Subgroups — C₂×C₆₇×#2935 #30739390

Order 17152.

2850 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#131×C₆₇	C₂	1	2	yes	maximal, complemented
2	C₂×#532×C₆₇	C₂	1	1	yes	maximal, characteristic
3	C₆₇×#2935	C₂	1	16	yes	maximal, direct product factor
4	C₂×#436×C₆₇	C₂	1	2	yes	maximal, complemented
5	C₂×#435×C₆₇	C₂	1	4	yes	maximal, complemented
6	C₂×C₈×D₄×C₆₇	C₂	1	2	yes	maximal, complemented
7	C₂²×C₄⋊C₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#408×C₆₇	C₂	1	2	yes	maximal, complemented
9	C₂×C₄×M₁₆×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#41×C₆₇	C₂²	1	2	yes	—
11	C₂×#131×C₆₇	—	2	16	no	—
12	C₂×#131×C₆₇	C₂²	1	16	yes	complemented
13	C₂²×M₁₆×C₆₇	C₂²	1	4	yes	—
14	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
15	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
16	C₂³×C₈×C₆₇	C₂²	1	2	yes	—
17	C₂³×C₈×C₆₇	C₂²	1	4	yes	—
18	#532×C₆₇	C₄	1	8	yes	—
19	#532×C₆₇	C₂²	1	8	yes	—
20	C₂×C₄⋊Q₈×C₆₇	C₄	1	1	yes	characteristic
21	C₂×#127×C₆₇	C₄	1	1	yes	characteristic
22	C₂×#124×C₆₇	C₄	1	2	yes	—
23	C₂×#121×C₆₇	C₄	1	2	yes	—
24	C₂×#121×C₆₇	C₄	1	2	yes	—
25	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
26	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
27	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
28	#436×C₆₇	C₂²	1	16	yes	complemented
29	#435×C₆₇	C₂²	1	32	yes	complemented
30	C₈×D₄×C₆₇	C₂²	1	16	yes	complemented
31	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
32	C₂×C₄⋊C₈×C₆₇	C₂²	1	2	yes	—
33	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
34	C₂×C₄⋊C₈×C₆₇	C₂²	1	8	yes	complemented
35	#408×C₆₇	C₂²	1	16	yes	complemented
36	C₂×C₂²⋊C₈×C₆₇	C₂²	1	4	yes	—
37	C₂×C₂²⋊C₈×C₆₇	C₂²	1	4	yes	—
38	C₄×M₁₆×C₆₇	C₂²	1	8	yes	complemented
39	C₂×#97×C₆₇	C₂²	1	2	yes	—
40	C₂×C₄×C₈×C₆₇	C₂²	1	2	yes	—
41	C₂×#41×C₆₇	—	2	8	no	—
42	C₂×#41×C₆₇	—	2	8	no	—
43	C₂×#41×C₆₇	C₂×C₄	1	8	yes	—
44	C₂×#41×C₆₇	C₂³	1	8	yes	—
45	C₂²×Q₈×C₆₇	C₂×C₄	1	2	yes	—
46	C₂²×D₄×C₆₇	C₂×C₄	1	2	yes	—
47	C₂²×D₄×C₆₇	C₂×C₄	1	4	yes	—
48	C₂²×D₄×C₆₇	C₂×C₄	1	2	yes	—
49	C₂²×D₄×C₆₇	C₂×C₄	1	2	yes	—
50	C₂³×C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
51	C₂³×C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
52	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
53	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
54	#131×C₆₇	—	2	64	no	—
55	C₂×M₁₆×C₆₇	—	2	4	no	—
56	C₂×M₁₆×C₆₇	—	2	16	no	—
57	C₂×M₁₆×C₆₇	D₄	1	8	yes	complemented
58	C₂×M₁₆×C₆₇	C₂³	1	16	yes	—
59	C₂×M₁₆×C₆₇	C₂³	1	4	yes	—
60	C₂×M₁₆×C₆₇	C₂³	1	4	yes	—
61	C₂²×C₈×C₆₇	—	2	8	no	—
62	C₂²×C₈×C₆₇	—	2	16	no	—
63	C₂²×C₈×C₆₇	C₂³	1	8	yes	—
64	C₂²×C₈×C₆₇	C₂³	1	16	yes	—
65	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
66	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
67	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
68	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
69	C₄⋊Q₈×C₆₇	C₂×C₄	1	8	yes	—
70	#127×C₆₇	C₂×C₄	1	8	yes	—
71	#124×C₆₇	C₂×C₄	1	16	yes	—
72	#121×C₆₇	C₂×C₄	1	16	yes	—
73	#121×C₆₇	C₂×C₄	1	16	yes	—
74	C₄×D₄×C₆₇	C₂×C₄	1	8	yes	—
75	C₄×D₄×C₆₇	C₂×C₄	1	8	yes	—
76	C₄×D₄×C₆₇	C₂³	1	8	yes	—
77	C₄×D₄×C₆₇	C₂³	1	8	yes	—
78	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
79	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
80	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	4	yes	—
81	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	4	yes	—
82	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
83	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
84	C₂×C₄²×C₆₇	C₂×C₄	1	4	yes	—
85	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
86	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
87	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
88	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
89	C₄⋊C₈×C₆₇	C₂³	1	8	yes	—
90	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
91	C₂²⋊C₈×C₆₇	C₂³	1	16	yes	—
92	C₂²⋊C₈×C₆₇	C₂³	1	16	yes	—
93	#97×C₆₇	C₂³	1	8	yes	—
94	C₄×C₈×C₆₇	C₂³	1	8	yes	—
95	C₂⁴×C₆₇	C₂²×C₄	1	4	yes	—
96	C₂⁴×C₆₇	C₂²×C₄	1	1	yes	characteristic
97	#41×C₆₇	—	2	32	no	—
98	#41×C₆₇	—	2	16	no	—
99	#41×C₆₇	—	2	16	no	—
100	C₂×Q₈×C₆₇	—	2	8	no	—
101	C₂×Q₈×C₆₇	C₂²×C₄	1	8	yes	—
102	C₂×D₄×C₆₇	—	2	16	no	—
103	C₂×D₄×C₆₇	—	2	8	no	—
104	C₂×D₄×C₆₇	—	2	8	no	—
105	C₂×D₄×C₆₇	—	4	4	no	—
106	C₂×D₄×C₆₇	C₂²×C₄	1	8	yes	—
107	C₂×D₄×C₆₇	C₂²×C₄	1	16	yes	—
108	C₂×D₄×C₆₇	C₂²×C₄	1	8	yes	—
109	C₂×D₄×C₆₇	C₂²×C₄	1	8	yes	—
110	C₂²×C₄×C₆₇	—	2	4	no	—
111	C₂²×C₄×C₆₇	—	2	8	no	—
112	C₂²×C₄×C₆₇	—	2	8	no	—
113	C₂²×C₄×C₆₇	—	4	2	no	—
114	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
115	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
116	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
117	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
118	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
119	C₂²×C₄×C₆₇	C₂²×C₄	1	8	yes	—
120	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
121	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
122	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
123	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
124	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
125	C₂²×C₄×C₆₇	#41	1	4	yes	—
126	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
127	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
128	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
129	M₁₆×C₆₇	—	2	8	no	—
130	M₁₆×C₆₇	—	2	32	no	—
131	M₁₆×C₆₇	C₂×D₄	1	16	yes	complemented
132	C₂×C₈×C₆₇	—	2	4	no	—
133	C₂×C₈×C₆₇	—	2	4	no	—
134	C₂×C₈×C₆₇	—	2	16	no	—
135	C₂×C₈×C₆₇	—	2	4	no	—
136	C₂×C₈×C₆₇	—	2	32	no	—
137	C₂×C₈×C₆₇	C₂×D₄	1	8	yes	—
138	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
139	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
140	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
141	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
142	C₄⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
143	C₄⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
144	C₂²⋊C₄×C₆₇	C₂²×C₄	1	16	yes	—
145	C₂²⋊C₄×C₆₇	C₂²×C₄	1	16	yes	—
146	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
147	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
148	C₄²×C₆₇	C₂²×C₄	1	4	yes	—
149	C₄²×C₆₇	C₂²×C₄	1	4	yes	—
150	C₄²×C₆₇	C₂⁴	1	2	yes	—
151	C₄²×C₆₇	C₂⁴	1	2	yes	—
152	C₂³×C₆₇	—	2	2	no	—
153	C₂³×C₆₇	—	2	2	no	—
154	C₂³×C₆₇	—	2	8	no	—
155	C₂³×C₆₇	—	2	8	no	—
156	C₂³×C₆₇	—	2	8	no	—
157	C₂³×C₆₇	C₄×D₄	1	4	yes	—
158	C₂³×C₆₇	C₂³×C₄	1	8	yes	—
159	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
160	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
161	Q₈×C₆₇	—	2	16	no	—
162	D₄×C₆₇	—	2	32	no	—
163	D₄×C₆₇	—	2	16	no	—
164	D₄×C₆₇	—	2	16	no	—
165	D₄×C₆₇	—	4	8	no	—
166	C₂×C₄×C₆₇	—	2	8	no	—
167	C₂×C₄×C₆₇	—	2	2	no	—
168	C₂×C₄×C₆₇	—	2	2	no	—
169	C₂×C₄×C₆₇	—	2	2	no	—
170	C₂×C₄×C₆₇	—	2	16	no	—
171	C₂×C₄×C₆₇	—	2	8	no	—
172	C₂×C₄×C₆₇	—	2	8	no	—
173	C₂×C₄×C₆₇	—	2	8	no	—
174	C₂×C₄×C₆₇	—	4	4	no	—
175	C₂×C₄×C₆₇	C₄×D₄	1	4	yes	—
176	C₂×C₄×C₆₇	C₄×D₄	1	8	yes	—
177	C₂×C₄×C₆₇	#131	1	4	yes	complemented
178	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
179	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
180	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
181	C₂×C₄×C₆₇	C₂³×C₄	1	8	yes	—
182	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
183	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
184	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
185	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
186	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
187	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
188	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
189	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
190	C₈×C₆₇	—	2	4	no	—
191	C₈×C₆₇	—	2	4	no	—
192	C₈×C₆₇	—	2	4	no	—
193	C₈×C₆₇	C₂²×D₄	1	8	yes	—
194	C₂²×C₆₇	—	2	8	no	—
195	C₂²×C₆₇	—	2	2	no	—
196	C₂²×C₆₇	—	2	2	no	—
197	C₂²×C₆₇	—	2	8	no	—
198	C₂²×C₆₇	—	2	8	no	—
199	C₂²×C₆₇	—	2	8	no	—
200	C₂²×C₆₇	—	4	16	no	—
201	C₂²×C₆₇	C₂×C₄×D₄	1	4	yes	—
202	C₂²×C₆₇	C₂×C₄×D₄	1	2	yes	—
203	C₂²×C₆₇	C₂×#131	1	2	yes	—
204	C₂²×C₆₇	#568	1	2	yes	—
205	C₂²×C₆₇	C₂⁴×C₄	1	1	yes	characteristic
206	C₄×C₆₇	—	2	8	no	—
207	C₄×C₆₇	—	2	2	no	—
208	C₄×C₆₇	—	2	2	no	—
209	C₄×C₆₇	—	2	2	no	—
210	C₄×C₆₇	C₂×C₄×D₄	1	2	yes	—
211	C₄×C₆₇	C₂×C₄×D₄	1	4	yes	—
212	C₄×C₆₇	C₂×#131	1	4	yes	complemented
213	C₄×C₆₇	C₂³×D₄	1	1	yes	characteristic
214	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
215	C₂×#2935	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
216	C₂×C₆₇	—	2	4	no	—
217	C₂×C₆₇	—	4	8	no	—
218	C₂×C₆₇	#2935	1	4	yes	direct product factor
219	C₂×C₆₇	C₂²×C₄×D₄	1	1	yes	characteristic
220	C₂×C₆₇	C₂²×#131	1	1	yes	characteristic
221	C₂×C₆₇	C₂×#568	1	1	yes	characteristic
222	C₂²×#131	C₂×C₆₇	1	2	yes	complemented
223	C₂×#532	C₂×C₆₇	1	1	yes	characteristic
224	#2935	C₂×C₆₇	1	16	yes	direct product factor
225	C₂×#436	C₂×C₆₇	1	2	yes	complemented
226	C₂×#435	C₂×C₆₇	1	4	yes	complemented
227	C₂×C₈×D₄	C₂×C₆₇	1	2	yes	complemented
228	C₂²×C₄⋊C₈	C₂×C₆₇	1	1	yes	characteristic, complemented
229	C₂×#408	C₂×C₆₇	1	2	yes	complemented
230	C₂×C₄×M₁₆	C₂×C₆₇	1	1	yes	characteristic, complemented
231	C₆₇	C₂×#2935	1	1	yes	characteristic, direct product factor, Sylow
232	C₂²×#41	C₂²×C₆₇	1	2	yes	—
233	C₂×#131	—	2	16	no	—
234	C₂×#131	C₂²×C₆₇	1	16	yes	complemented
235	C₂²×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
236	C₂²×M₁₆	C₂²×C₆₇	1	4	yes	—
237	C₂²×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
238	C₂³×C₈	C₂²×C₆₇	1	2	yes	—
239	C₂³×C₈	C₂²×C₆₇	1	4	yes	—
240	#532	C₄×C₆₇	1	8	yes	—
241	#532	C₂²×C₆₇	1	8	yes	—
242	C₂×C₄⋊Q₈	C₄×C₆₇	1	1	yes	characteristic
243	C₂×#127	C₄×C₆₇	1	1	yes	characteristic
244	C₂×#124	C₄×C₆₇	1	2	yes	—
245	C₂×#121	C₄×C₆₇	1	2	yes	—
246	C₂×#121	C₄×C₆₇	1	2	yes	—
247	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
248	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
249	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
250	#436	C₂²×C₆₇	1	16	yes	complemented
251	#435	C₂²×C₆₇	1	32	yes	complemented
252	C₈×D₄	C₂²×C₆₇	1	16	yes	complemented
253	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
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	8	yes	complemented
257	#408	C₂²×C₆₇	1	16	yes	complemented
258	C₂×C₂²⋊C₈	C₂²×C₆₇	1	4	yes	—
259	C₂×C₂²⋊C₈	C₂²×C₆₇	1	4	yes	—
260	C₄×M₁₆	C₂²×C₆₇	1	8	yes	complemented
261	C₂×#97	C₂²×C₆₇	1	2	yes	—
262	C₂×C₄×C₈	C₂²×C₆₇	1	2	yes	—
263	C₂×#41	—	2	8	no	—
264	C₂×#41	—	2	8	no	—
265	C₂×#41	C₂×C₄×C₆₇	1	8	yes	—
266	C₂×#41	C₂³×C₆₇	1	8	yes	—
267	C₂²×Q₈	C₂×C₄×C₆₇	1	2	yes	—
268	C₂²×D₄	C₂×C₄×C₆₇	1	2	yes	—
269	C₂²×D₄	C₂×C₄×C₆₇	1	4	yes	—
270	C₂²×D₄	C₂×C₄×C₆₇	1	2	yes	—
271	C₂²×D₄	C₂×C₄×C₆₇	1	2	yes	—
272	C₂³×C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
273	C₂³×C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
274	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
275	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
276	#131	—	2	64	no	—
277	C₂×M₁₆	—	2	4	no	—
278	C₂×M₁₆	—	2	16	no	—
279	C₂×M₁₆	D₄×C₆₇	1	8	yes	complemented
280	C₂×M₁₆	C₂³×C₆₇	1	16	yes	—
281	C₂×M₁₆	C₂³×C₆₇	1	4	yes	—
282	C₂×M₁₆	C₂³×C₆₇	1	4	yes	—
283	C₂²×C₈	—	2	8	no	—
284	C₂²×C₈	—	2	16	no	—
285	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
286	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
287	C₂²×C₈	C₂³×C₆₇	1	8	yes	—
288	C₂²×C₈	C₂³×C₆₇	1	16	yes	—
289	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
290	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
291	C₄⋊Q₈	C₂×C₄×C₆₇	1	8	yes	—
292	#127	C₂×C₄×C₆₇	1	8	yes	—
293	#124	C₂×C₄×C₆₇	1	16	yes	—
294	#121	C₂×C₄×C₆₇	1	16	yes	—
295	#121	C₂×C₄×C₆₇	1	16	yes	—
296	C₄×D₄	C₂×C₄×C₆₇	1	8	yes	—
297	C₄×D₄	C₂×C₄×C₆₇	1	8	yes	—
298	C₄×D₄	C₂³×C₆₇	1	8	yes	—
299	C₄×D₄	C₂³×C₆₇	1	8	yes	—
300	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	2	yes	—
301	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	2	yes	—
302	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	4	yes	—
303	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	4	yes	—
304	C₂×C₄²	C₂×C₄×C₆₇	1	1	yes	characteristic
305	C₂×C₄²	C₂×C₄×C₆₇	1	1	yes	characteristic
306	C₂×C₄²	C₂×C₄×C₆₇	1	4	yes	—
307	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
308	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
309	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
310	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
311	C₄⋊C₈	C₂³×C₆₇	1	8	yes	—
312	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
313	C₂²⋊C₈	C₂³×C₆₇	1	16	yes	—
314	C₂²⋊C₈	C₂³×C₆₇	1	16	yes	—
315	#97	C₂³×C₆₇	1	8	yes	—
316	C₄×C₈	C₂³×C₆₇	1	8	yes	—
317	C₂⁴	C₂²×C₄×C₆₇	1	4	yes	—
318	C₂⁴	C₂²×C₄×C₆₇	1	1	yes	characteristic
319	#41	—	2	32	no	—
320	#41	—	2	16	no	—
321	#41	—	2	16	no	—
322	C₂×Q₈	—	2	8	no	—
323	C₂×Q₈	C₂²×C₄×C₆₇	1	8	yes	—
324	C₂×D₄	—	2	16	no	—
325	C₂×D₄	—	2	8	no	—
326	C₂×D₄	—	2	8	no	—
327	C₂×D₄	—	4	4	no	—
328	C₂×D₄	C₂²×C₄×C₆₇	1	8	yes	—
329	C₂×D₄	C₂²×C₄×C₆₇	1	16	yes	—
330	C₂×D₄	C₂²×C₄×C₆₇	1	8	yes	—
331	C₂×D₄	C₂²×C₄×C₆₇	1	8	yes	—
332	C₂²×C₄	—	2	4	no	—
333	C₂²×C₄	—	2	8	no	—
334	C₂²×C₄	—	2	8	no	—
335	C₂²×C₄	—	4	2	no	—
336	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
337	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
338	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
339	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
340	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
341	C₂²×C₄	C₂²×C₄×C₆₇	1	8	yes	—
342	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
343	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
344	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
345	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
346	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
347	C₂²×C₄	#41×C₆₇	1	4	yes	—
348	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
349	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
350	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
351	M₁₆	—	2	8	no	—
352	M₁₆	—	2	32	no	—
353	M₁₆	C₂×D₄×C₆₇	1	16	yes	complemented
354	C₂×C₈	—	2	4	no	—
355	C₂×C₈	—	2	4	no	—
356	C₂×C₈	—	2	16	no	—
357	C₂×C₈	—	2	4	no	—
358	C₂×C₈	—	2	32	no	—
359	C₂×C₈	C₂×D₄×C₆₇	1	8	yes	—
360	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
361	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
362	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
363	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
364	C₄⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
365	C₄⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
366	C₂²⋊C₄	C₂²×C₄×C₆₇	1	16	yes	—
367	C₂²⋊C₄	C₂²×C₄×C₆₇	1	16	yes	—
368	C₄²	C₂²×C₄×C₆₇	1	2	yes	—
369	C₄²	C₂²×C₄×C₆₇	1	2	yes	—
370	C₄²	C₂²×C₄×C₆₇	1	4	yes	—
371	C₄²	C₂²×C₄×C₆₇	1	4	yes	—
372	C₄²	C₂⁴×C₆₇	1	2	yes	—
373	C₄²	C₂⁴×C₆₇	1	2	yes	—
374	C₂³	—	2	2	no	—
375	C₂³	—	2	2	no	—
376	C₂³	—	2	8	no	—
377	C₂³	—	2	8	no	—
378	C₂³	—	2	8	no	—
379	C₂³	C₄×D₄×C₆₇	1	4	yes	—
380	C₂³	C₂³×C₄×C₆₇	1	8	yes	—
381	C₂³	C₂³×C₄×C₆₇	1	2	yes	—
382	C₂³	C₂³×C₄×C₆₇	1	1	yes	characteristic
383	Q₈	—	2	16	no	—
384	D₄	—	2	32	no	—
385	D₄	—	2	16	no	—
386	D₄	—	2	16	no	—
387	D₄	—	4	8	no	—
388	C₂×C₄	—	2	8	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	16	no	—
393	C₂×C₄	—	2	8	no	—
394	C₂×C₄	—	2	8	no	—
395	C₂×C₄	—	2	8	no	—
396	C₂×C₄	—	4	4	no	—
397	C₂×C₄	C₄×D₄×C₆₇	1	4	yes	—
398	C₂×C₄	C₄×D₄×C₆₇	1	8	yes	—
399	C₂×C₄	#131×C₆₇	1	4	yes	complemented
400	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
401	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
402	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
403	C₂×C₄	C₂³×C₄×C₆₇	1	8	yes	—
404	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
405	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
406	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
407	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
408	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
409	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
410	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
411	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
412	C₈	—	2	4	no	—
413	C₈	—	2	4	no	—
414	C₈	—	2	4	no	—
415	C₈	C₂²×D₄×C₆₇	1	8	yes	—
416	C₂²	—	2	2	no	—
417	C₂²	—	2	2	no	—
418	C₂²	—	2	8	no	—
419	C₂²	—	2	8	no	—
420	C₂²	—	2	8	no	—
421	C₂²	—	2	8	no	—
422	C₂²	—	4	16	no	—
423	C₂²	C₂×C₄×D₄×C₆₇	1	4	yes	—
424	C₂²	C₂×C₄×D₄×C₆₇	1	2	yes	—
425	C₂²	C₂×#131×C₆₇	1	2	yes	—
426	C₂²	#568×C₆₇	1	2	yes	—
427	C₂²	C₂⁴×C₄×C₆₇	1	1	yes	characteristic
428	C₄	—	2	2	no	—
429	C₄	—	2	2	no	—
430	C₄	—	2	2	no	—
431	C₄	—	2	8	no	—
432	C₄	C₂×C₄×D₄×C₆₇	1	2	yes	—
433	C₄	C₂×C₄×D₄×C₆₇	1	4	yes	—
434	C₄	C₂×#131×C₆₇	1	4	yes	complemented
435	C₄	C₂³×D₄×C₆₇	1	1	yes	characteristic
436	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
437	C₂	—	2	4	no	—
438	C₂	—	4	8	no	—
439	C₂	C₆₇×#2935	1	4	yes	direct product factor
440	C₂	C₂²×C₄×D₄×C₆₇	1	1	yes	characteristic
441	C₂	C₂²×#131×C₆₇	1	1	yes	characteristic
442	C₂	C₂×#568×C₆₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₆₇	C₂⁴
commutator	C₂²	C₂⁴×C₄×C₆₇
Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
socle	C₂³×C₆₇	C₂³×C₄
prime radical	C₂×#532×C₆₇	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×#131×C₆₇	C₂	semidirect
3. C₆₇×#2935	C₂	direct (N × H)
4. C₂×#436×C₆₇	C₂	semidirect
5. C₂×#435×C₆₇	C₂	semidirect
6. C₂×C₈×D₄×C₆₇	C₂	semidirect
7. C₂²×C₄⋊C₈×C₆₇	C₂	semidirect
8. C₂×#408×C₆₇	C₂	semidirect
9. C₂×C₄×M₁₆×C₆₇	C₂	semidirect
12. C₂×#131×C₆₇	C₂²	semidirect
28. #436×C₆₇	C₂²	semidirect
29. #435×C₆₇	C₂²	semidirect
30. C₈×D₄×C₆₇	C₂²	semidirect
34. C₂×C₄⋊C₈×C₆₇	C₂²	semidirect
35. #408×C₆₇	C₂²	semidirect
38. C₄×M₁₆×C₆₇	C₂²	semidirect
57. C₂×M₁₆×C₆₇	D₄	semidirect
131. M₁₆×C₆₇	C₂×D₄	semidirect
177. C₂×C₄×C₆₇	#131	semidirect
212. C₄×C₆₇	C₂×#131	semidirect
215. C₂×#2935	C₆₇	direct (N × H)
218. C₂×C₆₇	#2935	direct (N × H)
222. C₂²×#131	C₂×C₆₇	semidirect
224. #2935	C₂×C₆₇	direct (N × H)
225. C₂×#436	C₂×C₆₇	semidirect
226. C₂×#435	C₂×C₆₇	semidirect
227. C₂×C₈×D₄	C₂×C₆₇	semidirect
228. C₂²×C₄⋊C₈	C₂×C₆₇	semidirect
229. C₂×#408	C₂×C₆₇	semidirect
230. C₂×C₄×M₁₆	C₂×C₆₇	semidirect
231. C₆₇	C₂×#2935	direct (N × H)
234. C₂×#131	C₂²×C₆₇	semidirect
250. #436	C₂²×C₆₇	semidirect
251. #435	C₂²×C₆₇	semidirect
252. C₈×D₄	C₂²×C₆₇	semidirect
256. C₂×C₄⋊C₈	C₂²×C₆₇	semidirect
257. #408	C₂²×C₆₇	semidirect
260. C₄×M₁₆	C₂²×C₆₇	semidirect
279. C₂×M₁₆	D₄×C₆₇	semidirect
353. M₁₆	C₂×D₄×C₆₇	semidirect
399. C₂×C₄	#131×C₆₇	semidirect
434. C₄	C₂×#131×C₆₇	semidirect
439. C₂	C₆₇×#2935	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×#131×C₆₇	2
C₂×#532×C₆₇	2
C₆₇×#2935	2
C₂×#436×C₆₇	2
C₂×#435×C₆₇	2
C₂×C₈×D₄×C₆₇	2
C₂²×C₄⋊C₈×C₆₇	2
C₂×#408×C₆₇	2
C₂×C₄×M₁₆×C₆₇	2
C₂×#2935	67

Subgroups — C2×C67×#2935 #30739390

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₇×#2935 #30739390