Subgroups — C₆₇×#61778 #30741029

Order 17152.

1806 conjugacy classes of subgroups.

The subgroup lattice has 1072 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3537	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#3493	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3355	C₂	1	2	yes	maximal, complemented
4	C₆₇×#3351	C₂	1	2	yes	maximal, complemented
5	C₆₇×#3350	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3347	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3325	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3324	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3318	C₂	1	2	yes	maximal, complemented
10	C₆₇×#3310	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3241	C₂	1	2	yes	maximal, complemented
12	C₆₇×#3198	C₂	1	2	yes	maximal, complemented
13	C₆₇×#3194	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3194	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#3119	C₂	1	2	yes	maximal, complemented
16	C₆₇×#3096	C₂	1	2	yes	maximal, complemented
17	C₆₇×#3094	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₇×#3094	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₇×#2978	C₂	1	1	yes	maximal, characteristic, complemented
20	#560×C₆₇	—	2	2	no	—
21	#556×C₆₇	—	2	1	no	—
22	#556×C₆₇	C₂²	1	2	yes	complemented
23	#555×C₆₇	—	2	1	no	—
24	#555×C₆₇	C₂²	1	2	yes	complemented
25	#553×C₆₇	—	2	1	no	—
26	#553×C₆₇	C₂²	1	2	yes	—
27	#553×C₆₇	C₂²	1	2	yes	—
28	#553×C₆₇	C₂²	1	2	yes	complemented
29	#552×C₆₇	—	2	1	no	—
30	#552×C₆₇	C₂²	1	2	yes	complemented
31	D₄²×C₆₇	—	2	2	no	—
32	D₄²×C₆₇	C₂²	1	2	yes	—
33	D₄²×C₆₇	C₂²	1	2	yes	—
34	#544×C₆₇	C₂²	1	1	yes	characteristic, complemented
35	#540×C₆₇	C₂²	1	2	yes	—
36	#538×C₆₇	—	2	1	no	—
37	#538×C₆₇	—	2	1	no	—
38	#538×C₆₇	—	2	2	no	—
39	#537×C₆₇	C₂²	1	1	yes	characteristic, complemented
40	#535×C₆₇	C₂²	1	2	yes	—
41	#534×C₆₇	—	2	1	no	—
42	#534×C₆₇	—	2	1	no	—
43	#529×C₆₇	—	2	2	no	—
44	#525×C₆₇	C₂²	1	1	yes	characteristic
45	#525×C₆₇	C₂²	1	1	yes	characteristic, complemented
46	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
47	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
48	#520×C₆₇	C₂²	1	1	yes	characteristic, complemented
49	#520×C₆₇	C₂²	1	1	yes	characteristic, complemented
50	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic, complemented
51	#501×C₆₇	C₂²	1	2	yes	complemented
52	#499×C₆₇	C₂²	1	2	yes	complemented
53	#490×C₆₇	C₂²	1	2	yes	complemented
54	#486×C₆₇	C₂²	1	2	yes	complemented
55	#485×C₆₇	C₂²	1	2	yes	complemented
56	#483×C₆₇	C₂²	1	1	yes	characteristic, complemented
57	#483×C₆₇	C₂²	1	1	yes	characteristic, complemented
58	#482×C₆₇	C₂²	1	2	yes	complemented
59	#482×C₆₇	C₂²	1	2	yes	complemented
60	#482×C₆₇	C₂²	1	2	yes	complemented
61	#482×C₆₇	C₂²	1	2	yes	complemented
62	#482×C₆₇	C₂²	1	2	yes	complemented
63	#482×C₆₇	C₂²	1	2	yes	complemented
64	#482×C₆₇	C₂²	1	2	yes	complemented
65	#482×C₆₇	C₂²	1	2	yes	complemented
66	#482×C₆₇	C₂²	1	2	yes	complemented
67	#481×C₆₇	C₂²	1	2	yes	complemented
68	#481×C₆₇	C₂²	1	2	yes	complemented
69	#481×C₆₇	C₂²	1	2	yes	complemented
70	#480×C₆₇	C₂²	1	2	yes	complemented
71	#480×C₆₇	C₂²	1	1	yes	characteristic, complemented
72	#480×C₆₇	C₂²	1	2	yes	complemented
73	#480×C₆₇	C₂²	1	2	yes	complemented
74	#480×C₆₇	C₂²	1	1	yes	characteristic, complemented
75	#479×C₆₇	C₂²	1	2	yes	complemented
76	#478×C₆₇	C₂²	1	2	yes	complemented
77	#478×C₆₇	C₂²	1	2	yes	complemented
78	#478×C₆₇	C₂²	1	2	yes	complemented
79	#476×C₆₇	C₂²	1	2	yes	complemented
80	#474×C₆₇	C₂²	1	2	yes	complemented
81	#469×C₆₇	C₂²	1	2	yes	complemented
82	#469×C₆₇	C₂²	1	2	yes	complemented
83	#469×C₆₇	C₂²	1	2	yes	complemented
84	#468×C₆₇	C₂²	1	2	yes	complemented
85	#468×C₆₇	C₂²	1	2	yes	complemented
86	#468×C₆₇	C₂²	1	2	yes	complemented
87	#466×C₆₇	C₂²	1	2	yes	complemented
88	#465×C₆₇	C₂²	1	2	yes	complemented
89	#460×C₆₇	C₂²	1	2	yes	complemented
90	#459×C₆₇	C₂²	1	2	yes	complemented
91	#450×C₆₇	C₂²	1	1	yes	characteristic, complemented
92	#450×C₆₇	C₂²	1	2	yes	complemented
93	#450×C₆₇	C₂²	1	1	yes	characteristic, complemented
94	#449×C₆₇	C₂²	1	2	yes	complemented
95	#449×C₆₇	C₂²	1	2	yes	complemented
96	#447×C₆₇	C₂²	1	1	yes	characteristic, complemented
97	#447×C₆₇	C₂²	1	2	yes	complemented
98	#447×C₆₇	C₂²	1	1	yes	characteristic, complemented
99	#442×C₆₇	C₂²	1	2	yes	complemented
100	#440×C₆₇	C₂²	1	2	yes	complemented
101	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
102	C₄×D₈×C₆₇	C₂²	1	2	yes	complemented
103	#436×C₆₇	C₂²	1	2	yes	complemented
104	#436×C₆₇	C₂²	1	2	yes	complemented
105	#435×C₆₇	C₂²	1	2	yes	complemented
106	#435×C₆₇	C₂²	1	2	yes	complemented
107	#433×C₆₇	C₂²	1	2	yes	complemented
108	#428×C₆₇	C₂²	1	2	yes	complemented
109	#428×C₆₇	C₂²	1	2	yes	complemented
110	#428×C₆₇	C₂²	1	2	yes	complemented
111	#427×C₆₇	C₂²	1	2	yes	complemented
112	#418×C₆₇	C₂²	1	2	yes	complemented
113	#418×C₆₇	C₂²	1	2	yes	complemented
114	#418×C₆₇	C₂²	1	2	yes	complemented
115	C₂×#102×C₆₇	C₂²	1	2	yes	complemented
116	#408×C₆₇	C₂²	1	2	yes	complemented
117	#407×C₆₇	C₂²	1	1	yes	characteristic, complemented
118	#407×C₆₇	C₂²	1	1	yes	characteristic, complemented
119	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
120	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
121	C₂²×D₄×C₆₇	—	2	1	no	—
122	C₂²×D₄×C₆₇	—	2	1	no	—
123	C₂²×D₄×C₆₇	—	2	2	no	—
124	C₂²×D₄×C₆₇	—	2	2	no	—
125	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
126	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
127	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
128	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
129	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
130	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
131	C₂×D₈×C₆₇	C₂³	1	2	yes	—
132	C₂×D₈×C₆₇	C₂³	1	2	yes	—
133	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
134	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
135	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
136	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
137	C₄⋊Q₈×C₆₇	—	2	1	no	—
138	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
139	#127×C₆₇	—	2	2	no	—
140	#127×C₆₇	C₂³	1	2	yes	—
141	#126×C₆₇	—	2	2	no	—
142	#126×C₆₇	—	2	2	no	—
143	#126×C₆₇	—	2	2	no	—
144	#126×C₆₇	—	2	2	no	—
145	#126×C₆₇	—	2	2	no	—
146	#126×C₆₇	—	2	2	no	—
147	#125×C₆₇	—	2	2	no	—
148	#125×C₆₇	—	2	1	no	—
149	#125×C₆₇	C₂³	1	2	yes	—
150	#125×C₆₇	C₂³	1	2	yes	—
151	#124×C₆₇	—	2	2	no	—
152	#124×C₆₇	—	2	2	no	—
153	#124×C₆₇	—	2	2	no	—
154	#124×C₆₇	—	2	2	no	—
155	#123×C₆₇	—	2	2	no	—
156	#123×C₆₇	—	2	1	no	—
157	#123×C₆₇	—	2	2	no	—
158	#123×C₆₇	—	2	2	no	—
159	#123×C₆₇	—	2	2	no	—
160	#123×C₆₇	—	2	2	no	—
161	#123×C₆₇	—	2	2	no	—
162	#123×C₆₇	D₄	1	2	yes	—
163	C₂²⋊Q₈×C₆₇	—	2	1	no	—
164	C₂²⋊Q₈×C₆₇	—	2	2	no	—
165	C₂²⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
166	C₂²⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
167	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
168	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
169	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
170	#121×C₆₇	—	2	2	no	—
171	#121×C₆₇	—	2	2	no	—
172	#121×C₆₇	—	2	2	no	—
173	#121×C₆₇	—	2	1	no	—
174	#121×C₆₇	—	2	2	no	—
175	#121×C₆₇	—	2	2	no	—
176	#121×C₆₇	—	2	1	no	—
177	#121×C₆₇	—	2	1	no	—
178	#121×C₆₇	—	2	1	no	—
179	#121×C₆₇	—	2	1	no	—
180	#121×C₆₇	—	2	2	no	—
181	#121×C₆₇	—	2	2	no	—
182	#121×C₆₇	—	2	2	no	—
183	#121×C₆₇	—	2	2	no	—
184	#121×C₆₇	D₄	1	1	yes	characteristic
185	#121×C₆₇	D₄	1	1	yes	characteristic
186	#121×C₆₇	C₂³	1	2	yes	—
187	#121×C₆₇	C₂³	1	2	yes	—
188	#121×C₆₇	C₂³	1	2	yes	—
189	#121×C₆₇	C₂³	1	2	yes	—
190	#121×C₆₇	C₂³	1	2	yes	—
191	#121×C₆₇	C₂³	1	2	yes	—
192	#121×C₆₇	C₂³	1	2	yes	—
193	#121×C₆₇	C₂³	1	1	yes	characteristic
194	#121×C₆₇	C₂³	1	1	yes	characteristic
195	#120×C₆₇	—	2	1	no	—
196	#120×C₆₇	—	2	2	no	—
197	#120×C₆₇	—	2	2	no	—
198	#120×C₆₇	—	2	2	no	—
199	#120×C₆₇	—	2	2	no	—
200	#120×C₆₇	—	2	2	no	—
201	#120×C₆₇	—	2	2	no	—
202	#120×C₆₇	D₄	1	2	yes	—
203	C₄×Q₈×C₆₇	—	2	1	no	—
204	C₄×Q₈×C₆₇	—	2	2	no	—
205	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
206	C₄×D₄×C₆₇	—	2	2	no	—
207	C₄×D₄×C₆₇	—	2	1	no	—
208	C₄×D₄×C₆₇	—	2	1	no	—
209	C₄×D₄×C₆₇	—	2	1	no	—
210	C₄×D₄×C₆₇	—	2	2	no	—
211	C₄×D₄×C₆₇	—	2	2	no	—
212	C₄×D₄×C₆₇	—	2	2	no	—
213	C₄×D₄×C₆₇	—	2	2	no	—
214	C₄×D₄×C₆₇	C₂³	1	2	yes	—
215	C₄×D₄×C₆₇	C₂³	1	2	yes	—
216	C₄×D₄×C₆₇	C₂³	1	2	yes	—
217	C₄×D₄×C₆₇	C₂³	1	2	yes	—
218	C₄×D₄×C₆₇	C₂³	1	2	yes	—
219	#117×C₆₇	—	2	1	no	—
220	#117×C₆₇	—	2	1	no	—
221	#117×C₆₇	—	2	1	no	—
222	#117×C₆₇	—	2	2	no	—
223	#117×C₆₇	—	2	2	no	—
224	#117×C₆₇	C₂³	1	1	yes	characteristic
225	#117×C₆₇	C₂³	1	2	yes	—
226	#117×C₆₇	C₂³	1	2	yes	—
227	#117×C₆₇	C₂³	1	2	yes	—
228	#117×C₆₇	C₂³	1	2	yes	—
229	#117×C₆₇	C₂³	1	1	yes	characteristic
230	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
231	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
232	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
233	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
234	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
235	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
236	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
237	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
238	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
239	C₂×C₄²×C₆₇	—	2	1	no	—
240	#107×C₆₇	C₂³	1	2	yes	—
241	#107×C₆₇	C₂³	1	2	yes	—
242	#107×C₆₇	C₂³	1	2	yes	—
243	#107×C₆₇	C₂³	1	2	yes	—
244	#107×C₆₇	C₂³	1	2	yes	—
245	#107×C₆₇	C₂³	1	2	yes	—
246	#106×C₆₇	C₂³	1	2	yes	—
247	#106×C₆₇	C₂³	1	2	yes	—
248	#106×C₆₇	C₂³	1	2	yes	—
249	#106×C₆₇	C₂³	1	2	yes	—
250	#106×C₆₇	C₂³	1	2	yes	—
251	#106×C₆₇	C₂³	1	2	yes	—
252	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
253	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
254	#103×C₆₇	C₂³	1	2	yes	—
255	#103×C₆₇	C₂³	1	2	yes	—
256	#102×C₆₇	C₂³	1	2	yes	—
257	#102×C₆₇	C₂³	1	2	yes	—
258	#102×C₆₇	C₂³	1	2	yes	—
259	#102×C₆₇	C₂³	1	2	yes	—
260	#102×C₆₇	C₂³	1	2	yes	—
261	#102×C₆₇	C₂³	1	2	yes	—
262	#102×C₆₇	C₂³	1	2	yes	—
263	#102×C₆₇	C₂³	1	2	yes	—
264	#102×C₆₇	C₂³	1	2	yes	—
265	#102×C₆₇	C₂³	1	2	yes	—
266	#102×C₆₇	C₂³	1	2	yes	—
267	#102×C₆₇	C₂³	1	2	yes	—
268	#102×C₆₇	C₂³	1	2	yes	—
269	#102×C₆₇	C₂³	1	2	yes	—
270	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
271	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
272	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
273	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
274	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
275	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
276	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
277	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
278	#97×C₆₇	C₂³	1	2	yes	—
279	C₄×C₈×C₆₇	C₂³	1	2	yes	—
280	C₂⁴×C₆₇	—	2	1	no	—
281	C₂⁴×C₆₇	—	2	1	no	—
282	C₂⁴×C₆₇	—	2	2	no	—
283	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
284	#41×C₆₇	—	4	2	no	—
285	#41×C₆₇	—	4	2	no	—
286	C₂×Q₈×C₆₇	—	2	2	no	—
287	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
288	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
289	C₂×D₄×C₆₇	—	2	1	no	—
290	C₂×D₄×C₆₇	—	2	2	no	—
291	C₂×D₄×C₆₇	—	2	2	no	—
292	C₂×D₄×C₆₇	—	2	1	no	—
293	C₂×D₄×C₆₇	—	2	1	no	—
294	C₂×D₄×C₆₇	—	2	2	no	—
295	C₂×D₄×C₆₇	—	2	2	no	—
296	C₂×D₄×C₆₇	—	2	2	no	—
297	C₂×D₄×C₆₇	—	2	2	no	—
298	C₂×D₄×C₆₇	—	2	2	no	—
299	C₂×D₄×C₆₇	—	2	1	no	—
300	C₂×D₄×C₆₇	—	2	1	no	—
301	C₂×D₄×C₆₇	—	2	2	no	—
302	C₂×D₄×C₆₇	—	2	2	no	—
303	C₂×D₄×C₆₇	—	2	2	no	—
304	C₂×D₄×C₆₇	—	4	2	no	—
305	C₂×D₄×C₆₇	—	4	2	no	—
306	C₂×D₄×C₆₇	—	4	2	no	—
307	C₂×D₄×C₆₇	—	4	2	no	—
308	C₂×D₄×C₆₇	—	8	4	no	—
309	C₂×D₄×C₆₇	—	8	4	no	—
310	C₂×D₄×C₆₇	—	8	2	no	—
311	C₂×D₄×C₆₇	—	8	2	no	—
312	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
313	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
314	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
315	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
316	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
317	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
318	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
319	C₂²×C₄×C₆₇	—	2	1	no	—
320	C₂²×C₄×C₆₇	—	2	1	no	—
321	C₂²×C₄×C₆₇	—	2	1	no	—
322	C₂²×C₄×C₆₇	—	2	1	no	—
323	C₂²×C₄×C₆₇	—	2	2	no	—
324	C₂²×C₄×C₆₇	—	2	1	no	—
325	C₂²×C₄×C₆₇	—	2	2	no	—
326	C₂²×C₄×C₆₇	—	2	2	no	—
327	C₂²×C₄×C₆₇	—	2	2	no	—
328	C₂²×C₄×C₆₇	—	4	2	no	—
329	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
330	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
331	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
332	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
333	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
334	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
335	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
336	SD₁₆×C₆₇	—	4	2	no	—
337	SD₁₆×C₆₇	—	4	2	no	—
338	D₈×C₆₇	—	4	2	no	—
339	D₈×C₆₇	—	4	2	no	—
340	M₁₆×C₆₇	—	4	2	no	—
341	M₁₆×C₆₇	—	4	2	no	—
342	M₁₆×C₆₇	—	4	2	no	—
343	C₂×C₈×C₆₇	—	4	2	no	—
344	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
345	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
346	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
347	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
348	C₄⋊C₄×C₆₇	—	2	1	no	—
349	C₄⋊C₄×C₆₇	—	2	2	no	—
350	C₄⋊C₄×C₆₇	—	2	1	no	—
351	C₄⋊C₄×C₆₇	—	2	2	no	—
352	C₄⋊C₄×C₆₇	—	2	1	no	—
353	C₄⋊C₄×C₆₇	—	2	1	no	—
354	C₄⋊C₄×C₆₇	—	2	1	no	—
355	C₄⋊C₄×C₆₇	—	2	2	no	—
356	C₄⋊C₄×C₆₇	—	2	2	no	—
357	C₄⋊C₄×C₆₇	—	2	1	no	—
358	C₄⋊C₄×C₆₇	—	2	2	no	—
359	C₄⋊C₄×C₆₇	—	2	2	no	—
360	C₄⋊C₄×C₆₇	—	2	2	no	—
361	C₄⋊C₄×C₆₇	—	2	2	no	—
362	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
363	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
364	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
365	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
366	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
367	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
368	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
369	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
370	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
371	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
372	C₂²⋊C₄×C₆₇	—	2	2	no	—
373	C₂²⋊C₄×C₆₇	—	2	2	no	—
374	C₂²⋊C₄×C₆₇	—	2	2	no	—
375	C₂²⋊C₄×C₆₇	—	2	1	no	—
376	C₂²⋊C₄×C₆₇	—	2	2	no	—
377	C₂²⋊C₄×C₆₇	—	2	2	no	—
378	C₂²⋊C₄×C₆₇	—	2	1	no	—
379	C₂²⋊C₄×C₆₇	—	2	1	no	—
380	C₂²⋊C₄×C₆₇	—	2	2	no	—
381	C₂²⋊C₄×C₆₇	—	2	2	no	—
382	C₂²⋊C₄×C₆₇	—	2	2	no	—
383	C₂²⋊C₄×C₆₇	—	2	2	no	—
384	C₂²⋊C₄×C₆₇	—	2	1	no	—
385	C₂²⋊C₄×C₆₇	—	2	2	no	—
386	C₂²⋊C₄×C₆₇	—	2	2	no	—
387	C₂²⋊C₄×C₆₇	—	2	1	no	—
388	C₂²⋊C₄×C₆₇	—	2	2	no	—
389	C₂²⋊C₄×C₆₇	—	2	2	no	—
390	C₂²⋊C₄×C₆₇	—	2	2	no	—
391	C₂²⋊C₄×C₆₇	—	2	2	no	—
392	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
393	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
394	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
395	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
396	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
397	C₄²×C₆₇	—	2	2	no	—
398	C₄²×C₆₇	—	2	2	no	—
399	C₄²×C₆₇	—	2	2	no	—
400	C₄²×C₆₇	—	2	2	no	—
401	C₄²×C₆₇	—	2	1	no	—
402	C₄²×C₆₇	—	2	2	no	—
403	C₄²×C₆₇	C₂⁴	1	2	yes	—
404	C₂³×C₆₇	—	2	1	no	—
405	C₂³×C₆₇	—	2	2	no	—
406	C₂³×C₆₇	—	2	2	no	—
407	C₂³×C₆₇	—	4	1	no	—
408	C₂³×C₆₇	—	4	1	no	—
409	C₂³×C₆₇	—	4	1	no	—
410	C₂³×C₆₇	—	4	2	no	—
411	C₂³×C₆₇	—	4	2	no	—
412	C₂³×C₆₇	—	8	1	no	—
413	C₂³×C₆₇	—	8	1	no	—
414	C₂³×C₆₇	—	8	2	no	—
415	C₂³×C₆₇	—	8	2	no	—
416	C₂³×C₆₇	—	8	1	no	—
417	C₂³×C₆₇	—	8	1	no	—
418	C₂³×C₆₇	—	8	2	no	—
419	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
420	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
421	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
422	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
423	Q₈×C₆₇	—	2	2	no	—
424	Q₈×C₆₇	—	4	1	no	—
425	Q₈×C₆₇	—	8	2	no	—
426	D₄×C₆₇	—	2	2	no	—
427	D₄×C₆₇	—	2	2	no	—
428	D₄×C₆₇	—	2	2	no	—
429	D₄×C₆₇	—	2	2	no	—
430	D₄×C₆₇	—	2	2	no	—
431	D₄×C₆₇	—	4	2	no	—
432	D₄×C₆₇	—	4	2	no	—
433	D₄×C₆₇	—	4	1	no	—
434	D₄×C₆₇	—	4	2	no	—
435	D₄×C₆₇	—	4	4	no	—
436	D₄×C₆₇	—	4	4	no	—
437	D₄×C₆₇	—	4	2	no	—
438	D₄×C₆₇	—	8	1	no	—
439	D₄×C₆₇	—	8	1	no	—
440	D₄×C₆₇	—	8	2	no	—
441	D₄×C₆₇	—	8	2	no	—
442	D₄×C₆₇	—	8	2	no	—
443	D₄×C₆₇	—	8	1	no	—
444	D₄×C₆₇	—	8	2	no	—
445	D₄×C₆₇	—	8	1	no	—
446	D₄×C₆₇	—	8	2	no	—
447	D₄×C₆₇	—	8	2	no	—
448	D₄×C₆₇	—	8	2	no	—
449	D₄×C₆₇	—	8	2	no	—
450	C₂×C₄×C₆₇	—	2	2	no	—
451	C₂×C₄×C₆₇	—	2	2	no	—
452	C₂×C₄×C₆₇	—	2	2	no	—
453	C₂×C₄×C₆₇	—	2	2	no	—
454	C₂×C₄×C₆₇	—	2	2	no	—
455	C₂×C₄×C₆₇	—	2	2	no	—
456	C₂×C₄×C₆₇	—	2	1	no	—
457	C₂×C₄×C₆₇	—	2	1	no	—
458	C₂×C₄×C₆₇	—	2	2	no	—
459	C₂×C₄×C₆₇	—	2	2	no	—
460	C₂×C₄×C₆₇	—	2	2	no	—
461	C₂×C₄×C₆₇	—	2	1	no	—
462	C₂×C₄×C₆₇	—	4	1	no	—
463	C₂×C₄×C₆₇	—	4	1	no	—
464	C₂×C₄×C₆₇	—	4	1	no	—
465	C₂×C₄×C₆₇	—	4	2	no	—
466	C₂×C₄×C₆₇	—	8	2	no	—
467	C₂×C₄×C₆₇	—	8	2	no	—
468	C₂×C₄×C₆₇	—	8	2	no	—
469	C₂×C₄×C₆₇	—	8	1	no	—
470	C₂×C₄×C₆₇	—	8	2	no	—
471	C₂×C₄×C₆₇	—	8	1	no	—
472	C₂×C₄×C₆₇	—	8	1	no	—
473	C₂×C₄×C₆₇	—	8	1	no	—
474	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
475	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
476	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
477	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
478	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
479	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
480	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
481	C₈×C₆₇	—	2	2	no	—
482	C₈×C₆₇	—	2	2	no	—
483	C₈×C₆₇	—	2	2	no	—
484	C₈×C₆₇	—	2	2	no	—
485	C₂²×C₆₇	—	2	2	no	—
486	C₂²×C₆₇	—	2	1	no	—
487	C₂²×C₆₇	—	2	1	no	—
488	C₂²×C₆₇	—	2	1	no	—
489	C₂²×C₆₇	—	2	1	no	—
490	C₂²×C₆₇	—	2	1	no	—
491	C₂²×C₆₇	—	2	1	no	—
492	C₂²×C₆₇	—	2	2	no	—
493	C₂²×C₆₇	—	2	1	no	—
494	C₂²×C₆₇	—	2	1	no	—
495	C₂²×C₆₇	—	2	1	no	—
496	C₂²×C₆₇	—	2	2	no	—
497	C₂²×C₆₇	—	4	1	no	—
498	C₂²×C₆₇	—	4	2	no	—
499	C₂²×C₆₇	—	4	2	no	—
500	C₂²×C₆₇	—	4	2	no	—
501	C₂²×C₆₇	—	4	2	no	—
502	C₂²×C₆₇	—	4	1	no	—
503	C₂²×C₆₇	—	4	1	no	—
504	C₂²×C₆₇	—	4	2	no	—
505	C₂²×C₆₇	—	4	2	no	—
506	C₂²×C₆₇	—	8	2	no	—
507	C₂²×C₆₇	—	16	2	no	—
508	C₂²×C₆₇	—	16	2	no	—
509	C₂²×C₆₇	—	16	4	no	—
510	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
511	C₄×C₆₇	—	2	2	no	—
512	C₄×C₆₇	—	2	2	no	—
513	C₄×C₆₇	—	2	1	no	—
514	C₄×C₆₇	—	2	1	no	—
515	C₄×C₆₇	—	2	1	no	—
516	C₄×C₆₇	—	2	2	no	—
517	C₄×C₆₇	—	4	2	no	—
518	C₄×C₆₇	—	4	2	no	—
519	C₄×C₆₇	—	4	2	no	—
520	C₄×C₆₇	—	4	1	no	—
521	C₄×C₆₇	—	4	2	no	—
522	C₄×C₆₇	—	4	1	no	—
523	C₄×C₆₇	—	4	1	no	—
524	C₄×C₆₇	#585	1	2	yes	—
525	#61778	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
526	C₂×C₆₇	—	4	1	no	—
527	C₂×C₆₇	—	4	1	no	—
528	C₂×C₆₇	—	4	1	no	—
529	C₂×C₆₇	—	4	2	no	—
530	C₂×C₆₇	—	8	1	no	—
531	C₂×C₆₇	—	8	2	no	—
532	C₂×C₆₇	—	8	2	no	—
533	C₂×C₆₇	#3485	1	1	yes	characteristic
534	C₂×C₆₇	#3585	1	1	yes	characteristic
535	C₂×C₆₇	#3585	1	1	yes	characteristic
536	#3537	C₂×C₆₇	1	1	yes	characteristic, complemented
537	#3493	C₂×C₆₇	1	1	yes	characteristic, complemented
538	#3355	C₂×C₆₇	1	2	yes	complemented
539	#3351	C₂×C₆₇	1	2	yes	complemented
540	#3350	C₂×C₆₇	1	2	yes	complemented
541	#3347	C₂×C₆₇	1	2	yes	complemented
542	#3325	C₂×C₆₇	1	2	yes	complemented
543	#3324	C₂×C₆₇	1	2	yes	complemented
544	#3318	C₂×C₆₇	1	2	yes	complemented
545	#3310	C₂×C₆₇	1	2	yes	complemented
546	#3241	C₂×C₆₇	1	2	yes	complemented
547	#3198	C₂×C₆₇	1	2	yes	complemented
548	#3194	C₂×C₆₇	1	1	yes	characteristic, complemented
549	#3194	C₂×C₆₇	1	1	yes	characteristic, complemented
550	#3119	C₂×C₆₇	1	2	yes	complemented
551	#3096	C₂×C₆₇	1	2	yes	complemented
552	#3094	C₂×C₆₇	1	1	yes	characteristic, complemented
553	#3094	C₂×C₆₇	1	1	yes	characteristic, complemented
554	#2978	C₂×C₆₇	1	1	yes	characteristic, complemented
555	C₆₇	#61778	1	1	yes	characteristic, direct product factor, Sylow
556	#560	—	2	2	no	—
557	#556	—	2	1	no	—
558	#556	C₂²×C₆₇	1	2	yes	complemented
559	#555	—	2	1	no	—
560	#555	C₂²×C₆₇	1	2	yes	complemented
561	#553	—	2	1	no	—
562	#553	C₂²×C₆₇	1	2	yes	—
563	#553	C₂²×C₆₇	1	2	yes	—
564	#553	C₂²×C₆₇	1	2	yes	complemented
565	#552	—	2	1	no	—
566	#552	C₂²×C₆₇	1	2	yes	complemented
567	D₄²	—	2	2	no	—
568	D₄²	C₂²×C₆₇	1	2	yes	—
569	D₄²	C₂²×C₆₇	1	2	yes	—
570	#544	C₂²×C₆₇	1	1	yes	characteristic, complemented
571	#540	C₂²×C₆₇	1	2	yes	—
572	#538	—	2	1	no	—
573	#538	—	2	1	no	—
574	#538	—	2	2	no	—
575	#537	C₂²×C₆₇	1	1	yes	characteristic, complemented
576	#535	C₂²×C₆₇	1	2	yes	—
577	#534	—	2	1	no	—
578	#534	—	2	1	no	—
579	#529	—	2	2	no	—
580	#525	C₂²×C₆₇	1	1	yes	characteristic
581	#525	C₂²×C₆₇	1	1	yes	characteristic, complemented
582	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
583	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
584	#520	C₂²×C₆₇	1	1	yes	characteristic, complemented
585	#520	C₂²×C₆₇	1	1	yes	characteristic, complemented
586	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic, complemented
587	#501	C₂²×C₆₇	1	2	yes	complemented
588	#499	C₂²×C₆₇	1	2	yes	complemented
589	#490	C₂²×C₆₇	1	2	yes	complemented
590	#486	C₂²×C₆₇	1	2	yes	complemented
591	#485	C₂²×C₆₇	1	2	yes	complemented
592	#483	C₂²×C₆₇	1	1	yes	characteristic, complemented
593	#483	C₂²×C₆₇	1	1	yes	characteristic, complemented
594	#482	C₂²×C₆₇	1	2	yes	complemented
595	#482	C₂²×C₆₇	1	2	yes	complemented
596	#482	C₂²×C₆₇	1	2	yes	complemented
597	#482	C₂²×C₆₇	1	2	yes	complemented
598	#482	C₂²×C₆₇	1	2	yes	complemented
599	#482	C₂²×C₆₇	1	2	yes	complemented
600	#482	C₂²×C₆₇	1	2	yes	complemented
601	#482	C₂²×C₆₇	1	2	yes	complemented
602	#482	C₂²×C₆₇	1	2	yes	complemented
603	#481	C₂²×C₆₇	1	2	yes	complemented
604	#481	C₂²×C₆₇	1	2	yes	complemented
605	#481	C₂²×C₆₇	1	2	yes	complemented
606	#480	C₂²×C₆₇	1	1	yes	characteristic, complemented
607	#480	C₂²×C₆₇	1	2	yes	complemented
608	#480	C₂²×C₆₇	1	2	yes	complemented
609	#480	C₂²×C₆₇	1	2	yes	complemented
610	#480	C₂²×C₆₇	1	1	yes	characteristic, complemented
611	#479	C₂²×C₆₇	1	2	yes	complemented
612	#478	C₂²×C₆₇	1	2	yes	complemented
613	#478	C₂²×C₆₇	1	2	yes	complemented
614	#478	C₂²×C₆₇	1	2	yes	complemented
615	#476	C₂²×C₆₇	1	2	yes	complemented
616	#474	C₂²×C₆₇	1	2	yes	complemented
617	#469	C₂²×C₆₇	1	2	yes	complemented
618	#469	C₂²×C₆₇	1	2	yes	complemented
619	#469	C₂²×C₆₇	1	2	yes	complemented
620	#468	C₂²×C₆₇	1	2	yes	complemented
621	#468	C₂²×C₆₇	1	2	yes	complemented
622	#468	C₂²×C₆₇	1	2	yes	complemented
623	#466	C₂²×C₆₇	1	2	yes	complemented
624	#465	C₂²×C₆₇	1	2	yes	complemented
625	#460	C₂²×C₆₇	1	2	yes	complemented
626	#459	C₂²×C₆₇	1	2	yes	complemented
627	#450	C₂²×C₆₇	1	1	yes	characteristic, complemented
628	#450	C₂²×C₆₇	1	1	yes	characteristic, complemented
629	#450	C₂²×C₆₇	1	2	yes	complemented
630	#449	C₂²×C₆₇	1	2	yes	complemented
631	#449	C₂²×C₆₇	1	2	yes	complemented
632	#447	C₂²×C₆₇	1	1	yes	characteristic, complemented
633	#447	C₂²×C₆₇	1	1	yes	characteristic, complemented
634	#447	C₂²×C₆₇	1	2	yes	complemented
635	#442	C₂²×C₆₇	1	2	yes	complemented
636	#440	C₂²×C₆₇	1	2	yes	complemented
637	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
638	C₄×D₈	C₂²×C₆₇	1	2	yes	complemented
639	#436	C₂²×C₆₇	1	2	yes	complemented
640	#436	C₂²×C₆₇	1	2	yes	complemented
641	#435	C₂²×C₆₇	1	2	yes	complemented
642	#435	C₂²×C₆₇	1	2	yes	complemented
643	#433	C₂²×C₆₇	1	2	yes	complemented
644	#428	C₂²×C₆₇	1	2	yes	complemented
645	#428	C₂²×C₆₇	1	2	yes	complemented
646	#428	C₂²×C₆₇	1	2	yes	complemented
647	#427	C₂²×C₆₇	1	2	yes	complemented
648	#418	C₂²×C₆₇	1	2	yes	complemented
649	#418	C₂²×C₆₇	1	2	yes	complemented
650	#418	C₂²×C₆₇	1	2	yes	complemented
651	C₂×#102	C₂²×C₆₇	1	2	yes	complemented
652	#408	C₂²×C₆₇	1	2	yes	complemented
653	#407	C₂²×C₆₇	1	1	yes	characteristic, complemented
654	#407	C₂²×C₆₇	1	1	yes	characteristic, complemented
655	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
656	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
657	C₂²×D₄	—	2	1	no	—
658	C₂²×D₄	—	2	1	no	—
659	C₂²×D₄	—	2	2	no	—
660	C₂²×D₄	—	2	2	no	—
661	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
662	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
663	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
664	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
665	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
666	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
667	C₂×D₈	C₂³×C₆₇	1	2	yes	—
668	C₂×D₈	C₂³×C₆₇	1	2	yes	—
669	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
670	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
671	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
672	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
673	C₄⋊Q₈	—	2	1	no	—
674	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
675	#127	—	2	2	no	—
676	#127	C₂³×C₆₇	1	2	yes	—
677	#126	—	2	2	no	—
678	#126	—	2	2	no	—
679	#126	—	2	2	no	—
680	#126	—	2	2	no	—
681	#126	—	2	2	no	—
682	#126	—	2	2	no	—
683	#125	—	2	2	no	—
684	#125	—	2	1	no	—
685	#125	C₂³×C₆₇	1	2	yes	—
686	#125	C₂³×C₆₇	1	2	yes	—
687	#124	—	2	2	no	—
688	#124	—	2	2	no	—
689	#124	—	2	2	no	—
690	#124	—	2	2	no	—
691	#123	—	2	2	no	—
692	#123	—	2	1	no	—
693	#123	—	2	2	no	—
694	#123	—	2	2	no	—
695	#123	—	2	2	no	—
696	#123	—	2	2	no	—
697	#123	—	2	2	no	—
698	#123	D₄×C₆₇	1	2	yes	—
699	C₂²⋊Q₈	—	2	1	no	—
700	C₂²⋊Q₈	—	2	2	no	—
701	C₂²⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
702	C₂²⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
703	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
704	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
705	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
706	#121	—	2	2	no	—
707	#121	—	2	2	no	—
708	#121	—	2	2	no	—
709	#121	—	2	1	no	—
710	#121	—	2	2	no	—
711	#121	—	2	2	no	—
712	#121	—	2	1	no	—
713	#121	—	2	1	no	—
714	#121	—	2	1	no	—
715	#121	—	2	1	no	—
716	#121	—	2	2	no	—
717	#121	—	2	2	no	—
718	#121	—	2	2	no	—
719	#121	—	2	2	no	—
720	#121	D₄×C₆₇	1	1	yes	characteristic
721	#121	D₄×C₆₇	1	1	yes	characteristic
722	#121	C₂³×C₆₇	1	2	yes	—
723	#121	C₂³×C₆₇	1	2	yes	—
724	#121	C₂³×C₆₇	1	2	yes	—
725	#121	C₂³×C₆₇	1	2	yes	—
726	#121	C₂³×C₆₇	1	1	yes	characteristic
727	#121	C₂³×C₆₇	1	1	yes	characteristic
728	#121	C₂³×C₆₇	1	2	yes	—
729	#121	C₂³×C₆₇	1	2	yes	—
730	#121	C₂³×C₆₇	1	2	yes	—
731	#120	—	2	1	no	—
732	#120	—	2	2	no	—
733	#120	—	2	2	no	—
734	#120	—	2	2	no	—
735	#120	—	2	2	no	—
736	#120	—	2	2	no	—
737	#120	—	2	2	no	—
738	#120	D₄×C₆₇	1	2	yes	—
739	C₄×Q₈	—	2	1	no	—
740	C₄×Q₈	—	2	2	no	—
741	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
742	C₄×D₄	—	2	2	no	—
743	C₄×D₄	—	2	1	no	—
744	C₄×D₄	—	2	1	no	—
745	C₄×D₄	—	2	1	no	—
746	C₄×D₄	—	2	2	no	—
747	C₄×D₄	—	2	2	no	—
748	C₄×D₄	—	2	2	no	—
749	C₄×D₄	—	2	2	no	—
750	C₄×D₄	C₂³×C₆₇	1	2	yes	—
751	C₄×D₄	C₂³×C₆₇	1	2	yes	—
752	C₄×D₄	C₂³×C₆₇	1	2	yes	—
753	C₄×D₄	C₂³×C₆₇	1	2	yes	—
754	C₄×D₄	C₂³×C₆₇	1	2	yes	—
755	#117	—	2	1	no	—
756	#117	—	2	1	no	—
757	#117	—	2	1	no	—
758	#117	—	2	2	no	—
759	#117	—	2	2	no	—
760	#117	C₂³×C₆₇	1	2	yes	—
761	#117	C₂³×C₆₇	1	2	yes	—
762	#117	C₂³×C₆₇	1	1	yes	characteristic
763	#117	C₂³×C₆₇	1	2	yes	—
764	#117	C₂³×C₆₇	1	2	yes	—
765	#117	C₂³×C₆₇	1	1	yes	characteristic
766	C₂×C₄⋊C₄	—	2	1	no	—
767	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
768	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
769	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
770	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
771	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
772	C₂×C₂²⋊C₄	—	2	1	no	—
773	C₂×C₂²⋊C₄	—	2	1	no	—
774	C₂×C₂²⋊C₄	—	2	1	no	—
775	C₂×C₄²	—	2	1	no	—
776	#107	C₂³×C₆₇	1	2	yes	—
777	#107	C₂³×C₆₇	1	2	yes	—
778	#107	C₂³×C₆₇	1	2	yes	—
779	#107	C₂³×C₆₇	1	2	yes	—
780	#107	C₂³×C₆₇	1	2	yes	—
781	#107	C₂³×C₆₇	1	2	yes	—
782	#106	C₂³×C₆₇	1	2	yes	—
783	#106	C₂³×C₆₇	1	2	yes	—
784	#106	C₂³×C₆₇	1	2	yes	—
785	#106	C₂³×C₆₇	1	2	yes	—
786	#106	C₂³×C₆₇	1	2	yes	—
787	#106	C₂³×C₆₇	1	2	yes	—
788	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
789	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
790	#103	C₂³×C₆₇	1	2	yes	—
791	#103	C₂³×C₆₇	1	2	yes	—
792	#102	C₂³×C₆₇	1	2	yes	—
793	#102	C₂³×C₆₇	1	2	yes	—
794	#102	C₂³×C₆₇	1	2	yes	—
795	#102	C₂³×C₆₇	1	2	yes	—
796	#102	C₂³×C₆₇	1	2	yes	—
797	#102	C₂³×C₆₇	1	2	yes	—
798	#102	C₂³×C₆₇	1	2	yes	—
799	#102	C₂³×C₆₇	1	2	yes	—
800	#102	C₂³×C₆₇	1	2	yes	—
801	#102	C₂³×C₆₇	1	2	yes	—
802	#102	C₂³×C₆₇	1	2	yes	—
803	#102	C₂³×C₆₇	1	2	yes	—
804	#102	C₂³×C₆₇	1	2	yes	—
805	#102	C₂³×C₆₇	1	2	yes	—
806	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
807	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
808	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
809	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
810	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
811	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
812	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
813	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
814	#97	C₂³×C₆₇	1	2	yes	—
815	C₄×C₈	C₂³×C₆₇	1	2	yes	—
816	C₂⁴	—	2	1	no	—
817	C₂⁴	—	2	1	no	—
818	C₂⁴	—	2	2	no	—
819	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
820	#41	—	4	2	no	—
821	#41	—	4	2	no	—
822	C₂×Q₈	—	2	2	no	—
823	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
824	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
825	C₂×D₄	—	2	1	no	—
826	C₂×D₄	—	2	2	no	—
827	C₂×D₄	—	2	2	no	—
828	C₂×D₄	—	2	1	no	—
829	C₂×D₄	—	2	1	no	—
830	C₂×D₄	—	2	2	no	—
831	C₂×D₄	—	2	2	no	—
832	C₂×D₄	—	2	2	no	—
833	C₂×D₄	—	2	2	no	—
834	C₂×D₄	—	2	2	no	—
835	C₂×D₄	—	2	1	no	—
836	C₂×D₄	—	2	1	no	—
837	C₂×D₄	—	2	2	no	—
838	C₂×D₄	—	2	2	no	—
839	C₂×D₄	—	2	2	no	—
840	C₂×D₄	—	4	2	no	—
841	C₂×D₄	—	4	2	no	—
842	C₂×D₄	—	4	2	no	—
843	C₂×D₄	—	4	2	no	—
844	C₂×D₄	—	8	4	no	—
845	C₂×D₄	—	8	4	no	—
846	C₂×D₄	—	8	2	no	—
847	C₂×D₄	—	8	2	no	—
848	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
849	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
850	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
851	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
852	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
853	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
854	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
855	C₂²×C₄	—	2	1	no	—
856	C₂²×C₄	—	2	1	no	—
857	C₂²×C₄	—	2	1	no	—
858	C₂²×C₄	—	2	1	no	—
859	C₂²×C₄	—	2	2	no	—
860	C₂²×C₄	—	2	1	no	—
861	C₂²×C₄	—	2	2	no	—
862	C₂²×C₄	—	2	2	no	—
863	C₂²×C₄	—	2	2	no	—
864	C₂²×C₄	—	4	2	no	—
865	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
866	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
867	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
868	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
869	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
870	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
871	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
872	SD₁₆	—	4	2	no	—
873	SD₁₆	—	4	2	no	—
874	D₈	—	4	2	no	—
875	D₈	—	4	2	no	—
876	M₁₆	—	4	2	no	—
877	M₁₆	—	4	2	no	—
878	M₁₆	—	4	2	no	—
879	C₂×C₈	—	4	2	no	—
880	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
881	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
882	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
883	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
884	C₄⋊C₄	—	2	1	no	—
885	C₄⋊C₄	—	2	2	no	—
886	C₄⋊C₄	—	2	1	no	—
887	C₄⋊C₄	—	2	2	no	—
888	C₄⋊C₄	—	2	1	no	—
889	C₄⋊C₄	—	2	1	no	—
890	C₄⋊C₄	—	2	1	no	—
891	C₄⋊C₄	—	2	2	no	—
892	C₄⋊C₄	—	2	2	no	—
893	C₄⋊C₄	—	2	1	no	—
894	C₄⋊C₄	—	2	2	no	—
895	C₄⋊C₄	—	2	2	no	—
896	C₄⋊C₄	—	2	2	no	—
897	C₄⋊C₄	—	2	2	no	—
898	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
899	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
900	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
901	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
902	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
903	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
904	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
905	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
906	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
907	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
908	C₂²⋊C₄	—	2	2	no	—
909	C₂²⋊C₄	—	2	2	no	—
910	C₂²⋊C₄	—	2	2	no	—
911	C₂²⋊C₄	—	2	1	no	—
912	C₂²⋊C₄	—	2	2	no	—
913	C₂²⋊C₄	—	2	2	no	—
914	C₂²⋊C₄	—	2	1	no	—
915	C₂²⋊C₄	—	2	1	no	—
916	C₂²⋊C₄	—	2	2	no	—
917	C₂²⋊C₄	—	2	2	no	—
918	C₂²⋊C₄	—	2	2	no	—
919	C₂²⋊C₄	—	2	2	no	—
920	C₂²⋊C₄	—	2	1	no	—
921	C₂²⋊C₄	—	2	2	no	—
922	C₂²⋊C₄	—	2	2	no	—
923	C₂²⋊C₄	—	2	1	no	—
924	C₂²⋊C₄	—	2	2	no	—
925	C₂²⋊C₄	—	2	2	no	—
926	C₂²⋊C₄	—	2	2	no	—
927	C₂²⋊C₄	—	2	2	no	—
928	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
929	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
930	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
931	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
932	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
933	C₄²	—	2	2	no	—
934	C₄²	—	2	2	no	—
935	C₄²	—	2	2	no	—
936	C₄²	—	2	2	no	—
937	C₄²	—	2	1	no	—
938	C₄²	—	2	2	no	—
939	C₄²	C₂⁴×C₆₇	1	2	yes	—
940	C₂³	—	2	1	no	—
941	C₂³	—	2	2	no	—
942	C₂³	—	2	2	no	—
943	C₂³	—	4	1	no	—
944	C₂³	—	4	1	no	—
945	C₂³	—	4	1	no	—
946	C₂³	—	4	2	no	—
947	C₂³	—	4	2	no	—
948	C₂³	—	8	1	no	—
949	C₂³	—	8	1	no	—
950	C₂³	—	8	2	no	—
951	C₂³	—	8	2	no	—
952	C₂³	—	8	1	no	—
953	C₂³	—	8	1	no	—
954	C₂³	—	8	2	no	—
955	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
956	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
957	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
958	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
959	Q₈	—	2	2	no	—
960	Q₈	—	4	1	no	—
961	Q₈	—	8	2	no	—
962	D₄	—	2	2	no	—
963	D₄	—	2	2	no	—
964	D₄	—	2	2	no	—
965	D₄	—	2	2	no	—
966	D₄	—	2	2	no	—
967	D₄	—	4	2	no	—
968	D₄	—	4	2	no	—
969	D₄	—	4	1	no	—
970	D₄	—	4	2	no	—
971	D₄	—	4	4	no	—
972	D₄	—	4	4	no	—
973	D₄	—	4	2	no	—
974	D₄	—	8	1	no	—
975	D₄	—	8	1	no	—
976	D₄	—	8	2	no	—
977	D₄	—	8	2	no	—
978	D₄	—	8	2	no	—
979	D₄	—	8	2	no	—
980	D₄	—	8	2	no	—
981	D₄	—	8	2	no	—
982	D₄	—	8	2	no	—
983	D₄	—	8	1	no	—
984	D₄	—	8	2	no	—
985	D₄	—	8	1	no	—
986	C₂×C₄	—	2	2	no	—
987	C₂×C₄	—	2	2	no	—
988	C₂×C₄	—	2	2	no	—
989	C₂×C₄	—	2	2	no	—
990	C₂×C₄	—	2	2	no	—
991	C₂×C₄	—	2	2	no	—
992	C₂×C₄	—	2	1	no	—
993	C₂×C₄	—	2	1	no	—
994	C₂×C₄	—	2	2	no	—
995	C₂×C₄	—	2	2	no	—
996	C₂×C₄	—	2	2	no	—
997	C₂×C₄	—	2	1	no	—
998	C₂×C₄	—	4	1	no	—
999	C₂×C₄	—	4	1	no	—
1000	C₂×C₄	—	4	1	no	—
1001	C₂×C₄	—	4	2	no	—
1002	C₂×C₄	—	8	2	no	—
1003	C₂×C₄	—	8	2	no	—
1004	C₂×C₄	—	8	2	no	—
1005	C₂×C₄	—	8	1	no	—
1006	C₂×C₄	—	8	1	no	—
1007	C₂×C₄	—	8	1	no	—
1008	C₂×C₄	—	8	2	no	—
1009	C₂×C₄	—	8	1	no	—
1010	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1011	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1012	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1013	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1014	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1015	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1016	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1017	C₈	—	2	2	no	—
1018	C₈	—	2	2	no	—
1019	C₈	—	2	2	no	—
1020	C₈	—	2	2	no	—
1021	C₂²	—	2	2	no	—
1022	C₂²	—	2	1	no	—
1023	C₂²	—	2	1	no	—
1024	C₂²	—	2	1	no	—
1025	C₂²	—	2	1	no	—
1026	C₂²	—	2	1	no	—
1027	C₂²	—	2	1	no	—
1028	C₂²	—	2	2	no	—
1029	C₂²	—	2	1	no	—
1030	C₂²	—	2	1	no	—
1031	C₂²	—	2	1	no	—
1032	C₂²	—	2	2	no	—
1033	C₂²	—	4	1	no	—
1034	C₂²	—	4	2	no	—
1035	C₂²	—	4	2	no	—
1036	C₂²	—	4	2	no	—
1037	C₂²	—	4	2	no	—
1038	C₂²	—	4	1	no	—
1039	C₂²	—	4	1	no	—
1040	C₂²	—	4	2	no	—
1041	C₂²	—	4	2	no	—
1042	C₂²	—	8	2	no	—
1043	C₂²	—	16	2	no	—
1044	C₂²	—	16	2	no	—
1045	C₂²	—	16	4	no	—
1046	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1047	C₄	—	2	2	no	—
1048	C₄	—	2	2	no	—
1049	C₄	—	2	1	no	—
1050	C₄	—	2	1	no	—
1051	C₄	—	2	1	no	—
1052	C₄	—	2	2	no	—
1053	C₄	—	4	2	no	—
1054	C₄	—	4	2	no	—
1055	C₄	—	4	2	no	—
1056	C₄	—	4	1	no	—
1057	C₄	—	4	2	no	—
1058	C₄	—	4	1	no	—
1059	C₄	—	4	1	no	—
1060	C₄	#585×C₆₇	1	2	yes	—
1061	C₂	—	4	1	no	—
1062	C₂	—	4	1	no	—
1063	C₂	—	4	1	no	—
1064	C₂	—	4	2	no	—
1065	C₂	—	8	2	no	—
1066	C₂	—	8	2	no	—
1067	C₂	—	8	1	no	—
1068	C₂	C₆₇×#3485	1	1	yes	characteristic
1069	C₂	C₆₇×#3585	1	1	yes	characteristic
1070	C₂	C₆₇×#3585	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 ◁ #525×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3537	C₂	semidirect
2. C₆₇×#3493	C₂	semidirect
3. C₆₇×#3355	C₂	semidirect
4. C₆₇×#3351	C₂	semidirect
5. C₆₇×#3350	C₂	semidirect
6. C₆₇×#3347	C₂	semidirect
7. C₆₇×#3325	C₂	semidirect
8. C₆₇×#3324	C₂	semidirect
9. C₆₇×#3318	C₂	semidirect
10. C₆₇×#3310	C₂	semidirect
11. C₆₇×#3241	C₂	semidirect
12. C₆₇×#3198	C₂	semidirect
13. C₆₇×#3194	C₂	semidirect
14. C₆₇×#3194	C₂	semidirect
15. C₆₇×#3119	C₂	semidirect
16. C₆₇×#3096	C₂	semidirect
17. C₆₇×#3094	C₂	semidirect
18. C₆₇×#3094	C₂	semidirect
19. C₆₇×#2978	C₂	semidirect
22. #556×C₆₇	C₂²	semidirect
24. #555×C₆₇	C₂²	semidirect
28. #553×C₆₇	C₂²	semidirect
30. #552×C₆₇	C₂²	semidirect
34. #544×C₆₇	C₂²	semidirect
39. #537×C₆₇	C₂²	semidirect
45. #525×C₆₇	C₂²	semidirect
48. #520×C₆₇	C₂²	semidirect
49. #520×C₆₇	C₂²	semidirect
50. C₂×#117×C₆₇	C₂²	semidirect
51. #501×C₆₇	C₂²	semidirect
52. #499×C₆₇	C₂²	semidirect
53. #490×C₆₇	C₂²	semidirect
54. #486×C₆₇	C₂²	semidirect
55. #485×C₆₇	C₂²	semidirect
56. #483×C₆₇	C₂²	semidirect
57. #483×C₆₇	C₂²	semidirect
58. #482×C₆₇	C₂²	semidirect
59. #482×C₆₇	C₂²	semidirect
60. #482×C₆₇	C₂²	semidirect
61. #482×C₆₇	C₂²	semidirect
62. #482×C₆₇	C₂²	semidirect
63. #482×C₆₇	C₂²	semidirect
64. #482×C₆₇	C₂²	semidirect
65. #482×C₆₇	C₂²	semidirect
66. #482×C₆₇	C₂²	semidirect
67. #481×C₆₇	C₂²	semidirect
68. #481×C₆₇	C₂²	semidirect
69. #481×C₆₇	C₂²	semidirect
70. #480×C₆₇	C₂²	semidirect
71. #480×C₆₇	C₂²	semidirect
72. #480×C₆₇	C₂²	semidirect
73. #480×C₆₇	C₂²	semidirect
74. #480×C₆₇	C₂²	semidirect
75. #479×C₆₇	C₂²	semidirect
76. #478×C₆₇	C₂²	semidirect
77. #478×C₆₇	C₂²	semidirect
78. #478×C₆₇	C₂²	semidirect
79. #476×C₆₇	C₂²	semidirect
80. #474×C₆₇	C₂²	semidirect
81. #469×C₆₇	C₂²	semidirect
82. #469×C₆₇	C₂²	semidirect
83. #469×C₆₇	C₂²	semidirect
84. #468×C₆₇	C₂²	semidirect
85. #468×C₆₇	C₂²	semidirect
86. #468×C₆₇	C₂²	semidirect
87. #466×C₆₇	C₂²	semidirect
88. #465×C₆₇	C₂²	semidirect
89. #460×C₆₇	C₂²	semidirect
90. #459×C₆₇	C₂²	semidirect
91. #450×C₆₇	C₂²	semidirect
92. #450×C₆₇	C₂²	semidirect
93. #450×C₆₇	C₂²	semidirect
94. #449×C₆₇	C₂²	semidirect
95. #449×C₆₇	C₂²	semidirect
96. #447×C₆₇	C₂²	semidirect
97. #447×C₆₇	C₂²	semidirect
98. #447×C₆₇	C₂²	semidirect
99. #442×C₆₇	C₂²	semidirect
100. #440×C₆₇	C₂²	semidirect
101. C₄×SD₁₆×C₆₇	C₂²	semidirect
102. C₄×D₈×C₆₇	C₂²	semidirect
103. #436×C₆₇	C₂²	semidirect
104. #436×C₆₇	C₂²	semidirect
105. #435×C₆₇	C₂²	semidirect
106. #435×C₆₇	C₂²	semidirect
107. #433×C₆₇	C₂²	semidirect
108. #428×C₆₇	C₂²	semidirect
109. #428×C₆₇	C₂²	semidirect
110. #428×C₆₇	C₂²	semidirect
111. #427×C₆₇	C₂²	semidirect
112. #418×C₆₇	C₂²	semidirect
113. #418×C₆₇	C₂²	semidirect
114. #418×C₆₇	C₂²	semidirect
115. C₂×#102×C₆₇	C₂²	semidirect
116. #408×C₆₇	C₂²	semidirect
117. #407×C₆₇	C₂²	semidirect
118. #407×C₆₇	C₂²	semidirect
525. #61778	C₆₇	direct (N × H)
536. #3537	C₂×C₆₇	semidirect
537. #3493	C₂×C₆₇	semidirect
538. #3355	C₂×C₆₇	semidirect
539. #3351	C₂×C₆₇	semidirect
540. #3350	C₂×C₆₇	semidirect
541. #3347	C₂×C₆₇	semidirect
542. #3325	C₂×C₆₇	semidirect
543. #3324	C₂×C₆₇	semidirect
544. #3318	C₂×C₆₇	semidirect
545. #3310	C₂×C₆₇	semidirect
546. #3241	C₂×C₆₇	semidirect
547. #3198	C₂×C₆₇	semidirect
548. #3194	C₂×C₆₇	semidirect
549. #3194	C₂×C₆₇	semidirect
550. #3119	C₂×C₆₇	semidirect
551. #3096	C₂×C₆₇	semidirect
552. #3094	C₂×C₆₇	semidirect
553. #3094	C₂×C₆₇	semidirect
554. #2978	C₂×C₆₇	semidirect
555. C₆₇	#61778	direct (N × H)
558. #556	C₂²×C₆₇	semidirect
560. #555	C₂²×C₆₇	semidirect
564. #553	C₂²×C₆₇	semidirect
566. #552	C₂²×C₆₇	semidirect
570. #544	C₂²×C₆₇	semidirect
575. #537	C₂²×C₆₇	semidirect
581. #525	C₂²×C₆₇	semidirect
584. #520	C₂²×C₆₇	semidirect
585. #520	C₂²×C₆₇	semidirect
586. C₂×#117	C₂²×C₆₇	semidirect
587. #501	C₂²×C₆₇	semidirect
588. #499	C₂²×C₆₇	semidirect
589. #490	C₂²×C₆₇	semidirect
590. #486	C₂²×C₆₇	semidirect
591. #485	C₂²×C₆₇	semidirect
592. #483	C₂²×C₆₇	semidirect
593. #483	C₂²×C₆₇	semidirect
594. #482	C₂²×C₆₇	semidirect
595. #482	C₂²×C₆₇	semidirect
596. #482	C₂²×C₆₇	semidirect
597. #482	C₂²×C₆₇	semidirect
598. #482	C₂²×C₆₇	semidirect
599. #482	C₂²×C₆₇	semidirect
600. #482	C₂²×C₆₇	semidirect
601. #482	C₂²×C₆₇	semidirect
602. #482	C₂²×C₆₇	semidirect
603. #481	C₂²×C₆₇	semidirect
604. #481	C₂²×C₆₇	semidirect
605. #481	C₂²×C₆₇	semidirect
606. #480	C₂²×C₆₇	semidirect
607. #480	C₂²×C₆₇	semidirect
608. #480	C₂²×C₆₇	semidirect
609. #480	C₂²×C₆₇	semidirect
610. #480	C₂²×C₆₇	semidirect
611. #479	C₂²×C₆₇	semidirect
612. #478	C₂²×C₆₇	semidirect
613. #478	C₂²×C₆₇	semidirect
614. #478	C₂²×C₆₇	semidirect
615. #476	C₂²×C₆₇	semidirect
616. #474	C₂²×C₆₇	semidirect
617. #469	C₂²×C₆₇	semidirect
618. #469	C₂²×C₆₇	semidirect
619. #469	C₂²×C₆₇	semidirect
620. #468	C₂²×C₆₇	semidirect
621. #468	C₂²×C₆₇	semidirect
622. #468	C₂²×C₆₇	semidirect
623. #466	C₂²×C₆₇	semidirect
624. #465	C₂²×C₆₇	semidirect
625. #460	C₂²×C₆₇	semidirect
626. #459	C₂²×C₆₇	semidirect
627. #450	C₂²×C₆₇	semidirect
628. #450	C₂²×C₆₇	semidirect
629. #450	C₂²×C₆₇	semidirect
630. #449	C₂²×C₆₇	semidirect
631. #449	C₂²×C₆₇	semidirect
632. #447	C₂²×C₆₇	semidirect
633. #447	C₂²×C₆₇	semidirect
634. #447	C₂²×C₆₇	semidirect
635. #442	C₂²×C₆₇	semidirect
636. #440	C₂²×C₆₇	semidirect
637. C₄×SD₁₆	C₂²×C₆₇	semidirect
638. C₄×D₈	C₂²×C₆₇	semidirect
639. #436	C₂²×C₆₇	semidirect
640. #436	C₂²×C₆₇	semidirect
641. #435	C₂²×C₆₇	semidirect
642. #435	C₂²×C₆₇	semidirect
643. #433	C₂²×C₆₇	semidirect
644. #428	C₂²×C₆₇	semidirect
645. #428	C₂²×C₆₇	semidirect
646. #428	C₂²×C₆₇	semidirect
647. #427	C₂²×C₆₇	semidirect
648. #418	C₂²×C₆₇	semidirect
649. #418	C₂²×C₆₇	semidirect
650. #418	C₂²×C₆₇	semidirect
651. C₂×#102	C₂²×C₆₇	semidirect
652. #408	C₂²×C₆₇	semidirect
653. #407	C₂²×C₆₇	semidirect
654. #407	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×#3537	2
C₆₇×#3493	2
C₆₇×#3355	2
C₆₇×#3351	2
C₆₇×#3350	2
C₆₇×#3347	2
C₆₇×#3325	2
C₆₇×#3324	2
C₆₇×#3318	2
C₆₇×#3310	2
C₆₇×#3241	2
C₆₇×#3198	2
C₆₇×#3194	2
C₆₇×#3119	2
C₆₇×#3096	2
C₆₇×#3094	2
C₆₇×#2978	2
#61778	67

Subgroups — C67×#61778 #30741029

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61778 #30741029