Subgroups — C₂²×C₄×SD₁₆×C₆₇ #30739400

Order 17152.

3262 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	C₂³×SD₁₆×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×Q₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₄×D₄×C₆₇	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×SD₁₆×C₆₇	C₂	1	24	yes	maximal, direct product factor
5	C₂²×#106×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#103×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×#102×C₆₇	C₂	1	1	yes	maximal, characteristic
8	C₂²×C₄×C₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×Q₈×C₆₇	C₂²	1	1	yes	characteristic
10	C₂³×D₄×C₆₇	C₂²	1	1	yes	characteristic
11	C₂⁴×C₄×C₆₇	—	2	1	no	—
12	C₂²×SD₁₆×C₆₇	C₄	1	16	yes	direct product factor
13	C₂²×SD₁₆×C₆₇	C₂²	1	12	yes	—
14	C₂³×C₈×C₆₇	C₂²	1	1	yes	characteristic
15	C₂³×C₈×C₆₇	C₂²	1	1	yes	characteristic
16	C₂×C₄×Q₈×C₆₇	—	2	6	no	—
17	C₂×C₄×Q₈×C₆₇	C₂²	1	12	yes	complemented
18	C₂×C₄×D₄×C₆₇	—	2	6	no	—
19	C₂×C₄×D₄×C₆₇	C₂²	1	12	yes	—
20	C₂²×C₄⋊C₄×C₆₇	—	2	1	no	—
21	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
22	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
23	C₂²×C₂²⋊C₄×C₆₇	—	2	1	no	—
24	C₂²×C₄²×C₆₇	—	2	1	no	—
25	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
26	C₄×SD₁₆×C₆₇	C₂²	1	64	yes	direct product factor
27	C₂×#106×C₆₇	C₂²	1	12	yes	complemented
28	C₂×#103×C₆₇	C₂²	1	12	yes	complemented
29	C₂×#102×C₆₇	C₂²	1	12	yes	—
30	C₂×C₄×C₈×C₆₇	C₂²	1	12	yes	complemented
31	C₂⁵×C₆₇	—	2	1	no	—
32	C₂²×Q₈×C₆₇	—	2	3	no	—
33	C₂²×Q₈×C₆₇	—	2	4	no	—
34	C₂²×Q₈×C₆₇	C₂×C₄	1	8	yes	complemented
35	C₂²×Q₈×C₆₇	C₂³	1	6	yes	—
36	C₂²×D₄×C₆₇	—	2	3	no	—
37	C₂²×D₄×C₆₇	—	2	4	no	—
38	C₂²×D₄×C₆₇	C₂×C₄	1	8	yes	—
39	C₂²×D₄×C₆₇	C₂³	1	6	yes	—
40	C₂³×C₄×C₆₇	—	2	1	no	—
41	C₂³×C₄×C₆₇	—	2	1	no	—
42	C₂³×C₄×C₆₇	—	2	1	no	—
43	C₂³×C₄×C₆₇	—	2	12	no	—
44	C₂³×C₄×C₆₇	—	4	8	no	—
45	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
46	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
47	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
48	C₂×SD₁₆×C₆₇	C₂×C₄	1	96	yes	direct product factor
49	C₂×SD₁₆×C₆₇	C₂³	1	16	yes	—
50	C₂²×C₈×C₆₇	—	2	4	no	—
51	C₂²×C₈×C₆₇	C₂×C₄	1	8	yes	complemented
52	C₂²×C₈×C₆₇	C₂³	1	6	yes	—
53	C₂²×C₈×C₆₇	C₂³	1	6	yes	—
54	C₄×Q₈×C₆₇	—	2	24	no	—
55	C₄×Q₈×C₆₇	C₂³	1	16	yes	complemented
56	C₄×D₄×C₆₇	—	2	24	no	—
57	C₄×D₄×C₆₇	C₂³	1	16	yes	—
58	C₂×C₄⋊C₄×C₆₇	—	2	12	no	—
59	C₂×C₄⋊C₄×C₆₇	—	2	3	no	—
60	C₂×C₄⋊C₄×C₆₇	—	2	3	no	—
61	C₂×C₄⋊C₄×C₆₇	C₂³	1	6	yes	—
62	C₂×C₄⋊C₄×C₆₇	C₂³	1	6	yes	—
63	C₂×C₂²⋊C₄×C₆₇	—	2	12	no	—
64	C₂×C₄²×C₆₇	—	2	12	no	—
65	C₂×C₄²×C₆₇	D₄	1	6	yes	—
66	C₂×C₄²×C₆₇	C₂³	1	6	yes	—
67	#106×C₆₇	C₂³	1	16	yes	complemented
68	#103×C₆₇	C₂³	1	16	yes	complemented
69	#102×C₆₇	C₂³	1	16	yes	—
70	C₄×C₈×C₆₇	C₂³	1	16	yes	complemented
71	C₂⁴×C₆₇	—	2	8	no	—
72	C₂⁴×C₆₇	—	2	6	no	—
73	C₂⁴×C₆₇	—	4	4	no	—
74	C₂⁴×C₆₇	—	4	4	no	—
75	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
76	C₂×Q₈×C₆₇	—	2	24	no	—
77	C₂×Q₈×C₆₇	—	2	6	no	—
78	C₂×Q₈×C₆₇	—	2	12	no	—
79	C₂×Q₈×C₆₇	C₂²×C₄	1	24	yes	complemented
80	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
81	C₂×D₄×C₆₇	—	2	24	no	—
82	C₂×D₄×C₆₇	—	2	6	no	—
83	C₂×D₄×C₆₇	—	2	12	no	—
84	C₂×D₄×C₆₇	C₂²×C₄	1	24	yes	—
85	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
86	C₂²×C₄×C₆₇	—	2	8	no	—
87	C₂²×C₄×C₆₇	—	2	4	no	—
88	C₂²×C₄×C₆₇	—	2	6	no	—
89	C₂²×C₄×C₆₇	—	2	6	no	—
90	C₂²×C₄×C₆₇	—	2	6	no	—
91	C₂²×C₄×C₆₇	—	2	16	no	—
92	C₂²×C₄×C₆₇	—	4	4	no	—
93	C₂²×C₄×C₆₇	—	4	4	no	—
94	C₂²×C₄×C₆₇	—	4	48	no	—
95	C₂²×C₄×C₆₇	SD₁₆	1	8	yes	direct product factor
96	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
97	C₂²×C₄×C₆₇	C₂×D₄	1	6	yes	—
98	C₂²×C₄×C₆₇	C₂×D₄	1	3	yes	—
99	C₂²×C₄×C₆₇	C₂×D₄	1	6	yes	—
100	C₂²×C₄×C₆₇	#41	1	4	yes	—
101	C₂²×C₄×C₆₇	C₂⁴	1	3	yes	—
102	SD₁₆×C₆₇	C₂²×C₄	1	64	yes	direct product factor
103	C₂×C₈×C₆₇	—	2	12	no	—
104	C₂×C₈×C₆₇	C₂²×C₄	1	24	yes	complemented
105	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
106	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
107	C₄⋊C₄×C₆₇	—	2	16	no	—
108	C₄⋊C₄×C₆₇	—	2	6	no	—
109	C₄⋊C₄×C₆₇	—	2	6	no	—
110	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
111	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
112	C₂²⋊C₄×C₆₇	—	2	16	no	—
113	C₄²×C₆₇	—	2	16	no	—
114	C₄²×C₆₇	C₂×D₄	1	12	yes	—
115	C₄²×C₆₇	C₂⁴	1	4	yes	—
116	C₂³×C₆₇	—	2	24	no	—
117	C₂³×C₆₇	—	2	4	no	—
118	C₂³×C₆₇	—	4	12	no	—
119	C₂³×C₆₇	—	4	12	no	—
120	C₂³×C₆₇	—	4	32	no	—
121	C₂³×C₆₇	C₄×D₄	1	4	yes	—
122	C₂³×C₆₇	C₂×SD₁₆	1	4	yes	—
123	C₂³×C₆₇	#135	1	4	yes	—
124	C₂³×C₆₇	C₂²×D₄	1	3	yes	—
125	Q₈×C₆₇	—	2	24	no	—
126	Q₈×C₆₇	—	2	4	no	—
127	Q₈×C₆₇	C₂³×C₄	1	8	yes	complemented
128	D₄×C₆₇	—	2	24	no	—
129	D₄×C₆₇	—	2	4	no	—
130	D₄×C₆₇	C₂³×C₄	1	8	yes	—
131	C₂×C₄×C₆₇	—	2	24	no	—
132	C₂×C₄×C₆₇	—	2	12	no	—
133	C₂×C₄×C₆₇	—	2	4	no	—
134	C₂×C₄×C₆₇	—	2	4	no	—
135	C₂×C₄×C₆₇	—	2	4	no	—
136	C₂×C₄×C₆₇	—	4	12	no	—
137	C₂×C₄×C₆₇	—	4	12	no	—
138	C₂×C₄×C₆₇	—	4	32	no	—
139	C₂×C₄×C₆₇	C₄×D₄	1	12	yes	—
140	C₂×C₄×C₆₇	C₂×SD₁₆	1	24	yes	direct product factor
141	C₂×C₄×C₆₇	C₂³×C₄	1	6	yes	—
142	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
143	C₂×C₄×C₆₇	C₂²×D₄	1	3	yes	—
144	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
145	C₂×C₄×C₆₇	C₂×#41	1	6	yes	—
146	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
147	C₈×C₆₇	—	2	4	no	—
148	C₈×C₆₇	C₂³×C₄	1	8	yes	complemented
149	C₂²×C₆₇	—	2	8	no	—
150	C₂²×C₆₇	—	4	48	no	—
151	C₂²×C₆₇	—	4	4	no	—
152	C₂²×C₆₇	—	4	4	no	—
153	C₂²×C₆₇	C₄×SD₁₆	1	16	yes	direct product factor
154	C₂²×C₆₇	C₂×C₄×D₄	1	6	yes	—
155	C₂²×C₆₇	C₂²×SD₁₆	1	6	yes	—
156	C₂²×C₆₇	C₂×#135	1	6	yes	—
157	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
158	C₄×C₆₇	—	2	8	no	—
159	C₄×C₆₇	—	2	4	no	—
160	C₄×C₆₇	—	4	4	no	—
161	C₄×C₆₇	—	4	4	no	—
162	C₄×C₆₇	C₂×C₄×D₄	1	6	yes	—
163	C₄×C₆₇	C₂²×SD₁₆	1	8	yes	direct product factor
164	C₄×C₆₇	C₂⁴×C₄	1	1	yes	characteristic
165	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
166	C₂²×C₄×SD₁₆	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
167	C₂×C₆₇	—	4	8	no	—
168	C₂×C₆₇	C₂×C₄×SD₁₆	1	12	yes	direct product factor
169	C₂×C₆₇	C₂²×C₄×D₄	1	1	yes	characteristic
170	C₂×C₆₇	C₂³×SD₁₆	1	1	yes	characteristic
171	C₂×C₆₇	C₂²×#135	1	1	yes	characteristic
172	C₂³×SD₁₆	C₂×C₆₇	1	1	yes	characteristic
173	C₂²×C₄×Q₈	C₂×C₆₇	1	1	yes	characteristic, complemented
174	C₂²×C₄×D₄	C₂×C₆₇	1	1	yes	characteristic
175	C₂×C₄×SD₁₆	C₂×C₆₇	1	24	yes	direct product factor
176	C₂²×#106	C₂×C₆₇	1	1	yes	characteristic, complemented
177	C₂²×#103	C₂×C₆₇	1	1	yes	characteristic, complemented
178	C₂²×#102	C₂×C₆₇	1	1	yes	characteristic
179	C₂²×C₄×C₈	C₂×C₆₇	1	1	yes	characteristic, complemented
180	C₆₇	C₂²×C₄×SD₁₆	1	1	yes	characteristic, direct product factor, Sylow
181	C₂³×Q₈	C₂²×C₆₇	1	1	yes	characteristic
182	C₂³×D₄	C₂²×C₆₇	1	1	yes	characteristic
183	C₂⁴×C₄	—	2	1	no	—
184	C₂²×SD₁₆	C₄×C₆₇	1	16	yes	direct product factor
185	C₂²×SD₁₆	C₂²×C₆₇	1	12	yes	—
186	C₂³×C₈	C₂²×C₆₇	1	1	yes	characteristic
187	C₂³×C₈	C₂²×C₆₇	1	1	yes	characteristic
188	C₂×C₄×Q₈	—	2	6	no	—
189	C₂×C₄×Q₈	C₂²×C₆₇	1	12	yes	complemented
190	C₂×C₄×D₄	—	2	6	no	—
191	C₂×C₄×D₄	C₂²×C₆₇	1	12	yes	—
192	C₂²×C₄⋊C₄	—	2	1	no	—
193	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
194	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
195	C₂²×C₂²⋊C₄	—	2	1	no	—
196	C₂²×C₄²	—	2	1	no	—
197	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
198	C₄×SD₁₆	C₂²×C₆₇	1	64	yes	direct product factor
199	C₂×#106	C₂²×C₆₇	1	12	yes	complemented
200	C₂×#103	C₂²×C₆₇	1	12	yes	complemented
201	C₂×#102	C₂²×C₆₇	1	12	yes	—
202	C₂×C₄×C₈	C₂²×C₆₇	1	12	yes	complemented
203	C₂⁵	—	2	1	no	—
204	C₂²×Q₈	—	2	3	no	—
205	C₂²×Q₈	—	2	4	no	—
206	C₂²×Q₈	C₂×C₄×C₆₇	1	8	yes	complemented
207	C₂²×Q₈	C₂³×C₆₇	1	6	yes	—
208	C₂²×D₄	—	2	3	no	—
209	C₂²×D₄	—	2	4	no	—
210	C₂²×D₄	C₂×C₄×C₆₇	1	8	yes	—
211	C₂²×D₄	C₂³×C₆₇	1	6	yes	—
212	C₂³×C₄	—	2	1	no	—
213	C₂³×C₄	—	2	1	no	—
214	C₂³×C₄	—	2	1	no	—
215	C₂³×C₄	—	2	12	no	—
216	C₂³×C₄	—	4	8	no	—
217	C₂³×C₄	D₄×C₆₇	1	1	yes	characteristic
218	C₂³×C₄	D₄×C₆₇	1	1	yes	characteristic
219	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
220	C₂×SD₁₆	C₂×C₄×C₆₇	1	96	yes	direct product factor
221	C₂×SD₁₆	C₂³×C₆₇	1	16	yes	—
222	C₂²×C₈	—	2	4	no	—
223	C₂²×C₈	C₂×C₄×C₆₇	1	8	yes	complemented
224	C₂²×C₈	C₂³×C₆₇	1	6	yes	—
225	C₂²×C₈	C₂³×C₆₇	1	6	yes	—
226	C₄×Q₈	—	2	24	no	—
227	C₄×Q₈	C₂³×C₆₇	1	16	yes	complemented
228	C₄×D₄	—	2	24	no	—
229	C₄×D₄	C₂³×C₆₇	1	16	yes	—
230	C₂×C₄⋊C₄	—	2	12	no	—
231	C₂×C₄⋊C₄	—	2	3	no	—
232	C₂×C₄⋊C₄	—	2	3	no	—
233	C₂×C₄⋊C₄	C₂³×C₆₇	1	6	yes	—
234	C₂×C₄⋊C₄	C₂³×C₆₇	1	6	yes	—
235	C₂×C₂²⋊C₄	—	2	12	no	—
236	C₂×C₄²	—	2	12	no	—
237	C₂×C₄²	D₄×C₆₇	1	6	yes	—
238	C₂×C₄²	C₂³×C₆₇	1	6	yes	—
239	#106	C₂³×C₆₇	1	16	yes	complemented
240	#103	C₂³×C₆₇	1	16	yes	complemented
241	#102	C₂³×C₆₇	1	16	yes	—
242	C₄×C₈	C₂³×C₆₇	1	16	yes	complemented
243	C₂⁴	—	2	8	no	—
244	C₂⁴	—	2	6	no	—
245	C₂⁴	—	4	4	no	—
246	C₂⁴	—	4	4	no	—
247	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
248	C₂×Q₈	—	2	24	no	—
249	C₂×Q₈	—	2	6	no	—
250	C₂×Q₈	—	2	12	no	—
251	C₂×Q₈	C₂²×C₄×C₆₇	1	24	yes	complemented
252	C₂×Q₈	C₂⁴×C₆₇	1	4	yes	—
253	C₂×D₄	—	2	24	no	—
254	C₂×D₄	—	2	6	no	—
255	C₂×D₄	—	2	12	no	—
256	C₂×D₄	C₂²×C₄×C₆₇	1	24	yes	—
257	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
258	C₂²×C₄	—	2	8	no	—
259	C₂²×C₄	—	2	4	no	—
260	C₂²×C₄	—	2	6	no	—
261	C₂²×C₄	—	2	6	no	—
262	C₂²×C₄	—	2	6	no	—
263	C₂²×C₄	—	2	16	no	—
264	C₂²×C₄	—	4	4	no	—
265	C₂²×C₄	—	4	4	no	—
266	C₂²×C₄	—	4	48	no	—
267	C₂²×C₄	SD₁₆×C₆₇	1	8	yes	direct product factor
268	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
269	C₂²×C₄	C₂×D₄×C₆₇	1	6	yes	—
270	C₂²×C₄	C₂×D₄×C₆₇	1	3	yes	—
271	C₂²×C₄	C₂×D₄×C₆₇	1	6	yes	—
272	C₂²×C₄	#41×C₆₇	1	4	yes	—
273	C₂²×C₄	C₂⁴×C₆₇	1	3	yes	—
274	SD₁₆	C₂²×C₄×C₆₇	1	64	yes	direct product factor
275	C₂×C₈	—	2	12	no	—
276	C₂×C₈	C₂²×C₄×C₆₇	1	24	yes	complemented
277	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
278	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
279	C₄⋊C₄	—	2	16	no	—
280	C₄⋊C₄	—	2	6	no	—
281	C₄⋊C₄	—	2	6	no	—
282	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
283	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
284	C₂²⋊C₄	—	2	16	no	—
285	C₄²	—	2	16	no	—
286	C₄²	C₂×D₄×C₆₇	1	12	yes	—
287	C₄²	C₂⁴×C₆₇	1	4	yes	—
288	C₂³	—	2	24	no	—
289	C₂³	—	2	4	no	—
290	C₂³	—	4	12	no	—
291	C₂³	—	4	12	no	—
292	C₂³	—	4	32	no	—
293	C₂³	C₄×D₄×C₆₇	1	4	yes	—
294	C₂³	C₂×SD₁₆×C₆₇	1	4	yes	—
295	C₂³	#135×C₆₇	1	4	yes	—
296	C₂³	C₂²×D₄×C₆₇	1	3	yes	—
297	Q₈	—	2	24	no	—
298	Q₈	—	2	4	no	—
299	Q₈	C₂³×C₄×C₆₇	1	8	yes	complemented
300	D₄	—	2	24	no	—
301	D₄	—	2	4	no	—
302	D₄	C₂³×C₄×C₆₇	1	8	yes	—
303	C₂×C₄	—	2	24	no	—
304	C₂×C₄	—	2	12	no	—
305	C₂×C₄	—	2	4	no	—
306	C₂×C₄	—	2	4	no	—
307	C₂×C₄	—	2	4	no	—
308	C₂×C₄	—	4	12	no	—
309	C₂×C₄	—	4	12	no	—
310	C₂×C₄	—	4	32	no	—
311	C₂×C₄	C₄×D₄×C₆₇	1	12	yes	—
312	C₂×C₄	C₂×SD₁₆×C₆₇	1	24	yes	direct product factor
313	C₂×C₄	C₂³×C₄×C₆₇	1	6	yes	—
314	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
315	C₂×C₄	C₂²×D₄×C₆₇	1	3	yes	—
316	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
317	C₂×C₄	C₂×#41×C₆₇	1	6	yes	—
318	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
319	C₈	—	2	4	no	—
320	C₈	C₂³×C₄×C₆₇	1	8	yes	complemented
321	C₂²	—	2	8	no	—
322	C₂²	—	4	4	no	—
323	C₂²	—	4	4	no	—
324	C₂²	—	4	48	no	—
325	C₂²	C₄×SD₁₆×C₆₇	1	16	yes	direct product factor
326	C₂²	C₂×C₄×D₄×C₆₇	1	6	yes	—
327	C₂²	C₂²×SD₁₆×C₆₇	1	6	yes	—
328	C₂²	C₂×#135×C₆₇	1	6	yes	—
329	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
330	C₄	—	2	4	no	—
331	C₄	—	2	8	no	—
332	C₄	—	4	4	no	—
333	C₄	—	4	4	no	—
334	C₄	C₂×C₄×D₄×C₆₇	1	6	yes	—
335	C₄	C₂²×SD₁₆×C₆₇	1	8	yes	direct product factor
336	C₄	C₂⁴×C₄×C₆₇	1	1	yes	characteristic
337	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
338	C₂	—	4	8	no	—
339	C₂	C₂×C₄×SD₁₆×C₆₇	1	12	yes	direct product factor
340	C₂	C₂²×C₄×D₄×C₆₇	1	1	yes	characteristic
341	C₂	C₂³×SD₁₆×C₆₇	1	1	yes	characteristic
342	C₂	C₂²×#135×C₆₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₄×C₆₇	D₄
commutator	C₄	C₂⁴×C₄×C₆₇
Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
socle	C₂⁴×C₆₇	C₂×D₄
prime radical	C₂³×D₄×C₆₇	C₂²
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄×C₆₇ ◁ C₂²×C₄²×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₄×Q₈×C₆₇	C₂	semidirect
4. C₂×C₄×SD₁₆×C₆₇	C₂	direct (N × H)
5. C₂²×#106×C₆₇	C₂	semidirect
6. C₂²×#103×C₆₇	C₂	semidirect
8. C₂²×C₄×C₈×C₆₇	C₂	semidirect
12. C₂²×SD₁₆×C₆₇	C₄	direct (N × H)
17. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
26. C₄×SD₁₆×C₆₇	C₂²	direct (N × H)
27. C₂×#106×C₆₇	C₂²	semidirect
28. C₂×#103×C₆₇	C₂²	semidirect
30. C₂×C₄×C₈×C₆₇	C₂²	semidirect
34. C₂²×Q₈×C₆₇	C₂×C₄	semidirect
48. C₂×SD₁₆×C₆₇	C₂×C₄	direct (N × H)
51. C₂²×C₈×C₆₇	C₂×C₄	semidirect
55. C₄×Q₈×C₆₇	C₂³	semidirect
67. #106×C₆₇	C₂³	semidirect
68. #103×C₆₇	C₂³	semidirect
70. C₄×C₈×C₆₇	C₂³	semidirect
79. C₂×Q₈×C₆₇	C₂²×C₄	semidirect
95. C₂²×C₄×C₆₇	SD₁₆	direct (N × H)
102. SD₁₆×C₆₇	C₂²×C₄	direct (N × H)
104. C₂×C₈×C₆₇	C₂²×C₄	semidirect
127. Q₈×C₆₇	C₂³×C₄	semidirect
140. C₂×C₄×C₆₇	C₂×SD₁₆	direct (N × H)
148. C₈×C₆₇	C₂³×C₄	semidirect
153. C₂²×C₆₇	C₄×SD₁₆	direct (N × H)
163. C₄×C₆₇	C₂²×SD₁₆	direct (N × H)
166. C₂²×C₄×SD₁₆	C₆₇	direct (N × H)
168. C₂×C₆₇	C₂×C₄×SD₁₆	direct (N × H)
173. C₂²×C₄×Q₈	C₂×C₆₇	semidirect
175. C₂×C₄×SD₁₆	C₂×C₆₇	direct (N × H)
176. C₂²×#106	C₂×C₆₇	semidirect
177. C₂²×#103	C₂×C₆₇	semidirect
179. C₂²×C₄×C₈	C₂×C₆₇	semidirect
180. C₆₇	C₂²×C₄×SD₁₆	direct (N × H)
184. C₂²×SD₁₆	C₄×C₆₇	direct (N × H)
189. C₂×C₄×Q₈	C₂²×C₆₇	semidirect
198. C₄×SD₁₆	C₂²×C₆₇	direct (N × H)
199. C₂×#106	C₂²×C₆₇	semidirect
200. C₂×#103	C₂²×C₆₇	semidirect
202. C₂×C₄×C₈	C₂²×C₆₇	semidirect
206. C₂²×Q₈	C₂×C₄×C₆₇	semidirect
220. C₂×SD₁₆	C₂×C₄×C₆₇	direct (N × H)
223. C₂²×C₈	C₂×C₄×C₆₇	semidirect
227. C₄×Q₈	C₂³×C₆₇	semidirect
239. #106	C₂³×C₆₇	semidirect
240. #103	C₂³×C₆₇	semidirect
242. C₄×C₈	C₂³×C₆₇	semidirect
251. C₂×Q₈	C₂²×C₄×C₆₇	semidirect
267. C₂²×C₄	SD₁₆×C₆₇	direct (N × H)
274. SD₁₆	C₂²×C₄×C₆₇	direct (N × H)
276. C₂×C₈	C₂²×C₄×C₆₇	semidirect
299. Q₈	C₂³×C₄×C₆₇	semidirect
312. C₂×C₄	C₂×SD₁₆×C₆₇	direct (N × H)
320. C₈	C₂³×C₄×C₆₇	semidirect
325. C₂²	C₄×SD₁₆×C₆₇	direct (N × H)
335. C₄	C₂²×SD₁₆×C₆₇	direct (N × H)
339. C₂	C₂×C₄×SD₁₆×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×SD₁₆×C₆₇	2
C₂²×C₄×Q₈×C₆₇	2
C₂²×C₄×D₄×C₆₇	2
C₂×C₄×SD₁₆×C₆₇	2
C₂²×#106×C₆₇	2
C₂²×#103×C₆₇	2
C₂²×#102×C₆₇	2
C₂²×C₄×C₈×C₆₇	2
C₂²×C₄×SD₁₆	67

Subgroups — C22×C4×SD16×C67 #30739400

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₄×SD₁₆×C₆₇ #30739400