Subgroups — C₆₇×#35143 #30714394

Order 17152.

2418 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#126×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×#41×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#2852	C₂	1	4	yes	maximal, complemented
4	C₆₇×#2637	C₂	1	2	yes	maximal, complemented
5	C₆₇×#2636	C₂	1	2	yes	maximal, complemented
6	C₆₇×#2604	C₂	1	2	yes	maximal, complemented
7	C₆₇×#2603	C₂	1	2	yes	maximal, complemented
8	C₆₇×#2601	C₂	1	4	yes	maximal, complemented
9	C₆₇×#2579	C₂	1	2	yes	maximal, complemented
10	C₆₇×#2534	C₂	1	2	yes	maximal, complemented
11	C₆₇×#2484	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#2482	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#2406	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#2404	C₂	1	1	yes	maximal, characteristic
15	C₆₇×#2322	C₂	1	2	yes	maximal, complemented
16	C₆₇×#2321	C₂	1	2	yes	maximal, complemented
17	C₆₇×#2283	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
19	C₂×#126×C₆₇	—	2	8	no	—
20	C₂×#126×C₆₇	C₂²	1	2	yes	—
21	C₂×#126×C₆₇	C₂²	1	2	yes	—
22	C₂×#126×C₆₇	C₂²	1	2	yes	—
23	C₂×#126×C₆₇	C₂²	1	2	yes	—
24	C₂×#123×C₆₇	C₂²	1	2	yes	—
25	C₂×#120×C₆₇	C₂²	1	2	yes	—
26	C₄×#41×C₆₇	—	2	8	no	—
27	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
30	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
31	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
33	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
34	C₂×#117×C₆₇	C₂²	1	2	yes	complemented
35	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
36	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
37	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
38	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
39	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
40	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
41	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
42	C₂²×C₄²×C₆₇	C₂²	1	2	yes	complemented
43	#400×C₆₇	C₂²	1	2	yes	complemented
44	#399×C₆₇	C₂²	1	2	yes	—
45	#398×C₆₇	C₂²	1	4	yes	complemented
46	#398×C₆₇	C₂²	1	2	yes	complemented
47	#397×C₆₇	C₂²	1	2	yes	—
48	#396×C₆₇	C₂²	1	4	yes	—
49	#396×C₆₇	C₂²	1	4	yes	complemented
50	#395×C₆₇	C₂²	1	2	yes	complemented
51	#394×C₆₇	C₂²	1	4	yes	—
52	#394×C₆₇	C₂²	1	2	yes	complemented
53	#393×C₆₇	C₂²	1	2	yes	—
54	#392×C₆₇	C₂²	1	2	yes	—
55	#390×C₆₇	C₂²	1	4	yes	—
56	#389×C₆₇	C₂²	1	4	yes	complemented
57	#388×C₆₇	C₂²	1	4	yes	—
58	#388×C₆₇	C₂²	1	4	yes	—
59	#388×C₆₇	C₂²	1	4	yes	—
60	#388×C₆₇	C₂²	1	4	yes	—
61	#388×C₆₇	C₂²	1	4	yes	complemented
62	#387×C₆₇	C₂²	1	4	yes	complemented
63	#387×C₆₇	C₂²	1	4	yes	complemented
64	#387×C₆₇	C₂²	1	4	yes	complemented
65	#386×C₆₇	C₂²	1	4	yes	—
66	#386×C₆₇	C₂²	1	2	yes	—
67	#386×C₆₇	C₂²	1	4	yes	—
68	#386×C₆₇	C₂²	1	2	yes	—
69	#386×C₆₇	C₂²	1	4	yes	—
70	#385×C₆₇	C₂²	1	2	yes	—
71	#385×C₆₇	C₂²	1	2	yes	—
72	#385×C₆₇	C₂²	1	4	yes	complemented
73	#385×C₆₇	C₂²	1	4	yes	complemented
74	#385×C₆₇	C₂²	1	4	yes	complemented
75	#383×C₆₇	C₂²	1	2	yes	complemented
76	#382×C₆₇	C₂²	1	2	yes	complemented
77	#381×C₆₇	C₂²	1	2	yes	—
78	#381×C₆₇	C₂²	1	1	yes	characteristic
79	#381×C₆₇	C₂²	1	1	yes	characteristic
80	#380×C₆₇	C₂²	1	2	yes	—
81	#379×C₆₇	C₂²	1	2	yes	—
82	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	complemented
83	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
84	#376×C₆₇	C₂²	1	2	yes	complemented
85	C₂⁵×C₆₇	C₂³	1	1	yes	characteristic
86	C₂×#41×C₆₇	—	2	8	no	—
87	C₂×#41×C₆₇	—	2	4	no	—
88	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
89	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
90	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
91	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
92	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
93	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
94	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
95	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
96	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
97	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
98	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
99	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
100	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
101	#126×C₆₇	—	2	8	no	—
102	#126×C₆₇	—	2	8	no	—
103	#126×C₆₇	—	2	8	no	—
104	#126×C₆₇	—	2	8	no	—
105	#123×C₆₇	—	2	8	no	—
106	#120×C₆₇	—	2	8	no	—
107	C₄×Q₈×C₆₇	—	2	4	no	—
108	C₄×Q₈×C₆₇	—	2	4	no	—
109	C₄×D₄×C₆₇	—	2	8	no	—
110	C₄×D₄×C₆₇	—	2	8	no	—
111	C₄×D₄×C₆₇	—	2	4	no	—
112	C₄×D₄×C₆₇	—	2	4	no	—
113	#117×C₆₇	—	2	4	no	—
114	#117×C₆₇	—	2	8	no	—
115	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
116	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
117	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
118	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
119	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
120	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
121	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
122	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
123	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
124	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
125	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
126	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
127	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
128	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
129	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
130	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
131	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
132	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
133	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
134	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
135	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
136	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
137	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
138	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
139	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
140	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
141	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
142	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
143	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
144	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
145	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
146	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
147	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
148	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
149	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
150	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
151	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
152	C₂×C₄²×C₆₇	—	2	8	no	—
153	C₂×C₄²×C₆₇	D₄	1	8	yes	complemented
154	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
155	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
156	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
157	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
158	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
159	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
160	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
161	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
162	#95×C₆₇	C₂³	1	4	yes	—
163	#95×C₆₇	C₂³	1	2	yes	—
164	#95×C₆₇	C₂³	1	2	yes	—
165	#95×C₆₇	C₂³	1	4	yes	—
166	#95×C₆₇	C₂³	1	2	yes	—
167	#95×C₆₇	C₂³	1	2	yes	—
168	#95×C₆₇	C₂³	1	4	yes	—
169	#95×C₆₇	C₂³	1	4	yes	—
170	#95×C₆₇	C₂³	1	4	yes	—
171	#95×C₆₇	C₂³	1	4	yes	—
172	#95×C₆₇	C₂³	1	4	yes	—
173	#95×C₆₇	C₂³	1	4	yes	—
174	C₂⁴×C₆₇	—	2	2	no	—
175	C₂⁴×C₆₇	—	2	4	no	—
176	C₂⁴×C₆₇	—	4	2	no	—
177	C₂⁴×C₆₇	—	4	2	no	—
178	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
179	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
180	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
181	#41×C₆₇	—	2	32	no	—
182	C₂×Q₈×C₆₇	—	2	2	no	—
183	C₂×Q₈×C₆₇	—	2	4	no	—
184	C₂×D₄×C₆₇	—	2	4	no	—
185	C₂×D₄×C₆₇	—	2	4	no	—
186	C₂×D₄×C₆₇	—	2	4	no	—
187	C₂×D₄×C₆₇	—	2	8	no	—
188	C₂×D₄×C₆₇	—	2	2	no	—
189	C₂×D₄×C₆₇	—	4	4	no	—
190	C₂×D₄×C₆₇	—	4	4	no	—
191	C₂×D₄×C₆₇	#41	1	8	yes	—
192	C₂²×C₄×C₆₇	—	2	4	no	—
193	C₂²×C₄×C₆₇	—	2	4	no	—
194	C₂²×C₄×C₆₇	—	2	4	no	—
195	C₂²×C₄×C₆₇	—	2	4	no	—
196	C₂²×C₄×C₆₇	—	2	2	no	—
197	C₂²×C₄×C₆₇	—	2	2	no	—
198	C₂²×C₄×C₆₇	—	2	2	no	—
199	C₂²×C₄×C₆₇	—	2	4	no	—
200	C₂²×C₄×C₆₇	—	2	4	no	—
201	C₂²×C₄×C₆₇	—	2	4	no	—
202	C₂²×C₄×C₆₇	—	4	2	no	—
203	C₂²×C₄×C₆₇	—	4	2	no	—
204	C₂²×C₄×C₆₇	—	4	4	no	—
205	C₂²×C₄×C₆₇	—	4	4	no	—
206	C₂²×C₄×C₆₇	—	4	2	no	—
207	C₂²×C₄×C₆₇	—	4	2	no	—
208	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
209	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
210	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
211	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
212	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
213	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
214	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
215	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
216	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
217	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
218	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
219	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
220	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
221	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
222	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
223	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
224	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
225	C₄⋊C₄×C₆₇	—	2	4	no	—
226	C₄⋊C₄×C₆₇	—	2	4	no	—
227	C₄⋊C₄×C₆₇	—	2	4	no	—
228	C₄⋊C₄×C₆₇	—	2	4	no	—
229	C₄⋊C₄×C₆₇	—	2	4	no	—
230	C₄⋊C₄×C₆₇	—	2	4	no	—
231	C₄⋊C₄×C₆₇	—	2	4	no	—
232	C₄⋊C₄×C₆₇	—	2	4	no	—
233	C₄⋊C₄×C₆₇	—	2	2	no	—
234	C₄⋊C₄×C₆₇	—	2	2	no	—
235	C₄⋊C₄×C₆₇	—	2	8	no	—
236	C₄⋊C₄×C₆₇	—	4	4	no	—
237	C₄⋊C₄×C₆₇	—	4	4	no	—
238	C₄⋊C₄×C₆₇	—	4	4	no	—
239	C₂²⋊C₄×C₆₇	—	2	4	no	—
240	C₂²⋊C₄×C₆₇	—	2	4	no	—
241	C₂²⋊C₄×C₆₇	—	2	4	no	—
242	C₂²⋊C₄×C₆₇	—	2	8	no	—
243	C₂²⋊C₄×C₆₇	—	2	4	no	—
244	C₂²⋊C₄×C₆₇	—	2	4	no	—
245	C₂²⋊C₄×C₆₇	—	2	4	no	—
246	C₂²⋊C₄×C₆₇	—	2	4	no	—
247	C₂²⋊C₄×C₆₇	—	2	4	no	—
248	C₂²⋊C₄×C₆₇	—	2	4	no	—
249	C₂²⋊C₄×C₆₇	—	2	4	no	—
250	C₂²⋊C₄×C₆₇	—	2	4	no	—
251	C₂²⋊C₄×C₆₇	—	2	8	no	—
252	C₂²⋊C₄×C₆₇	—	4	4	no	—
253	C₂²⋊C₄×C₆₇	—	4	4	no	—
254	C₂²⋊C₄×C₆₇	—	4	4	no	—
255	C₂²⋊C₄×C₆₇	—	4	4	no	—
256	C₄²×C₆₇	—	2	4	no	—
257	C₄²×C₆₇	—	2	4	no	—
258	C₄²×C₆₇	—	2	4	no	—
259	C₄²×C₆₇	—	4	4	no	—
260	C₄²×C₆₇	C₂×D₄	1	4	yes	—
261	C₄²×C₆₇	C₂×D₄	1	4	yes	—
262	C₄²×C₆₇	C₂×D₄	1	4	yes	—
263	C₄²×C₆₇	C₂×D₄	1	4	yes	—
264	C₂³×C₆₇	—	2	2	no	—
265	C₂³×C₆₇	—	2	2	no	—
266	C₂³×C₆₇	—	2	2	no	—
267	C₂³×C₆₇	—	2	2	no	—
268	C₂³×C₆₇	—	2	4	no	—
269	C₂³×C₆₇	—	2	4	no	—
270	C₂³×C₆₇	—	2	2	no	—
271	C₂³×C₆₇	—	2	4	no	—
272	C₂³×C₆₇	—	2	2	no	—
273	C₂³×C₆₇	—	2	4	no	—
274	C₂³×C₆₇	—	2	2	no	—
275	C₂³×C₆₇	—	4	4	no	—
276	C₂³×C₆₇	—	4	4	no	—
277	C₂³×C₆₇	—	4	4	no	—
278	C₂³×C₆₇	—	8	8	no	—
279	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
280	C₂³×C₆₇	C₂×#41	1	4	yes	—
281	C₂³×C₆₇	C₂×#41	1	4	yes	—
282	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
283	Q₈×C₆₇	—	2	8	no	—
284	D₄×C₆₇	—	2	8	no	—
285	D₄×C₆₇	—	2	16	no	—
286	D₄×C₆₇	—	8	8	no	—
287	C₂×C₄×C₆₇	—	2	16	no	—
288	C₂×C₄×C₆₇	—	2	8	no	—
289	C₂×C₄×C₆₇	—	2	2	no	—
290	C₂×C₄×C₆₇	—	2	2	no	—
291	C₂×C₄×C₆₇	—	2	2	no	—
292	C₂×C₄×C₆₇	—	2	2	no	—
293	C₂×C₄×C₆₇	—	2	2	no	—
294	C₂×C₄×C₆₇	—	2	2	no	—
295	C₂×C₄×C₆₇	—	2	2	no	—
296	C₂×C₄×C₆₇	—	2	2	no	—
297	C₂×C₄×C₆₇	—	2	2	no	—
298	C₂×C₄×C₆₇	—	2	2	no	—
299	C₂×C₄×C₆₇	—	2	2	no	—
300	C₂×C₄×C₆₇	—	2	2	no	—
301	C₂×C₄×C₆₇	—	2	2	no	—
302	C₂×C₄×C₆₇	—	2	4	no	—
303	C₂×C₄×C₆₇	—	2	4	no	—
304	C₂×C₄×C₆₇	—	2	4	no	—
305	C₂×C₄×C₆₇	—	2	4	no	—
306	C₂×C₄×C₆₇	—	2	4	no	—
307	C₂×C₄×C₆₇	—	2	4	no	—
308	C₂×C₄×C₆₇	—	2	2	no	—
309	C₂×C₄×C₆₇	—	2	4	no	—
310	C₂×C₄×C₆₇	—	2	4	no	—
311	C₂×C₄×C₆₇	—	2	4	no	—
312	C₂×C₄×C₆₇	—	2	2	no	—
313	C₂×C₄×C₆₇	—	2	4	no	—
314	C₂×C₄×C₆₇	—	4	4	no	—
315	C₂×C₄×C₆₇	—	4	4	no	—
316	C₂×C₄×C₆₇	—	4	8	no	—
317	C₂×C₄×C₆₇	—	4	8	no	—
318	C₂×C₄×C₆₇	—	4	4	no	—
319	C₂×C₄×C₆₇	—	4	4	no	—
320	C₂×C₄×C₆₇	—	4	4	no	—
321	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
322	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
323	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
324	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
325	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
326	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
327	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
328	C₂²×C₆₇	—	2	2	no	—
329	C₂²×C₆₇	—	2	2	no	—
330	C₂²×C₆₇	—	2	8	no	—
331	C₂²×C₆₇	—	2	4	no	—
332	C₂²×C₆₇	—	2	8	no	—
333	C₂²×C₆₇	—	4	2	no	—
334	C₂²×C₆₇	—	4	2	no	—
335	C₂²×C₆₇	—	4	4	no	—
336	C₂²×C₆₇	—	4	2	no	—
337	C₂²×C₆₇	—	4	2	no	—
338	C₂²×C₆₇	—	4	2	no	—
339	C₂²×C₆₇	—	4	4	no	—
340	C₂²×C₆₇	—	4	4	no	—
341	C₂²×C₆₇	—	8	8	no	—
342	C₂²×C₆₇	#525	1	4	yes	—
343	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
344	C₂²×C₆₇	C₂²×#41	1	2	yes	—
345	C₂²×C₆₇	#585	1	2	yes	—
346	C₂²×C₆₇	#585	1	2	yes	—
347	C₄×C₆₇	—	2	2	no	—
348	C₄×C₆₇	—	2	2	no	—
349	C₄×C₆₇	—	2	4	no	—
350	C₄×C₆₇	—	2	2	no	—
351	C₄×C₆₇	—	2	2	no	—
352	C₄×C₆₇	—	2	2	no	—
353	C₄×C₆₇	—	2	2	no	—
354	C₄×C₆₇	—	4	2	no	—
355	C₄×C₆₇	—	4	2	no	—
356	C₄×C₆₇	—	4	2	no	—
357	C₄×C₆₇	—	4	2	no	—
358	C₄×C₆₇	—	4	2	no	—
359	C₄×C₆₇	—	4	4	no	—
360	C₄×C₆₇	—	4	4	no	—
361	#35143	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
362	C₂×C₆₇	—	2	4	no	—
363	C₂×C₆₇	—	4	4	no	—
364	C₂×C₆₇	—	8	2	no	—
365	C₂×C₆₇	C₂×#525	1	1	yes	characteristic
366	C₂×C₆₇	#3449	1	1	yes	characteristic
367	C₂×C₆₇	#3449	1	1	yes	characteristic
368	C₂×C₆₇	#3521	1	4	yes	—
369	C₂²×#126	C₂×C₆₇	1	1	yes	characteristic, complemented
370	C₂×C₄×#41	C₂×C₆₇	1	1	yes	characteristic, complemented
371	#2852	C₂×C₆₇	1	4	yes	complemented
372	#2637	C₂×C₆₇	1	2	yes	complemented
373	#2636	C₂×C₆₇	1	2	yes	complemented
374	#2604	C₂×C₆₇	1	2	yes	complemented
375	#2603	C₂×C₆₇	1	2	yes	complemented
376	#2601	C₂×C₆₇	1	4	yes	complemented
377	#2579	C₂×C₆₇	1	2	yes	complemented
378	#2534	C₂×C₆₇	1	2	yes	complemented
379	#2484	C₂×C₆₇	1	1	yes	characteristic, complemented
380	#2482	C₂×C₆₇	1	1	yes	characteristic, complemented
381	#2406	C₂×C₆₇	1	1	yes	characteristic, complemented
382	#2404	C₂×C₆₇	1	1	yes	characteristic
383	#2322	C₂×C₆₇	1	2	yes	complemented
384	#2321	C₂×C₆₇	1	2	yes	complemented
385	#2283	C₂×C₆₇	1	1	yes	characteristic, complemented
386	C₆₇	#35143	1	1	yes	characteristic, direct product factor, Sylow
387	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
388	C₂×#126	—	2	8	no	—
389	C₂×#126	C₂²×C₆₇	1	2	yes	—
390	C₂×#126	C₂²×C₆₇	1	2	yes	—
391	C₂×#126	C₂²×C₆₇	1	2	yes	—
392	C₂×#126	C₂²×C₆₇	1	2	yes	—
393	C₂×#123	C₂²×C₆₇	1	2	yes	—
394	C₂×#120	C₂²×C₆₇	1	2	yes	—
395	C₄×#41	—	2	8	no	—
396	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
397	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
398	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
399	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
400	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
401	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
402	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
403	C₂×#117	C₂²×C₆₇	1	2	yes	complemented
404	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
405	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
406	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
407	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
408	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
409	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
410	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
411	C₂²×C₄²	C₂²×C₆₇	1	2	yes	complemented
412	#400	C₂²×C₆₇	1	2	yes	complemented
413	#399	C₂²×C₆₇	1	2	yes	—
414	#398	C₂²×C₆₇	1	4	yes	complemented
415	#398	C₂²×C₆₇	1	2	yes	complemented
416	#397	C₂²×C₆₇	1	2	yes	—
417	#396	C₂²×C₆₇	1	4	yes	—
418	#396	C₂²×C₆₇	1	4	yes	complemented
419	#395	C₂²×C₆₇	1	2	yes	complemented
420	#394	C₂²×C₆₇	1	4	yes	—
421	#394	C₂²×C₆₇	1	2	yes	complemented
422	#393	C₂²×C₆₇	1	2	yes	—
423	#392	C₂²×C₆₇	1	2	yes	—
424	#390	C₂²×C₆₇	1	4	yes	—
425	#389	C₂²×C₆₇	1	4	yes	complemented
426	#388	C₂²×C₆₇	1	4	yes	—
427	#388	C₂²×C₆₇	1	4	yes	—
428	#388	C₂²×C₆₇	1	4	yes	—
429	#388	C₂²×C₆₇	1	4	yes	—
430	#388	C₂²×C₆₇	1	4	yes	complemented
431	#387	C₂²×C₆₇	1	4	yes	complemented
432	#387	C₂²×C₆₇	1	4	yes	complemented
433	#387	C₂²×C₆₇	1	4	yes	complemented
434	#386	C₂²×C₆₇	1	2	yes	—
435	#386	C₂²×C₆₇	1	4	yes	—
436	#386	C₂²×C₆₇	1	2	yes	—
437	#386	C₂²×C₆₇	1	4	yes	—
438	#386	C₂²×C₆₇	1	4	yes	—
439	#385	C₂²×C₆₇	1	2	yes	—
440	#385	C₂²×C₆₇	1	2	yes	—
441	#385	C₂²×C₆₇	1	4	yes	complemented
442	#385	C₂²×C₆₇	1	4	yes	complemented
443	#385	C₂²×C₆₇	1	4	yes	complemented
444	#383	C₂²×C₆₇	1	2	yes	complemented
445	#382	C₂²×C₆₇	1	2	yes	complemented
446	#381	C₂²×C₆₇	1	2	yes	—
447	#381	C₂²×C₆₇	1	1	yes	characteristic
448	#381	C₂²×C₆₇	1	1	yes	characteristic
449	#380	C₂²×C₆₇	1	2	yes	—
450	#379	C₂²×C₆₇	1	2	yes	—
451	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	complemented
452	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
453	#376	C₂²×C₆₇	1	2	yes	complemented
454	C₂⁵	C₂³×C₆₇	1	1	yes	characteristic
455	C₂×#41	—	2	8	no	—
456	C₂×#41	—	2	4	no	—
457	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
458	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
459	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
460	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
461	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
462	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
463	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
464	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
465	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
466	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
467	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
468	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
469	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
470	#126	—	2	8	no	—
471	#126	—	2	8	no	—
472	#126	—	2	8	no	—
473	#126	—	2	8	no	—
474	#123	—	2	8	no	—
475	#120	—	2	8	no	—
476	C₄×Q₈	—	2	4	no	—
477	C₄×Q₈	—	2	4	no	—
478	C₄×D₄	—	2	8	no	—
479	C₄×D₄	—	2	8	no	—
480	C₄×D₄	—	2	4	no	—
481	C₄×D₄	—	2	4	no	—
482	#117	—	2	4	no	—
483	#117	—	2	8	no	—
484	C₂×C₄⋊C₄	—	2	4	no	—
485	C₂×C₄⋊C₄	—	2	4	no	—
486	C₂×C₄⋊C₄	—	2	4	no	—
487	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
488	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
489	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
490	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
491	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
492	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
493	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
494	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
495	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
496	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
497	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
498	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
499	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
500	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
501	C₂×C₂²⋊C₄	—	2	4	no	—
502	C₂×C₂²⋊C₄	—	2	4	no	—
503	C₂×C₂²⋊C₄	—	2	4	no	—
504	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
505	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
506	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
507	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
508	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
509	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
510	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
511	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
512	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
513	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
514	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
515	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
516	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
517	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
518	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
519	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
520	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
521	C₂×C₄²	—	2	8	no	—
522	C₂×C₄²	D₄×C₆₇	1	8	yes	complemented
523	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
524	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
525	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
526	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
527	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
528	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
529	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
530	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
531	#95	C₂³×C₆₇	1	4	yes	—
532	#95	C₂³×C₆₇	1	2	yes	—
533	#95	C₂³×C₆₇	1	2	yes	—
534	#95	C₂³×C₆₇	1	4	yes	—
535	#95	C₂³×C₆₇	1	2	yes	—
536	#95	C₂³×C₆₇	1	2	yes	—
537	#95	C₂³×C₆₇	1	4	yes	—
538	#95	C₂³×C₆₇	1	4	yes	—
539	#95	C₂³×C₆₇	1	4	yes	—
540	#95	C₂³×C₆₇	1	4	yes	—
541	#95	C₂³×C₆₇	1	4	yes	—
542	#95	C₂³×C₆₇	1	4	yes	—
543	C₂⁴	—	2	2	no	—
544	C₂⁴	—	2	4	no	—
545	C₂⁴	—	4	2	no	—
546	C₂⁴	—	4	2	no	—
547	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
548	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
549	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
550	#41	—	2	32	no	—
551	C₂×Q₈	—	2	2	no	—
552	C₂×Q₈	—	2	4	no	—
553	C₂×D₄	—	2	4	no	—
554	C₂×D₄	—	2	4	no	—
555	C₂×D₄	—	2	4	no	—
556	C₂×D₄	—	2	8	no	—
557	C₂×D₄	—	2	2	no	—
558	C₂×D₄	—	4	4	no	—
559	C₂×D₄	—	4	4	no	—
560	C₂×D₄	#41×C₆₇	1	8	yes	—
561	C₂²×C₄	—	2	4	no	—
562	C₂²×C₄	—	2	4	no	—
563	C₂²×C₄	—	2	4	no	—
564	C₂²×C₄	—	2	4	no	—
565	C₂²×C₄	—	2	2	no	—
566	C₂²×C₄	—	2	2	no	—
567	C₂²×C₄	—	2	2	no	—
568	C₂²×C₄	—	2	4	no	—
569	C₂²×C₄	—	2	4	no	—
570	C₂²×C₄	—	2	4	no	—
571	C₂²×C₄	—	4	2	no	—
572	C₂²×C₄	—	4	2	no	—
573	C₂²×C₄	—	4	4	no	—
574	C₂²×C₄	—	4	4	no	—
575	C₂²×C₄	—	4	2	no	—
576	C₂²×C₄	—	4	2	no	—
577	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
578	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
579	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
580	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
581	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
582	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
583	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
584	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
585	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
586	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
587	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
588	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
589	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
590	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
591	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
592	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
593	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
594	C₄⋊C₄	—	2	4	no	—
595	C₄⋊C₄	—	2	4	no	—
596	C₄⋊C₄	—	2	4	no	—
597	C₄⋊C₄	—	2	4	no	—
598	C₄⋊C₄	—	2	4	no	—
599	C₄⋊C₄	—	2	4	no	—
600	C₄⋊C₄	—	2	4	no	—
601	C₄⋊C₄	—	2	4	no	—
602	C₄⋊C₄	—	2	2	no	—
603	C₄⋊C₄	—	2	2	no	—
604	C₄⋊C₄	—	2	8	no	—
605	C₄⋊C₄	—	4	4	no	—
606	C₄⋊C₄	—	4	4	no	—
607	C₄⋊C₄	—	4	4	no	—
608	C₂²⋊C₄	—	2	4	no	—
609	C₂²⋊C₄	—	2	4	no	—
610	C₂²⋊C₄	—	2	4	no	—
611	C₂²⋊C₄	—	2	8	no	—
612	C₂²⋊C₄	—	2	4	no	—
613	C₂²⋊C₄	—	2	4	no	—
614	C₂²⋊C₄	—	2	4	no	—
615	C₂²⋊C₄	—	2	4	no	—
616	C₂²⋊C₄	—	2	4	no	—
617	C₂²⋊C₄	—	2	4	no	—
618	C₂²⋊C₄	—	2	4	no	—
619	C₂²⋊C₄	—	2	4	no	—
620	C₂²⋊C₄	—	2	8	no	—
621	C₂²⋊C₄	—	4	4	no	—
622	C₂²⋊C₄	—	4	4	no	—
623	C₂²⋊C₄	—	4	4	no	—
624	C₂²⋊C₄	—	4	4	no	—
625	C₄²	—	2	4	no	—
626	C₄²	—	2	4	no	—
627	C₄²	—	2	4	no	—
628	C₄²	—	4	4	no	—
629	C₄²	C₂×D₄×C₆₇	1	4	yes	—
630	C₄²	C₂×D₄×C₆₇	1	4	yes	—
631	C₄²	C₂×D₄×C₆₇	1	4	yes	—
632	C₄²	C₂×D₄×C₆₇	1	4	yes	—
633	C₂³	—	2	2	no	—
634	C₂³	—	2	2	no	—
635	C₂³	—	2	2	no	—
636	C₂³	—	2	2	no	—
637	C₂³	—	2	4	no	—
638	C₂³	—	2	4	no	—
639	C₂³	—	2	2	no	—
640	C₂³	—	2	4	no	—
641	C₂³	—	2	2	no	—
642	C₂³	—	2	4	no	—
643	C₂³	—	2	2	no	—
644	C₂³	—	4	4	no	—
645	C₂³	—	4	4	no	—
646	C₂³	—	4	4	no	—
647	C₂³	—	8	8	no	—
648	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
649	C₂³	C₂×#41×C₆₇	1	4	yes	—
650	C₂³	C₂×#41×C₆₇	1	4	yes	—
651	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
652	Q₈	—	2	8	no	—
653	D₄	—	2	8	no	—
654	D₄	—	2	16	no	—
655	D₄	—	8	8	no	—
656	C₂×C₄	—	2	16	no	—
657	C₂×C₄	—	2	8	no	—
658	C₂×C₄	—	2	2	no	—
659	C₂×C₄	—	2	2	no	—
660	C₂×C₄	—	2	2	no	—
661	C₂×C₄	—	2	2	no	—
662	C₂×C₄	—	2	2	no	—
663	C₂×C₄	—	2	2	no	—
664	C₂×C₄	—	2	2	no	—
665	C₂×C₄	—	2	2	no	—
666	C₂×C₄	—	2	2	no	—
667	C₂×C₄	—	2	2	no	—
668	C₂×C₄	—	2	2	no	—
669	C₂×C₄	—	2	2	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	4	no	—
672	C₂×C₄	—	2	4	no	—
673	C₂×C₄	—	2	4	no	—
674	C₂×C₄	—	2	4	no	—
675	C₂×C₄	—	2	4	no	—
676	C₂×C₄	—	2	4	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	4	no	—
679	C₂×C₄	—	2	4	no	—
680	C₂×C₄	—	2	4	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	4	no	—
683	C₂×C₄	—	4	4	no	—
684	C₂×C₄	—	4	4	no	—
685	C₂×C₄	—	4	8	no	—
686	C₂×C₄	—	4	8	no	—
687	C₂×C₄	—	4	4	no	—
688	C₂×C₄	—	4	4	no	—
689	C₂×C₄	—	4	4	no	—
690	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
691	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
692	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
693	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
694	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
695	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
696	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
697	C₂²	—	2	8	no	—
698	C₂²	—	2	2	no	—
699	C₂²	—	2	2	no	—
700	C₂²	—	2	8	no	—
701	C₂²	—	2	4	no	—
702	C₂²	—	4	4	no	—
703	C₂²	—	4	2	no	—
704	C₂²	—	4	2	no	—
705	C₂²	—	4	4	no	—
706	C₂²	—	4	4	no	—
707	C₂²	—	4	2	no	—
708	C₂²	—	4	2	no	—
709	C₂²	—	4	2	no	—
710	C₂²	—	8	8	no	—
711	C₂²	#525×C₆₇	1	4	yes	—
712	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
713	C₂²	C₂²×#41×C₆₇	1	2	yes	—
714	C₂²	#585×C₆₇	1	2	yes	—
715	C₂²	#585×C₆₇	1	2	yes	—
716	C₄	—	2	2	no	—
717	C₄	—	2	2	no	—
718	C₄	—	2	4	no	—
719	C₄	—	2	2	no	—
720	C₄	—	2	2	no	—
721	C₄	—	2	2	no	—
722	C₄	—	2	2	no	—
723	C₄	—	4	4	no	—
724	C₄	—	4	4	no	—
725	C₄	—	4	2	no	—
726	C₄	—	4	2	no	—
727	C₄	—	4	2	no	—
728	C₄	—	4	2	no	—
729	C₄	—	4	2	no	—
730	C₂	—	2	4	no	—
731	C₂	—	4	4	no	—
732	C₂	—	8	2	no	—
733	C₂	C₂×#525×C₆₇	1	1	yes	characteristic
734	C₂	C₆₇×#3449	1	1	yes	characteristic
735	C₂	C₆₇×#3449	1	1	yes	characteristic
736	C₂	C₆₇×#3521	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₇
prime radical	C₆₇×#2404	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×#126×C₆₇	C₂	semidirect
2. C₂×C₄×#41×C₆₇	C₂	semidirect
3. C₆₇×#2852	C₂	semidirect
4. C₆₇×#2637	C₂	semidirect
5. C₆₇×#2636	C₂	semidirect
6. C₆₇×#2604	C₂	semidirect
7. C₆₇×#2603	C₂	semidirect
8. C₆₇×#2601	C₂	semidirect
9. C₆₇×#2579	C₂	semidirect
10. C₆₇×#2534	C₂	semidirect
11. C₆₇×#2484	C₂	semidirect
12. C₆₇×#2482	C₂	semidirect
13. C₆₇×#2406	C₂	semidirect
15. C₆₇×#2322	C₂	semidirect
16. C₆₇×#2321	C₂	semidirect
17. C₆₇×#2283	C₂	semidirect
27. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
28. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
31. C₂×C₄×D₄×C₆₇	C₂²	semidirect
32. C₂×C₄×D₄×C₆₇	C₂²	semidirect
34. C₂×#117×C₆₇	C₂²	semidirect
42. C₂²×C₄²×C₆₇	C₂²	semidirect
43. #400×C₆₇	C₂²	semidirect
45. #398×C₆₇	C₂²	semidirect
46. #398×C₆₇	C₂²	semidirect
49. #396×C₆₇	C₂²	semidirect
50. #395×C₆₇	C₂²	semidirect
52. #394×C₆₇	C₂²	semidirect
56. #389×C₆₇	C₂²	semidirect
61. #388×C₆₇	C₂²	semidirect
62. #387×C₆₇	C₂²	semidirect
63. #387×C₆₇	C₂²	semidirect
64. #387×C₆₇	C₂²	semidirect
72. #385×C₆₇	C₂²	semidirect
73. #385×C₆₇	C₂²	semidirect
74. #385×C₆₇	C₂²	semidirect
75. #383×C₆₇	C₂²	semidirect
76. #382×C₆₇	C₂²	semidirect
82. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
84. #376×C₆₇	C₂²	semidirect
153. C₂×C₄²×C₆₇	D₄	semidirect
361. #35143	C₆₇	direct (N × H)
369. C₂²×#126	C₂×C₆₇	semidirect
370. C₂×C₄×#41	C₂×C₆₇	semidirect
371. #2852	C₂×C₆₇	semidirect
372. #2637	C₂×C₆₇	semidirect
373. #2636	C₂×C₆₇	semidirect
374. #2604	C₂×C₆₇	semidirect
375. #2603	C₂×C₆₇	semidirect
376. #2601	C₂×C₆₇	semidirect
377. #2579	C₂×C₆₇	semidirect
378. #2534	C₂×C₆₇	semidirect
379. #2484	C₂×C₆₇	semidirect
380. #2482	C₂×C₆₇	semidirect
381. #2406	C₂×C₆₇	semidirect
383. #2322	C₂×C₆₇	semidirect
384. #2321	C₂×C₆₇	semidirect
385. #2283	C₂×C₆₇	semidirect
386. C₆₇	#35143	direct (N × H)
396. C₂×C₄×Q₈	C₂²×C₆₇	semidirect
397. C₂×C₄×Q₈	C₂²×C₆₇	semidirect
400. C₂×C₄×D₄	C₂²×C₆₇	semidirect
401. C₂×C₄×D₄	C₂²×C₆₇	semidirect
403. C₂×#117	C₂²×C₆₇	semidirect
411. C₂²×C₄²	C₂²×C₆₇	semidirect
412. #400	C₂²×C₆₇	semidirect
414. #398	C₂²×C₆₇	semidirect
415. #398	C₂²×C₆₇	semidirect
418. #396	C₂²×C₆₇	semidirect
419. #395	C₂²×C₆₇	semidirect
421. #394	C₂²×C₆₇	semidirect
425. #389	C₂²×C₆₇	semidirect
430. #388	C₂²×C₆₇	semidirect
431. #387	C₂²×C₆₇	semidirect
432. #387	C₂²×C₆₇	semidirect
433. #387	C₂²×C₆₇	semidirect
441. #385	C₂²×C₆₇	semidirect
442. #385	C₂²×C₆₇	semidirect
443. #385	C₂²×C₆₇	semidirect
444. #383	C₂²×C₆₇	semidirect
445. #382	C₂²×C₆₇	semidirect
451. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
453. #376	C₂²×C₆₇	semidirect
522. C₂×C₄²	D₄×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#126×C₆₇	2
C₂×C₄×#41×C₆₇	2
C₆₇×#2852	2
C₆₇×#2637	2
C₆₇×#2636	2
C₆₇×#2604	2
C₆₇×#2603	2
C₆₇×#2601	2
C₆₇×#2579	2
C₆₇×#2534	2
C₆₇×#2484	2
C₆₇×#2482	2
C₆₇×#2406	2
C₆₇×#2404	2
C₆₇×#2322	2
C₆₇×#2321	2
C₆₇×#2283	2
#35143	67

Subgroups — C67×#35143 #30714394

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#35143 #30714394