Subgroups — C₂×C₆₇×#2546 #30714179

Order 17152.

3094 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄⋊Q₈×C₆₇	C₂	1	2	yes	maximal
2	C₂²×C₄⋊Q₈×C₆₇	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₄×Q₈×C₆₇	C₂	1	1	yes	maximal, characteristic
4	C₆₇×#2546	C₂	1	16	yes	maximal, direct product factor
5	C₂×#398×C₆₇	C₂	1	4	yes	maximal
6	C₂×#391×C₆₇	C₂	1	2	yes	maximal
7	C₂×#389×C₆₇	C₂	1	4	yes	maximal
8	C₂×C₄×C₄⋊C₄×C₆₇	C₂	1	1	yes	maximal, characteristic
9	C₂³×Q₈×C₆₇	C₂²	1	2	yes	—
10	C₂³×Q₈×C₆₇	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊Q₈×C₆₇	—	2	16	no	—
12	C₂×C₄⋊Q₈×C₆₇	—	2	8	no	—
13	C₂×C₄⋊Q₈×C₆₇	C₂²	1	16	yes	—
14	C₂×C₄⋊Q₈×C₆₇	C₂²	1	8	yes	—
15	C₂×C₄×Q₈×C₆₇	—	2	8	no	—
16	C₂×C₄×Q₈×C₆₇	C₂²	1	8	yes	—
17	C₂²×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
18	C₂²×C₄⋊C₄×C₆₇	C₂²	1	8	yes	—
19	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
20	C₂²×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
21	C₂²×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
22	C₂²×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
23	C₂²×C₄²×C₆₇	C₂²	1	2	yes	—
24	C₂²×C₄²×C₆₇	C₂²	1	2	yes	—
25	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
26	#398×C₆₇	C₂²	1	32	yes	—
27	#391×C₆₇	C₂²	1	16	yes	—
28	#389×C₆₇	C₂²	1	32	yes	—
29	C₄×C₄⋊C₄×C₆₇	C₂²	1	8	yes	—
30	C₂×#95×C₆₇	C₂²	1	2	yes	—
31	C₂×#95×C₆₇	C₂²	1	8	yes	—
32	C₂²×Q₈×C₆₇	—	2	4	no	—
33	C₂²×Q₈×C₆₇	—	2	8	no	—
34	C₂²×Q₈×C₆₇	—	2	8	no	—
35	C₂²×Q₈×C₆₇	—	2	4	no	—
36	C₂²×Q₈×C₆₇	—	2	8	no	—
37	C₂²×Q₈×C₆₇	D₄	1	8	yes	—
38	C₂²×Q₈×C₆₇	C₂³	1	8	yes	—
39	C₂²×Q₈×C₆₇	C₂³	1	4	yes	—
40	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
41	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
42	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
43	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
44	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
45	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
47	C₄⋊Q₈×C₆₇	—	2	64	no	—
48	C₄⋊Q₈×C₆₇	—	2	32	no	—
49	C₄×Q₈×C₆₇	—	2	32	no	—
50	C₂×C₄⋊C₄×C₆₇	—	2	8	no	—
51	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
52	C₂×C₄⋊C₄×C₆₇	—	2	32	no	—
53	C₂×C₄⋊C₄×C₆₇	—	2	8	no	—
54	C₂×C₄⋊C₄×C₆₇	—	2	8	no	—
55	C₂×C₄⋊C₄×C₆₇	Q₈	1	16	yes	complemented
56	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
57	C₂×C₄⋊C₄×C₆₇	C₂³	1	8	yes	—
58	C₂×C₄⋊C₄×C₆₇	C₂³	1	8	yes	—
59	C₂×C₄⋊C₄×C₆₇	C₂³	1	32	yes	—
60	C₂×C₄⋊C₄×C₆₇	C₂³	1	8	yes	—
61	C₂×C₄⋊C₄×C₆₇	C₂³	1	8	yes	—
62	C₂×C₄²×C₆₇	—	2	8	no	—
63	C₂×C₄²×C₆₇	—	2	8	no	—
64	C₂×C₄²×C₆₇	D₄	1	8	yes	—
65	C₂×C₄²×C₆₇	C₂³	1	8	yes	—
66	C₂×C₄²×C₆₇	C₂³	1	8	yes	—
67	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
68	#95×C₆₇	C₂³	1	8	yes	—
69	#95×C₆₇	C₂³	1	32	yes	—
70	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
71	C₂×Q₈×C₆₇	—	2	32	no	—
72	C₂×Q₈×C₆₇	—	2	8	no	—
73	C₂×Q₈×C₆₇	—	2	16	no	—
74	C₂×Q₈×C₆₇	—	2	16	no	—
75	C₂×Q₈×C₆₇	—	2	8	no	—
76	C₂×Q₈×C₆₇	—	2	16	no	—
77	C₂×Q₈×C₆₇	—	4	32	no	—
78	C₂×Q₈×C₆₇	C₂×D₄	1	16	yes	—
79	C₂²×C₄×C₆₇	—	2	8	no	—
80	C₂²×C₄×C₆₇	—	2	4	no	—
81	C₂²×C₄×C₆₇	—	2	4	no	—
82	C₂²×C₄×C₆₇	—	2	4	no	—
83	C₂²×C₄×C₆₇	—	2	8	no	—
84	C₂²×C₄×C₆₇	—	2	4	no	—
85	C₂²×C₄×C₆₇	—	2	8	no	—
86	C₂²×C₄×C₆₇	—	2	8	no	—
87	C₂²×C₄×C₆₇	—	2	8	no	—
88	C₂²×C₄×C₆₇	—	2	8	no	—
89	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
90	C₂²×C₄×C₆₇	C₂×D₄	1	8	yes	—
91	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
92	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
93	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
94	C₂²×C₄×C₆₇	C₂×Q₈	1	16	yes	—
95	C₂²×C₄×C₆₇	C₂×Q₈	1	8	yes	—
96	C₂²×C₄×C₆₇	#41	1	4	yes	—
97	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
98	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
99	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
100	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
101	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
102	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
103	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
104	C₄⋊C₄×C₆₇	—	2	16	no	—
105	C₄⋊C₄×C₆₇	—	2	8	no	—
106	C₄⋊C₄×C₆₇	—	2	64	no	—
107	C₄⋊C₄×C₆₇	—	2	16	no	—
108	C₄⋊C₄×C₆₇	—	2	16	no	—
109	C₄⋊C₄×C₆₇	C₂×Q₈	1	32	yes	complemented
110	C₄²×C₆₇	—	2	16	no	—
111	C₄²×C₆₇	—	2	16	no	—
112	C₄²×C₆₇	C₂×D₄	1	16	yes	—
113	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
114	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
115	C₂³×C₆₇	C₂²×Q₈	1	4	yes	—
116	C₂³×C₆₇	C₂×#41	1	2	yes	—
117	C₂³×C₆₇	2₋¹⁺⁴	1	4	yes	—
118	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
119	Q₈×C₆₇	—	2	32	no	—
120	Q₈×C₆₇	—	4	32	no	—
121	C₂×C₄×C₆₇	—	2	16	no	—
122	C₂×C₄×C₆₇	—	2	8	no	—
123	C₂×C₄×C₆₇	—	2	32	no	—
124	C₂×C₄×C₆₇	—	2	8	no	—
125	C₂×C₄×C₆₇	—	2	4	no	—
126	C₂×C₄×C₆₇	—	2	4	no	—
127	C₂×C₄×C₆₇	—	2	4	no	—
128	C₂×C₄×C₆₇	—	2	8	no	—
129	C₂×C₄×C₆₇	—	2	4	no	—
130	C₂×C₄×C₆₇	—	2	8	no	—
131	C₂×C₄×C₆₇	—	2	8	no	—
132	C₂×C₄×C₆₇	—	2	8	no	—
133	C₂×C₄×C₆₇	—	2	8	no	—
134	C₂×C₄×C₆₇	—	4	16	no	—
135	C₂×C₄×C₆₇	—	4	8	no	—
136	C₂×C₄×C₆₇	#121	1	16	yes	—
137	C₂×C₄×C₆₇	C₄⋊Q₈	1	16	yes	complemented
138	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
139	C₂×C₄×C₆₇	C₂²×D₄	1	8	yes	—
140	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
141	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
142	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
143	C₂×C₄×C₆₇	C₂²×Q₈	1	16	yes	—
144	C₂×C₄×C₆₇	C₂²×Q₈	1	8	yes	—
145	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
146	C₂²×C₆₇	C₂×#121	1	4	yes	—
147	C₂²×C₆₇	C₂×C₄⋊Q₈	1	4	yes	—
148	C₂²×C₆₇	#536	1	4	yes	—
149	C₂²×C₆₇	D₄×Q₈	1	8	yes	—
150	C₂²×C₆₇	#557	1	8	yes	—
151	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
152	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
153	C₂²×C₆₇	C₂³×Q₈	1	2	yes	—
154	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
155	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	2	yes	—
156	C₄×C₆₇	—	2	8	no	—
157	C₄×C₆₇	—	2	4	no	—
158	C₄×C₆₇	—	2	16	no	—
159	C₄×C₆₇	—	4	8	no	—
160	C₄×C₆₇	—	4	4	no	—
161	C₄×C₆₇	C₂×#121	1	8	yes	—
162	C₄×C₆₇	C₂×C₄⋊Q₈	1	8	yes	complemented
163	C₂×#2546	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
164	C₂×C₆₇	#2546	1	8	yes	direct product factor
165	C₂×C₆₇	C₂²×#121	1	1	yes	characteristic
166	C₂×C₆₇	C₂²×C₄⋊Q₈	1	1	yes	characteristic
167	C₂×C₆₇	C₂×#536	1	1	yes	characteristic
168	C₂×C₆₇	C₂×D₄×Q₈	1	2	yes	—
169	C₂×C₆₇	C₂×#557	1	2	yes	—
170	C₂²×C₄⋊Q₈	C₂×C₆₇	1	1	yes	characteristic
171	C₂²×C₄⋊Q₈	C₂×C₆₇	1	2	yes	—
172	C₂²×C₄×Q₈	C₂×C₆₇	1	1	yes	characteristic
173	#2546	C₂×C₆₇	1	16	yes	direct product factor
174	C₂×#398	C₂×C₆₇	1	4	yes	—
175	C₂×#391	C₂×C₆₇	1	2	yes	—
176	C₂×#389	C₂×C₆₇	1	4	yes	—
177	C₂×C₄×C₄⋊C₄	C₂×C₆₇	1	1	yes	characteristic
178	C₆₇	C₂×#2546	1	1	yes	characteristic, direct product factor, Sylow
179	C₂³×Q₈	C₂²×C₆₇	1	2	yes	—
180	C₂³×Q₈	C₂²×C₆₇	1	1	yes	characteristic
181	C₂×C₄⋊Q₈	—	2	16	no	—
182	C₂×C₄⋊Q₈	—	2	8	no	—
183	C₂×C₄⋊Q₈	C₂²×C₆₇	1	16	yes	—
184	C₂×C₄⋊Q₈	C₂²×C₆₇	1	8	yes	—
185	C₂×C₄×Q₈	—	2	8	no	—
186	C₂×C₄×Q₈	C₂²×C₆₇	1	8	yes	—
187	C₂²×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
188	C₂²×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
189	C₂²×C₄⋊C₄	C₂²×C₆₇	1	8	yes	—
190	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
191	C₂²×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
192	C₂²×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
193	C₂²×C₄²	C₂²×C₆₇	1	2	yes	—
194	C₂²×C₄²	C₂²×C₆₇	1	2	yes	—
195	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
196	#398	C₂²×C₆₇	1	32	yes	—
197	#391	C₂²×C₆₇	1	16	yes	—
198	#389	C₂²×C₆₇	1	32	yes	—
199	C₄×C₄⋊C₄	C₂²×C₆₇	1	8	yes	—
200	C₂×#95	C₂²×C₆₇	1	2	yes	—
201	C₂×#95	C₂²×C₆₇	1	8	yes	—
202	C₂²×Q₈	—	2	4	no	—
203	C₂²×Q₈	—	2	8	no	—
204	C₂²×Q₈	—	2	8	no	—
205	C₂²×Q₈	—	2	4	no	—
206	C₂²×Q₈	—	2	8	no	—
207	C₂²×Q₈	D₄×C₆₇	1	8	yes	—
208	C₂²×Q₈	C₂³×C₆₇	1	8	yes	—
209	C₂²×Q₈	C₂³×C₆₇	1	4	yes	—
210	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
211	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
212	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
213	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
214	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
215	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
216	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
217	C₄⋊Q₈	—	2	64	no	—
218	C₄⋊Q₈	—	2	32	no	—
219	C₄×Q₈	—	2	32	no	—
220	C₂×C₄⋊C₄	—	2	8	no	—
221	C₂×C₄⋊C₄	—	2	4	no	—
222	C₂×C₄⋊C₄	—	2	32	no	—
223	C₂×C₄⋊C₄	—	2	8	no	—
224	C₂×C₄⋊C₄	—	2	8	no	—
225	C₂×C₄⋊C₄	Q₈×C₆₇	1	16	yes	complemented
226	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
227	C₂×C₄⋊C₄	C₂³×C₆₇	1	8	yes	—
228	C₂×C₄⋊C₄	C₂³×C₆₇	1	8	yes	—
229	C₂×C₄⋊C₄	C₂³×C₆₇	1	32	yes	—
230	C₂×C₄⋊C₄	C₂³×C₆₇	1	8	yes	—
231	C₂×C₄⋊C₄	C₂³×C₆₇	1	8	yes	—
232	C₂×C₄²	—	2	8	no	—
233	C₂×C₄²	—	2	8	no	—
234	C₂×C₄²	D₄×C₆₇	1	8	yes	—
235	C₂×C₄²	C₂³×C₆₇	1	8	yes	—
236	C₂×C₄²	C₂³×C₆₇	1	8	yes	—
237	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
238	#95	C₂³×C₆₇	1	8	yes	—
239	#95	C₂³×C₆₇	1	32	yes	—
240	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
241	C₂×Q₈	—	2	32	no	—
242	C₂×Q₈	—	2	8	no	—
243	C₂×Q₈	—	2	16	no	—
244	C₂×Q₈	—	2	16	no	—
245	C₂×Q₈	—	2	8	no	—
246	C₂×Q₈	—	2	16	no	—
247	C₂×Q₈	—	4	32	no	—
248	C₂×Q₈	C₂×D₄×C₆₇	1	16	yes	—
249	C₂²×C₄	—	2	8	no	—
250	C₂²×C₄	—	2	4	no	—
251	C₂²×C₄	—	2	4	no	—
252	C₂²×C₄	—	2	4	no	—
253	C₂²×C₄	—	2	8	no	—
254	C₂²×C₄	—	2	4	no	—
255	C₂²×C₄	—	2	8	no	—
256	C₂²×C₄	—	2	8	no	—
257	C₂²×C₄	—	2	8	no	—
258	C₂²×C₄	—	2	8	no	—
259	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
260	C₂²×C₄	C₂×D₄×C₆₇	1	8	yes	—
261	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
262	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
263	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
264	C₂²×C₄	C₂×Q₈×C₆₇	1	16	yes	—
265	C₂²×C₄	C₂×Q₈×C₆₇	1	8	yes	—
266	C₂²×C₄	#41×C₆₇	1	4	yes	—
267	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
268	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
269	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
270	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
271	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
272	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
273	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
274	C₄⋊C₄	—	2	16	no	—
275	C₄⋊C₄	—	2	8	no	—
276	C₄⋊C₄	—	2	64	no	—
277	C₄⋊C₄	—	2	16	no	—
278	C₄⋊C₄	—	2	16	no	—
279	C₄⋊C₄	C₂×Q₈×C₆₇	1	32	yes	complemented
280	C₄²	—	2	16	no	—
281	C₄²	—	2	16	no	—
282	C₄²	C₂×D₄×C₆₇	1	16	yes	—
283	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
284	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
285	C₂³	C₂²×Q₈×C₆₇	1	4	yes	—
286	C₂³	C₂×#41×C₆₇	1	2	yes	—
287	C₂³	2₋¹⁺⁴×C₆₇	1	4	yes	—
288	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
289	Q₈	—	2	32	no	—
290	Q₈	—	4	32	no	—
291	C₂×C₄	—	2	16	no	—
292	C₂×C₄	—	2	8	no	—
293	C₂×C₄	—	2	32	no	—
294	C₂×C₄	—	2	8	no	—
295	C₂×C₄	—	2	4	no	—
296	C₂×C₄	—	2	4	no	—
297	C₂×C₄	—	2	4	no	—
298	C₂×C₄	—	2	8	no	—
299	C₂×C₄	—	2	4	no	—
300	C₂×C₄	—	2	8	no	—
301	C₂×C₄	—	2	8	no	—
302	C₂×C₄	—	2	8	no	—
303	C₂×C₄	—	2	8	no	—
304	C₂×C₄	—	4	16	no	—
305	C₂×C₄	—	4	8	no	—
306	C₂×C₄	#121×C₆₇	1	16	yes	—
307	C₂×C₄	C₄⋊Q₈×C₆₇	1	16	yes	complemented
308	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
309	C₂×C₄	C₂²×D₄×C₆₇	1	8	yes	—
310	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
311	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
312	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
313	C₂×C₄	C₂²×Q₈×C₆₇	1	16	yes	—
314	C₂×C₄	C₂²×Q₈×C₆₇	1	8	yes	—
315	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
316	C₂²	C₂×#121×C₆₇	1	4	yes	—
317	C₂²	C₂×C₄⋊Q₈×C₆₇	1	4	yes	—
318	C₂²	#536×C₆₇	1	4	yes	—
319	C₂²	D₄×Q₈×C₆₇	1	8	yes	—
320	C₂²	#557×C₆₇	1	8	yes	—
321	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
322	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
323	C₂²	C₂³×Q₈×C₆₇	1	2	yes	—
324	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
325	C₂²	C₂×2₋¹⁺⁴×C₆₇	1	2	yes	—
326	C₄	—	2	8	no	—
327	C₄	—	2	4	no	—
328	C₄	—	2	16	no	—
329	C₄	—	4	8	no	—
330	C₄	—	4	4	no	—
331	C₄	C₂×#121×C₆₇	1	8	yes	—
332	C₄	C₂×C₄⋊Q₈×C₆₇	1	8	yes	complemented
333	C₂	C₆₇×#2546	1	8	yes	direct product factor
334	C₂	C₂²×#121×C₆₇	1	1	yes	characteristic
335	C₂	C₂²×C₄⋊Q₈×C₆₇	1	1	yes	characteristic
336	C₂	C₂×#536×C₆₇	1	1	yes	characteristic
337	C₂	C₂×D₄×Q₈×C₆₇	1	2	yes	—
338	C₂	C₂×#557×C₆₇	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
4. C₆₇×#2546	C₂	direct (N × H)
55. C₂×C₄⋊C₄×C₆₇	Q₈	semidirect
109. C₄⋊C₄×C₆₇	C₂×Q₈	semidirect
137. C₂×C₄×C₆₇	C₄⋊Q₈	semidirect
162. C₄×C₆₇	C₂×C₄⋊Q₈	semidirect
163. C₂×#2546	C₆₇	direct (N × H)
164. C₂×C₆₇	#2546	direct (N × H)
173. #2546	C₂×C₆₇	direct (N × H)
178. C₆₇	C₂×#2546	direct (N × H)
225. C₂×C₄⋊C₄	Q₈×C₆₇	semidirect
279. C₄⋊C₄	C₂×Q₈×C₆₇	semidirect
307. C₂×C₄	C₄⋊Q₈×C₆₇	semidirect
332. C₄	C₂×C₄⋊Q₈×C₆₇	semidirect
333. C₂	C₆₇×#2546	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⋊Q₈×C₆₇	2
C₂²×C₄×Q₈×C₆₇	2
C₆₇×#2546	2
C₂×#398×C₆₇	2
C₂×#391×C₆₇	2
C₂×#389×C₆₇	2
C₂×C₄×C₄⋊C₄×C₆₇	2
C₂×#2546	67

Subgroups — C2×C67×#2546 #30714179

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₇×#2546 #30714179