Subgroups — C₂²×#418×C₆₇ #30739331

Order 17152.

7214 conjugacy classes of subgroups.

The subgroup lattice has 304 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×D₄×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₂³×M₁₆×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×#117×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#418×C₆₇	C₂	1	24	yes	maximal, direct product factor
5	C₂²×#102×C₆₇	C₂	1	4	yes	maximal, complemented
6	C₂⁶×C₆₇	—	2	1	no	—
7	C₂³×D₄×C₆₇	—	2	6	no	—
8	C₂³×D₄×C₆₇	—	2	1	no	—
9	C₂³×D₄×C₆₇	—	2	8	no	—
10	C₂³×D₄×C₆₇	C₄	1	16	yes	complemented
11	C₂³×D₄×C₆₇	C₂²	1	2	yes	—
12	C₂³×D₄×C₆₇	C₂²	1	12	yes	—
13	C₂⁴×C₄×C₆₇	C₂²	1	1	yes	characteristic
14	C₂²×M₁₆×C₆₇	—	2	8	no	—
15	C₂²×M₁₆×C₆₇	C₂²	1	12	yes	complemented
16	C₂³×C₈×C₆₇	C₂²	1	2	yes	complemented
17	C₂×#117×C₆₇	—	2	6	no	—
18	C₂×#117×C₆₇	C₂²	1	12	yes	complemented
19	C₂²×C₄⋊C₄×C₆₇	C₂²	1	2	yes	complemented
20	C₂²×C₂²⋊C₄×C₆₇	—	2	1	no	—
21	C₂²×C₄²×C₆₇	—	2	1	no	—
22	#418×C₆₇	C₂²	1	64	yes	direct product factor
23	C₂×#102×C₆₇	C₂²	1	48	yes	complemented
24	C₂⁵×C₆₇	—	2	16	no	—
25	C₂⁵×C₆₇	—	2	12	no	—
26	C₂⁵×C₆₇	—	2	2	no	—
27	C₂⁵×C₆₇	—	4	16	no	—
28	C₂⁵×C₆₇	D₄	1	1	yes	characteristic
29	C₂²×D₄×C₆₇	—	2	96	no	—
30	C₂²×D₄×C₆₇	—	2	16	no	—
31	C₂²×D₄×C₆₇	—	2	12	no	—
32	C₂²×D₄×C₆₇	—	2	6	no	—
33	C₂²×D₄×C₆₇	—	2	24	no	—
34	C₂²×D₄×C₆₇	—	2	8	no	—
35	C₂²×D₄×C₆₇	—	2	48	no	—
36	C₂²×D₄×C₆₇	C₂×C₄	1	16	yes	—
37	C₂²×D₄×C₆₇	C₂×C₄	1	96	yes	complemented
38	C₂²×D₄×C₆₇	C₂³	1	12	yes	—
39	C₂²×D₄×C₆₇	C₂³	1	16	yes	—
40	C₂³×C₄×C₆₇	—	2	2	no	—
41	C₂³×C₄×C₆₇	C₂×C₄	1	8	yes	—
42	C₂³×C₄×C₆₇	D₄	1	6	yes	—
43	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
44	C₂³×C₄×C₆₇	D₄	1	8	yes	—
45	C₂³×C₄×C₆₇	C₂³	1	6	yes	—
46	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
47	C₂×M₁₆×C₆₇	—	2	48	no	—
48	C₂×M₁₆×C₆₇	C₂³	1	16	yes	complemented
49	C₂²×C₈×C₆₇	—	2	8	no	—
50	C₂²×C₈×C₆₇	C₂³	1	12	yes	complemented
51	#117×C₆₇	—	2	24	no	—
52	#117×C₆₇	C₂³	1	16	yes	complemented
53	C₂×C₄⋊C₄×C₆₇	—	2	6	no	—
54	C₂×C₄⋊C₄×C₆₇	C₂³	1	12	yes	complemented
55	C₂×C₂²⋊C₄×C₆₇	—	2	12	no	—
56	C₂×C₄²×C₆₇	—	2	12	no	—
57	#102×C₆₇	C₂³	1	64	yes	complemented
58	C₂⁴×C₆₇	—	2	8	no	—
59	C₂⁴×C₆₇	—	2	16	no	—
60	C₂⁴×C₆₇	—	2	96	no	—
61	C₂⁴×C₆₇	—	2	12	no	—
62	C₂⁴×C₆₇	—	2	16	no	—
63	C₂⁴×C₆₇	—	4	96	no	—
64	C₂⁴×C₆₇	—	4	128	no	—
65	C₂⁴×C₆₇	—	4	16	no	—
66	C₂⁴×C₆₇	C₂²⋊C₄	1	8	yes	—
67	C₂⁴×C₆₇	C₂×D₄	1	6	yes	—
68	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
69	C₂×D₄×C₆₇	—	2	48	no	—
70	C₂×D₄×C₆₇	—	2	192	no	—
71	C₂×D₄×C₆₇	—	2	96	no	—
72	C₂×D₄×C₆₇	—	2	16	no	—
73	C₂×D₄×C₆₇	—	2	12	no	—
74	C₂×D₄×C₆₇	—	2	24	no	—
75	C₂×D₄×C₆₇	—	2	32	no	—
76	C₂×D₄×C₆₇	C₂²×C₄	1	48	yes	—
77	C₂×D₄×C₆₇	C₂²×C₄	1	64	yes	complemented
78	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
79	C₂²×C₄×C₆₇	—	2	12	no	—
80	C₂²×C₄×C₆₇	—	4	8	no	—
81	C₂²×C₄×C₆₇	C₂²⋊C₄	1	48	yes	—
82	C₂²×C₄×C₆₇	C₂²⋊C₄	1	8	yes	—
83	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
84	C₂²×C₄×C₆₇	C₂²×C₄	1	24	yes	—
85	C₂²×C₄×C₆₇	C₂×D₄	1	6	yes	—
86	C₂²×C₄×C₆₇	C₂×D₄	1	3	yes	—
87	C₂²×C₄×C₆₇	C₂×D₄	1	12	yes	—
88	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
89	C₂²×C₄×C₆₇	C₂×D₄	1	24	yes	—
90	C₂²×C₄×C₆₇	C₂⁴	1	3	yes	—
91	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
92	M₁₆×C₆₇	—	2	32	no	—
93	C₂×C₈×C₆₇	—	2	24	no	—
94	C₂×C₈×C₆₇	C₂⁴	1	8	yes	complemented
95	C₄⋊C₄×C₆₇	—	2	12	no	—
96	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	complemented
97	C₂²⋊C₄×C₆₇	—	2	16	no	—
98	C₄²×C₆₇	—	2	16	no	—
99	C₂³×C₆₇	—	2	24	no	—
100	C₂³×C₆₇	—	2	32	no	—
101	C₂³×C₆₇	—	2	48	no	—
102	C₂³×C₆₇	—	2	64	no	—
103	C₂³×C₆₇	—	2	8	no	—
104	C₂³×C₆₇	—	4	384	no	—
105	C₂³×C₆₇	—	4	64	no	—
106	C₂³×C₆₇	—	4	48	no	—
107	C₂³×C₆₇	—	4	64	no	—
108	C₂³×C₆₇	C₂×C₂²⋊C₄	1	24	yes	—
109	C₂³×C₆₇	C₂×C₂²⋊C₄	1	4	yes	—
110	C₂³×C₆₇	AGL(1,ℤ/8)	1	8	yes	—
111	C₂³×C₆₇	C₂²×D₄	1	4	yes	—
112	C₂³×C₆₇	C₂²×D₄	1	3	yes	—
113	D₄×C₆₇	—	2	48	no	—
114	D₄×C₆₇	—	2	64	no	—
115	D₄×C₆₇	—	2	8	no	—
116	D₄×C₆₇	C₂³×C₄	1	16	yes	—
117	C₂×C₄×C₆₇	—	2	8	no	—
118	C₂×C₄×C₆₇	—	4	24	no	—
119	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	48	yes	—
120	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	12	yes	—
121	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	24	yes	—
122	C₂×C₄×C₆₇	C₂³×C₄	1	6	yes	—
123	C₂×C₄×C₆₇	C₂³×C₄	1	8	yes	—
124	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
125	C₂×C₄×C₆₇	C₂²×D₄	1	3	yes	—
126	C₂×C₄×C₆₇	C₂²×D₄	1	6	yes	—
127	C₂×C₄×C₆₇	C₂²×D₄	1	8	yes	—
128	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
129	C₈×C₆₇	—	2	8	no	—
130	C₂²×C₆₇	—	2	48	no	—
131	C₂²×C₆₇	—	2	8	no	—
132	C₂²×C₆₇	—	2	16	no	—
133	C₂²×C₆₇	—	4	128	no	—
134	C₂²×C₆₇	—	4	96	no	—
135	C₂²×C₆₇	—	4	16	no	—
136	C₂²×C₆₇	#418	1	16	yes	direct product factor
137	C₂²×C₆₇	C₂²×C₂²⋊C₄	1	8	yes	—
138	C₂²×C₆₇	C₂²×C₂²⋊C₄	1	6	yes	—
139	C₂²×C₆₇	C₂×AGL(1,ℤ/8)	1	12	yes	—
140	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
141	C₄×C₆₇	—	4	8	no	—
142	C₄×C₆₇	C₂²×C₂²⋊C₄	1	6	yes	—
143	C₄×C₆₇	C₂²×C₂²⋊C₄	1	8	yes	—
144	C₄×C₆₇	C₂⁴×C₄	1	1	yes	characteristic
145	C₄×C₆₇	C₂³×D₄	1	1	yes	characteristic
146	C₂²×#418	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
147	C₂×C₆₇	—	2	8	no	—
148	C₂×C₆₇	—	4	16	no	—
149	C₂×C₆₇	C₂×#418	1	12	yes	direct product factor
150	C₂×C₆₇	C₂³×C₂²⋊C₄	1	1	yes	characteristic
151	C₂×C₆₇	C₂²×AGL(1,ℤ/8)	1	2	yes	—
152	C₂⁴×D₄	C₂×C₆₇	1	1	yes	characteristic
153	C₂³×M₁₆	C₂×C₆₇	1	1	yes	characteristic, complemented
154	C₂²×#117	C₂×C₆₇	1	1	yes	characteristic, complemented
155	C₂×#418	C₂×C₆₇	1	24	yes	direct product factor
156	C₂²×#102	C₂×C₆₇	1	4	yes	complemented
157	C₆₇	C₂²×#418	1	1	yes	characteristic, direct product factor, Sylow
158	C₂⁶	—	2	1	no	—
159	C₂³×D₄	—	2	6	no	—
160	C₂³×D₄	—	2	1	no	—
161	C₂³×D₄	—	2	8	no	—
162	C₂³×D₄	C₄×C₆₇	1	16	yes	complemented
163	C₂³×D₄	C₂²×C₆₇	1	2	yes	—
164	C₂³×D₄	C₂²×C₆₇	1	12	yes	—
165	C₂⁴×C₄	C₂²×C₆₇	1	1	yes	characteristic
166	C₂²×M₁₆	—	2	8	no	—
167	C₂²×M₁₆	C₂²×C₆₇	1	12	yes	complemented
168	C₂³×C₈	C₂²×C₆₇	1	2	yes	complemented
169	C₂×#117	—	2	6	no	—
170	C₂×#117	C₂²×C₆₇	1	12	yes	complemented
171	C₂²×C₄⋊C₄	C₂²×C₆₇	1	2	yes	complemented
172	C₂²×C₂²⋊C₄	—	2	1	no	—
173	C₂²×C₄²	—	2	1	no	—
174	#418	C₂²×C₆₇	1	64	yes	direct product factor
175	C₂×#102	C₂²×C₆₇	1	48	yes	complemented
176	C₂⁵	—	2	16	no	—
177	C₂⁵	—	2	2	no	—
178	C₂⁵	—	2	12	no	—
179	C₂⁵	—	4	16	no	—
180	C₂⁵	D₄×C₆₇	1	1	yes	characteristic
181	C₂²×D₄	—	2	96	no	—
182	C₂²×D₄	—	2	16	no	—
183	C₂²×D₄	—	2	12	no	—
184	C₂²×D₄	—	2	6	no	—
185	C₂²×D₄	—	2	24	no	—
186	C₂²×D₄	—	2	8	no	—
187	C₂²×D₄	—	2	48	no	—
188	C₂²×D₄	C₂×C₄×C₆₇	1	16	yes	—
189	C₂²×D₄	C₂×C₄×C₆₇	1	96	yes	complemented
190	C₂²×D₄	C₂³×C₆₇	1	12	yes	—
191	C₂²×D₄	C₂³×C₆₇	1	16	yes	—
192	C₂³×C₄	—	2	2	no	—
193	C₂³×C₄	C₂×C₄×C₆₇	1	8	yes	—
194	C₂³×C₄	D₄×C₆₇	1	6	yes	—
195	C₂³×C₄	D₄×C₆₇	1	1	yes	characteristic
196	C₂³×C₄	D₄×C₆₇	1	8	yes	—
197	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
198	C₂³×C₄	C₂³×C₆₇	1	6	yes	—
199	C₂×M₁₆	—	2	48	no	—
200	C₂×M₁₆	C₂³×C₆₇	1	16	yes	complemented
201	C₂²×C₈	—	2	8	no	—
202	C₂²×C₈	C₂³×C₆₇	1	12	yes	complemented
203	#117	—	2	24	no	—
204	#117	C₂³×C₆₇	1	16	yes	complemented
205	C₂×C₄⋊C₄	—	2	6	no	—
206	C₂×C₄⋊C₄	C₂³×C₆₇	1	12	yes	complemented
207	C₂×C₂²⋊C₄	—	2	12	no	—
208	C₂×C₄²	—	2	12	no	—
209	#102	C₂³×C₆₇	1	64	yes	complemented
210	C₂⁴	—	2	8	no	—
211	C₂⁴	—	2	16	no	—
212	C₂⁴	—	2	96	no	—
213	C₂⁴	—	2	12	no	—
214	C₂⁴	—	2	16	no	—
215	C₂⁴	—	4	96	no	—
216	C₂⁴	—	4	128	no	—
217	C₂⁴	—	4	16	no	—
218	C₂⁴	C₂²⋊C₄×C₆₇	1	8	yes	—
219	C₂⁴	C₂×D₄×C₆₇	1	6	yes	—
220	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
221	C₂×D₄	—	2	48	no	—
222	C₂×D₄	—	2	192	no	—
223	C₂×D₄	—	2	96	no	—
224	C₂×D₄	—	2	16	no	—
225	C₂×D₄	—	2	12	no	—
226	C₂×D₄	—	2	24	no	—
227	C₂×D₄	—	2	32	no	—
228	C₂×D₄	C₂²×C₄×C₆₇	1	48	yes	—
229	C₂×D₄	C₂²×C₄×C₆₇	1	64	yes	complemented
230	C₂×D₄	C₂⁴×C₆₇	1	8	yes	—
231	C₂²×C₄	—	2	12	no	—
232	C₂²×C₄	—	4	8	no	—
233	C₂²×C₄	C₂²⋊C₄×C₆₇	1	48	yes	—
234	C₂²×C₄	C₂²⋊C₄×C₆₇	1	8	yes	—
235	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
236	C₂²×C₄	C₂²×C₄×C₆₇	1	24	yes	—
237	C₂²×C₄	C₂×D₄×C₆₇	1	6	yes	—
238	C₂²×C₄	C₂×D₄×C₆₇	1	3	yes	—
239	C₂²×C₄	C₂×D₄×C₆₇	1	12	yes	—
240	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
241	C₂²×C₄	C₂×D₄×C₆₇	1	24	yes	—
242	C₂²×C₄	C₂⁴×C₆₇	1	3	yes	—
243	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
244	M₁₆	—	2	32	no	—
245	C₂×C₈	—	2	24	no	—
246	C₂×C₈	C₂⁴×C₆₇	1	8	yes	complemented
247	C₄⋊C₄	—	2	12	no	—
248	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	complemented
249	C₂²⋊C₄	—	2	16	no	—
250	C₄²	—	2	16	no	—
251	C₂³	—	2	24	no	—
252	C₂³	—	2	32	no	—
253	C₂³	—	2	48	no	—
254	C₂³	—	2	64	no	—
255	C₂³	—	2	8	no	—
256	C₂³	—	4	64	no	—
257	C₂³	—	4	384	no	—
258	C₂³	—	4	48	no	—
259	C₂³	—	4	64	no	—
260	C₂³	C₂×C₂²⋊C₄×C₆₇	1	24	yes	—
261	C₂³	C₂×C₂²⋊C₄×C₆₇	1	4	yes	—
262	C₂³	AGL(1,ℤ/8)×C₆₇	1	8	yes	—
263	C₂³	C₂²×D₄×C₆₇	1	4	yes	—
264	C₂³	C₂²×D₄×C₆₇	1	3	yes	—
265	D₄	—	2	48	no	—
266	D₄	—	2	64	no	—
267	D₄	—	2	8	no	—
268	D₄	C₂³×C₄×C₆₇	1	16	yes	—
269	C₂×C₄	—	2	8	no	—
270	C₂×C₄	—	4	24	no	—
271	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	48	yes	—
272	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	12	yes	—
273	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	24	yes	—
274	C₂×C₄	C₂³×C₄×C₆₇	1	6	yes	—
275	C₂×C₄	C₂³×C₄×C₆₇	1	8	yes	—
276	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
277	C₂×C₄	C₂²×D₄×C₆₇	1	3	yes	—
278	C₂×C₄	C₂²×D₄×C₆₇	1	6	yes	—
279	C₂×C₄	C₂²×D₄×C₆₇	1	8	yes	—
280	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
281	C₈	—	2	8	no	—
282	C₂²	—	2	8	no	—
283	C₂²	—	2	48	no	—
284	C₂²	—	2	16	no	—
285	C₂²	—	4	128	no	—
286	C₂²	—	4	16	no	—
287	C₂²	—	4	96	no	—
288	C₂²	#418×C₆₇	1	16	yes	direct product factor
289	C₂²	C₂²×C₂²⋊C₄×C₆₇	1	8	yes	—
290	C₂²	C₂²×C₂²⋊C₄×C₆₇	1	6	yes	—
291	C₂²	C₂×AGL(1,ℤ/8)×C₆₇	1	12	yes	—
292	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
293	C₄	—	4	8	no	—
294	C₄	C₂²×C₂²⋊C₄×C₆₇	1	6	yes	—
295	C₄	C₂²×C₂²⋊C₄×C₆₇	1	8	yes	—
296	C₄	C₂⁴×C₄×C₆₇	1	1	yes	characteristic
297	C₄	C₂³×D₄×C₆₇	1	1	yes	characteristic
298	C₂	—	2	8	no	—
299	C₂	—	4	16	no	—
300	C₂	C₂×#418×C₆₇	1	12	yes	direct product factor
301	C₂	C₂³×C₂²⋊C₄×C₆₇	1	1	yes	characteristic
302	C₂	C₂²×AGL(1,ℤ/8)×C₆₇	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
2. C₂³×M₁₆×C₆₇	C₂	semidirect
3. C₂²×#117×C₆₇	C₂	semidirect
4. C₂×#418×C₆₇	C₂	direct (N × H)
5. C₂²×#102×C₆₇	C₂	semidirect
10. C₂³×D₄×C₆₇	C₄	semidirect
15. C₂²×M₁₆×C₆₇	C₂²	semidirect
16. C₂³×C₈×C₆₇	C₂²	semidirect
18. C₂×#117×C₆₇	C₂²	semidirect
19. C₂²×C₄⋊C₄×C₆₇	C₂²	semidirect
22. #418×C₆₇	C₂²	direct (N × H)
23. C₂×#102×C₆₇	C₂²	semidirect
37. C₂²×D₄×C₆₇	C₂×C₄	semidirect
48. C₂×M₁₆×C₆₇	C₂³	semidirect
50. C₂²×C₈×C₆₇	C₂³	semidirect
52. #117×C₆₇	C₂³	semidirect
54. C₂×C₄⋊C₄×C₆₇	C₂³	semidirect
57. #102×C₆₇	C₂³	semidirect
77. C₂×D₄×C₆₇	C₂²×C₄	semidirect
94. C₂×C₈×C₆₇	C₂⁴	semidirect
96. C₄⋊C₄×C₆₇	C₂⁴	semidirect
136. C₂²×C₆₇	#418	direct (N × H)
146. C₂²×#418	C₆₇	direct (N × H)
149. C₂×C₆₇	C₂×#418	direct (N × H)
153. C₂³×M₁₆	C₂×C₆₇	semidirect
154. C₂²×#117	C₂×C₆₇	semidirect
155. C₂×#418	C₂×C₆₇	direct (N × H)
156. C₂²×#102	C₂×C₆₇	semidirect
157. C₆₇	C₂²×#418	direct (N × H)
162. C₂³×D₄	C₄×C₆₇	semidirect
167. C₂²×M₁₆	C₂²×C₆₇	semidirect
168. C₂³×C₈	C₂²×C₆₇	semidirect
170. C₂×#117	C₂²×C₆₇	semidirect
171. C₂²×C₄⋊C₄	C₂²×C₆₇	semidirect
174. #418	C₂²×C₆₇	direct (N × H)
175. C₂×#102	C₂²×C₆₇	semidirect
189. C₂²×D₄	C₂×C₄×C₆₇	semidirect
200. C₂×M₁₆	C₂³×C₆₇	semidirect
202. C₂²×C₈	C₂³×C₆₇	semidirect
204. #117	C₂³×C₆₇	semidirect
206. C₂×C₄⋊C₄	C₂³×C₆₇	semidirect
209. #102	C₂³×C₆₇	semidirect
229. C₂×D₄	C₂²×C₄×C₆₇	semidirect
246. C₂×C₈	C₂⁴×C₆₇	semidirect
248. C₄⋊C₄	C₂⁴×C₆₇	semidirect
288. C₂²	#418×C₆₇	direct (N × H)
300. C₂	C₂×#418×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
C₂⁴×D₄×C₆₇	2
C₂³×M₁₆×C₆₇	2
C₂²×#117×C₆₇	2
C₂×#418×C₆₇	2
C₂²×#102×C₆₇	2
C₂²×#418	67

Subgroups — C22×#418×C67 #30739331

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#418×C₆₇ #30739331