Subgroups — C₂×C₆₇×#2932 #30739387

Order 17152.

2806 conjugacy classes of subgroups.

The subgroup lattice has 344 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×#2932	C₂	1	16	yes	maximal, direct product factor
4	C₂×#435×C₆₇	C₂	1	8	yes	maximal, complemented
5	C₂×#423×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#408×C₆₇	C₂	1	2	yes	maximal, complemented
7	C₂²×#97×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#41×C₆₇	C₂²	1	2	yes	—
9	C₂×#131×C₆₇	—	2	16	no	—
10	C₂×#131×C₆₇	C₂²	1	16	yes	complemented
11	C₂²×M₁₆×C₆₇	C₂²	1	2	yes	—
12	C₂²×M₁₆×C₆₇	C₂²	1	4	yes	—
13	C₂³×C₈×C₆₇	C₂²	1	4	yes	—
14	C₂³×C₈×C₆₇	C₂²	1	1	yes	characteristic
15	C₂³×C₈×C₆₇	C₂²	1	1	yes	characteristic
16	#532×C₆₇	C₄	1	8	yes	—
17	#532×C₆₇	C₂²	1	8	yes	—
18	C₂×C₄⋊Q₈×C₆₇	C₄	1	1	yes	characteristic
19	C₂×#127×C₆₇	C₄	1	1	yes	characteristic
20	C₂×#124×C₆₇	C₄	1	2	yes	—
21	C₂×#121×C₆₇	C₄	1	4	yes	—
22	C₂×C₄×D₄×C₆₇	C₂²	1	4	yes	—
23	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
24	#435×C₆₇	C₂²	1	64	yes	complemented
25	#423×C₆₇	C₂²	1	8	yes	complemented
26	C₂×C₄⋊C₈×C₆₇	C₂²	1	4	yes	—
27	#408×C₆₇	C₂²	1	16	yes	complemented
28	C₂×C₂²⋊C₈×C₆₇	C₂²	1	8	yes	—
29	C₂×#97×C₆₇	C₂²	1	4	yes	—
30	C₂×#97×C₆₇	C₂²	1	8	yes	complemented
31	C₂×#41×C₆₇	—	2	8	no	—
32	C₂×#41×C₆₇	—	2	8	no	—
33	C₂×#41×C₆₇	C₂×C₄	1	8	yes	—
34	C₂×#41×C₆₇	C₂³	1	8	yes	—
35	C₂²×Q₈×C₆₇	C₂×C₄	1	2	yes	—
36	C₂²×D₄×C₆₇	C₂×C₄	1	4	yes	—
37	C₂²×D₄×C₆₇	C₂×C₄	1	2	yes	—
38	C₂²×D₄×C₆₇	C₂×C₄	1	4	yes	—
39	C₂³×C₄×C₆₇	C₂×C₄	1	2	yes	—
40	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
41	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
42	#131×C₆₇	—	2	64	no	—
43	C₂×M₁₆×C₆₇	—	2	8	no	—
44	C₂×M₁₆×C₆₇	—	2	16	no	—
45	C₂×M₁₆×C₆₇	C₂³	1	8	yes	—
46	C₂×M₁₆×C₆₇	C₂³	1	16	yes	—
47	C₂²×C₈×C₆₇	—	2	4	no	—
48	C₂²×C₈×C₆₇	—	2	16	no	—
49	C₂²×C₈×C₆₇	D₄	1	8	yes	complemented
50	C₂²×C₈×C₆₇	C₂³	1	16	yes	—
51	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
52	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
53	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
54	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
55	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
56	C₄⋊Q₈×C₆₇	C₂×C₄	1	8	yes	—
57	#127×C₆₇	C₂×C₄	1	8	yes	—
58	#124×C₆₇	C₂×C₄	1	16	yes	—
59	#121×C₆₇	C₂×C₄	1	32	yes	—
60	C₄×D₄×C₆₇	C₂×C₄	1	16	yes	—
61	C₄×D₄×C₆₇	C₂³	1	16	yes	—
62	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	4	yes	—
63	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	8	yes	—
64	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄²×C₆₇	C₂×C₄	1	4	yes	—
67	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
68	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
69	C₄⋊C₈×C₆₇	C₂³	1	16	yes	—
70	C₂²⋊C₈×C₆₇	C₂³	1	32	yes	—
71	#97×C₆₇	C₂³	1	16	yes	—
72	C₂⁴×C₆₇	C₂²×C₄	1	4	yes	—
73	C₂⁴×C₆₇	C₂²×C₄	1	1	yes	characteristic
74	#41×C₆₇	—	2	32	no	—
75	#41×C₆₇	—	2	16	no	—
76	#41×C₆₇	—	2	16	no	—
77	C₂×Q₈×C₆₇	—	2	8	no	—
78	C₂×Q₈×C₆₇	C₂²×C₄	1	8	yes	—
79	C₂×D₄×C₆₇	—	2	16	no	—
80	C₂×D₄×C₆₇	—	2	8	no	—
81	C₂×D₄×C₆₇	—	4	8	no	—
82	C₂×D₄×C₆₇	C₂²×C₄	1	16	yes	—
83	C₂×D₄×C₆₇	C₂²×C₄	1	8	yes	—
84	C₂×D₄×C₆₇	C₂²×C₄	1	16	yes	—
85	C₂²×C₄×C₆₇	—	2	8	no	—
86	C₂²×C₄×C₆₇	—	2	8	no	—
87	C₂²×C₄×C₆₇	—	4	4	no	—
88	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
89	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
90	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
91	C₂²×C₄×C₆₇	C₂²×C₄	1	8	yes	—
92	C₂²×C₄×C₆₇	C₂²×C₄	1	8	yes	—
93	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
94	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
95	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
96	C₂²×C₄×C₆₇	#41	1	4	yes	—
97	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
98	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
99	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
100	M₁₆×C₆₇	—	2	16	no	—
101	M₁₆×C₆₇	—	2	32	no	—
102	C₂×C₈×C₆₇	—	2	8	no	—
103	C₂×C₈×C₆₇	—	2	4	no	—
104	C₂×C₈×C₆₇	—	2	8	no	—
105	C₂×C₈×C₆₇	—	2	32	no	—
106	C₂×C₈×C₆₇	C₂×D₄	1	8	yes	—
107	C₂×C₈×C₆₇	C₂×D₄	1	16	yes	complemented
108	C₂×C₈×C₆₇	C₂⁴	1	8	yes	—
109	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
110	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
111	C₄⋊C₄×C₆₇	C₂²×C₄	1	16	yes	—
112	C₂²⋊C₄×C₆₇	C₂²×C₄	1	32	yes	—
113	C₄²×C₆₇	C₂²×C₄	1	4	yes	—
114	C₄²×C₆₇	C₂²×C₄	1	4	yes	—
115	C₄²×C₆₇	C₂²×C₄	1	4	yes	—
116	C₄²×C₆₇	C₂⁴	1	4	yes	—
117	C₂³×C₆₇	—	2	4	no	—
118	C₂³×C₆₇	—	2	8	no	—
119	C₂³×C₆₇	—	2	16	no	—
120	C₂³×C₆₇	C₄×D₄	1	4	yes	—
121	C₂³×C₆₇	C₂³×C₄	1	8	yes	—
122	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
123	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
124	Q₈×C₆₇	—	2	16	no	—
125	D₄×C₆₇	—	2	32	no	—
126	D₄×C₆₇	—	2	16	no	—
127	D₄×C₆₇	—	4	16	no	—
128	C₂×C₄×C₆₇	—	2	8	no	—
129	C₂×C₄×C₆₇	—	2	4	no	—
130	C₂×C₄×C₆₇	—	2	4	no	—
131	C₂×C₄×C₆₇	—	2	16	no	—
132	C₂×C₄×C₆₇	—	2	8	no	—
133	C₂×C₄×C₆₇	—	2	8	no	—
134	C₂×C₄×C₆₇	—	4	8	no	—
135	C₂×C₄×C₆₇	C₄×D₄	1	4	yes	—
136	C₂×C₄×C₆₇	C₄×D₄	1	8	yes	—
137	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
138	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
139	C₂×C₄×C₆₇	C₂³×C₄	1	8	yes	—
140	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
141	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
142	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
143	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
144	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
145	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
146	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
147	C₈×C₆₇	—	2	8	no	—
148	C₈×C₆₇	—	2	4	no	—
149	C₈×C₆₇	C₂²×D₄	1	8	yes	—
150	C₂²×C₆₇	—	2	8	no	—
151	C₂²×C₆₇	—	2	4	no	—
152	C₂²×C₆₇	—	2	8	no	—
153	C₂²×C₆₇	—	2	16	no	—
154	C₂²×C₆₇	—	4	16	no	—
155	C₂²×C₆₇	C₂×C₄×D₄	1	4	yes	—
156	C₂²×C₆₇	C₂×C₄×D₄	1	2	yes	—
157	C₂²×C₆₇	#568	1	4	yes	—
158	C₂²×C₆₇	C₂⁴×C₄	1	1	yes	characteristic
159	C₄×C₆₇	—	2	8	no	—
160	C₄×C₆₇	—	2	4	no	—
161	C₄×C₆₇	—	2	4	no	—
162	C₄×C₆₇	C₂×C₄×D₄	1	2	yes	—
163	C₄×C₆₇	C₂×C₄×D₄	1	4	yes	—
164	C₄×C₆₇	C₂³×D₄	1	1	yes	characteristic
165	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
166	C₂×#2932	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
167	C₂×C₆₇	—	2	4	no	—
168	C₂×C₆₇	—	4	8	no	—
169	C₂×C₆₇	#2932	1	4	yes	direct product factor
170	C₂×C₆₇	C₂²×C₄×D₄	1	1	yes	characteristic
171	C₂×C₆₇	C₂×#568	1	2	yes	—
172	C₂²×#131	C₂×C₆₇	1	2	yes	complemented
173	C₂×#532	C₂×C₆₇	1	1	yes	characteristic
174	#2932	C₂×C₆₇	1	16	yes	direct product factor
175	C₂×#435	C₂×C₆₇	1	8	yes	complemented
176	C₂×#423	C₂×C₆₇	1	1	yes	characteristic, complemented
177	C₂×#408	C₂×C₆₇	1	2	yes	complemented
178	C₂²×#97	C₂×C₆₇	1	1	yes	characteristic, complemented
179	C₆₇	C₂×#2932	1	1	yes	characteristic, direct product factor, Sylow
180	C₂²×#41	C₂²×C₆₇	1	2	yes	—
181	C₂×#131	—	2	16	no	—
182	C₂×#131	C₂²×C₆₇	1	16	yes	complemented
183	C₂²×M₁₆	C₂²×C₆₇	1	2	yes	—
184	C₂²×M₁₆	C₂²×C₆₇	1	4	yes	—
185	C₂³×C₈	C₂²×C₆₇	1	1	yes	characteristic
186	C₂³×C₈	C₂²×C₆₇	1	4	yes	—
187	C₂³×C₈	C₂²×C₆₇	1	1	yes	characteristic
188	#532	C₄×C₆₇	1	8	yes	—
189	#532	C₂²×C₆₇	1	8	yes	—
190	C₂×C₄⋊Q₈	C₄×C₆₇	1	1	yes	characteristic
191	C₂×#127	C₄×C₆₇	1	1	yes	characteristic
192	C₂×#124	C₄×C₆₇	1	2	yes	—
193	C₂×#121	C₄×C₆₇	1	4	yes	—
194	C₂×C₄×D₄	C₂²×C₆₇	1	4	yes	—
195	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
196	#435	C₂²×C₆₇	1	64	yes	complemented
197	#423	C₂²×C₆₇	1	8	yes	complemented
198	C₂×C₄⋊C₈	C₂²×C₆₇	1	4	yes	—
199	#408	C₂²×C₆₇	1	16	yes	complemented
200	C₂×C₂²⋊C₈	C₂²×C₆₇	1	8	yes	—
201	C₂×#97	C₂²×C₆₇	1	4	yes	—
202	C₂×#97	C₂²×C₆₇	1	8	yes	complemented
203	C₂×#41	—	2	8	no	—
204	C₂×#41	—	2	8	no	—
205	C₂×#41	C₂×C₄×C₆₇	1	8	yes	—
206	C₂×#41	C₂³×C₆₇	1	8	yes	—
207	C₂²×Q₈	C₂×C₄×C₆₇	1	2	yes	—
208	C₂²×D₄	C₂×C₄×C₆₇	1	4	yes	—
209	C₂²×D₄	C₂×C₄×C₆₇	1	2	yes	—
210	C₂²×D₄	C₂×C₄×C₆₇	1	4	yes	—
211	C₂³×C₄	C₂×C₄×C₆₇	1	2	yes	—
212	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
213	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
214	#131	—	2	64	no	—
215	C₂×M₁₆	—	2	8	no	—
216	C₂×M₁₆	—	2	16	no	—
217	C₂×M₁₆	C₂³×C₆₇	1	8	yes	—
218	C₂×M₁₆	C₂³×C₆₇	1	16	yes	—
219	C₂²×C₈	—	2	4	no	—
220	C₂²×C₈	—	2	16	no	—
221	C₂²×C₈	D₄×C₆₇	1	8	yes	complemented
222	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
223	C₂²×C₈	C₂³×C₆₇	1	16	yes	—
224	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
225	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
226	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
227	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
228	C₄⋊Q₈	C₂×C₄×C₆₇	1	8	yes	—
229	#127	C₂×C₄×C₆₇	1	8	yes	—
230	#124	C₂×C₄×C₆₇	1	16	yes	—
231	#121	C₂×C₄×C₆₇	1	32	yes	—
232	C₄×D₄	C₂×C₄×C₆₇	1	16	yes	—
233	C₄×D₄	C₂³×C₆₇	1	16	yes	—
234	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	4	yes	—
235	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	8	yes	—
236	C₂×C₄²	C₂×C₄×C₆₇	1	1	yes	characteristic
237	C₂×C₄²	C₂×C₄×C₆₇	1	1	yes	characteristic
238	C₂×C₄²	C₂×C₄×C₆₇	1	4	yes	—
239	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
240	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
241	C₄⋊C₈	C₂³×C₆₇	1	16	yes	—
242	C₂²⋊C₈	C₂³×C₆₇	1	32	yes	—
243	#97	C₂³×C₆₇	1	16	yes	—
244	C₂⁴	C₂²×C₄×C₆₇	1	4	yes	—
245	C₂⁴	C₂²×C₄×C₆₇	1	1	yes	characteristic
246	#41	—	2	32	no	—
247	#41	—	2	16	no	—
248	#41	—	2	16	no	—
249	C₂×Q₈	—	2	8	no	—
250	C₂×Q₈	C₂²×C₄×C₆₇	1	8	yes	—
251	C₂×D₄	—	2	16	no	—
252	C₂×D₄	—	2	8	no	—
253	C₂×D₄	—	4	8	no	—
254	C₂×D₄	C₂²×C₄×C₆₇	1	16	yes	—
255	C₂×D₄	C₂²×C₄×C₆₇	1	8	yes	—
256	C₂×D₄	C₂²×C₄×C₆₇	1	16	yes	—
257	C₂²×C₄	—	2	8	no	—
258	C₂²×C₄	—	2	8	no	—
259	C₂²×C₄	—	4	4	no	—
260	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
261	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
262	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
263	C₂²×C₄	C₂²×C₄×C₆₇	1	8	yes	—
264	C₂²×C₄	C₂²×C₄×C₆₇	1	8	yes	—
265	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
266	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
267	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
268	C₂²×C₄	#41×C₆₇	1	4	yes	—
269	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
270	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
271	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
272	M₁₆	—	2	16	no	—
273	M₁₆	—	2	32	no	—
274	C₂×C₈	—	2	8	no	—
275	C₂×C₈	—	2	4	no	—
276	C₂×C₈	—	2	8	no	—
277	C₂×C₈	—	2	32	no	—
278	C₂×C₈	C₂×D₄×C₆₇	1	8	yes	—
279	C₂×C₈	C₂×D₄×C₆₇	1	16	yes	complemented
280	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
281	C₂×C₈	C₂⁴×C₆₇	1	8	yes	—
282	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
283	C₄⋊C₄	C₂²×C₄×C₆₇	1	16	yes	—
284	C₂²⋊C₄	C₂²×C₄×C₆₇	1	32	yes	—
285	C₄²	C₂²×C₄×C₆₇	1	4	yes	—
286	C₄²	C₂²×C₄×C₆₇	1	4	yes	—
287	C₄²	C₂²×C₄×C₆₇	1	4	yes	—
288	C₄²	C₂⁴×C₆₇	1	4	yes	—
289	C₂³	—	2	4	no	—
290	C₂³	—	2	8	no	—
291	C₂³	—	2	16	no	—
292	C₂³	C₄×D₄×C₆₇	1	4	yes	—
293	C₂³	C₂³×C₄×C₆₇	1	8	yes	—
294	C₂³	C₂³×C₄×C₆₇	1	2	yes	—
295	C₂³	C₂³×C₄×C₆₇	1	1	yes	characteristic
296	Q₈	—	2	16	no	—
297	D₄	—	2	32	no	—
298	D₄	—	2	16	no	—
299	D₄	—	4	16	no	—
300	C₂×C₄	—	2	8	no	—
301	C₂×C₄	—	2	4	no	—
302	C₂×C₄	—	2	4	no	—
303	C₂×C₄	—	2	16	no	—
304	C₂×C₄	—	2	8	no	—
305	C₂×C₄	—	2	8	no	—
306	C₂×C₄	—	4	8	no	—
307	C₂×C₄	C₄×D₄×C₆₇	1	4	yes	—
308	C₂×C₄	C₄×D₄×C₆₇	1	8	yes	—
309	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
310	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
311	C₂×C₄	C₂³×C₄×C₆₇	1	8	yes	—
312	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
313	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
314	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
315	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
316	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
317	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
318	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
319	C₈	—	2	8	no	—
320	C₈	—	2	4	no	—
321	C₈	C₂²×D₄×C₆₇	1	8	yes	—
322	C₂²	—	2	4	no	—
323	C₂²	—	2	8	no	—
324	C₂²	—	2	16	no	—
325	C₂²	—	2	8	no	—
326	C₂²	—	4	16	no	—
327	C₂²	C₂×C₄×D₄×C₆₇	1	4	yes	—
328	C₂²	C₂×C₄×D₄×C₆₇	1	2	yes	—
329	C₂²	#568×C₆₇	1	4	yes	—
330	C₂²	C₂⁴×C₄×C₆₇	1	1	yes	characteristic
331	C₄	—	2	4	no	—
332	C₄	—	2	4	no	—
333	C₄	—	2	8	no	—
334	C₄	C₂×C₄×D₄×C₆₇	1	2	yes	—
335	C₄	C₂×C₄×D₄×C₆₇	1	4	yes	—
336	C₄	C₂³×D₄×C₆₇	1	1	yes	characteristic
337	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
338	C₂	—	2	4	no	—
339	C₂	—	4	8	no	—
340	C₂	C₆₇×#2932	1	4	yes	direct product factor
341	C₂	C₂²×C₄×D₄×C₆₇	1	1	yes	characteristic
342	C₂	C₂×#568×C₆₇	1	2	yes	—

	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×#2932	C₂	direct (N × H)
4. C₂×#435×C₆₇	C₂	semidirect
5. C₂×#423×C₆₇	C₂	semidirect
6. C₂×#408×C₆₇	C₂	semidirect
7. C₂²×#97×C₆₇	C₂	semidirect
10. C₂×#131×C₆₇	C₂²	semidirect
24. #435×C₆₇	C₂²	semidirect
25. #423×C₆₇	C₂²	semidirect
27. #408×C₆₇	C₂²	semidirect
30. C₂×#97×C₆₇	C₂²	semidirect
49. C₂²×C₈×C₆₇	D₄	semidirect
107. C₂×C₈×C₆₇	C₂×D₄	semidirect
166. C₂×#2932	C₆₇	direct (N × H)
169. C₂×C₆₇	#2932	direct (N × H)
172. C₂²×#131	C₂×C₆₇	semidirect
174. #2932	C₂×C₆₇	direct (N × H)
175. C₂×#435	C₂×C₆₇	semidirect
176. C₂×#423	C₂×C₆₇	semidirect
177. C₂×#408	C₂×C₆₇	semidirect
178. C₂²×#97	C₂×C₆₇	semidirect
179. C₆₇	C₂×#2932	direct (N × H)
182. C₂×#131	C₂²×C₆₇	semidirect
196. #435	C₂²×C₆₇	semidirect
197. #423	C₂²×C₆₇	semidirect
199. #408	C₂²×C₆₇	semidirect
202. C₂×#97	C₂²×C₆₇	semidirect
221. C₂²×C₈	D₄×C₆₇	semidirect
279. C₂×C₈	C₂×D₄×C₆₇	semidirect
340. C₂	C₆₇×#2932	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×#2932	2
C₂×#435×C₆₇	2
C₂×#423×C₆₇	2
C₂×#408×C₆₇	2
C₂²×#97×C₆₇	2
C₂×#2932	67

Subgroups — C2×C67×#2932 #30739387

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₇×#2932 #30739387