Subgroups — C₂²×#447×C₆₇ #30739598

Order 17152.

7470 conjugacy classes of subgroups.

The subgroup lattice has 372 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, complemented
2	C₂³×D₈×C₆₇	C₂	1	2	yes	maximal, complemented
3	C₂²×#121×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#447×C₆₇	C₂	1	24	yes	maximal, direct product factor
5	C₂²×#102×C₆₇	C₂	1	2	yes	maximal, complemented
6	C₂²×C₂²⋊C₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂⁶×C₆₇	—	2	1	no	—
8	C₂³×D₄×C₆₇	—	2	16	no	—
9	C₂³×D₄×C₆₇	—	2	1	no	—
10	C₂³×D₄×C₆₇	—	2	6	no	—
11	C₂³×D₄×C₆₇	—	2	1	no	—
12	C₂³×D₄×C₆₇	C₂²	1	2	yes	—
13	C₂³×D₄×C₆₇	C₂²	1	12	yes	complemented
14	C₂³×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
15	C₂⁴×C₄×C₆₇	C₂²	1	1	yes	characteristic
16	C₂²×D₈×C₆₇	—	2	16	no	—
17	C₂²×D₈×C₆₇	C₂²	1	24	yes	complemented
18	C₂³×C₈×C₆₇	C₂²	1	2	yes	complemented
19	C₂×#121×C₆₇	—	2	6	no	—
20	C₂×#121×C₆₇	C₂²	1	12	yes	complemented
21	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
22	C₂²×C₂²⋊C₄×C₆₇	—	2	1	no	—
23	#447×C₆₇	C₂²	1	64	yes	direct product factor
24	C₂×#102×C₆₇	C₂²	1	24	yes	complemented
25	C₂×C₂²⋊C₈×C₆₇	C₂²	1	12	yes	complemented
26	C₂⁵×C₆₇	—	2	16	no	—
27	C₂⁵×C₆₇	—	2	12	no	—
28	C₂⁵×C₆₇	—	2	2	no	—
29	C₂⁵×C₆₇	—	2	1	no	—
30	C₂⁵×C₆₇	—	4	8	no	—
31	C₂⁵×C₆₇	—	4	8	no	—
32	C₂⁵×C₆₇	D₄	1	1	yes	characteristic
33	C₂²×D₄×C₆₇	—	2	16	no	—
34	C₂²×D₄×C₆₇	—	2	96	no	—
35	C₂²×D₄×C₆₇	—	2	96	no	—
36	C₂²×D₄×C₆₇	—	2	12	no	—
37	C₂²×D₄×C₆₇	—	2	6	no	—
38	C₂²×D₄×C₆₇	—	2	8	no	—
39	C₂²×D₄×C₆₇	—	2	12	no	—
40	C₂²×D₄×C₆₇	—	2	24	no	—
41	C₂²×D₄×C₆₇	—	2	8	no	—
42	C₂²×D₄×C₆₇	—	2	3	no	—
43	C₂²×D₄×C₆₇	—	4	8	no	—
44	C₂²×D₄×C₆₇	D₄	1	16	yes	complemented
45	C₂²×D₄×C₆₇	C₂³	1	12	yes	—
46	C₂²×D₄×C₆₇	C₂³	1	16	yes	complemented
47	C₂²×D₄×C₆₇	C₂³	1	6	yes	complemented
48	C₂³×C₄×C₆₇	—	2	8	no	—
49	C₂³×C₄×C₆₇	—	2	1	no	—
50	C₂³×C₄×C₆₇	D₄	1	6	yes	—
51	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
52	C₂³×C₄×C₆₇	C₂³	1	6	yes	—
53	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
54	C₂×D₈×C₆₇	—	2	96	no	—
55	C₂×D₈×C₆₇	C₂³	1	32	yes	complemented
56	C₂²×C₈×C₆₇	—	2	8	no	—
57	C₂²×C₈×C₆₇	C₂³	1	12	yes	complemented
58	#121×C₆₇	—	2	24	no	—
59	#121×C₆₇	C₂³	1	16	yes	complemented
60	C₂×C₄⋊C₄×C₆₇	—	2	3	no	—
61	C₂×C₄⋊C₄×C₆₇	C₂³	1	6	yes	complemented
62	C₂×C₂²⋊C₄×C₆₇	—	2	12	no	—
63	#102×C₆₇	C₂³	1	32	yes	complemented
64	C₂²⋊C₈×C₆₇	C₂³	1	16	yes	complemented
65	C₂⁴×C₆₇	—	2	4	no	—
66	C₂⁴×C₆₇	—	2	4	no	—
67	C₂⁴×C₆₇	—	2	96	no	—
68	C₂⁴×C₆₇	—	2	16	no	—
69	C₂⁴×C₆₇	—	2	12	no	—
70	C₂⁴×C₆₇	—	2	16	no	—
71	C₂⁴×C₆₇	—	2	6	no	—
72	C₂⁴×C₆₇	—	4	48	no	—
73	C₂⁴×C₆₇	—	4	128	no	—
74	C₂⁴×C₆₇	—	4	8	no	—
75	C₂⁴×C₆₇	—	4	48	no	—
76	C₂⁴×C₆₇	—	4	8	no	—
77	C₂⁴×C₆₇	—	4	4	no	—
78	C₂⁴×C₆₇	—	4	4	no	—
79	C₂⁴×C₆₇	—	4	4	no	—
80	C₂⁴×C₆₇	D₈	1	8	yes	complemented
81	C₂⁴×C₆₇	C₂×D₄	1	6	yes	—
82	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
83	C₂×D₄×C₆₇	—	2	96	no	—
84	C₂×D₄×C₆₇	—	2	192	no	—
85	C₂×D₄×C₆₇	—	2	64	no	—
86	C₂×D₄×C₆₇	—	2	16	no	—
87	C₂×D₄×C₆₇	—	2	48	no	—
88	C₂×D₄×C₆₇	—	2	12	no	—
89	C₂×D₄×C₆₇	—	2	24	no	—
90	C₂×D₄×C₆₇	—	2	16	no	—
91	C₂×D₄×C₆₇	—	2	24	no	—
92	C₂×D₄×C₆₇	—	2	6	no	—
93	C₂×D₄×C₆₇	—	4	48	no	—
94	C₂×D₄×C₆₇	—	4	12	no	—
95	C₂×D₄×C₆₇	C₂×D₄	1	48	yes	complemented
96	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
97	C₂×D₄×C₆₇	C₂⁴	1	4	yes	complemented
98	C₂²×C₄×C₆₇	—	2	4	no	—
99	C₂²×C₄×C₆₇	—	2	24	no	—
100	C₂²×C₄×C₆₇	—	2	24	no	—
101	C₂²×C₄×C₆₇	—	2	6	no	—
102	C₂²×C₄×C₆₇	—	4	4	no	—
103	C₂²×C₄×C₆₇	C₂×D₄	1	6	yes	—
104	C₂²×C₄×C₆₇	C₂×D₄	1	12	yes	—
105	C₂²×C₄×C₆₇	C₂×D₄	1	3	yes	—
106	C₂²×C₄×C₆₇	C₂×D₄	1	8	yes	—
107	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
108	C₂²×C₄×C₆₇	C₂⁴	1	3	yes	—
109	D₈×C₆₇	—	2	64	no	—
110	C₂×C₈×C₆₇	—	2	24	no	—
111	C₂×C₈×C₆₇	C₂⁴	1	8	yes	complemented
112	C₄⋊C₄×C₆₇	—	2	6	no	—
113	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	complemented
114	C₂²⋊C₄×C₆₇	—	2	16	no	—
115	C₂³×C₆₇	—	2	12	no	—
116	C₂³×C₆₇	—	2	12	no	—
117	C₂³×C₆₇	—	2	32	no	—
118	C₂³×C₆₇	—	2	64	no	—
119	C₂³×C₆₇	—	2	48	no	—
120	C₂³×C₆₇	—	2	8	no	—
121	C₂³×C₆₇	—	2	4	no	—
122	C₂³×C₆₇	—	4	384	no	—
123	C₂³×C₆₇	—	4	32	no	—
124	C₂³×C₆₇	—	4	24	no	—
125	C₂³×C₆₇	—	4	32	no	—
126	C₂³×C₆₇	—	4	24	no	—
127	C₂³×C₆₇	—	4	64	no	—
128	C₂³×C₆₇	—	4	12	no	—
129	C₂³×C₆₇	—	4	12	no	—
130	C₂³×C₆₇	—	4	12	no	—
131	C₂³×C₆₇	—	8	16	no	—
132	C₂³×C₆₇	#120	1	4	yes	—
133	C₂³×C₆₇	C₂×D₈	1	4	yes	—
134	C₂³×C₆₇	C₂×D₈	1	24	yes	complemented
135	C₂³×C₆₇	AGL(1,ℤ/8)	1	4	yes	—
136	C₂³×C₆₇	C₂²×D₄	1	4	yes	—
137	C₂³×C₆₇	C₂²×D₄	1	3	yes	—
138	D₄×C₆₇	—	2	64	no	—
139	D₄×C₆₇	—	2	48	no	—
140	D₄×C₆₇	—	2	8	no	—
141	D₄×C₆₇	—	2	8	no	—
142	D₄×C₆₇	—	4	32	no	—
143	D₄×C₆₇	—	4	12	no	—
144	D₄×C₆₇	C₂²×D₄	1	16	yes	complemented
145	C₂×C₄×C₆₇	—	2	12	no	—
146	C₂×C₄×C₆₇	—	2	24	no	—
147	C₂×C₄×C₆₇	—	2	8	no	—
148	C₂×C₄×C₆₇	—	2	4	no	—
149	C₂×C₄×C₆₇	—	4	12	no	—
150	C₂×C₄×C₆₇	#120	1	12	yes	—
151	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
152	C₂×C₄×C₆₇	C₂²×D₄	1	3	yes	—
153	C₂×C₄×C₆₇	C₂²×D₄	1	12	yes	—
154	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
155	C₈×C₆₇	—	2	8	no	—
156	C₂²×C₆₇	—	2	4	no	—
157	C₂²×C₆₇	—	2	48	no	—
158	C₂²×C₆₇	—	2	4	no	—
159	C₂²×C₆₇	—	2	16	no	—
160	C₂²×C₆₇	—	4	128	no	—
161	C₂²×C₆₇	—	4	96	no	—
162	C₂²×C₆₇	—	4	8	no	—
163	C₂²×C₆₇	—	4	8	no	—
164	C₂²×C₆₇	—	4	4	no	—
165	C₂²×C₆₇	—	4	4	no	—
166	C₂²×C₆₇	—	4	4	no	—
167	C₂²×C₆₇	—	8	24	no	—
168	C₂²×C₆₇	#447	1	16	yes	direct product factor
169	C₂²×C₆₇	C₂×#120	1	6	yes	—
170	C₂²×C₆₇	C₂²×D₈	1	6	yes	—
171	C₂²×C₆₇	C₂²×D₈	1	8	yes	complemented
172	C₂²×C₆₇	C₂×AGL(1,ℤ/8)	1	6	yes	—
173	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
174	C₄×C₆₇	—	2	4	no	—
175	C₄×C₆₇	—	4	4	no	—
176	C₄×C₆₇	C₂×#120	1	6	yes	—
177	C₄×C₆₇	C₂³×D₄	1	2	yes	—
178	C₂²×#447	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
179	C₂×C₆₇	—	2	8	no	—
180	C₂×C₆₇	—	4	16	no	—
181	C₂×C₆₇	—	8	4	no	—
182	C₂×C₆₇	C₂×#447	1	12	yes	direct product factor
183	C₂×C₆₇	C₂²×#120	1	1	yes	characteristic
184	C₂×C₆₇	C₂³×D₈	1	1	yes	characteristic
185	C₂×C₆₇	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
186	C₂⁴×D₄	C₂×C₆₇	1	1	yes	characteristic, complemented
187	C₂³×D₈	C₂×C₆₇	1	2	yes	complemented
188	C₂²×#121	C₂×C₆₇	1	1	yes	characteristic, complemented
189	C₂×#447	C₂×C₆₇	1	24	yes	direct product factor
190	C₂²×#102	C₂×C₆₇	1	2	yes	complemented
191	C₂²×C₂²⋊C₈	C₂×C₆₇	1	1	yes	characteristic, complemented
192	C₆₇	C₂²×#447	1	1	yes	characteristic, direct product factor, Sylow
193	C₂⁶	—	2	1	no	—
194	C₂³×D₄	—	2	16	no	—
195	C₂³×D₄	—	2	1	no	—
196	C₂³×D₄	—	2	1	no	—
197	C₂³×D₄	—	2	6	no	—
198	C₂³×D₄	C₂²×C₆₇	1	2	yes	—
199	C₂³×D₄	C₂²×C₆₇	1	12	yes	complemented
200	C₂³×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
201	C₂⁴×C₄	C₂²×C₆₇	1	1	yes	characteristic
202	C₂²×D₈	—	2	16	no	—
203	C₂²×D₈	C₂²×C₆₇	1	24	yes	complemented
204	C₂³×C₈	C₂²×C₆₇	1	2	yes	complemented
205	C₂×#121	—	2	6	no	—
206	C₂×#121	C₂²×C₆₇	1	12	yes	complemented
207	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
208	C₂²×C₂²⋊C₄	—	2	1	no	—
209	#447	C₂²×C₆₇	1	64	yes	direct product factor
210	C₂×#102	C₂²×C₆₇	1	24	yes	complemented
211	C₂×C₂²⋊C₈	C₂²×C₆₇	1	12	yes	complemented
212	C₂⁵	—	2	16	no	—
213	C₂⁵	—	2	2	no	—
214	C₂⁵	—	2	12	no	—
215	C₂⁵	—	2	1	no	—
216	C₂⁵	—	4	8	no	—
217	C₂⁵	—	4	8	no	—
218	C₂⁵	D₄×C₆₇	1	1	yes	characteristic
219	C₂²×D₄	—	2	16	no	—
220	C₂²×D₄	—	2	96	no	—
221	C₂²×D₄	—	2	96	no	—
222	C₂²×D₄	—	2	12	no	—
223	C₂²×D₄	—	2	6	no	—
224	C₂²×D₄	—	2	8	no	—
225	C₂²×D₄	—	2	12	no	—
226	C₂²×D₄	—	2	24	no	—
227	C₂²×D₄	—	2	8	no	—
228	C₂²×D₄	—	2	3	no	—
229	C₂²×D₄	—	4	8	no	—
230	C₂²×D₄	D₄×C₆₇	1	16	yes	complemented
231	C₂²×D₄	C₂³×C₆₇	1	12	yes	—
232	C₂²×D₄	C₂³×C₆₇	1	16	yes	complemented
233	C₂²×D₄	C₂³×C₆₇	1	6	yes	complemented
234	C₂³×C₄	—	2	8	no	—
235	C₂³×C₄	—	2	1	no	—
236	C₂³×C₄	D₄×C₆₇	1	1	yes	characteristic
237	C₂³×C₄	D₄×C₆₇	1	6	yes	—
238	C₂³×C₄	C₂³×C₆₇	1	6	yes	—
239	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
240	C₂×D₈	—	2	96	no	—
241	C₂×D₈	C₂³×C₆₇	1	32	yes	complemented
242	C₂²×C₈	—	2	8	no	—
243	C₂²×C₈	C₂³×C₆₇	1	12	yes	complemented
244	#121	—	2	24	no	—
245	#121	C₂³×C₆₇	1	16	yes	complemented
246	C₂×C₄⋊C₄	—	2	3	no	—
247	C₂×C₄⋊C₄	C₂³×C₆₇	1	6	yes	complemented
248	C₂×C₂²⋊C₄	—	2	12	no	—
249	#102	C₂³×C₆₇	1	32	yes	complemented
250	C₂²⋊C₈	C₂³×C₆₇	1	16	yes	complemented
251	C₂⁴	—	2	4	no	—
252	C₂⁴	—	2	4	no	—
253	C₂⁴	—	2	96	no	—
254	C₂⁴	—	2	16	no	—
255	C₂⁴	—	2	12	no	—
256	C₂⁴	—	2	16	no	—
257	C₂⁴	—	2	6	no	—
258	C₂⁴	—	4	48	no	—
259	C₂⁴	—	4	128	no	—
260	C₂⁴	—	4	8	no	—
261	C₂⁴	—	4	48	no	—
262	C₂⁴	—	4	8	no	—
263	C₂⁴	—	4	4	no	—
264	C₂⁴	—	4	4	no	—
265	C₂⁴	—	4	4	no	—
266	C₂⁴	D₈×C₆₇	1	8	yes	complemented
267	C₂⁴	C₂×D₄×C₆₇	1	6	yes	—
268	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
269	C₂×D₄	—	2	96	no	—
270	C₂×D₄	—	2	192	no	—
271	C₂×D₄	—	2	64	no	—
272	C₂×D₄	—	2	16	no	—
273	C₂×D₄	—	2	48	no	—
274	C₂×D₄	—	2	12	no	—
275	C₂×D₄	—	2	24	no	—
276	C₂×D₄	—	2	16	no	—
277	C₂×D₄	—	2	24	no	—
278	C₂×D₄	—	2	6	no	—
279	C₂×D₄	—	4	48	no	—
280	C₂×D₄	—	4	12	no	—
281	C₂×D₄	C₂×D₄×C₆₇	1	48	yes	complemented
282	C₂×D₄	C₂⁴×C₆₇	1	8	yes	—
283	C₂×D₄	C₂⁴×C₆₇	1	4	yes	complemented
284	C₂²×C₄	—	2	4	no	—
285	C₂²×C₄	—	2	24	no	—
286	C₂²×C₄	—	2	24	no	—
287	C₂²×C₄	—	2	6	no	—
288	C₂²×C₄	—	4	4	no	—
289	C₂²×C₄	C₂×D₄×C₆₇	1	6	yes	—
290	C₂²×C₄	C₂×D₄×C₆₇	1	12	yes	—
291	C₂²×C₄	C₂×D₄×C₆₇	1	3	yes	—
292	C₂²×C₄	C₂×D₄×C₆₇	1	8	yes	—
293	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
294	C₂²×C₄	C₂⁴×C₆₇	1	3	yes	—
295	D₈	—	2	64	no	—
296	C₂×C₈	—	2	24	no	—
297	C₂×C₈	C₂⁴×C₆₇	1	8	yes	complemented
298	C₄⋊C₄	—	2	6	no	—
299	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	complemented
300	C₂²⋊C₄	—	2	16	no	—
301	C₂³	—	2	12	no	—
302	C₂³	—	2	12	no	—
303	C₂³	—	2	32	no	—
304	C₂³	—	2	64	no	—
305	C₂³	—	2	48	no	—
306	C₂³	—	2	8	no	—
307	C₂³	—	2	4	no	—
308	C₂³	—	4	32	no	—
309	C₂³	—	4	384	no	—
310	C₂³	—	4	24	no	—
311	C₂³	—	4	32	no	—
312	C₂³	—	4	24	no	—
313	C₂³	—	4	64	no	—
314	C₂³	—	4	12	no	—
315	C₂³	—	4	12	no	—
316	C₂³	—	4	12	no	—
317	C₂³	—	8	16	no	—
318	C₂³	#120×C₆₇	1	4	yes	—
319	C₂³	C₂×D₈×C₆₇	1	4	yes	—
320	C₂³	C₂×D₈×C₆₇	1	24	yes	complemented
321	C₂³	AGL(1,ℤ/8)×C₆₇	1	4	yes	—
322	C₂³	C₂²×D₄×C₆₇	1	4	yes	—
323	C₂³	C₂²×D₄×C₆₇	1	3	yes	—
324	D₄	—	2	64	no	—
325	D₄	—	2	48	no	—
326	D₄	—	2	8	no	—
327	D₄	—	2	8	no	—
328	D₄	—	4	32	no	—
329	D₄	—	4	12	no	—
330	D₄	C₂²×D₄×C₆₇	1	16	yes	complemented
331	C₂×C₄	—	2	12	no	—
332	C₂×C₄	—	2	24	no	—
333	C₂×C₄	—	2	8	no	—
334	C₂×C₄	—	2	4	no	—
335	C₂×C₄	—	4	12	no	—
336	C₂×C₄	#120×C₆₇	1	12	yes	—
337	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
338	C₂×C₄	C₂²×D₄×C₆₇	1	3	yes	—
339	C₂×C₄	C₂²×D₄×C₆₇	1	12	yes	—
340	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
341	C₈	—	2	8	no	—
342	C₂²	—	2	4	no	—
343	C₂²	—	2	4	no	—
344	C₂²	—	2	48	no	—
345	C₂²	—	2	16	no	—
346	C₂²	—	4	128	no	—
347	C₂²	—	4	8	no	—
348	C₂²	—	4	8	no	—
349	C₂²	—	4	96	no	—
350	C₂²	—	4	4	no	—
351	C₂²	—	4	4	no	—
352	C₂²	—	4	4	no	—
353	C₂²	—	8	24	no	—
354	C₂²	#447×C₆₇	1	16	yes	direct product factor
355	C₂²	C₂×#120×C₆₇	1	6	yes	—
356	C₂²	C₂²×D₈×C₆₇	1	6	yes	—
357	C₂²	C₂²×D₈×C₆₇	1	8	yes	complemented
358	C₂²	C₂×AGL(1,ℤ/8)×C₆₇	1	6	yes	—
359	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
360	C₄	—	2	4	no	—
361	C₄	—	4	4	no	—
362	C₄	C₂×#120×C₆₇	1	6	yes	—
363	C₄	C₂³×D₄×C₆₇	1	2	yes	—
364	C₂	—	2	8	no	—
365	C₂	—	4	16	no	—
366	C₂	—	8	4	no	—
367	C₂	C₂×#447×C₆₇	1	12	yes	direct product factor
368	C₂	C₂²×#120×C₆₇	1	1	yes	characteristic
369	C₂	C₂³×D₈×C₆₇	1	1	yes	characteristic
370	C₂	C₂²×AGL(1,ℤ/8)×C₆₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₆₇	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
LCS	G ▷ C₂×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
1. C₂⁴×D₄×C₆₇	C₂	semidirect
2. C₂³×D₈×C₆₇	C₂	semidirect
3. C₂²×#121×C₆₇	C₂	semidirect
4. C₂×#447×C₆₇	C₂	direct (N × H)
5. C₂²×#102×C₆₇	C₂	semidirect
6. C₂²×C₂²⋊C₈×C₆₇	C₂	semidirect
13. C₂³×D₄×C₆₇	C₂²	semidirect
14. C₂³×D₄×C₆₇	C₂²	semidirect
17. C₂²×D₈×C₆₇	C₂²	semidirect
18. C₂³×C₈×C₆₇	C₂²	semidirect
20. C₂×#121×C₆₇	C₂²	semidirect
21. C₂²×C₄⋊C₄×C₆₇	C₂²	semidirect
23. #447×C₆₇	C₂²	direct (N × H)
24. C₂×#102×C₆₇	C₂²	semidirect
25. C₂×C₂²⋊C₈×C₆₇	C₂²	semidirect
44. C₂²×D₄×C₆₇	D₄	semidirect
46. C₂²×D₄×C₆₇	C₂³	semidirect
47. C₂²×D₄×C₆₇	C₂³	semidirect
55. C₂×D₈×C₆₇	C₂³	semidirect
57. C₂²×C₈×C₆₇	C₂³	semidirect
59. #121×C₆₇	C₂³	semidirect
61. C₂×C₄⋊C₄×C₆₇	C₂³	semidirect
63. #102×C₆₇	C₂³	semidirect
64. C₂²⋊C₈×C₆₇	C₂³	semidirect
80. C₂⁴×C₆₇	D₈	semidirect
95. C₂×D₄×C₆₇	C₂×D₄	semidirect
97. C₂×D₄×C₆₇	C₂⁴	semidirect
111. C₂×C₈×C₆₇	C₂⁴	semidirect
113. C₄⋊C₄×C₆₇	C₂⁴	semidirect
134. C₂³×C₆₇	C₂×D₈	semidirect
144. D₄×C₆₇	C₂²×D₄	semidirect
168. C₂²×C₆₇	#447	direct (N × H)
171. C₂²×C₆₇	C₂²×D₈	semidirect
178. C₂²×#447	C₆₇	direct (N × H)
182. C₂×C₆₇	C₂×#447	direct (N × H)
186. C₂⁴×D₄	C₂×C₆₇	semidirect
187. C₂³×D₈	C₂×C₆₇	semidirect
188. C₂²×#121	C₂×C₆₇	semidirect
189. C₂×#447	C₂×C₆₇	direct (N × H)
190. C₂²×#102	C₂×C₆₇	semidirect
191. C₂²×C₂²⋊C₈	C₂×C₆₇	semidirect
192. C₆₇	C₂²×#447	direct (N × H)
199. C₂³×D₄	C₂²×C₆₇	semidirect
200. C₂³×D₄	C₂²×C₆₇	semidirect
203. C₂²×D₈	C₂²×C₆₇	semidirect
204. C₂³×C₈	C₂²×C₆₇	semidirect
206. C₂×#121	C₂²×C₆₇	semidirect
207. C₂²×C₄⋊C₄	C₂²×C₆₇	semidirect
209. #447	C₂²×C₆₇	direct (N × H)
210. C₂×#102	C₂²×C₆₇	semidirect
211. C₂×C₂²⋊C₈	C₂²×C₆₇	semidirect
230. C₂²×D₄	D₄×C₆₇	semidirect
232. C₂²×D₄	C₂³×C₆₇	semidirect
233. C₂²×D₄	C₂³×C₆₇	semidirect
241. C₂×D₈	C₂³×C₆₇	semidirect
243. C₂²×C₈	C₂³×C₆₇	semidirect
245. #121	C₂³×C₆₇	semidirect
247. C₂×C₄⋊C₄	C₂³×C₆₇	semidirect
249. #102	C₂³×C₆₇	semidirect
250. C₂²⋊C₈	C₂³×C₆₇	semidirect
266. C₂⁴	D₈×C₆₇	semidirect
281. C₂×D₄	C₂×D₄×C₆₇	semidirect
283. C₂×D₄	C₂⁴×C₆₇	semidirect
297. C₂×C₈	C₂⁴×C₆₇	semidirect
299. C₄⋊C₄	C₂⁴×C₆₇	semidirect
320. C₂³	C₂×D₈×C₆₇	semidirect
330. D₄	C₂²×D₄×C₆₇	semidirect
354. C₂²	#447×C₆₇	direct (N × H)
357. C₂²	C₂²×D₈×C₆₇	semidirect
367. C₂	C₂×#447×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×D₈×C₆₇	2
C₂²×#121×C₆₇	2
C₂×#447×C₆₇	2
C₂²×#102×C₆₇	2
C₂²×C₂²⋊C₈×C₆₇	2
C₂²×#447	67

Subgroups — C22×#447×C67 #30739598

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#447×C₆₇ #30739598