Subgroups — C₄×#452×C₆₇ #30700702

Order 17152.

1480 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#41×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₂×#452×C₆₇	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×Q₁₆×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄×SD₁₆×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×C₂²⋊Q₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#1878	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#1877	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#1873	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#1865	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#1862	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#1854	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#1788	C₂	1	1	yes	maximal, characteristic
13	C₄×#103×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×#102×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₂²⋊C₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
17	C₂²×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic
18	C₂²×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic
19	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
20	C₄×#41×C₆₇	—	2	4	no	—
21	C₄×#41×C₆₇	—	2	4	no	—
22	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
23	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
24	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₄×C₆₇	—	2	1	no	—
26	C₂×C₄×D₄×C₆₇	—	2	1	no	—
27	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
29	C₂×#117×C₆₇	—	2	1	no	—
30	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
31	C₂²×C₄²×C₆₇	—	2	1	no	—
32	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
33	#452×C₆₇	C₄	1	8	yes	direct product factor
34	C₄×Q₁₆×C₆₇	—	2	4	no	—
35	C₄×SD₁₆×C₆₇	—	2	4	no	—
36	C₂×#107×C₆₇	C₂²	1	1	yes	characteristic
37	C₂×#106×C₆₇	C₂²	1	1	yes	characteristic
38	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic
39	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic
40	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic
41	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic
42	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic
43	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
44	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
45	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
46	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
47	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
48	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
49	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
50	#391×C₆₇	C₂²	1	1	yes	characteristic
51	#389×C₆₇	C₂²	1	1	yes	characteristic
52	#387×C₆₇	—	2	1	no	—
53	#385×C₆₇	—	2	1	no	—
54	#380×C₆₇	C₂²	1	1	yes	characteristic
55	C₄×C₄⋊C₄×C₆₇	—	2	1	no	—
56	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
57	C₄×C₂²⋊C₄×C₆₇	—	2	1	no	—
58	#340×C₆₇	C₂²	1	1	yes	characteristic
59	#340×C₆₇	C₂²	1	1	yes	characteristic
60	#340×C₆₇	C₂²	1	1	yes	characteristic
61	#340×C₆₇	C₂²	1	1	yes	characteristic
62	#336×C₆₇	C₂²	1	1	yes	characteristic
63	#336×C₆₇	C₂²	1	1	yes	characteristic
64	C₂×#41×C₆₇	—	2	2	no	—
65	C₂×#41×C₆₇	—	2	2	no	—
66	C₂×#41×C₆₇	—	2	2	no	—
67	C₂×#41×C₆₇	—	2	2	no	—
68	C₂×#41×C₆₇	—	2	2	no	—
69	C₂×#41×C₆₇	C₂×C₄	1	4	yes	—
70	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
71	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
72	C₂²×D₄×C₆₇	—	2	1	no	—
73	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₆₇	—	2	1	no	—
75	C₂³×C₄×C₆₇	—	2	1	no	—
76	C₂³×C₄×C₆₇	—	2	1	no	—
77	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
78	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
79	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
80	C₂×Q₁₆×C₆₇	—	2	2	no	—
81	C₂×Q₁₆×C₆₇	—	2	2	no	—
82	C₂×Q₁₆×C₆₇	C₂×C₄	1	4	yes	complemented
83	C₂×SD₁₆×C₆₇	—	2	2	no	—
84	C₂×SD₁₆×C₆₇	—	2	2	no	—
85	C₂×SD₁₆×C₆₇	C₂×C₄	1	4	yes	complemented
86	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
87	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
88	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
89	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
90	C₂²⋊Q₈×C₆₇	—	2	2	no	—
91	C₂²⋊Q₈×C₆₇	C₂×C₄	1	4	yes	complemented
92	C₄×Q₈×C₆₇	—	2	2	no	—
93	C₄×Q₈×C₆₇	—	2	2	no	—
94	C₄×Q₈×C₆₇	—	2	2	no	—
95	C₄×Q₈×C₆₇	—	2	2	no	—
96	C₄×Q₈×C₆₇	—	2	2	no	—
97	C₄×Q₈×C₆₇	D₄	1	4	yes	—
98	C₄×D₄×C₆₇	—	2	8	no	—
99	C₄×D₄×C₆₇	—	2	8	no	—
100	C₄×D₄×C₆₇	—	2	2	no	—
101	C₄×D₄×C₆₇	—	2	2	no	—
102	C₄×D₄×C₆₇	—	2	2	no	—
103	C₄×D₄×C₆₇	D₄	1	4	yes	—
104	#117×C₆₇	—	2	8	no	—
105	#117×C₆₇	—	2	2	no	—
106	#117×C₆₇	—	2	2	no	—
107	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
108	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
109	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
110	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
111	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
112	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
113	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
114	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
115	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
116	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
117	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
118	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
119	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
120	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
121	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
122	C₂×C₄²×C₆₇	—	2	8	no	—
123	C₂×C₄²×C₆₇	—	2	1	no	—
124	C₂×C₄²×C₆₇	—	2	1	no	—
125	C₂×C₄²×C₆₇	—	2	1	no	—
126	C₂×C₄²×C₆₇	—	2	2	no	—
127	C₂×C₄²×C₆₇	—	2	2	no	—
128	C₂×C₄²×C₆₇	—	2	1	no	—
129	C₂×C₄²×C₆₇	—	2	1	no	—
130	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
131	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
132	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
133	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
134	#107×C₆₇	—	2	2	no	—
135	#106×C₆₇	—	2	2	no	—
136	#103×C₆₇	—	2	2	no	—
137	#103×C₆₇	—	2	2	no	—
138	#103×C₆₇	—	2	2	no	—
139	#103×C₆₇	—	2	2	no	—
140	#103×C₆₇	C₂×C₄	1	4	yes	complemented
141	#102×C₆₇	—	2	2	no	—
142	#102×C₆₇	—	2	2	no	—
143	#102×C₆₇	C₂×C₄	1	4	yes	complemented
144	C₂²⋊C₈×C₆₇	—	2	2	no	—
145	C₂²⋊C₈×C₆₇	C₂×C₄	1	4	yes	complemented
146	C₄×C₈×C₆₇	—	2	2	no	—
147	C₄×C₈×C₆₇	—	2	2	no	—
148	#95×C₆₇	—	2	1	no	—
149	#95×C₆₇	—	2	1	no	—
150	#95×C₆₇	—	2	1	no	—
151	#95×C₆₇	—	2	1	no	—
152	#95×C₆₇	—	2	1	no	—
153	C₂⁴×C₆₇	—	2	1	no	—
154	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
155	#41×C₆₇	—	2	8	no	—
156	#41×C₆₇	—	2	8	no	—
157	#41×C₆₇	—	2	8	no	—
158	#41×C₆₇	—	2	8	no	—
159	C₂×Q₈×C₆₇	—	2	1	no	—
160	C₂×Q₈×C₆₇	—	2	1	no	—
161	C₂×Q₈×C₆₇	—	2	1	no	—
162	C₂×Q₈×C₆₇	—	2	1	no	—
163	C₂×Q₈×C₆₇	—	2	1	no	—
164	C₂×Q₈×C₆₇	—	2	1	no	—
165	C₂×Q₈×C₆₇	—	2	1	no	—
166	C₂×Q₈×C₆₇	—	2	1	no	—
167	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
168	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
169	C₂×Q₈×C₆₇	C₂×D₄	1	2	yes	—
170	C₂×Q₈×C₆₇	#41	1	2	yes	—
171	C₂×D₄×C₆₇	—	2	4	no	—
172	C₂×D₄×C₆₇	—	2	4	no	—
173	C₂×D₄×C₆₇	—	2	4	no	—
174	C₂×D₄×C₆₇	—	2	1	no	—
175	C₂×D₄×C₆₇	—	2	1	no	—
176	C₂×D₄×C₆₇	—	2	1	no	—
177	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
178	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
179	C₂×D₄×C₆₇	#41	1	2	yes	—
180	C₂²×C₄×C₆₇	—	2	4	no	—
181	C₂²×C₄×C₆₇	—	2	4	no	—
182	C₂²×C₄×C₆₇	—	2	1	no	—
183	C₂²×C₄×C₆₇	—	2	4	no	—
184	C₂²×C₄×C₆₇	—	2	1	no	—
185	C₂²×C₄×C₆₇	—	2	1	no	—
186	C₂²×C₄×C₆₇	—	2	1	no	—
187	C₂²×C₄×C₆₇	—	2	1	no	—
188	C₂²×C₄×C₆₇	—	2	4	no	—
189	C₂²×C₄×C₆₇	—	2	1	no	—
190	C₂²×C₄×C₆₇	—	2	1	no	—
191	C₂²×C₄×C₆₇	—	2	1	no	—
192	C₂²×C₄×C₆₇	—	2	1	no	—
193	C₂²×C₄×C₆₇	—	2	2	no	—
194	C₂²×C₄×C₆₇	—	2	2	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	1	no	—
200	C₂²×C₄×C₆₇	—	2	1	no	—
201	C₂²×C₄×C₆₇	—	4	1	no	—
202	C₂²×C₄×C₆₇	—	4	2	no	—
203	C₂²×C₄×C₆₇	—	4	2	no	—
204	C₂²×C₄×C₆₇	—	4	2	no	—
205	C₂²×C₄×C₆₇	—	4	2	no	—
206	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
207	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
208	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
209	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
210	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
211	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
212	C₂²×C₄×C₆₇	#41	1	2	yes	—
213	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
214	Q₁₆×C₆₇	—	2	8	no	—
215	SD₁₆×C₆₇	—	2	8	no	—
216	C₂×C₈×C₆₇	—	2	1	no	—
217	C₂×C₈×C₆₇	—	2	1	no	—
218	C₂×C₈×C₆₇	—	2	1	no	—
219	C₂×C₈×C₆₇	—	2	1	no	—
220	C₂×C₈×C₆₇	—	2	1	no	—
221	C₂×C₈×C₆₇	—	2	1	no	—
222	C₂×C₈×C₆₇	—	2	1	no	—
223	C₂×C₈×C₆₇	—	2	1	no	—
224	C₂×C₈×C₆₇	—	2	1	no	—
225	C₂×C₈×C₆₇	—	2	1	no	—
226	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
227	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
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	1	no	—
232	C₄⋊C₄×C₆₇	—	2	1	no	—
233	C₄⋊C₄×C₆₇	—	2	1	no	—
234	C₄⋊C₄×C₆₇	—	2	1	no	—
235	C₄⋊C₄×C₆₇	—	2	1	no	—
236	C₄⋊C₄×C₆₇	—	2	1	no	—
237	C₄⋊C₄×C₆₇	—	2	1	no	—
238	C₄⋊C₄×C₆₇	—	4	2	no	—
239	C₄⋊C₄×C₆₇	—	4	2	no	—
240	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
241	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
242	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
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	—	4	2	no	—
248	C₄²×C₆₇	—	2	4	no	—
249	C₄²×C₆₇	—	2	4	no	—
250	C₄²×C₆₇	—	2	2	no	—
251	C₄²×C₆₇	—	2	4	no	—
252	C₄²×C₆₇	—	2	2	no	—
253	C₄²×C₆₇	—	2	1	no	—
254	C₄²×C₆₇	—	2	1	no	—
255	C₄²×C₆₇	—	4	2	no	—
256	C₄²×C₆₇	—	4	2	no	—
257	C₄²×C₆₇	C₂×D₄	1	2	yes	—
258	C₄²×C₆₇	C₂×D₄	1	2	yes	—
259	C₂³×C₆₇	—	2	2	no	—
260	C₂³×C₆₇	—	2	1	no	—
261	C₂³×C₆₇	—	2	2	no	—
262	C₂³×C₆₇	—	2	1	no	—
263	C₂³×C₆₇	—	2	2	no	—
264	C₂³×C₆₇	—	2	1	no	—
265	C₂³×C₆₇	—	2	1	no	—
266	C₂³×C₆₇	—	2	1	no	—
267	C₂³×C₆₇	—	2	1	no	—
268	C₂³×C₆₇	—	4	1	no	—
269	C₂³×C₆₇	—	4	1	no	—
270	C₂³×C₆₇	—	4	1	no	—
271	C₂³×C₆₇	—	4	1	no	—
272	C₂³×C₆₇	C₄×D₄	1	2	yes	—
273	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
274	Q₈×C₆₇	—	2	2	no	—
275	Q₈×C₆₇	—	2	2	no	—
276	Q₈×C₆₇	—	2	2	no	—
277	Q₈×C₆₇	—	2	2	no	—
278	Q₈×C₆₇	—	2	2	no	—
279	Q₈×C₆₇	—	4	1	no	—
280	Q₈×C₆₇	—	4	1	no	—
281	Q₈×C₆₇	C₄×D₄	1	4	yes	—
282	D₄×C₆₇	—	2	16	no	—
283	D₄×C₆₇	—	2	2	no	—
284	D₄×C₆₇	—	2	2	no	—
285	D₄×C₆₇	—	2	2	no	—
286	D₄×C₆₇	C₄×D₄	1	4	yes	—
287	C₂×C₄×C₆₇	—	2	16	no	—
288	C₂×C₄×C₆₇	—	2	2	no	—
289	C₂×C₄×C₆₇	—	2	1	no	—
290	C₂×C₄×C₆₇	—	2	1	no	—
291	C₂×C₄×C₆₇	—	2	2	no	—
292	C₂×C₄×C₆₇	—	2	1	no	—
293	C₂×C₄×C₆₇	—	2	2	no	—
294	C₂×C₄×C₆₇	—	2	1	no	—
295	C₂×C₄×C₆₇	—	2	1	no	—
296	C₂×C₄×C₆₇	—	2	1	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	2	no	—
303	C₂×C₄×C₆₇	—	2	1	no	—
304	C₂×C₄×C₆₇	—	2	2	no	—
305	C₂×C₄×C₆₇	—	2	2	no	—
306	C₂×C₄×C₆₇	—	2	1	no	—
307	C₂×C₄×C₆₇	—	2	1	no	—
308	C₂×C₄×C₆₇	—	4	4	no	—
309	C₂×C₄×C₆₇	—	4	8	no	—
310	C₂×C₄×C₆₇	—	4	1	no	—
311	C₂×C₄×C₆₇	—	4	1	no	—
312	C₂×C₄×C₆₇	—	4	1	no	—
313	C₂×C₄×C₆₇	—	4	1	no	—
314	C₂×C₄×C₆₇	—	4	1	no	—
315	C₂×C₄×C₆₇	—	4	1	no	—
316	C₂×C₄×C₆₇	—	4	1	no	—
317	C₂×C₄×C₆₇	—	4	1	no	—
318	C₂×C₄×C₆₇	—	4	4	no	—
319	C₂×C₄×C₆₇	—	4	8	no	—
320	C₂×C₄×C₆₇	—	4	1	no	—
321	C₂×C₄×C₆₇	—	4	1	no	—
322	C₂×C₄×C₆₇	—	4	1	no	—
323	C₂×C₄×C₆₇	—	4	1	no	—
324	C₂×C₄×C₆₇	—	4	1	no	—
325	C₂×C₄×C₆₇	—	4	1	no	—
326	C₂×C₄×C₆₇	C₄×D₄	1	2	yes	—
327	C₂×C₄×C₆₇	#120	1	2	yes	—
328	C₂×C₄×C₆₇	#120	1	2	yes	—
329	C₂×C₄×C₆₇	#135	1	2	yes	—
330	C₂×C₄×C₆₇	#135	1	2	yes	—
331	C₂×C₄×C₆₇	#137	1	2	yes	—
332	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
333	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
334	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
335	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
336	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
337	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
338	C₈×C₆₇	—	2	2	no	—
339	C₈×C₆₇	—	2	2	no	—
340	C₈×C₆₇	—	4	1	no	—
341	C₈×C₆₇	—	4	1	no	—
342	C₂²×C₆₇	—	2	2	no	—
343	C₂²×C₆₇	—	2	2	no	—
344	C₂²×C₆₇	—	2	2	no	—
345	C₂²×C₆₇	—	2	4	no	—
346	C₂²×C₆₇	—	4	1	no	—
347	C₂²×C₆₇	—	4	2	no	—
348	C₂²×C₆₇	—	4	1	no	—
349	C₂²×C₆₇	—	4	2	no	—
350	C₂²×C₆₇	—	4	2	no	—
351	C₂²×C₆₇	—	4	2	no	—
352	C₂²×C₆₇	—	4	1	no	—
353	C₂²×C₆₇	—	4	2	no	—
354	C₂²×C₆₇	—	4	1	no	—
355	C₂²×C₆₇	—	4	2	no	—
356	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
357	C₂²×C₆₇	C₂×#120	1	1	yes	characteristic
358	C₂²×C₆₇	#525	1	1	yes	characteristic
359	C₂²×C₆₇	C₂×#135	1	1	yes	characteristic
360	C₂²×C₆₇	C₂×#135	1	1	yes	characteristic
361	C₂²×C₆₇	C₂×#137	1	1	yes	characteristic
362	C₂²×C₆₇	#575	1	1	yes	characteristic
363	C₄×C₆₇	—	2	2	no	—
364	C₄×C₆₇	—	2	2	no	—
365	C₄×C₆₇	—	2	2	no	—
366	C₄×C₆₇	—	2	4	no	—
367	C₄×C₆₇	—	4	2	no	—
368	C₄×C₆₇	—	4	1	no	—
369	C₄×C₆₇	—	4	2	no	—
370	C₄×C₆₇	—	4	2	no	—
371	C₄×C₆₇	—	4	2	no	—
372	C₄×C₆₇	—	8	1	no	—
373	C₄×C₆₇	—	8	1	no	—
374	C₄×C₆₇	#452	1	4	yes	direct product factor
375	C₄×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
376	C₄×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
377	C₄×C₆₇	#525	1	1	yes	characteristic
378	C₄×C₆₇	#525	1	1	yes	characteristic
379	C₄×#452	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
380	C₂×C₆₇	—	4	2	no	—
381	C₂×C₆₇	—	4	4	no	—
382	C₂×C₆₇	C₄×#120	1	1	yes	characteristic
383	C₂×C₆₇	C₄×#135	1	1	yes	characteristic
384	C₂×C₆₇	C₄×#137	1	1	yes	characteristic
385	C₂×C₆₇	C₂×#452	1	1	yes	characteristic
386	C₂×C₆₇	#3002	1	1	yes	characteristic
387	C₂×C₆₇	#3102	1	1	yes	characteristic
388	C₂×C₆₇	#3107	1	1	yes	characteristic
389	C₂×C₄×#41	C₂×C₆₇	1	1	yes	characteristic
390	C₂×#452	C₂×C₆₇	1	1	yes	characteristic
391	C₂×C₄×Q₁₆	C₂×C₆₇	1	1	yes	characteristic, complemented
392	C₂×C₄×SD₁₆	C₂×C₆₇	1	1	yes	characteristic, complemented
393	C₄×C₂²⋊Q₈	C₂×C₆₇	1	1	yes	characteristic, complemented
394	#1878	C₂×C₆₇	1	1	yes	characteristic, complemented
395	#1877	C₂×C₆₇	1	1	yes	characteristic, complemented
396	#1873	C₂×C₆₇	1	1	yes	characteristic, complemented
397	#1865	C₂×C₆₇	1	1	yes	characteristic, complemented
398	#1862	C₂×C₆₇	1	1	yes	characteristic, complemented
399	#1854	C₂×C₆₇	1	1	yes	characteristic, complemented
400	#1788	C₂×C₆₇	1	1	yes	characteristic
401	C₄×#103	C₂×C₆₇	1	1	yes	characteristic, complemented
402	C₄×#102	C₂×C₆₇	1	1	yes	characteristic, complemented
403	C₄×C₂²⋊C₈	C₂×C₆₇	1	1	yes	characteristic, complemented
404	C₆₇	C₄×#452	1	1	yes	characteristic, direct product factor, Sylow
405	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
406	C₂²×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic
407	C₂²×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic
408	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
409	C₄×#41	—	2	4	no	—
410	C₄×#41	—	2	4	no	—
411	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
412	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
413	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
414	C₂×C₄×D₄	—	2	1	no	—
415	C₂×C₄×D₄	—	2	1	no	—
416	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
417	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
418	C₂×#117	—	2	1	no	—
419	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
420	C₂²×C₄²	—	2	1	no	—
421	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
422	#452	C₄×C₆₇	1	8	yes	direct product factor
423	C₄×Q₁₆	—	2	4	no	—
424	C₄×SD₁₆	—	2	4	no	—
425	C₂×#107	C₂²×C₆₇	1	1	yes	characteristic
426	C₂×#106	C₂²×C₆₇	1	1	yes	characteristic
427	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic
428	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic
429	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic
430	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic
431	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic
432	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
433	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
434	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
435	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
436	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
437	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic
438	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic
439	#391	C₂²×C₆₇	1	1	yes	characteristic
440	#389	C₂²×C₆₇	1	1	yes	characteristic
441	#387	—	2	1	no	—
442	#385	—	2	1	no	—
443	#380	C₂²×C₆₇	1	1	yes	characteristic
444	C₄×C₄⋊C₄	—	2	1	no	—
445	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
446	C₄×C₂²⋊C₄	—	2	1	no	—
447	#340	C₂²×C₆₇	1	1	yes	characteristic
448	#340	C₂²×C₆₇	1	1	yes	characteristic
449	#340	C₂²×C₆₇	1	1	yes	characteristic
450	#340	C₂²×C₆₇	1	1	yes	characteristic
451	#336	C₂²×C₆₇	1	1	yes	characteristic
452	#336	C₂²×C₆₇	1	1	yes	characteristic
453	C₂×#41	—	2	2	no	—
454	C₂×#41	—	2	2	no	—
455	C₂×#41	—	2	2	no	—
456	C₂×#41	—	2	2	no	—
457	C₂×#41	—	2	2	no	—
458	C₂×#41	C₂×C₄×C₆₇	1	4	yes	—
459	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
460	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
461	C₂²×D₄	—	2	1	no	—
462	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
463	C₂³×C₄	—	2	1	no	—
464	C₂³×C₄	—	2	1	no	—
465	C₂³×C₄	—	2	1	no	—
466	C₂³×C₄	D₄×C₆₇	1	1	yes	characteristic
467	C₂³×C₄	D₄×C₆₇	1	1	yes	characteristic
468	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
469	C₂×Q₁₆	—	2	2	no	—
470	C₂×Q₁₆	—	2	2	no	—
471	C₂×Q₁₆	C₂×C₄×C₆₇	1	4	yes	complemented
472	C₂×SD₁₆	—	2	2	no	—
473	C₂×SD₁₆	—	2	2	no	—
474	C₂×SD₁₆	C₂×C₄×C₆₇	1	4	yes	complemented
475	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
476	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
477	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
478	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
479	C₂²⋊Q₈	—	2	2	no	—
480	C₂²⋊Q₈	C₂×C₄×C₆₇	1	4	yes	complemented
481	C₄×Q₈	—	2	2	no	—
482	C₄×Q₈	—	2	2	no	—
483	C₄×Q₈	—	2	2	no	—
484	C₄×Q₈	—	2	2	no	—
485	C₄×Q₈	—	2	2	no	—
486	C₄×Q₈	D₄×C₆₇	1	4	yes	—
487	C₄×D₄	—	2	8	no	—
488	C₄×D₄	—	2	8	no	—
489	C₄×D₄	—	2	2	no	—
490	C₄×D₄	—	2	2	no	—
491	C₄×D₄	—	2	2	no	—
492	C₄×D₄	D₄×C₆₇	1	4	yes	—
493	#117	—	2	8	no	—
494	#117	—	2	2	no	—
495	#117	—	2	2	no	—
496	C₂×C₄⋊C₄	—	2	1	no	—
497	C₂×C₄⋊C₄	—	2	1	no	—
498	C₂×C₄⋊C₄	—	2	1	no	—
499	C₂×C₄⋊C₄	—	2	1	no	—
500	C₂×C₄⋊C₄	—	2	1	no	—
501	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
502	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
503	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
504	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
505	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
506	C₂×C₂²⋊C₄	—	2	1	no	—
507	C₂×C₂²⋊C₄	—	2	1	no	—
508	C₂×C₂²⋊C₄	—	2	1	no	—
509	C₂×C₂²⋊C₄	—	2	1	no	—
510	C₂×C₂²⋊C₄	—	2	1	no	—
511	C₂×C₄²	—	2	8	no	—
512	C₂×C₄²	—	2	1	no	—
513	C₂×C₄²	—	2	1	no	—
514	C₂×C₄²	—	2	1	no	—
515	C₂×C₄²	—	2	2	no	—
516	C₂×C₄²	—	2	2	no	—
517	C₂×C₄²	—	2	1	no	—
518	C₂×C₄²	—	2	1	no	—
519	C₂×C₄²	D₄×C₆₇	1	1	yes	characteristic
520	C₂×C₄²	D₄×C₆₇	1	1	yes	characteristic
521	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
522	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
523	#107	—	2	2	no	—
524	#106	—	2	2	no	—
525	#103	—	2	2	no	—
526	#103	—	2	2	no	—
527	#103	—	2	2	no	—
528	#103	—	2	2	no	—
529	#103	C₂×C₄×C₆₇	1	4	yes	complemented
530	#102	—	2	2	no	—
531	#102	—	2	2	no	—
532	#102	C₂×C₄×C₆₇	1	4	yes	complemented
533	C₂²⋊C₈	—	2	2	no	—
534	C₂²⋊C₈	C₂×C₄×C₆₇	1	4	yes	complemented
535	C₄×C₈	—	2	2	no	—
536	C₄×C₈	—	2	2	no	—
537	#95	—	2	1	no	—
538	#95	—	2	1	no	—
539	#95	—	2	1	no	—
540	#95	—	2	1	no	—
541	#95	—	2	1	no	—
542	C₂⁴	—	2	1	no	—
543	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
544	#41	—	2	8	no	—
545	#41	—	2	8	no	—
546	#41	—	2	8	no	—
547	#41	—	2	8	no	—
548	C₂×Q₈	—	2	1	no	—
549	C₂×Q₈	—	2	1	no	—
550	C₂×Q₈	—	2	1	no	—
551	C₂×Q₈	—	2	1	no	—
552	C₂×Q₈	—	2	1	no	—
553	C₂×Q₈	—	2	1	no	—
554	C₂×Q₈	—	2	1	no	—
555	C₂×Q₈	—	2	1	no	—
556	C₂×Q₈	C₂²×C₄×C₆₇	1	2	yes	—
557	C₂×Q₈	C₂²×C₄×C₆₇	1	2	yes	—
558	C₂×Q₈	C₂×D₄×C₆₇	1	2	yes	—
559	C₂×Q₈	#41×C₆₇	1	2	yes	—
560	C₂×D₄	—	2	4	no	—
561	C₂×D₄	—	2	4	no	—
562	C₂×D₄	—	2	4	no	—
563	C₂×D₄	—	2	1	no	—
564	C₂×D₄	—	2	1	no	—
565	C₂×D₄	—	2	1	no	—
566	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
567	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
568	C₂×D₄	#41×C₆₇	1	2	yes	—
569	C₂²×C₄	—	2	4	no	—
570	C₂²×C₄	—	2	4	no	—
571	C₂²×C₄	—	2	1	no	—
572	C₂²×C₄	—	2	4	no	—
573	C₂²×C₄	—	2	1	no	—
574	C₂²×C₄	—	2	1	no	—
575	C₂²×C₄	—	2	1	no	—
576	C₂²×C₄	—	2	1	no	—
577	C₂²×C₄	—	2	4	no	—
578	C₂²×C₄	—	2	1	no	—
579	C₂²×C₄	—	2	1	no	—
580	C₂²×C₄	—	2	1	no	—
581	C₂²×C₄	—	2	1	no	—
582	C₂²×C₄	—	2	2	no	—
583	C₂²×C₄	—	2	2	no	—
584	C₂²×C₄	—	2	4	no	—
585	C₂²×C₄	—	2	2	no	—
586	C₂²×C₄	—	2	2	no	—
587	C₂²×C₄	—	2	2	no	—
588	C₂²×C₄	—	2	1	no	—
589	C₂²×C₄	—	2	1	no	—
590	C₂²×C₄	—	4	1	no	—
591	C₂²×C₄	—	4	2	no	—
592	C₂²×C₄	—	4	2	no	—
593	C₂²×C₄	—	4	2	no	—
594	C₂²×C₄	—	4	2	no	—
595	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
596	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
597	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
598	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
599	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
600	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
601	C₂²×C₄	#41×C₆₇	1	2	yes	—
602	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
603	Q₁₆	—	2	8	no	—
604	SD₁₆	—	2	8	no	—
605	C₂×C₈	—	2	1	no	—
606	C₂×C₈	—	2	1	no	—
607	C₂×C₈	—	2	1	no	—
608	C₂×C₈	—	2	1	no	—
609	C₂×C₈	—	2	1	no	—
610	C₂×C₈	—	2	1	no	—
611	C₂×C₈	—	2	1	no	—
612	C₂×C₈	—	2	1	no	—
613	C₂×C₈	—	2	1	no	—
614	C₂×C₈	—	2	1	no	—
615	C₂×C₈	C₂²×C₄×C₆₇	1	2	yes	—
616	C₂×C₈	C₂²×C₄×C₆₇	1	2	yes	—
617	C₄⋊C₄	—	2	4	no	—
618	C₄⋊C₄	—	2	4	no	—
619	C₄⋊C₄	—	2	4	no	—
620	C₄⋊C₄	—	2	1	no	—
621	C₄⋊C₄	—	2	1	no	—
622	C₄⋊C₄	—	2	1	no	—
623	C₄⋊C₄	—	2	1	no	—
624	C₄⋊C₄	—	2	1	no	—
625	C₄⋊C₄	—	2	1	no	—
626	C₄⋊C₄	—	2	1	no	—
627	C₄⋊C₄	—	4	2	no	—
628	C₄⋊C₄	—	4	2	no	—
629	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
630	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
631	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
632	C₂²⋊C₄	—	2	4	no	—
633	C₂²⋊C₄	—	2	4	no	—
634	C₂²⋊C₄	—	2	4	no	—
635	C₂²⋊C₄	—	2	4	no	—
636	C₂²⋊C₄	—	4	2	no	—
637	C₄²	—	2	4	no	—
638	C₄²	—	2	4	no	—
639	C₄²	—	2	2	no	—
640	C₄²	—	2	4	no	—
641	C₄²	—	2	2	no	—
642	C₄²	—	2	1	no	—
643	C₄²	—	2	1	no	—
644	C₄²	—	4	2	no	—
645	C₄²	—	4	2	no	—
646	C₄²	C₂×D₄×C₆₇	1	2	yes	—
647	C₄²	C₂×D₄×C₆₇	1	2	yes	—
648	C₂³	—	2	2	no	—
649	C₂³	—	2	1	no	—
650	C₂³	—	2	2	no	—
651	C₂³	—	2	1	no	—
652	C₂³	—	2	2	no	—
653	C₂³	—	2	1	no	—
654	C₂³	—	2	1	no	—
655	C₂³	—	2	1	no	—
656	C₂³	—	2	1	no	—
657	C₂³	—	4	1	no	—
658	C₂³	—	4	1	no	—
659	C₂³	—	4	1	no	—
660	C₂³	—	4	1	no	—
661	C₂³	C₄×D₄×C₆₇	1	2	yes	—
662	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
663	Q₈	—	2	2	no	—
664	Q₈	—	2	2	no	—
665	Q₈	—	2	2	no	—
666	Q₈	—	2	2	no	—
667	Q₈	—	2	2	no	—
668	Q₈	—	4	1	no	—
669	Q₈	—	4	1	no	—
670	Q₈	C₄×D₄×C₆₇	1	4	yes	—
671	D₄	—	2	16	no	—
672	D₄	—	2	2	no	—
673	D₄	—	2	2	no	—
674	D₄	—	2	2	no	—
675	D₄	C₄×D₄×C₆₇	1	4	yes	—
676	C₂×C₄	—	2	16	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	1	no	—
679	C₂×C₄	—	2	1	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	1	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	1	no	—
684	C₂×C₄	—	2	1	no	—
685	C₂×C₄	—	2	1	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	1	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	1	no	—
696	C₂×C₄	—	2	1	no	—
697	C₂×C₄	—	4	4	no	—
698	C₂×C₄	—	4	8	no	—
699	C₂×C₄	—	4	1	no	—
700	C₂×C₄	—	4	1	no	—
701	C₂×C₄	—	4	1	no	—
702	C₂×C₄	—	4	1	no	—
703	C₂×C₄	—	4	1	no	—
704	C₂×C₄	—	4	1	no	—
705	C₂×C₄	—	4	1	no	—
706	C₂×C₄	—	4	1	no	—
707	C₂×C₄	—	4	4	no	—
708	C₂×C₄	—	4	8	no	—
709	C₂×C₄	—	4	1	no	—
710	C₂×C₄	—	4	1	no	—
711	C₂×C₄	—	4	1	no	—
712	C₂×C₄	—	4	1	no	—
713	C₂×C₄	—	4	1	no	—
714	C₂×C₄	—	4	1	no	—
715	C₂×C₄	C₄×D₄×C₆₇	1	2	yes	—
716	C₂×C₄	#120×C₆₇	1	2	yes	—
717	C₂×C₄	#120×C₆₇	1	2	yes	—
718	C₂×C₄	#135×C₆₇	1	2	yes	—
719	C₂×C₄	#135×C₆₇	1	2	yes	—
720	C₂×C₄	#137×C₆₇	1	2	yes	—
721	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
722	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
723	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
724	C₂×C₄	C₂×#41×C₆₇	1	1	yes	characteristic
725	C₂×C₄	C₂×#41×C₆₇	1	1	yes	characteristic
726	C₂×C₄	C₂×#41×C₆₇	1	1	yes	characteristic
727	C₈	—	2	2	no	—
728	C₈	—	2	2	no	—
729	C₈	—	4	1	no	—
730	C₈	—	4	1	no	—
731	C₂²	—	2	2	no	—
732	C₂²	—	2	4	no	—
733	C₂²	—	2	2	no	—
734	C₂²	—	2	2	no	—
735	C₂²	—	4	1	no	—
736	C₂²	—	4	2	no	—
737	C₂²	—	4	1	no	—
738	C₂²	—	4	2	no	—
739	C₂²	—	4	2	no	—
740	C₂²	—	4	2	no	—
741	C₂²	—	4	1	no	—
742	C₂²	—	4	2	no	—
743	C₂²	—	4	1	no	—
744	C₂²	—	4	2	no	—
745	C₂²	C₂×C₄×D₄×C₆₇	1	1	yes	characteristic
746	C₂²	C₂×#120×C₆₇	1	1	yes	characteristic
747	C₂²	#525×C₆₇	1	1	yes	characteristic
748	C₂²	C₂×#135×C₆₇	1	1	yes	characteristic
749	C₂²	C₂×#135×C₆₇	1	1	yes	characteristic
750	C₂²	C₂×#137×C₆₇	1	1	yes	characteristic
751	C₂²	#575×C₆₇	1	1	yes	characteristic
752	C₄	—	2	2	no	—
753	C₄	—	2	4	no	—
754	C₄	—	2	2	no	—
755	C₄	—	2	2	no	—
756	C₄	—	4	2	no	—
757	C₄	—	4	2	no	—
758	C₄	—	4	1	no	—
759	C₄	—	4	2	no	—
760	C₄	—	4	2	no	—
761	C₄	—	8	1	no	—
762	C₄	—	8	1	no	—
763	C₄	#452×C₆₇	1	4	yes	direct product factor
764	C₄	C₂×C₄×D₄×C₆₇	1	1	yes	characteristic
765	C₄	C₂×C₄×D₄×C₆₇	1	1	yes	characteristic
766	C₄	#525×C₆₇	1	1	yes	characteristic
767	C₄	#525×C₆₇	1	1	yes	characteristic
768	C₂	—	4	2	no	—
769	C₂	—	4	4	no	—
770	C₂	C₄×#120×C₆₇	1	1	yes	characteristic
771	C₂	C₄×#135×C₆₇	1	1	yes	characteristic
772	C₂	C₄×#137×C₆₇	1	1	yes	characteristic
773	C₂	C₂×#452×C₆₇	1	1	yes	characteristic
774	C₂	C₆₇×#3002	1	1	yes	characteristic
775	C₂	C₆₇×#3102	1	1	yes	characteristic
776	C₂	C₆₇×#3107	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₆₇	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₆₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₇
socle	C₂³×C₆₇	C₂²×D₄
prime radical	C₂²×#41×C₆₇	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₆₇ ◁ C₂²×C₄²×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×C₄×Q₁₆×C₆₇	C₂	semidirect
4. C₂×C₄×SD₁₆×C₆₇	C₂	semidirect
5. C₄×C₂²⋊Q₈×C₆₇	C₂	semidirect
6. C₆₇×#1878	C₂	semidirect
7. C₆₇×#1877	C₂	semidirect
8. C₆₇×#1873	C₂	semidirect
9. C₆₇×#1865	C₂	semidirect
10. C₆₇×#1862	C₂	semidirect
11. C₆₇×#1854	C₂	semidirect
13. C₄×#103×C₆₇	C₂	semidirect
14. C₄×#102×C₆₇	C₂	semidirect
15. C₄×C₂²⋊C₈×C₆₇	C₂	semidirect
33. #452×C₆₇	C₄	direct (N × H)
82. C₂×Q₁₆×C₆₇	C₂×C₄	semidirect
85. C₂×SD₁₆×C₆₇	C₂×C₄	semidirect
91. C₂²⋊Q₈×C₆₇	C₂×C₄	semidirect
140. #103×C₆₇	C₂×C₄	semidirect
143. #102×C₆₇	C₂×C₄	semidirect
145. C₂²⋊C₈×C₆₇	C₂×C₄	semidirect
374. C₄×C₆₇	#452	direct (N × H)
379. C₄×#452	C₆₇	direct (N × H)
391. C₂×C₄×Q₁₆	C₂×C₆₇	semidirect
392. C₂×C₄×SD₁₆	C₂×C₆₇	semidirect
393. C₄×C₂²⋊Q₈	C₂×C₆₇	semidirect
394. #1878	C₂×C₆₇	semidirect
395. #1877	C₂×C₆₇	semidirect
396. #1873	C₂×C₆₇	semidirect
397. #1865	C₂×C₆₇	semidirect
398. #1862	C₂×C₆₇	semidirect
399. #1854	C₂×C₆₇	semidirect
401. C₄×#103	C₂×C₆₇	semidirect
402. C₄×#102	C₂×C₆₇	semidirect
403. C₄×C₂²⋊C₈	C₂×C₆₇	semidirect
404. C₆₇	C₄×#452	direct (N × H)
422. #452	C₄×C₆₇	direct (N × H)
471. C₂×Q₁₆	C₂×C₄×C₆₇	semidirect
474. C₂×SD₁₆	C₂×C₄×C₆₇	semidirect
480. C₂²⋊Q₈	C₂×C₄×C₆₇	semidirect
529. #103	C₂×C₄×C₆₇	semidirect
532. #102	C₂×C₄×C₆₇	semidirect
534. C₂²⋊C₈	C₂×C₄×C₆₇	semidirect
763. C₄	#452×C₆₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄×#41×C₆₇	2
C₂×#452×C₆₇	2
C₂×C₄×Q₁₆×C₆₇	2
C₂×C₄×SD₁₆×C₆₇	2
C₄×C₂²⋊Q₈×C₆₇	2
C₆₇×#1878	2
C₆₇×#1877	2
C₆₇×#1873	2
C₆₇×#1865	2
C₆₇×#1862	2
C₆₇×#1854	2
C₆₇×#1788	2
C₄×#103×C₆₇	2
C₄×#102×C₆₇	2
C₄×C₂²⋊C₈×C₆₇	2
C₄×#452	67

Subgroups — C4×#452×C67 #30700702

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#452×C₆₇ #30700702