Subgroups — C₆₇×#34229 #30713480

Order 17152.

2314 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#529×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₆₇×#2361	C₂	1	2	yes	maximal
3	C₆₇×#2360	C₂	1	2	yes	maximal, complemented
4	C₆₇×#2359	C₂	1	4	yes	maximal, complemented
5	C₆₇×#2357	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#2356	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#2351	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#2349	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#2346	C₂	1	2	yes	maximal, complemented
10	C₆₇×#2343	C₂	1	2	yes	maximal, complemented
11	C₆₇×#2334	C₂	1	4	yes	maximal, complemented
12	C₆₇×#2318	C₂	1	2	yes	maximal, complemented
13	C₄×#125×C₆₇	C₂	1	2	yes	maximal, complemented
14	C₄×#124×C₆₇	C₂	1	2	yes	maximal, complemented
15	C₂×#382×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#2275	C₂	1	2	yes	maximal, complemented
17	C₄×#117×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
18	#529×C₆₇	C₄	1	16	yes	complemented
19	C₂×#126×C₆₇	C₂²	1	2	yes	—
20	C₂×#125×C₆₇	C₂²	1	1	yes	characteristic
21	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic
22	C₂×#123×C₆₇	C₂²	1	2	yes	—
23	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
24	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
25	C₂×C₄×Q₈×C₆₇	C₂²	1	2	yes	—
26	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
27	C₂×C₄×D₄×C₆₇	C₂²	1	4	yes	—
28	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
29	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
30	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
31	C₂×#117×C₆₇	C₂²	1	2	yes	—
32	C₂×#117×C₆₇	C₂²	1	2	yes	—
33	C₂²×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
34	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
35	#391×C₆₇	C₂²	1	2	yes	—
36	#390×C₆₇	C₂²	1	2	yes	—
37	#389×C₆₇	C₂²	1	2	yes	—
38	#389×C₆₇	C₂²	1	2	yes	—
39	#389×C₆₇	C₂²	1	4	yes	—
40	#389×C₆₇	C₂²	1	4	yes	—
41	#388×C₆₇	C₂²	1	4	yes	—
42	#388×C₆₇	C₂²	1	4	yes	—
43	#388×C₆₇	C₂²	1	4	yes	—
44	#388×C₆₇	C₂²	1	4	yes	—
45	#387×C₆₇	C₂²	1	4	yes	—
46	#387×C₆₇	C₂²	1	4	yes	—
47	#387×C₆₇	C₂²	1	4	yes	—
48	#387×C₆₇	C₂²	1	4	yes	—
49	#386×C₆₇	C₂²	1	4	yes	—
50	#385×C₆₇	C₂²	1	4	yes	—
51	#385×C₆₇	C₂²	1	4	yes	—
52	#385×C₆₇	C₂²	1	4	yes	—
53	#383×C₆₇	C₂²	1	2	yes	—
54	#382×C₆₇	C₂²	1	2	yes	—
55	#382×C₆₇	C₂²	1	2	yes	—
56	#382×C₆₇	C₂²	1	2	yes	—
57	#382×C₆₇	C₂²	1	1	yes	characteristic
58	#382×C₆₇	C₂²	1	1	yes	characteristic
59	#382×C₆₇	C₂²	1	2	yes	—
60	#381×C₆₇	C₂²	1	2	yes	—
61	#380×C₆₇	C₂²	1	2	yes	—
62	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
63	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
64	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
65	C₄×C₄⋊C₄×C₆₇	C₂²	1	4	yes	—
66	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
67	C₄×C₄⋊C₄×C₆₇	C₂²	1	4	yes	—
68	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
69	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
70	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
71	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
72	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
73	C₄×C₂²⋊C₄×C₆₇	C₂²	1	4	yes	—
74	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
75	C₄×C₂²⋊C₄×C₆₇	C₂²	1	4	yes	—
76	C₄×C₂²⋊C₄×C₆₇	C₂²	1	4	yes	—
77	#376×C₆₇	C₂²	1	1	yes	characteristic
78	#376×C₆₇	C₂²	1	1	yes	characteristic
79	#376×C₆₇	C₂²	1	2	yes	—
80	C₂×#95×C₆₇	C₂²	1	2	yes	—
81	C₂×#95×C₆₇	C₂²	1	2	yes	—
82	C₂×#95×C₆₇	C₂²	1	2	yes	—
83	C₄³×C₆₇	C₂²	1	2	yes	—
84	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
85	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
86	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
89	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
90	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
91	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
93	#126×C₆₇	C₂×C₄	1	16	yes	complemented
94	#125×C₆₇	C₂×C₄	1	8	yes	complemented
95	#124×C₆₇	C₂×C₄	1	8	yes	complemented
96	#123×C₆₇	C₂×C₄	1	16	yes	complemented
97	C₂²⋊Q₈×C₆₇	C₂×C₄	1	8	yes	complemented
98	#121×C₆₇	C₂×C₄	1	8	yes	—
99	C₄×Q₈×C₆₇	—	4	4	no	—
100	C₄×Q₈×C₆₇	C₂×C₄	1	8	yes	complemented
101	C₄×D₄×C₆₇	—	2	16	no	—
102	C₄×D₄×C₆₇	—	4	4	no	—
103	C₄×D₄×C₆₇	C₂×C₄	1	8	yes	complemented
104	C₄×D₄×C₆₇	C₂×C₄	1	16	yes	complemented
105	#117×C₆₇	—	2	8	no	—
106	#117×C₆₇	C₂×C₄	1	16	yes	complemented
107	C₂×C₄⋊C₄×C₆₇	—	4	4	no	—
108	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
109	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
110	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
111	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
112	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
113	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
114	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
115	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
116	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
117	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
118	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
119	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
120	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
121	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
122	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
123	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
124	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
125	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
126	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
127	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
128	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
129	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
130	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
131	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
132	C₂×C₄²×C₆₇	C₂×C₄	1	8	yes	complemented
133	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
134	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
135	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
136	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
137	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
138	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
139	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
140	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
141	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
142	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
143	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
144	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
145	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
146	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
147	#95×C₆₇	C₂³	1	1	yes	characteristic
148	#95×C₆₇	C₂³	1	2	yes	—
149	#95×C₆₇	C₂³	1	2	yes	—
150	#95×C₆₇	C₂³	1	4	yes	—
151	#95×C₆₇	C₂³	1	4	yes	—
152	#95×C₆₇	C₂³	1	4	yes	—
153	#95×C₆₇	C₂³	1	2	yes	—
154	#95×C₆₇	C₂³	1	2	yes	—
155	#95×C₆₇	C₂³	1	1	yes	characteristic
156	#95×C₆₇	C₂³	1	4	yes	—
157	#95×C₆₇	C₂³	1	1	yes	characteristic
158	#95×C₆₇	C₂³	1	1	yes	characteristic
159	#95×C₆₇	C₂³	1	2	yes	—
160	#95×C₆₇	C₂³	1	2	yes	—
161	#95×C₆₇	C₂³	1	4	yes	—
162	#95×C₆₇	C₂³	1	4	yes	—
163	#95×C₆₇	C₂³	1	4	yes	—
164	#95×C₆₇	C₂³	1	4	yes	—
165	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
166	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
167	C₂×Q₈×C₆₇	—	2	2	no	—
168	C₂×Q₈×C₆₇	—	2	2	no	—
169	C₂×Q₈×C₆₇	C₂²×C₄	1	4	yes	—
170	C₂×D₄×C₆₇	—	2	8	no	—
171	C₂×D₄×C₆₇	—	2	2	no	—
172	C₂×D₄×C₆₇	—	2	2	no	—
173	C₂×D₄×C₆₇	C₂²×C₄	1	8	yes	—
174	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
175	C₂²×C₄×C₆₇	—	2	4	no	—
176	C₂²×C₄×C₆₇	—	2	2	no	—
177	C₂²×C₄×C₆₇	—	2	2	no	—
178	C₂²×C₄×C₆₇	—	2	8	no	—
179	C₂²×C₄×C₆₇	—	2	8	no	—
180	C₂²×C₄×C₆₇	—	4	2	no	—
181	C₂²×C₄×C₆₇	—	4	4	no	—
182	C₂²×C₄×C₆₇	—	4	4	no	—
183	C₂²×C₄×C₆₇	—	4	4	no	—
184	C₂²×C₄×C₆₇	—	4	4	no	—
185	C₂²×C₄×C₆₇	—	4	4	no	—
186	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
187	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
188	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
189	C₂²×C₄×C₆₇	C₂²×C₄	1	8	yes	—
190	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
191	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
192	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
193	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
194	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
195	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
196	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
197	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
198	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
199	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
200	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
201	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
202	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
203	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
204	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
205	C₄⋊C₄×C₆₇	—	2	4	no	—
206	C₄⋊C₄×C₆₇	—	2	4	no	—
207	C₄⋊C₄×C₆₇	—	2	8	no	—
208	C₄⋊C₄×C₆₇	—	2	4	no	—
209	C₄⋊C₄×C₆₇	—	2	4	no	—
210	C₄⋊C₄×C₆₇	—	4	4	no	—
211	C₄⋊C₄×C₆₇	—	4	4	no	—
212	C₄⋊C₄×C₆₇	—	4	4	no	—
213	C₄⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
214	C₄⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
215	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
216	C₄⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
217	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
218	C₄⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
219	C₂²⋊C₄×C₆₇	—	2	4	no	—
220	C₂²⋊C₄×C₆₇	—	2	8	no	—
221	C₂²⋊C₄×C₆₇	—	4	4	no	—
222	C₂²⋊C₄×C₆₇	—	4	4	no	—
223	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
224	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
225	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
226	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
227	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
228	C₂²⋊C₄×C₆₇	#41	1	8	yes	—
229	C₄²×C₆₇	—	2	4	no	—
230	C₄²×C₆₇	—	2	4	no	—
231	C₄²×C₆₇	—	2	8	no	—
232	C₄²×C₆₇	—	2	4	no	—
233	C₄²×C₆₇	—	2	4	no	—
234	C₄²×C₆₇	—	4	2	no	—
235	C₄²×C₆₇	—	4	4	no	—
236	C₄²×C₆₇	—	4	2	no	—
237	C₄²×C₆₇	—	4	4	no	—
238	C₄²×C₆₇	C₂²×C₄	1	4	yes	—
239	C₄²×C₆₇	C₂²×C₄	1	4	yes	—
240	C₄²×C₆₇	C₂²×C₄	1	4	yes	—
241	C₄²×C₆₇	C₂²×C₄	1	4	yes	—
242	C₄²×C₆₇	C₂²×C₄	1	8	yes	—
243	C₂³×C₆₇	—	2	1	no	—
244	C₂³×C₆₇	—	2	1	no	—
245	C₂³×C₆₇	—	2	2	no	—
246	C₂³×C₆₇	—	2	4	no	—
247	C₂³×C₆₇	—	2	2	no	—
248	C₂³×C₆₇	—	2	2	no	—
249	C₂³×C₆₇	—	2	4	no	—
250	C₂³×C₆₇	C₂³×C₄	1	4	yes	—
251	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
252	C₂³×C₆₇	C₂×#41	1	4	yes	—
253	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
254	Q₈×C₆₇	—	2	8	no	—
255	D₄×C₆₇	—	2	16	no	—
256	D₄×C₆₇	—	2	8	no	—
257	C₂×C₄×C₆₇	—	2	8	no	—
258	C₂×C₄×C₆₇	—	2	2	no	—
259	C₂×C₄×C₆₇	—	2	4	no	—
260	C₂×C₄×C₆₇	—	2	2	no	—
261	C₂×C₄×C₆₇	—	2	2	no	—
262	C₂×C₄×C₆₇	—	2	2	no	—
263	C₂×C₄×C₆₇	—	2	1	no	—
264	C₂×C₄×C₆₇	—	2	2	no	—
265	C₂×C₄×C₆₇	—	2	1	no	—
266	C₂×C₄×C₆₇	—	2	2	no	—
267	C₂×C₄×C₆₇	—	2	2	no	—
268	C₂×C₄×C₆₇	—	2	2	no	—
269	C₂×C₄×C₆₇	—	2	4	no	—
270	C₂×C₄×C₆₇	—	2	2	no	—
271	C₂×C₄×C₆₇	—	2	2	no	—
272	C₂×C₄×C₆₇	—	2	8	no	—
273	C₂×C₄×C₆₇	—	2	2	no	—
274	C₂×C₄×C₆₇	—	2	2	no	—
275	C₂×C₄×C₆₇	—	2	4	no	—
276	C₂×C₄×C₆₇	—	2	4	no	—
277	C₂×C₄×C₆₇	—	2	2	no	—
278	C₂×C₄×C₆₇	—	2	4	no	—
279	C₂×C₄×C₆₇	—	2	4	no	—
280	C₂×C₄×C₆₇	—	2	2	no	—
281	C₂×C₄×C₆₇	—	2	2	no	—
282	C₂×C₄×C₆₇	—	2	4	no	—
283	C₂×C₄×C₆₇	—	2	2	no	—
284	C₂×C₄×C₆₇	—	2	4	no	—
285	C₂×C₄×C₆₇	—	4	4	no	—
286	C₂×C₄×C₆₇	—	4	8	no	—
287	C₂×C₄×C₆₇	—	8	8	no	—
288	C₂×C₄×C₆₇	—	8	8	no	—
289	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
290	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
291	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
292	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
293	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
294	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
295	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
296	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
297	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
298	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
299	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
300	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
301	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
302	C₂²×C₆₇	—	2	2	no	—
303	C₂²×C₆₇	—	2	2	no	—
304	C₂²×C₆₇	—	2	4	no	—
305	C₂²×C₆₇	—	2	4	no	—
306	C₂²×C₆₇	—	2	4	no	—
307	C₂²×C₆₇	—	2	4	no	—
308	C₂²×C₆₇	—	2	4	no	—
309	C₂²×C₆₇	—	4	4	no	—
310	C₂²×C₆₇	—	4	4	no	—
311	C₂²×C₆₇	C₄×#41	1	4	yes	—
312	C₂²×C₆₇	C₂⁴×C₄	1	1	yes	characteristic
313	C₂²×C₆₇	C₂²×#41	1	2	yes	—
314	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
315	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
316	C₂²×C₆₇	#585	1	2	yes	—
317	C₄×C₆₇	—	2	2	no	—
318	C₄×C₆₇	—	2	2	no	—
319	C₄×C₆₇	—	2	4	no	—
320	C₄×C₆₇	—	2	2	no	—
321	C₄×C₆₇	—	2	4	no	—
322	C₄×C₆₇	—	2	2	no	—
323	C₄×C₆₇	—	2	2	no	—
324	C₄×C₆₇	—	2	4	no	—
325	C₄×C₆₇	—	2	4	no	—
326	C₄×C₆₇	—	2	4	no	—
327	C₄×C₆₇	—	4	2	no	—
328	C₄×C₆₇	—	4	4	no	—
329	C₄×C₆₇	—	4	4	no	—
330	C₄×C₆₇	—	4	2	no	—
331	C₄×C₆₇	#520	1	4	yes	—
332	#34229	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
333	C₂×C₆₇	—	2	4	no	—
334	C₂×C₆₇	—	4	4	no	—
335	C₂×C₆₇	C₂×C₄×#41	1	1	yes	characteristic
336	C₂×C₆₇	C₂×#520	1	1	yes	characteristic
337	C₂×C₆₇	#3428	1	1	yes	characteristic
338	C₂×C₆₇	#3514	1	2	yes	—
339	C₂×C₆₇	#3515	1	2	yes	—
340	C₂×#529	C₂×C₆₇	1	1	yes	characteristic
341	#2361	C₂×C₆₇	1	2	yes	—
342	#2360	C₂×C₆₇	1	2	yes	complemented
343	#2359	C₂×C₆₇	1	4	yes	complemented
344	#2357	C₂×C₆₇	1	1	yes	characteristic, complemented
345	#2356	C₂×C₆₇	1	1	yes	characteristic, complemented
346	#2351	C₂×C₆₇	1	1	yes	characteristic, complemented
347	#2349	C₂×C₆₇	1	1	yes	characteristic, complemented
348	#2346	C₂×C₆₇	1	2	yes	complemented
349	#2343	C₂×C₆₇	1	2	yes	complemented
350	#2334	C₂×C₆₇	1	4	yes	complemented
351	#2318	C₂×C₆₇	1	2	yes	complemented
352	C₄×#125	C₂×C₆₇	1	2	yes	complemented
353	C₄×#124	C₂×C₆₇	1	2	yes	complemented
354	C₂×#382	C₂×C₆₇	1	1	yes	characteristic, complemented
355	#2275	C₂×C₆₇	1	2	yes	complemented
356	C₄×#117	C₂×C₆₇	1	1	yes	characteristic, complemented
357	C₆₇	#34229	1	1	yes	characteristic, direct product factor, Sylow
358	#529	C₄×C₆₇	1	16	yes	complemented
359	C₂×#126	C₂²×C₆₇	1	2	yes	—
360	C₂×#125	C₂²×C₆₇	1	1	yes	characteristic
361	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic
362	C₂×#123	C₂²×C₆₇	1	2	yes	—
363	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
364	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
365	C₂×C₄×Q₈	C₂²×C₆₇	1	2	yes	—
366	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
367	C₂×C₄×D₄	C₂²×C₆₇	1	4	yes	—
368	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
369	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
370	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
371	C₂×#117	C₂²×C₆₇	1	2	yes	—
372	C₂×#117	C₂²×C₆₇	1	2	yes	—
373	C₂²×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
374	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
375	#391	C₂²×C₆₇	1	2	yes	—
376	#390	C₂²×C₆₇	1	2	yes	—
377	#389	C₂²×C₆₇	1	2	yes	—
378	#389	C₂²×C₆₇	1	2	yes	—
379	#389	C₂²×C₆₇	1	4	yes	—
380	#389	C₂²×C₆₇	1	4	yes	—
381	#388	C₂²×C₆₇	1	4	yes	—
382	#388	C₂²×C₆₇	1	4	yes	—
383	#388	C₂²×C₆₇	1	4	yes	—
384	#388	C₂²×C₆₇	1	4	yes	—
385	#387	C₂²×C₆₇	1	4	yes	—
386	#387	C₂²×C₆₇	1	4	yes	—
387	#387	C₂²×C₆₇	1	4	yes	—
388	#387	C₂²×C₆₇	1	4	yes	—
389	#386	C₂²×C₆₇	1	4	yes	—
390	#385	C₂²×C₆₇	1	4	yes	—
391	#385	C₂²×C₆₇	1	4	yes	—
392	#385	C₂²×C₆₇	1	4	yes	—
393	#383	C₂²×C₆₇	1	2	yes	—
394	#382	C₂²×C₆₇	1	2	yes	—
395	#382	C₂²×C₆₇	1	2	yes	—
396	#382	C₂²×C₆₇	1	2	yes	—
397	#382	C₂²×C₆₇	1	2	yes	—
398	#382	C₂²×C₆₇	1	1	yes	characteristic
399	#382	C₂²×C₆₇	1	1	yes	characteristic
400	#381	C₂²×C₆₇	1	2	yes	—
401	#380	C₂²×C₆₇	1	2	yes	—
402	C₄×C₄⋊C₄	C₂²×C₆₇	1	4	yes	—
403	C₄×C₄⋊C₄	C₂²×C₆₇	1	4	yes	—
404	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
405	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
406	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
407	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
408	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
409	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
410	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
411	C₄×C₂²⋊C₄	C₂²×C₆₇	1	4	yes	—
412	C₄×C₂²⋊C₄	C₂²×C₆₇	1	4	yes	—
413	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
414	C₄×C₂²⋊C₄	C₂²×C₆₇	1	4	yes	—
415	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
416	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
417	#376	C₂²×C₆₇	1	1	yes	characteristic
418	#376	C₂²×C₆₇	1	1	yes	characteristic
419	#376	C₂²×C₆₇	1	2	yes	—
420	C₂×#95	C₂²×C₆₇	1	2	yes	—
421	C₂×#95	C₂²×C₆₇	1	2	yes	—
422	C₂×#95	C₂²×C₆₇	1	2	yes	—
423	C₄³	C₂²×C₆₇	1	2	yes	—
424	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
425	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
426	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
427	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
428	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
429	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
430	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
431	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
432	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
433	#126	C₂×C₄×C₆₇	1	16	yes	complemented
434	#125	C₂×C₄×C₆₇	1	8	yes	complemented
435	#124	C₂×C₄×C₆₇	1	8	yes	complemented
436	#123	C₂×C₄×C₆₇	1	16	yes	complemented
437	C₂²⋊Q₈	C₂×C₄×C₆₇	1	8	yes	complemented
438	#121	C₂×C₄×C₆₇	1	8	yes	—
439	C₄×Q₈	—	4	4	no	—
440	C₄×Q₈	C₂×C₄×C₆₇	1	8	yes	complemented
441	C₄×D₄	—	2	16	no	—
442	C₄×D₄	—	4	4	no	—
443	C₄×D₄	C₂×C₄×C₆₇	1	8	yes	complemented
444	C₄×D₄	C₂×C₄×C₆₇	1	16	yes	complemented
445	#117	—	2	8	no	—
446	#117	C₂×C₄×C₆₇	1	16	yes	complemented
447	C₂×C₄⋊C₄	—	4	4	no	—
448	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
449	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
450	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
451	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
452	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
453	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
454	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
455	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
456	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
457	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
458	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
459	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
460	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
461	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
462	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
463	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
464	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
465	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
466	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
467	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
468	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
469	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
470	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
471	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
472	C₂×C₄²	C₂×C₄×C₆₇	1	8	yes	complemented
473	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
474	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
475	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
476	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
477	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
478	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
479	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
480	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
481	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
482	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
483	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
484	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
485	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
486	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
487	#95	C₂³×C₆₇	1	1	yes	characteristic
488	#95	C₂³×C₆₇	1	2	yes	—
489	#95	C₂³×C₆₇	1	2	yes	—
490	#95	C₂³×C₆₇	1	4	yes	—
491	#95	C₂³×C₆₇	1	4	yes	—
492	#95	C₂³×C₆₇	1	4	yes	—
493	#95	C₂³×C₆₇	1	2	yes	—
494	#95	C₂³×C₆₇	1	2	yes	—
495	#95	C₂³×C₆₇	1	1	yes	characteristic
496	#95	C₂³×C₆₇	1	4	yes	—
497	#95	C₂³×C₆₇	1	1	yes	characteristic
498	#95	C₂³×C₆₇	1	1	yes	characteristic
499	#95	C₂³×C₆₇	1	2	yes	—
500	#95	C₂³×C₆₇	1	2	yes	—
501	#95	C₂³×C₆₇	1	4	yes	—
502	#95	C₂³×C₆₇	1	4	yes	—
503	#95	C₂³×C₆₇	1	4	yes	—
504	#95	C₂³×C₆₇	1	4	yes	—
505	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
506	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
507	C₂×Q₈	—	2	2	no	—
508	C₂×Q₈	—	2	2	no	—
509	C₂×Q₈	C₂²×C₄×C₆₇	1	4	yes	—
510	C₂×D₄	—	2	8	no	—
511	C₂×D₄	—	2	2	no	—
512	C₂×D₄	—	2	2	no	—
513	C₂×D₄	C₂²×C₄×C₆₇	1	8	yes	—
514	C₂×D₄	C₂²×C₄×C₆₇	1	4	yes	—
515	C₂²×C₄	—	2	4	no	—
516	C₂²×C₄	—	2	2	no	—
517	C₂²×C₄	—	2	2	no	—
518	C₂²×C₄	—	2	8	no	—
519	C₂²×C₄	—	2	8	no	—
520	C₂²×C₄	—	4	2	no	—
521	C₂²×C₄	—	4	4	no	—
522	C₂²×C₄	—	4	4	no	—
523	C₂²×C₄	—	4	4	no	—
524	C₂²×C₄	—	4	4	no	—
525	C₂²×C₄	—	4	4	no	—
526	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
527	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
528	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
529	C₂²×C₄	C₂²×C₄×C₆₇	1	8	yes	—
530	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
531	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
532	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
533	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
534	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
535	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
536	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
537	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
538	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
539	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
540	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
541	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
542	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
543	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
544	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
545	C₄⋊C₄	—	2	4	no	—
546	C₄⋊C₄	—	2	4	no	—
547	C₄⋊C₄	—	2	8	no	—
548	C₄⋊C₄	—	2	4	no	—
549	C₄⋊C₄	—	2	4	no	—
550	C₄⋊C₄	—	4	4	no	—
551	C₄⋊C₄	—	4	4	no	—
552	C₄⋊C₄	—	4	4	no	—
553	C₄⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
554	C₄⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
555	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
556	C₄⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
557	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
558	C₄⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
559	C₂²⋊C₄	—	2	4	no	—
560	C₂²⋊C₄	—	2	8	no	—
561	C₂²⋊C₄	—	4	4	no	—
562	C₂²⋊C₄	—	4	4	no	—
563	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
564	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
565	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
566	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
567	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
568	C₂²⋊C₄	#41×C₆₇	1	8	yes	—
569	C₄²	—	2	4	no	—
570	C₄²	—	2	4	no	—
571	C₄²	—	2	8	no	—
572	C₄²	—	2	4	no	—
573	C₄²	—	2	4	no	—
574	C₄²	—	4	4	no	—
575	C₄²	—	4	2	no	—
576	C₄²	—	4	4	no	—
577	C₄²	—	4	2	no	—
578	C₄²	C₂²×C₄×C₆₇	1	4	yes	—
579	C₄²	C₂²×C₄×C₆₇	1	4	yes	—
580	C₄²	C₂²×C₄×C₆₇	1	4	yes	—
581	C₄²	C₂²×C₄×C₆₇	1	4	yes	—
582	C₄²	C₂²×C₄×C₆₇	1	8	yes	—
583	C₂³	—	2	1	no	—
584	C₂³	—	2	1	no	—
585	C₂³	—	2	2	no	—
586	C₂³	—	2	4	no	—
587	C₂³	—	2	2	no	—
588	C₂³	—	2	2	no	—
589	C₂³	—	2	4	no	—
590	C₂³	C₂³×C₄×C₆₇	1	4	yes	—
591	C₂³	C₂³×C₄×C₆₇	1	2	yes	—
592	C₂³	C₂×#41×C₆₇	1	4	yes	—
593	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
594	Q₈	—	2	8	no	—
595	D₄	—	2	16	no	—
596	D₄	—	2	8	no	—
597	C₂×C₄	—	2	8	no	—
598	C₂×C₄	—	2	2	no	—
599	C₂×C₄	—	2	4	no	—
600	C₂×C₄	—	2	2	no	—
601	C₂×C₄	—	2	2	no	—
602	C₂×C₄	—	2	2	no	—
603	C₂×C₄	—	2	1	no	—
604	C₂×C₄	—	2	2	no	—
605	C₂×C₄	—	2	1	no	—
606	C₂×C₄	—	2	2	no	—
607	C₂×C₄	—	2	2	no	—
608	C₂×C₄	—	2	2	no	—
609	C₂×C₄	—	2	4	no	—
610	C₂×C₄	—	2	2	no	—
611	C₂×C₄	—	2	2	no	—
612	C₂×C₄	—	2	8	no	—
613	C₂×C₄	—	2	2	no	—
614	C₂×C₄	—	2	2	no	—
615	C₂×C₄	—	2	4	no	—
616	C₂×C₄	—	2	4	no	—
617	C₂×C₄	—	2	2	no	—
618	C₂×C₄	—	2	4	no	—
619	C₂×C₄	—	2	4	no	—
620	C₂×C₄	—	2	2	no	—
621	C₂×C₄	—	2	2	no	—
622	C₂×C₄	—	2	4	no	—
623	C₂×C₄	—	2	2	no	—
624	C₂×C₄	—	2	4	no	—
625	C₂×C₄	—	4	4	no	—
626	C₂×C₄	—	4	8	no	—
627	C₂×C₄	—	8	8	no	—
628	C₂×C₄	—	8	8	no	—
629	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
630	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
631	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
632	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
633	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
634	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
635	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
636	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
637	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
638	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
639	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
640	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
641	C₂×C₄	2₋¹⁺⁴×C₆₇	1	2	yes	—
642	C₂²	—	2	2	no	—
643	C₂²	—	2	2	no	—
644	C₂²	—	2	4	no	—
645	C₂²	—	2	4	no	—
646	C₂²	—	2	4	no	—
647	C₂²	—	2	4	no	—
648	C₂²	—	2	4	no	—
649	C₂²	—	4	4	no	—
650	C₂²	—	4	4	no	—
651	C₂²	C₄×#41×C₆₇	1	4	yes	—
652	C₂²	C₂⁴×C₄×C₆₇	1	1	yes	characteristic
653	C₂²	C₂²×#41×C₆₇	1	2	yes	—
654	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
655	C₂²	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
656	C₂²	#585×C₆₇	1	2	yes	—
657	C₄	—	2	2	no	—
658	C₄	—	2	2	no	—
659	C₄	—	2	4	no	—
660	C₄	—	2	2	no	—
661	C₄	—	2	4	no	—
662	C₄	—	2	2	no	—
663	C₄	—	2	2	no	—
664	C₄	—	2	4	no	—
665	C₄	—	2	4	no	—
666	C₄	—	2	4	no	—
667	C₄	—	4	4	no	—
668	C₄	—	4	4	no	—
669	C₄	—	4	2	no	—
670	C₄	—	4	2	no	—
671	C₄	#520×C₆₇	1	4	yes	—
672	C₂	—	2	4	no	—
673	C₂	—	4	4	no	—
674	C₂	C₂×C₄×#41×C₆₇	1	1	yes	characteristic
675	C₂	C₂×#520×C₆₇	1	1	yes	characteristic
676	C₂	C₆₇×#3428	1	1	yes	characteristic
677	C₂	C₆₇×#3514	1	2	yes	—
678	C₂	C₆₇×#3515	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₆₇
Frattini, cosocle	C₂³	C₂⁵×C₆₇
prime radical	C₂×#121×C₆₇	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₆₇×#2360	C₂	semidirect
4. C₆₇×#2359	C₂	semidirect
5. C₆₇×#2357	C₂	semidirect
6. C₆₇×#2356	C₂	semidirect
7. C₆₇×#2351	C₂	semidirect
8. C₆₇×#2349	C₂	semidirect
9. C₆₇×#2346	C₂	semidirect
10. C₆₇×#2343	C₂	semidirect
11. C₆₇×#2334	C₂	semidirect
12. C₆₇×#2318	C₂	semidirect
13. C₄×#125×C₆₇	C₂	semidirect
14. C₄×#124×C₆₇	C₂	semidirect
15. C₂×#382×C₆₇	C₂	semidirect
16. C₆₇×#2275	C₂	semidirect
17. C₄×#117×C₆₇	C₂	semidirect
18. #529×C₆₇	C₄	semidirect
93. #126×C₆₇	C₂×C₄	semidirect
94. #125×C₆₇	C₂×C₄	semidirect
95. #124×C₆₇	C₂×C₄	semidirect
96. #123×C₆₇	C₂×C₄	semidirect
97. C₂²⋊Q₈×C₆₇	C₂×C₄	semidirect
100. C₄×Q₈×C₆₇	C₂×C₄	semidirect
103. C₄×D₄×C₆₇	C₂×C₄	semidirect
104. C₄×D₄×C₆₇	C₂×C₄	semidirect
106. #117×C₆₇	C₂×C₄	semidirect
132. C₂×C₄²×C₆₇	C₂×C₄	semidirect
332. #34229	C₆₇	direct (N × H)
342. #2360	C₂×C₆₇	semidirect
343. #2359	C₂×C₆₇	semidirect
344. #2357	C₂×C₆₇	semidirect
345. #2356	C₂×C₆₇	semidirect
346. #2351	C₂×C₆₇	semidirect
347. #2349	C₂×C₆₇	semidirect
348. #2346	C₂×C₆₇	semidirect
349. #2343	C₂×C₆₇	semidirect
350. #2334	C₂×C₆₇	semidirect
351. #2318	C₂×C₆₇	semidirect
352. C₄×#125	C₂×C₆₇	semidirect
353. C₄×#124	C₂×C₆₇	semidirect
354. C₂×#382	C₂×C₆₇	semidirect
355. #2275	C₂×C₆₇	semidirect
356. C₄×#117	C₂×C₆₇	semidirect
357. C₆₇	#34229	direct (N × H)
358. #529	C₄×C₆₇	semidirect
433. #126	C₂×C₄×C₆₇	semidirect
434. #125	C₂×C₄×C₆₇	semidirect
435. #124	C₂×C₄×C₆₇	semidirect
436. #123	C₂×C₄×C₆₇	semidirect
437. C₂²⋊Q₈	C₂×C₄×C₆₇	semidirect
440. C₄×Q₈	C₂×C₄×C₆₇	semidirect
443. C₄×D₄	C₂×C₄×C₆₇	semidirect
444. C₄×D₄	C₂×C₄×C₆₇	semidirect
446. #117	C₂×C₄×C₆₇	semidirect
472. C₂×C₄²	C₂×C₄×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#529×C₆₇	2
C₆₇×#2361	2
C₆₇×#2360	2
C₆₇×#2359	2
C₆₇×#2357	2
C₆₇×#2356	2
C₆₇×#2351	2
C₆₇×#2349	2
C₆₇×#2346	2
C₆₇×#2343	2
C₆₇×#2334	2
C₆₇×#2318	2
C₄×#125×C₆₇	2
C₄×#124×C₆₇	2
C₂×#382×C₆₇	2
C₆₇×#2275	2
C₄×#117×C₆₇	2
#34229	67

Subgroups — C67×#34229 #30713480

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#34229 #30713480