Subgroups — C₆₇×#60327 #30739578

Order 17152.

1812 conjugacy classes of subgroups.

The subgroup lattice has 1022 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3529	C₂	1	1	yes	maximal, characteristic
2	C₆₇×#2995	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#2995	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#2994	C₂	1	2	yes	maximal, complemented
5	C₆₇×#2992	C₂	1	2	yes	maximal, complemented
6	C₆₇×#2981	C₂	1	2	yes	maximal, complemented
7	C₆₇×#2980	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#2977	C₂	1	2	yes	maximal, complemented
9	C₆₇×#2976	C₂	1	2	yes	maximal, complemented
10	C₆₇×#2976	C₂	1	2	yes	maximal, complemented
11	C₆₇×#2969	C₂	1	2	yes	maximal, complemented
12	C₆₇×#2967	C₂	1	2	yes	maximal, complemented
13	C₆₇×#2966	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#2966	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#2935	C₂	1	2	yes	maximal, complemented
16	C₆₇×#2933	C₂	1	2	yes	maximal, complemented
17	C₆₇×#2933	C₂	1	2	yes	maximal, complemented
18	C₆₇×#2931	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₇×#2930	C₂	1	2	yes	maximal, complemented
20	C₂×#131×C₆₇	C₂²	1	2	yes	—
21	C₂×#131×C₆₇	C₂²	1	1	yes	characteristic
22	C₂×#131×C₆₇	C₂²	1	1	yes	characteristic, complemented
23	C₂²×M₁₆×C₆₇	C₂²	1	2	yes	complemented
24	#563×C₆₇	C₄	1	1	yes	characteristic
25	#563×C₆₇	C₄	1	2	yes	—
26	#562×C₆₇	C₄	1	1	yes	characteristic
27	#562×C₆₇	C₄	1	2	yes	—
28	#562×C₆₇	C₄	1	2	yes	—
29	#562×C₆₇	C₄	1	1	yes	characteristic
30	H(3,𝔽₄)×C₆₇	C₄	1	1	yes	characteristic
31	#560×C₆₇	C₄	1	2	yes	—
32	#560×C₆₇	C₄	1	2	yes	—
33	#560×C₆₇	C₄	1	2	yes	—
34	#532×C₆₇	C₂²	1	1	yes	characteristic
35	#532×C₆₇	C₂²	1	2	yes	—
36	#529×C₆₇	C₂²	1	1	yes	characteristic
37	#529×C₆₇	C₂²	1	1	yes	characteristic
38	#529×C₆₇	C₂²	1	2	yes	—
39	#529×C₆₇	C₂²	1	2	yes	—
40	#525×C₆₇	C₂²	1	2	yes	—
41	#525×C₆₇	C₂²	1	2	yes	—
42	#525×C₆₇	C₂²	1	2	yes	—
43	#446×C₆₇	C₂²	1	1	yes	characteristic, complemented
44	#446×C₆₇	C₂²	1	1	yes	characteristic, complemented
45	#446×C₆₇	C₂²	1	2	yes	complemented
46	#446×C₆₇	C₂²	1	2	yes	complemented
47	C₈×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
48	C₈×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
49	#436×C₆₇	C₂²	1	1	yes	characteristic
50	#436×C₆₇	C₂²	1	2	yes	—
51	#436×C₆₇	C₂²	1	2	yes	—
52	#436×C₆₇	C₂²	1	1	yes	characteristic
53	#436×C₆₇	C₂²	1	2	yes	complemented
54	#436×C₆₇	C₂²	1	2	yes	complemented
55	#436×C₆₇	C₂²	1	2	yes	complemented
56	#436×C₆₇	C₂²	1	2	yes	complemented
57	#436×C₆₇	C₂²	1	2	yes	complemented
58	#436×C₆₇	C₂²	1	2	yes	complemented
59	#435×C₆₇	C₂²	1	2	yes	—
60	#435×C₆₇	C₂²	1	2	yes	—
61	#435×C₆₇	C₂²	1	2	yes	—
62	#435×C₆₇	C₂²	1	2	yes	—
63	#435×C₆₇	C₂²	1	2	yes	—
64	#435×C₆₇	C₂²	1	2	yes	—
65	#435×C₆₇	C₂²	1	2	yes	complemented
66	#435×C₆₇	C₂²	1	2	yes	complemented
67	#435×C₆₇	C₂²	1	2	yes	complemented
68	#435×C₆₇	C₂²	1	2	yes	complemented
69	#435×C₆₇	C₂²	1	2	yes	complemented
70	#435×C₆₇	C₂²	1	2	yes	complemented
71	#435×C₆₇	C₂²	1	2	yes	complemented
72	#435×C₆₇	C₂²	1	2	yes	complemented
73	#435×C₆₇	C₂²	1	2	yes	complemented
74	#435×C₆₇	C₂²	1	2	yes	complemented
75	#435×C₆₇	C₂²	1	2	yes	complemented
76	#435×C₆₇	C₂²	1	2	yes	complemented
77	C₈×D₄×C₆₇	C₂²	1	1	yes	characteristic
78	C₈×D₄×C₆₇	C₂²	1	2	yes	—
79	C₈×D₄×C₆₇	C₂²	1	1	yes	characteristic
80	C₈×D₄×C₆₇	C₂²	1	2	yes	—
81	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
82	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
83	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
84	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
85	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
86	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
87	#433×C₆₇	C₂²	1	2	yes	complemented
88	#433×C₆₇	C₂²	1	2	yes	complemented
89	#433×C₆₇	C₂²	1	2	yes	complemented
90	#433×C₆₇	C₂²	1	2	yes	complemented
91	#433×C₆₇	C₂²	1	2	yes	complemented
92	#433×C₆₇	C₂²	1	2	yes	complemented
93	#432×C₆₇	C₂²	1	1	yes	characteristic, complemented
94	#432×C₆₇	C₂²	1	1	yes	characteristic, complemented
95	#432×C₆₇	C₂²	1	2	yes	complemented
96	#431×C₆₇	C₂²	1	2	yes	complemented
97	#424×C₆₇	C₂²	1	2	yes	complemented
98	#424×C₆₇	C₂²	1	2	yes	complemented
99	#424×C₆₇	C₂²	1	2	yes	complemented
100	#423×C₆₇	C₂²	1	1	yes	characteristic, complemented
101	C₂×C₄⋊C₈×C₆₇	C₂²	1	2	yes	complemented
102	#408×C₆₇	C₂²	1	2	yes	—
103	#408×C₆₇	C₂²	1	1	yes	characteristic
104	#408×C₆₇	C₂²	1	2	yes	—
105	#408×C₆₇	C₂²	1	2	yes	—
106	#408×C₆₇	C₂²	1	2	yes	—
107	#408×C₆₇	C₂²	1	1	yes	characteristic, complemented
108	#408×C₆₇	C₂²	1	2	yes	complemented
109	#407×C₆₇	C₂²	1	2	yes	complemented
110	C₂×C₂²⋊C₈×C₆₇	C₂²	1	2	yes	complemented
111	C₂×C₂²⋊C₈×C₆₇	C₂²	1	2	yes	complemented
112	#405×C₆₇	C₂²	1	2	yes	complemented
113	#405×C₆₇	C₂²	1	2	yes	complemented
114	#405×C₆₇	C₂²	1	2	yes	complemented
115	C₄×M₁₆×C₆₇	C₂²	1	2	yes	complemented
116	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
117	C₂×#41×C₆₇	C₂³	1	2	yes	—
118	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
119	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
120	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
121	#131×C₆₇	—	4	4	no	—
122	#131×C₆₇	—	4	2	no	—
123	#131×C₆₇	—	4	2	no	—
124	C₂×M₁₆×C₆₇	—	4	4	no	—
125	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
126	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
127	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
128	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
129	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
130	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
131	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
132	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
133	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
134	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
135	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
136	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
137	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
138	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
139	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
140	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
141	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
142	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
143	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
144	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
145	C₄⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
146	C₄⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
147	#127×C₆₇	C₂×C₄	1	1	yes	characteristic
148	#127×C₆₇	C₂×C₄	1	2	yes	—
149	#126×C₆₇	C₂×C₄	1	2	yes	—
150	#126×C₆₇	C₂×C₄	1	2	yes	—
151	#126×C₆₇	C₂×C₄	1	2	yes	—
152	#126×C₆₇	C₂×C₄	1	2	yes	—
153	#126×C₆₇	C₂×C₄	1	2	yes	—
154	#126×C₆₇	C₂×C₄	1	2	yes	—
155	#125×C₆₇	C₂×C₄	1	1	yes	characteristic
156	#125×C₆₇	C₂×C₄	1	1	yes	characteristic
157	#125×C₆₇	C₂×C₄	1	2	yes	—
158	#125×C₆₇	C₂×C₄	1	2	yes	—
159	#124×C₆₇	C₂×C₄	1	1	yes	characteristic
160	#124×C₆₇	C₂×C₄	1	1	yes	characteristic
161	#124×C₆₇	C₂×C₄	1	2	yes	—
162	#124×C₆₇	C₂×C₄	1	2	yes	—
163	#124×C₆₇	C₂×C₄	1	1	yes	characteristic
164	#124×C₆₇	C₂×C₄	1	2	yes	—
165	#124×C₆₇	C₂×C₄	1	1	yes	characteristic
166	#124×C₆₇	C₂×C₄	1	2	yes	—
167	#123×C₆₇	C₂×C₄	1	2	yes	—
168	#123×C₆₇	C₂×C₄	1	2	yes	—
169	#123×C₆₇	C₂×C₄	1	2	yes	—
170	#123×C₆₇	C₂×C₄	1	2	yes	—
171	#123×C₆₇	C₂×C₄	1	2	yes	—
172	#123×C₆₇	C₂×C₄	1	2	yes	—
173	#123×C₆₇	C₂×C₄	1	2	yes	—
174	#123×C₆₇	C₂×C₄	1	2	yes	—
175	#123×C₆₇	C₂×C₄	1	2	yes	—
176	#123×C₆₇	C₂×C₄	1	2	yes	—
177	#123×C₆₇	C₂×C₄	1	2	yes	—
178	#123×C₆₇	C₂×C₄	1	2	yes	—
179	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
180	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
181	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
182	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
183	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
184	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
185	C₂²⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
186	C₂²⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
187	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
188	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
189	#121×C₆₇	C₂×C₄	1	2	yes	—
190	#121×C₆₇	C₂×C₄	1	2	yes	—
191	#121×C₆₇	C₂×C₄	1	2	yes	—
192	#121×C₆₇	C₂×C₄	1	2	yes	—
193	#121×C₆₇	C₂×C₄	1	2	yes	—
194	#121×C₆₇	C₂×C₄	1	2	yes	—
195	#121×C₆₇	C₂×C₄	1	1	yes	characteristic
196	#121×C₆₇	C₂×C₄	1	1	yes	characteristic
197	#121×C₆₇	C₂×C₄	1	2	yes	—
198	#121×C₆₇	C₂×C₄	1	2	yes	—
199	#121×C₆₇	C₂×C₄	1	2	yes	—
200	#121×C₆₇	C₂×C₄	1	2	yes	—
201	#121×C₆₇	C₂×C₄	1	2	yes	—
202	#121×C₆₇	C₂×C₄	1	2	yes	—
203	#121×C₆₇	C₂×C₄	1	2	yes	—
204	#121×C₆₇	C₂×C₄	1	2	yes	—
205	#120×C₆₇	C₂×C₄	1	2	yes	—
206	#120×C₆₇	C₂×C₄	1	2	yes	—
207	#120×C₆₇	C₂×C₄	1	2	yes	—
208	#120×C₆₇	C₂×C₄	1	2	yes	—
209	#120×C₆₇	C₂×C₄	1	2	yes	—
210	#120×C₆₇	C₂×C₄	1	2	yes	—
211	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
212	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
213	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
214	C₄×D₄×C₆₇	C₂³	1	2	yes	—
215	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
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	C₄×D₄×C₆₇	C₂³	1	2	yes	—
221	C₄×D₄×C₆₇	C₂³	1	2	yes	—
222	C₄×D₄×C₆₇	C₂³	1	2	yes	—
223	#117×C₆₇	C₂³	1	2	yes	—
224	#117×C₆₇	C₂³	1	2	yes	—
225	#117×C₆₇	C₂³	1	2	yes	—
226	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
227	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
228	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
229	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
230	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
231	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
232	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
233	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
234	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
235	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
236	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
237	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
238	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
239	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
240	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
241	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
242	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
243	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
244	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
245	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
246	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
247	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
248	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
249	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
250	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
251	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
252	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
253	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
254	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
255	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
256	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
257	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
258	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
259	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
260	#97×C₆₇	C₂³	1	2	yes	—
261	#97×C₆₇	C₂³	1	2	yes	—
262	#97×C₆₇	C₂³	1	2	yes	—
263	#97×C₆₇	C₂³	1	2	yes	—
264	#97×C₆₇	C₂³	1	2	yes	—
265	#97×C₆₇	C₂³	1	2	yes	—
266	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
267	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
268	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
269	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
270	C₄×C₈×C₆₇	C₂³	1	2	yes	—
271	C₄×C₈×C₆₇	C₂³	1	2	yes	—
272	C₄×C₈×C₆₇	C₂³	1	2	yes	—
273	C₄×C₈×C₆₇	C₂³	1	2	yes	—
274	C₂⁴×C₆₇	C₂²×C₄	1	2	yes	—
275	#41×C₆₇	—	4	2	no	—
276	#41×C₆₇	—	4	1	no	—
277	#41×C₆₇	—	4	1	no	—
278	#41×C₆₇	—	4	1	no	—
279	#41×C₆₇	—	4	2	no	—
280	#41×C₆₇	—	4	1	no	—
281	C₂×Q₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
282	C₂×Q₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
283	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
284	C₂×Q₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
285	C₂×Q₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
286	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
287	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
288	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
289	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
290	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
291	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
292	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
293	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
294	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
295	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
296	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
297	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
298	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
299	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
300	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
301	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
302	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
303	C₂²×C₄×C₆₇	—	4	2	no	—
304	C₂²×C₄×C₆₇	—	4	2	no	—
305	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
306	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
307	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
308	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
309	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
310	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
311	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
312	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
313	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
314	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
315	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
316	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
317	M₁₆×C₆₇	—	2	4	no	—
318	M₁₆×C₆₇	—	2	4	no	—
319	M₁₆×C₆₇	—	2	4	no	—
320	M₁₆×C₆₇	—	4	2	no	—
321	M₁₆×C₆₇	—	4	2	no	—
322	M₁₆×C₆₇	—	4	2	no	—
323	M₁₆×C₆₇	—	4	2	no	—
324	M₁₆×C₆₇	—	4	2	no	—
325	M₁₆×C₆₇	—	4	1	no	—
326	M₁₆×C₆₇	—	4	1	no	—
327	C₂×C₈×C₆₇	—	2	4	no	—
328	C₂×C₈×C₆₇	—	2	2	no	—
329	C₂×C₈×C₆₇	—	4	2	no	—
330	C₂×C₈×C₆₇	—	4	1	no	—
331	C₂×C₈×C₆₇	—	4	2	no	—
332	C₂×C₈×C₆₇	—	4	2	no	—
333	C₂×C₈×C₆₇	—	4	2	no	—
334	C₂×C₈×C₆₇	—	4	2	no	—
335	C₂×C₈×C₆₇	—	4	2	no	—
336	C₂×C₈×C₆₇	—	4	2	no	—
337	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
338	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
339	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
340	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
341	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
342	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
343	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
344	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
345	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
346	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
347	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
348	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
349	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
350	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
351	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
352	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
353	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
354	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
355	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
356	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
357	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
358	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
359	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
360	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
361	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
362	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
363	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
364	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
365	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
366	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
367	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
368	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
369	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
370	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
371	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
372	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
373	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
374	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
375	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
376	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
377	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
378	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
379	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
380	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
381	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
382	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
383	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
384	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
385	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
386	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
387	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
388	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
389	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
390	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
391	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
392	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
393	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
394	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
395	C₄²×C₆₇	C₂⁴	1	2	yes	—
396	C₄²×C₆₇	C₂⁴	1	2	yes	—
397	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
398	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
399	C₂³×C₆₇	—	4	2	no	—
400	C₂³×C₆₇	—	4	2	no	—
401	C₂³×C₆₇	—	4	2	no	—
402	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
403	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
404	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
405	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
406	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
407	Q₈×C₆₇	—	4	1	no	—
408	Q₈×C₆₇	—	4	1	no	—
409	Q₈×C₆₇	—	4	2	no	—
410	Q₈×C₆₇	—	4	1	no	—
411	Q₈×C₆₇	—	4	1	no	—
412	D₄×C₆₇	—	4	2	no	—
413	D₄×C₆₇	—	4	2	no	—
414	D₄×C₆₇	—	4	2	no	—
415	D₄×C₆₇	—	4	2	no	—
416	D₄×C₆₇	—	4	2	no	—
417	D₄×C₆₇	—	4	2	no	—
418	D₄×C₆₇	—	4	1	no	—
419	D₄×C₆₇	—	4	2	no	—
420	D₄×C₆₇	—	4	1	no	—
421	D₄×C₆₇	—	4	2	no	—
422	D₄×C₆₇	—	4	2	no	—
423	D₄×C₆₇	—	4	2	no	—
424	D₄×C₆₇	—	4	2	no	—
425	D₄×C₆₇	—	4	1	no	—
426	D₄×C₆₇	—	4	2	no	—
427	D₄×C₆₇	—	4	1	no	—
428	D₄×C₆₇	—	4	2	no	—
429	C₂×C₄×C₆₇	—	2	2	no	—
430	C₂×C₄×C₆₇	—	2	1	no	—
431	C₂×C₄×C₆₇	—	2	2	no	—
432	C₂×C₄×C₆₇	—	2	2	no	—
433	C₂×C₄×C₆₇	—	2	2	no	—
434	C₂×C₄×C₆₇	—	2	2	no	—
435	C₂×C₄×C₆₇	—	2	2	no	—
436	C₂×C₄×C₆₇	—	2	1	no	—
437	C₂×C₄×C₆₇	—	2	2	no	—
438	C₂×C₄×C₆₇	—	2	2	no	—
439	C₂×C₄×C₆₇	—	4	2	no	—
440	C₂×C₄×C₆₇	—	4	2	no	—
441	C₂×C₄×C₆₇	—	4	2	no	—
442	C₂×C₄×C₆₇	—	4	1	no	—
443	C₂×C₄×C₆₇	—	4	1	no	—
444	C₂×C₄×C₆₇	—	4	2	no	—
445	C₂×C₄×C₆₇	—	4	2	no	—
446	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
447	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
448	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
449	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
450	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
451	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
452	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
453	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
454	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
455	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
456	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
457	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
458	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
459	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
460	C₈×C₆₇	—	2	1	no	—
461	C₈×C₆₇	—	2	2	no	—
462	C₈×C₆₇	—	2	2	no	—
463	C₈×C₆₇	—	2	2	no	—
464	C₈×C₆₇	—	2	2	no	—
465	C₈×C₆₇	—	2	1	no	—
466	C₈×C₆₇	—	2	2	no	—
467	C₈×C₆₇	—	2	1	no	—
468	C₈×C₆₇	—	2	2	no	—
469	C₈×C₆₇	H(5,𝔽₂)	1	2	yes	—
470	C₂²×C₆₇	—	2	2	no	—
471	C₂²×C₆₇	—	2	2	no	—
472	C₂²×C₆₇	—	2	2	no	—
473	C₂²×C₆₇	—	2	1	no	—
474	C₂²×C₆₇	—	2	2	no	—
475	C₂²×C₆₇	—	2	1	no	—
476	C₂²×C₆₇	—	2	1	no	—
477	C₂²×C₆₇	—	2	2	no	—
478	C₂²×C₆₇	—	2	2	no	—
479	C₂²×C₆₇	—	2	2	no	—
480	C₂²×C₆₇	—	2	2	no	—
481	C₂²×C₆₇	—	2	2	no	—
482	C₂²×C₆₇	—	2	2	no	—
483	C₂²×C₆₇	—	2	2	no	—
484	C₂²×C₆₇	—	2	2	no	—
485	C₂²×C₆₇	—	8	4	no	—
486	C₂²×C₆₇	C₂⁴×C₄	1	1	yes	characteristic
487	C₄×C₆₇	—	2	2	no	—
488	C₄×C₆₇	—	2	2	no	—
489	C₄×C₆₇	—	2	2	no	—
490	C₄×C₆₇	—	2	1	no	—
491	C₄×C₆₇	—	2	2	no	—
492	C₄×C₆₇	—	2	1	no	—
493	C₄×C₆₇	—	2	1	no	—
494	C₄×C₆₇	—	2	2	no	—
495	C₄×C₆₇	—	2	2	no	—
496	C₄×C₆₇	—	2	1	no	—
497	C₄×C₆₇	—	2	1	no	—
498	C₄×C₆₇	—	2	2	no	—
499	C₄×C₆₇	—	2	2	no	—
500	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
501	C₄×C₆₇	#585	1	1	yes	characteristic
502	#60327	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
503	C₂×C₆₇	—	4	1	no	—
504	C₂×C₆₇	—	4	2	no	—
505	C₂×C₆₇	—	4	2	no	—
506	C₂×C₆₇	—	4	2	no	—
507	C₂×C₆₇	—	4	2	no	—
508	C₂×C₆₇	C₄×H(5,𝔽₂)	1	1	yes	characteristic
509	C₂×C₆₇	#3573	1	1	yes	characteristic
510	C₂×C₆₇	#3573	1	1	yes	characteristic
511	#3529	C₂×C₆₇	1	1	yes	characteristic
512	#2995	C₂×C₆₇	1	1	yes	characteristic, complemented
513	#2995	C₂×C₆₇	1	1	yes	characteristic, complemented
514	#2994	C₂×C₆₇	1	2	yes	complemented
515	#2992	C₂×C₆₇	1	2	yes	complemented
516	#2981	C₂×C₆₇	1	2	yes	complemented
517	#2980	C₂×C₆₇	1	1	yes	characteristic, complemented
518	#2977	C₂×C₆₇	1	2	yes	complemented
519	#2976	C₂×C₆₇	1	2	yes	complemented
520	#2976	C₂×C₆₇	1	2	yes	complemented
521	#2969	C₂×C₆₇	1	2	yes	complemented
522	#2967	C₂×C₆₇	1	2	yes	complemented
523	#2966	C₂×C₆₇	1	1	yes	characteristic, complemented
524	#2966	C₂×C₆₇	1	1	yes	characteristic, complemented
525	#2935	C₂×C₆₇	1	2	yes	complemented
526	#2933	C₂×C₆₇	1	2	yes	complemented
527	#2933	C₂×C₆₇	1	2	yes	complemented
528	#2931	C₂×C₆₇	1	1	yes	characteristic, complemented
529	#2930	C₂×C₆₇	1	2	yes	complemented
530	C₆₇	#60327	1	1	yes	characteristic, direct product factor, Sylow
531	C₂×#131	C₂²×C₆₇	1	2	yes	—
532	C₂×#131	C₂²×C₆₇	1	1	yes	characteristic
533	C₂×#131	C₂²×C₆₇	1	1	yes	characteristic, complemented
534	C₂²×M₁₆	C₂²×C₆₇	1	2	yes	complemented
535	#563	C₄×C₆₇	1	1	yes	characteristic
536	#563	C₄×C₆₇	1	2	yes	—
537	#562	C₄×C₆₇	1	1	yes	characteristic
538	#562	C₄×C₆₇	1	2	yes	—
539	#562	C₄×C₆₇	1	2	yes	—
540	#562	C₄×C₆₇	1	1	yes	characteristic
541	H(3,𝔽₄)	C₄×C₆₇	1	1	yes	characteristic
542	#560	C₄×C₆₇	1	2	yes	—
543	#560	C₄×C₆₇	1	2	yes	—
544	#560	C₄×C₆₇	1	2	yes	—
545	#532	C₂²×C₆₇	1	1	yes	characteristic
546	#532	C₂²×C₆₇	1	2	yes	—
547	#529	C₂²×C₆₇	1	1	yes	characteristic
548	#529	C₂²×C₆₇	1	1	yes	characteristic
549	#529	C₂²×C₆₇	1	2	yes	—
550	#529	C₂²×C₆₇	1	2	yes	—
551	#525	C₂²×C₆₇	1	2	yes	—
552	#525	C₂²×C₆₇	1	2	yes	—
553	#525	C₂²×C₆₇	1	2	yes	—
554	#446	C₂²×C₆₇	1	1	yes	characteristic, complemented
555	#446	C₂²×C₆₇	1	1	yes	characteristic, complemented
556	#446	C₂²×C₆₇	1	2	yes	complemented
557	#446	C₂²×C₆₇	1	2	yes	complemented
558	C₈×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
559	C₈×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
560	#436	C₂²×C₆₇	1	1	yes	characteristic
561	#436	C₂²×C₆₇	1	2	yes	—
562	#436	C₂²×C₆₇	1	2	yes	—
563	#436	C₂²×C₆₇	1	1	yes	characteristic
564	#436	C₂²×C₆₇	1	2	yes	complemented
565	#436	C₂²×C₆₇	1	2	yes	complemented
566	#436	C₂²×C₆₇	1	2	yes	complemented
567	#436	C₂²×C₆₇	1	2	yes	complemented
568	#436	C₂²×C₆₇	1	2	yes	complemented
569	#436	C₂²×C₆₇	1	2	yes	complemented
570	#435	C₂²×C₆₇	1	2	yes	—
571	#435	C₂²×C₆₇	1	2	yes	—
572	#435	C₂²×C₆₇	1	2	yes	—
573	#435	C₂²×C₆₇	1	2	yes	—
574	#435	C₂²×C₆₇	1	2	yes	—
575	#435	C₂²×C₆₇	1	2	yes	—
576	#435	C₂²×C₆₇	1	2	yes	complemented
577	#435	C₂²×C₆₇	1	2	yes	complemented
578	#435	C₂²×C₆₇	1	2	yes	complemented
579	#435	C₂²×C₆₇	1	2	yes	complemented
580	#435	C₂²×C₆₇	1	2	yes	complemented
581	#435	C₂²×C₆₇	1	2	yes	complemented
582	#435	C₂²×C₆₇	1	2	yes	complemented
583	#435	C₂²×C₆₇	1	2	yes	complemented
584	#435	C₂²×C₆₇	1	2	yes	complemented
585	#435	C₂²×C₆₇	1	2	yes	complemented
586	#435	C₂²×C₆₇	1	2	yes	complemented
587	#435	C₂²×C₆₇	1	2	yes	complemented
588	C₈×D₄	C₂²×C₆₇	1	1	yes	characteristic
589	C₈×D₄	C₂²×C₆₇	1	2	yes	—
590	C₈×D₄	C₂²×C₆₇	1	1	yes	characteristic
591	C₈×D₄	C₂²×C₆₇	1	2	yes	—
592	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
593	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
594	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
595	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
596	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
597	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
598	#433	C₂²×C₆₇	1	2	yes	complemented
599	#433	C₂²×C₆₇	1	2	yes	complemented
600	#433	C₂²×C₆₇	1	2	yes	complemented
601	#433	C₂²×C₆₇	1	2	yes	complemented
602	#433	C₂²×C₆₇	1	2	yes	complemented
603	#433	C₂²×C₆₇	1	2	yes	complemented
604	#432	C₂²×C₆₇	1	1	yes	characteristic, complemented
605	#432	C₂²×C₆₇	1	1	yes	characteristic, complemented
606	#432	C₂²×C₆₇	1	2	yes	complemented
607	#431	C₂²×C₆₇	1	2	yes	complemented
608	#424	C₂²×C₆₇	1	2	yes	complemented
609	#424	C₂²×C₆₇	1	2	yes	complemented
610	#424	C₂²×C₆₇	1	2	yes	complemented
611	#423	C₂²×C₆₇	1	1	yes	characteristic, complemented
612	C₂×C₄⋊C₈	C₂²×C₆₇	1	2	yes	complemented
613	#408	C₂²×C₆₇	1	2	yes	—
614	#408	C₂²×C₆₇	1	1	yes	characteristic
615	#408	C₂²×C₆₇	1	2	yes	—
616	#408	C₂²×C₆₇	1	2	yes	—
617	#408	C₂²×C₆₇	1	2	yes	—
618	#408	C₂²×C₆₇	1	1	yes	characteristic, complemented
619	#408	C₂²×C₆₇	1	2	yes	complemented
620	#407	C₂²×C₆₇	1	2	yes	complemented
621	C₂×C₂²⋊C₈	C₂²×C₆₇	1	2	yes	complemented
622	C₂×C₂²⋊C₈	C₂²×C₆₇	1	2	yes	complemented
623	#405	C₂²×C₆₇	1	2	yes	complemented
624	#405	C₂²×C₆₇	1	2	yes	complemented
625	#405	C₂²×C₆₇	1	2	yes	complemented
626	C₄×M₁₆	C₂²×C₆₇	1	2	yes	complemented
627	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
628	C₂×#41	C₂³×C₆₇	1	2	yes	—
629	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
630	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
631	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
632	#131	—	4	4	no	—
633	#131	—	4	2	no	—
634	#131	—	4	2	no	—
635	C₂×M₁₆	—	4	4	no	—
636	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
637	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
638	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
639	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
640	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
641	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
642	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
643	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
644	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
645	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
646	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
647	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
648	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
649	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
650	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
651	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
652	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
653	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
654	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
655	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
656	C₄⋊Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
657	C₄⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
658	#127	C₂×C₄×C₆₇	1	1	yes	characteristic
659	#127	C₂×C₄×C₆₇	1	2	yes	—
660	#126	C₂×C₄×C₆₇	1	2	yes	—
661	#126	C₂×C₄×C₆₇	1	2	yes	—
662	#126	C₂×C₄×C₆₇	1	2	yes	—
663	#126	C₂×C₄×C₆₇	1	2	yes	—
664	#126	C₂×C₄×C₆₇	1	2	yes	—
665	#126	C₂×C₄×C₆₇	1	2	yes	—
666	#125	C₂×C₄×C₆₇	1	1	yes	characteristic
667	#125	C₂×C₄×C₆₇	1	1	yes	characteristic
668	#125	C₂×C₄×C₆₇	1	2	yes	—
669	#125	C₂×C₄×C₆₇	1	2	yes	—
670	#124	C₂×C₄×C₆₇	1	1	yes	characteristic
671	#124	C₂×C₄×C₆₇	1	1	yes	characteristic
672	#124	C₂×C₄×C₆₇	1	2	yes	—
673	#124	C₂×C₄×C₆₇	1	2	yes	—
674	#124	C₂×C₄×C₆₇	1	1	yes	characteristic
675	#124	C₂×C₄×C₆₇	1	2	yes	—
676	#124	C₂×C₄×C₆₇	1	1	yes	characteristic
677	#124	C₂×C₄×C₆₇	1	2	yes	—
678	#123	C₂×C₄×C₆₇	1	2	yes	—
679	#123	C₂×C₄×C₆₇	1	2	yes	—
680	#123	C₂×C₄×C₆₇	1	2	yes	—
681	#123	C₂×C₄×C₆₇	1	2	yes	—
682	#123	C₂×C₄×C₆₇	1	2	yes	—
683	#123	C₂×C₄×C₆₇	1	2	yes	—
684	#123	C₂×C₄×C₆₇	1	2	yes	—
685	#123	C₂×C₄×C₆₇	1	2	yes	—
686	#123	C₂×C₄×C₆₇	1	2	yes	—
687	#123	C₂×C₄×C₆₇	1	2	yes	—
688	#123	C₂×C₄×C₆₇	1	2	yes	—
689	#123	C₂×C₄×C₆₇	1	2	yes	—
690	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
691	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
692	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
693	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
694	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
695	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
696	C₂²⋊Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
697	C₂²⋊Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
698	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
699	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
700	#121	C₂×C₄×C₆₇	1	2	yes	—
701	#121	C₂×C₄×C₆₇	1	2	yes	—
702	#121	C₂×C₄×C₆₇	1	2	yes	—
703	#121	C₂×C₄×C₆₇	1	2	yes	—
704	#121	C₂×C₄×C₆₇	1	2	yes	—
705	#121	C₂×C₄×C₆₇	1	2	yes	—
706	#121	C₂×C₄×C₆₇	1	1	yes	characteristic
707	#121	C₂×C₄×C₆₇	1	1	yes	characteristic
708	#121	C₂×C₄×C₆₇	1	2	yes	—
709	#121	C₂×C₄×C₆₇	1	2	yes	—
710	#121	C₂×C₄×C₆₇	1	2	yes	—
711	#121	C₂×C₄×C₆₇	1	2	yes	—
712	#121	C₂×C₄×C₆₇	1	2	yes	—
713	#121	C₂×C₄×C₆₇	1	2	yes	—
714	#121	C₂×C₄×C₆₇	1	2	yes	—
715	#121	C₂×C₄×C₆₇	1	2	yes	—
716	#120	C₂×C₄×C₆₇	1	2	yes	—
717	#120	C₂×C₄×C₆₇	1	2	yes	—
718	#120	C₂×C₄×C₆₇	1	2	yes	—
719	#120	C₂×C₄×C₆₇	1	2	yes	—
720	#120	C₂×C₄×C₆₇	1	2	yes	—
721	#120	C₂×C₄×C₆₇	1	2	yes	—
722	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
723	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
724	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
725	C₄×D₄	C₂³×C₆₇	1	2	yes	—
726	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
727	C₄×D₄	C₂³×C₆₇	1	2	yes	—
728	C₄×D₄	C₂³×C₆₇	1	2	yes	—
729	C₄×D₄	C₂³×C₆₇	1	2	yes	—
730	C₄×D₄	C₂³×C₆₇	1	2	yes	—
731	C₄×D₄	C₂³×C₆₇	1	2	yes	—
732	C₄×D₄	C₂³×C₆₇	1	2	yes	—
733	C₄×D₄	C₂³×C₆₇	1	2	yes	—
734	#117	C₂³×C₆₇	1	2	yes	—
735	#117	C₂³×C₆₇	1	2	yes	—
736	#117	C₂³×C₆₇	1	2	yes	—
737	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
738	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
739	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
740	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
741	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
742	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
743	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
744	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
745	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
746	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
747	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
748	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
749	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
750	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
751	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
752	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
753	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
754	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
755	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
756	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
757	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
758	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
759	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
760	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
761	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
762	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
763	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
764	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
765	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
766	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
767	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
768	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
769	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
770	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
771	#97	C₂³×C₆₇	1	2	yes	—
772	#97	C₂³×C₆₇	1	2	yes	—
773	#97	C₂³×C₆₇	1	2	yes	—
774	#97	C₂³×C₆₇	1	2	yes	—
775	#97	C₂³×C₆₇	1	2	yes	—
776	#97	C₂³×C₆₇	1	2	yes	—
777	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
778	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
779	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
780	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
781	C₄×C₈	C₂³×C₆₇	1	2	yes	—
782	C₄×C₈	C₂³×C₆₇	1	2	yes	—
783	C₄×C₈	C₂³×C₆₇	1	2	yes	—
784	C₄×C₈	C₂³×C₆₇	1	2	yes	—
785	C₂⁴	C₂²×C₄×C₆₇	1	2	yes	—
786	#41	—	4	2	no	—
787	#41	—	4	1	no	—
788	#41	—	4	1	no	—
789	#41	—	4	1	no	—
790	#41	—	4	2	no	—
791	#41	—	4	1	no	—
792	C₂×Q₈	C₂²×C₄×C₆₇	1	1	yes	characteristic
793	C₂×Q₈	C₂²×C₄×C₆₇	1	1	yes	characteristic
794	C₂×Q₈	C₂²×C₄×C₆₇	1	2	yes	—
795	C₂×Q₈	C₂²×C₄×C₆₇	1	1	yes	characteristic
796	C₂×Q₈	C₂²×C₄×C₆₇	1	1	yes	characteristic
797	C₂×D₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
798	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
799	C₂×D₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
800	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
801	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
802	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
803	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
804	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
805	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
806	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
807	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
808	C₂×D₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
809	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
810	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
811	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
812	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
813	C₂×D₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
814	C₂²×C₄	—	4	2	no	—
815	C₂²×C₄	—	4	2	no	—
816	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
817	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
818	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
819	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
820	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
821	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
822	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
823	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
824	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
825	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
826	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
827	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
828	M₁₆	—	2	4	no	—
829	M₁₆	—	2	4	no	—
830	M₁₆	—	2	4	no	—
831	M₁₆	—	4	2	no	—
832	M₁₆	—	4	2	no	—
833	M₁₆	—	4	2	no	—
834	M₁₆	—	4	1	no	—
835	M₁₆	—	4	1	no	—
836	M₁₆	—	4	2	no	—
837	M₁₆	—	4	2	no	—
838	C₂×C₈	—	2	4	no	—
839	C₂×C₈	—	2	2	no	—
840	C₂×C₈	—	4	2	no	—
841	C₂×C₈	—	4	2	no	—
842	C₂×C₈	—	4	2	no	—
843	C₂×C₈	—	4	2	no	—
844	C₂×C₈	—	4	2	no	—
845	C₂×C₈	—	4	2	no	—
846	C₂×C₈	—	4	1	no	—
847	C₂×C₈	—	4	2	no	—
848	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
849	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
850	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
851	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
852	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
853	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
854	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
855	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
856	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
857	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
858	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
859	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
860	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
861	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
862	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
863	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
864	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
865	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
866	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
867	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
868	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
869	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
870	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
871	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
872	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
873	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
874	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
875	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
876	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
877	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
878	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
879	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
880	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
881	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
882	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
883	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
884	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
885	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
886	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
887	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
888	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
889	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
890	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
891	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
892	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
893	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
894	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
895	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
896	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
897	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
898	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
899	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
900	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
901	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
902	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
903	C₄²	C₂²×C₄×C₆₇	1	2	yes	—
904	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
905	C₄²	C₂²×C₄×C₆₇	1	2	yes	—
906	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
907	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
908	C₄²	C₂⁴×C₆₇	1	2	yes	—
909	C₄²	C₂⁴×C₆₇	1	2	yes	—
910	C₂³	—	4	2	no	—
911	C₂³	—	4	2	no	—
912	C₂³	—	4	2	no	—
913	C₂³	C₂³×C₄×C₆₇	1	2	yes	—
914	C₂³	C₂³×C₄×C₆₇	1	2	yes	—
915	C₂³	C₂³×C₄×C₆₇	1	2	yes	—
916	C₂³	C₂³×C₄×C₆₇	1	1	yes	characteristic
917	C₂³	C₂³×C₄×C₆₇	1	2	yes	—
918	Q₈	—	4	2	no	—
919	Q₈	—	4	1	no	—
920	Q₈	—	4	1	no	—
921	Q₈	—	4	1	no	—
922	Q₈	—	4	1	no	—
923	D₄	—	4	2	no	—
924	D₄	—	4	2	no	—
925	D₄	—	4	2	no	—
926	D₄	—	4	1	no	—
927	D₄	—	4	2	no	—
928	D₄	—	4	1	no	—
929	D₄	—	4	2	no	—
930	D₄	—	4	2	no	—
931	D₄	—	4	2	no	—
932	D₄	—	4	2	no	—
933	D₄	—	4	2	no	—
934	D₄	—	4	2	no	—
935	D₄	—	4	2	no	—
936	D₄	—	4	1	no	—
937	D₄	—	4	2	no	—
938	D₄	—	4	1	no	—
939	D₄	—	4	2	no	—
940	C₂×C₄	—	2	2	no	—
941	C₂×C₄	—	2	1	no	—
942	C₂×C₄	—	2	2	no	—
943	C₂×C₄	—	2	2	no	—
944	C₂×C₄	—	2	2	no	—
945	C₂×C₄	—	2	2	no	—
946	C₂×C₄	—	2	2	no	—
947	C₂×C₄	—	2	1	no	—
948	C₂×C₄	—	2	2	no	—
949	C₂×C₄	—	2	2	no	—
950	C₂×C₄	—	4	2	no	—
951	C₂×C₄	—	4	2	no	—
952	C₂×C₄	—	4	2	no	—
953	C₂×C₄	—	4	1	no	—
954	C₂×C₄	—	4	1	no	—
955	C₂×C₄	—	4	2	no	—
956	C₂×C₄	—	4	2	no	—
957	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
958	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
959	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
960	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
961	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
962	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
963	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
964	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
965	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
966	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
967	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
968	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
969	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
970	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
971	C₈	—	2	1	no	—
972	C₈	—	2	2	no	—
973	C₈	—	2	2	no	—
974	C₈	—	2	2	no	—
975	C₈	—	2	2	no	—
976	C₈	—	2	1	no	—
977	C₈	—	2	2	no	—
978	C₈	—	2	1	no	—
979	C₈	—	2	2	no	—
980	C₈	H(5,𝔽₂)×C₆₇	1	2	yes	—
981	C₂²	—	2	1	no	—
982	C₂²	—	2	1	no	—
983	C₂²	—	2	2	no	—
984	C₂²	—	2	2	no	—
985	C₂²	—	2	2	no	—
986	C₂²	—	2	2	no	—
987	C₂²	—	2	2	no	—
988	C₂²	—	2	2	no	—
989	C₂²	—	2	2	no	—
990	C₂²	—	2	2	no	—
991	C₂²	—	2	2	no	—
992	C₂²	—	2	2	no	—
993	C₂²	—	2	2	no	—
994	C₂²	—	2	1	no	—
995	C₂²	—	2	2	no	—
996	C₂²	—	8	4	no	—
997	C₂²	C₂⁴×C₄×C₆₇	1	1	yes	characteristic
998	C₄	—	2	1	no	—
999	C₄	—	2	1	no	—
1000	C₄	—	2	2	no	—
1001	C₄	—	2	2	no	—
1002	C₄	—	2	1	no	—
1003	C₄	—	2	1	no	—
1004	C₄	—	2	2	no	—
1005	C₄	—	2	2	no	—
1006	C₄	—	2	2	no	—
1007	C₄	—	2	2	no	—
1008	C₄	—	2	2	no	—
1009	C₄	—	2	1	no	—
1010	C₄	—	2	2	no	—
1011	C₄	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1012	C₄	#585×C₆₇	1	1	yes	characteristic
1013	C₂	—	4	2	no	—
1014	C₂	—	4	2	no	—
1015	C₂	—	4	2	no	—
1016	C₂	—	4	1	no	—
1017	C₂	—	4	2	no	—
1018	C₂	C₄×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1019	C₂	C₆₇×#3573	1	1	yes	characteristic
1020	C₂	C₆₇×#3573	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₆₇	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₆₇
Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
socle	C₂²×C₆₇	C₂⁴×C₄
prime radical	C₆₇×#3529	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₆₇×#2995	C₂	semidirect
3. C₆₇×#2995	C₂	semidirect
4. C₆₇×#2994	C₂	semidirect
5. C₆₇×#2992	C₂	semidirect
6. C₆₇×#2981	C₂	semidirect
7. C₆₇×#2980	C₂	semidirect
8. C₆₇×#2977	C₂	semidirect
9. C₆₇×#2976	C₂	semidirect
10. C₆₇×#2976	C₂	semidirect
11. C₆₇×#2969	C₂	semidirect
12. C₆₇×#2967	C₂	semidirect
13. C₆₇×#2966	C₂	semidirect
14. C₆₇×#2966	C₂	semidirect
15. C₆₇×#2935	C₂	semidirect
16. C₆₇×#2933	C₂	semidirect
17. C₆₇×#2933	C₂	semidirect
18. C₆₇×#2931	C₂	semidirect
19. C₆₇×#2930	C₂	semidirect
22. C₂×#131×C₆₇	C₂²	semidirect
23. C₂²×M₁₆×C₆₇	C₂²	semidirect
43. #446×C₆₇	C₂²	semidirect
44. #446×C₆₇	C₂²	semidirect
45. #446×C₆₇	C₂²	semidirect
46. #446×C₆₇	C₂²	semidirect
47. C₈×Q₈×C₆₇	C₂²	semidirect
48. C₈×Q₈×C₆₇	C₂²	semidirect
53. #436×C₆₇	C₂²	semidirect
54. #436×C₆₇	C₂²	semidirect
55. #436×C₆₇	C₂²	semidirect
56. #436×C₆₇	C₂²	semidirect
57. #436×C₆₇	C₂²	semidirect
58. #436×C₆₇	C₂²	semidirect
65. #435×C₆₇	C₂²	semidirect
66. #435×C₆₇	C₂²	semidirect
67. #435×C₆₇	C₂²	semidirect
68. #435×C₆₇	C₂²	semidirect
69. #435×C₆₇	C₂²	semidirect
70. #435×C₆₇	C₂²	semidirect
71. #435×C₆₇	C₂²	semidirect
72. #435×C₆₇	C₂²	semidirect
73. #435×C₆₇	C₂²	semidirect
74. #435×C₆₇	C₂²	semidirect
75. #435×C₆₇	C₂²	semidirect
76. #435×C₆₇	C₂²	semidirect
81. C₈×D₄×C₆₇	C₂²	semidirect
82. C₈×D₄×C₆₇	C₂²	semidirect
83. C₈×D₄×C₆₇	C₂²	semidirect
84. C₈×D₄×C₆₇	C₂²	semidirect
85. C₈×D₄×C₆₇	C₂²	semidirect
86. C₈×D₄×C₆₇	C₂²	semidirect
87. #433×C₆₇	C₂²	semidirect
88. #433×C₆₇	C₂²	semidirect
89. #433×C₆₇	C₂²	semidirect
90. #433×C₆₇	C₂²	semidirect
91. #433×C₆₇	C₂²	semidirect
92. #433×C₆₇	C₂²	semidirect
93. #432×C₆₇	C₂²	semidirect
94. #432×C₆₇	C₂²	semidirect
95. #432×C₆₇	C₂²	semidirect
96. #431×C₆₇	C₂²	semidirect
97. #424×C₆₇	C₂²	semidirect
98. #424×C₆₇	C₂²	semidirect
99. #424×C₆₇	C₂²	semidirect
100. #423×C₆₇	C₂²	semidirect
101. C₂×C₄⋊C₈×C₆₇	C₂²	semidirect
107. #408×C₆₇	C₂²	semidirect
108. #408×C₆₇	C₂²	semidirect
109. #407×C₆₇	C₂²	semidirect
110. C₂×C₂²⋊C₈×C₆₇	C₂²	semidirect
111. C₂×C₂²⋊C₈×C₆₇	C₂²	semidirect
112. #405×C₆₇	C₂²	semidirect
113. #405×C₆₇	C₂²	semidirect
114. #405×C₆₇	C₂²	semidirect
115. C₄×M₁₆×C₆₇	C₂²	semidirect
116. C₂×C₄×C₈×C₆₇	C₂²	semidirect
502. #60327	C₆₇	direct (N × H)
512. #2995	C₂×C₆₇	semidirect
513. #2995	C₂×C₆₇	semidirect
514. #2994	C₂×C₆₇	semidirect
515. #2992	C₂×C₆₇	semidirect
516. #2981	C₂×C₆₇	semidirect
517. #2980	C₂×C₆₇	semidirect
518. #2977	C₂×C₆₇	semidirect
519. #2976	C₂×C₆₇	semidirect
520. #2976	C₂×C₆₇	semidirect
521. #2969	C₂×C₆₇	semidirect
522. #2967	C₂×C₆₇	semidirect
523. #2966	C₂×C₆₇	semidirect
524. #2966	C₂×C₆₇	semidirect
525. #2935	C₂×C₆₇	semidirect
526. #2933	C₂×C₆₇	semidirect
527. #2933	C₂×C₆₇	semidirect
528. #2931	C₂×C₆₇	semidirect
529. #2930	C₂×C₆₇	semidirect
530. C₆₇	#60327	direct (N × H)
533. C₂×#131	C₂²×C₆₇	semidirect
534. C₂²×M₁₆	C₂²×C₆₇	semidirect
554. #446	C₂²×C₆₇	semidirect
555. #446	C₂²×C₆₇	semidirect
556. #446	C₂²×C₆₇	semidirect
557. #446	C₂²×C₆₇	semidirect
558. C₈×Q₈	C₂²×C₆₇	semidirect
559. C₈×Q₈	C₂²×C₆₇	semidirect
564. #436	C₂²×C₆₇	semidirect
565. #436	C₂²×C₆₇	semidirect
566. #436	C₂²×C₆₇	semidirect
567. #436	C₂²×C₆₇	semidirect
568. #436	C₂²×C₆₇	semidirect
569. #436	C₂²×C₆₇	semidirect
576. #435	C₂²×C₆₇	semidirect
577. #435	C₂²×C₆₇	semidirect
578. #435	C₂²×C₆₇	semidirect
579. #435	C₂²×C₆₇	semidirect
580. #435	C₂²×C₆₇	semidirect
581. #435	C₂²×C₆₇	semidirect
582. #435	C₂²×C₆₇	semidirect
583. #435	C₂²×C₆₇	semidirect
584. #435	C₂²×C₆₇	semidirect
585. #435	C₂²×C₆₇	semidirect
586. #435	C₂²×C₆₇	semidirect
587. #435	C₂²×C₆₇	semidirect
592. C₈×D₄	C₂²×C₆₇	semidirect
593. C₈×D₄	C₂²×C₆₇	semidirect
594. C₈×D₄	C₂²×C₆₇	semidirect
595. C₈×D₄	C₂²×C₆₇	semidirect
596. C₈×D₄	C₂²×C₆₇	semidirect
597. C₈×D₄	C₂²×C₆₇	semidirect
598. #433	C₂²×C₆₇	semidirect
599. #433	C₂²×C₆₇	semidirect
600. #433	C₂²×C₆₇	semidirect
601. #433	C₂²×C₆₇	semidirect
602. #433	C₂²×C₆₇	semidirect
603. #433	C₂²×C₆₇	semidirect
604. #432	C₂²×C₆₇	semidirect
605. #432	C₂²×C₆₇	semidirect
606. #432	C₂²×C₆₇	semidirect
607. #431	C₂²×C₆₇	semidirect
608. #424	C₂²×C₆₇	semidirect
609. #424	C₂²×C₆₇	semidirect
610. #424	C₂²×C₆₇	semidirect
611. #423	C₂²×C₆₇	semidirect
612. C₂×C₄⋊C₈	C₂²×C₆₇	semidirect
618. #408	C₂²×C₆₇	semidirect
619. #408	C₂²×C₆₇	semidirect
620. #407	C₂²×C₆₇	semidirect
621. C₂×C₂²⋊C₈	C₂²×C₆₇	semidirect
622. C₂×C₂²⋊C₈	C₂²×C₆₇	semidirect
623. #405	C₂²×C₆₇	semidirect
624. #405	C₂²×C₆₇	semidirect
625. #405	C₂²×C₆₇	semidirect
626. C₄×M₁₆	C₂²×C₆₇	semidirect
627. C₂×C₄×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×#3529	2
C₆₇×#2995	2
C₆₇×#2994	2
C₆₇×#2992	2
C₆₇×#2981	2
C₆₇×#2980	2
C₆₇×#2977	2
C₆₇×#2976	2
C₆₇×#2969	2
C₆₇×#2967	2
C₆₇×#2966	2
C₆₇×#2935	2
C₆₇×#2933	2
C₆₇×#2931	2
C₆₇×#2930	2
#60327	67

Subgroups — C67×#60327 #30739578

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#60327 #30739578