Subgroups — C₄×#16863871 #31014066

Order 17152.

4186 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	C₂×#16863871	C₂	1	2	yes	maximal
2	#22562570	C₂	1	8	yes	maximal, complemented
3	#22562566	C₂	1	2	yes	maximal, complemented
4	#22562562	C₂	1	4	yes	maximal, complemented
5	C₄×D₄×Dic₆₇	C₂	1	8	yes	maximal, complemented
6	C₄×#14524002	C₂	1	2	yes	maximal, complemented
7	C₂×C₄×C₂²⋊Dic₆₇	C₂	1	4	yes	maximal, complemented
8	C₂²×C₄×D₄×C₆₇	C₂	1	1	yes	maximal, characteristic
9	#16863871	C₄	1	32	yes	direct product factor
10	C₂×D₄×Dic₆₇	C₂²	1	16	yes	—
11	C₂×#14524002	C₂²	1	4	yes	—
12	C₂²×C₂²⋊Dic₆₇	C₂²	1	8	yes	—
13	C₂²×C₄×Dic₆₇	C₂²	1	8	yes	complemented
14	C₄⋊C₄×Dic₆₇	C₂²	1	16	yes	complemented
15	C₄×C₄⋊Dic₆₇	C₂²	1	4	yes	complemented
16	C₄×C₄⋊Dic₆₇	C₂²	1	4	yes	complemented
17	C₂²⋊C₄×Dic₆₇	C₂²	1	32	yes	complemented
18	C₄×C₂²⋊Dic₆₇	C₂²	1	4	yes	—
19	C₄×C₂²⋊Dic₆₇	C₂²	1	8	yes	—
20	C₄×C₂²⋊Dic₆₇	C₂²	1	4	yes	—
21	C₄×C₂²⋊Dic₆₇	C₂²	1	8	yes	complemented
22	C₄×C₂²⋊Dic₆₇	C₂²	1	8	yes	complemented
23	#16863242	C₂²	1	4	yes	complemented
24	C₂×C₆₇⋊#95	C₂²	1	8	yes	complemented
25	C₄²×Dic₆₇	C₂²	1	4	yes	complemented
26	C₂³×D₄×C₆₇	C₂²	1	1	yes	characteristic
27	C₂⁴×C₄×C₆₇	C₂²	1	2	yes	—
28	C₂×C₄×D₄×C₆₇	C₄	1	16	yes	complemented
29	C₂×C₄×D₄×C₆₇	C₂²	1	4	yes	—
30	C₂×C₄×D₄×C₆₇	C₂²	1	4	yes	—
31	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
32	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
33	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
34	C₂³×Dic₆₇	C₂³	1	16	yes	—
35	D₄×Dic₆₇	C₂×C₄	1	128	yes	complemented
36	#14524002	C₂×C₄	1	32	yes	complemented
37	C₂×C₄⋊Dic₆₇	C₂³	1	8	yes	—
38	C₂×C₂²⋊Dic₆₇	C₂×C₄	1	64	yes	complemented
39	C₂×C₂²⋊Dic₆₇	C₂³	1	8	yes	—
40	C₂×C₂²⋊Dic₆₇	C₂³	1	16	yes	—
41	C₂×C₄×Dic₆₇	—	4	16	no	—
42	C₂×C₄×Dic₆₇	C₂³	1	8	yes	—
43	C₂×C₄×Dic₆₇	C₂³	1	8	yes	—
44	C₂×C₄×Dic₆₇	C₂³	1	16	yes	—
45	C₂×C₄×Dic₆₇	C₂³	1	8	yes	—
46	C₆₇⋊#95	C₂³	1	8	yes	—
47	C₆₇⋊#95	C₂³	1	16	yes	—
48	C₆₇⋊#95	C₂³	1	8	yes	—
49	C₂⁵×C₆₇	C₂³	1	2	yes	—
50	C₂²×D₄×C₆₇	C₂×C₄	1	16	yes	—
51	C₂²×D₄×C₆₇	C₂×C₄	1	8	yes	—
52	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
53	C₂³×C₄×C₆₇	—	4	8	no	—
54	C₂³×C₄×C₆₇	C₂×C₄	1	16	yes	complemented
55	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
56	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
57	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
58	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
59	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
60	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
61	C₄×D₄×C₆₇	C₂×C₄	1	32	yes	complemented
62	C₄×D₄×C₆₇	C₂×C₄	1	32	yes	complemented
63	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	8	yes	complemented
64	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
65	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	16	yes	complemented
66	C₂×C₂²⋊C₄×C₆₇	C₂³	1	8	yes	—
67	C₂×C₄²×C₆₇	C₂×C₄	1	8	yes	complemented
68	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
69	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
70	C₂²×Dic₆₇	—	4	16	no	—
71	C₂²×Dic₆₇	—	4	16	no	—
72	C₂²×Dic₆₇	C₂²×C₄	1	64	yes	complemented
73	C₂²×Dic₆₇	C₂⁴	1	16	yes	—
74	C₄⋊Dic₆₇	C₂²×C₄	1	32	yes	complemented
75	C₂²⋊Dic₆₇	C₂²×C₄	1	32	yes	—
76	C₂²⋊Dic₆₇	C₂²×C₄	1	64	yes	complemented
77	C₄×Dic₆₇	—	2	16	no	—
78	C₄×Dic₆₇	—	4	16	no	—
79	C₄×Dic₆₇	—	4	8	no	—
80	C₄×Dic₆₇	C₂²×C₄	1	32	yes	complemented
81	C₂⁴×C₆₇	—	4	4	no	—
82	C₂⁴×C₆₇	—	4	4	no	—
83	C₂⁴×C₆₇	C₂²×C₄	1	16	yes	—
84	C₂⁴×C₆₇	C₂²×C₄	1	8	yes	—
85	C₂⁴×C₆₇	C₂⁴	1	4	yes	—
86	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
87	C₂×D₄×C₆₇	C₄²	1	64	yes	complemented
88	C₂×D₄×C₆₇	C₂²×C₄	1	32	yes	—
89	C₂×D₄×C₆₇	C₂²×C₄	1	16	yes	—
90	C₂²×C₄×C₆₇	—	2	4	no	—
91	C₂²×C₄×C₆₇	—	2	16	no	—
92	C₂²×C₄×C₆₇	—	4	32	no	—
93	C₂²×C₄×C₆₇	—	4	8	no	—
94	C₂²×C₄×C₆₇	—	4	4	no	—
95	C₂²×C₄×C₆₇	—	4	2	no	—
96	C₂²×C₄×C₆₇	C₂²×C₄	1	8	yes	—
97	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
98	C₂²×C₄×C₆₇	C₂²×C₄	1	16	yes	—
99	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
100	C₂²×C₄×C₆₇	C₂²×C₄	1	8	yes	—
101	C₂²×C₄×C₆₇	C₂²×C₄	1	16	yes	—
102	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
103	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
104	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
105	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
106	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
107	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
108	C₄⋊C₄×C₆₇	C₂²×C₄	1	16	yes	—
109	C₂²⋊C₄×C₆₇	C₂²×C₄	1	32	yes	—
110	C₄²×C₆₇	C₂²×C₄	1	8	yes	—
111	C₄²×C₆₇	C₂²×C₄	1	8	yes	—
112	C₂³×C₆₇	—	2	2	no	—
113	C₂³×C₆₇	—	2	8	no	—
114	C₂³×C₆₇	—	2	2	no	—
115	C₂³×C₆₇	—	2	8	no	—
116	C₂³×C₆₇	—	4	8	no	—
117	C₂³×C₆₇	—	4	32	no	—
118	C₂³×C₆₇	—	4	8	no	—
119	C₂³×C₆₇	C₂×C₄²	1	32	yes	complemented
120	C₂³×C₆₇	C₂³×C₄	1	4	yes	—
121	C₂³×C₆₇	C₂³×C₄	1	16	yes	—
122	C₂³×C₆₇	C₂³×C₄	1	8	yes	—
123	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
124	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
125	D₄×C₆₇	C₂×C₄²	1	64	yes	complemented
126	C₂×C₄×C₆₇	—	2	2	no	—
127	C₂×C₄×C₆₇	—	2	8	no	—
128	C₂×C₄×C₆₇	—	2	4	no	—
129	C₂×C₄×C₆₇	—	2	8	no	—
130	C₂×C₄×C₆₇	—	2	32	no	—
131	C₂×C₄×C₆₇	—	4	16	no	—
132	C₂×C₄×C₆₇	—	4	8	no	—
133	C₂×C₄×C₆₇	—	4	4	no	—
134	C₂×C₄×C₆₇	C₂×C₄²	1	16	yes	complemented
135	C₂×C₄×C₆₇	C₂³×C₄	1	8	yes	—
136	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
137	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
138	C₂×C₄×C₆₇	C₂³×C₄	1	8	yes	—
139	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
140	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
141	C₂×C₄×C₆₇	H(5,𝔽₂)	1	4	yes	—
142	C₂×Dic₆₇	—	2	16	no	—
143	C₂×Dic₆₇	—	2	16	no	—
144	C₂×Dic₆₇	—	4	64	no	—
145	C₂×Dic₆₇	C₂³×C₄	1	32	yes	—
146	C₂²×C₆₇	—	2	2	no	—
147	C₂²×C₆₇	—	2	8	no	—
148	C₂²×C₆₇	—	2	2	no	—
149	C₂²×C₆₇	—	2	8	no	—
150	C₂²×C₆₇	—	2	32	no	—
151	C₂²×C₆₇	—	2	8	no	—
152	C₂²×C₆₇	—	4	32	no	—
153	C₂²×C₆₇	C₂²×C₄²	1	4	yes	—
154	C₂²×C₆₇	C₂²×C₄²	1	16	yes	—
155	C₂²×C₆₇	C₂⁴×C₄	1	2	yes	—
156	C₂²×C₆₇	C₂⁴×C₄	1	1	yes	characteristic
157	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
158	C₂²×C₆₇	#585	1	2	yes	—
159	C₄×C₆₇	—	2	2	no	—
160	C₄×C₆₇	—	2	8	no	—
161	C₄×C₆₇	—	2	4	no	—
162	C₄×C₆₇	C₂²×C₄²	1	8	yes	—
163	C₄×C₆₇	#518	1	4	yes	complemented
164	Dic₆₇	—	2	32	no	—
165	C₄×#518	—	67	1	no	maximal, Sylow
166	C₂×C₆₇	—	2	4	no	—
167	C₂×C₆₇	—	2	16	no	—
168	C₂×C₆₇	C₂³×C₄²	1	1	yes	characteristic
169	C₂×C₆₇	C₂×#518	1	1	yes	characteristic
170	C₂×C₆₇	#3428	1	1	yes	characteristic
171	C₂×C₆₇	C₄×H(5,𝔽₂)	1	4	yes	—
172	C₂×#518	—	67	2	no	—
173	C₂²×C₄×D₄	D₆₇	1	1	yes	characteristic
174	#2275	—	67	8	no	—
175	#2274	—	67	2	no	—
176	#2273	—	67	4	no	—
177	C₄²×D₄	—	67	8	no	—
178	C₄×#117	—	67	2	no	—
179	C₂×C₄×C₂²⋊C₄	—	67	4	no	—
180	C₆₇	C₄×#518	1	1	yes	characteristic, complemented, Sylow
181	C₂³×D₄	C₂×D₆₇	1	1	yes	characteristic
182	C₂⁴×C₄	C₂×D₆₇	1	2	yes	—
183	#518	—	67	32	no	—
184	C₂×C₄×D₄	—	67	16	no	—
185	C₂×C₄×D₄	Dic₆₇	1	16	yes	complemented
186	C₂×C₄×D₄	C₂×D₆₇	1	4	yes	—
187	C₂×C₄×D₄	C₂×D₆₇	1	4	yes	—
188	C₂×#117	—	67	4	no	—
189	C₂²×C₄⋊C₄	C₂×D₆₇	1	1	yes	characteristic
190	C₂²×C₂²⋊C₄	—	67	8	no	—
191	C₂²×C₂²⋊C₄	C₂×D₆₇	1	2	yes	—
192	C₂²×C₄²	—	67	8	no	—
193	C₂²×C₄²	C₂×D₆₇	1	1	yes	characteristic
194	C₄×C₄⋊C₄	—	67	16	no	—
195	C₄×C₄⋊C₄	—	67	4	no	—
196	C₄×C₄⋊C₄	—	67	4	no	—
197	C₄×C₂²⋊C₄	—	67	4	no	—
198	C₄×C₂²⋊C₄	—	67	8	no	—
199	C₄×C₂²⋊C₄	—	67	4	no	—
200	C₄×C₂²⋊C₄	—	67	8	no	—
201	C₄×C₂²⋊C₄	—	67	8	no	—
202	C₄×C₂²⋊C₄	—	67	32	no	—
203	#376	—	67	4	no	—
204	C₂×#95	—	67	8	no	—
205	C₄³	—	67	4	no	—
206	C₂⁵	C₂²×D₆₇	1	2	yes	—
207	C₂²×D₄	C₄×D₆₇	1	16	yes	—
208	C₂²×D₄	C₂×Dic₆₇	1	8	yes	—
209	C₂²×D₄	C₂²×D₆₇	1	4	yes	—
210	C₂³×C₄	—	4	8	no	—
211	C₂³×C₄	—	67	16	no	—
212	C₂³×C₄	C₂×Dic₆₇	1	16	yes	complemented
213	C₂³×C₄	C₂²×D₆₇	1	4	yes	—
214	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
215	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
216	C₂³×C₄	C₂²×D₆₇	1	2	yes	—
217	C₂³×C₄	C₂²×D₆₇	1	4	yes	—
218	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
219	C₄×D₄	—	67	128	no	—
220	C₄×D₄	C₂×Dic₆₇	1	32	yes	complemented
221	C₄×D₄	C₂×Dic₆₇	1	32	yes	complemented
222	#117	—	67	32	no	—
223	C₂×C₄⋊C₄	—	67	8	no	—
224	C₂×C₄⋊C₄	C₂×Dic₆₇	1	8	yes	complemented
225	C₂×C₄⋊C₄	C₂²×D₆₇	1	4	yes	—
226	C₂×C₂²⋊C₄	—	67	64	no	—
227	C₂×C₂²⋊C₄	—	67	8	no	—
228	C₂×C₂²⋊C₄	—	67	16	no	—
229	C₂×C₂²⋊C₄	C₂×Dic₆₇	1	16	yes	complemented
230	C₂×C₂²⋊C₄	C₂²×D₆₇	1	8	yes	—
231	C₂×C₄²	—	268	16	no	—
232	C₂×C₄²	—	67	8	no	—
233	C₂×C₄²	—	67	16	no	—
234	C₂×C₄²	—	67	8	no	—
235	C₂×C₄²	—	67	8	no	—
236	C₂×C₄²	C₂×Dic₆₇	1	8	yes	complemented
237	C₂×C₄²	C₂²×D₆₇	1	2	yes	—
238	C₂×C₄²	C₂²×D₆₇	1	2	yes	—
239	#95	—	67	8	no	—
240	#95	—	67	16	no	—
241	#95	—	67	8	no	—
242	C₂⁴	—	4	4	no	—
243	C₂⁴	—	4	4	no	—
244	C₂⁴	C₂×C₄×D₆₇	1	16	yes	—
245	C₂⁴	C₂²×Dic₆₇	1	8	yes	—
246	C₂⁴	C₂³×D₆₇	1	1	yes	characteristic
247	C₂⁴	C₂³×D₆₇	1	4	yes	—
248	C₂×D₄	C₄×Dic₆₇	1	64	yes	complemented
249	C₂×D₄	C₂×C₄×D₆₇	1	32	yes	—
250	C₂×D₄	C₂²×Dic₆₇	1	16	yes	—
251	C₂²×C₄	—	2	16	no	—
252	C₂²×C₄	—	2	4	no	—
253	C₂²×C₄	—	4	32	no	—
254	C₂²×C₄	—	4	4	no	—
255	C₂²×C₄	—	4	8	no	—
256	C₂²×C₄	—	4	2	no	—
257	C₂²×C₄	—	268	16	no	—
258	C₂²×C₄	—	268	16	no	—
259	C₂²×C₄	—	67	64	no	—
260	C₂²×C₄	—	67	16	no	—
261	C₂²×C₄	C₂×C₄×D₆₇	1	8	yes	—
262	C₂²×C₄	C₂²×Dic₆₇	1	4	yes	—
263	C₂²×C₄	C₂²×Dic₆₇	1	16	yes	—
264	C₂²×C₄	C₂²×Dic₆₇	1	4	yes	—
265	C₂²×C₄	C₂²×Dic₆₇	1	8	yes	—
266	C₂²×C₄	C₂²×Dic₆₇	1	16	yes	—
267	C₂²×C₄	C₂²×Dic₆₇	1	4	yes	—
268	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
269	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
270	C₂²×C₄	C₂³×D₆₇	1	4	yes	—
271	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
272	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
273	C₄⋊C₄	—	67	32	no	—
274	C₄⋊C₄	C₂²×Dic₆₇	1	16	yes	—
275	C₂²⋊C₄	—	67	32	no	—
276	C₂²⋊C₄	—	67	64	no	—
277	C₂²⋊C₄	C₂²×Dic₆₇	1	32	yes	—
278	C₄²	—	268	16	no	—
279	C₄²	—	268	8	no	—
280	C₄²	—	67	32	no	—
281	C₄²	—	134	16	no	—
282	C₄²	C₂²×Dic₆₇	1	8	yes	—
283	C₄²	C₂²×Dic₆₇	1	8	yes	—
284	C₂³	—	2	2	no	—
285	C₂³	—	2	8	no	—
286	C₂³	—	2	2	no	—
287	C₂³	—	2	8	no	—
288	C₂³	—	4	8	no	—
289	C₂³	—	4	32	no	—
290	C₂³	—	4	8	no	—
291	C₂³	C₂×C₄×Dic₆₇	1	32	yes	complemented
292	C₂³	C₂²×C₄×D₆₇	1	4	yes	—
293	C₂³	C₂²×C₄×D₆₇	1	16	yes	—
294	C₂³	C₂³×Dic₆₇	1	8	yes	—
295	C₂³	C₂³×Dic₆₇	1	2	yes	—
296	C₂³	C₂⁴×D₆₇	1	1	yes	characteristic
297	D₄	C₂×C₄×Dic₆₇	1	64	yes	complemented
298	C₂×C₄	—	2	8	no	—
299	C₂×C₄	—	2	2	no	—
300	C₂×C₄	—	2	4	no	—
301	C₂×C₄	—	2	8	no	—
302	C₂×C₄	—	2	32	no	—
303	C₂×C₄	—	4	16	no	—
304	C₂×C₄	—	4	8	no	—
305	C₂×C₄	—	4	4	no	—
306	C₂×C₄	—	268	64	no	—
307	C₂×C₄	—	67	32	no	—
308	C₂×C₄	—	134	16	no	—
309	C₂×C₄	—	134	16	no	—
310	C₂×C₄	C₂×C₄×Dic₆₇	1	16	yes	complemented
311	C₂×C₄	C₂²×C₄×D₆₇	1	8	yes	—
312	C₂×C₄	C₂³×Dic₆₇	1	4	yes	—
313	C₂×C₄	C₂³×Dic₆₇	1	2	yes	—
314	C₂×C₄	C₂³×Dic₆₇	1	8	yes	—
315	C₂×C₄	C₂³×Dic₆₇	1	4	yes	—
316	C₂×C₄	C₂³×Dic₆₇	1	2	yes	—
317	C₂×C₄	#14524088	1	4	yes	—
318	C₂²	—	2	2	no	—
319	C₂²	—	2	8	no	—
320	C₂²	—	2	2	no	—
321	C₂²	—	2	8	no	—
322	C₂²	—	2	32	no	—
323	C₂²	—	2	8	no	—
324	C₂²	—	4	32	no	—
325	C₂²	C₂²×C₄×Dic₆₇	1	4	yes	—
326	C₂²	C₂²×C₄×Dic₆₇	1	16	yes	—
327	C₂²	C₂³×C₄×D₆₇	1	2	yes	—
328	C₂²	C₂⁴×Dic₆₇	1	1	yes	characteristic
329	C₂²	C₂×#14524088	1	2	yes	—
330	C₂²	#16864232	1	2	yes	—
331	C₄	—	2	2	no	—
332	C₄	—	2	8	no	—
333	C₄	—	2	4	no	—
334	C₄	—	134	32	no	—
335	C₄	C₂²×C₄×Dic₆₇	1	8	yes	—
336	C₄	#16863871	1	4	yes	direct product factor
337	C₂	—	2	4	no	—
338	C₂	—	2	16	no	—
339	C₂	C₂³×C₄×Dic₆₇	1	1	yes	characteristic
340	C₂	C₂×#16863871	1	1	yes	characteristic
341	C₂	#22573412	1	1	yes	characteristic
342	C₂	C₄×#14524088	1	4	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂³×D₆₇
commutator	C₂×C₆₇	C₂³×C₄²
Frattini	C₂³	C₂⁴×D₆₇
Fitting	C₂²×C₄×D₄×C₆₇	C₂
socle, cosocle	C₂³×C₆₇	C₂⁵
prime radical	C₂³×D₄×C₆₇	C₂²
hypercenter	C₂²×C₄×D₄	D₆₇
hypocenter	C₆₇	C₄×#518
LCS	G ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄×D₄

Complements

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

N	H ≅ G/N	type
2. #22562570	C₂	semidirect
3. #22562566	C₂	semidirect
4. #22562562	C₂	semidirect
5. C₄×D₄×Dic₆₇	C₂	semidirect
6. C₄×#14524002	C₂	semidirect
7. C₂×C₄×C₂²⋊Dic₆₇	C₂	semidirect
9. #16863871	C₄	direct (N × H)
13. C₂²×C₄×Dic₆₇	C₂²	semidirect
14. C₄⋊C₄×Dic₆₇	C₂²	semidirect
15. C₄×C₄⋊Dic₆₇	C₂²	semidirect
16. C₄×C₄⋊Dic₆₇	C₂²	semidirect
17. C₂²⋊C₄×Dic₆₇	C₂²	semidirect
21. C₄×C₂²⋊Dic₆₇	C₂²	semidirect
22. C₄×C₂²⋊Dic₆₇	C₂²	semidirect
23. #16863242	C₂²	semidirect
24. C₂×C₆₇⋊#95	C₂²	semidirect
25. C₄²×Dic₆₇	C₂²	semidirect
28. C₂×C₄×D₄×C₆₇	C₄	semidirect
35. D₄×Dic₆₇	C₂×C₄	semidirect
36. #14524002	C₂×C₄	semidirect
38. C₂×C₂²⋊Dic₆₇	C₂×C₄	semidirect
54. C₂³×C₄×C₆₇	C₂×C₄	semidirect
61. C₄×D₄×C₆₇	C₂×C₄	semidirect
62. C₄×D₄×C₆₇	C₂×C₄	semidirect
63. C₂×C₄⋊C₄×C₆₇	C₂×C₄	semidirect
65. C₂×C₂²⋊C₄×C₆₇	C₂×C₄	semidirect
67. C₂×C₄²×C₆₇	C₂×C₄	semidirect
72. C₂²×Dic₆₇	C₂²×C₄	semidirect
74. C₄⋊Dic₆₇	C₂²×C₄	semidirect
76. C₂²⋊Dic₆₇	C₂²×C₄	semidirect
80. C₄×Dic₆₇	C₂²×C₄	semidirect
87. C₂×D₄×C₆₇	C₄²	semidirect
119. C₂³×C₆₇	C₂×C₄²	semidirect
125. D₄×C₆₇	C₂×C₄²	semidirect
134. C₂×C₄×C₆₇	C₂×C₄²	semidirect
163. C₄×C₆₇	#518	semidirect
180. C₆₇	C₄×#518	semidirect
185. C₂×C₄×D₄	Dic₆₇	semidirect
212. C₂³×C₄	C₂×Dic₆₇	semidirect
220. C₄×D₄	C₂×Dic₆₇	semidirect
221. C₄×D₄	C₂×Dic₆₇	semidirect
224. C₂×C₄⋊C₄	C₂×Dic₆₇	semidirect
229. C₂×C₂²⋊C₄	C₂×Dic₆₇	semidirect
236. C₂×C₄²	C₂×Dic₆₇	semidirect
248. C₂×D₄	C₄×Dic₆₇	semidirect
291. C₂³	C₂×C₄×Dic₆₇	semidirect
297. D₄	C₂×C₄×Dic₆₇	semidirect
310. C₂×C₄	C₂×C₄×Dic₆₇	semidirect
336. C₄	#16863871	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×#16863871	2
#22562570	2
#22562566	2
#22562562	2
C₄×D₄×Dic₆₇	2
C₄×#14524002	2
C₂×C₄×C₂²⋊Dic₆₇	2
C₂²×C₄×D₄×C₆₇	2
C₄×#518	67

Subgroups — C4×#16863871 #31014066

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#16863871 #31014066