Subgroups — C₆₇×#22670 #30701921

Order 17152.

1122 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#442×C₆₇	C₂	1	2	yes	maximal
2	C₂×C₄×D₈×C₆₇	C₂	1	1	yes	maximal, characteristic
3	D₄×C₄⋊C₄×C₆₇	C₂	1	2	yes	maximal, complemented
4	C₆₇×#1943	C₂	1	2	yes	maximal, complemented
5	C₆₇×#1864	C₂	1	4	yes	maximal, complemented
6	C₆₇×#1844	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#1802	C₂	1	2	yes	maximal, complemented
8	C₆₇×#1770	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×D₈×C₆₇	C₂²	1	1	yes	characteristic
10	C₂×C₄×D₄×C₆₇	C₂²	1	4	yes	—
11	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
12	C₂²×C₄⋊C₄×C₆₇	—	2	2	no	—
13	#442×C₆₇	—	2	8	no	—
14	C₄×D₈×C₆₇	C₄	1	8	yes	complemented
15	C₂×#107×C₆₇	C₂²	1	1	yes	characteristic
16	C₂×#106×C₆₇	C₂²	1	2	yes	—
17	C₂×#106×C₆₇	C₂²	1	2	yes	—
18	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
19	C₂×#102×C₆₇	C₂²	1	4	yes	—
20	C₂×#102×C₆₇	C₂²	1	2	yes	—
21	C₂×#97×C₆₇	C₂²	1	2	yes	—
22	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
23	#389×C₆₇	C₂²	1	4	yes	—
24	#385×C₆₇	—	2	4	no	—
25	#384×C₆₇	C₂²	1	2	yes	—
26	#380×C₆₇	—	2	2	no	—
27	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
28	#340×C₆₇	C₂²	1	4	yes	—
29	#336×C₆₇	C₂²	1	2	yes	—
30	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
31	C₂³×C₄×C₆₇	—	2	2	no	—
32	C₂³×C₄×C₆₇	—	2	4	no	—
33	C₂×D₈×C₆₇	C₂×C₄	1	4	yes	—
34	C₂×D₈×C₆₇	D₄	1	4	yes	—
35	C₂×D₈×C₆₇	Q₈	1	4	yes	—
36	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
37	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
38	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
39	C₄×D₄×C₆₇	—	2	8	no	—
40	C₄×D₄×C₆₇	—	2	4	no	—
41	C₄×D₄×C₆₇	—	4	4	no	—
42	C₄×D₄×C₆₇	C₂×C₄	1	8	yes	complemented
43	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
44	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
45	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
46	C₂×C₄⋊C₄×C₆₇	—	4	8	no	—
47	C₂×C₄⋊C₄×C₆₇	D₄	1	2	yes	—
48	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
49	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
50	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
51	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
52	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
53	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
54	#107×C₆₇	C₂×C₄	1	4	yes	complemented
55	#106×C₆₇	—	2	4	no	—
56	#106×C₆₇	—	4	2	no	—
57	C₄⋊C₈×C₆₇	—	2	2	no	—
58	#102×C₆₇	—	2	8	no	—
59	#102×C₆₇	C₂×C₄	1	8	yes	complemented
60	#97×C₆₇	—	2	4	no	—
61	C₄×C₈×C₆₇	C₂×C₄	1	4	yes	complemented
62	#95×C₆₇	—	2	4	no	—
63	#95×C₆₇	D₄	1	2	yes	—
64	C₂⁴×C₆₇	—	2	2	no	—
65	C₂×D₄×C₆₇	—	2	2	no	—
66	C₂×D₄×C₆₇	—	2	2	no	—
67	C₂×D₄×C₆₇	—	2	2	no	—
68	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
69	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	—
70	C₂×D₄×C₆₇	C₂×Q₈	1	4	yes	—
71	C₂²×C₄×C₆₇	—	2	2	no	—
72	C₂²×C₄×C₆₇	—	2	8	no	—
73	C₂²×C₄×C₆₇	—	2	4	no	—
74	C₂²×C₄×C₆₇	—	4	8	no	—
75	C₂²×C₄×C₆₇	—	4	8	no	—
76	C₂²×C₄×C₆₇	—	4	4	no	—
77	C₂²×C₄×C₆₇	—	4	4	no	—
78	C₂²×C₄×C₆₇	—	8	4	no	—
79	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
80	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
81	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
82	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
83	D₈×C₆₇	C₄⋊C₄	1	16	yes	complemented
84	C₂×C₈×C₆₇	—	2	1	no	—
85	C₂×C₈×C₆₇	—	2	1	no	—
86	C₂×C₈×C₆₇	—	2	2	no	—
87	C₂×C₈×C₆₇	—	2	2	no	—
88	C₂×C₈×C₆₇	—	2	2	no	—
89	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
90	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
91	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
92	C₂×C₈×C₆₇	C₂×Q₈	1	2	yes	—
93	C₄⋊C₄×C₆₇	—	2	4	no	—
94	C₄⋊C₄×C₆₇	—	2	2	no	—
95	C₄⋊C₄×C₆₇	—	2	4	no	—
96	C₄⋊C₄×C₆₇	—	2	4	no	—
97	C₄⋊C₄×C₆₇	—	4	8	no	—
98	C₄⋊C₄×C₆₇	—	4	4	no	—
99	C₄⋊C₄×C₆₇	—	8	2	no	—
100	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
101	C₂²⋊C₄×C₆₇	—	2	8	no	—
102	C₂²⋊C₄×C₆₇	—	4	8	no	—
103	C₄²×C₆₇	—	2	2	no	—
104	C₄²×C₆₇	—	2	2	no	—
105	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
106	C₄²×C₆₇	#41	1	2	yes	—
107	C₂³×C₆₇	—	2	4	no	—
108	C₂³×C₆₇	—	2	4	no	—
109	C₂³×C₆₇	—	2	4	no	—
110	C₂³×C₆₇	—	4	2	no	—
111	C₂³×C₆₇	—	4	2	no	—
112	C₂³×C₆₇	—	4	2	no	—
113	C₂³×C₆₇	—	4	2	no	—
114	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
115	D₄×C₆₇	—	2	4	no	—
116	D₄×C₆₇	—	2	4	no	—
117	D₄×C₆₇	—	2	4	no	—
118	D₄×C₆₇	C₂×C₄⋊C₄	1	8	yes	complemented
119	C₂×C₄×C₆₇	—	2	2	no	—
120	C₂×C₄×C₆₇	—	2	4	no	—
121	C₂×C₄×C₆₇	—	2	4	no	—
122	C₂×C₄×C₆₇	—	2	4	no	—
123	C₂×C₄×C₆₇	—	2	4	no	—
124	C₂×C₄×C₆₇	—	4	2	no	—
125	C₂×C₄×C₆₇	—	4	2	no	—
126	C₂×C₄×C₆₇	—	4	16	no	—
127	C₂×C₄×C₆₇	—	4	4	no	—
128	C₂×C₄×C₆₇	—	4	4	no	—
129	C₂×C₄×C₆₇	—	4	4	no	—
130	C₂×C₄×C₆₇	—	8	16	no	—
131	C₂×C₄×C₆₇	C₄×D₄	1	2	yes	—
132	C₂×C₄×C₆₇	C₄×D₄	1	2	yes	—
133	C₂×C₄×C₆₇	AGL(1,ℤ/8)	1	4	yes	—
134	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
135	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
136	C₂×C₄×C₆₇	C₂²×Q₈	1	1	yes	characteristic
137	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
138	C₂×C₄×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
139	C₂×C₄×C₆₇	2₋¹⁺⁴	1	1	yes	characteristic
140	C₈×C₆₇	—	2	2	no	—
141	C₈×C₆₇	—	4	2	no	—
142	C₈×C₆₇	C₂×C₄⋊C₄	1	4	yes	complemented
143	C₂²×C₆₇	—	2	8	no	—
144	C₂²×C₆₇	—	4	4	no	—
145	C₂²×C₆₇	—	4	4	no	—
146	C₂²×C₆₇	—	4	4	no	—
147	C₂²×C₆₇	—	4	4	no	—
148	C₂²×C₆₇	—	4	4	no	—
149	C₂²×C₆₇	—	4	4	no	—
150	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
151	C₂²×C₆₇	D₄²	1	1	yes	characteristic
152	C₂²×C₆₇	D₄×Q₈	1	1	yes	characteristic
153	C₂²×C₆₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
154	C₂²×C₆₇	#577	1	2	yes	—
155	C₄×C₆₇	—	2	2	no	—
156	C₄×C₆₇	—	4	4	no	—
157	C₄×C₆₇	—	4	4	no	—
158	C₄×C₆₇	—	8	4	no	—
159	C₄×C₆₇	#442	1	4	yes	complemented
160	C₄×C₆₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
161	C₄×C₆₇	#520	1	1	yes	characteristic
162	C₄×C₆₇	#547	1	1	yes	characteristic
163	C₄×C₆₇	#554	1	1	yes	characteristic
164	#22670	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
165	C₂×C₆₇	—	4	8	no	—
166	C₂×C₆₇	D₄×C₄⋊C₄	1	1	yes	characteristic
167	C₂×C₆₇	C₂×#442	1	1	yes	characteristic
168	C₂×C₆₇	#2952	1	1	yes	characteristic
169	C₂×C₆₇	#3272	1	2	yes	—
170	C₂×C₆₇	#3384	1	2	yes	—
171	C₂×#442	C₂×C₆₇	1	2	yes	—
172	C₂×C₄×D₈	C₂×C₆₇	1	1	yes	characteristic
173	D₄×C₄⋊C₄	C₂×C₆₇	1	2	yes	complemented
174	#1943	C₂×C₆₇	1	2	yes	complemented
175	#1864	C₂×C₆₇	1	4	yes	complemented
176	#1844	C₂×C₆₇	1	1	yes	characteristic, complemented
177	#1802	C₂×C₆₇	1	2	yes	complemented
178	#1770	C₂×C₆₇	1	1	yes	characteristic, complemented
179	C₆₇	#22670	1	1	yes	characteristic, direct product factor, Sylow
180	C₂²×D₈	C₂²×C₆₇	1	1	yes	characteristic
181	C₂×C₄×D₄	C₂²×C₆₇	1	4	yes	—
182	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
183	C₂²×C₄⋊C₄	—	2	2	no	—
184	#442	—	2	8	no	—
185	C₄×D₈	C₄×C₆₇	1	8	yes	complemented
186	C₂×#107	C₂²×C₆₇	1	1	yes	characteristic
187	C₂×#106	C₂²×C₆₇	1	2	yes	—
188	C₂×#106	C₂²×C₆₇	1	2	yes	—
189	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
190	C₂×#102	C₂²×C₆₇	1	4	yes	—
191	C₂×#102	C₂²×C₆₇	1	2	yes	—
192	C₂×#97	C₂²×C₆₇	1	2	yes	—
193	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic
194	#389	C₂²×C₆₇	1	4	yes	—
195	#385	—	2	4	no	—
196	#384	C₂²×C₆₇	1	2	yes	—
197	#380	—	2	2	no	—
198	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
199	#340	C₂²×C₆₇	1	4	yes	—
200	#336	C₂²×C₆₇	1	2	yes	—
201	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
202	C₂³×C₄	—	2	2	no	—
203	C₂³×C₄	—	2	4	no	—
204	C₂×D₈	C₂×C₄×C₆₇	1	4	yes	—
205	C₂×D₈	D₄×C₆₇	1	4	yes	—
206	C₂×D₈	Q₈×C₆₇	1	4	yes	—
207	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
208	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
209	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
210	C₄×D₄	—	2	8	no	—
211	C₄×D₄	—	2	4	no	—
212	C₄×D₄	—	4	4	no	—
213	C₄×D₄	C₂×C₄×C₆₇	1	8	yes	complemented
214	C₂×C₄⋊C₄	—	2	2	no	—
215	C₂×C₄⋊C₄	—	2	4	no	—
216	C₂×C₄⋊C₄	—	2	2	no	—
217	C₂×C₄⋊C₄	—	4	8	no	—
218	C₂×C₄⋊C₄	D₄×C₆₇	1	2	yes	—
219	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
220	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
221	C₂×C₂²⋊C₄	—	2	2	no	—
222	C₂×C₂²⋊C₄	—	2	4	no	—
223	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
224	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
225	#107	C₂×C₄×C₆₇	1	4	yes	complemented
226	#106	—	2	4	no	—
227	#106	—	4	2	no	—
228	C₄⋊C₈	—	2	2	no	—
229	#102	—	2	8	no	—
230	#102	C₂×C₄×C₆₇	1	8	yes	complemented
231	#97	—	2	4	no	—
232	C₄×C₈	C₂×C₄×C₆₇	1	4	yes	complemented
233	#95	—	2	4	no	—
234	#95	D₄×C₆₇	1	2	yes	—
235	C₂⁴	—	2	2	no	—
236	C₂×D₄	—	2	2	no	—
237	C₂×D₄	—	2	2	no	—
238	C₂×D₄	—	2	2	no	—
239	C₂×D₄	C₂²×C₄×C₆₇	1	4	yes	—
240	C₂×D₄	C₂×D₄×C₆₇	1	4	yes	—
241	C₂×D₄	C₂×Q₈×C₆₇	1	4	yes	—
242	C₂²×C₄	—	2	2	no	—
243	C₂²×C₄	—	2	8	no	—
244	C₂²×C₄	—	2	4	no	—
245	C₂²×C₄	—	4	8	no	—
246	C₂²×C₄	—	4	8	no	—
247	C₂²×C₄	—	4	4	no	—
248	C₂²×C₄	—	4	4	no	—
249	C₂²×C₄	—	8	4	no	—
250	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
251	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
252	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
253	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
254	D₈	C₄⋊C₄×C₆₇	1	16	yes	complemented
255	C₂×C₈	—	2	1	no	—
256	C₂×C₈	—	2	1	no	—
257	C₂×C₈	—	2	2	no	—
258	C₂×C₈	—	2	2	no	—
259	C₂×C₈	—	2	2	no	—
260	C₂×C₈	C₂²×C₄×C₆₇	1	2	yes	—
261	C₂×C₈	C₂²×C₄×C₆₇	1	2	yes	—
262	C₂×C₈	C₂×D₄×C₆₇	1	2	yes	—
263	C₂×C₈	C₂×Q₈×C₆₇	1	2	yes	—
264	C₄⋊C₄	—	2	4	no	—
265	C₄⋊C₄	—	2	2	no	—
266	C₄⋊C₄	—	2	4	no	—
267	C₄⋊C₄	—	2	4	no	—
268	C₄⋊C₄	—	4	8	no	—
269	C₄⋊C₄	—	4	4	no	—
270	C₄⋊C₄	—	8	2	no	—
271	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
272	C₂²⋊C₄	—	2	8	no	—
273	C₂²⋊C₄	—	4	8	no	—
274	C₄²	—	2	2	no	—
275	C₄²	—	2	2	no	—
276	C₄²	C₂²×C₄×C₆₇	1	2	yes	—
277	C₄²	#41×C₆₇	1	2	yes	—
278	C₂³	—	2	4	no	—
279	C₂³	—	2	4	no	—
280	C₂³	—	2	4	no	—
281	C₂³	—	4	2	no	—
282	C₂³	—	4	2	no	—
283	C₂³	—	4	2	no	—
284	C₂³	—	4	2	no	—
285	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
286	D₄	—	2	4	no	—
287	D₄	—	2	4	no	—
288	D₄	—	2	4	no	—
289	D₄	C₂×C₄⋊C₄×C₆₇	1	8	yes	complemented
290	C₂×C₄	—	2	2	no	—
291	C₂×C₄	—	2	4	no	—
292	C₂×C₄	—	2	4	no	—
293	C₂×C₄	—	2	4	no	—
294	C₂×C₄	—	2	4	no	—
295	C₂×C₄	—	4	2	no	—
296	C₂×C₄	—	4	2	no	—
297	C₂×C₄	—	4	16	no	—
298	C₂×C₄	—	4	4	no	—
299	C₂×C₄	—	4	4	no	—
300	C₂×C₄	—	4	4	no	—
301	C₂×C₄	—	8	16	no	—
302	C₂×C₄	C₄×D₄×C₆₇	1	2	yes	—
303	C₂×C₄	C₄×D₄×C₆₇	1	2	yes	—
304	C₂×C₄	AGL(1,ℤ/8)×C₆₇	1	4	yes	—
305	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
306	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
307	C₂×C₄	C₂²×Q₈×C₆₇	1	1	yes	characteristic
308	C₂×C₄	C₂×#41×C₆₇	1	1	yes	characteristic
309	C₂×C₄	H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
310	C₂×C₄	2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
311	C₈	—	2	2	no	—
312	C₈	—	4	2	no	—
313	C₈	C₂×C₄⋊C₄×C₆₇	1	4	yes	complemented
314	C₂²	—	2	8	no	—
315	C₂²	—	4	4	no	—
316	C₂²	—	4	4	no	—
317	C₂²	—	4	4	no	—
318	C₂²	—	4	4	no	—
319	C₂²	—	4	4	no	—
320	C₂²	—	4	4	no	—
321	C₂²	C₂×C₄×D₄×C₆₇	1	1	yes	characteristic
322	C₂²	D₄²×C₆₇	1	1	yes	characteristic
323	C₂²	D₄×Q₈×C₆₇	1	1	yes	characteristic
324	C₂²	C₂×AGL(1,ℤ/8)×C₆₇	1	2	yes	—
325	C₂²	#577×C₆₇	1	2	yes	—
326	C₄	—	2	2	no	—
327	C₄	—	4	4	no	—
328	C₄	—	4	4	no	—
329	C₄	—	8	4	no	—
330	C₄	#442×C₆₇	1	4	yes	complemented
331	C₄	C₂²×C₄⋊C₄×C₆₇	1	1	yes	characteristic
332	C₄	#520×C₆₇	1	1	yes	characteristic
333	C₄	#547×C₆₇	1	1	yes	characteristic
334	C₄	#554×C₆₇	1	1	yes	characteristic
335	C₂	—	4	8	no	—
336	C₂	D₄×C₄⋊C₄×C₆₇	1	1	yes	characteristic
337	C₂	C₂×#442×C₆₇	1	1	yes	characteristic
338	C₂	C₆₇×#2952	1	1	yes	characteristic
339	C₂	C₆₇×#3272	1	2	yes	—
340	C₂	C₆₇×#3384	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₆₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₇
prime radical	C₂²×D₈×C₆₇	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ C₄×C₄⋊C₄×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
3. D₄×C₄⋊C₄×C₆₇	C₂	semidirect
4. C₆₇×#1943	C₂	semidirect
5. C₆₇×#1864	C₂	semidirect
6. C₆₇×#1844	C₂	semidirect
7. C₆₇×#1802	C₂	semidirect
8. C₆₇×#1770	C₂	semidirect
14. C₄×D₈×C₆₇	C₄	semidirect
42. C₄×D₄×C₆₇	C₂×C₄	semidirect
54. #107×C₆₇	C₂×C₄	semidirect
59. #102×C₆₇	C₂×C₄	semidirect
61. C₄×C₈×C₆₇	C₂×C₄	semidirect
83. D₈×C₆₇	C₄⋊C₄	semidirect
118. D₄×C₆₇	C₂×C₄⋊C₄	semidirect
142. C₈×C₆₇	C₂×C₄⋊C₄	semidirect
159. C₄×C₆₇	#442	semidirect
164. #22670	C₆₇	direct (N × H)
173. D₄×C₄⋊C₄	C₂×C₆₇	semidirect
174. #1943	C₂×C₆₇	semidirect
175. #1864	C₂×C₆₇	semidirect
176. #1844	C₂×C₆₇	semidirect
177. #1802	C₂×C₆₇	semidirect
178. #1770	C₂×C₆₇	semidirect
179. C₆₇	#22670	direct (N × H)
185. C₄×D₈	C₄×C₆₇	semidirect
213. C₄×D₄	C₂×C₄×C₆₇	semidirect
225. #107	C₂×C₄×C₆₇	semidirect
230. #102	C₂×C₄×C₆₇	semidirect
232. C₄×C₈	C₂×C₄×C₆₇	semidirect
254. D₈	C₄⋊C₄×C₆₇	semidirect
289. D₄	C₂×C₄⋊C₄×C₆₇	semidirect
313. C₈	C₂×C₄⋊C₄×C₆₇	semidirect
330. C₄	#442×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#442×C₆₇	2
C₂×C₄×D₈×C₆₇	2
D₄×C₄⋊C₄×C₆₇	2
C₆₇×#1943	2
C₆₇×#1864	2
C₆₇×#1844	2
C₆₇×#1802	2
C₆₇×#1770	2
#22670	67

Subgroups — C67×#22670 #30701921

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#22670 #30701921