Subgroups — C₆₇×#61680 #30740931

Order 17152.

2096 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3550	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#3496	C₂	1	1	yes	maximal, characteristic
3	C₆₇×#3324	C₂	1	2	yes	maximal, complemented
4	C₆₇×#3311	C₂	1	4	yes	maximal, complemented
5	C₆₇×#3302	C₂	1	2	yes	maximal, complemented
6	D₄×SD₁₆×C₆₇	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3276	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3266	C₂	1	4	yes	maximal, complemented
9	C₆₇×#3216	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#3210	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#3201	C₂	1	4	yes	maximal, complemented
12	C₆₇×#3110	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3101	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3009	C₂	1	4	yes	maximal, complemented
15	C₆₇×#2981	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×H(5,𝔽₂)×C₆₇	C₂²	1	2	yes	—
17	C₂×#137×C₆₇	C₂²	1	4	yes	complemented
18	C₂²×SD₁₆×C₆₇	C₂²	1	4	yes	complemented
19	#563×C₆₇	—	2	2	no	—
20	#559×C₆₇	—	2	1	no	—
21	Q₈²×C₆₇	—	2	1	no	—
22	#556×C₆₇	C₂²	1	2	yes	complemented
23	#556×C₆₇	C₂²	1	2	yes	complemented
24	D₄×Q₈×C₆₇	C₂²	1	2	yes	complemented
25	D₄×Q₈×C₆₇	C₂²	1	2	yes	complemented
26	#547×C₆₇	—	2	1	no	—
27	#547×C₆₇	C₂²	1	2	yes	—
28	#546×C₆₇	—	2	2	no	—
29	#546×C₆₇	C₂²	1	4	yes	—
30	D₄²×C₆₇	—	2	1	no	—
31	D₄²×C₆₇	C₂²	1	2	yes	—
32	#542×C₆₇	—	2	2	no	—
33	#542×C₆₇	—	2	2	no	—
34	#537×C₆₇	C₂²	1	2	yes	—
35	#536×C₆₇	C₂²	1	4	yes	complemented
36	#534×C₆₇	—	2	2	no	—
37	#533×C₆₇	C₂²	1	1	yes	characteristic, complemented
38	#533×C₆₇	C₂²	1	1	yes	characteristic, complemented
39	#532×C₆₇	C₂²	1	1	yes	characteristic
40	#532×C₆₇	C₂²	1	1	yes	characteristic
41	C₂×#121×C₆₇	—	2	2	no	—
42	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
43	#497×C₆₇	C₂²	1	2	yes	complemented
44	#494×C₆₇	C₂²	1	1	yes	characteristic, complemented
45	#492×C₆₇	C₂²	1	1	yes	characteristic, complemented
46	#489×C₆₇	C₂²	1	2	yes	complemented
47	#487×C₆₇	C₂²	1	1	yes	characteristic, complemented
48	#486×C₆₇	C₂²	1	1	yes	characteristic, complemented
49	#485×C₆₇	C₂²	1	4	yes	complemented
50	#484×C₆₇	C₂²	1	2	yes	complemented
51	#483×C₆₇	C₂²	1	2	yes	complemented
52	#482×C₆₇	C₂²	1	4	yes	complemented
53	#476×C₆₇	C₂²	1	2	yes	complemented
54	#474×C₆₇	C₂²	1	2	yes	complemented
55	#470×C₆₇	C₂²	1	4	yes	complemented
56	#468×C₆₇	C₂²	1	4	yes	complemented
57	#467×C₆₇	C₂²	1	4	yes	complemented
58	#465×C₆₇	C₂²	1	4	yes	complemented
59	#464×C₆₇	C₂²	1	4	yes	complemented
60	#462×C₆₇	C₂²	1	2	yes	complemented
61	#461×C₆₇	C₂²	1	2	yes	complemented
62	#461×C₆₇	C₂²	1	2	yes	complemented
63	#460×C₆₇	C₂²	1	2	yes	complemented
64	#452×C₆₇	C₂²	1	4	yes	complemented
65	#452×C₆₇	C₂²	1	4	yes	complemented
66	#452×C₆₇	C₂²	1	4	yes	complemented
67	#452×C₆₇	C₂²	1	4	yes	complemented
68	#451×C₆₇	C₂²	1	4	yes	complemented
69	#450×C₆₇	C₂²	1	2	yes	—
70	#450×C₆₇	C₂²	1	2	yes	—
71	#450×C₆₇	C₂²	1	4	yes	complemented
72	#450×C₆₇	C₂²	1	4	yes	complemented
73	#448×C₆₇	C₂²	1	4	yes	complemented
74	#440×C₆₇	C₂²	1	4	yes	complemented
75	C₄×SD₁₆×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	complemented
80	#432×C₆₇	C₂²	1	1	yes	characteristic, complemented
81	#431×C₆₇	C₂²	1	1	yes	characteristic, complemented
82	#418×C₆₇	C₂²	1	4	yes	complemented
83	#416×C₆₇	C₂²	1	4	yes	complemented
84	#408×C₆₇	C₂²	1	4	yes	complemented
85	H(5,𝔽₂)×C₆₇	—	4	8	no	—
86	C₂×#41×C₆₇	—	2	2	no	—
87	C₂×#41×C₆₇	C₂³	1	4	yes	—
88	C₂×#41×C₆₇	C₂³	1	2	yes	—
89	C₂×#41×C₆₇	C₂³	1	2	yes	—
90	C₂²×Q₈×C₆₇	C₂³	1	4	yes	—
91	C₂²×D₄×C₆₇	—	2	4	no	—
92	C₂²×D₄×C₆₇	—	2	2	no	—
93	C₂²×D₄×C₆₇	—	2	2	no	—
94	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
95	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
96	C₂³×C₄×C₆₇	—	2	1	no	—
97	#137×C₆₇	—	4	8	no	—
98	C₂×Q₁₆×C₆₇	C₂³	1	4	yes	—
99	C₂×Q₁₆×C₆₇	C₂³	1	4	yes	—
100	C₂×SD₁₆×C₆₇	—	4	8	no	—
101	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
102	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
103	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
104	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
105	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
106	C₂×M₁₆×C₆₇	C₂³	1	4	yes	—
107	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
108	C₄⋊Q₈×C₆₇	—	2	4	no	—
109	C₄⋊Q₈×C₆₇	—	2	2	no	—
110	C₄⋊Q₈×C₆₇	—	2	2	no	—
111	C₄⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
112	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
113	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
114	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
115	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
116	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
117	#127×C₆₇	D₄	1	1	yes	characteristic
118	#127×C₆₇	C₂³	1	1	yes	characteristic
119	#126×C₆₇	—	2	4	no	—
120	#126×C₆₇	—	2	4	no	—
121	#125×C₆₇	—	2	1	no	—
122	#125×C₆₇	—	2	1	no	—
123	#124×C₆₇	—	2	4	no	—
124	#124×C₆₇	—	2	2	no	—
125	#124×C₆₇	—	2	2	no	—
126	#124×C₆₇	D₄	1	2	yes	—
127	#124×C₆₇	C₂³	1	2	yes	—
128	#123×C₆₇	—	2	4	no	—
129	#123×C₆₇	—	2	4	no	—
130	#123×C₆₇	—	2	4	no	—
131	#123×C₆₇	—	2	4	no	—
132	C₂²⋊Q₈×C₆₇	—	2	2	no	—
133	C₂²⋊Q₈×C₆₇	—	2	1	no	—
134	C₂²⋊Q₈×C₆₇	—	2	1	no	—
135	C₂²⋊Q₈×C₆₇	—	2	4	no	—
136	C₂²⋊Q₈×C₆₇	—	2	4	no	—
137	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
138	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
139	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
140	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
141	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
142	#121×C₆₇	—	2	4	no	—
143	#121×C₆₇	—	2	2	no	—
144	#121×C₆₇	—	2	2	no	—
145	#121×C₆₇	—	2	1	no	—
146	#121×C₆₇	—	2	1	no	—
147	#121×C₆₇	—	2	2	no	—
148	#121×C₆₇	—	2	4	no	—
149	#121×C₆₇	D₄	1	2	yes	—
150	#121×C₆₇	D₄	1	2	yes	—
151	#121×C₆₇	C₂³	1	4	yes	—
152	#120×C₆₇	—	2	4	no	—
153	#120×C₆₇	—	2	4	no	—
154	C₄×Q₈×C₆₇	—	2	2	no	—
155	C₄×Q₈×C₆₇	—	2	2	no	—
156	C₄×Q₈×C₆₇	—	2	1	no	—
157	C₄×Q₈×C₆₇	—	2	1	no	—
158	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
159	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
160	C₄×D₄×C₆₇	—	2	2	no	—
161	C₄×D₄×C₆₇	—	2	2	no	—
162	C₄×D₄×C₆₇	—	2	1	no	—
163	C₄×D₄×C₆₇	—	2	1	no	—
164	C₄×D₄×C₆₇	—	2	1	no	—
165	C₄×D₄×C₆₇	—	2	1	no	—
166	C₄×D₄×C₆₇	C₂³	1	2	yes	—
167	C₄×D₄×C₆₇	C₂³	1	2	yes	—
168	C₄×D₄×C₆₇	C₂³	1	2	yes	—
169	C₄×D₄×C₆₇	C₂³	1	2	yes	—
170	#117×C₆₇	—	2	1	no	—
171	#117×C₆₇	—	2	1	no	—
172	#117×C₆₇	C₂³	1	4	yes	—
173	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
174	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
175	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
176	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
177	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
178	#107×C₆₇	C₂³	1	4	yes	—
179	#106×C₆₇	C₂³	1	2	yes	—
180	#106×C₆₇	C₂³	1	2	yes	—
181	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
182	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
183	#103×C₆₇	C₂³	1	2	yes	—
184	#103×C₆₇	C₂³	1	4	yes	—
185	#103×C₆₇	C₂³	1	2	yes	—
186	#103×C₆₇	C₂³	1	4	yes	—
187	#103×C₆₇	C₂³	1	4	yes	—
188	#102×C₆₇	C₂³	1	2	yes	—
189	#102×C₆₇	C₂³	1	4	yes	—
190	#102×C₆₇	C₂³	1	2	yes	—
191	#102×C₆₇	C₂³	1	4	yes	—
192	#102×C₆₇	C₂³	1	4	yes	—
193	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
194	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
195	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
196	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
197	#97×C₆₇	C₂³	1	2	yes	—
198	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
199	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
200	C₂⁴×C₆₇	—	2	1	no	—
201	C₂⁴×C₆₇	—	2	4	no	—
202	#41×C₆₇	—	2	8	no	—
203	#41×C₆₇	—	4	4	no	—
204	#41×C₆₇	—	4	4	no	—
205	#41×C₆₇	—	4	4	no	—
206	#41×C₆₇	—	4	8	no	—
207	C₂×Q₈×C₆₇	—	2	1	no	—
208	C₂×Q₈×C₆₇	—	2	1	no	—
209	C₂×Q₈×C₆₇	—	2	4	no	—
210	C₂×Q₈×C₆₇	—	4	4	no	—
211	C₂×Q₈×C₆₇	—	4	4	no	—
212	C₂×Q₈×C₆₇	C₂×D₄	1	2	yes	—
213	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
214	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
215	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
216	C₂×D₄×C₆₇	—	2	4	no	—
217	C₂×D₄×C₆₇	—	2	8	no	—
218	C₂×D₄×C₆₇	—	2	4	no	—
219	C₂×D₄×C₆₇	—	2	2	no	—
220	C₂×D₄×C₆₇	—	2	4	no	—
221	C₂×D₄×C₆₇	—	2	1	no	—
222	C₂×D₄×C₆₇	—	2	1	no	—
223	C₂×D₄×C₆₇	—	2	4	no	—
224	C₂×D₄×C₆₇	—	2	1	no	—
225	C₂×D₄×C₆₇	—	4	4	no	—
226	C₂×D₄×C₆₇	—	4	8	no	—
227	C₂×D₄×C₆₇	—	4	16	no	—
228	C₂×D₄×C₆₇	—	8	4	no	—
229	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
230	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
231	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	—
232	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
233	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
234	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
235	C₂²×C₄×C₆₇	—	2	1	no	—
236	C₂²×C₄×C₆₇	—	2	4	no	—
237	C₂²×C₄×C₆₇	—	2	4	no	—
238	C₂²×C₄×C₆₇	—	2	2	no	—
239	C₂²×C₄×C₆₇	—	2	2	no	—
240	C₂²×C₄×C₆₇	—	2	2	no	—
241	C₂²×C₄×C₆₇	—	8	2	no	—
242	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
243	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
244	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
245	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
246	Q₁₆×C₆₇	—	4	4	no	—
247	Q₁₆×C₆₇	—	4	4	no	—
248	SD₁₆×C₆₇	—	2	4	no	—
249	SD₁₆×C₆₇	—	2	8	no	—
250	SD₁₆×C₆₇	—	2	4	no	—
251	SD₁₆×C₆₇	—	4	4	no	—
252	SD₁₆×C₆₇	—	4	4	no	—
253	M₁₆×C₆₇	—	4	4	no	—
254	C₂×C₈×C₆₇	—	4	4	no	—
255	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
256	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
257	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
258	C₄⋊C₄×C₆₇	—	2	1	no	—
259	C₄⋊C₄×C₆₇	—	2	4	no	—
260	C₄⋊C₄×C₆₇	—	2	1	no	—
261	C₄⋊C₄×C₆₇	—	2	1	no	—
262	C₄⋊C₄×C₆₇	—	2	1	no	—
263	C₄⋊C₄×C₆₇	—	2	1	no	—
264	C₄⋊C₄×C₆₇	—	2	1	no	—
265	C₄⋊C₄×C₆₇	—	2	1	no	—
266	C₄⋊C₄×C₆₇	—	2	1	no	—
267	C₄⋊C₄×C₆₇	—	2	1	no	—
268	C₄⋊C₄×C₆₇	—	2	4	no	—
269	C₄⋊C₄×C₆₇	—	2	4	no	—
270	C₄⋊C₄×C₆₇	—	2	2	no	—
271	C₄⋊C₄×C₆₇	—	2	2	no	—
272	C₄⋊C₄×C₆₇	—	2	2	no	—
273	C₄⋊C₄×C₆₇	—	2	2	no	—
274	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
275	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
276	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
277	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
278	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
279	C₂²⋊C₄×C₆₇	—	2	4	no	—
280	C₂²⋊C₄×C₆₇	—	2	2	no	—
281	C₂²⋊C₄×C₆₇	—	2	2	no	—
282	C₂²⋊C₄×C₆₇	—	2	4	no	—
283	C₂²⋊C₄×C₆₇	—	2	4	no	—
284	C₂²⋊C₄×C₆₇	—	2	4	no	—
285	C₂²⋊C₄×C₆₇	—	2	2	no	—
286	C₂²⋊C₄×C₆₇	—	2	2	no	—
287	C₂²⋊C₄×C₆₇	—	2	2	no	—
288	C₂²⋊C₄×C₆₇	—	2	4	no	—
289	C₂²⋊C₄×C₆₇	—	2	2	no	—
290	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
291	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
292	C₄²×C₆₇	—	2	2	no	—
293	C₄²×C₆₇	—	2	2	no	—
294	C₄²×C₆₇	—	2	4	no	—
295	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
296	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
297	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
298	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
299	C₂³×C₆₇	—	2	4	no	—
300	C₂³×C₆₇	—	2	2	no	—
301	C₂³×C₆₇	—	2	2	no	—
302	C₂³×C₆₇	—	4	8	no	—
303	C₂³×C₆₇	—	8	1	no	—
304	C₂³×C₆₇	—	8	1	no	—
305	C₂³×C₆₇	—	8	4	no	—
306	C₂³×C₆₇	—	8	4	no	—
307	C₂³×C₆₇	C₂²×D₄	1	4	yes	—
308	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
309	Q₈×C₆₇	—	2	2	no	—
310	Q₈×C₆₇	—	2	4	no	—
311	Q₈×C₆₇	—	2	2	no	—
312	Q₈×C₆₇	—	2	4	no	—
313	Q₈×C₆₇	—	4	2	no	—
314	Q₈×C₆₇	—	4	2	no	—
315	Q₈×C₆₇	—	4	2	no	—
316	Q₈×C₆₇	—	8	4	no	—
317	D₄×C₆₇	—	2	4	no	—
318	D₄×C₆₇	—	2	4	no	—
319	D₄×C₆₇	—	2	2	no	—
320	D₄×C₆₇	—	2	4	no	—
321	D₄×C₆₇	—	4	2	no	—
322	D₄×C₆₇	—	4	4	no	—
323	D₄×C₆₇	—	4	2	no	—
324	D₄×C₆₇	—	4	8	no	—
325	D₄×C₆₇	—	4	8	no	—
326	D₄×C₆₇	—	4	4	no	—
327	D₄×C₆₇	—	4	2	no	—
328	D₄×C₆₇	—	8	1	no	—
329	D₄×C₆₇	—	8	4	no	—
330	D₄×C₆₇	H(5,𝔽₂)	1	4	yes	—
331	C₂×C₄×C₆₇	—	2	2	no	—
332	C₂×C₄×C₆₇	—	2	4	no	—
333	C₂×C₄×C₆₇	—	2	4	no	—
334	C₂×C₄×C₆₇	—	2	2	no	—
335	C₂×C₄×C₆₇	—	2	2	no	—
336	C₂×C₄×C₆₇	—	2	2	no	—
337	C₂×C₄×C₆₇	—	2	2	no	—
338	C₂×C₄×C₆₇	—	2	2	no	—
339	C₂×C₄×C₆₇	—	2	2	no	—
340	C₂×C₄×C₆₇	—	2	2	no	—
341	C₂×C₄×C₆₇	—	4	1	no	—
342	C₂×C₄×C₆₇	—	4	8	no	—
343	C₂×C₄×C₆₇	—	4	4	no	—
344	C₂×C₄×C₆₇	—	4	4	no	—
345	C₂×C₄×C₆₇	—	8	2	no	—
346	C₂×C₄×C₆₇	—	8	1	no	—
347	C₂×C₄×C₆₇	—	8	4	no	—
348	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
349	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
350	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
351	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
352	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
353	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
354	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
355	C₈×C₆₇	—	2	2	no	—
356	C₈×C₆₇	—	2	4	no	—
357	C₈×C₆₇	—	2	2	no	—
358	C₂²×C₆₇	—	2	1	no	—
359	C₂²×C₆₇	—	2	4	no	—
360	C₂²×C₆₇	—	2	4	no	—
361	C₂²×C₆₇	—	2	1	no	—
362	C₂²×C₆₇	—	2	4	no	—
363	C₂²×C₆₇	—	2	1	no	—
364	C₂²×C₆₇	—	2	4	no	—
365	C₂²×C₆₇	—	4	2	no	—
366	C₂²×C₆₇	—	4	2	no	—
367	C₂²×C₆₇	—	4	2	no	—
368	C₂²×C₆₇	—	4	2	no	—
369	C₂²×C₆₇	—	4	2	no	—
370	C₂²×C₆₇	—	8	4	no	—
371	C₂²×C₆₇	—	16	8	no	—
372	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
373	C₄×C₆₇	—	2	1	no	—
374	C₄×C₆₇	—	2	1	no	—
375	C₄×C₆₇	—	2	1	no	—
376	C₄×C₆₇	—	2	4	no	—
377	C₄×C₆₇	—	2	1	no	—
378	C₄×C₆₇	—	4	2	no	—
379	C₄×C₆₇	—	4	2	no	—
380	C₄×C₆₇	—	4	2	no	—
381	C₄×C₆₇	—	4	2	no	—
382	C₄×C₆₇	—	4	2	no	—
383	C₄×C₆₇	—	4	2	no	—
384	C₄×C₆₇	#577	1	2	yes	—
385	C₄×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
386	#61680	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
387	C₂×C₆₇	—	4	1	no	—
388	C₂×C₆₇	—	4	4	no	—
389	C₂×C₆₇	—	4	4	no	—
390	C₂×C₆₇	—	8	2	no	—
391	C₂×C₆₇	#3484	1	1	yes	characteristic
392	C₂×C₆₇	C₂×#577	1	1	yes	characteristic
393	C₂×C₆₇	#3586	1	1	yes	characteristic
394	#3550	C₂×C₆₇	1	1	yes	characteristic, complemented
395	#3496	C₂×C₆₇	1	1	yes	characteristic
396	#3324	C₂×C₆₇	1	2	yes	complemented
397	#3311	C₂×C₆₇	1	4	yes	complemented
398	#3302	C₂×C₆₇	1	2	yes	complemented
399	D₄×SD₁₆	C₂×C₆₇	1	2	yes	complemented
400	#3276	C₂×C₆₇	1	2	yes	complemented
401	#3266	C₂×C₆₇	1	4	yes	complemented
402	#3216	C₂×C₆₇	1	1	yes	characteristic, complemented
403	#3210	C₂×C₆₇	1	1	yes	characteristic, complemented
404	#3201	C₂×C₆₇	1	4	yes	complemented
405	#3110	C₂×C₆₇	1	1	yes	characteristic, complemented
406	#3101	C₂×C₆₇	1	1	yes	characteristic, complemented
407	#3009	C₂×C₆₇	1	4	yes	complemented
408	#2981	C₂×C₆₇	1	1	yes	characteristic, complemented
409	C₆₇	#61680	1	1	yes	characteristic, direct product factor, Sylow
410	C₂×H(5,𝔽₂)	C₂²×C₆₇	1	2	yes	—
411	C₂×#137	C₂²×C₆₇	1	4	yes	complemented
412	C₂²×SD₁₆	C₂²×C₆₇	1	4	yes	complemented
413	#563	—	2	2	no	—
414	#559	—	2	1	no	—
415	Q₈²	—	2	1	no	—
416	#556	C₂²×C₆₇	1	2	yes	complemented
417	#556	C₂²×C₆₇	1	2	yes	complemented
418	D₄×Q₈	C₂²×C₆₇	1	2	yes	complemented
419	D₄×Q₈	C₂²×C₆₇	1	2	yes	complemented
420	#547	—	2	1	no	—
421	#547	C₂²×C₆₇	1	2	yes	—
422	#546	—	2	2	no	—
423	#546	C₂²×C₆₇	1	4	yes	—
424	D₄²	—	2	1	no	—
425	D₄²	C₂²×C₆₇	1	2	yes	—
426	#542	—	2	2	no	—
427	#542	—	2	2	no	—
428	#537	C₂²×C₆₇	1	2	yes	—
429	#536	C₂²×C₆₇	1	4	yes	complemented
430	#534	—	2	2	no	—
431	#533	C₂²×C₆₇	1	1	yes	characteristic, complemented
432	#533	C₂²×C₆₇	1	1	yes	characteristic, complemented
433	#532	C₂²×C₆₇	1	1	yes	characteristic
434	#532	C₂²×C₆₇	1	1	yes	characteristic
435	C₂×#121	—	2	2	no	—
436	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
437	#497	C₂²×C₆₇	1	2	yes	complemented
438	#494	C₂²×C₆₇	1	1	yes	characteristic, complemented
439	#492	C₂²×C₆₇	1	1	yes	characteristic, complemented
440	#489	C₂²×C₆₇	1	2	yes	complemented
441	#487	C₂²×C₆₇	1	1	yes	characteristic, complemented
442	#486	C₂²×C₆₇	1	1	yes	characteristic, complemented
443	#485	C₂²×C₆₇	1	4	yes	complemented
444	#484	C₂²×C₆₇	1	2	yes	complemented
445	#483	C₂²×C₆₇	1	2	yes	complemented
446	#482	C₂²×C₆₇	1	4	yes	complemented
447	#476	C₂²×C₆₇	1	2	yes	complemented
448	#474	C₂²×C₆₇	1	2	yes	complemented
449	#470	C₂²×C₆₇	1	4	yes	complemented
450	#468	C₂²×C₆₇	1	4	yes	complemented
451	#467	C₂²×C₆₇	1	4	yes	complemented
452	#465	C₂²×C₆₇	1	4	yes	complemented
453	#464	C₂²×C₆₇	1	4	yes	complemented
454	#462	C₂²×C₆₇	1	2	yes	complemented
455	#461	C₂²×C₆₇	1	2	yes	complemented
456	#461	C₂²×C₆₇	1	2	yes	complemented
457	#460	C₂²×C₆₇	1	2	yes	complemented
458	#452	C₂²×C₆₇	1	4	yes	complemented
459	#452	C₂²×C₆₇	1	4	yes	complemented
460	#452	C₂²×C₆₇	1	4	yes	complemented
461	#452	C₂²×C₆₇	1	4	yes	complemented
462	#451	C₂²×C₆₇	1	4	yes	complemented
463	#450	C₂²×C₆₇	1	2	yes	—
464	#450	C₂²×C₆₇	1	2	yes	—
465	#450	C₂²×C₆₇	1	4	yes	complemented
466	#450	C₂²×C₆₇	1	4	yes	complemented
467	#448	C₂²×C₆₇	1	4	yes	complemented
468	#440	C₂²×C₆₇	1	4	yes	complemented
469	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
470	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
471	#436	C₂²×C₆₇	1	2	yes	complemented
472	#435	C₂²×C₆₇	1	4	yes	complemented
473	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
474	#432	C₂²×C₆₇	1	1	yes	characteristic, complemented
475	#431	C₂²×C₆₇	1	1	yes	characteristic, complemented
476	#418	C₂²×C₆₇	1	4	yes	complemented
477	#416	C₂²×C₆₇	1	4	yes	complemented
478	#408	C₂²×C₆₇	1	4	yes	complemented
479	H(5,𝔽₂)	—	4	8	no	—
480	C₂×#41	—	2	2	no	—
481	C₂×#41	C₂³×C₆₇	1	4	yes	—
482	C₂×#41	C₂³×C₆₇	1	2	yes	—
483	C₂×#41	C₂³×C₆₇	1	2	yes	—
484	C₂²×Q₈	C₂³×C₆₇	1	4	yes	—
485	C₂²×D₄	—	2	4	no	—
486	C₂²×D₄	—	2	2	no	—
487	C₂²×D₄	—	2	2	no	—
488	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
489	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
490	C₂³×C₄	—	2	1	no	—
491	#137	—	4	8	no	—
492	C₂×Q₁₆	C₂³×C₆₇	1	4	yes	—
493	C₂×Q₁₆	C₂³×C₆₇	1	4	yes	—
494	C₂×SD₁₆	—	4	8	no	—
495	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
496	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
497	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
498	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
499	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
500	C₂×M₁₆	C₂³×C₆₇	1	4	yes	—
501	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
502	C₄⋊Q₈	—	2	4	no	—
503	C₄⋊Q₈	—	2	2	no	—
504	C₄⋊Q₈	—	2	2	no	—
505	C₄⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
506	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
507	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
508	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
509	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
510	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
511	#127	D₄×C₆₇	1	1	yes	characteristic
512	#127	C₂³×C₆₇	1	1	yes	characteristic
513	#126	—	2	4	no	—
514	#126	—	2	4	no	—
515	#125	—	2	1	no	—
516	#125	—	2	1	no	—
517	#124	—	2	4	no	—
518	#124	—	2	2	no	—
519	#124	—	2	2	no	—
520	#124	D₄×C₆₇	1	2	yes	—
521	#124	C₂³×C₆₇	1	2	yes	—
522	#123	—	2	4	no	—
523	#123	—	2	4	no	—
524	#123	—	2	4	no	—
525	#123	—	2	4	no	—
526	C₂²⋊Q₈	—	2	2	no	—
527	C₂²⋊Q₈	—	2	1	no	—
528	C₂²⋊Q₈	—	2	1	no	—
529	C₂²⋊Q₈	—	2	4	no	—
530	C₂²⋊Q₈	—	2	4	no	—
531	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
532	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
533	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
534	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
535	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
536	#121	—	2	4	no	—
537	#121	—	2	2	no	—
538	#121	—	2	2	no	—
539	#121	—	2	1	no	—
540	#121	—	2	1	no	—
541	#121	—	2	2	no	—
542	#121	—	2	4	no	—
543	#121	D₄×C₆₇	1	2	yes	—
544	#121	D₄×C₆₇	1	2	yes	—
545	#121	C₂³×C₆₇	1	4	yes	—
546	#120	—	2	4	no	—
547	#120	—	2	4	no	—
548	C₄×Q₈	—	2	2	no	—
549	C₄×Q₈	—	2	2	no	—
550	C₄×Q₈	—	2	1	no	—
551	C₄×Q₈	—	2	1	no	—
552	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
553	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
554	C₄×D₄	—	2	2	no	—
555	C₄×D₄	—	2	2	no	—
556	C₄×D₄	—	2	1	no	—
557	C₄×D₄	—	2	1	no	—
558	C₄×D₄	—	2	1	no	—
559	C₄×D₄	—	2	1	no	—
560	C₄×D₄	C₂³×C₆₇	1	2	yes	—
561	C₄×D₄	C₂³×C₆₇	1	2	yes	—
562	C₄×D₄	C₂³×C₆₇	1	2	yes	—
563	C₄×D₄	C₂³×C₆₇	1	2	yes	—
564	#117	—	2	1	no	—
565	#117	—	2	1	no	—
566	#117	C₂³×C₆₇	1	4	yes	—
567	C₂×C₄⋊C₄	—	2	2	no	—
568	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
569	C₂×C₂²⋊C₄	—	2	1	no	—
570	C₂×C₂²⋊C₄	—	2	4	no	—
571	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
572	#107	C₂³×C₆₇	1	4	yes	—
573	#106	C₂³×C₆₇	1	2	yes	—
574	#106	C₂³×C₆₇	1	2	yes	—
575	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
576	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
577	#103	C₂³×C₆₇	1	4	yes	—
578	#103	C₂³×C₆₇	1	4	yes	—
579	#103	C₂³×C₆₇	1	2	yes	—
580	#103	C₂³×C₆₇	1	2	yes	—
581	#103	C₂³×C₆₇	1	4	yes	—
582	#102	C₂³×C₆₇	1	2	yes	—
583	#102	C₂³×C₆₇	1	4	yes	—
584	#102	C₂³×C₆₇	1	2	yes	—
585	#102	C₂³×C₆₇	1	4	yes	—
586	#102	C₂³×C₆₇	1	4	yes	—
587	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
588	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
589	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
590	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
591	#97	C₂³×C₆₇	1	2	yes	—
592	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
593	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
594	C₂⁴	—	2	1	no	—
595	C₂⁴	—	2	4	no	—
596	#41	—	2	8	no	—
597	#41	—	4	4	no	—
598	#41	—	4	4	no	—
599	#41	—	4	4	no	—
600	#41	—	4	8	no	—
601	C₂×Q₈	—	2	1	no	—
602	C₂×Q₈	—	2	1	no	—
603	C₂×Q₈	—	2	4	no	—
604	C₂×Q₈	—	4	4	no	—
605	C₂×Q₈	—	4	4	no	—
606	C₂×Q₈	C₂×D₄×C₆₇	1	2	yes	—
607	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
608	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
609	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
610	C₂×D₄	—	2	4	no	—
611	C₂×D₄	—	2	8	no	—
612	C₂×D₄	—	2	4	no	—
613	C₂×D₄	—	2	2	no	—
614	C₂×D₄	—	2	4	no	—
615	C₂×D₄	—	2	1	no	—
616	C₂×D₄	—	2	1	no	—
617	C₂×D₄	—	2	4	no	—
618	C₂×D₄	—	2	1	no	—
619	C₂×D₄	—	4	4	no	—
620	C₂×D₄	—	4	8	no	—
621	C₂×D₄	—	4	16	no	—
622	C₂×D₄	—	8	4	no	—
623	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
624	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
625	C₂×D₄	C₂×D₄×C₆₇	1	4	yes	—
626	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
627	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
628	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
629	C₂²×C₄	—	2	1	no	—
630	C₂²×C₄	—	2	4	no	—
631	C₂²×C₄	—	2	4	no	—
632	C₂²×C₄	—	2	2	no	—
633	C₂²×C₄	—	2	2	no	—
634	C₂²×C₄	—	2	2	no	—
635	C₂²×C₄	—	8	2	no	—
636	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
637	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
638	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
639	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
640	Q₁₆	—	4	4	no	—
641	Q₁₆	—	4	4	no	—
642	SD₁₆	—	2	4	no	—
643	SD₁₆	—	2	8	no	—
644	SD₁₆	—	2	4	no	—
645	SD₁₆	—	4	4	no	—
646	SD₁₆	—	4	4	no	—
647	M₁₆	—	4	4	no	—
648	C₂×C₈	—	4	4	no	—
649	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
650	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
651	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
652	C₄⋊C₄	—	2	1	no	—
653	C₄⋊C₄	—	2	4	no	—
654	C₄⋊C₄	—	2	1	no	—
655	C₄⋊C₄	—	2	1	no	—
656	C₄⋊C₄	—	2	1	no	—
657	C₄⋊C₄	—	2	1	no	—
658	C₄⋊C₄	—	2	1	no	—
659	C₄⋊C₄	—	2	1	no	—
660	C₄⋊C₄	—	2	1	no	—
661	C₄⋊C₄	—	2	1	no	—
662	C₄⋊C₄	—	2	4	no	—
663	C₄⋊C₄	—	2	4	no	—
664	C₄⋊C₄	—	2	2	no	—
665	C₄⋊C₄	—	2	2	no	—
666	C₄⋊C₄	—	2	2	no	—
667	C₄⋊C₄	—	2	2	no	—
668	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
669	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
670	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
671	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
672	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
673	C₂²⋊C₄	—	2	4	no	—
674	C₂²⋊C₄	—	2	2	no	—
675	C₂²⋊C₄	—	2	2	no	—
676	C₂²⋊C₄	—	2	4	no	—
677	C₂²⋊C₄	—	2	4	no	—
678	C₂²⋊C₄	—	2	4	no	—
679	C₂²⋊C₄	—	2	2	no	—
680	C₂²⋊C₄	—	2	2	no	—
681	C₂²⋊C₄	—	2	2	no	—
682	C₂²⋊C₄	—	2	4	no	—
683	C₂²⋊C₄	—	2	2	no	—
684	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
685	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
686	C₄²	—	2	2	no	—
687	C₄²	—	2	2	no	—
688	C₄²	—	2	4	no	—
689	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
690	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
691	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
692	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
693	C₂³	—	2	4	no	—
694	C₂³	—	2	2	no	—
695	C₂³	—	2	2	no	—
696	C₂³	—	4	8	no	—
697	C₂³	—	8	1	no	—
698	C₂³	—	8	1	no	—
699	C₂³	—	8	4	no	—
700	C₂³	—	8	4	no	—
701	C₂³	C₂²×D₄×C₆₇	1	4	yes	—
702	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
703	Q₈	—	2	2	no	—
704	Q₈	—	2	4	no	—
705	Q₈	—	2	2	no	—
706	Q₈	—	2	4	no	—
707	Q₈	—	4	2	no	—
708	Q₈	—	4	2	no	—
709	Q₈	—	4	2	no	—
710	Q₈	—	8	4	no	—
711	D₄	—	2	4	no	—
712	D₄	—	2	4	no	—
713	D₄	—	2	2	no	—
714	D₄	—	2	4	no	—
715	D₄	—	4	2	no	—
716	D₄	—	4	4	no	—
717	D₄	—	4	2	no	—
718	D₄	—	4	8	no	—
719	D₄	—	4	8	no	—
720	D₄	—	4	4	no	—
721	D₄	—	4	2	no	—
722	D₄	—	8	1	no	—
723	D₄	—	8	4	no	—
724	D₄	H(5,𝔽₂)×C₆₇	1	4	yes	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	4	no	—
727	C₂×C₄	—	2	4	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	2	2	no	—
735	C₂×C₄	—	4	1	no	—
736	C₂×C₄	—	4	8	no	—
737	C₂×C₄	—	4	4	no	—
738	C₂×C₄	—	4	4	no	—
739	C₂×C₄	—	8	2	no	—
740	C₂×C₄	—	8	1	no	—
741	C₂×C₄	—	8	4	no	—
742	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
743	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
744	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
745	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
746	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
747	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
748	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
749	C₈	—	2	2	no	—
750	C₈	—	2	4	no	—
751	C₈	—	2	2	no	—
752	C₂²	—	2	1	no	—
753	C₂²	—	2	4	no	—
754	C₂²	—	2	1	no	—
755	C₂²	—	2	4	no	—
756	C₂²	—	2	4	no	—
757	C₂²	—	2	1	no	—
758	C₂²	—	2	4	no	—
759	C₂²	—	4	2	no	—
760	C₂²	—	4	2	no	—
761	C₂²	—	4	2	no	—
762	C₂²	—	4	2	no	—
763	C₂²	—	4	2	no	—
764	C₂²	—	8	4	no	—
765	C₂²	—	16	8	no	—
766	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
767	C₄	—	2	1	no	—
768	C₄	—	2	1	no	—
769	C₄	—	2	1	no	—
770	C₄	—	2	1	no	—
771	C₄	—	2	4	no	—
772	C₄	—	4	2	no	—
773	C₄	—	4	2	no	—
774	C₄	—	4	2	no	—
775	C₄	—	4	2	no	—
776	C₄	—	4	2	no	—
777	C₄	—	4	2	no	—
778	C₄	#577×C₆₇	1	2	yes	—
779	C₄	C₂×H(5,𝔽₂)×C₆₇	1	2	yes	—
780	C₂	—	4	1	no	—
781	C₂	—	4	4	no	—
782	C₂	—	4	4	no	—
783	C₂	—	8	2	no	—
784	C₂	C₆₇×#3484	1	1	yes	characteristic
785	C₂	C₂×#577×C₆₇	1	1	yes	characteristic
786	C₂	C₆₇×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
prime radical	C₆₇×#3496	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ #532×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3550	C₂	semidirect
3. C₆₇×#3324	C₂	semidirect
4. C₆₇×#3311	C₂	semidirect
5. C₆₇×#3302	C₂	semidirect
6. D₄×SD₁₆×C₆₇	C₂	semidirect
7. C₆₇×#3276	C₂	semidirect
8. C₆₇×#3266	C₂	semidirect
9. C₆₇×#3216	C₂	semidirect
10. C₆₇×#3210	C₂	semidirect
11. C₆₇×#3201	C₂	semidirect
12. C₆₇×#3110	C₂	semidirect
13. C₆₇×#3101	C₂	semidirect
14. C₆₇×#3009	C₂	semidirect
15. C₆₇×#2981	C₂	semidirect
17. C₂×#137×C₆₇	C₂²	semidirect
18. C₂²×SD₁₆×C₆₇	C₂²	semidirect
22. #556×C₆₇	C₂²	semidirect
23. #556×C₆₇	C₂²	semidirect
24. D₄×Q₈×C₆₇	C₂²	semidirect
25. D₄×Q₈×C₆₇	C₂²	semidirect
35. #536×C₆₇	C₂²	semidirect
37. #533×C₆₇	C₂²	semidirect
38. #533×C₆₇	C₂²	semidirect
43. #497×C₆₇	C₂²	semidirect
44. #494×C₆₇	C₂²	semidirect
45. #492×C₆₇	C₂²	semidirect
46. #489×C₆₇	C₂²	semidirect
47. #487×C₆₇	C₂²	semidirect
48. #486×C₆₇	C₂²	semidirect
49. #485×C₆₇	C₂²	semidirect
50. #484×C₆₇	C₂²	semidirect
51. #483×C₆₇	C₂²	semidirect
52. #482×C₆₇	C₂²	semidirect
53. #476×C₆₇	C₂²	semidirect
54. #474×C₆₇	C₂²	semidirect
55. #470×C₆₇	C₂²	semidirect
56. #468×C₆₇	C₂²	semidirect
57. #467×C₆₇	C₂²	semidirect
58. #465×C₆₇	C₂²	semidirect
59. #464×C₆₇	C₂²	semidirect
60. #462×C₆₇	C₂²	semidirect
61. #461×C₆₇	C₂²	semidirect
62. #461×C₆₇	C₂²	semidirect
63. #460×C₆₇	C₂²	semidirect
64. #452×C₆₇	C₂²	semidirect
65. #452×C₆₇	C₂²	semidirect
66. #452×C₆₇	C₂²	semidirect
67. #452×C₆₇	C₂²	semidirect
68. #451×C₆₇	C₂²	semidirect
71. #450×C₆₇	C₂²	semidirect
72. #450×C₆₇	C₂²	semidirect
73. #448×C₆₇	C₂²	semidirect
74. #440×C₆₇	C₂²	semidirect
75. C₄×SD₁₆×C₆₇	C₂²	semidirect
76. C₄×SD₁₆×C₆₇	C₂²	semidirect
77. #436×C₆₇	C₂²	semidirect
78. #435×C₆₇	C₂²	semidirect
79. C₈×D₄×C₆₇	C₂²	semidirect
80. #432×C₆₇	C₂²	semidirect
81. #431×C₆₇	C₂²	semidirect
82. #418×C₆₇	C₂²	semidirect
83. #416×C₆₇	C₂²	semidirect
84. #408×C₆₇	C₂²	semidirect
386. #61680	C₆₇	direct (N × H)
394. #3550	C₂×C₆₇	semidirect
396. #3324	C₂×C₆₇	semidirect
397. #3311	C₂×C₆₇	semidirect
398. #3302	C₂×C₆₇	semidirect
399. D₄×SD₁₆	C₂×C₆₇	semidirect
400. #3276	C₂×C₆₇	semidirect
401. #3266	C₂×C₆₇	semidirect
402. #3216	C₂×C₆₇	semidirect
403. #3210	C₂×C₆₇	semidirect
404. #3201	C₂×C₆₇	semidirect
405. #3110	C₂×C₆₇	semidirect
406. #3101	C₂×C₆₇	semidirect
407. #3009	C₂×C₆₇	semidirect
408. #2981	C₂×C₆₇	semidirect
409. C₆₇	#61680	direct (N × H)
411. C₂×#137	C₂²×C₆₇	semidirect
412. C₂²×SD₁₆	C₂²×C₆₇	semidirect
416. #556	C₂²×C₆₇	semidirect
417. #556	C₂²×C₆₇	semidirect
418. D₄×Q₈	C₂²×C₆₇	semidirect
419. D₄×Q₈	C₂²×C₆₇	semidirect
429. #536	C₂²×C₆₇	semidirect
431. #533	C₂²×C₆₇	semidirect
432. #533	C₂²×C₆₇	semidirect
437. #497	C₂²×C₆₇	semidirect
438. #494	C₂²×C₆₇	semidirect
439. #492	C₂²×C₆₇	semidirect
440. #489	C₂²×C₆₇	semidirect
441. #487	C₂²×C₆₇	semidirect
442. #486	C₂²×C₆₇	semidirect
443. #485	C₂²×C₆₇	semidirect
444. #484	C₂²×C₆₇	semidirect
445. #483	C₂²×C₆₇	semidirect
446. #482	C₂²×C₆₇	semidirect
447. #476	C₂²×C₆₇	semidirect
448. #474	C₂²×C₆₇	semidirect
449. #470	C₂²×C₆₇	semidirect
450. #468	C₂²×C₆₇	semidirect
451. #467	C₂²×C₆₇	semidirect
452. #465	C₂²×C₆₇	semidirect
453. #464	C₂²×C₆₇	semidirect
454. #462	C₂²×C₆₇	semidirect
455. #461	C₂²×C₆₇	semidirect
456. #461	C₂²×C₆₇	semidirect
457. #460	C₂²×C₆₇	semidirect
458. #452	C₂²×C₆₇	semidirect
459. #452	C₂²×C₆₇	semidirect
460. #452	C₂²×C₆₇	semidirect
461. #452	C₂²×C₆₇	semidirect
462. #451	C₂²×C₆₇	semidirect
465. #450	C₂²×C₆₇	semidirect
466. #450	C₂²×C₆₇	semidirect
467. #448	C₂²×C₆₇	semidirect
468. #440	C₂²×C₆₇	semidirect
469. C₄×SD₁₆	C₂²×C₆₇	semidirect
470. C₄×SD₁₆	C₂²×C₆₇	semidirect
471. #436	C₂²×C₆₇	semidirect
472. #435	C₂²×C₆₇	semidirect
473. C₈×D₄	C₂²×C₆₇	semidirect
474. #432	C₂²×C₆₇	semidirect
475. #431	C₂²×C₆₇	semidirect
476. #418	C₂²×C₆₇	semidirect
477. #416	C₂²×C₆₇	semidirect
478. #408	C₂²×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#3550	2
C₆₇×#3496	2
C₆₇×#3324	2
C₆₇×#3311	2
C₆₇×#3302	2
D₄×SD₁₆×C₆₇	2
C₆₇×#3276	2
C₆₇×#3266	2
C₆₇×#3216	2
C₆₇×#3210	2
C₆₇×#3201	2
C₆₇×#3110	2
C₆₇×#3101	2
C₆₇×#3009	2
C₆₇×#2981	2
#61680	67

Subgroups — C67×#61680 #30740931

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61680 #30740931