Subgroups — C₆₇×#61667 #30740918

Order 17152.

2064 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3548	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#3499	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3331	C₂	1	2	yes	maximal, complemented
4	C₆₇×#3330	C₂	1	2	yes	maximal, complemented
5	C₆₇×#3299	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3298	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3284	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3283	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3278	C₂	1	2	yes	maximal, complemented
10	C₆₇×#3276	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3209	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#3206	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3201	C₂	1	4	yes	maximal, complemented
14	C₆₇×#3107	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#3106	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#3013	C₂	1	4	yes	maximal, complemented
17	C₆₇×#2979	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×2₋¹⁺⁴×C₆₇	C₂²	1	2	yes	—
19	C₂×#137×C₆₇	C₂²	1	4	yes	—
20	C₂×#135×C₆₇	C₂²	1	4	yes	—
21	#562×C₆₇	—	2	2	no	—
22	#554×C₆₇	—	2	1	no	—
23	#554×C₆₇	C₂²	1	2	yes	—
24	#550×C₆₇	—	2	1	no	—
25	#550×C₆₇	C₂²	1	2	yes	—
26	D₄×Q₈×C₆₇	C₂²	1	2	yes	—
27	D₄×Q₈×C₆₇	C₂²	1	2	yes	—
28	#547×C₆₇	—	2	2	no	—
29	#547×C₆₇	—	2	2	no	—
30	#547×C₆₇	C₂²	1	2	yes	—
31	#547×C₆₇	C₂²	1	2	yes	—
32	#547×C₆₇	C₂²	1	2	yes	—
33	#547×C₆₇	C₂²	1	2	yes	—
34	#540×C₆₇	—	2	2	no	—
35	#537×C₆₇	—	2	2	no	—
36	#537×C₆₇	C₂²	1	4	yes	—
37	#536×C₆₇	—	2	2	no	—
38	#536×C₆₇	C₂²	1	2	yes	—
39	#533×C₆₇	C₂²	1	1	yes	characteristic
40	#532×C₆₇	—	2	1	no	—
41	#532×C₆₇	C₂²	1	1	yes	characteristic
42	#532×C₆₇	C₂²	1	1	yes	characteristic
43	C₂×C₄⋊Q₈×C₆₇	—	2	1	no	—
44	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
45	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
46	#494×C₆₇	C₂²	1	2	yes	—
47	#492×C₆₇	C₂²	1	2	yes	—
48	#487×C₆₇	C₂²	1	2	yes	—
49	#487×C₆₇	C₂²	1	2	yes	—
50	#485×C₆₇	C₂²	1	2	yes	—
51	#484×C₆₇	C₂²	1	4	yes	—
52	#483×C₆₇	C₂²	1	4	yes	—
53	#482×C₆₇	C₂²	1	2	yes	—
54	#477×C₆₇	C₂²	1	1	yes	characteristic
55	#476×C₆₇	C₂²	1	1	yes	characteristic
56	#475×C₆₇	C₂²	1	1	yes	characteristic
57	#474×C₆₇	C₂²	1	1	yes	characteristic
58	#470×C₆₇	C₂²	1	4	yes	—
59	#468×C₆₇	C₂²	1	4	yes	—
60	#467×C₆₇	C₂²	1	4	yes	—
61	#465×C₆₇	C₂²	1	4	yes	—
62	#462×C₆₇	C₂²	1	1	yes	characteristic
63	#462×C₆₇	C₂²	1	2	yes	—
64	#462×C₆₇	C₂²	1	2	yes	—
65	#461×C₆₇	C₂²	1	2	yes	—
66	#461×C₆₇	C₂²	1	1	yes	characteristic
67	#461×C₆₇	C₂²	1	2	yes	—
68	#460×C₆₇	C₂²	1	1	yes	characteristic
69	#459×C₆₇	C₂²	1	1	yes	characteristic
70	#452×C₆₇	C₂²	1	2	yes	—
71	#452×C₆₇	C₂²	1	4	yes	—
72	#452×C₆₇	C₂²	1	4	yes	—
73	#452×C₆₇	C₂²	1	4	yes	—
74	#451×C₆₇	C₂²	1	4	yes	—
75	#451×C₆₇	C₂²	1	4	yes	—
76	#449×C₆₇	C₂²	1	2	yes	—
77	#449×C₆₇	C₂²	1	4	yes	—
78	#448×C₆₇	C₂²	1	4	yes	—
79	#448×C₆₇	C₂²	1	4	yes	—
80	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	—
81	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	—
82	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	—
83	C₄×D₈×C₆₇	C₂²	1	2	yes	—
84	#436×C₆₇	C₂²	1	2	yes	—
85	#436×C₆₇	C₂²	1	2	yes	—
86	C₈×D₄×C₆₇	C₂²	1	2	yes	—
87	C₈×D₄×C₆₇	C₂²	1	2	yes	—
88	#431×C₆₇	C₂²	1	1	yes	characteristic
89	#431×C₆₇	C₂²	1	1	yes	characteristic
90	#417×C₆₇	C₂²	1	4	yes	—
91	C₂×#103×C₆₇	C₂²	1	4	yes	—
92	#408×C₆₇	C₂²	1	4	yes	—
93	2₋¹⁺⁴×C₆₇	—	4	4	no	—
94	2₋¹⁺⁴×C₆₇	—	4	4	no	—
95	C₂×#41×C₆₇	—	2	2	no	—
96	C₂×#41×C₆₇	—	2	4	no	—
97	C₂×#41×C₆₇	—	2	2	no	—
98	C₂×#41×C₆₇	—	2	1	no	—
99	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
100	C₂×#41×C₆₇	C₂³	1	4	yes	—
101	C₂×#41×C₆₇	C₂³	1	4	yes	—
102	C₂×#41×C₆₇	C₂³	1	2	yes	—
103	C₂²×Q₈×C₆₇	—	2	2	no	—
104	C₂²×Q₈×C₆₇	C₂³	1	4	yes	—
105	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
106	#137×C₆₇	—	4	8	no	—
107	#135×C₆₇	—	4	8	no	—
108	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
109	C₂×Q₁₆×C₆₇	C₂³	1	4	yes	—
110	C₂×Q₁₆×C₆₇	C₂³	1	4	yes	—
111	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
112	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
113	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
114	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
115	C₂×D₈×C₆₇	C₂³	1	2	yes	—
116	C₂×M₁₆×C₆₇	C₂³	1	4	yes	—
117	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
118	C₄⋊Q₈×C₆₇	—	2	2	no	—
119	C₄⋊Q₈×C₆₇	—	2	2	no	—
120	C₄⋊Q₈×C₆₇	—	2	2	no	—
121	C₄⋊Q₈×C₆₇	—	2	1	no	—
122	C₄⋊Q₈×C₆₇	—	2	1	no	—
123	C₄⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
124	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
125	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
126	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
127	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
128	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
129	#127×C₆₇	—	2	2	no	—
130	#127×C₆₇	D₄	1	1	yes	characteristic
131	#127×C₆₇	C₂³	1	1	yes	characteristic
132	#125×C₆₇	—	2	2	no	—
133	#125×C₆₇	—	2	1	no	—
134	#124×C₆₇	—	2	2	no	—
135	#124×C₆₇	—	2	1	no	—
136	#124×C₆₇	D₄	1	2	yes	—
137	#123×C₆₇	—	2	4	no	—
138	#123×C₆₇	—	2	4	no	—
139	#123×C₆₇	—	2	4	no	—
140	#123×C₆₇	—	2	4	no	—
141	#123×C₆₇	—	2	4	no	—
142	C₂²⋊Q₈×C₆₇	—	2	4	no	—
143	C₂²⋊Q₈×C₆₇	—	2	1	no	—
144	C₂²⋊Q₈×C₆₇	—	2	2	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	C₂³	1	2	yes	—
149	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
150	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
151	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
152	#121×C₆₇	—	2	2	no	—
153	#121×C₆₇	—	2	2	no	—
154	#121×C₆₇	—	2	4	no	—
155	#121×C₆₇	—	2	4	no	—
156	#121×C₆₇	—	2	2	no	—
157	#121×C₆₇	—	2	4	no	—
158	#121×C₆₇	—	2	1	no	—
159	#121×C₆₇	—	2	4	no	—
160	#121×C₆₇	D₄	1	2	yes	—
161	#121×C₆₇	D₄	1	2	yes	—
162	#121×C₆₇	C₂³	1	2	yes	—
163	#121×C₆₇	C₂³	1	4	yes	—
164	C₄×Q₈×C₆₇	—	2	1	no	—
165	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
166	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
167	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
168	C₄×D₄×C₆₇	—	2	2	no	—
169	C₄×D₄×C₆₇	—	2	2	no	—
170	C₄×D₄×C₆₇	—	2	2	no	—
171	C₄×D₄×C₆₇	—	2	1	no	—
172	C₄×D₄×C₆₇	—	2	1	no	—
173	C₄×D₄×C₆₇	—	2	2	no	—
174	C₄×D₄×C₆₇	—	2	1	no	—
175	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
176	C₄×D₄×C₆₇	C₂³	1	2	yes	—
177	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
178	C₄×D₄×C₆₇	C₂³	1	2	yes	—
179	C₄×D₄×C₆₇	C₂³	1	2	yes	—
180	#117×C₆₇	—	2	1	no	—
181	#117×C₆₇	—	2	1	no	—
182	#117×C₆₇	C₂³	1	1	yes	characteristic
183	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
184	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
185	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
186	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
187	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
188	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
189	C₂×C₄²×C₆₇	—	2	1	no	—
190	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
191	#107×C₆₇	C₂³	1	2	yes	—
192	#107×C₆₇	C₂³	1	2	yes	—
193	#106×C₆₇	C₂³	1	2	yes	—
194	#106×C₆₇	C₂³	1	2	yes	—
195	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
196	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
197	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
198	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
199	#103×C₆₇	C₂³	1	2	yes	—
200	#103×C₆₇	C₂³	1	4	yes	—
201	#103×C₆₇	C₂³	1	4	yes	—
202	#103×C₆₇	C₂³	1	4	yes	—
203	#103×C₆₇	C₂³	1	2	yes	—
204	#103×C₆₇	C₂³	1	4	yes	—
205	#103×C₆₇	C₂³	1	2	yes	—
206	#103×C₆₇	C₂³	1	2	yes	—
207	#102×C₆₇	C₂³	1	2	yes	—
208	#102×C₆₇	C₂³	1	2	yes	—
209	#102×C₆₇	C₂³	1	2	yes	—
210	#102×C₆₇	C₂³	1	2	yes	—
211	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
212	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
213	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
214	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
215	C₄×C₈×C₆₇	C₂³	1	2	yes	—
216	C₄×C₈×C₆₇	C₂³	1	2	yes	—
217	#41×C₆₇	—	2	2	no	—
218	#41×C₆₇	—	2	2	no	—
219	#41×C₆₇	—	2	8	no	—
220	#41×C₆₇	—	4	2	no	—
221	#41×C₆₇	—	4	2	no	—
222	#41×C₆₇	—	4	4	no	—
223	#41×C₆₇	—	4	8	no	—
224	#41×C₆₇	—	4	4	no	—
225	#41×C₆₇	—	4	4	no	—
226	#41×C₆₇	—	4	16	no	—
227	#41×C₆₇	—	8	2	no	—
228	#41×C₆₇	—	8	4	no	—
229	C₂×Q₈×C₆₇	—	2	1	no	—
230	C₂×Q₈×C₆₇	—	2	4	no	—
231	C₂×Q₈×C₆₇	—	2	2	no	—
232	C₂×Q₈×C₆₇	—	2	1	no	—
233	C₂×Q₈×C₆₇	—	2	8	no	—
234	C₂×Q₈×C₆₇	—	4	4	no	—
235	C₂×Q₈×C₆₇	—	4	2	no	—
236	C₂×Q₈×C₆₇	—	4	2	no	—
237	C₂×Q₈×C₆₇	—	4	8	no	—
238	C₂×Q₈×C₆₇	C₂×D₄	1	2	yes	—
239	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
240	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
241	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
242	C₂×D₄×C₆₇	—	2	1	no	—
243	C₂×D₄×C₆₇	—	2	4	no	—
244	C₂×D₄×C₆₇	—	2	2	no	—
245	C₂×D₄×C₆₇	—	2	4	no	—
246	C₂×D₄×C₆₇	—	2	4	no	—
247	C₂×D₄×C₆₇	—	2	1	no	—
248	C₂×D₄×C₆₇	—	2	1	no	—
249	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
250	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
251	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	—
252	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
253	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
254	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
255	C₂²×C₄×C₆₇	—	2	1	no	—
256	C₂²×C₄×C₆₇	—	2	2	no	—
257	C₂²×C₄×C₆₇	—	2	4	no	—
258	C₂²×C₄×C₆₇	—	2	4	no	—
259	C₂²×C₄×C₆₇	—	2	1	no	—
260	C₂²×C₄×C₆₇	—	2	1	no	—
261	C₂²×C₄×C₆₇	—	2	4	no	—
262	C₂²×C₄×C₆₇	—	2	2	no	—
263	C₂²×C₄×C₆₇	—	2	4	no	—
264	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
265	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
266	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
267	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
268	Q₁₆×C₆₇	—	2	4	no	—
269	Q₁₆×C₆₇	—	4	4	no	—
270	Q₁₆×C₆₇	—	4	4	no	—
271	SD₁₆×C₆₇	—	2	4	no	—
272	SD₁₆×C₆₇	—	2	4	no	—
273	SD₁₆×C₆₇	—	4	4	no	—
274	SD₁₆×C₆₇	—	4	4	no	—
275	D₈×C₆₇	—	2	4	no	—
276	M₁₆×C₆₇	—	4	4	no	—
277	C₂×C₈×C₆₇	—	4	4	no	—
278	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
279	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
280	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
281	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
282	C₄⋊C₄×C₆₇	—	2	2	no	—
283	C₄⋊C₄×C₆₇	—	2	2	no	—
284	C₄⋊C₄×C₆₇	—	2	1	no	—
285	C₄⋊C₄×C₆₇	—	2	4	no	—
286	C₄⋊C₄×C₆₇	—	2	2	no	—
287	C₄⋊C₄×C₆₇	—	2	2	no	—
288	C₄⋊C₄×C₆₇	—	2	4	no	—
289	C₄⋊C₄×C₆₇	—	2	4	no	—
290	C₄⋊C₄×C₆₇	—	2	4	no	—
291	C₄⋊C₄×C₆₇	—	2	1	no	—
292	C₄⋊C₄×C₆₇	—	2	1	no	—
293	C₄⋊C₄×C₆₇	—	2	1	no	—
294	C₄⋊C₄×C₆₇	—	2	1	no	—
295	C₄⋊C₄×C₆₇	—	2	1	no	—
296	C₄⋊C₄×C₆₇	—	2	2	no	—
297	C₄⋊C₄×C₆₇	—	2	2	no	—
298	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
299	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
300	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
301	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
302	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
303	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
304	C₂²⋊C₄×C₆₇	—	2	2	no	—
305	C₂²⋊C₄×C₆₇	—	2	1	no	—
306	C₂²⋊C₄×C₆₇	—	2	4	no	—
307	C₂²⋊C₄×C₆₇	—	2	4	no	—
308	C₂²⋊C₄×C₆₇	—	2	4	no	—
309	C₂²⋊C₄×C₆₇	—	2	1	no	—
310	C₂²⋊C₄×C₆₇	—	2	1	no	—
311	C₂²⋊C₄×C₆₇	—	2	4	no	—
312	C₂²⋊C₄×C₆₇	—	2	2	no	—
313	C₂²⋊C₄×C₆₇	—	2	2	no	—
314	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
315	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
316	C₄²×C₆₇	—	2	1	no	—
317	C₄²×C₆₇	—	2	1	no	—
318	C₄²×C₆₇	—	2	1	no	—
319	C₄²×C₆₇	—	2	2	no	—
320	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
321	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
322	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
323	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
324	C₂³×C₆₇	—	2	1	no	—
325	C₂³×C₆₇	—	2	2	no	—
326	C₂³×C₆₇	C₂²×D₄	1	4	yes	—
327	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
328	Q₈×C₆₇	—	2	1	no	—
329	Q₈×C₆₇	—	2	2	no	—
330	Q₈×C₆₇	—	2	4	no	—
331	Q₈×C₆₇	—	2	4	no	—
332	Q₈×C₆₇	—	2	2	no	—
333	Q₈×C₆₇	—	4	2	no	—
334	Q₈×C₆₇	—	4	8	no	—
335	Q₈×C₆₇	—	4	4	no	—
336	Q₈×C₆₇	—	4	2	no	—
337	Q₈×C₆₇	—	8	1	no	—
338	Q₈×C₆₇	H(5,𝔽₂)	1	2	yes	—
339	D₄×C₆₇	—	2	4	no	—
340	D₄×C₆₇	—	2	4	no	—
341	D₄×C₆₇	—	2	4	no	—
342	D₄×C₆₇	—	2	1	no	—
343	D₄×C₆₇	—	2	2	no	—
344	D₄×C₆₇	—	2	2	no	—
345	D₄×C₆₇	—	4	2	no	—
346	D₄×C₆₇	—	4	4	no	—
347	D₄×C₆₇	—	4	8	no	—
348	D₄×C₆₇	—	4	2	no	—
349	D₄×C₆₇	—	8	1	no	—
350	D₄×C₆₇	—	8	4	no	—
351	D₄×C₆₇	—	8	2	no	—
352	D₄×C₆₇	—	8	4	no	—
353	D₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
354	C₂×C₄×C₆₇	—	2	4	no	—
355	C₂×C₄×C₆₇	—	2	1	no	—
356	C₂×C₄×C₆₇	—	2	2	no	—
357	C₂×C₄×C₆₇	—	2	2	no	—
358	C₂×C₄×C₆₇	—	2	4	no	—
359	C₂×C₄×C₆₇	—	2	4	no	—
360	C₂×C₄×C₆₇	—	2	1	no	—
361	C₂×C₄×C₆₇	—	2	1	no	—
362	C₂×C₄×C₆₇	—	2	1	no	—
363	C₂×C₄×C₆₇	—	2	1	no	—
364	C₂×C₄×C₆₇	—	2	2	no	—
365	C₂×C₄×C₆₇	—	2	2	no	—
366	C₂×C₄×C₆₇	—	2	2	no	—
367	C₂×C₄×C₆₇	—	2	4	no	—
368	C₂×C₄×C₆₇	—	4	8	no	—
369	C₂×C₄×C₆₇	—	4	8	no	—
370	C₂×C₄×C₆₇	—	4	4	no	—
371	C₂×C₄×C₆₇	—	4	2	no	—
372	C₂×C₄×C₆₇	—	4	4	no	—
373	C₂×C₄×C₆₇	—	4	2	no	—
374	C₂×C₄×C₆₇	—	8	4	no	—
375	C₂×C₄×C₆₇	—	8	4	no	—
376	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
377	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
378	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
379	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
380	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
381	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
382	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
383	C₈×C₆₇	—	2	2	no	—
384	C₈×C₆₇	—	2	2	no	—
385	C₈×C₆₇	—	2	2	no	—
386	C₈×C₆₇	—	2	2	no	—
387	C₂²×C₆₇	—	2	1	no	—
388	C₂²×C₆₇	—	2	2	no	—
389	C₂²×C₆₇	—	2	4	no	—
390	C₂²×C₆₇	—	2	1	no	—
391	C₂²×C₆₇	—	2	4	no	—
392	C₂²×C₆₇	—	2	1	no	—
393	C₂²×C₆₇	—	2	4	no	—
394	C₂²×C₆₇	—	4	1	no	—
395	C₂²×C₆₇	—	4	1	no	—
396	C₂²×C₆₇	—	4	2	no	—
397	C₂²×C₆₇	—	4	2	no	—
398	C₂²×C₆₇	—	4	2	no	—
399	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
400	C₄×C₆₇	—	2	1	no	—
401	C₄×C₆₇	—	2	2	no	—
402	C₄×C₆₇	—	2	4	no	—
403	C₄×C₆₇	—	2	1	no	—
404	C₄×C₆₇	—	2	1	no	—
405	C₄×C₆₇	—	4	4	no	—
406	C₄×C₆₇	—	4	2	no	—
407	C₄×C₆₇	—	4	1	no	—
408	C₄×C₆₇	—	4	2	no	—
409	C₄×C₆₇	—	4	2	no	—
410	C₄×C₆₇	—	4	1	no	—
411	C₄×C₆₇	#577	1	2	yes	—
412	C₄×C₆₇	#578	1	2	yes	—
413	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
414	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
415	#61667	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
416	C₂×C₆₇	—	4	1	no	—
417	C₂×C₆₇	—	4	4	no	—
418	C₂×C₆₇	—	4	2	no	—
419	C₂×C₆₇	—	8	2	no	—
420	C₂×C₆₇	#3484	1	1	yes	characteristic
421	C₂×C₆₇	C₂×#577	1	1	yes	characteristic
422	C₂×C₆₇	C₂×#578	1	1	yes	characteristic
423	#3548	C₂×C₆₇	1	1	yes	characteristic, complemented
424	#3499	C₂×C₆₇	1	1	yes	characteristic, complemented
425	#3331	C₂×C₆₇	1	2	yes	complemented
426	#3330	C₂×C₆₇	1	2	yes	complemented
427	#3299	C₂×C₆₇	1	2	yes	complemented
428	#3298	C₂×C₆₇	1	2	yes	complemented
429	#3284	C₂×C₆₇	1	2	yes	complemented
430	#3283	C₂×C₆₇	1	2	yes	complemented
431	#3278	C₂×C₆₇	1	2	yes	complemented
432	#3276	C₂×C₆₇	1	2	yes	complemented
433	#3209	C₂×C₆₇	1	1	yes	characteristic, complemented
434	#3206	C₂×C₆₇	1	1	yes	characteristic, complemented
435	#3201	C₂×C₆₇	1	4	yes	complemented
436	#3107	C₂×C₆₇	1	1	yes	characteristic, complemented
437	#3106	C₂×C₆₇	1	1	yes	characteristic, complemented
438	#3013	C₂×C₆₇	1	4	yes	complemented
439	#2979	C₂×C₆₇	1	1	yes	characteristic, complemented
440	C₆₇	#61667	1	1	yes	characteristic, direct product factor, Sylow
441	C₂×2₋¹⁺⁴	C₂²×C₆₇	1	2	yes	—
442	C₂×#137	C₂²×C₆₇	1	4	yes	—
443	C₂×#135	C₂²×C₆₇	1	4	yes	—
444	#562	—	2	2	no	—
445	#554	—	2	1	no	—
446	#554	C₂²×C₆₇	1	2	yes	—
447	#550	—	2	1	no	—
448	#550	C₂²×C₆₇	1	2	yes	—
449	D₄×Q₈	C₂²×C₆₇	1	2	yes	—
450	D₄×Q₈	C₂²×C₆₇	1	2	yes	—
451	#547	—	2	2	no	—
452	#547	—	2	2	no	—
453	#547	C₂²×C₆₇	1	2	yes	—
454	#547	C₂²×C₆₇	1	2	yes	—
455	#547	C₂²×C₆₇	1	2	yes	—
456	#547	C₂²×C₆₇	1	2	yes	—
457	#540	—	2	2	no	—
458	#537	—	2	2	no	—
459	#537	C₂²×C₆₇	1	4	yes	—
460	#536	—	2	2	no	—
461	#536	C₂²×C₆₇	1	2	yes	—
462	#533	C₂²×C₆₇	1	1	yes	characteristic
463	#532	—	2	1	no	—
464	#532	C₂²×C₆₇	1	1	yes	characteristic
465	#532	C₂²×C₆₇	1	1	yes	characteristic
466	C₂×C₄⋊Q₈	—	2	1	no	—
467	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
468	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
469	#494	C₂²×C₆₇	1	2	yes	—
470	#492	C₂²×C₆₇	1	2	yes	—
471	#487	C₂²×C₆₇	1	2	yes	—
472	#487	C₂²×C₆₇	1	2	yes	—
473	#485	C₂²×C₆₇	1	2	yes	—
474	#484	C₂²×C₆₇	1	4	yes	—
475	#483	C₂²×C₆₇	1	4	yes	—
476	#482	C₂²×C₆₇	1	2	yes	—
477	#477	C₂²×C₆₇	1	1	yes	characteristic
478	#476	C₂²×C₆₇	1	1	yes	characteristic
479	#475	C₂²×C₆₇	1	1	yes	characteristic
480	#474	C₂²×C₆₇	1	1	yes	characteristic
481	#470	C₂²×C₆₇	1	4	yes	—
482	#468	C₂²×C₆₇	1	4	yes	—
483	#467	C₂²×C₆₇	1	4	yes	—
484	#465	C₂²×C₆₇	1	4	yes	—
485	#462	C₂²×C₆₇	1	2	yes	—
486	#462	C₂²×C₆₇	1	1	yes	characteristic
487	#462	C₂²×C₆₇	1	2	yes	—
488	#461	C₂²×C₆₇	1	2	yes	—
489	#461	C₂²×C₆₇	1	1	yes	characteristic
490	#461	C₂²×C₆₇	1	2	yes	—
491	#460	C₂²×C₆₇	1	1	yes	characteristic
492	#459	C₂²×C₆₇	1	1	yes	characteristic
493	#452	C₂²×C₆₇	1	4	yes	—
494	#452	C₂²×C₆₇	1	2	yes	—
495	#452	C₂²×C₆₇	1	4	yes	—
496	#452	C₂²×C₆₇	1	4	yes	—
497	#451	C₂²×C₆₇	1	4	yes	—
498	#451	C₂²×C₆₇	1	4	yes	—
499	#449	C₂²×C₆₇	1	4	yes	—
500	#449	C₂²×C₆₇	1	2	yes	—
501	#448	C₂²×C₆₇	1	4	yes	—
502	#448	C₂²×C₆₇	1	4	yes	—
503	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	—
504	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	—
505	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	—
506	C₄×D₈	C₂²×C₆₇	1	2	yes	—
507	#436	C₂²×C₆₇	1	2	yes	—
508	#436	C₂²×C₆₇	1	2	yes	—
509	C₈×D₄	C₂²×C₆₇	1	2	yes	—
510	C₈×D₄	C₂²×C₆₇	1	2	yes	—
511	#431	C₂²×C₆₇	1	1	yes	characteristic
512	#431	C₂²×C₆₇	1	1	yes	characteristic
513	#417	C₂²×C₆₇	1	4	yes	—
514	C₂×#103	C₂²×C₆₇	1	4	yes	—
515	#408	C₂²×C₆₇	1	4	yes	—
516	2₋¹⁺⁴	—	4	4	no	—
517	2₋¹⁺⁴	—	4	4	no	—
518	C₂×#41	—	2	2	no	—
519	C₂×#41	—	2	4	no	—
520	C₂×#41	—	2	2	no	—
521	C₂×#41	—	2	1	no	—
522	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
523	C₂×#41	C₂³×C₆₇	1	4	yes	—
524	C₂×#41	C₂³×C₆₇	1	4	yes	—
525	C₂×#41	C₂³×C₆₇	1	2	yes	—
526	C₂²×Q₈	—	2	2	no	—
527	C₂²×Q₈	C₂³×C₆₇	1	4	yes	—
528	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
529	#137	—	4	8	no	—
530	#135	—	4	8	no	—
531	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
532	C₂×Q₁₆	C₂³×C₆₇	1	4	yes	—
533	C₂×Q₁₆	C₂³×C₆₇	1	4	yes	—
534	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
535	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
536	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
537	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
538	C₂×D₈	C₂³×C₆₇	1	2	yes	—
539	C₂×M₁₆	C₂³×C₆₇	1	4	yes	—
540	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
541	C₄⋊Q₈	—	2	2	no	—
542	C₄⋊Q₈	—	2	2	no	—
543	C₄⋊Q₈	—	2	2	no	—
544	C₄⋊Q₈	—	2	1	no	—
545	C₄⋊Q₈	—	2	1	no	—
546	C₄⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
547	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
548	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
549	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
550	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
551	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
552	#127	—	2	2	no	—
553	#127	D₄×C₆₇	1	1	yes	characteristic
554	#127	C₂³×C₆₇	1	1	yes	characteristic
555	#125	—	2	2	no	—
556	#125	—	2	1	no	—
557	#124	—	2	2	no	—
558	#124	—	2	1	no	—
559	#124	D₄×C₆₇	1	2	yes	—
560	#123	—	2	4	no	—
561	#123	—	2	4	no	—
562	#123	—	2	4	no	—
563	#123	—	2	4	no	—
564	#123	—	2	4	no	—
565	C₂²⋊Q₈	—	2	4	no	—
566	C₂²⋊Q₈	—	2	1	no	—
567	C₂²⋊Q₈	—	2	2	no	—
568	C₂²⋊Q₈	—	2	4	no	—
569	C₂²⋊Q₈	—	2	4	no	—
570	C₂²⋊Q₈	—	2	4	no	—
571	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
572	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
573	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
574	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
575	#121	—	2	2	no	—
576	#121	—	2	2	no	—
577	#121	—	2	4	no	—
578	#121	—	2	4	no	—
579	#121	—	2	2	no	—
580	#121	—	2	4	no	—
581	#121	—	2	1	no	—
582	#121	—	2	4	no	—
583	#121	D₄×C₆₇	1	2	yes	—
584	#121	D₄×C₆₇	1	2	yes	—
585	#121	C₂³×C₆₇	1	2	yes	—
586	#121	C₂³×C₆₇	1	4	yes	—
587	C₄×Q₈	—	2	1	no	—
588	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
589	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
590	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
591	C₄×D₄	—	2	2	no	—
592	C₄×D₄	—	2	2	no	—
593	C₄×D₄	—	2	2	no	—
594	C₄×D₄	—	2	1	no	—
595	C₄×D₄	—	2	1	no	—
596	C₄×D₄	—	2	2	no	—
597	C₄×D₄	—	2	1	no	—
598	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
599	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
600	C₄×D₄	C₂³×C₆₇	1	2	yes	—
601	C₄×D₄	C₂³×C₆₇	1	2	yes	—
602	C₄×D₄	C₂³×C₆₇	1	2	yes	—
603	#117	—	2	1	no	—
604	#117	—	2	1	no	—
605	#117	C₂³×C₆₇	1	1	yes	characteristic
606	C₂×C₄⋊C₄	—	2	1	no	—
607	C₂×C₄⋊C₄	—	2	1	no	—
608	C₂×C₄⋊C₄	—	2	2	no	—
609	C₂×C₄⋊C₄	—	2	2	no	—
610	C₂×C₄⋊C₄	—	2	2	no	—
611	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
612	C₂×C₄²	—	2	1	no	—
613	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
614	#107	C₂³×C₆₇	1	2	yes	—
615	#107	C₂³×C₆₇	1	2	yes	—
616	#106	C₂³×C₆₇	1	2	yes	—
617	#106	C₂³×C₆₇	1	2	yes	—
618	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
619	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
620	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
621	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
622	#103	C₂³×C₆₇	1	2	yes	—
623	#103	C₂³×C₆₇	1	2	yes	—
624	#103	C₂³×C₆₇	1	4	yes	—
625	#103	C₂³×C₆₇	1	4	yes	—
626	#103	C₂³×C₆₇	1	4	yes	—
627	#103	C₂³×C₆₇	1	4	yes	—
628	#103	C₂³×C₆₇	1	2	yes	—
629	#103	C₂³×C₆₇	1	2	yes	—
630	#102	C₂³×C₆₇	1	2	yes	—
631	#102	C₂³×C₆₇	1	2	yes	—
632	#102	C₂³×C₆₇	1	2	yes	—
633	#102	C₂³×C₆₇	1	2	yes	—
634	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
635	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
636	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
637	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
638	C₄×C₈	C₂³×C₆₇	1	2	yes	—
639	C₄×C₈	C₂³×C₆₇	1	2	yes	—
640	#41	—	2	2	no	—
641	#41	—	2	2	no	—
642	#41	—	2	8	no	—
643	#41	—	4	2	no	—
644	#41	—	4	2	no	—
645	#41	—	4	4	no	—
646	#41	—	4	8	no	—
647	#41	—	4	4	no	—
648	#41	—	4	4	no	—
649	#41	—	4	16	no	—
650	#41	—	8	2	no	—
651	#41	—	8	4	no	—
652	C₂×Q₈	—	2	1	no	—
653	C₂×Q₈	—	2	4	no	—
654	C₂×Q₈	—	2	2	no	—
655	C₂×Q₈	—	2	1	no	—
656	C₂×Q₈	—	2	8	no	—
657	C₂×Q₈	—	4	4	no	—
658	C₂×Q₈	—	4	2	no	—
659	C₂×Q₈	—	4	2	no	—
660	C₂×Q₈	—	4	8	no	—
661	C₂×Q₈	C₂×D₄×C₆₇	1	2	yes	—
662	C₂×Q₈	C₂⁴×C₆₇	1	4	yes	—
663	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
664	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
665	C₂×D₄	—	2	1	no	—
666	C₂×D₄	—	2	4	no	—
667	C₂×D₄	—	2	2	no	—
668	C₂×D₄	—	2	4	no	—
669	C₂×D₄	—	2	4	no	—
670	C₂×D₄	—	2	1	no	—
671	C₂×D₄	—	2	1	no	—
672	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
673	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
674	C₂×D₄	C₂×D₄×C₆₇	1	4	yes	—
675	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
676	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
677	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
678	C₂²×C₄	—	2	1	no	—
679	C₂²×C₄	—	2	2	no	—
680	C₂²×C₄	—	2	4	no	—
681	C₂²×C₄	—	2	4	no	—
682	C₂²×C₄	—	2	1	no	—
683	C₂²×C₄	—	2	1	no	—
684	C₂²×C₄	—	2	4	no	—
685	C₂²×C₄	—	2	2	no	—
686	C₂²×C₄	—	2	4	no	—
687	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
688	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
689	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
690	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
691	Q₁₆	—	2	4	no	—
692	Q₁₆	—	4	4	no	—
693	Q₁₆	—	4	4	no	—
694	SD₁₆	—	2	4	no	—
695	SD₁₆	—	2	4	no	—
696	SD₁₆	—	4	4	no	—
697	SD₁₆	—	4	4	no	—
698	D₈	—	2	4	no	—
699	M₁₆	—	4	4	no	—
700	C₂×C₈	—	4	4	no	—
701	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
702	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
703	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
704	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
705	C₄⋊C₄	—	2	2	no	—
706	C₄⋊C₄	—	2	2	no	—
707	C₄⋊C₄	—	2	1	no	—
708	C₄⋊C₄	—	2	4	no	—
709	C₄⋊C₄	—	2	2	no	—
710	C₄⋊C₄	—	2	2	no	—
711	C₄⋊C₄	—	2	4	no	—
712	C₄⋊C₄	—	2	4	no	—
713	C₄⋊C₄	—	2	4	no	—
714	C₄⋊C₄	—	2	1	no	—
715	C₄⋊C₄	—	2	1	no	—
716	C₄⋊C₄	—	2	1	no	—
717	C₄⋊C₄	—	2	1	no	—
718	C₄⋊C₄	—	2	1	no	—
719	C₄⋊C₄	—	2	2	no	—
720	C₄⋊C₄	—	2	2	no	—
721	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
722	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
723	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
724	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
725	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
726	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
727	C₂²⋊C₄	—	2	2	no	—
728	C₂²⋊C₄	—	2	1	no	—
729	C₂²⋊C₄	—	2	4	no	—
730	C₂²⋊C₄	—	2	4	no	—
731	C₂²⋊C₄	—	2	4	no	—
732	C₂²⋊C₄	—	2	1	no	—
733	C₂²⋊C₄	—	2	1	no	—
734	C₂²⋊C₄	—	2	4	no	—
735	C₂²⋊C₄	—	2	2	no	—
736	C₂²⋊C₄	—	2	2	no	—
737	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
738	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
739	C₄²	—	2	1	no	—
740	C₄²	—	2	1	no	—
741	C₄²	—	2	1	no	—
742	C₄²	—	2	2	no	—
743	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
744	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
745	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
746	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
747	C₂³	—	2	1	no	—
748	C₂³	—	2	2	no	—
749	C₂³	C₂²×D₄×C₆₇	1	4	yes	—
750	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
751	Q₈	—	2	1	no	—
752	Q₈	—	2	2	no	—
753	Q₈	—	2	4	no	—
754	Q₈	—	2	4	no	—
755	Q₈	—	2	2	no	—
756	Q₈	—	4	2	no	—
757	Q₈	—	4	8	no	—
758	Q₈	—	4	4	no	—
759	Q₈	—	4	2	no	—
760	Q₈	—	8	1	no	—
761	Q₈	H(5,𝔽₂)×C₆₇	1	2	yes	—
762	D₄	—	2	4	no	—
763	D₄	—	2	4	no	—
764	D₄	—	2	4	no	—
765	D₄	—	2	1	no	—
766	D₄	—	2	2	no	—
767	D₄	—	2	2	no	—
768	D₄	—	4	2	no	—
769	D₄	—	4	4	no	—
770	D₄	—	4	8	no	—
771	D₄	—	4	2	no	—
772	D₄	—	8	1	no	—
773	D₄	—	8	4	no	—
774	D₄	—	8	2	no	—
775	D₄	—	8	4	no	—
776	D₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
777	C₂×C₄	—	2	4	no	—
778	C₂×C₄	—	2	1	no	—
779	C₂×C₄	—	2	2	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	4	no	—
782	C₂×C₄	—	2	4	no	—
783	C₂×C₄	—	2	1	no	—
784	C₂×C₄	—	2	1	no	—
785	C₂×C₄	—	2	1	no	—
786	C₂×C₄	—	2	1	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	4	no	—
791	C₂×C₄	—	4	8	no	—
792	C₂×C₄	—	4	8	no	—
793	C₂×C₄	—	4	4	no	—
794	C₂×C₄	—	4	4	no	—
795	C₂×C₄	—	4	2	no	—
796	C₂×C₄	—	4	2	no	—
797	C₂×C₄	—	8	4	no	—
798	C₂×C₄	—	8	4	no	—
799	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
800	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
801	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
802	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
803	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
804	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
805	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
806	C₈	—	2	2	no	—
807	C₈	—	2	2	no	—
808	C₈	—	2	2	no	—
809	C₈	—	2	2	no	—
810	C₂²	—	2	1	no	—
811	C₂²	—	2	4	no	—
812	C₂²	—	2	1	no	—
813	C₂²	—	2	4	no	—
814	C₂²	—	2	1	no	—
815	C₂²	—	2	2	no	—
816	C₂²	—	2	4	no	—
817	C₂²	—	4	1	no	—
818	C₂²	—	4	1	no	—
819	C₂²	—	4	2	no	—
820	C₂²	—	4	2	no	—
821	C₂²	—	4	2	no	—
822	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
823	C₄	—	2	1	no	—
824	C₄	—	2	1	no	—
825	C₄	—	2	1	no	—
826	C₄	—	2	2	no	—
827	C₄	—	2	4	no	—
828	C₄	—	4	2	no	—
829	C₄	—	4	1	no	—
830	C₄	—	4	2	no	—
831	C₄	—	4	1	no	—
832	C₄	—	4	4	no	—
833	C₄	—	4	2	no	—
834	C₄	#577×C₆₇	1	2	yes	—
835	C₄	#578×C₆₇	1	2	yes	—
836	C₄	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
837	C₄	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
838	C₂	—	4	1	no	—
839	C₂	—	4	4	no	—
840	C₂	—	4	2	no	—
841	C₂	—	8	2	no	—
842	C₂	C₆₇×#3484	1	1	yes	characteristic
843	C₂	C₂×#577×C₆₇	1	1	yes	characteristic
844	C₂	C₂×#578×C₆₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
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×#3548	C₂	semidirect
2. C₆₇×#3499	C₂	semidirect
3. C₆₇×#3331	C₂	semidirect
4. C₆₇×#3330	C₂	semidirect
5. C₆₇×#3299	C₂	semidirect
6. C₆₇×#3298	C₂	semidirect
7. C₆₇×#3284	C₂	semidirect
8. C₆₇×#3283	C₂	semidirect
9. C₆₇×#3278	C₂	semidirect
10. C₆₇×#3276	C₂	semidirect
11. C₆₇×#3209	C₂	semidirect
12. C₆₇×#3206	C₂	semidirect
13. C₆₇×#3201	C₂	semidirect
14. C₆₇×#3107	C₂	semidirect
15. C₆₇×#3106	C₂	semidirect
16. C₆₇×#3013	C₂	semidirect
17. C₆₇×#2979	C₂	semidirect
415. #61667	C₆₇	direct (N × H)
423. #3548	C₂×C₆₇	semidirect
424. #3499	C₂×C₆₇	semidirect
425. #3331	C₂×C₆₇	semidirect
426. #3330	C₂×C₆₇	semidirect
427. #3299	C₂×C₆₇	semidirect
428. #3298	C₂×C₆₇	semidirect
429. #3284	C₂×C₆₇	semidirect
430. #3283	C₂×C₆₇	semidirect
431. #3278	C₂×C₆₇	semidirect
432. #3276	C₂×C₆₇	semidirect
433. #3209	C₂×C₆₇	semidirect
434. #3206	C₂×C₆₇	semidirect
435. #3201	C₂×C₆₇	semidirect
436. #3107	C₂×C₆₇	semidirect
437. #3106	C₂×C₆₇	semidirect
438. #3013	C₂×C₆₇	semidirect
439. #2979	C₂×C₆₇	semidirect
440. C₆₇	#61667	direct (N × H)

Maximal subgroups

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

subgroup	index
C₆₇×#3548	2
C₆₇×#3499	2
C₆₇×#3331	2
C₆₇×#3330	2
C₆₇×#3299	2
C₆₇×#3298	2
C₆₇×#3284	2
C₆₇×#3283	2
C₆₇×#3278	2
C₆₇×#3276	2
C₆₇×#3209	2
C₆₇×#3206	2
C₆₇×#3201	2
C₆₇×#3107	2
C₆₇×#3106	2
C₆₇×#3013	2
C₆₇×#2979	2
#61667	67

Subgroups — C67×#61667 #30740918

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61667 #30740918