Subgroups — C₂×C₆₇×#2920 #30739368

Order 17152.

2806 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₄²×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₆₇×#2920	C₂	1	16	yes	maximal, direct product factor
3	C₂×#432×C₆₇	C₂	1	4	yes	maximal, complemented
4	C₂×#431×C₆₇	C₂	1	4	yes	maximal, complemented
5	C₂×#423×C₆₇	C₂	1	2	yes	maximal, complemented
6	C₂×#407×C₆₇	C₂	1	2	yes	maximal
7	C₂×C₄×M₁₆×C₆₇	C₂	1	2	yes	maximal, complemented
8	C₂⁴×C₄×C₆₇	C₄	1	2	yes	—
9	C₂⁴×C₄×C₆₇	C₂²	1	1	yes	characteristic
10	C₂²×M₁₆×C₆₇	C₂²	1	4	yes	—
11	C₂²×C₄²×C₆₇	C₄	1	8	yes	—
12	C₂²×C₄²×C₆₇	C₄	1	2	yes	—
13	C₂²×C₄²×C₆₇	C₄	1	2	yes	—
14	C₂²×C₄²×C₆₇	C₄	1	2	yes	—
15	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
16	C₂²×C₄²×C₆₇	C₂²	1	2	yes	—
17	C₂²×C₄²×C₆₇	C₂²	1	8	yes	—
18	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
19	C₂²×C₄²×C₆₇	C₂²	1	2	yes	—
20	#432×C₆₇	C₂²	1	32	yes	complemented
21	#431×C₆₇	C₂²	1	32	yes	complemented
22	#423×C₆₇	C₂²	1	16	yes	complemented
23	C₂×C₄⋊C₈×C₆₇	C₂²	1	8	yes	complemented
24	#407×C₆₇	C₂²	1	16	yes	—
25	C₂×C₂²⋊C₈×C₆₇	C₂²	1	8	yes	—
26	C₄×M₁₆×C₆₇	C₂²	1	16	yes	complemented
27	C₂×#97×C₆₇	C₂²	1	4	yes	complemented
28	C₂×C₄×C₈×C₆₇	C₂²	1	4	yes	complemented
29	C₂⁵×C₆₇	C₂×C₄	1	1	yes	characteristic
30	C₂³×C₄×C₆₇	—	2	16	no	—
31	C₂³×C₄×C₆₇	—	2	8	no	—
32	C₂³×C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
33	C₂³×C₄×C₆₇	C₂×C₄	1	4	yes	—
34	C₂³×C₄×C₆₇	C₂×C₄	1	2	yes	—
35	C₂³×C₄×C₆₇	C₂×C₄	1	2	yes	—
36	C₂³×C₄×C₆₇	C₂×C₄	1	2	yes	—
37	C₂³×C₄×C₆₇	C₂×C₄	1	2	yes	—
38	C₂³×C₄×C₆₇	C₂×C₄	1	2	yes	—
39	C₂³×C₄×C₆₇	C₂×C₄	1	2	yes	—
40	C₂³×C₄×C₆₇	C₂×C₄	1	16	yes	—
41	C₂³×C₄×C₆₇	C₂×C₄	1	2	yes	—
42	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
43	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
44	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
45	C₂×M₁₆×C₆₇	—	2	16	no	—
46	C₂×M₁₆×C₆₇	C₂³	1	16	yes	—
47	C₂²×C₈×C₆₇	C₂³	1	8	yes	—
48	C₂×C₄²×C₆₇	C₂×C₄	1	2	yes	—
49	C₂×C₄²×C₆₇	C₂×C₄	1	8	yes	—
50	C₂×C₄²×C₆₇	C₂×C₄	1	16	yes	—
51	C₂×C₄²×C₆₇	C₂×C₄	1	16	yes	—
52	C₂×C₄²×C₆₇	C₂×C₄	1	2	yes	—
53	C₂×C₄²×C₆₇	C₂×C₄	1	2	yes	—
54	C₂×C₄²×C₆₇	C₂×C₄	1	16	yes	—
55	C₂×C₄²×C₆₇	C₂×C₄	1	2	yes	—
56	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄²×C₆₇	C₂×C₄	1	4	yes	—
58	C₂×C₄²×C₆₇	C₂×C₄	1	2	yes	—
59	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄²×C₆₇	C₂×C₄	1	8	yes	—
61	C₂×C₄²×C₆₇	C₂×C₄	1	4	yes	—
62	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
63	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
64	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
65	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
66	C₂×C₄²×C₆₇	C₂³	1	8	yes	—
67	C₂×C₄²×C₆₇	C₂³	1	8	yes	—
68	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
69	C₄⋊C₈×C₆₇	C₂³	1	32	yes	complemented
70	C₂²⋊C₈×C₆₇	C₂³	1	32	yes	—
71	#97×C₆₇	C₂³	1	16	yes	complemented
72	C₄×C₈×C₆₇	C₂³	1	16	yes	complemented
73	C₂⁴×C₆₇	—	2	4	no	—
74	C₂⁴×C₆₇	—	2	8	no	—
75	C₂⁴×C₆₇	C₂²×C₄	1	4	yes	—
76	C₂⁴×C₆₇	C₂²×C₄	1	1	yes	characteristic
77	C₂⁴×C₆₇	C₂²×C₄	1	2	yes	—
78	C₂²×C₄×C₆₇	—	2	4	no	—
79	C₂²×C₄×C₆₇	—	2	8	no	—
80	C₂²×C₄×C₆₇	—	2	16	no	—
81	C₂²×C₄×C₆₇	—	2	8	no	—
82	C₂²×C₄×C₆₇	—	2	8	no	—
83	C₂²×C₄×C₆₇	—	2	8	no	—
84	C₂²×C₄×C₆₇	—	2	8	no	—
85	C₂²×C₄×C₆₇	—	2	8	no	—
86	C₂²×C₄×C₆₇	—	2	64	no	—
87	C₂²×C₄×C₆₇	—	2	8	no	—
88	C₂²×C₄×C₆₇	—	2	16	no	—
89	C₂²×C₄×C₆₇	M₁₆	1	16	yes	complemented
90	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
91	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
92	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
93	C₂²×C₄×C₆₇	C₂²×C₄	1	8	yes	—
94	C₂²×C₄×C₆₇	C₂²×C₄	1	8	yes	—
95	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
96	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
97	C₂²×C₄×C₆₇	C₂²×C₄	1	8	yes	—
98	C₂²×C₄×C₆₇	C₂²×C₄	1	8	yes	—
99	C₂²×C₄×C₆₇	C₂²×C₄	1	8	yes	—
100	C₂²×C₄×C₆₇	C₂²×C₄	1	8	yes	—
101	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
102	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
104	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
105	C₂²×C₄×C₆₇	C₂²×C₄	1	8	yes	—
106	C₂²×C₄×C₆₇	#41	1	8	yes	—
107	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
108	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
109	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
110	M₁₆×C₆₇	—	2	32	no	—
111	C₂×C₈×C₆₇	—	2	16	no	—
112	C₂×C₈×C₆₇	C₂⁴	1	16	yes	—
113	C₄²×C₆₇	C₂²×C₄	1	8	yes	—
114	C₄²×C₆₇	C₂²×C₄	1	8	yes	—
115	C₄²×C₆₇	C₂²×C₄	1	8	yes	—
116	C₄²×C₆₇	C₂²×C₄	1	8	yes	—
117	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
118	C₄²×C₆₇	C₂²×C₄	1	4	yes	—
119	C₄²×C₆₇	C₂²×C₄	1	8	yes	—
120	C₄²×C₆₇	C₂²×C₄	1	4	yes	—
121	C₄²×C₆₇	C₂²×C₄	1	4	yes	—
122	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
123	C₄²×C₆₇	C₂⁴	1	4	yes	—
124	C₄²×C₆₇	C₂⁴	1	2	yes	—
125	C₄²×C₆₇	C₂⁴	1	2	yes	—
126	C₂³×C₆₇	—	2	32	no	—
127	C₂³×C₆₇	—	2	8	no	—
128	C₂³×C₆₇	—	2	4	no	—
129	C₂³×C₆₇	—	2	16	no	—
130	C₂³×C₆₇	—	2	4	no	—
131	C₂³×C₆₇	—	2	4	no	—
132	C₂³×C₆₇	#117	1	4	yes	—
133	C₂³×C₆₇	C₂×M₁₆	1	8	yes	—
134	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
135	C₂³×C₆₇	C₂³×C₄	1	4	yes	—
136	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
137	C₂×C₄×C₆₇	—	2	8	no	—
138	C₂×C₄×C₆₇	—	2	4	no	—
139	C₂×C₄×C₆₇	—	2	16	no	—
140	C₂×C₄×C₆₇	—	2	4	no	—
141	C₂×C₄×C₆₇	—	2	4	no	—
142	C₂×C₄×C₆₇	—	2	8	no	—
143	C₂×C₄×C₆₇	—	2	16	no	—
144	C₂×C₄×C₆₇	—	2	16	no	—
145	C₂×C₄×C₆₇	—	2	16	no	—
146	C₂×C₄×C₆₇	—	2	16	no	—
147	C₂×C₄×C₆₇	—	2	16	no	—
148	C₂×C₄×C₆₇	—	2	8	no	—
149	C₂×C₄×C₆₇	#117	1	8	yes	—
150	C₂×C₄×C₆₇	#117	1	4	yes	—
151	C₂×C₄×C₆₇	C₂×M₁₆	1	8	yes	—
152	C₂×C₄×C₆₇	C₂×M₁₆	1	8	yes	—
153	C₂×C₄×C₆₇	C₂×M₁₆	1	32	yes	complemented
154	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
155	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
156	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
157	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
158	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
159	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
160	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
161	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
162	C₂×C₄×C₆₇	C₂×#41	1	8	yes	—
163	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
164	C₈×C₆₇	—	2	16	no	—
165	C₂²×C₆₇	—	2	32	no	—
166	C₂²×C₆₇	—	2	4	no	—
167	C₂²×C₆₇	—	2	8	no	—
168	C₂²×C₆₇	—	2	16	no	—
169	C₂²×C₆₇	—	2	4	no	—
170	C₂²×C₆₇	—	2	4	no	—
171	C₂²×C₆₇	C₂×#117	1	4	yes	—
172	C₂²×C₆₇	C₂×#117	1	2	yes	—
173	C₂²×C₆₇	C₂²×M₁₆	1	8	yes	—
174	C₂²×C₆₇	C₂²×M₁₆	1	4	yes	—
175	C₂²×C₆₇	C₂⁴×C₄	1	1	yes	characteristic
176	C₄×C₆₇	—	2	4	no	—
177	C₄×C₆₇	—	2	4	no	—
178	C₄×C₆₇	—	2	4	no	—
179	C₄×C₆₇	C₂×#117	1	2	yes	—
180	C₄×C₆₇	C₂×#117	1	4	yes	—
181	C₄×C₆₇	C₂²×M₁₆	1	8	yes	—
182	C₄×C₆₇	C₂²×M₁₆	1	8	yes	—
183	C₄×C₆₇	C₂²×#41	1	2	yes	—
184	C₂×#2920	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
185	C₂×C₆₇	—	2	4	no	—
186	C₂×C₆₇	—	2	8	no	—
187	C₂×C₆₇	#2920	1	4	yes	direct product factor
188	C₂×C₆₇	C₂²×#117	1	1	yes	characteristic
189	C₂×C₆₇	C₂³×M₁₆	1	2	yes	—
190	C₂³×C₄²	C₂×C₆₇	1	1	yes	characteristic
191	#2920	C₂×C₆₇	1	16	yes	direct product factor
192	C₂×#432	C₂×C₆₇	1	4	yes	complemented
193	C₂×#431	C₂×C₆₇	1	4	yes	complemented
194	C₂×#423	C₂×C₆₇	1	2	yes	complemented
195	C₂×#407	C₂×C₆₇	1	2	yes	—
196	C₂×C₄×M₁₆	C₂×C₆₇	1	2	yes	complemented
197	C₆₇	C₂×#2920	1	1	yes	characteristic, direct product factor, Sylow
198	C₂⁴×C₄	C₄×C₆₇	1	2	yes	—
199	C₂⁴×C₄	C₂²×C₆₇	1	1	yes	characteristic
200	C₂²×M₁₆	C₂²×C₆₇	1	4	yes	—
201	C₂²×C₄²	C₄×C₆₇	1	8	yes	—
202	C₂²×C₄²	C₄×C₆₇	1	2	yes	—
203	C₂²×C₄²	C₄×C₆₇	1	2	yes	—
204	C₂²×C₄²	C₄×C₆₇	1	2	yes	—
205	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
206	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
207	C₂²×C₄²	C₂²×C₆₇	1	2	yes	—
208	C₂²×C₄²	C₂²×C₆₇	1	2	yes	—
209	C₂²×C₄²	C₂²×C₆₇	1	8	yes	—
210	#432	C₂²×C₆₇	1	32	yes	complemented
211	#431	C₂²×C₆₇	1	32	yes	complemented
212	#423	C₂²×C₆₇	1	16	yes	complemented
213	C₂×C₄⋊C₈	C₂²×C₆₇	1	8	yes	complemented
214	#407	C₂²×C₆₇	1	16	yes	—
215	C₂×C₂²⋊C₈	C₂²×C₆₇	1	8	yes	—
216	C₄×M₁₆	C₂²×C₆₇	1	16	yes	complemented
217	C₂×#97	C₂²×C₆₇	1	4	yes	complemented
218	C₂×C₄×C₈	C₂²×C₆₇	1	4	yes	complemented
219	C₂⁵	C₂×C₄×C₆₇	1	1	yes	characteristic
220	C₂³×C₄	—	2	16	no	—
221	C₂³×C₄	—	2	8	no	—
222	C₂³×C₄	C₂×C₄×C₆₇	1	2	yes	—
223	C₂³×C₄	C₂×C₄×C₆₇	1	2	yes	—
224	C₂³×C₄	C₂×C₄×C₆₇	1	2	yes	—
225	C₂³×C₄	C₂×C₄×C₆₇	1	2	yes	—
226	C₂³×C₄	C₂×C₄×C₆₇	1	2	yes	—
227	C₂³×C₄	C₂×C₄×C₆₇	1	16	yes	—
228	C₂³×C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
229	C₂³×C₄	C₂×C₄×C₆₇	1	4	yes	—
230	C₂³×C₄	C₂×C₄×C₆₇	1	2	yes	—
231	C₂³×C₄	C₂×C₄×C₆₇	1	2	yes	—
232	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
233	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
234	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
235	C₂×M₁₆	—	2	16	no	—
236	C₂×M₁₆	C₂³×C₆₇	1	16	yes	—
237	C₂²×C₈	C₂³×C₆₇	1	8	yes	—
238	C₂×C₄²	C₂×C₄×C₆₇	1	2	yes	—
239	C₂×C₄²	C₂×C₄×C₆₇	1	8	yes	—
240	C₂×C₄²	C₂×C₄×C₆₇	1	16	yes	—
241	C₂×C₄²	C₂×C₄×C₆₇	1	16	yes	—
242	C₂×C₄²	C₂×C₄×C₆₇	1	2	yes	—
243	C₂×C₄²	C₂×C₄×C₆₇	1	2	yes	—
244	C₂×C₄²	C₂×C₄×C₆₇	1	8	yes	—
245	C₂×C₄²	C₂×C₄×C₆₇	1	16	yes	—
246	C₂×C₄²	C₂×C₄×C₆₇	1	2	yes	—
247	C₂×C₄²	C₂×C₄×C₆₇	1	4	yes	—
248	C₂×C₄²	C₂×C₄×C₆₇	1	1	yes	characteristic
249	C₂×C₄²	C₂×C₄×C₆₇	1	4	yes	—
250	C₂×C₄²	C₂×C₄×C₆₇	1	2	yes	—
251	C₂×C₄²	C₂×C₄×C₆₇	1	1	yes	characteristic
252	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
253	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
254	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
255	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
256	C₂×C₄²	C₂³×C₆₇	1	8	yes	—
257	C₂×C₄²	C₂³×C₆₇	1	8	yes	—
258	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
259	C₄⋊C₈	C₂³×C₆₇	1	32	yes	complemented
260	C₂²⋊C₈	C₂³×C₆₇	1	32	yes	—
261	#97	C₂³×C₆₇	1	16	yes	complemented
262	C₄×C₈	C₂³×C₆₇	1	16	yes	complemented
263	C₂⁴	—	2	4	no	—
264	C₂⁴	—	2	8	no	—
265	C₂⁴	C₂²×C₄×C₆₇	1	4	yes	—
266	C₂⁴	C₂²×C₄×C₆₇	1	1	yes	characteristic
267	C₂⁴	C₂²×C₄×C₆₇	1	2	yes	—
268	C₂²×C₄	—	2	4	no	—
269	C₂²×C₄	—	2	8	no	—
270	C₂²×C₄	—	2	16	no	—
271	C₂²×C₄	—	2	8	no	—
272	C₂²×C₄	—	2	8	no	—
273	C₂²×C₄	—	2	8	no	—
274	C₂²×C₄	—	2	8	no	—
275	C₂²×C₄	—	2	8	no	—
276	C₂²×C₄	—	2	64	no	—
277	C₂²×C₄	—	2	8	no	—
278	C₂²×C₄	—	2	16	no	—
279	C₂²×C₄	M₁₆×C₆₇	1	16	yes	complemented
280	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
281	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
282	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
283	C₂²×C₄	C₂²×C₄×C₆₇	1	8	yes	—
284	C₂²×C₄	C₂²×C₄×C₆₇	1	8	yes	—
285	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
286	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
287	C₂²×C₄	C₂²×C₄×C₆₇	1	8	yes	—
288	C₂²×C₄	C₂²×C₄×C₆₇	1	8	yes	—
289	C₂²×C₄	C₂²×C₄×C₆₇	1	8	yes	—
290	C₂²×C₄	C₂²×C₄×C₆₇	1	8	yes	—
291	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
292	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
293	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
294	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
295	C₂²×C₄	C₂²×C₄×C₆₇	1	8	yes	—
296	C₂²×C₄	#41×C₆₇	1	8	yes	—
297	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
298	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
299	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
300	M₁₆	—	2	32	no	—
301	C₂×C₈	—	2	16	no	—
302	C₂×C₈	C₂⁴×C₆₇	1	16	yes	—
303	C₄²	C₂²×C₄×C₆₇	1	8	yes	—
304	C₄²	C₂²×C₄×C₆₇	1	8	yes	—
305	C₄²	C₂²×C₄×C₆₇	1	8	yes	—
306	C₄²	C₂²×C₄×C₆₇	1	8	yes	—
307	C₄²	C₂²×C₄×C₆₇	1	2	yes	—
308	C₄²	C₂²×C₄×C₆₇	1	4	yes	—
309	C₄²	C₂²×C₄×C₆₇	1	8	yes	—
310	C₄²	C₂²×C₄×C₆₇	1	4	yes	—
311	C₄²	C₂²×C₄×C₆₇	1	4	yes	—
312	C₄²	C₂²×C₄×C₆₇	1	2	yes	—
313	C₄²	C₂⁴×C₆₇	1	2	yes	—
314	C₄²	C₂⁴×C₆₇	1	2	yes	—
315	C₄²	C₂⁴×C₆₇	1	4	yes	—
316	C₂³	—	2	32	no	—
317	C₂³	—	2	8	no	—
318	C₂³	—	2	4	no	—
319	C₂³	—	2	16	no	—
320	C₂³	—	2	4	no	—
321	C₂³	—	2	4	no	—
322	C₂³	#117×C₆₇	1	4	yes	—
323	C₂³	C₂×M₁₆×C₆₇	1	8	yes	—
324	C₂³	C₂³×C₄×C₆₇	1	2	yes	—
325	C₂³	C₂³×C₄×C₆₇	1	4	yes	—
326	C₂³	C₂³×C₄×C₆₇	1	1	yes	characteristic
327	C₂×C₄	—	2	8	no	—
328	C₂×C₄	—	2	4	no	—
329	C₂×C₄	—	2	16	no	—
330	C₂×C₄	—	2	4	no	—
331	C₂×C₄	—	2	4	no	—
332	C₂×C₄	—	2	8	no	—
333	C₂×C₄	—	2	16	no	—
334	C₂×C₄	—	2	16	no	—
335	C₂×C₄	—	2	16	no	—
336	C₂×C₄	—	2	16	no	—
337	C₂×C₄	—	2	16	no	—
338	C₂×C₄	—	2	8	no	—
339	C₂×C₄	#117×C₆₇	1	8	yes	—
340	C₂×C₄	#117×C₆₇	1	4	yes	—
341	C₂×C₄	C₂×M₁₆×C₆₇	1	8	yes	—
342	C₂×C₄	C₂×M₁₆×C₆₇	1	8	yes	—
343	C₂×C₄	C₂×M₁₆×C₆₇	1	32	yes	complemented
344	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
345	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
346	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
347	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
348	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
349	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
350	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
351	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
352	C₂×C₄	C₂×#41×C₆₇	1	8	yes	—
353	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
354	C₈	—	2	16	no	—
355	C₂²	—	2	32	no	—
356	C₂²	—	2	4	no	—
357	C₂²	—	2	4	no	—
358	C₂²	—	2	4	no	—
359	C₂²	—	2	8	no	—
360	C₂²	—	2	16	no	—
361	C₂²	C₂×#117×C₆₇	1	4	yes	—
362	C₂²	C₂×#117×C₆₇	1	2	yes	—
363	C₂²	C₂²×M₁₆×C₆₇	1	8	yes	—
364	C₂²	C₂²×M₁₆×C₆₇	1	4	yes	—
365	C₂²	C₂⁴×C₄×C₆₇	1	1	yes	characteristic
366	C₄	—	2	4	no	—
367	C₄	—	2	4	no	—
368	C₄	—	2	4	no	—
369	C₄	C₂×#117×C₆₇	1	2	yes	—
370	C₄	C₂×#117×C₆₇	1	4	yes	—
371	C₄	C₂²×M₁₆×C₆₇	1	8	yes	—
372	C₄	C₂²×M₁₆×C₆₇	1	8	yes	—
373	C₄	C₂²×#41×C₆₇	1	2	yes	—
374	C₂	—	2	4	no	—
375	C₂	—	2	8	no	—
376	C₂	C₆₇×#2920	1	4	yes	direct product factor
377	C₂	C₂²×#117×C₆₇	1	1	yes	characteristic
378	C₂	C₂³×M₁₆×C₆₇	1	2	yes	—

	subgroup	G/H
center	C₂×C₄²×C₆₇	C₂³
commutator	C₂²	C₂⁴×C₄×C₆₇
Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
socle	C₂³×C₆₇	C₂³×C₄
prime radical	C₂⁵×C₆₇	C₂×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄²×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₆₇×#2920	C₂	direct (N × H)
3. C₂×#432×C₆₇	C₂	semidirect
4. C₂×#431×C₆₇	C₂	semidirect
5. C₂×#423×C₆₇	C₂	semidirect
7. C₂×C₄×M₁₆×C₆₇	C₂	semidirect
20. #432×C₆₇	C₂²	semidirect
21. #431×C₆₇	C₂²	semidirect
22. #423×C₆₇	C₂²	semidirect
23. C₂×C₄⋊C₈×C₆₇	C₂²	semidirect
26. C₄×M₁₆×C₆₇	C₂²	semidirect
27. C₂×#97×C₆₇	C₂²	semidirect
28. C₂×C₄×C₈×C₆₇	C₂²	semidirect
69. C₄⋊C₈×C₆₇	C₂³	semidirect
71. #97×C₆₇	C₂³	semidirect
72. C₄×C₈×C₆₇	C₂³	semidirect
89. C₂²×C₄×C₆₇	M₁₆	semidirect
153. C₂×C₄×C₆₇	C₂×M₁₆	semidirect
184. C₂×#2920	C₆₇	direct (N × H)
187. C₂×C₆₇	#2920	direct (N × H)
191. #2920	C₂×C₆₇	direct (N × H)
192. C₂×#432	C₂×C₆₇	semidirect
193. C₂×#431	C₂×C₆₇	semidirect
194. C₂×#423	C₂×C₆₇	semidirect
196. C₂×C₄×M₁₆	C₂×C₆₇	semidirect
197. C₆₇	C₂×#2920	direct (N × H)
210. #432	C₂²×C₆₇	semidirect
211. #431	C₂²×C₆₇	semidirect
212. #423	C₂²×C₆₇	semidirect
213. C₂×C₄⋊C₈	C₂²×C₆₇	semidirect
216. C₄×M₁₆	C₂²×C₆₇	semidirect
217. C₂×#97	C₂²×C₆₇	semidirect
218. C₂×C₄×C₈	C₂²×C₆₇	semidirect
259. C₄⋊C₈	C₂³×C₆₇	semidirect
261. #97	C₂³×C₆₇	semidirect
262. C₄×C₈	C₂³×C₆₇	semidirect
279. C₂²×C₄	M₁₆×C₆₇	semidirect
343. C₂×C₄	C₂×M₁₆×C₆₇	semidirect
376. C₂	C₆₇×#2920	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₄²×C₆₇	2
C₆₇×#2920	2
C₂×#432×C₆₇	2
C₂×#431×C₆₇	2
C₂×#423×C₆₇	2
C₂×#407×C₆₇	2
C₂×C₄×M₁₆×C₆₇	2
C₂×#2920	67

Subgroups — C2×C67×#2920 #30739368

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₇×#2920 #30739368