Subgroups — C₆₇×#59421 #30738672

Order 17152.

2384 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#556×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₄×Q₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#2702	C₂	1	4	yes	maximal, complemented
4	C₆₇×#2582	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#2560	C₂	1	4	yes	maximal, complemented
6	C₆₇×#2537	C₂	1	1	yes	maximal, characteristic
7	C₆₇×#2492	C₂	1	2	yes	maximal, complemented
8	C₆₇×#2439	C₂	1	2	yes	maximal, complemented
9	C₆₇×#2436	C₂	1	2	yes	maximal, complemented
10	C₆₇×#2427	C₂	1	2	yes	maximal, complemented
11	C₆₇×#2426	C₂	1	2	yes	maximal, complemented
12	C₆₇×#2421	C₂	1	2	yes	maximal, complemented
13	C₆₇×#2363	C₂	1	2	yes	maximal, complemented
14	Q₈×C₂²⋊C₄×C₆₇	C₂	1	2	yes	maximal, complemented
15	C₄×C₄⋊Q₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×#124×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×#124×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂³×Q₈×C₆₇	C₂²	1	2	yes	—
19	#556×C₆₇	—	2	8	no	—
20	D₄×Q₈×C₆₇	—	2	8	no	—
21	C₂×C₄⋊Q₈×C₆₇	C₂²	1	2	yes	—
22	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
23	C₂×#126×C₆₇	C₂²	1	4	yes	—
24	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic
25	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic
26	C₂×#124×C₆₇	C₂²	1	2	yes	—
27	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	4	yes	—
28	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
29	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
30	C₂×#121×C₆₇	C₂²	1	2	yes	—
31	C₂×#121×C₆₇	C₂²	1	2	yes	—
32	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
33	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
34	C₂×C₄×Q₈×C₆₇	C₂²	1	2	yes	—
35	C₂×C₄×Q₈×C₆₇	C₂²	1	2	yes	—
36	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
37	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
38	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
39	C₂×#117×C₆₇	C₂²	1	2	yes	—
40	#400×C₆₇	C₂²	1	4	yes	—
41	#398×C₆₇	C₂²	1	4	yes	—
42	#397×C₆₇	C₂²	1	4	yes	—
43	#396×C₆₇	C₂²	1	4	yes	—
44	#394×C₆₇	C₂²	1	4	yes	—
45	#394×C₆₇	C₂²	1	4	yes	—
46	#393×C₆₇	C₂²	1	4	yes	—
47	#393×C₆₇	C₂²	1	4	yes	—
48	#391×C₆₇	C₂²	1	1	yes	characteristic
49	#391×C₆₇	C₂²	1	1	yes	characteristic
50	#391×C₆₇	C₂²	1	4	yes	—
51	#391×C₆₇	C₂²	1	2	yes	—
52	#391×C₆₇	C₂²	1	2	yes	—
53	#391×C₆₇	C₂²	1	2	yes	—
54	#391×C₆₇	C₂²	1	4	yes	—
55	#390×C₆₇	C₂²	1	1	yes	characteristic
56	#390×C₆₇	C₂²	1	1	yes	characteristic
57	#390×C₆₇	C₂²	1	4	yes	—
58	#389×C₆₇	C₂²	1	2	yes	—
59	#389×C₆₇	C₂²	1	2	yes	—
60	#389×C₆₇	C₂²	1	2	yes	—
61	#389×C₆₇	C₂²	1	2	yes	—
62	#388×C₆₇	C₂²	1	2	yes	—
63	#388×C₆₇	C₂²	1	2	yes	—
64	#388×C₆₇	C₂²	1	2	yes	—
65	#388×C₆₇	C₂²	1	2	yes	—
66	#388×C₆₇	C₂²	1	4	yes	—
67	#388×C₆₇	C₂²	1	4	yes	—
68	#387×C₆₇	C₂²	1	4	yes	—
69	#386×C₆₇	C₂²	1	4	yes	—
70	#386×C₆₇	C₂²	1	4	yes	—
71	#384×C₆₇	C₂²	1	1	yes	characteristic
72	#382×C₆₇	C₂²	1	1	yes	characteristic
73	#382×C₆₇	C₂²	1	1	yes	characteristic
74	#380×C₆₇	C₂²	1	2	yes	—
75	#380×C₆₇	C₂²	1	2	yes	—
76	#380×C₆₇	C₂²	1	4	yes	—
77	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
78	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
79	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
80	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
81	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
82	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
83	C₄×C₂²⋊C₄×C₆₇	C₂²	1	4	yes	—
84	C₄³×C₆₇	C₂²	1	1	yes	characteristic
85	C₂²×Q₈×C₆₇	—	2	8	no	—
86	C₂²×Q₈×C₆₇	—	2	8	no	—
87	C₂²×Q₈×C₆₇	—	4	4	no	—
88	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
89	C₂²×Q₈×C₆₇	C₂³	1	4	yes	—
90	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
91	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
92	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
93	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
94	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
95	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
96	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
97	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
98	C₄⋊Q₈×C₆₇	—	2	8	no	—
99	C₄⋊Q₈×C₆₇	D₄	1	8	yes	complemented
100	#126×C₆₇	—	2	16	no	—
101	#124×C₆₇	—	2	8	no	—
102	#124×C₆₇	—	2	4	no	—
103	#124×C₆₇	—	2	4	no	—
104	C₂²⋊Q₈×C₆₇	—	2	8	no	—
105	C₂²⋊Q₈×C₆₇	—	2	16	no	—
106	C₂²⋊Q₈×C₆₇	—	2	8	no	—
107	#121×C₆₇	—	2	8	no	—
108	#121×C₆₇	—	4	4	no	—
109	C₄×Q₈×C₆₇	—	2	8	no	—
110	C₄×Q₈×C₆₇	—	2	4	no	—
111	C₄×Q₈×C₆₇	—	2	4	no	—
112	C₄×Q₈×C₆₇	—	4	4	no	—
113	C₄×D₄×C₆₇	—	2	8	no	—
114	C₄×D₄×C₆₇	—	2	4	no	—
115	C₄×D₄×C₆₇	—	2	4	no	—
116	#117×C₆₇	—	2	8	no	—
117	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
118	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
119	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
120	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
121	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
122	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
123	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
124	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
125	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
126	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
127	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
128	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
129	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
130	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
131	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
132	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
133	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
134	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
135	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
136	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
137	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	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	4	yes	—
145	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
146	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
147	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
148	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
149	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
150	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
151	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
152	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
153	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
154	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
155	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
156	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
157	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
158	#95×C₆₇	C₂³	1	2	yes	—
159	#95×C₆₇	C₂³	1	2	yes	—
160	#95×C₆₇	C₂³	1	2	yes	—
161	#95×C₆₇	C₂³	1	2	yes	—
162	#95×C₆₇	C₂³	1	2	yes	—
163	#95×C₆₇	C₂³	1	2	yes	—
164	#95×C₆₇	C₂³	1	4	yes	—
165	#95×C₆₇	C₂³	1	2	yes	—
166	#95×C₆₇	C₂³	1	2	yes	—
167	#95×C₆₇	C₂³	1	4	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	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
173	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
174	C₂×Q₈×C₆₇	—	2	2	no	—
175	C₂×Q₈×C₆₇	—	2	2	no	—
176	C₂×Q₈×C₆₇	—	2	8	no	—
177	C₂×Q₈×C₆₇	—	2	4	no	—
178	C₂×Q₈×C₆₇	—	2	2	no	—
179	C₂×Q₈×C₆₇	—	2	8	no	—
180	C₂×Q₈×C₆₇	—	2	4	no	—
181	C₂×Q₈×C₆₇	—	2	2	no	—
182	C₂×Q₈×C₆₇	—	2	2	no	—
183	C₂×Q₈×C₆₇	—	4	4	no	—
184	C₂×Q₈×C₆₇	—	4	32	no	—
185	C₂×Q₈×C₆₇	C₂×D₄	1	8	yes	—
186	C₂×Q₈×C₆₇	#41	1	4	yes	—
187	C₂×D₄×C₆₇	—	2	8	no	—
188	C₂×D₄×C₆₇	—	2	2	no	—
189	C₂×D₄×C₆₇	—	2	2	no	—
190	C₂×D₄×C₆₇	—	2	2	no	—
191	C₂×D₄×C₆₇	—	2	2	no	—
192	C₂×D₄×C₆₇	—	2	2	no	—
193	C₂×D₄×C₆₇	—	4	4	no	—
194	C₂×D₄×C₆₇	—	4	4	no	—
195	C₂×D₄×C₆₇	#41	1	4	yes	—
196	C₂²×C₄×C₆₇	—	2	4	no	—
197	C₂²×C₄×C₆₇	—	2	8	no	—
198	C₂²×C₄×C₆₇	—	2	4	no	—
199	C₂²×C₄×C₆₇	—	2	4	no	—
200	C₂²×C₄×C₆₇	—	2	8	no	—
201	C₂²×C₄×C₆₇	—	2	4	no	—
202	C₂²×C₄×C₆₇	—	2	4	no	—
203	C₂²×C₄×C₆₇	—	2	4	no	—
204	C₂²×C₄×C₆₇	—	4	4	no	—
205	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
206	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
207	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
208	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
209	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
210	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
211	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
212	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
213	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
214	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
215	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
216	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
217	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
218	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
219	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
220	C₄⋊C₄×C₆₇	—	2	2	no	—
221	C₄⋊C₄×C₆₇	—	2	2	no	—
222	C₄⋊C₄×C₆₇	—	2	2	no	—
223	C₄⋊C₄×C₆₇	—	2	4	no	—
224	C₄⋊C₄×C₆₇	—	2	2	no	—
225	C₄⋊C₄×C₆₇	—	2	8	no	—
226	C₄⋊C₄×C₆₇	—	2	4	no	—
227	C₄⋊C₄×C₆₇	—	2	8	no	—
228	C₄⋊C₄×C₆₇	—	2	4	no	—
229	C₄⋊C₄×C₆₇	—	2	4	no	—
230	C₄⋊C₄×C₆₇	—	4	2	no	—
231	C₄⋊C₄×C₆₇	—	4	4	no	—
232	C₄⋊C₄×C₆₇	—	4	4	no	—
233	C₄⋊C₄×C₆₇	C₂×D₄	1	8	yes	—
234	C₄⋊C₄×C₆₇	C₂×D₄	1	8	yes	—
235	C₂²⋊C₄×C₆₇	—	2	8	no	—
236	C₂²⋊C₄×C₆₇	—	2	4	no	—
237	C₂²⋊C₄×C₆₇	—	2	4	no	—
238	C₂²⋊C₄×C₆₇	—	2	8	no	—
239	C₂²⋊C₄×C₆₇	—	2	8	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	—	4	2	no	—
248	C₂²⋊C₄×C₆₇	—	4	2	no	—
249	C₂²⋊C₄×C₆₇	—	4	4	no	—
250	C₄²×C₆₇	—	2	8	no	—
251	C₄²×C₆₇	—	2	4	no	—
252	C₄²×C₆₇	—	2	4	no	—
253	C₄²×C₆₇	—	2	2	no	—
254	C₄²×C₆₇	—	2	2	no	—
255	C₄²×C₆₇	—	2	2	no	—
256	C₄²×C₆₇	—	2	2	no	—
257	C₄²×C₆₇	—	2	2	no	—
258	C₄²×C₆₇	—	4	1	no	—
259	C₄²×C₆₇	—	4	4	no	—
260	C₄²×C₆₇	C₂×D₄	1	4	yes	—
261	C₂³×C₆₇	—	2	2	no	—
262	C₂³×C₆₇	—	2	2	no	—
263	C₂³×C₆₇	—	2	2	no	—
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	2	no	—
269	C₂³×C₆₇	—	2	2	no	—
270	C₂³×C₆₇	—	2	2	no	—
271	C₂³×C₆₇	—	2	2	no	—
272	C₂³×C₆₇	—	2	2	no	—
273	C₂³×C₆₇	—	2	2	no	—
274	C₂³×C₆₇	C₂×#41	1	4	yes	—
275	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
276	Q₈×C₆₇	—	2	8	no	—
277	Q₈×C₆₇	—	2	16	no	—
278	Q₈×C₆₇	—	4	16	no	—
279	Q₈×C₆₇	—	4	4	no	—
280	D₄×C₆₇	—	2	8	no	—
281	D₄×C₆₇	—	4	4	no	—
282	D₄×C₆₇	—	8	8	no	—
283	C₂×C₄×C₆₇	—	2	2	no	—
284	C₂×C₄×C₆₇	—	2	4	no	—
285	C₂×C₄×C₆₇	—	2	1	no	—
286	C₂×C₄×C₆₇	—	2	4	no	—
287	C₂×C₄×C₆₇	—	2	2	no	—
288	C₂×C₄×C₆₇	—	2	1	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	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	1	no	—
297	C₂×C₄×C₆₇	—	2	1	no	—
298	C₂×C₄×C₆₇	—	2	1	no	—
299	C₂×C₄×C₆₇	—	2	1	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	2	no	—
304	C₂×C₄×C₆₇	—	2	1	no	—
305	C₂×C₄×C₆₇	—	2	4	no	—
306	C₂×C₄×C₆₇	—	2	2	no	—
307	C₂×C₄×C₆₇	—	2	1	no	—
308	C₂×C₄×C₆₇	—	2	1	no	—
309	C₂×C₄×C₆₇	—	2	2	no	—
310	C₂×C₄×C₆₇	—	2	2	no	—
311	C₂×C₄×C₆₇	—	2	2	no	—
312	C₂×C₄×C₆₇	—	2	2	no	—
313	C₂×C₄×C₆₇	—	2	1	no	—
314	C₂×C₄×C₆₇	—	2	1	no	—
315	C₂×C₄×C₆₇	—	2	2	no	—
316	C₂×C₄×C₆₇	—	2	2	no	—
317	C₂×C₄×C₆₇	—	2	4	no	—
318	C₂×C₄×C₆₇	—	4	16	no	—
319	C₂×C₄×C₆₇	—	4	8	no	—
320	C₂×C₄×C₆₇	—	4	8	no	—
321	C₂×C₄×C₆₇	C₂²×D₄	1	8	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	C₂×#41	1	4	yes	—
326	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
327	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
328	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
329	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
330	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
331	C₂²×C₆₇	—	2	4	no	—
332	C₂²×C₆₇	—	2	4	no	—
333	C₂²×C₆₇	—	2	4	no	—
334	C₂²×C₆₇	—	4	2	no	—
335	C₂²×C₆₇	—	4	2	no	—
336	C₂²×C₆₇	—	4	2	no	—
337	C₂²×C₆₇	—	4	2	no	—
338	C₂²×C₆₇	—	4	2	no	—
339	C₂²×C₆₇	—	4	2	no	—
340	C₂²×C₆₇	—	4	2	no	—
341	C₂²×C₆₇	—	4	2	no	—
342	C₂²×C₆₇	—	4	2	no	—
343	C₂²×C₆₇	—	4	2	no	—
344	C₂²×C₆₇	—	4	2	no	—
345	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
346	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
347	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
348	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
349	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
350	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
351	C₂²×C₆₇	#585	1	1	yes	characteristic
352	C₄×C₆₇	—	2	4	no	—
353	C₄×C₆₇	—	2	8	no	—
354	C₄×C₆₇	—	2	2	no	—
355	C₄×C₆₇	—	2	2	no	—
356	C₄×C₆₇	—	4	2	no	—
357	C₄×C₆₇	—	4	2	no	—
358	C₄×C₆₇	—	4	2	no	—
359	C₄×C₆₇	—	4	1	no	—
360	C₄×C₆₇	—	4	2	no	—
361	C₄×C₆₇	—	4	2	no	—
362	C₄×C₆₇	—	4	1	no	—
363	C₄×C₆₇	—	4	4	no	—
364	C₄×C₆₇	—	4	1	no	—
365	C₄×C₆₇	#546	1	4	yes	—
366	C₄×C₆₇	#548	1	4	yes	—
367	#59421	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
368	C₂×C₆₇	—	4	4	no	—
369	C₂×C₆₇	—	8	2	no	—
370	C₂×C₆₇	C₂×#546	1	1	yes	characteristic
371	C₂×C₆₇	C₂×#548	1	1	yes	characteristic
372	C₂×C₆₇	#3482	1	1	yes	characteristic
373	C₂×C₆₇	#3497	1	1	yes	characteristic
374	C₂×C₆₇	#3514	1	1	yes	characteristic
375	C₂×C₆₇	#3518	1	1	yes	characteristic
376	C₂×C₆₇	#3552	1	1	yes	characteristic
377	C₂×#556	C₂×C₆₇	1	1	yes	characteristic, complemented
378	C₂×D₄×Q₈	C₂×C₆₇	1	1	yes	characteristic, complemented
379	#2702	C₂×C₆₇	1	4	yes	complemented
380	#2582	C₂×C₆₇	1	1	yes	characteristic, complemented
381	#2560	C₂×C₆₇	1	4	yes	complemented
382	#2537	C₂×C₆₇	1	1	yes	characteristic
383	#2492	C₂×C₆₇	1	2	yes	complemented
384	#2439	C₂×C₆₇	1	2	yes	complemented
385	#2436	C₂×C₆₇	1	2	yes	complemented
386	#2427	C₂×C₆₇	1	2	yes	complemented
387	#2426	C₂×C₆₇	1	2	yes	complemented
388	#2421	C₂×C₆₇	1	2	yes	complemented
389	#2363	C₂×C₆₇	1	2	yes	complemented
390	Q₈×C₂²⋊C₄	C₂×C₆₇	1	2	yes	complemented
391	C₄×C₄⋊Q₈	C₂×C₆₇	1	1	yes	characteristic, complemented
392	C₄×#124	C₂×C₆₇	1	1	yes	characteristic, complemented
393	C₄×#124	C₂×C₆₇	1	1	yes	characteristic, complemented
394	C₆₇	#59421	1	1	yes	characteristic, direct product factor, Sylow
395	C₂³×Q₈	C₂²×C₆₇	1	2	yes	—
396	#556	—	2	8	no	—
397	D₄×Q₈	—	2	8	no	—
398	C₂×C₄⋊Q₈	C₂²×C₆₇	1	2	yes	—
399	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
400	C₂×#126	C₂²×C₆₇	1	4	yes	—
401	C₂×#124	C₂²×C₆₇	1	2	yes	—
402	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic
403	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic
404	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	4	yes	—
405	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
406	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
407	C₂×#121	C₂²×C₆₇	1	2	yes	—
408	C₂×#121	C₂²×C₆₇	1	2	yes	—
409	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
410	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
411	C₂×C₄×Q₈	C₂²×C₆₇	1	2	yes	—
412	C₂×C₄×Q₈	C₂²×C₆₇	1	2	yes	—
413	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
414	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
415	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
416	C₂×#117	C₂²×C₆₇	1	2	yes	—
417	#400	C₂²×C₆₇	1	4	yes	—
418	#398	C₂²×C₆₇	1	4	yes	—
419	#397	C₂²×C₆₇	1	4	yes	—
420	#396	C₂²×C₆₇	1	4	yes	—
421	#394	C₂²×C₆₇	1	4	yes	—
422	#394	C₂²×C₆₇	1	4	yes	—
423	#393	C₂²×C₆₇	1	4	yes	—
424	#393	C₂²×C₆₇	1	4	yes	—
425	#391	C₂²×C₆₇	1	4	yes	—
426	#391	C₂²×C₆₇	1	2	yes	—
427	#391	C₂²×C₆₇	1	2	yes	—
428	#391	C₂²×C₆₇	1	2	yes	—
429	#391	C₂²×C₆₇	1	1	yes	characteristic
430	#391	C₂²×C₆₇	1	4	yes	—
431	#391	C₂²×C₆₇	1	1	yes	characteristic
432	#390	C₂²×C₆₇	1	4	yes	—
433	#390	C₂²×C₆₇	1	1	yes	characteristic
434	#390	C₂²×C₆₇	1	1	yes	characteristic
435	#389	C₂²×C₆₇	1	2	yes	—
436	#389	C₂²×C₆₇	1	2	yes	—
437	#389	C₂²×C₆₇	1	2	yes	—
438	#389	C₂²×C₆₇	1	2	yes	—
439	#388	C₂²×C₆₇	1	2	yes	—
440	#388	C₂²×C₆₇	1	2	yes	—
441	#388	C₂²×C₆₇	1	4	yes	—
442	#388	C₂²×C₆₇	1	4	yes	—
443	#388	C₂²×C₆₇	1	2	yes	—
444	#388	C₂²×C₆₇	1	2	yes	—
445	#387	C₂²×C₆₇	1	4	yes	—
446	#386	C₂²×C₆₇	1	4	yes	—
447	#386	C₂²×C₆₇	1	4	yes	—
448	#384	C₂²×C₆₇	1	1	yes	characteristic
449	#382	C₂²×C₆₇	1	1	yes	characteristic
450	#382	C₂²×C₆₇	1	1	yes	characteristic
451	#380	C₂²×C₆₇	1	2	yes	—
452	#380	C₂²×C₆₇	1	4	yes	—
453	#380	C₂²×C₆₇	1	2	yes	—
454	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
455	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
456	C₄×C₂²⋊C₄	C₂²×C₆₇	1	4	yes	—
457	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
458	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
459	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
460	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
461	C₄³	C₂²×C₆₇	1	1	yes	characteristic
462	C₂²×Q₈	—	2	8	no	—
463	C₂²×Q₈	—	2	8	no	—
464	C₂²×Q₈	—	4	4	no	—
465	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
466	C₂²×Q₈	C₂³×C₆₇	1	4	yes	—
467	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
468	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
469	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
470	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
471	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
472	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
473	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
474	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
475	C₄⋊Q₈	—	2	8	no	—
476	C₄⋊Q₈	D₄×C₆₇	1	8	yes	complemented
477	#126	—	2	16	no	—
478	#124	—	2	8	no	—
479	#124	—	2	4	no	—
480	#124	—	2	4	no	—
481	C₂²⋊Q₈	—	2	8	no	—
482	C₂²⋊Q₈	—	2	16	no	—
483	C₂²⋊Q₈	—	2	8	no	—
484	#121	—	2	8	no	—
485	#121	—	4	4	no	—
486	C₄×Q₈	—	2	8	no	—
487	C₄×Q₈	—	2	4	no	—
488	C₄×Q₈	—	2	4	no	—
489	C₄×Q₈	—	4	4	no	—
490	C₄×D₄	—	2	8	no	—
491	C₄×D₄	—	2	4	no	—
492	C₄×D₄	—	2	4	no	—
493	#117	—	2	8	no	—
494	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
495	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
496	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
497	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
498	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
499	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
500	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
501	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
502	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
503	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
504	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
505	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
506	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
507	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
508	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
509	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
510	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
511	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
512	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
513	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	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	2	yes	—
517	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
518	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
519	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
520	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
521	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
522	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
523	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
524	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
525	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
526	C₂×C₄²	C₂³×C₆₇	1	2	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	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
532	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
533	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
534	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
535	#95	C₂³×C₆₇	1	2	yes	—
536	#95	C₂³×C₆₇	1	2	yes	—
537	#95	C₂³×C₆₇	1	2	yes	—
538	#95	C₂³×C₆₇	1	2	yes	—
539	#95	C₂³×C₆₇	1	2	yes	—
540	#95	C₂³×C₆₇	1	2	yes	—
541	#95	C₂³×C₆₇	1	4	yes	—
542	#95	C₂³×C₆₇	1	2	yes	—
543	#95	C₂³×C₆₇	1	2	yes	—
544	#95	C₂³×C₆₇	1	4	yes	—
545	#95	C₂³×C₆₇	1	4	yes	—
546	#95	C₂³×C₆₇	1	4	yes	—
547	#95	C₂³×C₆₇	1	4	yes	—
548	#95	C₂³×C₆₇	1	4	yes	—
549	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
550	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
551	C₂×Q₈	—	2	2	no	—
552	C₂×Q₈	—	2	2	no	—
553	C₂×Q₈	—	2	8	no	—
554	C₂×Q₈	—	2	4	no	—
555	C₂×Q₈	—	2	2	no	—
556	C₂×Q₈	—	2	8	no	—
557	C₂×Q₈	—	2	4	no	—
558	C₂×Q₈	—	2	2	no	—
559	C₂×Q₈	—	2	2	no	—
560	C₂×Q₈	—	4	4	no	—
561	C₂×Q₈	—	4	32	no	—
562	C₂×Q₈	C₂×D₄×C₆₇	1	8	yes	—
563	C₂×Q₈	#41×C₆₇	1	4	yes	—
564	C₂×D₄	—	2	8	no	—
565	C₂×D₄	—	2	2	no	—
566	C₂×D₄	—	2	2	no	—
567	C₂×D₄	—	2	2	no	—
568	C₂×D₄	—	2	2	no	—
569	C₂×D₄	—	2	2	no	—
570	C₂×D₄	—	4	4	no	—
571	C₂×D₄	—	4	4	no	—
572	C₂×D₄	#41×C₆₇	1	4	yes	—
573	C₂²×C₄	—	2	4	no	—
574	C₂²×C₄	—	2	8	no	—
575	C₂²×C₄	—	2	4	no	—
576	C₂²×C₄	—	2	4	no	—
577	C₂²×C₄	—	2	8	no	—
578	C₂²×C₄	—	2	4	no	—
579	C₂²×C₄	—	2	4	no	—
580	C₂²×C₄	—	2	4	no	—
581	C₂²×C₄	—	4	4	no	—
582	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
583	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
584	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
585	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
586	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
587	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
588	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
589	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
590	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
591	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
592	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
593	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
594	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
595	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
596	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
597	C₄⋊C₄	—	2	2	no	—
598	C₄⋊C₄	—	2	2	no	—
599	C₄⋊C₄	—	2	2	no	—
600	C₄⋊C₄	—	2	4	no	—
601	C₄⋊C₄	—	2	2	no	—
602	C₄⋊C₄	—	2	8	no	—
603	C₄⋊C₄	—	2	4	no	—
604	C₄⋊C₄	—	2	8	no	—
605	C₄⋊C₄	—	2	4	no	—
606	C₄⋊C₄	—	2	4	no	—
607	C₄⋊C₄	—	4	4	no	—
608	C₄⋊C₄	—	4	2	no	—
609	C₄⋊C₄	—	4	4	no	—
610	C₄⋊C₄	C₂×D₄×C₆₇	1	8	yes	—
611	C₄⋊C₄	C₂×D₄×C₆₇	1	8	yes	—
612	C₂²⋊C₄	—	2	8	no	—
613	C₂²⋊C₄	—	2	4	no	—
614	C₂²⋊C₄	—	2	4	no	—
615	C₂²⋊C₄	—	2	8	no	—
616	C₂²⋊C₄	—	2	8	no	—
617	C₂²⋊C₄	—	2	4	no	—
618	C₂²⋊C₄	—	2	4	no	—
619	C₂²⋊C₄	—	2	8	no	—
620	C₂²⋊C₄	—	2	4	no	—
621	C₂²⋊C₄	—	2	4	no	—
622	C₂²⋊C₄	—	2	4	no	—
623	C₂²⋊C₄	—	2	4	no	—
624	C₂²⋊C₄	—	4	4	no	—
625	C₂²⋊C₄	—	4	2	no	—
626	C₂²⋊C₄	—	4	2	no	—
627	C₄²	—	2	8	no	—
628	C₄²	—	2	4	no	—
629	C₄²	—	2	4	no	—
630	C₄²	—	2	2	no	—
631	C₄²	—	2	2	no	—
632	C₄²	—	2	2	no	—
633	C₄²	—	2	2	no	—
634	C₄²	—	2	2	no	—
635	C₄²	—	4	4	no	—
636	C₄²	—	4	1	no	—
637	C₄²	C₂×D₄×C₆₇	1	4	yes	—
638	C₂³	—	2	2	no	—
639	C₂³	—	2	2	no	—
640	C₂³	—	2	2	no	—
641	C₂³	—	2	2	no	—
642	C₂³	—	2	2	no	—
643	C₂³	—	2	2	no	—
644	C₂³	—	2	2	no	—
645	C₂³	—	2	2	no	—
646	C₂³	—	2	2	no	—
647	C₂³	—	2	2	no	—
648	C₂³	—	2	2	no	—
649	C₂³	—	2	2	no	—
650	C₂³	—	2	2	no	—
651	C₂³	C₂×#41×C₆₇	1	4	yes	—
652	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
653	Q₈	—	2	8	no	—
654	Q₈	—	2	16	no	—
655	Q₈	—	4	16	no	—
656	Q₈	—	4	4	no	—
657	D₄	—	2	8	no	—
658	D₄	—	4	4	no	—
659	D₄	—	8	8	no	—
660	C₂×C₄	—	2	2	no	—
661	C₂×C₄	—	2	4	no	—
662	C₂×C₄	—	2	1	no	—
663	C₂×C₄	—	2	4	no	—
664	C₂×C₄	—	2	2	no	—
665	C₂×C₄	—	2	1	no	—
666	C₂×C₄	—	2	1	no	—
667	C₂×C₄	—	2	1	no	—
668	C₂×C₄	—	2	2	no	—
669	C₂×C₄	—	2	2	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	2	1	no	—
674	C₂×C₄	—	2	1	no	—
675	C₂×C₄	—	2	1	no	—
676	C₂×C₄	—	2	1	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	4	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	1	no	—
682	C₂×C₄	—	2	4	no	—
683	C₂×C₄	—	2	2	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	1	no	—
691	C₂×C₄	—	2	1	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	4	no	—
695	C₂×C₄	—	4	16	no	—
696	C₂×C₄	—	4	8	no	—
697	C₂×C₄	—	4	8	no	—
698	C₂×C₄	C₂²×D₄×C₆₇	1	8	yes	—
699	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
700	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
701	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
702	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
703	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
704	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
705	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
706	C₂×C₄	2₋¹⁺⁴×C₆₇	1	2	yes	—
707	C₂×C₄	2₋¹⁺⁴×C₆₇	1	2	yes	—
708	C₂²	—	2	4	no	—
709	C₂²	—	2	4	no	—
710	C₂²	—	2	4	no	—
711	C₂²	—	4	2	no	—
712	C₂²	—	4	2	no	—
713	C₂²	—	4	2	no	—
714	C₂²	—	4	2	no	—
715	C₂²	—	4	2	no	—
716	C₂²	—	4	2	no	—
717	C₂²	—	4	2	no	—
718	C₂²	—	4	2	no	—
719	C₂²	—	4	2	no	—
720	C₂²	—	4	2	no	—
721	C₂²	—	4	2	no	—
722	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
723	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
724	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
725	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
726	C₂²	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
727	C₂²	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
728	C₂²	#585×C₆₇	1	1	yes	characteristic
729	C₄	—	2	2	no	—
730	C₄	—	2	4	no	—
731	C₄	—	2	8	no	—
732	C₄	—	2	2	no	—
733	C₄	—	4	2	no	—
734	C₄	—	4	2	no	—
735	C₄	—	4	2	no	—
736	C₄	—	4	1	no	—
737	C₄	—	4	2	no	—
738	C₄	—	4	2	no	—
739	C₄	—	4	4	no	—
740	C₄	—	4	1	no	—
741	C₄	—	4	1	no	—
742	C₄	#546×C₆₇	1	4	yes	—
743	C₄	#548×C₆₇	1	4	yes	—
744	C₂	—	4	4	no	—
745	C₂	—	8	2	no	—
746	C₂	C₂×#546×C₆₇	1	1	yes	characteristic
747	C₂	C₂×#548×C₆₇	1	1	yes	characteristic
748	C₂	C₆₇×#3482	1	1	yes	characteristic
749	C₂	C₆₇×#3497	1	1	yes	characteristic
750	C₂	C₆₇×#3514	1	1	yes	characteristic
751	C₂	C₆₇×#3518	1	1	yes	characteristic
752	C₂	C₆₇×#3552	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₇
prime radical	C₆₇×#2537	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. C₂×#556×C₆₇	C₂	semidirect
2. C₂×D₄×Q₈×C₆₇	C₂	semidirect
3. C₆₇×#2702	C₂	semidirect
4. C₆₇×#2582	C₂	semidirect
5. C₆₇×#2560	C₂	semidirect
7. C₆₇×#2492	C₂	semidirect
8. C₆₇×#2439	C₂	semidirect
9. C₆₇×#2436	C₂	semidirect
10. C₆₇×#2427	C₂	semidirect
11. C₆₇×#2426	C₂	semidirect
12. C₆₇×#2421	C₂	semidirect
13. C₆₇×#2363	C₂	semidirect
14. Q₈×C₂²⋊C₄×C₆₇	C₂	semidirect
15. C₄×C₄⋊Q₈×C₆₇	C₂	semidirect
16. C₄×#124×C₆₇	C₂	semidirect
17. C₄×#124×C₆₇	C₂	semidirect
99. C₄⋊Q₈×C₆₇	D₄	semidirect
367. #59421	C₆₇	direct (N × H)
377. C₂×#556	C₂×C₆₇	semidirect
378. C₂×D₄×Q₈	C₂×C₆₇	semidirect
379. #2702	C₂×C₆₇	semidirect
380. #2582	C₂×C₆₇	semidirect
381. #2560	C₂×C₆₇	semidirect
383. #2492	C₂×C₆₇	semidirect
384. #2439	C₂×C₆₇	semidirect
385. #2436	C₂×C₆₇	semidirect
386. #2427	C₂×C₆₇	semidirect
387. #2426	C₂×C₆₇	semidirect
388. #2421	C₂×C₆₇	semidirect
389. #2363	C₂×C₆₇	semidirect
390. Q₈×C₂²⋊C₄	C₂×C₆₇	semidirect
391. C₄×C₄⋊Q₈	C₂×C₆₇	semidirect
392. C₄×#124	C₂×C₆₇	semidirect
393. C₄×#124	C₂×C₆₇	semidirect
394. C₆₇	#59421	direct (N × H)
476. C₄⋊Q₈	D₄×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#556×C₆₇	2
C₂×D₄×Q₈×C₆₇	2
C₆₇×#2702	2
C₆₇×#2582	2
C₆₇×#2560	2
C₆₇×#2537	2
C₆₇×#2492	2
C₆₇×#2439	2
C₆₇×#2436	2
C₆₇×#2427	2
C₆₇×#2426	2
C₆₇×#2421	2
C₆₇×#2363	2
Q₈×C₂²⋊C₄×C₆₇	2
C₄×C₄⋊Q₈×C₆₇	2
C₄×#124×C₆₇	2
#59421	67

Subgroups — C67×#59421 #30738672

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#59421 #30738672