Subgroups — C₆₇×#60560 #30739811

Order 17152.

2138 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3444	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×Q₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3117	C₂	1	4	yes	maximal, complemented
4	C₆₇×#3113	C₂	1	2	yes	maximal, complemented
5	C₆₇×#3112	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3108	C₂	1	4	yes	maximal, complemented
7	C₆₇×#3104	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3103	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3092	C₂	1	2	yes	maximal, complemented
10	C₆₇×#3078	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3037	C₂	1	2	yes	maximal, complemented
12	C₆₇×#3004	C₂	1	2	yes	maximal, complemented
13	C₄×#137×C₆₇	C₂	1	4	yes	maximal, complemented
14	C₆₇×#2920	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂³×Q₈×C₆₇	C₂²	1	1	yes	characteristic
16	C₂×#137×C₆₇	C₂²	1	4	yes	—
17	#533×C₆₇	C₂²	1	1	yes	characteristic
18	#533×C₆₇	C₂²	1	1	yes	characteristic
19	#533×C₆₇	C₂²	1	1	yes	characteristic
20	#532×C₆₇	C₂²	1	1	yes	characteristic
21	#532×C₆₇	C₂²	1	1	yes	characteristic
22	#532×C₆₇	C₂²	1	1	yes	characteristic
23	#529×C₆₇	—	2	1	no	—
24	#529×C₆₇	—	2	1	no	—
25	#529×C₆₇	—	2	1	no	—
26	#529×C₆₇	—	2	1	no	—
27	#529×C₆₇	C₂²	1	2	yes	—
28	#529×C₆₇	C₂²	1	2	yes	—
29	#525×C₆₇	—	2	1	no	—
30	#525×C₆₇	—	2	1	no	—
31	#525×C₆₇	C₂²	1	2	yes	—
32	C₄×#41×C₆₇	—	2	1	no	—
33	C₄×#41×C₆₇	—	2	1	no	—
34	C₄×#41×C₆₇	C₂²	1	2	yes	—
35	C₂×C₄×Q₈×C₆₇	—	2	1	no	—
36	C₂×C₄×Q₈×C₆₇	—	2	1	no	—
37	C₂×C₄×Q₈×C₆₇	—	2	1	no	—
38	C₂×C₄×Q₈×C₆₇	—	2	1	no	—
39	C₂×C₄×Q₈×C₆₇	—	2	1	no	—
40	C₂×C₄×Q₈×C₆₇	—	2	1	no	—
41	C₂×C₄×Q₈×C₆₇	C₂²	1	2	yes	—
42	C₂×C₄×Q₈×C₆₇	C₂²	1	2	yes	—
43	C₂×C₄×Q₈×C₆₇	C₂²	1	2	yes	—
44	C₂×C₄×Q₈×C₆₇	C₂²	1	2	yes	—
45	C₂×C₄×Q₈×C₆₇	C₂²	1	2	yes	—
46	C₂×C₄×Q₈×C₆₇	C₂²	1	2	yes	—
47	C₂²×C₄⋊C₄×C₆₇	—	2	1	no	—
48	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
49	C₂²×C₄²×C₆₇	—	2	1	no	—
50	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
51	#484×C₆₇	C₂²	1	4	yes	—
52	#483×C₆₇	C₂²	1	4	yes	—
53	#481×C₆₇	C₂²	1	4	yes	—
54	#480×C₆₇	C₂²	1	4	yes	—
55	#479×C₆₇	C₂²	1	8	yes	complemented
56	#477×C₆₇	C₂²	1	4	yes	complemented
57	#475×C₆₇	C₂²	1	4	yes	complemented
58	#464×C₆₇	C₂²	1	8	yes	complemented
59	#462×C₆₇	C₂²	1	4	yes	complemented
60	#460×C₆₇	C₂²	1	4	yes	complemented
61	#451×C₆₇	C₂²	1	4	yes	—
62	#451×C₆₇	C₂²	1	4	yes	—
63	#448×C₆₇	C₂²	1	4	yes	—
64	#448×C₆₇	C₂²	1	4	yes	—
65	#441×C₆₇	C₂²	1	8	yes	complemented
66	#440×C₆₇	C₂²	1	8	yes	complemented
67	C₄×Q₁₆×C₆₇	C₂²	1	8	yes	complemented
68	C₄×SD₁₆×C₆₇	C₂²	1	8	yes	complemented
69	#432×C₆₇	C₂²	1	2	yes	—
70	#432×C₆₇	C₂²	1	2	yes	—
71	#431×C₆₇	C₂²	1	2	yes	—
72	#431×C₆₇	C₂²	1	2	yes	—
73	#428×C₆₇	C₂²	1	4	yes	—
74	#423×C₆₇	C₂²	1	2	yes	—
75	#419×C₆₇	C₂²	1	4	yes	—
76	#417×C₆₇	C₂²	1	4	yes	—
77	#407×C₆₇	C₂²	1	2	yes	—
78	C₄×M₁₆×C₆₇	C₂²	1	2	yes	—
79	C₂×#41×C₆₇	—	2	1	no	—
80	C₂×#41×C₆₇	—	2	1	no	—
81	C₂×#41×C₆₇	C₂³	1	2	yes	—
82	C₂²×Q₈×C₆₇	—	2	8	no	—
83	C₂²×Q₈×C₆₇	—	2	1	no	—
84	C₂²×Q₈×C₆₇	—	2	1	no	—
85	C₂²×Q₈×C₆₇	—	2	1	no	—
86	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
87	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
88	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
89	C₂³×C₄×C₆₇	—	2	1	no	—
90	C₂³×C₄×C₆₇	—	2	1	no	—
91	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
92	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
93	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
94	#137×C₆₇	—	2	16	no	—
95	C₂×Q₁₆×C₆₇	C₂³	1	8	yes	—
96	C₂×SD₁₆×C₆₇	C₂³	1	8	yes	—
97	C₂×M₁₆×C₆₇	C₂³	1	4	yes	—
98	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
99	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
100	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
101	#127×C₆₇	C₂³	1	1	yes	characteristic
102	#126×C₆₇	—	2	2	no	—
103	#126×C₆₇	—	2	2	no	—
104	#125×C₆₇	—	2	1	no	—
105	#125×C₆₇	—	2	1	no	—
106	#125×C₆₇	C₂³	1	2	yes	—
107	#124×C₆₇	—	2	1	no	—
108	#124×C₆₇	—	2	1	no	—
109	#124×C₆₇	C₂³	1	2	yes	—
110	#123×C₆₇	—	2	2	no	—
111	#123×C₆₇	—	2	2	no	—
112	#123×C₆₇	—	2	2	no	—
113	C₂²⋊Q₈×C₆₇	—	2	1	no	—
114	C₂²⋊Q₈×C₆₇	—	2	1	no	—
115	C₂²⋊Q₈×C₆₇	—	2	1	no	—
116	C₂²⋊Q₈×C₆₇	—	2	1	no	—
117	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
118	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
119	#121×C₆₇	—	2	1	no	—
120	#121×C₆₇	—	2	1	no	—
121	#121×C₆₇	—	2	1	no	—
122	#121×C₆₇	—	2	1	no	—
123	#121×C₆₇	C₂³	1	2	yes	—
124	#121×C₆₇	C₂³	1	2	yes	—
125	#120×C₆₇	—	2	2	no	—
126	C₄×Q₈×C₆₇	—	2	2	no	—
127	C₄×Q₈×C₆₇	—	2	2	no	—
128	C₄×Q₈×C₆₇	—	2	2	no	—
129	C₄×Q₈×C₆₇	—	2	2	no	—
130	C₄×Q₈×C₆₇	—	2	2	no	—
131	C₄×Q₈×C₆₇	—	2	2	no	—
132	C₄×Q₈×C₆₇	—	2	2	no	—
133	C₄×Q₈×C₆₇	—	2	2	no	—
134	C₄×Q₈×C₆₇	—	2	2	no	—
135	C₄×Q₈×C₆₇	—	2	2	no	—
136	C₄×Q₈×C₆₇	—	2	2	no	—
137	C₄×Q₈×C₆₇	—	2	2	no	—
138	C₄×Q₈×C₆₇	—	2	1	no	—
139	C₄×Q₈×C₆₇	—	2	1	no	—
140	C₄×Q₈×C₆₇	—	2	1	no	—
141	C₄×Q₈×C₆₇	—	2	1	no	—
142	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
143	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
144	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
145	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
146	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
147	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
148	C₄×D₄×C₆₇	—	2	2	no	—
149	C₄×D₄×C₆₇	—	2	2	no	—
150	C₄×D₄×C₆₇	—	2	2	no	—
151	C₄×D₄×C₆₇	—	2	2	no	—
152	C₄×D₄×C₆₇	—	2	2	no	—
153	C₄×D₄×C₆₇	—	2	2	no	—
154	C₄×D₄×C₆₇	—	2	1	no	—
155	C₄×D₄×C₆₇	—	2	1	no	—
156	C₄×D₄×C₆₇	—	2	1	no	—
157	C₄×D₄×C₆₇	—	2	1	no	—
158	C₄×D₄×C₆₇	C₂³	1	2	yes	—
159	C₄×D₄×C₆₇	C₂³	1	2	yes	—
160	#117×C₆₇	—	2	1	no	—
161	#117×C₆₇	—	2	1	no	—
162	#117×C₆₇	—	2	2	no	—
163	#117×C₆₇	—	2	2	no	—
164	#117×C₆₇	—	2	2	no	—
165	#117×C₆₇	C₂³	1	2	yes	—
166	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
167	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
168	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
169	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
170	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
171	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
172	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
173	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
174	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
175	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
176	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
177	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
178	C₂×C₄²×C₆₇	—	2	2	no	—
179	C₂×C₄²×C₆₇	—	2	2	no	—
180	C₂×C₄²×C₆₇	—	2	2	no	—
181	C₂×C₄²×C₆₇	—	2	2	no	—
182	C₂×C₄²×C₆₇	—	2	2	no	—
183	C₂×C₄²×C₆₇	—	2	2	no	—
184	C₂×C₄²×C₆₇	—	2	2	no	—
185	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
186	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
187	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
188	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
189	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
190	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
191	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
192	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
193	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
194	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
195	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
196	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
197	#107×C₆₇	C₂³	1	8	yes	—
198	#106×C₆₇	C₂³	1	8	yes	—
199	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
200	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
201	#103×C₆₇	C₂³	1	8	yes	—
202	#103×C₆₇	C₂³	1	8	yes	—
203	#103×C₆₇	C₂³	1	8	yes	—
204	#102×C₆₇	C₂³	1	8	yes	—
205	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
206	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
207	#97×C₆₇	C₂³	1	4	yes	—
208	C₄×C₈×C₆₇	C₂³	1	4	yes	—
209	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
210	#41×C₆₇	—	2	8	no	—
211	#41×C₆₇	—	4	4	no	—
212	#41×C₆₇	—	4	4	no	—
213	C₂×Q₈×C₆₇	—	2	8	no	—
214	C₂×Q₈×C₆₇	—	2	8	no	—
215	C₂×Q₈×C₆₇	—	2	8	no	—
216	C₂×Q₈×C₆₇	—	2	8	no	—
217	C₂×Q₈×C₆₇	—	2	8	no	—
218	C₂×Q₈×C₆₇	—	2	2	no	—
219	C₂×Q₈×C₆₇	—	2	2	no	—
220	C₂×Q₈×C₆₇	—	2	2	no	—
221	C₂×Q₈×C₆₇	—	2	1	no	—
222	C₂×Q₈×C₆₇	—	2	1	no	—
223	C₂×Q₈×C₆₇	—	2	4	no	—
224	C₂×Q₈×C₆₇	#41	1	8	yes	complemented
225	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
226	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
227	C₂×D₄×C₆₇	—	2	2	no	—
228	C₂×D₄×C₆₇	—	2	2	no	—
229	C₂×D₄×C₆₇	—	2	2	no	—
230	C₂×D₄×C₆₇	—	2	1	no	—
231	C₂×D₄×C₆₇	—	2	1	no	—
232	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
233	C₂²×C₄×C₆₇	—	2	8	no	—
234	C₂²×C₄×C₆₇	—	2	2	no	—
235	C₂²×C₄×C₆₇	—	2	2	no	—
236	C₂²×C₄×C₆₇	—	2	2	no	—
237	C₂²×C₄×C₆₇	—	2	4	no	—
238	C₂²×C₄×C₆₇	—	2	4	no	—
239	C₂²×C₄×C₆₇	—	2	2	no	—
240	C₂²×C₄×C₆₇	—	2	2	no	—
241	C₂²×C₄×C₆₇	—	2	2	no	—
242	C₂²×C₄×C₆₇	—	2	2	no	—
243	C₂²×C₄×C₆₇	—	2	2	no	—
244	C₂²×C₄×C₆₇	—	2	2	no	—
245	C₂²×C₄×C₆₇	—	4	2	no	—
246	C₂²×C₄×C₆₇	—	4	4	no	—
247	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
248	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
249	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
250	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
251	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
252	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
253	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
254	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
255	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
256	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
257	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
258	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
259	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
260	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
261	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
262	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
263	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
264	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
265	Q₁₆×C₆₇	—	2	16	no	—
266	SD₁₆×C₆₇	—	2	16	no	—
267	M₁₆×C₆₇	—	2	8	no	—
268	C₂×C₈×C₆₇	C₂⁴	1	8	yes	—
269	C₄⋊C₄×C₆₇	—	2	4	no	—
270	C₄⋊C₄×C₆₇	—	2	4	no	—
271	C₄⋊C₄×C₆₇	—	2	4	no	—
272	C₄⋊C₄×C₆₇	—	2	4	no	—
273	C₄⋊C₄×C₆₇	—	2	2	no	—
274	C₄⋊C₄×C₆₇	—	2	2	no	—
275	C₄⋊C₄×C₆₇	—	2	2	no	—
276	C₄⋊C₄×C₆₇	—	2	1	no	—
277	C₄⋊C₄×C₆₇	—	2	1	no	—
278	C₄⋊C₄×C₆₇	—	2	1	no	—
279	C₄⋊C₄×C₆₇	—	2	1	no	—
280	C₄⋊C₄×C₆₇	—	2	2	no	—
281	C₄⋊C₄×C₆₇	—	2	2	no	—
282	C₄⋊C₄×C₆₇	—	2	2	no	—
283	C₄⋊C₄×C₆₇	—	2	2	no	—
284	C₄⋊C₄×C₆₇	—	2	2	no	—
285	C₄⋊C₄×C₆₇	—	2	2	no	—
286	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
287	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
288	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
289	C₂²⋊C₄×C₆₇	—	2	2	no	—
290	C₂²⋊C₄×C₆₇	—	2	2	no	—
291	C₂²⋊C₄×C₆₇	—	2	2	no	—
292	C₂²⋊C₄×C₆₇	—	2	2	no	—
293	C₂²⋊C₄×C₆₇	—	2	2	no	—
294	C₂²⋊C₄×C₆₇	—	2	2	no	—
295	C₂²⋊C₄×C₆₇	—	2	2	no	—
296	C₂²⋊C₄×C₆₇	—	2	2	no	—
297	C₂²⋊C₄×C₆₇	—	2	2	no	—
298	C₄²×C₆₇	—	2	4	no	—
299	C₄²×C₆₇	—	2	4	no	—
300	C₄²×C₆₇	—	2	4	no	—
301	C₄²×C₆₇	—	2	2	no	—
302	C₄²×C₆₇	—	2	2	no	—
303	C₄²×C₆₇	—	2	4	no	—
304	C₄²×C₆₇	—	2	2	no	—
305	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
306	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
307	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
308	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
309	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
310	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
311	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
312	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
313	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
314	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
315	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
316	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
317	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
318	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
319	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
320	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
321	C₂³×C₆₇	—	2	2	no	—
322	C₂³×C₆₇	—	2	2	no	—
323	C₂³×C₆₇	—	2	2	no	—
324	C₂³×C₆₇	—	2	2	no	—
325	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
326	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
327	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
328	Q₈×C₆₇	—	2	8	no	—
329	Q₈×C₆₇	—	2	8	no	—
330	Q₈×C₆₇	—	2	8	no	—
331	Q₈×C₆₇	—	2	4	no	—
332	Q₈×C₆₇	—	2	4	no	—
333	Q₈×C₆₇	—	4	2	no	—
334	Q₈×C₆₇	—	4	2	no	—
335	Q₈×C₆₇	C₂×#41	1	8	yes	—
336	D₄×C₆₇	—	2	4	no	—
337	D₄×C₆₇	—	4	2	no	—
338	D₄×C₆₇	—	4	4	no	—
339	D₄×C₆₇	—	4	4	no	—
340	D₄×C₆₇	—	4	4	no	—
341	D₄×C₆₇	—	4	2	no	—
342	C₂×C₄×C₆₇	—	2	8	no	—
343	C₂×C₄×C₆₇	—	2	8	no	—
344	C₂×C₄×C₆₇	—	2	8	no	—
345	C₂×C₄×C₆₇	—	2	2	no	—
346	C₂×C₄×C₆₇	—	2	2	no	—
347	C₂×C₄×C₆₇	—	2	2	no	—
348	C₂×C₄×C₆₇	—	2	2	no	—
349	C₂×C₄×C₆₇	—	2	4	no	—
350	C₂×C₄×C₆₇	—	2	2	no	—
351	C₂×C₄×C₆₇	—	2	2	no	—
352	C₂×C₄×C₆₇	—	2	2	no	—
353	C₂×C₄×C₆₇	—	2	2	no	—
354	C₂×C₄×C₆₇	—	2	2	no	—
355	C₂×C₄×C₆₇	—	2	2	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	2	no	—
360	C₂×C₄×C₆₇	—	2	2	no	—
361	C₂×C₄×C₆₇	—	2	2	no	—
362	C₂×C₄×C₆₇	—	4	1	no	—
363	C₂×C₄×C₆₇	—	4	1	no	—
364	C₂×C₄×C₆₇	—	4	1	no	—
365	C₂×C₄×C₆₇	—	4	1	no	—
366	C₂×C₄×C₆₇	—	4	4	no	—
367	C₂×C₄×C₆₇	—	4	4	no	—
368	C₂×C₄×C₆₇	—	4	4	no	—
369	C₂×C₄×C₆₇	—	4	4	no	—
370	C₂×C₄×C₆₇	—	4	4	no	—
371	C₂×C₄×C₆₇	—	4	4	no	—
372	C₂×C₄×C₆₇	#137	1	4	yes	complemented
373	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
374	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
375	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
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	1	yes	characteristic
380	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
381	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
382	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
383	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
384	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
385	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
386	C₈×C₆₇	—	2	8	no	—
387	C₂²×C₆₇	—	2	8	no	—
388	C₂²×C₆₇	—	2	1	no	—
389	C₂²×C₆₇	—	2	1	no	—
390	C₂²×C₆₇	—	2	1	no	—
391	C₂²×C₆₇	—	2	1	no	—
392	C₂²×C₆₇	—	2	1	no	—
393	C₂²×C₆₇	—	2	1	no	—
394	C₂²×C₆₇	—	4	2	no	—
395	C₂²×C₆₇	—	4	2	no	—
396	C₂²×C₆₇	—	4	2	no	—
397	C₂²×C₆₇	#525	1	2	yes	—
398	C₂²×C₆₇	C₂×#137	1	2	yes	—
399	C₂²×C₆₇	#575	1	2	yes	—
400	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
401	C₄×C₆₇	—	2	8	no	—
402	C₄×C₆₇	—	2	1	no	—
403	C₄×C₆₇	—	2	1	no	—
404	C₄×C₆₇	—	2	1	no	—
405	C₄×C₆₇	—	2	1	no	—
406	C₄×C₆₇	—	2	1	no	—
407	C₄×C₆₇	—	2	1	no	—
408	C₄×C₆₇	—	2	1	no	—
409	C₄×C₆₇	—	2	1	no	—
410	C₄×C₆₇	—	4	2	no	—
411	C₄×C₆₇	—	4	2	no	—
412	C₄×C₆₇	—	4	4	no	—
413	C₄×C₆₇	—	4	2	no	—
414	C₄×C₆₇	#525	1	2	yes	—
415	C₄×C₆₇	C₂×#137	1	2	yes	—
416	C₄×C₆₇	C₂×#137	1	2	yes	—
417	C₄×C₆₇	C₂²×#41	1	2	yes	—
418	#60560	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
419	C₂×C₆₇	—	2	2	no	—
420	C₂×C₆₇	—	2	2	no	—
421	C₂×C₆₇	—	2	2	no	—
422	C₂×C₆₇	—	8	2	no	—
423	C₂×C₆₇	C₂×#525	1	1	yes	characteristic
424	C₂×C₆₇	C₂²×#137	1	1	yes	characteristic
425	C₂×C₆₇	C₂×#575	1	1	yes	characteristic
426	#3444	C₂×C₆₇	1	1	yes	characteristic
427	C₂²×C₄×Q₈	C₂×C₆₇	1	1	yes	characteristic, complemented
428	#3117	C₂×C₆₇	1	4	yes	complemented
429	#3113	C₂×C₆₇	1	2	yes	complemented
430	#3112	C₂×C₆₇	1	2	yes	complemented
431	#3108	C₂×C₆₇	1	4	yes	complemented
432	#3104	C₂×C₆₇	1	2	yes	complemented
433	#3103	C₂×C₆₇	1	2	yes	complemented
434	#3092	C₂×C₆₇	1	2	yes	complemented
435	#3078	C₂×C₆₇	1	2	yes	complemented
436	#3037	C₂×C₆₇	1	2	yes	complemented
437	#3004	C₂×C₆₇	1	2	yes	complemented
438	C₄×#137	C₂×C₆₇	1	4	yes	complemented
439	#2920	C₂×C₆₇	1	1	yes	characteristic, complemented
440	C₆₇	#60560	1	1	yes	characteristic, direct product factor, Sylow
441	C₂³×Q₈	C₂²×C₆₇	1	1	yes	characteristic
442	C₂×#137	C₂²×C₆₇	1	4	yes	—
443	#533	C₂²×C₆₇	1	1	yes	characteristic
444	#533	C₂²×C₆₇	1	1	yes	characteristic
445	#533	C₂²×C₆₇	1	1	yes	characteristic
446	#532	C₂²×C₆₇	1	1	yes	characteristic
447	#532	C₂²×C₆₇	1	1	yes	characteristic
448	#532	C₂²×C₆₇	1	1	yes	characteristic
449	#529	—	2	1	no	—
450	#529	—	2	1	no	—
451	#529	—	2	1	no	—
452	#529	—	2	1	no	—
453	#529	C₂²×C₆₇	1	2	yes	—
454	#529	C₂²×C₆₇	1	2	yes	—
455	#525	—	2	1	no	—
456	#525	—	2	1	no	—
457	#525	C₂²×C₆₇	1	2	yes	—
458	C₄×#41	—	2	1	no	—
459	C₄×#41	—	2	1	no	—
460	C₄×#41	C₂²×C₆₇	1	2	yes	—
461	C₂×C₄×Q₈	—	2	1	no	—
462	C₂×C₄×Q₈	—	2	1	no	—
463	C₂×C₄×Q₈	—	2	1	no	—
464	C₂×C₄×Q₈	—	2	1	no	—
465	C₂×C₄×Q₈	—	2	1	no	—
466	C₂×C₄×Q₈	—	2	1	no	—
467	C₂×C₄×Q₈	C₂²×C₆₇	1	2	yes	—
468	C₂×C₄×Q₈	C₂²×C₆₇	1	2	yes	—
469	C₂×C₄×Q₈	C₂²×C₆₇	1	2	yes	—
470	C₂×C₄×Q₈	C₂²×C₆₇	1	2	yes	—
471	C₂×C₄×Q₈	C₂²×C₆₇	1	2	yes	—
472	C₂×C₄×Q₈	C₂²×C₆₇	1	2	yes	—
473	C₂²×C₄⋊C₄	—	2	1	no	—
474	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
475	C₂²×C₄²	—	2	1	no	—
476	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
477	#484	C₂²×C₆₇	1	4	yes	—
478	#483	C₂²×C₆₇	1	4	yes	—
479	#481	C₂²×C₆₇	1	4	yes	—
480	#480	C₂²×C₆₇	1	4	yes	—
481	#479	C₂²×C₆₇	1	8	yes	complemented
482	#477	C₂²×C₆₇	1	4	yes	complemented
483	#475	C₂²×C₆₇	1	4	yes	complemented
484	#464	C₂²×C₆₇	1	8	yes	complemented
485	#462	C₂²×C₆₇	1	4	yes	complemented
486	#460	C₂²×C₆₇	1	4	yes	complemented
487	#451	C₂²×C₆₇	1	4	yes	—
488	#451	C₂²×C₆₇	1	4	yes	—
489	#448	C₂²×C₆₇	1	4	yes	—
490	#448	C₂²×C₆₇	1	4	yes	—
491	#441	C₂²×C₆₇	1	8	yes	complemented
492	#440	C₂²×C₆₇	1	8	yes	complemented
493	C₄×Q₁₆	C₂²×C₆₇	1	8	yes	complemented
494	C₄×SD₁₆	C₂²×C₆₇	1	8	yes	complemented
495	#432	C₂²×C₆₇	1	2	yes	—
496	#432	C₂²×C₆₇	1	2	yes	—
497	#431	C₂²×C₆₇	1	2	yes	—
498	#431	C₂²×C₆₇	1	2	yes	—
499	#428	C₂²×C₆₇	1	4	yes	—
500	#423	C₂²×C₆₇	1	2	yes	—
501	#419	C₂²×C₆₇	1	4	yes	—
502	#417	C₂²×C₆₇	1	4	yes	—
503	#407	C₂²×C₆₇	1	2	yes	—
504	C₄×M₁₆	C₂²×C₆₇	1	2	yes	—
505	C₂×#41	—	2	1	no	—
506	C₂×#41	—	2	1	no	—
507	C₂×#41	C₂³×C₆₇	1	2	yes	—
508	C₂²×Q₈	—	2	8	no	—
509	C₂²×Q₈	—	2	1	no	—
510	C₂²×Q₈	—	2	1	no	—
511	C₂²×Q₈	—	2	1	no	—
512	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
513	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
514	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
515	C₂³×C₄	—	2	1	no	—
516	C₂³×C₄	—	2	1	no	—
517	C₂³×C₄	D₄×C₆₇	1	1	yes	characteristic
518	C₂³×C₄	D₄×C₆₇	1	1	yes	characteristic
519	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
520	#137	—	2	16	no	—
521	C₂×Q₁₆	C₂³×C₆₇	1	8	yes	—
522	C₂×SD₁₆	C₂³×C₆₇	1	8	yes	—
523	C₂×M₁₆	C₂³×C₆₇	1	4	yes	—
524	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
525	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
526	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
527	#127	C₂³×C₆₇	1	1	yes	characteristic
528	#126	—	2	2	no	—
529	#126	—	2	2	no	—
530	#125	—	2	1	no	—
531	#125	—	2	1	no	—
532	#125	C₂³×C₆₇	1	2	yes	—
533	#124	—	2	1	no	—
534	#124	—	2	1	no	—
535	#124	C₂³×C₆₇	1	2	yes	—
536	#123	—	2	2	no	—
537	#123	—	2	2	no	—
538	#123	—	2	2	no	—
539	C₂²⋊Q₈	—	2	1	no	—
540	C₂²⋊Q₈	—	2	1	no	—
541	C₂²⋊Q₈	—	2	1	no	—
542	C₂²⋊Q₈	—	2	1	no	—
543	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
544	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
545	#121	—	2	1	no	—
546	#121	—	2	1	no	—
547	#121	—	2	1	no	—
548	#121	—	2	1	no	—
549	#121	C₂³×C₆₇	1	2	yes	—
550	#121	C₂³×C₆₇	1	2	yes	—
551	#120	—	2	2	no	—
552	C₄×Q₈	—	2	2	no	—
553	C₄×Q₈	—	2	2	no	—
554	C₄×Q₈	—	2	2	no	—
555	C₄×Q₈	—	2	2	no	—
556	C₄×Q₈	—	2	2	no	—
557	C₄×Q₈	—	2	2	no	—
558	C₄×Q₈	—	2	2	no	—
559	C₄×Q₈	—	2	2	no	—
560	C₄×Q₈	—	2	2	no	—
561	C₄×Q₈	—	2	2	no	—
562	C₄×Q₈	—	2	2	no	—
563	C₄×Q₈	—	2	2	no	—
564	C₄×Q₈	—	2	1	no	—
565	C₄×Q₈	—	2	1	no	—
566	C₄×Q₈	—	2	1	no	—
567	C₄×Q₈	—	2	1	no	—
568	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
569	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
570	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
571	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
572	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
573	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
574	C₄×D₄	—	2	2	no	—
575	C₄×D₄	—	2	2	no	—
576	C₄×D₄	—	2	2	no	—
577	C₄×D₄	—	2	2	no	—
578	C₄×D₄	—	2	2	no	—
579	C₄×D₄	—	2	2	no	—
580	C₄×D₄	—	2	1	no	—
581	C₄×D₄	—	2	1	no	—
582	C₄×D₄	—	2	1	no	—
583	C₄×D₄	—	2	1	no	—
584	C₄×D₄	C₂³×C₆₇	1	2	yes	—
585	C₄×D₄	C₂³×C₆₇	1	2	yes	—
586	#117	—	2	1	no	—
587	#117	—	2	1	no	—
588	#117	—	2	2	no	—
589	#117	—	2	2	no	—
590	#117	—	2	2	no	—
591	#117	C₂³×C₆₇	1	2	yes	—
592	C₂×C₄⋊C₄	—	2	2	no	—
593	C₂×C₄⋊C₄	—	2	2	no	—
594	C₂×C₄⋊C₄	—	2	2	no	—
595	C₂×C₄⋊C₄	—	2	2	no	—
596	C₂×C₄⋊C₄	—	2	2	no	—
597	C₂×C₄⋊C₄	—	2	2	no	—
598	C₂×C₄⋊C₄	—	2	1	no	—
599	C₂×C₄⋊C₄	—	2	1	no	—
600	C₂×C₄⋊C₄	—	2	1	no	—
601	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
602	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
603	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
604	C₂×C₄²	—	2	2	no	—
605	C₂×C₄²	—	2	2	no	—
606	C₂×C₄²	—	2	2	no	—
607	C₂×C₄²	—	2	2	no	—
608	C₂×C₄²	—	2	2	no	—
609	C₂×C₄²	—	2	2	no	—
610	C₂×C₄²	—	2	2	no	—
611	C₂×C₄²	D₄×C₆₇	1	1	yes	characteristic
612	C₂×C₄²	D₄×C₆₇	1	1	yes	characteristic
613	C₂×C₄²	D₄×C₆₇	1	1	yes	characteristic
614	C₂×C₄²	D₄×C₆₇	1	1	yes	characteristic
615	C₂×C₄²	D₄×C₆₇	1	1	yes	characteristic
616	C₂×C₄²	D₄×C₆₇	1	1	yes	characteristic
617	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
618	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
619	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
620	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
621	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
622	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
623	#107	C₂³×C₆₇	1	8	yes	—
624	#106	C₂³×C₆₇	1	8	yes	—
625	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
626	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
627	#103	C₂³×C₆₇	1	8	yes	—
628	#103	C₂³×C₆₇	1	8	yes	—
629	#103	C₂³×C₆₇	1	8	yes	—
630	#102	C₂³×C₆₇	1	8	yes	—
631	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
632	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
633	#97	C₂³×C₆₇	1	4	yes	—
634	C₄×C₈	C₂³×C₆₇	1	4	yes	—
635	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
636	#41	—	2	8	no	—
637	#41	—	4	4	no	—
638	#41	—	4	4	no	—
639	C₂×Q₈	—	2	8	no	—
640	C₂×Q₈	—	2	8	no	—
641	C₂×Q₈	—	2	8	no	—
642	C₂×Q₈	—	2	8	no	—
643	C₂×Q₈	—	2	8	no	—
644	C₂×Q₈	—	2	2	no	—
645	C₂×Q₈	—	2	2	no	—
646	C₂×Q₈	—	2	2	no	—
647	C₂×Q₈	—	2	1	no	—
648	C₂×Q₈	—	2	1	no	—
649	C₂×Q₈	—	2	4	no	—
650	C₂×Q₈	#41×C₆₇	1	8	yes	complemented
651	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
652	C₂×Q₈	C₂⁴×C₆₇	1	4	yes	—
653	C₂×D₄	—	2	2	no	—
654	C₂×D₄	—	2	2	no	—
655	C₂×D₄	—	2	2	no	—
656	C₂×D₄	—	2	1	no	—
657	C₂×D₄	—	2	1	no	—
658	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
659	C₂²×C₄	—	2	8	no	—
660	C₂²×C₄	—	2	2	no	—
661	C₂²×C₄	—	2	2	no	—
662	C₂²×C₄	—	2	2	no	—
663	C₂²×C₄	—	2	4	no	—
664	C₂²×C₄	—	2	4	no	—
665	C₂²×C₄	—	2	2	no	—
666	C₂²×C₄	—	2	2	no	—
667	C₂²×C₄	—	2	2	no	—
668	C₂²×C₄	—	2	2	no	—
669	C₂²×C₄	—	2	2	no	—
670	C₂²×C₄	—	2	2	no	—
671	C₂²×C₄	—	4	2	no	—
672	C₂²×C₄	—	4	4	no	—
673	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
674	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
675	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
676	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
677	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
678	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
679	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
680	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
681	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
682	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
683	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
684	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
685	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
686	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
687	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
688	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
689	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
690	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
691	Q₁₆	—	2	16	no	—
692	SD₁₆	—	2	16	no	—
693	M₁₆	—	2	8	no	—
694	C₂×C₈	C₂⁴×C₆₇	1	8	yes	—
695	C₄⋊C₄	—	2	4	no	—
696	C₄⋊C₄	—	2	4	no	—
697	C₄⋊C₄	—	2	4	no	—
698	C₄⋊C₄	—	2	4	no	—
699	C₄⋊C₄	—	2	2	no	—
700	C₄⋊C₄	—	2	2	no	—
701	C₄⋊C₄	—	2	2	no	—
702	C₄⋊C₄	—	2	1	no	—
703	C₄⋊C₄	—	2	1	no	—
704	C₄⋊C₄	—	2	1	no	—
705	C₄⋊C₄	—	2	1	no	—
706	C₄⋊C₄	—	2	2	no	—
707	C₄⋊C₄	—	2	2	no	—
708	C₄⋊C₄	—	2	2	no	—
709	C₄⋊C₄	—	2	2	no	—
710	C₄⋊C₄	—	2	2	no	—
711	C₄⋊C₄	—	2	2	no	—
712	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
713	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
714	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
715	C₂²⋊C₄	—	2	2	no	—
716	C₂²⋊C₄	—	2	2	no	—
717	C₂²⋊C₄	—	2	2	no	—
718	C₂²⋊C₄	—	2	2	no	—
719	C₂²⋊C₄	—	2	2	no	—
720	C₂²⋊C₄	—	2	2	no	—
721	C₂²⋊C₄	—	2	2	no	—
722	C₂²⋊C₄	—	2	2	no	—
723	C₂²⋊C₄	—	2	2	no	—
724	C₄²	—	2	4	no	—
725	C₄²	—	2	4	no	—
726	C₄²	—	2	4	no	—
727	C₄²	—	2	4	no	—
728	C₄²	—	2	2	no	—
729	C₄²	—	2	2	no	—
730	C₄²	—	2	2	no	—
731	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
732	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
733	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
734	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
735	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
736	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
737	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
738	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
739	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
740	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
741	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
742	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
743	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
744	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
745	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
746	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
747	C₂³	—	2	2	no	—
748	C₂³	—	2	2	no	—
749	C₂³	—	2	2	no	—
750	C₂³	—	2	2	no	—
751	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
752	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
753	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
754	Q₈	—	2	8	no	—
755	Q₈	—	2	8	no	—
756	Q₈	—	2	8	no	—
757	Q₈	—	2	4	no	—
758	Q₈	—	2	4	no	—
759	Q₈	—	4	2	no	—
760	Q₈	—	4	2	no	—
761	Q₈	C₂×#41×C₆₇	1	8	yes	—
762	D₄	—	2	4	no	—
763	D₄	—	4	2	no	—
764	D₄	—	4	4	no	—
765	D₄	—	4	4	no	—
766	D₄	—	4	4	no	—
767	D₄	—	4	2	no	—
768	C₂×C₄	—	2	8	no	—
769	C₂×C₄	—	2	8	no	—
770	C₂×C₄	—	2	8	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	2	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	2	4	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	2	2	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	2	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	2	no	—
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	2	4	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	2	2	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	4	1	no	—
789	C₂×C₄	—	4	1	no	—
790	C₂×C₄	—	4	1	no	—
791	C₂×C₄	—	4	1	no	—
792	C₂×C₄	—	4	4	no	—
793	C₂×C₄	—	4	4	no	—
794	C₂×C₄	—	4	4	no	—
795	C₂×C₄	—	4	4	no	—
796	C₂×C₄	—	4	4	no	—
797	C₂×C₄	—	4	4	no	—
798	C₂×C₄	#137×C₆₇	1	4	yes	complemented
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	1	yes	characteristic
803	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
804	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
805	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
806	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
807	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
808	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
809	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
810	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
811	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
812	C₈	—	2	8	no	—
813	C₂²	—	2	8	no	—
814	C₂²	—	2	1	no	—
815	C₂²	—	2	1	no	—
816	C₂²	—	2	1	no	—
817	C₂²	—	2	1	no	—
818	C₂²	—	2	1	no	—
819	C₂²	—	2	1	no	—
820	C₂²	—	4	2	no	—
821	C₂²	—	4	2	no	—
822	C₂²	—	4	2	no	—
823	C₂²	#525×C₆₇	1	2	yes	—
824	C₂²	C₂×#137×C₆₇	1	2	yes	—
825	C₂²	#575×C₆₇	1	2	yes	—
826	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
827	C₄	—	2	1	no	—
828	C₄	—	2	1	no	—
829	C₄	—	2	1	no	—
830	C₄	—	2	1	no	—
831	C₄	—	2	1	no	—
832	C₄	—	2	1	no	—
833	C₄	—	2	8	no	—
834	C₄	—	2	1	no	—
835	C₄	—	2	1	no	—
836	C₄	—	4	2	no	—
837	C₄	—	4	4	no	—
838	C₄	—	4	2	no	—
839	C₄	—	4	2	no	—
840	C₄	#525×C₆₇	1	2	yes	—
841	C₄	C₂×#137×C₆₇	1	2	yes	—
842	C₄	C₂×#137×C₆₇	1	2	yes	—
843	C₄	C₂²×#41×C₆₇	1	2	yes	—
844	C₂	—	2	2	no	—
845	C₂	—	2	2	no	—
846	C₂	—	2	2	no	—
847	C₂	—	8	2	no	—
848	C₂	C₂×#525×C₆₇	1	1	yes	characteristic
849	C₂	C₂²×#137×C₆₇	1	1	yes	characteristic
850	C₂	C₂×#575×C₆₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₆₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
socle	C₂²×C₆₇	C₂³×D₄
prime radical	C₆₇×#3444	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₆₇ ◁ C₂²×C₄²×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₄×Q₈×C₆₇	C₂	semidirect
3. C₆₇×#3117	C₂	semidirect
4. C₆₇×#3113	C₂	semidirect
5. C₆₇×#3112	C₂	semidirect
6. C₆₇×#3108	C₂	semidirect
7. C₆₇×#3104	C₂	semidirect
8. C₆₇×#3103	C₂	semidirect
9. C₆₇×#3092	C₂	semidirect
10. C₆₇×#3078	C₂	semidirect
11. C₆₇×#3037	C₂	semidirect
12. C₆₇×#3004	C₂	semidirect
13. C₄×#137×C₆₇	C₂	semidirect
14. C₆₇×#2920	C₂	semidirect
55. #479×C₆₇	C₂²	semidirect
56. #477×C₆₇	C₂²	semidirect
57. #475×C₆₇	C₂²	semidirect
58. #464×C₆₇	C₂²	semidirect
59. #462×C₆₇	C₂²	semidirect
60. #460×C₆₇	C₂²	semidirect
65. #441×C₆₇	C₂²	semidirect
66. #440×C₆₇	C₂²	semidirect
67. C₄×Q₁₆×C₆₇	C₂²	semidirect
68. C₄×SD₁₆×C₆₇	C₂²	semidirect
224. C₂×Q₈×C₆₇	#41	semidirect
372. C₂×C₄×C₆₇	#137	semidirect
418. #60560	C₆₇	direct (N × H)
427. C₂²×C₄×Q₈	C₂×C₆₇	semidirect
428. #3117	C₂×C₆₇	semidirect
429. #3113	C₂×C₆₇	semidirect
430. #3112	C₂×C₆₇	semidirect
431. #3108	C₂×C₆₇	semidirect
432. #3104	C₂×C₆₇	semidirect
433. #3103	C₂×C₆₇	semidirect
434. #3092	C₂×C₆₇	semidirect
435. #3078	C₂×C₆₇	semidirect
436. #3037	C₂×C₆₇	semidirect
437. #3004	C₂×C₆₇	semidirect
438. C₄×#137	C₂×C₆₇	semidirect
439. #2920	C₂×C₆₇	semidirect
440. C₆₇	#60560	direct (N × H)
481. #479	C₂²×C₆₇	semidirect
482. #477	C₂²×C₆₇	semidirect
483. #475	C₂²×C₆₇	semidirect
484. #464	C₂²×C₆₇	semidirect
485. #462	C₂²×C₆₇	semidirect
486. #460	C₂²×C₆₇	semidirect
491. #441	C₂²×C₆₇	semidirect
492. #440	C₂²×C₆₇	semidirect
493. C₄×Q₁₆	C₂²×C₆₇	semidirect
494. C₄×SD₁₆	C₂²×C₆₇	semidirect
650. C₂×Q₈	#41×C₆₇	semidirect
798. C₂×C₄	#137×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#3444	2
C₂²×C₄×Q₈×C₆₇	2
C₆₇×#3117	2
C₆₇×#3113	2
C₆₇×#3112	2
C₆₇×#3108	2
C₆₇×#3104	2
C₆₇×#3103	2
C₆₇×#3092	2
C₆₇×#3078	2
C₆₇×#3037	2
C₆₇×#3004	2
C₄×#137×C₆₇	2
C₆₇×#2920	2
#60560	67

Subgroups — C67×#60560 #30739811

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#60560 #30739811