Subgroups — C₂²×#435×C₆₇ #30739382

Order 17152.

3350 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×M₁₆×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂⁴×C₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₄×D₄×C₆₇	C₂	1	1	yes	maximal, characteristic
4	C₂×#435×C₆₇	C₂	1	24	yes	maximal, direct product factor
5	C₂²×C₄⋊C₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₂²⋊C₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×C₂²⋊C₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#97×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×D₄×C₆₇	C₄	1	1	yes	characteristic
10	C₂⁴×C₄×C₆₇	C₂²	1	1	yes	characteristic
11	C₂⁴×C₄×C₆₇	C₂²	1	1	yes	characteristic
12	C₂²×M₁₆×C₆₇	—	2	8	no	—
13	C₂²×M₁₆×C₆₇	C₂²	1	12	yes	complemented
14	C₂³×C₈×C₆₇	—	2	8	no	—
15	C₂³×C₈×C₆₇	C₂²	1	1	yes	characteristic
16	C₂³×C₈×C₆₇	C₂²	1	1	yes	characteristic
17	C₂³×C₈×C₆₇	C₂²	1	1	yes	characteristic
18	C₂³×C₈×C₆₇	C₂²	1	1	yes	characteristic
19	C₂³×C₈×C₆₇	C₂²	1	12	yes	complemented
20	C₂×C₄×D₄×C₆₇	C₄	1	12	yes	—
21	C₂×C₄×D₄×C₆₇	C₂²	1	12	yes	—
22	C₂²×C₄⋊C₄×C₆₇	C₄	1	1	yes	characteristic
23	C₂²×C₂²⋊C₄×C₆₇	C₄	1	1	yes	characteristic
24	C₂²×C₂²⋊C₄×C₆₇	C₄	1	1	yes	characteristic
25	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
26	#435×C₆₇	C₂²	1	64	yes	direct product factor
27	C₂×C₄⋊C₈×C₆₇	C₂²	1	12	yes	complemented
28	C₂×C₂²⋊C₈×C₆₇	C₂²	1	12	yes	complemented
29	C₂×C₂²⋊C₈×C₆₇	C₂²	1	12	yes	complemented
30	C₂×#97×C₆₇	C₂²	1	12	yes	complemented
31	C₂⁵×C₆₇	C₂×C₄	1	1	yes	characteristic
32	C₂⁵×C₆₇	C₂×C₄	1	1	yes	characteristic
33	C₂²×D₄×C₆₇	—	2	8	no	—
34	C₂²×D₄×C₆₇	C₂×C₄	1	12	yes	—
35	C₂³×C₄×C₆₇	—	2	4	no	—
36	C₂³×C₄×C₆₇	—	2	4	no	—
37	C₂³×C₄×C₆₇	—	2	4	no	—
38	C₂³×C₄×C₆₇	—	2	4	no	—
39	C₂³×C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
40	C₂³×C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
41	C₂³×C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
42	C₂³×C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
43	C₂³×C₄×C₆₇	C₂×C₄	1	6	yes	—
44	C₂³×C₄×C₆₇	C₂×C₄	1	6	yes	—
45	C₂³×C₄×C₆₇	C₂³	1	6	yes	—
46	C₂³×C₄×C₆₇	C₂³	1	6	yes	—
47	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
48	C₂×M₁₆×C₆₇	—	2	48	no	—
49	C₂×M₁₆×C₆₇	C₂³	1	16	yes	complemented
50	C₂²×C₈×C₆₇	—	2	4	no	—
51	C₂²×C₈×C₆₇	—	2	4	no	—
52	C₂²×C₈×C₆₇	—	2	4	no	—
53	C₂²×C₈×C₆₇	—	2	48	no	—
54	C₂²×C₈×C₆₇	D₄	1	8	yes	complemented
55	C₂²×C₈×C₆₇	C₂³	1	6	yes	—
56	C₂²×C₈×C₆₇	C₂³	1	6	yes	—
57	C₂²×C₈×C₆₇	C₂³	1	6	yes	—
58	C₂²×C₈×C₆₇	C₂³	1	6	yes	—
59	C₂²×C₈×C₆₇	C₂³	1	16	yes	complemented
60	C₄×D₄×C₆₇	C₂×C₄	1	48	yes	—
61	C₄×D₄×C₆₇	C₂³	1	16	yes	—
62	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	12	yes	—
63	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	12	yes	—
64	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	12	yes	—
65	C₂×C₄²×C₆₇	C₂×C₄	1	6	yes	—
66	C₂×C₄²×C₆₇	C₂³	1	6	yes	—
67	C₄⋊C₈×C₆₇	C₂³	1	16	yes	complemented
68	C₂²⋊C₈×C₆₇	C₂³	1	16	yes	complemented
69	C₂²⋊C₈×C₆₇	C₂³	1	16	yes	complemented
70	#97×C₆₇	C₂³	1	16	yes	complemented
71	C₂⁴×C₆₇	—	2	4	no	—
72	C₂⁴×C₆₇	—	2	4	no	—
73	C₂⁴×C₆₇	—	2	4	no	—
74	C₂⁴×C₆₇	—	2	4	no	—
75	C₂⁴×C₆₇	—	2	4	no	—
76	C₂⁴×C₆₇	M₁₆	1	8	yes	complemented
77	C₂⁴×C₆₇	C₂²×C₄	1	6	yes	—
78	C₂⁴×C₆₇	C₂²×C₄	1	6	yes	—
79	C₂⁴×C₆₇	C₂²×C₄	1	1	yes	characteristic
80	C₂×D₄×C₆₇	—	2	48	no	—
81	C₂×D₄×C₆₇	C₂²×C₄	1	16	yes	—
82	C₂²×C₄×C₆₇	—	2	4	no	—
83	C₂²×C₄×C₆₇	—	2	4	no	—
84	C₂²×C₄×C₆₇	—	2	4	no	—
85	C₂²×C₄×C₆₇	—	2	4	no	—
86	C₂²×C₄×C₆₇	—	2	24	no	—
87	C₂²×C₄×C₆₇	—	2	24	no	—
88	C₂²×C₄×C₆₇	—	2	12	no	—
89	C₂²×C₄×C₆₇	—	2	12	no	—
90	C₂²×C₄×C₆₇	—	2	12	no	—
91	C₂²×C₄×C₆₇	—	2	12	no	—
92	C₂²×C₄×C₆₇	C₂²×C₄	1	6	yes	—
93	C₂²×C₄×C₆₇	C₂²×C₄	1	6	yes	—
94	C₂²×C₄×C₆₇	C₂²×C₄	1	6	yes	—
95	C₂²×C₄×C₆₇	C₂²×C₄	1	6	yes	—
96	C₂²×C₄×C₆₇	C₂²×C₄	1	12	yes	—
97	C₂²×C₄×C₆₇	C₂²×C₄	1	12	yes	—
98	C₂²×C₄×C₆₇	C₂²×C₄	1	3	yes	—
99	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
100	C₂²×C₄×C₆₇	#41	1	4	yes	—
101	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
102	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
103	C₂²×C₄×C₆₇	C₂⁴	1	3	yes	—
104	M₁₆×C₆₇	—	2	32	no	—
105	C₂×C₈×C₆₇	—	2	12	no	—
106	C₂×C₈×C₆₇	—	2	12	no	—
107	C₂×C₈×C₆₇	—	2	12	no	—
108	C₂×C₈×C₆₇	—	2	32	no	—
109	C₂×C₈×C₆₇	C₂×D₄	1	24	yes	complemented
110	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
111	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
112	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
113	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
114	C₄⋊C₄×C₆₇	C₂²×C₄	1	16	yes	—
115	C₂²⋊C₄×C₆₇	C₂²×C₄	1	16	yes	—
116	C₂²⋊C₄×C₆₇	C₂²×C₄	1	16	yes	—
117	C₄²×C₆₇	C₂²×C₄	1	12	yes	—
118	C₄²×C₆₇	C₂⁴	1	4	yes	—
119	C₂³×C₆₇	—	2	12	no	—
120	C₂³×C₆₇	—	2	12	no	—
121	C₂³×C₆₇	—	2	32	no	—
122	C₂³×C₆₇	—	2	12	no	—
123	C₂³×C₆₇	—	2	12	no	—
124	C₂³×C₆₇	—	2	12	no	—
125	C₂³×C₆₇	—	4	16	no	—
126	C₂³×C₆₇	C₄×D₄	1	4	yes	—
127	C₂³×C₆₇	C₂×M₁₆	1	4	yes	—
128	C₂³×C₆₇	C₂×M₁₆	1	24	yes	complemented
129	C₂³×C₆₇	#131	1	4	yes	—
130	C₂³×C₆₇	C₂³×C₄	1	4	yes	—
131	C₂³×C₆₇	C₂³×C₄	1	4	yes	—
132	C₂³×C₆₇	C₂³×C₄	1	3	yes	—
133	D₄×C₆₇	—	2	32	no	—
134	C₂×C₄×C₆₇	—	2	12	no	—
135	C₂×C₄×C₆₇	—	2	12	no	—
136	C₂×C₄×C₆₇	—	2	12	no	—
137	C₂×C₄×C₆₇	—	2	12	no	—
138	C₂×C₄×C₆₇	—	2	24	no	—
139	C₂×C₄×C₆₇	—	2	24	no	—
140	C₂×C₄×C₆₇	—	2	4	no	—
141	C₂×C₄×C₆₇	—	2	4	no	—
142	C₂×C₄×C₆₇	—	2	4	no	—
143	C₂×C₄×C₆₇	—	2	4	no	—
144	C₂×C₄×C₆₇	C₄×D₄	1	12	yes	—
145	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
146	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
147	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
148	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
149	C₂×C₄×C₆₇	C₂³×C₄	1	3	yes	—
150	C₂×C₄×C₆₇	C₂²×D₄	1	6	yes	—
151	C₂×C₄×C₆₇	C₂×#41	1	6	yes	—
152	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
153	C₈×C₆₇	—	2	4	no	—
154	C₈×C₆₇	—	2	4	no	—
155	C₈×C₆₇	—	2	4	no	—
156	C₈×C₆₇	C₂²×D₄	1	8	yes	complemented
157	C₂²×C₆₇	—	2	4	no	—
158	C₂²×C₆₇	—	2	48	no	—
159	C₂²×C₆₇	—	2	4	no	—
160	C₂²×C₆₇	—	2	4	no	—
161	C₂²×C₆₇	—	2	4	no	—
162	C₂²×C₆₇	—	2	4	no	—
163	C₂²×C₆₇	—	4	24	no	—
164	C₂²×C₆₇	#435	1	16	yes	direct product factor
165	C₂²×C₆₇	C₂×C₄×D₄	1	6	yes	—
166	C₂²×C₆₇	C₂²×M₁₆	1	6	yes	—
167	C₂²×C₆₇	C₂²×M₁₆	1	8	yes	complemented
168	C₂²×C₆₇	C₂×#131	1	6	yes	—
169	C₂²×C₆₇	C₂⁴×C₄	1	1	yes	characteristic
170	C₄×C₆₇	—	2	4	no	—
171	C₄×C₆₇	—	2	4	no	—
172	C₄×C₆₇	—	2	4	no	—
173	C₄×C₆₇	—	2	4	no	—
174	C₄×C₆₇	C₂×C₄×D₄	1	6	yes	—
175	C₄×C₆₇	C₂³×D₄	1	1	yes	characteristic
176	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
177	C₂²×#435	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
178	C₂×C₆₇	—	2	8	no	—
179	C₂×C₆₇	—	4	4	no	—
180	C₂×C₆₇	C₂×#435	1	12	yes	direct product factor
181	C₂×C₆₇	C₂²×C₄×D₄	1	1	yes	characteristic
182	C₂×C₆₇	C₂³×M₁₆	1	1	yes	characteristic
183	C₂×C₆₇	C₂²×#131	1	1	yes	characteristic
184	C₂³×M₁₆	C₂×C₆₇	1	1	yes	characteristic, complemented
185	C₂⁴×C₈	C₂×C₆₇	1	1	yes	characteristic, complemented
186	C₂²×C₄×D₄	C₂×C₆₇	1	1	yes	characteristic
187	C₂×#435	C₂×C₆₇	1	24	yes	direct product factor
188	C₂²×C₄⋊C₈	C₂×C₆₇	1	1	yes	characteristic, complemented
189	C₂²×C₂²⋊C₈	C₂×C₆₇	1	1	yes	characteristic, complemented
190	C₂²×C₂²⋊C₈	C₂×C₆₇	1	1	yes	characteristic, complemented
191	C₂²×#97	C₂×C₆₇	1	1	yes	characteristic, complemented
192	C₆₇	C₂²×#435	1	1	yes	characteristic, direct product factor, Sylow
193	C₂³×D₄	C₄×C₆₇	1	1	yes	characteristic
194	C₂⁴×C₄	C₂²×C₆₇	1	1	yes	characteristic
195	C₂⁴×C₄	C₂²×C₆₇	1	1	yes	characteristic
196	C₂²×M₁₆	—	2	8	no	—
197	C₂²×M₁₆	C₂²×C₆₇	1	12	yes	complemented
198	C₂³×C₈	—	2	8	no	—
199	C₂³×C₈	C₂²×C₆₇	1	1	yes	characteristic
200	C₂³×C₈	C₂²×C₆₇	1	1	yes	characteristic
201	C₂³×C₈	C₂²×C₆₇	1	1	yes	characteristic
202	C₂³×C₈	C₂²×C₆₇	1	1	yes	characteristic
203	C₂³×C₈	C₂²×C₆₇	1	12	yes	complemented
204	C₂×C₄×D₄	C₄×C₆₇	1	12	yes	—
205	C₂×C₄×D₄	C₂²×C₆₇	1	12	yes	—
206	C₂²×C₄⋊C₄	C₄×C₆₇	1	1	yes	characteristic
207	C₂²×C₂²⋊C₄	C₄×C₆₇	1	1	yes	characteristic
208	C₂²×C₂²⋊C₄	C₄×C₆₇	1	1	yes	characteristic
209	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
210	#435	C₂²×C₆₇	1	64	yes	direct product factor
211	C₂×C₄⋊C₈	C₂²×C₆₇	1	12	yes	complemented
212	C₂×C₂²⋊C₈	C₂²×C₆₇	1	12	yes	complemented
213	C₂×C₂²⋊C₈	C₂²×C₆₇	1	12	yes	complemented
214	C₂×#97	C₂²×C₆₇	1	12	yes	complemented
215	C₂⁵	C₂×C₄×C₆₇	1	1	yes	characteristic
216	C₂⁵	C₂×C₄×C₆₇	1	1	yes	characteristic
217	C₂²×D₄	—	2	8	no	—
218	C₂²×D₄	C₂×C₄×C₆₇	1	12	yes	—
219	C₂³×C₄	—	2	4	no	—
220	C₂³×C₄	—	2	4	no	—
221	C₂³×C₄	—	2	4	no	—
222	C₂³×C₄	—	2	4	no	—
223	C₂³×C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
224	C₂³×C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
225	C₂³×C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
226	C₂³×C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
227	C₂³×C₄	C₂×C₄×C₆₇	1	6	yes	—
228	C₂³×C₄	C₂×C₄×C₆₇	1	6	yes	—
229	C₂³×C₄	C₂³×C₆₇	1	6	yes	—
230	C₂³×C₄	C₂³×C₆₇	1	6	yes	—
231	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
232	C₂×M₁₆	—	2	48	no	—
233	C₂×M₁₆	C₂³×C₆₇	1	16	yes	complemented
234	C₂²×C₈	—	2	4	no	—
235	C₂²×C₈	—	2	4	no	—
236	C₂²×C₈	—	2	4	no	—
237	C₂²×C₈	—	2	48	no	—
238	C₂²×C₈	D₄×C₆₇	1	8	yes	complemented
239	C₂²×C₈	C₂³×C₆₇	1	6	yes	—
240	C₂²×C₈	C₂³×C₆₇	1	6	yes	—
241	C₂²×C₈	C₂³×C₆₇	1	6	yes	—
242	C₂²×C₈	C₂³×C₆₇	1	6	yes	—
243	C₂²×C₈	C₂³×C₆₇	1	16	yes	complemented
244	C₄×D₄	C₂×C₄×C₆₇	1	48	yes	—
245	C₄×D₄	C₂³×C₆₇	1	16	yes	—
246	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	12	yes	—
247	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	12	yes	—
248	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	12	yes	—
249	C₂×C₄²	C₂×C₄×C₆₇	1	6	yes	—
250	C₂×C₄²	C₂³×C₆₇	1	6	yes	—
251	C₄⋊C₈	C₂³×C₆₇	1	16	yes	complemented
252	C₂²⋊C₈	C₂³×C₆₇	1	16	yes	complemented
253	C₂²⋊C₈	C₂³×C₆₇	1	16	yes	complemented
254	#97	C₂³×C₆₇	1	16	yes	complemented
255	C₂⁴	—	2	4	no	—
256	C₂⁴	—	2	4	no	—
257	C₂⁴	—	2	4	no	—
258	C₂⁴	—	2	4	no	—
259	C₂⁴	—	2	4	no	—
260	C₂⁴	M₁₆×C₆₇	1	8	yes	complemented
261	C₂⁴	C₂²×C₄×C₆₇	1	6	yes	—
262	C₂⁴	C₂²×C₄×C₆₇	1	6	yes	—
263	C₂⁴	C₂²×C₄×C₆₇	1	1	yes	characteristic
264	C₂×D₄	—	2	48	no	—
265	C₂×D₄	C₂²×C₄×C₆₇	1	16	yes	—
266	C₂²×C₄	—	2	4	no	—
267	C₂²×C₄	—	2	4	no	—
268	C₂²×C₄	—	2	4	no	—
269	C₂²×C₄	—	2	4	no	—
270	C₂²×C₄	—	2	24	no	—
271	C₂²×C₄	—	2	24	no	—
272	C₂²×C₄	—	2	12	no	—
273	C₂²×C₄	—	2	12	no	—
274	C₂²×C₄	—	2	12	no	—
275	C₂²×C₄	—	2	12	no	—
276	C₂²×C₄	C₂²×C₄×C₆₇	1	6	yes	—
277	C₂²×C₄	C₂²×C₄×C₆₇	1	6	yes	—
278	C₂²×C₄	C₂²×C₄×C₆₇	1	6	yes	—
279	C₂²×C₄	C₂²×C₄×C₆₇	1	6	yes	—
280	C₂²×C₄	C₂²×C₄×C₆₇	1	12	yes	—
281	C₂²×C₄	C₂²×C₄×C₆₇	1	12	yes	—
282	C₂²×C₄	C₂²×C₄×C₆₇	1	3	yes	—
283	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
284	C₂²×C₄	#41×C₆₇	1	4	yes	—
285	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
286	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
287	C₂²×C₄	C₂⁴×C₆₇	1	3	yes	—
288	M₁₆	—	2	32	no	—
289	C₂×C₈	—	2	12	no	—
290	C₂×C₈	—	2	12	no	—
291	C₂×C₈	—	2	12	no	—
292	C₂×C₈	—	2	32	no	—
293	C₂×C₈	C₂×D₄×C₆₇	1	24	yes	complemented
294	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
295	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
296	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
297	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
298	C₄⋊C₄	C₂²×C₄×C₆₇	1	16	yes	—
299	C₂²⋊C₄	C₂²×C₄×C₆₇	1	16	yes	—
300	C₂²⋊C₄	C₂²×C₄×C₆₇	1	16	yes	—
301	C₄²	C₂²×C₄×C₆₇	1	12	yes	—
302	C₄²	C₂⁴×C₆₇	1	4	yes	—
303	C₂³	—	2	12	no	—
304	C₂³	—	2	12	no	—
305	C₂³	—	2	32	no	—
306	C₂³	—	2	12	no	—
307	C₂³	—	2	12	no	—
308	C₂³	—	2	12	no	—
309	C₂³	—	4	16	no	—
310	C₂³	C₄×D₄×C₆₇	1	4	yes	—
311	C₂³	C₂×M₁₆×C₆₇	1	4	yes	—
312	C₂³	C₂×M₁₆×C₆₇	1	24	yes	complemented
313	C₂³	#131×C₆₇	1	4	yes	—
314	C₂³	C₂³×C₄×C₆₇	1	4	yes	—
315	C₂³	C₂³×C₄×C₆₇	1	4	yes	—
316	C₂³	C₂³×C₄×C₆₇	1	3	yes	—
317	D₄	—	2	32	no	—
318	C₂×C₄	—	2	12	no	—
319	C₂×C₄	—	2	12	no	—
320	C₂×C₄	—	2	12	no	—
321	C₂×C₄	—	2	12	no	—
322	C₂×C₄	—	2	24	no	—
323	C₂×C₄	—	2	24	no	—
324	C₂×C₄	—	2	4	no	—
325	C₂×C₄	—	2	4	no	—
326	C₂×C₄	—	2	4	no	—
327	C₂×C₄	—	2	4	no	—
328	C₂×C₄	C₄×D₄×C₆₇	1	12	yes	—
329	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
330	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
331	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
332	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
333	C₂×C₄	C₂³×C₄×C₆₇	1	3	yes	—
334	C₂×C₄	C₂²×D₄×C₆₇	1	6	yes	—
335	C₂×C₄	C₂×#41×C₆₇	1	6	yes	—
336	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
337	C₈	—	2	4	no	—
338	C₈	—	2	4	no	—
339	C₈	—	2	4	no	—
340	C₈	C₂²×D₄×C₆₇	1	8	yes	complemented
341	C₂²	—	2	4	no	—
342	C₂²	—	2	4	no	—
343	C₂²	—	2	48	no	—
344	C₂²	—	2	4	no	—
345	C₂²	—	2	4	no	—
346	C₂²	—	2	4	no	—
347	C₂²	—	4	24	no	—
348	C₂²	#435×C₆₇	1	16	yes	direct product factor
349	C₂²	C₂×C₄×D₄×C₆₇	1	6	yes	—
350	C₂²	C₂²×M₁₆×C₆₇	1	6	yes	—
351	C₂²	C₂²×M₁₆×C₆₇	1	8	yes	complemented
352	C₂²	C₂×#131×C₆₇	1	6	yes	—
353	C₂²	C₂⁴×C₄×C₆₇	1	1	yes	characteristic
354	C₄	—	2	4	no	—
355	C₄	—	2	4	no	—
356	C₄	—	2	4	no	—
357	C₄	—	2	4	no	—
358	C₄	C₂×C₄×D₄×C₆₇	1	6	yes	—
359	C₄	C₂³×D₄×C₆₇	1	1	yes	characteristic
360	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
361	C₂	—	2	8	no	—
362	C₂	—	4	4	no	—
363	C₂	C₂×#435×C₆₇	1	12	yes	direct product factor
364	C₂	C₂²×C₄×D₄×C₆₇	1	1	yes	characteristic
365	C₂	C₂³×M₁₆×C₆₇	1	1	yes	characteristic
366	C₂	C₂²×#131×C₆₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₄×C₆₇	C₂³
commutator	C₂²	C₂⁴×C₄×C₆₇
Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
socle	C₂⁴×C₆₇	C₂²×C₄
prime radical	C₂³×D₄×C₆₇	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
1. C₂³×M₁₆×C₆₇	C₂	semidirect
2. C₂⁴×C₈×C₆₇	C₂	semidirect
4. C₂×#435×C₆₇	C₂	direct (N × H)
5. C₂²×C₄⋊C₈×C₆₇	C₂	semidirect
6. C₂²×C₂²⋊C₈×C₆₇	C₂	semidirect
7. C₂²×C₂²⋊C₈×C₆₇	C₂	semidirect
8. C₂²×#97×C₆₇	C₂	semidirect
13. C₂²×M₁₆×C₆₇	C₂²	semidirect
19. C₂³×C₈×C₆₇	C₂²	semidirect
26. #435×C₆₇	C₂²	direct (N × H)
27. C₂×C₄⋊C₈×C₆₇	C₂²	semidirect
28. C₂×C₂²⋊C₈×C₆₇	C₂²	semidirect
29. C₂×C₂²⋊C₈×C₆₇	C₂²	semidirect
30. C₂×#97×C₆₇	C₂²	semidirect
49. C₂×M₁₆×C₆₇	C₂³	semidirect
54. C₂²×C₈×C₆₇	D₄	semidirect
59. C₂²×C₈×C₆₇	C₂³	semidirect
67. C₄⋊C₈×C₆₇	C₂³	semidirect
68. C₂²⋊C₈×C₆₇	C₂³	semidirect
69. C₂²⋊C₈×C₆₇	C₂³	semidirect
70. #97×C₆₇	C₂³	semidirect
76. C₂⁴×C₆₇	M₁₆	semidirect
109. C₂×C₈×C₆₇	C₂×D₄	semidirect
128. C₂³×C₆₇	C₂×M₁₆	semidirect
156. C₈×C₆₇	C₂²×D₄	semidirect
164. C₂²×C₆₇	#435	direct (N × H)
167. C₂²×C₆₇	C₂²×M₁₆	semidirect
177. C₂²×#435	C₆₇	direct (N × H)
180. C₂×C₆₇	C₂×#435	direct (N × H)
184. C₂³×M₁₆	C₂×C₆₇	semidirect
185. C₂⁴×C₈	C₂×C₆₇	semidirect
187. C₂×#435	C₂×C₆₇	direct (N × H)
188. C₂²×C₄⋊C₈	C₂×C₆₇	semidirect
189. C₂²×C₂²⋊C₈	C₂×C₆₇	semidirect
190. C₂²×C₂²⋊C₈	C₂×C₆₇	semidirect
191. C₂²×#97	C₂×C₆₇	semidirect
192. C₆₇	C₂²×#435	direct (N × H)
197. C₂²×M₁₆	C₂²×C₆₇	semidirect
203. C₂³×C₈	C₂²×C₆₇	semidirect
210. #435	C₂²×C₆₇	direct (N × H)
211. C₂×C₄⋊C₈	C₂²×C₆₇	semidirect
212. C₂×C₂²⋊C₈	C₂²×C₆₇	semidirect
213. C₂×C₂²⋊C₈	C₂²×C₆₇	semidirect
214. C₂×#97	C₂²×C₆₇	semidirect
233. C₂×M₁₆	C₂³×C₆₇	semidirect
238. C₂²×C₈	D₄×C₆₇	semidirect
243. C₂²×C₈	C₂³×C₆₇	semidirect
251. C₄⋊C₈	C₂³×C₆₇	semidirect
252. C₂²⋊C₈	C₂³×C₆₇	semidirect
253. C₂²⋊C₈	C₂³×C₆₇	semidirect
254. #97	C₂³×C₆₇	semidirect
260. C₂⁴	M₁₆×C₆₇	semidirect
293. C₂×C₈	C₂×D₄×C₆₇	semidirect
312. C₂³	C₂×M₁₆×C₆₇	semidirect
340. C₈	C₂²×D₄×C₆₇	semidirect
348. C₂²	#435×C₆₇	direct (N × H)
351. C₂²	C₂²×M₁₆×C₆₇	semidirect
363. C₂	C₂×#435×C₆₇	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×M₁₆×C₆₇	2
C₂⁴×C₈×C₆₇	2
C₂²×C₄×D₄×C₆₇	2
C₂×#435×C₆₇	2
C₂²×C₄⋊C₈×C₆₇	2
C₂²×C₂²⋊C₈×C₆₇	2
C₂²×#97×C₆₇	2
C₂²×#435	67

Subgroups — C22×#435×C67 #30739382

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#435×C₆₇ #30739382