Subgroups — C₆₇×#61752 #30741003

Order 17152.

1862 conjugacy classes of subgroups.

The subgroup lattice has 1110 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×#3494	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3355	C₂	1	2	yes	maximal, complemented
4	C₆₇×#3347	C₂	1	2	yes	maximal, complemented
5	C₆₇×#3345	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3339	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3325	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3318	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3318	C₂	1	2	yes	maximal, complemented
10	C₆₇×#3294	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3241	C₂	1	2	yes	maximal, complemented
12	C₆₇×#3199	C₂	1	2	yes	maximal, complemented
13	C₆₇×#3192	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3186	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#3122	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	C₂×#482×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₇×#2976	C₂	1	1	yes	maximal, characteristic, complemented
20	#560×C₆₇	—	2	2	no	—
21	#555×C₆₇	C₂²	1	2	yes	complemented
22	#553×C₆₇	C₂²	1	2	yes	complemented
23	#553×C₆₇	C₂²	1	2	yes	complemented
24	#553×C₆₇	C₂²	1	2	yes	complemented
25	#553×C₆₇	C₂²	1	2	yes	complemented
26	#551×C₆₇	—	2	2	no	—
27	#547×C₆₇	C₂²	1	2	yes	complemented
28	#546×C₆₇	—	2	2	no	—
29	D₄²×C₆₇	—	2	2	no	—
30	D₄²×C₆₇	C₂²	1	2	yes	complemented
31	D₄²×C₆₇	C₂²	1	2	yes	complemented
32	#544×C₆₇	C₂²	1	1	yes	characteristic, complemented
33	#542×C₆₇	—	2	1	no	—
34	#540×C₆₇	—	2	1	no	—
35	#540×C₆₇	C₂²	1	2	yes	—
36	#538×C₆₇	—	2	1	no	—
37	#538×C₆₇	—	2	1	no	—
38	#535×C₆₇	C₂²	1	2	yes	—
39	#535×C₆₇	C₂²	1	1	yes	characteristic, complemented
40	#534×C₆₇	—	2	1	no	—
41	#534×C₆₇	—	2	1	no	—
42	#532×C₆₇	—	2	1	no	—
43	#529×C₆₇	—	2	1	no	—
44	#525×C₆₇	C₂²	1	1	yes	characteristic
45	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
46	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
47	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic, complemented
48	#520×C₆₇	C₂²	1	1	yes	characteristic, complemented
49	#518×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	#482×C₆₇	C₂²	1	2	yes	complemented
56	#482×C₆₇	C₂²	1	2	yes	complemented
57	#482×C₆₇	C₂²	1	2	yes	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	#481×C₆₇	C₂²	1	2	yes	complemented
66	#481×C₆₇	C₂²	1	2	yes	complemented
67	#481×C₆₇	C₂²	1	2	yes	complemented
68	#481×C₆₇	C₂²	1	2	yes	complemented
69	#480×C₆₇	C₂²	1	2	yes	complemented
70	#480×C₆₇	C₂²	1	2	yes	complemented
71	#480×C₆₇	C₂²	1	2	yes	complemented
72	#480×C₆₇	C₂²	1	2	yes	complemented
73	#478×C₆₇	C₂²	1	2	yes	complemented
74	#478×C₆₇	C₂²	1	2	yes	complemented
75	#478×C₆₇	C₂²	1	2	yes	complemented
76	#478×C₆₇	C₂²	1	2	yes	complemented
77	#476×C₆₇	C₂²	1	2	yes	complemented
78	#474×C₆₇	C₂²	1	2	yes	complemented
79	#469×C₆₇	C₂²	1	2	yes	complemented
80	#469×C₆₇	C₂²	1	2	yes	complemented
81	#469×C₆₇	C₂²	1	2	yes	complemented
82	#469×C₆₇	C₂²	1	2	yes	complemented
83	#466×C₆₇	C₂²	1	2	yes	complemented
84	#466×C₆₇	C₂²	1	2	yes	complemented
85	#466×C₆₇	C₂²	1	2	yes	complemented
86	#466×C₆₇	C₂²	1	2	yes	complemented
87	#459×C₆₇	C₂²	1	2	yes	complemented
88	#459×C₆₇	C₂²	1	2	yes	complemented
89	#447×C₆₇	C₂²	1	2	yes	complemented
90	#447×C₆₇	C₂²	1	2	yes	complemented
91	#447×C₆₇	C₂²	1	2	yes	complemented
92	#447×C₆₇	C₂²	1	2	yes	complemented
93	#447×C₆₇	C₂²	1	2	yes	complemented
94	#447×C₆₇	C₂²	1	2	yes	complemented
95	#442×C₆₇	C₂²	1	2	yes	complemented
96	#442×C₆₇	C₂²	1	2	yes	complemented
97	C₄×D₈×C₆₇	C₂²	1	2	yes	complemented
98	C₄×D₈×C₆₇	C₂²	1	2	yes	complemented
99	#436×C₆₇	C₂²	1	2	yes	complemented
100	#435×C₆₇	C₂²	1	2	yes	complemented
101	#435×C₆₇	C₂²	1	2	yes	complemented
102	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
103	#433×C₆₇	C₂²	1	2	yes	complemented
104	#428×C₆₇	C₂²	1	2	yes	complemented
105	#428×C₆₇	C₂²	1	1	yes	characteristic, complemented
106	#428×C₆₇	C₂²	1	1	yes	characteristic, complemented
107	#427×C₆₇	C₂²	1	2	yes	complemented
108	C₂×#107×C₆₇	C₂²	1	1	yes	characteristic, complemented
109	C₂×#106×C₆₇	C₂²	1	1	yes	characteristic, complemented
110	#418×C₆₇	C₂²	1	1	yes	characteristic, complemented
111	#418×C₆₇	C₂²	1	2	yes	complemented
112	#418×C₆₇	C₂²	1	1	yes	characteristic, complemented
113	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic, complemented
114	C₂×#102×C₆₇	C₂²	1	2	yes	complemented
115	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic, complemented
116	#408×C₆₇	C₂²	1	2	yes	complemented
117	#407×C₆₇	C₂²	1	1	yes	characteristic, complemented
118	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
119	C₂×#41×C₆₇	—	2	2	no	—
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	1	no	—
124	C₂²×D₄×C₆₇	—	2	2	no	—
125	C₂²×D₄×C₆₇	—	2	2	no	—
126	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
127	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
128	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
129	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
130	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
131	C₂×D₈×C₆₇	C₂³	1	2	yes	—
132	C₂×D₈×C₆₇	C₂³	1	2	yes	—
133	C₂×D₈×C₆₇	C₂³	1	2	yes	—
134	C₂×D₈×C₆₇	C₂³	1	2	yes	—
135	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
136	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
137	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
138	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
139	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
140	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
141	C₄⋊Q₈×C₆₇	—	2	1	no	—
142	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
143	#127×C₆₇	—	2	1	no	—
144	#127×C₆₇	—	2	2	no	—
145	#127×C₆₇	C₂³	1	2	yes	—
146	#126×C₆₇	—	2	2	no	—
147	#126×C₆₇	—	2	2	no	—
148	#126×C₆₇	—	2	2	no	—
149	#126×C₆₇	—	2	2	no	—
150	#125×C₆₇	—	2	1	no	—
151	#125×C₆₇	C₂³	1	2	yes	—
152	#125×C₆₇	C₂³	1	2	yes	—
153	#124×C₆₇	—	2	1	no	—
154	#124×C₆₇	—	2	2	no	—
155	#124×C₆₇	—	2	2	no	—
156	#124×C₆₇	—	2	2	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	—	2	2	no	—
163	#123×C₆₇	—	2	2	no	—
164	#123×C₆₇	—	2	2	no	—
165	#123×C₆₇	D₄	1	2	yes	—
166	C₂²⋊Q₈×C₆₇	—	2	2	no	—
167	C₂²⋊Q₈×C₆₇	—	2	2	no	—
168	C₂²⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
169	C₂²⋊Q₈×C₆₇	D₄	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	2	no	—
174	#121×C₆₇	—	2	2	no	—
175	#121×C₆₇	—	2	1	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	1	no	—
181	#121×C₆₇	—	2	2	no	—
182	#121×C₆₇	—	2	2	no	—
183	#121×C₆₇	—	2	2	no	—
184	#121×C₆₇	—	2	2	no	—
185	#121×C₆₇	D₄	1	1	yes	characteristic
186	#121×C₆₇	D₄	1	1	yes	characteristic
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	2	yes	—
194	#121×C₆₇	C₂³	1	2	yes	—
195	#121×C₆₇	C₂³	1	2	yes	—
196	#121×C₆₇	C₂³	1	2	yes	—
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	—	2	2	no	—
203	#120×C₆₇	—	2	2	no	—
204	#120×C₆₇	D₄	1	2	yes	—
205	C₄×Q₈×C₆₇	—	2	1	no	—
206	C₄×D₄×C₆₇	—	2	1	no	—
207	C₄×D₄×C₆₇	—	2	2	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	C₄×D₄×C₆₇	C₂³	1	2	yes	—
220	#117×C₆₇	—	2	1	no	—
221	#117×C₆₇	—	2	1	no	—
222	#117×C₆₇	—	2	2	no	—
223	#117×C₆₇	C₂³	1	1	yes	characteristic
224	#117×C₆₇	C₂³	1	1	yes	characteristic
225	#117×C₆₇	C₂³	1	1	yes	characteristic
226	#117×C₆₇	C₂³	1	1	yes	characteristic
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	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄×C₆₇	—	2	1	no	—
240	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
241	C₂×C₄²×C₆₇	—	2	1	no	—
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	#107×C₆₇	C₂³	1	2	yes	—
247	#107×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	#106×C₆₇	C₂³	1	2	yes	—
253	#106×C₆₇	C₂³	1	2	yes	—
254	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
255	C₄⋊C₈×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	#102×C₆₇	C₂³	1	2	yes	—
271	#102×C₆₇	C₂³	1	2	yes	—
272	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
273	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
274	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
275	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
276	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
277	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
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	1	no	—
283	C₂⁴×C₆₇	—	2	2	no	—
284	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
285	#41×C₆₇	—	4	1	no	—
286	#41×C₆₇	—	4	1	no	—
287	#41×C₆₇	—	8	4	no	—
288	C₂×Q₈×C₆₇	—	2	2	no	—
289	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
290	C₂×D₄×C₆₇	—	2	2	no	—
291	C₂×D₄×C₆₇	—	2	2	no	—
292	C₂×D₄×C₆₇	—	2	2	no	—
293	C₂×D₄×C₆₇	—	2	2	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	2	no	—
300	C₂×D₄×C₆₇	—	2	1	no	—
301	C₂×D₄×C₆₇	—	2	1	no	—
302	C₂×D₄×C₆₇	—	2	1	no	—
303	C₂×D₄×C₆₇	—	2	2	no	—
304	C₂×D₄×C₆₇	—	2	2	no	—
305	C₂×D₄×C₆₇	—	2	2	no	—
306	C₂×D₄×C₆₇	—	4	1	no	—
307	C₂×D₄×C₆₇	—	4	1	no	—
308	C₂×D₄×C₆₇	—	4	1	no	—
309	C₂×D₄×C₆₇	—	4	1	no	—
310	C₂×D₄×C₆₇	—	4	2	no	—
311	C₂×D₄×C₆₇	—	4	1	no	—
312	C₂×D₄×C₆₇	—	4	1	no	—
313	C₂×D₄×C₆₇	—	4	2	no	—
314	C₂×D₄×C₆₇	—	8	4	no	—
315	C₂×D₄×C₆₇	—	8	2	no	—
316	C₂×D₄×C₆₇	—	8	2	no	—
317	C₂×D₄×C₆₇	—	8	4	no	—
318	C₂×D₄×C₆₇	—	8	2	no	—
319	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
320	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
321	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
322	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
323	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
324	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
325	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
326	C₂²×C₄×C₆₇	—	2	1	no	—
327	C₂²×C₄×C₆₇	—	2	1	no	—
328	C₂²×C₄×C₆₇	—	2	1	no	—
329	C₂²×C₄×C₆₇	—	2	1	no	—
330	C₂²×C₄×C₆₇	—	2	1	no	—
331	C₂²×C₄×C₆₇	—	2	2	no	—
332	C₂²×C₄×C₆₇	—	2	2	no	—
333	C₂²×C₄×C₆₇	—	2	2	no	—
334	C₂²×C₄×C₆₇	—	2	2	no	—
335	C₂²×C₄×C₆₇	—	2	2	no	—
336	C₂²×C₄×C₆₇	—	4	1	no	—
337	C₂²×C₄×C₆₇	—	4	1	no	—
338	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
339	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
340	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
341	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
342	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
343	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
344	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
345	D₈×C₆₇	—	4	2	no	—
346	D₈×C₆₇	—	4	2	no	—
347	D₈×C₆₇	—	4	2	no	—
348	D₈×C₆₇	—	4	2	no	—
349	M₁₆×C₆₇	—	4	1	no	—
350	M₁₆×C₆₇	—	4	2	no	—
351	M₁₆×C₆₇	—	4	1	no	—
352	C₂×C₈×C₆₇	—	4	1	no	—
353	C₂×C₈×C₆₇	—	4	2	no	—
354	C₂×C₈×C₆₇	—	4	1	no	—
355	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
356	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
357	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
358	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
359	C₄⋊C₄×C₆₇	—	2	1	no	—
360	C₄⋊C₄×C₆₇	—	2	1	no	—
361	C₄⋊C₄×C₆₇	—	2	1	no	—
362	C₄⋊C₄×C₆₇	—	2	2	no	—
363	C₄⋊C₄×C₆₇	—	2	1	no	—
364	C₄⋊C₄×C₆₇	—	2	1	no	—
365	C₄⋊C₄×C₆₇	—	2	2	no	—
366	C₄⋊C₄×C₆₇	—	2	2	no	—
367	C₄⋊C₄×C₆₇	—	2	2	no	—
368	C₄⋊C₄×C₆₇	—	2	2	no	—
369	C₄⋊C₄×C₆₇	—	2	2	no	—
370	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
371	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
372	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
373	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
374	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
375	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
376	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
377	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
378	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
379	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
380	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
381	C₂²⋊C₄×C₆₇	—	2	1	no	—
382	C₂²⋊C₄×C₆₇	—	2	1	no	—
383	C₂²⋊C₄×C₆₇	—	2	1	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	2	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	—	2	2	no	—
393	C₂²⋊C₄×C₆₇	—	2	2	no	—
394	C₂²⋊C₄×C₆₇	—	2	2	no	—
395	C₂²⋊C₄×C₆₇	—	2	2	no	—
396	C₂²⋊C₄×C₆₇	—	2	2	no	—
397	C₂²⋊C₄×C₆₇	—	2	2	no	—
398	C₂²⋊C₄×C₆₇	—	2	2	no	—
399	C₂²⋊C₄×C₆₇	—	2	2	no	—
400	C₂²⋊C₄×C₆₇	—	2	2	no	—
401	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
402	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
403	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
404	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
405	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
406	C₄²×C₆₇	—	2	1	no	—
407	C₄²×C₆₇	—	2	1	no	—
408	C₄²×C₆₇	—	2	1	no	—
409	C₄²×C₆₇	—	2	1	no	—
410	C₄²×C₆₇	—	2	2	no	—
411	C₄²×C₆₇	—	2	2	no	—
412	C₄²×C₆₇	C₂⁴	1	2	yes	—
413	C₂³×C₆₇	—	2	2	no	—
414	C₂³×C₆₇	—	2	2	no	—
415	C₂³×C₆₇	—	2	2	no	—
416	C₂³×C₆₇	—	2	2	no	—
417	C₂³×C₆₇	—	4	1	no	—
418	C₂³×C₆₇	—	4	1	no	—
419	C₂³×C₆₇	—	4	2	no	—
420	C₂³×C₆₇	—	4	2	no	—
421	C₂³×C₆₇	—	4	2	no	—
422	C₂³×C₆₇	—	8	1	no	—
423	C₂³×C₆₇	—	8	1	no	—
424	C₂³×C₆₇	—	8	2	no	—
425	C₂³×C₆₇	—	8	1	no	—
426	C₂³×C₆₇	—	8	2	no	—
427	C₂³×C₆₇	—	8	2	no	—
428	C₂³×C₆₇	—	8	1	no	—
429	C₂³×C₆₇	—	8	1	no	—
430	C₂³×C₆₇	—	8	1	no	—
431	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
432	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
433	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
434	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
435	Q₈×C₆₇	—	4	1	no	—
436	Q₈×C₆₇	—	8	2	no	—
437	D₄×C₆₇	—	2	4	no	—
438	D₄×C₆₇	—	2	2	no	—
439	D₄×C₆₇	—	2	2	no	—
440	D₄×C₆₇	—	2	2	no	—
441	D₄×C₆₇	—	2	2	no	—
442	D₄×C₆₇	—	2	2	no	—
443	D₄×C₆₇	—	2	2	no	—
444	D₄×C₆₇	—	4	2	no	—
445	D₄×C₆₇	—	4	1	no	—
446	D₄×C₆₇	—	4	2	no	—
447	D₄×C₆₇	—	4	2	no	—
448	D₄×C₆₇	—	4	4	no	—
449	D₄×C₆₇	—	4	4	no	—
450	D₄×C₆₇	—	4	4	no	—
451	D₄×C₆₇	—	8	1	no	—
452	D₄×C₆₇	—	8	1	no	—
453	D₄×C₆₇	—	8	2	no	—
454	D₄×C₆₇	—	8	2	no	—
455	D₄×C₆₇	—	8	2	no	—
456	D₄×C₆₇	—	8	2	no	—
457	D₄×C₆₇	—	8	2	no	—
458	D₄×C₆₇	—	8	2	no	—
459	D₄×C₆₇	—	8	2	no	—
460	D₄×C₆₇	—	8	2	no	—
461	D₄×C₆₇	—	8	2	no	—
462	D₄×C₆₇	—	8	2	no	—
463	C₂×C₄×C₆₇	—	2	1	no	—
464	C₂×C₄×C₆₇	—	2	1	no	—
465	C₂×C₄×C₆₇	—	2	2	no	—
466	C₂×C₄×C₆₇	—	2	1	no	—
467	C₂×C₄×C₆₇	—	2	1	no	—
468	C₂×C₄×C₆₇	—	2	2	no	—
469	C₂×C₄×C₆₇	—	2	1	no	—
470	C₂×C₄×C₆₇	—	2	1	no	—
471	C₂×C₄×C₆₇	—	2	1	no	—
472	C₂×C₄×C₆₇	—	2	1	no	—
473	C₂×C₄×C₆₇	—	2	1	no	—
474	C₂×C₄×C₆₇	—	2	1	no	—
475	C₂×C₄×C₆₇	—	2	2	no	—
476	C₂×C₄×C₆₇	—	2	2	no	—
477	C₂×C₄×C₆₇	—	2	2	no	—
478	C₂×C₄×C₆₇	—	4	1	no	—
479	C₂×C₄×C₆₇	—	4	1	no	—
480	C₂×C₄×C₆₇	—	4	1	no	—
481	C₂×C₄×C₆₇	—	4	2	no	—
482	C₂×C₄×C₆₇	—	8	2	no	—
483	C₂×C₄×C₆₇	—	8	2	no	—
484	C₂×C₄×C₆₇	—	8	2	no	—
485	C₂×C₄×C₆₇	—	8	2	no	—
486	C₂×C₄×C₆₇	—	8	1	no	—
487	C₂×C₄×C₆₇	—	8	1	no	—
488	C₂×C₄×C₆₇	—	8	1	no	—
489	C₂×C₄×C₆₇	—	8	1	no	—
490	C₂×C₄×C₆₇	—	8	2	no	—
491	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
492	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
493	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
494	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
495	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
496	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
497	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
498	C₈×C₆₇	—	2	2	no	—
499	C₈×C₆₇	—	2	2	no	—
500	C₈×C₆₇	—	2	2	no	—
501	C₈×C₆₇	—	2	2	no	—
502	C₂²×C₆₇	—	2	1	no	—
503	C₂²×C₆₇	—	2	1	no	—
504	C₂²×C₆₇	—	2	1	no	—
505	C₂²×C₆₇	—	2	2	no	—
506	C₂²×C₆₇	—	2	1	no	—
507	C₂²×C₆₇	—	2	1	no	—
508	C₂²×C₆₇	—	2	1	no	—
509	C₂²×C₆₇	—	2	2	no	—
510	C₂²×C₆₇	—	2	2	no	—
511	C₂²×C₆₇	—	2	1	no	—
512	C₂²×C₆₇	—	2	1	no	—
513	C₂²×C₆₇	—	4	2	no	—
514	C₂²×C₆₇	—	4	2	no	—
515	C₂²×C₆₇	—	4	2	no	—
516	C₂²×C₆₇	—	4	2	no	—
517	C₂²×C₆₇	—	4	2	no	—
518	C₂²×C₆₇	—	4	2	no	—
519	C₂²×C₆₇	—	4	2	no	—
520	C₂²×C₆₇	—	4	2	no	—
521	C₂²×C₆₇	—	4	2	no	—
522	C₂²×C₆₇	—	8	2	no	—
523	C₂²×C₆₇	—	16	2	no	—
524	C₂²×C₆₇	—	16	2	no	—
525	C₂²×C₆₇	—	16	2	no	—
526	C₂²×C₆₇	—	16	4	no	—
527	C₂²×C₆₇	#576	1	2	yes	—
528	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
529	C₄×C₆₇	—	2	2	no	—
530	C₄×C₆₇	—	2	1	no	—
531	C₄×C₆₇	—	2	1	no	—
532	C₄×C₆₇	—	2	1	no	—
533	C₄×C₆₇	—	2	2	no	—
534	C₄×C₆₇	—	2	2	no	—
535	C₄×C₆₇	—	4	1	no	—
536	C₄×C₆₇	—	4	2	no	—
537	C₄×C₆₇	—	4	1	no	—
538	C₄×C₆₇	—	4	1	no	—
539	C₄×C₆₇	—	4	1	no	—
540	C₄×C₆₇	—	4	2	no	—
541	C₄×C₆₇	—	4	2	no	—
542	C₄×C₆₇	#585	1	1	yes	characteristic
543	C₄×C₆₇	#585	1	1	yes	characteristic
544	#61752	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
545	C₂×C₆₇	—	2	2	no	—
546	C₂×C₆₇	—	4	1	no	—
547	C₂×C₆₇	—	4	1	no	—
548	C₂×C₆₇	—	4	2	no	—
549	C₂×C₆₇	—	8	2	no	—
550	C₂×C₆₇	—	8	2	no	—
551	C₂×C₆₇	—	8	2	no	—
552	C₂×C₆₇	#3485	1	1	yes	characteristic
553	C₂×C₆₇	C₂×#576	1	1	yes	characteristic
554	C₂×C₆₇	#3585	1	1	yes	characteristic
555	#3537	C₂×C₆₇	1	1	yes	characteristic, complemented
556	#3494	C₂×C₆₇	1	1	yes	characteristic, complemented
557	#3355	C₂×C₆₇	1	2	yes	complemented
558	#3347	C₂×C₆₇	1	2	yes	complemented
559	#3345	C₂×C₆₇	1	2	yes	complemented
560	#3339	C₂×C₆₇	1	2	yes	complemented
561	#3325	C₂×C₆₇	1	2	yes	complemented
562	#3318	C₂×C₆₇	1	2	yes	complemented
563	#3318	C₂×C₆₇	1	2	yes	complemented
564	#3294	C₂×C₆₇	1	2	yes	complemented
565	#3241	C₂×C₆₇	1	2	yes	complemented
566	#3199	C₂×C₆₇	1	2	yes	complemented
567	#3192	C₂×C₆₇	1	1	yes	characteristic, complemented
568	#3186	C₂×C₆₇	1	1	yes	characteristic, complemented
569	#3122	C₂×C₆₇	1	2	yes	complemented
570	#3096	C₂×C₆₇	1	2	yes	complemented
571	#3094	C₂×C₆₇	1	1	yes	characteristic, complemented
572	C₂×#482	C₂×C₆₇	1	1	yes	characteristic, complemented
573	#2976	C₂×C₆₇	1	1	yes	characteristic, complemented
574	C₆₇	#61752	1	1	yes	characteristic, direct product factor, Sylow
575	#560	—	2	2	no	—
576	#555	C₂²×C₆₇	1	2	yes	complemented
577	#553	C₂²×C₆₇	1	2	yes	complemented
578	#553	C₂²×C₆₇	1	2	yes	complemented
579	#553	C₂²×C₆₇	1	2	yes	complemented
580	#553	C₂²×C₆₇	1	2	yes	complemented
581	#551	—	2	2	no	—
582	#547	C₂²×C₆₇	1	2	yes	complemented
583	#546	—	2	2	no	—
584	D₄²	—	2	2	no	—
585	D₄²	C₂²×C₆₇	1	2	yes	complemented
586	D₄²	C₂²×C₆₇	1	2	yes	complemented
587	#544	C₂²×C₆₇	1	1	yes	characteristic, complemented
588	#542	—	2	1	no	—
589	#540	—	2	1	no	—
590	#540	C₂²×C₆₇	1	2	yes	—
591	#538	—	2	1	no	—
592	#538	—	2	1	no	—
593	#535	C₂²×C₆₇	1	2	yes	—
594	#535	C₂²×C₆₇	1	1	yes	characteristic, complemented
595	#534	—	2	1	no	—
596	#534	—	2	1	no	—
597	#532	—	2	1	no	—
598	#529	—	2	1	no	—
599	#525	C₂²×C₆₇	1	1	yes	characteristic
600	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
601	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
602	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic, complemented
603	#520	C₂²×C₆₇	1	1	yes	characteristic, complemented
604	#518	C₂²×C₆₇	1	1	yes	characteristic, complemented
605	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic, complemented
606	#501	C₂²×C₆₇	1	2	yes	complemented
607	#499	C₂²×C₆₇	1	2	yes	complemented
608	#490	C₂²×C₆₇	1	2	yes	complemented
609	#486	C₂²×C₆₇	1	2	yes	complemented
610	#482	C₂²×C₆₇	1	2	yes	complemented
611	#482	C₂²×C₆₇	1	2	yes	complemented
612	#482	C₂²×C₆₇	1	2	yes	complemented
613	#482	C₂²×C₆₇	1	2	yes	complemented
614	#482	C₂²×C₆₇	1	2	yes	complemented
615	#482	C₂²×C₆₇	1	2	yes	complemented
616	#482	C₂²×C₆₇	1	2	yes	complemented
617	#482	C₂²×C₆₇	1	2	yes	complemented
618	#482	C₂²×C₆₇	1	2	yes	complemented
619	#482	C₂²×C₆₇	1	2	yes	complemented
620	#481	C₂²×C₆₇	1	2	yes	complemented
621	#481	C₂²×C₆₇	1	2	yes	complemented
622	#481	C₂²×C₆₇	1	2	yes	complemented
623	#481	C₂²×C₆₇	1	2	yes	complemented
624	#480	C₂²×C₆₇	1	2	yes	complemented
625	#480	C₂²×C₆₇	1	2	yes	complemented
626	#480	C₂²×C₆₇	1	2	yes	complemented
627	#480	C₂²×C₆₇	1	2	yes	complemented
628	#478	C₂²×C₆₇	1	2	yes	complemented
629	#478	C₂²×C₆₇	1	2	yes	complemented
630	#478	C₂²×C₆₇	1	2	yes	complemented
631	#478	C₂²×C₆₇	1	2	yes	complemented
632	#476	C₂²×C₆₇	1	2	yes	complemented
633	#474	C₂²×C₆₇	1	2	yes	complemented
634	#469	C₂²×C₆₇	1	2	yes	complemented
635	#469	C₂²×C₆₇	1	2	yes	complemented
636	#469	C₂²×C₆₇	1	2	yes	complemented
637	#469	C₂²×C₆₇	1	2	yes	complemented
638	#466	C₂²×C₆₇	1	2	yes	complemented
639	#466	C₂²×C₆₇	1	2	yes	complemented
640	#466	C₂²×C₆₇	1	2	yes	complemented
641	#466	C₂²×C₆₇	1	2	yes	complemented
642	#459	C₂²×C₆₇	1	2	yes	complemented
643	#459	C₂²×C₆₇	1	2	yes	complemented
644	#447	C₂²×C₆₇	1	2	yes	complemented
645	#447	C₂²×C₆₇	1	2	yes	complemented
646	#447	C₂²×C₆₇	1	2	yes	complemented
647	#447	C₂²×C₆₇	1	2	yes	complemented
648	#447	C₂²×C₆₇	1	2	yes	complemented
649	#447	C₂²×C₆₇	1	2	yes	complemented
650	#442	C₂²×C₆₇	1	2	yes	complemented
651	#442	C₂²×C₆₇	1	2	yes	complemented
652	C₄×D₈	C₂²×C₆₇	1	2	yes	complemented
653	C₄×D₈	C₂²×C₆₇	1	2	yes	complemented
654	#436	C₂²×C₆₇	1	2	yes	complemented
655	#435	C₂²×C₆₇	1	2	yes	complemented
656	#435	C₂²×C₆₇	1	2	yes	complemented
657	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
658	#433	C₂²×C₆₇	1	2	yes	complemented
659	#428	C₂²×C₆₇	1	2	yes	complemented
660	#428	C₂²×C₆₇	1	1	yes	characteristic, complemented
661	#428	C₂²×C₆₇	1	1	yes	characteristic, complemented
662	#427	C₂²×C₆₇	1	2	yes	complemented
663	C₂×#107	C₂²×C₆₇	1	1	yes	characteristic, complemented
664	C₂×#106	C₂²×C₆₇	1	1	yes	characteristic, complemented
665	#418	C₂²×C₆₇	1	1	yes	characteristic, complemented
666	#418	C₂²×C₆₇	1	1	yes	characteristic, complemented
667	#418	C₂²×C₆₇	1	2	yes	complemented
668	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic, complemented
669	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic, complemented
670	C₂×#102	C₂²×C₆₇	1	2	yes	complemented
671	#408	C₂²×C₆₇	1	2	yes	complemented
672	#407	C₂²×C₆₇	1	1	yes	characteristic, complemented
673	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
674	C₂×#41	—	2	2	no	—
675	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
676	C₂²×D₄	—	2	1	no	—
677	C₂²×D₄	—	2	1	no	—
678	C₂²×D₄	—	2	1	no	—
679	C₂²×D₄	—	2	2	no	—
680	C₂²×D₄	—	2	2	no	—
681	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
682	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
683	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
684	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
685	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
686	C₂×D₈	C₂³×C₆₇	1	2	yes	—
687	C₂×D₈	C₂³×C₆₇	1	2	yes	—
688	C₂×D₈	C₂³×C₆₇	1	2	yes	—
689	C₂×D₈	C₂³×C₆₇	1	2	yes	—
690	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
691	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
692	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
693	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
694	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
695	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
696	C₄⋊Q₈	—	2	1	no	—
697	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
698	#127	—	2	1	no	—
699	#127	—	2	2	no	—
700	#127	C₂³×C₆₇	1	2	yes	—
701	#126	—	2	2	no	—
702	#126	—	2	2	no	—
703	#126	—	2	2	no	—
704	#126	—	2	2	no	—
705	#125	—	2	1	no	—
706	#125	C₂³×C₆₇	1	2	yes	—
707	#125	C₂³×C₆₇	1	2	yes	—
708	#124	—	2	1	no	—
709	#124	—	2	2	no	—
710	#124	—	2	2	no	—
711	#124	—	2	2	no	—
712	#123	—	2	2	no	—
713	#123	—	2	2	no	—
714	#123	—	2	2	no	—
715	#123	—	2	2	no	—
716	#123	—	2	2	no	—
717	#123	—	2	2	no	—
718	#123	—	2	2	no	—
719	#123	—	2	2	no	—
720	#123	D₄×C₆₇	1	2	yes	—
721	C₂²⋊Q₈	—	2	2	no	—
722	C₂²⋊Q₈	—	2	2	no	—
723	C₂²⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
724	C₂²⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
725	#121	—	2	2	no	—
726	#121	—	2	2	no	—
727	#121	—	2	2	no	—
728	#121	—	2	2	no	—
729	#121	—	2	2	no	—
730	#121	—	2	1	no	—
731	#121	—	2	1	no	—
732	#121	—	2	1	no	—
733	#121	—	2	1	no	—
734	#121	—	2	1	no	—
735	#121	—	2	1	no	—
736	#121	—	2	2	no	—
737	#121	—	2	2	no	—
738	#121	—	2	2	no	—
739	#121	—	2	2	no	—
740	#121	D₄×C₆₇	1	1	yes	characteristic
741	#121	D₄×C₆₇	1	1	yes	characteristic
742	#121	C₂³×C₆₇	1	2	yes	—
743	#121	C₂³×C₆₇	1	2	yes	—
744	#121	C₂³×C₆₇	1	2	yes	—
745	#121	C₂³×C₆₇	1	2	yes	—
746	#121	C₂³×C₆₇	1	2	yes	—
747	#121	C₂³×C₆₇	1	2	yes	—
748	#121	C₂³×C₆₇	1	2	yes	—
749	#121	C₂³×C₆₇	1	2	yes	—
750	#121	C₂³×C₆₇	1	2	yes	—
751	#121	C₂³×C₆₇	1	2	yes	—
752	#120	—	2	2	no	—
753	#120	—	2	2	no	—
754	#120	—	2	2	no	—
755	#120	—	2	2	no	—
756	#120	—	2	2	no	—
757	#120	—	2	2	no	—
758	#120	—	2	2	no	—
759	#120	D₄×C₆₇	1	2	yes	—
760	C₄×Q₈	—	2	1	no	—
761	C₄×D₄	—	2	1	no	—
762	C₄×D₄	—	2	2	no	—
763	C₄×D₄	—	2	1	no	—
764	C₄×D₄	—	2	1	no	—
765	C₄×D₄	—	2	2	no	—
766	C₄×D₄	—	2	2	no	—
767	C₄×D₄	—	2	2	no	—
768	C₄×D₄	—	2	2	no	—
769	C₄×D₄	C₂³×C₆₇	1	2	yes	—
770	C₄×D₄	C₂³×C₆₇	1	2	yes	—
771	C₄×D₄	C₂³×C₆₇	1	2	yes	—
772	C₄×D₄	C₂³×C₆₇	1	2	yes	—
773	C₄×D₄	C₂³×C₆₇	1	2	yes	—
774	C₄×D₄	C₂³×C₆₇	1	2	yes	—
775	#117	—	2	1	no	—
776	#117	—	2	1	no	—
777	#117	—	2	2	no	—
778	#117	C₂³×C₆₇	1	1	yes	characteristic
779	#117	C₂³×C₆₇	1	1	yes	characteristic
780	#117	C₂³×C₆₇	1	1	yes	characteristic
781	#117	C₂³×C₆₇	1	1	yes	characteristic
782	#117	C₂³×C₆₇	1	2	yes	—
783	#117	C₂³×C₆₇	1	2	yes	—
784	#117	C₂³×C₆₇	1	1	yes	characteristic
785	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
786	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
787	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
788	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
789	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
790	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
791	C₂×C₂²⋊C₄	—	2	1	no	—
792	C₂×C₂²⋊C₄	—	2	1	no	—
793	C₂×C₂²⋊C₄	—	2	1	no	—
794	C₂×C₂²⋊C₄	—	2	1	no	—
795	C₂×C₂²⋊C₄	—	2	2	no	—
796	C₂×C₄²	—	2	1	no	—
797	#107	C₂³×C₆₇	1	2	yes	—
798	#107	C₂³×C₆₇	1	2	yes	—
799	#107	C₂³×C₆₇	1	2	yes	—
800	#107	C₂³×C₆₇	1	2	yes	—
801	#107	C₂³×C₆₇	1	2	yes	—
802	#107	C₂³×C₆₇	1	2	yes	—
803	#106	C₂³×C₆₇	1	2	yes	—
804	#106	C₂³×C₆₇	1	2	yes	—
805	#106	C₂³×C₆₇	1	2	yes	—
806	#106	C₂³×C₆₇	1	2	yes	—
807	#106	C₂³×C₆₇	1	2	yes	—
808	#106	C₂³×C₆₇	1	2	yes	—
809	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
810	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
811	#102	C₂³×C₆₇	1	2	yes	—
812	#102	C₂³×C₆₇	1	2	yes	—
813	#102	C₂³×C₆₇	1	2	yes	—
814	#102	C₂³×C₆₇	1	2	yes	—
815	#102	C₂³×C₆₇	1	2	yes	—
816	#102	C₂³×C₆₇	1	2	yes	—
817	#102	C₂³×C₆₇	1	2	yes	—
818	#102	C₂³×C₆₇	1	2	yes	—
819	#102	C₂³×C₆₇	1	2	yes	—
820	#102	C₂³×C₆₇	1	2	yes	—
821	#102	C₂³×C₆₇	1	2	yes	—
822	#102	C₂³×C₆₇	1	2	yes	—
823	#102	C₂³×C₆₇	1	2	yes	—
824	#102	C₂³×C₆₇	1	2	yes	—
825	#102	C₂³×C₆₇	1	2	yes	—
826	#102	C₂³×C₆₇	1	2	yes	—
827	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
828	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
829	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
830	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
831	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
832	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
833	#97	C₂³×C₆₇	1	2	yes	—
834	C₄×C₈	C₂³×C₆₇	1	2	yes	—
835	C₂⁴	—	2	1	no	—
836	C₂⁴	—	2	1	no	—
837	C₂⁴	—	2	1	no	—
838	C₂⁴	—	2	2	no	—
839	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
840	#41	—	4	1	no	—
841	#41	—	4	1	no	—
842	#41	—	8	4	no	—
843	C₂×Q₈	—	2	2	no	—
844	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
845	C₂×D₄	—	2	2	no	—
846	C₂×D₄	—	2	2	no	—
847	C₂×D₄	—	2	2	no	—
848	C₂×D₄	—	2	2	no	—
849	C₂×D₄	—	2	2	no	—
850	C₂×D₄	—	2	2	no	—
851	C₂×D₄	—	2	2	no	—
852	C₂×D₄	—	2	2	no	—
853	C₂×D₄	—	2	2	no	—
854	C₂×D₄	—	2	2	no	—
855	C₂×D₄	—	2	1	no	—
856	C₂×D₄	—	2	1	no	—
857	C₂×D₄	—	2	1	no	—
858	C₂×D₄	—	2	2	no	—
859	C₂×D₄	—	2	2	no	—
860	C₂×D₄	—	2	2	no	—
861	C₂×D₄	—	4	1	no	—
862	C₂×D₄	—	4	1	no	—
863	C₂×D₄	—	4	1	no	—
864	C₂×D₄	—	4	1	no	—
865	C₂×D₄	—	4	2	no	—
866	C₂×D₄	—	4	1	no	—
867	C₂×D₄	—	4	1	no	—
868	C₂×D₄	—	4	2	no	—
869	C₂×D₄	—	8	4	no	—
870	C₂×D₄	—	8	2	no	—
871	C₂×D₄	—	8	2	no	—
872	C₂×D₄	—	8	4	no	—
873	C₂×D₄	—	8	2	no	—
874	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
875	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
876	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
877	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
878	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
879	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
880	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
881	C₂²×C₄	—	2	1	no	—
882	C₂²×C₄	—	2	1	no	—
883	C₂²×C₄	—	2	1	no	—
884	C₂²×C₄	—	2	1	no	—
885	C₂²×C₄	—	2	1	no	—
886	C₂²×C₄	—	2	2	no	—
887	C₂²×C₄	—	2	2	no	—
888	C₂²×C₄	—	2	2	no	—
889	C₂²×C₄	—	2	2	no	—
890	C₂²×C₄	—	2	2	no	—
891	C₂²×C₄	—	4	1	no	—
892	C₂²×C₄	—	4	1	no	—
893	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
894	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
895	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
896	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
897	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
898	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
899	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
900	D₈	—	4	2	no	—
901	D₈	—	4	2	no	—
902	D₈	—	4	2	no	—
903	D₈	—	4	2	no	—
904	M₁₆	—	4	1	no	—
905	M₁₆	—	4	2	no	—
906	M₁₆	—	4	1	no	—
907	C₂×C₈	—	4	1	no	—
908	C₂×C₈	—	4	2	no	—
909	C₂×C₈	—	4	1	no	—
910	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
911	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
912	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
913	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
914	C₄⋊C₄	—	2	1	no	—
915	C₄⋊C₄	—	2	1	no	—
916	C₄⋊C₄	—	2	1	no	—
917	C₄⋊C₄	—	2	2	no	—
918	C₄⋊C₄	—	2	1	no	—
919	C₄⋊C₄	—	2	1	no	—
920	C₄⋊C₄	—	2	2	no	—
921	C₄⋊C₄	—	2	2	no	—
922	C₄⋊C₄	—	2	2	no	—
923	C₄⋊C₄	—	2	2	no	—
924	C₄⋊C₄	—	2	2	no	—
925	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
926	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
927	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
928	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
929	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
930	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
931	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
932	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
933	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
934	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
935	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
936	C₂²⋊C₄	—	2	1	no	—
937	C₂²⋊C₄	—	2	1	no	—
938	C₂²⋊C₄	—	2	1	no	—
939	C₂²⋊C₄	—	2	1	no	—
940	C₂²⋊C₄	—	2	2	no	—
941	C₂²⋊C₄	—	2	2	no	—
942	C₂²⋊C₄	—	2	2	no	—
943	C₂²⋊C₄	—	2	2	no	—
944	C₂²⋊C₄	—	2	2	no	—
945	C₂²⋊C₄	—	2	2	no	—
946	C₂²⋊C₄	—	2	2	no	—
947	C₂²⋊C₄	—	2	2	no	—
948	C₂²⋊C₄	—	2	2	no	—
949	C₂²⋊C₄	—	2	2	no	—
950	C₂²⋊C₄	—	2	2	no	—
951	C₂²⋊C₄	—	2	2	no	—
952	C₂²⋊C₄	—	2	2	no	—
953	C₂²⋊C₄	—	2	2	no	—
954	C₂²⋊C₄	—	2	2	no	—
955	C₂²⋊C₄	—	2	2	no	—
956	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
957	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
958	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
959	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
960	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
961	C₄²	—	2	1	no	—
962	C₄²	—	2	1	no	—
963	C₄²	—	2	1	no	—
964	C₄²	—	2	1	no	—
965	C₄²	—	2	2	no	—
966	C₄²	—	2	2	no	—
967	C₄²	C₂⁴×C₆₇	1	2	yes	—
968	C₂³	—	2	2	no	—
969	C₂³	—	2	2	no	—
970	C₂³	—	2	2	no	—
971	C₂³	—	2	2	no	—
972	C₂³	—	4	1	no	—
973	C₂³	—	4	1	no	—
974	C₂³	—	4	2	no	—
975	C₂³	—	4	2	no	—
976	C₂³	—	4	2	no	—
977	C₂³	—	8	1	no	—
978	C₂³	—	8	1	no	—
979	C₂³	—	8	2	no	—
980	C₂³	—	8	1	no	—
981	C₂³	—	8	2	no	—
982	C₂³	—	8	1	no	—
983	C₂³	—	8	1	no	—
984	C₂³	—	8	2	no	—
985	C₂³	—	8	1	no	—
986	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
987	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
988	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
989	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
990	Q₈	—	4	1	no	—
991	Q₈	—	8	2	no	—
992	D₄	—	2	4	no	—
993	D₄	—	2	2	no	—
994	D₄	—	2	2	no	—
995	D₄	—	2	2	no	—
996	D₄	—	2	2	no	—
997	D₄	—	2	2	no	—
998	D₄	—	2	2	no	—
999	D₄	—	4	2	no	—
1000	D₄	—	4	1	no	—
1001	D₄	—	4	2	no	—
1002	D₄	—	4	2	no	—
1003	D₄	—	4	4	no	—
1004	D₄	—	4	4	no	—
1005	D₄	—	4	4	no	—
1006	D₄	—	8	1	no	—
1007	D₄	—	8	1	no	—
1008	D₄	—	8	2	no	—
1009	D₄	—	8	2	no	—
1010	D₄	—	8	2	no	—
1011	D₄	—	8	2	no	—
1012	D₄	—	8	2	no	—
1013	D₄	—	8	2	no	—
1014	D₄	—	8	2	no	—
1015	D₄	—	8	2	no	—
1016	D₄	—	8	2	no	—
1017	D₄	—	8	2	no	—
1018	C₂×C₄	—	2	1	no	—
1019	C₂×C₄	—	2	1	no	—
1020	C₂×C₄	—	2	2	no	—
1021	C₂×C₄	—	2	1	no	—
1022	C₂×C₄	—	2	1	no	—
1023	C₂×C₄	—	2	2	no	—
1024	C₂×C₄	—	2	1	no	—
1025	C₂×C₄	—	2	1	no	—
1026	C₂×C₄	—	2	1	no	—
1027	C₂×C₄	—	2	1	no	—
1028	C₂×C₄	—	2	1	no	—
1029	C₂×C₄	—	2	1	no	—
1030	C₂×C₄	—	2	2	no	—
1031	C₂×C₄	—	2	2	no	—
1032	C₂×C₄	—	2	2	no	—
1033	C₂×C₄	—	4	1	no	—
1034	C₂×C₄	—	4	1	no	—
1035	C₂×C₄	—	4	1	no	—
1036	C₂×C₄	—	4	2	no	—
1037	C₂×C₄	—	8	2	no	—
1038	C₂×C₄	—	8	2	no	—
1039	C₂×C₄	—	8	2	no	—
1040	C₂×C₄	—	8	2	no	—
1041	C₂×C₄	—	8	1	no	—
1042	C₂×C₄	—	8	1	no	—
1043	C₂×C₄	—	8	1	no	—
1044	C₂×C₄	—	8	2	no	—
1045	C₂×C₄	—	8	1	no	—
1046	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1047	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1048	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1049	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1050	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1051	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1052	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1053	C₈	—	2	2	no	—
1054	C₈	—	2	2	no	—
1055	C₈	—	2	2	no	—
1056	C₈	—	2	2	no	—
1057	C₂²	—	2	1	no	—
1058	C₂²	—	2	1	no	—
1059	C₂²	—	2	2	no	—
1060	C₂²	—	2	1	no	—
1061	C₂²	—	2	1	no	—
1062	C₂²	—	2	1	no	—
1063	C₂²	—	2	2	no	—
1064	C₂²	—	2	1	no	—
1065	C₂²	—	2	1	no	—
1066	C₂²	—	2	1	no	—
1067	C₂²	—	2	2	no	—
1068	C₂²	—	4	2	no	—
1069	C₂²	—	4	2	no	—
1070	C₂²	—	4	2	no	—
1071	C₂²	—	4	2	no	—
1072	C₂²	—	4	2	no	—
1073	C₂²	—	4	2	no	—
1074	C₂²	—	4	2	no	—
1075	C₂²	—	4	2	no	—
1076	C₂²	—	4	2	no	—
1077	C₂²	—	8	2	no	—
1078	C₂²	—	16	2	no	—
1079	C₂²	—	16	2	no	—
1080	C₂²	—	16	2	no	—
1081	C₂²	—	16	4	no	—
1082	C₂²	#576×C₆₇	1	2	yes	—
1083	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1084	C₄	—	2	2	no	—
1085	C₄	—	2	2	no	—
1086	C₄	—	2	1	no	—
1087	C₄	—	2	1	no	—
1088	C₄	—	2	1	no	—
1089	C₄	—	2	2	no	—
1090	C₄	—	4	1	no	—
1091	C₄	—	4	1	no	—
1092	C₄	—	4	2	no	—
1093	C₄	—	4	2	no	—
1094	C₄	—	4	1	no	—
1095	C₄	—	4	2	no	—
1096	C₄	—	4	1	no	—
1097	C₄	#585×C₆₇	1	1	yes	characteristic
1098	C₄	#585×C₆₇	1	1	yes	characteristic
1099	C₂	—	2	2	no	—
1100	C₂	—	4	1	no	—
1101	C₂	—	4	1	no	—
1102	C₂	—	4	2	no	—
1103	C₂	—	8	2	no	—
1104	C₂	—	8	2	no	—
1105	C₂	—	8	2	no	—
1106	C₂	C₆₇×#3485	1	1	yes	characteristic
1107	C₂	C₂×#576×C₆₇	1	1	yes	characteristic
1108	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×#3494	C₂	semidirect
3. C₆₇×#3355	C₂	semidirect
4. C₆₇×#3347	C₂	semidirect
5. C₆₇×#3345	C₂	semidirect
6. C₆₇×#3339	C₂	semidirect
7. C₆₇×#3325	C₂	semidirect
8. C₆₇×#3318	C₂	semidirect
9. C₆₇×#3318	C₂	semidirect
10. C₆₇×#3294	C₂	semidirect
11. C₆₇×#3241	C₂	semidirect
12. C₆₇×#3199	C₂	semidirect
13. C₆₇×#3192	C₂	semidirect
14. C₆₇×#3186	C₂	semidirect
15. C₆₇×#3122	C₂	semidirect
16. C₆₇×#3096	C₂	semidirect
17. C₆₇×#3094	C₂	semidirect
18. C₂×#482×C₆₇	C₂	semidirect
19. C₆₇×#2976	C₂	semidirect
21. #555×C₆₇	C₂²	semidirect
22. #553×C₆₇	C₂²	semidirect
23. #553×C₆₇	C₂²	semidirect
24. #553×C₆₇	C₂²	semidirect
25. #553×C₆₇	C₂²	semidirect
27. #547×C₆₇	C₂²	semidirect
30. D₄²×C₆₇	C₂²	semidirect
31. D₄²×C₆₇	C₂²	semidirect
32. #544×C₆₇	C₂²	semidirect
39. #535×C₆₇	C₂²	semidirect
47. C₂×#121×C₆₇	C₂²	semidirect
48. #520×C₆₇	C₂²	semidirect
49. #518×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. #482×C₆₇	C₂²	semidirect
56. #482×C₆₇	C₂²	semidirect
57. #482×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. #481×C₆₇	C₂²	semidirect
66. #481×C₆₇	C₂²	semidirect
67. #481×C₆₇	C₂²	semidirect
68. #481×C₆₇	C₂²	semidirect
69. #480×C₆₇	C₂²	semidirect
70. #480×C₆₇	C₂²	semidirect
71. #480×C₆₇	C₂²	semidirect
72. #480×C₆₇	C₂²	semidirect
73. #478×C₆₇	C₂²	semidirect
74. #478×C₆₇	C₂²	semidirect
75. #478×C₆₇	C₂²	semidirect
76. #478×C₆₇	C₂²	semidirect
77. #476×C₆₇	C₂²	semidirect
78. #474×C₆₇	C₂²	semidirect
79. #469×C₆₇	C₂²	semidirect
80. #469×C₆₇	C₂²	semidirect
81. #469×C₆₇	C₂²	semidirect
82. #469×C₆₇	C₂²	semidirect
83. #466×C₆₇	C₂²	semidirect
84. #466×C₆₇	C₂²	semidirect
85. #466×C₆₇	C₂²	semidirect
86. #466×C₆₇	C₂²	semidirect
87. #459×C₆₇	C₂²	semidirect
88. #459×C₆₇	C₂²	semidirect
89. #447×C₆₇	C₂²	semidirect
90. #447×C₆₇	C₂²	semidirect
91. #447×C₆₇	C₂²	semidirect
92. #447×C₆₇	C₂²	semidirect
93. #447×C₆₇	C₂²	semidirect
94. #447×C₆₇	C₂²	semidirect
95. #442×C₆₇	C₂²	semidirect
96. #442×C₆₇	C₂²	semidirect
97. C₄×D₈×C₆₇	C₂²	semidirect
98. C₄×D₈×C₆₇	C₂²	semidirect
99. #436×C₆₇	C₂²	semidirect
100. #435×C₆₇	C₂²	semidirect
101. #435×C₆₇	C₂²	semidirect
102. C₈×D₄×C₆₇	C₂²	semidirect
103. #433×C₆₇	C₂²	semidirect
104. #428×C₆₇	C₂²	semidirect
105. #428×C₆₇	C₂²	semidirect
106. #428×C₆₇	C₂²	semidirect
107. #427×C₆₇	C₂²	semidirect
108. C₂×#107×C₆₇	C₂²	semidirect
109. C₂×#106×C₆₇	C₂²	semidirect
110. #418×C₆₇	C₂²	semidirect
111. #418×C₆₇	C₂²	semidirect
112. #418×C₆₇	C₂²	semidirect
113. C₂×#102×C₆₇	C₂²	semidirect
114. C₂×#102×C₆₇	C₂²	semidirect
115. C₂×#102×C₆₇	C₂²	semidirect
116. #408×C₆₇	C₂²	semidirect
117. #407×C₆₇	C₂²	semidirect
118. C₂×C₂²⋊C₈×C₆₇	C₂²	semidirect
544. #61752	C₆₇	direct (N × H)
555. #3537	C₂×C₆₇	semidirect
556. #3494	C₂×C₆₇	semidirect
557. #3355	C₂×C₆₇	semidirect
558. #3347	C₂×C₆₇	semidirect
559. #3345	C₂×C₆₇	semidirect
560. #3339	C₂×C₆₇	semidirect
561. #3325	C₂×C₆₇	semidirect
562. #3318	C₂×C₆₇	semidirect
563. #3318	C₂×C₆₇	semidirect
564. #3294	C₂×C₆₇	semidirect
565. #3241	C₂×C₆₇	semidirect
566. #3199	C₂×C₆₇	semidirect
567. #3192	C₂×C₆₇	semidirect
568. #3186	C₂×C₆₇	semidirect
569. #3122	C₂×C₆₇	semidirect
570. #3096	C₂×C₆₇	semidirect
571. #3094	C₂×C₆₇	semidirect
572. C₂×#482	C₂×C₆₇	semidirect
573. #2976	C₂×C₆₇	semidirect
574. C₆₇	#61752	direct (N × H)
576. #555	C₂²×C₆₇	semidirect
577. #553	C₂²×C₆₇	semidirect
578. #553	C₂²×C₆₇	semidirect
579. #553	C₂²×C₆₇	semidirect
580. #553	C₂²×C₆₇	semidirect
582. #547	C₂²×C₆₇	semidirect
585. D₄²	C₂²×C₆₇	semidirect
586. D₄²	C₂²×C₆₇	semidirect
587. #544	C₂²×C₆₇	semidirect
594. #535	C₂²×C₆₇	semidirect
602. C₂×#121	C₂²×C₆₇	semidirect
603. #520	C₂²×C₆₇	semidirect
604. #518	C₂²×C₆₇	semidirect
605. C₂×#117	C₂²×C₆₇	semidirect
606. #501	C₂²×C₆₇	semidirect
607. #499	C₂²×C₆₇	semidirect
608. #490	C₂²×C₆₇	semidirect
609. #486	C₂²×C₆₇	semidirect
610. #482	C₂²×C₆₇	semidirect
611. #482	C₂²×C₆₇	semidirect
612. #482	C₂²×C₆₇	semidirect
613. #482	C₂²×C₆₇	semidirect
614. #482	C₂²×C₆₇	semidirect
615. #482	C₂²×C₆₇	semidirect
616. #482	C₂²×C₆₇	semidirect
617. #482	C₂²×C₆₇	semidirect
618. #482	C₂²×C₆₇	semidirect
619. #482	C₂²×C₆₇	semidirect
620. #481	C₂²×C₆₇	semidirect
621. #481	C₂²×C₆₇	semidirect
622. #481	C₂²×C₆₇	semidirect
623. #481	C₂²×C₆₇	semidirect
624. #480	C₂²×C₆₇	semidirect
625. #480	C₂²×C₆₇	semidirect
626. #480	C₂²×C₆₇	semidirect
627. #480	C₂²×C₆₇	semidirect
628. #478	C₂²×C₆₇	semidirect
629. #478	C₂²×C₆₇	semidirect
630. #478	C₂²×C₆₇	semidirect
631. #478	C₂²×C₆₇	semidirect
632. #476	C₂²×C₆₇	semidirect
633. #474	C₂²×C₆₇	semidirect
634. #469	C₂²×C₆₇	semidirect
635. #469	C₂²×C₆₇	semidirect
636. #469	C₂²×C₆₇	semidirect
637. #469	C₂²×C₆₇	semidirect
638. #466	C₂²×C₆₇	semidirect
639. #466	C₂²×C₆₇	semidirect
640. #466	C₂²×C₆₇	semidirect
641. #466	C₂²×C₆₇	semidirect
642. #459	C₂²×C₆₇	semidirect
643. #459	C₂²×C₆₇	semidirect
644. #447	C₂²×C₆₇	semidirect
645. #447	C₂²×C₆₇	semidirect
646. #447	C₂²×C₆₇	semidirect
647. #447	C₂²×C₆₇	semidirect
648. #447	C₂²×C₆₇	semidirect
649. #447	C₂²×C₆₇	semidirect
650. #442	C₂²×C₆₇	semidirect
651. #442	C₂²×C₆₇	semidirect
652. C₄×D₈	C₂²×C₆₇	semidirect
653. C₄×D₈	C₂²×C₆₇	semidirect
654. #436	C₂²×C₆₇	semidirect
655. #435	C₂²×C₆₇	semidirect
656. #435	C₂²×C₆₇	semidirect
657. C₈×D₄	C₂²×C₆₇	semidirect
658. #433	C₂²×C₆₇	semidirect
659. #428	C₂²×C₆₇	semidirect
660. #428	C₂²×C₆₇	semidirect
661. #428	C₂²×C₆₇	semidirect
662. #427	C₂²×C₆₇	semidirect
663. C₂×#107	C₂²×C₆₇	semidirect
664. C₂×#106	C₂²×C₆₇	semidirect
665. #418	C₂²×C₆₇	semidirect
666. #418	C₂²×C₆₇	semidirect
667. #418	C₂²×C₆₇	semidirect
668. C₂×#102	C₂²×C₆₇	semidirect
669. C₂×#102	C₂²×C₆₇	semidirect
670. C₂×#102	C₂²×C₆₇	semidirect
671. #408	C₂²×C₆₇	semidirect
672. #407	C₂²×C₆₇	semidirect
673. C₂×C₂²⋊C₈	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×#3494	2
C₆₇×#3355	2
C₆₇×#3347	2
C₆₇×#3345	2
C₆₇×#3339	2
C₆₇×#3325	2
C₆₇×#3318	2
C₆₇×#3294	2
C₆₇×#3241	2
C₆₇×#3199	2
C₆₇×#3192	2
C₆₇×#3186	2
C₆₇×#3122	2
C₆₇×#3096	2
C₆₇×#3094	2
C₂×#482×C₆₇	2
C₆₇×#2976	2
#61752	67

Subgroups — C67×#61752 #30741003

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61752 #30741003