Subgroups — C₆₇×#34237 #30713488

Order 17152.

2186 conjugacy classes of subgroups.

The subgroup lattice has 666 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×#2370	C₂	1	2	yes	maximal, complemented
3	C₆₇×#2367	C₂	1	2	yes	maximal, complemented
4	C₆₇×#2363	C₂	1	2	yes	maximal
5	C₆₇×#2362	C₂	1	2	yes	maximal, complemented
6	C₆₇×#2357	C₂	1	2	yes	maximal, complemented
7	C₆₇×#2353	C₂	1	2	yes	maximal, complemented
8	C₆₇×#2346	C₂	1	2	yes	maximal, complemented
9	C₆₇×#2343	C₂	1	2	yes	maximal, complemented
10	C₆₇×#2335	C₂	1	4	yes	maximal, complemented
11	C₆₇×#2320	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#2319	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄×#126×C₆₇	C₂	1	4	yes	maximal, complemented
14	C₆₇×#2283	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#2276	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#2275	C₂	1	1	yes	maximal, characteristic, 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	2	yes	—
28	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
29	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
30	C₂×#117×C₆₇	C₂²	1	2	yes	—
31	C₂×#117×C₆₇	C₂²	1	2	yes	—
32	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
33	#391×C₆₇	C₂²	1	2	yes	—
34	#390×C₆₇	C₂²	1	2	yes	—
35	#390×C₆₇	C₂²	1	4	yes	—
36	#389×C₆₇	C₂²	1	2	yes	—
37	#389×C₆₇	C₂²	1	2	yes	—
38	#389×C₆₇	C₂²	1	4	yes	—
39	#388×C₆₇	C₂²	1	4	yes	—
40	#388×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	#383×C₆₇	C₂²	1	2	yes	—
52	#383×C₆₇	C₂²	1	2	yes	—
53	#382×C₆₇	C₂²	1	1	yes	characteristic
54	#382×C₆₇	C₂²	1	1	yes	characteristic
55	#382×C₆₇	C₂²	1	2	yes	—
56	#381×C₆₇	C₂²	1	1	yes	characteristic
57	#381×C₆₇	C₂²	1	1	yes	characteristic
58	#381×C₆₇	C₂²	1	2	yes	—
59	#380×C₆₇	C₂²	1	2	yes	—
60	#380×C₆₇	C₂²	1	2	yes	—
61	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
62	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
63	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
64	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
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	2	yes	—
68	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
69	C₄×C₄⋊C₄×C₆₇	C₂²	1	4	yes	—
70	C₄×C₄⋊C₄×C₆₇	C₂²	1	4	yes	—
71	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
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	2	yes	—
76	C₄×C₂²⋊C₄×C₆₇	C₂²	1	4	yes	—
77	C₄×C₂²⋊C₄×C₆₇	C₂²	1	4	yes	—
78	#376×C₆₇	C₂²	1	2	yes	—
79	#376×C₆₇	C₂²	1	1	yes	characteristic
80	#376×C₆₇	C₂²	1	1	yes	characteristic
81	#376×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	1	yes	characteristic
86	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
87	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
89	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
91	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
92	#126×C₆₇	C₂×C₄	1	16	yes	complemented
93	#125×C₆₇	C₂×C₄	1	8	yes	complemented
94	#124×C₆₇	C₂×C₄	1	8	yes	—
95	#123×C₆₇	C₂×C₄	1	16	yes	complemented
96	C₂²⋊Q₈×C₆₇	C₂×C₄	1	8	yes	complemented
97	#121×C₆₇	C₂×C₄	1	8	yes	—
98	C₄×Q₈×C₆₇	—	2	8	no	—
99	C₄×Q₈×C₆₇	C₂×C₄	1	8	yes	complemented
100	C₄×D₄×C₆₇	—	2	8	no	—
101	C₄×D₄×C₆₇	C₂×C₄	1	8	yes	—
102	C₄×D₄×C₆₇	C₂×C₄	1	16	yes	complemented
103	#117×C₆₇	—	2	8	no	—
104	#117×C₆₇	C₂×C₄	1	16	yes	complemented
105	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
106	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
107	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
108	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
109	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
110	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
111	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
112	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
113	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
114	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
115	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
116	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
117	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
118	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
119	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
120	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
121	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
122	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
123	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
124	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
125	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	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×C₄²×C₆₇	C₂×C₄	1	8	yes	complemented
130	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
131	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
132	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
133	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
134	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
135	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
136	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
137	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
138	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
139	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
140	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
141	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
142	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
143	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
144	#95×C₆₇	C₂³	1	1	yes	characteristic
145	#95×C₆₇	C₂³	1	2	yes	—
146	#95×C₆₇	C₂³	1	4	yes	—
147	#95×C₆₇	C₂³	1	1	yes	characteristic
148	#95×C₆₇	C₂³	1	2	yes	—
149	#95×C₆₇	C₂³	1	1	yes	characteristic
150	#95×C₆₇	C₂³	1	2	yes	—
151	#95×C₆₇	C₂³	1	4	yes	—
152	#95×C₆₇	C₂³	1	2	yes	—
153	#95×C₆₇	C₂³	1	1	yes	characteristic
154	#95×C₆₇	C₂³	1	4	yes	—
155	#95×C₆₇	C₂³	1	2	yes	—
156	#95×C₆₇	C₂³	1	2	yes	—
157	#95×C₆₇	C₂³	1	2	yes	—
158	#95×C₆₇	C₂³	1	4	yes	—
159	#95×C₆₇	C₂³	1	4	yes	—
160	#95×C₆₇	C₂³	1	2	yes	—
161	#95×C₆₇	C₂³	1	4	yes	—
162	#95×C₆₇	C₂³	1	4	yes	—
163	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
164	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
165	C₂×Q₈×C₆₇	—	2	4	no	—
166	C₂×Q₈×C₆₇	C₂²×C₄	1	4	yes	—
167	C₂×D₄×C₆₇	—	2	4	no	—
168	C₂×D₄×C₆₇	—	4	2	no	—
169	C₂×D₄×C₆₇	—	4	2	no	—
170	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
171	C₂×D₄×C₆₇	C₂²×C₄	1	8	yes	—
172	C₂²×C₄×C₆₇	—	2	4	no	—
173	C₂²×C₄×C₆₇	—	2	8	no	—
174	C₂²×C₄×C₆₇	—	4	1	no	—
175	C₂²×C₄×C₆₇	—	4	1	no	—
176	C₂²×C₄×C₆₇	—	4	2	no	—
177	C₂²×C₄×C₆₇	—	4	4	no	—
178	C₂²×C₄×C₆₇	—	4	4	no	—
179	C₂²×C₄×C₆₇	—	4	4	no	—
180	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
181	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
182	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
183	C₂²×C₄×C₆₇	C₂²×C₄	1	8	yes	—
184	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
185	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
186	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
187	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
188	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
189	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
190	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
191	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
192	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
193	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
194	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
195	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
196	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
197	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
198	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
199	C₄⋊C₄×C₆₇	—	2	4	no	—
200	C₄⋊C₄×C₆₇	—	2	8	no	—
201	C₄⋊C₄×C₆₇	—	4	4	no	—
202	C₄⋊C₄×C₆₇	—	4	2	no	—
203	C₄⋊C₄×C₆₇	—	4	2	no	—
204	C₄⋊C₄×C₆₇	—	4	4	no	—
205	C₄⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
206	C₄⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
207	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
208	C₄⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
209	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
210	C₄⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
211	C₄⋊C₄×C₆₇	#41	1	8	yes	—
212	C₂²⋊C₄×C₆₇	—	2	8	no	—
213	C₂²⋊C₄×C₆₇	—	2	8	no	—
214	C₂²⋊C₄×C₆₇	—	4	2	no	—
215	C₂²⋊C₄×C₆₇	—	4	4	no	—
216	C₂²⋊C₄×C₆₇	—	4	4	no	—
217	C₂²⋊C₄×C₆₇	—	4	2	no	—
218	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
219	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
220	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
221	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
222	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
223	C₄²×C₆₇	—	2	8	no	—
224	C₄²×C₆₇	—	2	4	no	—
225	C₄²×C₆₇	—	2	8	no	—
226	C₄²×C₆₇	—	2	4	no	—
227	C₄²×C₆₇	—	4	2	no	—
228	C₄²×C₆₇	—	4	4	no	—
229	C₄²×C₆₇	—	4	4	no	—
230	C₄²×C₆₇	—	4	4	no	—
231	C₄²×C₆₇	—	4	2	no	—
232	C₄²×C₆₇	C₂²×C₄	1	4	yes	—
233	C₄²×C₆₇	C₂²×C₄	1	4	yes	—
234	C₄²×C₆₇	C₂²×C₄	1	4	yes	—
235	C₄²×C₆₇	C₂²×C₄	1	4	yes	—
236	C₄²×C₆₇	C₂²×C₄	1	8	yes	—
237	C₂³×C₆₇	—	2	2	no	—
238	C₂³×C₆₇	—	2	4	no	—
239	C₂³×C₆₇	—	2	2	no	—
240	C₂³×C₆₇	—	2	2	no	—
241	C₂³×C₆₇	—	2	4	no	—
242	C₂³×C₆₇	—	2	2	no	—
243	C₂³×C₆₇	—	2	1	no	—
244	C₂³×C₆₇	—	2	1	no	—
245	C₂³×C₆₇	C₂³×C₄	1	4	yes	—
246	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
247	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
248	Q₈×C₆₇	—	2	8	no	—
249	D₄×C₆₇	—	2	8	no	—
250	D₄×C₆₇	—	4	8	no	—
251	C₂×C₄×C₆₇	—	2	2	no	—
252	C₂×C₄×C₆₇	—	2	4	no	—
253	C₂×C₄×C₆₇	—	2	1	no	—
254	C₂×C₄×C₆₇	—	2	2	no	—
255	C₂×C₄×C₆₇	—	2	1	no	—
256	C₂×C₄×C₆₇	—	2	4	no	—
257	C₂×C₄×C₆₇	—	2	4	no	—
258	C₂×C₄×C₆₇	—	2	2	no	—
259	C₂×C₄×C₆₇	—	2	4	no	—
260	C₂×C₄×C₆₇	—	2	1	no	—
261	C₂×C₄×C₆₇	—	2	1	no	—
262	C₂×C₄×C₆₇	—	2	2	no	—
263	C₂×C₄×C₆₇	—	2	2	no	—
264	C₂×C₄×C₆₇	—	2	8	no	—
265	C₂×C₄×C₆₇	—	2	2	no	—
266	C₂×C₄×C₆₇	—	2	2	no	—
267	C₂×C₄×C₆₇	—	2	4	no	—
268	C₂×C₄×C₆₇	—	2	2	no	—
269	C₂×C₄×C₆₇	—	2	2	no	—
270	C₂×C₄×C₆₇	—	2	2	no	—
271	C₂×C₄×C₆₇	—	2	2	no	—
272	C₂×C₄×C₆₇	—	2	4	no	—
273	C₂×C₄×C₆₇	—	2	4	no	—
274	C₂×C₄×C₆₇	—	2	2	no	—
275	C₂×C₄×C₆₇	—	2	2	no	—
276	C₂×C₄×C₆₇	—	2	2	no	—
277	C₂×C₄×C₆₇	—	2	2	no	—
278	C₂×C₄×C₆₇	—	2	2	no	—
279	C₂×C₄×C₆₇	—	2	2	no	—
280	C₂×C₄×C₆₇	—	4	4	no	—
281	C₂×C₄×C₆₇	—	4	8	no	—
282	C₂×C₄×C₆₇	—	4	4	no	—
283	C₂×C₄×C₆₇	—	8	8	no	—
284	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
285	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
286	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
287	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
288	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
289	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
290	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
291	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
292	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
293	C₂×C₄×C₆₇	C₂×#41	1	8	yes	—
294	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
295	C₂²×C₆₇	—	2	2	no	—
296	C₂²×C₆₇	—	2	4	no	—
297	C₂²×C₆₇	—	2	2	no	—
298	C₂²×C₆₇	—	2	2	no	—
299	C₂²×C₆₇	—	2	4	no	—
300	C₂²×C₆₇	—	2	4	no	—
301	C₂²×C₆₇	—	4	4	no	—
302	C₂²×C₆₇	—	4	2	no	—
303	C₂²×C₆₇	—	4	2	no	—
304	C₂²×C₆₇	—	4	4	no	—
305	C₂²×C₆₇	C₂⁴×C₄	1	1	yes	characteristic
306	C₂²×C₆₇	C₂²×#41	1	2	yes	—
307	C₂²×C₆₇	#585	1	1	yes	characteristic
308	C₂²×C₆₇	#585	1	2	yes	—
309	C₂²×C₆₇	#585	1	1	yes	characteristic
310	C₄×C₆₇	—	2	2	no	—
311	C₄×C₆₇	—	2	4	no	—
312	C₄×C₆₇	—	2	2	no	—
313	C₄×C₆₇	—	2	2	no	—
314	C₄×C₆₇	—	2	2	no	—
315	C₄×C₆₇	—	2	4	no	—
316	C₄×C₆₇	—	2	2	no	—
317	C₄×C₆₇	—	2	4	no	—
318	C₄×C₆₇	—	2	8	no	—
319	C₄×C₆₇	—	4	2	no	—
320	C₄×C₆₇	—	4	2	no	—
321	C₄×C₆₇	—	4	2	no	—
322	C₄×C₆₇	—	4	2	no	—
323	C₄×C₆₇	—	4	4	no	—
324	C₄×C₆₇	C₄×#41	1	4	yes	—
325	#34237	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
326	C₂×C₆₇	—	4	2	no	—
327	C₂×C₆₇	—	4	4	no	—
328	C₂×C₆₇	C₂×C₄×#41	1	1	yes	characteristic
329	C₂×C₆₇	#3428	1	1	yes	characteristic
330	C₂×C₆₇	#3428	1	1	yes	characteristic
331	C₂×C₆₇	#3521	1	2	yes	—
332	C₂×C₆₇	#3524	1	2	yes	—
333	C₂×#529	C₂×C₆₇	1	1	yes	characteristic
334	#2370	C₂×C₆₇	1	2	yes	complemented
335	#2367	C₂×C₆₇	1	2	yes	complemented
336	#2363	C₂×C₆₇	1	2	yes	—
337	#2362	C₂×C₆₇	1	2	yes	complemented
338	#2357	C₂×C₆₇	1	2	yes	complemented
339	#2353	C₂×C₆₇	1	2	yes	complemented
340	#2346	C₂×C₆₇	1	2	yes	complemented
341	#2343	C₂×C₆₇	1	2	yes	complemented
342	#2335	C₂×C₆₇	1	4	yes	complemented
343	#2320	C₂×C₆₇	1	1	yes	characteristic, complemented
344	#2319	C₂×C₆₇	1	1	yes	characteristic, complemented
345	C₄×#126	C₂×C₆₇	1	4	yes	complemented
346	#2283	C₂×C₆₇	1	1	yes	characteristic, complemented
347	#2276	C₂×C₆₇	1	1	yes	characteristic, complemented
348	#2275	C₂×C₆₇	1	1	yes	characteristic, complemented
349	C₄×#117	C₂×C₆₇	1	1	yes	characteristic, complemented
350	C₆₇	#34237	1	1	yes	characteristic, direct product factor, Sylow
351	#529	C₄×C₆₇	1	16	yes	complemented
352	C₂×#126	C₂²×C₆₇	1	2	yes	—
353	C₂×#125	C₂²×C₆₇	1	1	yes	characteristic
354	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic
355	C₂×#123	C₂²×C₆₇	1	2	yes	—
356	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
357	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
358	C₂×C₄×Q₈	C₂²×C₆₇	1	2	yes	—
359	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
360	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
361	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
362	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
363	C₂×#117	C₂²×C₆₇	1	2	yes	—
364	C₂×#117	C₂²×C₆₇	1	2	yes	—
365	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
366	#391	C₂²×C₆₇	1	2	yes	—
367	#390	C₂²×C₆₇	1	2	yes	—
368	#390	C₂²×C₆₇	1	4	yes	—
369	#389	C₂²×C₆₇	1	2	yes	—
370	#389	C₂²×C₆₇	1	2	yes	—
371	#389	C₂²×C₆₇	1	4	yes	—
372	#388	C₂²×C₆₇	1	4	yes	—
373	#388	C₂²×C₆₇	1	4	yes	—
374	#388	C₂²×C₆₇	1	4	yes	—
375	#388	C₂²×C₆₇	1	4	yes	—
376	#388	C₂²×C₆₇	1	4	yes	—
377	#388	C₂²×C₆₇	1	4	yes	—
378	#387	C₂²×C₆₇	1	4	yes	—
379	#387	C₂²×C₆₇	1	4	yes	—
380	#387	C₂²×C₆₇	1	4	yes	—
381	#387	C₂²×C₆₇	1	4	yes	—
382	#386	C₂²×C₆₇	1	4	yes	—
383	#385	C₂²×C₆₇	1	4	yes	—
384	#383	C₂²×C₆₇	1	2	yes	—
385	#383	C₂²×C₆₇	1	2	yes	—
386	#382	C₂²×C₆₇	1	2	yes	—
387	#382	C₂²×C₆₇	1	1	yes	characteristic
388	#382	C₂²×C₆₇	1	1	yes	characteristic
389	#381	C₂²×C₆₇	1	2	yes	—
390	#381	C₂²×C₆₇	1	1	yes	characteristic
391	#381	C₂²×C₆₇	1	1	yes	characteristic
392	#380	C₂²×C₆₇	1	2	yes	—
393	#380	C₂²×C₆₇	1	2	yes	—
394	C₄×C₄⋊C₄	C₂²×C₆₇	1	4	yes	—
395	C₄×C₄⋊C₄	C₂²×C₆₇	1	4	yes	—
396	C₄×C₄⋊C₄	C₂²×C₆₇	1	4	yes	—
397	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
398	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
399	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
400	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
401	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
402	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
403	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
404	C₄×C₂²⋊C₄	C₂²×C₆₇	1	4	yes	—
405	C₄×C₂²⋊C₄	C₂²×C₆₇	1	4	yes	—
406	C₄×C₂²⋊C₄	C₂²×C₆₇	1	4	yes	—
407	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
408	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
409	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
410	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
411	#376	C₂²×C₆₇	1	1	yes	characteristic
412	#376	C₂²×C₆₇	1	1	yes	characteristic
413	#376	C₂²×C₆₇	1	2	yes	—
414	#376	C₂²×C₆₇	1	2	yes	—
415	C₂×#95	C₂²×C₆₇	1	2	yes	—
416	C₄³	C₂²×C₆₇	1	2	yes	—
417	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
418	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
419	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
420	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
421	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
422	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
423	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
424	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
425	#126	C₂×C₄×C₆₇	1	16	yes	complemented
426	#125	C₂×C₄×C₆₇	1	8	yes	complemented
427	#124	C₂×C₄×C₆₇	1	8	yes	—
428	#123	C₂×C₄×C₆₇	1	16	yes	complemented
429	C₂²⋊Q₈	C₂×C₄×C₆₇	1	8	yes	complemented
430	#121	C₂×C₄×C₆₇	1	8	yes	—
431	C₄×Q₈	—	2	8	no	—
432	C₄×Q₈	C₂×C₄×C₆₇	1	8	yes	complemented
433	C₄×D₄	—	2	8	no	—
434	C₄×D₄	C₂×C₄×C₆₇	1	8	yes	—
435	C₄×D₄	C₂×C₄×C₆₇	1	16	yes	complemented
436	#117	—	2	8	no	—
437	#117	C₂×C₄×C₆₇	1	16	yes	complemented
438	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
439	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
440	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
441	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
442	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
443	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
444	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
445	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
446	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
447	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
448	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
449	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
450	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
451	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
452	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
453	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
454	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
455	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
456	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
457	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
458	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
459	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
460	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
461	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
462	C₂×C₄²	C₂×C₄×C₆₇	1	8	yes	complemented
463	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
464	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
465	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
466	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
467	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
468	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
469	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
470	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
471	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
472	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
473	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
474	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
475	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
476	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
477	#95	C₂³×C₆₇	1	1	yes	characteristic
478	#95	C₂³×C₆₇	1	2	yes	—
479	#95	C₂³×C₆₇	1	4	yes	—
480	#95	C₂³×C₆₇	1	1	yes	characteristic
481	#95	C₂³×C₆₇	1	2	yes	—
482	#95	C₂³×C₆₇	1	1	yes	characteristic
483	#95	C₂³×C₆₇	1	2	yes	—
484	#95	C₂³×C₆₇	1	4	yes	—
485	#95	C₂³×C₆₇	1	2	yes	—
486	#95	C₂³×C₆₇	1	1	yes	characteristic
487	#95	C₂³×C₆₇	1	4	yes	—
488	#95	C₂³×C₆₇	1	2	yes	—
489	#95	C₂³×C₆₇	1	2	yes	—
490	#95	C₂³×C₆₇	1	2	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	4	yes	—
495	#95	C₂³×C₆₇	1	4	yes	—
496	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
497	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
498	C₂×Q₈	—	2	4	no	—
499	C₂×Q₈	C₂²×C₄×C₆₇	1	4	yes	—
500	C₂×D₄	—	2	4	no	—
501	C₂×D₄	—	4	2	no	—
502	C₂×D₄	—	4	2	no	—
503	C₂×D₄	C₂²×C₄×C₆₇	1	4	yes	—
504	C₂×D₄	C₂²×C₄×C₆₇	1	8	yes	—
505	C₂²×C₄	—	2	4	no	—
506	C₂²×C₄	—	2	8	no	—
507	C₂²×C₄	—	4	1	no	—
508	C₂²×C₄	—	4	1	no	—
509	C₂²×C₄	—	4	2	no	—
510	C₂²×C₄	—	4	4	no	—
511	C₂²×C₄	—	4	4	no	—
512	C₂²×C₄	—	4	4	no	—
513	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
514	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
515	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
516	C₂²×C₄	C₂²×C₄×C₆₇	1	8	yes	—
517	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
518	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
519	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
520	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
521	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
522	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
523	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
524	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
525	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
526	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
527	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
528	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
529	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
530	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
531	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
532	C₄⋊C₄	—	2	4	no	—
533	C₄⋊C₄	—	2	8	no	—
534	C₄⋊C₄	—	4	4	no	—
535	C₄⋊C₄	—	4	2	no	—
536	C₄⋊C₄	—	4	2	no	—
537	C₄⋊C₄	—	4	4	no	—
538	C₄⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
539	C₄⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
540	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
541	C₄⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
542	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
543	C₄⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
544	C₄⋊C₄	#41×C₆₇	1	8	yes	—
545	C₂²⋊C₄	—	2	8	no	—
546	C₂²⋊C₄	—	2	8	no	—
547	C₂²⋊C₄	—	4	2	no	—
548	C₂²⋊C₄	—	4	4	no	—
549	C₂²⋊C₄	—	4	4	no	—
550	C₂²⋊C₄	—	4	2	no	—
551	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
552	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
553	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
554	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
555	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
556	C₄²	—	2	8	no	—
557	C₄²	—	2	4	no	—
558	C₄²	—	2	8	no	—
559	C₄²	—	2	4	no	—
560	C₄²	—	4	2	no	—
561	C₄²	—	4	4	no	—
562	C₄²	—	4	4	no	—
563	C₄²	—	4	4	no	—
564	C₄²	—	4	2	no	—
565	C₄²	C₂²×C₄×C₆₇	1	4	yes	—
566	C₄²	C₂²×C₄×C₆₇	1	4	yes	—
567	C₄²	C₂²×C₄×C₆₇	1	4	yes	—
568	C₄²	C₂²×C₄×C₆₇	1	4	yes	—
569	C₄²	C₂²×C₄×C₆₇	1	8	yes	—
570	C₂³	—	2	2	no	—
571	C₂³	—	2	4	no	—
572	C₂³	—	2	2	no	—
573	C₂³	—	2	2	no	—
574	C₂³	—	2	4	no	—
575	C₂³	—	2	2	no	—
576	C₂³	—	2	1	no	—
577	C₂³	—	2	1	no	—
578	C₂³	C₂³×C₄×C₆₇	1	4	yes	—
579	C₂³	C₂³×C₄×C₆₇	1	2	yes	—
580	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
581	Q₈	—	2	8	no	—
582	D₄	—	2	8	no	—
583	D₄	—	4	8	no	—
584	C₂×C₄	—	2	2	no	—
585	C₂×C₄	—	2	4	no	—
586	C₂×C₄	—	2	4	no	—
587	C₂×C₄	—	2	4	no	—
588	C₂×C₄	—	2	1	no	—
589	C₂×C₄	—	2	2	no	—
590	C₂×C₄	—	2	1	no	—
591	C₂×C₄	—	2	2	no	—
592	C₂×C₄	—	2	4	no	—
593	C₂×C₄	—	2	1	no	—
594	C₂×C₄	—	2	1	no	—
595	C₂×C₄	—	2	2	no	—
596	C₂×C₄	—	2	2	no	—
597	C₂×C₄	—	2	8	no	—
598	C₂×C₄	—	2	2	no	—
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	2	4	no	—
601	C₂×C₄	—	2	2	no	—
602	C₂×C₄	—	2	2	no	—
603	C₂×C₄	—	2	2	no	—
604	C₂×C₄	—	2	2	no	—
605	C₂×C₄	—	2	4	no	—
606	C₂×C₄	—	2	4	no	—
607	C₂×C₄	—	2	2	no	—
608	C₂×C₄	—	2	2	no	—
609	C₂×C₄	—	2	2	no	—
610	C₂×C₄	—	2	2	no	—
611	C₂×C₄	—	2	2	no	—
612	C₂×C₄	—	2	2	no	—
613	C₂×C₄	—	4	4	no	—
614	C₂×C₄	—	4	8	no	—
615	C₂×C₄	—	4	4	no	—
616	C₂×C₄	—	8	8	no	—
617	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
618	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
619	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
620	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
621	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
622	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
623	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
624	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
625	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
626	C₂×C₄	C₂×#41×C₆₇	1	8	yes	—
627	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
628	C₂²	—	2	2	no	—
629	C₂²	—	2	4	no	—
630	C₂²	—	2	2	no	—
631	C₂²	—	2	2	no	—
632	C₂²	—	2	4	no	—
633	C₂²	—	2	4	no	—
634	C₂²	—	4	4	no	—
635	C₂²	—	4	2	no	—
636	C₂²	—	4	2	no	—
637	C₂²	—	4	4	no	—
638	C₂²	C₂⁴×C₄×C₆₇	1	1	yes	characteristic
639	C₂²	C₂²×#41×C₆₇	1	2	yes	—
640	C₂²	#585×C₆₇	1	1	yes	characteristic
641	C₂²	#585×C₆₇	1	2	yes	—
642	C₂²	#585×C₆₇	1	1	yes	characteristic
643	C₄	—	2	8	no	—
644	C₄	—	2	2	no	—
645	C₄	—	2	4	no	—
646	C₄	—	2	2	no	—
647	C₄	—	2	2	no	—
648	C₄	—	2	2	no	—
649	C₄	—	2	4	no	—
650	C₄	—	2	2	no	—
651	C₄	—	2	4	no	—
652	C₄	—	4	2	no	—
653	C₄	—	4	2	no	—
654	C₄	—	4	2	no	—
655	C₄	—	4	2	no	—
656	C₄	—	4	4	no	—
657	C₄	C₄×#41×C₆₇	1	4	yes	—
658	C₂	—	4	2	no	—
659	C₂	—	4	4	no	—
660	C₂	C₂×C₄×#41×C₆₇	1	1	yes	characteristic
661	C₂	C₆₇×#3428	1	1	yes	characteristic
662	C₂	C₆₇×#3428	1	1	yes	characteristic
663	C₂	C₆₇×#3521	1	2	yes	—
664	C₂	C₆₇×#3524	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
2. C₆₇×#2370	C₂	semidirect
3. C₆₇×#2367	C₂	semidirect
5. C₆₇×#2362	C₂	semidirect
6. C₆₇×#2357	C₂	semidirect
7. C₆₇×#2353	C₂	semidirect
8. C₆₇×#2346	C₂	semidirect
9. C₆₇×#2343	C₂	semidirect
10. C₆₇×#2335	C₂	semidirect
11. C₆₇×#2320	C₂	semidirect
12. C₆₇×#2319	C₂	semidirect
13. C₄×#126×C₆₇	C₂	semidirect
14. C₆₇×#2283	C₂	semidirect
15. C₆₇×#2276	C₂	semidirect
16. C₆₇×#2275	C₂	semidirect
17. C₄×#117×C₆₇	C₂	semidirect
18. #529×C₆₇	C₄	semidirect
92. #126×C₆₇	C₂×C₄	semidirect
93. #125×C₆₇	C₂×C₄	semidirect
95. #123×C₆₇	C₂×C₄	semidirect
96. C₂²⋊Q₈×C₆₇	C₂×C₄	semidirect
99. C₄×Q₈×C₆₇	C₂×C₄	semidirect
102. C₄×D₄×C₆₇	C₂×C₄	semidirect
104. #117×C₆₇	C₂×C₄	semidirect
129. C₂×C₄²×C₆₇	C₂×C₄	semidirect
325. #34237	C₆₇	direct (N × H)
334. #2370	C₂×C₆₇	semidirect
335. #2367	C₂×C₆₇	semidirect
337. #2362	C₂×C₆₇	semidirect
338. #2357	C₂×C₆₇	semidirect
339. #2353	C₂×C₆₇	semidirect
340. #2346	C₂×C₆₇	semidirect
341. #2343	C₂×C₆₇	semidirect
342. #2335	C₂×C₆₇	semidirect
343. #2320	C₂×C₆₇	semidirect
344. #2319	C₂×C₆₇	semidirect
345. C₄×#126	C₂×C₆₇	semidirect
346. #2283	C₂×C₆₇	semidirect
347. #2276	C₂×C₆₇	semidirect
348. #2275	C₂×C₆₇	semidirect
349. C₄×#117	C₂×C₆₇	semidirect
350. C₆₇	#34237	direct (N × H)
351. #529	C₄×C₆₇	semidirect
425. #126	C₂×C₄×C₆₇	semidirect
426. #125	C₂×C₄×C₆₇	semidirect
428. #123	C₂×C₄×C₆₇	semidirect
429. C₂²⋊Q₈	C₂×C₄×C₆₇	semidirect
432. C₄×Q₈	C₂×C₄×C₆₇	semidirect
435. C₄×D₄	C₂×C₄×C₆₇	semidirect
437. #117	C₂×C₄×C₆₇	semidirect
462. 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×#2370	2
C₆₇×#2367	2
C₆₇×#2363	2
C₆₇×#2362	2
C₆₇×#2357	2
C₆₇×#2353	2
C₆₇×#2346	2
C₆₇×#2343	2
C₆₇×#2335	2
C₆₇×#2320	2
C₆₇×#2319	2
C₄×#126×C₆₇	2
C₆₇×#2283	2
C₆₇×#2276	2
C₆₇×#2275	2
C₄×#117×C₆₇	2
#34237	67

Subgroups — C67×#34237 #30713488

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#34237 #30713488