Subgroups — C₆₇×#61162 #30740413

Order 17152.

2162 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#554×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×#41×C₆₇	C₂	1	1	yes	maximal, characteristic
3	C₆₇×#3333	C₂	1	2	yes	maximal, complemented
4	C₆₇×#3331	C₂	1	2	yes	maximal, complemented
5	C₆₇×#3316	C₂	1	4	yes	maximal, complemented
6	C₆₇×#3314	C₂	1	4	yes	maximal, complemented
7	C₆₇×#3299	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3295	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3141	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#3092	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3079	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#3056	C₂	1	2	yes	maximal, complemented
13	C₆₇×#3037	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3007	C₂	1	2	yes	maximal, complemented
15	C₄×#137×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
16	D₄×M₁₆×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#417×C₆₇	C₂	1	2	yes	maximal, complemented
18	C₂²×#41×C₆₇	C₂²	1	2	yes	—
19	C₂×#137×C₆₇	C₂²	1	1	yes	characteristic
20	C₂×#137×C₆₇	C₂²	1	2	yes	complemented
21	C₂²×M₁₆×C₆₇	C₂²	1	2	yes	complemented
22	#554×C₆₇	—	2	1	no	—
23	#554×C₆₇	—	2	2	no	—
24	#554×C₆₇	—	2	1	no	—
25	#554×C₆₇	C₂²	1	2	yes	—
26	#554×C₆₇	C₂²	1	4	yes	complemented
27	#554×C₆₇	C₂²	1	2	yes	complemented
28	#550×C₆₇	C₂²	1	1	yes	characteristic
29	D₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
30	#548×C₆₇	C₂²	1	2	yes	—
31	#547×C₆₇	—	2	1	no	—
32	#547×C₆₇	C₂²	1	1	yes	characteristic
33	#546×C₆₇	—	2	2	no	—
34	#546×C₆₇	C₂²	1	2	yes	—
35	D₄²×C₆₇	—	2	1	no	—
36	D₄²×C₆₇	C₂²	1	1	yes	characteristic
37	#532×C₆₇	—	2	1	no	—
38	#532×C₆₇	C₂²	1	1	yes	characteristic
39	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
40	C₂×#125×C₆₇	—	2	1	no	—
41	#525×C₆₇	—	2	2	no	—
42	#525×C₆₇	C₂²	1	2	yes	—
43	C₂×C₂²⋊Q₈×C₆₇	—	2	2	no	—
44	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	complemented
45	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
46	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
47	C₂×C₄×D₄×C₆₇	—	2	1	no	—
48	C₂×C₄×D₄×C₆₇	—	2	1	no	—
49	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
50	C₂²×C₄⋊C₄×C₆₇	C₂²	1	2	yes	complemented
51	#489×C₆₇	C₂²	1	4	yes	complemented
52	#487×C₆₇	C₂²	1	2	yes	complemented
53	#486×C₆₇	C₂²	1	2	yes	complemented
54	#484×C₆₇	C₂²	1	4	yes	complemented
55	#483×C₆₇	C₂²	1	4	yes	complemented
56	#481×C₆₇	C₂²	1	4	yes	complemented
57	#480×C₆₇	C₂²	1	4	yes	complemented
58	#477×C₆₇	C₂²	1	2	yes	complemented
59	#476×C₆₇	C₂²	1	2	yes	complemented
60	#475×C₆₇	C₂²	1	2	yes	complemented
61	#474×C₆₇	C₂²	1	2	yes	complemented
62	#470×C₆₇	C₂²	1	4	yes	complemented
63	#468×C₆₇	C₂²	1	4	yes	complemented
64	#467×C₆₇	C₂²	1	4	yes	complemented
65	#465×C₆₇	C₂²	1	4	yes	complemented
66	#464×C₆₇	C₂²	1	4	yes	complemented
67	#462×C₆₇	C₂²	1	2	yes	complemented
68	#460×C₆₇	C₂²	1	2	yes	complemented
69	#452×C₆₇	C₂²	1	4	yes	complemented
70	#452×C₆₇	C₂²	1	4	yes	complemented
71	#451×C₆₇	C₂²	1	4	yes	complemented
72	#450×C₆₇	C₂²	1	4	yes	complemented
73	#441×C₆₇	C₂²	1	2	yes	complemented
74	#440×C₆₇	C₂²	1	2	yes	complemented
75	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	complemented
76	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
77	#436×C₆₇	C₂²	1	2	yes	complemented
78	#435×C₆₇	C₂²	1	4	yes	complemented
79	C₈×D₄×C₆₇	C₂²	1	2	yes	—
80	#428×C₆₇	C₂²	1	2	yes	complemented
81	#428×C₆₇	C₂²	1	1	yes	characteristic, complemented
82	#423×C₆₇	C₂²	1	1	yes	characteristic, complemented
83	#419×C₆₇	C₂²	1	1	yes	characteristic, complemented
84	#417×C₆₇	C₂²	1	2	yes	—
85	#417×C₆₇	C₂²	1	1	yes	characteristic
86	#417×C₆₇	C₂²	1	2	yes	complemented
87	#417×C₆₇	C₂²	1	2	yes	complemented
88	#417×C₆₇	C₂²	1	4	yes	complemented
89	#417×C₆₇	C₂²	1	4	yes	complemented
90	#417×C₆₇	C₂²	1	2	yes	complemented
91	C₂×#103×C₆₇	C₂²	1	4	yes	complemented
92	C₂×#102×C₆₇	C₂²	1	4	yes	complemented
93	#407×C₆₇	C₂²	1	2	yes	complemented
94	C₄×M₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
95	C₂×#41×C₆₇	—	2	2	no	—
96	C₂×#41×C₆₇	—	2	2	no	—
97	C₂×#41×C₆₇	—	2	8	no	—
98	C₂×#41×C₆₇	—	4	4	no	—
99	C₂×#41×C₆₇	C₂³	1	2	yes	—
100	C₂×#41×C₆₇	C₂³	1	2	yes	—
101	C₂×#41×C₆₇	C₂³	1	2	yes	—
102	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
103	C₂²×Q₈×C₆₇	—	2	1	no	—
104	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
105	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
106	C₂²×D₄×C₆₇	—	2	2	no	—
107	C₂²×D₄×C₆₇	—	2	1	no	—
108	C₂²×D₄×C₆₇	D₄	1	1	yes	characteristic
109	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
110	C₂³×C₄×C₆₇	—	2	2	no	—
111	C₂³×C₄×C₆₇	—	2	2	no	—
112	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
113	#137×C₆₇	—	2	4	no	—
114	#137×C₆₇	—	4	4	no	—
115	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
116	C₂×Q₁₆×C₆₇	C₂³	1	4	yes	—
117	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
118	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
119	C₂×M₁₆×C₆₇	—	4	4	no	—
120	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
121	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
122	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
123	C₂×M₁₆×C₆₇	C₂³	1	4	yes	—
124	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
125	C₄⋊Q₈×C₆₇	—	2	1	no	—
126	C₄⋊Q₈×C₆₇	—	2	1	no	—
127	C₄⋊Q₈×C₆₇	—	2	1	no	—
128	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
129	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
130	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
131	#127×C₆₇	—	2	1	no	—
132	#127×C₆₇	C₂³	1	1	yes	characteristic
133	#125×C₆₇	—	2	2	no	—
134	#125×C₆₇	—	2	2	no	—
135	#125×C₆₇	—	2	4	no	—
136	#124×C₆₇	—	2	2	no	—
137	#124×C₆₇	C₂³	1	2	yes	—
138	#123×C₆₇	—	2	2	no	—
139	#123×C₆₇	—	2	2	no	—
140	#123×C₆₇	—	2	2	no	—
141	C₂²⋊Q₈×C₆₇	—	2	2	no	—
142	C₂²⋊Q₈×C₆₇	—	2	2	no	—
143	C₂²⋊Q₈×C₆₇	—	2	2	no	—
144	C₂²⋊Q₈×C₆₇	—	2	4	no	—
145	C₂²⋊Q₈×C₆₇	—	2	4	no	—
146	C₂²⋊Q₈×C₆₇	—	2	4	no	—
147	C₂²⋊Q₈×C₆₇	—	2	4	no	—
148	C₂²⋊Q₈×C₆₇	—	2	2	no	—
149	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
150	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
151	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
152	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
153	#121×C₆₇	—	2	2	no	—
154	#121×C₆₇	—	2	1	no	—
155	#121×C₆₇	—	2	1	no	—
156	#121×C₆₇	—	2	1	no	—
157	#121×C₆₇	—	2	1	no	—
158	#121×C₆₇	—	2	2	no	—
159	#121×C₆₇	—	2	2	no	—
160	#121×C₆₇	C₂³	1	2	yes	—
161	#121×C₆₇	C₂³	1	2	yes	—
162	#120×C₆₇	—	2	2	no	—
163	#120×C₆₇	—	2	2	no	—
164	#120×C₆₇	—	2	2	no	—
165	C₄×Q₈×C₆₇	—	2	1	no	—
166	C₄×Q₈×C₆₇	—	2	1	no	—
167	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
168	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
169	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
170	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
171	C₄×D₄×C₆₇	—	2	1	no	—
172	C₄×D₄×C₆₇	—	2	2	no	—
173	C₄×D₄×C₆₇	—	2	4	no	—
174	C₄×D₄×C₆₇	—	2	2	no	—
175	C₄×D₄×C₆₇	—	2	2	no	—
176	C₄×D₄×C₆₇	—	2	1	no	—
177	C₄×D₄×C₆₇	—	2	1	no	—
178	C₄×D₄×C₆₇	—	2	2	no	—
179	C₄×D₄×C₆₇	—	2	1	no	—
180	C₄×D₄×C₆₇	—	2	2	no	—
181	C₄×D₄×C₆₇	—	2	1	no	—
182	C₄×D₄×C₆₇	—	2	1	no	—
183	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
184	C₄×D₄×C₆₇	D₄	1	2	yes	—
185	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
186	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
187	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
188	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
189	C₄×D₄×C₆₇	C₂³	1	2	yes	—
190	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
191	#117×C₆₇	—	2	1	no	—
192	#117×C₆₇	C₂³	1	1	yes	characteristic
193	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
194	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
195	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
196	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
197	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
198	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
199	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
200	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
201	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
202	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
203	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
204	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
205	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
206	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
207	C₂×C₂²⋊C₄×C₆₇	D₄	1	2	yes	—
208	C₂×C₄²×C₆₇	—	2	1	no	—
209	C₂×C₄²×C₆₇	—	2	1	no	—
210	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
211	#107×C₆₇	C₂³	1	4	yes	—
212	#107×C₆₇	C₂³	1	2	yes	—
213	#106×C₆₇	C₂³	1	4	yes	—
214	#106×C₆₇	C₂³	1	2	yes	—
215	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
216	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
217	#103×C₆₇	C₂³	1	4	yes	—
218	#103×C₆₇	C₂³	1	4	yes	—
219	#103×C₆₇	C₂³	1	4	yes	—
220	#103×C₆₇	C₂³	1	2	yes	—
221	#103×C₆₇	C₂³	1	2	yes	—
222	#103×C₆₇	C₂³	1	4	yes	—
223	#103×C₆₇	C₂³	1	2	yes	—
224	#102×C₆₇	C₂³	1	4	yes	—
225	#102×C₆₇	C₂³	1	4	yes	—
226	#102×C₆₇	C₂³	1	4	yes	—
227	#102×C₆₇	C₂³	1	4	yes	—
228	#102×C₆₇	C₂³	1	2	yes	—
229	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
230	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
231	#97×C₆₇	C₂³	1	2	yes	—
232	C₄×C₈×C₆₇	C₂³	1	2	yes	—
233	C₂⁴×C₆₇	—	2	2	no	—
234	C₂⁴×C₆₇	C₂×D₄	1	2	yes	—
235	#41×C₆₇	—	2	2	no	—
236	#41×C₆₇	—	2	4	no	—
237	#41×C₆₇	—	2	4	no	—
238	#41×C₆₇	—	2	4	no	—
239	#41×C₆₇	—	2	4	no	—
240	#41×C₆₇	—	4	8	no	—
241	#41×C₆₇	—	4	2	no	—
242	#41×C₆₇	—	4	2	no	—
243	#41×C₆₇	—	4	8	no	—
244	#41×C₆₇	#41	1	4	yes	—
245	C₂×Q₈×C₆₇	—	2	1	no	—
246	C₂×Q₈×C₆₇	—	2	2	no	—
247	C₂×Q₈×C₆₇	—	2	2	no	—
248	C₂×Q₈×C₆₇	—	2	2	no	—
249	C₂×Q₈×C₆₇	—	2	4	no	—
250	C₂×Q₈×C₆₇	—	2	2	no	—
251	C₂×Q₈×C₆₇	—	2	2	no	—
252	C₂×Q₈×C₆₇	—	4	2	no	—
253	C₂×Q₈×C₆₇	—	8	2	no	—
254	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
255	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
256	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
257	C₂×D₄×C₆₇	—	2	1	no	—
258	C₂×D₄×C₆₇	—	2	4	no	—
259	C₂×D₄×C₆₇	—	2	4	no	—
260	C₂×D₄×C₆₇	—	2	2	no	—
261	C₂×D₄×C₆₇	—	2	2	no	—
262	C₂×D₄×C₆₇	—	2	2	no	—
263	C₂×D₄×C₆₇	—	2	2	no	—
264	C₂×D₄×C₆₇	—	2	2	no	—
265	C₂×D₄×C₆₇	—	2	1	no	—
266	C₂×D₄×C₆₇	—	2	2	no	—
267	C₂×D₄×C₆₇	—	2	1	no	—
268	C₂×D₄×C₆₇	—	4	2	no	—
269	C₂×D₄×C₆₇	—	4	8	no	—
270	C₂×D₄×C₆₇	—	4	4	no	—
271	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
272	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
273	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
274	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
275	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
276	C₂²×C₄×C₆₇	—	2	1	no	—
277	C₂²×C₄×C₆₇	—	2	4	no	—
278	C₂²×C₄×C₆₇	—	2	4	no	—
279	C₂²×C₄×C₆₇	—	2	1	no	—
280	C₂²×C₄×C₆₇	—	2	1	no	—
281	C₂²×C₄×C₆₇	—	2	2	no	—
282	C₂²×C₄×C₆₇	—	2	2	no	—
283	C₂²×C₄×C₆₇	—	2	4	no	—
284	C₂²×C₄×C₆₇	—	2	4	no	—
285	C₂²×C₄×C₆₇	—	2	1	no	—
286	C₂²×C₄×C₆₇	—	2	2	no	—
287	C₂²×C₄×C₆₇	—	2	2	no	—
288	C₂²×C₄×C₆₇	—	2	2	no	—
289	C₂²×C₄×C₆₇	—	2	1	no	—
290	C₂²×C₄×C₆₇	—	4	8	no	—
291	C₂²×C₄×C₆₇	—	8	4	no	—
292	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
293	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
294	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
295	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
296	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
297	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
298	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
299	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
300	Q₁₆×C₆₇	—	2	4	no	—
301	Q₁₆×C₆₇	—	4	4	no	—
302	SD₁₆×C₆₇	—	2	4	no	—
303	SD₁₆×C₆₇	—	4	4	no	—
304	M₁₆×C₆₇	—	2	2	no	—
305	M₁₆×C₆₇	—	2	2	no	—
306	M₁₆×C₆₇	—	2	4	no	—
307	M₁₆×C₆₇	—	4	4	no	—
308	C₂×C₈×C₆₇	—	4	4	no	—
309	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
310	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
311	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
312	C₄⋊C₄×C₆₇	—	2	1	no	—
313	C₄⋊C₄×C₆₇	—	2	4	no	—
314	C₄⋊C₄×C₆₇	—	2	4	no	—
315	C₄⋊C₄×C₆₇	—	2	2	no	—
316	C₄⋊C₄×C₆₇	—	2	1	no	—
317	C₄⋊C₄×C₆₇	—	2	2	no	—
318	C₄⋊C₄×C₆₇	—	2	2	no	—
319	C₄⋊C₄×C₆₇	—	2	2	no	—
320	C₄⋊C₄×C₆₇	—	2	2	no	—
321	C₄⋊C₄×C₆₇	—	2	2	no	—
322	C₄⋊C₄×C₆₇	—	2	4	no	—
323	C₄⋊C₄×C₆₇	—	2	4	no	—
324	C₄⋊C₄×C₆₇	—	2	1	no	—
325	C₄⋊C₄×C₆₇	—	2	1	no	—
326	C₄⋊C₄×C₆₇	—	2	1	no	—
327	C₄⋊C₄×C₆₇	—	2	2	no	—
328	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
329	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
330	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
331	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
332	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
333	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
334	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
335	C₂²⋊C₄×C₆₇	—	2	2	no	—
336	C₂²⋊C₄×C₆₇	—	2	4	no	—
337	C₂²⋊C₄×C₆₇	—	2	4	no	—
338	C₂²⋊C₄×C₆₇	—	2	1	no	—
339	C₂²⋊C₄×C₆₇	—	2	2	no	—
340	C₂²⋊C₄×C₆₇	—	2	2	no	—
341	C₂²⋊C₄×C₆₇	—	2	2	no	—
342	C₂²⋊C₄×C₆₇	—	2	1	no	—
343	C₂²⋊C₄×C₆₇	—	2	1	no	—
344	C₂²⋊C₄×C₆₇	—	2	2	no	—
345	C₂²⋊C₄×C₆₇	—	2	2	no	—
346	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
347	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
348	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
349	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
350	C₄²×C₆₇	—	2	1	no	—
351	C₄²×C₆₇	—	2	1	no	—
352	C₄²×C₆₇	—	2	1	no	—
353	C₄²×C₆₇	—	2	2	no	—
354	C₄²×C₆₇	—	2	2	no	—
355	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
356	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
357	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
358	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
359	C₂³×C₆₇	—	2	4	no	—
360	C₂³×C₆₇	—	2	4	no	—
361	C₂³×C₆₇	—	2	1	no	—
362	C₂³×C₆₇	—	2	2	no	—
363	C₂³×C₆₇	—	4	2	no	—
364	C₂³×C₆₇	—	4	4	no	—
365	C₂³×C₆₇	—	4	4	no	—
366	C₂³×C₆₇	—	8	2	no	—
367	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
368	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
369	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
370	Q₈×C₆₇	—	2	1	no	—
371	Q₈×C₆₇	—	2	2	no	—
372	Q₈×C₆₇	—	2	2	no	—
373	Q₈×C₆₇	—	2	2	no	—
374	Q₈×C₆₇	—	2	2	no	—
375	Q₈×C₆₇	—	4	4	no	—
376	Q₈×C₆₇	—	4	2	no	—
377	Q₈×C₆₇	—	8	2	no	—
378	Q₈×C₆₇	—	8	2	no	—
379	Q₈×C₆₇	C₂×#41	1	2	yes	—
380	D₄×C₆₇	—	2	4	no	—
381	D₄×C₆₇	—	2	4	no	—
382	D₄×C₆₇	—	2	2	no	—
383	D₄×C₆₇	—	2	2	no	—
384	D₄×C₆₇	—	2	1	no	—
385	D₄×C₆₇	—	2	2	no	—
386	D₄×C₆₇	—	4	4	no	—
387	D₄×C₆₇	—	4	4	no	—
388	D₄×C₆₇	—	4	4	no	—
389	D₄×C₆₇	—	4	4	no	—
390	D₄×C₆₇	—	4	4	no	—
391	D₄×C₆₇	—	4	2	no	—
392	D₄×C₆₇	—	8	1	no	—
393	D₄×C₆₇	—	8	2	no	—
394	D₄×C₆₇	#137	1	4	yes	complemented
395	D₄×C₆₇	C₂×#41	1	2	yes	—
396	C₂×C₄×C₆₇	—	2	4	no	—
397	C₂×C₄×C₆₇	—	2	1	no	—
398	C₂×C₄×C₆₇	—	2	4	no	—
399	C₂×C₄×C₆₇	—	2	4	no	—
400	C₂×C₄×C₆₇	—	2	4	no	—
401	C₂×C₄×C₆₇	—	2	2	no	—
402	C₂×C₄×C₆₇	—	2	2	no	—
403	C₂×C₄×C₆₇	—	2	2	no	—
404	C₂×C₄×C₆₇	—	2	2	no	—
405	C₂×C₄×C₆₇	—	2	2	no	—
406	C₂×C₄×C₆₇	—	2	1	no	—
407	C₂×C₄×C₆₇	—	2	1	no	—
408	C₂×C₄×C₆₇	—	2	2	no	—
409	C₂×C₄×C₆₇	—	2	2	no	—
410	C₂×C₄×C₆₇	—	2	2	no	—
411	C₂×C₄×C₆₇	—	2	4	no	—
412	C₂×C₄×C₆₇	—	4	1	no	—
413	C₂×C₄×C₆₇	—	4	4	no	—
414	C₂×C₄×C₆₇	—	4	4	no	—
415	C₂×C₄×C₆₇	—	4	4	no	—
416	C₂×C₄×C₆₇	—	4	2	no	—
417	C₂×C₄×C₆₇	—	4	4	no	—
418	C₂×C₄×C₆₇	—	4	2	no	—
419	C₂×C₄×C₆₇	—	4	4	no	—
420	C₂×C₄×C₆₇	—	4	2	no	—
421	C₂×C₄×C₆₇	—	8	1	no	—
422	C₂×C₄×C₆₇	—	8	4	no	—
423	C₂×C₄×C₆₇	—	8	4	no	—
424	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
425	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
426	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
427	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
428	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
429	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
430	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
431	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
432	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
433	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
434	C₈×C₆₇	—	2	2	no	—
435	C₈×C₆₇	—	2	2	no	—
436	C₈×C₆₇	—	2	4	no	—
437	C₂²×C₆₇	—	2	1	no	—
438	C₂²×C₆₇	—	2	2	no	—
439	C₂²×C₆₇	—	2	2	no	—
440	C₂²×C₆₇	—	2	1	no	—
441	C₂²×C₆₇	—	2	2	no	—
442	C₂²×C₆₇	—	2	2	no	—
443	C₂²×C₆₇	—	2	2	no	—
444	C₂²×C₆₇	—	2	2	no	—
445	C₂²×C₆₇	—	4	8	no	—
446	C₂²×C₆₇	—	4	1	no	—
447	C₂²×C₆₇	—	4	1	no	—
448	C₂²×C₆₇	—	4	2	no	—
449	C₂²×C₆₇	—	4	2	no	—
450	C₂²×C₆₇	—	4	2	no	—
451	C₂²×C₆₇	—	8	8	no	—
452	C₂²×C₆₇	#546	1	2	yes	—
453	C₂²×C₆₇	C₂×#137	1	4	yes	—
454	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
455	C₄×C₆₇	—	2	1	no	—
456	C₄×C₆₇	—	2	1	no	—
457	C₄×C₆₇	—	2	2	no	—
458	C₄×C₆₇	—	2	2	no	—
459	C₄×C₆₇	—	2	2	no	—
460	C₄×C₆₇	—	2	1	no	—
461	C₄×C₆₇	—	4	2	no	—
462	C₄×C₆₇	—	4	4	no	—
463	C₄×C₆₇	—	4	1	no	—
464	C₄×C₆₇	—	4	2	no	—
465	C₄×C₆₇	—	4	2	no	—
466	C₄×C₆₇	—	4	1	no	—
467	C₄×C₆₇	#546	1	2	yes	—
468	C₄×C₆₇	C₂×#137	1	2	yes	—
469	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
470	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
471	#61162	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
472	C₂×C₆₇	—	2	2	no	—
473	C₂×C₆₇	—	2	4	no	—
474	C₂×C₆₇	—	4	2	no	—
475	C₂×C₆₇	—	4	2	no	—
476	C₂×C₆₇	—	8	2	no	—
477	C₂×C₆₇	C₂×#546	1	1	yes	characteristic
478	C₂×C₆₇	C₂²×#137	1	1	yes	characteristic
479	C₂×C₆₇	#3585	1	1	yes	characteristic
480	C₂×#554	C₂×C₆₇	1	1	yes	characteristic, complemented
481	D₄×#41	C₂×C₆₇	1	1	yes	characteristic
482	#3333	C₂×C₆₇	1	2	yes	complemented
483	#3331	C₂×C₆₇	1	2	yes	complemented
484	#3316	C₂×C₆₇	1	4	yes	complemented
485	#3314	C₂×C₆₇	1	4	yes	complemented
486	#3299	C₂×C₆₇	1	2	yes	complemented
487	#3295	C₂×C₆₇	1	2	yes	complemented
488	#3141	C₂×C₆₇	1	1	yes	characteristic, complemented
489	#3092	C₂×C₆₇	1	2	yes	complemented
490	#3079	C₂×C₆₇	1	1	yes	characteristic, complemented
491	#3056	C₂×C₆₇	1	2	yes	complemented
492	#3037	C₂×C₆₇	1	1	yes	characteristic, complemented
493	#3007	C₂×C₆₇	1	2	yes	complemented
494	C₄×#137	C₂×C₆₇	1	1	yes	characteristic, complemented
495	D₄×M₁₆	C₂×C₆₇	1	1	yes	characteristic, complemented
496	C₂×#417	C₂×C₆₇	1	2	yes	complemented
497	C₆₇	#61162	1	1	yes	characteristic, direct product factor, Sylow
498	C₂²×#41	C₂²×C₆₇	1	2	yes	—
499	C₂×#137	C₂²×C₆₇	1	1	yes	characteristic
500	C₂×#137	C₂²×C₆₇	1	2	yes	complemented
501	C₂²×M₁₆	C₂²×C₆₇	1	2	yes	complemented
502	#554	—	2	1	no	—
503	#554	—	2	2	no	—
504	#554	—	2	1	no	—
505	#554	C₂²×C₆₇	1	2	yes	—
506	#554	C₂²×C₆₇	1	2	yes	complemented
507	#554	C₂²×C₆₇	1	4	yes	complemented
508	#550	C₂²×C₆₇	1	1	yes	characteristic
509	D₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
510	#548	C₂²×C₆₇	1	2	yes	—
511	#547	—	2	1	no	—
512	#547	C₂²×C₆₇	1	1	yes	characteristic
513	#546	—	2	2	no	—
514	#546	C₂²×C₆₇	1	2	yes	—
515	D₄²	—	2	1	no	—
516	D₄²	C₂²×C₆₇	1	1	yes	characteristic
517	#532	—	2	1	no	—
518	#532	C₂²×C₆₇	1	1	yes	characteristic
519	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
520	C₂×#125	—	2	1	no	—
521	#525	—	2	2	no	—
522	#525	C₂²×C₆₇	1	2	yes	—
523	C₂×C₂²⋊Q₈	—	2	2	no	—
524	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	complemented
525	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
526	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
527	C₂×C₄×D₄	—	2	1	no	—
528	C₂×C₄×D₄	—	2	1	no	—
529	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
530	C₂²×C₄⋊C₄	C₂²×C₆₇	1	2	yes	complemented
531	#489	C₂²×C₆₇	1	4	yes	complemented
532	#487	C₂²×C₆₇	1	2	yes	complemented
533	#486	C₂²×C₆₇	1	2	yes	complemented
534	#484	C₂²×C₆₇	1	4	yes	complemented
535	#483	C₂²×C₆₇	1	4	yes	complemented
536	#481	C₂²×C₆₇	1	4	yes	complemented
537	#480	C₂²×C₆₇	1	4	yes	complemented
538	#477	C₂²×C₆₇	1	2	yes	complemented
539	#476	C₂²×C₆₇	1	2	yes	complemented
540	#475	C₂²×C₆₇	1	2	yes	complemented
541	#474	C₂²×C₆₇	1	2	yes	complemented
542	#470	C₂²×C₆₇	1	4	yes	complemented
543	#468	C₂²×C₆₇	1	4	yes	complemented
544	#467	C₂²×C₆₇	1	4	yes	complemented
545	#465	C₂²×C₆₇	1	4	yes	complemented
546	#464	C₂²×C₆₇	1	4	yes	complemented
547	#462	C₂²×C₆₇	1	2	yes	complemented
548	#460	C₂²×C₆₇	1	2	yes	complemented
549	#452	C₂²×C₆₇	1	4	yes	complemented
550	#452	C₂²×C₆₇	1	4	yes	complemented
551	#451	C₂²×C₆₇	1	4	yes	complemented
552	#450	C₂²×C₆₇	1	4	yes	complemented
553	#441	C₂²×C₆₇	1	2	yes	complemented
554	#440	C₂²×C₆₇	1	2	yes	complemented
555	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	complemented
556	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
557	#436	C₂²×C₆₇	1	2	yes	complemented
558	#435	C₂²×C₆₇	1	4	yes	complemented
559	C₈×D₄	C₂²×C₆₇	1	2	yes	—
560	#428	C₂²×C₆₇	1	2	yes	complemented
561	#428	C₂²×C₆₇	1	1	yes	characteristic, complemented
562	#423	C₂²×C₆₇	1	1	yes	characteristic, complemented
563	#419	C₂²×C₆₇	1	1	yes	characteristic, complemented
564	#417	C₂²×C₆₇	1	2	yes	—
565	#417	C₂²×C₆₇	1	1	yes	characteristic
566	#417	C₂²×C₆₇	1	4	yes	complemented
567	#417	C₂²×C₆₇	1	4	yes	complemented
568	#417	C₂²×C₆₇	1	2	yes	complemented
569	#417	C₂²×C₆₇	1	2	yes	complemented
570	#417	C₂²×C₆₇	1	2	yes	complemented
571	C₂×#103	C₂²×C₆₇	1	4	yes	complemented
572	C₂×#102	C₂²×C₆₇	1	4	yes	complemented
573	#407	C₂²×C₆₇	1	2	yes	complemented
574	C₄×M₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
575	C₂×#41	—	2	2	no	—
576	C₂×#41	—	2	2	no	—
577	C₂×#41	—	2	8	no	—
578	C₂×#41	—	4	4	no	—
579	C₂×#41	C₂³×C₆₇	1	2	yes	—
580	C₂×#41	C₂³×C₆₇	1	2	yes	—
581	C₂×#41	C₂³×C₆₇	1	2	yes	—
582	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
583	C₂²×Q₈	—	2	1	no	—
584	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
585	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
586	C₂²×D₄	—	2	2	no	—
587	C₂²×D₄	—	2	1	no	—
588	C₂²×D₄	D₄×C₆₇	1	1	yes	characteristic
589	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
590	C₂³×C₄	—	2	2	no	—
591	C₂³×C₄	—	2	2	no	—
592	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
593	#137	—	2	4	no	—
594	#137	—	4	4	no	—
595	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
596	C₂×Q₁₆	C₂³×C₆₇	1	4	yes	—
597	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
598	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
599	C₂×M₁₆	—	4	4	no	—
600	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
601	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
602	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
603	C₂×M₁₆	C₂³×C₆₇	1	4	yes	—
604	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
605	C₄⋊Q₈	—	2	1	no	—
606	C₄⋊Q₈	—	2	1	no	—
607	C₄⋊Q₈	—	2	1	no	—
608	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
609	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
610	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
611	#127	—	2	1	no	—
612	#127	C₂³×C₆₇	1	1	yes	characteristic
613	#125	—	2	2	no	—
614	#125	—	2	2	no	—
615	#125	—	2	4	no	—
616	#124	—	2	2	no	—
617	#124	C₂³×C₆₇	1	2	yes	—
618	#123	—	2	2	no	—
619	#123	—	2	2	no	—
620	#123	—	2	2	no	—
621	C₂²⋊Q₈	—	2	2	no	—
622	C₂²⋊Q₈	—	2	2	no	—
623	C₂²⋊Q₈	—	2	2	no	—
624	C₂²⋊Q₈	—	2	4	no	—
625	C₂²⋊Q₈	—	2	4	no	—
626	C₂²⋊Q₈	—	2	4	no	—
627	C₂²⋊Q₈	—	2	4	no	—
628	C₂²⋊Q₈	—	2	2	no	—
629	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
630	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
631	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
632	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
633	#121	—	2	2	no	—
634	#121	—	2	1	no	—
635	#121	—	2	1	no	—
636	#121	—	2	1	no	—
637	#121	—	2	1	no	—
638	#121	—	2	2	no	—
639	#121	—	2	2	no	—
640	#121	C₂³×C₆₇	1	2	yes	—
641	#121	C₂³×C₆₇	1	2	yes	—
642	#120	—	2	2	no	—
643	#120	—	2	2	no	—
644	#120	—	2	2	no	—
645	C₄×Q₈	—	2	1	no	—
646	C₄×Q₈	—	2	1	no	—
647	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
648	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
649	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
650	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
651	C₄×D₄	—	2	1	no	—
652	C₄×D₄	—	2	2	no	—
653	C₄×D₄	—	2	4	no	—
654	C₄×D₄	—	2	2	no	—
655	C₄×D₄	—	2	2	no	—
656	C₄×D₄	—	2	1	no	—
657	C₄×D₄	—	2	1	no	—
658	C₄×D₄	—	2	2	no	—
659	C₄×D₄	—	2	1	no	—
660	C₄×D₄	—	2	2	no	—
661	C₄×D₄	—	2	1	no	—
662	C₄×D₄	—	2	1	no	—
663	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
664	C₄×D₄	D₄×C₆₇	1	2	yes	—
665	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
666	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
667	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
668	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
669	C₄×D₄	C₂³×C₆₇	1	2	yes	—
670	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
671	#117	—	2	1	no	—
672	#117	C₂³×C₆₇	1	1	yes	characteristic
673	C₂×C₄⋊C₄	—	2	2	no	—
674	C₂×C₄⋊C₄	—	2	2	no	—
675	C₂×C₄⋊C₄	—	2	2	no	—
676	C₂×C₄⋊C₄	—	2	1	no	—
677	C₂×C₄⋊C₄	—	2	1	no	—
678	C₂×C₄⋊C₄	—	2	2	no	—
679	C₂×C₄⋊C₄	—	2	1	no	—
680	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
681	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
682	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
683	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
684	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
685	C₂×C₂²⋊C₄	—	2	2	no	—
686	C₂×C₂²⋊C₄	—	2	2	no	—
687	C₂×C₂²⋊C₄	D₄×C₆₇	1	2	yes	—
688	C₂×C₄²	—	2	1	no	—
689	C₂×C₄²	—	2	1	no	—
690	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
691	#107	C₂³×C₆₇	1	2	yes	—
692	#107	C₂³×C₆₇	1	4	yes	—
693	#106	C₂³×C₆₇	1	2	yes	—
694	#106	C₂³×C₆₇	1	4	yes	—
695	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
696	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
697	#103	C₂³×C₆₇	1	2	yes	—
698	#103	C₂³×C₆₇	1	4	yes	—
699	#103	C₂³×C₆₇	1	4	yes	—
700	#103	C₂³×C₆₇	1	4	yes	—
701	#103	C₂³×C₆₇	1	4	yes	—
702	#103	C₂³×C₆₇	1	2	yes	—
703	#103	C₂³×C₆₇	1	2	yes	—
704	#102	C₂³×C₆₇	1	2	yes	—
705	#102	C₂³×C₆₇	1	4	yes	—
706	#102	C₂³×C₆₇	1	4	yes	—
707	#102	C₂³×C₆₇	1	4	yes	—
708	#102	C₂³×C₆₇	1	4	yes	—
709	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
710	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
711	#97	C₂³×C₆₇	1	2	yes	—
712	C₄×C₈	C₂³×C₆₇	1	2	yes	—
713	C₂⁴	—	2	2	no	—
714	C₂⁴	C₂×D₄×C₆₇	1	2	yes	—
715	#41	—	2	2	no	—
716	#41	—	2	4	no	—
717	#41	—	2	4	no	—
718	#41	—	2	4	no	—
719	#41	—	2	4	no	—
720	#41	—	4	8	no	—
721	#41	—	4	2	no	—
722	#41	—	4	2	no	—
723	#41	—	4	8	no	—
724	#41	#41×C₆₇	1	4	yes	—
725	C₂×Q₈	—	2	1	no	—
726	C₂×Q₈	—	2	2	no	—
727	C₂×Q₈	—	2	2	no	—
728	C₂×Q₈	—	2	2	no	—
729	C₂×Q₈	—	2	4	no	—
730	C₂×Q₈	—	2	2	no	—
731	C₂×Q₈	—	2	2	no	—
732	C₂×Q₈	—	4	2	no	—
733	C₂×Q₈	—	8	2	no	—
734	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
735	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
736	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
737	C₂×D₄	—	2	1	no	—
738	C₂×D₄	—	2	4	no	—
739	C₂×D₄	—	2	4	no	—
740	C₂×D₄	—	2	2	no	—
741	C₂×D₄	—	2	2	no	—
742	C₂×D₄	—	2	2	no	—
743	C₂×D₄	—	2	2	no	—
744	C₂×D₄	—	2	2	no	—
745	C₂×D₄	—	2	1	no	—
746	C₂×D₄	—	2	2	no	—
747	C₂×D₄	—	2	1	no	—
748	C₂×D₄	—	4	2	no	—
749	C₂×D₄	—	4	8	no	—
750	C₂×D₄	—	4	4	no	—
751	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
752	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
753	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
754	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
755	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
756	C₂²×C₄	—	2	1	no	—
757	C₂²×C₄	—	2	4	no	—
758	C₂²×C₄	—	2	4	no	—
759	C₂²×C₄	—	2	1	no	—
760	C₂²×C₄	—	2	1	no	—
761	C₂²×C₄	—	2	2	no	—
762	C₂²×C₄	—	2	2	no	—
763	C₂²×C₄	—	2	4	no	—
764	C₂²×C₄	—	2	4	no	—
765	C₂²×C₄	—	2	1	no	—
766	C₂²×C₄	—	2	2	no	—
767	C₂²×C₄	—	2	2	no	—
768	C₂²×C₄	—	2	2	no	—
769	C₂²×C₄	—	2	1	no	—
770	C₂²×C₄	—	4	8	no	—
771	C₂²×C₄	—	8	4	no	—
772	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
773	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
774	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
775	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
776	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
777	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
778	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
779	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
780	Q₁₆	—	2	4	no	—
781	Q₁₆	—	4	4	no	—
782	SD₁₆	—	2	4	no	—
783	SD₁₆	—	4	4	no	—
784	M₁₆	—	2	2	no	—
785	M₁₆	—	2	2	no	—
786	M₁₆	—	2	4	no	—
787	M₁₆	—	4	4	no	—
788	C₂×C₈	—	4	4	no	—
789	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
790	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
791	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
792	C₄⋊C₄	—	2	1	no	—
793	C₄⋊C₄	—	2	4	no	—
794	C₄⋊C₄	—	2	4	no	—
795	C₄⋊C₄	—	2	2	no	—
796	C₄⋊C₄	—	2	1	no	—
797	C₄⋊C₄	—	2	2	no	—
798	C₄⋊C₄	—	2	2	no	—
799	C₄⋊C₄	—	2	2	no	—
800	C₄⋊C₄	—	2	2	no	—
801	C₄⋊C₄	—	2	2	no	—
802	C₄⋊C₄	—	2	4	no	—
803	C₄⋊C₄	—	2	4	no	—
804	C₄⋊C₄	—	2	1	no	—
805	C₄⋊C₄	—	2	1	no	—
806	C₄⋊C₄	—	2	1	no	—
807	C₄⋊C₄	—	2	2	no	—
808	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
809	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
810	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
811	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
812	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
813	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
814	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
815	C₂²⋊C₄	—	2	2	no	—
816	C₂²⋊C₄	—	2	4	no	—
817	C₂²⋊C₄	—	2	4	no	—
818	C₂²⋊C₄	—	2	1	no	—
819	C₂²⋊C₄	—	2	2	no	—
820	C₂²⋊C₄	—	2	2	no	—
821	C₂²⋊C₄	—	2	2	no	—
822	C₂²⋊C₄	—	2	1	no	—
823	C₂²⋊C₄	—	2	1	no	—
824	C₂²⋊C₄	—	2	2	no	—
825	C₂²⋊C₄	—	2	2	no	—
826	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
827	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
828	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
829	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
830	C₄²	—	2	1	no	—
831	C₄²	—	2	1	no	—
832	C₄²	—	2	1	no	—
833	C₄²	—	2	2	no	—
834	C₄²	—	2	2	no	—
835	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
836	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
837	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
838	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
839	C₂³	—	2	4	no	—
840	C₂³	—	2	4	no	—
841	C₂³	—	2	1	no	—
842	C₂³	—	2	2	no	—
843	C₂³	—	4	2	no	—
844	C₂³	—	4	4	no	—
845	C₂³	—	4	4	no	—
846	C₂³	—	8	2	no	—
847	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
848	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
849	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
850	Q₈	—	2	1	no	—
851	Q₈	—	2	2	no	—
852	Q₈	—	2	2	no	—
853	Q₈	—	2	2	no	—
854	Q₈	—	2	2	no	—
855	Q₈	—	4	4	no	—
856	Q₈	—	4	2	no	—
857	Q₈	—	8	2	no	—
858	Q₈	—	8	2	no	—
859	Q₈	C₂×#41×C₆₇	1	2	yes	—
860	D₄	—	2	4	no	—
861	D₄	—	2	4	no	—
862	D₄	—	2	2	no	—
863	D₄	—	2	2	no	—
864	D₄	—	2	1	no	—
865	D₄	—	2	2	no	—
866	D₄	—	4	4	no	—
867	D₄	—	4	4	no	—
868	D₄	—	4	4	no	—
869	D₄	—	4	4	no	—
870	D₄	—	4	4	no	—
871	D₄	—	4	2	no	—
872	D₄	—	8	1	no	—
873	D₄	—	8	2	no	—
874	D₄	#137×C₆₇	1	4	yes	complemented
875	D₄	C₂×#41×C₆₇	1	2	yes	—
876	C₂×C₄	—	2	4	no	—
877	C₂×C₄	—	2	1	no	—
878	C₂×C₄	—	2	4	no	—
879	C₂×C₄	—	2	4	no	—
880	C₂×C₄	—	2	4	no	—
881	C₂×C₄	—	2	2	no	—
882	C₂×C₄	—	2	2	no	—
883	C₂×C₄	—	2	2	no	—
884	C₂×C₄	—	2	2	no	—
885	C₂×C₄	—	2	2	no	—
886	C₂×C₄	—	2	1	no	—
887	C₂×C₄	—	2	1	no	—
888	C₂×C₄	—	2	2	no	—
889	C₂×C₄	—	2	2	no	—
890	C₂×C₄	—	2	2	no	—
891	C₂×C₄	—	2	4	no	—
892	C₂×C₄	—	4	1	no	—
893	C₂×C₄	—	4	4	no	—
894	C₂×C₄	—	4	4	no	—
895	C₂×C₄	—	4	4	no	—
896	C₂×C₄	—	4	2	no	—
897	C₂×C₄	—	4	4	no	—
898	C₂×C₄	—	4	2	no	—
899	C₂×C₄	—	4	4	no	—
900	C₂×C₄	—	4	2	no	—
901	C₂×C₄	—	8	1	no	—
902	C₂×C₄	—	8	4	no	—
903	C₂×C₄	—	8	4	no	—
904	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
905	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
906	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
907	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
908	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
909	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
910	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
911	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
912	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
913	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
914	C₈	—	2	2	no	—
915	C₈	—	2	2	no	—
916	C₈	—	2	4	no	—
917	C₂²	—	2	1	no	—
918	C₂²	—	2	1	no	—
919	C₂²	—	2	2	no	—
920	C₂²	—	2	2	no	—
921	C₂²	—	2	2	no	—
922	C₂²	—	2	2	no	—
923	C₂²	—	2	2	no	—
924	C₂²	—	2	2	no	—
925	C₂²	—	4	8	no	—
926	C₂²	—	4	1	no	—
927	C₂²	—	4	1	no	—
928	C₂²	—	4	2	no	—
929	C₂²	—	4	2	no	—
930	C₂²	—	4	2	no	—
931	C₂²	—	8	8	no	—
932	C₂²	#546×C₆₇	1	2	yes	—
933	C₂²	C₂×#137×C₆₇	1	4	yes	—
934	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
935	C₄	—	2	1	no	—
936	C₄	—	2	1	no	—
937	C₄	—	2	1	no	—
938	C₄	—	2	2	no	—
939	C₄	—	2	2	no	—
940	C₄	—	2	2	no	—
941	C₄	—	4	1	no	—
942	C₄	—	4	2	no	—
943	C₄	—	4	4	no	—
944	C₄	—	4	1	no	—
945	C₄	—	4	2	no	—
946	C₄	—	4	2	no	—
947	C₄	#546×C₆₇	1	2	yes	—
948	C₄	C₂×#137×C₆₇	1	2	yes	—
949	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
950	C₄	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
951	C₂	—	2	2	no	—
952	C₂	—	2	4	no	—
953	C₂	—	4	2	no	—
954	C₂	—	4	2	no	—
955	C₂	—	8	2	no	—
956	C₂	C₂×#546×C₆₇	1	1	yes	characteristic
957	C₂	C₂²×#137×C₆₇	1	1	yes	characteristic
958	C₂	C₆₇×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
prime radical	D₄×#41×C₆₇	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ C₂×C₄×D₄×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#554×C₆₇	C₂	semidirect
3. C₆₇×#3333	C₂	semidirect
4. C₆₇×#3331	C₂	semidirect
5. C₆₇×#3316	C₂	semidirect
6. C₆₇×#3314	C₂	semidirect
7. C₆₇×#3299	C₂	semidirect
8. C₆₇×#3295	C₂	semidirect
9. C₆₇×#3141	C₂	semidirect
10. C₆₇×#3092	C₂	semidirect
11. C₆₇×#3079	C₂	semidirect
12. C₆₇×#3056	C₂	semidirect
13. C₆₇×#3037	C₂	semidirect
14. C₆₇×#3007	C₂	semidirect
15. C₄×#137×C₆₇	C₂	semidirect
16. D₄×M₁₆×C₆₇	C₂	semidirect
17. C₂×#417×C₆₇	C₂	semidirect
20. C₂×#137×C₆₇	C₂²	semidirect
21. C₂²×M₁₆×C₆₇	C₂²	semidirect
26. #554×C₆₇	C₂²	semidirect
27. #554×C₆₇	C₂²	semidirect
39. C₂×C₄⋊Q₈×C₆₇	C₂²	semidirect
44. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
46. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
50. C₂²×C₄⋊C₄×C₆₇	C₂²	semidirect
51. #489×C₆₇	C₂²	semidirect
52. #487×C₆₇	C₂²	semidirect
53. #486×C₆₇	C₂²	semidirect
54. #484×C₆₇	C₂²	semidirect
55. #483×C₆₇	C₂²	semidirect
56. #481×C₆₇	C₂²	semidirect
57. #480×C₆₇	C₂²	semidirect
58. #477×C₆₇	C₂²	semidirect
59. #476×C₆₇	C₂²	semidirect
60. #475×C₆₇	C₂²	semidirect
61. #474×C₆₇	C₂²	semidirect
62. #470×C₆₇	C₂²	semidirect
63. #468×C₆₇	C₂²	semidirect
64. #467×C₆₇	C₂²	semidirect
65. #465×C₆₇	C₂²	semidirect
66. #464×C₆₇	C₂²	semidirect
67. #462×C₆₇	C₂²	semidirect
68. #460×C₆₇	C₂²	semidirect
69. #452×C₆₇	C₂²	semidirect
70. #452×C₆₇	C₂²	semidirect
71. #451×C₆₇	C₂²	semidirect
72. #450×C₆₇	C₂²	semidirect
73. #441×C₆₇	C₂²	semidirect
74. #440×C₆₇	C₂²	semidirect
75. C₄×Q₁₆×C₆₇	C₂²	semidirect
76. C₄×SD₁₆×C₆₇	C₂²	semidirect
77. #436×C₆₇	C₂²	semidirect
78. #435×C₆₇	C₂²	semidirect
80. #428×C₆₇	C₂²	semidirect
81. #428×C₆₇	C₂²	semidirect
82. #423×C₆₇	C₂²	semidirect
83. #419×C₆₇	C₂²	semidirect
86. #417×C₆₇	C₂²	semidirect
87. #417×C₆₇	C₂²	semidirect
88. #417×C₆₇	C₂²	semidirect
89. #417×C₆₇	C₂²	semidirect
90. #417×C₆₇	C₂²	semidirect
91. C₂×#103×C₆₇	C₂²	semidirect
92. C₂×#102×C₆₇	C₂²	semidirect
93. #407×C₆₇	C₂²	semidirect
94. C₄×M₁₆×C₆₇	C₂²	semidirect
394. D₄×C₆₇	#137	semidirect
471. #61162	C₆₇	direct (N × H)
480. C₂×#554	C₂×C₆₇	semidirect
482. #3333	C₂×C₆₇	semidirect
483. #3331	C₂×C₆₇	semidirect
484. #3316	C₂×C₆₇	semidirect
485. #3314	C₂×C₆₇	semidirect
486. #3299	C₂×C₆₇	semidirect
487. #3295	C₂×C₆₇	semidirect
488. #3141	C₂×C₆₇	semidirect
489. #3092	C₂×C₆₇	semidirect
490. #3079	C₂×C₆₇	semidirect
491. #3056	C₂×C₆₇	semidirect
492. #3037	C₂×C₆₇	semidirect
493. #3007	C₂×C₆₇	semidirect
494. C₄×#137	C₂×C₆₇	semidirect
495. D₄×M₁₆	C₂×C₆₇	semidirect
496. C₂×#417	C₂×C₆₇	semidirect
497. C₆₇	#61162	direct (N × H)
500. C₂×#137	C₂²×C₆₇	semidirect
501. C₂²×M₁₆	C₂²×C₆₇	semidirect
506. #554	C₂²×C₆₇	semidirect
507. #554	C₂²×C₆₇	semidirect
519. C₂×C₄⋊Q₈	C₂²×C₆₇	semidirect
524. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
526. C₂×C₄×Q₈	C₂²×C₆₇	semidirect
530. C₂²×C₄⋊C₄	C₂²×C₆₇	semidirect
531. #489	C₂²×C₆₇	semidirect
532. #487	C₂²×C₆₇	semidirect
533. #486	C₂²×C₆₇	semidirect
534. #484	C₂²×C₆₇	semidirect
535. #483	C₂²×C₆₇	semidirect
536. #481	C₂²×C₆₇	semidirect
537. #480	C₂²×C₆₇	semidirect
538. #477	C₂²×C₆₇	semidirect
539. #476	C₂²×C₆₇	semidirect
540. #475	C₂²×C₆₇	semidirect
541. #474	C₂²×C₆₇	semidirect
542. #470	C₂²×C₆₇	semidirect
543. #468	C₂²×C₆₇	semidirect
544. #467	C₂²×C₆₇	semidirect
545. #465	C₂²×C₆₇	semidirect
546. #464	C₂²×C₆₇	semidirect
547. #462	C₂²×C₆₇	semidirect
548. #460	C₂²×C₆₇	semidirect
549. #452	C₂²×C₆₇	semidirect
550. #452	C₂²×C₆₇	semidirect
551. #451	C₂²×C₆₇	semidirect
552. #450	C₂²×C₆₇	semidirect
553. #441	C₂²×C₆₇	semidirect
554. #440	C₂²×C₆₇	semidirect
555. C₄×Q₁₆	C₂²×C₆₇	semidirect
556. C₄×SD₁₆	C₂²×C₆₇	semidirect
557. #436	C₂²×C₆₇	semidirect
558. #435	C₂²×C₆₇	semidirect
560. #428	C₂²×C₆₇	semidirect
561. #428	C₂²×C₆₇	semidirect
562. #423	C₂²×C₆₇	semidirect
563. #419	C₂²×C₆₇	semidirect
566. #417	C₂²×C₆₇	semidirect
567. #417	C₂²×C₆₇	semidirect
568. #417	C₂²×C₆₇	semidirect
569. #417	C₂²×C₆₇	semidirect
570. #417	C₂²×C₆₇	semidirect
571. C₂×#103	C₂²×C₆₇	semidirect
572. C₂×#102	C₂²×C₆₇	semidirect
573. #407	C₂²×C₆₇	semidirect
574. C₄×M₁₆	C₂²×C₆₇	semidirect
874. D₄	#137×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#554×C₆₇	2
D₄×#41×C₆₇	2
C₆₇×#3333	2
C₆₇×#3331	2
C₆₇×#3316	2
C₆₇×#3314	2
C₆₇×#3299	2
C₆₇×#3295	2
C₆₇×#3141	2
C₆₇×#3092	2
C₆₇×#3079	2
C₆₇×#3056	2
C₆₇×#3037	2
C₆₇×#3007	2
C₄×#137×C₆₇	2
D₄×M₁₆×C₆₇	2
C₂×#417×C₆₇	2
#61162	67

Subgroups — C67×#61162 #30740413

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61162 #30740413