Subgroups — C₆₇×#34376 #30713627

Order 17152.

2630 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#123×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₆₇×#2376	C₂	1	4	yes	maximal, complemented
3	C₆₇×#2359	C₂	1	4	yes	maximal, complemented
4	C₆₇×#2345	C₂	1	2	yes	maximal, complemented
5	C₆₇×#2342	C₂	1	2	yes	maximal, complemented
6	C₆₇×#2342	C₂	1	2	yes	maximal, complemented
7	D₄×C₂²⋊C₄×C₆₇	C₂	1	2	yes	maximal
8	C₆₇×#2335	C₂	1	4	yes	maximal, complemented
9	C₆₇×#2322	C₂	1	4	yes	maximal, complemented
10	C₆₇×#2316	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#2315	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#2313	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#2312	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#2280	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#380×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×D₄×C₆₇	C₂²	1	1	yes	characteristic
17	C₂⁴×C₄×C₆₇	C₂²	1	1	yes	characteristic
18	C₂×#123×C₆₇	C₄	1	16	yes	complemented
19	C₂×#123×C₆₇	C₂²	1	2	yes	—
20	C₂×#123×C₆₇	C₂²	1	2	yes	—
21	C₂×#123×C₆₇	C₂²	1	2	yes	—
22	C₂×#123×C₆₇	C₂²	1	2	yes	—
23	C₂×C₄×D₄×C₆₇	C₂²	1	4	yes	—
24	C₂×#117×C₆₇	C₂²	1	2	yes	—
25	C₂×#117×C₆₇	C₂²	1	2	yes	complemented
26	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
27	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
28	C₂²×C₄⋊C₄×C₆₇	C₂²	1	2	yes	complemented
29	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
30	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
31	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
32	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
33	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
34	#390×C₆₇	C₂²	1	4	yes	—
35	#389×C₆₇	C₂²	1	4	yes	complemented
36	#389×C₆₇	C₂²	1	4	yes	complemented
37	#389×C₆₇	C₂²	1	4	yes	complemented
38	#388×C₆₇	C₂²	1	4	yes	complemented
39	#388×C₆₇	C₂²	1	4	yes	complemented
40	#388×C₆₇	C₂²	1	4	yes	complemented
41	#388×C₆₇	C₂²	1	4	yes	complemented
42	#388×C₆₇	C₂²	1	4	yes	complemented
43	#388×C₆₇	C₂²	1	4	yes	complemented
44	#387×C₆₇	C₂²	1	4	yes	complemented
45	#387×C₆₇	C₂²	1	4	yes	complemented
46	#387×C₆₇	C₂²	1	4	yes	complemented
47	#387×C₆₇	C₂²	1	4	yes	complemented
48	#386×C₆₇	C₂²	1	4	yes	—
49	#386×C₆₇	C₂²	1	4	yes	—
50	#385×C₆₇	C₂²	1	4	yes	complemented
51	#385×C₆₇	C₂²	1	4	yes	complemented
52	#385×C₆₇	C₂²	1	4	yes	complemented
53	#385×C₆₇	C₂²	1	4	yes	complemented
54	#381×C₆₇	C₂²	1	2	yes	—
55	#381×C₆₇	C₂²	1	2	yes	complemented
56	#380×C₆₇	C₂²	1	1	yes	characteristic
57	#380×C₆₇	C₂²	1	1	yes	characteristic
58	#380×C₆₇	C₂²	1	2	yes	—
59	#380×C₆₇	C₂²	1	1	yes	characteristic
60	#380×C₆₇	C₂²	1	1	yes	characteristic
61	#380×C₆₇	C₂²	1	2	yes	—
62	#380×C₆₇	C₂²	1	2	yes	—
63	#380×C₆₇	C₂²	1	2	yes	complemented
64	#380×C₆₇	C₂²	1	2	yes	complemented
65	#380×C₆₇	C₂²	1	2	yes	complemented
66	#379×C₆₇	C₂²	1	2	yes	—
67	#379×C₆₇	C₂²	1	2	yes	—
68	C₄×C₄⋊C₄×C₆₇	C₂²	1	4	yes	complemented
69	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
70	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
71	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
72	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
73	C₄×C₂²⋊C₄×C₆₇	C₂²	1	4	yes	complemented
74	C₄×C₂²⋊C₄×C₆₇	C₂²	1	4	yes	complemented
75	C₂×#95×C₆₇	C₂²	1	2	yes	complemented
76	C₂⁵×C₆₇	C₂³	1	1	yes	characteristic
77	C₂⁵×C₆₇	C₂³	1	1	yes	characteristic
78	C₂²×D₄×C₆₇	—	4	4	no	—
79	C₂²×D₄×C₆₇	C₂×C₄	1	8	yes	—
80	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
81	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
82	C₂³×C₄×C₆₇	—	4	4	no	—
83	C₂³×C₄×C₆₇	C₂×C₄	1	8	yes	complemented
84	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
85	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
86	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
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	1	yes	characteristic
92	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
93	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
94	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
95	#123×C₆₇	C₂×C₄	1	16	yes	complemented
96	#123×C₆₇	C₂×C₄	1	16	yes	complemented
97	#123×C₆₇	C₂×C₄	1	16	yes	complemented
98	#123×C₆₇	C₂×C₄	1	16	yes	complemented
99	C₄×D₄×C₆₇	—	4	8	no	—
100	#117×C₆₇	—	4	4	no	—
101	#117×C₆₇	—	4	4	no	—
102	C₂×C₄⋊C₄×C₆₇	—	4	4	no	—
103	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	8	yes	complemented
104	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	8	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	4	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	4	yes	—
112	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
113	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
114	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
115	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
116	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
117	C₂×C₂²⋊C₄×C₆₇	—	4	4	no	—
118	C₂×C₂²⋊C₄×C₆₇	—	4	4	no	—
119	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	8	yes	complemented
120	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	8	yes	complemented
121	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	8	yes	complemented
122	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
123	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
124	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	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	4	yes	—
128	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
129	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
130	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
131	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
132	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
133	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
134	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
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×C₄²×C₆₇	C₂³	1	4	yes	—
139	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
140	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
141	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
142	#95×C₆₇	C₂³	1	4	yes	—
143	#95×C₆₇	C₂³	1	2	yes	—
144	#95×C₆₇	C₂³	1	2	yes	—
145	#95×C₆₇	C₂³	1	4	yes	—
146	#95×C₆₇	C₂³	1	4	yes	—
147	#95×C₆₇	C₂³	1	4	yes	—
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	4	yes	—
154	C₂⁴×C₆₇	—	2	2	no	—
155	C₂⁴×C₆₇	—	2	4	no	—
156	C₂⁴×C₆₇	—	2	2	no	—
157	C₂⁴×C₆₇	—	2	2	no	—
158	C₂⁴×C₆₇	—	2	2	no	—
159	C₂⁴×C₆₇	—	4	2	no	—
160	C₂⁴×C₆₇	—	4	2	no	—
161	C₂⁴×C₆₇	—	4	2	no	—
162	C₂⁴×C₆₇	C₂²×C₄	1	4	yes	—
163	C₂⁴×C₆₇	C₂²×C₄	1	4	yes	—
164	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
165	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
166	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
167	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
168	C₂×D₄×C₆₇	—	2	8	no	—
169	C₂×D₄×C₆₇	—	4	4	no	—
170	C₂×D₄×C₆₇	—	4	16	no	—
171	C₂×D₄×C₆₇	C₂²×C₄	1	8	yes	—
172	C₂×D₄×C₆₇	C₂²×C₄	1	8	yes	—
173	C₂²×C₄×C₆₇	—	2	4	no	—
174	C₂²×C₄×C₆₇	—	2	2	no	—
175	C₂²×C₄×C₆₇	—	2	4	no	—
176	C₂²×C₄×C₆₇	—	2	2	no	—
177	C₂²×C₄×C₆₇	—	2	8	no	—
178	C₂²×C₄×C₆₇	—	4	16	no	—
179	C₂²×C₄×C₆₇	—	4	2	no	—
180	C₂²×C₄×C₆₇	—	4	2	no	—
181	C₂²×C₄×C₆₇	—	4	2	no	—
182	C₂²×C₄×C₆₇	—	4	2	no	—
183	C₂²×C₄×C₆₇	—	4	2	no	—
184	C₂²×C₄×C₆₇	—	4	2	no	—
185	C₂²×C₄×C₆₇	—	4	4	no	—
186	C₂²×C₄×C₆₇	—	4	4	no	—
187	C₂²×C₄×C₆₇	—	4	4	no	—
188	C₂²×C₄×C₆₇	—	4	4	no	—
189	C₂²×C₄×C₆₇	—	4	4	no	—
190	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
191	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
192	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
193	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
194	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
195	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
196	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
197	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
198	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
199	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
200	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
201	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
202	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
203	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
204	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
205	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
206	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
207	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
208	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
209	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
210	C₄⋊C₄×C₆₇	—	4	2	no	—
211	C₄⋊C₄×C₆₇	—	4	4	no	—
212	C₄⋊C₄×C₆₇	—	4	2	no	—
213	C₄⋊C₄×C₆₇	—	4	4	no	—
214	C₄⋊C₄×C₆₇	—	4	4	no	—
215	C₄⋊C₄×C₆₇	—	4	2	no	—
216	C₄⋊C₄×C₆₇	—	4	2	no	—
217	C₄⋊C₄×C₆₇	—	4	4	no	—
218	C₄⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
219	C₄⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
220	C₄⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
221	C₄⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
222	C₂²⋊C₄×C₆₇	—	2	4	no	—
223	C₂²⋊C₄×C₆₇	—	2	4	no	—
224	C₂²⋊C₄×C₆₇	—	2	4	no	—
225	C₂²⋊C₄×C₆₇	—	2	8	no	—
226	C₂²⋊C₄×C₆₇	—	2	4	no	—
227	C₂²⋊C₄×C₆₇	—	4	4	no	—
228	C₂²⋊C₄×C₆₇	—	4	4	no	—
229	C₂²⋊C₄×C₆₇	—	4	4	no	—
230	C₂²⋊C₄×C₆₇	—	4	4	no	—
231	C₂²⋊C₄×C₆₇	—	4	4	no	—
232	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
233	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
234	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
235	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
236	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
237	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
238	C₄²×C₆₇	—	4	4	no	—
239	C₄²×C₆₇	—	4	4	no	—
240	C₄²×C₆₇	—	4	4	no	—
241	C₄²×C₆₇	—	4	4	no	—
242	C₂³×C₆₇	—	2	1	no	—
243	C₂³×C₆₇	—	2	2	no	—
244	C₂³×C₆₇	—	2	1	no	—
245	C₂³×C₆₇	—	2	2	no	—
246	C₂³×C₆₇	—	2	2	no	—
247	C₂³×C₆₇	—	2	8	no	—
248	C₂³×C₆₇	—	2	8	no	—
249	C₂³×C₆₇	—	2	1	no	—
250	C₂³×C₆₇	—	2	2	no	—
251	C₂³×C₆₇	—	2	4	no	—
252	C₂³×C₆₇	—	2	2	no	—
253	C₂³×C₆₇	—	2	1	no	—
254	C₂³×C₆₇	—	2	2	no	—
255	C₂³×C₆₇	—	2	2	no	—
256	C₂³×C₆₇	—	2	4	no	—
257	C₂³×C₆₇	—	2	8	no	—
258	C₂³×C₆₇	—	4	4	no	—
259	C₂³×C₆₇	—	4	4	no	—
260	C₂³×C₆₇	—	4	4	no	—
261	C₂³×C₆₇	—	4	8	no	—
262	C₂³×C₆₇	—	4	8	no	—
263	C₂³×C₆₇	—	8	4	no	—
264	C₂³×C₆₇	—	8	4	no	—
265	C₂³×C₆₇	C₂³×C₄	1	4	yes	—
266	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
267	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
268	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
269	C₂³×C₆₇	H(5,𝔽₂)	1	4	yes	—
270	C₂³×C₆₇	H(5,𝔽₂)	1	2	yes	—
271	C₂³×C₆₇	2₋¹⁺⁴	1	2	yes	—
272	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
273	D₄×C₆₇	—	2	16	no	—
274	D₄×C₆₇	—	4	8	no	—
275	C₂×C₄×C₆₇	—	2	8	no	—
276	C₂×C₄×C₆₇	—	2	8	no	—
277	C₂×C₄×C₆₇	—	2	8	no	—
278	C₂×C₄×C₆₇	—	2	2	no	—
279	C₂×C₄×C₆₇	—	2	2	no	—
280	C₂×C₄×C₆₇	—	2	4	no	—
281	C₂×C₄×C₆₇	—	2	2	no	—
282	C₂×C₄×C₆₇	—	2	2	no	—
283	C₂×C₄×C₆₇	—	2	2	no	—
284	C₂×C₄×C₆₇	—	2	2	no	—
285	C₂×C₄×C₆₇	—	2	4	no	—
286	C₂×C₄×C₆₇	—	2	4	no	—
287	C₂×C₄×C₆₇	—	2	4	no	—
288	C₂×C₄×C₆₇	—	2	4	no	—
289	C₂×C₄×C₆₇	—	2	4	no	—
290	C₂×C₄×C₆₇	—	2	4	no	—
291	C₂×C₄×C₆₇	—	2	4	no	—
292	C₂×C₄×C₆₇	—	2	4	no	—
293	C₂×C₄×C₆₇	—	2	4	no	—
294	C₂×C₄×C₆₇	—	2	4	no	—
295	C₂×C₄×C₆₇	—	2	4	no	—
296	C₂×C₄×C₆₇	—	2	4	no	—
297	C₂×C₄×C₆₇	—	2	4	no	—
298	C₂×C₄×C₆₇	—	4	4	no	—
299	C₂×C₄×C₆₇	—	4	4	no	—
300	C₂×C₄×C₆₇	—	4	4	no	—
301	C₂×C₄×C₆₇	—	4	4	no	—
302	C₂×C₄×C₆₇	—	4	4	no	—
303	C₂×C₄×C₆₇	—	4	4	no	—
304	C₂×C₄×C₆₇	—	8	8	no	—
305	C₂×C₄×C₆₇	—	8	8	no	—
306	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
307	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
308	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
309	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
310	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
311	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
312	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
313	C₂²×C₆₇	—	2	2	no	—
314	C₂²×C₆₇	—	2	2	no	—
315	C₂²×C₆₇	—	2	2	no	—
316	C₂²×C₆₇	—	2	2	no	—
317	C₂²×C₆₇	—	2	4	no	—
318	C₂²×C₆₇	—	2	4	no	—
319	C₂²×C₆₇	—	2	4	no	—
320	C₂²×C₆₇	—	2	4	no	—
321	C₂²×C₆₇	—	2	2	no	—
322	C₂²×C₆₇	—	2	4	no	—
323	C₂²×C₆₇	—	2	2	no	—
324	C₂²×C₆₇	—	2	4	no	—
325	C₂²×C₆₇	—	2	2	no	—
326	C₂²×C₆₇	—	2	4	no	—
327	C₂²×C₆₇	—	4	16	no	—
328	C₂²×C₆₇	—	4	4	no	—
329	C₂²×C₆₇	—	4	2	no	—
330	C₂²×C₆₇	—	4	2	no	—
331	C₂²×C₆₇	—	4	4	no	—
332	C₂²×C₆₇	—	8	8	no	—
333	C₂²×C₆₇	#518	1	4	yes	—
334	C₂²×C₆₇	#520	1	4	yes	—
335	C₂²×C₆₇	C₂⁴×C₄	1	1	yes	characteristic
336	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
337	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
338	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
339	C₂²×C₆₇	#585	1	2	yes	—
340	C₄×C₆₇	—	2	2	no	—
341	C₄×C₆₇	—	2	2	no	—
342	C₄×C₆₇	—	2	2	no	—
343	C₄×C₆₇	—	2	2	no	—
344	C₄×C₆₇	—	2	4	no	—
345	C₄×C₆₇	—	2	4	no	—
346	C₄×C₆₇	—	2	4	no	—
347	C₄×C₆₇	—	4	4	no	—
348	C₄×C₆₇	—	4	4	no	—
349	C₄×C₆₇	—	4	4	no	—
350	C₄×C₆₇	—	4	4	no	—
351	#34376	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
352	C₂×C₆₇	—	2	4	no	—
353	C₂×C₆₇	—	2	4	no	—
354	C₂×C₆₇	—	4	2	no	—
355	C₂×C₆₇	—	4	4	no	—
356	C₂×C₆₇	C₂×#518	1	1	yes	characteristic
357	C₂×C₆₇	C₂×#520	1	1	yes	characteristic
358	C₂×C₆₇	#3428	1	1	yes	characteristic
359	C₂×C₆₇	#3534	1	2	yes	—
360	C₂×C₆₇	#3535	1	2	yes	—
361	C₂²×#123	C₂×C₆₇	1	1	yes	characteristic
362	#2376	C₂×C₆₇	1	4	yes	complemented
363	#2359	C₂×C₆₇	1	4	yes	complemented
364	#2345	C₂×C₆₇	1	2	yes	complemented
365	#2342	C₂×C₆₇	1	2	yes	complemented
366	#2342	C₂×C₆₇	1	2	yes	complemented
367	D₄×C₂²⋊C₄	C₂×C₆₇	1	2	yes	—
368	#2335	C₂×C₆₇	1	4	yes	complemented
369	#2322	C₂×C₆₇	1	4	yes	complemented
370	#2316	C₂×C₆₇	1	1	yes	characteristic, complemented
371	#2315	C₂×C₆₇	1	1	yes	characteristic, complemented
372	#2313	C₂×C₆₇	1	1	yes	characteristic, complemented
373	#2312	C₂×C₆₇	1	1	yes	characteristic, complemented
374	#2280	C₂×C₆₇	1	1	yes	characteristic, complemented
375	C₂×#380	C₂×C₆₇	1	1	yes	characteristic, complemented
376	C₆₇	#34376	1	1	yes	characteristic, direct product factor, Sylow
377	C₂³×D₄	C₂²×C₆₇	1	1	yes	characteristic
378	C₂⁴×C₄	C₂²×C₆₇	1	1	yes	characteristic
379	C₂×#123	C₄×C₆₇	1	16	yes	complemented
380	C₂×#123	C₂²×C₆₇	1	2	yes	—
381	C₂×#123	C₂²×C₆₇	1	2	yes	—
382	C₂×#123	C₂²×C₆₇	1	2	yes	—
383	C₂×#123	C₂²×C₆₇	1	2	yes	—
384	C₂×C₄×D₄	C₂²×C₆₇	1	4	yes	—
385	C₂×#117	C₂²×C₆₇	1	2	yes	—
386	C₂×#117	C₂²×C₆₇	1	2	yes	complemented
387	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
388	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
389	C₂²×C₄⋊C₄	C₂²×C₆₇	1	2	yes	complemented
390	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
391	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
392	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
393	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
394	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
395	#390	C₂²×C₆₇	1	4	yes	—
396	#389	C₂²×C₆₇	1	4	yes	complemented
397	#389	C₂²×C₆₇	1	4	yes	complemented
398	#389	C₂²×C₆₇	1	4	yes	complemented
399	#388	C₂²×C₆₇	1	4	yes	complemented
400	#388	C₂²×C₆₇	1	4	yes	complemented
401	#388	C₂²×C₆₇	1	4	yes	complemented
402	#388	C₂²×C₆₇	1	4	yes	complemented
403	#388	C₂²×C₆₇	1	4	yes	complemented
404	#388	C₂²×C₆₇	1	4	yes	complemented
405	#387	C₂²×C₆₇	1	4	yes	complemented
406	#387	C₂²×C₆₇	1	4	yes	complemented
407	#387	C₂²×C₆₇	1	4	yes	complemented
408	#387	C₂²×C₆₇	1	4	yes	complemented
409	#386	C₂²×C₆₇	1	4	yes	—
410	#386	C₂²×C₆₇	1	4	yes	—
411	#385	C₂²×C₆₇	1	4	yes	complemented
412	#385	C₂²×C₆₇	1	4	yes	complemented
413	#385	C₂²×C₆₇	1	4	yes	complemented
414	#385	C₂²×C₆₇	1	4	yes	complemented
415	#381	C₂²×C₆₇	1	2	yes	—
416	#381	C₂²×C₆₇	1	2	yes	complemented
417	#380	C₂²×C₆₇	1	1	yes	characteristic
418	#380	C₂²×C₆₇	1	1	yes	characteristic
419	#380	C₂²×C₆₇	1	1	yes	characteristic
420	#380	C₂²×C₆₇	1	1	yes	characteristic
421	#380	C₂²×C₆₇	1	2	yes	—
422	#380	C₂²×C₆₇	1	2	yes	—
423	#380	C₂²×C₆₇	1	2	yes	—
424	#380	C₂²×C₆₇	1	2	yes	complemented
425	#380	C₂²×C₆₇	1	2	yes	complemented
426	#380	C₂²×C₆₇	1	2	yes	complemented
427	#379	C₂²×C₆₇	1	2	yes	—
428	#379	C₂²×C₆₇	1	2	yes	—
429	C₄×C₄⋊C₄	C₂²×C₆₇	1	4	yes	complemented
430	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
431	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
432	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
433	C₄×C₂²⋊C₄	C₂²×C₆₇	1	4	yes	complemented
434	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
435	C₄×C₂²⋊C₄	C₂²×C₆₇	1	4	yes	complemented
436	C₂×#95	C₂²×C₆₇	1	2	yes	complemented
437	C₂⁵	C₂³×C₆₇	1	1	yes	characteristic
438	C₂⁵	C₂³×C₆₇	1	1	yes	characteristic
439	C₂²×D₄	—	4	4	no	—
440	C₂²×D₄	C₂×C₄×C₆₇	1	8	yes	—
441	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
442	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
443	C₂³×C₄	—	4	4	no	—
444	C₂³×C₄	C₂×C₄×C₆₇	1	8	yes	complemented
445	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
446	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
447	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
448	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
449	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
450	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
451	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
452	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
453	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
454	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
455	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
456	#123	C₂×C₄×C₆₇	1	16	yes	complemented
457	#123	C₂×C₄×C₆₇	1	16	yes	complemented
458	#123	C₂×C₄×C₆₇	1	16	yes	complemented
459	#123	C₂×C₄×C₆₇	1	16	yes	complemented
460	C₄×D₄	—	4	8	no	—
461	#117	—	4	4	no	—
462	#117	—	4	4	no	—
463	C₂×C₄⋊C₄	—	4	4	no	—
464	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	8	yes	complemented
465	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	8	yes	complemented
466	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
467	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
468	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
469	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
470	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
471	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
472	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
473	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
474	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
475	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
476	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
477	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
478	C₂×C₂²⋊C₄	—	4	4	no	—
479	C₂×C₂²⋊C₄	—	4	4	no	—
480	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	8	yes	complemented
481	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	8	yes	complemented
482	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	8	yes	complemented
483	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
484	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
485	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
486	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
487	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
488	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
489	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
490	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
491	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
492	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
493	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
494	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
495	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
496	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
497	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
498	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
499	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
500	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
501	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
502	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
503	#95	C₂³×C₆₇	1	4	yes	—
504	#95	C₂³×C₆₇	1	2	yes	—
505	#95	C₂³×C₆₇	1	2	yes	—
506	#95	C₂³×C₆₇	1	4	yes	—
507	#95	C₂³×C₆₇	1	4	yes	—
508	#95	C₂³×C₆₇	1	4	yes	—
509	#95	C₂³×C₆₇	1	2	yes	—
510	#95	C₂³×C₆₇	1	2	yes	—
511	#95	C₂³×C₆₇	1	4	yes	—
512	#95	C₂³×C₆₇	1	4	yes	—
513	#95	C₂³×C₆₇	1	4	yes	—
514	#95	C₂³×C₆₇	1	4	yes	—
515	C₂⁴	—	2	2	no	—
516	C₂⁴	—	2	4	no	—
517	C₂⁴	—	2	2	no	—
518	C₂⁴	—	2	2	no	—
519	C₂⁴	—	2	2	no	—
520	C₂⁴	—	4	2	no	—
521	C₂⁴	—	4	2	no	—
522	C₂⁴	—	4	2	no	—
523	C₂⁴	C₂²×C₄×C₆₇	1	4	yes	—
524	C₂⁴	C₂²×C₄×C₆₇	1	4	yes	—
525	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
526	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
527	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
528	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
529	C₂×D₄	—	2	8	no	—
530	C₂×D₄	—	4	4	no	—
531	C₂×D₄	—	4	16	no	—
532	C₂×D₄	C₂²×C₄×C₆₇	1	8	yes	—
533	C₂×D₄	C₂²×C₄×C₆₇	1	8	yes	—
534	C₂²×C₄	—	2	4	no	—
535	C₂²×C₄	—	2	2	no	—
536	C₂²×C₄	—	2	4	no	—
537	C₂²×C₄	—	2	2	no	—
538	C₂²×C₄	—	2	8	no	—
539	C₂²×C₄	—	4	16	no	—
540	C₂²×C₄	—	4	2	no	—
541	C₂²×C₄	—	4	2	no	—
542	C₂²×C₄	—	4	2	no	—
543	C₂²×C₄	—	4	2	no	—
544	C₂²×C₄	—	4	2	no	—
545	C₂²×C₄	—	4	2	no	—
546	C₂²×C₄	—	4	4	no	—
547	C₂²×C₄	—	4	4	no	—
548	C₂²×C₄	—	4	4	no	—
549	C₂²×C₄	—	4	4	no	—
550	C₂²×C₄	—	4	4	no	—
551	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
552	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
553	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
554	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
555	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
556	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
557	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
558	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
559	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
560	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
561	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
562	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
563	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
564	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
565	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
566	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
567	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
568	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
569	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
570	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
571	C₄⋊C₄	—	4	2	no	—
572	C₄⋊C₄	—	4	4	no	—
573	C₄⋊C₄	—	4	2	no	—
574	C₄⋊C₄	—	4	4	no	—
575	C₄⋊C₄	—	4	2	no	—
576	C₄⋊C₄	—	4	2	no	—
577	C₄⋊C₄	—	4	4	no	—
578	C₄⋊C₄	—	4	4	no	—
579	C₄⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
580	C₄⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
581	C₄⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
582	C₄⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
583	C₂²⋊C₄	—	2	4	no	—
584	C₂²⋊C₄	—	2	4	no	—
585	C₂²⋊C₄	—	2	4	no	—
586	C₂²⋊C₄	—	2	8	no	—
587	C₂²⋊C₄	—	2	4	no	—
588	C₂²⋊C₄	—	4	4	no	—
589	C₂²⋊C₄	—	4	4	no	—
590	C₂²⋊C₄	—	4	4	no	—
591	C₂²⋊C₄	—	4	4	no	—
592	C₂²⋊C₄	—	4	4	no	—
593	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
594	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
595	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
596	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
597	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
598	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
599	C₄²	—	4	4	no	—
600	C₄²	—	4	4	no	—
601	C₄²	—	4	4	no	—
602	C₄²	—	4	4	no	—
603	C₂³	—	2	1	no	—
604	C₂³	—	2	2	no	—
605	C₂³	—	2	1	no	—
606	C₂³	—	2	2	no	—
607	C₂³	—	2	2	no	—
608	C₂³	—	2	8	no	—
609	C₂³	—	2	8	no	—
610	C₂³	—	2	1	no	—
611	C₂³	—	2	2	no	—
612	C₂³	—	2	4	no	—
613	C₂³	—	2	2	no	—
614	C₂³	—	2	1	no	—
615	C₂³	—	2	2	no	—
616	C₂³	—	2	2	no	—
617	C₂³	—	2	4	no	—
618	C₂³	—	2	8	no	—
619	C₂³	—	4	4	no	—
620	C₂³	—	4	4	no	—
621	C₂³	—	4	4	no	—
622	C₂³	—	4	8	no	—
623	C₂³	—	4	8	no	—
624	C₂³	—	8	4	no	—
625	C₂³	—	8	4	no	—
626	C₂³	C₂³×C₄×C₆₇	1	4	yes	—
627	C₂³	C₂³×C₄×C₆₇	1	2	yes	—
628	C₂³	C₂³×C₄×C₆₇	1	2	yes	—
629	C₂³	C₂³×C₄×C₆₇	1	2	yes	—
630	C₂³	H(5,𝔽₂)×C₆₇	1	4	yes	—
631	C₂³	H(5,𝔽₂)×C₆₇	1	2	yes	—
632	C₂³	2₋¹⁺⁴×C₆₇	1	2	yes	—
633	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
634	D₄	—	2	16	no	—
635	D₄	—	4	8	no	—
636	C₂×C₄	—	2	8	no	—
637	C₂×C₄	—	2	8	no	—
638	C₂×C₄	—	2	8	no	—
639	C₂×C₄	—	2	2	no	—
640	C₂×C₄	—	2	2	no	—
641	C₂×C₄	—	2	4	no	—
642	C₂×C₄	—	2	2	no	—
643	C₂×C₄	—	2	2	no	—
644	C₂×C₄	—	2	2	no	—
645	C₂×C₄	—	2	2	no	—
646	C₂×C₄	—	2	4	no	—
647	C₂×C₄	—	2	4	no	—
648	C₂×C₄	—	2	4	no	—
649	C₂×C₄	—	2	4	no	—
650	C₂×C₄	—	2	4	no	—
651	C₂×C₄	—	2	4	no	—
652	C₂×C₄	—	2	4	no	—
653	C₂×C₄	—	2	4	no	—
654	C₂×C₄	—	2	4	no	—
655	C₂×C₄	—	2	4	no	—
656	C₂×C₄	—	2	4	no	—
657	C₂×C₄	—	2	4	no	—
658	C₂×C₄	—	2	4	no	—
659	C₂×C₄	—	4	4	no	—
660	C₂×C₄	—	4	4	no	—
661	C₂×C₄	—	4	4	no	—
662	C₂×C₄	—	4	4	no	—
663	C₂×C₄	—	4	4	no	—
664	C₂×C₄	—	4	4	no	—
665	C₂×C₄	—	8	8	no	—
666	C₂×C₄	—	8	8	no	—
667	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
668	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
669	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
670	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
671	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
672	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
673	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
674	C₂²	—	2	4	no	—
675	C₂²	—	2	4	no	—
676	C₂²	—	2	4	no	—
677	C₂²	—	2	4	no	—
678	C₂²	—	2	2	no	—
679	C₂²	—	2	2	no	—
680	C₂²	—	2	2	no	—
681	C₂²	—	2	2	no	—
682	C₂²	—	2	2	no	—
683	C₂²	—	2	4	no	—
684	C₂²	—	2	2	no	—
685	C₂²	—	2	4	no	—
686	C₂²	—	2	2	no	—
687	C₂²	—	2	4	no	—
688	C₂²	—	4	16	no	—
689	C₂²	—	4	4	no	—
690	C₂²	—	4	2	no	—
691	C₂²	—	4	2	no	—
692	C₂²	—	4	4	no	—
693	C₂²	—	8	8	no	—
694	C₂²	#518×C₆₇	1	4	yes	—
695	C₂²	#520×C₆₇	1	4	yes	—
696	C₂²	C₂⁴×C₄×C₆₇	1	1	yes	characteristic
697	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
698	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	2	yes	—
699	C₂²	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
700	C₂²	#585×C₆₇	1	2	yes	—
701	C₄	—	2	2	no	—
702	C₄	—	2	2	no	—
703	C₄	—	2	2	no	—
704	C₄	—	2	2	no	—
705	C₄	—	2	4	no	—
706	C₄	—	2	4	no	—
707	C₄	—	2	4	no	—
708	C₄	—	4	4	no	—
709	C₄	—	4	4	no	—
710	C₄	—	4	4	no	—
711	C₄	—	4	4	no	—
712	C₂	—	2	4	no	—
713	C₂	—	2	4	no	—
714	C₂	—	4	2	no	—
715	C₂	—	4	4	no	—
716	C₂	C₂×#518×C₆₇	1	1	yes	characteristic
717	C₂	C₂×#520×C₆₇	1	1	yes	characteristic
718	C₂	C₆₇×#3428	1	1	yes	characteristic
719	C₂	C₆₇×#3534	1	2	yes	—
720	C₂	C₆₇×#3535	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₆₇
Frattini, cosocle	C₂³	C₂⁵×C₆₇
prime radical	C₂³×D₄×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×#2376	C₂	semidirect
3. C₆₇×#2359	C₂	semidirect
4. C₆₇×#2345	C₂	semidirect
5. C₆₇×#2342	C₂	semidirect
6. C₆₇×#2342	C₂	semidirect
8. C₆₇×#2335	C₂	semidirect
9. C₆₇×#2322	C₂	semidirect
10. C₆₇×#2316	C₂	semidirect
11. C₆₇×#2315	C₂	semidirect
12. C₆₇×#2313	C₂	semidirect
13. C₆₇×#2312	C₂	semidirect
14. C₆₇×#2280	C₂	semidirect
15. C₂×#380×C₆₇	C₂	semidirect
18. C₂×#123×C₆₇	C₄	semidirect
25. C₂×#117×C₆₇	C₂²	semidirect
28. C₂²×C₄⋊C₄×C₆₇	C₂²	semidirect
35. #389×C₆₇	C₂²	semidirect
36. #389×C₆₇	C₂²	semidirect
37. #389×C₆₇	C₂²	semidirect
38. #388×C₆₇	C₂²	semidirect
39. #388×C₆₇	C₂²	semidirect
40. #388×C₆₇	C₂²	semidirect
41. #388×C₆₇	C₂²	semidirect
42. #388×C₆₇	C₂²	semidirect
43. #388×C₆₇	C₂²	semidirect
44. #387×C₆₇	C₂²	semidirect
45. #387×C₆₇	C₂²	semidirect
46. #387×C₆₇	C₂²	semidirect
47. #387×C₆₇	C₂²	semidirect
50. #385×C₆₇	C₂²	semidirect
51. #385×C₆₇	C₂²	semidirect
52. #385×C₆₇	C₂²	semidirect
53. #385×C₆₇	C₂²	semidirect
55. #381×C₆₇	C₂²	semidirect
63. #380×C₆₇	C₂²	semidirect
64. #380×C₆₇	C₂²	semidirect
65. #380×C₆₇	C₂²	semidirect
68. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
72. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
73. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
74. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
75. C₂×#95×C₆₇	C₂²	semidirect
83. C₂³×C₄×C₆₇	C₂×C₄	semidirect
95. #123×C₆₇	C₂×C₄	semidirect
96. #123×C₆₇	C₂×C₄	semidirect
97. #123×C₆₇	C₂×C₄	semidirect
98. #123×C₆₇	C₂×C₄	semidirect
103. C₂×C₄⋊C₄×C₆₇	C₂×C₄	semidirect
104. C₂×C₄⋊C₄×C₆₇	C₂×C₄	semidirect
119. C₂×C₂²⋊C₄×C₆₇	C₂×C₄	semidirect
120. C₂×C₂²⋊C₄×C₆₇	C₂×C₄	semidirect
121. C₂×C₂²⋊C₄×C₆₇	C₂×C₄	semidirect
351. #34376	C₆₇	direct (N × H)
362. #2376	C₂×C₆₇	semidirect
363. #2359	C₂×C₆₇	semidirect
364. #2345	C₂×C₆₇	semidirect
365. #2342	C₂×C₆₇	semidirect
366. #2342	C₂×C₆₇	semidirect
368. #2335	C₂×C₆₇	semidirect
369. #2322	C₂×C₆₇	semidirect
370. #2316	C₂×C₆₇	semidirect
371. #2315	C₂×C₆₇	semidirect
372. #2313	C₂×C₆₇	semidirect
373. #2312	C₂×C₆₇	semidirect
374. #2280	C₂×C₆₇	semidirect
375. C₂×#380	C₂×C₆₇	semidirect
376. C₆₇	#34376	direct (N × H)
379. C₂×#123	C₄×C₆₇	semidirect
386. C₂×#117	C₂²×C₆₇	semidirect
389. C₂²×C₄⋊C₄	C₂²×C₆₇	semidirect
396. #389	C₂²×C₆₇	semidirect
397. #389	C₂²×C₆₇	semidirect
398. #389	C₂²×C₆₇	semidirect
399. #388	C₂²×C₆₇	semidirect
400. #388	C₂²×C₆₇	semidirect
401. #388	C₂²×C₆₇	semidirect
402. #388	C₂²×C₆₇	semidirect
403. #388	C₂²×C₆₇	semidirect
404. #388	C₂²×C₆₇	semidirect
405. #387	C₂²×C₆₇	semidirect
406. #387	C₂²×C₆₇	semidirect
407. #387	C₂²×C₆₇	semidirect
408. #387	C₂²×C₆₇	semidirect
411. #385	C₂²×C₆₇	semidirect
412. #385	C₂²×C₆₇	semidirect
413. #385	C₂²×C₆₇	semidirect
414. #385	C₂²×C₆₇	semidirect
416. #381	C₂²×C₆₇	semidirect
424. #380	C₂²×C₆₇	semidirect
425. #380	C₂²×C₆₇	semidirect
426. #380	C₂²×C₆₇	semidirect
429. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
433. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
434. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
435. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
436. C₂×#95	C₂²×C₆₇	semidirect
444. C₂³×C₄	C₂×C₄×C₆₇	semidirect
456. #123	C₂×C₄×C₆₇	semidirect
457. #123	C₂×C₄×C₆₇	semidirect
458. #123	C₂×C₄×C₆₇	semidirect
459. #123	C₂×C₄×C₆₇	semidirect
464. C₂×C₄⋊C₄	C₂×C₄×C₆₇	semidirect
465. C₂×C₄⋊C₄	C₂×C₄×C₆₇	semidirect
480. C₂×C₂²⋊C₄	C₂×C₄×C₆₇	semidirect
481. C₂×C₂²⋊C₄	C₂×C₄×C₆₇	semidirect
482. C₂×C₂²⋊C₄	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
C₂²×#123×C₆₇	2
C₆₇×#2376	2
C₆₇×#2359	2
C₆₇×#2345	2
C₆₇×#2342	2
D₄×C₂²⋊C₄×C₆₇	2
C₆₇×#2335	2
C₆₇×#2322	2
C₆₇×#2316	2
C₆₇×#2315	2
C₆₇×#2313	2
C₆₇×#2312	2
C₆₇×#2280	2
C₂×#380×C₆₇	2
#34376	67

Subgroups — C67×#34376 #30713627

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#34376 #30713627