₆₇	#1939	direct (N × H)
178. #1939	C₂×C₆₇	direct (N × H)
180. C₆₇	C₂×#1939	direct (N × H)
216. C₂×C₄⋊C₄	C₈×C₆₇	semidirect
269. C₄⋊C₄	C₂×C₈×C₆₇	semidirect
294. C₂×C₄	C₄⋊C₈×C₆₇	semidirect
334. C₄	C₂×C₄⋊C₈×C₆₇	semidirect
339. C₂	C₆₇×#1939	direct (N × H)

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×C₄×C₈×C₆₇	2
C₂×C₄×C₄⋊C₄×C₆₇	2
C₆₇×#1939	2
C₂×#336×C₆₇	2
C₂×#1939	67

Subgroups — C2×C67×#1939 #30700392

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₇×#1939 #30700392